Finite Group Databasebeta

← #11887420

Subgroups — #11887420

Order 1152.

892 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
1C3×#5630C211yesmaximal, characteristic, complemented
2#10594995C211yesmaximal, characteristic, complemented
3#10592743C211yesmaximal, characteristic, complemented
4C3×#5048C211yesmaximal, characteristic, complemented
5#10591614C211yesmaximal, characteristic, complemented
6#10591586C211yesmaximal, characteristic, complemented
7#10591567C211yesmaximal, characteristic, complemented
8#10591556C211yesmaximal, characteristic, complemented
9#10591160C211yesmaximal, characteristic, complemented
10C3⋊C8×#67C211yesmaximal, characteristic, complemented
11C2×#63563C211yesmaximal, characteristic, complemented
12#10590545C211yesmaximal, characteristic, complemented
13#10590499C211yesmaximal, characteristic, complemented
14#10590452C211yesmaximal, characteristic, complemented
15#10590449C211yesmaximal, characteristic, complemented
16#83495—31nomaximal
17#80681—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C22×C3×D12C2211yescharacteristic
20C32×C22⋊Q8C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C3×#947C2211yescharacteristic
23C2×C3×#215C2211yescharacteristic, complemented
24C3×#930C2211yescharacteristic
25C3×C4×#67C2211yescharacteristic
26C22×C3×C3⋊C8C2211yescharacteristic
27C3×#895—21no—
28C3×#895C2211yescharacteristic
29C3×#894—21no—
30C3×#893C2211yescharacteristic
31C3×#882—21no—
32C3×D3×C22⋊C4—21no—
33#63980—21no—
34#67⋊Dic3—21no—
35#63908C2211yescharacteristic, complemented
36Dic3×D12C2211yescharacteristic, complemented
37#63891—21no—
38#63869C2211yescharacteristic, complemented
39#63861—21no—
40#63841C2211yescharacteristic, complemented
41C2×#3713C2211yescharacteristic
42C2×#3713C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44#63662C2211yescharacteristic, complemented
45#63662C2211yescharacteristic, complemented
46#63657C2211yescharacteristic
47#63634C2211yescharacteristic, complemented
48#63634C2211yescharacteristic, complemented
49C3×#835C2211yescharacteristic, complemented
50C3×#809C2211yescharacteristic, complemented
51C3×#808C2211yescharacteristic, complemented
52Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
53#63563C2211yescharacteristic
54#63563C2211yescharacteristic
55#63563C2211yescharacteristic
56#63563C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×#546—31no—
62#5630D311yescharacteristic, complemented
63#5618—31no—
64#5565—31no—
65C3×#465—31no—
66#5238—31no—
67#5233—31no—
68#5217—31no—
69C2×#832—31no—
70#5172—31no—
71#5165—31no—
72C2×#821—31no—
73C8×#67—31no—
74#5057—31no—
75#5056—31no—
76#5048D311yescharacteristic, complemented
77#5044—31no—
78#5044—31no—
79#5044—61no—
80#5038—31no—
81#5036—31no—
82#5035—31no—
83C4×#213—31no—
84D4×C3⋊C8—31no—
85#5009—31no—
86#4871—31no—
87#4866—31no—
88#4804—31no—
