Finite Group Databasebeta

← #11233448

Subgroups — #11233448

Order 768.

1934 conjugacy classes of subgroups.

The subgroup lattice has 1364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5701C211yesmaximal, characteristic
2C2×#5567C211yesmaximal, characteristic, complemented
3C3×#2469C211yesmaximal, characteristic
4#83101C211yesmaximal, characteristic
5#82471C211yesmaximal, characteristic, complemented
6#78181C211yesmaximal, characteristic, complemented
7#78137C211yesmaximal, characteristic, complemented
8#77298C211yesmaximal, characteristic
9#77282C211yesmaximal, characteristic
10#77185C211yesmaximal, characteristic, complemented
11#77175C211yesmaximal, characteristic, complemented
12#76830C211yesmaximal, characteristic
13#76793C211yesmaximal, characteristic
14#76117C211yesmaximal, characteristic, complemented
15#76060C211yesmaximal, characteristic, complemented
16#75702C211yesmaximal, characteristic
17#75695C211yesmaximal, characteristic
18#75565C211yesmaximal, characteristic
19#75564C211yesmaximal, characteristic
20#75544C211yesmaximal, characteristic
21#75500C211yesmaximal, characteristic
22#75500C211yesmaximal, characteristic
23#75460C211yesmaximal, characteristic
24#75168C211yesmaximal, characteristic, complemented
25#75166C211yesmaximal, characteristic, complemented
26#75165C211yesmaximal, characteristic, complemented
27#74988C211yesmaximal, characteristic, complemented
28#74969C211yesmaximal, characteristic, complemented
29#74967C211yesmaximal, characteristic, complemented
30#73713C211yesmaximal, characteristic, complemented
31#73652C211yesmaximal, characteristic, complemented
32#45343—31nomaximal, Sylow
33C2×C3×#126C2211yescharacteristic
34C2×C3×C4×Q8C2211yescharacteristic
35C2×#944C2211yescharacteristic
36C2×#944C2211yescharacteristic
37#5701—28no—
38#5567—28no—
39C2×#890C2211yescharacteristic
40C2×#889C2211yescharacteristic
41C2×#889C2211yescharacteristic
42C2×#889C2211yescharacteristic
43C2×#889C2211yescharacteristic
44C2×#889C2211yescharacteristic
45C2×#889C2211yescharacteristic
46C2×#888C2211yescharacteristic
47C2×#888C2211yescharacteristic
48C2×#888C2211yescharacteristic
49C2×#887C2211yescharacteristic
50C2×#887C2211yescharacteristic
51C2×#887C2211yescharacteristic
52C2×#879C2211yescharacteristic
53C2×#879C2211yescharacteristic
54C2×#879C2211yescharacteristic
55C2×#878C2211yescharacteristic
56C2×#878C2211yescharacteristic
57C2×#878C2211yescharacteristic
58C2×#877C2211yescharacteristic
59C2×#870C2211yescharacteristic
60C2×#870C2211yescharacteristic
61C2×#870C2211yescharacteristic
62C2×#869C2211yescharacteristic
63C2×C4×Dic6C2211yescharacteristic
64C2×C4×Dic6C2211yescharacteristic
65C2×C4×Dic6C2211yescharacteristic
66C2×C4×Dic6C2211yescharacteristic
67C3×#400C2211yescharacteristic
68C3×#396C2211yescharacteristic
69C3×#395C2211yescharacteristic
70C3×#393C2211yescharacteristic
71C3×#389C2211yescharacteristic
72C3×#388C2211yescharacteristic
73C3×#388C2211yescharacteristic
74C3×#388C2211yescharacteristic
75C3×#388C2211yescharacteristic
76C3×#387C2211yescharacteristic
77C3×#387C2211yescharacteristic
78C3×#387C2211yescharacteristic
79C3×C4×C4⋊C4C2211yescharacteristic
80#5229C2211yescharacteristic
81#5229C2211yescharacteristic
82#4986C2211yescharacteristic
83#4986C2211yescharacteristic
84#4985C2211yescharacteristic
85#4984C2211yescharacteristic
86#4984C2211yescharacteristic
87#4984C2211yescharacteristic
88#4983C2211yescharacteristic
