Finite Group Databasebeta

← #25263437

Subgroups — #25263437

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×#14583428C211yesmaximal, characteristic, complemented
2C2×C4×D4×D43C211yesmaximal, characteristic, complemented
3#19140496C214yesmaximal, complemented
4#19140466C211yesmaximal, characteristic, complemented
5#19140463C211yesmaximal, characteristic, complemented
6#19140448C211yesmaximal, characteristic, complemented
7#19140399C212yesmaximal, complemented
8#19140374C212yesmaximal, complemented
9#19140328C212yesmaximal, complemented
10#19140306C212yesmaximal, complemented
11#19137877C212yesmaximal, complemented
12#19137873C212yesmaximal, complemented
13#19137832C212yesmaximal, complemented
14#19137830C212yesmaximal, complemented
15#19137100C214yesmaximal, complemented
16#19136992C211yesmaximal, characteristic, complemented
17C43×#2631C211yesmaximal, characteristic, complemented
18C22×D4×D43C2211yescharacteristic
19C23×C4×D43C2212yes—
20#14583428—28no—
21C2×#13063318C2212yescomplemented
22C2×#13063317C2211yescharacteristic, complemented
23C2×#13063307C2212yes—
24C2×#13063301C2211yescharacteristic
25C2×#13063296C2211yescharacteristic
26C2×#13063293C2214yes—
27C2×Q8×Dic43C2211yescharacteristic, complemented
28C2×C4×D172C2211yescharacteristic
29C2×D4×Dic43C2211yescharacteristic
30C2×D4×Dic43C2211yescharacteristic, complemented
31C2×D4×Dic43C2214yescomplemented
32C2×#13063287C2211yescharacteristic
33C2×C4×C22⋊D43C2212yes—
34C2×(C22⋊D43)⋊C4C2212yes—
35C2×(C22⋊D43)⋊C4C2212yes—
36C2×(C22⋊D43)⋊C4C2214yescomplemented
37C4×D4×D43—28no—
38C2×#13063281C2212yescomplemented
39C2×C4⋊C4×D43C2211yescharacteristic
40C2×C22⋊C4×D43C2212yes—
41C2×C42×D43C2211yescharacteristic
42#14582841C2214yescomplemented
43#14582836C2212yescomplemented
44#14582835C2214yescomplemented
45#14582835C2212yescomplemented
46#14582831C2212yescomplemented
47#14582830C2212yescomplemented
48#14582826C2212yescomplemented
49#14582824C2212yescomplemented
50#14582824C2212yescomplemented
51#14582823C2214yescomplemented
52#14582822C2214yescomplemented
53#14582817C2212yes—
54#14582815C2214yes—
55#14582814C2214yescomplemented
56#14582813C2212yes—
57#14582813C2214yescomplemented
58#14582810C2212yescomplemented
59#14582808C2212yes—
60#14582807C2214yes—
61#14582807C2212yescomplemented
62#14582775C2214yes—
63#14582775C2214yescomplemented
64#14582773C2214yes—
65#14582773C2214yescomplemented
66#14582772C2214yescomplemented
67#14582767C2211yescharacteristic, complemented
68#14582763C2212yescomplemented
69#14582761C2212yes—
70#14582758C2212yes—
71#14582754C2214yes—
72#14582750C2212yescomplemented
73C22⋊C4×Dic43C2214yescomplemented
