Finite Group Databasebeta

← #14655542

Subgroups — #14655542

Order 2816.

528 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 105 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#13078992C211yesmaximal, characteristic
2C2×#10622701C211yesmaximal, characteristic
3#13069606C211yesmaximal, characteristic, complemented
4#13067283C211yesmaximal, characteristic
5#13067071C211yesmaximal, characteristic, complemented
6#13066452C211yesmaximal, characteristic, complemented
7C11×#3230C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×#66927C2211yescharacteristic
11C11×#500—21no—
12C11×#487—21no—
13C11×#484—22no—
14C11×#477—22no—
15C11×#431C2211yescharacteristic
16#10622701—21no—
17#10622701—21no—
18#10622701—22no—
19#10622701—22no—
20#10622680—22no—
21#10622614—22no—
22C2×#66873—22no—
23#10622537C2211yescharacteristic
24C4×#4318C2211yescharacteristic
25C2×C4×C11⋊C8C2211yescharacteristic
26Q8⋊(C11⋊C8)—22no—
27#10622168—22no—
28#10622123—22no—
29C22×Q8×C11—21no—
30C22×D44—21no—
31C22×D44—21no—
32C22×D44—21no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8D411yescharacteristic
38C11×C4⋊Q8D411yescharacteristic
39C11×#125—21no—
40C11×C22⋊Q8—21no—
41C11×C22⋊Q8—21no—
42C4×Q8×C11—21no—
43C4×Q8×C11—21no—
44C11×#117—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4D412yes—
47C2×C42×C11C2311yescharacteristic
48C2×#4318—21no—
49C2×#4318D412yes—
50C22×C11⋊C8—21no—
51#66927—21no—
52#66927—21no—
53#66927—21no—
54#66927D412yes—
55C11×#107—24no—
56C11×C4⋊C8D412yes—
57C11×#103—24no—
58C11×C22⋊C8—21no—
59C4×C8×C11—21no—
60#66873—28no—
61#66873—24no—
62#66873—24no—
63C4⋊(C11⋊C8)—21no—
64C4⋊(C11⋊C8)—21no—
65#66867—21no—
66C4×C11⋊C8—21no—
67C4×C11⋊C8—21no—
68C4×C11⋊C8D412yes—
69#10149—111nomaximal, Sylow
70C23×D11—41no—
71C2×Q8×C11—21no—
72C2×Q8×C11—21no—
73C2×Q8×C11—41no—
74C2×Q8×C11—41no—
75C2×Q8×C11—82no—
76C22×C4×C11—22no—
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11#4111yescharacteristic
80C2×D44—22no—
81C2×D44—22no—
82C2×D44—22no—
83C2×D44—44no—
84C2×D44—41no—
85C2×D44—41no—
86C2×D44—41no—
87C2×D44—42no—
88C2×D44—42no—
89C2×D44—82no—
90C2×C8×C11—22no—
91C11×C4⋊C4—22no—
92C11×C4⋊C4—21no—
93C11×C4⋊C4—21no—
94C11×C4⋊C4—22no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C11×C22⋊C4—41no—
102C42×C11—41no—
103C42×C11C2×D411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C42×C11C2×D411yescharacteristic
107#4318—22no—
108#4318—22no—
109#4318—42no—
110C2×C11⋊C8—22no—
111C2×C11⋊C8—22no—
112C2×C11⋊C8—42no—
113C2×C11⋊C8—41no—
114#3230D1111yescharacteristic, complemented
115#3138—111no—
116C2×#486—111no—
117#1997—111no—
118#1545—111no—
119#1493—111no—
120#1278—111no—
121C23×C11#12111yescharacteristic
122C22×D11—42no—
123C22×D11—82no—
124C22×D11—82no—
125C22×D11—82no—
126Q8×C11—42no—
127Q8×C11—42no—
128Q8×C11—82no—
129Q8×C11—82no—
130C2×C4×C11—22no—
131C2×C4×C11—22no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—42no—
135C2×C4×C11—82no—
136C2×C4×C11#12011yescharacteristic
137C2×C4×C11#12011yescharacteristic
138C2×C4×C11#12011yescharacteristic
139C2×C4×C11#12111yescharacteristic
140C2×C4×C11#12111yescharacteristic
141C2×C4×C11#12711yescharacteristic
142C2×C4×C11#13512yes—
143C2×C4×C11#13712yes—
144D44—44no—
145D44—44no—
146D44—82no—
147D44—82no—
148D44—82no—
149D44—81no—
150D44—81no—
151C8×C11—42no—
152C11⋊C8—42no—
153C11⋊C8—42no—
154C11⋊C8—81no—
155#533C2×D1111yescharacteristic
156C2×C4⋊Q8C2×D1111yescharacteristic
157C2×#127—111no—
158#500—21no—
159#490—222no—
160#487—21no—
161#486—222no—
162#486—222no—
163#486—221no—
164#486—221no—
165#484—22no—
166#477—22no—
167#431C2×D1111yescharacteristic
168#423—111no—
169#418—222no—
170C2×#102—222no—
171C4×M16—111no—
172C2×C4×C8—111no—
173#343—222no—
174#331—222no—
