Finite Group Databasebeta

← #14650428

Subgroups — #14650428

Order 2816.

490 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 113 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#13079538C211yesmaximal, characteristic
2#13077334C211yesmaximal, characteristic
3#13069588C211yesmaximal, characteristic, complemented
4#13067300C211yesmaximal, characteristic, complemented
5#13066474C211yesmaximal, characteristic, complemented
6#13066446C211yesmaximal, characteristic, complemented
7C11×#1517C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×#67001—21no—
10C2×#66922C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#382C2211yescharacteristic
13#10622847—21no—
14#10622706C412yescomplemented
15#10622689C412yescomplemented
16#10622653—22no—
17#10622632—22no—
18#10622624—22no—
19#10622624—22no—
20#10622538C2211yescharacteristic
21#10622537C2211yescharacteristic
22C2×#66867C2211yescharacteristic
23C11×#327—22no—
24#10622167—21no—
25#10622167—21no—
26#10622120—22no—
27C2×C11×#41—21no—
28C22×Dic22—21no—
29C11×C4⋊Q8C2×C411yescharacteristic
30C11×#127C2×C411yescharacteristic
31C11×#124—21no—
32C11×#121—21no—
33C11×#121D412yes—
34C4×D4×C11—21no—
35C4×D4×C11D412yes—
36C2×C11×C4⋊C4—21no—
37C2×C42×C11C2311yescharacteristic
38#67001—42no—
39#67001—42no—
40C2×#4324—24no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11—21no—
43C2×#4318—22no—
44C2×#4318—21no—
45C22×C11⋊C8—22no—
46C22×C11⋊C8D411yescharacteristic
47C22×C11⋊C8D411yescharacteristic
48#66922—21no—
49#66922—21no—
50#66922—21no—
51#66922C2×C412yes—
52C11×C4⋊C8—21no—
53C11×C22⋊C8—21no—
54C4×C8×C11—21no—
55C11×#95—21no—
56C11×#95—21no—
57C22⋊(C11⋊C8)—24no—
58C22⋊(C11⋊C8)—21no—
59#66874—24no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)D412yes—
63#66867—21no—
64#66867—21no—
65C4×C11⋊C8C2×C412yes—
66#9289—111nomaximal, Sylow
67C11×#41—41no—
68C11×#41—41no—
69C11×#41—41no—
70C11×#41—41no—
71C2×Q8×C11—21no—
72C2×D4×C11—22no—
73C2×D4×C11—21no—
74C2×D4×C11—21no—
75C2×D4×C11C22⋊C412yes—
76C22×C4×C11—22no—
77C22×C4×C11—41no—
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11#4111yescharacteristic
81C22×Dic11—41no—
82C2×Dic22—22no—
83C2×Dic22—41no—
84C2×Dic22—82no—
85C2×C8×C11—41no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4C22⋊C412yes—
90C11×C22⋊C4—22no—
91C11×C22⋊C4—22no—
92C42×C11C22×C411yescharacteristic
93C42×C11C2×D411yescharacteristic
94C42×C11C2×D411yescharacteristic
95C42×C11#4111yescharacteristic
96#4324—84no—
97C4⋊Dic11—22no—
98C4⋊Dic11—22no—
99C4⋊Dic11—41no—
100C4⋊Dic11—41no—
101#4318—44no—
102#4318—41no—
103#4318—41no—
104C2×C11⋊C8—22no—
105C2×C11⋊C8—21no—
106C2×C11⋊C8—21no—
107C2×C11⋊C8—22no—
108C2×C11⋊C8—21no—
109C2×C11⋊C8—21no—
110C2×C11⋊C8—21no—
111C2×C11⋊C8—44no—
112C2×C11⋊C8SD1612yescomplemented
113#3206—111no—
114#2932—111no—
115#1993—111no—
116#1549—111no—
117#1517D1111yescharacteristic
118#1286—111no—
119#1275—111no—
120C23×C11—22no—
121C23×C11#12111yescharacteristic
122Q8×C11—41no—
123Q8×C11—41no—
124D4×C11—42no—
125D4×C11—42no—
126D4×C11—42no—
127D4×C11—41no—
128D4×C11—41no—
129D4×C11—81no—
130C2×C4×C11—22no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—42no—
134C2×C4×C11—42no—
135C2×C4×C11—81no—
136C2×C4×C11—81no—
137C2×C4×C11—81no—
138C2×C4×C11C2×C22⋊C411yescharacteristic
139C2×C4×C11C4×D411yescharacteristic
140C2×C4×C11C4×D411yescharacteristic
141C2×C4×C11#12011yescharacteristic
142C2×C4×C11#12111yescharacteristic
143C2×C4×C11#12311yescharacteristic
144C2×C4×C11C2×SD1611yescharacteristic
145C2×C4×C11#13511yescharacteristic
146C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C11#13711yescharacteristic
148C2×Dic11—42no—
149C2×Dic11—82no—
150Dic22—44no—
151Dic22—82no—
152C8×C11—81no—
153C11⋊C8—22no—
154C11⋊C8—42no—
155C11⋊C8—42no—
156C11⋊C8—41no—
157C2×#131—221no—
158#532C2×D1111yescharacteristic
159C2×C4⋊Q8—111no—
160#492—112no—
161#487—112no—
162#461—222no—
163#448—222no—
164#435—222no—
165#435—222no—
166#431—111no—
167#431C2×D1111yescharacteristic
168#423—111no—
169#408—221no—
170C2×#97—111no—
171#382C2×D1111yescharacteristic
172#340—221no—
173#340—221no—
174#332—222no—
