Finite Group Databasebeta

← #11889268

Subgroups — #11889268

Order 1152.

898 conjugacy classes of subgroups.

The subgroup lattice has 811 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595411C211yesmaximal, characteristic, complemented
2#10595243C211yesmaximal, characteristic
3#10592868C211yesmaximal, characteristic, complemented
4C3×#5171C211yesmaximal, characteristic, complemented
5C3×#5166C211yesmaximal, characteristic, complemented
6#10591657C211yesmaximal, characteristic, complemented
7#10591600C211yesmaximal, characteristic, complemented
8#10591540C211yesmaximal, characteristic, complemented
9#10591488C211yesmaximal, characteristic, complemented
10#10591426C211yesmaximal, characteristic, complemented
11#10591422C211yesmaximal, characteristic, complemented
12#10590759C211yesmaximal, characteristic, complemented
13#10590727C211yesmaximal, characteristic, complemented
14#10590713C211yesmaximal, characteristic, complemented
15#10590690C211yesmaximal, characteristic, complemented
16#80686—31nomaximal
17#80617—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20C2×C32×SD16C2211yescharacteristic
21#64155C2211yescharacteristic
22C2×#3755C2211yescharacteristic
23C3×#946C2211yescharacteristic, complemented
24C3×Q8×Dic3C2211yescharacteristic, complemented
25C2×C3×#216C2211yescharacteristic, complemented
26C3×#938C2211yescharacteristic
27C3×#936C2211yescharacteristic
28C2×C3×D3×C8C2211yescharacteristic, complemented
29#63981—21no—
30#63975—21no—
31#63974—21no—
32#63958—21no—
33#63918C2211yescharacteristic, complemented
34C4×#626C2211yescharacteristic
35#63894C2211yescharacteristic
36#63871C2211yescharacteristic
37#63858—21no—
38#63852—21no—
39#63849C2211yescharacteristic
40#63848—21no—
41#63841C2211yescharacteristic, complemented
42#63837—21no—
43C2×#3712C2211yescharacteristic
44#63659C2211yescharacteristic
45#63648C2211yescharacteristic
46#63647C2211yescharacteristic
47C3×#835C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#817C2211yescharacteristic, complemented
51C3×#816C2211yescharacteristic, complemented
52C3×Dic3⋊C8C2211yescharacteristic, complemented
53#63576C2211yescharacteristic, complemented
54#63573C2211yescharacteristic, complemented
55#63566C2211yescharacteristic, complemented
56#63565C2211yescharacteristic, complemented
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60#63554C2211yescharacteristic, complemented
61#5676—31no—
62#5641—31no—
63#5612—31no—
64#5584—31no—
65C3×#465—31no—
66C3×#464—31no—
67#5189—31no—
68#5187—31no—
69#5171D311yescharacteristic, complemented
70#5169—31no—
71#5169—31no—
72#5169—61no—
73#5166D311yescharacteristic, complemented
74#5113—31no—
75#5111—31no—
76#5055—31no—
77#5047—31no—
78#5035—31no—
79#5026—31no—
80#4870—31no—
81#4868—31no—
82#4842—31no—
83#4836—31no—
84#4817—31no—
85#4816—31no—
86#4815—31no—
87#4804—31no—
88#4779—31no—
89#4770—31no—
90#4770—31no—
91#4765—31no—
92C23×C3⋊D3—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C2×#638—21no—
96D4×C3⋊D3—22no—
97D4×C3⋊D3—41no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4×C3⋊D3C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×Dic6C2311yescharacteristic
103C2×#627—21no—
104C2×#626—21no—
105C2×#626D411yescharacteristic
106C2×#624—21no—
107C2×#624—21no—
108#3799—22no—
109#3799—41no—
110C32×SD16—41no—
111C2×C32×C8C2311yescharacteristic
112#3755—22no—
