Finite Group Databasebeta

← #11044105

Subgroups — #11044105

Order 768.

1510 conjugacy classes of subgroups.

The subgroup lattice has 1304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2745C211yesmaximal, characteristic, complemented
2#78430C211yesmaximal, characteristic, complemented
3#78418C211yesmaximal, characteristic, complemented
4#78268C211yesmaximal, characteristic, complemented
5#78230C211yesmaximal, characteristic, complemented
6#78206C211yesmaximal, characteristic, complemented
7#78185C211yesmaximal, characteristic, complemented
8#77523C211yesmaximal, characteristic, complemented
9#77521C211yesmaximal, characteristic
10#77266C211yesmaximal, characteristic, complemented
11#77200C211yesmaximal, characteristic, complemented
12#76866C211yesmaximal, characteristic
13#76803C211yesmaximal, characteristic, complemented
14#76526C211yesmaximal, characteristic, complemented
15#76487C211yesmaximal, characteristic, complemented
16#75893C211yesmaximal, characteristic
17#75616C211yesmaximal, characteristic, complemented
18#75567C211yesmaximal, characteristic, complemented
19#75520C211yesmaximal, characteristic
20#75304C211yesmaximal, characteristic, complemented
21#75212C211yesmaximal, characteristic, complemented
22#75203C211yesmaximal, characteristic, complemented
23#75052C211yesmaximal, characteristic, complemented
24#74971C211yesmaximal, characteristic, complemented
25#74955C211yesmaximal, characteristic, complemented
26#74545C211yesmaximal, characteristic, complemented
27#74377C211yesmaximal, characteristic
28#74107C211yesmaximal, characteristic
29#74051C211yesmaximal, characteristic, complemented
30#73998C211yesmaximal, characteristic, complemented
31#73980C211yesmaximal, characteristic
32#38412—31nomaximal, Sylow
33C2×#946C2211yescharacteristic
34C22×C4×Dic3C2211yescharacteristic
35C2×#898C2211yescharacteristic
36C2×#892C2211yescharacteristic
37C2×#890C2211yescharacteristic
38C2×#67⋊C4C2211yescharacteristic
39C3×#401C2211yescharacteristic
40C3×#400C2211yescharacteristic
41C3×#400C2211yescharacteristic
42C3×#397C2211yescharacteristic
43C3×#395C2211yescharacteristic
44C3×#393C2211yescharacteristic
45C3×#391C2211yescharacteristic
46C3×#388C2211yescharacteristic
47C3×#388C2211yescharacteristic
48C3×#387C2211yescharacteristic
49C3×#387C2211yescharacteristic
50C3×#387C2211yescharacteristic
51C3×#385C2211yescharacteristic
52C3×#381C2211yescharacteristic
53C3×#380C2211yescharacteristic
54#5229C2211yescharacteristic
55#5229C2211yescharacteristic
56#5229C2211yescharacteristic
57#5213C2211yescharacteristic
58#5212C2211yescharacteristic
59#5211C2211yescharacteristic
60#4994C2211yescharacteristic
61#4993C2211yescharacteristic
62#4992C2211yescharacteristic
63#4990C2211yescharacteristic
64#4989C2211yescharacteristic
65#4986C2211yescharacteristic
66#4984C2211yescharacteristic
67#4984C2211yescharacteristic
68#4984C2211yescharacteristic
69#4983C2211yescharacteristic
70#4982C2211yescharacteristic
71#4982C2211yescharacteristic
72#4981C2211yescharacteristic
73#4980C2211yescharacteristic
74#4980C2211yescharacteristic
75#4978C2211yescharacteristic
76#4978C2211yescharacteristic
77#4978C2211yescharacteristic
78#4978C2211yescharacteristic
79#4978C2211yescharacteristic
80#4977C2211yescharacteristic
