Finite Group Databasebeta

← #11223210

Subgroups — #11223210

Order 768.

2890 conjugacy classes of subgroups.

The subgroup lattice has 1222 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5609C211yesmaximal, characteristic
2C2×#5603C211yesmaximal, characteristic, complemented
3C3×#2363C211yesmaximal, characteristic, complemented
4D4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
5#82381C211yesmaximal, characteristic, complemented
6#82277C211yesmaximal, characteristic, complemented
7#82269C211yesmaximal, characteristic, complemented
8#76469C212yesmaximal, complemented
9#76317C211yesmaximal, characteristic, complemented
10#76315C212yesmaximal, complemented
11#76315C211yesmaximal, characteristic, complemented
12#76218C211yesmaximal, characteristic, complemented
13#76011C211yesmaximal, characteristic, complemented
14#75918C212yesmaximal, complemented
15#75669C212yesmaximal, complemented
16#74918C212yesmaximal, complemented
17#74686C212yesmaximal, complemented
18#73788C211yesmaximal, characteristic, complemented
19#73654C211yesmaximal, characteristic, complemented
20#73604C212yesmaximal, complemented
21#73594C212yesmaximal, complemented
22#73588C211yesmaximal, characteristic, complemented
23#73583C211yesmaximal, characteristic, complemented
24#44874—31nomaximal, Sylow
25C22×D3×D4C2211yescharacteristic
26C22×D3×D4C2212yes—
27C23×D12C2211yescharacteristic
28C2×C3×#121C2211yescharacteristic
29C2×C3×C4×D4C2211yescharacteristic, complemented
30C2×C3×#117C2211yescharacteristic, complemented
31C2×#940C2211yescharacteristic
32C2×#937C2212yes—
33C2×#936C2212yescomplemented
34C2×#936C2211yescharacteristic, complemented
35C2×#935C2212yescomplemented
36C2×D4×Dic3C2211yescharacteristic, complemented
37C2×C4×#67C2211yescharacteristic
38C22×(C2×D3)⋊C4C2212yescomplemented
39C2×#926C2211yescharacteristic, complemented
40C2×#924C2211yescharacteristic, complemented
41#5609—28no—
42#5603—28no—
43C2×#897C2211yescharacteristic, complemented
44C2×#897C2212yescomplemented
45C2×#895C2211yescharacteristic
46C2×#893C2211yescharacteristic
47C2×#888C2211yescharacteristic, complemented
48C2×#887C2211yescharacteristic, complemented
49C2×#886C2212yescomplemented
50C2×#884C2212yes—
51C2×#882C2212yes—
52C2×#879C2212yescomplemented
53C2×#878C2212yescomplemented
54C2×#875C2211yescharacteristic
55C2×#875C2212yescomplemented
56C2×#875C2211yescharacteristic, complemented
57C3×#390C2211yescharacteristic, complemented
58C3×#390C2212yescomplemented
59C3×#389C2211yescharacteristic, complemented
60C3×#388C2212yescomplemented
61C3×#386C2212yescomplemented
62C3×C4×C4⋊C4C2211yescharacteristic, complemented
63C3×C4×C22⋊C4C2211yescharacteristic, complemented
64C3×C4×C22⋊C4C2212yescomplemented
65#5213C2212yescomplemented
66#5213C2212yescomplemented
67#5213C2212yescomplemented
68#4994C2212yescomplemented
69#4994C2212yescomplemented
70#4988C2211yescharacteristic
71#4988C2211yescharacteristic
72#4988C2212yescomplemented
73#4988C2211yescharacteristic, complemented
74#4988C2211yescharacteristic, complemented
75#4987C2211yescharacteristic, complemented
76#4984C2211yescharacteristic, complemented
77#4973C2211yescharacteristic, complemented
78#4961C2211yescharacteristic
79#4961C2212yes—
80#4961C2211yescharacteristic
81#4961C2212yescomplemented
82#4961C2212yescomplemented
83#4961C2212yescomplemented
84#4961C2212yescomplemented
85#4961C2212yescomplemented
86#4961C2212yescomplemented
87#4958C2212yescomplemented
88#4958C2212yescomplemented
89#4955C2212yescomplemented
