Finite Group Databasebeta

← #16945076

Subgroups — #16945076

Order 4352.

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

normal subgroups only

This group has 368 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#14528867C211yesmaximal, characteristic
2#14527118C211yesmaximal, characteristic
3#14526811C214yesmaximal, complemented
4C17×#2628C211yesmaximal, characteristic
5#11762866—21no—
6#11762773—21no—
7#11762578—21no—
8#11762578C2212yes—
9#11762535C2212yes—
10#11762533—21no—
11C2×C17×C4⋊Q8C411yescharacteristic
12C2×C17×#117C2211yescharacteristic
13C17×#400C2212yes—
14C17×#399C412yes—
15C17×#395—21no—
16C17×#393—21no—
17C17×#389—21no—
18C17×#382C411yescharacteristic
19C17×#380—21no—
20C22×Q8×C17—21no—
21C23×C4×C17D411yescharacteristic
22C17×C4⋊Q8—41no—
23C17×C4⋊Q8—41no—
24C17×#117—41no—
25C17×#117—41no—
26C2×C4⋊C4×C17—21no—
27C2×C4⋊C4×C17—21no—
28C2×C4⋊C4×C17—22no—
29C2×C4⋊C4×C17C2×C412yes—
30C2×C4⋊C4×C17D411yescharacteristic
31C2×C4⋊C4×C17C2311yescharacteristic
32C2×C22⋊C4×C17—22no—
33C2×C22⋊C4×C17C2×C411yescharacteristic
34C2×C22⋊C4×C17D411yescharacteristic
35C2×C42×C17C2×C411yescharacteristic
36C2×C42×C17D411yescharacteristic
37C2×#63223—22no—
38C17×#95—21no—
39C17×#95—22no—
40C17×#95—22no—
41C17×#95C2×C412yes—
42C22⋊#3622—22no—
43C22⋊#3622—41no—
44C22⋊#3622—41no—
45C4⋊#3622—41no—
46#10587474—41no—
47C24×C17C22⋊C411yescharacteristic
48C2×Q8×C17—42no—
49C2×Q8×C17—82no—
50C22×C4×C17—21no—
51C22×C4×C17—21no—
52C22×C4×C17—22no—
53C22×C4×C17—22no—
54C22×C4×C17—22no—
55C22×C4×C17—41no—
56C22×C4×C17C22⋊C411yescharacteristic
57C22×C4×C17C22⋊C411yescharacteristic
58C22×C4×C17C22⋊C411yescharacteristic
59C22×C4×C17C22×C411yescharacteristic
60C22×C4×C17C2×D411yescharacteristic
61C22×C4×C17C2×D411yescharacteristic
62C4⋊C4×C17—41no—
63C4⋊C4×C17—41no—
64C4⋊C4×C17—42no—
65C4⋊C4×C17—42no—
66C4⋊C4×C17—41no—
67C4⋊C4×C17—41no—
68C4⋊C4×C17—82no—
69C22⋊C4×C17—41no—
70C22⋊C4×C17—41no—
71C22⋊C4×C17—82no—
72C42×C17—21no—
73C42×C17—21no—
74C42×C17—21no—
75C42×C17—21no—
76#63223—42no—
77#63223—42no—
78C2×#3622—42no—
79C2×#3622—42no—
80#11818—171nomaximal, Sylow
81C23×C17—21no—
82C23×C17—21no—
83C23×C17—21no—
84C23×C17—41no—
85C23×C17—41no—
86C23×C17C2×C22⋊C411yescharacteristic
87Q8×C17—84no—
88C2×C4×C17—21no—
89C2×C4×C17—21no—
90C2×C4×C17—21no—
91C2×C4×C17—21no—
92C2×C4×C17—21no—
93C2×C4×C17—21no—
94C2×C4×C17—21no—
95C2×C4×C17—21no—
96C2×C4×C17—42no—
97C2×C4×C17—42no—
98C2×C4×C17—41no—
99C2×C4×C17—41no—
100C2×C4×C17—41no—
101C2×C4×C17—41no—
102C2×C4×C17—42no—
103C2×C4×C17—42no—
104C2×C4×C17—42no—
105C2×C4×C17—42no—
106C2×C4×C17—42no—
107C2×C4×C17—42no—
108C2×C4×C17#9911yescharacteristic
109C2×C4×C17#9911yescharacteristic
110C2×C4×C17#13712yes—
111#3622—82no—
112#3622—82no—
113#2628D1711yescharacteristic
114#1822—171no—
115#1464—171no—
116#1353—174no—
117C22×C17—21no—
118C22×C17—21no—
119C22×C17—42no—
120C22×C17—41no—
121C22×C17—41no—
122C22×C17—41no—
123C22×C17—81no—
124C22×C17C2×#9911yescharacteristic
125C22×C17#41911yescharacteristic
126C22×C17#42111yescharacteristic
127C4×C17—22no—
128C4×C17—21no—
129C4×C17—21no—
130C4×C17—41no—
131C4×C17—41no—
