Finite Group Databasebeta

← #14908118

Subgroups — #14908118

Order 2816.

680 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 680 conjugacy classes of subgroups — too many to draw. Only its 163 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×#10622808C211yesmaximal, characteristic
2C22×Dic88C211yesmaximal, characteristic, complemented
3#13079111C211yesmaximal, characteristic
4#13077483C211yesmaximal, characteristic, complemented
5#13070677C214yesmaximal, complemented
6#13070665C214yesmaximal, complemented
7#13070374C211yesmaximal, characteristic, complemented
8#13070335C211yesmaximal, characteristic, complemented
9C11×#2138C211yesmaximal, characteristic
10C2×C11×#135C2211yescharacteristic
11#10623356—21no—
12C2×#67004—21no—
13C22×Dic44C2211yescharacteristic
14C22×Dic44C2211yescharacteristic
15#10623047—21no—
16C22×C11×C16C2211yescharacteristic
17C11×#427C2211yescharacteristic
18#10622808—24no—
19#10622794C2212yes—
20C2×#66893C2212yes—
21#10622780—22no—
22#10622768C2212yes—
23C2×#66891C2212yes—
24#10622714C2211yescharacteristic
25C2×#66876C2211yescharacteristic
26#10622617—21no—
27C2×Dic88—24no—
28C2×Dic88C2214yes—
29#10622486C2214yes—
30#10622466—22no—
31C11×#358C2212yes—
32C11×#357C2212yes—
33Dic11⋊C16C2214yes—
34#10622130C2214yes—
35C2×C11×#41—21no—
36C22×Dic22—21no—
37C22×Dic22—21no—
38C11×#135—22no—
39C11×#135—22no—
40C2×C11×Q16C2311yescharacteristic
41C2×C11×SD16—21no—
42C2×C11×D8C2311yescharacteristic
43C22×C8×C11C2311yescharacteristic
44C11×#117—21no—
45#67004—44no—
46#66997—22no—
47C2×#4326—22no—
48#66989—22no—
49#66988—42no—
50C2×#4324—22no—
51#66979D411yescharacteristic
52#66977—42no—
53C2×#4318D411yescharacteristic
54C2×Dic44—21no—
55C2×Dic44—22no—
56C2×Dic44—22no—
57C2×Dic44—22no—
58C2×Dic44—21no—
59C2×Dic44D414yes—
60C2×Dic44C2312yes—
61C2×Dic44C2312yes—
62#66940—24no—
63#66930—42no—
64C4×Dic22—42no—
65C2×C11×C16—22no—
66C2×C11×C16C2312yes—
67C11×#107C2312yes—
68C11×#106—21no—
69#66893—24no—
70#66891—24no—
71#66879D412yes—
72C8×Dic11C2312yes—
73#66876—22no—
74C2×C11⋊C16C2312yes—
75#66874—24no—
76Dic88—28no—
77#33588—111nomaximal, Sylow
78C11×#41—42no—
79C11×#41—42no—
80C2×Q8×C11—21no—
81C2×D4×C11—21no—
82C2×D4×C11—41no—
83C22×C4×C11—41no—
84C22×C4×C11C2×D411yescharacteristic
85C22×Dic11—41no—
86C22×Dic11—41no—
87C2×Dic22—24no—
88C2×Dic22—22no—
89C2×Dic22—22no—
90C2×Dic22—42no—
91C2×Dic22—41no—
92C2×Dic22—41no—
93C2×Dic22—42no—
94C2×Dic22—42no—
95C11×Q16—21no—
96C11×Q16—21no—
97C11×SD16—42no—
98C11×D8—21no—
99C11×D8—21no—
100C2×C8×C11C2×D412yes—
101C2×C8×C11C2×D411yescharacteristic
102C2×C8×C11#4112yes—
103C2×C8×C11C2411yescharacteristic
104C11×C4⋊C4—22no—
105C11×C22⋊C4—41no—
106C42×C11—41no—
107C22⋊Dic11—44no—
108C22⋊Dic11D812yes—
109#4326—44no—
110#4324—44no—
111C4⋊Dic11D812yes—
112Dic11⋊C4—44no—
113Dic11⋊C4—44no—
114C4×Dic11—44no—
115C4×Dic11C2×D412yes—
116#4318—22no—
117C2×C11⋊C8C2×D412yes—
118Dic44—24no—
119Dic44—22no—
120Dic44—22no—
121Dic44—22no—
122Dic44—42no—
123Dic44C2×D414yes—
124C11×C16—22no—
125C11⋊C16—22no—
126C2×#510—111no—
127C22×Q32—111no—
128#3156—111no—
129#2950—111no—
130#2211—114no—
131#2209—114no—
132#2151—111no—
133#2141—111no—
134#2138D1111yescharacteristic
135C23×C11—41no—
136C23×C11C2×D811yescharacteristic
137Q8×C11—41no—
138Q8×C11—41no—
139D4×C11—41no—
140D4×C11—41no—
141D4×C11—82no—
142C2×C4×C11—42no—
143C2×C4×C11—41no—
144C2×C4×C11—82no—
145C2×C4×C11#12112yes—
146C2×C4×C11C2×D811yescharacteristic
147C2×C4×C11AGL(1,ℤ/8)12yes—
148C2×C4×C11C22×D411yescharacteristic
149C2×Dic11—42no—
150C2×Dic11—44no—
151C2×Dic11—42no—
152C2×Dic11—82no—
153C2×Dic11C2×D814yes—
154Dic22—24no—
155Dic22—42no—
156Dic22—44no—
157Dic22—42no—
158Dic22—42no—
159Dic22—82no—
160C8×C11#12112yes—
161C8×C11C22×D411yescharacteristic
162C8×C11C2×#4111yescharacteristic
163C11⋊C8—22no—
164C2×#137—221no—
165C2×#135C2×D1111yescharacteristic
166C22×Q16—111no—
167C22×Q16—111no—