81#4977C2211yescharacteristic
82Dic3×C4⋊C4C2211yescharacteristic
83Dic3×C4⋊C4C2211yescharacteristic
84#4972C2211yescharacteristic
85#4961C2211yescharacteristic
86#4959C2211yescharacteristic
87#4958C2211yescharacteristic
88#4956C2211yescharacteristic
89#4956C2211yescharacteristic
90#4952C2211yescharacteristic
91#4951C2211yescharacteristic
92#4951C2211yescharacteristic
93#4950C2211yescharacteristic
94#4950C2211yescharacteristic
95#4950C2211yescharacteristic
96#4949C2211yescharacteristic
97#4948C2211yescharacteristic
98#4948C2211yescharacteristic
99#4946C2211yescharacteristic
100#4946C2211yescharacteristic
101#4945C2211yescharacteristic
102#4944C2211yescharacteristic
103#4942C2211yescharacteristic
104#4942C2211yescharacteristic
105Dic3×C22⋊C4C2211yescharacteristic
106Dic3×C22⋊C4C2211yescharacteristic
107Dic3×C22⋊C4C2211yescharacteristic
108#4940C2211yescharacteristic
109C4×(C2×D3)⋊C4C2211yescharacteristic
110#4937C2211yescharacteristic
111C4×C4⋊Dic3C2211yescharacteristic
112C4×Dic3⋊C4C2211yescharacteristic
113C4×Dic3⋊C4C2211yescharacteristic
114#4928C2211yescharacteristic
115#4928C2211yescharacteristic
116#4674C2211yescharacteristic
117#4670C2211yescharacteristic
118#4670C2211yescharacteristic
119#4670C2211yescharacteristic
120#4669C2211yescharacteristic
121#4669C2211yescharacteristic
122#4668C2211yescharacteristic
123#4668C2211yescharacteristic
124#4668C2211yescharacteristic
125#4668C2211yescharacteristic
126#4668C2211yescharacteristic
127#4667C2211yescharacteristic
128#4666C2211yescharacteristic
129#4666C2211yescharacteristic
130#4664C2211yescharacteristic
131#4664C2211yescharacteristic
132#4664C2211yescharacteristic
133D3×#95C2211yescharacteristic
134C3⋊#401C2211yescharacteristic
135C3⋊#401C2211yescharacteristic
136#4661C2211yescharacteristic
137#4661C2211yescharacteristic
138#4660C2211yescharacteristic
139#4660C2211yescharacteristic
140#4660C2211yescharacteristic
141#4659C2211yescharacteristic
142#4659C2211yescharacteristic
143#4658C2211yescharacteristic
144#4658C2211yescharacteristic
145#4658C2211yescharacteristic
146#4658C2211yescharacteristic
147#4658C2211yescharacteristic
148#4657C2211yescharacteristic
149#4657C2211yescharacteristic
150#4657C2211yescharacteristic
151#4657C2211yescharacteristic
152#4657C2211yescharacteristic
153#4655C2211yescharacteristic
154#4655C2211yescharacteristic
155#4655C2211yescharacteristic
156#4655C2211yescharacteristic
157#4655C2211yescharacteristic
158#4655C2211yescharacteristic
159#4655C2211yescharacteristic
160#4655C2211yescharacteristic
161#4654C2211yescharacteristic
162#4654C2211yescharacteristic
163#4654C2211yescharacteristic
164#4654C2211yescharacteristic
165#4654C2211yescharacteristic
166#4654C2211yescharacteristic
167#4653C2211yescharacteristic
168#4653C2211yescharacteristic
169#4653C2211yescharacteristic
170#4653C2211yescharacteristic
171#4653C2211yescharacteristic
172#4653C2211yescharacteristic
173#4653C2211yescharacteristic
174#4651C2211yescharacteristic
175#4651C2211yescharacteristic
176#4651C2211yescharacteristic
177#4650C2211yescharacteristic
178#4650C2211yescharacteristic
179#4650C2211yescharacteristic
180#4649C2211yescharacteristic
181#4649C2211yescharacteristic
182#4649C2211yescharacteristic
183#4648C2211yescharacteristic
