Finite Group Databasebeta

← #14913504

Subgroups — #14913504

Order 2816.

2398 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#13071750C212yesmaximal, complemented
3#13071744C212yesmaximal, complemented
4#13071743C212yesmaximal, complemented
5#13071731C212yesmaximal, complemented
6#13071712C211yesmaximal, characteristic, complemented
7#13071710C211yesmaximal, characteristic, complemented
8#13071691C211yesmaximal, characteristic, complemented
9#13071659C211yesmaximal, characteristic
10#13071650C211yesmaximal, characteristic
11#13071648C211yesmaximal, characteristic, complemented
12#13071639C211yesmaximal, characteristic, complemented
13#13071110C212yesmaximal, complemented
14#13071091C211yesmaximal, characteristic, complemented
15#13071078C211yesmaximal, characteristic, complemented
16#13071076C212yesmaximal, complemented
17#13071052C212yesmaximal, complemented
18C4×Q8×Dic11C211yesmaximal, characteristic, complemented
19C4×D4×Dic11C211yesmaximal, characteristic, complemented
20C4×#66945C211yesmaximal, characteristic, complemented
21C4×#66945C211yesmaximal, characteristic, complemented
22C4×#66930C212yesmaximal, complemented
23C11×#2367C211yesmaximal, 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×C4×Dic11C2212yes—
34#10623211C4116yescomplemented
35C2×#66945C2211yescharacteristic
36C2×#66945C2211yescharacteristic
37C2×#66945C2211yescharacteristic
38C2×#66945C2211yescharacteristic
39C2×#66936C2212yes—
40C2×(C22⋊D11)⋊C4C2212yes—
41C2×#66932C2212yes—
42C2×#66930C2212yes—
43C2×#66930C2212yes—
44C2×C42×D11C2211yescharacteristic
45C2×#66923C2211yescharacteristic
46C11×#391C2211yescharacteristic
47C11×#390C2211yescharacteristic
48C11×#388C2212yes—
49C11×#388C2212yes—
50C11×#385C2212yes—
51C4×C11×C4⋊C4C2211yescharacteristic
52C4×C11×C4⋊C4C2211yescharacteristic
53C4×C11×C22⋊C4C2212yes—
54#10622843C2211yescharacteristic
55#10622834C2211yescharacteristic
56#10622826C2212yes—
57C4×C22⋊Dic11C2212yes—
58C4×C22⋊Dic11C2212yes—
59#10622603C2212yes—
60#10622591C2212yes—
61#10622591C2212yes—
62C4⋊C4×Dic11C2212yes—
63C4⋊C4×Dic11C2211yescharacteristic
64C4⋊C4×Dic11C2211yescharacteristic
65C4⋊C4×Dic11C2211yescharacteristic
66C4⋊C4×Dic11C2211yescharacteristic
67C4⋊C4×Dic11C2211yescharacteristic
68C4⋊C4×Dic11C2211yescharacteristic
69C4⋊C4×Dic11C2212yes—
70#10622586C2211yescharacteristic
71#10622586C2211yescharacteristic
72#10622585C2212yes—
73#10622571C2212yes—
74#10622570C2212yes—
75#10622570C2212yes—
76#10622564C2212yes—
77#10622564C2212yes—
78#10622563C2212yes—
79#10622558C2212yes—
80#10622558C2212yes—
81#10622557C2212yes—
82#10622557C2212yes—
83C22⋊C4×Dic11C2212yes—
84C22⋊C4×Dic11C2212yes—
85C22⋊C4×Dic11C2212yes—
86C22⋊C4×Dic11C2212yes—
87C22⋊C4×Dic11C2212yes—
88#10622553C2212yes—
89C4×(C2×D11)⋊C4C2211yescharacteristic
90C4×(C2×D11)⋊C4C2211yescharacteristic
