Finite Group Databasebeta

← #11887553

Subgroups — #11887553

Order 1152.

900 conjugacy classes of subgroups.

The subgroup lattice has 789 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595400C211yesmaximal, characteristic, complemented
2#10595134C211yesmaximal, characteristic
3#10592861C211yesmaximal, characteristic, complemented
4C3×#5171C211yesmaximal, characteristic, complemented
5C3×#5170C211yesmaximal, characteristic, complemented
6#10591549C211yesmaximal, characteristic, complemented
7D3×#835C211yesmaximal, characteristic, complemented
8#10591538C211yesmaximal, characteristic, complemented
9#10591517C211yesmaximal, characteristic, complemented
10#10591460C211yesmaximal, characteristic, complemented
11#10591445C211yesmaximal, characteristic, complemented
12#10590816C211yesmaximal, characteristic, complemented
13#10590717C211yesmaximal, characteristic, complemented
14#10590674C211yesmaximal, characteristic, complemented
15D3×#816C211yesmaximal, characteristic, complemented
16#80689—31nomaximal
17#80049—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×#3805—21no—
20C2×D3×Dic6C2211yescharacteristic
21C2×C32×SD16C2211yescharacteristic
22#64153C2211yescharacteristic
23D4×C3⋊Dic3C2211yescharacteristic
24C2×#3754C2211yescharacteristic
25C3×#946C2211yescharacteristic
26C3×#938C2211yescharacteristic
27C3×#938C2211yescharacteristic
28C2×C3×#214C2211yescharacteristic
29C2×C3×D3×C8C2211yescharacteristic
30#63982—21no—
31#63969—21no—
32#63969—21no—
33#63919C2211yescharacteristic
34C4×#625C2211yescharacteristic
35D3×C4⋊Dic3C2211yescharacteristic
36D3×C4⋊Dic3C2211yescharacteristic
37#63887—21no—
38#63879—21no—
39#63857C2211yescharacteristic
40#63851—21no—
41#63843C2211yescharacteristic
42#63839—21no—
43C2×D3×C3⋊C8C2211yescharacteristic
44#63662C2211yescharacteristic
45#63643C2211yescharacteristic
46#63641C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#817C2211yescharacteristic
52C3×#816C2211yescharacteristic
53#63574C2211yescharacteristic
54#63573C2211yescharacteristic
55#63567C2211yescharacteristic
56#63567C2211yescharacteristic
57#63566C2211yescharacteristic
58#63565C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63553C2211yescharacteristic
61Q8×#67—31no—
62#5632—31no—
63#5611—31no—
64#5611—31no—
65C3×#465—31no—
66C3×#448—31no—
67C2×#835—31no—
68#5171D311yescharacteristic, complemented
69#5170—31no—
70#5170D311yescharacteristic, complemented
71#5162—31no—
72#5162—31no—
73#5162—61no—
74Dic3×SD16—31no—
75C8×#67—31no—
76C2×#816—31no—
77#5043—31no—
78#5041—31no—
79#5040—31no—
80#4862—31no—
81#4854—31no—
82#4805—31no—
83D3×#103—31no—
84D3×#103—31no—
85#4792—31no—
86#4792—31no—
87#4791—31no—
88#4778—31no—
89#4758—31no—
90#67⋊C8—31no—
91#4721—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C32×D4C2311yescharacteristic
94C22×C3⋊Dic3—21no—
95C2×#634C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C3×D3×Q8—22no—
99C3×D3×Q8—41no—
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×Dic6—21no—
104C2×C3×Dic6C2311yescharacteristic
105C2×#627—21no—
106C2×#627—21no—
107C2×#625D411yescharacteristic
108#3805—44no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111C2×D3×Dic3—21no—
112D3×Dic6—22no—
