Finite Group Databasebeta

← #11860779

Subgroups — #11860779

Order 1152.

1045 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×D3×#204C211yesmaximal, characteristic
2#10594604C211yesmaximal, characteristic
3#10594357C211yesmaximal, characteristic, complemented
4#10592551C211yesmaximal, characteristic, complemented
5C3×#4860C211yesmaximal, characteristic, complemented
6C3×#4852C211yesmaximal, characteristic, complemented
7#10590775C211yesmaximal, characteristic, complemented
8#10590758C211yesmaximal, characteristic, complemented
9#10590692C211yesmaximal, characteristic, complemented
10#10590600C211yesmaximal, characteristic, complemented
11#10590592C211yesmaximal, characteristic
12#10590590C211yesmaximal, characteristic, complemented
13#10590484C211yesmaximal, characteristic, complemented
14#10590461C211yesmaximal, characteristic, complemented
15#10590457C211yesmaximal, characteristic, complemented
16#79649—31nomaximal
17#79168—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×D3×Dic6C2211yescharacteristic
20C2×#3744C2211yescharacteristic
21#64102C2211yescharacteristic
22#64096C2211yescharacteristic, complemented
23C2×C3×#204C2211yescharacteristic
24C2×C3×D3×C8C2211yescharacteristic
25C3×#893C2211yescharacteristic
26C3×#892C2211yescharacteristic
27C3×#892C2211yescharacteristic
28C3×#887C2211yescharacteristic, complemented
29#63921—21no—
30D3×(C2×D3)⋊C4—21no—
31C4×#627—21no—
32C4×#626—21no—
33#63898C2211yescharacteristic
34#63894C2211yescharacteristic
35#63880—21no—
36#63878—21no—
37#63877—21no—
38#63855C2211yescharacteristic
39#63844C2211yescharacteristic, complemented
40#63843C2211yescharacteristic, complemented
41#63837—21no—
42C2×#3717C2211yescharacteristic
43C2×#3716C2211yescharacteristic
44C2×#3711C2211yescharacteristic
45D3×#204C418yescomplemented
46C32×#106C2211yescharacteristic, complemented
47C8×C3⋊Dic3C2211yescharacteristic, complemented
48#63637C2211yescharacteristic, complemented
49#63636C2211yescharacteristic
50C3×#817C2211yescharacteristic, complemented
51C3×C8×Dic3C2211yescharacteristic, complemented
52C3×#810C2211yescharacteristic, complemented
53C3×#809C2211yescharacteristic
54C3×#807C2211yescharacteristic, complemented
55C3×#807C2211yescharacteristic, complemented
56#63567C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63564C2211yescharacteristic
59#63562C2211yescharacteristic
60#63555C2211yescharacteristic, complemented
61#63554C2211yescharacteristic, complemented
62C2×D3×SD16—31no—
63C22×#204—31no—
64#5572—31no—
65#5545—31no—
66#5521—31no—
67#5516—31no—
68C3×C4×SD16—31no—
69C3×#427—31no—
70Dic3×SD16—31no—
71#5101—31no—
72#5026—31no—
73#5018—31no—
74#5004—31no—
75#5001—31no—
76#4889—31no—
77#4889—31no—
78#4889—31no—
79#4889—31no—
80#4860D311yescharacteristic, complemented
81#4852—31no—
82#4852—31no—
83#4852—31no—
84#4852—31no—
85#4852—61no—
86#4852D311yescharacteristic, complemented
