Finite Group Databasebeta

← #11889749

Subgroups — #11889749

Order 1152.

882 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594005C211yesmaximal, characteristic
2#10593958C211yesmaximal, characteristic, complemented
3#10592405C211yesmaximal, characteristic, complemented
4C3×#4714C211yesmaximal, characteristic, complemented
5C3×#4710C211yesmaximal, characteristic, complemented
6#10590961C211yesmaximal, characteristic, complemented
7#10590957C211yesmaximal, characteristic, complemented
8#10590943C211yesmaximal, characteristic, complemented
9#10590940C211yesmaximal, characteristic, complemented
10#10590855C211yesmaximal, characteristic, complemented
11#10590842C211yesmaximal, characteristic, complemented
12#10590689C211yesmaximal, characteristic, complemented
13#10590650C211yesmaximal, characteristic, complemented
14#10590269C211yesmaximal, characteristic, complemented
15#10590267C211yesmaximal, characteristic, complemented
16#81700—31nomaximal
17#79802—31nomaximal
18C2×#3802C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20C2×#3743C2211yescharacteristic, complemented
21C2×C8×C3⋊D3C2211yescharacteristic
22C4×C4⋊(C3⋊D3)C2211yescharacteristic
23C2×C3×#204C2211yescharacteristic
24C3×#875C2211yescharacteristic
25C3×C4×D12C2211yescharacteristic
26C3×#869C2211yescharacteristic, complemented
27C3×C4×Dic6C2211yescharacteristic, complemented
28#63923—21no—
29D3×(C2×D3)⋊C4—21no—
30#63916C2211yescharacteristic
31#63906—21no—
32#63900C2211yescharacteristic
33#63900C2211yescharacteristic, complemented
34#63894—21no—
35#63891—21no—
36#63888—21no—
37#63888—21no—
38#63871C2211yescharacteristic
39#63871C2211yescharacteristic
40#63871C2211yescharacteristic, complemented
41#63869—21no—
42C2×#3718C2211yescharacteristic, complemented
43C2×#3715C2211yescharacteristic
44C32×#97C2211yescharacteristic, complemented
45#63647C2211yescharacteristic
46#63647C2211yescharacteristic, complemented
47C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
48C3×#821C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#818C2211yescharacteristic, complemented
52C3×#816C2211yescharacteristic, complemented
53C3×#816C2211yescharacteristic, complemented
54C3×#816C2211yescharacteristic, complemented
55#63576C2211yescharacteristic, complemented
56#63576C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63562C2211yescharacteristic
59#63562C2211yescharacteristic
60#63562C2211yescharacteristic
61#5730—31no—
62#5676—31no—
63#5579—31no—
64#5554—31no—
65C3×#489—31no—
66C3×#440—31no—
67#5173—31no—
68#5169—31no—
69#5087—31no—
70#5054—31no—
71#5028—31no—
72#5007—31no—
73#4884—31no—
74#4882—31no—
75#4813—31no—
76#4813—31no—
77#4812—31no—
78#4811—31no—
79#4808—31no—
80#4803—31no—
81#4780—31no—
82#4776—31no—
83#4774—31no—
84#4771—31no—
85D3×#102—31no—
86D3×#102—31no—
