Finite Group Databasebeta

← #11233282

Subgroups — #11233282

Order 768.

1922 conjugacy classes of subgroups.

The subgroup lattice has 1320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5685C211yesmaximal, characteristic
2C2×#5569C211yesmaximal, characteristic
3C3×#2462C211yesmaximal, characteristic
4#83049C211yesmaximal, characteristic
5#82472C211yesmaximal, characteristic
6#77859C211yesmaximal, characteristic
7#77785C211yesmaximal, characteristic
8#77752C211yesmaximal, characteristic
9#77747C211yesmaximal, characteristic
10#77191C211yesmaximal, characteristic
11#77178C211yesmaximal, characteristic
12#77177C211yesmaximal, characteristic
13#77171C211yesmaximal, characteristic
14#76118C211yesmaximal, characteristic
15#76117C211yesmaximal, characteristic
16#76060C211yesmaximal, characteristic
17#75982C211yesmaximal, characteristic
18#75168C211yesmaximal, characteristic
19#75167C211yesmaximal, characteristic
20#75166C211yesmaximal, characteristic
21#75165C211yesmaximal, characteristic
22#75090C211yesmaximal, characteristic
23#74998C211yesmaximal, characteristic
24#74993C211yesmaximal, characteristic
25#74986C211yesmaximal, characteristic
26#74985C211yesmaximal, characteristic
27#74985C211yesmaximal, characteristic
28#74948C211yesmaximal, characteristic
29#74948C211yesmaximal, characteristic
30#73678C211yesmaximal, characteristic
31#73637C211yesmaximal, characteristic
32#45334—31nomaximal, Sylow
33C2×C3×#125C2211yescharacteristic
34C2×C3×C4×Q8C2211yescharacteristic
35C2×Q8×Dic3C2211yescharacteristic
36C2×Q8×Dic3C2211yescharacteristic
37#5685—28no—
38#5569—28no—
39C2×#890C2211yescharacteristic
40C2×#890C2211yescharacteristic
41C2×#890C2211yescharacteristic
42C2×#890C2211yescharacteristic
43C2×#889C2211yescharacteristic
44C2×#889C2211yescharacteristic
45C2×#889C2211yescharacteristic
46C2×#889C2211yescharacteristic
47C2×#888C2211yescharacteristic
48C2×#888C2211yescharacteristic
49C2×#888C2211yescharacteristic
50C2×#888C2211yescharacteristic
51C2×#888C2211yescharacteristic
52C2×#888C2211yescharacteristic
53C2×#887C2211yescharacteristic
54C2×#887C2211yescharacteristic
55C2×#887C2211yescharacteristic
56C2×#887C2211yescharacteristic
57C2×#887C2211yescharacteristic
58C2×#870C2211yescharacteristic
59C2×#870C2211yescharacteristic
60C2×#870C2211yescharacteristic
61C2×C4×Dic6C2211yescharacteristic
62C2×C4×Dic6C2211yescharacteristic
63C2×C4×Dic6C2211yescharacteristic
64C2×C4×Dic6C2211yescharacteristic
65C2×C4×Dic6C2211yescharacteristic
66C2×C4×Dic6C2211yescharacteristic
67C3×#398C2211yescharacteristic
68C3×#398C2211yescharacteristic
69C3×#395C2211yescharacteristic
70C3×#395C2211yescharacteristic
71C3×#389C2211yescharacteristic
72C3×#389C2211yescharacteristic
73C3×#387C2211yescharacteristic
74C3×#387C2211yescharacteristic
75C3×#387C2211yescharacteristic
76C3×#387C2211yescharacteristic
77C3×#387C2211yescharacteristic
78C3×#387C2211yescharacteristic
79C3×C4×C4⋊C4C2211yescharacteristic
80#5230C2211yescharacteristic
