Finite Group Databasebeta

← #11889726

Subgroups — #11889726

Order 1152.

872 conjugacy classes of subgroups.

The subgroup lattice has 801 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594993C211yesmaximal, characteristic, complemented
2#10594886C211yesmaximal, characteristic
3#10592421C211yesmaximal, characteristic, complemented
4C3×#4731C211yesmaximal, characteristic, complemented
5C3×#4730C211yesmaximal, characteristic, complemented
6#10591187C211yesmaximal, characteristic, complemented
7C2×#63563C211yesmaximal, characteristic, complemented
8#10590960C211yesmaximal, characteristic, complemented
9#10590895C211yesmaximal, characteristic, complemented
10#10590859C211yesmaximal, characteristic, complemented
11#10590833C211yesmaximal, characteristic, complemented
12#10590766C211yesmaximal, characteristic, complemented
13#10590762C211yesmaximal, characteristic, complemented
14#10590680C211yesmaximal, characteristic, complemented
15#10590670C211yesmaximal, characteristic, complemented
16#80163—31nomaximal
17#79503—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21#64133C2211yescharacteristic
22C3×C4×#67C2211yescharacteristic
23C3×#924C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C2×C3×#204C2211yescharacteristic
26C2×C3×#204C2211yescharacteristic
27C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
28#63982—21no—
29#63976—21no—
30#67⋊Dic3—21no—
31D3×#217—21no—
32#63918C2211yescharacteristic, complemented
33#63908C2211yescharacteristic
34#63893—21no—
35Dic3×D12C2211yescharacteristic
36D3×C4⋊Dic3C2211yescharacteristic, complemented
37#63885—21no—
38#63884—21no—
39#63860C2211yescharacteristic
40#63856C2211yescharacteristic, complemented
41#63845—21no—
42Dic3×Dic6C2211yescharacteristic, complemented
43C2×#3719C2211yescharacteristic, complemented
44C32×C22⋊C8C2211yescharacteristic
45#63645C2211yescharacteristic, complemented
46#63645C2211yescharacteristic, complemented
47#63643C2211yescharacteristic, complemented
48#63643C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
52C3×#815C2211yescharacteristic, complemented
53C3×Dic3⋊C8C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63566C2211yescharacteristic, complemented
57#63563C2211yescharacteristic
58#63563C2211yescharacteristic
59#63563C2211yescharacteristic
60#63563C2211yescharacteristic
61#5806—31no—
62#5635—31no—
63#5550—31no—
64#5543—31no—
65C3×#450—31no—
66C3×#435—31no—
67C2×#832—31no—
68#5174—31no—
69#5173—31no—
70#5166—31no—
71#5164—31no—
72#5134—31no—
73#5133—31no—
74#5116—31no—
75C2×#821—31no—
76#5051—31no—
77#4846—31no—
78#4845—31no—
79#4774—31no—
80#4771—31no—
81#4765—31no—
82#4759—31no—
83#4736—31no—
84#4733—31no—
85#4731D311yescharacteristic, complemented
86#4730D311yescharacteristic, complemented
87#4722—31no—
88#4722—31no—
89#4722—61no—
90#4714—31no—
91#4710—31no—
92C23×C3×D3—21no—
93C22×C32×C4C2311yescharacteristic
94C22×C3⋊Dic3—21no—
95C2×#634C2311yescharacteristic
96C2×C3×#67D411yescharacteristic
97C2×C3×D12—22no—
98C2×C3×D12—21no—
99C2×C3×D12—41no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×#627—21no—
105C2×#625—21no—
106C2×#625—21no—
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110#3795—22no—
111#3795—41no—
112C2×C32×C8C2311yescharacteristic
113C2×C32×C8C2311yescharacteristic
