Finite Group Databasebeta

← #14669465

Subgroups — #14669465

Order 2816.

878 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 878 conjugacy classes of subgroups — too many to draw. Only its 159 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#13070352C212yesmaximal, complemented
2#13070336C212yesmaximal, complemented
3#13070237C211yesmaximal, characteristic, complemented
4#13068662C211yesmaximal, characteristic, complemented
5C2×C11×#578C211yesmaximal, characteristic
6C2×C11×2−1+4—21no—
7C11×#578—24no—
8C11×#578—24no—
9C2×C11×#137—21no—
10C2×C11×#137—22no—
11C2×C11×#135C412yescomplemented
12C2×C11×#135C2211yescharacteristic
13C22×C11×Q16C412yescomplemented
14C22×C11×Q16C2211yescharacteristic
15C2×C11×#131C2211yescharacteristic
16#10622853—21no—
17#10622719C2212yes—
18C2×#66876C2212yes—
19#10622204—24no—
20#10622202—24no—
21#10622195—21no—
22#10622191—22no—
23C11×2−1+4—28no—
24C11×2−1+4—44no—
25C2×C11×#41—22no—
26C2×C11×#41—21no—
27C2×C11×#41—42no—
28C2×C11×#41—41no—
29C2×C11×#41D411yescharacteristic
30C22×Q8×C11—22no—
31C22×Q8×C11—21no—
32C22×Q8×C11—41no—
33C11×#137—216no—
34C11×#137—28no—
35C11×#135—24no—
36C11×#135—24no—
37C11×#135—22no—
38C11×#135D414yes—
39C2×C11×Q16—24no—
40C2×C11×Q16—24no—
41C2×C11×Q16—22no—
42C2×C11×Q16—21no—
43C2×C11×Q16—22no—
44C2×C11×Q16C2×C411yescharacteristic
45C2×C11×Q16C2×C412yes—
46C2×C11×Q16D414yes—
47C2×C11×SD16—22no—
48C2×C11×SD16—21no—
49C2×C11×D8C2×C411yescharacteristic
50C11×#131—22no—
51C11×#131—22no—
52C2×C11×M16D411yescharacteristic
53C2×C11×M16D412yes—
54C22×C8×C11C2×C412yes—
55C22×C8×C11C2311yescharacteristic
56#66979—22no—
57#66898—42no—
58#66882—22no—
59#66881—22no—
60#66876—22no—
61#66876—22no—
62C2×C11⋊C16—22no—
63#12742—111nomaximal, Sylow
64C11×#41—22no—
65C11×#41—22no—
66C11×#41—28no—
67C11×#41—24no—
68C11×#41—44no—
69C11×#41—416no—
70C11×#41—48no—
71C11×#41—42no—
72C2×Q8×C11—28no—
73C2×Q8×C11—22no—
74C2×Q8×C11—21no—
75C2×Q8×C11—24no—
76C2×Q8×C11—44no—
77C2×Q8×C11—48no—
78C2×Q8×C11—42no—
79C2×Q8×C11—41no—
80C2×Q8×C11—42no—
81C2×Q8×C11SD1611yescharacteristic
82C2×D4×C11—21no—
83C2×D4×C11—42no—
84C2×D4×C11—41no—
85C2×D4×C11D812yes—
86C2×D4×C11SD1611yescharacteristic
87C22×C4×C11—42no—
88C22×C4×C11—41no—
89C22×C4×C11—42no—
90C22×C4×C11—41no—
91C22×C4×C11C22⋊C412yes—
92C22×C4×C11C2×D411yescharacteristic
93C11×Q16—28no—
94C11×Q16—21no—
95C11×Q16—22no—
96C11×Q16—24no—
97C11×Q16C22⋊C412yes—
98C11×Q16C22⋊C414yes—
99C11×SD16—28no—
100C11×SD16—24no—
101C11×D8—21no—
102C11×D8C22⋊C412yes—
103C11×M16—24no—
104C11×M16—22no—
105C2×C8×C11—22no—
106C2×C8×C11—22no—
107C2×C8×C11C22⋊C412yes—
