Finite Group Databasebeta

← #14914617

Subgroups — #14914617

Order 2816.

2286 conjugacy classes of subgroups.

The subgroup lattice has 998 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623211C211yesmaximal, characteristic
2#13071737C212yesmaximal, complemented
3#13071733C212yesmaximal, complemented
4#13071659C211yesmaximal, characteristic
5#13071650C211yesmaximal, characteristic
6#13071648C211yesmaximal, characteristic, complemented
7#13071639C211yesmaximal, characteristic, complemented
8#13071572C211yesmaximal, characteristic, complemented
9#13071564C211yesmaximal, characteristic, complemented
10#13071562C212yesmaximal, complemented
11#13071539C212yesmaximal, complemented
12Q8×Dic11⋊C4C211yesmaximal, characteristic, complemented
13D4×Dic11⋊C4C211yesmaximal, characteristic, complemented
14#13071408C212yesmaximal, complemented
15#13071404C212yesmaximal, complemented
16#13071220C212yesmaximal, complemented
17C4×#66923C211yesmaximal, characteristic, complemented
18#13071171C211yesmaximal, characteristic, complemented
19#124×Dic11C211yesmaximal, characteristic, complemented
20#13071022C211yesmaximal, characteristic, complemented
21#13070971C212yesmaximal, complemented
22C4×#66925C211yesmaximal, characteristic, complemented
23C4×C11×#124C211yesmaximal, characteristic, complemented
24C2×C11×#124C2211yescharacteristic
25C2×C4×Q8×C11C2211yescharacteristic
26C2×C4×D4×C11C2211yescharacteristic
27C2×#66999C2211yescharacteristic
28C2×Q8×Dic11C2211yescharacteristic
29C2×Q8×Dic11C2211yescharacteristic
30C2×#66991C2211yescharacteristic
31C2×D4×Dic11C2211yescharacteristic
32C2×D4×Dic11C2211yescharacteristic
33C22×Dic11⋊C4C2212yes—
34#10623211C4116yescomplemented
35C2×#66945C2211yescharacteristic
36C2×#66945C2211yescharacteristic
37C2×#66936C2212yes—
38C2×(C22⋊D11)⋊C4C2212yes—
39C2×#66932C2212yes—
40C2×#66930C2212yes—
41C2×#66930C2212yes—
42C2×#66925C2211yescharacteristic
43C2×#66925C2211yescharacteristic
44C2×C42×D11C2211yescharacteristic
45C2×#66923C2211yescharacteristic
46C11×#391C2211yescharacteristic
47C11×#390C2211yescharacteristic
48C11×#388C2212yes—
49C11×#388C2212yes—
50C11×#382C2211yescharacteristic
51C4×C11×C22⋊C4C2212yes—
52C4×C11×C22⋊C4C2212yes—
53C43×C11C2211yescharacteristic
54#10622843C2211yescharacteristic
55#10622834C2211yescharacteristic
56#10622826C2212yes—
57#10622823C2212yes—
58C4×C22⋊Dic11C2212yes—
59#10622603C2212yes—
60#10622591C2212yes—
61#10622589C2212yes—
62#10622589C2211yescharacteristic
63#10622589C2211yescharacteristic
64C4⋊C4×Dic11C2211yescharacteristic
65C4⋊C4×Dic11C2211yescharacteristic
66#10622586C2211yescharacteristic
67#10622586C2211yescharacteristic
68#10622586C2212yes—
69#10622571C2212yes—
70#10622570C2212yes—
71#10622570C2212yes—
72#10622564C2212yes—
73#10622564C2212yes—
74#10622559C2212yes—
75#10622558C2212yes—
76#10622558C2212yes—
77#10622557C2212yes—
78#10622557C2212yes—
79#10622555C2212yes—
80#10622555C2212yes—
81C22⋊C4×Dic11C2212yes—
