Finite Group Databasebeta

← #14657525

Subgroups — #14657525

Order 2816.

420 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 97 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#13068631C211yesmaximal, characteristic, complemented
2#13067388C211yesmaximal, characteristic, complemented
3#13067265C211yesmaximal, characteristic
4#13067176C211yesmaximal, characteristic
5#13066940C211yesmaximal, characteristic, complemented
6#13066476C211yesmaximal, characteristic, complemented
7C11×#3037C211yesmaximal, characteristic
8C2×C11×#137—21no—
9C11×#532C2211yescharacteristic
10C2×C4×Q8×C11C2211yescharacteristic
11C11×#464—22no—
12C11×#462—21no—
13C11×#460—21no—
14C11×#423C2211yescharacteristic
15C11×#417—21no—
16C2×#66899—21no—
17#10622549C2211yescharacteristic
18#10622538C2211yescharacteristic
19#10622538C2211yescharacteristic
20C2×C4⋊(C11⋊C8)C2211yescharacteristic
21#10622185—21no—
22#10622182—21no—
23#10622175—22no—
24#10622167—21no—
25#10622166—22no—
26#10622118—22no—
27C2×C11×#41—21no—
28C22×Q8×C11D411yescharacteristic
29C11×#137—42no—
30C11×#137—42no—
31C2×C11×Q16—22no—
32C2×C11×SD16—22no—
33C2×C11×M16—21no—
34C11×C4⋊Q8D411yescharacteristic
35C11×#127D411yescharacteristic
36C11×#124—21no—
37C11×#121—21no—
38C11×#121—21no—
39C4×Q8×C11—21no—
40C4×Q8×C11—21no—
41C4×Q8×C11—21no—
42C4×Q8×C11—21no—
43C4×D4×C11—21no—
44C4×D4×C11—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4D411yescharacteristic
47C2×C42×C11—21no—
48C2×C42×C11C2311yescharacteristic
49C2×C4⋊Dic11—21no—
50C22×C11⋊C8—21no—
51C11×C4⋊C8—21no—
52C11×C4⋊C8D412yes—
53C11×#103—22no—
54C11×#102—22no—
55#66899—42no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C22⋊(C11⋊C8)—21no—
59C22⋊(C11⋊C8)D412yes—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)—21no—
64C4×C11⋊C8—21no—
65C4×C11⋊C8—21no—
66#10467—111nomaximal, Sylow
67C11×#41—41no—
68C11×#41—41no—
69C11×#41—41no—
70C11×#41—41no—
71C2×Q8×C11—21no—
72C2×Q8×C11—21no—
73C2×Q8×C11—21no—
74C2×Q8×C11—21no—
75C2×Q8×C11—21no—
76C2×Q8×C11—21no—
77C2×Q8×C11SD1612yes—
78C2×D4×C11—21no—
79C2×D4×C11—21no—
80C2×D4×C11—21no—
81C2×D4×C11—41no—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—41no—
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11#4111yescharacteristic
88C22×Dic11—41no—
89C11×Q16—44no—
90C11×SD16—44no—
91C11×M16—41no—
92C11×M16—41no—
93C2×C8×C11—22no—
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×C22⋊C4—41no—
101C11×C22⋊C4—41no—
102C42×C11—41no—
103C42×C11—41no—
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C42×C11#4111yescharacteristic
107C42×C11#4111yescharacteristic
108C4⋊Dic11—41no—
109C4⋊Dic11—41no—
110C2×C11⋊C8—22no—
111C2×C11⋊C8—41no—
112C2×C11⋊C8—41no—
113C2×C11⋊C8—41no—
114C2×C11⋊C8—41no—
115#3037D1111yescharacteristic
116#1805—111no—
117#1570—111no—
118#1540—111no—
119#1517—111no—
120#1461—111no—
121#1286—111no—
122C23×C11—41no—
123C23×C11#12111yescharacteristic
124Q8×C11—22no—
125Q8×C11—22no—
126Q8×C11—41no—
127Q8×C11—41no—
128Q8×C11—41no—
129Q8×C11—41no—
130D4×C11—41no—
131D4×C11—41no—
132D4×C11—81no—
133D4×C11—81no—
134D4×C11—81no—
135D4×C11—81no—
136C2×C4×C11—22no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—81no—
144C2×C4×C11—81no—
145C2×C4×C11—81no—
146C2×C4×C11#12011yescharacteristic
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11#12111yescharacteristic
149C2×C4×C11#12311yescharacteristic
150C2×C4×C11#12311yescharacteristic
151C2×C4×C11#12411yescharacteristic
152C2×C4×C11C2×SD1611yescharacteristic
153C2×C4×C11#13511yescharacteristic
154C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
156C2×Dic11—81no—
157C2×Dic11—81no—
158C2×Dic11—81no—
159C8×C11—42no—
160C11⋊C8—42no—
161C11⋊C8—81no—
162C11⋊C8—81no—
163C2×#137—21no—
164#532C2×D1111yescharacteristic
165C2×C4×Q8C2×D1111yescharacteristic
166#464—22no—
167#462—21no—
168#460—21no—
169#431—111no—
170#431—111no—
171#423C2×D1111yescharacteristic
172C2×C4⋊C8—111no—
173#417—21no—
174C2×#103—221no—
175#382—111no—
176#340—221no—
177#334—222no—
178#332—221no—
179#331—221no—
180#327—222no—
