Finite Group Databasebeta

← #16927891

Subgroups — #16927891

Order 4352.

498 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 123 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#14531694C211yesmaximal, characteristic
2#14528776C211yesmaximal, characteristic
3#14526686C212yesmaximal, complemented
4#14526643C212yesmaximal, complemented
5C17×#1460C211yesmaximal, characteristic
6C2×D4×Dic17—21no—
7#11762833C2212yes—
8C2×#10587504—21no—
9#11762708—21no—
10#11762684—22no—
11#11762675C2211yescharacteristic
12#11762669C412yes—
13C4×C4⋊Dic17C2211yescharacteristic
14C2×#10587502C412yes—
15#11762578—21no—
16C2×C4×D4×C17C2211yescharacteristic
17C17×#431C2212yes—
18C17×#323—22no—
19C22×D4×C17D411yescharacteristic
20C23×C4×C17C2×C412yes—
21C23×Dic17—22no—
22C4×D4×C17—22no—
23C4×D4×C17—22no—
24C2×C4⋊C4×C17D411yescharacteristic
25C2×C22⋊C4×C17D412yes—
26C2×C42×C17C2311yescharacteristic
27C2×C22⋊Dic17—22no—
28D4×Dic17—42no—
29D4×Dic17—42no—
30C2×C4⋊Dic17—22no—
31C2×C4⋊Dic17—21no—
32C2×C4⋊Dic17—21no—
33C2×C4×Dic17—21no—
34C2×#63223—22no—
35C17×C4⋊C8—22no—
36C17×C22⋊C8—22no—
37C4×C8×C17—22no—
38#10587504—42no—
39#10587502—22no—
40#10587502—21no—
41#10587502C2×C411yescharacteristic
42#10587502C2×C412yes—
43#10587502C2×C411yescharacteristic
44C4⋊#3622—22no—
45C4⋊#3622—22no—
46C24×C17C22⋊C412yes—
47C2×D4×C17—22no—
48C2×D4×C17—22no—
49C2×D4×C17D812yes—
50C2×D4×C17SD1612yes—
51C22×C4×C17—22no—
52C22×C4×C17—22no—
53C22×C4×C17—82no—
54C22×C4×C17C22⋊C412yes—
55C22×C4×C17C22×C411yescharacteristic
56C22×C4×C17C2×D411yescharacteristic
57C22×C4×C17C2×D411yescharacteristic
58C22×Dic17—21no—
59C22×Dic17—22no—
60C22×Dic17—21no—
61C22×Dic17—44no—
62C22×Dic17—44no—
63C22×Dic17—82no—
64C2×C8×C17—42no—
65C4⋊C4×C17—22no—
66C22⋊C4×C17—24no—
67C42×C17#4112yes—
68C42×C17#4112yes—
69C22⋊Dic17—44no—
70C4⋊Dic17—42no—
71C4⋊Dic17—41no—
72C4⋊Dic17—41no—
73C4⋊Dic17—82no—
74C4×Dic17—41no—
75C4×Dic17—41no—
76#63223—42no—
77#63223—42no—
78C2×#3622—42no—
79#8764—171nomaximal, Sylow
80C23×C17—22no—
81C23×C17—22no—
82C23×C17—42no—
83C23×C17—42no—
84C23×C17#10214yes—
85C23×C17C2×C22⋊C411yescharacteristic
86D4×C17—24no—
87D4×C17—24no—
88C2×C4×C17—22no—
89C2×C4×C17—41no—
90C2×C4×C17—41no—
91C2×C4×C17—42no—
92C2×C4×C17—82no—
93C2×C4×C17—82no—
94C2×C4×C17#11711yescharacteristic
95C2×C4×C17#11711yescharacteristic
96C2×C4×C17#12312yes—
97C2×C4×C17#12312yes—
98C2×C4×C17C2×D811yescharacteristic
99C2×C4×C17C2×SD1611yescharacteristic
100C2×C4×C17#13712yes—
101C2×Dic17—22no—
102C2×Dic17—41no—
103C2×Dic17—41no—
104C2×Dic17—42no—
105C2×Dic17—42no—
106C2×Dic17—41no—
107C2×Dic17—41no—
108C2×Dic17—41no—
109C2×Dic17—42no—
110C2×Dic17—88no—
111C8×C17—82no—
112#3622—82no—
113#2349—171no—
114#1800—171no—
115#1460D1711yescharacteristic
116#1303—172no—
117#1286—172no—
118C22×C17—21no—
119C22×C17—21no—
120C22×C17—24no—
121C22×C17—44no—
122C22×C17—44no—
123C22×C17—42no—
124C22×C17—42no—
125C22×C17#38111yescharacteristic
126C22×C17C2×#10211yescharacteristic
127C22×C17#41911yescharacteristic
128C4×C17—22no—
129C4×C17—21no—
130C4×C17—21no—
131C4×C17—42no—
132C4×C17#48012yes—
133C4×C17#48312yes—
134Dic17—42no—
135Dic17—81no—
136Dic17—82no—
137C2×C4×D4—341no—
138C2×C4×D4C2×D1711yescharacteristic
