Finite Group Databasebeta

← C2×#24921397 #36312367

Subgroups — C2×#24921397 #36312367

Order 21248.

8082 conjugacy classes of subgroups.

The subgroup lattice has 1356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24921397C2132yesmaximal, direct product factor
2C2×#19128433C211yesmaximal, characteristic, complemented
3C2×#19128407C211yesmaximal, characteristic, complemented
4C2×#19128404C211yesmaximal, characteristic, complemented
5C2×#19128395C212yesmaximal, complemented
6C2×#19128393C211yesmaximal, characteristic, complemented
7C2×#19128380C212yesmaximal, complemented
8C2×#19128375C212yesmaximal, complemented
9C2×#19128351C211yesmaximal, characteristic, complemented
10C2×#19128346C212yesmaximal, complemented
11C2×#19128344C211yesmaximal, characteristic, complemented
12C2×#19128342C211yesmaximal, characteristic, complemented
13C2×#19128335C211yesmaximal, characteristic, complemented
14C2×#19128323C211yesmaximal, characteristic, complemented
15C2×#19128302C211yesmaximal, characteristic, complemented
16C2×#19128292C212yesmaximal, complemented
17C2×#19128290C212yesmaximal, complemented
18C2×#19128235C211yesmaximal, characteristic, complemented
19C2×#19128209C212yesmaximal, complemented
20C2×#123×D83C212yesmaximal, complemented
21C2×#19128183C211yesmaximal, characteristic, complemented
22C2×#19128173C211yesmaximal, characteristic, complemented
23C22×C4×D332C211yesmaximal, characteristic, complemented
24C2×#529×C83C211yesmaximal, characteristic, complemented
25C22×#13050591C2211yescharacteristic
26C22×#13050589C2212yescomplemented
27C23×D332C2211yescharacteristic
28C22×D4×D83C2211yescharacteristic
29C22×D4×D83C2212yes—
30C23×C4×D83C2212yescomplemented
31#19128433C22116yescomplemented
32#19128407C22116yescomplemented
33#19128404C22116yescomplemented
34#19128395C22132yescomplemented
35#19128393C22116yescomplemented
36#19128380C22132yescomplemented
37#19128375C22132yescomplemented
38#19128351C22116yescomplemented
39#19128346C22132yescomplemented
40#19128344C22116yescomplemented
41#19128342C22116yescomplemented
42#19128335C22116yescomplemented
43#19128323C22116yescomplemented
44#19128302C22116yescomplemented
45#19128292C22132yescomplemented
46#19128290C22132yescomplemented
47C2×#14581791C2211yescharacteristic, complemented
48C2×#14581788C2211yescharacteristic
49#19128235C22116yescomplemented
50C2×#14581787C2212yescomplemented
51C2×#14581787C2212yescomplemented
52C2×#14581786C2212yescomplemented
53C2×#14581786C2211yescharacteristic, complemented
54C2×#14581786C2211yescharacteristic, complemented
55C2×#14581784C2211yescharacteristic, complemented
56C2×#14581783C2212yescomplemented
57C2×#14581783C2211yescharacteristic, complemented
58C2×#14581781C2211yescharacteristic, complemented
59C2×#14581780C2212yescomplemented
60C2×#14581780C2211yescharacteristic, complemented
61C2×#14581778C2212yescomplemented
62#19128209C22132yescomplemented
63C2×#14581777C2212yescomplemented
64C2×#14581777C2212yescomplemented
65C2×#14581777C2212yescomplemented
66C2×#14581776C2212yes—
67C2×#14581776C2212yescomplemented
68C2×#14581775C2211yescharacteristic
69C2×#14581775C2211yescharacteristic, complemented
70C2×#14581775C2212yescomplemented
71C2×#14581774C2212yescomplemented
72C2×#14581774C2212yescomplemented
73C2×#14581774C2212yescomplemented
74C2×#14581774C2212yescomplemented
75C2×#14581773C2212yescomplemented
76#123×D83C22132yescomplemented
77C2×#14581772C2212yescomplemented
78C2×#14581771C2211yescharacteristic, complemented
79C2×#14581770C2212yescomplemented
80C2×#14581770C2212yescomplemented
81C2×#14581770C2212yescomplemented
82C2×#14581769C2212yescomplemented
83C2×#14581768C2211yescharacteristic, complemented
84C2×#14581767C2211yescharacteristic
85C2×#14581767C2212yescomplemented
86C2×#14581767C2211yescharacteristic, complemented
87C2×#14581767C2212yescomplemented
88C2×#14581766C2211yescharacteristic
89C2×#14581766C2212yescomplemented
90C2×#14581765C2212yes—
91C2×#14581765C2212yescomplemented
92C2×#14581765C2212yescomplemented
93C2×#14581763C2211yescharacteristic, complemented
94C2×#14581762C2212yes—
95C2×#14581762C2212yescomplemented
96C2×#14581762C2212yescomplemented
97C2×#14581760C2212yes—
98#19128183C22116yescomplemented
99#19128173C22116yescomplemented
100C2×Q8×Dic83C2211yescharacteristic, complemented
101C2×C4×Dic166C2211yescharacteristic, complemented
102C2×C4×D332C2211yescharacteristic
103C2×C4×D332C2211yescharacteristic
104C2×C4×D332C2211yescharacteristic, complemented
105C2×C4×D332C2212yescomplemented
106C2×C4×D332C2211yescharacteristic, complemented
107C2×C4×D332C2212yescomplemented
108C2×C4×D332C2211yescharacteristic, complemented
109C2×C4×D332C2212yescomplemented
110C2×C4×D332C22116yescomplemented
111C2×D4×Dic83C2211yescharacteristic, complemented
112C2×#14581754C2211yescharacteristic
113C2×#14581754C2211yescharacteristic
114C2×#14581754C2212yescomplemented
115C2×#14581754C2212yescomplemented
116C2×C4×C22⋊D83C2211yescharacteristic
117C2×C4×C22⋊D83C2212yescomplemented
