Finite Group Databasebeta

← #14784653

Subgroups — #14784653

Order 2816.

616 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077548C211yesmaximal, characteristic, complemented
2#13070195C211yesmaximal, characteristic, complemented
3#13070190C211yesmaximal, characteristic, complemented
4#13070066C212yesmaximal, complemented
5#13069919C211yesmaximal, characteristic
6#13069900C211yesmaximal, characteristic
7#13069786C212yesmaximal, complemented
8#13068451C212yesmaximal, complemented
9#13068416C212yesmaximal, complemented
10#13068371C211yesmaximal, characteristic, complemented
11C11×#2955C211yesmaximal, characteristic
12C11×#575C2211yescharacteristic
13C2×C11×#131C2212yes—
14#10623048C2211yescharacteristic
15C11×#444—22no—
16C11×#443—22no—
17C11×#430C2211yescharacteristic
18C11×#421C2212yes—
19C11×#405C2211yescharacteristic
20#10622853C2212yes—
21#10622850C2212yes—
22C2×#66901C2212yes—
23#10622846C2212yes—
24#10622732C2211yescharacteristic
25#10622731C2211yescharacteristic
26#10622714C2211yescharacteristic
27#10622714C2212yes—
28C2×C8×Dic11C2211yescharacteristic
29#10622612C2211yescharacteristic
30#10622314—22no—
31C8×Dic22—22no—
32C11⋊#338C2211yescharacteristic
33#10622196C2212yes—
34#10622195C2211yescharacteristic
35#10622194C2212yes—
36#10622194C2212yes—
37#10622193C2212yes—
38#10622169C2212yes—
39C2×C11×#41C2312yes—
40C11×#137—22no—
41C11×AGL(1,ℤ/8)—22no—
42C11×#135—22no—
43C11×#131—22no—
44C11×#131—22no—
45C11×#131—22no—
46C11×#131—22no—
47C2×C11×M16—22no—
48C2×C11×M16C2312yes—
49C2×C11×M16C2311yescharacteristic
50C22×C8×C11—22no—
51C22×C8×C11C2311yescharacteristic
52C11×#117C2311yescharacteristic
53#66979C2312yes—
54#66979C2311yescharacteristic
55C2×C4×Dic11C2311yescharacteristic
56C2×#4318C2311yescharacteristic
57C2×#4318C2312yes—
58C22×C11⋊C8C2311yescharacteristic
59#66943—21no—
60#66941—21no—
61#66931—22no—
62C4×Dic22—22no—
63C11×#108—22no—
64C11×#104—24no—
65C11×#97D412yes—
66C4×C8×C11D412yes—
67#66901—22no—
68#66901—22no—
69#66900—22no—
70#66899—22no—
71#66898—24no—
72#66897—22no—
73#66896—22no—
74#66879—21no—
75#66879—22no—
76Dic11⋊C8—22no—
77Dic11⋊C8—22no—
78C8×Dic11—21no—
79C8×Dic11—21no—
80C8×Dic11—21no—
81C8×Dic11—22no—
82C4⋊(C11⋊C8)—22no—
83#23833—111nomaximal, Sylow
84C11×#41—22no—
85C11×#41—22no—
86C11×#41—22no—
87C11×#41—22no—
88C2×Q8×C11#4112yes—
89C2×D4×C11—22no—
90C2×D4×C11#4112yes—
91C22×C4×C11—22no—
92C22×C4×C11C2411yescharacteristic
93C22×Dic11—21no—
94C2×Dic22—22no—
95C11×Q16—22no—
96C11×SD16—24no—
97C11×D8—22no—
98C11×M16—22no—
99C11×M16—22no—
100C11×M16—22no—
101C11×M16—42no—
102C11×M16—42no—
103C2×C8×C11—22no—
104C2×C8×C11—42no—
105C2×C8×C11—42no—
106C2×C8×C11C2×D412yes—
107C2×C8×C11C2×D411yescharacteristic
108C2×C8×C11C2×D411yescharacteristic
