Finite Group Databasebeta

← #11884114

Subgroups — #11884114

Order 1152.

1045 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#204C211yesmaximal, characteristic, complemented
2Dic6×#67C211yesmaximal, characteristic, complemented
3#10594886C211yesmaximal, characteristic
4C2×#63800C211yesmaximal, characteristic, complemented
5#10592815C211yesmaximal, characteristic, complemented
6C3×#5111C211yesmaximal, characteristic, complemented
7#10591186C211yesmaximal, characteristic, complemented
8#10591172C211yesmaximal, characteristic, complemented
9#10590960C211yesmaximal, characteristic, complemented
10#10590897C211yesmaximal, characteristic, complemented
11#10590859C211yesmaximal, characteristic, complemented
12#10590833C211yesmaximal, characteristic, complemented
13#10590822C211yesmaximal, characteristic, complemented
14#10590766C211yesmaximal, characteristic, complemented
15#10590752C211yesmaximal, characteristic, complemented
16#83866—31nomaximal
17#79495—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic
20C2×#3795C2211yescharacteristic
21C2×D3×Dic6C2211yescharacteristic, complemented
22C22×C32×C8C2211yescharacteristic
23#64133C2211yescharacteristic
24#64133C2211yescharacteristic
25C2×#3746C2211yescharacteristic, complemented
26C3×C4×#67C2211yescharacteristic
27C2×C3×#204—24no—
28C2×C3×#204C2211yescharacteristic
29C2×C3×#204C2211yescharacteristic
30C2×C3×#204C2211yescharacteristic
31C2×C3×#204C2211yescharacteristic
32C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
33#63976—21no—
34Dic3×#67—21no—
35D3×#217—21no—
36#63964—21no—
37#63908C2211yescharacteristic
38Dic3×D12C2211yescharacteristic
39#63887—21no—
40#63885—21no—
41#63884—21no—
42#63866C2211yescharacteristic, complemented
43#63860C2211yescharacteristic
44#63856C2211yescharacteristic, complemented
45Dic3×Dic6C2211yescharacteristic, complemented
46#63839—21no—
47C2×#3719C2211yescharacteristic, complemented
48C2×#3719C2211yescharacteristic, complemented
49C2×#3716C2211yescharacteristic
50C2×#3716C2211yescharacteristic
51#63800—24no—
52#63645C2211yescharacteristic, complemented
53#63643C2211yescharacteristic, complemented
54#63643C2211yescharacteristic, complemented
55C3×#830C2211yescharacteristic
56C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
57C3×#815C2211yescharacteristic, complemented
58C3×Dic3⋊C8C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63566C2211yescharacteristic, complemented
61#63563C2211yescharacteristic
62#63563C2211yescharacteristic
63C22×C3×SD16—31no—
64Q8×#67—31no—
65#5806—31no—
66C2×#915—31no—
67C2×#909—31no—
68C22×#204D311yescharacteristic, complemented
69#5550—31no—
70D4×Dic6—31no—
71C3×#435—31no—
72#5228—31no—
73#5218—31no—
