Finite Group Databasebeta

← #11860432

Subgroups — #11860432

Order 1152.

1049 conjugacy classes of subgroups.

The subgroup lattice has 771 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595190C211yesmaximal, characteristic
2C2×#63931C211yesmaximal, characteristic
3#10594363C211yesmaximal, characteristic, complemented
4#10592470C211yesmaximal, characteristic
5C3×#4758C211yesmaximal, characteristic, complemented
6C3×#4757C211yesmaximal, characteristic, complemented
7#10591440C211yesmaximal, characteristic, complemented
8Dic3×#214C211yesmaximal, characteristic, complemented
9#10590794C211yesmaximal, characteristic, complemented
10#10590793C211yesmaximal, characteristic, complemented
11#10590691C211yesmaximal, characteristic, complemented
12#10590664C211yesmaximal, characteristic, complemented
13#10590583C211yesmaximal, characteristic, complemented
14#10590481C211yesmaximal, characteristic, complemented
15#10590480C211yesmaximal, characteristic, complemented
16#79774—31nomaximal
17C4×#915—31nomaximal
18C2×#3830C2211yescharacteristic
19C2×#3797C2211yescharacteristic
20C2×#3743C2211yescharacteristic
21C4⋊C4×C3⋊D3C2211yescharacteristic
22C3×D4×Dic3C2211yescharacteristic
23C3×D4×Dic3C2211yescharacteristic
24C2×C3×#214C2211yescharacteristic
25C2×C3×#214C2211yescharacteristic
26C3×#887C2211yescharacteristic
27C3×#887C2211yescharacteristic
28#63957—21no—
29C2×Dic32—21no—
30#63952—21no—
31#63952—21no—
32#63931C418yescomplemented
33#63883—21no—
34C4×#624—21no—
35C4×#624C2211yescharacteristic
36#63849C2211yescharacteristic
37#63844C2211yescharacteristic
38#63844C2211yescharacteristic
39Dic3×Dic6C2211yescharacteristic
40Dic3×Dic6C2211yescharacteristic
41#63837—21no—
42#63837—21no—
43C2×#3719C2211yescharacteristic
44C2×#3719C2211yescharacteristic
45C2×#3712C2211yescharacteristic
46C32×#102C2211yescharacteristic
47#63659C2211yescharacteristic
48#63643C2211yescharacteristic
49#63637C2211yescharacteristic
50C3×#816C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×#815C2211yescharacteristic
53C3×C8×Dic3C2211yescharacteristic
54C3×#808C2211yescharacteristic
55C3×#807C2211yescharacteristic
56#63575C2211yescharacteristic
57#63573C2211yescharacteristic
58#63565C2211yescharacteristic
59#63565C2211yescharacteristic
60#63554C2211yescharacteristic
61Dic3×C3⋊C8C2211yescharacteristic
62C2×#915—31no—
63C2×#915—31no—
64C4×D3×Q8—31no—
65C4×D3×Q8—31no—
66C4×#237—31no—
67C4×#237—31no—
68C3×#440—31no—
69C3×C4×SD16—31no—
70#5164—31no—
71Dic3×SD16—31no—
72#5030—31no—
73C4×#216—31no—
74#5018—31no—
75C4×#214—31no—
76#4881—31no—
77#4873—31no—
78#4861—31no—
79#4853—31no—
80#4802—31no—
81#4802—31no—
82#4790—31no—
83#4789—31no—
84#4771—31no—
85#4771—31no—
86#4771—61no—
