Finite Group Databasebeta

← #11889727

Subgroups — #11889727

Order 1152.

896 conjugacy classes of subgroups.

The subgroup lattice has 813 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595431C211yesmaximal, characteristic
2#10594537C211yesmaximal, characteristic, complemented
3#10592507C211yesmaximal, characteristic, complemented
4C3×#4811C211yesmaximal, characteristic, complemented
5C3×#4794C211yesmaximal, characteristic, complemented
6#10591596C211yesmaximal, characteristic, complemented
7#10591577C211yesmaximal, characteristic, complemented
8#10591554C211yesmaximal, characteristic, complemented
9#10590946C211yesmaximal, characteristic, complemented
10#10590773C211yesmaximal, characteristic, complemented
11#10590728C211yesmaximal, characteristic, complemented
12#10590650C211yesmaximal, characteristic, complemented
13D3×#809C211yesmaximal, characteristic, complemented
14#10590506C211yesmaximal, characteristic, complemented
15#10590464C211yesmaximal, characteristic, complemented
16#81700—31nomaximal
17#81486—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C2×#3756C2211yescharacteristic, complemented
21C2×#3744C2211yescharacteristic
22#64106C2211yescharacteristic, complemented
23C3×#947C2211yescharacteristic
24C3×#946C2211yescharacteristic
25C3×D3×C4⋊C4C2211yescharacteristic
26C3×#888C2211yescharacteristic, complemented
27#63923—21no—
28#63921—21no—
29#63916C2211yescharacteristic
30#63910—21no—
31#63904—21no—
32C4×#626C2211yescharacteristic
33#63900C2211yescharacteristic, complemented
34#63894C2211yescharacteristic
35#63888—21no—
36#63857C2211yescharacteristic
37#63856—21no—
38#63853—21no—
39#63845—21no—
40#63844C2211yescharacteristic, complemented
41C2×#3716C2211yescharacteristic
42C2×#3712C2211yescharacteristic, complemented
43C2×D3×C3⋊C8C2211yescharacteristic
44C32×#103C2211yescharacteristic, complemented
45#63647C2211yescharacteristic, complemented
46#63636C2211yescharacteristic
47C3×#835C2211yescharacteristic, complemented
48C3×#835C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#818C2211yescharacteristic, complemented
52C3×#815C2211yescharacteristic, complemented
53C3×#809C2211yescharacteristic
54C3×#807C2211yescharacteristic, complemented
55#63576C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63564C2211yescharacteristic
59#63564C2211yescharacteristic
60#63562C2211yescharacteristic
61#5730—31no—
62#5676—31no—
63#5630—31no—
64#5511—31no—
65C3×#489—31no—
66C3×#484—31no—
67#5087—31no—
68#5054—31no—
69#5051—31no—
70C2×#809—31no—
71#4890—31no—
72#4889—31no—
73#4886—31no—
74#4882—31no—
75#4813—31no—
76#4811D311yescharacteristic, complemented
77#4808—31no—
78#4808—31no—
79#4808—61no—
80#4803—31no—
81#4803—31no—
82#4798—31no—
83#4794D311yescharacteristic, complemented
84#4780—31no—
85#4776—31no—
86#4774—31no—