89#4800—31no—
90#4775—31no—
91#4756—31no—
92C23×C3×D3—21no—
93C2×C32×Q8C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C22×C3⋊Dic3—21no—
96C2×C3×#67—21no—
97C2×C3×#67D411yescharacteristic
98C3×#239—22no—
99C3×#239—41no—
100C2×C3×D12—22no—
101C2×C3×D12—21no—
102C2×C3×D12—21no—
103C2×C3×D12—21no—
104C2×C3×D12—41no—
105C2×C3×D12C2311yescharacteristic
106C2×C3×D12C2311yescharacteristic
107C2×C3×D12C2311yescharacteristic
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3C2311yescharacteristic
111C2×#625—21no—
112C2×D3×Dic3—21no—
113C32×C4⋊C4—21no—
114C32×C4⋊C4C2311yescharacteristic
115C32×C22⋊C4—21no—
116C4⋊(C3⋊Dic3)—21no—
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C3×#217D411yescharacteristic
122C3×#215—41no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4D411yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4D411yescharacteristic
131C3×C4×Dic3C2311yescharacteristic
132C2×C3×C3⋊C8—41no—
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135#3724—21no—
136Dic3⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32—21no—
141#3713—22no—
142#3713—41no—
143D3×C3⋊C8—41no—
144#3297—91noSylow
145C2×C3×#41—31no—
146C22×C3×D4—31no—
147C2×#239C2×D311yescharacteristic
148C22×D12C2×D311yescharacteristic
149C2×C3×SD16—31no—
150C22×C3×C8—31no—
151C3×#124—31no—
152C3×#123—61no—
153C3×C22⋊Q8—21no—
154C3×C22⋊Q8C2×D311yescharacteristic
155C3×C22⋊Q8C2×D311yescharacteristic
156C3×#121—31no—
157C3×#121—31no—
158C3×#121—61no—
159C3×#120—61no—
160C3×C4×D4—31no—
161C3×C4×D4—31no—
162C2×C3×C22⋊C4—61no—
163#947C2×D311yescharacteristic
164C2×#215C2×D311yescharacteristic, complemented
165#939—61no—
166#939—61no—
167#938—31no—
168D4×Dic3—31no—
169D4×Dic3—61no—
170C2×#213—31no—
171C2×#213—31no—
172C2×#213—31no—
173C2×#213—31no—
174#930—31no—
175#930C2×D311yescharacteristic
176C4×#67C2×D311yescharacteristic
177#926—31no—
178C2×C4⋊Dic3—31no—
179C2×C4⋊Dic3—31no—
180C2×C4⋊Dic3—61no—
181C22×C3⋊C8—31no—
182C22×C3⋊C8C2×D311yescharacteristic
183C2×D3×C8—31no—
184#898—61no—
185#895—21no—
186#895C2×D311yescharacteristic
187#894—21no—
188#893C2×D311yescharacteristic
189#892—31no—
190#890—31no—
191#886—61no—
192#883—61no—
193#882—21no—
194#67⋊C4—61no—
195D3×C22⋊C4—21no—
196#879—61no—
197C4×D12—31no—
198#870—31no—
199C3×#106—31no—
200C3×#103—31no—
201C3×#102—31no—
202#835—31no—
203#835—31no—
204#835—31no—
205#835—31no—
206#835—61no—
207#835—61no—
208#835C2×D311yescharacteristic, complemented
209#832—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#832—31no—
214#832—31no—
215#830—31no—
216#830—31no—
217#830—31no—
218#830—61no—
219#821—31no—
220#821—31no—
221#821—31no—
222#821—31no—
223(C2×D3)⋊C8—31no—
224Dic3⋊C8—31no—
225C8×Dic3—31no—
226#809—31no—
227#809—31no—
228#809C2×D311yescharacteristic, complemented
229#808C2×D311yescharacteristic, complemented
230#807—31no—
231#807—31no—
