Finite Group Databasebeta

← C2×#23777211 #35196593

Subgroups — C2×#23777211 #35196593

Order 20224.

7478 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777211C2132yesmaximal, direct product factor
2C2×#19099293C212yesmaximal, complemented
3C2×#19099291C211yesmaximal, characteristic, complemented
4C2×#19099288C211yesmaximal, characteristic, complemented
5C2×#19099272C212yesmaximal, complemented
6C2×#19099267C214yesmaximal, complemented
7C2×D4×Dic158C211yesmaximal, characteristic, complemented
8C2×Q8×C22⋊D79C212yesmaximal, complemented
9C2×#19099226C212yesmaximal, complemented
10C2×#19099192C214yesmaximal, complemented
11C2×#19099190C212yesmaximal, complemented
12C2×#19099117C211yesmaximal, characteristic, complemented
13C2×#19099115C212yesmaximal, complemented
14C22×#14579159C212yesmaximal, complemented
15C2×C4⋊Q8×D79C211yesmaximal, characteristic, complemented
16C2×#19099042C212yesmaximal
17C2×C4×#11929623C211yesmaximal, characteristic
18C2×D4×Q8×C79C211yesmaximal, characteristic, complemented
19C22×#11929623C2211yescharacteristic
20C23×Dic158C2212yes—
21C22×Q8×D79C2212yes—
22#19099293C22132yescomplemented
23#19099291C22116yescomplemented
24#19099288C22116yescomplemented
25#19099272C22132yescomplemented
26#19099267C22164yescomplemented
27D4×Dic158C22116yescomplemented
28Q8×C22⋊D79C22132yescomplemented
29#19099226C22132yescomplemented
30#19099192C22164yescomplemented
31#19099190C22132yescomplemented
32#19099117C22116yescomplemented
33#19099115C22132yescomplemented
34C2×#14579161C2211yescharacteristic
35C2×#14579160C2212yes—
36C2×#14579160C2212yes—
37C2×#14579160C2214yes—
38C2×#14579160C2212yes—
39C2×#14579160C2211yescharacteristic
40C2×#14579159C2214yes—
41C2×#14579159C2214yes—
42C2×#14579159C2212yes—
43C2×#14579159C2212yes—
44C2×#14579159C2214yes—
45C2×#14579159C2212yes—
46C2×#14579159C2211yescharacteristic
47C2×#14579159C22132yescomplemented
48C4⋊Q8×D79C22116yescomplemented
49C2×#14579153C2212yes—
50C2×#14579152C2212yes—
51C2×#14579151C2214yes—
52C2×#14579151C2212yes—
53C2×#14579151C2214yes—
54C2×#14579151C2214yes—
55C2×#14579141C2211yescharacteristic
56C2×#14579140C2214yes—
57C2×#14579140C2212yes—
58C2×#14579139C2214yes—
59C2×#14579139C2212yes—
60C2×#14579138C2214yes—
61C2×#14579138C2214yes—
62C2×#14579138C2214yes—
63C2×#14579137C2214yes—
64C2×#14579137C2211yescharacteristic
65#19099042C22132yes—
66C4×#11929623C22116yes—
67C2×Q8×Dic79C2212yes—
68C2×C4×Dic158C2211yescharacteristic
69C2×C4×Dic158C2212yes—
70C2×C4×Dic158C2211yescharacteristic
71C2×C4×Dic158C2212yes—
72C2×#14579126C2211yescharacteristic
73C2×#14579126C2212yes—
74C2×#14579126C2212yes—
75C2×#14579126C2214yes—
76C2×D4×Dic79C2211yescharacteristic
