Finite Group Databasebeta

← #14911115

Subgroups — #14911115

Order 2816.

558 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#13080376C211yesmaximal, characteristic
2#13070841C211yesmaximal, characteristic, complemented
3#13070796C212yesmaximal, complemented
4#13070765C211yesmaximal, characteristic, complemented
5#13070731C212yesmaximal, complemented
6#13070656C211yesmaximal, characteristic, complemented
7#13070554C212yesmaximal, complemented
8C4×#66893C211yesmaximal, characteristic, complemented
9#13070448C211yesmaximal, characteristic, complemented
10#13070326C212yesmaximal, complemented
11C11×#3338C211yesmaximal, characteristic, complemented
12C11×#554—21no—
13C2×#66957C2212yes—
14#10623084—21no—
15C11×#500C2211yescharacteristic
16C11×#484—22no—
17C11×#477—21no—
18C11×#467C2212yes—
19C4×C11×Q16C2211yescharacteristic
20C8×D4×C11C2211yescharacteristic
21C2×C11×#107C2212yes—
22C2×#66893C2211yescharacteristic
23C2×#66892C2212yes—
24#10622728C2212yes—
25C2×#66876C2212yes—
26#10622461—21no—
27#10622347—22no—
28C4×Dic44C2211yescharacteristic
29#10622308C2211yescharacteristic
30#10622202C2211yescharacteristic
31C22⋊(C11⋊C16)C2212yes—
32#10622130C2211yescharacteristic
33#10622130C2212yes—
34#10622129C2212yes—
35#10622129C2212yes—
36#10622129C2212yes—
37#10622127C2211yescharacteristic
38#10622127C2212yes—
39C4⋊(C11⋊C16)C2211yescharacteristic
40C4×C11⋊C16C2211yescharacteristic
41C2×#4339—22no—
42C2×C11×Q16C2311yescharacteristic
43C22×C8×C11C2312yes—
44C11×C4⋊Q8—21no—
45C11×#125—41no—
46C11×C22⋊Q8—22no—
47C11×C22⋊Q8—42no—
48C4×Q8×C11—21no—
49C4×D4×C11—41no—
50C4×D4×C11D411yescharacteristic
51C2×C11×C4⋊C4—22no—
52#66993—41no—
53#66983—22no—
54C2×Dic44C2311yescharacteristic
55#66957—24no—
56#66957—42no—
57C2×D88—21no—
58C2×D88C2312yes—
59C2×#4314—22no—
60#66946—41no—
61#66937—42no—
62#66927—21no—
63C4×Dic22—21no—
64C11×#107—21no—
65C11×#107—22no—
66C11×#107C2312yes—
67C11×#107C2311yescharacteristic
68C11×C4⋊C8D411yescharacteristic
69C11×#103—21no—
70C11×#103—22no—
71C11×C22⋊C8D412yes—
72C4×C8×C11C2311yescharacteristic
73#66893—22no—
74#66892—42no—
75#66885—22no—
76#66882C2311yescharacteristic
77#66880—21no—
78#66876—42no—
79C2×C11⋊C16C2312yes—
80C2×C11⋊C16C2311yescharacteristic
81C2×C11⋊C16C2311yescharacteristic
82#33900—111nomaximal, Sylow
83C2×Q8×C11—21no—
84C2×Q8×C11—41no—
85C2×D4×C11D811yescharacteristic
86C22×C4×C11—42no—
87C22×C4×C11C2×D412yes—
88C2×C22⋊D11—42no—
89C2×C22⋊D11—42no—
90#4339—44no—
91#4339—82no—
92C2×D44—22no—
93C2×D44—41no—
94C2×D44—41no—
95C2×C4×D11—42no—
96C2×Dic22—21no—
97C11×Q16—21no—
98C11×Q16—21no—
99C2×C8×C11—22no—
100C2×C8×C11—22no—
101C2×C8×C11C2×D411yescharacteristic
102C2×C8×C11C2×D412yes—
103C2×C8×C11C2411yescharacteristic
104C11×C4⋊C4—21no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—42no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—42no—
