Finite Group Databasebeta

← #17958644

Subgroups — #17958644

Order 4352.

480 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 74 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#14544041C211yesmaximal, characteristic
2#14544021C211yesmaximal, characteristic
3#14543727C214yesmaximal, complemented
4#14533738C211yesmaximal, characteristic
5#11763780—21no—
6#11763777—21no—
7#11763654C2212yes—
8#11763654C2212yes—
9#11763653—21no—
10#11763653—21no—
11C2×#10587632—21no—
12C2×#10587632—21no—
13C2×C4×D68C2211yescharacteristic
14#11762744—21no—
15#11762744—21no—
16#11762710C412yes—
17#11762678C2212yes—
18C4×C4⋊Dic17C411yescharacteristic
19C2×C17×C4⋊Q8C411yescharacteristic
20C22×Q8×C17—21no—
21C22×D68C2×C411yescharacteristic
22C22×C4×D17D411yescharacteristic
23C22×C4×D17D411yescharacteristic
24C2×#63243—41no—
25C2×#63242—41no—
26C17×C4⋊Q8—41no—
27C17×C4⋊Q8—41no—
28C2×C4⋊C4×C17—21no—
29C2×C4⋊C4×C17C2×C412yes—
30C2×C42×C17C2×C411yescharacteristic
31#10587632—44no—
32#10587632—44no—
33C2×#63227—22no—
34C2×#63227—22no—
35C2×#63227D411yescharacteristic
36C2×#63227D411yescharacteristic
37C2×C4⋊Dic17—21no—
38C2×C4⋊Dic17C2311yescharacteristic
39C2×#63225—22no—
40C2×#63225—22no—
41C2×C4×Dic17C2×C412yes—
42C4×D68—41no—
43C4×D68—41no—
44C22⋊#3624—22no—
45C22⋊#3624—22no—
46#10587543—41no—
47#10587543—41no—
48#10587502—21no—
49C23×D17C22⋊C411yescharacteristic
50C23×D17C22⋊C411yescharacteristic
51C2×Q8×C17—42no—
52C2×Q8×C17—42no—
53C2×Q8×C17—41no—
54C2×Q8×C17—41no—
55C22×C4×C17—22no—
56C22×C4×C17C22⋊C411yescharacteristic
57C22×C4×C17C22⋊C411yescharacteristic
58C22×C4×C17C22×C411yescharacteristic
59C22×Dic17—22no—
60C22×Dic17C2×D411yescharacteristic
61C22×Dic17C2×D411yescharacteristic
62C2×D68—22no—
63C2×D68—22no—
64C2×D68—41no—
65C2×C4×D17—21no—
66C2×C4×D17—21no—
67C2×C4×D17—21no—
68C2×C4×D17—21no—
69C2×C4×D17—42no—
70C2×C4×D17—42no—
71C2×#3624—42no—
72C2×#3624—42no—
73#63243—82no—
74#63242—82no—
75C4⋊C4×C17—42no—
76C4⋊C4×C17—42no—
77C42×C17—21no—
78C42×C17—21no—
79#63227—41no—
80#63227—41no—
81#63227—44no—
82#63227—44no—
83C4⋊Dic17—24no—
84C4⋊Dic17—41no—
85#63225—44no—
86#63225—44no—
87C4×Dic17—24no—
88#11570—171nomaximal, Sylow
89C23×C17C2×C22⋊C411yescharacteristic
90C22×D17—21no—
91C22×D17—21no—
92C22×D17—21no—
93C22×D17—21no—
94C22×D17—21no—
95C22×D17—41no—
96C22×D17—41no—
97C22×D17—41no—
98C22×D17—41no—
99C22×D17#10112yes—
100Q8×C17—82no—
101Q8×C17—82no—
102C2×C4×C17—21no—
103C2×C4×C17—21no—
104C2×C4×C17—22no—
105C2×C4×C17—21no—
106C2×C4×C17—41no—
107C2×C4×C17—42no—
108C2×C4×C17—42no—
109C2×C4×C17—42no—
110C2×C4×C17#9911yescharacteristic
111C2×C4×C17#9911yescharacteristic
112C2×C4×C17#13112yes—
113C2×Dic17—24no—
114C2×Dic17—21no—
115C2×Dic17—21no—
116C2×Dic17—42no—
117C2×Dic17—42no—
118C2×Dic17—41no—
119C2×Dic17—41no—
120D68—44no—
121C4×D17—42no—
122C4×D17—42no—
123C4×D17—81no—
124C4×D17—81no—
125#3624—82no—
126#3624—82no—
127#2542—171no—
128#1465—171no—
129#1459—171no—
130#1325—174no—
131C22×C17—21no—
132C22×C17—21no—
133C22×C17#40811yescharacteristic
134C22×C17C2×#9911yescharacteristic
135C22×C17C2×#10111yescharacteristic
136C2×D17—22no—
137C2×D17—41no—
138C2×D17—41no—
139C2×D17—42no—
140C2×D17—42no—
141C2×D17—41no—
142C2×D17—41no—
143C2×D17—41no—
144C2×D17—81no—
145C2×D17—81no—
146C4×C17—21no—
147C4×C17—22no—
148C4×C17—41no—
149C4×C17—82no—
150C4×C17#35312yes—
151Dic17—44no—
152Dic17—41no—