114#3757—21no—
115C4⋊(C3⋊Dic3)—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119#3750—21no—
120C3×#217—21no—
121C3×#217D411yescharacteristic
122C3×(C2×D3)⋊C4D411yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4D411yescharacteristic
126C3×C4×Dic3C2311yescharacteristic
127C2×C3×C3⋊C8—41no—
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C3×#204—22no—
131C3×#204—41no—
132C3×ΓL(1,𝔽25)—41no—
133#3724—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142Dic32—21no—
143#3719—41no—
144#3314—91noSylow
145C22×C3×D4—31no—
146C2×#237—31no—
147C2×#235—31no—
148C22×D12C2×D311yescharacteristic
149C2×C3×SD16—31no—
150C2×C3×SD16—31no—
151C2×C3×M16—31no—
152C22×C3×C8—31no—
153C3×C22⋊Q8—31no—
154C3×C4×D4—31no—
155#953—61no—
156C2×#217—61no—
157#946—31no—
158Q8×Dic3—31no—
159C2×#216—31no—
160#939—61no—
161#938—31no—
162#937—61no—
163#936—31no—
164#935—61no—
165D4×Dic3—31no—
166D4×Dic3—61no—
167#930—31no—
168C4×#67C2×D311yescharacteristic
169C2×C4⋊Dic3—31no—
170C2×C4⋊Dic3—31no—
171C2×C4⋊Dic3—31no—
172C2×C4⋊Dic3—61no—
173#924—31no—
174#924—31no—
175#924—31no—
176#924—61no—
177#924C2×D311yescharacteristic
178C22×C3⋊C8C2×D311yescharacteristic
179C2×Dic12—31no—
180C2×#204C2×D311yescharacteristic
181C2×#204C2×D311yescharacteristic
182C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
183#897—61no—
184#894—61no—
185D3×C4⋊C4—31no—
186#890—61no—
187#889—61no—
188#888—31no—
189#884—61no—
190#67⋊C4—61no—
191D3×C22⋊C4—61no—
192#878—61no—
193#878—61no—
194#878—61no—
195#875—31no—
196C4×D12—31no—
197#869—31no—
198C4×Dic6—31no—
199C3×C4⋊C8—31no—
200C3×#102—31no—
201C3×#102—31no—
202C3×C22⋊C8—21no—
203C3×C22⋊C8—31no—
204C3×C22⋊C8C2×D311yescharacteristic
205C3×C22⋊C8C2×D311yescharacteristic
206C3×#97—31no—
207#835—31no—
208#832—31no—
209#832—31no—
210#832—31no—
211#832—31no—
212#821—31no—
213#821—31no—
214#821—31no—
215#821—31no—
216#821C2×D311yescharacteristic
217#821C2×D311yescharacteristic
218(C2×D3)⋊C8C2×D311yescharacteristic, complemented
219#818—31no—
220#818—31no—
221#818—31no—
222#818—31no—
223#818—31no—
224#818—61no—
225#818—61no—
226#816—31no—
227#816—31no—
228#816—31no—
229#816—31no—
230#816—31no—
231#816—31no—
232#816—61no—
233#816—61no—
234#815C2×D311yescharacteristic, complemented
235Dic3⋊C8C2×D311yescharacteristic, complemented
236#810—31no—
237#807—31no—
238C23×C32C2×D411yescharacteristic
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3—42no—
242C22×C3×D3—42no—
243C22×C3×D3—81no—
244C22×C3×D3C2×D411yescharacteristic
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—81no—
254#634—21no—
255#634—21no—
256C3×#67—22no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×D12—21no—
263C3×D12—21no—
264C3×D12—21no—
265C3×D12—42no—
266C3×D12#4112yes—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271#627—81no—
272#625—42no—
273#625—81no—
274D3×Dic3—42no—
275D3×Dic3—81no—
276D3×Dic3—81no—
277C32×C8—21no—
278C32×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—91no—
288#467—91no—
289#464—91no—
290#452—91no—
291#450—31no—
292#440—91no—
293#435—31no—
294#417—91no—
295C2×#102—91no—
296C24×C3—61no—
297C23×D3—21no—
298C2×C3×Q8—31no—
299C2×C3×D4—31no—
300C2×C3×D4—31no—
301C2×C3×D4—31no—
302C2×C3×D4—62no—
303C2×C3×D4—61no—
304C2×C3×D4—121no—
305C22×C3×C4—21no—
306C22×C3×C4—31no—
