Finite Group Databasebeta

← #11887653

Subgroups — #11887653

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
1#10595371C211yesmaximal, characteristic
2#10595361C211yesmaximal, characteristic
3#10592885C211yesmaximal, characteristic, complemented
4C3×#5188C211yesmaximal, characteristic, complemented
5C3×#5182C211yesmaximal, characteristic, complemented
6#10591653C211yesmaximal, characteristic, complemented
7#10591623C211yesmaximal, characteristic, complemented
8#10591601C211yesmaximal, characteristic, complemented
9#10591552C211yesmaximal, characteristic, complemented
10#10591551C211yesmaximal, characteristic, complemented
11#10591537C211yesmaximal, characteristic, complemented
12#10590805C211yesmaximal, characteristic, complemented
13#10590720C211yesmaximal, characteristic
14#10590689C211yesmaximal, characteristic, complemented
15D3×#816C211yesmaximal, characteristic, complemented
16#80781—31nomaximal
17#80491—31nomaximal
18C2×Q8×C3⋊D3C2211yescharacteristic
19C2×D3×Dic6C2211yescharacteristic
20C2×C32×Q16C2211yescharacteristic
21#64155C2211yescharacteristic
22C2×#3756C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C3×#946C2211yescharacteristic
25C3×Q8×Dic3C2211yescharacteristic
26C3×#944C2211yescharacteristic
27C2×C3×#216C2211yescharacteristic
28C2×C3×D3×C8C2211yescharacteristic
29#63918C2211yescharacteristic
30C4×#626C2211yescharacteristic
31#63900C2211yescharacteristic
32#63899—21no—
33#63896—21no—
34#63895—21no—
35D3×C4⋊Dic3C2211yescharacteristic
36#63881—21no—
37#63880—21no—
38#63871C2211yescharacteristic
39#63867—21no—
40#63865—21no—
41#63844C2211yescharacteristic
42#63840—21no—
43C2×#3710C2211yescharacteristic
44#63662C2211yescharacteristic
45#63647C2211yescharacteristic
46#63643C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#818C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×Dic3⋊C8C2211yescharacteristic
53#63576C2211yescharacteristic
54#63575C2211yescharacteristic
55#63567C2211yescharacteristic
56#63567C2211yescharacteristic
57#63566C2211yescharacteristic
58#63565C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5727—31no—
62#5635—31no—
63#5632—31no—
64#5579—31no—
65C3×#467—31no—
66C3×#462—31no—
67#5188—31no—
68#5188D311yescharacteristic, complemented
69#5186—31no—
70#5186—31no—
71#5186—31no—
72#5186—61no—
73#5182D311yescharacteristic, complemented
74C8×#67—31no—
75C2×#816—31no—
76#5079—31no—
77#5050—31no—
78#5044—31no—
79C4×#216—31no—
80#4884—31no—
81#4875—31no—
82#4850—31no—
83#4834—31no—
84#4813—31no—
85#4811—31no—
86#4811—31no—
87D3×#103—31no—
88D3×#103—31no—
89D3×#103—31no—
90#4792—31no—
91#4790—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C32×Q8C2311yescharacteristic
94Q8×C3⋊D3—22no—
95Q8×C3⋊D3—41no—
96C2×C4×C3⋊D3—21no—
97C2×C4×C3⋊D3C2311yescharacteristic
98C2×#634—21no—
99C2×#634C2311yescharacteristic
100C2×C3×C4×D3C2311yescharacteristic
101C2×C3×Dic6C2311yescharacteristic
102C2×#627—21no—
103C2×#627—21no—
104C2×#626D411yescharacteristic
105C2×#624—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108D3×Dic6—22no—
