Finite Group Databasebeta

← #14669640

Subgroups — #14669640

Order 2816.

728 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 728 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13070301C211yesmaximal, characteristic
2#13070270C212yesmaximal, complemented
3#13069169C212yesmaximal, complemented
4#13069000C211yesmaximal, characteristic
5C11×#3550C211yesmaximal, characteristic
6C11×#563—21no—
7C11×#563C412yescomplemented
8C11×#559C412yescomplemented
9Q82×C11—21no—
10C11×#556—22no—
11D4×Q8×C11—22no—
12C11×#542—24no—
13C11×#536—21no—
14C11×#536C2212yes—
15C11×#533—21no—
16C11×#532C2211yescharacteristic
17#10623350C2211yescharacteristic
18#10622853C2211yescharacteristic
19#10622850C2212yes—
20#10622849—21no—
21C2×#66900—22no—
22#10622186—21no—
23#10622180—21no—
24#10622177—24no—
25#10622171—22no—
26#10622161—21no—
27C2×C11×#41D411yescharacteristic
28C2×C11×#41C2311yescharacteristic
29C22×Q8×C11—21no—
30C22×Q8×C11D412yes—
31C11×C4⋊Q8—21no—
32C11×C4⋊Q8—21no—
33C11×C4⋊Q8—24no—
34C11×C4⋊Q8—22no—
35C11×C4⋊Q8—22no—
36C11×C4⋊Q8D411yescharacteristic
37C11×#127C2×C411yescharacteristic
38C11×#126—24no—
39C11×#126—24no—
40C11×#125—22no—
41C11×#124—22no—
42C11×#124—22no—
43C11×#124—24no—
44C11×#124C2×C411yescharacteristic
45C11×#124D411yescharacteristic
46C11×#123—22no—
47C11×#123—22no—
48C11×#123C2×C414yes—
49C11×#123D414yes—
50C11×C22⋊Q8—22no—
51C11×C22⋊Q8—22no—
52C11×C22⋊Q8—24no—
53C11×C22⋊Q8—24no—
54C11×C22⋊Q8—22no—
55C11×C22⋊Q8—22no—
56C11×#121—22no—
57C4×Q8×C11—22no—
58C4×Q8×C11—24no—
59C4×Q8×C11—22no—
60C4×D4×C11—24no—
61C4×D4×C11—22no—
62C11×#117—22no—
63C11×#117—21no—
64C11×#117D412yes—
65C2×C42×C11D411yescharacteristic
66#67001—42no—
67#66979—21no—
68C2×#4318—22no—
69C2×#4318—21no—
70C2×#4318—22no—
71#66901—42no—
72#66900—22no—
73#66900—44no—
74#66898—22no—
75#66897—22no—
76#12771—111nomaximal, Sylow
77C11×#41—41no—
78C11×#41—41no—
79C11×#41—41no—
80C11×#41—41no—
81C2×Q8×C11—22no—
82C2×Q8×C11—22no—
83C2×Q8×C11—22no—
84C2×Q8×C11—22no—
85C2×Q8×C11—42no—
86C2×Q8×C11—42no—
87C2×Q8×C11—81no—
88C2×Q8×C11—81no—
89C2×Q8×C11C22⋊C411yescharacteristic
90C2×Q8×C11C2×D411yescharacteristic
91C2×D4×C11—22no—
92C2×D4×C11—21no—
93C2×D4×C11C22⋊C411yescharacteristic
94C2×D4×C11C22×C411yescharacteristic
95C2×D4×C11C2×D412yes—
96C22×C4×C11—21no—
97C22×C4×C11—22no—
98C22×C4×C11—21no—
99C22×C4×C11C22⋊C414yes—
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D412yes—
102C11×C4⋊C4—22no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—24no—
106C11×C4⋊C4—24no—
107C11×C4⋊C4—24no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—24no—
111C11×C22⋊C4—22no—
112C11×C22⋊C4—24no—
113C11×C22⋊C4—22no—
114C11×C22⋊C4—24no—
115C11×C22⋊C4—24no—
116C11×C22⋊C4—22no—
117C11×C22⋊C4C22⋊C414yes—
118C42×C11—24no—
119C42×C11—22no—
120C42×C11—21no—
