Finite Group Databasebeta

← #11887383

Subgroups — #11887383

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×#5530C211yesmaximal, characteristic, complemented
2#10595067C211yesmaximal, characteristic, complemented
3#10592702C211yesmaximal, characteristic, complemented
4C3×#5002C211yesmaximal, characteristic, complemented
5#10591164C211yesmaximal, characteristic, complemented
6#10591161C211yesmaximal, characteristic, complemented
7C3⋊C8×#67C211yesmaximal, characteristic, complemented
8#10590595C211yesmaximal, characteristic, complemented
9D3×#809C211yesmaximal, characteristic, complemented
10#10590537C211yesmaximal, characteristic, complemented
11#10590534C211yesmaximal, characteristic, complemented
12#10590517C211yesmaximal, characteristic, complemented
13#10590514C211yesmaximal, characteristic, complemented
14#10590469C211yesmaximal, characteristic, complemented
15#10590452C211yesmaximal, characteristic, complemented
16#83614—31nomaximal
17#78846—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C32×#117C2211yescharacteristic, complemented
21#64139C2211yescharacteristic
22C3×#930C2211yescharacteristic, complemented
23C3×C4×#67C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic, complemented
25C3×#895C2211yescharacteristic
26C3×#893C2211yescharacteristic, complemented
27C3×D3×C4⋊C4C2211yescharacteristic
28C3×#890C2211yescharacteristic, complemented
29C3×#884—21no—
30C3×#883—21no—
31C3×#876—21no—
32C3×C4×D12—21no—
33#63983—21no—
34#63971—21no—
35D3×(C2×D3)⋊C4—21no—
36Dic3×D12C2211yescharacteristic
37#63864C2211yescharacteristic
38#63856C2211yescharacteristic
39#63850—21no—
40C2×#3715C2211yescharacteristic, complemented
41C2×#3714C2211yescharacteristic
42C2×#3713C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44#63657C2211yescharacteristic, complemented
45#63636C2211yescharacteristic
46#63636C2211yescharacteristic
47#63635C2211yescharacteristic, complemented
48#63634C2211yescharacteristic, complemented
49C3×#810C2211yescharacteristic, complemented
50C3×#810C2211yescharacteristic, complemented
51C3×#809C2211yescharacteristic
52C3×#809C2211yescharacteristic
53#63575C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63565C2211yescharacteristic, complemented
56#63564C2211yescharacteristic
57#63563C2211yescharacteristic, complemented
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×#553—31no—
62#5829—31no—
63#5550—31no—
64#5530D311yescharacteristic, complemented
65C3×#416—31no—
66#5238—31no—
67#5115—31no—
68C8×#67—31no—
69#5068—31no—
70#5066—31no—
71#5041—31no—
72#5038—31no—
73#5037—31no—
74#5036—31no—
75#5016—31no—
76C4×#213—31no—
77D4×C3⋊C8—31no—
78#5003—31no—
79#5003—31no—
80#5003—61no—
81#5002D311yescharacteristic, complemented
82#4970—31no—
83C2×#809—31no—
84#4819—31no—
85#4811—31no—
86#4807—31no—
87#4800—31no—
88#4773—31no—
89D3×#102—31no—
90#4766—31no—
91#4756—31no—
92C22×D32—21no—
93C22×C32×C4C2311yescharacteristic
94C2×#638—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C2×C3×#67D411yescharacteristic
99C3×#235—22no—
100C3×#235—41no—
101C2×C3×D12—21no—
102C2×C3×D12C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×#626—21no—
110C2×D3×Dic3—21no—
111D3×D12—22no—
112D3×D12—41no—
113C32×C4⋊C4C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115C32×C22⋊C4—21no—
