Finite Group Databasebeta

← #14648111

Subgroups — #14648111

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
1M16×Dic22C211yesmaximal, characteristic
2#13069391C211yesmaximal, characteristic
3#13067375C211yesmaximal, characteristic
4#13067046C211yesmaximal, characteristic
5C2×#10622094C211yesmaximal, characteristic
6#13066512C211yesmaximal, characteristic
7C11×#1278C211yesmaximal, characteristic
8C2×C4×Dic22C2211yescharacteristic
9C11×#431C2211yescharacteristic
10C4×C11×M16C2211yescharacteristic
11C2×C4×C8×C11C2211yescharacteristic
12C2×#66886—21no—
13#10622731—21no—
14M16×Dic11—21no—
15#10622537C2211yescharacteristic
16#10622537C2211yescharacteristic
17C2×C4⋊(C11⋊C8)C2211yescharacteristic
18#10622314—22no—
19#10622292—21no—
20C8×Dic22—21no—
21#10622196—21no—
22#10622096—22no—
23#10622094—21no—
24#10622094—21no—
25#10622094C411yescharacteristic
26#10622094C411yescharacteristic
27#10622094C411yescharacteristic
28#10622094C411yescharacteristic
29C22×Dic22Q811yescharacteristic
30C2×C11×M16D411yescharacteristic
31C2×C11×M16D411yescharacteristic
32C22×C8×C11—21no—
33C2×C42×C11C2311yescharacteristic
34C2×C4⋊Dic11Q811yescharacteristic
35C2×Dic11⋊C4—21no—
36C2×C4×Dic11—21no—
37C2×#4318—21no—
38C2×#4318—21no—
39C22×C11⋊C8—21no—
40C4×Dic22—21no—
41C4×Dic22—21no—
42C4×Dic22C2×C411yescharacteristic
43C4×Dic22C2×C411yescharacteristic
44C4×Dic22D411yescharacteristic
45C4×Dic22D411yescharacteristic
46C11×C4⋊C8—21no—
47C11×C22⋊C8—21no—
48C11×#97—21no—
49C4×C8×C11—21no—
50C4×C8×C11—21no—
51C4×C8×C11—21no—
52C4×C8×C11C2×C411yescharacteristic
53C4×C8×C11C2×C411yescharacteristic
54#66886—42no—
55#66879—22no—
56Dic11⋊C8—22no—
57Dic11⋊C8—22no—
58C8×Dic11—22no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)C2×C411yescharacteristic
64C4⋊(C11⋊C8)C2×C411yescharacteristic
65C4⋊(C11⋊C8)D412yes—
66#8907—111nomaximal, Sylow
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×Q811yescharacteristic
69C22×C4×C11#4111yescharacteristic
70C22×Dic11—21no—
71C22×Dic11—21no—
72C2×Dic22—22no—
73C2×Dic22—21no—
74C2×Dic22—41no—
75C2×Dic22C4⋊C411yescharacteristic
76C2×Dic22C4⋊C411yescharacteristic
77C11×M16—21no—
78C11×M16—21no—
79C11×M16—21no—
80C11×M16Q1612yes—
81C2×C8×C11—21no—
82C2×C8×C11—21no—
83C2×C8×C11—21no—
84C2×C8×C11—21no—
85C2×C8×C11—42no—
86C2×C8×C11—41no—
87C42×C11C22×C411yescharacteristic
88C42×C11C2×D411yescharacteristic
89C42×C11C2×D411yescharacteristic
90C42×C11#4111yescharacteristic
91C4⋊Dic11—21no—
92C4⋊Dic11C4⋊C411yescharacteristic
93C4⋊Dic11C4⋊C411yescharacteristic
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98C4×Dic11—21no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11—21no—
102#4318—41no—
103#4318—41no—
104#4318—41no—
105#4318—41no—
106C2×C11⋊C8—21no—
107C2×C11⋊C8—21no—
108C2×C11⋊C8—22no—
109C2×C11⋊C8—41no—
110C2×C11⋊C8—41no—
111C2×C11⋊C8—41no—
112Q8×M16—111no—
113#1950—111no—
114#1567—111no—
115#1487—111no—
116C2×Q8⋊C8—111no—
117#1301—111no—
118#1278D1111yescharacteristic
119C23×C11C22⋊Q811yescharacteristic
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—41no—
123C2×C4×C11C2×C4⋊C411yescharacteristic
124C2×C4×C11C4×D411yescharacteristic
125C2×C4×C11C4×D411yescharacteristic
126C2×C4×C11#12011yescharacteristic
127C2×C4×C11C22⋊Q811yescharacteristic
128C2×C4×C11#12311yescharacteristic
129C2×C4×C11C2×Q1611yescharacteristic
130C2×C4×C11#13511yescharacteristic
131C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C11#13711yescharacteristic
133C2×Dic11—21no—
134C2×Dic11—21no—
135C2×Dic11—21no—
136C2×Dic11—21no—
137C2×Dic11—42no—
138C2×Dic11—81no—
139Dic22—21no—
140Dic22—21no—
141Dic22—21no—
142Dic22—42no—
143Dic22#10812yescomplemented
144C8×C11—22no—
145C8×C11—22no—
146C8×C11—41no—
147C8×C11—41no—
148C8×C11—81no—
149C11⋊C8—41no—
150C11⋊C8—41no—
151C11⋊C8—42no—
152C11⋊C8—81no—
153C2×C4×Q8—111no—
154#446—221no—
155#446—222no—
156C8×Q8—221no—
157#431C2×D1111yescharacteristic
158C2×#108—221no—
159#423—111no—
160#423—111no—
161#423—221no—
162C2×C4⋊C8—111no—
163C4×M16—221no—
164C4×M16C2×D1111yescharacteristic
165C2×C4×C8C2×D1111yescharacteristic
166#341—221no—
167#335—222no—
