Finite Group Databasebeta

← #25968931

Subgroups — #25968931

Order 11008.

1788 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583433C211yesmaximal, characteristic
2#19145835C214yesmaximal, complemented
3#19145825C212yesmaximal, complemented
4#19145816C212yesmaximal, complemented
5#19145774C214yesmaximal, complemented
6#19145763C214yesmaximal, complemented
7#19145148C212yesmaximal, complemented
8#19144984C212yesmaximal, complemented
9#19144543C212yesmaximal, complemented
10#19144535C212yesmaximal
11#19144396C212yesmaximal, complemented
12#19144388C212yesmaximal, complemented
13#19143228C211yesmaximal, characteristic, complemented
14C2×C43×#533C211yesmaximal, characteristic, complemented
15#14583433—21no—
16#14583433—21no—
17#14583433—21no—
18#14583433—21no—
19#14583433C2212yes—
20#14583433C2212yes—
21#14583433C2212yes—
22#14583433C2212yes—
23C2×#13063319—21no—
24C2×#13063317C2211yescharacteristic
25C2×#13063313C2211yescharacteristic
26C2×#13063308—21no—
27C2×#13063304C2211yescharacteristic
28C2×#13063299C2211yescharacteristic
29C2×C4×Dic86C2211yescharacteristic
30C2×C4×D172C2211yescharacteristic
31C2×C4×C22⋊D43—21no—
32C2×#13063282—21no—
33#14583305C2214yescomplemented
34#14583305C2214yescomplemented
35#14583298C2218yescomplemented
36#14583261C2214yescomplemented
37#14583261C2214yescomplemented
38#14583256C2218yescomplemented
39#14583240C2218yescomplemented
40#14583234C2214yescomplemented
41#14583229C2214yescomplemented
42#14583223C2218yes—
43#14583217C2214yes—
44#14583212C2214yes—
45#14583203C2218yescomplemented
46#14583196C2218yescomplemented
47#14583191C2214yescomplemented
48#14583186C2214yescomplemented
49#14583181C2214yescomplemented
50#14583176C2214yescomplemented
51#14582956C2212yescomplemented
52#14582956C2212yescomplemented
53#14582952C2212yescomplemented
54#14582952C2212yescomplemented
55#14582942C2214yes—
56#14582942C2214yes—
57#14582923C2212yes—
58#14582907C2214yes—
59#14582903C2214yes—
60#14582863C2212yes—
61C4×#10621877C2212yes—
62C43×#533—21no—
63C43×#533—21no—
64C43×#533—21no—
65C43×#533—21no—
66C43×#533C2212yes—
67C43×#533C2212yes—
68C43×#533C2212yescomplemented
69C43×#533C2212yescomplemented
70C2×C4⋊Q8×C43C2211yescharacteristic, complemented
71C2×C4⋊Q8×C43C2211yescharacteristic, complemented
72C2×#125×C43C2212yescomplemented
73C2×C22⋊Q8×C43—21no—
74C2×C22⋊Q8×C43—21no—
75C2×C4×Q8×C43—21no—
76C2×C4×Q8×C43—21no—
77C2×#117×C43C2212yes—
78C22×C42×C43C2211yescharacteristic
79C22×Dic86C2311yescharacteristic
80C22×D172C2311yescharacteristic
81C22×C22⋊D43—21no—
82C22×C4×D43—21no—
83C2×#10621877C2314yes—
84#13063319—22no—
85#13063319—22no—
86#13063319—22no—
87#13063319—22no—
88#13063317—21no—
89#13063317—21no—
90#13063317C2312yes—
91#13063317C2312yes—
92#13063313—21no—
93#13063313—21no—
94#13063313C2312yes—
95#13063313C2312yes—
96#13063308—22no—
