Finite Group Databasebeta

← #25257060

Subgroups — #25257060

Order 11008.

2422 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊Q8×D43C211yesmaximal, characteristic
2#19137682C212yesmaximal, complemented
3#19137681C212yesmaximal, complemented
4#19137652C212yesmaximal, complemented
5#19137649C212yesmaximal, complemented
6#19137471C212yesmaximal
7#19137468C212yesmaximal
8#19137429C212yesmaximal
9Q8×(C2×D43)⋊C4C212yesmaximal
10#19137342C212yesmaximal, complemented
11#19137339C212yesmaximal, complemented
12#19137210C212yesmaximal
13C4⋊Q8×Dic43C211yesmaximal, characteristic, complemented
14C4×#13063325C211yesmaximal, characteristic, complemented
15#19137162C211yesmaximal, characteristic, complemented
16#19137000C211yesmaximal, characteristic
17#19136949C212yesmaximal
18C4×#13063282C211yesmaximal, characteristic
19C4×C4⋊Q8×C43C211yesmaximal, characteristic, complemented
20C22×Q8×D43C2212yes—
21C2×#13063325C2211yescharacteristic
22C2×#13063324C2212yes—
23C2×#13063324C2212yes—
24C2×#13063323C2212yes—
25C4⋊Q8×D43C4116yescomplemented
26C2×Q8×Dic43C2212yes—
27C2×C4×Dic86C2212yes—
28C2×#13063290C2212yes—
29C2×#13063283C2212yes—
30C2×#13063282C2211yescharacteristic
31C2×#13063282C2211yescharacteristic
32C2×C4⋊C4×D43C2212yes—
33C2×C4⋊C4×D43C2212yes—
34C2×C42×D43C2211yescharacteristic
35#14582806C2212yes—
36#14582805C2214yes—
37#14582805C2212yes—
38#14582804C2214yes—
39#14582804C2212yes—
40#14582803C2214yes—
41#14582803C2214yes—
42#14582798C2212yes—
43#14582798C2212yes—
44#14582797C2212yes—
45#14582797C2212yes—
46#14582796C2214yes—
47#14582795C2212yes—
48#14582795C2212yes—
49#14582794C2214yes—
50#14582786C2214yes—
51#14582783C2214yes—
52#14582781C2214yes—
53#14582780C2214yes—
54#14582769C2211yescharacteristic
55#14582764C2212yes—
56#14582758C2214yes—
57#14582756C2212yes—
58#14582756C2214yes—
59#14582756C2212yes—
60C4⋊C4×Dic43C2212yes—
61C4⋊C4×Dic43C2212yes—
62C4⋊C4×Dic43C2212yes—
63C4⋊C4×Dic43C2212yes—
64C4⋊C4×Dic43C2212yes—
65C4⋊C4×Dic43C2212yes—
66C4×Dic43⋊C4C2211yescharacteristic
67C4×Dic43⋊C4C2214yes—
68C4×Dic43⋊C4C2211yescharacteristic
69C4×Dic43⋊C4C2211yescharacteristic
70C4×Dic43⋊C4C2211yescharacteristic
71C4×C4⋊Dic43C2212yes—
72C4×C4⋊Dic43C2212yes—
73#14582750C2214yes—
74C4×(C2×D43)⋊C4C2211yescharacteristic
75C4×(C2×D43)⋊C4C2214yes—
76C4×(C2×D43)⋊C4C2211yescharacteristic
77C4×(C2×D43)⋊C4C2211yescharacteristic
78C4×(C2×D43)⋊C4C2211yescharacteristic
79#14582746C2214yes—
80#14582745C2211yescharacteristic
81#14582745C2211yescharacteristic
82C42×Dic43C2211yescharacteristic
83C2×C4⋊Q8×C43C2211yescharacteristic
