Finite Group Databasebeta

← #14664696

Subgroups — #14664696

Order 2816.

438 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 91 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#13068696C211yesmaximal, characteristic, complemented
2C2×#10622166C211yesmaximal, characteristic, complemented
3#13066643C212yesmaximal, complemented
4#13066619C212yesmaximal, complemented
5C11×#2591C211yesmaximal, characteristic
6C2×C11×#121C411yescharacteristic
7C22×C11×C4⋊C4C2211yescharacteristic
8C11×#400C411yescharacteristic
9C11×#400C2211yescharacteristic
10C11×#394C411yescharacteristic
11C11×#394C2211yescharacteristic
12C11×#388—21no—
13C11×#388—21no—
14C11×#386—21no—
15C11×#386—21no—
16C4×C11×C22⋊C4C411yescharacteristic
17#10622820—21no—
18C2×C22⋊(C11⋊C8)—21no—
19#10622168—21no—
20#10622168C2212yes—
21#10622166—21no—
22#10622166C2212yes—
23C22×D4×C11—21no—
24C22×D4×C11C2×C411yescharacteristic
25C23×C4×C11C2×C411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C23×C4×C11D411yescharacteristic
28C11×#121—41no—
29C11×#121—41no—
30C2×C11×C4⋊C4—41no—
31C2×C11×C4⋊C4—41no—
32C2×C11×C4⋊C4C2×C411yescharacteristic
33C2×C11×C4⋊C4C2×C411yescharacteristic
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C11×C4⋊C4D411yescharacteristic
36C2×C11×C4⋊C4C2311yescharacteristic
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4—21no—
43C2×C42×C11—21no—
44C2×#4318—22no—
45C22×C11⋊C8—41no—
46C11×#95—21no—
47C11×#95—21no—
48C11×#95—21no—
49C11×#95—21no—
50C11×#95C2×C411yescharacteristic
51C11×#95C2×C411yescharacteristic
52C22⋊(C11⋊C8)—22no—
53C22⋊(C11⋊C8)—41no—
54C22⋊(C11⋊C8)—41no—
55C22⋊(C11⋊C8)—41no—
56#11852—111nomaximal, Sylow
57C24×C11—21no—
58C24×C11C22⋊C411yescharacteristic
59C2×D4×C11—41no—
60C2×D4×C11—42no—
61C2×D4×C11—42no—
62C2×D4×C11—41no—
63C2×D4×C11—41no—
64C2×D4×C11—81no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—22no—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—41no—
76C22×C4×C11—81no—
77C22×C4×C11—81no—
78C22×C4×C11C22⋊C411yescharacteristic
79C22×C4×C11C22⋊C411yescharacteristic
80C22×C4×C11C22⋊C411yescharacteristic
81C22×C4×C11C22×C411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C11×C4⋊C4—41no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—41no—
89C11×C22⋊C4—42no—
90C11×C22⋊C4—42no—
91C11×C22⋊C4—42no—
92C11×C22⋊C4—42no—
93C11×C22⋊C4—81no—
94C11×C22⋊C4—81no—
95C42×C11—81no—
96#4318—42no—
97#4318—42no—
98C2×C11⋊C8—42no—
99C2×C11⋊C8—42no—
100C2×C11⋊C8—82no—
101#2591D1111yescharacteristic
102#1821—111no—
103C2×#324—111no—
104#1353—112no—
105#1345—112no—
106C23×C11—22no—
107C23×C11—21no—
108C23×C11—21no—
109C23×C11—41no—
110C23×C11—41no—
111C23×C11—41no—
112C23×C11—41no—
113C23×C11—41no—
114C23×C11—41no—
115C23×C11—41no—
116C23×C11—41no—
117C23×C11#9911yescharacteristic
118C23×C11#9911yescharacteristic
119C23×C11C2×C22⋊C411yescharacteristic
120D4×C11—82no—
121D4×C11—82no—
122D4×C11—82no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—42no—
133C2×C4×C11—42no—
134C2×C4×C11—42no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—81no—
149C2×C4×C11—81no—
150C2×C4×C11—81no—
151C2×C4×C11#13512yes—
152C11⋊C8—82no—
153C11⋊C8—82no—
154C2×#121Dic1111yescharacteristic
155C22×C4⋊C4C2×D1111yescharacteristic
156#407—221no—
157C2×C22⋊C8—221no—
158#400Dic1111yescharacteristic
159#400C2×D1111yescharacteristic
160#394Dic1111yescharacteristic
161#394C2×D1111yescharacteristic
162#388—21no—
163#388—21no—
164#386—21no—
165#386—21no—
166C4×C22⋊C4Dic1111yescharacteristic
167#343—112no—
168#343—221no—
169#324—112no—
170#324—221no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11—42no—
179C22×C11—42no—
180C22×C11—81no—
