Finite Group Databasebeta

← #17959724

Subgroups — #17959724

Order 4352.

476 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 80 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#14544650C211yesmaximal, characteristic, complemented
2#14544026C211yesmaximal, characteristic, complemented
3#14543766C214yesmaximal, complemented
4#14533787C211yesmaximal, characteristic
5#11763826—21no—
6#11763812—21no—
7C2×#10587545—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—42no—
33#10587622—42no—
34C2×C4⋊Dic17—21no—
35C2×C4⋊Dic17D411yescharacteristic
36C2×#63225C2×C411yescharacteristic
37C2×#63225C2311yescharacteristic
38C2×C4×Dic17—21no—
39C2×C4×Dic17D411yescharacteristic
40C2×C4×Dic17D411yescharacteristic
41C4×Dic34—41no—
42C4×Dic34—41no—
43C22⋊#3624—22no—
44#10587545—42no—
45#10587544—41no—
46#10587544—41no—
47C4⋊#3624—41no—
48C4×#3624—41no—
49#10587502C2×C412yes—
50C24×C17—22no—
51C2×D4×C17—42no—
52C2×D4×C17—42no—
53C2×D4×C17—42no—
54C2×D4×C17—42no—
55C2×D4×C17—42no—
56C2×D4×C17—41no—
57C2×D4×C17—41no—
58C2×D4×C17—42no—
59C2×D4×C17—82no—
60C22×C4×C17C22⋊C411yescharacteristic
61C22×C4×C17C22⋊C411yescharacteristic
62C22×C4×C17C22×C411yescharacteristic
63C22×Dic17—22no—
64C22×Dic17C22⋊C411yescharacteristic
65C22×Dic17C22⋊C411yescharacteristic
66C22×Dic17C2×D411yescharacteristic
67C22×Dic17C2×D411yescharacteristic
68C2×Dic34—41no—
69C2×Dic34—41no—
70C2×Dic34D812yes—
71C2×Dic34SD1612yes—
72#63247—42no—
73#63247—42no—
74C2×#3624—42no—
75C2×#3624—42no—
76C42×C17—21no—
77C42×C17—21no—
78C22⋊Dic17—44no—
79C22⋊Dic17—42no—
80C22⋊Dic17—42no—
81C22⋊Dic17—82no—
82C22⋊Dic17—82no—
83C4⋊Dic17—41no—
84C4⋊Dic17—42no—
85#63225—41no—
86#63225—41no—
87C4×Dic17—21no—
88C4×Dic17—21no—
89C4×Dic17—21no—
90C4×Dic17—21no—
91C4×Dic17—42no—
92#11882—171nomaximal, Sylow
93C23×C17—42no—
94C23×C17—42no—
95C23×C17—42no—
96C23×C17—42no—
97C23×C17—42no—
98C23×C17—42no—
99C23×C17—42no—
100C23×C17C2×C22⋊C411yescharacteristic
101D4×C17—82no—
102D4×C17—84no—
103D4×C17—84no—
104D4×C17—82no—
105C2×C4×C17—21no—
106C2×C4×C17—21no—
107C2×C4×C17—22no—
108C2×C4×C17—21no—
109C2×C4×C17—41no—
110C2×C4×C17#9911yescharacteristic
111C2×C4×C17#9911yescharacteristic
112C2×C4×C17#10212yes—
113C2×Dic17—21no—
114C2×Dic17—21no—
115C2×Dic17—21no—
116C2×Dic17—21no—
117C2×Dic17—21no—
118C2×Dic17—21no—
119C2×Dic17—41no—
120C2×Dic17—41no—
121C2×Dic17—42no—
122C2×Dic17—42no—
123C2×Dic17—42no—
124C2×Dic17#10212yes—
125C2×Dic17C2×D811yescharacteristic
126C2×Dic17C2×SD1611yescharacteristic
127Dic34—42no—
128Dic34—42no—
129#3624—82no—
130#3624—82no—
131#2548—171no—
132#1801—171no—
133#1461—171no—
134#1345—174no—
135C22×C17—21no—
136C22×C17—21no—
137C22×C17—82no—
138C22×C17—82no—
139C22×C17—82no—
140C22×C17—82no—
141C22×C17—82no—
142C22×C17—82no—
143C22×C17—82no—
144C22×C17C2×#9911yescharacteristic
145C22×C17C2×#10211yescharacteristic
146C22×C17#42111yescharacteristic
147C4×C17—21no—
148C4×C17—22no—
149C4×C17—41no—
150C4×C17#35512yes—
151Dic17—21no—
152Dic17—22no—
153Dic17—21no—
154Dic17—41no—
155Dic17—41no—
156Dic17—82no—
157C2×#127#59511yescharacteristic
158C2×#124—341no—
159C2×C4×Q8—171no—
