Finite Group Databasebeta

← C2×#19143286 #25960448

Subgroups — C2×#19143286 #25960448

Order 11008.

3046 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063333C211yesmaximal, characteristic, complemented
2C23×C8×D43C211yesmaximal, characteristic, complemented
3C2×#14583408C211yesmaximal, characteristic
4#19143286C2116yesmaximal, direct product factor
5C2×#14582972C211yesmaximal, characteristic, complemented
6C2×#14582970C211yesmaximal, characteristic, complemented
7C2×#14582968C211yesmaximal, characteristic, complemented
8C2×D4×C43⋊C8C211yesmaximal, characteristic, complemented
9C2×#14582964C211yesmaximal, characteristic, complemented
10C2×(C22⋊D43)⋊C8C211yesmaximal, characteristic, complemented
11C2×(C22⋊D43)⋊C8C211yesmaximal, characteristic, complemented
12C2×#14582924C211yesmaximal, characteristic, complemented
13C2×#14582864C211yesmaximal, characteristic, complemented
14C2×#14582861C211yesmaximal, characteristic, complemented
15C2×#14582856C211yesmaximal, characteristic, complemented
16C2×C43×#435C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C2×#13063333—28no—
20C2×#13063333C2218yescomplemented
21C22×#10621872C2211yescharacteristic
22C22×#10621872C2211yescharacteristic
23C22×#10621872C2211yescharacteristic, complemented
24C23×C43⋊C8C2211yescharacteristic
25C23×C43⋊C8C2211yescharacteristic, complemented
26C22×C8×D43—28no—
27C22×C8×D43C2211yescharacteristic
28C22×C8×D43C2211yescharacteristic
29C22×C8×D43C2211yescharacteristic
30C22×C8×D43C2211yescharacteristic
31C22×C8×D43C2218yescomplemented
32C22×C8×D43C2211yescharacteristic, complemented
33#14583408C418yes—
34#14583408C2218yes—
35C2×#13063310C411yescharacteristic
36C2×#13063307C411yescharacteristic
37C2×#13063303C411yescharacteristic
38C2×#13063302C411yescharacteristic
39C2×#13063298C411yescharacteristic
40C2×#13063297C411yescharacteristic
41C2×#13063295C411yescharacteristic
42C2×#13063293C411yescharacteristic
43C2×C4×D172C2211yescharacteristic
44C2×C4×C22⋊D43C2211yescharacteristic
45C2×C4×C22⋊D43C2211yescharacteristic
46C2×#13063282C2211yescharacteristic
47#14582972C2218yescomplemented
48#14582970C2218yescomplemented
49#14582968C2218yescomplemented
50D4×C43⋊C8C2218yescomplemented
51#14582964C2218yescomplemented
52(C22⋊D43)⋊C8C2218yescomplemented
53(C22⋊D43)⋊C8C2218yescomplemented
54#14582924C2218yescomplemented
55C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
56C2×Dic43⋊C8C2211yescharacteristic, complemented
57C2×Dic43⋊C8C2211yescharacteristic, complemented
58#14582864C2218yescomplemented
59#14582861C2218yescomplemented
60C2×C22⋊(C43⋊C8)C2211yescharacteristic
61C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
62C2×(C2×D43)⋊C8C2211yescharacteristic
63C2×(C2×D43)⋊C8C2211yescharacteristic
64C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
65C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
66#14582856C2218yescomplemented
