Finite Group Databasebeta

← #14908519

Subgroups — #14908519

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#13077534C211yesmaximal, characteristic
2#13070789C214yesmaximal, complemented
3#13070784C214yesmaximal, complemented
4#13070388C211yesmaximal, characteristic, complemented
5C2×#10622125C211yesmaximal, characteristic, complemented
6#13070382C211yesmaximal, characteristic, complemented
7#13070351C211yesmaximal, characteristic
8C2×#10622126C211yesmaximal, characteristic
9C11×#3163C211yesmaximal, characteristic, complemented
10C11×#544—21no—
11#10623276—21no—
12C2×#66957C2211yescharacteristic
13C11×#501—22no—
14C11×#499C2212yescomplemented
15C11×#498C2212yescomplemented
16C11×#428—21no—
17C11×#427C2211yescharacteristic
18C2×C11×#106C2211yescharacteristic
19C11×#405C2211yescharacteristic
20C2×#66883C2211yescharacteristic
21C2×#66876C2211yescharacteristic
22C2×#66876C2211yescharacteristic
23#10622618—21no—
24#10622330—22no—
25#10622313C2214yes—
26#10622126C2214yes—
27#10622126C2212yes—
28#10622126C2212yes—
29#10622125C2214yescomplemented
30#10622125C2212yescomplemented
31#10622125C2212yescomplemented
32#10622101C2214yescomplemented
33C2×#4339—21no—
34C2×C11×M16D411yescharacteristic
35C22×C8×C11C2311yescharacteristic
36C11×C4⋊Q8—22no—
37C11×C4⋊Q8—41no—
38C11×#125—22no—
39C11×#125—41no—
40C11×C22⋊Q8—42no—
41C11×#117—21no—
42C11×#117D411yescharacteristic
43C2×C11×C4⋊C4—21no—
44C2×#4318—21no—
45#66960—42no—
46M16×D11—42no—
47C2×Dic44Q811yescharacteristic, complemented
48#66957—21no—
49#66957—21no—
50#66957Q812yescomplemented
51#66957C2312yes—
52C2×D88Q811yescharacteristic, complemented
53C2×#4314—21no—
54#66954—24no—
55C11×#107—22no—
56C11×#107—21no—
57C11×#106—22no—
58C11×#106—21no—
59C11×#106C2311yescharacteristic
60C11×#106C2312yes—
61C11×#106C2311yescharacteristic
62C11×#97D412yes—
63C4×C8×C11C2312yes—
64#66883—21no—
65#66883C2312yes—
66#66876—21no—
67#66876—21no—
68#66876C2312yes—
69#66876C2312yes—
70C2×C11⋊C16—21no—
71C2×C11⋊C16—21no—
72#66869—24no—
73#33638—111nomaximal, Sylow
74C2×Q8×C11—42no—
75C22×C4×C11—41no—
76C22×C4×C11C2×D411yescharacteristic
77C2×C22⋊D11—41no—
78#4339—22no—
79#4339—22no—
80#4339—41no—
81#4339—41no—
82C2×D44—21no—
83C2×C4×D11—41no—
84C2×Dic22—21no—
85C11×M16SD1612yes—
86C11×M16SD1612yes—
87C2×C8×C11C2×D411yescharacteristic
88C2×C8×C11C2×D412yes—
89C2×C8×C11C2×Q811yescharacteristic
90C2×C8×C11C2×Q811yescharacteristic
91C2×C8×C11#4111yescharacteristic
92C2×C8×C11#4111yescharacteristic
93C2×C8×C11C2411yescharacteristic
94C11×C4⋊C4—21no—
95C11×C4⋊C4—22no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—42no—
99C11×C4⋊C4—42no—
100C11×C4⋊C4—42no—
101C11×C4⋊C4—41no—
102C11×C22⋊C4—21no—
103C11×C22⋊C4—41no—
104C42×C11—41no—
105C42×C11C2×D412yes—
106#4318—22no—
107#4318—41no—
108C2×C11⋊C8—41no—
109Dic44—21no—
110Dic44C2×Q812yes—
111D88—21no—
112D88C2×Q812yes—