118C2×C4×C22⋊D83C2211yescharacteristic, complemented
119C2×(C22⋊D83)⋊C4C2212yescomplemented
120C2×(C22⋊D83)⋊C4C2212yescomplemented
121C2×#14581750C2211yescharacteristic, complemented
122C2×#14581749C2211yescharacteristic, complemented
123C2×#14581749C2212yescomplemented
124C2×#14581749C2211yescharacteristic, complemented
125C2×#14581748C2212yescomplemented
126C22×C4⋊Dic83C2211yescharacteristic, complemented
127C2×C4⋊C4×D83C2211yescharacteristic, complemented
128C2×C4⋊C4×D83C2212yescomplemented
129C2×C4⋊C4×D83C2212yescomplemented
130C22×(C2×D83)⋊C4C2212yescomplemented
131C22×(C2×D83)⋊C4C2212yescomplemented
132C2×C22⋊C4×D83C2212yescomplemented
133C2×C22⋊C4×D83C2212yescomplemented
134C2×C22⋊C4×D83C2212yescomplemented
135#529×C83C22116yescomplemented
136C2×#126×C83C2212yescomplemented
137C2×#125×C83C2211yescharacteristic, complemented
138C2×#124×C83C2211yescharacteristic, complemented
139C2×#123×C83C2212yescomplemented
140C2×C22⋊Q8×C83C2211yescharacteristic, complemented
141C2×#121×C83C2211yescharacteristic
142C2×C4×Q8×C83C2211yescharacteristic, complemented
143C2×C4×D4×C83C2211yescharacteristic, complemented
144C2×C4×D4×C83C2212yescomplemented
145C2×#117×C83C2212yescomplemented
146C22×C42×C83C2211yescharacteristic, complemented
147C24×D83C2312yes—
148C24×D83C2312yes—
149C2×#13050591—28no—
150C2×#13050591C2318yes—
151C2×#13050589—48no—
152C2×#13050589C23116yescomplemented
153C22×Dic166C2311yescharacteristic
154C22×Dic166C2312yes—
155C22×D332—28no—
156C22×D332C2318yes—
157C22×D332C2312yes—
158C22×D332C2312yes—
159C22×D332C2311yescharacteristic
160C22×D332C2312yes—
161C22×D332C2311yescharacteristic
162C22×D332C2312yes—
163C22×D332C2311yescharacteristic
164C22×C22⋊D83C2312yes—
165C22×C22⋊D83C2311yescharacteristic
166C22×C22⋊D83C2311yescharacteristic
167C22×C22⋊D83C2312yes—
168C22×C22⋊D83C2312yes—
169C22×C22⋊D83C2312yes—
170C2×D4×D83—28no—
171C2×D4×D83—48no—
172C2×D4×D83C2318yes—
173C2×D4×D83C23116yes—
174C23×Dic83C2312yes—
175C23×Dic83C2312yes—
176C22×C4×D83—48no—
177C22×C4×D83C2312yes—
178C22×C4×D83C2311yescharacteristic
179C22×C4×D83C2311yescharacteristic
180C22×C4×D83C2312yes—
181C22×C4×D83C2312yes—
182C22×C4×D83C2312yes—
183C22×C4×D83C2312yes—
184C22×C4×D83C2312yes—
185C22×C4×D83C2312yes—
186C22×C4×D83C2312yes—
187C22×C4×D83C23116yescomplemented
188#14581791C2318yescomplemented
189#14581788C2318yes—
190#14581787C23116yescomplemented
191#14581787C23116yescomplemented
192#14581786C23116yescomplemented
193#14581786C2318yescomplemented
194#14581786C2318yescomplemented
195#14581784C2318yescomplemented
196#14581783C23116yescomplemented
197#14581783C2318yescomplemented
198#14581781C2318yescomplemented
199#14581780C23116yescomplemented
200#14581780C2318yescomplemented
201#14581778C23116yescomplemented
202#14581777C23116yescomplemented
203#14581777C23116yescomplemented
204#14581777C23116yescomplemented
205#14581776C23116yes—
206#14581776C23116yescomplemented
207#14581775C2318yes—
208#14581775C23116yescomplemented
209#14581775C2318yescomplemented
210#14581774C23116yescomplemented
211#14581774C23116yescomplemented
212#14581774C23116yescomplemented
213#14581774C23116yescomplemented
214#14581773C23116yescomplemented
215#14581772C23116yescomplemented
216#14581771C2318yescomplemented
217#14581770C23116yescomplemented
218#14581770C23116yescomplemented
219#14581770C23116yescomplemented
220#14581769C23116yescomplemented
221#14581768C2318yescomplemented
222#14581767C2318yes—
223#14581767C23116yescomplemented
224#14581767C2318yescomplemented
225#14581767C23116yescomplemented
226#14581766C2318yes—
227#14581766C23116yescomplemented
228#14581765C23116yes—
229#14581765C23116yescomplemented
230#14581765C23116yescomplemented
231#14581763C2318yescomplemented
232#14581762C23116yes—
233#14581762C23116yescomplemented
234#14581762C23116yescomplemented
235#14581760C23116yes—
236Q8×Dic83C2318yescomplemented
237C4×Dic166C2318yescomplemented
238C4×D332C2318yes—
239C4×D332C2318yes—
240C4×D332C2318yescomplemented
241C4×D332C2318yescomplemented
242C4×D332C23116yescomplemented
243C4×D332C23116yescomplemented
244C4×D332C2318yescomplemented
245C4×D332C23116yescomplemented
246D4×Dic83C2318yescomplemented
247#14581754C2318yes—
248#14581754C2318yes—
249#14581754C23116yescomplemented
250#14581754C23116yescomplemented
251C4×C22⋊D83C2318yes—
252C4×C22⋊D83C2318yescomplemented
253C4×C22⋊D83C23116yescomplemented
254(C22⋊D83)⋊C4C23116yescomplemented
255(C22⋊D83)⋊C4C23116yescomplemented
256#14581750C2318yescomplemented
257#14581749C2318yescomplemented
258#14581749C23116yescomplemented
259#14581749C2318yescomplemented
260#14581748C23116yescomplemented
261C2×C4⋊Dic83C2311yescharacteristic
262C2×C4⋊Dic83C2312yes—
263C2×C4⋊Dic83C2312yes—
264C2×C4⋊Dic83C2311yescharacteristic
265C2×C4⋊Dic83C2312yes—
266C2×C4⋊Dic83C2311yescharacteristic
267C2×C4⋊Dic83C2311yescharacteristic
268C2×C4⋊Dic83C2318yescomplemented
269C2×Dic83⋊C4C2312yes—
270C2×Dic83⋊C4C2311yescharacteristic
271C2×Dic83⋊C4C2311yescharacteristic
272C2×Dic83⋊C4C2312yes—
