Finite Group Databasebeta

← #11225903

Subgroups — #11225903

Order 768.

1644 conjugacy classes of subgroups.

The subgroup lattice has 1332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2791C211yesmaximal, characteristic, complemented
2#78298C211yesmaximal, characteristic, complemented
3#78130C211yesmaximal, characteristic
4#77985C211yesmaximal, characteristic
5#77906C211yesmaximal, characteristic
6#77877C211yesmaximal, characteristic, complemented
7#77871C211yesmaximal, characteristic
8#77804C211yesmaximal, characteristic
9#77785C211yesmaximal, characteristic, complemented
10#77768C211yesmaximal, characteristic, complemented
11#77748C211yesmaximal, characteristic, complemented
12#77748C211yesmaximal, characteristic, complemented
13#77745C211yesmaximal, characteristic
14#76227C211yesmaximal, characteristic
15#76071C211yesmaximal, characteristic, complemented
16#75981C211yesmaximal, characteristic, complemented
17#75971C211yesmaximal, characteristic
18#75248C211yesmaximal, characteristic
19#75186C211yesmaximal, characteristic, complemented
20#75107C211yesmaximal, characteristic
21#75090C211yesmaximal, characteristic, complemented
22#75043C211yesmaximal, characteristic, complemented
23#75038C211yesmaximal, characteristic, complemented
24#75029C211yesmaximal, characteristic, complemented
25#74999C211yesmaximal, characteristic
26#74983C211yesmaximal, characteristic
27#74967C211yesmaximal, characteristic, complemented
28#74966C211yesmaximal, characteristic
29#74965C211yesmaximal, characteristic
30#74359C211yesmaximal, characteristic
31#74340C211yesmaximal, characteristic, complemented
32#44997—31nomaximal, Sylow
33C2×#897C2211yescharacteristic
34C2×#896C2211yescharacteristic
35C2×#896C2211yescharacteristic
36C2×#892C2211yescharacteristic
37C2×D3×C4⋊C4C2211yescharacteristic
38C2×#888C2211yescharacteristic
39C2×#888C2211yescharacteristic
40C2×#888C2211yescharacteristic
41C2×#888C2211yescharacteristic
42C2×#887C2211yescharacteristic
43C2×#887C2211yescharacteristic
44C2×#887C2211yescharacteristic
45C2×#887C2211yescharacteristic
46C2×#872C2211yescharacteristic
47C2×C4×Dic6C2211yescharacteristic
48C2×C4×Dic6C2211yescharacteristic
49C3×#400C2211yescharacteristic
50C3×#398C2211yescharacteristic
51C3×#398C2211yescharacteristic
52C3×#398C2211yescharacteristic
53C3×#398C2211yescharacteristic
54C3×#398C2211yescharacteristic
55C3×#389C2211yescharacteristic
56C3×#389C2211yescharacteristic
57C3×#387C2211yescharacteristic
58C3×#387C2211yescharacteristic
59C3×#387C2211yescharacteristic
60C3×#387C2211yescharacteristic
61C3×#387C2211yescharacteristic
62C3×#387C2211yescharacteristic
63C3×#384C2211yescharacteristic
64#4994C2211yescharacteristic
65#4994C2211yescharacteristic
66#4993C2211yescharacteristic
67#4990C2211yescharacteristic
68#4990C2211yescharacteristic
69#4990C2211yescharacteristic
70#4989C2211yescharacteristic
71#4989C2211yescharacteristic
72#4989C2211yescharacteristic
73#4989C2211yescharacteristic
74#4989C2211yescharacteristic
75#4985C2211yescharacteristic
76#4984C2211yescharacteristic
77#4984C2211yescharacteristic
