Finite Group Databasebeta

← #17981166

Subgroups — #17981166

Order 4352.

230 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 45 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#14545856C212yesmaximal
2#14544915C211yesmaximal, characteristic
3#11763928—22no—
4C2×#10587549—22no—
5#11763768C2211yescharacteristic
6#11763753C411yescharacteristic
7C4⋊Q8×D17C411yescharacteristic
8C2×Q8×D17—21no—
9C2×C4⋊#595—21no—
10C2×#63242D412yes—
11#10587670—42no—
12#10587666—42no—
13#10587665—24no—
14C17×C4⋊Q8C811yescharacteristic
15#10587630—21no—
16C4⋊C4×D17—41no—
17#10587574—41no—
18C42×D17C2×C411yescharacteristic
19#10587555C811yescharacteristic
20#10587549—42no—
21#10587549—42no—
22(C2×#595)⋊C4—41no—
23#10587542—41no—
24C22×#595—41no—
25C2×Q8×C17—21no—
26Q8×D17—42no—
27Q8×D17—42no—
28C2×C4×D17—21no—
29C2×C4×D17—41no—
30C2×C4×D17C22⋊C411yescharacteristic
31C2×Dic34—21no—
32C2×Dic34—41no—
33C2×#3624—22no—
34C4⋊#595—42no—
35#63242—22no—
36#63242D812yes—
37#63242SD1612yes—
38#63241—44no—
39C4⋊C4×C17—41no—
40C42×C17C2×C811yescharacteristic
41C4⋊Dic17—41no—
42#63225—42no—
43C4×Dic17—21no—
44C4×Dic17M1611yescharacteristic
45#7117—171nomaximal, Sylow
46C22×D17#10011yescharacteristic
47C2×#595—82no—
48C2×#595—81no—
49Q8×C17—42no—
50C2×C4×C17—21no—
51C2×C4×C17—41no—
52C2×C4×C17C22⋊C811yescharacteristic
53C2×Dic17—21no—
54C2×Dic17—41no—
55C2×Dic17#9911yescharacteristic
56C4×D17—42no—
57C4×D17—81no—
58C4×D17—81no—
59C4×D17#10212yes—
60C4×D17#10412yes—
61Dic34—42no—
62Dic34—82no—
63#3624—22no—
64#3624—22no—
65#1960—171no—
66#1375—172no—
67C22×C17#32311yescharacteristic
68C2×D17—22no—
69C2×D17#32911yescharacteristic
70C2×D17#33111yescharacteristic
71#595—161no—
72C4×C17—41no—
73C4×C17—81no—
74C4×C17D4⋊C812yes—
75Dic17—41no—
76Dic17—81no—
77Dic17#32712yes—
78C2×C4⋊Q8—171no—
79C2×M32—342no—
80C2×#103—342no—
81C2×#97—171no—
82#382—171no—
83C2×C17—21no—
84C2×C17#127011yescharacteristic
85D17—21no—
86D17#135612yes—
87C22×Q8—341no—
88C22×C8—172no—
89C4⋊Q8—171no—
90C4⋊Q8—341no—
91C4⋊Q8—681no—
92C4⋊Q8#363311yescharacteristic
93C2×C4⋊C4—341no—
94C2×C4⋊C4—681no—
95C2×C42—171no—
96M32—682no—
97M32—682no—
98C2×C16—344no—
99#103—682no—
100#103—682no—
101#97—681no—
102#95—681no—
103C17#711711yescharacteristic, complemented, Sylow
104C2×Q8—21no—
105C2×Q8—341no—
106C2×Q8—681no—
107C2×Q8—682no—
108C2×Q8—682no—
109C22×C4—171no—
110C22×C4—341no—
111C22×C4—681no—
112C22×C4—681no—
113C2×C8—172no—
114C2×C8—172no—
115C2×C8—342no—
116C2×C8—342no—
117C4⋊C4—41no—
118C4⋊C4—681no—
119C4⋊C4—682no—
120C4⋊C4—682no—
121C42—171no—
122C42—341no—
123C42C2×#363311yescharacteristic
124C16—684no—
125C23—171no—
126Q8—42no—
127Q8—682no—
128Q8—1362no—
129C2×C4—21no—
130C2×C4—41no—
131C2×C4—171no—
132C2×C4—172no—
133C2×C4—172no—
134C2×C4—341no—
135C2×C4—682no—
136C2×C4—681no—
137C2×C4—1361no—
138C2×C4—1361no—
139C2×C4—1361no—
140C2×C4—1362no—
141C2×C4C22⋊#363311yescharacteristic
142C8—342no—
143C8—342no—
144C22—171no—
145C22—171no—
146C22—342no—
147C22#1176389411yescharacteristic
148C4—41no—
149C4—81no—
150C4—2721no—
151C4—172no—
152C4—681no—
153C4—1361no—
154C4D4⋊#363312yes—
155C2—21no—
156C2—172no—
157C2—341no—
158C2#1454578311yescharacteristic
subgroupG/H
centerC2#14545783
commutatorC42×C17C2×C8
FrattiniC42C2×#3633
FittingC17×C4⋊Q8C8
socleC2×C17#1270
prime radicalC22×D17#100
cosocle#11763768C22
hypercenterC4⋊Q8#3633
hypocenterC17#7117
LCSG ▷ C42×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C2×C4 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
103. C17#7117semidirect

Maximal subgroups

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

subgroupindex
#145458562
#145449152
#711717