Finite Group Databasebeta

← #14664117

Subgroups — #14664117

Order 2816.

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

normal subgroups only

This group has 486 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#13066937C211yesmaximal, characteristic, complemented
3#13066640C212yesmaximal, complemented
4#13066613C212yesmaximal, complemented
5C11×#2635C211yesmaximal, characteristic
6C2×C11×#121C411yescharacteristic, complemented
7C2×C4×D4×C11C2211yescharacteristic
8C11×#400C411yescharacteristic, complemented
9C11×#399C2211yescharacteristic
10C11×#394—21no—
11C11×#394C411yescharacteristic, complemented
12C11×#392—21no—
13C11×#392C2211yescharacteristic
14C11×#388—21no—
15C11×#386—21no—
16C11×#381C411yescharacteristic, complemented
17C2×#66898—21no—
18C4×C22⋊Dic11—21no—
19#10622538—21no—
20#10622164C2212yes—
21#10622163—21no—
22#10622163C2212yes—
23C22×D4×C11—21no—
24C22×D4×C11—21no—
25C22×D4×C11C2×C411yescharacteristic
26C22×D4×C11D411yescharacteristic
27C23×C4×C11C2×C411yescharacteristic
28C23×C4×C11D411yescharacteristic
29C11×#121—41no—
30C11×#121—41no—
31C4×D4×C11—41no—
32C4×D4×C11—41no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4C2×C411yescharacteristic
35C2×C11×C4⋊C4C2×C411yescharacteristic
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⋊C4—21no—
42C2×C11×C22⋊C4D411yescharacteristic
43C2×C11×C22⋊C4C2311yescharacteristic
44C2×C42×C11D411yescharacteristic
45C2×C22⋊Dic11—22no—
46C2×C4×Dic11—41no—
47C11×#95—21no—
48C11×#95—21no—
49C11×#95—21no—
50C11×#95C2×C411yescharacteristic
51C11×#95C2×C411yescharacteristic
52#66898—24no—
53C11⋊#95—41no—
54C22⋊(C11⋊C8)—22no—
55C4⋊(C11⋊C8)—41no—
56C4×C11⋊C8—41no—
57#11729—111nomaximal, Sylow
58C24×C11—21no—
59C24×C11C22⋊C411yescharacteristic
60C24×C11C2×D411yescharacteristic
61C2×D4×C11—22no—
62C2×D4×C11—22no—
63C2×D4×C11—41no—
64C2×D4×C11—41no—
65C2×D4×C11—42no—
66C2×D4×C11—42no—
67C2×D4×C11—81no—
68C2×D4×C11—81no—
69C2×D4×C11—81no—
70C2×D4×C11—81no—
71C2×D4×C11—81no—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11—81no—
80C22×C4×C11—81no—
81C22×C4×C11C22⋊C411yescharacteristic
82C22×C4×C11C22⋊C411yescharacteristic
83C22×C4×C11C22⋊C411yescharacteristic
84C22×C4×C11C22×C411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×Dic11—42no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—81no—
90C11×C22⋊C4—41no—
91C11×C22⋊C4—41no—
92C11×C22⋊C4—41no—
93C11×C22⋊C4—41no—
94C11×C22⋊C4—42no—
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—
105#2635D1111yescharacteristic
106C4×#99—111no—
107#1460—111no—
108#1352—112no—
109#1343—112no—
110C23×C11—21no—
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×C11C2×C22⋊C411yescharacteristic
127C23×C11#13512yes—
128D4×C11—44no—
129D4×C11—82no—
130D4×C11—84no—
131D4×C11—84no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—41no—
138C2×C4×C11—42no—
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—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—81no—
152C2×C4×C11—81no—
153C2×C4×C11—81no—
154C2×C4×C11#9911yescharacteristic
155C2×C4×C11#9911yescharacteristic
156C2×C4×C11#10412yes—
157C2×Dic11—44no—
158C2×Dic11—82no—
159C2×Dic11—82no—
160C11⋊C8—82no—
161C2×#121Dic1111yescharacteristic, complemented
162C2×C4×D4C2×D1111yescharacteristic
163#431—221no—
164C2×#99—221no—
165#400Dic1111yescharacteristic, complemented
166#399C2×D1111yescharacteristic
167#394—21no—
168#394Dic1111yescharacteristic, complemented
169#392—21no—
170#392C2×D1111yescharacteristic
171#388—21no—
172#386—21no—
173#381Dic1111yescharacteristic, complemented
174C4×C22⋊C4—221no—
175#342—112no—
176#323—112no—
177#323—221no—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11—22no—
181C22×C11—42no—
182C22×C11—41no—
183C22×C11—41no—
184C22×C11—41no—
185C22×C11—41no—
186C22×C11—41no—
187C22×C11—81no—
188C22×C11—81no—
189C22×C11—81no—
190C22×C11—81no—
191C22×C11—81no—
192C22×C11—81no—
193C22×C11—81no—
194C22×C11—81no—
195C22×C11—81no—
196C22×C11—81no—