87#4758D311yescharacteristic, complemented
88#4757D311yescharacteristic, complemented
89#4716—31no—
90#4707—31no—
91C4×Dic12—31no—
92C4×ΓL(1,𝔽25)—31no—
93C2×C32×D4C2311yescharacteristic
94C2×#638—21no—
95C22×C3⋊Dic3—21no—
96#3830—22no—
97#3830C2×C414yes—
98C2×C4×C3⋊D3—21no—
99C2×C4×C3⋊D3C2311yescharacteristic
100C2×#634C2311yescharacteristic
101C22×C3×Dic3—21no—
102C22×C3×Dic3—21no—
103C2×C3×Dic6C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×#627—21no—
106C2×#624—21no—
107C2×#624D411yescharacteristic
108C2×#624D411yescharacteristic
109#3797—22no—
110#3797C2×C414yescomplemented
111C2×C32×C8C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114#3750—21no—
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116#3743—22no—
117C3×#217—21no—
118C3×#217—21no—
119C3×#214C2×C414yescomplemented
120C3×#214C2×C414yescomplemented
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×Dic3⋊C4—21no—
124C3×Dic3⋊C4—21no—
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—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135#3722—21no—
136Dic32—21no—
137Dic32—21no—
138Dic32—21no—
139Dic32—21no—
140Dic32—21no—
141Dic32D411yescharacteristic
142Dic32D411yescharacteristic
143#3719C2×C414yescomplemented
144#3719C2×C414yescomplemented
145#3712C2×C414yescomplemented
146C4×#137—91noSylow
147C2×D3×Q8—31no—
148C2×D3×Q8—31no—
149C2×#237—31no—
150C2×#237—31no—
151C2×#237—61no—
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×Dic3—31no—
159Q8×Dic3—31no—
160C2×#216—31no—
161C2×#216—31no—
162D4×Dic3C2×D311yescharacteristic
163D4×Dic3C2×D311yescharacteristic
164C2×#214C2×D311yescharacteristic
165C2×#214C2×D311yescharacteristic
166C4×#67—61no—
167C4×#67—61no—
168C2×C4×Dic3—61no—
169C2×C4×Dic3—61no—
170#915—38no—
171#915—38no—
172C2×Dic12—31no—
173C2×Dic12—31no—
174C2×ΓL(1,𝔽25)—31no—
175C2×ΓL(1,𝔽25)—31no—
176C2×ΓL(1,𝔽25)—31no—
177C2×ΓL(1,𝔽25)—31no—
178C2×ΓL(1,𝔽25)—61no—
179#892—31no—
180#892—31no—
181D3×C4⋊C4—31no—
182D3×C4⋊C4—31no—
183D3×C4⋊C4—61no—
184D3×C4⋊C4—61no—
185D3×C4⋊C4—61no—
186#887—31no—
187#887—31no—
188#887—61no—
189#887—61no—
190#887C2×D311yescharacteristic
191#887C2×D311yescharacteristic
192#67⋊C4—61no—
193#67⋊C4—61no—
194#877—61no—
195#877—61no—
196C42×D3—31no—
197C42×D3—31no—
198C42×D3—61no—
199C42×D3—61no—
200C4×Dic6—31no—
201C4×Dic6—31no—
202C4×Dic6—31no—
203C4×Dic6—31no—
204C4×Dic6—61no—
205C4×Dic6—61no—
206C3×#107—31no—
207C3×#106—31no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#102—21no—
211C3×#102C2×D311yescharacteristic
212C3×#102C2×D311yescharacteristic
213C3×#97—31no—
214C3×C4×C8—31no—
215#835—31no—
216#835—31no—
217#832—31no—
218#832—31no—
219#832—61no—
220#818—31no—
221#817—31no—
222#816—31no—
223#816—31no—
224#816—61no—
