Finite Group Databasebeta

← #11889719

Subgroups — #11889719

Order 1152.

921 conjugacy classes of subgroups.

The subgroup lattice has 817 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595018C211yesmaximal, characteristic
2#10594993C211yesmaximal, characteristic, complemented
3C2×#63648C211yesmaximal, characteristic, complemented
4C3×#5116C211yesmaximal, characteristic, complemented
5C3×#5111C211yesmaximal, characteristic, complemented
6#10591183C211yesmaximal, characteristic, complemented
7#10591103C211yesmaximal, characteristic, complemented
8#10590966C211yesmaximal, characteristic, complemented
9#10590893C211yesmaximal, characteristic, complemented
10#10590850C211yesmaximal, characteristic, complemented
11#10590801C211yesmaximal, characteristic, complemented
12#10590795C211yesmaximal, characteristic, complemented
13#10590764C211yesmaximal, characteristic, complemented
14#10590679C211yesmaximal, characteristic, complemented
15#10590671C211yesmaximal, characteristic, complemented
16#80777—31nomaximal
17#79503—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20C22×C32×C8C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C3×C4×#67C2211yescharacteristic
23C3×#924C2211yescharacteristic
24C3×#924C2211yescharacteristic
25C2×C3×Dic12C2211yescharacteristic, complemented
26C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
27#63982—21no—
28#63981—21no—
29#63974—21no—
30#67⋊Dic3—21no—
31#63918C2211yescharacteristic, complemented
32#63910—21no—
33#63909C2211yescharacteristic
34#63897—21no—
35#63894C2211yescharacteristic
36#63893—21no—
37D3×C4⋊Dic3C2211yescharacteristic, complemented
38#63864C2211yescharacteristic
39#63856C2211yescharacteristic, complemented
40#63845—21no—
41Dic3×Dic6C2211yescharacteristic, complemented
42C2×#3717C2211yescharacteristic
43C2×#3717C2211yescharacteristic
44#63648C2211yescharacteristic
45#63648C2211yescharacteristic
46#63648C2211yescharacteristic
47#63648C2211yescharacteristic
48C3×#830C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
50C3×#818C2211yescharacteristic, complemented
51C3×#816C2211yescharacteristic, complemented
52C3×#816C2211yescharacteristic, complemented
53C3×#815C2211yescharacteristic, complemented
54C3×Dic3⋊C8C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56#63575C2211yescharacteristic, complemented
57#63566C2211yescharacteristic, complemented
58#63566C2211yescharacteristic, complemented
59#63564C2211yescharacteristic
60#63564C2211yescharacteristic
61#5635—31no—
62#5630—31no—
63#5550—31no—
64#5543—31no—
65C3×#467—31no—
66C3×#435—31no—
67#5187—31no—
68#5185—31no—
69#5134—31no—
70#5133—31no—
71#5116D311yescharacteristic, complemented
72C2×#821—31no—
73C2×#821—31no—
74C2×#821—61no—
75#5111D311yescharacteristic, complemented
76#5046—31no—
77#5044—31no—
78#4890—31no—
79#4882—31no—
80#4846—31no—
