Finite Group Databasebeta

← #17958970

Subgroups — #17958970

Order 4352.

354 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 84 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#14545146C211yesmaximal, characteristic
2#14544344C211yesmaximal, characteristic
3#14543745C214yesmaximal, complemented
4C2×#11762903C211yesmaximal, characteristic
5#11763830—21no—
6#11763730—21no—
7C22⋊#63216—21no—
8#11763698C2212yes—
9#11763673—21no—
10#11763670C2212yes—
11C22×Dic68C411yescharacteristic
12C2×#10587573—21no—
13#11762903—21no—
14#11762903—21no—
15#11762903C412yes—
16#11762903C2212yes—
17C2×#10587481—21no—
18C2×C8×Dic17C2211yescharacteristic
19C2×C17×#107C411yescharacteristic
20C22×Dic34—21no—
21C22×C8×C17C2×C411yescharacteristic
22C2×C4⋊C4×C17—21no—
23C2×#63225—41no—
24C2×C4×Dic17—41no—
25C2×C4×Dic17D411yescharacteristic
26C22×#3622D411yescharacteristic
27C2×Dic68—24no—
28C2×Dic68—21no—
29C2×Dic68C2×C412yes—
30#10587573—22no—
31#10587573—22no—
32#10587573—41no—
33#10587573—41no—
34C22⋊#3624—41no—
35#10587542—41no—
36C4⋊#3624—22no—
37C2×#63216—22no—
38C17×#107—21no—
39C17×#107C2×C412yes—
40C8×Dic17C2×C411yescharacteristic
41C8×Dic17D411yescharacteristic
42C8×Dic17D411yescharacteristic
43C8×Dic17C2311yescharacteristic
44#10587481—22no—
45#10587481—22no—
46C22×C4×C17—41no—
47C22×C4×C17C22⋊C411yescharacteristic
48C22×Dic17—41no—
49C22×Dic17D811yescharacteristic
50C22×Dic17SD1611yescharacteristic
51C2×Dic34—24no—
52C2×Dic34—22no—
53C2×Dic34—42no—
54C2×Dic34—41no—
55C2×#3624—42no—
56C2×C8×C17—22no—
57C2×C8×C17C22⋊C411yescharacteristic
58C2×C8×C17C22×C411yescharacteristic
59C4⋊C4×C17—22no—
60C4⋊C4×C17—41no—
61#63225—42no—
62#63225—42no—
63C4×Dic17—42no—
64C4×Dic17—42no—
65C4×Dic17C22⋊C411yescharacteristic
66C4×Dic17D811yescharacteristic
67C4×Dic17SD1611yescharacteristic
68C4×Dic17C2×D411yescharacteristic
69C2×#3622—41no—
70C2×#3622C22⋊C411yescharacteristic
71C2×#3622C2×D411yescharacteristic
72Dic68—24no—
73Dic68—22no—
74Dic68M1614yes—
75#63216—42no—
76#11668—171nomaximal, Sylow
77C23×C17#10211yescharacteristic
78C2×C4×C17—21no—
79C2×C4×C17—21no—
80C2×C4×C17—42no—
81C2×C4×C17—82no—
82C2×C4×C17#10211yescharacteristic
83C2×C4×C17C2×C22⋊C411yescharacteristic
84C2×Dic17—22no—
85C2×Dic17—41no—
86C2×Dic17—44no—
87C2×Dic17—42no—
88C2×Dic17#10211yescharacteristic
89C2×Dic17#10211yescharacteristic
90C2×Dic17C2×D811yescharacteristic
91C2×Dic17C2×SD1611yescharacteristic
92Dic34—24no—
93Dic34—44no—
94Dic34—42no—
95#3624—82no—
96C8×C17—21no—
97C8×C17C2×M1612yes—
98#3622—21no—
99#3622—21no—
100C2×C4×Q16—171no—
101#2163—171no—
102#1568—171no—
103#1334—174no—
104C22×C17—21no—
105C22×C17—21no—
106C22×C17#36212yes—
107C22×C17C2×#10211yescharacteristic
108C4×C17—21no—
109C4×C17—82no—
110C4×C17#40711yescharacteristic
111C4×C17#42111yescharacteristic
