Finite Group Databasebeta

← #17958641

Subgroups — #17958641

Order 4352.

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

normal subgroups only

This group has 424 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#14543725C214yesmaximal, complemented
4#14533958C211yesmaximal, characteristic
5#11763780—21no—
6#11763777—21no—
7#11763654C2212yes—
8#11763654C2212yes—
9#11763653—21no—
10#11763653—21no—
11C2×C4×D68C2211yescharacteristic
12#11762720—21no—
13#11762720—21no—
14#11762710C412yes—
15#11762674C2212yes—
16#11762666—21no—
17#11762666—21no—
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
31C2×#63227—22no—
32C2×#63227—22no—
33C2×#63227D411yescharacteristic
34C2×#63227D411yescharacteristic
35C2×C4⋊Dic17—21no—
36C2×C4⋊Dic17C2311yescharacteristic
37C2×C4×Dic17C2×C412yes—
38C4×D68—41no—
39C4×D68—41no—
40C22⋊#3624—22no—
41C22⋊#3624—22no—
42#10587543—41no—
43#10587543—41no—
44#10587502—21no—
45#10587502—22no—
46#10587502—22no—
47C23×D17C22⋊C411yescharacteristic
48C23×D17C22⋊C411yescharacteristic
49C2×Q8×C17—42no—
50C2×Q8×C17—82no—
51C22×C4×C17—22no—
52C22×C4×C17C22⋊C411yescharacteristic
53C22×C4×C17C22⋊C411yescharacteristic
54C22×C4×C17C22×C411yescharacteristic
55C22×Dic17—22no—
56C22×Dic17C2×D411yescharacteristic
57C22×Dic17C2×D411yescharacteristic
58C2×D68—22no—
59C2×D68—22no—
60C2×D68—41no—
61C2×C4×D17—21no—
62C2×C4×D17—21no—
63C2×C4×D17—21no—
64C2×C4×D17—21no—
65C2×C4×D17—42no—
66C2×C4×D17—42no—
67C2×#3624—42no—
68C2×#3624—42no—
69#63243—82no—
70#63242—82no—
71C4⋊C4×C17—42no—
72C4⋊C4×C17—41no—
73C4⋊C4×C17—41no—
74C42×C17—21no—
75C42×C17—21no—
76#63227—41no—
77#63227—41no—
78#63227—82no—
79#63227—82no—
80C4⋊Dic17—41no—
81C4⋊Dic17—42no—
82C4×Dic17—24no—
83#11569—171nomaximal, Sylow
84C23×C17C2×C22⋊C411yescharacteristic
85C22×D17—21no—
86C22×D17—21no—
87C22×D17—21no—
88C22×D17—21no—
89C22×D17—21no—
90C22×D17—41no—
91C22×D17—41no—
92C22×D17—41no—
93C22×D17—41no—
94C22×D17#10112yes—
95Q8×C17—84no—
96C2×C4×C17—21no—
97C2×C4×C17—21no—
98C2×C4×C17—22no—
99C2×C4×C17—21no—
100C2×C4×C17—41no—
101C2×C4×C17—42no—
102C2×C4×C17—42no—
103C2×C4×C17—42no—
104C2×C4×C17#9911yescharacteristic
105C2×C4×C17#9911yescharacteristic
106C2×C4×C17#13112yes—
107C2×Dic17—21no—
108C2×Dic17—21no—
109C2×Dic17—41no—
110C2×Dic17—41no—
111C2×Dic17—42no—
112C2×Dic17—42no—
113C2×Dic17—42no—
114D68—44no—
115C4×D17—42no—
116C4×D17—42no—
117C4×D17—81no—
118C4×D17—81no—
119#3624—82no—
120#3624—82no—
121#2563—171no—
122#1465—171no—
123#1459—171no—
124#1324—174no—
125C22×C17—21no—
126C22×C17—21no—
127C22×C17#40811yescharacteristic
128C22×C17C2×#9911yescharacteristic
129C22×C17C2×#10111yescharacteristic
130C2×D17—22no—
131C2×D17—41no—
132C2×D17—41no—
133C2×D17—42no—
134C2×D17—42no—
135C2×D17—41no—
136C2×D17—41no—
137C2×D17—41no—
138C2×D17—81no—
139C2×D17—81no—
140C4×C17—21no—
141C4×C17—22no—
142C4×C17—41no—
143C4×C17—82no—
144C4×C17#35412yes—
145Dic17—41no—
146Dic17—41no—
147Dic17—82no—
148C2×C4⋊Q8#59511yescharacteristic
149C2×C4×D4—171no—
150#407—341no—
151C2×C22⋊C8—341no—
