Finite Group Databasebeta

← #17948716

Subgroups — #17948716

Order 4352.

248 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 62 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#14545021C211yesmaximal, characteristic
2#14544539C211yesmaximal, characteristic
3#14530397C211yesmaximal, characteristic
4#11763865—21no—
5#11763795C411yescharacteristic
6#11763788C411yescharacteristic
7#11763772—21no—
8#11763706—21no—
9#11763705C412yescomplemented
10#11763691—21no—
11C2×#10587587C2211yescharacteristic
12C2×#10587483C411yescharacteristic, complemented
13#11762588—21no—
14#11762588—21no—
15C22×C16×C17C411yescharacteristic, complemented
16C2×#63252C2×C411yescharacteristic
17#10587677—21no—
18D17⋊M16—21no—
19C22×C8×C17C2×C411yescharacteristic
20C2×#63223C2×C411yescharacteristic
21#10587587—41no—
22#10587587—41no—
23C2×#63218D411yescharacteristic
24C2×#63218Q811yescharacteristic
25C2×C8×D17D411yescharacteristic
26C2×C8×D17D411yescharacteristic
27#10587553C812yes—
28#10587551C812yes—
29#10587545—21no—
30#10587539—21no—
31#10587538—22no—
32#10587532—41no—
33C8×#595—41no—
34#10587530—41no—
35#10587529—41no—
36C2×C16×C17—21no—
37C2×C16×C17—41no—
38#10587483—41no—
39C2×#63214—21no—
40C22×C4×C17C4211yescharacteristic
41C2×C22⋊D17C2×C811yescharacteristic
42C2×C22⋊D17C2×C811yescharacteristic
43#63252—41no—
44#63252—41no—
45C2×D68M1611yescharacteristic
46C2×C4×D17C22⋊C411yescharacteristic
47C2×C4×D17C4⋊C411yescharacteristic
48C2×Dic34M1611yescharacteristic
49C22⋊#595—22no—
50#63247—22no—
51C4⋊#595—41no—
52C4×#595—41no—
53#63243—41no—
54#63242—41no—
55C2×C8×C17—21no—
56C2×C8×C17—21no—
57C2×C8×C17C22⋊C411yescharacteristic
58C2×C8×C17C4⋊C411yescharacteristic
59#63223—41no—
60C2×#3622C22⋊C411yescharacteristic
61C2×#3622C4⋊C411yescharacteristic
62#63218—41no—
63#63218—41no—
64C8×D17—21no—
65C8×D17—21no—
66C8×D17—21no—
67C8×D17—21no—
68#63216—42no—
69C16×C17—41no—
70#63214—41no—
71#7207—171nomaximal, Sylow
72C23×C17C4×C811yescharacteristic
73C22×D17C22⋊C811yescharacteristic
74C22×D17C4⋊C811yescharacteristic
75C2×#595—42no—
76C2×C4×C17—21no—
77C2×C4×C17—21no—
78C2×C4×C17#9511yescharacteristic
79C2×C4×C17#9711yescharacteristic
80C22⋊D17—41no—
81C22⋊D17—41no—
82C2×Dic17C22⋊C811yescharacteristic
83C2×Dic17C4⋊C811yescharacteristic
84D68—41no—
85C4×D17—21no—
86C4×D17—21no—
87C4×D17—21no—
88C4×D17—21no—
89Dic34—41no—
90#3624—42no—
91C8×C17—21no—
92C8×C17#9911yescharacteristic
93C8×C17#9911yescharacteristic
94#3622—21no—
95#3622—21no—
96#2115—171no—
97#2113—171no—
98#1757—171no—
99C22×C17—21no—
100C22×C17—41no—
101C22×C17#33611yescharacteristic
102C2×D17—21no—
103C2×D17—21no—
104C2×D17—41no—
105C2×D17—41no—
106#595—82no—
107C4×C17—21no—
108C4×C17#34211yescharacteristic
109C4×C17#34411yescharacteristic
110Dic17—21no—
