Finite Group Databasebeta

← #11887821

Subgroups — #11887821

Order 1152.

828 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5677C211yesmaximal, characteristic
2#10593920C211yesmaximal, characteristic, complemented
3#10592753C211yesmaximal, characteristic, complemented
4C3×#5056C211yesmaximal, characteristic, complemented
5#10591596C211yesmaximal, characteristic, complemented
6#10591595C211yesmaximal, characteristic, complemented
7#10591558C211yesmaximal, characteristic, complemented
8D3×#835C211yesmaximal, characteristic, complemented
9#10591463C211yesmaximal, characteristic, complemented
10#10591460C211yesmaximal, characteristic, complemented
11#10591420C211yesmaximal, characteristic, complemented
12#10591413C211yesmaximal, characteristic, complemented
13C4×#3719C211yesmaximal, characteristic, complemented
14C3⋊C8×D12C211yesmaximal, characteristic, complemented
15#10590286C211yesmaximal, characteristic, complemented
16#83534—31nomaximal
17#81654—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C32×#124C2211yescharacteristic
21C2×#3756C2211yescharacteristic
22C2×#3754C2211yescharacteristic
23C4×#634C2211yescharacteristic
24C3×#946C2211yescharacteristic
25C3×#938C2211yescharacteristic
26C3×#885—21no—
27C3×#884—21no—
28C3×#67⋊C4—21no—
29C3×#878—21no—
30C3×C4×D12C2211yescharacteristic
31C3×#870C2211yescharacteristic
32C3×C4×Dic6C2211yescharacteristic
33D3×C4⋊Dic3C2211yescharacteristic
34#63884—21no—
35#63878—21no—
36#63862—21no—
37#63857C2211yescharacteristic
38#63857C2211yescharacteristic
39#63846—21no—
40#63841C2211yescharacteristic
41C2×#3719C2211yescharacteristic
42C2×D3×C3⋊C8C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44#63662C2211yescharacteristic
45#63659C2211yescharacteristic
46C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#832C2211yescharacteristic
51C3×C4×C3⋊C8C2211yescharacteristic
52#63576C2211yescharacteristic
53#63575C2211yescharacteristic
54#63574C2211yescharacteristic
55#63567C2211yescharacteristic
56#63566C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61C3×#548—31no—
62#5694—31no—
63#5677D311yescharacteristic
64#5541—31no—
65C3×#488—31no—
66#5239—31no—
67#5233—31no—
68#5228—31no—
69C2×#835—31no—
70#5063—31no—
71#5056D311yescharacteristic, complemented
72#5054—31no—
73#5054—31no—
74#5054—61no—
75#5051—31no—
76#5045—31no—
77#5041—31no—
78#5033—31no—
79C4×#216—31no—
80#5022—31no—
81D4×C3⋊C8—31no—
82#4814—31no—
83#4813—31no—
84#4809—31no—
85D3×#103—31no—
86#4783—31no—
87#4778—31no—
88#4774—31no—
89#4772—31no—
90C4×Dic12—31no—
91C8×D12—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C32×D4C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C2×C3×#67—21no—
96C2×C3×#67—21no—
97C22×C3×Dic3—21no—
98C3×D3×Q8—22no—
99C3×D3×Q8—41no—
100C3×#237—22no—
101C3×#237—41no—
102C2×C3×D12D411yescharacteristic
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6—21no—
107C2×C3×Dic6C2311yescharacteristic
108C2×D3×Dic3—21no—
109C32×C22⋊C4—21no—
110C32×C22⋊C4—21no—
111C32×C42C2311yescharacteristic
112#3756—41no—
113#3754—41no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115#3750—21no—