232#807—31no—
233#807—31no—
234#807—61no—
235#807—61no—
236C4⋊(C3⋊C8)—31no—
237C4×C3⋊C8—31no—
238C23×C32C2×D411yescharacteristic
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—42no—
243C22×C3×D3—42no—
244C22×C3×D3—81no—
245C22×C3×D3C2×D411yescharacteristic
246C32×Q8—21no—
247C32×Q8—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2411yescharacteristic
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3—81no—
257C3×#67—22no—
258C3×#67—42no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C3×D12—21no—
264C3×D12—21no—
265C3×D12—21no—
266C3×D12—21no—
267C3×D12—21no—
268C3×D12—42no—
269C3×D12—42no—
270C3×D12—81no—
271C3×D12#4112yes—
272C3×C4×D3—21no—
273C3×C4×D3—21no—
274C3×C4×D3—42no—
275C3×C4×D3—81no—
276#625—81no—
277D3×Dic3—81no—
278C3⋊(C3⋊C8)—21no—
279C3⋊(C3⋊C8)—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282#553—91no—
283#546—31no—
284#488—91no—
285#484—91no—
286#482—91no—
287#478—91no—
288#466—91no—
289#465—31no—
290#463—91no—
291#449—91no—
292#447—91no—
293C4×D8—91no—
294C8×D4—91no—
295#416—91no—
296C2×#102—91no—
297C24×C3—61no—
298C23×D3—21no—
299C3×#41—62no—
300C3×#41—121no—
301C2×C3×Q8—21no—
302C2×C3×Q8C22×D311yescharacteristic
303C2×C3×Q8C22×D311yescharacteristic
304C2×C3×D4—31no—
305C2×C3×D4—31no—
306C2×C3×D4—31no—
307C2×C3×D4—31no—
308C2×C3×D4—62no—
309C2×C3×D4—61no—
310C2×C3×D4—61no—
311C2×C3×D4—61no—
312C2×C3×D4—61no—
313C2×C3×D4—121no—
314C22×C3×C4—21no—
315C22×C3×C4—31no—
316C22×C3×C4—61no—
317C22×C3×C4—61no—
318C22×C3×C4C22×D311yescharacteristic
319C22×C3×C4C22×D311yescharacteristic
320C2×#67—21no—
321C2×#67—61no—
322C2×#67—61no—
323C2×#67#6711yescharacteristic
324C22×Dic3—61no—
325C22×Dic3—61no—
326C22×Dic3—61no—
327C22×Dic3—121no—
328#239—22no—
329#239—41no—
330C2×D12—22no—
331C2×D12—21no—
332C2×D12—21no—
333C2×D12—21no—
334C2×D12—41no—
335C2×D12C22×D311yescharacteristic
336C2×D12C22×D311yescharacteristic
337C2×D12C22×D311yescharacteristic
338C2×C4×D3—21no—
339C2×C4×D3—21no—
340C2×C4×D3—61no—
341C2×C4×D3C22×D311yescharacteristic
342C3×SD16—121no—
343C2×C3×C8—31no—
344C2×C3×C8—31no—
345C2×C3×C8—121no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—21no—
348C3×C4⋊C4—21no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—41no—
352C3×C4⋊C4C22×D311yescharacteristic
353C3×C4⋊C4C22×D311yescharacteristic
354C3×C22⋊C4—21no—
355C3×C22⋊C4—21no—
356C3×C22⋊C4—31no—
357C3×C22⋊C4—31no—
358C3×C22⋊C4—41no—
359C3×C22⋊C4—61no—
360C3×C22⋊C4—61no—
361C3×C22⋊C4—61no—
362C3×C22⋊C4—61no—
363C3×C22⋊C4—61no—
364C3×C42—31no—
365#217—61no—
366#217—61no—
367#217—61no—
368#217#6711yescharacteristic
369#215—41no—
370#213—62no—
371#213—62no—
372#213—121no—
373#213—121no—
374(C2×D3)⋊C4—21no—
375(C2×D3)⋊C4—21no—
376(C2×D3)⋊C4—21no—
377(C2×D3)⋊C4—21no—
378(C2×D3)⋊C4—21no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4#6711yescharacteristic
