Finite Group Databasebeta

← #14646905

Subgroups — #14646905

Order 2816.

466 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
1C2×D4×C11⋊C8C211yesmaximal, characteristic
2#13068753C211yesmaximal, 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—
13D4×C11⋊C8—21no—
14D4×C11⋊C8—21no—
15D4×C11⋊C8C412yes—
16D4×C11⋊C8C412yes—
17#10622538C2211yescharacteristic
18#10622537C2211yescharacteristic
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C2×C4×C11⋊C8C2211yescharacteristic
21C11×D4⋊C8—22no—
22#10622196—21no—
23#10622196—21no—
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—
53C4⋊(C11⋊C8)—21no—
54C4⋊(C11⋊C8)—21no—
55C4⋊(C11⋊C8)—21no—
56C4⋊(C11⋊C8)—21no—
57C4⋊(C11⋊C8)C2×C412yes—
58C4×C11⋊C8—21no—
59C4×C11⋊C8C2×C411yescharacteristic
60C4×C11⋊C8C2×C411yescharacteristic
61C4×C11⋊C8D411yescharacteristic
62C4×C11⋊C8D411yescharacteristic
63#8660—111nomaximal, Sylow
64C24×C11—21no—
65C2×D4×C11—24no—
66C2×D4×C11—21no—
67C2×D4×C11C4⋊C412yes—
68C22×C4×C11—21no—
69C22×C4×C11—22no—
70C22×C4×C11—22no—
71C22×C4×C11—41no—
72C22×C4×C11—41no—
73C22×C4×C11—41no—
74C22×C4×C11—41no—
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×Q811yescharacteristic
77C22×C4×C11#4111yescharacteristic
78C11×M16—41no—
79C11×M16—41no—
80C2×C8×C11—41no—
81C2×C8×C11—41no—
82C11×C4⋊C4—21no—
83C11×C4⋊C4C4⋊C412yes—
84C11×C22⋊C4—22no—
85C11×C22⋊C4—22no—
86C42×C11C22×C411yescharacteristic
87C42×C11C2×D411yescharacteristic
88C42×C11C2×D411yescharacteristic
89C42×C11#4111yescharacteristic
90#4318—41no—
91#4318—41no—
92C2×C11⋊C8—22no—
93C2×C11⋊C8—21no—
94C2×C11⋊C8—21no—
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×C8×D4—111no—
108#1837—111no—
109#1564—111no—
110#1486—111no—
111#1486D1111yescharacteristic
112#1301—111no—
113#1301—111no—
114C23×C11—24no—
115C23×C11—22no—
116C23×C11—42no—
117C23×C11—41no—
118C23×C11—41no—
119C23×C11C22⋊Q811yescharacteristic
120D4×C11—24no—
121D4×C11—22no—
122D4×C11#10814yes—
123C2×C4×C11—22no—
124C2×C4×C11—22no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—42no—
129C2×C4×C11—42no—
130C2×C4×C11—42no—
131C2×C4×C11—42no—
132C2×C4×C11C2×C22⋊C411yescharacteristic
133C2×C4×C11C2×C4⋊C411yescharacteristic
134C2×C4×C11#11711yescharacteristic
135C2×C4×C11#12111yescharacteristic
136C2×C4×C11#12111yescharacteristic
137C2×C4×C11C22⋊Q811yescharacteristic
138C2×C4×C11#13511yescharacteristic
139C2×C4×C11#13511yescharacteristic
140C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
142C8×C11—81no—
143C8×C11—81no—
144C11⋊C8—21no—
145C11⋊C8—21no—
146C11⋊C8—21no—
147C11⋊C8—21no—
148C11⋊C8—42no—
149C11⋊C8—81no—
150C11⋊C8—81no—
151C23×C8—221no—
152C2×C4×D4C2×D1111yescharacteristic
153C8×D4—112no—
154C8×D4—112no—
155C8×D4—221no—
156C8×D4—221no—
157#431—111no—
158#431C2×D1111yescharacteristic
159#423—111no—
160#423C2×D1111yescharacteristic
161C2×C4⋊C8—111no—
162C2×C22⋊C8—221no—
163C2×C4×C8—111no—
164#341—221no—
165#341—221no—
166#335—221no—
167#334—221no—
168D4⋊C8—22no—
169D4⋊C8—222no—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11—24no—
173C22×C11—44no—
174C22×C11—44no—
175C22×C11—42no—
176C22×C11—42no—
177C22×C11#38011yescharacteristic
178C22×C11#47811yescharacteristic
179C22×C11#47811yescharacteristic
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—42no—
184C4×C11#41611yescharacteristic
