Finite Group Databasebeta

← #14655464

Subgroups — #14655464

Order 2816.

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

normal subgroups only

This group has 468 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#13079808C211yesmaximal, characteristic
2#13079541C211yesmaximal, characteristic
3C2×#10622693C211yesmaximal, characteristic, complemented
4#13067228C211yesmaximal, characteristic
5#13066973C211yesmaximal, characteristic, complemented
6#13066514C211yesmaximal, characteristic, complemented
7C11×#1556C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9#10623008C2211yescharacteristic
10C2×#66923C2211yescharacteristic
11C11×#432C2211yescharacteristic
12C11×#432C2211yescharacteristic
13#10622840—22no—
14#10622698—21no—
15#10622696—22no—
16#10622694—21no—
17#10622693—22no—
18#10622693—22no—
19C2×#66872—21no—
20C2×#66871—21no—
21#10622538C2211yescharacteristic
22C2×#66867C2211yescharacteristic
23#10622460—22no—
24#10622349—21no—
25#10622348—21no—
26#10622326—21no—
27#10622315—21no—
28C11×#332—22no—
29#10622107—22no—
30#10622102—22no—
31C22×Q8×C11—21no—
32C2×#4339—21no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8D412yes—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—21no—
39C2×C42×C11C2311yescharacteristic
40C2×#4325—24no—
41#66983—21no—
42#66983—21no—
43C2×C4⋊Dic11D411yescharacteristic
44C2×C4⋊Dic11D411yescharacteristic
45C2×Dic11⋊C4—21no—
46C2×Dic11⋊C4—21no—
47C22×C11⋊C8—21no—
48#66928—21no—
49#66927D411yescharacteristic
50C4×D44—21no—
51C4×D44—21no—
52#66923—21no—
53#66923—21no—
54#66923—21no—
55#66923—21no—
56#66922D411yescharacteristic
57C11×C4⋊C8—21no—
58C11×C4⋊C8D412yes—
59C11×C22⋊C8—21no—
60C11×C22⋊C8—21no—
61C11×#97—21no—
62C11×#97—21no—
63#66899—24no—
64C22⋊(C11⋊C8)D412yes—
65#66885—22no—
66#66885—22no—
67#66882—22no—
68#66881—22no—
69#66872—24no—
70#66871—24no—
71C4⋊(C11⋊C8)—21no—
72#66867—21no—
73#66867D412yes—
74C4×C11⋊C8—21no—
75#10138—111nomaximal, Sylow
76C2×Q8×C11—22no—
77C2×Q8×C11—41no—
78C2×Q8×C11—82no—
79C22×C4×C11—41no—
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11#4111yescharacteristic
83C2×C22⋊D11—41no—
84C22×Dic11—21no—
85C22×Dic11—21no—
86#4339—82no—
87C2×D44—21no—
88C2×D44—21no—
89C2×D44—21no—
90C2×C4×D11—41no—
91C2×Dic22—21no—
92C2×C8×C11—22no—
93C2×C8×C11—41no—
94C11×C4⋊C4—22no—
95C11×C4⋊C4—22no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C42×C11C2×D411yescharacteristic
99C42×C11C2×D411yescharacteristic
100C42×C11C2×D411yescharacteristic
101C42×C11C2×D411yescharacteristic
102#4325—84no—
103(C2×D11)⋊C4—41no—
104(C2×D11)⋊C4—41no—
105C4⋊Dic11—21no—
106C4⋊Dic11—21no—
107C4⋊Dic11—21no—
108C4⋊Dic11—21no—
109C4⋊Dic11—21no—
110C4⋊Dic11—21no—
111Dic11⋊C4—41no—
112Dic11⋊C4—41no—
113Dic11⋊C4—41no—
114Dic11⋊C4—41no—
115C2×C11⋊C8—24no—
116C2×C11⋊C8—22no—
117C2×C11⋊C8—22no—
118#3234—111no—
119#3206—111no—
120C2×#501—111no—
121#1556D1111yescharacteristic, complemented
122#1530—111no—
123#1470—111no—
124#1302—111no—
125C23×C11#12111yescharacteristic
126C22×D11—41no—
127Q8×C11—44no—
128Q8×C11—82no—
129C2×C4×C11—22no—
130C2×C4×C11—22no—
131C2×C4×C11—41no—
132C2×C4×C11—42no—
133C2×C4×C11—82no—
134C2×C4×C11#12011yescharacteristic
135C2×C4×C11#12011yescharacteristic
136C2×C4×C11#12011yescharacteristic
137C2×C4×C11#12111yescharacteristic
138C2×C4×C11#12111yescharacteristic
139C2×C4×C11#12711yescharacteristic
140C22⋊D11—82no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—42no—
145C2×Dic11—81no—
146D44—42no—
147D44—42no—
148D44—81no—
149C4×D11—82no—
150Dic22—81no—
151C8×C11—42no—
152C8×C11—81no—
153C11⋊C8—24no—
154C11⋊C8—42no—
155#532—111no—
156C2×C4⋊Q8C2×D1111yescharacteristic
157C2×#125—111no—
158#501—221no—
159#501—222no—
160#501—222no—
161#492—221no—
162#490—221no—
163#487—221no—
164#481—221no—
165#480—221no—
