Finite Group Databasebeta

← #10957211

Subgroups — #10957211

Order 768.

3288 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#520C211yesmaximal, characteristic, complemented
2C2×#5829C211yesmaximal, characteristic
3C2×#5545C211yesmaximal, characteristic, complemented
4#84088C211yesmaximal, characteristic, complemented
5#82488C211yesmaximal, characteristic, complemented
6#82466C211yesmaximal, characteristic, complemented
7#82464C211yesmaximal, characteristic, complemented
8C4×#947C211yesmaximal, characteristic, complemented
9#82398C212yesmaximal, complemented
10D4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11#82395C212yesmaximal, complemented
12#82342C212yesmaximal, complemented
13#82334C211yesmaximal, characteristic, complemented
14C4×#939C212yesmaximal, complemented
15C4×D4×Dic3C211yesmaximal, characteristic, complemented
16#82271C212yesmaximal, complemented
17#82242C212yesmaximal, complemented
18#82236C211yesmaximal, characteristic, complemented
19#82225C211yesmaximal, characteristic, complemented
20#82163C211yesmaximal, characteristic, complemented
21#82161C211yesmaximal, characteristic, complemented
22#82158C212yesmaximal, complemented
23C2×#4990C212yesmaximal, complemented
24#34309—31nomaximal, Sylow
25C22×C3×#41C2211yescharacteristic
26C22×D3×D4C2211yescharacteristic
27C3×#520—28no—
28C2×C3×C4×Q8C2211yescharacteristic, complemented
29C2×C3×C4×Q8C2211yescharacteristic, complemented
30C2×C3×C4×D4C2211yescharacteristic
31C2×C3×C4×D4C2211yescharacteristic
32C2×C3×C4×D4C2212yescomplemented
33C2×C3×C4×D4C2212yescomplemented
34C2×C3×#117C2211yescharacteristic, complemented
35C2×C3×#117C2212yescomplemented
36C22×C3×C4⋊C4C2212yescomplemented
37C22×C3×C4⋊C4C2211yescharacteristic, complemented
38#5829C4116yescomplemented
39C2×#947C2211yescharacteristic
40C2×#946C2211yescharacteristic
41C2×#939C2212yes—
42C2×#937C2212yes—
43C2×D4×Dic3C2211yescharacteristic
44C2×D4×Dic3C2211yescharacteristic
45C2×D4×Dic3C2211yescharacteristic
46C2×#930C2211yescharacteristic
47C2×#929C2212yes—
48C2×C4×#67C2212yes—
49C2×C4×#67C2211yescharacteristic
50C2×C4×#67C2212yescomplemented
51C22×(C2×D3)⋊C4C2212yes—
52C22×(C2×D3)⋊C4C2212yes—
53C22×(C2×D3)⋊C4C2212yes—
54C22×C4×Dic3C2212yescomplemented
55#5545—28no—
56C2×#893C2211yescharacteristic
57C2×#892C2211yescharacteristic
58C2×#67⋊C4C2212yes—
59C2×D3×C22⋊C4C2212yes—
60C2×C4×D12C2211yescharacteristic
61C2×#872C2211yescharacteristic
62#5229C2211yescharacteristic, complemented
63#5229C2211yescharacteristic, complemented
64#5220C2212yescomplemented
65#5220C2212yescomplemented
66#5213C2212yes—
67#5213C2212yes—
68#5213C2212yescomplemented
69#5212C2211yescharacteristic, complemented
70#5211C2212yescomplemented
71#5210C2212yescomplemented
72C4×#217C2211yescharacteristic, complemented
73C4×#217C2212yescomplemented
74C4×#217C2212yescomplemented
75C2×C3⋊#95C2212yescomplemented
76C2×C3⋊#95C2212yescomplemented
77#4990C2212yes—
78#4990C2211yescharacteristic
79#4990C2211yescharacteristic
80#4990C2212yes—
81#4990C2212yes—
82#4990C2212yescomplemented
83#4990C2212yescomplemented
84#4990C2212yescomplemented
85#4990C2212yescomplemented
86#4990C2212yescomplemented
87#4989C2212yescomplemented
88#4989C2212yescomplemented
89#4989C2212yescomplemented
90#4988C2211yescharacteristic
91#4987C2211yescharacteristic
92#4978C2212yescomplemented
93#4978C2212yescomplemented
94#4977C2211yescharacteristic, complemented
95#4976C2211yescharacteristic, complemented
96#4976C2211yescharacteristic, complemented
97#4976C2212yescomplemented
