Finite Group Databasebeta

← #16950329

Subgroups — #16950329

Order 4352.

480 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 101 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#14531497C211yesmaximal, characteristic
2C2×#11762606C211yesmaximal, characteristic
3#14528778C212yesmaximal, complemented
4#14526910C212yesmaximal, complemented
5C2×C17×#355C211yesmaximal, characteristic
6C2×Q8×Dic17C2211yescharacteristic
7C2×D4×Dic17C411yescharacteristic
8#11762832—22no—
9C2×#10587507C2212yes—
10#11762716C2211yescharacteristic
11#11762712C411yescharacteristic
12#11762702—22no—
13#11762684—22no—
14#11762679C411yescharacteristic
15#11762655C411yescharacteristic
16#11762606—22no—
17#11762577—22no—
18C2×C17×#124C2211yescharacteristic
19C2×C17×#101C2212yes—
20C17×#355—22no—
21C22×Q8×C17C2311yescharacteristic
22C22×D4×C17C2×C411yescharacteristic
23C23×Dic17—21no—
24C2×M16×C17—22no—
25C17×#124—22no—
26C17×#124D412yes—
27C17×#124Q812yes—
28C2×C22⋊C4×C17—22no—
29C2×C42×C17C2×C411yescharacteristic
30C2×C22⋊Dic17—21no—
31C2×C22⋊Dic17—22no—
32Q8×Dic17—42no—
33D4×Dic17—42no—
34C2×C4⋊Dic17—22no—
35C2×C4⋊Dic17C2×C411yescharacteristic
36C2×C4⋊Dic17C2×C411yescharacteristic
37C2×C4⋊Dic17D412yes—
38C2×C4×Dic17C2×C411yescharacteristic
39C2×C4×Dic17C2×C411yescharacteristic
40C2×C4×Dic17D412yes—
41C2×#63223—22no—
42C17×#101—22no—
43C17×#101—22no—
44#10587507—22no—
45#10587507—22no—
46#10587502—22no—
47#10587502—21no—
48#10587502—21no—
49#10587485—44no—
50C24×C17—21no—
51C2×Q8×C17—41no—
52C2×Q8×C17—41no—
53C2×Q8×C17C2×D411yescharacteristic
54C2×Q8×C17C2×Q811yescharacteristic
55C2×Q8×C17#4112yes—
56C2×D4×C17—21no—
57C2×D4×C17—41no—
58C2×D4×C17—41no—
59C2×D4×C17C4⋊C412yes—
60C22×C4×C17—21no—
61C22×C4×C17C22×C411yescharacteristic
62C22×C4×C17C2×D412yes—
63C22×Dic17—21no—
64C22×Dic17—21no—
65C22×Dic17—42no—
66C22×Dic17—82no—
67C22×Dic17C22⋊C411yescharacteristic
68C22×Dic17C22⋊C412yes—
69C22×Dic17C22⋊C411yescharacteristic
70M16×C17—42no—
71M16×C17—42no—
72C2×C8×C17—42no—
73C22⋊C4×C17—24no—
74C22⋊C4×C17—24no—
75C42×C17—21no—
76C42×C17C4⋊C412yes—
77C22⋊Dic17—42no—
78C22⋊Dic17—82no—
79C4⋊Dic17—41no—
80C4⋊Dic17—42no—
81C4⋊Dic17—41no—
82C4⋊Dic17—82no—
83C4×Dic17—24no—
84C4×Dic17—22no—
85C4×Dic17—41no—
86#63223—42no—
87#63223—42no—
88C2×#3622—42no—
89#12803—171nomaximal, Sylow
90C23×C17—22no—
91C23×C17—42no—
92C23×C17—42no—
93C23×C17—41no—
94C23×C17—41no—
95C23×C17C2×C22⋊C411yescharacteristic
96Q8×C17—41no—
97Q8×C17—41no—
98Q8×C17—42no—
99D4×C17—42no—
100D4×C17—42no—
101C2×C4×C17—22no—
102C2×C4×C17—21no—
103C2×C4×C17—22no—
104C2×C4×C17—21no—
105C2×C4×C17—22no—
106C2×C4×C17—41no—
107C2×C4×C17—41no—
108C2×C4×C17C2×C4⋊C411yescharacteristic
109C2×C4×C17#11711yescharacteristic
110C2×C4×C17#12112yes—
111C2×C4×C17C22⋊Q812yes—
112C2×Dic17—21no—
113C2×Dic17—22no—
114C2×Dic17—41no—
115C2×Dic17—42no—
116C2×Dic17—41no—
117C2×Dic17—41no—
118C2×Dic17—41no—
119C2×Dic17—42no—
120C2×Dic17—41no—
121C2×Dic17—41no—
122C2×Dic17—84no—
123C2×Dic17#9912yes—
124C8×C17—82no—
125#3622—82no—
126#2326—171no—
127C2×#355—171no—
128C2×#355D1711yescharacteristic
129#1801—172no—
130#1394—172no—
131C22×C17—21no—
132C22×C17—21no—
133C22×C17—44no—
134C22×C17—42no—
135C22×C17—82no—
136C22×C17—81no—
137C22×C17—81no—
138C22×C17#38011yescharacteristic
139C22×C17C2×#9911yescharacteristic
140C22×C17#41011yescharacteristic
141C4×C17—22no—
142C4×C17—21no—
143C4×C17—21no—
144C4×C17—22no—
145C4×C17—42no—