74#14582746C2212yes—
75#14582746C2214yescomplemented
76#14582744C2212yescomplemented
77C2×#124×C43C2211yescharacteristic, complemented
78C2×C4×D4×C43C2211yescharacteristic
79C43×#397C2212yescomplemented
80C43×#393C2212yescomplemented
81C43×#392C2212yes—
82C43×#392C2212yescomplemented
83C43×#386C2214yescomplemented
84C43×#383C2211yescharacteristic, complemented
85C24×D43C2312yes—
86C22×D172C2311yescharacteristic
87C22×C22⋊D43C2312yes—
88C22×C22⋊D43C2312yes—
89C22×C22⋊D43C2314yes—
90C2×D4×D43—28no—
91C2×D4×D43—24no—
92C23×Dic43C2312yes—
93C23×Dic43C2312yes—
94C22×C4×D43—28no—
95C22×C4×D43—48no—
96C22×C4×D43C2312yes—
97C22×C4×D43C2311yescharacteristic
98C22×C4×D43C2311yescharacteristic
99C22×C4×D43C2312yes—
100C22×C4×D43C2312yes—
101C22×C4×D43C2311yescharacteristic
102#13063318—28no—
103#13063317—24no—
104#13063307—28no—
105#13063301—24no—
106#13063296—24no—
107#13063293—216no—
108Q8×Dic43—24no—
109C4×D172—24no—
110D4×Dic43—24no—
111D4×Dic43—24no—
112D4×Dic43—48no—
113#13063287—24no—
114C4×C22⋊D43—28no—
115(C22⋊D43)⋊C4—28no—
116(C22⋊D43)⋊C4—28no—
117(C22⋊D43)⋊C4—48no—
118#13063281—28no—
119C2×C4⋊Dic43C2312yes—
120C2×C4⋊Dic43C2311yescharacteristic
121C2×C4⋊Dic43C2311yescharacteristic
122C2×C4⋊Dic43C2311yescharacteristic
123C2×C4⋊Dic43C2314yes—
124C2×Dic43⋊C4C2312yes—
125C2×Dic43⋊C4C2312yes—
126C2×Dic43⋊C4C2312yes—
127C2×Dic43⋊C4C2312yes—
128C2×Dic43⋊C4C2314yes—
129C2×Dic43⋊C4C2314yes—
130C4⋊C4×D43—24no—
131C2×C22⋊Dic43C2312yes—
132C2×C22⋊Dic43C2314yes—
133C2×C22⋊Dic43C2312yes—
134C2×C22⋊Dic43C2312yes—
135C2×C22⋊Dic43C2314yes—
136C2×C22⋊Dic43C2314yes—
137C2×(C2×D43)⋊C4C2312yes—
138C2×(C2×D43)⋊C4C2312yes—
139C2×(C2×D43)⋊C4C2314yes—
140C2×(C2×D43)⋊C4C2312yes—
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⋊#95C2314yes—
152C43⋊#95C2312yes—
153C43⋊#95C2312yes—
154C43⋊#95C2314yes—
155C43⋊#95C2314yes—
156C43⋊#95C2314yes—
157C43⋊#95C2312yes—
158C22×Q8×C43C2311yescharacteristic
159C22×D4×C43C2311yescharacteristic
160C22×D4×C43C2314yes—
161C22×D4×C43C2311yescharacteristic
162C23×C4×C43C2312yes—
163#124×C43—24no—
164C4×D4×C43—24no—
165C2×C4⋊C4×C43C2311yescharacteristic
166C2×C22⋊C4×C43C2312yes—
167C2×C22⋊C4×C43C2312yes—
168C2×C22⋊C4×C43C2312yes—
169C2×C22⋊C4×C43C2314yes—
170C2×C22⋊C4×C43C2314yes—
171C2×C42×C43C2311yescharacteristic
172#95×C43C2312yes—
173#95×C43C2314yes—
174#95×C43C2312yes—
175#95×C43C2312yes—
176C24×C43C2412yes—
177C24×C43C2412yes—
178C23×D43—24no—
179C23×D43—24no—
180C23×D43—44no—
181C23×D43—44no—
182C23×D43#4118yes—
183C23×D43C2412yes—
184C23×D43C2411yescharacteristic
185C2×Q8×C43—22no—
186C2×Q8×C43—42no—
187C2×D4×C43—22no—
188C2×D4×C43—22no—
189C2×D4×C43—24no—
190C2×D4×C43—28no—
