Finite Group Databasebeta

← #11043495

Subgroups — #11043495

Order 768.

1652 conjugacy classes of subgroups.

The subgroup lattice has 1386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2419C211yesmaximal, characteristic, complemented
2#82891C211yesmaximal, characteristic
3#82857C211yesmaximal, characteristic, complemented
4#82385C211yesmaximal, characteristic, complemented
5#82342C211yesmaximal, characteristic
6#78256C211yesmaximal, characteristic, complemented
7#78222C211yesmaximal, characteristic, complemented
8#77897C211yesmaximal, characteristic, complemented
9#77781C211yesmaximal, characteristic, complemented
10#77707C211yesmaximal, characteristic, complemented
11#77593C211yesmaximal, characteristic, complemented
12#77562C211yesmaximal, characteristic, complemented
13#77512C211yesmaximal, characteristic, complemented
14#75355C211yesmaximal, characteristic, complemented
15#75301C211yesmaximal, characteristic, complemented
16#75211C211yesmaximal, characteristic, complemented
17#75202C211yesmaximal, characteristic, complemented
18#74771C211yesmaximal, characteristic
19#74735C211yesmaximal, characteristic, complemented
20#74550C211yesmaximal, characteristic, complemented
21#74472C211yesmaximal, characteristic, complemented
22#74465C211yesmaximal, characteristic, complemented
23#74388C211yesmaximal, characteristic, complemented
24#74110C211yesmaximal, characteristic, complemented
25#74083C211yesmaximal, characteristic, complemented
26#74065C211yesmaximal, characteristic, complemented
27#74051C211yesmaximal, characteristic, complemented
28#73889C211yesmaximal, characteristic, complemented
29#73879C211yesmaximal, characteristic, complemented
30#73352C211yesmaximal, characteristic, complemented
31C2×#4655C211yesmaximal, characteristic, complemented
32#38393—31nomaximal, Sylow
33C2×C3×#123C2211yescharacteristic
34C2×C3×C4×D4C2211yescharacteristic
35C2×#939C2211yescharacteristic
36C2×#929C2211yescharacteristic
37C22×C4⋊Dic3C2211yescharacteristic
38C2×#924C2211yescharacteristic
39C22×Dic3⋊C4C2211yescharacteristic
40C22×C4×Dic3C2211yescharacteristic
41C2×#896C2211yescharacteristic
42C2×#67⋊C4C2211yescharacteristic
43C2×#879C2211yescharacteristic
44C2×#878C2211yescharacteristic
45C3×#400C2211yescharacteristic
46C3×#398C2211yescharacteristic
47C3×#397C2211yescharacteristic
48C3×#397C2211yescharacteristic
49C3×#387C2211yescharacteristic
50C3×#387C2211yescharacteristic
51C3×#386C2211yescharacteristic
52C3×#385C2211yescharacteristic
53C3×#385C2211yescharacteristic
54C3×#381C2211yescharacteristic
55C3×#381C2211yescharacteristic
56C3×#380C2211yescharacteristic
57C2×C3×#95C2211yescharacteristic
58#5220C2211yescharacteristic
59#5220C2211yescharacteristic
60#5220C2211yescharacteristic
61#5213C2211yescharacteristic
62#5213C2211yescharacteristic
63#5213C2211yescharacteristic
64#5211C2211yescharacteristic
65#5210C2211yescharacteristic
66#5210C2211yescharacteristic
67C4×#217C2211yescharacteristic
68C4×#217C2211yescharacteristic
69C2×C3⋊#95C2211yescharacteristic
70C2×C3⋊#95C2211yescharacteristic
71C2×C3⋊#95C2211yescharacteristic
72#4994C2211yescharacteristic
73#4992C2211yescharacteristic
74#4990C2211yescharacteristic
75#4990C2211yescharacteristic
76#4990C2211yescharacteristic
77#4990C2211yescharacteristic
78#4986C2211yescharacteristic
79#4985C2211yescharacteristic
80#4985C2211yescharacteristic
81#4985C2211yescharacteristic
82#4984C2211yescharacteristic
83#4983C2211yescharacteristic
84#4982C2211yescharacteristic
85#4979C2211yescharacteristic
86#4979C2211yescharacteristic
87#4978C2211yescharacteristic
88#4978C2211yescharacteristic
