Finite Group Databasebeta

← #14908103

Subgroups — #14908103

Order 2816.

712 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 712 conjugacy classes of subgroups — too many to draw. Only its 171 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
1C2×#10622792C211yesmaximal, characteristic, complemented
2#13079097C211yesmaximal, characteristic
3#13077484C211yesmaximal, characteristic, complemented
4#13070676C214yesmaximal, complemented
5#13070654C214yesmaximal, complemented
6#13070374C211yesmaximal, characteristic, complemented
7#13070332C211yesmaximal, characteristic, complemented
8#13070324C211yesmaximal, characteristic, complemented
9C22×C11×SD32C211yesmaximal, characteristic, complemented
10C22×C11×Q16C2211yescharacteristic
11C22×C11×D8C2211yescharacteristic
12#10623343—21no—
13#10623336—21no—
14C2×#66985—21no—
15C2×#66957C2211yescharacteristic
16C2×C11×SD32—24no—
17C2×C11×SD32C2214yes—
18C22×C11×C16C2211yescharacteristic
19#10622838—21no—
20#10622797—22no—
21Q16×Dic11C2214yescomplemented
22C2×#66893C2212yescomplemented
23#10622792—24no—
24C2×#66892C2212yescomplemented
25#10622768C2212yes—
26#10622767—22no—
27#10622764C2212yes—
28#10622719C2211yescharacteristic
29#10622714C2211yescharacteristic
30C2×#66876C2211yescharacteristic
31#10622200C2214yes—
32#10622147C2212yescomplemented
33#10622141C2212yescomplemented
34Dic11⋊C16C2214yescomplemented
35C22×Q8×C11—21no—
36C22×D4×C11—21no—
37C2×#4339—21no—
38C2×C11×Q16—21no—
39C2×C11×Q16—22no—
40C2×C11×Q16D414yescomplemented
41C2×C11×Q16C2312yes—
42C2×C11×D8—22no—
43C2×C11×D8—21no—
44C2×C11×D8—22no—
45C2×C11×D8C2312yes—
46C22×C8×C11C2311yescharacteristic
47#67006—42no—
48Q8×Dic11—24no—
49Q8×Dic11—42no—
50#66993—22no—
51#66991—42no—
52#66989—22no—
53C2×#4324—22no—
54#66985—44no—
55C2×#4323—22no—
56#66979—21no—
57#66979—42no—
58#66979D411yescharacteristic
59C2×#4318D411yescharacteristic
60C2×Dic44C2311yescharacteristic
61#66957—22no—
62#66957—22no—
63C2×D88C2311yescharacteristic
64C2×#4314—21no—
65C11×SD32—28no—
66C2×C11×C16—22no—
67C2×C11×C16C2312yes—
68#66899—24no—
69#66893—24no—
70#66892—24no—
71#66882C2312yes—
72#66881—21no—
73#66879D412yes—
74C8×Dic11C2312yes—
75#66876—22no—
76C2×C11⋊C16C2312yes—
77#33587—111nomaximal, Sylow
78C24×C11—41no—
79C2×Q8×C11—24no—
80C2×Q8×C11—22no—
81C2×Q8×C11—41no—
82C2×Q8×C11—42no—
83C2×D4×C11—22no—
84C2×D4×C11—42no—
85C2×D4×C11—41no—
86C2×D4×C11—42no—
87C22×C4×C11—41no—
88C22×C4×C11C2×D411yescharacteristic
89C2×C22⋊D11—44no—
90C2×C22⋊D11—41no—
91#4339—42no—
92#4339—42no—
93C2×D44—21no—
94C2×C4×D11—41no—
95C2×Dic22—21no—
96C11×Q16—24no—
97C11×Q16—22no—
98C11×Q16C2×D414yes—
99C11×D8—22no—
100C11×D8—22no—
101C11×D8—42no—
102C2×C8×C11C2×D412yes—
103C2×C8×C11C2×D411yescharacteristic
104C2×C8×C11#4112yes—
105C2×C8×C11C2411yescharacteristic
