Finite Group Databasebeta

← #11889716

Subgroups — #11889716

Order 1152.

914 conjugacy classes of subgroups.

The subgroup lattice has 819 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5635C211yesmaximal, characteristic, complemented
2#10595018C211yesmaximal, characteristic
3#10592745C211yesmaximal, characteristic, complemented
4C3×#5051C211yesmaximal, characteristic, complemented
5#10591657C211yesmaximal, characteristic, complemented
6#10591607C211yesmaximal, characteristic, complemented
7#10591589C211yesmaximal, characteristic, complemented
8#10591540C211yesmaximal, characteristic, complemented
9#10591155C211yesmaximal, characteristic, complemented
10#10591132C211yesmaximal, characteristic, complemented
11C2×#63564C211yesmaximal, characteristic, complemented
12#10590609C211yesmaximal, characteristic, complemented
13#10590535C211yesmaximal, characteristic, complemented
14#10590464C211yesmaximal, characteristic, complemented
15#10590422C211yesmaximal, characteristic, complemented
16#83635—31nomaximal
17#80777—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20C32×C22⋊Q8C2211yescharacteristic
21C2×#3755C2211yescharacteristic
22C2×#3755C2211yescharacteristic
23C3×#946C2211yescharacteristic, complemented
24C3×Q8×Dic3C2211yescharacteristic, complemented
25C2×C3×#216C2211yescharacteristic, complemented
26C3×C4×#67C2211yescharacteristic
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C3×#924C2211yescharacteristic
29C22×C3×C3⋊C8C2211yescharacteristic
30C3×#897—21no—
31C3×D3×C4⋊C4C2211yescharacteristic, complemented
32C3×#889—21no—
33C3×#888C2211yescharacteristic, complemented
34C3×#67⋊C4—21no—
35C3×#878—21no—
36#63981—21no—
37#63974—21no—
38#63910—21no—
39#63909C2211yescharacteristic
40#63897—21no—
41#63894C2211yescharacteristic
42#63864C2211yescharacteristic
43C2×#3711C2211yescharacteristic, complemented
44#63657C2211yescharacteristic
45#63636C2211yescharacteristic
46#63636C2211yescharacteristic
47C3×#835C2211yescharacteristic, complemented
48C3×#810C2211yescharacteristic, complemented
49C3×#807C2211yescharacteristic, complemented
50#63576C2211yescharacteristic, complemented
51#63576C2211yescharacteristic, complemented
52Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
53#63565C2211yescharacteristic, complemented
54#63565C2211yescharacteristic, complemented
55#63564C2211yescharacteristic
56#63564C2211yescharacteristic
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60#63554C2211yescharacteristic, complemented
61C3×#554—31no—
62#5635D311yescharacteristic, complemented
63#5630—31no—
64#5550—31no—
65C3×#467—31no—
66#5187—31no—
67#5185—31no—
68C2×#821—31no—
69#5111—31no—
70#5089—31no—
71#5087—31no—
72#5051D311yescharacteristic, complemented
73#5049—31no—
74#5047—31no—
75#5046—31no—
76#5046—31no—
77#5046—61no—
78#5044—31no—
79#5028—31no—
80#5026—31no—
81#5011—31no—
82#4970—31no—
83#4967—31no—
