Finite Group Databasebeta

← #25263445

Subgroups — #25263445

Order 11008.

2934 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583434C211yesmaximal, characteristic, complemented
2C2×C4×D4×D43C211yesmaximal, characteristic, complemented
3#19140498C214yesmaximal, complemented
4#19140464C211yesmaximal, characteristic, complemented
5#19140450C211yesmaximal, characteristic, complemented
6#19140447C211yesmaximal, characteristic, complemented
7#19140401C212yesmaximal, complemented
8#19140376C212yesmaximal, complemented
9#19140330C212yesmaximal, complemented
10#19140308C212yesmaximal, complemented
11#19137880C212yesmaximal, complemented
12#19137875C212yesmaximal, complemented
13#19137836C212yesmaximal, complemented
14#19137834C212yesmaximal, complemented
15#19137096C214yesmaximal, complemented
16#19136992C211yesmaximal, characteristic, complemented
17C43×#2633C211yesmaximal, characteristic, complemented
18C22×D4×D43C2211yescharacteristic
19C23×C4×D43C2212yes—
20#14583434—28no—
21C2×#13063320C2212yescomplemented
22C2×#13063313C2211yescharacteristic, complemented
23C2×#13063310C2212yes—
24C2×#13063305C2211yescharacteristic
25C2×#13063300C2211yescharacteristic
26C2×#13063295C2214yes—
27C2×#13063290C2211yescharacteristic, complemented
28C2×C4×D172C2211yescharacteristic
29C2×D4×Dic43C2211yescharacteristic
30C2×#13063287C2211yescharacteristic
31C2×#13063287C2212yes—
32C2×#13063287C2211yescharacteristic, complemented
33C2×#13063287C2214yescomplemented
34C2×C4×C22⋊D43C2212yes—
35C2×(C22⋊D43)⋊C4C2212yes—
36C2×(C22⋊D43)⋊C4C2214yescomplemented
37C4×D4×D43—28no—
38C2×#13063283C2212yescomplemented
39C2×C4⋊C4×D43C2211yescharacteristic
40C2×C22⋊C4×D43C2212yes—
41C2×C42×D43C2211yescharacteristic
42#14582840C2214yescomplemented
43#14582834C2214yescomplemented
44#14582834C2212yescomplemented
45#14582829C2212yescomplemented
46#14582826C2212yescomplemented
47#14582825C2212yescomplemented
48#14582825C2212yescomplemented
49#14582822C2214yescomplemented
50#14582821C2214yescomplemented
51#14582817C2214yescomplemented
52#14582816C2212yes—
53#14582814C2214yes—
54#14582814C2214yescomplemented
55#14582812C2212yescomplemented
56#14582811C2212yescomplemented
57#14582809C2212yes—
58#14582809C2212yescomplemented
59#14582808C2214yes—
60#14582808C2212yescomplemented
61#14582807C2212yes—
62#14582778C2214yescomplemented
63#14582777C2214yes—
64#14582777C2214yescomplemented
65#14582770C2214yes—
66#14582770C2214yescomplemented
67#14582767C2211yescharacteristic, complemented
68#14582763C2212yescomplemented
69#14582761C2212yes—
70#14582758C2212yes—
71#14582754C2214yes—
72#14582750C2212yescomplemented
73C22⋊C4×Dic43C2214yescomplemented
