Finite Group Databasebeta

← #14534731

Subgroups — #14534731

Order 2176.

416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 133 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×#10587574C211yesmaximal, characteristic
2C2×#10587575C211yesmaximal, characteristic
3#11762751C212yesmaximal
4#11762750C212yesmaximal
5#11762749C211yesmaximal, characteristic
6#11762748C211yesmaximal, characteristic
7#11762747C211yesmaximal, characteristic
8#11762713C212yesmaximal
9#11762713C212yesmaximal
10#11762654C211yesmaximal, characteristic
11C17×#400C211yesmaximal, characteristic
12C22×Dic34C2212yes—
13C2×C4⋊C4×C17C2211yescharacteristic
14C2×C4⋊C4×C17C2211yescharacteristic
15C2×C4⋊Dic17C2211yescharacteristic
16C2×C4⋊Dic17C2211yescharacteristic
17C2×#63225C2211yescharacteristic
18C2×#63225C2211yescharacteristic
19C2×#63225C2211yescharacteristic
20C2×#63225C2211yescharacteristic
21C2×#63225C2212yes—
22C2×C4×Dic17C2212yes—
23C2×C4×Dic17C2211yescharacteristic
24#10587575—24no—
25#10587574—24no—
26C17×#95C2212yes—
27C17×#95C2212yes—
28C17×#95C2211yescharacteristic
29#10587502C2212yes—
30#10587502C2212yes—
31#10587502C2212yes—
32#10587502C2212yes—
33#10587502C2212yes—
34#10587502C2212yes—
35#10587502C2211yescharacteristic
36#10587502C2212yes—
37C22×C4×C17C2312yes—
38C22×C4×C17C2312yes—
39C22×C4×C17C2311yescharacteristic
40C22×C4×C17C2311yescharacteristic
41C22×C4×C17C2311yescharacteristic
42C22×Dic17C2312yes—
43C22×Dic17C2312yes—
44C22×Dic17C2311yescharacteristic
45C22×Dic17C2311yescharacteristic
46C22×Dic17C2311yescharacteristic
47C22×Dic17C2311yescharacteristic
48C2×Dic34—24no—
49C2×Dic34—28no—
50C4⋊C4×C17—22no—
51C4⋊C4×C17—22no—
52C4⋊Dic17—22no—
53C4⋊Dic17—22no—
54#63225—22no—
55#63225—24no—
56#63225—22no—
57#63225—22no—
58#63225—22no—
59C4×Dic17—24no—
60C4×Dic17D414yes—
61C23×C17C2411yescharacteristic
62C2×C4×C17—22no—
63C2×C4×C17—22no—
64C2×C4×C17—21no—
65C2×C4×C17—21no—
66C2×C4×C17—24no—
67C2×C4×C17—22no—
68C2×C4×C17—21no—
69C2×C4×C17—21no—
70C2×C4×C17—22no—
71C2×C4×C17—22no—
72C2×C4×C17—22no—
73C2×C4×C17C2×D412yes—
74C2×Dic17—21no—
75C2×Dic17—21no—
76C2×Dic17—22no—
77C2×Dic17—21no—
78C2×Dic17—21no—
79C2×Dic17—24no—
80C2×Dic17—22no—
81C2×Dic17—21no—
82C2×Dic17—22no—
83C2×Dic17—22no—
84C2×Dic17—21no—
85C2×Dic17—22no—
86C2×Dic17C2×D412yes—
87C2×Dic17C2×D412yes—
88C2×Dic17#4114yes—
89Dic34—48no—
90#2642—171nomaximal, Sylow
91C22×C17C22×D411yescharacteristic
92C22×C17C2×#4112yes—
93C22×C172−1+411yescharacteristic
94C22×C172−1+412yes—
95C22×C172−1+411yescharacteristic
96C4×C17—22no—
97C4×C17—42no—
98C4×C17—41no—
99C4×C17—41no—
100C4×C17—42no—
101Dic17—22no—
102Dic17—42no—
103Dic17—41no—
104Dic17—41no—
