Finite Group Databasebeta

← #29593722

Subgroups — #29593722

Order 15616.

282 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 69 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#21458711C211yesmaximal, characteristic
2#21448046C211yesmaximal, characteristic
3#21447866C211yesmaximal, characteristic
4#21443875C211yesmaximal, characteristic
5Q8⋊#11758185C211yesmaximal, characteristic
6#21443782C211yesmaximal, characteristic
7C61×#1670C211yesmaximal, characteristic
8#16840490—21no—
9C2×#14519723—21no—
10#16840167C2211yescharacteristic
11#16840164—21no—
12#16840070—22no—
13#16840048—21no—
14C4×Dic244—21no—
15C4×Dic244C2211yescharacteristic
16C4⋊#11758185C2211yescharacteristic
17#16839566—22no—
18#16839566—21no—
19C4×#11758185C2211yescharacteristic
20C61×#494C2211yescharacteristic
21C61×#475—21no—
22C8×Q8×C61C2211yescharacteristic
23C61×#335C2211yescharacteristic
24C61×#332—21no—
25C2×Dic244D411yescharacteristic
26#14519777—21no—
27#14519775—41no—
28#14519769—22no—
29#14519767—42no—
30C4×Dic122—22no—
31C4×Dic122—21no—
32#14519742—41no—
33#14519723—42no—
34C2×#11758185—21no—
35C2×#11758185—21no—
36#14519711—21no—
37#14519711D412yes—
38#14519711D411yescharacteristic
39#14519709—22no—
40#14519702—22no—
41#14519702—21no—
42C2×Q16×C61—21no—
43C2×Q16×C61—21no—
44C4⋊Q8×C61—21no—
45C4×Q8×C61D411yescharacteristic
46#106×C61—41no—
47C4⋊C8×C61—21no—
48C4⋊C8×C61—21no—
49C4⋊C8×C61D411yescharacteristic
50#103×C61—41no—
51C4×C8×C61—21no—
52C4×C8×C61C2311yescharacteristic
53C2×Q8×C61—41no—
54C2×Q8×C61D811yescharacteristic
55C2×Dic122—21no—
56C2×Dic122—41no—
57Q16×C61—42no—
58Q16×C61—41no—
59Q16×C61—41no—
60C2×C8×C61—21no—
61C2×C8×C61—41no—
62C2×C8×C61C2×D411yescharacteristic
63C2×C8×C61C2×D411yescharacteristic
64C4⋊C4×C61—21no—
65C4⋊C4×C61—41no—
66C4⋊C4×C61—41no—
67C4⋊C4×C61D811yescharacteristic
68C42×C61—21no—
69C42×C61C2×D411yescharacteristic
70C4⋊Dic61—21no—
71C4⋊Dic61—22no—
72C4⋊Dic61—41no—
73#11758196—42no—
74#11758196—42no—
75#11758196—42no—
76#11758196—41no—
77C4×Dic61—42no—
78C4×Dic61—41no—
79Dic244—21no—
80Dic244SD1612yes—
81#11758185—41no—
82#11758185—41no—
83Q8×C61—21no—
84Q8×C61—21no—
85Q8×C61—81no—
86Q8×C61—81no—
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—81no—
90C2×C4×C61#12011yescharacteristic
91C2×C4×C61C2×D811yescharacteristic
92C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
93C2×Dic61—41no—
94C2×Dic61—41no—
95C2×Dic61—42no—
96Dic122—22no—
97Dic122—41no—
98Dic122—81no—
99Dic122—81no—
100C8×C61—21no—
101C8×C61—41no—
102C8×C61—81no—
103C8×C61C2×SD1611yescharacteristic
104C8×C61#13711yescharacteristic
105#12357—611nomaximal, Sylow
106C22×C61#44711yescharacteristic
107C4×C61—21no—
108C4×C61—41no—
109C4×C61—41no—
110C4×C61—161no—
111C4×C61#44811yescharacteristic
112C4×C61#45411yescharacteristic
113C4×C61#50811yescharacteristic
114C4×C61#51011yescharacteristic
115Dic61—42no—
116Dic61—82no—
117Dic61—81no—
118#3383—611no—
119#2241—611no—
120#2209—611no—
