Finite Group Databasebeta

← #11887619

Subgroups — #11887619

Order 1152.

850 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5635C211yesmaximal, characteristic
2#10594915C211yesmaximal, characteristic
3#10592749C211yesmaximal, characteristic, complemented
4C3×#5051C211yesmaximal, characteristic, complemented
5#10591653C211yesmaximal, characteristic, complemented
6#10591625C211yesmaximal, characteristic, complemented
7#10591596C211yesmaximal, characteristic, complemented
8#10591537C211yesmaximal, characteristic, complemented
9C3⋊C8×#67C211yesmaximal, characteristic
10#10591132C211yesmaximal, characteristic, complemented
11C2×#63567C211yesmaximal, characteristic, complemented
12D3×#810C211yesmaximal, characteristic, complemented
13#10590560C211yesmaximal, characteristic, complemented
14#10590488C211yesmaximal, characteristic, complemented
15#10590427C211yesmaximal, characteristic, complemented
16#83640—31nomaximal
17#80781—31nomaximal
18C22×#634C2211yescharacteristic
19C2×D3×Dic6C2211yescharacteristic
20C32×C22⋊Q8C2211yescharacteristic
21C2×#3756C2211yescharacteristic
22C2×#3756C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C3×Q8×Dic3C2211yescharacteristic
25C2×C3×#216C2211yescharacteristic
26C3×C4×#67C2211yescharacteristic
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C3×#924C2211yescharacteristic
29C22×C3×C3⋊C8C2211yescharacteristic
30C3×#897—21no—
31C3×D3×C4⋊C4C2211yescharacteristic
32C3×#889—21no—
33C3×#888C2211yescharacteristic
34C3×#67⋊C4—21no—
35C3×#878—21no—
36#63982—21no—
37#67⋊Dic3—21no—
38#63896—21no—
39#63866C2211yescharacteristic
40#63857C2211yescharacteristic
41#63844C2211yescharacteristic
42#63840—21no—
43C2×D3×C3⋊C8C2211yescharacteristic
44#63657C2211yescharacteristic
45#63637C2211yescharacteristic
46#63637C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#810C2211yescharacteristic
49C3×#807C2211yescharacteristic
50#63576C2211yescharacteristic
51#63576C2211yescharacteristic
52Dic3⋊(C3⋊C8)C2211yescharacteristic
53#63567C2211yescharacteristic
54#63567C2211yescharacteristic
55#63567C2211yescharacteristic
56#63567C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#554—31no—
62#5635D311yescharacteristic
63#5632—31no—
64D4×Dic6—31no—
65C3×#467—31no—
66#5186—31no—
67#5182—31no—
68C8×#67—31no—
69C2×#816—31no—
70#5093—31no—
71#5091—31no—
72#5051—31no—
73#5051D311yescharacteristic, complemented
74#5050—31no—
75#5050—31no—
76#5050—31no—
77#5050—61no—
78#5044—31no—
79#5031—31no—
80C4×#216—31no—
81D4×C3⋊C8—31no—
82#4970—31no—
83#4970—31no—
84C2×#810—31no—
85C2×#810—31no—
86#4884—31no—
87#4875—31no—
88#4813—31no—
89D3×#103—31no—
90#4792—31no—
91#4790—31no—
92C2×C32×Q8C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C3⋊Dic3—21no—
95C2×#634—22no—
96C2×#634—21no—
97C2×#634—41no—
98C2×#634C2311yescharacteristic
99C2×#634C2311yescharacteristic
100C2×C3×#67D411yescharacteristic
101C22×C3×Dic3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×Dic6—21no—
105C2×C3×Dic6C2311yescharacteristic
106C2×#627—21no—
107C2×D3×Dic3—21no—
108D3×Dic6—22no—
