Finite Group Databasebeta

← #14912768

Subgroups — #14912768

Order 2816.

2094 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071422C214yesmaximal, complemented
2#13071374C214yesmaximal
3#13071365C212yesmaximal, complemented
4#13071336C212yesmaximal, complemented
5#13071300C214yesmaximal
6#13071114C214yesmaximal
7#13071094C214yesmaximal, complemented
8#13071094C212yesmaximal, complemented
9#13071014C211yesmaximal, characteristic
10C4×Q8×Dic11C212yesmaximal, complemented
11C4×#66979C211yesmaximal, characteristic
12C2×C11×#533C211yesmaximal, characteristic
13C11×#533C4116yescomplemented
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#125C2212yes—
17C2×C11×C22⋊Q8C2212yes—
18C2×C11×C22⋊Q8C2212yes—
19C2×C4×Q8×C11C2212yes—
20C2×C4×Q8×C11C2212yes—
21C2×C11×#117C2212yes—
22C22×C42×C11C2211yescharacteristic
23C2×Q8×Dic11C2214yes—
24C2×#66979C2212yes—
25#10622843C2218yes—
26#10622843C2214yes—
27#10622825C2212yes—
28#10622824C2212yes—
29C4×C22⋊Dic11C2212yes—
30C4×C22⋊Dic11C2212yes—
31C4×C22⋊Dic11C2212yes—
32#10622598C2214yes—
33#10622598C2218yes—
34#10622594C2218yes—
35#10622594C2218yes—
36#10622594C2218yes—
37#10622594C2218yes—
38#10622594C2218yes—
39C4⋊C4×Dic11C2214yes—
40C4⋊C4×Dic11C2218yes—
41#10622564C2218yes—
42#10622564C2218yes—
43#10622550C2212yes—
44#10622549C2212yes—
45C4×C4⋊Dic11C2214yes—
46C4×C4⋊Dic11C2214yes—
47C4×C4⋊Dic11C2212yes—
48C4×C4⋊Dic11C2212yes—
49C4×C4⋊Dic11C2212yes—
50#10622545C2212yes—
51#10622545C2214yes—
52#10622545C2212yes—
53C42×Dic11C2214yes—
54C42×Dic11C2211yescharacteristic
55C42×Dic11C2211yescharacteristic
56C22×Q8×C11C2312yes—
57C22×Q8×C11C2312yes—
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C11×C4⋊Q8C2×C418yes—
62C11×C4⋊Q8C2×C418yes—
63C11×#125C2×C4116yes—
64C11×C22⋊Q8C2×C4116yes—
65C11×C22⋊Q8C2×C4116yes—
66C4×Q8×C11C2×C4116yes—
67C4×Q8×C11C2×C4116yes—
68C11×#117C2×C4116yes—
69C2×C11×C4⋊C4C2314yes—
70C2×C11×C4⋊C4C2312yes—
71C2×C11×C4⋊C4C2312yes—
72C2×C11×C4⋊C4C2312yes—
73C2×C11×C4⋊C4C2312yes—
74C2×C11×C4⋊C4C2314yes—
75C2×C11×C22⋊C4C2314yes—
76C2×C42×C11C2×C418yes—
77C2×C42×C11C2311yescharacteristic
78C2×C42×C11C2314yes—
79C2×C42×C11C2311yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C2×C42×C11C2311yescharacteristic
82C2×C22⋊Dic11C2314yes—
83C2×C22⋊Dic11C2314yes—
84Q8×Dic11—216no—
85#66979—28no—
86C2×C4⋊Dic11C2314yes—
87C2×C4⋊Dic11C2314yes—
88C2×C4⋊Dic11C2318yes—
89C2×C4⋊Dic11C2318yes—
90C2×C4×Dic11C2312yes—
91C2×C4×Dic11C2314yes—
92C2×C4×Dic11C2312yes—
93C2×C4×Dic11C2312yes—
94C2×C4×Dic11C2318yes—
95C2×C4×Dic11C2312yes—
96C2×C4×Dic11C2312yes—
97C2×C4×Dic11C2318yes—