168#536—221no—
169#519—221no—
170#510—224no—
171C2×Q32—112no—
172C2×Q32—114no—
173C2×Q32—224no—
174C2×SD32—112no—
175C2×M32—111no—
176C22×C16C2×D1111yescharacteristic
177#497—222no—
178#495—112no—
179#494—112no—
180#441—222no—
181C4×Q16—114no—
182#427C2×D1111yescharacteristic
183#419—221no—
184#405—111no—
185C4⋊C16—114no—
186#358—114no—
187#358C2×D1112yes—
188#357C2×D1112yes—
189C22×C11—22no—
190C22×C11—82no—
191C22×C11—81no—
192C22×C11#45912yes—
193C22×C11C22×D811yescharacteristic
194C4×C11—82no—
195C4×C11—81no—
196C4×C11#45912yes—
197C4×C11C2×#12111yescharacteristic
198C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
199Dic11—24no—
200Dic11—44no—
201Dic11—82no—
202C2×#41—21no—
203C22×Q8—221no—
204C22×Q8—221no—
205#137—444no—
206#135—22no—
207#135—22no—
208C2×Q16—114no—
209C2×Q16—112no—
210C2×Q16—112no—
211C2×Q16—222no—
212C2×Q16—222no—
213C2×Q16—222no—
214C2×Q16—221no—
215C2×Q16—222no—
216C2×Q16—221no—
217C2×Q16C22×D1111yescharacteristic
218C2×SD16—21no—
219C2×SD16—222no—
220C2×D8C22×D1111yescharacteristic
221C2×M16—111no—
222C22×C8C22×D1111yescharacteristic
223C4⋊Q8—222no—
224#124—222no—
225#123—442no—
226C22⋊Q8—442no—
227C4×Q8—224no—
228C4×Q8—442no—
229#117—21no—
230#117—111no—
231#117—442no—
232Q32—228no—
233Q32—224no—
234SD32—224no—
235M32—222no—
236C2×C16—22no—
237C2×C16—112no—
238C2×C16C22×D1112yes—
239#107C22×D1112yes—
240#106—21no—
241#103—224no—
242#97—112no—
243C4×C8—112no—
244C2×C11—22no—
245C2×C11—161no—
246C2×C11C2×#45911yescharacteristic
247C2×C11#341712yes—
248#41—42no—
249#41—42no—
250C2×Q8—21no—
251C2×Q8—224no—
252C2×Q8—222no—
253C2×Q8—222no—
254C2×Q8—441no—
255C2×Q8—441no—
256C2×Q8—442no—
257C2×Q8—442no—
258C2×Q8—442no—
259C2×D4—21no—
260C2×D4—41no—
261C22×C4—41no—
262C22×C4—441no—
263C22×C4—441no—
264C22×C4D4×D1111yescharacteristic
265Q16—21no—
266Q16—21no—
267Q16—114no—
268Q16—224no—
269Q16—222no—
270Q16—222no—
271Q16—222no—
272Q16—444no—
273Q16—442no—
274SD16—42no—
275SD16—444no—
276D8—21no—
277D8—21no—
278M16—222no—
279C2×C8—112no—
280C2×C8#433912yes—
281C2×C8D4×D1111yescharacteristic
282C2×C8D4×D1112yes—
283C2×C8C23×D1111yescharacteristic
284C4⋊C4—22no—
285C4⋊C4—112no—
286C4⋊C4—444no—
287C4⋊C4—444no—
288C22⋊C4—41no—
289C22⋊C4—112no—
290C22⋊C4—444no—
291C42—41no—
292C42—112no—
293C42—444no—
294C16—22no—
295C16—222no—
296C11#3358811yescharacteristic, complemented, Sylow
297C23—41no—
298C23D8×D1111yescharacteristic
299Q8—41no—
300Q8—41no—
301Q8—224no—
302Q8—442no—
303Q8—444no—
304Q8—442no—
305Q8—442no—
306Q8—882no—
307D4—41no—
308D4—41no—
309D4—82no—
310C2×C4—42no—
311C2×C4—41no—
312C2×C4—82no—
313C2×C4—114no—
314C2×C4—442no—
315C2×C4—444no—
316C2×C4—442no—
317C2×C4—882no—
318C2×C4#6693712yes—
319C2×C4D8×D1111yescharacteristic
320C2×C4#6696712yes—
321C2×C4C2×D4×D1111yescharacteristic
322C8—222no—
323C8#6693712yes—
324C8C2×#433911yescharacteristic
325C8C2×D4×D1111yescharacteristic
326C22—22no—
327C22—81no—
328C22—82no—
329C22#1062239912yes—
330C22C2×D8×D1111yescharacteristic
331C4—81no—
332C4—82no—
333C4—224no—
334C4—444no—
335C4—882no—
336C4#1062239912yes—
337C4C2×#6693711yescharacteristic
338C4C2×#6696711yescharacteristic
339C2—22no—
340C2—161no—
341C2C2×#1062239911yescharacteristic
342C2#1308176612yes—
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2138C2
socleC22×C11C22×D8
prime radicalC2×C11×#135C22
hypercenter#2138D11
hypocenterC11#33588
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2138

Complements

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

NH ≅ G/Ntype
2. C22×Dic88C2semidirect
4. #13077483C2semidirect
5. #13070677C2semidirect
6. #13070665C2semidirect
7. #13070374C2semidirect
8. #13070335C2semidirect
296. C11#33588semidirect

Maximal subgroups

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

subgroupindex
C2×#106228082
C22×Dic882
#130791112
#130774832
#130706772
#130706652
#130703742
#130703352
C11×#21382
#3358811