Finite Group Databasebeta

← #17959722

Subgroups — #17959722

Order 4352.

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

normal subgroups only

This group has 460 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#14544648C211yesmaximal, characteristic
2#14544019C211yesmaximal, characteristic
3#14543769C214yesmaximal, complemented
4#14533093C211yesmaximal, characteristic
5#11763812—21no—
6C2×#10587553—21no—
7#11763777—21no—
8#11763689C2212yes—
9#11763655C2212yes—
10#11763652—21no—
11C2×#10587572—21no—
12C2×C4×C22⋊D17C2211yescharacteristic
13C22×C4⋊Dic17C411yescharacteristic
14#11762741C2212yes—
15#11762736C412yes—
16#11762708—21no—
17#11762670—21no—
18#11762666—21no—
19C17×#380C411yescharacteristic
20C23×C4×C17C2×C411yescharacteristic
21C22×C22⋊D17D411yescharacteristic
22C23×Dic17—21no—
23C22×C4×D17D411yescharacteristic
24C2×#63247—22no—
25C2×#63242—41no—
26C2×C4⋊C4×C17—21no—
27C2×C22⋊C4×C17—21no—
28C2×C22⋊Dic17D411yescharacteristic
29C4×C22⋊D17—41no—
30C4×C22⋊D17—41no—
31C2×#63227—22no—
32C2×#63227C2×C411yescharacteristic
33C2×C4⋊Dic17—21no—
34C2×C4⋊Dic17—22no—
35C2×C4⋊Dic17—41no—
36C2×C4⋊Dic17—41no—
37C2×C4⋊Dic17C2×C412yes—
38C2×#63225C2311yescharacteristic
39C2×C4×Dic17D411yescharacteristic
40#10587572—42no—
41#10587572—42no—
42#10587553—42no—
43C22⋊#3624—22no—
44#10587544—41no—
45#10587543—41no—
46C4⋊#3624—41no—
47C17×#95C2×C412yes—
48#10587502—22no—
49#10587502—22no—
50C24×C17C22⋊C411yescharacteristic
51C23×D17C22⋊C411yescharacteristic
52C22×C4×C17—21no—
53C22×C4×C17—21no—
54C22×C4×C17—22no—
55C22×C4×C17—42no—
56C22×C4×C17C22⋊C411yescharacteristic
57C22×C4×C17C22×C411yescharacteristic
58C2×C22⋊D17—41no—
59C2×C22⋊D17—41no—
60C2×C22⋊D17D812yes—
61C2×C22⋊D17SD1612yes—
62C22×Dic17—22no—
63C22×Dic17—42no—
64C22×Dic17—42no—
65C22×Dic17—42no—
66C22×Dic17C22⋊C411yescharacteristic
67C22×Dic17C2×D411yescharacteristic
68C22×Dic17C2×D411yescharacteristic
69C2×C4×D17—21no—
70C2×C4×D17—21no—
71C2×C4×D17—42no—
72#63247—42no—
73#63247—42no—
74C2×#3624—42no—
75C2×#3624—42no—
76#63242—82no—
77C4⋊C4×C17—42no—
78C22⋊C4×C17—42no—
79C22⋊Dic17—41no—
80#63227—41no—
81#63227—44no—
82C4⋊Dic17—41no—
83C4⋊Dic17—41no—
84C4⋊Dic17—42no—
85C4⋊Dic17—42no—
86C4⋊Dic17—42no—
87#63225—41no—
88C4×Dic17—21no—
89C4×Dic17—21no—
90#11881—171nomaximal, Sylow
91C23×C17—21no—
92C23×C17—21no—
93C23×C17—41no—
94C23×C17—41no—
95C23×C17#10212yes—
96C23×C17C2×C22⋊C411yescharacteristic
97C22×D17—21no—
98C22×D17—21no—
99C22×D17—41no—
100C22×D17—41no—
101C22×D17#10212yes—
102C2×C4×C17—22no—
103C2×C4×C17—21no—
104C2×C4×C17—42no—
105C2×C4×C17—42no—
106C2×C4×C17—41no—
107C2×C4×C17—42no—
108C2×C4×C17—42no—
109C2×C4×C17—42no—
110C2×C4×C17#9911yescharacteristic
111C2×C4×C17#9911yescharacteristic
112C22⋊D17—42no—
113C22⋊D17—42no—
114C2×Dic17—21no—
115C2×Dic17—21no—
116C2×Dic17—21no—
117C2×Dic17—21no—
118C2×Dic17—41no—
119C2×Dic17—41no—
120C2×Dic17—42no—
121C2×Dic17—42no—
122C2×Dic17—42no—
123C2×Dic17—84no—
124C2×Dic17C2×D811yescharacteristic
125C2×Dic17C2×SD1611yescharacteristic
126C4×D17—42no—
127C4×D17—81no—
128#3624—82no—
129#3624—82no—
130#2486—171no—
131#1800—171no—
132#1459—171no—
133#1346—174no—
134C22×C17—21no—
135C22×C17—21no—
136C22×C17—22no—
137C22×C17—42no—
138C22×C17—42no—
139C22×C17—41no—
140C22×C17—41no—
141C22×C17C2×#9911yescharacteristic
142C22×C17C2×#10211yescharacteristic
143C22×C17#42111yescharacteristic
144C2×D17—22no—
145C2×D17—41no—
146C2×D17—41no—
147C2×D17—42no—
148C2×D17—81no—
149C4×C17—21no—
150C4×C17—41no—
151C4×C17—82no—
152C4×C17#35212yes—