181C22×C11—81no—
182C22×C11—81no—
183C22×C11—81no—
184C22×C11—81no—
185C22×C11—81no—
186C22×C11—81no—
187C22×C11#35512yes—
188C22×C11C2×#9911yescharacteristic
189C22×C11#41611yescharacteristic
190C22×C11#42111yescharacteristic
191C4×C11—22no—
192C4×C11—41no—
193C4×C11—41no—
194C4×C11—41no—
195C4×C11—41no—
196C4×C11—41no—
197C4×C11—81no—
198C4×C11—81no—
199C4×C11—81no—
200C22×D4—21no—
201C22×D4C2×Dic1111yescharacteristic
202C23×C4C2×Dic1111yescharacteristic
203C23×C4C22⋊D1111yescharacteristic
204C23×C4C22⋊D1111yescharacteristic
205C2×M16—222no—
206C22×C8—441no—
207#121—41no—
208#121—41no—
209C2×C4⋊C4—41no—
210C2×C4⋊C4—41no—
211C2×C4⋊C4C2×Dic1111yescharacteristic
212C2×C4⋊C4C2×Dic1111yescharacteristic
213C2×C4⋊C4C22⋊D1111yescharacteristic
214C2×C4⋊C4C22⋊D1111yescharacteristic
215C2×C4⋊C4C22×D1111yescharacteristic
216C2×C22⋊C4—21no—
217C2×C22⋊C4—21no—
218C2×C22⋊C4—21no—
219C2×C22⋊C4—21no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C42—21no—
223C22⋊C8—222no—
224C22⋊C8—441no—
225C22⋊C8—441no—
226C22⋊C8—441no—
227#95—21no—
228#95—21no—
229#95—21no—
230#95—21no—
231#95C2×Dic1111yescharacteristic
232#95C2×Dic1111yescharacteristic
233C2×C11—21no—
234C2×C11—21no—
235C2×C11—22no—
236C2×C11—41no—
237C2×C11—161no—
238C2×C11#151611yescharacteristic
239C2×C11#212111yescharacteristic
240C2×C11C2×#35511yescharacteristic
241C24—21no—
242C24C22⋊Dic1111yescharacteristic
243C2×D4—41no—
244C2×D4—42no—
245C2×D4—42no—
246C2×D4—41no—
247C2×D4—41no—
248C2×D4—81no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—22no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—41no—
260C22×C4—81no—
261C22×C4—81no—
262C22×C4C22⋊Dic1111yescharacteristic
263C22×C4C22⋊Dic1111yescharacteristic
264C22×C4C22⋊Dic1111yescharacteristic
265C22×C4C22×Dic1111yescharacteristic
266C22×C4C2×C22⋊D1111yescharacteristic
267C22×C4C2×C22⋊D1111yescharacteristic
268M16—442no—
269M16—442no—
270C2×C8—442no—
271C2×C8—442no—
272C2×C8—882no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C22⋊C4—42no—
279C22⋊C4—42no—
280C22⋊C4—42no—
281C22⋊C4—42no—
282C22⋊C4—81no—
283C22⋊C4—81no—
284C42—81no—
285C11#1185211yescharacteristic, complemented, Sylow
286C23—21no—
287C23—21no—
288C23—22no—
289C23—41no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23#6689811yescharacteristic
298C23#6689811yescharacteristic
299C23C2×C22⋊Dic1111yescharacteristic
300D4—82no—
301D4—82no—
302D4—82no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4#6700312yes—
332C8—882no—
333C8—882no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—42no—
342C22—42no—
343C22—81no—
344C22—81no—
345C22—81no—
346C22—81no—
347C22—81no—
348C22—81no—
349C22—81no—
350C22#1062218012yes—
351C22C2×#6689811yescharacteristic
352C22#1062284611yescharacteristic
353C22#1062284911yescharacteristic
354C4—22no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—81no—
361C4—81no—
362C4—81no—
363C2—21no—
364C2—21no—
365C2—22no—
366C2—41no—
367C2—161no—
368C2#1306717211yescharacteristic
369C2#1307026211yescharacteristic
370C2C2×#1062218011yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2591C2
socleC22×C11C2×#99
prime radicalC2×C11×#121C4
cosocleC2×C11×C4⋊C4C23
hypercenter#2591D11
hypocenterC11#11852
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #2591

Complements

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

NH ≅ G/Ntype
1. #13068696C2semidirect
2. C2×#10622166C2semidirect
3. #13066643C2semidirect
4. #13066619C2semidirect
285. C11#11852semidirect

Maximal subgroups

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

subgroupindex
#130686962
C2×#106221662
#130666432
#130666192
C11×#25912
#1185211