Finite Group Databasebeta

← #14655439

Subgroups — #14655439

Order 2816.

456 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 83 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#13079802C211yesmaximal, characteristic
2#13079741C211yesmaximal, characteristic
3C2×#10622316C211yesmaximal, characteristic, complemented
4#13067332C211yesmaximal, characteristic, complemented
5#13066973C211yesmaximal, characteristic, complemented
6#13066515C211yesmaximal, characteristic, complemented
7C11×#1530C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×#66923C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#432C2211yescharacteristic
12C2×C11×#97C2211yescharacteristic
13C2×#66880—21no—
14C2×#66880—21no—
15#10622693—21no—
16#10622692—21no—
17#10622684—21no—
18#10622683—21no—
19#10622647—21no—
20#10622647—22no—
21#10622646—21no—
22#10622622—22no—
23#10622621—22no—
24#10622539C2211yescharacteristic
25#10622538C2211yescharacteristic
26#10622316—22no—
27#10622316—22no—
28C11×#329—22no—
29#10622124—22no—
30#10622107—22no—
31C2×C11×#41—21no—
32C22×Dic22—21no—
33C22×C8×C11—21no—
34C11×C4⋊Q8D411yescharacteristic
35C11×#127D411yescharacteristic
36C11×#124—21no—
37C11×#121—21no—
38C11×#121—21no—
39C4×D4×C11—21no—
40C4×D4×C11—21no—
41C2×C42×C11C2311yescharacteristic
42C2×C4⋊Dic11—21no—
43C2×C4⋊Dic11—21no—
44C2×C4⋊Dic11D411yescharacteristic
45C2×C4⋊Dic11D411yescharacteristic
46C2×Dic11⋊C4—21no—
47C2×Dic11⋊C4—21no—
48#66923—21no—
49#66923—21no—
50#66923—21no—
51#66923—21no—
52#66922—21no—
53#66922—21no—
54#66922—21no—
55#66922D412yes—
56C11×C4⋊C8—21no—
57C11×C22⋊C8—21no—
58C11×#97—21no—
59C11×#97—21no—
60C11×#97D412yes—
61#66896—24no—
62#66896—22no—
63#66896—22no—
64C22⋊(C11⋊C8)—21no—
65C22⋊(C11⋊C8)D412yes—
66#66880—24no—
67#66880—24no—
68#66872—24no—
69#66872—22no—
70#66871—22no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)D412yes—
73#66867—21no—
74C4×C11⋊C8—21no—
75#10134—111nomaximal, Sylow
76C11×#41—82no—
77C2×Q8×C11—21no—
78C2×D4×C11—21no—
79C2×D4×C11—21no—
80C2×D4×C11—21no—
81C2×D4×C11—41no—
82C22×C4×C11—41no—
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11#4111yescharacteristic
86C22×Dic11—21no—
87C22×Dic11—21no—
88C22×Dic11—41no—
89C2×Dic22—22no—
90C2×Dic22—44no—
91C2×Dic22—41no—
92C2×C8×C11—22no—
93C2×C8×C11—42no—
94C2×C8×C11—41no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—21no—
97C11×C22⋊C4—41no—
98C11×C22⋊C4—41no—
99C42×C11C2×D411yescharacteristic
100C42×C11C2×D411yescharacteristic
101C42×C11C2×D411yescharacteristic
102C42×C11C2×D411yescharacteristic
103C4⋊Dic11—21no—
104C4⋊Dic11—22no—
105C4⋊Dic11—21no—
106C4⋊Dic11—21no—
107C4⋊Dic11—21no—
108C4⋊Dic11—22no—
109C4⋊Dic11—41no—
110C4⋊Dic11—41no—
111Dic11⋊C4—41no—
112Dic11⋊C4—41no—
113Dic11⋊C4—41no—
114Dic11⋊C4—41no—
115C2×C11⋊C8—22no—
116C2×C11⋊C8—22no—
117#3234—111no—
118#3227—111no—
119C2×#491—111no—
120#1556—111no—
121#1530D1111yescharacteristic
122#1470—111no—
123#1302—111no—
124C23×C11—41no—
125C23×C11#12111yescharacteristic
126Q8×C11—81no—
127D4×C11—42no—
128D4×C11—42no—
129D4×C11—81no—
130D4×C11—82no—
131C2×C4×C11—22no—
132C2×C4×C11—22no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—82no—
136C2×C4×C11#12011yescharacteristic
137C2×C4×C11#12011yescharacteristic
138C2×C4×C11#12011yescharacteristic
139C2×C4×C11#12111yescharacteristic
140C2×C4×C11#12111yescharacteristic
141C2×C4×C11#12711yescharacteristic
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—42no—
145C2×Dic11—42no—
146C2×Dic11—82no—
147C2×Dic11—81no—
148Dic22—44no—
149Dic22—82no—
150C8×C11—42no—
151C8×C11—81no—
152C11⋊C8—42no—
153C11⋊C8—42no—
154#532C2×D1111yescharacteristic
155C2×C4⋊Q8—111no—
156C2×#125—111no—
157#501—221no—
158#498—221no—
159#491—222no—
160#491—222no—
161#490—221no—
162#486—221no—
163#481—222no—
