Finite Group Databasebeta

← #14913214

Subgroups — #14913214

Order 2816.

3142 conjugacy classes of subgroups.

The subgroup lattice has 1112 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic
2#13071586C212yesmaximal, complemented
3#13071551C212yesmaximal, complemented
4#13071550C212yesmaximal, complemented
5#13071522C212yesmaximal, complemented
6#13071494C211yesmaximal, characteristic, complemented
7#13071488C211yesmaximal, characteristic, complemented
8#13071466C211yesmaximal, characteristic, complemented
9#13071465C211yesmaximal, characteristic, complemented
10#13071458C211yesmaximal, characteristic, complemented
11C22⋊C4×C22⋊D11C211yesmaximal, characteristic
12#13071432C211yesmaximal, characteristic
13#13071076C212yesmaximal, complemented
14#13071058C212yesmaximal, complemented
15#13071052C212yesmaximal, complemented
16#13071007C211yesmaximal, characteristic, complemented
17#13070998C211yesmaximal, characteristic, complemented
18#13070994C211yesmaximal, characteristic, complemented
19C4×(C22⋊D11)⋊C4C212yesmaximal, complemented
20#117×Dic11C211yesmaximal, characteristic, complemented
21C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
22C4×C22⋊C4×D11C211yesmaximal, characteristic, complemented
23C11×#2342C211yesmaximal, characteristic, complemented
24C23×C22⋊D11C2211yescharacteristic
25C24×Dic11C2211yescharacteristic
26C23×C4×D11C2211yescharacteristic
27C2×C11×#117C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C11×C22⋊C4C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C2×C4×C22⋊D11C2212yes—
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C2×#66979C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C22×C4×Dic11C2211yescharacteristic
36C22×C4×Dic11C2212yescomplemented
37C2×#66945C2212yescomplemented
38C2×(C22⋊D11)⋊C4C4116yescomplemented
39C2×(C22⋊D11)⋊C4C2212yes—
40C2×(C22⋊D11)⋊C4C2211yescharacteristic
41C2×(C22⋊D11)⋊C4C2211yescharacteristic
42C2×(C22⋊D11)⋊C4C2211yescharacteristic
43C2×(C22⋊D11)⋊C4C2211yescharacteristic
44C2×(C22⋊D11)⋊C4C2211yescharacteristic
45C2×(C22⋊D11)⋊C4C2211yescharacteristic
46C2×(C22⋊D11)⋊C4C2211yescharacteristic
47C2×(C22⋊D11)⋊C4C2211yescharacteristic
48C2×C22⋊C4×D11C2211yescharacteristic
49C2×C22⋊C4×D11C2211yescharacteristic
50C2×#66930C2212yescomplemented
51C2×C42×D11C2212yescomplemented
52C11×#388C2212yescomplemented
53C11×#388C2212yescomplemented
54C11×#385C2212yescomplemented
55C11×#381C2211yescharacteristic
56C11×#380C2211yescharacteristic
57C11×#379C2211yescharacteristic
58C4×C11×C22⋊C4C2211yescharacteristic
59C4×C11×C22⋊C4C2212yescomplemented
60#10622860C2211yescharacteristic
61#10622826C2212yes—
62#10622825C2211yescharacteristic
63#10622824C2211yescharacteristic
64C4×C22⋊Dic11C2211yescharacteristic
65C2×C11⋊#95C2212yescomplemented
66#10622603C2212yescomplemented
67#10622602C2212yescomplemented
68#10622600C2212yescomplemented
69#10622591C2212yescomplemented
70C4⋊C4×Dic11C2212yescomplemented
71C4⋊C4×Dic11C2212yescomplemented
72#10622585C2212yescomplemented
73#10622571C2212yes—
74#10622570C2212yes—
75#10622570C2212yes—
76#10622569C2212yes—
77#10622569C2212yes—
78#10622568C2211yescharacteristic
79#10622568C2211yescharacteristic
80#10622564C2212yescomplemented
81#10622564C2212yescomplemented
82#10622563C2212yescomplemented
83#10622556C2212yescomplemented
84#10622555C2211yescharacteristic
85#10622555C2211yescharacteristic
86#10622555C2211yescharacteristic
87#10622555C2211yescharacteristic
88#10622555C2212yescomplemented
89C22⋊C4×Dic11C2211yescharacteristic