116C32×C42—21no—
117#3752—21no—
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C3×#217D411yescharacteristic
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4D411yescharacteristic
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4D411yescharacteristic
131C3×C4×Dic3C2311yescharacteristic
132C2×C3×C3⋊C8—41no—
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135#3724—21no—
136#3722—21no—
137#3722—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140#3715—41no—
141#3714—41no—
142#3713—22no—
143D3×C3⋊C8—41no—
144#3297—91noSylow
145C2×C3×#41—31no—
146C2×D3×D4—31no—
147C2×#235C2×D311yescharacteristic
148C22×D12—31no—
149C22×C3×C8—31no—
150C3×#126—61no—
151C3×#125—31no—
152C3×#123—61no—
153C3×#121—31no—
154C3×#121—31no—
155C3×#121—61no—
156C3×C4×D4—31no—
157C3×C4×D4—31no—
158C3×C4×D4—61no—
159C3×#117—21no—
160C3×#117C2×D311yescharacteristic, complemented
161C3×#117C2×D311yescharacteristic, complemented
162C2×C3×C4⋊C4—31no—
163#947—31no—
164#946—31no—
165C2×#215—31no—
166#939—61no—
167#937—61no—
168#937—61no—
169D4×Dic3—31no—
170C2×#214—31no—
171C2×#213—31no—
172C2×#213—31no—
173C2×#213—31no—
174#930—31no—
175#930—31no—
176#930—61no—
177#930C2×D311yescharacteristic, complemented
178#929—61no—
179C4×#67C2×D311yescharacteristic
180C2×(C2×D3)⋊C4—61no—
181#924—31no—
182C22×C3⋊C8—31no—
183C22×C3⋊C8C2×D311yescharacteristic, complemented
184C2×D24—31no—
185C2×D3×C8—31no—
186#895C2×D311yescharacteristic
187#894—61no—
188#893C2×D311yescharacteristic, complemented
189D3×C4⋊C4C2×D311yescharacteristic
190#890C2×D311yescharacteristic, complemented
191#884—21no—
192#884—61no—
193#883—21no—
194D3×C22⋊C4—61no—
195#876—21no—
196#875—31no—
197C4×D12—21no—
198C4×D12—31no—
199C3×#103—31no—
200C3×#103—31no—
201C3×#102—31no—
202C3×#102—31no—
203#835—31no—
204#832—31no—
205#832—31no—
206#830—31no—
207#830—31no—
208#830—31no—
209#830—61no—
210#821—31no—
211#821—31no—
212(C2×D3)⋊C8—31no—
213#818—31no—
214Dic3⋊C8—31no—
215C8×Dic3—31no—
216#810—31no—
217#810C2×D311yescharacteristic, complemented
218#810C2×D311yescharacteristic, complemented
219#809—31no—
220#809—31no—
221#809—31no—
222#809—31no—
223#809—31no—
224#809—31no—
225#809—61no—
226#809—61no—
227#809C2×D311yescharacteristic
228#809C2×D311yescharacteristic
229#808—31no—
230#808—31no—
231#808—61no—
232#807—31no—
233#807—31no—
234#807—31no—
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×D3C2×D411yescharacteristic
243C2×D32—42no—
244C2×D32—42no—
245C2×D32—81no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2411yescharacteristic
252#638—81no—
253C2×C3⋊Dic3—21no—
254C4⋊(C3⋊D3)—21no—
255C4⋊(C3⋊D3)—21no—
256C3×#67—22no—
257C3×#67—42no—
258C3×#67—81no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C3×D12—21no—
265C3×D12—21no—
266C3×D12—21no—
267C3×D12—42no—
268C3×D12#4112yes—
269C3×C4×D3—21no—
270C3×C4×D3—21no—
271C3×C4×D3—42no—
272C3×C4×D3—81no—
273C3×C4×D3—81no—
274C3×Dic6—21no—
275C3×Dic6—21no—
276#626—42no—
277D3×Dic3—81no—
278C3⋊(C3⋊C8)—21no—
279C3⋊(C3⋊C8)—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282#553—31no—
283#546—91no—
284#488—91no—
285#484—91no—
286#482—91no—
287#478—91no—
288#466—91no—
289#465—91no—
290#463—91no—
291#449—91no—
292#447—91no—
293C4×D8—91no—
294C8×D4—91no—