110C11×C4⋊C4D811yescharacteristic
111C11×C22⋊C4—42no—
112C11×C22⋊C4D812yes—
113C42×C11—41no—
114C42×C11C2×D411yescharacteristic
115(C2×D11)⋊C4—42no—
116C4⋊Dic11—21no—
117Dic11⋊C4—41no—
118C4×Dic11—41no—
119Dic44—21no—
120Dic44#4112yes—
121D88—22no—
122D88—22no—
123D88—81no—
124#4314—44no—
125C11⋊C16—21no—
126C11⋊C16—21no—
127C11⋊C16—22no—
128#3338D1111yescharacteristic, complemented
129#3287—111no—
130#2240—111no—
131#2232—112no—
132#2227—111no—
133#2220—112no—
134#2207—111no—
135#2189—112no—
136C4×Q32—111no—
137#2169—111no—
138#2139—112no—
139C23×C11C2×D812yes—
140C22×D11—42no—
141Q8×C11—41no—
142Q8×C11—41no—
143Q8×C11—161no—
144D4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—22no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—42no—
150C2×C4×C11—162no—
151C2×C4×C11C2×D811yescharacteristic
152C2×C4×C11C2×D812yes—
153C2×C4×C11C2×D811yescharacteristic
154C2×C4×C11C22×D411yescharacteristic
155C22⋊D11—84no—
156C22⋊D11—162no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159D44—42no—
160D44—42no—
161D44—82no—
162D44—161no—
163C4×D11—84no—
164Dic22—22no—
165Dic22—41no—
166C8×C11—22no—
167C8×C11—21no—
168C8×C11C2×#4111yescharacteristic
169C8×C11H(5,𝔽2)11yescharacteristic
170C2×#135—112no—
171#554—21no—
172#550—221no—
173C2×Q32—111no—
174C2×SD32—112no—
175C2×M32—112no—
176#500C2×D1111yescharacteristic
177#493—111no—
178#484—22no—
179#477—21no—
180#467C2×D1112yes—
181#466—112no—
182#460—221no—
183#449—222no—
184C4×Q16—111no—
185C4×Q16C2×D1111yescharacteristic
186C8×D4C2×D1111yescharacteristic
187C2×#107C2×D1112yes—
188#366—111no—
189#366—112no—
190C4⋊C16—111no—
191#358—111no—
192#358—111no—
193#358—112no—
194#357—112no—
195#357—112no—
196#357—112no—
197C22⋊C16—112no—
198C4×C16—111no—
199C22×C11—22no—
200C22×C11—22no—
201C22×C11—22no—
202C22×C11C22×D811yescharacteristic
203C2×D11—82no—
204C2×D11—82no—
205C2×D11—82no—
206C4×C11—21no—
207C4×C11—22no—
208C4×C11—81no—
209C4×C11—82no—
210C4×C11—81no—
211C4×C11#51012yes—
212C4×C11#54611yescharacteristic
213C4×C11#57711yescharacteristic
214Dic11—42no—
215Dic11—81no—
216C2×#41—222no—
217#135—224no—
218#135—442no—
219C2×Q16—111no—
220C2×Q16C22×D1111yescharacteristic
221C2×SD16—222no—
222C2×D8—112no—
223C2×D8—221no—
224C22×C8C22×D1112yes—
225C4⋊Q8—21no—
226#127—221no—
227#127—441no—
228#125—41no—
229C22⋊Q8—22no—
230C22⋊Q8—42no—
231#121—222no—
232#121—442no—
233C4×Q8—21no—
234C4×Q8—221no—
235C4×D4—41no—
236C4×D4—441no—
237C4×D4C22⋊D1111yescharacteristic
238C2×C4⋊C4—22no—
239Q32—222no—
240SD32—442no—
241M32—442no—
242C2×C16—111no—
243C2×C16—111no—
244C2×C16—112no—
245#107—22no—
246#107—21no—
247#107—111no—
248#107C22×D1111yescharacteristic
249#107C22×D1112yes—
250C4⋊C8C22⋊D1111yescharacteristic
251#103—21no—
252#103—22no—
253#103—221no—
254#102—222no—