84C2×C4×Q8×C43C2212yes—
85C43×#391C2212yes—
86C43×#389C2212yes—
87C43×#389C2212yes—
88C43×#384C2211yescharacteristic
89C4×C4⋊C4×C43C2212yes—
90C4×C4⋊C4×C43C2212yes—
91C43×C43C2211yescharacteristic
92C22×Dic86C2312yes—
93C22×Dic86C2314yes—
94C2×Q8×D43—44no—
95C2×Q8×D43—44no—
96C2×Q8×D43C2×C4116yes—
97C22×C4×D43C2311yescharacteristic
98C22×C4×D43C2311yescharacteristic
99C22×C4×D43C2314yes—
100C22×C4×D43C2311yescharacteristic
101#13063325C2×C418yes—
102#13063324C2×C4116yes—
103#13063324C2×C4116yes—
104#13063323C2×C4116yes—
105Q8×Dic43—44no—
106C4×Dic86—44no—
107#13063290—44no—
108#13063283—28no—
109#13063282—24no—
110#13063282Q818yescomplemented
111C2×C4⋊Dic43C2312yes—
112C2×C4⋊Dic43C2312yes—
113C2×C4⋊Dic43C2312yes—
114C2×C4⋊Dic43C2314yes—
115C2×C4⋊Dic43C2312yes—
116C2×C4⋊Dic43C2312yes—
117C2×Dic43⋊C4C2311yescharacteristic
118C2×Dic43⋊C4C2311yescharacteristic
119C2×Dic43⋊C4C2314yes—
120C2×Dic43⋊C4C2314yes—
121C2×Dic43⋊C4C2314yes—
122C2×Dic43⋊C4C2314yes—
123C2×Dic43⋊C4C2311yescharacteristic
124C2×Dic43⋊C4C2311yescharacteristic
125C4⋊C4×D43C2×C4116yes—
126C4⋊C4×D43C2×C4116yes—
127C2×(C2×D43)⋊C4C2311yescharacteristic
128C2×(C2×D43)⋊C4C2311yescharacteristic
129C2×(C2×D43)⋊C4C2314yes—
130C2×(C2×D43)⋊C4C2311yescharacteristic
131C2×(C2×D43)⋊C4C2311yescharacteristic
132C2×C4×Dic43C2314yes—
133C2×C4×Dic43C2311yescharacteristic
134C2×C4×Dic43C2311yescharacteristic
135C2×C4×Dic43C2311yescharacteristic
136C2×C4×Dic43C2311yescharacteristic
137C2×C4×Dic43C2311yescharacteristic
138C2×C4×Dic43C2314yes—
139C2×C4×Dic43C2314yes—
140C2×C4×Dic43C2314yes—
141C2×C4×Dic43C2311yescharacteristic
142C2×C4×Dic43C2311yescharacteristic
143C2×C4×Dic43C2311yescharacteristic
144C2×C4×Dic43C2311yescharacteristic
145C42×D43C2×C418yes—
146C43⋊#95C2311yescharacteristic
147C43⋊#95C2314yes—
148C43⋊#95C2314yes—
149C43⋊#95C2314yes—
150C43⋊#95C2314yes—
151C43⋊#95C2314yes—
152C43⋊#95C2314yes—
153C43⋊#95C2314yes—
154C43⋊#95C2311yescharacteristic
155C43⋊#95C2311yescharacteristic
156C43⋊#95C2314yes—
157C43⋊#95C2311yescharacteristic
158C43⋊#95C2311yescharacteristic
159C43⋊#95C2311yescharacteristic
160C43⋊#95C2311yescharacteristic
161C43⋊#95C2311yescharacteristic
162C22×Q8×C43C2312yes—
163C4⋊Q8×C43C2×C418yes—
164C4×Q8×C43—44no—
165C2×C4⋊C4×C43C2312yes—
166C2×C4⋊C4×C43C2312yes—
167C2×C4⋊C4×C43C2312yes—
168C2×C4⋊C4×C43C2314yes—
169C2×C4⋊C4×C43C2312yes—
170C2×C4⋊C4×C43C2312yes—
171C2×C42×C43C2311yescharacteristic
172C2×C42×C43C2311yescharacteristic
173C2×C42×C43C2311yescharacteristic
174C2×C42×C43C2311yescharacteristic
175C2×C42×C43C2311yescharacteristic
