Finite Group Databasebeta

← #16937818

Subgroups — #16937818

Order 4352.

386 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 91 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#14536852C211yesmaximal, characteristic
2#14529752C212yesmaximal
3C2×#11762550C212yesmaximal
4#14526665C211yesmaximal, characteristic
5C17×#1836C211yesmaximal, characteristic
6C2×#10587556C2212yes—
7C2×#10587474C2212yes—
8#11762749—22no—
9#11762741—22no—
10#11762739—22no—
11#11762571—22no—
12#11762571—22no—
13#11762550—24no—
14C2×C17×#97C2211yescharacteristic
15C17×#384C2211yescharacteristic
16C17×#382C2211yescharacteristic
17C17×#340—22no—
18C22×C8×C17—21no—
19C2×C4⋊C4×C17—21no—
20C2×C4⋊C4×C17—22no—
21C2×C4⋊C4×C17D412yes—
22C2×C42×C17C2311yescharacteristic
23C2×C4⋊Dic17—22no—
24C2×C4⋊Dic17D412yes—
25C2×C4⋊Dic17D412yes—
26C2×#63225—22no—
27C2×#63225—22no—
28C22×#3622—22no—
29#10587556—22no—
30#10587556—22no—
31#10587556—22no—
32#10587556—22no—
33C17×#97—21no—
34C17×#97D412yes—
35C17×#95—22no—
36#10587502—24no—
37#10587502—22no—
38#10587474—22no—
39#10587474—22no—
40C22×C4×C17—22no—
41C22×C4×C17—41no—
42C22×C4×C17C2×D412yes—
43C22×C4×C17C2×D411yescharacteristic
44C22×Dic17—22no—
45C22×Dic17—22no—
46C2×C8×C17—22no—
47C2×C8×C17—41no—
48C2×C8×C17—41no—
49C4⋊C4×C17—42no—
50C4⋊C4×C17—42no—
51C4⋊C4×C17—44no—
52C42×C17C2×D411yescharacteristic
53C42×C17#4111yescharacteristic
54C42×C17#4112yes—
55C4⋊Dic17—22no—
56C4⋊Dic17—22no—
57C4⋊Dic17—22no—
58C4⋊Dic17—22no—
59C4⋊Dic17—82no—
60#63225—42no—
61#63225—42no—
62#63225—42no—
63#63225—42no—
64C2×#3622—24no—
65C2×#3622—42no—
66C2×#3622—42no—
67#10428—171nomaximal, Sylow
68C23×C17#12011yescharacteristic
69C2×C4×C17—21no—
70C2×C4×C17—22no—
71C2×C4×C17—21no—
72C2×C4×C17—22no—
73C2×C4×C17—42no—
74C2×C4×C17—42no—
75C2×C4×C17—42no—
76C2×C4×C17—82no—
77C2×C4×C17—81no—
78C2×C4×C17#12112yes—
79C2×C4×C17#12111yescharacteristic
80C2×C4×C17#12312yes—
81C2×C4×C17#12411yescharacteristic
82C2×Dic17—42no—
83C2×Dic17—42no—
84C2×Dic17—42no—
85C2×Dic17—42no—
86C2×Dic17—42no—
87C2×Dic17—42no—
88C8×C17—42no—
89#3622—44no—
90#2822—171no—
91#1992—172no—
92#1836D1711yescharacteristic
93C2×#330—172no—
94#1295—171no—
95C22×C17#39411yescharacteristic
96C22×C17#45412yes—
97C22×C17#45411yescharacteristic
98C22×C17#45511yescharacteristic
99C22×C17#45612yes—
100C4×C17—22no—
101C4×C17—22no—
102C4×C17—21no—
103C4×C17—21no—
104C4×C17—82no—
105C4×C17—161no—
106Dic17—82no—
107Dic17—82no—
108C2×#125—172no—
109C2×#97—172no—
110C2×#97C2×D1711yescharacteristic
111#400—342no—
112#398—342no—
113#398—342no—
114#384C2×D1711yescharacteristic
115#382C2×D1711yescharacteristic
116#340—22no—
117#340—342no—
118#340—342no—
119#330—344no—
120C2×C17#165811yescharacteristic
121C2×C17#166311yescharacteristic
122C2×C17#166412yes—
123C2×C17#203812yes—
124C2×C17#204011yescharacteristic
125C22×C8—21no—
126C22×C8—342no—
127#125—342no—
128#125—342no—
129#125—342no—
130#125—342no—
131C2×C4⋊C4—22no—
132C2×C4⋊C4—21no—
133C2×C4⋊C4—172no—
134C2×C4⋊C4—172no—
135C2×C4⋊C4—342no—
136C2×C4⋊C4—342no—
137C2×C4⋊C4—342no—
138C2×C4⋊C4C22⋊D1712yes—
139C2×C42C22×D1711yescharacteristic
140#97—21no—
141#97—342no—
142#97—342no—
143#97D6812yes—
144#95—22no—
145#95—344no—
146#95—342no—
147C17#1042811yescharacteristic, complemented, Sylow
148C22×C4—22no—
149C22×C4—41no—
150C22×C4—342no—
151C22×C4—342no—
152C22×C4D4×D1712yes—
153C22×C4C2×C22⋊D1711yescharacteristic
154C2×C8—22no—
155C2×C8—41no—
156C2×C8—41no—
157C2×C8—344no—
158C2×C8—682no—
159C2×C8—682no—
160C4⋊C4—42no—
161C4⋊C4—44no—
162C4⋊C4—42no—
163C4⋊C4—342no—
164C4⋊C4—342no—
165C4⋊C4—342no—
166C4⋊C4—342no—
167C4⋊C4—682no—
168C4⋊C4—682no—
169C4⋊C4—682no—
170C4⋊C4—682no—
171C4⋊C4—1362no—
172C42C2×D6811yescharacteristic
173C42#6325211yescharacteristic
174C42#6325612yes—
175C23#1058762311yescharacteristic
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—82no—
184C2×C4—81no—
185C2×C4—682no—
186C2×C4—682no—
187C2×C4—682no—
188C2×C4—682no—
189C2×C4—682no—
190C2×C4—682no—
191C2×C4#1058758012yes—
192C2×C4#1058758112yes—
193C2×C4#1058761611yescharacteristic
194C2×C4#1058763311yescharacteristic
195C8—42no—
196C8—684no—
197C22#1176272611yescharacteristic
198C22#1176298012yes—
199C22#1176298111yescharacteristic
200C22#1176298611yescharacteristic
201C22#1176299012yes—
202C4—22no—
203C4—22no—
204C4—21no—
205C4—21no—
206C4—82no—
207C4—161no—
208C4—1362no—
209C4—1362no—
210C2#1452808511yescharacteristic
211C2#1452811011yescharacteristic
212C2#1452811712yes—
213C2#1453000312yes—
214C2#1453001311yescharacteristic
subgroupG/H
centerC23#10587623
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1836C2
socle, prime radicalC23×C17#120
hypercenter#1836D17
hypocenterC17#10428
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1836

Complements

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

NH ≅ G/Ntype
147. C17#10428semidirect

Maximal subgroups

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

subgroupindex
#145368522
#145297522
C2×#117625502
#145266652
C17×#18362
#1042817