87D3×#102—31no—
88#4731—31no—
89#4730—31no—
90#4710—31no—
91#4706—31no—
92C22×D32—21no—
93C2×C32×Q8C2311yescharacteristic
94#3832—22no—
95#3832—41no—
96C2×C4⋊(C3⋊D3)—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3—21no—
99C2×C4×C3⋊D3C2311yescharacteristic
100C2×#634C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×Dic6—21no—
105C2×#626—21no—
106C2×#626—21no—
107C2×#626D411yescharacteristic
108C2×#624—21no—
109C2×#624—21no—
110D3×D12—22no—
111D3×D12—41no—
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114#3756—41no—
115#3752—21no—
116C4⋊(C3⋊Dic3)—21no—
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118#3744—22no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131#3724—21no—
132#3724—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3D411yescharacteristic
135#3722—21no—
136#3722D411yescharacteristic
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3D411yescharacteristic
140Dic32—21no—
141#3716—41no—
142#3712—41no—
143D3×C3⋊C8—41no—
144#3314—91noSylow
145C2×#239—31no—
146C2×#239—31no—
147C2×#239—61no—
148C2×D3×D4—31no—
149C22×D12—31no—
150C3×C4⋊Q8—31no—
151C3×#124—31no—
152C3×C22⋊Q8—31no—
153C2×C3×C4⋊C4—31no—
154#947C2×D311yescharacteristic
155#946—61no—
156#946—61no—
157#946C2×D311yescharacteristic
158C2×#216—31no—
159C2×#216—31no—
160C2×#216—61no—
161#938—31no—
162C2×#214—31no—
163C4×#67—31no—
164C4×#67—61no—
165#924—31no—
166#924—61no—
167C22×C3⋊C8—31no—
168C2×#204—31no—
169C2×#204—31no—
170C2×#204—31no—
171C2×#204—61no—
172C2×ΓL(1,𝔽25)—31no—
173C2×ΓL(1,𝔽25)—31no—
174C2×D3×C8—31no—
175#897—31no—
176#897—31no—
177#897—31no—
178#897—61no—
179#896—61no—
180#895—31no—
181#895—61no—
182#894—61no—
183#893—31no—
184#893—61no—
185D3×C4⋊C4—31no—
186D3×C4⋊C4—31no—
187D3×C4⋊C4C2×D311yescharacteristic
188#890—61no—
189#889—61no—
190#888C2×D311yescharacteristic, complemented
191#887—31no—
192#884—61no—
193#883—61no—
194#882—61no—
195#882—61no—
196D3×C22⋊C4—61no—
197D3×C22⋊C4—61no—
198C4×D12—31no—
199C4×D12—31no—
200C4×Dic6—31no—
201C3×#107—31no—
202C3×#107—31no—
203C3×#103—21no—
204C3×#103—31no—
205C3×#103—31no—
206C3×#103C2×D311yescharacteristic, complemented
207C3×#103C2×D311yescharacteristic, complemented
208C3×#102—31no—
209C3×#102—31no—
210C3×C22⋊C8—31no—
211C3×#97—31no—
212#835C2×D311yescharacteristic, complemented
213#835C2×D311yescharacteristic, complemented
214#832—31no—
215#821—31no—
216#821—31no—
217#821C2×D311yescharacteristic
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8—61no—
221(C2×D3)⋊C8C2×D311yescharacteristic
222#818C2×D311yescharacteristic, complemented
223#816—31no—
224#815C2×D311yescharacteristic, complemented
225Dic3⋊C8—31no—
226#810—31no—
227#809—31no—
228#809—31no—
229#809—31no—
230#809—31no—
231#809—31no—
232#809—61no—
233#809C2×D311yescharacteristic
234#807—31no—
235#807—31no—
