Finite Group Databasebeta

← #14664909

Subgroups — #14664909

Order 2816.

508 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 107 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#13068604C211yesmaximal, characteristic
2#13066934C211yesmaximal, characteristic
3#13066640C214yesmaximal, complemented
4C11×#2542C211yesmaximal, characteristic
5C2×C11×C4⋊Q8C411yescharacteristic, complemented
6C2×C11×C22⋊Q8—21no—
7C2×C11×C22⋊Q8—21no—
8C2×C4×D4×C11C2211yescharacteristic
9C11×#399C412yescomplemented
10C11×#399C2212yes—
11C11×#390—21no—
12C11×#384—21no—
13C4×C11×C4⋊C4C411yescharacteristic, complemented
14C2×#66898—21no—
15#10622825—21no—
16C2×C22⋊(C11⋊C8)—21no—
17#10622166—21no—
18#10622164C2212yes—
19#10622163C2212yes—
20C22×Q8×C11—21no—
21C22×D4×C11D411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×C4×C11D411yescharacteristic
24C11×C4⋊Q8—41no—
25C11×C4⋊Q8—41no—
26C11×C22⋊Q8—44no—
27C11×C22⋊Q8—44no—
28C4×D4×C11—41no—
29C4×D4×C11—41no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—22no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—22no—
34C2×C11×C4⋊C4C2×C412yes—
35C2×C11×C4⋊C4D411yescharacteristic
36C2×C11×C22⋊C4—22no—
37C2×C11×C22⋊C4—22no—
38C2×C11×C22⋊C4C2×C411yescharacteristic
39C2×C11×C22⋊C4C2311yescharacteristic
40C2×C42×C11—21no—
41C2×C42×C11C2×C411yescharacteristic
42C2×C22⋊Dic11—22no—
43C2×C4⋊Dic11—41no—
44C22×C11⋊C8—41no—
45C11×#95C2×C412yes—
46#66898—42no—
47C11⋊#95—41no—
48C22⋊(C11⋊C8)—22no—
49C22⋊(C11⋊C8)—41no—
50#11901—111nomaximal, Sylow
51C24×C11C22⋊C411yescharacteristic
52C24×C11C2×D411yescharacteristic
53C2×Q8×C11—42no—
54C2×Q8×C11—42no—
55C2×Q8×C11—41no—
56C2×Q8×C11—41no—
57C2×D4×C11—41no—
58C2×D4×C11—41no—
59C2×D4×C11SD1612yes—
60C2×D4×C11Q1612yes—
61C22×C4×C11—22no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—22no—
67C22×C4×C11—42no—
68C22×C4×C11—42no—
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11C22×C411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×Dic11—42no—
75C11×C4⋊C4—24no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—44no—
78C11×C4⋊C4—44no—
79C11×C4⋊C4—42no—
80C11×C4⋊C4—42no—
81C11×C22⋊C4—41no—
82C11×C22⋊C4—41no—
83C11×C22⋊C4—44no—
84C11×C22⋊C4—44no—
85C42×C11—21no—
86C42×C11—21no—
87C42×C11—42no—
88C22⋊Dic11—42no—
89C22⋊Dic11—42no—
90C4⋊Dic11—82no—
91C2×C11⋊C8—42no—
92C2×C11⋊C8—82no—
93#2542D1111yescharacteristic
94#1799—111no—
95#1459—111no—
96#1352—114no—
97C23×C11—21no—
98C23×C11—21no—
99C23×C11—21no—
100C23×C11—21no—
101C23×C11—41no—
102C23×C11—41no—
103C23×C11—41no—
104C23×C11—41no—
105C23×C11#10312yes—
106C23×C11C2×C22⋊C411yescharacteristic
107C23×C11C2×SD1611yescharacteristic
108C23×C11C2×Q1611yescharacteristic
109Q8×C11—82no—
110Q8×C11—82no—
111D4×C11—42no—
112D4×C11—42no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—22no—
116C2×C4×C11—24no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—42no—
121C2×C4×C11—42no—
122C2×C4×C11—42no—
123C2×C4×C11—42no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—42no—
128C2×C4×C11—42no—
129C2×C4×C11—42no—
130C2×C4×C11—81no—
131C2×C4×C11—81no—
132C2×C4×C11#9911yescharacteristic
133C2×C4×C11#9911yescharacteristic
134C2×C4×C11#10312yes—
135C2×Dic11—82no—
136C2×Dic11—82no—
137C2×Dic11—82no—
138C11⋊C8—82no—
139C2×C4⋊Q8Dic1111yescharacteristic, complemented
140C2×C22⋊Q8—21no—
141C2×C22⋊Q8—21no—
142C2×C4×D4C2×D1111yescharacteristic
143C2×#99—221no—
144C2×C22⋊C8—221no—
145#399Dic1112yescomplemented
146#399C2×D1112yes—
147#390—21no—
148#384—21no—
149#380—221no—
150C4×C4⋊C4Dic1111yescharacteristic, complemented
151#342—112no—
152#324—221no—
153#323—112no—
154C22×C11—21no—
155C22×C11—21no—
156C22×C11—22no—
157C22×C11—21no—
158C22×C11—21no—
159C22×C11—42no—
160C22×C11—41no—
161C22×C11—41no—
162C22×C11—41no—
163C22×C11—41no—
164C22×C11—41no—
165C22×C11—41no—
166C22×C11—81no—
