Finite Group Databasebeta

← #17948912

Subgroups — #17948912

Order 4352.

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

normal subgroups only

This group has 218 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#14545001C211yesmaximal, characteristic
2#14544707C211yesmaximal, characteristic
3D17×#347C211yesmaximal, characteristic
4#11763865—21no—
5#11763755C411yescharacteristic
6#11763753C411yescharacteristic
7#11763702—21no—
8#11763701C412yescomplemented
9#11763683—21no—
10#11763683—21no—
11M32×D17—21no—
12#97×D17C2211yescharacteristic
13#11762587C411yescharacteristic, complemented
14#11762586—21no—
15C17×#347C411yescharacteristic, complemented
16C2×C4⋊#595—21no—
17C2×C4⋊#595—21no—
18C2×C4⋊#595—41no—
19C2×C8×D17D411yescharacteristic
20C2×C8×D17D411yescharacteristic
21C42×D17C2×C411yescharacteristic
22(C2×#595)⋊C4—41no—
23#10587538—22no—
24#10587530—22no—
25#10587529—22no—
26C17×M32—21no—
27C17×#97C2×C411yescharacteristic
28#10587486D411yescharacteristic
29#10587486Q811yescharacteristic
30#10587483—21no—
31#10587474C2×C411yescharacteristic
32#10587469—22no—
33C16×D17—22no—
34C22×#595—41no—
35C22×#595—41no—
36C2×C4×D17—21no—
37C2×C4×D17C22⋊C411yescharacteristic
38C4⋊#595—41no—
39C4⋊#595—41no—
40C4⋊#595—41no—
41C4⋊#595—41no—
42C4⋊#595—82no—
43C2×C8×C17C22⋊C411yescharacteristic
44C2×C8×C17C4⋊C411yescharacteristic
45C42×C17C4211yescharacteristic
46C4×Dic17—21no—
47C4×Dic17C4⋊C411yescharacteristic
48C2×#3622C22⋊C411yescharacteristic
49C2×#3622C4⋊C411yescharacteristic
50C8×D17—21no—
51C8×D17—21no—
52C8×D17—21no—
53C8×D17—21no—
54#63216—24no—
55C16×C17—22no—
56#63214—22no—
57#7266—171nomaximal, Sylow
58C22×D17#10011yescharacteristic
59C2×#595—82no—
60C2×#595—81no—
61C2×#595—81no—
62C2×#595—81no—
63C2×#595—81no—
64C2×C4×C17—21no—
65C2×C4×C17#9511yescharacteristic
66C2×Dic17—21no—
67C2×Dic17#10111yescharacteristic
68C4×D17—41no—
69C4×D17—41no—
70C4×D17#10411yescharacteristic
71C4×D17#10411yescharacteristic
72C4×D17#10411yescharacteristic
73C4×D17#10411yescharacteristic
74C8×C17—21no—
75C8×C17—21no—
76#3622—21no—
77#3622—21no—
78C2×#347—171no—
79C2×#347—171no—
80#1836—171no—
81C22×C17#34311yescharacteristic
82C2×D17—21no—
83C2×D17—21no—
84C2×D17#32911yescharacteristic
85C2×D17#32911yescharacteristic
86#595—161no—
87#595—161no—
88C4×C17—41no—
89C4×C17#33911yescharacteristic
90C4×C17#33911yescharacteristic
91Dic17—41no—
92Dic17#33011yescharacteristic
93Dic17#33011yescharacteristic
94C2×M32—341no—
95C2×M32—341no—
96C2×#97—171no—
97#384—171no—
98#382—171no—
99#347—172no—
100#347—171no—
101#347—341no—
102#347—341no—
103#347#59511yescharacteristic, complemented
104#340—341no—
105#340—341no—
106C2×C17—21no—
107C2×C17#129511yescharacteristic
108D17—21no—
109D17#135511yescharacteristic
110D17#135611yescharacteristic
111C22×C8—171no—
112C22×C8—171no—
113C2×C4⋊C4—341no—
114C2×C4⋊C4—341no—
115C2×C4⋊C4—681no—
116C2×C42—171no—
117M32—21no—
118M32—342no—
119M32—342no—
120M32—342no—
121M32—341no—
122C2×C16—342no—
123C2×C16—342no—
124#97—171no—
125#97—171no—
126#97—171no—
127#97C2×#59511yescharacteristic
128#95—681no—
129C17#726611yescharacteristic, complemented, Sylow
130C22×C4—171no—
131C22×C4—341no—
132C22×C4—681no—
133C22×C4—681no—
134C2×C8—171no—
135C2×C8—171no—
136C2×C8—341no—
137C2×C8—341no—
138C2×C8—341no—
139C2×C8—341no—
140C2×C8C4⋊#59511yescharacteristic
141C2×C8C22⋊#59511yescharacteristic
142C4⋊C4—681no—
143C4⋊C4—681no—
144C4⋊C4—681no—
145C4⋊C4—681no—
146C4⋊C4—1362no—
147C42—171no—
148C42—341no—
149C42C4×#59511yescharacteristic
150C16—22no—
151C16—342no—
152C16—344no—
153C23—171no—
154C2×C4—21no—
155C2×C4—171no—
156C2×C4—171no—
157C2×C4—171no—
158C2×C4—171no—
159C2×C4—171no—
160C2×C4—341no—
161C2×C4—681no—
162C2×C4—681no—
163C2×C4—1361no—
164C2×C4—1361no—
165C2×C4—1362no—
166C2×C4—1361no—
167C2×C4—1361no—
168C2×C4(C2×#595)⋊C411yescharacteristic
169C8—21no—
170C8—21no—
171C8—341no—
172C8—341no—
173C22—171no—
174C22—171no—
175C22—341no—
176C22—341no—
177C22#1176368811yescharacteristic
178C4—41no—
179C4—2721no—
180C4—2721no—
181C4—171no—
182C4—171no—
183C4—681no—
184C4#1176368011yescharacteristic
185C4#1176368111yescharacteristic
186C2—21no—
187C2—171no—
188C2—171no—
189C2—341no—
190C2#1454366111yescharacteristic
subgroupG/H
centerC2#14543661
commutatorC42×C17C42
Frattini#97C2×#595
FittingC17×#347C4
socleC2×C17#1295
prime radicalC22×D17#100
cosocle#97×D17C22
hypercenter#347#595
hypocenterC17#7266
LCSG ▷ C42×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #347

Complements

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

NH ≅ G/Ntype
8. #11763701C4semidirect
13. #11762587C4semidirect
15. C17×#347C4semidirect
103. #347#595semidirect
129. C17#7266semidirect

Maximal subgroups

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

subgroupindex
#145450012
#145447072
D17×#3472
#726617