87#4817—31no—
88#4802—31no—
89#4770—31no—
90#4757—31no—
91C4×#204—31no—
92#4689—31no—
93C22×D32—21no—
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C2×#634C2311yescharacteristic
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3C2311yescharacteristic
100C2×C3×Dic6C2311yescharacteristic
101C2×#627—21no—
102C2×#626—21no—
103C2×#624—21no—
104C2×D3×Dic3—21no—
105C2×D3×Dic3—21no—
106D3×D12—22no—
107D3×D12C2×C414yes—
108D3×Dic6—22no—
109D3×Dic6C2×C414yescomplemented
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113#3752—21no—
114#3750—21no—
115C4×C3⋊Dic3—21no—
116C4×C3⋊Dic3C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118#3744C2×C414yescomplemented
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×C4×Dic3—21no—
126C3×C4×Dic3—21no—
127C3×C4×Dic3—21no—
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×#204C2×C414yescomplemented
132C3×D3×C8C2×C414yescomplemented
133#3724—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3D411yescharacteristic
136Dic3⋊Dic3D411yescharacteristic
137#3722—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3D411yescharacteristic
140(C2×D3)⋊Dic3D411yescharacteristic
141Dic32—21no—
142Dic32—21no—
143#3717C2×C414yescomplemented
144#3716C2×C414yescomplemented
145#3711—22no—
146#2949—91noSylow
147C2×D3×Q8—31no—
148C2×D3×D4—31no—
149C22×D12—31no—
150C22×Dic6—31no—
151C2×C3×SD16—31no—
152C22×C3×C8—31no—
153C3×C4×Q8—31no—
154C3×C4×D4—31no—
155C3×#117—31no—
156C3×#117—31no—
157Q8×Dic3—31no—
158C2×#215—31no—
159D4×Dic3—31no—
160C2×#214—31no—
161C4×#67—61no—
162C2×(C2×D3)⋊C4—61no—
163#926—31no—
164C2×#208—31no—
165D3×SD16—38no—
166C2×#204—31no—
167C2×#204—31no—
168C2×#204—31no—
169C2×#204—31no—
170C2×#204—38no—
171C2×#204—61no—
172C2×#204C2×D311yescharacteristic
173C2×ΓL(1,𝔽25)—31no—
174C2×D3×C8C2×D311yescharacteristic
175#893—31no—
176#893—31no—
177#893—31no—
178#893—31no—
179#893—61no—
180#893C2×D311yescharacteristic
181#892—61no—
182#892C2×D311yescharacteristic
183#892C2×D311yescharacteristic
184#887—31no—
185#887—31no—
186#887—31no—
187#887—31no—
188#887—61no—
189#887—61no—
190#887C2×D311yescharacteristic, complemented
191#67⋊C4—61no—
192D3×C22⋊C4—61no—
193D3×C22⋊C4—61no—
194D3×C22⋊C4—61no—
195#877—61no—
196#877—61no—
197C4×D12—31no—
198C4×D12—61no—
199C4×D12—61no—
200#872—31no—
201#872—61no—
202C4×Dic6—31no—
203C4×Dic6—61no—
204C4×Dic6—61no—
205C4×Dic6—61no—
206C3×#107—31no—
207C3×#107—31no—
208C3×#106—21no—
209C3×#106—31no—
210C3×#106C2×D311yescharacteristic, complemented
211C3×#106C2×D311yescharacteristic, complemented
212C3×#103—31no—
213C3×#102—31no—
214C3×C4×C8—31no—
215#835—31no—
216#832—31no—
217#821—31no—
218#817C2×D311yescharacteristic, complemented
219#816—31no—
220#815—31no—
221#815—31no—
222#815—31no—
223C8×Dic3—31no—
224C8×Dic3—31no—
225C8×Dic3—61no—
226C8×Dic3C2×D311yescharacteristic, complemented
227#810—31no—
228#810—31no—
229#810—31no—
