Finite Group Databasebeta

← #17959494

Subgroups — #17959494

Order 4352.

368 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 66 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#14544685C211yesmaximal, characteristic
2#14544037C211yesmaximal, characteristic
3#14543785C214yesmaximal, complemented
4#14534606C211yesmaximal, characteristic
5#11763829—21no—
6#11763781—21no—
7#11763689—21no—
8#11763689C2212yes—
9#11763655C2212yes—
10#11763653—21no—
11C2×#10587558C2211yescharacteristic
12#11762747—21no—
13#11762744—21no—
14#11762728C2212yes—
15#11762720C412yes—
16#11762705—21no—
17#11762675C411yescharacteristic
18#11762666—21no—
19C2×C17×C4⋊Q8C411yescharacteristic
20C22×Q8×C17C2×C412yes—
21C22×C4×D17D411yescharacteristic
22C2×#63247—22no—
23C17×C4⋊Q8—41no—
24C17×C4⋊Q8—41no—
25C2×C4⋊C4×C17—21no—
26C2×C4⋊C4×C17—21no—
27C2×C42×C17C2×C411yescharacteristic
28C2×#63227—22no—
29C2×#63227C2×C411yescharacteristic
30C2×#63227D411yescharacteristic
31C2×C4⋊Dic17—21no—
32C2×#63225—22no—
33C2×#63225D411yescharacteristic
34C2×#63225C2311yescharacteristic
35C2×C4×Dic17D411yescharacteristic
36#10587558—41no—
37#10587558—41no—
38C22⋊#3624—22no—
39#10587544—41no—
40#10587543—41no—
41#10587543—41no—
42#10587542—41no—
43#10587502—21no—
44#10587502—22no—
45#10587502—22no—
46#10587502C2×C412yes—
47C23×D17C22⋊C411yescharacteristic
48C2×Q8×C17—42no—
49C2×Q8×C17—82no—
50C22×C4×C17—22no—
51C22×C4×C17C22⋊C411yescharacteristic
52C22×C4×C17C22⋊C411yescharacteristic
53C22×C4×C17C22×C411yescharacteristic
54C22×Dic17—22no—
55C22×Dic17C22⋊C411yescharacteristic
56C22×Dic17C2×D411yescharacteristic
57C22×Dic17C2×D411yescharacteristic
58C2×C4×D17—21no—
59C2×C4×D17—21no—
60C2×C4×D17—22no—
61C2×C4×D17—41no—
62#63247—42no—
63#63247—42no—
64C2×#3624—42no—
65C2×#3624—42no—
66C4⋊C4×C17—42no—
67C4⋊C4×C17—41no—
68C4⋊C4×C17—41no—
69C42×C17—21no—
70C42×C17—21no—
71#63227—41no—
72#63227—41no—
73#63227—82no—
74C4⋊Dic17—42no—
75#63225—41no—
76#63225—41no—
77#63225—82no—
78C4×Dic17—21no—
79C4×Dic17—21no—
80#11819—171nomaximal, Sylow
81C23×C17C2×C22⋊C411yescharacteristic
82C22×D17—21no—
83C22×D17—21no—
84C22×D17—21no—
85C22×D17—41no—
86C22×D17—41no—
87Q8×C17—84no—
88C2×C4×C17—21no—
89C2×C4×C17—21no—
90C2×C4×C17—21no—
91C2×C4×C17—21no—
92C2×C4×C17—41no—
93C2×C4×C17—41no—
94C2×C4×C17—42no—
95C2×C4×C17—42no—
96C2×C4×C17—42no—
97C2×C4×C17#9911yescharacteristic
98C2×C4×C17#9911yescharacteristic
99C2×Dic17—21no—
100C2×Dic17—21no—
101C2×Dic17—21no—
102C2×Dic17—21no—
103C2×Dic17—41no—
104C2×Dic17—41no—
105C2×Dic17—42no—
106C2×Dic17—42no—
107C2×Dic17—42no—
108C2×Dic17#13712yes—
109C4×D17—42no—
110C4×D17—42no—
111#3624—82no—
112#3624—82no—
113#2628—171no—
114#1822—171no—
115#1464—171no—
116#1354—174no—
117C22×C17—21no—
118C22×C17—21no—
119C22×C17C2×#9911yescharacteristic
120C22×C17#41911yescharacteristic
121C22×C17#42111yescharacteristic
122C2×D17—42no—
123C2×D17—41no—
124C2×D17—41no—
125C2×D17—41no—
126C2×D17—81no—
127C4×C17—21no—
128C4×C17—21no—
129C4×C17—41no—
130C4×C17—41no—
131C4×C17—82no—
132Dic17—22no—
