Finite Group Databasebeta

← #14655879

Subgroups — #14655879

Order 2816.

524 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 107 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#13079932C211yesmaximal, characteristic
2#13079538C211yesmaximal, characteristic
3#13079162C211yesmaximal, characteristic, complemented
4#13069564C211yesmaximal, characteristic, complemented
5#13067114C211yesmaximal, characteristic, complemented
6#13066467C211yesmaximal, characteristic, complemented
7C11×#1980C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9#10623001C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C2×C11×#104—22no—
12C4×C11×M16C2211yescharacteristic
13C4×C11×C4⋊C4C2211yescharacteristic
14#10622734—22no—
15#10622707—21no—
16#10622706—21no—
17#10622689—21no—
18#10622688—21no—
19#10622654—22no—
20#10622653—22no—
21#10622632—21no—
22#10622632—22no—
23#10622621—21no—
24#10622538C2211yescharacteristic
25C2×C4⋊(C11⋊C8)C2211yescharacteristic
26#10622315—22no—
27#10622295—21no—
28#10622293—21no—
29#10622167—22no—
30#10622090—22no—
31C2×C11×#41—21no—
32C22×Dic22—21no—
33C2×C11×M16D412yes—
34C11×C4⋊Q8D411yescharacteristic
35C11×#127D411yescharacteristic
36C11×#124—21no—
37C11×#121—21no—
38C11×#121—21no—
39C4×D4×C11—21no—
40C4×D4×C11—21no—
41C2×C11×C4⋊C4—21no—
42C2×C42×C11—21no—
43C2×C42×C11C2311yescharacteristic
44C2×#4324—24no—
45C2×#4324—22no—
46#66979—21no—
47C2×C4⋊Dic11—21no—
48C2×C4⋊Dic11—21no—
49#66977—21no—
50#66977—21no—
51C22×C11⋊C8D412yes—
52#66923—21no—
53#66922—21no—
54#66922—21no—
55#66922—21no—
56#66922D412yes—
57#66922D411yescharacteristic
58#66922D411yescharacteristic
59C4×Dic22—21no—
60C4×Dic22—21no—
61C11×#104—44no—
62C11×#97—21no—
63C4×C8×C11—21no—
64C11×#95—21no—
65#66896—22no—
66C22⋊(C11⋊C8)D412yes—
67#66882—24no—
68#66881—24no—
69#66874—24no—
70#66874—22no—
71#66872—22no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)—21no—
75C4×C11⋊C8—21no—
76#10197—111nomaximal, Sylow
77C11×#41—42no—
78C11×#41—42no—
79C2×Q8×C11—21no—
80C2×D4×C11—21no—
81C2×D4×C11—21no—
82C2×D4×C11—21no—
83C2×D4×C11—41no—
84C22×C4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×Dic11—41no—
90C2×Dic22—21no—
91C2×Dic22—22no—
92C2×Dic22—21no—
93C2×Dic22—41no—
94C2×Dic22—82no—
95C11×M16—22no—
96C11×M16SD1614yescomplemented
97C2×C8×C11—22no—
98C11×C4⋊C4—22no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—41no—
102C11×C22⋊C4—41no—
103C11×C22⋊C4—41no—
104C42×C11—42no—
105C42×C11C2×D411yescharacteristic
106C42×C11C2×D411yescharacteristic
107C42×C11C2×D411yescharacteristic
108C42×C11#4111yescharacteristic
109C22⋊Dic11—41no—
110#4324—84no—
111#4324—82no—
112C4⋊Dic11—21no—
113C4⋊Dic11—21no—
114C4⋊Dic11—22no—
115C4⋊Dic11—21no—
116C4⋊Dic11—21no—
117C4⋊Dic11—22no—
118C4⋊Dic11—41no—
119C4⋊Dic11—41no—
120Dic11⋊C4—41no—
121Dic11⋊C4—41no—
122C4×Dic11—41no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—42no—
126#3246—111no—
127#3206—111no—
128#3165—111no—
129#1987—111no—
130#1980D1111yescharacteristic
131#1503—111no—
132#1283—111no—
133C23×C11—41no—
134C23×C11#12711yescharacteristic
135Q8×C11—42no—
136D4×C11—42no—
137D4×C11—41no—
138D4×C11—41no—
139D4×C11—42no—
140D4×C11—81no—
141D4×C11—81no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—41no—
145C2×C4×C11—42no—
146C2×C4×C11—41no—
147C2×C4×C11—81no—
148C2×C4×C11—81no—
149C2×C4×C11—82no—
150C2×C4×C11#12011yescharacteristic
151C2×C4×C11#12011yescharacteristic
152C2×C4×C11#12011yescharacteristic
153C2×C4×C11#12111yescharacteristic
154C2×C4×C11#12111yescharacteristic
155C2×C4×C11#12111yescharacteristic
156C2×C4×C11C2×SD1612yes—
157C2×C4×C11#13712yes—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—42no—
161C2×Dic11—82no—
162Dic22—44no—
163Dic22—41no—
164Dic22—41no—
165Dic22—82no—
166Dic22—81no—
167C8×C11—24no—
168C11⋊C8—42no—
169C11⋊C8—42no—
170#533—111no—
171#532C2×D1111yescharacteristic
172C2×C4⋊Q8—111no—
173#501—222no—
174#500—221no—
175#498—221no—
176#492—221no—
177#487—221no—
178#476—221no—
179#475—221no—
180#465—222no—
181#461—222no—
182#461—221no—
183#460—221no—
184#448—222no—
185#431—111no—
186#428—222no—
187C2×C4⋊C8—111no—
188C2×#104—22no—
189C4×M16C2×D1111yescharacteristic
190C4×C4⋊C4C2×D1111yescharacteristic
191#340—222no—
