Finite Group Databasebeta

← #11044259

Subgroups — #11044259

Order 768.

1496 conjugacy classes of subgroups.

The subgroup lattice has 1300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2527C211yesmaximal, characteristic, complemented
2#78421C211yesmaximal, characteristic, complemented
3#78415C211yesmaximal, characteristic, complemented
4#78284C211yesmaximal, characteristic, complemented
5#78200C211yesmaximal, characteristic, complemented
6#77592C211yesmaximal, characteristic, complemented
7#77552C211yesmaximal, characteristic
8#76836C211yesmaximal, characteristic, complemented
9#76818C211yesmaximal, characteristic
10#76589C211yesmaximal, characteristic, complemented
11#76558C211yesmaximal, characteristic, complemented
12#76551C211yesmaximal, characteristic, complemented
13#76546C211yesmaximal, characteristic, complemented
14#75720C211yesmaximal, characteristic
15#75719C211yesmaximal, characteristic
16#75466C211yesmaximal, characteristic, complemented
17#75465C211yesmaximal, characteristic, complemented
18#75376C211yesmaximal, characteristic, complemented
19#75235C211yesmaximal, characteristic, complemented
20#75112C211yesmaximal, characteristic, complemented
21#75034C211yesmaximal, characteristic, complemented
22#75028C211yesmaximal, characteristic, complemented
23#74970C211yesmaximal, characteristic, complemented
24#74586C211yesmaximal, characteristic, complemented
25#74436C211yesmaximal, characteristic
26#74071C211yesmaximal, characteristic
27#74051C211yesmaximal, characteristic, complemented
28#73543C211yesmaximal, characteristic, complemented
29#73438C211yesmaximal, characteristic
30#73399C211yesmaximal, characteristic, complemented
31#73392C211yesmaximal, characteristic, complemented
32#38417—31nomaximal, Sylow
33C2×C4×#67C2211yescharacteristic
34C22×C4×Dic3C2211yescharacteristic
35C2×#889C2211yescharacteristic
36C2×#879C2211yescharacteristic
37C2×#879C2211yescharacteristic
38C2×#872C2211yescharacteristic
39C3×#401C2211yescharacteristic
40C3×#400C2211yescharacteristic
41C3×#397C2211yescharacteristic
42C3×#393C2211yescharacteristic
43C3×#391C2211yescharacteristic
44C3×#391C2211yescharacteristic
45C3×#388C2211yescharacteristic
46C3×#388C2211yescharacteristic
47C3×#387C2211yescharacteristic
48C3×#387C2211yescharacteristic
49C3×#387C2211yescharacteristic
50C3×#385C2211yescharacteristic
51C3×#381C2211yescharacteristic
52C3×C4×C22⋊C4C2211yescharacteristic
53C3×#376C2211yescharacteristic
54#5231C2211yescharacteristic
55#5230C2211yescharacteristic
56#5230C2211yescharacteristic
57#5229C2211yescharacteristic
58#5211C2211yescharacteristic
59#5210C2211yescharacteristic
60#4994C2211yescharacteristic
61#4993C2211yescharacteristic
62#4993C2211yescharacteristic
63#4990C2211yescharacteristic
64#4989C2211yescharacteristic
65#4983C2211yescharacteristic
66#4982C2211yescharacteristic
67#4982C2211yescharacteristic
68#4981C2211yescharacteristic
69#4980C2211yescharacteristic
70#4978C2211yescharacteristic
71#4978C2211yescharacteristic
72#4978C2211yescharacteristic
73#4976C2211yescharacteristic
74#4976C2211yescharacteristic
75#4976C2211yescharacteristic
76Dic3×C4⋊C4C2211yescharacteristic
77Dic3×C4⋊C4C2211yescharacteristic
78#4972C2211yescharacteristic
79#4961C2211yescharacteristic
80#4961C2211yescharacteristic
81#4959C2211yescharacteristic
82#4959C2211yescharacteristic
83#4958C2211yescharacteristic
84#4958C2211yescharacteristic
85#4953C2211yescharacteristic
86#4950C2211yescharacteristic
87#4949C2211yescharacteristic
88#4946C2211yescharacteristic
89#4946C2211yescharacteristic
90#4946C2211yescharacteristic
91#4945C2211yescharacteristic
92#4944C2211yescharacteristic
93#4944C2211yescharacteristic
94#4944C2211yescharacteristic
95#4942C2211yescharacteristic
96#4942C2211yescharacteristic
97#4942C2211yescharacteristic
