Finite Group Databasebeta

← #14648049

Subgroups — #14648049

Order 2816.

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

normal subgroups only

This group has 388 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
1#13077746C211yesmaximal, characteristic
2#13067407C211yesmaximal, characteristic, complemented
3#13067053C211yesmaximal, characteristic
4#13066999C211yesmaximal, characteristic
5#13066505C211yesmaximal, characteristic, complemented
6#13066453C211yesmaximal, characteristic, complemented
7C11×#1848C211yesmaximal, characteristic, complemented
8C4×#4339C2211yescharacteristic
9C2×C11×#108—22no—
10C11×#423C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C2×C4×C8×C11C2211yescharacteristic
13#10622741—22no—
14#10622538C2211yescharacteristic
15#10622538C2211yescharacteristic
16C4×#4318C2211yescharacteristic
17#10622451—21no—
18#10622450—21no—
19#10622446—21no—
20#10622443—21no—
21#10622122—21no—
22#10622121—21no—
23#10622118—21no—
24#10622117—21no—
25#10622097C411yescharacteristic
26#10622097C411yescharacteristic
27#10622094C411yescharacteristic
28#10622094C411yescharacteristic
29C2×#4339Q811yescharacteristic
30C2×C11×M16—21no—
31C2×C11×M16D412yes—
32C22×C8×C11—21no—
33C2×C42×C11C2311yescharacteristic
34C4×C22⋊D11—21no—
35C4×C22⋊D11—21no—
36#66979Q811yescharacteristic
37C2×#4318—21no—
38C2×#4313—22no—
39C4×D44C2×C411yescharacteristic
40C4×D44D411yescharacteristic
41#66925—21no—
42C42×D11—21no—
43C4×Dic22C2×C411yescharacteristic
44C4×Dic22D411yescharacteristic
45C11×#108—44no—
46C11×C4⋊C8—21no—
47C11×C4⋊C8—21no—
48C11×C4⋊C8—21no—
49C11×C4⋊C8—21no—
50C4×C8×C11—21no—
51C4×C8×C11C2×C411yescharacteristic
52C4×C8×C11C2×C411yescharacteristic
53C22⋊(C11⋊C8)—21no—
54C22⋊(C11⋊C8)—21no—
55(C2×D11)⋊C8—22no—
56Dic11⋊C8—22no—
57C8×Dic11—22no—
58C4⋊(C11⋊C8)C2×C411yescharacteristic
59C4⋊(C11⋊C8)C2×C411yescharacteristic
60C4⋊(C11⋊C8)D411yescharacteristic
61C4⋊(C11⋊C8)D411yescharacteristic
62#66867—21no—
63C4×C11⋊C8—21no—
64C4×C11⋊C8—21no—
65C4×C11⋊C8—21no—
66#8899—111nomaximal, Sylow
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×Q811yescharacteristic
69C22×C4×C11#4111yescharacteristic
70C2×C22⋊D11—21no—
71#4339—22no—
72#4339—41no—
73C2×D44C4⋊C411yescharacteristic
74C2×C4×D11—21no—
75C2×C4×D11—21no—
76C2×C4×D11—21no—
77C2×Dic22C4⋊C411yescharacteristic
78C11×M16—42no—
79C11×M16—42no—
80C2×C8×C11—22no—
81C2×C8×C11—22no—
82C2×C8×C11—21no—
83C2×C8×C11—21no—
84C2×C8×C11—22no—
85C2×C8×C11—41no—
86C42×C11C22×C411yescharacteristic
87C42×C11C2×D411yescharacteristic
88C42×C11C2×D411yescharacteristic
89C42×C11#4111yescharacteristic
90C22⋊Dic11—21no—
91(C2×D11)⋊C4—21no—
92(C2×D11)⋊C4—21no—
93C4⋊Dic11C4⋊C411yescharacteristic
94C4⋊Dic11C4⋊C411yescharacteristic
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97C4×Dic11—21no—
98C4×Dic11—21no—
99C4×Dic11—21no—
100#4318—22no—
101#4318—41no—
102C2×C11⋊C8—21no—
103C2×C11⋊C8—21no—
104C2×C11⋊C8—21no—
105C2×C11⋊C8—21no—
106C2×C11⋊C8—41no—
107#4313—82no—
108#2991—111no—
109#1848D1111yescharacteristic, complemented
110#1574—111no—
111#1489—111no—
112#1476—111no—
113#1299—111no—
114#1278—111no—
115C23×C11C22⋊Q811yescharacteristic
116C22×D11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11C2×C4⋊C411yescharacteristic
124C2×C4×C11C4×D411yescharacteristic
125C2×C4×C11C4×D411yescharacteristic
126C2×C4×C11#12011yescharacteristic
127C2×C4×C11C22⋊Q811yescharacteristic
128C2×C4×C11#12311yescharacteristic
129C22⋊D11—42no—
130C2×Dic11—21no—
131C2×Dic11—21no—
132C2×Dic11—21no—
133D44—21no—
134D44—21no—
135C4×D11—42no—
136C4×D11—41no—
137C4×D11—41no—
138C4×D11—41no—
139C4×D11—41no—
140Dic22—21no—
141Dic22#10812yescomplemented
142C8×C11—22no—
143C8×C11—22no—
144C8×C11—42no—
145C8×C11—81no—
146C11⋊C8—42no—
147C11⋊C8—41no—
148C11⋊C8—41no—
149C11⋊C8—41no—
150C11⋊C8—41no—
151C4×#41—111no—
152C8×Q8—221no—
153#436—221no—
154#436—222no—
155#431—111no—
156#431—111no—
157#431—221no—
158C2×#108—22no—
159#423—221no—
160#423C2×D1111yescharacteristic
161#423C2×D1111yescharacteristic
162C4×M16—111no—
