Finite Group Databasebeta

← #14909118

Subgroups — #14909118

Order 2816.

570 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079155C211yesmaximal, characteristic, complemented
2#13079110C211yesmaximal, characteristic
3#13070862C212yesmaximal, complemented
4#13070853C212yesmaximal, complemented
5#13070848C212yesmaximal, complemented
6#13070844C212yesmaximal, complemented
7#13070337C211yesmaximal, characteristic, complemented
8#13070329C211yesmaximal, characteristic
9#13070324C211yesmaximal, characteristic
10C2×#10622141C211yesmaximal, characteristic, complemented
11C11×#2108C211yesmaximal, characteristic, complemented
12C2×#66962—21no—
13C22×Dic44C2211yescharacteristic
14C2×#66957C2211yescharacteristic
15#10623057—21no—
16#10623050—21no—
17C2×C11×M32C2211yescharacteristic
18C22×C11×C16C2211yescharacteristic
19C11×#405C2211yescharacteristic
20#10622734—21no—
21#10622719C2211yescharacteristic
22C2×#66882C2211yescharacteristic
23#10622328—22no—
24#10622315—22no—
25#10622312C2212yes—
26#10622309C2212yes—
27#10622296C2212yes—
28#10622295C2212yes—
29C11×#346C2212yes—
30C4×C11×C16C2212yes—
31#10622147C2211yescharacteristic
32#10622147C2212yes—
33#10622147C2211yescharacteristic
34#10622141C2212yes—
35#10622141C2212yes—
36#10622141C2212yes—
37#10622141C2212yes—
38#10622141C2211yescharacteristic
39#10622141C2212yes—
40#10622141C2211yescharacteristic
41C2×#4339—21no—
42C22×Dic22—21no—
43C2×C11×M16D411yescharacteristic
44C22×C8×C11C2311yescharacteristic
45C11×#117D411yescharacteristic
46#66979—21no—
47C2×C4⋊Dic11—21no—
48#66962—44no—
49C2×Dic44—22no—
50C2×Dic44—22no—
51C2×Dic44—21no—
52C2×Dic44—22no—
53C2×Dic44C2311yescharacteristic
54C2×Dic44C2312yes—
55#66957—22no—
56#66957—22no—
57C2×D88C2311yescharacteristic
58C2×#4314—21no—
59C2×#4314—22no—
60#66950—41no—
61#66950—41no—
62#66943—41no—
63#66941—41no—
64#66939—42no—
65#66931—42no—
66#66928—22no—
67#66923—22no—
68#66922—22no—
69#66922—22no—
70C11×M32—22no—
71C2×C11×C16—22no—
72C2×C11×C16C2311yescharacteristic
73C2×C11×C16C2311yescharacteristic
74C2×C11×C16C2312yes—
75C11×#97D412yes—
76C4×C8×C11C2312yes—
77#66882—22no—
78#66882—21no—
79#66882C2311yescharacteristic
80#66882C2312yes—
81#66882C2311yescharacteristic
82#66881—22no—
83#66881—21no—
84#33703—111nomaximal, Sylow
85C22×C4×C11C2×D411yescharacteristic
86C2×C22⋊D11—41no—
87C22×Dic11—41no—
88C22×Dic11—41no—
89#4339—42no—
90#4339—42no—
91C2×D44—21no—
92C2×C4×D11—41no—
93C2×Dic22—21no—
94C2×Dic22—22no—
95C2×Dic22—42no—
96C2×Dic22—41no—
97C2×Dic22—42no—
98C2×Dic22—42no—
99C11×M16SD1614yes—
100C2×C8×C11C2×D411yescharacteristic
101C2×C8×C11C2×D412yes—
102C2×C8×C11#4112yes—
103C2×C8×C11#4112yes—
104C2×C8×C11C2411yescharacteristic
105C11×C4⋊C4D811yescharacteristic
106C11×C4⋊C4D811yescharacteristic
107C11×C22⋊C4D812yes—
108C42×C11C2×D412yes—
109C22⋊Dic11—41no—
110(C2×D11)⋊C4—42no—