273C2×Dic83⋊C4C2312yes—
274C2×Dic83⋊C4C2312yes—
275C2×Dic83⋊C4C2311yescharacteristic
276C2×Dic83⋊C4C2311yescharacteristic
277C2×Dic83⋊C4C2311yescharacteristic
278C2×Dic83⋊C4C2311yescharacteristic
279C2×Dic83⋊C4C2311yescharacteristic
280C2×Dic83⋊C4C2311yescharacteristic
281C4⋊C4×D83C2318yescomplemented
282C4⋊C4×D83C23116yescomplemented
283C4⋊C4×D83C23116yescomplemented
284C2×C22⋊Dic83C2311yescharacteristic
285C2×C22⋊Dic83C2312yes—
286C2×C22⋊Dic83C2312yes—
287C2×C22⋊Dic83C2311yescharacteristic
288C2×(C2×D83)⋊C4C2311yescharacteristic
289C2×(C2×D83)⋊C4C2311yescharacteristic
290C2×(C2×D83)⋊C4C2312yes—
291C2×(C2×D83)⋊C4C2312yes—
292C2×(C2×D83)⋊C4C2312yes—
293C2×(C2×D83)⋊C4C2312yes—
294C2×(C2×D83)⋊C4C2312yes—
295C2×(C2×D83)⋊C4C2311yescharacteristic
296C2×(C2×D83)⋊C4C2312yes—
297C2×(C2×D83)⋊C4C2312yes—
298C2×(C2×D83)⋊C4C2312yes—
299C2×(C2×D83)⋊C4C2312yes—
300C2×(C2×D83)⋊C4C2312yes—
301C2×(C2×D83)⋊C4C2311yescharacteristic
302C2×(C2×D83)⋊C4C2311yescharacteristic
303C2×(C2×D83)⋊C4C2312yes—
304C2×(C2×D83)⋊C4C2311yescharacteristic
305C2×(C2×D83)⋊C4C2311yescharacteristic
306C2×(C2×D83)⋊C4C2311yescharacteristic
307C2×(C2×D83)⋊C4C2312yes—
308C2×(C2×D83)⋊C4C23116yescomplemented
309C2×(C2×D83)⋊C4C23116yescomplemented
310C22⋊C4×D83C23116yescomplemented
311C22⋊C4×D83C23116yescomplemented
312C22⋊C4×D83C23116yescomplemented
313C2×C4×Dic83C2312yes—
314C2×C4×Dic83C2312yes—
315C2×C4×Dic83C2311yescharacteristic
316C2×C4×Dic83C2311yescharacteristic
317C22×Q8×C83C2311yescharacteristic
318C22×D4×C83C2312yes—
319C22×D4×C83C2311yescharacteristic
320C23×C4×C83C2311yescharacteristic
321C23×C4×C83C2311yescharacteristic
322C23×C4×C83C2311yescharacteristic
323C23×C4×C83C2312yes—
324#126×C83C23116yescomplemented
325#125×C83C2318yescomplemented
326#124×C83C2318yescomplemented
327#123×C83C23116yescomplemented
328C22⋊Q8×C83C2318yescomplemented
329#121×C83C2318yes—
330C4×Q8×C83C2318yescomplemented
331C4×D4×C83C23116yescomplemented
332C4×D4×C83C2318yescomplemented
333#117×C83C23116yescomplemented
334C2×C4⋊C4×C83C2312yes—
335C2×C4⋊C4×C83C2312yes—
336C2×C4⋊C4×C83C2311yescharacteristic
337C2×C4⋊C4×C83C2312yes—
338C2×C4⋊C4×C83C2311yescharacteristic
339C2×C4⋊C4×C83C2312yes—
340C2×C22⋊C4×C83C2312yes—
341C2×C22⋊C4×C83C2312yes—
342C2×C22⋊C4×C83C2312yes—
343C2×C22⋊C4×C83C2312yes—
344C2×C22⋊C4×C83C2312yes—
345C2×C42×C83C2311yescharacteristic
346C2×C42×C83C2311yescharacteristic
347C2×C42×C83C2311yescharacteristic
348C2×C42×C83C2311yescharacteristic
349C2×C42×C83C2312yes—
350C2×C42×C83C2318yescomplemented
351C23×D83—28no—
352C23×D83—28no—
353C23×D83—28no—
354C23×D83—44no—
355C23×D83—44no—
356C23×D83—44no—
357C23×D83C2411yescharacteristic
358C23×D83C2412yes—
359C23×D83C2411yescharacteristic
360C23×D83C2418yes—
361C23×D83C2412yes—
362C23×D83C2418yes—
363#13050591—232no—
364#13050589—432no—
365C2×Dic166—42no—
366C2×Dic166—44no—
367C2×Dic166C2418yes—
368C2×Dic166C2414yes—
369C2×D332—28no—
370C2×D332—28no—
371C2×D332—24no—
372C2×D332—232no—
373C2×D332—44no—
374C2×D332—44no—
375C2×D332—42no—
376C2×D332#4118yescomplemented
377C2×D332C2418yes—
378C2×D332C2418yes—
379C2×D332C2414yes—
380C2×D332C2418yes—
381C2×D332C2414yes—
382C2×D332C2418yes—
383C2×D332C2414yes—
384C2×C22⋊D83—24no—
385C2×C22⋊D83—24no—
386C2×C22⋊D83—28no—
387C2×C22⋊D83—44no—
388C2×C22⋊D83—44no—
389C2×C22⋊D83—44no—
390C2×C22⋊D83C2418yes—
391C2×C22⋊D83C2414yes—
392C2×C22⋊D83C2414yes—
393C2×C22⋊D83C2418yes—
394C2×C22⋊D83C2418yes—
395C2×C22⋊D83C2418yes—
396D4×D83—232no—
397D4×D83—432no—
398C22×Dic83—28no—
399C22×Dic83—44no—
400C22×Dic83C2418yes—
401C22×Dic83C2412yes—
402C22×Dic83C2411yescharacteristic
403C22×Dic83C2412yes—
404C22×Dic83C2411yescharacteristic
405C22×Dic83C2411yescharacteristic
406C22×Dic83C2411yescharacteristic
407C22×Dic83C2411yescharacteristic
408C22×Dic83C2411yescharacteristic
409C22×Dic83C2418yes—
410C2×C4×D83—28no—
411C2×C4×D83—24no—
412C2×C4×D83—24no—
413C2×C4×D83—44no—
414C2×C4×D83—44no—
415C2×C4×D83—44no—
416C2×C4×D83—44no—
417C2×C4×D83—432no—
418C2×C4×D83—44no—
419C2×C4×D83—44no—
420C2×C4×D83—44no—
421C2×C4×D83C2414yes—
422C2×C4×D83C2414yes—
423C2×C4×D83C2418yes—
424C2×C4×D83C2418yes—
425C2×C4×D83C2418yes—
426C2×C4×D83C2418yes—
427C2×C4×D83C2418yes—
428C2×C4×D83C2418yes—
429C2×C4×D83C2418yes—
430C2×C4×D83C2418yes—
431C4⋊Dic83C2414yes—
432C4⋊Dic83C2414yes—
433C4⋊Dic83C2418yes—
434C4⋊Dic83C2418yes—
435C4⋊Dic83C2414yes—
436C4⋊Dic83C2418yes—
437C4⋊Dic83C2414yes—
438Dic83⋊C4C2414yes—
439Dic83⋊C4C2418yes—
440Dic83⋊C4C2418yes—
441Dic83⋊C4C2414yes—
442Dic83⋊C4C2418yes—
443Dic83⋊C4C2414yes—
444Dic83⋊C4C2414yes—
445Dic83⋊C4C2418yes—
446Dic83⋊C4C2414yes—
447Dic83⋊C4C2414yes—
448Dic83⋊C4C2414yes—
449Dic83⋊C4C2414yes—
450C22⋊Dic83C2414yes—
451C22⋊Dic83C2418yes—
452C22⋊Dic83C2414yes—
453C22⋊Dic83C2418yes—
454(C2×D83)⋊C4C2418yes—
455(C2×D83)⋊C4C2418yes—
456(C2×D83)⋊C4C2414yes—
457(C2×D83)⋊C4C2418yes—
458(C2×D83)⋊C4C2418yes—
459(C2×D83)⋊C4C2418yes—
460(C2×D83)⋊C4C2418yes—
461(C2×D83)⋊C4C2414yes—
462(C2×D83)⋊C4C2414yes—
463(C2×D83)⋊C4C2414yes—