167C22×C11—81no—
168C22×C11C2×#9911yescharacteristic
169C22×C11C2×#10311yescharacteristic
170C22×C11#42111yescharacteristic
171C4×C11—21no—
172C4×C11—22no—
173C4×C11—44no—
174C4×C11—41no—
175C4×C11—41no—
176C4×C11—41no—
177C4×C11—82no—
178C4×C11#35312yes—
179Dic11—162no—
180C22×Q8—21no—
181C22×D4C22⋊D1111yescharacteristic
182C23×C4C22⋊D1111yescharacteristic
183C23×C4C22⋊D1111yescharacteristic
184C22×C8—441no—
185C4⋊Q8—41no—
186C4⋊Q8—41no—
187C22⋊Q8—44no—
188C22⋊Q8—44no—
189C4×D4—41no—
190C4×D4—41no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—22no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—22no—
195C2×C4⋊C4—441no—
196C2×C4⋊C4C2×Dic1112yes—
197C2×C4⋊C4C22⋊D1111yescharacteristic
198C2×C22⋊C4—22no—
199C2×C22⋊C4—22no—
200C2×C22⋊C4—222no—
201C2×C22⋊C4C2×Dic1111yescharacteristic
202C2×C22⋊C4C22×D1111yescharacteristic
203C2×C42—21no—
204C2×C42C2×Dic1111yescharacteristic
205#99—442no—
206C22⋊C8—222no—
207C22⋊C8—441no—
208#95—441no—
209#95C2×Dic1112yes—
210C2×C11—21no—
211C2×C11—21no—
212C2×C11—41no—
213C2×C11—42no—
214C2×C11—41no—
215C2×C11#152011yescharacteristic
216C2×C11#212311yescharacteristic
217C2×C11C2×#35311yescharacteristic
218C24C22⋊Dic1111yescharacteristic
219C24C2×C22⋊D1111yescharacteristic
220C2×Q8—42no—
221C2×Q8—42no—
222C2×Q8—41no—
223C2×Q8—41no—
224C2×D4—41no—
225C2×D4—41no—
226C2×D4#432512yes—
227C2×D4#432612yes—
228C22×C4—22no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—22no—
234C22×C4—42no—
235C22×C4—42no—
236C22×C4—442no—
237C22×C4C22⋊Dic1111yescharacteristic
238C22×C4C22⋊Dic1111yescharacteristic
239C22×C4C22⋊Dic1111yescharacteristic
240C22×C4C22×Dic1111yescharacteristic
241C22×C4C2×C22⋊D1111yescharacteristic
242C2×C8—442no—
243C2×C8—882no—
244C4⋊C4—24no—
245C4⋊C4—41no—
246C4⋊C4—42no—
247C4⋊C4—44no—
248C4⋊C4—44no—
249C4⋊C4—42no—
250C4⋊C4—882no—
251C22⋊C4—41no—
252C22⋊C4—41no—
253C22⋊C4—44no—
254C22⋊C4—44no—
255C22⋊C4—442no—
256C22⋊C4—442no—
257C42—21no—
258C42—21no—
259C42—42no—
260C11#1190111yescharacteristic, complemented, Sylow
261C23—21no—
262C23—21no—
263C23—21no—
264C23—21no—
265C23—41no—
266C23—41no—
267C23—41no—
268C23—41no—
269C23#6689912yes—
270C23C2×#432511yescharacteristic
271C23C2×#432611yescharacteristic
272C23C2×C22⋊Dic1111yescharacteristic
273Q8—82no—
274Q8—82no—
275D4—42no—
276D4—42no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—22no—
280C2×C4—24no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4—882no—
297C2×C4—882no—
298C2×C4—882no—
299C2×C4#6689811yescharacteristic
300C2×C4#6689811yescharacteristic
301C2×C4#6689912yes—
302C8—882no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22—22no—
307C22—21no—
308C22—42no—
309C22—41no—
310C22—41no—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—81no—
316C22—81no—
317C22C2×#6689811yescharacteristic
318C22C2×#6689911yescharacteristic
319C22#1062284911yescharacteristic
320C4—22no—
321C4—21no—
322C4—44no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—82no—
327C4—1762no—
328C4#1062218312yes—
329C2—21no—
330C2—21no—
331C2—41no—
332C2—42no—
333C2—41no—
334C2#1306718811yescharacteristic
335C2#1307027011yescharacteristic
336C2C2×#1062218311yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#2542C2
socleC22×C11C2×#99
prime radicalC22×D4×C11D4
cosocleC2×C11×C22⋊C4C23
hypercenter#2542D11
hypocenterC11#11901
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2542

Complements

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

NH ≅ G/Ntype
3. #13066640C2semidirect
5. C2×C11×C4⋊Q8C4semidirect
9. C11×#399C4semidirect
13. C4×C11×C4⋊C4C4semidirect
139. C2×C4⋊Q8Dic11semidirect
145. #399Dic11semidirect
150. C4×C4⋊C4Dic11semidirect
260. C11#11901semidirect

Maximal subgroups

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

subgroupindex
#130686042
#130669342
#130666402
C11×#25422
#1190111