Finite Group Databasebeta

← #14664912

Subgroups — #14664912

Order 2816.

452 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073792C211yesmaximal, characteristic
2#13066937C211yesmaximal, characteristic
3#13066639C212yesmaximal, complemented
4#13066636C212yesmaximal, complemented
5C11×#1799C211yesmaximal, characteristic
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66977C411yescharacteristic, complemented
8C2×C11×#99—21no—
9C11×#380—21no—
10#10622833—21no—
11#10622823—21no—
12C2×C11⋊#95C411yescharacteristic, complemented
13#10622599C411yescharacteristic, complemented
14#10622592C411yescharacteristic, complemented
15#10622562C2211yescharacteristic
16#10622560C2211yescharacteristic
17#10622555—21no—
18#10622546—21no—
19#10622538—21no—
20C11×#342C2212yes—
21#10622163—21no—
22#10622163C2212yes—
23C22×D4×C11D411yescharacteristic
24C23×C4×C11C2×C411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C23×Dic11—21no—
27C22×Dic22C2×C411yescharacteristic
28C4×D4×C11—41no—
29C4×D4×C11—41no—
30C2×C11×C4⋊C4—41no—
31C2×C11×C4⋊C4C2×C411yescharacteristic
32C2×C11×C22⋊C4—22no—
33C2×C11×C22⋊C4D411yescharacteristic
34C2×C11×C22⋊C4C2311yescharacteristic
35C2×C42×C11D411yescharacteristic
36C2×C22⋊Dic11—21no—
37C2×C22⋊Dic11—21no—
38C2×C22⋊Dic11—21no—
39C2×C4⋊Dic11C2×C411yescharacteristic
40#66977—41no—
41#66977—41no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C11×#99—42no—
46C11×#95—41no—
47C11⋊#95—21no—
48C11⋊#95—21no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95C2×C411yescharacteristic
53C11⋊#95C2×C411yescharacteristic
54C22⋊(C11⋊C8)—22no—
55C4⋊(C11⋊C8)—41no—
56C4×C11⋊C8—41no—
57#11902—111nomaximal, Sylow
58C24×C11C22⋊C411yescharacteristic
59C24×C11C2×D411yescharacteristic
60C2×D4×C11—41no—
61C2×D4×C11—41no—
62C2×D4×C11SD1612yes—
63C2×D4×C11Q1612yes—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—42no—
69C22×C4×C11—81no—
70C22×C4×C11—81no—
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22⋊C411yescharacteristic
74C22×C4×C11C22×C411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×Dic11—21no—
77C22×Dic11—21no—
78C22×Dic11—21no—
79C22×Dic11—21no—
80C22×Dic11—42no—
81C22×Dic11—42no—
82C22×Dic11—81no—
83C2×Dic22—41no—
84C2×Dic22—81no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—82no—
87C11×C22⋊C4—41no—
88C11×C22⋊C4—41no—
89C11×C22⋊C4—42no—
90C11×C22⋊C4—42no—
91C42×C11—21no—
92C42×C11—21no—
93C22⋊Dic11—42no—
94C22⋊Dic11—42no—
95C22⋊Dic11—81no—
96C4⋊Dic11—41no—
97Dic11⋊C4—42no—
98Dic11⋊C4—41no—
99Dic11⋊C4—41no—
100Dic11⋊C4—81no—
101C2×C11⋊C8—42no—
102#2564—111no—
103#1799D1111yescharacteristic
104#1460—111no—
105#1352—112no—
106#1351—112no—
107C23×C11—21no—
108C23×C11—21no—
109C23×C11—21no—
110C23×C11—21no—
111C23×C11—41no—
112C23×C11—41no—
113C23×C11—41no—
114C23×C11—41no—
115C23×C11#10312yes—
116C23×C11C2×C22⋊C411yescharacteristic
117C23×C11C2×SD1611yescharacteristic
118C23×C11C2×Q1611yescharacteristic
119D4×C11—42no—
120D4×C11—42no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—41no—
127C2×C4×C11—42no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—81no—
132C2×C4×C11—81no—
133C2×C4×C11—81no—
134C2×C4×C11—82no—
135C2×C4×C11—82no—
136C2×C4×C11—82no—
137C2×C4×C11#9911yescharacteristic
138C2×C4×C11#9911yescharacteristic
139C2×C4×C11#10312yes—
140C2×Dic11—22no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—84no—
153Dic22—82no—
154C11⋊C8—82no—
155C2×C22⋊Q8—111no—
156C2×C4×D4C2×D1111yescharacteristic
157#431—221no—
158C2×#99—21no—
159#400—111no—
160#399—111no—
161#395—111no—
162#393—111no—
163#387—221no—
164#386—221no—
165#385—221no—
166#380—21no—
167#380—221no—
168C2×#95—111no—
169#342C2×D1112yes—
170#323—112no—
171#323—221no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11—22no—
176C22×C11—21no—
177C22×C11—42no—
178C22×C11—41no—
179C22×C11—41no—
180C22×C11—42no—
181C22×C11—41no—
182C22×C11—41no—
183C22×C11—41no—
184C22×C11—41no—
185C22×C11—81no—
186C22×C11C2×#9911yescharacteristic