90C22⋊C4×Dic11C2211yescharacteristic
91C22⋊C4×Dic11C2211yescharacteristic
92C22⋊C4×Dic11C2211yescharacteristic
93C22⋊C4×Dic11C2211yescharacteristic
94C22⋊C4×Dic11C2211yescharacteristic
95C22⋊C4×Dic11C2211yescharacteristic
96C22⋊C4×Dic11C2211yescharacteristic
97C22⋊C4×Dic11C2212yescomplemented
98C22⋊C4×Dic11C2212yescomplemented
99C22⋊C4×Dic11C2212yescomplemented
100C22⋊C4×Dic11C2212yescomplemented
101#10622553C2212yescomplemented
102C4×(C2×D11)⋊C4C2212yescomplemented
103C4×(C2×D11)⋊C4C2212yescomplemented
104#10622546C2212yescomplemented
105#10622545C2212yescomplemented
106C4×Dic11⋊C4C2212yescomplemented
107C42×Dic11C2212yescomplemented
108#10622283C2212yescomplemented
109#10622282C2212yescomplemented
110#10622281C2212yescomplemented
111#10622279C2212yescomplemented
112#10622279C2212yescomplemented
113#10622279C2212yescomplemented
114#10622277C2212yescomplemented
115D11×#95C2212yescomplemented
116#10622268C2212yescomplemented
117#10622265C2212yescomplemented
118#10622264C2212yescomplemented
119#10622263C2212yescomplemented
120#10622262C2212yescomplemented
121#10622262C2212yescomplemented
122#10622261C2212yescomplemented
123#10622260C2212yescomplemented
124C25×C11C2311yescharacteristic
125C24×D11C2311yescharacteristic
126C23×C4×C11C2312yes—
127C23×C4×C11C2311yescharacteristic
128C23×C4×C11C2311yescharacteristic
129C22×C22⋊D11—28no—
130C22×C22⋊D11C2×C418yes—
131C22×C22⋊D11C2311yescharacteristic
132C22×C22⋊D11C2311yescharacteristic
133C22×C22⋊D11C2311yescharacteristic
134C22×C22⋊D11C2311yescharacteristic
135C23×Dic11—44no—
136C23×Dic11C2×C418yescomplemented
137C23×Dic11C2312yes—
138C23×Dic11C2311yescharacteristic
139C23×Dic11C2311yescharacteristic
140C23×Dic11C2311yescharacteristic
141C23×Dic11C2311yescharacteristic
142C23×Dic11C2311yescharacteristic
143C23×Dic11C2311yescharacteristic
144C23×Dic11C2311yescharacteristic
145C22×C4×D11—44no—
146C22×C4×D11C2×C418yescomplemented
147C22×C4×D11C2312yes—
148C22×C4×D11C2312yes—
149C22×C4×D11C2311yescharacteristic
150C22×C4×D11C2311yescharacteristic
151C22×C4×D11C2311yescharacteristic
152C22×C4×D11C2311yescharacteristic
153C11×#117—24no—
154C2×C11×C4⋊C4C2312yes—
155C2×C11×C4⋊C4C2312yes—
156C2×C11×C22⋊C4—24no—
157C2×C11×C22⋊C4C2×C418yescomplemented
158C2×C11×C22⋊C4C2311yescharacteristic
159C2×C11×C22⋊C4C2312yes—
160C2×C11×C22⋊C4C2311yescharacteristic
161C2×C11×C22⋊C4C2311yescharacteristic
162C2×C11×C22⋊C4C2312yes—
163C2×C11×C22⋊C4C2312yes—
164C2×C11×C22⋊C4C2311yescharacteristic
165C2×C11×C22⋊C4C2311yescharacteristic
166C2×C11×C22⋊C4C2311yescharacteristic
167C2×C11×C22⋊C4C2311yescharacteristic
168C2×C11×C22⋊C4C2311yescharacteristic
169C2×C42×C11C2312yes—
170C2×C42×C11C2312yes—
171C2×C22⋊Dic11—24no—
172C2×C22⋊Dic11C2311yescharacteristic
173C2×C22⋊Dic11C2311yescharacteristic
174C2×C22⋊Dic11C2312yes—
175C2×C22⋊Dic11C2311yescharacteristic
176C2×C22⋊Dic11C2312yes—
177C2×C22⋊Dic11C2312yes—
178C2×C22⋊Dic11C2311yescharacteristic
179C4×C22⋊D11—28no—
180C2×(C2×D11)⋊C4C2×C418yescomplemented
181C2×(C2×D11)⋊C4C2312yes—
182C2×(C2×D11)⋊C4C2312yes—
183C2×(C2×D11)⋊C4C2312yes—
184C2×(C2×D11)⋊C4C2312yes—
185C2×(C2×D11)⋊C4C2312yes—
186C2×(C2×D11)⋊C4C2312yes—
187C2×(C2×D11)⋊C4C2311yescharacteristic
188C2×(C2×D11)⋊C4C2311yescharacteristic
189C2×(C2×D11)⋊C4C2311yescharacteristic
190C2×(C2×D11)⋊C4C2311yescharacteristic
191#66979—24no—
192C2×C4⋊Dic11C2312yes—
193C2×C4⋊Dic11C2312yes—
194C2×Dic11⋊C4C2×C418yescomplemented
195C2×Dic11⋊C4C2312yes—
196C2×Dic11⋊C4C2312yes—
197C2×Dic11⋊C4C2312yes—
