Finite Group Databasebeta

← #14657393

Subgroups — #14657393

Order 2816.

408 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 95 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×#10622700C211yesmaximal, characteristic
2#13068605C211yesmaximal, characteristic
3#13067388C211yesmaximal, characteristic, complemented
4#13067301C211yesmaximal, characteristic, complemented
5#13067008C211yesmaximal, characteristic
6#13066512C211yesmaximal, characteristic, complemented
7C11×#1548C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C4×D44C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C2×#66887—21no—
13#10622700—22no—
14#10622700—22no—
15C2×#66873—21no—
16C2×#66871—21no—
17#10622538C2211yescharacteristic
18#10622537C2211yescharacteristic
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C11×#333—22no—
21#10622192—21no—
22#10622185—22no—
23#10622118—22no—
24#10622097—22no—
25C22×Q8×C11—21no—
26C22×D44D411yescharacteristic
27C22×C4×D11—21no—
28C2×C11×M16—21no—
29C11×C4⋊Q8—21no—
30C11×C4⋊Q8—21no—
31C11×C4⋊Q8—21no—
32C11×C4⋊Q8D412yes—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C42×C11C2311yescharacteristic
36C2×(C2×D11)⋊C4—21no—
37C2×C4⋊Dic11D411yescharacteristic
38C2×#4318—21no—
39C22×C11⋊C8—21no—
40C4×D44—21no—
41C4×D44—21no—
42C4×D44—21no—
43C4×D44—21no—
44C11×C4⋊C8—21no—
45C11×C4⋊C8—21no—
46C11×C4⋊C8—21no—
47C11×C22⋊C8—21no—
48C4×C8×C11—21no—
49C22⋊(C11⋊C8)—21no—
50#66887—42no—
51#66873—24no—
52#66871—24no—
53C4⋊(C11⋊C8)—21no—
54C4⋊(C11⋊C8)—21no—
55C4⋊(C11⋊C8)—21no—
56C4⋊(C11⋊C8)D412yes—
57C4⋊(C11⋊C8)D412yes—
58C4×C11⋊C8—21no—
59#10448—111nomaximal, Sylow
60C23×D11—21no—
61C2×Q8×C11—22no—
62C2×Q8×C11—41no—
63C2×Q8×C11—82no—
64C22×C4×C11—41no—
65C22×C4×C11C2×D411yescharacteristic
66C22×C4×C11#4111yescharacteristic
67C22×C4×C11#4111yescharacteristic
68C22×Dic11—21no—
69C2×D44—21no—
70C2×D44—21no—
71C2×D44—21no—
72C2×D44—21no—
73C2×D44—21no—
74C2×D44SD1612yes—
75C2×C4×D11—41no—
76C2×C4×D11—41no—
77C2×C4×D11—82no—
78C11×M16—41no—
79C11×M16—41no—
80C2×C8×C11—41no—
81C2×C8×C11—41no—
82C11×C4⋊C4—22no—
83C11×C4⋊C4—22no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—41no—
86C42×C11C2×D411yescharacteristic
87C42×C11C2×D411yescharacteristic
88C42×C11C2×D411yescharacteristic
89C42×C11#4111yescharacteristic
90(C2×D11)⋊C4—41no—
91(C2×D11)⋊C4—41no—
92C4⋊Dic11—21no—
93C4⋊Dic11—21no—
94#4318—41no—
95#4318—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#1800—111no—
103#1570—111no—
104#1549—111no—
105#1548D1111yescharacteristic, complemented
106#1478—111no—
107#1301—111no—
108C23×C11#12311yescharacteristic
109C22×D11—22no—
110C22×D11—41no—
111C22×D11—41no—
112C22×D11—81no—
113C22×D11—81no—
114Q8×C11—82no—
115Q8×C11—82no—
116C2×C4×C11—22no—
117C2×C4×C11—41no—
118C2×C4×C11—42no—
119C2×C4×C11—82no—
120C2×C4×C11#12011yescharacteristic
121C2×C4×C11#12111yescharacteristic
122C2×C4×C11#12111yescharacteristic
123C2×C4×C11#12111yescharacteristic
124C2×C4×C11#12311yescharacteristic
125C2×C4×C11#12411yescharacteristic
126C2×C4×C11C2×SD1611yescharacteristic
127C2×C4×C11#13511yescharacteristic
128C2×C4×C11#13711yescharacteristic
129C2×C4×C11#13711yescharacteristic
130C2×Dic11—41no—
131C2×Dic11—81no—
132D44—22no—
133D44—22no—
134D44—41no—
135D44—41no—
136C4×D11—82no—
137C4×D11—82no—
138C8×C11—81no—
139C8×C11—81no—
140C11⋊C8—42no—
141C11⋊C8—42no—
142C11⋊C8—81no—
143C2×C4⋊Q8C2×D1111yescharacteristic
144C2×C4×D4—111no—
145#474—222no—
146#474—222no—
147#431—111no—
148#431C2×D1111yescharacteristic
149C2×#107—221no—
150#423—111no—
151#423C2×D1111yescharacteristic
152C2×C4⋊C8—111no—
153C2×#102—221no—
154C2×#100—221no—
155#343—221no—
156#334—222no—
157#333—22no—
158#332—222no—
159D4⋊C8—222no—
160C22×C11—21no—
161C22×C11—21no—
162C22×C11#39411yescharacteristic
163C22×C11#48311yescharacteristic
