Finite Group Databasebeta

← #14648155

Subgroups — #14648155

Order 2816.

396 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 105 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#13071801C211yesmaximal, characteristic
2#13069584C211yesmaximal, characteristic
3#13068751C211yesmaximal, characteristic
4C2×#10622103C211yesmaximal, characteristic
5#13066498C211yesmaximal, characteristic
6#13066497C211yesmaximal, characteristic
7C11×#1836C211yesmaximal, characteristic
8C2×#66923C2211yescharacteristic
9C2×C11×#97C2211yescharacteristic
10C11×#384C2211yescharacteristic
11C11×#382C2211yescharacteristic
12#10622591—21no—
13#10622585—21no—
14#10622549C2211yescharacteristic
15C2×#66867C2211yescharacteristic
16C2×#66867C2211yescharacteristic
17#10622268—21no—
18#10622267—21no—
19#10622266—21no—
20#10622260—21no—
21C11×#340—21no—
22C11×#340—21no—
23#10622167—21no—
24#10622167—21no—
25#10622167—21no—
26#10622167—21no—
27#10622103C414yescomplemented
28C22×C8×C11—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C42×C11C2311yescharacteristic
35C2×C4⋊Dic11D411yescharacteristic
36C2×C4⋊Dic11D411yescharacteristic
37C2×C4⋊Dic11D411yescharacteristic
38C2×C4⋊Dic11D411yescharacteristic
39C2×Dic11⋊C4—21no—
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×C4×Dic11—21no—
44C2×C4×Dic11—21no—
45C22×C11⋊C8—21no—
46C22×C11⋊C8—21no—
47#66923—21no—
48#66923—21no—
49#66923C2×C412yes—
50#66923Q812yes—
51C11×#97—21no—
52C11×#97C2×C412yes—
53C11×#95—21no—
54C11×#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61#66867—21no—
62#66867—21no—
63#66867—21no—
64#66867C2×C412yes—
65#8915—111nomaximal, Sylow
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—41no—
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×Dic11—21no—
73C22×Dic11—21no—
74C22×Dic11—21no—
75C22×Dic11—21no—
76C2×C8×C11—22no—
77C2×C8×C11—41no—
78C2×C8×C11—41no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—42no—
82C11×C4⋊C4—42no—
83C11×C4⋊C4—42no—
84C42×C11C22×C411yescharacteristic
85C42×C11C2×Q811yescharacteristic
86C42×C11#4111yescharacteristic
87C42×C11#4111yescharacteristic
88C4⋊Dic11—21no—
89C4⋊Dic11—21no—
90C4⋊Dic11—41no—
91C4⋊Dic11—41no—
92C4⋊Dic11C4⋊C412yes—
93C4⋊Dic11C4⋊C412yes—
94Dic11⋊C4—22no—
95Dic11⋊C4—22no—
96Dic11⋊C4—22no—
97Dic11⋊C4—22no—
98Dic11⋊C4—81no—
99Dic11⋊C4—81no—
100C4×Dic11—81no—
101C4×Dic11—81no—
102C2×C11⋊C8—22no—
103C2×C11⋊C8—22no—
104C2×C11⋊C8—41no—
105C2×C11⋊C8—41no—
106C2×C11⋊C8—41no—
107C2×C11⋊C8—41no—
108#2382—111no—
109#1992—111no—
110#1836—111no—
111#1836D1111yescharacteristic
112C2×#330—111no—
113#1295—111no—
114#1295—111no—
115C23×C11#12011yescharacteristic
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—81no—
129C2×C4×C11—81no—
130C2×C4×C11—81no—
131C2×C4×C11C2×C4⋊C411yescharacteristic
132C2×C4×C11C4×D411yescharacteristic
133C2×C4×C11C4×D411yescharacteristic
134C2×C4×C11C22⋊Q811yescharacteristic
135C2×C4×C11C22⋊Q811yescharacteristic
136C2×C4×C11#12311yescharacteristic
137C2×Dic11—22no—
138C2×Dic11—22no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C8×C11—42no—
150C11⋊C8—42no—
151C11⋊C8—42no—
152C2×#125—111no—
153C2×#97—111no—
154C2×#97—111no—
155C2×#97C2×D1111yescharacteristic
156#389—221no—
157#389—221no—
158#387—221no—
159#387—221no—
160#387—221no—
161#387—221no—
162#384C2×D1111yescharacteristic
163#382—111no—
164#382C2×D1111yescharacteristic
165#340—21no—
166#340—21no—
167#340—221no—
168#340—221no—
169#340—221no—
170#340—221no—
171#330—114no—
172C22×C11#38511yescharacteristic
173C22×C11#45411yescharacteristic
174C22×C11#45411yescharacteristic
175C22×C11#45411yescharacteristic
176C22×C11#45511yescharacteristic
177C22×C11#45511yescharacteristic
178C22×C11#45611yescharacteristic
