Finite Group Databasebeta

← #14655717

Subgroups — #14655717

Order 2816.

578 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 109 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×#10622691C211yesmaximal, characteristic, complemented
2#13079076C211yesmaximal, characteristic
3#13069461C211yesmaximal, characteristic, complemented
4#13067287C211yesmaximal, characteristic, complemented
5#13067067C211yesmaximal, characteristic
6#13066452C211yesmaximal, characteristic, complemented
7C11×#3226C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×#67004—22no—
11C2×#66922C2211yescharacteristic
12C11×#500—21no—
13C11×#486—21no—
14C11×#480—22no—
15C11×#474—22no—
16C11×#431C2211yescharacteristic
17C2×#66900—22no—
18#10622705—21no—
19#10622691—22no—
20#10622691—22no—
21#10622689—21no—
22#10622673—22no—
23C2×#66871—22no—
24#10622537C2211yescharacteristic
25C4×#4318C2211yescharacteristic
26C2×C4×C11⋊C8C2211yescharacteristic
27D4⋊(C11⋊C8)—22no—
28#10622124—22no—
29C2×C11×#41—21no—
30C22×Q8×C11—21no—
31C22×Dic22—21no—
32C11×C4⋊Q8—21no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8D411yescharacteristic
37C11×#127D411yescharacteristic
38C11×#124—21no—
39C11×#121—21no—
40C11×#121—21no—
41C4×D4×C11—21no—
42C4×D4×C11—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4D412yes—
45C2×C42×C11C2311yescharacteristic
46#67004—44no—
47#67004—44no—
48C2×#4326—24no—
49C2×#4324—24no—
50C2×C4⋊Dic11—21no—
51C2×C4⋊Dic11—21no—
52C2×#4318—21no—
53C2×#4318D412yes—
54C22×C11⋊C8—21no—
55#66922—21no—
56#66922—21no—
57#66922—21no—
58#66922D412yes—
59C11×#107—24no—
60C11×C4⋊C8D412yes—
61C11×#102—24no—
62C11×C22⋊C8—21no—
63C4×C8×C11—21no—
64#66900—44no—
65#66871—28no—
66C4⋊(C11⋊C8)—21no—
67C4⋊(C11⋊C8)—21no—
68#66867—21no—
69C4×C11⋊C8—21no—
70C4×C11⋊C8—21no—
71C4×C11⋊C8D412yes—
72#10174—111nomaximal, Sylow
73C11×#41—42no—
74C11×#41—42no—
75C2×Q8×C11—21no—
76C2×Q8×C11—41no—
77C2×Q8×C11—41no—
78C2×Q8×C11—42no—
79C2×Q8×C11—42no—
80C2×D4×C11—21no—
81C2×D4×C11—21no—
82C2×D4×C11—21no—
83C2×D4×C11—41no—
84C22×C4×C11—22no—
85C22×C4×C11—41no—
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11#4111yescharacteristic
89C22×Dic11—41no—
90C2×Dic22—22no—
91C2×Dic22—41no—
92C2×Dic22—42no—
93C2×Dic22—42no—
94C2×C8×C11—22no—
95C11×C4⋊C4—22no—
96C11×C4⋊C4—22no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C11×C22⋊C4—41no—
102C11×C22⋊C4—41no—
103C42×C11C2×D411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C42×C11C2×D411yescharacteristic
107#4326—48no—
108#4324—48no—
109C4⋊Dic11—22no—
110C4⋊Dic11—22no—
111C4⋊Dic11—41no—
112C4⋊Dic11—41no—
113#4318—22no—
114#4318—42no—
115#4318D814yes—
116C2×C11⋊C8—24no—
117C2×C11⋊C8—22no—
118C2×C11⋊C8—22no—
119C2×C11⋊C8—41no—
120#3226D1111yescharacteristic
121C2×#500—111no—
122#3152—111no—
123#1966—111no—
124#1546—111no—
125#1492—111no—
126#1278—111no—
127C23×C11—41no—
128C23×C11#12111yescharacteristic
129Q8×C11—42no—
130Q8×C11—82no—
131Q8×C11—81no—
132Q8×C11—81no—
133D4×C11—42no—
134D4×C11—42no—
135D4×C11—42no—
136D4×C11—82no—
137C2×C4×C11—22no—
138C2×C4×C11—22no—
139C2×C4×C11—41no—
140C2×C4×C11—42no—
141C2×C4×C11—44no—
142C2×C4×C11—81no—
143C2×C4×C11—81no—
144C2×C4×C11#12011yescharacteristic
145C2×C4×C11#12011yescharacteristic
146C2×C4×C11#12011yescharacteristic
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11#12111yescharacteristic
149C2×C4×C11#12711yescharacteristic
150C2×C4×C11C2×D812yes—
151C2×C4×C11AGL(1,ℤ/8)12yes—
152C2×Dic11—42no—
153C2×Dic11—82no—
154Dic22—44no—
155Dic22—81no—
156Dic22—81no—
157C8×C11—42no—
158C11⋊C8—24no—
159C11⋊C8—24no—
160C11⋊C8—81no—
161C2×#137—222no—
162#532C2×D1111yescharacteristic
163C2×C4⋊Q8—111no—
164C2×C4⋊Q8C2×D1111yescharacteristic
165#500—21no—
166#500—222no—
167#500—222no—
168#497—222no—
169#494—221no—
170#492—221no—
171#486—21no—
172#480—22no—
173#474—22no—
174#431C2×D1111yescharacteristic
175C2×#107—222no—
176#423—111no—
177C2×#101—222no—
178C4×M16—111no—
