Finite Group Databasebeta

← #14646906

Subgroups — #14646906

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×#10622447C211yesmaximal, characteristic
2#13068753C211yesmaximal, characteristic, complemented
3#13067362C211yesmaximal, characteristic, complemented
4#13067042C211yesmaximal, characteristic
5#13067040C211yesmaximal, characteristic
6#13066513C211yesmaximal, characteristic, complemented
7C11×#1301C211yesmaximal, characteristic, complemented
8C22×C8×D11—21no—
9C2×C4×D44C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13C2×(C2×D11)⋊C8—21no—
14#10622538C2211yescharacteristic
15#10622537C2211yescharacteristic
16C2×C4×C11⋊C8C2211yescharacteristic
17#10622447—21no—
18#10622447—21no—
19#10622447C412yes—
20#10622447C412yes—
21#10622196—21no—
22#10622196—21no—
23#10622121—22no—
24#10622118—21no—
25#10622117—21no—
26#10622097—22no—
27C22×D44Q811yescharacteristic
28C22×C4×D11—21no—
29C2×C11×M16—21no—
30C22×C8×C11—21no—
31C2×C42×C11C2311yescharacteristic
32C2×(C2×D11)⋊C4—21no—
33C2×C4⋊Dic11Q811yescharacteristic
34C2×#4318—21no—
35C22×C11⋊C8D411yescharacteristic
36C22×C11⋊C8D411yescharacteristic
37C2×C8×D11—22no—
38C2×C8×D11—22no—
39C2×C8×D11—42no—
40C2×C8×D11—42no—
41C4×D44—21no—
42C4×D44—21no—
43C4×D44C2×C412yes—
44C4×D44D412yes—
45C11×C4⋊C8—21no—
46C11×C4⋊C8—21no—
47C11×C4⋊C8—21no—
48C11×C4⋊C8—21no—
49C11×C4⋊C8C2×C412yes—
50C11×C22⋊C8—21no—
51C4×C8×C11—21no—
52C22⋊(C11⋊C8)—21no—
53(C2×D11)⋊C8—22no—
54(C2×D11)⋊C8—22no—
55C4⋊(C11⋊C8)—21no—
56C4⋊(C11⋊C8)—21no—
57C4⋊(C11⋊C8)—21no—
58C4×C11⋊C8—21no—
59C4×C11⋊C8C2×C411yescharacteristic
60C4×C11⋊C8C2×C411yescharacteristic
61C4×C11⋊C8D411yescharacteristic
62C4×C11⋊C8D411yescharacteristic
63#8660—111nomaximal, Sylow
64C23×D11—21no—
65C22×C4×C11C2×D411yescharacteristic
66C22×C4×C11C2×Q811yescharacteristic
67C22×C4×C11#4111yescharacteristic
68C22×Dic11—21no—
69C2×D44—24no—
70C2×D44—21no—
71C2×D44C4⋊C412yes—
72C2×C4×D11—22no—
73C2×C4×D11—22no—
74C2×C4×D11—41no—
75C2×C4×D11—41no—
76C2×C4×D11—41no—
77C2×C4×D11—41no—
78C11×M16—41no—
79C11×M16—41no—
80C2×C8×C11—22no—
81C2×C8×C11—41no—
82C2×C8×C11—41no—
83C2×C8×C11—41no—
84C2×C8×C11—41no—
85C42×C11C22×C411yescharacteristic
86C42×C11C2×D411yescharacteristic
87C42×C11C2×D411yescharacteristic
88C42×C11#4111yescharacteristic
89(C2×D11)⋊C4—22no—
90(C2×D11)⋊C4—22no—
91C4⋊Dic11—21no—
92C4⋊Dic11C4⋊C412yes—
93#4318—41no—
94#4318—41no—
95C2×C11⋊C8—21no—
96C2×C11⋊C8—21no—
97C2×C11⋊C8—21no—
98C2×C11⋊C8—21no—
99C2×C11⋊C8—41no—
100C2×C11⋊C8—41no—
101C2×C11⋊C8C22⋊C411yescharacteristic
102C2×C11⋊C8C22⋊C411yescharacteristic
103C2×C11⋊C8C22⋊C411yescharacteristic
104C2×C11⋊C8C22⋊C411yescharacteristic
105C8×D11—44no—
106C8×D11—44no—
107C2×C8×D4—111no—
108#1837—111no—
109#1564—111no—
110#1486—111no—
111#1486—111no—
112#1301—111no—
113#1301D1111yescharacteristic, complemented
114C23×C11C22⋊Q811yescharacteristic
115C22×D11—24no—
116C22×D11—22no—
117C22×D11—42no—
118C22×D11—41no—
119C22×D11—41no—
120C2×C4×C11—22no—
121C2×C4×C11—41no—
122C2×C4×C11C2×C22⋊C411yescharacteristic
123C2×C4×C11C2×C4⋊C411yescharacteristic
124C2×C4×C11#11711yescharacteristic
125C2×C4×C11#12111yescharacteristic
126C2×C4×C11#12111yescharacteristic
127C2×C4×C11C22⋊Q811yescharacteristic
128C2×C4×C11#13511yescharacteristic
129C2×C4×C11#13511yescharacteristic
130C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
131C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
132C2×Dic11—22no—
133C2×Dic11—41no—
134C2×Dic11—41no—
135D44—24no—
136D44—22no—
137D44#10814yes—
138C4×D11—42no—
139C4×D11—42no—
140C4×D11—42no—
141C4×D11—42no—
142C8×C11—42no—
143C8×C11—81no—
144C8×C11—81no—
145C11⋊C8—21no—
146C11⋊C8—21no—
147C11⋊C8—21no—
148C11⋊C8—21no—
149C11⋊C8—81no—
150C11⋊C8—81no—
151C23×C8—221no—
152C2×C4×D4—111no—
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⋊C8C2×D1111yescharacteristic
162C2×C22⋊C8—221no—
163C2×C4×C8—111no—
164#341—221no—
165#341—221no—
166#335—221no—