90#4955C2212yescomplemented
91#4955C2212yescomplemented
92#4955C2212yescomplemented
93#4955C2212yescomplemented
94#4955C2212yescomplemented
95#4955C2212yescomplemented
96#4953C2212yescomplemented
97#4953C2211yescharacteristic, complemented
98#4953C2211yescharacteristic, complemented
99#4940C2212yescomplemented
100#4940C2212yescomplemented
101#4940C2212yescomplemented
102#4939C2211yescharacteristic
103#4939C2211yescharacteristic, complemented
104#4939C2212yescomplemented
105#4939C2212yescomplemented
106C4×(C2×D3)⋊C4C2211yescharacteristic, complemented
107C4×(C2×D3)⋊C4C2212yescomplemented
108C4×(C2×D3)⋊C4C2211yescharacteristic, complemented
109C4×C4⋊Dic3C2211yescharacteristic, complemented
110C4×C4⋊Dic3C2211yescharacteristic, complemented
111#4928C2212yescomplemented
112#4677C2211yescharacteristic, complemented
113#4674C2211yescharacteristic, complemented
114#4673C2212yescomplemented
115#4673C2212yescomplemented
116#4672C2212yescomplemented
117#4672C2212yescomplemented
118#4672C2212yescomplemented
119#4672C2212yescomplemented
120#4670C2212yescomplemented
121#4670C2212yescomplemented
122#4668C2212yescomplemented
123#4668C2212yescomplemented
124#4661C2211yescharacteristic, complemented
125#4659C2211yescharacteristic, complemented
126C2×D42—31no—
127C2×#542—31no—
128#2697—32no—
129#2685—32no—
130#2684—32no—
131#2681—32no—
132#2559—32no—
133#2544—31no—
134#2491—31no—
135#2472—32no—
136#2452—31no—
137#2445—31no—
138#2435—31no—
139#2435—32no—
140#2435—31no—
141#2426—31no—
142#2415—31no—
143#2405—32no—
144#2395—31no—
145#2367—31no—
146#2363D311yescharacteristic, complemented
147D4×C22⋊C4—31no—
148#2309—31no—
149C24×D3C2312yes—
150C24×D3C2312yes—
151C22×C3×D4C2311yescharacteristic
152C22×C3×D4C2312yes—
153C23×C3×C4C2311yescharacteristic
154C23×C3×C4C2312yes—
155C22×#67C2311yescharacteristic
156C22×#67C2312yes—
157C22×#67C2312yes—
158C22×#67C2312yes—
159C23×Dic3C2312yes—
160C2×D3×D4—28no—
161C2×D3×D4—24no—
162C2×D3×D4—24no—
163C2×D3×D4—42no—
164C2×D3×D4—44no—
165C2×D3×D4—44no—
166C22×D12—24no—
167C22×D12—24no—
168C22×D12—42no—
169C22×D12C2311yescharacteristic
170C22×D12C2312yes—
171C22×D12C2312yes—
172C22×D12C2311yescharacteristic
173C22×C4×D3C2311yescharacteristic
174C22×C4×D3C2312yes—
175C22×Dic6C2311yescharacteristic
176C22×Dic6C2312yes—
177C3×#121D418yes—
178C3×C4×D4—42no—
179C3×#117—42no—
180C2×C3×C4⋊C4C2311yescharacteristic
181C2×C3×C4⋊C4C2311yescharacteristic
182C2×C3×C4⋊C4C2312yes—
183C2×C3×C4⋊C4C2311yescharacteristic
184C2×C3×C22⋊C4C2311yescharacteristic
185C2×C3×C22⋊C4C2311yescharacteristic
186C2×C3×C22⋊C4C2312yes—
187C2×C3×C22⋊C4C2312yes—
188C2×C3×C22⋊C4C2312yes—
189C2×C3×C22⋊C4C2312yes—
190C2×C3×C22⋊C4C2312yes—
191C2×C3×C42C2311yescharacteristic
192C2×C3×C42C2311yescharacteristic
193C2×C3×C42C2312yes—
194C2×C3×C42C2312yes—
195C2×#217C2311yescharacteristic
196C2×#217C2312yes—
197C2×#217C2311yescharacteristic
198C2×#217C2311yescharacteristic
199C2×#217C2312yes—
200C2×#217C2312yes—
201C2×#217C2312yes—
202#940—24no—
203#937—28no—
204#936—28no—
205#936—24no—
206#935—28no—
207D4×Dic3—24no—
208C4×#67—24no—
209C2×(C2×D3)⋊C4—44no—
210C2×(C2×D3)⋊C4C2312yes—
211C2×(C2×D3)⋊C4C2312yes—
212C2×(C2×D3)⋊C4C2312yes—
213C2×(C2×D3)⋊C4C2311yescharacteristic
214C2×(C2×D3)⋊C4C2312yes—
215C2×(C2×D3)⋊C4C2312yes—
216C2×(C2×D3)⋊C4C2311yescharacteristic
217C2×(C2×D3)⋊C4C2311yescharacteristic
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)⋊C4C2311yescharacteristic
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)⋊C4C2311yescharacteristic
