Finite Group Databasebeta

← #14670623

Subgroups — #14670623

Order 2816.

416 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 85 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#13077680C211yesmaximal, characteristic
2#13070299C211yesmaximal, characteristic
3#13068997C211yesmaximal, characteristic
4#13068838C211yesmaximal, characteristic, complemented
5#13068835C211yesmaximal, characteristic, complemented
6#13066744C211yesmaximal, characteristic, complemented
7C11×#1395C211yesmaximal, characteristic, complemented
8#10623363C2211yescharacteristic
9#10623350C2211yescharacteristic
10C11×#413C2211yescharacteristic
11C11×#410C2211yescharacteristic
12C11×#408C2211yescharacteristic
13#10622850C2211yescharacteristic
14#10622847C2211yescharacteristic
15#10622741—21no—
16#10622738—21no—
17#10622737—21no—
18C8×C22⋊D11—21no—
19#10622618—21no—
20#10622342—21no—
21#10622340—21no—
22(C22⋊D11)⋊C8—21no—
23#10622331—21no—
24#10622196—21no—
25#10622190—21no—
26#10622170—21no—
27#10622116C412yescomplemented
28#10622115C412yescomplemented
29C2×C11×#41C2311yescharacteristic
30C2×#4339D411yescharacteristic
31C2×C11×M16—21no—
32C2×C11×M16D411yescharacteristic
33C22×C8×C11D411yescharacteristic
34C11×#117—21no—
35#67001—42no—
36#67000C2×C411yescharacteristic
37#66997C2×C411yescharacteristic
38#66993Q811yescharacteristic
39#66992—21no—
40#66992—21no—
41#66989Q811yescharacteristic
42C4×C22⋊D11—21no—
43C4×C22⋊D11—21no—
44C2×C4×Dic11D411yescharacteristic
45C2×#4318—21no—
46C2×#4318—21no—
47C2×#4318—21no—
48C2×#4318—21no—
49C2×#4318D411yescharacteristic
50C22×C11⋊C8D411yescharacteristic
51C2×#4313—21no—
52C2×C8×D11—21no—
53C11×#101C2×C412yes—
54C11×#100—21no—
55C11×#99—21no—
56C11×#99—21no—
57C11×C22⋊C8—21no—
58C11×C22⋊C8—21no—
59#66900C2×C412yes—
60#66897—21no—
61C22⋊(C11⋊C8)—21no—
62C22⋊(C11⋊C8)—21no—
63#66886—42no—
64(C2×D11)⋊C8—21no—
65(C2×D11)⋊C8—21no—
66#66883—42no—
67Dic11⋊C8—21no—
68Dic11⋊C8—21no—
69C8×Dic11—21no—
70C8×Dic11—21no—
71#66869—42no—
72#12975—111nomaximal, Sylow
73C11×#41—41no—
74C11×#41—41no—
75C2×Q8×C11C22×C411yescharacteristic
76C2×D4×C11C2×Q811yescharacteristic
77C2×D4×C11#4111yescharacteristic
78C2×D4×C11#4111yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C2×C22⋊D11—21no—
83C2×C22⋊D11—21no—
84C2×C22⋊D11—21no—
85C22×Dic11—21no—
86#4339—41no—
87#4339—41no—
88C2×D44C4⋊C411yescharacteristic
89C2×C4×D11—21no—
90C2×Dic22C4⋊C411yescharacteristic
91C11×M16—22no—
92C11×M16—41no—
93C11×M16—41no—
94C2×C8×C11—21no—
95C2×C8×C11—21no—
96C2×C8×C11—41no—
97C2×C8×C11—41no—
98C11×C4⋊C4—41no—
99C11×C22⋊C4—41no—
100C42×C11—41no—
101C22⋊Dic11—21no—
102C22⋊Dic11—21no—
103(C2×D11)⋊C4—21no—
104(C2×D11)⋊C4—21no—
105Dic11⋊C4—21no—
106Dic11⋊C4—21no—
107C4×Dic11—21no—
