Finite Group Databasebeta

← #14913217

Subgroups — #14913217

Order 2816.

3142 conjugacy classes of subgroups.

The subgroup lattice has 1146 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D11C211yesmaximal, characteristic
2#13071586C212yesmaximal, complemented
3#13071555C212yesmaximal, complemented
4#13071554C212yesmaximal, complemented
5#13071522C212yesmaximal, complemented
6#13071490C212yesmaximal, complemented
7#13071464C212yesmaximal, complemented
8#13071463C212yesmaximal, complemented
9#13071434C212yesmaximal
10#13071079C211yesmaximal, characteristic, complemented
11#13071075C211yesmaximal, characteristic, complemented
12#13071061C211yesmaximal, characteristic, complemented
13#13071060C211yesmaximal, characteristic, complemented
14#13071057C211yesmaximal, characteristic, complemented
15#13071008C211yesmaximal, characteristic, complemented
16#13070997C211yesmaximal, characteristic, complemented
17#13070995C211yesmaximal, characteristic, complemented
18C42×C22⋊D11C211yesmaximal, characteristic, complemented
19C4×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
20C4×#66945C211yesmaximal, characteristic, complemented
21C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
22C4×C22⋊C4×D11C211yesmaximal, characteristic, complemented
23C11×#2290C211yesmaximal, characteristic, complemented
24C22×D4×D11C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C23×C4×D11C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C2×C11×#117C2211yescharacteristic, complemented
29C22×C42×C11C2211yescharacteristic, complemented
30C2×D4×Dic11C2211yescharacteristic
31C2×C4×C22⋊D11C2212yes—
32C2×C4×C22⋊D11C2211yescharacteristic
33C2×C4×C22⋊D11C2211yescharacteristic
34C22×(C2×D11)⋊C4C2212yes—
35C2×#66979C2211yescharacteristic, complemented
36C22×C4×Dic11C2211yescharacteristic, complemented
37C4×D4×D11C4116yescomplemented
38C2×#66946C2211yescharacteristic
39C2×#66945C2212yes—
40C2×C4⋊C4×D11C2211yescharacteristic
41C2×(C22⋊D11)⋊C4C2212yes—
42C2×(C22⋊D11)⋊C4C2211yescharacteristic
43C2×(C22⋊D11)⋊C4C2211yescharacteristic
44C2×C22⋊C4×D11C2212yes—
45C2×C22⋊C4×D11C2211yescharacteristic
46C2×C22⋊C4×D11C2211yescharacteristic
47C2×C4×D44C2211yescharacteristic
48C2×#66925C2211yescharacteristic, complemented
49C2×#66925C2211yescharacteristic, complemented
50C2×C42×D11C2211yescharacteristic
51C2×C42×D11C2211yescharacteristic, complemented
52C2×C42×D11C2211yescharacteristic, complemented
53C11×#388C2212yescomplemented
54C11×#387C2212yescomplemented
55C11×#386C2212yes—
56C11×#385C2212yescomplemented
57C4×C11×C4⋊C4C2211yescharacteristic, complemented
58C4×C11×C22⋊C4C2211yescharacteristic, complemented
59C4×C11×C22⋊C4C2211yescharacteristic, complemented
60C11×#376C2211yescharacteristic, complemented
61#10622833C2212yes—
62C4×C22⋊Dic11C2211yescharacteristic, complemented
63C4×C22⋊Dic11C2212yescomplemented
64C4×C22⋊Dic11C2211yescharacteristic, complemented
65C2×C11⋊#95C2212yescomplemented
66#10622603C2212yescomplemented
67#10622603C2212yescomplemented
68#10622602C2212yescomplemented
69#10622600C2212yes—
70#10622600C2212yescomplemented
71#10622594C2212yescomplemented
72C4⋊C4×Dic11C2212yescomplemented
73#10622585C2212yescomplemented
74#10622570C2212yes—
75#10622570C2212yes—
76#10622568C2212yes—
77#10622568C2212yes—
78#10622564C2212yescomplemented
79#10622563C2212yescomplemented
80#10622558C2212yescomplemented
81#10622557C2212yescomplemented
82#10622556C2212yescomplemented
83#10622555C2212yescomplemented
84C22⋊C4×Dic11C2212yescomplemented
85C22⋊C4×Dic11C2212yescomplemented
86C4×(C2×D11)⋊C4C2211yescharacteristic
87C4×(C2×D11)⋊C4C2211yescharacteristic
