Finite Group Databasebeta

← #14655607

Subgroups — #14655607

Order 2816.

514 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 103 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#13079734C211yesmaximal, characteristic
2#13079009C211yesmaximal, characteristic
3C2×#10622294C211yesmaximal, characteristic, complemented
4#13069459C211yesmaximal, characteristic, complemented
5#13067302C211yesmaximal, characteristic, complemented
6#13066453C211yesmaximal, characteristic, complemented
7C11×#1492C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×#66922C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C2×C4×C8×C11C2211yescharacteristic
13#10622845—22no—
14C2×#66888—22no—
15C2×#66880—22no—
16#10622694—21no—
17#10622691—21no—
18#10622683—21no—
19#10622683—21no—
20#10622668—22no—
21#10622646—22no—
22#10622620—22no—
23#10622538C2211yescharacteristic
24C4×#4318C2211yescharacteristic
25#10622294—22no—
26#10622294—22no—
27C11×D4⋊C8—22no—
28#10622124—22no—
29C2×C11×#41—21no—
30C22×Dic22—21no—
31C22×Dic22—21no—
32C2×C11×M16—21no—
33C22×C8×C11—21no—
34C11×C4⋊Q8D411yescharacteristic
35C11×#127D411yescharacteristic
36C11×#124—21no—
37C11×#121—21no—
38C11×#121—21no—
39C4×D4×C11—21no—
40C4×D4×C11—21no—
41C2×C42×C11C2311yescharacteristic
42C2×C4⋊Dic11—21no—
43C2×C4⋊Dic11—21no—
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11D412yes—
46C2×#4318D412yes—
47#66922—21no—
48#66922—21no—
49#66922—21no—
50#66922—21no—
51#66922—21no—
52#66922—21no—
53#66922—21no—
54#66922D412yes—
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C4×C8×C11—21no—
58C4×C8×C11D412yes—
59#66899—24no—
60#66896—24no—
61#66896—24no—
62C22⋊(C11⋊C8)—21no—
63#66888—44no—
64#66880—28no—
65#66871—24no—
66C4⋊(C11⋊C8)D412yes—
67#66867—21no—
68C4×C11⋊C8—21no—
69C4×C11⋊C8—21no—
70#10158—111nomaximal, Sylow
71C11×#41—42no—
72C11×#41—42no—
73C2×Q8×C11—21no—
74C2×D4×C11—21no—
75C2×D4×C11—21no—
76C2×D4×C11—21no—
77C2×D4×C11—41no—
78C22×C4×C11—41no—
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11#4111yescharacteristic
82C22×Dic11—22no—
83C22×Dic11—41no—
84C2×Dic22—22no—
85C2×Dic22—44no—
86C2×Dic22—41no—
87C2×Dic22—41no—
88C2×Dic22—41no—
89C2×Dic22—42no—
90C2×Dic22—42no—
91C11×M16—42no—
92C2×C8×C11—22no—
93C2×C8×C11—42no—
94C2×C8×C11—41no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—21no—
97C11×C22⋊C4—41no—
98C11×C22⋊C4—41no—
99C42×C11C2×D411yescharacteristic
100C42×C11C2×D411yescharacteristic
101C42×C11C2×D411yescharacteristic
102C42×C11C2×D411yescharacteristic
103C4⋊Dic11—22no—
104C4⋊Dic11—22no—
105C4⋊Dic11—22no—
106C4⋊Dic11—22no—
107C4⋊Dic11—41no—
108C4⋊Dic11—41no—
109C4⋊Dic11—41no—
110C4⋊Dic11—41no—
111#4318—22no—
112#4318—22no—
113C2×C11⋊C8—22no—
114C2×C11⋊C8—22no—
115#3226—111no—
116#3141—111no—
117C2×#487—111no—
118#1966—111no—
119#1549—111no—
120#1492D1111yescharacteristic
121#1278—111no—
122C23×C11—41no—
123C23×C11#12111yescharacteristic
124Q8×C11—42no—
125D4×C11—42no—
126D4×C11—42no—
127D4×C11—42no—
128D4×C11—82no—
129C2×C4×C11—22no—
130C2×C4×C11—22no—
131C2×C4×C11—41no—
132C2×C4×C11—81no—
133C2×C4×C11—81no—
134C2×C4×C11#12011yescharacteristic
135C2×C4×C11#12011yescharacteristic
136C2×C4×C11#12011yescharacteristic
137C2×C4×C11#12111yescharacteristic
138C2×C4×C11#12111yescharacteristic
139C2×C4×C11#12711yescharacteristic
140C2×C4×C11#13512yes—
141C2×C4×C11AGL(1,ℤ/8)12yes—
142C2×Dic11—42no—
143C2×Dic11—42no—
144C2×Dic11—44no—
145C2×Dic11—82no—
146Dic22—44no—
147Dic22—82no—
148Dic22—82no—
149Dic22—81no—
150Dic22—81no—
151C8×C11—42no—
152C8×C11—81no—
153C11⋊C8—42no—
154C11⋊C8—42no—
155#532C2×D1111yescharacteristic
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#431—111no—
168#423C2×D1111yescharacteristic
169#417—222no—
170C2×#103—222no—
171C2×#101—222no—
172C4×M16—111no—
173C2×C4×C8C2×D1111yescharacteristic
174#332—222no—