108C4×Dic11C4⋊C411yescharacteristic
109C4×Dic11C4⋊C411yescharacteristic
110#4318—22no—
111#4318—22no—
112#4318—22no—
113#4318—22no—
114#4318—41no—
115#4318—41no—
116#4318—41no—
117C2×C11⋊C8—21no—
118C2×C11⋊C8—21no—
119C2×C11⋊C8—41no—
120C2×C11⋊C8—41no—
121C2×C11⋊C8—41no—
122C2×C11⋊C8—41no—
123C2×C11⋊C8—41no—
124#4313—81no—
125C8×D11—81no—
126#2979—111no—
127#2132—111no—
128#1884—111no—
129#1858—111no—
130#1858—111no—
131#1395—111no—
132#1395D1111yescharacteristic, complemented
133C23×C11C22⋊Q811yescharacteristic
134C23×C11C22⋊Q811yescharacteristic
135C23×C11#12311yescharacteristic
136C22×D11—21no—
137Q8×C11—41no—
138D4×C11—41no—
139D4×C11—41no—
140D4×C11—41no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—81no—
148C2×C4×C11C2×C4⋊C411yescharacteristic
149C2×C4×C11C4×D411yescharacteristic
150C2×C4×C11C4×D411yescharacteristic
151C2×C4×C11#12011yescharacteristic
152C22⋊D11—42no—
153C22⋊D11—42no—
154C22⋊D11—81no—
155C2×Dic11—21no—
156C2×Dic11—21no—
157C2×Dic11—21no—
158C2×Dic11—42no—
159D44—41no—
160C4×D11—41no—
161C4×D11—41no—
162Dic22—41no—
163C8×C11—42no—
164C8×C11—41no—
165C8×C11—41no—
166C11⋊C8—42no—
167C11⋊C8—41no—
168C11⋊C8—42no—
169C11⋊C8—41no—
170#568—111no—
171#532—111no—
172#436—221no—
173#436—221no—
174C8×D4—221no—
175C8×D4—221no—
176#431—221no—
177#430—221no—
178#430—221no—
179#421—221no—
180#413—111no—
181#413C2×D1111yescharacteristic
182#410C2×D1111yescharacteristic
183#408—111no—
184#408—221no—
185#408C2×D1111yescharacteristic
186#356—112no—
187#355—112no—
188#341—221no—
189#341—221no—
190#339—221no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—41no—
195C22×C11—41no—
196C22×C11—41no—
197C22×C11#38511yescharacteristic
198C2×D11—41no—
199C2×D11—41no—
200C2×D11—41no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—161no—
205C4×C11B(4,𝔽2)11yescharacteristic
206C4×C11#45811yescharacteristic
207Dic11—22no—
208Dic11—41no—
209Dic11—41no—
210C2×#41—111no—
211C2×#41C22×D1111yescharacteristic
212#131—442no—
213C2×M16—21no—
214C2×M16—111no—
215C2×M16—221no—
216C2×M16—221no—
217C2×M16—221no—
218C2×M16—221no—
219C2×M16—221no—
220C2×M16D4411yescharacteristic
221C22×C8—111no—
222C22×C8—221no—
223C22×C8D4411yescharacteristic
224C4⋊Q8—111no—
225#127—111no—
226#124—111no—
227#124—111no—
228#121—221no—
229#121—221no—
230C4×D4—221no—
231C4×D4—221no—
232#117—21no—
233C2×C42—111no—
234#108—442no—
235#108—442no—
236C4⋊C8—221no—
237C4⋊C8—221no—
238#104—442no—
239#101—112no—
240#101C4×D1112yes—
241#100—21no—
242#100—221no—
243#99—21no—
244#99—21no—
245C22⋊C8—21no—
246C22⋊C8—21no—
247C22⋊C8—221no—
248C22⋊C8—221no—
249C22⋊C8—221no—
250C22⋊C8—221no—
251C4×C8—221no—
252C4×C8—221no—
253C2×C11—21no—
254C2×C11—41no—
255C2×C11—41no—
256C2×C11—41no—
257C2×C11#186711yescharacteristic
258D11—81no—