98Dic3×C4⋊C4C2211yescharacteristic, complemented
99Dic3×C4⋊C4C2211yescharacteristic, complemented
100#4972C2211yescharacteristic, complemented
101#4958C2212yes—
102#4957C2211yescharacteristic
103#4957C2211yescharacteristic
104#4957C2212yescomplemented
105#4956C2212yescomplemented
106#4955C2212yes—
107#4946C2212yescomplemented
108#4945C2211yescharacteristic, complemented
109#4945C2211yescharacteristic, complemented
110#4942C2212yescomplemented
111Dic3×C22⋊C4C2212yescomplemented
112Dic3×C22⋊C4C2212yescomplemented
113#4940C2212yes—
114#4940C2212yes—
115#4940C2212yescomplemented
116#4939C2211yescharacteristic
117C4×(C2×D3)⋊C4C2211yescharacteristic
118C4×(C2×D3)⋊C4C2212yescomplemented
119C4×(C2×D3)⋊C4C2212yescomplemented
120C4×(C2×D3)⋊C4C2212yescomplemented
121C4×C4⋊Dic3C2211yescharacteristic, complemented
122#4933C2212yescomplemented
123C4×Dic3⋊C4C2212yescomplemented
124C4×Dic3⋊C4C2211yescharacteristic, complemented
125C42×Dic3C2211yescharacteristic, complemented
126#4928C2211yescharacteristic, complemented
127C2×#546—31no—
128C2×#520D311yescharacteristic, complemented
129C2×#518—31no—
130#2367—31no—
131#2364—32no—
132#2362—31no—
133#2361—31no—
134#2359—32no—
135#2358—32no—
136#2352—31no—
137#2349—31no—
138#2342—32no—
139#2339—31no—
140D4×C22⋊C4—31no—
141#2324—31no—
142#2323—31no—
143#2322—32no—
144#2321—32no—
145C4×#124—31no—
146C4×#121—32no—
147#2293—31no—
148C2×#388—32no—
149C42×D4—31no—
150C24×D3C2312yes—
151C2×C3×#41—24no—
152C2×C3×#41—24no—
153C2×C3×#41C2×C418yescomplemented
154C22×C3×Q8C2311yescharacteristic
155C22×C3×D4C2312yes—
156C22×C3×D4C2311yescharacteristic
157C23×C3×C4C2312yes—
158C23×C3×C4C2311yescharacteristic
159C23×C3×C4C2312yes—
160C23×C3×C4C2312yes—
161C23×C3×C4C2312yes—
162C22×#67C2312yes—
163C22×#67C2312yes—
164C22×#67C2311yescharacteristic
165C23×Dic3C2312yes—
166C23×Dic3C2312yes—
167C23×Dic3C2312yes—
168C2×D3×D4—24no—
169C2×D3×D4—24no—
170C2×D3×D4C2×C418yescomplemented
171C22×D12C2311yescharacteristic
172C22×C4×D3C2311yescharacteristic
173C22×C4×D3C2312yes—
174C22×C4×D3C2312yes—
175C3×C4×Q8—24no—
176C3×C4×Q8—24no—
177C3×C4×D4—24no—
178C3×C4×D4—28no—
179C3×C4×D4—28no—
180C3×C4×D4D418yescomplemented
181C3×#117—28no—
182C3×#117—24no—
183C2×C3×C4⋊C4—28no—
184C2×C3×C4⋊C4—24no—
185C2×C3×C4⋊C4C2311yescharacteristic
186C2×C3×C4⋊C4C2311yescharacteristic
187C2×C3×C4⋊C4C2311yescharacteristic
188C2×C3×C4⋊C4C2312yes—
189C2×C3×C4⋊C4C2312yes—
190C2×C3×C4⋊C4C2312yes—
191C2×C3×C4⋊C4C2311yescharacteristic
192C2×C3×C22⋊C4C2312yes—
193C2×C3×C22⋊C4C2311yescharacteristic
194C2×C3×C22⋊C4C2311yescharacteristic
195C2×C3×C22⋊C4C2312yes—
196C2×C3×C42C2311yescharacteristic
197C2×C3×C42C2312yes—
198C2×C3×C42C2312yes—
199C2×C3×C42C2311yescharacteristic
200C2×#217C2312yes—
201C2×#217C2312yes—
202C2×#217C2311yescharacteristic
203C2×#217C2311yescharacteristic
204C2×#217C2312yes—
205C2×#217C2312yes—
206C2×#217C2311yescharacteristic
207#947C2×C418yescomplemented
208#946C2×C418yescomplemented
209#939C2×C4116yescomplemented
210#937C2×C4116yescomplemented
211D4×Dic3—24no—
212D4×Dic3—24no—
213D4×Dic3C2×C418yescomplemented
214#930C2×C418yescomplemented
215#929C2×C4116yescomplemented
216C4×#67—28no—
217C4×#67—44no—
218C4×#67C2×C418yescomplemented
219C2×(C2×D3)⋊C4—28no—
220C2×(C2×D3)⋊C4—44no—
221C2×(C2×D3)⋊C4C2×C4116yescomplemented
222C2×(C2×D3)⋊C4C2311yescharacteristic
223C2×(C2×D3)⋊C4C2312yes—
224C2×(C2×D3)⋊C4C2311yescharacteristic
225C2×(C2×D3)⋊C4C2312yes—
226C2×(C2×D3)⋊C4C2312yes—
227C2×(C2×D3)⋊C4C2311yescharacteristic
228C2×(C2×D3)⋊C4C2312yes—