113#3752—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115#3750—21no—
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C3×#217—21no—
118C3×#217—21no—
119C3×#217—21no—
120C3×#216—41no—
121C3×(C2×D3)⋊C4—21no—
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×C4×Dic3—21no—
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×D3×C8—41no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3D411yescharacteristic
135#3722—21no—
136#3722—21no—
137#3722—21no—
138#3722D411yescharacteristic
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3D411yescharacteristic
141Dic32—21no—
142Dic32—21no—
143#3712—41no—
144#3311—91noSylow
145C2×#239—31no—
146C2×D3×D4—31no—
147C2×D3×D4—31no—
148C2×D3×D4—61no—
149C2×#235—31no—
150C2×C3×Q16—31no—
151C2×C3×SD16—21no—
152C2×C3×SD16C2×D311yescharacteristic
153C2×C3×SD16C2×D311yescharacteristic
154C22×C3×C8—31no—
155C3×#124—31no—
156C3×C22⋊Q8—31no—
157C3×#121—31no—
158C3×C4×Q8—31no—
159#946—31no—
160#946—31no—
161#946—31no—
162#946—61no—
163#946C2×D311yescharacteristic, complemented
164Q8×Dic3C2×D311yescharacteristic, complemented
165C2×#216C2×D311yescharacteristic, complemented
166C2×#215—31no—
167C2×#215—31no—
168C2×#215—61no—
169#938—61no—
170#938C2×D311yescharacteristic
171#937—61no—
172#936C2×D311yescharacteristic
173C4×#67—31no—
174#926—31no—
175C2×ΓL(1,𝔽25)—31no—
176C2×ΓL(1,𝔽25)—31no—
177C2×D3×C8C2×D311yescharacteristic, complemented
178#898—61no—
179#898—61no—
180#898—61no—
181#897—31no—
182#893—31no—
183#892—31no—
184#892—31no—
185#892—31no—
186#888—31no—
187#887—61no—
188#885—61no—
189#884—61no—
190#883—61no—
191#883—61no—
192#882—61no—
193D3×C22⋊C4—61no—
194D3×C22⋊C4—61no—
195#879—61no—
196#875—61no—
197C4×D12—31no—
198C4×D12—31no—
199#869—31no—
200C4×Dic6—61no—
201C3×#106—31no—
202C3×C4⋊C8—31no—
203C3×#103—31no—
204C3×#103—31no—
205C3×#102—31no—
206C3×#102—31no—
207#835—31no—
208#835—31no—
209#835C2×D311yescharacteristic, complemented
210#832—31no—
211#832—31no—
212#832—61no—
213#832C2×D311yescharacteristic
214#832C2×D311yescharacteristic
215#830—31no—
216#821—31no—
217#821—31no—
218#821—31no—
219#821—31no—
220#821—61no—
221(C2×D3)⋊C8—31no—
222(C2×D3)⋊C8—31no—
223(C2×D3)⋊C8—31no—
224(C2×D3)⋊C8—61no—
225#817—31no—
226#817C2×D311yescharacteristic, complemented
227#816—31no—
228#816C2×D311yescharacteristic, complemented
229#815—31no—
230Dic3⋊C8C2×D311yescharacteristic, complemented
231#810—31no—
232#809—31no—
233#809—31no—
234#808—31no—
235#807—31no—
236#807—31no—
237#803—31no—
238C23×C32—21no—
239C22×C3⋊D3—21no—
240C22×C3⋊D3—42no—
241C22×C3⋊D3—42no—
242C22×C3⋊D3—81no—
243C22×C3⋊D3C2×D411yescharacteristic
244C22×C3×D3C2×D411yescharacteristic
245C32×Q8—21no—
246C32×Q8—21no—
247C32×D4—21no—
248C32×D4—21no—
249C2×C32×C4—21no—
250C2×C32×C4C2411yescharacteristic
251#638—42no—
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3C2×D411yescharacteristic
254C4⋊(C3⋊D3)—21no—
255C4⋊(C3⋊D3)#4112yes—
256C4×C3⋊D3—21no—
257C4×C3⋊D3—21no—
258C3×#67—81no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270#627—42no—
271#626—41no—
272#626—42no—
273#624—42no—
274#624—81no—
275C32×C8—21no—
276C3⋊(C3⋊C8)—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#556—91no—
280#546—91no—
281#489—91no—
282#485—91no—
283#482—91no—
284#476—91no—
285#470—91no—
286#465—31no—
287#464—31no—
288#452—91no—
289#450—91no—
290#440—91no—
291#435—91no—
292#418—91no—
293#416—91no—
294C23×D3—61no—