109D3×Dic6—41no—
110C32×Q16—41no—
111C2×C32×C8C2311yescharacteristic
112#3756—22no—
113#3752—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115#3750—21no—
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C3×#216—41no—
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4—21no—
120C3×C4⋊Dic3—21no—
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×C4×Dic3—21no—
129C3×C4×Dic3C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C3×D3×C8—41no—
133#3724—21no—
134#3724—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3D411yescharacteristic
139#3722—21no—
140#3722D411yescharacteristic
141(C2×D3)⋊Dic3D411yescharacteristic
142Dic32—21no—
143#3710—41no—
144#3299—91noSylow
145C2×D3×Q8—31no—
146C2×D3×Q8—31no—
147C2×D3×Q8—31no—
148C2×D3×Q8—61no—
149C22×Dic6—31no—
150C2×C3×Q16—21no—
151C2×C3×Q16—31no—
152C2×C3×Q16C2×D311yescharacteristic
153C2×C3×Q16C2×D311yescharacteristic
154C22×C3×C8—31no—
155C3×C4⋊Q8—31no—
156C3×C22⋊Q8—31no—
157C3×C22⋊Q8—31no—
158C3×C4×Q8—31no—
159#946—31no—
160#946—31no—
161#946—31no—
162#946—61no—
163#946C2×D311yescharacteristic
164#946C2×D311yescharacteristic
165Q8×Dic3C2×D311yescharacteristic
166#944C2×D311yescharacteristic
167C2×#216—31no—
168C2×#216—31no—
169C2×#216—61no—
170C2×#216C2×D311yescharacteristic
171C4×#67—31no—
172C2×C4⋊Dic3—31no—
173C2×D3×C8—31no—
174C2×D3×C8—31no—
175C2×D3×C8C2×D311yescharacteristic
176#897—31no—
177#897—61no—
178#896—61no—
179#896—61no—
180#896—61no—
181#896—61no—
182#896—61no—
183#893—61no—
184D3×C4⋊C4—31no—
185D3×C4⋊C4—31no—
186D3×C4⋊C4—31no—
187#889—61no—
188#888—31no—
189#888—61no—
190#888—61no—
191#887—31no—
192#67⋊C4—61no—
193#67⋊C4—61no—
194#878—61no—
195#878—61no—
196C4×D12—31no—
197C4×D12—61no—
198#870—61no—
199#869—31no—
200C4×Dic6—31no—
201C3×#107—31no—
202C3×C4⋊C8—31no—
203C3×#103—31no—
204C3×#103—31no—
205C3×#103—31no—
206C3×#103—31no—
207#835—31no—
208#835—31no—
209#835—31no—
210#835—31no—
211#835—61no—
212#835C2×D311yescharacteristic
213#835C2×D311yescharacteristic
214#835C2×D311yescharacteristic
215#830—31no—
216(C2×D3)⋊C8—31no—
217(C2×D3)⋊C8—31no—
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8—61no—
220#818—31no—
221#818C2×D311yescharacteristic
222#816—31no—
223#816—31no—
224#816—31no—
225#816—31no—
226#816—31no—
227#816—61no—
228#816C2×D311yescharacteristic
229Dic3⋊C8C2×D311yescharacteristic
230C8×Dic3—31no—
231#810—31no—
232#810—31no—
233#810—31no—
234#807—31no—
235#807—31no—
236#807—31no—
237C4×C3⋊C8—31no—
238C22×C3⋊D3C2×D411yescharacteristic
239C22×C3×D3C2×D411yescharacteristic
240C32×Q8—21no—
241C32×Q8—21no—
242C32×Q8—21no—
243C32×Q8—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4C2411yescharacteristic
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3C2×D411yescharacteristic
250C4×C3⋊D3—21no—
251C4×C3⋊D3—21no—
252C4×C3⋊D3—42no—
253#634—21no—
254#634—42no—
255#634#4112yes—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C3×C4×D3—21no—
264C3×C4×D3—21no—
265C3×Dic6—21no—
266C3×Dic6—21no—
267#627—42no—
268#627—81no—
269#626Q1614yescomplemented
