Finite Group Databasebeta

← #14664111

Subgroups — #14664111

Order 2816.

470 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 73 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#13071898C211yesmaximal, characteristic
2#13068403C211yesmaximal, characteristic
3#13066931C211yesmaximal, characteristic
4#13066637C211yesmaximal, characteristic, complemented
5#13066617C211yesmaximal, characteristic, complemented
6#13066615C211yesmaximal, characteristic, complemented
7C11×#1351C211yesmaximal, characteristic, complemented
8C2×Q8×Dic11C411yescharacteristic, complemented
9C2×(C22⋊D11)⋊C4C2211yescharacteristic
10C11×#393C2211yescharacteristic
11#10622844C411yescharacteristic, complemented
12#10622574—21no—
13C2×#66870—21no—
14#10622566C2211yescharacteristic
15C22⋊C4×Dic11—21no—
16C22⋊C4×Dic11—21no—
17D11×C22⋊C8—21no—
18#10622287C411yescharacteristic, complemented
19#10622279—21no—
20#10622273—21no—
21#10622261C411yescharacteristic, complemented
22C11×#342C2211yescharacteristic
23C11×#323C2211yescharacteristic
24#10622164C2211yescharacteristic
25#10622163C2211yescharacteristic
26#10622107—21no—
27C22×Q8×C11C2×C411yescharacteristic
28C22×C22⋊D11D411yescharacteristic
29C23×Dic11D411yescharacteristic
30C22×C4×D11D411yescharacteristic
31C2×C11×C22⋊C4—21no—
32C2×C11×C22⋊C4—21no—
33C2×C11×C22⋊C4C2311yescharacteristic
34C2×C22⋊Dic11—21no—
35C2×C22⋊Dic11—21no—
36Q8×Dic11—41no—
37Q8×Dic11—41no—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4C2×C411yescharacteristic
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11C2×C411yescharacteristic
43C2×Dic11⋊C4D411yescharacteristic
44C2×C4×Dic11—21no—
45C2×C4×Dic11—21no—
46C2×C4×Dic11—41no—
47C2×C4×Dic11C2×C411yescharacteristic
48C2×C8×D11—41no—
49(C22⋊D11)⋊C4—41no—
50(C22⋊D11)⋊C4—41no—
51C11×C22⋊C8—21no—
52C11×#95—21no—
53C11×#95C2×C411yescharacteristic
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—41no—
59C11⋊#95C2×C411yescharacteristic
60C22⋊(C11⋊C8)—21no—
61(C2×D11)⋊C8—41no—
62#66870—24no—
63#11728—111nomaximal, Sylow
64C24×C11C2×D411yescharacteristic
65C23×D11C22⋊C411yescharacteristic
66C2×Q8×C11—42no—
67C2×Q8×C11—41no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—41no—
71C22×C4×C11C22×C411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C2×C22⋊D11—21no—
74C2×C22⋊D11—21no—
75C2×C22⋊D11—22no—
76C2×C22⋊D11—41no—
77C22×Dic11—21no—
78C22×Dic11—21no—
79C22×Dic11—21no—
80C22×Dic11—21no—
81C22×Dic11—41no—
82C22×Dic11—42no—
83C22×Dic11C22⋊C411yescharacteristic
84C22×Dic11C22⋊C411yescharacteristic
85C22×Dic11C22⋊C411yescharacteristic
86C2×C4×D11—21no—
87C2×C4×D11—21no—
88C2×C4×D11—42no—
89C2×C8×C11—41no—
90C11×C22⋊C4—22no—
91C11×C22⋊C4—41no—
92C11×C22⋊C4—42no—
93C11×C22⋊C4—41no—
94C22⋊Dic11—22no—
95C22⋊Dic11—41no—
96C22⋊Dic11—41no—
97C22⋊Dic11—41no—
98(C2×D11)⋊C4—41no—
99(C2×D11)⋊C4—42no—
100(C2×D11)⋊C4—42no—
101C4⋊Dic11—41no—
102C4⋊Dic11—42no—
103Dic11⋊C4—41no—
