Finite Group Databasebeta

← #16943809

Subgroups — #16943809

Order 4352.

424 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 75 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#14531494C211yesmaximal, characteristic
2#14527126C212yesmaximal, complemented
3#14526729C212yesmaximal, complemented
4#14526716C211yesmaximal, characteristic
5C17×#1318C211yesmaximal, characteristic
6C2×#10587622C411yescharacteristic
7C2×#10587573C2211yescharacteristic
8C2×D4×Dic17C411yescharacteristic
9#11762863—22no—
10#11762715C411yescharacteristic
11#11762703—22no—
12#11762681—22no—
13#11762678C2211yescharacteristic
14#11762655C411yescharacteristic
15#11762535C2212yes—
16#11762534—22no—
17C17×#390C2211yescharacteristic
18C17×#324C2212yes—
19C22×D4×C17C2×C411yescharacteristic
20C23×Dic17—21no—
21C22×Dic34C2×C411yescharacteristic
22C2×C4⋊C4×C17C2311yescharacteristic
23C2×C22⋊C4×C17—22no—
24C2×C42×C17C2×C411yescharacteristic
25C2×C22⋊Dic17—22no—
26C2×C22⋊Dic17—21no—
27#10587622—22no—
28#10587622—22no—
29D4×Dic17—42no—
30C2×C4⋊Dic17C2×C411yescharacteristic
31C2×#63225—22no—
32C2×#63225D412yes—
33C2×C4×Dic17C2×C411yescharacteristic
34C2×C4×Dic17C2×C411yescharacteristic
35C2×C4×Dic17D412yes—
36#10587573—42no—
37C17×C22⋊C8—22no—
38#10587502—21no—
39#10587502—22no—
40#10587502—21no—
41C22⋊#3622—22no—
42#10587486—42no—
43#10587485—42no—
44C24×C17—21no—
45C2×D4×C17—21no—
46C2×D4×C17—41no—
47C2×D4×C17—41no—
48C2×D4×C17M1612yes—
49C22×C4×C17—21no—
50C22×C4×C17C22×C411yescharacteristic
51C22×C4×C17C2×D412yes—
52C22×Dic17—21no—
53C22×Dic17—21no—
54C22×Dic17—42no—
55C22×Dic17—82no—
56C22×Dic17C22⋊C412yes—
57C22×Dic17C22⋊C411yescharacteristic
58C22×Dic17C22⋊C411yescharacteristic
59C2×Dic34—21no—
60C2×Dic34—21no—
61C2×Dic34—41no—
62C2×Dic34—41no—
63C2×C8×C17—42no—
64C4⋊C4×C17—41no—
65C22⋊C4×C17—82no—
66C42×C17—41no—
67C22⋊Dic17—28no—
68C22⋊Dic17—42no—
69C4⋊Dic17—41no—
70#63225—42no—
71#63225—82no—
72C4×Dic17—21no—
73C4×Dic17—22no—
74C4×Dic17—22no—
75C4×Dic17—22no—
76C4×Dic17M1612yes—
77C2×#3622—42no—
78#11534—171nomaximal, Sylow
79C23×C17—22no—
80C23×C17—42no—
81C23×C17—42no—
82C23×C17—41no—
83C23×C17—41no—
84C23×C17C2×C22⋊C411yescharacteristic
85D4×C17—42no—
86D4×C17—42no—
87C2×C4×C17—21no—
88C2×C4×C17—21no—
89C2×C4×C17—22no—
90C2×C4×C17—42no—
91C2×C4×C17—41no—
92C2×C4×C17—41no—
93C2×C4×C17—41no—
94C2×C4×C17C2×M1611yescharacteristic
95C2×C4×C17C2×M1611yescharacteristic
96C2×Dic17—22no—
97C2×Dic17—22no—
98C2×Dic17—22no—
99C2×Dic17—21no—
100C2×Dic17—22no—
101C2×Dic17—41no—
102C2×Dic17—41no—
103C2×Dic17—41no—
104C2×Dic17—41no—
105C2×Dic17—42no—
106C2×Dic17—41no—
107C2×Dic17—84no—
108C2×Dic17#9912yes—
109Dic34—42no—
110Dic34—42no—
111C8×C17—82no—
112#3622—82no—
113#2326—171no—
114#1467—172no—
115#1325—172no—
116#1318—171no—
117#1318D1711yescharacteristic
118C22×C17—21no—
119C22×C17—21no—
120C22×C17—44no—
121C22×C17—42no—
122C22×C17—82no—
123C22×C17—81no—
124C22×C17—81no—
125C22×C17#40711yescharacteristic
126C22×C17C2×#9911yescharacteristic
127C22×C17#41311yescharacteristic
128C4×C17—21no—
129C4×C17—21no—
130C4×C17—42no—
131C4×C17—81no—
132Dic17—22no—
133Dic17—42no—