139#431C2×D1712yes—
140#423—172no—
141C2×#100—341no—
142#389—341no—
143#385—342no—
144#382—171no—
145#380—172no—
146C4×C4⋊C4—171no—
147C2×#95—172no—
148#343—341no—
149#323—22no—
150C2×C17—21no—
151C2×C17—21no—
152C2×C17—44no—
153C2×C17#182311yescharacteristic
154C2×C17#182711yescharacteristic
155C2×C17#182911yescharacteristic
156C22×D4D6811yescharacteristic
157C23×C4—342no—
158C23×C4C4×D1712yes—
159C2×M16—342no—
160C4×D4—22no—
161C4×D4—22no—
162C4×D4—682no—
163C4×D4—682no—
164C2×C4⋊C4—341no—
165C2×C4⋊C4—341no—
166C2×C4⋊C4—342no—
167C2×C4⋊C4D6811yescharacteristic
168C2×C22⋊C4—342no—
169C2×C22⋊C4C22⋊D1712yes—
170C2×C42—341no—
171C2×C42C22×D1711yescharacteristic
172C4⋊C8—22no—
173C4⋊C8—342no—
174C4⋊C8—342no—
175#100—682no—
176C22⋊C8—22no—
177C4×C8—22no—
178#95—171no—
179#95—172no—
180#95—171no—
181#95—341no—
182#95—342no—
183C17#876411yescharacteristic, complemented, Sylow
184C24#6322712yes—
185C2×D4—22no—
186C2×D4—22no—
187C2×D4#6321912yes—
188C2×D4D13612yes—
189C22×C4—22no—
190C22×C4—22no—
191C22×C4—82no—
192C22×C4—341no—
193C22×C4—342no—
194C22×C4—341no—
195C22×C4—684no—
196C22×C4—684no—
197C22×C4—1362no—
198C22×C4#6322712yes—
199C22×C4C2×C4×D1711yescharacteristic
200C22×C4C2×D6811yescharacteristic
201C22×C4C2×C22⋊D1711yescharacteristic
202M16—682no—
203M16—682no—
204C2×C8—42no—
205C2×C8—682no—
206C4⋊C4—22no—
207C4⋊C4—682no—
208C4⋊C4—681no—
209C4⋊C4—681no—
210C4⋊C4—1362no—
211C22⋊C4—24no—
212C22⋊C4—684no—
213C42—681no—
214C42—681no—
215C42#6325412yes—
216C42#6325412yes—
217C23—22no—
218C23—22no—
219C23—42no—
220C23—42no—
221C23#1058749214yes—
222C23C2×#6322711yescharacteristic
223D4—24no—
224D4—24no—
225C2×C4—22no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—42no—
229C2×C4—82no—
230C2×C4—82no—
231C2×C4—342no—
232C2×C4—681no—
233C2×C4—681no—
234C2×C4—681no—
235C2×C4—681no—
236C2×C4—682no—
237C2×C4—682no—
238C2×C4—681no—
239C2×C4—682no—
240C2×C4—1368no—
241C2×C4#1058756311yescharacteristic
242C2×C4#1058756311yescharacteristic
243C2×C4#1058757212yes—
244C2×C4C2×#6321911yescharacteristic
245C2×C4C2×D13611yescharacteristic
246C2×C4#1058759512yes—
247C2×C4#1058762112yes—
248C8—82no—
249C8—1362no—
250C22—21no—
251C22—21no—
252C22—24no—
253C22—44no—
254C22—44no—
255C22—42no—
256C22—42no—
257C22#1176267011yescharacteristic
258C22C2×#1058749211yescharacteristic
259C22#1176281911yescharacteristic
260C4—22no—
261C4—21no—
262C4—21no—
263C4—42no—
264C4—682no—
265C4—1362no—
266C4—1361no—
267C4#1176312312yes—
268C4#1176314012yes—
269C2—21no—
270C2—21no—
271C2—44no—
272C2#1452887111yescharacteristic
273C2#1452888511yescharacteristic
274C2#1452889311yescharacteristic
subgroupG/H
centerC22#11762670
commutatorC22×C4×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#1460C2
socleC22×C17#381
prime radicalC22×D4×C17D4
cosocleC2×C42×C17C23
hypercenter#1460D17
hypocenterC17#8764
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1460

Complements

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

NH ≅ G/Ntype
3. #14526686C2semidirect
4. #14526643C2semidirect
183. C17#8764semidirect

Maximal subgroups

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

subgroupindex
#145316942
#145287762
#145266862
#145266432
C17×#14602
#876417