Finite Group Databasebeta

← #14657672

Subgroups — #14657672

Order 2816.

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

normal subgroups only

This group has 446 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#13069457C211yesmaximal, characteristic, complemented
2#13067404C211yesmaximal, characteristic, complemented
3#13067351C211yesmaximal, characteristic, complemented
4#13067284C211yesmaximal, characteristic, complemented
5#13067033C211yesmaximal, characteristic, complemented
6#13066507C211yesmaximal, characteristic, complemented
7C11×#3205C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×C11×#127C2211yescharacteristic
10C11×#493—21no—
11C11×#486—21no—
12C11×#459—21no—
13C11×#459—21no—
14C11×#447—22no—
15C11×#431C2211yescharacteristic
16C2×#66897—22no—
17#10622538C2211yescharacteristic
18#10622537C2211yescharacteristic
19#10622537C2211yescharacteristic
20C4×#4318C2211yescharacteristic
21#10622184—21no—
22#10622182—21no—
23#10622182—22no—
24D4⋊(C11⋊C8)—22no—
25#10622118—21no—
26#10622117—21no—
27C2×C11×#41—21no—
28C22×D4×C11—21no—
29C22×D4×C11—21no—
30C22×D4×C11D412yes—
31C2×C11×D8—22no—
32C2×C11×D8—22no—
33C11×C4⋊Q8D411yescharacteristic
34C11×#127—21no—
35C11×#127—21no—
36C11×#127—21no—
37C11×#127—21no—
38C11×#127D411yescharacteristic
39C11×#124—21no—
40C11×#121—21no—
41C11×#121—21no—
42C4×D4×C11—21no—
43C4×D4×C11—21no—
44C2×C42×C11C2311yescharacteristic
45C2×#4318—21no—
46C2×#4318—21no—
47C2×#4318—21no—
48C11×C4⋊C8D411yescharacteristic
49C11×C4⋊C8D411yescharacteristic
50C11×#102—22no—
51C11×#102—22no—
52C11×C22⋊C8—21no—
53C4×C8×C11—21no—
54#66897—44no—
55C22⋊(C11⋊C8)—21no—
56C4⋊(C11⋊C8)—21no—
57C4⋊(C11⋊C8)—21no—
58C4⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)D412yes—
61#66867—21no—
62C4×C11⋊C8—21no—
63C4×C11⋊C8—21no—
64#10488—111nomaximal, Sylow
65C24×C11—22no—
66C11×#41—82no—
67C2×Q8×C11—21no—
68C2×D4×C11—22no—
69C2×D4×C11—21no—
70C2×D4×C11—21no—
71C2×D4×C11—22no—
72C2×D4×C11—21no—
73C2×D4×C11—42no—
74C2×D4×C11—42no—
75C2×D4×C11—41no—
76C2×D4×C11—41no—
77C2×D4×C11—41no—
78C2×D4×C11—41no—
79C2×D4×C11—41no—
80C2×D4×C11—81no—
81C2×D4×C11—81no—
82C2×D4×C11—82no—
83C22×C4×C11—41no—
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11#4111yescharacteristic
86C22×C4×C11#4111yescharacteristic
87C11×D8—82no—
88C11×D8—82no—
89C2×C8×C11—21no—
90C2×C8×C11—21no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4—21no—
93C11×C22⋊C4—41no—
94C11×C22⋊C4—41no—
95C42×C11C2×D411yescharacteristic
96C42×C11C2×D411yescharacteristic
97C42×C11C2×D411yescharacteristic
98C42×C11#4111yescharacteristic
99#4318—22no—
100#4318—41no—
101#4318—42no—
102#4318—81no—
103C2×C11⋊C8—22no—
104C2×C11⋊C8—41no—
105C2×C11⋊C8—41no—
106C2×C11⋊C8—41no—
107#3205D1111yescharacteristic
108#1965—111no—
109#1574—111no—
110#1560—111no—
111#1545—111no—
112#1484—111no—
113#1299—111no—
114C23×C11—44no—
115C23×C11—41no—
116C23×C11—42no—
117C23×C11—82no—
118C23×C11—82no—
119C23×C11#12311yescharacteristic
120Q8×C11—81no—
121D4×C11—41no—
122D4×C11—42no—
123D4×C11—41no—
124D4×C11—42no—
125D4×C11—41no—
126D4×C11—41no—
127D4×C11—82no—
128D4×C11—81no—
129D4×C11—82no—
130D4×C11—82no—
131D4×C11—82no—
132D4×C11—81no—
133D4×C11—82no—
134D4×C11—81no—
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—82no—
142C2×C4×C11#12011yescharacteristic
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11#12111yescharacteristic
145C2×C4×C11#12111yescharacteristic
146C2×C4×C11#12311yescharacteristic
147C2×C4×C11#12411yescharacteristic
148C8×C11—41no—
149C8×C11—41no—
150C11⋊C8—42no—
151C11⋊C8—42no—
152C11⋊C8—81no—
153C11⋊C8—81no—
154#532C2×D1111yescharacteristic
155C2×#127C2×D1111yescharacteristic
156#493—21no—
157#486—21no—
158#459—21no—
159#459—21no—
160#447—22no—
161#431—111no—
162#431C2×D1111yescharacteristic
163#423—111no—
164#423—111no—
165C2×#100—222no—
166C4×M16—111no—
167#335—221no—
168#334—221no—
169#333—221no—
170#331—222no—
171#331—221no—