116C4×C3⋊Dic3—21no—
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×#217—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4D411yescharacteristic
122C3×(C2×D3)⋊C4D411yescharacteristic
123C3×C4⋊Dic3D411yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×C4×Dic3—21no—
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32—21no—
141#3719—22no—
142D3×C3⋊C8—41no—
143D3×C3⋊C8—41no—
144#3300—91noSylow
145C2×C3×#41—31no—
146C22×C3×Q8—31no—
147C2×D3×Q8C2×D311yescharacteristic
148C2×#237C2×D311yescharacteristic
149C3×#125—31no—
150C3×#124—21no—
151C3×#124—61no—
152C3×#124C2×D311yescharacteristic
153C3×#124C2×D311yescharacteristic
154C3×C22⋊Q8—31no—
155C3×C22⋊Q8—61no—
156C3×#121—31no—
157C3×#121—61no—
158C3×C4×Q8—31no—
159C3×C4×D4—31no—
160C3×C4×D4—61no—
161#946C2×D311yescharacteristic
162C2×#216—31no—
163C2×#216—31no—
164C2×#216—31no—
165C2×#216—61no—
166#938C2×D311yescharacteristic
167#935—61no—
168C2×#214—31no—
169C2×#214—31no—
170C2×#214—61no—
171#926—31no—
172C2×C4⋊Dic3—31no—
173#924—31no—
174#924—31no—
175C22×C3⋊C8—31no—
176C22×C3⋊C8—31no—
177C2×Dic12—31no—
178C2×D3×C8—31no—
179C2×D3×C8—31no—
180#898—61no—
181#897—31no—
182#897—31no—
183#894—61no—
184#892—31no—
185#892—61no—
186D3×C4⋊C4—31no—
187#890—61no—
188#889—61no—
189#885—21no—
190#884—21no—
191#67⋊C4—21no—
192#879—61no—
193#878—21no—
194#877—61no—
195C4×D12C2×D311yescharacteristic
196#870C2×D311yescharacteristic
197C4×Dic6—31no—
198C4×Dic6—31no—
199C4×Dic6—61no—
200C4×Dic6C2×D311yescharacteristic
201C3×#103—31no—
202C3×#103—31no—
203C3×#102—31no—
204C3×#102—31no—
205C3×C4×C8—31no—
206#835—31no—
207#835—31no—
208#835—31no—
209#835—31no—
210#835—31no—
211#835—61no—
212#835C2×D311yescharacteristic
213#835C2×D311yescharacteristic
214#832—31no—
215#832—31no—
216#832—61no—
217#832C2×D311yescharacteristic
218#832C2×D311yescharacteristic
219#830—31no—
220#830—31no—
221(C2×D3)⋊C8—31no—
222(C2×D3)⋊C8—31no—
223#818—31no—
224#816—31no—
225#816—31no—
226#810—31no—
227#810—31no—
228#810—31no—
229#808—31no—
230#808—31no—
231#807—31no—
232#807—31no—
233#807—31no—
234C4⋊(C3⋊C8)—31no—
235C4⋊(C3⋊C8)—31no—
236C4⋊(C3⋊C8)—61no—
237C4×C3⋊C8C2×D311yescharacteristic
238C23×C32—21no—
239C22×C3×D3C2×D411yescharacteristic
240C22×C3×D3C2×D411yescharacteristic
241C32×Q8—21no—
242C32×Q8—21no—
243C32×D4—21no—
244C32×D4—21no—
245C2×C32×C4—21no—
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
251#634—21no—
252#634—21no—
253C3×#67—42no—
254C3×#67—42no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—42no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×D12—22no—
263C3×C4×D3—21no—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—42no—
268C3×Dic6—21no—
269C3×Dic6—42no—
270C3×Dic6#4112yes—
271D3×Dic3—42no—
272C3⋊(C3⋊C8)—21no—
273C3⋊(C3⋊C8)—21no—
274C3×C3⋊C8—21no—
275C3×C3⋊C8—21no—
276#552—91no—
277#548—31no—
278#488—31no—
279#485—91no—
280#480—91no—
281#479—91no—
282#467—91no—
283#465—91no—
284#464—91no—
285#452—91no—
286#451—91no—
287C4×Q16—91no—
288C8×D4—91no—
289#416—91no—
290C2×#103—91no—
291C3×#41—62no—
