Finite Group Databasebeta

← #11887455

Subgroups — #11887455

Order 1152.

893 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5612C211yesmaximal, characteristic, complemented
2#10594945C211yesmaximal, characteristic, complemented
3#10592734C211yesmaximal, characteristic, complemented
4C3×#5038C211yesmaximal, characteristic, complemented
5#10591478C211yesmaximal, characteristic, complemented
6#10591447C211yesmaximal, characteristic, complemented
7#10591431C211yesmaximal, characteristic, complemented
8D3×#832C211yesmaximal, characteristic, complemented
9#10591161C211yesmaximal, characteristic, complemented
10C3⋊C8×#67C211yesmaximal, characteristic, complemented
11#10591084C211yesmaximal, characteristic, complemented
12#10590542C211yesmaximal, characteristic, complemented
13#10590501C211yesmaximal, characteristic, complemented
14#10590452C211yesmaximal, characteristic, complemented
15#10590440C211yesmaximal, characteristic, complemented
16#83495—31nomaximal
17#80725—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C32×#121C2211yescharacteristic
21#64135C2211yescharacteristic, complemented
22C3×#938—21no—
23C3×#937—21no—
24C3×#936C2211yescharacteristic
25C2×C3×#213C2211yescharacteristic
26C3×#930C2211yescharacteristic, complemented
27C3×C4×#67C2211yescharacteristic
28C22×C3×C3⋊C8C2211yescharacteristic, complemented
29C3×#897C2211yescharacteristic
30C3×#893C2211yescharacteristic
31C3×#883—21no—
32C3×D3×C22⋊C4—21no—
33#63970—21no—
34#63969—21no—
35#63908C2211yescharacteristic
36#63902—21no—
37Dic3×D12C2211yescharacteristic, complemented
38D3×C4⋊Dic3C2211yescharacteristic
39#63869C2211yescharacteristic, complemented
40#63862—21no—
41C2×#3715C2211yescharacteristic, complemented
42C2×#3713C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44#63659C2211yescharacteristic
45#63659C2211yescharacteristic
46#63657C2211yescharacteristic, complemented
47#63635C2211yescharacteristic, complemented
48#63634C2211yescharacteristic, complemented
49C3×#832C2211yescharacteristic
50C3×#809C2211yescharacteristic, complemented
51C3×#807C2211yescharacteristic, complemented
52Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
53#63566C2211yescharacteristic, complemented
54#63566C2211yescharacteristic, complemented
55#63565C2211yescharacteristic, complemented
56#63563C2211yescharacteristic
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×#546—31no—
62#5614—31no—
63#5612D311yescharacteristic, complemented
64#5565—31no—
65C3×#466—31no—
66#5238—31no—
67#5233—31no—
68#5217—31no—
69C2×#832—31no—
70#5156—31no—
71#5153—31no—
72#5113—31no—
73C8×#67—31no—
74#5057—31no—
75#5056—31no—
76#5048—31no—
77#5044—31no—
78#5038D311yescharacteristic, complemented
79#5037—31no—
80#5035—31no—
81#5035—31no—
82#5035—61no—
83C4×#213—31no—
84D4×C3⋊C8—31no—
85#5009—31no—
86#4891—31no—
87#4884—31no—
88#4778—31no—
89D3×#102—31no—
90#4768—31no—
91#4756—31no—
92C23×C3×D3—21no—
93C2×C32×D4—21no—
94C2×C32×D4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C2×C3×#67D411yescharacteristic
100C3×D3×D4—22no—
101C3×D3×D4—41no—
102C3×#235—22no—
103C3×#235—41no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110C2×#625—21no—
