Finite Group Databasebeta

← #14655134

Subgroups — #14655134

Order 2816.

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

normal subgroups only

This group has 560 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#13079076C211yesmaximal, characteristic
2#13074737C211yesmaximal, characteristic, complemented
3#13067341C211yesmaximal, characteristic, complemented
4#13067218C211yesmaximal, characteristic, complemented
5#13067124C211yesmaximal, characteristic
6#13066508C211yesmaximal, characteristic, complemented
7C11×#3234C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×C11×#125C2211yescharacteristic
10C2×#67004—22no—
11C2×#66922C2211yescharacteristic
12C11×#501—21no—
13C11×#490—21no—
14C11×#481—21no—
15C11×#480—21no—
16C11×#478—22no—
17C11×#432C2211yescharacteristic
18#10622705—21no—
19#10622689—21no—
20#10622673—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#10622119—22no—
31C2×C11×#41—21no—
32C22×Dic22D412yes—
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
49#67004—48no—
50C2×#4326—24no—
51C2×#4324—24no—
52C2×C4⋊Dic11—21no—
53C2×C4⋊Dic11—21no—
54C2×Dic11⋊C4—24no—
55C2×C4×Dic11—21no—
56C2×#4318—21no—
57#66922—21no—
58#66922—21no—
59#66922—21no—
60#66922—21no—
61C11×#107—22no—
62C11×#106—22no—
63C11×C4⋊C8D412yes—
64C11×#102—22no—
65C11×#102—22no—
66C11×C22⋊C8—21no—
67C11×#97—21no—
68C11⋊#95—24no—
69C11⋊#95—21no—
70C11⋊#95D412yes—
71C22⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)—21no—
73#66867—21no—
74#66867D412yes—
75C4×C11⋊C8—21no—
76#10091—111nomaximal, Sylow
77C11×#41—44no—
78C2×Q8×C11—21no—
79C2×D4×C11—21no—
80C2×D4×C11—21no—
81C2×D4×C11—21no—
82C2×D4×C11—41no—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—41no—
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×Dic11—22no—
90C22×Dic11—22no—
91C2×Dic22—22no—
92C2×Dic22—22no—
93C2×Dic22—44no—
94C2×C8×C11—22no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C11×C22⋊C4—41no—
106C11×C22⋊C4—41no—
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110C42×C11#4111yescharacteristic
111#4326—48no—
112#4324—48no—
113C4⋊Dic11—41no—
114C4⋊Dic11—41no—
115C4⋊Dic11—41no—
116C4⋊Dic11—41no—
117Dic11⋊C4—84no—
118C4×Dic11—24no—
119#4318—24no—
120C2×C11⋊C8—22no—
121C2×C11⋊C8—41no—
122#3234D1111yescharacteristic
123#3152—111no—
124#2660—111no—
125#1558—111no—
126#1528—111no—
127#1505—111no—
128#1300—111no—
129C23×C11—41no—
130C23×C11#12011yescharacteristic
131Q8×C11—42no—
132D4×C11—42no—
133D4×C11—42no—
134D4×C11—81no—
135D4×C11—82no—
136C2×C4×C11—22no—
137C2×C4×C11—22no—
138C2×C4×C11—41no—
139C2×C4×C11—42no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—42no—
144C2×C4×C11—82no—
145C2×C4×C11#12011yescharacteristic
146C2×C4×C11#12011yescharacteristic
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11#12111yescharacteristic
149C2×C4×C11#12111yescharacteristic
150C2×C4×C11#12711yescharacteristic
151C2×Dic11—24no—
152C2×Dic11—42no—
153C2×Dic11—42no—
154C2×Dic11—42no—
155C2×Dic11—44no—
156Dic22—44no—
157Dic22—82no—
158C8×C11—42no—
159C11⋊C8—24no—
160C11⋊C8—81no—
161C2×#137—222no—
162#532C2×D1111yescharacteristic
163C2×C4⋊Q8—111no—
164C2×#125C2×D1111yescharacteristic
165#501—21no—
166#497—222no—
167#494—221no—
168#492—221no—
169#490—21no—
170#481—21no—
171#480—21no—
172#478—22no—
173#432—111no—
174#432C2×D1111yescharacteristic
175C4×M16—111no—
176#398—222no—
177#395—222no—
178#384—221no—
179#382—221no—
180#376—111no—
181#333—222no—
