Finite Group Databasebeta

← #17950083

Subgroups — #17950083

Order 4352.

562 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 562 conjugacy classes of subgroups — too many to draw. Only its 116 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
1C4×#10587543C211yesmaximal, characteristic
2#14544448C211yesmaximal, characteristic
3#14543602C214yesmaximal, complemented
4#14537137C211yesmaximal, characteristic
5C22×#63243—21no—
6C2×#10587543—21no—
7C2×C4×#3624—21no—
8#11763675—21no—
9#11763675C2212yes—
10#11763675C2212yes—
11C2×#10587555C411yescharacteristic
12C2×#10587583—21no—
13C2×C42×D17C2211yescharacteristic
14#11762714—21no—
15#11762708—21no—
16#11762708C2212yes—
17#11762666—21no—
18#11762666C412yes—
19C17×#384C411yescharacteristic
20C22×C4×D17C2×C411yescharacteristic
21C22×C4×D17D411yescharacteristic
22C22×C4×D17D411yescharacteristic
23C22×Dic34—21no—
24C22×#3624—22no—
25C22×#3624—22no—
26C2×#63243—24no—
27C2×#63243—42no—
28C2×#63243—42no—
29C2×C4⋊C4×C17—21no—
30C2×C4⋊C4×C17—21no—
31C2×C4⋊C4×C17C2×C412yes—
32C2×C42×C17C2×C411yescharacteristic
33C2×#63227—22no—
34C2×C4⋊Dic17—21no—
35C2×C4⋊Dic17—22no—
36C2×C4⋊Dic17C2×C412yes—
37C2×C4×Dic17D411yescharacteristic
38C2×C4×Dic17D411yescharacteristic
39C2×C4×Dic17C2311yescharacteristic
40#10587583—42no—
41#10587583—42no—
42C42×D17—42no—
43#10587555—42no—
44#10587543—24no—
45C4×#3624—42no—
46#10587502—22no—
47#10587502—22no—
48C23×D17C22⋊C411yescharacteristic
49C22×C4×C17—22no—
50C22×C4×C17C22⋊C411yescharacteristic
51C22×C4×C17C22⋊C411yescharacteristic
52C22×C4×C17C22×C411yescharacteristic
53C22×Dic17—22no—
54C22×Dic17C22⋊C411yescharacteristic
55C22×Dic17C2×D411yescharacteristic
56C22×Dic17C2×D411yescharacteristic
57C2×C4×D17—22no—
58C2×C4×D17—22no—
59C2×C4×D17—22no—
60C2×C4×D17—22no—
61C2×C4×D17—22no—
62C2×C4×D17—22no—
63C2×C4×D17—41no—
64C2×C4×D17—41no—
65C2×C4×D17D812yes—
66C2×C4×D17SD1612yes—
67C2×Dic34—42no—
68C2×Dic34—42no—
69C2×Dic34—42no—
70C2×#3624—24no—
71C2×#3624—24no—
72C2×#3624—42no—
73C2×#3624—42no—
74C2×#3624—42no—
75C2×#3624—42no—
76#63243—48no—
77C4⋊C4×C17—24no—
78C4⋊C4×C17—42no—
79C4⋊C4×C17—42no—
80C42×C17—22no—
81#63227—44no—
82C4⋊Dic17—42no—
83C4⋊Dic17—42no—
84C4⋊Dic17—42no—
85C4⋊Dic17—42no—
86C4×Dic17—22no—
87C4×Dic17—41no—
88C4×Dic17—41no—
89#7685—171nomaximal, Sylow
90C23×C17C2×C22⋊C411yescharacteristic
91C22×D17—21no—
92C22×D17—21no—
93C22×D17—21no—
94C22×D17—21no—
95C22×D17—21no—
96C22×D17—21no—
97C22×D17#10212yes—
98C2×C4×C17—21no—
99C2×C4×C17—21no—
100C2×C4×C17—21no—
101C2×C4×C17—21no—
102C2×C4×C17—42no—
103C2×C4×C17—42no—
104C2×C4×C17—42no—
105C2×C4×C17#9912yes—
106C2×C4×C17#10212yes—
107C2×C4×C17#10412yes—
108C2×C4×C17#10412yes—
109C2×C4×C17#13112yes—
110C2×Dic17—21no—
111C2×Dic17—21no—
112C2×Dic17—21no—
113C2×Dic17—21no—
114C2×Dic17—21no—
115C2×Dic17—21no—
116C2×Dic17—42no—
117C2×Dic17—42no—
118C2×Dic17—42no—
119C2×Dic17#10112yes—
120C2×Dic17C2×D811yescharacteristic
121C2×Dic17C2×SD1611yescharacteristic
122C2×Dic17#13712yes—
123C4×D17—24no—
124C4×D17—24no—
125C4×D17—44no—
126C4×D17—44no—
127Dic34—84no—
128#3624—44no—
129#3624—44no—
130#2857—171no—
131C4×C22⋊C8—171no—
132#1728—171no—
133#1271—174no—
134C22×C17#40811yescharacteristic
135C22×C17C2×#9911yescharacteristic
136C22×C17C2×#10111yescharacteristic
137C22×C17C2×#10211yescharacteristic
138C22×C17#41911yescharacteristic
139C22×C17C2×#10411yescharacteristic
140C22×C17C2×#10411yescharacteristic
141C2×D17—22no—
142C2×D17—22no—
143C2×D17—22no—
144C2×D17—41no—
145C2×D17—41no—
146C2×D17—41no—
147C2×D17—41no—
148C4×C17—22no—
149C4×C17—22no—
150C4×C17—82no—
151C4×C17#32714yes—
152Dic17—22no—
