Finite Group Databasebeta

← #17958521

Subgroups — #17958521

Order 4352.

348 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 70 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#14545158C212yesmaximal, complemented
2#14543718C212yesmaximal, complemented
3#14543717C212yesmaximal, complemented
4#14537476C211yesmaximal, characteristic
5#11763731—22no—
6#11763705C2214yes—
7#11763702—22no—
8C22×C8×D17C411yescharacteristic
9#11763316C411yescharacteristic
10#11762878—22no—
11C8×C22⋊D17—22no—
12#11762837C411yescharacteristic
13#11762776C2211yescharacteristic
14#11762772C2211yescharacteristic
15#11762764C2211yescharacteristic
16C2×C17×#131C411yescharacteristic
17C2×#41×C17C2×C411yescharacteristic
18C22×C4×D17C2×C411yescharacteristic
19C17×#131—42no—
20C2×M16×C17—21no—
21C2×M16×C17C2×C411yescharacteristic
22C22×C8×C17—21no—
23C22×C8×C17C2×C411yescharacteristic
24#10587632—21no—
25#10587624—21no—
26#10587623—21no—
27#10587621—21no—
28C4×C22⋊D17—22no—
29#10587612C2×C411yescharacteristic
30C2×#63223C2311yescharacteristic
31C22×#3622C2×C411yescharacteristic
32C2×C8×D17—21no—
33C2×C8×D17—21no—
34C2×C8×D17—42no—
35#10587538—24no—
36C22⋊#3622—22no—
37#10587491—22no—
38#10587486D412yes—
39#10587485—22no—
40C8×Dic17D412yes—
41C23×D17M1611yescharacteristic
42#41×C17—41no—
43#41×C17—41no—
44C2×Q8×C17M1611yescharacteristic
45C2×D4×C17—21no—
46C2×D4×C17M1611yescharacteristic
47C22×C4×C17—21no—
48C22×C4×C17C22×C411yescharacteristic
49C2×C22⋊D17—22no—
50C22×Dic17M1611yescharacteristic
51C2×C4×D17—21no—
52C2×C4×D17—21no—
53C2×C4×D17—41no—
54C2×C4×D17—41no—
55M16×C17—42no—
56M16×C17—41no—
57C2×C8×C17—22no—
58C2×C8×C17—21no—
59C2×C8×C17—42no—
60C2×C8×C17C22⋊C411yescharacteristic
61C2×C8×C17C22⋊C411yescharacteristic
62C22⋊Dic17—22no—
63C22⋊Dic17—21no—
64#63227—22no—
65C4⋊Dic17—21no—
66#63225—22no—
67C4×Dic17C22⋊C412yes—
68#63223—41no—
69C2×#3622—21no—
70C2×#3622—41no—
71C2×#3622C2×D412yes—
72C8×D17—42no—
73C8×D17—42no—
74#63216—44no—
75#11537—171nomaximal, Sylow
76C23×C17—21no—
77C23×C17C2×M1611yescharacteristic
78C22×D17—21no—
79C22×D17—42no—
80C22×D17—41no—
81Q8×C17—41no—
82D4×C17—41no—
83D4×C17—42no—
84C2×C4×C17—21no—
85C2×C4×C17—21no—
86C2×C4×C17—21no—
87C2×C4×C17—41no—
88C2×C4×C17—41no—
89C2×C4×C17C2×C22⋊C411yescharacteristic
90C2×C4×C17C2×M1611yescharacteristic
91C22⋊D17—44no—
92C2×Dic17—21no—
93C2×Dic17—22no—
94C2×Dic17—41no—
95C4×D17—42no—
96C4×D17—41no—
97C4×D17—41no—
98C8×C17—21no—
99C8×C17—41no—
100C8×C17#10012yes—
101#3622—22no—
102#3622—41no—
103#2929—171no—
104#2166—172no—
105#1321—172no—
106#1320—172no—
107C22×C17—21no—
108C22×C17—41no—
109C22×C17—42no—
110C22×C17—41no—
111C22×C17#40711yescharacteristic
112C2×D17—22no—
113C2×D17—41no—
114C2×D17—42no—
115C2×D17—41no—
116C2×D17—42no—
117C4×C17—21no—
118C4×C17—41no—
119C4×C17#41011yescharacteristic
120C4×C17C2×#10011yescharacteristic
