Finite Group Databasebeta

← #17958271

Subgroups — #17958271

Order 4352.

398 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 90 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#14543723C212yesmaximal, complemented
3#14543706C212yesmaximal, complemented
4#14537476C211yesmaximal, characteristic
5C2×#10587529—22no—
6#11763704—22no—
7C22⋊#63216C2214yes—
8C22×C8×D17C2211yescharacteristic
9#11763316C411yescharacteristic
10#11762878—22no—
11C8×C22⋊D17—22no—
12#11762837C2211yescharacteristic
13#11762776C2211yescharacteristic
14#11762772C411yescharacteristic
15#11762764C411yescharacteristic
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#10587632C812yes—
25#10587624C812yes—
26#10587623—21no—
27#10587621—21no—
28C4×C22⋊D17—22no—
29#10587612C2×C411yescharacteristic
30C2×#63223C2×C411yescharacteristic
31C22×#3622C2311yescharacteristic
32C2×C8×D17—42no—
33C2×C8×D17D412yes—
34C2×C8×D17D412yes—
35C2×#63216—24no—
36#10587529—44no—
37C22⋊#3622—22no—
38#10587491—22no—
39#10587486—21no—
40#10587485—22no—
41C8×Dic17—21no—
42C23×D17M1611yescharacteristic
43#41×C17—41no—
44#41×C17—41no—
45C2×Q8×C17C2×C811yescharacteristic
46C2×D4×C17—21no—
47C2×D4×C17C2×C811yescharacteristic
48C22×C4×C17—21no—
49C22×C4×C17C22×C411yescharacteristic
50C2×C22⋊D17—22no—
51C22×Dic17M1611yescharacteristic
52C2×C4×D17—41no—
53C2×C4×D17—41no—
54C2×C4×D17C22⋊C412yes—
55C2×C4×D17C2×C812yes—
56M16×C17—42no—
57M16×C17—41no—
58C2×C8×C17—22no—
59C2×C8×C17—21no—
60C2×C8×C17—42no—
61C2×C8×C17C22⋊C411yescharacteristic
62C2×C8×C17C22⋊C411yescharacteristic
63C22⋊Dic17—21no—
64C22⋊Dic17—22no—
65#63227—22no—
66C4⋊Dic17C2×C812yes—
67#63225—22no—
68C4×Dic17—21no—
69#63223—41no—
70C2×#3622—21no—
71C2×#3622—41no—
72C2×#3622C2×D412yes—
73C8×D17—24no—
74C8×D17—42no—
75#63216—44no—
76#11468—171nomaximal, Sylow
77C23×C17—21no—
78C23×C17C2×M1611yescharacteristic
79C22×D17—24no—
80C22×D17—41no—
81C22×D17C22⋊C812yes—
82Q8×C17—41no—
83D4×C17—41no—
84D4×C17—42no—
85C2×C4×C17—21no—
86C2×C4×C17—21no—
87C2×C4×C17—21no—
88C2×C4×C17—41no—
89C2×C4×C17—41no—
90C2×C4×C17C2×C22⋊C411yescharacteristic
91C2×C4×C17C22×C811yescharacteristic
92C22⋊D17—44no—
93C2×Dic17—22no—
94C2×Dic17—41no—
95C2×Dic17C22⋊C812yes—
96C4×D17—22no—
97C4×D17—22no—
98C4×D17—42no—
99C8×C17—21no—
100C8×C17—41no—
101C8×C17#9912yes—
102#3622—22no—
103#3622—41no—
104#2929—171no—
105C2×C22⋊C16—172no—
106#1323—172no—
107#1315—172no—
108C22×C17—22no—
109C22×C17—21no—
110C22×C17—42no—
111C22×C17—41no—
112C22×C17C2×C22⋊C811yescharacteristic
113C2×D17—22no—
114C2×D17—22no—
115C2×D17—44no—
116C2×D17#35014yes—
117C4×C17—21no—
118C4×C17—41no—
119C4×C17C2×#9911yescharacteristic
120C4×C17#41311yescharacteristic
121Dic17—22no—
122Dic17—42no—
