Finite Group Databasebeta

← #11889759

Subgroups — #11889759

Order 1152.

876 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595407C211yesmaximal, characteristic, complemented
2#10595228C211yesmaximal, characteristic
3#10592865C211yesmaximal, characteristic, complemented
4C3×#5174C211yesmaximal, characteristic, complemented
5C3×#5169C211yesmaximal, characteristic, complemented
6#10591655C211yesmaximal, characteristic, complemented
7#10591596C211yesmaximal, characteristic, complemented
8#10591572C211yesmaximal, characteristic, complemented
9#10591496C211yesmaximal, characteristic, complemented
10#10591413C211yesmaximal, characteristic, complemented
11D3×#832C211yesmaximal, characteristic, complemented
12#10590778C211yesmaximal, characteristic, complemented
13#10590724C211yesmaximal, characteristic, complemented
14#10590684C211yesmaximal, characteristic, complemented
15#10590670C211yesmaximal, characteristic, complemented
16#80823—31nomaximal
17#80163—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×ΓL(1,𝔽25)C2211yescharacteristic, complemented
29#63976—21no—
30#63970—21no—
31#63969—21no—
32D3×#217—21no—
33#63919C2211yescharacteristic, complemented
34#63902—21no—
35C4×#625C2211yescharacteristic
36#63898C2211yescharacteristic
37#63893—21no—
38#63893—21no—
39D3×C4⋊Dic3C2211yescharacteristic
40D3×C4⋊Dic3C2211yescharacteristic, complemented
41#63870—21no—
42#63857C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44#63659C2211yescharacteristic
45#63643C2211yescharacteristic, complemented
46#63641C2211yescharacteristic, complemented
47C3×#835C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×#818C2211yescharacteristic, complemented
53#63576C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, 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#5635—31no—
63#5635—31no—
64#5612—31no—
65C3×#468—31no—
66C3×#450—31no—
67C2×#832—31no—
68#5174D311yescharacteristic, complemented
69#5173—31no—
70#5169D311yescharacteristic, complemented
71#5166—31no—
72#5166—31no—
73#5166—61no—
74#5164—31no—
75#5133—31no—
76#5127—31no—
77#5051—31no—
78#5047—31no—
79#5033—31no—
80#4890—31no—
81#4884—31no—
82#4817—31no—
83#4813—31no—
84#4774—31no—
85#4771—31no—
86D3×#102—31no—
87#4765—31no—
88#4765—31no—
89#4759—31no—
90#4730—31no—
91#4722—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—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110#3795—22no—
111#3795—41no—
112C32×SD16—41no—
113C2×C32×C8C2311yescharacteristic
114#3757—21no—
115#3757—21no—
116#3756—41no—
117C4⋊(C3⋊Dic3)—21no—
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119C4×C3⋊Dic3—21no—
120C4×C3⋊Dic3C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C3×#217—21no—
123C3×#215—22no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C3×ΓL(1,𝔽25)—41no—
134#3724—21no—
135#3724D411yescharacteristic
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3D411yescharacteristic
142(C2×D3)⋊Dic3D411yescharacteristic
143D3×C3⋊C8—41no—
144#3314—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
153C2×C3×M16—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—
179C2×C4⋊Dic3—31no—
180C2×C4⋊Dic3—31no—
181#924—31no—
182C22×C3⋊C8—31no—
183C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
184C2×D3×C8—31no—
185#897—31no—
186#897—61no—
187#897—61no—
188#893—31no—
189D3×C4⋊C4—31no—
190D3×C4⋊C4—31no—
191#889—61no—
192#889—61no—
193#888—31no—
194#888—31no—
195#883—61no—
196#67⋊C4—61no—
197#67⋊C4—61no—
198D3×C22⋊C4—61no—
199#878—61no—
200#878—61no—
