Finite Group Databasebeta

← #11867179

Subgroups — #11867179

Order 1152.

1158 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#938C211yesmaximal, characteristic, complemented
2C2×#63932C211yesmaximal, characteristic, complemented
3C2×#63791C211yesmaximal, characteristic, complemented
4#10594626C211yesmaximal, characteristic, complemented
5#10592477C211yesmaximal, characteristic, complemented
6C3×#4782C211yesmaximal, characteristic, complemented
7C3×#4770C211yesmaximal, characteristic, complemented
8#10591462C211yesmaximal, characteristic, complemented
9#10591455C211yesmaximal, characteristic, complemented
10#10590839C211yesmaximal, characteristic, complemented
11#10590828C211yesmaximal, characteristic, complemented
12#10590670C211yesmaximal, characteristic, complemented
13#10590507C211yesmaximal, characteristic, complemented
14#10590504C211yesmaximal, characteristic, complemented
15#10590437C211yesmaximal, characteristic, complemented
16#80864—31nomaximal
17#78930—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×D3×#67—21no—
20C2×C4×D32C2211yescharacteristic
21C2×#3795C2211yescharacteristic
22#64147C2211yescharacteristic
23C2×#3754C2211yescharacteristic, complemented
24C2×C8×C3⋊D3C2211yescharacteristic, complemented
25#64106C2211yescharacteristic, complemented
26C3×#938C2211yescharacteristic
27C2×C3×#213C2211yescharacteristic, complemented
28C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
29C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
30C3×#895C2211yescharacteristic, complemented
31C3×#892C2211yescharacteristic
32#63970—21no—
33D3×#217—21no—
34#63958—21no—
35#63932—24no—
36#63922—21no—
37#63916C2211yescharacteristic
38#63916C2211yescharacteristic, complemented
39#63908C2211yescharacteristic
40Dic3×D12—21no—
41#63891—21no—
42D3×C4⋊Dic3C2211yescharacteristic
43#63880—21no—
44#63857C2211yescharacteristic, complemented
45C2×#3716C2211yescharacteristic, complemented
46C2×#3713C2211yescharacteristic, complemented
47C2×#3711C2211yescharacteristic
48C2×#3711C2211yescharacteristic, complemented
49C2×#3710C2211yescharacteristic, complemented
50#63791—24no—
51C32×#102C2211yescharacteristic, complemented
52#63643C2211yescharacteristic, complemented
53#63635C2211yescharacteristic, complemented
54C3×#832C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic, complemented
56C3×#821C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic, complemented
58C3×#808C2211yescharacteristic, complemented
59#63576C2211yescharacteristic, complemented
60#63575C2211yescharacteristic, complemented
61#63567C2211yescharacteristic, complemented
62#63563C2211yescharacteristic, complemented
63C2×#938—31no—
64C2×#932—31no—
65C2×#911—31no—
66C2×D3×M16—31no—
67C2×D3×M16—31no—
68#5606—31no—
69D3×#121—31no—
70#5524—31no—
71C3×#469—31no—
72C3×#418—31no—
73#5157—31no—
74#5134—31no—
75#5133—31no—
76#5042—31no—
77#5039—31no—
