Finite Group Databasebeta

← #14808247

Subgroups — #14808247

Order 2816.

920 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079169C211yesmaximal, characteristic, complemented
2#13078438C211yesmaximal, characteristic
3#13074566C211yesmaximal, characteristic, complemented
4#13069830C214yesmaximal
5#13069598C211yesmaximal, characteristic, complemented
6#13069461C211yesmaximal, characteristic, complemented
7#13068831C214yesmaximal, complemented
8#13068426C211yesmaximal, characteristic
9C11×#3509C211yesmaximal, characteristic
10C11×#557—22no—
11C11×#556—22no—
12C11×#552—24no—
13C11×#541—22no—
14C11×#536C2212yes—
15C11×#533—22no—
16C11×#533C2211yescharacteristic
17C2×C11×C4⋊Q8C2211yescharacteristic
18C11×#519C2212yes—
19C4×C11×#41C2211yescharacteristic
20C2×#66923C2211yescharacteristic
21C2×#66901C2212yes—
22#10622845C2212yes—
23#10622843C2214yes—
24C2×#66900C2214yes—
25#10622693—22no—
26#10622677—22no—
27#10622635—22no—
28#10622622—22no—
29#10622608C2214yes—
30#10622608C2212yes—
31#10622595—24no—
32#10622545C2211yescharacteristic
33#10622537C2211yescharacteristic
34C4×#4318C2211yescharacteristic
35#10622170C2214yes—
36#10622170C2212yes—
37C2×C11×#41C2311yescharacteristic
38C22×Q8×C11C2312yes—
39C11×C4⋊Q8—22no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—22no—
43C11×C4⋊Q8D412yes—
44C11×#126—28no—
45C11×#125—24no—
46C11×#125—28no—
47C11×#125D412yes—
48C11×#124—22no—
49C11×#123—24no—
50C11×C22⋊Q8—24no—
51C11×C22⋊Q8—22no—
52C11×C22⋊Q8—24no—
53C4×Q8×C11—24no—
54C4×Q8×C11—24no—
55C4×Q8×C11—24no—
56C4×Q8×C11—22no—
57C4×Q8×C11D412yes—
58C4×D4×C11—22no—
59C4×D4×C11D412yes—
60C11×#117—24no—
61C11×#117—24no—
62C11×#117—21no—
63C11×#117C2311yescharacteristic
64C11×#117C2312yes—
65C2×C11×C4⋊C4D414yes—
66C2×C42×C11—21no—
67C2×C42×C11C2311yescharacteristic
68C2×C4⋊Dic11C2312yes—
69C2×Dic11⋊C4—22no—
70C2×C4×Dic11C2312yes—
71C2×#4318C2312yes—
72C2×#4318C2312yes—
73#66923—22no—
74#66923—21no—
75#66923—21no—
76#66901—24no—
77#66900—28no—
78#66899—22no—
79#66896—22no—
80C11⋊#95—22no—
81C11⋊#95—28no—
82#66872—22no—
83#66872—24no—
84#66871—22no—
85#66871—24no—
86C4⋊(C11⋊C8)—22no—
87#66867—21no—
88C4×C11⋊C8—21no—
89#25691—111nomaximal, Sylow
90C11×#41—22no—
91C11×#41—22no—
92C2×Q8×C11—22no—
93C2×Q8×C11—22no—
94C2×Q8×C11—22no—
95C2×Q8×C11—24no—
96C2×Q8×C11—24no—
97C2×Q8×C11C2×D411yescharacteristic
98C2×D4×C11—21no—
99C2×D4×C11C2×D411yescharacteristic
100C22×C4×C11—22no—
101C22×C4×C11—21no—
102C22×C4×C11C2×D414yes—
103C22×C4×C11C2×D412yes—
104C22×C4×C11C2411yescharacteristic
105C22×Dic11—22no—
106C22×Dic11—22no—
107C11×C4⋊C4—28no—
108C11×C4⋊C4—28no—
109C11×C4⋊C4—24no—
110C11×C4⋊C4—24no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—24no—
114C11×C4⋊C4C2×D412yes—
115C11×C4⋊C4C2×D414yes—
116C11×C22⋊C4—28no—
