Finite Group Databasebeta

← #14646895

Subgroups — #14646895

Order 2816.

482 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C11⋊C8C211yesmaximal, characteristic
2#13068787C211yesmaximal, characteristic, complemented
3#13067362C211yesmaximal, characteristic, complemented
4#13067041C211yesmaximal, characteristic
5#13066512C211yesmaximal, characteristic, complemented
6#13066511C211yesmaximal, characteristic, complemented
7C11×#1486C211yesmaximal, characteristic
8C2×C4×D4×C11C2211yescharacteristic
9C23×C11⋊C8—21no—
10C11×#431C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C2×C22⋊(C11⋊C8)—21no—
13C2×#66886—21no—
14C2×#66886—21no—
15D4×C11⋊C8—21no—
16D4×C11⋊C8—21no—
17D4×C11⋊C8C412yes—
18D4×C11⋊C8C412yes—
19#10622538C2211yescharacteristic
20#10622537C2211yescharacteristic
21C2×C4⋊(C11⋊C8)C2211yescharacteristic
22C2×C4×C11⋊C8C2211yescharacteristic
23C11×D4⋊C8—22no—
24D4⋊(C11⋊C8)—22no—
25#10622118—21no—
26#10622117—21no—
27C22×D4×C11Q811yescharacteristic
28C23×C4×C11—21no—
29C2×C11×M16—21no—
30C4×D4×C11—21no—
31C4×D4×C11—21no—
32C4×D4×C11C2×C412yes—
33C4×D4×C11D412yes—
34C2×C11×C4⋊C4Q811yescharacteristic
35C2×C11×C22⋊C4—21no—
36C2×C42×C11C2311yescharacteristic
37C2×#4318—21no—
38C22×C11⋊C8—21no—
39C22×C11⋊C8—22no—
40C22×C11⋊C8—22no—
41C22×C11⋊C8—42no—
42C22×C11⋊C8—42no—
43C22×C11⋊C8D411yescharacteristic
44C22×C11⋊C8D411yescharacteristic
45C11×C4⋊C8—21no—
46C11×C4⋊C8—21no—
47C11×C4⋊C8—21no—
48C11×C22⋊C8—21no—
49C4×C8×C11—21no—
50C22⋊(C11⋊C8)—22no—
51C22⋊(C11⋊C8)—22no—
52C22⋊(C11⋊C8)—21no—
53#66886—42no—
54#66886—42no—
55C4⋊(C11⋊C8)—21no—
56C4⋊(C11⋊C8)—21no—
57C4⋊(C11⋊C8)—21no—
58C4⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)C2×C412yes—
60C4×C11⋊C8—21no—
61C4×C11⋊C8C2×C411yescharacteristic
62C4×C11⋊C8C2×C411yescharacteristic
63C4×C11⋊C8D411yescharacteristic
64C4×C11⋊C8D411yescharacteristic
65#8658—111nomaximal, Sylow
66C24×C11—21no—
67C2×D4×C11—24no—
68C2×D4×C11—21no—
69C2×D4×C11C4⋊C412yes—
70C22×C4×C11—21no—
71C22×C4×C11—22no—
72C22×C4×C11—22no—
73C22×C4×C11—41no—
74C22×C4×C11—41no—
75C22×C4×C11—41no—
76C22×C4×C11—41no—
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×Q811yescharacteristic
79C22×C4×C11#4111yescharacteristic
80C11×M16—41no—
81C11×M16—41no—
82C2×C8×C11—41no—
83C2×C8×C11—41no—
84C11×C4⋊C4—21no—
85C11×C4⋊C4C4⋊C412yes—
86C11×C22⋊C4—22no—
87C11×C22⋊C4—22no—
88C42×C11C22×C411yescharacteristic
89C42×C11C2×D411yescharacteristic
90C42×C11C2×D411yescharacteristic
91C42×C11#4111yescharacteristic
92#4318—41no—
93#4318—41no—
94C2×C11⋊C8—22no—
95C2×C11⋊C8—21no—
96C2×C11⋊C8—21no—
97C2×C11⋊C8—44no—
98C2×C11⋊C8—44no—
99C2×C11⋊C8—41no—
100C2×C11⋊C8—41no—
101C2×C11⋊C8—41no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8C22⋊C411yescharacteristic
104C2×C11⋊C8C22⋊C411yescharacteristic
