Finite Group Databasebeta

← #14657387

Subgroups — #14657387

Order 2816.

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

normal subgroups only

This group has 408 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
1C2×#10622703C211yesmaximal, characteristic
2#13068609C211yesmaximal, characteristic
3#13067387C211yesmaximal, characteristic
4#13067288C211yesmaximal, characteristic
5#13067010C211yesmaximal, characteristic
6#13066511C211yesmaximal, characteristic
7C11×#1546C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C22×#4326—21no—
10C2×C4×Dic22C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#423C2211yescharacteristic
13C2×#66899—21no—
14C2×#66888—21no—
15#10622703—22no—
16#10622703—22no—
17#10622538C2211yescharacteristic
18#10622537C2211yescharacteristic
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C11×#332—22no—
21#10622192—21no—
22#10622185—22no—
23#10622122—22no—
24#10622095—22no—
25C22×Q8×C11—21no—
26C22×Dic22D411yescharacteristic
27C2×C11×M16—21no—
28C11×C4⋊Q8—21no—
29C11×C4⋊Q8—21no—
30C11×C4⋊Q8—21no—
31C11×C4⋊Q8D412yes—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C42×C11C2311yescharacteristic
35C2×#4326—24no—
36C2×#4326—42no—
37C2×#4326—42no—
38C2×C4⋊Dic11D411yescharacteristic
39C2×Dic11⋊C4—21no—
40C2×C4×Dic11—21no—
41C2×#4318—21no—
42C22×C11⋊C8—21no—
43C4×Dic22—21no—
44C4×Dic22—21no—
45C4×Dic22—21no—
46C4×Dic22—21no—
47C11×C4⋊C8—21no—
48C11×C4⋊C8—21no—
49C11×C4⋊C8D412yes—
50C11×C22⋊C8—21no—
51C4×C8×C11—21no—
52#66899—24no—
53C22⋊(C11⋊C8)—21no—
54#66888—42no—
55C4⋊(C11⋊C8)—21no—
56C4⋊(C11⋊C8)—21no—
57C4⋊(C11⋊C8)—21no—
58C4⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)D412yes—
60C4×C11⋊C8—21no—
61#10447—111nomaximal, Sylow
62C2×Q8×C11—22no—
63C2×Q8×C11—41no—
64C2×Q8×C11—41no—
65C2×Q8×C11—41no—
66C2×Q8×C11—41no—
67C2×Q8×C11—41no—
68C22×C4×C11—41no—
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11#4111yescharacteristic
71C22×C4×C11#4111yescharacteristic
72C22×Dic11—21no—
73C22×Dic11—21no—
74C2×Dic22—21no—
75C2×Dic22—21no—
76C2×Dic22—21no—
77C2×Dic22—21no—
78C2×Dic22—21no—
79C2×Dic22SD1612yes—
80C11×M16—41no—
81C11×M16—41no—
82C2×C8×C11—22no—
83C2×C8×C11—41no—
84C11×C4⋊C4—22no—
85C11×C4⋊C4—22no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C42×C11C2×D411yescharacteristic
89C42×C11C2×D411yescharacteristic
90C42×C11C2×D411yescharacteristic
91C42×C11#4111yescharacteristic
92#4326—48no—
93C4⋊Dic11—21no—
94C4⋊Dic11—21no—
95Dic11⋊C4—41no—
96Dic11⋊C4—41no—
97C4×Dic11—41no—
98C4×Dic11—41no—
99#4318—41no—
100#4318—41no—
101C2×C11⋊C8—22no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8—41no—
104C2×C11⋊C8—41no—
105C2×C11⋊C8—41no—
106C2×#462—111no—
107#1801—111no—
108#1570—111no—
109#1546—111no—
110#1546D1111yescharacteristic
111#1479—111no—
112#1301—111no—
113C23×C11#12311yescharacteristic
114Q8×C11—42no—
115Q8×C11—42no—
116Q8×C11—81no—
117Q8×C11—81no—
118C2×C4×C11—22no—
119C2×C4×C11—41no—
120C2×C4×C11—42no—
121C2×C4×C11—81no—
122C2×C4×C11—81no—
123C2×C4×C11#12011yescharacteristic
124C2×C4×C11#12111yescharacteristic
125C2×C4×C11#12111yescharacteristic
126C2×C4×C11#12111yescharacteristic
127C2×C4×C11#12311yescharacteristic
128C2×C4×C11#12411yescharacteristic
129C2×C4×C11C2×SD1611yescharacteristic
130C2×C4×C11#13511yescharacteristic
131C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
133C2×Dic11—22no—
134C2×Dic11—41no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—81no—
138Dic22—22no—
139Dic22—22no—
140Dic22—41no—
141Dic22—41no—
142C8×C11—42no—
143C8×C11—81no—
144C11⋊C8—42no—
145C11⋊C8—81no—
146C11⋊C8—81no—
147C22×Q16—221no—
148C2×C4⋊Q8C2×D1111yescharacteristic
149C2×C4×Q8—111no—
150#462—222no—
151#462—222no—
152#431—111no—
153#431C2×D1111yescharacteristic
154#423—111no—
155#423C2×D1111yescharacteristic
156C2×C4⋊C8—111no—
157C2×#103—221no—