255C22⋊C8C22⋊D1112yes—
256C4×C8C22×D1111yescharacteristic
257C2×C11—42no—
258C2×C11#329411yescharacteristic
259C2×C11C2×#51011yescharacteristic
260C2×C11#341511yescharacteristic
261D11—162no—
262#41—444no—
263#41—882no—
264C2×Q8—21no—
265C2×Q8—41no—
266C2×Q8—221no—
267C2×D4—222no—
268C2×D4—442no—
269C2×D4—442no—
270C2×D4—441no—
271C2×D4—441no—
272C2×D4#432311yescharacteristic
273C22×C4—42no—
274C22×C4—442no—
275C22×C4C2×C22⋊D1112yes—
276Q16—21no—
277Q16—21no—
278Q16—112no—
279Q16—221no—
280SD16—444no—
281D8—222no—
282D8—222no—
283D8—881no—
284C2×C8—22no—
285C2×C8—22no—
286C2×C8C2×C22⋊D1111yescharacteristic
287C2×C8C2×C22⋊D1112yes—
288C2×C8C23×D1111yescharacteristic
289C4⋊C4—21no—
290C4⋊C4—22no—
291C4⋊C4—42no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—42no—
295C4⋊C4—221no—
296C4⋊C4—441no—
297C4⋊C4#432311yescharacteristic
298C22⋊C4—42no—
299C22⋊C4—442no—
300C22⋊C4#432312yes—
301C42—41no—
302C42—441no—
303C42C2×C22⋊D1111yescharacteristic
304C16—221no—
305C16—221no—
306C16—222no—
307C11#3390011yescharacteristic, complemented, Sylow
308C23—442no—
309C23C2×#432312yes—
310Q8—41no—
311Q8—41no—
312Q8—161no—
313Q8—222no—
314Q8—441no—
315D4—22no—
316D4—442no—
317D4—442no—
318D4—884no—
319D4—882no—
320D4—1761no—
321D4—1762no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—42no—
327C2×C4—162no—
328C2×C4—441no—
329C2×C4—441no—
330C2×C4—884no—
331C2×C4C2×#432311yescharacteristic
332C2×C4C2×#432312yes—
333C2×C4C2×#432311yescharacteristic
334C2×C4C22×C22⋊D1111yescharacteristic
335C8—22no—
336C8—21no—
337C8#41×D1111yescharacteristic
338C8#6704211yescharacteristic
339C22—22no—
340C22—22no—
341C22—22no—
342C22—882no—
343C22—882no—
344C22—882no—
345C22C22×#432311yescharacteristic
346C4—22no—
347C4—21no—
348C4—81no—
349C4—81no—
350C4—82no—
351C4—442no—
352C4—881no—
353C4#1062279212yes—
354C4#1062336011yescharacteristic
355C4#1062336811yescharacteristic
356C2—42no—
357C2—1762no—
358C2#1308042311yescharacteristic
359C2C2×#1062279211yescharacteristic
360C2#1308175511yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3338C2
socleC22×C11C22×D8
prime radical#13080376C2
hypercenter#3338D11
hypocenterC11#33900
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3338

Complements

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

NH ≅ G/Ntype
2. #13070841C2semidirect
3. #13070796C2semidirect
4. #13070765C2semidirect
5. #13070731C2semidirect
6. #13070656C2semidirect
7. #13070554C2semidirect
8. C4×#66893C2semidirect
9. #13070448C2semidirect
10. #13070326C2semidirect
11. C11×#3338C2semidirect
128. #3338D11semidirect
307. C11#33900semidirect

Maximal subgroups

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

subgroupindex
#130803762
#130708412
#130707962
#130707652
#130707312
#130706562
#130705542
C4×#668932
#130704482
#130703262
C11×#33382
#3390011