78#4983C2211yescharacteristic
79#4983C2211yescharacteristic
80#4981C2211yescharacteristic
81#4980C2211yescharacteristic
82#4980C2211yescharacteristic
83#4979C2211yescharacteristic
84#4979C2211yescharacteristic
85#4979C2211yescharacteristic
86#4979C2211yescharacteristic
87#4979C2211yescharacteristic
88#4979C2211yescharacteristic
89#4979C2211yescharacteristic
90#4978C2211yescharacteristic
91#4978C2211yescharacteristic
92#4978C2211yescharacteristic
93#4978C2211yescharacteristic
94#4977C2211yescharacteristic
95#4976C2211yescharacteristic
96#4976C2211yescharacteristic
97#4976C2211yescharacteristic
98#4976C2211yescharacteristic
99#4976C2211yescharacteristic
100#4976C2211yescharacteristic
101#4976C2211yescharacteristic
102#4976C2211yescharacteristic
103#4976C2211yescharacteristic
104#4976C2211yescharacteristic
105#4976C2211yescharacteristic
106#4976C2211yescharacteristic
107#4975C2211yescharacteristic
108#4975C2211yescharacteristic
109#4975C2211yescharacteristic
110#4975C2211yescharacteristic
111Dic3×C4⋊C4C2211yescharacteristic
112#4973C2211yescharacteristic
113#4973C2211yescharacteristic
114#4972C2211yescharacteristic
115#4940C2211yescharacteristic
116C4×(C2×D3)⋊C4C2211yescharacteristic
117#4936C2211yescharacteristic
118#4933C2211yescharacteristic
119C4×Dic3⋊C4C2211yescharacteristic
120C4×Dic3⋊C4C2211yescharacteristic
121C4×Dic3⋊C4C2211yescharacteristic
122#4929C2211yescharacteristic
123#4928C2211yescharacteristic
124#4676C2211yescharacteristic
125#4676C2211yescharacteristic
126#4673C2211yescharacteristic
127#4673C2211yescharacteristic
128#4673C2211yescharacteristic
129#4670C2211yescharacteristic
130#4669C2211yescharacteristic
131#4669C2211yescharacteristic
132#4669C2211yescharacteristic
133#4668C2211yescharacteristic
134#4668C2211yescharacteristic
135#4668C2211yescharacteristic
136#4667C2211yescharacteristic
137#4666C2211yescharacteristic
138#4666C2211yescharacteristic
139#4666C2211yescharacteristic
140#4661C2211yescharacteristic
141#4661C2211yescharacteristic
142#4660C2211yescharacteristic
143#4660C2211yescharacteristic
144#4660C2211yescharacteristic
145#4658C2211yescharacteristic
146#4658C2211yescharacteristic
147#4657C2211yescharacteristic
148#4657C2211yescharacteristic
149#4657C2211yescharacteristic
150#4657C2211yescharacteristic
151#4657C2211yescharacteristic
152#4657C2211yescharacteristic
153#4656C2211yescharacteristic
154#4656C2211yescharacteristic
155#4655C2211yescharacteristic
156#4655C2211yescharacteristic
157#4655C2211yescharacteristic
158#4655C2211yescharacteristic
159#4655C2211yescharacteristic
160#4655C2211yescharacteristic
161#4654C2211yescharacteristic
162#4653C2211yescharacteristic
163#4653C2211yescharacteristic
164#4652C2211yescharacteristic
165#4652C2211yescharacteristic
166#4650C2211yescharacteristic
167#4649C2211yescharacteristic
168#4649C2211yescharacteristic
169#4649C2211yescharacteristic
170#4649C2211yescharacteristic
171#4649C2211yescharacteristic
172#4649C2211yescharacteristic
173#4647C2211yescharacteristic
174#4647C2211yescharacteristic
175#4647C2211yescharacteristic
176#4647C2211yescharacteristic
177#4647C2211yescharacteristic