158C2×#101—221no—
159#343—221no—
160#334—222no—
161#332—22no—
162#332—222no—
163Q8⋊C8—222no—
164C22×C11—21no—
165C22×C11—21no—
166C22×C11#39411yescharacteristic
167C22×C11#48111yescharacteristic
168C22×C11#48211yescharacteristic
169C4×C11—21no—
170C4×C11—21no—
171C4×C11—21no—
172C4×C11—82no—
173C4×C11#44911yescharacteristic
174C4×C11#45011yescharacteristic
175C4×C11#46511yescharacteristic
176C4×C11#46911yescharacteristic
177C4×C11#47312yes—
178Dic11—42no—
179Dic11—81no—
180C22×Q8—21no—
181C22×Q8—111no—
182C2×Q16—224no—
183C2×Q16—442no—
184C2×Q16—442no—
185C2×M16—21no—
186C2×M16—221no—
187C22×C8—221no—
188C4⋊Q8—21no—
189C4⋊Q8—21no—
190C4⋊Q8—21no—
191C4⋊Q8D4412yes—
192C4×Q8—221no—
193C4×Q8—221no—
194C4×Q8—221no—
195C4×Q8—221no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—111no—
199C2×C4⋊C4—221no—
200C2×C42—221no—
201C2×C42C22×D1111yescharacteristic
202C4⋊C8—21no—
203C4⋊C8—21no—
204C4⋊C8—112no—
205C4⋊C8—221no—
206C4⋊C8—221no—
207C4⋊C8—221no—
208C4⋊C8—221no—
209C4⋊C8C22⋊D1112yes—
210#103—224no—
211#101—442no—
212C22⋊C8—21no—
213C22⋊C8—221no—
214C4×C8—21no—
215C4×C8—221no—
216C2×C11—21no—
217C2×C11—21no—
218C2×C11#203411yescharacteristic
219C2×C11#204711yescharacteristic
220C2×C11#204911yescharacteristic
221C2×Q8—22no—
222C2×Q8—41no—
223C2×Q8—41no—
224C2×Q8—41no—
225C2×Q8—41no—
226C2×Q8—41no—
227C2×Q8—112no—
228C2×Q8—221no—
229C2×Q8—221no—
230C2×Q8—221no—
231C2×Q8—221no—
232C2×Q8—221no—
233C22×C4—41no—
234C22×C4—221no—
235C22×C4—221no—
236C22×C4#433911yescharacteristic
237C22×C4D4×D1111yescharacteristic
238C22×C4#434111yescharacteristic
239Q16—448no—
240M16—41no—
241M16—41no—
242M16—441no—
243M16—441no—
244C2×C8—22no—
245C2×C8—41no—
246C2×C8—222no—
247C2×C8—441no—
248C2×C8—441no—
249C2×C8—441no—
250C2×C8—441no—
251C4⋊C4—22no—
252C4⋊C4—22no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—221no—
256C4⋊C4—221no—
257C4⋊C4—441no—
258C4⋊C4—441no—
259C42—441no—
260C42—441no—
261C42C2×D4411yescharacteristic
262C42D4×D1111yescharacteristic
263C42#434111yescharacteristic
264C42C2×C22⋊D1111yescharacteristic
265C11#1044711yescharacteristic, complemented, Sylow
266C23#6693611yescharacteristic
267Q8—42no—
268Q8—42no—
269Q8—81no—
270Q8—81no—
271Q8—222no—
272Q8—222no—
273Q8—441no—
274Q8—441no—
275C2×C4—22no—
276C2×C4—41no—
277C2×C4—42no—
278C2×C4—81no—
279C2×C4—81no—
280C2×C4—222no—
281C2×C4—441no—
282C2×C4—441no—
283C2×C4—441no—
284C2×C4—881no—
285C2×C4#6693511yescharacteristic
286C2×C4#6693811yescharacteristic
287C2×C4#6693911yescharacteristic
288C2×C4#6696411yescharacteristic
289C2×C4#6696411yescharacteristic
290C2×C4SD16×D1111yescharacteristic
291C2×C4#6696911yescharacteristic
292C2×C4#6698311yescharacteristic
293C2×C4#6699111yescharacteristic
294C2×C4#6699211yescharacteristic
295C8—42no—
296C8—81no—
297C8—442no—
298C8—881no—
299C8—881no—
300C22—21no—
301C22—21no—
302C22#1062239011yescharacteristic
303C22#1062239211yescharacteristic
304C22#1062257411yescharacteristic
305C4—21no—
306C4—21no—
307C4—21no—
308C4—82no—
309C4—442no—
310C4—881no—
311C4#1062238911yescharacteristic
312C4#1062239411yescharacteristic
313C4#1062277211yescharacteristic
314C4#1062278411yescharacteristic
315C4#1062281712yes—
316C2—21no—
317C2—21no—
318C2#1306980411yescharacteristic
319C2#1306988311yescharacteristic
320C2#1306989511yescharacteristic
subgroupG/H
centerC22#10622574
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1546C2
socleC22×C11#394
prime radicalC23×C11#123
hypercenter#1546D11
hypocenterC11#10447
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1546

Complements

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

NH ≅ G/Ntype
265. C11#10447semidirect

Maximal subgroups

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

subgroupindex
C2×#106227032
#130686092
#130673872
#130672882
#130670102
#130665112
C11×#15462
#1044711