Finite Group Databasebeta

← #17958259

Subgroups — #17958259

Order 4352.

454 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 108 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, complemented
2#14543721C212yesmaximal, complemented
3#14543704C212yesmaximal, complemented
4C2×C8×C22⋊D17C211yesmaximal, characteristic
5C2×#10587529—22no—
6#11763704—22no—
7C22⋊#63216C2214yes—
8C22×C8×D17C2211yescharacteristic
9C2×C4×C22⋊D17C411yescharacteristic
10C8×C22⋊D17—22no—
11C8×C22⋊D17—22no—
12C2×#10587485C2211yescharacteristic
13C2×C22⋊#3622C2211yescharacteristic
14C2×#10587491C411yescharacteristic
15C2×C8×Dic17C411yescharacteristic
16C23×C8×C17C411yescharacteristic
17C23×C4×C17C2×C411yescharacteristic
18C22×C22⋊D17C811yescharacteristic
19C22×C4×D17C2×C411yescharacteristic
20C22×C8×C17—21no—
21C22×C8×C17—21no—
22C22×C8×C17—42no—
23C22×C8×C17C2×C411yescharacteristic
24C22×C8×C17C2×C411yescharacteristic
25C2×C22⋊Dic17C811yescharacteristic
26C4×C22⋊D17—22no—
27C4×C22⋊D17—22no—
28C2×#63227C811yescharacteristic
29C2×#63225C811yescharacteristic
30C2×C4×Dic17C2×C411yescharacteristic
31C22×#3622C2×C411yescharacteristic
32C22×#3622C2311yescharacteristic
33C2×C8×D17—42no—
34C2×C8×D17D412yes—
35C2×C8×D17D412yes—
36C2×#63216—24no—
37#10587529—44no—
38C22⋊#3622—22no—
39#10587491—22no—
40#10587485—22no—
41C8×Dic17—21no—
42C8×Dic17—21no—
43C24×C17C2×C811yescharacteristic
44C23×D17C2×C811yescharacteristic
45C22×C4×C17—21no—
46C22×C4×C17—21no—
47C22×C4×C17—41no—
48C22×C4×C17—41no—
49C22×C4×C17C2×C811yescharacteristic
50C22×C4×C17C22×C411yescharacteristic
51C2×C22⋊D17—22no—
52C2×C22⋊D17—22no—
53C2×C22⋊D17C1614yescomplemented
54C22×Dic17C2×C811yescharacteristic
55C22×Dic17C2×C811yescharacteristic
56C22×Dic17C2×C811yescharacteristic
57C2×C4×D17—41no—
58C2×C4×D17—41no—
59C2×C4×D17C22⋊C412yes—
60C2×C4×D17M1612yes—
61C2×C8×C17—22no—
62C2×C8×C17—21no—
63C2×C8×C17—42no—
64C2×C8×C17—42no—
65C2×C8×C17—41no—
66C2×C8×C17C22⋊C411yescharacteristic
67C2×C8×C17C22⋊C411yescharacteristic
68C22⋊Dic17—22no—
69#63227—22no—
70#63225—22no—
71C4×Dic17—21no—
72C4×Dic17—21no—
73C2×#3622—21no—
74C2×#3622—41no—
75C2×#3622—41no—
76C2×#3622C2×D412yes—
77C8×D17—24no—
78C8×D17—42no—
79#63216—44no—
80#11465—171nomaximal, Sylow
81C23×C17—21no—
82C23×C17—21no—
83C23×C17—41no—
84C23×C17—41no—
85C23×C17C2×C1612yescomplemented
86C23×C17C22×C811yescharacteristic
87C22×D17—41no—
88C22×D17—41no—
89C22×D17C22⋊C812yes—
90C22×D17C2×C1612yes—
91C22×D17M3212yes—
92C2×C4×C17—21no—
93C2×C4×C17—21no—
94C2×C4×C17—21no—
95C2×C4×C17—42no—
96C2×C4×C17—41no—
97C2×C4×C17—41no—
98C2×C4×C17—41no—
99C2×C4×C17C2×C22⋊C411yescharacteristic
100C2×C4×C17C2×M1611yescharacteristic
101C22⋊D17—28no—
102C2×Dic17—21no—
103C2×Dic17—21no—
104C2×Dic17—21no—
105C2×Dic17—41no—
106C2×Dic17—41no—
107C2×Dic17C22⋊C812yes—
108C2×Dic17C2×C1612yescomplemented
109C4×D17—22no—
110C4×D17—22no—
111C4×D17—42no—
112C8×C17—21no—
113C8×C17—41no—
114C8×C17#9912yes—
115#3622—22no—
116#3622—41no—
117C2×C8×D4—171no—
118C2×C22⋊C16—172no—
119#1322—172no—
120#1314—172no—
121C22×C17—21no—
122C22×C17—21no—
123C22×C17—22no—
124C22×C17—42no—
125C22×C17—42no—
126C22×C17—41no—
127C22×C17—41no—
128C22×C17C2×C22⋊C811yescharacteristic
129C22×C17C22×C1611yescharacteristic
130C22×C17C2×M3211yescharacteristic
131C2×D17—22no—
132C2×D17—22no—
133C2×D17—42no—
134C2×D17—42no—
135C2×D17C22⋊C1614yes—
136C4×C17—21no—
137C4×C17—41no—
138C4×C17C2×#9911yescharacteristic
139C4×C17#41311yescharacteristic
140Dic17—22no—
141Dic17—22no—
142Dic17—41no—
143C23×C8—171no—
