Finite Group Databasebeta

← #14908478

Subgroups — #14908478

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#13077493C211yesmaximal, characteristic
2#13070777C212yesmaximal, complemented
3#13070770C212yesmaximal, complemented
4#13070765C212yesmaximal, complemented
5#13070750C212yesmaximal, complemented
6#13070405C211yesmaximal, characteristic, complemented
7C2×#10622127C211yesmaximal, characteristic, complemented
8#13070375C211yesmaximal, characteristic, complemented
9#13070326C211yesmaximal, characteristic
10#13070321C211yesmaximal, characteristic
11C11×#3164C211yesmaximal, characteristic, complemented
12C11×#544—21no—
13C2×#66957C2211yescharacteristic
14#10623054—21no—
15C11×#501—22no—
16C11×#500C2212yes—
17C11×#499C2212yes—
18C11×#428—21no—
19C11×#427C2211yescharacteristic
20C2×C11×#107C2211yescharacteristic
21C11×#405C2211yescharacteristic
22#10622746—21no—
23C2×#66882C2211yescharacteristic
24C2×#66876C2211yescharacteristic
25C22×C11⋊C16C2211yescharacteristic
26#10622323—22no—
27C4×Dic44C2212yes—
28C4×D88C2212yes—
29#10622130C2211yescharacteristic
30#10622130C2212yes—
31#10622130C2211yescharacteristic
32#10622129C2211yescharacteristic
33#10622129C2212yes—
34#10622129C2211yescharacteristic
35#10622128C2212yes—
36#10622127C2212yes—
37#10622127C2212yes—
38#10622127C2212yes—
39C4⋊(C11⋊C16)C2212yes—
40C4⋊(C11⋊C16)C2212yes—
41C2×#4339—21no—
42C2×C11×M16D411yescharacteristic
43C22×C8×C11C2311yescharacteristic
44C11×C4⋊Q8—22no—
45C11×C4⋊Q8—41no—
46C11×#125—22no—
47C11×#125—41no—
48C11×C22⋊Q8—42no—
49C11×#117—21no—
50C11×#117D411yescharacteristic
51C2×C11×C4⋊C4—21no—
52C2×C4⋊Dic11—21no—
53C2×Dic44C2311yescharacteristic
54#66957—22no—
55#66957Q814yescomplemented
56C2×D88C2311yescharacteristic
57C2×#4314—21no—
58#66945—41no—
59C4⋊C4×D11—41no—
60(C22⋊D11)⋊C4—42no—
61C4×D44—22no—
62C4×Dic22—22no—
63C11×#107—22no—
64C11×#107—21no—
65C11×#107C2311yescharacteristic
66C11×#107C2312yes—
67C11×#107C2311yescharacteristic
68C11×#106—22no—
69C11×#106—21no—
70C11×#97D412yes—
71C4×C8×C11C2312yes—
72#66885—22no—
73#66882—21no—
74#66882C2312yes—
75#66880—22no—
76#66876—22no—
77C2×C11⋊C16—22no—
78C2×C11⋊C16C2311yescharacteristic
79C2×C11⋊C16C2311yescharacteristic
80C2×C11⋊C16C2312yes—
81#33633—111nomaximal, Sylow
82C2×Q8×C11—42no—
83C22×C4×C11—41no—
84C22×C4×C11C2×D411yescharacteristic
85C2×C22⋊D11—41no—
86C22×Dic11—41no—
87#4339—24no—
88#4339—42no—
89C2×D44—21no—
90C2×C4×D11—41no—
91C2×C4×D11—42no—
92C2×Dic22—21no—
93C11×M16—22no—
94C2×C8×C11C2×D412yes—
95C2×C8×C11C2×D411yescharacteristic
96C2×C8×C11C2×Q812yes—
97C2×C8×C11#4112yes—
98C2×C8×C11C2411yescharacteristic
99C11×C4⋊C4—21no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—42no—
104C11×C4⋊C4—42no—
105C11×C4⋊C4—42no—
106C11×C4⋊C4D811yescharacteristic
107C11×C4⋊C4D811yescharacteristic
108C11×C22⋊C4—41no—
109C11×C22⋊C4D812yes—
110C42×C11—41no—
111C42×C11C2×D412yes—
112(C2×D11)⋊C4—42no—
113C4⋊Dic11—22no—
114C4⋊Dic11—41no—
115Dic11⋊C4—42no—
116C4×Dic11—42no—
117Dic44—21no—
118Dic44C2×Q812yes—
119D88—21no—
120D88C2×Q812yes—
121#4314—24no—
122C11⋊C16—21no—
123C11⋊C16—21no—
124C11⋊C16—22no—
125#3164D1111yescharacteristic, complemented
126#2951—111no—
127#2229—112no—
128#2228—112no—
129#2227—112no—
130#2224—112no—
131#2159—111no—
132C2×#366—111no—
133#2151—111no—
134#2139—111no—
135#2138—111no—
136C23×C11C2×D811yescharacteristic
137C22×D11—41no—
138Q8×C11—162no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—42no—
142C2×C4×C11—161no—
143C2×C4×C11C22⋊Q812yes—
144C2×C4×C11C2×D812yes—
145C2×C4×C11C2×D812yes—
146C2×C4×C11C2×D811yescharacteristic
147C2×C4×C11#13712yes—
148C2×C4×C11C22×D411yescharacteristic
149C22⋊D11—44no—
150C2×Dic11—41no—
151C2×Dic11—42no—
152C2×Dic11—161no—
153D44—22no—
154D44—41no—
155C4×D11—44no—
156C4×D11—162no—
157Dic22—22no—
158Dic22—41no—
159C8×C11—22no—
160C8×C11C22⋊Q812yes—
161C8×C11C22×Q811yescharacteristic
162C8×C11C2×#4111yescharacteristic
163C2×#135—111no—
164#544—21no—
165#520—221no—
166C2×M32—111no—
167C22×C16—111no—
168#501—22no—
