Finite Group Databasebeta

← #17958550

Subgroups — #17958550

Order 4352.

380 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 66 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#14544036C211yesmaximal, characteristic
2#14544016C211yesmaximal, characteristic
3#14543729C212yesmaximal
4#14543711C212yesmaximal
5#14533070C211yesmaximal, characteristic
6#11763830—21no—
7#11763826—21no—
8#11763655—21no—
9#11763655—21no—
10#11763652C2212yes—
11#11763652C2212yes—
12C2×#10587563C2211yescharacteristic
13C22×C4⋊Dic17C411yescharacteristic
14#11762751—21no—
15#11762742—21no—
16#11762696—21no—
17#11762695—21no—
18#11762682C2211yescharacteristic
19#11762670C411yescharacteristic
20#11762670C411yescharacteristic
21#11762670C2211yescharacteristic
22C17×#385C411yescharacteristic
23C23×C4×C17C2×C411yescharacteristic
24C23×Dic17C2×C411yescharacteristic
25C23×Dic17C2×C411yescharacteristic
26C2×C4⋊C4×C17—21no—
27C2×C22⋊C4×C17C2×C411yescharacteristic
28C2×C22⋊C4×C17C2×C411yescharacteristic
29C2×C22⋊Dic17C2×C411yescharacteristic
30C2×C22⋊Dic17C2311yescharacteristic
31C2×C4⋊Dic17—21no—
32C2×C4⋊Dic17—21no—
33C2×C4⋊Dic17—41no—
34C2×C4⋊Dic17—41no—
35C2×#63225—21no—
36C2×#63225D411yescharacteristic
37C2×#63225D411yescharacteristic
38C2×C4×Dic17D411yescharacteristic
39C2×C4×Dic17D411yescharacteristic
40#10587563—41no—
41#10587563—41no—
42C22⋊#3624—22no—
43C22⋊#3624—22no—
44#10587544—41no—
45#10587542—41no—
46C4⋊#3624—41no—
47C4×#3624—41no—
48C17×#95—21no—
49#10587502—21no—
50#10587502—21no—
51#10587502—21no—
52#10587502—21no—
53#10587502—21no—
54#10587502—21no—
55#10587502—21no—
56C24×C17C22×C411yescharacteristic
57C22×C4×C17—21no—
58C22×C4×C17—21no—
59C22×C4×C17—42no—
60C22×C4×C17—41no—
61C22×C4×C17C22⋊C411yescharacteristic
62C22×C4×C17C22⋊C411yescharacteristic
63C22×Dic17—22no—
64C22×Dic17—21no—
65C22×Dic17—21no—
66C22×Dic17—21no—
67C22×Dic17—21no—
68C22×Dic17—22no—
69C22×Dic17—41no—
70C22×Dic17—41no—
71C22×Dic17—41no—
72C22×Dic17C22⋊C411yescharacteristic
73C22×Dic17C22⋊C411yescharacteristic
74C22×Dic17C2×D411yescharacteristic
75C22×Dic17C2×D411yescharacteristic
76C2×#3624—42no—
77C2×#3624—42no—
78C4⋊C4×C17—42no—
79C22⋊C4×C17—41no—
80C22⋊C4×C17—41no—
81C22⋊Dic17—22no—
82C22⋊Dic17—41no—
83C4⋊Dic17—42no—
84C4⋊Dic17—41no—
85C4⋊Dic17—41no—
86#63225—41no—
87#63225—41no—
88#63225—42no—
89C4×Dic17—21no—
90C4×Dic17—21no—
91C4×Dic17—21no—
92C4×Dic17—21no—
93#11544—171nomaximal, Sylow
94C23×C17—21no—
95C23×C17—21no—
96C23×C17—41no—
97C23×C17—41no—
98C23×C17C2×C22⋊C411yescharacteristic
99C23×C17#13112yes—
100C2×C4×C17—22no—
101C2×C4×C17—21no—
102C2×C4×C17—21no—
103C2×C4×C17—41no—
104C2×C4×C17—42no—
105C2×C4×C17—41no—
106C2×C4×C17—41no—
107C2×C4×C17—41no—
108C2×C4×C17—42no—
109C2×C4×C17—41no—
110C2×C4×C17—41no—
111C2×C4×C17—41no—
112C2×Dic17—21no—
113C2×Dic17—21no—
114C2×Dic17—21no—
115C2×Dic17—21no—
116C2×Dic17—21no—
117C2×Dic17—21no—
118C2×Dic17—21no—
119C2×Dic17—42no—
120C2×Dic17—42no—
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—82no—
130C2×Dic17#9911yescharacteristic
131C2×Dic17#9911yescharacteristic
132#3624—82no—
133#3624—82no—
134#2484—171no—
135#1464—171no—
136#1458—171no—
137#1326—172no—
138#1317—172no—
139C22×C17—21no—
140C22×C17—21no—
141C22×C17—22no—
142C22×C17—42no—
143C22×C17—42no—
144C22×C17—41no—
145C22×C17—41no—
146C22×C17#40811yescharacteristic
147C22×C17C2×#9911yescharacteristic
148C22×C17#41311yescharacteristic
149C4×C17—41no—
150C4×C17—42no—
151C4×C17—41no—
152C4×C17—81no—
