Finite Group Databasebeta

← #29581351

Subgroups — #29581351

Order 15616.

500 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 97 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×#16840171C212yesmaximal
2#21453887C211yesmaximal, characteristic
3#21446638C211yesmaximal, characteristic
4C2×#16839503C212yesmaximal
5C61×#1295C211yesmaximal, characteristic
6C2×#14519777C2211yescharacteristic
7C2×#14519769C2212yes—
8#16840171—24no—
9#16840171—24no—
10C2×#14519711—22no—
11C2×#14519709—22no—
12C2×#14519700—22no—
13C2×#14519688C2211yescharacteristic
14#16839702—22no—
15#16839694—22no—
16#16839692—22no—
17#16839503—24no—
18C2×#97×C61C2212yes—
19C61×#382C2211yescharacteristic
20C22×Dic122—21no—
21C22×#92418—21no—
22#14519777—22no—
23#14519777—21no—
24#14519777D412yes—
25#14519769—22no—
26#14519769—22no—
27#14519769—22no—
28#14519769—22no—
29C2×C4⋊Dic61—22no—
30C2×C4⋊Dic61—22no—
31C2×C4⋊Dic61D412yes—
32C2×C4⋊Dic61D412yes—
33C2×#11758196—22no—
34C2×#11758196—22no—
35#14519711—28no—
36#14519709—28no—
37#14519700—44no—
38#14519688—22no—
39#14519684—24no—
40#14519684—22no—
41C22×C8×C61—22no—
42C2×C4⋊C4×C61D412yes—
43C2×C42×C61C2311yescharacteristic
44#97×C61—22no—
45#97×C61D414yes—
46#95×C61—22no—
47C22×C4×C61—22no—
48C22×C4×C61C2×D412yes—
49C22×C4×C61C2×D411yescharacteristic
50C22×Dic61—22no—
51C22×Dic61—22no—
52C22×Dic61—41no—
53C2×Dic122—22no—
54C2×Dic122—42no—
55C2×Dic122—42no—
56C2×Dic122—41no—
57C2×C8×C61—28no—
58C2×C8×C61—24no—
59C4⋊C4×C61—42no—
60C42×C61C2×D411yescharacteristic
61C42×C61C2×D412yes—
62C42×C61#4111yescharacteristic
63C4⋊Dic61—22no—
64C4⋊Dic61—24no—
65C4⋊Dic61—22no—
66C4⋊Dic61—22no—
67C4⋊Dic61—22no—
68C4⋊Dic61—42no—
69C4⋊Dic61—82no—
70#11758196—42no—
71#11758196—42no—
72#11758196—42no—
73#11758196—42no—
74C2×#92418—22no—
75C2×#92418—41no—
76C2×#92418—41no—
77C23×C61#12011yescharacteristic
78C2×C4×C61—21no—
79C2×C4×C61—21no—
80C2×C4×C61—24no—
81C2×C4×C61—42no—
82C2×C4×C61—44no—
83C2×C4×C61#12012yes—
84C2×C4×C61#12111yescharacteristic
85C2×C4×C61#12112yes—
86C2×C4×C61#12711yescharacteristic
87C2×Dic61—42no—
88C2×Dic61—42no—
89C2×Dic61—42no—
90C2×Dic61—42no—
91C2×Dic61—42no—
92C2×Dic61—44no—
93C2×Dic61—81no—
94C2×Dic61—81no—
95Dic122—44no—
96Dic122—82no—
97C8×C61—28no—
98#92418—42no—
99#10087—611nomaximal, Sylow
100C22×C61#39211yescharacteristic
101C22×C61#45311yescharacteristic
102C22×C61#45411yescharacteristic
103C22×C61#45614yes—
104C4×C61—22no—
105C4×C61—22no—
106C4×C61—21no—
107C4×C61—21no—
108C4×C61—82no—
109Dic61—82no—
110Dic61—82no—
111Dic61—82no—
112C2×#501—612no—
113#2822—611no—
114#1960—611no—
115C2×#330—612no—