146Dic17—22no—
147Dic17—42no—
148Dic17—41no—
149Dic17—81no—
150Dic17—81no—
151C2×#124C2×D1711yescharacteristic
152C2×C4×Q8—171no—
153C2×C4×D4—171no—
154#423—342no—
155C2×#101—172no—
156C2×#101C2×D1712yes—
157#391—171no—
158#390—171no—
159#388—342no—
160#385—342no—
161#384—171no—
162#376—171no—
163#355—22no—
164#355—342no—
165#343—342no—
166C2×C17—21no—
167C2×C17—21no—
168C2×C17—82no—
169C2×C17#179911yescharacteristic
170C2×C17#213311yescharacteristic
171C2×C17#213411yescharacteristic
172C22×Q8C22×D1711yescharacteristic
173C22×D4C4×D1711yescharacteristic
174C23×C4—341no—
175C2×M16—22no—
176C2×M16—342no—
177#124—22no—
178#124Dic3412yes—
179#124C22⋊D1712yes—
180C4×Q8—682no—
181C4×D4—682no—
182C2×C4⋊C4—171no—
183C2×C4⋊C4—172no—
184C2×C4⋊C4—171no—
185C2×C4⋊C4—342no—
186C2×C22⋊C4—22no—
187C2×C22⋊C4—341no—
188C2×C22⋊C4—342no—
189C2×C42—171no—
190C2×C42—172no—
191C2×C42—171no—
192C2×C42C4×D1711yescharacteristic
193C4⋊C8—684no—
194#101—22no—
195#101—22no—
196#101—342no—
197#101—342no—
198#95—341no—
199#95—341no—
200#95—342no—
201C17#1280311yescharacteristic, complemented, Sylow
202C24—21no—
203C2×Q8—41no—
204C2×Q8—41no—
205C2×Q8C2×Dic3411yescharacteristic
206C2×Q8#6325412yes—
207C2×Q8C2×C22⋊D1711yescharacteristic
208C2×D4—21no—
209C2×D4—41no—
210C2×D4—41no—
211C2×D4#6322512yes—
212C22×C4—21no—
213C22×C4—171no—
214C22×C4—171no—
215C22×C4—172no—
216C22×C4—341no—
217C22×C4—341no—
218C22×C4—682no—
219C22×C4—1362no—
220C22×C4C2×C4×D1711yescharacteristic
221C22×C4D4×D1712yes—
222M16—42no—
223M16—42no—
224M16—682no—
225M16—682no—
226C2×C8—42no—
227C2×C8—682no—
228C4⋊C4—681no—
229C4⋊C4—682no—
230C4⋊C4—681no—
231C4⋊C4—1362no—
232C22⋊C4—24no—
233C22⋊C4—24no—
234C22⋊C4—682no—
235C22⋊C4—1362no—
236C42—21no—
237C42—344no—
238C42—342no—
239C42—681no—
240C42#6322512yes—
241C23—22no—
242C23—42no—
243C23—42no—
244C23—41no—
245C23—41no—
246C23C22⋊C4×D1711yescharacteristic
247Q8—41no—
248Q8—42no—
249Q8—41no—
250D4—42no—
251D4—42no—
252C2×C4—21no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—172no—
260C2×C4—341no—
261C2×C4—342no—
262C2×C4—681no—
263C2×C4—682no—
264C2×C4—681no—
265C2×C4—681no—
266C2×C4—682no—
267C2×C4—681no—
268C2×C4—681no—
269C2×C4—681no—
270C2×C4—1364no—
271C2×C4#1058756311yescharacteristic
272C2×C4#1058756412yes—
273C2×C4C2×#6322511yescharacteristic
274C2×C4#1058762512yes—
275C8—82no—
276C8—1362no—
277C22—21no—
278C22—21no—
279C22—44no—
280C22—42no—
281C22—82no—
282C22—81no—
283C22—81no—
284C22#1176266711yescharacteristic
285C22#99×D1711yescharacteristic
286C22#1176278111yescharacteristic
287C4—22no—
288C4—21no—
289C4—22no—
290C4—21no—
291C4—42no—
292C4—342no—
293C4—681no—
294C4—682no—
295C4—1361no—
296C4—1361no—
297C2—21no—
298C2—21no—
299C2—82no—
300C2#1452877011yescharacteristic
301C2#1453047011yescharacteristic
302C2#1453047411yescharacteristic
subgroupG/H
centerC22#99×D17
commutatorC22×C4×C17C22×C4
FrattiniC22×Q8C22×D17
FittingC2×C17×#355C2
socleC22×C17C2×#99
prime radicalC22×D4×C17C2×C4
cosocleC22×Q8×C17C23
hypercenterC2×#355D17
hypocenterC17#12803
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#355

Complements

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

NH ≅ G/Ntype
3. #14528778C2semidirect
4. #14526910C2semidirect
201. C17#12803semidirect

Maximal subgroups

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

subgroupindex
#145314972
C2×#117626062
#145287782
#145269102
C2×C17×#3552
#1280317