Finite Group Databasebeta

← #16931734

Subgroups — #16931734

Order 4352.

486 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 119 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#14533769C211yesmaximal, characteristic
2#14528780C211yesmaximal, characteristic
3#14527455C212yesmaximal
4#14526686C212yesmaximal
5C17×#2983C211yesmaximal, characteristic
6C2×#10587555C2211yescharacteristic
7C2×#10587630—21no—
8#11762833C2212yes—
9C2×#10587507—21no—
10#11762739C414yes—
11#11762714—21no—
12#11762707—22no—
13C4×C4⋊Dic17C2211yescharacteristic
14#11762578—21no—
15#11762554—24no—
16C2×C4×Q8×C17C2211yescharacteristic
17C17×#446—24no—
18C17×#432—22no—
19C17×#431C2212yes—
20C22×Q8×C17D411yescharacteristic
21C22×Dic34—21no—
22C4×Q8×C17—22no—
23C4×Q8×C17—22no—
24C2×C4⋊C4×C17C2×C412yes—
25C2×C4⋊C4×C17D411yescharacteristic
26C2×C42×C17D412yes—
27C2×C42×C17C2311yescharacteristic
28#10587630—44no—
29C2×C4⋊Dic17—21no—
30C2×C4⋊Dic17—21no—
31C2×C4⋊Dic17C2×C412yes—
32C2×#63225—24no—
33C2×C4×Dic17—21no—
34C2×#63223—22no—
35#10587555—22no—
36#10587555—22no—
37C17×C4⋊C8—24no—
38C17×C4⋊C8D414yes—
39C17×C22⋊C8—22no—
40C17×#97—24no—
41C4×C8×C17—22no—
42#10587507—42no—
43#10587502—24no—
44#10587502C2×C412yes—
45C4⋊#3622—22no—
46C4⋊#3622—22no—
47C2×Q8×C17—22no—
48C2×Q8×C17—21no—
49C2×Q8×C17—22no—
50C2×Q8×C17—21no—
51C22×C4×C17C22⋊C412yes—
52C22×C4×C17C22⋊C412yes—
53C22×C4×C17C22×C411yescharacteristic
54C22×C4×C17C2×D411yescharacteristic
55C22×C4×C17C2×D411yescharacteristic
56C22×Dic17—22no—
57C22×Dic17—22no—
58C2×Dic34—42no—
59C2×Dic34—41no—
60C2×Dic34—42no—
61C2×Dic34—41no—
62C2×C8×C17—24no—
63C4⋊C4×C17—24no—
64C4⋊C4×C17—22no—
65C42×C17—22no—
66C42×C17—22no—
67C42×C17C2×D412yes—
68C42×C17#4112yes—
69C4⋊Dic17—24no—
70C4⋊Dic17—24no—
71C4⋊Dic17—41no—
72C4⋊Dic17—41no—
73#63225—48no—
74C4×Dic17—42no—
75#63223—42no—
76#63223—42no—
77C2×#3622—42no—
78#9402—171nomaximal, Sylow
79C23×C17C2×C22⋊C411yescharacteristic
80Q8×C17—42no—
81Q8×C17—42no—
82C2×C4×C17—22no—
83C2×C4×C17—22no—
84C2×C4×C17—22no—
85C2×C4×C17—22no—
86C2×C4×C17—22no—
87C2×C4×C17—41no—
88C2×C4×C17—42no—
89C2×C4×C17C4×D412yes—
90C2×C4×C17#12011yescharacteristic
91C2×C4×C17#12112yes—
92C2×C4×C17#12311yescharacteristic
93C2×C4×C17AGL(1,ℤ/8)12yes—
94C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
95C2×C4×C17#13711yescharacteristic
96C2×Dic17—24no—
97C2×Dic17—42no—
98C2×Dic17—42no—
99C2×Dic17—42no—
100C2×Dic17—42no—
101C2×Dic17—42no—
102Dic34—82no—
103Dic34—82no—
104C8×C17—44no—
105#3622—82no—
106#2983D1711yescharacteristic
107#2546—171no—
108#1801—171no—
109#1546—172no—
110#1303—172no—
111C22×C17—21no—
112C22×C17—21no—
113C22×C17#38611yescharacteristic
114C22×C17#41711yescharacteristic
115C22×C17#41811yescharacteristic
116C4×C17—21no—
117C4×C17—22no—
118C4×C17—42no—
119C4×C17—42no—
120C4×C17#45612yes—
121C4×C17#46812yes—
122C4×C17#46912yes—
123Dic17—44no—
124Dic17—82no—
125C2×C4⋊Q8—171no—
126C2×C4⋊Q8—341no—
