Finite Group Databasebeta

← #17959203

Subgroups — #17959203

Order 4352.

402 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 72 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
2#14544026C211yesmaximal, characteristic
3#14543784C212yesmaximal
4#14543769C212yesmaximal
5#14532077C211yesmaximal, characteristic
6#11763826—21no—
7C2×#10587545—21no—
8C4×#63247—21no—
9#11763689C2212yes—
10#11763655C2212yes—
11#11763654—21no—
12C2×C4×Dic34C411yescharacteristic
13C2×C4×Dic34C2211yescharacteristic
14#11762741—21no—
15#11762741C411yescharacteristic
16#11762741C2211yescharacteristic
17#11762730—21no—
18#11762730C411yescharacteristic
19#11762730C2211yescharacteristic
20C4×C4⋊Dic17—21no—
21C4×C4⋊Dic17—21no—
22C17×#376C411yescharacteristic
23C22×Dic34C2×C411yescharacteristic
24C22×Dic34D411yescharacteristic
25C2×#63247—22no—
26C2×C42×C17—21no—
27C2×C42×C17C2×C411yescharacteristic
28C2×C4⋊Dic17—21no—
29C2×C4⋊Dic17—21no—
30C2×C4⋊Dic17—21no—
31C2×C4⋊Dic17—21no—
32C2×C4⋊Dic17C2×C411yescharacteristic
33C2×C4⋊Dic17D411yescharacteristic
34C2×#63225—21no—
35C2×#63225C2×C411yescharacteristic
36C2×#63225C2311yescharacteristic
37C2×C4×Dic17—21no—
38C2×C4×Dic17D411yescharacteristic
39C2×C4×Dic17D411yescharacteristic
40C4×Dic34—41no—
41C4×Dic34—41no—
42C4×Dic34—41no—
43C4×Dic34—41no—
44C22⋊#3624—22no—
45#10587545—24no—
46#10587544—41no—
47#10587542—41no—
48C4×#3624—41no—
49C4×#3624—41no—
50C17×#95—21no—
51C17×#95C2×C411yescharacteristic
52C17×#95C2×C411yescharacteristic
53#10587502—21no—
54#10587502—21no—
55#10587502—21no—
56#10587502—21no—
57C22×C4×C17—21no—
58C22×C4×C17—21no—
59C22×C4×C17C22⋊C411yescharacteristic
60C22×C4×C17C22⋊C411yescharacteristic
61C22×C4×C17C22×C411yescharacteristic
62C22×Dic17—21no—
63C22×Dic17—21no—
64C22×Dic17C22⋊C411yescharacteristic
65C22×Dic17C22⋊C411yescharacteristic
66C22×Dic17C2×D411yescharacteristic
67C22×Dic17C2×D411yescharacteristic
68C2×Dic34—22no—
69C2×Dic34—22no—
70C2×Dic34—41no—
71C2×Dic34—41no—
72C2×Dic34—42no—
73#63247—24no—
74#63247—42no—
75C2×#3624—42no—
76C2×#3624—42no—
77C42×C17—24no—
78C42×C17—21no—
79C42×C17—21no—
80C4⋊Dic17—41no—
81C4⋊Dic17—42no—
82C4⋊Dic17—42no—
83C4⋊Dic17—42no—
84C4⋊Dic17—42no—
85C4⋊Dic17—41no—
86#63225—41no—
87#63225—41no—
88#63225—42no—
89C4×Dic17—21no—
90C4×Dic17—21no—
91C4×Dic17—21no—
92C4×Dic17—21no—
93C4×Dic17—41no—
94C4×Dic17—41no—
95#11736—171nomaximal, Sylow
96C23×C17C2×C22⋊C411yescharacteristic
97C2×C4×C17—22no—
98C2×C4×C17—22no—
99C2×C4×C17—22no—
100C2×C4×C17—21no—
101C2×C4×C17—21no—
102C2×C4×C17—21no—
103C2×C4×C17—21no—
104C2×C4×C17—41no—
105C2×C4×C17—41no—
106C2×C4×C17—41no—
107C2×C4×C17—41no—
108C2×C4×C17—41no—
109C2×C4×C17#9911yescharacteristic
110C2×C4×C17#9911yescharacteristic
111C2×Dic17—21no—
112C2×Dic17—21no—
113C2×Dic17—21no—
114C2×Dic17—21no—
115C2×Dic17—22no—
116C2×Dic17—21no—
117C2×Dic17—21no—
118C2×Dic17—41no—
119C2×Dic17—41no—
120C2×Dic17—41no—
121C2×Dic17—41no—
122C2×Dic17—41no—
123C2×Dic17—41no—
124C2×Dic17—41no—
125C2×Dic17#10412yes—
126C2×Dic17#13512yes—
127Dic34—44no—
128Dic34—42no—
129Dic34—42no—
130#3624—44no—
131#3624—82no—
132#2399—171no—
133C4×#101—171no—
134#1461—171no—
135#1354—172no—
136#1346—172no—
137C22×C17—21no—
138C22×C17—21no—
139C22×C17C2×#9911yescharacteristic
140C22×C17#41611yescharacteristic
141C22×C17C2×#10411yescharacteristic
142C4×C17—21no—
143C4×C17—42no—
144C4×C17—42no—