77C2×D4×Dic79C2212yes—
78C2×C4×C22⋊D79C2212yes—
79C2×C4×C22⋊D79C2214yes—
80C2×(C22⋊D79)⋊C4C2212yes—
81C2×(C22⋊D79)⋊C4C2214yes—
82C2×#14579119C2211yescharacteristic
83C2×#14579118C2212yes—
84C2×#14579117C2212yes—
85C2×#14579117C2214yes—
86C22×Dic79⋊C4C2214yes—
87C22×Dic79⋊C4C2214yes—
88C2×C4⋊C4×D79C2212yes—
89C2×C4⋊C4×D79C2212yes—
90C22×C4×Dic79C2212yes—
91C2×C42×D79C2211yescharacteristic
92C23×Q8×C79C2212yes—
93D4×Q8×C79C22116yescomplemented
94C2×C4⋊Q8×C79C2212yes—
95C2×C4⋊Q8×C79C2211yescharacteristic
96C2×C22⋊Q8×C79C2214yes—
97C2×C22⋊Q8×C79C2212yes—
98C2×C4×Q8×C79C2211yescharacteristic
99C2×C4×D4×C79C2211yescharacteristic
100C2×C4×D4×C79C2212yes—
101C2×#11929623Q8116yescomplemented
102C2×#11929623C2318yes—
103C22×Dic158—48no—
104C22×Dic158C2312yes—
105C22×Dic158C2312yes—
106C22×Dic158C2311yescharacteristic
107C22×Dic158C23116yes—
108C22×Dic158C2314yes—
109C22×Dic158C2314yes—
110C22×Dic158C2311yescharacteristic
111C2×Q8×D79—48no—
112C2×Q8×D79C23116yes—
113C22×C22⋊D79C2312yes—
114C23×Dic79C2312yes—
115C23×Dic79C2314yes—
116C23×Dic79C2312yes—
117C22×C4×D79C2311yescharacteristic
118C22×C4×D79C2311yescharacteristic
119C22×C4×D79C2314yes—
120C22×C4×D79C2311yescharacteristic
121#14579161C2318yes—
122#14579160C23116yes—
123#14579160C23116yes—
124#14579160C23132yes—
125#14579160C23116yes—
126#14579160C2318yes—
127#14579159C23132yes—
128#14579159C23132yes—
129#14579159C23116yes—
130#14579159C23116yes—
131#14579159C23132yes—
132#14579159C23116yes—
133#14579159C2318yes—
134#14579153C23116yes—
135#14579152C23116yes—
136#14579151C23132yes—
137#14579151C23116yes—
138#14579151C23132yes—
139#14579151C23132yes—
140#14579141C2318yes—
141#14579140C23132yes—
142#14579140C23116yes—
143#14579139C23132yes—
144#14579139C23116yes—
145#14579138C23132yes—
146#14579138C23132yes—
147#14579138C23132yes—
148#14579137C23132yes—
149#14579137C2318yes—
150Q8×Dic79C23116yes—
151C4×Dic158C2318yes—
152C4×Dic158C23116yes—
153C4×Dic158C2318yes—
154C4×Dic158C23116yes—
155#14579126C23116yes—
156#14579126C23132yes—
157#14579126C2318yes—
158#14579126C23116yes—
159D4×Dic79C23116yes—
160D4×Dic79C2318yes—
161C4×C22⋊D79C23116yes—
162C4×C22⋊D79C23132yes—
163(C22⋊D79)⋊C4C23132yes—
164(C22⋊D79)⋊C4C23116yes—
165#14579119C2318yes—
166#14579118C23116yes—
167#14579117C23116yes—
168#14579117C23132yes—
169C2×C4⋊Dic79C2312yes—
170C2×C4⋊Dic79C2312yes—
171C2×C4⋊Dic79C2311yescharacteristic
172C2×C4⋊Dic79C2311yescharacteristic
173C2×C4⋊Dic79C2312yes—
174C2×C4⋊Dic79C2314yes—
175C2×Dic79⋊C4C23132yes—
176C2×Dic79⋊C4C23132yes—
177C2×Dic79⋊C4C2314yes—
178C2×Dic79⋊C4C2314yes—
179C2×Dic79⋊C4C2312yes—
180C2×Dic79⋊C4C2312yes—
181C2×Dic79⋊C4C2314yes—
182C2×Dic79⋊C4C2314yes—