176C2×C42×C43C2314yes—
177C2×C42×C43C2311yescharacteristic
178C2×C42×C43C2311yescharacteristic
179#95×C43C2314yes—
180#95×C43C2314yes—
181C23×D43C2411yescharacteristic
182C2×Q8×C43—24no—
183C2×Q8×C43—24no—
184C2×Q8×C43C22×C418yes—
185C22×C4×C43C2411yescharacteristic
186C22×C4×C43C2414yes—
187C22×C4×C43C2411yescharacteristic
188C22×C4×C43C2414yes—
189C22×C4×C43C2411yescharacteristic
190C22×C4×C43C2411yescharacteristic
191C22×C4×C43C2411yescharacteristic
192C22×C4×C43C2411yescharacteristic
193C22×C4×C43C2411yescharacteristic
194C22×Dic43C2411yescharacteristic
195C22×Dic43C2411yescharacteristic
196C22×Dic43C2414yes—
197C22×Dic43C2411yescharacteristic
198C22×Dic43C2411yescharacteristic
199C22×Dic43C2414yes—
200C22×Dic43C2411yescharacteristic
201C22×Dic43C2411yescharacteristic
202C22×Dic43C2411yescharacteristic
203Q8×D43—432no—
204C2×C4×D43—22no—
205C2×C4×D43—22no—
206C2×C4×D43—22no—
207C2×C4×D43—22no—
208C2×C4×D43—44no—
209C2×C4×D43—44no—
210C2×C4×D43C22×C414yes—
211C2×C4×D43C22×C414yes—
212C2×C4×D43C22×C4116yes—
213C2×C4×D43C22×C414yes—
214C2×C4×D43C2×Q814yes—
215C2×C4×D43#4114yes—
216C2×Dic86—24no—
217C2×Dic86—24no—
218C2×Dic86—44no—
219C2×Dic86—44no—
220C2×Dic86C22×C418yes—
221C2×Dic86C22×C4116yes—
222C4⋊C4×C43—24no—
223C4⋊C4×C43—24no—
224C4⋊C4×C43—24no—
225C4⋊C4×C43—44no—
226C4⋊C4×C43C22×C418yes—
227C4⋊C4×C43C22×C418yes—
228C42×C43—22no—
229C42×C43—22no—
230C42×C43—22no—
231C42×C43—22no—
232C42×C43—22no—
233C42×C43—44no—
234C42×C43C22×C414yes—
235C42×C43C2×Q814yescomplemented
236(C2×D43)⋊C4—22no—
237(C2×D43)⋊C4—22no—
238(C2×D43)⋊C4—28no—
239(C2×D43)⋊C4C2×Q814yes—
240(C2×D43)⋊C4C2×Q814yes—
241C4⋊Dic43—24no—
242C4⋊Dic43—24no—
243C4⋊Dic43—24no—
244C4⋊Dic43—44no—
245C4⋊Dic43C22×C418yes—
246C4⋊Dic43C22×C418yes—
247Dic43⋊C4—22no—
248Dic43⋊C4—22no—
249Dic43⋊C4—44no—
250Dic43⋊C4—44no—
251Dic43⋊C4C22×C4116yes—
252Dic43⋊C4C22×C4116yes—
253Dic43⋊C4C2×Q814yescomplemented
254Dic43⋊C4C2×Q814yescomplemented
255C4×Dic43—22no—
256C4×Dic43—22no—
257C4×Dic43—22no—
258C4×Dic43—22no—
259C4×Dic43—22no—
260C4×Dic43—28no—
261C4×Dic43—44no—
262C4×Dic43—44no—
263C4×Dic43—44no—
264C4×Dic43C22×C414yes—
265C4×Dic43C22×C414yes—
266C4×Dic43C22×C414yes—
267C4×Dic43C2×Q814yescomplemented
268C23×C43C2511yescharacteristic
269C22×D43—21no—
270C22×D43—21no—
271C22×D43—21no—
272C22×D43—21no—
273C22×D43C23×C412yes—
274C22×D43C22×Q812yes—
275C22×D43C2×#4112yes—
276Q8×C43—216no—
277C2×C4×C43—21no—
278C2×C4×C43—24no—
279C2×C4×C43—21no—
280C2×C4×C43—24no—
281C2×C4×C43—21no—
282C2×C4×C43—21no—
283C2×C4×C43—24no—
284C2×C4×C43—21no—