175Q8⋊C8—222no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11#39211yescharacteristic
179C22×C11#46412yes—
180C2×D11—82no—
181C2×D11—82no—
182C2×D11—82no—
183C2×D11—164no—
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—81no—
187C4×C11—82no—
188C4×C11—81no—
189C4×C11#45212yes—
190C4×C11#45412yes—
191C4×C11#47212yes—
192C4×C11#49511yescharacteristic
193C4×C11#49711yescharacteristic
194C22×Q8—21no—
195C22×D4—221no—
196C22×D4—221no—
197C22×D4—221no—
198C2×M16—112no—
199C2×M16—221no—
200C22×C8—221no—
201C4⋊Q8—21no—
202C4⋊Q8—21no—
203C4⋊Q8—21no—
204C4⋊Q8—21no—
205C4⋊Q8C22⋊D1111yescharacteristic
206C4⋊Q8C22⋊D1111yescharacteristic
207#127—112no—
208#127—221no—
209#127—221no—
210#127—221no—
211#125—21no—
212C22⋊Q8—21no—
213C22⋊Q8—21no—
214C4×Q8—21no—
215C4×Q8—21no—
216#117—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4C22⋊D1112yes—
219C2×C42C22×D1111yescharacteristic
220#107—24no—
221C4⋊C8—221no—
222C4⋊C8—221no—
223C4⋊C8C22⋊D1112yes—
224#103—24no—
225#102—228no—
226#102—224no—
227#102—224no—
228C22⋊C8—21no—
229#97—221no—
230C4×C8—21no—
231C4×C8—112no—
232C4×C8—221no—
233C4×C8—221no—
234C2×C11—22no—
235C2×C11#200311yescharacteristic
236C2×C11#201511yescharacteristic
237C2×C11#201811yescharacteristic
238D11—162no—
239C24—441no—
240C2×Q8—21no—
241C2×Q8—21no—
242C2×Q8—41no—
243C2×Q8—41no—
244C2×Q8—82no—
245C2×D4—222no—
246C2×D4—222no—
247C2×D4—222no—
248C2×D4—444no—
249C2×D4—442no—
250C2×D4—442no—
251C2×D4—441no—
252C2×D4—441no—
253C2×D4—441no—
254C2×D4—882no—
255C22×C4—22no—
256C22×C4D4×D1111yescharacteristic
257C22×C4#434111yescharacteristic
258C22×C4C2×C22⋊D1111yescharacteristic
259M16—222no—
260M16—222no—
261M16—442no—
262C2×C8—22no—
263C2×C8—222no—
264C2×C8—222no—
265C2×C8—442no—
266C2×C8—441no—
267C4⋊C4—22no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—22no—
272C4⋊C4—21no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C22⋊C4—41no—
278C42—41no—
279C42D4×D1111yescharacteristic
280C42D4×D1111yescharacteristic
281C42C2×C22⋊D1111yescharacteristic
282C42C2×C22⋊D1111yescharacteristic
283C11#1014911yescharacteristic, complemented, Sylow
284C23—442no—
285C23—882no—
286C23—882no—
287C23—882no—
288C23#6699211yescharacteristic
289Q8—42no—
290Q8—42no—
291Q8—82no—
292Q8—82no—
293D4—444no—
294D4—444no—
295D4—882no—
296D4—881no—
297D4—881no—
298D4—882no—
299D4—882no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—42no—
305C2×C4—82no—
306C2×C4#6697112yes—
307C2×C4#6697212yes—
308C2×C4#6699011yescharacteristic
309C2×C4#6699011yescharacteristic
310C2×C4#6699111yescharacteristic
311C2×C4#6699211yescharacteristic
312C2×C4#6699311yescharacteristic
313C2×C4#6700611yescharacteristic
314C8—42no—
315C8—442no—
316C8—442no—
317C8—881no—
318C22—21no—
319C22—21no—
320C22—882no—
321C22—882no—
322C22—882no—
323C22—1764no—
324C22#1062279812yes—
325C22#1062283611yescharacteristic
326C4—21no—
327C4—21no—
328C4—81no—
329C4—82no—
330C4—81no—
331C4#1062280012yes—
332C4#1062280311yescharacteristic
333C4#1062280411yescharacteristic
334C4#1062281212yes—
335C4#1062285812yes—
336C2—22no—
337C2—1762no—
338C2#1306963611yescharacteristic
339C2#1306970711yescharacteristic
340C2#1306972211yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3230C2
socleC22×C11#392
prime radicalC2×#66927C22
hypercenter#3230D11
hypocenterC11#10149
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3230

Complements

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

NH ≅ G/Ntype
3. #13069606C2semidirect
5. #13067071C2semidirect
6. #13066452C2semidirect
7. C11×#3230C2semidirect
114. #3230D11semidirect
283. C11#10149semidirect

Maximal subgroups

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

subgroupindex
#130789922
C2×#106227012
#130696062
#130672832
#130670712
#130664522
C11×#32302
#1014911