Finite Group Databasebeta

← #14655905

Subgroups — #14655905

Order 2816.

528 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 103 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#13079933C211yesmaximal, characteristic
2#13079744C211yesmaximal, characteristic
3#13079158C211yesmaximal, characteristic, complemented
4#13069534C211yesmaximal, characteristic
5#13067114C211yesmaximal, characteristic, complemented
6#13066466C211yesmaximal, characteristic, complemented
7C11×#1981C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9#10623008C2211yescharacteristic
10#10623001C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×C11×#103—22no—
13C4×C11×C4⋊C4C2211yescharacteristic
14#10622727—22no—
15#10622701—21no—
16#10622697—22no—
17#10622693—22no—
18#10622692—21no—
19#10622692—21no—
20#10622691—21no—
21#10622581—22no—
22#10622577—22no—
23C2×#66869—22no—
24#10622538C2211yescharacteristic
25C4×#4318C2211yescharacteristic
26#10622464—21no—
27#10622461—21no—
28#10622455—21no—
29#10622454—21no—
30#10622090—22no—
31C22×Q8×C11—21no—
32C2×#4339—21no—
33C22×C8×C11D412yes—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8D412yes—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—21no—
41C2×C42×C11—21no—
42C2×C42×C11C2311yescharacteristic
43#66983—21no—
44#66983—21no—
45#66979—21no—
46#66977—21no—
47#66977—21no—
48C2×#4318D412yes—
49C2×#4314—22no—
50#66928—21no—
51#66927D411yescharacteristic
52C4×D44—21no—
53C4×D44—21no—
54#66923—21no—
55#66922D411yescharacteristic
56#66922D411yescharacteristic
57#66922D411yescharacteristic
58C4×Dic22—21no—
59C4×Dic22—21no—
60C11×C4⋊C8—21no—
61C11×C4⋊C8—21no—
62C11×#103—44no—
63C11×#95—21no—
64C22⋊(C11⋊C8)D412yes—
65#66885—22no—
66#66881—22no—
67#66880—22no—
68#66873—24no—
69#66872—24no—
70#66872—24no—
71#66871—24no—
72#66869—44no—
73C4⋊(C11⋊C8)—21no—
74#66867—21no—
75C4×C11⋊C8—21no—
76C4×C11⋊C8—21no—
77#10201—111nomaximal, Sylow
78C2×Q8×C11—22no—
79C2×Q8×C11—42no—
80C2×Q8×C11—42no—
81C2×Q8×C11—41no—
82C22×C4×C11—41no—
83C22×C4×C11—41no—
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C2×C22⋊D11—41no—
88#4339—42no—
89#4339—42no—
90C2×D44—21no—
91C2×D44—21no—
92C2×D44—21no—
93C2×C4×D11—41no—
94C2×Dic22—21no—
95C2×Dic22—21no—
96C2×Dic22—21no—
97C2×C8×C11—22no—
98C2×C8×C11—42no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C42×C11—42no—
106C42×C11C2×D411yescharacteristic
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11#4111yescharacteristic
110C22⋊Dic11—41no—
111(C2×D11)⋊C4—41no—
112(C2×D11)⋊C4—41no—
113C4⋊Dic11—21no—
114C4⋊Dic11—21no—
115C4⋊Dic11—21no—
116C4⋊Dic11—21no—
117C4⋊Dic11—21no—
118C4⋊Dic11—21no—
119Dic11⋊C4—41no—
120Dic11⋊C4—41no—
121C4×Dic11—41no—
122#4318—22no—
123#4318SD1614yescomplemented
124C2×C11⋊C8—22no—
125C2×C11⋊C8—22no—
126#4314—82no—
127#3246—111no—
128#3227—111no—
129#3165—111no—
130#1981D1111yescharacteristic, complemented
131#1980—111no—
132#1503—111no—
133#1283—111no—
134C23×C11#12711yescharacteristic
135C22×D11—41no—
136Q8×C11—44no—
137Q8×C11—81no—
138Q8×C11—81no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—41no—
142C2×C4×C11—42no—
143C2×C4×C11—42no—
144C2×C4×C11—81no—
145C2×C4×C11—82no—
146C2×C4×C11—81no—
147C2×C4×C11#12011yescharacteristic
148C2×C4×C11#12011yescharacteristic
149C2×C4×C11#12011yescharacteristic
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11C2×SD1612yes—
154C2×C4×C11#13712yes—
155C22⋊D11—81no—
156C22⋊D11—81no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160D44—42no—
161D44—41no—
162D44—41no—
163D44—42no—
164C4×D11—82no—
165Dic22—41no—
166Dic22—41no—
167Dic22—42no—
168Dic22—81no—
169C8×C11—42no—
170C11⋊C8—24no—
171C11⋊C8—42no—
172#533—111no—
173#532—111no—
174C2×C4⋊Q8C2×D1111yescharacteristic
175#501—222no—
176#500—221no—
177#498—221no—
178#498—221no—
179#486—221no—
180#481—222no—
181#476—221no—
182#476—222no—
183#475—221no—
184#465—222no—
185#461—221no—
186#460—221no—
187#431—111no—
188#428—222no—
189C2×C4⋊C8C2×D1111yescharacteristic
190C2×#104—222no—
191C2×#103—22no—
192C4×M16—111no—
193C4×C4⋊C4C2×D1111yescharacteristic
194#328—222no—