183C2×Dic79⋊C4C2314yes—
184C2×Dic79⋊C4C2314yes—
185C2×Dic79⋊C4C2312yes—
186C2×Dic79⋊C4C2312yes—
187C2×Dic79⋊C4C2312yes—
188C2×Dic79⋊C4C2314yes—
189C2×Dic79⋊C4C2314yes—
190C2×Dic79⋊C4C2312yes—
191C2×Dic79⋊C4C2312yes—
192C4⋊C4×D79C23116yes—
193C4⋊C4×D79C23116yes—
194C2×C22⋊Dic79C2312yes—
195C2×C22⋊Dic79C2314yes—
196C2×(C2×D79)⋊C4C2312yes—
197C2×(C2×D79)⋊C4C2312yes—
198C2×(C2×D79)⋊C4C2312yes—
199C2×C4×Dic79C2311yescharacteristic
200C2×C4×Dic79C2311yescharacteristic
201C2×C4×Dic79C2311yescharacteristic
202C2×C4×Dic79C2312yes—
203C2×C4×Dic79C2312yes—
204C2×C4×Dic79C2312yes—
205C2×C4×Dic79C23116yes—
206C2×C4×Dic79C2314yes—
207C2×C4×Dic79C2314yes—
208C2×C4×Dic79C2312yes—
209C42×D79C2318yes—
210C22×Q8×C79—48no—
211C22×Q8×C79C2311yescharacteristic
212C22×Q8×C79C2312yes—
213C22×Q8×C79C23116yes—
214C22×Q8×C79C2314yes—
215C22×D4×C79C2311yescharacteristic
216C23×C4×C79C2312yes—
217C23×C4×C79C2314yes—
218C4⋊Q8×C79C23116yes—
219C4⋊Q8×C79C2318yes—
220C22⋊Q8×C79C23132yes—
221C22⋊Q8×C79C23116yes—
222C4×Q8×C79C2318yes—
223C4×D4×C79C2318yes—
224C4×D4×C79C23116yes—
225C2×C4⋊C4×C79C2312yes—
226C2×C4⋊C4×C79C2311yescharacteristic
227C2×C4⋊C4×C79C2311yescharacteristic
228C2×C4⋊C4×C79C2312yes—
229C2×C4⋊C4×C79C2312yes—
230C2×C4⋊C4×C79C2314yes—
231C2×C22⋊C4×C79C2312yes—
232C2×C22⋊C4×C79C2314yes—
233C2×C42×C79C2311yescharacteristic
234C2×C42×C79C2312yes—
235C23×D79C2411yescharacteristic
236#11929623C2×Q8164yescomplemented
237C2×Dic158—28no—
238C2×Dic158—28no—
239C2×Dic158—24no—
240C2×Dic158—432no—
241C2×Dic158—48no—
242C2×Dic158—48no—
243C2×Dic158C2×Q818yescomplemented
244C2×Dic158C2418yes—
245C2×Dic158C2414yes—
246C2×Dic158C2418yes—
247C2×Dic158C24116yes—
248C2×Dic158C24116yes—
249C2×Dic158C2414yes—
250Q8×D79—432no—
251C2×C22⋊D79C2×Q8116yescomplemented
252C2×C22⋊D79C2418yes—
253C22×Dic79—28no—
254C22×Dic79—48no—
255C22×Dic79C2×Q8116yescomplemented
256C22×Dic79C2411yescharacteristic
257C22×Dic79C2412yes—
258C22×Dic79C2414yes—
259C22×Dic79C2412yes—
260C22×Dic79C2412yes—
261C22×Dic79C2418yes—
262C22×Dic79C24116yes—
263C22×Dic79C2412yes—
264C22×Dic79C2411yescharacteristic
265C22×Dic79C2418yes—
266C22×Dic79C2411yescharacteristic
267C2×C4×D79—24no—
268C2×C4×D79—24no—
269C2×C4×D79—48no—
270C2×C4×D79C2×Q818yescomplemented
271C2×C4×D79C2414yes—
272C2×C4×D79C2414yes—
273C2×C4×D79C24116yes—
274C2×C4×D79C2414yes—
275C4⋊Dic79C2418yes—
276C4⋊Dic79C2418yes—
277C4⋊Dic79C2414yes—
278C4⋊Dic79C2414yes—
279C4⋊Dic79C2418yes—
280C4⋊Dic79C24116yes—
281Dic79⋊C4C24116yes—
282Dic79⋊C4C24116yes—
283Dic79⋊C4C2418yes—
284Dic79⋊C4C2418yes—
285Dic79⋊C4C24116yes—
286Dic79⋊C4C24116yes—
287Dic79⋊C4C24116yes—
288Dic79⋊C4C24116yes—
289Dic79⋊C4C2418yes—