307C22×C3×C4C22×D311yescharacteristic
308C22×C3×C4C22×D311yescharacteristic
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—61no—
313C2×#67D1211yescharacteristic
314C22×Dic3—61no—
315C22×Dic3—61no—
316C22×Dic3—61no—
317C22×Dic3—61no—
318C22×Dic3—61no—
319C22×Dic3—121no—
320#237—62no—
321#237—121no—
322#235—62no—
323#235—121no—
324C2×D12—22no—
325C2×D12—21no—
326C2×D12—41no—
327C2×D12C22×D311yescharacteristic
328C2×D12C22×D311yescharacteristic
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3C22×D311yescharacteristic
333C2×Dic6—31no—
334C2×Dic6—31no—
335C2×Dic6—61no—
336C2×Dic6—61no—
337C2×Dic6—61no—
338C2×Dic6C22×D311yescharacteristic
339C3×SD16—62no—
340C3×SD16—121no—
341C3×M16—121no—
342C2×C3×C8—21no—
343C2×C3×C8—21no—
344C2×C3×C8—31no—
345C2×C3×C8—31no—
346C2×C3×C8—121no—
347C2×C3×C8C22×D311yescharacteristic
348C2×C3×C8C22×D311yescharacteristic
349C2×C3×C8C22×D311yescharacteristic
350C2×C3×C8C22×D311yescharacteristic
351C3×C4⋊C4—31no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—61no—
354C3×C22⋊C4—31no—
355C3×C22⋊C4—31no—
356C3×C22⋊C4—61no—
357C3×C42—31no—
358#217—21no—
359#217—61no—
360#217—61no—
361#217—61no—
362#217—61no—
363#217—61no—
364#217—61no—
365#217—61no—
366#217—121no—
367#217D1211yescharacteristic
368#216—121no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4D1211yescharacteristic
375C4⋊Dic3—31no—
376C4⋊Dic3—31no—
377C4⋊Dic3—31no—
378C4⋊Dic3—31no—
379C4⋊Dic3—31no—
380C4⋊Dic3—31no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3—61no—
389C4⋊Dic3—121no—
390C4⋊Dic3C22×D311yescharacteristic
391Dic3⋊C4—21no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—121no—
400Dic3⋊C4D1211yescharacteristic
401C4×Dic3—61no—
402C4×Dic3—61no—
403C4×Dic3C22×D311yescharacteristic
404C2×C3⋊C8—41no—
405C2×C3⋊C8C22×D311yescharacteristic
406C2×C3⋊C8C22×D311yescharacteristic
407Dic12—121no—
408#204—22no—
409#204—41no—
410ΓL(1,𝔽25)—41no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32#13712yes—
414C22×C32C22×D411yescharacteristic
415C2×C3×D3—22no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—84no—
425C32×C4—21no—
426C32×C4C2×#4111yescharacteristic
427C32×C4H(5,𝔽2)11yescharacteristic
428C3⋊Dic3—41no—
429C3⋊Dic3—41no—
430C3⋊Dic3—41no—
431C3⋊Dic3—41no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C2×#41—91no—
438C22×D4—31no—
439C2×Q16—91no—
440C2×SD16—31no—
441C2×SD16—31no—
442C2×M16—31no—
443C22×C8—31no—
444C4⋊Q8—91no—
445#125—181no—
446#124—91no—
447#123—181no—
448C22⋊Q8—31no—
449C22⋊Q8—91no—
450C22⋊Q8—91no—
451C22⋊Q8—181no—
452C22⋊Q8—181no—
453#121—91no—
454#121—181no—
455#120—181no—
456C4×Q8—91no—
457C4×D4—31no—
458C4×D4—91no—
459C4×D4—181no—
460C2×C4⋊C4—91no—
461C2×C4⋊C4—91no—
462C2×C22⋊C4—181no—
463#107—91no—
464#107—91no—
465#107—91no—
466C4⋊C8—31no—
467#103—91no—
468#103—91no—
469#103—91no—
470#103—91no—
471#102—31no—
472#102—31no—
473#102—91no—
474#102—91no—
475#102—91no—
476#102—91no—
477C22⋊C8—31no—
478C22⋊C8D3211yescharacteristic
479#97—31no—
480C23×C3—21no—
481C23×C3—31no—
482C23×C3—61no—
483C23×C3—61no—
484C23×C3—122no—
485C23×C3—122no—
486C23×C3—241no—
487C23×C3C2×D1211yescharacteristic
488C23×C3D3×D411yescharacteristic
489C22×D3—21no—
490C22×D3—21no—
491C22×D3—42no—
492C22×D3—42no—
493C22×D3—81no—
494C22×D3C2×D1211yescharacteristic
495C3×Q8—61no—