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—121no—
393C4⋊Dic3C22×D311yescharacteristic
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4#6711yescharacteristic
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3C22×D311yescharacteristic
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—41no—
406C2×C3⋊C8—61no—
407C2×C3⋊C8—61no—
408C2×C3⋊C8—121no—
409C2×C3⋊C8C22×D311yescharacteristic
410C2×C3⋊C8C22×D311yescharacteristic
411D3×C8—121no—
412C22×C32—21no—
413C22×C32—21no—
414C22×C32#13512yes—
415C22×C32C22×D411yescharacteristic
416C2×C3×D3—21no—
417C2×C3×D3—22no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428C2×C3×D3—84no—
429C32×C4—21no—
430C32×C4—41no—
431C32×C4—41no—
432C32×C4C2×#4111yescharacteristic
433C32×C4H(5,𝔽2)11yescharacteristic
434C3⋊Dic3—41no—
435C3⋊Dic3—41no—
436C3×Dic3—21no—
437C3×Dic3—21no—
438C3×Dic3—21no—
439C3×Dic3—41no—
440C2×#41—31no—
441C22×D4—31no—
442C2×SD16—31no—
443C2×D8—91no—
444C2×D8—91no—
445C22×C8—31no—
446C22×C8—91no—
447#126—181no—
448#125—91no—
449#124—31no—
450#123—61no—
451#123—181no—
452C22⋊Q8D3211yescharacteristic
453#121—31no—
454#121—31no—
455#121—61no—
456#121—91no—
457#121—181no—
458#120—61no—
459C4×D4—31no—
460C4×D4—31no—
461C4×D4—91no—
462C4×D4—181no—
463#117—91no—
464C2×C4⋊C4—91no—
465C2×C22⋊C4—61no—
466#107—91no—
467#107—91no—
468#106—31no—
469C4⋊C8—91no—
470#103—31no—
471#103—91no—
472#103—91no—
473#102—31no—
474#102—91no—
475#102—91no—
476#102—91no—
477#102—91no—
478#102—91no—
479#102—91no—
480C22⋊C8—91no—
481C22⋊C8—91no—
482C4×C8—91no—
483C23×C3—21no—
484C23×C3—31no—
485C23×C3—61no—
486C23×C3—61no—
487C23×C3—61no—
488C23×C3—122no—
489C23×C3—122no—
490C23×C3—241no—
491C23×C3D3×D411yescharacteristic
492C23×C3C2×#6711yescharacteristic
493C22×D3—21no—
494C22×D3—21no—
495C22×D3—21no—
496C22×D3—42no—
497C22×D3—42no—
498C22×D3—81no—
499C22×D3C2×#6711yescharacteristic
500C3×Q8—21no—
501C3×Q8—21no—
502C3×Q8—21no—
503C3×Q8—21no—
504C3×Q8—41no—
505C3×Q8—41no—
506C3×D4—32no—
507C3×D4—62no—
508C3×D4—61no—
509C3×D4—61no—
510C3×D4—61no—
511C3×D4—61no—
512C3×D4—61no—
513C3×D4—122no—
514C3×D4—122no—
515C3×D4—122no—
516C3×D4—241no—
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—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—31no—
528C2×C3×C4—31no—
529C2×C3×C4—31no—
530C2×C3×C4—41no—
531C2×C3×C4—41no—
532C2×C3×C4—41no—
533C2×C3×C4—41no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—122no—
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—42no—
545#67—241no—
546#67—241no—
547C2×Dic3—21no—
548C2×Dic3—61no—
549C2×Dic3—61no—
550C2×Dic3—61no—
551C2×Dic3—61no—
552C2×Dic3—121no—
553C2×Dic3—121no—
554C2×Dic3—241no—
555C2×Dic3—241no—
556C2×Dic3—241no—
557C2×Dic3—242no—
558C2×Dic3C2×#6711yescharacteristic
559C2×Dic3C2×#6711yescharacteristic
560C2×Dic3C2×#6711yescharacteristic
561D12—21no—
562D12—21no—
