Finite Group Databasebeta

← #11887649

Subgroups — #11887649

Order 1152.

833 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5632C211yesmaximal, characteristic
2#10594988C211yesmaximal, characteristic
3#10592750C211yesmaximal, characteristic, complemented
4C3×#5044C211yesmaximal, characteristic, complemented
5#10591623C211yesmaximal, characteristic, complemented
6#10591595C211yesmaximal, characteristic, complemented
7#10591575C211yesmaximal, characteristic, complemented
8D3×#835C211yesmaximal, characteristic, complemented
9#10591186C211yesmaximal, characteristic, complemented
10#67⋊(C3⋊C8)C211yesmaximal, characteristic
11C2×#63565C211yesmaximal, characteristic, complemented
12#10590579C211yesmaximal, characteristic, complemented
13#10590557C211yesmaximal, characteristic, complemented
14#10590481C211yesmaximal, characteristic, complemented
15#10590440C211yesmaximal, characteristic, complemented
16#83551—31nomaximal
17#81490—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic
20C32×C22⋊Q8C2211yescharacteristic
21C2×#3756C2211yescharacteristic
22#64133C2211yescharacteristic
23C22×C3⋊(C3⋊C8)C2211yescharacteristic
24C3×#944C2211yescharacteristic
25C3×C4×#67C2211yescharacteristic
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C3×#897C2211yescharacteristic
28C3×#896—21no—
29C3×#888—21no—
30C3×#887C2211yescharacteristic
31C3×#67⋊C4—21no—
32C3×#878—21no—
33Dic3×#67—21no—
34#63964—21no—
35#63918C2211yescharacteristic
36#63899—21no—
37D3×C4⋊Dic3C2211yescharacteristic
38#63857C2211yescharacteristic
39#63846—21no—
40#63844C2211yescharacteristic
41C2×#3719C2211yescharacteristic
42C2×#3719C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44#63662C2211yescharacteristic
45#63637C2211yescharacteristic
46#63634C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#830C2211yescharacteristic
50C3×#807C2211yescharacteristic
51C3×#807C2211yescharacteristic
52Dic3⋊(C3⋊C8)C2211yescharacteristic
53#63566C2211yescharacteristic
54#63566C2211yescharacteristic
55#63565C2211yescharacteristic
56#63565C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×D4×Q8—31no—
62#5632D311yescharacteristic
63#5543—31no—
64#5511—31no—
65C3×#484—31no—
66#5228—31no—
67#5228—31no—
68C2×#835—31no—
69C2×#835—31no—
70#5090—31no—
71#5079—31no—
72#5051—31no—
73#5051—31no—
74#5051—31no—
75#5051—61no—
76#5044—31no—
77#5044D311yescharacteristic, complemented
78C4×#216—31no—
79#5021—31no—
80D4×C3⋊C8—31no—
81C2×#810—31no—
82#4887—31no—
83#4884—31no—
84#4875—31no—
85#4873—31no—
86#4809—31no—
87D3×#103—31no—
88#4795—31no—
89#4792—31no—
90#4739—31no—
91#67⋊C8—31no—
92C2×C32×Q8C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C2×C3×#67D411yescharacteristic
96C22×C3×Dic3—21no—
97C22×C3×Dic3—21no—
98C3×D3×Q8—22no—
99C3×D3×Q8—41no—
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×Dic6—22no—
103C2×C3×Dic6—21no—
104C2×C3×Dic6—21no—
105C2×C3×Dic6—41no—
106C2×C3×Dic6C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C2×#627—21no—
109C2×D3×Dic3—21no—
110C32×C4⋊C4—21no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C22⋊C4—21no—
113#3757—21no—