292C3×#41—121no—
293C2×C3×Q8—21no—
294C2×C3×Q8—31no—
295C2×C3×Q8—61no—
296C2×C3×Q8—62no—
297C2×C3×Q8—121no—
298C2×C3×Q8C22×D311yescharacteristic
299C2×C3×Q8C22×D311yescharacteristic
300C2×C3×D4—21no—
301C2×C3×D4—31no—
302C2×C3×D4—61no—
303C2×C3×D4—61no—
304C2×C3×D4C22×D311yescharacteristic
305C2×C3×D4C22×D311yescharacteristic
306C22×C3×C4—31no—
307C22×C3×C4—31no—
308C22×C3×C4—61no—
309C22×C3×C4—61no—
310C2×#67—21no—
311C2×#67—21no—
312C22×Dic3—21no—
313C22×Dic3—61no—
314D3×Q8—22no—
315D3×Q8—41no—
316#237—22no—
317#237—41no—
318C2×D12#6711yescharacteristic
319C2×C4×D3—21no—
320C2×C4×D3—61no—
321C2×C4×D3C22×D311yescharacteristic
322C2×C4×D3C22×D311yescharacteristic
323C2×Dic6—21no—
324C2×Dic6—31no—
325C2×Dic6—31no—
326C2×Dic6—61no—
327C2×Dic6C22×D311yescharacteristic
328C2×C3×C8—31no—
329C2×C3×C8—31no—
330C3×C4⋊C4—31no—
331C3×C4⋊C4—31no—
332C3×C4⋊C4—31no—
333C3×C4⋊C4—31no—
334C3×C4⋊C4—61no—
335C3×C4⋊C4—61no—
336C3×C4⋊C4—61no—
337C3×C4⋊C4—61no—
338C3×C22⋊C4—21no—
339C3×C22⋊C4—21no—
340C3×C22⋊C4—21no—
341C3×C22⋊C4—21no—
342C3×C22⋊C4—31no—
343C3×C22⋊C4—31no—
344C3×C22⋊C4—41no—
345C3×C22⋊C4—41no—
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C42—21no—
349C3×C42—61no—
350C3×C42C22×D311yescharacteristic
351C3×C42C22×D311yescharacteristic
352#217—21no—
353#217—61no—
354#217—61no—
355#217—61no—
356#216—62no—
357#216—121no—
358#216—121no—
359#216—122no—
360#214—121no—
361#214—121no—
362#214—122no—
363(C2×D3)⋊C4—21no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4#6711yescharacteristic
368(C2×D3)⋊C4#6711yescharacteristic
369C4⋊Dic3—31no—
370C4⋊Dic3—31no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3#6711yescharacteristic
376C4⋊Dic3C22×D311yescharacteristic
377C4⋊Dic3C22×D311yescharacteristic
378C4⋊Dic3C22×D311yescharacteristic
379Dic3⋊C4—21no—
380Dic3⋊C4—21no—
381Dic3⋊C4—21no—
382Dic3⋊C4—21no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—121no—
389C4×Dic3—21no—
390C4×Dic3—61no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3—121no—
395C2×C3⋊C8—31no—
396C2×C3⋊C8—31no—
397C2×C3⋊C8—31no—
398C2×C3⋊C8—31no—
399C2×C3⋊C8—61no—
400C2×C3⋊C8—61no—
401C2×C3⋊C8—121no—
402C2×C3⋊C8—121no—
403C2×C3⋊C8C22×D311yescharacteristic
404C2×C3⋊C8C22×D311yescharacteristic
405Dic12—62no—
406D3×C8—121no—
407D3×C8—121no—
408C22×C32—41no—
409C22×C32—41no—
410C22×C32—41no—
411C22×C32C22×D411yescharacteristic
412C2×C3×D3—21no—
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3#13512yes—
418C32×C4—21no—
419C32×C4—21no—
420C32×C4—41no—
421C32×C4C2×#4111yescharacteristic
422C32×C4H(5,𝔽2)11yescharacteristic
423C3⋊Dic3—41no—
424C3⋊Dic3—41no—
425C3×Dic3—22no—
426C3×Dic3—21no—
427C3×Dic3—21no—
428C3×Dic3—41no—
429C3×Dic3—41no—
430C3×Dic3—41no—
431C2×#41—31no—
432C22×Q8—31no—
433C2×Q16—91no—
434C2×Q16—91no—
435C2×SD16—91no—
436C22×C8—91no—
437C22×C8—91no—
438#126—181no—
439#125—31no—
440#125—181no—
441#124—61no—
442#124D3211yescharacteristic
443#123—181no—
444C22⋊Q8—31no—
445C22⋊Q8—61no—
446C22⋊Q8—91no—
447C22⋊Q8—91no—
448#121—31no—
449#121—61no—
450C4×Q8—31no—
451C4×Q8—91no—
452C4×D4—31no—
453C4×D4—61no—