496C3×Q8—61no—
497C3×D4—32no—
498C3×D4—62no—
499C3×D4—61no—
500C3×D4—61no—
501C3×D4—61no—
502C3×D4—122no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—31no—
510C2×C3×C4—31no—
511C2×C3×C4—31no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4C2×D1211yescharacteristic
519C2×C3×C4D3×D411yescharacteristic
520C2×C3×C4C23×D311yescharacteristic
521C2×C3×C4C23×D311yescharacteristic
522#67—22no—
523#67—122no—
524#67—122no—
525#67—241no—
526#67—241no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—121no—
538C2×Dic3—121no—
539C2×Dic3—121no—
540C2×Dic3—121no—
541C2×Dic3—122no—
542C2×Dic3—241no—
543C2×Dic3—241no—
544C2×Dic3—241no—
545C2×Dic3—241no—
546C2×Dic3—242no—
547C2×Dic3C2×D1211yescharacteristic
548C2×Dic3C2×D1211yescharacteristic
549C2×Dic3C2×D1211yescharacteristic
550D12—21no—
551D12—21no—
552D12—21no—
553D12—42no—
554D12#23712yes—
555C4×D3—21no—
556C4×D3—21no—
557C4×D3—122no—
558C4×D3—241no—
559C4×D3—241no—
560Dic6—21no—
561Dic6—21no—
562Dic6—61no—
563Dic6—61no—
564Dic6—61no—
565Dic6—61no—
566Dic6—121no—
567Dic6—121no—
568Dic6—241no—
569Dic6—241no—
570C3×C8—21no—
571C3×C8—21no—
572C3×C8—21no—
573C3×C8—21no—
574C3×C8—41no—
575C3×C8—41no—
576C3×C8—61no—
577C3×C8—61no—
578C3⋊C8—21no—
579C3⋊C8—21no—
580C2×C32—22no—
581C2×C32#54611yescharacteristic
582C2×C32C2×#13711yescharacteristic
583C2×C32#57611yescharacteristic
584C3×D3—41no—
585C3×D3—42no—
586C3×D3—81no—
587C24—61no—
588#41—182no—
589#41—361no—
590C2×Q8—31no—
591C2×Q8—91no—
592C2×Q8—181no—
593C2×D4—31no—
594C2×D4—31no—
595C2×D4—31no—
596C2×D4—62no—
597C2×D4—61no—
598C2×D4—121no—
599C2×D4—181no—
600C2×D4—181no—
601C22×C4—31no—
602C22×C4—181no—
603C22×C4—181no—
604C22×C4—181no—
605C22×C4—181no—
606C22×C4C2×D3211yescharacteristic
607Q16—361no—
608SD16—62no—
609SD16—121no—
610M16—121no—
611C2×C8—31no—
612C2×C8—31no—
613C2×C8—121no—
614C2×C8C2×D3211yescharacteristic
615C2×C8C2×D3211yescharacteristic
616C4⋊C4—31no—
617C4⋊C4—31no—
618C4⋊C4—61no—
619C4⋊C4—91no—
620C4⋊C4—91no—
621C4⋊C4—91no—
622C4⋊C4—181no—
623C4⋊C4—181no—
624C4⋊C4—181no—
625C4⋊C4—181no—
626C4⋊C4—181no—
627C4⋊C4—181no—
628C22⋊C4—31no—
629C22⋊C4—31no—
630C22⋊C4—61no—
631C22⋊C4—181no—
632C22⋊C4—181no—
633C22⋊C4—181no—
634C22⋊C4—181no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C42—31no—
638C42—181no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—22no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—61no—
648C22×C3—61no—
649C22×C3—62no—
650C22×C3—61no—
651C22×C3—121no—
652C22×C3—121no—
653C22×C3—121no—
654C22×C3—121no—
655C22×C3—121no—
656C22×C3—244no—
657C22×C3#90912yes—
658C22×C3#91512yes—
659C22×C3C22×D1211yescharacteristic
660C22×C3C2×D3×D411yescharacteristic
661C2×D3—21no—
662C2×D3—21no—
663C2×D3—21no—
664C2×D3—22no—
665C2×D3—41no—
666C2×D3—41no—
667C2×D3—41no—
668C2×D3—41no—
669C2×D3—41no—
670C2×D3—84no—
671C3×C4—21no—
672C3×C4—21no—
673C3×C4—21no—
674C3×C4—21no—
675C3×C4—41no—
676C3×C4—61no—
677C3×C4—61no—
678C3×C4—61no—
679C3×C4—121no—
680C3×C4—121no—
681C3×C4C2×#23711yescharacteristic
682C3×C4#100411yescharacteristic
683C3×C4#100411yescharacteristic
684C3×C4D3×#4111yescharacteristic
685Dic3—21no—
686Dic3—21no—
687Dic3—21no—
688Dic3—41no—
689Dic3—41no—
690Dic3—121no—
691Dic3—121no—
692Dic3—121no—
693Dic3—121no—
694Dic3—121no—
695Dic3—121no—
696Dic3—121no—