98#4942C2211yescharacteristic
99Dic3×C22⋊C4C2211yescharacteristic
100Dic3×C22⋊C4C2211yescharacteristic
101#4940C2211yescharacteristic
102#4940C2211yescharacteristic
103C4×(C2×D3)⋊C4C2211yescharacteristic
104#4936C2211yescharacteristic
105#4933C2211yescharacteristic
106#4933C2211yescharacteristic
107#4933C2211yescharacteristic
108#4933C2211yescharacteristic
109#4933C2211yescharacteristic
110#4932C2211yescharacteristic
111C4×Dic3⋊C4C2211yescharacteristic
112C4×Dic3⋊C4C2211yescharacteristic
113C4×Dic3⋊C4C2211yescharacteristic
114C4×Dic3⋊C4C2211yescharacteristic
115#4928C2211yescharacteristic
116#4676C2211yescharacteristic
117#4675C2211yescharacteristic
118#4675C2211yescharacteristic
119#4675C2211yescharacteristic
120#4675C2211yescharacteristic
121#4675C2211yescharacteristic
122#4670C2211yescharacteristic
123#4670C2211yescharacteristic
124#4670C2211yescharacteristic
125#4670C2211yescharacteristic
126#4669C2211yescharacteristic
127#4669C2211yescharacteristic
128#4669C2211yescharacteristic
129#4669C2211yescharacteristic
130#4669C2211yescharacteristic
131#4668C2211yescharacteristic
132#4667C2211yescharacteristic
133#4666C2211yescharacteristic
134C3⋊#401C2211yescharacteristic
135#4661C2211yescharacteristic
136#4660C2211yescharacteristic
137#4659C2211yescharacteristic
138#4659C2211yescharacteristic
139#4658C2211yescharacteristic
140#4658C2211yescharacteristic
141#4658C2211yescharacteristic
142#4658C2211yescharacteristic
143#4658C2211yescharacteristic
144#4657C2211yescharacteristic
145#4657C2211yescharacteristic
146#4657C2211yescharacteristic
147#4657C2211yescharacteristic
148#4655C2211yescharacteristic
149#4655C2211yescharacteristic
150#4655C2211yescharacteristic
151#4655C2211yescharacteristic
152#4654C2211yescharacteristic
153#4654C2211yescharacteristic
154#4654C2211yescharacteristic
155#4654C2211yescharacteristic
156#4653C2211yescharacteristic
157#4653C2211yescharacteristic
158#4653C2211yescharacteristic
159#4652C2211yescharacteristic
160#4652C2211yescharacteristic
161#4652C2211yescharacteristic
162#4652C2211yescharacteristic
163#4652C2211yescharacteristic
164#4652C2211yescharacteristic
165#4652C2211yescharacteristic
166#4652C2211yescharacteristic
167#4652C2211yescharacteristic
168#4651C2211yescharacteristic
169#4651C2211yescharacteristic
170#4650C2211yescharacteristic
171#4650C2211yescharacteristic
172#4650C2211yescharacteristic
173#4650C2211yescharacteristic
174#4650C2211yescharacteristic
175#4649C2211yescharacteristic
176#4649C2211yescharacteristic
177#4649C2211yescharacteristic
178#4648C2211yescharacteristic
179#4648C2211yescharacteristic
180#4647C2211yescharacteristic
181#4647C2211yescharacteristic
182#4647C2211yescharacteristic
183#4647C2211yescharacteristic
184#4647C2211yescharacteristic
185#4647C2211yescharacteristic
186#4647C2211yescharacteristic
187#4647C2211yescharacteristic
188#2851—31no—
189#2777—31no—
190#2776—31no—
191#2775—31no—
192#2766—31no—
193#2742—31no—
194#2741—31no—
195#2741—31no—
196#2722—31no—
197#2653—31no—
198#2649—31no—
199#2612—31no—
200#2611—31no—
201#2596—31no—
202#2594—31no—
203#2590—31no—
204#2588—31no—
205#2575—31no—
206#2574—31no—
207#2528—31no—
208#2527D311yescharacteristic, complemented
209#2517—31no—
210#2508—31no—
211#2468—31no—
212#2466—31no—
213#2371—31no—
214#2346—31no—
215#2334—31no—
216#2334—31no—
217#2290—31no—
218#2283—31no—
219C22×C3×Q8C2311yescharacteristic
220C23×C3×C4C2311yescharacteristic
221C22×#67C2311yescharacteristic
222C23×Dic3C2311yescharacteristic
223C23×Dic3C2311yescharacteristic
224C22×C4×D3C2311yescharacteristic
225C2×C3×C4⋊C4C2311yescharacteristic
226C2×C3×C4⋊C4C2311yescharacteristic
227C2×C3×C4⋊C4C2311yescharacteristic
228C2×C3×C4⋊C4C2311yescharacteristic
229C2×C3×C4⋊C4C2311yescharacteristic
230C2×C3×C22⋊C4C2311yescharacteristic