81#5230C2211yescharacteristic
82#4986C2211yescharacteristic
83#4986C2211yescharacteristic
84#4985C2211yescharacteristic
85#4984C2211yescharacteristic
86#4984C2211yescharacteristic
87#4983C2211yescharacteristic
88#4982C2211yescharacteristic
89#4982C2211yescharacteristic
90#4982C2211yescharacteristic
91#4982C2211yescharacteristic
92#4982C2211yescharacteristic
93#4982C2211yescharacteristic
94#4982C2211yescharacteristic
95#4981C2211yescharacteristic
96#4981C2211yescharacteristic
97#4981C2211yescharacteristic
98#4981C2211yescharacteristic
99#4980C2211yescharacteristic
100#4980C2211yescharacteristic
101#4980C2211yescharacteristic
102#4980C2211yescharacteristic
103#4980C2211yescharacteristic
104#4980C2211yescharacteristic
105#4979C2211yescharacteristic
106#4978C2211yescharacteristic
107#4978C2211yescharacteristic
108#4978C2211yescharacteristic
109#4978C2211yescharacteristic
110#4977C2211yescharacteristic
111#4976C2211yescharacteristic
112#4976C2211yescharacteristic
113#4976C2211yescharacteristic
114#4976C2211yescharacteristic
115#4976C2211yescharacteristic
116#4976C2211yescharacteristic
117#4976C2211yescharacteristic
118#4976C2211yescharacteristic
119Dic3×C4⋊C4C2211yescharacteristic
120Dic3×C4⋊C4C2211yescharacteristic
121Dic3×C4⋊C4C2211yescharacteristic
122#4972C2211yescharacteristic
123#4936C2211yescharacteristic
124#4933C2211yescharacteristic
125#4933C2211yescharacteristic
126#4933C2211yescharacteristic
127#4933C2211yescharacteristic
128#4933C2211yescharacteristic
129#4933C2211yescharacteristic
130C4×Dic3⋊C4C2211yescharacteristic
131#4928C2211yescharacteristic
132#4928C2211yescharacteristic
133#4928C2211yescharacteristic
134#4661C2211yescharacteristic
135#4661C2211yescharacteristic
136#4661C2211yescharacteristic
137#4660C2211yescharacteristic
138#4660C2211yescharacteristic
139#4659C2211yescharacteristic
140#4659C2211yescharacteristic
141#4659C2211yescharacteristic
142#4658C2211yescharacteristic
143#4658C2211yescharacteristic
144#4658C2211yescharacteristic
145#4658C2211yescharacteristic
146#4657C2211yescharacteristic
147#4657C2211yescharacteristic
148#4657C2211yescharacteristic
149#4656C2211yescharacteristic
150#4656C2211yescharacteristic
151#4656C2211yescharacteristic
152#4655C2211yescharacteristic
153#4655C2211yescharacteristic
154#4655C2211yescharacteristic
155#4655C2211yescharacteristic
156#4655C2211yescharacteristic
157#4655C2211yescharacteristic
158#4654C2211yescharacteristic
159#4654C2211yescharacteristic
160#4654C2211yescharacteristic
161#4654C2211yescharacteristic
162#4653C2211yescharacteristic
163#4653C2211yescharacteristic
164#4653C2211yescharacteristic
165#4653C2211yescharacteristic
166#4652C2211yescharacteristic
167#4652C2211yescharacteristic
168#4652C2211yescharacteristic
169#4652C2211yescharacteristic
170#4650C2211yescharacteristic
171#4650C2211yescharacteristic
172#4650C2211yescharacteristic
173#4650C2211yescharacteristic
174#4649C2211yescharacteristic
175#4649C2211yescharacteristic
176#4649C2211yescharacteristic