91C4×(C2×D11)⋊C4C2212yes—
92C4×C4⋊Dic11C2211yescharacteristic
93C4×C4⋊Dic11C2211yescharacteristic
94C4×C4⋊Dic11C2211yescharacteristic
95C4×C4⋊Dic11C2211yescharacteristic
96C4×C4⋊Dic11C2212yes—
97#10622546C2212yes—
98C4×Dic11⋊C4C2212yes—
99C4×Dic11⋊C4C2212yes—
100C42×Dic11C2212yes—
101C42×Dic11C2212yes—
102C42×Dic11C2211yescharacteristic
103C42×Dic11C2211yescharacteristic
104#10622541C2211yescharacteristic
105#10622541C2211yescharacteristic
106#10622283C2212yes—
107#10622282C2212yes—
108#10622279C2211yescharacteristic
109#10622279C2211yescharacteristic
110#10622279C2212yes—
111#10622268C2212yes—
112#10622268C2212yes—
113#10622267C2212yes—
114#10622266C2212yes—
115#10622265C2212yes—
116#10622262C2212yes—
117#10622262C2212yes—
118#10622262C2212yes—
119#10622261C2211yescharacteristic
120#10622261C2211yescharacteristic
121#10622261C2212yes—
122#10622261C2212yes—
123#10622260C2212yes—
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—24no—
135C4×D4×C11—24no—
136C2×C11×C4⋊C4C2311yescharacteristic
137C2×C11×C4⋊C4C2311yescharacteristic
138C2×C11×C4⋊C4C2311yescharacteristic
139C2×C11×C4⋊C4C2312yes—
140C2×C11×C4⋊C4C2311yescharacteristic
141C2×C11×C22⋊C4C2312yes—
142C2×C11×C22⋊C4C2312yes—
143C2×C11×C22⋊C4C2312yes—
144C2×C11×C22⋊C4C2312yes—
145C2×C11×C22⋊C4C2312yes—
146C2×C42×C11C2311yescharacteristic
147C2×C42×C11C2311yescharacteristic
148C2×C42×C11C2312yes—
149C2×C42×C11C2312yes—
150C2×C42×C11C2311yescharacteristic
151C2×C22⋊Dic11C2312yes—
152C2×C22⋊Dic11C2312yes—
153C2×C22⋊Dic11C2312yes—
154C2×C22⋊Dic11C2312yes—
155C2×C22⋊Dic11C2312yes—
156#66999C2×C418yescomplemented
157Q8×Dic11—24no—
158Q8×Dic11C2×C418yescomplemented
159#66991C2×C418yes—
160D4×Dic11—24no—
161D4×Dic11C2×C418yes—
162C2×(C2×D11)⋊C4C2311yescharacteristic
163C2×(C2×D11)⋊C4C2312yes—
164C2×(C2×D11)⋊C4C2311yescharacteristic
165C2×(C2×D11)⋊C4C2311yescharacteristic
166C2×(C2×D11)⋊C4C2312yes—
167C2×(C2×D11)⋊C4C2311yescharacteristic
168C2×(C2×D11)⋊C4C2312yes—
169C2×C4⋊Dic11C2311yescharacteristic
170C2×C4⋊Dic11C2311yescharacteristic
171C2×C4⋊Dic11C2311yescharacteristic
172C2×C4⋊Dic11C2312yes—
173C2×C4⋊Dic11C2311yescharacteristic
174C2×C4⋊Dic11C2311yescharacteristic
175C2×C4⋊Dic11C2312yes—
176C2×C4⋊Dic11C2311yescharacteristic
177C2×Dic11⋊C4C2312yes—
178C2×Dic11⋊C4C2312yes—
179C2×Dic11⋊C4C2312yes—
180C2×Dic11⋊C4C2312yes—
181C2×Dic11⋊C4C2312yes—
182C2×Dic11⋊C4C2312yes—
183C2×Dic11⋊C4C2312yes—
184C2×C4×Dic11—28no—
185C2×C4×Dic11C2312yes—
186C2×C4×Dic11C2311yescharacteristic
187C2×C4×Dic11C2312yes—
188C2×C4×Dic11C2312yes—
189C2×C4×Dic11C2311yescharacteristic
190C2×C4×Dic11C2312yes—
191C2×C4×Dic11C2312yes—
192C2×C4×Dic11C2312yes—
193C2×C4×Dic11C2312yes—
194C2×C4×Dic11C2311yescharacteristic
195C2×C4×Dic11C2311yescharacteristic
196C2×C4×Dic11C2312yes—
197C2×C4×Dic11C2312yes—