74#5174—31no—
75#5173—31no—
76#5170—31no—
77#5167—31no—
78#5166—31no—
79#5164—31no—
80#5162—31no—
81#5134—31no—
82#5116—31no—
83#5116—31no—
84#5116—61no—
85#5111D311yescharacteristic, complemented
86#4845—31no—
87#4841—31no—
88#4739—31no—
89#4738—31no—
90#4733—31no—
91#4731—31no—
92#4715—31no—
93#4710—31no—
94C23×C3×D3—21no—
95C22×C32×C4C2311yescharacteristic
96C2×#634C2311yescharacteristic
97C2×#634C2311yescharacteristic
98C2×C3×#67D411yescharacteristic
99C22×C3×Dic3—21no—
100C2×C3×D12—22no—
101C2×C3×D12—21no—
102C2×C3×D12—41no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6—22no—
107C2×C3×Dic6—21no—
108C2×C3×Dic6—41no—
109C2×C3×Dic6C2311yescharacteristic
110C2×C3×Dic6C2311yescharacteristic
111C2×#627—21no—
112C2×#625—21no—
113C2×#625—21no—
114C2×D3×Dic3—21no—
115C2×D3×Dic3—21no—
116C2×D3×Dic3—21no—
117#3795—22no—
118#3795—41no—
119D3×Dic6—22no—
120D3×Dic6—41no—
121C2×C32×C8—22no—
122C2×C32×C8C2311yescharacteristic
123C2×C32×C8C2311yescharacteristic
124#3757—21no—
125#3757—21no—
126C4⋊(C3⋊Dic3)C2311yescharacteristic
127C4⋊(C3⋊Dic3)C2311yescharacteristic
128#3750—21no—
129#3750—21no—
130#3746—22no—
131C3×#217D411yescharacteristic
132C3×(C2×D3)⋊C4D411yescharacteristic
133C3×Dic3⋊C4D411yescharacteristic
134C3×C4×Dic3C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C3×#204—22no—
138C3×#204—22no—
139C3×#204—22no—
140C3×#204D414yescomplemented
141C3×ΓL(1,𝔽25)—22no—
142#3724—21no—
143Dic3⋊Dic3—21no—
144Dic3⋊Dic3—21no—
145Dic3⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151Dic32—21no—
152#3719—22no—
153#3719—41no—
154#3716—22no—
155#3716—41no—
156#3266—91noSylow
157C22×C3×Q8—31no—
158C22×C3×D4—31no—
159C2×D3×Q8—31no—
160C2×#237—31no—
161C2×#235—31no—
162C22×D12C2×D311yescharacteristic
163C22×Dic6—31no—
164C22×Dic6C2×D311yescharacteristic
165C2×C3×SD16—31no—
166C2×C3×SD16—31no—
167C2×C3×SD16—31no—
168C2×C3×SD16—31no—
169C2×C3×SD16—64no—
170C2×C3×M16—31no—
171C22×C3×C8—21no—
172C22×C3×C8C2×D311yescharacteristic
173C22×C3×C8C2×D311yescharacteristic
174C3×C4×D4—31no—
175#953—61no—
176C2×#217—61no—
177#946—31no—
178#946—61no—
179Q8×Dic3—31no—
180#944—31no—
181#944—61no—
182C2×#216—31no—
183C2×#216—31no—
184#939—61no—
185#938—31no—
186#937—61no—
187#936—31no—
188#935—61no—
189D4×Dic3—31no—
190D4×Dic3—61no—
191C2×#214—31no—
192C2×#214—31no—
193#930—31no—
194C4×#67—61no—
195C4×#67C2×D311yescharacteristic
196#924—31no—
197#924—31no—
198#924—31no—
199#924—31no—
200#924—31no—
201#924—61no—
202#924—61no—
203#924—61no—
204#915—64no—
205#909—64no—
206C2×Dic12—31no—
207C2×Dic12—31no—
208C2×Dic12—31no—
209C2×Dic12—31no—
210C2×Dic12—61no—
211C2×#204—24no—
212C2×#204—31no—
213C2×#204—31no—
214C2×#204C2×D311yescharacteristic
215C2×#204C2×D311yescharacteristic
