Finite Group Databasebeta

← #11634064

Subgroups — #11634064

Order 768.

2842 conjugacy classes of subgroups.

The subgroup lattice has 1226 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5550C211yesmaximal, characteristic, complemented
2C2×#5479C211yesmaximal, characteristic, complemented
3C3×C4×#123C211yesmaximal, characteristic, complemented
4#82901C212yesmaximal, complemented
5#82352C211yesmaximal, characteristic, complemented
6C2×#4939C211yesmaximal, characteristic, complemented
7#75930C212yesmaximal, complemented
8#75495C212yesmaximal, complemented
9#75153C212yesmaximal, complemented
10#75007C212yesmaximal, complemented
11#74893C212yesmaximal, complemented
12#74596C212yesmaximal, complemented
13#74126C212yesmaximal, complemented
14#73712C211yesmaximal, characteristic, complemented
15#73677C211yesmaximal, characteristic, complemented
16#73673C211yesmaximal, characteristic, complemented
17#73653C211yesmaximal, characteristic, complemented
18#73587C211yesmaximal, characteristic, complemented
19#73586C211yesmaximal, characteristic, complemented
20#73506C211yesmaximal, characteristic, complemented
21#73487C211yesmaximal, characteristic, complemented
22#73465C211yesmaximal, characteristic, complemented
23#73454C211yesmaximal, characteristic, complemented
24#59046—31nomaximal, Sylow
25C22×#235C2211yescharacteristic
26C23×D12C2211yescharacteristic
27C2×C3×#123C2211yescharacteristic
28C2×C3×C4×D4C2211yescharacteristic
29C22×C3×C42C2211yescharacteristic
30C2×#939C2212yes—
31C2×#937C2212yes—
32C2×#930C2211yescharacteristic
33C2×#930C2211yescharacteristic
34C2×#930C2211yescharacteristic, complemented
35C2×#929C2212yes—
36C2×C4×#67C2212yes—
37C22×(C2×D3)⋊C4C2212yes—
38C22×(C2×D3)⋊C4C2212yes—
39C22×C4⋊Dic3C2211yescharacteristic
40C2×#924C2211yescharacteristic
41#5550—28no—
42C2×#894C2212yes—
43C2×#893C2212yescomplemented
44C2×#884C2212yes—
45C2×#884C2212yescomplemented
46C2×#882C2212yes—
47C2×#882C2212yes—
48C2×D3×C22⋊C4C2212yes—
49#5479—28no—
50C2×#876C2212yescomplemented
51C2×#875C2211yescharacteristic
52C2×#875C2211yescharacteristic, complemented
53C2×#874C2211yescharacteristic
54C2×#874C2211yescharacteristic
55C2×C4×D12C2211yescharacteristic
56C2×C4×D12C2211yescharacteristic, complemented
57C2×#872C2212yescomplemented
58C2×#870C2211yescharacteristic, complemented
59C2×C4×Dic6C2211yescharacteristic, complemented
60C2×C4×Dic6C2211yescharacteristic, complemented
61C3×#388C2211yescharacteristic, complemented
62C3×#388C2211yescharacteristic, complemented
63C3×#387C2211yescharacteristic, complemented
64C3×#387C2211yescharacteristic, complemented
65C3×#386C2211yescharacteristic
66C3×#385C2211yescharacteristic
67C3×#381C2211yescharacteristic
68C3×C4×C4⋊C4C2211yescharacteristic, complemented
69C3×C4×C4⋊C4C2211yescharacteristic, complemented
70C3×C4×C22⋊C4C2211yescharacteristic
71C3×C4×C22⋊C4C2211yescharacteristic, complemented
72C3×C4×C22⋊C4C2211yescharacteristic, complemented
73#5212C2211yescharacteristic, complemented
74#4994C2212yescomplemented
75#4993C2212yescomplemented
76#4993C2212yescomplemented
77#4990C2212yescomplemented
78#4989C2212yescomplemented
79#4988C2212yescomplemented
80#4988C2212yescomplemented
81#4988C2212yescomplemented
82#4961C2212yescomplemented
83#4960C2212yescomplemented
84#4960C2212yescomplemented
85#4960C2212yescomplemented
86#4959C2212yescomplemented
87#4958C2212yes—
88#4957C2212yescomplemented
89#4957C2212yescomplemented
90#4957C2212yescomplemented
91#4946C2212yes—
92Dic3×C22⋊C4C2212yes—
93#4939C2211yescharacteristic
