Finite Group Databasebeta

← #17958183

Subgroups — #17958183

Order 4352.

394 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 98 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#14545009C212yesmaximal
2#14543723C212yesmaximal, complemented
3#14543722C212yesmaximal, complemented
4D17×#424C211yesmaximal, characteristic
5C2×#10587529—22no—
6#11763704—22no—
7C22⋊#63216C2214yes—
8C2×M16×D17C411yescharacteristic
9C22×C8×D17C2211yescharacteristic
10#117×D17C411yescharacteristic
11#11762837C2211yescharacteristic
12#11762836C2211yescharacteristic
13#11762835C411yescharacteristic
14#11762834—22no—
15C4⋊C8×D17—22no—
16C17×#424C411yescharacteristic
17C22×C4×D17C2×C411yescharacteristic
18C2×M16×C17C2×C411yescharacteristic
19C22×C8×C17C2×C411yescharacteristic
20C17×#117C2×C411yescharacteristic
21#10587612C2×C411yescharacteristic
22C2×#63223C2×C411yescharacteristic
23C22×#3622C2311yescharacteristic
24M16×D17—42no—
25C2×#63218—21no—
26C2×C8×D17—21no—
27C2×C8×D17—42no—
28C2×C8×D17D412yes—
29C2×C8×D17D412yes—
30#10587578C812yes—
31C4⋊C4×D17C812yes—
32C22⋊C4×D17—21no—
33#10587563—21no—
34#10587558—21no—
35C42×D17—21no—
36C2×#63216—24no—
37#10587529—44no—
38C17×C4⋊C8—22no—
39#10587485—22no—
40#10587485—22no—
41C4⋊#3622—22no—
42C23×D17M1611yescharacteristic
43C22×C4×C17C22×C411yescharacteristic
44C22×Dic17M1611yescharacteristic
45C2×C4×D17—22no—
46C2×C4×D17—22no—
47C2×C4×D17—22no—
48C2×C4×D17C22⋊C411yescharacteristic
49C2×C4×D17C22⋊C411yescharacteristic
50C2×C4×D17C2×C811yescharacteristic
51C2×C4×D17C2×C811yescharacteristic
52M16×C17—41no—
53C2×C8×C17—21no—
54C2×C8×C17—41no—
55C2×C8×C17C22⋊C412yes—
56C4⋊C4×C17C2×C812yes—
57C22⋊C4×C17—21no—
58C42×C17—21no—
59C22⋊Dic17—21no—
60#63227—22no—
61C4⋊Dic17C2×C812yes—
62#63225—22no—
63C4×Dic17—21no—
64C4×Dic17—22no—
65#63223—41no—
66C2×#3622—21no—
67C2×#3622—41no—
68C2×#3622C2×D412yes—
69#63218—42no—
70C8×D17—24no—
71C8×D17—42no—
72C8×D17—42no—
73#63216—44no—
74C2×#1323—171nomaximal, Sylow
75C23×C17C2×M1611yescharacteristic
76C22×D17—22no—
77C22×D17—24no—
78C22×D17C22⋊C811yescharacteristic
79C22×D17C22⋊C811yescharacteristic
80C2×C4×C17—21no—
81C2×C4×C17—21no—
82C2×C4×C17—22no—
83C2×C4×C17C2×C22⋊C411yescharacteristic
84C2×C4×C17C22×C811yescharacteristic
85C2×Dic17—22no—
86C2×Dic17—22no—
87C2×Dic17C22⋊C811yescharacteristic
88C2×Dic17C22⋊C811yescharacteristic
89C4×D17—22no—
90C4×D17—21no—
91C4×D17—21no—
92C4×D17—22no—
93C4×D17—44no—
94C4×D17#9912yes—
95C4×D17#10112yes—
96C8×C17—22no—
97C8×C17—41no—
98#3622—22no—
99#3622—41no—
100C2×#424—171no—
101C2×C22⋊C16—172no—
102#1323—172no—
103#1323—172no—
104C22×C17—22no—
105C22×C17—21no—
106C22×C17C2×C22⋊C811yescharacteristic
107C2×D17—22no—
108C2×D17—21no—
109C2×D17—44no—
110C2×D17#32412yes—
111C2×D17#35014yes—
112C4×C17—21no—
113C4×C17—42no—
114C4×C17C2×#9911yescharacteristic
115C4×C17C2×#10111yescharacteristic