82C22⋊C4×Dic11C2212yes—
83C22⋊C4×Dic11C2212yes—
84#10622553C2212yes—
85C4×(C2×D11)⋊C4C2211yescharacteristic
86C4×(C2×D11)⋊C4C2211yescharacteristic
87C4×(C2×D11)⋊C4C2211yescharacteristic
88C4×(C2×D11)⋊C4C2211yescharacteristic
89#10622549C2211yescharacteristic
90C4×C4⋊Dic11C2211yescharacteristic
91C4×C4⋊Dic11C2211yescharacteristic
92#10622546C2212yes—
93#10622546C2212yes—
94#10622545C2211yescharacteristic
95#10622545C2211yescharacteristic
96C4×Dic11⋊C4C2212yes—
97C4×Dic11⋊C4C2212yes—
98C4×Dic11⋊C4C2212yes—
99C4×Dic11⋊C4C2211yescharacteristic
100C4×Dic11⋊C4C2211yescharacteristic
101C4×Dic11⋊C4C2211yescharacteristic
102C4×Dic11⋊C4C2211yescharacteristic
103C4×Dic11⋊C4C2212yes—
104C42×Dic11C2211yescharacteristic
105#10622541C2211yescharacteristic
106#10622541C2211yescharacteristic
107#10622541C2212yes—
108#10622283C2212yes—
109#10622282C2212yes—
110#10622280C2212yes—
111#10622280C2212yes—
112#10622268C2212yes—
113#10622267C2212yes—
114#10622266C2212yes—
115#10622265C2212yes—
116#10622265C2212yes—
117#10622263C2212yes—
118#10622262C2212yes—
119#10622262C2212yes—
120#10622262C2212yes—
121#10622262C2212yes—
122#10622262C2212yes—
123#10622262C2212yes—
124C22×Q8×C11C2311yescharacteristic
125C22×D4×C11C2311yescharacteristic
126C23×C4×C11C2312yes—
127C22×C22⋊D11C2312yes—
128C23×Dic11C2312yes—
129C23×Dic11C2312yes—
130C22×C4×D11C2311yescharacteristic
131C22×C4×D11C2311yescharacteristic
132C22×C4×D11C2311yescharacteristic
133C11×#124C2×C418yes—
134C4×Q8×C11—42no—
135C4×D4×C11—42no—
136C2×C11×C4⋊C4C2311yescharacteristic
137C2×C11×C4⋊C4C2311yescharacteristic
138C2×C11×C4⋊C4C2312yes—
139C2×C11×C22⋊C4C2312yes—
140C2×C11×C22⋊C4C2312yes—
141C2×C11×C22⋊C4C2312yes—
142C2×C11×C22⋊C4C2312yes—
143C2×C11×C22⋊C4C2312yes—
144C2×C42×C11C2311yescharacteristic
145C2×C42×C11C2311yescharacteristic
146C2×C42×C11C2311yescharacteristic
147C2×C42×C11C2311yescharacteristic
148C2×C42×C11C2312yes—
149C2×C42×C11C2311yescharacteristic
150C2×C42×C11C2311yescharacteristic
151C2×C42×C11C2311yescharacteristic
152C2×C22⋊Dic11C2312yes—
153C2×C22⋊Dic11C2312yes—
154C2×C22⋊Dic11C2312yes—
155C2×C22⋊Dic11C2312yes—
156C2×C22⋊Dic11C2312yes—
157#66999C2×C418yescomplemented
158Q8×Dic11—42no—
159Q8×Dic11C2×C418yescomplemented
160#66991C2×C418yes—
161D4×Dic11—42no—
162D4×Dic11C2×C418yes—
163C2×(C2×D11)⋊C4C2311yescharacteristic
164C2×(C2×D11)⋊C4C2311yescharacteristic
165C2×(C2×D11)⋊C4C2311yescharacteristic
166C2×(C2×D11)⋊C4C2311yescharacteristic
167C2×(C2×D11)⋊C4C2312yes—
168C2×(C2×D11)⋊C4C2312yes—
169C2×(C2×D11)⋊C4C2312yes—
170C2×C4⋊Dic11C2311yescharacteristic
171C2×C4⋊Dic11C2311yescharacteristic
172C2×C4⋊Dic11C2312yes—
173C2×C4⋊Dic11C2311yescharacteristic
174C2×C4⋊Dic11C2311yescharacteristic
175C2×C4⋊Dic11C2312yes—
176C2×Dic11⋊C4—28no—
177C2×Dic11⋊C4C2311yescharacteristic
178C2×Dic11⋊C4C2311yescharacteristic
179C2×Dic11⋊C4C2312yes—
180C2×Dic11⋊C4C2312yes—
181C2×Dic11⋊C4C2312yes—
182C2×Dic11⋊C4C2312yes—
183C2×Dic11⋊C4C2312yes—
