Finite Group Databasebeta

← #14657526

Subgroups — #14657526

Order 2816.

420 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 91 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#13078084C211yesmaximal, characteristic
2#13068632C211yesmaximal, characteristic, complemented
3#13067386C211yesmaximal, characteristic, complemented
4#13067176C211yesmaximal, characteristic
5#13066939C211yesmaximal, characteristic, complemented
6#13066475C211yesmaximal, characteristic, complemented
7C11×#1540C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×#67004—21no—
10C2×C4×Dic22C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13#10622845—21no—
14C2×#66880—21no—
15#10622703—21no—
16#10622688—21no—
17#10622667—22no—
18#10622549C2211yescharacteristic
19#10622538C2211yescharacteristic
20#10622537C2211yescharacteristic
21C11×#332—21no—
22C11×#331—21no—
23#10622189—21no—
24#10622175—22no—
25#10622118—22no—
26#10622107—22no—
27C2×C11×#41—21no—
28C22×Dic22D411yescharacteristic
29C22×C8×C11—21no—
30C11×C4⋊Q8D411yescharacteristic
31C11×#127D411yescharacteristic
32C11×#124—21no—
33C11×#121—21no—
34C11×#121—21no—
35C4×D4×C11—21no—
36C4×D4×C11—21no—
37C2×C42×C11C2311yescharacteristic
38#67004—42no—
39#67004—42no—
40C2×#4326—22no—
41C2×#4324—22no—
42C2×C4⋊Dic11—21no—
43C2×C4⋊Dic11D411yescharacteristic
44C2×Dic11⋊C4—21no—
45C2×C4×Dic11—21no—
46C2×#4318—21no—
47C4×Dic22—21no—
48C4×Dic22—21no—
49C4×Dic22—21no—
50C4×Dic22—21no—
51C11×C4⋊C8—21no—
52C11×C4⋊C8—21no—
53C11×C4⋊C8—21no—
54C11×C22⋊C8—21no—
55C4×C8×C11—21no—
56#66899—22no—
57#66896—22no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C22⋊(C11⋊C8)D412yes—
61#66880—42no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)—21no—
64C4⋊(C11⋊C8)D412yes—
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×D4×C11—21no—
73C2×D4×C11—21no—
74C2×D4×C11—21no—
75C2×D4×C11—41no—
76C22×C4×C11—41no—
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11#4111yescharacteristic
80C22×Dic11—21no—
81C22×Dic11—21no—
82C22×Dic11—41no—
83C2×Dic22—21no—
84C2×Dic22—21no—
85C2×Dic22—21no—
86C2×Dic22—21no—
87C2×Dic22—21no—
88C2×Dic22SD1612yes—
89C2×C8×C11—41no—
90C2×C8×C11—41no—
91C2×C8×C11—41no—
92C2×C8×C11—41no—
93C11×C4⋊C4—21no—
94C11×C4⋊C4—21no—
95C11×C22⋊C4—41no—
96C11×C22⋊C4—41no—
97C42×C11C2×D411yescharacteristic
98C42×C11C2×D411yescharacteristic
99C42×C11#4111yescharacteristic
100C42×C11#4111yescharacteristic
101#4326—44no—
102#4324—44no—
103C4⋊Dic11—21no—
104C4⋊Dic11—21no—
105C4⋊Dic11—41no—
106C4⋊Dic11—41no—
107Dic11⋊C4—41no—
108Dic11⋊C4—41no—
109C4×Dic11—41no—
110C4×Dic11—41no—
111#4318—41no—
112#4318—41no—
113C2×C11⋊C8—22no—
114C2×C11⋊C8—22no—
115#3037—111no—
116#1805—111no—
117#1570—111no—
118#1540D1111yescharacteristic
119#1517—111no—
120#1461—111no—
121#1286—111no—
122C23×C11—41no—
123C23×C11#12111yescharacteristic
124Q8×C11—41no—
125Q8×C11—41no—
126D4×C11—41no—
127D4×C11—41no—
128D4×C11—81no—
129D4×C11—81no—
130D4×C11—81no—
131D4×C11—81no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—81no—
136C2×C4×C11—81no—
137C2×C4×C11#12011yescharacteristic
138C2×C4×C11#12111yescharacteristic
139C2×C4×C11#12111yescharacteristic
140C2×C4×C11#12311yescharacteristic
141C2×C4×C11#12311yescharacteristic
142C2×C4×C11#12411yescharacteristic
143C2×C4×C11C2×SD1611yescharacteristic
144C2×C4×C11#13511yescharacteristic
145C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
147C2×Dic11—22no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—81no—
152C2×Dic11—81no—
153C2×Dic11—81no—
154C2×Dic11—81no—
155Dic22—22no—
156Dic22—22no—
157Dic22—41no—
158Dic22—41no—
159C8×C11—81no—
160C8×C11—81no—
161C11⋊C8—42no—
162C11⋊C8—42no—
163C2×#137—221no—
164#532C2×D1111yescharacteristic
165C2×C4×Q8—111no—
166#464—222no—
167#462—221no—
168#460—221no—
169#431—111no—
170#431C2×D1111yescharacteristic
171#423—111no—
172C2×C4⋊C8C2×D1111yescharacteristic