134Dic17—41no—
135Dic17—42no—
136Dic17—81no—
137C2×#124—171no—
138C2×C4×Q8—171no—
139C2×C4×D4—171no—
140#432—342no—
141#391—171no—
142#390C2×D1711yescharacteristic
143#388—342no—
144#385—342no—
145#384—171no—
146#376—171no—
147#324—172no—
148#324—342no—
149#324C2×D1712yes—
150C2×C17—21no—
151C2×C17—21no—
152C2×C17—82no—
153C2×C17#146511yescharacteristic
154C2×C17#212811yescharacteristic
155C2×C17#213311yescharacteristic
156C22×Q8—171no—
157C22×D4C4×D1711yescharacteristic
158C23×C4—341no—
159#124—342no—
160#124—342no—
161C4×Q8—682no—
162C4×D4—682no—
163C2×C4⋊C4—172no—
164C2×C4⋊C4—171no—
165C2×C4⋊C4—342no—
166C2×C4⋊C4C22×D1711yescharacteristic
167C2×C22⋊C4—22no—
168C2×C22⋊C4—342no—
169C2×C22⋊C4—341no—
170C2×C42—171no—
171C2×C42—171no—
172C2×C42—172no—
173C2×C42C4×D1711yescharacteristic
174C4⋊C8—682no—
175C22⋊C8—22no—
176C22⋊C8—342no—
177#97—682no—
178#95—341no—
179#95—341no—
180#95—342no—
181C17#1153411yescharacteristic, complemented, Sylow
182C24—21no—
183C2×Q8—341no—
184C2×Q8—341no—
185C2×Q8—681no—
186C2×Q8—681no—
187C2×D4—21no—
188C2×D4—41no—
189C2×D4—41no—
190C2×D4#6321812yes—
191C22×C4—21no—
192C22×C4—171no—
193C22×C4—172no—
194C22×C4—171no—
195C22×C4—341no—
196C22×C4—341no—
197C22×C4—682no—
198C22×C4—1362no—
199C22×C4C2×C4×D1711yescharacteristic
200C22×C4D4×D1712yes—
201C2×C8—42no—
202C2×C8—682no—
203C4⋊C4—41no—
204C4⋊C4—682no—
205C4⋊C4—681no—
206C4⋊C4—1362no—
207C22⋊C4—82no—
208C22⋊C4—348no—
209C22⋊C4—682no—
210C42—41no—
211C42—172no—
212C42—342no—
213C42—342no—
214C42—342no—
215C42—341no—
216C23—22no—
217C23—42no—
218C23—42no—
219C23—41no—
220C23—41no—
221C23C22⋊C4×D1711yescharacteristic
222Q8—682no—
223Q8—682no—
224D4—42no—
225D4—42no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—42no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—172no—
234C2×C4—342no—
235C2×C4—342no—
236C2×C4—341no—
237C2×C4—342no—
238C2×C4—342no—
239C2×C4—681no—
240C2×C4—681no—
241C2×C4—681no—
242C2×C4—681no—
243C2×C4—682no—
244C2×C4—681no—
245C2×C4—1364no—
246C2×C4C2×#6321811yescharacteristic
247C2×C4M16×D1711yescharacteristic
248C8—82no—
249C8—1362no—
250C22—21no—
251C22—21no—
252C22—44no—
253C22—42no—
254C22—82no—
255C22—81no—
256C22—81no—
257C22#1176277111yescharacteristic
258C22#99×D1711yescharacteristic
259C22#1176279011yescharacteristic
260C4—21no—
261C4—21no—
262C4—42no—
263C4—81no—
264C4—342no—
265C4—682no—
266C4—682no—
267C4—681no—
268C4—1361no—
269C2—21no—
270C2—21no—
271C2—82no—
272C2#1452711911yescharacteristic
273C2#1453045411yescharacteristic
274C2#1453047011yescharacteristic
subgroupG/H
centerC22#99×D17
commutatorC22×C4×C17C22×C4
FrattiniC2×C4⋊C4C22×D17
FittingC17×#1318C2
socleC22×C17C2×#99
prime radicalC22×D4×C17C2×C4
cosocleC2×C4⋊C4×C17C23
hypercenter#1318D17
hypocenterC17#11534
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1318

Complements

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

NH ≅ G/Ntype
2. #14527126C2semidirect
3. #14526729C2semidirect
181. C17#11534semidirect

Maximal subgroups

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

subgroupindex
#145314942
#145271262
#145267292
#145267162
C17×#13182
#1153417