Finite Group Databasebeta

← #14910722

Subgroups — #14910722

Order 2816.

556 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081047C211yesmaximal, characteristic, complemented
2#13070839C211yesmaximal, characteristic, complemented
3#13070804C212yesmaximal, complemented
4#13070758C211yesmaximal, characteristic, complemented
5#13070710C212yesmaximal, complemented
6#13070653C211yesmaximal, characteristic, complemented
7#13070556C212yesmaximal, complemented
8C4×#66893C211yesmaximal, characteristic, complemented
9D4×C11⋊C16C211yesmaximal, characteristic, complemented
10#13070323C212yesmaximal, complemented
11C11×#3287C211yesmaximal, characteristic
12C2×C11×#135C2212yes—
13C11×#550—21no—
14#10623073—21no—
15C11×#493C2211yescharacteristic
16C11×#466C2212yes—
17C11×#460—21no—
18C11×#449—22no—
19C4×C11×Q16C2211yescharacteristic
20C8×D4×C11C2211yescharacteristic
21C2×#66893C2211yescharacteristic
22C2×#66891C2212yes—
23#10622729C2212yes—
24#10622719C2212yes—
25C22×C11⋊C16C2212yes—
26#10622464—21no—
27#10622336—22no—
28C4×Dic44C2211yescharacteristic
29#10622295C2211yescharacteristic
30#10622202C2211yescharacteristic
31#10622202C2212yes—
32#10622200C2212yes—
33#10622200C2212yes—
34#10622200C2212yes—
35C22⋊(C11⋊C16)C2212yes—
36#10622130C2211yescharacteristic
37#10622128C2212yes—
38#10622127C2211yescharacteristic
39C4⋊(C11⋊C16)C2211yescharacteristic
40C4×C11⋊C16C2211yescharacteristic
41C2×C11×#41—22no—
42C11×#135—24no—
43C11×#135—42no—
44C2×C11×Q16C2311yescharacteristic
45C2×C11×SD16—22no—
46C2×C11×D8—21no—
47C2×C11×D8C2312yes—
48C22×C8×C11C2312yes—
49C11×#127—21no—
50C11×#127—41no—
51C11×#121—22no—
52C11×#121—42no—
53C4×Q8×C11—21no—
54C4×D4×C11—41no—
55C4×D4×C11D411yescharacteristic
56#66989—41no—
57#66979—22no—
58#66977—22no—
59C2×Dic44C2311yescharacteristic
60#66940—41no—
61#66932—42no—
62#66922—21no—
63C4×Dic22—21no—
64C11×#107C2311yescharacteristic
65C11×C4⋊C8D411yescharacteristic
66C11×#103—21no—
67C11×#102—22no—
68C11×C22⋊C8D412yes—
69C4×C8×C11C2311yescharacteristic
70#66893—22no—
71#66891—42no—
72#66882—21no—
73#66882C2312yes—
74#66882C2311yescharacteristic
75#66881—22no—
76#66880—22no—
77#66880—21no—
78C2×C11⋊C16—42no—
79C2×C11⋊C16C2312yes—
80C2×C11⋊C16C2311yescharacteristic
81C2×C11⋊C16C2311yescharacteristic
82#33871—111nomaximal, Sylow
83C11×#41—44no—
84C11×#41—82no—
85C2×Q8×C11—21no—
86C2×D4×C11—22no—
87C2×D4×C11—42no—
88C2×D4×C11—42no—
89C2×D4×C11—41no—
90C2×D4×C11—41no—
91C2×D4×C11D811yescharacteristic
92C22×C4×C11—42no—
93C22×C4×C11C2×D412yes—
94C2×Dic22—21no—
95C2×Dic22—41no—
96C11×Q16—21no—
97C11×Q16#4112yes—
98C11×SD16—44no—
99C11×D8—22no—
100C11×D8—22no—
101C11×D8—81no—
102C2×C8×C11—22no—
103C2×C8×C11—22no—
104C2×C8×C11C2×D412yes—
105C2×C8×C11C2×D411yescharacteristic
106C2×C8×C11C2411yescharacteristic
