Finite Group Databasebeta

← #11889270

Subgroups — #11889270

Order 1152.

860 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595413C211yesmaximal, characteristic, complemented
2#10595228C211yesmaximal, characteristic
3#10592865C211yesmaximal, characteristic, complemented
4C3×#5171C211yesmaximal, characteristic, complemented
5C3×#5169C211yesmaximal, characteristic, complemented
6#10591655C211yesmaximal, characteristic, complemented
7#10591598C211yesmaximal, characteristic, complemented
8#10591572C211yesmaximal, characteristic, complemented
9#10591496C211yesmaximal, characteristic, complemented
10#10591423C211yesmaximal, characteristic, complemented
11#10591421C211yesmaximal, characteristic, complemented
12#10590954C211yesmaximal, characteristic, complemented
13#10590776C211yesmaximal, characteristic, complemented
14#10590723C211yesmaximal, characteristic, complemented
15#10590709C211yesmaximal, characteristic, complemented
16#80686—31nomaximal
17#80162—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20C2×C32×SD16C2211yescharacteristic
21Q8×C3⋊Dic3C2211yescharacteristic, complemented
22C2×#3756C2211yescharacteristic, complemented
23#64145C2211yescharacteristic
24C3×#946C2211yescharacteristic
25C3×#946C2211yescharacteristic, complemented
26C2×C3×#215C2211yescharacteristic
27C3×#938C2211yescharacteristic
28C2×C3×D3×C8C2211yescharacteristic, complemented
29#63976—21no—
30#63970—21no—
31#63969—21no—
32D3×#217—21no—
33#63919C2211yescharacteristic, complemented
34#63915—21no—
35C4×#625C2211yescharacteristic
36#63898C2211yescharacteristic
37#63861—21no—
38#63861—21no—
39#63857C2211yescharacteristic
40#63841C2211yescharacteristic
41#63841C2211yescharacteristic, complemented
42#63838—21no—
43C2×#3711C2211yescharacteristic
44#63659C2211yescharacteristic
45#63643C2211yescharacteristic, complemented
46#63641C2211yescharacteristic, complemented
47C3×#835C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×#817C2211yescharacteristic, complemented
53#63575C2211yescharacteristic, complemented
54#63574C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63567C2211yescharacteristic, complemented
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60#63555C2211yescharacteristic, complemented
61#5806—31no—
62#5641—31no—
63#5641—31no—
64#5612—31no—
65C3×#465—31no—
66C3×#450—31no—
67#5215—31no—
68#5173—31no—
69#5171D311yescharacteristic, complemented
70#5169D311yescharacteristic, complemented
71#5166—31no—
72#5166—31no—
73#5166—61no—
74#5164—31no—
75#5113—31no—
76#5111—31no—
77#5052—31no—
78#5047—31no—
79#5035—31no—
80#4870—31no—
81#4868—31no—
82#4817—31no—
83#4816—31no—
84#4784—31no—
85#4772—31no—
86#4770—31no—
87#4765—31no—
88#4765—31no—
89#4761—31no—
90#4728—31no—
91#4723—31no—
92C23×C3×D3—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C2×#634C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C3×D3×D4—22no—
99C3×D3×D4—41no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×C4×D3C2311yescharacteristic
103C2×#627—21no—
104C2×#625—21no—
105C2×#625D411yescharacteristic
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108#3795—22no—
109#3795—41no—
110C32×SD16—41no—
