Finite Group Databasebeta

← #14908520

Subgroups — #14908520

Order 2816.

514 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079144C211yesmaximal, characteristic, complemented
2#13077533C211yesmaximal, characteristic
3#13070790C214yesmaximal, complemented
4#13070785C214yesmaximal, complemented
5#13070389C211yesmaximal, characteristic, complemented
6C2×#10622125C211yesmaximal, characteristic, complemented
7#13070381C211yesmaximal, characteristic, complemented
8#13070352C211yesmaximal, characteristic
9C2×C11×#360C211yesmaximal, characteristic
10C2×C11×#135C2211yescharacteristic
11#10623350—21no—
12#10623031—21no—
13C2×C11×M32C2211yescharacteristic
14C2×C11×#106C2211yescharacteristic
15#10622849—21no—
16#10622810—22no—
17#10622809C2214yes—
18C2×#66883C2211yescharacteristic
19#10622719C2211yescharacteristic
20#10622714C2211yescharacteristic
21C2×#66876C2211yescharacteristic
22#10622577—21no—
23#10622471C2212yescomplemented
24#10622469—22no—
25#10622468C2212yescomplemented
26C11×#360C2214yes—
27#10622204C2212yes—
28#10622204C2212yes—
29#10622151C2212yescomplemented
30#10622151C2212yescomplemented
31#10622149C2214yescomplemented
32#10622125C2214yescomplemented
33C2×C11×#41—21no—
34C11×#135—21no—
35C11×#135—21no—
36C11×#135Q812yescomplemented
37C11×#135C2312yes—
38C2×C11×Q16Q811yescharacteristic, complemented
39C2×C11×SD16—21no—
40C2×C11×D8Q811yescharacteristic, complemented
41C22×C8×C11C2311yescharacteristic
42C2×C11×C4⋊C4—21no—
43#67001—24no—
44#67001—42no—
45#66979—21no—
46#66979D411yescharacteristic
47#66977—42no—
48C2×#4318—21no—
49C2×#4318—42no—
50C2×#4318D411yescharacteristic
51#66943—22no—
52#66943—41no—
53#66941—22no—
54#66941—41no—
55C11×M32—21no—
56C11×M32C2312yes—
57C2×C11×C16—21no—
58C11×#106—21no—
59C11×#106C2312yes—
60#66901—24no—
61#66883—21no—
62#66883C2312yes—
63#66882—21no—
64#66881C2311yescharacteristic
65#66881C2311yescharacteristic
66#66879D412yes—
67C8×Dic11C2312yes—
68#66876—21no—
69#66876C2312yes—
70C2×C11⋊C16—21no—
71#66872—22no—
72#66871—22no—
73#33638—111nomaximal, Sylow
74C11×#41—22no—
75C11×#41—22no—
76C11×#41—41no—
77C11×#41—41no—
78C2×Q8×C11—21no—
79C2×D4×C11—21no—
80C2×D4×C11—41no—
81C22×C4×C11—41no—
82C22×C4×C11—41no—
83C22×C4×C11C2×D411yescharacteristic
84C2×Dic22—42no—
85C11×Q16—21no—
86C11×Q16C2×Q812yes—
87C11×SD16—22no—
88C11×SD16—22no—
89C11×D8—21no—
90C11×D8C2×Q812yes—
91C2×C8×C11C2×D411yescharacteristic
92C2×C8×C11C2×Q811yescharacteristic
93C2×C8×C11C2×Q811yescharacteristic
94C2×C8×C11#4111yescharacteristic
95C2×C8×C11#4111yescharacteristic
96C2×C8×C11C2411yescharacteristic
97C11×C4⋊C4—22no—
98C11×C4⋊C4—41no—
99C22⋊Dic11—21no—
100C22⋊Dic11—41no—
101C4⋊Dic11—21no—
102C4⋊Dic11—21no—
103C4⋊Dic11—21no—
104C4⋊Dic11—42no—
105Dic11⋊C4—42no—
106Dic11⋊C4—42no—
107C4×Dic11—41no—
108C4×Dic11C2×D412yes—
109#4318—22no—
110#4318—44no—
111#4318—41no—