198C2×C4×Dic11C2312yes—
199C2×C4×Dic11C2311yescharacteristic
200C2×C4×Dic11C2311yescharacteristic
201C2×C4×Dic11C2311yescharacteristic
202C2×C4×Dic11C2311yescharacteristic
203C2×C4×Dic11C2311yescharacteristic
204C2×C4×Dic11C2311yescharacteristic
205C2×C4×Dic11C2311yescharacteristic
206C2×C4×Dic11C2312yes—
207C2×C4×Dic11C2311yescharacteristic
208C2×C4×Dic11C2311yescharacteristic
209#66945—24no—
210#66945—24no—
211#66945—24no—
212#66945—24no—
213#66936C2×C4116yescomplemented
214(C22⋊D11)⋊C4C2×C4116yescomplemented
215#66932C2×C4116yescomplemented
216#66930—28no—
217#66930C2×C4116yescomplemented
218C42×D11C2×C418yescomplemented
219#66923C2×C418yescomplemented
220C11×#95C2312yes—
221C11×#95C2311yescharacteristic
222C11×#95C2312yes—
223C11×#95C2311yescharacteristic
224C11×#95C2312yes—
225C11⋊#95C2312yes—
226C11⋊#95C2311yescharacteristic
227C11⋊#95C2312yes—
228C11⋊#95C2312yes—
229C11⋊#95C2312yes—
230C11⋊#95C2312yes—
231C11⋊#95C2311yescharacteristic
232C11⋊#95C2311yescharacteristic
233C11⋊#95C2311yescharacteristic
234C11⋊#95C2312yes—
235C11⋊#95C2311yescharacteristic
236C11⋊#95C2312yes—
237C11⋊#95C2311yescharacteristic
238C11⋊#95C2312yes—
239C11⋊#95C2312yes—
240C11⋊#95C2312yes—
241C11⋊#95C2312yes—
242C11⋊#95C2312yes—
243C11⋊#95C2312yes—
244#34151—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—24no—
255C22×C4×C11—42no—
256C22×C4×C11C2411yescharacteristic
257C22×C4×C11C2412yes—
258C22×C4×C11C2411yescharacteristic
259C22×C4×C11C2411yescharacteristic
260C22×C4×C11C2412yes—
261C22×C4×C11C2411yescharacteristic
262C22×C4×C11C2411yescharacteristic
263C22×C4×C11C2412yes—
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—24no—
273C22×Dic11—42no—
274C22×Dic11C22×C418yes—
275C22×Dic11C2412yes—
276C22×Dic11C2411yescharacteristic
277C22×Dic11C2411yescharacteristic
278C22×Dic11C2411yescharacteristic
279C22×Dic11C2411yescharacteristic
280C22×Dic11C2412yes—
281C22×Dic11C2412yes—
282C22×Dic11C2411yescharacteristic
283C22×Dic11C2412yes—
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—22no—
298C11×C4⋊C4—24no—
299C11×C4⋊C4#4114yes—
300C11×C22⋊C4—24no—
301C11×C22⋊C4—24no—
302C11×C22⋊C4—42no—
303C11×C22⋊C4C22×C418yes—
304C11×C22⋊C4C22×C418yes—
305C42×C11—22no—
306C42×C11—24no—
307C42×C11—22no—
308C42×C11—42no—
309C42×C11C22×C414yes—
310C22⋊Dic11—24no—
311C22⋊Dic11—24no—
312C22⋊Dic11—42no—
313C22⋊Dic11C22×C418yes—
314C22⋊Dic11C22×C418yes—
315(C2×D11)⋊C4—22no—
316(C2×D11)⋊C4—24no—
317(C2×D11)⋊C4—22no—
318(C2×D11)⋊C4—24no—
319(C2×D11)⋊C4—22no—
320(C2×D11)⋊C4—22no—
321(C2×D11)⋊C4C22×C418yes—
322C4⋊Dic11—22no—
323C4⋊Dic11—22no—
324C4⋊Dic11—24no—
325C4⋊Dic11—22no—
326C4⋊Dic11C22×C414yes—
327C4⋊Dic11C22×C414yes—
328C4⋊Dic11C22×C418yes—
329C4⋊Dic11#4114yes—
330Dic11⋊C4—24no—
331Dic11⋊C4—24no—
332Dic11⋊C4—42no—
333Dic11⋊C4—42no—
334Dic11⋊C4C22×C418yes—
