Finite Group Databasebeta

← #16945381

Subgroups — #16945381

Order 4352.

408 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 99 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#14533769C211yesmaximal, characteristic
2#14527108C211yesmaximal, characteristic
3#14526789C214yesmaximal
4C17×#1801C211yesmaximal, characteristic
5C2×#10587555C411yescharacteristic
6C2×#10587630—21no—
7#11762862—21no—
8#11762739C412yes—
9#11762739C2212yes—
10#11762714—21no—
11#11762707—21no—
12#11762707—21no—
13C4×C4⋊Dic17C411yescharacteristic
14#11762535—21no—
15#11762535C2212yes—
16C2×C4×Q8×C17C2211yescharacteristic
17C17×#423—21no—
18C2×C17×#101—21no—
19C17×#343C2212yes—
20C22×Q8×C17D411yescharacteristic
21C22×Dic34—21no—
22C2×M16×C17—22no—
23C4×Q8×C17—41no—
24C4×Q8×C17—41no—
25C2×C4⋊C4×C17C2×C411yescharacteristic
26C2×C4⋊C4×C17D411yescharacteristic
27C2×C4⋊C4×C17C2311yescharacteristic
28C2×C42×C17C2×C411yescharacteristic
29C2×C42×C17D411yescharacteristic
30C2×C42×C17D411yescharacteristic
31#10587630—42no—
32#10587630—42no—
33C2×C4⋊Dic17—21no—
34C2×C4⋊Dic17—21no—
35C2×C4⋊Dic17C2×C412yes—
36C2×#63225—22no—
37C2×#63225—22no—
38C2×C4×Dic17—21no—
39#10587555—41no—
40#10587555—41no—
41C17×C4⋊C8—41no—
42C17×C4⋊C8—41no—
43C17×#101—42no—
44#10587502—22no—
45#10587502—22no—
46#10587502C2×C412yes—
47C22⋊#3622—22no—
48C4⋊#3622—41no—
49C4×#3622—41no—
50C2×Q8×C17—41no—
51C2×Q8×C17—41no—
52C2×Q8×C17D812yes—
53C2×Q8×C17SD1612yes—
54C22×C4×C17C22⋊C411yescharacteristic
55C22×C4×C17C22⋊C411yescharacteristic
56C22×C4×C17C22⋊C411yescharacteristic
57C22×C4×C17C22⋊C411yescharacteristic
58C22×C4×C17C22×C411yescharacteristic
59C22×C4×C17C2×D411yescharacteristic
60C22×C4×C17C2×D411yescharacteristic
61C22×Dic17—22no—
62C22×Dic17—22no—
63C2×Dic34—42no—
64C2×Dic34—42no—
65C2×Dic34—42no—
66M16×C17—42no—
67M16×C17—42no—
68C2×C8×C17—42no—
69C4⋊C4×C17—41no—
70C4⋊C4×C17—41no—
71C4⋊C4×C17—41no—
72C42×C17—21no—
73C42×C17—21no—
74C42×C17—21no—
75C42×C17—21no—
76C42×C17—21no—
77C42×C17—21no—
78C4⋊Dic17—24no—
79C4⋊Dic17—41no—
80C4⋊Dic17—41no—
81C4⋊Dic17—42no—
82#63225—44no—
83#63225—42no—
84#63225—42no—
85C4×Dic17—42no—
86C2×#3622—42no—
87#11883—171nomaximal, Sylow
88C23×C17C2×C22⋊C411yescharacteristic
89Q8×C17—42no—
90Q8×C17—42no—
91C2×C4×C17—21no—
92C2×C4×C17—21no—
93C2×C4×C17—21no—
94C2×C4×C17—21no—
95C2×C4×C17—21no—
96C2×C4×C17—21no—
97C2×C4×C17—22no—
98C2×C4×C17—21no—
99C2×C4×C17—21no—
100C2×C4×C17—21no—
101C2×C4×C17—41no—
102C2×C4×C17—41no—
103C2×C4×C17—41no—
104C2×C4×C17#9911yescharacteristic
105C2×C4×C17#9911yescharacteristic
106C2×C4×C17#10212yes—
107C2×C4×C17#10212yes—
108C2×C4×C17C2×D811yescharacteristic
109C2×C4×C17C2×SD1611yescharacteristic
110C2×Dic17—24no—
111C2×Dic17—42no—
112C2×Dic17—42no—
113C2×Dic17—42no—
114C2×Dic17—42no—
115C2×Dic17—42no—
116Dic34—84no—
117C8×C17—82no—
118#3622—82no—
119#2546—171no—
120#1801D1711yescharacteristic
121#1461—171no—
122#1346—174no—
123C22×C17—21no—
124C22×C17—21no—
125C22×C17C2×#9911yescharacteristic
126C22×C17C2×#10211yescharacteristic
127C22×C17#42111yescharacteristic
128C4×C17—21no—
129C4×C17—21no—
130C4×C17—22no—
131C4×C17—22no—
132C4×C17—21no—
133C4×C17—41no—
134C4×C17—41no—
135C4×C17—41no—
136C4×C17#35612yes—
