Finite Group Databasebeta

← #16944277

Subgroups — #16944277

Order 4352.

296 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 93 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#14537713C211yesmaximal, characteristic
2#14530586C211yesmaximal, characteristic
3#14530581C211yesmaximal, characteristic
4#14526764C211yesmaximal, characteristic, complemented
5Q8⋊#63214C211yesmaximal, characteristic, complemented
6#14526762C211yesmaximal, characteristic, complemented
7C17×Q8⋊C16C211yesmaximal, characteristic, complemented
8#11763363C411yescharacteristic
9#11762940C411yescharacteristic
10#11762938—21no—
11#11762936C411yescharacteristic
12C8×Dic34—21no—
13C8×Dic34C2211yescharacteristic
14#11762834—21no—
15#11762831C411yescharacteristic
16#11762763—21no—
17C4×C8×D17C2211yescharacteristic
18C4⋊#63214C2211yescharacteristic
19#11762627—21no—
20#11762588—21no—
21#11762588—21no—
22#11762584—21no—
23C4×#63214C2211yescharacteristic
24C8×Q8×C17C2211yescharacteristic
25C17×C4⋊C16C2211yescharacteristic
26C4×C16×C17C2211yescharacteristic
27C4×Q8×C17C2×C411yescharacteristic
28#10587632C811yescharacteristic
29#10587630C811yescharacteristic
30C2×#63218—21no—
31C2×C8×D17D411yescharacteristic
32C2×C8×D17D411yescharacteristic
33#10587583C811yescharacteristic
34#10587582—21no—
35#10587575—21no—
36#10587574C811yescharacteristic
37#10587558—21no—
38C42×D17C2×C411yescharacteristic
39C4×Dic34—21no—
40C4×Dic34C2×C411yescharacteristic
41C2×C16×C17—21no—
42C2×C16×C17—21no—
43C17×C4⋊C8—21no—
44C17×C4⋊C8C2×C411yescharacteristic
45C4×C8×C17—21no—
46C4×C8×C17C2311yescharacteristic
47#10587486—21no—
48#10587485—21no—
49#10587485—21no—
50#10587485—21no—
51C8×Dic17—21no—
52C8×Dic17D411yescharacteristic
53C8×Dic17D411yescharacteristic
54C2×#63214—21no—
55C2×#63214—21no—
56C4⋊#3622—21no—
57C4⋊#3622C2×C411yescharacteristic
58#10587474—21no—
59C4×#3622C2×C411yescharacteristic
60C2×Q8×C17C2×C811yescharacteristic
61C2×C4×D17C22⋊C411yescharacteristic
62C2×C4×D17C2×C811yescharacteristic
63C2×C4×D17M1611yescharacteristic
64C2×Dic34—21no—
65C2×Dic34C2×C811yescharacteristic
66C2×C8×C17—21no—
67C2×C8×C17C2×D411yescharacteristic
68C2×C8×C17C2×D411yescharacteristic
69C4⋊C4×C17—21no—
70C4⋊C4×C17C2×C811yescharacteristic
71C42×C17—21no—
72C42×C17C22×C411yescharacteristic
73#63227—21no—
74#63227—21no—
75C4⋊Dic17—21no—
76C4⋊Dic17C2×C811yescharacteristic
77#63225—21no—
78#63225—21no—
79#63225—21no—
80#63225—21no—
81#63225—21no—
82C4×Dic17—21no—
83C4×Dic17C22⋊C411yescharacteristic
84C4×Dic17C2×C811yescharacteristic
85C4×Dic17M1611yescharacteristic
86C2×#3622—21no—
87C2×#3622C22⋊C411yescharacteristic
88C2×#3622C22⋊C411yescharacteristic
89#63218—42no—
90C8×D17—21no—
91C8×D17—21no—
92C8×D17—41no—
93C16×C17—41no—
94C16×C17—41no—
95#63214—41no—
96#63214—41no—
97#11640—171nomaximal, Sylow
98C22×D17C22⋊C811yescharacteristic
99Q8×C17—21no—
100Q8×C17—21no—
101C2×C4×C17—21no—
102C2×C4×C17—21no—
103C2×C4×C17C2×C22⋊C411yescharacteristic
104C2×C4×C17C22×C811yescharacteristic
105C2×C4×C17C2×M1611yescharacteristic
106C2×Dic17—21no—
107C2×Dic17—21no—
108C2×Dic17C22⋊C811yescharacteristic
109C2×Dic17C22⋊C811yescharacteristic
110C2×Dic17C22⋊C811yescharacteristic
111C4×D17—21no—
112C4×D17—21no—
113C4×D17—21no—
114C4×D17—21no—
115C4×D17—41no—
116Dic34—21no—
117Dic34—21no—
118Dic34—42no—
119C8×C17—21no—
120C8×C17—41no—
121C8×C17#13711yescharacteristic
122C8×C17#13711yescharacteristic
123#3622—21no—
124#3622—21no—
125#3622—41no—
126#2960—171no—
127#2163—171no—
128#2162—171no—
129Q8⋊C16—171no—
130Q8⋊C16—171no—
131Q8⋊C16—171no—
132Q8⋊C16D1711yescharacteristic, complemented
133C22×C17C2×C22⋊C811yescharacteristic
134C2×D17—21no—
135C2×D17—21no—
136C2×D17—21no—
137C4×C17—21no—