167#334—221no—
168D4⋊C8—222no—
169D4⋊C8—222no—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11#38011yescharacteristic
173C22×C11#47811yescharacteristic
174C22×C11#47811yescharacteristic
175C2×D11—24no—
176C2×D11—44no—
177C2×D11—44no—
178C2×D11—42no—
179C2×D11—42no—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11#41611yescharacteristic
184C4×C11#41811yescharacteristic
185C4×C11C2×#10812yes—
186C4×C11#46311yescharacteristic
187C4×C11#46311yescharacteristic
188Dic11—42no—
189C22×D4—111no—
190C23×C4—221no—
191C2×M16—21no—
192C2×M16—221no—
193C22×C8—21no—
194C22×C8—111no—
195C22×C8—111no—
196C22×C8—222no—
197C22×C8—222no—
198C22×C8—442no—
199C22×C8—442no—
200C4×D4—112no—
201C4×D4—112no—
202C4×D4—221no—
203C4×D4—221no—
204C2×C4⋊C4—111no—
205C2×C22⋊C4—221no—
206C2×C42C22×D1111yescharacteristic
207C4⋊C8—21no—
208C4⋊C8—21no—
209C4⋊C8—21no—
210C4⋊C8—21no—
211C4⋊C8—221no—
212C4⋊C8—221no—
213C4⋊C8—221no—
214C4⋊C8C4×D1112yes—
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#180411yescharacteristic
228C2×C11#181011yescharacteristic
229C2×C11#181411yescharacteristic
230D11—44no—
231C24—221no—
232C2×D4—112no—
233C2×D4—224no—
234C2×D4—221no—
235C22×C4—221no—
236C22×C4—222no—
237C22×C4—222no—
238C22×C4—441no—
239C22×C4—441no—
240C22×C4—441no—
241C22×C4—441no—
242C22×C4#433911yescharacteristic
243C22×C4D4×D1111yescharacteristic
244C22×C4Q8×D1111yescharacteristic
245M16—41no—
246M16—41no—
247M16—441no—
248M16—441no—
249C2×C8—22no—
250C2×C8—41no—
251C2×C8—41no—
252C2×C8—41no—
253C2×C8—41no—
254C2×C8—111no—
255C2×C8—111no—
256C2×C8—111no—
257C2×C8—111no—
258C2×C8—221no—
259C2×C8—221no—
260C2×C8—221no—
261C2×C8—221no—
262C2×C8—444no—
263C2×C8—444no—
264C2×C8—441no—
265C2×C8—441no—
266C4⋊C4—112no—
267C4⋊C4—221no—
268C22⋊C4—222no—
269C22⋊C4—222no—
270C42C2×C4×D1111yescharacteristic
271C42#433911yescharacteristic
272C42D4×D1111yescharacteristic
273C42D4×D1111yescharacteristic
274C11#866011yescharacteristic, complemented, Sylow
275C23—224no—
276C23—222no—
277C23—442no—
278C23—441no—
279C23—441no—
280C23#6694911yescharacteristic
281D4—114no—
282D4—224no—
283D4—222no—
284C2×C4—22no—
285C2×C4—41no—
286C2×C4—222no—
287C2×C4—441no—
288C2×C4—441no—
289C2×C4—442no—
290C2×C4—442no—
291C2×C4—442no—
292C2×C4—442no—
293C2×C4#6692511yescharacteristic
294C2×C4C22⋊C4×D1111yescharacteristic
295C2×C4#6693711yescharacteristic
296C2×C4#6693711yescharacteristic
297C2×C4C4⋊C4×D1111yescharacteristic
298C2×C4#6694911yescharacteristic
299C2×C4#6696411yescharacteristic
300C2×C4#6696711yescharacteristic
301C2×C4#6696911yescharacteristic
302C2×C4#6697211yescharacteristic
303C8—42no—
304C8—81no—
305C8—81no—
306C8—221no—
307C8—221no—
308C8—221no—
309C8—221no—
310C8—881no—
311C8—881no—
312C22—21no—
313C22—21no—
314C22—224no—
315C22—444no—
316C22—444no—
317C22—442no—
318C22—442no—
319C22#1062228011yescharacteristic
320C22#1062248411yescharacteristic
321C22#1062250411yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—442no—
326C4#1062238311yescharacteristic
327C4#1062240011yescharacteristic
328C4#1062241711yescharacteristic
329C4#1062243211yescharacteristic
330C4D11×#10812yes—
331C2—21no—
332C2—21no—
333C2—444no—
334C2#1306862511yescharacteristic
335C2#1306865311yescharacteristic
336C2#1306866911yescharacteristic
subgroupG/H
centerC2×C4#66937
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1301C2
socleC22×C11#380
prime radicalC22×D44Q8
cosocleC2×C42×C11C23
hypercenter#1301D11
hypocenterC11#8660
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1301

Complements

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

NH ≅ G/Ntype
2. #13068753C2semidirect
3. #13067362C2semidirect
6. #13066513C2semidirect
7. C11×#1301C2semidirect
113. #1301D11semidirect
274. C11#8660semidirect

Maximal subgroups

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

subgroupindex
C2×#106224472
#130687532
#130673622
#130670422
#130670402
#130665132
C11×#13012
#866011