Finite Group Databasebeta

← #14655148

Subgroups — #14655148

Order 2816.

496 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 85 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#13079009C211yesmaximal, characteristic
2#13074737C211yesmaximal, characteristic, complemented
3#13067332C211yesmaximal, characteristic, complemented
4#13067218C211yesmaximal, characteristic, complemented
5#13067124C211yesmaximal, characteristic
6#13066508C211yesmaximal, characteristic, complemented
7C11×#3234C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×C11×#125C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#501—21no—
12C11×#490—21no—
13C11×#481—21no—
14C11×#480—21no—
15C11×#478—22no—
16C11×#432C2211yescharacteristic
17#10622845—22no—
18#10622694—21no—
19#10622683—21no—
20#10622668—22no—
21#10622596—22no—
22#10622592—22no—
23#10622590—21no—
24#10622589—21no—
25#10622545C2211yescharacteristic
26#10622539C2211yescharacteristic
27C4×#4318C2211yescharacteristic
28#10622181—22no—
29#10622175—22no—
30#10622124—22no—
31C2×C11×#41—21no—
32C22×Dic22—21no—
33C11×C4⋊Q8D411yescharacteristic
34C11×#127D411yescharacteristic
35C11×#125—21no—
36C11×#125—21no—
37C11×#125—21no—
38C11×#125—21no—
39C11×#124—21no—
40C11×#121—21no—
41C11×#121—21no—
42C4×D4×C11—21no—
43C4×D4×C11—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4D411yescharacteristic
47C2×C11×C4⋊C4D411yescharacteristic
48C2×C42×C11C2311yescharacteristic
49C2×C4⋊Dic11—21no—
50C2×C4⋊Dic11D412yes—
51C2×Dic11⋊C4—24no—
52C2×C4×Dic11—21no—
53C2×#4318—21no—
54#66922—21no—
55#66922—21no—
56#66922—21no—
57#66922—21no—
58C11×#107—22no—
59C11×#106—22no—
60C11×C4⋊C8D412yes—
61C11×#102—22no—
62C11×#102—22no—
63C11×C22⋊C8—21no—
64C11×#97—21no—
65#66899—24no—
66#66896—24no—
67C11⋊#95—24no—
68C11⋊#95—21no—
69C11⋊#95D412yes—
70C22⋊(C11⋊C8)—21no—
71C4⋊(C11⋊C8)—21no—
72#66867—21no—
73#66867D412yes—
74C4×C11⋊C8—21no—
75#10093—111nomaximal, Sylow
76C11×#41—44no—
77C2×Q8×C11—21no—
78C2×D4×C11—21no—
79C2×D4×C11—21no—
80C2×D4×C11—21no—
81C2×D4×C11—41no—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—41no—
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×Dic11—22no—
89C22×Dic11—22no—
90C2×Dic22—41no—
91C2×Dic22—41no—
92C2×Dic22—82no—
93C2×C8×C11—22no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C11×C22⋊C4—41no—
105C11×C22⋊C4—41no—
106C42×C11C2×D411yescharacteristic
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11#4111yescharacteristic
110C4⋊Dic11—22no—
111C4⋊Dic11—22no—
112C4⋊Dic11—41no—
113C4⋊Dic11—41no—
114Dic11⋊C4—84no—
115C4×Dic11—24no—
116#4318—42no—
117C2×C11⋊C8—22no—
118C2×C11⋊C8—41no—
119#3234D1111yescharacteristic
120#3141—111no—
121#2660—111no—
122#1556—111no—
123#1528—111no—
124#1505—111no—
125#1300—111no—
126C23×C11—41no—
127C23×C11#12011yescharacteristic
128Q8×C11—42no—
129D4×C11—42no—
130D4×C11—42no—
131D4×C11—81no—
132D4×C11—82no—
133C2×C4×C11—22no—
134C2×C4×C11—22no—
135C2×C4×C11—41no—
136C2×C4×C11—42no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—42no—
141C2×C4×C11—82no—
142C2×C4×C11#12011yescharacteristic
143C2×C4×C11#12011yescharacteristic
144C2×C4×C11#12111yescharacteristic
145C2×C4×C11#12111yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12711yescharacteristic
148C2×Dic11—24no—
149C2×Dic11—42no—
150C2×Dic11—42no—
151C2×Dic11—44no—
152C2×Dic11—42no—
153Dic22—82no—
154Dic22—82no—
155C8×C11—42no—
156C11⋊C8—42no—
157C11⋊C8—81no—
158#532C2×D1111yescharacteristic
159C2×C4⋊Q8—111no—
160C2×#125C2×D1111yescharacteristic
161#501—21no—
162#490—21no—
163#489—222no—
164#487—221no—
165#486—221no—
166#481—21no—
167#480—21no—
168#478—22no—
169#432—111no—
170#432C2×D1111yescharacteristic
171#417—222no—