89#4982C2211yescharacteristic
90#4982C2211yescharacteristic
91#4982C2211yescharacteristic
92#4982C2211yescharacteristic
93#4982C2211yescharacteristic
94#4982C2211yescharacteristic
95#4982C2211yescharacteristic
96#4981C2211yescharacteristic
97#4980C2211yescharacteristic
98#4979C2211yescharacteristic
99#4979C2211yescharacteristic
100#4978C2211yescharacteristic
101#4976C2211yescharacteristic
102#4976C2211yescharacteristic
103#4976C2211yescharacteristic
104Dic3×C4⋊C4C2211yescharacteristic
105Dic3×C4⋊C4C2211yescharacteristic
106Dic3×C4⋊C4C2211yescharacteristic
107#4972C2211yescharacteristic
108#4972C2211yescharacteristic
109#4953C2211yescharacteristic
110#4952C2211yescharacteristic
111#4951C2211yescharacteristic
112#4951C2211yescharacteristic
113#4951C2211yescharacteristic
114#4949C2211yescharacteristic
115#4948C2211yescharacteristic
116#4948C2211yescharacteristic
117#4948C2211yescharacteristic
118#4948C2211yescharacteristic
119#4948C2211yescharacteristic
120#4947C2211yescharacteristic
121#4947C2211yescharacteristic
122#4945C2211yescharacteristic
123#4944C2211yescharacteristic
124#4944C2211yescharacteristic
125#4944C2211yescharacteristic
126#4944C2211yescharacteristic
127#4942C2211yescharacteristic
128Dic3×C22⋊C4C2211yescharacteristic
129Dic3×C22⋊C4C2211yescharacteristic
130#4936C2211yescharacteristic
131C4×C4⋊Dic3C2211yescharacteristic
132#4933C2211yescharacteristic
133#4933C2211yescharacteristic
134#4933C2211yescharacteristic
135C4×Dic3⋊C4C2211yescharacteristic
136C4×Dic3⋊C4C2211yescharacteristic
137#4928C2211yescharacteristic
138#4928C2211yescharacteristic
139#4928C2211yescharacteristic
140#4928C2211yescharacteristic
141#4928C2211yescharacteristic
142#4661C2211yescharacteristic
143#4661C2211yescharacteristic
144#4660C2211yescharacteristic
145#4659C2211yescharacteristic
146#4659C2211yescharacteristic
147#4659C2211yescharacteristic
148#4658C2211yescharacteristic
149#4658C2211yescharacteristic
150#4658C2211yescharacteristic
151#4657C2211yescharacteristic
152#4657C2211yescharacteristic
153#4657C2211yescharacteristic
154#4655C2211yescharacteristic
155#4655C2211yescharacteristic
156#4655C2211yescharacteristic
157#4654C2211yescharacteristic
158#4654C2211yescharacteristic
159#4653C2211yescharacteristic
160#4653C2211yescharacteristic
161#4653C2211yescharacteristic
162#4653C2211yescharacteristic
163#4652C2211yescharacteristic
164#4650C2211yescharacteristic
165#4650C2211yescharacteristic
166#4650C2211yescharacteristic
167#4649C2211yescharacteristic
168#4649C2211yescharacteristic
169#4649C2211yescharacteristic
170#4649C2211yescharacteristic
171#4649C2211yescharacteristic
172#4647C2211yescharacteristic
173#4647C2211yescharacteristic
174#4647C2211yescharacteristic
175#4647C2211yescharacteristic
176#4647C2211yescharacteristic
177#4647C2211yescharacteristic
178#4647C2211yescharacteristic
179#4646C2211yescharacteristic
180#4646C2211yescharacteristic
181#4646C2211yescharacteristic
182#4646C2211yescharacteristic
183#4646C2211yescharacteristic
184#4646C2211yescharacteristic
185#4646C2211yescharacteristic
186#4646C2211yescharacteristic
187#4646C2211yescharacteristic
188#4646C2211yescharacteristic
189#4646C2211yescharacteristic
190C2×#557—31no—
191C2×#541—31no—
192#2725—31no—
193#2725—31no—
194#2719—31no—
195#2719—31no—
196#2719—31no—
197#2719—31no—
198#2716—31no—
199#2716—31no—
200#2568—31no—
201#2550—31no—
202#2550—31no—
203#2546—31no—
204#2519—31no—
205#2519—31no—
206#2492—31no—