184C2×Dic11⋊C4C2312yes—
185C2×Dic11⋊C4C2312yes—
186C2×Dic11⋊C4C2312yes—
187C2×Dic11⋊C4C2312yes—
188C2×Dic11⋊C4C2312yes—
189C2×Dic11⋊C4C2312yes—
190C2×Dic11⋊C4C2311yescharacteristic
191C2×Dic11⋊C4C2311yescharacteristic
192C2×C4×Dic11C2311yescharacteristic
193C2×C4×Dic11C2311yescharacteristic
194C2×C4×Dic11C2312yes—
195C2×C4×Dic11C2312yes—
196C2×C4×Dic11C2311yescharacteristic
197C2×C4×Dic11C2311yescharacteristic
198C2×C4×Dic11C2312yes—
199C2×C4×Dic11C2312yes—
200C2×C4×Dic11C2312yes—
201C2×C4×Dic11C2311yescharacteristic
202C2×C4×Dic11C2312yes—
203C2×C4×Dic11C2312yes—
204C2×C4×Dic11C2311yescharacteristic
205C2×C4×Dic11C2311yescharacteristic
206C2×C4×Dic11C2311yescharacteristic
207C2×C4×Dic11C2311yescharacteristic
208C2×C4×Dic11C2312yes—
209#66945—42no—
210#66945—42no—
211#66936C2×C4116yescomplemented
212(C22⋊D11)⋊C4C2×C4116yescomplemented
213#66932C2×C4116yescomplemented
214#66930—28no—
215#66930C2×C4116yescomplemented
216#66925—24no—
217#66925—24no—
218C42×D11C2×C418yescomplemented
219#66923C2×C418yescomplemented
220C11×#95C2312yes—
221C11×#95C2312yes—
222C11×#95C2312yes—
223C11×#95C2312yes—
224C11⋊#95C2311yescharacteristic
225C11⋊#95C2312yes—
226C11⋊#95C2312yes—
227C11⋊#95C2312yes—
228C11⋊#95C2312yes—
229C11⋊#95C2312yes—
230C11⋊#95C2312yes—
231C11⋊#95C2312yes—
232C11⋊#95C2312yes—
233C11⋊#95C2312yes—
234C11⋊#95C2311yescharacteristic
235C11⋊#95C2311yescharacteristic
236C11⋊#95C2311yescharacteristic
237C11⋊#95C2312yes—
238C11⋊#95C2312yes—
239C11⋊#95C2311yescharacteristic
240C11⋊#95C2312yes—
241C11⋊#95C2311yescharacteristic
242C11⋊#95C2311yescharacteristic
243C11⋊#95C2311yescharacteristic
244#34242—111nomaximal, Sylow
245C24×C11C2412yes—
246C23×D11C2411yescharacteristic
247C2×Q8×C11—22no—
248C2×Q8×C11—22no—
249C2×Q8×C11C22×C414yes—
250C2×D4×C11—22no—
251C2×D4×C11—22no—
252C2×D4×C11C22×C414yes—
253C22×C4×C11—24no—
254C22×C4×C11—42no—
255C22×C4×C11—42no—
256C22×C4×C11C2411yescharacteristic
257C22×C4×C11C2411yescharacteristic
258C22×C4×C11C2412yes—
259C22×C4×C11C2412yes—
260C22×C4×C11C2411yescharacteristic
261C22×C4×C11C2411yescharacteristic
262C22×C4×C11C2412yes—
263C22×C4×C11C2411yescharacteristic
264C22×C4×C11C2411yescharacteristic
265C22×C4×C11C2411yescharacteristic
266C2×C22⋊D11—42no—
267C2×C22⋊D11—42no—
268C2×C22⋊D11C22×C418yes—
269C22×Dic11—24no—
270C22×Dic11—24no—
271C22×Dic11—24no—
272C22×Dic11—42no—
273C22×Dic11—42no—
274C22×Dic11C22×C418yes—
275C22×Dic11C2411yescharacteristic
276C22×Dic11C2412yes—
277C22×Dic11C2411yescharacteristic
278C22×Dic11C2412yes—
279C22×Dic11C2411yescharacteristic
280C22×Dic11C2412yes—
281C22×Dic11C2412yes—
282C22×Dic11C2411yescharacteristic
283C22×Dic11C2411yescharacteristic
284C22×Dic11C2411yescharacteristic
285C22×Dic11C2411yescharacteristic
286C2×C4×D11—22no—
287C2×C4×D11—22no—
288C2×C4×D11—22no—
289C2×C4×D11—22no—
290C2×C4×D11—41no—
291C2×C4×D11—41no—
292C2×C4×D11C22×C414yes—
293C2×C4×D11C22×C414yes—
294C2×C4×D11C22×C414yes—
295C11×C4⋊C4—22no—
