Finite Group Databasebeta

← #11223030

Subgroups — #11223030

Order 768.

1542 conjugacy classes of subgroups.

The subgroup lattice has 1286 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2581C211yesmaximal, characteristic, complemented
2#82485C211yesmaximal, characteristic
3#82467C211yesmaximal, characteristic, complemented
4#82465C211yesmaximal, characteristic, complemented
5#82464C211yesmaximal, characteristic
6#78284C211yesmaximal, characteristic, complemented
7#78258C211yesmaximal, characteristic, complemented
8#78253C211yesmaximal, characteristic
9#78170C211yesmaximal, characteristic
10#77261C211yesmaximal, characteristic
11#77225C211yesmaximal, characteristic, complemented
12#77214C211yesmaximal, characteristic
13#77175C211yesmaximal, characteristic, complemented
14#76588C211yesmaximal, characteristic, complemented
15#76583C211yesmaximal, characteristic
16#76549C211yesmaximal, characteristic, complemented
17#76546C211yesmaximal, characteristic
18#76227C211yesmaximal, characteristic
19#76099C211yesmaximal, characteristic, complemented
20#76063C211yesmaximal, characteristic, complemented
21#76053C211yesmaximal, characteristic
22#75068C211yesmaximal, characteristic
23#75061C211yesmaximal, characteristic, complemented
24#75015C211yesmaximal, characteristic
25#75004C211yesmaximal, characteristic
26#74970C211yesmaximal, characteristic, complemented
27#74964C211yesmaximal, characteristic, complemented
28#74948C211yesmaximal, characteristic, complemented
29#74947C211yesmaximal, characteristic
30#74179C211yesmaximal, characteristic
31#74176C211yesmaximal, characteristic, complemented
32#44866—31nomaximal, Sylow
33C2×C3×C4×Q8C2211yescharacteristic
34C2×C3×C4×Q8C2211yescharacteristic
35C2×#946C2211yescharacteristic
36C2×#944C2211yescharacteristic
37C2×#896C2211yescharacteristic
38C2×#892C2211yescharacteristic
39C2×#889C2211yescharacteristic
40C2×#888C2211yescharacteristic
41C2×#887C2211yescharacteristic
42C2×#887C2211yescharacteristic
43C2×#876C2211yescharacteristic
44C2×C4×Dic6C2211yescharacteristic
45C3×#400C2211yescharacteristic
46C3×#400C2211yescharacteristic
47C3×#395C2211yescharacteristic
48C3×#395C2211yescharacteristic
49C3×#391C2211yescharacteristic
50C3×#391C2211yescharacteristic
51C3×#389C2211yescharacteristic
52C3×#389C2211yescharacteristic
53C3×#387C2211yescharacteristic
54C3×#387C2211yescharacteristic
55C3×#387C2211yescharacteristic
56C3×#387C2211yescharacteristic
57C3×#382C2211yescharacteristic
58#5231C2211yescharacteristic
59#5230C2211yescharacteristic
60#5230C2211yescharacteristic
61#5230C2211yescharacteristic
62#5229C2211yescharacteristic
63#5229C2211yescharacteristic
64#4994C2211yescharacteristic
65#4993C2211yescharacteristic
66#4990C2211yescharacteristic
67#4990C2211yescharacteristic
68#4990C2211yescharacteristic
69#4990C2211yescharacteristic
70#4990C2211yescharacteristic
71#4990C2211yescharacteristic
72#4990C2211yescharacteristic
73#4989C2211yescharacteristic
74#4985C2211yescharacteristic
75#4984C2211yescharacteristic
76#4983C2211yescharacteristic
77#4983C2211yescharacteristic
78#4982C2211yescharacteristic