207#2489—31no—
208#2469—31no—
209#2469D311yescharacteristic
210#2453—31no—
211#2453—31no—
212#2453—31no—
213#2451—31no—
214#2429—31no—
215#2429—31no—
216#2396—31no—
217#2370—31no—
218#2365—31no—
219#2365—31no—
220#2323—31no—
221C22×C3×Q8C2311yescharacteristic
222C23×Dic3C2311yescharacteristic
223C22×Dic6C2311yescharacteristic
224C22×Dic6C2311yescharacteristic
225C22×Dic6C2311yescharacteristic
226C22×Dic6C2311yescharacteristic
227C22×Dic6C2311yescharacteristic
228C3×#126—24no—
229C3×C4×Q8—24no—
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×C22⋊C4C2311yescharacteristic
241C2×C3×C22⋊C4C2311yescharacteristic
242C2×C3×C22⋊C4C2311yescharacteristic
243C2×C3×C22⋊C4C2311yescharacteristic
244C2×C3×C22⋊C4C2311yescharacteristic
245C2×C3×C22⋊C4C2311yescharacteristic
246C2×C3×C22⋊C4C2311yescharacteristic
247C2×C3×C42C2311yescharacteristic
248C2×C3×C42C2311yescharacteristic
249C2×C3×C42C2311yescharacteristic
250C2×C3×C42C2311yescharacteristic
251C2×C3×C42C2311yescharacteristic
252C2×#217C2311yescharacteristic
253C2×#217C2311yescharacteristic
254C2×#217C2311yescharacteristic
255C2×#217C2311yescharacteristic
256C2×#217C2311yescharacteristic
257C2×#217C2311yescharacteristic
258C2×#217C2311yescharacteristic
259#944—24no—
260#944—24no—
261C2×C4⋊Dic3C2311yescharacteristic
262C2×C4⋊Dic3C2311yescharacteristic
263C2×C4⋊Dic3C2311yescharacteristic
264C2×C4⋊Dic3C2311yescharacteristic
265C2×C4⋊Dic3C2311yescharacteristic
266C2×C4⋊Dic3C2311yescharacteristic
267C2×C4⋊Dic3C2311yescharacteristic
268C2×C4⋊Dic3C2311yescharacteristic
269C2×C4⋊Dic3C2311yescharacteristic
270C2×C4⋊Dic3C2311yescharacteristic
271C2×C4⋊Dic3C2311yescharacteristic
272C2×C4⋊Dic3C2311yescharacteristic
273C2×C4⋊Dic3C2311yescharacteristic
274C2×C4⋊Dic3C2311yescharacteristic
275C2×C4⋊Dic3C2311yescharacteristic
276C2×C4⋊Dic3C2311yescharacteristic
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×Dic3⋊C4C2311yescharacteristic
302C2×Dic3⋊C4C2311yescharacteristic
303C2×Dic3⋊C4C2311yescharacteristic
304C2×Dic3⋊C4C2311yescharacteristic
305C2×Dic3⋊C4C2311yescharacteristic
306C2×Dic3⋊C4C2311yescharacteristic
307C2×Dic3⋊C4C2311yescharacteristic
308C2×Dic3⋊C4C2311yescharacteristic
309C2×Dic3⋊C4C2311yescharacteristic
310C2×Dic3⋊C4C2311yescharacteristic
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
320C2×C4×Dic3C2311yescharacteristic
321C2×C4×Dic3C2311yescharacteristic
322C2×C4×Dic3C2311yescharacteristic
323C2×C4×Dic3C2311yescharacteristic
324C2×C4×Dic3C2311yescharacteristic
325C2×C4×Dic3C2311yescharacteristic
326C2×C4×Dic3C2311yescharacteristic
327C2×C4×Dic3C2311yescharacteristic
328#890—24no—
329#889—24no—
330#889—24no—
331#889—24no—
332#889—24no—
333#889—24no—
334#889D418yes—
335#888—24no—
336#888—24no—
337#888—24no—
338#887—24no—
339#887—24no—
340#887—24no—
341#879—24no—
342#879—24no—
343#879—24no—
344#878—24no—
345#878—24no—
346#878—24no—
347#877—24no—
348#870—24no—
349#870—24no—
350#870—24no—
351#869—24no—
352C4×Dic6—24no—
353C4×Dic6—24no—
354C4×Dic6—24no—
355C4×Dic6—24no—
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
390C3⋊#95C2311yescharacteristic
391C3⋊#95C2311yescharacteristic
392C3⋊#95C2311yescharacteristic
393C3⋊#95C2311yescharacteristic
394C3⋊#95C2311yescharacteristic
395C3⋊#95C2311yescharacteristic
396C3⋊#95C2311yescharacteristic
397C3⋊#95C2311yescharacteristic
398C3⋊#95C2311yescharacteristic
399C3⋊#95C2311yescharacteristic
400C3⋊#95C2311yescharacteristic
401C3⋊#95C2311yescharacteristic