94#4939C2211yescharacteristic
95#4939C2211yescharacteristic
96#4939C2211yescharacteristic
97#4939C2211yescharacteristic
98#4939C2212yes—
99#4939C2211yescharacteristic
100#4939C2212yes—
101#4939C2211yescharacteristic, complemented
102C4×C4⋊Dic3C2211yescharacteristic, complemented
103#4929C2211yescharacteristic, complemented
104#4928C2211yescharacteristic, complemented
105#4928C2211yescharacteristic, complemented
106#4676C2212yescomplemented
107#4675C2212yescomplemented
108#4675C2212yescomplemented
109#4672C2212yescomplemented
110#4672C2212yescomplemented
111#4672C2212yescomplemented
112#4671C2212yes—
113#4671C2212yes—
114#4669C2212yescomplemented
115#4669C2212yescomplemented
116#4667C2212yescomplemented
117#4667C2212yescomplemented
118#4666C2212yescomplemented
119#4665C2212yescomplemented
120#4665C2212yescomplemented
121#4665C2212yescomplemented
122#4665C2212yescomplemented
123#4665C2212yescomplemented
124#4655C2212yescomplemented
125#4647C2212yescomplemented
126C2×#546—31no—
127C2×#529—31no—
128#2714—32no—
129#2705—32no—
130#2548—31no—
131#2539—32no—
132#2490—31no—
133#2471—32no—
134#2454—31no—
135#2448—31no—
136#2433—31no—
137#2431—31no—
138#2428—31no—
139#2424—32no—
140#2416—31no—
141#2414—32no—
142#2412—32no—
143#2366—31no—
144#2360—31no—
145#2358—32no—
146#2341—31no—
147C4×#123D311yescharacteristic, complemented
148C2×#390—31no—
149C24×D3C2312yes—
150C22×C3×D4C2311yescharacteristic
151C23×C3×C4C2311yescharacteristic
152C23×C3×C4C2311yescharacteristic
153C23×C3×C4C2311yescharacteristic
154C23×C3×C4C2311yescharacteristic
155C22×#67C2312yes—
156C22×#67C2312yes—
157C22×#67C2312yes—
158C22×#67C2312yes—
159C23×Dic3C2312yes—
160C2×#235—24no—
161C2×#235—24no—
162C2×#235—42no—
163C22×D12—24no—
164C22×D12—24no—
165C22×D12—42no—
166C22×D12C2311yescharacteristic
167C22×D12C2311yescharacteristic
168C22×D12C2312yes—
169C22×D12C2312yes—
170C22×D12C2311yescharacteristic
171C22×D12C2312yes—
172C22×D12C2312yes—
173C22×D12C2312yes—
174C22×C4×D3C2312yes—
175C22×C4×D3C2312yes—
176C22×C4×D3C2312yes—
177C22×Dic6C2311yescharacteristic
178C3×#123—24no—
179C3×C4×D4—24no—
180C2×C3×C4⋊C4C2311yescharacteristic
181C2×C3×C4⋊C4C2311yescharacteristic
182C2×C3×C4⋊C4C2311yescharacteristic
183C2×C3×C4⋊C4C2311yescharacteristic
184C2×C3×C4⋊C4C2311yescharacteristic
185C2×C3×C22⋊C4C2311yescharacteristic
186C2×C3×C22⋊C4C2311yescharacteristic
187C2×C3×C22⋊C4C2311yescharacteristic
188C2×C3×C22⋊C4C2311yescharacteristic
189C2×C3×C22⋊C4C2311yescharacteristic
190C2×C3×C22⋊C4C2311yescharacteristic
191C2×C3×C22⋊C4C2311yescharacteristic
192C2×C3×C22⋊C4C2311yescharacteristic
193C2×C3×C42—24no—
194C2×C3×C42C2311yescharacteristic
195C2×C3×C42C2311yescharacteristic
196C2×C3×C42C2311yescharacteristic
197C2×C3×C42C2311yescharacteristic
198C2×C3×C42C2311yescharacteristic
199C2×C3×C42C2311yescharacteristic
200C2×C3×C42C2311yescharacteristic
201C2×#217C2312yes—
202C2×#217C2312yes—
203#939—44no—
204#937—28no—
205#930—24no—
206#930—24no—
207#930—42no—
208#929—28no—
209C4×#67—28no—
210C2×(C2×D3)⋊C4—44no—
211C2×(C2×D3)⋊C4—44no—
212C2×(C2×D3)⋊C4C2312yes—
213C2×(C2×D3)⋊C4C2312yes—
214C2×(C2×D3)⋊C4C2312yes—
215C2×(C2×D3)⋊C4C2312yes—
216C2×(C2×D3)⋊C4C2312yes—
217C2×(C2×D3)⋊C4C2312yes—
218C2×(C2×D3)⋊C4C2312yes—
219C2×(C2×D3)⋊C4C2312yes—
220C2×(C2×D3)⋊C4C2312yes—
221C2×(C2×D3)⋊C4C2312yes—
222C2×(C2×D3)⋊C4C2312yes—
223C2×(C2×D3)⋊C4C2312yes—
224C2×(C2×D3)⋊C4C2312yes—
225C2×(C2×D3)⋊C4C2312yes—
226C2×(C2×D3)⋊C4C2312yes—
227C2×(C2×D3)⋊C4C2312yes—
228C2×(C2×D3)⋊C4C2312yes—
229C2×(C2×D3)⋊C4C2312yes—
230C2×(C2×D3)⋊C4C2312yes—