296C11×C4⋊C4—22no—
297C11×C4⋊C4—42no—
298C11×C22⋊C4—24no—
299C11×C22⋊C4—42no—
300C11×C22⋊C4—42no—
301C11×C22⋊C4C22×C418yes—
302C11×C22⋊C4C22×C418yes—
303C42×C11—22no—
304C42×C11—22no—
305C42×C11—22no—
306C42×C11—22no—
307C42×C11—41no—
308C42×C11—41no—
309C42×C11—42no—
310C42×C11C22×C414yes—
311C22⋊Dic11—24no—
312C22⋊Dic11—42no—
313C22⋊Dic11—42no—
314C22⋊Dic11C22×C418yes—
315C22⋊Dic11C22×C418yes—
316(C2×D11)⋊C4—22no—
317(C2×D11)⋊C4—22no—
318(C2×D11)⋊C4—22no—
319(C2×D11)⋊C4—22no—
320(C2×D11)⋊C4—42no—
321(C2×D11)⋊C4—42no—
322(C2×D11)⋊C4C22×C418yes—
323C4⋊Dic11—22no—
324C4⋊Dic11—22no—
325C4⋊Dic11—42no—
326C4⋊Dic11C22×C414yes—
327C4⋊Dic11C22×C414yes—
328C4⋊Dic11C22×C418yes—
329Dic11⋊C4—22no—
330Dic11⋊C4—22no—
331Dic11⋊C4—24no—
332Dic11⋊C4—24no—
333Dic11⋊C4—24no—
334Dic11⋊C4—24no—
335Dic11⋊C4—42no—
336Dic11⋊C4—42no—
337Dic11⋊C4—42no—
338Dic11⋊C4—42no—
339Dic11⋊C4C22×C418yes—
340Dic11⋊C4C22×C418yes—
341Dic11⋊C4C22×C418yes—
342Dic11⋊C4#4114yes—
343Dic11⋊C4#4114yes—
344C4×Dic11—22no—
345C4×Dic11—22no—
346C4×Dic11—24no—
347C4×Dic11—24no—
348C4×Dic11—22no—
349C4×Dic11—22no—
350C4×Dic11—42no—
351C4×Dic11—42no—
352C4×Dic11—42no—
353C4×Dic11—41no—
354C4×Dic11—41no—
355C4×Dic11—42no—
356C4×Dic11—42no—
357C4×Dic11C22×C414yes—
358C4×Dic11C22×C414yes—
359C4×Dic11C22×C414yes—
360C4×Dic11C22×C418yes—
361C2×#529—111no—
362#2373—112no—
363#2373—112no—
364#2363—111no—
365#2363—111no—
366#2362—111no—
367#2362—111no—
368#2355—111no—
369#2354—111no—
370#2354—112no—
371#2352—112no—
372Q8×C4⋊C4—111no—
373D4×C4⋊C4—111no—
374#2335—112no—
375#2335—112no—
376#2314—112no—
377C4×#125—111no—
378C4×#125—111no—
379C4×#124—111no—
380C4×#124D1111yescharacteristic, complemented
381#2285—111no—
382#2274—112no—
383C4×#117—111no—
384C23×C11—22no—
385C23×C11—22no—
386C23×C11—22no—
387C23×C11—22no—
388C23×C11—22no—
389C23×C11—22no—
390C23×C11C23×C414yes—
391C23×C11C2511yescharacteristic
392C22×D11—21no—
393C22×D11—21no—
394C22×D11—21no—
395C22×D11—21no—
396C22×D11—21no—
397C22×D11—21no—
398C22×D11C23×C412yes—
399Q8×C11—28no—
400D4×C11—28no—
401C2×C4×C11—21no—
402C2×C4×C11—21no—
403C2×C4×C11—22no—
404C2×C4×C11—21no—
405C2×C4×C11—21no—
406C2×C4×C11—22no—
407C2×C4×C11—21no—
408C2×C4×C11—21no—
409C2×C4×C11—21no—
410C2×C4×C11—21no—
411C2×C4×C11—22no—
412C2×C4×C11—22no—
413C2×C4×C11—21no—
414C2×C4×C11—21no—
415C2×C4×C11—22no—
416C2×C4×C11—22no—
417C2×C4×C11—21no—
418C2×C4×C11—21no—
419C2×C4×C11—22no—
420C2×C4×C11—21no—
421C2×C4×C11—22no—
422C2×C4×C11—21no—
423C2×C4×C11—84no—
424C2×C4×C11C23×C412yes—
425C2×C4×C11C23×C412yes—
426C2×C4×C11C23×C414yes—
427C2×C4×C11C23×C412yes—
428C2×C4×C11C2×#4112yes—
429C2×C4×C11C2×#4112yes—
430C2×C4×C11H(5,𝔽2)12yes—
431C2×C4×C112−1+412yes—
432C22⋊D11—48no—
433C2×Dic11—22no—
434C2×Dic11—22no—
435C2×Dic11—21no—
436C2×Dic11—21no—
437C2×Dic11—21no—
438C2×Dic11—21no—
439C2×Dic11—21no—
440C2×Dic11—22no—
441C2×Dic11—21no—
442C2×Dic11—21no—
443C2×Dic11—21no—
444C2×Dic11—22no—
445C2×Dic11—216no—