179C2×C4×C8—111no—
180#332—222no—
181D4⋊C8—222no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—81no—
185C22×C11—81no—
186C22×C11—81no—
187C22×C11#39211yescharacteristic
188C22×C11#45912yes—
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—82no—
192C4×C11—81no—
193C4×C11#44712yes—
194C4×C11#45612yes—
195C4×C11#47312yes—
196C4×C11#49311yescharacteristic
197C4×C11#49611yescharacteristic
198Dic11—82no—
199C2×#41—21no—
200C22×Q8—21no—
201C22×Q8—221no—
202#137—444no—
203#137—444no—
204C2×Q16—224no—
205C2×SD16—224no—
206C2×M16—112no—
207C2×M16—221no—
208C22×C8—221no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8—21no—
212C4⋊Q8—21no—
213C4⋊Q8—112no—
214C4⋊Q8—221no—
215C4⋊Q8—221no—
216C4⋊Q8—221no—
217C4⋊Q8C22⋊D1111yescharacteristic
218#127C22⋊D1111yescharacteristic
219#124—21no—
220#121—21no—
221#121—21no—
222C4×D4—21no—
223C4×D4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—221no—
226C2×C4⋊C4—221no—
227C2×C4⋊C4C22⋊D1112yes—
228C2×C42C22×D1111yescharacteristic
229#107—24no—
230#107—228no—
231C4⋊C8—221no—
232C4⋊C8—221no—
233C4⋊C8C22⋊D1112yes—
234#102—24no—
235#101—444no—
236C22⋊C8—21no—
237#97—221no—
238C4×C8—21no—
239C4×C8—112no—
240C4×C8—221no—
241C4×C8—221no—
242C2×C11—22no—
243C2×C11—161no—
244C2×C11#200511yescharacteristic
245C2×C11#201111yescharacteristic
246C2×C11#202011yescharacteristic
247#41—42no—
248#41—42no—
249C2×Q8—21no—
250C2×Q8—42no—
251C2×Q8—42no—
252C2×Q8—41no—
253C2×Q8—41no—
254C2×Q8—222no—
255C2×Q8—441no—
256C2×Q8—442no—
257C2×Q8—442no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—41no—
262C22×C4—22no—
263C22×C4—41no—
264C22×C4—441no—
265C22×C4D4×D1111yescharacteristic
266C22×C4#434111yescharacteristic
267C22×C4C2×C22⋊D1111yescharacteristic
268Q16—448no—
269SD16—448no—
270M16—114no—
271M16—222no—
272M16—442no—
273C2×C8—22no—
274C2×C8—224no—
275C2×C8—222no—
276C2×C8—222no—
277C2×C8—441no—
278C4⋊C4—22no—
279C4⋊C4—21no—
280C4⋊C4—22no—
281C4⋊C4—21no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—222no—
285C4⋊C4—222no—
286C4⋊C4—441no—
287C4⋊C4—441no—
288C22⋊C4—41no—
289C22⋊C4—41no—
290C42D4×D1111yescharacteristic
291C42D4×D1111yescharacteristic
292C42C2×C22⋊D1111yescharacteristic
293C42C2×C22⋊D1111yescharacteristic
294C11#1017411yescharacteristic, complemented, Sylow
295C23—41no—
296C23#6699211yescharacteristic
297Q8—42no—
298Q8—81no—
299Q8—81no—
300Q8—82no—
301Q8—444no—
302Q8—881no—
303Q8—881no—
304D4—42no—
305D4—42no—
306D4—42no—
307D4—82no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—44no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—442no—
316C2×C4—882no—
317C2×C4D8×D1112yes—
318C2×C4#6696412yes—
319C2×C4#6699011yescharacteristic
320C2×C4#6699011yescharacteristic
321C2×C4#6699111yescharacteristic
322C2×C4#6699211yescharacteristic
323C2×C4#6699311yescharacteristic
324C2×C4#6700611yescharacteristic
325C8—42no—
326C8—224no—
327C8—224no—
328C8—881no—
329C22—21no—
330C22—21no—
331C22—81no—
332C22—81no—
333C22—81no—
334C22#1062276312yes—
335C22#1062283611yescharacteristic
336C4—21no—
337C4—21no—
338C4—82no—
339C4—81no—
340C4—882no—
341C4#1062276411yescharacteristic
342C4#1062276711yescharacteristic
343C4#1062276912yes—
344C4#1062281712yes—
345C4#1062285912yes—
346C2—22no—
347C2—161no—
348C2#1306965011yescharacteristic
349C2#1306968511yescharacteristic
350C2#1306973411yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3226C2
socleC22×C11#392
prime radicalC11×#532C22
hypercenter#3226D11
hypocenterC11#10174
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3226

Complements

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

NH ≅ G/Ntype
1. C2×#10622691C2semidirect
3. #13069461C2semidirect
4. #13067287C2semidirect
6. #13066452C2semidirect
294. C11#10174semidirect

Maximal subgroups

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

subgroupindex
C2×#106226912
#130790762
#130694612
#130672872
#130670672
#130664522
C11×#32262
#1017411