235#926—24no—
236C2×C4⋊Dic3C2311yescharacteristic
237C2×C4⋊Dic3C2311yescharacteristic
238C2×C4⋊Dic3C2311yescharacteristic
239C2×C4⋊Dic3C2311yescharacteristic
240C2×C4⋊Dic3C2312yes—
241C2×C4⋊Dic3C2311yescharacteristic
242C2×C4⋊Dic3C2311yescharacteristic
243C2×C4⋊Dic3C2312yes—
244C2×C4⋊Dic3C2311yescharacteristic
245#924—24no—
246C2×Dic3⋊C4C2311yescharacteristic
247C2×Dic3⋊C4C2312yes—
248C2×Dic3⋊C4C2312yes—
249C2×Dic3⋊C4C2312yes—
250C2×C4×Dic3C2312yes—
251C2×C4×Dic3C2311yescharacteristic
252C2×C4×Dic3C2311yescharacteristic
253C2×C4×Dic3C2311yescharacteristic
254#897—44no—
255#897—42no—
256#895—24no—
257#893—24no—
258#888—24no—
259#887—24no—
260#886—44no—
261#884—28no—
262#882—28no—
263#879—28no—
264#878—28no—
265#875—24no—
266#875—44no—
267#875—42no—
268C3×#95C2311yescharacteristic
269C3×#95C2311yescharacteristic
270C3×#95C2312yes—
271C3×#95C2312yes—
272C3⋊#95C2311yescharacteristic
273C3⋊#95C2311yescharacteristic
274C3⋊#95C2311yescharacteristic
275C3⋊#95C2311yescharacteristic
276C3⋊#95C2311yescharacteristic
277C3⋊#95C2311yescharacteristic
278C3⋊#95C2312yes—
279C3⋊#95C2312yes—
280C3⋊#95C2312yes—
281C3⋊#95C2311yescharacteristic
282C3⋊#95C2312yes—
283C3⋊#95C2311yescharacteristic
284C23×D4—31no—
285C23×D4—32no—
286C23×D4—31no—
287D42—68no—
288#542—68no—
289C2×C4⋊Q8—31no—
290C2×#127—31no—
291C2×#126—32no—
292C2×#124—32no—
293C2×#124—31no—
294C2×#124—31no—
295C2×#124—31no—
296C2×#124—32no—
297C2×#123—32no—
298C2×#123—32no—
299C2×C22⋊Q8—31no—
300C2×C22⋊Q8—31no—
301C2×C22⋊Q8—32no—
302C2×C22⋊Q8—32no—
303C2×#121—31no—
304C2×#121—32no—
305C2×#121C2×D311yescharacteristic
306C2×#120—32no—
307C2×#120—32no—
308C2×C4×Q8—31no—
309C2×C4×D4—31no—
310C2×C4×D4—31no—
311C2×C4×D4—31no—
312C2×C4×D4C2×D311yescharacteristic, complemented
313C2×#117—31no—
314C2×#117C2×D311yescharacteristic, complemented
315C22×C22⋊C4—32no—
316#400—31no—
317#399—31no—
318#398—31no—
319#397—31no—
320#397—31no—
321#397—32no—
322#397—31no—
323#396—32no—
324#396—32no—
325#394—31no—
326#394—31no—
327#394—32no—
328#394—32no—
329#394—32no—
330#394—32no—
331#394—32no—
332#394—32no—
333#394—32no—
334#394—32no—
335#394—32no—
336#394—32no—
337#394—32no—
338#393—32no—
339#393—32no—
340#391—31no—
341#390—31no—
342#390—31no—
343#390—31no—
344#390—31no—
345#390—32no—
346#390—32no—
347#390—32no—
348#390—31no—
349#390—31no—
350#390C2×D312yescomplemented
351#390C2×D311yescharacteristic, complemented
352#389—31no—
353#389—32no—
354#389C2×D311yescharacteristic, complemented
355#388—32no—
356#388—32no—
357#388—32no—
358#388—32no—
359#388—32no—
360#388C2×D312yescomplemented
361#386—32no—
362#386—32no—
363#386—32no—
364#386—32no—
365#386—32no—
366#386C2×D312yescomplemented
367#385—32no—
368#385—32no—
369#380—31no—
370#379—32no—
371#379—32no—
372#379—32no—
373#379—32no—
374#379—32no—
375#379—32no—
376#379—32no—
377C4×C4⋊C4—31no—
378C4×C4⋊C4—31no—
379C4×C4⋊C4C2×D311yescharacteristic, complemented
380C4×C22⋊C4—31no—
381C4×C22⋊C4—32no—
382C4×C22⋊C4—31no—
383C4×C22⋊C4C2×D311yescharacteristic, complemented
384C4×C22⋊C4C2×D312yescomplemented
385C24×C3C2411yescharacteristic
386C24×C3C2412yes—
387C23×D3—24no—
388C23×D3—24no—
389C23×D3—24no—
390C23×D3—24no—
391C23×D3—24no—
392C23×D3—42no—
393C23×D3—42no—
394C23×D3—42no—
395C23×D3—42no—
396C23×D3—42no—
397C23×D3—42no—
398C23×D3—42no—
399C23×D3—42no—
400C23×D3—42no—
401C23×D3C2412yes—
402C23×D3C2412yes—
403C23×D3C2411yescharacteristic
404C2×C3×D4—22no—
405C2×C3×D4—22no—
406C2×C3×D4—42no—
407C2×C3×D4—42no—
408C2×C3×D4C2×D414yes—