152#393—341no—
153#393—341no—
154#390—172no—
155#382—172no—
156#380—341no—
157#380—341no—
158C4×C4⋊C4—171no—
159#324—172no—
160#324—172no—
161#323—341no—
162#323—341no—
163C2×C17—21no—
164C2×C17—21no—
165C2×C17#147211yescharacteristic
166C2×C17C2×#35411yescharacteristic
167C2×C17#213411yescharacteristic
168D17—42no—
169D17—81no—
170C22×Q8—21no—
171C22×D4—171no—
172C23×C4—171no—
173C23×C4—171no—
174C2×M16—681no—
175C22×C8—681no—
176C4⋊Q8—41no—
177C4⋊Q8—41no—
178C4×D4—681no—
179C4×D4—681no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—171no—
182C2×C4⋊C4—341no—
183C2×C4⋊C4C2×#59512yes—
184C2×C22⋊C4—171no—
185C2×C22⋊C4—171no—
186C2×C22⋊C4—342no—
187C2×C22⋊C4—342no—
188C2×C42—172no—
189C2×C42C2×#59511yescharacteristic
190C22⋊C8—342no—
191C22⋊C8—342no—
192C22⋊C8—681no—
193C22⋊C8—681no—
194#95—342no—
195#95—342no—
196#95—341no—
197C17#1156911yescharacteristic, complemented, Sylow
198C24—171no—
199C24—171no—
200C2×Q8—42no—
201C2×Q8—82no—
202C2×D4—342no—
203C2×D4—342no—
204C2×D4—681no—
205C22×C4—22no—
206C22×C4—171no—
207C22×C4—171no—
208C22×C4—341no—
209C22×C4—341no—
210C22×C4—341no—
211C22×C4—341no—
212C22×C4—342no—
213C22×C4—682no—
214C22×C4—682no—
215C22×C4C22⋊#59511yescharacteristic
216C22×C4C22⋊#59511yescharacteristic
217C22×C4C22×#59511yescharacteristic
218M16—1362no—
219C2×C8—682no—
220C2×C8—682no—
221C2×C8—1362no—
222C4⋊C4—42no—
223C4⋊C4—41no—
224C4⋊C4—41no—
225C4⋊C4—681no—
226C4⋊C4—682no—
227C22⋊C4—681no—
228C22⋊C4—681no—
229C22⋊C4—1362no—
230C22⋊C4—1362no—
231C42—21no—
232C42—21no—
233C42—344no—
234C23—172no—
235C23—341no—
236C23—341no—
237C23—341no—
238C23—341no—
239C23—341no—
240C23—681no—
241C23—681no—
242C23—681no—
243C23—681no—
244C23C2×C22⋊#59511yescharacteristic
245Q8—84no—
246D4—684no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—21no—
251C2×C4—41no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—341no—
256C2×C4—341no—
257C2×C4—682no—
258C2×C4—682no—
259C2×C4—681no—
260C2×C4—681no—
261C2×C4—682no—
262C2×C4—682no—
263C2×C4—682no—
264C2×C4—1361no—
265C2×C4—1361no—
266C2×C4#1058755111yescharacteristic
267C2×C4#1058755111yescharacteristic
268C2×C4#1058768012yes—
269C8—1362no—
270C8—1362no—
271C22—21no—
272C22—21no—
273C22—342no—
274C22—682no—
275C22—682no—
276C22—681no—
277C22—681no—
278C22—681no—
279C22—681no—
280C22—681no—
281C22—1361no—
282C22—1361no—
283C22#1176378411yescharacteristic
284C22C2×#1058755111yescharacteristic
285C22D17⋊#10111yescharacteristic
286C4—21no—
287C4—22no—
288C4—41no—
289C4—82no—
290C4—681no—
291C4—681no—
292C4—1362no—
293C4#1176371512yes—
294C2—21no—
295C2—21no—
296C2—682no—
297C2—1361no—
298C2#1454406411yescharacteristic
299C2C2×#1176371511yescharacteristic
300C2#1454508311yescharacteristic
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#11569
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. #14543725C2semidirect
197. C17#11569semidirect

Maximal subgroups

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

subgroupindex
#145440412
#145440212
#145437252
#145339582
#1156917