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—81no—
186C4×C11—81no—
187C4×C11—161no—
188Dic11—42no—
189Dic11—42no—
190Dic11—81no—
191Dic11—81no—
192C22×C8—21no—
193C22×C8—221no—
194C22×C8—221no—
195#125—112no—
196#125—112no—
197#125—221no—
198#125—221no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—111no—
203C2×C4⋊C4—111no—
204C2×C4⋊C4—111no—
205C2×C4⋊C4—111no—
206C2×C4⋊C4—221no—
207C2×C4⋊C4—221no—
208C2×C4⋊C4—221no—
209C2×C4⋊C4—221no—
210C2×C4⋊C4C22⋊D1111yescharacteristic
211C2×C4⋊C4C22⋊D1111yescharacteristic
212C2×C42—221no—
213C2×C42—221no—
214C2×C42C22×D1111yescharacteristic
215#97—21no—
216#97—112no—
217#97—221no—
218#97—221no—
219#97—221no—
220#97C4×D1112yes—
221#95—21no—
222#95—21no—
223#95—221no—
224#95—221no—
225#95—221no—
226#95—221no—
227#95—221no—
228#95—221no—
229C2×C11#165811yescharacteristic
230C2×C11#166211yescharacteristic
231C2×C11#166411yescharacteristic
232C2×C11#166411yescharacteristic
233C2×C11#185711yescharacteristic
234C2×C11#186011yescharacteristic
235C2×C11#186011yescharacteristic
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—41no—
239C22×C4—221no—
240C22×C4—221no—
241C22×C4—221no—
242C22×C4—221no—
243C22×C4D4×D1111yescharacteristic
244C22×C4D4×D1111yescharacteristic
245C22×C4C2×C22⋊D1111yescharacteristic
246C2×C8—22no—
247C2×C8—41no—
248C2×C8—41no—
249C2×C8—222no—
250C2×C8—222no—
251C2×C8—441no—
252C2×C8—441no—
253C2×C8—441no—
254C2×C8—441no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—42no—
258C4⋊C4—42no—
259C4⋊C4—42no—
260C4⋊C4—112no—
261C4⋊C4—112no—
262C4⋊C4—222no—
263C4⋊C4—221no—
264C4⋊C4—221no—
265C4⋊C4—222no—
266C4⋊C4—222no—
267C4⋊C4—222no—
268C4⋊C4—441no—
269C4⋊C4—441no—
270C4⋊C4—881no—
271C4⋊C4—881no—
272C42—881no—
273C42—881no—
274C42C2×C4×D1111yescharacteristic
275C42#433911yescharacteristic
276C42Q8×D1111yescharacteristic
277C42#434311yescharacteristic
278C11#891511yescharacteristic, complemented, Sylow
279C23#6699011yescharacteristic
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—81no—
293C2×C4—81no—
294C2×C4—81no—
295C2×C4—222no—
296C2×C4—222no—
297C2×C4—441no—
298C2×C4—441no—
299C2×C4—441no—
300C2×C4—441no—
301C2×C4—441no—
302C2×C4—441no—
303C2×C4—441no—
304C2×C4—441no—
305C2×C4—441no—
306C2×C4—441no—
307C2×C4C4⋊C4×D1111yescharacteristic
308C2×C4#6694611yescharacteristic
309C2×C4#6694711yescharacteristic
310C2×C4#6694911yescharacteristic
311C2×C4C4×C22⋊D1111yescharacteristic
312C2×C4#6699911yescharacteristic
313C8—42no—
314C8—442no—
315C8—442no—
316C22#1062260211yescharacteristic
317C22#1062267411yescharacteristic
318C22#1062267511yescharacteristic
319C22#1062281411yescharacteristic
320C22#1062281411yescharacteristic
321C22#1062281511yescharacteristic
322C22#1062281811yescharacteristic
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—81no—
330C4—81no—
331C4—161no—
332C4—442no—
333C4—442no—
334C4—881no—
335C4—881no—
336C2#1306791711yescharacteristic
337C2#1306793811yescharacteristic
338C2#1306794711yescharacteristic
339C2#1306794911yescharacteristic
340C2#1306882911yescharacteristic
341C2#1306884611yescharacteristic
342C2#1306884811yescharacteristic
subgroupG/H
centerC23#66990
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1836C2
socle, prime radicalC23×C11#120
cosocleC2×C42×C11C23
hypercenter#1836D11
hypocenterC11#8915
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1836

Complements

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

NH ≅ G/Ntype
27. #10622103C4semidirect
278. C11#8915semidirect

Maximal subgroups

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

subgroupindex
#130718012
#130695842
#130687512
C2×#106221032
#130664982
#130664972
C11×#18362
#891511