84#4966—31no—
85C2×#809—31no—
86#4890—31no—
87#4882—31no—
88#4817—31no—
89#4812—31no—
90#4803—31no—
91#4794—31no—
92C23×C3⋊D3—21no—
93C2×C32×Q8C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
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
101C22×C3×Dic3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×Dic6—21no—
105C2×C3×Dic6C2311yescharacteristic
106C2×#626—21no—
107C2×#626—21no—
108C2×#624—21no—
109C2×#624—21no—
110#3799—22no—
111#3799—41no—
112C32×C4⋊C4—21no—
113C32×C4⋊C4C2311yescharacteristic
114C32×C22⋊C4—21no—
115#3755—22no—
116#3755—41no—
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×#217—21no—
120C3×#217D411yescharacteristic
121C3×#216—41no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4D411yescharacteristic
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4D411yescharacteristic
134C3×C4×Dic3—21no—
135C3×C4×Dic3C2311yescharacteristic
136C2×C3×C3⋊C8—41no—
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139#3722—21no—
140#3722—21no—
141#3722—21no—
142#3722—21no—
143#3711—41no—
144#3314—91noSylow
145C2×#239—31no—
146C2×#235—31no—
147C22×D12—31no—
148C22×D12—31no—
149C22×D12—61no—
150C2×C3×Q16—31no—
151C22×C3×C8—31no—
152C3×C4⋊Q8—31no—
153C3×#125—61no—
154C3×C22⋊Q8—21no—
155C3×C22⋊Q8—31no—
156C3×C22⋊Q8—31no—
157C3×C22⋊Q8—61no—
158C3×C22⋊Q8—61no—
159C3×C22⋊Q8C2×D311yescharacteristic
160C3×C22⋊Q8C2×D311yescharacteristic
161C3×C4×Q8—31no—
162C3×C4×D4—31no—
163C3×C4×D4—61no—
164C2×C3×C4⋊C4—31no—
165C2×C3×C4⋊C4—31no—
166#947—31no—
167#946C2×D311yescharacteristic, complemented
168Q8×Dic3C2×D311yescharacteristic, complemented
169C2×#216C2×D311yescharacteristic, complemented
170C2×#215—31no—
171C2×#215—31no—
172C2×#215—31no—
173C2×#215—31no—
174C2×#215—61no—
175C2×#215—61no—
176#937—61no—
177#930—31no—
178C4×#67C2×D311yescharacteristic
179C2×C4⋊Dic3C2×D311yescharacteristic
180#924C2×D311yescharacteristic
181C2×#208—31no—
182C22×C3⋊C8C2×D311yescharacteristic
183C2×ΓL(1,𝔽25)—31no—
184#897—21no—
185#895—31no—
186#895—61no—
187#894—61no—
188#894—61no—
189#893—31no—
190D3×C4⋊C4C2×D311yescharacteristic, complemented
191#889—21no—
192#888C2×D311yescharacteristic, complemented
193#884—61no—
194#882—61no—
195#67⋊C4—21no—
196D3×C22⋊C4—61no—
197D3×C22⋊C4—61no—
198#878—21no—
199#875—31no—
200C4×D12—31no—
201C3×#107—31no—
202C3×#103—31no—
203C3×#103—31no—
204#835—31no—
205#835—31no—
206#835C2×D311yescharacteristic, complemented
207#830—31no—
208#830—31no—
209#830—31no—
210#830—61no—
211#821—31no—
212#821—31no—
213#821—31no—
214#821—31no—
215(C2×D3)⋊C8—31no—
216#815—31no—
217Dic3⋊C8—31no—
218#810—31no—
219#810—31no—
220#810C2×D311yescharacteristic, complemented
221#809—31no—
222#809—31no—
223#809—31no—
224#809—31no—
225#809—31no—
226#809—31no—
227#809—31no—
228#809—31no—
229#809—61no—
230#809—61no—
231#807—31no—
232#807—31no—
233#807—31no—
234#807—31no—
235#807C2×D311yescharacteristic, complemented
