Finite Group Databasebeta

← #14664914

Subgroups — #14664914

Order 2816.

452 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 103 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#13066937C211yesmaximal, characteristic
3#13066640C212yesmaximal, complemented
4#13066637C212yesmaximal, complemented
5C11×#2564C211yesmaximal, characteristic
6C2×C11×C22⋊Q8C411yescharacteristic, complemented
7C2×C4×D4×C11C2211yescharacteristic
8C11×#400C411yescharacteristic, complemented
9C11×#399C2211yescharacteristic
10C11×#395C411yescharacteristic, complemented
11C11×#393C2211yescharacteristic
12C11×#387—21no—
13C11×#386—21no—
14C11×#385—21no—
15C11×#380—21no—
16C2×C11×#95C411yescharacteristic, complemented
17C2×#66898—21no—
18#10622825—21no—
19#10622538—21no—
20#10622164C2212yes—
21#10622163—21no—
22#10622163C2212yes—
23C22×Q8×C11C2×C411yescharacteristic
24C22×D4×C11D411yescharacteristic
25C23×C4×C11—21no—
26C23×C4×C11C2×C411yescharacteristic
27C23×C4×C11D411yescharacteristic
28C11×C22⋊Q8—41no—
29C11×C22⋊Q8—41no—
30C4×D4×C11—41no—
31C4×D4×C11—41no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4C2×C411yescharacteristic
36C2×C11×C4⋊C4C2×C411yescharacteristic
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4D411yescharacteristic
41C2×C11×C22⋊C4C2311yescharacteristic
42C2×C42×C11D411yescharacteristic
43C2×C22⋊Dic11—22no—
44C2×C4⋊Dic11—41no—
45C11×#95—21no—
46C11×#95—21no—
47C11×#95—21no—
48C11×#95—21no—
49C11×#95—21no—
50C11×#95C2×C411yescharacteristic
51C11×#95C2×C411yescharacteristic
52#66898—42no—
53C11⋊#95—41no—
54C22⋊(C11⋊C8)—22no—
55C4⋊(C11⋊C8)—41no—
56C4×C11⋊C8—41no—
57#11902—111nomaximal, Sylow
58C24×C11C22⋊C411yescharacteristic
59C24×C11C2×D411yescharacteristic
60C2×Q8×C11—41no—
61C2×Q8×C11—81no—
62C2×D4×C11—41no—
63C2×D4×C11—41no—
64C2×D4×C11SD1612yes—
65C2×D4×C11Q1612yes—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—42no—
75C22×C4×C11—42no—
76C22×C4×C11—81no—
77C22×C4×C11—81no—
78C22×C4×C11—81no—
79C22×C4×C11C22⋊C411yescharacteristic
80C22×C4×C11C22⋊C411yescharacteristic
81C22×C4×C11C22⋊C411yescharacteristic
82C22×C4×C11C22×C411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×Dic11—42no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—42no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—81no—
91C11×C22⋊C4—41no—
92C11×C22⋊C4—41no—
93C11×C22⋊C4—42no—
94C11×C22⋊C4—42no—
95C11×C22⋊C4—81no—
96C42×C11—21no—
97C42×C11—21no—
98C22⋊Dic11—42no—
99C22⋊Dic11—42no—
100C4⋊Dic11—82no—
101C2×C11⋊C8—42no—
102#2564D1111yescharacteristic
103#1799—111no—
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
119Q8×C11—82no—
120D4×C11—42no—
121D4×C11—42no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—22no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—41no—
129C2×C4×C11—42no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
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—81no—
145C2×C4×C11—81no—
146C2×C4×C11—81no—
147C2×C4×C11—84no—
148C2×C4×C11#9911yescharacteristic
149C2×C4×C11#9911yescharacteristic
150C2×C4×C11#10312yes—
151C2×Dic11—82no—
152C2×Dic11—82no—
153C2×Dic11—82no—
154C11⋊C8—82no—
155C2×C22⋊Q8Dic1111yescharacteristic, complemented
156C2×C4×D4C2×D1111yescharacteristic
157#431—221no—
158C2×#99—221no—
159#400Dic1111yescharacteristic, complemented
160#399C2×D1111yescharacteristic
161#395Dic1111yescharacteristic, complemented
162#393C2×D1111yescharacteristic
163#387—21no—
164#386—21no—
165#385—21no—
166#380—21no—
167#380—221no—
168C2×#95Dic1111yescharacteristic, complemented
169#342—112no—
170#323—112no—
171#323—221no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11—22no—
175C22×C11—21no—
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—42no—