409C2×C3×D4C2×D418yes—
410C22×C3×C4—22no—
411C22×C3×C4—22no—
412C22×C3×C4—42no—
413C22×C3×C4—42no—
414C22×C3×C4—42no—
415C22×C3×C4C2×D414yes—
416C22×C3×C4C2411yescharacteristic
417C22×C3×C4C2411yescharacteristic
418C22×C3×C4C2412yes—
419C22×C3×C4C2411yescharacteristic
420C22×C3×C4C2412yes—
421C22×C3×C4C2411yescharacteristic
422C22×C3×C4C2412yes—
423C22×C3×C4C2411yescharacteristic
424C22×C3×C4C2411yescharacteristic
425C2×#67—22no—
426C2×#67—22no—
427C2×#67—24no—
428C2×#67—24no—
429C2×#67—24no—
430C2×#67—24no—
431C2×#67—22no—
432C2×#67—24no—
433C2×#67—42no—
434C2×#67—42no—
435C2×#67—42no—
436C2×#67—42no—
437C22×Dic3—24no—
438C22×Dic3—42no—
439C22×Dic3—42no—
440C22×Dic3C2411yescharacteristic
441C22×Dic3C2411yescharacteristic
442C22×Dic3C2411yescharacteristic
443C22×Dic3C2411yescharacteristic
444C22×Dic3C2411yescharacteristic
445C22×Dic3C2412yes—
446C22×Dic3C2411yescharacteristic
447C22×Dic3C2412yes—
448C22×Dic3C2411yescharacteristic
449D3×D4—416no—
450D3×D4—432no—
451C2×D12—22no—
452C2×D12—22no—
453C2×D12—24no—
454C2×D12—24no—
455C2×D12—24no—
456C2×D12—24no—
457C2×D12—22no—
458C2×D12—22no—
459C2×D12—22no—
460C2×D12—416no—
461C2×D12—42no—
462C2×D12—42no—
463C2×D12#4114yes—
464C2×C4×D3—24no—
465C2×C4×D3—22no—
466C2×C4×D3—22no—
467C2×C4×D3—22no—
468C2×C4×D3—24no—
469C2×C4×D3—42no—
470C2×Dic6—22no—
471C2×Dic6—22no—
472C2×Dic6—22no—
473C2×Dic6—24no—
474C2×Dic6—42no—
475C2×Dic6—42no—
476C3×C4⋊C4—22no—
477C3×C4⋊C4—22no—
478C3×C4⋊C4—42no—
479C3×C4⋊C4C2×D414yes—
480C3×C22⋊C4—42no—
481C3×C22⋊C4—41no—
482C3×C22⋊C4—41no—
483C3×C22⋊C4—42no—
484C3×C22⋊C4—42no—
485C3×C22⋊C4—42no—
486C3×C22⋊C4C2×D418yes—
487C3×C42—22no—
488C3×C42—22no—
489C3×C42—42no—
490C3×C42—42no—
491#217—24no—
492#217—24no—
493#217—24no—
494#217—24no—
495#217—22no—
496#217—22no—
497#217—22no—
498(C2×D3)⋊C4—24no—
499(C2×D3)⋊C4—24no—
500(C2×D3)⋊C4—22no—
501(C2×D3)⋊C4—24no—
502(C2×D3)⋊C4—22no—
503(C2×D3)⋊C4—22no—
504(C2×D3)⋊C4—24no—
505(C2×D3)⋊C4—24no—
506(C2×D3)⋊C4—42no—
507(C2×D3)⋊C4—42no—
508(C2×D3)⋊C4—42no—
509(C2×D3)⋊C4—42no—
510(C2×D3)⋊C4—42no—
511(C2×D3)⋊C4—42no—
512(C2×D3)⋊C4—42no—
513(C2×D3)⋊C4—42no—
514(C2×D3)⋊C4—42no—
515(C2×D3)⋊C4—42no—
516(C2×D3)⋊C4—42no—
517(C2×D3)⋊C4—42no—
518(C2×D3)⋊C4—42no—
519(C2×D3)⋊C4—41no—
520(C2×D3)⋊C4—41no—
521(C2×D3)⋊C4—42no—
522(C2×D3)⋊C4—42no—
523C4⋊Dic3—22no—
524C4⋊Dic3—22no—
525C4⋊Dic3—22no—
526C4⋊Dic3—22no—
527C4⋊Dic3—24no—
528C4⋊Dic3—22no—
529C4⋊Dic3—42no—
530C4⋊Dic3—41no—
531C4⋊Dic3—41no—
532Dic3⋊C4—24no—
533Dic3⋊C4—24no—
534Dic3⋊C4—24no—
535Dic3⋊C4—22no—
536C4×Dic3—24no—
537C4×Dic3—22no—
538C4×Dic3—22no—
539C4×Dic3—22no—
540C25—32no—
541C25—32no—
542C22×Q8—31no—
543C22×Q8—32no—
544C22×D4—31no—
545C22×D4—32no—
546C22×D4—32no—
547C22×D4—32no—
548C22×D4—31no—
549C22×D4—31no—
550C22×D4—32no—
551C22×D4—32no—
552C22×D4—64no—
553C22×D4—64no—
554C22×D4—68no—
555C22×D4—64no—
556C22×D4—64no—
557C22×D4—122no—
558C22×D4—122no—
559C22×D4—124no—
560C22×D4—124no—
561C22×D4C22×D311yescharacteristic
562C22×D4C22×D312yes—
563C23×C4—32no—
564C23×C4—31no—
565C23×C4—32no—
566C23×C4C22×D311yescharacteristic
567C23×C4C22×D312yes—
568C4⋊Q8—64no—
569#127—64no—
570#126—68no—
571#124—64no—
572#124—64no—
573#124—68no—
574#124—122no—
575#124—124no—
576#123—68no—
577#123—124no—
578C22⋊Q8—64no—
579C22⋊Q8—68no—
580C22⋊Q8—122no—
581C22⋊Q8—124no—
582#121—64no—
583#121—68no—
584#121D1218yes—
585#120—68no—
586#120—68no—
587C4×Q8—64no—
588C4×D4—42no—
589C4×D4—64no—
590C4×D4—64no—
591C4×D4—64no—
592#117—42no—
593#117—64no—
594C2×C4⋊C4—31no—
595C2×C4⋊C4—31no—