111Dic17—21no—
112C2×#131—171no—
113C2×M32—171no—
114C2×M32—341no—
115C22×C16#59511yescharacteristic, complemented
116#413—171no—
117#410—171no—
118#405—341no—
119#349—172no—
120#349—341no—
121C22⋊C16—341no—
122C22⋊C16—341no—
123#344—341no—
124C2×C17—21no—
125C2×C17—41no—
126C2×C17#128211yescharacteristic
127D17—41no—
128D17—41no—
129C2×#41—171no—
130#131—681no—
131#131—681no—
132C2×M16—171no—
133C2×M16—171no—
134C2×M16—171no—
135C2×M16—341no—
136C22×C8—171no—
137C22×C8—171no—
138C22×C8C2×#59511yescharacteristic
139#117—341no—
140M32—342no—
141M32—681no—
142M32—681no—
143C2×C16—21no—
144C2×C16—41no—
145C2×C16—341no—
146C2×C16—681no—
147#101—341no—
148#100—172no—
149#99—172no—
150#99—341no—
151#97—681no—
152C4×C8—681no—
153C17#720711yescharacteristic, complemented, Sylow
154#41—681no—
155#41—681no—
156C2×Q8—171no—
157C2×D4—171no—
158C2×D4—171no—
159C2×D4—171no—
160C22×C4—171no—
161C22×C4—171no—
162C22×C4C4×#59511yescharacteristic
163M16—342no—
164M16—681no—
165M16—681no—
166M16—681no—
167M16—681no—
168C2×C8—21no—
169C2×C8—21no—
170C2×C8—171no—
171C2×C8—171no—
172C2×C8—341no—
173C2×C8—341no—
174C2×C8—341no—
175C2×C8—341no—
176C2×C8—681no—
177C2×C8C4⋊#59511yescharacteristic
178C2×C8C22⋊#59511yescharacteristic
179C4⋊C4—681no—
180C22⋊C4—342no—
181C42—681no—
182C16—41no—
183C16—682no—
184C16—681no—
185C23—171no—
186C23—171no—
187C23C8×#59511yescharacteristic
188Q8—681no—
189D4—681no—
190D4—681no—
191D4—681no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—171no—
195C2×C4—171no—
196C2×C4—341no—
197C2×C4—341no—
198C2×C4—341no—
199C2×C4—341no—
200C2×C4—682no—
201C2×C4#1058753211yescharacteristic
202C2×C4(C2×#595)⋊C411yescharacteristic
203C8—21no—
204C8—341no—
205C8—341no—
206C8—682no—
207C8#1058753911yescharacteristic
208C8#1058755111yescharacteristic
209C22—21no—
210C22—41no—
211C22—341no—
212C22—341no—
213C22—681no—
214C22—681no—
215C22#1176367411yescharacteristic
216C4—21no—
217C4—341no—
218C4—341no—
219C4—1362no—
220C4#1176368711yescharacteristic
221C4#1176369111yescharacteristic
222C2—21no—
223C2—41no—
224C2—681no—
225C2—681no—
226C2#1454362611yescharacteristic
subgroupG/H
centerC8#10587551
commutatorC23×C17C4×C8
FrattiniC22×C8C2×#595
FittingC22×C16×C17C4
socleC2×C17#1282
prime radicalC2×#63252C2×C4
cosocleC2×#10587587C22
hypercenterC22×C16#595
hypocenterC17#7207
LCSG ▷ C23×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C8 ◁ C2×C8 ◁ C22×C8 ◁ C22×C16

Complements

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

NH ≅ G/Ntype
9. #11763705C4semidirect
12. C2×#10587483C4semidirect
15. C22×C16×C17C4semidirect
115. C22×C16#595semidirect
153. C17#7207semidirect

Maximal subgroups

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

subgroupindex
#145450212
#145445392
#145303972
#720717