153Dic17—21no—
154Dic17—21no—
155Dic17—41no—
156Dic17—41no—
157Dic17—82no—
158C2×#123—341no—
159C2×C4×D4—171no—
160C22×C4⋊C4—171no—
161#423—341no—
162C2×#100—341no—
163C2×C22⋊C8—341no—
164#398—172no—
165#397—172no—
166#389—341no—
167#381—341no—
168#380—341no—
169#380#59511yescharacteristic
170#343—172no—
171#324—172no—
172#323—341no—
173C2×C17—21no—
174C2×C17—21no—
175C2×C17—42no—
176C2×C17#151911yescharacteristic
177C2×C17C2×#35211yescharacteristic
178C2×C17#213511yescharacteristic
179D17—42no—
180C22×D4—171no—
181C23×C4—171no—
182C23×C4—341no—
183C23×C4C2×#59511yescharacteristic
184C2×M16—342no—
185C22×C8—681no—
186#123—682no—
187#123—682no—
188C4×D4—681no—
189C4×D4—681no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—171no—
192C2×C4⋊C4—172no—
193C2×C4⋊C4—342no—
194C2×C4⋊C4—341no—
195C2×C4⋊C4—681no—
196C2×C4⋊C4—681no—
197C2×C22⋊C4—21no—
198C2×C22⋊C4—171no—
199C2×C22⋊C4—171no—
200C2×C22⋊C4—342no—
201C2×C42—171no—
202C4⋊C8—681no—
203C4⋊C8—681no—
204#100—682no—
205C22⋊C8—342no—
206C22⋊C8—681no—
207#95—342no—
208#95—342no—
209#95C2×#59512yes—
210C17#1188111yescharacteristic, complemented, Sylow
211C24—171no—
212C24C22⋊#59511yescharacteristic
213C2×D4—172no—
214C2×D4—172no—
215C2×D4—681no—
216C2×D4—681no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—22no—
220C22×C4—42no—
221C22×C4—171no—
222C22×C4—171no—
223C22×C4—171no—
224C22×C4—341no—
225C22×C4—341no—
226C22×C4—342no—
227C22×C4—682no—
228C22×C4—682no—
229C22×C4—682no—
230C22×C4—682no—
231C22×C4C22⋊#59511yescharacteristic
232C22×C4C22×#59511yescharacteristic
233M16—682no—
234M16—682no—
235C2×C8—682no—
236C2×C8—682no—
237C2×C8—1362no—
238C4⋊C4—42no—
239C4⋊C4—681no—
240C4⋊C4—682no—
241C4⋊C4—682no—
242C4⋊C4—682no—
243C4⋊C4—681no—
244C4⋊C4—681no—
245C22⋊C4—42no—
246C22⋊C4—681no—
247C22⋊C4—684no—
248C22⋊C4—681no—
249C42—341no—
250C42—341no—
251C23—21no—
252C23—21no—
253C23—41no—
254C23—41no—
255C23—172no—
256C23—341no—
257C23—341no—
258C23—681no—
259C23—681no—
260C23#1058754712yes—
261C23C2×C22⋊#59511yescharacteristic
262D4—682no—
263D4—682no—
264C2×C4—22no—
265C2×C4—21no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—41no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—171no—
273C2×C4—171no—
274C2×C4—341no—
275C2×C4—341no—
276C2×C4—341no—
277C2×C4—341no—
278C2×C4—682no—
279C2×C4—681no—
280C2×C4—681no—
281C2×C4—682no—
282C2×C4—682no—
283C2×C4—682no—
284C2×C4—1361no—
285C2×C4—1364no—
286C2×C4#1058753911yescharacteristic
287C2×C4#1058753911yescharacteristic
288C8—1362no—
289C8—1362no—
290C22—21no—
291C22—21no—
292C22—22no—
293C22—42no—
294C22—42no—
295C22—41no—
296C22—41no—
297C22—342no—
298C22—682no—
299C22—681no—
300C22—681no—
301C22—1361no—
302C22C2×#1058753911yescharacteristic
303C22C2×#1058754711yescharacteristic
304C22#1176380811yescharacteristic
305C4—21no—
306C4—41no—
307C4—82no—
308C4—341no—
309C4—341no—
310C4—681no—
311C4—681no—
312C4—1362no—
313C4#1176371212yes—
314C2—21no—
315C2—21no—
316C2—42no—
317C2—682no—
318C2#1454422111yescharacteristic
319C2C2×#1176371211yescharacteristic
320C2#1454508811yescharacteristic
subgroupG/H
centerC22C2×#10587539
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC17×#380C4
socleC22×C17C2×#99
prime radicalC22×C22⋊D17D4
cosocleC2×#63225C23
hypercenter#380#595
hypocenterC17#11881
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
3. #14543769C2semidirect
210. C17#11881semidirect

Maximal subgroups

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

subgroupindex
#145446482
#145440192
#145437692
#145330932
#1188117