596C2×C4⋊C4—31no—
597C2×C4⋊C4—31no—
598C2×C4⋊C4—32no—
599C2×C4⋊C4—32no—
600C2×C4⋊C4—31no—
601C2×C4⋊C4—32no—
602C2×C4⋊C4—31no—
603C2×C4⋊C4—32no—
604C2×C4⋊C4—32no—
605C2×C4⋊C4—31no—
606C2×C4⋊C4—31no—
607C2×C4⋊C4C22×D311yescharacteristic
608C2×C4⋊C4C22×D311yescharacteristic
609C2×C4⋊C4C22×D312yes—
610C2×C4⋊C4C22×D311yescharacteristic
611C2×C22⋊C4—31no—
612C2×C22⋊C4—31no—
613C2×C22⋊C4—31no—
614C2×C22⋊C4—32no—
615C2×C22⋊C4—32no—
616C2×C22⋊C4—32no—
617C2×C22⋊C4—32no—
618C2×C22⋊C4—31no—
619C2×C22⋊C4—32no—
620C2×C22⋊C4—32no—
621C2×C22⋊C4—31no—
622C2×C22⋊C4—32no—
623C2×C22⋊C4—31no—
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—31no—
639C2×C22⋊C4—31no—
640C2×C22⋊C4—32no—
641C2×C22⋊C4—32no—
642C2×C22⋊C4—32no—
643C2×C22⋊C4—124no—
644C2×C22⋊C4C22×D312yes—
645C2×C22⋊C4C22×D312yes—
646C2×C22⋊C4C22×D312yes—
647C2×C22⋊C4C22×D311yescharacteristic
648C2×C22⋊C4C22×D311yescharacteristic
649C2×C22⋊C4C22×D312yes—
650C2×C22⋊C4C22×D312yes—
651C2×C42—31no—
652C2×C42—31no—
653C2×C42—31no—
654C2×C42—32no—
655C2×C42C22×D311yescharacteristic
656C2×C42C22×D311yescharacteristic
657C2×C42C22×D312yes—
658C2×C42C22×D312yes—
659#95—31no—
660#95—32no—
661#95—31no—
662#95—31no—
663#95—31no—
664#95—31no—
665#95—31no—
666#95—31no—
667#95—31no—
668#95—32no—
669#95—32no—
670#95—32no—
671#95C22×D311yescharacteristic
672#95C22×D312yes—
673#95C22×D311yescharacteristic
674#95C22×D312yes—
675C23×C3—22no—
676C23×C3—21no—
677C23×C3—21no—
678C23×C3—22no—
679C23×C3—22no—
680C23×C3—22no—
681C23×C3—21no—
682C23×C3—21no—
683C23×C3—22no—
684C23×C3—21no—
685C23×C3—21no—
686C23×C3—22no—
687C23×C3C22×D412yes—
688C23×C3C22×D414yes—
689C23×C3C2511yescharacteristic
690C22×D3—22no—
691C22×D3—21no—
692C22×D3—21no—
693C22×D3—21no—
694C22×D3—22no—
695C22×D3—22no—
696C22×D3—22no—
697C22×D3—21no—
698C22×D3—21no—
699C22×D3—22no—
700C22×D3—22no—
701C22×D3—21no—
702C22×D3—22no—
703C22×D3—22no—
704C22×D3—22no—
705C22×D3—22no—
706C22×D3—22no—
707C22×D3—22no—
708C22×D3—22no—
709C22×D3—48no—
710C22×D3—48no—
711C22×D3—48no—
712C22×D3—48no—
713C22×D3—48no—
714C22×D3—84no—
715C22×D3—84no—
716C22×D3—84no—
717C22×D3—84no—
718C22×D3—84no—
719C22×D3—84no—
720C22×D3—84no—
721C22×D3—84no—
722C22×D3—84no—
723C22×D3C2×#4114yes—
724C22×D3H(5,𝔽2)12yes—
725C3×D4—28no—
726C3×D4—48no—
727C2×C3×C4—21no—
728C2×C3×C4—21no—
729C2×C3×C4—22no—
730C2×C3×C4—22no—
731C2×C3×C4—28no—
732C2×C3×C4—21no—
733C2×C3×C4—21no—
734C2×C3×C4—21no—
735C2×C3×C4—22no—
736C2×C3×C4—21no—
737C2×C3×C4—22no—
738C2×C3×C4—21no—
739C2×C3×C4—22no—
740C2×C3×C4—21no—
741C2×C3×C4—21no—
742C2×C3×C4—21no—
743C2×C3×C4—22no—
744C2×C3×C4—21no—
745C2×C3×C4—21no—
746C2×C3×C4—22no—
747C2×C3×C4—22no—
748C2×C3×C4—21no—
749C2×C3×C4—21no—
750C2×C3×C4—84no—
751C2×C3×C4C22×D414yes—
752C2×C3×C4C22×D412yes—
753C2×C3×C4C22×D412yes—
754C2×C3×C4C2×#4112yes—
755C2×C3×C4H(5,𝔽2)12yes—
756#67—28no—
757#67—48no—
758#67—48no—
759#67—84no—
760C2×Dic3—21no—
761C2×Dic3—21no—
762C2×Dic3—21no—
763C2×Dic3—21no—
764C2×Dic3—21no—
765C2×Dic3—22no—
766C2×Dic3—21no—
767C2×Dic3—21no—
768C2×Dic3—22no—
769C2×Dic3—21no—
770C2×Dic3—22no—
771C2×Dic3—21no—
772C2×Dic3—21no—
773C2×Dic3—22no—
774C2×Dic3—21no—
775C2×Dic3—21no—
776C2×Dic3—22no—
777C2×Dic3—21no—
778C2×Dic3—22no—
779C2×Dic3—21no—
780C2×Dic3—21no—
781C2×Dic3—21no—
782C2×Dic3—21no—
783C2×Dic3—21no—
784C2×Dic3—21no—
785C2×Dic3—21no—
786C2×Dic3—84no—
787C2×Dic3H(5,𝔽2)12yes—
788D12—28no—
789D12—48no—
790D12—48no—
791D12—44no—
792C4×D3—48no—
793C4×D3—44no—
794Dic6—44no—
795Dic6—84no—
796C24—32no—
797C24—31no—