172C4×M16—111no—
173#398—222no—
174#395—222no—
175#384—221no—
176#382—221no—
177#376—111no—
178#332—222no—
179#330—222no—
180#327—222no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11—81no—
184C22×C11—81no—
185C22×C11—81no—
186C22×C11#39211yescharacteristic
187C22×C11#45412yes—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—81no—
194C4×C11—81no—
195C4×C11—81no—
196C4×C11#45612yes—
197Dic11—44no—
198Dic11—82no—
199C2×#41—21no—
200C22×Q8—221no—
201C2×M16—221no—
202C4⋊Q8—221no—
203C4⋊Q8—221no—
204C4⋊Q8—221no—
205C4⋊Q8—221no—
206C4⋊Q8C22⋊D1111yescharacteristic
207#127C22⋊D1111yescharacteristic
208#125—21no—
209#125—21no—
210#125—21no—
211#125—21no—
212#124—21no—
213#121—21no—
214#121—21no—
215C4×D4—21no—
216C4×D4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—112no—
220C2×C4⋊C4—221no—
221C2×C4⋊C4—224no—
222C2×C4⋊C4C22⋊D1111yescharacteristic
223C2×C4⋊C4C22⋊D1111yescharacteristic
224C2×C42—221no—
225C2×C42C22×D1111yescharacteristic
226#107—22no—
227#106—22no—
228C4⋊C8—221no—
229C4⋊C8C22⋊D1112yes—
230#103—224no—
231#102—22no—
232#102—22no—
233#102—224no—
234C22⋊C8—21no—
235C22⋊C8—221no—
236#97—21no—
237#97—112no—
238#97—221no—
239C4×C8—221no—
240#95—112no—
241#95—224no—
242#95—221no—
243C2×C11—22no—
244C2×C11—161no—
245C2×C11#200311yescharacteristic
246C2×C11#200511yescharacteristic
247C2×C11#200811yescharacteristic
248#41—44no—
249C2×Q8—21no—
250C2×Q8—441no—
251C2×Q8—441no—
252C2×Q8—882no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4—21no—
256C2×D4—41no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—41no—
260C22×C4—222no—
261C22×C4—222no—
262C22×C4D4×D1111yescharacteristic
263C22×C4D4×D1111yescharacteristic
264C22×C4C2×C22⋊D1111yescharacteristic
265M16—442no—
266C2×C8—22no—
267C2×C8—222no—
268C2×C8—441no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—222no—
280C4⋊C4—222no—
281C4⋊C4—441no—
282C4⋊C4—441no—
283C4⋊C4—884no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C42—224no—
287C42D4×D1111yescharacteristic
288C42#434111yescharacteristic
289C42C2×C22⋊D1111yescharacteristic
290C42C2×C22⋊D1111yescharacteristic
291C11#1009311yescharacteristic, complemented, Sylow
292C23—41no—
293C23#6699011yescharacteristic
294Q8—42no—
295Q8—882no—
296Q8—882no—
297D4—42no—
298D4—42no—
299D4—81no—
300D4—82no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—41no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—82no—
310C2×C4—224no—
311C2×C4—442no—
312C2×C4—442no—
313C2×C4—444no—
314C2×C4—442no—
315C2×C4#6699011yescharacteristic
316C2×C4#6699111yescharacteristic
317C2×C4#6699211yescharacteristic
318C2×C4#6699211yescharacteristic
319C2×C4#6699311yescharacteristic
320C2×C4#6700611yescharacteristic
321C8—42no—
322C8—442no—
323C8—881no—
324C22—21no—
325C22—21no—
326C22—81no—
327C22—81no—
328C22—81no—
329C22#1062281412yes—
330C22#1062283611yescharacteristic
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—81no—
337C4—81no—
338C4—81no—
339C4—444no—
340C4—882no—
341C4#1062285912yes—
342C2—22no—
343C2—161no—
344C2#1306963511yescharacteristic
345C2#1306965011yescharacteristic
346C2#1306966611yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3234C2
socleC22×C11#392
prime radicalC11×#532C22
hypercenter#3234D11
hypocenterC11#10093
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3234

Complements

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

NH ≅ G/Ntype
2. #13074737C2semidirect
3. #13067332C2semidirect
4. #13067218C2semidirect
6. #13066508C2semidirect
291. C11#10093semidirect

Maximal subgroups

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

subgroupindex
#130790092
#130747372
#130673322
#130672182
#130671242
#130665082
C11×#32342
#1009311