173#417—221no—
174C2×#103—221no—
175#382—111no—
176#340—221no—
177#334—222no—
178#332—21no—
179#331—21no—
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—81no—
195C4×C11#44911yescharacteristic
196C4×C11#45011yescharacteristic
197C4×C11#48111yescharacteristic
198C4×C11#48211yescharacteristic
199Dic11—42no—
200Dic11—81no—
201Dic11—161no—
202C2×#41—21no—
203C22×Q8—111no—
204#137—442no—
205#137—442no—
206C2×Q16—222no—
207C2×SD16—222no—
208C2×M16—221no—
209C22×C8—21no—
210C4⋊Q8C22⋊D1111yescharacteristic
211#127C22⋊D1111yescharacteristic
212#124—21no—
213#121—21no—
214#121—21no—
215C4×Q8—221no—
216C4×Q8—221no—
217C4×Q8—221no—
218C4×Q8—221no—
219C4×D4—21no—
220C4×D4—21no—
221C2×C4⋊C4—111no—
222C2×C4⋊C4—221no—
223C2×C4⋊C4—221no—
224C2×C42—221no—
225C2×C42C22×D1111yescharacteristic
226C4⋊C8—21no—
227C4⋊C8—21no—
228C4⋊C8—21no—
229C4⋊C8—112no—
230C4⋊C8—221no—
231C4⋊C8—221no—
232#103—222no—
233#103—442no—
234#102—222no—
235C22⋊C8—21no—
236C22⋊C8—112no—
237C4×C8—21no—
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—112no—
253C2×Q8—221no—
254C2×Q8—221no—
255C2×Q8—221no—
256C2×Q8—221no—
257C2×Q8—221no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—41no—
262C22×C4—41no—
263C22×C4—221no—
264C22×C4—221no—
265C22×C4—441no—
266C22×C4#433911yescharacteristic
267C22×C4D4×D1111yescharacteristic
268C22×C4D4×D1111yescharacteristic
269Q16—444no—
270SD16—444no—
271M16—441no—
272M16—441no—
273C2×C8—41no—
274C2×C8—41no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8—222no—
278C2×C8—222no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—221no—
282C4⋊C4—221no—
283C4⋊C4—441no—
284C4⋊C4—441no—
285C4⋊C4—441no—
286C4⋊C4—441no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C42—441no—
290C42—441no—
291C42#433911yescharacteristic
292C42D4×D1111yescharacteristic
293C42#434111yescharacteristic
294C42C2×C22⋊D1111yescharacteristic
295C11#1046711yescharacteristic, complemented, Sylow
296C23—41no—
297C23#6693711yescharacteristic
298Q8—41no—
299Q8—41no—
300Q8—222no—
301Q8—222no—
302Q8—441no—
303Q8—441no—
304D4—41no—
305D4—41no—
306D4—81no—
307D4—81no—
308D4—81no—
309D4—81no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—222no—
316C2×C4—441no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4—881no—
320C2×C4—881no—
321C2×C4—881no—
322C2×C4—881no—
323C2×C4#6693611yescharacteristic
324C2×C4#6693711yescharacteristic
325C2×C4#6693811yescharacteristic
326C2×C4#6696411yescharacteristic
327C2×C4#6696511yescharacteristic
328C2×C4SD16×D1111yescharacteristic
329C2×C4#6696711yescharacteristic
330C2×C4#6698211yescharacteristic
331C2×C4#6699011yescharacteristic
332C2×C4#6699211yescharacteristic
333C8—81no—
334C8—81no—
335C8—442no—
336C8—442no—
337C22—21no—
338C22—21no—
339C22—81no—
340C22—81no—
341C22—81no—
342C22#1062239111yescharacteristic
343C22#1062239511yescharacteristic
344C22#1062257211yescharacteristic
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—81no—
350C4—442no—
351C4—881no—
352C4—1761no—
353C4#1062239011yescharacteristic
354C4#1062239711yescharacteristic
355C4#1062277111yescharacteristic
356C4#1062278211yescharacteristic
357C2—21no—
358C2—21no—
359C2—161no—
360C2#1306980311yescharacteristic
361C2#1306989611yescharacteristic
362C2#1306992011yescharacteristic
subgroupG/H
centerC22#10622572
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1540C2
socleC22×C11#394
prime radicalC11×#532C22
hypercenter#1540D11
hypocenterC11#10467
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1540

Complements

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

NH ≅ G/Ntype
2. #13068632C2semidirect
3. #13067386C2semidirect
5. #13066939C2semidirect
6. #13066475C2semidirect
295. C11#10467semidirect

Maximal subgroups

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

subgroupindex
#130780842
#130686322
#130673862
#130671762
#130669392
#130664752
C11×#15402
#1046711