Finite Group Databasebeta

← #17948691

Subgroups — #17948691

Order 4352.

286 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 66 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#14545013C211yesmaximal, characteristic
2#14544520C211yesmaximal, characteristic
3#14530393C211yesmaximal, characteristic
4C2×#10587538C412yescomplemented
5#11763777C411yescharacteristic
6C2×#10587532—21no—
7C4×C22⋊#595C411yescharacteristic
8#11763704—21no—
9#11763704—21no—
10#11763674—21no—
11C22×C8×D17C2211yescharacteristic
12C2×#10587469—21no—
13C22⋊#63214C411yescharacteristic, complemented
14#11762588—21no—
15C17×C22⋊C16C411yescharacteristic, complemented
16C22×C4×D17C2×C411yescharacteristic
17C2×C22⋊#595C812yes—
18C2×C4×#595—21no—
19C2×#63242—21no—
20C22×C8×C17C2×C411yescharacteristic
21C22×#3622C2×C411yescharacteristic
22C2×C8×D17—42no—
23C2×C8×D17D411yescharacteristic
24C2×C8×D17D411yescharacteristic
25C2×C8×D17D411yescharacteristic
26C2×C8×D17Q811yescharacteristic
27C22⋊#3624C812yes—
28(C2×#595)⋊C4—21no—
29#10587543—21no—
30#10587538—42no—
31C2×#63216—22no—
32#10587532—42no—
33C2×C16×C17—21no—
34C2×#63214—21no—
35#10587469—42no—
36C23×D17C2×C811yescharacteristic
37C22×#595—22no—
38C22×C4×C17C4211yescharacteristic
39C22×Dic17C2×C811yescharacteristic
40C2×C4×D17—41no—
41C2×C4×D17—41no—
42C2×C4×D17C22⋊C411yescharacteristic
43C2×C4×D17C4⋊C411yescharacteristic
44C2×C4×D17M1611yescharacteristic
45C2×C4×D17M1611yescharacteristic
46C22⋊#595—42no—
47C2×#3624—22no—
48C4×#595—41no—
49C4×#595—41no—
50#63242—41no—
51#63242—41no—
52C2×C8×C17—41no—
53C2×C8×C17C22⋊C411yescharacteristic
54C2×C8×C17C4⋊C411yescharacteristic
55C2×#3622—22no—
56C2×#3622C22⋊C411yescharacteristic
57C2×#3622C4⋊C411yescharacteristic
58C8×D17—22no—
59C8×D17—22no—
60C8×D17—41no—
61C8×D17—41no—
62#63216—42no—
63C16×C17—41no—
64#63214—41no—
65#7201—171nomaximal, Sylow
66C23×C17C4×C811yescharacteristic
67C22×D17—22no—
68C22×D17—41no—
69C22×D17—41no—
70C22×D17C22⋊C811yescharacteristic
71C22×D17C4⋊C811yescharacteristic
72C2×#595—42no—
73C2×#595—42no—
74C2×#595—42no—
75C2×C4×C17—21no—
76C2×C4×C17—21no—
77C2×C4×C17#9511yescharacteristic
78C2×C4×C17#9711yescharacteristic
79C2×Dic17—41no—
80C2×Dic17C22⋊C811yescharacteristic
81C2×Dic17C4⋊C811yescharacteristic
82C4×D17—21no—
83C4×D17—21no—
84C4×D17—21no—
85C4×D17—21no—
86C4×D17—41no—
87C4×D17—41no—
88#3624—42no—
89C8×C17—21no—
90C8×C17—21no—
91#3622—21no—
92#3622#9912yes—
93#2112—171no—
94#2112—171no—
95#1752—171no—
96C22×C17—21no—
97C22×C17—21no—
98C22×C17—21no—
99C22×C17#33611yescharacteristic
100C2×D17—21no—
101C2×D17—21no—
102C2×D17—21no—
103C2×D17—21no—
104C2×D17—21no—
105C2×D17—44no—
106C2×D17#34912yes—
107#595—82no—
108C4×C17—21no—
109C4×C17#34211yescharacteristic
110C4×C17#34411yescharacteristic
111Dic17—21no—
112Dic17—21no—
113C23×C8—171no—
114C2×M32—172no—