87#4714D311yescharacteristic, complemented
88#4710D311yescharacteristic, complemented
89#4706—31no—
90#4706—31no—
91#4706—61no—
92C22×D32—21no—
93C2×C4⋊(C3⋊D3)D411yescharacteristic
94C2×C4×C3⋊D3C2311yescharacteristic
95C2×C4×C3⋊D3C2311yescharacteristic
96C2×C3×D12C2311yescharacteristic
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3—21no—
99C2×C3×Dic6—21no—
100C2×C3×Dic6C2311yescharacteristic
101C2×C3×Dic6C2311yescharacteristic
102C2×#626—21no—
103C2×#626—21no—
104C2×#625—21no—
105C2×#624—21no—
106C2×#624—21no—
107C2×D3×Dic3—21no—
108#3802—22no—
109#3802—41no—
110#3796—22no—
111#3796—41no—
112C2×C32×C8C2311yescharacteristic
113C2×C32×C8C2311yescharacteristic
114C32×C42C2311yescharacteristic
115#3752D411yescharacteristic
116#3752D411yescharacteristic
117C4⋊(C3⋊Dic3)D411yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120#3743—41no—
121C8×C3⋊D3—41no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C3×C4×Dic3—21no—
132C3×#204—22no—
133#3724—21no—
134#3724—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138#3722—21no—
139#3722—21no—
140#3722—21no—
141(C2×D3)⋊Dic3—21no—
142#3718—41no—
143#3715—41no—
144#3314—91noSylow
145C2×#239—31no—
146C2×#237—31no—
147C2×D3×D4—31no—
148C2×D3×D4—31no—
149C2×C3×SD16—31no—
150C3×C4⋊Q8—31no—
151C3×#124—31no—
152C3×C4×Q8—31no—
153C3×C4×D4—31no—
154#946—31no—
155#946—31no—
156#946—31no—
157#946—61no—
158#946—61no—
159C2×#216—31no—
160C2×#216—31no—
161C2×#215—31no—
162#938—31no—
163C2×#214—31no—
164#930—61no—
165C2×(C2×D3)⋊C4—61no—
166C2×#204C2×D311yescharacteristic
167C2×ΓL(1,𝔽25)—31no—
168C2×ΓL(1,𝔽25)—31no—
169C2×ΓL(1,𝔽25)—61no—
170C2×D3×C8—31no—
171C2×D3×C8—31no—
172C2×D3×C8—61no—
173#897—31no—
174#897—31no—
175#897—31no—
176#896—61no—
177#896—61no—
178#895—31no—
179#893—61no—
180D3×C4⋊C4—31no—
181D3×C4⋊C4—31no—
182D3×C4⋊C4—31no—
183D3×C4⋊C4—31no—
184#890—61no—
185#886—61no—
186#884—61no—
187#883—61no—
188#882—61no—
189#882—61no—
190D3×C22⋊C4—61no—
191#875C2×D311yescharacteristic
192C4×D12—31no—
193C4×D12—31no—
194C4×D12—61no—
195C4×D12—61no—
196C4×D12C2×D311yescharacteristic
197#870—61no—
198#869C2×D311yescharacteristic, complemented
199C4×Dic6C2×D311yescharacteristic, complemented
200C3×#107—31no—
201C3×#103—31no—
202C3×#103—31no—
203C3×#103—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×#102—31no—
207C3×#97—21no—
208C3×#97C2×D311yescharacteristic, complemented
209C3×#97C2×D311yescharacteristic, complemented
210#835—31no—
211#832—31no—
212#832—31no—
213#832—31no—
214#821C2×D311yescharacteristic
215#821C2×D311yescharacteristic
216#821C2×D311yescharacteristic
217(C2×D3)⋊C8—31no—
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8—61no—
222(C2×D3)⋊C8—61no—
223#818C2×D311yescharacteristic, complemented
224#816C2×D311yescharacteristic, complemented
225#816C2×D311yescharacteristic, complemented