198C2×Dic11⋊C4C2312yes—
199C2×Dic11⋊C4C2311yescharacteristic
200C2×Dic11⋊C4C2311yescharacteristic
201C2×Dic11⋊C4C2311yescharacteristic
202C2×Dic11⋊C4C2311yescharacteristic
203C2×C4×Dic11—44no—
204C2×C4×Dic11C2×C418yescomplemented
205C2×C4×Dic11C2312yes—
206C2×C4×Dic11C2312yes—
207C2×C4×Dic11C2312yes—
208C2×C4×Dic11C2312yes—
209C2×C4×Dic11C2312yes—
210C2×C4×Dic11C2312yes—
211C2×C4×Dic11C2312yes—
212C2×C4×Dic11C2312yes—
213C2×C4×Dic11C2312yes—
214C2×C4×Dic11C2312yes—
215C2×C4×Dic11C2311yescharacteristic
216C2×C4×Dic11C2311yescharacteristic
217C2×C4×Dic11C2311yescharacteristic
218C2×C4×Dic11C2311yescharacteristic
219#66945—44no—
220(C22⋊D11)⋊C4—28no—
221(C22⋊D11)⋊C4C2×C418yes—
222(C22⋊D11)⋊C4C2×C418yes—
223(C22⋊D11)⋊C4C2×C418yescomplemented
224(C22⋊D11)⋊C4C2×C418yescomplemented
225(C22⋊D11)⋊C4C2×C418yescomplemented
226(C22⋊D11)⋊C4C2×C418yescomplemented
227(C22⋊D11)⋊C4C2×C418yescomplemented
228(C22⋊D11)⋊C4C2×C418yescomplemented
229C22⋊C4×D11—24no—
230C22⋊C4×D11—24no—
231#66930—44no—
232C42×D11—44no—
233C11×#95C2312yes—
234C11×#95C2312yes—
235C11×#95C2312yes—
236C11×#95C2312yes—
237C11⋊#95C2312yes—
238C11⋊#95C2312yes—
239C11⋊#95C2312yes—
240C11⋊#95C2312yes—
241C11⋊#95C2312yes—
242C11⋊#95C2312yes—
243C11⋊#95C2312yes—
244C11⋊#95C2312yes—
245C11⋊#95C2312yes—
246C11⋊#95C2312yes—
247C11⋊#95C2312yes—
248C11⋊#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253#34126—111nomaximal, Sylow
254C24×C11—22no—
255C24×C11—22no—
256C24×C11—24no—
257C24×C11—42no—
258C24×C11C22×C414yes—
259C24×C11C2411yescharacteristic
260C24×C11C2411yescharacteristic
261C24×C11C2411yescharacteristic
262C23×D11—22no—
263C23×D11—22no—
264C23×D11—24no—
265C23×D11—42no—
266C23×D11C22×C414yes—
267C23×D11C2411yescharacteristic
268C23×D11C2411yescharacteristic
269C22×C4×C11—22no—
270C22×C4×C11—22no—
271C22×C4×C11—24no—
272C22×C4×C11—24no—
273C22×C4×C11—42no—
274C22×C4×C11—42no—
275C22×C4×C11C22×C414yes—
276C22×C4×C11C22×C414yes—
277C22×C4×C11C2412yes—
278C22×C4×C11C2412yes—
279C22×C4×C11C2412yes—
280C22×C4×C11C2411yescharacteristic
281C22×C4×C11C2411yescharacteristic
282C22×C4×C11C2411yescharacteristic
283C22×C4×C11C2411yescharacteristic
284C22×C4×C11C2412yes—
285C2×C22⋊D11—232no—
286C2×C22⋊D11—24no—
287C2×C22⋊D11—24no—
288C2×C22⋊D11—24no—
289C2×C22⋊D11C22×C414yes—
290C2×C22⋊D11C22×C414yes—
291C2×C22⋊D11C22×C414yes—
292C2×C22⋊D11C22×C414yes—
293C2×C22⋊D11#4118yes—
294C22×Dic11—24no—
295C22×Dic11—24no—
296C22×Dic11—24no—
297C22×Dic11—24no—
298C22×Dic11—24no—
299C22×Dic11—24no—
300C22×Dic11—42no—
301C22×Dic11—42no—
302C22×Dic11—42no—
303C22×Dic11—42no—
304C22×Dic11—416no—
305C22×Dic11C22×C414yes—
306C22×Dic11C22×C414yes—
307C22×Dic11C22×C414yes—
308C22×Dic11C22×C414yes—
309C22×Dic11C22×C414yes—
310C22×Dic11C22×C414yes—
311C22×Dic11C22×C414yes—
312C22×Dic11C2412yes—
313C22×Dic11C2412yes—
314C22×Dic11C2412yes—
315C22×Dic11C2411yescharacteristic
316C22×Dic11C2411yescharacteristic
317C22×Dic11C2411yescharacteristic
318C22×Dic11C2411yescharacteristic
319C22×Dic11C2412yes—
320C22×Dic11C2411yescharacteristic
321C22×Dic11C2411yescharacteristic
322C2×C4×D11—24no—
323C2×C4×D11—24no—
324C2×C4×D11—24no—
325C2×C4×D11—24no—
326C2×C4×D11—24no—
327C2×C4×D11—24no—
328C2×C4×D11—42no—
329C2×C4×D11—42no—
330C2×C4×D11—42no—
331C2×C4×D11—42no—
332C2×C4×D11—416no—
333C2×C4×D11C22×C414yes—
334C2×C4×D11C22×C414yes—
335C2×C4×D11C22×C414yes—
336C2×C4×D11C22×C414yes—
337C11×C4⋊C4—24no—
338C11×C4⋊C4—42no—
339C11×C22⋊C4—22no—
340C11×C22⋊C4—24no—
341C11×C22⋊C4—22no—
342C11×C22⋊C4—22no—
