Finite Group Databasebeta

← #17953586

Subgroups — #17953586

Order 4352.

482 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 94 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#14544510C211yesmaximal, characteristic
2#14544510C211yesmaximal, characteristic
3#14543660C212yesmaximal, complemented
4#14543660C212yesmaximal, complemented
5#14531179C211yesmaximal, characteristic
6C2×C22⋊#3624—21no—
7C2×C22⋊#3624—21no—
8C2×#10587542C2212yes—
9C2×#10587542C2212yes—
10#11763675—21no—
11#11763675—21no—
12C22×C4×Dic17C2211yescharacteristic
13#11762676—21no—
14#11762674C2211yescharacteristic
15#11762674C2211yescharacteristic
16#11762670—21no—
17#11762669C411yescharacteristic
18C4⋊C4×Dic17C411yescharacteristic
19C4⋊C4×Dic17C411yescharacteristic
20C22⋊C4×Dic17—21no—
21#11762654—21no—
22C17×#380C411yescharacteristic
23C23×C4×C17C2×C411yescharacteristic
24C23×Dic17D411yescharacteristic
25C23×Dic17D411yescharacteristic
26C22×#3624—22no—
27C22×#3624—22no—
28C2×C4⋊C4×C17C2×C411yescharacteristic
29C2×C4⋊C4×C17C2×C411yescharacteristic
30C2×C22⋊C4×C17—21no—
31C2×C22⋊Dic17—21no—
32C2×C4⋊Dic17C2×C411yescharacteristic
33C2×C4⋊Dic17C2×C411yescharacteristic
34C2×C4×Dic17—24no—
35C2×C4×Dic17—21no—
36C2×C4×Dic17—21no—
37C2×C4×Dic17C2×C411yescharacteristic
38C2×C4×Dic17D411yescharacteristic
39C2×C4×Dic17D411yescharacteristic
40C2×C4×Dic17C2311yescharacteristic
41C22⋊#3624—24no—
42C22⋊#3624—24no—
43#10587542—24no—
44#10587542—24no—
45C17×#95—21no—
46#10587502—21no—
47#10587502—21no—
48#10587502—21no—
49#10587502—21no—
50#10587502—21no—
51#10587502—21no—
52#10587502—21no—
53C24×C17C22⋊C411yescharacteristic
54C22×C4×C17—22no—
55C22×C4×C17—21no—
56C22×C4×C17—21no—
57C22×C4×C17—41no—
58C22×C4×C17—41no—
59C22×C4×C17C22⋊C411yescharacteristic
60C22×C4×C17C22×C411yescharacteristic
61C22×Dic17—22no—
62C22×Dic17—22no—
63C22×Dic17—22no—
64C22×Dic17—22no—
65C22×Dic17—21no—
66C22×Dic17—21no—
67C22×Dic17—41no—
68C22×Dic17—41no—
69C22×Dic17C22⋊C411yescharacteristic
70C22×Dic17C22⋊C411yescharacteristic
71C22×Dic17C2×D411yescharacteristic
72C22×Dic17C2×D411yescharacteristic
73C2×#3624—24no—
74C2×#3624—24no—
75C2×#3624—42no—
76C2×#3624—42no—
77C2×#3624—42no—
78C2×#3624—42no—
79C4⋊C4×C17—41no—
80C4⋊C4×C17—41no—
81C22⋊C4×C17—42no—
82C22⋊Dic17—42no—
83C4⋊Dic17—41no—
84C4⋊Dic17—41no—
85C4×Dic17—22no—
86C4×Dic17—22no—
87C4×Dic17—22no—
88C4×Dic17—42no—
89C4×Dic17—42no—
90C4×Dic17#4114yes—
91#8720—171nomaximal, Sylow
92C23×C17—21no—
93C23×C17—21no—
94C23×C17—21no—
95C23×C17—21no—
96C23×C17—21no—
97C23×C17—21no—
98C23×C17#10412yes—
99C23×C17C2×C22⋊C411yescharacteristic
100C2×C4×C17—21no—
101C2×C4×C17—21no—
102C2×C4×C17—21no—
103C2×C4×C17—21no—
104C2×C4×C17—21no—
105C2×C4×C17—44no—
106C2×C4×C17—41no—
107C2×C4×C17—41no—
108C2×C4×C17—41no—
109C2×C4×C17—41no—
110C2×C4×C17—41no—
111C2×C4×C17—41no—
112C2×C4×C17#11712yes—
113C2×Dic17—21no—
114C2×Dic17—21no—
115C2×Dic17—21no—
116C2×Dic17—21no—
117C2×Dic17—21no—
118C2×Dic17—21no—
119C2×Dic17—21no—
120C2×Dic17—21no—
121C2×Dic17—21no—
122C2×Dic17—44no—
123C2×Dic17—44no—
124C2×Dic17—41no—
125C2×Dic17—41no—
126C2×Dic17—41no—
127C2×Dic17—41no—
128C2×Dic17—41no—
129C2×Dic17—41no—
130C2×Dic17#10412yes—
131C2×Dic17#12312yes—
132C2×Dic17#12312yes—
133#3624—44no—
134#3624—44no—
135#2283—171no—
136#1749—171no—
137#1749—171no—
138#1295—172no—
139#1295—172no—
140C22×C17—22no—
141C22×C17—22no—
142C22×C17—22no—
143C22×C17—41no—
144C22×C17—41no—
145C22×C17—41no—
146C22×C17—41no—
147C22×C17#38111yescharacteristic
148C22×C17#41311yescharacteristic
149C22×C17#41311yescharacteristic
150C22×C17C2×#10411yescharacteristic
151C22×C17C2×#10411yescharacteristic
152C22×C17#42111yescharacteristic
153C22×C17#42111yescharacteristic
154C4×C17—22no—
155C4×C17—41no—