88C4×(C2×D11)⋊C4C2212yes—
89C4×(C2×D11)⋊C4C2211yescharacteristic
90C4×(C2×D11)⋊C4C2211yescharacteristic
91C4×(C2×D11)⋊C4C2212yescomplemented
92C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
93C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
94C4×(C2×D11)⋊C4C2212yescomplemented
95C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
96C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
97C4×C4⋊Dic11C2211yescharacteristic, complemented
98#10622545C2211yescharacteristic, complemented
99C4×Dic11⋊C4C2211yescharacteristic, complemented
100C4×Dic11⋊C4C2212yescomplemented
101C4×Dic11⋊C4C2211yescharacteristic, complemented
102C42×Dic11C2211yescharacteristic, complemented
103C42×Dic11C2211yescharacteristic, complemented
104#10622283C2212yescomplemented
105#10622283C2212yescomplemented
106#10622281C2212yescomplemented
107#10622280C2212yes—
108#10622280C2212yes—
109#10622279C2212yes—
110#10622279C2212yes—
111#10622279C2212yescomplemented
112#10622278C2212yes—
113#10622278C2212yes—
114#10622277C2212yes—
115#10622277C2212yescomplemented
116D11×#95C2212yescomplemented
117#10622267C2212yescomplemented
118#10622266C2212yescomplemented
119#10622264C2212yescomplemented
120#10622263C2212yescomplemented
121#10622262C2212yescomplemented
122#10622261C2212yescomplemented
123#10622260C2212yescomplemented
124C24×D11C2311yescharacteristic
125C24×D11C2311yescharacteristic
126C22×D4×C11C2311yescharacteristic
127C23×C4×C11C2312yes—
128C23×C4×C11C2311yescharacteristic
129C23×C4×C11C2311yescharacteristic
130C22×C22⋊D11C2311yescharacteristic
131C22×C22⋊D11C2311yescharacteristic
132C23×Dic11C2312yes—
133C23×Dic11C2311yescharacteristic
134C23×Dic11C2311yescharacteristic
135C2×D4×D11—28no—
136C2×D4×D11C2×C418yes—
137C22×D44C2311yescharacteristic
138C22×C4×D11—42no—
139C22×C4×D11—42no—
140C22×C4×D11—42no—
141C22×C4×D11—42no—
142C22×C4×D11C2×C418yescomplemented
143C22×C4×D11C2×C418yescomplemented
144C22×C4×D11C2312yes—
145C22×C4×D11C2312yes—
146C22×C4×D11C2311yescharacteristic
147C22×C4×D11C2311yescharacteristic
148C22×C4×D11C2311yescharacteristic
149C22×C4×D11C2311yescharacteristic
150C22×C4×D11C2311yescharacteristic
151C22×C4×D11C2311yescharacteristic
152C22×C4×D11C2311yescharacteristic
153C22×C4×D11C2311yescharacteristic
154C22×C4×D11C2311yescharacteristic
155C4×D4×C11C2×C418yescomplemented
156C11×#117—42no—
157C2×C11×C4⋊C4C2312yes—
158C2×C11×C4⋊C4C2312yes—
159C2×C11×C4⋊C4C2311yescharacteristic
160C2×C11×C22⋊C4C2312yes—
161C2×C11×C22⋊C4C2312yes—
162C2×C11×C22⋊C4C2312yes—
163C2×C11×C22⋊C4C2311yescharacteristic
164C2×C11×C22⋊C4C2311yescharacteristic
165C2×C42×C11—42no—
166C2×C42×C11C2311yescharacteristic
167C2×C42×C11C2311yescharacteristic
168C2×C42×C11C2311yescharacteristic
169C2×C42×C11C2311yescharacteristic
170C2×C42×C11C2312yes—
171C2×C42×C11C2311yescharacteristic
172C2×C22⋊Dic11C2312yes—
173C2×C22⋊Dic11C2312yes—
174C2×C22⋊Dic11C2312yes—
175C2×C22⋊Dic11C2311yescharacteristic
176C2×C22⋊Dic11C2311yescharacteristic
177D4×Dic11C2×C418yescomplemented
178C4×C22⋊D11—28no—
179C4×C22⋊D11C2×C418yes—
180C4×C22⋊D11C2×C418yescomplemented
181C2×(C2×D11)⋊C4—28no—
182C2×(C2×D11)⋊C4C2312yes—
183C2×(C2×D11)⋊C4C2312yes—
184C2×(C2×D11)⋊C4C2312yes—
185C2×(C2×D11)⋊C4C2312yes—
186C2×(C2×D11)⋊C4C2312yes—
187C2×(C2×D11)⋊C4C2312yes—
188C2×(C2×D11)⋊C4C2312yes—
189C2×(C2×D11)⋊C4C2312yes—
190C2×(C2×D11)⋊C4C2312yes—
191C2×(C2×D11)⋊C4C2311yescharacteristic
192C2×(C2×D11)⋊C4C2311yescharacteristic
193C2×(C2×D11)⋊C4C2311yescharacteristic
194C2×(C2×D11)⋊C4C2311yescharacteristic
195C2×(C2×D11)⋊C4C2312yes—
196#66979—42no—
197C2×C4⋊Dic11C2312yes—
198C2×C4⋊Dic11C2312yes—
199C2×C4⋊Dic11C2311yescharacteristic
