Finite Group Databasebeta

← #14911492

Subgroups — #14911492

Order 2816.

532 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081591C211yesmaximal, characteristic, complemented
2#13081484C211yesmaximal, characteristic, complemented
3#13070858C212yesmaximal, complemented
4#13070840C211yesmaximal, characteristic, complemented
5#13070774C212yesmaximal, complemented
6#13070764C211yesmaximal, characteristic, complemented
7#13070652C211yesmaximal, characteristic, complemented
8#13070652C212yesmaximal, complemented
9#13070493C212yesmaximal, complemented
10C4×D176C211yesmaximal, characteristic, complemented
11C11×#2183C211yesmaximal, characteristic, complemented
12#10623110—21no—
13#10623108—21no—
14C8×Q8×C11C2211yescharacteristic
15C2×D176C2211yescharacteristic
16C2×D176C2212yes—
17#10622460—22no—
18#10622456—21no—
19#10622456—22no—
20#10622455—21no—
21#10622308C2212yes—
22#10622308C2211yescharacteristic
23C4×D88C2211yescharacteristic
24C4×D88C2212yes—
25C4×D88C2211yescharacteristic
26C4×D88C2212yes—
27#10622296C2212yes—
28#10622295C2211yescharacteristic
29C11×C4⋊C16C2211yescharacteristic
30C11×C4⋊C16C2212yes—
31C11×#346C2212yes—
32C4×C11×C16C2211yescharacteristic
33#10622147C2211yescharacteristic
34#10622147C2212yes—
35#10622147C2212yes—
36#10622147C2212yes—
37#10622147C2212yes—
38#10622147C2211yescharacteristic
39#10622143C2212yes—
40#10622142C2211yescharacteristic
41C2×#4343—41no—
42C4×Q8×C11D411yescharacteristic
43#66999—41no—
44C2×D88—22no—
45C2×D88—21no—
46C2×D88C2311yescharacteristic
47C2×D88C2312yes—
48C2×D88C2311yescharacteristic
49#66949—42no—
50#66948—41no—
51#66948—42no—
52C4⋊C4×D11—41no—
53#66927—21no—
54#66927—22no—
55C4×D44—21no—
56C4×D44—22no—
57C4×D44—21no—
58C4×D44—22no—
59#66923—22no—
60#66922—21no—
61C2×C11×C16C2311yescharacteristic
62C2×C11×C16C2311yescharacteristic
63C2×C11×C16C2312yes—
64C11×C4⋊C8D411yescharacteristic
65C11×C4⋊C8D412yes—
66C4×C8×C11C2311yescharacteristic
67C4×C8×C11C2312yes—
68#66885—22no—
69#66885—22no—
70#66885—21no—
71#66885—21no—
72#66882—21no—
73#66882C2312yes—
74#66882C2311yescharacteristic
75#66882C2311yescharacteristic
76#66881—22no—
77D176—22no—
78D176—24no—
79#33933—111nomaximal, Sylow
80C2×Q8×C11D811yescharacteristic
81#4343—84no—
82C2×D44—21no—
83C2×D44—22no—
84C2×D44—21no—
85C2×D44—42no—
86C2×D44—41no—
87C2×D44—42no—
88C2×D44—41no—
89C2×C4×D11—41no—
90C2×C4×D11—42no—
91C2×C4×D11—41no—
92C2×C4×D11—42no—
93C2×Dic22—41no—
94C2×C8×C11C2×D412yes—
95C2×C8×C11C2×D411yescharacteristic
96C2×C8×C11C2411yescharacteristic
97C11×C4⋊C4D811yescharacteristic
98C11×C4⋊C4D812yes—
99C42×C11C2×D411yescharacteristic
100C42×C11C2×D412yes—
101(C2×D11)⋊C4—42no—
102(C2×D11)⋊C4—41no—
103(C2×D11)⋊C4—41no—
104(C2×D11)⋊C4—42no—