153Dic17—21no—
154Dic17—21no—
155Dic17—41no—
156Dic17—41no—
157Dic17—41no—
158Dic17—81no—
159Dic17—81no—
160C2×#117—171no—
161C22×C4⋊C4—171no—
162#432—341no—
163#431—341no—
164#400—341no—
165#398—341no—
166#387—341no—
167#387—341no—
168#385—171no—
169#385#59511yescharacteristic
170#381—171no—
171#381—171no—
172#381—171no—
173#324—341no—
174#324—341no—
175#323—172no—
176#323—172no—
177C2×C17—21no—
178C2×C17—21no—
179C2×C17—42no—
180C2×C17#146811yescharacteristic
181C2×C17#212011yescharacteristic
182C2×C17#212311yescharacteristic
183C23×C4—171no—
184C23×C4—171no—
185C23×C4C2×#59511yescharacteristic
186#117—681no—
187#117—681no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—171no—
190C2×C4⋊C4—171no—
191C2×C4⋊C4—341no—
192C2×C4⋊C4—341no—
193C2×C4⋊C4—341no—
194C2×C4⋊C4—681no—
195C2×C4⋊C4—681no—
196C2×C22⋊C4—171no—
197C2×C22⋊C4—171no—
198C2×C22⋊C4C2×#59511yescharacteristic
199C2×C22⋊C4C2×#59511yescharacteristic
200C2×C42—171no—
201C2×C42—171no—
202C4⋊C8—681no—
203C4⋊C8—681no—
204C22⋊C8—342no—
205C22⋊C8—342no—
206#97—681no—
207C4×C8—681no—
208#95—21no—
209#95—341no—
210#95—341no—
211#95—341no—
212#95—341no—
213#95—341no—
214#95—341no—
215#95—341no—
216C17#1154411yescharacteristic, complemented, Sylow
217C24C22×#59511yescharacteristic
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—42no—
221C22×C4—41no—
222C22×C4—171no—
223C22×C4—171no—
224C22×C4—171no—
225C22×C4—171no—
226C22×C4—341no—
227C22×C4—341no—
228C22×C4—342no—
229C22×C4—341no—
230C22×C4—341no—
231C22×C4—342no—
232C22×C4—681no—
233C22×C4—681no—
234C22×C4—681no—
235C22×C4C22⋊#59511yescharacteristic
236C22×C4C22⋊#59511yescharacteristic
237C2×C8—682no—
238C2×C8—682no—
239C4⋊C4—42no—
240C4⋊C4—681no—
241C4⋊C4—681no—
242C4⋊C4—682no—
243C4⋊C4—681no—
244C4⋊C4—681no—
245C4⋊C4—682no—
246C22⋊C4—41no—
247C22⋊C4—41no—
248C22⋊C4—342no—
249C22⋊C4—681no—
250C42—341no—
251C42—341no—
252C42—341no—
253C42—341no—
254C23—21no—
255C23—21no—
256C23—41no—
257C23—41no—
258C23#1058768012yes—
259C23C2×C22⋊#59511yescharacteristic
260C2×C4—22no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—41no—
264C2×C4—42no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—42no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—171no—
273C2×C4—171no—
274C2×C4—341no—
275C2×C4—341no—
276C2×C4—341no—
277C2×C4—341no—
278C2×C4—341no—
279C2×C4—341no—
280C2×C4—341no—
281C2×C4—682no—
282C2×C4—682no—
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—1362no—
292C8—1362no—
293C8—1362no—
294C22—21no—
295C22—21no—
296C22—22no—
297C22—42no—
298C22—42no—
299C22—41no—
300C22—41no—
301C22#1176378411yescharacteristic
302C22D17⋊#9911yescharacteristic
303C22#1176379511yescharacteristic
304C4—42no—
305C4—41no—
306C4—41no—
307C4—81no—
308C4—341no—
309C4—341no—
310C4—681no—
311C4—681no—
312C4—681no—
313C4—1361no—
314C4—1361no—
315C2—21no—
316C2—21no—
317C2—42no—
318C2#1454405211yescharacteristic
319C2#1454503611yescharacteristic
320C2#1454504711yescharacteristic
subgroupG/H
centerC22D17⋊#99
commutator, prime radicalC24×C17C22×C4
FrattiniC24C22×#595
FittingC17×#385C4
socleC22×C17C2×#99
cosocleC2×C22⋊Dic17C23
hypercenter#385#595
hypocenterC17#11544
LCSG ▷ C24×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #385

Complements

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

NH ≅ G/Ntype
216. C17#11544semidirect

Maximal subgroups

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

subgroupindex
#145440362
#145440162
#145437292
#145437112
#145330702
#1154417