Finite Group Databasebeta

← #14664146

Subgroups — #14664146

Order 2816.

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

normal subgroups only

This group has 440 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#13071882C211yesmaximal, characteristic
2#13068407C211yesmaximal, characteristic
3#13066933C211yesmaximal, characteristic
4#13066643C211yesmaximal, characteristic, complemented
5#13066623C211yesmaximal, characteristic, complemented
6#13066621C211yesmaximal, characteristic, complemented
7C11×#1353C211yesmaximal, characteristic, complemented
8C2×#66946C2211yescharacteristic
9C2×#66945C411yescharacteristic
10C11×#400C2211yescharacteristic
11C2×#66887—21no—
12M16×Dic11—21no—
13#10622605C411yescharacteristic
14#10622596C2211yescharacteristic
15D11×C22⋊C8—21no—
16#10622288—21no—
17#10622287C411yescharacteristic
18#10622285—21no—
19#10622279—21no—
20#10622279C411yescharacteristic
21#10622262—21no—
22C11×#343C2211yescharacteristic
23C11×#324C2211yescharacteristic
24#10622168C2211yescharacteristic
25#10622166C2211yescharacteristic
26#10622106—21no—
27C22×D44D411yescharacteristic
28C22×C4×D11C2×C411yescharacteristic
29C22×C4×D11D411yescharacteristic
30C2×C11×M16—21no—
31C2×C11×C4⋊C4C2×C411yescharacteristic
32C2×C11×C4⋊C4C2311yescharacteristic
33C2×(C2×D11)⋊C4—21no—
34C2×(C2×D11)⋊C4—21no—
35C2×(C2×D11)⋊C4—21no—
36C2×(C2×D11)⋊C4—21no—
37C2×(C2×D11)⋊C4C2×C411yescharacteristic
38C2×(C2×D11)⋊C4D411yescharacteristic
39C2×C4⋊Dic11C2×C411yescharacteristic
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×C4×Dic11—21no—
43C2×C4×Dic11—21no—
44C2×C4×Dic11D411yescharacteristic
45C2×#4318—21no—
46C2×C8×D11—41no—
47#66946—41no—
48#66946—41no—
49#66945—41no—
50#66945—41no—
51C11×C22⋊C8—21no—
52C11×#95—21no—
53C11×#95—21no—
54C11×#95C2×C411yescharacteristic
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95C2×C411yescharacteristic
58C22⋊(C11⋊C8)—21no—
59#66887—24no—
60(C2×D11)⋊C8—41no—
61#66879—41no—
62C8×Dic11—41no—
63#11735—111nomaximal, Sylow
64C23×D11C22⋊C411yescharacteristic
65C23×D11C22⋊C411yescharacteristic
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11C22×C411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×Dic11—21no—
72C22×Dic11—21no—
73C22×Dic11C22⋊C411yescharacteristic
74C22×Dic11C22⋊C411yescharacteristic
75C2×D44—22no—
76C2×D44—21no—
77C2×D44—21no—
78C2×D44—41no—
79C2×C4×D11—21no—
80C2×C4×D11—21no—
81C2×C4×D11—21no—
82C2×C4×D11—21no—
83C2×C4×D11—42no—
84C2×C4×D11—42no—
85C11×M16—22no—
86C11×M16—41no—
87C2×C8×C11—41no—
88C2×C8×C11—41no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91(C2×D11)⋊C4—41no—
92(C2×D11)⋊C4—41no—
93(C2×D11)⋊C4—42no—
94(C2×D11)⋊C4—42no—
95(C2×D11)⋊C4—42no—
96(C2×D11)⋊C4—42no—
97C4⋊Dic11—41no—
98Dic11⋊C4—42no—
99Dic11⋊C4—41no—
100Dic11⋊C4—41no—
101C4×Dic11—21no—
102C4×Dic11—21no—
103C4×Dic11—42no—
104C4×Dic11—41no—
105C4×Dic11—41no—
106#4318—22no—
107#4318—41no—
108C2×C11⋊C8—41no—
109C2×C11⋊C8—41no—
110C8×D11—82no—
111#2395—111no—
112C4×#100—111no—
113#1459—111no—
114#1353—111no—
115#1353D1111yescharacteristic, complemented
116#1346—111no—
117#1346—111no—
118C23×C11C2×C22⋊C411yescharacteristic
119C22×D11—21no—
120C22×D11—21no—
121C22×D11—21no—
122C22×D11—21no—
123C22×D11—21no—
124C22×D11—41no—
125C22×D11—41no—
126C22×D11—41no—
127C22×D11—41no—
128C22×D11#10412yes—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
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#13511yescharacteristic
142C2×C4×C11#13511yescharacteristic
143C2×Dic11—22no—
144C2×Dic11—22no—
145C2×Dic11—21no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11#9911yescharacteristic
153C2×Dic11#9911yescharacteristic
154D44—42no—
155D44—42no—
156C4×D11—42no—
157C4×D11—42no—
158C4×D11—42no—
159C4×D11—81no—
160C8×C11—42no—
161C8×C11—81no—
162C11⋊C8—42no—
163C11⋊C8—81no—
164C2×C4×D4—111no—
165C2×#117—111no—
166C2×#100—221no—
167C2×C22⋊C8—221no—
168C4×M16—221no—
169#400C2×D1111yescharacteristic
170#399—111no—
171#398—111no—
172#397—111no—
173#397—221no—
174#394—221no—
175C4×C4⋊C4—221no—
176C4×C22⋊C4—111no—
177C4×C22⋊C4—221no—
178#343—111no—