236#807C2×D311yescharacteristic, complemented
237C4⋊(C3⋊C8)—31no—
238C22×C3⋊D3—21no—
239C22×C3⋊D3C2×D411yescharacteristic
240C22×C3×D3—21no—
241C22×C3×D3C2×D411yescharacteristic
242C2×D32—42no—
243C2×D32—42no—
244C2×D32—81no—
245C32×Q8—21no—
246C32×Q8—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4C2411yescharacteristic
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3C2×D411yescharacteristic
252C4⋊(C3⋊D3)—21no—
253C4⋊(C3⋊D3)—42no—
254C4⋊(C3⋊D3)#4112yes—
255C4×C3⋊D3—21no—
256C4×C3⋊D3—21no—
257C4×C3⋊D3—42no—
258#634—21no—
259#634—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C3×D12—21no—
267C3×D12—21no—
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×C4×D3—81no—
271C3×Dic6—81no—
272#626—22no—
273#626—42no—
274#626—81no—
275#624—81no—
276#624—81no—
277C32×C8—21no—
278C3⋊(C3⋊C8)—21no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281#554—91no—
282#546—91no—
283#489—31no—
284#484—31no—
285#480—91no—
286#474—91no—
287#468—91no—
288#467—91no—
289#464—91no—
290#452—91no—
291#450—91no—
292#440—91no—
293#435—91no—
294#417—91no—
295C2×#102—91no—
296C23×D3—61no—
297C23×D3—61no—
298C2×C3×Q8—21no—
299C2×C3×Q8—61no—
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×D4—31no—
303C22×C3×C4—31no—
304C22×C3×C4—61no—
305C2×#67—31no—
306C2×#67—61no—
307C2×#67—61no—
308#239—62no—
309#239—62no—
310#239—122no—
311#239—121no—
312#239—121no—
313#239—122no—
314D3×D4—62no—
315D3×D4—121no—
316C2×D12—31no—
317C2×D12—31no—
318C2×D12—31no—
319C2×D12—61no—
320C2×D12—62no—
321C2×D12—61no—
322C2×D12—61no—
323C2×D12—61no—
324C2×D12—61no—
325C2×D12—121no—
326C2×D12—121no—
327C2×D12C22×D311yescharacteristic
328C2×C4×D3—21no—
329C2×C4×D3—31no—
330C2×C4×D3—31no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×C4×D3—61no—
336C2×C4×D3—61no—
337C2×C4×D3—61no—
338C2×C4×D3—121no—
339C2×C4×D3C22×D311yescharacteristic
340C2×Dic6—21no—
341C2×Dic6—31no—
342C2×Dic6—31no—
343C2×Dic6—61no—
344C2×C3×C8—21no—
345C2×C3×C8—31no—
346C2×C3×C8—31no—
347C2×C3×C8C22×D311yescharacteristic
348C2×C3×C8C22×D311yescharacteristic
349C3×C4⋊C4—21no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4—61no—
356C3×C4⋊C4C22×D311yescharacteristic
357C3×C4⋊C4C22×D311yescharacteristic
358C3×C22⋊C4—61no—
359C3×C22⋊C4—61no—
360C3×C22⋊C4—61no—
361C3×C42—31no—
362#217—31no—
363#217—61no—
364#217—61no—
365#216—121no—
366#216—121no—
367#216—122no—
368#214—121no—
369(C2×D3)⋊C4—21no—
370(C2×D3)⋊C4—21no—
371(C2×D3)⋊C4—21no—
372(C2×D3)⋊C4—31no—
373(C2×D3)⋊C4—31no—
374(C2×D3)⋊C4—31no—
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—121no—
382C4⋊Dic3—31no—
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—21no—
393Dic3⋊C4—31no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3C22×D311yescharacteristic
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—61no—
405C2×C3⋊C8—121no—