270#624—81no—
271D3×Dic3—42no—
272D3×Dic3—81no—
273C32×C8—21no—
274C3⋊(C3⋊C8)—21no—
275C3×C3⋊C8—21no—
276C3×C3⋊C8—21no—
277#554—91no—
278D4×Q8—91no—
279#487—91no—
280#484—91no—
281#484—91no—
282#477—91no—
283#467—31no—
284#467—91no—
285#462—31no—
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—21no—
294C2×C3×Q8—31no—
295C2×C3×Q8C22×D311yescharacteristic
296C2×C3×Q8C22×D311yescharacteristic
297C2×C3×Q8C22×D311yescharacteristic
298C2×C3×Q8C22×D311yescharacteristic
299C22×C3×C4—31no—
300C2×#67—31no—
301C22×Dic3—61no—
302C22×Dic3—61no—
303D3×Q8—62no—
304D3×Q8—62no—
305D3×Q8—62no—
306D3×Q8—122no—
307D3×Q8—121no—
308D3×Q8—121no—
309D3×Q8—121no—
310D3×Q8—122no—
311C2×D12—31no—
312C2×C4×D3—31no—
313C2×C4×D3—31no—
314C2×C4×D3—61no—
315C2×C4×D3—61no—
316C2×C4×D3—61no—
317C2×C4×D3—61no—
318C2×C4×D3—61no—
319C2×C4×D3—61no—
320C2×C4×D3—61no—
321C2×C4×D3—121no—
322C2×C4×D3C22×D311yescharacteristic
323C2×Dic6—31no—
324C2×Dic6—31no—
325C2×Dic6—61no—
326C2×Dic6—62no—
327C2×Dic6—61no—
328C2×Dic6—61no—
329C2×Dic6—61no—
330C2×Dic6—61no—
331C2×Dic6—61no—
332C2×Dic6—61no—
333C2×Dic6—121no—
334C2×Dic6—121no—
335C2×Dic6C22×D311yescharacteristic
336C3×Q16—41no—
337C3×Q16—41no—
338C3×Q16—42no—
339C3×Q16—121no—
340C2×C3×C8—21no—
341C2×C3×C8—31no—
342C2×C3×C8—31no—
343C2×C3×C8—121no—
344C2×C3×C8C22×D311yescharacteristic
345C2×C3×C8C22×D311yescharacteristic
346C3×C4⋊C4—31no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—61no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
354C3×C22⋊C4—61no—
355C3×C22⋊C4—61no—
356C3×C42—31no—
357C3×C42—61no—
358#217—31no—
359#216—41no—
360#216—62no—
361#216—62no—
362#216—122no—
363(C2×D3)⋊C4—21no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—31no—
366(C2×D3)⋊C4—31no—
367(C2×D3)⋊C4—31no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—121no—
373C4⋊Dic3—21no—
374C4⋊Dic3—31no—
375C4⋊Dic3—31no—
376C4⋊Dic3—31no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3C22×D311yescharacteristic
382C4⋊Dic3C22×D311yescharacteristic
383C4⋊Dic3C22×D311yescharacteristic
384Dic3⋊C4—21no—
385Dic3⋊C4—21no—
386Dic3⋊C4—21no—
387Dic3⋊C4—21no—
388Dic3⋊C4—31no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—121no—
399C4×Dic3—21no—
400C4×Dic3—61no—
401C4×Dic3—61no—
402C4×Dic3C22×D311yescharacteristic
403C2×C3⋊C8—31no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—61no—
406C2×C3⋊C8C22×D311yescharacteristic
407C2×C3⋊C8C22×D311yescharacteristic
408D3×C8—41no—
409D3×C8—121no—
410D3×C8—121no—
411C22×C32C22×D411yescharacteristic
412C2×C3⋊D3—21no—
413C2×C3⋊D3—21no—
414C2×C3⋊D3C2×Q1612yes—
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3C2×Q1612yes—
418C32×C4—41no—
419C32×C4—41no—
420C32×C4C2×#4111yescharacteristic
421C32×C4H(5,𝔽2)11yescharacteristic
422C3⋊Dic3—22no—
423C3⋊Dic3—21no—
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×Q16D3211yescharacteristic
437C22×C8—31no—
438C22×C8—91no—
439C4⋊Q8—31no—
440C4⋊Q8—91no—
441C4⋊Q8—181no—
442#125—181no—
443C22⋊Q8—31no—
444C22⋊Q8—31no—
445C22⋊Q8—91no—
446C22⋊Q8—91no—
447C22⋊Q8—181no—