446C2×Dic11—21no—
447C2×Dic11—21no—
448C2×Dic11—22no—
449C2×Dic11—22no—
450C2×Dic11—21no—
451C2×Dic11—22no—
452C2×Dic11—22no—
453C2×Dic11—21no—
454C2×Dic11—21no—
455C2×Dic11—22no—
456C2×Dic11—21no—
457C2×Dic11—22no—
458C2×Dic11—84no—
459C2×Dic11C23×C412yes—
460C2×Dic11C23×C412yes—
461C2×Dic11C23×C414yes—
462C2×Dic11C23×C414yes—
463C2×Dic11C23×C412yes—
464C2×Dic11C2×#4112yes—
465C2×Dic11C2×#4112yes—
466C2×Dic11C2×#4112yes—
467C2×Dic11C2×#4112yes—
468C4×D11—28no—
469C4×D11—28no—
470C4×D11—44no—
471#529—1116no—
472C2×#126—112no—
473C2×#125—111no—
474C2×#124C2×D1111yescharacteristic
475C2×#123—112no—
476C2×C22⋊Q8—111no—
477C2×#121—111no—
478C2×C4×Q8—111no—
479C2×C4×Q8—111no—
480C2×C4×Q8C2×D1111yescharacteristic
481C2×C4×D4—111no—
482C2×C4×D4—111no—
483C2×C4×D4—112no—
484C2×C4×D4C2×D1111yescharacteristic
485C2×#117—111no—
486C2×#117—111no—
487C2×#117—112no—
488C2×#117—112no—
489C2×#117—111no—
490C2×#117—111no—
491C22×C4⋊C4—112no—
492C22×C42—111no—
493#391—111no—
494#391C2×D1111yescharacteristic
495#390—111no—
496#390—112no—
497#390—112no—
498#390C2×D1111yescharacteristic
499#389—111no—
500#389—111no—
501#389—112no—
502#389—111no—
503#389—111no—
504#389—112no—
505#388—112no—
506#388—112no—
507#388—112no—
508#388—112no—
509#388—112no—
510#388—112no—
511#388—112no—
512#388—112no—
513#388—112no—
514#388—112no—
515#388C2×D1112yes—
516#388C2×D1112yes—
517#387—112no—
518#387—112no—
519#387—112no—
520#387—112no—
521#387—112no—
522#387—112no—
523#387—112no—
524#387—112no—
525#386—112no—
526#386—112no—
527#385—112no—
528#385—112no—
529#384—112no—
530#384—111no—
531#384—111no—
532#382—111no—
533#382—112no—
534#382C2×D1111yescharacteristic
535#380—112no—
536#380—112no—
537#380—112no—
538#380—112no—
539C4×C4⋊C4—111no—
540C4×C4⋊C4—111no—
541C4×C4⋊C4—112no—
542C4×C4⋊C4—111no—
543C4×C4⋊C4—112no—
544C4×C4⋊C4—111no—
545C4×C4⋊C4—111no—
546C4×C4⋊C4—111no—
547C4×C4⋊C4—112no—
548C4×C4⋊C4—111no—
549C4×C4⋊C4—112no—
550C4×C4⋊C4—111no—
551C4×C4⋊C4—112no—
552C4×C4⋊C4—112no—
553C4×C4⋊C4—112no—
554C4×C4⋊C4—112no—
555C4×C4⋊C4—112no—
556C4×C4⋊C4—112no—
557C4×C22⋊C4—112no—
558C4×C22⋊C4—112no—
559C4×C22⋊C4—112no—
560C4×C22⋊C4—112no—
561C4×C22⋊C4—111no—
562C4×C22⋊C4—111no—
563C4×C22⋊C4—111no—
564C4×C22⋊C4—111no—
565C4×C22⋊C4C2×D1112yes—
566C4×C22⋊C4C2×D1112yes—
567#376—111no—
568#376—111no—
569C43—111no—
570C43C2×D1111yescharacteristic
571C22×C11—24no—
572C22×C11—24no—
573C22×C11—24no—
574C22×C11—42no—
575C22×C11—42no—
576C22×C11—42no—
577C22×C11—42no—
578C22×C11C24×C411yescharacteristic
579C22×C11C22×#4111yescharacteristic
580C22×C11C22×#4111yescharacteristic
581C22×C11C2×H(5,𝔽2)11yescharacteristic
582C22×C11C2×2−1+411yescharacteristic
583C22×C11#58511yescharacteristic
584C22×C11#58511yescharacteristic
585C2×D11—22no—
586C2×D11—22no—
587C2×D11—22no—
588C2×D11—41no—
589C2×D11—41no—
590C2×D11—41no—
591C2×D11—41no—
592C4×C11—22no—
593C4×C11—24no—
594C4×C11—22no—
595C4×C11—22no—
596C4×C11—22no—
597C4×C11—42no—