67C2×#13063235C2211yescharacteristic, complemented
68C2×C4×C43⋊C8C2211yescharacteristic, complemented
69C2×C8×Dic43C2211yescharacteristic, complemented
70C22×M16×C43C2211yescharacteristic, complemented
71C23×C8×C43C2211yescharacteristic
72C2×C4×D4×C43C2211yescharacteristic
73C43×#435C2218yescomplemented
74C2×C4⋊C8×C43C2211yescharacteristic, complemented
75C2×C22⋊C8×C43C2211yescharacteristic
76C2×C22⋊C8×C43C2211yescharacteristic, complemented
77C2×#97×C43C2211yescharacteristic, complemented
78C24×D43C2×C411yescharacteristic
79C2×#10621898—24no—
80C2×#10621898—24no—
81C2×#10621898C2×C414yes—
82C2×#10621898C2314yes—
83C22×Dic86C2×C411yescharacteristic
84C22×D172C2×C411yescharacteristic
85C22×D172C2×C411yescharacteristic
86C22×C22⋊D43C2×C411yescharacteristic
87C22×C22⋊D43C2×C411yescharacteristic
88C22×C22⋊D43C2×C411yescharacteristic
89C22×C22⋊D43C2×C411yescharacteristic
90C23×Dic43C2×C411yescharacteristic
91C22×C4×D43—24no—
92C22×C4×D43—24no—
93C22×C4×D43C2×C411yescharacteristic
94C22×C4×D43C2×C411yescharacteristic
95C22×C4×D43C2×C414yes—
96C22×C4×D43C2311yescharacteristic
97C22×C4×D43C2311yescharacteristic
98C22×C4×D43C2314yes—
99C22×C4×D43C2311yescharacteristic
100#13063333—232no—
101C2×#10621872—24no—
102C2×#10621872—24no—
103C2×#10621872—24no—
104C2×#10621872C2314yes—
105C2×#10621872C2314yes—
106C2×#10621872C2314yescomplemented
107C22×C43⋊C8—24no—
108C22×C43⋊C8—24no—
109C22×C43⋊C8C2311yescharacteristic
110C22×C43⋊C8C2311yescharacteristic
111C22×C43⋊C8C2311yescharacteristic
112C22×C43⋊C8C2314yes—
113C22×C43⋊C8C2311yescharacteristic
114C22×C43⋊C8C2314yescomplemented
115C2×C8×D43—24no—
116C2×C8×D43—24no—
117C2×C8×D43—24no—
118C2×C8×D43—24no—
119C2×C8×D43—232no—
120C2×C8×D43D418yescomplemented
121C2×C8×D43C2314yes—
122C2×C8×D43C2314yes—
123C2×C8×D43C2314yes—
124C2×C8×D43C2314yes—
125C2×C8×D43C2314yescomplemented
126#13063310C2×C418yes—
127#13063307C2×C418yes—
128#13063303C2×C418yes—
129#13063302C2×C418yes—
130#13063298C2×C418yes—
131#13063297C2×C418yes—
132#13063295C2×C418yes—
133#13063293C2×C418yes—
134C4×D172C2×C414yes—
135C4×D172C2314yes—
136C4×C22⋊D43C2×C414yes—
137C4×C22⋊D43C2×C414yes—
138C4×C22⋊D43C2314yes—
139C4×C22⋊D43C2314yes—
140#13063282C2×C414yes—
141#13063282C2314yes—
142C2×C4⋊Dic43C2×C411yescharacteristic
143C2×Dic43⋊C4C2×C411yescharacteristic
144C2×Dic43⋊C4C2×C411yescharacteristic
145C2×Dic43⋊C4C2×C411yescharacteristic
146C2×Dic43⋊C4C2×C411yescharacteristic
147C2×C22⋊Dic43C2×C411yescharacteristic
148C2×C22⋊Dic43C2×C411yescharacteristic
149C2×(C2×D43)⋊C4C2×C411yescharacteristic
150C2×(C2×D43)⋊C4C2×C411yescharacteristic
151C2×(C2×D43)⋊C4C2×C411yescharacteristic
152C2×(C2×D43)⋊C4C2×C411yescharacteristic
153C2×(C2×D43)⋊C4C2×C411yescharacteristic
154C2×(C2×D43)⋊C4C2×C411yescharacteristic
155C2×C4×Dic43C2311yescharacteristic
156C4⋊(C43⋊C8)C2314yescomplemented
157Dic43⋊C8C2314yescomplemented
