Finite Group Databasebeta

← #14726267

Subgroups — #14726267

Order 2816.

930 conjugacy classes of subgroups; only the 183 normal subgroups are shown.

normal subgroups only

This group has 930 conjugacy classes of subgroups — too many to draw. Only its 183 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#13078560C212yesmaximal
2#13072903C211yesmaximal, characteristic
3#13067658C214yesmaximal, complemented
4#13067624C214yesmaximal, complemented
5#13067149C212yesmaximal
6#13066946C211yesmaximal, characteristic
7C2×C11×#544C211yesmaximal, characteristic
8C11×#544—24no—
9C11×#544—22no—
10C11×#544C2214yes—
11C2×C11×C4⋊Q8—22no—
12C2×C11×#125—22no—
13C2×C11×C22⋊Q8—21no—
14C2×C11×C22⋊Q8C2212yes—
15C2×C11×#117—21no—
16C22×C11×C4⋊C4C2211yescharacteristic
17C2×#66979C2211yescharacteristic
18#10622838—22no—
19#10622824—21no—
20#10622824C2211yescharacteristic
21#10622823—21no—
22#10622820C2212yes—
23#10622658—24no—
24#10622657C2214yes—
25#10622656C2214yes—
26#10622599C2212yes—
27#10622596C2212yes—
28#10622591—22no—
29#10622577—22no—
30#10622176C2218yes—
31#10622166C2214yes—
32C22×Q8×C11—21no—
33C22×Q8×C11D412yes—
34C23×C4×C11D411yescharacteristic
35C23×C4×C11D411yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C11×C4⋊Q8—28no—
38C11×C4⋊Q8—28no—
39C11×#125—28no—
40C11×#125—28no—
41C11×C22⋊Q8—24no—
42C11×C22⋊Q8—24no—
43C11×C22⋊Q8—22no—
44C11×C22⋊Q8—22no—
45C11×C22⋊Q8D414yes—
46C11×C22⋊Q8C2314yes—
47C11×#117—24no—
48C11×#117—24no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4D412yes—
57C2×C11×C4⋊C4D412yes—
58C2×C11×C4⋊C4C2312yes—
59C2×C11×C22⋊C4—22no—
60C2×C42×C11—22no—
61C2×C22⋊Dic11—21no—
62C2×C22⋊Dic11—21no—
63#66979—22no—
64#66979—22no—
65C2×C4⋊Dic11C2311yescharacteristic
66C2×C4⋊Dic11C2311yescharacteristic
67C2×Dic11⋊C4—22no—
68C2×C4×Dic11—21no—
69C2×#4318—22no—
70#66899—24no—
71#66899—24no—
72C11⋊#95—22no—
73C11⋊#95—22no—
74C11⋊#95—22no—
75C11⋊#95—21no—
76C11⋊#95C2312yes—
77C22⋊(C11⋊C8)—22no—
78C22⋊(C11⋊C8)C2314yes—
79#66872—24no—
80#66871—24no—
81#18148—111nomaximal, Sylow
82C24×C11C2×D411yescharacteristic
83C2×Q8×C11—24no—
84C2×Q8×C11—22no—
85C2×Q8×C11—44no—
86C2×Q8×C11—82no—
87C2×Q8×C11C2×D414yes—
88C22×C4×C11—21no—
89C22×C4×C11—21no—
90C22×C4×C11—24no—
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11—42no—
96C22×C4×C11—42no—
97C22×C4×C11C2×D412yes—
98C22×C4×C11C2×D412yes—
99C22×C4×C11C2×D412yes—
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D412yes—
102C22×C4×C11C2411yescharacteristic
103C22×Dic11—22no—
104C22×Dic11—21no—
105C22×Dic11—21no—
106C11×C4⋊C4—24no—
107C11×C4⋊C4—24no—
108C11×C4⋊C4—24no—
109C11×C4⋊C4—28no—
110C11×C4⋊C4—24no—