201C3×#107—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#818C2×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#807—31no—
236#807—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—81no—
271#625—22no—
272#625—42no—
273D3×Dic3—42no—
274D3×Dic3—81no—
275D3×Dic3—81no—
276D3×Dic3—81no—
277C32×C8—21no—
278C3⋊(C3⋊C8)—21no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281#554—91no—
282#546—91no—
283#489—91no—
284#484—91no—
285#480—91no—
286#474—91no—
287#468—31no—
288#467—91no—
289#464—91no—
290#452—91no—
291#450—31no—
292#440—91no—
293#435—91no—
294#417—91no—
295C2×#102—91no—
296C24×C3—61no—
297C23×D3—21no—
298C2×C3×Q8—21no—
299C2×C3×Q8C22×D311yescharacteristic
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×D4—21no—
302C2×C3×D4—31no—
303C2×C3×D4—61no—
304C2×C3×D4—62no—
305C2×C3×D4—61no—
306C2×C3×D4—121no—
307C2×C3×D4C22×D311yescharacteristic
308C2×C3×D4C22×D311yescharacteristic
309C22×C3×C4—31no—
310C22×C3×C4—31no—
311C2×#67—21no—
312C2×#67—21no—
313C2×#67—31no—
314C2×#67—31no—
315C2×#67—61no—
316C2×#67—61no—
317C22×Dic3—61no—
318C22×Dic3—61no—
319C22×Dic3—61no—
320C22×Dic3—61no—
321#237—62no—
322#237—121no—
323D3×D4—22no—
324D3×D4—41no—
325#235—62no—
326#235—121no—
327C2×D12C22×D311yescharacteristic
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3C22×D311yescharacteristic
333C2×C4×D3C22×D311yescharacteristic
334C2×Dic6—31no—
335C2×Dic6—31no—
336C2×Dic6—61no—
337C2×Dic6—61no—
338C2×Dic6—61no—
339C3×SD16—41no—
340C3×SD16—41no—
341C3×SD16—42no—
342C3×SD16—62no—
343C3×M16—121no—
344C2×C3×C8—21no—
345C2×C3×C8—31no—
346C2×C3×C8—31no—
347C2×C3×C8C22×D311yescharacteristic
348C2×C3×C8C22×D311yescharacteristic
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
354C3×C22⋊C4—61no—
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357#217—21no—
358#217—31no—
359#217—31no—
360#217—61no—
361#217—61no—
362#217—61no—
363#217—61no—
364#217—61no—
365#217—61no—
366#217—121no—
367#217—121no—
368#216—121no—
369#216—121no—
370#216—122no—
371#215—22no—
372(C2×D3)⋊C4—21no—
373(C2×D3)⋊C4—21no—
374(C2×D3)⋊C4—31no—
375(C2×D3)⋊C4—31no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
378C4⋊Dic3—31no—
379C4⋊Dic3—31no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3—121no—
387C4⋊Dic3C22×D311yescharacteristic
388C4⋊Dic3C22×D311yescharacteristic
389C4⋊Dic3C22×D311yescharacteristic
390Dic3⋊C4—21no—
391Dic3⋊C4—21no—
392Dic3⋊C4—31no—
393Dic3⋊C4—31no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399C4×Dic3—31no—
400C4×Dic3—31no—
401C4×Dic3—61no—
402C4×Dic3—61no—
403C4×Dic3—61no—
404C4×Dic3—121no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—31no—
407C2×C3⋊C8—61no—
408C2×C3⋊C8—121no—
409C2×C3⋊C8C22×D311yescharacteristic
410C2×C3⋊C8C22×D311yescharacteristic
411ΓL(1,𝔽25)—41no—
412D3×C8—121no—
413C22×C32—41no—
414C22×C32—41no—
415C22×C32—41no—
416C22×C32C22×D411yescharacteristic
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—22no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—21no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3—84no—
426C2×C3×D3#13712yes—
427C32×C4—41no—
428C32×C4C2×#4111yescharacteristic
429C32×C4H(5,𝔽2)11yescharacteristic
430C3⋊Dic3—21no—
431C3⋊Dic3—21no—
432C3⋊Dic3—41no—
433C3⋊Dic3—41no—
434C3×Dic3—21no—
435C3×Dic3—21no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C3×Dic3—41no—
439C2×#41—91no—
440C22×D4—31no—
441C2×Q16—91no—
442C2×SD16—31no—
443C2×SD16D3211yescharacteristic
444C2×M16—31no—
445C22×C8—91no—
446C4⋊Q8—91no—