89#4977C2211yescharacteristic
90#4976C2211yescharacteristic
91#4976C2211yescharacteristic
92#4976C2211yescharacteristic
93Dic3×C4⋊C4C2211yescharacteristic
94Dic3×C4⋊C4C2211yescharacteristic
95#4973C2211yescharacteristic
96#4972C2211yescharacteristic
97#4972C2211yescharacteristic
98#4972C2211yescharacteristic
99#4961C2211yescharacteristic
100#4961C2211yescharacteristic
101#4958C2211yescharacteristic
102#4958C2211yescharacteristic
103#4957C2211yescharacteristic
104#4957C2211yescharacteristic
105#4956C2211yescharacteristic
106#4953C2211yescharacteristic
107#4952C2211yescharacteristic
108#4951C2211yescharacteristic
109#4951C2211yescharacteristic
110#4950C2211yescharacteristic
111#4949C2211yescharacteristic
112#4948C2211yescharacteristic
113#4947C2211yescharacteristic
114#4947C2211yescharacteristic
115#4945C2211yescharacteristic
116#4945C2211yescharacteristic
117#4945C2211yescharacteristic
118#4945C2211yescharacteristic
119#4945C2211yescharacteristic
120#4945C2211yescharacteristic
121#4942C2211yescharacteristic
122#4942C2211yescharacteristic
123#4942C2211yescharacteristic
124#4942C2211yescharacteristic
125Dic3×C22⋊C4C2211yescharacteristic
126Dic3×C22⋊C4C2211yescharacteristic
127Dic3×C22⋊C4C2211yescharacteristic
128C4×(C2×D3)⋊C4C2211yescharacteristic
129#4933C2211yescharacteristic
130#4933C2211yescharacteristic
131#4933C2211yescharacteristic
132#4676C2211yescharacteristic
133#4675C2211yescharacteristic
134#4675C2211yescharacteristic
135#4675C2211yescharacteristic
136#4674C2211yescharacteristic
137#4673C2211yescharacteristic
138#4670C2211yescharacteristic
139#4670C2211yescharacteristic
140#4670C2211yescharacteristic
141#4669C2211yescharacteristic
142#4669C2211yescharacteristic
143#4668C2211yescharacteristic
144#4667C2211yescharacteristic
145#4664C2211yescharacteristic
146C3⋊#401C2211yescharacteristic
147#4660C2211yescharacteristic
148#4660C2211yescharacteristic
149#4660C2211yescharacteristic
150#4660C2211yescharacteristic
151#4658C2211yescharacteristic
152#4658C2211yescharacteristic
153#4658C2211yescharacteristic
154#4657C2211yescharacteristic
155#4657C2211yescharacteristic
156#4657C2211yescharacteristic
157#4656C2211yescharacteristic
158#4655C2211yescharacteristic
159#4655C2211yescharacteristic
160#4655C2211yescharacteristic
161#4655C2211yescharacteristic
162#4655C2211yescharacteristic
163#4655C2211yescharacteristic
164#4655C2211yescharacteristic
165#4655C2211yescharacteristic
166#4654C2211yescharacteristic
167#4653C2211yescharacteristic
168#4653C2211yescharacteristic
169#4653C2211yescharacteristic
170#4653C2211yescharacteristic
171#4653C2211yescharacteristic
172#4652C2211yescharacteristic
173#4652C2211yescharacteristic
174#4651C2211yescharacteristic
175#4651C2211yescharacteristic
176#4651C2211yescharacteristic
177#4650C2211yescharacteristic
178#4650C2211yescharacteristic
179#4650C2211yescharacteristic
180#4649C2211yescharacteristic
181#4649C2211yescharacteristic
182#4648C2211yescharacteristic
183#4648C2211yescharacteristic
184#4646C2211yescharacteristic
185#4646C2211yescharacteristic
186#4646C2211yescharacteristic
187#4646C2211yescharacteristic
188#2854—31no—
189#2774—31no—
190#2767—31no—
191#2766—31no—
192#2761—31no—
193#2758—31no—
194#2757—31no—
195#2737—31no—
196#2723—31no—
197#2654—31no—
198#2650—31no—
199#2591—31no—
200#2564—31no—
201#2549—31no—
202#2532—31no—
203#2530—31no—
204#2529—31no—
205#2527—31no—
206#2510—31no—
207#2488—31no—
208#2488—31no—
209#2481—31no—
210#2419—31no—
211#2419D311yescharacteristic, complemented
212#2417—31no—
213#2364—31no—
214#2345—31no—
215#2334—31no—
216#2332—31no—
217C2×#387—31no—
218#2283—31no—