74#14582746C2212yes—
75#14582746C2214yescomplemented
76#14582744C2212yescomplemented
77C2×#125×C43C2211yescharacteristic, complemented
78C2×C4×D4×C43C2211yescharacteristic
79C43×#399C2212yescomplemented
80C43×#398C2212yescomplemented
81C43×#397C2212yescomplemented
82C43×#394C2212yes—
83C43×#385C2214yescomplemented
84C43×#383C2211yescharacteristic, complemented
85C24×D43C2312yes—
86C22×Dic86C2311yescharacteristic
87C22×D172C2311yescharacteristic
88C22×D172C2312yes—
89C22×D172C2314yes—
90C22×D172C2311yescharacteristic
91C22×C22⋊D43C2312yes—
92C22×C22⋊D43C2314yes—
93C2×D4×D43—28no—
94C2×D4×D43—24no—
95C23×Dic43C2312yes—
96C22×C4×D43—28no—
97C22×C4×D43—48no—
98C22×C4×D43C2312yes—
99C22×C4×D43C2312yes—
100C22×C4×D43C2311yescharacteristic
101C22×C4×D43C2311yescharacteristic
102C22×C4×D43C2312yes—
103C22×C4×D43C2312yes—
104C22×C4×D43C2311yescharacteristic
105#13063320—28no—
106#13063313—24no—
107#13063310—28no—
108#13063305—24no—
109#13063300—24no—
110#13063295—216no—
111#13063290—24no—
112C4×D172—24no—
113D4×Dic43—24no—
114#13063287—28no—
115#13063287—24no—
116#13063287—24no—
117#13063287—48no—
118C4×C22⋊D43—28no—
119(C22⋊D43)⋊C4—28no—
120(C22⋊D43)⋊C4—48no—
121#13063283—28no—
122C2×C4⋊Dic43C2312yes—
123C2×C4⋊Dic43C2311yescharacteristic
124C2×Dic43⋊C4C2312yes—
125C2×Dic43⋊C4C2312yes—
126C2×Dic43⋊C4C2314yes—
127C2×Dic43⋊C4C2314yes—
128C4⋊C4×D43—24no—
129C2×C22⋊Dic43C2312yes—
130C2×C22⋊Dic43C2314yes—
131C2×(C2×D43)⋊C4C2312yes—
132C2×(C2×D43)⋊C4C2312yes—
133C2×(C2×D43)⋊C4C2312yes—
134C2×(C2×D43)⋊C4C2314yes—
135C2×(C2×D43)⋊C4C2312yes—
136C2×(C2×D43)⋊C4C2312yes—
137C2×(C2×D43)⋊C4C2312yes—
138C2×(C2×D43)⋊C4C2312yes—
139C2×(C2×D43)⋊C4C2314yes—
140C2×(C2×D43)⋊C4C2314yes—
141C2×(C2×D43)⋊C4C2314yes—
142C2×(C2×D43)⋊C4C2314yes—
143C2×(C2×D43)⋊C4C2314yes—
144C22⋊C4×D43—28no—
145C2×C4×Dic43C2312yes—
146C2×C4×Dic43C2314yes—
147C2×C4×Dic43C2311yescharacteristic
148C2×C4×Dic43C2311yescharacteristic
149C2×C4×Dic43C2311yescharacteristic
150C42×D43D418yescomplemented
151C43⋊#95C2312yes—
152C43⋊#95C2314yes—
153C43⋊#95C2312yes—
154C43⋊#95C2314yes—
155C43⋊#95C2314yes—
156C43⋊#95C2314yes—
157C43⋊#95C2312yes—
158C22×D4×C43C2311yescharacteristic
159C23×C4×C43C2312yes—
160#125×C43—24no—
161C4×D4×C43—24no—
162C2×C4⋊C4×C43C2311yescharacteristic
163C2×C4⋊C4×C43C2312yes—
164C2×C4⋊C4×C43C2311yescharacteristic
165C2×C4⋊C4×C43C2311yescharacteristic
166C2×C4⋊C4×C43C2312yes—
167C2×C4⋊C4×C43C2314yes—
168C2×C22⋊C4×C43C2312yes—
169C2×C22⋊C4×C43C2314yes—
170C2×C22⋊C4×C43C2314yes—
171C2×C42×C43C2311yescharacteristic
172#95×C43C2312yes—
173#95×C43C2312yes—
174#95×C43C2314yes—
175#95×C43C2312yes—
176C24×C43C2412yes—
177C23×D43—24no—