285C2×C4×C43—21no—
286C2×C4×C43—24no—
287C2×C4×C43—21no—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
291C2×C4×C43—24no—
292C2×C4×C43C23×C418yes—
293C2×C4×C43C23×C412yes—
294C2×C4×C43C23×C412yes—
295C2×C4×C43C23×C412yes—
296C2×C4×C43C22×Q812yes—
297C2×C4×C43C22×Q812yes—
298C2×C4×C43C22×Q812yes—
299C2×C4×C43C2×#4112yes—
300C2×C4×C43H(5,𝔽2)12yes—
301C2×C4×C43H(5,𝔽2)12yes—
302C2×C4×C432−1+412yes—
303C2×C4×C432−1+412yes—
304C2×Dic43—21no—
305C2×Dic43—21no—
306C2×Dic43—24no—
307C2×Dic43—24no—
308C2×Dic43—21no—
309C2×Dic43—21no—
310C2×Dic43—21no—
311C2×Dic43—21no—
312C2×Dic43—21no—
313C2×Dic43—21no—
314C2×Dic43—21no—
315C2×Dic43—21no—
316C2×Dic43—24no—
317C2×Dic43—21no—
318C2×Dic43—21no—
319C2×Dic43—24no—
320C2×Dic43—21no—
321C2×Dic43—21no—
322C2×Dic43—24no—
323C2×Dic43C23×C412yes—
324C2×Dic43C23×C412yes—
325C2×Dic43C23×C418yes—
326C2×Dic43C23×C412yes—
327C2×Dic43C22×Q812yes—
328C2×Dic43C22×Q812yes—
329C2×Dic43C22×Q812yes—
330C2×Dic43C2×#4112yes—
331C4×D43—28no—
332C4×D43—28no—
333C4×D43—416no—
334C4×D43C4×Q8116yescomplemented
335Dic86—216no—
336Dic86—416no—
337#34216—431nomaximal, Sylow
338C22×C43C24×C411yescharacteristic
339C22×C43C23×Q811yescharacteristic
340C22×C43C22×#4111yescharacteristic
341C22×C43C2×H(5,𝔽2)11yescharacteristic
342C22×C43C2×H(5,𝔽2)11yescharacteristic
343C22×C43C2×2−1+411yescharacteristic
344C22×C43C2×2−1+411yescharacteristic
345C2×D43—22no—
346C2×D43—22no—
347C2×D43—22no—
348C2×D43—22no—
349C2×D43—22no—
350C2×D43—22no—
351C2×D43C2×C4×Q814yes—
352C4×C43—28no—
353C4×C43—22no—
354C4×C43—22no—
355C4×C43—44no—
356C4×C43—41no—
357C4×C43—41no—
358C4×C43C2×C4×Q814yes—
359C4×C43#51814yes—
360C4×C43#51914yes—
361Dic43—28no—
362Dic43—22no—
363Dic43—22no—
364Dic43—22no—
365Dic43—22no—
366Dic43—41no—
367Dic43—41no—
368Dic43—44no—
369Dic43C2×C4×Q814yes—
370C22×C4⋊Q8—431no—
371#2369—432no—
372#2369—432no—
373#2365—432no—
374#2365—432no—
375#2345—432no—
376#2345—432no—
377Q8×C22⋊C4—432no—
378Q8×C22⋊C4—432no—
379#2331—432no—
380#2331—432no—
381#2316—432no—
382C4×C4⋊Q8—431no—
383C4×C4⋊Q8—431no—
384C4×C4⋊Q8—431no—
385C4×C4⋊Q8D4311yescharacteristic, complemented
386#2285—431no—
387#2274—432no—
388C4×#117—431no—
389C2×C43C22×C4×Q811yescharacteristic
390C2×C43C2×#51811yescharacteristic
391C2×C43C2×#51911yescharacteristic
392C2×C43#350311yescharacteristic
393C2×C43#350311yescharacteristic
394C2×C43#351111yescharacteristic
395C2×C43#351111yescharacteristic
396D43—24no—
397C23×Q8—432no—
398C2×C4⋊Q8—432no—
399C2×C4⋊Q8—4316no—
400C2×C4⋊Q8—432no—
401C2×C4⋊Q8—432no—
402C2×C4⋊Q8—431no—
