Finite Group Databasebeta

← #30608405

Subgroups — #30608405

Order 15616.

312 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 60 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×#16840673C212yesmaximal
2#21460962C212yesmaximal, complemented
3#21460961C212yesmaximal, complemented
4#21456201C211yesmaximal, characteristic
5C2×#14519838—22no—
6#16840673—22no—
7#16840673C2214yes—
8C2×#14519777C2211yescharacteristic
9#16840132C411yescharacteristic
10#16840132C411yescharacteristic
11#16840132C2211yescharacteristic
12#16840132C2211yescharacteristic
13#16840114—22no—
14#16839770—22no—
15C4×#11758194C411yescharacteristic
16C61×#533C411yescharacteristic
17C2×#11758217—42no—
18#14519838—24no—
19#14519838—42no—
20C22×Dic122D412yes—
21C2×#11758194—21no—
22#14519777—41no—
23#14519777C2×C411yescharacteristic
24#14519777D412yes—
25#14519777C2311yescharacteristic
26C2×C4⋊Dic61—41no—
27#14519700—22no—
28#14519700—22no—
29#14519700—22no—
30#14519700—22no—
31#14519688C2×C411yescharacteristic
32#14519688C2×C411yescharacteristic
33C4×#92418—21no—
34C4⋊Q8×C61—21no—
35#125×C61C2×C411yescharacteristic
36#125×C61C2×C411yescharacteristic
37C22⋊Q8×C61—41no—
38C4×Q8×C61—41no—
39#117×C61—21no—
40C2×C42×C61C2×C411yescharacteristic
41C2×Q8×C61—41no—
42C22×C4×C61—21no—
43C22×C4×C61C22⋊C411yescharacteristic
44C22×Dic61—22no—
45C2×Dic122—22no—
46C2×Dic122—42no—
47C2×Dic122—42no—
48C2×Dic122C22⋊C412yes—
49C2×Dic122C2×D412yes—
50#11758217—44no—
51#11758217—82no—
52C2×#92420—82no—
53C4⋊C4×C61—21no—
54C4⋊C4×C61—21no—
55C4⋊C4×C61—41no—
56C4⋊C4×C61—41no—
57C4⋊C4×C61—41no—
58C22⋊C4×C61—41no—
59C42×C61—21no—
60C42×C61—41no—
61C42×C61C22⋊C411yescharacteristic
62C42×C61C22×C411yescharacteristic
63C4⋊Dic61—41no—
64C4⋊Dic61—42no—
65C4⋊Dic61—41no—
66#11758194—42no—
67C2×#92418—21no—
68C2×#92418—21no—
69C23×C61#9911yescharacteristic
70Q8×C61—82no—
71C2×C4×C61—22no—
72C2×C4×C61—21no—
73C2×C4×C61—21no—
74C2×C4×C61—42no—
75C2×C4×C61—41no—
76C2×C4×C61—41no—
77C2×C4×C61#9911yescharacteristic
78C2×C4×C61C2×C22⋊C411yescharacteristic
79C2×Dic61—22no—
80C2×Dic61—22no—
81C2×Dic61—42no—
82C2×Dic61—42no—
83Dic122—42no—
84Dic122—42no—
85Dic122—82no—
86#92420—84no—
87#92418—41no—
88#92418—41no—
89#13599—611nomaximal, Sylow
90C22×C61—41no—
91C22×C61#35412yes—
92C22×C61C2×#9911yescharacteristic
93C4×C61—22no—
94C4×C61—21no—
95C4×C61—21no—
96C4×C61—41no—
97C4×C61—81no—
98C4×C61—81no—
99Dic61—42no—
100Dic61—42no—
101#3139—611no—
102C2×#356—612no—
103#1413—612no—
104#1413—612no—
105C2×C61—21no—
106C2×C61—22no—
107C2×C61C2×#35411yescharacteristic
108#533#692311yescharacteristic
109C2×C4⋊Q8—611no—
110#491—611no—
111#491—611no—
112#491—611no—
113#491—611no—
114#487—1222no—
115#419—1222no—
116C2×#101—1222no—
117C4×M16—611no—
118#356—614no—
119#356—1222no—
120C61#1359911yescharacteristic, complemented, Sylow
121C22×Q8—612no—
122C2×M16—1221no—
123C2×M16—2442no—
124C4⋊Q8—21no—
125C4⋊Q8—612no—
126C4⋊Q8—611no—
127C4⋊Q8—611no—
128C4⋊Q8—2441no—
129#125C2×#692311yescharacteristic
130#125C2×#692311yescharacteristic
131C22⋊Q8—41no—
132C4×Q8—41no—
133#117—21no—
134C2×C4⋊C4—2441no—
135C2×C42C2×#692311yescharacteristic
136#103—1222no—
137#103—1222no—
138#103—1222no—
139#103—1222no—
140#101—1224no—
141#101—2442no—
142#97—611no—
143#97—611no—
144C4×C8—1221no—
145C2×Q8—41no—
146C2×Q8—612no—
147C2×Q8—612no—
148C2×Q8—1222no—
149C2×Q8—2442no—
150C2×Q8—2442no—
151C22×C4—21no—
152C22×C4—1222no—
153C22×C4C22⋊#692311yescharacteristic
154M16—4882no—
155M16—2444no—
156M16—2442no—
157C2×C8—1221no—
158C2×C8—1221no—
159C2×C8—4882no—
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—41no—
163C4⋊C4—41no—
164C4⋊C4—41no—
165C4⋊C4—2442no—
166C4⋊C4—2441no—
167C4⋊C4—2441no—
168C22⋊C4—41no—
169C42—21no—
170C42—41no—
171C42C22⋊#692311yescharacteristic
172C42C22×#692311yescharacteristic
173C23#1451983511yescharacteristic
174Q8—82no—
175Q8—4882no—
176Q8—2442no—
177Q8—2442no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—21no—
181C2×C4—42no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—1222no—
185C2×C4—1222no—
186C2×C4—2442no—
187C2×C4—2442no—
188C2×C4#1451983511yescharacteristic
189C2×C4C2×C22⋊#692311yescharacteristic
190C8—4884no—
191C8—2441no—
192C8—2441no—
193C22—41no—
194C22#1684066812yes—
195C22C2×#1451983511yescharacteristic
196C4—22no—
197C4—21no—
198C4—21no—
199C4—41no—
200C4—81no—
201C4—81no—
202C4—2442no—
203C4—2442no—
204C2—21no—
205C2—22no—
206C2C2×#1684066811yescharacteristic
subgroupG/H
centerC2C2×#16840668
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#533C4
socleC2×C61C2×#354
prime radicalC23×C61#99
cosocle#14519777C23
hypercenter#533#6923
hypocenterC61#13599
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #21460962C2semidirect
3. #21460961C2semidirect
120. C61#13599semidirect

Maximal subgroups

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

subgroupindex
C2×#168406732
#214609622
#214609612
#214562012
#1359961