178C23×D43—24no—
179C23×D43—44no—
180C23×D43—44no—
181C23×D43#4118yes—
182C23×D43C2412yes—
183C23×D43C2412yes—
184C23×D43C2411yescharacteristic
185C2×D4×C43—22no—
186C2×D4×C43—24no—
187C22×C4×C43—24no—
188C22×C4×C43—44no—
189C22×C4×C43C2414yes—
190C22×C4×C43C2412yes—
191C22×C4×C43C2412yes—
192C22×C4×C43C2412yes—
193C22×C4×C43C2411yescharacteristic
194C22×C4×C43C2411yescharacteristic
195C22×C4×C43C2411yescharacteristic
196C2×C22⋊D43—24no—
197C2×C22⋊D43—24no—
198C2×C22⋊D43—28no—
199C2×C22⋊D43—24no—
200C2×C22⋊D43—44no—
201C2×C22⋊D43—44no—
202C22×Dic43—24no—
203C22×Dic43—28no—
204C22×Dic43C2414yes—
205C22×Dic43C2412yes—
206C22×Dic43C2412yes—
207C22×Dic43C2411yescharacteristic
208C22×Dic43C2411yescharacteristic
209C22×Dic43C2411yescharacteristic
210D4×D43—232no—
211C2×D172—22no—
212C2×D172—22no—
213C2×D172—24no—
214C2×D172—24no—
215C2×D172—28no—
216C2×D172—28no—
217C2×D172—44no—
218C2×D172—44no—
219C2×D172—42no—
220C2×C4×D43—24no—
221C2×C4×D43—24no—
222C2×C4×D43—24no—
223C2×C4×D43—24no—
224C2×C4×D43—24no—
225C2×C4×D43—24no—
226C2×C4×D43—28no—
227C2×C4×D43—24no—
228C2×C4×D43—24no—
229C2×C4×D43—44no—
230C2×C4×D43—44no—
231C2×C4×D43—42no—
232C2×C4×D43—432no—
233C2×C4×D43C2×D414yes—
234C2×C4×D43C2×D414yes—
235C2×C4×D43C2×D414yes—
236C2×Dic86—22no—
237C2×Dic86—42no—
238C4⋊C4×C43—22no—
239C4⋊C4×C43—24no—
240C4⋊C4×C43—22no—
241C4⋊C4×C43—24no—
242C4⋊C4×C43—22no—
243C4⋊C4×C43—44no—
244C22⋊C4×C43—24no—
245C22⋊C4×C43—28no—
246C22⋊C4×C43—44no—
247C42×C43C2×D414yes—
248C22⋊Dic43—24no—
249C22⋊Dic43—44no—
250(C2×D43)⋊C4—24no—
251(C2×D43)⋊C4—24no—
252(C2×D43)⋊C4—24no—
253(C2×D43)⋊C4—24no—
254(C2×D43)⋊C4—24no—
255(C2×D43)⋊C4—24no—
256(C2×D43)⋊C4—24no—
257(C2×D43)⋊C4—28no—
258(C2×D43)⋊C4—28no—
259(C2×D43)⋊C4—44no—
260(C2×D43)⋊C4—44no—
261(C2×D43)⋊C4—44no—
262(C2×D43)⋊C4—44no—
263C4⋊Dic43—22no—
264C4⋊Dic43—24no—
265Dic43⋊C4—24no—
266Dic43⋊C4—24no—
267Dic43⋊C4—44no—
268Dic43⋊C4—44no—
269C4×Dic43—24no—
270C4×Dic43—28no—
271C4×Dic43C2×D414yes—
272C4×Dic43C2×D414yes—
273C4×Dic43C2×D414yes—
274C23×C43—22no—
275C23×C43—22no—
276C23×C43—24no—
277C23×C43—24no—
278C23×C43C2×#4114yes—
279C23×C43C2511yescharacteristic
280C22×D43—22no—
281C22×D43—22no—
282C22×D43—22no—
283C22×D43—22no—
284C22×D43—24no—
285C22×D43—24no—
286C22×D43—216no—
287C22×D43—22no—
288C22×D43—24no—
289C22×D43—22no—
290C22×D43—22no—
291C22×D43—24no—
292C22×D43—416no—
293C22×D43—48no—
294C22×D43—48no—
295C22×D43—416no—
296C22×D43C22×D412yes—
297C22×D43C2×#4114yes—
298C22×D43C2×#4114yes—
299D4×C43—28no—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—22no—
303C2×C4×C43—22no—
304C2×C4×C43—22no—
305C2×C4×C43—22no—
306C2×C4×C43—24no—
307C2×C4×C43—24no—