81#4845—31no—
82#4817—31no—
83#4812—31no—
84#4803—31no—
85#4794—31no—
86#4736—31no—
87#4733—31no—
88#4731—31no—
89#4722—31no—
90#4714—31no—
91#4710—31no—
92C23×C3⋊D3—21no—
93C22×C32×C4C2311yescharacteristic
94C22×C3⋊Dic3—21no—
95C2×C4⋊(C3⋊D3)—22no—
96C2×C4⋊(C3⋊D3)—21no—
97C2×C4⋊(C3⋊D3)—41no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C3×#67D411yescharacteristic
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×Dic6C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×#627—21no—
105C2×#626—21no—
106C2×#626—21no—
107C2×#624—21no—
108C2×#624—21no—
109C2×D3×Dic3—21no—
110#3799—22no—
111#3799—41no—
112C2×C32×C8—41no—
113C2×C32×C8C2311yescharacteristic
114C2×C32×C8C2311yescharacteristic
115C4⋊(C3⋊Dic3)—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C3×#217—21no—
119C3×#217—21no—
120C3×#217D411yescharacteristic
121C3×(C2×D3)⋊C4D411yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4D411yescharacteristic
127C3×C4×Dic3C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C3×Dic12—41no—
131C3×ΓL(1,𝔽25)—41no—
132#3724—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136#3722—21no—
137#3722—21no—
138#3722—21no—
139#3722—21no—
140(C2×D3)⋊Dic3—21no—
141Dic32—21no—
142#3717—22no—
143#3717—41no—
144#3314—91noSylow
145C2×#239—31no—
146C2×#235—31no—
147C22×D12—31no—
148C22×D12—31no—
149C22×D12—61no—
150C2×C3×Q16—31no—
151C2×C3×M16—31no—
152C22×C3×C8—21no—
153C22×C3×C8C2×D311yescharacteristic
154C22×C3×C8C2×D311yescharacteristic
155C3×C22⋊Q8—31no—
156C3×C22⋊Q8—31no—
157C3×C4×D4—31no—
158#947—31no—
159#946—31no—
160Q8×Dic3—31no—
161C2×#215—31no—
162C2×#215—31no—
163#937—61no—
164D4×Dic3—61no—
165#930—31no—
166C4×#67C2×D311yescharacteristic
167C2×C4⋊Dic3—31no—
168C2×C4⋊Dic3—31no—
169C2×C4⋊Dic3—31no—
170C2×C4⋊Dic3—61no—
171#924—31no—
172#924C2×D311yescharacteristic
173#924C2×D311yescharacteristic
174C2×Dic12C2×D311yescharacteristic, complemented
175C2×#204—31no—
176C2×#204—31no—
177C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
178#897—61no—
179#895—31no—
180#895—61no—
181#894—61no—
182#894—61no—
183#893—31no—
184D3×C4⋊C4—31no—
185#890—61no—
186#889—61no—
187#888—31no—
188#884—61no—
189#882—61no—
190#67⋊C4—61no—
191D3×C22⋊C4—61no—
192D3×C22⋊C4—61no—
193#878—61no—
194#878—61no—
195#878—61no—
196#875—31no—
197C4×D12—31no—
198#869—31no—
199C4×Dic6—31no—
200C3×#107—31no—
201C3×C4⋊C8—31no—
202C3×#103—31no—
203C3×#103—31no—
204C3×C22⋊C8—31no—
205C3×C22⋊C8—31no—
206C3×#97—31no—
207#835—31no—
208#835—31no—
209#830C2×D311yescharacteristic
210#821—31no—
211#821—31no—
212#821—31no—
213#821—31no—
214#821—31no—
215#821—31no—
216#821—31no—
217#821—31no—
218#821—31no—
219#821—31no—
220#821—61no—
221#821—61no—
222#821—61no—
223#821—61no—
224(C2×D3)⋊C8C2×D311yescharacteristic, complemented
225#818—31no—
226#818—31no—
227#818C2×D311yescharacteristic, complemented