402C3⋊#95C2311yescharacteristic
403C3⋊#95C2311yescharacteristic
404C3⋊#95C2311yescharacteristic
405C3⋊#95C2311yescharacteristic
406C3⋊#95C2311yescharacteristic
407C3⋊#95C2311yescharacteristic
408#557—68no—
409#541—68no—
410C2×C4⋊Q8—31no—
411C2×C4⋊Q8—31no—
412C2×C4⋊Q8—31no—
413C2×C4⋊Q8—31no—
414C2×C4⋊Q8—31no—
415C2×C4⋊Q8—31no—
416C2×#126—31no—
417C2×#126—31no—
418C2×#126—31no—
419C2×#126C2×D311yescharacteristic
420C2×#125—31no—
421C2×#125—31no—
422C2×#125—31no—
423C2×#125—31no—
424C2×#125—31no—
425C2×#125—31no—
426C2×#125—31no—
427C2×#125—31no—
428C2×#125—31no—
429C2×#125—31no—
430C2×C22⋊Q8—31no—
431C2×C22⋊Q8—31no—
432C2×C22⋊Q8—31no—
433C2×C4×Q8—31no—
434C2×C4×Q8—31no—
435C2×C4×Q8—31no—
436C2×C4×Q8—31no—
437C2×C4×Q8—31no—
438C2×C4×Q8—31no—
439C2×C4×Q8—31no—
440C2×C4×Q8C2×D311yescharacteristic
441C2×#117—31no—
442#400—31no—
443#400—31no—
444#400—31no—
445#400—31no—
446#400—31no—
447#400—31no—
448#400—31no—
449#400—31no—
450#400—31no—
451#400—31no—
452#400C2×D311yescharacteristic
453#399—31no—
454#398—31no—
455#398—31no—
456#398—31no—
457#398—31no—
458#398—31no—
459#398—31no—
460#398—31no—
461#398—31no—
462#398—31no—
463#398—31no—
464#398—31no—
465#398—31no—
466#398—31no—
467#398—31no—
468#397—31no—
469#397—31no—
470#396—31no—
471#396—31no—
472#396—31no—
473#396—31no—
474#396—31no—
475#396C2×D311yescharacteristic
476#395—31no—
477#395—31no—
478#395C2×D311yescharacteristic
479#393—31no—
480#393—31no—
481#393C2×D311yescharacteristic
482#391—31no—
483#391—31no—
484#391—31no—
485#391—31no—
486#391—31no—
487#391—31no—
488#391—31no—
489#391—31no—
490#391—31no—
491#391—31no—
492#391—31no—
493#391—31no—
494#391—31no—
495#389—31no—
496#389—31no—
497#389—31no—
498#389—31no—
499#389—31no—
500#389—31no—
501#389—31no—
502#389—31no—
503#389—31no—
504#389—31no—
505#389—31no—
506#389—31no—
507#389—31no—
508#389—31no—
509#389—31no—
510#389—31no—
511#389—31no—
512#389—31no—
513#389—31no—
514#389—31no—
515#389C2×D311yescharacteristic
516#388—31no—
517#388—31no—
518#388—31no—
519#388—31no—
520#388—31no—
521#388—31no—
522#388—31no—
523#388—31no—
524#388C2×D311yescharacteristic
525#388C2×D311yescharacteristic
526#388C2×D311yescharacteristic
527#388C2×D311yescharacteristic
528#387—31no—
529#387—31no—
530#387—31no—
531#387—31no—
532#387—31no—
533#387—31no—
534#387—31no—
535#387—31no—
536#387—31no—
537#387—31no—
538#387—31no—
539#387—31no—
540#387—31no—
541#387—31no—
542#387—31no—
543#387C2×D311yescharacteristic
544#387C2×D311yescharacteristic
545#387C2×D311yescharacteristic
546#382—31no—
547#382—31no—
548#382—31no—
549#382—31no—
550#380—31no—
551C4×C4⋊C4—31no—
552C4×C4⋊C4—31no—
553C4×C4⋊C4—31no—
554C4×C4⋊C4—31no—
555C4×C4⋊C4—31no—
556C4×C4⋊C4—31no—
557C4×C4⋊C4—31no—
558C4×C4⋊C4—31no—
559C4×C4⋊C4—31no—
560C4×C4⋊C4—31no—
561C4×C4⋊C4—31no—
562C4×C4⋊C4C2×D311yescharacteristic
563C4×C22⋊C4—31no—
564C4×C22⋊C4—31no—
565C24×C3C2411yescharacteristic
566C2×C3×Q8—22no—
567C2×C3×Q8—22no—
568C2×C3×Q8—41no—
569C22×C3×C4C2411yescharacteristic
570C22×C3×C4C2411yescharacteristic
571C22×C3×C4C2411yescharacteristic
572C22×C3×C4C2411yescharacteristic
573C22×C3×C4C2411yescharacteristic
574C22×C3×C4C2411yescharacteristic
575C22×C3×C4C2411yescharacteristic
576C22×C3×C4C2411yescharacteristic
577C22×C3×C4C2411yescharacteristic
578C22×C3×C4C2411yescharacteristic
579C22×C3×C4C2411yescharacteristic
580C22×C3×C4C2411yescharacteristic
581C22×C3×C4C2411yescharacteristic
582C22×C3×C4C2411yescharacteristic
583C22×Dic3—22no—