164#481—221no—
165#480—221no—
166#478—222no—
167#476—222no—
168#432—111no—
169#432C2×D1111yescharacteristic
170#431—111no—
171C2×#103—221no—
172C2×#103—221no—
173C2×#97C2×D1111yescharacteristic
174#332—222no—
175#329—22no—
176#324—222no—
177C22×C11—21no—
178C22×C11—21no—
179C22×C11—81no—
180C22×C11—81no—
181C22×C11—81no—
182C22×C11#39211yescharacteristic
183C22×C11#47112yes—
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—21no—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—81no—
190C4×C11#45412yes—
191Dic11—82no—
192Dic11—81no—
193Dic11—81no—
194C2×#41—21no—
195C22×Q8—221no—
196C22×C8—21no—
197C4⋊Q8—112no—
198C4⋊Q8—221no—
199C4⋊Q8—221no—
200C4⋊Q8—221no—
201C4⋊Q8D4411yescharacteristic
202#127D4411yescharacteristic
203#125—221no—
204#125—221no—
205#125—221no—
206#125—221no—
207#124—21no—
208#121—21no—
209#121—21no—
210C4×D4—21no—
211C4×D4—21no—
212C2×C4⋊C4—111no—
213C2×C4⋊C4—111no—
214C2×C4⋊C4—221no—
215C2×C4⋊C4—221no—
216C2×C4⋊C4—221no—
217C2×C4⋊C4—221no—
218C2×C42C22×D1111yescharacteristic
219#107—222no—
220#106—224no—
221#106—222no—
222C4⋊C8—21no—
223C4⋊C8—112no—
224C4⋊C8—221no—
225#103—224no—
226#103—224no—
227#102—224no—
228#102—222no—
229#102—222no—
230C22⋊C8—21no—
231C22⋊C8—112no—
232C22⋊C8—221no—
233#97—21no—
234#97—21no—
235#97—221no—
236#97C22⋊D1112yes—
237C4×C8—221no—
238C2×C11—22no—
239C2×C11—161no—
240C2×C11#200311yescharacteristic
241C2×C11#200911yescharacteristic
242C2×C11#201911yescharacteristic
243#41—82no—
244C2×Q8—21no—
245C2×Q8—222no—
246C2×Q8—444no—
247C2×Q8—441no—
248C2×D4—21no—
249C2×D4—21no—
250C2×D4—21no—
251C2×D4—41no—
252C22×C4—41no—
253C22×C4—221no—
254C22×C4—221no—
255C22×C4—441no—
256C22×C4#433911yescharacteristic
257C22×C4D4×D1111yescharacteristic
258C22×C4D4×D1111yescharacteristic
259C2×C8—22no—
260C2×C8—42no—
261C2×C8—41no—
262C2×C8—222no—
263C2×C8—222no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—221no—
267C4⋊C4—222no—
268C4⋊C4—221no—
269C4⋊C4—222no—
270C4⋊C4—221no—
271C4⋊C4—221no—
272C4⋊C4—441no—
273C4⋊C4—441no—
274C4⋊C4—441no—
275C4⋊C4—441no—
276C4⋊C4—441no—
277C4⋊C4—441no—
278C22⋊C4—41no—
279C22⋊C4—41no—
280C42C2×D4411yescharacteristic
281C42D4×D1111yescharacteristic
282C42D4×D1111yescharacteristic
283C42C2×C22⋊D1111yescharacteristic
284C11#1013411yescharacteristic, complemented, Sylow
285C23—41no—
286C23#6693711yescharacteristic
287Q8—81no—
288Q8—444no—
289Q8—882no—
290D4—42no—
291D4—42no—
292D4—81no—
293D4—82no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—82no—
299C2×C4—441no—
300C2×C4—441no—
301C2×C4—442no—
302C2×C4—442no—
303C2×C4—882no—
304C2×C4—881no—
305C2×C4#6693511yescharacteristic
306C2×C4#6693511yescharacteristic
307C2×C4#6693711yescharacteristic
308C2×C4#6698311yescharacteristic
309C2×C4#6699011yescharacteristic
310C2×C4#6699311yescharacteristic
311C8—42no—
312C8—81no—
313C8—442no—
314C8—442no—
315C22—21no—
316C22—21no—
317C22—81no—
318C22—81no—
319C22—81no—
320C22#1062236112yes—
321C22#1062257311yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—81no—
328C4—882no—
329C4—881no—
330C4—881no—
331C4#1062244012yes—
332C2—22no—
333C2—161no—
334C2#1306963711yescharacteristic
335C2#1306967711yescharacteristic
336C2#1306973211yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1530C2
socleC22×C11#392
prime radicalC11×#532C22
hypercenter#1530D11
hypocenterC11#10134
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1530

Complements

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

NH ≅ G/Ntype
3. C2×#10622316C2semidirect
4. #13067332C2semidirect
5. #13066973C2semidirect
6. #13066515C2semidirect
284. C11#10134semidirect

Maximal subgroups

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

subgroupindex
#130798022
#130797412
C2×#106223162
#130673322
#130669732
#130665152
C11×#15302
#1013411