464(C2×D83)⋊C4C2414yes—
465(C2×D83)⋊C4C2418yes—
466(C2×D83)⋊C4C2414yes—
467(C2×D83)⋊C4C2418yes—
468(C2×D83)⋊C4C2418yes—
469(C2×D83)⋊C4C2418yes—
470(C2×D83)⋊C4C2418yes—
471(C2×D83)⋊C4C2414yes—
472(C2×D83)⋊C4C2414yes—
473(C2×D83)⋊C4C2418yes—
474C4×Dic83C2418yes—
475C4×Dic83C2414yes—
476C4×Dic83C2418yes—
477C4×Dic83C2414yes—
478C24×C83C2412yes—
479C24×C83C2411yescharacteristic
480C2×Q8×C83—24no—
481C2×Q8×C83C2414yes—
482C2×D4×C83—28no—
483C2×D4×C83—24no—
484C2×D4×C83C2418yes—
485C2×D4×C83C2414yes—
486C22×C4×C83—24no—
487C22×C4×C83—24no—
488C22×C4×C83—44no—
489C22×C4×C83—42no—
490C22×C4×C83C2414yes—
491C22×C4×C83C2411yescharacteristic
492C22×C4×C83C2411yescharacteristic
493C22×C4×C83C2412yes—
494C22×C4×C83C2412yes—
495C22×C4×C83C2412yes—
496C22×C4×C83C2411yescharacteristic
497C22×C4×C83C2414yes—
498C22×C4×C83C2411yescharacteristic
499C22×C4×C83C2411yescharacteristic
500C22×C4×C83C2414yes—
501C22×C4×C83C2418yes—
502C22×C4×C83C2411yescharacteristic
503C4⋊C4×C83C2414yes—
504C4⋊C4×C83C2418yes—
505C4⋊C4×C83C2418yes—
506C4⋊C4×C83C2414yes—
507C4⋊C4×C83C2418yes—
508C4⋊C4×C83C2418yes—
509C22⋊C4×C83C2418yes—
510C22⋊C4×C83C2418yes—
511C22⋊C4×C83C2418yes—
512C22⋊C4×C83C2418yes—
513C22⋊C4×C83C2418yes—
514C42×C83C2414yes—
515C42×C83C2418yes—
516C42×C83C2414yes—
517C42×C83C2414yes—
518C42×C83C2414yes—
519C23×C83—22no—
520C23×C83—22no—
521C23×C83—24no—
522C23×C83—24no—
523C23×C83—24no—
524C23×C83H(5,𝔽2)14yes—
525C23×C83C2514yes—
526C23×C83C2512yes—
527C23×C83C2511yescharacteristic
528C22×D83—24no—
529C22×D83—24no—
530C22×D83—22no—
531C22×D83—22no—
532C22×D83—24no—
533C22×D83—216no—
534C22×D83—22no—
535C22×D83—24no—
536C22×D83—22no—
537C22×D83—24no—
538C22×D83—22no—
539C22×D83—22no—
540C22×D83—216no—
541C22×D83—216no—
542C22×D83—48no—
543C22×D83—48no—
544C22×D83—48no—
545C22×D83—432no—
546C22×D83—816no—
547C22×D83C2×#4118yes—
548C22×D83C2512yes—
549C22×D83C2514yes—
550C22×D83C2512yes—
551C22×D83C2514yes—
552Q8×C83—28no—
553D4×C83—216no—
554D4×C83—28no—
555C2×C4×C83—22no—
556C2×C4×C83—24no—
557C2×C4×C83—28no—
558C2×C4×C83—22no—
559C2×C4×C83—22no—
560C2×C4×C83—24no—
561C2×C4×C83—22no—
562C2×C4×C83—24no—
563C2×C4×C83—22no—
564C2×C4×C83—28no—
565C2×C4×C83—44no—
566C2×C4×C83—48no—
567C2×C4×C83C2×#4114yes—
568C2×C4×C83C2512yes—
569C2×C4×C83C2512yes—
570C2×C4×C83C2512yes—
571C2×C4×C83C2512yes—
572C2×C4×C83C2512yes—
573C2×C4×C83C2514yes—
574C2×C4×C83C2514yes—
575C2×C4×C83C2514yes—
576C2×C4×C83C2512yes—
577C22⋊D83—28no—
578C22⋊D83—28no—
579C22⋊D83—216no—
580C22⋊D83—48no—
581C22⋊D83—48no—
582C22⋊D83—48no—
583C2×Dic83—22no—
584C2×Dic83—22no—
585C2×Dic83—24no—
586C2×Dic83—24no—
587C2×Dic83—216no—
588C2×Dic83—22no—
589C2×Dic83—22no—
590C2×Dic83—22no—
591C2×Dic83—22no—
592C2×Dic83—48no—
593C2×Dic83C2512yes—
594C2×Dic83C2512yes—
595C2×Dic83C2514yes—
596C2×Dic83C2512yes—
597C2×Dic83C2512yes—
598C2×Dic83C2512yes—
599C2×Dic83C2512yes—
600C2×Dic83C2514yes—
601D332—216no—
602D332—216no—
603D332—28no—
604D332—48no—
605D332—44no—
606D332—48no—
607D332C2×#41116yescomplemented
608C4×D83—216no—
609C4×D83—28no—
610C4×D83—28no—
611C4×D83—48no—
612C4×D83—48no—
613C4×D83—48no—
614C4×D83—48no—
615C4×D83—48no—
616C4×D83—48no—
617C4×D83—48no—
618Dic166—44no—
619Dic166—48no—
620C22×C83—22no—
621C22×C83—22no—
622C22×C83—28no—
623C22×C83—24no—
624C22×C83—24no—
625C22×C83—24no—
626C22×C83—48no—
627C22×C83C22×#4112yes—
628C22×C83C2×H(5,𝔽2)14yes—
629C22×C83C2×H(5,𝔽2)12yes—
630C22×C83#58512yes—
631C22×C83C2611yescharacteristic
632C2×D83—24no—
633C2×D83—24no—
634C2×D83—216no—
635C2×D83—22no—
636C2×D83—22no—
637C2×D83—24no—
638C2×D83—24no—
639C2×D83—22no—
640C2×D83—22no—
641C2×D83—22no—
642C2×D83—24no—
643C2×D83—22no—
644C2×D83—432no—
645C2×D83—44no—
646C2×D83—48no—
647C2×D83—44no—
648C2×D83—816no—
649C2×D83C22×#4118yes—
650C4×C83—24no—
651C4×C83—22no—
652C4×C83—24no—
653C4×C83—22no—
654C4×C83—22no—
655C4×C83—22no—
656C4×C83—24no—
657C4×C83—22no—
658C4×C83C22×#4114yes—
659Dic83—22no—
660Dic83—22no—
661Dic83—22no—
662Dic83—24no—
663Dic83—24no—
664Dic83—22no—
665Dic83—22no—
666Dic83—22no—
667C2×#3513—831nomaximal, Sylow
668C2×C83—24no—
669C2×C83—44no—
670C2×C83#351314yescomplemented
671C2×C83C23×#4111yescharacteristic
672C2×C83C22×H(5,𝔽2)11yescharacteristic
673C2×C83C2×#58511yescharacteristic
674D83—28no—
675D83—42no—
676D83—44no—
677D83—42no—
678#3513—8332no—
679C2×#559—831no—
680C2×#554—831no—
681C2×#553—831no—
682C2×#553—832no—
683C2×#552—831no—
684C2×#551—832no—
685C2×#551—832no—
686C2×#547—831no—
687C2×#546—831no—
688C2×#546—831no—
689C2×#546—832no—
690C2×D42—831no—
691C2×#542—831no—
692C2×#540—831no—
693C2×#539—832no—
694C2×#538—832no—
695C2×#529—831no—
696C2×#529D8311yescharacteristic, complemented
697C2×#525—832no—
698C22×#123—832no—
699C2×#520—831no—
700C2×#518—831no—
701C22×C4×D4—831no—
702C83C2×#351311yescharacteristic, complemented, Sylow
703C22×#41—831no—
704C22×#41—832no—
705C23×D4—832no—
706C23×D4—831no—
707C23×D4—831no—
708C24×C4—832no—
709#559—8316no—
710#554—8316no—
711#553—8316no—
712#553—8332no—
713#552—8316no—