105C4⋊Dic11—21no—
106C4⋊Dic11—22no—
107C4⋊Dic11—21no—
108C4⋊Dic11—41no—
109Dic11⋊C4—42no—
110Dic11⋊C4—42no—
111D88—21no—
112D88—22no—
113D88—21no—
114D88—21no—
115D88—22no—
116D88—82no—
117D88—81no—
118D88#4112yescomplemented
119C11×C16—21no—
120C11×C16—22no—
121C11×C16—21no—
122#3391—111no—
123#3380—111no—
124#2244—112no—
125#2240—111no—
126#2228—112no—
127#2226—111no—
128#2206—112no—
129#2206—111no—
130#2183D1111yescharacteristic, complemented
131#2177—112no—
132C4×D16—111no—
133C22×D11—41no—
134C22×D11—42no—
135C22×D11—41no—
136Q8×C11—22no—
137C2×C4×C11C2×D812yes—
138C2×C4×C11C2×D812yes—
139C2×C4×C11C2×D811yescharacteristic
140C2×C4×C11C2×D811yescharacteristic
141C2×C4×C11C22×D411yescharacteristic
142C2×Dic11—41no—
143C2×Dic11—42no—
144C2×Dic11—41no—
145D44—22no—
146D44—41no—
147D44—42no—
148D44—41no—
149D44—41no—
150D44—42no—
151D44—84no—
152D44—82no—
153D44—161no—
154D44—162no—
155C4×D11—84no—
156C4×D11—82no—
157C4×D11—82no—
158C4×D11—162no—
159Dic22—161no—
160C8×C11—22no—
161C8×C11—21no—
162C8×C11C2×#4111yescharacteristic
163C8×C112−1+411yescharacteristic
164#554—221no—
165#550—221no—
166C2×D16—111no—
167C2×D16—112no—
168#500—111no—
169#499—112no—
170#493—111no—
171#493—112no—
172#478—222no—
173#476—221no—
174#459—221no—
175#459—222no—
176C8×Q8C2×D1111yescharacteristic
177C4×D8—111no—
178C4×D8—112no—
179C4×D8—111no—
180C4×D8—112no—
181#367—112no—
182#366—111no—
183C4⋊C16C2×D1111yescharacteristic
184C4⋊C16C2×D1112yes—
185#357—111no—
186#357—111no—
187#357—112no—
188#357—112no—
189#357—112no—
190#357—112no—
191#346C2×D1112yes—
192C4×C16C2×D1111yescharacteristic
193C22×C11C22×D811yescharacteristic
194C2×D11—42no—
195C2×D11—81no—
196C2×D11—81no—
197C2×D11—82no—
198C2×D11—81no—
199C2×D11—82no—
200C2×D11—81no—
201C2×D11—82no—
202C2×D11—81no—
203C4×C11—22no—
204C4×C11—21no—
205C4×C11—22no—
206C4×C11#50912yes—
207C4×C11#54811yescharacteristic
208C4×C11#57711yescharacteristic
209Dic11—81no—
210Dic11—81no—
211Dic11—82no—
212C2×#41—441no—
213C2×D8—111no—
214C2×D8—111no—
215C2×D8—112no—
216C2×D8—222no—
217C2×D8—221no—
218C4⋊Q8—221no—
219#127—222no—
220#127—221no—
221#125—222no—
222C22⋊Q8—441no—
223C22⋊Q8—442no—
224#121—441no—
225#121—442no—
226C4×Q8D4411yescharacteristic
227C4×D4—222no—
228C4×D4—221no—
229C4×D4—221no—
230C4×D4—222no—
231C2×C4⋊C4—441no—
232D16—222no—
233D16—224no—
234C2×C16C22×D1111yescharacteristic
235C2×C16C22×D1111yescharacteristic
236C2×C16C22×D1112yes—
237#107—111no—
238#107—112no—
239#107—111no—
240#107—221no—
241#106—222no—
242C4⋊C8D4411yescharacteristic
243C4⋊C8D4412yes—
244#102—222no—
245#102—221no—
246#102—222no—
247#102—221no—
248C4×C8C22×D1111yescharacteristic
249C4×C8C22×D1112yes—
250C2×C11#335811yescharacteristic
251C2×C11C2×#50911yescharacteristic