98C2×C4×Dic11C2312yes—
99C11⋊#95C2314yes—
100C11⋊#95C2314yes—
101C11⋊#95C2314yes—
102C11⋊#95C2314yes—
103C11⋊#95C2318yes—
104C11⋊#95C2318yes—
105C11⋊#95C2314yes—
106C11⋊#95C2318yes—
107C11⋊#95C2318yes—
108C11⋊#95C2314yes—
109#34085—111nomaximal, Sylow
110C24×C11C2411yescharacteristic
111C2×Q8×C11—28no—
112C2×Q8×C11—44no—
113C2×Q8×C11C22×C418yes—
114C2×Q8×C11C22×C418yes—
115C22×C4×C11—24no—
116C22×C4×C11—24no—
117C22×C4×C11—42no—
118C22×C4×C11C22×C414yes—
119C22×C4×C11C22×C414yes—
120C22×C4×C11C22×C414yes—
121C22×C4×C11C2411yescharacteristic
122C22×C4×C11C2411yescharacteristic
123C22×C4×C11C2411yescharacteristic
124C22×C4×C11C2414yes—
125C22×C4×C11C2414yes—
126C22×C4×C11C2411yescharacteristic
127C22×C4×C11C2411yescharacteristic
128C22×C4×C11C2411yescharacteristic
129C22×Dic11C2418yes—
130C22×Dic11C2414yes—
131C22×Dic11C2414yes—
132C11×C4⋊C4C22×C418yes—
133C11×C4⋊C4C22×C418yes—
134C11×C4⋊C4C22×C4116yes—
135C11×C4⋊C4C22×C4116yes—
136C11×C4⋊C4C22×C418yes—
137C11×C4⋊C4C22×C418yes—
138C11×C22⋊C4C22×C4116yes—
139C42×C11C22×C414yes—
140C42×C11C22×C414yes—
141C42×C11C22×C414yes—
142C42×C11C22×C414yes—
143C42×C11C22×C4116yes—
144C22⋊Dic11—28no—
145C22⋊Dic11—44no—
146C4⋊Dic11—28no—
147C4⋊Dic11—216no—
148C4⋊Dic11—28no—
149C4⋊Dic11—48no—
150C4×Dic11—216no—
151C4×Dic11—24no—
152C4×Dic11—24no—
153C4×Dic11—28no—
154C4×Dic11—24no—
155C4×Dic11—42no—
156C4×Dic11—42no—
157C4×Dic11—48no—
158C4×Dic11#4118yes—
159C2×#533D1111yescharacteristic
160#2336—114no—
161#2332—114no—
162#2331—112no—
163#2327—112no—
164#2323—114no—
165#2298—114no—
166#2295—112no—
167#2295—114no—
168#2283—111no—
169C42×Q8—112no—
170C4×#117—111no—
171C23×C11—22no—
172C23×C11—22no—
173C23×C11—22no—
174C23×C11C23×C412yes—
175C23×C11C2511yescharacteristic
176Q8×C11—216no—
177Q8×C11—48no—
178C2×C4×C11—28no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—28no—
183C2×C4×C11—22no—
184C2×C4×C11—28no—
185C2×C4×C11—28no—
186C2×C4×C11—44no—
187C2×C4×C11C23×C412yes—
188C2×C4×C11C23×C412yes—
189C2×C4×C11C23×C412yes—
190C2×C4×C11C23×C412yes—
191C2×C4×C11C23×C418yes—
192C2×C4×C11C23×C418yes—
193C2×C4×C11C23×C412yes—
194C2×C4×C11C23×C412yes—
195C2×C4×C11C2×#4114yes—
196C2×C4×C112−1+414yes—
197C2×Dic11—24no—
198C2×Dic11—24no—
199C2×Dic11—28no—
200C2×Dic11—24no—
201C2×Dic11—28no—
202C2×Dic11—24no—
203C2×Dic11—24no—
204C2×Dic11—28no—
205C2×Dic11C2×#4118yes—
206#533Dic11116yescomplemented
207C2×C4⋊Q8C2×D1111yescharacteristic
208C2×C4⋊Q8C2×D1111yescharacteristic
209C2×#125C2×D1112yes—
210C2×C22⋊Q8C2×D1112yes—
211C2×C22⋊Q8C2×D1112yes—
212C2×C4×Q8—114no—
213C2×C4×Q8C2×D1112yes—
