Finite Group Databasebeta

← #16945195

Subgroups — #16945195

Order 4352.

390 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 79 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#14534361C211yesmaximal, characteristic
2#14527098C211yesmaximal, characteristic
3#14526804C212yesmaximal
4#14526783C212yesmaximal
5C17×#1820C211yesmaximal, characteristic
6C2×C4×Dic34C411yescharacteristic, complemented
7#11762862—21no—
8#11762739C411yescharacteristic, complemented
9#11762734C2211yescharacteristic
10#11762729C411yescharacteristic, complemented
11#11762721C2211yescharacteristic
12#11762697—21no—
13#11762693—21no—
14#11762690—21no—
15#11762682—21no—
16#11762677C411yescharacteristic, complemented
17#11762535—21no—
18#11762533C2212yes—
19C2×C17×#117C2211yescharacteristic
20C17×#381—21no—
21C17×#342—21no—
22C17×#342C2212yes—
23C23×C4×C17D411yescharacteristic
24C22×Dic34C2×C411yescharacteristic
25C17×#117—41no—
26C17×#117—41no—
27C2×C4⋊C4×C17C2×C411yescharacteristic
28C2×C4⋊C4×C17D411yescharacteristic
29C2×C22⋊C4×C17—22no—
30C2×C22⋊C4×C17D411yescharacteristic
31C2×C22⋊C4×C17C2311yescharacteristic
32C2×C42×C17C2×C411yescharacteristic
33C2×C42×C17D411yescharacteristic
34C2×C22⋊Dic17—21no—
35C2×C22⋊Dic17—21no—
36C2×C4⋊Dic17C2×C411yescharacteristic
37C2×#63225—21no—
38C2×#63225—21no—
39C2×#63225—21no—
40C2×C4×Dic17—21no—
41C4×Dic34—41no—
42C4×Dic34—41no—
43C17×#95—41no—
44C17×#95—41no—
45#10587502—21no—
46#10587502—21no—
47#10587502—21no—
48#10587502—21no—
49#10587502—21no—
50#10587502—21no—
51#10587502C2×C411yescharacteristic
52#10587502C2×C411yescharacteristic
53C22⋊#3622—22no—
54C4⋊#3622—41no—
55C4×#3622—41no—
56C24×C17C2×D411yescharacteristic
57C22×C4×C17—22no—
58C22×C4×C17—21no—
59C22×C4×C17—21no—
60C22×C4×C17—41no—
61C22×C4×C17—42no—
62C22×C4×C17C22⋊C411yescharacteristic
63C22×C4×C17C22⋊C411yescharacteristic
64C22×C4×C17C22⋊C411yescharacteristic
65C22×C4×C17C22⋊C411yescharacteristic
66C22×C4×C17C22×C411yescharacteristic
67C22×C4×C17C2×D411yescharacteristic
68C22×Dic17—21no—
69C22×Dic17—21no—
70C22×Dic17—21no—
71C22×Dic17—21no—
72C2×Dic34—41no—
73C2×Dic34—42no—
74C4⋊C4×C17—41no—
75C4⋊C4×C17—41no—
76C22⋊C4×C17—41no—
77C22⋊C4×C17—41no—
78C22⋊C4×C17—42no—
79C22⋊C4×C17—42no—
80C42×C17—21no—
81C42×C17—21no—
82C42×C17—21no—
83C42×C17—21no—
84C22⋊Dic17—42no—
85C22⋊Dic17—42no—
86C4⋊Dic17—41no—
87#63225—42no—
88#63225—42no—
89#63225—41no—
90#63225—41no—
91C4×Dic17—42no—
92C2×#3622—42no—
93#11842—171nomaximal, Sylow
94C23×C17—21no—
95C23×C17—21no—
96C23×C17—41no—
97C23×C17—41no—
98C23×C17C2×C22⋊C411yescharacteristic
99C23×C17#13512yes—
100C2×C4×C17—21no—
101C2×C4×C17—21no—
102C2×C4×C17—21no—
103C2×C4×C17—21no—
104C2×C4×C17—21no—
105C2×C4×C17—21no—
106C2×C4×C17—21no—
107C2×C4×C17—21no—
108C2×C4×C17—21no—
109C2×C4×C17—42no—
110C2×C4×C17—42no—
111C2×C4×C17—41no—
112C2×C4×C17—41no—
113C2×C4×C17—41no—
114C2×C4×C17—41no—
115C2×C4×C17—82no—
116C2×C4×C17—82no—
117C2×C4×C17—82no—
118C2×C4×C17#9911yescharacteristic
119C2×C4×C17#9911yescharacteristic
120C2×Dic17—22no—
121C2×Dic17—41no—
122C2×Dic17—41no—
123C2×Dic17—41no—
124C2×Dic17—41no—
125C2×Dic17—41no—
126C2×Dic17—41no—
127C2×Dic17—41no—
128C2×Dic17—41no—
129C2×Dic17—41no—
130C2×Dic17—41no—
131C2×Dic17—41no—
132Dic34—42no—
133Dic34—42no—
134#3622—82no—
135#2599—171no—
136#1820D1711yescharacteristic
137#1458—171no—
138#1351—172no—
139#1344—172no—
140C22×C17—21no—
141C22×C17—21no—
142C22×C17—22no—
143C22×C17—42no—
144C22×C17—41no—
145C22×C17—41no—
146C22×C17—81no—
147C22×C17C2×#9911yescharacteristic
148C22×C17#41611yescharacteristic
149C22×C17#42111yescharacteristic
150C4×C17—21no—
151C4×C17—21no—
152C4×C17—41no—
153C4×C17—41no—
154C4×C17—41no—