219C22×C3×D4C2311yescharacteristic
220C23×C3×C4C2311yescharacteristic
221C23×C3×C4C2311yescharacteristic
222C23×C3×C4C2311yescharacteristic
223C23×C3×C4C2311yescharacteristic
224C22×#67C2311yescharacteristic
225C22×#67C2311yescharacteristic
226C23×Dic3C2311yescharacteristic
227C23×Dic3C2311yescharacteristic
228C23×Dic3C2311yescharacteristic
229C23×Dic3C2311yescharacteristic
230C22×C4×D3C2311yescharacteristic
231C22×Dic6C2311yescharacteristic
232C22×Dic6C2311yescharacteristic
233C3×#123—42no—
234C3×C4×D4—42no—
235C2×C3×C4⋊C4C2311yescharacteristic
236C2×C3×C4⋊C4C2311yescharacteristic
237C2×C3×C4⋊C4C2311yescharacteristic
238C2×C3×C4⋊C4C2311yescharacteristic
239C2×C3×C4⋊C4C2311yescharacteristic
240C2×C3×C4⋊C4C2311yescharacteristic
241C2×C3×C4⋊C4C2311yescharacteristic
242C2×C3×C22⋊C4C2311yescharacteristic
243C2×C3×C22⋊C4C2311yescharacteristic
244C2×C3×C22⋊C4C2311yescharacteristic
245C2×C3×C22⋊C4C2311yescharacteristic
246C2×C3×C22⋊C4C2311yescharacteristic
247C2×C3×C22⋊C4C2311yescharacteristic
248C2×C3×C22⋊C4C2311yescharacteristic
249C2×C3×C22⋊C4C2311yescharacteristic
250C2×C3×C42C2311yescharacteristic
251C2×#217C2311yescharacteristic
252C2×#217C2311yescharacteristic
253C2×#217C2311yescharacteristic
254C2×#217C2311yescharacteristic
255C2×#217C2311yescharacteristic
256C2×#217C2311yescharacteristic
257C2×#217C2311yescharacteristic
258C2×#217C2311yescharacteristic
259C2×#217C2311yescharacteristic
260C2×#217C2311yescharacteristic
261#939—24no—
262#929—42no—
263C2×(C2×D3)⋊C4C2311yescharacteristic
264C2×(C2×D3)⋊C4C2311yescharacteristic
265C2×(C2×D3)⋊C4C2311yescharacteristic
266C2×(C2×D3)⋊C4C2311yescharacteristic
267C2×(C2×D3)⋊C4C2311yescharacteristic
268C2×(C2×D3)⋊C4C2311yescharacteristic
269C2×(C2×D3)⋊C4C2311yescharacteristic
270C2×(C2×D3)⋊C4C2311yescharacteristic
271C2×(C2×D3)⋊C4C2311yescharacteristic
272C2×(C2×D3)⋊C4C2311yescharacteristic
273C2×(C2×D3)⋊C4C2311yescharacteristic
274C2×(C2×D3)⋊C4C2311yescharacteristic
275C2×C4⋊Dic3—24no—
276C2×C4⋊Dic3C2311yescharacteristic
277C2×C4⋊Dic3C2311yescharacteristic
278C2×C4⋊Dic3C2311yescharacteristic
279C2×C4⋊Dic3C2311yescharacteristic
280C2×C4⋊Dic3C2311yescharacteristic
281C2×C4⋊Dic3C2311yescharacteristic
282C2×C4⋊Dic3C2311yescharacteristic
283C2×C4⋊Dic3C2311yescharacteristic
284#924—42no—
285C2×Dic3⋊C4—24no—
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×Dic3⋊C4C2311yescharacteristic
297C2×Dic3⋊C4C2311yescharacteristic
298C2×Dic3⋊C4C2311yescharacteristic
299C2×Dic3⋊C4C2311yescharacteristic
300C2×Dic3⋊C4C2311yescharacteristic
301C2×Dic3⋊C4C2311yescharacteristic
302C2×Dic3⋊C4C2311yescharacteristic
303C2×Dic3⋊C4C2311yescharacteristic
304C2×Dic3⋊C4C2311yescharacteristic
305C2×Dic3⋊C4C2311yescharacteristic
306C2×C4×Dic3—24no—
307C2×C4×Dic3C2311yescharacteristic
308C2×C4×Dic3C2311yescharacteristic
309C2×C4×Dic3C2311yescharacteristic
310C2×C4×Dic3C2311yescharacteristic
311C2×C4×Dic3C2311yescharacteristic
312C2×C4×Dic3C2311yescharacteristic
313C2×C4×Dic3C2311yescharacteristic
314C2×C4×Dic3C2311yescharacteristic
315C2×C4×Dic3C2311yescharacteristic
316C2×C4×Dic3C2311yescharacteristic
317C2×C4×Dic3C2311yescharacteristic
318C2×C4×Dic3C2311yescharacteristic
319C2×C4×Dic3C2311yescharacteristic
320#896—24no—
321#67⋊C4—42no—
322#879—24no—
323#878—42no—
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×#126—31no—
387C2×#123—31no—
388C2×#123C2×D311yescharacteristic
389C2×C22⋊Q8—31no—
390C2×C22⋊Q8—31no—
391C2×C22⋊Q8—31no—
392C2×#121—31no—
393C2×C4×D4—31no—
394C2×C4×D4C2×D311yescharacteristic
395C22×C4⋊C4—31no—
396C22×C4⋊C4—31no—
397C22×C42—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#400—31no—