158Dic43⋊C8C2314yescomplemented
159C22⋊(C43⋊C8)C2314yes—
160C22⋊(C43⋊C8)C2314yescomplemented
161(C2×D43)⋊C8C2314yes—
162(C2×D43)⋊C8C2314yes—
163(C2×D43)⋊C8C2314yescomplemented
164(C2×D43)⋊C8C2314yescomplemented
165#13063235C2314yescomplemented
166C4×C43⋊C8C2314yescomplemented
167C8×Dic43C2314yescomplemented
168C22×D4×C43C2×C411yescharacteristic
169C23×C4×C43C2311yescharacteristic
170C23×C4×C43C2311yescharacteristic
171C2×M16×C43—24no—
172C2×M16×C43C2314yescomplemented
173C22×C8×C43—24no—
174C22×C8×C43C2311yescharacteristic
175C22×C8×C43C2311yescharacteristic
176C22×C8×C43C2314yes—
177C22×C8×C43C2311yescharacteristic
178C22×C8×C43C2311yescharacteristic
179C4×D4×C43C2×C414yes—
180C4×D4×C43C2314yes—
181C2×C4⋊C4×C43C2×C411yescharacteristic
182C2×C22⋊C4×C43C2×C411yescharacteristic
183C2×C22⋊C4×C43C2×C411yescharacteristic
184C2×C42×C43C2311yescharacteristic
185C4⋊C8×C43C2314yescomplemented
186C22⋊C8×C43C2314yes—
187C22⋊C8×C43C2314yescomplemented
188#97×C43C2314yescomplemented
189C24×C43C22×C411yescharacteristic
190C24×C43C22×C411yescharacteristic
191C23×D43—24no—
192C23×D43—24no—
193C23×D43—24no—
194C23×D43C22×C411yescharacteristic
195C23×D43C22×C414yes—
196C23×D43C22×C411yescharacteristic
197C23×D43C22×C411yescharacteristic
198C2×D4×C43—24no—
199C2×D4×C43C22×C414yes—
200C22×C4×C43—22no—
201C22×C4×C43—22no—
202C22×C4×C43—22no—
203C22×C4×C43—22no—
204C22×C4×C43C22×C411yescharacteristic
205C22×C4×C43C22×C411yescharacteristic
206C22×C4×C43C22×C411yescharacteristic
207C22×C4×C43C22×C411yescharacteristic
208C22×C4×C43C22×C412yes—
209C22×C4×C43C22×C412yes—
210C22×C4×C43C2412yes—
211C22×C4×C43C2412yes—
212C22×C4×C43C2411yescharacteristic
213C2×C22⋊D43—24no—
214C2×C22⋊D43—24no—
215C2×C22⋊D43—24no—
216C2×C22⋊D43—24no—
217C2×C22⋊D43C22×C414yes—
218C2×C22⋊D43C22×C414yes—
219C2×C22⋊D43C22×C414yes—
220C2×C22⋊D43C22×C414yes—
221C22×Dic43—24no—
222C22×Dic43C22×C411yescharacteristic
223C22×Dic43C22×C411yescharacteristic
224C22×Dic43C22×C411yescharacteristic
225C22×Dic43C22×C411yescharacteristic
226C22×Dic43C22×C414yes—
227C22×Dic43C22×C411yescharacteristic
228#10621898—216no—
229#10621898—28no—
230#10621898—28no—
231C2×D172—24no—
232C2×D172—24no—
233C2×D172C22×C414yes—
234C2×D172C22×C414yes—
235C2×C4×D43—22no—
236C2×C4×D43—22no—
237C2×C4×D43—22no—
238C2×C4×D43—22no—
239C2×C4×D43—24no—
240C2×C4×D43—216no—
241C2×C4×D43—28no—
242C2×C4×D43—28no—
243C2×C4×D43—24no—
244C2×C4×D43C22×C412yes—
245C2×C4×D43C22×C412yes—
246C2×C4×D43C22×C414yes—
247C2×C4×D43C22×C414yes—
248C2×C4×D43C22×C412yes—
249C2×C4×D43C2×D414yes—
250C2×C4×D43#4114yes—
251C2×C4×D43C2412yes—
252C2×C4×D43C2412yes—
253C2×C4×D43C2412yes—
254C2×Dic86—24no—
255C2×Dic86C22×C414yes—
256M16×C43—28no—
257C2×C8×C43—22no—
258C2×C8×C43—22no—
259C2×C8×C43—22no—
260C2×C8×C43—28no—
261C2×C8×C43C2×D414yes—
262C2×C8×C43C2412yes—
263C2×C8×C43C2412yes—
264C2×C8×C43C2412yes—