116#1295D6111yescharacteristic
117C2×C61#166012yes—
118C2×C61#166312yes—
119C2×C61#200512yes—
120C2×C61#200611yescharacteristic
121C2×C4⋊Q8—611no—
122C2×#125—612no—
123#501—1224no—
124#501—1224no—
125C2×#107—1222no—
126C2×#106—1222no—
127C2×#103—1222no—
128C2×#97—611no—
129C2×#97C2×D6112yes—
130#400—1222no—
131#398—1222no—
132#398—1222no—
133#382C2×D6111yescharacteristic
134#330—1224no—
135C61#1008711yescharacteristic, complemented, Sylow
136C22×Q8—1221no—
137C22×C8—22no—
138C22×C8—1221no—
139C4⋊Q8—612no—
140C4⋊Q8—1222no—
141C4⋊Q8—1221no—
142#125—1222no—
143#125—1222no—
144#125—1222no—
145#125—1222no—
146C2×C4⋊C4—612no—
147C2×C4⋊C4—612no—
148C2×C4⋊C4—1222no—
149C2×C4⋊C4—1222no—
150C2×C4⋊C4—1222no—
151C2×C4⋊C4—1222no—
152C2×C4⋊C4D24412yes—
153C2×C42C22×D6111yescharacteristic
154#107—1228no—
155#106—1228no—
156#103—2444no—
157#97—22no—
158#97—1222no—
159#97D24414yes—
160#95—22no—
161#95—1224no—
162#95—1222no—
163C2×Q8—1222no—
164C2×Q8—2442no—
165C2×Q8—2442no—
166C2×Q8—2441no—
167C22×C4—22no—
168C22×C4—1222no—
169C22×C4—1222no—
170C22×C4—2441no—
171C22×C4C2×D24411yescharacteristic
172C22×C4D4×D6112yes—
173C2×C8—28no—
174C2×C8—24no—
175C2×C8—1222no—
176C2×C8—2441no—
177C2×C8—2441no—
178C4⋊C4—42no—
179C4⋊C4—1222no—
180C4⋊C4—1224no—
181C4⋊C4—1222no—
182C4⋊C4—1222no—
183C4⋊C4—1222no—
184C4⋊C4—4882no—
185C4⋊C4—2442no—
186C4⋊C4—2442no—
187C4⋊C4—2442no—
188C4⋊C4—2442no—
189C4⋊C4—2442no—
190C42C2×D24412yes—
191C42D4×D6111yescharacteristic
192C42#1175822611yescharacteristic
193C23#1451974711yescharacteristic
194Q8—4882no—
195Q8—2444no—
196C2×C4—21no—
197C2×C4—24no—
198C2×C4—21no—
199C2×C4—44no—
200C2×C4—42no—
201C2×C4—4881no—
202C2×C4—4881no—
203C2×C4—2442no—
204C2×C4—2444no—
205C2×C4—2442no—
206C2×C4—2442no—
207C2×C4—2442no—
208C2×C4—2442no—
209C2×C4#1451974712yes—
210C2×C4#1451975212yes—
211C2×C4#1451975211yescharacteristic
212C2×C4#1451977411yescharacteristic
213C8—28no—
214C8—2442no—
215C22#1683967211yescharacteristic
216C22#1683993211yescharacteristic
217C22#1683993711yescharacteristic
218C22#1683994614yes—
219C4—22no—
220C4—22no—
221C4—21no—
222C4—21no—
223C4—82no—
224C4—4882no—
225C4—4882no—
226C4—4882no—
227C2#2144513112yes—
228C2#2144514812yes—
229C2#2144685812yes—
230C2#2144686311yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1295C2
socle, prime radicalC23×C61#120
hypercenter#1295D61
hypocenterC61#10087
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
135. C61#10087semidirect

Maximal subgroups

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

subgroupindex
C2×#168401712
#214538872
#214466382
C2×#168395032
C61×#12952
#1008761