111C2×D3×Dic3—21no—
112C2×D3×Dic3—21no—
113C32×C4⋊C4C2311yescharacteristic
114C32×C22⋊C4—21no—
115#3757—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C4×C3⋊Dic3—21no—
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C3×#217—21no—
122C3×#217—21no—
123C3×#217D411yescharacteristic
124C3×#213—41no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4D411yescharacteristic
129C3×C4⋊Dic3—21no—
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4D411yescharacteristic
132C3×C4×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8—41no—
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136#3724—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141#3715—41no—
142#3713—22no—
143D3×C3⋊C8—41no—
144#3297—91noSylow
145C2×C3×#41—31no—
146C22×C3×D4—31no—
147C2×D3×D4C2×D311yescharacteristic
148C2×#235C2×D311yescharacteristic
149C2×C3×D8—31no—
150C22×C3×C8—31no—
151C3×#124—31no—
152C3×#123—61no—
153C3×C22⋊Q8—31no—
154C3×#121—21no—
155C3×#121—31no—
156C3×#121—61no—
157C3×#121C2×D311yescharacteristic
158C3×#121C2×D311yescharacteristic
159C3×#120—61no—
160C3×C4×D4—31no—
161C3×C4×D4—31no—
162C2×C3×C22⋊C4—61no—
163C2×#215—31no—
164#939—61no—
165#938—21no—
166#938—31no—
167#938—61no—
168#937—21no—
169#936C2×D311yescharacteristic
170#935—61no—
171D4×Dic3—31no—
172C2×#214—31no—
173C2×#213—31no—
174C2×#213—31no—
175C2×#213C2×D311yescharacteristic
176#930—31no—
177#930C2×D311yescharacteristic, complemented
178C4×#67C2×D311yescharacteristic
179#926—31no—
180#926—31no—
181#926—61no—
182C2×C4⋊Dic3—31no—
183C22×C3⋊C8—31no—
184C22×C3⋊C8C2×D311yescharacteristic, complemented
185C2×D3×C8—31no—
186#898—61no—
187#897C2×D311yescharacteristic
188#893C2×D311yescharacteristic
189D3×C4⋊C4—31no—
190#890—31no—
191#883—21no—
192#883—61no—
193#67⋊C4—61no—
194#67⋊C4—61no—
195D3×C22⋊C4—21no—
196#879—61no—
197C4×D12—31no—
198#870—31no—
199C3×#107—31no—
200C3×#102—31no—
201C3×#102—31no—
202#835—31no—
203#835—31no—
204#835—31no—
205#832—31no—
206#832—31no—
207#832—31no—
208#832—31no—
209#832—31no—
210#832—31no—
211#832—31no—
212#832—61no—
213#832—61no—
214#832C2×D311yescharacteristic
215#830—31no—
216#830—31no—
217#830—31no—
218#830—61no—
219#821—31no—
220#821—31no—
221(C2×D3)⋊C8—31no—
222#816—31no—
223#816—31no—
224Dic3⋊C8—31no—
225C8×Dic3—31no—
226#810—31no—
227#809—31no—
228#809C2×D311yescharacteristic, complemented
229#808—31no—
230#808—31no—
231#808—61no—
232#807—31no—
233#807—31no—
234#807—61no—
235#807C2×D311yescharacteristic, complemented
236C4⋊(C3⋊C8)—31no—
237C4×C3⋊C8—31no—
238C23×C32—21no—
239C23×C32C2×D411yescharacteristic
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×D4—21no—
247C32×D4—21no—
248C32×D4—81no—
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—
256C3×#67—22no—
257C3×#67—42no—
258C3×#67—42no—
259C3×#67—81no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×D12—21no—
266C3×D12—21no—
267C3×D12—21no—
268C3×D12#4112yes—
269C3×C4×D3—21no—
270C3×C4×D3—21no—
271C3×C4×D3—42no—
272C3×C4×D3—81no—
273C3×Dic6—21no—
274C3×Dic6—21no—
275#625—42no—
276D3×Dic3—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—31no—
289#465—91no—
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—31no—