714#551—8332no—
715#551—8332no—
716#547—8316no—
717#546—8316no—
718#546—8316no—
719#546—8332no—
720D42—8316no—
721#542—8316no—
722#540—8316no—
723#539—8332no—
724#538—8332no—
725C2×C4⋊Q8—831no—
726C2×#127—831no—
727#529—8316no—
728#529C2×D83116yescomplemented
729C2×#126—832no—
730C2×#126—832no—
731C2×#126—831no—
732C2×#126—831no—
733C2×#126—832no—
734C2×#126C2×D8312yescomplemented
735C2×#125—832no—
736C2×#125—831no—
737C2×#125—831no—
738C2×#125C2×D8311yescharacteristic, complemented
739C2×#124—831no—
740C2×#124—832no—
741C2×#124—831no—
742C2×#124—832no—
743C2×#124C2×D8311yescharacteristic, complemented
744#525—8332no—
745C2×#123—832no—
746C2×#123—831no—
747C2×#123—831no—
748C2×#123—832no—
749C2×#123—8332no—
750C2×#123—832no—
751C2×#123—832no—
752C2×#123—832no—
753C2×#123—832no—
754C2×#123—832no—
755C2×#123—832no—
756C2×#123—832no—
757C2×#123—832no—
758C2×#123—832no—
759C2×#123C2×D8312yescomplemented
760C2×C22⋊Q8—831no—
761C2×C22⋊Q8—831no—
762C2×C22⋊Q8—832no—
763C2×C22⋊Q8—832no—
764C2×C22⋊Q8—832no—
765C2×C22⋊Q8—832no—
766C2×C22⋊Q8—832no—
767C2×C22⋊Q8C2×D8311yescharacteristic, complemented
768C2×#121—831no—
769C2×#121—831no—
770C2×#121—832no—
771C2×#121—832no—
772C2×#121—832no—
773C2×#121—831no—
774C2×#121—831no—
775C2×#121—832no—
776C2×#121—832no—
777C2×#121—832no—
778C2×#121C2×D8311yescharacteristic
779C2×#120—832no—
780C2×#120—832no—
781C2×#120—832no—
782C2×#120—832no—
783#520—8316no—
784#518—8316no—
785C2×C4×Q8—831no—
786C2×C4×Q8—831no—
787C2×C4×Q8C2×D8311yescharacteristic, complemented
788C2×C4×D4—831no—
789C2×C4×D4—831no—
790C2×C4×D4—832no—
791C2×C4×D4—831no—
792C2×C4×D4—831no—
793C2×C4×D4—831no—
794C2×C4×D4—832no—
795C2×C4×D4—832no—
796C2×C4×D4—832no—
797C2×C4×D4—832no—
798C2×C4×D4—831no—
799C2×C4×D4—831no—
800C2×C4×D4—832no—
801C2×C4×D4—831no—
802C2×C4×D4—832no—
803C2×C4×D4—831no—
804C2×C4×D4—832no—
805C2×C4×D4—831no—
806C2×C4×D4—8316no—
807C2×C4×D4C2×D8311yescharacteristic, complemented
808C2×C4×D4C2×D8312yescomplemented
809C2×#117—831no—
810C2×#117—832no—
811C2×#117—831no—
812C2×#117—831no—
813C2×#117—832no—
814C2×#117C2×D8312yescomplemented
815C22×C4⋊C4—831no—
816C22×C4⋊C4—832no—
817C22×C4⋊C4—831no—
818C22×C4⋊C4—832no—
819C22×C22⋊C4—832no—
820C22×C22⋊C4—832no—
821C22×C22⋊C4—832no—
822C22×C22⋊C4—832no—
823C22×C22⋊C4—832no—
824C22×C42C2×D8311yescharacteristic, complemented
825C25—832no—
826C25—832no—
827C2×#41—3328no—
828C2×#41—838no—
829C2×#41—8316no—
830C2×#41—1668no—
831C22×Q8—831no—
832C22×Q8—832no—
833C22×Q8C22×D8311yescharacteristic
834C22×D4—3328no—
835C22×D4—832no—
836C22×D4—832no—
837C22×D4—832no—
838C22×D4—8316no—
839C22×D4—832no—
840C22×D4—831no—
841C22×D4—831no—
842C22×D4—838no—
843C22×D4—831no—
844C22×D4—832no—
845C22×D4—832no—
846C22×D4—831no—
847C22×D4—832no—
848C22×D4—832no—
849C22×D4—831no—
850C22×D4—838no—
851C22×D4—1668no—
852C22×D4—1668no—
853C22×D4C22×D8311yescharacteristic
854C22×D4C22×D8312yes—
855C23×C4—3328no—
856C23×C4—832no—
857C23×C4—832no—
858C23×C4—832no—
859C23×C4—832no—
860C23×C4—832no—
861C23×C4—832no—
862C23×C4—832no—
863C23×C4—832no—
864C23×C4—8316no—
865C23×C4—832no—
866C23×C4—832no—
867C23×C4—831no—
868C23×C4—831no—
869C23×C4C22×D8311yescharacteristic
870C23×C4C22×D8311yescharacteristic
871C23×C4C22×D8311yescharacteristic
872C23×C4C22×D8312yes—
873C4⋊Q8—838no—
874#127—838no—
875#126—8316no—
876#126—8316no—
877#126—838no—
878#126—838no—
879#126—8316no—
880#126C22×D83116yescomplemented
881#125—8316no—
882#125—838no—
883#125—838no—
884#125C22×D8318yescomplemented
885#124—838no—
886#124—8316no—
887#124—838no—
888#124—8316no—
889#124C22×D8318yescomplemented
890#123—8316no—
891#123—838no—
892#123—838no—
893#123—8316no—
894#123—8316no—
895#123—8316no—
896#123—8316no—
897#123—8316no—
898#123—8316no—
899#123—8316no—
900#123—8316no—
901#123—8316no—
902#123—8316no—
903#123C22×D83116yescomplemented
904C22⋊Q8—838no—
905C22⋊Q8—838no—
906C22⋊Q8—8316no—
907C22⋊Q8—8316no—
908C22⋊Q8—8316no—
909C22⋊Q8—8316no—
910C22⋊Q8—8316no—
911C22⋊Q8C22×D8318yescomplemented
912#121—838no—
913#121—838no—
914#121—8316no—
915#121—838no—
916#121—8316no—
917#121—8316no—
918#121—838no—
919#121—8316no—
920#121—8316no—
921#121—8316no—
922#121C22×D8318yes—
923#120—8316no—
924#120—8316no—
925#120—8316no—
926#120—8316no—
927C4×Q8—838no—
928C4×Q8—838no—
929C4×Q8C22×D8318yescomplemented
930C4×D4—838no—
931C4×D4—8316no—
932C4×D4—838no—
933C4×D4—838no—
934C4×D4—838no—
935C4×D4—8316no—
936C4×D4—838no—
937C4×D4—8316no—
938C4×D4—8316no—
939C4×D4—8316no—
940C4×D4—838no—
941C4×D4—8316no—
942C4×D4—838no—
943C4×D4—838no—
944C4×D4—8316no—
945C4×D4—838no—
946C4×D4—8316no—
947C4×D4—838no—
948C4×D4C22×D8318yescomplemented
949C4×D4C22×D83116yescomplemented
950#117—838no—
951#117—8316no—
952#117—838no—
953#117—838no—
954#117—8316no—
955#117C22×D83116yescomplemented
956C2×C4⋊C4—831no—
957C2×C4⋊C4—832no—
958C2×C4⋊C4—831no—
959C2×C4⋊C4—831no—
960C2×C4⋊C4—831no—
961C2×C4⋊C4—832no—
962C2×C4⋊C4—838no—
963C2×C4⋊C4—832no—
964C2×C4⋊C4—832no—
965C2×C4⋊C4—832no—
966C2×C4⋊C4—831no—