121#1670D6111yescharacteristic
122#1364—611no—
123Q8⋊C16—611no—
124#1332—611no—
125C2×C61#162711yescharacteristic
126C2×C61#218911yescharacteristic
127C2×C61#219511yescharacteristic
128#557—1221no—
129C2×Q32—1221no—
130#500—611no—
131#499—1221no—
132#494C2×D6111yescharacteristic
133#479—1222no—
134#475—21no—
135#475—1221no—
136C8×Q8C2×D6111yescharacteristic
137C4×Q16—611no—
138C4×Q16—1221no—
139C4⋊C16—611no—
140#358—1221no—
141#358—1222no—
142C4×C16—611no—
143#335C2×D6111yescharacteristic
144#332—21no—
145C61#1235711yescharacteristic, complemented, Sylow
146C2×Q16—21no—
147C2×Q16—21no—
148C2×Q16—611no—
149C4⋊Q8—21no—
150C4⋊Q8—1221no—
151C4⋊Q8—2441no—
152#125—1222no—
153#125—2442no—
154C4×Q8—1222no—
155C4×Q8—1221no—
156C4×Q8—2441no—
157C4×Q8C22⋊D6111yescharacteristic
158Q32—2442no—
159C2×C16—1221no—
160C2×C16—1221no—
161#107—611no—
162#107—612no—
163#107—1221no—
164#106—41no—
165#106—1222no—
166C4⋊C8—21no—
167C4⋊C8—21no—
168C4⋊C8C22⋊D6111yescharacteristic
169#103—41no—
170#103—1222no—
171#103—1221no—
172C4×C8—21no—
173C4×C8C22×D6111yescharacteristic
174C2×Q8—41no—
175C2×Q8—1221no—
176C2×Q8—2441no—
177C2×Q8#1175819911yescharacteristic
178Q16—42no—
179Q16—41no—
180Q16—41no—
181Q16—612no—
182Q16—1221no—
183C2×C8—21no—
184C2×C8—41no—
185C2×C8D4×D6111yescharacteristic
186C2×C8D4×D6111yescharacteristic
187C4⋊C4—21no—
188C4⋊C4—41no—
189C4⋊C4—41no—
190C4⋊C4—1221no—
191C4⋊C4—1222no—
192C4⋊C4—2442no—
193C4⋊C4—2442no—
194C4⋊C4—2442no—
195C4⋊C4—2441no—
196C4⋊C4—2441no—
197C4⋊C4#1175819911yescharacteristic
198C42—21no—
199C42—2442no—
200C42—2441no—
201C42C2×C22⋊D6111yescharacteristic
202C16—2441no—
203C16—2441no—
204Q8—21no—
205Q8—21no—
206Q8—81no—
207Q8—81no—
208Q8—1222no—
209Q8—4881no—
210Q8—4881no—
211Q8—2441no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—81no—
215C2×C4—2441no—
216C2×C4—2442no—
217C2×C4—2441no—
218C2×C4#1451974511yescharacteristic
219C2×C4C2×#1175819911yescharacteristic
220C2×C4#1451980211yescharacteristic
221C8—21no—
222C8—41no—
223C8—81no—
224C8SD16×D6111yescharacteristic
225C8#1451980611yescharacteristic
226C22#1683989511yescharacteristic
227C4—21no—
228C4—41no—
229C4—41no—
230C4—161no—
231C4—4882no—
232C4—4881no—
233C4—2442no—
234C4#1683989911yescharacteristic
235C4#1683993311yescharacteristic
236C4#1684019211yescharacteristic
237C4#1684020311yescharacteristic
238C2#2144492011yescharacteristic
239C2#2144775711yescharacteristic
240C2#2144779511yescharacteristic
subgroupG/H
centerC22#16839895
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1670C2
socle, prime radicalC22×C61#447
hypercenter#1670D61
hypocenterC61#12357
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ #1670

Complements

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

NH ≅ G/Ntype
145. C61#12357semidirect

Maximal subgroups

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

subgroupindex
#214587112
#214480462
#214478662
#214438752
Q8⋊#117581852
#214437822
C61×#16702
#1235761