113D3×Dic6—41no—
114C32×SD16—41no—
115C2×C32×C8C2311yescharacteristic
116#3757—21no—
117#3754—41no—
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119#3750—21no—
120#3750—21no—
121C4×C3⋊Dic3C2311yescharacteristic
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C3×#217—21no—
124C3×#217—21no—
125C3×#214—22no—
126C3×(C2×D3)⋊C4—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C3×D3×C8—41no—
134#3724—21no—
135#3724D411yescharacteristic
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139Dic3⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3D411yescharacteristic
142(C2×D3)⋊Dic3D411yescharacteristic
143Dic32—21no—
144D3×C3⋊C8—41no—
145#3298—91noSylow
146C22×C3×Q8—31no—
147C2×D3×Q8—31no—
148C2×D3×Q8C2×D311yescharacteristic
149C2×#237—61no—
150C2×#237—61no—
151C22×Dic6—31no—
152C2×C3×SD16—21no—
153C2×C3×SD16—31no—
154C2×C3×SD16C2×D311yescharacteristic
155C2×C3×SD16C2×D311yescharacteristic
156C22×C3×C8—31no—
157C3×C22⋊Q8—31no—
158C3×#121—31no—
159C3×#121—31no—
160#946—61no—
161#946C2×D311yescharacteristic
162Q8×Dic3—31no—
163#944—31no—
164#944—31no—
165#944—61no—
166#944—61no—
167#938C2×D311yescharacteristic
168#938C2×D311yescharacteristic
169#935—61no—
170#935—61no—
171D4×Dic3—31no—
172D4×Dic3—31no—
173D4×Dic3—61no—
174C2×#214—31no—
175C2×#214—31no—
176C2×#214—61no—
177C2×#214C2×D311yescharacteristic
178C4×#67—31no—
179C4×#67—31no—
180C4×#67—61no—
181C2×C4⋊Dic3—31no—
182C2×C4⋊Dic3—31no—
183#924—31no—
184#924—61no—
185C22×C3⋊C8—31no—
186C2×D3×C8—31no—
187C2×D3×C8C2×D311yescharacteristic
188#897—31no—
189#896—61no—
190D3×C4⋊C4—31no—
191D3×C4⋊C4—31no—
192#888—31no—
193#888—31no—
194#888—61no—
195#887—31no—
196#883—61no—
197#883—61no—
198#67⋊C4—61no—
199#878—61no—
200#878—61no—
201#878—61no—
202C3×#106—31no—
203C3×#103—31no—
204C3×#103—31no—
205C3×#103—31no—
206C3×#102—31no—
207C3×C22⋊C8—31no—
208#835—31no—
209#835—31no—
210#835—31no—
211#835—31no—
212#835—61no—
213#835C2×D311yescharacteristic
214#835C2×D311yescharacteristic
215#832C2×D311yescharacteristic
216#830—31no—
217(C2×D3)⋊C8—31no—
218(C2×D3)⋊C8C2×D311yescharacteristic
219#817—31no—
220#817C2×D311yescharacteristic
221#816—31no—
222#816—31no—
223#816—31no—
224#816—31no—
225#816—31no—
226#816—61no—
227#816C2×D311yescharacteristic
228Dic3⋊C8—31no—
229Dic3⋊C8—31no—
230Dic3⋊C8—61no—
231C8×Dic3—31no—
232C8×Dic3—31no—
233#810—31no—
234#810—31no—
235#810—31no—
236#808—31no—
237#808—31no—
238#808—31no—
239C23×C32—21no—
240C22×C3×D3C2×D411yescharacteristic
241C22×C3×D3C2×D411yescharacteristic
242C32×Q8—21no—
243C32×Q8—21no—
244C32×D4—21no—
245C32×D4—21no—
246C2×C32×C4—21no—
247C2×C32×C4C2411yescharacteristic
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—42no—
251C2×C3⋊Dic3C2×D411yescharacteristic
252C2×C3⋊Dic3C2×D411yescharacteristic
253#634—21no—
254#634—21no—
255C3×#67—42no—
256C3×#67—42no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
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#4112yescomplemented
271#627—42no—
272#627—42no—
273#625SD1614yescomplemented
274D3×Dic3—42no—
275D3×Dic3—42no—
276D3×Dic3—42no—
277C32×C8—21no—
278C3⋊(C3⋊C8)—21no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281D4×Q8—91no—
282#547—91no—