563D12—21no—
564D12—21no—
565D12—21no—
566D12—42no—
567D12—42no—
568D12—81no—
569D12#23712yes—
570C4×D3—21no—
571C4×D3—21no—
572C4×D3—42no—
573C4×D3—81no—
574C4×D3—241no—
575C3×C8—61no—
576C3×C8—61no—
577C3⋊C8—21no—
578C3⋊C8—21no—
579C3⋊C8—61no—
580C3⋊C8—61no—
581C3⋊C8—61no—
582C3⋊C8—61no—
583C3⋊C8—121no—
584C3⋊C8—121no—
585C2×C32—22no—
586C2×C32#54611yescharacteristic
587C2×C32C2×#13511yescharacteristic
588C2×C32#57611yescharacteristic
589C3×D3—41no—
590C3×D3—42no—
591C3×D3—81no—
592C3×D3—81no—
593C24—61no—
594#41—62no—
595#41—121no—
596C2×Q8C2×D3211yescharacteristic
597C2×D4—31no—
598C2×D4—31no—
599C2×D4—31no—
600C2×D4—31no—
601C2×D4—62no—
602C2×D4—61no—
603C2×D4—61no—
604C2×D4—61no—
605C2×D4—61no—
606C2×D4—121no—
607C2×D4—181no—
608C22×C4—31no—
609C22×C4—61no—
610C22×C4—61no—
611C22×C4—181no—
612C22×C4—181no—
613C22×C4C2×D3211yescharacteristic
614SD16—121no—
615D8—182no—
616D8—361no—
617C2×C8—31no—
618C2×C8—31no—
619C2×C8—91no—
620C2×C8—91no—
621C2×C8—121no—
622C2×C8—361no—
623C4⋊C4—21no—
624C4⋊C4—31no—
625C4⋊C4—31no—
626C4⋊C4—91no—
627C4⋊C4—91no—
628C4⋊C4—181no—
629C4⋊C4—181no—
630C4⋊C4—181no—
631C4⋊C4C2×D3211yescharacteristic
632C22⋊C4—21no—
633C22⋊C4—31no—
634C22⋊C4—31no—
635C22⋊C4—61no—
636C22⋊C4—61no—
637C22⋊C4—61no—
638C22⋊C4—61no—
639C22⋊C4—61no—
640C22⋊C4—181no—
641C22⋊C4—181no—
642C22⋊C4—181no—
643C42—31no—
644C42—181no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—22no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—61no—
654C22×C3—61no—
655C22×C3—61no—
656C22×C3—62no—
657C22×C3—121no—
658C22×C3—121no—
659C22×C3—121no—
660C22×C3—121no—
661C22×C3—121no—
662C22×C3—121no—
663C22×C3—121no—
664C22×C3—121no—
665C22×C3—244no—
666C22×C3#91612yes—
667C22×C3#95012yes—
668C22×C3C2×D3×D411yescharacteristic
669C22×C3C22×#6711yescharacteristic
670C2×D3—21no—
671C2×D3—22no—
672C2×D3—21no—
673C2×D3—21no—
674C2×D3—41no—
675C2×D3—41no—
676C2×D3—41no—
677C2×D3—41no—
678C2×D3—41no—
679C2×D3—41no—
680C2×D3—41no—
681C2×D3—41no—
682C2×D3—84no—
683C3×C4—21no—
684C3×C4—21no—
685C3×C4—21no—
686C3×C4—21no—
687C3×C4—41no—
688C3×C4—41no—
689C3×C4—41no—
690C3×C4—41no—
691C3×C4—41no—
692C3×C4—61no—
693C3×C4—61no—
694C3×C4—61no—
695C3×C4—81no—
696C3×C4—81no—
697C3×C4—121no—
698C3×C4C2×#23711yescharacteristic
699C3×C4#100411yescharacteristic
700C3×C4#100411yescharacteristic
701C3×C4D3×#4111yescharacteristic
702Dic3—21no—
703Dic3—21no—
704Dic3—21no—
705Dic3—41no—
706Dic3—121no—
707Dic3—121no—
708Dic3—121no—
709Dic3—121no—
710Dic3—241no—
711Dic3—241no—
712C32#329711yescharacteristic, complemented, Sylow
713C23—31no—
714C23—61no—
715C23—61no—
716C23—61no—
717C23—122no—
718C23—122no—
719C23—241no—
720C23D3×#6711yescharacteristic
721Q8—21no—
722Q8—21no—
723D4—32no—
724D4—62no—
725D4—61no—
726D4—61no—
727D4—61no—
728D4—61no—
729D4—61no—
730D4—122no—
731D4—122no—
732D4—122no—
733D4—241no—