121C42×C11—22no—
122C42×C11C22⋊C411yescharacteristic
123C42×C11C22⋊C411yescharacteristic
124C22⋊Dic11—41no—
125C4⋊Dic11—41no—
126C4×Dic11—41no—
127#4318—24no—
128#4318—22no—
129#4318—42no—
130#4318—41no—
131#4318—42no—
132C2×C11⋊C8—42no—
133C2×C11⋊C8—41no—
134C2×C11⋊C8—42no—
135#3550D1111yescharacteristic
136#2132—111no—
137#2123—112no—
138#1915—112no—
139#1884—111no—
140C23×C11—21no—
141C23×C11C2×C22⋊C412yes—
142C23×C11#12011yescharacteristic
143Q8×C11—41no—
144Q8×C11—41no—
145Q8×C11—44no—
146Q8×C11—42no—
147Q8×C11—42no—
148Q8×C11—82no—
149Q8×C11—82no—
150D4×C11—41no—
151D4×C11—42no—
152D4×C11—41no—
153D4×C11—44no—
154D4×C11—81no—
155C2×C4×C11—21no—
156C2×C4×C11—22no—
157C2×C4×C11—21no—
158C2×C4×C11—22no—
159C2×C4×C11—21no—
160C2×C4×C11—24no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—24no—
164C2×C4×C11—42no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—44no—
168C2×C4×C11—82no—
169C2×C4×C11C2×C22⋊C411yescharacteristic
170C2×C4×C11#12012yes—
171C2×C4×C11#12011yescharacteristic
172C2×Dic11—81no—
173C11⋊C8—42no—
174C11⋊C8—82no—
175#568—111no—
176#563—21no—
177#563Dic1112yescomplemented
178#559Dic1112yescomplemented
179Q82—21no—
180#556—22no—
181D4×Q8—22no—
182#542—24no—
183#536—21no—
184#536C2×D1112yes—
185#533—21no—
186#532C2×D1111yescharacteristic
187#421—221no—
188#413—112no—
189C2×#101—222no—
190#410—111no—
191#356—221no—
192#355—221no—
193#352—224no—
194#344—222no—
195#339—221no—
196C22×C11—22no—
197C22×C11—21no—
198C22×C11—41no—
199C22×C11—42no—
200C22×C11—42no—
201C22×C11—41no—
202C22×C11#37911yescharacteristic
203C4×C11—22no—
204C4×C11—21no—
205C4×C11—22no—
206C4×C11—41no—
207C4×C11—44no—
208C4×C11—41no—
209C4×C11—44no—
210C4×C11B(4,𝔽2)11yescharacteristic
211C4×C11#45811yescharacteristic
212Dic11—161no—
213C2×#41C22⋊D1111yescharacteristic
214C2×#41C22×D1111yescharacteristic
215C22×Q8—21no—
216C22×Q8C22⋊D1112yes—
217#131—442no—
218C2×M16—221no—
219C2×M16—222no—
220C2×M16—222no—
221C4⋊Q8—21no—
222C4⋊Q8—21no—
223C4⋊Q8—24no—
224C4⋊Q8—22no—
225C4⋊Q8—22no—
226C4⋊Q8C22⋊D1111yescharacteristic
227#127C2×Dic1111yescharacteristic
228#126—24no—
229#126—24no—
230#125—22no—
231#124—22no—
232#124—22no—
233#124—24no—
234#124C2×Dic1111yescharacteristic
235#124C22⋊D1111yescharacteristic
236#123—22no—
237#123—22no—
238#123C2×Dic1114yes—
239#123C22⋊D1114yes—
240C22⋊Q8—22no—
241C22⋊Q8—22no—
242C22⋊Q8—24no—
243C22⋊Q8—24no—
244C22⋊Q8—22no—
245C22⋊Q8—22no—
246#121—22no—
247C4×Q8—22no—
248C4×Q8—24no—
249C4×Q8—22no—
250C4×D4—24no—
251C4×D4—22no—
252#117—22no—
253#117—21no—
254#117—221no—
255#117C22⋊D1112yes—
256C2×C42C22⋊D1111yescharacteristic
257#104—442no—
258#101—222no—
259#101—444no—
260#100—222no—
261#99—222no—
262C2×C11—21no—
263C2×C11—41no—
264C2×C11—42no—
265C2×C11—81no—
266C2×C11#179011yescharacteristic
