Finite Group Databasebeta

← #17958844

Subgroups — #17958844

Order 4352.

430 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 106 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#14545144C211yesmaximal, characteristic, complemented
2#14545143C211yesmaximal, characteristic, complemented
3#14543735C212yesmaximal, complemented
4D4⋊#63216C212yesmaximal, complemented
5C8×D4×D17C211yesmaximal, characteristic
6#11763730—21no—
7C4⋊#63216C2212yescomplemented
8#11763704—21no—
9#11763704—21no—
10#11763695—21no—
11C4×#63216C2212yescomplemented
12C22×C8×D17—21no—
13C4×D4×D17C411yescharacteristic
14C8×D68C411yescharacteristic
15D4×#3622C2211yescharacteristic
16#11762874C2211yescharacteristic
17C8×C22⋊D17—21no—
18#11762872—21no—
19C4⋊C8×D17C411yescharacteristic
20C22⋊C8×D17—21no—
21C4×C8×D17C2211yescharacteristic
22C8×D4×C17C411yescharacteristic
23C2×D4×D17C811yescharacteristic
24C22×C4×D17—21no—
25C22×C8×C17—21no—
26C4×D4×C17C2×C411yescharacteristic
27D4×Dic17C811yescharacteristic
28C4×C22⋊D17—21no—
29C22×#3622—21no—
30C2×C8×D17—21no—
31C2×C8×D17—21no—
32C2×C8×D17—21no—
33C2×C8×D17—44no—
34C2×C8×D17D411yescharacteristic
35C2×C8×D17D411yescharacteristic
36#10587579C811yescharacteristic
37C4⋊C4×D17C811yescharacteristic
38#10587567—21no—
39C22⋊C4×D17—21no—
40C4×D68C2×C411yescharacteristic
41C42×D17C2×C411yescharacteristic
42C2×#63216—22no—
43C2×#63216—22no—
44C17×C4⋊C8C2×C411yescharacteristic
45C17×C22⋊C8—21no—
46C4×C8×C17C2×C411yescharacteristic
47C22⋊#3622—21no—
48#10587491—21no—
49#10587491—21no—
50#10587485—21no—
51C8×Dic17D411yescharacteristic
52C8×Dic17D411yescharacteristic
53C4⋊#3622C2×C411yescharacteristic
54C4×#3622C2311yescharacteristic
55C23×D17—21no—
56C2×D4×C17C2×C811yescharacteristic
57C22×C4×C17—21no—
58C2×C22⋊D17—21no—
59C22×Dic17—21no—
60D4×D17—22no—
61D4×D17C1614yescomplemented
62C2×D68C2×C811yescharacteristic
63C2×C4×D17—21no—
64C2×C4×D17—21no—
65C2×C4×D17—21no—
66C2×C4×D17—42no—
67C2×C4×D17—42no—
68C2×C4×D17C22⋊C411yescharacteristic
69C2×C4×D17C2×C811yescharacteristic
70C2×C4×D17M1611yescharacteristic
71C2×C8×C17—21no—
72C2×C8×C17—42no—
73C2×C8×C17C22⋊C411yescharacteristic
74C2×C8×C17C22⋊C411yescharacteristic
75C4⋊C4×C17C2×C811yescharacteristic
76C22⋊C4×C17—21no—
77C42×C17C22×C411yescharacteristic
78C22⋊Dic17—21no—
79#63227—21no—
80#63227—21no—
81C4⋊Dic17C2×C811yescharacteristic
82#63225—21no—
83C4×Dic17C22⋊C411yescharacteristic
84C4×Dic17C2×C811yescharacteristic
85C4×Dic17M1611yescharacteristic
86C2×#3622—21no—
87C2×#3622—42no—
88C2×#3622C2×D411yescharacteristic
89C2×#3622C2×D411yescharacteristic