184#4648C2211yescharacteristic
185#4648C2211yescharacteristic
186#4647C2211yescharacteristic
187#4647C2211yescharacteristic
188#2851—31no—
189#2768—31no—
190#2767—31no—
191#2766—31no—
192#2746—31no—
193#2745D311yescharacteristic, complemented
194#2744—31no—
195#2743—31no—
196#2698—31no—
197#2655—31no—
198#2655—31no—
199#2612—31no—
200#2611—31no—
201#2589—31no—
202#2587—31no—
203#2578—31no—
204#2577—31no—
205#2576—31no—
206#2573—31no—
207#2524—31no—
208#2522—31no—
209#2514—31no—
210#2493—31no—
211#2468—31no—
212#2450—31no—
213#2371—31no—
214#2343—31no—
215#2334—31no—
216#2332—31no—
217#2290—31no—
218#2283—31no—
219C22×C3×Q8C2311yescharacteristic
220C23×C3×C4C2311yescharacteristic
221C22×#67C2311yescharacteristic
222C23×Dic3C2311yescharacteristic
223C23×Dic3C2311yescharacteristic
224C22×C4×D3C2311yescharacteristic
225C22×C4×D3C2311yescharacteristic
226C22×C4×D3C2311yescharacteristic
227C2×C3×C4⋊C4C2311yescharacteristic
228C2×C3×C4⋊C4C2311yescharacteristic
229C2×C3×C4⋊C4C2311yescharacteristic
230C2×C3×C4⋊C4C2311yescharacteristic
231C2×C3×C4⋊C4C2311yescharacteristic
232C2×C3×C4⋊C4C2311yescharacteristic
233C2×C3×C4⋊C4C2311yescharacteristic
234C2×C3×C22⋊C4C2311yescharacteristic
235C2×C3×C22⋊C4C2311yescharacteristic
236C2×C3×C22⋊C4C2311yescharacteristic
237C2×C3×C22⋊C4C2311yescharacteristic
238C2×C3×C22⋊C4C2311yescharacteristic
239C2×C3×C22⋊C4C2311yescharacteristic
240C2×C3×C42C2311yescharacteristic
241C2×C3×C42C2311yescharacteristic
242C2×#217C2311yescharacteristic
243C2×#217C2311yescharacteristic
244C2×#217C2311yescharacteristic
245C2×#217C2311yescharacteristic
246C2×#217C2311yescharacteristic
247#946—24no—
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×C4⋊Dic3C2311yescharacteristic
268C2×C4⋊Dic3C2311yescharacteristic
269C2×C4⋊Dic3C2311yescharacteristic
270C2×C4⋊Dic3C2311yescharacteristic
271C2×C4⋊Dic3C2311yescharacteristic
272C2×C4⋊Dic3C2311yescharacteristic
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×C4×Dic3—24no—
293C2×C4×Dic3C2311yescharacteristic
294C2×C4×Dic3C2311yescharacteristic
295C2×C4×Dic3C2311yescharacteristic
296C2×C4×Dic3C2311yescharacteristic
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
308#898—24no—
309#892—24no—
310#890—24no—
311#67⋊C4—24no—
312C3×#95C2311yescharacteristic
313C3×#95C2311yescharacteristic
314C3×#95C2311yescharacteristic
315C3×#95C2311yescharacteristic
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×#125—31no—
382C2×C22⋊Q8—31no—
383C2×C4×D4—31no—
384C2×#117—31no—
385C22×C42—31no—
386#401—31no—
387#401—31no—
388#401C2×D311yescharacteristic
389#400—31no—
390#400—31no—
391#400—31no—
392#400—31no—
393#400—31no—
394#400—31no—
395#400—31no—
396#400—31no—
397#400—31no—
398#400—31no—
399#400—31no—
400#400C2×D311yescharacteristic
401#400C2×D311yescharacteristic
402#399—31no—
403#399—31no—
404#398—31no—
405#398—31no—
406#398—31no—
407#398—31no—
408#398—31no—
409#398—31no—
410#398—31no—
411#398—31no—
412#398—31no—
413#398—31no—
414#398—31no—
415#397—31no—
416#397—31no—
417#397—31no—
418#397C2×D311yescharacteristic
419#396—31no—
420#396—31no—
421#396—31no—
422#395C2×D311yescharacteristic
423#394—31no—
424#394—31no—
425#393C2×D311yescharacteristic
426#391—31no—
427#391—31no—
428#391—31no—
429#391C2×D311yescharacteristic
