Finite Group Databasebeta

← #14664122

Subgroups — #14664122

Order 2816.

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

normal subgroups only

This group has 500 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
1C4×#66898C211yesmaximal, characteristic, complemented
2#13066934C211yesmaximal, characteristic, complemented
3#13066637C212yesmaximal, complemented
4#13066613C212yesmaximal, complemented
5C11×#2631C211yesmaximal, characteristic
6C2×C11×#124C411yescharacteristic, complemented
7C2×C4×D4×C11C2211yescharacteristic
8C11×#397—21no—
9C11×#393C411yescharacteristic, complemented
10C11×#393C2211yescharacteristic
11C11×#392—21no—
12C11×#392C411yescharacteristic, complemented
13C11×#392C2211yescharacteristic
14C11×#386—21no—
15C11×#386—21no—
16C11×#383C411yescharacteristic, complemented
17C2×#66898—21no—
18C4×C22⋊Dic11—21no—
19C2×C22⋊(C11⋊C8)—21no—
20#10622166—21no—
21#10622164C2212yes—
22#10622163C2212yes—
23C22×Q8×C11C2×C411yescharacteristic
24C22×D4×C11—21no—
25C22×D4×C11—21no—
26C22×D4×C11C2×C411yescharacteristic
27C22×D4×C11D411yescharacteristic
28C23×C4×C11D411yescharacteristic
29C23×C4×C11D411yescharacteristic
30C11×#124—41no—
31C11×#124—41no—
32C4×D4×C11—41no—
33C4×D4×C11—41no—
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4C2×C411yescharacteristic
42C2×C11×C22⋊C4C2311yescharacteristic
43C2×C42×C11C2×C411yescharacteristic
44C2×C22⋊Dic11—22no—
45C2×C4×Dic11—41no—
46C22×C11⋊C8—41no—
47C11×#95—21no—
48C11×#95—21no—
49C11×#95—21no—
50C11×#95—21no—
51C11×#95C2×C411yescharacteristic
52C11×#95C2×C411yescharacteristic
53#66898—24no—
54C11⋊#95—41no—
55C22⋊(C11⋊C8)—22no—
56C22⋊(C11⋊C8)—41no—
57#11730—111nomaximal, Sylow
58C24×C11—21no—
59C24×C11C22⋊C411yescharacteristic
60C24×C11C2×D411yescharacteristic
61C2×Q8×C11—41no—
62C2×Q8×C11—81no—
63C2×D4×C11—22no—
64C2×D4×C11—22no—
65C2×D4×C11—41no—
66C2×D4×C11—41no—
67C2×D4×C11—42no—
68C2×D4×C11—42no—
69C2×D4×C11—81no—
70C2×D4×C11—81no—
71C2×D4×C11—81no—
72C2×D4×C11—81no—
73C2×D4×C11—81no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11—81no—
82C22×C4×C11—81no—
83C22×C4×C11C22⋊C411yescharacteristic
84C22×C4×C11C22⋊C411yescharacteristic
85C22×C4×C11C22⋊C411yescharacteristic
86C22×C4×C11C22×C411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×Dic11—42no—
89C11×C4⋊C4—41no—
90C11×C22⋊C4—41no—
91C11×C22⋊C4—41no—
92C11×C22⋊C4—42no—
93C11×C22⋊C4—41no—
94C11×C22⋊C4—41no—
95C11×C22⋊C4—81no—
96C11×C22⋊C4—81no—
97C11×C22⋊C4—81no—
98C11×C22⋊C4—81no—
99C42×C11—21no—
100C42×C11—21no—
101C22⋊Dic11—24no—
102C22⋊Dic11—42no—
103C4×Dic11—82no—
104C2×C11⋊C8—42no—
105C2×C11⋊C8—82no—
106#2631D1111yescharacteristic
107C4×#99—111no—
108#1459—111no—
109#1351—112no—
110#1343—112no—
111C23×C11—21no—
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—41no—
116C23×C11—41no—
117C23×C11—41no—
118C23×C11—41no—
119C23×C11—41no—
120C23×C11—41no—
121C23×C11—41no—
122C23×C11—41no—
123C23×C11—41no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11#10412yes—
127C23×C11C2×C22⋊C411yescharacteristic
128C23×C11#13512yes—
129Q8×C11—82no—
130D4×C11—44no—
131D4×C11—82no—
132D4×C11—84no—
133D4×C11—84no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—41no—
141C2×C4×C11—42no—
142C2×C4×C11—42no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—81no—
156C2×C4×C11—81no—
157C2×C4×C11#9911yescharacteristic
158C2×C4×C11#9911yescharacteristic
159C2×Dic11—44no—
160C2×Dic11—82no—
161C2×Dic11—82no—
162C11⋊C8—82no—
163C2×#124Dic1111yescharacteristic, complemented
164C2×C4×D4C2×D1111yescharacteristic
165C2×#99—221no—
166C2×C22⋊C8—221no—
167#397—21no—
168#393Dic1111yescharacteristic, complemented
169#393C2×D1111yescharacteristic
170#392—21no—
171#392Dic1111yescharacteristic, complemented
172#392C2×D1111yescharacteristic
173#386—21no—
174#386—21no—
175#383Dic1111yescharacteristic, complemented
176C4×C22⋊C4—221no—
177#342—112no—
178#324—221no—
179#323—112no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11—22no—
183C22×C11—22no—
184C22×C11—42no—
185C22×C11—42no—
186C22×C11—41no—
187C22×C11—41no—
188C22×C11—41no—
189C22×C11—41no—
190C22×C11—81no—
191C22×C11—81no—
192C22×C11—81no—
193C22×C11—81no—