113#4314—22no—
114#4314—22no—
115#4313—44no—
116C8×D11—44no—
117C11⋊C16—22no—
118C11⋊C16—22no—
119#3163D1111yescharacteristic, complemented
120#2957—111no—
121#2231—114no—
122#2230—114no—
123#2155—111no—
124C2×#365—111no—
125#2153—111no—
126#2145—111no—
127C2×#360—111no—
128C23×C11AGL(1,ℤ/8)11yescharacteristic
129C22×D11—41no—
130Q8×C11—162no—
131C2×C4×C11—22no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—42no—
135C2×C4×C11—161no—
136C2×C4×C11C22⋊Q811yescharacteristic
137C2×C4×C11C22⋊Q811yescharacteristic
138C2×C4×C11C2×SD1611yescharacteristic
139C2×C4×C11C2×SD1611yescharacteristic
140C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C11C22×D411yescharacteristic
142C22⋊D11—42no—
143C22⋊D11—42no—
144C2×Dic11—41no—
145D44—22no—
146D44—41no—
147C4×D11—42no—
148C4×D11—42no—
149Dic22—22no—
150Dic22—41no—
151C8×C11C22⋊Q811yescharacteristic
152C8×C11C22⋊Q811yescharacteristic
153C8×C11C2×SD1614yes—
154C8×C11C22×Q811yescharacteristic
155C8×C11C2×#4111yescharacteristic
156C11⋊C8—42no—
157C2×#135—111no—
158#568—221no—
159#544—21no—
160C2×M32—111no—
161C2×M32—111no—
162#501—22no—
163#499C2×D1112yescomplemented
164#498C2×D1112yescomplemented
165#444—222no—
166#443—114no—
167C2×#108—111no—
168#428—21no—
169#427C2×D1111yescharacteristic
170C2×#106C2×D1111yescharacteristic
171#421—221no—
172#405C2×D1111yescharacteristic
173#365—114no—
174#365—112no—
175#365—112no—
176#364—114no—
177#360—114no—
178#360—112no—
179#360—112no—
180C22×C11—41no—
181C22×C11#47611yescharacteristic
182C22×C11#47611yescharacteristic
183C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
184C2×D11—42no—
185C2×D11—161no—
186C4×C11—42no—
187C4×C11—81no—
188C4×C11—82no—
189C4×C11—81no—
190C4×C11#47611yescharacteristic
191C4×C11#47611yescharacteristic
192C4×C11C2×C22⋊Q811yescharacteristic
193C4×C11C22×SD1611yescharacteristic
194Dic11—42no—
195C2×#41—221no—
196#135—112no—
197#135—112no—
198#135—221no—
199#135—221no—
200C2×Q16—111no—
201C2×SD16—221no—
202C2×D8—111no—
203#131—224no—
204#131—442no—
205C2×M16—221no—
206C2×M16—442no—
207C2×M16C22⋊D1111yescharacteristic
208C22×C8C22×D1111yescharacteristic
209C4⋊Q8—22no—
210C4⋊Q8—41no—
211#125—22no—
212#125—41no—
213C22⋊Q8—42no—
214#117—21no—
215#117C22⋊D1111yescharacteristic
216C2×C4⋊C4—21no—
217M32—112no—
218M32—112no—
219M32—221no—
220M32—221no—
221C2×C16—221no—
222C2×C16—221no—
223#108—112no—
224#108—221no—
225#107—21no—
226#107—22no—
227#106—21no—
228#106—22no—
229#106C22×D1112yes—
230#106C22×D1111yescharacteristic
231#106C22×D1111yescharacteristic
232#104—224no—
233#97C22⋊D1112yes—
234C4×C8C22×D1112yes—
235C2×C11—21no—
236C2×C11—21no—
237C2×C11—21no—
238C2×C11C2×#47611yescharacteristic
239D11—82no—
240#41—222no—
241#41—222no—
242#41—441no—
243#41—441no—
244C2×Q8—42no—
245C2×Q8—221no—
246C2×D4—221no—
247C2×D4—441no—
248C22×C4—41no—
249C22×C4—441no—