97#13063308—22no—
98#13063308—22no—
99#13063308—22no—
100#13063304—21no—
101#13063304—21no—
102#13063304C2312yes—
103#13063304C2312yes—
104#13063299—21no—
105#13063299—21no—
106#13063299C2312yes—
107#13063299C2312yes—
108C4×Dic86—21no—
109C4×Dic86—21no—
110C4×Dic86C2312yes—
111C4×Dic86C2312yes—
112C4×D172—21no—
113C4×D172—21no—
114C4×D172C2312yes—
115C4×D172C2312yes—
116C4×C22⋊D43—22no—
117C4×C22⋊D43—22no—
118C4×C22⋊D43—22no—
119C4×C22⋊D43—22no—
120#13063282—22no—
121#13063282—22no—
122#13063282—22no—
123#13063282—22no—
124C2×C4⋊Dic43C2311yescharacteristic
125C2×C4⋊Dic43C2311yescharacteristic
126C2×Dic43⋊C4—21no—
127C2×Dic43⋊C4—21no—
128C2×Dic43⋊C4—21no—
129C2×Dic43⋊C4—21no—
130C2×C22⋊Dic43—21no—
131C2×(C2×D43)⋊C4—21no—
132C2×(C2×D43)⋊C4—21no—
133C2×(C2×D43)⋊C4—21no—
134C2×(C2×D43)⋊C4—21no—
135C2×C4×Dic43—21no—
136#13063258C2318yes—
137#13063258C2318yes—
138#13063256C2318yes—
139#13063256C2318yes—
140C4⋊(C43⋊C8)C2314yes—
141C4⋊(C43⋊C8)C2314yes—
142#13063248C2318yes—
143#13063248C2318yes—
144#13063245C2318yes—
145#13063245C2318yes—
146C22⋊(C43⋊C8)C2314yes—
147C22⋊(C43⋊C8)C2314yes—
148#13063236C2314yes—
149C4×C43⋊C8C2314yes—
150C22×Q8×C43—21no—
151C22×Q8×C43—21no—
152C23×C4×C43D411yescharacteristic
153C23×C4×C43D411yescharacteristic
154C23×C4×C43C2311yescharacteristic
155C4⋊Q8×C43—21no—
156C4⋊Q8×C43—21no—
157C4⋊Q8×C43—21no—
158C4⋊Q8×C43—21no—
159C4⋊Q8×C43C2312yes—
160C4⋊Q8×C43C2312yes—
161C4⋊Q8×C43C2312yes—
162C4⋊Q8×C43C2312yes—
163#125×C43—22no—
164#125×C43—22no—
165#125×C43C2314yes—
166#125×C43C2314yes—
167C22⋊Q8×C43—22no—
168C22⋊Q8×C43—22no—
169C22⋊Q8×C43—22no—
170C22⋊Q8×C43—22no—
171C22⋊Q8×C43—22no—
172C22⋊Q8×C43—22no—
173C22⋊Q8×C43—22no—
174C22⋊Q8×C43—22no—
175C4×Q8×C43—22no—
176C4×Q8×C43—22no—
177C4×Q8×C43—22no—
178C4×Q8×C43—22no—
179C4×Q8×C43—22no—
180C4×Q8×C43—22no—
181C4×Q8×C43—22no—
182C4×Q8×C43—22no—
183#117×C43—22no—
184#117×C43—22no—
185#117×C43C2314yes—
186#117×C43C2314yes—
187C2×C4⋊C4×C43—22no—
188C2×C4⋊C4×C43—22no—
189C2×C4⋊C4×C43—21no—
190C2×C4⋊C4×C43—21no—
191C2×C4⋊C4×C43C2312yes—
192C2×C4⋊C4×C43C2312yes—
193C2×C22⋊C4×C43—22no—
194C2×C42×C43—22no—
195C2×C42×C43D411yescharacteristic
196C2×C42×C43D411yescharacteristic
197C2×C42×C43D411yescharacteristic
198C2×C42×C43D411yescharacteristic
199C2×C42×C43D411yescharacteristic
200C2×C42×C43D411yescharacteristic
201C2×C42×C43C2311yescharacteristic
202C2×C42×C43C2311yescharacteristic
203C2×C42×C43C2311yescharacteristic
204C2×C42×C43C2311yescharacteristic
205C2×C42×C43C2311yescharacteristic
206C2×C42×C43C2311yescharacteristic
207C24×C43C2×D411yescharacteristic
208C23×D43—21no—
209C2×Q8×C43—22no—
210C2×Q8×C43—22no—
211C2×Q8×C43—22no—
212C2×Q8×C43—22no—
213C2×Q8×C43—44no—
214C2×Q8×C43—44no—
215C22×C4×C43—24no—
216C22×C4×C43—22no—
217C22×C4×C43—22no—
218C22×C4×C43—42no—
219C22×C4×C43—42no—
220C22×C4×C43C2×D411yescharacteristic