155C4×C17—41no—
156C4×C17—41no—
157C4×C17—162no—
158Dic17—42no—
159Dic17—81no—
160Dic17—81no—
161Dic17—81no—
162C2×C4×Q8—171no—
163C2×#117C2×D1711yescharacteristic
164#431—341no—
165#398—171no—
166#397—171no—
167#395—171no—
168#393—171no—
169#388—341no—
170#387—341no—
171#387—341no—
172#385—341no—
173#383—171no—
174#381—21no—
175#342—21no—
176#342C2×D1712yes—
177#324—341no—
178#323—172no—
179C2×C17—21no—
180C2×C17—21no—
181C2×C17—42no—
182C2×C17#151611yescharacteristic
183C2×C17#212011yescharacteristic
184C2×C17#212911yescharacteristic
185C22×Q8—171no—
186C23×C4C22⋊D1711yescharacteristic
187C4×Q8—681no—
188C4×Q8—681no—
189#117—41no—
190#117—41no—
191C2×C4⋊C4—171no—
192C2×C4⋊C4—341no—
193C2×C4⋊C4—341no—
194C2×C4⋊C4—341no—
195C2×C4⋊C4C4×D1711yescharacteristic
196C2×C4⋊C4D6811yescharacteristic
197C2×C22⋊C4—22no—
198C2×C22⋊C4—341no—
199C2×C22⋊C4—341no—
200C2×C22⋊C4C22⋊D1711yescharacteristic
201C2×C22⋊C4C22×D1711yescharacteristic
202C2×C42—341no—
203C2×C42C4×D1711yescharacteristic
204C2×C42D6811yescharacteristic
205C4⋊C8—681no—
206C22⋊C8—342no—
207C4×C8—681no—
208#95—41no—
209#95—41no—
210#95—171no—
211#95—171no—
212#95—341no—
213#95—341no—
214#95—341no—
215#95—341no—
216#95—341no—
217#95—341no—
218C17#1184211yescharacteristic, complemented, Sylow
219C24C2×C22⋊D1711yescharacteristic
220C2×Q8—681no—
221C2×Q8—682no—
222C22×C4—22no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—41no—
226C22×C4—42no—
227C22×C4—341no—
228C22×C4—341no—
229C22×C4—341no—
230C22×C4—341no—
231C22×C4#6322711yescharacteristic
232C22×C4#6322711yescharacteristic
233C22×C4#6322711yescharacteristic
234C22×C4#6322711yescharacteristic
235C22×C4C2×C4×D1711yescharacteristic
236C22×C4C2×D6811yescharacteristic
237C2×C8—682no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—681no—
241C4⋊C4—682no—
242C4⋊C4—682no—
243C4⋊C4—681no—
244C4⋊C4—681no—
245C22⋊C4—41no—
246C22⋊C4—41no—
247C22⋊C4—42no—
248C22⋊C4—42no—
249C22⋊C4—682no—
250C22⋊C4—682no—
251C42—21no—
252C42—21no—
253C42—21no—
254C42—21no—
255C42—682no—
256C23—21no—
257C23—21no—
258C23—41no—
259C23—41no—
260C23C2×#6322711yescharacteristic
261C23#1058763612yes—
262Q8—682no—
263Q8—682no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—82no—
280C2×C4—82no—
281C2×C4—82no—
282C2×C4—342no—
283C2×C4—681no—
284C2×C4—681no—
285C2×C4—681no—
286C2×C4—681no—
287C2×C4—681no—
288C2×C4—681no—
289C2×C4—681no—
290C2×C4—681no—
291C2×C4—681no—
292C2×C4—681no—
293C2×C4—681no—
294C2×C4#1058747711yescharacteristic
295C2×C4#1058747711yescharacteristic
296C8—1362no—
297C22—21no—
298C22—21no—
299C22—22no—
300C22—42no—
301C22—41no—
302C22—41no—
303C22—81no—
304C22C2×#1058747711yescharacteristic
305C22#1176280311yescharacteristic
306C22#1176282711yescharacteristic
307C4—21no—
308C4—21no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—41no—
314C4—162no—
315C4—682no—
316C4—1361no—
317C4—1361no—
318C4—1361no—
319C2—21no—
320C2—21no—
321C2—42no—
322C2#1452733811yescharacteristic
323C2#1453042311yescharacteristic
324C2#1453045811yescharacteristic
subgroupG/H
centerC22C2×#10587477
commutatorC22×C4×C17C22×C4
FrattiniC2×C22⋊C4C22×D17
FittingC17×#1820C2
socleC22×C17C2×#99
prime radicalC24×C17C2×D4
cosocleC2×C22⋊C4×C17C23
hypercenter#1820D17
hypocenterC17#11842
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1820

Complements

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

NH ≅ G/Ntype
6. C2×C4×Dic34C4semidirect
8. #11762739C4semidirect
10. #11762729C4semidirect
16. #11762677C4semidirect
218. C17#11842semidirect

Maximal subgroups

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

subgroupindex
#145343612
#145270982
#145268042
#145267832
C17×#18202
#1184217