Finite Group Databasebeta

← #14908492

Subgroups — #14908492

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#13079156C211yesmaximal, characteristic, complemented
2#13077490C211yesmaximal, characteristic
3#13070779C212yesmaximal, complemented
4#13070776C212yesmaximal, complemented
5#13070762C212yesmaximal, complemented
6#13070757C212yesmaximal, complemented
7C2×#10622128C211yesmaximal, characteristic, complemented
8#13070376C211yesmaximal, characteristic, complemented
9#13070329C211yesmaximal, characteristic
10#13070321C211yesmaximal, characteristic
11C11×#2159C211yesmaximal, characteristic, complemented
12C2×#66957C2211yescharacteristic
13#10623050—21no—
14#10623035—21no—
15C2×C11×M32C2211yescharacteristic
16C11×#427C2211yescharacteristic
17C2×C11×#107C2211yescharacteristic
18C2×#66882C2211yescharacteristic
19#10622714C2211yescharacteristic
20C22×C11⋊C16C2211yescharacteristic
21#10622608—21no—
22#10622579—21no—
23#10622502—22no—
24#10622491C2212yes—
25#10622487C2212yes—
26#10622486C2212yes—
27#10622485C2212yes—
28#10622469—22no—
29C11×#367C2212yes—
30C11×#366C2212yes—
31#10622147C2212yes—
32#10622141C2212yes—
33Dic11⋊C16C2212yes—
34Dic11⋊C16C2212yes—
35#10622130C2211yescharacteristic
36#10622130C2211yescharacteristic
37#10622129C2211yescharacteristic
38#10622129C2211yescharacteristic
39#10622128C2212yes—
40#10622128C2212yes—
41C2×#4339—21no—
42C22×C8×C11C2311yescharacteristic
43C11×#117—21no—
44C2×C11×C4⋊C4—21no—
45C4×C22⋊D11—42no—
46#66979D411yescharacteristic
47C2×C4⋊Dic11—21no—
48C2×#4318D411yescharacteristic
49C2×Dic44C2311yescharacteristic
50#66957—22no—
51#66957Q814yescomplemented
52C2×D88C2311yescharacteristic
53C2×#4314—21no—
54#66946—22no—
55#66945—41no—
56C4⋊C4×D11—41no—
57#66943—22no—
58#66941—22no—
59#66940—22no—
60#66931—42no—
61#66923—41no—
62#66922—41no—
63C11×M32—22no—
64C2×C11×C16C2312yes—
65C11×#107—21no—
66C11×#107C2312yes—
67C11×#107C2311yescharacteristic
68C11×#107C2311yescharacteristic
69C11×#106—21no—
70#66882—21no—
71#66882C2312yes—
72#66879D412yes—
73C8×Dic11C2312yes—
74C2×C11⋊C16—22no—
75C2×C11⋊C16C2311yescharacteristic
76C2×C11⋊C16C2311yescharacteristic
77#66874—22no—
78#66873—22no—
79#66872—22no—
80#66871—22no—
81#33634—111nomaximal, Sylow
82C22×C4×C11—41no—
83C22×C4×C11C2×D411yescharacteristic
84C2×C22⋊D11—41no—
85C22×Dic11—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—21no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—41no—
101C11×C22⋊C4—41no—
102C42×C11—41no—
103C22⋊Dic11D812yes—
104(C2×D11)⋊C4—42no—
105C4⋊Dic11—22no—
106C4⋊Dic11—42no—
107C4⋊Dic11—41no—
108C4⋊Dic11D811yescharacteristic
109C4⋊Dic11D811yescharacteristic
110Dic11⋊C4—42no—
111Dic11⋊C4—42no—
112Dic11⋊C4—42no—
113C4×Dic11—42no—
114C4×Dic11C2×D412yes—
115#4318—22no—
116C2×C11⋊C8C2×D412yes—
117Dic44—21no—
118Dic44C2×Q812yes—
119D88—21no—
120D88C2×Q812yes—
121#4314—24no—
122C11×C16—22no—
123C11⋊C16—21no—
124C11⋊C16—21no—
125#3164—111no—
126#2951—111no—
127#2229—112no—
128#2228—112no—
129#2226—112no—
130#2225—112no—
131#2159D1111yescharacteristic, complemented
132C2×#367—111no—
133#2151—111no—
134#2139—111no—
135#2138—111no—
136C23×C11C2×D811yescharacteristic
137C22×D11—41no—
138C2×C4×C11—42no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
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—42no—