107C11×C4⋊C4—21no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4D811yescharacteristic
110C11×C22⋊C4—42no—
111C11×C22⋊C4D812yes—
112C42×C11—41no—
113C42×C11C2×D411yescharacteristic
114C22⋊Dic11—42no—
115C22⋊Dic11—42no—
116C4⋊Dic11—21no—
117C4⋊Dic11—22no—
118C4⋊Dic11—41no—
119Dic11⋊C4—41no—
120Dic11⋊C4—42no—
121C4×Dic11—41no—
122C4×Dic11—42no—
123Dic44—21no—
124Dic44—21no—
125C11⋊C16—21no—
126C11⋊C16—21no—
127C11⋊C16—22no—
128#3342—111no—
129#3287D1111yescharacteristic
130#2240—111no—
131#2234—112no—
132#2225—111no—
133#2217—112no—
134#2207—111no—
135#2189—112no—
136C4×Q32—111no—
137D4×C16—111no—
138#2138—112no—
139C23×C11—42no—
140C23×C11C2×D812yes—
141Q8×C11—22no—
142Q8×C11—41no—
143D4×C11—22no—
144D4×C11—42no—
145D4×C11—42no—
146D4×C11—84no—
147D4×C11—82no—
148D4×C11—161no—
149D4×C11—162no—
150C2×C4×C11—22no—
151C2×C4×C11—22no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—84no—
155C2×C4×C11C2×D812yes—
156C2×C4×C11C2×D811yescharacteristic
157C2×C4×C11C2×D811yescharacteristic
158C2×C4×C11C22×D411yescharacteristic
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—42no—
162Dic22—41no—
163Dic22—41no—
164Dic22—82no—
165C8×C11—22no—
166C8×C11—21no—
167C8×C11C2×#4111yescharacteristic
168C8×C11H(5,𝔽2)11yescharacteristic
169C2×#135C2×D1112yes—
170#556—221no—
171#550—21no—
172C2×Q32—111no—
173C2×SD32—112no—
174C22×C16—112no—
175#500—111no—
176#493C2×D1111yescharacteristic
177#485—222no—
178#475—221no—
179#467—112no—
180#466C2×D1112yes—
181#460—21no—
182#449—22no—
183C4×Q16—111no—
184C4×Q16C2×D1111yescharacteristic
185C8×D4C2×D1111yescharacteristic
186#427—112no—
187#367—112no—
188#366—111no—
189C4⋊C16—111no—
190#358—111no—
191#358—112no—
192#358—111no—
193#357—112no—
194#357—112no—
195#357—112no—
196C22⋊C16—112no—
197C4×C16—111no—
198C22×C11—22no—
199C22×C11—22no—
200C22×C11—22no—
201C22×C11—82no—
202C22×C11—82no—
203C22×C11—82no—
204C22×C11C22×D811yescharacteristic
205C4×C11—21no—
206C4×C11—22no—
207C4×C11—42no—
208C4×C11—81no—
209C4×C11#50812yes—
210C4×C11#54611yescharacteristic
211C4×C11#57711yescharacteristic
212Dic11—82no—
213Dic11—81no—
214Dic11—81no—
215C2×#41—22no—
216#135—24no—
217#135—42no—
218C2×Q16—111no—
219C2×Q16C22×D1111yescharacteristic
220C2×SD16—22no—
221C2×D8—21no—
222C2×D8C22×D1112yes—
223C22×C8C22×D1112yes—
224C4⋊Q8—221no—
225#127—21no—
226#127—41no—
227#126—442no—
228#124—441no—
229C22⋊Q8—222no—
230#121—22no—
231#121—42no—
232C4×Q8—21no—
233C4×Q8—221no—
234C4×Q8—441no—
235C4×D4—41no—
236C4×D4C22⋊D1111yescharacteristic
237#117—222no—
238Q32—222no—
239SD32—442no—
240C2×C16—111no—
241C2×C16—111no—
242C2×C16—112no—
243C2×C16—442no—
244#107—111no—
245#107—112no—
246#107—221no—
247#107C22×D1111yescharacteristic
248#106—222no—
249C4⋊C8C22⋊D1111yescharacteristic
250#103—21no—
251#103—221no—
252#103—222no—