335Dic11⋊C4C22×C418yes—
336Dic11⋊C4C22×C418yes—
337C4×Dic11—24no—
338C4×Dic11—24no—
339C4×Dic11—22no—
340C4×Dic11—22no—
341C4×Dic11—24no—
342C4×Dic11—24no—
343C4×Dic11—24no—
344C4×Dic11—24no—
345C4×Dic11—24no—
346C4×Dic11—22no—
347C4×Dic11—22no—
348C4×Dic11—41no—
349C4×Dic11—42no—
350C4×Dic11—42no—
351C4×Dic11—42no—
352C4×Dic11—41no—
353C4×Dic11—41no—
354C4×Dic11—41no—
355C4×Dic11C22×C414yes—
356C4×Dic11C22×C414yes—
357C4×Dic11C22×C414yes—
358C4×Dic11C22×C418yes—
359C4×Dic11#4114yes—
360C4×Dic11#4114yes—
361C2×#529—111no—
362#2374—112no—
363#2374—112no—
364#2373—112no—
365#2373—112no—
366#2370—111no—
367#2370—111no—
368#2367—111no—
369#2367D1111yescharacteristic, complemented
370#2363—111no—
371#2363—111no—
372#2362—111no—
373#2362—111no—
374#2298—112no—
375#2295—111no—
376#2293—111no—
377#2293—112no—
378#2290—112no—
379C42×Q8—111no—
380C42×D4—111no—
381C4×#117—111no—
382C4×#117—111no—
383C4×#117—112no—
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—22no—
402C2×C4×C11—22no—
403C2×C4×C11—21no—
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—22no—
411C2×C4×C11—21no—
412C2×C4×C11—21no—
413C2×C4×C11—22no—
414C2×C4×C11—21no—
415C2×C4×C11—22no—
416C2×C4×C11—21no—
417C2×C4×C11—21no—
418C2×C4×C11—21no—
419C2×C4×C11—21no—
420C2×C4×C11—21no—
421C2×C4×C11—22no—
422C2×C4×C11—48no—
423C2×C4×C11C23×C412yes—
424C2×C4×C11C23×C412yes—
425C2×C4×C11C23×C414yes—
426C2×C4×C11C23×C412yes—
427C2×C4×C11C2×#4114yes—
428C2×C4×C11C2×#4112yes—
429C2×C4×C11C2×#4112yes—
430C2×C4×C11C2×#4112yes—
431C2×C4×C11C2×#4112yes—
432C22⋊D11—48no—
433C2×Dic11—21no—
434C2×Dic11—21no—
435C2×Dic11—21no—
436C2×Dic11—22no—
437C2×Dic11—22no—
438C2×Dic11—21no—
439C2×Dic11—22no—
440C2×Dic11—21no—
441C2×Dic11—21no—
442C2×Dic11—21no—
443C2×Dic11—22no—
444C2×Dic11—22no—
445C2×Dic11—22no—
446C2×Dic11—21no—
447C2×Dic11—216no—
448C2×Dic11—22no—
449C2×Dic11—21no—
450C2×Dic11—22no—
451C2×Dic11—21no—
452C2×Dic11—21no—
453C2×Dic11—21no—
454C2×Dic11—21no—
455C2×Dic11—22no—
456C2×Dic11—21no—
457C2×Dic11—48no—
458C2×Dic11C23×C412yes—
459C2×Dic11C23×C412yes—
460C2×Dic11C23×C414yes—
461C2×Dic11C23×C414yes—
462C2×Dic11C23×C412yes—
463C2×Dic11C2×#4112yes—
464C2×Dic11C2×#4114yes—
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—111no—
488C2×#117—111no—
489C2×#117—112no—
490C2×#117—112no—
491C22×C42—111no—
492C22×C42—112no—
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#385C2×D1112yes—
529C4×C4⋊C4—111no—
530C4×C4⋊C4—111no—
531C4×C4⋊C4—111no—
532C4×C4⋊C4—111no—
533C4×C4⋊C4—112no—
534C4×C4⋊C4—111no—
535C4×C4⋊C4—111no—
536C4×C4⋊C4—112no—
537C4×C4⋊C4—111no—
538C4×C4⋊C4—112no—
539C4×C4⋊C4—111no—
540C4×C4⋊C4—111no—
541C4×C4⋊C4—111no—
542C4×C4⋊C4—112no—
543C4×C4⋊C4—112no—
544C4×C4⋊C4—112no—
545C4×C4⋊C4—112no—
546C4×C4⋊C4—112no—
547C4×C4⋊C4C2×D1111yescharacteristic