231C2×(C2×D3)⋊C4C2312yes—
232C2×(C2×D3)⋊C4C2312yes—
233C2×(C2×D3)⋊C4C2312yes—
234C2×(C2×D3)⋊C4C2312yes—
235C2×C4⋊Dic3—42no—
236C2×C4⋊Dic3C2311yescharacteristic
237C2×C4⋊Dic3C2311yescharacteristic
238C2×C4⋊Dic3C2311yescharacteristic
239C2×C4⋊Dic3C2312yes—
240C2×C4⋊Dic3C2311yescharacteristic
241#924D418yescomplemented
242C2×Dic3⋊C4C2312yes—
243C2×Dic3⋊C4C2312yes—
244C2×Dic3⋊C4C2312yes—
245C2×Dic3⋊C4C2312yes—
246C2×Dic3⋊C4C2312yes—
247C2×Dic3⋊C4C2312yes—
248C2×Dic3⋊C4C2312yes—
249C2×C4×Dic3C2312yes—
250C2×C4×Dic3C2312yes—
251C2×C4×Dic3C2312yes—
252#894—28no—
253#893—44no—
254#884—28no—
255#884—44no—
256#882—28no—
257#882—44no—
258D3×C22⋊C4—28no—
259#876—28no—
260#875—24no—
261#875—24no—
262#874—24no—
263#874—42no—
264C4×D12—24no—
265C4×D12—24no—
266#872—28no—
267#870—24no—
268C4×Dic6—24no—
269C4×Dic6—42no—
270C3×#95C2311yescharacteristic
271C3×#95C2311yescharacteristic
272C3×#95C2311yescharacteristic
273C3×#95C2311yescharacteristic
274C3×#95C2311yescharacteristic
275C3×#95C2311yescharacteristic
276C3×#95C2311yescharacteristic
277C3×#95C2311yescharacteristic
278C3×#95C2311yescharacteristic
279C3×#95C2311yescharacteristic
280C3⋊#95C2312yes—
281C3⋊#95C2312yes—
282C3⋊#95C2312yes—
283C3⋊#95C2312yes—
284C3⋊#95C2312yes—
285C3⋊#95C2312yes—
286C22×#41—31no—
287C23×D4—31no—
288#546—68no—
289C2×#127—31no—
290C2×#127—31no—
291#529—68no—
292C2×#126—32no—
293C2×#125—31no—
294C2×#124—31no—
295C2×#124—31no—
296C2×#123—32no—
297C2×#123—32no—
298C2×#123C2×D311yescharacteristic
299C2×C22⋊Q8—31no—
300C2×#121—31no—
301C2×#121—31no—
302C2×#121—32no—
303C2×#121—31no—
304C2×#121—32no—
305C2×#121—32no—
306C2×#120—32no—
307C2×#120—32no—
308C2×#120—32no—
309C2×C4×Q8—31no—
310C2×C4×Q8—31no—
311C2×C4×D4—32no—
312C2×C4×D4—32no—
313C2×C4×D4—31no—
314C2×C4×D4—31no—
315C2×C4×D4C2×D311yescharacteristic
316C2×#117—32no—
317C22×C4⋊C4—31no—
318C22×C22⋊C4—32no—
319C22×C22⋊C4—32no—
320C22×C22⋊C4—32no—
321C22×C42C2×D311yescharacteristic
322#399—32no—
323#399—32no—
324#397—32no—
325#397—32no—
326#396—32no—
327#396—32no—
328#394—32no—
329#394—32no—
330#394—32no—
331#394—32no—
332#394—32no—
333#392—32no—
334#392—32no—
335#392—32no—
336#392—32no—
337#392—32no—
338#391—31no—
339#390—32no—
340#390—32no—
341#390—32no—
342#390—32no—
343#390—32no—
344#390—32no—
345#390—31no—
346#390—31no—
347#390—31no—
348#390—32no—
349#390—31no—
350#390—31no—
351#390—31no—
352#390—32no—
353#390—31no—
354#389—31no—
355#389—31no—
356#389—32no—
357#388—32no—
358#388—32no—
359#388—32no—
360#388C2×D311yescharacteristic, complemented
361#388C2×D311yescharacteristic, complemented
362#387—32no—
363#387C2×D311yescharacteristic, complemented
364#387C2×D311yescharacteristic, complemented
365#386—32no—
366#386—32no—
367#386—32no—
368#386—32no—
369#386—32no—
370#386—32no—
371#386C2×D311yescharacteristic
372#385—32no—
373#385—32no—
374#385C2×D311yescharacteristic
375#381C2×D311yescharacteristic
376#380—31no—
377#380—32no—
378#380—32no—
379C4×C4⋊C4—31no—
380C4×C4⋊C4C2×D311yescharacteristic, complemented
381C4×C4⋊C4C2×D311yescharacteristic, complemented
382C4×C22⋊C4—32no—
383C4×C22⋊C4—32no—
384C4×C22⋊C4C2×D311yescharacteristic
385C4×C22⋊C4C2×D311yescharacteristic, complemented
386C4×C22⋊C4C2×D311yescharacteristic, complemented
387C24×C3C2411yescharacteristic
388C24×C3C2411yescharacteristic
389C23×D3—24no—
390C23×D3—24no—
391C23×D3—24no—
392C23×D3—24no—
393C23×D3—42no—
394C23×D3—42no—
395C23×D3—42no—
396C23×D3C2412yes—
397C23×D3C2412yes—
398C23×D3C2412yes—
399C2×C3×D4—22no—
400C2×C3×D4—22no—
401C2×C3×D4—22no—