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#388—31no—
439#388—31no—
440#388—31no—
441#388—31no—
442#388—31no—
443#388—31no—
444#388—31no—
445#388—31no—
446#388—31no—
447#388—31no—
448#388—31no—
449#388C2×D311yescharacteristic
450#388C2×D311yescharacteristic
451#387—31no—
452#387—31no—
453#387—31no—
454#387—31no—
455#387—31no—
456#387—31no—
457#387—31no—
458#387—31no—
459#387—31no—
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#387C2×D311yescharacteristic
480#387C2×D311yescharacteristic
481#387C2×D311yescharacteristic
482#386—31no—
483#386—31no—
484#386—31no—
485#386—31no—
486#385—31no—
487#385—31no—
488#385—31no—
489#385—31no—
490#385—31no—
491#385—31no—
492#385—31no—
493#385—31no—
494#385—31no—
495#385—31no—
496#385—31no—
497#385C2×D311yescharacteristic
498#383—31no—
499#383—31no—
500#383—31no—
501#383—31no—
502#382—31no—
503#382—31no—
504#382—31no—
505#382—31no—
506#382—31no—
507#381—31no—
508#381—31no—
509#381—31no—
510#381—31no—
511#381C2×D311yescharacteristic
512#380—31no—
513#380—31no—
514#380—31no—
515#380—31no—
516#380C2×D311yescharacteristic
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×C22⋊C4—31no—
526C4×C22⋊C4—31no—
527C4×C22⋊C4—31no—
528C4×C22⋊C4—31no—
529C4×C22⋊C4—31no—
530C4×C22⋊C4—31no—
531#376—31no—
532#376—31no—
533#376—31no—
534C2×#95—31no—
535C24×C3C2411yescharacteristic
536C23×D3C2411yescharacteristic
537C2×C3×Q8—22no—
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—22no—
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—22no—
584C2×C4×D3—41no—
585C2×C4×D3—41no—
586C2×C4×D3—41no—
587C2×C4×D3—41no—
588C2×C4×D3—41no—
589C2×C4×D3—41no—
590C3×C4⋊C4—22no—
591C3×C4⋊C4—22no—
592C3×C4⋊C4—22no—
593C3×C4⋊C4—41no—
594C3×C4⋊C4—41no—
595C3×C4⋊C4—41no—
596C3×C4⋊C4—41no—
597C3×C22⋊C4—22no—
598C3×C22⋊C4—22no—
599C3×C22⋊C4—22no—
600C3×C22⋊C4—41no—
601C3×C22⋊C4—41no—
602C3×C22⋊C4—41no—
603C3×C42—41no—
604C3×C42—41no—
605#217—22no—
606#217—41no—
607#217—41no—
608#217—41no—
609#217—41no—
610(C2×D3)⋊C4—22no—
611(C2×D3)⋊C4—22no—
612(C2×D3)⋊C4—22no—
613(C2×D3)⋊C4—22no—
614(C2×D3)⋊C4—22no—
615(C2×D3)⋊C4—41no—
616(C2×D3)⋊C4—41no—
617(C2×D3)⋊C4—41no—
618(C2×D3)⋊C4—41no—
619(C2×D3)⋊C4—41no—
620(C2×D3)⋊C4#4114yes—
621C4⋊Dic3—22no—
622C4⋊Dic3—22no—
623C4⋊Dic3—22no—
624C4⋊Dic3—22no—
625C4⋊Dic3—22no—
626C4⋊Dic3—22no—
627C4⋊Dic3—41no—
628C4⋊Dic3—41no—
629C4⋊Dic3—41no—
630C4⋊Dic3—41no—
631C4⋊Dic3—41no—
632C4⋊Dic3—41no—
633C4⋊Dic3—41no—
634C4⋊Dic3—41no—
635Dic3⋊C4—22no—
636Dic3⋊C4—22no—
637Dic3⋊C4—22no—
638Dic3⋊C4—22no—
639Dic3⋊C4—22no—
640Dic3⋊C4—22no—
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×C4—31no—
675C23×C4—31no—
676C23×C4C22×D311yescharacteristic
677#126—64no—
678#125—64no—
679C22⋊Q8—64no—
680C4×D4—64no—
681#117—64no—
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⋊C4C22×D311yescharacteristic
716C2×C4⋊C4C22×D311yescharacteristic
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⋊C4C22×D311yescharacteristic
739C2×C22⋊C4C22×D311yescharacteristic
740C2×C22⋊C4C22×D311yescharacteristic
741C2×C22⋊C4C22×D311yescharacteristic
742C2×C22⋊C4C22×D311yescharacteristic
743C2×C22⋊C4C22×D311yescharacteristic
744C2×C42—31no—
745C2×C42—31no—
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—64no—
760C2×C42C22×D311yescharacteristic
761C2×C42C22×D311yescharacteristic
