Finite Group Databasebeta

← #14541586

Subgroups — #14541586

Order 2176.

326 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 115 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#11763537C211yesmaximal, characteristic
2#11763534C211yesmaximal, characteristic
3#11763176C212yesmaximal
4#11763161C211yesmaximal, characteristic
5#11763119C212yesmaximal
6#11763020C211yesmaximal, characteristic
7#11763018C212yesmaximal
8#11762936C211yesmaximal, characteristic
9#11762915C212yesmaximal
10C4×#63231C211yesmaximal, characteristic
11C17×#475C211yesmaximal, characteristic
12C17×C4⋊Q8C2211yescharacteristic
13C4×Q8×C17C2211yescharacteristic
14Q8×Dic17—21no—
15#10587630—21no—
16#10587630C2212yes—
17C2×#63231C2211yescharacteristic
18C2×Dic68C2212yes—
19#10587576C2212yes—
20#10587575—22no—
21#10587575—22no—
22#10587573C2212yes—
23#10587573C2212yes—
24#10587556—21no—
25#10587555C2211yescharacteristic
26C4×Dic34—21no—
27C4×Dic34C2211yescharacteristic
28C4×Dic34C2211yescharacteristic
29C17×#106C2212yes—
30C17×C4⋊C8C2211yescharacteristic
31C17×#103C2212yes—
32#10587506C2211yescharacteristic
33#10587487C2212yes—
34#10587486C2212yes—
35#10587485C2212yes—
36#10587481C2212yes—
37#10587481C2211yescharacteristic
38#10587481C2212yes—
39#10587478C2211yescharacteristic
40C4×#3622C2211yescharacteristic
41C2×Q8×C17—21no—
42C2×Q8×C17C2311yescharacteristic
43C2×Dic34D411yescharacteristic
44C2×Dic34C2312yes—
45C2×Dic34C2311yescharacteristic
46C2×C8×C17C2312yes—
47C4⋊C4×C17—21no—
48C4⋊C4×C17—21no—
49C4⋊C4×C17C2312yes—
50C4⋊C4×C17C2311yescharacteristic
51C42×C17—21no—
52C42×C17C2311yescharacteristic
53#63231—22no—
54C4⋊Dic17—21no—
55C4⋊Dic17—21no—
56C4⋊Dic17—22no—
57C4⋊Dic17D411yescharacteristic
58C4⋊Dic17C2311yescharacteristic
59#63225—21no—
60#63225—22no—
61#63225—22no—
62#63225—22no—
63#63225—22no—
64#63225—22no—
65#63225D412yes—
66C4×Dic17—21no—
67C4×Dic17—22no—
68C4×Dic17—22no—
69C4×Dic17C2312yes—
70C2×#3622C2311yescharacteristic
71C2×#3622C2311yescharacteristic
72Dic68—24no—
73Q8×C17—21no—
74Q8×C17—21no—
75Q8×C17—42no—
76C2×C4×C17—21no—
77C2×C4×C17—21no—
78C2×C4×C17—22no—
79C2×C4×C17C2×D411yescharacteristic
80C2×C4×C17C2×D411yescharacteristic
81C2×C4×C17C2411yescharacteristic
82C2×Dic17—21no—
83C2×Dic17—22no—
84C2×Dic17—21no—
85C2×Dic17C2×D412yes—
86C2×Dic17C2×D412yes—
87Dic34—22no—
88Dic34—21no—
89Dic34—22no—
90Dic34—22no—
91Dic34#4112yes—
92C8×C17—22no—
93#3622—21no—
94#3622—21no—
95#3374—171nomaximal, Sylow
96C22×C17C22×D411yescharacteristic
97C4×C17—21no—
98C4×C17—41no—
99C4×C17—42no—
100C4×C17—41no—
101C4×C17#13712yes—
102C4×C17C2×#4111yescharacteristic
103C4×C172−1+411yescharacteristic
104Dic17—22no—