112#4318SD1612yes—
113#4318SD1612yes—
114C2×C11⋊C8—44no—
115C2×C11⋊C8—41no—
116C2×C11⋊C8C2×D412yes—
117C11×C16—22no—
118C11⋊C16—22no—
119#3163—111no—
120#2957—111no—
121#2231—114no—
122#2230—114no—
123#2155—111no—
124C2×#365—111no—
125#2153—111no—
126#2145—111no—
127C2×#360D1111yescharacteristic
128C23×C11—41no—
129C23×C11AGL(1,ℤ/8)11yescharacteristic
130Q8×C11—22no—
131Q8×C11—41no—
132D4×C11—22no—
133D4×C11—42no—
134D4×C11—42no—
135D4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—42no—
138C2×C4×C11—42no—
139C2×C4×C11—42no—
140C2×C4×C11—161no—
141C2×C4×C11C22⋊Q811yescharacteristic
142C2×C4×C11C22⋊Q811yescharacteristic
143C2×C4×C11C2×SD1611yescharacteristic
144C2×C4×C11C2×SD1611yescharacteristic
145C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C11C22×D411yescharacteristic
147C2×Dic11—22no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150Dic22—162no—
151C8×C11C22⋊Q811yescharacteristic
152C8×C11C22⋊Q811yescharacteristic
153C8×C11C22×Q811yescharacteristic
154C8×C11C2×#4111yescharacteristic
155C11⋊C8—42no—
156C11⋊C8C2×SD1614yes—
157C2×#135C2×D1111yescharacteristic
158#568—221no—
159#544—221no—
160C2×M32—111no—
161C2×M32C2×D1111yescharacteristic
162#501—222no—
163#499—112no—
164#498—112no—
165#444—222no—
166#443—114no—
167C2×#108—111no—
168#428—221no—
169#427—111no—
170C2×#106C2×D1111yescharacteristic
171#421—221no—
172#405—111no—
173#365—112no—
174#365—112no—
175#365—114no—
176#364—114no—
177#360—112no—
178#360—112no—
179#360C2×D1114yes—
180C22×C11—41no—
181C22×C11—42no—
182C22×C11—161no—
183C22×C11#47611yescharacteristic
184C22×C11#47611yescharacteristic
185C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
186C4×C11—42no—
187C4×C11—82no—
188C4×C11#47611yescharacteristic
189C4×C11#47611yescharacteristic
190C4×C11C2×C22⋊Q811yescharacteristic
191C4×C11C22×SD1611yescharacteristic
192Dic11—42no—
193Dic11—81no—
194Dic11—81no—
195C2×#41—21no—
196#135—21no—
197#135—21no—
198#135Dic2212yescomplemented
199#135C22×D1112yes—
200C2×Q16Dic2211yescharacteristic, complemented
201C2×SD16—21no—
202C2×D8Dic2211yescharacteristic, complemented
203#131—224no—
204#131—442no—
205C2×M16—111no—
206C2×M16—221no—
207C2×M16—442no—
208C22×C8C22×D1111yescharacteristic
209C4⋊Q8—222no—
210C4⋊Q8—441no—
211#125—222no—
212#125—441no—
213C22⋊Q8—442no—
214#117—111no—
215#117—221no—
216C2×C4⋊C4—21no—
217M32—21no—
218M32—112no—
219M32—221no—
220M32C22×D1112yes—
221C2×C16—21no—
222C2×C16—221no—
223#108—112no—
224#108—221no—
225#107—222no—
226#107—221no—
227#106—21no—
228#106—111no—
229#106—111no—
230#106—222no—
231#106C22×D1112yes—
232#104—224no—
233#97—112no—
234C4×C8—112no—
235C2×C11—21no—
236C2×C11—21no—
237C2×C11—21no—
238C2×C11—82no—
239C2×C11C2×#47611yescharacteristic
240#41—22no—
241#41—22no—
242#41—41no—
243#41—41no—
244C2×Q8—21no—
245C2×Q8—442no—
246C2×D4—21no—