111C11×C4⋊C4—24no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—24no—
114C11×C4⋊C4—24no—
115C11×C4⋊C4C2×D414yes—
116C11×C22⋊C4—24no—
117C11×C22⋊C4—24no—
118C42×C11—28no—
119C22⋊Dic11—42no—
120C22⋊Dic11—41no—
121C22⋊Dic11—41no—
122C4⋊Dic11—22no—
123C4⋊Dic11—22no—
124Dic11⋊C4—44no—
125C4×Dic11—42no—
126#4318—44no—
127C2×C11⋊C8—24no—
128C2×#544D1111yescharacteristic
129#3095—112no—
130#2484—111no—
131#1617—114no—
132#1611—114no—
133#1511—112no—
134#1463—111no—
135C23×C11—22no—
136C23×C11—22no—
137C23×C11—41no—
138C23×C11#12011yescharacteristic
139C23×C11#12011yescharacteristic
140C23×C11C22×D411yescharacteristic
141Q8×C11—44no—
142Q8×C11—82no—
143Q8×C11—84no—
144C2×C4×C11—24no—
145C2×C4×C11—24no—
146C2×C4×C11—22no—
147C2×C4×C11—22no—
148C2×C4×C11—24no—
149C2×C4×C11—24no—
150C2×C4×C11—24no—
151C2×C4×C11—22no—
152C2×C4×C11—41no—
153C2×C4×C11—42no—
154C2×C4×C11—41no—
155C2×C4×C11—44no—
156C2×C4×C11—42no—
157C2×C4×C11—44no—
158C2×C4×C11—42no—
159C2×C4×C11—81no—
160C2×C4×C11#12012yes—
161C2×C4×C11#13714yes—
162C2×C4×C11C22×D412yes—
163C2×Dic11—42no—
164C2×Dic11—42no—
165C2×Dic11—42no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—42no—
169C2×Dic11—42no—
170C11⋊C8—44no—
171#544—24no—
172#544—22no—
173#544C2×D1114yes—
174C2×C4⋊Q8—22no—
175C2×#125—22no—
176C2×C22⋊Q8—21no—
177C2×C22⋊Q8C2×D1112yes—
178C2×#117—21no—
179C2×#117—111no—
180C22×C4⋊C4C2×D1111yescharacteristic
181#485—224no—
182#484—114no—
183#483—114no—
184#428—222no—
185#419—222no—
186#407—112no—
187#400—112no—
188#398—112no—
189#387—222no—
190#385—221no—
191#381—111no—
192#381—221no—
193#328—118no—
194#324—114no—
195C22×C11—21no—
196C22×C11—21no—
197C22×C11—21no—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11—21no—
201C22×C11—21no—
202C22×C11—44no—
203C22×C11#45812yes—
204C22×C11C2×#12011yescharacteristic
205C22×C11C2×#13712yes—
206C4×C11—24no—
207C4×C11—22no—
208C4×C11—22no—
209C4×C11—44no—
210C4×C11—42no—
211C4×C11—44no—
212Dic11—82no—
213Dic11—81no—
214Dic11—81no—
215C22×Q8—21no—
216C22×Q8C22⋊D1112yes—
217C23×C4C22⋊D1111yescharacteristic
218C23×C4C22⋊D1111yescharacteristic
219C23×C4C22×D1111yescharacteristic
220C2×M16—222no—
221C4⋊Q8—28no—
222C4⋊Q8—28no—
223#125—28no—
224#125—28no—
225C22⋊Q8—24no—
226C22⋊Q8—24no—
227C22⋊Q8—22no—
228C22⋊Q8—22no—
229C22⋊Q8C22⋊D1114yes—
230C22⋊Q8C22×D1114yes—
231#117—24no—
232#117—24no—
233#117—222no—
234#117—222no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—22no—
239C2×C4⋊C4—22no—
240C2×C4⋊C4—22no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4—111no—
243C2×C4⋊C4—111no—
244C2×C4⋊C4—222no—
245C2×C4⋊C4C22⋊D1112yes—
246C2×C4⋊C4C22⋊D1112yes—
247C2×C4⋊C4C22×D1112yes—
248C2×C22⋊C4—22no—
249C2×C22⋊C4—221no—
250C2×C22⋊C4—221no—