123C2×#131#59511yescharacteristic
124C23×C8—171no—
125#525—171no—
126C22×C16—342no—
127#435—342no—
128C8×D4—342no—
129#424—171no—
130#408—171no—
131#407—171no—
132#405—171no—
133C22⋊C16—174no—
134C22⋊C16—342no—
135C2×C17—41no—
136C2×C17—81no—
137C2×C17#145911yescharacteristic
138C2×C17C2×#35012yes—
139D17—24no—
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—172no—
149C22×C8—172no—
150C22×C8—682no—
151C22×C8C2×#59511yescharacteristic
152#123—341no—
153C22⋊Q8—172no—
154#121—172no—
155#120—341no—
156C4×D4—342no—
157#117—171no—
158C2×C16—344no—
159C2×C16—684no—
160C4⋊C8—342no—
161C22⋊C8—342no—
162C22⋊C8—342no—
163#97—341no—
164C4×C8—341no—
165C17#1146811yescharacteristic, complemented, Sylow
166C24—171no—
167#41—41no—
168#41—41no—
169C2×Q8#6324211yescharacteristic
170C2×D4—21no—
171C2×D4—342no—
172C2×D4#6324211yescharacteristic
173C22×C4—21no—
174C22×C4—171no—
175C22×C4—172no—
176C22×C4—172no—
177C22×C4—681no—
178C22×C4—681no—
179C22×C4C22×#59511yescharacteristic
180M16—42no—
181M16—41no—
182M16—681no—
183C2×C8—22no—
184C2×C8—21no—
185C2×C8—42no—
186C2×C8—172no—
187C2×C8—344no—
188C2×C8—341no—
189C2×C8—682no—
190C2×C8—681no—
191C2×C8C22⋊#59511yescharacteristic
192C2×C8C22⋊#59511yescharacteristic
193C4⋊C4—172no—
194C4⋊C4—342no—
195C22⋊C4—342no—
196C22⋊C4—342no—
197C22⋊C4—341no—
198C42—341no—
199C16—684no—
200C23—21no—
201C23—172no—
202C23—344no—
203C23—681no—
204C23D17⋊M1611yescharacteristic
205Q8—41no—
206D4—41no—
207D4—42no—
208D4—684no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—172no—
215C2×C4—342no—
216C2×C4—342no—
217C2×C4—342no—
218C2×C4—682no—
219C2×C4—681no—
220C2×C4C2×#6324211yescharacteristic
221C2×C4C2×C22⋊#59511yescharacteristic
222C8—21no—
223C8—41no—
224C8—342no—
225C8—681no—
226C8#1058755112yes—
227C22—22no—
228C22—21no—
229C22—42no—
230C22—41no—
231C22—174no—
232C22—342no—
233C22—342no—
234C22—684no—
235C22#1176377711yescharacteristic
236C4—21no—
237C4—41no—
238C4—342no—
239C4—682no—
240C4C2×#1058755111yescharacteristic
241C4#1176379511yescharacteristic
242C2—41no—
243C2—81no—
244C2—344no—
245C2#1454401911yescharacteristic
246C2#1454502412yes—
subgroupG/H
centerC2×C8C22⋊#595
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC2×C17×#131C4
socleC22×C17C2×C22⋊C8
prime radical#11763316C4
cosocleC22×#3622C23
hypercenterC2×#131#595
hypocenterC17#11468
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ C2×#131

Complements

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

NH ≅ G/Ntype
1. #14545009C2semidirect
2. #14543723C2semidirect
3. #14543706C2semidirect
165. C17#11468semidirect

Maximal subgroups

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

subgroupindex
#145450092
#145437232
#145437062
#145374762
#1146817