Finite Group Databasebeta

← #14658149

Subgroups — #14658149

Order 2816.

438 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 81 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#13069085C211yesmaximal, characteristic
2#13069050C211yesmaximal, characteristic
3#13068820C211yesmaximal, characteristic
4#13067188C211yesmaximal, characteristic
5#13066980C211yesmaximal, characteristic
6#13066521C211yesmaximal, characteristic
7C11×#3195C211yesmaximal, characteristic
8C2×C11×C22⋊Q8C2211yescharacteristic
9C2×C11×C22⋊Q8C2211yescharacteristic
10C22×#4318C2211yescharacteristic
11C11×#483—21no—
12C11×#483—21no—
13C11×#470—21no—
14C11×#470—21no—
15C11×#451—21no—
16C11×#451—21no—
17C11×#407C2211yescharacteristic
18C2×#66900—21no—
19C2×#66899—21no—
20#10622825C2211yescharacteristic
21#10622820C2211yescharacteristic
22C2×C22⋊(C11⋊C8)C2211yescharacteristic
23C2×#66886—21no—
24#10622196—21no—
25#10622176—22no—
26#10622168—21no—
27#10622167—21no—
28#10622166—22no—
29C22×Q8×C11D411yescharacteristic
30C22×Q8×C11D411yescharacteristic
31C23×C4×C11C2311yescharacteristic
32C2×C11×Q16—21no—
33C2×C11×Q16—21no—
34C2×C11×M16D411yescharacteristic
35C2×C11×M16D411yescharacteristic
36C11×C22⋊Q8—21no—
37C11×C22⋊Q8—21no—
38C11×C22⋊Q8—21no—
39C11×C22⋊Q8—21no—
40C11×C22⋊Q8—21no—
41C11×C22⋊Q8—21no—
42C11×C22⋊Q8—21no—
43C11×C22⋊Q8—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4D411yescharacteristic
47C2×C11×C4⋊C4D411yescharacteristic
48C2×C11×C22⋊C4—21no—
49C2×C11×C22⋊C4—21no—
50C2×C22⋊Dic11—21no—
51C2×C4⋊Dic11—21no—
52C2×#4318—21no—
53C2×#4318—21no—
54C2×#4318—21no—
55C2×#4318—42no—
56C22×C11⋊C8—21no—
57C22×C11⋊C8—21no—
58C11×#106—21no—
59C11×#106—21no—
60C11×#103—21no—
61C11×#103—21no—
62C11×#103—21no—
63C11×#103—21no—
64C11×C22⋊C8—21no—
65C11×C22⋊C8—21no—
66#66900—42no—
67#66899—42no—
68C11⋊#95—21no—
69C22⋊(C11⋊C8)—21no—
70C22⋊(C11⋊C8)—21no—
71C22⋊(C11⋊C8)—21no—
72C22⋊(C11⋊C8)D412yes—
73#66886—42no—
74#10563—111nomaximal, Sylow
75C24×C11#4111yescharacteristic
76C2×Q8×C11—21no—
77C2×Q8×C11—21no—
78C2×Q8×C11—21no—
79C2×Q8×C11—21no—
80C2×Q8×C11—41no—
81C2×Q8×C11—41no—
82C2×Q8×C11—41no—
83C2×Q8×C11—41no—
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—21no—
88C22×C4×C11—41no—
89C22×C4×C11—41no—
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11#4111yescharacteristic
95C22×C4×C11#4111yescharacteristic
96C22×Dic11—41no—
97C11×Q16—81no—
98C11×Q16—81no—
99C11×M16—41no—
100C11×M16—41no—
101C2×C8×C11—21no—
102C2×C8×C11—21no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4—41no—
111C11×C22⋊C4—41no—
112C11×C22⋊C4—41no—
113C11×C22⋊C4—41no—
114C11×C22⋊C4—41no—
115C22⋊Dic11—81no—
116C4⋊Dic11—41no—
117C4⋊Dic11—41no—
118#4318—22no—
119#4318—22no—
120#4318—41no—
121#4318—41no—
122#4318—41no—
123#4318—41no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—41no—
127C2×C11⋊C8—41no—
128C2×C11⋊C8—41no—
129C2×C11⋊C8—41no—
130C2×C11⋊C8—41no—
131#3195D1111yescharacteristic
132#1901—111no—
133#1894—111no—
134#1855—111no—
135#1520—111no—
136#1472—111no—
137#1305—111no—
138C23×C11—21no—
139C23×C11—21no—
140C23×C11—41no—
141C23×C11—41no—
142C23×C11#12111yescharacteristic
143C23×C11#12311yescharacteristic
144C23×C11#12411yescharacteristic
145Q8×C11—42no—
146Q8×C11—41no—
147Q8×C11—41no—
148Q8×C11—41no—
149Q8×C11—41no—
150Q8×C11—81no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—42no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—81no—
168C2×C4×C11—81no—
169C2×C4×C11#12011yescharacteristic
170C2×C4×C11#12111yescharacteristic
171C2×C4×C11#12111yescharacteristic
172C2×C4×C11#12311yescharacteristic
173C2×Dic11—81no—
174C2×Dic11—81no—
175C2×Dic11—81no—
176C8×C11—41no—
177C8×C11—41no—
178C11⋊C8—42no—
179C11⋊C8—42no—
180C11⋊C8—81no—
181C22×M16—111no—
182C2×C22⋊Q8C2×D1111yescharacteristic
183C2×C22⋊Q8C2×D1111yescharacteristic
184#483—21no—
185#483—21no—
186#470—21no—
187#470—21no—
188#451—21no—
189#451—21no—
190C2×#108—221no—
191C2×#103—221no—
192C2×#101—221no—
193#407—111no—
194#407C2×D1111yescharacteristic
195C2×C22⋊C8—111no—
196#380—111no—
197#343—221no—
198#341—221no—
