Finite Group Databasebeta

← #14655466

Subgroups — #14655466

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#13079806C211yesmaximal, characteristic
2#13079543C211yesmaximal, characteristic
3C2×#10622678C211yesmaximal, characteristic, complemented
4#13067334C211yesmaximal, characteristic, complemented
5#13067228C211yesmaximal, characteristic
6#13066516C211yesmaximal, characteristic, complemented
7C11×#1470C211yesmaximal, characteristic, complemented
8C2×C11×#125C2211yescharacteristic
9#10623008C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#432C2211yescharacteristic
12C11×#431C2211yescharacteristic
13#10622680—21no—
14#10622679—22no—
15#10622678—22no—
16#10622678—21no—
17#10622678—22no—
18#10622581—21no—
19#10622580—21no—
20C2×#66872—21no—
21C2×#66871—21no—
22#10622539C2211yescharacteristic
23C2×#66867C2211yescharacteristic
24#10622454—22no—
25#10622351—22no—
26#10622306—21no—
27#10622294—21no—
28C11×#324—22no—
29#10622120—22no—
30#10622102—22no—
31C2×#4339—21no—
32C22×Dic22—21no—
33C11×#125—21no—
34C11×#125—21no—
35C11×#125—21no—
36C11×#125—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4D411yescharacteristic
40C2×C11×C4⋊C4D411yescharacteristic
41C2×C42×C11C2311yescharacteristic
42#66983—21no—
43#66983—21no—
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11—21no—
46C22×C11⋊C8—21no—
47C2×#4314—24no—
48#66928—21no—
49#66927D411yescharacteristic
50C4×D44—21no—
51C4×D44—21no—
52#66922—21no—
53#66922—21no—
54#66922—21no—
55#66922D412yes—
56#66922D411yescharacteristic
57C11×C4⋊C8—21no—
58C11×C4⋊C8—21no—
59C11×C22⋊C8—21no—
60C11×C22⋊C8D412yes—
61C11×#97—21no—
62C4×C8×C11—21no—
63C22⋊(C11⋊C8)—21no—
64#66880—24no—
65#66873—22no—
66#66873—22no—
67#66872—24no—
68#66872—22no—
69#66871—24no—
70#66871—22no—
71C4⋊(C11⋊C8)D412yes—
72#66867—21no—
73#66867—21no—
74#66867D412yes—
75#10138—111nomaximal, Sylow
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11#4111yescharacteristic
81C2×C22⋊D11—41no—
82C22×Dic11—41no—
83#4339—82no—
84C2×D44—21no—
85C2×D44—21no—
86C2×D44—21no—
87C2×C4×D11—41no—
88C2×Dic22—22no—
89C2×Dic22—21no—
90C2×Dic22—41no—
91C2×Dic22—82no—
92C2×C8×C11—22no—
93C2×C8×C11—41no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—41no—
102C42×C11C2×D411yescharacteristic
103C42×C11C2×D411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106(C2×D11)⋊C4—41no—
107(C2×D11)⋊C4—41no—
108C4⋊Dic11—22no—
109C4⋊Dic11—21no—
110C4⋊Dic11—21no—
111C4⋊Dic11—22no—
112C4⋊Dic11—41no—
113C4⋊Dic11—41no—
114C2×C11⋊C8—24no—
115C2×C11⋊C8—22no—
116C2×C11⋊C8—22no—
117#4314—84no—
118#3234—111no—
119#3206—111no—
120C2×#501—111no—
121#1556—111no—
122#1530—111no—
123#1470D1111yescharacteristic, complemented
124#1302—111no—
125C23×C11#12111yescharacteristic
126C22×D11—41no—
127C2×C4×C11—22no—
128C2×C4×C11—22no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—42no—
133C2×C4×C11—81no—
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—42no—
142C2×Dic11—41no—
143C2×Dic11—82no—
144D44—42no—
145D44—42no—
146D44—81no—
147C4×D11—82no—
148Dic22—44no—
149Dic22—82no—
150Dic22—81no—
151C8×C11—42no—
152C8×C11—81no—
153C11⋊C8—24no—
154C11⋊C8—42no—
155#532—111no—
156C2×C4⋊Q8—111no—
157C2×#125C2×D1111yescharacteristic
158#501—222no—
159#501—222no—
160#501—221no—
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#432—111no—