114#3756—41no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116#3750—21no—
117C2×C3⋊(C3⋊C8)—41no—
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C3×#217D411yescharacteristic
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4D411yescharacteristic
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4D411yescharacteristic
131C3×C4×Dic3—21no—
132C3×C4×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135#3724—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32—21no—
141#3719—22no—
142#3719—41no—
143D3×C3⋊C8—41no—
144#3299—91noSylow
145C22×C3×Q8—31no—
146C22×C3×Q8—31no—
147C2×D3×Q8C2×D311yescharacteristic
148C22×Dic6C2×D311yescharacteristic
149C3×C4⋊Q8—31no—
150C3×C4⋊Q8—61no—
151C3×C22⋊Q8—21no—
152C3×C22⋊Q8—31no—
153C3×C22⋊Q8—61no—
154C3×C22⋊Q8—61no—
155C3×C22⋊Q8C2×D311yescharacteristic
156C3×C22⋊Q8C2×D311yescharacteristic
157C3×C4×Q8—31no—
158C3×C4×D4—31no—
159C3×C4×D4—61no—
160C2×C3×C4⋊C4—31no—
161#944C2×D311yescharacteristic
162C2×#216—31no—
163C2×#216—31no—
164C2×#216—31no—
165C2×#216—31no—
166C2×#216—61no—
167D4×Dic3—61no—
168C4×#67—61no—
169C4×#67C2×D311yescharacteristic
170C2×C4⋊Dic3—31no—
171C2×C4⋊Dic3C2×D311yescharacteristic
172#924—31no—
173#924—31no—
174#924—31no—
175#924—61no—
176#924—61no—
177C22×C3⋊C8—31no—
178C22×C3⋊C8—31no—
179C22×C3⋊C8—31no—
180C22×C3⋊C8—61no—
181C2×Dic12—31no—
182C2×Dic12—31no—
183C2×D3×C8—31no—
184#897—31no—
185#897C2×D311yescharacteristic
186#896—21no—
187#896—61no—
188D3×C4⋊C4—31no—
189#890—61no—
190#889—61no—
191#888—21no—
192#888—31no—
193#887—31no—
194#887C2×D311yescharacteristic
195#67⋊C4—21no—
196#878—21no—
197#878—61no—
198#878—61no—
199#869—31no—
200C4×Dic6—31no—
201C3×#107—31no—
202C3×#107—31no—
203C3×#103—31no—
204C3×#103—31no—
205C3×C22⋊C8—31no—
206#835—31no—
207#835—31no—
208#835—31no—
209#835—31no—
210#835—31no—
211#835—31no—
212#835—31no—
213#835—31no—
214#835—61no—
215#835C2×D311yescharacteristic
216#835C2×D311yescharacteristic
217#830—31no—
218#830C2×D311yescharacteristic
219(C2×D3)⋊C8—31no—
220#816—31no—
221#816—31no—
222Dic3⋊C8—31no—
223C8×Dic3—31no—
224#810—31no—
225#810—31no—
226#810—31no—
227#810—31no—
228#810—31no—
229#810—31no—
230#810—61no—
231#807—31no—
232#807—31no—
233#807—61no—
234#807C2×D311yescharacteristic
235#807C2×D311yescharacteristic
236C4⋊(C3⋊C8)—31no—
237C4×C3⋊C8—31no—
238C23×C32C2×D411yescharacteristic
239C22×C3×D3C2×D411yescharacteristic
240C32×Q8—21no—
241C32×Q8—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2411yescharacteristic
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250#634—21no—
251#634—21no—
252C3×#67Q1614yescomplemented
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—42no—
258C2×C3×Dic3—81no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×C4×D3—21no—
263C3×C4×D3—21no—
264C3×C4×D3—42no—
265C3×Dic6—21no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268C3×Dic6—42no—
269C3×Dic6—42no—
270C3×Dic6#4112yes—
271#627—81no—
272D3×Dic3—81no—
273C3⋊(C3⋊C8)—21no—
274C3⋊(C3⋊C8)—21no—
275C3×C3⋊C8—21no—
276C3×C3⋊C8—21no—
277#554—91no—
278D4×Q8—31no—
279#487—91no—
280#484—31no—
281#484—91no—
282#477—91no—