229C2×(C2×D3)⋊C4C2311yescharacteristic
230C2×(C2×D3)⋊C4C2312yes—
231C2×(C2×D3)⋊C4C2312yes—
232C2×(C2×D3)⋊C4C2312yes—
233C2×(C2×D3)⋊C4C2312yes—
234C2×(C2×D3)⋊C4C2312yes—
235C2×(C2×D3)⋊C4C2312yes—
236C2×(C2×D3)⋊C4C2312yes—
237C2×(C2×D3)⋊C4C2312yes—
238C2×(C2×D3)⋊C4C2311yescharacteristic
239C2×C4⋊Dic3C2311yescharacteristic
240C2×C4⋊Dic3C2311yescharacteristic
241C2×C4⋊Dic3C2311yescharacteristic
242C2×Dic3⋊C4C2311yescharacteristic
243C2×Dic3⋊C4C2311yescharacteristic
244C2×Dic3⋊C4C2312yes—
245C2×Dic3⋊C4C2311yescharacteristic
246C2×Dic3⋊C4C2311yescharacteristic
247C2×Dic3⋊C4C2312yes—
248C2×Dic3⋊C4C2312yes—
249C2×Dic3⋊C4C2311yescharacteristic
250C2×C4×Dic3—44no—
251C2×C4×Dic3C2311yescharacteristic
252C2×C4×Dic3C2311yescharacteristic
253C2×C4×Dic3C2312yes—
254C2×C4×Dic3C2311yescharacteristic
255C2×C4×Dic3C2312yes—
256C2×C4×Dic3C2311yescharacteristic
257C2×C4×Dic3C2311yescharacteristic
258C2×C4×Dic3C2311yescharacteristic
259C2×C4×Dic3C2312yes—
260C2×C4×Dic3C2312yes—
261C2×C4×Dic3C2311yescharacteristic
262#893—24no—
263#892—24no—
264#67⋊C4—28no—
265D3×C22⋊C4—28no—
266C4×D12—24no—
267#872—24no—
268C3⋊#95C2312yes—
269C3⋊#95C2311yescharacteristic
270C3⋊#95C2311yescharacteristic
271C3⋊#95C2312yes—
272C3⋊#95C2311yescharacteristic
273C3⋊#95C2312yes—
274C3⋊#95C2312yes—
275C3⋊#95C2312yes—
276C3⋊#95C2312yes—
277C3⋊#95C2311yescharacteristic
278C3⋊#95C2312yes—
279C3⋊#95C2312yes—
280C3⋊#95C2312yes—
281C3⋊#95C2312yes—
282C3⋊#95C2312yes—
283C3⋊#95C2312yes—
284C3⋊#95C2311yescharacteristic
285C3⋊#95C2312yes—
286C3⋊#95C2311yescharacteristic
287C22×#41C2×D311yescharacteristic
288C23×D4—31no—
289#546—316no—
290C2×#124—31no—
291C2×#123—32no—
292C2×C22⋊Q8—31no—
293C2×#121—32no—
294C2×#121—31no—
295C2×#120—32no—
296#520—28no—
297#518—68no—
298C2×C4×Q8C2×D311yescharacteristic, complemented
299C2×C4×Q8C2×D311yescharacteristic, complemented
300C2×C4×D4—31no—
301C2×C4×D4—31no—
302C2×C4×D4—31no—
303C2×C4×D4—31no—
304C2×C4×D4—32no—
305C2×C4×D4—32no—
306C2×C4×D4—31no—
307C2×C4×D4—32no—
308C2×C4×D4—31no—
309C2×C4×D4C2×D311yescharacteristic
310C2×C4×D4C2×D311yescharacteristic
311C2×C4×D4C2×D312yescomplemented
312C2×C4×D4C2×D312yescomplemented
313C2×#117—31no—
314C2×#117—31no—
315C2×#117C2×D311yescharacteristic, complemented
316C2×#117C2×D312yescomplemented
317C22×C4⋊C4C2×D312yescomplemented
318C22×C4⋊C4C2×D311yescharacteristic, complemented
319C22×C22⋊C4—32no—
320C22×C22⋊C4—32no—
321C22×C22⋊C4—32no—
322C22×C22⋊C4—32no—
323C22×C42—32no—
324#391—31no—
325#391—31no—
326#390—31no—
327#390—31no—
328#390—32no—
329#390—31no—
330#390—31no—
331#389—31no—
332#389—32no—
333#389—31no—
334#389—31no—
335#389—31no—
336#388—32no—
337#388—32no—
338#388—32no—
339#388—31no—
340#388—32no—
341#388—32no—
342#388—32no—
343#388—32no—
344#388—31no—
345#388—32no—
346#388—31no—
347#388—31no—
348#388—32no—
349#388—32no—
350#388—32no—
351#387—32no—
352#387—32no—
353#387—32no—
354#386—32no—
355#386—32no—
356#386—32no—
357#386—32no—
358#386—32no—
359#386—32no—
360#386—32no—
361#385—32no—
362#385—32no—
363#385—32no—
364#385—32no—
365#385—32no—
366#382—31no—
367#381—32no—
368#380—31no—
369#380—31no—
370#380—32no—
371#379—32no—
372C4×C4⋊C4—31no—
373C4×C4⋊C4—31no—
374C4×C4⋊C4—31no—
375C4×C4⋊C4—31no—
376C4×C4⋊C4—32no—
377C4×C22⋊C4—32no—
378C4×C22⋊C4—31no—
379C4×C22⋊C4—32no—
380C4×C22⋊C4—32no—
381C4×C22⋊C4—32no—
382C4×C22⋊C4—31no—
383C4×C22⋊C4—32no—
384C4×C22⋊C4—32no—
385C4×C22⋊C4—32no—
386C2×#95—32no—
387C2×#95—32no—
388C43—31no—
389C24×C3C2411yescharacteristic
390C24×C3C2412yes—
391C23×D3—24no—
392C23×D3—24no—
393C23×D3—42no—