407#400—31no—
408#400—31no—
409#400—31no—
410#400C2×D311yescharacteristic
411#399—31no—
412#398—31no—
413#398—31no—
414#398—31no—
415#398—31no—
416#398—31no—
417#398C2×D311yescharacteristic
418#397—31no—
419#397—31no—
420#397—31no—
421#397—31no—
422#397—31no—
423#397—31no—
424#397—31no—
425#397C2×D311yescharacteristic
426#397C2×D311yescharacteristic
427#396—31no—
428#396—31no—
429#396—31no—
430#395—31no—
431#395—31no—
432#395—31no—
433#394—31no—
434#394—31no—
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#390—31no—
444#390—31no—
445#389—31no—
446#389—31no—
447#389—31no—
448#389—31no—
449#389—31no—
450#389—31no—
451#389—31no—
452#388—31no—
453#388—31no—
454#388—31no—
455#388—31no—
456#388—31no—
457#388—31no—
458#388—31no—
459#388—31no—
460#388—31no—
461#388—31no—
462#388—31no—
463#388—31no—
464#388—31no—
465#388—31no—
466#388—31no—
467#388—31no—
468#388—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#387—31no—
490#387C2×D311yescharacteristic
491#387C2×D311yescharacteristic
492#386—31no—
493#386—31no—
494#386—31no—
495#386—31no—
496#386—31no—
497#386—31no—
498#386—31no—
499#386—31no—
500#386—31no—
501#386C2×D311yescharacteristic
502#385—31no—
503#385—31no—
504#385—31no—
505#385—31no—
506#385C2×D311yescharacteristic
507#385C2×D311yescharacteristic
508#383—31no—
509#383—31no—
510#383—31no—
511#382—31no—
512#382—31no—
513#382—31no—
514#382—31no—
515#381—31no—
516#381—31no—
517#381C2×D311yescharacteristic
518#381C2×D311yescharacteristic
519#380—31no—
520#380—31no—
521#380—31no—
522#380—31no—
523#380—31no—
524#380C2×D311yescharacteristic
525C4×C4⋊C4—31no—
526C4×C4⋊C4—31no—
527C4×C4⋊C4—31no—
528C4×C4⋊C4—31no—
529C4×C22⋊C4—31no—
530C4×C22⋊C4—31no—
531C4×C22⋊C4—31no—
532C4×C22⋊C4—31no—
533C4×C22⋊C4—31no—
534C4×C22⋊C4—31no—
535#376—31no—
536#376—31no—
537C2×#95—31no—
538C2×#95—31no—
539C2×#95—31no—
540C2×#95C2×D311yescharacteristic
541C24×C3C2411yescharacteristic
542C24×C3C2411yescharacteristic
543C23×D3C2411yescharacteristic
544C2×C3×D4—22no—
545C2×C3×D4—22no—
546C2×C3×D4—22no—
547C22×C3×C4—22no—
548C22×C3×C4—22no—
549C22×C3×C4—22no—
550C22×C3×C4—22no—
551C22×C3×C4—22no—
552C22×C3×C4—22no—
553C22×C3×C4—41no—
554C22×C3×C4—41no—
555C22×C3×C4—41no—
556C22×C3×C4—41no—
557C22×C3×C4—41no—
558C22×C3×C4—41no—
559C22×C3×C4C2411yescharacteristic
560C22×C3×C4C2411yescharacteristic
561C22×C3×C4C2411yescharacteristic
562C22×C3×C4C2411yescharacteristic
563C22×C3×C4C2411yescharacteristic
564C22×C3×C4C2411yescharacteristic
565C22×C3×C4C2411yescharacteristic
566C22×C3×C4C2411yescharacteristic
567C22×C3×C4C2411yescharacteristic
568C22×C3×C4C2411yescharacteristic
569C22×C3×C4C2411yescharacteristic
570C22×C3×C4C2411yescharacteristic
571C22×C3×C4C2411yescharacteristic
572C2×#67—22no—
573C2×#67—22no—
574C2×#67—22no—
575C2×#67—22no—
576C2×#67—41no—
577C2×#67—41no—
578C22×Dic3—22no—
579C22×Dic3—22no—
580C22×Dic3—22no—
581C22×Dic3—22no—
582C22×Dic3—22no—
583C22×Dic3—41no—
584C22×Dic3—41no—
585C22×Dic3—41no—
586C22×Dic3—41no—
587C22×Dic3—41no—
588C22×Dic3—41no—
589C22×Dic3#4114yes—
590C22×Dic3C2411yescharacteristic
591C22×Dic3C2411yescharacteristic
592C22×Dic3C2411yescharacteristic
593C22×Dic3C2411yescharacteristic
594C22×Dic3C2411yescharacteristic
595C22×Dic3C2411yescharacteristic
596C22×Dic3C2411yescharacteristic
597C22×Dic3C2411yescharacteristic
598C22×Dic3C2411yescharacteristic
599C22×Dic3C2411yescharacteristic
600C22×Dic3C2411yescharacteristic
601C22×Dic3C2411yescharacteristic
602C22×Dic3C2411yescharacteristic
603C22×Dic3C2411yescharacteristic
604C22×Dic3C2411yescharacteristic
605C2×C4×D3—22no—
606C2×C4×D3—41no—
607C2×C4×D3—41no—
