Finite Group Databasebeta

← #14650413

Subgroups — #14650413

Order 2816.

478 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 107 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#13079744C211yesmaximal, characteristic
2#13077333C211yesmaximal, characteristic
3#13069590C211yesmaximal, characteristic, complemented
4#13067177C211yesmaximal, characteristic
5#13066476C211yesmaximal, characteristic, complemented
6#13066446C211yesmaximal, characteristic, complemented
7C11×#1548C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×#66960—21no—
10#10623008C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#423C2211yescharacteristic
13#10622742—21no—
14#10622701C412yescomplemented
15#10622697—22no—
16#10622692C412yescomplemented
17#10622581—22no—
18#10622549C2211yescharacteristic
19#10622538C2211yescharacteristic
20C2×#66867C2211yescharacteristic
21#10622449—22no—
22#10622449—22no—
23C11×#333—22no—
24#10622167—21no—
25#10622167—21no—
26#10622108—22no—
27C22×Q8×C11—21no—
28C2×#4339—21no—
29C2×C11×M16—21no—
30C11×C4⋊Q8—21no—
31C11×C4⋊Q8—21no—
32C11×C4⋊Q8—21no—
33C11×C4⋊Q8C2×C412yes—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×C42×C11C2311yescharacteristic
37#66983—21no—
38#66983D412yes—
39C2×C4⋊Dic11—21no—
40C22×C11⋊C8D411yescharacteristic
41C22×C11⋊C8D411yescharacteristic
42#66960—42no—
43#66960—42no—
44C2×#4313—22no—
45C2×C8×D11—22no—
46#66928—21no—
47#66927C2×C411yescharacteristic
48C4×D44—21no—
49C4×D44D412yes—
50#66922C2×C411yescharacteristic
51C11×C4⋊C8—21no—
52C11×C4⋊C8—21no—
53C11×C4⋊C8D412yes—
54C11×C22⋊C8—21no—
55C4×C8×C11—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C22⋊(C11⋊C8)—21no—
59(C2×D11)⋊C8—24no—
60#66873—24no—
61#66872—24no—
62C4⋊(C11⋊C8)—21no—
63#66867—21no—
64#66867—21no—
65C4×C11⋊C8C2×C412yes—
66#9287—111nomaximal, Sylow
67C2×Q8×C11—22no—
68C2×Q8×C11—41no—
69C2×Q8×C11—82no—
70C22×C4×C11—41no—
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11#4111yescharacteristic
74C2×C22⋊D11—22no—
75C22×Dic11—41no—
76#4339—41no—
77#4339—41no—
78#4339—41no—
79#4339—41no—
80C2×D44—21no—
81C2×D44—21no—
82C2×D44C22⋊C412yes—
83C2×C4×D11—22no—
84C2×Dic22—21no—
85C11×M16—41no—
86C11×M16—41no—
87C2×C8×C11—22no—
88C2×C8×C11—41no—
89C11×C4⋊C4—22no—
90C11×C4⋊C4—22no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—41no—
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—41no—
101C4⋊Dic11—41no—
102C4⋊Dic11C22⋊C412yes—
103C2×C11⋊C8—22no—
104C2×C11⋊C8—21no—
105C2×C11⋊C8—21no—
106C2×C11⋊C8—21no—
107C2×C11⋊C8—21no—
108C2×C11⋊C8—21no—
109C2×C11⋊C8SD1612yes—
110#4313—44no—
111C8×D11—44no—
112#3227—111no—
113#2932—111no—
114#1993—111no—
115#1548D1111yescharacteristic, complemented
116#1517—111no—
117#1286—111no—
118#1275—111no—
119C23×C11#12111yescharacteristic
120C22×D11—22no—
121Q8×C11—82no—
122Q8×C11—82no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—42no—
126C2×C4×C11—82no—
127C2×C4×C11C2×C22⋊C411yescharacteristic
128C2×C4×C11C4×D411yescharacteristic
129C2×C4×C11C4×D411yescharacteristic
130C2×C4×C11#12011yescharacteristic
131C2×C4×C11#12111yescharacteristic
132C2×C4×C11#12311yescharacteristic
133C2×C4×C11C2×SD1611yescharacteristic
134C2×C4×C11#13511yescharacteristic
135C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C11#13711yescharacteristic
137C22⋊D11—42no—
138C22⋊D11—42no—
139C2×Dic11—22no—
140C2×Dic11—81no—
141C2×Dic11—81no—
142C2×Dic11—81no—
143D44—42no—
144D44—41no—
145D44—41no—
146D44—81no—
147C4×D11—42no—
148C4×D11—42no—
149Dic22—41no—
150Dic22—41no—
151C8×C11—42no—
152C8×C11—81no—
153C11⋊C8—22no—
154C11⋊C8—42no—
155C11⋊C8—41no—
156C2×#131—221no—
157#532—111no—
158C2×C4⋊Q8C2×D1111yescharacteristic
159#498—112no—
160#486—112no—
161#481—222no—
162#476—222no—
163#435—222no—
164#435—222no—
165#431—111no—
166#431C2×D1111yescharacteristic
167#423C2×D1111yescharacteristic
168#408—221no—
169C2×#97—111no—
170#382—111no—
171#340—221no—
172#340—221no—
173#333—22no—
174#327—222no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11#38611yescharacteristic