394C23×D3—42no—
395C23×D3—42no—
396C23×D3—42no—
397C23×D3C22×C418yes—
398C23×D3C2411yescharacteristic
399C23×D3C2412yes—
400C3×#41—232no—
401C2×C3×Q8—22no—
402C2×C3×Q8—22no—
403C2×C3×Q8C22×C414yes—
404C2×C3×D4—24no—
405C2×C3×D4—24no—
406C2×C3×D4C22×C418yes—
407C2×C3×D4C22×C414yes—
408C2×C3×D4C2×D414yes—
409C2×C3×D4#4114yes—
410C22×C3×C4—24no—
411C22×C3×C4—24no—
412C22×C3×C4—22no—
413C22×C3×C4—22no—
414C22×C3×C4—24no—
415C22×C3×C4—24no—
416C22×C3×C4—42no—
417C22×C3×C4—42no—
418C22×C3×C4—42no—
419C22×C3×C4—42no—
420C22×C3×C4—42no—
421C22×C3×C4—42no—
422C22×C3×C4C22×C418yes—
423C22×C3×C4C22×C414yes—
424C22×C3×C4C2×D418yes—
425C22×C3×C4C2412yes—
426C22×C3×C4C2411yescharacteristic
427C22×C3×C4C2411yescharacteristic
428C22×C3×C4C2412yes—
429C22×C3×C4C2411yescharacteristic
430C22×C3×C4C2412yes—
431C22×C3×C4C2411yescharacteristic
432C22×C3×C4C2411yescharacteristic
433C22×C3×C4C2411yescharacteristic
434C2×#67—24no—
435C2×#67—24no—
436C2×#67—42no—
437C2×#67—41no—
438C2×#67—41no—
439C2×#67—42no—
440C2×#67C22×C418yes—
441C2×#67C22×C414yes—
442C2×#67C22×C418yes—
443C22×Dic3—24no—
444C22×Dic3—24no—
445C22×Dic3—24no—
446C22×Dic3—42no—
447C22×Dic3—42no—
448C22×Dic3—42no—
449C22×Dic3—42no—
450C22×Dic3—42no—
451C22×Dic3C22×C418yes—
452C22×Dic3C2411yescharacteristic
453C22×Dic3C2412yes—
454C22×Dic3C2411yescharacteristic
455C22×Dic3C2412yes—
456C22×Dic3C2411yescharacteristic
457C22×Dic3C2411yescharacteristic
458C22×Dic3C2411yescharacteristic
459C22×Dic3C2411yescharacteristic
460C22×Dic3C2412yes—
461C22×Dic3C2411yescharacteristic
462D3×D4—232no—
463C2×D12—22no—
464C2×D12—22no—
465C2×D12C22×C414yes—
466C2×C4×D3—22no—
467C2×C4×D3—22no—
468C2×C4×D3—24no—
469C2×C4×D3—24no—
470C2×C4×D3—42no—
471C2×C4×D3—42no—
472C2×C4×D3—42no—
473C2×C4×D3—42no—
474C2×C4×D3C22×C414yes—
475C3×C4⋊C4—24no—
476C3×C4⋊C4—22no—
477C3×C4⋊C4—24no—
478C3×C4⋊C4—24no—
479C3×C4⋊C4—22no—
480C3×C4⋊C4—22no—
481C3×C4⋊C4C2×D414yes—
482C3×C22⋊C4—24no—
483C3×C22⋊C4—22no—
484C3×C22⋊C4—22no—
485C3×C22⋊C4C2×D418yes—
486C3×C42—24no—
487C3×C42—24no—
488C3×C42—22no—
489C3×C42C2×D414yes—
490#217—24no—
491#217—24no—
492#217—22no—
493#217—41no—
494#217—42no—
495#217C22×C414yes—
496#217C22×C418yes—
497(C2×D3)⋊C4—22no—
498(C2×D3)⋊C4—22no—
499(C2×D3)⋊C4—24no—
500(C2×D3)⋊C4—24no—
501(C2×D3)⋊C4—24no—
502(C2×D3)⋊C4—22no—
503(C2×D3)⋊C4—24no—
504(C2×D3)⋊C4—42no—
505(C2×D3)⋊C4—42no—
506(C2×D3)⋊C4—42no—
507(C2×D3)⋊C4—41no—
508(C2×D3)⋊C4—42no—
509(C2×D3)⋊C4C22×C414yes—
510(C2×D3)⋊C4C22×C418yes—
511(C2×D3)⋊C4C22×C418yes—
512(C2×D3)⋊C4C22×C418yes—
513(C2×D3)⋊C4C22×C418yes—
514C4⋊Dic3—22no—
515C4⋊Dic3—22no—
516C4⋊Dic3C22×C414yes—
517Dic3⋊C4—22no—
518Dic3⋊C4—22no—
519Dic3⋊C4—41no—
520Dic3⋊C4—41no—
521Dic3⋊C4—42no—
522Dic3⋊C4—42no—
523Dic3⋊C4C22×C414yes—
524Dic3⋊C4C22×C418yes—
525C4×Dic3—22no—
526C4×Dic3—24no—
527C4×Dic3—22no—
528C4×Dic3—22no—
529C4×Dic3—24no—
530C4×Dic3—42no—
531C4×Dic3—42no—
532C4×Dic3—41no—
533C4×Dic3—41no—
534C4×Dic3—41no—
535C4×Dic3C22×C414yes—
536C25—32no—
537C2×#41—24no—
538C2×#41—24no—
539C2×#41C4×D318yescomplemented
540C22×Q8C22×D311yescharacteristic
541C22×D4—32no—
542C22×D4—31no—
543C22×D4—32no—
544C22×D4—38no—
545C22×D4—31no—
546C22×D4—64no—
547C22×D4—64no—
548C22×D4C22×D312yes—
549C22×D4C22×D311yescharacteristic
550C23×C4—32no—
551C23×C4—31no—
552C23×C4—32no—
553C23×C4—32no—
554C23×C4—32no—
555C23×C4—32no—
556C23×C4C22×D312yes—
557C23×C4C22×D311yescharacteristic
558C23×C4C22×D312yes—
559C23×C4C22×D312yes—
560C23×C4C22×D312yes—
561#124—38no—
562#123—316no—
563C22⋊Q8—38no—
564#121—316no—
565#121—38no—