191C2×D4×C43—44no—
192C2×D4×C43—42no—
193C2×D4×C43—44no—
194C22×C4×C43—24no—
195C22×C4×C43—44no—
196C22×C4×C43C2414yes—
197C22×C4×C43C2412yes—
198C22×C4×C43C2412yes—
199C22×C4×C43C2411yescharacteristic
200C22×C4×C43C2411yescharacteristic
201C22×C4×C43C2411yescharacteristic
202C2×C22⋊D43—24no—
203C2×C22⋊D43—24no—
204C2×C22⋊D43—24no—
205C2×C22⋊D43—24no—
206C2×C22⋊D43—28no—
207C2×C22⋊D43—28no—
208C2×C22⋊D43—44no—
209C2×C22⋊D43—44no—
210C22×Dic43—24no—
211C22×Dic43—24no—
212C22×Dic43—24no—
213C22×Dic43—24no—
214C22×Dic43—28no—
215C22×Dic43C2414yes—
216C22×Dic43C2412yes—
217C22×Dic43C2412yes—
218C22×Dic43C2412yes—
219C22×Dic43C2411yescharacteristic
220C22×Dic43C2411yescharacteristic
221C22×Dic43C2411yescharacteristic
222D4×D43—232no—
223C2×D172—22no—
224C2×D172—24no—
225C2×C4×D43—24no—
226C2×C4×D43—24no—
227C2×C4×D43—24no—
228C2×C4×D43—28no—
229C2×C4×D43—24no—
230C2×C4×D43—24no—
231C2×C4×D43—44no—
232C2×C4×D43—44no—
233C2×C4×D43—42no—
234C2×C4×D43—432no—
235C2×C4×D43C2×D414yes—
236C2×C4×D43C2×D414yes—
237C2×C4×D43C2×D414yes—
238C4⋊C4×C43—22no—
239C22⋊C4×C43—24no—
240C22⋊C4×C43—24no—
241C22⋊C4×C43—24no—
242C22⋊C4×C43—44no—
243C22⋊C4×C43—44no—
244C42×C43C2×D414yes—
245C22⋊Dic43—24no—
246C22⋊Dic43—24no—
247C22⋊Dic43—24no—
248C22⋊Dic43—28no—
249C22⋊Dic43—44no—
250C22⋊Dic43—44no—
251(C2×D43)⋊C4—24no—
252(C2×D43)⋊C4—24no—
253(C2×D43)⋊C4—24no—
254(C2×D43)⋊C4—28no—
255(C2×D43)⋊C4—28no—
256(C2×D43)⋊C4—44no—
257(C2×D43)⋊C4—44no—
258C4⋊Dic43—22no—
259C4⋊Dic43—22no—
260C4⋊Dic43—22no—
261C4⋊Dic43—24no—
262C4⋊Dic43—44no—
263Dic43⋊C4—24no—
264Dic43⋊C4—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×C43—22no—
279C23×C43—24no—
280C23×C43—22no—
281C23×C43—22no—
282C23×C43—24no—
283C23×C43C2×#4114yes—
284C23×C43C2511yescharacteristic
285C22×D43—22no—
286C22×D43—22no—
287C22×D43—22no—
288C22×D43—22no—
289C22×D43—24no—
290C22×D43—24no—
291C22×D43—216no—
292C22×D43—416no—
293C22×D43—48no—
294C22×D43—48no—
295C22×D43—416no—
296C22×D43C22×D412yes—
297C22×D43C2×#4114yes—
298C22×D43C2×#4114yes—
299Q8×C43—44no—
300D4×C43—28no—
301D4×C43—44no—
302D4×C43—416no—
303C2×C4×C43—22no—
304C2×C4×C43—22no—
305C2×C4×C43—22no—
306C2×C4×C43—22no—
307C2×C4×C43—22no—
308C2×C4×C43—24no—
309C2×C4×C43—24no—
310C2×C4×C43—24no—
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—
319C22⋊D43—48no—
320C2×Dic43—22no—
321C2×Dic43—22no—
322C2×Dic43—22no—
323C2×Dic43—22no—
324C2×Dic43—22no—
325C2×Dic43—24no—
326C2×Dic43—24no—
327C2×Dic43—24no—
328C2×Dic43—22no—
329C2×Dic43—22no—
330C2×Dic43—24no—
331C2×Dic43—24no—
332C2×Dic43—48no—
333C2×Dic43—48no—
334C2×Dic43C22×D412yes—
335C2×Dic43C22×D412yes—
336C2×Dic43C22×D412yes—