447#125—181no—
448#124—91no—
449#123—181no—
450C22⋊Q8—31no—
451C22⋊Q8—31no—
452C22⋊Q8—91no—
453C22⋊Q8—181no—
454C22⋊Q8—181no—
455#121—31no—
456#121—181no—
457#120—181no—
458C4×Q8—91no—
459C4×D4—91no—
460C4×D4—91no—
461C4×D4—181no—
462C2×C4⋊C4—91no—
463C2×C4⋊C4—91no—
464C2×C22⋊C4—181no—
465#107—31no—
466#107—91no—
467#107—91no—
468C4⋊C8—91no—
469#103—31no—
470#103—91no—
471#103—91no—
472#103—91no—
473#102—31no—
474#102—31no—
475#102—31no—
476#102—91no—
477#102—91no—
478#102—91no—
479C22⋊C8—31no—
480C22⋊C8—91no—
481#97—91no—
482C23×C3—21no—
483C23×C3—21no—
484C23×C3—31no—
485C23×C3—31no—
486C23×C3—41no—
487C23×C3—61no—
488C23×C3—122no—
489C23×C3—122no—
490C23×C3—241no—
491C22×D3—21no—
492C22×D3—42no—
493C22×D3—42no—
494C22×D3—81no—
495C22×D3D3×D411yescharacteristic
496C22×D3D3×D411yescharacteristic
497C3×Q8—22no—
498C3×Q8—21no—
499C3×Q8—21no—
500C3×Q8—21no—
501C3×Q8—21no—
502C3×Q8—41no—
503C3×D4—21no—
504C3×D4—21no—
505C3×D4—21no—
506C3×D4—21no—
507C3×D4—32no—
508C3×D4—41no—
509C3×D4—41no—
510C3×D4—61no—
511C3×D4—122no—
512C3×D4—241no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—31no—
517C2×C3×C4—31no—
518C2×C3×C4—41no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4C23×D311yescharacteristic
527C2×C3×C4C23×D311yescharacteristic
528#67—42no—
529#67—62no—
530#67—62no—
531#67—81no—
532#67—122no—
533#67—122no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—31no—
538C2×Dic3—31no—
539C2×Dic3—31no—
540C2×Dic3—31no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—121no—
548C2×Dic3—121no—
549C2×Dic3—122no—
550C2×Dic3—241no—
551C2×Dic3—241no—
552C2×Dic3—241no—
553C2×Dic3D3×D411yescharacteristic
554C2×Dic3D3×D411yescharacteristic
555D12—21no—
556D12#23712yes—
557C4×D3—21no—
558C4×D3—21no—
559C4×D3—21no—
560C4×D3—21no—
561C4×D3—122no—
562C4×D3—241no—
563C4×D3—241no—
564C4×D3—241no—
565Dic6—61no—
566Dic6—61no—
567Dic6—61no—
568Dic6—61no—
569Dic6—121no—
570Dic6—121no—
571Dic6—241no—
572Dic6—241no—
573C3×C8—21no—
574C3×C8—21no—
575C3×C8—41no—
576C3×C8—61no—
577C3×C8—61no—
578C3⋊C8—21no—
579C3⋊C8—21no—
580C3⋊C8—61no—
581C3⋊C8—61no—
582C3⋊C8—121no—
583C2×C32—81no—
584C2×C32#54611yescharacteristic
585C2×C32C2×#13711yescharacteristic
586C2×C32#57611yescharacteristic
587C3×D3—22no—
588C3×D3—41no—
589C3×D3—42no—
590C24—61no—
591#41—182no—
592#41—361no—
593C2×Q8—91no—
594C2×Q8—181no—
595C2×Q8C2×D3211yescharacteristic
596C2×D4—31no—
597C2×D4—61no—
598C2×D4—62no—
599C2×D4—61no—
600C2×D4—91no—
601C2×D4—121no—
602C2×D4—181no—
603C2×D4C2×D3211yescharacteristic
604C22×C4—31no—
605C22×C4—31no—
606C22×C4—181no—
607C22×C4—181no—
608C22×C4—181no—
609C22×C4—181no—
610Q16—361no—
611SD16—41no—
612SD16—62no—
613M16—121no—
614C2×C8—31no—
615C2×C8—31no—
616C2×C8—91no—
617C2×C8—361no—
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—
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—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C42—91no—
641C42—181no—
642C22×C3—21no—
643C22×C3—32no—
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—61no—
655C22×C3—62no—
656C22×C3—81no—
657C22×C3—81no—
658C22×C3—81no—
659C22×C3—121no—
660C22×C3—121no—
661C22×C3—244no—
662C22×C3C2×D3×D411yescharacteristic
663C22×C3C2×D3×D411yescharacteristic
664C2×D3—21no—
665C2×D3—21no—
666C2×D3—21no—
667C2×D3—21no—
668C2×D3—22no—
669C2×D3—21no—
670C2×D3—41no—
671C2×D3—41no—
672C2×D3—84no—
673C2×D3#91512yes—
674C3×C4—21no—
675C3×C4—21no—
676C3×C4—42no—
677C3×C4—41no—
678C3×C4—41no—
679C3×C4—61no—
680C3×C4—61no—
681C3×C4—121no—
