Finite Group Databasebeta

← #14650466

Subgroups — #14650466

Order 2816.

490 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 107 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#13079559C211yesmaximal, characteristic
2#13077553C211yesmaximal, characteristic, complemented
3#13069439C211yesmaximal, characteristic
4#13067285C211yesmaximal, characteristic
5#13067179C211yesmaximal, characteristic, complemented
6#13066446C211yesmaximal, characteristic, complemented
7C11×#1286C211yesmaximal, characteristic, complemented
8C2×#66927C2211yescharacteristic
9#10623001C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C11×#382C2211yescharacteristic
13#10622735—21no—
14#10622732—21no—
15C2×#66873—21no—
16C2×#66873—21no—
17#10622538C2211yescharacteristic
18C2×#66867C2211yescharacteristic
19#10622461—22no—
20#10622441—22no—
21#10622441—22no—
22#10622344—22no—
23#10622307C412yescomplemented
24#10622306C412yescomplemented
25#10622123—22no—
26#10622090—22no—
27C22×D44—21no—
28C22×D44—21no—
29C22×D44—21no—
30C2×C11×M16—21no—
31C2×C11×C4⋊C4—21no—
32C2×C42×C11C2311yescharacteristic
33#66979—21no—
34#66977—21no—
35#66977D412yes—
36C22×C11⋊C8D411yescharacteristic
37C22×C11⋊C8D411yescharacteristic
38C2×#4314—24no—
39#66927—21no—
40#66927—21no—
41#66927—21no—
42#66927C2×C412yes—
43#66923—21no—
44#66922C2×C411yescharacteristic
45#66922C2×C411yescharacteristic
46C4×Dic22—21no—
47C4×Dic22D412yes—
48C11×C4⋊C8—21no—
49C11×C4⋊C8—21no—
50C11×C4⋊C8D412yes—
51C11×C22⋊C8—21no—
52C4×C8×C11C2×C412yes—
53C11×#95—21no—
54C11×#95—21no—
55C22⋊(C11⋊C8)—21no—
56#66885—24no—
57#66879—22no—
58Dic11⋊C8—24no—
59C8×Dic11—22no—
60#66873—42no—
61#66873—42no—
62C4⋊(C11⋊C8)—21no—
63#66867—21no—
64#66867—21no—
65C4×C11⋊C8—21no—
66#9294—111nomaximal, Sylow
67C23×D11—41no—
68C22×C4×C11—41no—
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11#4111yescharacteristic
72C2×D44—22no—
73C2×D44—22no—
74C2×D44—22no—
75C2×D44—41no—
76C2×D44—41no—
77C2×D44—41no—
78C2×D44—41no—
79C2×D44—41no—
80C2×D44—41no—
81C2×D44—41no—
82C2×D44—82no—
83C2×D44—82no—
84C2×Dic22—21no—
85C2×Dic22C22⋊C412yes—
86C11×M16—41no—
87C11×M16—41no—
88C2×C8×C11—22no—
89C2×C8×C11—22no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C42×C11C22×C411yescharacteristic
93C42×C11C2×D411yescharacteristic
94C42×C11C2×D411yescharacteristic
95C42×C11#4111yescharacteristic
96C22⋊Dic11—22no—
97C4⋊Dic11—21no—
98C4⋊Dic11—21no—
99C4⋊Dic11—21no—
100C4⋊Dic11C22⋊C412yes—
101Dic11⋊C4—22no—
102Dic11⋊C4—22no—
103C4×Dic11—22no—
104C2×C11⋊C8—21no—
105C2×C11⋊C8—21no—
106C2×C11⋊C8—21no—
107C2×C11⋊C8—21no—
108C2×C11⋊C8—21no—
109C2×C11⋊C8—41no—
110C2×C11⋊C8SD1612yescomplemented
111#4314—84no—
112#3208—111no—
113#2961—111no—
114#1961—111no—
115#1545—111no—
116#1518—111no—
117#1286D1111yescharacteristic, complemented
118#1275—111no—
119C23×C11#12111yescharacteristic
120C22×D11—42no—
121C22×D11—82no—
122C22×D11—82no—
123C22×D11—81no—
124C22×D11—81no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—81no—
128C2×C4×C11—81no—
129C2×C4×C11—81no—
130C2×C4×C11C2×C22⋊C411yescharacteristic
131C2×C4×C11C4×D411yescharacteristic
132C2×C4×C11C4×D411yescharacteristic
133C2×C4×C11#12011yescharacteristic
134C2×C4×C11#12111yescharacteristic
135C2×C4×C11#12311yescharacteristic
136C2×C4×C11C2×SD1611yescharacteristic
137C2×C4×C11#13511yescharacteristic
138C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C11#13711yescharacteristic
140C2×Dic11—22no—
141C2×Dic11—22no—
142D44—44no—
143D44—42no—
144D44—42no—
145D44—82no—
146D44—82no—
147D44—82no—
148D44—81no—
149D44—81no—
150Dic22—42no—
151Dic22—81no—
152C8×C11—42no—
153C8×C11—42no—
154C11⋊C8—22no—
155C11⋊C8—41no—
156C11⋊C8—81no—
157#533—111no—
158C2×#127—111no—
159#492—112no—
160#486—112no—
161#460—222no—
162#450—222no—
163#446—222no—
164#446—222no—
165#431—111no—
166#431C2×D1111yescharacteristic
167#424—221no—
168#423C2×D1111yescharacteristic
169C2×#102—221no—
170C2×#102—221no—
171#405—221no—
172C2×#97—111no—
173#382C2×D1111yescharacteristic
174#331—222no—
175#328—222no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11#38611yescharacteristic