253#102—22no—
254C22⋊C8C22⋊D1112yes—
255C4×C8C22×D1111yescharacteristic
256C2×C11—42no—
257C2×C11—162no—
258C2×C11#329411yescharacteristic
259C2×C11C2×#50811yescharacteristic
260C2×C11#341611yescharacteristic
261#41—44no—
262#41—82no—
263C2×Q8—21no—
264C2×Q8—221no—
265C2×Q8—441no—
266C2×D4—22no—
267C2×D4—42no—
268C2×D4—42no—
269C2×D4—41no—
270C2×D4—41no—
271C2×D4#432311yescharacteristic
272C22×C4—42no—
273C22×C4C2×C22⋊D1112yes—
274Q16—21no—
275Q16—221no—
276Q16—221no—
277Q16#434112yes—
278SD16—44no—
279D8—22no—
280D8—22no—
281D8—81no—
282C2×C8—22no—
283C2×C8—22no—
284C2×C8C2×C22⋊D1111yescharacteristic
285C2×C8C2×C22⋊D1112yes—
286C2×C8C23×D1111yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—41no—
289C4⋊C4—221no—
290C4⋊C4—222no—
291C4⋊C4—441no—
292C4⋊C4—442no—
293C4⋊C4—441no—
294C4⋊C4#432311yescharacteristic
295C22⋊C4—42no—
296C22⋊C4—442no—
297C22⋊C4—442no—
298C22⋊C4#432312yes—
299C42—41no—
300C42—442no—
301C42—441no—
302C42C2×C22⋊D1111yescharacteristic
303C16—221no—
304C16—221no—
305C16—222no—
306C11#3387111yescharacteristic, complemented, Sylow
307C23—42no—
308C23C2×#432312yes—
309Q8—22no—
310Q8—41no—
311Q8—441no—
312Q8—441no—
313Q8—882no—
314D4—22no—
315D4—42no—
316D4—42no—
317D4—84no—
318D4—82no—
319D4—161no—
320D4—162no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—84no—
326C2×C4—441no—
327C2×C4—442no—
328C2×C4—441no—
329C2×C4C2×#432312yes—
330C2×C4C2×#432311yescharacteristic
331C2×C4C2×#432311yescharacteristic
332C2×C4C22×C22⋊D1111yescharacteristic
333C8—22no—
334C8—21no—
335C8C2×#434111yescharacteristic
336C8#6703711yescharacteristic
337C22—22no—
338C22—22no—
339C22—22no—
340C22—82no—
341C22—82no—
342C22—82no—
343C22C22×#432311yescharacteristic
344C4—22no—
345C4—21no—
346C4—42no—
347C4—81no—
348C4—881no—
349C4—882no—
350C4—881no—
351C4#1062280712yes—
352C4#1062333711yescharacteristic
353C4#1062336711yescharacteristic
354C2—42no—
355C2—162no—
356C2#1308042911yescharacteristic
357C2C2×#1062280711yescharacteristic
358C2#1308176311yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
Fitting, prime radicalC11×#3287C2
socleC22×C11C22×D8
hypercenter#3287D11
hypocenterC11#33871
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3287

Complements

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

NH ≅ G/Ntype
1. #13081047C2semidirect
2. #13070839C2semidirect
3. #13070804C2semidirect
4. #13070758C2semidirect
5. #13070710C2semidirect
6. #13070653C2semidirect
7. #13070556C2semidirect
8. C4×#66893C2semidirect
9. D4×C11⋊C16C2semidirect
10. #13070323C2semidirect
306. C11#33871semidirect

Maximal subgroups

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

subgroupindex
#130810472
#130708392
#130708042
#130707582
#130707102
#130706532
#130705562
C4×#668932
D4×C11⋊C162
#130703232
C11×#32872
#3387111