584C22×Dic3—22no—
585C22×Dic3—22no—
586C22×Dic3C2411yescharacteristic
587C22×Dic3C2411yescharacteristic
588C22×Dic3C2411yescharacteristic
589C22×Dic3C2411yescharacteristic
590C22×Dic3C2411yescharacteristic
591C22×Dic3C2411yescharacteristic
592C22×Dic3C2411yescharacteristic
593C22×Dic3C2411yescharacteristic
594C22×Dic3C2411yescharacteristic
595C22×Dic3C2411yescharacteristic
596C22×Dic3C2411yescharacteristic
597C22×Dic3C2411yescharacteristic
598C22×Dic3C2411yescharacteristic
599C22×Dic3C2411yescharacteristic
600C22×Dic3C2411yescharacteristic
601C22×Dic3C2411yescharacteristic
602C2×Dic6—22no—
603C2×Dic6—22no—
604C2×Dic6—22no—
605C2×Dic6—22no—
606C2×Dic6—22no—
607C2×Dic6—22no—
608C2×Dic6—22no—
609C2×Dic6—22no—
610C2×Dic6—22no—
611C2×Dic6—22no—
612C2×Dic6—22no—
613C2×Dic6—22no—
614C2×Dic6—41no—
615C2×Dic6—41no—
616C2×Dic6#4114yes—
617C3×C4⋊C4—22no—
618C3×C4⋊C4—22no—
619C3×C4⋊C4—22no—
620C3×C4⋊C4—22no—
621C3×C4⋊C4—22no—
622C3×C4⋊C4—22no—
623C3×C4⋊C4—22no—
624C3×C4⋊C4—22no—
625C3×C4⋊C4—41no—
626C3×C4⋊C4C2×D414yes—
627C3×C22⋊C4—22no—
628C3×C22⋊C4—22no—
629C3×C22⋊C4—22no—
630C3×C22⋊C4—22no—
631C3×C22⋊C4—22no—
632C3×C22⋊C4—22no—
633C3×C22⋊C4—41no—
634C3×C42—22no—
635C3×C42—22no—
636C3×C42—22no—
637C3×C42—22no—
638C3×C42—22no—
639#217—22no—
640#217—22no—
641#217—22no—
642#217—22no—
643#217—22no—
644#217—41no—
645#217—41no—
646C4⋊Dic3—22no—
647C4⋊Dic3—22no—
648C4⋊Dic3—22no—
649C4⋊Dic3—22no—
650C4⋊Dic3—22no—
651C4⋊Dic3—22no—
652C4⋊Dic3—22no—
653C4⋊Dic3—22no—
654C4⋊Dic3—22no—
655C4⋊Dic3—22no—
656C4⋊Dic3—22no—
657C4⋊Dic3—22no—
658C4⋊Dic3—22no—
659C4⋊Dic3—22no—
660C4⋊Dic3—41no—
661C4⋊Dic3C2×D414yes—
662Dic3⋊C4—22no—
663Dic3⋊C4—22no—
664Dic3⋊C4—22no—
665Dic3⋊C4—22no—
666Dic3⋊C4—22no—
667Dic3⋊C4—22no—
668Dic3⋊C4—22no—
669Dic3⋊C4—22no—
670Dic3⋊C4—22no—
671Dic3⋊C4—22no—
672Dic3⋊C4—22no—
673Dic3⋊C4—22no—
674Dic3⋊C4—22no—
675Dic3⋊C4—22no—
676Dic3⋊C4—22no—
677Dic3⋊C4—22no—
678Dic3⋊C4—22no—
679Dic3⋊C4—22no—
680Dic3⋊C4—22no—
681Dic3⋊C4—22no—
682Dic3⋊C4—22no—
683Dic3⋊C4—22no—
684Dic3⋊C4—22no—
685Dic3⋊C4—22no—
686Dic3⋊C4—22no—
687Dic3⋊C4—22no—
688Dic3⋊C4—22no—
689Dic3⋊C4—41no—
690Dic3⋊C4—41no—
691Dic3⋊C4—41no—
692Dic3⋊C4C2×D414yes—
693Dic3⋊C4C2×D414yes—
694Dic3⋊C4C2×D414yes—
695Dic3⋊C4C2×D414yes—
696C4×Dic3—22no—
697C4×Dic3—22no—
698C4×Dic3—22no—
699C4×Dic3—22no—
700C4×Dic3—22no—
701C4×Dic3—22no—
702C4×Dic3—22no—
703C4×Dic3—22no—
704C4×Dic3—22no—
705C4×Dic3—22no—
706C4×Dic3—22no—
707C4×Dic3—22no—
708C4×Dic3—41no—
709C4×Dic3—41no—
710C4×Dic3—41no—
711C4×Dic3—41no—
712C4×Dic3C2×D414yes—
713C22×Q8—31no—
714C22×Q8—31no—
715C22×Q8—31no—
716C22×Q8—31no—
717C22×Q8—31no—
718C22×Q8C22×D311yescharacteristic
719C23×C4—31no—
720C4⋊Q8—64no—
721C4⋊Q8—64no—
722C4⋊Q8—64no—
723C4⋊Q8—64no—
724C4⋊Q8—64no—
725C4⋊Q8—64no—
726#126—24no—
727#126—64no—
728#126—64no—
729#126—64no—
730#125—38no—
731#125—64no—
732#125—64no—
733#125—64no—
734#125—64no—
735#125—64no—
736#125—64no—
737#125—64no—
738#125—64no—
739#125—64no—
740C22⋊Q8—64no—
741C22⋊Q8—64no—
742C22⋊Q8—64no—
743C4×Q8—24no—
744C4×Q8—64no—
745C4×Q8—64no—
746C4×Q8—64no—
747C4×Q8—64no—
748C4×Q8—64no—
749C4×Q8—64no—
750C4×Q8—64no—
751#117—64no—
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—31no—
760C2×C4⋊C4—31no—
761C2×C4⋊C4—31no—
762C2×C4⋊C4—31no—
763C2×C4⋊C4—31no—
764C2×C4⋊C4—31no—
765C2×C4⋊C4—31no—
766C2×C4⋊C4—31no—
767C2×C4⋊C4—31no—
768C2×C4⋊C4—31no—
769C2×C4⋊C4—31no—
770C2×C4⋊C4—31no—
771C2×C4⋊C4—31no—
772C2×C4⋊C4—31no—
773C2×C4⋊C4—31no—
