Finite Group Databasebeta

← #14533995

Subgroups — #14533995

Order 2176.

468 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 151 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×#10587573C211yesmaximal, characteristic
3#11762749C211yesmaximal, characteristic
4#11762748C211yesmaximal, characteristic
5#11762747C211yesmaximal, characteristic
6#11762713C212yesmaximal
7#11762713C212yesmaximal
8#11762713C212yesmaximal
9#11762673C212yesmaximal
10#11762660C211yesmaximal, characteristic
11C17×#400C211yesmaximal, characteristic
12C22×Dic34C2212yes—
13C22×Dic34C2211yescharacteristic
14C2×C4⋊C4×C17C2211yescharacteristic
15C2×C4⋊C4×C17C2211yescharacteristic
16C2×C4⋊Dic17C2211yescharacteristic
17C2×#63225C2212yes—
18C2×#63225C2212yes—
19C2×#63225C2211yescharacteristic
20C2×#63225C2211yescharacteristic
21C2×C4×Dic17C2211yescharacteristic
22C2×C4×Dic17C2211yescharacteristic
23C2×C4×Dic17C2212yes—
24C2×C4×Dic17C2211yescharacteristic
25#10587574—24no—
26#10587573—24no—
27C17×#95C2212yes—
28C17×#95C2212yes—
29C17×#95C2211yescharacteristic
30#10587502C2212yes—
31#10587502C2212yes—
32#10587502C2212yes—
33#10587502C2212yes—
34#10587502C2212yes—
35#10587502C2212yes—
36#10587502C2211yescharacteristic
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—22no—
49C2×Dic34—22no—
50C2×Dic34—24no—
51C2×Dic34—28no—
52C2×Dic34Q814yescomplemented
53C4⋊C4×C17—22no—
54C4⋊C4×C17—22no—
55C4⋊Dic17—22no—
56#63225—22no—
57#63225—22no—
58#63225—24no—
59#63225—24no—
60C4×Dic17—22no—
61C4×Dic17—22no—
62C4×Dic17—24no—
63C4×Dic17D414yes—
64C23×C17C2411yescharacteristic
65C2×C4×C17—21no—
66C2×C4×C17—21no—
67C2×C4×C17—22no—
68C2×C4×C17—22no—
69C2×C4×C17—21no—
70C2×C4×C17—24no—
71C2×C4×C17—22no—
72C2×C4×C17—22no—
73C2×C4×C17—22no—
74C2×C4×C17—22no—
75C2×C4×C17C2×D412yes—
76C2×C4×C17C2×Q812yes—
77C2×Dic17—21no—
78C2×Dic17—21no—
79C2×Dic17—22no—
80C2×Dic17—21no—
81C2×Dic17—24no—
82C2×Dic17—22no—
83C2×Dic17—22no—
84C2×Dic17—22no—
85C2×Dic17—22no—
86C2×Dic17C2×D412yes—
87C2×Dic17C2×D412yes—
88C2×Dic17C2×Q812yes—
89C2×Dic17C2×Q812yes—
90C2×Dic17#4112yes—
91C2×Dic17#4114yes—
92Dic34—28no—
93Dic34—48no—
94#2568—171nomaximal, Sylow
95C22×C17C22×D411yescharacteristic
96C22×C17C22×Q811yescharacteristic
97C22×C17C2×#4111yescharacteristic
98C22×C17C2×#4112yes—
99C22×C172−1+412yes—
100C4×C17—22no—
101C4×C17—22no—
102C4×C17—42no—
103C4×C17—41no—
104C4×C17—42no—
105Dic17—22no—
106Dic17—42no—
107Dic17—41no—
108Dic17—42no—
109Dic17C22⋊Q814yes—
110Dic17#12414yes—
111C2×C4⋊Q8—171no—
112C2×C4×Q8—171no—
113#400—171no—
114#400—171no—
115#400—171no—
116#400D1711yescharacteristic
117#391—172no—
118#391—172no—
119#391—172no—
120#382—172no—
121C4×C4⋊C4—171no—
122C2×C17C2×C22⋊Q811yescharacteristic
123C2×C17C2×#12411yescharacteristic
124C2×C17#53611yescharacteristic
125C2×C17#55612yes—
126C2×C17#55712yes—
127C22×Q8—171no—
128C22×Q8—172no—
129C4⋊Q8—344no—
130C4×Q8—344no—
131C2×C4⋊C4—171no—
132C2×C4⋊C4—171no—
133C2×C4⋊C4—172no—
134C2×C4⋊C4—171no—
135C2×C4⋊C4—172no—
136C2×C4⋊C4C2×D1711yescharacteristic
137C2×C4⋊C4C2×D1711yescharacteristic
138C2×C42—171no—
139C2×C42—171no—
140C2×C42—171no—
141C2×C42—172no—
142#95—171no—
143#95—172no—
144#95—172no—
145#95—172no—
146#95—172no—
147#95—172no—
148#95—172no—
149#95C2×D1711yescharacteristic
150#95C2×D1712yes—
151#95C2×D1712yes—
152C17#256811yescharacteristic, complemented, Sylow
153C2×Q8—174no—
154C2×Q8—342no—
155C2×Q8—342no—
156C2×Q8—344no—
157C2×Q8—348no—
158C22×C4—171no—
159C22×C4—171no—
160C22×C4—171no—
161C22×C4—172no—
162C22×C4—171no—
163C22×C4—172no—
164C22×C4C22×D1712yes—
165C22×C4C22×D1711yescharacteristic
166C22×C4C22×D1712yes—
167C22×C4C22×D1711yescharacteristic
168C22×C4C22×D1711yescharacteristic
169C4⋊C4—22no—
170C4⋊C4—22no—
171C4⋊C4—342no—
172C4⋊C4—344no—
173C4⋊C4—344no—
174C4⋊C4—342no—
175C4⋊C4—342no—
176C42—174no—
177C42—342no—
178C42—342no—
179C42—344no—
180C23C23×D1711yescharacteristic
181Q8—348no—
182Q8—688no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—24no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—172no—
194C2×C4—172no—
195C2×C4—172no—
196C2×C4—172no—
197C2×C4—174no—
198C2×C4—172no—
199C2×C4—341no—
200C2×C4—341no—
201C2×C4—341no—
202C2×C4—342no—
203C2×C4—342no—
204C2×C4—342no—
205C2×C4—344no—
206C2×C4—342no—
207C2×C4—342no—
208C2×C4D4×D1712yes—
209C2×C4Q8×D1712yes—
210C22C2×D4×D1711yescharacteristic
211C22C2×Q8×D1711yescharacteristic
212C22#41×D1711yescharacteristic
213C22#41×D1712yes—
214C22#1058769712yes—
215C4—22no—
216C4—22no—
217C4—42no—
218C4—42no—
219C4—41no—
220C4—174no—
221C4—174no—
222C4—342no—
223C4—682no—
224C4—682no—
225C4—681no—
226C2C22⋊Q8×D1711yescharacteristic
227C2#124×D1711yescharacteristic
228C2#1176338111yescharacteristic
229C2#1176352612yes—
230C2#1176353612yes—
subgroupG/H
center, FrattiniC23C23×D17
commutator, socle, prime radical, cosocleC23×C17C24
FittingC17×#400C2
hypercenter#400D17
hypocenterC17#2568
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
52. C2×Dic34Q8semidirect
152. C17#2568semidirect

Maximal subgroups

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

subgroupindex
C2×#105875742
C2×#105875732
#117627492
#117627482
#117627472
#117627132
#117626732
#117626602
C17×#4002
#256817