295#416—31no—
296C2×#102—91no—
297C23×D3—61no—
298C23×D3—61no—
299C3×#41—62no—
300C3×#41—121no—
301C2×C3×Q8—31no—
302C2×C3×D4—31no—
303C2×C3×D4—31no—
304C2×C3×D4—31no—
305C2×C3×D4—61no—
306C2×C3×D4—61no—
307C2×C3×D4—61no—
308C22×C3×C4—21no—
309C22×C3×C4—31no—
310C22×C3×C4—61no—
311C22×C3×C4—61no—
312C22×C3×C4—61no—
313C22×C3×C4C22×D311yescharacteristic
314C22×C3×C4C22×D311yescharacteristic
315C2×#67—21no—
316C2×#67—21no—
317C2×#67—61no—
318C2×#67—61no—
319C2×#67—61no—
320C2×#67—121no—
321C2×#67#6711yescharacteristic
322C22×Dic3—61no—
323D3×D4—62no—
324D3×D4—121no—
325#235—22no—
326#235—41no—
327C2×D12—21no—
328C2×D12—31no—
329C2×D12—31no—
330C2×D12—61no—
331C2×D12—62no—
332C2×D12—61no—
333C2×D12—121no—
334C2×D12C22×D311yescharacteristic
335C2×D12C22×D311yescharacteristic
336C2×C4×D3—21no—
337C2×C4×D3—21no—
338C2×C4×D3—21no—
339C2×C4×D3—61no—
340C2×C4×D3C22×D311yescharacteristic
341C2×Dic6C22×D311yescharacteristic
342C2×C3×C8—31no—
343C2×C3×C8—31no—
344C2×C3×C8—121no—
345C3×C4⋊C4—21no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—61no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4C22×D311yescharacteristic
353C3×C4⋊C4C22×D311yescharacteristic
354C3×C4⋊C4C22×D311yescharacteristic
355C3×C4⋊C4C22×D311yescharacteristic
356C3×C22⋊C4—21no—
357C3×C22⋊C4—21no—
358C3×C22⋊C4—31no—
359C3×C22⋊C4—31no—
360C3×C22⋊C4—41no—
361C3×C22⋊C4—61no—
362C3×C22⋊C4—61no—
363C3×C22⋊C4—61no—
364C3×C42—21no—
365C3×C42—21no—
366C3×C42—31no—
367C3×C42—41no—
368#217—61no—
369#217—61no—
370#217#6711yescharacteristic
371#215—121no—
372#214—121no—
373#213—62no—
374#213—62no—
375#213—121no—
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—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—121no—
388(C2×D3)⋊C4#6711yescharacteristic
389C4⋊Dic3—21no—
390C4⋊Dic3—31no—
391C4⋊Dic3—31no—
392C4⋊Dic3—61no—
393C4⋊Dic3C22×D311yescharacteristic
394Dic3⋊C4—21no—
395Dic3⋊C4—21no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4#6711yescharacteristic
399C4×Dic3C22×D311yescharacteristic
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—41no—
405C2×C3⋊C8—61no—
406C2×C3⋊C8—61no—
407C2×C3⋊C8—121no—
408C2×C3⋊C8C22×D311yescharacteristic
409C2×C3⋊C8C22×D311yescharacteristic
410D24—121no—
411D3×C8—121no—
412C22×C32—21no—
413C22×C32—21no—
414C22×C32—21no—
415C22×C32C22×D411yescharacteristic
416C2×C3⋊D3—41no—
417C2×C3⋊D3—41no—
418C2×C3⋊D3—41no—
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#13512yes—
428D32—84no—
429C32×C4—21no—
430C32×C4—41no—
431C32×C4—41no—
432C32×C4C2×#4111yescharacteristic
433C32×C4H(5,𝔽2)11yescharacteristic
434C3⋊Dic3—41no—
435C3×Dic3—21no—
436C3×Dic3—21no—
437C3×Dic3—21no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C2×#41—31no—
441C22×D4—91no—
442C2×SD16—91no—
443C2×D8—91no—
444C2×D8—91no—
445C22×C8—31no—
446C22×C8—91no—
447#126—61no—
448#125—31no—
449#124—91no—
450#123—61no—
451#123—181no—
452C22⋊Q8—91no—
453#121—31no—
454#121—31no—
455#121—61no—
456#121—91no—
457#121—181no—
458#120—181no—
459C4×D4—31no—
460C4×D4—31no—
461C4×D4—61no—
462C4×D4—91no—
463#117D3211yescharacteristic, complemented
464C2×C4⋊C4—31no—
465C2×C22⋊C4—181no—
466#107—91no—
467#107—91no—
468#106—91no—
469C4⋊C8—91no—
470#103—31no—
471#103—31no—
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—31no—