403C2×C4⋊Q8C2×D4311yescharacteristic
404C2×C4×Q8—432no—
405C2×C4×Q8—432no—
406C2×C4×Q8—432no—
407C2×C4×Q8C2×D4312yes—
408C2×#117—432no—
409C2×#117—431no—
410C2×#117—431no—
411C22×C4⋊C4—432no—
412C22×C4⋊C4—432no—
413C22×C42—431no—
414#391—432no—
415#391—432no—
416#391—434no—
417#391—432no—
418#391—434no—
419#391—434no—
420#391—434no—
421#391C2×D4312yes—
422#389—432no—
423#389—432no—
424#389—432no—
425#389—432no—
426#389—434no—
427#389—432no—
428#389—432no—
429#389—434no—
430#389C2×D4312yes—
431#389C2×D4312yes—
432#387—434no—
433#387—434no—
434#387—434no—
435#387—434no—
436#384—431no—
437#384C2×D4311yescharacteristic
438#382—432no—
439#380—434no—
440#380—432no—
441#380—432no—
442#380—434no—
443C4×C4⋊C4—432no—
444C4×C4⋊C4—432no—
445C4×C4⋊C4—432no—
446C4×C4⋊C4—432no—
447C4×C4⋊C4—432no—
448C4×C4⋊C4—432no—
449C4×C4⋊C4—432no—
450C4×C4⋊C4—432no—
451C4×C4⋊C4—431no—
452C4×C4⋊C4—431no—
453C4×C4⋊C4—434no—
454C4×C4⋊C4—431no—
455C4×C4⋊C4—431no—
456C4×C4⋊C4—434no—
457C4×C4⋊C4C2×D4312yes—
458C4×C4⋊C4C2×D4312yes—
459C4×C22⋊C4—431no—
460C4×C22⋊C4—431no—
461C4×C22⋊C4—434no—
462C4×C22⋊C4—431no—
463C4×C22⋊C4—431no—
464C4×C22⋊C4—434no—
465#376—431no—
466#376—431no—
467C43—431no—
468C43C2×D4311yescharacteristic
469C43#3421611yescharacteristic, complemented, Sylow
470C22×Q8—4316no—
471C22×Q8—432no—
472C22×Q8—434no—
473C22×Q8—1724no—
474C22×Q8—1724no—
475C22×Q8C22×D4312yes—
476C23×C4—431no—
477C23×C4—431no—
478C23×C4—431no—
479C23×C4—434no—
480C4⋊Q8—4316no—
481C4⋊Q8—4316no—
482C4⋊Q8—4316no—
483C4⋊Q8—438no—
484C4⋊Q8C4×D4318yes—
485C4×Q8—44no—
486C4×Q8—1724no—
487C4×Q8—1724no—
488C4×Q8—1724no—
489#117—438no—
490#117—864no—
491#117—868no—
492C2×C4⋊C4—434no—
493C2×C4⋊C4—434no—
494C2×C4⋊C4—432no—
495C2×C4⋊C4—432no—
496C2×C4⋊C4—431no—
497C2×C4⋊C4—431no—
498C2×C4⋊C4—4316no—
499C2×C4⋊C4—4316no—
500C2×C4⋊C4—431no—
501C2×C4⋊C4—431no—
502C2×C4⋊C4—432no—
503C2×C4⋊C4—432no—
504C2×C4⋊C4—432no—
505C2×C4⋊C4—434no—
506C2×C4⋊C4—434no—
507C2×C4⋊C4—434no—
508C2×C4⋊C4C22×D4312yes—
509C2×C4⋊C4C22×D4312yes—
510C2×C4⋊C4C22×D4312yes—
511C2×C4⋊C4C22×D4314yes—
512C2×C4⋊C4C22×D4312yes—
513C2×C4⋊C4C22×D4312yes—
514C2×C22⋊C4—431no—
515C2×C22⋊C4—431no—
516C2×C22⋊C4—431no—
517C2×C22⋊C4—434no—
518C2×C22⋊C4—431no—
519C2×C42—431no—
520C2×C42—431no—
521C2×C42—431no—
522C2×C42—431no—
523C2×C42—438no—
524C2×C42—431no—
525C2×C42—434no—
526C2×C42—431no—
527C2×C42—431no—
528C2×C42—431no—
529C2×C42—431no—
530C2×C42—434no—
531C2×C42—434no—
532C2×C42—434no—
533C2×C42C22×D4311yescharacteristic
534C2×C42C22×D4311yescharacteristic
535C2×C42C22×D4311yescharacteristic
536C2×C42C22×D4311yescharacteristic