548C4×C4⋊C4C2×D1111yescharacteristic
549C4×C22⋊C4—112no—
550C4×C22⋊C4—112no—
551C4×C22⋊C4—112no—
552C4×C22⋊C4—112no—
553C4×C22⋊C4—112no—
554C4×C22⋊C4—112no—
555C4×C22⋊C4—112no—
556C4×C22⋊C4—111no—
557C4×C22⋊C4—111no—
558C4×C22⋊C4—112no—
559C4×C22⋊C4—111no—
560C4×C22⋊C4—111no—
561C4×C22⋊C4—112no—
562C4×C22⋊C4C2×D1112yes—
563#376—112no—
564#376—111no—
565#376—112no—
566#376—111no—
567C43—112no—
568C43—111no—
569C43—112no—
570C43—111no—
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×C11C22×#4111yescharacteristic
582C22×C11C22×#4111yescharacteristic
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—24no—
593C4×C11—22no—
594C4×C11—22no—
595C4×C11—22no—
596C4×C11—24no—
597C4×C11—22no—
598C4×C11—41no—
599C4×C11—41no—
600C4×C11—42no—
601C4×C11C4×#4114yes—
602Dic11—22no—
603Dic11—24no—
604Dic11—22no—
605Dic11—24no—
606Dic11—22no—
607Dic11—24no—
608Dic11—22no—
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—24no—
629C4×Q8—118no—
630C4×Q8—224no—
631C4×D4—24no—
632C4×D4—118no—
633C4×D4—1116no—
634C4×D4—224no—
635#117—1116no—
636#117—228no—
637#117—224no—
638#117—224no—
639#117—224no—
640#117—224no—
641C2×C4⋊C4—111no—
642C2×C4⋊C4—112no—
643C2×C4⋊C4—112no—
644C2×C4⋊C4—111no—
645C2×C4⋊C4—112no—
646C2×C4⋊C4—111no—
647C2×C4⋊C4—112no—
648C2×C4⋊C4—111no—
649C2×C4⋊C4—112no—
650C2×C4⋊C4—112no—
651C2×C4⋊C4—111no—
652C2×C4⋊C4—111no—
653C2×C4⋊C4—112no—
654C2×C4⋊C4—112no—
655C2×C4⋊C4—112no—
656C2×C4⋊C4C22×D1111yescharacteristic
657C2×C4⋊C4C22×D1111yescharacteristic
658C2×C4⋊C4C22×D1111yescharacteristic
659C2×C4⋊C4C22×D1112yes—
660C2×C4⋊C4C22×D1111yescharacteristic
661C2×C22⋊C4—112no—
662C2×C22⋊C4—112no—
663C2×C22⋊C4—112no—
664C2×C22⋊C4—112no—
665C2×C22⋊C4—112no—
666C2×C22⋊C4—111no—
667C2×C22⋊C4—111no—
668C2×C22⋊C4—112no—
669C2×C22⋊C4—112no—
670C2×C22⋊C4—111no—
671C2×C22⋊C4—111no—
672C2×C22⋊C4—112no—
673C2×C22⋊C4C22×D1112yes—
674C2×C22⋊C4C22×D1112yes—
675C2×C22⋊C4C22×D1112yes—
676C2×C22⋊C4C22×D1112yes—
677C2×C22⋊C4C22×D1112yes—
678C2×C42—111no—
679C2×C42—111no—
680C2×C42—112no—
681C2×C42—111no—
682C2×C42—111no—
683C2×C42—111no—
684C2×C42—118no—
685C2×C42—111no—
686C2×C42—111no—
687C2×C42—112no—
688C2×C42—112no—
689C2×C42—112no—
690C2×C42—111no—
691C2×C42—112no—
692C2×C42—111no—
693C2×C42—112no—
694C2×C42—112no—
695C2×C42—112no—
696C2×C42—111no—
697C2×C42—111no—
698C2×C42—112no—
699C2×C42—111no—
700C2×C42—111no—
701C2×C42—112no—
702C2×C42—112no—
703C2×C42—228no—
704C2×C42C22×D1111yescharacteristic
705C2×C42C22×D1111yescharacteristic
706C2×C42C22×D1112yes—
707C2×C42C22×D1112yes—
708C2×C42C22×D1111yescharacteristic
709#95—111no—
710#95—111no—
711#95—112no—
712#95—111no—
713#95—112no—
714#95—112no—
715#95—112no—
716#95—112no—
717#95—111no—
718#95—112no—
719#95—111no—
720#95—111no—
721#95—112no—
722#95—112no—
723#95—112no—
724#95—112no—
725#95—112no—
726#95—112no—
