Finite Group Databasebeta

← #14908491

Subgroups — #14908491

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#13077492C211yesmaximal, characteristic
3#13070778C212yesmaximal, complemented
4#13070775C212yesmaximal, complemented
5#13070761C212yesmaximal, complemented
6#13070756C212yesmaximal, complemented
7#13070405C211yesmaximal, characteristic, complemented
8C2×#10622143C211yesmaximal, characteristic, complemented
9#13070374C211yesmaximal, characteristic, complemented
10#13070328C211yesmaximal, characteristic
11C11×#2138C211yesmaximal, characteristic
12C2×C11×#135C2211yescharacteristic
13#10623358—21no—
14#10623050—21no—
15C22×C11×C16C2211yescharacteristic
16C11×#427C2211yescharacteristic
17#10622845—21no—
18Q16×Dic11C2212yes—
19#10622777—22no—
20D8×Dic11C2212yes—
21C2×#66882C2211yescharacteristic
22C2×#66882C2211yescharacteristic
23#10622714C2211yescharacteristic
24C2×#66876C2211yescharacteristic
25#10622608—21no—
26#10622491C2212yes—
27#10622487C2212yes—
28#10622469—22no—
29C11×#358C2211yescharacteristic
30C11×#358C2211yescharacteristic
31C11×#357C2211yescharacteristic
32C11×#357C2211yescharacteristic
33#10622202C2212yes—
34#10622200C2212yes—
35#10622143C2212yes—
36#10622143C2212yes—
37Dic11⋊C16C2212yes—
38Dic11⋊C16C2212yes—
39#10622128C2212yes—
40#10622127C2212yes—
41C2×C11×#41—21no—
42C11×#135—22no—
43C11×#135Q814yescomplemented
44C2×C11×Q16C2311yescharacteristic
45C2×C11×SD16—21no—
46C2×C11×D8C2311yescharacteristic
47C22×C8×C11C2311yescharacteristic
48C11×#117—21no—
49Q8×Dic11—22no—
50D4×Dic11—22no—
51D4×Dic11—42no—
52#66979—41no—
53#66979D411yescharacteristic
54C2×C4⋊Dic11—21no—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11—41no—
57C2×#4318D411yescharacteristic
58#66943—22no—
59#66941—22no—
60#66931—42no—
61#66923—41no—
62#66922—41no—
63C2×C11×C16—22no—
64C2×C11×C16C2311yescharacteristic
65C2×C11×C16C2311yescharacteristic
66C11×#107C2311yescharacteristic
67C11×#107C2311yescharacteristic
68C11×#106—21no—
69#66899—22no—
70#66896—22no—
71#66882—21no—
72#66882—21no—
73#66882C2312yes—
74#66882C2312yes—
75#66879D412yes—
76C8×Dic11C2312yes—
77#66876—22no—
78C2×C11⋊C16C2312yes—
79#66872—22no—
80#66871—22no—
81#33634—111nomaximal, Sylow
82C11×#41—24no—
83C11×#41—42no—
84C2×Q8×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11C2×D411yescharacteristic
89C22×Dic11—42no—
90C22×Dic11—41no—
91C22×Dic11—41no—
92C2×Dic22—42no—
93C11×Q16—21no—
94C11×Q16C2×Q812yes—
95C11×SD16—24no—
96C11×D8—21no—
97C11×D8C2×Q812yes—
98C2×C8×C11C2×D411yescharacteristic
99C2×C8×C11C2×Q812yes—
100C2×C8×C11#4112yes—
101C2×C8×C11C2411yescharacteristic
102C11×C4⋊C4—21no—
103C11×C4⋊C4—21no—
104C11×C22⋊C4—41no—
105C42×C11—41no—
106C22⋊Dic11—42no—
107C22⋊Dic11D812yes—
108C4⋊Dic11—22no—
109C4⋊Dic11—22no—
110C4⋊Dic11—42no—
111C4⋊Dic11—42no—
112C4⋊Dic11—41no—
113C4⋊Dic11—41no—
114C4⋊Dic11D811yescharacteristic
115C4⋊Dic11D811yescharacteristic
116Dic11⋊C4—42no—
117Dic11⋊C4—42no—
118C4×Dic11—42no—
119C4×Dic11C2×D412yes—
120#4318—22no—
121C2×C11⋊C8C2×D412yes—
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#2151—111no—
134#2139—111no—
135#2138D1111yescharacteristic
136C23×C11—41no—
137C23×C11C2×D811yescharacteristic
138Q8×C11—22no—
139Q8×C11—41no—
140D4×C11—22no—
141D4×C11—44no—
142D4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—44no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11C22⋊Q812yes—
148C2×C4×C11C2×D811yescharacteristic
149C2×C4×C11#13712yes—
150C2×C4×C11C22×D411yescharacteristic
151C2×Dic11—42no—
152C2×Dic11—42no—
153C2×Dic11—162no—
154C2×Dic11—161no—
155C2×Dic11—161no—
156C2×Dic11C2×D812yes—
157C2×Dic11C2×D812yes—
158Dic22—162no—
159C8×C11C22⋊Q812yes—
160C8×C11C22×Q811yescharacteristic
161C8×C11C2×#4111yescharacteristic
162C11⋊C8—22no—
163C2×#135C2×D1111yescharacteristic
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#427C2×D1111yescharacteristic
176C2×#107—111no—
177C2×#107—111no—