252C2×C11#341511yescharacteristic
253D11—82no—
254D11—162no—
255D11—161no—
256#41—884no—
257C2×Q8—441no—
258C2×Q8D8811yescharacteristic
259C2×D4—221no—
260C2×D4—222no—
261C2×D4—221no—
262C2×D4—442no—
263C2×D4—441no—
264C2×D4—441no—
265C2×D4—442no—
266C22×C4—441no—
267C22×C4—442no—
268C22×C4—441no—
269C22×C4—442no—
270D8—112no—
271D8—221no—
272D8—221no—
273D8—222no—
274D8—221no—
275D8—222no—
276D8—882no—
277D8—881no—
278C2×C8C2×D4412yes—
279C2×C8C2×D4411yescharacteristic
280C2×C8C23×D1111yescharacteristic
281C4⋊C4—221no—
282C4⋊C4—221no—
283C4⋊C4—222no—
284C4⋊C4—442no—
285C4⋊C4—441no—
286C4⋊C4—442no—
287C4⋊C4D8811yescharacteristic
288C4⋊C4D8812yes—
289C22⋊C4—441no—
290C22⋊C4—442no—
291C22⋊C4—441no—
292C22⋊C4—442no—
293C42C2×D4412yes—
294C42C2×D4411yescharacteristic
295C16—21no—
296C16—21no—
297C16—22no—
298C11#3393311yescharacteristic, complemented, Sylow
299C23—441no—
300C23—442no—
301C23—441no—
302Q8—22no—
303Q8—1761no—
304D4—222no—
305D4—441no—
306D4—441no—
307D4—442no—
308D4—441no—
309D4—442no—
310D4—884no—
311D4—882no—
312D4—1762no—
313D4—1761no—
314C2×C4—441no—
315C2×C4—441no—
316C2×C4—442no—
317C2×C4—884no—
318C2×C4—882no—
319C2×C4—882no—
320C2×C4—1762no—
321C2×C4C2×D8811yescharacteristic
322C2×C4C2×D8812yes—
323C2×C4C2×D8812yes—
324C2×C4C2×D8811yescharacteristic
325C2×C4C22×D4411yescharacteristic
326C8—22no—
327C8—21no—
328C8#6704011yescharacteristic
329C8#41×D1111yescharacteristic
330C22—442no—
331C22—881no—
332C22—881no—
333C22—882no—
334C22—881no—
335C22—881no—
336C22—882no—
337C22—882no—
338C22—881no—
339C22C22×D8811yescharacteristic
340C4—22no—
341C4—22no—
342C4—21no—
343C4—881no—
344C4—881no—
345C4—882no—
346C4#1062252112yes—
347C4#1062310711yescharacteristic
348C4#1062328211yescharacteristic
349C2—882no—
350C2—1762no—
351C2—1761no—
352C2#1308125211yescharacteristic
353C2C2×#1062252111yescharacteristic
354C2#1308175711yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2183C2
socleC22×C11C22×D8
hypercenter#2183D11
hypocenterC11#33933
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×Q8 ◁ C8×Q8 ◁ #2183

Complements

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

NH ≅ G/Ntype
1. #13081591C2semidirect
2. #13081484C2semidirect
3. #13070858C2semidirect
4. #13070840C2semidirect
5. #13070774C2semidirect
6. #13070764C2semidirect
7. #13070652C2semidirect
8. #13070652C2semidirect
9. #13070493C2semidirect
10. C4×D176C2semidirect
11. C11×#2183C2semidirect
118. D88#41semidirect
130. #2183D11semidirect
298. C11#33933semidirect

Maximal subgroups

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

subgroupindex
#130815912
#130814842
#130708582
#130708402
#130707742
#130707642
#130706522
#130704932
C4×D1762
C11×#21832
#3393311