774C2×C4⋊C4—31no—
775C2×C4⋊C4—31no—
776C2×C4⋊C4—31no—
777C2×C4⋊C4—31no—
778C2×C4⋊C4—31no—
779C2×C4⋊C4—31no—
780C2×C4⋊C4—31no—
781C2×C4⋊C4—31no—
782C2×C4⋊C4—31no—
783C2×C4⋊C4—31no—
784C2×C4⋊C4—31no—
785C2×C4⋊C4—31no—
786C2×C4⋊C4—31no—
787C2×C4⋊C4—31no—
788C2×C4⋊C4—31no—
789C2×C4⋊C4—31no—
790C2×C4⋊C4—31no—
791C2×C4⋊C4—31no—
792C2×C4⋊C4—31no—
793C2×C4⋊C4—31no—
794C2×C4⋊C4—31no—
795C2×C4⋊C4—31no—
796C2×C4⋊C4—31no—
797C2×C4⋊C4—31no—
798C2×C4⋊C4—31no—
799C2×C4⋊C4—31no—
800C2×C4⋊C4—31no—
801C2×C4⋊C4—31no—
802C2×C4⋊C4C22×D311yescharacteristic
803C2×C4⋊C4C22×D311yescharacteristic
804C2×C4⋊C4C22×D311yescharacteristic
805C2×C4⋊C4C22×D311yescharacteristic
806C2×C4⋊C4C22×D311yescharacteristic
807C2×C4⋊C4C22×D311yescharacteristic
808C2×C4⋊C4C22×D311yescharacteristic
809C2×C4⋊C4C22×D311yescharacteristic
810C2×C4⋊C4C22×D311yescharacteristic
811C2×C4⋊C4C22×D311yescharacteristic
812C2×C22⋊C4—31no—
813C2×C22⋊C4—31no—
814C2×C22⋊C4—31no—
815C2×C22⋊C4—31no—
816C2×C22⋊C4—31no—
817C2×C22⋊C4—31no—
818C2×C22⋊C4—31no—
819C2×C22⋊C4C22×D311yescharacteristic
820C2×C22⋊C4C22×D311yescharacteristic
821C2×C22⋊C4C22×D311yescharacteristic
822C2×C22⋊C4C22×D311yescharacteristic
823C2×C22⋊C4C22×D311yescharacteristic
824C2×C22⋊C4C22×D311yescharacteristic
825C2×C22⋊C4C22×D311yescharacteristic
826C2×C42—31no—
827C2×C42—31no—
828C2×C42—31no—
829C2×C42—31no—
830C2×C42—31no—
831C2×C42—31no—
832C2×C42—31no—
833C2×C42—31no—
834C2×C42—31no—
835C2×C42—31no—
836C2×C42—31no—
837C2×C42—31no—
838C2×C42—31no—
839C2×C42—31no—
840C2×C42—31no—
841C2×C42—31no—
842C2×C42—31no—
843C2×C42C22×D311yescharacteristic
844C2×C42C22×D311yescharacteristic
845C2×C42C22×D311yescharacteristic
846C2×C42C22×D311yescharacteristic
847C2×C42C22×D311yescharacteristic
848#95—31no—
849#95—31no—
850#95—31no—
851#95—31no—
852#95—31no—
853#95—31no—
854#95—31no—
855#95—31no—
856#95—31no—
857#95—31no—
858#95—31no—
859#95—31no—
860#95—31no—
861#95—31no—
862#95—31no—
863#95—31no—
864#95—31no—
865#95—31no—
866#95—31no—
867#95—31no—
868#95—31no—
869#95—31no—
870#95—31no—
871#95—31no—
872#95—31no—
873#95—31no—
874#95—31no—
875#95—31no—
876#95—31no—
877#95—31no—
878#95—31no—
879#95—31no—
880#95—31no—
881#95—31no—
882#95—31no—
883#95—31no—
884#95—31no—
885#95—31no—
886#95—31no—
887#95—31no—
888#95C22×D311yescharacteristic
889#95C22×D311yescharacteristic
890#95C22×D311yescharacteristic
891#95C22×D311yescharacteristic
892#95C22×D311yescharacteristic
893#95C22×D311yescharacteristic
894#95C22×D311yescharacteristic
895#95C22×D311yescharacteristic
896#95C22×D311yescharacteristic
897#95C22×D311yescharacteristic
898#95C22×D311yescharacteristic
899#95C22×D311yescharacteristic
900C23×C3—21no—
901C23×C3—21no—
902C23×C3—21no—
903C23×C3—21no—
904C23×C3—21no—
905C23×C3—21no—
906C23×C3—21no—
907C23×C3C2511yescharacteristic
908C3×Q8—44no—
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—21no—
922C2×C3×C4—21no—
923C2×C3×C4—21no—
924C2×C3×C4—21no—
925C2×C3×C4—21no—
926C2×C3×C4—21no—
927C2×C3×C4—21no—
928C2×C3×C4—21no—
929C2×C3×C4—21no—
930C2×C3×C4—21no—
931C2×C3×C4—21no—
932C2×C3×C4—21no—
933C2×C3×C4—21no—
934C2×C3×C4—21no—
935C2×C3×C4—21no—
936C2×C3×C4—21no—
937C2×C3×C4—21no—
938C2×C3×C4—21no—
939C2×C3×C4—21no—
940C2×C3×C4—21no—
941C2×C3×C4—21no—
942C2×C3×C4—21no—
943C2×C3×C4—21no—
944C2×C3×C4—21no—
945C2×C3×C4C22×D412yes—
946C2×C3×C4C22×D412yes—
947C2×C3×C4C22×D412yes—
948C2×C3×C4C2×#4112yes—
949C2×C3×C42−1+412yes—
950C2×C3×C42−1+412yes—