302C2×C3×D4—21no—
303C2×C3×D4—21no—
304C2×C3×D4—21no—
305C2×C3×D4—31no—
306C2×C3×D4—31no—
307C2×C3×D4—31no—
308C2×C3×D4—41no—
309C2×C3×D4—61no—
310C2×C3×D4—62no—
311C2×C3×D4—61no—
312C2×C3×D4—61no—
313C2×C3×D4—121no—
314C2×C3×D4C22×D311yescharacteristic
315C2×C3×D4C22×D311yescharacteristic
316C22×C3×C4—21no—
317C22×C3×C4—31no—
318C22×C3×C4—61no—
319C22×C3×C4—61no—
320C22×C3×C4C22×D311yescharacteristic
321C22×C3×C4C22×D311yescharacteristic
322C2×#67—21no—
323C2×#67—21no—
324C2×#67—21no—
325C2×#67—61no—
326C2×#67—61no—
327C2×#67#6711yescharacteristic
328C22×Dic3—61no—
329C22×Dic3—61no—
330D3×D4—22no—
331D3×D4—41no—
332#235—22no—
333#235—41no—
334C2×D12C22×D311yescharacteristic
335C2×D12C22×D311yescharacteristic
336C2×C4×D3—21no—
337C2×C4×D3—21no—
338C2×C4×D3—61no—
339C2×C4×D3—61no—
340C2×C4×D3C22×D311yescharacteristic
341C2×Dic6C22×D311yescharacteristic
342C3×D8—121no—
343C2×C3×C8—31no—
344C2×C3×C8—31no—
345C2×C3×C8—121no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—61no—
350C3×C4⋊C4C22×D311yescharacteristic
351C3×C4⋊C4C22×D311yescharacteristic
352C3×C22⋊C4—21no—
353C3×C22⋊C4—21no—
354C3×C22⋊C4—31no—
355C3×C22⋊C4—31no—
356C3×C22⋊C4—41no—
357C3×C22⋊C4—61no—
358C3×C22⋊C4—61no—
359C3×C22⋊C4—61no—
360C3×C22⋊C4—61no—
361C3×C22⋊C4—61no—
362C3×C42—31no—
363#217—21no—
364#217—21no—
365#217—61no—
366#217—61no—
367#217—61no—
368#217—61no—
369#217—121no—
370#217#6711yescharacteristic
371#215—121no—
372#214—121no—
373#213—41no—
374#213—62no—
375#213—62no—
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#6711yescharacteristic
382C4⋊Dic3—21no—
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⋊Dic3C22×D311yescharacteristic
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4#6711yescharacteristic
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—121no—
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—21no—
415C22×C32—41no—
416C22×C32—41no—
417C22×C32—41no—
418C22×C32C22×D411yescharacteristic
419C2×C3×D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—22no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3—84no—
428C2×C3×D3#13512yes—
429C32×C4—21no—
430C32×C4—41no—
431C32×C4C2×#4111yescharacteristic
432C32×C4H(5,𝔽2)11yescharacteristic
433C3⋊Dic3—41no—
434C3⋊Dic3—41no—
435C3×Dic3—21no—
436C3×Dic3—21no—
437C3×Dic3—21no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C2×#41—31no—
441C22×D4—31no—
442C2×SD16—91no—
443C2×D8—31no—
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⋊Q8—31no—
453#121—31no—
454#121—61no—
455#121—91no—
456#121—181no—
457#121D3211yescharacteristic
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—31no—
467#107—91no—
468#106—91no—
469C4⋊C8—91no—
470#103—91no—
471#103—91no—
472#103—91no—
473#102—31no—
474#102—31no—
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—21no—
485C23×C3—21no—
486C23×C3—31no—
487C23×C3—41no—
488C23×C3—61no—
489C23×C3—61no—
490C23×C3—122no—
491C23×C3—122no—
492C23×C3—241no—
493C23×C3D3×D411yescharacteristic
494C23×C3C2×#6711yescharacteristic
495C22×D3—21no—
496C22×D3—21no—
497C22×D3—42no—
498C22×D3—42no—
499C22×D3—81no—
500C22×D3C2×#6711yescharacteristic
501C3×Q8—61no—
502C3×Q8—61no—
503C3×D4—21no—