163C2×C4×C8C2×D1111yescharacteristic
164#335—221no—
165#334—221no—
166Q8⋊C8—111no—
167Q8⋊C8—111no—
168Q8⋊C8—221no—
169D4⋊C8—111no—
170D4⋊C8—111no—
171D4⋊C8—221no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11#38511yescharacteristic
176C2×D11—41no—
177C2×D11—41no—
178C2×D11—41no—
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11C2×#10811yescharacteristic
183C4×C11#43011yescharacteristic
184C4×C11#44311yescharacteristic
185C4×C11#44411yescharacteristic
186C4×C11#45311yescharacteristic
187C4×C11#45611yescharacteristic
188Dic11—22no—
189Dic11—41no—
190Dic11—41no—
191C2×#41—111no—
192C2×M16—21no—
193C2×M16—222no—
194C2×M16—221no—
195C2×M16C22⋊D1112yes—
196C22×C8—21no—
197C4×Q8—111no—
198C4×Q8—111no—
199C4×D4—111no—
200C4×D4—111no—
201C4×D4—221no—
202C4×D4—221no—
203#117—111no—
204#117—221no—
205C2×C42—221no—
206C2×C42C22×D1111yescharacteristic
207#108—44no—
208C4⋊C8—21no—
209C4⋊C8—21no—
210C4⋊C8—21no—
211C4⋊C8—21no—
212C4⋊C8—111no—
213C4⋊C8—111no—
214C4⋊C8—111no—
215C4⋊C8—111no—
216C4⋊C8—222no—
217C22⋊C8—222no—
218C22⋊C8—221no—
219C22⋊C8—221no—
220#97—221no—
221C4×C8—21no—
222C4×C8—222no—
223C4×C8—221no—
224C4×C8—221no—
225C4×C8—221no—
226C4×C8C4×D1111yescharacteristic
227C4×C8C4×D1111yescharacteristic
228C2×C11—41no—
229C2×C11#185511yescharacteristic
230C2×C11#185911yescharacteristic
231C2×C11#186611yescharacteristic
232D11—81no—
233#41—222no—
234#41—441no—
235C2×Q8—111no—
236C2×D4—111no—
237C2×D4—221no—
238C22×C4—221no—
239C22×C4—221no—
240C22×C4—221no—
241C22×C4Q8×D1111yescharacteristic
242C22×C4#434311yescharacteristic
243C22×C4C2×C22⋊D1111yescharacteristic
244M16—42no—
245M16—42no—
246M16—222no—
247M16—441no—
248M16—882no—
249C2×C8—22no—
250C2×C8—22no—
251C2×C8—21no—
252C2×C8—21no—
253C2×C8—22no—
254C2×C8—41no—
255C2×C8—221no—
256C2×C8—221no—
257C2×C8—221no—
258C2×C8—221no—
259C2×C8—441no—
260C4⋊C4—111no—
261C4⋊C4—111no—
262C4⋊C4—221no—
263C4⋊C4—221no—
264C22⋊C4—221no—
265C22⋊C4—221no—
266C22⋊C4—221no—
267C42—221no—
268C42—221no—
269C42—221no—
270C42C2×C4×D1111yescharacteristic
271C42#433911yescharacteristic
272C42D4×D1111yescharacteristic
273C42D4×D1111yescharacteristic
274C11#889911yescharacteristic, complemented, Sylow
275C23—221no—
276C23#6699911yescharacteristic
277Q8—112no—
278Q8—221no—
279D4—221no—
280D4—221no—
281D4—442no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—221no—
289C2×C4—221no—
290C2×C4—221no—
291C2×C4—442no—
292C2×C4—441no—
293C2×C4—441no—
294C2×C4—441no—
295C2×C4—441no—
296C2×C4C4⋊C4×D1111yescharacteristic
297C2×C4#6694611yescharacteristic
298C2×C4#6694711yescharacteristic
299C2×C4#6694911yescharacteristic
300C2×C4C4×C22⋊D1111yescharacteristic
301C2×C4#6699011yescharacteristic
302C8—22no—
303C8—22no—
304C8—42no—
305C8—81no—
306C8—442no—
307C8—441no—
308C8—441no—
309C8—441no—
310C8—441no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—441no—
315C22—441no—
316C22—441no—
317C22#1062260211yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—222no—
322C4—441no—
323C4—441no—
324C4D11×#10811yescharacteristic
325C4#1062250611yescharacteristic
326C4#1062250711yescharacteristic
327C4#1062250811yescharacteristic
328C4#1062269011yescharacteristic
329C4#1062270811yescharacteristic
330C2—41no—
331C2—881no—
332C2#1306881911yescharacteristic
333C2#1306884111yescharacteristic
334C2#1306888811yescharacteristic
subgroupG/H
centerC2×C4#66990
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1848C2
socleC22×C11#385
prime radicalC2×#4339Q8
cosocleC2×C42×C11C23
hypercenter#1848D11
hypocenterC11#8899
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1848

Complements

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

NH ≅ G/Ntype
2. #13067407C2semidirect
5. #13066505C2semidirect
6. #13066453C2semidirect
7. C11×#1848C2semidirect
109. #1848D11semidirect
141. Dic22#108semidirect
274. C11#8899semidirect

Maximal subgroups

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

subgroupindex
#130777462
#130674072
#130670532
#130669992
#130665052
#130664532
C11×#18482
#889911