Finite Group Databasebeta

← #14648110

Subgroups — #14648110

Order 2816.

376 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#4318C211yesmaximal, characteristic
2#13069392C211yesmaximal, characteristic
3#13067375C211yesmaximal, characteristic
4#13067045C211yesmaximal, characteristic
5#13066513C211yesmaximal, characteristic
6#13066453C211yesmaximal, characteristic
7C2×C11×Q8⋊C8C211yesmaximal, characteristic
8C2×C4×Q8×C11C2211yescharacteristic
9C2×C11×C4⋊C8C2211yescharacteristic
10C2×C4×C8×C11C2211yescharacteristic
11C2×#66883—21no—
12#10622637—21no—
13#10622637—22no—
14Q8×C11⋊C8—21no—
15#10622538C2211yescharacteristic
16#10622537—21no—
17#10622537C2211yescharacteristic
18#10622537C2211yescharacteristic
19C4×#4318—21no—
20C4×#4318C2211yescharacteristic
21C11×Q8⋊C8C411yescharacteristic
22C11×Q8⋊C8C411yescharacteristic
23C11×Q8⋊C8C411yescharacteristic
24C11×Q8⋊C8C411yescharacteristic
25#10622190—21no—
26Q8⋊(C11⋊C8)—21no—
27Q8⋊(C11⋊C8)—21no—
28#10622096—22no—
29C22×Q8×C11Q811yescharacteristic
30C22×C8×C11—21no—
31C22×C8×C11—21no—
32C4×Q8×C11—21no—
33C4×Q8×C11—21no—
34C4×Q8×C11C2×C411yescharacteristic
35C4×Q8×C11C2×C411yescharacteristic
36C4×Q8×C11D411yescharacteristic
37C4×Q8×C11D411yescharacteristic
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4Q811yescharacteristic
40C2×C42×C11—21no—
41C2×C42×C11C2311yescharacteristic
42C2×#4318—21no—
43C2×#4318—21no—
44C2×#4318D411yescharacteristic
45C2×#4318D411yescharacteristic
46C11×C4⋊C8—21no—
47C11×C4⋊C8C2×C411yescharacteristic
48C11×C4⋊C8C2×C411yescharacteristic
49C4×C8×C11—21no—
50C4×C8×C11C2×C411yescharacteristic
51C4×C8×C11C2×C411yescharacteristic
52C22⋊(C11⋊C8)—21no—
53#66883—42no—
54C4⋊(C11⋊C8)—22no—
55C4⋊(C11⋊C8)—22no—
56C4⋊(C11⋊C8)—21no—
57C4⋊(C11⋊C8)—21no—
58C4⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)D412yes—
61#66867—22no—
62#66867—21no—
63C4×C11⋊C8—22no—
64C4×C11⋊C8—21no—
65C4×C11⋊C8—21no—
66#8907—111nomaximal, Sylow
67C2×Q8×C11—21no—
68C2×Q8×C11—22no—
69C2×Q8×C11—41no—
70C2×Q8×C11C4⋊C411yescharacteristic
71C2×Q8×C11C4⋊C411yescharacteristic
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×Q811yescharacteristic
76C22×C4×C11#4111yescharacteristic
77C2×C8×C11—21no—
78C2×C8×C11—21no—
79C2×C8×C11—21no—
80C2×C8×C11—21no—
81C2×C8×C11—42no—
82C2×C8×C11—41no—
83C2×C8×C11—41no—
84C11×C4⋊C4—21no—
85C11×C4⋊C4—21no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4C4⋊C411yescharacteristic
90C11×C4⋊C4C4⋊C411yescharacteristic
91C42×C11—21no—
92C42×C11—21no—
93C42×C11—21no—
94C42×C11—21no—
95C42×C11C22×C411yescharacteristic
96C42×C11C2×D411yescharacteristic
97C42×C11C2×D411yescharacteristic
98C42×C11#4111yescharacteristic
99#4318—21no—
100#4318—21no—
101#4318—21no—
102#4318—41no—
103#4318—41no—
104#4318—41no—