228#816—31no—
229#816—31no—
230#816C2×D311yescharacteristic, complemented
231#816C2×D311yescharacteristic, complemented
232#815C2×D311yescharacteristic, complemented
233Dic3⋊C8C2×D311yescharacteristic, complemented
234#809—31no—
235#809—31no—
236#807—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—81no—
252C4⋊(C3⋊D3)—21no—
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)—21no—
255C4⋊(C3⋊D3)—42no—
256C4⋊(C3⋊D3)#4112yes—
257C3×#67—22no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271#627—81no—
272#626—42no—
273#626—81no—
274#624—42no—
275#624—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—31no—
289#464—91no—
290#452—91no—
291#450—91no—
292#440—91no—
293#435—31no—
294#417—91no—
295C2×#102—91no—
296C23×D3—61no—
297C23×D3—61no—
298C23×D3—121no—
299C2×C3×Q8—31no—
300C2×C3×Q8—31no—
301C2×C3×D4—31no—
302C22×C3×C4—21no—
303C22×C3×C4—31no—
304C22×C3×C4C22×D311yescharacteristic
305C22×C3×C4C22×D311yescharacteristic
306C2×#67—61no—
307C2×#67—61no—
308C2×#67D1211yescharacteristic
309C22×Dic3—61no—
310C22×Dic3—61no—
311C22×Dic3—61no—
312C22×Dic3—121no—
313#239—62no—
314#239—121no—
315#235—62no—
316#235—121no—
317C2×D12—31no—
318C2×D12—31no—
319C2×D12—31no—
320C2×D12—31no—
321C2×D12—61no—
322C2×D12—61no—
323C2×D12—62no—
324C2×D12—62no—
325C2×D12—64no—
326C2×D12—61no—
327C2×D12—61no—
328C2×D12—61no—
329C2×D12—61no—
330C2×D12—121no—
331C2×D12—121no—
332C2×D12—121no—
333C2×D12—122no—
334C2×C4×D3—61no—
335C2×C4×D3—61no—
336C2×C4×D3—61no—
337C2×C4×D3—61no—
338C2×C4×D3—61no—
339C2×C4×D3C22×D311yescharacteristic
340C2×Dic6—61no—
341C2×Dic6—61no—
342C2×Dic6C22×D311yescharacteristic
343C2×Dic6C22×D311yescharacteristic
344C3×Q16—121no—
345C3×M16—121no—
346C2×C3×C8—21no—
347C2×C3×C8—21no—
348C2×C3×C8—31no—
349C2×C3×C8—31no—
350C2×C3×C8—41no—
351C2×C3×C8—41no—
352C2×C3×C8—42no—
353C2×C3×C8C22×D311yescharacteristic
354C2×C3×C8C22×D311yescharacteristic
355C2×C3×C8C22×D311yescharacteristic
356C2×C3×C8C22×D311yescharacteristic
357C3×C4⋊C4—31no—
358C3×C4⋊C4—31no—
359C3×C4⋊C4—31no—
360C3×C4⋊C4—61no—
361C3×C4⋊C4—61no—
362C3×C22⋊C4—31no—
363C3×C22⋊C4—31no—
364C3×C22⋊C4—61no—
365C3×C22⋊C4—61no—
366C3×C42—31no—
367#217—21no—
368#217—21no—
369#217—61no—
370#217D1211yescharacteristic
371#215—62no—
372#215—121no—
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—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4D1211yescharacteristic
383C4⋊Dic3—31no—
384C4⋊Dic3—31no—
385C4⋊Dic3—31no—
386C4⋊Dic3—31no—
387C4⋊Dic3—61no—
388C4⋊Dic3—61no—
389C4⋊Dic3—61no—
390C4⋊Dic3—61no—
391C4⋊Dic3—61no—
392C4⋊Dic3—61no—
393C4⋊Dic3—61no—
394C4⋊Dic3—121no—
395C4⋊Dic3C22×D311yescharacteristic
396C4⋊Dic3C22×D311yescharacteristic
397Dic3⋊C4—21no—
398Dic3⋊C4—21no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4—61no—
403Dic3⋊C4—61no—
404Dic3⋊C4D1211yescharacteristic
