Finite Group Databasebeta

← #29594054

Subgroups — #29594054

Order 15616.

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

normal subgroups only

This group has 276 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#21448094C211yesmaximal, characteristic
3#21447962C211yesmaximal, characteristic
4#21445213C211yesmaximal, characteristic
5#21443873C211yesmaximal, characteristic
6#21443784C211yesmaximal, characteristic
7C61×Q8⋊C16C211yesmaximal, characteristic
8#16840490—21no—
9#16840167C2211yescharacteristic
10#16840167C2211yescharacteristic
11#16840164—21no—
12#16840070—22no—
13#16840048—21no—
14#16839972—21no—
15C4×Dic244—21no—
16C4×Dic244C2211yescharacteristic
17#16839590—21no—
18#16839588—22no—
19#16839567—21no—
20#16839515C2211yescharacteristic
21#16839507—21no—
22C8×Q8×C61C2211yescharacteristic
23C61×C4⋊C16C2211yescharacteristic
24C4×C16×C61C2211yescharacteristic
25C2×Dic244D411yescharacteristic
26C2×#11758202—41no—
27#14519777—21no—
28#14519777—21no—
29#14519775—41no—
30#14519769—22no—
31#14519767—42no—
32C4×Dic122—22no—
33C4×Dic122—21no—
34#14519742—41no—
35#14519711—21no—
36#14519711—21no—
37#14519711—21no—
38#14519711D412yes—
39#14519711D411yescharacteristic
40#14519709—22no—
41C4⋊#92418—21no—
42#14519702—22no—
43#14519702—21no—
44#14519700—41no—
45C4×Q8×C61D411yescharacteristic
46C2×C16×C61—21no—
47C2×C16×C61—21no—
48C4⋊C8×C61—21no—
49C4⋊C8×C61D411yescharacteristic
50C4×C8×C61—21no—
51C4×C8×C61C2311yescharacteristic
52C2×Q8×C61D811yescharacteristic
53C2×Dic122—21no—
54C2×Dic122—41no—
55C2×Dic122—41no—
56C2×C8×C61—21no—
57C2×C8×C61C2×D411yescharacteristic
58C2×C8×C61C2×D411yescharacteristic
59C4⋊C4×C61—21no—
60C4⋊C4×C61D811yescharacteristic
61C42×C61—21no—
62C42×C61C2×D411yescharacteristic
63#11758202—82no—
64C4⋊Dic61—21no—
65C4⋊Dic61—22no—
66C4⋊Dic61—41no—
67C4⋊Dic61—41no—
68C4⋊Dic61—41no—
69#11758196—42no—
70#11758196—42no—
71#11758196—42no—
72#11758196—41no—
73C4×Dic61—42no—
74C4×Dic61—41no—
75C2×#92418—41no—
76Dic244—21no—
77Dic244Q1612yescomplemented
78C16×C61—22no—
79C16×C61—41no—
80Q8×C61—21no—
81Q8×C61—21no—
82C2×C4×C61—21no—
83C2×C4×C61—21no—
84C2×C4×C61#12011yescharacteristic
85C2×C4×C61C2×D811yescharacteristic
86C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
87C2×Dic61—41no—
88C2×Dic61—41no—
89C2×Dic61—42no—
90C2×Dic61—81no—
91Dic122—22no—
92Dic122—41no—
93Dic122—81no—
94Dic122—81no—
95Dic122—81no—
96Dic122—81no—
97C8×C61—21no—
98C8×C61—41no—
99C8×C61C2×Q1611yescharacteristic
100C8×C61#13711yescharacteristic
101#92418—81no—
102#12405—611nomaximal, Sylow
103C22×C61#44711yescharacteristic
104C4×C61—21no—
105C4×C61—41no—
106C4×C61—41no—
107C4×C61#45111yescharacteristic
108C4×C61#45611yescharacteristic
109C4×C61#50811yescharacteristic
110C4×C61#50911yescharacteristic
111Dic61—42no—
112Dic61—82no—
113Dic61—81no—
114Dic61—161no—
115#3383—611no—
116#2252—611no—
117#2225—611no—
118#1674—611no—
119#1364—611no—