216C2×#204C2×D311yescharacteristic
217C2×#204C2×D311yescharacteristic
218C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
219#894—61no—
220#888—61no—
221#884—61no—
222D3×C22⋊C4—61no—
223#878—61no—
224#878—61no—
225#875—31no—
226C4×D12—31no—
227#869—31no—
228C4×Dic6—31no—
229C3×C4⋊C8—31no—
230C3×C22⋊C8—31no—
231C3×C22⋊C8—31no—
232C3×#97—31no—
233#835—31no—
234#835—31no—
235#832—31no—
236#832—31no—
237#830C2×D311yescharacteristic
238#821—31no—
239#821—31no—
240(C2×D3)⋊C8C2×D311yescharacteristic, complemented
241#818—31no—
242#818—31no—
243#818—61no—
244#816—31no—
245#816—31no—
246#816—31no—
247#816—31no—
248#816—31no—
249#816—31no—
250#816—61no—
251#816—61no—
252#815C2×D311yescharacteristic, complemented
253Dic3⋊C8C2×D311yescharacteristic, complemented
254C23×C32C2×D411yescharacteristic
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—42no—
258C22×C3×D3—42no—
259C22×C3×D3—81no—
260C22×C3×D3C2×D411yescharacteristic
261C2×C32×C4—21no—
262C2×C32×C4—21no—
263C2×C32×C4C2×D411yescharacteristic
264C2×C32×C4C2411yescharacteristic
265C2×C3⋊Dic3—21no—
266C2×C3⋊Dic3—21no—
267C2×C3⋊Dic3—21no—
268C2×C3⋊Dic3—21no—
269#634—21no—
270#634—21no—
271#634—21no—
272#634—21no—
273C3×#67—22no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—42no—
277C2×C3×Dic3C2×D411yescharacteristic
278C2×C3×Dic3C2×D411yescharacteristic
279C2×C3×Dic3C2×D411yescharacteristic
280C3×D12—21no—
281C3×D12—21no—
282C3×D12—21no—
283C3×D12—42no—
284C3×D12C2×D412yes—
285C3×C4×D3—21no—
286C3×C4×D3—21no—
287C3×Dic6—21no—
288C3×Dic6—21no—
289C3×Dic6—21no—
290C3×Dic6—42no—
291C3×Dic6C2×D412yes—
292#627—42no—
293#625—42no—
294#625—81no—
295D3×Dic3—42no—
296D3×Dic3—42no—
297D3×Dic3—81no—
298C32×C8—21no—
299C32×C8C2×D412yes—
300C3×C3⋊C8—21no—
301C3×C3⋊C8—21no—
302C2×#137—91no—
303C22×SD16—31no—
304D4×Q8—91no—
305#546—91no—
306#497—91no—
307#468—91no—
308#467—91no—
309#464—91no—
310#461—91no—
311#452—91no—
312#451—91no—
313#450—91no—
314#448—91no—
315#440—91no—
316#435—31no—
317C24×C3—61no—
318C23×D3—21no—
319C2×C3×Q8—31no—
320C2×C3×Q8—31no—
321C2×C3×Q8—62no—
322C2×C3×Q8—61no—
323C2×C3×Q8—121no—
324C2×C3×D4—31no—
325C2×C3×D4—31no—
326C2×C3×D4—31no—
327C2×C3×D4—62no—
328C2×C3×D4—61no—
329C2×C3×D4—121no—
330C22×C3×C4—21no—
331C22×C3×C4—31no—
332C22×C3×C4—61no—
333C22×C3×C4C22×D311yescharacteristic
334C22×C3×C4C22×D311yescharacteristic
335C2×#67—61no—
336C2×#67—61no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67D1211yescharacteristic
340C22×Dic3—21no—
341C22×Dic3—61no—
342C22×Dic3—61no—
343C22×Dic3—61no—
344D3×Q8—62no—
345D3×Q8—121no—
346#237—62no—
347#237—121no—
348#235—62no—
349#235—121no—
350C2×D12—22no—
351C2×D12—21no—
352C2×D12—41no—
353C2×D12C22×D311yescharacteristic