405C4×Dic3—61no—
406C4×Dic3—61no—
407C4×Dic3C22×D311yescharacteristic
408C2×C3⋊C8C22×D311yescharacteristic
409C2×C3⋊C8C22×D311yescharacteristic
410Dic12—41no—
411#204—62no—
412#204—121no—
413ΓL(1,𝔽25)—41no—
414C22×C32—21no—
415C22×C32—21no—
416C22×C32#13712yes—
417C22×C32C22×D411yescharacteristic
418C2×C3⋊D3—22no—
419C2×C3⋊D3—41no—
420C2×C3⋊D3—41no—
421C2×C3⋊D3—41no—
422C2×C3⋊D3—41no—
423C2×C3⋊D3—41no—
424C2×C3⋊D3—84no—
425C2×C3×D3—21no—
426C2×C3×D3—21no—
427C2×C3×D3—21no—
428C32×C4—21no—
429C32×C4C2×#4111yescharacteristic
430C32×C4H(5,𝔽2)11yescharacteristic
431C3⋊Dic3—41no—
432C3⋊Dic3—41no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—21no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C2×#41—91no—
441C22×D4—91no—
442C2×Q16—31no—
443C2×SD16—91no—
444C2×SD16—91no—
445C2×M16—31no—
446C22×C8D3211yescharacteristic
447C4⋊Q8—91no—
448#125—181no—
449#124—91no—
450#123—181no—
451C22⋊Q8—31no—
452C22⋊Q8—31no—
453C22⋊Q8—91no—
454C22⋊Q8—181no—
455C22⋊Q8—181no—
456#121—91no—
457#121—181no—
458#120—181no—
459C4×Q8—91no—
460C4×D4—31no—
461C4×D4—91no—
462C4×D4—181no—
463C2×C4⋊C4—91no—
464C2×C4⋊C4—91no—
465C2×C22⋊C4—181no—
466#107—31no—
467#107—91no—
468#107—91no—
469C4⋊C8—31no—
470#103—31no—
471#103—31no—
472#103—91no—
473#103—91no—
474#102—91no—
475#102—91no—
476#102—91no—
477#102—91no—
478#102—91no—
479#102—91no—
480C22⋊C8—31no—
481C22⋊C8—31no—
482#97—31no—
483C23×C3—21no—
484C23×C3—31no—
485C23×C3C2×D1211yescharacteristic
486C23×C3D3×D411yescharacteristic
487C22×D3—61no—
488C22×D3—61no—
489C22×D3—61no—
490C22×D3—61no—
491C22×D3—121no—
492C22×D3—121no—
493C22×D3—122no—
494C22×D3—122no—
495C22×D3—124no—
496C22×D3—122no—
497C22×D3—122no—
498C22×D3—242no—
499C22×D3—241no—
500C22×D3—241no—
501C22×D3—242no—
502C22×D3C2×D1211yescharacteristic
503C3×Q8—61no—
504C3×Q8—61no—
505C3×Q8—61no—
506C3×Q8—61no—
507C3×D4—62no—
508C2×C3×C4—22no—
509C2×C3×C4—22no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—31no—
517C2×C3×C4—31no—
518C2×C3×C4—31no—
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×C4C2×D1211yescharacteristic
526C2×C3×C4D3×D411yescharacteristic
527C2×C3×C4C23×D311yescharacteristic
528C2×C3×C4C23×D311yescharacteristic
529#67—22no—
530#67—122no—
531#67—241no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—121no—
541C2×Dic3—121no—
542C2×Dic3—241no—
543C2×Dic3—241no—
544C2×Dic3—241no—
545C2×Dic3—242no—
546C2×Dic3C2×D1211yescharacteristic
547C2×Dic3C2×D1211yescharacteristic
548C2×Dic3C2×D1211yescharacteristic
549D12—32no—
550D12—32no—
551D12—62no—
552D12—62no—
553D12—61no—
554D12—61no—
555D12—61no—
556D12—61no—
557D12—61no—
558D12—61no—
559D12—121no—
560D12—121no—
561D12—122no—
562D12—122no—
563D12—124no—
564D12—122no—
565D12—241no—
566C4×D3—21no—
567C4×D3—21no—
568C4×D3—122no—
569C4×D3—122no—
570C4×D3—241no—
571C4×D3—241no—
572C4×D3—241no—
573Dic6—21no—