109C2×C8×C11#4112yes—
110C2×C8×C11#4112yes—
111C11×C4⋊C4—21no—
112C11×C22⋊C4—21no—
113C42×C11C2×D412yes—
114C22⋊Dic11—22no—
115C22⋊Dic11#4112yes—
116C4⋊Dic11—22no—
117C4⋊Dic11—21no—
118C4⋊Dic11—22no—
119Dic11⋊C4—22no—
120Dic11⋊C4—22no—
121C4×Dic11—21no—
122C4×Dic11—21no—
123C4×Dic11—22no—
124C4×Dic11#4111yescharacteristic
125C4×Dic11#4111yescharacteristic
126#4318—22no—
127#4318—22no—
128#4318—22no—
129C2×C11⋊C8—21no—
130C2×C11⋊C8—21no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—22no—
133#2960—111no—
134#2955D1111yescharacteristic
135#2103—111no—
136#2102—111no—
137#2080—112no—
138#2053—111no—
139#2050—111no—
140#2031—112no—
141#1764—112no—
142#1757—112no—
143#1747—111no—
144C23×C11—22no—
145C23×C11C2×#4111yescharacteristic
146Q8×C11—22no—
147Q8×C11—22no—
148D4×C11—22no—
149D4×C11—22no—
150D4×C11—42no—
151D4×C11—42no—
152C2×C4×C11—22no—
153C2×C4×C11—22no—
154C2×C4×C11—42no—
155C2×C4×C11—42no—
156C2×C4×C11C22×D411yescharacteristic
157C2×C4×C11C2×#4112yes—
158C2×C4×C11C2×#4112yes—
159C2×C4×C11C2×#4111yescharacteristic
160C2×Dic11—21no—
161C2×Dic11—21no—
162C2×Dic11—22no—
163C2×Dic11—42no—
164C2×Dic11—42no—
165Dic22—44no—
166C8×C11—22no—
167C8×C11—42no—
168C8×C11#12412yes—
169C8×C11#12411yescharacteristic
170C8×C11#12411yescharacteristic
171C11⋊C8—41no—
172C11⋊C8—41no—
173C11⋊C8—42no—
174#575C2×D1111yescharacteristic
175C2×#131C2×D1112yes—
176#533—111no—
177#446—222no—
178C8×Q8—222no—
179#444—22no—
180#443—22no—
181#430C2×D1111yescharacteristic
182#424—111no—
183#424—111no—
184#423—111no—
185#421C2×D1112yes—
186C2×#104—112no—
187#416—112no—
188#413—112no—
189#410—112no—
190#405—111no—
191#405—112no—
192#405C2×D1111yescharacteristic
193C2×C4×C8—111no—
194#344—112no—
195#344—112no—
196#341—112no—
197#339—112no—
198#338—111no—
199H(3,ℤ/4)—111no—
200H(3,ℤ/4)—112no—
201C22×C11—41no—
202C22×C11—42no—
203C22×C11—82no—
204C22×C11#52511yescharacteristic
205C22×C11#52912yes—
206C4×C11—42no—
207C4×C11—42no—
208C4×C11#52511yescharacteristic
209C4×C11C2×#12411yescharacteristic
210C4×C11#52912yes—
211Dic11—22no—
212Dic11—42no—
213Dic11—41no—
214Dic11—82no—
215C2×#41C22×D1112yes—
216#137—22no—
217AGL(1,ℤ/8)—22no—
218#135—22no—
219#131—22no—
220#131—22no—
221#131—22no—
222#131—22no—
223C2×M16—22no—
224C2×M16—112no—
225C2×M16—111no—
226C2×M16C22×D1112yes—
227C2×M16C22×D1111yescharacteristic
228C22×C8—22no—
229C22×C8—111no—
230C22×C8C22×D1111yescharacteristic
231C4⋊Q8—221no—
232#125—221no—
233C22⋊Q8—222no—
234C4×Q8—222no—
235#117—111no—
236#117—112no—
237#117C22×D1111yescharacteristic
238C2×C42—111no—
239#108—22no—
240C4⋊C8—222no—
241C4⋊C8—222no—
242C4⋊C8—222no—
243#104—24no—
244#104—222no—
245#104—222no—
246#103—222no—
247#102—222no—
248#101—222no—
249#100—222no—
250#99—224no—