236C4⋊(C3⋊C8)—31no—
237#803—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
245C32×Q8—21no—
246C32×Q8—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2411yescharacteristic
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)—21no—
255C4⋊(C3⋊D3)—21no—
256C4⋊(C3⋊D3)—42no—
257C4⋊(C3⋊D3)#4112yes—
258C3×#67—22no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—81no—
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×C4×D3—81no—
270C3×Dic6—21no—
271C3×Dic6—21no—
272C3×Dic6—81no—
273#626—42no—
274#626—81no—
275#624—42no—
276#624—81no—
277C3⋊(C3⋊C8)—21no—
278C3⋊(C3⋊C8)—21no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281#554—31no—
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—91no—
294#417—91no—
295C2×#102—91no—
296C23×D3—61no—
297C23×D3—61no—
298C23×D3—121no—
299C2×C3×Q8—21no—
300C2×C3×Q8—31no—
301C2×C3×Q8—61no—
302C2×C3×Q8C22×D311yescharacteristic
303C2×C3×Q8C22×D311yescharacteristic
304C2×C3×D4—31no—
305C22×C3×C4—21no—
306C22×C3×C4—31no—
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C22×C3×C4C22×D311yescharacteristic
310C22×C3×C4C22×D311yescharacteristic
311C2×#67—61no—
312C2×#67—61no—
313C2×#67#6711yescharacteristic
314C22×Dic3—21no—
315#239—62no—
316#239—121no—
317#235—62no—
318#235—121no—
319C2×D12—31no—
320C2×D12—31no—
321C2×D12—31no—
322C2×D12—31no—
323C2×D12—61no—
324C2×D12—61no—
325C2×D12—62no—
326C2×D12—62no—
327C2×D12—61no—
328C2×D12—61no—
329C2×D12—61no—
330C2×D12—61no—
331C2×D12—122no—
332C2×D12—121no—
333C2×D12—121no—
334C2×D12—121no—
335C2×D12—122no—
336C2×C4×D3—21no—
337C2×C4×D3—61no—
338C2×C4×D3—61no—
339C2×C4×D3—61no—
340C2×C4×D3—61no—
341C2×C4×D3C22×D311yescharacteristic
342C2×Dic6—21no—
343C2×Dic6C22×D311yescharacteristic
344C3×Q16—121no—
345C2×C3×C8—31no—
346C2×C3×C8—31no—
347C2×C3×C8—121no—
348C3×C4⋊C4—21no—
349C3×C4⋊C4—21no—
350C3×C4⋊C4—21no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—31no—
354C3×C4⋊C4—31no—
355C3×C4⋊C4—41no—
356C3×C4⋊C4—61no—
357C3×C4⋊C4—61no—
358C3×C4⋊C4—61no—
359C3×C4⋊C4—61no—
360C3×C4⋊C4—61no—
361C3×C4⋊C4—61no—
362C3×C4⋊C4C22×D311yescharacteristic
363C3×C4⋊C4C22×D311yescharacteristic
364C3×C22⋊C4—21no—
365C3×C22⋊C4—21no—
366C3×C22⋊C4—31no—
367C3×C22⋊C4—31no—
368C3×C22⋊C4—41no—
369C3×C22⋊C4—61no—
370C3×C22⋊C4—61no—
371C3×C42—31no—
372C3×C42—61no—
373#217—21no—
374#217#6711yescharacteristic
375#216—41no—
376#215—62no—
377#215—62no—
378#215—122no—
379#215—121no—
380#215—121no—
381#215—122no—
382(C2×D3)⋊C4—21no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—61no—
388(C2×D3)⋊C4—61no—
389(C2×D3)⋊C4—61no—
390(C2×D3)⋊C4—61no—
391(C2×D3)⋊C4#6711yescharacteristic
392C4⋊Dic3—21no—
393C4⋊Dic3—21no—
394C4⋊Dic3C22×D311yescharacteristic
395C4⋊Dic3C22×D311yescharacteristic
396C4⋊Dic3C22×D311yescharacteristic
397Dic3⋊C4—21no—
398Dic3⋊C4—21no—
399Dic3⋊C4—21no—
400Dic3⋊C4—21no—
401Dic3⋊C4#6711yescharacteristic
402C4×Dic3—21no—