566#120—316no—
567C4×Q8—24no—
568C4×Q8—24no—
569C4×D4—24no—
570C4×D4—28no—
571C4×D4—28no—
572C4×D4—38no—
573C4×D4—38no—
574C4×D4—64no—
575C4×D4—64no—
576C4×D4—68no—
577C4×D4—64no—
578C4×D4—68no—
579C4×D4—64no—
580C4×D4—124no—
581C4×D4#6718yescomplemented
582#117—28no—
583#117—24no—
584#117—64no—
585#117—64no—
586C2×C4⋊C4—28no—
587C2×C4⋊C4—24no—
588C2×C4⋊C4—31no—
589C2×C4⋊C4—31no—
590C2×C4⋊C4—32no—
591C2×C4⋊C4—31no—
592C2×C4⋊C4—31no—
593C2×C4⋊C4—31no—
594C2×C4⋊C4—31no—
595C2×C4⋊C4—32no—
596C2×C4⋊C4—32no—
597C2×C4⋊C4—31no—
598C2×C4⋊C4—31no—
599C2×C4⋊C4C22×D312yes—
600C2×C4⋊C4C22×D311yescharacteristic
601C2×C4⋊C4C22×D311yescharacteristic
602C2×C4⋊C4C22×D312yes—
603C2×C4⋊C4C22×D312yes—
604C2×C4⋊C4C22×D311yescharacteristic
605C2×C4⋊C4C22×D311yescharacteristic
606C2×C22⋊C4—32no—
607C2×C22⋊C4—31no—
608C2×C22⋊C4—316no—
609C2×C22⋊C4—31no—
610C2×C22⋊C4—32no—
611C2×C22⋊C4—32no—
612C2×C22⋊C4—32no—
613C2×C22⋊C4—32no—
614C2×C22⋊C4—32no—
615C2×C22⋊C4—31no—
616C2×C22⋊C4—32no—
617C2×C22⋊C4—32no—
618C2×C22⋊C4—31no—
619C2×C22⋊C4—31no—
620C2×C22⋊C4—31no—
621C2×C22⋊C4—32no—
622C2×C22⋊C4—32no—
623C2×C22⋊C4—32no—
624C2×C22⋊C4—32no—
625C2×C22⋊C4—31no—
626C2×C22⋊C4—32no—
627C2×C22⋊C4—32no—
628C2×C22⋊C4—31no—
629C2×C22⋊C4—32no—
630C2×C22⋊C4—32no—
631C2×C22⋊C4—68no—
632C2×C22⋊C4—68no—
633C2×C22⋊C4—124no—
634C2×C22⋊C4C22×D312yes—
635C2×C22⋊C4C22×D311yescharacteristic
636C2×C22⋊C4C22×D311yescharacteristic
637C2×C22⋊C4C22×D312yes—
638C2×C42—31no—
639C2×C42—32no—
640C2×C42—31no—
641C2×C42—31no—
642C2×C42—32no—
643C2×C42—31no—
644C2×C42—31no—
645C2×C42—31no—
646C2×C42—31no—
647C2×C42—32no—
648C2×C42—32no—
649C2×C42—124no—
650C2×C42C22×D311yescharacteristic
651C2×C42C22×D312yes—
652C2×C42C22×D312yes—
653C2×C42C22×D311yescharacteristic
654#95—31no—
655#95—31no—
656#95—32no—
657#95—32no—
658#95—32no—
659#95—32no—
660#95—32no—
661#95—32no—
662#95—31no—
663#95—32no—
664#95—32no—
665#95—32no—
666#95—31no—
667#95—32no—
668#95—31no—
669#95—32no—
670#95—32no—
671#95—32no—
672#95—31no—
673C23×C3—22no—
674C23×C3—22no—
675C23×C3—22no—
676C23×C3—22no—
677C23×C3—21no—
678C23×C3—21no—
679C23×C3—21no—
680C23×C3—21no—
681C23×C3—21no—
682C23×C3—21no—
683C23×C3C23×C412yes—
684C23×C3C23×C414yes—
685C23×C3C22×D414yes—
686C23×C3C2×#4114yes—
687C23×C3C2511yescharacteristic
688C22×D3—21no—
689C22×D3—22no—
690C22×D3—21no—
691C22×D3—22no—
692C22×D3—21no—
693C22×D3—22no—
694C22×D3—22no—
695C22×D3—22no—
696C22×D3—21no—
697C22×D3—22no—
698C22×D3—21no—
699C22×D3—21no—
700C22×D3—216no—
701C22×D3—48no—
702C22×D3—48no—
703C22×D3—84no—
704C22×D3—84no—
705C22×D3—84no—
706C22×D3—84no—
707C22×D3C23×C412yes—
708C22×D3C23×C414yes—
709C3×Q8—28no—
710C3×D4—216no—
711C3×D4C4×D4116yescomplemented
712C2×C3×C4—216no—
713C2×C3×C4—22no—
714C2×C3×C4—21no—
715C2×C3×C4—21no—
716C2×C3×C4—22no—
717C2×C3×C4—21no—
718C2×C3×C4—22no—
719C2×C3×C4—21no—
720C2×C3×C4—21no—
721C2×C3×C4—21no—
722C2×C3×C4—22no—
723C2×C3×C4—28no—
724C2×C3×C4—21no—
725C2×C3×C4—22no—
726C2×C3×C4—21no—
727C2×C3×C4—22no—
728C2×C3×C4—21no—
729C2×C3×C4—21no—
730C2×C3×C4—21no—
731C2×C3×C4—21no—
732C2×C3×C4—22no—
733C2×C3×C4—48no—
734C2×C3×C4—84no—
735C2×C3×C4—84no—
736C2×C3×C4C23×C412yes—
737C2×C3×C4C23×C414yes—
738C2×C3×C4C23×C412yes—
739C2×C3×C4C22×D414yes—
740C2×C3×C4C22×D412yes—
741C2×C3×C4C22×D412yes—
742C2×C3×C4C22×D412yes—
743C2×C3×C4C2×#4112yes—
744#67—216no—
745#67—44no—
746#67—48no—
747C2×Dic3—21no—
748C2×Dic3—21no—
749C2×Dic3—21no—
750C2×Dic3—21no—
751C2×Dic3—22no—
752C2×Dic3—21no—
753C2×Dic3—21no—
754C2×Dic3—21no—
755C2×Dic3—21no—
756C2×Dic3—22no—