454#117—91no—
455#117—181no—
456C2×C4⋊C4—91no—
457#107—91no—
458#107—91no—
459#106—91no—
460C4⋊C8—91no—
461#103—31no—
462#103—31no—
463#103—91no—
464#103—91no—
465#103—91no—
466#103—91no—
467#103—91no—
468#102—31no—
469#102—31no—
470#102—91no—
471C22⋊C8—91no—
472C22⋊C8—91no—
473C4×C8—31no—
474C23×C3—21no—
475C23×C3—21no—
476C23×C3—31no—
477C23×C3—31no—
478C23×C3—41no—
479C22×D3C2×#6711yescharacteristic
480C22×D3C2×#6711yescharacteristic
481C3×Q8—21no—
482C3×Q8—21no—
483C3×Q8—21no—
484C3×Q8—21no—
485C3×Q8—32no—
486C3×Q8—41no—
487C3×Q8—41no—
488C3×Q8—61no—
489C3×Q8—122no—
490C3×D4—21no—
491C3×D4—21no—
492C3×D4—21no—
493C3×D4—21no—
494C3×D4—41no—
495C3×D4—41no—
496C3×D4—62no—
497C3×D4—122no—
498C3×D4—122no—
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—31no—
506C2×C3×C4—41no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—122no—
516C2×C3×C4—122no—
517C2×C3×C4D3×D411yescharacteristic
518C2×C3×C4D3×D411yescharacteristic
519C2×C3×C4C2×#6711yescharacteristic
520C2×C3×C4C2×#6711yescharacteristic
521C2×C3×C4C23×D311yescharacteristic
522C2×C3×C4C23×D311yescharacteristic
523#67—42no—
524#67—42no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—42no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—121no—
535C2×Dic3—121no—
536C2×Dic3—122no—
537C2×Dic3C2×#6711yescharacteristic
538C2×Dic3C2×#6711yescharacteristic
539D12—22no—
540C4×D3—21no—
541C4×D3—21no—
542C4×D3—21no—
543C4×D3—21no—
544C4×D3—42no—
545C4×D3—122no—
546Dic6—21no—
547Dic6—42no—
548Dic6—62no—
549Dic6—61no—
550Dic6—61no—
551Dic6—61no—
552Dic6—61no—
553Dic6—121no—
554Dic6#23712yes—
555C3×C8—61no—
556C3×C8—61no—
557C3⋊C8—21no—
558C3⋊C8—21no—
559C3⋊C8—61no—
560C3⋊C8—61no—
561C3⋊C8—61no—
562C3⋊C8—61no—
563C3⋊C8—121no—
564C3⋊C8—121no—
565C2×C32—81no—
566C2×C32#54611yescharacteristic
567C2×C32C2×#13511yescharacteristic
568C2×C32#57811yescharacteristic
569C3×D3—22no—
570C3×D3—41no—
571#41—62no—
572#41—121no—
573C2×Q8—31no—
574C2×Q8—61no—
575C2×Q8—62no—
576C2×Q8—91no—
577C2×Q8—121no—
578C2×Q8C2×D3211yescharacteristic
579C2×D4—31no—
580C2×D4—61no—
581C2×D4—61no—
582C2×D4C2×D3211yescharacteristic
583C22×C4—31no—
584C22×C4—31no—
585C22×C4—61no—
586C22×C4—61no—
587C22×C4—181no—
588Q16—182no—
589Q16—361no—
590SD16—361no—
591C2×C8—31no—
592C2×C8—31no—
593C2×C8—91no—
594C2×C8—91no—
595C2×C8—361no—
596C2×C8—361no—
597C4⋊C4—31no—
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—31no—
601C4⋊C4—61no—
602C4⋊C4—61no—
603C4⋊C4—61no—
604C4⋊C4—61no—
605C4⋊C4—91no—
606C4⋊C4—181no—
607C4⋊C4—181no—
608C4⋊C4—181no—
609C4⋊C4—181no—
610C22⋊C4—21no—
611C22⋊C4—21no—
612C22⋊C4—31no—
613C22⋊C4—31no—
614C22⋊C4—61no—
615C22⋊C4—61no—
616C22⋊C4—181no—
617C22⋊C4—181no—
618C22⋊C4—181no—
619C42—61no—
620C42—181no—
621C42—181no—
622C42C2×D3211yescharacteristic
623C22×C3—21no—
624C22×C3—32no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3—41no—
631C22×C3—61no—
632C22×C3—61no—
633C22×C3—61no—
634C22×C3—61no—
635C22×C3—61no—
636C22×C3—81no—
637C22×C3—81no—
638C22×C3—81no—
639C22×C3C2×D3×D411yescharacteristic
640C22×C3C22×#6711yescharacteristic
641C2×D3—21no—