403C4×Dic3C22×D311yescharacteristic
404#208—121no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—31no—
407C2×C3⋊C8—31no—
408C2×C3⋊C8—31no—
409C2×C3⋊C8—41no—
410C2×C3⋊C8—61no—
411C2×C3⋊C8—61no—
412C2×C3⋊C8C22×D311yescharacteristic
413C2×C3⋊C8C22×D311yescharacteristic
414ΓL(1,𝔽25)—121no—
415C22×C32—21no—
416C22×C32—21no—
417C22×C32#13712yes—
418C22×C32C22×D411yescharacteristic
419C2×C3⋊D3—22no—
420C2×C3⋊D3—41no—
421C2×C3⋊D3—41no—
422C2×C3⋊D3—41no—
423C2×C3⋊D3—41no—
424C2×C3⋊D3—41no—
425C2×C3⋊D3—84no—
426C2×C3×D3—21no—
427C2×C3×D3—21no—
428C2×C3×D3—21no—
429C32×C4—21no—
430C32×C4—41no—
431C32×C4—41no—
432C32×C4C2×#4111yescharacteristic
433C32×C4H(5,𝔽2)11yescharacteristic
434C3×Dic3—21no—
435C3×Dic3—21no—
436C3×Dic3—21no—
437C3×Dic3—41no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C3×Dic3—41no—
441C2×#41—91no—
442C22×D4—91no—
443C2×Q16—31no—
444C2×SD16—91no—
445C2×SD16—91no—
446C2×M16—91no—
447C22×C8—31no—
448C4⋊Q8—31no—
449#125—61no—
450#124—91no—
451#123—181no—
452C22⋊Q8—31no—
453C22⋊Q8—31no—
454C22⋊Q8—61no—
455C22⋊Q8—61no—
456C22⋊Q8D3211yescharacteristic
457#121—91no—
458#121—181no—
459#120—181no—
460C4×Q8—31no—
461C4×D4—31no—
462C4×D4—61no—
463C4×D4—91no—
464C2×C4⋊C4—31no—
465C2×C4⋊C4—31no—
466C2×C22⋊C4—181no—
467#107—31no—
468#107—91no—
469#107—91no—
470C4⋊C8—91no—
471#103—31no—
472#103—31no—
473#103—91no—
474#103—91no—
475#102—91no—
476#102—91no—
477#102—91no—
478#102—91no—
479#102—91no—
480#102—91no—
481C22⋊C8—91no—
482C22⋊C8—91no—
483#97—91no—
484C23×C3—21no—
485C23×C3—31no—
486C23×C3D3×D411yescharacteristic
487C23×C3C2×#6711yescharacteristic
488C22×D3—61no—
489C22×D3—61no—
490C22×D3—61no—
491C22×D3—61no—
492C22×D3—121no—
493C22×D3—121no—
494C22×D3—122no—
495C22×D3—122no—
496C22×D3—124no—
497C22×D3—122no—
498C22×D3—122no—
499C22×D3—242no—
500C22×D3—241no—
501C22×D3—241no—
502C22×D3—242no—
503C22×D3C2×#6711yescharacteristic
504C3×Q8—21no—
505C3×Q8—21no—
506C3×Q8—21no—
507C3×Q8—21no—
508C3×Q8—41no—
509C3×Q8—41no—
510C3×Q8—61no—
511C3×Q8—61no—
512C3×Q8—241no—
513C3×D4—62no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—31no—
525C2×C3×C4—31no—
526C2×C3×C4—31no—
527C2×C3×C4—41no—
528C2×C3×C4—41no—
529C2×C3×C4—41no—
530C2×C3×C4—41no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—241no—
538C2×C3×C4—241no—
539C2×C3×C4D3×D411yescharacteristic
540C2×C3×C4C2×#6711yescharacteristic
541C2×C3×C4C23×D311yescharacteristic
542C2×C3×C4C23×D311yescharacteristic
543#67—22no—
544#67—122no—
545#67—241no—
546C2×Dic3—21no—
547C2×Dic3—21no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3—81no—
551C2×Dic3C2×#6711yescharacteristic
552C2×Dic3C2×#6711yescharacteristic
553C2×Dic3C2×#6711yescharacteristic
554D12—32no—
555D12—32no—
556D12—62no—
557D12—62no—
558D12—61no—
559D12—61no—
560D12—61no—
561D12—61no—
562D12—61no—
563D12—61no—
564D12—121no—
565D12—121no—
566D12—122no—
567D12—122no—
568D12—124no—
569D12—122no—
570D12—241no—
