Finite Group Databasebeta

← #17962702

Subgroups — #17962702

Order 4352.

388 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 60 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
1C2×#11763714C212yesmaximal
2#14543924C212yesmaximal, complemented
3#14543923C212yesmaximal, complemented
4#14539160C211yesmaximal, characteristic
5C2×#10587539—22no—
6#11763714—22no—
7#11763714C2214yes—
8C2×#10587560C2211yescharacteristic
9#11763175C411yescharacteristic, complemented
10#11763175C411yescharacteristic, complemented
11#11763175C2211yescharacteristic
12#11763175C2211yescharacteristic
13#11763157—22no—
14#11762813—22no—
15C4×#63223C411yescharacteristic, complemented
16C17×#533C411yescharacteristic, complemented
17C22×D68—41no—
18C22×D68D412yes—
19C2×C22⋊#595—42no—
20C17×C4⋊Q8—21no—
21C17×#125C2×C411yescharacteristic, complemented
22C17×#125C2×C411yescharacteristic, complemented
23C17×C22⋊Q8—41no—
24C4×Q8×C17—41no—
25C17×#117—21no—
26C2×C42×C17C2×C411yescharacteristic
27C2×#63223—21no—
28#10587560—41no—
29#10587560C2×C411yescharacteristic
30#10587560D412yes—
31#10587560C2311yescharacteristic
32#10587539—24no—
33#10587539—42no—
34#10587480—22no—
35#10587480—22no—
36#10587480—22no—
37#10587480—22no—
38#10587474C2×C411yescharacteristic, complemented
39#10587474C2×C411yescharacteristic, complemented
40C4×#3622—21no—
41C23×D17—22no—
42C22×#595—82no—
43C2×Q8×C17—41no—
44C22×C4×C17—21no—
45C22×C4×C17C22⋊C411yescharacteristic
46C2×D68—22no—
47C2×D68—42no—
48C2×D68—42no—
49C2×D68—41no—
50C2×D68—42no—
51C2×D68—41no—
52C2×D68—84no—
53C2×D68C22⋊C412yes—
54C2×D68C2×D412yes—
55C22⋊#595—44no—
56C22⋊#595—82no—
57C4⋊C4×C17—21no—
58C4⋊C4×C17—21no—
59C4⋊C4×C17—41no—
60C4⋊C4×C17—41no—
61C4⋊C4×C17—41no—
62C22⋊C4×C17—41no—
63C42×C17—21no—
64C42×C17—41no—
65C42×C17C22⋊C411yescharacteristic
66C42×C17C22×C411yescharacteristic
67#63223—42no—
68C2×#3622—21no—
69C2×#3622—21no—
70#13595—171nomaximal, Sylow
71C23×C17#9911yescharacteristic
72C22×D17—22no—
73C22×D17—22no—
74C22×D17—42no—
75C22×D17—42no—
76C22×D17—84no—
77C2×#595—84no—
78C2×#595—164no—
79Q8×C17—82no—
80C2×C4×C17—22no—
81C2×C4×C17—21no—
82C2×C4×C17—21no—
83C2×C4×C17—42no—
84C2×C4×C17—41no—
85C2×C4×C17—41no—
86C2×C4×C17#9911yescharacteristic
87C2×C4×C17C2×C22⋊C411yescharacteristic
88D68—42no—
89D68—42no—
90D68—82no—
91D68—84no—
92D68—82no—
93D68—82no—
94#3622—41no—
95#3622—41no—
96#3138—171no—
97C2×#353—172no—
98#1412—172no—
99#1412—172no—
100C22×C17—41no—
101C22×C17#35412yes—
102C22×C17C2×#9911yescharacteristic
103C2×D17—42no—
104C2×D17—42no—
105C2×D17—84no—
106C2×D17—82no—
107C2×D17—82no—
108C2×D17—162no—
109#595—164no—
110C4×C17—22no—
111C4×C17—21no—
112C4×C17—21no—
113C4×C17—41no—
114C4×C17—81no—
115C4×C17—81no—
116#533#59511yescharacteristic, complemented
117C2×#127—171no—
118#490—171no—
119#490—171no—
120#490—171no—