127C2×C4×Q8C2×D1711yescharacteristic
128#446—24no—
129#432—22no—
130#431C2×D1712yes—
131#423—172no—
132C2×#101—341no—
133#398—174no—
134#391—341no—
135#389—342no—
136C4×C4⋊C4—171no—
137#343—341no—
138#332—344no—
139C2×C17—21no—
140C2×C17—21no—
141C2×C17#188611yescharacteristic
142C2×C17#189511yescharacteristic
143C2×C17#191511yescharacteristic
144C22×Q8—341no—
145C22×Q8D6811yescharacteristic
146C2×M16—342no—
147C4⋊Q8—342no—
148C4⋊Q8—342no—
149C4⋊Q8—684no—
150C4×Q8—22no—
151C4×Q8—22no—
152C2×C4⋊C4—172no—
153C2×C4⋊C4—341no—
154C2×C4⋊C4—341no—
155C2×C4⋊C4—344no—
156C2×C4⋊C4C4×D1712yes—
157C2×C4⋊C4D6811yescharacteristic
158C2×C42—341no—
159C2×C42C22⋊D1712yes—
160C2×C42C22×D1711yescharacteristic
161C4⋊C8—24no—
162C4⋊C8—342no—
163C4⋊C8—342no—
164C4⋊C8C22⋊D1714yes—
165#101—682no—
166C22⋊C8—22no—
167#97—24no—
168C4×C8—22no—
169#95—172no—
170#95—344no—
171C17#940211yescharacteristic, complemented, Sylow
172C2×Q8—21no—
173C2×Q8—22no—
174C2×Q8—21no—
175C2×Q8—22no—
176C2×Q8—682no—
177C2×Q8—681no—
178C2×Q8—681no—
179C2×Q8—682no—
180C22×C4—342no—
181C22×C4—342no—
182C22×C4#6322712yes—
183C22×C4#6322712yes—
184C22×C4C2×C4×D1711yescharacteristic
185C22×C4C2×D6811yescharacteristic
186C22×C4C2×C22⋊D1711yescharacteristic
187M16—682no—
188M16—682no—
189C2×C8—24no—
190C2×C8—682no—
191C4⋊C4—24no—
192C4⋊C4—22no—
193C4⋊C4—344no—
194C4⋊C4—344no—
195C4⋊C4—688no—
196C4⋊C4—681no—
197C4⋊C4—681no—
198C42—22no—
199C42—22no—
200C42—682no—
201C42#6325212yes—
202C42C2×C22⋊D1712yes—
203C23C2×#6322711yescharacteristic
204Q8—42no—
205Q8—42no—
206Q8—1362no—
207Q8—1362no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—41no—
214C2×C4—42no—
215C2×C4—344no—
216C2×C4—682no—
217C2×C4—682no—
218C2×C4—682no—
219C2×C4—682no—
220C2×C4—682no—
221C2×C4#1058759412yes—
222C2×C4#1058759411yescharacteristic
223C2×C4#1058759511yescharacteristic
224C2×C4C4×C22⋊D1712yes—
225C2×C4#1058761511yescharacteristic
226C2×C4#1058761612yes—
227C2×C4#1058763911yescharacteristic
228C8—44no—
229C8—1362no—
230C22—21no—
231C22—21no—
232C22#1176268811yescharacteristic
233C22#1176281111yescharacteristic
234C22#1176281511yescharacteristic
235C4—22no—
236C4—21no—
237C4—42no—
238C4—42no—
239C4—684no—
240C4—1362no—
241C4#1176299212yes—
242C4#1176305512yes—
243C4#1176306212yes—
244C2—21no—
245C2—21no—
246C2#1452917711yescharacteristic
247C2#1452922211yescharacteristic
248C2#1452933611yescharacteristic
subgroupG/H
centerC22#11762688
commutatorC22×C4×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#2983C2
socleC22×C17#386
prime radicalC23×C17C2×C22⋊C4
cosocleC2×C42×C17C23
hypercenter#2983D17
hypocenterC17#9402
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2983

Complements

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

NH ≅ G/Ntype
171. C17#9402semidirect

Maximal subgroups

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

subgroupindex
#145337692
#145287802
#145274552
#145266862
C17×#29832
#940217