Finite Group Databasebeta

← #11860742

Subgroups — #11860742

Order 1152.

1059 conjugacy classes of subgroups.

The subgroup lattice has 787 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595339C211yesmaximal, characteristic, complemented
2C2×#63940C211yesmaximal, characteristic
3#10594606C211yesmaximal, characteristic
4#10592501C211yesmaximal, characteristic, complemented
5C3×#4817C211yesmaximal, characteristic, complemented
6C3×#4788C211yesmaximal, characteristic, complemented
7#10591566C211yesmaximal, characteristic, complemented
8Dic3×#215C211yesmaximal, characteristic, complemented
9#10590941C211yesmaximal, characteristic
10#10590910C211yesmaximal, characteristic, complemented
11#10590747C211yesmaximal, characteristic, complemented
12#10590744C211yesmaximal, characteristic, complemented
13#10590590C211yesmaximal, characteristic, complemented
14#10590574C211yesmaximal, characteristic, complemented
15#10590479C211yesmaximal, characteristic, complemented
16#79777—31nomaximal
17#79649—31nomaximal
18C2×Q8×C3⋊D3C2211yescharacteristic
19C2×#3802C2211yescharacteristic
20C2×#3743C2211yescharacteristic
21#64101C2211yescharacteristic
22C3×Q8×Dic3C2211yescharacteristic, complemented
23C3×Q8×Dic3C2211yescharacteristic, complemented
24C2×C3×#215C2211yescharacteristic
25C2×C3×#215C2211yescharacteristic
26C3×#893C2211yescharacteristic
27C3×#893C2211yescharacteristic
28#63940C418yescomplemented
29D3×(C2×D3)⋊C4—21no—
30D3×(C2×D3)⋊C4—21no—
31#63902—21no—
32C4×#625—21no—
33Dic3×D12C2211yescharacteristic
34Dic3×D12C2211yescharacteristic
35#63874—21no—
36#63874C2211yescharacteristic
37#63849—21no—
38#63849C2211yescharacteristic
39#63844—21no—
40#63844—21no—
41#63844C2211yescharacteristic, complemented
42#63844C2211yescharacteristic, complemented
43C2×#3716C2211yescharacteristic
44C2×#3716C2211yescharacteristic
45C2×#3710C2211yescharacteristic
46C32×#103C2211yescharacteristic, complemented
47#63662C2211yescharacteristic, complemented
48#63643C2211yescharacteristic, complemented
49#63637C2211yescharacteristic, complemented
50C3×#821C2211yescharacteristic
51C3×#821C2211yescharacteristic
52C3×#815C2211yescharacteristic, complemented
53C3×C8×Dic3C2211yescharacteristic, complemented
54C3×#808C2211yescharacteristic, complemented
55C3×#807C2211yescharacteristic, complemented
56#63575C2211yescharacteristic, complemented
57#63573C2211yescharacteristic, complemented
58#63562C2211yescharacteristic
59#63562C2211yescharacteristic
60#63554C2211yescharacteristic, complemented
61Dic3×C3⋊C8C2211yescharacteristic, complemented
62C2×D3×SD16—31no—
63C2×D3×SD16—31no—
64#5572—31no—
65#5572—31no—
66#5545—31no—
67#5545—31no—
68C3×#440—31no—
69C3×C4×SD16—31no—
70#5164—31no—
71Dic3×SD16—31no—
72#5026—31no—
73C4×#215—31no—
74#5018—31no—
75C4×#214—31no—
76#4889—31no—
77#4880—31no—
78#4860—31no—
79#4852—31no—
80#4817D311yescharacteristic, complemented
81#4802—31no—