642C2×D3—21no—
643C2×D3—21no—
644C2×D3—21no—
645C2×D3—21no—
646C2×D3#95012yes—
647C3×C4—21no—
648C3×C4—21no—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—41no—
654C3×C4—41no—
655C3×C4—41no—
656C3×C4—41no—
657C3×C4—61no—
658C3×C4—61no—
659C3×C4—62no—
660C3×C4—81no—
661C3×C4—121no—
662C3×C4—121no—
663C3×C4—121no—
664C3×C4C2×#23711yescharacteristic
665C3×C4#100411yescharacteristic
666C3×C4D3×#4111yescharacteristic
667C3×C4#100911yescharacteristic
668Dic3—22no—
669Dic3—21no—
670Dic3—21no—
671Dic3—41no—
672Dic3—41no—
673Dic3—41no—
674Dic3—122no—
675Dic3—121no—
676Dic3—121no—
677Dic3—121no—
678Dic3—121no—
679Dic3—241no—
680C32#330011yescharacteristic, complemented, Sylow
681C23—21no—
682C23—31no—
683C23—31no—
684Q8—21no—
685Q8—21no—
686Q8—32no—
687Q8—61no—
688Q8—122no—
689Q8—181no—
690Q8—181no—
691D4—21no—
692D4—21no—
693D4—62no—
694D4—122no—
695D4—122no—
696C2×C4—21no—
697C2×C4—31no—
698C2×C4—31no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—122no—
708C2×C4—122no—
709C2×C4—181no—
710C2×C4—181no—
711C2×C4—362no—
712C2×C4D3×#6711yescharacteristic
713C2×C4D3×#6711yescharacteristic
714C2×C4C22×D3211yescharacteristic
715C8—61no—
716C8—61no—
717C8—181no—
718C8—181no—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3—21no—
722C2×C3—62no—
723C2×C3—81no—
724C2×C3—81no—
725C2×C3—121no—
726C2×C3—161no—
727C2×C3#567611yescharacteristic
728C2×C3D3×#13511yescharacteristic
729C2×C3#577111yescharacteristic
730C2×C3#580611yescharacteristic
731C2×C3C2×#95011yescharacteristic
732C2×C3#583811yescharacteristic
733D3—22no—
734D3—41no—
735C22—32no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—61no—
740C22—61no—
741C22—61no—
742C22—61no—
743C22—61no—
744C22C2×D3×#6711yescharacteristic
745C4—21no—
746C4—21no—
747C4—41no—
748C4—61no—
749C4—61no—
750C4—62no—
751C4—121no—
752C4—121no—
753C4—121no—
754C4—361no—
755C4—361no—
756C4D3×#23711yescharacteristic
757C4#6431411yescharacteristic
758C3—21no—
759C3#8165411yescharacteristic, complemented
760C3#8353411yescharacteristic, complemented
761C2—62no—
762C2—81no—
763C2—121no—
764C2#1059522911yescharacteristic
765C2D3×#95011yescharacteristic
766C2#1059546711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#124C22
socleC22×C32C22×D4
prime radicalC3×#5677C2
hypercenter#124D32
hypocenterC32#3300
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
2. #10593920C2semidirect
3. #10592753C2semidirect
4. C3×#5056C2semidirect
5. #10591596C2semidirect
6. #10591595C2semidirect
7. #10591558C2semidirect
8. D3×#835C2semidirect
9. #10591463C2semidirect
10. #10591460C2semidirect
11. #10591420C2semidirect
12. #10591413C2semidirect
13. C4×#3719C2semidirect
14. C3⋊C8×D12C2semidirect
15. #10590286C2semidirect
71. #5056D3semidirect
680. C32#3300semidirect
759. C3#81654semidirect
760. C3#83534semidirect

Maximal subgroups

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

subgroupindex
C3×#56772
#105939202
#105927532
C3×#50562
#105915962
#105915952
#105915582
D3×#8352
#105914632
#105914602
#105914202
#105914132
C4×#37192
C3⋊C8×D122
#105902862
#835343
#816543