225#816C2×D311yescharacteristic
226#816C2×D311yescharacteristic
227#815—31no—
228#815C2×D311yescharacteristic
229C8×Dic3—31no—
230C8×Dic3C2×D311yescharacteristic
231#810—31no—
232#810—31no—
233#810—31no—
234#810—31no—
235#810—61no—
236#808—31no—
237#808C2×D311yescharacteristic
238#807—31no—
239#807C2×D311yescharacteristic
240#803—31no—
241C4×C3⋊C8—31no—
242C23×C32—21no—
243C22×C3⋊D3C2×D411yescharacteristic
244C32×D4—21no—
245C32×D4C22×C412yes—
246C2×C32×C4—21no—
247C2×C32×C4C2411yescharacteristic
248#638—24no—
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—24no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3C2×D411yescharacteristic
253C4×C3⋊D3—42no—
254C4×C3⋊D3C22×C412yes—
255C4×C3⋊D3#4112yes—
256#634—21no—
257#634C22×C412yes—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—42no—
263C2×C3×Dic3—42no—
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6C22×C412yes—
271C3×Dic6C22×C412yes—
272#627—24no—
273#624—24no—
274#624—22no—
275#624—41no—
276C32×C8—21no—
277C3⋊(C3⋊C8)—21no—
278C3×C3⋊C8C22×C412yes—
279C3×C3⋊C8C22×C412yes—
280C2×#137—91no—
281C4×#41—91no—
282C2×C4×Q8—91no—
283#441—91no—
284#441—91no—
285#440—31no—
286#440—91no—
287C4×Q16—91no—
288C4×Q16—91no—
289C4×SD16—31no—
290C4×SD16—91no—
291#428—91no—
292#419—91no—
293#417—91no—
294C4×M16—91no—
295C2×C3×Q8—31no—
296C2×C3×Q8—31no—
297C2×C3×D4—21no—
298C2×C3×D4C22×D311yescharacteristic
299C2×C3×D4C22×D311yescharacteristic
300C22×C3×C4—61no—
301C22×C3×C4—61no—
302C2×#67—61no—
303C2×#67—61no—
304C2×#67—121no—
305C22×Dic3—21no—
306C22×Dic3—21no—
307C22×Dic3—61no—
308C22×Dic3—61no—
309C22×Dic3—121no—
310D3×Q8—34no—
311D3×Q8—34no—
312D3×Q8—62no—
313D3×Q8—62no—
314#237—34no—
315#237—34no—
316#237—64no—
317#237—62no—
318#237—62no—
319#237—122no—
320C2×C4×D3—31no—
321C2×C4×D3—31no—
322C2×C4×D3—31no—
323C2×C4×D3—31no—
324C2×C4×D3—31no—
325C2×C4×D3—31no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—121no—
332C2×Dic6—31no—
333C2×Dic6—31no—
334C2×Dic6—61no—
335C2×Dic6—61no—
336C2×Dic6—61no—
337C2×Dic6C22×D311yescharacteristic
338C2×Dic6C22×D311yescharacteristic
339C3×SD16—34no—
340C3×SD16—34no—
341C2×C3×C8—21no—
342C2×C3×C8—31no—
343C2×C3×C8—31no—
344C2×C3×C8C22×D311yescharacteristic
345C2×C3×C8C22×D311yescharacteristic
346C3×C4⋊C4—21no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—61no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4C22×D311yescharacteristic
352C3×C4⋊C4C22×D311yescharacteristic
353C3×C22⋊C4—61no—
354C3×C22⋊C4—61no—
355C3×C42—31no—
356C3×C42—31no—
357C3×C42—61no—
358C3×C42—61no—
359#217—21no—
360#217—21no—
361#216—34no—
362#216—34no—
363#214C4×D314yescomplemented
364#214C4×D314yescomplemented
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—61no—
