Finite Group Databasebeta

← #14545075

Subgroups — #14545075

Order 2176.

250 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 54 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#11763795C212yesmaximal, complemented
2#11763719C212yesmaximal, complemented
3#11763717C212yesmaximal, complemented
4#11763355C211yesmaximal, characteristic
5C2×#41×C17C411yescharacteristic
6C2×#63252C2211yescharacteristic
7D17⋊M16—22no—
8#10587633C411yescharacteristic
9#10587630C2211yescharacteristic
10#10587626C411yescharacteristic
11#10587625—22no—
12#10587622C2211yescharacteristic
13C4×C22⋊D17—22no—
14C2×C4×Dic17C411yescharacteristic
15#10587553—22no—
16#10587545C2214yes—
17#41×C17—41no—
18#41×C17—41no—
19C2×Q8×C17C2×C411yescharacteristic
20C2×D4×C17—21no—
21C2×D4×C17C2×C411yescharacteristic
22C22×C4×C17—21no—
23C22×C4×C17C2×C411yescharacteristic
24C2×C22⋊D17—22no—
25C2×C22⋊D17D412yes—
26C22×Dic17—21no—
27#63252—41no—
28#63252—41no—
29C2×D68C2×C411yescharacteristic
30C2×C4×D17D412yes—
31C2×Dic34C2311yescharacteristic
32#63247—24no—
33#63243—42no—
34#63242—42no—
35C22⋊Dic17—22no—
36#63227—22no—
37#63225—22no—
38C4×Dic17—21no—
39C4×Dic17C2×C411yescharacteristic
40C4×Dic17C2×C411yescharacteristic
41C23×C17—21no—
42C23×C17C22⋊C411yescharacteristic
43C22×D17C22⋊C412yes—
44Q8×C17—41no—
45D4×C17—41no—
46D4×C17—42no—
47C2×C4×C17—21no—
48C2×C4×C17—21no—
49C2×C4×C17—21no—
50C2×C4×C17—41no—
51C2×C4×C17—41no—
52C2×C4×C17C22⋊C411yescharacteristic
53C2×C4×C17C22×C411yescharacteristic
54C22⋊D17—42no—
55C22⋊D17—44no—
56C2×Dic17—21no—
57C2×Dic17—21no—
58C2×Dic17—42no—
59C2×Dic17C2×D412yes—
60D68—41no—
61C4×D17—22no—
62C4×D17—22no—
63Dic34—41no—
64#3624—44no—
65#2132—171nomaximal, Sylow
66C22×C17—21no—
67C22×C17—41no—
68C22×C17—42no—
69C22×C17—41no—
70C22×C17C2×C22⋊C411yescharacteristic
71C2×D17—22no—
72C2×D17—42no—
73C4×C17—21no—
74C4×C17—41no—
75C4×C17#9911yescharacteristic
76C4×C17#9911yescharacteristic
77Dic17—22no—
78Dic17—22no—
79Dic17—41no—
80#532—171no—
81#413—172no—
82#356—172no—
83#355—172no—
84C2×C17—21no—
85C2×C17—41no—
86C2×C17—81no—
87C2×C17C2×#9911yescharacteristic
88D17—42no—
89C2×#41—171no—
90C2×#41#59511yescharacteristic
91C2×M16—342no—
92C4⋊Q8—171no—
93#127—171no—
94#124—171no—
95#124—171no—
96#121—342no—
97C4×D4—342no—
98C2×C42—171no—
99#101—174no—
100#100—342no—
101C17#213211yescharacteristic, complemented, Sylow
102#41—41no—
103#41—41no—
104#41—681no—
105#41—681no—
106C2×Q8—171no—
107C2×Q8C2×#59511yescharacteristic
108C2×D4—21no—
109C2×D4—172no—
110C2×D4—171no—
111C2×D4—342no—
112C2×D4C2×#59511yescharacteristic
113C22×C4—21no—
114C22×C4—172no—
115C22×C4—341no—
116C22×C4C2×#59511yescharacteristic
117M16—344no—
118M16—682no—
119C2×C8—682no—
120C4⋊C4—342no—
121C22⋊C4—342no—
122C22⋊C4—342no—
123C42—171no—
124C42—171no—
125C42—341no—
126C23—21no—
127C23—172no—
128C23C22⋊#59511yescharacteristic
129Q8—41no—
130Q8—681no—
131D4—41no—
132D4—42no—
133D4—681no—
134D4—682no—
135D4—684no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—172no—
142C2×C4—341no—
143C2×C4—342no—
144C2×C4—342no—
145C2×C4—341no—
146C2×C4—682no—
147C2×C4C22⋊#59511yescharacteristic
148C2×C4C22×#59511yescharacteristic
149C8—684no—
150C22—21no—
151C22—41no—
152C22—42no—
153C22—41no—
154C22—342no—
155C22—682no—
156C22C2×C22⋊#59511yescharacteristic
157C4—21no—
158C4—41no—
159C4—342no—
160C4—342no—
161C4—681no—
162C4#1058755111yescharacteristic
163C4#1058755111yescharacteristic
164C2—21no—
165C2—41no—
166C2—81no—
167C2—682no—
168C2C2×#1058755111yescharacteristic
subgroupG/H
centerC4#10587551
commutatorC2×C4×C17C22×C4
FrattiniC2×C4C22×#595
FittingC2×#41×C17C4
socleC2×C17C2×#99
prime radical#11763355C2
cosocleC2×Dic34C23
hypercenterC2×#41#595
hypocenterC17#2132
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #11763795C2semidirect
2. #11763719C2semidirect
3. #11763717C2semidirect
101. C17#2132semidirect

Maximal subgroups

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

subgroupindex
#117637952
#117637192
#117637172
#117633552
#213217