178#4646C2211yescharacteristic
179#4646C2211yescharacteristic
180#4646C2211yescharacteristic
181#4646C2211yescharacteristic
182#4646C2211yescharacteristic
183#4646C2211yescharacteristic
184#4646C2211yescharacteristic
185#4646C2211yescharacteristic
186#4646C2211yescharacteristic
187#4646C2211yescharacteristic
188#2791—31no—
189#2791D311yescharacteristic, complemented
190#2790—31no—
191#2790—31no—
192#2755—31no—
193#2755—31no—
194#2729—31no—
195#2729—31no—
196#2589—31no—
197#2589—31no—
198#2581—31no—
199#2567—31no—
200#2567—31no—
201#2546—31no—
202#2520—31no—
203#2520—31no—
204#2509—31no—
205#2507—31no—
206#2465—31no—
207#2465—31no—
208#2451—31no—
209#2451—31no—
210#2440—31no—
211#2439—31no—
212#2396—31no—
213#2365—31no—
214#2362—31no—
215#2360—31no—
216Q8×C4⋊C4—31no—
217#2323—31no—
218#2317—31no—
219C22×C4×D3C2311yescharacteristic
220C22×C4×D3C2311yescharacteristic
221C22×C4×D3C2311yescharacteristic
222C22×Dic6C2311yescharacteristic
223C22×Dic6C2311yescharacteristic
224C22×Dic6C2311yescharacteristic
225C22×Dic6C2311yescharacteristic
226C22×Dic6C2311yescharacteristic
227C22×Dic6C2311yescharacteristic
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×C4⋊C4C2311yescharacteristic
240C2×C3×C4⋊C4C2311yescharacteristic
241C2×C3×C4⋊C4C2311yescharacteristic
242C2×C3×C4⋊C4C2311yescharacteristic
243C2×C3×C4⋊C4C2311yescharacteristic
244C2×C3×C42C2311yescharacteristic
245C2×C3×C42C2311yescharacteristic
246C2×C3×C42C2311yescharacteristic
247C2×(C2×D3)⋊C4C2311yescharacteristic
248C2×(C2×D3)⋊C4C2311yescharacteristic
249C2×(C2×D3)⋊C4C2311yescharacteristic
250C2×(C2×D3)⋊C4C2311yescharacteristic
251C2×(C2×D3)⋊C4C2311yescharacteristic
252C2×(C2×D3)⋊C4C2311yescharacteristic
253C2×(C2×D3)⋊C4C2311yescharacteristic
254C2×(C2×D3)⋊C4C2311yescharacteristic
255C2×(C2×D3)⋊C4C2311yescharacteristic
256C2×(C2×D3)⋊C4C2311yescharacteristic
257C2×(C2×D3)⋊C4C2311yescharacteristic
258C2×(C2×D3)⋊C4C2311yescharacteristic
259C2×C4⋊Dic3C2311yescharacteristic
260C2×C4⋊Dic3C2311yescharacteristic
261C2×C4⋊Dic3C2311yescharacteristic
262C2×C4⋊Dic3C2311yescharacteristic
263C2×C4⋊Dic3C2311yescharacteristic
264C2×C4⋊Dic3C2311yescharacteristic
265C2×C4⋊Dic3C2311yescharacteristic
266C2×C4⋊Dic3C2311yescharacteristic
267C2×C4⋊Dic3C2311yescharacteristic
268C2×C4⋊Dic3C2311yescharacteristic
269C2×Dic3⋊C4C2311yescharacteristic
270C2×Dic3⋊C4C2311yescharacteristic
271C2×Dic3⋊C4C2311yescharacteristic
272C2×Dic3⋊C4C2311yescharacteristic
273C2×Dic3⋊C4C2311yescharacteristic
274C2×Dic3⋊C4C2311yescharacteristic
275C2×Dic3⋊C4C2311yescharacteristic
276C2×Dic3⋊C4C2311yescharacteristic
277C2×Dic3⋊C4C2311yescharacteristic
278C2×Dic3⋊C4C2311yescharacteristic
279C2×Dic3⋊C4C2311yescharacteristic
280C2×Dic3⋊C4C2311yescharacteristic
281C2×Dic3⋊C4C2311yescharacteristic
282C2×Dic3⋊C4C2311yescharacteristic
283C2×Dic3⋊C4C2311yescharacteristic
284C2×Dic3⋊C4C2311yescharacteristic
285C2×Dic3⋊C4C2311yescharacteristic
286C2×Dic3⋊C4C2311yescharacteristic
287C2×Dic3⋊C4C2311yescharacteristic
288C2×Dic3⋊C4C2311yescharacteristic
289C2×Dic3⋊C4C2311yescharacteristic
290C2×Dic3⋊C4C2311yescharacteristic
