Finite Group Databasebeta

← #16937820

Subgroups — #16937820

Order 4352.

402 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 93 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#14529754C212yesmaximal
2#14528953C211yesmaximal, characteristic
3C2×#11762551C212yesmaximal
4#14526665C211yesmaximal, characteristic
5C17×#2822C211yesmaximal, characteristic
6C2×#10587478—21no—
7C2×#10587479—21no—
8C2×#10587474C2212yes—
9C2×#10587474C2211yescharacteristic
10#11762679C2211yescharacteristic
11#11762571—22no—
12#11762571—22no—
13#11762551—24no—
14C2×C17×#125C2212yes—
15C17×#400—22no—
16C17×#398—21no—
17C17×#398—21no—
18C17×#398—22no—
19C17×#382C2211yescharacteristic
20C17×#125—22no—
21C17×#125—22no—
22C17×#125—22no—
23C17×#125—22no—
24C2×C4⋊C4×C17—22no—
25C2×C4⋊C4×C17—22no—
26C2×C4⋊C4×C17—21no—
27C2×C4⋊C4×C17—21no—
28C2×C4⋊C4×C17D412yes—
29C2×C4⋊C4×C17D412yes—
30C2×C4⋊C4×C17D411yescharacteristic
31C2×C4⋊C4×C17D411yescharacteristic
32C2×C42×C17C2311yescharacteristic
33C2×C4⋊Dic17—22no—
34C2×C4⋊Dic17—21no—
35C22×#3622—21no—
36C22×#3622—22no—
37C17×#95—22no—
38C17×#95—22no—
39C17×#95—21no—
40C17×#95—21no—
41C17×#95—22no—
42#10587479—42no—
43#10587478—42no—
44#10587474—22no—
45#10587474—21no—
46#10587474—22no—
47#10587474D412yes—
48C22×C4×C17—21no—
49C22×C4×C17—21no—
50C22×C4×C17—22no—
51C22×C4×C17—22no—
52C22×C4×C17C2×D412yes—
53C22×C4×C17C2×D411yescharacteristic
54C22×Dic17—41no—
55C4⋊C4×C17—22no—
56C4⋊C4×C17—22no—
57C4⋊C4×C17—22no—
58C4⋊C4×C17—22no—
59C4⋊C4×C17—41no—
60C4⋊C4×C17—41no—
61C4⋊C4×C17—42no—
62C4⋊C4×C17—42no—
63C4⋊C4×C17—42no—
64C4⋊C4×C17—42no—
65C4⋊C4×C17—81no—
66C4⋊C4×C17—81no—
67C42×C17C2×D411yescharacteristic
68C42×C17#4111yescharacteristic
69C42×C17#4112yes—
70C4⋊Dic17—41no—
71C4⋊Dic17—41no—
72C4⋊Dic17—44no—
73C2×#3622—22no—
74C2×#3622—22no—
75C2×#3622—22no—
76C2×#3622—24no—
77C2×#3622—42no—
78C2×#3622—42no—
79#10429—171nomaximal, Sylow
80C23×C17#12011yescharacteristic
81C2×C4×C17—21no—
82C2×C4×C17—22no—
83C2×C4×C17—22no—
84C2×C4×C17—21no—
85C2×C4×C17—42no—
86C2×C4×C17—42no—
87C2×C4×C17—41no—
88C2×C4×C17—41no—
89C2×C4×C17—42no—
90C2×C4×C17—42no—
91C2×C4×C17—42no—
92C2×C4×C17—42no—
93C2×C4×C17—42no—
94C2×C4×C17—42no—
95C2×C4×C17#12111yescharacteristic
96C2×C4×C17#12112yes—
97C2×C4×C17#12312yes—
98C2×C4×C17#12411yescharacteristic
99C2×Dic17—81no—
100C2×Dic17—82no—
101#3622—24no—
102#3622—44no—
103#2822D1711yescharacteristic
104#1992—172no—
105#1847—171no—
106C2×#330—172no—
107#1295—171no—
108C22×C17#39411yescharacteristic
109C22×C17#45311yescharacteristic
110C22×C17#45412yes—
111C22×C17#45612yes—
112C22×C17#45611yescharacteristic
113C4×C17—22no—
114C4×C17—22no—
115C4×C17—21no—
116C4×C17—21no—
117C4×C17—81no—
118C4×C17—81no—
