Finite Group Databasebeta

← #17953616

Subgroups — #17953616

Order 4352.

404 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 88 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#14544015C211yesmaximal, characteristic
2#14544015C211yesmaximal, characteristic
3#14543612C212yesmaximal, complemented
4#14543608C212yesmaximal, complemented
5#14531280C211yesmaximal, characteristic
6#11763825C2212yes—
7#11763825C2212yes—
8#11763654—21no—
9#11763654—21no—
10#11763652—21no—
11#11763652—21no—
12C2×#10587612C2211yescharacteristic
13#11762703—21no—
14#11762697—21no—
15#11762694—21no—
16#11762692—21no—
17C4×#63225C411yescharacteristic
18C4×#63225C411yescharacteristic
19C4×C22⋊Dic17C411yescharacteristic
20#11762655C2211yescharacteristic
21C42×Dic17C2211yescharacteristic
22C4×C22⋊C4×C17C411yescharacteristic
23C23×C4×C17C2×C411yescharacteristic
24C2×C22⋊C4×C17—21no—
25C2×C42×C17C2×C411yescharacteristic
26C2×C42×C17C2×C411yescharacteristic
27C2×C22⋊Dic17—21no—
28C2×C22⋊Dic17D411yescharacteristic
29C2×C22⋊Dic17D411yescharacteristic
30#10587612—22no—
31#10587612—22no—
32C2×C4⋊Dic17D411yescharacteristic
33C2×C4⋊Dic17D411yescharacteristic
34C2×#63225—21no—
35C2×#63225—21no—
36C2×C4×Dic17—21no—
37C2×C4×Dic17—21no—
38C2×C4×Dic17C2×C411yescharacteristic
39C2×C4×Dic17C2×C411yescharacteristic
40C2×C4×Dic17C2×C411yescharacteristic
41C2×C4×Dic17C2311yescharacteristic
42C22⋊#3624—22no—
43C22⋊#3624—22no—
44C4⋊#3624—22no—
45C4⋊#3624—22no—
46C4×#3624—22no—
47C4×#3624—22no—
48C17×#95—21no—
49#10587502—21no—
50#10587502—21no—
51#10587502—21no—
52#10587502—21no—
53#10587502—21no—
54C24×C17C22⋊C411yescharacteristic
55C22×C4×C17—21no—
56C22×C4×C17—21no—
57C22×C4×C17—21no—
58C22×C4×C17—22no—
59C22×C4×C17—22no—
60C22×C4×C17—21no—
61C22×C4×C17C22⋊C411yescharacteristic
62C22×C4×C17C22×C411yescharacteristic
63C22×Dic17—21no—
64C22×Dic17—21no—
65C22×Dic17C22⋊C411yescharacteristic
66C22×Dic17C22⋊C411yescharacteristic
67C22×Dic17C2×D411yescharacteristic
68C22×Dic17C2×D411yescharacteristic
69C2×#3624—42no—
70C2×#3624—42no—
71C22⋊C4×C17—42no—
72C42×C17—22no—
73C42×C17—22no—
74C22⋊Dic17—22no—
75C22⋊Dic17—22no—
76C22⋊Dic17—42no—
77C4⋊Dic17—22no—
78C4⋊Dic17—22no—
79#63225—42no—
80#63225—42no—
81C4×Dic17—21no—
82C4×Dic17—21no—
83C4×Dic17—22no—
84C4×Dic17—22no—
85C4×Dic17—42no—
86C4×Dic17—42no—
87C4×Dic17#4112yes—
88C4×Dic17#4112yes—
89#8733—171nomaximal, Sylow
90C23×C17—21no—
91C23×C17—21no—
92C23×C17—21no—
93C23×C17—41no—
94C23×C17—41no—
95C23×C17C2×C22⋊C411yescharacteristic
96C2×C4×C17—22no—
97C2×C4×C17—21no—
98C2×C4×C17—21no—
99C2×C4×C17—21no—
100C2×C4×C17—41no—
101C2×C4×C17—41no—
102C2×C4×C17—42no—
103C2×C4×C17—42no—
104C2×C4×C17—41no—
105C2×C4×C17—41no—
106C2×C4×C17—41no—
107C2×C4×C17#11711yescharacteristic
108C2×C4×C17#11711yescharacteristic
109C2×C4×C17#13112yes—
110C2×C4×C17#13112yes—
111C2×Dic17—22no—
112C2×Dic17—21no—
113C2×Dic17—21no—
114C2×Dic17—41no—
115C2×Dic17—41no—
116C2×Dic17—41no—
117C2×Dic17—41no—
118C2×Dic17—41no—
119C2×Dic17—41no—
120C2×Dic17—41no—
121C2×Dic17—41no—
122C2×Dic17—41no—
123C2×Dic17#12312yes—
124C2×Dic17#12312yes—
125#3624—82no—
126#3624—82no—
127#2298—171no—
128#1458—171no—
129#1458—171no—
130#1276—172no—
131#1274—172no—
132C22×C17—21no—
133C22×C17—21no—
134C22×C17—41no—
135C22×C17—41no—
136C22×C17—41no—
137C22×C17—81no—
138C22×C17—81no—
139C22×C17#38111yescharacteristic
140C22×C17#40811yescharacteristic