608C2×Dic6—22no—
609C2×Dic6—41no—
610C2×Dic6—41no—
611C2×Dic6—41no—
612C2×Dic6—41no—
613C2×Dic6—41no—
614C3×C4⋊C4—22no—
615C3×C4⋊C4—41no—
616C3×C4⋊C4—41no—
617C3×C4⋊C4—41no—
618C3×C4⋊C4—41no—
619C3×C4⋊C4—41no—
620C3×C4⋊C4—41no—
621C3×C22⋊C4—22no—
622C3×C22⋊C4—22no—
623C3×C22⋊C4—22no—
624C3×C22⋊C4—22no—
625C3×C22⋊C4—41no—
626C3×C22⋊C4—41no—
627C3×C22⋊C4—41no—
628C3×C22⋊C4—41no—
629C3×C42—41no—
630#217—22no—
631#217—22no—
632#217—22no—
633#217—22no—
634#217—22no—
635#217—22no—
636#217—41no—
637#217—41no—
638#217—41no—
639#217—41no—
640(C2×D3)⋊C4—22no—
641(C2×D3)⋊C4—22no—
642(C2×D3)⋊C4—22no—
643(C2×D3)⋊C4—41no—
644(C2×D3)⋊C4—41no—
645(C2×D3)⋊C4—41no—
646(C2×D3)⋊C4—41no—
647(C2×D3)⋊C4—41no—
648(C2×D3)⋊C4—41no—
649(C2×D3)⋊C4—41no—
650(C2×D3)⋊C4—41no—
651(C2×D3)⋊C4—41no—
652C4⋊Dic3—22no—
653C4⋊Dic3—22no—
654C4⋊Dic3—22no—
655C4⋊Dic3—22no—
656C4⋊Dic3—22no—
657C4⋊Dic3—41no—
658C4⋊Dic3—41no—
659C4⋊Dic3—41no—
660Dic3⋊C4—22no—
661Dic3⋊C4—22no—
662Dic3⋊C4—22no—
663Dic3⋊C4—22no—
664Dic3⋊C4—22no—
665Dic3⋊C4—22no—
666Dic3⋊C4—41no—
667Dic3⋊C4—41no—
668Dic3⋊C4—41no—
669Dic3⋊C4—41no—
670Dic3⋊C4—41no—
671Dic3⋊C4—41no—
672Dic3⋊C4—41no—
673Dic3⋊C4—41no—
674Dic3⋊C4—41no—
675Dic3⋊C4—41no—
676Dic3⋊C4—41no—
677Dic3⋊C4—41no—
678Dic3⋊C4—41no—
679Dic3⋊C4#4114yes—
680C4×Dic3—22no—
681C4×Dic3—22no—
682C4×Dic3—22no—
683C4×Dic3—22no—
684C4×Dic3—22no—
685C4×Dic3—41no—
686C4×Dic3—41no—
687C4×Dic3—41no—
688C4×Dic3—41no—
689C4×Dic3—41no—
690C4×Dic3—41no—
691C4×Dic3—41no—
692C4×Dic3—41no—
693C22×Q8—31no—
694C22×Q8—31no—
695C22×D4—31no—
696C22×D4—31no—
697C22×D4C22×D311yescharacteristic
698C23×C4—31no—
699C23×C4—31no—
700C23×C4—31no—
701C23×C4—31no—
702C23×C4—31no—
703C23×C4C22×D311yescharacteristic
704C23×C4C22×D311yescharacteristic
705C23×C4C22×D311yescharacteristic
706C23×C4C22×D311yescharacteristic
707#126—64no—
708#123—42no—
709#123—122no—
710C22⋊Q8—64no—
711C22⋊Q8—122no—
712C22⋊Q8—122no—
713#121—64no—
714C4×D4—42no—
715C4×D4—122no—
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⋊C4—31no—
727C2×C4⋊C4—31no—
728C2×C4⋊C4—31no—
729C2×C4⋊C4—31no—
730C2×C4⋊C4—31no—
731C2×C4⋊C4—31no—
732C2×C4⋊C4—31no—
733C2×C4⋊C4—31no—
734C2×C4⋊C4—31no—
735C2×C4⋊C4—31no—
736C2×C4⋊C4—31no—
737C2×C4⋊C4—31no—
738C2×C4⋊C4—31no—
739C2×C4⋊C4—31no—
740C2×C4⋊C4—31no—
741C2×C4⋊C4—31no—
742C2×C4⋊C4—31no—
743C2×C4⋊C4—31no—
744C2×C4⋊C4—64no—
745C2×C4⋊C4—64no—
746C2×C4⋊C4C22×D311yescharacteristic
747C2×C4⋊C4C22×D311yescharacteristic
748C2×C4⋊C4C22×D311yescharacteristic
749C2×C4⋊C4C22×D311yescharacteristic
750C2×C4⋊C4C22×D311yescharacteristic
751C2×C4⋊C4C22×D311yescharacteristic
752C2×C4⋊C4C22×D311yescharacteristic
753C2×C22⋊C4—31no—
754C2×C22⋊C4—31no—
755C2×C22⋊C4—31no—
756C2×C22⋊C4—31no—
757C2×C22⋊C4—31no—
758C2×C22⋊C4—31no—
759C2×C22⋊C4—31no—
760C2×C22⋊C4—31no—
761C2×C22⋊C4—31no—
762C2×C22⋊C4—31no—
763C2×C22⋊C4—31no—
764C2×C22⋊C4—31no—
765C2×C22⋊C4—31no—
766C2×C22⋊C4—31no—
767C2×C22⋊C4—31no—
768C2×C22⋊C4—31no—
769C2×C22⋊C4—31no—
770C2×C22⋊C4—31no—
771C2×C22⋊C4—31no—
772C2×C22⋊C4—31no—
773C2×C22⋊C4—31no—
774C2×C22⋊C4—31no—
775C2×C22⋊C4C22×D311yescharacteristic
776C2×C22⋊C4C22×D311yescharacteristic
777C2×C22⋊C4C22×D311yescharacteristic
778C2×C22⋊C4C22×D311yescharacteristic
779C2×C22⋊C4C22×D311yescharacteristic
780C2×C22⋊C4C22×D311yescharacteristic
781C2×C22⋊C4C22×D311yescharacteristic
782C2×C22⋊C4C22×D311yescharacteristic
783C2×C42—31no—
784C2×C42—31no—
785C2×C42—31no—
786C2×C42—31no—
787C2×C42—31no—
788C2×C42—31no—
789C2×C42—31no—
790C2×C42—31no—
791C2×C42—31no—
792C2×C42—31no—
793C2×C42—31no—
794C2×C42—31no—
795C2×C42—31no—
796C2×C42—64no—
797C2×C42C22×D311yescharacteristic