145C4×C17—41no—
146C4×C17—41no—
147C4×C17#35612yes—
148Dic17—22no—
149Dic17—22no—
150Dic17—41no—
151Dic17—42no—
152Dic17—41no—
153Dic17—81no—
154C2×C4×Q8—171no—
155C2×C4×Q8—171no—
156#431—341no—
157C2×#101—341no—
158C4×M16—341no—
159#398—171no—
160#398—171no—
161#398—341no—
162#395—171no—
163#395—171no—
164#395—341no—
165C4×C4⋊C4—341no—
166C4×C4⋊C4—341no—
167#376#59511yescharacteristic
168#343—172no—
169#324—172no—
170#324—341no—
171C2×C17—21no—
172C2×C17—21no—
173C2×C17#150111yescharacteristic
174C2×C17#212011yescharacteristic
175C2×C17C2×#35611yescharacteristic
176C22×Q8—171no—
177C22×Q8—171no—
178C2×M16—342no—
179C4×Q8—681no—
180C4×Q8—681no—
181C4×Q8—681no—
182C4×Q8—681no—
183C2×C4⋊C4—171no—
184C2×C4⋊C4—171no—
185C2×C4⋊C4—171no—
186C2×C4⋊C4—171no—
187C2×C4⋊C4—341no—
188C2×C4⋊C4—341no—
189C2×C4⋊C4—341no—
190C2×C4⋊C4—341no—
191C2×C4⋊C4—341no—
192C2×C42—21no—
193C2×C42—171no—
194C2×C42—171no—
195C2×C42—341no—
196C2×C42C2×#59511yescharacteristic
197C4⋊C8—681no—
198#101—344no—
199C22⋊C8—342no—
200#97—681no—
201C4×C8—681no—
202C4×C8—681no—
203#95—21no—
204#95—341no—
205#95—341no—
206#95—341no—
207#95—341no—
208#95C2×#59511yescharacteristic
209#95C2×#59511yescharacteristic
210C17#1173611yescharacteristic, complemented, Sylow
211C2×Q8—342no—
212C2×Q8—342no—
213C2×Q8—681no—
214C2×Q8—681no—
215C2×Q8—682no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—171no—
219C22×C4—171no—
220C22×C4—171no—
221C22×C4—171no—
222C22×C4—341no—
223C22×C4—341no—
224C22×C4C22⋊#59511yescharacteristic
225C22×C4C22⋊#59511yescharacteristic
226C22×C4C22×#59511yescharacteristic
227M16—344no—
228M16—682no—
229C2×C8—682no—
230C2×C8—682no—
231C4⋊C4—681no—
232C4⋊C4—681no—
233C4⋊C4—681no—
234C4⋊C4—681no—
235C4⋊C4—682no—
236C4⋊C4—682no—
237C4⋊C4—682no—
238C4⋊C4—682no—
239C4⋊C4—682no—
240C42—24no—
241C42—21no—
242C42—21no—
243C42—341no—
244C42—341no—
245C42—341no—
246C42—341no—
247C42—681no—
248C42—681no—
249C23C2×C22⋊#59511yescharacteristic
250Q8—684no—
251Q8—682no—
252Q8—682no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—172no—
266C2×C4—172no—
267C2×C4—341no—
268C2×C4—341no—
269C2×C4—341no—
270C2×C4—341no—
271C2×C4—342no—
272C2×C4—341no—
273C2×C4—341no—
274C2×C4—681no—
275C2×C4—681no—
276C2×C4—681no—
277C2×C4—681no—
278C2×C4—681no—
279C2×C4—681no—
280C2×C4—681no—
281C2×C4#1058753911yescharacteristic
282C2×C4#1058753911yescharacteristic
283C8—684no—
284C8—1362no—
285C22—21no—
286C22—21no—
287C22C2×#1058753911yescharacteristic
288C22#1176379911yescharacteristic
289C22D17⋊#10411yescharacteristic
290C4—21no—
291C4—42no—
292C4—42no—
293C4—41no—
294C4—41no—
295C4—342no—
296C4—342no—
297C4—681no—
298C4—682no—
299C4—681no—
300C4—1361no—
301C4#1176372012yes—
302C2—21no—
303C2—21no—
304C2#1454416111yescharacteristic
305C2#1454503711yescharacteristic
306C2C2×#1176372011yescharacteristic
subgroupG/H
centerC2×C4#10587539
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC17×#376C4
socleC22×C17C2×#99
prime radicalC23×C17C2×C22⋊C4
cosocleC2×#63225C23
hypercenter#376#595
hypocenterC17#11736
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ #376

Complements

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

NH ≅ G/Ntype
210. C17#11736semidirect

Maximal subgroups

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

subgroupindex
C4×#105875452
#145440262
#145437842
#145437692
#145320772
#1173617