367C4⋊Dic3—31no—
368C4⋊Dic3—31no—
369C4⋊Dic3—61no—
370C4⋊Dic3—61no—
371C4⋊Dic3—61no—
372C4⋊Dic3C22×D311yescharacteristic
373C4⋊Dic3C22×D311yescharacteristic
374Dic3⋊C4—21no—
375Dic3⋊C4—21no—
376Dic3⋊C4—61no—
377Dic3⋊C4—61no—
378Dic3⋊C4—61no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—121no—
385C4×Dic3—21no—
386C4×Dic3—21no—
387C4×Dic3—31no—
388C4×Dic3—31no—
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—61no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3C22×D311yescharacteristic
402C4×Dic3C22×D311yescharacteristic
403C2×C3⋊C8—31no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—61no—
406C2×C3⋊C8C22×D311yescharacteristic
407C2×C3⋊C8C22×D311yescharacteristic
408Dic12—34no—
409Dic12—34no—
410ΓL(1,𝔽25)—34no—
411ΓL(1,𝔽25)—34no—
412ΓL(1,𝔽25)—62no—
413ΓL(1,𝔽25)—62no—
414ΓL(1,𝔽25)—122no—
415C22×C32—22no—
416C22×C32—41no—
417C22×C32—41no—
418C22×C32C22×D411yescharacteristic
419C2×C3⋊D3—21no—
420C2×C3⋊D3—21no—
421C2×C3⋊D3C4×D412yes—
422C32×C4—41no—
423C32×C4C23×C411yescharacteristic
424C32×C4C2×#4111yescharacteristic
425C3⋊Dic3—22no—
426C3⋊Dic3—41no—
427C3⋊Dic3C4×D412yes—
428C3×Dic3—22no—
429C3×Dic3—22no—
430C3×Dic3—21no—
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C3×Dic3#13712yescomplemented
436C2×#41—91no—
437C22×Q8—91no—
438#137—98no—
439C2×Q16—91no—
440C2×Q16—91no—
441C2×SD16—31no—
442C2×SD16—31no—
443C2×M16—91no—
444C2×M16—91no—
445C4×Q8—31no—
446C4×Q8—31no—
447C4×Q8—91no—
448C4×Q8—91no—
449C4×Q8—91no—
450C4×Q8—91no—
451C4×Q8—181no—
452C4×Q8—181no—
453C4×D4—31no—
454C4×D4—31no—
455C4×D4—181no—
456C4×D4—181no—
457#117—91no—
458#117—181no—
459C2×C4⋊C4—91no—
460C2×C4⋊C4—181no—
461C2×C42—91no—
462C2×C42—181no—
463C2×C42—181no—
464#107—31no—
465#107—91no—
466#106—31no—
467#106—91no—
468#103—31no—
469#103—31no—
470#103—91no—
471#103—91no—
472#103—91no—
473#103—91no—
474#102—91no—
475#102D3211yescharacteristic
476#97—31no—
477#97—91no—
478C4×C8—31no—
479C4×C8—91no—
480C23×C3—21no—
481C23×C3—21no—
482C23×C3—41no—
483C22×D3—31no—
484C22×D3—31no—
485C22×D3—61no—
486C3×Q8—32no—
487C3×Q8—32no—
488C3×Q8—61no—
489C3×Q8—61no—
490C3×D4—21no—
491C3×D4—21no—
492C3×D4—22no—
493C3×D4—41no—
494C3×D4C2×C4×D312yes—
495C3×D4C2×C4×D312yes—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—31no—
500C2×C3×C4—31no—
501C2×C3×C4—31no—
502C2×C3×C4—31no—
503C2×C3×C4—41no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—122no—
509C2×C3×C4—122no—
510C2×C3×C4C23×D311yescharacteristic
511C2×C3×C4C23×D311yescharacteristic
512#67—64no—
513#67—64no—
514#67—124no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—31no—
520C2×Dic3—31no—
521C2×Dic3—42no—
522C2×Dic3—42no—
523C2×Dic3—61no—
524C2×Dic3—64no—