251C2×C42—22no—
252C2×C42—221no—
253#107—224no—
254#106—224no—
255#103—224no—
256#103—224no—
257C22⋊C8—114no—
258C22⋊C8—222no—
259#95—112no—
260#95—221no—
261#95—222no—
262#95—222no—
263#95—222no—
264C2×C11—22no—
265C2×C11—22no—
266C2×C11—41no—
267C2×C11#300411yescharacteristic
268C2×C11#302011yescharacteristic
269C2×C11C2×#45811yescharacteristic
270C24C2×C22⋊D1111yescharacteristic
271C2×Q8—24no—
272C2×Q8—22no—
273C2×Q8—44no—
274C2×Q8—82no—
275C2×Q8C2×C22⋊D1114yes—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—24no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—222no—
286C22×C4—221no—
287C22×C4—221no—
288C22×C4C2×C22⋊D1112yes—
289C22×C4C2×C22⋊D1112yes—
290C22×C4C2×C22⋊D1112yes—
291C22×C4C2×C22⋊D1111yescharacteristic
292C22×C4C2×C22⋊D1112yes—
293C22×C4C23×D1111yescharacteristic
294M16—444no—
295C2×C8—224no—
296C4⋊C4—24no—
297C4⋊C4—24no—
298C4⋊C4—24no—
299C4⋊C4—28no—
300C4⋊C4—24no—
301C4⋊C4—24no—
302C4⋊C4—22no—
303C4⋊C4—24no—
304C4⋊C4—24no—
305C4⋊C4—222no—
306C4⋊C4—222no—
307C4⋊C4—444no—
308C4⋊C4C2×C22⋊D1114yes—
309C22⋊C4—24no—
310C22⋊C4—24no—
311C22⋊C4—442no—
312C22⋊C4—441no—
313C22⋊C4—441no—
314C42—28no—
315C42—442no—
316C11#1814811yescharacteristic, complemented, Sylow
317C23—22no—
318C23—22no—
319C23—41no—
320C23#6700611yescharacteristic
321C23#6700611yescharacteristic
322C23C22×C22⋊D1111yescharacteristic
323Q8—44no—
324Q8—82no—
325Q8—84no—
326C2×C4—24no—
327C2×C4—24no—
328C2×C4—22no—
329C2×C4—24no—
330C2×C4—22no—
331C2×C4—24no—
332C2×C4—24no—
333C2×C4—22no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—44no—
338C2×C4—42no—
339C2×C4—44no—
340C2×C4—42no—
341C2×C4—81no—
342C2×C4—442no—
343C2×C4—442no—
344C2×C4—442no—
345C2×C4—442no—
346C2×C4—442no—
347C2×C4—441no—
348C2×C4—441no—
349C2×C4#6699514yes—
350C2×C4#6700612yes—
351C2×C4C22×C22⋊D1112yes—
352C8—444no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—44no—
361C22#1062285612yes—
362C22C2×#6699512yes—
363C22C2×#6700611yescharacteristic
364C4—24no—
365C4—22no—
366C4—22no—
367C4—44no—
368C4—42no—
369C4—44no—
370C4—882no—
371C4—881no—
372C4—881no—
373C2—22no—
374C2—22no—
375C2—41no—
376C2#1307785011yescharacteristic
377C2#1307798011yescharacteristic
378C2C2×#1062285611yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#544C2
socleC22×C11C2×#120
prime radicalC24×C11C2×D4
hypercenterC2×#544D11
hypocenterC11#18148
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
3. #13067658C2semidirect
4. #13067624C2semidirect
316. C11#18148semidirect

Maximal subgroups

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

subgroupindex
#130785602
#130729032
#130676582
#130676242
#130671492
#130669462
C2×C11×#5442
#1814811