105#4318—41no—
106#4318Q1612yes—
107C2×C11⋊C8—21no—
108C2×C11⋊C8—21no—
109C2×C11⋊C8—22no—
110C2×C11⋊C8—41no—
111C2×C11⋊C8—41no—
112Q8×M16—111no—
113#1950—111no—
114#1567—111no—
115#1487—111no—
116C2×Q8⋊C8D1111yescharacteristic
117#1301—111no—
118#1278—111no—
119C23×C11C22⋊Q811yescharacteristic
120Q8×C11—21no—
121Q8×C11—21no—
122Q8×C11—21no—
123Q8×C11—42no—
124Q8×C11#10812yescomplemented
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—41no—
132C2×C4×C11—42no—
133C2×C4×C11—81no—
134C2×C4×C11C2×C4⋊C411yescharacteristic
135C2×C4×C11C4×D411yescharacteristic
136C2×C4×C11C4×D411yescharacteristic
137C2×C4×C11#12011yescharacteristic
138C2×C4×C11C22⋊Q811yescharacteristic
139C2×C4×C11#12311yescharacteristic
140C2×C4×C11C2×Q1611yescharacteristic
141C2×C4×C11#13511yescharacteristic
142C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C11#13711yescharacteristic
144C8×C11—22no—
145C8×C11—41no—
146C8×C11—41no—
147C8×C11—41no—
148C11⋊C8—22no—
149C11⋊C8—41no—
150C11⋊C8—42no—
151C11⋊C8—81no—
152C11⋊C8—81no—
153C2×C4×Q8C2×D1111yescharacteristic
154#446—222no—
155#446—221no—
156C8×Q8—221no—
157#431—111no—
158C2×#108—221no—
159#423—111no—
160#423—111no—
161#423—221no—
162C2×C4⋊C8C2×D1111yescharacteristic
163C4×M16—111no—
164C4×M16—221no—
165C2×C4×C8C2×D1111yescharacteristic
166#341—221no—
167#335—222no—
168Q8⋊C8—221no—
169Q8⋊C8—221no—
170Q8⋊C8Dic1111yescharacteristic
171Q8⋊C8Dic1111yescharacteristic
172Q8⋊C8Dic1111yescharacteristic
173Q8⋊C8Dic1111yescharacteristic
174C22×C11—21no—
175C22×C11—21no—
176C22×C11#38511yescharacteristic
177C22×C11#47711yescharacteristic
178C22×C11#47911yescharacteristic
179C4×C11—21no—
180C4×C11—22no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—41no—
184C4×C11—41no—
185C4×C11—41no—
186C4×C11C2×#10811yescharacteristic
187C4×C11#43011yescharacteristic
188C4×C11C4×Q1611yescharacteristic
189C4×C11#44011yescharacteristic
190C4×C11#44911yescharacteristic
191C4×C11#45111yescharacteristic
192C22×Q8Dic2211yescharacteristic
193C2×M16—111no—
194C2×M16—111no—
195C2×M16—221no—
196C2×M16—221no—
197C22×C8—21no—
198C22×C8—21no—
199C4×Q8—21no—
200C4×Q8—21no—
201C4×Q8D4411yescharacteristic
202C4×Q8D4411yescharacteristic
203C4×Q8C2×Dic1111yescharacteristic
204C4×Q8C2×Dic1111yescharacteristic
205C2×C4⋊C4—21no—
206C2×C4⋊C4Dic2211yescharacteristic
207C2×C42—21no—
208C2×C42C22×D1111yescharacteristic
209#108—442no—
210C4⋊C8—21no—
211C4⋊C8—112no—
212C4⋊C8—222no—
213C4⋊C8—222no—
214C4⋊C8—221no—
215C4⋊C8—221no—
216C4⋊C8—221no—
217C4⋊C8—221no—
218C4⋊C8C2×Dic1111yescharacteristic
219C4⋊C8C2×Dic1111yescharacteristic
220C22⋊C8—221no—
221#97—222no—
222#97—221no—
223C4×C8—21no—
224C4×C8—222no—
225C4×C8—221no—
226C4×C8—221no—
227C4×C8C2×Dic1111yescharacteristic
228C4×C8C2×Dic1111yescharacteristic