295C23×D3—61no—
296C23×D3—121no—
297C2×C3×Q8—21no—
298C2×C3×Q8—31no—
299C2×C3×Q8C22×D311yescharacteristic
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×D4—21no—
302C2×C3×D4—61no—
303C2×C3×D4C22×D311yescharacteristic
304C2×C3×D4C22×D311yescharacteristic
305C22×C3×C4—31no—
306C2×#67—21no—
307C2×#67—31no—
308C2×#67—61no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—121no—
312#239—62no—
313#239—121no—
314D3×D4—62no—
315D3×D4—62no—
316D3×D4—122no—
317D3×D4—121no—
318D3×D4—121no—
319D3×D4—122no—
320#235—62no—
321#235—121no—
322C2×D12—31no—
323C2×D12—31no—
324C2×D12—31no—
325C2×D12—61no—
326C2×D12—61no—
327C2×C4×D3—31no—
328C2×C4×D3—31no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3C22×D311yescharacteristic
335C2×Dic6—61no—
336C2×Dic6—61no—
337C2×Dic6C22×D311yescharacteristic
338C3×Q16—121no—
339C3×SD16—41no—
340C3×SD16—41no—
341C3×SD16—42no—
342C2×C3×C8—21no—
343C2×C3×C8—31no—
344C2×C3×C8—31no—
345C2×C3×C8—121no—
346C2×C3×C8C22×D311yescharacteristic
347C2×C3×C8C22×D311yescharacteristic
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4—61no—
353C3×C22⋊C4—61no—
354C3×C22⋊C4—61no—
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C42—31no—
358C3×C42—61no—
359#217—21no—
360#217—21no—
361#217—21no—
362#217—31no—
363#217—61no—
364#216—41no—
365#215—62no—
366#215—62no—
367#215—122no—
368(C2×D3)⋊C4—21no—
369(C2×D3)⋊C4—31no—
370(C2×D3)⋊C4—31no—
371(C2×D3)⋊C4—31no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—121no—
382C4⋊Dic3—21no—
383C4⋊Dic3—31no—
384C4⋊Dic3—31no—
385C4⋊Dic3—31no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3—61no—
389C4⋊Dic3C22×D311yescharacteristic
390C4⋊Dic3C22×D311yescharacteristic
391C4⋊Dic3C22×D311yescharacteristic
392Dic3⋊C4—21no—
393Dic3⋊C4—31no—
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×Dic3—61no—
403C4×Dic3—61no—
404C4×Dic3C22×D311yescharacteristic
405C2×C3⋊C8—31no—
406C2×C3⋊C8—31no—
407C2×C3⋊C8—61no—
408C2×C3⋊C8C22×D311yescharacteristic
409C2×C3⋊C8C22×D311yescharacteristic
410ΓL(1,𝔽25)—121no—
411ΓL(1,𝔽25)—121no—
412D3×C8—41no—
413C22×C32—41no—
414C22×C32—41no—
415C22×C32—41no—
416C22×C32C22×D411yescharacteristic
417C2×C3⋊D3—21no—
418C2×C3⋊D3—22no—
419C2×C3⋊D3—21no—
420C2×C3⋊D3—21no—
421C2×C3⋊D3—41no—
422C2×C3⋊D3—41no—
423C2×C3⋊D3—84no—
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C2×C3×D3—21no—
427C32×C4—41no—
428C32×C4C2×#4111yescharacteristic
429C32×C4H(5,𝔽2)11yescharacteristic
430C3⋊Dic3—21no—
431C3⋊Dic3—41no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C3×Dic3—41no—
439C2×#41—91no—
440C22×D4—91no—
441C2×Q16—31no—
442C2×SD16—91no—
443C2×SD16D3211yescharacteristic
444C2×M16—91no—
445C22×C8—31no—
446C4⋊Q8—91no—
447#126—181no—
448#126—181no—
449#124—31no—
450#124—181no—
451#123—181no—
452C22⋊Q8—31no—
453C22⋊Q8—91no—
454C22⋊Q8—91no—
455#121—31no—
456#121—181no—
457#120—181no—
458C4×Q8—31no—
459C4×Q8—181no—
460C4×D4—91no—
461C4×D4—91no—
462#117—91no—
463#117—91no—
464C2×C22⋊C4—181no—
465#107—91no—
466#106—31no—
467#106—91no—
468C4⋊C8—31no—
469#103—31no—
470#103—31no—
471#103—91no—
472#103—91no—
473#102—31no—
474#102—31no—
475#102—91no—
476#102—91no—
477#102—91no—
478#102—91no—
479C22⋊C8—91no—
480C22⋊C8—91no—
481#97—91no—
482C23×C3—21no—
483C23×C3—21no—
484C23×C3—31no—
485C23×C3—41no—
486C22×D3—31no—
487C22×D3—31no—
488C22×D3—61no—
489C22×D3—61no—
490C22×D3—61no—
491C22×D3—121no—
492C22×D3—122no—