82#4802—31no—
83#4802—61no—
84#4788D311yescharacteristic, complemented
85#4770—31no—
86#4770—31no—
87#4758—31no—
88#4757—31no—
89#4710—31no—
90#4708—31no—
91C4×#204—31no—
92#4689—31no—
93C22×D32—21no—
94C2×C32×Q8C2311yescharacteristic
95Q8×C3⋊D3—22no—
96Q8×C3⋊D3C2×C414yescomplemented
97C2×C4×C3⋊D3—21no—
98C2×C4×C3⋊D3C2311yescharacteristic
99C2×#634—21no—
100C2×#634C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—21no—
105C2×#625—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108#3802—22no—
109#3802C2×C414yes—
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112#3752—21no—
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114C4×C3⋊Dic3—21no—
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116#3743—22no—
117C3×#215C2×C414yescomplemented
118C3×#215C2×C414yescomplemented
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4×Dic3—21no—
126C3×C4×Dic3—21no—
127C3×C4×Dic3C2311yescharacteristic
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131#3724—21no—
132#3724—21no—
133#3724D411yescharacteristic
134#3724D411yescharacteristic
135#3722—21no—
136#3722D411yescharacteristic
137#3722D411yescharacteristic
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32—21no—
141Dic32—21no—
142Dic32—21no—
143#3716C2×C414yescomplemented
144#3716C2×C414yescomplemented
145#3710C2×C414yescomplemented
146#2949—91noSylow
147C2×D3×Q8—31no—
148C2×D3×Q8—31no—
149C2×D3×Q8—61no—
150C2×D3×D4—31no—
151C2×D3×D4—31no—
152C2×C3×SD16—31no—
153C2×C3×SD16—31no—
154C3×C4×Q8—31no—
155C3×C4×Q8—31no—
156C3×C4×D4—31no—
157C3×C4×D4—31no—
158Q8×Dic3C2×D311yescharacteristic, complemented
159Q8×Dic3C2×D311yescharacteristic, complemented
160C2×#215C2×D311yescharacteristic
161C2×#215C2×D311yescharacteristic
162D4×Dic3—31no—
163D4×Dic3—31no—
164C2×#214—31no—
165C2×#214—31no—
166C4×#67—61no—
167C4×#67—61no—
168C2×(C2×D3)⋊C4—61no—
169C2×(C2×D3)⋊C4—61no—
170D3×SD16—38no—
171D3×SD16—38no—
172C2×#204—31no—
173C2×#204—31no—
174C2×ΓL(1,𝔽25)—31no—
175C2×ΓL(1,𝔽25)—31no—
176C2×ΓL(1,𝔽25)—61no—
177C2×D3×C8—31no—
178C2×D3×C8—31no—
179#893C2×D311yescharacteristic
180#893C2×D311yescharacteristic
181#892—31no—
182#892—31no—
183#892—31no—
184#892—31no—
185#892—61no—
186#892—61no—
187#892—61no—
188#887—31no—
189#887—31no—
190#887—61no—
191#887—61no—
192#67⋊C4—61no—
193#67⋊C4—61no—
194D3×C22⋊C4—61no—
195D3×C22⋊C4—61no—
196C4×D12—31no—
197C4×D12—31no—
198#872—31no—
199#872—31no—
200#872—61no—
201#872—61no—
202C4×Dic6—31no—
203C4×Dic6—31no—
204C4×Dic6—61no—
205C4×Dic6—61no—
206C3×#107—31no—
207C3×#106—31no—
208C3×#103—21no—
209C3×#103C2×D311yescharacteristic, complemented
210C3×#103C2×D311yescharacteristic, complemented
211C3×#102—31no—
212C3×#102—31no—
213C3×#97—31no—
214C3×C4×C8—31no—
215#835—31no—
216#835—31no—
217#835—61no—
218#832—31no—
219#832—31no—
220#821C2×D311yescharacteristic
221#821C2×D311yescharacteristic
222#818—31no—
223#817—31no—
224#816—31no—
225#816—31no—
