Finite Group Databasebeta

← #14650429

Subgroups — #14650429

Order 2816.

490 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 109 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#13079543C211yesmaximal, characteristic
2#13077335C211yesmaximal, characteristic
3#13069589C211yesmaximal, characteristic, complemented
4#13067300C211yesmaximal, characteristic, complemented
5#13067177C211yesmaximal, characteristic
6#13066475C211yesmaximal, characteristic, complemented
7C11×#1275C211yesmaximal, characteristic, complemented
8C2×#66954—21no—
9#10623008C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#431C2211yescharacteristic
13C2×C11×#97C2211yescharacteristic
14#10622723—21no—
15#10622549C2211yescharacteristic
16#10622537C2211yescharacteristic
17#10622454—22no—
18#10622351—22no—
19#10622319—22no—
20#10622319—22no—
21#10622306C412yescomplemented
22#10622294C412yescomplemented
23#10622189—21no—
24#10622189—21no—
25#10622120—22no—
26#10622108—22no—
27C2×#4339—21no—
28C22×Dic22—21no—
29C22×C8×C11D411yescharacteristic
30C22×C8×C11D411yescharacteristic
31C2×C42×C11C2311yescharacteristic
32#66983—21no—
33#66983D412yes—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—21no—
37C2×#4318—21no—
38C2×#4314—24no—
39#66954—42no—
40#66954—42no—
41C2×#4313—22no—
42C2×C8×D11—22no—
43#66928—21no—
44#66927C2×C411yescharacteristic
45C4×D44—21no—
46C4×D44D412yes—
47#66922—21no—
48#66922—21no—
49#66922—21no—
50#66922C2×C412yes—
51#66922C2×C411yescharacteristic
52C11×C4⋊C8—21no—
53C11×C4⋊C8—21no—
54C11×C22⋊C8—21no—
55C11×C22⋊C8—21no—
56C11×#97—21no—
57C11×#97—21no—
58C4×C8×C11—21no—
59C4×C8×C11C2×C412yes—
60C11⋊#95—21no—
61C11⋊#95—21no—
62(C2×D11)⋊C8—24no—
63#66880—24no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)D412yes—
66#9289—111nomaximal, Sylow
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11#4111yescharacteristic
70C2×C22⋊D11—22no—
71C22×Dic11—41no—
72C22×Dic11—41no—
73#4339—41no—
74#4339—41no—
75#4339—41no—
76#4339—41no—
77C2×D44—21no—
78C2×D44—21no—
79C2×D44C22⋊C412yes—
80C2×C4×D11—22no—
81C2×Dic22—22no—
82C2×Dic22—21no—
83C2×Dic22—41no—
84C2×Dic22—82no—
85C2×C8×C11—22no—
86C2×C8×C11—21no—
87C2×C8×C11—21no—
88C2×C8×C11—21no—
89C2×C8×C11—21no—
90C2×C8×C11—21no—
91C2×C8×C11—41no—
92C2×C8×C11SD1612yescomplemented
93C42×C11C22×C411yescharacteristic
94C42×C11C2×D411yescharacteristic
95C42×C11C2×D411yescharacteristic
96C42×C11#4111yescharacteristic
97(C2×D11)⋊C4—22no—
98(C2×D11)⋊C4—22no—
99C4⋊Dic11—21no—
100C4⋊Dic11—22no—
101C4⋊Dic11—22no—
102C4⋊Dic11—41no—
103C4⋊Dic11—41no—
104C4⋊Dic11—41no—
105C4⋊Dic11—41no—
106C4⋊Dic11C22⋊C412yes—
107#4318—41no—
108#4318—41no—
109C2×C11⋊C8—22no—
110#4314—84no—
111#4313—44no—
112C8×D11—44no—
113#3206—111no—
114#2932—111no—
115#1993—111no—
116#1549—111no—
117#1517—111no—
118#1286—111no—
119#1275D1111yescharacteristic, complemented
120C23×C11#12111yescharacteristic
121C22×D11—22no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11C2×C22⋊C411yescharacteristic
125C2×C4×C11C4×D411yescharacteristic
126C2×C4×C11C4×D411yescharacteristic
127C2×C4×C11#12011yescharacteristic
128C2×C4×C11#12111yescharacteristic
129C2×C4×C11#12311yescharacteristic
130C2×C4×C11C2×SD1611yescharacteristic
131C2×C4×C11#13511yescharacteristic
132C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C11#13711yescharacteristic
134C22⋊D11—42no—
135C22⋊D11—42no—
136C2×Dic11—22no—
137C2×Dic11—42no—
138C2×Dic11—82no—
139C2×Dic11—81no—
140C2×Dic11—81no—
141C2×Dic11—81no—
142D44—42no—
143D44—41no—
144D44—41no—
145D44—81no—
146C4×D11—42no—
147C4×D11—42no—
148Dic22—41no—
149Dic22—41no—
150Dic22—44no—
151Dic22—82no—
152C8×C11—22no—
153C8×C11—42no—
154C8×C11—41no—
155C8×C11—81no—
156C11⋊C8—42no—
157C2×#131—221no—
158#532—111no—
159C2×C4⋊Q8—111no—
160#492—112no—
161#487—112no—
162#461—222no—
163#448—222no—
164#435—222no—
165#435—222no—
166#431C2×D1111yescharacteristic
167#431C2×D1111yescharacteristic
168#423—111no—
169#408—221no—
170C2×#97C2×D1111yescharacteristic
171#382—111no—
172#340—221no—
173#340—221no—
174#332—222no—
175#327—222no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11#38611yescharacteristic
179C22×C11#46111yescharacteristic