156C4×C17—81no—
157C4×C17—81no—
158Dic17—22no—
159Dic17—22no—
160Dic17—22no—
161Dic17—41no—
162Dic17—81no—
163Dic17—81no—
164C22×C42—171no—
165C2×C22⋊C8—341no—
166C2×C22⋊C8—341no—
167C2×#97—172no—
168C2×#97—172no—
169#383—341no—
170#382—171no—
171#382—171no—
172#381—341no—
173#380—171no—
174#380#59511yescharacteristic
175C4×C4⋊C4—171no—
176C4×C4⋊C4—171no—
177C4×C22⋊C4—341no—
178#376—341no—
179#336—341no—
180#336—341no—
181C2×C17—42no—
182C2×C17#152411yescharacteristic
183C2×C17#152911yescharacteristic
184C2×C17#153211yescharacteristic
185C2×C17#153511yescharacteristic
186C2×C17#182211yescharacteristic
187C2×C17#182611yescharacteristic
188C2×C17#182611yescharacteristic
189C23×C4—171no—
190C23×C4—171no—
191C23×C4C2×#59511yescharacteristic
192C22×C8—342no—
193C22×C8—342no—
194C2×C4⋊C4—171no—
195C2×C4⋊C4—171no—
196C2×C4⋊C4C2×#59511yescharacteristic
197C2×C4⋊C4C2×#59511yescharacteristic
198C2×C22⋊C4—21no—
199C2×C22⋊C4—341no—
200C2×C42—171no—
201C2×C42—171no—
202C2×C42—171no—
203C2×C42—171no—
204C2×C42—344no—
205C2×C42—341no—
206C2×C42—341no—
207C22⋊C8—344no—
208C22⋊C8—344no—
209#97—344no—
210#97—344no—
211#95—21no—
212#95—341no—
213#95—341no—
214#95—341no—
215#95—341no—
216#95—341no—
217#95—341no—
218#95—341no—
219C17#872011yescharacteristic, complemented, Sylow
220C24C22⋊#59511yescharacteristic
221C22×C4—22no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—41no—
225C22×C4—41no—
226C22×C4—171no—
227C22×C4—171no—
228C22×C4—171no—
229C22×C4—171no—
230C22×C4—342no—
231C22×C4—342no—
232C22×C4—342no—
233C22×C4—342no—
234C22×C4—341no—
235C22×C4—341no—
236C22×C4—681no—
237C22×C4—681no—
238C22×C4C22⋊#59511yescharacteristic
239C22×C4C22×#59511yescharacteristic
240C2×C8—344no—
241C2×C8—344no—
242C2×C8—682no—
243C2×C8—682no—
244C2×C8—682no—
245C2×C8—682no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—681no—
249C4⋊C4—681no—
250C22⋊C4—42no—
251C22⋊C4—682no—
252C42—174no—
253C42—342no—
254C42—342no—
255C42—342no—
256C42—682no—
257C42—682no—
258C23—21no—
259C23—21no—
260C23—21no—
261C23—21no—
262C23—21no—
263C23—21no—
264C23#1058755012yes—
265C23C2×C22⋊#59511yescharacteristic
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—44no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—172no—
279C2×C4—172no—
280C2×C4—172no—
281C2×C4—341no—
282C2×C4—341no—
283C2×C4—341no—
284C2×C4—341no—
285C2×C4—341no—
286C2×C4—341no—
287C2×C4—341no—
288C2×C4—341no—
289C2×C4—341no—
290C2×C4—684no—
291C2×C4—684no—
292C2×C4—681no—
293C2×C4—681no—
294C2×C4—681no—
295C2×C4—681no—
296C2×C4—681no—
297C2×C4—681no—
298C2×C4#1058767712yes—
299C8—684no—
300C8—684no—
301C22—22no—
302C22—22no—
303C22—22no—
304C22—41no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22#1176375211yescharacteristic
309C22#1176379611yescharacteristic
310C22#1176379611yescharacteristic
311C22D17⋊#10411yescharacteristic
312C22C2×#1058755011yescharacteristic
313C22#1176380611yescharacteristic
314C22#1176380711yescharacteristic
315C4—22no—
316C4—41no—
317C4—81no—
318C4—81no—
319C4—342no—
320C4—342no—
321C4—342no—
322C4—681no—
323C4—1361no—
324C4—1361no—
325C2—42no—
326C2#1454423711yescharacteristic
327C2#1454425011yescharacteristic
328C2#1454426211yescharacteristic
329C2#1454426911yescharacteristic
330C2#1454468611yescharacteristic
331C2#1454469111yescharacteristic
332C2#1454469211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC17×#380C4
socleC23×C17C2×C22⋊C4
prime radicalC24×C17C22⋊C4
cosocleC2×C4×Dic17C23
hypercenter#380#595
hypocenterC17#8720
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
3. #14543660C2semidirect
4. #14543660C2semidirect
219. C17#8720semidirect

Maximal subgroups

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

subgroupindex
#145445102
#145436602
#145311792
#872017