Finite Group Databasebeta

← #14655608

Subgroups — #14655608

Order 2816.

514 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 105 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#13079739C211yesmaximal, characteristic
2#13079010C211yesmaximal, characteristic
3C2×#10622294C211yesmaximal, characteristic, complemented
4#13069460C211yesmaximal, characteristic, complemented
5#13067300C211yesmaximal, characteristic, complemented
6#13067068C211yesmaximal, characteristic
7C11×#1278C211yesmaximal, characteristic, complemented
8#10623008C2211yescharacteristic
9C2×#66922C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C4×C11×M16C2211yescharacteristic
13C2×C4×C8×C11C2211yescharacteristic
14C2×#66888—22no—
15#10622746—22no—
16C2×#66880—22no—
17#10622537C2211yescharacteristic
18#10622459—22no—
19#10622349—22no—
20#10622327—22no—
21#10622307—21no—
22#10622307—21no—
23#10622295—21no—
24#10622294—22no—
25#10622294—21no—
26#10622294—22no—
27#10622120—22no—
28#10622097—22no—
29C2×#4339—21no—
30C22×Dic22—21no—
31C22×Dic22—21no—
32C2×C11×M16D412yes—
33C22×C8×C11—21no—
34C2×C42×C11C2311yescharacteristic
35#66983—21no—
36#66983—21no—
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11D412yes—
41C2×#4318—21no—
42#66928—21no—
43#66927D411yescharacteristic
44C4×D44—21no—
45C4×D44—21no—
46#66922—21no—
47#66922—21no—
48#66922—21no—
49#66922—21no—
50#66922—21no—
51#66922—21no—
52#66922—21no—
53#66922D412yes—
54#66922D411yescharacteristic
55C11×C4⋊C8D412yes—
56C11×C22⋊C8—21no—
57C11×#97—21no—
58C4×C8×C11—21no—
59C4×C8×C11—21no—
60C4×C8×C11—21no—
61C4×C8×C11D412yes—
62#66888—44no—
63#66885—24no—
64#66885—24no—
65#66882—24no—
66#66880—24no—
67#66880—28no—
68C4⋊(C11⋊C8)—21no—
69C4⋊(C11⋊C8)—21no—
70#10158—111nomaximal, Sylow
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11#4111yescharacteristic
74C2×C22⋊D11—41no—
75C22×Dic11—22no—
76C22×Dic11—41no—
77#4339—42no—
78#4339—42no—
79C2×D44—21no—
80C2×D44—21no—
81C2×D44—21no—
82C2×C4×D11—41no—
83C2×Dic22—22no—
84C2×Dic22—21no—
85C2×Dic22—44no—
86C2×Dic22—41no—
87C2×Dic22—41no—
88C2×Dic22—41no—
89C2×Dic22—42no—
90C2×Dic22—42no—
91C11×M16—22no—
92C11×M16—22no—
93C2×C8×C11—22no—
94C2×C8×C11—22no—
95C2×C8×C11—22no—
96C2×C8×C11—42no—
97C42×C11C2×D411yescharacteristic
98C42×C11C2×D411yescharacteristic
99C42×C11C2×D411yescharacteristic
100C42×C11C2×D411yescharacteristic
101(C2×D11)⋊C4—41no—
102(C2×D11)⋊C4—41no—
103C4⋊Dic11—22no—
104C4⋊Dic11—22no—
105C4⋊Dic11—21no—
106C4⋊Dic11—22no—
107C4⋊Dic11—22no—
108C4⋊Dic11—21no—
109C4⋊Dic11—41no—
110C4⋊Dic11—41no—
111C4⋊Dic11—41no—
112C4⋊Dic11—41no—
113#4318—42no—
114C2×C11⋊C8—41no—
115#3226—111no—
116#3141—111no—
117C2×#487—111no—
118#1966—111no—
119#1549—111no—
120#1492—111no—
121#1278D1111yescharacteristic, complemented
122C23×C11#12111yescharacteristic
123C22×D11—41no—
124C2×C4×C11—22no—
125C2×C4×C11—22no—
126C2×C4×C11#12011yescharacteristic
127C2×C4×C11#12011yescharacteristic
128C2×C4×C11#12011yescharacteristic
129C2×C4×C11#12111yescharacteristic
130C2×C4×C11#12111yescharacteristic
131C2×C4×C11#12711yescharacteristic
132C2×C4×C11#13512yes—
133C2×C4×C11AGL(1,ℤ/8)12yes—
134C22⋊D11—82no—
135C2×Dic11—42no—
136C2×Dic11—42no—
137C2×Dic11—41no—
138C2×Dic11—44no—
139C2×Dic11—82no—
140D44—42no—
141D44—42no—
142D44—42no—
143C4×D11—81no—
144C4×D11—81no—
145Dic22—44no—
146Dic22—42no—
147Dic22—82no—
148Dic22—82no—
149Dic22—81no—
150Dic22—81no—
151C8×C11—42no—
152C8×C11—42no—
153C8×C11—42no—
154C11⋊C8—81no—
155#532—111no—
156C2×C4⋊Q8—111no—
157C2×C4⋊Q8—111no—
158#500—221no—
159#489—222no—
160#487—222no—
161#487—221no—
162#487—222no—
163#486—221no—
164#486—221no—
165#480—222no—
166#474—222no—
167#431C2×D1111yescharacteristic
168#423—111no—
169#417—222no—
170C2×#103—222no—
171C2×#101—222no—
172C4×M16C2×D1111yescharacteristic
173C2×C4×C8C2×D1111yescharacteristic