230#810—31no—
231#810—61no—
232#810C2×D311yescharacteristic, complemented
233#809—31no—
234#809—31no—
235#809—31no—
236#809—31no—
237#809—61no—
238#809C2×D311yescharacteristic
239#807C2×D311yescharacteristic, complemented
240#807C2×D311yescharacteristic, complemented
241#803—31no—
242C22×C3⋊D3—21no—
243C22×C3×D3—21no—
244C22×C3×D3C2×D411yescharacteristic
245C2×D32—24no—
246C2×D32—81no—
247C2×D32—81no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4C2411yescharacteristic
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3C2×D411yescharacteristic
253C2×C3⋊Dic3C2×D411yescharacteristic
254C4⋊(C3⋊D3)—21no—
255C4⋊(C3⋊D3)C22×C412yes—
256C4×C3⋊D3—81no—
257#634—21no—
258#634C22×C412yes—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×D12—21no—
266C3×D12C22×C412yes—
267C3×C4×D3—81no—
268C3×C4×D3C22×C412yes—
269C3×C4×D3#4112yes—
270C3×Dic6—21no—
271C3×Dic6C22×C412yes—
272#627—24no—
273#626—24no—
274#624—81no—
275D3×Dic3—24no—
276D3×Dic3—81no—
277C32×C8C22×C412yes—
278C3⋊(C3⋊C8)—21no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8C22×C412yes—
281C22×SD16—91no—
282#519—91no—
283#518—91no—
284#440—91no—
285#440—91no—
286#440—91no—
287#440—91no—
288C4×SD16—31no—
289C4×SD16—91no—
290C4×SD16—91no—
291C4×SD16—91no—
292#427—31no—
293#419—91no—
294#418—91no—
295#405—91no—
296C23×D3—61no—
297C23×D3—61no—
298C2×C3×Q8—31no—
299C2×C3×D4—31no—
300C22×C3×C4—31no—
301C22×C3×C4—61no—
302C2×#67—61no—
303C22×Dic3—61no—
304C22×Dic3—61no—
305D3×Q8—34no—
306D3×Q8—62no—
307D3×D4—34no—
308D3×D4—62no—
309C2×D12—31no—
310C2×D12—31no—
311C2×D12—34no—
312C2×D12—61no—
313C2×D12—62no—
314C2×D12—61no—
315C2×D12C22×D311yescharacteristic
316C2×C4×D3—21no—
317C2×C4×D3—61no—
318C2×C4×D3—61no—
319C2×C4×D3—61no—
320C2×C4×D3—61no—
321C2×C4×D3—61no—
322C2×C4×D3—61no—
323C2×C4×D3—121no—
324C2×C4×D3C22×D311yescharacteristic
325C2×Dic6—31no—
326C2×Dic6—31no—
327C2×Dic6—34no—
328C2×Dic6—61no—
329C2×Dic6—62no—
330C2×Dic6—61no—
331C2×Dic6—61no—
332C2×Dic6C22×D311yescharacteristic
333C3×SD16—34no—
334C2×C3×C8—21no—
335C2×C3×C8—31no—
336C2×C3×C8—34no—
337C2×C3×C8—31no—
338C2×C3×C8C22×D311yescharacteristic
339C2×C3×C8C22×D311yescharacteristic
340C3×C4⋊C4—21no—
341C3×C4⋊C4—21no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4C22×D311yescharacteristic
346C3×C4⋊C4C22×D311yescharacteristic
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C4⋊C4C22×D311yescharacteristic
349C3×C22⋊C4—61no—
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C42—31no—
353C3×C42—61no—
354C3×C42—61no—
355C3×C42—61no—
356#217—31no—
357#217—31no—
358#217—61no—
359#215—34no—
360#214—34no—
361(C2×D3)⋊C4—21no—
362(C2×D3)⋊C4—21no—
363(C2×D3)⋊C4—21no—
364(C2×D3)⋊C4—31no—
365(C2×D3)⋊C4—31no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—121no—
372C4⋊Dic3—31no—
373C4⋊Dic3—31no—
374C4⋊Dic3—61no—
375C4⋊Dic3C22×D311yescharacteristic
376C4⋊Dic3C22×D311yescharacteristic