493C22×D3—122no—
494C22×D3—122no—
495C22×D3—122no—
496C22×D3—124no—
497C22×D3—242no—
498C22×D3—241no—
499C22×D3—241no—
500C22×D3—242no—
501C22×D3D3×D411yescharacteristic
502C3×Q8—21no—
503C3×Q8—21no—
504C3×Q8—21no—
505C3×Q8—21no—
506C3×Q8—41no—
507C3×Q8—41no—
508C3×Q8—61no—
509C3×Q8—61no—
510C3×D4—22no—
511C3×D4—21no—
512C3×D4—21no—
513C3×D4—21no—
514C3×D4—21no—
515C3×D4—41no—
516C3×D4—241no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—31no—
521C2×C3×C4—31no—
522C2×C3×C4—31no—
523C2×C3×C4—41no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4C23×D311yescharacteristic
531C2×C3×C4C23×D311yescharacteristic
532#67—81no—
533#67—121no—
534#67—122no—
535#67—122no—
536#67—122no—
537#67—124no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—31no—
543C2×Dic3—31no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—121no—
548C2×Dic3D3×D411yescharacteristic
549C2×Dic3D3×D411yescharacteristic
550C2×Dic3D3×D411yescharacteristic
551D12—32no—
552D12—32no—
553D12—62no—
554D12—61no—
555D12—61no—
556D12—121no—
557D12—121no—
558D12—122no—
559C4×D3—21no—
560C4×D3—21no—
561C4×D3—61no—
562C4×D3—61no—
563C4×D3—61no—
564C4×D3—61no—
565C4×D3—121no—
566C4×D3—121no—
567C4×D3—122no—
568C4×D3—122no—
569C4×D3—241no—
570C4×D3—241no—
571Dic6—21no—
572Dic6—21no—
573Dic6—122no—
574Dic6—122no—
575C3×C8—21no—
576C3×C8—21no—
577C3×C8—41no—
578C3×C8—61no—
579C3×C8—61no—
580C3⋊C8—21no—
581C3⋊C8—21no—
582C3⋊C8—61no—
583C3⋊C8—61no—
584C3⋊C8—121no—
585C2×C32—81no—
586C2×C32#54611yescharacteristic
587C2×C32#57511yescharacteristic
588C2×C32#57711yescharacteristic
589C3⋊D3—41no—
590C3⋊D3—42no—
591C3×D3—41no—
592C24—181no—
593#41—182no—
594#41—361no—
595C2×Q8—31no—
596C2×Q8—181no—
597C2×Q8C2×D3211yescharacteristic
598C2×D4—61no—
599C2×D4—91no—
600C2×D4—91no—
601C2×D4—181no—
602C2×D4—181no—
603C2×D4—182no—
604C2×D4—361no—
605C2×D4C2×D3211yescharacteristic
606C22×C4—31no—
607C22×C4—91no—
608C22×C4—181no—
609C22×C4—181no—
610Q16—121no—
611SD16—41no—
612SD16—182no—
613M16—361no—
614C2×C8—31no—
615C2×C8—31no—
616C2×C8—91no—
617C2×C8—121no—
618C2×C8C2×D3211yescharacteristic
619C4⋊C4—31no—
620C4⋊C4—31no—
621C4⋊C4—31no—
622C4⋊C4—61no—
623C4⋊C4—61no—
624C4⋊C4—91no—
625C4⋊C4—91no—
626C4⋊C4—181no—
627C4⋊C4—181no—
628C4⋊C4—181no—
629C22⋊C4—61no—
630C22⋊C4—61no—
631C22⋊C4—61no—
632C22⋊C4—61no—
633C22⋊C4—91no—
634C22⋊C4—91no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C42—31no—
641C42—61no—
642C42—181no—
643C42—181no—
644C22×C3—21no—
645C22×C3—42no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—61no—
653C22×C3—61no—
654C22×C3—61no—
655C22×C3—81no—
656C22×C3—81no—
657C22×C3C2×D3×D411yescharacteristic
658C22×C3C2×D3×D411yescharacteristic
659C2×D3—21no—
660C2×D3—21no—
661C2×D3—21no—
662C2×D3—62no—
663C2×D3—61no—
664C2×D3—61no—
665C2×D3—61no—
666C2×D3—61no—
667C2×D3—61no—
668C2×D3—62no—
669C2×D3—61no—
670C2×D3—62no—
671C2×D3—121no—
672C2×D3—121no—
673C2×D3—122no—
674C2×D3—121no—
675C2×D3—121no—
676C2×D3—121no—
677C2×D3—121no—
678C2×D3—241no—
679C2×D3—241no—
680C2×D3—244no—
681C2×D3—244no—
682C2×D3—248no—
683C3×C4—21no—
684C3×C4—21no—
685C3×C4—41no—
686C3×C4—41no—
687C3×C4—61no—
688C3×C4—61no—
689C3×C4—61no—
690C3×C4—81no—
691C3×C4—121no—
692C3×C4—121no—
693C3×C4—121no—
694C3×C4—121no—
695C3×C4#100411yescharacteristic
696C3×C4#100411yescharacteristic
697C3×C4D3×#4111yescharacteristic
698C3×C4D3×#4111yescharacteristic
