Finite Group Databasebeta

← #14657395

Subgroups — #14657395

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×#10622620C211yesmaximal, characteristic
2#13067388C211yesmaximal, characteristic, complemented
3#13067302C211yesmaximal, characteristic, complemented
4#13067298C211yesmaximal, characteristic, complemented
5#13067007C211yesmaximal, characteristic
6#13066511C211yesmaximal, characteristic, complemented
7C11×#1800C211yesmaximal, characteristic
8C2×C4×D4×C11C2211yescharacteristic
9C2×#66922C2211yescharacteristic
10C11×#423C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C2×C11×#100—21no—
13C2×#66896—21no—
14#10622620—22no—
15#10622620—22no—
16C2×#66871—21no—
17#10622538C2211yescharacteristic
18#10622538C2211yescharacteristic
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C11×#343—21no—
21D4⋊(C11⋊C8)—22no—
22#10622124—22no—
23#10622119—22no—
24#10622118—22no—
25C22×D4×C11D411yescharacteristic
26C23×C4×C11—21no—
27C22×Dic22—21no—
28C2×C11×M16—21no—
29C2×C11×M16—21no—
30C4×D4×C11—21no—
31C4×D4×C11—21no—
32C4×D4×C11—21no—
33C4×D4×C11—21no—
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C11×C22⋊C4—21no—
36C2×C42×C11C2311yescharacteristic
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11—21no—
39C22×C11⋊C8—21no—
40#66922—21no—
41#66922—21no—
42#66922—21no—
43#66922D412yes—
44C11×C4⋊C8—21no—
45C11×C4⋊C8—21no—
46C11×C4⋊C8—21no—
47C11×C4⋊C8—21no—
48C11×#100—42no—
49#66896—24no—
50C22⋊(C11⋊C8)—21no—
51C22⋊(C11⋊C8)—21no—
52#66871—24no—
53C4⋊(C11⋊C8)—21no—
54C4⋊(C11⋊C8)—21no—
55C4⋊(C11⋊C8)D412yes—
56C4⋊(C11⋊C8)D412yes—
57C4×C11⋊C8—21no—
58C4×C11⋊C8—21no—
59#10448—111nomaximal, Sylow
60C24×C11—21no—
61C2×D4×C11—21no—
62C2×D4×C11—21no—
63C2×D4×C11—21no—
64C2×D4×C11—21no—
65C2×D4×C11—21no—
66C2×D4×C11SD1612yes—
67C22×C4×C11—21no—
68C22×C4×C11—41no—
69C22×C4×C11—41no—
70C22×C4×C11—82no—
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11#4111yescharacteristic
73C22×C4×C11#4111yescharacteristic
74C22×Dic11—41no—
75C2×Dic22—22no—
76C2×Dic22—41no—
77C2×Dic22—82no—
78C11×M16—41no—
79C11×M16—41no—
80C11×M16—41no—
81C11×M16—41no—
82C2×C8×C11—41no—
83C2×C8×C11—41no—
84C11×C4⋊C4—21no—
85C11×C4⋊C4—21no—
86C11×C22⋊C4—41no—
87C11×C22⋊C4—41no—
88C42×C11C2×D411yescharacteristic
89C42×C11C2×D411yescharacteristic
90C42×C11C2×D411yescharacteristic
91C42×C11#4111yescharacteristic
92C4⋊Dic11—22no—
93C4⋊Dic11—22no—
94C4⋊Dic11—41no—
95C4⋊Dic11—41no—
96C2×C11⋊C8—22no—
97C2×C11⋊C8—22no—
98C2×C11⋊C8—41no—
99C2×C11⋊C8—41no—
100C2×C11⋊C8—41no—
101C2×#474—111no—
102#1800D1111yescharacteristic
103#1570—111no—
104#1549—111no—
105#1548—111no—
106#1478—111no—
107#1301—111no—
108C23×C11—22no—
109C23×C11—41no—
110C23×C11—41no—
111C23×C11—81no—
112C23×C11—81no—
113C23×C11#12311yescharacteristic
114D4×C11—22no—
115D4×C11—22no—
116D4×C11—41no—
117D4×C11—41no—
118C2×C4×C11—22no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—82no—
122C2×C4×C11—82no—
123C2×C4×C11—81no—
124C2×C4×C11#12011yescharacteristic
125C2×C4×C11#12111yescharacteristic
126C2×C4×C11#12111yescharacteristic
127C2×C4×C11#12111yescharacteristic
128C2×C4×C11#12311yescharacteristic
129C2×C4×C11#12411yescharacteristic
130C2×C4×C11C2×SD1611yescharacteristic
131C2×C4×C11#13511yescharacteristic
132C2×C4×C11#13711yescharacteristic
133C2×C4×C11#13711yescharacteristic
134C2×Dic11—42no—
135C2×Dic11—82no—
136Dic22—82no—
137Dic22—82no—
138C8×C11—81no—
139C8×C11—81no—
140C11⋊C8—42no—
141C11⋊C8—42no—
142C11⋊C8—81no—
143C2×C4⋊Q8—111no—
144C2×C4×D4C2×D1111yescharacteristic
145#474—222no—
146#474—222no—
147#431—111no—
148#431—111no—
149C2×#107—221no—
150#423C2×D1111yescharacteristic
151#423C2×D1111yescharacteristic
152C2×C4⋊C8—111no—
153C2×#102—221no—
154C2×#100—21no—
155#343—21no—
156#334—222no—
157#333—222no—
158#332—222no—
159D4⋊C8—222no—
160C22×C11—21no—
161C22×C11—21no—
162C22×C11—42no—
163C22×C11—82no—
164C22×C11—82no—