525C2×Dic3—64no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—124no—
531C2×Dic3—121no—
532C2×Dic3—121no—
533C2×Dic3D3×D411yescharacteristic
534C2×Dic3D3×D411yescharacteristic
535C2×Dic3D3×D411yescharacteristic
536C2×Dic3D3×D411yescharacteristic
537C4×D3—32no—
538C4×D3—32no—
539C4×D3—32no—
540C4×D3—32no—
541C4×D3—62no—
542C4×D3—62no—
543C4×D3—62no—
544C4×D3—64no—
545C4×D3—64no—
546C4×D3—62no—
547C4×D3—121no—
548C4×D3—121no—
549C4×D3—122no—
550C4×D3—122no—
551C4×D3—242no—
552Dic6—21no—
553Dic6—21no—
554Dic6—32no—
555Dic6—32no—
556Dic6—62no—
557Dic6—64no—
558Dic6—64no—
559Dic6—61no—
560Dic6—61no—
561Dic6—121no—
562Dic6C2×C4×D312yes—
563Dic6C2×C4×D312yes—
564C3×C8—21no—
565C3×C8—21no—
566C3×C8—32no—
567C3×C8—32no—
568C3×C8—41no—
569C3⋊C8—61no—
570C3⋊C8—61no—
571C3⋊C8—121no—
572C3⋊C8C2×C4×D312yes—
573C3⋊C8C2×C4×D312yes—
574C2×C32—42no—
575C2×C32C2×C4×D411yescharacteristic
576C2×C32C2×#13711yescharacteristic
577C2×C32#57511yescharacteristic
578C3⋊D3—22no—
579#41—94no—
580#41—182no—
581C2×Q8—31no—
582C2×Q8—31no—
583C2×Q8—94no—
584C2×Q8—91no—
585C2×Q8—181no—
586C2×Q8—182no—
587C2×D4—181no—
588C2×D4C2×D3211yescharacteristic
589C22×C4—61no—
590C22×C4—61no—
591C22×C4—91no—
592C22×C4—91no—
593C22×C4—91no—
594C22×C4—181no—
595C22×C4—181no—
596C22×C4—181no—
597Q16—94no—
598Q16—94no—
599SD16—34no—
600SD16—34no—
601M16—94no—
602M16—182no—
603C2×C8—31no—
604C2×C8—31no—
605C2×C8—91no—
606C2×C8C2×D3211yescharacteristic
607C4⋊C4—31no—
608C4⋊C4—31no—
609C4⋊C4—61no—
610C4⋊C4—61no—
611C4⋊C4—91no—
612C4⋊C4—181no—
613C4⋊C4—181no—
614C4⋊C4—181no—
615C4⋊C4—181no—
616C4⋊C4—181no—
617C4⋊C4C2×D3211yescharacteristic
618C22⋊C4—61no—
619C22⋊C4—61no—
620C22⋊C4—181no—
621C42—31no—
622C42—31no—
623C42—61no—
624C42—61no—
625C42—91no—
626C42—91no—
627C42—181no—
628C42—181no—
629C42—181no—
630C42—181no—
631C42—181no—
632C22×C3—22no—
633C22×C3—22no—
634C22×C3—21no—
635C22×C3—42no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—81no—
641C22×C3—81no—
642C22×C3C2×D3×D411yescharacteristic
643C22×C3C2×D3×D411yescharacteristic
644C2×D3—32no—
645C2×D3—32no—
646C2×D3—62no—
647C2×D3—61no—
648C2×D3—61no—
649C2×D3—61no—
650C2×D3—61no—
651C2×D3—121no—
652C2×D3—121no—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—32no—
656C3×C4—41no—
657C3×C4—41no—
658C3×C4—61no—
659C3×C4—61no—
660C3×C4—61no—
661C3×C4—62no—
662C3×C4—62no—
663C3×C4—81no—
664C3×C4—121no—
665C3×C4—121no—
666C3×C4C22×C4×D311yescharacteristic
667C3×C4C22×C4×D311yescharacteristic
668C3×C4D3×#4111yescharacteristic
669C3×C4D3×#4111yescharacteristic
670Dic3—21no—
671Dic3—21no—
672Dic3—21no—
673Dic3—22no—
674Dic3—22no—
675Dic3—32no—
676Dic3—32no—
677Dic3—41no—
678Dic3—41no—
679Dic3—62no—
680Dic3—62no—
681Dic3—62no—
682Dic3—122no—
683Dic3—121no—
684Dic3—121no—