734D4—721no—
735C2×C4—21no—
736C2×C4—21no—
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—122no—
746C2×C4—181no—
747C2×C4—181no—
748C2×C4—241no—
749C2×C4—721no—
750C2×C4—721no—
751C2×C4D3×#6711yescharacteristic
752C2×C4C22×D3211yescharacteristic
753C8—61no—
754C8—61no—
755C8—181no—
756C8—181no—
757C2×C3—22no—
758C2×C3—22no—
759C2×C3—21no—
760C2×C3—21no—
761C2×C3—21no—
762C2×C3—42no—
763C2×C3—121no—
764C2×C3—122no—
765C2×C3—241no—
766C2×C3—241no—
767C2×C3#561011yescharacteristic
768C2×C3C2×#91611yescharacteristic
769C2×C3#576911yescharacteristic
770C2×C3#580611yescharacteristic
771C2×C3C2×#95011yescharacteristic
772C2×C3#583511yescharacteristic
773D3—41no—
774D3—42no—
775D3—81no—
776D3—81no—
777C22—21no—
778C22—21no—
779C22—61no—
780C22—61no—
781C22—62no—
782C22—61no—
783C22—121no—
784C22—121no—
785C22—121no—
786C22—121no—
787C22—121no—
788C22—121no—
789C22—121no—
790C22—121no—
791C22—244no—
792C22#6394712yes—
793C22C2×D3×#6711yescharacteristic
794C4—21no—
795C4—41no—
796C4—41no—
797C4—61no—
798C4—61no—
799C4—61no—
800C4—121no—
801C4—361no—
802C4—361no—
803C4D3×#23711yescharacteristic
804C4#6431311yescharacteristic
805C3—21no—
806C3#8068111yescharacteristic, complemented
807C3#8349511yescharacteristic, complemented
808C2—22no—
809C2—121no—
810C2—122no—
811C2—241no—
812C2—241no—
813C2#1059515011yescharacteristic
814C2C2×#6394711yescharacteristic
815C2#1059545611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
hypercenterC22⋊Q8D32
hypocenterC32#3297
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×#5630C2semidirect
2. #10594995C2semidirect
3. #10592743C2semidirect
4. C3×#5048C2semidirect
5. #10591614C2semidirect
6. #10591586C2semidirect
7. #10591567C2semidirect
8. #10591556C2semidirect
9. #10591160C2semidirect
10. C3⋊C8×#67C2semidirect
11. C2×#63563C2semidirect
12. #10590545C2semidirect
13. #10590499C2semidirect
14. #10590452C2semidirect
15. #10590449C2semidirect
23. C2×C3×#215C22semidirect
35. #63908C22semidirect
36. Dic3×D12C22semidirect
38. #63869C22semidirect
40. #63841C22semidirect
43. C2×D3×C3⋊C8C22semidirect
44. #63662C22semidirect
45. #63662C22semidirect
47. #63634C22semidirect
48. #63634C22semidirect
49. C3×#835C22semidirect
50. C3×#809C22semidirect
51. C3×#808C22semidirect
52. Dic3⋊(C3⋊C8)C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. Dic3×C3⋊C8C22semidirect
62. #5630D3semidirect
76. #5048D3semidirect
164. C2×#215C2×D3semidirect
208. #835C2×D3semidirect
228. #809C2×D3semidirect
229. #808C2×D3semidirect
712. C32#3297semidirect
806. C3#80681semidirect
807. C3#83495semidirect

Maximal subgroups

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

subgroupindex
C3×#56302
#105949952
#105927432
C3×#50482
#105916142
#105915862
#105915672
#105915562
#105911602
C3⋊C8×#672
C2×#635632
#105905452
#105904992
#105904522
#105904492
#834953
#806813