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#95—31no—
825#95—31no—
826#95—31no—
827#95—31no—
828#95—31no—
829#95—31no—
830#95—31no—
831#95—31no—
832#95—31no—
833#95—31no—
834#95—31no—
835#95—31no—
836#95—31no—
837#95—31no—
838#95—31no—
839#95—31no—
840#95—31no—
841#95—31no—
842#95—31no—
843#95—31no—
844#95—31no—
845#95—31no—
846#95C22×D311yescharacteristic
847#95C22×D311yescharacteristic
848#95C22×D311yescharacteristic
849#95C22×D311yescharacteristic
850#95C22×D311yescharacteristic
851#95C22×D311yescharacteristic
852#95C22×D311yescharacteristic
853#95C22×D311yescharacteristic
854#95C22×D311yescharacteristic
855#95C22×D311yescharacteristic
856#95C22×D311yescharacteristic
857#95C22×D311yescharacteristic
858#95C22×D311yescharacteristic
859#95C22×D311yescharacteristic
860C23×C3—21no—
861C23×C3—21no—
862C23×C3—21no—
863C23×C3—21no—
864C23×C3—21no—
865C23×C3—21no—
866C23×C3—21no—
867C23×C3—21no—
868C23×C3—21no—
869C23×C3—21no—
870C23×C3—21no—
871C23×C3C2×#4112yes—
872C23×C3H(5,𝔽2)12yes—
873C23×C32−1+412yes—
874C23×C3C2511yescharacteristic
875C22×D3—21no—
876C22×D3—21no—
877C22×D3—21no—
878C22×D3—21no—
879C22×D3—21no—
880C22×D3—21no—
881C22×D3—21no—
882C3×D4—44no—
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×C4—21no—
892C2×C3×C4—21no—
893C2×C3×C4—21no—
894C2×C3×C4—21no—
895C2×C3×C4—21no—
896C2×C3×C4—21no—
897C2×C3×C4—21no—
898C2×C3×C4—21no—
899C2×C3×C4—21no—
900C2×C3×C4—21no—
901C2×C3×C4—21no—
902C2×C3×C4—21no—
903C2×C3×C4—21no—
904C2×C3×C4—21no—
905C2×C3×C4—21no—
906C2×C3×C4—21no—
907C2×C3×C4—21no—
908C2×C3×C4—21no—
909C2×C3×C4—21no—
910C2×C3×C4—21no—
911C2×C3×C4—21no—
912C2×C3×C4—21no—
913C2×C3×C4—21no—
914C2×C3×C4—21no—
915C2×C3×C4—21no—
916C2×C3×C4—21no—
917C2×C3×C4—21no—
918C2×C3×C4—21no—
919C2×C3×C4—21no—
920C2×C3×C4—21no—
921C2×C3×C4—44no—
922C2×C3×C4—44no—
923C2×C3×C4—82no—
924C2×C3×C4—82no—
925C2×C3×C4C2×#4112yes—
926#67—44no—
927#67—82no—
928C2×Dic3—21no—
929C2×Dic3—21no—
930C2×Dic3—21no—
931C2×Dic3—21no—
932C2×Dic3—21no—
933C2×Dic3—21no—
934C2×Dic3—21no—
935C2×Dic3—21no—
936C2×Dic3—21no—
937C2×Dic3—21no—
938C2×Dic3—21no—
939C2×Dic3—21no—
940C2×Dic3—21no—
941C2×Dic3—21no—
942C2×Dic3—21no—
943C2×Dic3—21no—
944C2×Dic3—21no—
945C2×Dic3—21no—
946C2×Dic3—21no—
947C2×Dic3—21no—
948C2×Dic3—21no—
949C2×Dic3—21no—
950C2×Dic3—21no—
951C2×Dic3—21no—
952C2×Dic3—21no—
953C2×Dic3—21no—
954C2×Dic3—21no—
955C2×Dic3—21no—
956C2×Dic3—21no—
957C2×Dic3—21no—
958C2×Dic3—21no—
959C2×Dic3—21no—
960C2×Dic3—21no—
961C2×Dic3—21no—
962C2×Dic3—21no—
963C2×Dic3—21no—
964C2×Dic3—21no—
965C2×Dic3—21no—
966C2×Dic3—21no—
967C2×Dic3—21no—
968C2×Dic3—21no—
969C2×Dic3—44no—
970C2×Dic3—44no—
971C2×Dic3—44no—
972C2×Dic3—82no—
973C2×Dic3C2×#4112yes—
974C2×Dic3C2×#4112yes—
975C2×Dic3C2×#4112yes—
976C2×Dic3C2×#4112yes—
977C4×D3—82no—
978Dic6—82no—
979Dic6—82no—
980C24—31no—
981C24C23×D311yescharacteristic
982C24C23×D311yescharacteristic
983C2×Q8—62no—
984C2×Q8—121no—
985C2×Q8—121no—
986C2×Q8—121no—
987C2×Q8—121no—
988C2×Q8—121no—
989C2×D4—22no—
990C2×D4—22no—
991C2×D4—22no—
992C2×D4—62no—
993C2×D4—62no—
994C2×D4—62no—
995C2×D4—62no—
996C2×D4—121no—
997C2×D4—121no—
998C22×C4—22no—
999C22×C4—22no—
1000C22×C4—22no—
1001C22×C4—22no—
1002C22×C4—22no—
1003C22×C4—22no—
1004C22×C4—31no—
1005C22×C4—31no—
1006C22×C4—31no—
1007C22×C4—31no—
1008C22×C4—34no—
1009C22×C4—31no—
1010C22×C4—31no—
1011C22×C4—31no—
1012C22×C4—31no—
1013C22×C4—31no—
1014C22×C4—31no—
1015C22×C4—31no—
1016C22×C4—31no—
1017C22×C4—31no—
1018C22×C4—31no—
1019C22×C4—31no—
1020C22×C4—41no—
1021C22×C4—41no—
1022C22×C4—41no—
1023C22×C4—41no—
1024C22×C4—41no—
1025C22×C4—41no—
1026C22×C4—62no—
1027C22×C4—62no—