111C2×C32×C8C2311yescharacteristic
112#3757—21no—
113#3757—21no—
114#3756—41no—
115C4⋊(C3⋊Dic3)—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C4×C3⋊Dic3—21no—
118C4×C3⋊Dic3C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C3×#217—21no—
121C3×#215—22no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×D3×C8—41no—
132#3724—21no—
133#3724D411yescharacteristic
134Dic3⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3D411yescharacteristic
140(C2×D3)⋊Dic3D411yescharacteristic
141Dic32—21no—
142Dic32—21no—
143#3711—41no—
144#3311—91noSylow
145C22×C3×D4—31no—
146C2×#237—31no—
147C2×D3×D4C2×D311yescharacteristic
148C2×#235—31no—
149C2×C3×SD16—21no—
150C2×C3×SD16—31no—
151C2×C3×SD16C2×D311yescharacteristic
152C2×C3×SD16C2×D311yescharacteristic
153C22×C3×C8—31no—
154C3×C22⋊Q8—31no—
155C3×C22⋊Q8—31no—
156C3×#121—31no—
157#953—61no—
158C2×#217—61no—
159#946C2×D311yescharacteristic
160#946C2×D311yescharacteristic, complemented
161Q8×Dic3—31no—
162Q8×Dic3—31no—
163Q8×Dic3—61no—
164C2×#216—31no—
165C2×#216—31no—
166C2×#216—61no—
167C2×#215C2×D311yescharacteristic
168#939—61no—
169#938—61no—
170#938C2×D311yescharacteristic
171#937—61no—
172#936—31no—
173#936—31no—
174#936—61no—
175#935—61no—
176D4×Dic3—31no—
177C4×#67—31no—
178C4×#67—31no—
179#926—31no—
180#926—31no—
181#924—31no—
182C2×#208—31no—
183C2×ΓL(1,𝔽25)—31no—
184C2×D3×C8C2×D311yescharacteristic, complemented
185#898—61no—
186#898—61no—
187#897—31no—
188#893—31no—
189#892—31no—
190#892—31no—
191#888—31no—
192#888—31no—
193#887—61no—
194#887—61no—
195#885—61no—
196#885—61no—
197#883—61no—
198D3×C22⋊C4—61no—
199#879—61no—
200#879—61no—
201C3×#106—31no—
202C3×#103—31no—
203C3×#102—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×C22⋊C8—31no—
207#835C2×D311yescharacteristic, complemented
208#832—31no—
209#832—31no—
210#832—31no—
211#832—31no—
212#832—61no—
213#832C2×D311yescharacteristic
214#832C2×D311yescharacteristic
215#830—31no—
216#821—31no—
217#821C2×D311yescharacteristic
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8C2×D311yescharacteristic
220#818—31no—
221#817C2×D311yescharacteristic, complemented
222#816—31no—
223#816—31no—
224#816—31no—
225#816—31no—
226#816—61no—
227#815—31no—
228#815—31no—
229Dic3⋊C8—31no—
230Dic3⋊C8—31no—
231Dic3⋊C8—61no—
232#810—31no—
233#810—31no—
234#809—31no—
235#808—31no—
236#808—31no—
237#807—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
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3C2×D411yescharacteristic
254C2×C3⋊Dic3C2×D411yescharacteristic
255#634—21no—
256#634—21no—
257C3×#67—42no—
258C3×#67—81no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C3×D12—21no—
265C3×D12#4112yes—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270#627—42no—
271#625—41no—
272#625—42no—
273D3×Dic3—42no—
274D3×Dic3—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—91no—
288#452—91no—
289#450—31no—
290#440—91no—
291#435—91no—
292#418—91no—
293#416—91no—
294C24×C3—61no—
295C23×D3—21no—
296C2×C3×Q8—21no—
297C2×C3×Q8C22×D311yescharacteristic
298C2×C3×Q8C22×D311yescharacteristic
299C2×C3×D4—21no—
300C2×C3×D4—31no—
301C2×C3×D4—61no—
302C2×C3×D4—62no—