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—21no—
970C2×Dic3—21no—
971C2×Dic3—21no—
972C2×Dic3—21no—
973C2×Dic3—21no—
974C2×Dic3—21no—
975C2×Dic3—21no—
976C2×Dic3—21no—
977C2×Dic3—21no—
978C2×Dic3—21no—
979C2×Dic3—21no—
980C2×Dic3—21no—
981C2×Dic3—21no—
982C2×Dic3—21no—
983C2×Dic3—21no—
984C2×Dic3—21no—
985C2×Dic3—21no—
986C2×Dic3—21no—
987C2×Dic3—21no—
988C2×Dic3—21no—
989C2×Dic3—21no—
990C2×Dic3—21no—
991C2×Dic3—44no—
992C2×Dic3C22×D412yes—
993C2×Dic3C22×D412yes—
994C2×Dic3C22×D412yes—
995C2×Dic3C22×D412yes—
996C2×Dic3C2×#4112yes—
997C2×Dic3C2×#4112yes—
998C2×Dic32−1+412yes—
999C2×Dic32−1+412yes—
1000Dic6—28no—
1001Dic6—44no—
1002Dic6—44no—
1003Dic6—44no—
1004Dic6—44no—
1005C24C23×D311yescharacteristic
1006C2×Q8—22no—
1007C2×Q8—22no—
1008C2×Q8—34no—
1009C2×Q8—41no—
1010C2×Q8—62no—
1011C2×Q8—62no—
1012C2×Q8—62no—
1013C2×Q8—62no—
1014C2×Q8—62no—
1015C2×Q8—62no—
1016C2×Q8—62no—
1017C2×Q8—62no—
1018C2×Q8—62no—
1019C2×Q8—62no—
1020C2×Q8—62no—
1021C2×Q8—62no—
1022C2×Q8—121no—
1023C2×Q8—121no—
1024C22×C4—31no—
1025C22×C4—31no—
1026C22×C4—31no—
1027C22×C4—31no—
1028C22×C4—31no—
1029C22×C4—31no—
1030C22×C4—31no—
1031C22×C4—31no—
1032C22×C4—31no—
1033C22×C4—31no—
1034C22×C4—31no—
1035C22×C4—31no—
1036C22×C4—31no—
1037C22×C4—31no—
1038C22×C4—31no—
1039C22×C4—31no—
1040C22×C4—62no—
1041C22×C4—62no—
1042C22×C4—62no—
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
1053C22×C4C23×D311yescharacteristic
1054C22×C4C23×D311yescharacteristic
1055C22×C4C23×D311yescharacteristic
1056C22×C4C23×D311yescharacteristic
1057C4⋊C4—22no—
1058C4⋊C4—22no—
1059C4⋊C4—22no—
1060C4⋊C4—22no—
1061C4⋊C4—22no—
1062C4⋊C4—22no—
1063C4⋊C4—22no—
1064C4⋊C4—22no—
1065C4⋊C4—34no—
1066C4⋊C4—34no—
1067C4⋊C4—34no—
1068C4⋊C4—34no—
1069C4⋊C4—34no—
1070C4⋊C4—41no—
1071C4⋊C4—62no—
1072C4⋊C4—62no—
1073C4⋊C4—62no—
1074C4⋊C4—62no—
1075C4⋊C4—62no—
1076C4⋊C4—62no—
1077C4⋊C4—62no—
1078C4⋊C4—62no—
1079C4⋊C4—62no—
1080C4⋊C4—62no—
1081C4⋊C4—62no—
1082C4⋊C4—62no—
1083C4⋊C4—62no—
1084C4⋊C4—62no—
1085C4⋊C4—62no—
1086C4⋊C4—62no—
1087C4⋊C4—62no—
1088C4⋊C4—62no—
1089C4⋊C4—62no—
1090C4⋊C4—62no—
1091C4⋊C4—62no—
1092C4⋊C4—62no—
1093C4⋊C4—62no—
1094C4⋊C4—62no—
1095C4⋊C4—62no—
1096C4⋊C4—62no—
1097C4⋊C4—62no—
1098C4⋊C4—62no—
1099C4⋊C4—62no—
1100C4⋊C4—62no—
1101C4⋊C4—62no—
1102C4⋊C4—62no—
1103C4⋊C4—62no—
1104C4⋊C4—62no—
1105C4⋊C4—62no—
1106C4⋊C4—62no—
1107C4⋊C4—62no—
1108C4⋊C4—62no—
1109C4⋊C4—62no—
1110C4⋊C4—62no—
1111C4⋊C4—62no—
1112C4⋊C4—121no—
1113C4⋊C4—121no—
1114C4⋊C4—121no—
1115C4⋊C4—121no—
1116C4⋊C4D3×D414yes—
1117C22⋊C4—22no—
1118C22⋊C4—22no—
1119C22⋊C4—22no—
1120C22⋊C4—22no—
1121C22⋊C4—22no—
1122C22⋊C4—22no—
1123C22⋊C4—41no—
1124C22⋊C4—62no—
1125C22⋊C4—62no—
1126C22⋊C4—62no—
1127C22⋊C4—62no—
1128C22⋊C4—62no—
1129C22⋊C4—121no—
1130C22⋊C4—121no—
1131C42—22no—
1132C42—22no—
1133C42—22no—
1134C42—22no—
1135C42—22no—
1136C42—34no—
1137C42—62no—
1138C42—62no—
1139C42—62no—
1140C42—62no—
1141C42—62no—
1142C42—62no—
1143C42—62no—
1144C42—62no—
1145C42—62no—
1146C42—62no—
1147C42—62no—
1148C42—62no—
1149C42—121no—
1150C42—121no—
1151C42—121no—
1152C42—121no—
1153C22×C3—41no—
1154C22×C3—41no—
1155C22×C3—41no—
1156C22×C3—41no—
1157C22×C3—41no—
1158C22×C3—41no—
1159C22×C3—41no—
1160C22×C3C23×D411yescharacteristic
1161C22×C3C22×#4111yescharacteristic
1162C22×C3C2×2−1+411yescharacteristic
1163C22×C3C2×2−1+411yescharacteristic
1164C22×C3C2×2−1+411yescharacteristic
1165C22×C3C2×2−1+411yescharacteristic
1166C22×C3#58511yescharacteristic