226#816C2×D311yescharacteristic, complemented
227#810—31no—
228#809—31no—
229#809—31no—
230#809—31no—
231#807—31no—
232#807—31no—
233#807—31no—
234#807—31no—
235C4⋊(C3⋊C8)—31no—
236C4⋊(C3⋊C8)—31no—
237C4⋊(C3⋊C8)—61no—
238C22×C3⋊D3C2×D411yescharacteristic
239C22×C3⋊D3C2×D411yescharacteristic
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C2×D32—42no—
243C2×D32—42no—
244C2×D32—81no—
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2411yescharacteristic
248C2×C3⋊Dic3C2×D411yescharacteristic
249C2×C3⋊Dic3C2×D411yescharacteristic
250C4⋊(C3⋊D3)—22no—
251C4×C3⋊D3—21no—
252C4×C3⋊D3—21no—
253C4×C3⋊D3—21no—
254C4×C3⋊D3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C3×D12—21no—
262C3×D12—21no—
263C3×D12—21no—
264C3×D12#4112yes—
265C3×C4×D3—81no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—81no—
271#626—42no—
272#626—81no—
273#625—42no—
274#624—81no—
275#624—81no—
276D3×Dic3—42no—
277C32×C8—21no—
278C32×C8—21no—
279C3⋊(C3⋊C8)—21no—
280C3⋊(C3⋊C8)—21no—
281#554—91no—
282#546—91no—
283#489—31no—
284#484—91no—
285#480—91no—
286#474—91no—
287#468—91no—
288#467—91no—
289#464—91no—
290#452—91no—
291#450—91no—
292#440—31no—
293#435—91no—
294#417—91no—
295C2×#102—91no—
296C23×D3—61no—
297C23×D3—61no—
298C2×C3×Q8—31no—
299C2×C3×Q8—31no—
300C2×C3×Q8—61no—
301C2×C3×D4—31no—
302C2×C3×D4—31no—
303C22×C3×C4—61no—
304C2×#67—61no—
305C2×#67—61no—
306C2×#67—61no—
307C2×#67—61no—
308C22×Dic3—61no—
309#239—62no—
310#239—121no—
311#237—62no—
312#237—121no—
313D3×D4—62no—
314D3×D4—62no—
315D3×D4—121no—
316D3×D4—121no—
317C2×D12—31no—
318C2×D12—31no—
319C2×D12—61no—
320C2×D12—61no—
321C2×D12—61no—
322C2×D12C22×D311yescharacteristic
323C2×D12C22×D311yescharacteristic
324C2×C4×D3—21no—
325C2×C4×D3—31no—
326C2×C4×D3—31no—
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×D3—61no—
335C2×C4×D3—61no—
336C2×Dic6—21no—
337C2×Dic6C22×D311yescharacteristic
338C2×Dic6C22×D311yescharacteristic
339C3×SD16—62no—
340C2×C3×C8—21no—
341C2×C3×C8—21no—
342C2×C3×C8C22×D311yescharacteristic
343C2×C3×C8C22×D311yescharacteristic
344C2×C3×C8C22×D311yescharacteristic
345C2×C3×C8C22×D311yescharacteristic
346C3×C4⋊C4—31no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4—61no—
352C3×C22⋊C4—61no—
353C3×C22⋊C4—61no—
354C3×C22⋊C4—61no—
355C3×C42—21no—
356C3×C42—61no—
357C3×C42C22×D311yescharacteristic
358C3×C42C22×D311yescharacteristic
359#217—61no—
360#216—121no—
361#216—121no—
362#215—121no—
363#214—121no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—21no—
366(C2×D3)⋊C4—21no—
367(C2×D3)⋊C4—31no—
368(C2×D3)⋊C4—31no—
369(C2×D3)⋊C4—31no—
370(C2×D3)⋊C4—31no—
371(C2×D3)⋊C4—61no—
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—
380C4⋊Dic3—21no—
381C4⋊Dic3—31no—
382C4⋊Dic3—31no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3C22×D311yescharacteristic