574Dic6—21no—
575Dic6—21no—
576Dic6—21no—
577Dic6—241no—
578Dic6—241no—
579C3×C8—21no—
580C3×C8—21no—
581C3×C8—21no—
582C3×C8—21no—
583C3×C8—41no—
584C3×C8—41no—
585C3×C8—61no—
586C3×C8—61no—
587C3⋊C8—21no—
588C3⋊C8—21no—
589C2×C32—22no—
590C2×C32#54611yescharacteristic
591C2×C32C2×#13711yescharacteristic
592C2×C32#57611yescharacteristic
593C3⋊D3—42no—
594C3⋊D3—81no—
595C3×D3—41no—
596C24—181no—
597#41—182no—
598#41—361no—
599C2×Q8—31no—
600C2×Q8—31no—
601C2×Q8—181no—
602C2×D4—31no—
603C2×D4—91no—
604C2×D4—91no—
605C2×D4—182no—
606C2×D4—181no—
607C2×D4—181no—
608C2×D4—181no—
609C2×D4—361no—
610C22×C4—31no—
611C22×C4—181no—
612C22×C4—181no—
613C22×C4—181no—
614C22×C4—181no—
615C22×C4C2×D3211yescharacteristic
616Q16—121no—
617SD16—182no—
618SD16—361no—
619M16—121no—
620C2×C8—31no—
621C2×C8—31no—
622C2×C8—41no—
623C2×C8C2×D3211yescharacteristic
624C2×C8C2×D3211yescharacteristic
625C4⋊C4—31no—
626C4⋊C4—31no—
627C4⋊C4—31no—
628C4⋊C4—61no—
629C4⋊C4—61no—
630C4⋊C4—91no—
631C4⋊C4—91no—
632C4⋊C4—181no—
633C4⋊C4—181no—
634C4⋊C4—181no—
635C4⋊C4—181no—
636C4⋊C4—181no—
637C22⋊C4—31no—
638C22⋊C4—31no—
639C22⋊C4—61no—
640C22⋊C4—61no—
641C22⋊C4—181no—
642C22⋊C4—181no—
643C22⋊C4—181no—
644C22⋊C4—181no—
645C22⋊C4—181no—
646C42—31no—
647C42—181no—
648C22×C3—22no—
649C22×C3—22no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—22no—
656C22×C3—61no—
657C22×C3—61no—
658C22×C3—61no—
659C22×C3#90912yes—
660C22×C3#91812yes—
661C22×C3C22×D1211yescharacteristic
662C22×C3C2×D3×D411yescharacteristic
663C2×D3—21no—
664C2×D3—21no—
665C2×D3—21no—
666C2×D3—62no—
667C2×D3—62no—
668C2×D3—122no—
669C2×D3—121no—
670C2×D3—121no—
671C2×D3—121no—
672C2×D3—121no—
673C2×D3—122no—
674C2×D3—121no—
675C2×D3—121no—
676C2×D3—121no—
677C2×D3—121no—
678C2×D3—121no—
679C2×D3—121no—
680C2×D3—241no—
681C2×D3—241no—
682C2×D3—241no—
683C2×D3—241no—
684C2×D3—244no—
685C2×D3—244no—
686C2×D3—248no—
687C3×C4—22no—
688C3×C4—21no—
689C3×C4—21no—
690C3×C4—21no—
691C3×C4—21no—
692C3×C4—61no—
693C3×C4—61no—
694C3×C4—61no—
695C3×C4—121no—
696C3×C4—121no—
697C3×C4—121no—
698C3×C4—121no—
699C3×C4#100411yescharacteristic
700C3×C4#100411yescharacteristic
701C3×C4D3×#4111yescharacteristic
702C3×C4D3×#4111yescharacteristic
703Dic3—21no—
704Dic3—21no—
705Dic3—21no—
706Dic3—41no—
707Dic3—41no—
708Dic3—41no—
709Dic3—41no—
710Dic3—121no—
711Dic3—121no—
712Dic3—121no—
713Dic3—121no—
714Dic3—241no—
715Dic3—241no—
716C32#331411yescharacteristic, complemented, Sylow
717C23—31no—
718C23—181no—
719C23—181no—
720C23—362no—
721C23—362no—
722C23—721no—
723C23D3×D1211yescharacteristic
724Q8—61no—
725Q8—61no—
726Q8—61no—
727Q8—61no—
728Q8—721no—
729D4—62no—
730D4—92no—
731D4—181no—
732D4—181no—
733D4—181no—
734D4—362no—
735D4—362no—
736D4—721no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—31no—
740C2×C4—31no—