226#816—61no—
227#815—31no—
228#815C2×D311yescharacteristic, complemented
229C8×Dic3—31no—
230C8×Dic3C2×D311yescharacteristic, complemented
231#810—31no—
232#810—31no—
233#810—61no—
234#809—31no—
235#809—31no—
236#808—31no—
237#808C2×D311yescharacteristic, complemented
238#807—31no—
239#807C2×D311yescharacteristic, complemented
240#803—31no—
241C4×C3⋊C8—31no—
242C22×C3⋊D3C2×D411yescharacteristic
243C22×C3×D3—21no—
244C22×C3×D3—21no—
245C2×D32—24no—
246C2×D32—81no—
247C2×D32—81no—
248C32×Q8—21no—
249C32×Q8C22×C412yes—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4C2411yescharacteristic
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3C2×D411yescharacteristic
256C4×C3⋊D3—24no—
257C4×C3⋊D3C22×C412yes—
258C4×C3⋊D3#4112yes—
259#634—21no—
260#634—24no—
261#634C22×C412yes—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C3×D12—21no—
269C3×D12—21no—
270C3×D12C22×C412yes—
271C3×D12C22×C412yes—
272C3×C4×D3—81no—
273C3×C4×D3—81no—
274#625—24no—
275D3×Dic3—81no—
276D3×Dic3—81no—
277C32×C8—21no—
278C3⋊(C3⋊C8)—21no—
279C3×C3⋊C8C22×C412yes—
280C3×C3⋊C8C22×C412yes—
281C22×SD16—91no—
282#519—91no—
283#518—91no—
284#440—31no—
285#440—91no—
286#440—91no—
287#440—91no—
288C4×SD16—31no—
289C4×SD16—91no—
290C4×SD16—91no—
291C4×SD16—91no—
292#427—91no—
293#419—91no—
294#418—91no—
295#405—91no—
296C23×D3—61no—
297C23×D3—61no—
298C2×C3×Q8—21no—
299C2×C3×Q8C22×D311yescharacteristic
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×D4—31no—
302C2×C3×D4—31no—
303C22×C3×C4—61no—
304C22×C3×C4—61no—
305C2×#67—61no—
306C2×#67—61no—
307C22×Dic3—61no—
308C22×Dic3—61no—
309D3×Q8—34no—
310D3×Q8—34no—
311D3×Q8—64no—
312D3×Q8—62no—
313D3×Q8—62no—
314D3×Q8—122no—
315D3×D4—34no—
316D3×D4—34no—
317D3×D4—62no—
318D3×D4—62no—
319C2×D12C22×D311yescharacteristic
320C2×D12C22×D311yescharacteristic
321C2×C4×D3—21no—
322C2×C4×D3—21no—
323C2×C4×D3—31no—
324C2×C4×D3—31no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—121no—
331C2×Dic6—31no—
332C2×Dic6—31no—
333C2×Dic6—61no—
334C2×Dic6—61no—
335C2×Dic6—61no—
336C2×Dic6—121no—
337C3×SD16—34no—
338C3×SD16—34no—
339C2×C3×C8—21no—
340C2×C3×C8—31no—
341C2×C3×C8—31no—
342C2×C3×C8C22×D311yescharacteristic
343C2×C3×C8C22×D311yescharacteristic
344C3×C4⋊C4—21no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4C22×D311yescharacteristic
350C3×C4⋊C4C22×D311yescharacteristic
351C3×C22⋊C4—61no—
352C3×C22⋊C4—61no—
353C3×C42—31no—
354C3×C42—31no—
355C3×C42—61no—
356C3×C42—61no—
357#217—61no—
358#217—61no—
359#215C4×D314yescomplemented
360#215C4×D314yescomplemented
361#214—34no—
362#214—34no—
363(C2×D3)⋊C4—21no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—31no—
366(C2×D3)⋊C4—31no—
367(C2×D3)⋊C4—31no—
368(C2×D3)⋊C4—31no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—121no—
376C4⋊Dic3—21no—
377C4⋊Dic3—21no—
378C4⋊Dic3—31no—
379C4⋊Dic3—31no—
380C4⋊Dic3—61no—
381C4⋊Dic3C22×D311yescharacteristic