402C22×C3×C4—22no—
403C22×C3×C4—22no—
404C22×C3×C4—22no—
405C22×C3×C4—22no—
406C22×C3×C4—22no—
407C22×C3×C4—22no—
408C22×C3×C4—22no—
409C22×C3×C4—22no—
410C22×C3×C4—22no—
411C22×C3×C4—22no—
412C22×C3×C4—41no—
413C22×C3×C4C2×D414yes—
414C22×C3×C4C2411yescharacteristic
415C22×C3×C4C2411yescharacteristic
416C22×C3×C4C2411yescharacteristic
417C22×C3×C4C2411yescharacteristic
418C22×C3×C4C2411yescharacteristic
419C22×C3×C4C2411yescharacteristic
420C22×C3×C4C2411yescharacteristic
421C22×C3×C4C2411yescharacteristic
422C22×C3×C4C2411yescharacteristic
423C22×C3×C4C2411yescharacteristic
424C22×C3×C4C2411yescharacteristic
425C22×C3×C4C2411yescharacteristic
426C22×C3×C4C2411yescharacteristic
427C2×#67—24no—
428C2×#67—24no—
429C2×#67—24no—
430C2×#67—24no—
431C2×#67—24no—
432C2×#67—24no—
433C2×#67—42no—
434C2×#67—42no—
435C2×#67—42no—
436C2×#67—42no—
437C2×#67—42no—
438C2×#67—42no—
439C22×Dic3—24no—
440C22×Dic3—42no—
441C22×Dic3—42no—
442C22×Dic3C2412yes—
443C22×Dic3C2412yes—
444C22×Dic3C2412yes—
445C22×Dic3C2412yes—
446C22×Dic3C2412yes—
447#235—416no—
448C2×D12—22no—
449C2×D12—22no—
450C2×D12—24no—
451C2×D12—24no—
452C2×D12—22no—
453C2×D12—22no—
454C2×D12—24no—
455C2×D12—22no—
456C2×D12—24no—
457C2×D12—22no—
458C2×D12—22no—
459C2×D12—22no—
460C2×D12—24no—
461C2×D12—24no—
462C2×D12—416no—
463C2×D12—42no—
464C2×D12—42no—
465C2×D12—42no—
466C2×D12—42no—
467C2×D12—42no—
468C2×D12—42no—
469C2×D12—42no—
470C2×D12—42no—
471C2×D12—42no—
472C2×D12#4114yes—
473C2×C4×D3—24no—
474C2×C4×D3—24no—
475C2×C4×D3—24no—
476C2×C4×D3—24no—
477C2×C4×D3—24no—
478C2×C4×D3—42no—
479C2×C4×D3—42no—
480C2×C4×D3—42no—
481C2×C4×D3—42no—
482C2×Dic6—22no—
483C2×Dic6—22no—
484C2×Dic6C2×D414yes—
485C3×C4⋊C4—22no—
486C3×C4⋊C4—22no—
487C3×C4⋊C4—22no—
488C3×C4⋊C4—22no—
489C3×C4⋊C4—41no—
490C3×C22⋊C4—22no—
491C3×C22⋊C4—22no—
492C3×C22⋊C4—22no—
493C3×C22⋊C4—22no—
494C3×C22⋊C4—22no—
495C3×C22⋊C4—22no—
496C3×C22⋊C4—41no—
497C3×C22⋊C4#4114yescomplemented
498C3×C42—22no—
499C3×C42—22no—
500C3×C42—22no—
501C3×C42—22no—
502C3×C42—22no—
503C3×C42—22no—
504C3×C42—22no—
505#217—42no—
506#217C2×D418yes—
507(C2×D3)⋊C4—24no—
508(C2×D3)⋊C4—24no—
509(C2×D3)⋊C4—24no—
510(C2×D3)⋊C4—24no—
511(C2×D3)⋊C4—24no—
512(C2×D3)⋊C4—24no—
513(C2×D3)⋊C4—24no—
514(C2×D3)⋊C4—24no—
515(C2×D3)⋊C4—24no—
516(C2×D3)⋊C4—24no—
517(C2×D3)⋊C4—24no—
518(C2×D3)⋊C4—24no—
519(C2×D3)⋊C4—42no—
520(C2×D3)⋊C4—42no—
521(C2×D3)⋊C4—42no—
522(C2×D3)⋊C4—42no—
523(C2×D3)⋊C4—42no—
524(C2×D3)⋊C4—42no—
525(C2×D3)⋊C4—42no—
526(C2×D3)⋊C4—42no—
527(C2×D3)⋊C4—42no—
528(C2×D3)⋊C4—42no—
529(C2×D3)⋊C4—42no—
530C4⋊Dic3—22no—
531C4⋊Dic3—22no—
532C4⋊Dic3—22no—
533C4⋊Dic3—42no—
534C4⋊Dic3C2×D414yes—
535Dic3⋊C4—24no—
536Dic3⋊C4—24no—
537Dic3⋊C4—24no—
538Dic3⋊C4—42no—
539Dic3⋊C4—42no—
540Dic3⋊C4—42no—
541Dic3⋊C4C2×D418yes—
542C4×Dic3—24no—
543C4×Dic3—42no—
544C4×Dic3—42no—
545C25—32no—
546C2×#41—64no—
547C2×#41—64no—
548C2×#41—122no—
549C22×Q8—31no—
550C22×D4—32no—
551C22×D4—32no—
552C22×D4—32no—
553C22×D4—32no—
554C22×D4—31no—
555C22×D4—31no—
556C22×D4—31no—
557C22×D4—32no—
558C22×D4—32no—
559C22×D4—32no—
560C22×D4—32no—
561C22×D4—32no—
562C22×D4—64no—
563C22×D4—64no—
564C22×D4—122no—
565C22×D4C22×D311yescharacteristic
566C23×C4—32no—
567C23×C4—32no—
568C23×C4—32no—
569C23×C4—32no—
570C23×C4C22×D311yescharacteristic
571C23×C4C22×D311yescharacteristic
572C23×C4C22×D311yescharacteristic
573C23×C4C22×D311yescharacteristic
574#127—64no—
575#127—122no—
576#126—68no—
577#125—64no—
578#124—64no—
579#124—64no—
580#123—24no—
581#123—68no—
582#123—68no—
583C22⋊Q8—38no—
