Finite Group Databasebeta

← #30601092

Subgroups — #30601092

Order 15616.

400 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 78 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#21462729C211yesmaximal, characteristic
2#21461359C211yesmaximal, characteristic
3#21461335C212yesmaximal
4#21460704C212yesmaximal
5#21456198C211yesmaximal, characteristic
6#16840814—22no—
7#16840811—22no—
8#16840787—22no—
9#16840780C2212yes—
10#16840767C2212yes—
11#16840621—22no—
12#16840621—22no—
13#16840621—22no—
14#16840318C2211yescharacteristic
15C4⋊Q8×D61C2211yescharacteristic
16#16840132C411yescharacteristic
17#16840131C411yescharacteristic
18#16840130C411yescharacteristic
19#16840111—22no—
20#16839769—22no—
21#16839714C2211yescharacteristic
22C61×#491C411yescharacteristic
23C2×#11758213—22no—
24#14519844—22no—
25#14519844—22no—
26#14519844—22no—
27#14519844D412yes—
28#14519844D412yes—
29C4⋊#92420—22no—
30#14519834—22no—
31#14519832—22no—
32C4×#92420—22no—
33C4×#92420—22no—
34C2×Q8×D61—21no—
35C2×#11758189—21no—
36#14519777C2×C411yescharacteristic
37#14519776—22no—
38#14519776D412yes—
39#14519775—21no—
40#14519769C2×C411yescharacteristic
41#14519755—22no—
42#14519742—22no—
43#14519735D412yes—
44C4⋊C4×D61—22no—
45C42×D61C2311yescharacteristic
46#14519702—22no—
47#14519701—22no—
48#14519700—22no—
49#14519688C2×C411yescharacteristic
50C8×Dic61—21no—
51C4⋊Q8×C61C2×C411yescharacteristic
52#125×C61C2×C411yescharacteristic
53#103×C61—22no—
54#97×C61C2×C411yescharacteristic
55C2×Q8×C61—21no—
56Q8×D61—44no—
57C2×C4×D61—41no—
58C2×C4×D61C2×D411yescharacteristic
59C2×C4×D61#4112yes—
60C2×Dic122—22no—
61C2×Dic122—21no—
62C2×Dic122—41no—
63C2×#92420—22no—
64C2×#92420—22no—
65C2×#92420—42no—
66#11758213—82no—
67C2×C8×C61—21no—
68C4⋊C4×C61—22no—
69C4⋊C4×C61—22no—
70C4⋊C4×C61C22⋊C412yes—
71C42×C61C22×C411yescharacteristic
72#11758198—22no—
73C4⋊Dic61—22no—
74C4⋊Dic61C22⋊C412yes—
75#11758196—22no—
76#11758196—22no—
77#11758196—42no—
78C4×Dic61—22no—
79C4×Dic61C2×D412yes—
80C4×Dic61C2×D411yescharacteristic
81C2×#92418—21no—
82#11758189—42no—
83C22×D61#12311yescharacteristic
84Q8×C61—42no—
85C2×C4×C61—22no—
86C2×C4×C61—41no—
87C2×C4×C61C2×C22⋊C411yescharacteristic
88C2×C4×C61C4×D412yes—
89C2×Dic61—22no—
90C2×Dic61—41no—
91C2×Dic61#12011yescharacteristic
92C2×Dic61#12112yes—
93C4×D61—22no—
94C4×D61—22no—
95C4×D61—22no—
96C4×D61—82no—
97Dic122—42no—
98Dic122—42no—
99Dic122—42no—
100Dic122—82no—
101#92420—42no—
102#92420—42no—
103#92420—82no—
104C8×C61—41no—
105#92418—41no—
106#9436—611nomaximal, Sylow
107C22×C61#38611yescharacteristic
108C2×D61—21no—
109C2×D61—22no—
110C4×C61—21no—
111C4×C61—22no—
112C4×C61—42no—
113C4×C61—81no—
114Dic61—42no—