221C22×C4×C43C2×D411yescharacteristic
222C22×C4×C43C2×D411yescharacteristic
223C22×C4×C43C2×D411yescharacteristic
224C22×C4×C43C2×D411yescharacteristic
225C22×C4×C43C2×D411yescharacteristic
226C22×C4×C43C2×D411yescharacteristic
227C22×C4×C43C2×D411yescharacteristic
228C22×C4×C43C2×D411yescharacteristic
229C22×C4×C43C2×D411yescharacteristic
230C22×C4×C43C2×D411yescharacteristic
231C22×C4×C43C2×D411yescharacteristic
232C22×C4×C43C2×D411yescharacteristic
233C22×C4×C43C2×D411yescharacteristic
234C22×C4×C43C2×D411yescharacteristic
235C22×C4×C43C2411yescharacteristic
236C22×C4×C43C2411yescharacteristic
237C22×C4×C43C2411yescharacteristic
238C2×C22⋊D43—22no—
239C2×C22⋊D43—22no—
240C2×C22⋊D43—44no—
241C22×Dic43—21no—
242C22×Dic43—21no—
243C22×Dic43—21no—
244C2×D172—21no—
245C2×D172—24no—
246C2×D172C2412yes—
247C2×C4×D43—22no—
248C2×C4×D43—22no—
249C2×C4×D43—44no—
250C2×Dic86—24no—
251C2×Dic86—21no—
252C2×Dic86C2412yes—
253C4⋊C4×C43—24no—
254C4⋊C4×C43—24no—
255C4⋊C4×C43—24no—
256C4⋊C4×C43—24no—
257C4⋊C4×C43—22no—
258C4⋊C4×C43—22no—
259C4⋊C4×C43—22no—
260C4⋊C4×C43—22no—
261C4⋊C4×C43—22no—
262C4⋊C4×C43—22no—
263C4⋊C4×C43C2414yes—
264C4⋊C4×C43C2414yes—
265C22⋊C4×C43—24no—
266C22⋊C4×C43—24no—
267C42×C43—24no—
268C42×C43—24no—
269C42×C43C2×D411yescharacteristic
270C42×C43C2×D411yescharacteristic
271C42×C43C2×D411yescharacteristic
272C42×C43C2×D411yescharacteristic
273C42×C43C2×D411yescharacteristic
274C42×C43C2×D411yescharacteristic
275C42×C43C2×D411yescharacteristic
276C42×C43C2×D411yescharacteristic
277C42×C43C2×D411yescharacteristic
278C42×C43C2×D411yescharacteristic
279C42×C43C2×D411yescharacteristic
280C42×C43C2×D411yescharacteristic
281C42×C43C2411yescharacteristic
282C42×C43C2411yescharacteristic
283C42×C43C2411yescharacteristic
284C42×C43C2411yescharacteristic
285C22⋊Dic43—22no—
286C22⋊Dic43—22no—
287(C2×D43)⋊C4—22no—
288(C2×D43)⋊C4—22no—
289(C2×D43)⋊C4—22no—
290(C2×D43)⋊C4—22no—
291(C2×D43)⋊C4—22no—
292(C2×D43)⋊C4—22no—
293(C2×D43)⋊C4—22no—
294(C2×D43)⋊C4—22no—
295C4⋊Dic43—21no—
296C4⋊Dic43—21no—
297C4⋊Dic43C2412yes—
298C4⋊Dic43C2412yes—
299Dic43⋊C4—22no—
300Dic43⋊C4—22no—
301Dic43⋊C4—22no—
302Dic43⋊C4—22no—
303Dic43⋊C4—22no—
304Dic43⋊C4—22no—
305Dic43⋊C4—22no—
306Dic43⋊C4—22no—
307C4×Dic43—22no—
308C4×Dic43—22no—
309#10621877—28no—
310C2×C43⋊C8C2418yes—
311C23×C43—22no—
312C23×C43—22no—
313C23×C43—41no—
314C23×C43C22×D411yescharacteristic
315C23×C43C22×D411yescharacteristic
316C23×C43C22×D411yescharacteristic
317C22×D43—22no—
318C22×D43—42no—
319C22×D43—42no—
320C22×D43—42no—
321Q8×C43—44no—
322Q8×C43—44no—
323Q8×C43—44no—
324Q8×C43—44no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43—22no—
331C2×C4×C43—22no—
332C2×C4×C43—22no—
333C2×C4×C43—22no—
334C2×C4×C43—22no—
335C2×C4×C43—24no—
336C2×C4×C43—24no—
337C2×C4×C43—41no—
338C2×C4×C43—41no—