537C2×C42C22×D4311yescharacteristic
538C2×C42C22×D4314yes—
539C2×C42C22×D4311yescharacteristic
540C2×C42C22×D4311yescharacteristic
541#95—431no—
542#95—431no—
543#95—431no—
544#95—431no—
545#95—431no—
546#95—431no—
547#95—431no—
548#95—431no—
549#95—434no—
550#95—434no—
551#95—434no—
552#95—434no—
553#95—434no—
554#95—434no—
555#95—434no—
556#95—434no—
557#95C22×D4314yes—
558#95C22×D4314yes—
559C24—431no—
560C2×Q8—24no—
561C2×Q8—24no—
562C2×Q8—438no—
563C2×Q8—4316no—
564C2×Q8—864no—
565C2×Q8—864no—
566C2×Q8—1724no—
567C2×Q8—1724no—
568C2×Q8—17232no—
569C2×Q8C2×C4×D4318yes—
570C22×C4—431no—
571C22×C4—434no—
572C22×C4—434no—
573C22×C4—434no—
574C22×C4—431no—
575C22×C4—431no—
576C22×C4—431no—
577C22×C4—431no—
578C22×C4—434no—
579C22×C4—434no—
580C22×C4—434no—
581C22×C4—4316no—
582C22×C4—431no—
583C22×C4—431no—
584C22×C4—434no—
585C22×C4—862no—
586C22×C4—862no—
587C22×C4—862no—
588C22×C4—862no—
589C22×C4—1724no—
590C22×C4—1724no—
591C22×C4C23×D4311yescharacteristic
592C22×C4C23×D4314yes—
593C22×C4C23×D4311yescharacteristic
594C22×C4C23×D4314yes—
595C22×C4C23×D4311yescharacteristic
596C22×C4C23×D4311yescharacteristic
597C22×C4C23×D4311yescharacteristic
598C22×C4C23×D4311yescharacteristic
599C22×C4C23×D4311yescharacteristic
600C4⋊C4—24no—
601C4⋊C4—24no—
602C4⋊C4—24no—
603C4⋊C4—44no—
604C4⋊C4—4316no—
605C4⋊C4—4316no—
606C4⋊C4—438no—
607C4⋊C4—438no—
608C4⋊C4—434no—
609C4⋊C4—434no—
610C4⋊C4—862no—
611C4⋊C4—862no—
612C4⋊C4—864no—
613C4⋊C4—864no—
614C4⋊C4—864no—
615C4⋊C4—1724no—
616C4⋊C4—1724no—
617C4⋊C4—1724no—
618C4⋊C4C2×C4×D4318yes—
619C4⋊C4C2×C4×D4318yes—
620C22⋊C4—434no—
621C22⋊C4—434no—
622C22⋊C4—862no—
623C22⋊C4—862no—
624C22⋊C4—868no—
625C42—22no—
626C42—22no—
627C42—22no—
628C42—22no—
629C42—22no—
630C42—44no—
631C42—434no—
632C42—434no—
633C42—434no—
634C42—434no—
635C42—868no—
636C42—862no—
637C42—862no—
638C42—862no—
639C42—862no—
640C42—862no—
641C42—1724no—
642C42—1724no—
643C42—1724no—
644C42C2×C4×D4314yes—
645C42Q8×D4314yescomplemented
646C23—432no—
647C23—432no—
648C23—432no—
649C23—861no—
650C23—861no—
651C23—861no—
652C23—861no—
653C23C24×D4311yescharacteristic
654Q8—216no—
655Q8—8616no—
656Q8—17216no—
657C2×C4—21no—
658C2×C4—24no—
659C2×C4—21no—
660C2×C4—24no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—24no—
666C2×C4—21no—
667C2×C4—24no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—24no—
671C2×C4—21no—
672C2×C4—432no—
673C2×C4—432no—
674C2×C4—432no—
675C2×C4—4316no—
676C2×C4—432no—
677C2×C4—432no—
678C2×C4—438no—
679C2×C4—432no—
680C2×C4—432no—
681C2×C4—861no—