337C2×Dic43H(5,𝔽2)14yes—
338D172—28no—
339C4×D43—28no—
340C4×D43—28no—
341C4×D43—44no—
342C4×D43—48no—
343C4×D43—48no—
344C4×D43—48no—
345#34593—431nomaximal, Sylow
346C22×C43—24no—
347C22×C43—28no—
348C22×C43—42no—
349C22×C43—42no—
350C22×C43—44no—
351C22×C43—42no—
352C22×C43—42no—
353C22×C43—42no—
354C22×C43—44no—
355C22×C43—44no—
356C22×C43C23×D411yescharacteristic
357C22×C43C22×#4112yes—
358C22×C43C2×H(5,𝔽2)12yes—
359C22×C43#58512yes—
360C2×D43—22no—
361C2×D43—22no—
362C2×D43—28no—
363C2×D43—24no—
364C2×D43—28no—
365C2×D43—432no—
366C2×D43—42no—
367C2×D43—42no—
368C2×D43—44no—
369C2×D43#52514yes—
370C4×C43—22no—
371C4×C43—22no—
372C4×C43—22no—
373C4×C43—42no—
374C4×C43—42no—
375C4×C43—44no—
376Dic43—22no—
377Dic43—22no—
378Dic43—42no—
379Dic43—42no—
380Dic43—42no—
381Dic43—44no—
382Dic43#53514yes—
383C2×#529—431no—
384C22×C4×D4—431no—
385#2636—434no—
386#2633—431no—
387#2633—431no—
388#2631—431no—
389#2631D4311yescharacteristic, complemented
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×C43—82no—
402C2×C43C2×#52511yescharacteristic
403C2×C43C2×#53511yescharacteristic
404C2×C43#344911yescharacteristic
405C2×C43#345914yes—
406D43—24no—
407D43—44no—
408C23×D4—431no—
409C24×C4—432no—
410#529—868no—
411C2×#126—432no—
412C2×#125—431no—
413C2×#124C2×D4311yescharacteristic, complemented
414C2×#123—432no—
415C2×C22⋊Q8—431no—
416C2×#121—431no—
417C2×#120—434no—
418C2×C4×Q8—431no—
419C2×C4×D4—431no—
420C2×C4×D4—431no—
421C2×C4×D4—432no—
422C2×C4×D4—434no—
423C2×C4×D4—431no—
424C2×C4×D4—432no—
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#399—432no—
438#398—432no—
439#398—432no—
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#394—432no—
451#393—432no—
452#393C2×D4312yescomplemented
453#392—434no—
454#392—432no—
455#392—432no—
456#392C2×D4312yes—
457#392C2×D4312yescomplemented
458#386—434no—
459#386—434no—
460#386C2×D4314yescomplemented
461#385—434no—
462#385—434no—
463#385—434no—
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×Q8C22×D4311yescharacteristic
478C22×D4—432no—
479C22×D4—432no—
480C22×D4—434no—
481C22×D4—431no—
482C22×D4—864no—
483C22×D4—868no—
484C22×D4C22×D4311yescharacteristic
485C22×D4C22×D4314yes—
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—864no—
500#124—24no—
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—868no—
510C4×D4—864no—
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—431no—
522C2×C4⋊C4—432no—
523C2×C4⋊C4—431no—
524C2×C4⋊C4—432no—
525C2×C4⋊C4—434no—
526C2×C4⋊C4—434no—
527C2×C4⋊C4—434no—
528C2×C4⋊C4—864no—
529C2×C4⋊C4C22×D4311yescharacteristic
530C2×C22⋊C4—432no—
531C2×C22⋊C4—432no—
532C2×C22⋊C4—432no—
533C2×C22⋊C4—434no—