109D3×Dic6—41no—
110C32×C4⋊C4—21no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C22⋊C4—21no—
113#3756—22no—
114#3756—41no—
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C3×#217—21no—
118C3×#217D411yescharacteristic
119C3×#216—41no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4D411yescharacteristic
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3—21no—
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×Dic3⋊C4D411yescharacteristic
132C3×C4×Dic3—21no—
133C3×C4×Dic3C2311yescharacteristic
134C2×C3×C3⋊C8—41no—
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137#3724—21no—
138Dic3⋊Dic3—21no—
139Dic3⋊Dic3—21no—
140Dic3⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142Dic32—21no—
143D3×C3⋊C8—41no—
144#3299—91noSylow
145C2×D3×Q8—31no—
146C22×Dic6—31no—
147C22×Dic6—31no—
148C22×Dic6—31no—
149C22×Dic6—61no—
150C2×C3×Q16—31no—
151C22×C3×C8—31no—
152C3×C4⋊Q8—31no—
153C3×#125—61no—
154C3×C22⋊Q8—21no—
155C3×C22⋊Q8—31no—
156C3×C22⋊Q8—31no—
157C3×C22⋊Q8—61no—
158C3×C22⋊Q8—61no—
159C3×C22⋊Q8C2×D311yescharacteristic
160C3×C22⋊Q8C2×D311yescharacteristic
161C3×C4×Q8—31no—
162C3×C4×D4—31no—
163C3×C4×D4—61no—
164C2×C3×C4⋊C4—31no—
165C2×C3×C4⋊C4—31no—
166#946C2×D311yescharacteristic
167Q8×Dic3C2×D311yescharacteristic
168#944—31no—
169C2×#216—31no—
170C2×#216—31no—
171C2×#216—31no—
172C2×#216—31no—
173C2×#216—61no—
174C2×#216—61no—
175C2×#216C2×D311yescharacteristic
176D4×Dic3—61no—
177C4×#67C2×D311yescharacteristic
178C2×C4⋊Dic3C2×D311yescharacteristic
179#924—31no—
180#924C2×D311yescharacteristic
181C22×C3⋊C8—31no—
182C22×C3⋊C8C2×D311yescharacteristic
183C2×D3×C8—31no—
184#897—21no—
185#897—31no—
186#896—61no—
187D3×C4⋊C4C2×D311yescharacteristic
188#889—21no—
189#888—61no—
190#888—61no—
191#888C2×D311yescharacteristic
192#887—31no—
193#67⋊C4—21no—
194#67⋊C4—61no—
195#878—21no—
196#878—61no—
197#878—61no—
198#878—61no—
199#869—31no—
200C4×Dic6—31no—
201C3×#107—31no—
202C3×#103—31no—
203C3×#103—31no—
204#835—31no—
205#835—31no—
206#835C2×D311yescharacteristic
207#830—31no—
208#830—31no—
209#830—31no—
210#830—61no—
211(C2×D3)⋊C8—31no—
212#816—31no—
213#816—31no—
214#816—31no—
215#816—31no—
216Dic3⋊C8—31no—
217C8×Dic3—31no—
218#810—31no—
219#810—31no—
220#810—31no—
221#810—31no—
222#810—31no—
223#810—31no—
224#810—31no—
225#810—31no—
226#810—31no—
227#810—31no—
228#810—61no—
229#810—61no—
230#810C2×D311yescharacteristic
231#807—31no—
232#807—31no—
233#807—31no—
234#807—31no—
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—
250C2×C3⋊Dic3—42no—
251#634—21no—
252#634—21no—
253#634—21no—
254#634—42no—
255#634#4112yes—
256C3×#67Q1614yescomplemented
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—81no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—81no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—81no—
271#627—42no—
272D3×Dic3—42no—
273C3⋊(C3⋊C8)—21no—
274C3⋊(C3⋊C8)—21no—
275C3×C3⋊C8—21no—
276C3×C3⋊C8—21no—
277#554—31no—
278D4×Q8—91no—
279#487—91no—
280#484—91no—
281#484—91no—
282#477—91no—
283#467—31no—
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—61no—