308C2×C4×C43—24no—
309C2×C4×C43—22no—
310C2×C4×C43—22no—
311C2×C4×C43—24no—
312C2×C4×C43—24no—
313C2×C4×C43—48no—
314C2×C4×C43C22×D412yes—
315C2×C4×C43C22×D412yes—
316C2×C4×C43C22×D412yes—
317C22⋊D43—216no—
318C22⋊D43—416no—
319C2×Dic43—22no—
320C2×Dic43—22no—
321C2×Dic43—22no—
322C2×Dic43—22no—
323C2×Dic43—24no—
324C2×Dic43—24no—
325C2×Dic43—24no—
326C2×Dic43—24no—
327C2×Dic43—24no—
328C2×Dic43—48no—
329C2×Dic43C22×D412yes—
330C2×Dic43C22×D412yes—
331C2×Dic43C22×D412yes—
332C2×Dic43H(5,𝔽2)14yes—
333D172—28no—
334D172—44no—
335D172—416no—
336D172—48no—
337C4×D43—28no—
338C4×D43—28no—
339C4×D43—44no—
340C4×D43—48no—
341C4×D43—48no—
342C4×D43—48no—
343C4×D43—48no—
344Dic86—44no—
345#34593—431nomaximal, Sylow
346C22×C43—24no—
347C22×C43—28no—
348C22×C43—42no—
349C22×C43—42no—
350C22×C43—44no—
351C22×C43C23×D411yescharacteristic
352C22×C43C22×#4112yes—
353C22×C43C2×H(5,𝔽2)12yes—
354C22×C43#58512yes—
355C2×D43—22no—
356C2×D43—22no—
357C2×D43—28no—
358C2×D43—24no—
359C2×D43—28no—
360C2×D43—432no—
361C2×D43—42no—
362C2×D43—42no—
363C2×D43—44no—
364C2×D43—42no—
365C2×D43—42no—
366C2×D43—42no—
367C2×D43—44no—
368C2×D43—44no—
369C2×D43#52514yes—
370C4×C43—22no—
371C4×C43—22no—
372C4×C43—22no—
373C4×C43—42no—
374C4×C43—42no—
375C4×C43—42no—
376C4×C43—44no—
377Dic43—22no—
378Dic43—22no—
379Dic43—42no—
380Dic43—42no—
381Dic43—44no—
382Dic43#53514yes—
383C2×#529—431no—
384C22×C4×D4—431no—
385#2636—434no—
386#2633—431no—
387#2633D4311yescharacteristic, complemented
388#2631—431no—
389#2631—431no—
390#2626—432no—
391#2623—432no—
392#2617—432no—
393#2613—432no—
394#2398—432no—
395#2397—432no—
396#2392—432no—
397#2392—432no—
398C4×#120—434no—
399#2283—431no—
400C2×C43—44no—
401C2×C43C2×#52511yescharacteristic
402C2×C43C2×#53511yescharacteristic
403C2×C43#344911yescharacteristic
404C2×C43#345914yes—
405D43—24no—
406D43—44no—
407D43—82no—
408C23×D4—431no—
409C24×C4—432no—
410#529—868no—
411C2×#126—432no—
412C2×#125C2×D4311yescharacteristic, complemented
413C2×#124—431no—
414C2×#123—432no—
415C2×C22⋊Q8—431no—
416C2×#121—431no—
417C2×#120—434no—
418C2×C4×Q8—431no—
419C2×C4×D4—431no—
420C2×C4×D4—432no—
421C2×C4×D4—431no—
422C2×C4×D4—432no—
423C2×C4×D4—431no—
424C2×C4×D4—434no—
425C2×C4×D4—432no—
426C2×C4×D4—434no—
427C2×C4×D4—431no—
428C2×C4×D4—868no—
429C2×C4×D4C2×D4311yescharacteristic
430C2×#117—432no—
431C22×C4⋊C4—431no—
432C22×C22⋊C4—432no—
433C22×C42—431no—
434#400—434no—
435#399—434no—
436#399—432no—
437#399C2×D4312yescomplemented
438#398—432no—
439#398C2×D4312yescomplemented
440#397—432no—
441#397—432no—
442#397—432no—
443#397C2×D4312yescomplemented
444#396—434no—
445#396—434no—
446#394—432no—
447#394—434no—
