Finite Group Databasebeta

← #14655416

Subgroups — #14655416

Order 2816.

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

normal subgroups only

This group has 498 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#13079554C211yesmaximal, characteristic
2C2×#10622680C211yesmaximal, characteristic
3#13067329C211yesmaximal, characteristic
4#13067231C211yesmaximal, characteristic, complemented
5#13066972C211yesmaximal, characteristic, complemented
6#13066514C211yesmaximal, characteristic, complemented
7C11×#3236C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×C11×#125C2211yescharacteristic
10C2×#66927C2211yescharacteristic
11C11×#501—21no—
12C11×#491—21no—
13C11×#484—21no—
14C11×#483—21no—
15C11×#479—22no—
16C11×#432C2211yescharacteristic
17#10622701—21no—
18#10622698—21no—
19#10622680—22no—
20#10622680—22no—
21#10622659—22no—
22#10622640—22no—
23C2×#66873—21no—
24C2×#66873—21no—
25#10622539C2211yescharacteristic
26#10622538C2211yescharacteristic
27C2×#66867C2211yescharacteristic
28#10622181—22no—
29#10622166—22no—
30#10622123—22no—
31C22×D44—21no—
32C22×D44—21no—
33C22×D44—21no—
34C11×C4⋊Q8D411yescharacteristic
35C11×C4⋊Q8D411yescharacteristic
36C11×#125—21no—
37C11×#125—21no—
38C11×#125—21no—
39C11×#125—21no—
40C11×#125—21no—
41C11×C22⋊Q8—21no—
42C11×C22⋊Q8—21no—
43C4×Q8×C11—21no—
44C4×Q8×C11—21no—
45C11×#117—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4D411yescharacteristic
49C2×C11×C4⋊C4D411yescharacteristic
50C2×C42×C11C2311yescharacteristic
51C2×#4325—24no—
52C22×C11⋊C8—21no—
53#66927—21no—
54#66927—21no—
55#66927—21no—
56#66927D412yes—
57C11×#107—22no—
58C11×#106—22no—
59C11×C4⋊C8D412yes—
60C11×#103—22no—
61C11×#103—22no—
62C11×C22⋊C8—21no—
63C11×#97—21no—
64C22⋊(C11⋊C8)—21no—
65C22⋊(C11⋊C8)D412yes—
66#66873—24no—
67#66873—24no—
68#66873—24no—
69C4⋊(C11⋊C8)—21no—
70C4⋊(C11⋊C8)—21no—
71#66867—21no—
72#66867—21no—
73#66867D412yes—
74C4×C11⋊C8—21no—
75#10131—111nomaximal, Sylow
76C23×D11—41no—
77C2×Q8×C11—21no—
78C2×Q8×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11#4111yescharacteristic
84C2×D44—22no—
85C2×D44—22no—
86C2×D44—22no—
87C2×D44—44no—
88C2×D44—41no—
89C2×D44—41no—
90C2×D44—41no—
91C2×D44—82no—
92C2×D44—82no—
93C2×C8×C11—22no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C22⋊C4—41no—
109C42×C11—41no—
110C42×C11C2×D411yescharacteristic
111C42×C11C2×D411yescharacteristic
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114#4325—84no—
115C2×C11⋊C8—22no—
116C2×C11⋊C8—22no—
117C2×C11⋊C8—42no—
118C2×C11⋊C8—41no—
119#3236D1111yescharacteristic, complemented
120#3208—111no—
121C2×#490—111no—
122#1555—111no—
123#1531—111no—
124#1470—111no—
125#1302—111no—
126C23×C11#12111yescharacteristic
127C22×D11—42no—
128C22×D11—82no—
129C22×D11—82no—
130C22×D11—82no—
131Q8×C11—42no—
132Q8×C11—42no—
133C2×C4×C11—22no—
134C2×C4×C11—22no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—42no—
141C2×C4×C11—81no—
142C2×C4×C11#12011yescharacteristic
143C2×C4×C11#12011yescharacteristic
144C2×C4×C11#12011yescharacteristic
145C2×C4×C11#12111yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12711yescharacteristic
148D44—44no—
149D44—44no—
150D44—82no—
151D44—82no—
152D44—82no—
153D44—82no—
154C8×C11—42no—
155C11⋊C8—42no—
156C11⋊C8—42no—
157C11⋊C8—81no—
158#533C2×D1111yescharacteristic
159C2×#127—111no—
160C2×#125C2×D1111yescharacteristic
161#501—21no—
162#492—221no—
163#491—21no—
164#490—222no—
165#490—222no—
166#486—221no—
167#484—21no—
168#483—21no—
169#479—22no—
170#460—222no—
171#450—222no—
172#432—111no—
173#432C2×D1111yescharacteristic
174#431—111no—