295C2×C3×Q8C22×D311yescharacteristic
296C2×C3×Q8C22×D311yescharacteristic
297C2×C3×D4—31no—
298C22×C3×C4—21no—
299C22×C3×C4—31no—
300C22×C3×C4—61no—
301C22×C3×C4—61no—
302C22×C3×C4C22×D311yescharacteristic
303C22×C3×C4C22×D311yescharacteristic
304C2×#67#6711yescharacteristic
305C22×Dic3—21no—
306C22×Dic3—61no—
307C22×Dic3—61no—
308C22×Dic3—61no—
309C22×Dic3—121no—
310D3×Q8—62no—
311D3×Q8—121no—
312C2×C4×D3—21no—
313C2×C4×D3—61no—
314C2×C4×D3C22×D311yescharacteristic
315C2×Dic6—21no—
316C2×Dic6—31no—
317C2×Dic6—31no—
318C2×Dic6—31no—
319C2×Dic6—31no—
320C2×Dic6—61no—
321C2×Dic6—61no—
322C2×Dic6—62no—
323C2×Dic6—62no—
324C2×Dic6—62no—
325C2×Dic6—61no—
326C2×Dic6—61no—
327C2×Dic6—61no—
328C2×Dic6—61no—
329C2×Dic6—122no—
330C2×Dic6—121no—
331C2×Dic6—121no—
332C2×Dic6—121no—
333C2×Dic6—121no—
334C2×Dic6—122no—
335C2×Dic6C22×D311yescharacteristic
336C3×Q16—121no—
337C2×C3×C8—31no—
338C2×C3×C8—31no—
339C2×C3×C8—121no—
340C3×C4⋊C4—21no—
341C3×C4⋊C4—21no—
342C3×C4⋊C4—21no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—41no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4—61no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4C22×D311yescharacteristic
355C3×C4⋊C4C22×D311yescharacteristic
356C3×C22⋊C4—21no—
357C3×C22⋊C4—21no—
358C3×C22⋊C4—31no—
359C3×C22⋊C4—31no—
360C3×C22⋊C4—41no—
361C3×C22⋊C4—61no—
362C3×C22⋊C4—61no—
363C3×C42—31no—
364C3×C42—61no—
365#217—21no—
366#217—61no—
367#217#6711yescharacteristic
368#216—41no—
369#216—62no—
370#216—62no—
371#216—122no—
372#216—121no—
373#216—121no—
374#216—122no—
375(C2×D3)⋊C4—21no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4#6711yescharacteristic
378C4⋊Dic3—21no—
379C4⋊Dic3—21no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3C22×D311yescharacteristic
384C4⋊Dic3C22×D311yescharacteristic
385C4⋊Dic3C22×D311yescharacteristic
386Dic3⋊C4—21no—
387Dic3⋊C4—21no—
388Dic3⋊C4—21no—
389Dic3⋊C4—21no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4#6711yescharacteristic
396C4×Dic3—21no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3C22×D311yescharacteristic
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—41no—
405C2×C3⋊C8—61no—
406C2×C3⋊C8—61no—
407C2×C3⋊C8—121no—
408C2×C3⋊C8C22×D311yescharacteristic
409C2×C3⋊C8C22×D311yescharacteristic
410D3×C8—121no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32C2×Q1612yes—
414C22×C32C22×D411yescharacteristic
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3C2×Q1612yes—
418C32×C4—21no—
419C32×C4—41no—
420C32×C4—41no—
421C32×C4C2×#4111yescharacteristic
422C32×C4H(5,𝔽2)11yescharacteristic
423C3⋊Dic3—22no—
424C3⋊Dic3—41no—
425C3×Dic3—21no—
426C3×Dic3—21no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C3×Dic3—41no—
430C3×Dic3—41no—
431C3×Dic3C2×Q1612yes—
432C22×Q8—91no—
433C22×Q8—91no—
434C2×Q16—31no—
435C2×Q16—91no—
436C2×Q16—91no—
437C22×C8—31no—
438C22×C8—91no—
439C4⋊Q8—31no—
440C4⋊Q8—91no—
441C4⋊Q8—181no—
442#125—61no—
443C22⋊Q8—31no—
444C22⋊Q8—31no—
445C22⋊Q8—61no—
446C22⋊Q8—61no—
447C22⋊Q8—91no—
448C22⋊Q8—181no—
449C22⋊Q8—181no—
