Finite Group Databasebeta

← #17958277

Subgroups — #17958277

Order 4352.

386 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 86 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#14545012C212yesmaximal, complemented
2#14543722C212yesmaximal, complemented
3#14543707C212yesmaximal, complemented
4#14537480C211yesmaximal, characteristic
5C2×#10587530—22no—
6#11763704—22no—
7C22⋊#63216C2214yes—
8C2×#10587587C411yescharacteristic
9C22×C8×D17C2211yescharacteristic
10#11763321C411yescharacteristic
11#11762882—22no—
12C8×D68—22no—
13#11762836C2211yescharacteristic
14#11762777C2211yescharacteristic
15#11762772C411yescharacteristic
16C17×#405C411yescharacteristic
17C2×#63252C2×C411yescharacteristic
18C22×C4×D17C2×C411yescharacteristic
19C2×M16×C17C2×C411yescharacteristic
20C22×C8×C17C2×C411yescharacteristic
21C17×#117C2×C411yescharacteristic
22C2×#63223C2×C411yescharacteristic
23C22×#3622C2311yescharacteristic
24#10587587—42no—
25C2×#63218—21no—
26C2×C8×D17—21no—
27C2×C8×D17—42no—
28C2×C8×D17D412yes—
29C2×C8×D17D412yes—
30#10587583C812yes—
31#10587581C812yes—
32#10587572—21no—
33#10587568—21no—
34C4×D68—22no—
35C2×#63216—24no—
36#10587530—44no—
37C17×#97—21no—
38C4×C8×C17—21no—
39#10587491—22no—
40#10587491—22no—
41C4⋊#3622—22no—
42C23×D17M1611yescharacteristic
43C22×C4×C17C22×C411yescharacteristic
44C2×C22⋊D17—21no—
45C22×Dic17M1611yescharacteristic
46#63252—41no—
47#63252—41no—
48C2×D68—22no—
49C2×D68C2×C811yescharacteristic
50C2×C4×D17—21no—
51C2×C4×D17—41no—
52C2×C4×D17—41no—
53C2×C4×D17C22⋊C412yes—
54C2×C4×D17C2×C812yes—
55C2×Dic34C2×C811yescharacteristic
56M16×C17—41no—
57C2×C8×C17—22no—
58C2×C8×C17—21no—
59C2×C8×C17C22⋊C411yescharacteristic
60C2×C8×C17C22⋊C411yescharacteristic
61C4⋊C4×C17C2×C812yes—
62C22⋊C4×C17—21no—
63C42×C17—21no—
64#63227—22no—
65#63227—22no—
66C4⋊Dic17—22no—
67#63223—41no—
68C2×#3622—21no—
69C2×#3622—41no—
70C2×#3622C2×D412yes—
71#63218—42no—
72C8×D17—24no—
73C8×D17—42no—
74C8×D17—42no—
75#63216—44no—
76#11469—171nomaximal, Sylow
77C23×C17C2×M1611yescharacteristic
78C22×D17—21no—
79C22×D17—41no—
80C22×D17—42no—
81C22×D17C22⋊C812yes—
82C2×C4×C17—21no—
83C2×C4×C17—21no—
84C2×C4×C17—22no—
85C2×C4×C17C2×C22⋊C411yescharacteristic
86C2×C4×C17C22×C811yescharacteristic
87C22⋊D17—42no—
88C2×Dic17—21no—
89C2×Dic17—41no—
90C2×Dic17C22⋊C812yes—
91D68—41no—
92D68—44no—
93C4×D17—22no—
94C4×D17—22no—
95C4×D17—42no—
96C4×D17—41no—
97C4×D17—41no—
98Dic34—41no—
99C8×C17—21no—
100C8×C17—41no—
101C8×C17#9912yes—
102#3622—22no—
103#3622—41no—
104#2929—171no—
105#2112—172no—
106#1323—172no—
107#1315—172no—
108C22×C17—22no—
109C22×C17—21no—
110C22×C17C2×C22⋊C811yescharacteristic
111C2×D17—22no—
112C2×D17—22no—
113C2×D17—22no—
114C2×D17—44no—
115C2×D17—42no—
116C2×D17—41no—
117C4×C17—21no—
118C4×C17—42no—
119C4×C17C2×#9911yescharacteristic
120C4×C17#41311yescharacteristic
121Dic17—22no—
