Finite Group Databasebeta

← #14646708

Subgroups — #14646708

Order 2816.

454 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622451C211yesmaximal, characteristic
2#13068605C211yesmaximal, characteristic
3#13068605C211yesmaximal, characteristic
4#13067374C211yesmaximal, characteristic, complemented
5#13067371C211yesmaximal, characteristic, complemented
6#13066491C211yesmaximal, characteristic, complemented
7C11×#1292C211yesmaximal, characteristic, complemented
8C22×#4313C412yes—
9C2×C4×D44C2211yescharacteristic
10C11×#423C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13C2×#66887—21no—
14C2×#66887—21no—
15C2×(C2×D11)⋊C8C412yes—
16#10622537C2211yescharacteristic
17#10622537C2211yescharacteristic
18C2×C4×C11⋊C8C2211yescharacteristic
19#10622451—21no—
20#10622451—21no—
21#10622451—21no—
22#10622451—21no—
23#10622192—21no—
24#10622192—21no—
25#10622118—21no—
26#10622118—21no—
27#10622117—21no—
28#10622117—21no—
29C22×D44D411yescharacteristic
30C22×C4×D11C2×C412yes—
31C2×C11×M16—21no—
32C2×C11×M16—21no—
33C22×C8×C11C2×C412yes—
34C2×C42×C11C2311yescharacteristic
35C2×(C2×D11)⋊C4Q812yes—
36C2×C4⋊Dic11D411yescharacteristic
37C2×#4318—21no—
38C2×#4318—21no—
39C22×C11⋊C8C2×C411yescharacteristic
40C22×C11⋊C8C2×C411yescharacteristic
41C2×#4313—22no—
42C2×#4313—22no—
43C2×#4313—44no—
44C4×D44—21no—
45C4×D44—21no—
46C4×D44—21no—
47C4×D44—21no—
48C11×C4⋊C8—21no—
49C11×C4⋊C8—21no—
50C11×C4⋊C8—21no—
51C11×C4⋊C8—21no—
52C11×C4⋊C8—21no—
53C11×C4⋊C8—21no—
54#66887—42no—
55#66887—42no—
56(C2×D11)⋊C8—22no—
57(C2×D11)⋊C8—22no—
58C4⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62C4×C11⋊C8D411yescharacteristic
63C4×C11⋊C8D411yescharacteristic
64C4×C11⋊C8D411yescharacteristic
65C4×C11⋊C8D411yescharacteristic
66#8618—111nomaximal, Sylow
67C23×D11C4⋊C412yes—
68C22×C4×C11C22×C411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×Q811yescharacteristic
71C22×Dic11C4⋊C412yes—
72C2×D44—21no—
73C2×D44—21no—
74C2×D44—21no—
75C2×D44—21no—
76C2×D44—21no—
77C2×D44—21no—
78C2×C4×D11—22no—
79C2×C4×D11—22no—
80C2×C4×D11—42no—
81C2×C4×D11—42no—
82C11×M16—41no—
83C11×M16—41no—
84C11×M16—41no—
85C11×M16—41no—
86C2×C8×C11—22no—
87C2×C8×C11—42no—
88C2×C8×C11—41no—
89C2×C8×C11—41no—
90C42×C11C2×D411yescharacteristic
91C42×C11C2×D411yescharacteristic
92C42×C11#4111yescharacteristic
93C42×C11#4111yescharacteristic
94(C2×D11)⋊C4—22no—
95(C2×D11)⋊C4—22no—
96C4⋊Dic11—21no—
97C4⋊Dic11—21no—
98#4318—41no—
99#4318—41no—
100#4318—41no—
101#4318—41no—
102C2×C11⋊C8—22no—
103C2×C11⋊C8—41no—
104C2×C11⋊C8—41no—
105C2×C11⋊C8—41no—
106C2×C11⋊C8C22⋊C411yescharacteristic
107C2×C11⋊C8C22⋊C411yescharacteristic
108C2×C11⋊C8C22⋊C411yescharacteristic
109C2×C11⋊C8C22⋊C411yescharacteristic
110#4313—44no—
111#4313—44no—
112C2×#436—111no—
113#1800—111no—