406C2×C3⋊C8C22×D311yescharacteristic
407C2×C3⋊C8C22×D311yescharacteristic
408#204—62no—
409#204—62no—
410#204—122no—
411#204—121no—
412ΓL(1,𝔽25)—121no—
413ΓL(1,𝔽25)—121no—
414D3×C8—121no—
415C22×C32C22×D411yescharacteristic
416C2×C3⋊D3—22no—
417C2×C3⋊D3—21no—
418C2×C3⋊D3—21no—
419C2×C3⋊D3—21no—
420C2×C3⋊D3—41no—
421C2×C3⋊D3—41no—
422C2×C3×D3—21no—
423C2×C3×D3—21no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3#13712yes—
428D32—84no—
429C32×C4—41no—
430C32×C4—41no—
431C32×C4C2×#4111yescharacteristic
432C32×C4H(5,𝔽2)11yescharacteristic
433C3⋊Dic3—21no—
434C3⋊Dic3—41no—
435C3×Dic3—21no—
436C3×Dic3—21no—
437C3×Dic3—21no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C3×Dic3—41no—
441C2×#41—91no—
442C22×D4—91no—
443C2×Q16—91no—
444C2×SD16—91no—
445C2×SD16—91no—
446C2×M16—91no—
447C22×C8—91no—
448C4⋊Q8—31no—
449#125—181no—
450#124—31no—
451#123—181no—
452C22⋊Q8—31no—
453C22⋊Q8—91no—
454C22⋊Q8—91no—
455C22⋊Q8—181no—
456C22⋊Q8—181no—
457#121—91no—
458#121—181no—
459#120—181no—
460C4×Q8—91no—
461C4×D4—91no—
462C4×D4—91no—
463C4×D4—181no—
464C2×C4⋊C4—31no—
465C2×C4⋊C4—91no—
466C2×C22⋊C4—181no—
467#107—31no—
468#107—31no—
469#107—91no—
470C4⋊C8—91no—
471#103—31no—
472#103—31no—
473#103—91no—
474#103D3211yescharacteristic, complemented
475#102—31no—
476#102—31no—
477#102—91no—
478#102—91no—
479#102—91no—
480#102—91no—
481C22⋊C8—31no—
482C22⋊C8—91no—
483#97—31no—
484C23×C3—31no—
485C23×C3—61no—
486C22×D3—21no—
487C22×D3—31no—
488C22×D3—31no—
489C22×D3—61no—
490C22×D3—61no—
491C22×D3—61no—
492C22×D3—121no—
493C22×D3—122no—
494C22×D3—122no—
495C22×D3—122no—
496C22×D3—122no—
497C22×D3—241no—
498C22×D3—241no—
499C22×D3D3×D411yescharacteristic
500C3×Q8—22no—
501C3×Q8—21no—
502C3×Q8—21no—
503C3×Q8—21no—
504C3×Q8—21no—
505C3×Q8—41no—
506C3×Q8—241no—
507C3×D4—61no—
508C3×D4—61no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—31no—
515C2×C3×C4—31no—
516C2×C3×C4—31no—
517C2×C3×C4—41no—
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—241no—
525C2×C3×C4C23×D311yescharacteristic
526C2×C3×C4C23×D311yescharacteristic
527#67—62no—
528#67—122no—
529#67—241no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—31no—
534C2×Dic3—31no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—121no—
539C2×Dic3D3×D411yescharacteristic
540C2×Dic3D3×D411yescharacteristic
541C2×Dic3D3×D411yescharacteristic
542D12—21no—
543D12—21no—
544D12—32no—
545D12—32no—
546D12—62no—
547D12—62no—
548D12—61no—
549D12—61no—
550D12—121no—
551D12—122no—
552D12—122no—
553D12—124no—
554D12—122no—
555D12—241no—
556C4×D3—21no—
557C4×D3—21no—
558C4×D3—61no—
559C4×D3—61no—
560C4×D3—61no—
561C4×D3—61no—
562C4×D3—81no—
563C4×D3—121no—
564C4×D3—121no—
565C4×D3—122no—
566C4×D3—122no—
567C4×D3—124no—
568C4×D3—241no—
569C4×D3—241no—
570C4×D3—241no—
571C4×D3—241no—
572Dic6—61no—