200C2×Dic11⋊C4C2312yes—
201C2×Dic11⋊C4C2312yes—
202C2×Dic11⋊C4C2312yes—
203C2×Dic11⋊C4C2312yes—
204C2×Dic11⋊C4C2311yescharacteristic
205C2×Dic11⋊C4C2311yescharacteristic
206C2×C4×Dic11—42no—
207C2×C4×Dic11C2311yescharacteristic
208C2×C4×Dic11C2311yescharacteristic
209C2×C4×Dic11C2311yescharacteristic
210C2×C4×Dic11C2312yes—
211C2×C4×Dic11C2312yes—
212C2×C4×Dic11C2312yes—
213C2×C4×Dic11C2312yes—
214C2×C4×Dic11C2311yescharacteristic
215C2×C4×Dic11C2312yes—
216C2×C4×Dic11C2312yes—
217C2×C4×Dic11C2312yes—
218C2×C4×Dic11C2311yescharacteristic
219C2×C4×Dic11C2311yescharacteristic
220C2×C4×Dic11C2311yescharacteristic
221#66946C2×C418yescomplemented
222#66945—28no—
223C4⋊C4×D11C2×C418yescomplemented
224(C22⋊D11)⋊C4—28no—
225(C22⋊D11)⋊C4C2×C418yes—
226(C22⋊D11)⋊C4C2×C418yescomplemented
227C22⋊C4×D11—28no—
228C22⋊C4×D11C2×C418yescomplemented
229C22⋊C4×D11C2×C418yescomplemented
230C4×D44C2×C418yescomplemented
231#66925—42no—
232#66925—42no—
233C42×D11—42no—
234C42×D11—42no—
235C42×D11C2×C418yescomplemented
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—
253C11⋊#95C2312yes—
254C11⋊#95C2312yes—
255C11⋊#95C2312yes—
256#34126—111nomaximal, Sylow
257C24×C11C2411yescharacteristic
258C24×C11C2411yescharacteristic
259C23×D11—24no—
260C23×D11—24no—
261C23×D11—24no—
262C23×D11—24no—
263C23×D11—41no—
264C23×D11—41no—
265C23×D11—41no—
266C23×D11—41no—
267C23×D11C22×C414yes—
268C23×D11C22×C414yes—
269C23×D11C2411yescharacteristic
270C23×D11C2411yescharacteristic
271C23×D11C2411yescharacteristic
272C2×D4×C11—24no—
273C2×D4×C11C22×C414yes—
274C22×C4×C11—22no—
275C22×C4×C11—22no—
276C22×C4×C11—22no—
277C22×C4×C11—22no—
278C22×C4×C11—24no—
279C22×C4×C11—24no—
280C22×C4×C11—42no—
281C22×C4×C11C22×C414yes—
282C22×C4×C11C22×C414yes—
283C22×C4×C11C2412yes—
284C22×C4×C11C2412yes—
285C22×C4×C11C2412yes—
286C22×C4×C11C2411yescharacteristic
287C22×C4×C11C2411yescharacteristic
288C22×C4×C11C2411yescharacteristic
289C22×C4×C11C2411yescharacteristic
290C22×C4×C11C2412yes—
291C22×C4×C11C2411yescharacteristic
292C2×C22⋊D11—24no—
293C2×C22⋊D11C22×C414yes—
294C2×C22⋊D11C22×C414yes—
295C2×C22⋊D11#4118yes—
296C22×Dic11—24no—
297C22×Dic11—24no—
298C22×Dic11—42no—
299C22×Dic11—41no—
300C22×Dic11—41no—
301C22×Dic11—41no—
302C22×Dic11—41no—
303C22×Dic11C22×C414yes—
304C22×Dic11C22×C414yes—
305C22×Dic11C2412yes—
306C22×Dic11C2412yes—
307C22×Dic11C2412yes—
308C22×Dic11C2411yescharacteristic
309C22×Dic11C2411yescharacteristic
310C22×Dic11C2411yescharacteristic
311C22×Dic11C2411yescharacteristic
312C22×Dic11C2412yes—
313C22×Dic11C2411yescharacteristic
314D4×D11—232no—
315C2×D44—24no—
316C2×D44C22×C414yes—
317C2×C4×D11—24no—
318C2×C4×D11—24no—
319C2×C4×D11—24no—
320C2×C4×D11—24no—
321C2×C4×D11—24no—
322C2×C4×D11—24no—
323C2×C4×D11—22no—
324C2×C4×D11—22no—
325C2×C4×D11—22no—
326C2×C4×D11—22no—
327C2×C4×D11—22no—
328C2×C4×D11—22no—
329C2×C4×D11—42no—
330C2×C4×D11—42no—
331C2×C4×D11—41no—
332C2×C4×D11—41no—
333C2×C4×D11—41no—
334C2×C4×D11—41no—
335C2×C4×D11—41no—
336C2×C4×D11—41no—
337C2×C4×D11—41no—
338C2×C4×D11—41no—
339C2×C4×D11—416no—
340C2×C4×D11—416no—
341C2×C4×D11C22×C414yes—
342C2×C4×D11C22×C414yes—
343C2×C4×D11C22×C414yes—
344C2×C4×D11C22×C414yes—
345C2×C4×D11C22×C414yes—
346C2×C4×D11C22×C414yes—
347C2×C4×D11C22×C414yes—
348C2×C4×D11C22×C414yes—
349C2×C4×D11C22×C414yes—
350C11×C4⋊C4—24no—
351C11×C4⋊C4—42no—
352C11×C4⋊C4C22×C414yes—
353C11×C22⋊C4—24no—
354C11×C22⋊C4—24no—
355C11×C22⋊C4—42no—
356C11×C22⋊C4C22×C414yes—
357C11×C22⋊C4C22×C414yes—
358C42×C11—22no—
359C42×C11—22no—
360C42×C11—22no—
361C42×C11—22no—
362C42×C11—42no—
363C42×C11C22×C414yes—
364C22⋊Dic11—24no—