283#467—91no—
284#467—91no—
285#462—91no—
286#451—91no—
287#451—91no—
288C4×Q16—91no—
289C8×D4—91no—
290C2×#103—91no—
291C2×#103—91no—
292C2×C3×Q8—21no—
293C2×C3×Q8—31no—
294C2×C3×Q8—31no—
295C2×C3×Q8—61no—
296C2×C3×Q8—62no—
297C2×C3×Q8—61no—
298C2×C3×Q8—62no—
299C2×C3×Q8—121no—
300C2×C3×Q8—121no—
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×Q8C22×D311yescharacteristic
303C2×C3×D4—31no—
304C22×C3×C4—21no—
305C22×C3×C4—31no—
306C22×C3×C4—61no—
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C22×C3×C4C22×D311yescharacteristic
310C22×C3×C4C22×D311yescharacteristic
311C2×#67#6711yescharacteristic
312C22×Dic3—21no—
313C22×Dic3—21no—
314C22×Dic3—61no—
315D3×Q8—22no—
316D3×Q8—41no—
317C2×C4×D3—21no—
318C2×C4×D3—61no—
319C2×C4×D3C22×D311yescharacteristic
320C2×Dic6—22no—
321C2×Dic6—21no—
322C2×Dic6—21no—
323C2×Dic6—31no—
324C2×Dic6—31no—
325C2×Dic6—41no—
326C2×Dic6—61no—
327C2×Dic6—61no—
328C2×Dic6—61no—
329C2×Dic6C22×D311yescharacteristic
330C2×Dic6C22×D311yescharacteristic
331C2×C3×C8—31no—
332C2×C3×C8—31no—
333C3×C4⋊C4—21no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4—21no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—41no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4C22×D311yescharacteristic
346C3×C4⋊C4C22×D311yescharacteristic
347C3×C22⋊C4—21no—
348C3×C22⋊C4—21no—
349C3×C22⋊C4—31no—
350C3×C22⋊C4—31no—
351C3×C22⋊C4—41no—
352C3×C22⋊C4—61no—
353C3×C42—31no—
354C3×C42—61no—
355#217—61no—
356#217—61no—
357#217—61no—
358#217—121no—
359#217#6711yescharacteristic
360#216—62no—
361#216—121no—
362#216—121no—
363#216—121no—
364#216—122no—
365(C2×D3)⋊C4—21no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4#6711yescharacteristic
368C4⋊Dic3—21no—
369C4⋊Dic3—21no—
370C4⋊Dic3—31no—
371C4⋊Dic3—31no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3C22×D311yescharacteristic
377C4⋊Dic3C22×D311yescharacteristic
378Dic3⋊C4—21no—
379Dic3⋊C4—21no—
380Dic3⋊C4—21no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—121no—
389Dic3⋊C4#6711yescharacteristic
390C4×Dic3—21no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3C22×D311yescharacteristic
394C2×C3⋊C8—31no—
395C2×C3⋊C8—31no—
396C2×C3⋊C8—31no—
397C2×C3⋊C8—31no—
398C2×C3⋊C8—61no—
399C2×C3⋊C8—61no—
400C2×C3⋊C8—121no—
401C2×C3⋊C8—121no—
402C2×C3⋊C8—121no—
403C2×C3⋊C8—122no—
404C2×C3⋊C8C22×D311yescharacteristic
405C2×C3⋊C8C22×D311yescharacteristic
406Dic12—62no—
407Dic12—121no—
408D3×C8—121no—
409C22×C32—21no—
410C22×C32—21no—
411C22×C32C2×Q1612yes—
412C22×C32C22×D411yescharacteristic
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3C2×Q1612yes—
416C32×C4—21no—
417C32×C4—41no—
418C32×C4—41no—
419C32×C4C2×#4111yescharacteristic
420C32×C4H(5,𝔽2)11yescharacteristic
421C3⋊Dic3—41no—
422C3⋊Dic3—41no—
423C3×Dic3—22no—
424C3×Dic3—21no—
425C3×Dic3—21no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C3×Dic3C2×Q1612yes—
430C22×Q8—31no—
431C22×Q8—31no—
432C2×Q16—91no—
433C2×Q16—91no—
434C2×Q16—91no—
435C22×C8—91no—
436C22×C8—91no—
437C4⋊Q8—31no—
438C4⋊Q8—61no—
439C4⋊Q8—91no—
440#125—181no—
441C22⋊Q8—31no—
442C22⋊Q8—61no—
443C22⋊Q8—61no—