1028C22×C4—62no—
1029C22×C4—62no—
1030C22×C4—62no—
1031C22×C4—62no—
1032C22×C4—121no—
1033C22×C4—121no—
1034C22×C4—121no—
1035C22×C4—121no—
1036C22×C4—121no—
1037C22×C4—121no—
1038C22×C4—121no—
1039C22×C4—121no—
1040C22×C4C23×D311yescharacteristic
1041C22×C4C23×D311yescharacteristic
1042C22×C4C23×D311yescharacteristic
1043C22×C4C23×D311yescharacteristic
1044C22×C4C23×D311yescharacteristic
1045C22×C4C23×D311yescharacteristic
1046C22×C4C23×D311yescharacteristic
1047C22×C4C23×D311yescharacteristic
1048C22×C4C23×D311yescharacteristic
1049C22×C4C23×D311yescharacteristic
1050C22×C4C23×D311yescharacteristic
1051C22×C4C23×D311yescharacteristic
1052C22×C4C23×D311yescharacteristic
1053C4⋊C4—22no—
1054C4⋊C4—34no—
1055C4⋊C4—41no—
1056C4⋊C4—41no—
1057C4⋊C4—41no—
1058C4⋊C4—41no—
1059C4⋊C4—41no—
1060C4⋊C4—41no—
1061C4⋊C4—62no—
1062C4⋊C4—62no—
1063C4⋊C4—62no—
1064C4⋊C4—62no—
1065C4⋊C4—62no—
1066C4⋊C4—62no—
1067C4⋊C4—62no—
1068C4⋊C4—62no—
1069C4⋊C4—62no—
1070C4⋊C4—62no—
1071C4⋊C4—62no—
1072C4⋊C4—121no—
1073C4⋊C4—121no—
1074C4⋊C4—121no—
1075C4⋊C4—121no—
1076C4⋊C4—121no—
1077C4⋊C4—121no—
1078C4⋊C4—121no—
1079C4⋊C4—121no—
1080C4⋊C4—121no—
1081C4⋊C4—121no—
1082C4⋊C4—121no—
1083C4⋊C4—121no—
1084C4⋊C4—121no—
1085C4⋊C4—121no—
1086C4⋊C4—121no—
1087C4⋊C4—121no—
1088C22⋊C4—22no—
1089C22⋊C4—22no—
1090C22⋊C4—22no—
1091C22⋊C4—22no—
1092C22⋊C4—41no—
1093C22⋊C4—41no—
1094C22⋊C4—41no—
1095C22⋊C4—41no—
1096C22⋊C4—62no—
1097C22⋊C4—62no—
1098C22⋊C4—62no—
1099C22⋊C4—62no—
1100C22⋊C4—62no—
1101C22⋊C4—62no—
1102C22⋊C4—62no—
1103C22⋊C4—62no—
1104C22⋊C4—62no—
1105C22⋊C4—121no—
1106C22⋊C4—121no—
1107C22⋊C4—121no—
1108C22⋊C4—121no—
1109C22⋊C4—121no—
1110C22⋊C4—121no—
1111C22⋊C4—121no—
1112C22⋊C4—121no—
1113C22⋊C4—121no—
1114C22⋊C4—121no—
1115C22⋊C4—121no—
1116C22⋊C4—121no—
1117C22⋊C4—121no—
1118C42—41no—
1119C42—62no—
1120C42—62no—
1121C42—62no—
1122C42—62no—
1123C42—62no—
1124C42—121no—
1125C42—121no—
1126C42—121no—
1127C42—121no—
1128C42—121no—
1129C42—121no—
1130C42—121no—
1131C42—121no—
1132C22×C3—22no—
1133C22×C3—22no—
1134C22×C3—22no—
1135C22×C3—22no—
1136C22×C3—22no—
1137C22×C3—22no—
1138C22×C3—41no—
1139C22×C3—41no—
1140C22×C3—41no—
1141C22×C3—41no—
1142C22×C3—41no—
1143C22×C3—41no—
1144C22×C3—41no—
1145C22×C3#54214yes—
1146C22×C3C22×#4111yescharacteristic
1147C22×C3C22×#4111yescharacteristic
1148C22×C3C2×H(5,𝔽2)11yescharacteristic
1149C22×C3C2×2−1+411yescharacteristic
1150C22×C3#58511yescharacteristic
1151C22×C3#58511yescharacteristic
1152C22×C3#58511yescharacteristic
1153C2×D3—41no—
1154C2×D3—41no—
1155C2×D3—41no—
1156C2×D3—41no—
1157C2×D3—41no—
1158C2×D3—41no—
1159C2×D3—41no—
1160C3×C4—22no—
1161C3×C4—41no—
1162C3×C4—41no—
1163C3×C4—41no—
1164C3×C4—41no—
1165C3×C4—41no—
1166C3×C4—41no—
1167C3×C4—41no—
1168C3×C4—41no—
1169C3×C4—41no—
1170C3×C4—41no—
1171C3×C4—41no—
1172C3×C4—41no—
1173Dic3—22no—
1174Dic3—22no—
1175Dic3—22no—
1176Dic3—22no—
1177Dic3—41no—
1178Dic3—41no—
1179Dic3—41no—
1180Dic3—41no—
1181Dic3—41no—
1182Dic3—41no—
1183Dic3—41no—
1184Dic3—41no—
1185Dic3—41no—
1186Dic3—41no—
1187Dic3—41no—
1188C23—21no—
1189C23—21no—
1190C23—21no—
1191C23—21no—
1192C23—21no—
1193C23—21no—
1194C23—21no—
1195C23—21no—
1196C23—21no—
1197C23—21no—
1198C23—21no—
1199C23—61no—
1200C23—61no—
1201C23—61no—
1202C23—61no—
1203C23—61no—
1204C23—61no—
1205C23—61no—
1206C23#100412yes—
1207C23D3×#4112yes—
1208C23#101012yes—
1209C23C24×D311yescharacteristic
1210Q8—242no—
1211Q8—242no—
1212D4—44no—
1213D4—124no—
1214D4—242no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—32no—
1254C2×C4—32no—
1255C2×C4—32no—
1256C2×C4—32no—
1257C2×C4—44no—
1258C2×C4—44no—
1259C2×C4—61no—