682C2×C4—864no—
683C2×C4—861no—
684C2×C4—861no—
685C2×C4—864no—
686C2×C4—861no—
687C2×C4—861no—
688C2×C4—861no—
689C2×C4—861no—
690C2×C4—861no—
691C2×C4—868no—
692C2×C4—868no—
693C2×C4—861no—
694C2×C4—864no—
695C2×C4—861no—
696C2×C4—861no—
697C2×C4—861no—
698C2×C4—864no—
699C2×C4—861no—
700C2×C4—861no—
701C2×C4—864no—
702C2×C4—17216no—
703C2×C4C22×C4×D4318yes—
704C2×C4C22×C4×D4312yes—
705C2×C4C22×C4×D4312yes—
706C2×C4C22×C4×D4312yes—
707C2×C4C2×Q8×D4312yes—
708C2×C4C2×Q8×D4312yes—
709C2×C4C2×Q8×D4312yes—
710C2×C4#41×D4312yes—
711C2×C4#1306337012yes—
712C2×C4#1306337112yes—
713C2×C4#1306337212yes—
714C2×C4#1306337312yes—
715C22—434no—
716C22—862no—
717C22—862no—
718C22—862no—
719C22—862no—
720C22—862no—
721C22—862no—
722C22C23×C4×D4311yescharacteristic
723C22C22×Q8×D4311yescharacteristic
724C22C2×#41×D4311yescharacteristic
725C22C2×#1306337011yescharacteristic
726C22C2×#1306337111yescharacteristic
727C22C2×#1306337211yescharacteristic
728C22C2×#1306337311yescharacteristic
729C4—28no—
730C4—22no—
731C4—22no—
732C4—41no—
733C4—44no—
734C4—41no—
735C4—434no—
736C4—862no—
737C4—868no—
738C4—862no—
739C4—862no—
740C4—862no—
741C4—1721no—
742C4—1721no—
743C4—1724no—
744C4C4×Q8×D4314yes—
745C4#1458337114yes—
746C4#1458337514yes—
747C2—864no—
748C2C2×C4×Q8×D4311yescharacteristic
749C2C2×#1458337111yescharacteristic
750C2C2×#1458337511yescharacteristic
751C2#1914840711yescharacteristic
752C2#1914841111yescharacteristic
753C2#1914849611yescharacteristic
754C2#1914850711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D43
commutatorC22×C43C24×C4
FittingC4×C4⋊Q8×C43C2
socle, cosocleC23×C43C25
prime radicalC23×D43C24
hypercenterC4×C4⋊Q8D43
hypocenterC43#34216
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #19137682C2semidirect
3. #19137681C2semidirect
4. #19137652C2semidirect
5. #19137649C2semidirect
10. #19137342C2semidirect
11. #19137339C2semidirect
13. C4⋊Q8×Dic43C2semidirect
14. C4×#13063325C2semidirect
15. #19137162C2semidirect
19. C4×C4⋊Q8×C43C2semidirect
25. C4⋊Q8×D43C4semidirect
110. #13063282Q8semidirect
235. C42×C43C2×Q8semidirect
253. Dic43⋊C4C2×Q8semidirect
254. Dic43⋊C4C2×Q8semidirect
267. C4×Dic43C2×Q8semidirect
334. C4×D43C4×Q8semidirect
385. C4×C4⋊Q8D43semidirect
469. C43#34216semidirect
645. C42Q8×D43semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊Q8×D432
#191376822
#191376812
#191376522
#191376492
#191374712
#191374682
#191374292
Q8×(C2×D43)⋊C42
#191373422
#191373392
#191372102
C4⋊Q8×Dic432
C4×#130633252
#191371622
#191370002
#191369492
C4×#130632822
C4×C4⋊Q8×C432
#3421643