78#4995—31no—
79#4864—31no—
80#4861—31no—
81#4782—31no—
82#4782D311yescharacteristic, complemented
83#4780—31no—
84#4780—31no—
85#4778—31no—
86#4778—31no—
87#4778—31no—
88#4778—61no—
89#4775—31no—
90#4775—31no—
91#4775—31no—
92#4771—31no—
93#4770D311yescharacteristic, complemented
94C23×C3×D3—21no—
95C22×D32D411yescharacteristic
96C2×C32×D4C2311yescharacteristic
97C2×#638—21no—
98C2×C4×C3⋊D3C2311yescharacteristic
99C2×#634C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C3×D3×D4—22no—
103C3×D3×D4—22no—
104C2×C3×D12—21no—
105C2×C3×D12C2311yescharacteristic
106C2×C3×D12C2311yescharacteristic
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×C4×D3C2311yescharacteristic
109D3×#67—44no—
110C2×#626—21no—
111C2×#626—21no—
112C2×#625—21no—
113C2×#625—21no—
114C2×#624D411yescharacteristic
115C2×D3×Dic3—21no—
116C2×D3×Dic3—21no—
117C2×D3×Dic3D411yescharacteristic
118C2×D3×Dic3D411yescharacteristic
119C4×D32—22no—
120C4×D32—22no—
121#3795—22no—
122#3795—22no—
123C2×C32×C8C2311yescharacteristic
124C32×C4⋊C4C2311yescharacteristic
125#3757—21no—
126#3754—22no—
127#3752—21no—
128C4⋊(C3⋊Dic3)—21no—
129C4⋊(C3⋊Dic3)C2311yescharacteristic
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131C8×C3⋊D3—22no—
132C3×#217—21no—
133C3×#213—22no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×C4⋊Dic3C2311yescharacteristic
137C3×C4⋊Dic3C2311yescharacteristic
138C3×C4×Dic3—21no—
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C3×ΓL(1,𝔽25)—22no—
142C3×ΓL(1,𝔽25)—22no—
143Dic3⋊Dic3—21no—
144Dic3⋊Dic3—21no—
145(C2×D3)⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149#3716—22no—
150#3713—22no—
151#3711—22no—
152#3711D414yescomplemented
153#3710—22no—
154#3055—91noSylow
155C22×C3×D4—31no—
156C22×#67—61no—
157C2×#237—31no—
158C2×D3×D4—61no—
159C2×D3×D4C2×D311yescharacteristic
160C2×#235—31no—
161C22×C4×D3—31no—
162C22×C4×D3—31no—
163C2×C3×D8—31no—
164C2×C3×M16—31no—
165C2×C3×M16—31no—
166C3×#121—31no—
167C3×#121—31no—
168C3×#117—31no—
169C2×#217—61no—
170#939—61no—
171#938—31no—
172#938—31no—
173#938—31no—
174#938—31no—
175#938—31no—
176#938—61no—
177#938—61no—
178#938—61no—
179#938C2×D311yescharacteristic
180#937—61no—
181D4×Dic3—61no—
182C2×#214—31no—
183C2×#214—31no—
184C2×#214—31no—
185C2×#214—61no—
186#932—64no—
187C2×#213—31no—
188C2×#213—31no—
189C2×#213C2×D311yescharacteristic, complemented
190#930—31no—
191C2×C4⋊Dic3—31no—
192#924—31no—
193C2×#208—31no—
194C2×#208—31no—
195#911—64no—
196D3×M16—64no—
197D3×M16—64no—
198C2×#204—31no—
199C2×ΓL(1,𝔽25)—31no—
200C2×ΓL(1,𝔽25)—31no—
201C2×ΓL(1,𝔽25)C2×D311yescharacteristic
202C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
203C2×D3×C8—31no—
204C2×D3×C8—31no—
205C2×D3×C8—31no—
206C2×D3×C8—31no—
207C2×D3×C8—61no—
208#897—31no—
209#897—31no—
210#897—31no—
211#897—61no—
212#895—31no—
213#895—31no—
214#895C2×D311yescharacteristic, complemented