165C22×C11—81no—
166C22×C11—81no—
167C22×C11#39411yescharacteristic
168C22×C11#48311yescharacteristic
169C22×C11#48511yescharacteristic
170C4×C11—21no—
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—81no—
174C4×C11#44811yescharacteristic
175C4×C11#45211yescharacteristic
176C4×C11#46511yescharacteristic
177C4×C11#47011yescharacteristic
178C4×C11#47212yes—
179Dic11—82no—
180C22×Q8—221no—
181C22×D4C22⋊D1111yescharacteristic
182C23×C4—21no—
183C2×M16—21no—
184C2×M16—21no—
185C22×C8—221no—
186C4⋊Q8—112no—
187C4⋊Q8—221no—
188C4⋊Q8—221no—
189C4⋊Q8—221no—
190C4×D4—21no—
191C4×D4—21no—
192C4×D4—21no—
193C4×D4—21no—
194C2×C4⋊C4—221no—
195C2×C4⋊C4—221no—
196C2×C4⋊C4C22⋊D1111yescharacteristic
197C2×C22⋊C4—21no—
198C2×C42C22×D1111yescharacteristic
199#107—224no—
200C4⋊C8—21no—
201C4⋊C8—21no—
202C4⋊C8—21no—
203C4⋊C8—21no—
204C4⋊C8—112no—
205C4⋊C8—112no—
206C4⋊C8—221no—
207C4⋊C8—221no—
208#102—224no—
209#100—42no—
210C22⋊C8—221no—
211C22⋊C8—221no—
212C4×C8—221no—
213C4×C8—221no—
214C2×C11—21no—
215C2×C11—21no—
216C2×C11—82no—
217C2×C11#203511yescharacteristic
218C2×C11#204511yescharacteristic
219C2×C11#204911yescharacteristic
220C24—21no—
221C2×Q8—222no—
222C2×Q8—441no—
223C2×Q8—882no—
224C2×D4—21no—
225C2×D4—21no—
226C2×D4—21no—
227C2×D4—21no—
228C2×D4—21no—
229C2×D4#432412yes—
230C22×C4—21no—
231C22×C4—41no—
232C22×C4—41no—
233C22×C4—82no—
234C22×C4—441no—
235C22×C4#433911yescharacteristic
236C22×C4#433911yescharacteristic
237C22×C4C2×C22⋊D1111yescharacteristic
238M16—41no—
239M16—41no—
240M16—41no—
241M16—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—222no—
245C2×C8—222no—
246C2×C8—441no—
247C2×C8—441no—
248C2×C8—441no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—222no—
252C4⋊C4—222no—
253C4⋊C4—441no—
254C4⋊C4—441no—
255C22⋊C4—41no—
256C22⋊C4—41no—
257C42D4×D1111yescharacteristic
258C42D4×D1111yescharacteristic
259C42D4×D1111yescharacteristic
260C42#434111yescharacteristic
261C11#1044811yescharacteristic, complemented, Sylow
262C23—22no—
263C23—41no—
264C23—41no—
265C23—81no—
266C23—81no—
267C23#6698211yescharacteristic
268Q8—882no—
269Q8—882no—
270D4—22no—
271D4—22no—
272D4—41no—
273D4—41no—
274C2×C4—22no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—82no—
278C2×C4—82no—
279C2×C4—81no—
280C2×C4—442no—
281C2×C4—882no—
282C2×C4#6693611yescharacteristic
283C2×C4#6693711yescharacteristic
284C2×C4#6693711yescharacteristic
285C2×C4#6693811yescharacteristic
286C2×C4C2×#432411yescharacteristic
287C2×C4#6699011yescharacteristic
288C2×C4#6699211yescharacteristic
289C2×C4#6699511yescharacteristic
290C2×C4#6700311yescharacteristic
291C2×C4#6700411yescharacteristic
292C8—81no—
293C8—81no—
294C8—442no—
295C8—442no—
296C8—881no—
297C22—21no—
298C22—21no—
299C22—42no—
300C22—82no—
301C22—82no—
302C22—81no—
303C22—81no—
304C22#1062257211yescharacteristic
305C22#1062258411yescharacteristic
306C22#1062260911yescharacteristic
307C4—21no—
308C4—21no—
309C4—21no—
310C4—81no—
311C4—882no—
312C4#1062236212yes—
313C4#1062265311yescharacteristic
314C4#1062265411yescharacteristic
315C4#1062266011yescharacteristic
316C4#1062266511yescharacteristic
317C2—21no—
318C2—21no—
319C2—82no—
320C2#1306981211yescharacteristic
321C2#1306987011yescharacteristic
322C2#1306989611yescharacteristic
subgroupG/H
centerC22#10622572
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1800C2
socleC22×C11#394
prime radicalC22×D4×C11D4
hypercenter#1800D11
hypocenterC11#10448
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1800

Complements

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

NH ≅ G/Ntype
2. #13067388C2semidirect
3. #13067302C2semidirect
4. #13067298C2semidirect
6. #13066511C2semidirect
261. C11#10448semidirect

Maximal subgroups

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

subgroupindex
C2×#106226202
#130673882
#130673022
#130672982
#130670072
#130665112
C11×#18002
#1044811