444C22⋊Q8—91no—
445C22⋊Q8—91no—
446C22⋊Q8—181no—
447C22⋊Q8—181no—
448C22⋊Q8D3211yescharacteristic
449C4×Q8—31no—
450C4×Q8—91no—
451C4×D4—31no—
452C4×D4—61no—
453C4×D4—181no—
454C2×C4⋊C4—31no—
455C2×C4⋊C4—91no—
456#107—31no—
457#107—31no—
458#107—91no—
459C4⋊C8—91no—
460#103—31no—
461#103—31no—
462#103—91no—
463#103—91no—
464#103—91no—
465#103—91no—
466#103—91no—
467#103—91no—
468#103—91no—
469#103—91no—
470C22⋊C8—31no—
471C22⋊C8—91no—
472C4×C8—91no—
473C23×C3—21no—
474C23×C3—31no—
475C23×C3D3×D411yescharacteristic
476C23×C3C2×#6711yescharacteristic
477C22×D3C2×#6711yescharacteristic
478C3×Q8—21no—
479C3×Q8—21no—
480C3×Q8—21no—
481C3×Q8—21no—
482C3×Q8—32no—
483C3×Q8—41no—
484C3×Q8—41no—
485C3×Q8—61no—
486C3×Q8—61no—
487C3×Q8—61no—
488C3×Q8—122no—
489C3×Q8—122no—
490C3×D4—34no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—31no—
502C2×C3×C4—31no—
503C2×C3×C4—31no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
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—122no—
515C2×C3×C4—122no—
516C2×C3×C4—241no—
517C2×C3×C4D3×D411yescharacteristic
518C2×C3×C4C2×#6711yescharacteristic
519C2×C3×C4C23×D311yescharacteristic
520C2×C3×C4C23×D311yescharacteristic
521#67#21614yescomplemented
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—42no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—81no—
532C2×Dic3—121no—
533C2×Dic3—121no—
534C2×Dic3—241no—
535C2×Dic3C2×#6711yescharacteristic
536C2×Dic3C2×#6711yescharacteristic
537C2×Dic3C2×#6711yescharacteristic
538C4×D3—21no—
539C4×D3—21no—
540C4×D3—42no—
541C4×D3—241no—
542Dic6—21no—
543Dic6—21no—
544Dic6—21no—
545Dic6—42no—
546Dic6—42no—
547Dic6—61no—
548Dic6—61no—
549Dic6—61no—
550Dic6—61no—
551Dic6—121no—
552Dic6—121no—
553Dic6—241no—
554Dic6—241no—
555Dic6#23712yes—
556C3×C8—61no—
557C3×C8—61no—
558C3⋊C8—21no—
559C3⋊C8—21no—
560C3⋊C8—62no—
561C3⋊C8—61no—
562C3⋊C8—61no—
563C3⋊C8—61no—
564C3⋊C8—61no—
565C3⋊C8—121no—
566C2×C32—22no—
567C2×C32#54611yescharacteristic
568C2×C32C22×Q1611yescharacteristic
569C2×C32#57711yescharacteristic
570C3×D3—22no—
571C2×Q8—31no—
572C2×Q8—31no—
573C2×Q8—61no—
574C2×Q8—62no—
575C2×Q8—61no—
576C2×Q8—62no—
577C2×Q8—91no—
578C2×Q8—121no—
579C2×Q8—121no—
580C2×Q8—181no—
581C2×Q8C2×D3211yescharacteristic
582C2×D4—31no—
583C22×C4—31no—
584C22×C4—61no—
585C22×C4—61no—
586C22×C4—61no—
587C22×C4—181no—
588C22×C4C2×D3211yescharacteristic
589Q16—182no—
590Q16—361no—
591Q16—361no—
592C2×C8—31no—
593C2×C8—31no—
594C2×C8—91no—
595C2×C8—91no—
596C2×C8—361no—
597C2×C8—361no—
598C4⋊C4—21no—
599C4⋊C4—31no—
600C4⋊C4—31no—
601C4⋊C4—31no—
602C4⋊C4—61no—
603C4⋊C4—61no—
604C4⋊C4—61no—
605C4⋊C4—61no—
606C4⋊C4—61no—
607C4⋊C4—91no—
608C4⋊C4—181no—
609C4⋊C4—181no—
610C4⋊C4—181no—
611C4⋊C4—181no—
612C4⋊C4—181no—
613C4⋊C4C2×D3211yescharacteristic
614C22⋊C4—21no—
615C22⋊C4—31no—
616C22⋊C4—31no—
617C22⋊C4—61no—
618C22⋊C4—181no—
619C22⋊C4—181no—
620C42—31no—
621C42—61no—
622C42—181no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—22no—
629C22×C3—32no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3—61no—
633C22×C3—61no—
634C22×C3D3×Q1612yes—
635C22×C3C2×#21612yes—