291C2×Dic3⋊C4C2311yescharacteristic
292C2×Dic3⋊C4C2311yescharacteristic
293C2×Dic3⋊C4C2311yescharacteristic
294C2×Dic3⋊C4C2311yescharacteristic
295C2×Dic3⋊C4C2311yescharacteristic
296C2×Dic3⋊C4C2311yescharacteristic
297C2×Dic3⋊C4C2311yescharacteristic
298C2×Dic3⋊C4C2311yescharacteristic
299C2×Dic3⋊C4C2311yescharacteristic
300C2×Dic3⋊C4C2311yescharacteristic
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
312C2×C4×Dic3C2311yescharacteristic
313C2×C4×Dic3C2311yescharacteristic
314C2×C4×Dic3C2311yescharacteristic
315C2×C4×Dic3C2311yescharacteristic
316C2×C4×Dic3C2311yescharacteristic
317C2×C4×Dic3C2311yescharacteristic
318#897—42no—
319#896—42no—
320#896Q818yescomplemented
321#892—42no—
322D3×C4⋊C4—42no—
323#888—24no—
324#888—42no—
325#888—42no—
326#888—42no—
327#887—24no—
328#887—42no—
329#887—42no—
330#887—42no—
331#872—24no—
332C4×Dic6—42no—
333C4×Dic6—42no—
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
386C3⋊#95C2311yescharacteristic
387C3⋊#95C2311yescharacteristic
388C3⋊#95C2311yescharacteristic
389C3⋊#95C2311yescharacteristic
390C2×C4⋊Q8—31no—
391C2×C4⋊Q8—31no—
392C2×C4⋊Q8—31no—
393C2×C4⋊Q8—31no—
394C2×C22⋊Q8—31no—
395C2×C22⋊Q8—31no—
396C2×C22⋊Q8—31no—
397C2×C4×Q8—31no—
398C2×C4×Q8—31no—
399C2×C4×Q8—31no—
400C2×C4×Q8—31no—
401C2×C4×Q8—31no—
402C2×C4×Q8—31no—
403C2×#117—31no—
404C2×#117—31no—
405C22×C4⋊C4—31no—
406#400—31no—
407#400—31no—
408#400—31no—
409#400—31no—
410#400—31no—
411#400—31no—
412#400C2×D311yescharacteristic
413#399—31no—
414#398—31no—
415#398—31no—
416#398—31no—
417#398—31no—
418#398—31no—
419#398—31no—
420#398—31no—
421#398—31no—
422#398—31no—
423#398—31no—
424#398—31no—
425#398C2×D311yescharacteristic
426#398C2×D311yescharacteristic
427#398C2×D311yescharacteristic
428#398C2×D311yescharacteristic
429#398C2×D311yescharacteristic
430#396—31no—
431#396—31no—
432#396—31no—
433#396—31no—
434#395—31no—
435#395—31no—
436#395—31no—
437#395—31no—
438#395—31no—
439#395—31no—
440#395—31no—
441#395—31no—
442#395—31no—
443#393—31no—
444#393—31no—
445#393—31no—
446#391—31no—
447#391—31no—
448#391—31no—
449#391—31no—
450#391—31no—
451#391—31no—
452#391—31no—
453#391—31no—
454#391—31no—
455#391—31no—
456#391—31no—
457#391—31no—
458#391—31no—
459#389—31no—
460#389—31no—
461#389—31no—
462#389—31no—
463#389—31no—
464#389—31no—
465#389—31no—
466#389—31no—
467#389—31no—
468#389—31no—
469#389—31no—
470#389—31no—
471#389—31no—
472#389—31no—
473#389—31no—
474#389—31no—
475#389—31no—
476#389—31no—
477#389—31no—
478#389—31no—
479#389—31no—
480#389C2×D311yescharacteristic
481#389C2×D311yescharacteristic
482#388—31no—
483#388—31no—
484#388—31no—
485#388—31no—
486#388—31no—
487#388—31no—
488#388—31no—
489#388—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#387C2×D311yescharacteristic
509#387C2×D311yescharacteristic
510#387C2×D311yescharacteristic
511#387C2×D311yescharacteristic
512#387C2×D311yescharacteristic
513#387C2×D311yescharacteristic
514#385—31no—
515#385—31no—
516#385—31no—
517#385—31no—
518#385—31no—
519#385—31no—
520#385—31no—
521#385—31no—
522#384—31no—
523#384—31no—
524#384—31no—
525#384—31no—