504C3×D4—21no—
505C3×D4—21no—
506C3×D4—21no—
507C3×D4—32no—
508C3×D4—41no—
509C3×D4—41no—
510C3×D4—62no—
511C3×D4—61no—
512C3×D4—61no—
513C3×D4—61no—
514C3×D4—81no—
515C3×D4—81no—
516C3×D4—82no—
517C3×D4—122no—
518C3×D4—122no—
519C3×D4—241no—
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—21no—
528C2×C3×C4—31no—
529C2×C3×C4—31no—
530C2×C3×C4—31no—
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—61no—
538C2×C3×C4—122no—
539C2×C3×C4—241no—
540C2×C3×C4D3×D411yescharacteristic
541C2×C3×C4C2×#6711yescharacteristic
542C2×C3×C4C23×D311yescharacteristic
543C2×C3×C4C23×D311yescharacteristic
544#67—22no—
545#67—42no—
546#67—42no—
547#67—81no—
548#67—122no—
549#67—122no—
550C2×Dic3—21no—
551C2×Dic3—21no—
552C2×Dic3—61no—
553C2×Dic3—61no—
554C2×Dic3—61no—
555C2×Dic3—61no—
556C2×Dic3—121no—
557C2×Dic3—121no—
558C2×Dic3—241no—
559C2×Dic3—241no—
560C2×Dic3C2×#6711yescharacteristic
561C2×Dic3C2×#6711yescharacteristic
562C2×Dic3C2×#6711yescharacteristic
563D12—21no—
564D12—21no—
565D12—21no—
566D12#23712yes—
567C4×D3—21no—
568C4×D3—21no—
569C4×D3—42no—
570C4×D3—81no—
571C4×D3—241no—
572C4×D3—241no—
573Dic6—21no—
574Dic6—21no—
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—41no—
586C2×C32—81no—
587C2×C32#54611yescharacteristic
588C2×C32C2×#13511yescharacteristic
589C2×C32#57611yescharacteristic
590C3×D3—22no—
591C3×D3—42no—
592C3×D3—81no—
593C24—61no—
594#41—62no—
595#41—121no—
596C2×Q8—31no—
597C2×D4—21no—
598C2×D4—31no—
599C2×D4—31no—
600C2×D4—31no—
601C2×D4—61no—
602C2×D4—62no—
603C2×D4—61no—
604C2×D4—61no—
605C2×D4—121no—
606C2×D4—181no—
607C2×D4C2×D3211yescharacteristic
608C22×C4—31no—
609C22×C4—61no—
610C22×C4—61no—
611C22×C4—181no—
612C22×C4—181no—
613C22×C4C2×D3211yescharacteristic
614SD16—361no—
615D8—121no—
616D8—182no—
617C2×C8—31no—
618C2×C8—31no—
619C2×C8—91no—
620C2×C8—91no—
621C2×C8—121no—
622C2×C8—361no—
623C4⋊C4—31no—
624C4⋊C4—31no—
625C4⋊C4—61no—
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—21no—
651C22×C3—21no—
652C22×C3—32no—
653C22×C3—41no—
654C22×C3—41no—
655C22×C3—41no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—41no—
659C22×C3—41no—
660C22×C3—41no—
661C22×C3—41no—
662C22×C3—61no—
663C22×C3—61no—
664C22×C3—62no—
665C22×C3—81no—
666C22×C3—81no—
667C22×C3—81no—
668C22×C3—121no—
669C22×C3—121no—
670C22×C3—121no—
671C22×C3—121no—
672C22×C3—121no—
673C22×C3—244no—
674C22×C3C2×D3×D411yescharacteristic
675C22×C3C22×#6711yescharacteristic
676C2×D3—21no—
677C2×D3—21no—
678C2×D3—22no—
679C2×D3—41no—
680C2×D3—41no—
681C2×D3—41no—
682C2×D3—41no—
683C2×D3—41no—
684C2×D3—84no—
685C2×D3#95012yes—
686C3×C4—21no—
687C3×C4—21no—
688C3×C4—21no—
689C3×C4—21no—
690C3×C4—41no—
691C3×C4—41no—
692C3×C4—41no—
693C3×C4—61no—
694C3×C4—61no—
695C3×C4—61no—
696C3×C4—81no—
697C3×C4—121no—
698C3×C4—121no—
699C3×C4C2×#23711yescharacteristic
700C3×C4#100411yescharacteristic
701C3×C4#100411yescharacteristic
702C3×C4D3×#4111yescharacteristic
703Dic3—21no—
704Dic3—21no—
705Dic3—21no—
706Dic3—41no—
707Dic3—41no—
708Dic3—121no—
709Dic3—121no—
710Dic3—121no—
711Dic3—121no—
712Dic3—241no—
713Dic3—241no—
714C32#329711yescharacteristic, complemented, Sylow
715C23—21no—