343C11×C22⋊C4—24no—
344C11×C22⋊C4—42no—
345C11×C22⋊C4C22×C414yes—
346C11×C22⋊C4C22×C414yes—
347C11×C22⋊C4C22×C414yes—
348C11×C22⋊C4C22×C414yes—
349C11×C22⋊C4#4114yes—
350C42×C11—24no—
351C42×C11—42no—
352C22⋊Dic11—24no—
353C22⋊Dic11—22no—
354C22⋊Dic11—22no—
355C22⋊Dic11—24no—
356C22⋊Dic11—22no—
357C22⋊Dic11—42no—
358C22⋊Dic11#4114yes—
359(C2×D11)⋊C4—24no—
360(C2×D11)⋊C4—24no—
361(C2×D11)⋊C4—24no—
362(C2×D11)⋊C4—24no—
363(C2×D11)⋊C4—42no—
364(C2×D11)⋊C4—42no—
365(C2×D11)⋊C4C22×C414yes—
366(C2×D11)⋊C4C22×C414yes—
367(C2×D11)⋊C4C22×C414yes—
368(C2×D11)⋊C4C22×C414yes—
369C4⋊Dic11—24no—
370C4⋊Dic11—42no—
371Dic11⋊C4—24no—
372Dic11⋊C4—24no—
373Dic11⋊C4—42no—
374Dic11⋊C4—42no—
375Dic11⋊C4C22×C414yes—
376Dic11⋊C4C22×C414yes—
377Dic11⋊C4C22×C414yes—
378Dic11⋊C4C22×C414yes—
379C4×Dic11—24no—
380C4×Dic11—24no—
381C4×Dic11—24no—
382C4×Dic11—24no—
383C4×Dic11—24no—
384C4×Dic11—24no—
385C4×Dic11—24no—
386C4×Dic11—42no—
387C4×Dic11—42no—
388C4×Dic11—42no—
389C4×Dic11C22×C414yes—
390C4×Dic11C22×C414yes—
391C4×Dic11C22×C414yes—
392C4×Dic11C22×C414yes—
393C22×C4×D4—111no—
394#2357—112no—
395#2353—112no—
396#2353—112no—
397#2349—112no—
398#2345—111no—
399#2345—111no—
400#2342—111no—
401#2342—111no—
402#2342—111no—
403#2342D1111yescharacteristic, complemented
404D4×C22⋊C4—111no—
405D4×C22⋊C4—111no—
406#2293—112no—
407#2290—112no—
408#2290—112no—
409#2283—111no—
410#2280—111no—
411#2280—111no—
412C42×D4—112no—
413C4×#117—111no—
414C2×C4×C22⋊C4—111no—
415C2×C4×C22⋊C4—111no—
416C23×C11—21no—
417C23×C11—22no—
418C23×C11—21no—
419C23×C11—22no—
420C23×C11—22no—
421C23×C11—28no—
422C23×C11—28no—
423C23×C11—21no—
424C23×C11—21no—
425C23×C11—22no—
426C23×C11—22no—
427C23×C11—44no—
428C23×C11—48no—
429C23×C11—48no—
430C23×C11C23×C412yes—
431C23×C11C23×C412yes—
432C23×C11C23×C412yes—
433C23×C11C2×#4112yes—
434C23×C11C2×#4114yes—
435C23×C11C2×#4112yes—
436C23×C11C2511yescharacteristic
437C22×D11—21no—
438C22×D11—21no—
439C22×D11—22no—
440C22×D11—28no—
441C22×D11—21no—
442C22×D11—21no—
443C22×D11—22no—
444C22×D11—22no—
445C22×D11—28no—
446C22×D11—44no—
447C22×D11—48no—
448C22×D11—48no—
449C22×D11C23×C412yes—
450C22×D11C23×C412yes—
451C22×D11C2×#4114yes—
452C2×C4×C11—28no—
453C2×C4×C11—21no—
454C2×C4×C11—22no—
455C2×C4×C11—21no—
456C2×C4×C11—21no—
457C2×C4×C11—21no—
458C2×C4×C11—22no—
459C2×C4×C11—22no—
460C2×C4×C11—22no—
461C2×C4×C11—22no—
462C2×C4×C11—22no—
463C2×C4×C11—22no—
464C2×C4×C11—22no—
465C2×C4×C11—22no—
466C2×C4×C11—22no—
467C2×C4×C11—22no—
468C2×C4×C11—22no—
469C2×C4×C11—22no—
470C2×C4×C11—44no—
471C2×C4×C11—48no—
472C2×C4×C11C23×C412yes—
473C2×C4×C11C23×C412yes—
474C2×C4×C11C23×C412yes—
475C2×C4×C11C23×C412yes—
476C2×C4×C11C2×#4114yes—
477C22⋊D11—28no—
478C22⋊D11—28no—
479C22⋊D11—28no—
480C22⋊D11#117116yescomplemented
481C2×Dic11—22no—
482C2×Dic11—22no—
483C2×Dic11—22no—
484C2×Dic11—22no—
485C2×Dic11—22no—
486C2×Dic11—22no—
487C2×Dic11—28no—
488C2×Dic11—28no—
489C2×Dic11—28no—
490C2×Dic11—28no—
491C2×Dic11—22no—
492C2×Dic11—22no—
493C2×Dic11—22no—
494C2×Dic11—22no—
495C2×Dic11—22no—
496C2×Dic11—22no—
497C2×Dic11—22no—
498C2×Dic11—22no—
499C2×Dic11—22no—
500C2×Dic11—44no—
501C2×Dic11—44no—
502C2×Dic11—44no—
503C2×Dic11—48no—
504C2×Dic11C23×C412yes—
505C2×Dic11C23×C412yes—
506C2×Dic11C23×C412yes—
507C2×Dic11C23×C412yes—
508C2×Dic11C23×C412yes—
509C2×Dic11C23×C412yes—
510C2×Dic11C2×#4114yes—
511C2×Dic11C2×#4114yes—
512C2×Dic11H(5,𝔽2)14yes—
513C4×D11—28no—
514C4×D11—28no—
515C4×D11—44no—
516C4×D11—44no—
517C4×D11—48no—
518C4×D11—48no—
