Finite Group Databasebeta

← #16935662

Subgroups — #16935662

Order 4352.

500 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 97 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×#11763218C212yesmaximal
2#14536852C211yesmaximal, characteristic
3#14529603C211yesmaximal, characteristic
4C2×#11762550C212yesmaximal
5C17×#1295C211yesmaximal, characteristic
6C2×#10587555C2211yescharacteristic
7C2×#10587556C2212yes—
8#11763218—24no—
9#11763218—24no—
10C2×#10587489—22no—
11C2×#10587488—22no—
12C2×#10587481—22no—
13C2×#10587474C2211yescharacteristic
14#11762749—22no—
15#11762741—22no—
16#11762739—22no—
17#11762550—24no—
18C2×C17×#97C2212yes—
19C17×#382C2211yescharacteristic
20C22×Dic34—21no—
21C22×C8×C17—22no—
22C2×C4⋊C4×C17D412yes—
23C2×C42×C17C2311yescharacteristic
24C2×C4⋊Dic17—22no—
25C2×C4⋊Dic17—22no—
26C2×C4⋊Dic17D412yes—
27C2×C4⋊Dic17D412yes—
28C2×#63225—22no—
29C2×#63225—22no—
30C22×#3622—21no—
31#10587556—22no—
32#10587556—22no—
33#10587556—22no—
34#10587556—22no—
35#10587555—22no—
36#10587555—21no—
37#10587555D412yes—
38C17×#97—22no—
39C17×#97D414yes—
40C17×#95—22no—
41#10587502—24no—
42#10587502—22no—
43#10587489—28no—
44#10587488—28no—
45#10587481—44no—
46#10587474—22no—
47C22×C4×C17—22no—
48C22×C4×C17C2×D411yescharacteristic
49C22×C4×C17C2×D412yes—
50C22×Dic17—22no—
51C22×Dic17—22no—
52C22×Dic17—41no—
53C2×Dic34—22no—
54C2×Dic34—42no—
55C2×Dic34—42no—
56C2×Dic34—41no—
57C2×C8×C17—28no—
58C2×C8×C17—24no—
59C4⋊C4×C17—42no—
60C42×C17C2×D412yes—
61C42×C17C2×D411yescharacteristic
62C42×C17#4111yescharacteristic
63C4⋊Dic17—22no—
64C4⋊Dic17—24no—
65C4⋊Dic17—22no—
66C4⋊Dic17—22no—
67C4⋊Dic17—22no—
68C4⋊Dic17—42no—
69C4⋊Dic17—82no—
70#63225—42no—
71#63225—42no—
72#63225—42no—
73#63225—42no—
74C2×#3622—22no—
75C2×#3622—41no—
76C2×#3622—41no—
77#10087—171nomaximal, Sylow
78C23×C17#12011yescharacteristic
79C2×C4×C17—21no—
80C2×C4×C17—21no—
81C2×C4×C17—24no—
82C2×C4×C17—42no—
83C2×C4×C17—44no—
84C2×C4×C17#12012yes—
85C2×C4×C17#12111yescharacteristic
86C2×C4×C17#12112yes—
87C2×C4×C17#12711yescharacteristic
88C2×Dic17—42no—
89C2×Dic17—42no—
90C2×Dic17—42no—
91C2×Dic17—42no—
92C2×Dic17—42no—
93C2×Dic17—44no—
94C2×Dic17—81no—
95C2×Dic17—81no—
96Dic34—44no—
97Dic34—82no—
98C8×C17—28no—
99#3622—42no—
100C2×#501—172no—
101#2822—171no—
102#1960—171no—
103C2×#330—172no—
104#1295D1711yescharacteristic
105C22×C17#39211yescharacteristic
106C22×C17#45311yescharacteristic
107C22×C17#45411yescharacteristic
108C22×C17#45614yes—
109C4×C17—22no—
110C4×C17—22no—
111C4×C17—21no—
112C4×C17—21no—
113C4×C17—82no—
114Dic17—82no—
115Dic17—82no—
