Finite Group Databasebeta

← #14646648

Subgroups — #14646648

Order 2816.

462 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#66954C211yesmaximal, characteristic
2#13067364C211yesmaximal, characteristic, complemented
3#13067001C212yesmaximal
4#13066466C212yesmaximal, complemented
5C2×C11×#334C211yesmaximal, characteristic, complemented
6C2×#66954C411yescharacteristic
7C2×#66954C411yescharacteristic
8C4×#4339C2211yescharacteristic
9C2×C11×C4⋊C8C2212yes—
10C2×C4×C8×C11C2211yescharacteristic
11#10622714C411yescharacteristic
12#10622714C411yescharacteristic
13#10622538C2212yes—
14C4×#4318C2211yescharacteristic
15#10622302—21no—
16#10622302—21no—
17C4×#4313—21no—
18C4×C8×D11—21no—
19C11×#334—21no—
20C11×#334—21no—
21#10622122—22no—
22#10622121—22no—
23#10622096—21no—
24#10622095—21no—
25C2×#4339C2×C411yescharacteristic
26C22×C8×C11—22no—
27C22×C8×C11C2×C411yescharacteristic
28C22×C8×C11C2×C411yescharacteristic
29C2×C42×C11C2311yescharacteristic
30C4×C22⋊D11—21no—
31C4×C22⋊D11—21no—
32#66979C2×C411yescharacteristic
33C2×#4318C2×C411yescharacteristic
34C2×#4318C2×C411yescharacteristic
35#66954—22no—
36#66954—22no—
37#66954—22no—
38#66954C814yescomplemented
39C2×#4313—21no—
40C2×#4313—21no—
41C2×C8×D11—21no—
42C2×C8×D11—21no—
43C4×D44D411yescharacteristic
44C4×D44Q811yescharacteristic
45#66925—21no—
46C42×D11—21no—
47C4×Dic22D411yescharacteristic
48C4×Dic22Q811yescharacteristic
49C11×C4⋊C8—22no—
50C11×C4⋊C8—22no—
51C4×C8×C11D411yescharacteristic
52C4×C8×C11D411yescharacteristic
53C4×C8×C11D411yescharacteristic
54C4×C8×C11D411yescharacteristic
55C22⋊(C11⋊C8)—22no—
56#66879—21no—
57#66879—21no—
58C8×Dic11—21no—
59C8×Dic11—21no—
60C4⋊(C11⋊C8)—22no—
61#66867—21no—
62C4×C11⋊C8—21no—
63C4×C11⋊C8—22no—
64#8604—111nomaximal, Sylow
65C22×C4×C11C22×C411yescharacteristic
66C22×C4×C11#4111yescharacteristic
67C22×C4×C11#4111yescharacteristic
68C2×C22⋊D11—21no—
69#4339—21no—
70#4339—21no—
71#4339C2×C812yes—
72#4339M1612yes—
73C2×D44C4⋊C411yescharacteristic
74C2×C4×D11—21no—
75C2×C4×D11—21no—
76C2×C4×D11—21no—
77C2×Dic22C4⋊C411yescharacteristic
78C2×C8×C11—21no—
79C2×C8×C11—21no—
80C2×C8×C11—42no—
81C2×C8×C11—82no—
82C2×C8×C11C22⋊C411yescharacteristic
83C2×C8×C11C22⋊C411yescharacteristic
84C2×C8×C11C22⋊C411yescharacteristic
85C2×C8×C11C22⋊C411yescharacteristic
86C2×C8×C11C2×C812yes—
87C2×C8×C11M1612yes—
88C42×C11C2×D411yescharacteristic
89C42×C11C2×D411yescharacteristic
90C42×C11C2×D411yescharacteristic
91C42×C11C2×Q811yescharacteristic
92C22⋊Dic11—21no—
93(C2×D11)⋊C4—21no—
94(C2×D11)⋊C4—21no—
95C4⋊Dic11C4⋊C411yescharacteristic
96C4⋊Dic11C4⋊C411yescharacteristic
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11—21no—
102#4318—21no—
103#4318—21no—
104#4318C2×C812yes—
105#4318M1612yes—
106C2×C11⋊C8—21no—
107C2×C11⋊C8—21no—
108C2×C11⋊C8—42no—
109#4313—24no—
110#4313—24no—