584#121—68no—
585#121—64no—
586#121—64no—
587#121—124no—
588#121—122no—
589#121—124no—
590#120—68no—
591#120—68no—
592#120—124no—
593C4×Q8—64no—
594C4×Q8—122no—
595C4×D4—24no—
596C4×D4—64no—
597C4×D4—64no—
598C4×D4—68no—
599C4×D4—124no—
600#117—68no—
601C2×C4⋊C4—32no—
602C2×C4⋊C4—31no—
603C2×C4⋊C4—31no—
604C2×C4⋊C4—31no—
605C2×C4⋊C4—32no—
606C2×C4⋊C4—32no—
607C2×C4⋊C4—31no—
608C2×C4⋊C4—32no—
609C2×C4⋊C4—32no—
610C2×C4⋊C4—32no—
611C2×C4⋊C4—32no—
612C2×C4⋊C4—32no—
613C2×C4⋊C4—122no—
614C2×C4⋊C4C22×D311yescharacteristic
615C2×C4⋊C4C22×D311yescharacteristic
616C2×C4⋊C4C22×D311yescharacteristic
617C2×C4⋊C4C22×D311yescharacteristic
618C2×C4⋊C4C22×D311yescharacteristic
619C2×C22⋊C4—32no—
620C2×C22⋊C4—32no—
621C2×C22⋊C4—32no—
622C2×C22⋊C4—32no—
623C2×C22⋊C4—32no—
624C2×C22⋊C4—32no—
625C2×C22⋊C4—32no—
626C2×C22⋊C4—32no—
627C2×C22⋊C4—32no—
628C2×C22⋊C4—32no—
629C2×C22⋊C4—32no—
630C2×C22⋊C4—32no—
631C2×C22⋊C4—32no—
632C2×C22⋊C4—32no—
633C2×C22⋊C4—32no—
634C2×C22⋊C4—32no—
635C2×C22⋊C4—32no—
636C2×C22⋊C4—32no—
637C2×C22⋊C4—32no—
638C2×C22⋊C4—32no—
639C2×C22⋊C4—32no—
640C2×C22⋊C4—32no—
641C2×C22⋊C4—32no—
642C2×C22⋊C4—32no—
643C2×C22⋊C4—32no—
644C2×C22⋊C4—68no—
645C2×C22⋊C4—124no—
646C2×C22⋊C4—124no—
647C2×C22⋊C4C22×D311yescharacteristic
648C2×C22⋊C4C22×D311yescharacteristic
649C2×C22⋊C4C22×D311yescharacteristic
650C2×C22⋊C4C22×D311yescharacteristic
651C2×C22⋊C4C22×D311yescharacteristic
652C2×C22⋊C4C22×D311yescharacteristic
653C2×C22⋊C4C22×D311yescharacteristic
654C2×C22⋊C4C22×D311yescharacteristic
655C2×C42—24no—
656C2×C42—32no—
657C2×C42—32no—
658C2×C42—32no—
659C2×C42C22×D311yescharacteristic
660C2×C42C22×D311yescharacteristic
661C2×C42C22×D311yescharacteristic
662C2×C42C22×D311yescharacteristic
663C2×C42C22×D311yescharacteristic
664C2×C42C22×D311yescharacteristic
665C2×C42C22×D311yescharacteristic
666#95—32no—
667#95—32no—
668#95—32no—
669#95—32no—
670#95—32no—
671#95—32no—
672#95C22×D311yescharacteristic
673#95C22×D311yescharacteristic
674#95C22×D311yescharacteristic
675#95C22×D311yescharacteristic
676#95C22×D311yescharacteristic
677#95C22×D311yescharacteristic
678#95C22×D311yescharacteristic
679#95C22×D311yescharacteristic
680#95C22×D311yescharacteristic
681#95C22×D311yescharacteristic
682C23×C3—21no—
683C23×C3—21no—
684C23×C3—21no—
685C23×C3—21no—
686C23×C3—21no—
687C23×C3—21no—
688C23×C3—21no—
689C23×C3—21no—
690C23×C3—21no—
691C23×C3—21no—
692C23×C3—21no—
693C23×C3C22×D412yes—
694C23×C3C2×#4112yes—
695C23×C3H(5,𝔽2)12yes—
696C23×C3C2511yescharacteristic
697C22×D3—22no—
698C22×D3—22no—
699C22×D3—22no—
700C22×D3—22no—
701C22×D3—22no—
702C22×D3—22no—
703C22×D3—22no—
704C22×D3—22no—
705C22×D3—22no—
706C22×D3—22no—
707C22×D3—22no—
708C22×D3—22no—
709C22×D3—22no—
710C22×D3—22no—
711C22×D3—22no—
712C22×D3—22no—
713C22×D3—22no—
714C22×D3—22no—
715C22×D3—22no—
716C22×D3—22no—
717C22×D3—48no—
718C22×D3—48no—
719C22×D3—48no—
720C22×D3—48no—
721C22×D3—84no—
722C22×D3—84no—
723C22×D3—84no—
724C22×D3C2×#4114yes—
725C3×D4—44no—
726C2×C3×C4—21no—
727C2×C3×C4—21no—
728C2×C3×C4—21no—
729C2×C3×C4—21no—
730C2×C3×C4—21no—
731C2×C3×C4—21no—
732C2×C3×C4—21no—
733C2×C3×C4—21no—
734C2×C3×C4—28no—
735C2×C3×C4—21no—
736C2×C3×C4—21no—
737C2×C3×C4—21no—
738C2×C3×C4—21no—
739C2×C3×C4—21no—
740C2×C3×C4—21no—
741C2×C3×C4—21no—
742C2×C3×C4—21no—
743C2×C3×C4—21no—
744C2×C3×C4—21no—
745C2×C3×C4—21no—
746C2×C3×C4—21no—
747C2×C3×C4—21no—
748C2×C3×C4—21no—
749C2×C3×C4—21no—
750C2×C3×C4—21no—
751C2×C3×C4—21no—
752C2×C3×C4—21no—
753C2×C3×C4—21no—
754C2×C3×C4—21no—
755C2×C3×C4—21no—
756C2×C3×C4—21no—
