Finite Group Databasebeta

← #14908495

Subgroups — #14908495

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#13079155C211yesmaximal, characteristic, complemented
2#13077493C211yesmaximal, characteristic
3#13070781C212yesmaximal, complemented
4#13070774C212yesmaximal, complemented
5#13070764C212yesmaximal, complemented
6#13070759C212yesmaximal, complemented
7#13070404C211yesmaximal, characteristic, complemented
8C2×#10622143C211yesmaximal, characteristic, complemented
9#13070329C211yesmaximal, characteristic
10#13070324C211yesmaximal, characteristic
11C11×#2151C211yesmaximal, characteristic, complemented
12C2×#66957C2211yescharacteristic
13#10623054—21no—
14#10623050—21no—
15C2×C11×M32C2211yescharacteristic
16C22×C11×C16C2211yescharacteristic
17C11×#405C2211yescharacteristic
18#10622746—21no—
19#10622734—21no—
20#10622719C2211yescharacteristic
21C2×#66882C2211yescharacteristic
22C2×#66882C2211yescharacteristic
23#10622323—22no—
24#10622315—22no—
25C4×Dic44C2212yes—
26C4×D88C2212yes—
27#10622296C2212yes—
28#10622295C2212yes—
29C11×C4⋊C16C2212yes—
30C11×C4⋊C16C2212yes—
31#10622147C2211yescharacteristic
32#10622147C2212yes—
33#10622147C2211yescharacteristic
34#10622143C2212yes—
35#10622143C2212yes—
36#10622143C2212yes—
37#10622142C2212yes—
38#10622141C2211yescharacteristic
39#10622141C2212yes—
40#10622141C2211yescharacteristic
41C2×#4339—21no—
42C2×C11×M16D411yescharacteristic
43C22×C8×C11C2311yescharacteristic
44C11×#117D411yescharacteristic
45#66979—21no—
46C2×C4⋊Dic11—21no—
47C2×C4⋊Dic11—21no—
48C2×Dic44C2311yescharacteristic
49#66957—22no—
50#66957Q814yescomplemented
51C2×D88C2311yescharacteristic
52C2×#4314—21no—
53#66945—41no—
54C4⋊C4×D11—41no—
55#66943—41no—
56#66941—41no—
57(C22⋊D11)⋊C4—42no—
58#66931—42no—
59C4×D44—22no—
60#66923—22no—
61#66922—22no—
62C4×Dic22—22no—
63C11×M32—22no—
64C2×C11×C16—22no—
65C2×C11×C16C2311yescharacteristic
66C2×C11×C16C2311yescharacteristic
67C2×C11×C16C2312yes—
68C11×#97D412yes—
69C4×C8×C11C2312yes—
70#66885—22no—
71#66882—22no—
72#66882—21no—
73#66882—21no—
74#66882C2311yescharacteristic
75#66882C2312yes—
76#66882C2311yescharacteristic
77#66882C2312yes—
78#66881—22no—
79#66881—21no—
80#66880—22no—
81#33634—111nomaximal, Sylow
82C22×C4×C11C2×D411yescharacteristic
83C2×C22⋊D11—41no—
84C22×Dic11—41no—
85C22×Dic11—41no—
86#4339—24no—
87#4339—42no—
88C2×D44—21no—
89C2×C4×D11—41no—
90C2×C4×D11—42no—
91C2×Dic22—21no—
92C2×Dic22—42no—
93C11×M16—22no—
94C2×C8×C11C2×D412yes—
95C2×C8×C11C2×D411yescharacteristic
96C2×C8×C11C2×Q812yes—
97C2×C8×C11#4112yes—
98C2×C8×C11C2411yescharacteristic
99C11×C4⋊C4D811yescharacteristic
100C11×C4⋊C4D811yescharacteristic
101C11×C22⋊C4D812yes—
102C42×C11C2×D412yes—
103C22⋊Dic11—41no—
104(C2×D11)⋊C4—42no—
105C4⋊Dic11—22no—
106C4⋊Dic11—21no—
107C4⋊Dic11—21no—
108C4⋊Dic11—22no—
109C4⋊Dic11—42no—
110C4⋊Dic11—41no—
111C4⋊Dic11—41no—
112Dic11⋊C4—42no—
113Dic11⋊C4—42no—
114Dic11⋊C4—42no—
115C4×Dic11—42no—
116C4×Dic11—41no—
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×#367—111no—
133#2151D1111yescharacteristic, complemented
134#2139—111no—
135#2138—111no—
136C23×C11C2×D811yescharacteristic
137C22×D11—41no—
138C2×C4×C11C22⋊Q812yes—
139C2×C4×C11C2×D812yes—
140C2×C4×C11C2×D812yes—
141C2×C4×C11C2×D811yescharacteristic
142C2×C4×C11#13712yes—
143C2×C4×C11C22×D411yescharacteristic
144C22⋊D11—44no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—42no—
148C2×Dic11—41no—
149C2×Dic11—42no—
150C2×Dic11—161no—
151C2×Dic11—161no—
152D44—22no—
153D44—41no—
154C4×D11—44no—
155C4×D11—162no—
156Dic22—22no—
157Dic22—41no—
158Dic22—162no—
159C8×C11—22no—
160C8×C11C22⋊Q812yes—
161C8×C11C22×Q811yescharacteristic
162C8×C11C2×#4111yescharacteristic