716C23—31no—
717C23—61no—
718C23—61no—
719C23—122no—
720C23—122no—
721C23—241no—
722C23D3×#6711yescharacteristic
723Q8—61no—
724Q8—61no—
725D4—21no—
726D4—21no—
727D4—32no—
728D4—62no—
729D4—61no—
730D4—61no—
731D4—61no—
732D4—81no—
733D4—122no—
734D4—122no—
735D4—241no—
736D4—362no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—31no—
741C2×C4—31no—
742C2×C4—31no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—122no—
748C2×C4—181no—
749C2×C4—181no—
750C2×C4—241no—
751C2×C4—721no—
752C2×C4—721no—
753C2×C4D3×#6711yescharacteristic
754C2×C4C22×D3211yescharacteristic
755C8—61no—
756C8—61no—
757C8—181no—
758C8—181no—
759C2×C3—21no—
760C2×C3—21no—
761C2×C3—21no—
762C2×C3—41no—
763C2×C3—41no—
764C2×C3—62no—
765C2×C3—81no—
766C2×C3—81no—
767C2×C3—81no—
768C2×C3—122no—
769C2×C3—161no—
770C2×C3—241no—
771C2×C3#561011yescharacteristic
772C2×C3#575711yescharacteristic
773C2×C3D3×#13511yescharacteristic
774C2×C3#580611yescharacteristic
775C2×C3C2×#95011yescharacteristic
776C2×C3#583511yescharacteristic
777D3—22no—
778D3—42no—
779D3—81no—
780C22—21no—
781C22—21no—
782C22—21no—
783C22—32no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—61no—
788C22—61no—
789C22—62no—
790C22—121no—
791C22—121no—
792C22—121no—
793C22—121no—
794C22—121no—
795C22—244no—
796C22C2×D3×#6711yescharacteristic
797C4—21no—
798C4—41no—
799C4—61no—
800C4—61no—
801C4—61no—
802C4—121no—
803C4—121no—
804C4—361no—
805C4—361no—
806C4D3×#23711yescharacteristic
807C4#6431311yescharacteristic
808C3—21no—
809C3#8072511yescharacteristic, complemented
810C3#8349511yescharacteristic, complemented
811C2—41no—
812C2—62no—
813C2—81no—
814C2—122no—
815C2—241no—
816C2#1059509611yescharacteristic
817C2#1059515011yescharacteristic
818C2D3×#95011yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
hypercenter#121D32
hypocenterC32#3297
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C3×#5612C2semidirect
2. #10594945C2semidirect
3. #10592734C2semidirect
4. C3×#5038C2semidirect
5. #10591478C2semidirect
6. #10591447C2semidirect
7. #10591431C2semidirect
8. D3×#832C2semidirect
9. #10591161C2semidirect
10. C3⋊C8×#67C2semidirect
11. #10591084C2semidirect
12. #10590542C2semidirect
13. #10590501C2semidirect
14. #10590452C2semidirect
15. #10590440C2semidirect
21. #64135C22semidirect
26. C3×#930C22semidirect
28. C22×C3×C3⋊C8C22semidirect
37. Dic3×D12C22semidirect
39. #63869C22semidirect
41. C2×#3715C22semidirect
46. #63657C22semidirect
47. #63635C22semidirect
48. #63634C22semidirect
50. C3×#809C22semidirect
51. C3×#807C22semidirect
52. Dic3⋊(C3⋊C8)C22semidirect
53. #63566C22semidirect
54. #63566C22semidirect
55. #63565C22semidirect
60. Dic3×C3⋊C8C22semidirect
63. #5612D3semidirect
78. #5038D3semidirect
177. #930C2×D3semidirect
184. C22×C3⋊C8C2×D3semidirect
228. #809C2×D3semidirect
235. #807C2×D3semidirect
714. C32#3297semidirect
809. C3#80725semidirect
810. C3#83495semidirect

Maximal subgroups

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

subgroupindex
C3×#56122
#105949452
#105927342
C3×#50382
#105914782
#105914472
#105914312
D3×#8322
#105911612
C3⋊C8×#672
#105910842
#105905422
#105905012
#105904522
#105904402
#834953
#807253