598C4×C11—42no—
599C4×C11—41no—
600C4×C11—41no—
601C4×C11#52014yes—
602Dic11—24no—
603Dic11—22no—
604Dic11—22no—
605Dic11—24no—
606Dic11—22no—
607Dic11—22no—
608Dic11—42no—
609Dic11—41no—
610Dic11—42no—
611Dic11—41no—
612Dic11C4×#4114yes—
613C22×Q8C22×D1111yescharacteristic
614C22×D4—112no—
615C22×D4C22×D1111yescharacteristic
616C23×C4—112no—
617C23×C4—111no—
618C23×C4—111no—
619C23×C4—111no—
620C23×C4—112no—
621C23×C4C22×D1112yes—
622#126—1116no—
623#125—118no—
624#124C4×D1118yes—
625#123—1116no—
626C22⋊Q8—118no—
627#121—118no—
628C4×Q8—42no—
629C4×Q8—118no—
630C4×Q8—442no—
631C4×D4—42no—
632C4×D4—118no—
633C4×D4—1116no—
634C4×D4—442no—
635#117—1116no—
636#117—224no—
637#117—224no—
638#117—228no—
639#117—442no—
640#117—442no—
641C2×C4⋊C4—111no—
642C2×C4⋊C4—111no—
643C2×C4⋊C4—112no—
644C2×C4⋊C4—112no—
645C2×C4⋊C4—111no—
646C2×C4⋊C4—112no—
647C2×C4⋊C4—111no—
648C2×C4⋊C4—112no—
649C2×C4⋊C4—112no—
650C2×C4⋊C4—112no—
651C2×C4⋊C4—112no—
652C2×C4⋊C4—111no—
653C2×C4⋊C4—111no—
654C2×C4⋊C4—111no—
655C2×C4⋊C4—111no—
656C2×C4⋊C4—112no—
657C2×C4⋊C4—112no—
658C2×C4⋊C4—112no—
659C2×C4⋊C4—112no—
660C2×C4⋊C4—112no—
661C2×C4⋊C4—112no—
662C2×C4⋊C4—228no—
663C2×C4⋊C4C22×D1111yescharacteristic
664C2×C4⋊C4C22×D1111yescharacteristic
665C2×C4⋊C4C22×D1112yes—
666C2×C22⋊C4—112no—
667C2×C22⋊C4—112no—
668C2×C22⋊C4—112no—
669C2×C22⋊C4—112no—
670C2×C22⋊C4—111no—
671C2×C22⋊C4—111no—
672C2×C22⋊C4—111no—
673C2×C22⋊C4—111no—
674C2×C22⋊C4—112no—
675C2×C22⋊C4—112no—
676C2×C22⋊C4—112no—
677C2×C22⋊C4—112no—
678C2×C22⋊C4C22×D1112yes—
679C2×C22⋊C4C22×D1112yes—
680C2×C22⋊C4C22×D1112yes—
681C2×C22⋊C4C22×D1112yes—
682C2×C22⋊C4C22×D1112yes—
683C2×C42—111no—
684C2×C42—112no—
685C2×C42—111no—
686C2×C42—111no—
687C2×C42—118no—
688C2×C42—111no—
689C2×C42—111no—
690C2×C42—112no—
691C2×C42—112no—
692C2×C42—111no—
693C2×C42—111no—
694C2×C42—112no—
695C2×C42—112no—
696C2×C42—112no—
697C2×C42—111no—
698C2×C42—111no—
699C2×C42—112no—
700C2×C42—112no—
701C2×C42C22×D1111yescharacteristic
702C2×C42C22×D1111yescharacteristic
703C2×C42C22×D1111yescharacteristic
704C2×C42C22×D1111yescharacteristic
705C2×C42C22×D1112yes—
706C2×C42C22×D1111yescharacteristic
707C2×C42C22×D1111yescharacteristic
708C2×C42C22×D1111yescharacteristic
709#95—111no—
710#95—111no—
711#95—111no—
712#95—111no—
713#95—111no—
714#95—111no—
715#95—111no—
716#95—111no—
717#95—112no—
718#95—112no—
719#95—112no—
720#95—112no—
721#95—112no—
722#95—112no—
723#95—112no—
724#95—112no—
725#95—112no—
726#95—112no—
727#95—112no—
728#95—112no—
729#95C22×D1112yes—
730#95C22×D1112yes—
731#95C22×D1112yes—
732#95C22×D1112yes—
733C2×C11—44no—
734C2×C11C2×C4×#4111yescharacteristic
735C2×C11C2×#52011yescharacteristic
736C2×C11#342811yescharacteristic
737C2×C11#351411yescharacteristic
738C2×C11#351511yescharacteristic
739C2×C11#351711yescharacteristic
740C2×C11#351811yescharacteristic
741D11—42no—
742C24—111no—
743C24C23×D1112yes—
744C2×Q8—22no—
745C2×Q8—22no—
746C2×Q8C2×C4×D1114yes—