534C2×C22⋊C4—432no—
535C2×C22⋊C4—432no—
536C2×C22⋊C4—432no—
537C2×C22⋊C4—434no—
538C2×C22⋊C4—434no—
539C2×C22⋊C4—434no—
540C2×C22⋊C4—434no—
541C2×C22⋊C4—434no—
542C2×C22⋊C4—434no—
543C2×C22⋊C4—868no—
544C2×C22⋊C4C22×D4312yes—
545C2×C22⋊C4C22×D4312yes—
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—864no—
571C24—864no—
572C24—1724no—
573C24—1724no—
574C24C23×D4312yes—
575C24C23×D4312yes—
576C2×Q8—22no—
577C2×Q8—42no—
578C2×D4—24no—
579C2×D4—28no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—44no—
583C2×D4—42no—
584C2×D4—44no—
585C2×D4—864no—
586C2×D4—864no—
587C2×D4—8632no—
588C2×D4—864no—
589C2×D4—864no—
590C2×D4—864no—
591C2×D4—868no—
592C2×D4—868no—
593C2×D4—862no—
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—432no—
608C22×C4—864no—
609C22×C4—864no—
610C22×C4—868no—
611C22×C4—864no—
612C22×C4—864no—
613C22×C4—864no—
614C22×C4—864no—
615C22×C4—864no—
616C22×C4—864no—
617C22×C4—868no—
618C22×C4—864no—
619C22×C4—1724no—
620C22×C4—1724no—
621C22×C4—1722no—
622C22×C4—17232no—
623C22×C4C23×D4314yes—
624C22×C4C23×D4312yes—
625C22×C4C23×D4312yes—
626C22×C4C23×D4311yescharacteristic
627C22×C4C23×D4311yescharacteristic
628C22×C4C23×D4311yescharacteristic
629C4⋊C4—22no—
630C4⋊C4—864no—
631C4⋊C4—864no—
632C4⋊C4—864no—
633C4⋊C4—862no—
634C4⋊C4—864no—
635C4⋊C4—862no—
636C4⋊C4—864no—
637C4⋊C4—862no—
638C4⋊C4—1724no—
639C4⋊C4—1724no—
640C4⋊C4—1724no—
641C22⋊C4—24no—
642C22⋊C4—24no—
643C22⋊C4—24no—
644C22⋊C4—44no—
645C22⋊C4—44no—
646C22⋊C4—864no—
647C22⋊C4—864no—
648C22⋊C4—868no—
649C22⋊C4—868no—
650C22⋊C4—864no—
651C22⋊C4—864no—
652C22⋊C4—864no—
653C22⋊C4—868no—
654C22⋊C4—864no—
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—22no—
670C23—24no—
671C23—22no—
672C23—22no—
673C23—24no—
674C23—432no—
675C23—434no—
676C23—434no—
677C23—8616no—
678C23—862no—
679C23—862no—
680C23—862no—
681C23—862no—
682C23—864no—
683C23—864no—
684C23—17216no—
685C23—1728no—
686C23—1728no—
687C23—17216no—
688C23#41×D4314yes—
689C23C24×D4311yescharacteristic
690Q8—44no—
691D4—28no—
692D4—44no—
693D4—416no—
694D4—868no—
695D4—8616no—
696D4—1728no—
697D4—17216no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—48no—
709C2×C4—432no—
710C2×C4—434no—
711C2×C4—432no—
712C2×C4—432no—
713C2×C4—868no—
714C2×C4—868no—
715C2×C4—862no—
716C2×C4—862no—
717C2×C4—862no—
718C2×C4—862no—
719C2×C4—862no—
720C2×C4—864no—
721C2×C4—864no—
722C2×C4—864no—
723C2×C4—862no—
724C2×C4—862no—
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—42no—
742C22—42no—
743C22—42no—
744C22—44no—
745C22—44no—
746C22—434no—
747C22—862no—
748C22—862no—
749C22—868no—
750C22—864no—
751C22—868no—
752C22—17232no—
753C22—1722no—