571C4×D3—21no—
572C4×D3—21no—
573C4×D3—81no—
574C4×D3—122no—
575C4×D3—122no—
576C4×D3—241no—
577C4×D3—241no—
578Dic6—21no—
579Dic6—21no—
580Dic6—81no—
581C3×C8—61no—
582C3×C8—61no—
583C3⋊C8—21no—
584C3⋊C8—21no—
585C3⋊C8—61no—
586C3⋊C8—61no—
587C3⋊C8—61no—
588C3⋊C8—61no—
589C3⋊C8—121no—
590C3⋊C8—121no—
591C2×C32—22no—
592C2×C32#54611yescharacteristic
593C2×C32C2×#13711yescharacteristic
594C2×C32#57611yescharacteristic
595C3⋊D3—42no—
596C3⋊D3—81no—
597C3×D3—41no—
598C24—181no—
599#41—182no—
600#41—361no—
601C2×Q8—31no—
602C2×Q8—61no—
603C2×Q8C2×D3211yescharacteristic
604C2×D4—31no—
605C2×D4—91no—
606C2×D4—91no—
607C2×D4—182no—
608C2×D4—181no—
609C2×D4—181no—
610C2×D4—181no—
611C2×D4—361no—
612C22×C4—31no—
613C22×C4—61no—
614C22×C4—61no—
615C22×C4—181no—
616C22×C4—181no—
617C22×C4C2×D3211yescharacteristic
618Q16—121no—
619SD16—182no—
620SD16—361no—
621M16—361no—
622C2×C8—31no—
623C2×C8—31no—
624C2×C8—91no—
625C2×C8—91no—
626C2×C8—121no—
627C4⋊C4—21no—
628C4⋊C4—31no—
629C4⋊C4—31no—
630C4⋊C4—31no—
631C4⋊C4—31no—
632C4⋊C4—61no—
633C4⋊C4—61no—
634C4⋊C4—61no—
635C4⋊C4—61no—
636C4⋊C4—61no—
637C4⋊C4—61no—
638C4⋊C4C2×D3211yescharacteristic
639C22⋊C4—21no—
640C22⋊C4—31no—
641C22⋊C4—31no—
642C22⋊C4—61no—
643C22⋊C4—61no—
644C22⋊C4—181no—
645C22⋊C4—181no—
646C22⋊C4—181no—
647C22⋊C4—181no—
648C42—31no—
649C42—61no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—22no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—61no—
659C22×C3—61no—
660C22×C3—61no—
661C22×C3#91812yes—
662C22×C3#94212yes—
663C22×C3C2×D3×D411yescharacteristic
664C22×C3C22×#6711yescharacteristic
665C2×D3—21no—
666C2×D3—21no—
667C2×D3—21no—
668C2×D3—62no—
669C2×D3—62no—
670C2×D3—122no—
671C2×D3—121no—
672C2×D3—121no—
673C2×D3—121no—
674C2×D3—121no—
675C2×D3—122no—
676C2×D3—121no—
677C2×D3—121no—
678C2×D3—121no—
679C2×D3—121no—
680C2×D3—121no—
681C2×D3—121no—
682C2×D3—241no—
683C2×D3—241no—
684C2×D3—241no—
685C2×D3—241no—
686C2×D3—244no—
687C2×D3—244no—
688C2×D3—248no—
689C3×C4—21no—
690C3×C4—21no—
691C3×C4—21no—
692C3×C4—21no—
693C3×C4—41no—
694C3×C4—41no—
695C3×C4—41no—
696C3×C4—41no—
697C3×C4—41no—
698C3×C4—61no—
699C3×C4—61no—
700C3×C4—61no—
701C3×C4—81no—
702C3×C4—81no—
703C3×C4—121no—
704C3×C4—121no—
705C3×C4—121no—
706C3×C4—121no—
707C3×C4#100411yescharacteristic
708C3×C4D3×#4111yescharacteristic
709C3×C4D3×#4111yescharacteristic
710C3×C4#100911yescharacteristic
711Dic3—21no—
712Dic3—21no—
713Dic3—21no—
714Dic3—41no—
715Dic3—41no—
716Dic3—41no—
717Dic3—41no—
718C32#331411yescharacteristic, complemented, Sylow
719C23—31no—
720C23—181no—
721C23—181no—
722C23—362no—
723C23—362no—
724C23—721no—
725C23D3×#6711yescharacteristic
726Q8—21no—
727Q8—21no—
728Q8—61no—
729Q8—61no—
730Q8—241no—
731D4—62no—
732D4—92no—
733D4—181no—
734D4—181no—
735D4—181no—
736D4—362no—
737D4—362no—
738D4—721no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—31no—
744C2×C4—31no—