121Dic17—42no—
122Dic17—41no—
123C2×#131#59511yescharacteristic
124C23×C8—171no—
125#525—171no—
126#435—342no—
127C8×D4—342no—
128#424—171no—
129#408—171no—
130#407—171no—
131#405—171no—
132#364—342no—
133#349—174no—
134#347—342no—
135C2×C17—21no—
136C2×C17—41no—
137C2×C17—81no—
138C2×C17#146611yescharacteristic
139D17—42no—
140C2×#41C2×#59511yescharacteristic
141C23×C4—171no—
142#131—42no—
143C2×M16—21no—
144C2×M16—171no—
145C2×M16C2×#59511yescharacteristic
146C22×C8—21no—
147C22×C8—171no—
148C22×C8—341no—
149C22×C8—341no—
150C22×C8—682no—
151C22×C8C2×#59511yescharacteristic
152#123—341no—
153C22⋊Q8—341no—
154#121—341no—
155#120—341no—
156C4×D4—342no—
157#117—171no—
158M32—344no—
159C4⋊C8—342no—
160C22⋊C8—342no—
161C22⋊C8—342no—
162#97—172no—
163C4×C8—172no—
164C17#1153711yescharacteristic, complemented, Sylow
165C24—171no—
166#41—41no—
167#41—41no—
168C2×Q8#6324311yescharacteristic
169C2×D4—21no—
170C2×D4—342no—
171C2×D4#6324311yescharacteristic
172C22×C4—21no—
173C22×C4—171no—
174C22×C4—341no—
175C22×C4—341no—
176C22×C4—681no—
177C22×C4—681no—
178C22×C4C22×#59511yescharacteristic
179M16—42no—
180M16—41no—
181M16—681no—
182C2×C8—22no—
183C2×C8—21no—
184C2×C8—42no—
185C2×C8—172no—
186C2×C8—341no—
187C2×C8—682no—
188C2×C8—682no—
189C2×C8—681no—
190C2×C8C22⋊#59511yescharacteristic
191C2×C8C22⋊#59511yescharacteristic
192C4⋊C4—342no—
193C4⋊C4—341no—
194C22⋊C4—342no—
195C22⋊C4—342no—
196C22⋊C4—341no—
197C42—172no—
198C16—684no—
199C23—21no—
200C23—341no—
201C23—681no—
202C23—682no—
203C23D17⋊M1611yescharacteristic
204Q8—41no—
205D4—41no—
206D4—42no—
207D4—684no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—342no—
214C2×C4—341no—
215C2×C4—682no—
216C2×C4—681no—
217C2×C4—681no—
218C2×C4—681no—
219C2×C4C2×#6324311yescharacteristic
220C2×C4C2×C22⋊#59511yescharacteristic
221C8—21no—
222C8—41no—
223C8—342no—
224C8—681no—
225C8#1058755312yes—
226C22—21no—
227C22—41no—
228C22—42no—
229C22—41no—
230C22—342no—
231C22—681no—
232C22—682no—
233C22—682no—
234C22—681no—
235C22#1176378011yescharacteristic
236C4—21no—
237C4—41no—
238C4—682no—
239C4—681no—
240C4#1176378811yescharacteristic
241C4C2×#1058755311yescharacteristic
242C2—21no—
243C2—41no—
244C2—81no—
245C2—682no—
246C2#1454404311yescharacteristic
subgroupG/H
centerC4#11763788
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC2×C17×#131C4
socleC2×C17#1466
prime radical#11763316C4
cosocleC2×#63223C23
hypercenterC2×#131#595
hypocenterC17#11537
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C4 ◁ C2×C8 ◁ C22×C8 ◁ C2×#131

Complements

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

NH ≅ G/Ntype
1. #14545158C2semidirect
2. #14543718C2semidirect
3. #14543717C2semidirect
164. C17#11537semidirect

Maximal subgroups

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

subgroupindex
#145451582
#145437182
#145437172
#145374762
#1153717