967C2×C4⋊C4—831no—
968C2×C4⋊C4—831no—
969C2×C4⋊C4—832no—
970C2×C4⋊C4—832no—
971C2×C4⋊C4—831no—
972C2×C4⋊C4—831no—
973C2×C4⋊C4—831no—
974C2×C4⋊C4—831no—
975C2×C4⋊C4—831no—
976C2×C4⋊C4—8316no—
977C2×C4⋊C4—838no—
978C2×C4⋊C4—8316no—
979C2×C4⋊C4C22×D8312yes—
980C2×C4⋊C4C22×D8311yescharacteristic
981C2×C4⋊C4C22×D8312yes—
982C2×C4⋊C4C22×D8311yescharacteristic
983C2×C4⋊C4C22×D8312yes—
984C2×C4⋊C4C22×D8312yes—
985C2×C22⋊C4—831no—
986C2×C22⋊C4—832no—
987C2×C22⋊C4—832no—
988C2×C22⋊C4—831no—
989C2×C22⋊C4—832no—
990C2×C22⋊C4—832no—
991C2×C22⋊C4—831no—
992C2×C22⋊C4—831no—
993C2×C22⋊C4—831no—
994C2×C22⋊C4—832no—
995C2×C22⋊C4—832no—
996C2×C22⋊C4—832no—
997C2×C22⋊C4—832no—
998C2×C22⋊C4—8316no—
999C2×C22⋊C4—8316no—
1000C2×C22⋊C4—832no—
1001C2×C22⋊C4—832no—
1002C2×C22⋊C4—832no—
1003C2×C22⋊C4—832no—
1004C2×C22⋊C4—831no—
1005C2×C22⋊C4—831no—
1006C2×C22⋊C4—831no—
1007C2×C22⋊C4—831no—
1008C2×C22⋊C4—832no—
1009C2×C22⋊C4—832no—
1010C2×C22⋊C4—831no—
1011C2×C22⋊C4—8316no—
1012C2×C22⋊C4—8316no—
1013C2×C22⋊C4—8316no—
1014C2×C22⋊C4C22×D8312yes—
1015C2×C22⋊C4C22×D8312yes—
1016C2×C22⋊C4C22×D8312yes—
1017C2×C22⋊C4C22×D8312yes—
1018C2×C22⋊C4C22×D8312yes—
1019C2×C42—832no—
1020C2×C42—832no—
1021C2×C42—831no—
1022C2×C42—831no—
1023C2×C42C22×D8311yescharacteristic
1024C2×C42C22×D8312yes—
1025C2×C42C22×D8311yescharacteristic
1026C2×C42C22×D8311yescharacteristic
1027C2×C42C22×D8311yescharacteristic
1028C2×C42C22×D8318yescomplemented
1029C24—3324no—
1030C24—3324no—
1031C24—3324no—
1032C24—838no—
1033C24—838no—
1034C24—832no—
1035C24—831no—
1036C24—832no—
1037C24—831no—
1038C24—1668no—
1039C24—1668no—
1040C24—1668no—
1041C24C23×D8312yes—
1042C24C23×D8311yescharacteristic
1043#41—33232no—
1044#41—16632no—
1045C2×Q8—24no—
1046C2×Q8—3324no—
1047C2×Q8—3322no—
1048C2×Q8—834no—
1049C2×Q8—838no—
1050C2×Q8C23×D8314yes—
1051C2×D4—28no—
1052C2×D4—24no—
1053C2×D4—3324no—
1054C2×D4—3324no—
1055C2×D4—3322no—
1056C2×D4—33232no—
1057C2×D4—3324no—
1058C2×D4—3324no—
1059C2×D4—3324no—
1060C2×D4—838no—
1061C2×D4—838no—
1062C2×D4—838no—
1063C2×D4—838no—
1064C2×D4—834no—
1065C2×D4—834no—
1066C2×D4—838no—
1067C2×D4—834no—
1068C2×D4—838no—
1069C2×D4—838no—
1070C2×D4—834no—
1071C2×D4—838no—
1072C2×D4—838no—
1073C2×D4—834no—
1074C2×D4—16632no—
1075C2×D4—1668no—
1076C2×D4—1668no—
1077C2×D4—16632no—
1078C2×D4—1668no—
1079C2×D4—1664no—
1080C2×D4—1664no—
1081C2×D4—1664no—
1082C2×D4C23×D8314yes—
1083C2×D4C23×D8318yes—
1084C22×C4—24no—
1085C22×C4—24no—
1086C22×C4—44no—
1087C22×C4—42no—
1088C22×C4—3324no—
1089C22×C4—3324no—
1090C22×C4—3324no—
1091C22×C4—3324no—
1092C22×C4—33232no—
1093C22×C4—3324no—
1094C22×C4—3324no—
1095C22×C4—3324no—
1096C22×C4—3324no—
1097C22×C4—838no—
1098C22×C4—838no—
1099C22×C4—838no—
1100C22×C4—838no—
1101C22×C4—838no—
1102C22×C4—838no—
1103C22×C4—838no—
1104C22×C4—838no—
1105C22×C4—838no—
1106C22×C4—831no—
1107C22×C4—831no—
1108C22×C4—832no—
1109C22×C4—831no—
1110C22×C4—831no—
1111C22×C4—831no—
1112C22×C4—831no—
1113C22×C4—832no—
1114C22×C4—838no—
1115C22×C4—834no—
1116C22×C4—834no—
1117C22×C4—1668no—
1118C22×C4—1668no—
1119C22×C4—1664no—
1120C22×C4—1664no—
1121C22×C4C23×D8314yes—
1122C22×C4C23×D8314yes—
1123C22×C4C23×D8312yes—
1124C22×C4C23×D8312yes—
1125C22×C4C23×D8311yescharacteristic
1126C22×C4C23×D8311yescharacteristic
1127C22×C4C23×D8311yescharacteristic
1128C22×C4C23×D8311yescharacteristic
1129C22×C4C23×D8311yescharacteristic
1130C22×C4C23×D8312yes—
1131C22×C4C23×D8314yes—
1132C22×C4C23×D8318yes—
1133C22×C4C23×D8311yescharacteristic
1134C4⋊C4—834no—
1135C4⋊C4—838no—
1136C4⋊C4—834no—
1137C4⋊C4—834no—
1138C4⋊C4—834no—
1139C4⋊C4—838no—
1140C4⋊C4—838no—
1141C4⋊C4—838no—
1142C4⋊C4—838no—
1143C4⋊C4—834no—
1144C4⋊C4—834no—
1145C4⋊C4—834no—
1146C4⋊C4—838no—
1147C4⋊C4—838no—
1148C4⋊C4—834no—
1149C4⋊C4—834no—
1150C4⋊C4—834no—
1151C4⋊C4—834no—
1152C4⋊C4—834no—
1153C4⋊C4C23×D8318yes—
1154C4⋊C4C23×D8314yes—
1155C4⋊C4C23×D8318yes—
1156C4⋊C4C23×D8314yes—
1157C4⋊C4C23×D8318yes—
1158C4⋊C4C23×D8318yes—
1159C22⋊C4—834no—
1160C22⋊C4—838no—
1161C22⋊C4—838no—
1162C22⋊C4—834no—
1163C22⋊C4—838no—
1164C22⋊C4—838no—
1165C22⋊C4—834no—
1166C22⋊C4—834no—
1167C22⋊C4—834no—
1168C22⋊C4—838no—
1169C22⋊C4—838no—
1170C22⋊C4—838no—
1171C22⋊C4—838no—
1172C22⋊C4—838no—
1173C22⋊C4—838no—
1174C22⋊C4—838no—
1175C22⋊C4—838no—
1176C22⋊C4—834no—
1177C22⋊C4—834no—
1178C22⋊C4—834no—
1179C22⋊C4—834no—
1180C22⋊C4—838no—
1181C22⋊C4—838no—
1182C22⋊C4—834no—
1183C22⋊C4C23×D8318yes—
1184C22⋊C4C23×D8318yes—
1185C22⋊C4C23×D8318yes—
1186C22⋊C4C23×D8318yes—
1187C22⋊C4C23×D8318yes—
1188C42—838no—
1189C42—838no—
1190C42—834no—
1191C42—834no—
1192C42C23×D8314yes—
1193C42C23×D8314yes—
1194C42C23×D8314yes—
1195C42C23×D8314yes—
1196C42C23×D8318yes—
1197C23—22no—
1198C23—22no—
1199C23—24no—
1200C23—24no—
1201C23—24no—
1202C23—33232no—
1203C23—3328no—
1204C23—3328no—
1205C23—3328no—
1206C23—838no—
1207C23—834no—
1208C23—832no—
1209C23—834no—
1210C23—832no—
1211C23—66416no—
1212C23—16616no—
1213C23—16616no—
1214C23—1662no—
1215C23—1662no—
1216C23—1664no—
1217C23—1662no—