757C2×Dic3—21no—
758C2×Dic3—21no—
759C2×Dic3—22no—
760C2×Dic3—21no—
761C2×Dic3—22no—
762C2×Dic3—22no—
763C2×Dic3—21no—
764C2×Dic3—21no—
765C2×Dic3—21no—
766C2×Dic3—21no—
767C2×Dic3—22no—
768C2×Dic3—21no—
769C2×Dic3—22no—
770C2×Dic3—22no—
771C2×Dic3—21no—
772C2×Dic3—48no—
773C2×Dic3—48no—
774C2×Dic3—84no—
775C2×Dic3C23×C412yes—
776C2×Dic3C23×C412yes—
777C2×Dic3C23×C412yes—
778C2×Dic3C23×C414yes—
779C2×Dic3H(5,𝔽2)12yes—
780D12—28no—
781C4×D3—28no—
782C4×D3—84no—
783C4×D3—84no—
784C24—31no—
785C24—32no—
786C24—38no—
787C24—64no—
788C24—64no—
789C24—122no—
790C24—122no—
791C24—122no—
792C24—122no—
793C24C23×D311yescharacteristic
794C24C23×D312yes—
795#41—232no—
796C2×Q8—22no—
797C2×Q8—22no—
798C2×Q8C2×C4×D314yes—
799C2×D4—24no—
800C2×D4—24no—
801C2×D4—38no—
802C2×D4—34no—
803C2×D4—38no—
804C2×D4—34no—
805C2×D4—64no—
806C2×D4—64no—
807C2×D4—632no—
808C2×D4—62no—
809C2×D4—62no—
810C2×D4—122no—
811C2×D4—121no—
812C2×D4—121no—
813C2×D4—122no—
814C2×D4C2×C4×D318yes—
815C2×D4C2×C4×D314yes—
816C2×D4#23514yes—
817C2×D4C2×#6714yes—
818C22×C4—24no—
819C22×C4—24no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—24no—
823C22×C4—24no—
824C22×C4—31no—
825C22×C4—31no—
826C22×C4—31no—
827C22×C4—32no—
828C22×C4—31no—
829C22×C4—38no—
830C22×C4—34no—
831C22×C4—31no—
832C22×C4—32no—
833C22×C4—31no—
834C22×C4—32no—
835C22×C4—31no—
836C22×C4—42no—
837C22×C4—42no—
838C22×C4—42no—
839C22×C4—42no—
840C22×C4—42no—
841C22×C4—42no—
842C22×C4—64no—
843C22×C4—62no—
844C22×C4—62no—
845C22×C4—64no—
846C22×C4—64no—
847C22×C4—64no—
848C22×C4—64no—
849C22×C4—122no—
850C22×C4—122no—
851C22×C4—122no—
852C22×C4—122no—
853C22×C4—122no—
854C22×C4—122no—
855C22×C4—122no—
856C22×C4—122no—
857C22×C4—122no—
858C22×C4C2×C4×D318yes—
859C22×C4C2×C4×D314yes—
860C22×C4C2×#6718yes—
861C22×C4C23×D311yescharacteristic
862C22×C4C23×D312yes—
863C22×C4C23×D311yescharacteristic
864C22×C4C23×D312yes—
865C22×C4C23×D311yescharacteristic
866C22×C4C23×D312yes—
867C22×C4C23×D311yescharacteristic
868C22×C4C23×D311yescharacteristic
869C22×C4C23×D311yescharacteristic
870C4⋊C4—24no—
871C4⋊C4—22no—
872C4⋊C4—24no—
873C4⋊C4—24no—
874C4⋊C4—22no—
875C4⋊C4—22no—
876C4⋊C4—34no—
877C4⋊C4—34no—
878C4⋊C4—38no—
879C4⋊C4—62no—
880C4⋊C4—62no—
881C4⋊C4—62no—
882C4⋊C4—62no—
883C4⋊C4—122no—
884C4⋊C4—121no—
885C4⋊C4—121no—
886C4⋊C4—122no—
887C4⋊C4C2×#6714yes—
888C22⋊C4—24no—
889C22⋊C4—22no—
890C22⋊C4—22no—
891C22⋊C4—38no—
892C22⋊C4—34no—
893C22⋊C4—34no—
894C22⋊C4—38no—
895C22⋊C4—38no—
896C22⋊C4—38no—
897C22⋊C4—38no—
898C22⋊C4—62no—
899C22⋊C4—64no—
900C22⋊C4—62no—
901C22⋊C4—64no—
902C22⋊C4—64no—
903C22⋊C4—62no—
904C22⋊C4—64no—
905C22⋊C4—62no—
906C22⋊C4—64no—
907C22⋊C4—64no—
908C22⋊C4—122no—
909C22⋊C4—122no—
910C22⋊C4—122no—
911C22⋊C4—122no—
912C22⋊C4—121no—
913C22⋊C4—121no—
914C22⋊C4—122no—
915C22⋊C4C2×#6718yes—
916C42—24no—
917C42—24no—
918C42—22no—
919C42—34no—
920C42—62no—
921C42—64no—
922C42—62no—
923C42—64no—
924C42—62no—
925C42—122no—
926C42—122no—
927C42—121no—
928C42—121no—
929C42—121no—
930C42C2×#6714yes—
931C22×C3—24no—
932C22×C3—24no—
933C22×C3—24no—
934C22×C3—24no—
935C22×C3—24no—
936C22×C3—24no—
937C22×C3—22no—
938C22×C3—22no—
939C22×C3—22no—
940C22×C3—41no—
941C22×C3—41no—
942C22×C3—41no—
943C22×C3—41no—
944C22×C3C2×C4×D418yes—
945C22×C3C24×C411yescharacteristic
946C22×C3C23×D411yescharacteristic
947C22×C3C22×#4111yescharacteristic
948C22×C3C2×H(5,𝔽2)11yescharacteristic
949C22×C3#58511yescharacteristic
950C22×C3#58511yescharacteristic
951C22×C3#58511yescharacteristic
952C2×D3—22no—
953C2×D3—24no—
954C2×D3—22no—
