Finite Group Databasebeta

← #14643036

Subgroups — #14643036

Order 2816.

446 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 91 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#13070179C211yesmaximal, characteristic, complemented
2#13070154C211yesmaximal, characteristic, complemented
3#13070149C211yesmaximal, characteristic
4#13066442C211yesmaximal, characteristic, complemented
5#13066439C211yesmaximal, characteristic, complemented
6#13066437C211yesmaximal, characteristic
7C11×#2732C211yesmaximal, characteristic
8C2×C11×C22⋊Q8—21no—
9C11×#399—21no—
10C11×#398—21no—
11C11×#396—21no—
12C11×#391C2211yescharacteristic
13C11×#390C2211yescharacteristic
14C11×#389C2211yescharacteristic
15C11×#386—21no—
16C11×#385—21no—
17C2×#66899—21no—
18C2×#66896—21no—
19C2×#66872—21no—
20C2×#66871—21no—
21#10622548C2211yescharacteristic
22#10622167—21no—
23#10622167—21no—
24#10622162C2211yescharacteristic
25#10622162C2211yescharacteristic
26#10622162C2211yescharacteristic
27C22×Q8×C11D411yescharacteristic
28C22×D4×C11D411yescharacteristic
29C23×C4×C11—21no—
30C11×C22⋊Q8—42no—
31C11×C22⋊Q8—42no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4D411yescharacteristic
37C2×C11×C4⋊C4D411yescharacteristic
38C2×C11×C4⋊C4D411yescharacteristic
39C2×C11×C4⋊C4D411yescharacteristic
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4—21no—
44C2×C11×C22⋊C4—21no—
45C2×C42×C11C2311yescharacteristic
46C2×C4⋊Dic11—21no—
47C2×C4⋊Dic11—21no—
48C2×C4⋊Dic11—21no—
49C22×C11⋊C8—21no—
50C22×C11⋊C8—21no—
51C22×C11⋊C8—21no—
52C11×#95—21no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95—21no—
56#66899—42no—
57#66896—42no—
58#66872—42no—
59#66871—42no—
60#7823—111nomaximal, Sylow
61C24×C11—21no—
62C2×Q8×C11—21no—
63C2×Q8×C11—41no—
64C2×Q8×C11—41no—
65C2×Q8×C11SD1612yes—
66C2×D4×C11—21no—
67C2×D4×C11—41no—
68C2×D4×C11—41no—
69C2×D4×C11Q1612yes—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—42no—
76C22×C4×C11—81no—
77C22×C4×C11—81no—
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×Dic11—41no—
82C11×C4⋊C4—21no—
83C11×C4⋊C4—21no—
84C11×C4⋊C4—42no—
85C11×C4⋊C4—42no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—81no—
92C11×C22⋊C4—42no—
93C11×C22⋊C4—41no—
94C11×C22⋊C4—41no—
95C11×C22⋊C4—41no—
96C11×C22⋊C4—41no—
97C11×C22⋊C4—81no—
98C11×C22⋊C4—81no—
99C42×C11—41no—
100C4⋊Dic11—41no—
101C4⋊Dic11—41no—
102C4⋊Dic11—41no—
103C4⋊Dic11—41no—
104C4⋊Dic11—42no—
105C2×C11⋊C8—22no—
106C2×C11⋊C8—22no—
107C2×C11⋊C8—41no—
108C2×C11⋊C8—41no—
109C2×C11⋊C8—41no—
110C2×C11⋊C8—41no—
111C2×C11⋊C8—41no—
112C2×C11⋊C8—41no—
113C2×C11⋊C8—41no—
114#2732D1111yescharacteristic
115#2100—111no—
116#2095—111no—
117#2094—111no—
118#1272—111no—
119#1271—111no—
120#1270—111no—
121C23×C11—22no—
122C23×C11—41no—
123C23×C11—41no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11—41no—
127C23×C11—41no—
128C23×C11#12011yescharacteristic
129Q8×C11—42no—
130Q8×C11—81no—
131D4×C11—42no—
132D4×C11—81no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—22no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—84no—
155C2×C4×C11C2×SD1611yescharacteristic
156C2×C4×C11C2×Q1611yescharacteristic
157C2×C4×C11#13511yescharacteristic
158C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C11#13711yescharacteristic
160C2×C4×C11#13711yescharacteristic
161C2×Dic11—81no—
162C2×Dic11—81no—
163C2×Dic11—81no—
164C11⋊C8—42no—
165C11⋊C8—42no—
166C11⋊C8—81no—
167C2×C22⋊Q8—21no—
168C2×#107—221no—
169C2×#106—221no—
170C2×#103—221no—
171C2×#102—221no—
172#399—21no—
173#398—21no—
174#396—21no—
175#391C2×D1111yescharacteristic
176#390C2×D1111yescharacteristic
177#389C2×D1111yescharacteristic
178#386—21no—
179#385—21no—
180#384—111no—
181#340—221no—
182#340—221no—
183#336—111no—
184#336—111no—
185#336—111no—
186C22×C11—42no—
187C22×C11—42no—
188C22×C11—42no—
189C22×C11—81no—
190C22×C11—81no—
191C22×C11—81no—
192C22×C11—81no—
193C22×C11#45011yescharacteristic
194C22×C11#45111yescharacteristic
195C22×C11#45211yescharacteristic
