Finite Group Databasebeta

← #16923636

Subgroups — #16923636

Order 4352.

350 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 83 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#14536772C211yesmaximal, characteristic
2#14530348C212yesmaximal
3#14530322C211yesmaximal, characteristic
4#14526608C212yesmaximal
5C17×#1272C211yesmaximal, characteristic
6C2×#10587478—21no—
7C2×#10587506—21no—
8#11762748—21no—
9#11762741—22no—
10#11762716—21no—
11#11762707C2212yes—
12#11762696—22no—
13#11762679C2211yescharacteristic
14#11762572—22no—
15#11762572—22no—
16#11762564C2211yescharacteristic
17C17×#391C2211yescharacteristic
18C17×#336C2212yes—
19C22×Q8×C17D411yescharacteristic
20C22×C8×C17—22no—
21C2×C4⋊C4×C17D411yescharacteristic
22C2×C42×C17C2311yescharacteristic
23C2×C4⋊Dic17—21no—
24C2×C4⋊Dic17—21no—
25C2×C4⋊Dic17—21no—
26C2×C4⋊Dic17—22no—
27C2×C4⋊Dic17D412yes—
28C2×C4⋊Dic17D412yes—
29C2×#63225—22no—
30C2×C4×Dic17—21no—
31C22×#3622—21no—
32C17×#95—22no—
33#10587506—42no—
34#10587502—21no—
35#10587502—22no—
36#10587502—22no—
37#10587502—22no—
38#10587478—42no—
39C2×Q8×C17—21no—
40C2×Q8×C17—41no—
41C2×Q8×C17—41no—
42C2×Q8×C17Q1612yes—
43C22×C4×C17—21no—
44C22×C4×C17—21no—
45C22×C4×C17C2×D411yescharacteristic
46C22×C4×C17C2×D412yes—
47C22×Dic17—22no—
48C22×Dic17—22no—
49C22×Dic17—41no—
50C2×C8×C17—42no—
51C2×C8×C17—42no—
52C2×C8×C17—42no—
53C4⋊C4×C17—41no—
54C42×C17—41no—
55C4⋊Dic17—22no—
56C4⋊Dic17—22no—
57C4⋊Dic17—42no—
58C4⋊Dic17—41no—
59C4⋊Dic17—41no—
60C4⋊Dic17—44no—
61C4⋊Dic17—81no—
62C4⋊Dic17—81no—
63#63225—42no—
64#63225—42no—
65C4×Dic17—81no—
66C2×#3622—22no—
67C2×#3622—41no—
68C2×#3622—41no—
69#7831—171nomaximal, Sylow
70C23×C17#12011yescharacteristic
71Q8×C17—42no—
72Q8×C17—81no—
73C2×C4×C17—21no—
74C2×C4×C17—22no—
75C2×C4×C17—22no—
76C2×C4×C17—21no—
77C2×C4×C17—22no—
78C2×C4×C17—41no—
79C2×C4×C17—41no—
80C2×C4×C17—41no—
81C2×C4×C17—42no—
82C2×C4×C17C2×Q1611yescharacteristic
83C2×C4×C17#13512yes—
84C2×C4×C17#13711yescharacteristic
85C2×C4×C17#13712yes—
86C2×Dic17—42no—
87C2×Dic17—42no—
88C2×Dic17—42no—
89C2×Dic17—42no—
90C2×Dic17—42no—
91C2×Dic17—42no—
92C2×Dic17—81no—
93C2×Dic17—82no—
94C8×C17—82no—
95#3622—42no—
96#2809—171no—
97#2100—172no—
98#2095—171no—
99#1272D1711yescharacteristic
100#1271—172no—
101C22×C17#45111yescharacteristic
102C22×C17#45212yes—
103C22×C17#45311yescharacteristic
104C22×C17#45412yes—
105C22×C17#45811yescharacteristic
106C4×C17—21no—
107C4×C17—21no—
108C4×C17—22no—
109C4×C17—22no—
110C4×C17—42no—
111C4×C17—81no—
112Dic17—82no—
113Dic17—82no—
114Dic17—161no—
115C2×#107—341no—
116C2×#103—341no—
117#400—341no—
118#398—342no—
119#391—341no—
120#391C2×D1711yescharacteristic
121#389—172no—
122#387—342no—
123#384—171no—
124#340—342no—
125#340—342no—
126#336—171no—
127#336C2×D1712yes—
128C2×C17#161411yescharacteristic
129C2×C17#161512yes—
130C2×C17#163411yescharacteristic
131C2×C17#163612yes—
132C2×C17#165711yescharacteristic
133C22×Q8D6811yescharacteristic
134C22×C8—22no—
135C22×C8—341no—
136C2×C4⋊C4—172no—
137C2×C4⋊C4—172no—
138C2×C4⋊C4—342no—
139C2×C4⋊C4—341no—
140C2×C4⋊C4—342no—
141C2×C4⋊C4—341no—
142C2×C4⋊C4—341no—
143C2×C4⋊C4D6811yescharacteristic
144C2×C42—341no—
145C2×C42C22×D1711yescharacteristic
146#107—682no—
147#103—682no—
148#95—22no—
149#95—341no—
150#95—342no—
151#95—342no—
152#95—342no—
153C17#783111yescharacteristic, complemented, Sylow
154C2×Q8—21no—
155C2×Q8—41no—
156C2×Q8—41no—
157C2×Q8Dic6812yes—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—342no—
161C22×C4—342no—
162C22×C4—681no—
163C22×C4C2×D6811yescharacteristic
164C22×C4D4×D1712yes—
165C2×C8—42no—
166C2×C8—42no—
167C2×C8—42no—
168C2×C8—342no—
169C2×C8—681no—
170C2×C8—681no—
171C4⋊C4—41no—
172C4⋊C4—342no—
173C4⋊C4—342no—
174C4⋊C4—682no—
175C4⋊C4—681no—
176C4⋊C4—681no—
177C4⋊C4—684no—
178C4⋊C4—682no—
179C4⋊C4—682no—
180C4⋊C4—1361no—
181C4⋊C4—1361no—
182C42—41no—
183C42—1361no—
184C23#1058756811yescharacteristic
185Q8—42no—
186Q8—81no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—42no—
196C2×C4—682no—
197C2×C4—682no—
198C2×C4—682no—
199C2×C4—682no—
200C2×C4—682no—
201C2×C4—682no—
202C2×C4—1361no—
203C2×C4—1362no—
204C2×C4C2×Dic6811yescharacteristic
205C2×C4#1058759511yescharacteristic
206C2×C4#1058760212yes—
207C2×C4#1058760412yes—
208C8—82no—
209C8—682no—
210C22#1176296711yescharacteristic
211C22#1176297412yes—
212C22#1176297911yescharacteristic
213C22#1176298312yes—
214C22#1176300011yescharacteristic
215C4—21no—
216C4—21no—
217C4—22no—
218C4—22no—
219C4—42no—
220C4—81no—
221C4—2721no—
222C4—1362no—
223C4—1362no—
224C2#1452781111yescharacteristic
225C2#1452781812yes—
226C2#1452793011yescharacteristic
227C2#1452794512yes—
228C2#1452808311yescharacteristic
subgroupG/H
centerC23#10587568
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1272C2
socle, prime radicalC23×C17#120
hypercenter#1272D17
hypocenterC17#7831
LCSG ▷ C2×C42×C17 ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
153. C17#7831semidirect

Maximal subgroups

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

subgroupindex
#145367722
#145303482
#145303222
#145266082
C17×#12722
#783117