757C2×C3×C4—21no—
758C2×C3×C4—21no—
759C2×C3×C4—44no—
760C2×C3×C4—44no—
761C2×C3×C4—44no—
762C2×C3×C4C22×D412yes—
763C2×C3×C4C22×D412yes—
764C2×C3×C4C2×#4112yes—
765C2×C3×C4C2×#4112yes—
766C2×C3×C4C2×#4112yes—
767C2×C3×C4H(5,𝔽2)12yes—
768C2×C3×C4H(5,𝔽2)12yes—
769#67—48no—
770#67—48no—
771#67—84no—
772#67—84no—
773C2×Dic3—22no—
774C2×Dic3—22no—
775C2×Dic3—22no—
776C2×Dic3—22no—
777C2×Dic3—22no—
778C2×Dic3—22no—
779C2×Dic3—22no—
780C2×Dic3—22no—
781C2×Dic3—22no—
782C2×Dic3—22no—
783C2×Dic3—22no—
784C2×Dic3—22no—
785C2×Dic3—22no—
786C2×Dic3—84no—
787C2×Dic3C22×D414yes—
788C2×Dic3C22×D414yes—
789D12—28no—
790D12—48no—
791D12—48no—
792D12—44no—
793D12—44no—
794D12—84no—
795D12—84no—
796D12—84no—
797C4×D3—48no—
798C4×D3—48no—
799C4×D3—84no—
800Dic6—28no—
801C24—32no—
802C24—32no—
803C24—32no—
804C24—64no—
805C24—64no—
806C24—64no—
807C24—64no—
808C24—122no—
809C24—122no—
810C24—122no—
811C24C23×D311yescharacteristic
812C24C23×D311yescharacteristic
813#41—1216no—
814C2×Q8—34no—
815C2×Q8—62no—
816C2×Q8—62no—
817C2×D4—22no—
818C2×D4—22no—
819C2×D4—22no—
820C2×D4—34no—
821C2×D4—64no—
822C2×D4—64no—
823C2×D4—64no—
824C2×D4—64no—
825C2×D4—64no—
826C2×D4—64no—
827C2×D4—64no—
828C2×D4—64no—
829C2×D4—64no—
830C2×D4—64no—
831C2×D4—64no—
832C2×D4—62no—
833C2×D4—62no—
834C2×D4—64no—
835C2×D4—62no—
836C2×D4—62no—
837C2×D4—62no—
838C2×D4—62no—
839C2×D4—62no—
840C2×D4—62no—
841C2×D4—1216no—
842C2×D4—122no—
843C2×D4—122no—
844C2×D4—122no—
845C2×D4—122no—
846C2×D4—122no—
847C2×D4—122no—
848C2×D4—122no—
849C2×D4—122no—
850C2×D4—122no—
851C2×D4—122no—
852C2×D4—122no—
853C2×D4—122no—
854C2×D4—122no—
855C2×D4—122no—
856C2×D4—122no—
857C22×C4—22no—
858C22×C4—22no—
859C22×C4—22no—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—22no—
867C22×C4—32no—
868C22×C4—32no—
869C22×C4—32no—
870C22×C4—32no—
871C22×C4—32no—
872C22×C4—41no—
873C22×C4—64no—
874C22×C4—64no—
875C22×C4—64no—
876C22×C4—64no—
877C22×C4—64no—
878C22×C4—64no—
879C22×C4—122no—
880C22×C4—122no—
881C22×C4—122no—
882C22×C4—122no—
883C22×C4—122no—
884C22×C4—122no—
885C22×C4D3×D414yes—
886C22×C4C23×D311yescharacteristic
887C22×C4C23×D311yescharacteristic
888C22×C4C23×D311yescharacteristic
889C22×C4C23×D311yescharacteristic
890C22×C4C23×D311yescharacteristic
891C22×C4C23×D311yescharacteristic
892C22×C4C23×D311yescharacteristic
893C22×C4C23×D311yescharacteristic
894C22×C4C23×D311yescharacteristic
895C22×C4C23×D311yescharacteristic
896C22×C4C23×D311yescharacteristic
897C22×C4C23×D311yescharacteristic
898C22×C4C23×D311yescharacteristic
899C4⋊C4—22no—
900C4⋊C4—22no—
901C4⋊C4—22no—
902C4⋊C4—22no—
903C4⋊C4—38no—
904C4⋊C4—34no—
905C4⋊C4—41no—
906C4⋊C4—64no—
907C4⋊C4—64no—
908C4⋊C4—64no—
909C4⋊C4—62no—
910C4⋊C4—62no—
911C4⋊C4—62no—
912C4⋊C4—122no—
913C4⋊C4—122no—
914C4⋊C4—122no—
915C4⋊C4—122no—
916C22⋊C4—22no—
917C22⋊C4—22no—
918C22⋊C4—22no—
919C22⋊C4—22no—
920C22⋊C4—22no—
921C22⋊C4—22no—
922C22⋊C4—38no—
923C22⋊C4—41no—
924C22⋊C4—64no—
925C22⋊C4—64no—
926C22⋊C4—64no—
927C22⋊C4—64no—
928C22⋊C4—64no—
929C22⋊C4—64no—
930C22⋊C4—64no—
931C22⋊C4—64no—
932C22⋊C4—64no—
933C22⋊C4—64no—
934C22⋊C4—64no—
935C22⋊C4—64no—
936C22⋊C4—122no—
937C22⋊C4—122no—
938C22⋊C4—122no—
939C22⋊C4—122no—
940C22⋊C4—122no—
941C22⋊C4—122no—
942C22⋊C4—122no—
943C22⋊C4—122no—
944C22⋊C4—122no—
945C22⋊C4—122no—
946C22⋊C4—122no—
947C22⋊C4—122no—
948C22⋊C4#23514yescomplemented
949C42—22no—
950C42—22no—
951C42—22no—
952C42—22no—
953C42—22no—
954C42—22no—
955C42—22no—
956C42—64no—
957C42—122no—
958C42—122no—
959C22×C3—22no—
960C22×C3—22no—
961C22×C3—22no—