727#95—112no—
728#95C22×D1111yescharacteristic
729#95C22×D1112yes—
730#95C22×D1111yescharacteristic
731#95C22×D1112yes—
732#95C22×D1112yes—
733C2×C11—44no—
734C2×C11C2×C4×#4111yescharacteristic
735C2×C11C2×C4×#4111yescharacteristic
736C2×C11#342811yescharacteristic
737C2×C11#347511yescharacteristic
738C2×C11#347511yescharacteristic
739C2×C11#348011yescharacteristic
740C2×C11#348011yescharacteristic
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—24no—
755C22×C4—42no—
756C22×C4—111no—
757C22×C4—118no—
758C22×C4—111no—
759C22×C4—111no—
760C22×C4—111no—
761C22×C4—112no—
762C22×C4—112no—
763C22×C4—112no—
764C22×C4—111no—
765C22×C4—114no—
766C22×C4—114no—
767C22×C4—114no—
768C22×C4—112no—
769C22×C4—111no—
770C22×C4—111no—
771C22×C4—222no—
772C22×C4—222no—
773C22×C4—224no—
774C22×C4—224no—
775C22×C4—224no—
776C22×C4—224no—
777C22×C4—222no—
778C22×C4—222no—
779C22×C4—441no—
780C22×C4—441no—
781C22×C4—442no—
782C22×C4C23×D1111yescharacteristic
783C22×C4C23×D1111yescharacteristic
784C22×C4C23×D1112yes—
785C22×C4C23×D1111yescharacteristic
786C22×C4C23×D1112yes—
787C22×C4C23×D1111yescharacteristic
788C22×C4C23×D1112yes—
789C22×C4C23×D1111yescharacteristic
790C22×C4C23×D1111yescharacteristic
791C22×C4C23×D1111yescharacteristic
792C4⋊C4—24no—
793C4⋊C4—22no—
794C4⋊C4—22no—
795C4⋊C4—22no—
796C4⋊C4—118no—
797C4⋊C4—118no—
798C4⋊C4—114no—
799C4⋊C4—118no—
800C4⋊C4—114no—
801C4⋊C4—118no—
802C4⋊C4—114no—
803C4⋊C4—224no—
804C4⋊C4—222no—
805C4⋊C4—222no—
806C4⋊C4—224no—
807C4⋊C4—222no—
808C4⋊C4—224no—
809C4⋊C4—442no—
810C4⋊C4—442no—
811C4⋊C4#434114yes—
812C22⋊C4—24no—
813C22⋊C4—24no—
814C22⋊C4—42no—
815C22⋊C4—118no—
816C22⋊C4—118no—
817C22⋊C4—118no—
818C22⋊C4—222no—
819C22⋊C4—222no—
820C22⋊C4—224no—
821C22⋊C4—224no—
822C22⋊C4—224no—
823C22⋊C4—224no—
824C22⋊C4—222no—
825C22⋊C4—222no—
826C22⋊C4—442no—
827C22⋊C4C2×C4×D1118yes—
828C22⋊C4C2×C4×D1118yes—
829C42—22no—
830C42—24no—
831C42—22no—
832C42—42no—
833C42—114no—
834C42—114no—
835C42—114no—
836C42—118no—
837C42—114no—
838C42—114no—
839C42—224no—
840C42—224no—
841C42—224no—
842C42—222no—
843C42—222no—
844C42—224no—
845C42—224no—
846C42—224no—
847C42—224no—
848C42—222no—
849C42—222no—
850C42—442no—
851C42—441no—
852C42—442no—
853C42—441no—
854C42—442no—
855C42—441no—
856C42—441no—
857C42C2×C4×D1114yes—
858C11#3415111yescharacteristic, 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—22no—
881C2×C4—22no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—22no—
886C2×C4—21no—
887C2×C4—21no—
888C2×C4—21no—
889C2×C4—21no—
890C2×C4—21no—
891C2×C4—22no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—48no—
899C2×C4—112no—
900C2×C4—112no—
901C2×C4—112no—
902C2×C4—112no—
903C2×C4—112no—
904C2×C4—114no—
905C2×C4—114no—
906C2×C4—112no—
907C2×C4—112no—
908C2×C4—114no—
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—222no—