290Dic79⋊C4C2418yes—
291Dic79⋊C4C2418yes—
292Dic79⋊C4C24116yes—
293Dic79⋊C4C24116yes—
294Dic79⋊C4C2418yes—
295Dic79⋊C4C2418yes—
296C22⋊Dic79C24116yes—
297C22⋊Dic79C2418yes—
298(C2×D79)⋊C4C2418yes—
299(C2×D79)⋊C4C2418yes—
300(C2×D79)⋊C4C2418yes—
301C4×Dic79C2414yes—
302C4×Dic79C2414yes—
303C4×Dic79C2414yes—
304C4×Dic79C2418yes—
305C4×Dic79C2418yes—
306C4×Dic79C2418yes—
307C4×Dic79C24116yes—
308C4×Dic79C24116yes—
309C4×Dic79C2418yes—
310C24×C79C2412yes—
311C2×Q8×C79—28no—
312C2×Q8×C79—24no—
313C2×Q8×C79—48no—
314C2×Q8×C79—432no—
315C2×Q8×C79C2418yes—
316C2×Q8×C79C2414yes—
317C2×Q8×C79C24116yes—
318C2×D4×C79C2×Q818yescomplemented
319C2×D4×C79C2414yes—
320C22×C4×C79—28no—
321C22×C4×C79—48no—
322C22×C4×C79C2412yes—
323C22×C4×C79C2418yes—
324C22×C4×C79C2412yes—
325C22×C4×C79C2414yes—
326C22×C4×C79C2411yescharacteristic
327C22×C4×C79C2412yes—
328C22×C4×C79C24116yes—
329C22×C4×C79C2411yescharacteristic
330C22×C4×C79C2411yescharacteristic
331C4⋊C4×C79C2418yes—
332C4⋊C4×C79C2414yes—
333C4⋊C4×C79C2414yes—
334C4⋊C4×C79C2418yes—
335C4⋊C4×C79C2418yes—
336C4⋊C4×C79C24116yes—
337C22⋊C4×C79C24116yes—
338C22⋊C4×C79C2418yes—
339C42×C79C2414yes—
340C42×C79C2418yes—
341C23×C79—24no—
342C23×C79—24no—
343C23×C79C22×Q818yes—
344C23×C79C2514yes—
345C23×C79C2511yescharacteristic
346C22×D79—22no—
347C22×D79—22no—
348C22×D79C22×Q814yes—
349C22×D79C2512yes—
350Q8×C79—216no—
351Q8×C79—28no—
352Q8×C79—416no—
353D4×C79C22×Q8116yescomplemented
354C2×C4×C79—28no—
355C2×C4×C79—24no—
356C2×C4×C79—24no—
357C2×C4×C79—22no—
358C2×C4×C79—24no—
359C2×C4×C79—216no—
360C2×C4×C79—416no—
361C2×C4×C79C22×Q814yes—
362C2×C4×C79H(5,𝔽2)14yes—
363C2×C4×C79C2514yes—
364C2×C4×C79C2514yes—
365C2×C4×C79C2512yes—
366C2×C4×C79C2518yes—
367C2×C4×C79C2514yes—
368C2×C4×C79C2512yes—
369C2×C4×C79C2512yes—
370C22⋊D79C22×Q8132yescomplemented
371C2×Dic79—22no—
372C2×Dic79—28no—
373C2×Dic79—24no—
374C2×Dic79—24no—
375C2×Dic79—24no—
376C2×Dic79—216no—
377C2×Dic79—416no—
378C2×Dic79C22×Q814yes—
379C2×Dic79C22×Q818yes—
380C2×Dic79C22×Q8132yescomplemented
381C2×Dic792−1+414yes—
382C2×Dic79C2514yes—
383C2×Dic79C2514yes—
384C2×Dic79C2512yes—
385C2×Dic79C2514yes—
386C2×Dic79C2518yes—
387C2×Dic79C2514yes—
388C2×Dic79C2512yes—
389C2×Dic79C2512yes—
390C4×D79—28no—
391C4×D79—28no—
392C4×D79—416no—
393C4×D79C22×Q8116yescomplemented
394Dic158—216no—
395Dic158—28no—
396Dic158—216no—
397Dic158—416no—
398Dic158—416no—
399Dic158C22×Q8116yescomplemented
400C22×C79—24no—
401C22×C79—24no—
402C22×C79—216no—
403C22×C79C23×Q818yes—
404C22×C79C23×Q812yes—
405C22×C79C2×H(5,𝔽2)12yes—
406C22×C79C2×2−1+412yes—
407C22×C79C2611yescharacteristic
408C2×D79—22no—
409C2×D79—22no—
410C2×D79—28no—
411C2×D79C23×Q814yes—