114#1800—111no—
115#1567—111no—
116#1566—111no—
117#1292—111no—
118#1292D1111yescharacteristic, complemented
119C23×C11C2×C4⋊C411yescharacteristic
120C22×D11—22no—
121C22×D11—22no—
122C22×D11—22no—
123C22×D11—42no—
124C22×D11—42no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—41no—
128C2×C4×C11C2×C22⋊C411yescharacteristic
129C2×C4×C11#11711yescharacteristic
130C2×C4×C11#12111yescharacteristic
131C2×C4×C11#12111yescharacteristic
132C2×C4×C11C22⋊Q811yescharacteristic
133C2×C4×C11C22⋊Q811yescharacteristic
134C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C11#13711yescharacteristic
137C2×C4×C11#13711yescharacteristic
138C2×Dic11—22no—
139C2×Dic11—42no—
140D44—41no—
141D44—41no—
142D44—41no—
143D44—41no—
144C4×D11—44no—
145C4×D11—42no—
146C4×D11—42no—
147C8×C11—42no—
148C8×C11—81no—
149C8×C11—81no—
150C11⋊C8—21no—
151C11⋊C8—21no—
152C11⋊C8—21no—
153C11⋊C8—81no—
154C11⋊C8—81no—
155C11⋊C8#10012yescomplemented
156C22×M16—112no—
157C2×C4×D4—111no—
158#436—221no—
159#436—221no—
160#436—221no—
161#436—221no—
162#423—111no—
163#423—111no—
164#423C2×D1111yescharacteristic
165#423C2×D1111yescharacteristic
166C2×C4⋊C8C2×D1111yescharacteristic
167C2×#100—221no—
168C2×#100—221no—
169C2×C22⋊C8—112no—
170C2×C4×C8—111no—
171#343—221no—
172#343—221no—
173#335—221no—
174#335—221no—
175#334—221no—
176#334—221no—
177C22×C11—21no—
178C22×C11—21no—
179C22×C11#38011yescharacteristic
180C22×C11#42811yescharacteristic
181C22×C11#42811yescharacteristic
182C2×D11—42no—
183C2×D11—42no—
184C2×D11—42no—
185C2×D11—82no—
186C2×D11—82no—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11C2×#10011yescharacteristic
191C4×C11#41311yescharacteristic
192C4×C11#46811yescharacteristic
193C4×C11#46811yescharacteristic
194C4×C11#46911yescharacteristic
195C4×C11#47011yescharacteristic
196Dic11—42no—
197C22×D4—111no—
198C23×C4—112no—
199C2×M16—21no—
200C2×M16—21no—
201C2×M16—222no—
202C2×M16—222no—
203C2×M16—221no—
204C2×M16—221no—
205C2×M16—444no—
206C22×C8—111no—
207C22×C8—111no—
208C22×C8C4×D1112yes—
209C4×D4—221no—
210C4×D4—221no—
211C4×D4—221no—
212C4×D4—221no—
213C2×C4⋊C4—111no—
214C2×C22⋊C4—112no—
215C2×C42C22×D1111yescharacteristic
216C4⋊C8—21no—
217C4⋊C8—21no—
218C4⋊C8—21no—
219C4⋊C8—21no—
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8—221no—
223C4⋊C8—221no—
224C4⋊C8—221no—
225C4⋊C8—221no—
226#100—442no—
227#100—442no—
228C22⋊C8—222no—
229C22⋊C8—222no—
230C4×C8—111no—
231C4×C8—111no—
232C4×C8—111no—
233C4×C8—111no—
234C2×C11—21no—
235C2×C11—21no—
236C2×C11#180011yescharacteristic
237C2×C11#180911yescharacteristic
238C2×C11#181311yescharacteristic
239D11—82no—
240C24—112no—
241C2×D4—221no—
242C2×D4—221no—
243C2×D4—221no—
244C2×D4—221no—
245C2×D4—221no—
246C2×D4—221no—
247C22×C4—112no—
248C22×C4—222no—