104C4×Dic11—21no—
105C4×Dic11—21no—
106C4×Dic11—42no—
107C4×Dic11—41no—
108C4×Dic11—41no—
109C4×Dic11—82no—
110C2×C11⋊C8—41no—
111C8×D11—82no—
112#2398—111no—
113C4×#99—111no—
114#1459—111no—
115#1351—111no—
116#1351D1111yescharacteristic, complemented
117#1344—111no—
118#1344—111no—
119C23×C11—21no—
120C23×C11—21no—
121C23×C11—41no—
122C23×C11—41no—
123C23×C11C2×C22⋊C411yescharacteristic
124C23×C11#13511yescharacteristic
125C23×C11#13511yescharacteristic
126C22×D11—21no—
127C22×D11—21no—
128C22×D11—41no—
129C22×D11—41no—
130C22×D11#10412yes—
131Q8×C11—42no—
132Q8×C11—42no—
133C2×C4×C11—22no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—42no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—81no—
145C2×C4×C11—81no—
146C22⋊D11—42no—
147C22⋊D11—42no—
148C2×Dic11—22no—
149C2×Dic11—21no—
150C2×Dic11—21no—
151C2×Dic11—21no—
152C2×Dic11—21no—
153C2×Dic11—42no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—42no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—81no—
163C2×Dic11—81no—
164C2×Dic11—81no—
165C2×Dic11#9911yescharacteristic
166C2×Dic11#9911yescharacteristic
167C4×D11—42no—
168C4×D11—81no—
169C8×C11—81no—
170C11⋊C8—81no—
171C2×C4×Q8—111no—
172C2×C4×D4—111no—
173C2×#99—221no—
174C2×C22⋊C8—221no—
175#400—221no—
176#397—111no—
177#397—111no—
178#394—221no—
179#393—111no—
180#393C2×D1111yescharacteristic
181C4×C22⋊C4—221no—
182C4×C22⋊C4—221no—
183C4×C22⋊C4—221no—
184#376—111no—
185#342—111no—
186#342C2×D1111yescharacteristic
187#324—221no—
188#323—111no—
189#323C2×D1111yescharacteristic
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—41no—
195C22×C11—41no—
196C22×C11—41no—
197C22×C11—41no—
198C22×C11—81no—
199C22×C11C2×#9911yescharacteristic
200C22×C11#41611yescharacteristic
201C22×C11C2×#10411yescharacteristic
202C2×D11—22no—
203C2×D11—41no—
204C2×D11—41no—
205C2×D11—42no—
206C2×D11—81no—
207C4×C11—42no—
208C4×C11—41no—
209C4×C11—41no—
210C4×C11—81no—
211C4×C11—82no—
212Dic11—21no—
213Dic11—41no—
214Dic11—41no—
215Dic11—81no—
216Dic11—82no—
217Dic11—81no—
218Dic11#35412yes—
219C22×Q8C4×D1111yescharacteristic
220C22×D4—111no—
221C23×C4—111no—
222C23×C4—111no—
223C22×C8—441no—
224C4×Q8—441no—
225C4×Q8—441no—
226C4×D4—441no—
227C4×D4—441no—
228C2×C4⋊C4—111no—
229C2×C4⋊C4—111no—
230C2×C4⋊C4—221no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—111no—
234C2×C22⋊C4—221no—
235C2×C22⋊C4—221no—
236C2×C22⋊C4—221no—
237C2×C22⋊C4—221no—
238C2×C22⋊C4C22×D1111yescharacteristic
239C2×C42—111no—
240C2×C42—221no—
241C2×C42—221no—
242C2×C42—441no—
243#99—224no—
244C22⋊C8—21no—
245C22⋊C8—221no—
246C22⋊C8—441no—
247#95—21no—
248#95—111no—
249#95—221no—
250#95—221no—
251#95—221no—
252#95—221no—
253#95—441no—
254#95C4×D1111yescharacteristic
255C2×C11—21no—
256C2×C11—21no—
257C2×C11—41no—
258C2×C11—41no—
259C2×C11#150111yescharacteristic
260C2×C11#212011yescharacteristic
261C2×C11C2×#35411yescharacteristic