116Dic17—82no—
117C2×C4⋊Q8—171no—
118C2×#125—172no—
119#501—344no—
120#501—344no—
121C2×#107—342no—
122C2×#106—342no—
123C2×#103—342no—
124C2×#97—171no—
125C2×#97C2×D1712yes—
126#400—342no—
127#398—342no—
128#398—342no—
129#382C2×D1711yescharacteristic
130#330—344no—
131C2×C17#166012yes—
132C2×C17#166312yes—
133C2×C17#200512yes—
134C2×C17#200611yescharacteristic
135C22×Q8—341no—
136C22×C8—22no—
137C22×C8—341no—
138C4⋊Q8—172no—
139C4⋊Q8—342no—
140C4⋊Q8—341no—
141#125—342no—
142#125—342no—
143#125—342no—
144#125—342no—
145C2×C4⋊C4—172no—
146C2×C4⋊C4—172no—
147C2×C4⋊C4—342no—
148C2×C4⋊C4—342no—
149C2×C4⋊C4—342no—
150C2×C4⋊C4—342no—
151C2×C4⋊C4D6812yes—
152C2×C42C22×D1711yescharacteristic
153#107—348no—
154#106—348no—
155#103—684no—
156#97—22no—
157#97—342no—
158#97D6814yes—
159#95—22no—
160#95—344no—
161#95—342no—
162C17#1008711yescharacteristic, complemented, Sylow
163C2×Q8—342no—
164C2×Q8—682no—
165C2×Q8—682no—
166C2×Q8—681no—
167C22×C4—22no—
168C22×C4—342no—
169C22×C4—342no—
170C22×C4—681no—
171C22×C4C2×D6811yescharacteristic
172C22×C4D4×D1712yes—
173C2×C8—28no—
174C2×C8—24no—
175C2×C8—342no—
176C2×C8—681no—
177C2×C8—681no—
178C4⋊C4—42no—
179C4⋊C4—342no—
180C4⋊C4—344no—
181C4⋊C4—342no—
182C4⋊C4—342no—
183C4⋊C4—342no—
184C4⋊C4—682no—
185C4⋊C4—682no—
186C4⋊C4—682no—
187C4⋊C4—682no—
188C4⋊C4—682no—
189C4⋊C4—1362no—
190C42C2×D6812yes—
191C42D4×D1711yescharacteristic
192C42#6325611yescharacteristic
193C23#1058756811yescharacteristic
194Q8—684no—
195Q8—1362no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—24no—
199C2×C4—42no—
200C2×C4—44no—
201C2×C4—682no—
202C2×C4—682no—
203C2×C4—682no—
204C2×C4—682no—
205C2×C4—682no—
206C2×C4—684no—
207C2×C4—1361no—
208C2×C4—1361no—
209C2×C4#1058756011yescharacteristic
210C2×C4#1058756812yes—
211C2×C4#1058758112yes—
212C2×C4#1058758111yescharacteristic
213C8—28no—
214C8—682no—
215C22#1176271911yescharacteristic
216C22#1176297911yescharacteristic
217C22#1176298411yescharacteristic
218C22#1176299314yes—
219C4—22no—
220C4—22no—
221C4—21no—
222C4—21no—
223C4—82no—
224C4—1362no—
225C4—1362no—
226C4—1362no—
227C2#1452809612yes—
228C2#1452811312yes—
229C2#1452982312yes—
230C2#1452982811yescharacteristic
subgroupG/H
centerC23#10587568
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1295C2
socle, prime radicalC23×C17#120
hypercenter#1295D17
hypocenterC17#10087
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
162. C17#10087semidirect

Maximal subgroups

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

subgroupindex
C2×#117632182
#145368522
#145296032
C2×#117625502
C17×#12952
#1008717