388C4⋊Dic3C22×D311yescharacteristic
389C4⋊Dic3C22×D311yescharacteristic
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—
399C4×Dic3—21no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—61no—
405C2×C3⋊C8—61no—
406#204—22no—
407ΓL(1,𝔽25)—121no—
408ΓL(1,𝔽25)—121no—
409ΓL(1,𝔽25)—122no—
410D3×C8—121no—
411D3×C8—121no—
412D3×C8—122no—
413C22×C32C22×D411yescharacteristic
414C2×C3⋊D3—21no—
415C2×C3⋊D3—21no—
416C2×C3⋊D3—21no—
417C2×C3⋊D3—21no—
418C2×C3⋊D3—21no—
419C2×C3⋊D3#13712yes—
420C2×C3×D3—22no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426D32—84no—
427C32×C4—21no—
428C32×C4—21no—
429C32×C4C2×#4111yescharacteristic
430C32×C4H(5,𝔽2)11yescharacteristic
431C3⋊Dic3—21no—
432C3⋊Dic3—21no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C3×Dic3—41no—
439C2×#41—91no—
440C22×D4—91no—
441C2×Q16—91no—
442C2×SD16—31no—
443C2×SD16—91no—
444C2×M16—91no—
445C22×C8—91no—
446C4⋊Q8—31no—
447#125—181no—
448#124—31no—
449#123—181no—
450C22⋊Q8—91no—
451C22⋊Q8—91no—
452C22⋊Q8—91no—
453C22⋊Q8—181no—
454C22⋊Q8—181no—
455#121—91no—
456#121—181no—
457#120—181no—
458C4×Q8—31no—
459C4×D4—31no—
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—31no—
471#103—31no—
472#103—91no—
473#102—31no—
474#102—31no—
475#102—31no—
476#102—91no—
477#102—91no—
478#102—91no—
479C22⋊C8—91no—
480C22⋊C8—91no—
481#97D3211yescharacteristic, complemented
482C23×C3—61no—
483C23×C3—61no—
484C22×D3—21no—
485C22×D3—21no—
486C22×D3—31no—
487C22×D3—31no—
488C22×D3—31no—
489C22×D3—31no—
490C22×D3—61no—
491C22×D3—61no—
492C22×D3—122no—
493C22×D3—122no—
494C22×D3—122no—
495C22×D3—122no—
496C22×D3—241no—
497C22×D3—241no—
498C3×Q8—61no—
499C3×Q8—61no—
500C3×Q8—61no—
501C3×Q8—61no—
502C3×Q8—241no—
503C3×D4—32no—
504C3×D4—61no—
505C3×D4—61no—
506C3×D4—61no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—241no—
517C2×C3×C4D3×D411yescharacteristic
518C2×C3×C4D3×D411yescharacteristic
519C2×C3×C4D3×D411yescharacteristic
520C2×C3×C4D3×D411yescharacteristic
521C2×C3×C4C23×D311yescharacteristic
522C2×C3×C4C23×D311yescharacteristic
523#67—122no—
524#67—122no—
525#67—122no—
526#67—241no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—31no—
534C2×Dic3—31no—
535C2×Dic3—31no—
536C2×Dic3—31no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—122no—
540D12—21no—
541D12—21no—
542D12—21no—
543D12—62no—
544D12—62no—
545D12—122no—
546D12—122no—
547D12—241no—
548D12#23512yes—
549C4×D3—61no—
550C4×D3—61no—
551C4×D3—61no—
552C4×D3—61no—
553C4×D3—61no—
554C4×D3—61no—
555C4×D3—61no—
556C4×D3—61no—
557C4×D3—81no—
558C4×D3—121no—
559C4×D3—121no—
560C4×D3—121no—
561C4×D3—121no—
562C4×D3—122no—
563C4×D3—241no—
564C4×D3—241no—
565C4×D3—241no—
566C4×D3—241no—
567Dic6—21no—
568Dic6—21no—
569Dic6—21no—
570Dic6—21no—
571Dic6—81no—
572C3×C8—22no—
573C3×C8—21no—
574C3×C8—21no—