163C2×#135—111no—
164#544—221no—
165#520—221no—
166C2×M32C2×D1111yescharacteristic
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×#107—111no—
177C2×#107—111no—
178#417—221no—
179#405C2×D1111yescharacteristic
180#367—112no—
181#367—112no—
182#367—112no—
183#366—112no—
184C4⋊C16C2×D1112yes—
185C4⋊C16C2×D1112yes—
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—22no—
200C4×C11—22no—
201C4×C11#47412yes—
202C4×C11C2×C22⋊Q811yescharacteristic
203C4×C11C2×#13711yescharacteristic
204Dic11—42no—
205Dic11—81no—
206Dic11—82no—
207Dic11—82no—
208Dic11—81no—
209C2×#41—221no—
210#135—114no—
211#135—222no—
212C2×Q16—111no—
213C2×SD16—221no—
214C2×D8—111no—
215C2×M16D4411yescharacteristic
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—221no—
226#117—441no—
227#117D4411yescharacteristic
228C2×C4⋊C4—221no—
229C2×C4⋊C4—221no—
230C2×C4⋊C4—441no—
231M32—22no—
232C2×C16—22no—
233C2×C16C22×D1112yes—
234C2×C16C22×D1111yescharacteristic
235C2×C16C22×D1111yescharacteristic
236#107—111no—
237#107—112no—
238#107—111no—
239#107—112no—
240#107—221no—
241#107—221no—
242#107—222no—
243#106—221no—
244#106—222no—
245#103—222no—
246#102—222no—
247#97D4412yes—
248C4×C8C22×D1112yes—
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—441no—
261C22×C4—441no—
262C22×C4—441no—
263C22×C4—442no—
264C22×C4C2×D4411yescharacteristic
265Q16—112no—
266Q16—221no—
267SD16—224no—
268D8—112no—
269D8—221no—
270M16—22no—
271C2×C8C2×D4412yes—
272C2×C8C2×D4411yescharacteristic
273C2×C8#434112yes—
274C2×C8Q8×D1112yes—
275C2×C8C23×D1111yescharacteristic
276C4⋊C4—222no—
277C4⋊C4—221no—
278C4⋊C4—222no—
279C4⋊C4—221no—
280C4⋊C4—441no—
281C4⋊C4—441no—
282C4⋊C4—442no—
283C4⋊C4—442no—
284C4⋊C4—442no—
285C4⋊C4—442no—
286C4⋊C4D8811yescharacteristic
287C4⋊C4D8811yescharacteristic
288C22⋊C4—441no—
289C22⋊C4—442no—
290C22⋊C4D8812yes—
291C42—441no—
292C42—442no—
293C42C2×D4412yes—
294C16—21no—
295C16—21no—
296C16—22no—
297C11#3363411yescharacteristic, complemented, Sylow
298C23—441no—
299C23C2×D8811yescharacteristic
300Q8—222no—
301Q8—441no—
302Q8—1762no—
303D4—222no—
304D4—444no—
305D4—441no—
306C2×C4—441no—
307C2×C4—444no—
308C2×C4—441no—
309C2×C4—442no—
310C2×C4—441no—
311C2×C4—442no—
312C2×C4—1762no—
313C2×C4—1761no—
314C2×C4—1761no—
315C2×C4#6695012yes—
316C2×C4C2×D8812yes—
317C2×C4C2×D8812yes—
318C2×C4C2×D8811yescharacteristic
319C2×C4#6696212yes—
320C2×C4C22×D4411yescharacteristic
321C8—22no—
322C8#6695012yes—
323C8C2×#434111yescharacteristic
324C8C2×Q8×D1111yescharacteristic
325C22—21no—
326C22—21no—
327C22—442no—
328C22—881no—
329C22—881no—
330C22#1062245912yes—
331C22C22×D8811yescharacteristic
332C4—22no—
333C4—22no—
334C4—442no—
335C4—882no—
336C4—882no—
337C4—881no—
338C4—881no—
339C4#1062245912yes—
340C4C2×#6695011yescharacteristic
341C4C2×#6696211yescharacteristic
342C2—22no—
343C2—882no—
344C2C2×#1062245911yescharacteristic
345C2#1308176411yescharacteristic
346C2#1308176411yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2151C2
socleC22×C11C22×D8
prime radicalC2×#66957C22
hypercenter#2151D11
hypocenterC11#33634
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #2151

Complements

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

NH ≅ G/Ntype
1. #13079155C2semidirect
3. #13070781C2semidirect
4. #13070774C2semidirect
5. #13070764C2semidirect
6. #13070759C2semidirect
7. #13070404C2semidirect
8. C2×#10622143C2semidirect
11. C11×#2151C2semidirect
50. #66957Q8semidirect
133. #2151D11semidirect
297. C11#33634semidirect

Maximal subgroups

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

subgroupindex
#130791552
#130774932
#130707812
#130707742
#130707642
#130707592
#130704042
C2×#106221432
#130703292
#130703242
C11×#21512
#3363411