111(C2×D11)⋊C4—42no—
112C4⋊Dic11—21no—
113C4⋊Dic11—21no—
114C4⋊Dic11—22no—
115C4⋊Dic11—42no—
116C4⋊Dic11—42no—
117C4⋊Dic11—42no—
118C4⋊Dic11—41no—
119Dic11⋊C4—42no—
120Dic11⋊C4—42no—
121C4×Dic11—41no—
122Dic44—21no—
123Dic44—21no—
124Dic44—22no—
125Dic44—22no—
126Dic44—42no—
127Dic44—44no—
128D88—21no—
129D88—21no—
130#4314—42no—
131#4314—44no—
132C11×C16—21no—
133C11×C16—21no—
134C11×C16—22no—
135#3164—111no—
136#3156—111no—
137#2245—112no—
138#2243—112no—
139#2242—112no—
140#2241—112no—
141#2141—111no—
142#2139—111no—
143#2138—111no—
144C2×#358—111no—
145#2108D1111yescharacteristic, complemented
146C23×C11C2×D811yescharacteristic
147C22×D11—41no—
148C2×C4×C11#12412yes—
149C2×C4×C11C2×D812yes—
150C2×C4×C11C2×D812yes—
151C2×C4×C11C2×D811yescharacteristic
152C2×C4×C11C2×SD1612yes—
153C2×C4×C11C22×D411yescharacteristic
154C22⋊D11—82no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—42no—
158C2×Dic11—41no—
159C2×Dic11—42no—
160C2×Dic11—82no—
161C2×Dic11—161no—
162D44—41no—
163D44—41no—
164C4×D11—82no—
165Dic22—41no—
166Dic22—42no—
167Dic22—42no—
168Dic22—41no—
169Dic22—82no—
170Dic22—162no—
171C8×C11#12412yes—
172C8×C11C2×SD1614yes—
173C8×C11C2×#4111yescharacteristic
174C8×C11C2×#4111yescharacteristic
175C2×#137—221no—
176C2×#135—111no—
177C22×Q16—111no—
178#544—221no—
179#536—221no—
180C2×M32C2×D1111yescharacteristic
181C22×C16C2×D1111yescharacteristic
182#501—222no—
183#500—112no—
184#499—112no—
185#497—222no—
186#495—112no—
187#494—112no—
188#428—221no—
189#427—111no—
190C2×#107—111no—
191#405C2×D1111yescharacteristic
192#358—112no—
193#358—112no—
194#358—111no—
195#358—111no—
196#358—112no—
197#358—112no—
198#358—112no—
199#357—111no—
200#357—111no—
201#357—112no—
202#346C2×D1112yes—
203C4×C16C2×D1112yes—
204C22×C11—21no—
205C22×C11—21no—
206C22×C11#48612yes—
207C22×C11C22×D811yescharacteristic
208C2×D11—81no—
209C2×D11—81no—
210C2×D11—81no—
211C4×C11—22no—
212C4×C11—22no—
213C4×C11#48612yes—
214C4×C11C2×#12411yescharacteristic
215C4×C11C22×SD1611yescharacteristic
216Dic11—82no—
217Dic11—81no—
218Dic11—81no—
219Dic11—82no—
220Dic11—81no—
221C2×#41—221no—
222C22×Q8—221no—
223#137—444no—
224#135—222no—
225#135—222no—
226C2×Q16—112no—
227C2×Q16—111no—
228C2×Q16—221no—
229C2×Q16—222no—
230C2×Q16—222no—
231C2×Q16—222no—
232C2×SD16—221no—
233C2×SD16—222no—
234C2×D8—111no—
235C2×M16D4411yescharacteristic
236C22×C8C22×D1111yescharacteristic
237C4⋊Q8—222no—
238C4⋊Q8—222no—
239C4⋊Q8—441no—
240#125—222no—
241#125—441no—
242#124—222no—
243#123—442no—
244C22⋊Q8—441no—
245C22⋊Q8—441no—
246C22⋊Q8—442no—
247#117—221no—
248#117D4411yescharacteristic
249C2×C4⋊C4—221no—
250M32—22no—
251C2×C16—22no—
252C2×C16C22×D1111yescharacteristic
253C2×C16C22×D1112yes—
254C2×C16C22×D1111yescharacteristic
255#107—112no—
256#107—111no—
257#107—111no—
258#107—221no—
259#107—222no—
260#106—221no—
261#106—222no—