144C23×C8#59511yescharacteristic
145C2×C4×D4—171no—
146C22×C16—342no—
147C8×D4—342no—
148C8×D4—342no—
149C2×C4⋊C8—171no—
150C2×C22⋊C8—171no—
151C2×C22⋊C8—171no—
152C2×C4×C8—171no—
153C22⋊C16—174no—
154C22⋊C16—342no—
155C2×C17—21no—
156C2×C17—21no—
157C2×C17—42no—
158C2×C17#145911yescharacteristic
159C2×C17C2×C22⋊C1611yescharacteristic
160C2×C17#211511yescharacteristic
161D17—24no—
162C22×D4—171no—
163C23×C4—171no—
164C23×C4C2×#59511yescharacteristic
165C22×C8—21no—
166C22×C8—21no—
167C22×C8—42no—
168C22×C8—171no—
169C22×C8—172no—
170C22×C8—172no—
171C22×C8—171no—
172C22×C8—682no—
173C22×C8C2×#59511yescharacteristic
174C22×C8C2×#59511yescharacteristic
175C4×D4—342no—
176C4×D4—342no—
177C2×C4⋊C4—171no—
178C2×C22⋊C4—171no—
179C2×C22⋊C4—171no—
180C2×C42—171no—
181C2×C16—344no—
182C2×C16—684no—
183C4⋊C8—342no—
184C22⋊C8—342no—
185C22⋊C8—342no—
186C4×C8—341no—
187C4×C8—341no—
188C17#1146511yescharacteristic, complemented, Sylow
189C24—171no—
190C24#6324211yescharacteristic
191C2×D4—174no—
192C2×D4—342no—
193C2×D4—342no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—41no—
197C22×C4—41no—
198C22×C4—171no—
199C22×C4—171no—
200C22×C4—172no—
201C22×C4—172no—
202C22×C4—171no—
203C22×C4—681no—
204C22×C4—681no—
205C22×C4#6324211yescharacteristic
206C22×C4C22×#59511yescharacteristic
207C2×C8—22no—
208C2×C8—21no—
209C2×C8—42no—
210C2×C8—42no—
211C2×C8—41no—
212C2×C8—172no—
213C2×C8—344no—
214C2×C8—341no—
215C2×C8—682no—
216C2×C8—681no—
217C2×C8—681no—
218C2×C8C22⋊#59511yescharacteristic
219C2×C8C22⋊#59511yescharacteristic
220C4⋊C4—342no—
221C22⋊C4—342no—
222C22⋊C4—342no—
223C42—341no—
224C42—341no—
225C16—684no—
226C23—21no—
227C23—21no—
228C23—41no—
229C23—41no—
230C23—172no—
231C23—172no—
232C23—172no—
233C23—681no—
234C23—681no—
235C23#1058752912yescomplemented
236C23C2×#6324211yescharacteristic
237D4—348no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—42no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—172no—
246C2×C4—172no—
247C2×C4—341no—
248C2×C4—341no—
249C2×C4—342no—
250C2×C4—342no—
251C2×C4—341no—
252C2×C4—682no—
253C2×C4—681no—
254C2×C4—681no—
255C2×C4D17⋊M1611yescharacteristic
256C2×C4C2×C22⋊#59511yescharacteristic
257C8—21no—
258C8—41no—
259C8—342no—
260C8—681no—
261C8#1058755112yes—
262C22—21no—
263C22—21no—
264C22—22no—
265C22—42no—
266C22—42no—
267C22—41no—
268C22—41no—
269C22—174no—
270C22—342no—
271C22—342no—
272C22—682no—
273C22—682no—
274C22#1176377711yescharacteristic
275C22C2×#1058752911yescharacteristic
276C22#1176386511yescharacteristic
277C4—21no—
278C4—41no—
279C4—342no—
280C4—342no—
281C4—681no—
282C4C2×#1058755111yescharacteristic
283C4#1176379511yescharacteristic
284C2—21no—
285C2—21no—
286C2—42no—
287C2—344no—
288C2#1454401911yescharacteristic
289C2#1454500911yescharacteristic
290C2#1454502111yescharacteristic
subgroupG/H
centerC2×C8C22⋊#595
commutatorC22×C17C22×C16
FrattiniC22×C4C22×#595
FittingC23×C8×C17C4
socleC22×C17C2×C22⋊C8
prime radicalC22×C22⋊D17C8
cosocleC22×#3622C23
hypercenterC23×C8#595
hypocenterC17#11465
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ C23×C8

Complements

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

NH ≅ G/Ntype
1. #14545009C2semidirect
2. #14543721C2semidirect
3. #14543704C2semidirect
53. C2×C22⋊D17C16semidirect
85. C23×C17C2×C16semidirect
108. C2×Dic17C2×C16semidirect
188. C17#11465semidirect
235. C23#10587529semidirect

Maximal subgroups

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

subgroupindex
#145450092
#145437212
#145437042
C2×C8×C22⋊D172
#1146517