105C2×C11⋊C8C22⋊C411yescharacteristic
106C2×C11⋊C8C22⋊C411yescharacteristic
107C2×C11⋊C8D812yes—
108C2×C11⋊C8SD1612yes—
109C2×C8×D4—111no—
110#1848—111no—
111#1564—111no—
112#1486—111no—
113#1486D1111yescharacteristic
114#1301—111no—
115#1301—111no—
116C23×C11—24no—
117C23×C11—22no—
118C23×C11—42no—
119C23×C11—41no—
120C23×C11—41no—
121C23×C11C22⋊Q811yescharacteristic
122D4×C11—24no—
123D4×C11—22no—
124D4×C11#10814yescomplemented
125C2×C4×C11—22no—
126C2×C4×C11—22no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—42no—
131C2×C4×C11—42no—
132C2×C4×C11—42no—
133C2×C4×C11—42no—
134C2×C4×C11C2×C22⋊C411yescharacteristic
135C2×C4×C11C2×C4⋊C411yescharacteristic
136C2×C4×C11#11711yescharacteristic
137C2×C4×C11#12111yescharacteristic
138C2×C4×C11#12111yescharacteristic
139C2×C4×C11C22⋊Q811yescharacteristic
140C2×C4×C11C2×D811yescharacteristic
141C2×C4×C11C2×SD1611yescharacteristic
142C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C11#13711yescharacteristic
144C8×C11—81no—
145C8×C11—81no—
146C11⋊C8—21no—
147C11⋊C8—21no—
148C11⋊C8—42no—
149C11⋊C8—81no—
150C11⋊C8—81no—
151C11⋊C8#10212yes—
152C11⋊C8#10212yes—
153C23×C8—221no—
154C2×C4×D4C2×D1111yescharacteristic
155C8×D4—112no—
156C8×D4—112no—
157C8×D4—221no—
158C8×D4—221no—
159#431—111no—
160#431C2×D1111yescharacteristic
161C2×#108—221no—
162C2×#108—221no—
163#423—111no—
164#423C2×D1111yescharacteristic
165C2×C4⋊C8—111no—
166C2×C22⋊C8—221no—
167C2×C4×C8—111no—
168#335—221no—
169#334—221no—
170D4⋊C8—22no—
171D4⋊C8—222no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11—24no—
175C22×C11—44no—
176C22×C11—44no—
177C22×C11—42no—
178C22×C11—42no—
179C22×C11#38011yescharacteristic
180C22×C11#47411yescharacteristic
181C22×C11#47611yescharacteristic
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—42no—
186C4×C11C2×#10211yescharacteristic
187C4×C11#41711yescharacteristic
188C4×C11C2×#10812yes—
189C4×C11#45911yescharacteristic
190C4×C11#46111yescharacteristic
191C22×D4Dic2211yescharacteristic
192C23×C4—21no—
193C2×M16—21no—
194C2×M16—221no—
195C22×C8—111no—
196C22×C8—111no—
197C22×C8—222no—
198C22×C8—222no—
199C22×C8—221no—
200C22×C8—442no—
201C22×C8—442no—
202C4×D4—21no—
203C4×D4—21no—
204C4×D4C4×D1112yes—
205C4×D4C22⋊D1112yes—
206C2×C4⋊C4Dic2211yescharacteristic
207C2×C22⋊C4—21no—
208C2×C42C22×D1111yescharacteristic
209#108—442no—
210#108—442no—
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8—21no—
214C4⋊C8—112no—
215C4⋊C8—221no—
216C4⋊C8—221no—
217C4⋊C8—221no—
218C4⋊C8—221no—
219C22⋊C8—21no—
220C22⋊C8—222no—
221C22⋊C8—222no—
222C22⋊C8—221no—
223C4×C8—21no—
224C4×C8—111no—
225C4×C8—111no—
226C4×C8—111no—
227C4×C8—111no—
228C4×C8—221no—
229C2×C11—21no—
230C2×C11—21no—
231C2×C11—44no—
232C2×C11#180211yescharacteristic