450C22⋊Q8D3211yescharacteristic
451C4×Q8—31no—
452C4×Q8—91no—
453C4×D4—31no—
454C4×D4—61no—
455C4×D4—181no—
456C2×C4⋊C4—31no—
457C2×C4⋊C4—31no—
458#107—31no—
459#107—91no—
460#107—91no—
461C4⋊C8—91no—
462#103—31no—
463#103—31no—
464#103—91no—
465#103—91no—
466#103—91no—
467#103—91no—
468#103—91no—
469#103—91no—
470#103—91no—
471#103—91no—
472C22⋊C8—91no—
473C22⋊C8—91no—
474C4×C8—91no—
475C23×C3—21no—
476C23×C3—31no—
477C23×C3D3×D411yescharacteristic
478C23×C3C2×#6711yescharacteristic
479C22×D3C2×#6711yescharacteristic
480C3×Q8—21no—
481C3×Q8—21no—
482C3×Q8—21no—
483C3×Q8—21no—
484C3×Q8—41no—
485C3×Q8—41no—
486C3×Q8—61no—
487C3×Q8—61no—
488C3×Q8—241no—
489C3×D4—34no—
490C2×C3×C4—21no—
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—31no—
501C2×C3×C4—31no—
502C2×C3×C4—31no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
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—241no—
514C2×C3×C4—241no—
515C2×C3×C4D3×D411yescharacteristic
516C2×C3×C4C2×#6711yescharacteristic
517C2×C3×C4C23×D311yescharacteristic
518C2×C3×C4C23×D311yescharacteristic
519#67#21614yescomplemented
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—81no—
529C2×Dic3—121no—
530C2×Dic3—121no—
531C2×Dic3—122no—
532C2×Dic3—122no—
533C2×Dic3—122no—
534C2×Dic3—124no—
535C2×Dic3C2×#6711yescharacteristic
536C2×Dic3C2×#6711yescharacteristic
537C2×Dic3C2×#6711yescharacteristic
538C4×D3—21no—
539C4×D3—21no—
540C4×D3—81no—
541C4×D3—122no—
542Dic6—21no—
543Dic6—21no—
544Dic6—32no—
545Dic6—32no—
546Dic6—62no—
547Dic6—61no—
548Dic6—61no—
549Dic6—62no—
550Dic6—61no—
551Dic6—61no—
552Dic6—61no—
553Dic6—61no—
554Dic6—81no—
555Dic6—121no—
556Dic6—121no—
557Dic6—122no—
558Dic6—122no—
559Dic6—122no—
560Dic6—122no—
561Dic6—124no—
562C3×C8—61no—
563C3×C8—61no—
564C3⋊C8—21no—
565C3⋊C8—21no—
566C3⋊C8—61no—
567C3⋊C8—61no—
568C3⋊C8—61no—
569C3⋊C8—61no—
570C3⋊C8—121no—
571C3⋊C8—121no—
572C2×C32—22no—
573C2×C32#54611yescharacteristic
574C2×C32C22×Q1611yescharacteristic
575C2×C32#57711yescharacteristic
576C3×D3—22no—
577C2×Q8—31no—
578C2×Q8—61no—
579C2×Q8—91no—
580C2×Q8—91no—
581C2×Q8—182no—
582C2×Q8—181no—
583C2×Q8—182no—
584C2×Q8—181no—
585C2×Q8—361no—
586C2×Q8—361no—
587C2×Q8C2×D3211yescharacteristic
588C2×D4—31no—
589C22×C4—31no—
590C22×C4—61no—
591C22×C4—61no—
592C22×C4—181no—
593C22×C4—181no—
594C22×C4C2×D3211yescharacteristic
595Q16—121no—
596Q16—182no—
597Q16—361no—
598C2×C8—31no—
599C2×C8—31no—
600C2×C8—91no—
601C2×C8—91no—
602C2×C8—121no—
603C2×C8—361no—
604C4⋊C4—21no—
605C4⋊C4—31no—
606C4⋊C4—31no—
607C4⋊C4—31no—
608C4⋊C4—31no—
609C4⋊C4—61no—
610C4⋊C4—61no—
611C4⋊C4—61no—
612C4⋊C4—61no—
613C4⋊C4—61no—
614C4⋊C4—61no—
615C4⋊C4—181no—
616C4⋊C4—181no—
617C4⋊C4—181no—
618C4⋊C4—181no—
619C4⋊C4C2×D3211yescharacteristic
620C22⋊C4—21no—
621C22⋊C4—31no—
622C22⋊C4—31no—
623C22⋊C4—61no—
624C22⋊C4—61no—
625C22⋊C4—181no—
626C42—31no—
627C42—61no—
628C42—181no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—22no—
635C22×C3—32no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—61no—
639C22×C3—61no—