365C22⋊Dic11—24no—
366C22⋊Dic11—42no—
367C22⋊Dic11C22×C414yes—
368C22⋊Dic11C22×C414yes—
369(C2×D11)⋊C4—24no—
370(C2×D11)⋊C4—24no—
371(C2×D11)⋊C4—24no—
372(C2×D11)⋊C4—24no—
373(C2×D11)⋊C4—24no—
374(C2×D11)⋊C4—24no—
375(C2×D11)⋊C4—24no—
376(C2×D11)⋊C4—42no—
377(C2×D11)⋊C4—42no—
378(C2×D11)⋊C4C22×C414yes—
379(C2×D11)⋊C4C22×C414yes—
380(C2×D11)⋊C4C22×C414yes—
381(C2×D11)⋊C4C22×C414yes—
382(C2×D11)⋊C4#4118yes—
383C4⋊Dic11—24no—
384C4⋊Dic11—42no—
385C4⋊Dic11C22×C414yes—
386Dic11⋊C4—24no—
387Dic11⋊C4—24no—
388Dic11⋊C4—42no—
389Dic11⋊C4—42no—
390Dic11⋊C4C22×C414yes—
391Dic11⋊C4C22×C414yes—
392C4×Dic11—24no—
393C4×Dic11—24no—
394C4×Dic11—24no—
395C4×Dic11—24no—
396C4×Dic11—22no—
397C4×Dic11—22no—
398C4×Dic11—22no—
399C4×Dic11—22no—
400C4×Dic11—42no—
401C4×Dic11—42no—
402C4×Dic11—42no—
403C4×Dic11C22×C414yes—
404C4×Dic11C22×C414yes—
405C4×Dic11C22×C414yes—
406C22×C4×D4—111no—
407#2357—112no—
408#2353—112no—
409#2353—112no—
410#2349—112no—
411#2345—112no—
412#2342—112no—
413#2342—112no—
414D4×C22⋊C4—112no—
415#2293—111no—
416#2293—111no—
417#2290—111no—
418#2290—111no—
419#2290—111no—
420#2290D1111yescharacteristic, complemented
421#2283—111no—
422#2280—111no—
423#2280—111no—
424C42×D4—111no—
425C42×D4—111no—
426C4×#117—111no—
427C2×C4×C22⋊C4—111no—
428C2×C4×C22⋊C4—111no—
429C23×C11—22no—
430C23×C11—21no—
431C23×C11—21no—
432C23×C11—22no—
433C23×C11—22no—
434C23×C11—21no—
435C23×C11—21no—
436C23×C11C23×C412yes—
437C23×C11C23×C412yes—
438C23×C11C2×#4114yes—
439C23×C11C2511yescharacteristic
440C22×D11—22no—
441C22×D11—22no—
442C22×D11—21no—
443C22×D11—21no—
444C22×D11—21no—
445C22×D11—21no—
446C22×D11—28no—
447C22×D11—22no—
448C22×D11—22no—
449C22×D11—21no—
450C22×D11—21no—
451C22×D11—28no—
452C22×D11—28no—
453C22×D11—28no—
454C22×D11—44no—
455C22×D11—44no—
456C22×D11—48no—
457C22×D11—48no—
458C22×D11—48no—
459C22×D11—48no—
460C22×D11C23×C412yes—
461C22×D11C23×C412yes—
462C22×D11C23×C412yes—
463C22×D11C2×#4114yes—
464C22×D11C2×#4114yes—
465D4×C11—28no—
466C2×C4×C11—22no—
467C2×C4×C11—22no—
468C2×C4×C11—22no—
469C2×C4×C11—21no—
470C2×C4×C11—22no—
471C2×C4×C11—21no—
472C2×C4×C11—21no—
473C2×C4×C11—21no—
474C2×C4×C11—28no—
475C2×C4×C11—28no—
476C2×C4×C11—22no—
477C2×C4×C11—22no—
478C2×C4×C11—22no—
479C2×C4×C11—22no—
480C2×C4×C11—22no—
481C2×C4×C11—22no—
482C2×C4×C11—22no—
483C2×C4×C11—22no—
484C2×C4×C11—22no—
485C2×C4×C11—48no—
486C2×C4×C11C23×C412yes—
487C2×C4×C11C23×C412yes—
488C2×C4×C11C23×C412yes—
489C2×C4×C11C23×C412yes—
490C2×C4×C11C23×C412yes—
491C2×C4×C11C2×#4114yes—
492C2×C4×C11H(5,𝔽2)12yes—
493C2×C4×C11H(5,𝔽2)12yes—
494C22⋊D11—28no—
495C22⋊D11#117116yescomplemented
496C2×Dic11—22no—
497C2×Dic11—22no—
498C2×Dic11—22no—
499C2×Dic11—21no—
500C2×Dic11—21no—
501C2×Dic11—21no—
502C2×Dic11—21no—
503C2×Dic11—21no—
504C2×Dic11—21no—
505C2×Dic11—22no—
506C2×Dic11—22no—
507C2×Dic11—22no—
508C2×Dic11—22no—
509C2×Dic11—22no—
510C2×Dic11—22no—
511C2×Dic11—22no—
512C2×Dic11—22no—
513C2×Dic11—22no—
514C2×Dic11—44no—
515C2×Dic11—44no—
516C2×Dic11—48no—
517C2×Dic11C23×C412yes—
518C2×Dic11C23×C412yes—
519C2×Dic11C23×C412yes—
520C2×Dic11C23×C412yes—
521C2×Dic11C23×C412yes—
522C2×Dic11C2×#4114yes—
523C2×Dic11C2×#4114yes—
524D44—28no—
525C4×D11—28no—
526C4×D11—28no—
527C4×D11—28no—
528C4×D11—28no—
529C4×D11—28no—
530C4×D11—44no—
531C4×D11—44no—
532C4×D11—44no—
533C4×D11—44no—
534C4×D11—48no—
535C4×D11—48no—
536C23×D4—111no—
537C24×C4—111no—
538C24×C4—111no—
539C2×C4×D4—111no—
540C2×C4×D4—111no—
541C2×C4×D4—111no—
542C2×C4×D4—1116no—
543C2×C4×D4—112no—
544C2×C4×D4—111no—
545C2×C4×D4—111no—
546C2×C4×D4—111no—
547C2×C4×D4—112no—
548C2×C4×D4—111no—