117C11×C22⋊C4—21no—
118C11×C22⋊C4—22no—
119C11×C22⋊C4—22no—
120C42×C11—28no—
121C42×C11—22no—
122C42×C11—21no—
123C42×C11—22no—
124C42×C11C2×D411yescharacteristic
125C42×C11C2×D411yescharacteristic
126C42×C11C2×D412yes—
127C4⋊Dic11—22no—
128C4⋊Dic11—22no—
129Dic11⋊C4—42no—
130Dic11⋊C4—42no—
131C4×Dic11—22no—
132C4×Dic11—22no—
133#4318—24no—
134#4318—22no—
135#4318#4114yes—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—22no—
138#3509D1111yescharacteristic
139#3166—111no—
140#3080—111no—
141#2642—111no—
142#2038—114no—
143#1995—111no—
144#1966—111no—
145#1857—114no—
146#1759—111no—
147C23×C11—21no—
148C23×C11C22×D411yescharacteristic
149Q8×C11—21no—
150Q8×C11—21no—
151Q8×C11—44no—
152Q8×C11—42no—
153Q8×C11—42no—
154Q8×C11—44no—
155D4×C11—21no—
156D4×C11—21no—
157D4×C11—42no—
158C2×C4×C11—22no—
159C2×C4×C11—24no—
160C2×C4×C11—24no—
161C2×C4×C11—21no—
162C2×C4×C11—28no—
163C2×C4×C11—42no—
164C2×C4×C11—44no—
165C2×C4×C11—42no—
166C2×C4×C11#12012yes—
167C2×C4×C11#12012yes—
168C2×C4×C11C22×D411yescharacteristic
169C2×C4×C11C22×D411yescharacteristic
170C2×C4×C11C2×#4112yes—
171C2×C4×C112−1+412yes—
172C2×Dic11—44no—
173C2×Dic11—44no—
174C2×Dic11—42no—
175C2×Dic11—42no—
176C11⋊C8—24no—
177C11⋊C8—42no—
178#557—22no—
179#556—22no—
180#552—24no—
181#541—22no—
182#536C2×D1112yes—
183#533—22no—
184#533C2×D1111yescharacteristic
185C2×C4⋊Q8C2×D1111yescharacteristic
186C2×#125—111no—
187#519C2×D1112yes—
188C4×#41C2×D1111yescharacteristic
189#501—222no—
190#499—222no—
191#479—222no—
192#478—222no—
193#428—112no—
194#428—114no—
195#423—111no—
196C2×#104—112no—
197#417—112no—
198C2×#101—114no—
199C4×M16—111no—
200#400—224no—
201#391—114no—
202#376—111no—
203#339—112no—
204#339—114no—
205C22×C11—22no—
206C22×C11—41no—
207C22×C11—42no—
208C22×C11C2×#12011yescharacteristic
209C22×C11#54712yes—
210C4×C11—22no—
211C4×C11—22no—
212C4×C11—44no—
213C4×C11—41no—
214C4×C11—42no—
215C4×C11—44no—
216C4×C11#53211yescharacteristic
217C4×C11#53611yescharacteristic
218C4×C11#54812yes—
219Dic11—82no—
220Dic11—82no—
221C2×#41C22×D1111yescharacteristic
222C22×Q8C22×D1112yes—
223C2×M16—112no—
224C2×M16—112no—
225C4⋊Q8—22no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—22no—
229C4⋊Q8C22⋊D1112yes—
230#126—28no—
231#125—24no—
232#125—28no—
233#125—222no—
234#125—221no—
235#125—221no—
236#125C22⋊D1112yes—
237#124—22no—
238#123—24no—
239C22⋊Q8—24no—
240C22⋊Q8—22no—
241C22⋊Q8—24no—
242C4×Q8—24no—
243C4×Q8—24no—
244C4×Q8—24no—
245C4×Q8—22no—
246C4×Q8C22⋊D1112yes—
247C4×D4—22no—
248C4×D4C22⋊D1112yes—
249#117—24no—
250#117—24no—
251#117—21no—
252#117C22×D1111yescharacteristic
253#117C22×D1112yes—
254C2×C4⋊C4—112no—
255C2×C4⋊C4—222no—
256C2×C4⋊C4C22⋊D1114yes—
257C2×C42—21no—
258C2×C42—112no—
259C2×C42C22×D1111yescharacteristic