412C4×C79—24no—
413C4×C79—24no—
414C4×C79—28no—
415C4×C79—24no—
416C4×C79—22no—
417C4×C79C23×Q814yes—
418C4×C79C2×H(5,𝔽2)14yes—
419Dic79—28no—
420Dic79—24no—
421Dic79—22no—
422Dic79—24no—
423Dic79—24no—
424Dic79C23×Q818yes—
425Dic79C23×Q814yes—
426Dic79C2×2−1+414yes—
427C2×#3503—791nomaximal, Sylow
428C2×C79—28no—
429C2×C79#350314yescomplemented
430C2×C79C24×Q811yescharacteristic
431C2×C79C22×H(5,𝔽2)11yescharacteristic
432C2×C79C22×2−1+411yescharacteristic
433D79—24no—
434#3503—7932no—
435C2×Q82—792no—
436C2×#557—791no—
437C2×#557—791no—
438C2×#554—794no—
439C2×#554—792no—
440C2×D4×Q8—792no—
441C2×D4×Q8—792no—
442C2×D4×Q8—791no—
443C2×D4×Q8D7911yescharacteristic, complemented
444C2×#544—792no—
445C2×#544—794no—
446C2×#533—792no—
447C2×#533—791no—
448C22×C4⋊Q8—792no—
449C22×C4⋊Q8—791no—
450C2×#520—792no—
451C2×C4×#41—791no—
452C79C2×#350311yescharacteristic, complemented, Sylow
453C22×#41—791no—
454C23×Q8—792no—
455C23×Q8—792no—
456C23×Q8C2×D7912yes—
457Q82—7932no—
458#557—7916no—
459#557—7916no—
460#554—7964no—
461#554—7932no—
462D4×Q8—7932no—
463D4×Q8—7932no—
464D4×Q8—7916no—
465D4×Q8C2×D79116yescomplemented
466#544—7932no—
467#544—7964no—
468#533—7932no—
469#533—7916no—
470C2×C4⋊Q8—792no—
471C2×C4⋊Q8—791no—
472C2×C4⋊Q8—794no—
473C2×C4⋊Q8—792no—
474C2×C4⋊Q8—792no—
475C2×C4⋊Q8—794no—
476C2×C4⋊Q8—7932no—
477C2×C4⋊Q8—794no—
478C2×C4⋊Q8—7916no—
479C2×C4⋊Q8—792no—
480C2×C4⋊Q8—792no—
481C2×C4⋊Q8—791no—
482C2×C4⋊Q8—794no—
483C2×C4⋊Q8—792no—
484C2×C4⋊Q8—791no—
485C2×C4⋊Q8C2×D7911yescharacteristic
486C2×C4⋊Q8C2×D7912yes—
487C2×#125—794no—
488C2×#125—792no—
489C2×#125—794no—
490C2×#125—794no—
491C2×#125—792no—
492C2×#125—792no—
493C2×C22⋊Q8—791no—
494C2×C22⋊Q8—794no—
495C2×C22⋊Q8—792no—
496C2×C22⋊Q8—794no—
497C2×C22⋊Q8—791no—
498C2×C22⋊Q8—792no—
499C2×C22⋊Q8—794no—
500C2×C22⋊Q8—794no—
501C2×C22⋊Q8—794no—
502C2×C22⋊Q8—794no—
503C2×C22⋊Q8C2×D7912yes—
504C2×C22⋊Q8C2×D7914yes—
505#520—7932no—
506C4×#41—7916no—
507C2×C4×Q8—792no—
508C2×C4×Q8—791no—
509C2×C4×Q8—792no—
510C2×C4×Q8—792no—
511C2×C4×Q8—794no—
512C2×C4×Q8—791no—
513C2×C4×Q8—792no—
514C2×C4×Q8—791no—
515C2×C4×Q8—792no—
516C2×C4×Q8C2×D7911yescharacteristic
517C2×C4×D4—791no—
518C2×C4×D4—792no—
519C2×C4×D4—792no—
520C2×C4×D4—794no—
521C2×C4×D4—792no—
522C2×C4×D4—794no—
523C2×C4×D4C2×D7911yescharacteristic
524C2×C4×D4C2×D7912yes—
525C2×#117—791no—
526C2×#117—792no—
527C2×#117—794no—
528C2×#117—792no—
529C22×C4⋊C4—794no—
530C22×C4⋊C4—794no—
531C22×C4⋊C4—792no—
532C22×C4⋊C4—792no—
533C22×C42—792no—
534C22×C42—791no—
535C2×#41—7916no—
536C2×#41—798no—
537C22×Q8—48no—
538C22×Q8—3168no—
539C22×Q8—3168no—
540C22×Q8—7916no—
541C22×Q8—794no—
542C22×Q8—794no—