214C2×C4×Q8C2×D1112yes—
215C2×#117—112no—
216C2×#117C2×D1112yes—
217C22×C42C2×D1111yescharacteristic
218#391—114no—
219#391—118no—
220#389—114no—
221#389—118no—
222#388—118no—
223#388—118no—
224#387—118no—
225#387—118no—
226#387—118no—
227#387—118no—
228#387—118no—
229#383—112no—
230#382—112no—
231#381—112no—
232#380—112no—
233C4×C4⋊C4—114no—
234C4×C4⋊C4—118no—
235C4×C4⋊C4—112no—
236C4×C4⋊C4—112no—
237C4×C4⋊C4—112no—
238C4×C4⋊C4—114no—
239C4×C4⋊C4—114no—
240C4×C22⋊C4—112no—
241C4×C22⋊C4—112no—
242C4×C22⋊C4—112no—
243#376—112no—
244#376—112no—
245#376—114no—
246C43—111no—
247C43—111no—
248C43—114no—
249C22×C11—22no—
250C22×C11—22no—
251C22×C11—22no—
252C22×C11—44no—
253C22×C11C24×C411yescharacteristic
254C22×C11C22×#4112yes—
255C22×C11C2×2−1+412yes—
256C22×C11#58512yes—
257C4×C11—22no—
258C4×C11—28no—
259C4×C11—22no—
260C4×C11—22no—
261C4×C11—22no—
262C4×C11—28no—
263C4×C11C4×#4114yes—
264C4×C11#51914yes—
265Dic11—28no—
266Dic11—48no—
267Dic11—44no—
268C22×Q8C22×D1112yes—
269C22×Q8C22×D1112yes—
270C23×C4C22×D1111yescharacteristic
271C23×C4C22×D1111yescharacteristic
272C23×C4C22×D1111yescharacteristic
273C4⋊Q8C2×Dic1118yes—
274C4⋊Q8C2×Dic1118yes—
275#125C2×Dic11116yes—
276C22⋊Q8C2×Dic11116yes—
277C22⋊Q8C2×Dic11116yes—
278C4×Q8—2216no—
279C4×Q8C2×Dic11116yes—
280C4×Q8C2×Dic11116yes—
281#117—228no—
282#117C2×Dic11116yes—
283C2×C4⋊C4—114no—
284C2×C4⋊C4—114no—
285C2×C4⋊C4—118no—
286C2×C4⋊C4—118no—
287C2×C4⋊C4C22×D1112yes—
288C2×C4⋊C4C22×D1112yes—
289C2×C4⋊C4C22×D1114yes—
290C2×C4⋊C4C22×D1114yes—
291C2×C4⋊C4C22×D1112yes—
292C2×C4⋊C4C22×D1112yes—
293C2×C22⋊C4—114no—
294C2×C22⋊C4—114no—
295C2×C22⋊C4C22×D1114yes—
296C2×C42—112no—
297C2×C42—112no—
298C2×C42—118no—
299C2×C42—112no—
300C2×C42—112no—
301C2×C42—114no—
302C2×C42—112no—
303C2×C42—112no—
304C2×C42—118no—
305C2×C42C2×Dic1118yes—
306C2×C42C22×D1111yescharacteristic
307C2×C42C22×D1111yescharacteristic
308C2×C42C22×D1114yes—
309C2×C42C22×D1111yescharacteristic
310C2×C42C22×D1111yescharacteristic
311#95—114no—
312#95—114no—
313#95—114no—
314#95—114no—
315#95—118no—
316#95—118no—
317#95—114no—
318#95—114no—
319#95—118no—
320#95—118no—
321C2×C11—42no—
322C2×C11C2×C4×#4111yescharacteristic
323C2×C11C2×#51911yescharacteristic
324C2×C11#342811yescharacteristic
325C2×C11#346114yes—
326C24C23×D1111yescharacteristic
327C2×Q8—28no—
328C2×Q8—44no—
329C2×Q8C22×Dic1118yes—
330C2×Q8C22×Dic1118yes—
331C22×C4—24no—
332C22×C4—24no—
333C22×C4—42no—
334C22×C4—114no—
335C22×C4—114no—
336C22×C4—118no—
337C22×C4C22×Dic1114yes—
338C22×C4C22×Dic1114yes—
339C22×C4C22×Dic1114yes—