231C2×C3×C22⋊C4C2311yescharacteristic
232C2×C3×C22⋊C4C2311yescharacteristic
233C2×C3×C22⋊C4C2311yescharacteristic
234C2×C3×C22⋊C4C2311yescharacteristic
235C2×C3×C22⋊C4C2311yescharacteristic
236C2×C3×C42C2311yescharacteristic
237C2×C3×C42C2311yescharacteristic
238C2×C3×C42C2311yescharacteristic
239C2×C3×C42C2311yescharacteristic
240C2×#217C2311yescharacteristic
241C2×#217C2311yescharacteristic
242C2×#217C2311yescharacteristic
243C2×#217C2311yescharacteristic
244C2×#217C2311yescharacteristic
245C4×#67—24no—
246C2×(C2×D3)⋊C4C2311yescharacteristic
247C2×(C2×D3)⋊C4C2311yescharacteristic
248C2×(C2×D3)⋊C4C2311yescharacteristic
249C2×(C2×D3)⋊C4C2311yescharacteristic
250C2×(C2×D3)⋊C4C2311yescharacteristic
251C2×(C2×D3)⋊C4C2311yescharacteristic
252C2×(C2×D3)⋊C4C2311yescharacteristic
253C2×(C2×D3)⋊C4C2311yescharacteristic
254C2×(C2×D3)⋊C4C2311yescharacteristic
255C2×(C2×D3)⋊C4C2311yescharacteristic
256C2×(C2×D3)⋊C4C2311yescharacteristic
257C2×(C2×D3)⋊C4C2311yescharacteristic
258C2×(C2×D3)⋊C4C2311yescharacteristic
259C2×C4⋊Dic3C2311yescharacteristic
260C2×C4⋊Dic3C2311yescharacteristic
261C2×C4⋊Dic3C2311yescharacteristic
262C2×C4⋊Dic3C2311yescharacteristic
263C2×C4⋊Dic3C2311yescharacteristic
264C2×C4⋊Dic3C2311yescharacteristic
265C2×C4⋊Dic3C2311yescharacteristic
266C2×C4⋊Dic3C2311yescharacteristic
267C2×Dic3⋊C4C2311yescharacteristic
268C2×Dic3⋊C4C2311yescharacteristic
269C2×Dic3⋊C4C2311yescharacteristic
270C2×Dic3⋊C4C2311yescharacteristic
271C2×Dic3⋊C4C2311yescharacteristic
272C2×Dic3⋊C4C2311yescharacteristic
273C2×Dic3⋊C4C2311yescharacteristic
274C2×Dic3⋊C4C2311yescharacteristic
275C2×Dic3⋊C4C2311yescharacteristic
276C2×Dic3⋊C4C2311yescharacteristic
277C2×Dic3⋊C4C2311yescharacteristic
278C2×Dic3⋊C4C2311yescharacteristic
279C2×Dic3⋊C4C2311yescharacteristic
280C2×Dic3⋊C4C2311yescharacteristic
281C2×Dic3⋊C4C2311yescharacteristic
282C2×Dic3⋊C4C2311yescharacteristic
283C2×Dic3⋊C4C2311yescharacteristic
284C2×Dic3⋊C4C2311yescharacteristic
285C2×Dic3⋊C4C2311yescharacteristic
286C2×Dic3⋊C4C2311yescharacteristic
287C2×Dic3⋊C4C2311yescharacteristic
288C2×Dic3⋊C4C2311yescharacteristic
289C2×Dic3⋊C4C2311yescharacteristic
290C2×Dic3⋊C4C2311yescharacteristic
291C2×Dic3⋊C4C2311yescharacteristic
292C2×Dic3⋊C4C2311yescharacteristic
293C2×Dic3⋊C4C2311yescharacteristic
294C2×Dic3⋊C4C2311yescharacteristic
295C2×Dic3⋊C4C2311yescharacteristic
296C2×C4×Dic3—24no—
297C2×C4×Dic3C2311yescharacteristic
298C2×C4×Dic3C2311yescharacteristic
299C2×C4×Dic3C2311yescharacteristic
300C2×C4×Dic3C2311yescharacteristic
301C2×C4×Dic3C2311yescharacteristic
302C2×C4×Dic3C2311yescharacteristic
303C2×C4×Dic3C2311yescharacteristic
304C2×C4×Dic3C2311yescharacteristic
305C2×C4×Dic3C2311yescharacteristic
306C2×C4×Dic3C2311yescharacteristic
307C2×C4×Dic3C2311yescharacteristic
308C2×C4×Dic3C2311yescharacteristic
309C2×C4×Dic3C2311yescharacteristic
310C2×C4×Dic3C2311yescharacteristic
311C2×C4×Dic3C2311yescharacteristic
312#889—24no—
313#879—24no—
314#879—24no—
315#872—24no—
316C3×#95C2311yescharacteristic
317C3×#95C2311yescharacteristic
318C3×#95C2311yescharacteristic
319C3×#95C2311yescharacteristic
320C3×#95C2311yescharacteristic
321C3×#95C2311yescharacteristic
322C3×#95C2311yescharacteristic
323C3×#95C2311yescharacteristic
324C3×#95C2311yescharacteristic
325C3×#95C2311yescharacteristic
326C3×#95C2311yescharacteristic
327C3×#95C2311yescharacteristic
328C3×#95C2311yescharacteristic
329C3×#95C2311yescharacteristic
330C3×#95C2311yescharacteristic
331C3×#95C2311yescharacteristic
332C3×#95C2311yescharacteristic
333C3×#95C2311yescharacteristic
334C3⋊#95C2311yescharacteristic
335C3⋊#95C2311yescharacteristic
336C3⋊#95C2311yescharacteristic
337C3⋊#95C2311yescharacteristic
338C3⋊#95C2311yescharacteristic
339C3⋊#95C2311yescharacteristic
340C3⋊#95C2311yescharacteristic