339C2×C4×C43—41no—
340C2×C4×C43—41no—
341C2×C4×C43—41no—
342C2×C4×C43—41no—
343C2×C4×C43—41no—
344C2×C4×C43—44no—
345C2×C4×C43—44no—
346C2×C4×C43C22×D411yescharacteristic
347C2×C4×C43C22×D411yescharacteristic
348C2×C4×C43C22×D411yescharacteristic
349C2×C4×C43C22×D411yescharacteristic
350C2×C4×C43C22×D411yescharacteristic
351C2×C4×C43C22×D411yescharacteristic
352C2×C4×C43C22×D411yescharacteristic
353C2×C4×C43C22×D411yescharacteristic
354C2×C4×C43C22×D411yescharacteristic
355C2×C4×C43C22×D411yescharacteristic
356C2×C4×C43C22×D411yescharacteristic
357C2×C4×C432−1+414yes—
358C2×C4×C43C2511yescharacteristic
359C22⋊D43—44no—
360C22⋊D43—44no—
361C2×Dic43—22no—
362C2×Dic43—22no—
363C2×Dic43—22no—
364C2×Dic43—42no—
365C2×Dic43—42no—
366C2×Dic43—42no—
367D172—24no—
368D172—42no—
369C4×D43—44no—
370C4×D43—44no—
371Dic86—24no—
372Dic86—42no—
373C43⋊C8—28no—
374#60866—431nomaximal, Sylow
375C22×C43—21no—
376C22×C43—21no—
377C22×C43—21no—
378C22×C43—21no—
379C22×C43—21no—
380C22×C43—21no—
381C22×C43—21no—
382C22×C43—44no—
383C22×C43#53612yes—
384C22×C43#57512yes—
385C22×C43C23×D411yescharacteristic
386C2×D43—42no—
387C2×D43—42no—
388C2×D43—42no—
389C2×D43—84no—
390C4×C43—21no—
391C4×C43—21no—
392C4×C43—21no—
393C4×C43—21no—
394C4×C43—21no—
395C4×C43—21no—
396C4×C43—21no—
397C4×C43—21no—
398C4×C43—21no—
399C4×C43—44no—
400C4×C43—44no—
401C4×C43#53612yes—
402C4×C43#57512yes—
403C4×C43C2×2−1+412yes—
404Dic43—42no—
405Dic43—42no—
406Dic43—42no—
407C2×#533D4311yescharacteristic, complemented
408C2×#529—431no—
409#3240—434no—
410#3239—432no—
411#3238—432no—
412#3233—434no—
413#3232—434no—
414#3166—432no—
415#3140—432no—
416#3095—432no—
417#3094—432no—
418#3078—432no—
419#3077—432no—
420#2920—431no—
421C2×C43—22no—
422C2×C43—22no—
423C2×C43—41no—
424C2×C43C2×#53611yescharacteristic
425C2×C43C2×#57511yescharacteristic
426C2×C43C2×#57511yescharacteristic
427D43—82no—
428#533—21no—
429#533—21no—
430#533—21no—
431#533—21no—
432#533C2×D4312yes—
433#533C2×D4312yes—
434#533C2×D4312yescomplemented
435#533C2×D4312yescomplemented
436C2×C4⋊Q8C2×D4311yescharacteristic, complemented
437C2×C4⋊Q8C2×D4311yescharacteristic, complemented
438#529—432no—
439#529—432no—
440#529—432no—
441#529—432no—
442#529—861no—
443#529—861no—
444#529—861no—
445#529—861no—
446C2×#126—861no—
447C2×#125—431no—
448C2×#125C2×D4312yescomplemented
449C2×#124—431no—
450C2×#123—861no—
451C2×C22⋊Q8—21no—
452C2×C22⋊Q8—21no—
453C2×C22⋊Q8—431no—
454C2×#121—431no—
455C2×C4×Q8—21no—
456C2×C4×Q8—21no—
457C2×C4×Q8—431no—
458C2×C4×D4—431no—
459C2×C4×D4—861no—
460C2×#117—861no—
461C2×#117C2×D4312yes—
462C22×C42C2×D4311yescharacteristic
463#501—434no—
464#501—434no—
465#499—438no—
466#489—434no—
467#489—434no—
468#488—438no—
469#485—438no—
470#484—434no—
471#483—434no—
472#482—438no—
473#481—434no—
474#480—434no—
475#479—438no—
476#478—438no—