573Dic6—61no—
574Dic6—61no—
575Dic6—61no—
576Dic6—81no—
577Dic6—121no—
578Dic6—121no—
579C3×C8—21no—
580C3×C8—21no—
581C3×C8—41no—
582C3×C8—61no—
583C3×C8—61no—
584C3⋊C8—21no—
585C3⋊C8—21no—
586C3⋊C8—61no—
587C3⋊C8—61no—
588C3⋊C8—121no—
589C2×C32#54611yescharacteristic
590C2×C32C2×#13711yescharacteristic
591C2×C32#57611yescharacteristic
592C3⋊D3—42no—
593C3⋊D3—41no—
594C3×D3—22no—
595C3×D3—81no—
596C24—181no—
597#41—182no—
598#41—361no—
599C2×Q8—61no—
600C2×Q8—91no—
601C2×Q8C2×D3211yescharacteristic
602C2×D4—31no—
603C2×D4—91no—
604C2×D4—91no—
605C2×D4—181no—
606C2×D4—181no—
607C2×D4—182no—
608C2×D4—181no—
609C2×D4—361no—
610C22×C4—31no—
611C22×C4—61no—
612C22×C4—91no—
613C22×C4—181no—
614C22×C4—181no—
615C22×C4—181no—
616Q16—361no—
617SD16—182no—
618SD16—361no—
619M16—361no—
620C2×C8—31no—
621C2×C8—31no—
622C2×C8—91no—
623C2×C8—361no—
624C2×C8C2×D3211yescharacteristic
625C4⋊C4—31no—
626C4⋊C4—31no—
627C4⋊C4—31no—
628C4⋊C4—61no—
629C4⋊C4—61no—
630C4⋊C4—61no—
631C4⋊C4—91no—
632C4⋊C4—181no—
633C4⋊C4—181no—
634C4⋊C4—181no—
635C4⋊C4—181no—
636C4⋊C4C2×D3211yescharacteristic
637C22⋊C4—61no—
638C22⋊C4—61no—
639C22⋊C4—61no—
640C22⋊C4—91no—
641C22⋊C4—91no—
642C22⋊C4—181no—
643C22⋊C4—181no—
644C22⋊C4—181no—
645C22⋊C4—181no—
646C42—31no—
647C42—181no—
648C22×C3—21no—
649C22×C3—32no—
650C22×C3—61no—
651C22×C3—61no—
652C22×C3—121no—
653C22×C3—121no—
654C22×C3—121no—
655C22×C3C2×D3×D411yescharacteristic
656C22×C3C2×D3×D411yescharacteristic
657C2×D3—21no—
658C2×D3—21no—
659C2×D3—41no—
660C2×D3—41no—
661C2×D3—41no—
662C2×D3—61no—
663C2×D3—62no—
664C2×D3—61no—
665C2×D3—62no—
666C2×D3—61no—
667C2×D3—61no—
668C2×D3—61no—
669C2×D3—61no—
670C2×D3—122no—
671C2×D3—121no—
672C2×D3—121no—
673C2×D3—121no—
674C2×D3—121no—
675C2×D3—121no—
676C2×D3—121no—
677C2×D3—121no—
678C2×D3—241no—
679C2×D3—241no—
680C2×D3—244no—
681C2×D3—244no—
682C2×D3#91812yes—
683C3×C4—21no—
684C3×C4—21no—
685C3×C4—42no—
686C3×C4—41no—
687C3×C4—41no—
688C3×C4—41no—
689C3×C4—41no—
690C3×C4—61no—
691C3×C4—61no—
692C3×C4—61no—
693C3×C4—81no—
694C3×C4—121no—
695C3×C4—121no—
696C3×C4—121no—
697C3×C4D3×#4111yescharacteristic
698C3×C4D3×#4111yescharacteristic
699C3×C4#100911yescharacteristic
700C3×C4#100911yescharacteristic
701Dic3—21no—
702Dic3—21no—
703Dic3—21no—
704Dic3—41no—
705Dic3—41no—
706Dic3—41no—
707Dic3—61no—
708Dic3—61no—
709Dic3—121no—
710Dic3—121no—
711Dic3—121no—
712Dic3—241no—
713C32#331411yescharacteristic, complemented, Sylow
714C23—31no—
715C23—61no—
716C23—91no—
717C23—181no—
718C23—362no—
719C23—362no—
720C23—721no—
721Q8—21no—
722Q8—21no—
723Q8—181no—
724Q8—181no—
725Q8—241no—
726D4—61no—
727D4—61no—
728D4—92no—
729D4—182no—
730D4—181no—
731D4—362no—
732D4—362no—
733D4—721no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—31no—
737C2×C4—31no—