177#4648C2211yescharacteristic
178#4647C2211yescharacteristic
179#4647C2211yescharacteristic
180#4647C2211yescharacteristic
181#4647C2211yescharacteristic
182#4646C2211yescharacteristic
183#4646C2211yescharacteristic
184#4646C2211yescharacteristic
185#4646C2211yescharacteristic
186#4646C2211yescharacteristic
187#4646C2211yescharacteristic
188#4646C2211yescharacteristic
189#4646C2211yescharacteristic
190C2×#557—31no—
191C2×#557—31no—
192#2719—31no—
193#2719—31no—
194#2719—31no—
195#2719—31no—
196#2719—31no—
197#2719—31no—
198#2719—31no—
199#2719—31no—
200#2581—31no—
201#2581—31no—
202#2546—31no—
203#2546—31no—
204#2462—31no—
205#2462—31no—
206#2462—31no—
207#2462—31no—
208#2462—31no—
209#2462—31no—
210#2462—31no—
211#2462D311yescharacteristic
212#2446—31no—
213#2446—31no—
214#2446—31no—
215#2446—31no—
216#2399—31no—
217#2351—31no—
218#2351—31no—
219#2327—31no—
220#2327—31no—
221C22×C3×Q8C2311yescharacteristic
222C22×Dic6C2311yescharacteristic
223C22×Dic6C2311yescharacteristic
224C22×Dic6C2311yescharacteristic
225C22×Dic6C2311yescharacteristic
226C22×Dic6C2311yescharacteristic
227C3×#125—24no—
228C3×C4×Q8—24no—
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×C3×C42C2311yescharacteristic
248C2×C3×C42C2311yescharacteristic
249Q8×Dic3—24no—
250Q8×Dic3—24no—
251C2×C4⋊Dic3C2311yescharacteristic
252C2×C4⋊Dic3C2311yescharacteristic
253C2×C4⋊Dic3C2311yescharacteristic
254C2×C4⋊Dic3C2311yescharacteristic
255C2×C4⋊Dic3C2311yescharacteristic
256C2×C4⋊Dic3C2311yescharacteristic
257C2×C4⋊Dic3C2311yescharacteristic
258C2×C4⋊Dic3C2311yescharacteristic
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×Dic3⋊C4C2311yescharacteristic
269C2×Dic3⋊C4C2311yescharacteristic
270C2×Dic3⋊C4C2311yescharacteristic
271C2×Dic3⋊C4C2311yescharacteristic
272C2×Dic3⋊C4C2311yescharacteristic
273C2×Dic3⋊C4C2311yescharacteristic
274C2×Dic3⋊C4C2311yescharacteristic
275C2×Dic3⋊C4C2311yescharacteristic
276C2×Dic3⋊C4C2311yescharacteristic
277C2×Dic3⋊C4C2311yescharacteristic
278C2×Dic3⋊C4C2311yescharacteristic
279C2×Dic3⋊C4C2311yescharacteristic
280C2×Dic3⋊C4C2311yescharacteristic
281C2×Dic3⋊C4C2311yescharacteristic
282C2×Dic3⋊C4C2311yescharacteristic
283C2×Dic3⋊C4C2311yescharacteristic
284C2×Dic3⋊C4C2311yescharacteristic
285C2×Dic3⋊C4C2311yescharacteristic
286C2×Dic3⋊C4C2311yescharacteristic
287C2×Dic3⋊C4C2311yescharacteristic
288C2×Dic3⋊C4C2311yescharacteristic
289C2×Dic3⋊C4C2311yescharacteristic
290C2×Dic3⋊C4C2311yescharacteristic
291C2×Dic3⋊C4C2311yescharacteristic
292C2×Dic3⋊C4C2311yescharacteristic
293C2×Dic3⋊C4C2311yescharacteristic
294C2×Dic3⋊C4C2311yescharacteristic
295C2×Dic3⋊C4C2311yescharacteristic
296C2×Dic3⋊C4C2311yescharacteristic
297C2×Dic3⋊C4C2311yescharacteristic
298C2×Dic3⋊C4C2311yescharacteristic
299C2×Dic3⋊C4C2311yescharacteristic
300C2×Dic3⋊C4C2311yescharacteristic
301C2×Dic3⋊C4C2311yescharacteristic
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
318C2×C4×Dic3C2311yescharacteristic