178#417—221no—
179#405—111no—
180#367—112no—
181#367—112no—
182#367—112no—
183#366—112no—
184C4⋊C16—112no—
185C4⋊C16—112no—
186#358—112no—
187#358C2×D1111yescharacteristic
188#358C2×D1111yescharacteristic
189#357—112no—
190#357C2×D1111yescharacteristic
191#357C2×D1111yescharacteristic
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—42no—
195C22×C11—81no—
196C22×C11—81no—
197C22×C11#47412yes—
198C22×C11C22×D811yescharacteristic
199C4×C11—42no—
200C4×C11—81no—
201C4×C11—81no—
202C4×C11#47412yes—
203C4×C11C2×C22⋊Q811yescharacteristic
204C4×C11C2×#13711yescharacteristic
205Dic11—22no—
206Dic11—22no—
207Dic11—82no—
208Dic11—82no—
209C2×#41—21no—
210#135—22no—
211#135Dic2214yescomplemented
212C2×Q16C22×D1111yescharacteristic
213C2×SD16—21no—
214C2×D8C22×D1111yescharacteristic
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—221no—
229C2×C4⋊C4—221no—
230C2×C4⋊C4—441no—
231M32—222no—
232C2×C16—22no—
233C2×C16—112no—
234C2×C16C22×D1111yescharacteristic
235C2×C16C22×D1111yescharacteristic
236#107—112no—
237#107—112no—
238#107—222no—
239#107—221no—
240#107—221no—
241#107C22×D1111yescharacteristic
242#107C22×D1111yescharacteristic
243#106—21no—
244#106—222no—
245#103—222no—
246#102—222no—
247#97—112no—
248C4×C8—112no—
249C2×C11—22no—
250C2×C11—82no—
251C2×C11C2×#47411yescharacteristic
252C2×C11#341611yescharacteristic
253C2×C11#341611yescharacteristic
254#41—24no—
255#41—42no—
256C2×Q8—21no—
257C2×Q8—442no—
258C2×D4—21no—
259C2×D4—41no—
260C22×C4—41no—
261C22×C4—442no—
262C22×C4—441no—
263C22×C4—441no—
264C22×C4D4×D1111yescharacteristic
265Q16—21no—
266Q16C2×Dic2212yes—
267SD16—24no—
268D8—21no—
269D8C2×Dic2212yes—
270M16—222no—
271C2×C8—112no—
272C2×C8C2×Dic2212yes—
273C2×C8D4×D1111yescharacteristic
274C2×C8#434112yes—
275C2×C8C23×D1111yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—111no—
279C4⋊C4—111no—
280C4⋊C4—222no—
281C4⋊C4—222no—
282C4⋊C4—442no—
283C4⋊C4—442no—
284C4⋊C4—442no—
285C4⋊C4—442no—
286C4⋊C4—441no—
287C4⋊C4—441no—
288C22⋊C4—41no—
289C22⋊C4—112no—
290C22⋊C4—442no—
291C42—41no—
292C42—112no—
293C42—442no—
294C16—21no—
295C16—21no—
296C16—222no—
297C11#3363411yescharacteristic, complemented, Sylow
298C23—41no—
299C23D8×D1111yescharacteristic
300Q8—22no—
301Q8—41no—
302Q8—1762no—
303D4—22no—
304D4—44no—
305D4—41no—
306C2×C4—41no—
307C2×C4—44no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—112no—
311C2×C4—112no—
312C2×C4—442no—
313C2×C4—442no—
314C2×C4—1762no—
315C2×C4—1761no—
316C2×C4—1761no—
317C2×C4#6693112yes—
318C2×C4D8×D1111yescharacteristic
319C2×C4#6696812yes—
320C2×C4C2×D4×D1111yescharacteristic
321C8—222no—
322C8#6693112yes—
323C8C22×Dic2211yescharacteristic
324C8C2×#434111yescharacteristic
325C22—21no—
326C22—21no—
327C22—42no—
328C22—81no—
329C22—81no—
330C22#1062237212yes—
331C22C2×D8×D1111yescharacteristic
332C4—42no—
333C4—81no—
334C4—81no—
335C4—222no—
336C4—222no—
337C4—882no—
338C4—882no—
339C4#1062237212yes—
340C4C2×#6693111yescharacteristic
341C4C2×#6696811yescharacteristic
342C2—22no—
343C2—82no—
344C2C2×#1062237211yescharacteristic
345C2#1308175911yescharacteristic
346C2#1308175911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2138C2
socleC22×C11C22×D8
prime radicalC2×C11×#135C22
hypercenter#2138D11
hypocenterC11#33634
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2138

Complements

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

NH ≅ G/Ntype
1. #13079156C2semidirect
3. #13070778C2semidirect
4. #13070775C2semidirect
5. #13070761C2semidirect
6. #13070756C2semidirect
7. #13070405C2semidirect
8. C2×#10622143C2semidirect
9. #13070374C2semidirect
43. C11×#135Q8semidirect
211. #135Dic22semidirect
297. C11#33634semidirect

Maximal subgroups

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

subgroupindex
#130791562
#130774922
#130707782
#130707752
#130707612
#130707562
#130704052
C2×#106221432
#130703742
#130703282
C11×#21382
#3363411