194C22×C11—81no—
195C22×C11—81no—
196C22×C11—81no—
197C22×C11—81no—
198C22×C11—81no—
199C22×C11C2×#9911yescharacteristic
200C22×C11#41611yescharacteristic
201C22×C11C2×#10411yescharacteristic
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—41no—
205C4×C11—41no—
206C4×C11—41no—
207C4×C11—41no—
208C4×C11—81no—
209C4×C11—81no—
210C4×C11—81no—
211Dic11—84no—
212C22×Q8C2×Dic1111yescharacteristic
213C22×D4—21no—
214C22×D4—21no—
215C22×D4C2×Dic1111yescharacteristic
216C22×D4C22⋊D1111yescharacteristic
217C23×C4C22⋊D1111yescharacteristic
218C23×C4C22⋊D1111yescharacteristic
219C22×C8—441no—
220#124—41no—
221#124—41no—
222C4×D4—41no—
223C4×D4—41no—
224C2×C4⋊C4C22⋊D1111yescharacteristic
225C2×C22⋊C4—21no—
226C2×C22⋊C4—21no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C2×C22⋊C4—21no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4—222no—
232C2×C22⋊C4C2×Dic1111yescharacteristic
233C2×C22⋊C4C22×D1111yescharacteristic
234C2×C42—441no—
235C2×C42C2×Dic1111yescharacteristic
236#99—224no—
237C22⋊C8—222no—
238C22⋊C8—441no—
239#95—21no—
240#95—21no—
241#95—21no—
242#95—21no—
243#95—441no—
244#95C2×Dic1111yescharacteristic
245#95C2×Dic1111yescharacteristic
246C2×C11—21no—
247C2×C11—21no—
248C2×C11—42no—
249C2×C11—42no—
250C2×C11—161no—
251C2×C11#150111yescharacteristic
252C2×C11#212211yescharacteristic
253C2×C11#212711yescharacteristic
254C24—21no—
255C24C22⋊Dic1111yescharacteristic
256C24C2×C22⋊D1111yescharacteristic
257C2×Q8—41no—
258C2×Q8—81no—
259C2×D4—22no—
260C2×D4—22no—
261C2×D4—41no—
262C2×D4—41no—
263C2×D4—42no—
264C2×D4—42no—
265C2×D4—81no—
266C2×D4—81no—
267C2×D4—81no—
268C2×D4—81no—
269C2×D4—81no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—81no—
278C22×C4—81no—
279C22×C4—442no—
280C22×C4C22⋊Dic1111yescharacteristic
281C22×C4C22⋊Dic1111yescharacteristic
282C22×C4C22⋊Dic1111yescharacteristic
283C22×C4C22×Dic1111yescharacteristic
284C22×C4C2×C22⋊D1111yescharacteristic
285C2×C8—442no—
286C2×C8—882no—
287C4⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—41no—
290C22⋊C4—42no—
291C22⋊C4—41no—
292C22⋊C4—41no—
293C22⋊C4—81no—
294C22⋊C4—81no—
295C22⋊C4—81no—
296C22⋊C4—81no—
297C22⋊C4—224no—
298C22⋊C4—442no—
299C42—21no—
300C42—21no—
301C42—882no—
302C11#1173011yescharacteristic, complemented, Sylow
303C23—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—41no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23#6690112yes—
319C23#6700312yes—
320C23C2×C22⋊Dic1111yescharacteristic
321Q8—82no—
322D4—44no—
323D4—82no—
324D4—84no—
325D4—84no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4—444no—
350C2×C4—882no—
351C2×C4—882no—
352C2×C4#6689811yescharacteristic
353C2×C4#6689811yescharacteristic
354C8—882no—
355C22—21no—
356C22—21no—
357C22—22no—
358C22—22no—
359C22—42no—
360C22—42no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—81no—
366C22—81no—
367C22—81no—
368C22—81no—
369C22—81no—
370C22—81no—
371C22—81no—
372C22—81no—
373C22—81no—
374C22C2×#6689811yescharacteristic
375C22#1062284611yescharacteristic
376C22C2×#6690111yescharacteristic
377C4—21no—
378C4—21no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—41no—
383C4—81no—
384C4—81no—
385C4—81no—
386C4—884no—
387C2—21no—
388C2—21no—
389C2—42no—
390C2—42no—
391C2—161no—
392C2#1306710711yescharacteristic
393C2#1307026611yescharacteristic
394C2#1307028511yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
Fitting, prime radicalC11×#2631C2
socleC22×C11C2×#99
cosocleC2×C11×C22⋊C4C23
hypercenter#2631D11
hypocenterC11#11730
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2631

Complements

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

NH ≅ G/Ntype
1. C4×#66898C2semidirect
2. #13066934C2semidirect
3. #13066637C2semidirect
4. #13066613C2semidirect
6. C2×C11×#124C4semidirect
9. C11×#393C4semidirect
12. C11×#392C4semidirect
16. C11×#383C4semidirect
163. C2×#124Dic11semidirect
168. #393Dic11semidirect
171. #392Dic11semidirect
175. #383Dic11semidirect
302. C11#11730semidirect

Maximal subgroups

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

subgroupindex
C4×#668982
#130669342
#130666372
#130666132
C11×#26312
#1173011