341C3⋊#95C2311yescharacteristic
342C3⋊#95C2311yescharacteristic
343C3⋊#95C2311yescharacteristic
344C3⋊#95C2311yescharacteristic
345C3⋊#95C2311yescharacteristic
346C3⋊#95C2311yescharacteristic
347C3⋊#95C2311yescharacteristic
348C3⋊#95C2311yescharacteristic
349C3⋊#95C2311yescharacteristic
350C3⋊#95C2311yescharacteristic
351C3⋊#95C2311yescharacteristic
352C3⋊#95C2311yescharacteristic
353C3⋊#95C2311yescharacteristic
354C3⋊#95C2311yescharacteristic
355C3⋊#95C2311yescharacteristic
356C3⋊#95C2311yescharacteristic
357C3⋊#95C2311yescharacteristic
358C3⋊#95C2311yescharacteristic
359C3⋊#95C2311yescharacteristic
360C3⋊#95C2311yescharacteristic
361C3⋊#95C2311yescharacteristic
362C3⋊#95C2311yescharacteristic
363C3⋊#95C2311yescharacteristic
364C3⋊#95C2311yescharacteristic
365C3⋊#95C2311yescharacteristic
366C3⋊#95C2311yescharacteristic
367C3⋊#95C2311yescharacteristic
368C3⋊#95C2311yescharacteristic
369C3⋊#95C2311yescharacteristic
370C3⋊#95C2311yescharacteristic
371C3⋊#95C2311yescharacteristic
372C3⋊#95C2311yescharacteristic
373C3⋊#95C2311yescharacteristic
374C3⋊#95C2311yescharacteristic
375C3⋊#95C2311yescharacteristic
376C3⋊#95C2311yescharacteristic
377C3⋊#95C2311yescharacteristic
378C3⋊#95C2311yescharacteristic
379C3⋊#95C2311yescharacteristic
380C2×#126—31no—
381C2×#126—31no—
382C2×#125—31no—
383C2×C4×D4—31no—
384C2×#117—31no—
385C22×C42—31no—
386#401—31no—
387#401C2×D311yescharacteristic
388#400—31no—
389#400—31no—
390#400—31no—
391#400—31no—
392#400—31no—
393#400—31no—
394#400—31no—
395#400—31no—
396#400C2×D311yescharacteristic
397#399—31no—
398#399—31no—
399#399—31no—
400#398—31no—
401#398—31no—
402#398—31no—
403#398—31no—
404#398—31no—
405#398—31no—
406#398—31no—
407#398—31no—
408#398—31no—
409#397—31no—
410#397—31no—
411#397—31no—
412#397—31no—
413#397—31no—
414#397—31no—
415#397C2×D311yescharacteristic
416#396—31no—
417#396—31no—
418#395—31no—
419#395—31no—
420#394—31no—
421#394—31no—
422#394—31no—
423#394—31no—
424#393—31no—
425#393C2×D311yescharacteristic
426#391—31no—
427#391C2×D311yescharacteristic
428#391C2×D311yescharacteristic
429#389—31no—
430#389—31no—
431#389—31no—
432#389—31no—
433#389—31no—
434#389—31no—
435#389—31no—
436#389—31no—
437#389—31no—
438#389—31no—
439#389—31no—
440#389—31no—
441#389—31no—
442#388—31no—
443#388—31no—
444#388—31no—
445#388—31no—
446#388—31no—
447#388—31no—
448#388—31no—
449#388—31no—
450#388—31no—
451#388—31no—
452#388—31no—
453#388—31no—
454#388—31no—
455#388—31no—
456#388—31no—
457#388—31no—
458#388C2×D311yescharacteristic
459#388C2×D311yescharacteristic
460#387—31no—
461#387—31no—
462#387—31no—
463#387—31no—
464#387—31no—
465#387—31no—
466#387—31no—
467#387—31no—
468#387—31no—
469#387—31no—
470#387—31no—
471#387—31no—
472#387—31no—
473#387—31no—
474#387—31no—
475#387—31no—
476#387—31no—
477#387—31no—
478#387—31no—
479#387—31no—
480#387—31no—
481#387—31no—
482#387—31no—
483#387—31no—
484#387—31no—
485#387—31no—
486#387—31no—
487#387—31no—
488#387—31no—
489#387C2×D311yescharacteristic
490#387C2×D311yescharacteristic
491#387C2×D311yescharacteristic
492#386—31no—
493#386—31no—
494#385—31no—
495#385—31no—
496#385—31no—
497#385—31no—
498#385—31no—
499#385—31no—
500#385—31no—
501#385C2×D311yescharacteristic
502#383—31no—
503#383—31no—
504#382—31no—
505#382—31no—
506#382—31no—
507#382—31no—
508#382—31no—
509#382—31no—
510#381—31no—
511#381C2×D311yescharacteristic
512#380—31no—
513#380—31no—
514#380—31no—
515#380—31no—
516#380—31no—
517C4×C4⋊C4—31no—
518C4×C4⋊C4—31no—
519C4×C4⋊C4—31no—
520C4×C4⋊C4—31no—
521C4×C4⋊C4—31no—
522C4×C4⋊C4—31no—
523C4×C4⋊C4—31no—
524C4×C4⋊C4—31no—
525C4×C4⋊C4—31no—
526C4×C22⋊C4—31no—
527C4×C22⋊C4—31no—
528C4×C22⋊C4—31no—
529C4×C22⋊C4—31no—
530C4×C22⋊C4C2×D311yescharacteristic
531#376—31no—
532#376—31no—
533#376—31no—