185C4×C11#41811yescharacteristic
186C4×C11C2×#10812yes—
187C4×C11#46311yescharacteristic
188C4×C11#46311yescharacteristic
189C22×D4Dic2211yescharacteristic
190C23×C4—21no—
191C2×M16—21no—
192C2×M16—221no—
193C22×C8—111no—
194C22×C8—111no—
195C22×C8—222no—
196C22×C8—222no—
197C22×C8—221no—
198C22×C8—442no—
199C22×C8—442no—
200C4×D4—21no—
201C4×D4—21no—
202C4×D4C4×D1112yes—
203C4×D4C22⋊D1112yes—
204C2×C4⋊C4Dic2211yescharacteristic
205C2×C22⋊C4—21no—
206C2×C42C22×D1111yescharacteristic
207C4⋊C8—21no—
208C4⋊C8—21no—
209C4⋊C8—21no—
210C4⋊C8—112no—
211C4⋊C8—221no—
212C4⋊C8—221no—
213C4⋊C8—221no—
214C4⋊C8—221no—
215C22⋊C8—21no—
216C22⋊C8—222no—
217C22⋊C8—222no—
218C22⋊C8—221no—
219C4×C8—21no—
220C4×C8—111no—
221C4×C8—111no—
222C4×C8—111no—
223C4×C8—111no—
224C4×C8—221no—
225C2×C11—21no—
226C2×C11—21no—
227C2×C11—44no—
228C2×C11#180411yescharacteristic
229C2×C11#181011yescharacteristic
230C2×C11#181411yescharacteristic
231C24—21no—
232C2×D4—24no—
233C2×D4—21no—
234C2×D4Dic11⋊C412yes—
235C22×C4—21no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4C2×Dic2211yescharacteristic
243C22×C4D4×D1111yescharacteristic
244C22×C4#434111yescharacteristic
245M16—41no—
246M16—41no—
247M16—441no—
248M16—441no—
249C2×C8—41no—
250C2×C8—41no—
251C2×C8—111no—
252C2×C8—111no—
253C2×C8—111no—
254C2×C8—111no—
255C2×C8—221no—
256C2×C8—221no—
257C2×C8—221no—
258C2×C8—221no—
259C2×C8—222no—
260C2×C8—444no—
261C2×C8—444no—
262C2×C8—441no—
263C2×C8—441no—
264C2×C8—441no—
265C2×C8—441no—
266C4⋊C4—21no—
267C4⋊C4Dic11⋊C412yes—
268C22⋊C4—22no—
269C22⋊C4—22no—
270C42C2×C4×D1111yescharacteristic
271C42D4×D1111yescharacteristic
272C42#434111yescharacteristic
273C42C2×C22⋊D1111yescharacteristic
274C11#866011yescharacteristic, complemented, Sylow
275C23—24no—
276C23—22no—
277C23—42no—
278C23—41no—
279C23—41no—
280C23#6693111yescharacteristic
281D4—24no—
282D4—22no—
283D4#6688614yes—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4#6693011yescharacteristic
294C2×C4#6693111yescharacteristic
295C2×C4C22⋊C4×D1111yescharacteristic
296C2×C4#6696411yescharacteristic
297C2×C4#6696511yescharacteristic
298C2×C4#6696711yescharacteristic
299C2×C4#6696911yescharacteristic
300C2×C4C2×Dic11⋊C411yescharacteristic
301C2×C4#6699211yescharacteristic
302C2×C4#6699211yescharacteristic
303C8—81no—
304C8—81no—
305C8—221no—
306C8—221no—
307C8—221no—
308C8—221no—
309C8—442no—
310C8—881no—
311C8—881no—
312C22—21no—
313C22—21no—
314C22—24no—
315C22—44no—
316C22—44no—
317C22—42no—
318C22—42no—
319C22#1062237611yescharacteristic
320C22#1062237911yescharacteristic
321C22#1062255511yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—42no—
326C4#1062238311yescharacteristic
327C4#1062238511yescharacteristic
328C4C2×#6688612yes—
329C4#1062276611yescharacteristic
330C4#1062277811yescharacteristic
331C2—21no—
332C2—21no—
333C2—44no—
334C2#1306862411yescharacteristic
335C2#1306865211yescharacteristic
336C2#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#8660
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. #13068753C2semidirect
3. #13067362C2semidirect
5. #13066512C2semidirect
6. #13066511C2semidirect
274. C11#8660semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C11⋊C82
#130687532
#130673622
#130670412
#130665122
#130665112
C11×#14862
#866011