Finite Group Databasebeta

← #17959366

Subgroups — #17959366

Order 4352.

482 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 74 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
1C4×#10587545C211yesmaximal, characteristic, complemented
2#14544046C211yesmaximal, characteristic, complemented
3#14543766C214yesmaximal, complemented
4#14533787C211yesmaximal, characteristic
5#11763830—21no—
6C2×#10587545—21no—
7C4×#63247—21no—
8#11763689C2212yes—
9#11763655C2212yes—
10#11763654—21no—
11C2×#10587622—21no—
12C2×C4×Dic34C2211yescharacteristic
13#11762723C412yes—
14#11762723C2212yes—
15#11762712—21no—
16#11762712—21no—
17#11762712—21no—
18C4×C4⋊Dic17C411yescharacteristic
19C2×C17×#127C411yescharacteristic
20C22×D4×C17—21no—
21C22×D4×C17—21no—
22C22×D4×C17C2×C412yes—
23C22×Dic34D411yescharacteristic
24C2×#63247—22no—
25C17×#127—41no—
26C17×#127—41no—
27C2×C42×C17C2×C411yescharacteristic
28C2×C22⋊Dic17—22no—
29C2×C22⋊Dic17—22no—
30C2×C22⋊Dic17—22no—
31C2×C22⋊Dic17—22no—
32#10587622—44no—
33C2×C4⋊Dic17—21no—
34C2×C4⋊Dic17D411yescharacteristic
35C2×#63225C2×C411yescharacteristic
36C2×#63225C2311yescharacteristic
37C2×C4×Dic17—21no—
38C2×C4×Dic17D411yescharacteristic
39C2×C4×Dic17D411yescharacteristic
40C4×Dic34—41no—
41C4×Dic34—41no—
42C22⋊#3624—22no—
43#10587545—24no—
44#10587542—41no—
45#10587542—41no—
46C4⋊#3624—41no—
47C4×#3624—41no—
48#10587502C2×C412yes—
49C24×C17—22no—
50C2×D4×C17—42no—
51C2×D4×C17—42no—
52C2×D4×C17—42no—
53C2×D4×C17—42no—
54C2×D4×C17—42no—
55C2×D4×C17—41no—
56C2×D4×C17—41no—
57C2×D4×C17—42no—
58C2×D4×C17—82no—
59C22×C4×C17C22⋊C411yescharacteristic
60C22×C4×C17C22⋊C411yescharacteristic
61C22×C4×C17C22×C411yescharacteristic
62C22×Dic17—22no—
63C22×Dic17C22⋊C411yescharacteristic
64C22×Dic17C22⋊C411yescharacteristic
65C22×Dic17C2×D411yescharacteristic
66C22×Dic17C2×D411yescharacteristic
67C2×Dic34—22no—
68C2×Dic34—22no—
69C2×Dic34—41no—
70#63247—24no—
71#63247—42no—
72C2×#3624—42no—
73C2×#3624—42no—
74C42×C17—21no—
75C42×C17—21no—
76C22⋊Dic17—44no—
77C22⋊Dic17—44no—
78C22⋊Dic17—82no—
79C22⋊Dic17—82no—
80C4⋊Dic17—41no—
81C4⋊Dic17—42no—
82#63225—41no—
83#63225—41no—
84C4×Dic17—21no—
85C4×Dic17—21no—
86C4×Dic17—21no—
87C4×Dic17—21no—
88C4×Dic17—42no—
89#11781—171nomaximal, Sylow
90C23×C17—42no—
91C23×C17—42no—
92C23×C17—42no—
93C23×C17—42no—
94C23×C17—42no—
95C23×C17—42no—
96C23×C17—42no—
97C23×C17C2×C22⋊C411yescharacteristic
98D4×C17—82no—
99D4×C17—84no—
100D4×C17—84no—
101D4×C17—82no—
102C2×C4×C17—21no—
103C2×C4×C17—21no—
104C2×C4×C17—22no—
105C2×C4×C17—21no—
106C2×C4×C17—41no—
107C2×C4×C17#9911yescharacteristic
108C2×C4×C17#9911yescharacteristic
109C2×C4×C17#10412yes—
110C2×Dic17—21no—
111C2×Dic17—21no—
112C2×Dic17—21no—
113C2×Dic17—21no—
114C2×Dic17—21no—
115C2×Dic17—21no—
116C2×Dic17—21no—
117C2×Dic17—41no—
118C2×Dic17—41no—
119C2×Dic17—42no—
120C2×Dic17—42no—
121C2×Dic17—42no—
122C2×Dic17AGL(1,ℤ/8)12yes—
123Dic34—44no—
124#3624—44no—
125#3624—82no—
126#2548—171no—
127C4×#101—171no—
128#1467—171no—
129#1345—174no—
130C22×C17—21no—
131C22×C17—21no—
132C22×C17—82no—
133C22×C17—82no—
134C22×C17—82no—
135C22×C17—82no—
136C22×C17—82no—
137C22×C17—82no—
138C22×C17—82no—
139C22×C17C2×#9911yescharacteristic
140C22×C17#41811yescharacteristic
141C22×C17C2×#10411yescharacteristic
142C4×C17—21no—
143C4×C17—22no—
144C4×C17—41no—
145C4×C17#35512yes—