115C2×M32—341no—
116C2×C22⋊C8—171no—
117C2×#97—341no—
118C4×C22⋊C4—171no—
119C22⋊C16—171no—
120C22⋊C16—341no—
121C22⋊C16—341no—
122C22⋊C16—341no—
123C22⋊C16#59511yescharacteristic, complemented
124#336—341no—
125C2×C17—41no—
126C2×C17#128211yescharacteristic
127C2×C17#137711yescharacteristic
128C2×C17#137811yescharacteristic
129D17—22no—
130D17—41no—
131C23×C4—171no—
132C22×C8—171no—
133C22×C8—171no—
134C22×C8—171no—
135C22×C8—171no—
136C22×C8—171no—
137C22×C8—341no—
138C22×C8—682no—
139C22×C8C2×#59511yescharacteristic
140C2×C22⋊C4—172no—
141C2×C42—341no—
142M32—682no—
143M32—682no—
144C2×C16—21no—
145C2×C16—342no—
146C2×C16—341no—
147C22⋊C8—172no—
148C22⋊C8—341no—
149#97—682no—
150#95—341no—
151C17#720111yescharacteristic, complemented, Sylow
152C24—171no—
153C22×C4—171no—
154C22×C4—171no—
155C22×C4—171no—
156C22×C4—171no—
157C22×C4—171no—
158C22×C4—342no—
159C22×C4—681no—
160C22×C4—681no—
161C22×C4C4×#59511yescharacteristic
162C2×C8—41no—
163C2×C8—171no—
164C2×C8—171no—
165C2×C8—342no—
166C2×C8—342no—
167C2×C8—342no—
168C2×C8—342no—
169C2×C8—681no—
170C2×C8—681no—
171C2×C8—681no—
172C2×C8—681no—
173C2×C8C4⋊#59511yescharacteristic
174C2×C8C22⋊#59511yescharacteristic
175C22⋊C4—682no—
176C42—681no—
177C42—681no—
178C16—41no—
179C16—681no—
180C16—682no—
181C23—171no—
182C23—171no—
183C23—342no—
184C23—681no—
185C23—681no—
186C23C8×#59511yescharacteristic
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—171no—
190C2×C4—171no—
191C2×C4—341no—
192C2×C4—341no—
193C2×C4—341no—
194C2×C4—341no—
195C2×C4—681no—
196C2×C4—681no—
197C2×C4—681no—
198C2×C4—682no—
199C2×C4—682no—
200C2×C4—682no—
201C2×C4#1058753211yescharacteristic
202C2×C4(C2×#595)⋊C411yescharacteristic
203C8—21no—
204C8—21no—
205C8—172no—
206C8—341no—
207C8—682no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—172no—
212C22—341no—
213C22—341no—
214C22—341no—
215C22—341no—
216C22—341no—
217C22—684no—
218C22#1176367411yescharacteristic
219C4—21no—
220C4—341no—
221C4—341no—
222C4—1362no—
223C4#1176368611yescharacteristic
224C4#1176369211yescharacteristic
225C2—41no—
226C2—342no—
227C2—681no—
228C2#1454362511yescharacteristic
229C2#1454383011yescharacteristic
230C2#1454383311yescharacteristic
subgroupG/H
centerC2×C4(C2×#595)⋊C4
commutatorC23×C17C4×C8
FrattiniC22×C8C2×#595
FittingC17×C22⋊C16C4
socleC22×C17#336
prime radicalC23×D17C2×C8
cosocleC22×C8×D17C22
hypercenterC22⋊C16#595
hypocenterC17#7201
LCSG ▷ C23×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C22⋊C16

Complements

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

NH ≅ G/Ntype
4. C2×#10587538C4semidirect
13. C22⋊#63214C4semidirect
15. C17×C22⋊C16C4semidirect
123. C22⋊C16#595semidirect
151. C17#7201semidirect

Maximal subgroups

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

subgroupindex
#145450132
#145445202
#145303932
#720117