Finite Group Databasebeta

← #14672000

Subgroups — #14672000

Order 2816.

522 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×#10622804C211yesmaximal, characteristic
2C2×#10622202C211yesmaximal, characteristic, complemented
3C2×#10622147C211yesmaximal, characteristic
4C2×#10622129C211yesmaximal, characteristic
5C2×#10622140C211yesmaximal, characteristic, complemented
6#13068774C211yesmaximal, characteristic, complemented
7C2×C11×#358C211yesmaximal, characteristic, complemented
8C22×C11×Q16C2211yescharacteristic
9C2×#67000—21no—
10C22×#4325—21no—
11C22×D88C2211yescharacteristic
12C22×C11×C16C2211yescharacteristic
13C2×C11×#107C2211yescharacteristic
14#10622804—22no—
15#10622804C414yescomplemented
16C2×#66882C2211yescharacteristic
17C2×C8×Dic11C2211yescharacteristic
18C22×C11⋊C16C2211yescharacteristic
19#10622589—21no—
20C2×#66871—21no—
21C11×#358—22no—
22#10622202—22no—
23#10622147—22no—
24#10622140—22no—
25#10622129—22no—
26C22×Q8×C11—21no—
27C22×D44—21no—
28C2×C11×Q16—21no—
29C2×C11×Q16—21no—
30C2×C11×Q16—21no—
31C2×C11×Q16—21no—
32C2×C11×Q16—21no—
33C2×C11×Q16C2×C412yes—
34C22×C8×C11C2311yescharacteristic
35C2×C11×C4⋊C4—21no—
36#67000—24no—
37#67000—42no—
38C2×#4325—24no—
39C2×#4325—42no—
40C2×#4325—42no—
41C2×(C2×D11)⋊C4—42no—
42C2×C4⋊Dic11—21no—
43C2×Dic11⋊C4—42no—
44C2×C4×Dic11D411yescharacteristic
45C22×C11⋊C8D411yescharacteristic
46C2×D88—21no—
47C2×D88—21no—
48C2×D88—21no—
49C2×D88—21no—
50C2×D88—21no—
51C2×D88C2×C412yes—
52C2×C11×C16—21no—
53C2×C11×C16—21no—
54C2×C11×C16D412yes—
55C11×#107—21no—
56C11×#107—21no—
57#66882—21no—
58#66882—21no—
59C8×Dic11C2×C412yes—
60C8×Dic11D412yes—
61C2×C11⋊C16—21no—
62C2×C11⋊C16—21no—
63C2×C11⋊C16D412yes—
64#66871—42no—
65#13205—111nomaximal, Sylow
66C23×D11—41no—
67C2×Q8×C11—22no—
68C2×Q8×C11—41no—
69C2×Q8×C11—41no—
70C2×Q8×C11—41no—
71C2×Q8×C11—41no—
72C2×Q8×C11—41no—
73C22×C4×C11—41no—
74C22×C4×C11—41no—
75C22×C4×C11C2×D411yescharacteristic
76C22×Dic11—41no—
77C22×Dic11D812yes—
78C2×D44—22no—
79C2×D44—41no—
80C2×D44—41no—
81C2×D44—41no—
82C2×D44—41no—
83C2×D44—41no—
84C11×Q16—22no—
85C11×Q16—22no—
86C11×Q16—41no—
87C11×Q16—41no—
88C2×C8×C11C22×C411yescharacteristic
89C2×C8×C11C2×D411yescharacteristic
90C2×C8×C11C2×D411yescharacteristic
91C2×C8×C11C2×D411yescharacteristic
92C2×C8×C11#4111yescharacteristic
93C2×C8×C11#4111yescharacteristic
94C11×C4⋊C4—41no—
95C11×C4⋊C4—41no—
96#4325—48no—
97(C2×D11)⋊C4—48no—
98C4⋊Dic11—41no—
99C4⋊Dic11—41no—
100Dic11⋊C4—84no—
101C4×Dic11C22⋊C412yes—
102C4×Dic11SD1612yes—
103C2×C11⋊C8C22⋊C412yes—
104C2×C11⋊C8D812yes—
105C2×C11⋊C8SD1612yes—
106D88—22no—
107D88—22no—
108D88—41no—
109D88—41no—
110C11×C16—22no—
111C11⋊C16—22no—
112C2×#495—111no—
113C2×#358—111no—
114C2×#358D1111yescharacteristic, complemented