519C23×D4—111no—
520C24×C4—111no—
521C24×C4—111no—
522C2×C4×D4—112no—
523C2×C4×D4—111no—
524C2×C4×D4—111no—
525C2×C4×D4—111no—
526C2×C4×D4—111no—
527C2×C4×D4—111no—
528C2×C4×D4—111no—
529C2×C4×D4—111no—
530C2×C4×D4—111no—
531C2×C4×D4—112no—
532C2×C4×D4—1116no—
533C2×#117—111no—
534C2×#117—112no—
535C2×#117—112no—
536C2×#117C2×D1111yescharacteristic
537C22×C4⋊C4—111no—
538C22×C22⋊C4—111no—
539C22×C22⋊C4—111no—
540C22×C22⋊C4—111no—
541C22×C22⋊C4—111no—
542C22×C22⋊C4C2×D1111yescharacteristic
543C22×C22⋊C4C2×D1111yescharacteristic
544C22×C42—111no—
545C22×C42—112no—
546C22×C42—112no—
547#390—112no—
548#390—112no—
549#389—112no—
550#389—112no—
551#388—112no—
552#388—112no—
553#388—112no—
554#388—112no—
555#388—112no—
556#388—112no—
557#388C2×D1112yescomplemented
558#388C2×D1112yescomplemented
559#387—112no—
560#387—112no—
561#387—112no—
562#387—112no—
563#386—112no—
564#386—112no—
565#386—112no—
566#386—112no—
567#385—112no—
568#385—112no—
569#385—112no—
570#385C2×D1112yescomplemented
571#383—112no—
572#382—112no—
573#381—111no—
574#381—112no—
575#381—112no—
576#381C2×D1111yescharacteristic
577#380—111no—
578#380—112no—
579#380—111no—
580#380—111no—
581#380—111no—
582#380—111no—
583#380—112no—
584#380C2×D1111yescharacteristic
585#379—111no—
586#379—111no—
587#379—111no—
588#379C2×D1111yescharacteristic
589C4×C4⋊C4—112no—
590C4×C4⋊C4—112no—
591C4×C4⋊C4—112no—
592C4×C4⋊C4—112no—
593C4×C4⋊C4—112no—
594C4×C22⋊C4—111no—
595C4×C22⋊C4—111no—
596C4×C22⋊C4—111no—
597C4×C22⋊C4—111no—
598C4×C22⋊C4—111no—
599C4×C22⋊C4—112no—
600C4×C22⋊C4—112no—
601C4×C22⋊C4—111no—
602C4×C22⋊C4—111no—
603C4×C22⋊C4—111no—
604C4×C22⋊C4—111no—
605C4×C22⋊C4—112no—
606C4×C22⋊C4—112no—
607C4×C22⋊C4—112no—
608C4×C22⋊C4—112no—
609C4×C22⋊C4—112no—
610C4×C22⋊C4—112no—
611C4×C22⋊C4—112no—
612C4×C22⋊C4C2×D1111yescharacteristic
613C4×C22⋊C4C2×D1112yescomplemented
614#376—112no—
615#376—112no—
616C2×#95—112no—
617C2×#95—112no—
618C43—112no—
619C22×C11—22no—
620C22×C11—22no—
621C22×C11—22no—
622C22×C11—22no—
623C22×C11—24no—
624C22×C11—24no—
625C22×C11—24no—
626C22×C11—24no—
627C22×C11—22no—
628C22×C11—22no—
629C22×C11—22no—
630C22×C11—416no—
631C22×C11—42no—
632C22×C11—42no—
633C22×C11C2×#11714yes—
634C22×C11C4×#4114yes—
635C22×C11C24×C411yescharacteristic
636C22×C11C22×#4111yescharacteristic
637C22×C11C22×#4112yes—
638C22×C11C22×#4111yescharacteristic
639C22×C11C2×H(5,𝔽2)12yes—
640C2×D11—22no—
641C2×D11—22no—
642C2×D11—24no—
643C2×D11—24no—
644C2×D11—22no—
645C2×D11—22no—
646C2×D11—22no—
647C2×D11—416no—
648C2×D11—42no—
649C2×D11—42no—
650C2×D11C2×#11714yes—
651C4×C11—22no—
652C4×C11—22no—
653C4×C11—22no—
654C4×C11—22no—
655C4×C11—24no—
656C4×C11—42no—
657C4×C11—42no—
658C4×C11—42no—
659Dic11—22no—
660Dic11—22no—
661Dic11—22no—
662Dic11—22no—
663Dic11—24no—
664Dic11—42no—
665Dic11—42no—
666Dic11—42no—
667Dic11C2×#11714yes—
668Dic11#51814yes—
669C25—111no—
670C25C22×D1111yescharacteristic
671C22×D4—111no—
672C22×D4—118no—
673C22×D4—111no—
674C22×D4—111no—
675C22×D4—111no—
676C22×D4—228no—
677C23×C4—111no—
678C23×C4—111no—
679C23×C4—111no—
680C23×C4—111no—
681C23×C4—118no—
682C23×C4—111no—
683C23×C4—111no—
684C23×C4—111no—
685C23×C4—111no—
686C23×C4—111no—
687C23×C4—118no—
688C23×C4—111no—
689C23×C4—111no—
690C23×C4—112no—
691C23×C4—112no—
692C23×C4—112no—
693C23×C4—444no—
694C23×C4—444no—
695C23×C4C22×D1112yes—
696C23×C4C22×D1111yescharacteristic
697C23×C4C22×D1111yescharacteristic
698C4×D4—118no—
699C4×D4—118no—
700C4×D4—118no—
701C4×D4—118no—