354C2×D12C22×D311yescharacteristic
355C2×C4×D3—61no—
356C2×C4×D3—61no—
357C2×C4×D3—61no—
358C2×C4×D3C22×D311yescharacteristic
359C2×Dic6—22no—
360C2×Dic6—21no—
361C2×Dic6—31no—
362C2×Dic6—31no—
363C2×Dic6—31no—
364C2×Dic6—31no—
365C2×Dic6—41no—
366C2×Dic6—61no—
367C2×Dic6—61no—
368C2×Dic6—62no—
369C2×Dic6—61no—
370C2×Dic6—61no—
371C2×Dic6—121no—
372C2×Dic6C22×D311yescharacteristic
373C2×Dic6C22×D311yescharacteristic
374C3×SD16—34no—
375C3×SD16—62no—
376C3×SD16—62no—
377C3×SD16—62no—
378C3×M16—62no—
379C2×C3×C8—22no—
380C2×C3×C8—22no—
381C2×C3×C8—21no—
382C2×C3×C8—21no—
383C2×C3×C8—31no—
384C2×C3×C8—31no—
385C2×C3×C8—42no—
386C2×C3×C8C22×D311yescharacteristic
387C2×C3×C8C22×D311yescharacteristic
388C2×C3×C8C22×D311yescharacteristic
389C2×C3×C8C22×D311yescharacteristic
390C3×C4⋊C4—31no—
391C3×C22⋊C4—31no—
392C3×C22⋊C4—31no—
393C3×C42—31no—
394#217—61no—
395#217—61no—
396#217—61no—
397#217—61no—
398#217—61no—
399#217—61no—
400#217—61no—
401#217—61no—
402#217—61no—
403#217—121no—
404#217—121no—
405#217D1211yescharacteristic
406#216—62no—
407#216—121no—
408#214—62no—
409#214—121no—
410(C2×D3)⋊C4—61no—
411(C2×D3)⋊C4—61no—
412(C2×D3)⋊C4—61no—
413(C2×D3)⋊C4—61no—
414(C2×D3)⋊C4—61no—
415(C2×D3)⋊C4D1211yescharacteristic
416C4⋊Dic3—31no—
417C4⋊Dic3—31no—
418C4⋊Dic3—31no—
419C4⋊Dic3—31no—
420C4⋊Dic3—61no—
421C4⋊Dic3—61no—
422C4⋊Dic3—61no—
423C4⋊Dic3—61no—
424C4⋊Dic3—61no—
425Dic3⋊C4—61no—
426Dic3⋊C4—61no—
427Dic3⋊C4—61no—
428Dic3⋊C4—61no—
429Dic3⋊C4—61no—
430Dic3⋊C4—61no—
431Dic3⋊C4—61no—
432Dic3⋊C4—61no—
433Dic3⋊C4—61no—
434Dic3⋊C4—121no—
435Dic3⋊C4—121no—
436Dic3⋊C4D1211yescharacteristic
437C4×Dic3—61no—
438C4×Dic3—61no—
439C4×Dic3C22×D311yescharacteristic
440C2×C3⋊C8C22×D311yescharacteristic
441C2×C3⋊C8C22×D311yescharacteristic
442Dic12—62no—
443Dic12—62no—
444Dic12—62no—
445Dic12—122no—
446Dic12—121no—
447#204—22no—
448#204—22no—
449#204—22no—
450#204—62no—
451#204—121no—
452#204#6714yescomplemented
453ΓL(1,𝔽25)—22no—
454C22×C32—21no—
455C22×C32—21no—
456C22×C32#13712yescomplemented
457C22×C32C22×D411yescharacteristic
458C2×C3×D3—21no—
459C2×C3×D3—22no—
460C2×C3×D3—21no—
461C2×C3×D3—21no—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
467C2×C3×D3—84no—
468C32×C4—21no—
469C32×C4C22×D411yescharacteristic
470C32×C4H(5,𝔽2)11yescharacteristic
471C3⋊Dic3—41no—
472C3⋊Dic3—41no—
473C3⋊Dic3—41no—
474C3⋊Dic3—41no—
475C3×Dic3—21no—
476C3×Dic3—22no—
477C3×Dic3—21no—
478C3×Dic3—21no—
479C3×Dic3—41no—
480C2×#41—91no—
481C22×Q8—31no—
482C22×Q8—91no—
483C22×D4—31no—
484#137—184no—
485C2×Q16—91no—
486C2×Q16—91no—
487C2×Q16—91no—
488C2×SD16—31no—
489C2×SD16—31no—
490C2×SD16—31no—
491C2×SD16—31no—
492C2×SD16—64no—
493C2×SD16—91no—
494C2×SD16—91no—