115C2×#357—111no—
116C2×#357—111no—
117C2×#346—111no—
118#1845—111no—
119C23×C11C2×D811yescharacteristic
120C22×D11—42no—
121C22×D11—81no—
122C22×D11—81no—
123C22×D11—82no—
124C22×D11—82no—
125Q8×C11—42no—
126Q8×C11—42no—
127Q8×C11—81no—
128Q8×C11—81no—
129C2×C4×C11—42no—
130C2×C4×C11—81no—
131C2×C4×C11—81no—
132C2×C4×C11—81no—
133C2×C4×C11—82no—
134C2×C4×C11C2×C22⋊C411yescharacteristic
135C2×C4×C11#12411yescharacteristic
136C2×C4×C11#12711yescharacteristic
137C2×C4×C11C2×D811yescharacteristic
138C2×C4×C11C2×SD1611yescharacteristic
139C2×C4×C11C2×SD1611yescharacteristic
140C2×Dic11—22no—
141C2×Dic11—22no—
142C2×Dic11—81no—
143C2×Dic11—82no—
144C2×Dic11#10214yes—
145D44—42no—
146D44—42no—
147D44—81no—
148D44—81no—
149C8×C11C4×D411yescharacteristic
150C8×C11C4×D411yescharacteristic
151C8×C11#12111yescharacteristic
152C8×C11#12111yescharacteristic
153C11⋊C8#10214yes—
154C22×Q16C2×D1111yescharacteristic
155C22×SD16—221no—
156C22×D8—111no—
157C2×#124—221no—
158C22×C16—111no—
159C22×C16C2×D1111yescharacteristic
160#495—114no—
161#495—222no—
162C2×#107—111no—
163C2×#107—221no—
164C2×#107C2×D1111yescharacteristic
165C2×C4×C8—111no—
166#384—221no—
167#358—22no—
168#358—222no—
169#357—222no—
170#357—222no—
171#346—222no—
172C22×C11C2×#10211yescharacteristic
173C22×C11#48611yescharacteristic
174C22×C11#49311yescharacteristic
175C22×C11#50912yes—
176C22×C11#51012yes—
177C2×D11—84no—
178C2×D11—82no—
179C2×D11—162no—
180C2×D11—161no—
181C2×D11—161no—
182C4×C11—82no—
183C4×C11—161no—
184C4×C11#39011yescharacteristic
185C4×C11C2×#10211yescharacteristic
186C4×C11#48611yescharacteristic
187C4×C11#49211yescharacteristic
188Dic11—24no—
189Dic11—161no—
190C22×Q8—21no—
191C22×D4—221no—
192C2×Q16—21no—
193C2×Q16—21no—
194C2×Q16—21no—
195C2×Q16—21no—
196C2×Q16—21no—
197C2×Q16C4×D1112yes—
198C2×SD16—224no—
199C2×SD16—442no—
200C2×SD16—442no—
201C2×D8—112no—
202C2×D8—221no—
203C2×D8—221no—
204C2×D8—221no—
205C2×D8—221no—
206C2×D8—221no—
207C22×C8—111no—
208C22×C8C22×D1111yescharacteristic
209#124—224no—
210#124—442no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—221no—
213C2×C4⋊C4—442no—
214C2×C22⋊C4—442no—
215C2×C42—111no—
216C2×C16—21no—
217C2×C16—21no—
218C2×C16—112no—
219C2×C16—221no—
220C2×C16—221no—
221C2×C16C22⋊D1112yes—
222#107—21no—
223#107—21no—
224#107—221no—
225#107—221no—
226#107—442no—
227C4×C8—112no—
228C4×C8—112no—
229C2×C11#195711yescharacteristic
230C2×C11#213912yes—
231C2×C11#224312yes—
232C2×C11#225011yescharacteristic
233C2×C11#225111yescharacteristic
234D11—162no—
235C24—441no—
236C2×Q8—22no—
237C2×Q8—41no—
238C2×Q8—41no—
239C2×Q8—41no—
240C2×Q8—41no—
241C2×Q8—41no—
242C2×D4—222no—
243C2×D4—441no—
244C2×D4—441no—
245C2×D4—441no—
246C2×D4—441no—