251#97—222no—
252#97—221no—
253#97C22⋊D1112yes—
254C4×C8—222no—
255C4×C8—221no—
256C4×C8—221no—
257C4×C8—221no—
258C4×C8C22⋊D1112yes—
259C2×C11—21no—
260C2×C11—22no—
261C2×C11—82no—
262C2×C11#239811yescharacteristic
263#41—22no—
264#41—22no—
265#41—22no—
266#41—22no—
267C2×Q8—222no—
268C2×Q8#433912yes—
269C2×D4—22no—
270C2×D4#433912yes—
271C22×C4—22no—
272C22×C4—221no—
273C22×C4C23×D1111yescharacteristic
274Q16—22no—
275SD16—24no—
276D8—22no—
277M16—22no—
278M16—22no—
279M16—22no—
280M16—42no—
281M16—42no—
282M16—222no—
283M16—222no—
284M16—222no—
285C2×C8—22no—
286C2×C8—42no—
287C2×C8—42no—
288C2×C8—222no—
289C2×C8—222no—
290C2×C8—221no—
291C2×C8—221no—
292C2×C8#434112yes—
293C2×C8#434112yes—
294C2×C8C2×C22⋊D1112yes—
295C2×C8C2×C22⋊D1111yescharacteristic
296C2×C8C2×C22⋊D1111yescharacteristic
297C4⋊C4—21no—
298C4⋊C4—222no—
299C4⋊C4—222no—
300C4⋊C4—222no—
301C4⋊C4—221no—
302C4⋊C4—222no—
303C22⋊C4—21no—
304C22⋊C4—112no—
305C22⋊C4—222no—
306C42—111no—
307C42—111no—
308C42—221no—
309C42—221no—
310C42—222no—
311C42C2×C22⋊D1112yes—
312C11#2383311yescharacteristic, complemented, Sylow
313C23—22no—
314C23#41×D1111yescharacteristic
315Q8—22no—
316Q8—22no—
317Q8—444no—
318D4—22no—
319D4—22no—
320D4—42no—
321D4—42no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—221no—
327C2×C4—221no—
328C2×C4—222no—
329C2×C4—442no—
330C2×C4—442no—
331C2×C4C2×#433912yes—
332C2×C4C2×#434112yes—
333C2×C4#41×D1111yescharacteristic
334C2×C4C22×C22⋊D1111yescharacteristic
335C8—22no—
336C8—42no—
337C8—441no—
338C8—441no—
339C8—442no—
340C8#6698912yes—
341C8#6698911yescharacteristic
342C8#6698911yescharacteristic
343C22—41no—
344C22—42no—
345C22—82no—
346C22#1062306912yes—
347C22#1062335911yescharacteristic
348C4—42no—
349C4—42no—
350C4—222no—
351C4—441no—
352C4—442no—
353C4—882no—
354C4#1062306912yes—
355C4#1062332211yescharacteristic
356C4C2×#6698911yescharacteristic
357C2—21no—
358C2—22no—
359C2—82no—
360C2#1307190011yescharacteristic
subgroupG/H
centerC8#66989
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2955C2
socleC2×C11#2398
prime radicalC11×#575C22
hypercenter#2955D11
hypocenterC11#23833
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C8 ◁ C22×C8 ◁ #2955

Complements

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

NH ≅ G/Ntype
1. #13077548C2semidirect
2. #13070195C2semidirect
3. #13070190C2semidirect
4. #13070066C2semidirect
7. #13069786C2semidirect
8. #13068451C2semidirect
9. #13068416C2semidirect
10. #13068371C2semidirect
312. C11#23833semidirect

Maximal subgroups

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

subgroupindex
#130775482
#130701952
#130701902
#130700662
#130699192
#130699002
#130697862
#130684512
#130684162
#130683712
C11×#29552
#2383311