534#376C2×D311yescharacteristic
535C24×C3C2411yescharacteristic
536C23×D3C2411yescharacteristic
537C2×C3×Q8—41no—
538C2×C3×Q8—41no—
539C2×C3×Q8—41no—
540C22×C3×C4—22no—
541C22×C3×C4—22no—
542C22×C3×C4—41no—
543C22×C3×C4C2411yescharacteristic
544C22×C3×C4C2411yescharacteristic
545C22×C3×C4C2411yescharacteristic
546C22×C3×C4C2411yescharacteristic
547C22×C3×C4C2411yescharacteristic
548C22×C3×C4C2411yescharacteristic
549C22×C3×C4C2411yescharacteristic
550C22×C3×C4C2411yescharacteristic
551C22×C3×C4C2411yescharacteristic
552C22×C3×C4C2411yescharacteristic
553C22×C3×C4C2411yescharacteristic
554C22×C3×C4C2411yescharacteristic
555C22×C3×C4C2411yescharacteristic
556C22×C3×C4C2411yescharacteristic
557C2×#67—22no—
558C2×#67—41no—
559C2×#67—41no—
560C22×Dic3—22no—
561C22×Dic3—22no—
562C22×Dic3—22no—
563C22×Dic3—41no—
564C22×Dic3—41no—
565C22×Dic3—41no—
566C22×Dic3C2411yescharacteristic
567C22×Dic3C2411yescharacteristic
568C22×Dic3C2411yescharacteristic
569C22×Dic3C2411yescharacteristic
570C22×Dic3C2411yescharacteristic
571C22×Dic3C2411yescharacteristic
572C22×Dic3C2411yescharacteristic
573C22×Dic3C2411yescharacteristic
574C22×Dic3C2411yescharacteristic
575C22×Dic3C2411yescharacteristic
576C22×Dic3C2411yescharacteristic
577C22×Dic3C2411yescharacteristic
578C22×Dic3C2411yescharacteristic
579C22×Dic3C2411yescharacteristic
580C22×Dic3C2411yescharacteristic
581C2×C4×D3—22no—
582C2×C4×D3—22no—
583C2×C4×D3—41no—
584C3×C4⋊C4—22no—
585C3×C4⋊C4—41no—
586C3×C4⋊C4—41no—
587C3×C4⋊C4—41no—
588C3×C4⋊C4—41no—
589C3×C22⋊C4—22no—
590C3×C22⋊C4—22no—
591C3×C22⋊C4—41no—
592C3×C22⋊C4—41no—
593C3×C22⋊C4—41no—
594C3×C22⋊C4—41no—
595C3×C42—22no—
596C3×C42—41no—
597C3×C42—41no—
598C3×C42—41no—
599#217—22no—
600#217—22no—
601#217—41no—
602#217—41no—
603#217#4114yes—
604(C2×D3)⋊C4—22no—
605(C2×D3)⋊C4—22no—
606(C2×D3)⋊C4—22no—
607(C2×D3)⋊C4—22no—
608(C2×D3)⋊C4—41no—
609(C2×D3)⋊C4—41no—
610(C2×D3)⋊C4—41no—
611(C2×D3)⋊C4—41no—
612(C2×D3)⋊C4—41no—
613(C2×D3)⋊C4—41no—
614(C2×D3)⋊C4—41no—
615(C2×D3)⋊C4—41no—
616(C2×D3)⋊C4—41no—
617C4⋊Dic3—22no—
618C4⋊Dic3—22no—
619C4⋊Dic3—22no—
620C4⋊Dic3—41no—
621C4⋊Dic3—41no—
622C4⋊Dic3—41no—
623C4⋊Dic3—41no—
624C4⋊Dic3—41no—
625Dic3⋊C4—22no—
626Dic3⋊C4—22no—
627Dic3⋊C4—22no—
628Dic3⋊C4—22no—
629Dic3⋊C4—22no—
630Dic3⋊C4—22no—
631Dic3⋊C4—22no—
632Dic3⋊C4—22no—
633Dic3⋊C4—22no—
634Dic3⋊C4—22no—
635Dic3⋊C4—22no—
636Dic3⋊C4—22no—
637Dic3⋊C4—22no—
638Dic3⋊C4—22no—
639Dic3⋊C4—41no—
640Dic3⋊C4—41no—
641Dic3⋊C4—41no—
642Dic3⋊C4—41no—
643Dic3⋊C4—41no—
644Dic3⋊C4—41no—
645Dic3⋊C4—41no—
646Dic3⋊C4—41no—
647Dic3⋊C4—41no—
648Dic3⋊C4—41no—
649Dic3⋊C4—41no—
650Dic3⋊C4—41no—
651Dic3⋊C4—41no—
652Dic3⋊C4—41no—
653Dic3⋊C4—41no—
654C4×Dic3—22no—
655C4×Dic3—22no—
656C4×Dic3—22no—
657C4×Dic3—22no—
658C4×Dic3—22no—
659C4×Dic3—22no—
660C4×Dic3—41no—
661C4×Dic3—41no—
662C4×Dic3—41no—
663C4×Dic3—41no—
664C4×Dic3—41no—
665C4×Dic3—41no—
666C4×Dic3—41no—
667C4×Dic3—41no—
668C4×Dic3#4114yes—
669C22×Q8C22×D311yescharacteristic
670C22×D4—31no—
671C23×C4—31no—
672C23×C4—31no—
673C23×C4—31no—
674C23×C4C22×D311yescharacteristic
675#126—64no—
676#126—64no—
677#125—64no—
678C4×D4—64no—
679#117—64no—
680C2×C4⋊C4—31no—
681C2×C4⋊C4—31no—
682C2×C4⋊C4—31no—
683C2×C4⋊C4—31no—
684C2×C4⋊C4—31no—
685C2×C4⋊C4—31no—
686C2×C4⋊C4—31no—
687C2×C4⋊C4—31no—
688C2×C4⋊C4—31no—
689C2×C4⋊C4—31no—
690C2×C4⋊C4—31no—
691C2×C4⋊C4—31no—
692C2×C4⋊C4—31no—
693C2×C4⋊C4—31no—
694C2×C4⋊C4—31no—
695C2×C4⋊C4—31no—
696C2×C4⋊C4—31no—
697C2×C4⋊C4—31no—
698C2×C4⋊C4—31no—
699C2×C4⋊C4—31no—
700C2×C4⋊C4—31no—
701C2×C4⋊C4—31no—
702C2×C4⋊C4—31no—
703C2×C4⋊C4—31no—
704C2×C4⋊C4—31no—
705C2×C4⋊C4—31no—
706C2×C4⋊C4—31no—
707C2×C4⋊C4—31no—
708C2×C4⋊C4—31no—
709C2×C4⋊C4—31no—
710C2×C4⋊C4—31no—
711C2×C4⋊C4—31no—
712C2×C4⋊C4—31no—
713C2×C4⋊C4—31no—
714C2×C4⋊C4—31no—
715C2×C4⋊C4—31no—
716C2×C4⋊C4—31no—