215#892C2×D311yescharacteristic
216D3×C4⋊C4—31no—
217#886—61no—
218#884—61no—
219#883—61no—
220#882—61no—
221#67⋊C4—61no—
222D3×C22⋊C4—61no—
223C4×D12—61no—
224C4×D12—61no—
225C3×#106—31no—
226C3×#102—21no—
227C3×#102—31no—
228C3×#102—31no—
229C3×#102—31no—
230C3×#102—31no—
231C3×#102C2×D311yescharacteristic, complemented
232C3×#102C2×D311yescharacteristic, complemented
233#832—31no—
234#832C2×D311yescharacteristic, complemented
235#821—31no—
236#821C2×D311yescharacteristic, complemented
237#821C2×D311yescharacteristic, complemented
238#818—31no—
239#816—31no—
240#816—31no—
241#816—31no—
242#816—61no—
243#810—31no—
244#809C2×D311yescharacteristic, complemented
245#808—31no—
246#808—31no—
247#808—61no—
248#808C2×D311yescharacteristic, complemented
249#807—31no—
250#807—31no—
251#807—31no—
252C23×C32—21no—
253C22×C3⋊D3C2×D411yescharacteristic
254C22×C3×D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3—42no—
257C22×C3×D3—42no—
258C22×C3×D3—42no—
259C22×C3×D3C2×D411yescharacteristic
260C22×C3×D3C2×D411yescharacteristic
261C2×D32—22no—
262C2×D32—22no—
263C2×D32—41no—
264C32×D4—21no—
265C32×D4—21no—
266C2×C32×C4—21no—
267C2×C32×C4C2411yescharacteristic
268#638—42no—
269C2×C3⋊Dic3—21no—
270C2×C3⋊Dic3—21no—
271C2×C3⋊Dic3C2×D411yescharacteristic
272C4×C3⋊D3—21no—
273C4×C3⋊D3—21no—
274#634—21no—
275#634—21no—
276C3×#67—42no—
277C3×#67—42no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3C2×D411yescharacteristic
281C2×C3×Dic3C2×D411yescharacteristic
282C3×D12—21no—
283C3×D12—21no—
284C3×D12—21no—
285C3×D12—21no—
286C3×D12—42no—
287C3×C4×D3—21no—
288C3×C4×D3—21no—
289C3×C4×D3C2×D412yes—
290C3×C4×D3#4112yes—
291#626—42no—
292#626—42no—
293#625—42no—
294#625—42no—
295#624—22no—
296D3×Dic3—22no—
297D3×Dic3—22no—
298D3×Dic3—42no—
299D3×Dic3—42no—
300C32×C8—21no—
301C3⋊(C3⋊C8)C2×D412yescomplemented
302C3×C3⋊C8—21no—
303C3×C3⋊C8C2×D412yescomplemented
304C2×AGL(1,ℤ/8)—91no—
305C22×M16—91no—
306#525—91no—
307C2×#121—91no—
308#469—31no—
309#469—91no—
310#468—91no—
311#468—91no—
312#466—91no—
313#466—91no—
314#465—91no—
315#465—91no—
316#428—91no—
317#418—31no—
318#417—91no—
319C24×C3—61no—
320C23×D3—21no—
321C23×D3—31no—
322C23×D3—31no—
323C2×C3×D4—21no—
324C2×C3×D4—31no—
325C2×C3×D4—31no—
326C2×C3×D4—61no—
327C2×C3×D4—62no—
328C2×C3×D4—62no—
329C2×C3×D4—61no—
330C2×C3×D4—61no—
331C2×C3×D4C22×D311yescharacteristic
332C2×C3×D4C22×D311yescharacteristic
333C22×C3×C4—31no—
334C22×C3×C4—31no—
335C2×#67—21no—
336C2×#67—21no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67—61no—
345C2×#67—121no—
346C2×#67—124no—
347C22×Dic3—31no—
348C22×Dic3—31no—
349C22×Dic3—61no—
350C22×Dic3—61no—
351#237—62no—
352#237—62no—
353D3×D4—22no—
354D3×D4—22no—
355D3×D4—124no—
356#235—62no—
357#235—62no—
358C2×D12—21no—
359C2×D12—61no—
360C2×D12—61no—
361C2×D12C22×D311yescharacteristic
362C2×D12C22×D311yescharacteristic
363C2×C4×D3—31no—
364C2×C4×D3—31no—