153Dic17—21no—
154Dic17—21no—
155Dic17—22no—
156Dic17—82no—
157C22×M16—341no—
158C2×C4⋊Q8—171no—
159C2×C22⋊Q8—341no—
160C22×C42—171no—
161C2×C22⋊C8—341no—
162C2×C4×C8—341no—
163#391—341no—
164#389—172no—
165#389—341no—
166#384#59511yescharacteristic
167#380—172no—
168#380—341no—
169#336—172no—
170#336—172no—
171#336—341no—
172C2×C17#147211yescharacteristic
173C2×C17#148511yescharacteristic
174C2×C17#149211yescharacteristic
175C2×C17C2×#32711yescharacteristic
176C2×C17#150811yescharacteristic
177C2×C17#152611yescharacteristic
178C2×C17#154611yescharacteristic
179D17—42no—
180C22×Q8—341no—
181C23×C4—171no—
182C23×C4—171no—
183C23×C4—171no—
184C2×M16—344no—
185C2×M16—682no—
186C2×M16—682no—
187C22×C8—342no—
188C22×C8—342no—
189C4⋊Q8—682no—
190C22⋊Q8—682no—
191C22⋊Q8—682no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—172no—
195C2×C4⋊C4—342no—
196C2×C4⋊C4—341no—
197C2×C4⋊C4C2×#59512yes—
198C2×C22⋊C4—342no—
199C2×C42—171no—
200C2×C42—171no—
201C2×C42—171no—
202C2×C42—682no—
203C2×C42C2×#59511yescharacteristic
204C22⋊C8—344no—
205C4×C8—682no—
206#95—342no—
207#95—342no—
208C17#768511yescharacteristic, complemented, Sylow
209C24—171no—
210C2×Q8—682no—
211C2×Q8—682no—
212C2×Q8—682no—
213C22×C4—22no—
214C22×C4—171no—
215C22×C4—171no—
216C22×C4—171no—
217C22×C4—172no—
218C22×C4—172no—
219C22×C4—342no—
220C22×C4—342no—
221C22×C4—342no—
222C22×C4—342no—
223C22×C4—342no—
224C22×C4—342no—
225C22×C4—342no—
226C22×C4—681no—
227C22×C4—681no—
228C22×C4C22⋊#59511yescharacteristic
229C22×C4C22⋊#59511yescharacteristic
230C22×C4C22×#59511yescharacteristic
231M16—688no—
232C2×C8—344no—
233C2×C8—344no—
234C2×C8—682no—
235C2×C8—682no—
236C2×C8—682no—
237C2×C8—682no—
238C4⋊C4—24no—
239C4⋊C4—42no—
240C4⋊C4—42no—
241C4⋊C4—682no—
242C4⋊C4—682no—
243C4⋊C4—682no—
244C4⋊C4—682no—
245C22⋊C4—684no—
246C42—22no—
247C42—342no—
248C42—681no—
249C42—681no—
250C23—172no—
251C23—341no—
252C23—341no—
253C23—341no—
254C23—341no—
255C23—341no—
256C23—341no—
257C23C2×C22⋊#59511yescharacteristic
258Q8—1364no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—172no—
267C2×C4—171no—
268C2×C4—171no—
269C2×C4—172no—
270C2×C4—341no—
271C2×C4—341no—
272C2×C4—341no—
273C2×C4—341no—
274C2×C4—341no—
275C2×C4—341no—
276C2×C4—344no—
277C2×C4—344no—
278C2×C4—684no—
279C2×C4—684no—
280C2×C4—682no—
281C2×C4—682no—
282C2×C4—682no—
283C2×C4#1058753912yes—
284C2×C4#1058754712yes—
285C2×C4#1058754812yes—
286C2×C4#1058755012yes—
287C2×C4#1058767812yes—
288C8—684no—
289C8—684no—
290C22—342no—
291C22—342no—
292C22—342no—
293C22—681no—
294C22—681no—
295C22—681no—
296C22—681no—
297C22#1176378311yescharacteristic
298C22C2×#1058753911yescharacteristic
299C22D17⋊#10111yescharacteristic
300C22C2×#1058754711yescharacteristic
301C22#1176380211yescharacteristic
302C22C2×#1058754811yescharacteristic
303C22C2×#1058755011yescharacteristic
304C4—22no—
305C4—22no—
306C4—82no—
307C4—341no—
308C4—341no—
309C4—342no—
310C4—342no—
311C4—1362no—
312C4#1176366114yes—
313C2—682no—
314C2#1454406211yescharacteristic
315C2#1454410711yescharacteristic
316C2#1454413011yescharacteristic
317C2C2×#1176366111yescharacteristic
318C2#1454418311yescharacteristic
319C2#1454424211yescharacteristic
320C2#1454429411yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC17×#384C4
socleC23×C17C2×C22⋊C4
prime radicalC23×D17C22⋊C4
cosocleC2×C4×Dic17C23
hypercenter#384#595
hypocenterC17#7685
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
3. #14543602C2semidirect
208. C17#7685semidirect

Maximal subgroups

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

subgroupindex
C4×#105875432
#145444482
#145436022
#145371372
#768517