108C2×C8×C11C22×C411yescharacteristic
109C2×C8×C11C2×D411yescharacteristic
110C2×C8×C11C2×D412yes—
111C2×C8×C11C2×D412yes—
112C22⋊Dic11—42no—
113C4⋊Dic11—42no—
114C4×Dic11—42no—
115C11⋊C16—42no—
116C2×#578D1111yescharacteristic
117#2145—112no—
118#2141—112no—
119#2115—111no—
120#1812—111no—
121C23×C11—41no—
122C23×C11#10212yes—
123C23×C11C2×D811yescharacteristic
124Q8×C11—22no—
125Q8×C11—24no—
126Q8×C11—22no—
127Q8×C11—48no—
128Q8×C11—41no—
129Q8×C11—42no—
130Q8×C11—44no—
131D4×C11—24no—
132D4×C11—22no—
133D4×C11—22no—
134D4×C11—48no—
135D4×C11—44no—
136D4×C11—41no—
137C2×C4×C11—22no—
138C2×C4×C11—22no—
139C2×C4×C11—48no—
140C2×C4×C11—48no—
141C2×C4×C11—41no—
142C2×C4×C11—42no—
143C2×C4×C11—44no—
144C2×C4×C11—44no—
145C2×C4×C11#10212yes—
146C2×C4×C11C2×C22⋊C411yescharacteristic
147C2×C4×C11#12012yes—
148C2×C4×C11C2×SD1611yescharacteristic
149C2×C4×C11AGL(1,ℤ/8)12yes—
150C2×Dic11—82no—
151C8×C11—22no—
152C8×C11C2×C22⋊C411yescharacteristic
153C8×C11C2×C22⋊C411yescharacteristic
154C8×C11#12012yes—
155C2×2−1+4—21no—
156#578—24no—
157#578—24no—
158C2×#137—21no—
159C2×#137—22no—
160C2×#135Dic1112yescomplemented
161C2×#135C2×D1111yescharacteristic
162C22×Q16Dic1112yescomplemented
163C22×Q16C2×D1111yescharacteristic
164C2×#131C2×D1111yescharacteristic
165C2×M32—112no—
166#427—112no—
167#410—221no—
168#360—224no—
169#358—224no—
170#349—222no—
171H(3,ℤ/4)—221no—
172C22×C11—22no—
173C22×C11—41no—
174C22×C11—42no—
175C22×C11—42no—
176C22×C11—82no—
177C22×C11C2×#10211yescharacteristic
178C22×C11#44712yes—
179C4×C11—22no—
180C4×C11—44no—
181C4×C11—42no—
182C4×C11#37911yescharacteristic
183C4×C11#41811yescharacteristic
184C4×C11#45012yes—
185Dic11—162no—
1862−1+4—28no—
1872−1+4—44no—
188C2×#41—22no—
189C2×#41—21no—
190C2×#41—42no—
191C2×#41—41no—
192C2×#41C22⋊D1111yescharacteristic
193C22×Q8—22no—
194C22×Q8—21no—
195C22×Q8—41no—
196#137—28no—
197#137—216no—
198#135—24no—
199#135—24no—
200#135—22no—
201#135C22⋊D1114yes—
202C2×Q16—24no—
203C2×Q16—24no—
204C2×Q16—22no—
205C2×Q16—21no—
206C2×Q16—22no—
207C2×Q16C2×Dic1111yescharacteristic
208C2×Q16C2×Dic1112yes—
209C2×Q16C22⋊D1114yes—
210C2×SD16—22no—
211C2×SD16—21no—
212C2×D8C2×Dic1111yescharacteristic
213#131—22no—
214#131—22no—
215C2×M16C22⋊D1111yescharacteristic
216C2×M16C22⋊D1112yes—
217C22×C8C2×Dic1112yes—
218C22×C8C22×D1111yescharacteristic
219#117—222no—
220M32—222no—
221M32—222no—
222C2×C16—222no—
223#107—222no—
224#106—222no—
225#99—442no—
226C2×C11—22no—
227C2×C11—21no—
228C2×C11—42no—
229C2×C11—82no—
230C2×C11#178611yescharacteristic
231#41—22no—
232#41—22no—
233#41—28no—
234#41—24no—
235#41—44no—
236#41—416no—