636C22×C3C2×D3×D411yescharacteristic
637C22×C3C22×#6711yescharacteristic
638C2×D3—21no—
639C2×D3—21no—
640C2×D3C2×#21612yes—
641C3×C4—21no—
642C3×C4—21no—
643C3×C4—21no—
644C3×C4—21no—
645C3×C4—32no—
646C3×C4—41no—
647C3×C4—41no—
648C3×C4—41no—
649C3×C4—41no—
650C3×C4—41no—
651C3×C4—61no—
652C3×C4—62no—
653C3×C4—61no—
654C3×C4—81no—
655C3×C4—81no—
656C3×C4—121no—
657C3×C4—121no—
658C3×C4—121no—
659C3×C4C2×#23711yescharacteristic
660C3×C4#100411yescharacteristic
661C3×C4D3×#4111yescharacteristic
662C3×C4#100911yescharacteristic
663Dic3—22no—
664Dic3—21no—
665Dic3—21no—
666Dic3—41no—
667Dic3—41no—
668Dic3—41no—
669Dic3—121no—
670Dic3—121no—
671Dic3—121no—
672Dic3—121no—
673Dic3—241no—
674Dic3—241no—
675Dic3C2×#21612yes—
676C32#329911yescharacteristic, complemented, Sylow
677C23—31no—
678C23D3×#6711yescharacteristic
679Q8—21no—
680Q8—21no—
681Q8—32no—
682Q8—61no—
683Q8—61no—
684Q8—61no—
685Q8—122no—
686Q8—122no—
687Q8—181no—
688Q8—181no—
689Q8—721no—
690D4—34no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—31no—
696C2×C4—31no—
697C2×C4—31no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—122no—
705C2×C4—122no—
706C2×C4—181no—
707C2×C4—181no—
708C2×C4—241no—
709C2×C4—721no—
710C2×C4D3×#6711yescharacteristic
711C2×C4C22×D3211yescharacteristic
712C8—61no—
713C8—61no—
714C8—181no—
715C8—181no—
716C2×C3—22no—
717C2×C3—22no—
718C2×C3—21no—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3—42no—
722C2×C3—62no—
723C2×C3#565411yescharacteristic
724C2×C3C2×D3×Q1611yescharacteristic
725C2×C3#577511yescharacteristic
726C2×C3#580611yescharacteristic
727C2×C3C22×#21611yescharacteristic
728C2×C3#583711yescharacteristic
729D3—22no—
730C22—21no—
731C22—21no—
732C22—32no—
733C22—61no—
734C22—61no—
735C22D3×#21612yes—
736C22C2×D3×#6711yescharacteristic
737C4—21no—
738C4—32no—
739C4—41no—
740C4—41no—
741C4—61no—
742C4—62no—
743C4—61no—
744C4—121no—
745C4—121no—
746C4—121no—
747C4—361no—
748C4—361no—
749C4D3×#23711yescharacteristic
750C4#6431411yescharacteristic
751C3—21no—
752C3#8149011yescharacteristic, complemented
753C3#8355111yescharacteristic, complemented
754C2—22no—
755C2—62no—
756C2#1059514811yescharacteristic
757C2C2×D3×#21611yescharacteristic
758C2#1059545511yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×C3×#67D4
hypercenterC22⋊Q8D32
hypocenterC32#3299
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #10592750C2semidirect
4. C3×#5044C2semidirect
5. #10591623C2semidirect
6. #10591595C2semidirect
7. #10591575C2semidirect
8. D3×#835C2semidirect
9. #10591186C2semidirect
11. C2×#63565C2semidirect
12. #10590579C2semidirect
13. #10590557C2semidirect
14. #10590481C2semidirect
15. #10590440C2semidirect
77. #5044D3semidirect
252. C3×#67Q16semidirect
521. #67#216semidirect
676. C32#3299semidirect
752. C3#81490semidirect
753. C3#83551semidirect

Maximal subgroups

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

subgroupindex
C3×#56322
#105949882
#105927502
C3×#50442
#105916232
#105915952
#105915752
D3×#8352
#105911862
#67⋊(C3⋊C8)2
C2×#635652
#105905792
#105905572
#105904812
#105904402
#835513
#814903