798C24—32no—
799C24—64no—
800C24—64no—
801C24—64no—
802C24—64no—
803C24—64no—
804C24—122no—
805C24—122no—
806C24—122no—
807C24—122no—
808C24—122no—
809C24—122no—
810C24—122no—
811C24—122no—
812C24—122no—
813C24C23×D311yescharacteristic
814C24C23×D312yes—
815C2×Q8—62no—
816C2×Q8—64no—
817C2×Q8—62no—
818C2×Q8—62no—
819C2×Q8—122no—
820C2×Q8—122no—
821C2×D4—22no—
822C2×D4—22no—
823C2×D4—34no—
824C2×D4—42no—
825C2×D4—42no—
826C2×D4—64no—
827C2×D4—64no—
828C2×D4—62no—
829C2×D4—64no—
830C2×D4—62no—
831C2×D4—62no—
832C2×D4—64no—
833C2×D4—64no—
834C2×D4—64no—
835C2×D4—64no—
836C2×D4—62no—
837C2×D4—64no—
838C2×D4—64no—
839C2×D4—62no—
840C2×D4—62no—
841C2×D4—62no—
842C2×D4—62no—
843C2×D4—1216no—
844C2×D4—122no—
845C2×D4—122no—
846C2×D4—122no—
847C2×D4—122no—
848C2×D4—122no—
849C2×D4—122no—
850C2×D4—1216no—
851C2×D4—1232no—
852C2×D4C2×D1214yes—
853C2×D4C2×D1218yes—
854C22×C4—22no—
855C22×C4—22no—
856C22×C4—31no—
857C22×C4—31no—
858C22×C4—31no—
859C22×C4—31no—
860C22×C4—31no—
861C22×C4—32no—
862C22×C4—31no—
863C22×C4—31no—
864C22×C4—32no—
865C22×C4—42no—
866C22×C4—42no—
867C22×C4—42no—
868C22×C4—64no—
869C22×C4—64no—
870C22×C4—64no—
871C22×C4—62no—
872C22×C4—62no—
873C22×C4—62no—
874C22×C4—122no—
875C22×C4—122no—
876C22×C4—122no—
877C22×C4C2×D1214yes—
878C22×C4C23×D311yescharacteristic
879C22×C4C23×D311yescharacteristic
880C22×C4C23×D312yes—
881C22×C4C23×D311yescharacteristic
882C22×C4C23×D311yescharacteristic
883C22×C4C23×D312yes—
884C22×C4C23×D312yes—
885C22×C4C23×D311yescharacteristic
886C22×C4C23×D311yescharacteristic
887C4⋊C4—22no—
888C4⋊C4—22no—
889C4⋊C4—42no—
890C4⋊C4—62no—
891C4⋊C4—64no—
892C4⋊C4—62no—
893C4⋊C4—62no—
894C4⋊C4—62no—
895C4⋊C4—62no—
896C4⋊C4—62no—
897C4⋊C4—64no—
898C4⋊C4—64no—
899C4⋊C4—64no—
900C4⋊C4—122no—
901C4⋊C4—121no—
902C4⋊C4—121no—
903C4⋊C4C2×D1214yes—
904C22⋊C4—42no—
905C22⋊C4—42no—
906C22⋊C4—42no—
907C22⋊C4—42no—
908C22⋊C4—41no—
909C22⋊C4—41no—
910C22⋊C4—62no—
911C22⋊C4—64no—
912C22⋊C4—64no—
913C22⋊C4—64no—
914C22⋊C4—62no—
915C22⋊C4—62no—
916C22⋊C4—62no—
917C22⋊C4—62no—
918C22⋊C4—64no—
919C22⋊C4—64no—
920C22⋊C4—64no—
921C22⋊C4—64no—
922C22⋊C4—64no—
923C22⋊C4—62no—
924C22⋊C4—64no—
925C22⋊C4—122no—
926C22⋊C4—122no—
927C22⋊C4—122no—
928C22⋊C4—122no—
929C22⋊C4—122no—
930C22⋊C4—122no—
931C22⋊C4—122no—
932C22⋊C4—122no—
933C22⋊C4—122no—
934C22⋊C4—122no—
935C22⋊C4—122no—
936C22⋊C4—122no—
937C22⋊C4—122no—
938C22⋊C4—121no—
939C22⋊C4—121no—
940C22⋊C4—122no—
941C22⋊C4—122no—
942C22⋊C4C2×D1218yes—
943C42—22no—
944C42—22no—
945C42—42no—
946C42—42no—
947C42—62no—
948C42—62no—
949C42—62no—
950C42—64no—
951C22×C3—24no—
952C22×C3—22no—
953C22×C3—24no—
954C22×C3—22no—
955C22×C3—24no—
956C22×C3—22no—
957C22×C3—42no—
958C22×C3—41no—
959C22×C3—41no—
960C22×C3—42no—
961C22×C3—41no—
962C22×C3—42no—
963C22×C3—42no—
964C22×C3—41no—
965C22×C3C23×D411yescharacteristic
966C22×C3C22×#4111yescharacteristic
967C22×C3C2×H(5,𝔽2)11yescharacteristic
968C22×C3C2×H(5,𝔽2)11yescharacteristic
969C22×C3C2×H(5,𝔽2)11yescharacteristic
970C22×C3#58511yescharacteristic
971C22×C3#58511yescharacteristic
972C2×D3—24no—
973C2×D3—22no—
974C2×D3—22no—
975C2×D3—24no—
976C2×D3—24no—
977C2×D3—22no—
978C2×D3—41no—
979C2×D3—42no—
980C2×D3—42no—
981C2×D3—41no—
982C2×D3—41no—
983C2×D3—42no—
984C2×D3—41no—
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—816no—
994C2×D3—816no—
995C3×C4—22no—
996C3×C4—24no—
997C3×C4—41no—
998C3×C4—41no—
999C3×C4—42no—
1000C3×C4—41no—
1001C3×C4—42no—
1002C3×C4—41no—
1003C3×C4#54614yes—
1004Dic3—22no—
1005Dic3—42no—