119C4×C17—82no—
120C4×C17—82no—
121Dic17—161no—
122C2×#125C2×D1712yes—
123C2×#107—341no—
124C2×#106—341no—
125C2×#97—171no—
126C2×#97—172no—
127#400—22no—
128#398—21no—
129#398—21no—
130#398—22no—
131#384—171no—
132#382C2×D1711yescharacteristic
133#340—342no—
134#340—342no—
135#330—344no—
136C2×C17#165711yescharacteristic
137C2×C17#166011yescharacteristic
138C2×C17#166312yes—
139C2×C17#203812yes—
140C2×C17#203911yescharacteristic
141C22×C8—341no—
142C22×C8—342no—
143#125—22no—
144#125—22no—
145#125—22no—
146#125—22no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—342no—
152C2×C4⋊C4—341no—
153C2×C4⋊C4C22⋊D1712yes—
154C2×C4⋊C4C22⋊D1712yes—
155C2×C4⋊C4C22⋊D1711yescharacteristic
156C2×C4⋊C4C22⋊D1711yescharacteristic
157C2×C42C22×D1711yescharacteristic
158#107—682no—
159#106—682no—
160#97—172no—
161#97—342no—
162#97—341no—
163#97—342no—
164#95—22no—
165#95—22no—
166#95—21no—
167#95—21no—
168#95—22no—
169C17#1042911yescharacteristic, complemented, Sylow
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—22no—
173C22×C4—22no—
174C22×C4—681no—
175C22×C4C2×C22⋊D1712yes—
176C22×C4C2×C22⋊D1711yescharacteristic
177C2×C8—342no—
178C2×C8—342no—
179C2×C8—342no—
180C2×C8—344no—
181C2×C8—682no—
182C2×C8—682no—
183C4⋊C4—22no—
184C4⋊C4—22no—
185C4⋊C4—22no—
186C4⋊C4—22no—
187C4⋊C4—41no—
188C4⋊C4—41no—
189C4⋊C4—42no—
190C4⋊C4—42no—
191C4⋊C4—42no—
192C4⋊C4—42no—
193C4⋊C4—81no—
194C4⋊C4—81no—
195C4⋊C4—681no—
196C4⋊C4—681no—
197C4⋊C4—684no—
198C42D4×D1711yescharacteristic
199C42#6325411yescharacteristic
200C42#6325412yes—
201C23#1058763911yescharacteristic
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—1361no—
217C2×C4—1362no—
218C2×C4#1058762112yes—
219C2×C4#1058762211yescharacteristic
220C2×C4#1058762411yescharacteristic
221C2×C4#1058762512yes—
222C8—344no—
223C8—684no—
224C22#1176272311yescharacteristic
225C22#1176297711yescharacteristic
226C22#1176298212yes—
227C22#1176299212yes—
228C22#1176299211yescharacteristic
229C4—22no—
230C4—22no—
231C4—21no—
232C4—21no—
233C4—81no—
234C4—81no—
235C4—82no—
236C4—82no—
237C4—2721no—
238C2#1452808211yescharacteristic
239C2#1452809511yescharacteristic
240C2#1452811212yes—
241C2#1452999812yes—
242C2#1453000511yescharacteristic
subgroupG/H
centerC23#10587639
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#2822C2
socle, prime radicalC23×C17#120
hypercenter#2822D17
hypocenterC17#10429
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2822

Complements

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

NH ≅ G/Ntype
169. C17#10429semidirect

Maximal subgroups

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

subgroupindex
#145297542
#145289532
C2×#117625512
#145266652
C17×#28222
#1042917