382C4⋊Dic3C22×D311yescharacteristic
383Dic3⋊C4—31no—
384Dic3⋊C4—31no—
385Dic3⋊C4—31no—
386Dic3⋊C4—31no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391C4×Dic3—21no—
392C4×Dic3—21no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3—121no—
402C4×Dic3C22×D311yescharacteristic
403C4×Dic3C22×D311yescharacteristic
404C2×C3⋊C8—31no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—61no—
407C2×C3⋊C8C22×D311yescharacteristic
408C2×C3⋊C8C22×D311yescharacteristic
409#204—34no—
410#204—34no—
411ΓL(1,𝔽25)—62no—
412ΓL(1,𝔽25)—62no—
413ΓL(1,𝔽25)—122no—
414D3×C8—34no—
415D3×C8—34no—
416C22×C32C22×D411yescharacteristic
417C2×C3⋊D3—21no—
418C2×C3⋊D3—21no—
419C2×C3⋊D3C4×D412yes—
420C2×C3×D3—22no—
421C2×C3×D3—22no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426D32—84no—
427C32×C4—22no—
428C32×C4—41no—
429C32×C4C23×C411yescharacteristic
430C32×C4C2×#4111yescharacteristic
431C3⋊Dic3—22no—
432C3⋊Dic3—41no—
433C3⋊Dic3C4×D412yes—
434C3×Dic3—21no—
435C3×Dic3—21no—
436C3×Dic3—21no—
437C3×Dic3—21no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C22×Q8—91no—
441C22×D4—91no—
442C2×SD16—31no—
443C2×SD16—31no—
444C2×SD16—91no—
445C2×SD16—91no—
446C2×SD16—98no—
447C2×M16—91no—
448C22×C8—91no—
449C4×Q8—31no—
450C4×Q8—31no—
451C4×Q8—91no—
452C4×Q8—91no—
453C4×Q8—181no—
454C4×Q8—181no—
455C4×D4—31no—
456C4×D4—31no—
457C4×D4—91no—
458C4×D4—91no—
459C4×D4—181no—
460C4×D4—181no—
461#117—91no—
462#117—91no—
463#117—91no—
464#117—181no—
465#117—181no—
466C2×C22⋊C4—181no—
467C2×C22⋊C4—181no—
468#107—31no—
469#107—91no—
470#106—31no—
471#106—91no—
472#103—91no—
473#103—91no—
474#103—91no—
475#103D3211yescharacteristic, complemented
476#102—31no—
477#102—31no—
478#102—91no—
479#102—91no—
480#97—31no—
481#97—91no—
482C4×C8—31no—
483C4×C8—91no—
484C23×C3—61no—
485C23×C3—61no—
486C22×D3—21no—
487C22×D3—21no—
488C22×D3—31no—
489C22×D3—31no—
490C22×D3—61no—
491C22×D3—64no—
492C22×D3—64no—
493C22×D3—241no—
494C22×D3—241no—
495C22×D3—241no—
496C22×D3—241no—
497C3×Q8—21no—
498C3×Q8—21no—
499C3×Q8—22no—
500C3×Q8—41no—
501C3×Q8C2×C4×D312yes—
502C3×Q8C2×C4×D312yes—
503C3×D4—32no—
504C3×D4—32no—
505C3×D4—61no—
506C3×D4—61no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—31no—
513C2×C3×C4—31no—
514C2×C3×C4—31no—
515C2×C3×C4—31no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—241no—
521C2×C3×C4—241no—
522C2×C3×C4C23×D311yescharacteristic
523C2×C3×C4C23×D311yescharacteristic
524#67—64no—
525#67—64no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—31no—
529C2×Dic3—31no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—121no—
536C2×Dic3—121no—
537C2×Dic3—241no—
538C2×Dic3—241no—
539C2×Dic3D3×D411yescharacteristic
540C2×Dic3D3×D411yescharacteristic
541C2×Dic3D3×D411yescharacteristic
542C2×Dic3D3×D411yescharacteristic
543D12—21no—
544D12—21no—
545D12C2×C4×D312yes—
546D12C2×C4×D312yes—
547C4×D3—32no—
548C4×D3—32no—
549C4×D3—32no—
550C4×D3—32no—
551C4×D3—62no—
