Finite Group Databasebeta

← #14908498

Subgroups — #14908498

Order 2816.

534 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079152C211yesmaximal, characteristic, complemented
2#13077490C211yesmaximal, characteristic
3#13070783C212yesmaximal, complemented
4#13070772C212yesmaximal, complemented
5#13070762C212yesmaximal, complemented
6#13070757C212yesmaximal, complemented
7#13070402C211yesmaximal, characteristic, complemented
8#13070374C211yesmaximal, characteristic, complemented
9#13070326C211yesmaximal, characteristic
10#13070324C211yesmaximal, characteristic
11C2×C11×#367C211yesmaximal, characteristic, complemented
12C2×#66957C2211yescharacteristic
13#10623035—21no—
14#10623031—21no—
15C22×C11×C16C2211yescharacteristic
16C2×C11×#107C2211yescharacteristic
17C2×C11×#107C2211yescharacteristic
18#10622719C2211yescharacteristic
19#10622714C2211yescharacteristic
20C2×#66876C2211yescharacteristic
21#10622579—21no—
22#10622577—21no—
23#10622502—22no—
24#10622491C2212yes—
25#10622489—22no—
26#10622487C2212yes—
27#10622486C2212yes—
28#10622485C2212yes—
29C11×#367C2212yes—
30C11×#367C2212yes—
31#10622147C2211yescharacteristic
32#10622147C2211yescharacteristic
33#10622141C2211yescharacteristic
34#10622141C2211yescharacteristic
35Dic11⋊C16C2212yes—
36Dic11⋊C16C2212yes—
37#10622130C2212yes—
38#10622129C2212yes—
39#10622128C2212yes—
40#10622127C2212yes—
41C2×#4339—21no—
42C22×C8×C11C2311yescharacteristic
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—21no—
45C4×C22⋊D11—42no—
46#66979—21no—
47#66979D411yescharacteristic
48#66977—42no—
49C2×#4318D411yescharacteristic
50C2×Dic44C2311yescharacteristic
51#66957—22no—
52#66957Q814yescomplemented
53C2×D88C2311yescharacteristic
54C2×#4314—21no—
55#66946—22no—
56#66945—41no—
57C4⋊C4×D11—41no—
58#66943—22no—
59#66943—41no—
60#66941—22no—
61#66941—41no—
62#66940—22no—
63C2×C11×C16—22no—
64C2×C11×C16C2311yescharacteristic
65C2×C11×C16C2311yescharacteristic
66C11×#107—21no—
67C11×#107—21no—
68C11×#107C2312yes—
69C11×#107C2312yes—
70#66882C2311yescharacteristic
71#66882C2311yescharacteristic
72#66881—21no—
73#66879D412yes—
74C8×Dic11C2312yes—
75#66876—22no—
76C2×C11⋊C16C2312yes—
77#66874—22no—
78#66873—22no—
79#66872—22no—
80#66871—22no—
81#33634—111nomaximal, Sylow
82C22×C4×C11—41no—
83C22×C4×C11—41no—
84C22×C4×C11C2×D411yescharacteristic
85C2×C22⋊D11—41no—
86#4339—24no—
87#4339—42no—
88C2×D44—21no—
89C2×C4×D11—42no—
90C2×C4×D11—41no—
91C2×Dic22—21no—
92C2×Dic22—42no—
93C2×C8×C11C2×D411yescharacteristic
94C2×C8×C11C2×Q812yes—
95C2×C8×C11#4112yes—
96C2×C8×C11C2411yescharacteristic
97C11×C4⋊C4—22no—
98C11×C4⋊C4—22no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C22⋊Dic11—41no—
102C22⋊Dic11D812yes—
103(C2×D11)⋊C4—42no—
104C4⋊Dic11—21no—
105C4⋊Dic11—21no—
106C4⋊Dic11—42no—
107C4⋊Dic11D811yescharacteristic
108C4⋊Dic11D811yescharacteristic
109Dic11⋊C4—42no—
110Dic11⋊C4—42no—
111Dic11⋊C4—42no—
112C4×Dic11—42no—
113C4×Dic11—41no—
114C4×Dic11C2×D412yes—
115#4318—22no—
116C2×C11⋊C8C2×D412yes—
117Dic44—21no—
118Dic44C2×Q812yes—
119D88—21no—
120D88C2×Q812yes—
121#4314—24no—
122C11×C16—21no—
123C11×C16—21no—
124C11⋊C16—22no—
125#3164—111no—
126#2951—111no—
127#2229—112no—
128#2228—112no—
129#2226—112no—
130#2225—112no—
131#2159—111no—
132C2×#367D1111yescharacteristic, complemented
133#2151—111no—
134#2139—111no—
135#2138—111no—
136C23×C11C2×D811yescharacteristic
137C22×D11—41no—
138C2×C4×C11—42no—
139C2×C4×C11—42no—
140C2×C4×C11—161no—
141C2×C4×C11—161no—
142C2×C4×C11C22⋊Q812yes—
143C2×C4×C11C2×D811yescharacteristic
144C2×C4×C11#13712yes—
145C2×C4×C11C22×D411yescharacteristic
146C22⋊D11—44no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11C2×D812yes—
151C2×Dic11C2×D812yes—
152D44—22no—
153D44—41no—
154C4×D11—44no—
155C4×D11—162no—
156Dic22—22no—
157Dic22—41no—
158Dic22—162no—
159C8×C11C22⋊Q812yes—
160C8×C11C22×Q811yescharacteristic
161C8×C11C2×#4111yescharacteristic
162C11⋊C8—22no—
163C2×#135—111no—
164#544—221no—
165#520—221no—
166C2×M32—111no—
167C22×C16C2×D1111yescharacteristic
168#501—222no—
169#500—112no—
170#499—112no—
171#440—222no—