741C2×C4—31no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—181no—
749C2×C4—181no—
750C2×C4—362no—
751C2×C4—721no—
752C2×C4—721no—
753C2×C4—721no—
754C2×C4D3×D1211yescharacteristic
755C2×C4C22×D3211yescharacteristic
756C8—21no—
757C8—21no—
758C8—61no—
759C8—61no—
760C2×C3—24no—
761C2×C3—22no—
762C2×C3—22no—
763C2×C3—21no—
764C2×C3—21no—
765C2×C3—21no—
766C2×C3—121no—
767C2×C3#555411yescharacteristic
768C2×C3#561011yescharacteristic
769C2×C3C2×#90911yescharacteristic
770C2×C3#575211yescharacteristic
771C2×C3C2×#91811yescharacteristic
772C2×C3#576911yescharacteristic
773D3—41no—
774D3—122no—
775D3—122no—
776D3—242no—
777D3—242no—
778D3—241no—
779D3—241no—
780C22—21no—
781C22—21no—
782C22—61no—
783C22—61no—
784C22—61no—
785C22—182no—
786C22—361no—
787C22—361no—
788C22—361no—
789C22—361no—
790C22—361no—
791C22—724no—
792C22#6380112yes—
793C22C2×D3×D1211yescharacteristic
794C4—21no—
795C4—61no—
796C4—61no—
797C4—61no—
798C4—121no—
799C4—121no—
800C4—121no—
801C4—121no—
802C4—361no—
803C4—361no—
804C4#6430611yescharacteristic
805C4#6433011yescharacteristic
806C3—21no—
807C3#7950311yescharacteristic, complemented
808C3#8077711yescharacteristic, complemented
809C2—22no—
810C2—121no—
811C2—362no—
812C2—721no—
813C2#1059468011yescharacteristic
814C2C2×#6380111yescharacteristic
815C2#1059507511yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
prime radical#10595018C2
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
2. #10594993C2semidirect
3. C2×#63648C2semidirect
4. C3×#5116C2semidirect
5. C3×#5111C2semidirect
6. #10591183C2semidirect
7. #10591103C2semidirect
8. #10590966C2semidirect
9. #10590893C2semidirect
10. #10590850C2semidirect
11. #10590801C2semidirect
12. #10590795C2semidirect
13. #10590764C2semidirect
14. #10590679C2semidirect
15. #10590671C2semidirect
25. C2×C3×Dic12C22semidirect
26. C2×C3×ΓL(1,𝔽25)C22semidirect
31. #63918C22semidirect
37. D3×C4⋊Dic3C22semidirect
39. #63856C22semidirect
41. Dic3×Dic6C22semidirect
49. C3×(C2×D3)⋊C8C22semidirect
50. C3×#818C22semidirect
51. C3×#816C22semidirect
52. C3×#816C22semidirect
53. C3×#815C22semidirect
54. C3×Dic3⋊C8C22semidirect
55. #63575C22semidirect
56. #63575C22semidirect
57. #63566C22semidirect
58. #63566C22semidirect
71. #5116D3semidirect
75. #5111D3semidirect
174. C2×Dic12C2×D3semidirect
177. C2×ΓL(1,𝔽25)C2×D3semidirect
224. (C2×D3)⋊C8C2×D3semidirect
227. #818C2×D3semidirect
230. #816C2×D3semidirect
231. #816C2×D3semidirect
232. #815C2×D3semidirect
233. Dic3⋊C8C2×D3semidirect
716. C32#3314semidirect
807. C3#79503semidirect
808. C3#80777semidirect

Maximal subgroups

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

subgroupindex
#105950182
#105949932
C2×#636482
C3×#51162
C3×#51112
#105911832
#105911032
#105909662
#105908932
#105908502
#105908012
#105907952
#105907642
#105906792
#105906712
#807773
#795033