149C2×Dic11—161no—
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×M32C2×D1111yescharacteristic
167C22×C16—111no—
168#501—222no—
169#500—112no—
170#499—112no—
171#440—222no—
172C4×Q16—112no—
173C4×D8—112no—
174#428—221no—
175#427C2×D1111yescharacteristic
176C2×#107—111no—
177C2×#107C2×D1111yescharacteristic
178#417—221no—
179#405—111no—
180#367—112no—
181#367—112no—
182#367C2×D1112yes—
183#366C2×D1112yes—
184C4⋊C16—112no—
185C4⋊C16—112no—
186#358—112no—
187#358—111no—
188#358—111no—
189#357—112no—
190#357—111no—
191#357—111no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11#47412yes—
195C22×C11C22×D811yescharacteristic
196C2×D11—42no—
197C2×D11—81no—
198C2×D11—81no—
199C4×C11—81no—
200C4×C11—82no—
201C4×C11—81no—
202C4×C11#47412yes—
203C4×C11C2×C22⋊Q811yescharacteristic
204C4×C11C2×#13711yescharacteristic
205Dic11—22no—
206Dic11—22no—
207Dic11—42no—
208Dic11—82no—
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—21no—
226#117—111no—
227#117—441no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—221no—
230C2×C4⋊C4—441no—
231M32—22no—
232C2×C16—111no—
233C2×C16—111no—
234C2×C16—222no—
235C2×C16C22×D1112yes—
236#107—21no—
237#107—112no—
238#107—222no—
239#107—221no—
240#107C22×D1111yescharacteristic
241#107C22×D1111yescharacteristic
242#107C22×D1112yes—
243#106—21no—
244#106—222no—
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—442no—
262C22×C4—441no—
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—21no—
278C4⋊C4—21no—
279C4⋊C4—41no—
280C4⋊C4—111no—
281C4⋊C4—111no—
282C4⋊C4—222no—
283C4⋊C4—442no—
284C4⋊C4—442no—
285C4⋊C4—442no—
286C4⋊C4—442no—
287C4⋊C4—441no—
288C22⋊C4—41no—
289C22⋊C4—112no—
290C22⋊C4—442no—
291C42—41no—
292C42—112no—
293C42—442no—
294C16—22no—
295C16—221no—
296C16—221no—
297C11#3363411yescharacteristic, complemented, Sylow
298C23—441no—
299C23D8×D1111yescharacteristic
300Q8—222no—
301Q8—441no—
302Q8—1762no—
303D4—222no—
304D4—444no—
305D4—441no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—42no—
309C2×C4—112no—
310C2×C4—112no—
311C2×C4—161no—
312C2×C4—441no—
313C2×C4—444no—
314C2×C4—442no—
315C2×C4—1762no—
316C2×C4—1761no—
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—81no—
333C4—82no—
334C4—81no—
335C4—222no—
336C4—222no—
337C4—442no—
338C4—882no—
339C4#1062250312yes—
340C4C2×#6694911yescharacteristic
341C4C2×#6697111yescharacteristic
342C2—22no—
343C2—882no—
344C2C2×#1062250311yescharacteristic
345C2#1308176111yescharacteristic
346C2#1308176211yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2159C2
socleC22×C11C22×D8
prime radicalC2×#66957C22
hypercenter#2159D11
hypocenterC11#33634
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2159

Complements

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

NH ≅ G/Ntype
1. #13079156C2semidirect
3. #13070779C2semidirect
4. #13070776C2semidirect
5. #13070762C2semidirect
6. #13070757C2semidirect
7. C2×#10622128C2semidirect
8. #13070376C2semidirect
11. C11×#2159C2semidirect
51. #66957Q8semidirect
131. #2159D11semidirect
297. C11#33634semidirect

Maximal subgroups

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

subgroupindex
#130791562
#130774902
#130707792
#130707762
#130707622
#130707572
C2×#106221282
#130703762
#130703292
#130703212
C11×#21592
#3363411