1218C23—16616no—
1219C23—1664no—
1220C23—1662no—
1221C23—1662no—
1222C23—1664no—
1223C23—1662no—
1224C23—1664no—
1225C23—1664no—
1226C23#1458183814yes—
1227C23C24×D8314yes—
1228C23C24×D8312yes—
1229C23C24×D8311yescharacteristic
1230Q8—28no—
1231Q8—3328no—
1232Q8—3324no—
1233D4—216no—
1234D4—28no—
1235D4—3328no—
1236D4—3328no—
1237D4—3324no—
1238D4—3328no—
1239D4—3328no—
1240D4—3328no—
1241D4—8316no—
1242D4—16616no—
1243D4—16616no—
1244D4—16616no—
1245D4—1668no—
1246D4—1668no—
1247D4—1668no—
1248C2×C4—22no—
1249C2×C4—24no—
1250C2×C4—28no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—24no—
1254C2×C4—22no—
1255C2×C4—24no—
1256C2×C4—22no—
1257C2×C4—28no—
1258C2×C4—48no—
1259C2×C4—44no—
1260C2×C4—3328no—
1261C2×C4—3328no—
1262C2×C4—3328no—
1263C2×C4—3328no—
1264C2×C4—3328no—
1265C2×C4—3328no—
1266C2×C4—3328no—
1267C2×C4—3328no—
1268C2×C4—832no—
1269C2×C4—832no—
1270C2×C4—834no—
1271C2×C4—832no—
1272C2×C4—832no—
1273C2×C4—832no—
1274C2×C4—832no—
1275C2×C4—834no—
1276C2×C4—16616no—
1277C2×C4—1662no—
1278C2×C4—1662no—
1279C2×C4—1664no—
1280C2×C4—1664no—
1281C2×C4—16616no—
1282C2×C4—1662no—
1283C2×C4—1662no—
1284C2×C4—1662no—
1285C2×C4—1662no—
1286C2×C4—1668no—
1287C2×C4—1668no—
1288C2×C4#41×D8314yes—
1289C2×C4C24×D8314yes—
1290C2×C4C24×D8314yes—
1291C2×C4C24×D8312yes—
1292C2×C4C24×D8312yes—
1293C2×C4C24×D8312yes—
1294C2×C4C24×D8312yes—
1295C2×C4C24×D8312yes—
1296C2×C4C24×D8314yes—
1297C2×C4C24×D8312yes—
1298C22—28no—
1299C22—22no—
1300C22—22no—
1301C22—24no—
1302C22—24no—
1303C22—24no—
1304C22—48no—
1305C22—33232no—
1306C22—3328no—
1307C22—3324no—
1308C22—3324no—
1309C22—838no—
1310C22—66416no—
1311C22—1662no—
1312C22—1662no—
1313C22—1664no—
1314C22—1662no—
1315C22—1664no—
1316C22—1662no—
1317C22—1662no—
1318C22—1664no—
1319C22—1662no—
1320C22—16616no—
1321C22—1664no—
1322C22—1664no—
1323C22C2×#41×D8312yes—
1324C22C2×#1458183814yes—
1325C22C2×#1458183812yes—
1326C22#1912853712yes—
1327C22C25×D8311yescharacteristic
1328C4—22no—
1329C4—24no—
1330C4—22no—
1331C4—22no—
1332C4—24no—
1333C4—22no—
1334C4—24no—
1335C4—22no—
1336C4—1662no—
1337C4—1662no—
1338C4—1664no—
1339C4—1664no—
1340C4—1662no—
1341C4—1662no—
1342C4—1662no—
1343C4—1662no—
1344C4C2×#41×D8314yes—
1345C2—24no—
1346C2—44no—
1347C2—3324no—
1348C2—3322no—
1349C2—3322no—
1350C2—1668no—
1351C2#2492139714yesdirect product factor
1352C2C22×#41×D8311yescharacteristic
1353C2C22×#1458183811yescharacteristic
1354C2C2×#1912853711yescharacteristic
subgroupG/H
centerC23C24×D83
commutator, cosocleC22×C83C26
FrattiniC22C25×D83
FittingC2×#529×C83C2
socleC23×C83C25
hypercenterC2×#529D83
hypocenterC83C2×#3513
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#529

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #24921397C2direct (N × H)
2. C2×#19128433C2semidirect
3. C2×#19128407C2semidirect
4. C2×#19128404C2semidirect
5. C2×#19128395C2semidirect
6. C2×#19128393C2semidirect
7. C2×#19128380C2semidirect
8. C2×#19128375C2semidirect
9. C2×#19128351C2semidirect
10. C2×#19128346C2semidirect
11. C2×#19128344C2semidirect
12. C2×#19128342C2semidirect
13. C2×#19128335C2semidirect
14. C2×#19128323C2semidirect
15. C2×#19128302C2semidirect
16. C2×#19128292C2semidirect
17. C2×#19128290C2semidirect
18. C2×#19128235C2semidirect
19. C2×#19128209C2semidirect
20. C2×#123×D83C2semidirect
21. C2×#19128183C2semidirect
22. C2×#19128173C2semidirect
23. C22×C4×D332C2semidirect
24. C2×#529×C83C2semidirect
26. C22×#13050589C22semidirect
30. C23×C4×D83C22semidirect
31. #19128433C22semidirect
32. #19128407C22semidirect
33. #19128404C22semidirect
34. #19128395C22semidirect
35. #19128393C22semidirect
36. #19128380C22semidirect
37. #19128375C22semidirect
38. #19128351C22semidirect
39. #19128346C22semidirect
40. #19128344C22semidirect
41. #19128342C22semidirect
42. #19128335C22semidirect
43. #19128323C22semidirect
44. #19128302C22semidirect
45. #19128292C22semidirect
46. #19128290C22semidirect
47. C2×#14581791C22semidirect
49. #19128235C22semidirect
50. C2×#14581787C22semidirect
51. C2×#14581787C22semidirect
52. C2×#14581786C22semidirect
53. C2×#14581786C22semidirect
54. C2×#14581786C22semidirect
55. C2×#14581784C22semidirect
56. C2×#14581783C22semidirect
57. C2×#14581783C22semidirect
58. C2×#14581781C22semidirect
59. C2×#14581780C22semidirect
60. C2×#14581780C22semidirect
61. C2×#14581778C22semidirect
62. #19128209C22semidirect
63. C2×#14581777C22semidirect
64. C2×#14581777C22semidirect
65. C2×#14581777C22semidirect
67. C2×#14581776C22semidirect
69. C2×#14581775C22semidirect
70. C2×#14581775C22semidirect
71. C2×#14581774C22semidirect
72. C2×#14581774C22semidirect
73. C2×#14581774C22semidirect
74. C2×#14581774C22semidirect
75. C2×#14581773C22semidirect
76. #123×D83C22semidirect
77. C2×#14581772C22semidirect
78. C2×#14581771C22semidirect
79. C2×#14581770C22semidirect
80. C2×#14581770C22semidirect
81. C2×#14581770C22semidirect
82. C2×#14581769C22semidirect
83. C2×#14581768C22semidirect
85. C2×#14581767C22semidirect
86. C2×#14581767C22semidirect