448#394—434no—
449#394—434no—
450#394C2×D4312yes—
451#393—432no—
452#393—432no—
453#392—432no—
454#392—434no—
455#392—432no—
456#392—432no—
457#392—432no—
458#386—434no—
459#386—434no—
460#386—434no—
461#385—434no—
462#385—434no—
463#385C2×D4314yescomplemented
464#383—431no—
465#383C2×D4311yescharacteristic, complemented
466#382—432no—
467#381—432no—
468#380—432no—
469#379—434no—
470C4×C4⋊C4—432no—
471C4×C22⋊C4—434no—
472C4×C22⋊C4—434no—
473C4×C22⋊C4—432no—
474#376—432no—
475C43#3459311yescharacteristic, complemented, Sylow
476C25—432no—
477C22×Q8—431no—
478C22×D4—432no—
479C22×D4—434no—
480C22×D4—431no—
481C22×D4—432no—
482C22×D4—434no—
483C22×D4—431no—
484C22×D4—864no—
485C22×D4—868no—
486C22×D4C22×D4311yescharacteristic
487C23×C4—431no—
488C23×C4—431no—
489C23×C4—431no—
490C23×C4—432no—
491C23×C4—432no—
492C23×C4—432no—
493C23×C4—432no—
494C23×C4—432no—
495C23×C4—868no—
496C23×C4—1728no—
497C23×C4C22×D4312yes—
498#126—868no—
499#125—24no—
500#124—864no—
501#123—868no—
502C22⋊Q8—864no—
503#121—864no—
504#120—8616no—
505C4×Q8—864no—
506C4×D4—24no—
507C4×D4—868no—
508C4×D4—864no—
509C4×D4—864no—
510C4×D4—868no—
511C4×D4—864no—
512C4×D4—868no—
513C4×D4—864no—
514C4×D4—1728no—
515C4×D4—1728no—
516#117—868no—
517C2×C4⋊C4—432no—
518C2×C4⋊C4—431no—
519C2×C4⋊C4—432no—
520C2×C4⋊C4—432no—
521C2×C4⋊C4—434no—
522C2×C4⋊C4—434no—
523C2×C4⋊C4—864no—
524C2×C4⋊C4C22×D4311yescharacteristic
525C2×C4⋊C4C22×D4312yes—
526C2×C4⋊C4C22×D4311yescharacteristic
527C2×C4⋊C4C22×D4312yes—
528C2×C4⋊C4C22×D4311yescharacteristic
529C2×C4⋊C4C22×D4314yes—
530C2×C22⋊C4—432no—
531C2×C22⋊C4—432no—
532C2×C22⋊C4—432no—
533C2×C22⋊C4—432no—
534C2×C22⋊C4—432no—
535C2×C22⋊C4—432no—
536C2×C22⋊C4—432no—
537C2×C22⋊C4—432no—
538C2×C22⋊C4—434no—
539C2×C22⋊C4—434no—
540C2×C22⋊C4—434no—
541C2×C22⋊C4—434no—
542C2×C22⋊C4—434no—
543C2×C22⋊C4—434no—
544C2×C22⋊C4—434no—
545C2×C22⋊C4—868no—
546C2×C22⋊C4C22×D4312yes—
547C2×C22⋊C4C22×D4314yes—
548C2×C22⋊C4C22×D4314yes—
549C2×C42—431no—
550C2×C42—431no—
551C2×C42—431no—
552C2×C42—438no—
553C2×C42—432no—
554C2×C42—434no—
555C2×C42C22×D4311yescharacteristic
556#95—432no—
557#95—434no—
558#95—432no—
559#95—434no—
560#95—434no—
561#95—434no—
562#95—432no—
563#95C22×D4312yes—
564#95C22×D4312yes—
565#95C22×D4314yes—
566#95C22×D4312yes—
567C24—431no—
568C24—432no—
569C24—438no—
570C24—432no—
571C24—864no—
572C24—864no—
573C24—1724no—
574C24—1724no—
575C24C23×D4312yes—
576C2×Q8—862no—
577C2×Q8—1722no—
578C2×D4—24no—
579C2×D4—22no—
580C2×D4—864no—
581C2×D4—864no—
582C2×D4—868no—
583C2×D4—868no—
584C2×D4—864no—
585C2×D4—8632no—
586C2×D4—864no—
587C2×D4—864no—
588C2×D4—868no—
589C2×D4—862no—
590C2×D4—862no—