106C22⋊Dic11—44no—
107C22⋊Dic11—41no—
108C22⋊Dic11D812yes—
109#4324—44no—
110#4323—44no—
111C4⋊Dic11—22no—
112C4⋊Dic11—44no—
113C4⋊Dic11D812yes—
114C4×Dic11—44no—
115C4×Dic11—41no—
116C4×Dic11C2×D412yes—
117#4318—22no—
118C2×C11⋊C8C2×D412yes—
119Dic44—21no—
120Dic44—21no—
121D88—21no—
122D88—21no—
123#4314—42no—
124C11×C16—22no—
125C11⋊C16—22no—
126C2×#510—111no—
127C22×SD32D1111yescharacteristic, complemented
128#3155—111no—
129#2950—111no—
130#2211—114no—
131#2207—114no—
132#2151—111no—
133#2140—111no—
134#2138—111no—
135C23×C11—42no—
136C23×C11—82no—
137C23×C11—162no—
138C23×C11C2×D811yescharacteristic
139C22×D11—41no—
140Q8×C11—24no—
141Q8×C11—42no—
142Q8×C11—44no—
143D4×C11—42no—
144D4×C11—42no—
145D4×C11—82no—
146C2×C4×C11—42no—
147C2×C4×C11—44no—
148C2×C4×C11#12112yes—
149C2×C4×C11C2×D811yescharacteristic
150C2×C4×C11AGL(1,ℤ/8)12yes—
151C2×C4×C11C22×D411yescharacteristic
152C22⋊D11—82no—
153C22⋊D11—164no—
154C2×Dic11—42no—
155C2×Dic11—41no—
156C2×Dic11C2×D814yes—
157D44—41no—
158D44—41no—
159C4×D11—82no—
160Dic22—41no—
161Dic22—41no—
162C8×C11#12112yes—
163C8×C11C22×D411yescharacteristic
164C8×C11C2×#4111yescharacteristic
165C11⋊C8—22no—
166C2×AGL(1,ℤ/8)—221no—
167C2×#135—111no—
168C22×Q16C2×D1111yescharacteristic
169C22×D8C2×D1111yescharacteristic
170#535—221no—
171#519—221no—
172#510—224no—
173C2×Q32—112no—
174C2×SD32—24no—
175C2×SD32—112no—
176C2×SD32C2×D1114yes—
177C2×M32—111no—
178C22×C16C2×D1111yescharacteristic
179#496—222no—
180#495—112no—
181#493—112no—
182#441—222no—
183C4×Q16—114no—
184#427—111no—
185#419—221no—
186#405—111no—
187C4⋊C16—114no—
188#358—112no—
189#357—114no—
190#357—112no—
191C22×C11—22no—
192C22×C11—84no—
193C22×C11—82no—
194C22×C11—164no—
195C22×C11#45912yes—
196C22×C11C22×D811yescharacteristic
197C2×D11—82no—
198C2×D11—81no—
199C4×C11—44no—
200C4×C11#45912yes—
201C4×C11C2×#12111yescharacteristic
202C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
203Dic11—24no—
204Dic11—82no—
205Dic11—81no—
206C2×#41—221no—
207C22×Q8—21no—
208C22×D4—21no—
209AGL(1,ℤ/8)—444no—
210#135—222no—
211#135—222no—
212C2×Q16—21no—
213C2×Q16—22no—
214C2×Q16—111no—
215C2×Q16C22⋊D1114yescomplemented
216C2×Q16C22×D1112yes—
217C2×SD16—222no—
218C2×SD16—221no—
219C2×D8—21no—
220C2×D8—22no—
221C2×D8—22no—
222C2×D8—111no—
223C2×D8—222no—
224C2×D8C22×D1112yes—
225C2×M16—111no—
226C22×C8C22×D1111yescharacteristic
227#127—222no—
228#124—222no—
229#121—442no—
230#120—442no—
231C4×Q8—224no—
232C4×Q8—442no—
233#117—111no—
234#117—221no—
235#117—442no—
236Q32—224no—
237SD32—28no—
238SD32—224no—
239M32—222no—
240C2×C16—22no—
241C2×C16—112no—
242C2×C16C22×D1112yes—
243#107—112no—
244#106—221no—
245#103—224no—
246#97—112no—
247C4×C8—112no—
248C2×C11—22no—
249C2×C11—162no—
250C2×C11C2×#45911yescharacteristic