319C2×C4×Dic3C2311yescharacteristic
320#890—24no—
321#890—24no—
322#890—24no—
323#890—24no—
324#889—24no—
325#889—24no—
326#889—24no—
327#889—24no—
328#888—24no—
329#888—24no—
330#888—24no—
331#888—24no—
332#888—24no—
333#888D418yes—
334#887—24no—
335#887—24no—
336#887—24no—
337#887—24no—
338#887—24no—
339#870—24no—
340#870—24no—
341#870—24no—
342C4×Dic6—24no—
343C4×Dic6—24no—
344C4×Dic6—24no—
345C4×Dic6—24no—
346C4×Dic6—24no—
347C4×Dic6—24no—
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
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#557—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×#125—31no—
417C2×#125—31no—
418C2×#125—31no—
419C2×#125—31no—
420C2×#125—31no—
421C2×#125—31no—
422C2×#125—31no—
423C2×#125—31no—
424C2×#125—31no—
425C2×#125—31no—
426C2×#125—31no—
427C2×#125C2×D311yescharacteristic
428C2×C4×Q8—31no—
429C2×C4×Q8—31no—
430C2×C4×Q8—31no—
431C2×C4×Q8—31no—
432C2×C4×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×Q8—31no—
441C2×C4×Q8C2×D311yescharacteristic
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#400—31no—
453#400—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#398—31no—
469#398—31no—
470#398—31no—
471#398—31no—
472#398C2×D311yescharacteristic
473#398C2×D311yescharacteristic
474#395—31no—
475#395—31no—
476#395—31no—
477#395—31no—
478#395—31no—
479#395—31no—
480#395C2×D311yescharacteristic
481#395C2×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#389—31no—
491#389—31no—
492#389—31no—
493#389—31no—
494#389—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#389C2×D311yescharacteristic
509#389C2×D311yescharacteristic
510#387—31no—
511#387—31no—
512#387—31no—
513#387—31no—
514#387—31no—
515#387—31no—
516#387—31no—
517#387—31no—
518#387—31no—
519#387—31no—
520#387—31no—
521#387—31no—
522#387—31no—
523#387—31no—
524#387—31no—
525#387—31no—
526#387—31no—
527#387—31no—
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#387—31no—
544#387C2×D311yescharacteristic
545#387C2×D311yescharacteristic
546#387C2×D311yescharacteristic
547#387C2×D311yescharacteristic
548#387C2×D311yescharacteristic
549#387C2×D311yescharacteristic
550#382—31no—
551#382—31no—
552#382—31no—
553#382—31no—
554#382—31no—
555#382—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⋊C4—31no—
563C4×C4⋊C4C2×D311yescharacteristic
564#376—31no—
565C2×C3×Q8—22no—
566C2×C3×Q8—22no—
567C2×C3×Q8—22no—
568C22×C3×C4C2411yescharacteristic
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×Dic3C2411yescharacteristic
584C22×Dic3C2411yescharacteristic
585C22×Dic3C2411yescharacteristic
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
599C2×Dic6—22no—
600C2×Dic6—22no—
601C2×Dic6—22no—
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×Dic6C2×D414yes—
613C2×Dic6C2×D414yes—
614C3×C4⋊C4—22no—
615C3×C4⋊C4—22no—
616C3×C4⋊C4—22no—
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—22no—
626C3×C4⋊C4—22no—
627C3×C4⋊C4—22no—
628C3×C4⋊C4C2×D414yes—
629C3×C42—22no—
630C3×C42—22no—
631C3×C42—22no—
632C3×C42—22no—
