Finite Group Databasebeta

← #17959668

Subgroups — #17959668

Order 4352.

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

normal subgroups only

This group has 300 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#14544709C211yesmaximal, characteristic
3#14543777C214yesmaximal
4#14539371C211yesmaximal, characteristic
5#11763814—21no—
6#11763730—21no—
7#11763704C2212yes—
8#11763697—21no—
9#11763685—21no—
10#11763685C2212yes—
11#11763364—21no—
12#11763189C411yescharacteristic
13#11763161—21no—
14#11763051—21no—
15#11763051C2212yes—
16#11762903—21no—
17#11762903C412yes—
18C4×C8×D17C2211yescharacteristic
19C17×#500C411yescharacteristic
20C2×#63243—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#10587544—41no—
35#10587544—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
45C2×Q8×C17—41no—
46C2×C4×D17SD1611yescharacteristic
47C2×C4×D17SD1611yescharacteristic
48C2×C4×D17C2×D411yescharacteristic
49C2×Dic34—22no—
50C2×#3624—42no—
51#63243—42no—
52#63243—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×Dic17D811yescharacteristic
66C4×Dic17D811yescharacteristic
67C2×#3622C22⋊C411yescharacteristic
68C2×#3622C2×D411yescharacteristic
69Dic68—42no—
70Dic68—42no—
71C8×D17—41no—
72C8×D17—41no—
73#63216—42no—
74#11865—171nomaximal, Sylow
75C22×D17C2×SD1611yescharacteristic
76Q8×C17—82no—
77C2×C4×C17—42no—
78C2×C4×C17#10211yescharacteristic
79C2×C4×C17#10211yescharacteristic
80C2×C4×C17C2×C22⋊C411yescharacteristic
81C2×Dic17—42no—
82C2×Dic17#10211yescharacteristic
83C2×Dic17#10211yescharacteristic
84C2×Dic17C2×D811yescharacteristic
85C4×D17—21no—
86C4×D17—21no—
87C4×D17—22no—
88C4×D17—41no—
89Dic34—42no—
90Dic34—42no—
91#3624—82no—
92C8×C17—21no—
93C8×C17—21no—
94#3622—21no—
95#3622—21no—
96#3170—171no—
97#2163—171no—
98#1837—171no—
99#1350—174no—
100C22×C17C2×#10211yescharacteristic
101C2×D17—21no—
102C2×D17—21no—
103C2×D17—21no—
104C4×C17—21no—
105C4×C17—21no—
106C4×C17—82no—
107C4×C17#41011yescharacteristic
108C4×C17#42111yescharacteristic
109Dic17—21no—
110Dic17—21no—
111Dic17—82no—
112Dic17#36212yes—
113#533—341no—
114#500#59511yescharacteristic
115#494—171no—
116#487—341no—
117#467—172no—
118#467—341no—
119C4×Q16—172no—
120C4×Q16—341no—
121#423—341no—
122C2×C4×C8—171no—
123C4⋊C16—341no—
124C22⋊C16—172no—
125#346—341no—
126#341—172no—
127#341—341no—
128C2×C17#151711yescharacteristic
129C2×C17#214311yescharacteristic
130C2×C17C2×#36211yescharacteristic
131D17—41no—
132C2×Q16—172no—
133C2×Q16—341no—
134C2×M16—342no—
135C22×C8—171no—
136C22×C8—171no—
137C4⋊Q8—21no—
138C4⋊Q8—341no—
139#125—681no—
140C22⋊Q8—342no—
141C22⋊Q8—681no—
142C4×Q8—342no—
143C4×Q8—681no—
144#117—681no—
145C2×C42—171no—
146C2×C16—342no—
147#107—21no—
148#107C2×#59512yes—
149C4⋊C8—681no—
150C4⋊C8—681no—
151#103—342no—
152#103—342no—
153C4×C8—171no—
154C4×C8—171no—
155C4×C8—171no—
156C4×C8C2×#59511yescharacteristic
157C17#1186511yescharacteristic, complemented, Sylow
158C2×Q8—41no—
159C2×Q8—342no—
160C22×C4—171no—
161C22×C4—171no—
162C22×C4—171no—
163Q16—682no—
164Q16—682no—
165M16—682no—
166M16—682no—
167C2×C8—171no—
168C2×C8—171no—
169C2×C8—681no—
170C2×C8—681no—
171C2×C8—682no—
172C2×C8C22⋊#59511yescharacteristic
173C2×C8C22×#59511yescharacteristic
174C4⋊C4—22no—
175C4⋊C4—41no—
176C4⋊C4—682no—
177C4⋊C4—682no—
178C4⋊C4—681no—
179C4⋊C4—681no—
180C22⋊C4—682no—
181C42—171no—
182C42—171no—
183C42—171no—
184C42—682no—
185C42C22⋊#59511yescharacteristic
186C16—682no—
187C23—171no—
188Q8—82no—
189Q8—682no—
190Q8—682no—
191C2×C4—42no—
192C2×C4—171no—
193C2×C4—171no—
194C2×C4—171no—
195C2×C4—342no—
196C2×C4—341no—
197C2×C4—341no—
198C2×C4—681no—
199C2×C4—682no—
200C2×C4#1058754711yescharacteristic
201C2×C4#1058754711yescharacteristic
202C2×C4C2×C22⋊#59511yescharacteristic
203C8—21no—
204C8—21no—
205C8—341no—
206C8—341no—
207C8—1362no—
208C22—341no—
209C22—341no—
210C22—341no—
211C22C2×#1058754711yescharacteristic
212C4—21no—
213C4—21no—
214C4—82no—
215C4—172no—
216C4—341no—
217C4—341no—
218C4—1362no—
219C4#1176379011yescharacteristic
220C4#1176380811yescharacteristic
221C2—681no—
222C2#1454421511yescharacteristic
223C2#1454509911yescharacteristic
224C2D17⋊#36211yescharacteristic
subgroupG/H
centerC22C2×#10587547
commutatorC2×C8×C17C22×C4
FrattiniC2×C8C22×#595
FittingC17×#500C4
socleC22×C17C2×#102
prime radicalC22×D17C2×SD16
cosocleC2×C8×D17C23
hypercenter#500#595
hypocenterC17#11865
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
157. C17#11865semidirect

Maximal subgroups

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

subgroupindex
#145451472
#145447092
#145437772
#145393712
#1186517