591C2×D4—1724no—
592C2×D4—1722no—
593C2×D4—1724no—
594C2×D4—1724no—
595C2×D4—1724no—
596C22×C4—24no—
597C22×C4—44no—
598C22×C4—431no—
599C22×C4—431no—
600C22×C4—431no—
601C22×C4—434no—
602C22×C4—434no—
603C22×C4—434no—
604C22×C4—434no—
605C22×C4—432no—
606C22×C4—432no—
607C22×C4—864no—
608C22×C4—864no—
609C22×C4—864no—
610C22×C4—864no—
611C22×C4—864no—
612C22×C4—868no—
613C22×C4—864no—
614C22×C4—864no—
615C22×C4—864no—
616C22×C4—868no—
617C22×C4—864no—
618C22×C4—1724no—
619C22×C4—1724no—
620C22×C4—1722no—
621C22×C4—17232no—
622C22×C4C23×D4314yes—
623C22×C4C23×D4312yes—
624C22×C4C23×D4312yes—
625C22×C4C23×D4312yes—
626C22×C4C23×D4311yescharacteristic
627C22×C4C23×D4311yescharacteristic
628C22×C4C23×D4311yescharacteristic
629C4⋊C4—22no—
630C4⋊C4—24no—
631C4⋊C4—22no—
632C4⋊C4—24no—
633C4⋊C4—22no—
634C4⋊C4—44no—
635C4⋊C4—864no—
636C4⋊C4—864no—
637C4⋊C4—864no—
638C4⋊C4—862no—
639C4⋊C4—1724no—
640C4⋊C4—1724no—
641C22⋊C4—28no—
642C22⋊C4—24no—
643C22⋊C4—44no—
644C22⋊C4—864no—
645C22⋊C4—864no—
646C22⋊C4—864no—
647C22⋊C4—864no—
648C22⋊C4—868no—
649C22⋊C4—868no—
650C22⋊C4—864no—
651C22⋊C4—864no—
652C22⋊C4—864no—
653C22⋊C4—864no—
654C22⋊C4—1724no—
655C22⋊C4—1724no—
656C22⋊C4—1724no—
657C22⋊C4—1724no—
658C22⋊C4—1724no—
659C42—434no—
660C42—434no—
661C42—434no—
662C42—864no—
663C42—868no—
664C42D4×D4314yes—
665C23—22no—
666C23—22no—
667C23—24no—
668C23—24no—
669C23—432no—
670C23—434no—
671C23—434no—
672C23—8616no—
673C23—862no—
674C23—862no—
675C23—862no—
676C23—862no—
677C23—864no—
678C23—864no—
679C23—862no—
680C23—864no—
681C23—862no—
682C23—862no—
683C23—864no—
684C23—17216no—
685C23—1728no—
686C23—1728no—
687C23—17216no—
688C23#41×D4314yes—
689C23C24×D4311yescharacteristic
690Q8—1724no—
691D4—28no—
692D4—868no—
693D4—8616no—
694D4—1724no—
695D4—1728no—
696D4—17216no—
697D4—17216no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—48no—
712C2×C4—432no—
713C2×C4—434no—
714C2×C4—432no—
715C2×C4—432no—
716C2×C4—868no—
717C2×C4—868no—
718C2×C4—862no—
719C2×C4—862no—
720C2×C4—862no—
721C2×C4—862no—
722C2×C4—864no—
723C2×C4—864no—
724C2×C4—864no—
725C2×C4—864no—
726C2×C4—864no—
727C2×C4—1724no—
728C2×C4—1728no—
729C2×C4—1728no—
730C2×C4—1728no—
731C2×C4—1728no—
732C2×C4—1728no—
733C2×C4C2×D4×D4312yes—
734C2×C4C2×D4×D4312yes—
735C2×C4C2×D4×D4312yes—
736C22—24no—
737C22—28no—
738C22—42no—
739C22—42no—
740C22—44no—
741C22—434no—
742C22—862no—
743C22—862no—
744C22—868no—
745C22—864no—
746C22—868no—
747C22—17232no—
748C22—1722no—
749C22—1722no—
750C22—1722no—
751C22—1724no—
752C22—1724no—
753C22—1722no—
754C22—1722no—
755C22—1724no—
756C22C22×D4×D4311yescharacteristic
757C22C2×#41×D4312yes—