682C3×C4—121no—
683C3×C4—121no—
684C3×C4C2×#23711yescharacteristic
685C3×C4#100411yescharacteristic
686C3×C4#100411yescharacteristic
687C3×C4D3×#4111yescharacteristic
688Dic3—21no—
689Dic3—21no—
690Dic3—41no—
691Dic3—41no—
692Dic3—41no—
693Dic3—61no—
694Dic3—61no—
695Dic3—61no—
696Dic3—61no—
697Dic3—121no—
698Dic3—121no—
699Dic3—121no—
700Dic3—121no—
701Dic3—121no—
702Dic3—121no—
703Dic3—241no—
704Dic3—241no—
705C32#331411yescharacteristic, complemented, Sylow
706C23—21no—
707C23—31no—
708C23—31no—
709C23—61no—
710C23—122no—
711C23—122no—
712C23—241no—
713Q8—21no—
714Q8—21no—
715Q8—181no—
716Q8—181no—
717Q8—721no—
718D4—21no—
719D4—21no—
720D4—32no—
721D4—61no—
722D4—122no—
723D4—182no—
724D4—241no—
725D4—362no—
726C2×C4—21no—
727C2×C4—31no—
728C2×C4—31no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—91no—
737C2×C4—91no—
738C2×C4—181no—
739C2×C4—181no—
740C2×C4—362no—
741C2×C4—721no—
742C2×C4—721no—
743C2×C4—721no—
744C2×C4C22×D3211yescharacteristic
745C8—21no—
746C8—61no—
747C8—61no—
748C8—181no—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—62no—
753C2×C3—81no—
754C2×C3—81no—
755C2×C3—121no—
756C2×C3—122no—
757C2×C3—161no—
758C2×C3#559111yescharacteristic
759C2×C3#561011yescharacteristic
760C2×C3C2×#91511yescharacteristic
761C2×C3#577411yescharacteristic
762C2×C3#577411yescharacteristic
763C2×C3D3×#13711yescharacteristic
764D3—22no—
765D3—42no—
766D3—41no—
767C22—32no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—61no—
772C22—61no—
773C22—61no—
774C22—61no—
775C22—61no—
776C22—62no—
777C22—121no—
778C22—121no—
779C22—244no—
780C22D32×D411yescharacteristic
781C4—41no—
782C4—61no—
783C4—61no—
784C4—121no—
785C4—121no—
786C4—121no—
787C4—181no—
788C4—181no—
789C4—361no—
790C4—361no—
791C4D3×#23711yescharacteristic
792C4#6433011yescharacteristic
793C3—21no—
794C3#8016311yescharacteristic, complemented
795C3#8082311yescharacteristic, complemented
796C2—62no—
797C2—81no—
798C2—121no—
799C2—122no—
800C2D3×#91511yescharacteristic
801C2#1059475011yescharacteristic
802C2#1059529011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
prime radical#10595228C2
hypercenterC2×SD16D32
hypocenterC32#3314
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. #10595407C2semidirect
3. #10592865C2semidirect
4. C3×#5174C2semidirect
5. C3×#5169C2semidirect
6. #10591655C2semidirect
7. #10591596C2semidirect
8. #10591572C2semidirect
9. #10591496C2semidirect
10. #10591413C2semidirect
11. D3×#832C2semidirect
12. #10590778C2semidirect
13. #10590724C2semidirect
14. #10590684C2semidirect
15. #10590670C2semidirect
21. Q8×C3⋊Dic3C22semidirect
22. C2×#3756C22semidirect
25. C3×#946C22semidirect
28. C2×C3×ΓL(1,𝔽25)C22semidirect
33. #63919C22semidirect
40. D3×C4⋊Dic3C22semidirect
45. #63643C22semidirect
46. #63641C22semidirect
47. C3×#835C22semidirect
52. C3×#818C22semidirect
53. #63576C22semidirect
54. #63575C22semidirect
55. #63567C22semidirect
56. #63567C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. #63555C22semidirect
68. #5174D3semidirect
70. #5169D3semidirect
160. #946C2×D3semidirect
183. C2×ΓL(1,𝔽25)C2×D3semidirect
207. #835C2×D3semidirect
221. #818C2×D3semidirect
705. C32#3314semidirect
794. C3#80163semidirect
795. C3#80823semidirect

Maximal subgroups

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

subgroupindex
#105954072
#105952282
#105928652
C3×#51742
C3×#51692
#105916552
#105915962
#105915722
#105914962
#105914132
D3×#8322
#105907782
#105907242
#105906842
#105906702
#808233
#801633