549C2×C4×D4C2×D1111yescharacteristic
550C2×#117—111no—
551C2×#117—112no—
552C2×#117—111no—
553C2×#117—111no—
554C2×#117C2×D1111yescharacteristic, complemented
555C22×C4⋊C4—111no—
556C22×C22⋊C4—111no—
557C22×C22⋊C4—111no—
558C22×C22⋊C4—112no—
559C22×C22⋊C4—112no—
560C22×C42—111no—
561C22×C42—111no—
562C22×C42—111no—
563C22×C42—111no—
564C22×C42C2×D1111yescharacteristic, complemented
565#390—112no—
566#390—112no—
567#389—112no—
568#389—112no—
569#388—112no—
570#388—112no—
571#388—112no—
572#388—112no—
573#388—112no—
574#388—112no—
575#388—112no—
576#388C2×D1112yescomplemented
577#387—112no—
578#387—112no—
579#387—112no—
580#387C2×D1112yescomplemented
581#386—112no—
582#386—112no—
583#386—112no—
584#386C2×D1112yes—
585#385—112no—
586#385—112no—
587#385—112no—
588#385C2×D1112yescomplemented
589#383—112no—
590#382—112no—
591#381—112no—
592#381—112no—
593#381—112no—
594#380—112no—
595#380—112no—
596#380—112no—
597#380—112no—
598#380—112no—
599#379—112no—
600#379—112no—
601C4×C4⋊C4—112no—
602C4×C4⋊C4—112no—
603C4×C4⋊C4—111no—
604C4×C4⋊C4—111no—
605C4×C4⋊C4—111no—
606C4×C4⋊C4—112no—
607C4×C4⋊C4C2×D1111yescharacteristic, complemented
608C4×C22⋊C4—112no—
609C4×C22⋊C4—111no—
610C4×C22⋊C4—111no—
611C4×C22⋊C4—112no—
612C4×C22⋊C4—112no—
613C4×C22⋊C4—112no—
614C4×C22⋊C4—112no—
615C4×C22⋊C4—112no—
616C4×C22⋊C4—111no—
617C4×C22⋊C4—111no—
618C4×C22⋊C4—111no—
619C4×C22⋊C4—111no—
620C4×C22⋊C4—111no—
621C4×C22⋊C4—111no—
622C4×C22⋊C4—111no—
623C4×C22⋊C4—111no—
624C4×C22⋊C4—112no—
625C4×C22⋊C4—112no—
626C4×C22⋊C4—112no—
627C4×C22⋊C4C2×D1111yescharacteristic, complemented
628C4×C22⋊C4C2×D1111yescharacteristic, complemented
629#376—111no—
630#376—112no—
631#376C2×D1111yescharacteristic, complemented
632C2×#95—112no—
633C2×#95—112no—
634C43—111no—
635C43—111no—
636C22×C11—22no—
637C22×C11—22no—
638C22×C11—24no—
639C22×C11—24no—
640C22×C11—22no—
641C22×C11—22no—
642C22×C11—22no—
643C22×C11—42no—
644C22×C11—42no—
645C22×C11C2×#11714yes—
646C22×C11C24×C411yescharacteristic
647C22×C11C22×#4112yes—
648C22×C11C22×#4112yes—
649C22×C11C2×H(5,𝔽2)11yescharacteristic
650C22×C11C2×H(5,𝔽2)11yescharacteristic
651C2×D11—22no—
652C2×D11—22no—
653C2×D11—22no—
654C2×D11—22no—
655C2×D11—24no—
656C2×D11—24no—
657C2×D11—24no—
658C2×D11—24no—
659C2×D11—22no—
660C2×D11—22no—
661C2×D11—22no—
662C2×D11—416no—
663C2×D11—416no—
664C2×D11—42no—
665C2×D11—42no—
666C2×D11C2×#11714yes—
667C2×D11C4×#4114yes—
668C4×C11—22no—
669C4×C11—22no—
670C4×C11—22no—
671C4×C11—22no—
672C4×C11—24no—
673C4×C11—42no—
674C4×C11—42no—
675C4×C11—42no—
676C4×C11#51814yes—
677Dic11—22no—
678Dic11—22no—
679Dic11—22no—
680Dic11—22no—
681Dic11—24no—
682Dic11—42no—
683Dic11—42no—
684Dic11—42no—
685Dic11C2×#11714yes—
686C25—111no—
687C25—111no—
688C22×D4—111no—
689C22×D4—111no—
690C22×D4—118no—
691C22×D4—111no—
692C22×D4—228no—
693C22×D4C22×D1111yescharacteristic
694C23×C4—111no—
695C23×C4—111no—
696C23×C4—111no—
697C23×C4—111no—
698C23×C4—111no—
699C23×C4—111no—
700C23×C4—111no—
701C23×C4—118no—
702C23×C4—118no—
703C23×C4—111no—
704C23×C4—111no—
705C23×C4—111no—
706C23×C4—111no—
707C23×C4—112no—
708C23×C4—112no—
709C23×C4—112no—
710C23×C4—442no—
711C23×C4—442no—
712C23×C4—442no—
713C23×C4—442no—
714C23×C4C22×D1112yes—
715C23×C4C22×D1111yescharacteristic
716C23×C4C22×D1111yescharacteristic
717C4×D4—118no—
718C4×D4—118no—
719C4×D4—118no—
720C4×D4—118no—
721C4×D4—118no—
722C4×D4—118no—
723C4×D4—118no—
724C4×D4—228no—
725C4×D4—228no—
726C4×D4C4×D1118yescomplemented
727#117—42no—
728#117—228no—
729#117—442no—
730#117—442no—
731#117—442no—
732C2×C4⋊C4—111no—
733C2×C4⋊C4—111no—
734C2×C4⋊C4—111no—
735C2×C4⋊C4—118no—
736C2×C4⋊C4—112no—