754C22—1722no—
755C22—1724no—
756C22C22×D4×D4311yescharacteristic
757C22C2×#41×D4312yes—
758C22H(5,𝔽2)×D4312yes—
759C22#1458373412yes—
760C4—22no—
761C4—22no—
762C4—22no—
763C4—42no—
764C4—42no—
765C4—44no—
766C4—434no—
767C4—862no—
768C4—862no—
769C4—1722no—
770C4—1722no—
771C4—1722no—
772C4—1724no—
773C2—44no—
774C2—82no—
775C2—864no—
776C2—1724no—
777C2#525×D4311yescharacteristic
778C2#535×D4311yescharacteristic
779C2#1914792611yescharacteristic
780C2#1914800614yes—
subgroupG/H
center, FrattiniC23C24×D43
commutator, socle, cosocleC23×C43C25
FittingC43×#2631C2
hypercenter#2631D43
hypocenterC43#34593
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2631

Complements

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

NH ≅ G/Ntype
1. C2×#14583428C2semidirect
2. C2×C4×D4×D43C2semidirect
3. #19140496C2semidirect
4. #19140466C2semidirect
5. #19140463C2semidirect
6. #19140448C2semidirect
7. #19140399C2semidirect
8. #19140374C2semidirect
9. #19140328C2semidirect
10. #19140306C2semidirect
11. #19137877C2semidirect
12. #19137873C2semidirect
13. #19137832C2semidirect
14. #19137830C2semidirect
15. #19137100C2semidirect
16. #19136992C2semidirect
17. C43×#2631C2semidirect
21. C2×#13063318C22semidirect
22. C2×#13063317C22semidirect
27. C2×Q8×Dic43C22semidirect
30. C2×D4×Dic43C22semidirect
31. C2×D4×Dic43C22semidirect
36. C2×(C22⋊D43)⋊C4C22semidirect
38. C2×#13063281C22semidirect
42. #14582841C22semidirect
43. #14582836C22semidirect
44. #14582835C22semidirect
45. #14582835C22semidirect
46. #14582831C22semidirect
47. #14582830C22semidirect
48. #14582826C22semidirect
49. #14582824C22semidirect
50. #14582824C22semidirect
51. #14582823C22semidirect
52. #14582822C22semidirect
55. #14582814C22semidirect
57. #14582813C22semidirect
58. #14582810C22semidirect
61. #14582807C22semidirect
63. #14582775C22semidirect
65. #14582773C22semidirect
66. #14582772C22semidirect
67. #14582767C22semidirect
68. #14582763C22semidirect
72. #14582750C22semidirect
73. C22⋊C4×Dic43C22semidirect
75. #14582746C22semidirect
76. #14582744C22semidirect
77. C2×#124×C43C22semidirect
79. C43×#397C22semidirect
80. C43×#393C22semidirect
82. C43×#392C22semidirect
83. C43×#386C22semidirect
84. C43×#383C22semidirect
150. C42×D43D4semidirect
389. #2631D43semidirect
413. C2×#124C2×D43semidirect
443. #397C2×D43semidirect
452. #393C2×D43semidirect
457. #392C2×D43semidirect
460. #386C2×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×#145834282
C2×C4×D4×D432
#191404962
#191404662
#191404632
#191404482
#191403992
#191403742
#191403282
#191403062
#191378772
#191378732
#191378322
#191378302
#191371002
#191369922
C43×#26312
#3459343