233C2×C11#181011yescharacteristic
234C2×C11#181411yescharacteristic
235C24—21no—
236C2×D4—24no—
237C2×D4—21no—
238C2×D4Dic11⋊C412yes—
239C22×C4—21no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—41no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4C2×Dic2211yescharacteristic
247C22×C4D4×D1111yescharacteristic
248C22×C4#434111yescharacteristic
249M16—41no—
250M16—41no—
251M16—441no—
252M16—441no—
253C2×C8—41no—
254C2×C8—41no—
255C2×C8—111no—
256C2×C8—111no—
257C2×C8—112no—
258C2×C8—112no—
259C2×C8—111no—
260C2×C8—111no—
261C2×C8—221no—
262C2×C8—221no—
263C2×C8—222no—
264C2×C8—444no—
265C2×C8—444no—
266C2×C8—441no—
267C2×C8—441no—
268C2×C8—441no—
269C2×C8—441no—
270C4⋊C4—21no—
271C4⋊C4Dic11⋊C412yes—
272C22⋊C4—22no—
273C22⋊C4—22no—
274C42C2×C4×D1111yescharacteristic
275C42D4×D1111yescharacteristic
276C42#434111yescharacteristic
277C42C2×C22⋊D1111yescharacteristic
278C11#865811yescharacteristic, complemented, Sylow
279C23—24no—
280C23—22no—
281C23—42no—
282C23—41no—
283C23—41no—
284C23#6693111yescharacteristic
285D4—24no—
286D4—22no—
287D4#6688614yescomplemented
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4#6693011yescharacteristic
298C2×C4#6693111yescharacteristic
299C2×C4C22⋊C4×D1111yescharacteristic
300C2×C4D8×D1111yescharacteristic
301C2×C4#6696411yescharacteristic
302C2×C4SD16×D1111yescharacteristic
303C2×C4#6696811yescharacteristic
304C2×C4C2×Dic11⋊C411yescharacteristic
305C2×C4#6699211yescharacteristic
306C2×C4#6699211yescharacteristic
307C8—81no—
308C8—81no—
309C8—112no—
310C8—112no—
311C8—221no—
312C8—221no—
313C8—442no—
314C8—881no—
315C8—881no—
316C22—21no—
317C22—21no—
318C22—24no—
319C22—44no—
320C22—44no—
321C22—42no—
322C22—42no—
323C22#1062237211yescharacteristic
324C22#1062237411yescharacteristic
325C22#1062255511yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—42no—
330C4D11×#10211yescharacteristic
331C4#1062238411yescharacteristic
332C4C2×#6688612yes—
333C4#1062276311yescharacteristic
334C4#1062277511yescharacteristic
335C2—21no—
336C2—21no—
337C2—44no—
338C2#1306861411yescharacteristic
339C2#1306865211yescharacteristic
340C2#1306866811yescharacteristic
subgroupG/H
centerC2×C4#66992
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1486C2
socleC22×C11#380
prime radicalC22×D4×C11Q8
cosocleC2×C42×C11C23
hypercenter#1486D11
hypocenterC11#8658
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1486

Complements

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

NH ≅ G/Ntype
2. #13068787C2semidirect
3. #13067362C2semidirect
5. #13066512C2semidirect
6. #13066511C2semidirect
124. D4×C11#108semidirect
278. C11#8658semidirect
287. D4#66886semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C11⋊C82
#130687872
#130673622
#130670412
#130665122
#130665112
C11×#14862
#865811