267#41—41no—
268#41—41no—
269#41—41no—
270#41—41no—
271C2×Q8—22no—
272C2×Q8—22no—
273C2×Q8—22no—
274C2×Q8—22no—
275C2×Q8—42no—
276C2×Q8—42no—
277C2×Q8—81no—
278C2×Q8—81no—
279C2×Q8C22⋊Dic1111yescharacteristic
280C2×Q8C2×C22⋊D1111yescharacteristic
281C2×D4—22no—
282C2×D4—21no—
283C2×D4C22⋊Dic1111yescharacteristic
284C2×D4C22×Dic1111yescharacteristic
285C2×D4C2×C22⋊D1112yes—
286C22×C4—21no—
287C22×C4—22no—
288C22×C4—21no—
289C22×C4C22⋊Dic1114yes—
290C22×C4C2×C22⋊D1111yescharacteristic
291C22×C4C2×C22⋊D1112yes—
292M16—224no—
293M16—222no—
294M16—441no—
295M16—442no—
296M16—442no—
297C2×C8—441no—
298C2×C8—442no—
299C2×C8—442no—
300C4⋊C4—22no—
301C4⋊C4—22no—
302C4⋊C4—22no—
303C4⋊C4—24no—
304C4⋊C4—24no—
305C4⋊C4—24no—
306C4⋊C4—22no—
307C4⋊C4—24no—
308C4⋊C4—22no—
309C4⋊C4—441no—
310C22⋊C4—22no—
311C22⋊C4—24no—
312C22⋊C4—22no—
313C22⋊C4—24no—
314C22⋊C4—24no—
315C22⋊C4—22no—
316C22⋊C4—441no—
317C22⋊C4C22⋊Dic1114yes—
318C42—24no—
319C42—22no—
320C42—22no—
321C42—21no—
322C42—441no—
323C42C22⋊Dic1111yescharacteristic
324C42C22⋊Dic1111yescharacteristic
325C11#1277111yescharacteristic, complemented, Sylow
326C23—21no—
327C23C2×C22⋊Dic1112yes—
328C23#6700611yescharacteristic
329Q8—41no—
330Q8—41no—
331Q8—44no—
332Q8—42no—
333Q8—42no—
334Q8—82no—
335Q8—82no—
336D4—41no—
337D4—42no—
338D4—41no—
339D4—44no—
340D4—81no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—22no—
344C2×C4—21no—
345C2×C4—22no—
346C2×C4—24no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—24no—
350C2×C4—42no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—44no—
354C2×C4—82no—
355C2×C4—881no—
356C2×C4C2×C22⋊Dic1111yescharacteristic
357C2×C4#6700612yes—
358C2×C4#6700611yescharacteristic
359C8—442no—
360C8—882no—
361C22—22no—
362C22—21no—
363C22—41no—
364C22—42no—
365C22—42no—
366C22—41no—
367C22#1062286011yescharacteristic
368C4—22no—
369C4—22no—
370C4—21no—
371C4—41no—
372C4—44no—
373C4—41no—
374C4—44no—
375C4—1761no—
376C4#1062285611yescharacteristic
377C4#1062285711yescharacteristic
378C2—21no—
379C2—41no—
380C2—42no—
381C2—81no—
382C2#1306856411yescharacteristic
subgroupG/H
centerC2#13068564
commutatorC2×D4×C11C22×C4
FrattiniC2×#41C22×D11
FittingC11×#3550C2
socleC2×C11#1790
prime radicalC11×#532C22
cosocleC2×C11×#41C23
hypercenter#3550D11
hypocenterC11#12771
LCSG ▷ C2×D4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #3550

Complements

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

NH ≅ G/Ntype
2. #13070270C2semidirect
3. #13069169C2semidirect
7. C11×#563C4semidirect
8. C11×#559C4semidirect
177. #563Dic11semidirect
178. #559Dic11semidirect
325. C11#12771semidirect

Maximal subgroups

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

subgroupindex
#130703012
#130702702
#130691692
#130690002
C11×#35502
#1277111