745C2×C4—31no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—61no—
749C2×C4—61no—
750C2×C4—61no—
751C2×C4—61no—
752C2×C4—241no—
753C2×C4—241no—
754C2×C4—362no—
755C2×C4—721no—
756C2×C4D3×#6711yescharacteristic
757C2×C4C22×D3211yescharacteristic
758C8—61no—
759C8—61no—
760C8—181no—
761C8—181no—
762C2×C3—22no—
763C2×C3—22no—
764C2×C3—21no—
765C2×C3—21no—
766C2×C3—21no—
767C2×C3—42no—
768C2×C3—121no—
769C2×C3#561011yescharacteristic
770C2×C3C2×#91811yescharacteristic
771C2×C3#576911yescharacteristic
772C2×C3C2×#94211yescharacteristic
773C2×C3#582911yescharacteristic
774C2×C3#583511yescharacteristic
775D3—41no—
776D3—122no—
777D3—122no—
778D3—242no—
779D3—242no—
780D3—241no—
781D3—241no—
782C22—21no—
783C22—21no—
784C22—61no—
785C22—61no—
786C22—61no—
787C22—182no—
788C22—361no—
789C22—361no—
790C22—361no—
791C22—361no—
792C22—361no—
793C22—724no—
794C22#6394812yes—
795C22C2×D3×#6711yescharacteristic
796C4—21no—
797C4—41no—
798C4—41no—
799C4—61no—
800C4—61no—
801C4—61no—
802C4—121no—
803C4—121no—
804C4—121no—
805C4—121no—
806C4#6431211yescharacteristic
807C4#6431411yescharacteristic
808C3—21no—
809C3#8077711yescharacteristic, complemented
810C3#8363511yescharacteristic, complemented
811C2—22no—
812C2—121no—
813C2—362no—
814C2—721no—
815C2#1059530511yescharacteristic
816C2C2×#6394811yescharacteristic
817C2#1059545611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radical#10595018C2
hypercenterC22⋊Q8D32
hypocenterC32#3314
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5635C2semidirect
3. #10592745C2semidirect
4. C3×#5051C2semidirect
5. #10591657C2semidirect
6. #10591607C2semidirect
7. #10591589C2semidirect
8. #10591540C2semidirect
9. #10591155C2semidirect
10. #10591132C2semidirect
11. C2×#63564C2semidirect
12. #10590609C2semidirect
13. #10590535C2semidirect
14. #10590464C2semidirect
15. #10590422C2semidirect
23. C3×#946C22semidirect
24. C3×Q8×Dic3C22semidirect
25. C2×C3×#216C22semidirect
31. C3×D3×C4⋊C4C22semidirect
33. C3×#888C22semidirect
43. C2×#3711C22semidirect
47. C3×#835C22semidirect
48. C3×#810C22semidirect
49. C3×#807C22semidirect
50. #63576C22semidirect
51. #63576C22semidirect
52. Dic3⋊(C3⋊C8)C22semidirect
53. #63565C22semidirect
54. #63565C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. #63554C22semidirect
62. #5635D3semidirect
72. #5051D3semidirect
167. #946C2×D3semidirect
168. Q8×Dic3C2×D3semidirect
169. C2×#216C2×D3semidirect
190. D3×C4⋊C4C2×D3semidirect
192. #888C2×D3semidirect
206. #835C2×D3semidirect
220. #810C2×D3semidirect
235. #807C2×D3semidirect
718. C32#3314semidirect
809. C3#80777semidirect
810. C3#83635semidirect

Maximal subgroups

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

subgroupindex
C3×#56352
#105950182
#105927452
C3×#50512
#105916572
#105916072
#105915892
#105915402
#105911552
#105911322
C2×#635642
#105906092
#105905352
#105904642
#105904222
#836353
#807773