141C22×C17#40811yescharacteristic
142C4×C17—42no—
143C4×C17—41no—
144C4×C17—81no—
145C4×C17#43312yes—
146C4×C17#43312yes—
147Dic17—22no—
148Dic17—22no—
149Dic17—42no—
150Dic17—41no—
151Dic17—41no—
152Dic17—81no—
153C2×#117—171no—
154#431—172no—
155#431—172no—
156#388—341no—
157#388—341no—
158#387—341no—
159#387—341no—
160C4×C4⋊C4—171no—
161C4×C4⋊C4—171no—
162C4×C22⋊C4—171no—
163C4×C22⋊C4#59511yescharacteristic
164#376—171no—
165C43—171no—
166#324—341no—
167#324—341no—
168#323—341no—
169#323—341no—
170C2×C17—21no—
171C2×C17—21no—
172C2×C17—81no—
173C2×C17#181811yescharacteristic
174C2×C17#182711yescharacteristic
175C2×C17#182711yescharacteristic
176C23×C4C2×#59511yescharacteristic
177#117—342no—
178#117—342no—
179C2×C4⋊C4—171no—
180C2×C4⋊C4—171no—
181C2×C4⋊C4—341no—
182C2×C4⋊C4—341no—
183C2×C22⋊C4—21no—
184C2×C22⋊C4—171no—
185C2×C22⋊C4—171no—
186C2×C22⋊C4—341no—
187C2×C42—171no—
188C2×C42—171no—
189C2×C42—171no—
190C2×C42—171no—
191C2×C42—341no—
192C2×C42—341no—
193C2×C42C2×#59511yescharacteristic
194C2×C42C2×#59511yescharacteristic
195C4⋊C8—342no—
196C4⋊C8—342no—
197C22⋊C8—342no—
198C22⋊C8—342no—
199C4×C8—342no—
200C4×C8—342no—
201#95—21no—
202#95—341no—
203#95—341no—
204#95—341no—
205#95—341no—
206#95—341no—
207C17#873311yescharacteristic, complemented, Sylow
208C24C22⋊#59511yescharacteristic
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—21no—
215C22×C4—171no—
216C22×C4—171no—
217C22×C4—171no—
218C22×C4—171no—
219C22×C4—341no—
220C22×C4—341no—
221C22×C4C22⋊#59511yescharacteristic
222C22×C4C22×#59511yescharacteristic
223C2×C8—682no—
224C2×C8—682no—
225C4⋊C4—342no—
226C4⋊C4—342no—
227C4⋊C4—682no—
228C4⋊C4—682no—
229C22⋊C4—42no—
230C22⋊C4—342no—
231C22⋊C4—342no—
232C22⋊C4—682no—
233C42—22no—
234C42—22no—
235C42—172no—
236C42—172no—
237C42—341no—
238C42—341no—
239C42—342no—
240C42—342no—
241C42—682no—
242C42—682no—
243C23—21no—
244C23—21no—
245C23—21no—
246C23—41no—
247C23—41no—
248C23C2×C22⋊#59511yescharacteristic
249C2×C4—22no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—172no—
261C2×C4—172no—
262C2×C4—342no—
263C2×C4—341no—
264C2×C4—341no—
265C2×C4—681no—
266C2×C4—681no—
267C2×C4—681no—
268C2×C4—681no—
269C2×C4—681no—
270C2×C4—681no—
271C2×C4—681no—
272C2×C4—681no—
273C2×C4—681no—
274C2×C4#1058767711yescharacteristic
275C2×C4#1058767711yescharacteristic
276C2×C4#1058767812yes—
277C2×C4#1058767812yes—
278C8—1362no—
279C8—1362no—
280C22—21no—
281C22—21no—
282C22—41no—
283C22—41no—
284C22—41no—
285C22—81no—
286C22—81no—
287C22#1176375211yescharacteristic
288C22#1176378211yescharacteristic
289C22#1176378211yescharacteristic
290C4—42no—
291C4—41no—
292C4—81no—
293C4—342no—
294C4—342no—
295C4—682no—
296C4—681no—
297C4—681no—
298C4—1361no—
299C4#1176383312yes—
300C4#1176383312yes—
301C2—21no—
302C2—21no—
303C2—81no—
304C2#1454467711yescharacteristic
305C2#1454469311yescharacteristic
306C2#1454469411yescharacteristic
subgroupG/H
centerC2×C4#10587677
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC4×C22⋊C4×C17C4
socleC22×C17#381
prime radicalC24×C17C22⋊C4
cosocleC2×C4×Dic17C23
hypercenterC4×C22⋊C4#595
hypocenterC17#8733
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #14543612C2semidirect
4. #14543608C2semidirect
207. C17#8733semidirect

Maximal subgroups

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

subgroupindex
#145440152
#145436122
#145436082
#145312802
#873317