170#432C2×D1111yescharacteristic
171#431C2×D1111yescharacteristic
172C2×#107—221no—
173C2×#106—221no—
174C2×#97—111no—
175#332—222no—
176#329—222no—
177#324—22no—
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—81no—
191C4×C11—81no—
192C4×C11#45612yes—
193Dic11—82no—
194Dic11—81no—
195C2×#41—221no—
196C22×Q8—221no—
197C2×SD16—224no—
198C22×C8—221no—
199C4⋊Q8—112no—
200C4⋊Q8—111no—
201C4⋊Q8—221no—
202C4⋊Q8—221no—
203C4⋊Q8—221no—
204#127—111no—
205#125—21no—
206#125—21no—
207#125—21no—
208#125—21no—
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—221no—
217C2×C4⋊C4—221no—
218C2×C4⋊C4D4411yescharacteristic
219C2×C4⋊C4D4411yescharacteristic
220C2×C42C22×D1111yescharacteristic
221#107—224no—
222#107—222no—
223#106—224no—
224#106—222no—
225C4⋊C8—21no—
226C4⋊C8—21no—
227C4⋊C8—112no—
228#103—224no—
229#102—222no—
230#102—222no—
231C22⋊C8—21no—
232C22⋊C8—221no—
233C22⋊C8C22⋊D1112yes—
234#97—21no—
235#97—112no—
236#97—221no—
237#97—221no—
238C4×C8—21no—
239C2×C11—22no—
240C2×C11#200511yescharacteristic
241C2×C11#200811yescharacteristic
242C2×C11#201911yescharacteristic
243D11—161no—
244#41—882no—
245C2×Q8—221no—
246C2×Q8—222no—
247C2×Q8—441no—
248C2×Q8—882no—
249C2×D4—221no—
250C2×D4—221no—
251C2×D4—221no—
252C2×D4—441no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—441no—
256C22×C4—441no—
257C22×C4C2×D4411yescharacteristic
258C22×C4#433911yescharacteristic
259C22×C4C2×C22⋊D1111yescharacteristic
260SD16—884no—
261C2×C8—22no—
262C2×C8—41no—
263C2×C8—224no—
264C2×C8—222no—
265C2×C8—222no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—222no—
275C4⋊C4—221no—
276C4⋊C4—222no—
277C4⋊C4—221no—
278C4⋊C4—441no—
279C4⋊C4—441no—
280C22⋊C4—441no—
281C22⋊C4—441no—
282C42D4×D1111yescharacteristic
283C42D4×D1111yescharacteristic
284C42D4×D1111yescharacteristic
285C42D4×D1111yescharacteristic
286C11#1013811yescharacteristic, complemented, Sylow
287C23—441no—
288C23#6698311yescharacteristic
289Q8—444no—
290Q8—881no—
291Q8—882no—
292D4—442no—
293D4—442no—
294D4—881no—
295D4—882no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—81no—
303C2×C4—441no—
304C2×C4—442no—
305C2×C4—882no—
306C2×C4—882no—
307C2×C4#6693511yescharacteristic
308C2×C4#6693511yescharacteristic
309C2×C4#6693711yescharacteristic
310C2×C4#6693711yescharacteristic
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#1062257311yescharacteristic
323C22#1062275412yes—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—81no—
330C4—81no—
331C4—882no—
332C4—881no—
333C4#1062236512yes—
334C2—22no—
335C2—1761no—
336C2#1306965411yescharacteristic
337C2#1306966811yescharacteristic
338C2#1306973111yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1470C2
socleC22×C11#392
prime radical#10623008C22
hypercenter#1470D11
hypocenterC11#10138
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1470

Complements

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

NH ≅ G/Ntype
3. C2×#10622678C2semidirect
4. #13067334C2semidirect
6. #13066516C2semidirect
7. C11×#1470C2semidirect
123. #1470D11semidirect
286. C11#10138semidirect

Maximal subgroups

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

subgroupindex
#130798062
#130795432
C2×#106226782
#130673342
#130672282
#130665162
C11×#14702
#1013811