122Dic17—41no—
123C2×#131—171no—
124C23×C8—171no—
125#525—171no—
126C2×M32—342no—
127#435—342no—
128C8×D4—342no—
129#424—171no—
130#408—171no—
131#407—171no—
132#405#59511yescharacteristic
133C22⋊C16—174no—
134C22⋊C16—342no—
135C2×C17—41no—
136C2×C17#145911yescharacteristic
137C2×C17#211712yes—
138D17—42no—
139D17—81no—
140C2×#41—171no—
141C23×C4—171no—
142#131—682no—
143C2×M16—171no—
144C2×M16—341no—
145C2×M16C2×#59511yescharacteristic
146C22×C8—171no—
147C22×C8—172no—
148C22×C8—172no—
149C22×C8—341no—
150C22×C8—682no—
151C22×C8C2×#59511yescharacteristic
152#123—341no—
153C22⋊Q8—172no—
154#121—172no—
155#120—341no—
156C4×D4—342no—
157#117C2×#59511yescharacteristic
158M32—684no—
159C2×C16—344no—
160C4⋊C8—342no—
161C22⋊C8—342no—
162C22⋊C8—342no—
163#97—21no—
164C4×C8—21no—
165C17#1146911yescharacteristic, complemented, Sylow
166C24—171no—
167#41—681no—
168#41—681no—
169C2×Q8—171no—
170C2×D4—171no—
171C2×D4—342no—
172C2×D4—341no—
173C22×C4—171no—
174C22×C4—172no—
175C22×C4—172no—
176C22×C4—341no—
177C22×C4—681no—
178C22×C4—681no—
179C22×C4C22×#59511yescharacteristic
180M16—41no—
181M16—682no—
182M16—681no—
183C2×C8—22no—
184C2×C8—21no—
185C2×C8—172no—
186C2×C8—344no—
187C2×C8—341no—
188C2×C8—682no—
189C2×C8—681no—
190C2×C8—682no—
191C2×C8C22⋊#59511yescharacteristic
192C2×C8C22⋊#59511yescharacteristic
193C4⋊C4—342no—
194C4⋊C4#6324212yes—
195C22⋊C4—21no—
196C22⋊C4—342no—
197C22⋊C4—342no—
198C42—21no—
199C16—684no—
200C23—172no—
201C23—341no—
202C23—681no—
203C23—682no—
204C23D17⋊M1611yescharacteristic
205Q8—681no—
206D4—681no—
207D4—684no—
208D4—682no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—172no—
213C2×C4—342no—
214C2×C4—342no—
215C2×C4—341no—
216C2×C4—682no—
217C2×C4—681no—
218C2×C4—681no—
219C2×C4—681no—
220C2×C4C2×#6324211yescharacteristic
221C2×C4C2×C22⋊#59511yescharacteristic
222C8—21no—
223C8—41no—
224C8—342no—
225C8—681no—
226C8#1058753912yes—
227C22—22no—
228C22—21no—
229C22—342no—
230C22—342no—
231C22—342no—
232C22—684no—
233C22—682no—
234C22—681no—
235C22#1176377711yescharacteristic
236C4—21no—
237C4—42no—
238C4—342no—
239C4—681no—
240C4C2×#1058753911yescharacteristic
241C4#1176379511yescharacteristic
242C2—41no—
243C2—682no—
244C2—1361no—
245C2#1454402111yescharacteristic
246C2#1454502712yes—
subgroupG/H
centerC2×C4C2×C22⋊#595
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC17×#405C4
socleC22×C17C2×C22⋊C8
prime radical#11763321C4
cosocleC22×#3622C23
hypercenter#405#595
hypocenterC17#11469
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #405

Complements

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

NH ≅ G/Ntype
1. #14545012C2semidirect
2. #14543722C2semidirect
3. #14543707C2semidirect
165. C17#11469semidirect

Maximal subgroups

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

subgroupindex
#145450122
#145437222
#145437072
#145374802
#1146917