477#477—434no—
478#476—434no—
479#475—434no—
480#474—434no—
481#432—432no—
482#432—432no—
483#431—432no—
484#431—432no—
485#428—434no—
486#428—434no—
487#423—432no—
488#419—434no—
489#418—434no—
490#407—432no—
491C4×M16—432no—
492C43#6086611yescharacteristic, complemented, Sylow
493C22×Q8—21no—
494C22×Q8—21no—
495C22×Q8—431no—
496C22×D4—431no—
497C22×D4—861no—
498C23×C4—861no—
499C23×C4C22⋊D4311yescharacteristic
500C23×C4C22⋊D4311yescharacteristic
501C23×C4C22×D4311yescharacteristic
502C2×M16—434no—
503C4⋊Q8—21no—
504C4⋊Q8—21no—
505C4⋊Q8—21no—
506C4⋊Q8—21no—
507C4⋊Q8C22×D4312yes—
508C4⋊Q8C22×D4312yes—
509C4⋊Q8C22×D4312yes—
510C4⋊Q8C22×D4312yes—
511#126—862no—
512#126—862no—
513#126—862no—
514#126—862no—
515#125—22no—
516#125—22no—
517#125—432no—
518#125—432no—
519#125—861no—
520#125—861no—
521#125C22×D4314yes—
522#125C22×D4314yes—
523#124—432no—
524#124—432no—
525#124—861no—
526#124—861no—
527#123—862no—
528#123—862no—
529#123—862no—
530#123—862no—
531C22⋊Q8—22no—
532C22⋊Q8—22no—
533C22⋊Q8—22no—
534C22⋊Q8—22no—
535C22⋊Q8—22no—
536C22⋊Q8—22no—
537C22⋊Q8—22no—
538C22⋊Q8—22no—
539C22⋊Q8—432no—
540C22⋊Q8—432no—
541C22⋊Q8—861no—
542C22⋊Q8—861no—
543#121—432no—
544#121—432no—
545#121—861no—
546#121—861no—
547C4×Q8—22no—
548C4×Q8—22no—
549C4×Q8—22no—
550C4×Q8—22no—
551C4×Q8—22no—
552C4×Q8—22no—
553C4×Q8—22no—
554C4×Q8—22no—
555C4×Q8—432no—
556C4×Q8—432no—
557C4×Q8—861no—
558C4×Q8—861no—
559C4×D4—432no—
560C4×D4—432no—
561C4×D4—862no—
562C4×D4—862no—
563C4×D4—862no—
564C4×D4—862no—
565C4×D4—861no—
566C4×D4—861no—
567#117—22no—
568#117—22no—
569#117—862no—
570#117—862no—
571#117—862no—
572#117—862no—
573#117C22×D4314yes—
574#117C22×D4314yes—
575C2×C4⋊C4—22no—
576C2×C4⋊C4—22no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—431no—
580C2×C4⋊C4—431no—
581C2×C4⋊C4—861no—
582C2×C4⋊C4—861no—
583C2×C4⋊C4—861no—
584C2×C4⋊C4—861no—
585C2×C4⋊C4C22×D4312yes—
586C2×C4⋊C4C22×D4312yes—
587C2×C22⋊C4—22no—
588C2×C22⋊C4—861no—
589C2×C22⋊C4—861no—
590C2×C22⋊C4—861no—
591C2×C22⋊C4—861no—
592C2×C22⋊C4—861no—
593C2×C42—22no—
594C2×C42—861no—
595C2×C42C22⋊D4311yescharacteristic
596C2×C42C22⋊D4311yescharacteristic
597C2×C42C22⋊D4311yescharacteristic
598C2×C42C22⋊D4311yescharacteristic
599C2×C42C22⋊D4311yescharacteristic
600C2×C42C22⋊D4311yescharacteristic
601C2×C42C22×D4311yescharacteristic
602C2×C42C22×D4311yescharacteristic
603C2×C42C22×D4311yescharacteristic
604C2×C42C22×D4311yescharacteristic
605C2×C42C22×D4311yescharacteristic
606C2×C42C22×D4311yescharacteristic
607#107—438no—
608#107—438no—
609#106—438no—
610#106—438no—
611C4⋊C8—434no—
612C4⋊C8—434no—
613#103—438no—
614#103—438no—
615#102—438no—
616#102—438no—
617C22⋊C8—434no—
618C22⋊C8—434no—
619#97—434no—
620C4×C8—434no—
621C24—861no—
622C24C2×C22⋊D4311yescharacteristic
623C2×Q8—22no—
624C2×Q8—22no—
625C2×Q8—22no—
626C2×Q8—22no—