168Q8⋊C8—111no—
169Q8⋊C8—111no—
170Q8⋊C8—111no—
171Q8⋊C8—111no—
172Q8⋊C8—221no—
173Q8⋊C8—221no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11#38511yescharacteristic
177C22×C11#47711yescharacteristic
178C22×C11#47911yescharacteristic
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11C2×#10811yescharacteristic
183C4×C11#43011yescharacteristic
184C4×C11C4×Q1611yescharacteristic
185C4×C11#44011yescharacteristic
186C4×C11#44911yescharacteristic
187C4×C11#45111yescharacteristic
188Dic11—22no—
189Dic11—41no—
190Dic11—41no—
191Dic11—41no—
192C22×Q8—111no—
193C2×M16—221no—
194C2×M16—221no—
195C2×M16D4411yescharacteristic
196C2×M16D4411yescharacteristic
197C22×C8—21no—
198C22×C8—221no—
199C4×Q8—111no—
200C4×Q8—111no—
201C4×Q8—111no—
202C4×Q8—111no—
203C4×Q8—221no—
204C4×Q8—221no—
205C2×C4⋊C4—111no—
206C2×C4⋊C4—221no—
207C2×C42—221no—
208C2×C42C22×D1111yescharacteristic
209#108—442no—
210C4⋊C8—21no—
211C4⋊C8—111no—
212C4⋊C8—111no—
213C4⋊C8—112no—
214C4⋊C8—222no—
215C4⋊C8—222no—
216C4⋊C8—221no—
217C4⋊C8—221no—
218C4⋊C8—221no—
219C4⋊C8—221no—
220C22⋊C8—21no—
221#97—21no—
222#97—222no—
223C4×C8—21no—
224C4×C8—21no—
225C4×C8—21no—
226C4×C8—222no—
227C4×C8C4×D1111yescharacteristic
228C4×C8C4×D1111yescharacteristic
229C2×C11—21no—
230C2×C11—21no—
231C2×C11#185511yescharacteristic
232C2×C11#186111yescharacteristic
233C2×C11#186311yescharacteristic
234C2×Q8—111no—
235C2×Q8—111no—
236C2×Q8—222no—
237C2×Q8—221no—
238C2×Q8—441no—
239C22×C4—221no—
240C22×C4—221no—
241C22×C4C2×D4411yescharacteristic
242C22×C4#434111yescharacteristic
243C22×C4Q8×D1111yescharacteristic
244M16—21no—
245M16—21no—
246M16—21no—
247M16—441no—
248M16—441no—
249M16—441no—
250M16—441no—
251M16Dic4412yes—
252C2×C8—21no—
253C2×C8—21no—
254C2×C8—21no—
255C2×C8—21no—
256C2×C8—42no—
257C2×C8—41no—
258C2×C8—221no—
259C2×C8—221no—
260C2×C8—222no—
261C2×C8—441no—
262C2×C8—441no—
263C2×C8—441no—
264C4⋊C4—111no—
265C4⋊C4—111no—
266C4⋊C4—221no—
267C4⋊C4—221no—
268C4⋊C4—221no—
269C4⋊C4—221no—
270C4⋊C4—221no—
271C42—221no—
272C42—221no—
273C42—221no—
274C42—221no—
275C42C2×C4×D1111yescharacteristic
276C42#433911yescharacteristic
277C42D4×D1111yescharacteristic
278C42D4×D1111yescharacteristic
279C11#890711yescharacteristic, complemented, Sylow
280C23#6695011yescharacteristic
281Q8—112no—
282Q8—221no—
283Q8—221no—
284Q8—221no—
285Q8—442no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—41no—
289C2×C4—221no—
290C2×C4—221no—
291C2×C4—221no—
292C2×C4—221no—
293C2×C4—442no—
294C2×C4—881no—
295C2×C4C4×D4411yescharacteristic
296C2×C4(C22⋊D11)⋊C411yescharacteristic
297C2×C4#6693511yescharacteristic
298C2×C4#6693611yescharacteristic
299C2×C4C4⋊C4×D1111yescharacteristic
300C2×C4#6694911yescharacteristic
301C2×C4#6695711yescharacteristic
302C2×C4C2×Dic4411yescharacteristic
303C2×C4#6696111yescharacteristic
304C2×C4#6696211yescharacteristic
305C8—22no—
306C8—22no—
307C8—41no—
308C8—41no—
309C8—81no—
310C8—441no—
311C8—441no—
312C8—442no—
313C8—881no—
314C22—21no—
315C22—21no—
316C22#1062228111yescharacteristic
317C22#1062244211yescharacteristic
318C22#1062246311yescharacteristic
319C4—21no—
320C4—21no—
321C4—21no—
322C4—222no—
323C4—441no—
324C4—441no—
325C4—441no—
326C4C4×Dic4411yescharacteristic
327C4#1062232311yescharacteristic
328C4#1062234711yescharacteristic
329C4#1062235211yescharacteristic
330C4D11×#10811yescharacteristic
331C4#1062250611yescharacteristic
332C2—21no—
333C2—21no—
334C2#1306882211yescharacteristic
335C2#1306885711yescharacteristic
336C2#1306887311yescharacteristic
subgroupG/H
centerC2×C4#66935
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1278C2
socleC22×C11#385
prime radicalC23×C11C22⋊Q8
cosocleC2×C42×C11C23
hypercenter#1278D11
hypocenterC11#8907
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1278

Complements

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

NH ≅ G/Ntype
143. Dic22#108semidirect
279. C11#8907semidirect

Maximal subgroups

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

subgroupindex
M16×Dic222
#130693912
#130673752
#130670462
C2×#106220942
#130665122
C11×#12782
#890711