172D4⋊C8—222no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—81no—
177C22×C11—82no—
178C22×C11—82no—
179C22×C11—81no—
180C22×C11—81no—
181C22×C11—82no—
182C22×C11—164no—
183C22×C11#39411yescharacteristic
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—21no—
187C4×C11—81no—
188C4×C11#45311yescharacteristic
189C4×C11#45511yescharacteristic
190C4×C11#47111yescharacteristic
191C4×C11#47212yes—
192C4×C11#47211yescharacteristic
193C2×#41—21no—
194C22×D4—21no—
195C22×D4—21no—
196C22×D4C22⋊D1112yes—
197C2×D8—22no—
198C2×D8—22no—
199C2×M16—221no—
200C2×M16—221no—
201C2×M16—221no—
202C4⋊Q8C22⋊D1111yescharacteristic
203#127—21no—
204#127—21no—
205#127—21no—
206#127—21no—
207#127C22⋊D1111yescharacteristic
208#124—21no—
209#121—21no—
210#121—21no—
211C4×D4—21no—
212C4×D4—21no—
213C2×C42C22×D1111yescharacteristic
214C4⋊C8—112no—
215C4⋊C8—221no—
216C4⋊C8—221no—
217C4⋊C8—221no—
218C4⋊C8—221no—
219C4⋊C8C22⋊D1111yescharacteristic
220C4⋊C8C22⋊D1111yescharacteristic
221#102—22no—
222#102—22no—
223#100—444no—
224C22⋊C8—21no—
225C22⋊C8—221no—
226#97—221no—
227C4×C8—21no—
228C4×C8—221no—
229C4×C8—221no—
230C2×C11—41no—
231C2×C11—161no—
232C2×C11—162no—
233C2×C11#203711yescharacteristic
234C2×C11#204511yescharacteristic
235C2×C11#205111yescharacteristic
236C24—22no—
237#41—82no—
238C2×Q8—21no—
239C2×D4—21no—
240C2×D4—21no—
241C2×D4—22no—
242C2×D4—22no—
243C2×D4—21no—
244C2×D4—42no—
245C2×D4—42no—
246C2×D4—41no—
247C2×D4—41no—
248C2×D4—41no—
249C2×D4—41no—
250C2×D4—41no—
251C2×D4—82no—
252C2×D4—81no—
253C2×D4—81no—
254C22×C4—41no—
255C22×C4#434111yescharacteristic
256C22×C4#434111yescharacteristic
257C22×C4C2×C22⋊D1111yescharacteristic
258D8—82no—
259D8—82no—
260M16—222no—
261M16—441no—
262M16—442no—
263M16—881no—
264C2×C8—21no—
265C2×C8—21no—
266C2×C8—222no—
267C2×C8—441no—
268C2×C8—441no—
269C2×C8—441no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C22⋊C4—41no—
273C22⋊C4—41no—
274C42D4×D1111yescharacteristic
275C42#434111yescharacteristic
276C42C2×C22⋊D1111yescharacteristic
277C42C2×C22⋊D1111yescharacteristic
278C11#1048811yescharacteristic, complemented, Sylow
279C23—44no—
280C23—41no—
281C23—42no—
282C23—82no—
283C23—82no—
284C23#6698811yescharacteristic
285Q8—81no—
286D4—41no—
287D4—41no—
288D4—41no—
289D4—42no—
290D4—41no—
291D4—42no—
292D4—82no—
293D4—81no—
294D4—82no—
295D4—82no—
296D4—82no—
297D4—82no—
298D4—81no—
299D4—81no—
300C2×C4—22no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—41no—
306C2×C4—82no—
307C2×C4#6698811yescharacteristic
308C2×C4#6698911yescharacteristic
309C2×C4#6699111yescharacteristic
310C2×C4#6699211yescharacteristic
311C2×C4#6699211yescharacteristic
312C2×C4#6700611yescharacteristic
313C8—41no—
314C8—41no—
315C8—442no—
316C8—442no—
317C8—881no—
318C8—881no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—81no—
323C22—82no—
324C22—81no—
325C22—82no—
326C22—82no—
327C22—81no—
328C22—164no—
329C22#1062283511yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—81no—
334C4#1062277312yes—
335C4#1062281211yescharacteristic
336C4#1062281311yescharacteristic
337C4#1062285411yescharacteristic
338C4#1062285511yescharacteristic
339C2—41no—
340C2—162no—
341C2—161no—
342C2#1306982311yescharacteristic
343C2#1306986911yescharacteristic
344C2#1306990511yescharacteristic
subgroupG/H
centerC22#10622835
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
Fitting, prime radicalC11×#3205C2
socleC22×C11#394
hypercenter#3205D11
hypocenterC11#10488
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3205

Complements

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

NH ≅ G/Ntype
1. #13069457C2semidirect
2. #13067404C2semidirect
3. #13067351C2semidirect
4. #13067284C2semidirect
5. #13067033C2semidirect
6. #13066507C2semidirect
278. C11#10488semidirect

Maximal subgroups

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

subgroupindex
#130694572
#130674042
#130673512
#130672842
#130670332
#130665072
C11×#32052
#1048811