90C8×D17—22no—
91C8×D17—41no—
92C8×D17—42no—
93C8×D17—42no—
94C8×D17—42no—
95#63216—42no—
96#63216—42no—
97#11629—171nomaximal, Sylow
98C23×C17—21no—
99C22×D17—21no—
100C22×D17—24no—
101C22×D17—42no—
102C22×D17—42no—
103C22×D17C22⋊C811yescharacteristic
104D4×C17—21no—
105D4×C17C2×C1612yes—
106C2×C4×C17—21no—
107C2×C4×C17—41no—
108C2×C4×C17—41no—
109C2×C4×C17C2×C22⋊C411yescharacteristic
110C2×C4×C17C22×C811yescharacteristic
111C2×C4×C17C2×M1611yescharacteristic
112C22⋊D17—24no—
113C2×Dic17—21no—
114C2×Dic17—42no—
115C2×Dic17C22⋊C811yescharacteristic
116C2×Dic17C22⋊C811yescharacteristic
117C2×Dic17C22⋊C811yescharacteristic
118D68—21no—
119D68C2×C1612yes—
120C4×D17—21no—
121C4×D17—21no—
122C4×D17—41no—
123C4×D17—42no—
124C4×D17—42no—
125C4×D17—41no—
126C4×D17—41no—
127C4×D17C2×C1612yes—
128C4×D17M3212yes—
129C8×C17—21no—
130C8×C17—21no—
131C8×C17—41no—
132#3622—21no—
133#3622—41no—
134#3622AGL(1,ℤ/8)12yes—
135C2×C8×D4—171no—
136#2162—171no—
137#2162—171no—
138D4⋊C16—172no—
139D4⋊C16—172no—
140C22×C17—22no—
141C22×C17—41no—
142C22×C17—41no—
143C22×C17C2×C22⋊C811yescharacteristic
144C2×D17—21no—
145C2×D17—21no—
146C2×D17—22no—
147C2×D17—48no—
148C2×D17—41no—
149C2×D17—41no—
150C2×D17C22⋊C1612yes—
151C4×C17—21no—
152C4×C17—41no—
153C4×C17#41811yescharacteristic
154C4×C17#42111yescharacteristic
155C4×C17C22×C1611yescharacteristic
156C4×C17C2×M3211yescharacteristic
157Dic17—21no—
158Dic17—21no—
159Dic17—41no—
160Dic17C22⋊C1612yes—
161C23×C8—341no—
162C2×C4×D4—171no—
163C8×D4—171no—
164C8×D4—171no—
165C8×D4—171no—
166C8×D4—341no—
167C8×D4—341no—
168C8×D4#59511yescharacteristic
169C2×C4⋊C8—171no—
170C2×C22⋊C8—341no—
171C2×C4×C8—171no—
172C4⋊C16—172no—
173C4⋊C16—341no—
174C22⋊C16—341no—
175C22⋊C16—341no—
176C4×C16—172no—
177C4×C16—341no—
178C2×C17—42no—
179C2×C17#147811yescharacteristic
180C2×C17C2×C22⋊C1611yescharacteristic
181C2×C17#211711yescharacteristic
182D17—22no—
183D17—42no—
184C22×D4—171no—
185C23×C4—341no—
186C22×C8—21no—
187C22×C8—171no—
188C22×C8—171no—
189C22×C8—341no—
190C22×C8—341no—
191C22×C8—341no—
192C22×C8—341no—
193C22×C8—684no—
194C4×D4—171no—
195C4×D4—171no—
196C4×D4—171no—
197C4×D4—341no—
198C4×D4—341no—
199C4×D4C2×#59511yescharacteristic
200C2×C4⋊C4—171no—
201C2×C22⋊C4—341no—
202C2×C42—171no—
203C2×C16—342no—
204C2×C16—342no—
205C4⋊C8—171no—
206C4⋊C8—341no—
207C4⋊C8C2×#59511yescharacteristic
208C22⋊C8—21no—
209C22⋊C8—341no—
210C22⋊C8—341no—
211C22⋊C8—341no—
212C4×C8—171no—
213C4×C8—171no—
214C4×C8—171no—
215C4×C8C2×#59511yescharacteristic
216C17#1162911yescharacteristic, complemented, Sylow