199#340—221no—
200#328—222no—
201#324—222no—
202C22×C11—21no—
203C22×C11—21no—
204C22×C11—21no—
205C22×C11—21no—
206C22×C11—21no—
207C22×C11—21no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—81no—
211C22×C11—81no—
212C22×C11#39411yescharacteristic
213C22×C11#47111yescharacteristic
214C22×C11#47311yescharacteristic
215C4×C11—21no—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—81no—
219C4×C11—81no—
220C4×C11—81no—
221C4×C11—81no—
222C4×C11B(4,𝔽2)11yescharacteristic
223C4×C11#45811yescharacteristic
224Dic11—161no—
225C22×Q8C22⋊D1111yescharacteristic
226C22×Q8C22⋊D1111yescharacteristic
227C23×C4C22×D1111yescharacteristic
228C2×Q16—21no—
229C2×Q16—21no—
230C2×M16—221no—
231C2×M16—221no—
232C2×M16—221no—
233C2×M16—442no—
234C2×M16C22⋊D1111yescharacteristic
235C2×M16C22⋊D1111yescharacteristic
236C22×C8—221no—
237C22×C8—221no—
238C22⋊Q8—21no—
239C22⋊Q8—21no—
240C22⋊Q8—21no—
241C22⋊Q8—21no—
242C22⋊Q8—21no—
243C22⋊Q8—21no—
244C22⋊Q8—21no—
245C22⋊Q8—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—221no—
249C2×C4⋊C4C22⋊D1111yescharacteristic
250C2×C4⋊C4C22⋊D1111yescharacteristic
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—221no—
254#108—442no—
255#106—21no—
256#106—21no—
257#103—21no—
258#103—21no—
259#103—21no—
260#103—21no—
261#103—442no—
262#101—442no—
263C22⋊C8—21no—
264C22⋊C8—21no—
265C22⋊C8—112no—
266C22⋊C8—221no—
267C22⋊C8—221no—
268C22⋊C8—221no—
269#95—221no—
270C2×C11—21no—
271C2×C11—21no—
272C2×C11—41no—
273C2×C11—41no—
274C2×C11#204411yescharacteristic
275C2×C11#204911yescharacteristic
276C2×C11#205211yescharacteristic
277C24#434111yescharacteristic
278C2×Q8—21no—
279C2×Q8—21no—
280C2×Q8—21no—
281C2×Q8—21no—
282C2×Q8—41no—
283C2×Q8—41no—
284C2×Q8—41no—
285C2×Q8—41no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—441no—
293C22×C4D4×D1111yescharacteristic
294C22×C4#434111yescharacteristic
295C22×C4#434111yescharacteristic
296C22×C4C2×C22⋊D1111yescharacteristic
297C22×C4C2×C22⋊D1111yescharacteristic
298C22×C4C2×C22⋊D1111yescharacteristic
299Q16—81no—
300Q16—81no—
301M16—41no—
302M16—41no—
303M16—222no—
304M16—222no—
305M16—441no—
306M16—441no—
307M16—441no—
308M16—441no—
309C2×C8—21no—
310C2×C8—21no—
311C2×C8—222no—
312C2×C8—222no—
313C2×C8—441no—
314C2×C8—441no—
315C2×C8—441no—
316C2×C8—441no—
317C2×C8—441no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—441no—
327C4⋊C4—441no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—881no—
333C11#1056311yescharacteristic, complemented, Sylow
334C23—21no—
335C23—21no—
336C23—41no—
337C23—41no—
338C23#6698811yescharacteristic
339C23#6698911yescharacteristic
340C23#6699211yescharacteristic
341Q8—42no—
342Q8—41no—
343Q8—41no—
344Q8—41no—
345Q8—41no—
346Q8—81no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—81no—
364C2×C4—81no—
365C2×C4—881no—
366C2×C4—881no—
367C2×C4—881no—
368C2×C4#6698811yescharacteristic
369C2×C4#6699111yescharacteristic
370C2×C4#6699211yescharacteristic
371C2×C4#6700611yescharacteristic
372C8—41no—
373C8—41no—
374C8—442no—
375C8—442no—
376C8—881no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—81no—
386C22—81no—
387C22#1062281611yescharacteristic
388C22#1062281711yescharacteristic
389C22#1062283511yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—81no—
394C4—81no—
395C4—81no—
396C4—81no—
397C4—1761no—
398C4#1062285611yescharacteristic
399C4#1062285711yescharacteristic
400C2—21no—
401C2—21no—
402C2—41no—
403C2—41no—
404C2#1306986411yescharacteristic
405C2#1306989311yescharacteristic
406C2#1306991211yescharacteristic
subgroupG/H
centerC22#10622835
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#3195C2
socleC22×C11#394
prime radicalC24×C11#41
hypercenter#3195D11
hypocenterC11#10563
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3195

Complements

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

NH ≅ G/Ntype
333. C11#10563semidirect

Maximal subgroups

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

subgroupindex
#130690852
#130690502
#130688202
#130671882
#130669802
#130665212
C11×#31952
#1056311