543C22×Q8—7916no—
544C22×Q8—791no—
545C22×Q8—792no—
546C22×Q8—792no—
547C22×Q8—791no—
548C22×Q8C22×D7912yes—
549C22×Q8C22×D7911yescharacteristic
550C22×Q8C22×D7914yes—
551C22×Q8C22×D79116yes—
552C22×D4—792no—
553C22×D4C22×D7911yescharacteristic
554C23×C4—794no—
555C23×C4—794no—
556C23×C4—792no—
557C23×C4—791no—
558C23×C4—792no—
559C23×C4—791no—
560C23×C4—791no—
561C23×C4C22×D7912yes—
562C23×C4C22×D7914yes—
563C4⋊Q8—7916no—
564C4⋊Q8—798no—
565C4⋊Q8—7932no—
566C4⋊Q8—7916no—
567C4⋊Q8—7916no—
568C4⋊Q8—7932no—
569C4⋊Q8—7932no—
570C4⋊Q8—7916no—
571C4⋊Q8—7916no—
572C4⋊Q8—798no—
573C4⋊Q8—7932no—
574C4⋊Q8—7916no—
575C4⋊Q8—798no—
576C4⋊Q8C22×D7918yes—
577C4⋊Q8C22×D79116yes—
578#125—7932no—
579#125—7916no—
580#125—7932no—
581#125—7932no—
582#125—7916no—
583#125—7916no—
584C22⋊Q8—798no—
585C22⋊Q8—7932no—
586C22⋊Q8—7916no—
587C22⋊Q8—7932no—
588C22⋊Q8—798no—
589C22⋊Q8—7916no—
590C22⋊Q8—7932no—
591C22⋊Q8—7932no—
592C22⋊Q8—7932no—
593C22⋊Q8—7932no—
594C22⋊Q8C22×D79116yes—
595C22⋊Q8C22×D79132yes—
596C4×Q8—7916no—
597C4×Q8—798no—
598C4×Q8—7916no—
599C4×Q8—7916no—
600C4×Q8—7932no—
601C4×Q8—798no—
602C4×Q8—7916no—
603C4×Q8—798no—
604C4×Q8—7916no—
605C4×Q8C22×D7918yes—
606C4×D4—798no—
607C4×D4—7916no—
608C4×D4—7916no—
609C4×D4—7932no—
610C4×D4—7916no—
611C4×D4—7932no—
612C4×D4C22×D7918yes—
613C4×D4C22×D79116yes—
614#117—798no—
615#117—7916no—
616#117—7932no—
617#117—7916no—
618C2×C4⋊C4—794no—
619C2×C4⋊C4—792no—
620C2×C4⋊C4—794no—
621C2×C4⋊C4—792no—
622C2×C4⋊C4—794no—
623C2×C4⋊C4—794no—
624C2×C4⋊C4—792no—
625C2×C4⋊C4—7932no—
626C2×C4⋊C4—794no—
627C2×C4⋊C4—794no—
628C2×C4⋊C4—792no—
629C2×C4⋊C4—7932no—
630C2×C4⋊C4—792no—
631C2×C4⋊C4—792no—
632C2×C4⋊C4—791no—
633C2×C4⋊C4—792no—
634C2×C4⋊C4—791no—
635C2×C4⋊C4—792no—
636C2×C4⋊C4—794no—
637C2×C4⋊C4—794no—
638C2×C4⋊C4—792no—
639C2×C4⋊C4—794no—
640C2×C4⋊C4—792no—
641C2×C4⋊C4—7916no—
642C2×C4⋊C4—7916no—
643C2×C4⋊C4C22×D7912yes—
644C2×C4⋊C4C22×D7912yes—
645C2×C4⋊C4C22×D7911yescharacteristic
646C2×C4⋊C4C22×D7911yescharacteristic
647C2×C4⋊C4C22×D7914yes—
648C2×C4⋊C4C22×D7912yes—
649C2×C22⋊C4—794no—
650C2×C22⋊C4—792no—
651C2×C22⋊C4—792no—
652C2×C22⋊C4—792no—
653C2×C22⋊C4—792no—
654C2×C22⋊C4C22×D7914yes—
655C2×C22⋊C4C22×D7912yes—
656C2×C42—792no—
657C2×C42—791no—
658C2×C42—794no—
659C2×C42—794no—
660C2×C42—792no—
661C2×C42—792no—
662C2×C42—792no—
663C2×C42—791no—
664C2×C42—7916no—
665C2×C42—791no—
666C2×C42—798no—
667C2×C42C22×D7912yes—
668C2×C42C22×D7911yescharacteristic
669C24—791no—
670C24C23×D7912yes—
671#41—7964no—
672C2×Q8—24no—
673C2×Q8—28no—
674C2×Q8—48no—
675C2×Q8—432no—
676C2×Q8—31632no—
677C2×Q8—3168no—
678C2×Q8—3168no—
679C2×Q8—31632no—
680C2×Q8—798no—
681C2×Q8—7916no—
682C2×Q8—7916no—