365C2×C4×D3—31no—
366C2×C4×D3—31no—
367C2×C4×D3—31no—
368C2×C4×D3—31no—
369C2×C4×D3—61no—
370C2×C4×D3—62no—
371C2×C4×D3—62no—
372C2×C4×D3—62no—
373C2×C4×D3—62no—
374C2×C4×D3—61no—
375C2×C4×D3—61no—
376C2×C4×D3C22×D311yescharacteristic
377C2×C4×D3C22×D311yescharacteristic
378C2×Dic6—31no—
379C2×Dic6—31no—
380C2×Dic6—61no—
381C3×D8—62no—
382C3×M16—62no—
383C3×M16—62no—
384C2×C3×C8—21no—
385C2×C3×C8—31no—
386C2×C3×C8—31no—
387C2×C3×C8C22×D311yescharacteristic
388C2×C3×C8C22×D311yescharacteristic
389C3×C4⋊C4—21no—
390C3×C4⋊C4—31no—
391C3×C4⋊C4—31no—
392C3×C4⋊C4C22×D311yescharacteristic
393C3×C4⋊C4C22×D311yescharacteristic
394C3×C22⋊C4—61no—
395C3×C22⋊C4—61no—
396C3×C22⋊C4—61no—
397C3×C42—61no—
398#217—21no—
399#217—61no—
400#217—61no—
401#217—61no—
402#217—61no—
403#217—61no—
404#217—61no—
405#217—121no—
406#214—62no—
407#214—62no—
408#214—62no—
409#214—122no—
410#213—22no—
411#213—62no—
412#213—62no—
413(C2×D3)⋊C4—21no—
414(C2×D3)⋊C4—21no—
415(C2×D3)⋊C4—61no—
416(C2×D3)⋊C4—61no—
417(C2×D3)⋊C4—61no—
418(C2×D3)⋊C4—61no—
419(C2×D3)⋊C4—61no—
420(C2×D3)⋊C4—61no—
421(C2×D3)⋊C4—121no—
422C4⋊Dic3—31no—
423C4⋊Dic3—31no—
424C4⋊Dic3—61no—
425C4⋊Dic3—61no—
426C4⋊Dic3—61no—
427C4⋊Dic3—61no—
428C4⋊Dic3—61no—
429C4⋊Dic3—121no—
430C4⋊Dic3C22×D311yescharacteristic
431C4⋊Dic3C22×D311yescharacteristic
432Dic3⋊C4—61no—
433Dic3⋊C4—61no—
434C4×Dic3—21no—
435#208—34no—
436#208—62no—
437C2×C3⋊C8—31no—
438C2×C3⋊C8—31no—
439C2×C3⋊C8—61no—
440C2×C3⋊C8C22×D311yescharacteristic
441C2×C3⋊C8C22×D311yescharacteristic
442#204—62no—
443ΓL(1,𝔽25)—22no—
444ΓL(1,𝔽25)—22no—
445ΓL(1,𝔽25)—34no—
446ΓL(1,𝔽25)—62no—
447D3×C8—62no—
448D3×C8—62no—
449D3×C8—62no—
450D3×C8—62no—
451D3×C8—122no—
452C22×C32—41no—
453C22×C32—41no—
454C22×C32—41no—
455C22×C32C22×D411yescharacteristic
456C2×C3⋊D3—21no—
457C2×C3⋊D3—21no—
458C2×C3⋊D3AGL(1,ℤ/8)12yescomplemented
459C2×C3×D3—21no—
460C2×C3×D3—21no—
461C2×C3×D3—21no—
462C2×C3×D3—21no—
463C2×C3×D3—21no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
467C2×C3×D3—41no—
468C2×C3×D3—41no—
469C2×C3×D3—41no—
470C2×C3×D3—84no—
471C2×C3×D3#12112yes—
472D32—44no—
473C32×C4—41no—
474C32×C4C22×D411yescharacteristic
475C32×C4C2×#4111yescharacteristic
476C3⋊Dic3—21no—
477C3⋊Dic3—41no—
478C3⋊Dic3—41no—
479C3×Dic3—21no—
480C3×Dic3—41no—
481C3×Dic3—41no—
482C3×Dic3#12112yes—
483C2×#41—91no—
484C22×D4—31no—
485C22×D4—181no—
486C23×C4—91no—
487AGL(1,ℤ/8)—184no—
488C2×SD16—91no—
489C2×SD16—91no—
490C2×D8—31no—
491C2×D8—91no—
492C2×M16—31no—
493C2×M16—31no—
494C2×M16—91no—
495C2×M16—91no—
496C2×M16—184no—
497C22×C8—91no—
498C22×C8—91no—
499#123—181no—
500C22⋊Q8—91no—
501C22⋊Q8—91no—
502#121—31no—
503#121—31no—
504#121—91no—
505#121—91no—
506#121—91no—
507#121—91no—
508#121—181no—
509#121—181no—
510#120—181no—
511C4×D4—181no—
512C4×D4—181no—
513#117—31no—
514C2×C4⋊C4—91no—
515C2×C22⋊C4—181no—
516#107—91no—
517#107—91no—
518#106—31no—