179C22×C11#46011yescharacteristic
180C22×C11#46411yescharacteristic
181C2×D11—82no—
182C2×D11—82no—
183C2×D11—82no—
184C2×D11—162no—
185C2×D11—162no—
186C4×C11—21no—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—161no—
191C4×C11C4×SD1611yescharacteristic
192C4×C11#44011yescharacteristic
193C4×C11#44811yescharacteristic
194C4×C11#44911yescharacteristic
195Dic11—42no—
196Dic11—42no—
197C22×D4—221no—
198C22×D4—221no—
199C22×D4—221no—
200C2×SD16—224no—
201C2×M16—21no—
202C22×C8—111no—
203C22×C8—111no—
204C4⋊Q8—111no—
205C4⋊Q8—111no—
206#127—112no—
207#127—221no—
208#127—221no—
209#127—221no—
210#125—221no—
211C22⋊Q8—112no—
212C22⋊Q8—221no—
213C4×Q8—112no—
214C4×Q8—221no—
215#117—221no—
216C2×C4⋊C4—21no—
217C2×C42C22×D1111yescharacteristic
218C4⋊C8—21no—
219C4⋊C8—21no—
220C4⋊C8—224no—
221C4⋊C8—221no—
222C4⋊C8D4412yes—
223#102—224no—
224#102—442no—
225#102—442no—
226C22⋊C8—21no—
227C22⋊C8—221no—
228#97—222no—
229#97—221no—
230#97—221no—
231C4×C8—222no—
232C4×C8—221no—
233C4×C8C4×D1112yes—
234#95—21no—
235#95—21no—
236C2×C11—21no—
237C2×C11—21no—
238C2×C11#188011yescharacteristic
239C2×C11#190311yescharacteristic
240C2×C11#191011yescharacteristic
241D11—162no—
242C24—441no—
243C2×Q8—112no—
244C2×Q8—221no—
245C2×D4—222no—
246C2×D4—222no—
247C2×D4—222no—
248C2×D4—441no—
249C2×D4—441no—
250C2×D4—441no—
251C2×D4—441no—
252C2×D4—441no—
253C2×D4—441no—
254C2×D4—441no—
255C2×D4—882no—
256C2×D4—882no—
257C22×C4—41no—
258C22×C4#433911yescharacteristic
259C22×C4D4×D1111yescharacteristic
260C22×C4D4×D1111yescharacteristic
261SD16—884no—
262M16—41no—
263M16—41no—
264C2×C8—22no—
265C2×C8—22no—
266C2×C8—112no—
267C2×C8—221no—
268C2×C8—221no—
269C2×C8—221no—
270C2×C8—221no—
271C2×C8—221no—
272C2×C8—441no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—112no—
276C4⋊C4—221no—
277C4⋊C4—221no—
278C4⋊C4—221no—
279C4⋊C4—222no—
280C4⋊C4—222no—
281C22⋊C4—222no—
282C42—222no—
283C42C2×C4×D1111yescharacteristic
284C42C2×D4411yescharacteristic
285C42D4×D1111yescharacteristic
286C42#434311yescharacteristic
287C11#929411yescharacteristic, complemented, Sylow
288C23—442no—
289C23—882no—
290C23—882no—
291C23—881no—
292C23—881no—
293C23#6693711yescharacteristic
294Q8—442no—
295Q8—881no—
296D4—444no—
297D4—442no—
298D4—442no—
299D4—882no—
300D4—882no—
301D4—882no—
302D4—881no—
303D4—881no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4—222no—
310C2×C4—222no—
311C2×C4C4×D4411yescharacteristic
312C2×C4C22⋊C4×D1111yescharacteristic
313C2×C4#6693511yescharacteristic
314C2×C4#6694611yescharacteristic
315C2×C4#6694711yescharacteristic
316C2×C4#6694811yescharacteristic
317C2×C4#6696411yescharacteristic
318C2×C4SD16×D1111yescharacteristic
319C2×C4#6696911yescharacteristic
320C2×C4#6697111yescharacteristic
321C8—42no—
322C8—42no—
323C8—222no—
324C8—441no—
325C8—881no—
326C22—21no—
327C22—21no—
328C22—882no—
329C22—882no—
330C22—882no—
331C22—1762no—
332C22—1762no—
333C22#1062227811yescharacteristic
334C22#1062237511yescharacteristic
335C22#1062241111yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—161no—
341C4—442no—
342C4—442no—
343C4#1062239411yescharacteristic
344C4#1062241911yescharacteristic
345C4#1062246511yescharacteristic
346C4#1062250211yescharacteristic
347C2—21no—
348C2—21no—
349C2—1762no—
350C2#1306897211yescharacteristic
351C2#1306909511yescharacteristic
352C2#1306914211yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1286C2
socleC22×C11#386
prime radicalC2×#66927C22
cosocleC2×C42×C11C23
hypercenter#1286D11
hypocenterC11#9294
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1286

Complements

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

NH ≅ G/Ntype
2. #13077553C2semidirect
5. #13067179C2semidirect
6. #13066446C2semidirect
7. C11×#1286C2semidirect
23. #10622307C4semidirect
24. #10622306C4semidirect
110. C2×C11⋊C8SD16semidirect
117. #1286D11semidirect
287. C11#9294semidirect

Maximal subgroups

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

subgroupindex
#130795592
#130775532
#130694392
#130672852
#130671792
#130664462
C11×#12862
#929411