79#4982C2211yescharacteristic
80#4982C2211yescharacteristic
81#4981C2211yescharacteristic
82#4981C2211yescharacteristic
83#4981C2211yescharacteristic
84#4981C2211yescharacteristic
85#4980C2211yescharacteristic
86#4980C2211yescharacteristic
87#4979C2211yescharacteristic
88#4979C2211yescharacteristic
89#4979C2211yescharacteristic
90#4979C2211yescharacteristic
91#4978C2211yescharacteristic
92#4978C2211yescharacteristic
93#4978C2211yescharacteristic
94#4978C2211yescharacteristic
95#4978C2211yescharacteristic
96#4978C2211yescharacteristic
97#4978C2211yescharacteristic
98#4976C2211yescharacteristic
99#4976C2211yescharacteristic
100#4976C2211yescharacteristic
101#4976C2211yescharacteristic
102#4976C2211yescharacteristic
103Dic3×C4⋊C4C2211yescharacteristic
104Dic3×C4⋊C4C2211yescharacteristic
105Dic3×C4⋊C4C2211yescharacteristic
106#4940C2211yescharacteristic
107#4940C2211yescharacteristic
108#4940C2211yescharacteristic
109C4×(C2×D3)⋊C4C2211yescharacteristic
110#4933C2211yescharacteristic
111#4933C2211yescharacteristic
112#4933C2211yescharacteristic
113#4932C2211yescharacteristic
114#4932C2211yescharacteristic
115C4×Dic3⋊C4C2211yescharacteristic
116C4×Dic3⋊C4C2211yescharacteristic
117C4×Dic3⋊C4C2211yescharacteristic
118C4×Dic3⋊C4C2211yescharacteristic
119C4×Dic3⋊C4C2211yescharacteristic
120C4×Dic3⋊C4C2211yescharacteristic
121C4×Dic3⋊C4C2211yescharacteristic
122#4929C2211yescharacteristic
123#4928C2211yescharacteristic
124#4676C2211yescharacteristic
125#4675C2211yescharacteristic
126#4675C2211yescharacteristic
127#4675C2211yescharacteristic
128#4674C2211yescharacteristic
129#4673C2211yescharacteristic
130#4673C2211yescharacteristic
131#4670C2211yescharacteristic
132#4670C2211yescharacteristic
133#4669C2211yescharacteristic
134#4669C2211yescharacteristic
135#4669C2211yescharacteristic
136#4669C2211yescharacteristic
137#4669C2211yescharacteristic
138#4668C2211yescharacteristic
139#4667C2211yescharacteristic
140C3⋊#401C2211yescharacteristic
141#4660C2211yescharacteristic
142#4660C2211yescharacteristic
143#4660C2211yescharacteristic
144#4658C2211yescharacteristic
145#4658C2211yescharacteristic
146#4658C2211yescharacteristic
147#4657C2211yescharacteristic
148#4657C2211yescharacteristic
149#4655C2211yescharacteristic
150#4655C2211yescharacteristic
151#4655C2211yescharacteristic
152#4655C2211yescharacteristic
153#4654C2211yescharacteristic
154#4654C2211yescharacteristic
155#4654C2211yescharacteristic
156#4654C2211yescharacteristic
157#4653C2211yescharacteristic
158#4653C2211yescharacteristic
159#4652C2211yescharacteristic
160#4652C2211yescharacteristic
161#4652C2211yescharacteristic
162#4652C2211yescharacteristic
163#4652C2211yescharacteristic
164#4652C2211yescharacteristic
165#4652C2211yescharacteristic
166#4652C2211yescharacteristic
167#4651C2211yescharacteristic
168#4651C2211yescharacteristic
169#4651C2211yescharacteristic
170#4650C2211yescharacteristic
171#4650C2211yescharacteristic
172#4650C2211yescharacteristic
173#4649C2211yescharacteristic
174#4649C2211yescharacteristic
175#4648C2211yescharacteristic