955C2×D3—24no—
956C2×D3—24no—
957C2×D3—22no—
958C2×D3—42no—
959C2×D3—41no—
960C2×D3—42no—
961C2×D3—41no—
962C2×D3—42no—
963C2×D3—41no—
964C2×D3—42no—
965C2×D3—41no—
966C2×D3—816no—
967C3×C4—22no—
968C3×C4—24no—
969C3×C4—24no—
970C3×C4—22no—
971C3×C4—22no—
972C3×C4—42no—
973C3×C4—41no—
974C3×C4—41no—
975C3×C4C2×C4×D414yes—
976Dic3—22no—
977Dic3—22no—
978Dic3—22no—
979Dic3—24no—
980Dic3—22no—
981Dic3—41no—
982Dic3—42no—
983Dic3—41no—
984Dic3—42no—
985Dic3—41no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—21no—
991C23—21no—
992C23—21no—
993C23—21no—
994C23—21no—
995C23—21no—
996C23—32no—
997C23—34no—
998C23—61no—
999C23—62no—
1000C23—61no—
1001C23—62no—
1002C23—62no—
1003C23—61no—
1004C23—62no—
1005C23—61no—
1006C23—62no—
1007C23—61no—
1008C23—61no—
1009C23—62no—
1010C23—616no—
1011C23—128no—
1012C23—128no—
1013C23—244no—
1014C23—244no—
1015C23—244no—
1016C23—244no—
1017C23C22×C4×D312yes—
1018C23C22×C4×D314yes—
1019C23C2×#23514yes—
1020C23C22×#6714yes—
1021C23C24×D311yescharacteristic
1022Q8—28no—
1023D4—216no—
1024D4—616no—
1025D4—68no—
1026D4—124no—
1027D4—128no—
1028D4C4×#67116yescomplemented
1029C2×C4—21no—
1030C2×C4—22no—
1031C2×C4—21no—
1032C2×C4—22no—
1033C2×C4—21no—
1034C2×C4—22no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—22no—
1038C2×C4—21no—
1039C2×C4—216no—
1040C2×C4—28no—
1041C2×C4—21no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—22no—
1049C2×C4—21no—
1050C2×C4—32no—
1051C2×C4—32no—
1052C2×C4—34no—
1053C2×C4—32no—
1054C2×C4—32no—
1055C2×C4—48no—
1056C2×C4—61no—
1057C2×C4—61no—
1058C2×C4—61no—
1059C2×C4—62no—
1060C2×C4—61no—
1061C2×C4—61no—
1062C2×C4—61no—
1063C2×C4—61no—
1064C2×C4—62no—
1065C2×C4—61no—
1066C2×C4—68no—
1067C2×C4—61no—
1068C2×C4—62no—
1069C2×C4—62no—
1070C2×C4—61no—
1071C2×C4—61no—
1072C2×C4—61no—
1073C2×C4—61no—
1074C2×C4—62no—
1075C2×C4—62no—
1076C2×C4—61no—
1077C2×C4—61no—
1078C2×C4—62no—
1079C2×C4—61no—
1080C2×C4—62no—
1081C2×C4—61no—
1082C2×C4—84no—
1083C2×C4—84no—
1084C2×C4—128no—
1085C2×C4—128no—
1086C2×C4—244no—
1087C2×C4—244no—
1088C2×C4—244no—
1089C2×C4C22×C4×D312yes—
1090C2×C4C22×C4×D314yes—
1091C2×C4C22×C4×D312yes—
1092C2×C4C2×#23512yes—
1093C2×C4C22×#6712yes—
1094C2×C4C22×#6714yes—
1095C2×C4C22×#6712yes—
1096C2×C4C22×#6712yes—
1097C2×C3—28no—
1098C2×C3—42no—
1099C2×C3C22×C4×D411yescharacteristic
1100C2×C3#342811yescharacteristic
1101C2×C3C4×H(5,𝔽2)11yescharacteristic
1102C2×C3#349611yescharacteristic
1103C2×C3#350011yescharacteristic
1104C2×C3#351311yescharacteristic
1105C2×C3#352111yescharacteristic
1106D3—44no—
1107D3—42no—
1108C22—24no—
1109C22—24no—
1110C22—24no—
1111C22—24no—
1112C22—24no—
1113C22—24no—
1114C22—22no—
1115C22—22no—
1116C22—22no—
1117C22—41no—
1118C22—41no—
1119C22—41no—
1120C22—41no—
1121C22—62no—
1122C22—64no—
1123C22—64no—
1124C22—62no—
1125C22—62no—
1126C22—64no—
1127C22—121no—
1128C22—122no—
1129C22—121no—
1130C22—122no—
1131C22—122no—
1132C22—121no—
1133C22—122no—
1134C22—121no—
1135C22—2416no—
1136C22C2×C4×#6718yes—
1137C22C23×C4×D311yescharacteristic
1138C22C22×#23511yescharacteristic
1139C22D3×H(5,𝔽2)11yescharacteristic
1140C22#596611yescharacteristic
1141C22#596811yescharacteristic
1142C22#596811yescharacteristic
1143C22C23×#6711yescharacteristic
1144C4—22no—
1145C4—24no—
1146C4—22no—
1147C4—24no—
1148C4—22no—
1149C4—41no—
1150C4—42no—
1151C4—41no—
1152C4—62no—
1153C4—62no—
1154C4—64no—
1155C4—62no—
1156C4—62no—
1157C4—121no—
1158C4—122no—
1159C4—121no—
1160C4—122no—
1161C4—121no—
1162C4C2×C4×#6714yes—
1163C3#3430911yescharacteristic, complemented, Sylow