265C2×C8×C43C2412yes—
266C4⋊C4×C43C22×C414yes—
267C22⋊C4×C43C22×C414yes—
268C22⋊C4×C43C22×C414yes—
269C42×C43C22×C412yes—
270C42×C43C2412yes—
271C22⋊Dic43C22×C414yes—
272C22⋊Dic43C22×C414yes—
273(C2×D43)⋊C4C22×C414yes—
274(C2×D43)⋊C4C22×C414yes—
275(C2×D43)⋊C4C22×C414yes—
276(C2×D43)⋊C4C22×C414yes—
277(C2×D43)⋊C4C22×C414yes—
278(C2×D43)⋊C4C22×C414yes—
279C4⋊Dic43C22×C414yes—
280Dic43⋊C4C22×C414yes—
281Dic43⋊C4C22×C414yes—
282Dic43⋊C4C22×C414yes—
283Dic43⋊C4C22×C414yes—
284C4×Dic43C22×C412yes—
285C4×Dic43C2412yes—
286C2×C43⋊C8—22no—
287C2×C43⋊C8—22no—
288C2×C43⋊C8—22no—
289C2×C43⋊C8—28no—
290C2×C43⋊C8—28no—
291C2×C43⋊C8C2×D414yes—
292C2×C43⋊C8C2412yes—
293C2×C43⋊C8C2412yes—
294C2×C43⋊C8C2412yes—
295C2×C43⋊C8C2412yes—
296#10621872—28no—
297#10621872—28no—
298#10621872—28no—
299C8×D43—28no—
300C8×D43—28no—
301C8×D43—28no—
302C8×D43—28no—
303C8×D43C2×D4116yescomplemented
304C23×C43—22no—
305C23×C43—22no—
306C23×C43—22no—
307C23×C43—22no—
308C23×C43—22no—
309C23×C43#13114yescomplemented
310C23×C43C23×C412yes—
311C23×C43C23×C412yes—
312C23×C43C23×C411yescharacteristic
313C22×D43—232no—
314C22×D43—22no—
315C22×D43—22no—
316C22×D43—22no—
317C22×D43—22no—
318C22×D43—28no—
319C22×D43—28no—
320C22×D43—28no—
321C22×D43—22no—
322C22×D43—22no—
323C22×D43—22no—
324C22×D43C4×D414yes—
325C22×D43#13114yescomplemented
326C22×D43C23×C412yes—
327C22×D43C23×C412yes—
328C22×D43C23×C412yes—
329D4×C43—28no—
330C2×C4×C43—22no—
331C2×C4×C43—22no—
332C2×C4×C43—22no—
333C2×C4×C43—22no—
334C2×C4×C43—24no—
335C2×C4×C43—24no—
336C2×C4×C43—22no—
337C2×C4×C43—22no—
338C2×C4×C43—22no—
339C2×C4×C43—22no—
340C2×C4×C43C23×C412yes—
341C2×C4×C43C23×C412yes—
342C2×C4×C43C23×C412yes—
343C2×C4×C43C23×C412yes—
344C2×C4×C43C23×C411yescharacteristic
345C2×C4×C43C22×D412yes—
346C2×C4×C43C2×#4112yes—
347C2×C4×C43C2511yescharacteristic
348C22⋊D43—28no—
349C22⋊D43—28no—
350C22⋊D43—28no—
351C22⋊D43—28no—
352C2×Dic43—22no—
353C2×Dic43—22no—
354C2×Dic43—22no—
355C2×Dic43—22no—
356C2×Dic43—28no—
357C2×Dic43C4×D414yes—
358C2×Dic43C23×C412yes—
359C2×Dic43C23×C412yes—
360C2×Dic43C23×C412yes—
361C2×Dic43C23×C412yes—
362C2×Dic43C23×C412yes—
363D172—28no—
364D172—28no—
365C4×D43—28no—
366C4×D43—24no—
367C4×D43—24no—
368C4×D43—22no—
369C4×D43—22no—
370C4×D43—22no—
371C4×D43—22no—
372C4×D43—28no—
373C4×D43C4×D418yes—
374C4×D43C22×D414yes—
375C4×D43C2×#4114yes—
376Dic86—28no—
377C8×C43—22no—
378C8×C43—22no—
379C8×C43—22no—
380C8×C43C22×D414yes—
381C43⋊C8—22no—
382C43⋊C8—22no—
383C43⋊C8—22no—
384C43⋊C8C22×D414yes—
385C2×#2929—431nomaximal, Sylow
386C22×C43—22no—
387C22×C43—28no—
388C22×C43—22no—
389C22×C43—22no—
390C22×C43—22no—
391C22×C43—22no—
392C22×C43—44no—
393C22×C43C2×C4×D412yes—
394C22×C43C2×#13112yes—
395C22×C43C2×#13112yes—
396C22×C43C2×#13114yescomplemented
397C22×C43C24×C411yescharacteristic
398C2×D43—232no—
399C2×D43—22no—
400C2×D43—28no—
401C2×D43—28no—
402C2×D43—22no—