702C4×D4—118no—
703C4×D4—118no—
704C4×D4—118no—
705C4×D4—118no—
706C4×D4—228no—
707C4×D4—228no—
708#117—24no—
709#117—224no—
710#117—444no—
711#117—444no—
712C2×C4⋊C4—118no—
713C2×C4⋊C4—111no—
714C2×C4⋊C4—111no—
715C2×C4⋊C4—111no—
716C2×C4⋊C4—111no—
717C2×C4⋊C4—112no—
718C2×C4⋊C4—112no—
719C2×C4⋊C4—112no—
720C2×C4⋊C4—112no—
721C2×C4⋊C4—112no—
722C2×C4⋊C4—112no—
723C2×C4⋊C4C22×D1112yes—
724C2×C4⋊C4C22×D1112yes—
725C2×C22⋊C4—24no—
726C2×C22⋊C4—111no—
727C2×C22⋊C4—118no—
728C2×C22⋊C4—111no—
729C2×C22⋊C4—111no—
730C2×C22⋊C4—111no—
731C2×C22⋊C4—111no—
732C2×C22⋊C4—111no—
733C2×C22⋊C4—111no—
734C2×C22⋊C4—112no—
735C2×C22⋊C4—111no—
736C2×C22⋊C4—112no—
737C2×C22⋊C4—112no—
738C2×C22⋊C4—112no—
739C2×C22⋊C4—112no—
740C2×C22⋊C4—112no—
741C2×C22⋊C4—112no—
742C2×C22⋊C4—112no—
743C2×C22⋊C4—112no—
744C2×C22⋊C4—224no—
745C2×C22⋊C4—224no—
746C2×C22⋊C4—224no—
747C2×C22⋊C4C4×D1118yescomplemented
748C2×C22⋊C4C22×D1111yescharacteristic
749C2×C22⋊C4C22×D1111yescharacteristic
750C2×C22⋊C4C22×D1112yes—
751C2×C22⋊C4C22×D1111yescharacteristic
752C2×C22⋊C4C22×D1112yes—
753C2×C22⋊C4C22×D1112yes—
754C2×C22⋊C4C22×D1111yescharacteristic
755C2×C22⋊C4C22×D1111yescharacteristic
756C2×C22⋊C4C22×D1111yescharacteristic
757C2×C22⋊C4C22×D1111yescharacteristic
758C2×C22⋊C4C22×D1111yescharacteristic
759C2×C42—118no—
760C2×C42—111no—
761C2×C42—111no—
762C2×C42—111no—
763C2×C42—111no—
764C2×C42—112no—
765C2×C42—112no—
766C2×C42—112no—
767C2×C42—112no—
768C2×C42—112no—
769C2×C42—112no—
770C2×C42—112no—
771C2×C42—112no—
772C2×C42—112no—
773C2×C42—112no—
774C2×C42—444no—
775C2×C42—444no—
776C2×C42C22×D1112yes—
777C2×C42C22×D1112yes—
778#95—112no—
779#95—112no—
780#95—112no—
781#95—112no—
782#95—112no—
783#95—112no—
784#95—112no—
785#95—112no—
786#95—112no—
787#95—112no—
788#95—112no—
789#95—112no—
790#95—112no—
791#95—112no—
792#95—112no—
793#95—112no—
794#95C22×D1112yes—
795#95C22×D1112yes—
796#95C22×D1112yes—
797#95C22×D1112yes—
798C2×C11—24no—
799C2×C11—24no—
800C2×C11—42no—
801C2×C11C22×#11711yescharacteristic
802C2×C11C2×C4×#4111yescharacteristic
803C2×C11C2×#51811yescharacteristic
804C2×C11#348112yes—
805C2×C11#348112yes—
806D11—24no—
807D11—42no—
808C24—22no—
809C24—22no—
810C24—24no—
811C24—42no—
812C24—111no—
813C24—111no—
814C24—114no—
815C24—224no—
816C24—222no—
817C24—222no—
818C24—442no—
819C24C2×C4×D1114yes—
820C24C23×D1111yescharacteristic
821C24C23×D1111yescharacteristic
822C24C23×D1111yescharacteristic
823C2×D4—114no—
824C2×D4—118no—
825C2×D4—114no—
826C2×D4—114no—
827C2×D4—114no—
828C2×D4—224no—
829C2×D4—2232no—
830C2×D4—224no—
831C2×D4—224no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—24no—
835C22×C4—24no—
836C22×C4—42no—
837C22×C4—42no—
838C22×C4—111no—
839C22×C4—111no—
840C22×C4—114no—
841C22×C4—114no—
842C22×C4—114no—
843C22×C4—114no—
844C22×C4—111no—
845C22×C4—111no—
846C22×C4—112no—
847C22×C4—111no—
848C22×C4—111no—
849C22×C4—114no—
850C22×C4—114no—
851C22×C4—114no—
852C22×C4—114no—
853C22×C4—114no—
854C22×C4—114no—
855C22×C4—114no—
856C22×C4—112no—
857C22×C4—112no—
858C22×C4—112no—
859C22×C4—224no—
860C22×C4—224no—
861C22×C4—224no—
862C22×C4—224no—
863C22×C4—224no—
864C22×C4—224no—
865C22×C4—224no—
866C22×C4—224no—
867C22×C4—224no—
868C22×C4—224no—
869C22×C4—224no—
870C22×C4—224no—
871C22×C4—442no—
872C22×C4—442no—
873C22×C4—442no—
874C22×C4—442no—
875C22×C4—4416no—
876C22×C4—4416no—
877C22×C4—442no—
878C22×C4—442no—
879C22×C4—442no—
880C22×C4—442no—
881C22×C4C2×C4×D1114yes—
882C22×C4C2×C4×D1114yes—
883C22×C4C23×D1112yes—