176#4648C2211yescharacteristic
177#4647C2211yescharacteristic
178#4647C2211yescharacteristic
179#4647C2211yescharacteristic
180#4647C2211yescharacteristic
181#4646C2211yescharacteristic
182#4646C2211yescharacteristic
183#4646C2211yescharacteristic
184#4646C2211yescharacteristic
185#4646C2211yescharacteristic
186#4646C2211yescharacteristic
187#4646C2211yescharacteristic
188#2776—31no—
189#2774—31no—
190#2759—31no—
191#2758—31no—
192#2755—31no—
193#2754—31no—
194#2690—31no—
195#2677—31no—
196#2606—31no—
197#2604—31no—
198#2586—31no—
199#2581D311yescharacteristic, complemented
200#2574—31no—
201#2550—31no—
202#2532—31no—
203#2529—31no—
204#2529—31no—
205#2528—31no—
206#2525—31no—
207#2520—31no—
208#2478—31no—
209#2469—31no—
210#2465—31no—
211#2451—31no—
212#2399—31no—
213#2371—31no—
214#2365—31no—
215#2362—31no—
216#2356—31no—
217#2327—31no—
218#2323—31no—
219C22×C3×Q8C2311yescharacteristic
220C22×C3×Q8C2311yescharacteristic
221C22×C4×D3C2311yescharacteristic
222C22×Dic6C2311yescharacteristic
223C22×Dic6C2311yescharacteristic
224C22×Dic6C2311yescharacteristic
225C3×C4×Q8—42no—
226C3×C4×Q8—42no—
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×C4⋊C4C2311yescharacteristic
235C2×C3×C4⋊C4C2311yescharacteristic
236C2×C3×C4⋊C4C2311yescharacteristic
237C2×C3×C4⋊C4C2311yescharacteristic
238C2×C3×C4⋊C4C2311yescharacteristic
239C2×C3×C42C2311yescharacteristic
240C2×C3×C42C2311yescharacteristic
241C2×C3×C42C2311yescharacteristic
242C2×C3×C42C2311yescharacteristic
243C2×C3×C42C2311yescharacteristic
244#946—24no—
245#944—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×(C2×D3)⋊C4C2311yescharacteristic
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×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
308C2×C4×Dic3C2311yescharacteristic
309C2×C4×Dic3C2311yescharacteristic
310C2×C4×Dic3C2311yescharacteristic
311C2×C4×Dic3C2311yescharacteristic
312#896—24no—
313#892—42no—
314#889—24no—
315#888—24no—
316#887—24no—
317#887—42no—
318#876—42no—
319C4×Dic6—42no—
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
380C3⋊#95C2311yescharacteristic
381C3⋊#95C2311yescharacteristic
382C3⋊#95C2311yescharacteristic
383C3⋊#95C2311yescharacteristic
384C3⋊#95C2311yescharacteristic
385C3⋊#95C2311yescharacteristic
386C2×C4⋊Q8—31no—
387C2×C4⋊Q8—31no—
388C2×#126—31no—
389C2×#125—31no—
390C2×C22⋊Q8—31no—
391C2×C22⋊Q8—31no—
392C2×C4×Q8—31no—
393C2×C4×Q8—31no—
394C2×C4×Q8—31no—
395C2×C4×Q8C2×D311yescharacteristic
396C2×C4×Q8C2×D311yescharacteristic
397C2×#117—31no—
398#401—31no—
399#400—31no—
400#400—31no—
401#400—31no—
402#400—31no—
403#400—31no—
404#400—31no—
405#400—31no—
406#400C2×D311yescharacteristic
407#400C2×D311yescharacteristic
408#399—31no—
409#398—31no—
410#398—31no—
411#398—31no—
412#398—31no—
413#398—31no—
414#398—31no—
415#398—31no—
416#398—31no—
417#398—31no—
418#398—31no—
419#398—31no—
420#397—31no—
421#397—31no—
422#397—31no—
423#397—31no—
424#396—31no—
425#396—31no—
426#395—31no—
427#395—31no—
428#395—31no—
429#395—31no—
430#395—31no—
431#395—31no—
432#395—31no—
433#395C2×D311yescharacteristic
434#395C2×D311yescharacteristic
435#393—31no—