169#500C2×D1112yes—
170#499C2×D1112yes—
171#440—222no—
172C4×Q16—112no—
173C4×D8—112no—
174#428—21no—
175#427C2×D1111yescharacteristic
176C2×#107—111no—
177C2×#107C2×D1111yescharacteristic
178#417—221no—
179#405C2×D1111yescharacteristic
180#367—112no—
181#366—112no—
182#366—112no—
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—22no—
200C4×C11—22no—
201C4×C11—82no—
202C4×C11—81no—
203C4×C11—81no—
204C4×C11#47412yes—
205C4×C11C2×C22⋊Q811yescharacteristic
206C4×C11C2×#13711yescharacteristic
207Dic11—42no—
208Dic11—82no—
209C2×#41—221no—
210#135—114no—
211#135—222no—
212C2×Q16—111no—
213C2×SD16—221no—
214C2×D8—111no—
215C2×M16C22⋊D1111yescharacteristic
216C22×C8C22×D1111yescharacteristic
217C4⋊Q8—22no—
218C4⋊Q8—41no—
219#125—22no—
220#125—41no—
221C22⋊Q8—42no—
222C4×Q8—222no—
223C4×D4—222no—
224C4×D4—442no—
225#117—21no—
226#117—441no—
227#117C22⋊D1111yescharacteristic
228C2×C4⋊C4—21no—
229C2×C4⋊C4—221no—
230C2×C4⋊C4—441no—
231M32—222no—
232C2×C16—111no—
233C2×C16—111no—
234C2×C16—112no—
235C2×C16—222no—
236#107—21no—
237#107—22no—
238#107—112no—
239#107—221no—
240#107C22×D1112yes—
241#107C22×D1111yescharacteristic
242#107C22×D1111yescharacteristic
243#106—21no—
244#106—22no—
245#103—222no—
246#102—222no—
247#97C22⋊D1112yes—
248C4×C8C22×D1112yes—
249C2×C11—22no—
250C2×C11C2×#47411yescharacteristic
251C2×C11#341511yescharacteristic
252C2×C11#341711yescharacteristic
253D11—82no—
254#41—224no—
255#41—442no—
256C2×Q8—42no—
257C2×Q8—221no—
258C2×D4—221no—
259C2×D4—441no—
260C22×C4—41no—
261C22×C4—441no—
262C22×C4—441no—
263C22×C4—442no—
264C22×C4C2×C22⋊D1111yescharacteristic
265Q16—112no—
266Q16—221no—
267SD16—224no—
268D8—112no—
269D8—221no—
270M16—22no—
271C2×C8Q8×D1112yes—
272C2×C8#434312yes—
273C2×C8C2×C22⋊D1112yes—
274C2×C8C2×C22⋊D1111yescharacteristic
275C2×C8C23×D1111yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—22no—
278C4⋊C4—21no—
279C4⋊C4—41no—
280C4⋊C4—42no—
281C4⋊C4—42no—
282C4⋊C4—42no—
283C4⋊C4—222no—
284C4⋊C4—441no—
285C4⋊C4—442no—
286C4⋊C4#432311yescharacteristic
287C4⋊C4#432311yescharacteristic
288C22⋊C4—41no—
289C22⋊C4—442no—
290C22⋊C4#432312yes—
291C42—41no—
292C42—442no—
293C42C2×C22⋊D1112yes—
294C16—221no—
295C16—221no—
296C16—222no—
297C11#3363311yescharacteristic, complemented, Sylow
298C23—441no—
299C23C2×#432311yescharacteristic
300Q8—162no—
301Q8—222no—
302Q8—441no—
303D4—222no—
304D4—444no—
305D4—441no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—42no—
309C2×C4—161no—
310C2×C4—441no—
311C2×C4—444no—
312C2×C4—442no—
313C2×C4—1762no—
314C2×C4—1761no—
315C2×C4C2×#432312yes—
316C2×C4C2×#432312yes—
317C2×C4C2×#432311yescharacteristic
318C2×C4#6699512yes—
319C2×C4#6699912yes—
320C2×C4C22×C22⋊D1111yescharacteristic
321C8—22no—
322C8#6699912yes—
323C8C2×Q8×D1111yescharacteristic
324C8C2×#434311yescharacteristic
325C22—21no—
326C22—21no—
327C22—442no—
328C22—881no—
329C22—881no—
330C22#1062270012yes—
331C22C22×#432311yescharacteristic
332C4—22no—
333C4—22no—
334C4—82no—
335C4—81no—
336C4—81no—
337C4—442no—
338C4—882no—
339C4#1062270012yes—
340C4C2×#6699511yescharacteristic
341C4C2×#6699911yescharacteristic
342C2—22no—
343C2—882no—
344C2C2×#1062270011yescharacteristic
345C2#1308175511yescharacteristic
346C2#1308176711yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3164C2
socleC22×C11C22×D8
prime radicalC2×#66957C22
hypercenter#3164D11
hypocenterC11#33633
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #3164

Complements

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

NH ≅ G/Ntype
2. #13070777C2semidirect
3. #13070770C2semidirect
4. #13070765C2semidirect
5. #13070750C2semidirect
6. #13070405C2semidirect
7. C2×#10622127C2semidirect
8. #13070375C2semidirect
11. C11×#3164C2semidirect
55. #66957Q8semidirect
125. #3164D11semidirect
297. C11#33633semidirect

Maximal subgroups

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

subgroupindex
#130774932
#130707772
#130707702
#130707652
#130707502
#130704052
C2×#106221272
#130703752
#130703262
#130703212
C11×#31642
#3363311