762#95—31no—
763#95—31no—
764#95—31no—
765#95—31no—
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×C32−1+412yes—
837C23×C3C2511yescharacteristic
838C22×D3—21no—
839C22×D3—21no—
840C22×D3—21no—
841C22×D3—21no—
842C22×D3—21no—
843C22×D3—21no—
844C22×D3C2×#4112yes—
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—44no—
887C2×C3×C4C2×#4112yes—
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—21no—
931C2×Dic3—21no—
932C2×Dic3—44no—
933C2×Dic3—44no—
934C2×Dic3C2×#4112yes—
935C2×Dic3C2×#4112yes—
936C2×Dic3C2×#4112yes—
937C4×D3—44no—
938C4×D3—82no—
939C4×D3—82no—
940C24—31no—
941C24C23×D311yescharacteristic
942C2×Q8—22no—
943C2×Q8—41no—
944C2×Q8—41no—
945C2×D4—62no—
946C2×D4—62no—
947C2×D4—121no—
948C22×C4—22no—
949C22×C4—22no—
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—31no—
964C22×C4—31no—
965C22×C4—41no—
966C22×C4—62no—
967C22×C4—62no—
968C22×C4—62no—
969C22×C4—62no—
970C22×C4—62no—
971C22×C4—62no—
972C22×C4—121no—
973C22×C4—121no—
974C22×C4—121no—
975C22×C4—121no—
976C22×C4—121no—
977C22×C4—121no—
978C22×C4—121no—
979C22×C4—121no—
980C22×C4—121no—
981C22×C4C23×D311yescharacteristic
982C22×C4C23×D311yescharacteristic
983C22×C4C23×D311yescharacteristic
984C22×C4C23×D311yescharacteristic
985C22×C4C23×D311yescharacteristic
986C22×C4C23×D311yescharacteristic
987C22×C4C23×D311yescharacteristic
988C22×C4C23×D311yescharacteristic
989C22×C4C23×D311yescharacteristic
990C22×C4C23×D311yescharacteristic
991C22×C4C23×D311yescharacteristic
992C22×C4C23×D311yescharacteristic
993C22×C4C23×D311yescharacteristic
994C22×C4C23×D311yescharacteristic
995C4⋊C4—22no—
996C4⋊C4—22no—
997C4⋊C4—22no—
998C4⋊C4—41no—
999C4⋊C4—41no—
1000C4⋊C4—41no—
1001C4⋊C4—41no—
1002C4⋊C4—62no—
1003C4⋊C4—62no—
1004C4⋊C4—62no—
1005C4⋊C4—62no—
1006C4⋊C4—62no—
1007C4⋊C4—62no—
1008C4⋊C4—62no—
1009C4⋊C4—62no—
1010C4⋊C4—62no—
1011C4⋊C4—62no—
1012C4⋊C4—62no—
1013C4⋊C4—62no—
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—
1029C4⋊C4—121no—
1030C4⋊C4—121no—
1031C4⋊C4—121no—
1032C4⋊C4—121no—
1033C4⋊C4—121no—
1034C4⋊C4—121no—
1035C22⋊C4—22no—
1036C22⋊C4—22no—
1037C22⋊C4—22no—
1038C22⋊C4—34no—
1039C22⋊C4—41no—
1040C22⋊C4—41no—
1041C22⋊C4—41no—
1042C22⋊C4—62no—
1043C22⋊C4—62no—
1044C22⋊C4—62no—
1045C22⋊C4—62no—
1046C22⋊C4—62no—
1047C22⋊C4—62no—
1048C22⋊C4—121no—
1049C22⋊C4—121no—
1050C22⋊C4—121no—
1051C22⋊C4—121no—
1052C22⋊C4—121no—
1053C22⋊C4—121no—
1054C22⋊C4—121no—
1055C22⋊C4—121no—
1056C22⋊C4—121no—
1057C42—34no—
1058C42—41no—
1059C42—41no—
1060C42—62no—
1061C42—62no—
1062C42—62no—
1063C42—62no—
1064C42—62no—
1065C42—62no—
1066C42—121no—
1067C42—121no—
1068C42—121no—
1069C42—121no—
1070C42—121no—
1071C42—121no—
1072C42—121no—
1073C42—121no—
1074C22×C3—22no—
1075C22×C3—22no—
1076C22×C3—22no—
1077C22×C3—41no—
1078C22×C3—41no—
1079C22×C3—41no—
1080C22×C3—41no—
1081C22×C3C22×#4111yescharacteristic
1082C22×C3C22×#4111yescharacteristic
1083C22×C3C2×2−1+411yescharacteristic
1084C22×C3#58511yescharacteristic
1085C22×C3#58511yescharacteristic
1086C22×C3#58511yescharacteristic
1087C22×C3#58511yescharacteristic
1088C2×D3—22no—
1089C2×D3—22no—
1090C2×D3—22no—
1091C2×D3—41no—
1092C2×D3—41no—
1093C2×D3—41no—
1094C2×D3—41no—
1095C3×C4—22no—
1096C3×C4—22no—
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—