166#478—222no—
167#461—222no—
168#448—222no—
169#432C2×D1111yescharacteristic
170#432C2×D1111yescharacteristic
171#431—111no—
172C2×#107—221no—
173C2×#106—221no—
174C2×#97—111no—
175#332—22no—
176#329—222no—
177#324—222no—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11#39211yescharacteristic
181C22×C11#47112yes—
182C2×D11—81no—
183C2×D11—81no—
184C2×D11—81no—
185C4×C11—21no—
186C4×C11—21no—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—82no—
191C4×C11#45612yes—
192Dic11—81no—
193Dic11—81no—
194Dic11—81no—
195C2×#41—221no—
196C22×Q8—21no—
197C2×SD16—224no—
198C22×C8—221no—
199C4⋊Q8—21no—
200C4⋊Q8—21no—
201C4⋊Q8—21no—
202C4⋊Q8—111no—
203C4⋊Q8D4412yes—
204#127—111no—
205#125—221no—
206#125—221no—
207#125—221no—
208#125—221no—
209#124—221no—
210#121—221no—
211#121—221no—
212C4×D4—221no—
213C4×D4—221no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—111no—
217C2×C4⋊C4—111no—
218C2×C4⋊C4—221no—
219C2×C4⋊C4—221no—
220C2×C42C22×D1111yescharacteristic
221#107—224no—
222#107—222no—
223#106—224no—
224#106—222no—
225C4⋊C8—21no—
226C4⋊C8—221no—
227C4⋊C8C22⋊D1112yes—
228#103—224no—
229#102—222no—
230#102—222no—
231C22⋊C8—21no—
232C22⋊C8—21no—
233C22⋊C8—112no—
234#97—21no—
235#97—21no—
236#97—112no—
237#97—221no—
238C4×C8—221no—
239C2×C11—22no—
240C2×C11#200511yescharacteristic
241C2×C11#200811yescharacteristic
242C2×C11#201911yescharacteristic
243D11—161no—
244#41—882no—
245C2×Q8—22no—
246C2×Q8—41no—
247C2×Q8—82no—
248C2×Q8—221no—
249C2×D4—221no—
250C2×D4—221no—
251C2×D4—221no—
252C2×D4—441no—
253C22×C4—41no—
254C22×C4—221no—
255C22×C4—221no—
256C22×C4—441no—
257C22×C4#433911yescharacteristic
258C22×C4D4×D1111yescharacteristic
259C22×C4D4×D1111yescharacteristic
260SD16—884no—
261C2×C8—22no—
262C2×C8—41no—
263C2×C8—224no—
264C2×C8—222no—
265C2×C8—222no—
266C4⋊C4—22no—
267C4⋊C4—22no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—221no—
271C4⋊C4—221no—
272C4⋊C4—221no—
273C4⋊C4—221no—
274C4⋊C4—221no—
275C4⋊C4—221no—
276C4⋊C4—441no—
277C4⋊C4—441no—
278C4⋊C4—441no—
279C4⋊C4—441no—
280C22⋊C4—441no—
281C22⋊C4—441no—
282C42C2×D4411yescharacteristic
283C42D4×D1111yescharacteristic
284C42D4×D1111yescharacteristic
285C42C2×C22⋊D1111yescharacteristic
286C11#1013811yescharacteristic, complemented, Sylow
287C23—441no—
288C23#6693711yescharacteristic
289Q8—44no—
290Q8—82no—
291Q8—881no—
292D4—442no—
293D4—442no—
294D4—881no—
295D4—882no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—82no—
301C2×C4—441no—
302C2×C4—441no—
303C2×C4—441no—
304C2×C4—442no—
305C2×C4—882no—
306C2×C4—881no—
307C2×C4#6693511yescharacteristic
308C2×C4#6693511yescharacteristic
309C2×C4#6693711yescharacteristic
310C2×C4#6698311yescharacteristic
311C2×C4#6699011yescharacteristic
312C2×C4#6699311yescharacteristic
313C8—42no—
314C8—81no—
315C8—224no—
316C8—442no—
317C22—21no—
318C22—21no—
319C22—881no—
320C22—881no—
321C22—881no—
322C22#1062236712yes—
323C22#1062257311yescharacteristic
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—82no—
330C4—881no—
331C4—881no—
332C4—881no—
333C4#1062281812yes—
334C2—22no—
335C2—1761no—
336C2#1306965311yescharacteristic
337C2#1306967111yescharacteristic
338C2#1306972911yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1556C2
socleC22×C11#392
prime radical#10623008C22
hypercenter#1556D11
hypocenterC11#10138
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1556

Complements

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

NH ≅ G/Ntype
3. C2×#10622693C2semidirect
5. #13066973C2semidirect
6. #13066514C2semidirect
7. C11×#1556C2semidirect
121. #1556D11semidirect
286. C11#10138semidirect

Maximal subgroups

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

subgroupindex
#130798082
#130795412
C2×#106226932
#130672282
#130669732
#130665142
C11×#15562
#1013811