132C4×C17—41no—
133C4×C17—41no—
134C4×C17—82no—
135C4×C17—82no—
136C2×C4⋊Q8Dic1711yescharacteristic
137C2×#117C2×D1711yescharacteristic
138#432—341no—
139#407—341no—
140#400C2×D1712yes—
141#399Dic1712yes—
142#395—21no—
143#393—21no—
144#389—21no—
145#382Dic1711yescharacteristic
146#380—21no—
147#343—172no—
148#343—341no—
149#324—172no—
150#323—341no—
151C2×C17—21no—
152C2×C17—21no—
153C2×C17—81no—
154C2×C17#151111yescharacteristic
155C2×C17#212311yescharacteristic
156C2×C17#213411yescharacteristic
157C22×Q8—21no—
158C23×C4C22⋊D1711yescharacteristic
159C2×M16—342no—
160C4⋊Q8—41no—
161C4⋊Q8—41no—
162#117—41no—
163#117—41no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4C2×Dic1712yes—
168C2×C4⋊C4C22⋊D1711yescharacteristic
169C2×C4⋊C4C22×D1711yescharacteristic
170C2×C22⋊C4—22no—
171C2×C22⋊C4C2×Dic1711yescharacteristic
172C2×C22⋊C4C22⋊D1711yescharacteristic
173C2×C42C2×Dic1711yescharacteristic
174C2×C42C22⋊D1711yescharacteristic
175C4⋊C8—681no—
176C22⋊C8—342no—
177C22⋊C8—681no—
178C22⋊C8—681no—
179#97—681no—
180#95—21no—
181#95—22no—
182#95—22no—
183#95C2×Dic1712yes—
184C17#1181811yescharacteristic, complemented, Sylow
185C24C22⋊Dic1711yescharacteristic
186C2×Q8—42no—
187C2×Q8—82no—
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—22no—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—41no—
194C22×C4C22⋊Dic1711yescharacteristic
195C22×C4C22⋊Dic1711yescharacteristic
196C22×C4C22⋊Dic1711yescharacteristic
197C22×C4C22×Dic1711yescharacteristic
198C22×C4C2×C22⋊D1711yescharacteristic
199C22×C4C2×C22⋊D1711yescharacteristic
200M16—682no—
201M16—682no—
202C2×C8—682no—
203C2×C8—682no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—42no—
207C4⋊C4—42no—
208C4⋊C4—41no—
209C4⋊C4—41no—
210C4⋊C4—82no—
211C22⋊C4—41no—
212C22⋊C4—41no—
213C22⋊C4—82no—
214C42—21no—
215C42—21no—
216C42—21no—
217C42—21no—
218C23—21no—
219C23—21no—
220C23—21no—
221C23—41no—
222C23—41no—
223C23C2×C22⋊Dic1711yescharacteristic
224Q8—84no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4#1058750511yescharacteristic
246C2×C4#1058750511yescharacteristic
247C2×C4#1058762812yes—
248C8—1362no—
249C8—1362no—
250C22—21no—
251C22—21no—
252C22—42no—
253C22—41no—
254C22—41no—
255C22—41no—
256C22—81no—
257C22C2×#1058750511yescharacteristic
258C22#1176281811yescharacteristic
259C22#1176282611yescharacteristic
260C4—22no—
261C4—21no—
262C4—21no—
263C4—41no—
264C4—41no—
265C4—41no—
266C4—41no—
267C4—82no—
268C4—82no—
269C2—21no—
270C2—21no—
271C2—81no—
272C2#1452731711yescharacteristic
273C2#1453043811yescharacteristic
274C2#1453047611yescharacteristic
subgroupG/H
centerC22C2×#10587505
commutatorC22×C4×C17C22×C4
FrattiniC2×C4⋊C4C22×D17
FittingC17×#2628C2
socleC22×C17C2×#99
prime radicalC24×C17C22⋊C4
cosocleC2×C4⋊C4×C17C23
hypercenter#2628D17
hypocenterC17#11818
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #2628

Complements

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

NH ≅ G/Ntype
3. #14526811C2semidirect
184. C17#11818semidirect

Maximal subgroups

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

subgroupindex
#145288672
#145271182
#145268112
C17×#26282
#1181817