699Dic3—21no—
700Dic3—21no—
701Dic3—21no—
702Dic3—41no—
703Dic3—41no—
704Dic3—41no—
705Dic3—41no—
706Dic3—61no—
707Dic3—61no—
708Dic3—121no—
709Dic3—121no—
710Dic3—121no—
711Dic3—241no—
712C32#331111yescharacteristic, complemented, Sylow
713C23—21no—
714C23—31no—
715C23—91no—
716C23—181no—
717C23—362no—
718C23—362no—
719C23—721no—
720Q8—21no—
721Q8—21no—
722Q8—61no—
723Q8—61no—
724Q8—362no—
725D4—21no—
726D4—21no—
727D4—92no—
728D4—181no—
729D4—241no—
730D4—361no—
731D4—362no—
732D4—362no—
733C2×C4—21no—
734C2×C4—31no—
735C2×C4—31no—
736C2×C4—31no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—91no—
744C2×C4—181no—
745C2×C4—181no—
746C2×C4—181no—
747C2×C4—362no—
748C2×C4—721no—
749C2×C4C22×D3211yescharacteristic
750C8—21no—
751C8—61no—
752C8—61no—
753C8—181no—
754C2×C3—21no—
755C2×C3—21no—
756C2×C3—21no—
757C2×C3—82no—
758C2×C3—81no—
759C2×C3—81no—
760C2×C3—121no—
761C2×C3#561011yescharacteristic
762C2×C3#561211yescharacteristic
763C2×C3#576211yescharacteristic
764C2×C3#576811yescharacteristic
765C2×C3#577011yescharacteristic
766C2×C3#577711yescharacteristic
767D3—41no—
768D3—122no—
769D3—121no—
770D3—122no—
771D3—121no—
772D3—122no—
773D3—242no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—61no—
778C22—61no—
779C22—61no—
780C22—181no—
781C22—181no—
782C22—181no—
783C22—182no—
784C22—361no—
785C22—361no—
786C22—724no—
787C22D32×D411yescharacteristic
788C4—41no—
789C4—61no—
790C4—61no—
791C4—61no—
792C4—121no—
793C4—121no—
794C4—121no—
795C4—121no—
796C4—181no—
797C4—361no—
798C4#6431211yescharacteristic
799C4#6433011yescharacteristic
800C3—21no—
801C3#8061711yescharacteristic, complemented
802C3#8068611yescharacteristic, complemented
803C2—81no—
804C2—121no—
805C2—361no—
806C2—362no—
807C2#1059474611yescharacteristic
808C2#1059475311yescharacteristic
809C2#1059529611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
prime radical#10595243C2
hypercenterC2×SD16D32
hypocenterC32#3311
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. #10595411C2semidirect
3. #10592868C2semidirect
4. C3×#5171C2semidirect
5. C3×#5166C2semidirect
6. #10591657C2semidirect
7. #10591600C2semidirect
8. #10591540C2semidirect
9. #10591488C2semidirect
10. #10591426C2semidirect
11. #10591422C2semidirect
12. #10590759C2semidirect
13. #10590727C2semidirect
14. #10590713C2semidirect
15. #10590690C2semidirect
23. C3×#946C22semidirect
24. C3×Q8×Dic3C22semidirect
25. C2×C3×#216C22semidirect
28. C2×C3×D3×C8C22semidirect
33. #63918C22semidirect
41. #63841C22semidirect
47. C3×#835C22semidirect
50. C3×#817C22semidirect
51. C3×#816C22semidirect
52. C3×Dic3⋊C8C22semidirect
53. #63576C22semidirect
54. #63573C22semidirect
55. #63566C22semidirect
56. #63565C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. #63554C22semidirect
69. #5171D3semidirect
73. #5166D3semidirect
163. #946C2×D3semidirect
164. Q8×Dic3C2×D3semidirect
165. C2×#216C2×D3semidirect
177. C2×D3×C8C2×D3semidirect
209. #835C2×D3semidirect
226. #817C2×D3semidirect
228. #816C2×D3semidirect
230. Dic3⋊C8C2×D3semidirect
712. C32#3311semidirect
801. C3#80617semidirect
802. C3#80686semidirect

Maximal subgroups

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

subgroupindex
#105954112
#105952432
#105928682
C3×#51712
C3×#51662
#105916572
#105916002
#105915402
#105914882
#105914262
#105914222
#105907592
#105907272
#105907132
#105906902
#806863
#806173