137Dic17—44no—
138Dic17—82no—
139C2×C4⋊Q8—171no—
140C2×C4⋊Q8—341no—
141C2×C4×Q8C2×D1711yescharacteristic
142#431—341no—
143#423—21no—
144C2×#101—21no—
145#398—172no—
146#398—172no—
147#391—341no—
148#389—341no—
149#389—341no—
150C4×C4⋊C4—171no—
151#343C2×D1712yes—
152#324—172no—
153#324—341no—
154C2×C17—21no—
155C2×C17—21no—
156C2×C17#151911yescharacteristic
157C2×C17#212311yescharacteristic
158C2×C17C2×#35611yescharacteristic
159C22×Q8—341no—
160C22×Q8C22⋊D1711yescharacteristic
161C2×M16—22no—
162C4⋊Q8—681no—
163C4⋊Q8—681no—
164C4⋊Q8—682no—
165C4⋊Q8—682no—
166C4×Q8—41no—
167C4×Q8—41no—
168C2×C4⋊C4—172no—
169C2×C4⋊C4—341no—
170C2×C4⋊C4—342no—
171C2×C4⋊C4—342no—
172C2×C4⋊C4—341no—
173C2×C4⋊C4C4×D1711yescharacteristic
174C2×C4⋊C4D6811yescharacteristic
175C2×C4⋊C4C22×D1711yescharacteristic
176C2×C42—341no—
177C2×C42C4×D1711yescharacteristic
178C2×C42D6811yescharacteristic
179C2×C42C22⋊D1711yescharacteristic
180C4⋊C8—41no—
181C4⋊C8—41no—
182C4⋊C8—681no—
183#101—42no—
184C22⋊C8—342no—
185C4×C8—681no—
186#95—172no—
187#95—342no—
188#95—342no—
189C17#1188311yescharacteristic, complemented, Sylow
190C2×Q8—41no—
191C2×Q8—41no—
192C2×Q8—682no—
193C2×Q8—682no—
194C2×Q8—682no—
195C2×Q8#6322812yes—
196C2×Q8#6323012yes—
197C22×C4—342no—
198C22×C4—342no—
199C22×C4#6322711yescharacteristic
200C22×C4#6322711yescharacteristic
201C22×C4#6322711yescharacteristic
202C22×C4#6322711yescharacteristic
203C22×C4C2×C4×D1711yescharacteristic
204C22×C4C2×D6811yescharacteristic
205C22×C4C2×C22⋊D1711yescharacteristic
206M16—42no—
207M16—42no—
208C2×C8—42no—
209C2×C8—682no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—344no—
214C4⋊C4—682no—
215C4⋊C4—681no—
216C4⋊C4—681no—
217C4⋊C4—684no—
218C4⋊C4—682no—
219C4⋊C4—682no—
220C42—21no—
221C42—21no—
222C42—21no—
223C42—21no—
224C42—21no—
225C42—21no—
226C42—682no—
227C23C2×#6322711yescharacteristic
228Q8—42no—
229Q8—42no—
230Q8—1364no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—344no—
245C2×C4—682no—
246C2×C4—682no—
247C2×C4—682no—
248C2×C4—682no—
249C2×C4—682no—
250C2×C4#1058747711yescharacteristic
251C2×C4#1058747711yescharacteristic
252C2×C4#1058748012yes—
253C2×C4#1058748012yes—
254C2×C4C2×#6322811yescharacteristic
255C2×C4C2×#6323011yescharacteristic
256C8—82no—
257C8—1362no—
258C22—21no—
259C22—21no—
260C22C2×#1058747711yescharacteristic
261C22C2×#1058748011yescharacteristic
262C22#1176282711yescharacteristic
263C4—21no—
264C4—22no—
265C4—22no—
266C4—21no—
267C4—21no—
268C4—41no—
269C4—41no—
270C4—41no—
271C4—684no—
272C4—1362no—
273C4#1176260712yes—
274C2—21no—
275C2—21no—
276C2#1452735111yescharacteristic
277C2#1453043911yescharacteristic
278C2C2×#1176260711yescharacteristic
subgroupG/H
centerC22C2×#10587477
commutatorC22×C4×C17C22×C4
FrattiniC2×C4⋊C4C22×D17
FittingC17×#1801C2
socleC22×C17C2×#99
prime radicalC23×C17C2×C22⋊C4
cosocleC2×C4⋊C4×C17C23
hypercenter#1801D17
hypocenterC17#11883
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1801

Complements

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

NH ≅ G/Ntype
189. C17#11883semidirect

Maximal subgroups

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

subgroupindex
#145337692
#145271082
#145267892
C17×#18012
#1188317