251C2×C11#341612yes—
252D11—161no—
253C24—41no—
254#41—442no—
255#41—442no—
256C2×Q8—24no—
257C2×Q8—22no—
258C2×Q8—41no—
259C2×Q8—42no—
260C2×Q8—221no—
261C2×D4—22no—
262C2×D4—41no—
263C2×D4—42no—
264C2×D4—42no—
265C2×D4—221no—
266C2×D4—444no—
267C2×D4—441no—
268C22×C4—41no—
269C22×C4—441no—
270C22×C4D4×D1111yescharacteristic
271Q16—24no—
272Q16—22no—
273Q16—221no—
274Q16—221no—
275Q16C2×C22⋊D1114yes—
276SD16—444no—
277SD16—442no—
278D8—22no—
279D8—22no—
280D8—42no—
281D8—221no—
282D8—221no—
283D8—444no—
284M16—222no—
285C2×C8—112no—
286C2×C8D4×D1111yescharacteristic
287C2×C8#434112yes—
288C2×C8C2×C22⋊D1112yes—
289C2×C8C23×D1111yescharacteristic
290C4⋊C4—112no—
291C4⋊C4—222no—
292C4⋊C4—444no—
293C22⋊C4—112no—
294C22⋊C4—444no—
295C22⋊C4—441no—
296C42—112no—
297C42—444no—
298C42—441no—
299C16—22no—
300C16—222no—
301C11#3358711yescharacteristic, complemented, Sylow
302C23—42no—
303C23—82no—
304C23—162no—
305C23—441no—
306C23D8×D1111yescharacteristic
307Q8—24no—
308Q8—44no—
309Q8—42no—
310Q8—441no—
311Q8—441no—
312D4—42no—
313D4—42no—
314D4—82no—
315D4—441no—
316D4—441no—
317D4—882no—
318D4—1764no—
319C2×C4—44no—
320C2×C4—42no—
321C2×C4—114no—
322C2×C4—442no—
323C2×C4—441no—
324C2×C4—882no—
325C2×C4D8×D1111yescharacteristic
326C2×C4#6696412yes—
327C2×C4#6699212yes—
328C2×C4C2×D4×D1111yescharacteristic
329C8—222no—
330C8#6699212yes—
331C8C2×#434111yescharacteristic
332C8C22×C22⋊D1111yescharacteristic
333C22—22no—
334C22—82no—
335C22—84no—
336C22—164no—
337C22—881no—
338C22—882no—
339C22#1062276312yes—
340C22C2×D8×D1111yescharacteristic
341C4—44no—
342C4—224no—
343C4—881no—
344C4—882no—
345C4#1062276312yes—
346C4C2×#6696411yescharacteristic
347C4C2×#6699211yescharacteristic
348C2—22no—
349C2—162no—
350C2—1761no—
351C2C2×#1062276311yescharacteristic
352C2#1308175812yes—
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC22×C11×SD32C2
socleC22×C11C22×D8
prime radical#13079097C2
hypercenterC22×SD32D11
hypocenterC11#33587
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×SD32

Complements

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

NH ≅ G/Ntype
1. C2×#10622792C2semidirect
3. #13077484C2semidirect
4. #13070676C2semidirect
5. #13070654C2semidirect
6. #13070374C2semidirect
7. #13070332C2semidirect
8. #13070324C2semidirect
9. C22×C11×SD32C2semidirect
21. Q16×Dic11C22semidirect
22. C2×#66893C22semidirect
24. C2×#66892C22semidirect
32. #10622147C22semidirect
33. #10622141C22semidirect
34. Dic11⋊C16C22semidirect
40. C2×C11×Q16D4semidirect
127. C22×SD32D11semidirect
215. C2×Q16C22⋊D11semidirect
301. C11#33587semidirect

Maximal subgroups

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

subgroupindex
C2×#106227922
#130790972
#130774842
#130706762
#130706542
#130703742
#130703322
#130703242
C22×C11×SD322
#3358711