283#487—91no—
284#483—91no—
285#483—91no—
286#475—91no—
287#465—31no—
288#465—91no—
289#461—91no—
290#448—31no—
291#448—91no—
292C4×SD16—91no—
293C8×D4—91no—
294C2×#103—91no—
295C2×#103—91no—
296C2×C3×Q8—21no—
297C2×C3×Q8—31no—
298C2×C3×Q8—61no—
299C2×C3×Q8—62no—
300C2×C3×Q8—121no—
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×Q8C22×D311yescharacteristic
303C2×C3×D4—21no—
304C2×C3×D4—61no—
305C2×C3×D4—61no—
306C2×C3×D4C22×D311yescharacteristic
307C2×C3×D4C22×D311yescharacteristic
308C22×C3×C4—31no—
309C22×C3×C4—31no—
310C22×C3×C4—61no—
311C2×#67—21no—
312C2×#67—21no—
313C2×#67—31no—
314C2×#67—31no—
315C22×Dic3—61no—
316C22×Dic3—61no—
317C22×Dic3—61no—
318C22×Dic3—61no—
319C22×Dic3—61no—
320C22×Dic3—121no—
321D3×Q8—22no—
322D3×Q8—41no—
323D3×Q8—62no—
324D3×Q8—121no—
325#237—124no—
326#237—124no—
327C2×C4×D3—21no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3C22×D311yescharacteristic
332C2×C4×D3C22×D311yescharacteristic
333C2×Dic6—21no—
334C2×Dic6—31no—
335C2×Dic6—31no—
336C2×Dic6—61no—
337C2×Dic6—62no—
338C2×Dic6—61no—
339C2×Dic6—61no—
340C2×Dic6—61no—
341C2×Dic6—61no—
342C2×Dic6—121no—
343C2×Dic6C22×D311yescharacteristic
344C3×SD16—41no—
345C3×SD16—41no—
346C3×SD16—42no—
347C3×SD16—62no—
348C2×C3×C8—21no—
349C2×C3×C8—31no—
350C2×C3×C8—31no—
351C2×C3×C8—121no—
352C2×C3×C8C22×D311yescharacteristic
353C2×C3×C8C22×D311yescharacteristic
354C3×C4⋊C4—31no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—61no—
358C3×C22⋊C4—61no—
359C3×C22⋊C4—61no—
360C3×C22⋊C4—61no—
361#217—21no—
362#217—21no—
363#217—31no—
364#217—31no—
365#217—61no—
366#217—61no—
367#217—61no—
368#217—121no—
369#214—22no—
370#214—121no—
371#214—121no—
372#214—122no—
373(C2×D3)⋊C4—21no—
374(C2×D3)⋊C4—31no—
375(C2×D3)⋊C4—31no—
376(C2×D3)⋊C4—61no—
377C4⋊Dic3—31no—
378C4⋊Dic3—31no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3C22×D311yescharacteristic
385C4⋊Dic3C22×D311yescharacteristic
386C4⋊Dic3C22×D311yescharacteristic
387Dic3⋊C4—21no—
388Dic3⋊C4—31no—
389Dic3⋊C4—31no—
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—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—121no—
401Dic3⋊C4—121no—
402C4×Dic3—31no—
403C4×Dic3—31no—
404C4×Dic3—61no—
405C4×Dic3—61no—
406C4×Dic3—61no—
407C2×C3⋊C8—31no—
408C2×C3⋊C8—31no—
409C2×C3⋊C8—61no—
410C2×C3⋊C8—121no—
411C2×C3⋊C8C22×D311yescharacteristic
412C2×C3⋊C8C22×D311yescharacteristic
413D3×C8—41no—
414D3×C8—121no—
415C22×C32—41no—
416C22×C32—41no—
417C22×C32—41no—
418C22×C32C22×D411yescharacteristic
419C2×C3×D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—21no—
423C2×C3×D3C2×SD1612yes—
424C2×C3×D3C2×SD1612yes—
425C32×C4—41no—
426C32×C4C2×#4111yescharacteristic
427C32×C4H(5,𝔽2)11yescharacteristic
428C3⋊Dic3—21no—
429C3⋊Dic3—41no—
430C3⋊Dic3—41no—
431C3⋊Dic3C2×SD1612yes—
432C3×Dic3—22no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C2×#41—181no—
439C22×Q8—31no—
440C22×Q8—91no—
441C2×SD16—31no—
442C2×SD16—91no—
443C2×SD16D3211yescharacteristic
444C22×C8—31no—
445C22×C8—91no—
446C4⋊Q8—91no—
447C4⋊Q8—91no—
448C4⋊Q8—181no—
449#123—181no—
450#123—181no—
451C22⋊Q8—31no—
452C22⋊Q8—91no—
453C22⋊Q8—181no—
454C22⋊Q8—181no—
455C22⋊Q8—181no—
456#121—31no—
457#121—31no—
458C4×Q8—91no—