133Dic17—41no—
134Dic17—41no—
135Dic17—82no—
136C2×C4⋊Q8#59511yescharacteristic
137C2×#117—171no—
138#432—341no—
139#407—341no—
140#400—341no—
141#399—341no—
142#395—172no—
143#393—172no—
144#389—341no—
145#382—171no—
146#380—341no—
147#343—172no—
148#343—341no—
149#324—172no—
150#323—341no—
151C2×C17—21no—
152C2×C17—21no—
153C2×C17#151111yescharacteristic
154C2×C17#212211yescharacteristic
155C2×C17#213511yescharacteristic
156D17—81no—
157C22×Q8C2×#59512yes—
158C23×C4—171no—
159C2×M16—342no—
160C4⋊Q8—41no—
161C4⋊Q8—41no—
162#117—681no—
163#117—681no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—171no—
167C2×C4⋊C4—171no—
168C2×C4⋊C4—341no—
169C2×C4⋊C4—342no—
170C2×C22⋊C4—171no—
171C2×C22⋊C4—171no—
172C2×C22⋊C4—342no—
173C2×C42—171no—
174C2×C42C2×#59511yescharacteristic
175C4⋊C8—681no—
176C22⋊C8—342no—
177C22⋊C8—681no—
178C22⋊C8—681no—
179#97—681no—
180#95—172no—
181#95—342no—
182#95—342no—
183#95—341no—
184C17#1181911yescharacteristic, complemented, Sylow
185C24—171no—
186C2×Q8—42no—
187C2×Q8—82no—
188C22×C4—22no—
189C22×C4—171no—
190C22×C4—171no—
191C22×C4—171no—
192C22×C4—342no—
193C22×C4—341no—
194C22×C4—341no—
195C22×C4—342no—
196C22×C4—681no—
197C22×C4C22⋊#59511yescharacteristic
198C22×C4C22⋊#59511yescharacteristic
199C22×C4C22×#59511yescharacteristic
200M16—682no—
201M16—682no—
202C2×C8—682no—
203C2×C8—682no—
204C4⋊C4—42no—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C4⋊C4—681no—
208C4⋊C4—681no—
209C4⋊C4—682no—
210C4⋊C4—1362no—
211C22⋊C4—681no—
212C22⋊C4—681no—
213C22⋊C4—1362no—
214C42—21no—
215C42—21no—
216C42—341no—
217C42—341no—
218C23—341no—
219C23—341no—
220C23—341no—
221C23—681no—
222C23—681no—
223C23C2×C22⋊#59511yescharacteristic
224Q8—84no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—42no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—172no—
235C2×C4—341no—
236C2×C4—341no—
237C2×C4—341no—
238C2×C4—341no—
239C2×C4—682no—
240C2×C4—682no—
241C2×C4—681no—
242C2×C4—681no—
243C2×C4—682no—
244C2×C4—682no—
245C2×C4—682no—
246C2×C4#1058755111yescharacteristic
247C2×C4#1058755111yescharacteristic
248C8—1362no—
249C8—1362no—
250C22—21no—
251C22—21no—
252C22—682no—
253C22—681no—
254C22—681no—
255C22—681no—
256C22—1361no—
257C22C2×#1058755111yescharacteristic
258C22#1176380211yescharacteristic
259C22#1176380811yescharacteristic
260C4—21no—
261C4—21no—
262C4—41no—
263C4—41no—
264C4—82no—
265C4—342no—
266C4—681no—
267C4—681no—
268C4—1362no—
269C2—21no—
270C2—21no—
271C2—1361no—
272C2#1454419411yescharacteristic
273C2#1454504311yescharacteristic
274C2#1454508611yescharacteristic
subgroupG/H
centerC22C2×#10587551
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC2×C17×C4⋊Q8C4
socleC22×C17C2×#99
prime radicalC23×D17C22⋊C4
cosocleC2×#63225C23
hypercenterC2×C4⋊Q8#595
hypocenterC17#11819
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. #14543785C2semidirect
184. C17#11819semidirect

Maximal subgroups

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

subgroupindex
#145446852
#145440372
#145437852
#145346062
#1181917