737C2×C4⋊C4—112no—
738C2×C4⋊C4—112no—
739C2×C4⋊C4—112no—
740C2×C4⋊C4—112no—
741C2×C4⋊C4—112no—
742C2×C4⋊C4C22×D1112yes—
743C2×C4⋊C4C22×D1112yes—
744C2×C4⋊C4C22×D1111yescharacteristic
745C2×C22⋊C4—111no—
746C2×C22⋊C4—111no—
747C2×C22⋊C4—112no—
748C2×C22⋊C4—111no—
749C2×C22⋊C4—111no—
750C2×C22⋊C4—111no—
751C2×C22⋊C4—111no—
752C2×C22⋊C4—118no—
753C2×C22⋊C4—118no—
754C2×C22⋊C4—112no—
755C2×C22⋊C4—112no—
756C2×C22⋊C4—112no—
757C2×C22⋊C4—112no—
758C2×C22⋊C4—112no—
759C2×C22⋊C4—112no—
760C2×C22⋊C4—112no—
761C2×C22⋊C4—112no—
762C2×C22⋊C4—112no—
763C2×C22⋊C4—112no—
764C2×C22⋊C4—112no—
765C2×C22⋊C4—112no—
766C2×C22⋊C4—228no—
767C2×C22⋊C4—228no—
768C2×C22⋊C4C22×D1112yes—
769C2×C22⋊C4C22×D1112yes—
770C2×C22⋊C4C22×D1112yes—
771C2×C22⋊C4C22×D1111yescharacteristic
772C2×C22⋊C4C22×D1111yescharacteristic
773C2×C42—42no—
774C2×C42—111no—
775C2×C42—111no—
776C2×C42—111no—
777C2×C42—118no—
778C2×C42—112no—
779C2×C42—112no—
780C2×C42—112no—
781C2×C42—112no—
782C2×C42—111no—
783C2×C42—111no—
784C2×C42—111no—
785C2×C42—111no—
786C2×C42—112no—
787C2×C42—112no—
788C2×C42—112no—
789C2×C42—442no—
790C2×C42—442no—
791C2×C42—442no—
792C2×C42C22×D1111yescharacteristic
793C2×C42C22×D1111yescharacteristic
794C2×C42C22×D1111yescharacteristic
795C2×C42C22×D1111yescharacteristic
796C2×C42C22×D1112yes—
797C2×C42C22×D1111yescharacteristic
798#95—112no—
799#95—112no—
800#95—112no—
801#95—112no—
802#95—112no—
803#95—112no—
804#95—112no—
805#95—112no—
806#95—112no—
807#95—112no—
808#95—112no—
809#95—112no—
810#95—112no—
811#95—112no—
812#95—112no—
813#95C22×D1112yes—
814#95C22×D1112yes—
815#95C22×D1112yes—
816#95C22×D1112yes—
817#95C22×D1112yes—
818C2×C11—24no—
819C2×C11—42no—
820C2×C11C22×#11711yescharacteristic
821C2×C11C2×C4×#4111yescharacteristic
822C2×C11C2×#51811yescharacteristic
823C2×C11#348112yes—
824C2×C11#348112yes—
825D11—24no—
826D11—24no—
827D11—42no—
828C24—111no—
829C24—111no—
830C24—111no—
831C24—114no—
832C24—114no—
833C24—224no—
834C24—224no—
835C24—224no—
836C24—224no—
837C24—441no—
838C24—441no—
839C24—441no—
840C24—441no—
841C24C23×D1111yescharacteristic
842C24C23×D1111yescharacteristic
843C2×D4—24no—
844C2×D4—114no—
845C2×D4—118no—
846C2×D4—114no—
847C2×D4—114no—
848C2×D4—224no—
849C2×D4—224no—
850C2×D4—2232no—
851C2×D4C2×C4×D1114yes—
852C22×C4—22no—
853C22×C4—22no—
854C22×C4—22no—
855C22×C4—22no—
856C22×C4—24no—
857C22×C4—24no—
858C22×C4—42no—
859C22×C4—111no—
860C22×C4—111no—
861C22×C4—111no—
862C22×C4—112no—
863C22×C4—111no—
864C22×C4—111no—
865C22×C4—114no—
866C22×C4—114no—
867C22×C4—114no—
868C22×C4—114no—
869C22×C4—114no—
870C22×C4—114no—
871C22×C4—114no—
872C22×C4—114no—
873C22×C4—114no—
874C22×C4—114no—
875C22×C4—114no—
876C22×C4—112no—
877C22×C4—112no—
878C22×C4—112no—
879C22×C4—224no—
880C22×C4—224no—
881C22×C4—224no—
882C22×C4—224no—
883C22×C4—224no—
884C22×C4—224no—
885C22×C4—222no—
886C22×C4—222no—
887C22×C4—222no—
888C22×C4—222no—
889C22×C4—222no—
890C22×C4—222no—
891C22×C4—224no—
892C22×C4—224no—
893C22×C4—4416no—
894C22×C4—4416no—
895C22×C4—442no—
896C22×C4—442no—
897C22×C4—441no—
898C22×C4—441no—
899C22×C4—441no—
900C22×C4—441no—
901C22×C4—441no—
902C22×C4—441no—
903C22×C4—441no—
904C22×C4—441no—
905C22×C4—442no—
906C22×C4—441no—
907C22×C4—441no—
908C22×C4—441no—
909C22×C4—441no—
910C22×C4C2×C4×D1114yes—
911C22×C4C2×C4×D1114yes—
912C22×C4C23×D1112yes—
913C22×C4C23×D1112yes—
914C22×C4C23×D1112yes—
915C22×C4C23×D1111yescharacteristic
916C22×C4C23×D1111yescharacteristic
917C22×C4C23×D1111yescharacteristic
918C22×C4C23×D1111yescharacteristic
919C22×C4C23×D1112yes—
920C22×C4C23×D1111yescharacteristic
921C4⋊C4—24no—
922C4⋊C4—42no—