962C22×C3—22no—
963C22×C3—22no—
964C22×C3—22no—
965C22×C3—41no—
966C22×C3—41no—
967C22×C3—41no—
968C22×C3—41no—
969C22×C3—41no—
970C22×C3—41no—
971C22×C3—41no—
972C22×C3#55014yes—
973C22×C3C23×D411yescharacteristic
974C22×C3C22×#4111yescharacteristic
975C22×C3C22×#4111yescharacteristic
976C22×C3C2×H(5,𝔽2)11yescharacteristic
977C22×C3C2×H(5,𝔽2)11yescharacteristic
978C22×C3C2×H(5,𝔽2)11yescharacteristic
979C22×C3#58511yescharacteristic
980C2×D3—24no—
981C2×D3—24no—
982C2×D3—24no—
983C2×D3—42no—
984C2×D3—42no—
985C2×D3—42no—
986C2×D3—42no—
987C2×D3—42no—
988C2×D3—42no—
989C2×D3—42no—
990C2×D3—42no—
991C2×D3—42no—
992C2×D3—42no—
993C2×D3—42no—
994C2×D3—42no—
995C2×D3—42no—
996C2×D3—42no—
997C2×D3—42no—
998C2×D3—42no—
999C2×D3—42no—
1000C2×D3—42no—
1001C2×D3—816no—
1002C3×C4—22no—
1003C3×C4—22no—
1004C3×C4—22no—
1005C3×C4—22no—
1006C3×C4—41no—
1007C3×C4—41no—
1008C3×C4—41no—
1009C3×C4—41no—
1010C3×C4—41no—
1011C3×C4—41no—
1012C3×C4—41no—
1013C3×C4—41no—
1014C3×C4#54614yes—
1015Dic3—24no—
1016Dic3—24no—
1017Dic3—42no—
1018Dic3—42no—
1019Dic3—42no—
1020C23—21no—
1021C23—21no—
1022C23—21no—
1023C23—21no—
1024C23—21no—
1025C23—21no—
1026C23—21no—
1027C23—21no—
1028C23—21no—
1029C23—21no—
1030C23—21no—
1031C23—34no—
1032C23—62no—
1033C23—62no—
1034C23—62no—
1035C23—62no—
1036C23—62no—
1037C23—62no—
1038C23—62no—
1039C23—62no—
1040C23—62no—
1041C23—62no—
1042C23—62no—
1043C23—62no—
1044C23—62no—
1045C23—62no—
1046C23—62no—
1047C23—62no—
1048C23—62no—
1049C23—62no—
1050C23—62no—
1051C23—62no—
1052C23—128no—
1053C23—128no—
1054C23—128no—
1055C23—128no—
1056C23—244no—
1057C23—244no—
1058C23—244no—
1059C23C2×#23512yes—
1060C23C2×D3×D412yes—
1061C23#100912yes—
1062C23C24×D311yescharacteristic
1063Q8—68no—
1064D4—44no—
1065D4—68no—
1066D4—128no—
1067D4—128no—
1068D4—128no—
1069D4—128no—
1070D4—124no—
1071D4—124no—
1072D4—244no—
1073D4—244no—
1074D4—244no—
1075D4—244no—
1076D4—244no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—28no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—34no—
1111C2×C4—34no—
1112C2×C4—44no—
1113C2×C4—44no—
1114C2×C4—44no—
1115C2×C4—62no—
1116C2×C4—62no—
1117C2×C4—62no—
1118C2×C4—62no—
1119C2×C4—62no—
1120C2×C4—62no—
1121C2×C4—62no—
1122C2×C4—62no—
1123C2×C4—62no—
1124C2×C4—62no—
1125C2×C4—62no—
1126C2×C4—62no—
1127C2×C4—62no—
1128C2×C4—128no—
1129C2×C4—128no—
1130C2×C4—244no—
1131C2×C4—244no—
1132C2×C4C2×#23512yes—
1133C2×C4C2×#23512yes—
1134C2×C4C2×D3×D412yes—
1135C2×C4C2×D3×D412yes—
1136C2×C4D3×#4112yes—
1137C2×C4#100912yes—
1138C2×C4#100912yes—
1139C2×C3—24no—
1140C2×C3—81no—
1141C2×C3C2×#54611yescharacteristic
1142C2×C3C2×#55011yescharacteristic
1143C2×C3#348111yescharacteristic
1144C2×C3#348811yescharacteristic
1145C2×C3#351311yescharacteristic
1146C2×C3#351411yescharacteristic
1147C2×C3#354311yescharacteristic
1148D3—44no—
1149D3—82no—
1150D3—82no—
1151C22—22no—
1152C22—22no—
1153C22—22no—
1154C22—22no—
1155C22—22no—
1156C22—22no—
1157C22—41no—
1158C22—41no—
1159C22—41no—
1160C22—41no—
1161C22—41no—
1162C22—41no—
1163C22—41no—
1164C22—64no—
1165C22—64no—
1166C22—64no—
1167C22—122no—
1168C22—122no—
1169C22—122no—
1170C22—122no—
1171C22—122no—
1172C22—122no—
1173C22—122no—
1174C22—122no—
1175C22—122no—
1176C22—122no—
1177C22—122no—
1178C22—122no—
1179C22—122no—
1180C22—122no—
1181C22—122no—
1182C22—122no—
1183C22—122no—
1184C22—122no—
1185C22—2416no—
1186C22#555314yes—
1187C22C22×#23511yescharacteristic
1188C22C22×D3×D411yescharacteristic
1189C22C2×D3×#4111yescharacteristic
1190C22C2×#100911yescharacteristic