697Dic3—121no—
698Dic3—241no—
699Dic3—241no—
700Dic3—241no—
701Dic3—241no—
702C32#331411yescharacteristic, complemented, Sylow
703C23—31no—
704C23—61no—
705C23—61no—
706C23—122no—
707C23—122no—
708C23—241no—
709C23D3×D1211yescharacteristic
710Q8—61no—
711Q8—61no—
712Q8—181no—
713Q8—181no—
714Q8—721no—
715D4—32no—
716D4—62no—
717D4—61no—
718D4—61no—
719D4—61no—
720D4—122no—
721D4—362no—
722D4—721no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—31no—
726C2×C4—31no—
727C2×C4—31no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—181no—
733C2×C4—181no—
734C2×C4—181no—
735C2×C4—181no—
736C2×C4—362no—
737C2×C4—721no—
738C2×C4—721no—
739C2×C4—721no—
740C2×C4D3×D1211yescharacteristic
741C2×C4C22×D3211yescharacteristic
742C8—21no—
743C8—21no—
744C8—61no—
745C8—61no—
746C2×C3—22no—
747C2×C3—22no—
748C2×C3—21no—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—42no—
752C2×C3—121no—
753C2×C3—122no—
754C2×C3—241no—
755C2×C3#555411yescharacteristic
756C2×C3#559111yescharacteristic
757C2×C3C2×#90911yescharacteristic
758C2×C3#575211yescharacteristic
759C2×C3C2×#91511yescharacteristic
760C2×C3#577411yescharacteristic
761D3—42no—
762D3—41no—
763D3—81no—
764C22—21no—
765C22—21no—
766C22—61no—
767C22—61no—
768C22—61no—
769C22—62no—
770C22—121no—
771C22—121no—
772C22—121no—
773C22—121no—
774C22—121no—
775C22—244no—
776C22#6380012yes—
777C22C2×D3×D1211yescharacteristic
778C4—21no—
779C4—61no—
780C4—61no—
781C4—61no—
782C4—121no—
783C4—121no—
784C4—361no—
785C4—361no—
786C4—361no—
787C4—361no—
788C4D3×#23711yescharacteristic
789C4#6431311yescharacteristic
790C3—21no—
791C3#7950311yescharacteristic, complemented
792C3#8016311yescharacteristic, complemented
793C2—22no—
794C2—121no—
795C2—122no—
796C2—241no—
797C2#1059429211yescharacteristic
798C2C2×#6380011yescharacteristic
799C2#1059471411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radical#10594886C2
hypercenterC22⋊C8D32
hypocenterC32#3314
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. #10594993C2semidirect
3. #10592421C2semidirect
4. C3×#4731C2semidirect
5. C3×#4730C2semidirect
6. #10591187C2semidirect
7. C2×#63563C2semidirect
8. #10590960C2semidirect
9. #10590895C2semidirect
10. #10590859C2semidirect
11. #10590833C2semidirect
12. #10590766C2semidirect
13. #10590762C2semidirect
14. #10590680C2semidirect
15. #10590670C2semidirect
27. C2×C3×ΓL(1,𝔽25)C22semidirect
32. #63918C22semidirect
36. D3×C4⋊Dic3C22semidirect
40. #63856C22semidirect
42. Dic3×Dic6C22semidirect
43. C2×#3719C22semidirect
45. #63645C22semidirect
46. #63645C22semidirect
47. #63643C22semidirect
48. #63643C22semidirect
51. C3×(C2×D3)⋊C8C22semidirect
52. C3×#815C22semidirect
53. C3×Dic3⋊C8C22semidirect
54. #63575C22semidirect
55. #63567C22semidirect
56. #63566C22semidirect
85. #4731D3semidirect
86. #4730D3semidirect
182. C2×ΓL(1,𝔽25)C2×D3semidirect
218. (C2×D3)⋊C8C2×D3semidirect
234. #815C2×D3semidirect
235. Dic3⋊C8C2×D3semidirect
702. C32#3314semidirect
791. C3#79503semidirect
792. C3#80163semidirect

Maximal subgroups

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

subgroupindex
#105949932
#105948862
#105924212
C3×#47312
C3×#47302
#105911872
C2×#635632
#105909602
#105908952
#105908592
#105908332
#105907662
#105907622
#105906802
#105906702
#801633
#795033