526#384C2×D311yescharacteristic
527#382—31no—
528#382—31no—
529#382—31no—
530#380—31no—
531C4×C4⋊C4—31no—
532C4×C4⋊C4—31no—
533C4×C4⋊C4—31no—
534C4×C4⋊C4—31no—
535C4×C4⋊C4—31no—
536C4×C4⋊C4—31no—
537C4×C4⋊C4—31no—
538C4×C4⋊C4—31no—
539C4×C4⋊C4—31no—
540C4×C4⋊C4—31no—
541C4×C22⋊C4—31no—
542C4×C22⋊C4—31no—
543C4×C22⋊C4—31no—
544C4×C22⋊C4—31no—
545C23×D3C2411yescharacteristic
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
557C22×C3×C4C2411yescharacteristic
558C22×C3×C4C2411yescharacteristic
559C22×C3×C4C2411yescharacteristic
560C22×C3×C4C2411yescharacteristic
561C22×Dic3C2411yescharacteristic
562C22×Dic3C2411yescharacteristic
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
576C2×C4×D3—22no—
577C2×C4×D3—22no—
578C2×C4×D3—41no—
579C2×C4×D3—41no—
580C2×C4×D3—41no—
581C2×C4×D3—41no—
582C2×C4×D3—41no—
583C2×C4×D3—41no—
584C2×C4×D3C2×Q814yes—
585C2×Dic6—22no—
586C2×Dic6—22no—
587C2×Dic6—22no—
588C2×Dic6—22no—
589C2×Dic6—22no—
590C2×Dic6—22no—
591C2×Dic6—22no—
592C2×Dic6—22no—
593C2×Dic6—22no—
594C2×Dic6—41no—
595C2×Dic6—41no—
596C2×Dic6—41no—
597C2×Dic6—41no—
598C2×Dic6—41no—
599C2×Dic6—41no—
600C2×Dic6—41no—
601C2×Dic6—41no—
602C2×Dic6C2×Q814yes—
603C3×C4⋊C4—22no—
604C3×C4⋊C4—22no—
605C3×C4⋊C4—41no—
606C3×C4⋊C4—41no—
607C3×C4⋊C4—41no—
608C3×C4⋊C4—41no—
609C3×C4⋊C4—41no—
610C3×C4⋊C4—41no—
611C3×C4⋊C4—41no—
612C3×C4⋊C4—41no—
613C3×C4⋊C4—41no—
614C3×C4⋊C4—41no—
615C3×C4⋊C4—41no—
616C3×C4⋊C4—41no—
617C3×C4⋊C4—41no—
618C3×C4⋊C4C2×Q814yes—
619C3×C42—22no—
620C3×C42—41no—
621C3×C42—41no—
622(C2×D3)⋊C4—22no—
623(C2×D3)⋊C4—22no—
624(C2×D3)⋊C4—22no—
625(C2×D3)⋊C4—22no—
626(C2×D3)⋊C4—22no—
627(C2×D3)⋊C4—41no—
628(C2×D3)⋊C4—41no—
629(C2×D3)⋊C4—41no—
630(C2×D3)⋊C4—41no—
631(C2×D3)⋊C4—41no—
632(C2×D3)⋊C4C2×Q814yes—
633(C2×D3)⋊C4C2×Q814yes—
634C4⋊Dic3—22no—
635C4⋊Dic3—22no—
636C4⋊Dic3—22no—
637C4⋊Dic3—41no—
638C4⋊Dic3—41no—
639C4⋊Dic3—41no—
640C4⋊Dic3—41no—
641C4⋊Dic3—41no—
642C4⋊Dic3—41no—
643C4⋊Dic3—41no—
644Dic3⋊C4—22no—
645Dic3⋊C4—22no—
646Dic3⋊C4—22no—
647Dic3⋊C4—22no—
648Dic3⋊C4—22no—
649Dic3⋊C4—22no—
650Dic3⋊C4—22no—
651Dic3⋊C4—22no—
652Dic3⋊C4—22no—
653Dic3⋊C4—22no—
654Dic3⋊C4—22no—
655Dic3⋊C4—22no—
656Dic3⋊C4—22no—
657Dic3⋊C4—41no—
658Dic3⋊C4—41no—
659Dic3⋊C4—41no—
660Dic3⋊C4—41no—
661Dic3⋊C4—41no—
662Dic3⋊C4—41no—
663Dic3⋊C4—41no—
664Dic3⋊C4—41no—
665Dic3⋊C4—41no—
666Dic3⋊C4—41no—
667Dic3⋊C4—41no—
668Dic3⋊C4—41no—
669Dic3⋊C4—41no—
670Dic3⋊C4—41no—
671Dic3⋊C4—41no—
672Dic3⋊C4—41no—
673Dic3⋊C4C2×Q814yes—
674Dic3⋊C4C2×Q814yes—
675Dic3⋊C4#4114yes—
676C4×Dic3—22no—
677C4×Dic3—22no—
678C4×Dic3—22no—
679C4×Dic3—22no—
680C4×Dic3—22no—
681C4×Dic3—22no—
682C4×Dic3—22no—
683C4×Dic3—22no—
684C4×Dic3—22no—
685C4×Dic3—22no—
686C4×Dic3—22no—
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×Q8—31no—
696C22×Q8—31no—
697C22×Q8—31no—
698C22×Q8—31no—
699C23×C4—31no—
700C23×C4—31no—
701C23×C4—31no—
702C4⋊Q8—64no—
703C4⋊Q8—122no—
704C4⋊Q8—122no—
705C4⋊Q8—122no—
706C22⋊Q8—38no—
707C22⋊Q8—122no—
708C22⋊Q8—122no—
709C4×Q8—64no—
710C4×Q8—122no—
711C4×Q8—122no—
712C4×Q8—122no—
713C4×Q8—122no—
714C4×Q8—122no—
715#117—64no—
716#117—122no—