250C22×C4C2×C22⋊D1111yescharacteristic
251Q16—112no—
252Q16—221no—
253SD16—222no—
254SD16—222no—
255D8—112no—
256D8—221no—
257M16—222no—
258M16—441no—
259M16—444no—
260M16#432512yes—
261M16#432512yes—
262C2×C8—441no—
263C2×C8—444no—
264C2×C8Q8×D1111yescharacteristic
265C2×C8Q8×D1111yescharacteristic
266C2×C8#434311yescharacteristic
267C2×C8#434311yescharacteristic
268C2×C8C2×C22⋊D1112yes—
269C2×C8C2×C22⋊D1111yescharacteristic
270C2×C8C23×D1111yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—22no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—42no—
276C4⋊C4—42no—
277C4⋊C4—42no—
278C4⋊C4—41no—
279C22⋊C4—21no—
280C22⋊C4—41no—
281C42—41no—
282C42C2×C22⋊D1112yes—
283C16—222no—
284C16—222no—
285C11#3363811yescharacteristic, complemented, Sylow
286C23—441no—
287C23#6698511yescharacteristic
288Q8—162no—
289Q8—222no—
290Q8—441no—
291D4—222no—
292D4—442no—
293D4—442no—
294D4—441no—
295C2×C4—22no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—42no—
299C2×C4—161no—
300C2×C4—441no—
301C2×C4—442no—
302C2×C4—442no—
303C2×C4#6698511yescharacteristic
304C2×C4C2×#432511yescharacteristic
305C2×C4C2×#432511yescharacteristic
306C2×C4#6699911yescharacteristic
307C2×C4#6699911yescharacteristic
308C2×C4C22×C22⋊D1111yescharacteristic
309C8—442no—
310C8C2×#432514yes—
311C8#6699911yescharacteristic
312C8#6699911yescharacteristic
313C8C2×Q8×D1111yescharacteristic
314C8C2×#434311yescharacteristic
315C22—41no—
316C22—442no—
317C22—1761no—
318C22#1062269711yescharacteristic
319C22#1062269711yescharacteristic
320C22C2×#6698511yescharacteristic
321C4—42no—
322C4—82no—
323C4—81no—
324C4—81no—
325C4—442no—
326C4#1062269711yescharacteristic
327C4#1062269711yescharacteristic
328C4C22×#432511yescharacteristic
329C4C2×#6699911yescharacteristic
330C2—21no—
331C2—21no—
332C2—21no—
333C2—882no—
334C2C2×#1062269711yescharacteristic
subgroupG/H
centerC2C2×#10622697
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3163C2
socleC2×C11C2×#476
prime radicalC2×#66957C22
hypercenter#3163D11
hypocenterC11#33638
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ #405 ◁ #3163

Complements

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

NH ≅ G/Ntype
2. #13070789C2semidirect
3. #13070784C2semidirect
4. #13070388C2semidirect
5. C2×#10622125C2semidirect
6. #13070382C2semidirect
9. C11×#3163C2semidirect
14. C11×#499C22semidirect
15. C11×#498C22semidirect
29. #10622125C22semidirect
30. #10622125C22semidirect
31. #10622125C22semidirect
32. #10622101C22semidirect
47. C2×Dic44Q8semidirect
50. #66957Q8semidirect
52. C2×D88Q8semidirect
119. #3163D11semidirect
163. #499C2×D11semidirect
164. #498C2×D11semidirect
285. C11#33638semidirect

Maximal subgroups

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

subgroupindex
#130775342
#130707892
#130707842
#130703882
C2×#106221252
#130703822
#130703512
C2×#106221262
C11×#31632
#3363811