717C2×C4⋊C4C22×D311yescharacteristic
718C2×C4⋊C4C22×D311yescharacteristic
719C2×C4⋊C4C22×D311yescharacteristic
720C2×C4⋊C4C22×D311yescharacteristic
721C2×C4⋊C4C22×D311yescharacteristic
722C2×C22⋊C4—31no—
723C2×C22⋊C4—31no—
724C2×C22⋊C4—31no—
725C2×C22⋊C4—31no—
726C2×C22⋊C4—31no—
727C2×C22⋊C4—31no—
728C2×C22⋊C4—31no—
729C2×C22⋊C4—31no—
730C2×C22⋊C4—31no—
731C2×C22⋊C4—31no—
732C2×C22⋊C4—31no—
733C2×C22⋊C4—31no—
734C2×C22⋊C4—31no—
735C2×C22⋊C4—31no—
736C2×C22⋊C4—31no—
737C2×C22⋊C4—31no—
738C2×C22⋊C4—31no—
739C2×C22⋊C4—31no—
740C2×C22⋊C4C22×D311yescharacteristic
741C2×C22⋊C4C22×D311yescharacteristic
742C2×C22⋊C4C22×D311yescharacteristic
743C2×C22⋊C4C22×D311yescharacteristic
744C2×C22⋊C4C22×D311yescharacteristic
745C2×C22⋊C4C22×D311yescharacteristic
746C2×C42—31no—
747C2×C42—31no—
748C2×C42—31no—
749C2×C42—31no—
750C2×C42—31no—
751C2×C42—31no—
752C2×C42—31no—
753C2×C42—31no—
754C2×C42—31no—
755C2×C42—31no—
756C2×C42—31no—
757C2×C42—31no—
758C2×C42—31no—
759C2×C42—31no—
760C2×C42—31no—
761C2×C42—64no—
762C2×C42C22×D311yescharacteristic
763C2×C42C22×D311yescharacteristic
764C2×C42C22×D311yescharacteristic
765C2×C42C22×D311yescharacteristic
766#95—31no—
767#95—31no—
768#95—31no—
769#95—31no—
770#95—31no—
771#95—31no—
772#95—31no—
773#95—31no—
774#95—31no—
775#95—31no—
776#95—31no—
777#95—31no—
778#95—31no—
779#95—31no—
780#95—31no—
781#95—31no—
782#95—31no—
783#95—31no—
784#95—31no—
785#95—31no—
786#95—31no—
787#95—31no—
788#95—31no—
789#95—31no—
790#95—31no—
791#95—31no—
792#95—31no—
793#95—31no—
794#95—31no—
795#95—31no—
796#95—31no—
797#95—31no—
798#95—31no—
799#95—31no—
800#95—31no—
801#95—31no—
802#95—31no—
803#95—31no—
804#95—31no—
805#95—31no—
806#95—31no—
807#95—31no—
808#95—31no—
809#95—31no—
810#95—31no—
811#95—31no—
812#95C22×D311yescharacteristic
813#95C22×D311yescharacteristic
814#95C22×D311yescharacteristic
815#95C22×D311yescharacteristic
816#95C22×D311yescharacteristic
817#95C22×D311yescharacteristic
818#95C22×D311yescharacteristic
819#95C22×D311yescharacteristic
820#95C22×D311yescharacteristic
821#95C22×D311yescharacteristic
822#95C22×D311yescharacteristic
823#95C22×D311yescharacteristic
824#95C22×D311yescharacteristic
825#95C22×D311yescharacteristic
826#95C22×D311yescharacteristic
827#95C22×D311yescharacteristic
828#95C22×D311yescharacteristic
829#95C22×D311yescharacteristic
830C23×C3—21no—
831C23×C3—21no—
832C23×C3—21no—
833C23×C3—21no—
834C23×C3—21no—
835C23×C3—21no—
836C23×C3C2×#4112yes—
837C23×C3C2511yescharacteristic
838C22×D3—21no—
839C22×D3—21no—
840C22×D3—21no—
841C22×D3—21no—
842C22×D3—21no—
843C22×D3—21no—
844C22×D3—21no—
845C3×Q8—82no—
846C2×C3×C4—21no—
847C2×C3×C4—21no—
848C2×C3×C4—21no—
849C2×C3×C4—21no—
850C2×C3×C4—21no—
851C2×C3×C4—21no—
852C2×C3×C4—21no—
853C2×C3×C4—21no—
854C2×C3×C4—21no—
855C2×C3×C4—21no—
856C2×C3×C4—21no—
857C2×C3×C4—21no—
858C2×C3×C4—21no—
859C2×C3×C4—21no—
860C2×C3×C4—21no—
861C2×C3×C4—21no—
862C2×C3×C4—21no—
863C2×C3×C4—21no—
864C2×C3×C4—21no—
865C2×C3×C4—21no—
866C2×C3×C4—21no—
867C2×C3×C4—21no—
868C2×C3×C4—21no—
869C2×C3×C4—21no—
870C2×C3×C4—21no—
871C2×C3×C4—21no—
872C2×C3×C4—21no—
873C2×C3×C4—21no—
874C2×C3×C4—21no—
875C2×C3×C4—21no—
876C2×C3×C4—21no—
877C2×C3×C4—21no—
878C2×C3×C4—21no—
879C2×C3×C4—21no—
880C2×C3×C4—21no—
881C2×C3×C4—21no—
882C2×C3×C4—21no—
883C2×C3×C4—21no—
884C2×C3×C4—21no—
885C2×C3×C4—21no—
886C2×C3×C4—21no—
887C2×C3×C4—44no—
888C2×C3×C4C2×#4112yes—
889#67—44no—
890C2×Dic3—21no—
891C2×Dic3—21no—
892C2×Dic3—21no—
893C2×Dic3—21no—
894C2×Dic3—21no—
895C2×Dic3—21no—
896C2×Dic3—21no—
897C2×Dic3—21no—
898C2×Dic3—21no—
899C2×Dic3—21no—
900C2×Dic3—21no—
901C2×Dic3—21no—
902C2×Dic3—21no—
903C2×Dic3—21no—
904C2×Dic3—21no—
905C2×Dic3—21no—
906C2×Dic3—21no—
907C2×Dic3—21no—
908C2×Dic3—21no—
909C2×Dic3—21no—
910C2×Dic3—21no—