116Dic17—21no—
117Dic17—42no—
118Dic17#32412yes—
119C22×M16—171no—
120C23×C8—171no—
121C2×#117—171no—
122C22×C16—342no—
123#424—171no—
124#424—171no—
125#424—171no—
126#424—342no—
127#424#59511yescharacteristic
128C2×C4⋊C8—342no—
129C22⋊C16—174no—
130C22⋊C16—342no—
131C2×C17—41no—
132C2×C17C2×#32411yescharacteristic
133C2×C17C2×#35012yes—
134D17—41no—
135D17#132314yescomplemented
136C23×C4—171no—
137C2×M16—171no—
138C2×M16—341no—
139C2×M16—682no—
140C2×M16C2×#59511yescharacteristic
141C22×C8—171no—
142C22×C8—172no—
143C22×C8—172no—
144C22×C8—341no—
145C22×C8—682no—
146C22×C8C2×#59511yescharacteristic
147#117—171no—
148#117—172no—
149#117—341no—
150#117—341no—
151#117C2×#59511yescharacteristic
152C2×C4⋊C4—172no—
153C2×C22⋊C4—341no—
154C2×C42—341no—
155C2×C16—344no—
156C2×C16—684no—
157C4⋊C8—22no—
158C4⋊C8—342no—
159C4⋊C8—342no—
160C4⋊C8—342no—
161C17C2×#132311yescharacteristic, complemented, Sylow
162C24—171no—
163C22×C4—171no—
164C22×C4—171no—
165C22×C4—171no—
166C22×C4—171no—
167C22×C4—171no—
168C22×C4—342no—
169C22×C4—342no—
170C22×C4—342no—
171C22×C4C22×#59511yescharacteristic
172M16—41no—
173M16—682no—
174M16—681no—
175C2×C8—21no—
176C2×C8—41no—
177C2×C8—172no—
178C2×C8—344no—
179C2×C8—341no—
180C2×C8—682no—
181C2×C8—682no—
182C2×C8—681no—
183C2×C8C22⋊#59512yes—
184C4⋊C4—172no—
185C4⋊C4—342no—
186C4⋊C4#6324212yes—
187C22⋊C4—21no—
188C22⋊C4—342no—
189C22⋊C4—341no—
190C42—21no—
191C42—342no—
192C42—341no—
193C16—684no—
194C23—171no—
195C23—171no—
196C23—342no—
197C23—344no—
198C23D17⋊M1611yescharacteristic
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—171no—
203C2×C4—172no—
204C2×C4—172no—
205C2×C4—171no—
206C2×C4—342no—
207C2×C4—342no—
208C2×C4—342no—
209C2×C4—341no—
210C2×C4—341no—
211C2×C4—342no—
212C2×C4—684no—
213C2×C4C2×#6324211yescharacteristic
214C2×C4C2×C22⋊#59511yescharacteristic
215C8—22no—
216C8—41no—
217C8—342no—
218C8—681no—
219C22—22no—
220C22—21no—
221C22—174no—
222C22—172no—
223C22—342no—
224C22—341no—
225C22—684no—
226C22#1176377711yescharacteristic
227C4—21no—
228C4—42no—
229C4—172no—
230C4—341no—
231C4—682no—
232C4D17⋊#9911yescharacteristic
233C4D17⋊#10111yescharacteristic
234C2—41no—
235C2—174no—
236C2—681no—
237C2#1454401311yescharacteristic
238C2#1454502412yes—
subgroupG/H
centerC2×C4C2×C22⋊#595
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC17×#424C4
socleC22×C17C2×C22⋊C8
prime radicalC23×D17M16
cosocleC22×#3622C23
hypercenter#424#595
hypocenterC17C2×#1323
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #424

Complements

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

NH ≅ G/Ntype
2. #14543723C2semidirect
3. #14543722C2semidirect
135. D17#1323semidirect
161. C17C2×#1323semidirect

Maximal subgroups

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

subgroupindex
#145450092
#145437232
#145437222
D17×#4242
C2×#132317