519#106—91no—
520#103—91no—
521#103—91no—
522#102—31no—
523#102—31no—
524#102—31no—
525#102—31no—
526#102—91no—
527#102D3211yescharacteristic, complemented
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—31no—
531C23×C3—31no—
532C23×C3—41no—
533C23×C3—61no—
534C23×C3—61no—
535C23×C3—122no—
536C23×C3—122no—
537C23×C3—122no—
538C22×D3—21no—
539C22×D3—21no—
540C22×D3—31no—
541C22×D3—31no—
542C22×D3—42no—
543C22×D3—42no—
544C22×D3—42no—
545C22×D3—61no—
546C22×D3—62no—
547C22×D3—62no—
548C22×D3—62no—
549C22×D3—62no—
550C22×D3—121no—
551C22×D3—121no—
552C22×D3D3×D411yescharacteristic
553C22×D3D3×D411yescharacteristic
554C3×D4—21no—
555C3×D4—21no—
556C3×D4—21no—
557C3×D4—21no—
558C3×D4—41no—
559C3×D4—41no—
560C3×D4—61no—
561C3×D4—61no—
562C3×D4—61no—
563C3×D4—61no—
564C3×D4—122no—
565C3×D4—122no—
566C3×D4—122no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—31no—
571C2×C3×C4—32no—
572C2×C3×C4—32no—
573C2×C3×C4—31no—
574C2×C3×C4—41no—
575C2×C3×C4—61no—
576C2×C3×C4—61no—
577C2×C3×C4—61no—
578C2×C3×C4—61no—
579C2×C3×C4C23×D311yescharacteristic
580C2×C3×C4C23×D311yescharacteristic
581#67—42no—
582#67—42no—
583#67—122no—
584#67—122no—
585#67—122no—
586#67—122no—
587#67—122no—
588#67—122no—
589#67—122no—
590#67—122no—
591#67—242no—
592C2×Dic3—21no—
593C2×Dic3—21no—
594C2×Dic3—31no—
595C2×Dic3—31no—
596C2×Dic3—61no—
597C2×Dic3—62no—
598C2×Dic3—62no—
599C2×Dic3—61no—
600C2×Dic3—61no—
601C2×Dic3—61no—
602C2×Dic3—61no—
603C2×Dic3—121no—
604C2×Dic3—121no—
605C2×Dic3—122no—
606C2×Dic3—122no—
607C2×Dic3D3×D411yescharacteristic
608C2×Dic3D3×D411yescharacteristic
609D12—21no—
610D12—21no—
611D12—21no—
612D12—21no—
613D12—42no—
614D12—122no—
615D12—122no—
616C4×D3—21no—
617C4×D3—21no—
618C4×D3—62no—
619C4×D3—62no—
620C4×D3—62no—
621C4×D3—61no—
622C4×D3—61no—
623C4×D3—61no—
624C4×D3—61no—
625C4×D3—62no—
626C4×D3—121no—
627C4×D3—121no—
628C4×D3—122no—
629C4×D3—122no—
630C4×D3#23512yes—
631C4×D3D3×D412yes—
632Dic6—61no—
633Dic6—61no—
634Dic6—61no—
635Dic6—61no—
636Dic6—121no—
637Dic6—121no—
638C3×C8—21no—
639C3×C8—21no—
640C3×C8—32no—
641C3×C8—41no—
642C3×C8—61no—
643C3⋊C8—21no—
644C3⋊C8—32no—
645C3⋊C8—32no—
646C3⋊C8—62no—
647C3⋊C8D3×D412yescomplemented
648C2×C32—81no—
649C2×C32C2×#12111yescharacteristic
650C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
651C2×C32#57511yescharacteristic
652C3⋊D3—22no—
653C3×D3—22no—
654C3×D3—41no—
655C3×D3—81no—
656C3×D3—81no—
657C24—61no—
658C24—91no—
659#41—182no—
660#41—182no—
661C2×Q8—91no—
662C2×D4—31no—
663C2×D4—31no—
664C2×D4—61no—
665C2×D4—62no—
666C2×D4—62no—
667C2×D4—61no—
668C2×D4—61no—
669C2×D4—181no—
670C2×D4—181no—
671C2×D4—181no—
672C2×D4—181no—
673C2×D4—181no—
674C2×D4—364no—
675C2×D4C2×D3211yescharacteristic
676C22×C4—31no—
677C22×C4—31no—
678C22×C4—91no—
679C22×C4—91no—
680C22×C4—91no—
681C22×C4—91no—
682C22×C4—182no—
683C22×C4—182no—
684C22×C4—181no—
685C22×C4—181no—