436#393—31no—
437#393—31no—
438#391—31no—
439#391—31no—
440#391—31no—
441#391—31no—
442#391—31no—
443#391—31no—
444#391—31no—
445#391—31no—
446#391—31no—
447#391—31no—
448#391C2×D311yescharacteristic
449#391C2×D311yescharacteristic
450#389—31no—
451#389—31no—
452#389—31no—
453#389—31no—
454#389—31no—
455#389—31no—
456#389—31no—
457#389—31no—
458#389—31no—
459#389—31no—
460#389—31no—
461#389C2×D311yescharacteristic
462#389C2×D311yescharacteristic
463#388—31no—
464#388—31no—
465#388—31no—
466#388—31no—
467#388—31no—
468#388—31no—
469#388—31no—
470#388—31no—
471#388—31no—
472#388—31no—
473#388—31no—
474#388—31no—
475#388—31no—
476#388—31no—
477#388—31no—
478#388—31no—
479#388—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#387—31no—
490#387—31no—
491#387—31no—
492#387—31no—
493#387—31no—
494#387—31no—
495#387—31no—
496#387—31no—
497#387—31no—
498#387—31no—
499#387—31no—
500#387—31no—
501#387—31no—
502#387—31no—
503#387—31no—
504#387—31no—
505#387—31no—
506#387—31no—
507#387—31no—
508#387—31no—
509#387—31no—
510#387C2×D311yescharacteristic
511#387C2×D311yescharacteristic
512#387C2×D311yescharacteristic
513#387C2×D311yescharacteristic
514#385—31no—
515#385—31no—
516#383—31no—
517#383—31no—
518#383—31no—
519#382—31no—
520#382—31no—
521#382—31no—
522#382C2×D311yescharacteristic
523#380—31no—
524C4×C4⋊C4—31no—
525C4×C4⋊C4—31no—
526C4×C4⋊C4—31no—
527C4×C4⋊C4—31no—
528C4×C4⋊C4—31no—
529C4×C4⋊C4—31no—
530C4×C4⋊C4—31no—
531C4×C4⋊C4—31no—
532C4×C4⋊C4—31no—
533C4×C4⋊C4—31no—
534C4×C4⋊C4—31no—
535C4×C4⋊C4—31no—
536C4×C22⋊C4—31no—
537#376—31no—
538#376—31no—
539#376—31no—
540#376—31no—
541C23×D3C2411yescharacteristic
542C2×C3×Q8—22no—
543C2×C3×Q8—22no—
544C2×C3×Q8—22no—
545C2×C3×Q8—41no—
546C2×C3×Q8—41no—
547C2×C3×Q8—41no—
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
557C22×C3×C4C2411yescharacteristic
558C22×C3×C4C2411yescharacteristic
559C22×C3×C4C2411yescharacteristic
560C22×C3×C4C2411yescharacteristic
561C22×C3×C4C2411yescharacteristic
562C22×C3×C4C2411yescharacteristic
563C22×Dic3C2411yescharacteristic
564C22×Dic3C2411yescharacteristic
565C22×Dic3C2411yescharacteristic
566C22×Dic3C2411yescharacteristic
567C22×Dic3C2411yescharacteristic
568C22×Dic3C2411yescharacteristic
569C22×Dic3C2411yescharacteristic
570C22×Dic3C2411yescharacteristic
571C22×Dic3C2411yescharacteristic
572C22×Dic3C2411yescharacteristic
573C22×Dic3C2411yescharacteristic
574C22×Dic3C2411yescharacteristic
575C22×Dic3C2411yescharacteristic
576C22×Dic3C2411yescharacteristic
577C22×Dic3C2411yescharacteristic
578C2×C4×D3—22no—
579C2×C4×D3—22no—
580C2×C4×D3—41no—
581C2×Dic6—22no—
582C2×Dic6—22no—
583C2×Dic6—22no—
584C2×Dic6—22no—
585C2×Dic6—22no—
586C2×Dic6—22no—
587C2×Dic6—41no—
588C2×Dic6—41no—
589C2×Dic6—41no—
590C3×C4⋊C4—22no—
591C3×C4⋊C4—22no—
592C3×C4⋊C4—22no—
593C3×C4⋊C4—22no—
594C3×C4⋊C4—22no—
595C3×C4⋊C4—22no—
596C3×C4⋊C4—41no—
597C3×C4⋊C4—41no—
598C3×C4⋊C4—41no—
599C3×C4⋊C4—41no—
600C3×C4⋊C4—41no—
601C3×C4⋊C4—41no—
602C3×C42—22no—
603C3×C42—22no—
604C3×C42—22no—
605C3×C42—41no—
606C3×C42—41no—
607(C2×D3)⋊C4—22no—
608(C2×D3)⋊C4—22no—
