Finite Group Databasebeta

← #14738575

Subgroups — #14738575

Order 2816.

608 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#13079643C212yesmaximal
2#13077591C211yesmaximal, characteristic
3#13068131C212yesmaximal, complemented
4#13068126C212yesmaximal, complemented
5#13068007C212yesmaximal, complemented
6#13068002C212yesmaximal, complemented
7#13067379C211yesmaximal, characteristic, complemented
8#13067333C212yesmaximal, complemented
9C2×C11×#500C211yesmaximal, characteristic, complemented
10C2×C11×C4⋊Q8C2212yes—
11#10623010C2211yescharacteristic
12C11×#500—21no—
13C11×#500—21no—
14C11×#500C2212yes—
15C11×#500C2212yes—
16C2×C11×#107—21no—
17C2×C11×#107—21no—
18C2×C4×C8×C11C2211yescharacteristic
19#10622841—22no—
20#10622840—22no—
21#10622724—21no—
22C8×C22⋊D11—21no—
23#10622703C2214yes—
24#10622699—22no—
25#10622696C2214yes—
26#10622695—22no—
27#10622539C2211yescharacteristic
28#10622539C2212yes—
29#10622303—21no—
30#10622302—21no—
31#10622301C2211yescharacteristic
32C8×D44C2211yescharacteristic
33#10622292C2211yescharacteristic
34C8×Dic22C2211yescharacteristic
35#10622185C2214yes—
36#10622185C2214yes—
37#10622096C2212yes—
38#10622095C2212yes—
39C22×Q8×C11—22no—
40C22×C8×C11D411yescharacteristic
41C22×C8×C11D411yescharacteristic
42C11×C4⋊Q8—22no—
43C11×C4⋊Q8—22no—
44C11×C4⋊Q8—22no—
45C11×C4⋊Q8C2314yes—
46C2×C11×C4⋊C4—22no—
47C2×C11×C4⋊C4—22no—
48C2×C42×C11C2311yescharacteristic
49C2×#4326—24no—
50C2×#4325—24no—
51#66983D411yescharacteristic
52#66982—21no—
53C4×C22⋊D11—21no—
54#66977D411yescharacteristic
55C2×#4313—21no—
56C2×C8×D11—21no—
57#66929—21no—
58#66928D411yescharacteristic
59C4×D44C2311yescharacteristic
60#66925—21no—
61#66923D411yescharacteristic
62C4×Dic22C2311yescharacteristic
63C11×#107—22no—
64C11×#107—22no—
65C11×#107—22no—
66C11×#107—22no—
67C4×C8×C11D411yescharacteristic
68C4×C8×C11D411yescharacteristic
69C4×C8×C11C2311yescharacteristic
70C4×C8×C11C2311yescharacteristic
71#66899—24no—
72#66899—24no—
73C22⋊(C11⋊C8)—21no—
74C22⋊(C11⋊C8)—22no—
75(C2×D11)⋊C8—21no—
76(C2×D11)⋊C8—21no—
77#66879—21no—
78Dic11⋊C8—21no—
79Dic11⋊C8—21no—
80C8×Dic11—21no—
81C4⋊(C11⋊C8)C2311yescharacteristic
82C4⋊(C11⋊C8)C2311yescharacteristic
83C4⋊(C11⋊C8)C2314yes—
84#66867—21no—
85#66867—22no—
86#19358—111nomaximal, Sylow
87C2×Q8×C11—24no—
88C2×Q8×C11—42no—
89C2×Q8×C11—84no—
90C22×C4×C11—42no—
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11#4111yescharacteristic
94C2×C22⋊D11—21no—
95C2×D44C2×D411yescharacteristic
96C2×C4×D11—21no—
97C2×Dic22C2×D411yescharacteristic
98C2×C8×C11—22no—
99C2×C8×C11—22no—
100C2×C8×C11C2×D411yescharacteristic
101C2×C8×C11C2×D411yescharacteristic
102C2×C8×C11C2×D411yescharacteristic
103C2×C8×C11C2×D411yescharacteristic
104C11×C4⋊C4—24no—
105C11×C4⋊C4—24no—
106C11×C4⋊C4—42no—
107C11×C4⋊C4—42no—
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110C42×C11#4111yescharacteristic
111C42×C11C2411yescharacteristic
