Finite Group Databasebeta

← #14670554

Subgroups — #14670554

Order 2816.

426 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 95 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#13070257C211yesmaximal, characteristic
2#13069035C211yesmaximal, characteristic
3#13068901C211yesmaximal, characteristic, complemented
4#13068835C211yesmaximal, characteristic, complemented
5#13066745C211yesmaximal, characteristic, complemented
6#13066739C211yesmaximal, characteristic, complemented
7C11×#2977C211yesmaximal, characteristic
8C11×#525C2211yescharacteristic
9#10623350C2211yescharacteristic
10C11×#435—21no—
11C11×#435—21no—
12C8×D4×C11—21no—
13C8×D4×C11—21no—
14C11×#433—21no—
15C11×#408C2211yescharacteristic
16C11×#408C2211yescharacteristic
17C2×C11×C22⋊C8—21no—
18#10622853C2211yescharacteristic
19#10622850C2211yescharacteristic
20#10622850C2211yescharacteristic
21#10622820—21no—
22#10622737—21no—
23#10622715—21no—
24#10622197—21no—
25#10622190—21no—
26#10622177C412yes—
27#10622174C412yes—
28#10622171—21no—
29C2×C11×#41C2311yescharacteristic
30C23×C4×C11D411yescharacteristic
31C2×C11×M16D411yescharacteristic
32C2×C11×M16D411yescharacteristic
33C22×C8×C11—21no—
34C22×C8×C11—21no—
35C22×C8×C11D411yescharacteristic
36C22×C8×C11D411yescharacteristic
37C11×#123C2×C411yescharacteristic
38C11×#123Q811yescharacteristic
39C11×C22⋊Q8—21no—
40C11×#121—21no—
41C11×#120C2×C411yescharacteristic
42C11×#120Q811yescharacteristic
43C4×D4×C11—21no—
44C4×D4×C11—21no—
45C11×#117D411yescharacteristic
46#67001—42no—
47#66979—21no—
48C2×#4318—21no—
49C2×#4318—21no—
50C2×#4318—21no—
51C2×#4318—21no—
52C2×#4318—21no—
53C11×C4⋊C8—21no—
54C11×C4⋊C8—21no—
55C11×C22⋊C8—21no—
56C11×C22⋊C8—21no—
57C11×C22⋊C8—21no—
58C11×C22⋊C8—21no—
59C11×C22⋊C8—21no—
60C11×C22⋊C8—21no—
61C11×#97—21no—
62C4×C8×C11—21no—
63#66900—21no—
64#66900—21no—
65#66898—21no—
66#66898C2×C412yes—
67#66897—21no—
68#66897C2×C412yes—
69C22⋊(C11⋊C8)—42no—
70#66886—42no—
71Dic11⋊C8—42no—
72#12962—111nomaximal, Sylow
73C24×C11C4⋊C411yescharacteristic
74C11×#41—41no—
75C11×#41—41no—
76C2×Q8×C11#4111yescharacteristic
77C2×D4×C11—21no—
78C2×D4×C11—21no—
79C2×D4×C11C22×C411yescharacteristic
80C2×D4×C11C2×Q811yescharacteristic
81C2×D4×C11#4111yescharacteristic
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11C4⋊C411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C11×M16—41no—
91C11×M16—41no—
92C2×C8×C11—21no—
93C2×C8×C11—21no—
94C2×C8×C11—21no—
95C2×C8×C11—21no—
96C2×C8×C11—41no—
97C2×C8×C11—41no—
98C2×C8×C11—81no—
99C2×C8×C11—81no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C22⋊C4—21no—
104C11×C22⋊C4—21no—
105C11×C22⋊C4—21no—
106C11×C22⋊C4—21no—
107C11×C22⋊C4C4⋊C411yescharacteristic
108C11×C22⋊C4C4⋊C411yescharacteristic
109C42×C11—21no—
110C22⋊Dic11—22no—
111C4⋊Dic11—41no—
112C4×Dic11—41no—
113#4318—22no—
114#4318—22no—
115#4318—41no—
116#4318—41no—
117#4318—41no—
118#4318—41no—
119#4318—41no—
120#4318—41no—
121C2×C11⋊C8—22no—
122C2×C11⋊C8—22no—
123C2×C11⋊C8—41no—
124C2×C11⋊C8—41no—
125C2×C11⋊C8—41no—
126#2977D1111yescharacteristic
127#2120—111no—
128#1891—111no—
129#1868—111no—
130#1858—111no—
131#1395—111no—
132#1392—111no—
133C23×C11—21no—
134C23×C11—41no—
135C23×C11—42no—
136C23×C11C2×C4⋊C411yescharacteristic
137C23×C11C4×D411yescharacteristic
138C23×C11C22⋊Q811yescharacteristic
139Q8×C11—41no—
140D4×C11—41no—
141D4×C11—41no—
142D4×C11—41no—
143D4×C11—42no—
144D4×C11—42no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—81no—
158C2×C4×C11C4×D411yescharacteristic
159C2×C4×C11#12011yescharacteristic
160C2×C4×C11C22⋊Q811yescharacteristic
161C2×C4×C11#12311yescharacteristic
162C2×Dic11—42no—
163C8×C11—41no—
164C8×C11—41no—
165C8×C11—41no—
166C8×C11—41no—
167C11⋊C8—42no—
168C11⋊C8—42no—
169C11⋊C8—81no—
170#568—111no—
171#525C2×D1111yescharacteristic
172#435—21no—
173#435—21no—
174C8×D4—21no—
175C8×D4—21no—
176#433—21no—
177#430—221no—
178#424—221no—
179#413—111no—
180#413—111no—
181#410—111no—
182#408C2×D1111yescharacteristic
183#408C2×D1111yescharacteristic
184#407—221no—
185C2×C22⋊C8—21no—
186#352—112no—