738C2×C4—31no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—91no—
745C2×C4—181no—
746C2×C4—181no—
747C2×C4—181no—
748C2×C4—241no—
749C2×C4—362no—
750C2×C4—721no—
751C2×C4—721no—
752C2×C4C22×D3211yescharacteristic
753C8—21no—
754C8—61no—
755C8—61no—
756C8—181no—
757C2×C3—21no—
758C2×C3—21no—
759C2×C3—21no—
760C2×C3—62no—
761C2×C3—241no—
762C2×C3#565411yescharacteristic
763C2×C3#567611yescharacteristic
764C2×C3C2×#91811yescharacteristic
765C2×C3#577411yescharacteristic
766C2×C3#577411yescharacteristic
767C2×C3D3×#13711yescharacteristic
768D3—22no—
769D3—81no—
770D3—121no—
771D3—122no—
772D3—121no—
773D3—122no—
774D3—241no—
775D3—242no—
776C22—32no—
777C22—61no—
778C22—61no—
779C22—121no—
780C22—121no—
781C22—121no—
782C22—181no—
783C22—181no—
784C22—181no—
785C22—182no—
786C22—361no—
787C22—361no—
788C22—724no—
789C22D32×D411yescharacteristic
790C4—41no—
791C4—41no—
792C4—61no—
793C4—61no—
794C4—61no—
795C4—121no—
796C4—121no—
797C4—121no—
798C4—181no—
799C4—361no—
800C4#6430811yescharacteristic
801C4#6431211yescharacteristic
802C3—21no—
803C3#8148611yescharacteristic, complemented
804C3#8170011yescharacteristic, complemented
805C2—62no—
806C2—241no—
807C2—361no—
808C2—362no—
809C2#1059428211yescharacteristic
810C2#1059475011yescharacteristic
811C2D3×#91811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radical#10595431C2
hypercenter#103D32
hypocenterC32#3314
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
2. #10594537C2semidirect
3. #10592507C2semidirect
4. C3×#4811C2semidirect
5. C3×#4794C2semidirect
6. #10591596C2semidirect
7. #10591577C2semidirect
8. #10591554C2semidirect
9. #10590946C2semidirect
10. #10590773C2semidirect
11. #10590728C2semidirect
12. #10590650C2semidirect
13. D3×#809C2semidirect
14. #10590506C2semidirect
15. #10590464C2semidirect
20. C2×#3756C22semidirect
22. #64106C22semidirect
26. C3×#888C22semidirect
33. #63900C22semidirect
40. #63844C22semidirect
42. C2×#3712C22semidirect
44. C32×#103C22semidirect
45. #63647C22semidirect
47. C3×#835C22semidirect
48. C3×#835C22semidirect
51. C3×#818C22semidirect
52. C3×#815C22semidirect
54. C3×#807C22semidirect
55. #63576C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63567C22semidirect
76. #4811D3semidirect
83. #4794D3semidirect
190. #888C2×D3semidirect
206. C3×#103C2×D3semidirect
207. C3×#103C2×D3semidirect
212. #835C2×D3semidirect
213. #835C2×D3semidirect
222. #818C2×D3semidirect
224. #815C2×D3semidirect
236. #807C2×D3semidirect
474. #103D32semidirect
713. C32#3314semidirect
803. C3#81486semidirect
804. C3#81700semidirect

Maximal subgroups

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

subgroupindex
#105954312
#105945372
#105925072
C3×#48112
C3×#47942
#105915962
#105915772
#105915542
#105909462
#105907732
#105907282
#105906502
D3×#8092
#105905062
#105904642
#817003
#814863