175D4⋊C8—22no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11—81no—
179C22×C11—81no—
180C22×C11—81no—
181C22×C11#39211yescharacteristic
182C22×C11#46312yes—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—81no—
186C4×C11#44912yes—
187C4×C11#45412yes—
188C4×C11#47312yes—
189C4×C11#49511yescharacteristic
190C4×C11#49611yescharacteristic
191Dic11—82no—
192Dic11—82no—
193C2×#41—21no—
194C22×Q8—221no—
195C22×Q8—221no—
196C2×M16—21no—
197C2×M16—112no—
198C22×C8—21no—
199C4⋊Q8—112no—
200C4⋊Q8—221no—
201C4⋊Q8—221no—
202C4⋊Q8—221no—
203C4⋊Q8—221no—
204C4⋊Q8—221no—
205C4⋊Q8—221no—
206C4⋊Q8—221no—
207C4⋊Q8D4411yescharacteristic
208#127D4411yescharacteristic
209#124—21no—
210#121—21no—
211#121—21no—
212C4×D4—21no—
213C4×D4—21no—
214C2×C4⋊C4—112no—
215C2×C4⋊C4—221no—
216C2×C4⋊C4—221no—
217C2×C4⋊C4—221no—
218C2×C42C22×D1111yescharacteristic
219#107—224no—
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8—112no—
223#103—228no—
224#103—224no—
225#102—224no—
226#102—224no—
227#101—444no—
228C22⋊C8—221no—
229#97—221no—
230C4×C8—21no—
231C4×C8—221no—
232C4×C8—221no—
233C4×C8C22⋊D1112yes—
234C2×C11—22no—
235C2×C11—161no—
236C2×C11#200311yescharacteristic
237C2×C11#201211yescharacteristic
238C2×C11#202011yescharacteristic
239#41—42no—
240#41—42no—
241C2×Q8—21no—
242C2×Q8—222no—
243C2×Q8—444no—
244C2×Q8—441no—
245C2×Q8—441no—
246C2×Q8—442no—
247C2×Q8—442no—
248C2×Q8—441no—
249C2×D4—21no—
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—41no—
253C22×C4—41no—
254C22×C4—222no—
255C22×C4—441no—
256C22×C4#433911yescharacteristic
257C22×C4D4×D1111yescharacteristic
258C22×C4D4×D1111yescharacteristic
259M16—42no—
260M16—222no—
261M16—222no—
262C2×C8—22no—
263C2×C8—42no—
264C2×C8—41no—
265C2×C8—222no—
266C2×C8—222no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—222no—
270C4⋊C4—222no—
271C4⋊C4—222no—
272C4⋊C4—222no—
273C4⋊C4—441no—
274C4⋊C4—441no—
275C4⋊C4—441no—
276C4⋊C4—441no—
277C22⋊C4—41no—
278C22⋊C4—41no—
279C42C2×D4411yescharacteristic
280C42D4×D1111yescharacteristic
281C42D4×D1111yescharacteristic
282C42C2×C22⋊D1111yescharacteristic
283C11#1015811yescharacteristic, complemented, Sylow
284C23—41no—
285C23#6693711yescharacteristic
286Q8—42no—
287Q8—444no—
288Q8—881no—
289Q8—881no—
290Q8—882no—
291Q8—882no—
292D4—42no—
293D4—42no—
294D4—42no—
295D4—82no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—41no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—442no—
302C2×C4—442no—
303C2×C4—444no—
304C2×C4—882no—
305C2×C4#6693511yescharacteristic
306C2×C4#6693511yescharacteristic
307C2×C4#6693711yescharacteristic
308C2×C4#6696412yes—
309C2×C4#6696912yes—
310C2×C4#6698311yescharacteristic
311C2×C4#6699011yescharacteristic
312C2×C4#6699311yescharacteristic
313C8—42no—
314C8—81no—
315C8—442no—
316C8—442no—
317C22—21no—
318C22—21no—
319C22—81no—
320C22—81no—
321C22—81no—
322C22#1062240012yes—
323C22#1062257311yescharacteristic
324C4—21no—
325C4—21no—
326C4—81no—
327C4—882no—
328C4—882no—
329C4#1062239412yes—
330C4#1062244012yes—
331C4#1062275612yes—
332C4#1062276711yescharacteristic
333C4#1062278111yescharacteristic
334C2—22no—
335C2—161no—
336C2#1306963711yescharacteristic
337C2#1306969511yescharacteristic
338C2#1306973711yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1492C2
socleC22×C11#392
prime radicalC11×#532C22
hypercenter#1492D11
hypocenterC11#10158
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1492

Complements

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

NH ≅ G/Ntype
3. C2×#10622294C2semidirect
4. #13069459C2semidirect
5. #13067302C2semidirect
6. #13066453C2semidirect
283. C11#10158semidirect

Maximal subgroups

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

subgroupindex
#130797342
#130790092
C2×#106222942
#130694592
#130673022
#130664532
C11×#14922
#1015811