229C2×C11—21no—
230C2×C11—21no—
231C2×C11#185511yescharacteristic
232C2×C11#186111yescharacteristic
233C2×C11#186311yescharacteristic
234C2×Q8—21no—
235C2×Q8—22no—
236C2×Q8—41no—
237C2×Q8C4⋊Dic1111yescharacteristic
238C2×Q8C4⋊Dic1111yescharacteristic
239C22×C4—21no—
240C22×C4—21no—
241C22×C4C2×Dic2211yescharacteristic
242C22×C4D4×D1111yescharacteristic
243C22×C4#434111yescharacteristic
244M16—112no—
245M16—221no—
246M16—221no—
247M16—221no—
248M16—441no—
249M16—441no—
250M16—441no—
251M16—441no—
252C2×C8—21no—
253C2×C8—21no—
254C2×C8—21no—
255C2×C8—21no—
256C2×C8—42no—
257C2×C8—41no—
258C2×C8—41no—
259C2×C8—221no—
260C2×C8—222no—
261C2×C8—221no—
262C2×C8—441no—
263C2×C8—441no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4C4⋊Dic1111yescharacteristic
270C4⋊C4C4⋊Dic1111yescharacteristic
271C42—21no—
272C42—21no—
273C42—21no—
274C42—21no—
275C42C2×D4411yescharacteristic
276C42D4×D1111yescharacteristic
277C42#434111yescharacteristic
278C42C22×Dic1111yescharacteristic
279C11#890711yescharacteristic, complemented, Sylow
280C23#6693111yescharacteristic
281Q8—21no—
282Q8—21no—
283Q8—21no—
284Q8—42no—
285Q8#6688312yescomplemented
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—81no—
295C2×C4#6693111yescharacteristic
296C2×C4#6693511yescharacteristic
297C2×C4#6693911yescharacteristic
298C2×C4#6696711yescharacteristic
299C2×C4#6696811yescharacteristic
300C2×C4Q16×D1111yescharacteristic
301C2×C4#6697211yescharacteristic
302C2×C4C2×C4⋊Dic1111yescharacteristic
303C2×C4D4×Dic1111yescharacteristic
304C2×C4D4×Dic1111yescharacteristic
305C8—22no—
306C8—41no—
307C8—41no—
308C8—41no—
309C8—222no—
310C8—441no—
311C8—442no—
312C8—881no—
313C8—881no—
314C22—21no—
315C22—21no—
316C22#1062240711yescharacteristic
317C22#1062240911yescharacteristic
318C22#1062256311yescharacteristic
319C4—21no—
320C4—22no—
321C4—21no—
322C4—21no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4#1062242111yescharacteristic
327C4#1062242411yescharacteristic
328C4C2×#6688311yescharacteristic
329C4#1062273811yescharacteristic
330C4#1062277711yescharacteristic
331C4Q16×Dic1111yescharacteristic
332C2—21no—
333C2—21no—
334C2#1306882311yescharacteristic
335C2#1306885811yescharacteristic
336C2#1306887211yescharacteristic
subgroupG/H
centerC2×C4#66935
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×Q8⋊C8C2
socleC22×C11#385
prime radicalC23×C11C22⋊Q8
cosocleC2×C42×C11C23
hypercenterC2×Q8⋊C8D11
hypocenterC11#8907
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
124. Q8×C11#108semidirect
279. C11#8907semidirect
285. Q8#66883semidirect

Maximal subgroups

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

subgroupindex
Q8×#43182
#130693922
#130673752
#130670452
#130665132
#130664532
C2×C11×Q8⋊C82
#890711