686SD16—182no—
687SD16—182no—
688D8—62no—
689D8—182no—
690M16—62no—
691M16—62no—
692M16—94no—
693M16—182no—
694C2×C8—31no—
695C2×C8—31no—
696C2×C8—91no—
697C2×C8—182no—
698C2×C8—182no—
699C2×C8C2×D3211yescharacteristic
700C4⋊C4—31no—
701C4⋊C4—31no—
702C4⋊C4—91no—
703C4⋊C4—181no—
704C4⋊C4—181no—
705C4⋊C4—181no—
706C4⋊C4C2×D3211yescharacteristic
707C22⋊C4—61no—
708C22⋊C4—61no—
709C22⋊C4—61no—
710C22⋊C4—181no—
711C22⋊C4—181no—
712C22⋊C4—181no—
713C22⋊C4—181no—
714C22⋊C4—181no—
715C22⋊C4—181no—
716C42—61no—
717C22×C3—21no—
718C22×C3—32no—
719C22×C3—41no—
720C22×C3—41no—
721C22×C3—41no—
722C22×C3—41no—
723C22×C3—41no—
724C22×C3—41no—
725C22×C3—61no—
726C22×C3—61no—
727C22×C3—61no—
728C22×C3—61no—
729C22×C3—61no—
730C22×C3—81no—
731C22×C3—81no—
732C22×C3—81no—
733C22×C3—121no—
734C22×C3—121no—
735C22×C3—121no—
736C22×C3—121no—
737C22×C3—121no—
738C22×C3—121no—
739C22×C3—244no—
740C22×C3C2×D3×D411yescharacteristic
741C22×C3C2×D3×D411yescharacteristic
742C2×D3—21no—
743C2×D3—21no—
744C2×D3—21no—
745C2×D3—21no—
746C2×D3—21no—
747C2×D3—32no—
748C2×D3—32no—
749C2×D3—41no—
750C2×D3—41no—
751C2×D3—41no—
752C2×D3—41no—
753C2×D3—41no—
754C2×D3—41no—
755C2×D3—62no—
756C2×D3—61no—
757C2×D3—61no—
758C2×D3—61no—
759C2×D3—61no—
760C2×D3—84no—
761C2×D3—121no—
762C2×D3—121no—
763C2×D3—124no—
764C2×D3—124no—
765C2×D3#88412yes—
766C3×C4—21no—
767C3×C4—21no—
768C3×C4—32no—
769C3×C4—41no—
770C3×C4—41no—
771C3×C4—61no—
772C3×C4—81no—
773C3×C4—121no—
774C3×C4—121no—
775C3×C4C2×#23511yescharacteristic
776C3×C4C2×D3×D411yescharacteristic
777C3×C4C2×D3×D411yescharacteristic
778C3×C4D3×#4111yescharacteristic
779Dic3—21no—
780Dic3—41no—
781Dic3—41no—
782Dic3—61no—
783Dic3—61no—
784Dic3—121no—
785Dic3—121no—
786Dic3—121no—
787Dic3—121no—
788Dic3—121no—
789Dic3—241no—
790Dic3—241no—
791Dic3#88412yes—
792C32#305511yescharacteristic, complemented, Sylow
793C23—21no—
794C23—31no—
795C23—31no—
796C23—61no—
797C23—61no—
798C23—91no—
799C23—122no—
800C23—122no—
801C23—122no—
802C23—182no—
803C23—182no—
804C23—361no—
805Q8—181no—
806Q8—181no—
807D4—21no—
808D4—21no—
809D4—61no—
810D4—61no—
811D4—61no—
812D4—61no—
813D4—122no—
814D4—122no—
815D4—122no—
816D4—362no—
817D4—362no—
818D4—362no—
819D4—362no—
820D4—362no—
821C2×C4—21no—
822C2×C4—31no—
823C2×C4—32no—
824C2×C4—32no—
825C2×C4—31no—
826C2×C4—61no—
827C2×C4—61no—
828C2×C4—61no—
829C2×C4—61no—
830C2×C4—91no—
831C2×C4—182no—
832C2×C4—182no—
833C2×C4—182no—
834C2×C4—181no—
835C2×C4—181no—
836C2×C4—181no—
837C2×C4—181no—
838C2×C4—362no—
839C2×C4—362no—
840C2×C4C22×D3211yescharacteristic
841C8—21no—
842C8—32no—
843C8—61no—
844C8—92no—
845C2×C3—21no—
846C2×C3—21no—
847C2×C3—21no—
848C2×C3—62no—
849C2×C3—81no—
850C2×C3—81no—
851C2×C3—121no—
852C2×C3—161no—
853C2×C3—241no—
854C2×C3—241no—
855C2×C3C2×#88411yescharacteristic
856C2×C3D3×#12111yescharacteristic
857C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