403C2×D43—22no—
404C2×D43—22no—
405C2×D43—22no—
406C2×D43—22no—
407C2×D43—22no—
408C2×D43—44no—
409C2×D43C2×C4×D414yes—
410C2×D43C2×#13114yescomplemented
411C4×C43—22no—
412C4×C43—22no—
413C4×C43—22no—
414C4×C43—22no—
415C4×C43C2×C4×D412yes—
416C4×C43C23×D411yescharacteristic
417C4×C43C22×#4111yescharacteristic
418Dic43—22no—
419Dic43—22no—
420Dic43—22no—
421Dic43—22no—
422Dic43C2×C4×D414yes—
423C22×#131—431no—
424C24×C8—431no—
425C2×#525—431no—
426#2929—4316no—
427C2×#435—431no—
428C2×#435—431no—
429C2×#435—431no—
430C2×#435D4311yescharacteristic, complemented
431C2×C8×D4—431no—
432C2×C8×D4—431no—
433C2×C8×D4—431no—
434C2×C8×D4—431no—
435C2×#424—431no—
436C2×#408—431no—
437C2×#407—431no—
438C2×#405—431no—
439C2×C43—24no—
440C2×C43—42no—
441C2×C43#292914yescomplemented
442C2×C43C22×C4×D411yescharacteristic
443C2×C43C22×#13111yescharacteristic
444C2×C43C22×#13111yescharacteristic
445D43—24no—
446D43—24no—
447D43—42no—
448C22×#41—431no—
449C24×C4—431no—
450C2×#131—438no—
451C2×#131—868no—
452C22×M16—431no—
453C22×M16—431no—
454C22×M16—431no—
455C22×M16C2×D4311yescharacteristic, complemented
456C23×C8—431no—
457C23×C8—431no—
458C23×C8—431no—
459C23×C8—431no—
460C23×C8—431no—
461C23×C8—431no—
462C23×C8—431no—
463C23×C8—438no—
464C23×C8—868no—
465C23×C8C2×D4311yescharacteristic
466#525—438no—
467#525—438no—
468C2×#123—431no—
469C2×#123—431no—
470C2×C22⋊Q8—431no—
471C2×C22⋊Q8—431no—
472C2×#121—431no—
473C2×#121—431no—
474C2×#120—431no—
475C2×#120—431no—
476C2×C4×D4—431no—
477C2×C4×D4—431no—
478C2×C4×D4—431no—
479C2×C4×D4C2×D4311yescharacteristic
480C2×#117—431no—
481#435—438no—
482#435—438no—
483#435—438no—
484#435C2×D4318yescomplemented
485C8×D4—438no—
486C8×D4—438no—
487C8×D4—438no—
488C8×D4—438no—
489#424—438no—
490C2×C4⋊C8—431no—
491C2×C4⋊C8—431no—
492C2×C4⋊C8—431no—
493C2×C4⋊C8C2×D4311yescharacteristic, complemented
494#408—438no—
495#407—438no—
496C2×C22⋊C8—431no—
497C2×C22⋊C8—431no—
498C2×C22⋊C8—431no—
499C2×C22⋊C8—431no—
500C2×C22⋊C8—431no—
501C2×C22⋊C8—431no—
502C2×C22⋊C8C2×D4311yescharacteristic
503C2×C22⋊C8C2×D4311yescharacteristic, complemented
504#405—438no—
505C2×#97—431no—
506C2×#97C2×D4311yescharacteristic, complemented
507C2×C4×C8—431no—
508C2×C4×C8—431no—
509C43C2×#292911yescharacteristic, complemented, Sylow
510C25—431no—
511C2×#41—434no—
512C2×#41—434no—
513C2×#41—864no—
514C2×#41—864no—
515C22×Q8—431no—
516C22×D4—431no—
517C22×D4—431no—
518C22×D4—431no—
519C22×D4—431no—
520C22×D4—431no—
521C22×D4—431no—
522C22×D4C4×D4311yescharacteristic
523C23×C4—431no—
524C23×C4—431no—
525C23×C4—431no—
526C23×C4—431no—
527C23×C4—434no—
528C23×C4—434no—
529C23×C4—431no—
530C23×C4—431no—
531C23×C4—864no—
532C23×C4—864no—
533C23×C4C22×D4311yescharacteristic
534C23×C4C22×D4311yescharacteristic
535#131—8632no—
536C2×M16—24no—
537C2×M16—434no—
538C2×M16—434no—
539C2×M16—434no—
540C2×M16—864no—
541C2×M16—864no—