247C2×D4—41no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4D4×D1111yescharacteristic
251Q16—21no—
252Q16C2×Dic2212yes—
253SD16—22no—
254SD16—22no—
255D8—21no—
256D8C2×Dic2212yes—
257M16—112no—
258M16—112no—
259M16—222no—
260M16—444no—
261M16—441no—
262C2×C8—112no—
263C2×C8—444no—
264C2×C8—441no—
265C2×C8C2×Dic2211yescharacteristic
266C2×C8C2×Dic2211yescharacteristic
267C2×C8D4×D1111yescharacteristic
268C2×C8#434111yescharacteristic
269C2×C8#434111yescharacteristic
270C2×C8C23×D1111yescharacteristic
271C4⋊C4—22no—
272C4⋊C4—41no—
273C4⋊C4—221no—
274C4⋊C4—221no—
275C4⋊C4—221no—
276C4⋊C4—442no—
277C4⋊C4—442no—
278C4⋊C4—442no—
279C22⋊C4—221no—
280C22⋊C4—441no—
281C42—112no—
282C42—441no—
283C16—22no—
284C16—222no—
285C11#3363811yescharacteristic, complemented, Sylow
286C23—41no—
287C23#6696411yescharacteristic
288Q8—22no—
289Q8—41no—
290Q8—1762no—
291D4—22no—
292D4—42no—
293D4—42no—
294D4—41no—
295C2×C4—41no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—161no—
300C2×C4—222no—
301C2×C4—441no—
302C2×C4—441no—
303C2×C4#6693111yescharacteristic
304C2×C4#6693111yescharacteristic
305C2×C4#6696411yescharacteristic
306C2×C4SD16×D1111yescharacteristic
307C2×C4SD16×D1111yescharacteristic
308C2×C4C2×D4×D1111yescharacteristic
309C8—114no—
310C8—442no—
311C8#6693111yescharacteristic
312C8#6693111yescharacteristic
313C8C22×Dic2211yescharacteristic
314C8C2×#434111yescharacteristic
315C22—41no—
316C22—42no—
317C22—161no—
318C22#1062237411yescharacteristic
319C22#1062237411yescharacteristic
320C22C2×#6696411yescharacteristic
321C4—42no—
322C4—82no—
323C4—442no—
324C4—881no—
325C4—881no—
326C4#1062237411yescharacteristic
327C4#1062237411yescharacteristic
328C4C2×#6693111yescharacteristic
329C4C2×SD16×D1111yescharacteristic
330C2—21no—
331C2—21no—
332C2—21no—
333C2—82no—
334C2C2×#1062237411yescharacteristic
subgroupG/H
centerC2C2×#10622374
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#360C2
socleC2×C11C2×#476
prime radicalC2×C11×#135C22
hypercenterC2×#360D11
hypocenterC11#33638
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×C8 ◁ C2×#360

Complements

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

NH ≅ G/Ntype
1. #13079144C2semidirect
3. #13070790C2semidirect
4. #13070785C2semidirect
5. #13070389C2semidirect
6. C2×#10622125C2semidirect
7. #13070381C2semidirect
23. #10622471C22semidirect
25. #10622468C22semidirect
29. #10622151C22semidirect
30. #10622151C22semidirect
31. #10622149C22semidirect
32. #10622125C22semidirect
36. C11×#135Q8semidirect
38. C2×C11×Q16Q8semidirect
40. C2×C11×D8Q8semidirect
198. #135Dic22semidirect
200. C2×Q16Dic22semidirect
202. C2×D8Dic22semidirect
285. C11#33638semidirect

Maximal subgroups

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

subgroupindex
#130791442
#130775332
#130707902
#130707852
#130703892
C2×#106221252
#130703812
#130703522
C2×C11×#3602
#3363811