747C2×D4—22no—
748C2×D4—22no—
749C2×D4—118no—
750C2×D4—442no—
751C2×D4—442no—
752C2×D4C2×C4×D1114yes—
753C22×C4—24no—
754C22×C4—42no—
755C22×C4—42no—
756C22×C4—111no—
757C22×C4—118no—
758C22×C4—111no—
759C22×C4—111no—
760C22×C4—111no—
761C22×C4—112no—
762C22×C4—111no—
763C22×C4—112no—
764C22×C4—114no—
765C22×C4—114no—
766C22×C4—114no—
767C22×C4—111no—
768C22×C4—112no—
769C22×C4—111no—
770C22×C4—112no—
771C22×C4—222no—
772C22×C4—222no—
773C22×C4—224no—
774C22×C4—224no—
775C22×C4—224no—
776C22×C4—222no—
777C22×C4—222no—
778C22×C4—441no—
779C22×C4—441no—
780C22×C4—442no—
781C22×C4—442no—
782C22×C4C23×D1111yescharacteristic
783C22×C4C23×D1111yescharacteristic
784C22×C4C23×D1112yes—
785C22×C4C23×D1112yes—
786C22×C4C23×D1111yescharacteristic
787C22×C4C23×D1111yescharacteristic
788C22×C4C23×D1112yes—
789C22×C4C23×D1111yescharacteristic
790C22×C4C23×D1111yescharacteristic
791C22×C4C23×D1111yescharacteristic
792C4⋊C4—22no—
793C4⋊C4—22no—
794C4⋊C4—42no—
795C4⋊C4—118no—
796C4⋊C4—118no—
797C4⋊C4—114no—
798C4⋊C4—118no—
799C4⋊C4—114no—
800C4⋊C4—118no—
801C4⋊C4—114no—
802C4⋊C4—114no—
803C4⋊C4—224no—
804C4⋊C4—224no—
805C4⋊C4—222no—
806C4⋊C4—222no—
807C4⋊C4—224no—
808C4⋊C4—222no—
809C4⋊C4—222no—
810C4⋊C4—224no—
811C4⋊C4—442no—
812C4⋊C4—442no—
813C4⋊C4—442no—
814C4⋊C4—442no—
815C4⋊C4—442no—
816C22⋊C4—24no—
817C22⋊C4—42no—
818C22⋊C4—42no—
819C22⋊C4—118no—
820C22⋊C4—118no—
821C22⋊C4—118no—
822C22⋊C4—222no—
823C22⋊C4—222no—
824C22⋊C4—224no—
825C22⋊C4—222no—
826C22⋊C4—222no—
827C22⋊C4—442no—
828C22⋊C4—442no—
829C22⋊C4—442no—
830C22⋊C4—442no—
831C22⋊C4C2×C4×D1118yes—
832C22⋊C4C2×C4×D1118yes—
833C42—22no—
834C42—22no—
835C42—22no—
836C42—22no—
837C42—42no—
838C42—41no—
839C42—41no—
840C42—114no—
841C42—114no—
842C42—114no—
843C42—118no—
844C42—222no—
845C42—222no—
846C42—224no—
847C42—222no—
848C42—224no—
849C42—222no—
850C42—442no—
851C42—442no—
852C42—442no—
853C42—442no—
854C42—441no—
855C42—441no—
856C42—442no—
857C42C2×C4×D1114yes—
858C11#3424211yescharacteristic, complemented, Sylow
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—112no—
866C23—221no—
867C23—221no—
868C23—221no—
869C23—221no—
870C23—221no—
871C23—221no—
872C23C22×C4×D1114yes—
873C23C24×D1111yescharacteristic
874Q8—28no—
875D4—28no—
876D4—448no—
877C2×C4—21no—
878C2×C4—22no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—22no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—21no—
886C2×C4—21no—
887C2×C4—21no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—21no—
891C2×C4—21no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—21no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—84no—
900C2×C4—112no—
901C2×C4—112no—
902C2×C4—112no—
903C2×C4—112no—
904C2×C4—112no—
905C2×C4—114no—
906C2×C4—114no—
907C2×C4—112no—
908C2×C4—112no—
909C2×C4—228no—
910C2×C4—2216no—
911C2×C4—221no—
912C2×C4—221no—
913C2×C4—222no—
914C2×C4—222no—
915C2×C4—221no—
916C2×C4—221no—
917C2×C4—221no—
918C2×C4—222no—