542C2×M16—864no—
543C2×M16C22×D4314yescomplemented
544C22×C8—24no—
545C22×C8—431no—
546C22×C8—438no—
547C22×C8—434no—
548C22×C8—434no—
549C22×C8—434no—
550C22×C8—431no—
551C22×C8—431no—
552C22×C8—431no—
553C22×C8—434no—
554C22×C8—434no—
555C22×C8—434no—
556C22×C8—434no—
557C22×C8—864no—
558C22×C8—8632no—
559C22×C8—864no—
560C22×C8—864no—
561C22×C8—864no—
562C22×C8—864no—
563C22×C8—864no—
564C22×C8C22×D4314yes—
565C22×C8C22×D4311yescharacteristic
566C22×C8C22×D4311yescharacteristic
567C22×C8C22×D4311yescharacteristic
568C22×C8C22×D4311yescharacteristic
569#123—438no—
570#123—438no—
571C22⋊Q8—438no—
572C22⋊Q8—438no—
573#121—438no—
574#121—438no—
575#120—438no—
576#120—438no—
577C4×D4—434no—
578C4×D4—434no—
579C4×D4—434no—
580C4×D4—434no—
581C4×D4—434no—
582C4×D4—434no—
583C4×D4C4×D4314yes—
584C4×D4C22×D4314yes—
585#117—434no—
586#117—434no—
587C2×C4⋊C4—431no—
588C2×C4⋊C4—431no—
589C2×C4⋊C4—431no—
590C2×C4⋊C4—431no—
591C2×C4⋊C4—431no—
592C2×C4⋊C4C4×D4311yescharacteristic
593C2×C22⋊C4—431no—
594C2×C22⋊C4—431no—
595C2×C22⋊C4—431no—
596C2×C22⋊C4—431no—
597C2×C22⋊C4—431no—
598C2×C22⋊C4—431no—
599C2×C22⋊C4—431no—
600C2×C22⋊C4—431no—
601C2×C22⋊C4C4×D4311yescharacteristic
602C2×C22⋊C4C4×D4311yescharacteristic
603C2×C42—431no—
604C2×C42C22×D4311yescharacteristic
605C4⋊C8—434no—
606C4⋊C8—434no—
607C4⋊C8—434no—
608C4⋊C8C22×D4314yescomplemented
609C22⋊C8—434no—
610C22⋊C8—434no—
611C22⋊C8—434no—
612C22⋊C8—434no—
613C22⋊C8—434no—
614C22⋊C8—434no—
615C22⋊C8C22×D4314yes—
616C22⋊C8C22×D4314yescomplemented
617#97—434no—
618#97C22×D4314yescomplemented
619C4×C8—434no—
620C4×C8—434no—
621C24—431no—
622C24—431no—
623C24—431no—
624C24—434no—
625C24—864no—
626C24—864no—
627C24—864no—
628C24C2×C4×D4311yescharacteristic
629C24C2×C4×D4311yescharacteristic
630#41—868no—
631#41—8616no—
632#41—868no—
633C2×Q8—434no—
634C2×Q8—864no—
635C2×D4—24no—
636C2×D4—434no—
637C2×D4—434no—
638C2×D4—434no—
639C2×D4—434no—
640C2×D4—434no—
641C2×D4—434no—
642C2×D4—864no—
643C2×D4—864no—
644C2×D4—864no—
645C2×D4—864no—
646C2×D4—864no—
647C2×D4—864no—
648C2×D4C2×C4×D4314yes—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—431no—
654C22×C4—432no—
655C22×C4—434no—
656C22×C4—434no—
657C22×C4—432no—
658C22×C4—431no—
659C22×C4—431no—
660C22×C4—431no—
661C22×C4—431no—
662C22×C4—434no—
663C22×C4—432no—
664C22×C4—432no—
665C22×C4—434no—
666C22×C4—434no—
667C22×C4—432no—
668C22×C4—432no—
669C22×C4—868no—
670C22×C4—864no—
671C22×C4—8616no—
672C22×C4—868no—
673C22×C4—864no—
674C22×C4—864no—
675C22×C4—862no—
676C22×C4—862no—
677C22×C4—862no—
678C22×C4—862no—
679C22×C4C2×C4×D4311yescharacteristic
680C22×C4C2×C4×D4311yescharacteristic
681C22×C4C2×C4×D4311yescharacteristic
682C22×C4C2×C4×D4311yescharacteristic
683C22×C4C2×C4×D4312yes—
684C22×C4C2×C4×D4312yes—
685C22×C4C23×D4312yes—
686C22×C4C23×D4312yes—
687C22×C4C23×D4311yescharacteristic
688M16—28no—