683C2×Q8—794no—
684C2×Q8—798no—
685C2×Q8—798no—
686C2×Q8—794no—
687C2×Q8—1588no—
688C2×Q8—1588no—
689C2×Q8—1584no—
690C2×Q8C23×D7918yes—
691C2×Q8C23×D7914yes—
692C2×Q8C23×D79116yes—
693C2×D4—7916no—
694C2×D4—798no—
695C2×D4Q8×D7918yescomplemented
696C2×D4C23×D7914yes—
697C22×C4—28no—
698C22×C4—48no—
699C22×C4—3168no—
700C22×C4—3168no—
701C22×C4—7916no—
702C22×C4—7916no—
703C22×C4—7916no—
704C22×C4—798no—
705C22×C4—792no—
706C22×C4—791no—
707C22×C4—791no—
708C22×C4—798no—
709C22×C4—794no—
710C22×C4—798no—
711C22×C4—792no—
712C22×C4—792no—
713C22×C4—791no—
714C22×C4—792no—
715C22×C4—794no—
716C22×C4—794no—
717C22×C4—794no—
718C22×C4—1584no—
719C22×C4—1588no—
720C22×C4—1584no—
721C22×C4C23×D7918yes—
722C22×C4C23×D7912yes—
723C22×C4C23×D7912yes—
724C22×C4C23×D7911yescharacteristic
725C22×C4C23×D7914yes—
726C22×C4C23×D7912yes—
727C22×C4C23×D79116yes—
728C22×C4C23×D7911yescharacteristic
729C22×C4C23×D7911yescharacteristic
730C4⋊C4—7916no—
731C4⋊C4—798no—
732C4⋊C4—7916no—
733C4⋊C4—798no—
734C4⋊C4—7916no—
735C4⋊C4—7916no—
736C4⋊C4—7916no—
737C4⋊C4—7916no—
738C4⋊C4—798no—
739C4⋊C4—798no—
740C4⋊C4—798no—
741C4⋊C4—798no—
742C4⋊C4—7916no—
743C4⋊C4—798no—
744C4⋊C4—7916no—
745C4⋊C4—798no—
746C4⋊C4—798no—
747C4⋊C4—794no—
748C4⋊C4—794no—
749C4⋊C4—7916no—
750C4⋊C4—798no—
751C4⋊C4C23×D7918yes—
752C4⋊C4C23×D7918yes—
753C4⋊C4C23×D7914yes—
754C4⋊C4C23×D7914yes—
755C4⋊C4C23×D79116yes—
756C4⋊C4C23×D7918yes—
757C22⋊C4—7916no—
758C22⋊C4—798no—
759C22⋊C4—798no—
760C22⋊C4—798no—
761C22⋊C4—798no—
762C22⋊C4C23×D79116yes—
763C22⋊C4C23×D7918yes—
764C42—794no—
765C42—798no—
766C42—794no—
767C42—798no—
768C42—798no—
769C42—794no—
770C42—7916no—
771C42—7916no—
772C42—798no—
773C42C23×D7914yes—
774C42C23×D7918yes—
775C23—24no—
776C23—24no—
777C23—792no—
778C23—794no—
779C23—1582no—
780C23—1582no—
781C23C2×Q8×D7918yes—
782C23C24×D7914yes—
783C23C24×D7911yescharacteristic
784Q8—28no—
785Q8—216no—
786Q8—416no—
787Q8—31616no—
788Q8—31616no—
789Q8—7916no—
790Q8—15816no—
791Q8—1588no—
792Q8—15816no—
793D4—7932no—
794D4C2×Q8×D79116yescomplemented
795C2×C4—24no—
796C2×C4—24no—
797C2×C4—28no—
798C2×C4—22no—
799C2×C4—24no—
800C2×C4—216no—
801C2×C4—416no—
802C2×C4—31616no—
803C2×C4—31616no—
804C2×C4—794no—
805C2×C4—794no—
806C2×C4—792no—
807C2×C4—792no—
808C2×C4—794no—
809C2×C4—798no—
810C2×C4—7932no—
811C2×C4—7916no—
812C2×C4—794no—
813C2×C4—794no—
814C2×C4—792no—
815C2×C4—798no—
816C2×C4—794no—
817C2×C4—1588no—
818C2×C4—15816no—
819C2×C4—1588no—
820C2×C4—1584no—
821C2×C4—1582no—
822C2×C4—1584no—
823C2×C4—1584no—
824C2×C4—1588no—
825C2×C4C2×Q8×D7914yes—
826C2×C4#1457920614yes—
827C2×C4C24×D7914yes—
828C2×C4C24×D7914yes—
829C2×C4C24×D7912yes—