495C2×M16—31no—
496C22×C8D3211yescharacteristic
497C4⋊Q8—91no—
498C4⋊Q8—181no—
499#124—91no—
500#123—181no—
501C22⋊Q8—91no—
502C22⋊Q8—91no—
503C22⋊Q8—91no—
504C22⋊Q8—181no—
505C22⋊Q8—181no—
506#121—91no—
507#121—181no—
508#120—181no—
509C4×Q8—91no—
510C4×D4—31no—
511C4×D4—91no—
512C4×D4—181no—
513C2×C22⋊C4—181no—
514#107—91no—
515C4⋊C8—31no—
516#103—91no—
517#103—91no—
518#103—91no—
519#103—91no—
520#102—91no—
521#102—91no—
522C22⋊C8—31no—
523C22⋊C8—31no—
524#97—31no—
525C23×C3—21no—
526C23×C3—31no—
527C23×C3—61no—
528C23×C3—61no—
529C23×C3—122no—
530C23×C3—122no—
531C23×C3—241no—
532C23×C3C2×D1211yescharacteristic
533C23×C3D3×D411yescharacteristic
534C22×D3—21no—
535C22×D3—21no—
536C22×D3—42no—
537C22×D3—42no—
538C22×D3—81no—
539C22×D3C2×D1211yescharacteristic
540C3×Q8—32no—
541C3×Q8—61no—
542C3×Q8—61no—
543C3×Q8—61no—
544C3×Q8—122no—
545C3×D4—32no—
546C3×D4—62no—
547C3×D4—61no—
548C3×D4—61no—
549C3×D4—61no—
550C3×D4—122no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—31no—
558C2×C3×C4—31no—
559C2×C3×C4—31no—
560C2×C3×C4—41no—
561C2×C3×C4—41no—
562C2×C3×C4—61no—
563C2×C3×C4—61no—
564C2×C3×C4—61no—
565C2×C3×C4—61no—
566C2×C3×C4—122no—
567C2×C3×C4C2×D1211yescharacteristic
568C2×C3×C4D3×D411yescharacteristic
569C2×C3×C4C23×D311yescharacteristic
570C2×C3×C4C23×D311yescharacteristic
571#67—22no—
572#67—122no—
573#67—122no—
574#67—241no—
575#67—241no—
576C2×Dic3—21no—
577C2×Dic3—21no—
578C2×Dic3—42no—
579C2×Dic3—61no—
580C2×Dic3—61no—
581C2×Dic3—61no—
582C2×Dic3—61no—
583C2×Dic3—61no—
584C2×Dic3—61no—
585C2×Dic3—61no—
586C2×Dic3—61no—
587C2×Dic3—121no—
588C2×Dic3—121no—
589C2×Dic3—121no—
590C2×Dic3—121no—
591C2×Dic3—122no—
592C2×Dic3—122no—
593C2×Dic3—241no—
594C2×Dic3C2×D1211yescharacteristic
595C2×Dic3C2×D1211yescharacteristic
596C2×Dic3C2×D1211yescharacteristic
597D12—21no—
598D12—21no—
599D12—21no—
600D12—42no—
601D12C2×#6712yes—
602C4×D3—21no—
603C4×D3—21no—
604C4×D3—122no—
605C4×D3—122no—
606C4×D3—241no—
607Dic6—21no—
608Dic6—21no—
609Dic6—21no—
610Dic6—42no—
611Dic6—61no—
612Dic6—61no—
613Dic6—61no—
614Dic6—61no—
615Dic6—61no—
616Dic6—61no—
617Dic6—61no—
618Dic6—61no—
619Dic6—121no—
620Dic6—121no—
621Dic6—121no—
622Dic6—121no—
623Dic6—122no—
624Dic6—122no—
625Dic6C2×#6712yes—
626C3×C8—21no—
627C3×C8—21no—
628C3×C8—22no—
629C3×C8—41no—
630C3×C8—61no—
631C3×C8—61no—
632C3×C8D3×D412yes—
633C3×C8C2×#6712yes—
634C3⋊C8—21no—
635C3⋊C8—21no—
636C2×C32—22no—
637C2×C32D4211yescharacteristic
638C2×C32C2×#13711yescharacteristic
639C2×C32#57711yescharacteristic
640C3×D3—41no—
641C3×D3—42no—
642C3×D3—81no—
643C24—61no—
644#41—182no—
645#41—361no—
646C2×Q8—31no—
647C2×Q8—31no—
648C2×Q8—62no—
649C2×Q8—61no—
650C2×Q8—91no—
651C2×Q8—91no—