923C4⋊C4—114no—
924C4⋊C4—114no—
925C4⋊C4—114no—
926C4⋊C4—224no—
927C4⋊C4—224no—
928C4⋊C4—224no—
929C4⋊C4—442no—
930C4⋊C4—442no—
931C4⋊C4—442no—
932C4⋊C4C2×C4×D1114yes—
933C22⋊C4—24no—
934C22⋊C4—24no—
935C22⋊C4—42no—
936C22⋊C4—114no—
937C22⋊C4—114no—
938C22⋊C4—114no—
939C22⋊C4—114no—
940C22⋊C4—114no—
941C22⋊C4—114no—
942C22⋊C4—118no—
943C22⋊C4—224no—
944C22⋊C4—224no—
945C22⋊C4—224no—
946C22⋊C4—224no—
947C22⋊C4—224no—
948C22⋊C4—224no—
949C22⋊C4—224no—
950C22⋊C4—224no—
951C22⋊C4—224no—
952C22⋊C4—442no—
953C22⋊C4—442no—
954C22⋊C4—442no—
955C22⋊C4C2×C4×D1114yes—
956C22⋊C4C2×C4×D1114yes—
957C42—22no—
958C42—22no—
959C42—22no—
960C42—22no—
961C42—42no—
962C42—114no—
963C42—114no—
964C42—114no—
965C42—224no—
966C42—224no—
967C42—224no—
968C42—222no—
969C42—224no—
970C42—222no—
971C42—222no—
972C42—222no—
973C42—442no—
974C42—442no—
975C42—442no—
976C42C2×C4×D1114yes—
977C11#3412611yescharacteristic, complemented, Sylow
978C23—21no—
979C23—22no—
980C23—21no—
981C23—21no—
982C23—22no—
983C23—22no—
984C23—21no—
985C23—112no—
986C23—112no—
987C23—114no—
988C23—114no—
989C23—112no—
990C23—228no—
991C23—228no—
992C23—228no—
993C23—221no—
994C23—221no—
995C23—222no—
996C23—222no—
997C23—221no—
998C23—221no—
999C23—228no—
1000C23—221no—
1001C23—222no—
1002C23—222no—
1003C23—221no—
1004C23—444no—
1005C23—444no—
1006C23—448no—
1007C23—448no—
1008C23—448no—
1009C23—448no—
1010C23C22×C4×D1112yes—
1011C23C22×C4×D1112yes—
1012C23#41×D1114yes—
1013C23C24×D1111yescharacteristic
1014D4—28no—
1015D4—1116no—
1016D4—228no—
1017D4—228no—
1018C2×C4—22no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—28no—
1027C2×C4—28no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—48no—
1038C2×C4—112no—
1039C2×C4—114no—
1040C2×C4—112no—
1041C2×C4—112no—
1042C2×C4—112no—
1043C2×C4—112no—
1044C2×C4—114no—
1045C2×C4—228no—
1046C2×C4—228no—
1047C2×C4—221no—
1048C2×C4—221no—
1049C2×C4—221no—
1050C2×C4—222no—
1051C2×C4—222no—
1052C2×C4—222no—
1053C2×C4—221no—
1054C2×C4—221no—
1055C2×C4—221no—
1056C2×C4—228no—
1057C2×C4—228no—
1058C2×C4—228no—
1059C2×C4—222no—
1060C2×C4—222no—
1061C2×C4—222no—
1062C2×C4—222no—
1063C2×C4—222no—
1064C2×C4—222no—
1065C2×C4—222no—
1066C2×C4—222no—
1067C2×C4—222no—
1068C2×C4—444no—
1069C2×C4—444no—
1070C2×C4—444no—
1071C2×C4—444no—
1072C2×C4—448no—
1073C2×C4—448no—
1074C2×C4—444no—
1075C2×C4—444no—
1076C2×C4—448no—
1077C2×C4C22×C4×D1112yes—
1078C2×C4C22×C4×D1112yes—
1079C2×C4C22×C4×D1112yes—
1080C2×C4C22×C4×D1112yes—
1081C2×C4C22×C4×D1112yes—
1082C2×C4#6703712yes—
1083C2×C4#41×D1114yes—
1084C2×C4#6704212yes—
1085C22—24no—
1086C22—24no—
1087C22—22no—
1088C22—22no—
1089C22—22no—
1090C22—22no—
1091C22—22no—
1092C22—42no—
1093C22—42no—
1094C22—114no—
1095C22—114no—
1096C22—224no—
1097C22—224no—
1098C22—224no—
1099C22—224no—
1100C22—222no—
1101C22—222no—
1102C22—222no—
1103C22—222no—
1104C22—222no—
1105C22—222no—
1106C22—222no—
1107C22—4416no—
1108C22—4416no—
1109C22—442no—
1110C22—442no—
1111C22D11×#11714yes—
1112C22C23×C4×D1111yescharacteristic
1113C22C2×#6703711yescharacteristic
1114C22C2×#41×D1112yes—
1115C22C2×#41×D1112yes—
1116C22C2×#6704211yescharacteristic
1117C4—24no—
1118C4—22no—
1119C4—22no—
1120C4—22no—
1121C4—22no—
1122C4—42no—
1123C4—42no—
1124C4—42no—
1125C4—114no—
1126C4—224no—
1127C4—222no—
1128C4—222no—
1129C4—222no—
1130C4—222no—
1131C4—442no—
1132C4—442no—
1133C4—442no—
1134C4#1062307614yes—
1135C2—24no—
1136C2—42no—
1137C2—224no—
1138C2—224no—
1139C2—442no—
1140C2C2×D11×#11711yescharacteristic
1141C2C4×#41×D1111yescharacteristic
1142C2C2×#1062307611yescharacteristic
1143C2#1308221812yes—
1144C2#1308222212yes—