911C2×Dic3—21no—
912C2×Dic3—21no—
913C2×Dic3—21no—
914C2×Dic3—21no—
915C2×Dic3—21no—
916C2×Dic3—21no—
917C2×Dic3—21no—
918C2×Dic3—21no—
919C2×Dic3—21no—
920C2×Dic3—21no—
921C2×Dic3—21no—
922C2×Dic3—21no—
923C2×Dic3—21no—
924C2×Dic3—21no—
925C2×Dic3—21no—
926C2×Dic3—21no—
927C2×Dic3—21no—
928C2×Dic3—21no—
929C2×Dic3—21no—
930C2×Dic3—44no—
931C2×Dic3—44no—
932C2×Dic3C2×#4112yes—
933C2×Dic3C2×#4112yes—
934C2×Dic3C2×#4112yes—
935C2×Dic3C2×#4112yes—
936C2×Dic32−1+412yes—
937C4×D3—44no—
938C24—31no—
939C24C23×D311yescharacteristic
940C2×Q8—41no—
941C2×Q8—41no—
942C2×Q8—41no—
943C2×D4—62no—
944C2×D4—121no—
945C2×D4—121no—
946C22×C4—22no—
947C22×C4—22no—
948C22×C4—31no—
949C22×C4—31no—
950C22×C4—31no—
951C22×C4—31no—
952C22×C4—31no—
953C22×C4—31no—
954C22×C4—31no—
955C22×C4—31no—
956C22×C4—31no—
957C22×C4—31no—
958C22×C4—31no—
959C22×C4—31no—
960C22×C4—31no—
961C22×C4—31no—
962C22×C4—31no—
963C22×C4—41no—
964C22×C4—62no—
965C22×C4—62no—
966C22×C4—62no—
967C22×C4—62no—
968C22×C4—62no—
969C22×C4—121no—
970C22×C4—121no—
971C22×C4—121no—
972C22×C4—121no—
973C22×C4C23×D311yescharacteristic
974C22×C4C23×D311yescharacteristic
975C22×C4C23×D311yescharacteristic
976C22×C4C23×D311yescharacteristic
977C22×C4C23×D311yescharacteristic
978C22×C4C23×D311yescharacteristic
979C22×C4C23×D311yescharacteristic
980C22×C4C23×D311yescharacteristic
981C22×C4C23×D311yescharacteristic
982C22×C4C23×D311yescharacteristic
983C22×C4C23×D311yescharacteristic
984C22×C4C23×D311yescharacteristic
985C22×C4C23×D311yescharacteristic
986C22×C4C23×D311yescharacteristic
987C4⋊C4—22no—
988C4⋊C4—41no—
989C4⋊C4—41no—
990C4⋊C4—41no—
991C4⋊C4—41no—
992C4⋊C4—62no—
993C4⋊C4—62no—
994C4⋊C4—62no—
995C4⋊C4—62no—
996C4⋊C4—62no—
997C4⋊C4—62no—
998C4⋊C4—62no—
999C4⋊C4—62no—
1000C4⋊C4—62no—
1001C4⋊C4—62no—
1002C4⋊C4—62no—
1003C4⋊C4—62no—
1004C4⋊C4—62no—
1005C4⋊C4—62no—
1006C4⋊C4—62no—
1007C4⋊C4—62no—
1008C4⋊C4—62no—
1009C4⋊C4—121no—
1010C4⋊C4—121no—
1011C4⋊C4—121no—
1012C4⋊C4—121no—
1013C4⋊C4—121no—
1014C4⋊C4—121no—
1015C4⋊C4—121no—
1016C4⋊C4—121no—
1017C4⋊C4—121no—
1018C4⋊C4—121no—
1019C4⋊C4—121no—
1020C4⋊C4—121no—
1021C4⋊C4—121no—
1022C4⋊C4—121no—
1023C4⋊C4—121no—
1024C4⋊C4—121no—
1025C4⋊C4—121no—
1026C4⋊C4—121no—
1027C4⋊C4—121no—
1028C4⋊C4—121no—
1029C22⋊C4—22no—
1030C22⋊C4—22no—
1031C22⋊C4—34no—
1032C22⋊C4—41no—
1033C22⋊C4—41no—
1034C22⋊C4—41no—
1035C22⋊C4—41no—
1036C22⋊C4—62no—
1037C22⋊C4—62no—
1038C22⋊C4—62no—
1039C22⋊C4—62no—
1040C22⋊C4—62no—
1041C22⋊C4—62no—
1042C22⋊C4—121no—
1043C22⋊C4—121no—
1044C22⋊C4—121no—
1045C22⋊C4—121no—
1046C22⋊C4—121no—
1047C22⋊C4—121no—
1048C22⋊C4—121no—
1049C22⋊C4—121no—
1050C22⋊C4—121no—
1051C22⋊C4—121no—
1052C22⋊C4—121no—
1053C42—22no—
1054C42—34no—
1055C42—41no—
1056C42—41no—
1057C42—41no—
1058C42—62no—
1059C42—62no—
1060C42—62no—
1061C42—62no—
1062C42—62no—
1063C42—62no—
1064C42—121no—
1065C42—121no—
1066C42—121no—
1067C42—121no—
1068C42—121no—
1069C42—121no—
1070C42—121no—
1071C42—121no—
1072C22×C3—22no—
1073C22×C3—22no—
1074C22×C3—22no—
1075C22×C3—41no—
1076C22×C3—41no—
1077C22×C3—41no—
1078C22×C3—41no—
1079C22×C3C22×#4111yescharacteristic
1080C22×C3C22×#4111yescharacteristic
1081C22×C3C2×2−1+411yescharacteristic
1082C22×C3#58511yescharacteristic
1083C22×C3#58511yescharacteristic
1084C22×C3#58511yescharacteristic
1085C22×C3#58511yescharacteristic
1086C2×D3—41no—
1087C2×D3—41no—
1088C2×D3—41no—
1089C2×D3—41no—
1090C2×D3—41no—
1091C2×D3—41no—
1092C2×D3—41no—
1093C3×C4—22no—
1094C3×C4—41no—
1095C3×C4—41no—
1096C3×C4—41no—
1097C3×C4—41no—
1098C3×C4—41no—
1099C3×C4—41no—
1100C3×C4—41no—
1101C3×C4—41no—
1102C3×C4—41no—
1103C3×C4—41no—
1104C3×C4—41no—
1105C3×C4—41no—
1106C3×C4—41no—
1107Dic3—22no—
1108Dic3—22no—
1109Dic3—22no—
1110Dic3—22no—
1111Dic3—22no—
1112Dic3—41no—
1113Dic3—41no—
1114Dic3—41no—
1115Dic3—41no—