164C22×C11#48511yescharacteristic
165C2×D11—42no—
166C2×D11—82no—
167C2×D11—81no—
168C2×D11—81no—
169C2×D11—82no—
170C4×C11—21no—
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—82no—
174C4×C11#44811yescharacteristic
175C4×C11#45211yescharacteristic
176C4×C11#46511yescharacteristic
177C4×C11#47011yescharacteristic
178C4×C11#47212yes—
179Dic11—81no—
180C22×Q8—21no—
181C22×D4—111no—
182C23×C4—221no—
183C2×M16—21no—
184C2×M16—221no—
185C22×C8—221no—
186C4⋊Q8—21no—
187C4⋊Q8—21no—
188C4⋊Q8—21no—
189C4⋊Q8C22⋊D1112yes—
190C4×D4—221no—
191C4×D4—221no—
192C4×D4—221no—
193C4×D4—221no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—111no—
197C2×C22⋊C4—221no—
198C2×C42C22×D1111yescharacteristic
199#107—224no—
200C4⋊C8—21no—
201C4⋊C8—21no—
202C4⋊C8—21no—
203C4⋊C8—112no—
204C4⋊C8—112no—
205C4⋊C8—221no—
206C4⋊C8—221no—
207C4⋊C8—221no—
208#102—224no—
209#100—442no—
210C22⋊C8—21no—
211C22⋊C8—221no—
212C4×C8—21no—
213C4×C8—221no—
214C2×C11—21no—
215C2×C11—21no—
216C2×C11#203511yescharacteristic
217C2×C11#204511yescharacteristic
218C2×C11#204911yescharacteristic
219D11—82no—
220C24—221no—
221C2×Q8—22no—
222C2×Q8—41no—
223C2×Q8—82no—
224C2×D4—112no—
225C2×D4—221no—
226C2×D4—221no—
227C2×D4—221no—
228C2×D4—221no—
229C2×D4—221no—
230C22×C4—41no—
231C22×C4—221no—
232C22×C4—441no—
233C22×C4—441no—
234C22×C4—882no—
235C22×C4#433911yescharacteristic
236C22×C4D4×D1111yescharacteristic
237C22×C4#434111yescharacteristic
238M16—41no—
239M16—41no—
240M16—441no—
241M16—441no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—222no—
245C2×C8—222no—
246C2×C8—441no—
247C2×C8—441no—
248C2×C8—441no—
249C4⋊C4—22no—
250C4⋊C4—22no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—221no—
254C4⋊C4—221no—
255C22⋊C4—441no—
256C22⋊C4—441no—
257C42#433911yescharacteristic
258C42D4×D1111yescharacteristic
259C42D4×D1111yescharacteristic
260C42C2×C22⋊D1111yescharacteristic
261C11#1044811yescharacteristic, complemented, Sylow
262C23—222no—
263C23—441no—
264C23—441no—
265C23—881no—
266C23—881no—
267C23#6693611yescharacteristic
268Q8—82no—
269Q8—82no—
270D4—222no—
271D4—222no—
272D4—441no—
273D4—441no—
274C2×C4—22no—
275C2×C4—41no—
276C2×C4—42no—
277C2×C4—82no—
278C2×C4—441no—
279C2×C4—882no—
280C2×C4—882no—
281C2×C4—881no—
282C2×C4#6693711yescharacteristic
283C2×C4#6693711yescharacteristic
284C2×C4#6693811yescharacteristic
285C2×C4SD16×D1111yescharacteristic
286C2×C4#6696811yescharacteristic
287C2×C4#6697111yescharacteristic
288C2×C4#6697211yescharacteristic
289C2×C4#6698211yescharacteristic
290C2×C4#6699011yescharacteristic
291C2×C4#6699211yescharacteristic
292C8—81no—
293C8—81no—
294C8—442no—
295C8—442no—
296C8—881no—
297C22—21no—
298C22—21no—
299C22—442no—
300C22—882no—
301C22—882no—
302C22—881no—
303C22—881no—
304C22#1062241811yescharacteristic
305C22#1062242711yescharacteristic
306C22#1062257211yescharacteristic
307C4—21no—
308C4—21no—
309C4—21no—
310C4—82no—
311C4—881no—
312C4#1062236212yes—
313C4#1062242011yescharacteristic
314C4#1062242911yescharacteristic
315C4#1062278311yescharacteristic
316C4#1062280011yescharacteristic
317C2—21no—
318C2—21no—
319C2—882no—
320C2#1306981011yescharacteristic
321C2#1306987011yescharacteristic
322C2#1306989411yescharacteristic
subgroupG/H
centerC22#10622572
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1548C2
socleC22×C11#394
prime radicalC22×D44D4
hypercenter#1548D11
hypocenterC11#10448
LCSG ▷ C2×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. #13067388C2semidirect
4. #13067301C2semidirect
6. #13066512C2semidirect
7. C11×#1548C2semidirect
105. #1548D11semidirect
261. C11#10448semidirect

Maximal subgroups

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

subgroupindex
C2×#106227002
#130686052
#130673882
#130673012
#130670082
#130665122
C11×#15482
#1044811