627C2×Q8—44no—
628C2×Q8—44no—
629C2×Q8—432no—
630C2×Q8—861no—
631C2×Q8—864no—
632C2×D4—432no—
633C2×D4—862no—
634C2×D4—862no—
635C2×D4—861no—
636C2×D4—864no—
637C2×D4—1724no—
638C22×C4—24no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—861no—
644C22×C4—861no—
645C22×C4—861no—
646C22×C4—862no—
647C22×C4—862no—
648C22×C4—1724no—
649C22×C4C2×C22⋊D4311yescharacteristic
650C22×C4C2×C22⋊D4311yescharacteristic
651C22×C4C2×C22⋊D4311yescharacteristic
652C22×C4C2×C22⋊D4311yescharacteristic
653C22×C4C2×C22⋊D4311yescharacteristic
654C22×C4C2×C22⋊D4311yescharacteristic
655C22×C4C2×C22⋊D4311yescharacteristic
656C22×C4C2×C22⋊D4311yescharacteristic
657C22×C4C2×C22⋊D4311yescharacteristic
658C22×C4C2×C22⋊D4311yescharacteristic
659C22×C4C2×C22⋊D4311yescharacteristic
660C22×C4C2×C22⋊D4311yescharacteristic
661C22×C4C2×C22⋊D4311yescharacteristic
662C22×C4C2×C22⋊D4311yescharacteristic
663C22×C4C2×C22⋊D4311yescharacteristic
664C22×C4C23×D4311yescharacteristic
665C22×C4C23×D4311yescharacteristic
666C22×C4C23×D4311yescharacteristic
667M16—868no—
668C2×C8—438no—
669C4⋊C4—24no—
670C4⋊C4—24no—
671C4⋊C4—24no—
672C4⋊C4—24no—
673C4⋊C4—22no—
674C4⋊C4—22no—
675C4⋊C4—22no—
676C4⋊C4—22no—
677C4⋊C4—22no—
678C4⋊C4—22no—
679C4⋊C4—432no—
680C4⋊C4—432no—
681C4⋊C4—861no—
682C4⋊C4—861no—
683C4⋊C4—862no—
684C4⋊C4—862no—
685C4⋊C4—862no—
686C4⋊C4—862no—
687C4⋊C4—862no—
688C4⋊C4—862no—
689C4⋊C4—862no—
690C4⋊C4—862no—
691C4⋊C4C23×D4314yes—
692C4⋊C4C23×D4314yes—
693C22⋊C4—24no—
694C22⋊C4—24no—
695C22⋊C4—862no—
696C22⋊C4—862no—
697C22⋊C4—862no—
698C22⋊C4—862no—
699C22⋊C4—862no—
700C22⋊C4—862no—
701C22⋊C4—862no—
702C22⋊C4—862no—
703C22⋊C4—862no—
704C22⋊C4—862no—
705C42—24no—
706C42—24no—
707C42—862no—
708C42—862no—
709C42C2×C22⋊D4311yescharacteristic
710C42C2×C22⋊D4311yescharacteristic
711C42C2×C22⋊D4311yescharacteristic
712C42C2×C22⋊D4311yescharacteristic
713C42C2×C22⋊D4311yescharacteristic
714C42C2×C22⋊D4311yescharacteristic
715C42C2×C22⋊D4311yescharacteristic
716C42C2×C22⋊D4311yescharacteristic
717C42C2×C22⋊D4311yescharacteristic
718C42C2×C22⋊D4311yescharacteristic
719C42C2×C22⋊D4311yescharacteristic
720C42C2×C22⋊D4311yescharacteristic
721C42C23×D4311yescharacteristic
722C42C23×D4311yescharacteristic
723C42C23×D4311yescharacteristic
724C42C23×D4311yescharacteristic
725C23—22no—
726C23—22no—
727C23—41no—
728C23—862no—
729C23—1722no—
730C23—1722no—
731C23—1722no—
732C23C22×C22⋊D4311yescharacteristic
733C23C22×C22⋊D4311yescharacteristic
734C23C22×C22⋊D4311yescharacteristic
735Q8—44no—
736Q8—44no—
737Q8—44no—
738Q8—44no—
739Q8—864no—
740Q8—1722no—
741D4—864no—
742D4—1724no—
743D4—1724no—
744D4—1722no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—862no—
767C2×C4—862no—
768C2×C4—862no—
769C2×C4—1724no—
770C2×C4—1722no—
771C2×C4—1722no—
772C2×C4—1722no—
773C2×C4—1724no—
774C2×C4C22×C22⋊D4311yescharacteristic