105Dic17—22no—
106Dic17—22no—
107Dic17—42no—
108Dic17—41no—
109#557—171no—
110#557—171no—
111#491—172no—
112#487—171no—
113#479—172no—
114#475D1711yescharacteristic
115#462—171no—
116#462—172no—
117#446—171no—
118#441—172no—
119C4×Q16—171no—
120C2×C17#54811yescharacteristic
121C2×C17C2×#13711yescharacteristic
122C2×C17#57811yescharacteristic
123C2×Q16—171no—
124C2×Q16—172no—
125C4⋊Q8—172no—
126C4⋊Q8—171no—
127C4⋊Q8—341no—
128C4⋊Q8C2×D1711yescharacteristic
129#125—172no—
130#125—341no—
131#125—342no—
132#125—342no—
133C4×Q8—171no—
134C4×Q8—172no—
135C4×Q8—172no—
136C4×Q8—171no—
137C4×Q8—341no—
138C4×Q8—341no—
139C4×Q8C2×D1711yescharacteristic
140#107—171no—
141#106C2×D1712yes—
142C4⋊C8—172no—
143C4⋊C8C2×D1711yescharacteristic
144#103—171no—
145#103—172no—
146#103—171no—
147#103—172no—
148#103—172no—
149#103C2×D1712yes—
150#97—172no—
151C4×C8—171no—
152C17#337411yescharacteristic, complemented, Sylow
153C2×Q8—21no—
154C2×Q8—171no—
155C2×Q8—171no—
156C2×Q8—172no—
157C2×Q8C22×D1711yescharacteristic
158Q16—344no—
159Q16—342no—
160C2×C8—171no—
161C2×C8—171no—
162C2×C8C22×D1712yes—
163C4⋊C4—21no—
164C4⋊C4—21no—
165C4⋊C4—171no—
166C4⋊C4—172no—
167C4⋊C4—171no—
168C4⋊C4—342no—
169C4⋊C4—342no—
170C4⋊C4—342no—
171C4⋊C4—342no—
172C4⋊C4—342no—
173C4⋊C4—342no—
174C4⋊C4—341no—
175C4⋊C4—341no—
176C4⋊C4—341no—
177C4⋊C4C22×D1712yes—
178C4⋊C4C22×D1711yescharacteristic
179C42—21no—
180C42—172no—
181C42—342no—
182C42—342no—
183C42—341no—
184C42C22×D1711yescharacteristic
185Q8—21no—
186Q8—21no—
187Q8—42no—
188Q8—172no—
189Q8—341no—
190Q8—342no—
191Q8—342no—
192Q8—342no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—172no—
197C2×C4—172no—
198C2×C4—341no—
199C2×C4—341no—
200C2×C4—342no—
201C2×C4D4×D1711yescharacteristic
202C2×C4D4×D1711yescharacteristic
203C2×C4C23×D1711yescharacteristic
204C8—22no—
205C8—341no—
206C8—341no—
207C22C2×D4×D1711yescharacteristic
208C4—21no—
209C4—41no—
210C4—42no—
211C4—41no—
212C4—342no—
213C4—342no—
214C4—342no—
215C4—682no—
216C4—681no—
217C4#1058760112yes—
218C4#1058769411yescharacteristic
219C4#41×D1711yescharacteristic
220C2#1176346911yescharacteristic
221C2C2×#1058760111yescharacteristic
222C2#1176362511yescharacteristic
subgroupG/H
centerC22C2×D4×D17
commutator, cosocleC2×C4×C17C24
FrattiniC2×C4C23×D17
FittingC17×#475C2
socle, prime radicalC22×C17C22×D4
hypercenter#475D17
hypocenterC17#3374
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
152. C17#3374semidirect

Maximal subgroups

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

subgroupindex
#117635372
#117635342
#117631762
#117631612
#117631192
#117630202
#117630182
#117629362
#117629152
C4×#632312
C17×#4752
#337417