179#343C2×D1111yescharacteristic
180#324—111no—
181#324C2×D1111yescharacteristic
182#323—221no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11C2×#9911yescharacteristic
186C22×C11#41611yescharacteristic
187C22×C11C2×#10411yescharacteristic
188C2×D11—22no—
189C2×D11—41no—
190C2×D11—41no—
191C2×D11—42no—
192C2×D11—41no—
193C2×D11—41no—
194C2×D11—41no—
195C2×D11—81no—
196C2×D11—81no—
197C2×D11—81no—
198C4×C11—21no—
199C4×C11—21no—
200C4×C11—41no—
201C4×C11—41no—
202C4×C11—81no—
203C4×C11—81no—
204Dic11—21no—
205Dic11—42no—
206Dic11—41no—
207Dic11—81no—
208Dic11#35212yes—
209C22×D4—111no—
210C23×C4—111no—
211C23×C4—111no—
212C2×M16—21no—
213C2×M16—221no—
214C22×C8—441no—
215C4×D4—441no—
216C4×D4—441no—
217#117—441no—
218#117—441no—
219C2×C4⋊C4—111no—
220C2×C4⋊C4—221no—
221C2×C4⋊C4—221no—
222C2×C4⋊C4C4×D1111yescharacteristic
223C2×C4⋊C4C22×D1111yescharacteristic
224C2×C22⋊C4—111no—
225C2×C22⋊C4—111no—
226C2×C22⋊C4—221no—
227C2×C22⋊C4—221no—
228C2×C22⋊C4—221no—
229C2×C22⋊C4—221no—
230C2×C42—111no—
231C2×C42—221no—
232C2×C42—221no—
233#100—224no—
234C22⋊C8—21no—
235C22⋊C8—221no—
236C22⋊C8—441no—
237#97—441no—
238C4×C8—441no—
239#95—21no—
240#95—21no—
241#95—111no—
242#95—221no—
243#95—221no—
244#95C4×D1111yescharacteristic
245C2×C11—21no—
246C2×C11—21no—
247C2×C11#150111yescharacteristic
248C2×C11C2×#35211yescharacteristic
249C2×C11#213211yescharacteristic
250D11—42no—
251D11—81no—
252C24—111no—
253C24—111no—
254C2×D4—222no—
255C2×D4—221no—
256C2×D4—221no—
257C2×D4—441no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—111no—
261C22×C4—111no—
262C22×C4—221no—
263C22×C4—221no—
264C22×C4—221no—
265C22×C4—221no—
266C22×C4—221no—
267C22×C4—221no—
268C22×C4—442no—
269C22×C4—442no—
270C22×C4C2×C4×D1111yescharacteristic
271C22×C4D4×D1111yescharacteristic
272C22×C4D4×D1111yescharacteristic
273M16—22no—
274M16—41no—
275M16—222no—
276M16—441no—
277C2×C8—41no—
278C2×C8—41no—
279C2×C8—441no—
280C2×C8—441no—
281C2×C8—882no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—441no—
285C4⋊C4—442no—
286C4⋊C4—441no—
287C4⋊C4—441no—
288C22⋊C4—441no—
289C22⋊C4—441no—
290C22⋊C4—442no—
291C22⋊C4—442no—
292C22⋊C4—442no—
293C22⋊C4—442no—
294C42—221no—
295C42—221no—
296C42—441no—
297C42—441no—
298C42—442no—
299C11#1173511yescharacteristic, complemented, Sylow
300C23—112no—
301C23—221no—
302C23—221no—
303C23—221no—
304C23—221no—
305C23—221no—
306C23—441no—
307C23—441no—
308C23—441no—
309C23—441no—
310C23C22⋊C4×D1111yescharacteristic
311D4—442no—
312D4—442no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—111no—
326C2×C4—111no—
327C2×C4—222no—
328C2×C4—222no—
329C2×C4—221no—
330C2×C4—442no—
331C2×C4—442no—
332C2×C4—442no—
333C2×C4—441no—
334C2×C4—441no—
335C2×C4—441no—
336C2×C4—441no—
337C2×C4—441no—
338C2×C4—441no—
339C2×C4—881no—
340C2×C4#6696911yescharacteristic
341C2×C4#6697211yescharacteristic
342C8—42no—
343C8—81no—
344C8—442no—
345C8—881no—
346C22—21no—
347C22—21no—
348C22—222no—
349C22—442no—
350C22—441no—
351C22—441no—
352C22—441no—
353C22—441no—
354C22—441no—
355C22—881no—
356C22—881no—
357C22—881no—
358C22D11×#9911yescharacteristic
359C22#1062241711yescharacteristic
360C22D11×#10411yescharacteristic
361C4—21no—
362C4—21no—
363C4—41no—
364C4—41no—
365C4—81no—
366C4—81no—
367C4—112no—
368C4—221no—
369C4—442no—
370C4—441no—
371C4—881no—
372C2—21no—
373C2—21no—
374C2—442no—
375C2—881no—
376C2#1306710611yescharacteristic
377C2D11×#35211yescharacteristic
378C2#1307029811yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1353C2
socleC22×C11C2×#99
prime radicalC22×D44D4
cosocleC2×C11×C4⋊C4C23
hypercenter#1353D11
hypocenterC11#11735
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1353

Complements

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

NH ≅ G/Ntype
4. #13066643C2semidirect
5. #13066623C2semidirect
6. #13066621C2semidirect
7. C11×#1353C2semidirect
115. #1353D11semidirect
299. C11#11735semidirect

Maximal subgroups

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

subgroupindex
#130718822
#130684072
#130669332
#130666432
#130666232
#130666212
C11×#13532
#1173511