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—31no—
745C2×C4⋊C4—31no—
746C2×C4⋊C4—31no—
747C2×C4⋊C4—31no—
748C2×C4⋊C4—31no—
749C2×C4⋊C4—31no—
750C2×C4⋊C4—31no—
751C2×C4⋊C4—31no—
752C2×C4⋊C4—31no—
753C2×C4⋊C4—31no—
754C2×C4⋊C4—31no—
755C2×C4⋊C4—31no—
756C2×C4⋊C4—31no—
757C2×C4⋊C4—31no—
758C2×C4⋊C4—31no—
759C2×C4⋊C4—122no—
760C2×C4⋊C4C22×D311yescharacteristic
761C2×C4⋊C4C22×D311yescharacteristic
762C2×C4⋊C4C22×D311yescharacteristic
763C2×C4⋊C4C22×D311yescharacteristic
764C2×C4⋊C4C22×D311yescharacteristic
765C2×C4⋊C4C22×D311yescharacteristic
766C2×C4⋊C4C22×D311yescharacteristic
767C2×C4⋊C4C22×D311yescharacteristic
768C2×C4⋊C4C22×D311yescharacteristic
769C2×C4⋊C4C22×D311yescharacteristic
770C2×C4⋊C4C22×D311yescharacteristic
771C2×C4⋊C4C22×D311yescharacteristic
772C2×C4⋊C4C22×D311yescharacteristic
773C2×C4⋊C4C22×D311yescharacteristic
774C2×C4⋊C4C22×D311yescharacteristic
775C2×C4⋊C4C22×D311yescharacteristic
776C2×C22⋊C4—31no—
777C2×C22⋊C4—31no—
778C2×C22⋊C4—31no—
779C2×C22⋊C4—31no—
780C2×C22⋊C4—31no—
781C2×C22⋊C4—31no—
782C2×C22⋊C4—31no—
783C2×C22⋊C4—31no—
784C2×C22⋊C4—31no—
785C2×C22⋊C4—31no—
786C2×C22⋊C4—31no—
787C2×C22⋊C4—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—31no—
797C2×C42—31no—
798C2×C42—31no—
799C2×C42—31no—
800C2×C42—31no—
801C2×C42—31no—
802C2×C42—31no—
803C2×C42—31no—
804C2×C42—31no—
805C2×C42C22×D311yescharacteristic
806C2×C42C22×D311yescharacteristic
807C2×C42C22×D311yescharacteristic
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#95—31no—
847#95—31no—
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
860#95C22×D311yescharacteristic
861#95C22×D311yescharacteristic
862#95C22×D311yescharacteristic
863#95C22×D311yescharacteristic
864C23×C3C2511yescharacteristic
865C22×D3—21no—
866C22×D3—21no—
867C22×D3—21no—
868C22×D3—21no—
869C22×D3—21no—
870C22×D3—21no—
871C22×D3C22×Q812yes—
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×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×C4C22×Q812yes—
914C2×C3×C4C22×Q812yes—
915C2×C3×C4C22×Q812yes—
916C2×C3×C4C2×#4112yes—
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×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×Dic3C22×Q812yes—
954C2×Dic3C22×Q812yes—
955C2×Dic3C22×Q812yes—
956C2×Dic3C2×#4112yes—
957C2×Dic3C2×#4112yes—
958C2×Dic3H(5,𝔽2)12yes—
959C2×Dic3H(5,𝔽2)12yes—
960C2×Dic32−1+412yes—
961C2×Dic32−1+412yes—
962C4×D3—28no—
963C4×D3—82no—
964C4×D3—82no—
965Dic6—28no—
966Dic6—44no—
967Dic6—44no—
968Dic6—44no—
969Dic6—82no—
970Dic6—82no—
971C24—31no—
972C2×Q8—34no—
973C2×Q8—62no—
974C2×Q8—62no—
975C2×Q8—62no—
976C2×Q8—62no—
977C2×Q8—62no—
978C2×Q8—62no—
979C2×Q8—62no—
980C2×Q8—62no—
981C2×Q8—62no—
982C2×Q8—121no—
983C2×Q8—121no—
984C2×Q8—121no—
985C2×Q8—121no—
986C2×Q8—121no—
987C2×Q8—121no—
988C2×Q8—121no—
989C2×Q8—121no—
990C22×C4—31no—
991C22×C4—31no—
992C22×C4—31no—
993C22×C4—31no—
994C22×C4—31no—
995C22×C4—31no—
996C22×C4—31no—
997C22×C4—34no—
998C22×C4—31no—
999C22×C4—31no—
1000C22×C4—31no—
1001C22×C4—31no—
1002C22×C4—31no—
1003C22×C4—31no—
1004C22×C4—31no—
1005C22×C4—31no—
1006C22×C4—62no—
1007C22×C4—62no—
1008C22×C4—121no—