217C24—341no—
218C2×D4—174no—
219C2×D4—171no—
220C2×D4—342no—
221C2×D4—341no—
222C2×D4#6324211yescharacteristic
223C22×C4—21no—
224C22×C4—171no—
225C22×C4—171no—
226C22×C4—171no—
227C22×C4—341no—
228C22×C4—341no—
229C22×C4—341no—
230C22×C4—341no—
231C22×C4—682no—
232C22×C4—682no—
233C2×C8—21no—
234C2×C8—42no—
235C2×C8—171no—
236C2×C8—171no—
237C2×C8—342no—
238C2×C8—341no—
239C2×C8—681no—
240C2×C8—682no—
241C2×C8—682no—
242C2×C8—682no—
243C2×C8—682no—
244C2×C8C22⋊#59511yescharacteristic
245C2×C8C22⋊#59511yescharacteristic
246C4⋊C4—171no—
247C4⋊C4—341no—
248C4⋊C4#6324211yescharacteristic
249C22⋊C4—21no—
250C22⋊C4—341no—
251C22⋊C4—341no—
252C22⋊C4—341no—
253C42—171no—
254C42—171no—
255C42—171no—
256C42C22×#59511yescharacteristic
257C16—682no—
258C16—682no—
259C23—21no—
260C23—171no—
261C23—344no—
262C23—341no—
263C23—682no—
264C23—682no—
265D4—21no—
266D4—172no—
267D4—344no—
268D4—341no—
269D4#1058752912yes—
270C2×C4—21no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—171no—
274C2×C4—172no—
275C2×C4—172no—
276C2×C4—171no—
277C2×C4—171no—
278C2×C4—341no—
279C2×C4—341no—
280C2×C4—341no—
281C2×C4—681no—
282C2×C4—682no—
283C2×C4—682no—
284C2×C4—682no—
285C2×C4—681no—
286C2×C4—681no—
287C2×C4C2×#6324211yescharacteristic
288C2×C4D17⋊M1611yescharacteristic
289C2×C4C2×C22⋊#59511yescharacteristic
290C8—21no—
291C8—21no—
292C8—41no—
293C8—172no—
294C8—341no—
295C8—681no—
296C22—22no—
297C22—41no—
298C22—41no—
299C22—172no—
300C22—341no—
301C22—341no—
302C22—342no—
303C22—688no—
304C22—681no—
305C22—681no—
306C22#1176377711yescharacteristic
307C4—21no—
308C4—41no—
309C4—172no—
310C4—341no—
311C4—341no—
312C4—681no—
313C4#1176380111yescharacteristic
314C4#1176380611yescharacteristic
315C4C2×#1058752911yescharacteristic
316C4#1176386511yescharacteristic
317C2—42no—
318C2—342no—
319C2—682no—
320C2#1454408411yescharacteristic
321C2#1454500911yescharacteristic
322C2#1454502711yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#595
commutatorC4×C17C22×C16
FrattiniC42C22×#595
FittingC8×D4×C17C4
socleC22×C17C2×C22⋊C8
prime radicalC2×D4×D17C8
cosocleC4×#3622C23
hypercenterC8×D4#595
hypocenterC17#11629
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #14545144C2semidirect
2. #14545143C2semidirect
3. #14543735C2semidirect
4. D4⋊#63216C2semidirect
7. C4⋊#63216C22semidirect
11. C4×#63216C22semidirect
61. D4×D17C16semidirect
216. C17#11629semidirect

Maximal subgroups

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

subgroupindex
#145451442
#145451432
#145437352
D4⋊#632162
C8×D4×D172
#1162917