918C2×C4—221no—
919C2×C4—221no—
920C2×C4—222no—
921C2×C4—222no—
922C2×C4—221no—
923C2×C4—222no—
924C2×C4—221no—
925C2×C4—228no—
926C2×C4—222no—
927C2×C4—221no—
928C2×C4—221no—
929C2×C4—222no—
930C2×C4—221no—
931C2×C4—221no—
932C2×C4—221no—
933C2×C4—221no—
934C2×C4—222no—
935C2×C4—444no—
936C2×C4—448no—
937C2×C4C22×C4×D1112yes—
938C2×C4C22×C4×D1112yes—
939C2×C4C22×C4×D1114yes—
940C2×C4C22×C4×D1112yes—
941C2×C4C2×#434114yes—
942C2×C4C2×#434112yes—
943C2×C4#41×D1112yes—
944C2×C4#41×D1112yes—
945C2×C4#41×D1112yes—
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
961C22C22×#434111yescharacteristic
962C22C2×#41×D1111yescharacteristic
963C22C2×#41×D1111yescharacteristic
964C22C2×#41×D1111yescharacteristic
965C22#1062345511yescharacteristic
966C22#1062345711yescharacteristic
967C4—22no—
968C4—24no—
969C4—22no—
970C4—22no—
971C4—24no—
972C4—22no—
973C4—41no—
974C4—41no—
975C4—42no—
976C4—114no—
977C4—222no—
978C4—224no—
979C4—222no—
980C4—224no—
981C4—222no—
982C4—222no—
983C4—224no—
984C4—441no—
985C4—442no—
986C4—441no—
987C4C4×#434114yes—
988C2—44no—
989C2—442no—
990C2C4×#41×D1111yescharacteristic
991C2C2×C4×#434111yescharacteristic
992C2#1308181611yescharacteristic
993C2#1308216711yescharacteristic
994C2#1308217711yescharacteristic
995C2#1308220611yescharacteristic
996C2#1308221211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2367C2
socle, cosocleC23×C11C25
prime radicalC2×#66991C22
hypercenter#2367D11
hypocenterC11#34151
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2367

Complements

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

NH ≅ G/Ntype
2. #13071750C2semidirect
3. #13071744C2semidirect
4. #13071743C2semidirect
5. #13071731C2semidirect
6. #13071712C2semidirect
7. #13071710C2semidirect
8. #13071691C2semidirect
11. #13071648C2semidirect
12. #13071639C2semidirect
13. #13071110C2semidirect
14. #13071091C2semidirect
15. #13071078C2semidirect
16. #13071076C2semidirect
17. #13071052C2semidirect
18. C4×Q8×Dic11C2semidirect
19. C4×D4×Dic11C2semidirect
20. C4×#66945C2semidirect
21. C4×#66945C2semidirect
22. C4×#66930C2semidirect
23. C11×#2367C2semidirect
34. #10623211C4semidirect
156. #66999C2×C4semidirect
158. Q8×Dic11C2×C4semidirect
213. #66936C2×C4semidirect
214. (C22⋊D11)⋊C4C2×C4semidirect
215. #66932C2×C4semidirect
217. #66930C2×C4semidirect
218. C42×D11C2×C4semidirect
219. #66923C2×C4semidirect
369. #2367D11semidirect
858. C11#34151semidirect

Maximal subgroups

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

subgroupindex
C2×#106232112
#130717502
#130717442
#130717432
#130717312
#130717122
#130717102
#130716912
#130716592
#130716502
#130716482
#130716392
#130711102
#130710912
#130710782
#130710762
#130710522
C4×Q8×Dic112
C4×D4×Dic112
C4×#669452
C4×#669302
C11×#23672
#3415111