633C3×C42—22no—
634C4⋊Dic3—22no—
635C4⋊Dic3—22no—
636C4⋊Dic3—22no—
637C4⋊Dic3—22no—
638C4⋊Dic3—22no—
639C4⋊Dic3—22no—
640C4⋊Dic3—22no—
641C4⋊Dic3—22no—
642C4⋊Dic3—22no—
643C4⋊Dic3—22no—
644C4⋊Dic3—22no—
645C4⋊Dic3—22no—
646C4⋊Dic3—22no—
647C4⋊Dic3—22no—
648C4⋊Dic3—22no—
649C4⋊Dic3—22no—
650C4⋊Dic3C2×D414yes—
651Dic3⋊C4—22no—
652Dic3⋊C4—22no—
653Dic3⋊C4—22no—
654Dic3⋊C4—22no—
655Dic3⋊C4—22no—
656Dic3⋊C4—22no—
657Dic3⋊C4—22no—
658Dic3⋊C4—22no—
659Dic3⋊C4—22no—
660Dic3⋊C4—22no—
661Dic3⋊C4—22no—
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⋊C4C2×D414yes—
684Dic3⋊C4C2×D414yes—
685C4×Dic3—22no—
686C4×Dic3—22no—
687C4×Dic3—22no—
688C4×Dic3—22no—
689C4×Dic3—22no—
690C4×Dic3—22no—
691C4×Dic3—22no—
692C4×Dic3—22no—
693C4×Dic3—22no—
694C4×Dic3—22no—
695C4×Dic3—22no—
696C4×Dic3—22no—
697C4×Dic3—22no—
698C4×Dic3—22no—
699C4×Dic3—22no—
700C4×Dic3—22no—
701C4×Dic3C2×D414yes—
702C4×Dic3#4114yes—
703C22×Q8—31no—
704C22×Q8—31no—
705C22×Q8—31no—
706C22×Q8—31no—
707C22×Q8—31no—
708C22×Q8C22×D311yescharacteristic
709C4⋊Q8—38no—
710C4⋊Q8—64no—
711C4⋊Q8—64no—
712C4⋊Q8—64no—
713C4⋊Q8—64no—
714C4⋊Q8—64no—
715#125—24no—
716#125—64no—
717#125—64no—
718#125—64no—
719#125—64no—
720#125—64no—
721#125—64no—
722#125—64no—
723#125—64no—
724#125—64no—
725#125—64no—
726#125—64no—
727C4×Q8—24no—
728C4×Q8—64no—
729C4×Q8—64no—
730C4×Q8—64no—
731C4×Q8—64no—
732C4×Q8—64no—
733C4×Q8—64no—
734C4×Q8—64no—
735C4×Q8—64no—
736C4×Q8—64no—
737C4×Q8—64no—
738C4×Q8—64no—
739C4×Q8—64no—
740C4×Q8—64no—
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—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⋊C4C22×D311yescharacteristic
793C2×C4⋊C4C22×D311yescharacteristic
794C2×C4⋊C4C22×D311yescharacteristic
795C2×C4⋊C4C22×D311yescharacteristic
796C2×C4⋊C4C22×D311yescharacteristic
797C2×C4⋊C4C22×D311yescharacteristic
798C2×C4⋊C4C22×D311yescharacteristic
799C2×C4⋊C4C22×D311yescharacteristic
800C2×C4⋊C4C22×D311yescharacteristic
801C2×C4⋊C4C22×D311yescharacteristic
802C2×C4⋊C4C22×D311yescharacteristic
803C2×C4⋊C4C22×D311yescharacteristic
804C2×C4⋊C4C22×D311yescharacteristic
805C2×C4⋊C4C22×D311yescharacteristic
806C2×C4⋊C4C22×D311yescharacteristic
807C2×C42—31no—
808C2×C42—31no—
809C2×C42—31no—
810C2×C42—31no—
811C2×C42—31no—
812C2×C42—31no—
813C2×C42—31no—
814C2×C42—31no—
815C2×C42—31no—
816C2×C42—31no—
817C2×C42—31no—
818C2×C42—31no—
819C2×C42—31no—
820C2×C42—31no—
821C2×C42—31no—
822C2×C42—31no—
823C2×C42—31no—
824C2×C42—31no—
825C2×C42C22×D311yescharacteristic
826C2×C42C22×D311yescharacteristic
827C2×C42C22×D311yescharacteristic
828C2×C42C22×D311yescharacteristic
829C2×C42C22×D311yescharacteristic
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#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#95C22×D311yescharacteristic
877#95C22×D311yescharacteristic
878#95C22×D311yescharacteristic
879#95C22×D311yescharacteristic
880#95C22×D311yescharacteristic
881#95C22×D311yescharacteristic
882#95C22×D311yescharacteristic
883#95C22×D311yescharacteristic