485C23×C3—61no—
486C23×C3—61no—
487C23×C3D3×D411yescharacteristic
488C23×C3C2×#6711yescharacteristic
489C22×D3—21no—
490C22×D3—21no—
491C22×D3—61no—
492C22×D3—61no—
493C22×D3—121no—
494C22×D3—122no—
495C22×D3—122no—
496C22×D3—122no—
497C22×D3—122no—
498C22×D3—241no—
499C22×D3—241no—
500C22×D3C2×#6711yescharacteristic
501C3×Q8—61no—
502C3×Q8—61no—
503C3×D4—32no—
504C3×D4—62no—
505C3×D4—61no—
506C3×D4—61no—
507C3×D4—61no—
508C3×D4—122no—
509C3×D4—122no—
510C3×D4—241no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
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—31no—
522C2×C3×C4—31no—
523C2×C3×C4—31no—
524C2×C3×C4—41no—
525C2×C3×C4—41no—
526C2×C3×C4—41no—
527C2×C3×C4—41no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—122no—
533C2×C3×C4—241no—
534C2×C3×C4—241no—
535C2×C3×C4D3×D411yescharacteristic
536C2×C3×C4C2×#6711yescharacteristic
537C2×C3×C4C23×D311yescharacteristic
538C2×C3×C4C23×D311yescharacteristic
539#67—22no—
540#67—42no—
541#67—81no—
542#67—122no—
543#67—241no—
544#67—241no—
545#67—242no—
546C2×Dic3—21no—
547C2×Dic3—21no—
548C2×Dic3—61no—
549C2×Dic3—61no—
550C2×Dic3—121no—
551C2×Dic3—241no—
552C2×Dic3C2×#6711yescharacteristic
553C2×Dic3C2×#6711yescharacteristic
554C2×Dic3C2×#6711yescharacteristic
555D12—21no—
556D12—21no—
557D12—21no—
558D12—42no—
559D12—61no—
560D12—61no—
561D12—61no—
562D12—61no—
563D12—121no—
564D12—121no—
565D12—122no—
566D12#23512yes—
567C4×D3—21no—
568C4×D3—21no—
569C4×D3—42no—
570C4×D3—81no—
571C4×D3—81no—
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#54611yescharacteristic
587C2×C32C2×#13511yescharacteristic
588C2×C32#57611yescharacteristic
589C3⋊D3—81no—
590C3×D3—22no—
591C3×D3—42no—
592C3×D3—81no—
593C24—181no—
594#41—62no—
595#41—121no—
596C2×Q8—31no—
597C2×D4—31no—
598C2×D4—31no—
599C2×D4—31no—
600C2×D4—61no—
601C2×D4—61no—
602C2×D4—61no—
603C2×D4—91no—
604C2×D4—181no—
605C2×D4—182no—
606C2×D4—181no—
607C2×D4—361no—
608C22×C4—31no—
609C22×C4—61no—
610C22×C4—61no—
611C22×C4—61no—
612C22×C4—181no—
613C22×C4C2×D3211yescharacteristic
614SD16—361no—
615D8—182no—
616D8—361no—
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—61no—
627C4⋊C4—61no—
628C4⋊C4—91no—
629C4⋊C4—181no—
630C4⋊C4C2×D3211yescharacteristic
631C4⋊C4C2×D3211yescharacteristic
632C22⋊C4—21no—
633C22⋊C4—31no—
634C22⋊C4—31no—
635C22⋊C4—61no—
636C22⋊C4—61no—
637C22⋊C4—61no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C22⋊C4—181no—
641C22⋊C4—181no—
642C22⋊C4—181no—
643C42—21no—
644C42—31no—
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—61no—
657C22×C3—61no—
658C22×C3—62no—
659C22×C3—121no—
660C22×C3—121no—
661C22×C3—121no—
662C22×C3—121no—
663C22×C3—121no—
664C22×C3C2×D3×D411yescharacteristic
665C22×C3C22×#6711yescharacteristic
666C2×D3—21no—
667C2×D3—21no—
668C2×D3—22no—
669C2×D3—41no—
670C2×D3—41no—
671C2×D3—41no—
672C2×D3—41no—
673C2×D3—41no—
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—244no—
684C2×D3—244no—
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—41no—
694C3×C4—41no—
695C3×C4—61no—
696C3×C4—61no—
697C3×C4—61no—
698C3×C4—81no—
699C3×C4—81no—
700C3×C4—121no—
701C3×C4—121no—
702C3×C4C2×#23511yescharacteristic
703C3×C4#100411yescharacteristic
704C3×C4D3×#4111yescharacteristic
705C3×C4#100911yescharacteristic