1167C3×C4—22no—
1168C3×C4—22no—
1169C3×C4—22no—
1170C3×C4—22no—
1171C3×C4—22no—
1172C3×C4—22no—
1173C3×C4—41no—
1174C3×C4—41no—
1175C3×C4—41no—
1176C3×C4—41no—
1177C3×C4—41no—
1178C3×C4—41no—
1179C3×C4—41no—
1180C3×C4—41no—
1181Dic3—22no—
1182Dic3—22no—
1183Dic3—22no—
1184Dic3—22no—
1185Dic3—22no—
1186Dic3—41no—
1187Dic3—41no—
1188Dic3—41no—
1189Dic3—41no—
1190Dic3—41no—
1191Dic3—41no—
1192Dic3—41no—
1193Dic3—41no—
1194Dic3—41no—
1195Dic3—41no—
1196Dic3#54814yes—
1197C23—21no—
1198C23—21no—
1199C23—21no—
1200C23—21no—
1201C23—21no—
1202C23—21no—
1203C23—21no—
1204C23C24×D311yescharacteristic
1205Q8—44no—
1206Q8—68no—
1207Q8—124no—
1208Q8—124no—
1209Q8—124no—
1210Q8—124no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
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—32no—
1248C2×C4—32no—
1249C2×C4—32no—
1250C2×C4—32no—
1251C2×C4—32no—
1252C2×C4—32no—
1253C2×C4—32no—
1254C2×C4—32no—
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—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—124no—
1296C2×C4C2×D3×D412yes—
1297C2×C4C2×D3×D412yes—
1298C2×C4C2×D3×D412yes—
1299C2×C4D3×#4112yes—
1300C2×C4#101012yes—
1301C2×C4#101012yes—
1302C2×C3—81no—
1303C2×C3C2×#54811yescharacteristic
1304C2×C3#348911yescharacteristic
1305C2×C3#349911yescharacteristic
1306C2×C3#351611yescharacteristic
1307C2×C3#352311yescharacteristic
1308C2×C3#355511yescharacteristic
1309C2×C3#355611yescharacteristic
1310C22—41no—
1311C22—41no—
1312C22—41no—
1313C22—41no—
1314C22—41no—
1315C22—41no—
1316C22—41no—
1317C22C22×D3×D411yescharacteristic
1318C22C2×D3×#4111yescharacteristic
1319C22C2×#101011yescharacteristic
1320C22C2×#101011yescharacteristic
1321C22#596411yescharacteristic
1322C22D3×2−1+411yescharacteristic
1323C22D3×2−1+411yescharacteristic
1324C4—22no—
1325C4—22no—
1326C4—22no—
1327C4—22no—
1328C4—22no—
1329C4—22no—
1330C4—34no—
1331C4—41no—
1332C4—41no—
1333C4—41no—
1334C4—41no—
1335C4—41no—
1336C4—41no—
1337C4—41no—
1338C4—41no—
1339C4—62no—
1340C4—62no—
1341C4—62no—
1342C4—62no—
1343C4—62no—
1344C4—121no—
1345C4—121no—
1346C4—121no—
1347C4—121no—
1348C4—121no—
1349C4—121no—
1350C4—121no—
1351C4—121no—
1352C4—121no—
1353C4—121no—
1354C3#4534311yescharacteristic, complemented, Sylow
1355C2—81no—
1356C2#8604211yescharacteristic
1357C2#8612911yescharacteristic
1358C2#8650211yescharacteristic
1359C2#8667911yescharacteristic
1360C2D3×#54811yescharacteristic
1361C2#8698711yescharacteristic
1362C2#8699611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2469C2
prime radicalC24×C3C24
hypercenter#2469D3
hypocenterC3#45343
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2469

Complements

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

NH ≅ G/Ntype
2. C2×#5567C2semidirect
5. #82471C2semidirect
6. #78181C2semidirect
7. #78137C2semidirect
10. #77185C2semidirect
11. #77175C2semidirect
14. #76117C2semidirect
15. #76060C2semidirect
24. #75168C2semidirect
25. #75166C2semidirect
26. #75165C2semidirect
27. #74988C2semidirect
28. #74969C2semidirect
29. #74967C2semidirect
30. #73713C2semidirect
31. #73652C2semidirect
1354. C3#45343semidirect

Maximal subgroups

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

subgroupindex
C2×#57012
C2×#55672
C3×#24692
#831012
#824712
#781812
#781372
#772982
#772822
#771852
#771752
#768302
#767932
#761172
#760602
#757022
#756952
#755652
#755642
#755442
#755002
#754602
#751682
#751662
#751652
#749882
#749692
#749672
#737132
#736522
#453433