112C22⋊Dic11—21no—
113#4326—84no—
114#4325—84no—
115(C2×D11)⋊C4—21no—
116(C2×D11)⋊C4—21no—
117(C2×D11)⋊C4—21no—
118(C2×D11)⋊C4—21no—
119C4⋊Dic11C2×D411yescharacteristic
120C4⋊Dic11C2×D411yescharacteristic
121Dic11⋊C4—21no—
122Dic11⋊C4—21no—
123Dic11⋊C4—21no—
124Dic11⋊C4—21no—
125C4×Dic11—21no—
126C2×C11⋊C8—21no—
127C2×C11⋊C8—21no—
128C2×C11⋊C8—24no—
129#4313—42no—
130C8×D11—42no—
131#3218—112no—
132C2×#500D1111yescharacteristic, complemented
133#2966—111no—
134#1694—112no—
135#1693—112no—
136#1674—112no—
137#1673—112no—
138#1568—111no—
139#1556—112no—
140C23×C11#12111yescharacteristic
141C22×D11—21no—
142Q8×C11—44no—
143Q8×C11—44no—
144Q8×C11—84no—
145C2×C4×C11—22no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—22no—
149C2×C4×C11—44no—
150C2×C4×C11—84no—
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11#12111yescharacteristic
154C2×C4×C11C22×D411yescharacteristic
155C2×C4×C11C22×D411yescharacteristic
156C2×C4×C11C2×#4111yescharacteristic
157C22⋊D11—42no—
158C2×Dic11—21no—
159C2×Dic11—21no—
160C2×Dic11—21no—
161D44—22no—
162C4×D11—41no—
163C4×D11—41no—
164Dic22—22no—
165C8×C11—21no—
166C8×C11—21no—
167C8×C11#13712yes—
168C8×C11#13712yes—
169C11⋊C8—41no—
170C11⋊C8—41no—
171C11⋊C8—44no—
172C2×C4⋊Q8C2×D1112yes—
173#529—111no—
174#500—21no—
175#500—21no—
176#500C2×D1112yes—
177#500C2×D1112yes—
178#497—222no—
179#491—222no—
180#462—114no—
181#461—114no—
182#451—222no—
183#448—222no—
184#446—111no—
185C8×Q8—111no—
186#436—111no—
187#435—221no—
188C8×D4—111no—
189C8×D4—221no—
190#433—221no—
191#432—111no—
192#432—112no—
193C2×#107—21no—
194C2×#107—21no—
195#405—221no—
196C2×C4×C8C2×D1111yescharacteristic
197#335—112no—
198#334—112no—
199#332—114no—
200#332—114no—
201C22×C11—21no—
202C22×C11—21no—
203C22×C11#47312yes—
204C22×C11C2×#12111yescharacteristic
205C2×D11—41no—
206C2×D11—41no—
207C2×D11—41no—
208C4×C11—21no—
209C4×C11—21no—
210C4×C11—21no—
211C4×C11—21no—
212C4×C11—84no—
213C4×C11C2×#13711yescharacteristic
214C4×C11C2×#13711yescharacteristic
215C4×C11#57612yes—
216Dic11—41no—
217Dic11—41no—
218Dic11—41no—
219C22×Q8—22no—
220C2×Q16—224no—
221C2×SD16—224no—
222C2×M16—221no—
223C22×C8—221no—
224C22×C8C22⋊D1111yescharacteristic
225C22×C8C22⋊D1111yescharacteristic
226C4⋊Q8—22no—
227C4⋊Q8—22no—
228C4⋊Q8—22no—
229C4⋊Q8C22×D1114yes—
230#126—221no—
231#125—111no—
232#124—111no—
233#123—221no—
234C22⋊Q8—111no—
235#121—111no—
236C4×Q8—111no—
237C4×D4—111no—
238C4×D4—221no—
239#117—221no—
240C2×C4⋊C4—22no—
241C2×C4⋊C4—22no—
242C2×C42C22×D1111yescharacteristic
243#107—22no—
244#107—22no—
245#107—22no—
246#107—22no—
247C4⋊C8—111no—
248C4⋊C8—111no—
249C4⋊C8—114no—
250C4⋊C8—221no—
251C4⋊C8—221no—
252#103—224no—
253#103—224no—
254C22⋊C8—222no—
255C22⋊C8—221no—
256C22⋊C8—221no—
257C22⋊C8—221no—
258#97—221no—
259#97—222no—
260#97—221no—
261C4×C8—221no—
262C4×C8C22⋊D1111yescharacteristic
263C4×C8C22⋊D1111yescharacteristic