174#332—222no—
175D4⋊C8—222no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11#39211yescharacteristic
179C22×C11#46312yes—
180C2×D11—81no—
181C2×D11—81no—
182C2×D11—81no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11#44912yes—
186C4×C11#45412yes—
187C4×C11#47312yes—
188C4×C11#49511yescharacteristic
189C4×C11#49611yescharacteristic
190Dic11—82no—
191Dic11—81no—
192Dic11—82no—
193C2×#41—221no—
194C22×Q8—221no—
195C22×Q8—221no—
196C2×M16—221no—
197C2×M16D4412yes—
198C22×C8—21no—
199C4⋊Q8—112no—
200C4⋊Q8—111no—
201C4⋊Q8—221no—
202C4⋊Q8—221no—
203C4⋊Q8—221no—
204C4⋊Q8—221no—
205C4⋊Q8—221no—
206C4⋊Q8—221no—
207C4⋊Q8—221no—
208#127—111no—
209#124—221no—
210#121—221no—
211#121—221no—
212C4×D4—221no—
213C4×D4—221no—
214C2×C4⋊C4—112no—
215C2×C4⋊C4—221no—
216C2×C4⋊C4—221no—
217C2×C4⋊C4—221no—
218C2×C42C22×D1111yescharacteristic
219#107—224no—
220C4⋊C8—221no—
221C4⋊C8—221no—
222C4⋊C8D4412yes—
223#103—228no—
224#103—224no—
225#102—224no—
226#102—224no—
227#101—444no—
228C22⋊C8—21no—
229#97—21no—
230C4×C8—21no—
231C4×C8—21no—
232C4×C8—21no—
233C4×C8D4412yes—
234C2×C11—22no—
235C2×C11#200311yescharacteristic
236C2×C11#201211yescharacteristic
237C2×C11#202011yescharacteristic
238D11—161no—
239#41—442no—
240#41—442no—
241C2×Q8—221no—
242C2×Q8—222no—
243C2×Q8—444no—
244C2×Q8—441no—
245C2×Q8—441no—
246C2×Q8—441no—
247C2×Q8—442no—
248C2×Q8—442no—
249C2×D4—221no—
250C2×D4—221no—
251C2×D4—221no—
252C2×D4—441no—
253C22×C4—222no—
254C22×C4—441no—
255C22×C4—441no—
256C22×C4C2×D4411yescharacteristic
257C22×C4D4×D1111yescharacteristic
258C22×C4#434311yescharacteristic
259M16—22no—
260M16—22no—
261M16—442no—
262C2×C8—22no—
263C2×C8—22no—
264C2×C8—22no—
265C2×C8—42no—
266C2×C8—441no—
267C4⋊C4—222no—
268C4⋊C4—222no—
269C4⋊C4—222no—
270C4⋊C4—221no—
271C4⋊C4—222no—
272C4⋊C4—221no—
273C4⋊C4—441no—
274C4⋊C4—441no—
275C4⋊C4—441no—
276C4⋊C4—441no—
277C22⋊C4—441no—
278C22⋊C4—441no—
279C42C2×D4411yescharacteristic
280C42C2×D4411yescharacteristic
281C42D4×D1111yescharacteristic
282C42D4×D1111yescharacteristic
283C11#1015811yescharacteristic, complemented, Sylow
284C23—441no—
285C23#6694811yescharacteristic
286Q8—444no—
287Q8—442no—
288Q8—881no—
289Q8—881no—
290Q8—882no—
291Q8—882no—
292D4—442no—
293D4—442no—
294D4—442no—
295D4—882no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—441no—
299C2×C4—442no—
300C2×C4—442no—
301C2×C4—444no—
302C2×C4—882no—
303C2×C4—881no—
304C2×C4—881no—
305C2×C4#6692711yescharacteristic
306C2×C4#6693511yescharacteristic
307C2×C4#6693511yescharacteristic
308C2×C4#6693511yescharacteristic
309C2×C4#6694811yescharacteristic
310C2×C4#6694811yescharacteristic
311C2×C4#6695712yes—
312C2×C4#6696112yes—
313C8—42no—
314C8—42no—
315C8—42no—
316C8—881no—
317C22—21no—
318C22—21no—
319C22—881no—
320C22—881no—
321C22—881no—
322C22#1062228411yescharacteristic
323C22#1062245712yes—
324C4—21no—
325C4—21no—
326C4—882no—
327C4—882no—
328C4—881no—
329C4#1062230911yescharacteristic
330C4#1062232511yescharacteristic
331C4#1062234712yes—
332C4#1062244012yes—
333C4#1062250912yes—
334C2—22no—
335C2—1761no—
336C2#1306964111yescharacteristic
337C2#1306969611yescharacteristic
338C2#1306973811yescharacteristic
subgroupG/H
centerC22#10622284
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1278C2
socleC22×C11#392
prime radical#10623008C22
hypercenter#1278D11
hypocenterC11#10158
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1278

Complements

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

NH ≅ G/Ntype
3. C2×#10622294C2semidirect
4. #13069460C2semidirect
5. #13067300C2semidirect
7. C11×#1278C2semidirect
121. #1278D11semidirect
283. C11#10158semidirect

Maximal subgroups

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

subgroupindex
#130797392
#130790102
C2×#106222942
#130694602
#130673002
#130670682
C11×#12782
#1015811