172C4×Q16—112no—
173C4×D8—112no—
174#428—221no—
175#427—111no—
176C2×#107C2×D1111yescharacteristic
177C2×#107C2×D1111yescharacteristic
178#417—221no—
179#405—111no—
180#367—112no—
181#367C2×D1112yes—
182#367C2×D1112yes—
183#366—112no—
184C4⋊C16—112no—
185C4⋊C16—112no—
186#358—111no—
187#358—111no—
188#358—112no—
189#357—111no—
190#357—111no—
191#357—112no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11#47412yes—
195C22×C11C22×D811yescharacteristic
196C2×D11—42no—
197C2×D11—81no—
198C2×D11—81no—
199C4×C11—82no—
200C4×C11—82no—
201C4×C11#47412yes—
202C4×C11C2×C22⋊Q811yescharacteristic
203C4×C11C2×#13711yescharacteristic
204Dic11—22no—
205Dic11—22no—
206Dic11—42no—
207Dic11—81no—
208Dic11—81no—
209C2×#41—221no—
210#135—114no—
211#135—222no—
212C2×Q16—111no—
213C2×SD16—221no—
214C2×D8—111no—
215C2×M16—111no—
216C22×C8C22×D1111yescharacteristic
217C4⋊Q8—222no—
218C4⋊Q8—441no—
219#125—222no—
220#125—441no—
221C22⋊Q8—442no—
222C4×Q8—222no—
223C4×D4—222no—
224C4×D4—442no—
225#117—111no—
226#117—221no—
227#117—441no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—441no—
231M32—222no—
232C2×C16—22no—
233C2×C16—112no—
234C2×C16C22×D1111yescharacteristic
235C2×C16C22×D1111yescharacteristic
236#107—21no—
237#107—21no—
238#107—111no—
239#107—111no—
240#107—222no—
241#107C22×D1112yes—
242#107C22×D1112yes—
243#106—222no—
244#106—221no—
245#103—222no—
246#102—222no—
247#97—112no—
248C4×C8—112no—
249C2×C11—22no—
250C2×C11C2×#47411yescharacteristic
251C2×C11#341611yescharacteristic
252C2×C11#341611yescharacteristic
253D11—82no—
254#41—224no—
255#41—442no—
256C2×Q8—221no—
257C2×Q8—442no—
258C2×D4—221no—
259C2×D4—441no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—442no—
263C22×C4—441no—
264C22×C4D4×D1111yescharacteristic
265Q16—112no—
266Q16—221no—
267SD16—224no—
268D8—112no—
269D8—221no—
270M16—222no—
271C2×C8—112no—
272C2×C8#433912yes—
273C2×C8D4×D1111yescharacteristic
274C2×C8Q8×D1112yes—
275C2×C8C23×D1111yescharacteristic
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—111no—
281C4⋊C4—111no—
282C4⋊C4—221no—
283C4⋊C4—221no—
284C4⋊C4—442no—
285C4⋊C4—442no—
286C4⋊C4—442no—
287C4⋊C4—442no—
288C22⋊C4—112no—
289C22⋊C4—442no—
290C22⋊C4—441no—
291C42—112no—
292C42—442no—
293C42—441no—
294C16—21no—
295C16—21no—
296C16—222no—
297C11#3363411yescharacteristic, complemented, Sylow
298C23—441no—
299C23D8×D1111yescharacteristic
300Q8—222no—
301Q8—441no—
302Q8—1762no—
303D4—222no—
304D4—444no—
305D4—441no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—112no—
309C2×C4—112no—
310C2×C4—161no—
311C2×C4—161no—
312C2×C4—441no—
313C2×C4—444no—
314C2×C4—441no—
315C2×C4—441no—
316C2×C4—1762no—
317C2×C4#6694912yes—
318C2×C4D8×D1111yescharacteristic
319C2×C4#6697112yes—
320C2×C4C2×D4×D1111yescharacteristic
321C8—222no—
322C8#6694912yes—
323C8C2×#433911yescharacteristic
324C8C2×Q8×D1111yescharacteristic
325C22—21no—
326C22—21no—
327C22—442no—
328C22—881no—
329C22—881no—
330C22#1062250312yes—
331C22C2×D8×D1111yescharacteristic
332C4—82no—
333C4—82no—
334C4—222no—
335C4—222no—
336C4—442no—
337C4—881no—
338C4—881no—
339C4#1062250312yes—
340C4C2×#6694911yescharacteristic
341C4C2×#6697111yescharacteristic
342C2—22no—
343C2—882no—
344C2C2×#1062250311yescharacteristic
345C2#1308175811yescharacteristic
346C2#1308175811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#367C2
socleC22×C11C22×D8
prime radicalC2×#66957C22
hypercenterC2×#367D11
hypocenterC11#33634
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#367

Complements

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

NH ≅ G/Ntype
1. #13079152C2semidirect
3. #13070783C2semidirect
4. #13070772C2semidirect
5. #13070762C2semidirect
6. #13070757C2semidirect
7. #13070402C2semidirect
8. #13070374C2semidirect
11. C2×C11×#367C2semidirect
52. #66957Q8semidirect
132. C2×#367D11semidirect
297. C11#33634semidirect

Maximal subgroups

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

subgroupindex
#130791522
#130774902
#130707832
#130707722
#130707622
#130707572
#130704022
#130703742
#130703262
#130703242
C2×C11×#3672
#3363411