609(C2×D3)⋊C4—22no—
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—41no—
621C4⋊Dic3—22no—
622C4⋊Dic3—22no—
623C4⋊Dic3—22no—
624C4⋊Dic3—22no—
625C4⋊Dic3—41no—
626C4⋊Dic3—41no—
627C4⋊Dic3—41no—
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—22no—
640Dic3⋊C4—22no—
641Dic3⋊C4—22no—
642Dic3⋊C4—22no—
643Dic3⋊C4—22no—
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—
654Dic3⋊C4#4114yes—
655Dic3⋊C4#4114yes—
656C4×Dic3—22no—
657C4×Dic3—22no—
658C4×Dic3—22no—
659C4×Dic3—22no—
660C4×Dic3—22no—
661C4×Dic3—22no—
662C4×Dic3—22no—
663C4×Dic3—22no—
664C4×Dic3—22no—
665C4×Dic3—22no—
666C4×Dic3—22no—
667C4×Dic3—22no—
668C4×Dic3—41no—
669C4×Dic3—41no—
670C4×Dic3—41no—
671C4×Dic3—41no—
672C4×Dic3—41no—
673C22×Q8—31no—
674C22×Q8—31no—
675C22×Q8—31no—
676C22×Q8C22×D311yescharacteristic
677C22×Q8C22×D311yescharacteristic
678C23×C4—31no—
679C4⋊Q8—64no—
680C4⋊Q8—64no—
681#126—122no—
682#125—64no—
683C22⋊Q8—64no—
684C22⋊Q8—64no—
685C4×Q8—42no—
686C4×Q8—42no—
687C4×Q8—64no—
688C4×Q8—122no—
689C4×Q8—122no—
690#117—122no—
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⋊C4—31no—
718C2×C4⋊C4—31no—
719C2×C4⋊C4—31no—
720C2×C4⋊C4—31no—
721C2×C4⋊C4—31no—
722C2×C4⋊C4—31no—
723C2×C4⋊C4—31no—
724C2×C4⋊C4—31no—
725C2×C4⋊C4—31no—
726C2×C4⋊C4C22×D311yescharacteristic
727C2×C4⋊C4C22×D311yescharacteristic
728C2×C4⋊C4C22×D311yescharacteristic
729C2×C4⋊C4C22×D311yescharacteristic
730C2×C4⋊C4C22×D311yescharacteristic
731C2×C4⋊C4C22×D311yescharacteristic
732C2×C4⋊C4C22×D311yescharacteristic
733C2×C4⋊C4C22×D311yescharacteristic
734C2×C4⋊C4C22×D311yescharacteristic
735C2×C4⋊C4C22×D311yescharacteristic
736C2×C4⋊C4C22×D311yescharacteristic
737C2×C4⋊C4C22×D311yescharacteristic
738C2×C22⋊C4—31no—
739C2×C22⋊C4—31no—
740C2×C22⋊C4—31no—
741C2×C22⋊C4—31no—
742C2×C22⋊C4—31no—
743C2×C22⋊C4—31no—
744C2×C22⋊C4—31no—
745C2×C22⋊C4—31no—
746C2×C22⋊C4—31no—
747C2×C22⋊C4—31no—
748C2×C22⋊C4—31no—
749C2×C22⋊C4—31no—
750C2×C22⋊C4—31no—
751C2×C22⋊C4—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—31no—
762C2×C42—31no—
763C2×C42—31no—
764C2×C42—31no—
765C2×C42—31no—
766C2×C42—31no—
767C2×C42—31no—
768C2×C42—31no—
769C2×C42C22×D311yescharacteristic
770C2×C42C22×D311yescharacteristic
771C2×C42C22×D311yescharacteristic
772C2×C42C22×D311yescharacteristic
773C2×C42C22×D311yescharacteristic
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#95—31no—
813#95—31no—
814#95—31no—
815#95—31no—
816#95—31no—
817#95—31no—
818#95—31no—
819#95—31no—
820#95—31no—
821#95—31no—
822#95—31no—
823#95—31no—
824#95C22×D311yescharacteristic
825#95C22×D311yescharacteristic
826#95C22×D311yescharacteristic
827#95C22×D311yescharacteristic
828#95C22×D311yescharacteristic
829#95C22×D311yescharacteristic
830#95C22×D311yescharacteristic
831#95C22×D311yescharacteristic
832#95C22×D311yescharacteristic
833#95C22×D311yescharacteristic
834#95C22×D311yescharacteristic
835#95C22×D311yescharacteristic
836#95C22×D311yescharacteristic
837#95C22×D311yescharacteristic
838#95C22×D311yescharacteristic
839#95C22×D311yescharacteristic
840C23×C3C2511yescharacteristic
841C22×D3—21no—
842C22×D3—21no—
843C22×D3—21no—