303C2×C3×D4—61no—
304C2×C3×D4—121no—
305C2×C3×D4C22×D311yescharacteristic
306C2×C3×D4C22×D311yescharacteristic
307C22×C3×C4—31no—
308C22×C3×C4—31no—
309C2×#67—21no—
310C2×#67—21no—
311C2×#67—31no—
312C2×#67—31no—
313C2×#67—61no—
314C2×#67—61no—
315C22×Dic3—61no—
316C22×Dic3—61no—
317#237—62no—
318#237—121no—
319D3×D4—22no—
320D3×D4—41no—
321#235—62no—
322#235—121no—
323C2×D12C22×D311yescharacteristic
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3C22×D311yescharacteristic
327C2×C4×D3C22×D311yescharacteristic
328C2×Dic6—31no—
329C2×Dic6—31no—
330C2×Dic6—61no—
331C2×Dic6—61no—
332C2×Dic6—61no—
333C3×SD16—41no—
334C3×SD16—41no—
335C3×SD16—42no—
336C3×SD16—62no—
337C2×C3×C8—21no—
338C2×C3×C8—31no—
339C2×C3×C8—31no—
340C2×C3×C8—121no—
341C2×C3×C8C22×D311yescharacteristic
342C2×C3×C8C22×D311yescharacteristic
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C22⋊C4—61no—
351#217—21no—
352#217—31no—
353#217—31no—
354#217—61no—
355#217—61no—
356#217—61no—
357#217—61no—
358#217—61no—
359#217—61no—
360#217—61no—
361#217—61no—
362#217—121no—
363#217—121no—
364#216—121no—
365#216—121no—
366#216—122no—
367#215—22no—
368(C2×D3)⋊C4—21no—
369(C2×D3)⋊C4—21no—
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—
376C4⋊Dic3—31no—
377C4⋊Dic3—31no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3—121no—
383C4⋊Dic3C22×D311yescharacteristic
384C4⋊Dic3C22×D311yescharacteristic
385C4⋊Dic3C22×D311yescharacteristic
386Dic3⋊C4—21no—
387Dic3⋊C4—21no—
388Dic3⋊C4—31no—
389Dic3⋊C4—31no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393C4×Dic3—31no—
394C4×Dic3—31no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3—61no—
402C4×Dic3—121no—
403#208—121no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—61no—
407C2×C3⋊C8C22×D311yescharacteristic
408C2×C3⋊C8C22×D311yescharacteristic
409ΓL(1,𝔽25)—121no—
410D3×C8—41no—
411C22×C32—41no—
412C22×C32—41no—
413C22×C32—41no—
414C22×C32C22×D411yescharacteristic
415C2×C3×D3—22no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—84no—
425C32×C4—41no—
426C32×C4C2×#4111yescharacteristic
427C32×C4H(5,𝔽2)11yescharacteristic
428C3⋊Dic3—21no—
429C3⋊Dic3—21no—
430C3⋊Dic3—41no—
431C3⋊Dic3—41no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C2×#41—91no—
438C22×D4—31no—
439C2×Q16—91no—
440C2×SD16—31no—
441C2×SD16D3211yescharacteristic
442C2×M16—91no—
443C22×C8—31no—
444C4⋊Q8—91no—
445#126—181no—
446#126—181no—
447#124—91no—
448#124—181no—
449#123—181no—
450C22⋊Q8—31no—
451C22⋊Q8—31no—
452C22⋊Q8—91no—
453#121—31no—
454#121—181no—
455#120—181no—
456C4×Q8—91no—
457C4×Q8—181no—
458C4×D4—91no—
459C4×D4—91no—
460#117—91no—
461#117—91no—
462C2×C22⋊C4—181no—
463#107—91no—
464#106—31no—
465#106—91no—
466C4⋊C8—91no—
467#103—31no—
468#103—91no—
469#103—91no—
470#103—91no—
471#102—31no—
472#102—31no—
473#102—31no—
474#102—91no—
475#102—91no—
476#102—91no—
477C22⋊C8—31no—
478C22⋊C8—91no—
479#97—91no—
480C23×C3—21no—
481C23×C3—21no—
482C23×C3—31no—
483C23×C3—31no—
484C23×C3—41no—
485C23×C3—61no—
486C23×C3—122no—
487C23×C3—122no—
488C23×C3—241no—
489C22×D3—21no—
490C22×D3—42no—
491C22×D3—42no—
492C22×D3—81no—
493C22×D3D3×D411yescharacteristic
494C22×D3D3×D411yescharacteristic