706Dic3—21no—
707Dic3—21no—
708Dic3—21no—
709Dic3—41no—
710Dic3—41no—
711Dic3—121no—
712Dic3—121no—
713Dic3—241no—
714C32#329711yescharacteristic, complemented, Sylow
715C23—31no—
716C23—61no—
717C23—61no—
718C23—181no—
719C23—362no—
720C23—362no—
721C23—721no—
722C23D3×#6711yescharacteristic
723Q8—61no—
724Q8—61no—
725D4—32no—
726D4—62no—
727D4—61no—
728D4—61no—
729D4—61no—
730D4—122no—
731D4—122no—
732D4—181no—
733D4—181no—
734D4—241no—
735D4—362no—
736D4—721no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—31no—
742C2×C4—31no—
743C2×C4—31no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—122no—
749C2×C4—181no—
750C2×C4—241no—
751C2×C4—241no—
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—122no—
767C2×C3—241no—
768C2×C3#549011yescharacteristic
769C2×C3D3×#13511yescharacteristic
770C2×C3#576911yescharacteristic
771C2×C3C2×#95011yescharacteristic
772C2×C3#582911yescharacteristic
773C2×C3#583511yescharacteristic
774D3—22no—
775D3—42no—
776D3—81no—
777D3—241no—
778D3—241no—
779D3—481no—
780C22—21no—
781C22—21no—
782C22—21no—
783C22—32no—
784C22—61no—
785C22—61no—
786C22—62no—
787C22—121no—
788C22—121no—
789C22—121no—
790C22—121no—
791C22—121no—
792C22—361no—
793C22—361no—
794C22—361no—
795C22—724no—
796C22C2×D3×#6711yescharacteristic
797C4—21no—
798C4—41no—
799C4—41no—
800C4—61no—
801C4—61no—
802C4—61no—
803C4—121no—
804C4—121no—
805C4—361no—
806C4D3×#23511yescharacteristic
807C4#6430711yescharacteristic
808C3—21no—
809C3#7884611yescharacteristic, complemented
810C3#8361411yescharacteristic, complemented
811C2—41no—
812C2—62no—
813C2—122no—
814C2—241no—
815C2—721no—
816C2#1059506511yescharacteristic
817C2D3×#95011yescharacteristic
818C2#1059545611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
hypercenter#117D32
hypocenterC32#3297
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C3×#5530C2semidirect
2. #10595067C2semidirect
3. #10592702C2semidirect
4. C3×#5002C2semidirect
5. #10591164C2semidirect
6. #10591161C2semidirect
7. C3⋊C8×#67C2semidirect
8. #10590595C2semidirect
9. D3×#809C2semidirect
10. #10590537C2semidirect
11. #10590534C2semidirect
12. #10590517C2semidirect
13. #10590514C2semidirect
14. #10590469C2semidirect
15. #10590452C2semidirect
20. C32×#117C22semidirect
22. C3×#930C22semidirect
24. C22×C3×C3⋊C8C22semidirect
26. C3×#893C22semidirect
28. C3×#890C22semidirect
40. C2×#3715C22semidirect
44. #63657C22semidirect
47. #63635C22semidirect
48. #63634C22semidirect
49. C3×#810C22semidirect
50. C3×#810C22semidirect
53. #63575C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63565C22semidirect
57. #63563C22semidirect
60. Dic3×C3⋊C8C22semidirect
64. #5530D3semidirect
81. #5002D3semidirect
160. C3×#117C2×D3semidirect
161. C3×#117C2×D3semidirect
177. #930C2×D3semidirect
183. C22×C3⋊C8C2×D3semidirect
188. #893C2×D3semidirect
190. #890C2×D3semidirect
217. #810C2×D3semidirect
218. #810C2×D3semidirect
463. #117D32semidirect
714. C32#3297semidirect
809. C3#78846semidirect
810. C3#83614semidirect

Maximal subgroups

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

subgroupindex
C3×#55302
#105950672
#105927022
C3×#50022
#105911642
#105911612
C3⋊C8×#672
#105905952
D3×#8092
#105905372
#105905342
#105905172
#105905142
#105904692
#105904522
#836143
#788463