138C4×C17—41no—
139C4×C17—41no—
140C4×C17#41911yescharacteristic
141C4×C17#42111yescharacteristic
142C4×C17#50411yescharacteristic
143C4×C17#50411yescharacteristic
144Dic17—21no—
145Dic17—21no—
146Dic17—21no—
147Dic17—41no—
148Dic17—41no—
149#533—171no—
150#446—171no—
151#446—171no—
152#446—341no—
153C8×Q8—171no—
154C8×Q8—341no—
155C8×Q8C2×D1711yescharacteristic
156#424—341no—
157#423—171no—
158#405—341no—
159C2×C4×C8—171no—
160C4⋊C16—171no—
161C4⋊C16—341no—
162C4⋊C16C2×D1711yescharacteristic
163C22⋊C16—341no—
164C22⋊C16—341no—
165#346—341no—
166C4×C16—171no—
167C4×C16C2×D1711yescharacteristic
168C2×C17#147911yescharacteristic
169C2×C17#211311yescharacteristic
170C2×C17#211711yescharacteristic
171D17—41no—
172C2×M16—341no—
173C22×C8—171no—
174C22×C8—171no—
175C4⋊Q8—171no—
176C4⋊Q8—171no—
177#125—341no—
178C22⋊Q8—171no—
179C22⋊Q8—171no—
180C22⋊Q8—341no—
181C4×Q8—171no—
182C4×Q8—341no—
183C4×Q8C4×D1711yescharacteristic
184#117—341no—
185C2×C42—171no—
186C2×C16—21no—
187C2×C16—21no—
188C2×C16—341no—
189C2×C16—341no—
190C4⋊C8—21no—
191C4⋊C8—171no—
192C4⋊C8—341no—
193C4⋊C8—341no—
194C4⋊C8—341no—
195C4⋊C8—341no—
196C4⋊C8C4×D1711yescharacteristic
197#97—341no—
198#97—341no—
199C4×C8—21no—
200C4×C8—171no—
201C4×C8—171no—
202C4×C8—171no—
203C4×C8—341no—
204C4×C8C22×D1711yescharacteristic
205C17#1164011yescharacteristic, complemented, Sylow
206C2×Q8—171no—
207C2×Q8—341no—
208C2×Q8C8×D1711yescharacteristic
209C22×C4—171no—
210C22×C4—171no—
211C22×C4—171no—
212M16—682no—
213C2×C8—21no—
214C2×C8—171no—
215C2×C8—171no—
216C2×C8—341no—
217C2×C8—341no—
218C2×C8—341no—
219C2×C8—681no—
220C2×C8D4×D1711yescharacteristic
221C2×C8D4×D1711yescharacteristic
222C4⋊C4—21no—
223C4⋊C4—171no—
224C4⋊C4—341no—
225C4⋊C4—341no—
226C4⋊C4—341no—
227C4⋊C4—341no—
228C4⋊C4—341no—
229C4⋊C4—341no—
230C4⋊C4C8×D1711yescharacteristic
231C22⋊C4—341no—
232C22⋊C4—341no—
233C42—21no—
234C42—171no—
235C42—171no—
236C42—171no—
237C42—341no—
238C42C2×C4×D1711yescharacteristic
239C16—41no—
240C16—41no—
241C16—681no—
242C16—681no—
243C23—171no—
244Q8—21no—
245Q8—21no—
246Q8—341no—
247Q8—341no—
248Q8—682no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—171no—
252C2×C4—171no—
253C2×C4—171no—
254C2×C4—341no—
255C2×C4—341no—
256C2×C4—341no—
257C2×C4—341no—
258C2×C4—341no—
259C2×C4—341no—
260C2×C4—681no—
261C2×C4C22⋊C4×D1711yescharacteristic
262C2×C4C2×C8×D1711yescharacteristic
263C2×C4M16×D1711yescharacteristic
264C8—21no—
265C8—41no—
266C8—341no—
267C8—341no—
268C8—681no—
269C8#1058760111yescharacteristic
270C8#1058760411yescharacteristic
271C22—341no—
272C22—341no—
273C22—341no—
274C22C22⋊C8×D1711yescharacteristic
275C4—21no—
276C4—41no—
277C4—41no—
278C4—341no—
279C4—341no—
280C4—341no—
281C4—681no—
282C4—681no—
283C4#1176281611yescharacteristic
284C4#1176282411yescharacteristic
285C4#1176322511yescharacteristic
286C4#1176322711yescharacteristic
287C2—681no—
288C2#1452717711yescharacteristic
289C2#1453039611yescharacteristic
290C2#1453041011yescharacteristic
subgroupG/H
centerC2×C8D4×D17
commutatorC2×C4×C17C22×C8
FrattiniC4×C8C22×D17
FittingC17×Q8⋊C16C2
socleC22×C17C2×C22⋊C8
prime radicalC22×D17C22⋊C8
cosocleC4×C8×C17C23
hypercenterQ8⋊C16D17
hypocenterC17#11640
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C8 ◁ C4×C8 ◁ Q8⋊C16

Complements

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

NH ≅ G/Ntype
4. #14526764C2semidirect
5. Q8⋊#63214C2semidirect
6. #14526762C2semidirect
7. C17×Q8⋊C16C2semidirect
132. Q8⋊C16D17semidirect
205. C17#11640semidirect

Maximal subgroups

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

subgroupindex
#145377132
#145305862
#145305812
#145267642
Q8⋊#632142
#145267622
C17×Q8⋊C162
#1164017