153Dic17—41no—
154C2×C4⋊Q8#59511yescharacteristic
155C2×C22⋊Q8—341no—
156C2×C22⋊Q8—341no—
157C2×C4×D4—171no—
158#407—341no—
159C2×C22⋊C8—341no—
160#399—341no—
161#399—341no—
162#390—172no—
163#384—172no—
164C4×C4⋊C4—171no—
165#324—172no—
166#324—172no—
167#323—341no—
168#323—341no—
169C2×C17—21no—
170C2×C17—21no—
171C2×C17#147211yescharacteristic
172C2×C17C2×#35311yescharacteristic
173C2×C17#213511yescharacteristic
174D17—42no—
175D17—81no—
176C22×Q8—21no—
177C22×D4—171no—
178C23×C4—171no—
179C23×C4—171no—
180C2×M16—681no—
181C22×C8—681no—
182C4⋊Q8—41no—
183C4⋊Q8—41no—
184C22⋊Q8—684no—
185C22⋊Q8—684no—
186C4×D4—681no—
187C4×D4—681no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—171no—
190C2×C4⋊C4—341no—
191C2×C4⋊C4—342no—
192C2×C4⋊C4—342no—
193C2×C4⋊C4C2×#59512yes—
194C2×C22⋊C4—171no—
195C2×C22⋊C4—171no—
196C2×C22⋊C4—342no—
197C2×C22⋊C4—342no—
198C2×C42—172no—
199C2×C42C2×#59511yescharacteristic
200C22⋊C8—342no—
201C22⋊C8—342no—
202C22⋊C8—681no—
203C22⋊C8—681no—
204#95—341no—
205C17#1157011yescharacteristic, complemented, Sylow
206C24—171no—
207C24—171no—
208C2×Q8—42no—
209C2×Q8—42no—
210C2×Q8—41no—
211C2×Q8—41no—
212C2×D4—342no—
213C2×D4—342no—
214C2×D4—681no—
215C22×C4—22no—
216C22×C4—171no—
217C22×C4—171no—
218C22×C4—342no—
219C22×C4—341no—
220C22×C4—341no—
221C22×C4—341no—
222C22×C4—341no—
223C22×C4—682no—
224C22×C4—682no—
225C22×C4C22⋊#59511yescharacteristic
226C22×C4C22⋊#59511yescharacteristic
227C22×C4C22×#59511yescharacteristic
228M16—1362no—
229C2×C8—682no—
230C2×C8—682no—
231C2×C8—1362no—
232C4⋊C4—42no—
233C4⋊C4—42no—
234C4⋊C4—344no—
235C4⋊C4—681no—
236C4⋊C4—684no—
237C4⋊C4—684no—
238C22⋊C4—681no—
239C22⋊C4—681no—
240C22⋊C4—684no—
241C22⋊C4—684no—
242C42—21no—
243C42—21no—
244C42—344no—
245C23—172no—
246C23—341no—
247C23—341no—
248C23—341no—
249C23—341no—
250C23—341no—
251C23—681no—
252C23—681no—
253C23—681no—
254C23—681no—
255C23C2×C22⋊#59511yescharacteristic
256Q8—82no—
257Q8—82no—
258D4—684no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—41no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—344no—
268C2×C4—341no—
269C2×C4—341no—
270C2×C4—682no—
271C2×C4—682no—
272C2×C4—682no—
273C2×C4—682no—
274C2×C4—681no—
275C2×C4—681no—
276C2×C4—1361no—
277C2×C4—1361no—
278C2×C4#1058755111yescharacteristic
279C2×C4#1058755111yescharacteristic
280C2×C4#1058768012yes—
281C8—1362no—
282C8—1362no—
283C22—21no—
284C22—21no—
285C22—342no—
286C22—682no—
287C22—682no—
288C22—681no—
289C22—681no—
290C22—681no—
291C22—681no—
292C22—681no—
293C22—1361no—
294C22—1361no—
295C22#1176378411yescharacteristic
296C22C2×#1058755111yescharacteristic
297C22D17⋊#10111yescharacteristic
298C4—21no—
299C4—22no—
300C4—41no—
301C4—82no—
302C4—684no—
303C4—681no—
304C4—681no—
305C4#1176371312yes—
306C2—21no—
307C2—21no—
308C2—682no—
309C2—1361no—
310C2#1454406411yescharacteristic
311C2C2×#1176371311yescharacteristic
312C2#1454508611yescharacteristic
subgroupG/H
centerC22C2×#10587551
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC2×C17×C4⋊Q8C4
socleC22×C17C2×#99
prime radicalC22×D68C2×C4
cosocleC2×C4⋊Dic17C23
hypercenterC2×C4⋊Q8#595
hypocenterC17#11570
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. #14543727C2semidirect
205. C17#11570semidirect

Maximal subgroups

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

subgroupindex
#145440412
#145440212
#145437272
#145337382
#1157017