146Dic17—22no—
147Dic17—41no—
148Dic17—41no—
149Dic17—41no—
150Dic17—82no—
151C2×#127#59511yescharacteristic
152C2×#124—341no—
153C2×C4×Q8—171no—
154#432—341no—
155C2×#101—341no—
156C4×M16—341no—
157#394—172no—
158#394—172no—
159#390—341no—
160#390—341no—
161#390—341no—
162C4×C4⋊C4—171no—
163#343—172no—
164#324—172no—
165#324—341no—
166C2×C17—21no—
167C2×C17—21no—
168C2×C17—162no—
169C2×C17#150711yescharacteristic
170C2×C17#212211yescharacteristic
171C2×C17C2×#35511yescharacteristic
172C22×Q8—171no—
173C22×D4—21no—
174C22×D4—21no—
175C22×D4C2×#59512yes—
176C2×M16—342no—
177#127—41no—
178#127—41no—
179#124—684no—
180C4×Q8—681no—
181C4×Q8—681no—
182C2×C4⋊C4—171no—
183C2×C4⋊C4—171no—
184C2×C4⋊C4—171no—
185C2×C4⋊C4—341no—
186C2×C22⋊C4—342no—
187C2×C22⋊C4—342no—
188C2×C22⋊C4—342no—
189C2×C22⋊C4—342no—
190C2×C42—171no—
191C2×C42—171no—
192C2×C42—341no—
193C2×C42C2×#59511yescharacteristic
194C4⋊C8—681no—
195#101—344no—
196C22⋊C8—342no—
197#97—681no—
198#97—681no—
199C4×C8—681no—
200#95—172no—
201C17#1178111yescharacteristic, complemented, Sylow
202C24—22no—
203C2×Q8—342no—
204C2×Q8—342no—
205C2×Q8—681no—
206C2×D4—42no—
207C2×D4—42no—
208C2×D4—42no—
209C2×D4—42no—
210C2×D4—42no—
211C2×D4—42no—
212C2×D4—41no—
213C2×D4—41no—
214C2×D4—82no—
215C22×C4—171no—
216C22×C4—171no—
217C22×C4—171no—
218C22×C4—171no—
219C22×C4—342no—
220C22×C4C22⋊#59511yescharacteristic
221C22×C4C22⋊#59511yescharacteristic
222C22×C4C22×#59511yescharacteristic
223M16—344no—
224M16—682no—
225C2×C8—682no—
226C2×C8—682no—
227C4⋊C4—681no—
228C4⋊C4—681no—
229C4⋊C4—681no—
230C4⋊C4—682no—
231C22⋊C4—684no—
232C22⋊C4—684no—
233C22⋊C4—1362no—
234C22⋊C4—1362no—
235C42—21no—
236C42—21no—
237C42—341no—
238C42—341no—
239C42—341no—
240C42—341no—
241C42—682no—
242C23—42no—
243C23—42no—
244C23—42no—
245C23—42no—
246C23—42no—
247C23—42no—
248C23—42no—
249C23C2×C22⋊#59511yescharacteristic
250Q8—684no—
251D4—84no—
252D4—82no—
253D4—84no—
254D4—82no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—21no—
259C2×C4—41no—
260C2×C4—172no—
261C2×C4—341no—
262C2×C4—341no—
263C2×C4—341no—
264C2×C4—341no—
265C2×C4—341no—
266C2×C4—341no—
267C2×C4—341no—
268C2×C4—681no—
269C2×C4—681no—
270C2×C4—682no—
271C2×C4—682no—
272C2×C4—682no—
273C2×C4#1058754812yes—
274C2×C4#1058755111yescharacteristic
275C2×C4#1058755111yescharacteristic
276C8—684no—
277C8—1362no—
278C22—21no—
279C22—21no—
280C22—82no—
281C22—82no—
282C22—82no—
283C22—82no—
284C22—82no—
285C22—82no—
286C22—82no—
287C22C2×#1058755111yescharacteristic
288C22#1176380111yescharacteristic
289C22C2×#1058754811yescharacteristic
290C4—22no—
291C4—21no—
292C4—41no—
293C4—342no—
294C4—681no—
295C4—681no—
296C4—681no—
297C4—1362no—
298C4#1176371712yes—
299C2—21no—
300C2—21no—
301C2—162no—
302C2#1454418011yescharacteristic
303C2#1454504311yescharacteristic
304C2C2×#1176371711yescharacteristic
subgroupG/H
centerC22C2×#10587551
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
Fitting, prime radicalC2×C17×#127C4
socleC22×C17C2×#99
cosocleC2×#63225C23
hypercenterC2×#127#595
hypocenterC17#11781
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C4×#10587545C2semidirect
2. #14544046C2semidirect
3. #14543766C2semidirect
201. C17#11781semidirect

Maximal subgroups

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

subgroupindex
C4×#105875452
#145440462
#145437662
#145337872
#1178117