652C2×Q8—121no—
653C2×Q8—181no—
654C2×Q8—182no—
655C2×Q8—361no—
656C2×D4—31no—
657C2×D4—31no—
658C2×D4—31no—
659C2×D4—62no—
660C2×D4—61no—
661C2×D4—121no—
662C2×D4—181no—
663C2×D4—181no—
664C22×C4—31no—
665C22×C4—61no—
666C22×C4—181no—
667C22×C4—181no—
668C22×C4—181no—
669C22×C4C2×D3211yescharacteristic
670Q16—182no—
671Q16—182no—
672Q16—361no—
673SD16—34no—
674SD16—62no—
675SD16—62no—
676SD16—62no—
677SD16—182no—
678SD16—361no—
679M16—62no—
680C2×C8—22no—
681C2×C8—31no—
682C2×C8—31no—
683C2×C8C2×D3211yescharacteristic
684C2×C8C2×D3211yescharacteristic
685C4⋊C4—31no—
686C4⋊C4—91no—
687C4⋊C4—91no—
688C4⋊C4—181no—
689C4⋊C4—181no—
690C4⋊C4—181no—
691C4⋊C4—181no—
692C4⋊C4—181no—
693C4⋊C4—181no—
694C22⋊C4—31no—
695C22⋊C4—31no—
696C22⋊C4—181no—
697C22⋊C4—181no—
698C22⋊C4—181no—
699C22⋊C4—181no—
700C22⋊C4—181no—
701C22⋊C4—181no—
702C22⋊C4—181no—
703C42—31no—
704C42—181no—
705C22×C3—21no—
706C22×C3—21no—
707C22×C3—21no—
708C22×C3—21no—
709C22×C3—21no—
710C22×C3—22no—
711C22×C3—41no—
712C22×C3—41no—
713C22×C3—61no—
714C22×C3—61no—
715C22×C3—61no—
716C22×C3—62no—
717C22×C3—121no—
718C22×C3—121no—
719C22×C3—121no—
720C22×C3—121no—
721C22×C3—121no—
722C22×C3—244no—
723C22×C3#90912yescomplemented
724C22×C3#91512yescomplemented
725C22×C3C22×D1211yescharacteristic
726C22×C3C2×D3×D411yescharacteristic
727C2×D3—21no—
728C2×D3—21no—
729C2×D3—22no—
730C2×D3—21no—
731C2×D3—41no—
732C2×D3—41no—
733C2×D3—41no—
734C2×D3—41no—
735C2×D3—41no—
736C2×D3—84no—
737C3×C4—21no—
738C3×C4—21no—
739C3×C4—21no—
740C3×C4—21no—
741C3×C4—41no—
742C3×C4—61no—
743C3×C4—61no—
744C3×C4—61no—
745C3×C4—62no—
746C3×C4—121no—
747C3×C4C2×D3×D411yescharacteristic
748C3×C4#100411yescharacteristic
749C3×C4#100911yescharacteristic
750C3×C4C22×#6711yescharacteristic
751Dic3—21no—
752Dic3—21no—
753Dic3—22no—
754Dic3—21no—
755Dic3—41no—
756Dic3—121no—
757Dic3—121no—
758Dic3—121no—
759Dic3—121no—
760Dic3—121no—
761Dic3—121no—
762Dic3—121no—
763Dic3—121no—
764Dic3—241no—
765Dic3—241no—
766Dic3—241no—
767Dic3—241no—
768C32#326611yescharacteristic, complemented, Sylow
769C23—31no—
770C23—61no—
771C23—61no—
772C23—122no—
773C23—122no—
774C23—241no—
775C23D3×D1211yescharacteristic
776Q8—32no—
777Q8—61no—
778Q8—61no—
779Q8—61no—
780Q8—122no—
781Q8—181no—
782Q8—181no—
783Q8—181no—
784Q8—181no—
785Q8—362no—
786D4—32no—
787D4—62no—
788D4—61no—
789D4—61no—
790D4—61no—
791D4—122no—
792D4—362no—
793D4—721no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—31no—
797C2×C4—31no—
798C2×C4—31no—
799C2×C4—61no—
800C2×C4—61no—
801C2×C4—61no—
802C2×C4—61no—
803C2×C4—122no—
804C2×C4—181no—
805C2×C4—181no—
806C2×C4—181no—
807C2×C4—181no—
808C2×C4—362no—
809C2×C4—362no—
810C2×C4—721no—
811C2×C4D3×D1211yescharacteristic