121#490—171no—
122#486—342no—
123#418—342no—
124C2×#99—342no—
125C4×M16—171no—
126#353—174no—
127#353—342no—
128C2×C17—21no—
129C2×C17—22no—
130C2×C17C2×#35411yescharacteristic
131D17—82no—
132D17—82no—
133C22×D4—172no—
134C22×D4—681no—
135C2×M16—341no—
136C4⋊Q8—21no—
137#127—172no—
138#127—171no—
139#127—171no—
140#127—681no—
141#125C2×#59511yescharacteristic, complemented
142#125C2×#59511yescharacteristic, complemented
143C22⋊Q8—41no—
144C4×Q8—41no—
145#117—21no—
146C2×C22⋊C4—682no—
147C2×C42C2×#59511yescharacteristic
148#102—342no—
149#102—342no—
150#102—342no—
151#102—342no—
152#99—344no—
153#99—682no—
154#97—171no—
155#97—171no—
156C4×C8—341no—
157C17#1359511yescharacteristic, complemented, Sylow
158C24—342no—
159C2×Q8—41no—
160C2×D4—172no—
161C2×D4—172no—
162C2×D4—342no—
163C2×D4—682no—
164C2×D4—682no—
165C2×D4—682no—
166C2×D4—681no—
167C2×D4—681no—
168C2×D4—1364no—
169C22×C4—21no—
170C22×C4—1362no—
171C22×C4C22⋊#59511yescharacteristic
172M16—682no—
173C2×C8—341no—
174C2×C8—341no—
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—41no—
178C4⋊C4—41no—
179C4⋊C4—41no—
180C22⋊C4—41no—
181C22⋊C4—684no—
182C22⋊C4—1362no—
183C42—21no—
184C42—41no—
185C42C22⋊#59511yescharacteristic
186C42C22×#59511yescharacteristic
187C23—342no—
188C23—342no—
189C23—682no—
190C23—682no—
191C23—1364no—
192C23#1058755111yescharacteristic
193Q8—82no—
194D4—682no—
195D4—682no—
196D4—1362no—
197D4—1364no—
198D4—1362no—
199D4—1362no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—42no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—2724no—
207C2×C4—1364no—
208C2×C4#1058755111yescharacteristic
209C2×C4C2×C22⋊#59511yescharacteristic
210C8—681no—
211C8—681no—
212C22—41no—
213C22—2722no—
214C22—682no—
215C22—682no—
216C22—1362no—
217C22—1362no—
218C22—1364no—
219C22#1176371512yes—
220C22C2×#1058755111yescharacteristic
221C4—22no—
222C4—21no—
223C4—21no—
224C4—41no—
225C4—81no—
226C4—81no—
227C4—2724no—
228C2—21no—
229C2—22no—
230C2—1362no—
231C2—1362no—
232C2C2×#1176371511yescharacteristic
subgroupG/H
centerC2C2×#11763715
commutatorC42×C17C22×C4
FrattiniC42C22×#595
FittingC17×#533C4
socleC2×C17C2×#354
prime radicalC2×#10587560C22
cosocle#10587560C23
hypercenter#533#595
hypocenterC17#13595
LCSG ▷ C42×C17 ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #14543924C2semidirect
3. #14543923C2semidirect
9. #11763175C4semidirect
10. #11763175C4semidirect
15. C4×#63223C4semidirect
16. C17×#533C4semidirect
21. C17×#125C2×C4semidirect
22. C17×#125C2×C4semidirect
38. #10587474C2×C4semidirect
39. #10587474C2×C4semidirect
116. #533#595semidirect
141. #125C2×#595semidirect
142. #125C2×#595semidirect
157. C17#13595semidirect

Maximal subgroups

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

subgroupindex
C2×#117637142
#145439242
#145439232
#145391602
#1359517