237#41—48no—
238#41—42no—
239C2×Q8—28no—
240C2×Q8—22no—
241C2×Q8—21no—
242C2×Q8—24no—
243C2×Q8—44no—
244C2×Q8—48no—
245C2×Q8—42no—
246C2×Q8—42no—
247C2×Q8—41no—
248C2×Q8#432411yescharacteristic
249C2×D4—21no—
250C2×D4—42no—
251C2×D4—41no—
252C2×D4#432312yes—
253C2×D4#432411yescharacteristic
254C22×C4—42no—
255C22×C4—41no—
256C22×C4—42no—
257C22×C4—41no—
258C22×C4C22⋊Dic1112yes—
259C22×C4C2×C22⋊D1111yescharacteristic
260Q16—28no—
261Q16—21no—
262Q16—22no—
263Q16—24no—
264Q16C22⋊Dic1112yes—
265Q16C22⋊Dic1114yes—
266SD16—28no—
267SD16—24no—
268D8—21no—
269D8C22⋊Dic1112yes—
270M16—22no—
271M16—24no—
272C2×C8—22no—
273C2×C8—22no—
274C2×C8C22⋊Dic1112yes—
275C2×C8C22×Dic1111yescharacteristic
276C2×C8C2×C22⋊D1112yes—
277C2×C8C2×C22⋊D1112yes—
278C2×C8C2×C22⋊D1111yescharacteristic
279C4⋊C4—442no—
280C22⋊C4—442no—
281C42—442no—
282C16—442no—
283C11#1274211yescharacteristic, complemented, Sylow
284C23—41no—
285C23#6689612yes—
286C23C2×#432311yescharacteristic
287Q8—22no—
288Q8—24no—
289Q8—22no—
290Q8—48no—
291Q8—41no—
292Q8—42no—
293Q8—44no—
294D4—24no—
295D4—22no—
296D4—22no—
297D4—48no—
298D4—44no—
299D4—41no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—48no—
303C2×C4—48no—
304C2×C4—41no—
305C2×C4—42no—
306C2×C4—44no—
307C2×C4—44no—
308C2×C4—882no—
309C2×C4#6689612yes—
310C2×C4#6698512yes—
311C2×C4C2×#432411yescharacteristic
312C2×C4C2×C22⋊Dic1111yescharacteristic
313C2×C4#6700612yes—
314C8—22no—
315C8C2×C22⋊Dic1111yescharacteristic
316C8C2×C22⋊Dic1111yescharacteristic
317C8#6700612yes—
318C22—22no—
319C22—41no—
320C22—42no—
321C22—42no—
322C22—82no—
323C22C2×#6689611yescharacteristic
324C22#1062283012yes—
325C4—22no—
326C4—44no—
327C4—42no—
328C4—1762no—
329C4#1062282811yescharacteristic
330C4#1062283112yes—
331C4#1062286011yescharacteristic
332C2—22no—
333C2—21no—
334C2—42no—
335C2—82no—
336C2#1306854711yescharacteristic
subgroupG/H
centerC2#13068547
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
Fitting, prime radicalC2×C11×#578C2
socleC2×C11#1786
cosocleC22×C8×C11C23
hypercenterC2×#578D11
hypocenterC11#12742
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#131 ◁ C2×#578

Complements

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

NH ≅ G/Ntype
1. #13070352C2semidirect
2. #13070336C2semidirect
3. #13070237C2semidirect
4. #13068662C2semidirect
11. C2×C11×#135C4semidirect
13. C22×C11×Q16C4semidirect
160. C2×#135Dic11semidirect
162. C22×Q16Dic11semidirect
283. C11#12742semidirect

Maximal subgroups

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

subgroupindex
#130703522
#130703362
#130702372
#130686622
C2×C11×#5782
#1274211