495C3×Q8—22no—
496C3×Q8—21no—
497C3×Q8—21no—
498C3×Q8—21no—
499C3×Q8—21no—
500C3×Q8—41no—
501C3×D4—21no—
502C3×D4—21no—
503C3×D4—21no—
504C3×D4—21no—
505C3×D4—32no—
506C3×D4—41no—
507C3×D4—41no—
508C3×D4—61no—
509C3×D4—122no—
510C3×D4—241no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—31no—
515C2×C3×C4—31no—
516C2×C3×C4—41no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4C23×D311yescharacteristic
525C2×C3×C4C23×D311yescharacteristic
526#67—42no—
527#67—81no—
528#67—121no—
529#67—121no—
530#67—122no—
531#67—122no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—31no—
536C2×Dic3—31no—
537C2×Dic3—31no—
538C2×Dic3—31no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—121no—
546C2×Dic3—121no—
547C2×Dic3—122no—
548C2×Dic3—241no—
549C2×Dic3D3×D411yescharacteristic
550C2×Dic3D3×D411yescharacteristic
551D12—21no—
552D12#23712yes—
553C4×D3—21no—
554C4×D3—21no—
555C4×D3—21no—
556C4×D3—21no—
557C4×D3—122no—
558C4×D3—241no—
559Dic6—61no—
560Dic6—61no—
561Dic6—61no—
562Dic6—61no—
563Dic6—121no—
564Dic6—121no—
565Dic6—122no—
566Dic6—122no—
567C3×C8—21no—
568C3×C8—21no—
569C3×C8—41no—
570C3×C8—61no—
571C3×C8—61no—
572C3⋊C8—21no—
573C3⋊C8—21no—
574C3⋊C8—61no—
575C3⋊C8—61no—
576C3⋊C8—121no—
577C2×C32—81no—
578C2×C32#54611yescharacteristic
579C2×C32#57511yescharacteristic
580C2×C32#57711yescharacteristic
581C3×D3—41no—
582C3×D3—41no—
583C3×D3—42no—
584C24—61no—
585#41—182no—
586#41—361no—
587C2×Q8—91no—
588C2×Q8—181no—
589C2×Q8C2×D3211yescharacteristic
590C2×D4—31no—
591C2×D4—61no—
592C2×D4—62no—
593C2×D4—61no—
594C2×D4—91no—
595C2×D4—121no—
596C2×D4—181no—
597C2×D4C2×D3211yescharacteristic
598C22×C4—31no—
599C22×C4—31no—
600C22×C4—181no—
601C22×C4—181no—
602Q16—361no—
603SD16—41no—
604SD16—62no—
605M16—361no—
606C2×C8—31no—
607C2×C8—31no—
608C2×C8—91no—
609C2×C8—121no—
610C2×C8C2×D3211yescharacteristic
611C4⋊C4—31no—
612C4⋊C4—31no—
613C4⋊C4—31no—
614C4⋊C4—61no—
615C4⋊C4—61no—
616C4⋊C4—91no—
617C4⋊C4—91no—
618C4⋊C4—181no—
619C4⋊C4—181no—
620C4⋊C4—181no—
621C22⋊C4—61no—
622C22⋊C4—61no—
623C22⋊C4—61no—
624C22⋊C4—91no—
625C22⋊C4—91no—
626C22⋊C4—181no—
627C22⋊C4—181no—
628C22⋊C4—181no—
629C22⋊C4—181no—
630C22⋊C4—181no—
631C22⋊C4—181no—
632C42—91no—
633C42—181no—
634C42—181no—
635C42—181no—
636C22×C3—21no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—61no—
644C22×C3—61no—
645C22×C3—61no—
646C22×C3—61no—
647C22×C3—61no—
648C22×C3—62no—
649C22×C3—61no—
650C22×C3—81no—
651C22×C3—81no—
652C22×C3—81no—
653C22×C3—121no—
654C22×C3—121no—
655C22×C3—244no—
656C22×C3C2×D3×D411yescharacteristic
657C22×C3C2×D3×D411yescharacteristic
658C2×D3—21no—
659C2×D3—21no—
660C2×D3—21no—
661C2×D3—21no—
662C2×D3—21no—
663C2×D3—22no—
664C2×D3—21no—
665C2×D3—41no—
666C2×D3—41no—
667C2×D3—84no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—42no—
671C3×C4—41no—
672C3×C4—41no—
673C3×C4—61no—
674C3×C4—61no—
675C3×C4—121no—
676C3×C4—121no—
677C3×C4—121no—
678C3×C4C2×#23711yescharacteristic
679C3×C4#100411yescharacteristic
680C3×C4#100411yescharacteristic
681C3×C4D3×#4111yescharacteristic
682Dic3—21no—
683Dic3—21no—
684Dic3—41no—
685Dic3—41no—
686Dic3—41no—
687Dic3—61no—