178C22×C11#46111yescharacteristic
179C22×C11#46311yescharacteristic
180C2×D11—42no—
181C2×D11—42no—
182C2×D11—42no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—21no—
187C4×C11—82no—
188C4×C11C4×SD1611yescharacteristic
189C4×C11#44011yescharacteristic
190C4×C11#45011yescharacteristic
191C4×C11#45211yescharacteristic
192Dic11—42no—
193Dic11—161no—
194C2×#41—221no—
195C22×Q8—21no—
196#131—442no—
197#131—442no—
198C2×M16—21no—
199C2×M16—222no—
200C22×C8—111no—
201C22×C8—111no—
202C22×C8—222no—
203C4⋊Q8—21no—
204C4⋊Q8—21no—
205C4⋊Q8—21no—
206C4⋊Q8—111no—
207C4⋊Q8C4×D1112yes—
208#127—111no—
209#124—221no—
210#121—112no—
211#121—221no—
212C4×D4—112no—
213C4×D4—221no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—221no—
217C2×C42C22×D1111yescharacteristic
218#106—224no—
219C4⋊C8—21no—
220C4⋊C8—21no—
221C4⋊C8—221no—
222C4⋊C8C22⋊D1112yes—
223#102—224no—
224C22⋊C8—21no—
225C22⋊C8—224no—
226C22⋊C8—221no—
227#97—221no—
228#97—221no—
229C4×C8—21no—
230C4×C8—112no—
231#95—221no—
232#95—221no—
233C2×C11—21no—
234C2×C11—21no—
235C2×C11#187711yescharacteristic
236C2×C11#190311yescharacteristic
237C2×C11#190911yescharacteristic
238D11—82no—
239#41—441no—
240#41—441no—
241#41—441no—
242#41—441no—
243C2×Q8—22no—
244C2×Q8—41no—
245C2×Q8—82no—
246C2×Q8—221no—
247C2×D4—112no—
248C2×D4—222no—
249C2×D4—221no—
250C2×D4—221no—
251C22×C4—41no—
252C22×C4—222no—
253C22×C4—441no—
254C22×C4#433911yescharacteristic
255C22×C4D4×D1111yescharacteristic
256C22×C4D4×D1111yescharacteristic
257M16—41no—
258M16—41no—
259M16—444no—
260C2×C8—22no—
261C2×C8—41no—
262C2×C8—112no—
263C2×C8—221no—
264C2×C8—221no—
265C2×C8—222no—
266C2×C8—221no—
267C2×C8—221no—
268C2×C8—221no—
269C2×C8—444no—
270C4⋊C4—22no—
271C4⋊C4—22no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—112no—
275C4⋊C4—221no—
276C4⋊C4—441no—
277C4⋊C4—441no—
278C22⋊C4—222no—
279C22⋊C4—222no—
280C42C2×C4×D1111yescharacteristic
281C42D4×D1111yescharacteristic
282C42#434111yescharacteristic
283C42C2×C22⋊D1111yescharacteristic
284C11#928711yescharacteristic, complemented, Sylow
285C23—222no—
286C23#6693711yescharacteristic
287Q8—82no—
288Q8—82no—
289Q8—441no—
290Q8—441no—
291D4—442no—
292D4—442no—
293D4—442no—
294D4—441no—
295D4—441no—
296D4—881no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—82no—
301C2×C4—222no—
302C2×C4—442no—
303C2×C4—442no—
304C2×C4—881no—
305C2×C4—881no—
306C2×C4—881no—
307C2×C4C22⋊C4×D1111yescharacteristic
308C2×C4(C22⋊D11)⋊C411yescharacteristic
309C2×C4#6693611yescharacteristic
310C2×C4SD16×D1111yescharacteristic
311C2×C4#6696711yescharacteristic
312C2×C4#6697111yescharacteristic
313C2×C4#6697211yescharacteristic
314C2×C4C4×C22⋊D1111yescharacteristic
315C2×C4#6699011yescharacteristic
316C2×C4#6699111yescharacteristic
317C8—42no—
318C8—81no—
319C8—222no—
320C8—442no—
321C8—441no—
322C22—21no—
323C22—21no—
324C22—442no—
325C22—442no—
326C22—442no—
327C22#1062243111yescharacteristic
328C22#1062243211yescharacteristic
329C22#1062256911yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—82no—
335C4—442no—
336C4—1761no—
337C4#1062240111yescharacteristic
338C4#1062243011yescharacteristic
339C4#1062278211yescharacteristic
340C4#1062280011yescharacteristic
341C2—21no—
342C2—21no—
343C2—882no—
344C2#1306894711yescharacteristic
345C2#1306909911yescharacteristic
346C2#1306913511yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1548C2
socleC22×C11#386
prime radical#10623008C22
cosocleC2×C42×C11C23
hypercenter#1548D11
hypocenterC11#9287
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1548

Complements

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

NH ≅ G/Ntype
3. #13069590C2semidirect
5. #13066476C2semidirect
6. #13066446C2semidirect
7. C11×#1548C2semidirect
14. #10622701C4semidirect
16. #10622692C4semidirect
115. #1548D11semidirect
284. C11#9287semidirect

Maximal subgroups

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

subgroupindex
#130797442
#130773332
#130695902
#130671772
#130664762
#130664462
C11×#15482
#928711