884C22×C4C23×D1112yes—
885C22×C4C23×D1112yes—
886C22×C4C23×D1111yescharacteristic
887C22×C4C23×D1111yescharacteristic
888C22×C4C23×D1111yescharacteristic
889C22×C4C23×D1111yescharacteristic
890C22×C4C23×D1112yes—
891C4⋊C4—24no—
892C4⋊C4—42no—
893C4⋊C4—114no—
894C4⋊C4—114no—
895C4⋊C4—114no—
896C4⋊C4—114no—
897C4⋊C4—224no—
898C4⋊C4—224no—
899C4⋊C4—224no—
900C4⋊C4—442no—
901C4⋊C4—442no—
902C4⋊C4—442no—
903C22⋊C4—22no—
904C22⋊C4—22no—
905C22⋊C4—22no—
906C22⋊C4—24no—
907C22⋊C4—24no—
908C22⋊C4—42no—
909C22⋊C4—114no—
910C22⋊C4—114no—
911C22⋊C4—114no—
912C22⋊C4—114no—
913C22⋊C4—114no—
914C22⋊C4—224no—
915C22⋊C4—224no—
916C22⋊C4—224no—
917C22⋊C4—224no—
918C22⋊C4—222no—
919C22⋊C4—222no—
920C22⋊C4—222no—
921C22⋊C4—224no—
922C22⋊C4—224no—
923C22⋊C4—442no—
924C22⋊C4—442no—
925C22⋊C4—442no—
926C22⋊C4C2×C4×D1114yes—
927C22⋊C4C2×C4×D1114yes—
928C22⋊C4C2×C4×D1114yes—
929C22⋊C4C2×C4×D1114yes—
930C22⋊C4#434114yes—
931C42—24no—
932C42—42no—
933C42—114no—
934C42—114no—
935C42—114no—
936C42—114no—
937C42—224no—
938C42—224no—
939C42—224no—
940C42—224no—
941C42—224no—
942C42—224no—
943C42—224no—
944C42—442no—
945C42—442no—
946C42—442no—
947C11#3412611yescharacteristic, complemented, Sylow
948C23—21no—
949C23—21no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—28no—
954C23—28no—
955C23—21no—
956C23—21no—
957C23—22no—
958C23—22no—
959C23—44no—
960C23—48no—
961C23—48no—
962C23—112no—
963C23—114no—
964C23—112no—
965C23—228no—
966C23—221no—
967C23—221no—
968C23—222no—
969C23—228no—
970C23—221no—
971C23—221no—
972C23—222no—
973C23—222no—
974C23—444no—
975C23—448no—
976C23—448no—
977C23C22×C4×D1112yes—
978C23C22×C4×D1112yes—
979C23C22×C4×D1112yes—
980C23C2×#434112yes—
981C23#41×D1114yes—
982C23#41×D1112yes—
983C23C24×D1111yescharacteristic
984D4—1116no—
985D4—228no—
986D4—228no—
987D4—228no—
988C2×C4—28no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—22no—
993C2×C4—21no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—44no—
1007C2×C4—48no—
1008C2×C4—112no—
1009C2×C4—112no—
1010C2×C4—114no—
1011C2×C4—114no—
1012C2×C4—112no—
1013C2×C4—112no—
1014C2×C4—112no—
1015C2×C4—112no—
1016C2×C4—114no—
1017C2×C4—228no—
1018C2×C4—228no—
1019C2×C4—228no—
1020C2×C4—228no—
1021C2×C4—228no—
1022C2×C4—228no—
1023C2×C4—222no—
1024C2×C4—222no—
1025C2×C4—222no—
1026C2×C4—222no—
1027C2×C4—222no—
1028C2×C4—222no—
1029C2×C4—222no—
1030C2×C4—222no—
1031C2×C4—222no—
1032C2×C4—222no—
1033C2×C4—222no—
1034C2×C4—222no—
1035C2×C4—222no—
1036C2×C4—222no—
1037C2×C4—222no—
1038C2×C4—444no—
1039C2×C4—444no—
1040C2×C4—448no—
1041C2×C4—448no—
1042C2×C4—444no—
1043C2×C4—444no—
1044C2×C4—444no—
1045C2×C4—448no—
1046C2×C4C22×C4×D1112yes—
1047C2×C4C22×C4×D1112yes—
1048C2×C4C22×C4×D1112yes—
1049C2×C4C22×C4×D1112yes—
1050C2×C4C2×#434114yes—
1051C22—24no—
1052C22—24no—
1053C22—24no—
1054C22—24no—
1055C22—22no—
1056C22—22no—
1057C22—22no—
1058C22—22no—
1059C22—22no—
1060C22—22no—
1061C22—22no—
1062C22—416no—
1063C22—42no—
1064C22—42no—
1065C22—114no—
1066C22—224no—
1067C22—224no—
1068C22—222no—
1069C22—222no—
1070C22—222no—
1071C22—222no—
1072C22—222no—
1073C22—4416no—
1074C22—442no—
1075C22—442no—
1076C22D11×#11714yes—
1077C22C4×#434114yes—
1078C22C23×C4×D1111yescharacteristic
1079C22C22×#434111yescharacteristic
1080C22C2×#41×D1111yescharacteristic
1081C22C2×#41×D1112yes—
1082C22D11×H(5,𝔽2)12yes—
1083C4—24no—
1084C4—22no—
1085C4—22no—
1086C4—22no—
1087C4—22no—
1088C4—42no—
1089C4—42no—
1090C4—42no—
1091C4—114no—
1092C4—114no—
1093C4—224no—
1094C4—222no—
1095C4—222no—