640C22×C3D3×Q1612yes—
641C22×C3C2×#21612yes—
642C22×C3C2×D3×D411yescharacteristic
643C22×C3C22×#6711yescharacteristic
644C2×D3—21no—
645C2×D3—21no—
646C2×D3C2×#21612yes—
647C3×C4—21no—
648C3×C4—21no—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—32no—
652C3×C4—41no—
653C3×C4—41no—
654C3×C4—41no—
655C3×C4—41no—
656C3×C4—41no—
657C3×C4—61no—
658C3×C4—61no—
659C3×C4—81no—
660C3×C4—81no—
661C3×C4—121no—
662C3×C4—121no—
663C3×C4—121no—
664C3×C4—121no—
665C3×C4#100411yescharacteristic
666C3×C4D3×#4111yescharacteristic
667C3×C4D3×#4111yescharacteristic
668C3×C4#100911yescharacteristic
669Dic3—21no—
670Dic3—21no—
671Dic3—41no—
672Dic3—41no—
673Dic3—41no—
674Dic3—41no—
675Dic3—62no—
676Dic3—62no—
677Dic3—122no—
678Dic3—122no—
679Dic3—121no—
680Dic3—121no—
681Dic3C2×#21612yes—
682C32#329911yescharacteristic, complemented, Sylow
683C23—31no—
684C23D3×#6711yescharacteristic
685Q8—21no—
686Q8—21no—
687Q8—61no—
688Q8—61no—
689Q8—92no—
690Q8—181no—
691Q8—181no—
692Q8—181no—
693Q8—241no—
694Q8—362no—
695Q8—362no—
696D4—34no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—31no—
702C2×C4—31no—
703C2×C4—31no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—181no—
711C2×C4—181no—
712C2×C4—241no—
713C2×C4—241no—
714C2×C4—362no—
715C2×C4—362no—
716C2×C4D3×#6711yescharacteristic
717C2×C4C22×D3211yescharacteristic
718C8—61no—
719C8—61no—
720C8—181no—
721C8—181no—
722C2×C3—22no—
723C2×C3—22no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—21no—
727C2×C3—42no—
728C2×C3—62no—
729C2×C3#561011yescharacteristic
730C2×C3C2×D3×Q1611yescharacteristic
731C2×C3#577011yescharacteristic
732C2×C3C22×#21611yescharacteristic
733C2×C3#582911yescharacteristic
734C2×C3#583611yescharacteristic
735D3—22no—
736C22—21no—
737C22—21no—
738C22—32no—
739C22—61no—
740C22—61no—
741C22D3×#21612yes—
742C22C2×D3×#6711yescharacteristic
743C4—21no—
744C4—32no—
745C4—41no—
746C4—41no—
747C4—61no—
748C4—61no—
749C4—121no—
750C4—121no—
751C4—121no—
752C4—121no—
753C4—182no—
754C4—361no—
755C4#6431211yescharacteristic
756C4#6431411yescharacteristic
757C3—21no—
758C3#8078111yescharacteristic, complemented
759C3#8364011yescharacteristic, complemented
760C2—22no—
761C2—62no—
762C2#1059530511yescharacteristic
763C2C2×D3×#21611yescharacteristic
764C2#1059546611yescharacteristic
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. #10592749C2semidirect
4. C3×#5051C2semidirect
5. #10591653C2semidirect
6. #10591625C2semidirect
7. #10591596C2semidirect
8. #10591537C2semidirect
10. #10591132C2semidirect
11. C2×#63567C2semidirect
12. D3×#810C2semidirect
13. #10590560C2semidirect
14. #10590488C2semidirect
15. #10590427C2semidirect
73. #5051D3semidirect
256. C3×#67Q16semidirect
519. #67#216semidirect
682. C32#3299semidirect
758. C3#80781semidirect
759. C3#83640semidirect

Maximal subgroups

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

subgroupindex
C3×#56352
#105949152
#105927492
C3×#50512
#105916532
#105916252
#105915962
#105915372
C3⋊C8×#672
#105911322
C2×#635672
D3×#8102
#105905602
#105904882
#105904272
#836403
#807813