830C2×C4C24×D7918yes—
831C2×C4C24×D7914yes—
832C2×C4C24×D7912yes—
833C2×C4C24×D7912yes—
834C22—24no—
835C22—24no—
836C22—216no—
837C22—794no—
838C22—1582no—
839C22—1582no—
840C22—1588no—
841C22C22×Q8×D7918yes—
842C22C22×Q8×D7912yes—
843C22C2×#1457920612yes—
844C222−1+4×D7912yes—
845C22C25×D7911yescharacteristic
846C4—24no—
847C4—24no—
848C4—28no—
849C4—22no—
850C4—24no—
851C4—794no—
852C4—798no—
853C4—794no—
854C4—1588no—
855C4—1584no—
856C4—1582no—
857C4—1584no—
858C4—1584no—
859C4C22×Q8×D7914yes—
860C4C2×#1457920614yes—
861C2—28no—
862C2—1584no—
863C2#2377721114yesdirect product factor
864C2C23×Q8×D7911yescharacteristic
865C2C22×#1457920611yescharacteristic
866C2C2×2−1+4×D7911yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×D4×Q8×C79C2
socleC23×C79C25
prime radicalC22×#11929623C22
hypercenterC2×D4×Q8D79
hypocenterC79C2×#3503
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. #23777211C2direct (N × H)
2. C2×#19099293C2semidirect
3. C2×#19099291C2semidirect
4. C2×#19099288C2semidirect
5. C2×#19099272C2semidirect
6. C2×#19099267C2semidirect
7. C2×D4×Dic158C2semidirect
8. C2×Q8×C22⋊D79C2semidirect
9. C2×#19099226C2semidirect
10. C2×#19099192C2semidirect
11. C2×#19099190C2semidirect
12. C2×#19099117C2semidirect
13. C2×#19099115C2semidirect
14. C22×#14579159C2semidirect
15. C2×C4⋊Q8×D79C2semidirect
18. C2×D4×Q8×C79C2semidirect
22. #19099293C22semidirect
23. #19099291C22semidirect
24. #19099288C22semidirect
25. #19099272C22semidirect
26. #19099267C22semidirect
27. D4×Dic158C22semidirect
28. Q8×C22⋊D79C22semidirect
29. #19099226C22semidirect
30. #19099192C22semidirect
31. #19099190C22semidirect
32. #19099117C22semidirect
33. #19099115C22semidirect
47. C2×#14579159C22semidirect
48. C4⋊Q8×D79C22semidirect
93. D4×Q8×C79C22semidirect
101. C2×#11929623Q8semidirect
236. #11929623C2×Q8semidirect
243. C2×Dic158C2×Q8semidirect
251. C2×C22⋊D79C2×Q8semidirect
255. C22×Dic79C2×Q8semidirect
270. C2×C4×D79C2×Q8semidirect
318. C2×D4×C79C2×Q8semidirect
353. D4×C79C22×Q8semidirect
370. C22⋊D79C22×Q8semidirect
380. C2×Dic79C22×Q8semidirect
393. C4×D79C22×Q8semidirect
399. Dic158C22×Q8semidirect
429. C2×C79#3503semidirect
443. C2×D4×Q8D79semidirect
452. C79C2×#3503semidirect
465. D4×Q8C2×D79semidirect
695. C2×D4Q8×D79semidirect
794. D4C2×Q8×D79semidirect
863. C2#23777211direct (N × H)

Maximal subgroups

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

subgroupindex
#237772112
C2×#190992932
C2×#190992912
C2×#190992882
C2×#190992722
C2×#190992672
C2×D4×Dic1582
C2×Q8×C22⋊D792
C2×#190992262
C2×#190991922
C2×#190991902
C2×#190991172
C2×#190991152
C22×#145791592
C2×C4⋊Q8×D792
C2×#190990422
C2×C4×#119296232
C2×D4×Q8×C792
C2×#350379