262#97D4412yes—
263C4×C8C22×D1112yes—
264C2×C11—22no—
265C2×C11C2×#48611yescharacteristic
266C2×C11#341611yescharacteristic
267C2×C11#341711yescharacteristic
268D11—161no—
269#41—442no—
270#41—442no—
271C2×Q8—222no—
272C2×Q8—221no—
273C2×Q8—441no—
274C2×Q8—442no—
275C2×Q8—442no—
276C2×Q8—442no—
277C2×D4—221no—
278C2×D4—441no—
279C22×C4—441no—
280C22×C4—441no—
281C22×C4—441no—
282C22×C4C2×D4411yescharacteristic
283Q16—222no—
284Q16—222no—
285Q16—221no—
286Q16—221no—
287Q16—442no—
288Q16—444no—
289SD16—442no—
290SD16—444no—
291D8—221no—
292D8—221no—
293M16#431414yes—
294C2×C8C2×D4411yescharacteristic
295C2×C8C2×D4412yes—
296C2×C8#433912yes—
297C2×C8#433912yes—
298C2×C8C23×D1111yescharacteristic
299C4⋊C4—221no—
300C4⋊C4—222no—
301C4⋊C4—221no—
302C4⋊C4—441no—
303C4⋊C4—442no—
304C4⋊C4—442no—
305C4⋊C4—442no—
306C4⋊C4—442no—
307C4⋊C4—442no—
308C4⋊C4D8811yescharacteristic
309C4⋊C4D8811yescharacteristic
310C22⋊C4—441no—
311C22⋊C4—442no—
312C22⋊C4—442no—
313C22⋊C4D8812yes—
314C42—441no—
315C42C2×D4412yes—
316C16—21no—
317C16—21no—
318C16—22no—
319C11#3370311yescharacteristic, complemented, Sylow
320C23—441no—
321C23C2×D8811yescharacteristic
322Q8—441no—
323Q8—442no—
324Q8—442no—
325Q8—441no—
326Q8—882no—
327Q8—1762no—
328D4—441no—
329D4—441no—
330D4—882no—
331C2×C4—441no—
332C2×C4—441no—
333C2×C4—442no—
334C2×C4—442no—
335C2×C4—441no—
336C2×C4—882no—
337C2×C4—882no—
338C2×C4—1761no—
339C2×C4#6692812yes—
340C2×C4C2×#431412yes—
341C2×C4C2×D8812yes—
342C2×C4C2×D8812yes—
343C2×C4C2×D8811yescharacteristic
344C2×C4C22×D4411yescharacteristic
345C8#6692812yes—
346C8C2×#431414yes—
347C8C2×#433911yescharacteristic
348C8C2×#433911yescharacteristic
349C22—21no—
350C22—21no—
351C22—881no—
352C22—881no—
353C22—881no—
354C22#1062230712yes—
355C22C22×D8811yescharacteristic
356C4—22no—
357C4—22no—
358C4—881no—
359C4—882no—
360C4—882no—
361C4—881no—
362C4—881no—
363C4#1062230712yes—
364C4C2×#6692811yescharacteristic
365C4C22×#431411yescharacteristic
366C2—22no—
367C2—1761no—
368C2C2×#1062230711yescharacteristic
369C2#1308176411yescharacteristic
370C2#1308176911yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2108C2
socleC22×C11C22×D8
prime radicalC2×#66957C22
hypercenter#2108D11
hypocenterC11#33703
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #2108

Complements

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

NH ≅ G/Ntype
1. #13079155C2semidirect
3. #13070862C2semidirect
4. #13070853C2semidirect
5. #13070848C2semidirect
6. #13070844C2semidirect
7. #13070337C2semidirect
10. C2×#10622141C2semidirect
11. C11×#2108C2semidirect
145. #2108D11semidirect
319. C11#33703semidirect

Maximal subgroups

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

subgroupindex
#130791552
#130791102
#130708622
#130708532
#130708482
#130708442
#130703372
#130703292
#130703242
C2×#106221412
C11×#21082
#3370311