192#328—222no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—81no—
196C22×C11—81no—
197C22×C11—81no—
198C22×C11#39211yescharacteristic
199C22×C11#49211yescharacteristic
200C22×C11#49711yescharacteristic
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—82no—
205C4×C11—81no—
206C4×C11#44812yes—
207C4×C11#45511yescharacteristic
208C4×C11#45611yescharacteristic
209C4×C11#46112yes—
210Dic11—81no—
211Dic11—82no—
212Dic11—81no—
213C2×#41—21no—
214C22×Q8—221no—
215C2×SD16—224no—
216C2×SD16—222no—
217C2×M16C22⋊D1112yes—
218C22×C8—112no—
219C4⋊Q8—112no—
220C4⋊Q8—111no—
221C4⋊Q8—111no—
222C4⋊Q8—221no—
223C4⋊Q8—221no—
224C4⋊Q8—221no—
225C4⋊Q8D4411yescharacteristic
226#127D4411yescharacteristic
227#125—221no—
228#124—21no—
229C22⋊Q8—221no—
230C22⋊Q8—221no—
231#121—21no—
232#121—21no—
233C4×Q8—221no—
234C4×Q8—221no—
235C4×D4—21no—
236C4×D4—21no—
237#117—221no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—221no—
240C2×C4⋊C4—221no—
241C2×C42—21no—
242C2×C42C22×D1111yescharacteristic
243#107—224no—
244#106—222no—
245#106—224no—
246C4⋊C8—221no—
247C4⋊C8—221no—
248C4⋊C8—221no—
249#104—44no—
250#103—224no—
251#103—222no—
252#102—222no—
253C22⋊C8—112no—
254#97—21no—
255C4×C8—21no—
256C4×C8—221no—
257#95—21no—
258C2×C11—21no—
259C2×C11—21no—
260C2×C11—161no—
261C2×C11#200711yescharacteristic
262C2×C11#200811yescharacteristic
263C2×C11#201311yescharacteristic
264#41—42no—
265#41—42no—
266C2×Q8—21no—
267C2×Q8—221no—
268C2×Q8—222no—
269C2×Q8—221no—
270C2×Q8—441no—
271C2×Q8—882no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—41no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—441no—
279C22×C4D4×D1111yescharacteristic
280C22×C4D4×D1111yescharacteristic
281C22×C4C2×C22⋊D1111yescharacteristic
282SD16—884no—
283SD16—882no—
284M16—22no—
285M16#432414yescomplemented
286C2×C8—22no—
287C2×C8—222no—
288C2×C8—222no—
289C2×C8—442no—
290C4⋊C4—22no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—41no—
294C4⋊C4—221no—
295C4⋊C4—222no—
296C4⋊C4—221no—
297C4⋊C4—221no—
298C4⋊C4—222no—
299C4⋊C4—221no—
300C4⋊C4—441no—
301C4⋊C4—441no—
302C4⋊C4—441no—
303C4⋊C4—441no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—441no—
307C42—42no—
308C42—441no—
309C42C2×D4411yescharacteristic
310C42#433911yescharacteristic
311C42D4×D1111yescharacteristic
312C42D4×D1111yescharacteristic
313C11#1019711yescharacteristic, complemented, Sylow
314C23—41no—
315C23#6699311yescharacteristic
316Q8—42no—
317Q8—444no—
318Q8—441no—
319Q8—441no—
320Q8—881no—
321Q8—882no—
322D4—42no—
323D4—42no—
324D4—41no—
325D4—41no—
326D4—81no—
327D4—81no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—41no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—82no—
336C2×C4—441no—
337C2×C4—441no—
338C2×C4—442no—
339C2×C4—882no—
340C2×C4#6693511yescharacteristic
341C2×C4#6693511yescharacteristic
342C2×C4#6693711yescharacteristic
343C2×C4#6693711yescharacteristic
344C2×C4#6698311yescharacteristic
345C2×C4C2×#432412yes—
346C2×C4#6699011yescharacteristic
347C2×C4#6700412yes—
348C8—24no—
349C8—442no—
350C8—442no—
351C22—21no—
352C22—21no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22#1062257311yescharacteristic
357C22#1062267311yescharacteristic
358C22#1062268911yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—82no—
363C4—81no—
364C4—881no—
365C4—882no—
366C4—881no—
367C4#1062243811yescharacteristic
368C4#1062243911yescharacteristic
369C4#1062263212yes—
370C4#1062265312yes—
371C2—21no—
372C2—21no—
373C2—161no—
374C2#1306966411yescharacteristic
375C2#1306967011yescharacteristic
376C2#1306969811yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1980C2
socleC22×C11#392
prime radicalC11×#532C22
hypercenter#1980D11
hypocenterC11#10197
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1980

Complements

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

NH ≅ G/Ntype
3. #13079162C2semidirect
4. #13069564C2semidirect
5. #13067114C2semidirect
6. #13066467C2semidirect
96. C11×M16SD16semidirect
285. M16#4324semidirect
313. C11#10197semidirect

Maximal subgroups

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

subgroupindex
#130799322
#130795382
#130791622
#130695642
#130671142
#130664672
C11×#19802
#1019711