858C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
859C2×C3#577311yescharacteristic
860C2×C3#577311yescharacteristic
861D3—22no—
862D3—41no—
863D3—62no—
864D3—62no—
865D3—81no—
866D3—81no—
867D3—122no—
868C22—32no—
869C22—41no—
870C22—41no—
871C22—41no—
872C22—61no—
873C22—61no—
874C22—61no—
875C22—61no—
876C22—61no—
877C22—92no—
878C22—121no—
879C22—121no—
880C22—121no—
881C22—121no—
882C22—121no—
883C22—121no—
884C22—181no—
885C22—181no—
886C22—244no—
887C22—364no—
888C22D32×D411yescharacteristic
889C4—32no—
890C4—41no—
891C4—61no—
892C4—121no—
893C4—121no—
894C4—181no—
895C4—361no—
896C4—361no—
897C4D3×#23511yescharacteristic
898C4D32×D411yescharacteristic
899C3—21no—
900C3#7893011yescharacteristic, complemented
901C3#8086411yescharacteristic, complemented
902C2—62no—
903C2—81no—
904C2—121no—
905C2—182no—
906C2—241no—
907C2—241no—
908C2D3×#88411yescharacteristic
909C2#1059472811yescharacteristic
910C2#1059474011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32#3055
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. D3×#938C2semidirect
2. C2×#63932C2semidirect
3. C2×#63791C2semidirect
4. #10594626C2semidirect
5. #10592477C2semidirect
6. C3×#4782C2semidirect
7. C3×#4770C2semidirect
8. #10591462C2semidirect
9. #10591455C2semidirect
10. #10590839C2semidirect
11. #10590828C2semidirect
12. #10590670C2semidirect
13. #10590507C2semidirect
14. #10590504C2semidirect
15. #10590437C2semidirect
23. C2×#3754C22semidirect
24. C2×C8×C3⋊D3C22semidirect
25. #64106C22semidirect
27. C2×C3×#213C22semidirect
29. C2×C3×ΓL(1,𝔽25)C22semidirect
30. C3×#895C22semidirect
38. #63916C22semidirect
44. #63857C22semidirect
45. C2×#3716C22semidirect
46. C2×#3713C22semidirect
48. C2×#3711C22semidirect
49. C2×#3710C22semidirect
51. C32×#102C22semidirect
52. #63643C22semidirect
53. #63635C22semidirect
54. C3×#832C22semidirect
55. C3×#821C22semidirect
56. C3×#821C22semidirect
57. C3×#809C22semidirect
58. C3×#808C22semidirect
59. #63576C22semidirect
60. #63575C22semidirect
61. #63567C22semidirect
62. #63563C22semidirect
82. #4782D3semidirect
93. #4770D3semidirect
152. #3711D4semidirect
189. C2×#213C2×D3semidirect
202. C2×ΓL(1,𝔽25)C2×D3semidirect
214. #895C2×D3semidirect
231. C3×#102C2×D3semidirect
232. C3×#102C2×D3semidirect
234. #832C2×D3semidirect
236. #821C2×D3semidirect
237. #821C2×D3semidirect
244. #809C2×D3semidirect
248. #808C2×D3semidirect
301. C3⋊(C3⋊C8)C2×D4semidirect
303. C3×C3⋊C8C2×D4semidirect
458. C2×C3⋊D3AGL(1,ℤ/8)semidirect
527. #102D32semidirect
647. C3⋊C8D3×D4semidirect
792. C32#3055semidirect
900. C3#78930semidirect
901. C3#80864semidirect

Maximal subgroups

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

subgroupindex
D3×#9382
C2×#639322
C2×#637912
#105946262
#105924772
C3×#47822
C3×#47702
#105914622
#105914552
#105908392
#105908282
#105906702
#105905072
#105905042
#105904372
#808643
#789303