195C22×C11—21no—
196C22×C11—21no—
197C22×C11#39211yescharacteristic
198C22×C11#49211yescharacteristic
199C22×C11#49711yescharacteristic
200C2×D11—81no—
201C2×D11—81no—
202C2×D11—81no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—82no—
207C4×C11—82no—
208C4×C11#44812yes—
209C4×C11#45311yescharacteristic
210C4×C11#45411yescharacteristic
211C4×C11#46112yes—
212Dic11—81no—
213Dic11—81no—
214Dic11—81no—
215C2×#41—221no—
216C22×Q8—21no—
217C2×SD16—222no—
218C2×M16—112no—
219C22×C8C22⋊D1112yes—
220C4⋊Q8—21no—
221C4⋊Q8—21no—
222C4⋊Q8—21no—
223C4⋊Q8—111no—
224C4⋊Q8—111no—
225C4⋊Q8—111no—
226C4⋊Q8D4412yes—
227#127—111no—
228#125—221no—
229#124—221no—
230C22⋊Q8—221no—
231C22⋊Q8—221no—
232#121—221no—
233#121—221no—
234C4×Q8—221no—
235C4×Q8—221no—
236C4×D4—221no—
237C4×D4—221no—
238#117—221no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C42—21no—
243C2×C42C22×D1111yescharacteristic
244#107—224no—
245#106—224no—
246#106—224no—
247#106—222no—
248C4⋊C8—21no—
249C4⋊C8—21no—
250C4⋊C8—221no—
251#104—444no—
252#103—44no—
253#103—222no—
254#102—224no—
255#102—222no—
256C22⋊C8—112no—
257#97—221no—
258C4×C8—221no—
259C4×C8—221no—
260#95—21no—
261C2×C11—21no—
262C2×C11—21no—
263C2×C11#200611yescharacteristic
264C2×C11#200911yescharacteristic
265C2×C11#201311yescharacteristic
266D11—161no—
267#41—442no—
268#41—442no—
269C2×Q8—22no—
270C2×Q8—42no—
271C2×Q8—42no—
272C2×Q8—41no—
273C2×Q8—221no—
274C2×Q8—221no—
275C2×Q8—221no—
276C2×D4—221no—
277C2×D4—221no—
278C2×D4—221no—
279C2×D4—441no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—441no—
283C22×C4D4×D1111yescharacteristic
284C22×C4D4×D1111yescharacteristic
285C22×C4C2×C22⋊D1111yescharacteristic
286SD16—882no—
287M16—114no—
288M16—222no—
289C2×C8—22no—
290C2×C8—42no—
291C2×C8—222no—
292C2×C8—222no—
293C4⋊C4—22no—
294C4⋊C4—22no—
295C4⋊C4—22no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—221no—
300C4⋊C4—221no—
301C4⋊C4—221no—
302C4⋊C4—221no—
303C4⋊C4—221no—
304C4⋊C4—221no—
305C4⋊C4—441no—
306C4⋊C4—441no—
307C22⋊C4—441no—
308C22⋊C4—441no—
309C22⋊C4—441no—
310C42—42no—
311C42—441no—
312C42C2×D4411yescharacteristic
313C42#433911yescharacteristic
314C42D4×D1111yescharacteristic
315C42D4×D1111yescharacteristic
316C11#1020111yescharacteristic, complemented, Sylow
317C23—441no—
318C23#6699311yescharacteristic
319Q8—44no—
320Q8—81no—
321Q8—81no—
322Q8—441no—
323Q8—442no—
324Q8—441no—
325Q8—881no—
326D4—442no—
327D4—441no—
328D4—442no—
329D4—441no—
330D4—881no—
331D4—881no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—81no—
338C2×C4—82no—
339C2×C4—81no—
340C2×C4—441no—
341C2×C4—441no—
342C2×C4—441no—
343C2×C4—882no—
344C2×C4#6693511yescharacteristic
345C2×C4#6693511yescharacteristic
346C2×C4#6693711yescharacteristic
347C2×C4#6693711yescharacteristic
348C2×C4SD16×D1112yes—
349C2×C4#6697112yes—
350C2×C4#6698311yescharacteristic
351C2×C4#6699011yescharacteristic
352C8—42no—
353C8—224no—
354C8—442no—
355C22—21no—
356C22—21no—
357C22—881no—
358C22—881no—
359C22—881no—
360C22#1062257311yescharacteristic
361C22#1062278811yescharacteristic
362C22#1062280311yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—82no—
367C4—82no—
368C4—881no—
369C4—881no—
370C4—881no—
371C4#1062241912yes—
372C4#1062243112yes—
373C4#1062267511yescharacteristic
374C4#1062269011yescharacteristic
375C2—21no—
376C2—21no—
377C2—1761no—
378C2#1306965711yescharacteristic
379C2#1306967811yescharacteristic
380C2#1306970011yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1981C2
socleC22×C11#392
prime radical#10623008C22
hypercenter#1981D11
hypocenterC11#10201
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1981

Complements

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

NH ≅ G/Ntype
3. #13079158C2semidirect
5. #13067114C2semidirect
6. #13066466C2semidirect
7. C11×#1981C2semidirect
123. #4318SD16semidirect
130. #1981D11semidirect
316. C11#10201semidirect

Maximal subgroups

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

subgroupindex
#130799332
#130797442
#130791582
#130695342
#130671142
#130664662
C11×#19812
#1020111