187AΣL(1,𝔽16)—112no—
188#344—221no—
189#344—221no—
190#341—221no—
191C22×C11—22no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—41no—
196C22×C11—41no—
197C22×C11—41no—
198C22×C11—41no—
199C22×C11—42no—
200C22×C11—41no—
201C22×C11—81no—
202C22×C11#38511yescharacteristic
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—41no—
207C4×C11—41no—
208C4×C11—41no—
209C4×C11B(4,𝔽2)11yescharacteristic
210C4×C11#45811yescharacteristic
211Dic11—82no—
212C2×#41C22×D1111yescharacteristic
213C23×C4C22⋊D1111yescharacteristic
214#131—442no—
215C2×M16—221no—
216C2×M16—221no—
217C2×M16—221no—
218C2×M16—221no—
219C2×M16—221no—
220C2×M16C22⋊D1111yescharacteristic
221C2×M16C22⋊D1111yescharacteristic
222C22×C8—21no—
223C22×C8—21no—
224C22×C8C22⋊D1111yescharacteristic
225C22×C8C22⋊D1111yescharacteristic
226#123Dic2211yescharacteristic
227#123C4×D1111yescharacteristic
228C22⋊Q8—21no—
229#121—21no—
230#120Dic2211yescharacteristic
231#120C4×D1111yescharacteristic
232C4×D4—21no—
233C4×D4—21no—
234#117—221no—
235#117C22⋊D1111yescharacteristic
236#108—442no—
237C4⋊C8—21no—
238C4⋊C8—21no—
239C4⋊C8—442no—
240#101—221no—
241#101—221no—
242#100—112no—
243#100—221no—
244#99—112no—
245#99—221no—
246C22⋊C8—21no—
247C22⋊C8—21no—
248C22⋊C8—21no—
249C22⋊C8—21no—
250C22⋊C8—21no—
251C22⋊C8—21no—
252C22⋊C8—442no—
253#97—21no—
254C4×C8—21no—
255C2×C11—21no—
256C2×C11—41no—
257C2×C11—41no—
258C2×C11—42no—
259C2×C11—41no—
260C2×C11#186711yescharacteristic
261C24Dic11⋊C411yescharacteristic
262#41—41no—
263#41—41no—
264C2×Q8#433911yescharacteristic
265C2×D4—21no—
266C2×D4—21no—
267C2×D4C2×Dic2211yescharacteristic
268C2×D4C2×C4×D1111yescharacteristic
269C2×D4#433911yescharacteristic
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4Dic11⋊C411yescharacteristic
275C22×C4C2×C22⋊D1111yescharacteristic
276C22×C4C2×C22⋊D1111yescharacteristic
277C22×C4C2×C22⋊D1111yescharacteristic
278M16—41no—
279M16—41no—
280M16—222no—
281M16—222no—
282M16—441no—
283M16—441no—
284M16—441no—
285M16—441no—
286M16—441no—
287M16—441no—
288C2×C8—21no—
289C2×C8—21no—
290C2×C8—21no—
291C2×C8—21no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—81no—
295C2×C8—81no—
296C2×C8—222no—
297C2×C8—222no—
298C2×C8—441no—
299C2×C8—441no—
300C2×C8—441no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—441no—
305C22⋊C4—21no—
306C22⋊C4—21no—
307C22⋊C4—21no—
308C22⋊C4—21no—
309C22⋊C4—222no—
310C22⋊C4Dic11⋊C411yescharacteristic
311C22⋊C4Dic11⋊C411yescharacteristic
312C42—21no—
313C42—441no—
314C11#1296211yescharacteristic, complemented, Sylow
315C23—21no—
316C23—41no—
317C23—42no—
318C23C2×Dic11⋊C411yescharacteristic
319C23#6697711yescharacteristic
320C23C4×C22⋊D1111yescharacteristic
321Q8—41no—
322D4—41no—
323D4—41no—
324D4—41no—
325D4—42no—
326D4—42no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—81no—
340C2×C4—442no—
341C2×C4#6697711yescharacteristic
342C2×C4C4×C22⋊D1111yescharacteristic
343C2×C4#6698211yescharacteristic
344C2×C4#6700611yescharacteristic
345C8—41no—
346C8—41no—
347C8—41no—
348C8—41no—
349C8—442no—
350C8—442no—
351C8—881no—
352C22—22no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—42no—
361C22—41no—
362C22—81no—
363C22#1062282311yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—882no—
371C4#1062285611yescharacteristic
372C4#1062285711yescharacteristic
373C2—21no—
374C2—41no—
375C2—42no—
376C2—41no—
377C2—41no—
378C2#1306889711yescharacteristic
subgroupG/H
centerC4#10622857
commutatorC2×D4×C11C22×C4
FrattiniC2×#41C22×D11
FittingC11×#2977C2
socleC2×C11#1867
prime radicalC11×#525C22
cosocleC2×C11×#41C23
hypercenter#2977D11
hypocenterC11#12962
LCSG ▷ C2×D4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #2977

Complements

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

NH ≅ G/Ntype
3. #13068901C2semidirect
4. #13068835C2semidirect
5. #13066745C2semidirect
6. #13066739C2semidirect
314. C11#12962semidirect

Maximal subgroups

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

subgroupindex
#130702572
#130690352
#130689012
#130688352
#130667452
#130667392
C11×#29772
#1296211