87. C2×#14581767C22semidirect
89. C2×#14581766C22semidirect
91. C2×#14581765C22semidirect
92. C2×#14581765C22semidirect
93. C2×#14581763C22semidirect
95. C2×#14581762C22semidirect
96. C2×#14581762C22semidirect
98. #19128183C22semidirect
99. #19128173C22semidirect
100. C2×Q8×Dic83C22semidirect
101. C2×C4×Dic166C22semidirect
104. C2×C4×D332C22semidirect
105. C2×C4×D332C22semidirect
106. C2×C4×D332C22semidirect
107. C2×C4×D332C22semidirect
108. C2×C4×D332C22semidirect
109. C2×C4×D332C22semidirect
110. C2×C4×D332C22semidirect
111. C2×D4×Dic83C22semidirect
114. C2×#14581754C22semidirect
115. C2×#14581754C22semidirect
117. C2×C4×C22⋊D83C22semidirect
118. C2×C4×C22⋊D83C22semidirect
119. C2×(C22⋊D83)⋊C4C22semidirect
120. C2×(C22⋊D83)⋊C4C22semidirect
121. C2×#14581750C22semidirect
122. C2×#14581749C22semidirect
123. C2×#14581749C22semidirect
124. C2×#14581749C22semidirect
125. C2×#14581748C22semidirect
126. C22×C4⋊Dic83C22semidirect
127. C2×C4⋊C4×D83C22semidirect
128. C2×C4⋊C4×D83C22semidirect
129. C2×C4⋊C4×D83C22semidirect
130. C22×(C2×D83)⋊C4C22semidirect
131. C22×(C2×D83)⋊C4C22semidirect
132. C2×C22⋊C4×D83C22semidirect
133. C2×C22⋊C4×D83C22semidirect
134. C2×C22⋊C4×D83C22semidirect
135. #529×C83C22semidirect
136. C2×#126×C83C22semidirect
137. C2×#125×C83C22semidirect
138. C2×#124×C83C22semidirect
139. C2×#123×C83C22semidirect
140. C2×C22⋊Q8×C83C22semidirect
142. C2×C4×Q8×C83C22semidirect
143. C2×C4×D4×C83C22semidirect
144. C2×C4×D4×C83C22semidirect
145. C2×#117×C83C22semidirect
146. C22×C42×C83C22semidirect
152. C2×#13050589C23semidirect
187. C22×C4×D83C23semidirect
188. #14581791C23semidirect
190. #14581787C23semidirect
191. #14581787C23semidirect
192. #14581786C23semidirect
193. #14581786C23semidirect
194. #14581786C23semidirect
195. #14581784C23semidirect
196. #14581783C23semidirect
197. #14581783C23semidirect
198. #14581781C23semidirect
199. #14581780C23semidirect
200. #14581780C23semidirect
201. #14581778C23semidirect
202. #14581777C23semidirect
203. #14581777C23semidirect
204. #14581777C23semidirect
206. #14581776C23semidirect
208. #14581775C23semidirect
209. #14581775C23semidirect
210. #14581774C23semidirect
211. #14581774C23semidirect
212. #14581774C23semidirect
213. #14581774C23semidirect
214. #14581773C23semidirect
215. #14581772C23semidirect
216. #14581771C23semidirect
217. #14581770C23semidirect
218. #14581770C23semidirect
219. #14581770C23semidirect
220. #14581769C23semidirect
221. #14581768C23semidirect
223. #14581767C23semidirect
224. #14581767C23semidirect
225. #14581767C23semidirect
227. #14581766C23semidirect
229. #14581765C23semidirect
230. #14581765C23semidirect
231. #14581763C23semidirect
233. #14581762C23semidirect
234. #14581762C23semidirect
236. Q8×Dic83C23semidirect
237. C4×Dic166C23semidirect
240. C4×D332C23semidirect
241. C4×D332C23semidirect
242. C4×D332C23semidirect
243. C4×D332C23semidirect
244. C4×D332C23semidirect
245. C4×D332C23semidirect
246. D4×Dic83C23semidirect
249. #14581754C23semidirect
250. #14581754C23semidirect
252. C4×C22⋊D83C23semidirect
253. C4×C22⋊D83C23semidirect
254. (C22⋊D83)⋊C4C23semidirect
255. (C22⋊D83)⋊C4C23semidirect
256. #14581750C23semidirect
257. #14581749C23semidirect
258. #14581749C23semidirect
259. #14581749C23semidirect
260. #14581748C23semidirect
268. C2×C4⋊Dic83C23semidirect
281. C4⋊C4×D83C23semidirect
282. C4⋊C4×D83C23semidirect
283. C4⋊C4×D83C23semidirect
308. C2×(C2×D83)⋊C4C23semidirect
309. C2×(C2×D83)⋊C4C23semidirect
310. C22⋊C4×D83C23semidirect
311. C22⋊C4×D83C23semidirect
312. C22⋊C4×D83C23semidirect
324. #126×C83C23semidirect
325. #125×C83C23semidirect
326. #124×C83C23semidirect
327. #123×C83C23semidirect
328. C22⋊Q8×C83C23semidirect
330. C4×Q8×C83C23semidirect
331. C4×D4×C83C23semidirect
332. C4×D4×C83C23semidirect
333. #117×C83C23semidirect
350. C2×C42×C83C23semidirect
376. C2×D332#41semidirect
607. D332C2×#41semidirect
670. C2×C83#3513semidirect
696. C2×#529D83semidirect
702. C83C2×#3513semidirect
728. #529C2×D83semidirect
734. C2×#126C2×D83semidirect
738. C2×#125C2×D83semidirect
743. C2×#124C2×D83semidirect
759. C2×#123C2×D83semidirect
767. C2×C22⋊Q8C2×D83semidirect
787. C2×C4×Q8C2×D83semidirect
807. C2×C4×D4C2×D83semidirect
808. C2×C4×D4C2×D83semidirect
814. C2×#117C2×D83semidirect
824. C22×C42C2×D83semidirect
880. #126C22×D83semidirect
884. #125C22×D83semidirect
889. #124C22×D83semidirect
903. #123C22×D83semidirect
911. C22⋊Q8C22×D83semidirect
929. C4×Q8C22×D83semidirect
948. C4×D4C22×D83semidirect
949. C4×D4C22×D83semidirect
955. #117C22×D83semidirect
1028. C2×C42C22×D83semidirect
1351. C2#24921397direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#249213972
C2×#191284332
C2×#191284072
C2×#191284042
C2×#191283952
C2×#191283932
C2×#191283802
C2×#191283752
C2×#191283512
C2×#191283462
C2×#191283442
C2×#191283422
C2×#191283352
C2×#191283232
C2×#191283022
C2×#191282922
C2×#191282902
C2×#191282352
C2×#191282092
C2×#123×D832
C2×#191281832
C2×#191281732
C22×C4×D3322
C2×#529×C832
C2×#351383