249C22×C4—222no—
250C22×C4—442no—
251C22×C4—442no—
252C22×C4C2×C4×D1111yescharacteristic
253C22×C4D4×D1111yescharacteristic
254C22×C4Q8×D1111yescharacteristic
255M16—41no—
256M16—41no—
257M16—41no—
258M16—41no—
259M16—444no—
260M16—444no—
261M16—441no—
262M16—441no—
263M16—441no—
264M16—441no—
265C2×C8—22no—
266C2×C8—42no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8—111no—
270C2×C8—111no—
271C2×C8—111no—
272C2×C8—111no—
273C2×C8—222no—
274C2×C8—441no—
275C2×C8—441no—
276C2×C8—441no—
277C4⋊C4—221no—
278C4⋊C4—221no—
279C22⋊C4—222no—
280C22⋊C4—222no—
281C42#433911yescharacteristic
282C42#433911yescharacteristic
283C42D4×D1111yescharacteristic
284C42D4×D1111yescharacteristic
285C11#861811yescharacteristic, complemented, Sylow
286C23—222no—
287C23—222no—
288C23—222no—
289C23—442no—
290C23—442no—
291C23C4⋊C4×D1111yescharacteristic
292D4—441no—
293D4—441no—
294D4—441no—
295D4—441no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—41no—
299C2×C4—222no—
300C2×C4—444no—
301C2×C4—442no—
302C2×C4—442no—
303C2×C4—442no—
304C2×C4#6692511yescharacteristic
305C2×C4C22⋊C4×D1111yescharacteristic
306C2×C4#6693711yescharacteristic
307C2×C4#6693711yescharacteristic
308C2×C4#6694911yescharacteristic
309C2×C4#6694911yescharacteristic
310C2×C4#6696411yescharacteristic
311C2×C4#6696711yescharacteristic
312C2×C4#6696811yescharacteristic
313C2×C4#6697111yescharacteristic
314C8—42no—
315C8—81no—
316C8—81no—
317C8—112no—
318C8—221no—
319C8—221no—
320C8—221no—
321C8—881no—
322C8—881no—
323C22—21no—
324C22—21no—
325C22—442no—
326C22—442no—
327C22—442no—
328C22—882no—
329C22—882no—
330C22#1062228011yescharacteristic
331C22#1062247411yescharacteristic
332C22#1062249411yescharacteristic
333C4—21no—
334C4—21no—
335C4—21no—
336C4—442no—
337C4D11×#10011yescharacteristic
338C4#1062236411yescharacteristic
339C4#1062239311yescharacteristic
340C4#1062239511yescharacteristic
341C4#1062242511yescharacteristic
342C4#1062242911yescharacteristic
343C2—21no—
344C2—21no—
345C2—882no—
346C2#1306860711yescharacteristic
347C2#1306864811yescharacteristic
348C2#1306866511yescharacteristic
subgroupG/H
centerC22#10622280
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1292C2
socleC22×C11#380
prime radicalC22×D44D4
cosocleC2×C42×C11C23
hypercenter#1292D11
hypocenterC11#8618
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1292

Complements

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

NH ≅ G/Ntype
4. #13067374C2semidirect
5. #13067371C2semidirect
6. #13066491C2semidirect
7. C11×#1292C2semidirect
118. #1292D11semidirect
155. C11⋊C8#100semidirect
285. C11#8618semidirect

Maximal subgroups

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

subgroupindex
C2×#106224512
#130686052
#130673742
#130673712
#130664912
C11×#12922
#861811