247C2×D4—441no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—112no—
251C22×C4—441no—
252C22×C4D4×D1111yescharacteristic
253Q16—22no—
254Q16—22no—
255Q16—41no—
256Q16—41no—
257SD16—448no—
258D8—222no—
259D8—222no—
260D8—441no—
261D8—441no—
262C2×C8—112no—
263C2×C8—112no—
264C2×C8—112no—
265C2×C8C2×C4×D1111yescharacteristic
266C2×C8#433911yescharacteristic
267C2×C8D4×D1111yescharacteristic
268C2×C8D4×D1111yescharacteristic
269C2×C8#434111yescharacteristic
270C2×C8C2×C22⋊D1111yescharacteristic
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—441no—
274C4⋊C4—441no—
275C4⋊C4—884no—
276C22⋊C4—448no—
277C42—112no—
278C42—112no—
279C16—22no—
280C16—222no—
281C11#1320511yescharacteristic, complemented, Sylow
282C23—442no—
283C23—881no—
284C23—882no—
285C23—882no—
286C23—881no—
287C23D8×D1111yescharacteristic
288Q8—42no—
289Q8—42no—
290Q8—81no—
291Q8—81no—
292D4—442no—
293D4—442no—
294D4—881no—
295D4—881no—
296C2×C4—42no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4—82no—
301C2×C4—114no—
302C2×C4—222no—
303C2×C4—222no—
304C2×C4—881no—
305C2×C4—882no—
306C2×C4C22⋊C4×D1111yescharacteristic
307C2×C4#6693811yescharacteristic
308C2×C4D8×D1111yescharacteristic
309C2×C4SD16×D1111yescharacteristic
310C2×C4SD16×D1111yescharacteristic
311C2×C4#6699311yescharacteristic
312C8—114no—
313C8(C22⋊D11)⋊C411yescharacteristic
314C8#6693711yescharacteristic
315C8C4×C22⋊D1111yescharacteristic
316C8#6699211yescharacteristic
317C22—882no—
318C22—884no—
319C22—1762no—
320C22—1761no—
321C22—1761no—
322C22#1062237311yescharacteristic
323C22D11×#10211yescharacteristic
324C22#1062252712yes—
325C22#1062253112yes—
326C22#1062276411yescharacteristic
327C4—82no—
328C4—161no—
329C4—224no—
330C4—1761no—
331C4#1062237311yescharacteristic
332C4D11×#10211yescharacteristic
333C4#1062257011yescharacteristic
334C4#1062278811yescharacteristic
335C2—1762no—
336C2#1306942011yescharacteristic
337C2#1307032712yes—
338C2#1307085412yes—
339C2#1307088111yescharacteristic
340C2#1307088411yescharacteristic
subgroupG/H
centerC23D8×D11
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC2×C11×#358C2
socleC23×C11C2×D8
prime radicalC22×D88C22
cosocleC22×C8×C11C23
hypercenterC2×#358D11
hypocenterC11#13205
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#358

Complements

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

NH ≅ G/Ntype
2. C2×#10622202C2semidirect
5. C2×#10622140C2semidirect
6. #13068774C2semidirect
7. C2×C11×#358C2semidirect
15. #10622804C4semidirect
114. C2×#358D11semidirect
281. C11#13205semidirect

Maximal subgroups

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

subgroupindex
C2×#106228042
C2×#106222022
C2×#106221472
C2×#106221292
C2×#106221402
#130687742
C2×C11×#3582
#1320511