Finite Group Databasebeta

← #14650128

Subgroups — #14650128

Order 2816.

406 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C2×#10622442C211yesmaximal, characteristic
2#13077703C211yesmaximal, characteristic
3#13067217C211yesmaximal, characteristic
4#13067064C211yesmaximal, characteristic
5#13066971C211yesmaximal, characteristic
6#13066486C211yesmaximal, characteristic
7C11×#1283C211yesmaximal, characteristic
8C2×#66923C2211yescharacteristic
9C2×C4×Dic22C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C4×C11×M16C2211yescharacteristic
13C2×#66882C411yescharacteristic
14C2×#66881C411yescharacteristic
15C2×#66880C411yescharacteristic
16C2×#66880C411yescharacteristic
17#10622539C2211yescharacteristic
18#10622539C2211yescharacteristic
19#10622442—21no—
20#10622442—21no—
21#10622442—21no—
22#10622442—21no—
23#10622441—22no—
24#10622332—21no—
25#10622331—21no—
26#10622292—21no—
27C8×Dic22—21no—
28#10622107—21no—
29#10622107—21no—
30#10622103—22no—
31#10622094—21no—
32#10622094—21no—
33C22×Dic22C2×C411yescharacteristic
34C2×C11×M16—21no—
35C22×C8×C11C2×C411yescharacteristic
36C22×C8×C11C2×C411yescharacteristic
37C2×C42×C11C2311yescharacteristic
38C2×C4⋊Dic11C2×C411yescharacteristic
39C2×C4⋊Dic11C2×C411yescharacteristic
40C2×C4⋊Dic11C2×C411yescharacteristic
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×C4×Dic11—21no—
45#66923—21no—
46#66923—21no—
47#66923—21no—
48#66923—21no—
49C4×Dic22—21no—
50C4×Dic22—21no—
51C4×Dic22D411yescharacteristic
52C4×Dic22D411yescharacteristic
53C4×Dic22D411yescharacteristic
54C4×Dic22D411yescharacteristic
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C11×C4⋊C8—21no—
58C11×C22⋊C8D411yescharacteristic
59C11×C22⋊C8D411yescharacteristic
60C11×#97—21no—
61C4×C8×C11—21no—
62C4×C8×C11—21no—
63C22⋊(C11⋊C8)—21no—
64C22⋊(C11⋊C8)—21no—
65#66882—21no—
66#66882—21no—
67#66881—21no—
68#66881—21no—
69#66880—21no—
70#66880—21no—
71#66880—21no—
72#66880—21no—
73#66879—22no—
74Dic11⋊C8—22no—
75Dic11⋊C8—22no—
76C8×Dic11—22no—
77C4⋊(C11⋊C8)—21no—
78C4⋊(C11⋊C8)—21no—
79#66867—21no—
80#66867D412yes—
81#9246—111nomaximal, Sylow
82C22×C4×C11C22×C411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11#4111yescharacteristic
85C22×Dic11—21no—
86C22×Dic11—21no—
87C22×Dic11—21no—
88C22×Dic11—21no—
89C2×Dic22—22no—
90C2×Dic22—21no—
91C2×Dic22—41no—
92C2×Dic22C22⋊C411yescharacteristic
93C2×Dic22C22⋊C411yescharacteristic
94C11×M16—22no—
95C11×M16—41no—
96C2×C8×C11—21no—
97C2×C8×C11—21no—
98C2×C8×C11—21no—
99C2×C8×C11—21no—
100C2×C8×C11—41no—
101C2×C8×C11—41no—
102C2×C8×C11—41no—
103C42×C11C2×D411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C42×C11#4111yescharacteristic
107C4⋊Dic11—21no—
108C4⋊Dic11—21no—
109C4⋊Dic11—21no—
110C4⋊Dic11—21no—
111C4⋊Dic11—21no—
112C4⋊Dic11C22⋊C411yescharacteristic
113C4⋊Dic11C22⋊C411yescharacteristic
114Dic11⋊C4—21no—
115Dic11⋊C4—21no—
116Dic11⋊C4—21no—
117Dic11⋊C4—21no—
118Dic11⋊C4—41no—
119Dic11⋊C4—41no—
120Dic11⋊C4—41no—
121Dic11⋊C4—41no—
122C4×Dic11—21no—
123C4×Dic11—21no—
124C4×Dic11—21no—
125C4×Dic11—21no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—41no—
128C2×#479—111no—
129#2984—111no—
130#1528—111no—
131#1491—111no—
132#1470—111no—
133#1290—111no—
134#1283D1111yescharacteristic
135C23×C11C4×D411yescharacteristic
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—41no—
141C2×C4×C11C2×C22⋊C411yescharacteristic
142C2×C4×C11C4×D411yescharacteristic
143C2×C4×C11#12011yescharacteristic
144C2×C4×C11#12111yescharacteristic
145C2×C4×C11#12111yescharacteristic
146C2×C4×C11#12311yescharacteristic
147C2×Dic11—21no—
148C2×Dic11—21no—
149C2×Dic11—21no—
150C2×Dic11—21no—
151C2×Dic11—42no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—81no—
159Dic22—21no—
160Dic22—21no—
161Dic22—21no—
162Dic22—42no—
163Dic22#10112yes—
164C8×C11—41no—
165C8×C11—41no—
166C8×C11—42no—
167C8×C11—41no—
168C8×C11—41no—
169C11⋊C8—42no—
170C11⋊C8—81no—
171C2×#125—111no—
172C2×C4×Q8—111no—
173#479—221no—
174#479—221no—
175#479—221no—
176#479—221no—
177#446—221no—
178#446—222no—
179C8×Q8—221no—
180#432—111no—
181#432—111no—
182#432—221no—
183#431—221no—