552C4×D3—62no—
553C4×D3—64no—
554C4×D3—64no—
555C4×D3—81no—
556C4×D3—81no—
557C4×D3—124no—
558C4×D3—241no—
559C4×D3—241no—
560Dic6—32no—
561Dic6—32no—
562Dic6—62no—
563Dic6—64no—
564Dic6—64no—
565Dic6—61no—
566Dic6—61no—
567Dic6—124no—
568Dic6—121no—
569C3×C8—21no—
570C3×C8—21no—
571C3×C8—32no—
572C3×C8—32no—
573C3×C8—41no—
574C3⋊C8—61no—
575C3⋊C8—61no—
576C3⋊C8—121no—
577C3⋊C8C2×C4×D312yes—
578C3⋊C8C2×C4×D312yes—
579C2×C32C2×C4×D411yescharacteristic
580C2×C32#57711yescharacteristic
581C2×C32#57711yescharacteristic
582C3⋊D3—22no—
583C3×D3—42no—
584C3×D3—42no—
585C24—181no—
586C2×Q8—94no—
587C2×Q8—91no—
588C2×Q8—181no—
589C2×Q8—182no—
590C2×Q8C2×D3211yescharacteristic
591C2×D4—31no—
592C2×D4—31no—
593C2×D4—94no—
594C2×D4—182no—
595C2×D4—181no—
596C22×C4—61no—
597C22×C4—61no—
598C22×C4—91no—
599C22×C4—181no—
600C22×C4—181no—
601C22×C4—181no—
602SD16—34no—
603SD16—34no—
604SD16—94no—
605SD16—94no—
606M16—182no—
607C2×C8—31no—
608C2×C8—31no—
609C2×C8—94no—
610C2×C8—91no—
611C2×C8C2×D3211yescharacteristic
612C4⋊C4—31no—
613C4⋊C4—31no—
614C4⋊C4—61no—
615C4⋊C4—61no—
616C4⋊C4—91no—
617C4⋊C4—91no—
618C4⋊C4—91no—
619C4⋊C4—181no—
620C4⋊C4—181no—
621C4⋊C4C2×D3211yescharacteristic
622C22⋊C4—61no—
623C22⋊C4—61no—
624C22⋊C4—91no—
625C22⋊C4—91no—
626C22⋊C4—181no—
627C22⋊C4—181no—
628C22⋊C4—181no—
629C22⋊C4—181no—
630C42—31no—
631C42—31no—
632C42—61no—
633C42—61no—
634C42—181no—
635C42—181no—
636C42—181no—
637C42—181no—
638C22×C3—21no—
639C22×C3—62no—
640C22×C3—62no—
641C22×C3—121no—
642C22×C3—121no—
643C22×C3—121no—
644C22×C3—121no—
645C22×C3C2×D3×D411yescharacteristic
646C22×C3C2×D3×D411yescharacteristic
647C2×D3—22no—
648C2×D3—22no—
649C2×D3—32no—
650C2×D3—32no—
651C2×D3—41no—
652C2×D3—41no—
653C2×D3—41no—
654C2×D3—41no—
655C2×D3—62no—
656C2×D3—61no—
657C2×D3—61no—
658C2×D3—61no—
659C2×D3—61no—
660C2×D3—121no—
661C2×D3—121no—
662C2×D3—244no—
663C2×D3—244no—
664C3×C4—22no—
665C3×C4—22no—
666C3×C4—21no—
667C3×C4—21no—
668C3×C4—42no—
669C3×C4—41no—
670C3×C4—41no—
671C3×C4—61no—
672C3×C4—61no—
673C3×C4—61no—
674C3×C4—61no—
675C3×C4—81no—
676C3×C4—121no—
677C3×C4—121no—
678C3×C4C22×C4×D311yescharacteristic
679C3×C4C22×C4×D311yescharacteristic
680C3×C4D3×#4111yescharacteristic
681C3×C4D3×#4111yescharacteristic
682Dic3—21no—
683Dic3—21no—
684Dic3—21no—
685Dic3—21no—
686Dic3—32no—
687Dic3—32no—
688Dic3—41no—
689Dic3—41no—
690Dic3—62no—
691Dic3—62no—
692Dic3—62no—
693Dic3—122no—
694Dic3—121no—
695Dic3—121no—
696Dic3—241no—
697C32#294911yescharacteristic, complemented, Sylow
698C23—61no—
699C23—61no—
700C23—91no—
701C23—184no—
702C23—721no—
703C23—721no—
704Q8—21no—
705Q8—92no—
706Q8—184no—
707Q8—181no—
708Q8C4×D3212yes—
709D4—32no—
710D4—32no—
711D4—61no—
712D4—61no—
713D4—184no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—31no—
717C2×C4—31no—
718C2×C4—31no—
719C2×C4—31no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—91no—
723C2×C4—92no—
