Finite Group Databasebeta

← #29600355

Subgroups — #29600355

Order 15616.

398 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 79 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#21447504C212yesmaximal
2#21443988C214yesmaximal, complemented
3C61×#3152C211yesmaximal, characteristic
4#16839746—22no—
5#16839561C2214yes—
6#16839559—22no—
7C2×#137×C61—22no—
8C61×#532C2211yescharacteristic
9C2×C4⋊Q8×C61C411yescharacteristic
10C61×#497—22no—
11C61×#494C2212yes—
12C61×#492C412yes—
13C4×M16×C61C411yescharacteristic
14C2×#11758194—42no—
15#14519696—24no—
16#14519694—42no—
17C2×#41×C61D412yes—
18C22×Q8×C61—21no—
19#137×C61—44no—
20#137×C61—44no—
21C2×Q16×C61—24no—
22C2×SD16×C61—24no—
23C2×M16×C61—21no—
24C4⋊Q8×C61—21no—
25C4⋊Q8×C61—41no—
26C4⋊Q8×C61C2×C412yes—
27C4⋊Q8×C61C2311yescharacteristic
28#127×C61C2×C411yescharacteristic
29#124×C61D412yes—
30#121×C61—41no—
31C4×D4×C61—41no—
32C2×C4⋊C4×C61—41no—
33C2×C42×C61C2×C411yescharacteristic
34#97×C61—21no—
35C4×C8×C61C2×C412yes—
36#41×C61—42no—
37#41×C61—42no—
38C2×Q8×C61—22no—
39C2×Q8×C61—42no—
40C2×Q8×C61—42no—
41C2×Q8×C61—41no—
42C2×Q8×C61C2×D412yes—
43C2×D4×C61—22no—
44C2×D4×C61—41no—
45C2×D4×C61C22⋊C412yes—
46C22×C4×C61—21no—
47C22×C4×C61—22no—
48C22×C4×C61—41no—
49C22×C4×C61C22⋊C411yescharacteristic
50Q16×C61—48no—
51SD16×C61—48no—
52M16×C61—24no—
53C2×C8×C61—22no—
54C4⋊C4×C61—41no—
55C4⋊C4×C61—42no—
56C4⋊C4×C61—42no—
57C22⋊C4×C61—42no—
58C42×C61—21no—
59C42×C61C22⋊C411yescharacteristic
60C42×C61C22×C411yescharacteristic
61#11758194—44no—
62#11758194—82no—
63C2×#92418—82no—
64C23×C61—22no—
65C23×C61#9911yescharacteristic
66Q8×C61—42no—
67Q8×C61—44no—
68Q8×C61—82no—
69D4×C61—42no—
70D4×C61—82no—
71D4×C61—82no—
72C2×C4×C61—21no—
73C2×C4×C61—22no—
74C2×C4×C61—22no—
75C2×C4×C61—21no—
76C2×C4×C61—42no—
77C2×C4×C61—42no—
78C2×C4×C61—42no—
79C2×C4×C61—42no—
80C2×C4×C61—81no—
81C2×C4×C61—81no—
82C2×C4×C61#9911yescharacteristic
83C2×C4×C61C2×C22⋊C411yescharacteristic
84C8×C61—24no—
85#92418—84no—
86#13592—611nomaximal, Sylow
87C22×C61—21no—
88C22×C61—41no—
89C22×C61—42no—
90C22×C61—82no—
91C22×C61C2×#9911yescharacteristic
92C4×C61—22no—
93C4×C61—21no—
94C4×C61—41no—
95C4×C61—42no—
96C4×C61—82no—
97C4×C61#35312yes—
98#3152D6111yescharacteristic
99#2132—612no—
100#1411—614no—
101C2×C61—21no—
102C2×C61—41no—
103C2×C61—82no—
104C2×C61C2×#35311yescharacteristic
105C2×#137—22no—
106#532C2×D6111yescharacteristic
107C2×C4⋊Q8Dic6111yescharacteristic
108#497—22no—
109#494C2×D6112yes—
110#492Dic6112yes—
111#413—1222no—
112C4×M16Dic6111yescharacteristic
113#356—614no—
114#355—1222no—
115C61#1359211yescharacteristic, complemented, Sylow
116C2×#41C22⋊D6112yes—
117C22×Q8—21no—
118#137—44no—
119#137—44no—
120C2×Q16—24no—
121C2×SD16—24no—
122C2×M16—21no—
123C2×M16—2442no—
124C4⋊Q8—21no—
125C4⋊Q8—41no—
126C4⋊Q8C2×Dic6112yes—
127C4⋊Q8C22×D6111yescharacteristic
128#127C2×Dic6111yescharacteristic
129#124C22⋊D6112yes—
130#121—41no—
131C4×D4—41no—
132C2×C4⋊C4—41no—
133C2×C42C2×Dic6111yescharacteristic
134#101—1224no—
135#100—2442no—
136#97—21no—
137C4×C8C2×Dic6112yes—
138#41—42no—
139#41—42no—
140C2×Q8—22no—
141C2×Q8—42no—
142C2×Q8—42no—
143C2×Q8—41no—
144C2×Q8C2×C22⋊D6112yes—
145C2×D4—22no—
146C2×D4—41no—
147C2×D4C22⋊Dic6112yes—
148C22×C4—21no—
149C22×C4—22no—
150C22×C4—41no—
151C22×C4C22⋊Dic6111yescharacteristic
152Q16—48no—
153SD16—48no—
154M16—24no—
155M16—4882no—
156M16—2444no—
157C2×C8—22no—
158C2×C8—4882no—
159C4⋊C4—41no—
160C4⋊C4—42no—
161C4⋊C4—42no—
162C22⋊C4—42no—
163C42—21no—
164C42C22⋊Dic6111yescharacteristic
165C42C22×Dic6111yescharacteristic
166C23—22no—
167C23#1451969211yescharacteristic
168Q8—42no—
169Q8—44no—
170Q8—82no—
171D4—42no—
172D4—82no—
173D4—82no—
174C2×C4—21no—
175C2×C4—22no—
176C2×C4—21no—
177C2×C4—22no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—81no—
183C2×C4—81no—
184C2×C4#1451969211yescharacteristic
185C2×C4C2×C22⋊Dic6111yescharacteristic
186C8—24no—
187C8—4884no—
188C22—21no—
189C22—41no—
190C22—42no—
191C22—82no—
192C22C2×#1451969211yescharacteristic
193C4—22no—
194C4—21no—
195C4—41no—
196C4—42no—
197C4—82no—
198C4#1683955512yes—
199C2—21no—
200C2—41no—
201C2—82no—
202C2C2×#1683955511yescharacteristic
subgroupG/H
centerC2C2×#16839555
commutatorC42×C61C22×C4
FrattiniC4⋊Q8C22×D61
FittingC61×#3152C2
socleC2×C61C2×#353
prime radicalC61×#532C22
cosocleC4⋊Q8×C61C23
hypercenter#3152D61
hypocenterC61#13592
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ #532 ◁ #3152

Complements

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

NH ≅ G/Ntype
2. #21443988C2semidirect
115. C61#13592semidirect

Maximal subgroups

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

subgroupindex
#214475042
#214439882
C61×#31522
#1359261