1009C22×C4—121no—
1010C22×C4—121no—
1011C22×C4—121no—
1012C22×C4—121no—
1013C22×C4—121no—
1014C22×C4C23×D311yescharacteristic
1015C22×C4C23×D311yescharacteristic
1016C22×C4C23×D311yescharacteristic
1017C22×C4C23×D311yescharacteristic
1018C22×C4C23×D311yescharacteristic
1019C22×C4C23×D311yescharacteristic
1020C22×C4C23×D311yescharacteristic
1021C22×C4C23×D311yescharacteristic
1022C22×C4C23×D311yescharacteristic
1023C22×C4C23×D311yescharacteristic
1024C22×C4C23×D311yescharacteristic
1025C22×C4C23×D311yescharacteristic
1026C22×C4C23×D311yescharacteristic
1027C22×C4C23×D311yescharacteristic
1028C22×C4C23×D311yescharacteristic
1029C4⋊C4—22no—
1030C4⋊C4—22no—
1031C4⋊C4—34no—
1032C4⋊C4—34no—
1033C4⋊C4—34no—
1034C4⋊C4—41no—
1035C4⋊C4—41no—
1036C4⋊C4—41no—
1037C4⋊C4—41no—
1038C4⋊C4—41no—
1039C4⋊C4—41no—
1040C4⋊C4—41no—
1041C4⋊C4—41no—
1042C4⋊C4—41no—
1043C4⋊C4—41no—
1044C4⋊C4—41no—
1045C4⋊C4—41no—
1046C4⋊C4—41no—
1047C4⋊C4—62no—
1048C4⋊C4—62no—
1049C4⋊C4—62no—
1050C4⋊C4—62no—
1051C4⋊C4—62no—
1052C4⋊C4—62no—
1053C4⋊C4—62no—
1054C4⋊C4—62no—
1055C4⋊C4—62no—
1056C4⋊C4—62no—
1057C4⋊C4—62no—
1058C4⋊C4—62no—
1059C4⋊C4—62no—
1060C4⋊C4—62no—
1061C4⋊C4—62no—
1062C4⋊C4—62no—
1063C4⋊C4—121no—
1064C4⋊C4—121no—
1065C4⋊C4—121no—
1066C4⋊C4—121no—
1067C4⋊C4—121no—
1068C4⋊C4—121no—
1069C4⋊C4—121no—
1070C4⋊C4—121no—
1071C4⋊C4—121no—
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⋊C4D3×Q814yes—
1087C22⋊C4—34no—
1088C22⋊C4—34no—
1089C22⋊C4—62no—
1090C22⋊C4—62no—
1091C22⋊C4—62no—
1092C22⋊C4—62no—
1093C22⋊C4—62no—
1094C22⋊C4—121no—
1095C22⋊C4—121no—
1096C22⋊C4—121no—
1097C22⋊C4—121no—
1098C22⋊C4—121no—
1099C42—22no—
1100C42—41no—
1101C42—41no—
1102C42—62no—
1103C42—62no—
1104C42—62no—
1105C42—62no—
1106C42—62no—
1107C42—62no—
1108C42—62no—
1109C42—62no—
1110C42—62no—
1111C42—62no—
1112C42—62no—
1113C42—121no—
1114C42—121no—
1115C42—121no—
1116C42—121no—
1117C42—121no—
1118C42—121no—
1119C22×C3C23×Q811yescharacteristic
1120C22×C3C22×#4111yescharacteristic
1121C22×C3C2×H(5,𝔽2)11yescharacteristic
1122C22×C3C2×H(5,𝔽2)11yescharacteristic
1123C22×C3C2×2−1+411yescharacteristic
1124C22×C3C2×2−1+411yescharacteristic
1125C22×C3#58511yescharacteristic
1126C2×D3—22no—
1127C2×D3—22no—
1128C2×D3—22no—
1129C2×D3—41no—
1130C2×D3—41no—
1131C2×D3—41no—
1132C2×D3—41no—
1133C3×C4—22no—
1134C3×C4—22no—
1135C3×C4—22no—
1136C3×C4—22no—
1137C3×C4—41no—
1138C3×C4—41no—
1139C3×C4—41no—
1140C3×C4—41no—
1141C3×C4—41no—
1142C3×C4—41no—
1143C3×C4—41no—
1144C3×C4—41no—
1145C3×C4—41no—
1146C3×C4—41no—
1147C3×C4—41no—
1148Dic3—22no—
1149Dic3—22no—
1150Dic3—22no—
1151Dic3—22no—
1152Dic3—22no—
1153Dic3—22no—
1154Dic3—41no—
1155Dic3—41no—
1156Dic3—41no—
1157Dic3—41no—
1158Dic3—41no—
1159Dic3—41no—
1160Dic3—41no—
1161Dic3—41no—
1162Dic3#55414yes—
1163C23—32no—
1164C23—61no—
1165C23—61no—
1166C23—61no—
1167C23—61no—
1168C23—61no—
1169C23—61no—
1170C23C24×D311yescharacteristic
1171Q8—68no—
1172Q8—124no—
1173Q8—124no—
1174Q8—124no—
1175Q8—242no—
1176Q8—242no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—32no—
1219C2×C4—32no—
1220C2×C4—32no—
1221C2×C4—32no—
1222C2×C4—32no—
1223C2×C4—32no—