112Dic17—21no—
113Dic17—21no—
114Dic17—21no—
115Dic17—21no—
116Dic17—44no—
117C22×Q16—171no—
118C2×C4×Q8—341no—
119C4×Q16—172no—
120C4×Q16—172no—
121C4×Q16—341no—
122C4×Q16—341no—
123#432—341no—
124C2×#107#59511yescharacteristic
125C2×#103—341no—
126C2×C4×C8—171no—
127C4⋊C16—341no—
128C22⋊C16—341no—
129#346—172no—
130#335—341no—
131#334—172no—
132C2×C17—22no—
133C2×C17#148611yescharacteristic
134C2×C17#214511yescharacteristic
135C2×C17C2×#36211yescharacteristic
136C22×Q8—341no—
137C2×Q16—172no—
138C2×Q16—344no—
139C2×Q16—341no—
140C22×C8—171no—
141C22×C8C2×#59511yescharacteristic
142C4×Q8—342no—
143C4×Q8—342no—
144C4×Q8—681no—
145C4×Q8—681no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—681no—
148C2×C42—171no—
149C2×C42—681no—
150C2×C16—342no—
151#107—21no—
152#107C2×#59512yes—
153C4⋊C8—342no—
154#103—342no—
155#103—342no—
156C22⋊C8—681no—
157#97—681no—
158C4×C8—171no—
159C4×C8—171no—
160C4×C8—171no—
161C4×C8—171no—
162C17#1166811yescharacteristic, complemented, Sylow
163C2×Q8—344no—
164C2×Q8—342no—
165C2×Q8—682no—
166C2×Q8—681no—
167C22×C4—41no—
168C22×C4—171no—
169C22×C4—171no—
170C22×C4—681no—
171C22×C4C22⋊#59511yescharacteristic
172Q16—174no—
173Q16—344no—
174Q16—342no—
175C2×C8—22no—
176C2×C8—171no—
177C2×C8—171no—
178C2×C8—681no—
179C2×C8—682no—
180C2×C8C22⋊#59511yescharacteristic
181C2×C8C22×#59511yescharacteristic
182C4⋊C4—22no—
183C4⋊C4—41no—
184C4⋊C4—682no—
185C4⋊C4—682no—
186C42—171no—
187C42—171no—
188C42—171no—
189C42—171no—
190C42—682no—
191C42—682no—
192C16—682no—
193C23#1058754711yescharacteristic
194Q8—344no—
195Q8—684no—
196Q8—682no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—42no—
200C2×C4—82no—
201C2×C4—171no—
202C2×C4—171no—
203C2×C4—171no—
204C2×C4—171no—
205C2×C4—342no—
206C2×C4—681no—
207C2×C4—684no—
208C2×C4—682no—
209C2×C4#1058754711yescharacteristic
210C2×C4C2×C22⋊#59511yescharacteristic
211C8—21no—
212C8—341no—
213C8—341no—
214C8—1362no—
215C8D17⋊M1612yes—
216C22—21no—
217C22—21no—
218C22#1176372812yes—
219C22C2×#1058754711yescharacteristic
220C4—21no—
221C4—82no—
222C4—341no—
223C4—341no—
224C4—341no—
225C4—341no—
226C4—684no—
227C4#1176378111yescharacteristic
228C4#1176380811yescharacteristic
229C2—22no—
230C2#1454411111yescharacteristic
231C2#1454510511yescharacteristic
232C2C2×#1176372811yescharacteristic
subgroupG/H
centerC22C2×#10587547
commutatorC2×C8×C17C22×C4
FrattiniC2×C8C22×#595
FittingC2×C17×#107C4
socleC22×C17C2×#102
prime radicalC23×C17#102
cosocleC8×Dic17C23
hypercenterC2×#107#595
hypocenterC17#11668
LCSG ▷ C2×C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
3. #14543745C2semidirect
162. C17#11668semidirect

Maximal subgroups

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

subgroupindex
#145451462
#145443442
#145437452
C2×#117629032
#1166817