844C22×D3—21no—
845C22×D3—21no—
846C22×D3—21no—
847C22×D3—21no—
848C3×Q8—44no—
849C3×Q8—44no—
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—21no—
888C2×C3×C4—21no—
889C2×C3×C4—21no—
890C2×C3×C4—21no—
891C2×C3×C4C2×#4112yes—
892C2×C3×C4C2×#4112yes—
893C2×C3×C4H(5,𝔽2)12yes—
894C2×C3×C42−1+412yes—
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—21no—
933C2×Dic3—21no—
934C2×Dic3C2×#4112yes—
935C2×Dic3C2×#4112yes—
936C2×Dic3C2×#4112yes—
937C2×Dic3C2×#4112yes—
938C2×Dic32−1+412yes—
939C2×Dic32−1+412yes—
940C4×D3—44no—
941Dic6—44no—
942Dic6—44no—
943Dic6—44no—
944C24—31no—
945C2×Q8—22no—
946C2×Q8—22no—
947C2×Q8—22no—
948C2×Q8—41no—
949C2×Q8—41no—
950C2×Q8—41no—
951C2×Q8—62no—
952C2×Q8—62no—
953C2×Q8—62no—
954C2×Q8—62no—
955C2×Q8—62no—
956C2×Q8—62no—
957C2×Q8—121no—
958C2×Q8—121no—
959C2×Q8—121no—
960C22×C4—31no—
961C22×C4—31no—
962C22×C4—31no—
963C22×C4—31no—
964C22×C4—31no—
965C22×C4—31no—
966C22×C4—31no—
967C22×C4—31no—
968C22×C4—31no—
969C22×C4—31no—
970C22×C4—31no—
971C22×C4—31no—
972C22×C4—31no—
973C22×C4—31no—
974C22×C4—31no—
975C22×C4—62no—
976C22×C4—62no—
977C22×C4—121no—
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
987C22×C4C23×D311yescharacteristic
988C22×C4C23×D311yescharacteristic
989C22×C4C23×D311yescharacteristic
990C22×C4C23×D311yescharacteristic
991C22×C4C23×D311yescharacteristic
992C22×C4C23×D311yescharacteristic
993C4⋊C4—22no—
994C4⋊C4—22no—
995C4⋊C4—22no—
996C4⋊C4—22no—
997C4⋊C4—22no—
998C4⋊C4—22no—
999C4⋊C4—34no—
1000C4⋊C4—34no—
1001C4⋊C4—41no—
1002C4⋊C4—41no—
1003C4⋊C4—41no—
1004C4⋊C4—41no—
1005C4⋊C4—41no—
1006C4⋊C4—41no—
1007C4⋊C4—62no—
1008C4⋊C4—62no—
1009C4⋊C4—62no—
1010C4⋊C4—62no—
1011C4⋊C4—62no—
1012C4⋊C4—62no—
1013C4⋊C4—62no—
1014C4⋊C4—62no—
1015C4⋊C4—62no—
1016C4⋊C4—62no—
1017C4⋊C4—62no—
1018C4⋊C4—62no—
1019C4⋊C4—62no—
1020C4⋊C4—62no—
1021C4⋊C4—62no—
1022C4⋊C4—62no—
1023C4⋊C4—62no—
1024C4⋊C4—62no—
1025C4⋊C4—62no—
1026C4⋊C4—62no—
1027C4⋊C4—121no—
1028C4⋊C4—121no—
1029C4⋊C4—121no—
1030C4⋊C4—121no—
1031C4⋊C4—121no—
1032C4⋊C4—121no—
1033C4⋊C4—121no—
1034C4⋊C4—121no—
1035C4⋊C4—121no—
1036C4⋊C4—121no—
1037C4⋊C4—121no—
1038C4⋊C4—121no—
1039C4⋊C4—121no—
1040C22⋊C4—62no—
1041C22⋊C4—62no—
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—
1054C42—22no—
1055C42—22no—
1056C42—22no—
1057C42—41no—
1058C42—41no—
1059C42—62no—
1060C42—62no—
1061C42—62no—
1062C42—62no—
1063C42—62no—
1064C42—62no—
1065C42—62no—
1066C42—62no—
1067C42—62no—
1068C42—62no—
1069C42—62no—
1070C42—62no—
1071C42—121no—
1072C42—121no—
1073C42—121no—
1074C42—121no—
1075C42—121no—
1076C22×C3C22×#4111yescharacteristic
1077C22×C3C22×#4111yescharacteristic
1078C22×C3C2×H(5,𝔽2)11yescharacteristic
1079C22×C3C2×2−1+411yescharacteristic
1080C22×C3C2×2−1+411yescharacteristic
1081C22×C3C2×2−1+411yescharacteristic
1082C22×C3#58511yescharacteristic
1083C2×D3—41no—
1084C2×D3—41no—
1085C2×D3—41no—
1086C2×D3—41no—
1087C2×D3—41no—
1088C2×D3—41no—
1089C2×D3—41no—
1090C3×C4—22no—
1091C3×C4—22no—
1092C3×C4—22no—
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—
1105Dic3—22no—
1106Dic3—22no—
1107Dic3—22no—
1108Dic3—22no—