775C2×C4C22×C22⋊D4311yescharacteristic
776C2×C4C22×C22⋊D4311yescharacteristic
777C2×C4C22×C22⋊D4311yescharacteristic
778C2×C4C22×C22⋊D4311yescharacteristic
779C2×C4C22×C22⋊D4311yescharacteristic
780C2×C4C22×C22⋊D4311yescharacteristic
781C2×C4C22×C22⋊D4311yescharacteristic
782C2×C4C22×C22⋊D4311yescharacteristic
783C2×C4C22×C22⋊D4311yescharacteristic
784C2×C4C22×C22⋊D4311yescharacteristic
785C2×C4#1306337314yes—
786C2×C4C24×D4311yescharacteristic
787C8—868no—
788C22—21no—
789C22—21no—
790C22—21no—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—21no—
795C22—44no—
796C22—3444no—
797C22—1722no—
798C22—1722no—
799C22—1722no—
800C22#1458347312yes—
801C22#1458369712yes—
802C22C23×C22⋊D4311yescharacteristic
803C4—21no—
804C4—21no—
805C4—21no—
806C4—21no—
807C4—21no—
808C4—21no—
809C4—21no—
810C4—21no—
811C4—21no—
812C4—44no—
813C4—44no—
814C4—1722no—
815C4—1722no—
816C4—1722no—
817C4#1458347312yes—
818C4#1458369712yes—
819C4C2×#1306337312yes—
820C2—22no—
821C2—22no—
822C2—41no—
823C2—3442no—
824C2C2×#1458347311yescharacteristic
825C2C2×#1458369711yescharacteristic
826C2C2×#1458369711yescharacteristic
subgroupG/H
centerC22C23×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#533C2
socleC22×C43C23×D4
prime radicalC2×#13063299C22
hypercenterC2×#533D43
hypocenterC43#60866
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C42 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
2. #19145835C2semidirect
3. #19145825C2semidirect
4. #19145816C2semidirect
5. #19145774C2semidirect
6. #19145763C2semidirect
7. #19145148C2semidirect
8. #19144984C2semidirect
9. #19144543C2semidirect
11. #19144396C2semidirect
12. #19144388C2semidirect
13. #19143228C2semidirect
14. C2×C43×#533C2semidirect
33. #14583305C22semidirect
34. #14583305C22semidirect
35. #14583298C22semidirect
36. #14583261C22semidirect
37. #14583261C22semidirect
38. #14583256C22semidirect
39. #14583240C22semidirect
40. #14583234C22semidirect
41. #14583229C22semidirect
45. #14583203C22semidirect
46. #14583196C22semidirect
47. #14583191C22semidirect
48. #14583186C22semidirect
49. #14583181C22semidirect
50. #14583176C22semidirect
51. #14582956C22semidirect
52. #14582956C22semidirect
53. #14582952C22semidirect
54. #14582952C22semidirect
68. C43×#533C22semidirect
69. C43×#533C22semidirect
70. C2×C4⋊Q8×C43C22semidirect
71. C2×C4⋊Q8×C43C22semidirect
72. C2×#125×C43C22semidirect
407. C2×#533D43semidirect
434. #533C2×D43semidirect
435. #533C2×D43semidirect
436. C2×C4⋊Q8C2×D43semidirect
437. C2×C4⋊Q8C2×D43semidirect
448. C2×#125C2×D43semidirect
492. C43#60866semidirect

Maximal subgroups

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

subgroupindex
C2×#145834332
#191458352
#191458252
#191458162
#191457742
#191457632
#191451482
#191449842
#191445432
#191445352
#191443962
#191443882
#191432282
C2×C43×#5332
#6086643