1260C2×C4—61no—
1261C2×C4—61no—
1262C2×C4—61no—
1263C2×C4—61no—
1264C2×C4—61no—
1265C2×C4—61no—
1266C2×C4—61no—
1267C2×C4—61no—
1268C2×C4—61no—
1269C2×C4—61no—
1270C2×C4—61no—
1271C2×C4—61no—
1272C2×C4—61no—
1273C2×C4—61no—
1274C2×C4—61no—
1275C2×C4—61no—
1276C2×C4—61no—
1277C2×C4—61no—
1278C2×C4—61no—
1279C2×C4—61no—
1280C2×C4—61no—
1281C2×C4—61no—
1282C2×C4—61no—
1283C2×C4—61no—
1284C2×C4—61no—
1285C2×C4—61no—
1286C2×C4—61no—
1287C2×C4—61no—
1288C2×C4—61no—
1289C2×C4—61no—
1290C2×C4—61no—
1291C2×C4—61no—
1292C2×C4—61no—
1293C2×C4—61no—
1294C2×C4—61no—
1295C2×C4—61no—
1296C2×C4—61no—
1297C2×C4—61no—
1298C2×C4—61no—
1299C2×C4—61no—
1300C2×C4—82no—
1301C2×C4—82no—
1302C2×C4—124no—
1303C2×C4—124no—
1304C2×C4—124no—
1305C2×C4—242no—
1306C2×C4—242no—
1307C2×C4D3×#4112yes—
1308C2×C3—24no—
1309C2×C3—81no—
1310C2×C3C2×#54211yescharacteristic
1311C2×C3#347511yescharacteristic
1312C2×C3#349111yescharacteristic
1313C2×C3#349411yescharacteristic
1314C2×C3#351611yescharacteristic
1315C2×C3#355311yescharacteristic
1316C2×C3#356011yescharacteristic
1317D3—81no—
1318C22—22no—
1319C22—22no—
1320C22—22no—
1321C22—22no—
1322C22—22no—
1323C22—22no—
1324C22—41no—
1325C22—41no—
1326C22—41no—
1327C22—41no—
1328C22—41no—
1329C22—41no—
1330C22—41no—
1331C22—121no—
1332C22—121no—
1333C22—121no—
1334C22—121no—
1335C22—121no—
1336C22—121no—
1337C22—121no—
1338C22#566214yes—
1339C22C2×#100411yescharacteristic
1340C22C2×D3×#4111yescharacteristic
1341C22C2×D3×#4111yescharacteristic
1342C22C2×#101011yescharacteristic
1343C22#596411yescharacteristic
1344C22#596611yescharacteristic
1345C22#596811yescharacteristic
1346C4—22no—
1347C4—41no—
1348C4—41no—
1349C4—41no—
1350C4—41no—
1351C4—41no—
1352C4—41no—
1353C4—41no—
1354C4—41no—
1355C4—41no—
1356C4—41no—
1357C4—41no—
1358C4—41no—
1359C4—62no—
1360C4—62no—
1361C4—62no—
1362C4—62no—
1363C4—121no—
1364C4—121no—
1365C4—121no—
1366C4—121no—
1367C4—121no—
1368C4—121no—
1369C4—121no—
1370C4—121no—
1371C4—121no—
1372C4—121no—
1373C4—121no—
1374C3#3839311yescharacteristic, complemented, Sylow
1375C2—24no—
1376C2—81no—
1377C2—241no—
1378C2C2×#566211yescharacteristic
1379C2#8612511yescharacteristic
1380C2#8643911yescharacteristic
1381C2#8665611yescharacteristic
1382C2#8667811yescharacteristic
1383C2#8679011yescharacteristic
1384C2#8685911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2419C2
prime radicalC2×#939C22
hypercenter#2419D3
hypocenterC3#38393
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2419

Complements

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

NH ≅ G/Ntype
1. C3×#2419C2semidirect
3. #82857C2semidirect
4. #82385C2semidirect
6. #78256C2semidirect
7. #78222C2semidirect
8. #77897C2semidirect
9. #77781C2semidirect
10. #77707C2semidirect
11. #77593C2semidirect
12. #77562C2semidirect
13. #77512C2semidirect
14. #75355C2semidirect
15. #75301C2semidirect
16. #75211C2semidirect
17. #75202C2semidirect
19. #74735C2semidirect
20. #74550C2semidirect
21. #74472C2semidirect
22. #74465C2semidirect
23. #74388C2semidirect
24. #74110C2semidirect
25. #74083C2semidirect
26. #74065C2semidirect
27. #74051C2semidirect
28. #73889C2semidirect
29. #73879C2semidirect
30. #73352C2semidirect
31. C2×#4655C2semidirect
211. #2419D3semidirect
1374. C3#38393semidirect

Maximal subgroups

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

subgroupindex
C3×#24192
#828912
#828572
#823852
#823422
#782562
#782222
#778972
#777812
#777072
#775932
#775622
#775122
#753552
#753012
#752112
#752022
#747712
#747352
#745502
#744722
#744652
#743882
#741102
#740832
#740652
#740512
#738892
#738792
#733522
C2×#46552
#383933