1164C2—28no—
1165C2—42no—
1166C2—122no—
1167C2—124no—
1168C2#8588511yescharacteristic
1169C2#8588611yescharacteristic
1170C2#8589711yescharacteristic
1171C2#8590511yescharacteristic
1172C2C22×C4×#6711yescharacteristic
1173C2#8728111yescharacteristic
1174C2#8729311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutatorC22×C3C24×C4
FittingC2×C3×#520C2
socle, cosocleC23×C3C25
prime radicalC2×#5829C2
hypercenterC2×#520D3
hypocenterC3#34309
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. C2×C3×#520C2semidirect
3. C2×#5545C2semidirect
4. #84088C2semidirect
5. #82488C2semidirect
6. #82466C2semidirect
7. #82464C2semidirect
8. C4×#947C2semidirect
9. #82398C2semidirect
10. D4×(C2×D3)⋊C4C2semidirect
11. #82395C2semidirect
12. #82342C2semidirect
13. #82334C2semidirect
14. C4×#939C2semidirect
15. C4×D4×Dic3C2semidirect
16. #82271C2semidirect
17. #82242C2semidirect
18. #82236C2semidirect
19. #82225C2semidirect
20. #82163C2semidirect
21. #82161C2semidirect
22. #82158C2semidirect
23. C2×#4990C2semidirect
28. C2×C3×C4×Q8C22semidirect
29. C2×C3×C4×Q8C22semidirect
32. C2×C3×C4×D4C22semidirect
33. C2×C3×C4×D4C22semidirect
34. C2×C3×#117C22semidirect
35. C2×C3×#117C22semidirect
36. C22×C3×C4⋊C4C22semidirect
37. C22×C3×C4⋊C4C22semidirect
38. #5829C4semidirect
50. C2×C4×#67C22semidirect
54. C22×C4×Dic3C22semidirect
62. #5229C22semidirect
63. #5229C22semidirect
64. #5220C22semidirect
65. #5220C22semidirect
68. #5213C22semidirect
69. #5212C22semidirect
70. #5211C22semidirect
71. #5210C22semidirect
72. C4×#217C22semidirect
73. C4×#217C22semidirect
74. C4×#217C22semidirect
75. C2×C3⋊#95C22semidirect
76. C2×C3⋊#95C22semidirect
82. #4990C22semidirect
83. #4990C22semidirect
84. #4990C22semidirect
85. #4990C22semidirect
86. #4990C22semidirect
87. #4989C22semidirect
88. #4989C22semidirect
89. #4989C22semidirect
92. #4978C22semidirect
93. #4978C22semidirect
94. #4977C22semidirect
95. #4976C22semidirect
96. #4976C22semidirect
97. #4976C22semidirect
98. Dic3×C4⋊C4C22semidirect
99. Dic3×C4⋊C4C22semidirect
100. #4972C22semidirect
104. #4957C22semidirect
105. #4956C22semidirect
107. #4946C22semidirect
108. #4945C22semidirect
109. #4945C22semidirect
110. #4942C22semidirect
111. Dic3×C22⋊C4C22semidirect
112. Dic3×C22⋊C4C22semidirect
115. #4940C22semidirect
118. C4×(C2×D3)⋊C4C22semidirect
119. C4×(C2×D3)⋊C4C22semidirect
120. C4×(C2×D3)⋊C4C22semidirect
121. C4×C4⋊Dic3C22semidirect
122. #4933C22semidirect
123. C4×Dic3⋊C4C22semidirect
124. C4×Dic3⋊C4C22semidirect
125. C42×Dic3C22semidirect
126. #4928C22semidirect
128. C2×#520D3semidirect
153. C2×C3×#41C2×C4semidirect
170. C2×D3×D4C2×C4semidirect
180. C3×C4×D4D4semidirect
207. #947C2×C4semidirect
208. #946C2×C4semidirect
209. #939C2×C4semidirect
210. #937C2×C4semidirect
213. D4×Dic3C2×C4semidirect
214. #930C2×C4semidirect
215. #929C2×C4semidirect
218. C4×#67C2×C4semidirect
221. C2×(C2×D3)⋊C4C2×C4semidirect
298. C2×C4×Q8C2×D3semidirect
299. C2×C4×Q8C2×D3semidirect
311. C2×C4×D4C2×D3semidirect
312. C2×C4×D4C2×D3semidirect
315. C2×#117C2×D3semidirect
316. C2×#117C2×D3semidirect
317. C22×C4⋊C4C2×D3semidirect
318. C22×C4⋊C4C2×D3semidirect
539. C2×#41C4×D3semidirect
581. C4×D4#67semidirect
711. C3×D4C4×D4semidirect
1028. D4C4×#67semidirect
1163. C3#34309semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5202
C2×#58292
C2×#55452
#840882
#824882
#824662
#824642
C4×#9472
#823982
D4×(C2×D3)⋊C42
#823952
#823422
#823342
C4×#9392
C4×D4×Dic32
#822712
#822422
#822362
#822252
#821632
#821612
#821582
C2×#49902
#343093