Finite Group Databasebeta

← #17959153

Subgroups — #17959153

Order 4352.

432 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 88 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#14544489C211yesmaximal, characteristic
2#14544017C211yesmaximal, characteristic
3#14543783C214yesmaximal, complemented
4#14534606C211yesmaximal, characteristic
5C2×D17⋊M16—21no—
6#11763825—21no—
7#11763689—21no—
8#11763689C2212yes—
9#11763655C2212yes—
10#11763653—21no—
11C2×#10587558C2211yescharacteristic
12#11762747C2212yes—
13#11762744C412yes—
14#11762728—21no—
15#11762720—21no—
16#11762705—21no—
17#11762675C411yescharacteristic
18#11762666—21no—
19C2×C17×C4⋊Q8C411yescharacteristic
20C22×Q8×C17—21no—
21C22×C4×D17D411yescharacteristic
22C2×#63247—22no—
23D17⋊M16—24no—
24D17⋊M16—42no—
25C2×#63243—41no—
26C2×#63242—41no—
27C17×C4⋊Q8—41no—
28C17×C4⋊Q8—41no—
29C2×C4⋊C4×C17—21no—
30C2×C4⋊C4×C17C2×C412yes—
31C2×C42×C17C2×C411yescharacteristic
32C2×#63227—22no—
33C2×#63227C2×C411yescharacteristic
34C2×#63227D411yescharacteristic
35C2×C4⋊Dic17—21no—
36C2×#63225—22no—
37C2×#63225D411yescharacteristic
38C2×#63225C2311yescharacteristic
39C2×C4×Dic17D411yescharacteristic
40#10587558—41no—
41#10587558—41no—
42C22⋊#3624—22no—
43C4⋊#3624—41no—
44C4×#3624—41no—
45#10587502—21no—
46#10587502—22no—
47#10587502—22no—
48#10587502C2×C412yes—
49C23×D17C22⋊C411yescharacteristic
50C2×Q8×C17—42no—
51C2×Q8×C17—82no—
52C22×C4×C17—22no—
53C22×C4×C17C22⋊C411yescharacteristic
54C22×C4×C17C22⋊C411yescharacteristic
55C22×C4×C17C22×C411yescharacteristic
56C22×Dic17—22no—
57C22×Dic17C22⋊C411yescharacteristic
58C22×Dic17C2×D411yescharacteristic
59C22×Dic17C2×D411yescharacteristic
60C2×C4×D17—21no—
61C2×C4×D17—21no—
62C2×C4×D17—22no—
63C2×C4×D17SD1612yes—
64C2×C4×D17Q1612yes—
65#63247—24no—
66#63247—42no—
67C2×#3624—42no—
68C2×#3624—42no—
69#63243—44no—
70#63242—44no—
71C4⋊C4×C17—42no—
72C4⋊C4×C17—41no—
73C4⋊C4×C17—41no—
74C42×C17—21no—
75C42×C17—21no—
76#63227—41no—
77#63227—41no—
78#63227—82no—
79C4⋊Dic17—42no—
80#63225—41no—
81#63225—41no—
82#63225—82no—
83C4×Dic17—21no—
84C4×Dic17—21no—
85#11723—171nomaximal, Sylow
86C23×C17C2×C22⋊C411yescharacteristic
87C22×D17—21no—
88C22×D17—21no—
89C22×D17—41no—
90C22×D17—41no—
91C22×D17#10312yes—
92Q8×C17—84no—
93C2×C4×C17—21no—
94C2×C4×C17—21no—
95C2×C4×C17—41no—
96C2×C4×C17—41no—
97C2×C4×C17—42no—
98C2×C4×C17—42no—
99C2×C4×C17—42no—
100C2×C4×C17#9911yescharacteristic
101C2×C4×C17#9911yescharacteristic
102C2×C4×C17#10312yes—
103C2×C4×C17#10412yes—
104C2×Dic17—21no—
105C2×Dic17—21no—
106C2×Dic17—21no—
107C2×Dic17—21no—
108C2×Dic17—41no—
109C2×Dic17—41no—
110C2×Dic17—42no—
111C2×Dic17—42no—
112C2×Dic17—42no—
113C2×Dic17C2×SD1611yescharacteristic
114C2×Dic17C2×Q1611yescharacteristic
115C4×D17—22no—
116C4×D17—22no—
117C4×D17—22no—
118C4×D17—22no—
119#3624—44no—
120#3624—82no—
121#2628—171no—
122#1742—171no—
123#1458—171no—
124#1353—174no—
125C22×C17—21no—
126C22×C17—21no—
127C22×C17C2×#9911yescharacteristic
128C22×C17C2×#10311yescharacteristic
129C22×C17C2×#10411yescharacteristic
130C2×D17—22no—
131C2×D17—41no—
132C2×D17—41no—
133C2×D17—42no—
134C2×D17—81no—
135C4×C17—41no—