182#330—222no—
183#327—222no—
184C22×C11—21no—
185C22×C11—21no—
186C22×C11—81no—
187C22×C11—81no—
188C22×C11—81no—
189C22×C11#39211yescharacteristic
190C22×C11#45312yes—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—81no—
197C4×C11—81no—
198C4×C11—81no—
199C4×C11#45612yes—
200Dic11—44no—
201Dic11—82no—
202C2×#41—21no—
203C22×Q8—112no—
204#137—448no—
205C2×Q16—224no—
206C2×SD16—224no—
207C2×M16—221no—
208C4⋊Q8—221no—
209C4⋊Q8—221no—
210C4⋊Q8—221no—
211C4⋊Q8—221no—
212C4⋊Q8C22⋊D1111yescharacteristic
213#127C22⋊D1111yescharacteristic
214#125—21no—
215#125—21no—
216#125—21no—
217#125—21no—
218#124—21no—
219#121—21no—
220#121—21no—
221C4×D4—21no—
222C4×D4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—221no—
226C2×C4⋊C4—221no—
227C2×C4⋊C4—224no—
228C2×C4⋊C4C22⋊D1111yescharacteristic
229C2×C4⋊C4C22⋊D1111yescharacteristic
230C2×C42—221no—
231C2×C42C22×D1111yescharacteristic
232#107—22no—
233#106—22no—
234C4⋊C8—221no—
235C4⋊C8C22⋊D1112yes—
236#102—22no—
237#102—22no—
238C22⋊C8—21no—
239C22⋊C8—221no—
240#97—21no—
241#97—112no—
242#97—221no—
243C4×C8—221no—
244#95—112no—
245#95—224no—
246#95—221no—
247C2×C11—22no—
248C2×C11—161no—
249C2×C11#200211yescharacteristic
250C2×C11#200511yescharacteristic
251C2×C11#200911yescharacteristic
252#41—44no—
253C2×Q8—21no—
254C2×Q8—222no—
255C2×Q8—222no—
256C2×Q8—444no—
257C2×D4—21no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—41no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—41no—
264C22×C4—222no—
265C22×C4—222no—
266C22×C4D4×D1111yescharacteristic
267C22×C4D4×D1111yescharacteristic
268C22×C4C2×C22⋊D1111yescharacteristic
269Q16—448no—
270SD16—448no—
271M16—224no—
272C2×C8—22no—
273C2×C8—222no—
274C2×C8—441no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—441no—
286C4⋊C4—441no—
287C4⋊C4—441no—
288C4⋊C4—441no—
289C4⋊C4—884no—
290C22⋊C4—41no—
291C22⋊C4—41no—
292C42—224no—
293C42D4×D1111yescharacteristic
294C42#434111yescharacteristic
295C42C2×C22⋊D1111yescharacteristic
296C42C2×C22⋊D1111yescharacteristic
297C11#1009111yescharacteristic, complemented, Sylow
298C23—41no—
299C23#6699011yescharacteristic
300Q8—42no—
301Q8—444no—
302Q8—882no—
303D4—42no—
304D4—42no—
305D4—81no—
306D4—82no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—82no—
316C2×C4—224no—
317C2×C4—442no—
318C2×C4—442no—
319C2×C4—444no—
320C2×C4—442no—
321C2×C4#6699011yescharacteristic
322C2×C4#6699111yescharacteristic
323C2×C4#6699211yescharacteristic
324C2×C4#6699211yescharacteristic
325C2×C4#6699311yescharacteristic
326C2×C4#6700611yescharacteristic
327C8—42no—
328C8—224no—
329C8—881no—
330C22—21no—
331C22—21no—
332C22—81no—
333C22—81no—
334C22—81no—
335C22#1062281112yes—
336C22#1062283611yescharacteristic
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—81no—
343C4—81no—
344C4—81no—
345C4—444no—
346C4—882no—
347C4#1062285912yes—
348C2—22no—
349C2—161no—
350C2#1306962811yescharacteristic
351C2#1306965011yescharacteristic
352C2#1306967311yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3234C2
socleC22×C11#392
prime radicalC11×#532C22
hypercenter#3234D11
hypocenterC11#10091
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. #13067341C2semidirect
4. #13067218C2semidirect
6. #13066508C2semidirect
297. C11#10091semidirect

Maximal subgroups

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

subgroupindex
#130790762
#130747372
#130673412
#130672182
#130671242
#130665082
C11×#32342
#1009111