259#41—41no—
260#41—41no—
261#41—441no—
262#41—441no—
263C2×Q8—111no—
264C2×Q8C2×C4×D1111yescharacteristic
265C2×D4—111no—
266C2×D4—221no—
267C2×D4—221no—
268C2×D4—221no—
269C2×D4#433911yescharacteristic
270C2×D4#434111yescharacteristic
271C2×D4Q8×D1111yescharacteristic
272C22×C4—221no—
273C22×C4—221no—
274C22×C4C2×D4411yescharacteristic
275C22×C4D4×D1111yescharacteristic
276C22×C4D4×D1111yescharacteristic
277M16—22no—
278M16—41no—
279M16—41no—
280M16—222no—
281M16—222no—
282M16—222no—
283M16—222no—
284M16—441no—
285M16—441no—
286M16—441no—
287M16—881no—
288C2×C8—21no—
289C2×C8—21no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—221no—
293C2×C8—221no—
294C2×C8—441no—
295C2×C8—441no—
296C2×C8—441no—
297C2×C8—441no—
298C2×C8—441no—
299C2×C8—881no—
300C4⋊C4—41no—
301C4⋊C4—221no—
302C4⋊C4—221no—
303C22⋊C4—41no—
304C22⋊C4—221no—
305C22⋊C4—221no—
306C22⋊C4—221no—
307C22⋊C4—221no—
308C42—41no—
309C42—111no—
310C42—111no—
311C42—221no—
312C11#1297511yescharacteristic, complemented, Sylow
313C23—221no—
314C23#6693611yescharacteristic
315C23#6694911yescharacteristic
316C23#6695011yescharacteristic
317Q8—41no—
318Q8—441no—
319D4—41no—
320D4—41no—
321D4—41no—
322D4—441no—
323D4—442no—
324D4—442no—
325D4—881no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—81no—
333C2×C4—221no—
334C2×C4—221no—
335C2×C4—221no—
336C2×C4—442no—
337C2×C4—441no—
338C2×C4—441no—
339C2×C4C4×D4411yescharacteristic
340C2×C4(C22⋊D11)⋊C411yescharacteristic
341C2×C4#6693511yescharacteristic
342C2×C4C4⋊C4×D1111yescharacteristic
343C8—42no—
344C8—41no—
345C8—41no—
346C8—442no—
347C8—441no—
348C8—442no—
349C8—441no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—441no—
357C22—441no—
358C22—441no—
359C22#1062228111yescharacteristic
360C4—21no—
361C4—21no—
362C4—21no—
363C4—161no—
364C4—222no—
365C4—441no—
366C4—441no—
367C4#1062235411yescharacteristic
368C4#1062235511yescharacteristic
369C2—21no—
370C2—41no—
371C2—41no—
372C2—41no—
373C2—881no—
374C2#1306889811yescharacteristic
subgroupG/H
centerC4#10622354
commutatorC2×Q8×C11C22×C4
FrattiniC2×#41C22×D11
FittingC11×#1395C2
socleC2×C11#1867
prime radical#10623363C22
cosocleC2×C11×#41C23
hypercenter#1395D11
hypocenterC11#12975
LCSG ▷ C2×Q8×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #1395

Complements

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

NH ≅ G/Ntype
4. #13068838C2semidirect
5. #13068835C2semidirect
6. #13066744C2semidirect
7. C11×#1395C2semidirect
27. #10622116C4semidirect
28. #10622115C4semidirect
132. #1395D11semidirect
312. C11#12975semidirect

Maximal subgroups

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

subgroupindex
#130776802
#130702992
#130689972
#130688382
#130688352
#130667442
C11×#13952
#1297511