Finite Group Databasebeta

← #17959648

Subgroups — #17959648

Order 4352.

314 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 74 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#14545147C211yesmaximal, characteristic
2#14544706C211yesmaximal, characteristic
3#14543773C214yesmaximal
4#14539371C211yesmaximal, characteristic
5#11763753—21no—
6#11763730—21no—
7#11763704C2212yes—
8#11763697—21no—
9#11763683—21no—
10#11763683C2212yes—
11#11763364—21no—
12#11763189C411yescharacteristic, complemented
13#11763161—21no—
14#11763051—21no—
15#11763051C2212yes—
16#11762903—21no—
17#11762903C412yescomplemented
18C4×C8×D17C2211yescharacteristic
19C17×#500C411yescharacteristic, complemented
20C2×C4⋊#595—22no—
21C17×C4⋊Q8—21no—
22#10587632—41no—
23Q8×Dic17—41no—
24C2×Dic68—21no—
25C2×Dic68C2×C412yes—
26C2×C8×D17D411yescharacteristic
27C2×C8×D17C2311yescharacteristic
28#10587583—22no—
29#10587578—41no—
30#10587576—41no—
31#10587573—22no—
32C42×D17D411yescharacteristic
33#10587555—21no—
34(C2×#595)⋊C4—41no—
35(C2×#595)⋊C4—41no—
36C2×#63216—22no—
37C17×#107—21no—
38C17×#107C2×C412yes—
39C4×C8×C17C2×C411yescharacteristic
40C8×Dic17C2×C411yescharacteristic
41C8×Dic17D411yescharacteristic
42#10587481—22no—
43#10587481—22no—
44C4×#3622D411yescharacteristic
45C22×#595—42no—
46C2×Q8×C17—41no—
47C2×C4×D17D811yescharacteristic
48C2×C4×D17D811yescharacteristic
49C2×C4×D17C2×D411yescharacteristic
50C2×Dic34—22no—
51C4⋊#595—42no—
52C4⋊#595—42no—
53C2×C8×C17C22⋊C411yescharacteristic
54C2×C8×C17C22×C411yescharacteristic
55C4⋊C4×C17—22no—
56C4⋊C4×C17—41no—
57C42×C17C22⋊C411yescharacteristic
58#63227—42no—
59C4⋊Dic17—41no—
60C4⋊Dic17—41no—
61C4⋊Dic17—42no—
62#63225—42no—
63C4×Dic17—42no—
64C4×Dic17C22⋊C411yescharacteristic
65C4×Dic17SD1611yescharacteristic
66C4×Dic17SD1611yescharacteristic
67C2×#3622C22⋊C411yescharacteristic
68C2×#3622C2×D411yescharacteristic
69Dic68—42no—
70Dic68—42no—
71C8×D17—41no—
72C8×D17—41no—
73#63216—42no—
74#11859—171nomaximal, Sylow
75C22×D17C2×D811yescharacteristic
76C2×#595—82no—
77C2×#595—82no—
78C2×#595—82no—
79Q8×C17—82no—
80C2×C4×C17—42no—
81C2×C4×C17#10211yescharacteristic
82C2×C4×C17#10211yescharacteristic
83C2×C4×C17C2×C22⋊C411yescharacteristic
84C2×Dic17—42no—
85C2×Dic17#10211yescharacteristic
86C2×Dic17#10211yescharacteristic
87C2×Dic17C2×SD1611yescharacteristic
88C4×D17—22no—
89C4×D17—21no—
90C4×D17—21no—
91C4×D17—41no—
92Dic34—42no—
93Dic34—42no—
94C8×C17—21no—
95C8×C17—21no—
96#3622—21no—
97#3622—21no—
98#3170—171no—
99#2163—171no—
100#1835—171no—
101#1348—174no—
102C22×C17C2×#10211yescharacteristic
103C2×D17—21no—
104C2×D17—21no—
105C2×D17#51012yes—
106#595—162no—
107C4×C17—21no—
108C4×C17—21no—
109C4×C17—82no—
110C4×C17#41011yescharacteristic
111C4×C17#42111yescharacteristic
112Dic17—21no—
113Dic17—21no—
114Dic17—21no—