448C22⋊Q8—181no—
449C22⋊Q8—181no—
450C22⋊Q8—181no—
451C4×Q8—31no—
452C4×Q8—91no—
453C4×D4—91no—
454C4×D4—181no—
455C4×D4—181no—
456C2×C4⋊C4—91no—
457C2×C4⋊C4—91no—
458#107—31no—
459#107—91no—
460#107—91no—
461C4⋊C8—31no—
462#103—31no—
463#103—31no—
464#103—31no—
465#103—31no—
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—31no—
476C22×D3—31no—
477C22×D3—31no—
478C22×D3—61no—
479C22×D3D3×D411yescharacteristic
480C3×Q8—22no—
481C3×Q8—21no—
482C3×Q8—21no—
483C3×Q8—21no—
484C3×Q8—21no—
485C3×Q8—21no—
486C3×Q8—21no—
487C3×Q8—21no—
488C3×Q8—21no—
489C3×Q8—41no—
490C3×Q8—41no—
491C3×Q8—41no—
492C3×Q8—61no—
493C3×Q8—61no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
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—41no—
503C2×C3×C4—41no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4C23×D311yescharacteristic
511C2×C3×C4C23×D311yescharacteristic
512#67—34no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—31no—
518C2×Dic3—31no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—121no—
525C2×Dic3—121no—
526C2×Dic3—122no—
527C2×Dic3—241no—
528C2×Dic3D3×D411yescharacteristic
529C2×Dic3D3×D411yescharacteristic
530C2×Dic3D3×D411yescharacteristic
531D12—34no—
532C4×D3—21no—
533C4×D3—21no—
534C4×D3—61no—
535C4×D3—61no—
536C4×D3—61no—
537C4×D3—61no—
538C4×D3—121no—
539C4×D3—121no—
540C4×D3—122no—
541C4×D3—122no—
542C4×D3—122no—
543C4×D3—124no—
544C4×D3—241no—
545C4×D3—241no—
546C4×D3—241no—
547Dic6—21no—
548Dic6—21no—
549Dic6—32no—
550Dic6—32no—
551Dic6—62no—
552Dic6—61no—
553Dic6—61no—
554Dic6—121no—
555Dic6—122no—
556Dic6—122no—
557Dic6—122no—
558Dic6—122no—
559Dic6—124no—
560Dic6—241no—
561Dic6—241no—
562C3×C8—21no—
563C3×C8—21no—
564C3×C8—41no—
565C3×C8—61no—
566C3×C8—61no—
567C3⋊C8—21no—
568C3⋊C8—21no—
569C3⋊C8—61no—
570C3⋊C8—61no—
571C3⋊C8—121no—
572C2×C32#54611yescharacteristic
573C2×C32C22×Q1611yescharacteristic
574C2×C32#57711yescharacteristic
575C3⋊D3—22no—
576C3×D3—22no—
577C2×Q8—31no—
578C2×Q8—91no—
579C2×Q8—181no—
580C2×Q8—181no—
581C2×Q8—181no—
582C2×Q8—182no—
583C2×Q8—182no—
584C2×Q8—361no—
585C2×Q8—361no—
586C2×Q8C2×D3211yescharacteristic
587C2×Q8C2×D3211yescharacteristic
588C2×D4—91no—
589C22×C4—31no—
590C22×C4—91no—
591C22×C4—181no—
592C22×C4—181no—
593C22×C4—181no—
594C22×C4—181no—
595Q16—41no—
596Q16—121no—
597Q16—182no—
598C2×C8—31no—
599C2×C8—31no—
600C2×C8—91no—
601C2×C8—121no—
602C2×C8—361no—
603C2×C8C2×D3211yescharacteristic
604C4⋊C4—31no—
605C4⋊C4—31no—
606C4⋊C4—31no—
607C4⋊C4—61no—
608C4⋊C4—61no—
609C4⋊C4—61no—
610C4⋊C4—61no—
611C4⋊C4—61no—
612C4⋊C4—91no—
613C4⋊C4—91no—
614C4⋊C4—181no—
615C4⋊C4—181no—
616C4⋊C4—181no—
617C4⋊C4—181no—
618C4⋊C4—181no—
619C4⋊C4—181no—
620C22⋊C4—61no—
621C22⋊C4—61no—
622C22⋊C4—91no—
623C22⋊C4—91no—
624C22⋊C4—181no—
625C22⋊C4—181no—
626C42—31no—
627C42—61no—
628C42—181no—
629C22×C3—21no—
630C22×C3—32no—
631C22×C3—61no—
632C22×C3—61no—
633C22×C3C2×D3×D411yescharacteristic
634C22×C3C2×D3×D411yescharacteristic
635C2×D3—21no—
636C2×D3—21no—
637C2×D3—32no—
638C2×D3—32no—
639C2×D3—62no—
640C2×D3—61no—