197C22×C11C2×#9911yescharacteristic
198C22×C11#41611yescharacteristic
199C22×C11C2×#10411yescharacteristic
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—22no—
203C4×C11—41no—
204C4×C11—41no—
205C4×C11—41no—
206C4×C11—81no—
207C4×C11—81no—
208C4×C11—81no—
209Dic11—84no—
210C22×D4—21no—
211C22×D4—21no—
212C22×D4C2×Dic1111yescharacteristic
213C22×D4C22⋊D1111yescharacteristic
214C23×C4C2×Dic1111yescharacteristic
215C23×C4C22⋊D1111yescharacteristic
216#121—41no—
217#121—41no—
218C4×D4—41no—
219C4×D4—41no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4C2×Dic1111yescharacteristic
222C2×C4⋊C4C2×Dic1111yescharacteristic
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—21no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C2×C22⋊C4—222no—
230C2×C22⋊C4C22⋊D1111yescharacteristic
231C2×C22⋊C4C22×D1111yescharacteristic
232C2×C42—441no—
233C2×C42C22⋊D1111yescharacteristic
234C4⋊C8—441no—
235#99—224no—
236C22⋊C8—222no—
237C4×C8—441no—
238#95—21no—
239#95—21no—
240#95—21no—
241#95—441no—
242#95C2×Dic1111yescharacteristic
243#95C2×Dic1111yescharacteristic
244C2×C11—21no—
245C2×C11—21no—
246C2×C11—42no—
247C2×C11—81no—
248C2×C11—161no—
249C2×C11#150111yescharacteristic
250C2×C11#212111yescharacteristic
251C2×C11#212811yescharacteristic
252C24—21no—
253C24C22⋊Dic1111yescharacteristic
254C24C2×C22⋊D1111yescharacteristic
255C2×D4—22no—
256C2×D4—22no—
257C2×D4—41no—
258C2×D4—41no—
259C2×D4—42no—
260C2×D4—42no—
261C2×D4—81no—
262C2×D4—81no—
263C2×D4—81no—
264C2×D4—81no—
265C2×D4—81no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—81no—
274C22×C4—81no—
275C22×C4—442no—
276C22×C4C22⋊Dic1111yescharacteristic
277C22×C4C22⋊Dic1111yescharacteristic
278C22×C4C22⋊Dic1111yescharacteristic
279C22×C4C22×Dic1111yescharacteristic
280C22×C4C2×C22⋊D1111yescharacteristic
281C2×C8—442no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—81no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—42no—
290C22⋊C4—81no—
291C22⋊C4—81no—
292C22⋊C4—81no—
293C22⋊C4—81no—
294C22⋊C4—224no—
295C22⋊C4—442no—
296C42—21no—
297C42—21no—
298C42—882no—
299C11#1172911yescharacteristic, complemented, Sylow
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23#6700312yes—
317C23C2×C22⋊Dic1111yescharacteristic
318D4—44no—
319D4—82no—
320D4—84no—
321D4—84no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—41no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—444no—
345C2×C4—882no—
346C2×C4—882no—
347C2×C4#6689811yescharacteristic
348C2×C4#6689811yescharacteristic
349C2×C4#6690112yes—
350C8—882no—
351C22—21no—
352C22—21no—
353C22—22no—
354C22—42no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—81no—
361C22—81no—
362C22—81no—
363C22—81no—
364C22—81no—
365C22—81no—
366C22—81no—
367C22—81no—
368C22—81no—
369C22—81no—
370C22C2×#6689811yescharacteristic
371C22#1062284611yescharacteristic
372C22C2×#6690111yescharacteristic
373C4—22no—
374C4—21no—
375C4—21no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—81no—
380C4—81no—
381C4—81no—
382C4—884no—
383C2—21no—
384C2—21no—
385C2—42no—
386C2—81no—
387C2—161no—
388C2#1306710711yescharacteristic
389C2#1307026211yescharacteristic
390C2#1307028811yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
Fitting, prime radicalC11×#2635C2
socleC22×C11C2×#99
cosocleC2×C11×C22⋊C4C23
hypercenter#2635D11
hypocenterC11#11729
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2635

Complements

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

NH ≅ G/Ntype
1. C4×#66898C2semidirect
2. #13066937C2semidirect
3. #13066640C2semidirect
4. #13066613C2semidirect
6. C2×C11×#121C4semidirect
8. C11×#400C4semidirect
11. C11×#394C4semidirect
16. C11×#381C4semidirect
161. C2×#121Dic11semidirect
165. #400Dic11semidirect
168. #394Dic11semidirect
173. #381Dic11semidirect
299. C11#11729semidirect

Maximal subgroups

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

subgroupindex
C4×#668982
#130669372
#130666402
#130666132
C11×#26352
#1172911