260#107—222no—
261#107—224no—
262#106—222no—
263#106—224no—
264C4⋊C8—222no—
265#104—224no—
266#103—222no—
267#102—222no—
268#101—228no—
269#97—221no—
270C4×C8—221no—
271#95—222no—
272#95—228no—
273C2×C11—22no—
274C2×C11—81no—
275C2×C11#243211yescharacteristic
276C2×C11#302012yes—
277#41—22no—
278#41—22no—
279C2×Q8—22no—
280C2×Q8—24no—
281C2×Q8—24no—
282C2×Q8—22no—
283C2×Q8—22no—
284C2×Q8C2×C22⋊D1111yescharacteristic
285C2×D4—21no—
286C2×D4C2×C22⋊D1111yescharacteristic
287C22×C4—22no—
288C22×C4—21no—
289C22×C4—222no—
290C22×C4—222no—
291C22×C4C2×C22⋊D1114yes—
292C22×C4C2×C22⋊D1112yes—
293C22×C4C23×D1111yescharacteristic
294M16—114no—
295M16—222no—
296M16—224no—
297C2×C8—222no—
298C2×C8—222no—
299C4⋊C4—28no—
300C4⋊C4—28no—
301C4⋊C4—24no—
302C4⋊C4—24no—
303C4⋊C4—22no—
304C4⋊C4—22no—
305C4⋊C4—24no—
306C4⋊C4—222no—
307C4⋊C4—222no—
308C4⋊C4—442no—
309C4⋊C4—442no—
310C4⋊C4C2×C22⋊D1112yes—
311C4⋊C4C2×C22⋊D1114yes—
312C22⋊C4—28no—
313C22⋊C4—21no—
314C22⋊C4—22no—
315C22⋊C4—22no—
316C42—28no—
317C42—22no—
318C42—21no—
319C42—22no—
320C42—222no—
321C42—222no—
322C42C2×C22⋊D1111yescharacteristic
323C42C2×C22⋊D1111yescharacteristic
324C42C2×C22⋊D1112yes—
325C11#2569111yescharacteristic, complemented, Sylow
326C23—21no—
327C23C22×C22⋊D1111yescharacteristic
328Q8—21no—
329Q8—21no—
330Q8—44no—
331Q8—42no—
332Q8—44no—
333Q8—42no—
334D4—21no—
335D4—21no—
336D4—42no—
337C2×C4—28no—
338C2×C4—22no—
339C2×C4—24no—
340C2×C4—24no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—44no—
344C2×C4—42no—
345C2×C4—444no—
346C2×C4—444no—
347C2×C4—442no—
348C2×C4—442no—
349C2×C4#6700612yes—
350C2×C4#6700612yes—
351C2×C4#41×D1112yes—
352C2×C4#6704312yes—
353C2×C4C22×C22⋊D1111yescharacteristic
354C2×C4C22×C22⋊D1111yescharacteristic
355C8—224no—
356C8—442no—
357C22—22no—
358C22—41no—
359C22—42no—
360C22#1062335512yes—
361C22C2×#6700611yescharacteristic
362C4—22no—
363C4—22no—
364C4—44no—
365C4—41no—
366C4—42no—
367C4—44no—
368C4—882no—
369C4—882no—
370C4#1062335611yescharacteristic
371C4#1062336212yes—
372C4#1062336311yescharacteristic
373C2—22no—
374C2—81no—
375C2#1307224011yescharacteristic
376C2#1307798012yes—
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3509C2
socleC22×C11C2×#120
prime radicalC2×C11×#41C23
hypercenter#3509D11
hypocenterC11#25691
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3509

Complements

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

NH ≅ G/Ntype
1. #13079169C2semidirect
3. #13074566C2semidirect
5. #13069598C2semidirect
6. #13069461C2semidirect
7. #13068831C2semidirect
325. C11#25691semidirect

Maximal subgroups

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

subgroupindex
#130791692
#130784382
#130745662
#130698302
#130695982
#130694612
#130688312
#130684262
C11×#35092
#2569111