264C4×C8C22×D1111yescharacteristic
265C4×C8C22×D1111yescharacteristic
266C2×C11—22no—
267C2×C11#303911yescharacteristic
268C2×C11#305811yescharacteristic
269C2×C11C2×#47311yescharacteristic
270D11—81no—
271C2×Q8—24no—
272C2×Q8—42no—
273C2×Q8—84no—
274C2×Q8—111no—
275C2×D4—111no—
276C2×D4—221no—
277C22×C4—42no—
278C22×C4—221no—
279C22×C4D4×D1111yescharacteristic
280C22×C4#434111yescharacteristic
281C22×C4C2×C22⋊D1111yescharacteristic
282Q16—884no—
283SD16—884no—
284M16—442no—
285C2×C8—22no—
286C2×C8—22no—
287C2×C8—224no—
288C2×C8—221no—
289C2×C8—221no—
290C2×C8—442no—
291C2×C8C2×C22⋊D1111yescharacteristic
292C2×C8C2×C22⋊D1111yescharacteristic
293C2×C8C2×C22⋊D1111yescharacteristic
294C2×C8C2×C22⋊D1111yescharacteristic
295C4⋊C4—24no—
296C4⋊C4—24no—
297C4⋊C4—42no—
298C4⋊C4—42no—
299C4⋊C4—111no—
300C4⋊C4—111no—
301C4⋊C4—221no—
302C4⋊C4—221no—
303C4⋊C4—221no—
304C4⋊C4—221no—
305C22⋊C4—221no—
306C22⋊C4—221no—
307C22⋊C4—221no—
308C22⋊C4—221no—
309C22⋊C4—221no—
310C42—221no—
311C42D4×D1111yescharacteristic
312C42#434111yescharacteristic
313C42C2×C22⋊D1111yescharacteristic
314C42C23×D1111yescharacteristic
315C11#1935811yescharacteristic, complemented, Sylow
316C23—221no—
317C23#6699111yescharacteristic
318Q8—44no—
319Q8—44no—
320Q8—84no—
321Q8—222no—
322D4—222no—
323D4—442no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—44no—
329C2×C4—84no—
330C2×C4—221no—
331C2×C4—221no—
332C2×C4—221no—
333C2×C4—441no—
334C2×C4—441no—
335C2×C4#6699111yescharacteristic
336C2×C4#6699111yescharacteristic
337C2×C4#6699111yescharacteristic
338C2×C4C2×D4×D1111yescharacteristic
339C2×C4C2×#434111yescharacteristic
340C2×C4C22×C22⋊D1111yescharacteristic
341C8—21no—
342C8—21no—
343C8—444no—
344C8—441no—
345C8—441no—
346C8#6699512yes—
347C8#6699512yes—
348C22—21no—
349C22—21no—
350C22—441no—
351C22—441no—
352C22—441no—
353C22#1062280512yes—
354C22C2×#6699111yescharacteristic
355C4—21no—
356C4—21no—
357C4—21no—
358C4—21no—
359C4—84no—
360C4—441no—
361C4—441no—
362C4—441no—
363C4#1062328812yes—
364C4C2×#6699511yescharacteristic
365C4C2×#6699511yescharacteristic
366C2—22no—
367C2—881no—
368C2#1307809911yescharacteristic
369C2#1307826011yescharacteristic
370C2C2×#1062280511yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#500C2
socleC22×C11C2×#121
prime radical#66983D4
hypercenterC2×#500D11
hypocenterC11#19358
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#500

Complements

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

NH ≅ G/Ntype
3. #13068131C2semidirect
4. #13068126C2semidirect
5. #13068007C2semidirect
6. #13068002C2semidirect
7. #13067379C2semidirect
8. #13067333C2semidirect
9. C2×C11×#500C2semidirect
132. C2×#500D11semidirect
315. C11#19358semidirect

Maximal subgroups

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

subgroupindex
#130796432
#130775912
#130681312
#130681262
#130680072
#130680022
#130673792
#130673332
C2×C11×#5002
#1935811