115Dic17—82no—
116#533—341no—
117#500#59511yescharacteristic, complemented
118#494—171no—
119#487—341no—
120#467—172no—
121#467—341no—
122C4×Q16—172no—
123C4×Q16—341no—
124C2×C4×C8—171no—
125#382—341no—
126C4⋊C16—341no—
127C22⋊C16—172no—
128#346—341no—
129#340—172no—
130#340—341no—
131C2×C17#151711yescharacteristic
132C2×C17#214111yescharacteristic
133C2×C17#214511yescharacteristic
134D17—22no—
135C2×Q16—172no—
136C2×Q16—341no—
137C22×C8—171no—
138C22×C8—171no—
139C4⋊Q8—21no—
140C4⋊Q8—341no—
141#125—681no—
142C22⋊Q8—342no—
143C22⋊Q8—681no—
144C4×Q8—342no—
145C4×Q8—681no—
146#117—681no—
147C2×C4⋊C4—342no—
148C2×C42—171no—
149C2×C16—342no—
150#107—21no—
151#107C2×#59512yes—
152#103—342no—
153#103—342no—
154C4×C8—171no—
155C4×C8—171no—
156C4×C8—171no—
157C4×C8C2×#59511yescharacteristic
158#95—681no—
159#95—681no—
160C17#1185911yescharacteristic, complemented, Sylow
161C2×Q8—41no—
162C2×Q8—342no—
163C22×C4—171no—
164C22×C4—171no—
165C22×C4—171no—
166C22×C4—682no—
167Q16—682no—
168Q16—682no—
169C2×C8—171no—
170C2×C8—171no—
171C2×C8—681no—
172C2×C8—681no—
173C2×C8C22⋊#59511yescharacteristic
174C2×C8C22×#59511yescharacteristic
175C4⋊C4—22no—
176C4⋊C4—41no—
177C4⋊C4—682no—
178C4⋊C4—682no—
179C4⋊C4—682no—
180C4⋊C4—682no—
181C4⋊C4—681no—
182C4⋊C4—681no—
183C22⋊C4—682no—
184C42—171no—
185C42—171no—
186C42—171no—
187C42—682no—
188C42C22⋊#59511yescharacteristic
189C16—682no—
190C23—171no—
191Q8—82no—
192Q8—682no—
193Q8—682no—
194C2×C4—42no—
195C2×C4—171no—
196C2×C4—171no—
197C2×C4—171no—
198C2×C4—342no—
199C2×C4—341no—
200C2×C4—341no—
201C2×C4—681no—
202C2×C4—682no—
203C2×C4—1362no—
204C2×C4—1362no—
205C2×C4—1362no—
206C2×C4#1058754711yescharacteristic
207C2×C4#1058754711yescharacteristic
208C2×C4C2×C22⋊#59511yescharacteristic
209C8—21no—
210C8—21no—
211C8—341no—
212C8—341no—
213C22—172no—
214C22—341no—
215C22—341no—
216C22C2×#1058754711yescharacteristic
217C4—21no—
218C4—21no—
219C4—82no—
220C4—2722no—
221C4—341no—
222C4—341no—
223C4—341no—
224C4—1362no—
225C4#1176379011yescharacteristic
226C4#1176380811yescharacteristic
227C2—342no—
228C2#1454421511yescharacteristic
229C2#1454509411yescharacteristic
230C2#1454510511yescharacteristic
subgroupG/H
centerC22C2×#10587547
commutatorC2×C8×C17C22×C4
FrattiniC2×C8C22×#595
FittingC17×#500C4
socleC22×C17C2×#102
prime radicalC22×D17C2×D8
cosocleC2×C8×D17C23
hypercenter#500#595
hypocenterC17#11859
LCSG ▷ C2×C8×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #500

Complements

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

NH ≅ G/Ntype
12. #11763189C4semidirect
17. #11762903C4semidirect
19. C17×#500C4semidirect
117. #500#595semidirect
160. C17#11859semidirect

Maximal subgroups

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

subgroupindex
#145451472
#145447062
#145437732
#145393712
#1185917