1096C4—222no—
1097C4—222no—
1098C4—442no—
1099C4—442no—
1100C4—442no—
1101C2—24no—
1102C2—24no—
1103C2—42no—
1104C2—224no—
1105C2—442no—
1106C2C2×D11×#11711yescharacteristic
1107C2C2×C4×#434111yescharacteristic
1108C2D11×#51811yescharacteristic
1109C2#1308221912yes—
1110C2#1308222112yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2342C2
socle, cosocleC23×C11C25
prime radicalC23×C22⋊D11C22
hypercenter#2342D11
hypocenterC11#34126
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2342

Complements

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

NH ≅ G/Ntype
2. #13071586C2semidirect
3. #13071551C2semidirect
4. #13071550C2semidirect
5. #13071522C2semidirect
6. #13071494C2semidirect
7. #13071488C2semidirect
8. #13071466C2semidirect
9. #13071465C2semidirect
10. #13071458C2semidirect
13. #13071076C2semidirect
14. #13071058C2semidirect
15. #13071052C2semidirect
16. #13071007C2semidirect
17. #13070998C2semidirect
18. #13070994C2semidirect
19. C4×(C22⋊D11)⋊C4C2semidirect
20. #117×Dic11C2semidirect
21. C2×C22⋊C4×Dic11C2semidirect
22. C4×C22⋊C4×D11C2semidirect
23. C11×#2342C2semidirect
36. C22×C4×Dic11C22semidirect
37. C2×#66945C22semidirect
38. C2×(C22⋊D11)⋊C4C4semidirect
50. C2×#66930C22semidirect
51. C2×C42×D11C22semidirect
52. C11×#388C22semidirect
53. C11×#388C22semidirect
54. C11×#385C22semidirect
59. C4×C11×C22⋊C4C22semidirect
65. C2×C11⋊#95C22semidirect
66. #10622603C22semidirect
67. #10622602C22semidirect
68. #10622600C22semidirect
69. #10622591C22semidirect
70. C4⋊C4×Dic11C22semidirect
71. C4⋊C4×Dic11C22semidirect
72. #10622585C22semidirect
80. #10622564C22semidirect
81. #10622564C22semidirect
82. #10622563C22semidirect
83. #10622556C22semidirect
88. #10622555C22semidirect
97. C22⋊C4×Dic11C22semidirect
98. C22⋊C4×Dic11C22semidirect
99. C22⋊C4×Dic11C22semidirect
100. C22⋊C4×Dic11C22semidirect
101. #10622553C22semidirect
102. C4×(C2×D11)⋊C4C22semidirect
103. C4×(C2×D11)⋊C4C22semidirect
104. #10622546C22semidirect
105. #10622545C22semidirect
106. C4×Dic11⋊C4C22semidirect
107. C42×Dic11C22semidirect
108. #10622283C22semidirect
109. #10622282C22semidirect
110. #10622281C22semidirect
111. #10622279C22semidirect
112. #10622279C22semidirect
113. #10622279C22semidirect
114. #10622277C22semidirect
115. D11×#95C22semidirect
116. #10622268C22semidirect
117. #10622265C22semidirect
118. #10622264C22semidirect
119. #10622263C22semidirect
120. #10622262C22semidirect
121. #10622262C22semidirect
122. #10622261C22semidirect
123. #10622260C22semidirect
136. C23×Dic11C2×C4semidirect
146. C22×C4×D11C2×C4semidirect
157. C2×C11×C22⋊C4C2×C4semidirect
180. C2×(C2×D11)⋊C4C2×C4semidirect
194. C2×Dic11⋊C4C2×C4semidirect
204. C2×C4×Dic11C2×C4semidirect
223. (C22⋊D11)⋊C4C2×C4semidirect
224. (C22⋊D11)⋊C4C2×C4semidirect
225. (C22⋊D11)⋊C4C2×C4semidirect
226. (C22⋊D11)⋊C4C2×C4semidirect
227. (C22⋊D11)⋊C4C2×C4semidirect
228. (C22⋊D11)⋊C4C2×C4semidirect
403. #2342D11semidirect
480. C22⋊D11#117semidirect
557. #388C2×D11semidirect
558. #388C2×D11semidirect
570. #385C2×D11semidirect
613. C4×C22⋊C4C2×D11semidirect
747. C2×C22⋊C4C4×D11semidirect
947. C11#34126semidirect

Maximal subgroups

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

subgroupindex
C22×(C22⋊D11)⋊C42
#130715862
#130715512
#130715502
#130715222
#130714942
#130714882
#130714662
#130714652
#130714582
C22⋊C4×C22⋊D112
#130714322
#130710762
#130710582
#130710522
#130710072
#130709982
#130709942
C4×(C22⋊D11)⋊C42
#117×Dic112
C2×C22⋊C4×Dic112
C4×C22⋊C4×D112
C11×#23422
#3412611