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC11×#2290C2
socle, cosocleC23×C11C25
prime radicalC22×D4×D11C22
hypercenter#2290D11
hypocenterC11#34126
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2290

Complements

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

NH ≅ G/Ntype
2. #13071586C2semidirect
3. #13071555C2semidirect
4. #13071554C2semidirect
5. #13071522C2semidirect
6. #13071490C2semidirect
7. #13071464C2semidirect
8. #13071463C2semidirect
10. #13071079C2semidirect
11. #13071075C2semidirect
12. #13071061C2semidirect
13. #13071060C2semidirect
14. #13071057C2semidirect
15. #13071008C2semidirect
16. #13070997C2semidirect
17. #13070995C2semidirect
18. C42×C22⋊D11C2semidirect
19. C4×(C22⋊D11)⋊C4C2semidirect
20. C4×#66945C2semidirect
21. C2×C4×(C2×D11)⋊C4C2semidirect
22. C4×C22⋊C4×D11C2semidirect
23. C11×#2290C2semidirect
28. C2×C11×#117C22semidirect
29. C22×C42×C11C22semidirect
35. C2×#66979C22semidirect
36. C22×C4×Dic11C22semidirect
37. C4×D4×D11C4semidirect
48. C2×#66925C22semidirect
49. C2×#66925C22semidirect
51. C2×C42×D11C22semidirect
52. C2×C42×D11C22semidirect
53. C11×#388C22semidirect
54. C11×#387C22semidirect
56. C11×#385C22semidirect
57. C4×C11×C4⋊C4C22semidirect
58. C4×C11×C22⋊C4C22semidirect
59. C4×C11×C22⋊C4C22semidirect
60. C11×#376C22semidirect
62. C4×C22⋊Dic11C22semidirect
63. C4×C22⋊Dic11C22semidirect
64. C4×C22⋊Dic11C22semidirect
65. C2×C11⋊#95C22semidirect
66. #10622603C22semidirect
67. #10622603C22semidirect
68. #10622602C22semidirect
70. #10622600C22semidirect
71. #10622594C22semidirect
72. C4⋊C4×Dic11C22semidirect
73. #10622585C22semidirect
78. #10622564C22semidirect
79. #10622563C22semidirect
80. #10622558C22semidirect
81. #10622557C22semidirect
82. #10622556C22semidirect
83. #10622555C22semidirect
84. C22⋊C4×Dic11C22semidirect
85. C22⋊C4×Dic11C22semidirect
91. C4×(C2×D11)⋊C4C22semidirect
92. C4×(C2×D11)⋊C4C22semidirect
93. C4×(C2×D11)⋊C4C22semidirect
94. C4×(C2×D11)⋊C4C22semidirect
95. C4×(C2×D11)⋊C4C22semidirect
96. C4×(C2×D11)⋊C4C22semidirect
97. C4×C4⋊Dic11C22semidirect
98. #10622545C22semidirect
99. C4×Dic11⋊C4C22semidirect
100. C4×Dic11⋊C4C22semidirect
101. C4×Dic11⋊C4C22semidirect
102. C42×Dic11C22semidirect
103. C42×Dic11C22semidirect
104. #10622283C22semidirect
105. #10622283C22semidirect
106. #10622281C22semidirect
111. #10622279C22semidirect
115. #10622277C22semidirect
116. D11×#95C22semidirect
117. #10622267C22semidirect
118. #10622266C22semidirect
119. #10622264C22semidirect
120. #10622263C22semidirect
121. #10622262C22semidirect
122. #10622261C22semidirect
123. #10622260C22semidirect
142. C22×C4×D11C2×C4semidirect
143. C22×C4×D11C2×C4semidirect
155. C4×D4×C11C2×C4semidirect
177. D4×Dic11C2×C4semidirect
180. C4×C22⋊D11C2×C4semidirect
221. #66946C2×C4semidirect
223. C4⋊C4×D11C2×C4semidirect
226. (C22⋊D11)⋊C4C2×C4semidirect
228. C22⋊C4×D11C2×C4semidirect
229. C22⋊C4×D11C2×C4semidirect
230. C4×D44C2×C4semidirect
235. C42×D11C2×C4semidirect
420. #2290D11semidirect
495. C22⋊D11#117semidirect
554. C2×#117C2×D11semidirect
564. C22×C42C2×D11semidirect
576. #388C2×D11semidirect
580. #387C2×D11semidirect
588. #385C2×D11semidirect
607. C4×C4⋊C4C2×D11semidirect
627. C4×C22⋊C4C2×D11semidirect
628. C4×C22⋊C4C2×D11semidirect
631. #376C2×D11semidirect
726. C4×D4C4×D11semidirect
977. C11#34126semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×D112
#130715862
#130715552
#130715542
#130715222
#130714902
#130714642
#130714632
#130714342
#130710792
#130710752
#130710612
#130710602
#130710572
#130710082
#130709972
#130709952
C42×C22⋊D112
C4×(C22⋊D11)⋊C42
C4×#669452
C2×C4×(C2×D11)⋊C42
C4×C22⋊C4×D112
C11×#22902
#3412611