685Dic3—241no—
686Dic3#91512yescomplemented
687C32C4×#13711yescharacteristic, complemented, Sylow
688C23—21no—
689C23—91no—
690Q8—32no—
691Q8—32no—
692Q8—61no—
693Q8—61no—
694Q8—92no—
695Q8—184no—
696Q8—181no—
697D4—21no—
698D4—184no—
699D4C4×D3212yes—
700C2×C4—21no—
701C2×C4—31no—
702C2×C4—31no—
703C2×C4—31no—
704C2×C4—31no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—91no—
710C2×C4—92no—
711C2×C4—92no—
712C2×C4—122no—
713C2×C4—122no—
714C2×C4—182no—
715C2×C4—184no—
716C2×C4—184no—
717C2×C4—181no—
718C2×C4—181no—
719C2×C4—362no—
720C2×C4—361no—
721C2×C4C22×D3211yescharacteristic
722C8—21no—
723C8—32no—
724C8—32no—
725C8—181no—
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—21no—
729C2×C3—42no—
730C2×C3—42no—
731C2×C3—82no—
732C2×C3C4×D3×D411yescharacteristic
733C2×C3C4×D3×D411yescharacteristic
734C2×C3C2×#91511yescharacteristic
735C2×C3#576811yescharacteristic
736C2×C3#577311yescharacteristic
737C2×C3D3×#13711yescharacteristic
738D3—62no—
739D3—62no—
740D3—122no—
741C22—22no—
742C22—41no—
743C22—41no—
744C22—92no—
745C22—181no—
746C22—181no—
747C22D32×D411yescharacteristic
748C4—32no—
749C4—41no—
750C4—61no—
751C4—61no—
752C4—61no—
753C4—62no—
754C4—62no—
755C4—92no—
756C4—121no—
757C4—121no—
758C4—182no—
759C4—361no—
760C4C2×C4×D3211yescharacteristic
761C4#6431211yescharacteristic
762C3—21no—
763C3C4×#91511yescharacteristic, complemented
764C3#7977411yescharacteristic, complemented
765C2—42no—
766C2—182no—
767C2#1059425511yescharacteristic
768C2#1059472911yescharacteristic
769C2D3×#91511yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalC2×#3830C22
cosocleC2×C32×C4C24
hypercenter#102D32
hypocenterC32C4×#137
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
3. #10594363C2semidirect
5. C3×#4758C2semidirect
6. C3×#4757C2semidirect
7. #10591440C2semidirect
8. Dic3×#214C2semidirect
9. #10590794C2semidirect
10. #10590793C2semidirect
11. #10590691C2semidirect
12. #10590664C2semidirect
13. #10590583C2semidirect
14. #10590481C2semidirect
15. #10590480C2semidirect
32. #63931C4semidirect
87. #4758D3semidirect
88. #4757D3semidirect
110. #3797C2×C4semidirect
119. C3×#214C2×C4semidirect
120. C3×#214C2×C4semidirect
143. #3719C2×C4semidirect
144. #3719C2×C4semidirect
145. #3712C2×C4semidirect
363. #214C4×D3semidirect
364. #214C4×D3semidirect
435. C3×Dic3#137semidirect
686. Dic3#915semidirect
687. C32C4×#137semidirect
763. C3C4×#915semidirect
764. C3#79774semidirect

Maximal subgroups

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

subgroupindex
#105951902
C2×#639312
#105943632
#105924702
C3×#47582
C3×#47572
#105914402
Dic3×#2142
#105907942
#105907932
#105906912
#105906642
#105905832
#105904812
#105904802
#797743
C4×#9153