184#431C2×D1111yescharacteristic
185C2×#107—111no—
186C2×#106—111no—
187C2×C4⋊C8C2×D1111yescharacteristic
188C2×#103—111no—
189C2×#103—111no—
190C4×M16C2×D1111yescharacteristic
191#330—222no—
192Q8⋊C8—221no—
193Q8⋊C8—221no—
194#324—221no—
195#324—221no—
196C22×C11—21no—
197C22×C11—21no—
198C22×C11#38611yescharacteristic
199C22×C11#44311yescharacteristic
200C22×C11#44411yescharacteristic
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11C2×#10111yescharacteristic
207C4×C11#41311yescharacteristic
208Dic11—22no—
209Dic11—41no—
210Dic11—41no—
211Dic11—41no—
212Dic11—81no—
213Dic11—81no—
214C22×Q8—111no—
215C2×M16—21no—
216C22×C8C4×D1111yescharacteristic
217C22×C8C4×D1111yescharacteristic
218#125—221no—
219#125—221no—
220#125—221no—
221#125—221no—
222C4×Q8—111no—
223C4×Q8—111no—
224C4×Q8—111no—
225C4×Q8—111no—
226C4×Q8—221no—
227C4×Q8—221no—
228C2×C4⋊C4—111no—
229C2×C4⋊C4—111no—
230C2×C4⋊C4—111no—
231C2×C4⋊C4—221no—
232C2×C4⋊C4—221no—
233C2×C4⋊C4—221no—
234C2×C42—221no—
235C2×C42C22×D1111yescharacteristic
236#107—221no—
237#107—221no—
238#106—221no—
239#106—221no—
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8—222no—
244C4⋊C8—222no—
245C4⋊C8—221no—
246C4⋊C8—221no—
247#103—221no—
248#103—221no—
249#103—221no—
250#103—221no—
251C22⋊C8—221no—
252C22⋊C8—221no—
253C22⋊C8D4411yescharacteristic
254C22⋊C8D4411yescharacteristic
255#97—21no—
256#97—112no—
257#97—222no—
258#97—221no—
259C4×C8—21no—
260C4×C8—21no—
261C4×C8—222no—
262C2×C11—21no—
263C2×C11—21no—
264C2×C11#187611yescharacteristic
265C2×C11#190111yescharacteristic
266C2×C11#190511yescharacteristic
267C2×Q8—111no—
268C2×Q8—111no—
269C2×Q8—222no—
270C2×Q8—221no—
271C2×Q8—441no—
272C22×C4—221no—
273C22×C4—221no—
274C22×C4—221no—
275C22×C4—221no—
276C22×C4C2×C4×D1111yescharacteristic
277C22×C4C2×D4411yescharacteristic
278C22×C4#433911yescharacteristic
279M16—22no—
280M16—41no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—21no—
285C2×C8—41no—
286C2×C8—41no—
287C2×C8—41no—
288C2×C8—222no—
289C2×C8—441no—
290C4⋊C4—111no—
291C4⋊C4—111no—
292C4⋊C4—221no—
293C4⋊C4—221no—
294C4⋊C4—221no—
295C4⋊C4—221no—
296C4⋊C4—221no—
297C4⋊C4—221no—
298C4⋊C4—221no—
299C4⋊C4—221no—
300C4⋊C4—221no—
301C4⋊C4—441no—
302C4⋊C4—441no—
303C4⋊C4—441no—
304C4⋊C4—441no—
305C42—221no—
306C42—221no—
307C42—221no—
308C42—221no—
309C42D4×D1111yescharacteristic
310C42D4×D1111yescharacteristic
311C42D4×D1111yescharacteristic
312C42#434311yescharacteristic
313C11#924611yescharacteristic, complemented, Sylow
314C23C4×D4411yescharacteristic
315Q8—112no—
316Q8—221no—
317Q8—221no—
318Q8—221no—
319Q8—442no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—41no—
325C2×C4—221no—
326C2×C4—221no—
327C2×C4—221no—
328C2×C4—221no—
329C2×C4—442no—
330C2×C4—441no—
331C2×C4—441no—
332C2×C4—441no—
333C2×C4—441no—
334C2×C4—441no—
335C2×C4—441no—
336C2×C4—881no—
337C2×C4C22⋊C4×D1111yescharacteristic
338C2×C4#6693511yescharacteristic
339C2×C4#6693711yescharacteristic
340C2×C4#6694611yescharacteristic
341C2×C4#6694711yescharacteristic
342C2×C4#6694811yescharacteristic
343C8—41no—
344C8—41no—
345C8—42no—
346C8—41no—
347C8—41no—
348C8—442no—
349C8—881no—
350C22—21no—
351C22—21no—
352C22#1062227811yescharacteristic
353C22#1062231311yescharacteristic
354C22#1062233011yescharacteristic
355C4—21no—
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—222no—
361C4—441no—
362C4—441no—
363C4—441no—
364C4—881no—
365C4—881no—
366C4#1062235811yescharacteristic
367C4D11×#10111yescharacteristic
368C2—21no—
369C2—21no—
370C2#1306894211yescharacteristic
371C2#1306908311yescharacteristic
372C2#1306910911yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1283C2
socleC22×C11#386
prime radicalC23×C11C4×D4
cosocleC2×C42×C11C23
hypercenter#1283D11
hypocenterC11#9246
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1283

Complements

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

NH ≅ G/Ntype
313. C11#9246semidirect

Maximal subgroups

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

subgroupindex
C2×#106224422
#130777032
#130672172
#130670642
#130669712
#130664862
C11×#12832
#924611