689M16—868no—
690M16—868no—
691M16—868no—
692C2×C8—22no—
693C2×C8—22no—
694C2×C8—22no—
695C2×C8—28no—
696C2×C8—434no—
697C2×C8—432no—
698C2×C8—4316no—
699C2×C8—432no—
700C2×C8—432no—
701C2×C8—432no—
702C2×C8—868no—
703C2×C8—868no—
704C2×C8—868no—
705C2×C8—868no—
706C2×C8—868no—
707C2×C8—862no—
708C2×C8—862no—
709C2×C8—862no—
710C2×C8—868no—
711C2×C8D4×D4314yes—
712C2×C8C23×D4312yes—
713C2×C8C23×D4312yes—
714C2×C8C23×D4312yes—
715C2×C8C23×D4312yes—
716C4⋊C4—434no—
717C4⋊C4—434no—
718C4⋊C4—434no—
719C4⋊C4—434no—
720C4⋊C4—434no—
721C4⋊C4C2×C4×D4314yes—
722C22⋊C4—434no—
723C22⋊C4—434no—
724C22⋊C4—434no—
725C22⋊C4—434no—
726C22⋊C4—434no—
727C22⋊C4—434no—
728C22⋊C4—434no—
729C22⋊C4—434no—
730C22⋊C4C2×C4×D4314yes—
731C22⋊C4C2×C4×D4314yes—
732C42—432no—
733C42—432no—
734C42C2×C4×D4312yes—
735C42C23×D4312yes—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—434no—
742C23—434no—
743C23—432no—
744C23—432no—
745C23—432no—
746C23—868no—
747C23—868no—
748C23—8632no—
749C23—862no—
750C23—862no—
751C23—862no—
752C23—862no—
753C23—868no—
754C23—862no—
755C23—862no—
756C23—862no—
757C23#1306333314yescomplemented
758C23C22×C4×D4312yes—
759C23C22×C4×D4312yes—
760C23C22×C4×D4311yescharacteristic
761Q8—868no—
762D4—28no—
763D4—868no—
764D4—868no—
765D4—868no—
766D4—868no—
767D4—868no—
768D4—868no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—434no—
780C2×C4—432no—
781C2×C4—438no—
782C2×C4—434no—
783C2×C4—434no—
784C2×C4—432no—
785C2×C4—432no—
786C2×C4—432no—
787C2×C4—432no—
788C2×C4—868no—
789C2×C4—868no—
790C2×C4—868no—
791C2×C4—862no—
792C2×C4—862no—
793C2×C4—862no—
794C2×C4—862no—
795C2×C4—864no—
796C2×C4—864no—
797C2×C4—862no—
798C2×C4—862no—
799C2×C4—862no—
800C2×C4—862no—
801C2×C4C22×C4×D4312yes—
802C2×C4C22×C4×D4312yes—
803C2×C4C22×C4×D4312yes—
804C2×C4C22×C4×D4312yes—
805C2×C4C22×C4×D4311yescharacteristic
806C2×C4C2×D4×D4312yes—
807C2×C4#41×D4312yes—
808C2×C4C24×D4311yescharacteristic
809C8—22no—
810C8—22no—
811C8—22no—
812C8—434no—
813C8—862no—
814C8—862no—
815C8—862no—
816C8C2×D4×D4314yes—
817C22—28no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—22no—
823C22—44no—
824C22—434no—
825C22—434no—
826C22—8632no—
827C22—868no—
828C22—868no—
829C22—862no—
830C22—862no—
831C22—862no—
832C22—862no—
833C22—862no—
834C22—862no—
835C22—862no—
836C22—1724no—
837C22C4×D4×D4312yes—
838C22#131×D4312yes—
839C22C2×#1306333312yes—
840C22C2×#1306333314yescomplemented
841C22C23×C4×D4311yescharacteristic
842C4—22no—
843C4—22no—
844C4—22no—
845C4—22no—
846C4—434no—
847C4—862no—
848C4—862no—
849C4—862no—
850C4—862no—
851C4C4×D4×D4312yes—
852C4C22×D4×D4311yescharacteristic
853C4C2×#41×D4311yescharacteristic
854C2—24no—
855C2—42no—
856C2—864no—
857C2—864no—
858C2—1722no—
859C2#1914328614yesdirect product factor
860C2C2×C4×D4×D4311yescharacteristic
861C2C2×#131×D4311yescharacteristic
862C2C22×#1306333311yescharacteristic
subgroupG/H