1107C3×C4—41no—
1108C3×C4—41no—
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—
1122Dic3—41no—
1123Dic3—41no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—32no—
1131C23—61no—
1132C23—61no—
1133C23—61no—
1134C23—61no—
1135C23—61no—
1136C23—61no—
1137C23#101012yes—
1138C23C24×D311yescharacteristic
1139Q8—82no—
1140D4—124no—
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—21no—
1181C2×C4—32no—
1182C2×C4—32no—
1183C2×C4—32no—
1184C2×C4—44no—
1185C2×C4—61no—
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—61no—
1227C2×C4—124no—
1228C2×C4—124no—
1229C2×C4—124no—
1230C2×C4—242no—
1231C2×C4—242no—
1232C2×C4D3×#4112yes—
1233C2×C4D3×#4112yes—
1234C2×C3—42no—
1235C2×C3#345511yescharacteristic
1236C2×C3#347511yescharacteristic
1237C2×C3#349511yescharacteristic
1238C2×C3#349511yescharacteristic
1239C2×C3#352111yescharacteristic
1240C2×C3#355311yescharacteristic
1241C2×C3#356611yescharacteristic
1242D3—42no—
1243C22—22no—
1244C22—22no—
1245C22—22no—
1246C22—41no—
1247C22—41no—
1248C22—41no—
1249C22—41no—
1250C22—62no—
1251C22—62no—
1252C22—62no—
1253C22—121no—
1254C22—121no—
1255C22—121no—
1256C22—121no—
1257C22C2×D3×#4111yescharacteristic
1258C22C2×D3×#4111yescharacteristic
1259C22C2×#101011yescharacteristic
1260C22#596611yescharacteristic
1261C22#596611yescharacteristic
1262C22#596811yescharacteristic
1263C22#596811yescharacteristic
1264C4—22no—
1265C4—22no—
1266C4—41no—
1267C4—41no—
1268C4—41no—
1269C4—41no—
1270C4—41no—
1271C4—41no—
1272C4—41no—
1273C4—41no—
1274C4—41no—
1275C4—41no—
1276C4—41no—
1277C4—41no—
1278C4—62no—
1279C4—62no—
1280C4—62no—
1281C4—121no—
1282C4—121no—
1283C4—121no—
1284C4—121no—
1285C4—121no—
1286C4—121no—
1287C4—121no—
1288C4—121no—
1289C4—121no—
1290C4—121no—
1291C4—121no—
1292C4—121no—
1293C3#3841211yescharacteristic, complemented, Sylow
1294C2—42no—
1295C2—122no—
1296C2#8639311yescharacteristic
1297C2#8643911yescharacteristic
1298C2#8652311yescharacteristic
1299C2#8679311yescharacteristic
1300C2#8683011yescharacteristic
1301C2#8697911yescharacteristic
1302C2#8712511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2745C2
prime radicalC22×#67C23
hypercenter#2745D3
hypocenterC3#38412
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2745

Complements

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

NH ≅ G/Ntype
1. C3×#2745C2semidirect
2. #78430C2semidirect
3. #78418C2semidirect
4. #78268C2semidirect
5. #78230C2semidirect
6. #78206C2semidirect
7. #78185C2semidirect
8. #77523C2semidirect
10. #77266C2semidirect
11. #77200C2semidirect
13. #76803C2semidirect
14. #76526C2semidirect
15. #76487C2semidirect
17. #75616C2semidirect
18. #75567C2semidirect
20. #75304C2semidirect
21. #75212C2semidirect
22. #75203C2semidirect
23. #75052C2semidirect
24. #74971C2semidirect
25. #74955C2semidirect
26. #74545C2semidirect
29. #74051C2semidirect
30. #73998C2semidirect
193. #2745D3semidirect
1293. C3#38412semidirect

Maximal subgroups

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

subgroupindex
C3×#27452
#784302
#784182
#782682
#782302
#782062
#781852
#775232
#775212
#772662
#772002
#768662
#768032
#765262
#764872
#758932
#756162
#755672
#755202
#753042
#752122
#752032
#750522
#749712
#749552
#745452
#743772
#741072
#740512
#739982
#739802
#384123