377Dic3⋊C4—21no—
378Dic3⋊C4—31no—
379Dic3⋊C4—31no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—121no—
386C4×Dic3—21no—
387C4×Dic3—21no—
388C4×Dic3—21no—
389C4×Dic3—31no—
390C4×Dic3—31no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—121no—
399C4×Dic3C22×D311yescharacteristic
400#208—62no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—61no—
404C2×C3⋊C8C22×D311yescharacteristic
405C2×C3⋊C8C22×D311yescharacteristic
406#204—34no—
407#204—34no—
408#204—34no—
409#204—34no—
410#204—64no—
411#204C4×D314yescomplemented
412ΓL(1,𝔽25)—62no—
413D3×C8C4×D314yescomplemented
414C22×C32C22×D411yescharacteristic
415C2×C3⋊D3—22no—
416C2×C3⋊D3—41no—
417C2×C3⋊D3—41no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—22no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3C4×D412yes—
424D32—84no—
425C32×C4—41no—
426C32×C4—41no—
427C32×C4C23×C411yescharacteristic
428C32×C4C2×#4111yescharacteristic
429C3⋊Dic3—21no—
430C3⋊Dic3—22no—
431C3⋊Dic3—21no—
432C3×Dic3—22no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3C4×D412yes—
438C22×Q8—91no—
439C22×D4—91no—
440C2×SD16—31no—
441C2×SD16—98no—
442C2×SD16—91no—
443C2×SD16—91no—
444C2×SD16—91no—
445C2×M16—91no—
446C22×C8—31no—
447C4×Q8—31no—
448C4×Q8—91no—
449C4×Q8—91no—
450C4×Q8—91no—
451C4×Q8—181no—
452C4×Q8—181no—
453C4×D4—31no—
454C4×D4—91no—
455C4×D4—91no—
456C4×D4—91no—
457C4×D4—181no—
458C4×D4—181no—
459#117—31no—
460#117—31no—
461#117—91no—
462#117—181no—
463#117—181no—
464C2×C22⋊C4—181no—
465C2×C22⋊C4—181no—
466#107—31no—
467#107—31no—
468#106—31no—
469#106D3211yescharacteristic, complemented
470#103—31no—
471#103—91no—
472#103—91no—
473#103—91no—
474#102—31no—
475#102—91no—
476#102—91no—
477#102—91no—
478#97—91no—
479#97—91no—
480C4×C8—31no—
481C4×C8—91no—
482C23×C3—31no—
483C23×C3—61no—
484C22×D3—21no—
485C22×D3—64no—
486C22×D3—61no—
487C22×D3—61no—
488C22×D3—64no—
489C22×D3—121no—
490C22×D3—241no—
491C22×D3—241no—
492C22×D3—241no—
493C22×D3—241no—
494C22×D3D3×D411yescharacteristic
495C3×Q8—32no—
496C3×Q8—61no—
497C3×D4—32no—
498C3×D4—61no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—31no—
505C2×C3×C4—32no—
506C2×C3×C4—32no—
507C2×C3×C4—31no—
508C2×C3×C4—31no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—241no—
515C2×C3×C4C23×D311yescharacteristic
516C2×C3×C4C23×D311yescharacteristic
517#67—64no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—31no—
522C2×Dic3—31no—
523C2×Dic3—31no—
524C2×Dic3—31no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—64no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—121no—
531C2×Dic3—241no—
532C2×Dic3D3×D411yescharacteristic
533C2×Dic3D3×D411yescharacteristic
534C2×Dic3D3×D411yescharacteristic
535D12—21no—
536D12—32no—
537D12—32no—
538D12—62no—
539D12—64no—
540D12—61no—
541D12—61no—
542D12—121no—
543D12C2×C4×D312yes—
544C4×D3—64no—
545C4×D3—81no—
546C4×D3—241no—
547C4×D3—241no—
548C4×D3—241no—