459C4×D4—91no—
460C4×D4—91no—
461C4×D4—181no—
462C2×C4⋊C4—91no—
463C2×C4⋊C4—91no—
464#106—31no—
465#106—91no—
466#106—91no—
467C4⋊C8—91no—
468#103—31no—
469#103—31no—
470#103—31no—
471#103—91no—
472#103—91no—
473#103—91no—
474#103—91no—
475#103—91no—
476#103—91no—
477#102—31no—
478C22⋊C8—31no—
479C22⋊C8—91no—
480C4×C8—91no—
481C23×C3—21no—
482C23×C3—21no—
483C23×C3—31no—
484C23×C3—31no—
485C23×C3—41no—
486C22×D3D3×D411yescharacteristic
487C22×D3D3×D411yescharacteristic
488C3×Q8—21no—
489C3×Q8—21no—
490C3×Q8—21no—
491C3×Q8—21no—
492C3×Q8—32no—
493C3×Q8—41no—
494C3×Q8—41no—
495C3×Q8—61no—
496C3×Q8—122no—
497C3×D4—22no—
498C3×D4—21no—
499C3×D4—21no—
500C3×D4—21no—
501C3×D4—21no—
502C3×D4—41no—
503C3×D4—122no—
504C3×D4—122no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—31no—
509C2×C3×C4—31no—
510C2×C3×C4—41no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—122no—
520C2×C3×C4C23×D311yescharacteristic
521C2×C3×C4C23×D311yescharacteristic
522#67—34no—
523#67—34no—
524#67—42no—
525#67—42no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—31no—
531C2×Dic3—31no—
532C2×Dic3—31no—
533C2×Dic3—31no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—121no—
541C2×Dic3—121no—
542C2×Dic3—122no—
543C2×Dic3—122no—
544C2×Dic3—122no—
545C2×Dic3—122no—
546C2×Dic3—122no—
547C2×Dic3—242no—
548C2×Dic3D3×D411yescharacteristic
549C2×Dic3D3×D411yescharacteristic
550C4×D3—21no—
551C4×D3—21no—
552C4×D3—21no—
553C4×D3—21no—
554C4×D3—42no—
555C4×D3—122no—
556C4×D3—122no—
557C4×D3—122no—
558Dic6—21no—
559Dic6—42no—
560Dic6—61no—
561Dic6—61no—
562Dic6—61no—
563Dic6—61no—
564Dic6—121no—
565Dic6—121no—
566Dic6—122no—
567Dic6—122no—
568Dic6—122no—
569Dic6—122no—
570Dic6#23712yescomplemented
571C3×C8—21no—
572C3×C8—21no—
573C3×C8—41no—
574C3×C8—61no—
575C3×C8—61no—
576C3⋊C8—21no—
577C3⋊C8—21no—
578C3⋊C8—61no—
579C3⋊C8—61no—
580C3⋊C8—121no—
581C2×C32—81no—
582C2×C32#54611yescharacteristic
583C2×C32C22×SD1611yescharacteristic
584C2×C32#57811yescharacteristic
585C3×D3—22no—
586C3×D3—22no—
587#41—364no—
588C2×Q8—31no—
589C2×Q8—61no—
590C2×Q8—62no—
591C2×Q8—91no—
592C2×Q8—121no—
593C2×Q8—181no—
594C2×Q8—181no—
595C2×Q8—182no—
596C2×Q8—361no—
597C2×Q8C2×D3211yescharacteristic
598C2×D4—61no—
599C2×D4—61no—
600C2×D4—91no—
601C2×D4C2×D3211yescharacteristic
602C22×C4—31no—
603C22×C4—31no—
604C22×C4—61no—
605C22×C4—181no—
606C22×C4—181no—
607C22×C4—181no—
608C22×C4—181no—
609SD16—41no—
610SD16—62no—
611SD16—361no—
612C2×C8—31no—
613C2×C8—31no—
614C2×C8—91no—
615C2×C8—121no—
616C2×C8—361no—
617C2×C8C2×D3211yescharacteristic
618C4⋊C4—31no—
619C4⋊C4—31no—
620C4⋊C4—31no—
621C4⋊C4—61no—
622C4⋊C4—91no—
623C4⋊C4—91no—
624C4⋊C4—181no—
625C4⋊C4—181no—
626C4⋊C4—181no—
627C4⋊C4—181no—
628C4⋊C4—181no—
629C4⋊C4—181no—
630C4⋊C4—181no—
631C22⋊C4—61no—
632C22⋊C4—61no—
633C22⋊C4—61no—
634C22⋊C4—91no—
635C22⋊C4—91no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C42—91no—
639C42—181no—
640C22×C3—21no—
641C22×C3—32no—
642C22×C3—32no—
643C22×C3—42no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—61no—
651C22×C3—61no—
652C22×C3—61no—
653C22×C3—61no—
654C22×C3—81no—
655C22×C3—81no—
656C22×C3C2×D3×D411yescharacteristic
657C22×C3C2×D3×D411yescharacteristic