175#327—22no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11—42no—
179C22×C11—42no—
180C22×C11—42no—
181C22×C11#38611yescharacteristic
182C22×C11#46111yescharacteristic
183C22×C11#46311yescharacteristic
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—21no—
187C4×C11—21no—
188C4×C11—42no—
189C4×C11—161no—
190C4×C11C4×SD1611yescharacteristic
191C4×C11#44011yescharacteristic
192C4×C11#45011yescharacteristic
193C4×C11#45211yescharacteristic
194Dic11—82no—
195C2×#41—21no—
196C22×Q8—221no—
197C2×SD16—224no—
198#131—442no—
199#131—442no—
200C2×M16—222no—
201C2×M16—221no—
202C22×C8—111no—
203C22×C8—111no—
204C22×C8—222no—
205C4⋊Q8—112no—
206C4⋊Q8—221no—
207C4⋊Q8—221no—
208C4⋊Q8—221no—
209C4⋊Q8C4×D1111yescharacteristic
210#127C4×D1111yescharacteristic
211#124—21no—
212#121—21no—
213#121C22⋊D1112yes—
214C4×D4—21no—
215C4×D4D4412yes—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—221no—
218C2×C4⋊C4—221no—
219C2×C42C22×D1111yescharacteristic
220C4⋊C8—21no—
221C4⋊C8—112no—
222C4⋊C8—221no—
223C4⋊C8—221no—
224#103—224no—
225C22⋊C8—21no—
226C22⋊C8—224no—
227C22⋊C8—221no—
228#97—221no—
229#97—221no—
230C4×C8—21no—
231C4×C8—112no—
232#95—21no—
233#95—21no—
234C2×C11—21no—
235C2×C11—21no—
236C2×C11—82no—
237C2×C11#187711yescharacteristic
238C2×C11#190211yescharacteristic
239C2×C11#191011yescharacteristic
240#41—41no—
241#41—41no—
242#41—41no—
243#41—41no—
244C2×Q8—21no—
245C2×Q8—222no—
246C2×Q8—441no—
247C2×Q8—882no—
248C2×D4—22no—
249C2×D4—21no—
250C2×D4—21no—
251C2×D4(C2×D11)⋊C412yes—
252C22×C4—22no—
253C22×C4—41no—
254C22×C4—441no—
255C22×C4D4×D1111yescharacteristic
256C22×C4#434111yescharacteristic
257C22×C4C2×C22⋊D1111yescharacteristic
258SD16—884no—
259M16—444no—
260M16—441no—
261M16—441no—
262C2×C8—41no—
263C2×C8—112no—
264C2×C8—221no—
265C2×C8—221no—
266C2×C8—221no—
267C2×C8—222no—
268C2×C8—221no—
269C2×C8—221no—
270C2×C8—222no—
271C2×C8—444no—
272C4⋊C4—21no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—222no—
276C4⋊C4—222no—
277C4⋊C4—441no—
278C4⋊C4—441no—
279C4⋊C4(C2×D11)⋊C412yes—
280C22⋊C4—22no—
281C22⋊C4—22no—
282C42C2×C4×D1111yescharacteristic
283C42C2×D4411yescharacteristic
284C42D4×D1111yescharacteristic
285C42#434111yescharacteristic
286C11#928911yescharacteristic, complemented, Sylow
287C23—22no—
288C23#6699211yescharacteristic
289Q8—41no—
290Q8—41no—
291Q8—444no—
292Q8—882no—
293D4—42no—
294D4—42no—
295D4—42no—
296D4—41no—
297D4—41no—
298D4—81no—
299C2×C4—22no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4—442no—
308C2×C4—882no—
309C2×C4(C22⋊D11)⋊C411yescharacteristic
310C2×C4(C22⋊D11)⋊C411yescharacteristic
311C2×C4#6693511yescharacteristic
312C2×C4#6693911yescharacteristic
313C2×C4#6696411yescharacteristic
314C2×C4#6696511yescharacteristic
315C2×C4SD16×D1111yescharacteristic
316C2×C4#6696811yescharacteristic
317C2×C4C2×(C2×D11)⋊C411yescharacteristic
318C2×C4#6699211yescharacteristic
319C8—81no—
320C8—222no—
321C8—442no—
322C8—442no—
323C8—441no—
324C22—21no—
325C22—21no—
326C22—42no—
327C22—42no—
328C22—42no—
329C22#1062257111yescharacteristic
330C22#1062276611yescharacteristic
331C22#1062277511yescharacteristic
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—42no—
337C4—161no—
338C4—882no—
339C4#1062237011yescharacteristic
340C4#1062237111yescharacteristic
341C4#1062238911yescharacteristic
342C4#1062239611yescharacteristic
343C2—21no—
344C2—21no—
345C2—82no—
346C2#1306894811yescharacteristic
347C2#1306908711yescharacteristic
348C2#1306914111yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1517C2
socleC22×C11#386
prime radicalC11×#532C22
cosocleC2×C42×C11C23
hypercenter#1517D11
hypocenterC11#9289
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1517

Complements

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

NH ≅ G/Ntype
3. #13069588C2semidirect
4. #13067300C2semidirect
5. #13066474C2semidirect
6. #13066446C2semidirect
14. #10622706C4semidirect
15. #10622689C4semidirect
112. C2×C11⋊C8SD16semidirect
286. C11#9289semidirect

Maximal subgroups

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

subgroupindex
#130795382
#130773342
#130695882
#130673002
#130664742
#130664462
C11×#15172
#928911