1006Dic3—41no—
1007Dic3—41no—
1008Dic3—42no—
1009Dic3—41no—
1010Dic3—41no—
1011Dic3—41no—
1012Dic3—41no—
1013C23—21no—
1014C23—22no—
1015C23—21no—
1016C23—22no—
1017C23—22no—
1018C23—21no—
1019C23—21no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—21no—
1024C23—21no—
1025C23—34no—
1026C23—32no—
1027C23—62no—
1028C23—61no—
1029C23—61no—
1030C23—62no—
1031C23—61no—
1032C23—61no—
1033C23—62no—
1034C23—61no—
1035C23—62no—
1036C23—62no—
1037C23—62no—
1038C23—61no—
1039C23—62no—
1040C23—62no—
1041C23—62no—
1042C23—62no—
1043C23—62no—
1044C23—62no—
1045C23—62no—
1046C23—128no—
1047C23—128no—
1048C23—128no—
1049C23—128no—
1050C23—128no—
1051C23—244no—
1052C23—244no—
1053C23—244no—
1054C23—244no—
1055C23—244no—
1056C23—244no—
1057C23—244no—
1058C23—244no—
1059C23—244no—
1060C23C22×D1212yes—
1061C23C22×D1214yes—
1062C23C24×D311yescharacteristic
1063Q8—124no—
1064Q8—244no—
1065D4—28no—
1066D4—48no—
1067D4—68no—
1068D4—68no—
1069D4—128no—
1070D4—128no—
1071D4—128no—
1072D4—128no—
1073D4—124no—
1074D4—244no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—28no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—22no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—22no—
1092C2×C4—21no—
1093C2×C4—22no—
1094C2×C4—21no—
1095C2×C4—22no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—32no—
1099C2×C4—61no—
1100C2×C4—61no—
1101C2×C4—61no—
1102C2×C4—61no—
1103C2×C4—61no—
1104C2×C4—62no—
1105C2×C4—61no—
1106C2×C4—61no—
1107C2×C4—61no—
1108C2×C4—62no—
1109C2×C4—62no—
1110C2×C4—61no—
1111C2×C4—62no—
1112C2×C4—61no—
1113C2×C4—61no—
1114C2×C4—61no—
1115C2×C4—61no—
1116C2×C4—61no—
1117C2×C4—61no—
1118C2×C4—61no—
1119C2×C4—61no—
1120C2×C4—62no—
1121C2×C4—61no—
1122C2×C4—61no—
1123C2×C4—62no—
1124C2×C4—61no—
1125C2×C4—84no—
1126C2×C4—128no—
1127C2×C4—124no—
1128C2×C4—244no—
1129C2×C4C22×D1214yes—
1130C2×C4C22×D1212yes—
1131C2×C4C22×D1212yes—
1132C2×C4#100412yes—
1133C2×C4D3×#4112yes—
1134C2×C3—42no—
1135C2×C3—44no—
1136C2×C3C2×#54611yescharacteristic
1137C2×C3#348411yescharacteristic
1138C2×C3#350011yescharacteristic
1139C2×C3#351311yescharacteristic
1140C2×C3#351411yescharacteristic
1141C2×C3#354611yescharacteristic
1142C2×C3#355811yescharacteristic
1143D3—44no—
1144D3—42no—
1145D3—82no—
1146C22—22no—
1147C22—24no—
1148C22—24no—
1149C22—22no—
1150C22—24no—
1151C22—22no—
1152C22—42no—
1153C22—41no—
1154C22—42no—
1155C22—41no—
1156C22—41no—
1157C22—42no—
1158C22—41no—
1159C22—42no—
1160C22—64no—
1161C22—62no—
1162C22—64no—
1163C22—62no—
1164C22—62no—
1165C22—64no—
1166C22—121no—
1167C22—122no—
1168C22—121no—
1169C22—122no—
1170C22—122no—
1171C22—121no—
1172C22—121no—
1173C22—122no—
1174C22—122no—
1175C22—122no—
1176C22—122no—
1177C22—122no—
1178C22—122no—
1179C22—122no—
1180C22—122no—
1181C22—2416no—
1182C22—2416no—
1183C22C23×D1211yescharacteristic
1184C22C2×#100411yescharacteristic
1185C22C2×D3×#4111yescharacteristic
1186C22#596411yescharacteristic
1187C22#596411yescharacteristic
1188C22D3×H(5,𝔽2)11yescharacteristic
1189C22D3×H(5,𝔽2)11yescharacteristic
1190C4—22no—
1191C4—24no—
1192C4—41no—
1193C4—41no—
1194C4—42no—
1195C4—41no—
1196C4—41no—
1197C4—42no—
1198C4—62no—
1199C4—121no—
1200C4—122no—
1201C4—121no—
1202C4—121no—
1203C4—121no—
1204C4—121no—
1205C4—122no—
1206C4—121no—
1207C4#555414yes—
1208C3#4487411yescharacteristic, complemented, Sylow
1209C2—42no—
1210C2—44no—
1211C2—124no—
1212C2—122no—
1213C2—242no—
1214C2C2×#555411yescharacteristic
1215C2#8584711yescharacteristic
1216C2#8586711yescharacteristic