105Dic17—42no—
106Dic17#12414yes—
107C2×C4⋊Q8—171no—
108C2×#125—171no—
109#400—171no—
110#400—171no—
111#400—171no—
112#400—172no—
113#400—172no—
114#400D1711yescharacteristic
115#391—172no—
116#391—172no—
117#376—171no—
118C2×C17C2×#12411yescharacteristic
119C2×C17#53611yescharacteristic
120C2×C17#53611yescharacteristic
121C2×C17#54112yes—
122C2×C17#54112yes—
123C22×Q8—172no—
124C4⋊Q8—344no—
125#125—344no—
126C2×C4⋊C4—171no—
127C2×C4⋊C4—171no—
128C2×C4⋊C4—171no—
129C2×C4⋊C4—171no—
130C2×C4⋊C4—171no—
131C2×C4⋊C4—172no—
132C2×C4⋊C4—171no—
133C2×C4⋊C4C2×D1711yescharacteristic
134C2×C4⋊C4C2×D1711yescharacteristic
135C2×C42—171no—
136C2×C42—172no—
137#95—172no—
138#95—171no—
139#95—172no—
140#95—172no—
141#95—172no—
142#95—172no—
143#95—172no—
144#95—172no—
145#95C2×D1711yescharacteristic
146#95C2×D1712yes—
147#95C2×D1712yes—
148C17#264211yescharacteristic, complemented, Sylow
149C2×Q8—344no—
150C2×Q8—348no—
151C22×C4—171no—
152C22×C4—171no—
153C22×C4—172no—
154C22×C4—171no—
155C22×C4—171no—
156C22×C4—172no—
157C22×C4C22×D1712yes—
158C22×C4C22×D1711yescharacteristic
159C22×C4C22×D1711yescharacteristic
160C22×C4C22×D1712yes—
161C22×C4C22×D1711yescharacteristic
162C4⋊C4—22no—
163C4⋊C4—22no—
164C4⋊C4—342no—
165C4⋊C4—342no—
166C4⋊C4—342no—
167C4⋊C4—342no—
168C4⋊C4—344no—
169C4⋊C4—342no—
170C4⋊C4—342no—
171C42—174no—
172C42—344no—
173C23C23×D1711yescharacteristic
174Q8—688no—
175C2×C4—22no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—24no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—172no—
187C2×C4—174no—
188C2×C4—172no—
189C2×C4—341no—
190C2×C4—341no—
191C2×C4—341no—
192C2×C4—341no—
193C2×C4—342no—
194C2×C4—341no—
195C2×C4—342no—
196C2×C4—342no—
197C2×C4—344no—
198C2×C4—342no—
199C2×C4—341no—
200C2×C4—342no—
201C2×C4D4×D1712yes—
202C22C2×D4×D1711yescharacteristic
203C22#1058769411yescharacteristic
204C22#41×D1712yes—
205C22#1058769712yes—
206C22#1058769711yescharacteristic
207C4—22no—
208C4—42no—
209C4—41no—
210C4—41no—
211C4—42no—
212C4—174no—
213C4—342no—
214C4—682no—
215C4—681no—
216C4—681no—
217C4—682no—
218C2#124×D1711yescharacteristic
219C2#1176338111yescharacteristic
220C2#1176338211yescharacteristic
221C2#1176341612yes—
222C2#1176341812yes—
subgroupG/H
center, FrattiniC23C23×D17
commutator, socle, prime radical, cosocleC23×C17C24
FittingC17×#400C2
hypercenter#400D17
hypocenterC17#2642
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
148. C17#2642semidirect

Maximal subgroups

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

subgroupindex
C2×#105875742
C2×#105875752
#117627512
#117627502
#117627492
#117627482
#117627472
#117627132
#117626542
C17×#4002
#264217