160#431—341no—
161#423—341no—
162C2×#101—341no—
163#394—172no—
164#394—172no—
165#390—341no—
166#390—341no—
167#390—341no—
168C4×C4⋊C4—171no—
169#343—172no—
170#324—172no—
171#324—341no—
172C2×C17—21no—
173C2×C17—21no—
174C2×C17—162no—
175C2×C17#151911yescharacteristic
176C2×C17#212211yescharacteristic
177C2×C17C2×#35511yescharacteristic
178C22×Q8—171no—
179C22×D4—21no—
180C22×D4—21no—
181C22×D4C2×#59512yes—
182C2×M16—342no—
183#127—41no—
184#127—41no—
185#124—682no—
186#124—682no—
187C4×Q8—681no—
188C4×Q8—681no—
189C2×C4⋊C4—171no—
190C2×C4⋊C4—171no—
191C2×C4⋊C4—171no—
192C2×C4⋊C4—341no—
193C2×C22⋊C4—342no—
194C2×C22⋊C4—342no—
195C2×C22⋊C4—342no—
196C2×C22⋊C4—342no—
197C2×C42—171no—
198C2×C42—171no—
199C2×C42—341no—
200C2×C42C2×#59511yescharacteristic
201C4⋊C8—681no—
202C4⋊C8—681no—
203C4⋊C8—681no—
204#101—682no—
205C22⋊C8—342no—
206C4×C8—681no—
207#95—172no—
208C17#1188211yescharacteristic, complemented, Sylow
209C24—22no—
210C2×Q8—172no—
211C2×Q8—172no—
212C2×Q8—681no—
213C2×Q8—681no—
214C2×D4—42no—
215C2×D4—42no—
216C2×D4—42no—
217C2×D4—42no—
218C2×D4—42no—
219C2×D4—42no—
220C2×D4—41no—
221C2×D4—41no—
222C2×D4—82no—
223C22×C4—171no—
224C22×C4—171no—
225C22×C4—171no—
226C22×C4—171no—
227C22×C4—342no—
228C22×C4C22⋊#59511yescharacteristic
229C22×C4C22⋊#59511yescharacteristic
230C22×C4C22×#59511yescharacteristic
231M16—682no—
232M16—682no—
233C2×C8—682no—
234C2×C8—682no—
235C4⋊C4—681no—
236C4⋊C4—681no—
237C4⋊C4—681no—
238C4⋊C4—682no—
239C22⋊C4—682no—
240C22⋊C4—684no—
241C22⋊C4—682no—
242C22⋊C4—1362no—
243C22⋊C4—1362no—
244C42—21no—
245C42—21no—
246C42—341no—
247C42—341no—
248C42—341no—
249C42—341no—
250C42—682no—
251C23—42no—
252C23—42no—
253C23—42no—
254C23—42no—
255C23—42no—
256C23—42no—
257C23—42no—
258C23C2×C22⋊#59511yescharacteristic
259Q8—682no—
260Q8—682no—
261D4—84no—
262D4—82no—
263D4—84no—
264D4—82no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—41no—
270C2×C4—171no—
271C2×C4—172no—
272C2×C4—171no—
273C2×C4—341no—
274C2×C4—341no—
275C2×C4—341no—
276C2×C4—341no—
277C2×C4—341no—
278C2×C4—341no—
279C2×C4—681no—
280C2×C4—681no—
281C2×C4—682no—
282C2×C4—682no—
283C2×C4—682no—
284C2×C4#1058754712yes—
285C2×C4#1058755111yescharacteristic
286C2×C4#1058755111yescharacteristic
287C8—1362no—
288C8—1362no—
289C22—21no—
290C22—21no—
291C22—82no—
292C22—82no—
293C22—82no—
294C22—82no—
295C22—82no—
296C22—82no—
297C22—82no—
298C22C2×#1058755111yescharacteristic
299C22C2×#1058754711yescharacteristic
300C22#1176380711yescharacteristic
301C4—22no—
302C4—21no—
303C4—41no—
304C4—341no—
305C4—342no—
306C4—341no—
307C4—681no—
308C4—681no—
309C4—1362no—
310C4#1176371712yes—
311C2—21no—
312C2—21no—
313C2—162no—
314C2#1454422011yescharacteristic
315C2#1454504311yescharacteristic
316C2C2×#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#11882
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. #14544650C2semidirect
2. #14544026C2semidirect
3. #14543766C2semidirect
208. C17#11882semidirect

Maximal subgroups

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

subgroupindex
#145446502
#145440262
#145437662
#145337872
#1188217