111C8×D11—24no—
112C8×D11—24no—
113C4×#131—111no—
114#1564—111no—
115C2×#334D1111yescharacteristic, complemented
116#1477—112no—
117#1283—112no—
118C23×C11#11711yescharacteristic
119C22×D11—21no—
120C2×C4×C11—22no—
121C2×C4×C11—41no—
122C2×C4×C11C2×C22⋊C411yescharacteristic
123C2×C4×C11C2×C4⋊C411yescharacteristic
124C2×C4×C11#12111yescharacteristic
125C2×C4×C11#12111yescharacteristic
126C2×C4×C11C22⋊Q811yescharacteristic
127C2×C4×C11C22⋊Q811yescharacteristic
128C2×C4×C11C22×C811yescharacteristic
129C2×C4×C11C2×M1611yescharacteristic
130C2×C4×C11C2×M1611yescharacteristic
131C2×C4×C11C2×M1611yescharacteristic
132C22⋊D11—22no—
133C22⋊D11—22no—
134C2×Dic11—21no—
135C2×Dic11—21no—
136C2×Dic11—21no—
137D44—21no—
138D44C4⋊C812yes—
139C4×D11—22no—
140C4×D11—22no—
141C4×D11—42no—
142C4×D11—42no—
143Dic22—21no—
144Dic22C4⋊C812yes—
145C8×C11—21no—
146C8×C11—21no—
147C8×C11—82no—
148C8×C11C22⋊C812yes—
149C8×C11C22⋊C812yes—
150C11⋊C8—22no—
151C11⋊C8—22no—
152C11⋊C8—82no—
153C2×#131—111no—
154C2×#131—111no—
155C4×#41—111no—
156#431—112no—
157C2×C4⋊C8C2×D1112yes—
158#405—111no—
159#405—111no—
160#405—221no—
161#405—221no—
162C4×M16—111no—
163C4×M16—221no—
164C2×C4×C8—221no—
165C2×C4×C8C2×D1111yescharacteristic
166#335—221no—
167#334—21no—
168#334—21no—
169#334—221no—
170Q8⋊C8—222no—
171D4⋊C8—222no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11#38011yescharacteristic
175C22×C11#43111yescharacteristic
176C22×C11#43211yescharacteristic
177C2×D11—22no—
178C2×D11—41no—
179C2×D11—41no—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11C2×C22⋊C811yescharacteristic
184C4×C11#40711yescharacteristic
185C4×C11C2×C4⋊C811yescharacteristic
186C4×C11#42311yescharacteristic
187C4×C11#47112yes—
188Dic11—22no—
189Dic11—41no—
190Dic11—41no—
191C2×#41—111no—
192#131—114no—
193#131—222no—
194#131—222no—
195#131—222no—
196C2×M16—111no—
197C2×M16—111no—
198C2×M16—221no—
199C2×M16—221no—
200C22×C8—22no—
201C22×C8—221no—
202C22×C8—221no—
203C22×C8C4×D1111yescharacteristic
204C22×C8C4×D1111yescharacteristic
205C4×Q8—111no—
206C4×Q8—111no—
207C4×D4—111no—
208C4×D4—111no—
209C4×D4—221no—
210C4×D4—221no—
211#117—111no—
212#117—221no—
213C2×C42—221no—
214C2×C42C22×D1111yescharacteristic
215C4⋊C8—22no—
216C4⋊C8—22no—
217C4⋊C8—222no—
218C22⋊C8—222no—
219#97—221no—
220#97—221no—
221#97—221no—
222C4×C8—221no—
223C4×C8—221no—
224C4×C8—222no—
225C4×C8—221no—
226C4×C8D4411yescharacteristic
227C4×C8D4411yescharacteristic
228C4×C8C22⋊D1111yescharacteristic
229C4×C8C22⋊D1111yescharacteristic
230C2×C11—21no—
231C2×C11—21no—
232C2×C11#179711yescharacteristic
233C2×C11#181411yescharacteristic
234C2×C11#181511yescharacteristic
235D11—42no—
236#41—112no—
237#41—112no—
238#41—221no—
239#41—221no—
240C2×Q8—111no—
241C2×D4—111no—
242C2×D4—221no—
243C22×C4—221no—
244C22×C4—221no—
245C22×C4—221no—