262D11—42no—
263C24—111no—
264C24D4×D1111yescharacteristic
265C2×Q8—42no—
266C2×Q8—41no—
267C2×D4—222no—
268C2×D4—221no—
269C2×D4—221no—
270C2×D4—441no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—41no—
274C22×C4—111no—
275C22×C4—111no—
276C22×C4—111no—
277C22×C4—221no—
278C22×C4—221no—
279C22×C4—221no—
280C22×C4—221no—
281C22×C4—221no—
282C22×C4—221no—
283C22×C4—442no—
284C22×C4—442no—
285C22×C4—441no—
286C22×C4C2×C4×D1111yescharacteristic
287C22×C4D4×D1111yescharacteristic
288C2×C8—41no—
289C2×C8—441no—
290C2×C8—882no—
291C4⋊C4—441no—
292C4⋊C4—441no—
293C4⋊C4—442no—
294C22⋊C4—22no—
295C22⋊C4—41no—
296C22⋊C4—42no—
297C22⋊C4—41no—
298C22⋊C4—222no—
299C22⋊C4—441no—
300C22⋊C4—442no—
301C22⋊C4—442no—
302C22⋊C4—441no—
303C22⋊C4—441no—
304C22⋊C4—441no—
305C42—221no—
306C42—221no—
307C42—441no—
308C42—441no—
309C42—442no—
310C42—882no—
311C11#1172811yescharacteristic, complemented, Sylow
312C23—21no—
313C23—21no—
314C23—41no—
315C23—41no—
316C23—112no—
317C23—221no—
318C23—221no—
319C23—441no—
320C23—441no—
321C23C22⋊C4×D1111yescharacteristic
322C23#6696911yescharacteristic
323C23#6697211yescharacteristic
324Q8—42no—
325Q8—42no—
326D4—442no—
327D4—442no—
328C2×C4—22no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—111no—
342C2×C4—111no—
343C2×C4—222no—
344C2×C4—221no—
345C2×C4—221no—
346C2×C4—221no—
347C2×C4—221no—
348C2×C4—442no—
349C2×C4—442no—
350C2×C4—441no—
351C2×C4—441no—
352C2×C4—442no—
353C2×C4—441no—
354C2×C4—441no—
355C2×C4—441no—
356C2×C4—441no—
357C2×C4—441no—
358C2×C4—881no—
359C2×C4—881no—
360C2×C4—881no—
361C2×C4—881no—
362C8—81no—
363C8—881no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—81no—
373C22—222no—
374C22—442no—
375C22—441no—
376C22—441no—
377C22—881no—
378C22D11×#9911yescharacteristic
379C22#1062241711yescharacteristic
380C22D11×#10411yescharacteristic
381C4—42no—
382C4—41no—
383C4—41no—
384C4—81no—
385C4—82no—
386C4—112no—
387C4—221no—
388C4—441no—
389C4—441no—
390C4—881no—
391C4—882no—
392C4—881no—
393C2—21no—
394C2—21no—
395C2—41no—
396C2—41no—
397C2—442no—
398C2#1306710611yescharacteristic
399C2#1307025411yescharacteristic
400C2D11×#35411yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1351C2
socleC22×C11C2×#99
prime radicalC22×C22⋊D11D4
cosocleC2×C11×C22⋊C4C23
hypercenter#1351D11
hypocenterC11#11728
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1351

Complements

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

NH ≅ G/Ntype
4. #13066637C2semidirect
5. #13066617C2semidirect
6. #13066615C2semidirect
7. C11×#1351C2semidirect
8. C2×Q8×Dic11C4semidirect
11. #10622844C4semidirect
18. #10622287C4semidirect
21. #10622261C4semidirect
116. #1351D11semidirect
311. C11#11728semidirect

Maximal subgroups

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

subgroupindex
#130718982
#130684032
#130669312
#130666372
#130666172
#130666152
C11×#13512
#1172811