575C3×C8—21no—
576C3×C8—21no—
577C3×C8—41no—
578C3⋊C8—61no—
579C3⋊C8—61no—
580C3⋊C8—61no—
581C3⋊C8—61no—
582C3⋊C8—121no—
583C3⋊C8—121no—
584C2×C32#54611yescharacteristic
585C2×C32C2×#13711yescharacteristic
586C2×C32#57611yescharacteristic
587C3⋊D3—22no—
588C3⋊D3—41no—
589C3×D3—42no—
590C3×D3—81no—
591C24—181no—
592#41—182no—
593#41—361no—
594C2×Q8—31no—
595C2×Q8—31no—
596C2×Q8—61no—
597C2×D4—31no—
598C2×D4—31no—
599C2×D4—91no—
600C2×D4—181no—
601C2×D4—181no—
602C2×D4—181no—
603C2×D4—182no—
604C2×D4—361no—
605C22×C4—61no—
606C22×C4—91no—
607C22×C4—91no—
608C22×C4—181no—
609C22×C4—181no—
610C22×C4—181no—
611Q16—361no—
612SD16—62no—
613SD16—361no—
614M16—361no—
615C2×C8—91no—
616C2×C8—91no—
617C2×C8—361no—
618C2×C8C2×D3211yescharacteristic
619C2×C8C2×D3211yescharacteristic
620C4⋊C4—31no—
621C4⋊C4—31no—
622C4⋊C4—31no—
623C4⋊C4—31no—
624C4⋊C4—61no—
625C4⋊C4—61no—
626C4⋊C4—91no—
627C4⋊C4—181no—
628C4⋊C4—181no—
629C4⋊C4—181no—
630C4⋊C4—181no—
631C4⋊C4—181no—
632C22⋊C4—61no—
633C22⋊C4—61no—
634C22⋊C4—61no—
635C22⋊C4—91no—
636C22⋊C4—91no—
637C22⋊C4—181no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C22⋊C4—181no—
641C42—61no—
642C42C2×D3211yescharacteristic
643C22×C3—21no—
644C22×C3—62no—
645C22×C3—121no—
646C22×C3—121no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3—121no—
650C22×C3C2×D3×D411yescharacteristic
651C22×C3C2×D3×D411yescharacteristic
652C2×D3—22no—
653C2×D3—32no—
654C2×D3—32no—
655C2×D3—41no—
656C2×D3—41no—
657C2×D3—41no—
658C2×D3—41no—
659C2×D3—41no—
660C2×D3—62no—
661C2×D3—61no—
662C2×D3—61no—
663C2×D3—61no—
664C2×D3—61no—
665C2×D3—61no—
666C2×D3—61no—
667C2×D3—61no—
668C2×D3—61no—
669C2×D3—61no—
670C2×D3—61no—
671C2×D3—121no—
672C2×D3—121no—
673C2×D3—121no—
674C2×D3—121no—
675C2×D3—121no—
676C2×D3—244no—
677C2×D3—244no—
678C3×C4—21no—
679C3×C4—21no—
680C3×C4—21no—
681C3×C4—21no—
682C3×C4—21no—
683C3×C4—21no—
684C3×C4—41no—
685C3×C4—41no—
686C3×C4—121no—
687C3×C4—121no—
688C3×C4—121no—
689C3×C4—121no—
690C3×C4—121no—
691C3×C4—121no—
692C3×C4C2×#23511yescharacteristic
693C3×C4D3×#4111yescharacteristic
694C3×C4#100911yescharacteristic
695C3×C4#100911yescharacteristic
696Dic3—41no—
697Dic3—41no—
698Dic3—41no—
699Dic3—41no—
700Dic3—41no—
701Dic3—41no—
702Dic3—61no—
703Dic3—61no—
704Dic3—61no—
705Dic3—61no—
706Dic3—121no—
707Dic3—121no—
708C32#331411yescharacteristic, complemented, Sylow
709C23—61no—
710C23—61no—
711C23—91no—
712C23—91no—
713C23—362no—
714C23—362no—
715C23—721no—
716Q8—61no—
717Q8—61no—
718Q8—61no—
719Q8—61no—
720Q8—241no—
721D4—32no—
722D4—61no—
723D4—61no—
724D4—61no—
725D4—182no—
726D4—362no—
727D4—362no—
728D4—721no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—91no—
736C2×C4—91no—
737C2×C4—181no—
738C2×C4—181no—
739C2×C4—181no—
740C2×C4—181no—
741C2×C4—241no—
742C2×C4—362no—