340C22×C4C23×D1111yescharacteristic
341C22×C4C23×D1111yescharacteristic
342C22×C4C23×D1111yescharacteristic
343C22×C4C23×D1114yes—
344C22×C4C23×D1114yes—
345C22×C4C23×D1111yescharacteristic
346C22×C4C23×D1111yescharacteristic
347C22×C4C23×D1111yescharacteristic
348C4⋊C4—228no—
349C4⋊C4—2216no—
350C4⋊C4—228no—
351C4⋊C4—448no—
352C4⋊C4C22×Dic1118yes—
353C4⋊C4C22×Dic1118yes—
354C4⋊C4C22×Dic11116yes—
355C4⋊C4C22×Dic11116yes—
356C4⋊C4C22×Dic1118yes—
357C4⋊C4C22×Dic1118yes—
358C22⋊C4—228no—
359C22⋊C4—444no—
360C22⋊C4C22×Dic11116yes—
361C42—118no—
362C42—2216no—
363C42—224no—
364C42—224no—
365C42—228no—
366C42—224no—
367C42—442no—
368C42—442no—
369C42—448no—
370C42C22×Dic1114yes—
371C42C22×Dic1114yes—
372C42C22×Dic1114yes—
373C42C22×Dic1114yes—
374C42C22×Dic11116yes—
375C11#3408511yescharacteristic, complemented, Sylow
376C23—22no—
377C23—22no—
378C23—22no—
379C23C23×Dic1112yes—
380C23C24×D1111yescharacteristic
381Q8—216no—
382Q8—48no—
383C2×C4—22no—
384C2×C4—28no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—28no—
388C2×C4—22no—
389C2×C4—28no—
390C2×C4—28no—
391C2×C4—44no—
392C2×C4—118no—
393C2×C4—224no—
394C2×C4—224no—
395C2×C4—224no—
396C2×C4—228no—
397C2×C4—224no—
398C2×C4—228no—
399C2×C4—228no—
400C2×C4—224no—
401C2×C4#6704014yes—
402C2×C4#41×D1114yes—
403C2×C4C23×Dic1112yes—
404C2×C4C23×Dic1112yes—
405C2×C4C23×Dic1112yes—
406C2×C4C23×Dic1112yes—
407C2×C4C23×Dic1118yes—
408C2×C4C23×Dic1118yes—
409C2×C4C23×Dic1112yes—
410C2×C4C23×Dic1112yes—
411C22—22no—
412C22—22no—
413C22—22no—
414C22—44no—
415C22C2×#6704012yes—
416C22C2×#41×D1112yes—
417C22#1062345312yes—
418C22C24×Dic1111yescharacteristic
419C4—22no—
420C4—28no—
421C4—22no—
422C4—22no—
423C4—22no—
424C4—28no—
425C4—228no—
426C4—444no—
427C4—448no—
428C4#1062334314yes—
429C4#41×Dic1114yes—
430C2—42no—
431C2C2×#41×Dic1111yescharacteristic
432C2C2×#1062334311yescharacteristic
433C2#1308181911yescharacteristic
434C2#1308204714yes—
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C11×#533C2
socle, cosocleC23×C11C25
prime radicalC24×C11C24
hypercenterC2×#533D11
hypocenterC11#34085
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #13071422C2semidirect
3. #13071365C2semidirect
4. #13071336C2semidirect
7. #13071094C2semidirect
8. #13071094C2semidirect
10. C4×Q8×Dic11C2semidirect
13. C11×#533C4semidirect
206. #533Dic11semidirect
375. C11#34085semidirect

Maximal subgroups

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

subgroupindex
#130714222
#130713742
#130713652
#130713362
#130713002
#130711142
#130710942
#130710142
C4×Q8×Dic112
C4×#669792
C2×C11×#5332
#3408511