549C4×D3—241no—
550C4×D3—242no—
551C4×D3—241no—
552C4×D3C2×C4×D312yes—
553C4×D3#23912yes—
554Dic6—21no—
555Dic6—32no—
556Dic6—32no—
557Dic6—62no—
558Dic6—64no—
559Dic6—61no—
560Dic6—61no—
561Dic6—64no—
562Dic6—121no—
563Dic6C2×C4×D312yes—
564C3×C8—22no—
565C3×C8—32no—
566C3×C8—61no—
567C3×C8C2×C4×D312yes—
568C3×C8C2×C4×D312yes—
569C3⋊C8—21no—
570C3⋊C8—61no—
571C3⋊C8—61no—
572C3⋊C8—121no—
573C3⋊C8C2×C4×D312yes—
574C2×C32C2×C4×D411yescharacteristic
575C2×C32#57711yescharacteristic
576C2×C32#57711yescharacteristic
577C3⋊D3—42no—
578C3×D3—22no—
579C3×D3—42no—
580C24—181no—
581C2×Q8—31no—
582C2×Q8—94no—
583C2×Q8—91no—
584C2×Q8—181no—
585C2×Q8—182no—
586C2×D4—31no—
587C2×D4—94no—
588C2×D4—91no—
589C2×D4—182no—
590C2×D4—181no—
591C22×C4—31no—
592C22×C4—61no—
593C22×C4—181no—
594C22×C4—181no—
595C22×C4—181no—
596C22×C4—181no—
597SD16—34no—
598SD16—94no—
599SD16—94no—
600SD16—94no—
601M16—182no—
602C2×C8—31no—
603C2×C8—34no—
604C2×C8—31no—
605C2×C8—91no—
606C2×C8C2×D3211yescharacteristic
607C4⋊C4—31no—
608C4⋊C4—31no—
609C4⋊C4—61no—
610C4⋊C4—91no—
611C4⋊C4—91no—
612C4⋊C4—181no—
613C4⋊C4—181no—
614C4⋊C4—181no—
615C4⋊C4C2×D3211yescharacteristic
616C4⋊C4C2×D3211yescharacteristic
617C22⋊C4—61no—
618C22⋊C4—61no—
619C22⋊C4—61no—
620C22⋊C4—91no—
621C22⋊C4—91no—
622C22⋊C4—181no—
623C22⋊C4—181no—
624C22⋊C4—181no—
625C42—31no—
626C42—61no—
627C42—61no—
628C42—61no—
629C42—91no—
630C42—181no—
631C42—181no—
632C42—181no—
633C22×C3—21no—
634C22×C3—32no—
635C22×C3—61no—
636C22×C3—61no—
637C22×C3—62no—
638C22×C3—121no—
639C22×C3—121no—
640C22×C3C2×D3×D411yescharacteristic
641C22×C3C2×D3×D411yescharacteristic
642C2×D3—21no—
643C2×D3—21no—
644C2×D3—22no—
645C2×D3—41no—
646C2×D3—41no—
647C2×D3—62no—
648C2×D3—62no—
649C2×D3—122no—
650C2×D3—121no—
651C2×D3—121no—
652C2×D3—121no—
653C2×D3—121no—
654C2×D3—241no—
655C2×D3—241no—
656C2×D3—244no—
657C2×D3—244no—
658C2×D3#89312yes—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—32no—
662C3×C4—41no—
663C3×C4—41no—
664C3×C4—41no—
665C3×C4—41no—
666C3×C4—62no—
667C3×C4—61no—
668C3×C4—61no—
669C3×C4—81no—
670C3×C4—81no—
671C3×C4—121no—
672C3×C4—121no—
673C3×C4C22×C4×D311yescharacteristic
674C3×C4C22×C4×D311yescharacteristic
675C3×C4C2×#23911yescharacteristic
676C3×C4D3×#4111yescharacteristic
677Dic3—21no—
678Dic3—21no—
679Dic3—22no—
680Dic3—41no—
681Dic3—41no—
682Dic3—62no—
683Dic3—62no—
684Dic3—61no—
685Dic3—61no—
686Dic3—61no—
687Dic3—61no—
688Dic3—62no—
689Dic3—122no—
690Dic3—121no—
691Dic3#89312yes—
692C32#294911yescharacteristic, complemented, Sylow
693C23—31no—
694C23—61no—
695C23—184no—
696C23—181no—
697C23—721no—
698C23—721no—
699Q8—32no—
700Q8—61no—
701Q8—92no—
702Q8—184no—
703Q8—181no—
704D4—32no—
705D4—61no—
706D4—92no—
707D4—184no—
708D4—181no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—31no—
712C2×C4—32no—
713C2×C4—32no—
714C2×C4—31no—
715C2×C4—31no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—91no—