180C22×C11#46311yescharacteristic
181C2×D11—42no—
182C2×D11—42no—
183C2×D11—42no—
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—21no—
187C4×C11—21no—
188C4×C11C4×SD1611yescharacteristic
189C4×C11#44011yescharacteristic
190C4×C11#45011yescharacteristic
191C4×C11#45211yescharacteristic
192Dic11—42no—
193Dic11—82no—
194Dic11—161no—
195C2×#41—221no—
196C22×Q8—221no—
197C2×SD16—224no—
198#131—442no—
199#131—442no—
200C2×M16—222no—
201C2×M16—221no—
202C22×C8—222no—
203C22×C8D4411yescharacteristic
204C22×C8D4411yescharacteristic
205C4⋊Q8—111no—
206C4⋊Q8—112no—
207C4⋊Q8—221no—
208C4⋊Q8—221no—
209C4⋊Q8—221no—
210#127—111no—
211#124—221no—
212#121—112no—
213#121—221no—
214C4×D4—112no—
215C4×D4—221no—
216C2×C4⋊C4—221no—
217C2×C4⋊C4—221no—
218C2×C4⋊C4—221no—
219C2×C42C22×D1111yescharacteristic
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8—112no—
223C4⋊C8—221no—
224#103—224no—
225C22⋊C8—21no—
226C22⋊C8—21no—
227C22⋊C8—224no—
228#97—21no—
229#97—21no—
230C4×C8—21no—
231C4×C8C4×D1112yes—
232#95—221no—
233#95—221no—
234C2×C11—21no—
235C2×C11—21no—
236C2×C11#187711yescharacteristic
237C2×C11#190211yescharacteristic
238C2×C11#191011yescharacteristic
239D11—82no—
240#41—441no—
241#41—441no—
242#41—441no—
243#41—441no—
244C2×Q8—221no—
245C2×Q8—222no—
246C2×Q8—441no—
247C2×Q8—882no—
248C2×D4—112no—
249C2×D4—222no—
250C2×D4—221no—
251C2×D4—221no—
252C22×C4—222no—
253C22×C4—441no—
254C22×C4—441no—
255C22×C4C2×D4411yescharacteristic
256C22×C4D4×D1111yescharacteristic
257C22×C4#434311yescharacteristic
258SD16—884no—
259M16—444no—
260M16—441no—
261M16—441no—
262C2×C8—21no—
263C2×C8—21no—
264C2×C8—22no—
265C2×C8—21no—
266C2×C8—21no—
267C2×C8—21no—
268C2×C8—41no—
269C2×C8—222no—
270C2×C8—444no—
271C2×C8#431412yescomplemented
272C4⋊C4—112no—
273C4⋊C4—221no—
274C4⋊C4—222no—
275C4⋊C4—222no—
276C4⋊C4—441no—
277C4⋊C4—441no—
278C4⋊C4—441no—
279C4⋊C4—441no—
280C22⋊C4—222no—
281C22⋊C4—222no—
282C42C2×C4×D1111yescharacteristic
283C42#433911yescharacteristic
284C42D4×D1111yescharacteristic
285C42D4×D1111yescharacteristic
286C11#928911yescharacteristic, complemented, Sylow
287C23—222no—
288C23#6694811yescharacteristic
289Q8—444no—
290Q8—441no—
291Q8—441no—
292Q8—882no—
293D4—442no—
294D4—442no—
295D4—442no—
296D4—441no—
297D4—441no—
298D4—881no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—222no—
302C2×C4—442no—
303C2×C4—442no—
304C2×C4—442no—
305C2×C4—882no—
306C2×C4—881no—
307C2×C4—881no—
308C2×C4—881no—
309C2×C4C4×D4411yescharacteristic
310C2×C4C22⋊C4×D1111yescharacteristic
311C2×C4#6693511yescharacteristic
312C2×C4#6693711yescharacteristic
313C2×C4#6694611yescharacteristic
314C2×C4#6694711yescharacteristic
315C2×C4C2×#431411yescharacteristic
316C2×C4#6695711yescharacteristic
317C2×C4#6696111yescharacteristic
318C2×C4#6696211yescharacteristic
319C8—22no—
320C8—42no—
321C8—41no—
322C8—81no—
323C8—442no—
324C22—21no—
325C22—21no—
326C22—442no—
327C22—442no—
328C22—442no—
329C22#1062227811yescharacteristic
330C22#1062245411yescharacteristic
331C22#1062245711yescharacteristic
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—442no—
337C4—882no—
338C4—1761no—
339C4C4×#431411yescharacteristic
340C4#1062232311yescharacteristic
341C4#1062234411yescharacteristic
342C4#1062234611yescharacteristic
343C2—21no—
344C2—21no—
345C2—882no—
346C2#1306894911yescharacteristic
347C2#1306909011yescharacteristic
348C2#1306914211yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1275C2
socleC22×C11#386
prime radical#10623008C22
cosocleC2×C42×C11C23
hypercenter#1275D11
hypocenterC11#9289
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1275

Complements

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

NH ≅ G/Ntype
3. #13069589C2semidirect
4. #13067300C2semidirect
6. #13066475C2semidirect
7. C11×#1275C2semidirect
21. #10622306C4semidirect
22. #10622294C4semidirect
92. C2×C8×C11SD16semidirect
119. #1275D11semidirect
271. C2×C8#4314semidirect
286. C11#9289semidirect

Maximal subgroups

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

subgroupindex
#130795432
#130773352
#130695892
#130673002
#130671772
#130664752
C11×#12752
#928911