115Dic61—81no—
116Dic61#45412yes—
117Dic61#47112yes—
118Dic61#47312yes—
119#3139—611no—
120#2986—611no—
121#1561—611no—
122#1549—612no—
123#1299—612no—
124C2×C61#188811yescharacteristic
125C2×C61#190812yes—
126D61—41no—
127#533—611no—
128C2×C4⋊Q8—611no—
129#491—611no—
130#491—611no—
131#491—611no—
132#491#692311yescharacteristic
133#487—1222no—
134#446—1222no—
135C8×Q8—1222no—
136#433—1222no—
137#431—612no—
138#423—612no—
139#419—1222no—
140C4×M16—611no—
141#332—1222no—
142#332—1222no—
143#332—1222no—
144C61#943611yescharacteristic, complemented, Sylow
145C22×Q8—1221no—
146C2×M16—1221no—
147C2×M16—1222no—
148C4⋊Q8—612no—
149C4⋊Q8—611no—
150C4⋊Q8—1222no—
151C4⋊Q8—1221no—
152C4⋊Q8C2×#692311yescharacteristic
153#125—611no—
154#125C2×#692311yescharacteristic
155C22⋊Q8—1222no—
156C4×Q8—1222no—
157#117—612no—
158C2×C4⋊C4—1222no—
159C2×C42—611no—
160C4⋊C8—612no—
161C4⋊C8—612no—
162C4⋊C8—1222no—
163C4⋊C8—1222no—
164C4⋊C8—1222no—
165C4⋊C8—1222no—
166#103—22no—
167#103—1222no—
168#103—1222no—
169#103—1222no—
170C22⋊C8—1222no—
171#97—611no—
172#97—1222no—
173#97C2×#692311yescharacteristic
174C4×C8—1221no—
175C4×C8—1222no—
176C4×C8—1222no—
177C2×Q8—21no—
178C2×Q8—1222no—
179C2×Q8—1221no—
180C2×Q8—2441no—
181C2×Q8—2444no—
182C22×C4—611no—
183C22×C4—612no—
184C22×C4—2441no—
185M16—4882no—
186M16—2442no—
187C2×C8—21no—
188C2×C8—1222no—
189C2×C8—1222no—
190C2×C8—1221no—
191C2×C8—2442no—
192C4⋊C4—22no—
193C4⋊C4—22no—
194C4⋊C4—612no—
195C4⋊C4—1222no—
196C4⋊C4—1222no—
197C4⋊C4—1222no—
198C4⋊C4—2442no—
199C4⋊C4C22⋊#692312yes—
200C22⋊C4—1222no—
201C42—611no—
202C42—612no—
203C42—1222no—
204C42C22×#692311yescharacteristic
205C23—611no—
206Q8—42no—
207Q8—4882no—
208Q8—2442no—
209Q8—2442no—
210Q8—2442no—
211C2×C4—22no—
212C2×C4—41no—
213C2×C4—611no—
214C2×C4—612no—
215C2×C4—1222no—
216C2×C4—1222no—
217C2×C4—1222no—
218C2×C4—1222no—
219C2×C4—4882no—
220C2×C4—2441no—
221C2×C4C2×C22⋊#692311yescharacteristic
222C2×C4D4×#692312yes—
223C8—41no—
224C8—4882no—
225C8—2441no—
226C8—2442no—
227C8—2442no—
228C22—1221no—
229C22—1222no—
230C22#1684071011yescharacteristic
231C4—21no—
232C4—22no—
233C4—42no—
234C4—81no—
235C4—612no—
236C4—612no—
237C4—612no—
238C4—4881no—
239C4—2442no—
240C2—2441no—
241C2#2146182711yescharacteristic
242C2#2146185912yes—
subgroupG/H
centerC22#16840710
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#491C4
socleC22×C61#386
prime radicalC22×D61#123
cosocleC42×D61C23
hypercenter#491#6923
hypocenterC61#9436
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
144. C61#9436semidirect

Maximal subgroups

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

subgroupindex
#214627292
#214613592
#214613352
#214607042
#214561982
#943661