1191C22C2×#100911yescharacteristic
1192C22C2×#100911yescharacteristic
1193C22#596411yescharacteristic
1194C4—22no—
1195C4—22no—
1196C4—22no—
1197C4—22no—
1198C4—41no—
1199C4—41no—
1200C4—41no—
1201C4—41no—
1202C4—41no—
1203C4—41no—
1204C4—41no—
1205C4—41no—
1206C4—64no—
1207C4—64no—
1208C4—122no—
1209C4—122no—
1210C4—122no—
1211C4#565414yes—
1212C3#5904611yescharacteristic, complemented, Sylow
1213C2—24no—
1214C2—81no—
1215C2—124no—
1216C2—242no—
1217C2—242no—
1218C2C2×#555311yescharacteristic
1219C2#8584311yescharacteristic
1220C2#8585211yescharacteristic
1221C2C2×#565411yescharacteristic
1222C2#8604111yescharacteristic
1223C2#8616111yescharacteristic
1224C2#8617211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×C4×#123C2
hypercenterC4×#123D3
hypocenterC3#59046
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C4×#123

Complements

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

NH ≅ G/Ntype
1. C2×#5550C2semidirect
2. C2×#5479C2semidirect
3. C3×C4×#123C2semidirect
4. #82901C2semidirect
5. #82352C2semidirect
6. C2×#4939C2semidirect
7. #75930C2semidirect
8. #75495C2semidirect
9. #75153C2semidirect
10. #75007C2semidirect
11. #74893C2semidirect
12. #74596C2semidirect
13. #74126C2semidirect
14. #73712C2semidirect
15. #73677C2semidirect
16. #73673C2semidirect
17. #73653C2semidirect
18. #73587C2semidirect
19. #73586C2semidirect
20. #73506C2semidirect
21. #73487C2semidirect
22. #73465C2semidirect
23. #73454C2semidirect
34. C2×#930C22semidirect
43. C2×#893C22semidirect
45. C2×#884C22semidirect
50. C2×#876C22semidirect
52. C2×#875C22semidirect
56. C2×C4×D12C22semidirect
57. C2×#872C22semidirect
58. C2×#870C22semidirect
59. C2×C4×Dic6C22semidirect
60. C2×C4×Dic6C22semidirect
61. C3×#388C22semidirect
62. C3×#388C22semidirect
63. C3×#387C22semidirect
64. C3×#387C22semidirect
68. C3×C4×C4⋊C4C22semidirect
69. C3×C4×C4⋊C4C22semidirect
71. C3×C4×C22⋊C4C22semidirect
72. C3×C4×C22⋊C4C22semidirect
73. #5212C22semidirect
74. #4994C22semidirect
75. #4993C22semidirect
76. #4993C22semidirect
77. #4990C22semidirect
78. #4989C22semidirect
79. #4988C22semidirect
80. #4988C22semidirect
81. #4988C22semidirect
82. #4961C22semidirect
83. #4960C22semidirect
84. #4960C22semidirect
85. #4960C22semidirect
86. #4959C22semidirect
88. #4957C22semidirect
89. #4957C22semidirect
90. #4957C22semidirect
101. #4939C22semidirect
102. C4×C4⋊Dic3C22semidirect
103. #4929C22semidirect
104. #4928C22semidirect
105. #4928C22semidirect
106. #4676C22semidirect
107. #4675C22semidirect
108. #4675C22semidirect
109. #4672C22semidirect
110. #4672C22semidirect
111. #4672C22semidirect
114. #4669C22semidirect
115. #4669C22semidirect
116. #4667C22semidirect
117. #4667C22semidirect
118. #4666C22semidirect
119. #4665C22semidirect
120. #4665C22semidirect
121. #4665C22semidirect
122. #4665C22semidirect
123. #4665C22semidirect
124. #4655C22semidirect
125. #4647C22semidirect
147. C4×#123D3semidirect
241. #924D4semidirect
360. #388C2×D3semidirect
361. #388C2×D3semidirect
363. #387C2×D3semidirect
364. #387C2×D3semidirect
380. C4×C4⋊C4C2×D3semidirect
381. C4×C4⋊C4C2×D3semidirect
385. C4×C22⋊C4C2×D3semidirect
386. C4×C22⋊C4C2×D3semidirect
497. C3×C22⋊C4#41semidirect
948. C22⋊C4#235semidirect
1212. C3#59046semidirect

Maximal subgroups

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

subgroupindex
C2×#55502
C2×#54792
C3×C4×#1232
#829012
#823522
C2×#49392
#759302
#754952
#751532
#750072
#748932
#745962
#741262
#737122
#736772
#736732
#736532
#735872
#735862
#735062
#734872
#734652
#734542
#590463