120Q8⋊C16D6111yescharacteristic
121#1332—611no—
122C2×C61#164911yescharacteristic
123C2×C61#218611yescharacteristic
124C2×C61#219511yescharacteristic
125#557—1221no—
126#500—611no—
127#500—611no—
128#499—1221no—
129#479—1222no—
130#475—1221no—
131#462—1221no—
132C8×Q8C2×D6111yescharacteristic
133C4×Q16—611no—
134C4×Q16—1221no—
135#367—1221no—
136#366—1222no—
137C4⋊C16C2×D6111yescharacteristic
138#358—1221no—
139C4×C16C2×D6111yescharacteristic
140#335—611no—
141#332—1221no—
142C61#1240511yescharacteristic, complemented, Sylow
143C2×Q16—611no—
144C2×Q16—2441no—
145C4⋊Q8—1221no—
146C4⋊Q8—1221no—
147C4⋊Q8—2441no—
148#125—1222no—
149#125—2442no—
150C4×Q8—1222no—
151C4×Q8—1221no—
152C4×Q8—2441no—
153C4×Q8D24411yescharacteristic
154C2×C16—21no—
155C2×C16—21no—
156#107—612no—
157#107—611no—
158#107—1221no—
159#107—1221no—
160#107—1221no—
161#106—1222no—
162C4⋊C8—21no—
163C4⋊C8—1221no—
164C4⋊C8D24411yescharacteristic
165#103—1222no—
166#103—1221no—
167#103—2441no—
168C4×C8—21no—
169C4×C8C22×D6111yescharacteristic
170C2×Q8—1221no—
171C2×Q8—2441no—
172C2×Q8—2441no—
173C2×Q8D48811yescharacteristic
174Q16—612no—
175Q16—1221no—
176Q16—4882no—
177C2×C8—21no—
178C2×C8—2441no—
179C2×C8D4×D6111yescharacteristic
180C2×C8D4×D6111yescharacteristic
181C4⋊C4—21no—
182C4⋊C4—1221no—
183C4⋊C4—1222no—
184C4⋊C4—2442no—
185C4⋊C4—2442no—
186C4⋊C4—2442no—
187C4⋊C4—2441no—
188C4⋊C4—2441no—
189C4⋊C4—2441no—
190C4⋊C4—2441no—
191C4⋊C4D48811yescharacteristic
192C42—21no—
193C42—2442no—
194C42—2441no—
195C42C2×D24411yescharacteristic
196C16—22no—
197C16—41no—
198Q8—21no—
199Q8—21no—
200Q8—1222no—
201Q8—4881no—
202Q8—4881no—
203Q8—4881no—
204Q8—4881no—
205Q8—2441no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—4881no—
209C2×C4—2441no—
210C2×C4—2442no—
211C2×C4—2441no—
212C2×C4#1451974711yescharacteristic
213C2×C4C2×D48811yescharacteristic
214C2×C4#1451980511yescharacteristic
215C8—21no—
216C8—41no—
217C8—4881no—
218C8Q16×D6111yescharacteristic
219C8#1451980611yescharacteristic
220C22#1683989811yescharacteristic
221C4—21no—
222C4—41no—
223C4—41no—
224C4—9761no—
225C4—4882no—
226C4—4881no—
227C4—2442no—
228C4#1683991911yescharacteristic
229C4#1683994611yescharacteristic
230C4#1684019411yescharacteristic
231C4#1684020011yescharacteristic
232C2#2144507011yescharacteristic
233C2#2144774411yescharacteristic
234C2#2144779911yescharacteristic
subgroupG/H
centerC22#16839898
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×Q8⋊C16C2
socle, prime radicalC22×C61#447
hypercenterQ8⋊C16D61
hypocenterC61#12405
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ Q8⋊C16

Complements

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

NH ≅ G/Ntype
77. Dic244Q16semidirect
142. C61#12405semidirect

Maximal subgroups

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

subgroupindex
#214587112
#214480942
#214479622
#214452132
#214438732
#214437842
C61×Q8⋊C162
#1240561