720C2×C4—91no—
721C2×C4—184no—
722C2×C4—181no—
723C2×C4—241no—
724C2×C4—721no—
725C2×C4—721no—
726C2×C4—721no—
727C2×C4C22×D3211yescharacteristic
728C8—32no—
729C8—61no—
730C8—181no—
731C8C4×D3212yes—
732C2×C3—21no—
733C2×C3—21no—
734C2×C3—21no—
735C2×C3—62no—
736C2×C3—122no—
737C2×C3C2×#89311yescharacteristic
738C2×C3C4×D3×D411yescharacteristic
739C2×C3#576211yescharacteristic
740C2×C3#577011yescharacteristic
741C2×C3#577011yescharacteristic
742C2×C3#577011yescharacteristic
743D3—22no—
744D3—42no—
745D3—122no—
746D3—122no—
747D3—242no—
748C22—32no—
749C22—61no—
750C22—61no—
751C22—62no—
752C22—121no—
753C22—121no—
754C22—182no—
755C22—361no—
756C22—361no—
757C22—724no—
758C22D32×D411yescharacteristic
759C4—32no—
760C4—41no—
761C4—41no—
762C4—62no—
763C4—61no—
764C4—61no—
765C4—121no—
766C4—121no—
767C4—182no—
768C4—181no—
769C4—181no—
770C4C2×C4×D3211yescharacteristic
771C4D3×#23911yescharacteristic
772C3—21no—
773C3#7916811yescharacteristic, complemented
774C3#7964911yescharacteristic, complemented
775C2—62no—
776C2—122no—
777C2—362no—
778C2D3×#89311yescharacteristic
779C2#1059475311yescharacteristic
780C2#1059475711yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radicalC2×D3×D12C22
cosocleC2×C32×C4C24
hypercenter#106D32
hypocenterC32#2949
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
3. #10594357C2semidirect
4. #10592551C2semidirect
5. C3×#4860C2semidirect
6. C3×#4852C2semidirect
7. #10590775C2semidirect
8. #10590758C2semidirect
9. #10590692C2semidirect
10. #10590600C2semidirect
12. #10590590C2semidirect
13. #10590484C2semidirect
14. #10590461C2semidirect
15. #10590457C2semidirect
22. #64096C22semidirect
28. C3×#887C22semidirect
39. #63844C22semidirect
40. #63843C22semidirect
45. D3×#204C4semidirect
46. C32×#106C22semidirect
47. C8×C3⋊Dic3C22semidirect
48. #63637C22semidirect
50. C3×#817C22semidirect
51. C3×C8×Dic3C22semidirect
52. C3×#810C22semidirect
54. C3×#807C22semidirect
55. C3×#807C22semidirect
56. #63567C22semidirect
57. #63565C22semidirect
60. #63555C22semidirect
61. #63554C22semidirect
80. #4860D3semidirect
86. #4852D3semidirect
109. D3×Dic6C2×C4semidirect
118. #3744C2×C4semidirect
131. C3×#204C2×C4semidirect
132. C3×D3×C8C2×C4semidirect
143. #3717C2×C4semidirect
144. #3716C2×C4semidirect
190. #887C2×D3semidirect
210. C3×#106C2×D3semidirect
211. C3×#106C2×D3semidirect
218. #817C2×D3semidirect
226. C8×Dic3C2×D3semidirect
232. #810C2×D3semidirect
239. #807C2×D3semidirect
240. #807C2×D3semidirect
411. #204C4×D3semidirect
413. D3×C8C4×D3semidirect
469. #106D32semidirect
692. C32#2949semidirect
773. C3#79168semidirect
774. C3#79649semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2042
#105946042
#105943572
#105925512
C3×#48602
C3×#48522
#105907752
#105907582
#105906922
#105906002
#105905922
#105905902
#105904842
#105904612
#105904572
#796493
#791683