Finite Group Databasebeta

← #14657396

Subgroups — #14657396

Order 2816.

408 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 99 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#13068608C211yesmaximal, characteristic
3#13067387C211yesmaximal, characteristic, complemented
4#13067300C211yesmaximal, characteristic, complemented
5#13067296C211yesmaximal, characteristic, complemented
6#13066512C211yesmaximal, characteristic, complemented
7C11×#1478C211yesmaximal, characteristic
8C2×C4×D4×C11C2211yescharacteristic
9C2×#66922C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C2×#66897—21no—
13C2×#66896—21no—
14#10622620—22no—
15#10622620—22no—
16C2×#66871—21no—
17#10622537C2211yescharacteristic
18#10622537C2211yescharacteristic
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C11×D4⋊C8—22no—
21#10622168—21no—
22#10622120—22no—
23#10622119—22no—
24#10622095—22no—
25C22×D4×C11D411yescharacteristic
26C23×C4×C11—21no—
27C22×Dic22—21no—
28C4×D4×C11—21no—
29C4×D4×C11—21no—
30C4×D4×C11—21no—
31C4×D4×C11—21no—
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C11×C22⋊C4—21no—
34C2×C42×C11C2311yescharacteristic
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—21no—
37C2×#4318—21no—
38C2×#4318—21no—
39C22×C11⋊C8—21no—
40#66922—21no—
41#66922—21no—
42#66922—21no—
43#66922D412yes—
44C11×C4⋊C8—21no—
45C11×C4⋊C8D412yes—
46C11×C22⋊C8—21no—
47C11×C22⋊C8—21no—
48C4×C8×C11—21no—
49C4×C8×C11—21no—
50#66897—42no—
51#66896—24no—
52#66871—24no—
53C4⋊(C11⋊C8)—21no—
54C4⋊(C11⋊C8)—21no—
55C4⋊(C11⋊C8)—21no—
56C4⋊(C11⋊C8)—21no—
57C4⋊(C11⋊C8)—21no—
58C4⋊(C11⋊C8)D412yes—
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—
78C2×C8×C11—22no—
79C2×C8×C11—41no—
80C11×C4⋊C4—21no—
81C11×C4⋊C4—21no—
82C11×C22⋊C4—41no—
83C11×C22⋊C4—41no—
84C42×C11C2×D411yescharacteristic
85C42×C11C2×D411yescharacteristic
86C42×C11C2×D411yescharacteristic
87C42×C11#4111yescharacteristic
88C4⋊Dic11—22no—
89C4⋊Dic11—22no—
90C4⋊Dic11—41no—
91C4⋊Dic11—41no—
92#4318—41no—
93#4318—41no—
94#4318—41no—
95#4318—41no—
96C2×C11⋊C8—22no—
97C2×C11⋊C8—41no—
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#1548—111no—
106#1478D1111yescharacteristic
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—42no—
139C8×C11—81no—
140C11⋊C8—42no—
141C11⋊C8—81no—
142C11⋊C8—81no—
143C2×C4⋊Q8—111no—
144C2×C4×D4C2×D1111yescharacteristic
145#474—222no—
146#474—222no—
147#431C2×D1111yescharacteristic
148#431C2×D1111yescharacteristic
149C2×#107—221no—
150#423—111no—
151#423—111no—
152C2×C4⋊C8—111no—
153C2×#102—221no—
154C2×#100—221no—
155#343—221no—
156#334—222no—
157#333—222no—
158#332—222no—
159D4⋊C8—22no—
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×D4D4411yescharacteristic
182C23×C4—21no—
183C2×M16—221no—
184C2×M16—221no—
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⋊C4D4411yescharacteristic
197C2×C22⋊C4—21no—
198C2×C42C22×D1111yescharacteristic
199#107—224no—
200C4⋊C8—21no—
201C4⋊C8—112no—
202C4⋊C8—221no—
203C4⋊C8—221no—
204C4⋊C8—221no—
205C4⋊C8—221no—
206C4⋊C8—221no—
207C4⋊C8C22⋊D1112yes—
208#102—224no—
209#100—442no—
210C22⋊C8—21no—
211C22⋊C8—21no—
212C4×C8—21no—
213C4×C8—21no—
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#431412yes—
230C22×C4—21no—
231C22×C4—41no—
232C22×C4—41no—
233C22×C4—82no—
234C22×C4—441no—
235C22×C4C2×D4411yescharacteristic
236C22×C4#434111yescharacteristic
237C22×C4#434111yescharacteristic
238M16—441no—
239M16—441no—
240M16—441no—
241M16—441no—
242C2×C8—22no—
243C2×C8—41no—
244C2×C8—222no—
245C2×C8—441no—
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—
257C42#433911yescharacteristic
258C42D4×D1111yescharacteristic
259C42D4×D1111yescharacteristic
260C42C2×C22⋊D1111yescharacteristic
261C11#1044811yescharacteristic, complemented, Sylow
262C23—22no—
263C23—41no—
264C23—41no—
265C23—81no—
266C23—81no—
267C23#6693911yescharacteristic
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#6693511yescharacteristic
283C2×C4#6693611yescharacteristic
284C2×C4#6693811yescharacteristic
285C2×C4C2×#431411yescharacteristic
286C2×C4#6695711yescharacteristic
287C2×C4#6696211yescharacteristic
288C2×C4#6696211yescharacteristic
289C2×C4#6698311yescharacteristic
290C2×C4#6699111yescharacteristic
291C2×C4#6699211yescharacteristic
292C8—42no—
293C8—81no—
294C8—442no—
295C8—881no—
296C8—881no—
297C22—21no—
298C22—21no—
299C22—42no—
300C22—82no—
301C22—82no—
302C22—81no—
303C22—81no—
304C22#1062233411yescharacteristic
305C22#1062233611yescharacteristic
306C22#1062257411yescharacteristic
307C4—21no—
308C4—21no—
309C4—21no—
310C4—81no—
311C4—882no—
312C4#1062234611yescharacteristic
313C4#1062235111yescharacteristic
314C4#1062272711yescharacteristic
315C4#1062275011yescharacteristic
316C4#1062281212yes—
317C2—21no—
318C2—21no—
319C2—82no—
320C2#1306981311yescharacteristic
321C2#1306987111yescharacteristic
322C2#1306989711yescharacteristic
subgroupG/H
centerC22#10622574
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1478C2
socleC22×C11#394
prime radicalC22×D4×C11D4
hypercenter#1478D11
hypocenterC11#10448
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1478

Complements

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

NH ≅ G/Ntype
3. #13067387C2semidirect
4. #13067300C2semidirect
5. #13067296C2semidirect
6. #13066512C2semidirect
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
#130686082
#130673872
#130673002
#130672962
#130665122
C11×#14782
#1044811