187C22×C11C2×#10311yescharacteristic
188C22×C11#42111yescharacteristic
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—22no—
192C4×C11—41no—
193C4×C11—41no—
194C4×C11—41no—
195C4×C11—162no—
196Dic11—42no—
197Dic11—81no—
198Dic11—81no—
199Dic11—81no—
200C22×Q8—111no—
201C22×D4C22⋊D1111yescharacteristic
202C23×C4—221no—
203C23×C4C4×D1111yescharacteristic
204C23×C4C22⋊D1111yescharacteristic
205C22⋊Q8—441no—
206C22⋊Q8—441no—
207C4×D4—41no—
208C4×D4—41no—
209C2×C4⋊C4—41no—
210C2×C4⋊C4—111no—
211C2×C4⋊C4—221no—
212C2×C4⋊C4—221no—
213C2×C4⋊C4—221no—
214C2×C4⋊C4C4×D1111yescharacteristic
215C2×C22⋊C4—22no—
216C2×C22⋊C4—221no—
217C2×C22⋊C4—221no—
218C2×C22⋊C4—221no—
219C2×C22⋊C4D4411yescharacteristic
220C2×C22⋊C4C22×D1111yescharacteristic
221C2×C42D4411yescharacteristic
222C4⋊C8—441no—
223#99—42no—
224C22⋊C8—222no—
225C4×C8—441no—
226#95—41no—
227#95—111no—
228#95—111no—
229#95—221no—
230#95—221no—
231#95—221no—
232#95—221no—
233#95—221no—
234C2×C11—21no—
235C2×C11—21no—
236C2×C11—41no—
237C2×C11—42no—
238C2×C11—41no—
239C2×C11#152011yescharacteristic
240C2×C11#212111yescharacteristic
241C2×C11#212611yescharacteristic
242C24(C2×D11)⋊C411yescharacteristic
243C24C2×C22⋊D1111yescharacteristic
244C2×Q8—441no—
245C2×Q8—881no—
246C2×D4—41no—
247C2×D4—41no—
248C2×D4#432412yes—
249C2×D4#432612yes—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—42no—
255C22×C4—81no—
256C22×C4—81no—
257C22×C4—221no—
258C22×C4—221no—
259C22×C4—221no—
260C22×C4—221no—
261C22×C4—442no—
262C22×C4—442no—
263C22×C4—881no—
264C22×C4(C2×D11)⋊C411yescharacteristic
265C22×C4(C2×D11)⋊C411yescharacteristic
266C22×C4(C2×D11)⋊C411yescharacteristic
267C22×C4C2×C4×D1111yescharacteristic
268C22×C4C2×D4411yescharacteristic
269C2×C8—442no—
270C4⋊C4—41no—
271C4⋊C4—82no—
272C4⋊C4—441no—
273C4⋊C4—442no—
274C4⋊C4—441no—
275C4⋊C4—441no—
276C4⋊C4—881no—
277C22⋊C4—41no—
278C22⋊C4—41no—
279C22⋊C4—42no—
280C22⋊C4—42no—
281C22⋊C4—442no—
282C22⋊C4—442no—
283C22⋊C4—881no—
284C42—21no—
285C42—21no—
286C11#1190211yescharacteristic, complemented, Sylow
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23#6687412yes—
296C23C2×(C2×D11)⋊C411yescharacteristic
297C23C2×#432411yescharacteristic
298C23C2×#432611yescharacteristic
299Q8—882no—
300D4—42no—
301D4—42no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—41no—
308C2×C4—42no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—82no—
316C2×C4—82no—
317C2×C4—82no—
318C2×C4—222no—
319C2×C4—441no—
320C2×C4—441no—
321C2×C4—441no—
322C2×C4—441no—
323C2×C4—441no—
324C2×C4—441no—
325C2×C4—441no—
326C2×C4—441no—
327C2×C4—441no—
328C2×C4—441no—
329C2×C4—441no—
330C2×C4—884no—
331C2×C4#6687011yescharacteristic
332C2×C4#6687011yescharacteristic
333C2×C4#6687412yes—
334C8—882no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—22no—
339C22—21no—
340C22—42no—
341C22—41no—
342C22—41no—
343C22—42no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—81no—
349C22C2×#6687011yescharacteristic
350C22C2×#6687411yescharacteristic
351C22#1062261811yescharacteristic
352C4—22no—
353C4—21no—
354C4—21no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—162no—
359C4—442no—
360C4—881no—
361C4—881no—
362C4—881no—
363C2—21no—
364C2—21no—
365C2—41no—
366C2—42no—
367C2—41no—
368C2#1306718711yescharacteristic
369C2#1307026011yescharacteristic
370C2#1307027911yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1799C2
socleC22×C11C2×#99
prime radicalC22×D4×C11D4
cosocleC2×C11×C22⋊C4C23
hypercenter#1799D11
hypocenterC11#11902
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1799

Complements

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

NH ≅ G/Ntype
3. #13066639C2semidirect
4. #13066636C2semidirect
7. C2×#66977C4semidirect
12. C2×C11⋊#95C4semidirect
13. #10622599C4semidirect
14. #10622592C4semidirect
286. C11#11902semidirect

Maximal subgroups

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

subgroupindex
#130737922
#130669372
#130666392
#130666362
C11×#17992
#1190211