641C2×D3—61no—
642C2×D3—61no—
643C2×D3—61no—
644C2×D3—121no—
645C2×D3—121no—
646C2×D3D3×Q1612yes—
647C3×C4—21no—
648C3×C4—21no—
649C3×C4—32no—
650C3×C4—42no—
651C3×C4—41no—
652C3×C4—41no—
653C3×C4—41no—
654C3×C4—41no—
655C3×C4—61no—
656C3×C4—61no—
657C3×C4—81no—
658C3×C4—121no—
659C3×C4—121no—
660C3×C4—121no—
661C3×C4—121no—
662C3×C4#100411yescharacteristic
663C3×C4#100411yescharacteristic
664C3×C4D3×#4111yescharacteristic
665C3×C4D3×#4111yescharacteristic
666Dic3—21no—
667Dic3—21no—
668Dic3—41no—
669Dic3—41no—
670Dic3—41no—
671Dic3—41no—
672Dic3—62no—
673Dic3—61no—
674Dic3—62no—
675Dic3—61no—
676Dic3—122no—
677Dic3—121no—
678Dic3—121no—
679Dic3—121no—
680Dic3—241no—
681Dic3D3×Q1612yes—
682C32#329911yescharacteristic, complemented, Sylow
683C23—31no—
684C23—91no—
685Q8—21no—
686Q8—21no—
687Q8—21no—
688Q8—21no—
689Q8—61no—
690Q8—61no—
691Q8—92no—
692Q8—181no—
693Q8—362no—
694Q8—362no—
695Q8—721no—
696D4—94no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—31no—
700C2×C4—31no—
701C2×C4—31no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—91no—
709C2×C4—181no—
710C2×C4—181no—
711C2×C4—181no—
712C2×C4—181no—
713C2×C4—362no—
714C2×C4—362no—
715C2×C4—721no—
716C2×C4—721no—
717C2×C4C22×D3211yescharacteristic
718C8—21no—
719C8—61no—
720C8—61no—
721C8—181no—
722C2×C3—21no—
723C2×C3—21no—
724C2×C3—21no—
725C2×C3—62no—
726C2×C3#561011yescharacteristic
727C2×C3#561211yescharacteristic
728C2×C3C2×D3×Q1611yescharacteristic
729C2×C3C2×D3×Q1611yescharacteristic
730C2×C3#577011yescharacteristic
731C2×C3#577811yescharacteristic
732D3—22no—
733D3—62no—
734D3—62no—
735D3—122no—
736C22—32no—
737C22—61no—
738C22—61no—
739C22—92no—
740C22—181no—
741C22—181no—
742C22D32×D411yescharacteristic
743C4—32no—
744C4—41no—
745C4—41no—
746C4—61no—
747C4—61no—
748C4—121no—
749C4—121no—
750C4—121no—
751C4—121no—
752C4—181no—
753C4—182no—
754C4—361no—
755C4#6431211yescharacteristic
756C4#6433011yescharacteristic
757C3—21no—
758C3#8049111yescharacteristic, complemented
759C3#8078111yescharacteristic, complemented
760C2—62no—
761C2—182no—
762C2D32×Q1611yescharacteristic
763C2#1059477011yescharacteristic
764C2#1059529611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
prime radicalC2×#626D4
hypercenterC2×Q16D32
hypocenterC32#3299
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
3. #10592885C2semidirect
4. C3×#5188C2semidirect
5. C3×#5182C2semidirect
6. #10591653C2semidirect
7. #10591623C2semidirect
8. #10591601C2semidirect
9. #10591552C2semidirect
10. #10591551C2semidirect
11. #10591537C2semidirect
12. #10590805C2semidirect
14. #10590689C2semidirect
15. D3×#816C2semidirect
68. #5188D3semidirect
73. #5182D3semidirect
269. #626Q16semidirect
682. C32#3299semidirect
758. C3#80491semidirect
759. C3#80781semidirect

Maximal subgroups

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

subgroupindex
#105953712
#105953612
#105928852
C3×#51882
C3×#51822
#105916532
#105916232
#105916012
#105915522
#105915512
#105915372
#105908052
#105907202
#105906892
D3×#8162
#807813
#804913