193C4×C11—41no—
194C4×C11—41no—
195C4×C11—41no—
196C4×C11—81no—
197C4×C11—81no—
198C4×C11—81no—
199Dic11—162no—
200C22×Q8C2×Dic1111yescharacteristic
201C22×D4C22⋊D1111yescharacteristic
202C23×C4—21no—
203C23×C4C2×Dic1111yescharacteristic
204C23×C4C22⋊D1111yescharacteristic
205C22⋊Q8—41no—
206C22⋊Q8—41no—
207C4×D4—41no—
208C4×D4—41no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—441no—
213C2×C4⋊C4C2×Dic1111yescharacteristic
214C2×C4⋊C4C2×Dic1111yescharacteristic
215C2×C22⋊C4—21no—
216C2×C22⋊C4—21no—
217C2×C22⋊C4—21no—
218C2×C22⋊C4—222no—
219C2×C22⋊C4C22⋊D1111yescharacteristic
220C2×C22⋊C4C22×D1111yescharacteristic
221C2×C42C22⋊D1111yescharacteristic
222C4⋊C8—441no—
223#99—442no—
224C22⋊C8—222no—
225C4×C8—441no—
226#95—21no—
227#95—21no—
228#95—21no—
229#95—21no—
230#95—21no—
231#95—441no—
232#95C2×Dic1111yescharacteristic
233#95C2×Dic1111yescharacteristic
234C2×C11—21no—
235C2×C11—21no—
236C2×C11—41no—
237C2×C11—42no—
238C2×C11—41no—
239C2×C11#152011yescharacteristic
240C2×C11#212111yescharacteristic
241C2×C11#212611yescharacteristic
242C24C22⋊Dic1111yescharacteristic
243C24C2×C22⋊D1111yescharacteristic
244C2×Q8—41no—
245C2×Q8—81no—
246C2×D4—41no—
247C2×D4—41no—
248C2×D4#432512yes—
249C2×D4#432612yes—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—42no—
259C22×C4—42no—
260C22×C4—81no—
261C22×C4—81no—
262C22×C4—81no—
263C22×C4—442no—
264C22×C4C22⋊Dic1111yescharacteristic
265C22×C4C22⋊Dic1111yescharacteristic
266C22×C4C22⋊Dic1111yescharacteristic
267C22×C4C22×Dic1111yescharacteristic
268C22×C4C2×C22⋊D1111yescharacteristic
269C2×C8—442no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—42no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—81no—
276C4⋊C4—882no—
277C22⋊C4—41no—
278C22⋊C4—41no—
279C22⋊C4—42no—
280C22⋊C4—42no—
281C22⋊C4—81no—
282C22⋊C4—442no—
283C22⋊C4—442no—
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#6689912yes—
296C23C2×#432511yescharacteristic
297C23C2×#432611yescharacteristic
298C23C2×C22⋊Dic1111yescharacteristic
299Q8—82no—
300D4—42no—
301D4—42no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—22no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—41no—
309C2×C4—42no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
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—81no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4—84no—
328C2×C4—882no—
329C2×C4—882no—
330C2×C4—882no—
331C2×C4#6689811yescharacteristic
332C2×C4#6689811yescharacteristic
333C2×C4#6689912yes—
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×#6689811yescharacteristic
350C22C2×#6689911yescharacteristic
351C22#1062284911yescharacteristic
352C4—22no—
353C4—21no—
354C4—21no—
355C4—42no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—81no—
360C4—81no—
361C4—81no—
362C4—1762no—
363C2—21no—
364C2—21no—
365C2—41no—
366C2—42no—
367C2—41no—
368C2#1306718811yescharacteristic
369C2#1307026211yescharacteristic
370C2#1307028111yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#2564C2
socleC22×C11C2×#99
prime radicalC22×D4×C11D4
cosocleC2×C11×C22⋊C4C23
hypercenter#2564D11
hypocenterC11#11902
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2564

Complements

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

NH ≅ G/Ntype
3. #13066640C2semidirect
4. #13066637C2semidirect
6. C2×C11×C22⋊Q8C4semidirect
8. C11×#400C4semidirect
10. C11×#395C4semidirect
16. C2×C11×#95C4semidirect
155. C2×C22⋊Q8Dic11semidirect
159. #400Dic11semidirect
161. #395Dic11semidirect
168. C2×#95Dic11semidirect
286. C11#11902semidirect

Maximal subgroups

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

subgroupindex
#130686042
#130669372
#130666402
#130666372
C11×#25642
#1190211