758C22H(5,𝔽2)×D4312yes—
759C22#1458373612yes—
760C4—22no—
761C4—22no—
762C4—22no—
763C4—42no—
764C4—42no—
765C4—42no—
766C4—44no—
767C4—434no—
768C4—862no—
769C4—862no—
770C4—1722no—
771C4—1722no—
772C4—1724no—
773C2—44no—
774C2—864no—
775C2—3442no—
776C2—1724no—
777C2#525×D4311yescharacteristic
778C2#535×D4311yescharacteristic
779C2#1914792711yescharacteristic
780C2#1914800314yes—
subgroupG/H
center, FrattiniC23C24×D43
commutator, socle, cosocleC23×C43C25
FittingC43×#2633C2
hypercenter#2633D43
hypocenterC43#34593
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2633

Complements

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

NH ≅ G/Ntype
1. C2×#14583434C2semidirect
2. C2×C4×D4×D43C2semidirect
3. #19140498C2semidirect
4. #19140464C2semidirect
5. #19140450C2semidirect
6. #19140447C2semidirect
7. #19140401C2semidirect
8. #19140376C2semidirect
9. #19140330C2semidirect
10. #19140308C2semidirect
11. #19137880C2semidirect
12. #19137875C2semidirect
13. #19137836C2semidirect
14. #19137834C2semidirect
15. #19137096C2semidirect
16. #19136992C2semidirect
17. C43×#2633C2semidirect
21. C2×#13063320C22semidirect
22. C2×#13063313C22semidirect
27. C2×#13063290C22semidirect
32. C2×#13063287C22semidirect
33. C2×#13063287C22semidirect
36. C2×(C22⋊D43)⋊C4C22semidirect
38. C2×#13063283C22semidirect
42. #14582840C22semidirect
43. #14582834C22semidirect
44. #14582834C22semidirect
45. #14582829C22semidirect
46. #14582826C22semidirect
47. #14582825C22semidirect
48. #14582825C22semidirect
49. #14582822C22semidirect
50. #14582821C22semidirect
51. #14582817C22semidirect
54. #14582814C22semidirect
55. #14582812C22semidirect
56. #14582811C22semidirect
58. #14582809C22semidirect
60. #14582808C22semidirect
62. #14582778C22semidirect
64. #14582777C22semidirect
66. #14582770C22semidirect
67. #14582767C22semidirect
68. #14582763C22semidirect
72. #14582750C22semidirect
73. C22⋊C4×Dic43C22semidirect
75. #14582746C22semidirect
76. #14582744C22semidirect
77. C2×#125×C43C22semidirect
79. C43×#399C22semidirect
80. C43×#398C22semidirect
81. C43×#397C22semidirect
83. C43×#385C22semidirect
84. C43×#383C22semidirect
150. C42×D43D4semidirect
387. #2633D43semidirect
412. C2×#125C2×D43semidirect
437. #399C2×D43semidirect
439. #398C2×D43semidirect
443. #397C2×D43semidirect
463. #385C2×D43semidirect
465. #383C2×D43semidirect
475. C43#34593semidirect

Maximal subgroups

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

subgroupindex
C2×#145834342
C2×C4×D4×D432
#191404982
#191404642
#191404502
#191404472
#191404012
#191403762
#191403302
#191403082
#191378802
#191378752
#191378362
#191378342
#191370962
#191369922
C43×#26332
#3459343