175C2×#102—221no—
176C2×#102—221no—
177C2×#97—111no—
178#331—222no—
179#330—222no—
180#324—222no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11#39211yescharacteristic
184C22×C11#47112yes—
185C2×D11—82no—
186C2×D11—82no—
187C2×D11—82no—
188C2×D11—164no—
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—81no—
195C4×C11—81no—
196C4×C11—81no—
197C4×C11—81no—
198C4×C11#45412yes—
199C22×D4—221no—
200C22×D4—221no—
201C22×D4—221no—
202C2×SD16—224no—
203C22×C8—221no—
204C4⋊Q8C22⋊D1111yescharacteristic
205C4⋊Q8C22⋊D1111yescharacteristic
206#127—112no—
207#127—221no—
208#127—221no—
209#127—221no—
210#125—21no—
211#125—21no—
212#125—21no—
213#125—21no—
214#125—21no—
215C22⋊Q8—21no—
216C22⋊Q8—21no—
217C4×Q8—21no—
218C4×Q8—21no—
219#117—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4C22⋊D1111yescharacteristic
223C2×C4⋊C4C22⋊D1111yescharacteristic
224C2×C42C22×D1111yescharacteristic
225#107—22no—
226#106—22no—
227C4⋊C8—221no—
228C4⋊C8—221no—
229C4⋊C8C22⋊D1112yes—
230#103—22no—
231#103—22no—
232#102—224no—
233#102—224no—
234#102—224no—
235C22⋊C8—21no—
236C22⋊C8—112no—
237C22⋊C8—221no—
238#97—21no—
239#97—112no—
240#97—221no—
241#97—221no—
242C4×C8—221no—
243C2×C11—22no—
244C2×C11#200311yescharacteristic
245C2×C11#200811yescharacteristic
246C2×C11#201911yescharacteristic
247D11—162no—
248C24—441no—
249C2×Q8—21no—
250C2×Q8—21no—
251C2×D4—222no—
252C2×D4—222no—
253C2×D4—222no—
254C2×D4—444no—
255C2×D4—441no—
256C2×D4—441no—
257C2×D4—441no—
258C2×D4—882no—
259C2×D4—882no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4D4×D1111yescharacteristic
263C22×C4#434111yescharacteristic
264C22×C4C2×C22⋊D1111yescharacteristic
265SD16—884no—
266C2×C8—22no—
267C2×C8—222no—
268C2×C8—222no—
269C2×C8—442no—
270C2×C8—441no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C22⋊C4—41no—
286C42—41no—
287C42D4×D1111yescharacteristic
288C42D4×D1111yescharacteristic
289C42C2×C22⋊D1111yescharacteristic
290C42C2×C22⋊D1111yescharacteristic
291C11#1013111yescharacteristic, complemented, Sylow
292C23—442no—
293C23—882no—
294C23—882no—
295C23—882no—
296C23#6699211yescharacteristic
297Q8—42no—
298Q8—42no—
299D4—444no—
300D4—444no—
301D4—882no—
302D4—882no—
303D4—882no—
304D4—882no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—41no—
308C2×C4—42no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—81no—
314C2×C4#6699011yescharacteristic
315C2×C4#6699011yescharacteristic
316C2×C4#6699111yescharacteristic
317C2×C4#6699211yescharacteristic
318C2×C4#6699311yescharacteristic
319C2×C4#6700611yescharacteristic
320C8—42no—
321C8—442no—
322C8—442no—
323C8—881no—
324C22—21no—
325C22—21no—
326C22—882no—
327C22—882no—
328C22—882no—
329C22—1764no—
330C22#1062281612yes—
331C22#1062283611yescharacteristic
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—21no—
337C4—81no—
338C4—81no—
339C4—81no—
340C4—81no—
341C4#1062285812yes—
342C2—22no—
343C2—1762no—
344C2#1306963611yescharacteristic
345C2#1306966611yescharacteristic
346C2#1306972711yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3236C2
socleC22×C11#392
prime radicalC2×#66927C22
hypercenter#3236D11
hypocenterC11#10131
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3236

Complements

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

NH ≅ G/Ntype
4. #13067231C2semidirect
5. #13066972C2semidirect
6. #13066514C2semidirect
7. C11×#3236C2semidirect
119. #3236D11semidirect
291. C11#10131semidirect

Maximal subgroups

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

subgroupindex
#130795542
C2×#106226802
#130673292
#130672312
#130669722
#130665142
C11×#32362
#1013111