743C2×C4—721no—
744C2×C4—721no—
745C2×C4#380211yescharacteristic
746C2×C4#380211yescharacteristic
747C2×C4C22×D3211yescharacteristic
748C8—21no—
749C8—21no—
750C8—181no—
751C8—181no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—21no—
755C2×C3—122no—
756C2×C3—241no—
757C2×C3#555011yescharacteristic
758C2×C3#567611yescharacteristic
759C2×C3#577411yescharacteristic
760C2×C3#577411yescharacteristic
761C2×C3D3×#13711yescharacteristic
762C2×C3D3×#13711yescharacteristic
763D3—42no—
764D3—62no—
765D3—62no—
766D3—81no—
767D3—122no—
768D3—121no—
769D3—121no—
770D3—241no—
771C22—62no—
772C22—92no—
773C22—121no—
774C22—121no—
775C22—121no—
776C22—121no—
777C22—121no—
778C22—181no—
779C22—181no—
780C22—181no—
781C22—181no—
782C22—181no—
783C22—724no—
784C22C2×#380211yescharacteristic
785C4—21no—
786C4—21no—
787C4—121no—
788C4—121no—
789C4—121no—
790C4—121no—
791C4—121no—
792C4—121no—
793C4—181no—
794C4—181no—
795C4D3×#23511yescharacteristic
796C4#6430811yescharacteristic
797C3—21no—
798C3#7980211yescharacteristic, complemented
799C3#8170011yescharacteristic, complemented
800C2—122no—
801C2—182no—
802C2—241no—
803C2—361no—
804C2#1059400711yescharacteristic
805C2#1059471711yescharacteristic
806C2#1059472011yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#97C22
socleC22×C32C22×D4
prime radical#10594005C2
hypercenter#97D32
hypocenterC32#3314
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
2. #10593958C2semidirect
3. #10592405C2semidirect
4. C3×#4714C2semidirect
5. C3×#4710C2semidirect
6. #10590961C2semidirect
7. #10590957C2semidirect
8. #10590943C2semidirect
9. #10590940C2semidirect
10. #10590855C2semidirect
11. #10590842C2semidirect
12. #10590689C2semidirect
13. #10590650C2semidirect
14. #10590269C2semidirect
15. #10590267C2semidirect
20. C2×#3743C22semidirect
26. C3×#869C22semidirect
27. C3×C4×Dic6C22semidirect
33. #63900C22semidirect
40. #63871C22semidirect
42. C2×#3718C22semidirect
44. C32×#97C22semidirect
46. #63647C22semidirect
47. C4⋊(C3⋊(C3⋊C8))C22semidirect
51. C3×#818C22semidirect
52. C3×#816C22semidirect
53. C3×#816C22semidirect
54. C3×#816C22semidirect
55. #63576C22semidirect
56. #63576C22semidirect
57. #63565C22semidirect
87. #4714D3semidirect
88. #4710D3semidirect
198. #869C2×D3semidirect
199. C4×Dic6C2×D3semidirect
208. C3×#97C2×D3semidirect
209. C3×#97C2×D3semidirect
223. #818C2×D3semidirect
224. #816C2×D3semidirect
225. #816C2×D3semidirect
226. #816C2×D3semidirect
481. #97D32semidirect
708. C32#3314semidirect
798. C3#79802semidirect
799. C3#81700semidirect

Maximal subgroups

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

subgroupindex
#105940052
#105939582
#105924052
C3×#47142
C3×#47102
#105909612
#105909572
#105909432
#105909402
#105908552
#105908422
#105906892
#105906502
#105902692
#105902672
#817003
#798023