658C2×D3—21no—
659C2×D3—21no—
660C2×D3—21no—
661C2×D3—21no—
662C2×D3D3×SD1612yes—
663C2×D3D3×SD1612yes—
664C3×C4—21no—
665C3×C4—21no—
666C3×C4—41no—
667C3×C4—41no—
668C3×C4—61no—
669C3×C4—62no—
670C3×C4—61no—
671C3×C4—81no—
672C3×C4—121no—
673C3×C4—121no—
674C3×C4—121no—
675C3×C4C2×#23711yescharacteristic
676C3×C4#100411yescharacteristic
677C3×C4#100411yescharacteristic
678C3×C4D3×#4111yescharacteristic
679Dic3—22no—
680Dic3—21no—
681Dic3—21no—
682Dic3—32no—
683Dic3—32no—
684Dic3—41no—
685Dic3—41no—
686Dic3—41no—
687Dic3—62no—
688Dic3—61no—
689Dic3—61no—
690Dic3—121no—
691Dic3—121no—
692Dic3—121no—
693Dic3—121no—
694Dic3—121no—
695Dic3—241no—
696Dic3—241no—
697C32#329811yescharacteristic, complemented, Sylow
698C23—21no—
699C23—31no—
700C23—31no—
701Q8—21no—
702Q8—21no—
703Q8—32no—
704Q8—61no—
705Q8—122no—
706Q8—181no—
707Q8—181no—
708Q8—362no—
709Q8—362no—
710D4—21no—
711D4—21no—
712D4—94no—
713D4—122no—
714D4—122no—
715C2×C4—21no—
716C2×C4—31no—
717C2×C4—31no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—91no—
727C2×C4—91no—
728C2×C4—122no—
729C2×C4—181no—
730C2×C4—181no—
731C2×C4—362no—
732C2×C4—362no—
733C2×C4—362no—
734C2×C4—362no—
735C2×C4C22×D3211yescharacteristic
736C8—21no—
737C8—61no—
738C8—61no—
739C8—181no—
740C2×C3—21no—
741C2×C3—21no—
742C2×C3—21no—
743C2×C3—62no—
744C2×C3—62no—
745C2×C3—82no—
746C2×C3—81no—
747C2×C3—81no—
748C2×C3#559111yescharacteristic
749C2×C3#561011yescharacteristic
750C2×C3C2×D3×SD1611yescharacteristic
751C2×C3C2×D3×SD1611yescharacteristic
752C2×C3#577111yescharacteristic
753C2×C3#577911yescharacteristic
754D3—22no—
755D3—22no—
756C22—32no—
757C22—32no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—61no—
762C22—61no—
763C22—61no—
764C22—61no—
765C22D32×D411yescharacteristic
766C4—41no—
767C4—61no—
768C4—61no—
769C4—62no—
770C4—92no—
771C4—121no—
772C4—121no—
773C4—121no—
774C4—181no—
775C4—361no—
776C4—361no—
777C4D3×#23711yescharacteristic
778C4#6433011yescharacteristic
779C3—21no—
780C3#8004911yescharacteristic, complemented
781C3#8068911yescharacteristic, complemented
782C2—62no—
783C2—62no—
784C2—81no—
785C2D32×SD1611yescharacteristic
786C2#1059475611yescharacteristic
787C2#1059529011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
prime radical#10595134C2
hypercenterC2×SD16D32
hypocenterC32#3298
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. #10595400C2semidirect
3. #10592861C2semidirect
4. C3×#5171C2semidirect
5. C3×#5170C2semidirect
6. #10591549C2semidirect
7. D3×#835C2semidirect
8. #10591538C2semidirect
9. #10591517C2semidirect
10. #10591460C2semidirect
11. #10591445C2semidirect
12. #10590816C2semidirect
13. #10590717C2semidirect
14. #10590674C2semidirect
15. D3×#816C2semidirect
68. #5171D3semidirect
70. #5170D3semidirect
270. C3×Dic6#41semidirect
273. #625SD16semidirect
570. Dic6#237semidirect
697. C32#3298semidirect
780. C3#80049semidirect
781. C3#80689semidirect

Maximal subgroups

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

subgroupindex
#105954002
#105951342
#105928612
C3×#51712
C3×#51702
#105915492
D3×#8352
#105915382
#105915172
#105914602
#105914452
#105908162
#105907172
#105906742
D3×#8162
#806893
#800493