919C2×C4—221no—
920C2×C4—221no—
921C2×C4—221no—
922C2×C4—222no—
923C2×C4—228no—
924C2×C4—221no—
925C2×C4—222no—
926C2×C4—222no—
927C2×C4—221no—
928C2×C4—221no—
929C2×C4—222no—
930C2×C4—222no—
931C2×C4—221no—
932C2×C4—221no—
933C2×C4—221no—
934C2×C4—222no—
935C2×C4—222no—
936C2×C4—444no—
937C2×C4—884no—
938C2×C4C22×C4×D1112yes—
939C2×C4C22×C4×D1112yes—
940C2×C4C22×C4×D1114yes—
941C2×C4C22×C4×D1112yes—
942C2×C4#6703712yes—
943C2×C4#41×D1112yes—
944C2×C4#41×D1112yes—
945C2×C4#6704312yes—
946C22—24no—
947C22—24no—
948C22—24no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—222no—
954C22—222no—
955C22—222no—
956C22—441no—
957C22—441no—
958C22—441no—
959C22—441no—
960C22C23×C4×D1111yescharacteristic
961C22C2×#6703711yescharacteristic
962C22C2×#41×D1111yescharacteristic
963C22C2×#41×D1111yescharacteristic
964C22C2×#6704311yescharacteristic
965C22#1062345311yescharacteristic
966C22#1062345311yescharacteristic
967C4—22no—
968C4—22no—
969C4—24no—
970C4—22no—
971C4—22no—
972C4—41no—
973C4—42no—
974C4—41no—
975C4—42no—
976C4—114no—
977C4—224no—
978C4—222no—
979C4—222no—
980C4—222no—
981C4—222no—
982C4—224no—
983C4—441no—
984C4—442no—
985C4—441no—
986C4—442no—
987C4#1062307714yes—
988C2—44no—
989C2—442no—
990C2C4×#41×D1111yescharacteristic
991C2C2×#1062307711yescharacteristic
992C2#1308181511yescharacteristic
993C2#1308257111yescharacteristic
994C2#1308258211yescharacteristic
995C2#1308261411yescharacteristic
996C2#1308263111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC4×C11×#124C2
socle, cosocleC23×C11C25
prime radicalC2×#66991C22
hypercenterC4×#124D11
hypocenterC11#34242
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×#124

Complements

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

NH ≅ G/Ntype
2. #13071737C2semidirect
3. #13071733C2semidirect
6. #13071648C2semidirect
7. #13071639C2semidirect
8. #13071572C2semidirect
9. #13071564C2semidirect
10. #13071562C2semidirect
11. #13071539C2semidirect
12. Q8×Dic11⋊C4C2semidirect
13. D4×Dic11⋊C4C2semidirect
14. #13071408C2semidirect
15. #13071404C2semidirect
16. #13071220C2semidirect
17. C4×#66923C2semidirect
18. #13071171C2semidirect
19. #124×Dic11C2semidirect
20. #13071022C2semidirect
21. #13070971C2semidirect
22. C4×#66925C2semidirect
23. C4×C11×#124C2semidirect
34. #10623211C4semidirect
157. #66999C2×C4semidirect
159. Q8×Dic11C2×C4semidirect
211. #66936C2×C4semidirect
212. (C22⋊D11)⋊C4C2×C4semidirect
213. #66932C2×C4semidirect
215. #66930C2×C4semidirect
218. C42×D11C2×C4semidirect
219. #66923C2×C4semidirect
380. C4×#124D11semidirect
858. C11#34242semidirect

Maximal subgroups

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

subgroupindex
C2×#106232112
#130717372
#130717332
#130716592
#130716502
#130716482
#130716392
#130715722
#130715642
#130715622
#130715392
Q8×Dic11⋊C42
D4×Dic11⋊C42
#130714082
#130714042
#130712202
C4×#669232
#130711712
#124×Dic112
#130710222
#130709712
C4×#669252
C4×C11×#1242
#3424211