1109Dic3—22no—
1110Dic3—22no—
1111Dic3—41no—
1112Dic3—41no—
1113Dic3—41no—
1114Dic3—41no—
1115Dic3—41no—
1116Dic3—41no—
1117Dic3—41no—
1118Dic3—41no—
1119Dic3—41no—
1120C23—61no—
1121C23—61no—
1122C23—61no—
1123C23—61no—
1124C23—61no—
1125C23—61no—
1126C23—61no—
1127C23C24×D311yescharacteristic
1128Q8—44no—
1129Q8—44no—
1130Q8—124no—
1131Q8—124no—
1132Q8—124no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
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—32no—
1175C2×C4—32no—
1176C2×C4—32no—
1177C2×C4—32no—
1178C2×C4—32no—
1179C2×C4—32no—
1180C2×C4—61no—
1181C2×C4—61no—
1182C2×C4—61no—
1183C2×C4—61no—
1184C2×C4—61no—
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—124no—
1220C2×C4#100412yes—
1221C2×C4#100712yes—
1222C2×C4D3×#4112yes—
1223C2×C4D3×#4112yes—
1224C2×C3#348111yescharacteristic
1225C2×C3#349511yescharacteristic
1226C2×C3#350911yescharacteristic
1227C2×C3#351811yescharacteristic
1228C2×C3#352311yescharacteristic
1229C2×C3#354111yescharacteristic
1230C2×C3#354411yescharacteristic
1231D3—81no—
1232C22—121no—
1233C22—121no—
1234C22—121no—
1235C22—121no—
1236C22—121no—
1237C22—121no—
1238C22—121no—
1239C22C2×#100411yescharacteristic
1240C22C2×#100711yescharacteristic
1241C22C2×D3×#4111yescharacteristic
1242C22C2×D3×#4111yescharacteristic
1243C22#596411yescharacteristic
1244C22D3×2−1+411yescharacteristic
1245C22D3×2−1+411yescharacteristic
1246C4—22no—
1247C4—22no—
1248C4—22no—
1249C4—22no—
1250C4—41no—
1251C4—41no—
1252C4—41no—
1253C4—41no—
1254C4—41no—
1255C4—41no—
1256C4—41no—
1257C4—41no—
1258C4—41no—
1259C4—41no—
1260C4—41no—
1261C4—62no—
1262C4—62no—
1263C4—62no—
1264C4—62no—
1265C4—62no—
1266C4—62no—
1267C4—121no—
1268C4—121no—
1269C4—121no—
1270C4—121no—
1271C4—121no—
1272C4—121no—
1273C4—121no—
1274C4—121no—
1275C4—121no—
1276C3#4486611yescharacteristic, complemented, Sylow
1277C2—241no—
1278C2#8599111yescharacteristic
1279C2#8603811yescharacteristic
1280C2#8634611yescharacteristic
1281C2#8698211yescharacteristic
1282C2#8698811yescharacteristic
1283C2#8702011yescharacteristic
1284C2#8702511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2581C2
prime radicalC23×D3C24
hypercenter#2581D3
hypocenterC3#44866
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2581

Complements

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

NH ≅ G/Ntype
1. C3×#2581C2semidirect
3. #82467C2semidirect
4. #82465C2semidirect
6. #78284C2semidirect
7. #78258C2semidirect
11. #77225C2semidirect
13. #77175C2semidirect
14. #76588C2semidirect
16. #76549C2semidirect
19. #76099C2semidirect
20. #76063C2semidirect
23. #75061C2semidirect
26. #74970C2semidirect
27. #74964C2semidirect
28. #74948C2semidirect
31. #74176C2semidirect
199. #2581D3semidirect
1276. C3#44866semidirect

Maximal subgroups

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

subgroupindex
C3×#25812
#824852
#824672
#824652
#824642
#782842
#782582
#782532
#781702
#772612
#772252
#772142
#771752
#765882
#765832
#765492
#765462
#762272
#760992
#760632
#760532
#750682
#750612
#750152
#750042
#749702
#749642
#749482
#749472
#741792
#741762
#448663