812C2×C4C22×D3211yescharacteristic
813C8—21no—
814C8—61no—
815C8—61no—
816C8D3×#6712yes—
817C2×C3—22no—
818C2×C3—22no—
819C2×C3—21no—
820C2×C3—21no—
821C2×C3—21no—
822C2×C3—42no—
823C2×C3—122no—
824C2×C3—121no—
825C2×C3—241no—
826C2×C3D4×D1211yescharacteristic
827C2×C3C2×#90911yescharacteristic
828C2×C3#575111yescharacteristic
829C2×C3C2×#91511yescharacteristic
830C2×C3#576211yescharacteristic
831C2×C3D4×#6711yescharacteristic
832D3—41no—
833D3—42no—
834D3—81no—
835C22—21no—
836C22—21no—
837C22—61no—
838C22—61no—
839C22—61no—
840C22—62no—
841C22—121no—
842C22—121no—
843C22—121no—
844C22—121no—
845C22—121no—
846C22—244no—
847C22#6380012yescomplemented
848C22C2×D3×D1211yescharacteristic
849C4—21no—
850C4—61no—
851C4—61no—
852C4—61no—
853C4—62no—
854C4—121no—
855C4—361no—
856C4—361no—
857C4—361no—
858C4—361no—
859C4#6430711yescharacteristic
860C4C2×D3×#6711yescharacteristic
861C3—21no—
862C3#7949511yescharacteristic, complemented
863C3#8386611yescharacteristic, complemented
864C2—22no—
865C2—121no—
866C2—122no—
867C2—241no—
868C2#1059467711yescharacteristic
869C2C2×#6380011yescharacteristic
870C2D12×#6711yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
prime radical#10594886C2
hypercenterC22×C8D32
hypocenterC32#3266
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C22×C3×#204C2semidirect
2. Dic6×#67C2semidirect
4. C2×#63800C2semidirect
5. #10592815C2semidirect
6. C3×#5111C2semidirect
7. #10591186C2semidirect
8. #10591172C2semidirect
9. #10590960C2semidirect
10. #10590897C2semidirect
11. #10590859C2semidirect
12. #10590833C2semidirect
13. #10590822C2semidirect
14. #10590766C2semidirect
15. #10590752C2semidirect
21. C2×D3×Dic6C22semidirect
25. C2×#3746C22semidirect
32. C2×C3×ΓL(1,𝔽25)C22semidirect
42. #63866C22semidirect
44. #63856C22semidirect
45. Dic3×Dic6C22semidirect
47. C2×#3719C22semidirect
48. C2×#3719C22semidirect
52. #63645C22semidirect
53. #63643C22semidirect
54. #63643C22semidirect
56. C3×(C2×D3)⋊C8C22semidirect
57. C3×#815C22semidirect
58. C3×Dic3⋊C8C22semidirect
59. #63566C22semidirect
60. #63566C22semidirect
68. C22×#204D3semidirect
85. #5111D3semidirect
140. C3×#204D4semidirect
218. C2×ΓL(1,𝔽25)C2×D3semidirect
240. (C2×D3)⋊C8C2×D3semidirect
252. #815C2×D3semidirect
253. Dic3⋊C8C2×D3semidirect
452. #204#67semidirect
456. C22×C32#137semidirect
723. C22×C3#909semidirect
724. C22×C3#915semidirect
768. C32#3266semidirect
847. C22#63800semidirect
862. C3#79495semidirect
863. C3#83866semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2042
Dic6×#672
#105948862
C2×#638002
#105928152
C3×#51112
#105911862
#105911722
#105909602
#105908972
#105908592
#105908332
#105908222
#105907662
#105907522
#838663
#794953