196C22×C11#45311yescharacteristic
197C22×C11#45311yescharacteristic
198C22×C11#45411yescharacteristic
199C22×C11#45811yescharacteristic
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—42no—
207C4×C11—81no—
208C4×C11—81no—
209C4×C11—81no—
210C4×C11—81no—
211Dic11—161no—
212C22×Q8C22⋊D1111yescharacteristic
213C22×D4C22⋊D1111yescharacteristic
214C23×C4—21no—
215C22×C8—221no—
216C22×C8—221no—
217C22×C8—221no—
218C22⋊Q8—42no—
219C22⋊Q8—42no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—221no—
225C2×C4⋊C4—221no—
226C2×C4⋊C4—221no—
227C2×C4⋊C4C22⋊D1111yescharacteristic
228C2×C4⋊C4C22⋊D1111yescharacteristic
229C2×C4⋊C4C22⋊D1111yescharacteristic
230C2×C4⋊C4C22⋊D1111yescharacteristic
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C42C22×D1111yescharacteristic
237#107—442no—
238#106—442no—
239#103—442no—
240#102—442no—
241#95—21no—
242#95—21no—
243#95—21no—
244#95—21no—
245C2×C11—82no—
246C2×C11#161311yescharacteristic
247C2×C11#161411yescharacteristic
248C2×C11#161511yescharacteristic
249C2×C11#163111yescharacteristic
250C2×C11#163211yescharacteristic
251C2×C11#163711yescharacteristic
252C2×C11#165611yescharacteristic
253C24—21no—
254C2×Q8—21no—
255C2×Q8—41no—
256C2×Q8—41no—
257C2×Q8#432412yes—
258C2×D4—21no—
259C2×D4—41no—
260C2×D4—41no—
261C2×D4#432612yes—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—42no—
268C22×C4—81no—
269C22×C4—81no—
270C22×C4—441no—
271C22×C4C2×C22⋊D1111yescharacteristic
272C22×C4C2×C22⋊D1111yescharacteristic
273C22×C4C2×C22⋊D1111yescharacteristic
274C2×C8—222no—
275C2×C8—222no—
276C2×C8—441no—
277C2×C8—441no—
278C2×C8—441no—
279C2×C8—441no—
280C2×C8—441no—
281C2×C8—441no—
282C2×C8—441no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—42no—
289C4⋊C4—42no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—81no—
293C4⋊C4—441no—
294C4⋊C4—441no—
295C4⋊C4—441no—
296C4⋊C4—441no—
297C4⋊C4—442no—
298C22⋊C4—42no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—41no—
302C22⋊C4—41no—
303C22⋊C4—81no—
304C22⋊C4—81no—
305C42—41no—
306C11#782311yescharacteristic, complemented, Sylow
307C23—22no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23#6700611yescharacteristic
315Q8—42no—
316Q8—81no—
317D4—42no—
318D4—81no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—22no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—84no—
341C2×C4—881no—
342C2×C4—881no—
343C2×C4—881no—
344C2×C4#6698511yescharacteristic
345C2×C4C2×#432411yescharacteristic
346C2×C4#6699511yescharacteristic
347C2×C4C2×#432611yescharacteristic
348C2×C4#6700311yescharacteristic
349C2×C4#6700411yescharacteristic
350C8—442no—
351C8—442no—
352C8—881no—
353C22—42no—
354C22—42no—
355C22—42no—
356C22—81no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22#1062283111yescharacteristic
361C22#1062284111yescharacteristic
362C22#1062285211yescharacteristic
363C22#1062285411yescharacteristic
364C22#1062285411yescharacteristic
365C22#1062285611yescharacteristic
366C22#1062285811yescharacteristic
367C4—21no—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—42no—
374C4—81no—
375C4—81no—
376C4—81no—
377C4—81no—
378C4—1761no—
379C2—82no—
380C2#1306763611yescharacteristic
381C2#1306764111yescharacteristic
382C2#1306764711yescharacteristic
383C2#1306774311yescharacteristic
384C2#1306775011yescharacteristic
385C2#1306778111yescharacteristic
386C2#1306790911yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2732C2
socleC23×C11#120
prime radicalC22×D4×C11D4
hypercenter#2732D11
hypocenterC11#7823
LCSG ▷ C2×C42×C11 ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2732

Complements

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

NH ≅ G/Ntype
1. #13070179C2semidirect
2. #13070154C2semidirect
4. #13066442C2semidirect
5. #13066439C2semidirect
306. C11#7823semidirect

Maximal subgroups

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

subgroupindex
#130701792
#130701542
#130701492
#130664422
#130664392
#130664372
C11×#27322
#782311