724C2×C4—92no—
725C2×C4—184no—
726C2×C4—181no—
727C2×C4—181no—
728C2×C4—241no—
729C2×C4—241no—
730C2×C4—721no—
731C2×C4—721no—
732C2×C4C22×D3211yescharacteristic
733C8—21no—
734C8—32no—
735C8—32no—
736C8—181no—
737C2×C3—21no—
738C2×C3—21no—
739C2×C3—21no—
740C2×C3—122no—
741C2×C3—122no—
742C2×C3C4×D3×D411yescharacteristic
743C2×C3C4×D3×D411yescharacteristic
744C2×C3#576211yescharacteristic
745C2×C3#577011yescharacteristic
746C2×C3#577511yescharacteristic
747C2×C3#577811yescharacteristic
748D3—42no—
749D3—42no—
750D3—62no—
751D3—62no—
752D3—122no—
753C22—62no—
754C22—62no—
755C22—92no—
756C22—121no—
757C22—121no—
758C22—121no—
759C22—121no—
760C22—181no—
761C22—181no—
762C22—724no—
763C22D32×D411yescharacteristic
764C4—22no—
765C4—41no—
766C4—61no—
767C4—61no—
768C4—61no—
769C4—61no—
770C4—92no—
771C4—121no—
772C4—121no—
773C4—182no—
774C4—361no—
775C4C2×C4×D3211yescharacteristic
776C4#6431211yescharacteristic
777C3—21no—
778C3#7964911yescharacteristic, complemented
779C3#7977711yescharacteristic, complemented
780C2—122no—
781C2—122no—
782C2—182no—
783C2#1059425511yescharacteristic
784C2#1059474911yescharacteristic
785C2#1059477011yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC2×#3802C22
cosocleC2×C32×C4C24
hypercenter#103D32
hypocenterC32#2949
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. #10595339C2semidirect
4. #10592501C2semidirect
5. C3×#4817C2semidirect
6. C3×#4788C2semidirect
7. #10591566C2semidirect
8. Dic3×#215C2semidirect
10. #10590910C2semidirect
11. #10590747C2semidirect
12. #10590744C2semidirect
13. #10590590C2semidirect
14. #10590574C2semidirect
15. #10590479C2semidirect
22. C3×Q8×Dic3C22semidirect
23. C3×Q8×Dic3C22semidirect
28. #63940C4semidirect
41. #63844C22semidirect
42. #63844C22semidirect
46. C32×#103C22semidirect
47. #63662C22semidirect
48. #63643C22semidirect
49. #63637C22semidirect
52. C3×#815C22semidirect
53. C3×C8×Dic3C22semidirect
54. C3×#808C22semidirect
55. C3×#807C22semidirect
56. #63575C22semidirect
57. #63573C22semidirect
60. #63554C22semidirect
61. Dic3×C3⋊C8C22semidirect
80. #4817D3semidirect
84. #4788D3semidirect
96. Q8×C3⋊D3C2×C4semidirect
117. C3×#215C2×C4semidirect
118. C3×#215C2×C4semidirect
143. #3716C2×C4semidirect
144. #3716C2×C4semidirect
145. #3710C2×C4semidirect
158. Q8×Dic3C2×D3semidirect
159. Q8×Dic3C2×D3semidirect
209. C3×#103C2×D3semidirect
210. C3×#103C2×D3semidirect
228. #815C2×D3semidirect
230. C8×Dic3C2×D3semidirect
237. #808C2×D3semidirect
239. #807C2×D3semidirect
359. #215C4×D3semidirect
360. #215C4×D3semidirect
475. #103D32semidirect
697. C32#2949semidirect
778. C3#79649semidirect
779. C3#79777semidirect

Maximal subgroups

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

subgroupindex
#105953392
C2×#639402
#105946062
#105925012
C3×#48172
C3×#47882
#105915662
Dic3×#2152
#105909412
#105909102
#105907472
#105907442
#105905902
#105905742
#105904792
#797773
#796493