884#95C22×D311yescharacteristic
885#95C22×D311yescharacteristic
886#95C22×D311yescharacteristic
887#95C22×D311yescharacteristic
888#95C22×D311yescharacteristic
889#95C22×D311yescharacteristic
890C23×C3C2511yescharacteristic
891C3×Q8—28no—
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—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×C4C22×D412yes—
931C2×C3×C4C22×D412yes—
932C2×C3×C4C22×D412yes—
933C2×C3×C4C2×#4112yes—
934C2×C3×C42−1+412yes—
935C2×C3×C42−1+412yes—
936C2×C3×C42−1+412yes—
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—21no—
970C2×Dic3—21no—
971C2×Dic3—21no—
972C2×Dic3—21no—
973C2×Dic3—21no—
974C2×Dic3—21no—
975C2×Dic3—21no—
976C2×Dic3—21no—
977C2×Dic3C22×D412yes—
978C2×Dic3C22×D412yes—
979C2×Dic3C22×D412yes—
980C2×Dic3C22×D412yes—
981C2×Dic3C2×#4112yes—
982C2×Dic3C2×#4112yes—
983C2×Dic32−1+412yes—
984C2×Dic32−1+412yes—
985Dic6—28no—
986Dic6—28no—
987Dic6—28no—
988Dic6—44no—
989Dic6—44no—
990C2×Q8—22no—
991C2×Q8—22no—
992C2×Q8—22no—
993C2×Q8—34no—
994C2×Q8—34no—
995C2×Q8—62no—
996C2×Q8—62no—
997C2×Q8—62no—
998C2×Q8—62no—
999C2×Q8—62no—
1000C2×Q8—62no—
1001C2×Q8—62no—
1002C2×Q8—62no—
1003C2×Q8—62no—
1004C2×Q8—62no—
1005C2×Q8—62no—
1006C2×Q8—62no—
1007C2×Q8—62no—
1008C22×C4—31no—
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—31no—
1021C22×C4—31no—
1022C22×C4—31no—
1023C22×C4—31no—
1024C22×C4C23×D311yescharacteristic
1025C22×C4C23×D311yescharacteristic
1026C22×C4C23×D311yescharacteristic
1027C22×C4C23×D311yescharacteristic
1028C22×C4C23×D311yescharacteristic
1029C22×C4C23×D311yescharacteristic
1030C22×C4C23×D311yescharacteristic
1031C22×C4C23×D311yescharacteristic
1032C22×C4C23×D311yescharacteristic
1033C22×C4C23×D311yescharacteristic
1034C22×C4C23×D311yescharacteristic
1035C22×C4C23×D311yescharacteristic
1036C22×C4C23×D311yescharacteristic
1037C22×C4C23×D311yescharacteristic
1038C22×C4C23×D311yescharacteristic
1039C4⋊C4—22no—
1040C4⋊C4—22no—
1041C4⋊C4—22no—
1042C4⋊C4—22no—
1043C4⋊C4—22no—
1044C4⋊C4—22no—
1045C4⋊C4—22no—
1046C4⋊C4—22no—
1047C4⋊C4—22no—
1048C4⋊C4—22no—
1049C4⋊C4—22no—
1050C4⋊C4—22no—
1051C4⋊C4—22no—
1052C4⋊C4—22no—
1053C4⋊C4—34no—
1054C4⋊C4—34no—
1055C4⋊C4—34no—
1056C4⋊C4—62no—
1057C4⋊C4—62no—
1058C4⋊C4—62no—
1059C4⋊C4—62no—
1060C4⋊C4—62no—
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—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⋊C4D3×D414yes—
1105C42—22no—
1106C42—22no—
1107C42—22no—
1108C42—22no—
1109C42—22no—
1110C42—34no—
1111C42—34no—
1112C42—62no—
1113C42—62no—
1114C42—62no—
1115C42—62no—
1116C42—62no—
1117C42—62no—
1118C42—62no—
1119C42—62no—
1120C42—62no—
1121C42—62no—
1122C42—62no—
1123C42—62no—
1124C42—62no—
1125C42—62no—
1126C42—62no—
1127C42—62no—
1128C22×C3C23×D411yescharacteristic
1129C22×C3C22×#4111yescharacteristic
1130C22×C3C2×2−1+411yescharacteristic
1131C22×C3C2×2−1+411yescharacteristic
1132C22×C3C2×2−1+411yescharacteristic
1133C22×C3C2×2−1+411yescharacteristic
1134C22×C3C2×2−1+411yescharacteristic
1135C3×C4—22no—