688Dic3—61no—
689Dic3—61no—
690Dic3—61no—
691Dic3—121no—
692Dic3—121no—
693Dic3—121no—
694Dic3—121no—
695Dic3—121no—
696Dic3—121no—
697Dic3—241no—
698Dic3—241no—
699C32#331111yescharacteristic, complemented, Sylow
700C23—21no—
701C23—31no—
702C23—31no—
703C23—61no—
704C23—122no—
705C23—122no—
706C23—241no—
707Q8—21no—
708Q8—21no—
709Q8—181no—
710Q8—181no—
711Q8—362no—
712D4—21no—
713D4—21no—
714D4—32no—
715D4—61no—
716D4—122no—
717D4—241no—
718D4—361no—
719D4—362no—
720C2×C4—21no—
721C2×C4—31no—
722C2×C4—31no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—91no—
731C2×C4—91no—
732C2×C4—181no—
733C2×C4—181no—
734C2×C4—362no—
735C2×C4—721no—
736C2×C4C22×D3211yescharacteristic
737C8—21no—
738C8—61no—
739C8—61no—
740C8—181no—
741C2×C3—21no—
742C2×C3—21no—
743C2×C3—21no—
744C2×C3—81no—
745C2×C3—81no—
746C2×C3—121no—
747C2×C3—121no—
748C2×C3—122no—
749C2×C3—161no—
750C2×C3#559111yescharacteristic
751C2×C3#561011yescharacteristic
752C2×C3#576211yescharacteristic
753C2×C3#576211yescharacteristic
754C2×C3#576811yescharacteristic
755C2×C3#577311yescharacteristic
756D3—41no—
757D3—42no—
758D3—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—61no—
763C22—61no—
764C22—61no—
765C22—61no—
766C22—61no—
767C22—61no—
768C22—62no—
769C22—121no—
770C22—121no—
771C22—244no—
772C22D32×D411yescharacteristic
773C4—41no—
774C4—61no—
775C4—61no—
776C4—121no—
777C4—121no—
778C4—121no—
779C4—181no—
780C4—181no—
781C4—361no—
782C4—361no—
783C4D3×#23711yescharacteristic
784C4#6433011yescharacteristic
785C3—21no—
786C3#8016211yescharacteristic, complemented
787C3#8068611yescharacteristic, complemented
788C2—81no—
789C2—121no—
790C2—121no—
791C2—122no—
792C2#1059474511yescharacteristic
793C2#1059474811yescharacteristic
794C2#1059529011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
prime radical#10595228C2
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. #10595413C2semidirect
3. #10592865C2semidirect
4. C3×#5171C2semidirect
5. C3×#5169C2semidirect
6. #10591655C2semidirect
7. #10591598C2semidirect
8. #10591572C2semidirect
9. #10591496C2semidirect
10. #10591423C2semidirect
11. #10591421C2semidirect
12. #10590954C2semidirect
13. #10590776C2semidirect
14. #10590723C2semidirect
15. #10590709C2semidirect
21. Q8×C3⋊Dic3C22semidirect
22. C2×#3756C22semidirect
25. C3×#946C22semidirect
28. C2×C3×D3×C8C22semidirect
33. #63919C22semidirect
41. #63841C22semidirect
45. #63643C22semidirect
46. #63641C22semidirect
47. C3×#835C22semidirect
52. C3×#817C22semidirect
53. #63575C22semidirect
54. #63574C22semidirect
55. #63567C22semidirect
56. #63567C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. #63555C22semidirect
69. #5171D3semidirect
70. #5169D3semidirect
160. #946C2×D3semidirect
184. C2×D3×C8C2×D3semidirect
207. #835C2×D3semidirect
221. #817C2×D3semidirect
699. C32#3311semidirect
786. C3#80162semidirect
787. C3#80686semidirect

Maximal subgroups

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

subgroupindex
#105954132
#105952282
#105928652
C3×#51712
C3×#51692
#105916552
#105915982
#105915722
#105914962
#105914232
#105914212
#105909542
#105907762
#105907232
#105907092
#806863
#801623