centerC22×C4C23×D43
commutatorC22×C43C24×C4
FrattiniC2×C4C24×D43
FittingC2×C43×#435C2
socleC23×C43C23×C4
prime radicalC2×#14583408C2
cosocleC2×C4×C43C25
hypercenterC2×#435D43
hypocenterC43C2×#2929
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C22×#13063333C2semidirect
2. C23×C8×D43C2semidirect
4. #19143286C2direct (N × H)
5. C2×#14582972C2semidirect
6. C2×#14582970C2semidirect
7. C2×#14582968C2semidirect
8. C2×D4×C43⋊C8C2semidirect
9. C2×#14582964C2semidirect
10. C2×(C22⋊D43)⋊C8C2semidirect
11. C2×(C22⋊D43)⋊C8C2semidirect
12. C2×#14582924C2semidirect
13. C2×#14582864C2semidirect
14. C2×#14582861C2semidirect
15. C2×#14582856C2semidirect
16. C2×C43×#435C2semidirect
20. C2×#13063333C22semidirect
23. C22×#10621872C22semidirect
25. C23×C43⋊C8C22semidirect
31. C22×C8×D43C22semidirect
32. C22×C8×D43C22semidirect
47. #14582972C22semidirect
48. #14582970C22semidirect
49. #14582968C22semidirect
50. D4×C43⋊C8C22semidirect
51. #14582964C22semidirect
52. (C22⋊D43)⋊C8C22semidirect
53. (C22⋊D43)⋊C8C22semidirect
54. #14582924C22semidirect
55. C2×C4⋊(C43⋊C8)C22semidirect
56. C2×Dic43⋊C8C22semidirect
57. C2×Dic43⋊C8C22semidirect
58. #14582864C22semidirect
59. #14582861C22semidirect
61. C2×C22⋊(C43⋊C8)C22semidirect
64. C2×(C2×D43)⋊C8C22semidirect
65. C2×(C2×D43)⋊C8C22semidirect
66. #14582856C22semidirect
67. C2×#13063235C22semidirect
68. C2×C4×C43⋊C8C22semidirect
69. C2×C8×Dic43C22semidirect
70. C22×M16×C43C22semidirect
73. C43×#435C22semidirect
74. C2×C4⋊C8×C43C22semidirect
76. C2×C22⋊C8×C43C22semidirect
77. C2×#97×C43C22semidirect
106. C2×#10621872C23semidirect
114. C22×C43⋊C8C23semidirect
120. C2×C8×D43D4semidirect
125. C2×C8×D43C23semidirect
156. C4⋊(C43⋊C8)C23semidirect
157. Dic43⋊C8C23semidirect
158. Dic43⋊C8C23semidirect
160. C22⋊(C43⋊C8)C23semidirect
163. (C2×D43)⋊C8C23semidirect
164. (C2×D43)⋊C8C23semidirect
165. #13063235C23semidirect
166. C4×C43⋊C8C23semidirect
167. C8×Dic43C23semidirect
172. C2×M16×C43C23semidirect
185. C4⋊C8×C43C23semidirect
187. C22⋊C8×C43C23semidirect
188. #97×C43C23semidirect
303. C8×D43C2×D4semidirect
309. C23×C43#131semidirect
325. C22×D43#131semidirect
396. C22×C43C2×#131semidirect
410. C2×D43C2×#131semidirect
430. C2×#435D43semidirect
441. C2×C43#2929semidirect
455. C22×M16C2×D43semidirect
484. #435C2×D43semidirect
493. C2×C4⋊C8C2×D43semidirect
503. C2×C22⋊C8C2×D43semidirect
506. C2×#97C2×D43semidirect
509. C43C2×#2929semidirect
543. C2×M16C22×D43semidirect
608. C4⋊C8C22×D43semidirect
616. C22⋊C8C22×D43semidirect
618. #97C22×D43semidirect
757. C23#13063333semidirect
840. C22C2×#13063333semidirect
859. C2#19143286direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633332
C23×C8×D432
C2×#145834082
#191432862
C2×#145829722
C2×#145829702
C2×#145829682
C2×D4×C43⋊C82
C2×#145829642
C2×(C22⋊D43)⋊C82
C2×#145829242
C2×#145828642
C2×#145828612
C2×#145828562
C2×C43×#4352
C2×#292943