Finite Group Databasebeta

← #16923634

Subgroups — #16923634

Order 4352.

350 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 87 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#14530347C212yesmaximal
2#14530322C211yesmaximal, characteristic
3#14526610C211yesmaximal, characteristic
4#14526607C212yesmaximal
5C17×#2809C211yesmaximal, characteristic
6C2×#10587478—21no—
7C2×#10587506—21no—
8#11762679C2211yescharacteristic
9#11762571—22no—
10#11762571—22no—
11#11762564C2211yescharacteristic
12#11762564C2212yes—
13C17×#400—21no—
14C17×#398—22no—
15C17×#391—21no—
16C17×#391C2211yescharacteristic
17C17×#389C2212yes—
18C17×#387—22no—
19C22×Q8×C17D411yescharacteristic
20C2×C4⋊C4×C17—22no—
21C2×C4⋊C4×C17—21no—
22C2×C4⋊C4×C17—21no—
23C2×C4⋊C4×C17D412yes—
24C2×C4⋊C4×C17D412yes—
25C2×C4⋊C4×C17D411yescharacteristic
26C2×C42×C17—21no—
27C2×C42×C17C2311yescharacteristic
28C2×C4⋊Dic17—21no—
29C2×C4⋊Dic17—22no—
30C22×#3622—21no—
31C22×#3622—22no—
32C17×#95—21no—
33C17×#95—22no—
34C17×#95—22no—
35C17×#95—22no—
36C17×#95—22no—
37#10587506—42no—
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×C17—22no—
46C22×C4×C17—22no—
47C22×C4×C17C2×D411yescharacteristic
48C22×C4×C17C2×D412yes—
49C22×Dic17—41no—
50C4⋊C4×C17—22no—
51C4⋊C4×C17—22no—
52C4⋊C4×C17—41no—
53C4⋊C4×C17—42no—
54C4⋊C4×C17—42no—
55C4⋊C4×C17—42no—
56C4⋊C4×C17—81no—
57C4⋊C4×C17—81no—
58C42×C17—41no—
59C42×C17—81no—
60C4⋊Dic17—41no—
61C4⋊Dic17—41no—
62C4⋊Dic17—44no—
63C2×#3622—22no—
64C2×#3622—41no—
65C2×#3622—41no—
66C2×#3622—42no—
67C2×#3622—42no—
68C2×#3622—42no—
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—42no—
81C2×C4×C17—42no—
82C2×C4×C17—42no—
83C2×C4×C17—41no—
84C2×C4×C17—42no—
85C2×C4×C17—42no—
86C2×C4×C17—42no—
87C2×C4×C17—42no—
88C2×C4×C17C2×Q1611yescharacteristic
89C2×C4×C17#13512yes—
90C2×C4×C17#13711yescharacteristic
91C2×C4×C17#13712yes—
92C2×Dic17—81no—
93C2×Dic17—82no—
94#3622—42no—
95#3622—82no—
96#2809D1711yescharacteristic
97#2100—172no—
98#2095—171no—
99#1272—171no—
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—82no—
112C4×C17—82no—
113C4×C17—81no—
114Dic17—161no—
115C2×#107—341no—
116C2×#103—341no—
117#400—21no—
118#398—22no—
119#391—21no—
120#391C2×D1711yescharacteristic
121#389C2×D1712yes—
122#387—22no—
123#384—171no—
124#340—342no—
125#340—342no—
126#336—171no—
127#336—172no—
128C2×C17#161411yescharacteristic
129C2×C17#161512yes—
130C2×C17#163411yescharacteristic
131C2×C17#163612yes—
132C2×C17#165711yescharacteristic
133C22×Q8C22⋊D1711yescharacteristic
134C22×C8—341no—
135C22×C8—342no—
136C2×C4⋊C4—22no—
137C2×C4⋊C4—21no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4—342no—
140C2×C4⋊C4—341no—
141C2×C4⋊C4C22⋊D1712yes—
142C2×C4⋊C4C22⋊D1712yes—
143C2×C4⋊C4C22⋊D1711yescharacteristic
144C2×C42—21no—
145C2×C42C22×D1711yescharacteristic
146#107—682no—
147#103—682no—
148#95—21no—
149#95—22no—
150#95—22no—
151#95—22no—
152#95—22no—
153C17#783111yescharacteristic, complemented, Sylow
154C2×Q8—21no—
155C2×Q8—41no—
156C2×Q8—41no—
157C2×Q8#6323112yes—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—22no—
161C22×C4—22no—
162C22×C4—681no—
163C22×C4C2×C22⋊D1711yescharacteristic
164C22×C4C2×C22⋊D1712yes—
165C2×C8—342no—
166C2×C8—681no—
167C2×C8—681no—
168C2×C8—682no—
169C2×C8—682no—
170C2×C8—682no—
171C4⋊C4—22no—
172C4⋊C4—22no—
173C4⋊C4—41no—
174C4⋊C4—42no—
175C4⋊C4—42no—
176C4⋊C4—42no—
177C4⋊C4—81no—
178C4⋊C4—81no—
179C4⋊C4—681no—
180C4⋊C4—681no—
181C4⋊C4—684no—
182C42—41no—
183C42—81no—
184C23#1058763911yescharacteristic
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—42no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4—41no—
198C2×C4—42no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—42no—
202C2×C4—1361no—
203C2×C4—1362no—
204C2×C4#1058762811yescharacteristic
205C2×C4C2×#6323111yescharacteristic
206C2×C4#1058763612yes—
207C2×C4#1058763712yes—
208C8—682no—
209C8—1362no—
210C22#1176296511yescharacteristic
211C22#1176297112yes—
212C22#1176297711yescharacteristic
213C22#1176298212yes—
214C22#1176299911yescharacteristic
215C4—21no—
216C4—21no—
217C4—22no—
218C4—22no—
219C4—42no—
220C4—82no—
221C4—81no—
222C4—82no—
223C4—2721no—
224C2#1452780911yescharacteristic
225C2#1452781512yes—
226C2#1452792911yescharacteristic
227C2#1452794212yes—
228C2#1452808211yescharacteristic
subgroupG/H
centerC23#10587639
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#2809C2
socle, prime radicalC23×C17#120
hypercenter#2809D17
hypocenterC17#7831
LCSG ▷ C2×C42×C17 ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2809

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
#145303472
#145303222
#145266102
#145266072
C17×#28092
#783117