181#324—222no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—81no—
185C22×C11—81no—
186C22×C11—81no—
187C22×C11#39411yescharacteristic
188C22×C11#46511yescharacteristic
189C22×C11#46911yescharacteristic
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—42no—
195C4×C11—81no—
196C4×C11—81no—
197C4×C11#44911yescharacteristic
198C4×C11#45011yescharacteristic
199C4×C11#48111yescharacteristic
200C4×C11#48211yescharacteristic
201Dic11—161no—
202C2×#41—21no—
203C22×Q8C22⋊D1111yescharacteristic
204#137—42no—
205#137—42no—
206C2×Q16—22no—
207C2×SD16—22no—
208C2×M16—21no—
209C22×C8—221no—
210C4⋊Q8C22⋊D1111yescharacteristic
211#127C22⋊D1111yescharacteristic
212#124—21no—
213#121—21no—
214#121—21no—
215C4×Q8—21no—
216C4×Q8—21no—
217C4×Q8—21no—
218C4×Q8—21no—
219C4×D4—21no—
220C4×D4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—221no—
223C2×C4⋊C4C22⋊D1111yescharacteristic
224C2×C42—21no—
225C2×C42C22×D1111yescharacteristic
226C4⋊C8—21no—
227C4⋊C8—221no—
228C4⋊C8—221no—
229C4⋊C8—221no—
230C4⋊C8—221no—
231C4⋊C8C22⋊D1112yes—
232#103—22no—
233#103—442no—
234#102—22no—
235C22⋊C8—112no—
236C22⋊C8—221no—
237C4×C8—221no—
238C4×C8—221no—
239#95—221no—
240#95—221no—
241C2×C11—21no—
242C2×C11—21no—
243C2×C11—161no—
244C2×C11#203411yescharacteristic
245C2×C11#204911yescharacteristic
246C2×C11#205311yescharacteristic
247#41—41no—
248#41—41no—
249#41—41no—
250#41—41no—
251C2×Q8—21no—
252C2×Q8—21no—
253C2×Q8—21no—
254C2×Q8—21no—
255C2×Q8—21no—
256C2×Q8—21no—
257C2×Q8#432412yes—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—41no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—41no—
265C22×C4—441no—
266C22×C4D4×D1111yescharacteristic
267C22×C4#434111yescharacteristic
268C22×C4C2×C22⋊D1111yescharacteristic
269Q16—44no—
270SD16—44no—
271M16—41no—
272M16—41no—
273C2×C8—22no—
274C2×C8—222no—
275C2×C8—441no—
276C2×C8—441no—
277C2×C8—441no—
278C2×C8—441no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—441no—
286C4⋊C4—441no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C42—41no—
290C42—41no—
291C42#434111yescharacteristic
292C42#434111yescharacteristic
293C42C2×C22⋊D1111yescharacteristic
294C42C2×C22⋊D1111yescharacteristic
295C11#1046711yescharacteristic, complemented, Sylow
296C23—41no—
297C23#6699211yescharacteristic
298Q8—22no—
299Q8—22no—
300Q8—41no—
301Q8—41no—
302Q8—41no—
303Q8—41no—
304D4—41no—
305D4—41no—
306D4—81no—
307D4—81no—
308D4—81no—
309D4—81no—
310C2×C4—22no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—881no—
321C2×C4—881no—
322C2×C4—881no—
323C2×C4#6698511yescharacteristic
324C2×C4C2×#432411yescharacteristic
325C2×C4#6698811yescharacteristic
326C2×C4#6698811yescharacteristic
327C2×C4#6698911yescharacteristic
328C2×C4#6699111yescharacteristic
329C2×C4#6699211yescharacteristic
330C2×C4#6700211yescharacteristic
331C2×C4#6700311yescharacteristic
332C2×C4#6700611yescharacteristic
333C8—42no—
334C8—442no—
335C8—881no—
336C8—881no—
337C22—21no—
338C22—21no—
339C22—81no—
340C22—81no—
341C22—81no—
342C22#1062265211yescharacteristic
343C22#1062265411yescharacteristic
344C22#1062283511yescharacteristic
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—42no—
350C4—81no—
351C4—81no—
352C4—1761no—
353C4#1062264711yescharacteristic
354C4#1062264811yescharacteristic
355C4#1062283111yescharacteristic
356C4#1062285111yescharacteristic
357C2—21no—
358C2—21no—
359C2—161no—
360C2#1306980211yescharacteristic
361C2#1306989311yescharacteristic
362C2#1306991911yescharacteristic
subgroupG/H
centerC22#10622835
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3037C2
socleC22×C11#394
prime radicalC11×#532C22
hypercenter#3037D11
hypocenterC11#10467
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3037

Complements

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

NH ≅ G/Ntype
1. #13068631C2semidirect
2. #13067388C2semidirect
5. #13066940C2semidirect
6. #13066476C2semidirect
295. C11#10467semidirect

Maximal subgroups

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

subgroupindex
#130686312
#130673882
#130672652
#130671762
#130669402
#130664762
C11×#30372
#1046711