1224C2×C4—32no—
1225C2×C4—32no—
1226C2×C4—32no—
1227C2×C4—68no—
1228C2×C4—61no—
1229C2×C4—61no—
1230C2×C4—61no—
1231C2×C4—61no—
1232C2×C4—61no—
1233C2×C4—61no—
1234C2×C4—61no—
1235C2×C4—61no—
1236C2×C4—61no—
1237C2×C4—61no—
1238C2×C4—61no—
1239C2×C4—61no—
1240C2×C4—61no—
1241C2×C4—61no—
1242C2×C4—61no—
1243C2×C4—61no—
1244C2×C4—61no—
1245C2×C4—61no—
1246C2×C4—61no—
1247C2×C4—61no—
1248C2×C4—61no—
1249C2×C4—61no—
1250C2×C4—61no—
1251C2×C4—61no—
1252C2×C4—61no—
1253C2×C4—61no—
1254C2×C4—61no—
1255C2×C4—61no—
1256C2×C4—61no—
1257C2×C4—61no—
1258C2×C4—61no—
1259C2×C4—61no—
1260C2×C4—61no—
1261C2×C4—61no—
1262C2×C4—61no—
1263C2×C4—61no—
1264C2×C4—242no—
1265C2×C4—242no—
1266C2×C4C2×D3×Q812yes—
1267C2×C4C2×D3×Q812yes—
1268C2×C4C2×D3×Q812yes—
1269C2×C4D3×#4112yes—
1270C2×C3C2×#55411yescharacteristic
1271C2×C3#350211yescharacteristic
1272C2×C3#350311yescharacteristic
1273C2×C3#351611yescharacteristic
1274C2×C3#352011yescharacteristic
1275C2×C3#354211yescharacteristic
1276C2×C3#355011yescharacteristic
1277D3—42no—
1278C22—62no—
1279C22—62no—
1280C22—62no—
1281C22—121no—
1282C22—121no—
1283C22—121no—
1284C22—121no—
1285C22C22×D3×Q811yescharacteristic
1286C22C2×D3×#4111yescharacteristic
1287C22#596411yescharacteristic
1288C22D3×H(5,𝔽2)11yescharacteristic
1289C22D3×H(5,𝔽2)11yescharacteristic
1290C22D3×2−1+411yescharacteristic
1291C22D3×2−1+411yescharacteristic
1292C4—22no—
1293C4—22no—
1294C4—22no—
1295C4—22no—
1296C4—34no—
1297C4—41no—
1298C4—41no—
1299C4—41no—
1300C4—41no—
1301C4—41no—
1302C4—41no—
1303C4—41no—
1304C4—41no—
1305C4—41no—
1306C4—41no—
1307C4—41no—
1308C4—62no—
1309C4—62no—
1310C4—62no—
1311C4—62no—
1312C4—62no—
1313C4—62no—
1314C4—121no—
1315C4—121no—
1316C4—121no—
1317C4—121no—
1318C4—121no—
1319C4—121no—
1320C4—121no—
1321C4—121no—
1322C3#4499711yescharacteristic, complemented, Sylow
1323C2—122no—
1324C2#8645611yescharacteristic
1325C2#8647411yescharacteristic
1326C2#8658611yescharacteristic
1327C2#8683811yescharacteristic
1328C2D3×#55411yescharacteristic
1329C2#8703211yescharacteristic
1330C2#8711911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2791C2
prime radicalC23×D3C24
hypercenter#2791D3
hypocenterC3#44997
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2791

Complements

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

NH ≅ G/Ntype
1. C3×#2791C2semidirect
2. #78298C2semidirect
6. #77877C2semidirect
9. #77785C2semidirect
10. #77768C2semidirect
11. #77748C2semidirect
12. #77748C2semidirect
15. #76071C2semidirect
16. #75981C2semidirect
19. #75186C2semidirect
21. #75090C2semidirect
22. #75043C2semidirect
23. #75038C2semidirect
24. #75029C2semidirect
27. #74967C2semidirect
31. #74340C2semidirect
189. #2791D3semidirect
320. #896Q8semidirect
1322. C3#44997semidirect

Maximal subgroups

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

subgroupindex
C3×#27912
#782982
#781302
#779852
#779062
#778772
#778712
#778042
#777852
#777682
#777482
#777452
#762272
#760712
#759812
#759712
#752482
#751862
#751072
#750902
#750432
#750382
#750292
#749992
#749832
#749672
#749662
#749652
#743592
#743402
#449973