1116Dic3—41no—
1117Dic3—41no—
1118Dic3—41no—
1119Dic3—41no—
1120Dic3—41no—
1121Dic3—41no—
1122C23—21no—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—61no—
1129C23—61no—
1130C23—61no—
1131C23—61no—
1132C23—61no—
1133C23—61no—
1134C23—61no—
1135C23D3×#4112yes—
1136C23C24×D311yescharacteristic
1137Q8—82no—
1138D4—124no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—32no—
1181C2×C4—32no—
1182C2×C4—32no—
1183C2×C4—32no—
1184C2×C4—32no—
1185C2×C4—44no—
1186C2×C4—61no—
1187C2×C4—61no—
1188C2×C4—61no—
1189C2×C4—61no—
1190C2×C4—61no—
1191C2×C4—61no—
1192C2×C4—61no—
1193C2×C4—61no—
1194C2×C4—61no—
1195C2×C4—61no—
1196C2×C4—61no—
1197C2×C4—61no—
1198C2×C4—61no—
1199C2×C4—61no—
1200C2×C4—61no—
1201C2×C4—61no—
1202C2×C4—61no—
1203C2×C4—61no—
1204C2×C4—61no—
1205C2×C4—61no—
1206C2×C4—61no—
1207C2×C4—61no—
1208C2×C4—61no—
1209C2×C4—61no—
1210C2×C4—61no—
1211C2×C4—61no—
1212C2×C4—61no—
1213C2×C4—61no—
1214C2×C4—61no—
1215C2×C4—61no—
1216C2×C4—61no—
1217C2×C4—61no—
1218C2×C4—61no—
1219C2×C4—61no—
1220C2×C4—61no—
1221C2×C4—61no—
1222C2×C4—61no—
1223C2×C4—61no—
1224C2×C4—61no—
1225C2×C4—61no—
1226C2×C4—124no—
1227C2×C4—124no—
1228C2×C4—124no—
1229C2×C4D3×#4112yes—
1230C2×C3—42no—
1231C2×C3#345511yescharacteristic
1232C2×C3#347511yescharacteristic
1233C2×C3#349311yescharacteristic
1234C2×C3#349511yescharacteristic
1235C2×C3#351511yescharacteristic
1236C2×C3#355711yescharacteristic
1237C2×C3#356611yescharacteristic
1238D3—81no—
1239C22—22no—
1240C22—22no—
1241C22—22no—
1242C22—41no—
1243C22—41no—
1244C22—41no—
1245C22—41no—
1246C22—121no—
1247C22—121no—
1248C22—121no—
1249C22—121no—
1250C22—121no—
1251C22—121no—
1252C22—121no—
1253C22C2×D3×#4111yescharacteristic
1254C22C2×D3×#4111yescharacteristic
1255C22#596411yescharacteristic
1256C22#596411yescharacteristic
1257C22#596411yescharacteristic
1258C22#596611yescharacteristic
1259C22D3×2−1+411yescharacteristic
1260C4—22no—
1261C4—41no—
1262C4—41no—
1263C4—41no—
1264C4—41no—
1265C4—41no—
1266C4—41no—
1267C4—41no—
1268C4—41no—
1269C4—41no—
1270C4—41no—
1271C4—41no—
1272C4—41no—
1273C4—41no—
1274C4—62no—
1275C4—62no—
1276C4—62no—
1277C4—62no—
1278C4—62no—
1279C4—121no—
1280C4—121no—
1281C4—121no—
1282C4—121no—
1283C4—121no—
1284C4—121no—
1285C4—121no—
1286C4—121no—
1287C4—121no—
1288C4—121no—
1289C3#3841711yescharacteristic, complemented, Sylow
1290C2—42no—
1291C2—241no—
1292C2#8612111yescharacteristic
1293C2#8614611yescharacteristic
1294C2#8653911yescharacteristic
1295C2#8679011yescharacteristic
1296C2#8681211yescharacteristic
1297C2#8683511yescharacteristic
1298C2#8698211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2527C2
prime radicalC22×#67C23
hypercenter#2527D3
hypocenterC3#38417
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2527

Complements

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

NH ≅ G/Ntype
1. C3×#2527C2semidirect
2. #78421C2semidirect
3. #78415C2semidirect
4. #78284C2semidirect
5. #78200C2semidirect
6. #77592C2semidirect
8. #76836C2semidirect
10. #76589C2semidirect
11. #76558C2semidirect
12. #76551C2semidirect
13. #76546C2semidirect
16. #75466C2semidirect
17. #75465C2semidirect
18. #75376C2semidirect
19. #75235C2semidirect
20. #75112C2semidirect
21. #75034C2semidirect
22. #75028C2semidirect
23. #74970C2semidirect
24. #74586C2semidirect
27. #74051C2semidirect
28. #73543C2semidirect
30. #73399C2semidirect
31. #73392C2semidirect
208. #2527D3semidirect
1289. C3#38417semidirect

Maximal subgroups

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

subgroupindex
C3×#25272
#784212
#784152
#782842
#782002
#775922
#775522
#768362
#768182
#765892
#765582
#765512
#765462
#757202
#757192
#754662
#754652
#753762
#752352
#751122
#750342
#750282
#749702
#745862
#744362
#740712
#740512
#735432
#734382
#733992
#733922
#384173