1136C3×C4—22no—
1137C3×C4—22no—
1138C3×C4—22no—
1139C3×C4—22no—
1140C3×C4—22no—
1141C3×C4—22no—
1142C3×C4—41no—
1143C3×C4—41no—
1144C3×C4—41no—
1145C3×C4—41no—
1146C3×C4—41no—
1147C3×C4—41no—
1148C3×C4—41no—
1149C3×C4—41no—
1150Dic3—22no—
1151Dic3—22no—
1152Dic3—22no—
1153Dic3—22no—
1154Dic3—22no—
1155Dic3—41no—
1156Dic3—41no—
1157Dic3—41no—
1158Dic3—41no—
1159Dic3—41no—
1160Dic3—41no—
1161Dic3—41no—
1162Dic3—41no—
1163Dic3—41no—
1164Dic3—41no—
1165Dic3#54714yes—
1166C23C24×D311yescharacteristic
1167Q8—28no—
1168Q8—68no—
1169Q8—68no—
1170Q8—68no—
1171Q8—124no—
1172Q8—124no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—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—32no—
1212C2×C4—32no—
1213C2×C4—32no—
1214C2×C4—32no—
1215C2×C4—32no—
1216C2×C4—32no—
1217C2×C4—32no—
1218C2×C4—32no—
1219C2×C4—61no—
1220C2×C4—61no—
1221C2×C4—61no—
1222C2×C4—61no—
1223C2×C4—61no—
1224C2×C4—61no—
1225C2×C4—61no—
1226C2×C4—61no—
1227C2×C4—61no—
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×C4C2×D3×D412yes—
1260C2×C4C2×D3×D412yes—
1261C2×C4C2×D3×D412yes—
1262C2×C4#100712yes—
1263C2×C4D3×#4112yes—
1264C2×C4#101012yes—
1265C2×C4#101012yes—
1266C2×C3C2×#54711yescharacteristic
1267C2×C3#348611yescharacteristic
1268C2×C3#348611yescharacteristic
1269C2×C3#350911yescharacteristic
1270C2×C3#350911yescharacteristic
1271C2×C3#355611yescharacteristic
1272C2×C3#355611yescharacteristic
1273C22C22×D3×D411yescharacteristic
1274C22C2×#100711yescharacteristic
1275C22C2×D3×#4111yescharacteristic
1276C22C2×#101011yescharacteristic
1277C22C2×#101011yescharacteristic
1278C22D3×2−1+411yescharacteristic
1279C22D3×2−1+411yescharacteristic
1280C4—22no—
1281C4—22no—
1282C4—22no—
1283C4—22no—
1284C4—22no—
1285C4—22no—
1286C4—22no—
1287C4—34no—
1288C4—41no—
1289C4—41no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—41no—
1294C4—41no—
1295C4—41no—
1296C4—62no—
1297C4—62no—
1298C4—62no—
1299C4—62no—
1300C4—62no—
1301C4—121no—
1302C4—121no—
1303C4—121no—
1304C4—121no—
1305C4—121no—
1306C4—121no—
1307C4—121no—
1308C4—121no—
1309C4—121no—
1310C4—121no—
1311C3#4533411yescharacteristic, complemented, Sylow
1312C2#8602211yescharacteristic
1313C2#8628311yescharacteristic
1314C2#8650211yescharacteristic
1315C2D3×#54711yescharacteristic
1316C2#8675911yescharacteristic
1317C2#8683211yescharacteristic
1318C2#8702711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, prime radical, cosocleC23×C3C25
FittingC3×#2462C2
hypercenter#2462D3
hypocenterC3#45334
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2462

Complements

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

NH ≅ G/Ntype
1311. C3#45334semidirect

Maximal subgroups

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

subgroupindex
C2×#56852
C2×#55692
C3×#24622
#830492
#824722
#778592
#777852
#777522
#777472
#771912
#771782
#771772
#771712
#761182
#761172
#760602
#759822
#751682
#751672
#751662
#751652
#750902
#749982
#749932
#749862
#749852
#749482
#736782
#736372
#453343