246C22×C4C2×C4×D1111yescharacteristic
247C22×C4#434111yescharacteristic
248C22×C4#434311yescharacteristic
249M16—112no—
250M16—112no—
251M16—224no—
252M16—221no—
253M16—221no—
254M16—224no—
255C2×C8—21no—
256C2×C8—21no—
257C2×C8—42no—
258C2×C8—82no—
259C2×C8—224no—
260C2×C8—221no—
261C2×C8—221no—
262C2×C8—224no—
263C2×C8—442no—
264C2×C8C8×D1112yes—
265C2×C8#431312yes—
266C2×C8(C2×D11)⋊C411yescharacteristic
267C2×C8(C2×D11)⋊C411yescharacteristic
268C2×C8(C2×D11)⋊C411yescharacteristic
269C2×C8(C2×D11)⋊C411yescharacteristic
270C4⋊C4—111no—
271C4⋊C4—111no—
272C4⋊C4—221no—
273C4⋊C4—221no—
274C22⋊C4—221no—
275C22⋊C4—221no—
276C22⋊C4—221no—
277C42—221no—
278C42—221no—
279C42—221no—
280C42C2×D4411yescharacteristic
281C42D4×D1111yescharacteristic
282C42Q8×D1111yescharacteristic
283C42C2×C22⋊D1111yescharacteristic
284C11#860411yescharacteristic, complemented, Sylow
285C23—221no—
286C23#6694511yescharacteristic
287Q8—112no—
288Q8—221no—
289D4—112no—
290D4—222no—
291D4—222no—
292D4—221no—
293C2×C4—22no—
294C2×C4—41no—
295C2×C4—221no—
296C2×C4—222no—
297C2×C4—222no—
298C2×C4—221no—
299C2×C4—221no—
300C2×C4—442no—
301C2×C4—442no—
302C2×C4C4⋊C4×D1111yescharacteristic
303C2×C4#6694811yescharacteristic
304C2×C4#6695011yescharacteristic
305C2×C4C2×C8×D1111yescharacteristic
306C2×C4C2×#431311yescharacteristic
307C2×C4M16×D1111yescharacteristic
308C2×C4M16×D1111yescharacteristic
309C2×C4C2×(C2×D11)⋊C411yescharacteristic
310C2×C4#6699111yescharacteristic
311C2×C4#6699911yescharacteristic
312C8—21no—
313C8—21no—
314C8—82no—
315C8—222no—
316C8—222no—
317C8—882no—
318C8(C2×D11)⋊C812yes—
319C8(C2×D11)⋊C812yes—
320C22—21no—
321C22—21no—
322C22—222no—
323C22—441no—
324C22—441no—
325C22#1062244611yescharacteristic
326C22#1062244811yescharacteristic
327C22#1062260011yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—222no—
332C4—441no—
333C4—441no—
334C4D11×C4⋊C811yescharacteristic
335C4#1062245011yescharacteristic
336C4C2×(C2×D11)⋊C811yescharacteristic
337C4#1062273911yescharacteristic
338C4#1062279012yes—
339C2—21no—
340C2—21no—
341C2—442no—
342C2#1306859311yescharacteristic
343C2#1306867111yescharacteristic
344C2#1306867611yescharacteristic
subgroupG/H
centerC2×C4#66991
commutatorC2×C4×C11C22×C8
FrattiniC2×C42C22×D11
FittingC2×C11×#334C2
socleC22×C11#380
prime radicalC2×#4339C2×C4
cosocleC2×C42×C11C23
hypercenterC2×#334D11
hypocenterC11#8604
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×#334

Complements

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

NH ≅ G/Ntype
2. #13067364C2semidirect
4. #13066466C2semidirect
5. C2×C11×#334C2semidirect
38. #66954C8semidirect
115. C2×#334D11semidirect
284. C11#8604semidirect

Maximal subgroups

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

subgroupindex
C4×#669542
#130673642
#130670012
#130664662
C2×C11×#3342
#860411