136C4×C17—41no—
137C4×C17—82no—
138C4×C17#32812yes—
139C4×C17#32812yes—
140Dic17—21no—
141Dic17—21no—
142Dic17—41no—
143Dic17—41no—
144Dic17—82no—
145C22×M16—341no—
146C2×C4⋊Q8#59511yescharacteristic
147C2×#117—171no—
148#431—341no—
149#400—172no—
150#399—172no—
151#395—341no—
152#393—341no—
153#389—341no—
154#382—171no—
155#380—341no—
156#343—172no—
157#343—341no—
158#324—172no—
159#323—341no—
160C2×C17—21no—
161C2×C17—21no—
162C2×C17C2×#32811yescharacteristic
163C2×C17#212311yescharacteristic
164C2×C17#213411yescharacteristic
165D17—42no—
166C22×Q8—21no—
167C23×C4—171no—
168C2×M16—342no—
169C2×M16—344no—
170C2×M16—682no—
171C2×M16—681no—
172C22×C8—681no—
173C4⋊Q8—41no—
174C4⋊Q8—41no—
175#117—681no—
176#117—681no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—171no—
179C2×C4⋊C4—171no—
180C2×C4⋊C4—341no—
181C2×C4⋊C4—342no—
182C2×C4⋊C4C2×#59512yes—
183C2×C22⋊C4—171no—
184C2×C22⋊C4—171no—
185C2×C22⋊C4—342no—
186C2×C42—171no—
187C2×C42C2×#59511yescharacteristic
188C4⋊C8—681no—
189C22⋊C8—342no—
190C4×C8—681no—
191#95—172no—
192#95—342no—
193#95—342no—
194#95—341no—
195C17#1172311yescharacteristic, complemented, Sylow
196C24—171no—
197C2×Q8—42no—
198C2×Q8—82no—
199C22×C4—22no—
200C22×C4—171no—
201C22×C4—172no—
202C22×C4—172no—
203C22×C4—171no—
204C22×C4—171no—
205C22×C4—342no—
206C22×C4—341no—
207C22×C4—341no—
208C22×C4—342no—
209C22×C4C22⋊#59511yescharacteristic
210C22×C4C22⋊#59511yescharacteristic
211C22×C4C22×#59511yescharacteristic
212M16—344no—
213M16—682no—
214M16—684no—
215C2×C8—684no—
216C2×C8—682no—
217C2×C8—682no—
218C4⋊C4—42no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—681no—
222C4⋊C4—681no—
223C4⋊C4—682no—
224C4⋊C4—1362no—
225C22⋊C4—681no—
226C22⋊C4—681no—
227C22⋊C4—1362no—
228C42—21no—
229C42—21no—
230C42—341no—
231C42—341no—
232C23—172no—
233C23—341no—
234C23—341no—
235C23—681no—
236C23—681no—
237C23C2×C22⋊#59511yescharacteristic
238Q8—84no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—171no—
247C2×C4—171no—
248C2×C4—341no—
249C2×C4—341no—
250C2×C4—342no—
251C2×C4—342no—
252C2×C4—342no—
253C2×C4—342no—
254C2×C4—341no—
255C2×C4—341no—
256C2×C4—681no—
257C2×C4—681no—
258C2×C4—682no—
259C2×C4—682no—
260C2×C4—682no—
261C2×C4#1058754912yes—
262C2×C4#1058755012yes—
263C2×C4#1058755111yescharacteristic
264C2×C4#1058755111yescharacteristic
265C8—684no—
266C8—1362no—
267C22—21no—
268C22—21no—
269C22—342no—
270C22—682no—
271C22—681no—
272C22—681no—
273C22—1361no—
274C22C2×#1058755111yescharacteristic
275C22C2×#1058754911yescharacteristic
276C22C2×#1058755011yescharacteristic
277C4—41no—
278C4—41no—
279C4—82no—
280C4—341no—
281C4—341no—
282C4—681no—
283C4—681no—
284C4—1362no—
285C4#1176366312yes—
286C4#1176366312yes—
287C2—21no—
288C2—21no—
289C2—682no—
290C2C2×#1176366311yescharacteristic
291C2#1454504611yescharacteristic
292C2#1454508311yescharacteristic
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#11723
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. #14543783C2semidirect
195. C17#11723semidirect

Maximal subgroups

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

subgroupindex
#145444892
#145440172
#145437832
#145346062
#1172317