1217C2#8667311yescharacteristic
1218C2#8677911yescharacteristic
1219C2#8688311yescharacteristic
1220C2#8696211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2363C2
prime radicalC2×#5609C2
hypercenter#2363D3
hypocenterC3#44874
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2363

Complements

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

NH ≅ G/Ntype
2. C2×#5603C2semidirect
3. C3×#2363C2semidirect
4. D4×(C2×D3)⋊C4C2semidirect
5. #82381C2semidirect
6. #82277C2semidirect
7. #82269C2semidirect
8. #76469C2semidirect
9. #76317C2semidirect
10. #76315C2semidirect
11. #76315C2semidirect
12. #76218C2semidirect
13. #76011C2semidirect
14. #75918C2semidirect
15. #75669C2semidirect
16. #74918C2semidirect
17. #74686C2semidirect
18. #73788C2semidirect
19. #73654C2semidirect
20. #73604C2semidirect
21. #73594C2semidirect
22. #73588C2semidirect
23. #73583C2semidirect
29. C2×C3×C4×D4C22semidirect
30. C2×C3×#117C22semidirect
33. C2×#936C22semidirect
34. C2×#936C22semidirect
35. C2×#935C22semidirect
36. C2×D4×Dic3C22semidirect
38. C22×(C2×D3)⋊C4C22semidirect
39. C2×#926C22semidirect
40. C2×#924C22semidirect
43. C2×#897C22semidirect
44. C2×#897C22semidirect
47. C2×#888C22semidirect
48. C2×#887C22semidirect
49. C2×#886C22semidirect
52. C2×#879C22semidirect
53. C2×#878C22semidirect
55. C2×#875C22semidirect
56. C2×#875C22semidirect
57. C3×#390C22semidirect
58. C3×#390C22semidirect
59. C3×#389C22semidirect
60. C3×#388C22semidirect
61. C3×#386C22semidirect
62. C3×C4×C4⋊C4C22semidirect
63. C3×C4×C22⋊C4C22semidirect
64. C3×C4×C22⋊C4C22semidirect
65. #5213C22semidirect
66. #5213C22semidirect
67. #5213C22semidirect
68. #4994C22semidirect
69. #4994C22semidirect
72. #4988C22semidirect
73. #4988C22semidirect
74. #4988C22semidirect
75. #4987C22semidirect
76. #4984C22semidirect
77. #4973C22semidirect
81. #4961C22semidirect
82. #4961C22semidirect
83. #4961C22semidirect
84. #4961C22semidirect
85. #4961C22semidirect
86. #4961C22semidirect
87. #4958C22semidirect
88. #4958C22semidirect
89. #4955C22semidirect
90. #4955C22semidirect
91. #4955C22semidirect
92. #4955C22semidirect
93. #4955C22semidirect
94. #4955C22semidirect
95. #4955C22semidirect
96. #4953C22semidirect
97. #4953C22semidirect
98. #4953C22semidirect
99. #4940C22semidirect
100. #4940C22semidirect
101. #4940C22semidirect
103. #4939C22semidirect
104. #4939C22semidirect
105. #4939C22semidirect
106. C4×(C2×D3)⋊C4C22semidirect
107. C4×(C2×D3)⋊C4C22semidirect
108. C4×(C2×D3)⋊C4C22semidirect
109. C4×C4⋊Dic3C22semidirect
110. C4×C4⋊Dic3C22semidirect
111. #4928C22semidirect
112. #4677C22semidirect
113. #4674C22semidirect
114. #4673C22semidirect
115. #4673C22semidirect
116. #4672C22semidirect
117. #4672C22semidirect
118. #4672C22semidirect
119. #4672C22semidirect
120. #4670C22semidirect
121. #4670C22semidirect
122. #4668C22semidirect
123. #4668C22semidirect
124. #4661C22semidirect
125. #4659C22semidirect
146. #2363D3semidirect
312. C2×C4×D4C2×D3semidirect
314. C2×#117C2×D3semidirect
350. #390C2×D3semidirect
351. #390C2×D3semidirect
354. #389C2×D3semidirect
360. #388C2×D3semidirect
366. #386C2×D3semidirect
379. C4×C4⋊C4C2×D3semidirect
383. C4×C22⋊C4C2×D3semidirect
384. C4×C22⋊C4C2×D3semidirect
1208. C3#44874semidirect

Maximal subgroups

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

subgroupindex
C2×#56092
C2×#56032
C3×#23632
D4×(C2×D3)⋊C42
#823812
#822772
#822692
#764692
#763172
#763152
#762182
#760112
#759182
#756692
#749182
#746862
#737882
#736542
#736042
#735942
#735882
#735832
#448743