Finite Group Databasebeta

← #17948709

Subgroups — #17948709

Order 4352.

372 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 70 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×#10587539C211yesmaximal, characteristic
2#14544021C211yesmaximal, characteristic
3#14529577C211yesmaximal, characteristic
4C2×#10587539C412yes—
5#11763777—21no—
6C4×C22⋊#595—21no—
7#11763687—21no—
8#11763654C412yescomplemented
9#11763653—21no—
10C2×C4×D68C2211yescharacteristic
11C2×#10587491—21no—
12C2×#10587491—21no—
13C2×C4×#3622C411yescharacteristic, complemented
14C2×C17×C4⋊C8C411yescharacteristic, complemented
15C22×D68C2×C411yescharacteristic
16C22×C4×D17D411yescharacteristic
17C22×C4×D17D411yescharacteristic
18C2×C22⋊#595—22no—
19C2×C4×#595—41no—
20C2×#63242—41no—
21C22×C8×C17—21no—
22C2×C42×C17C2×C411yescharacteristic
23C2×#63227D411yescharacteristic
24C2×#63227Q811yescharacteristic
25C2×C4⋊Dic17C2×C411yescharacteristic
26C22×#3622—21no—
27C4×D68—41no—
28C4×D68—41no—
29C22⋊#3624—22no—
30(C2×#595)⋊C4—41no—
31#10587543—41no—
32#10587539—22no—
33#10587539C814yescomplemented
34C17×C4⋊C8—41no—
35#10587491—42no—
36#10587491—42no—
37C4×#3622—41no—
38C23×D17C22⋊C411yescharacteristic
39C23×D17C4⋊C411yescharacteristic
40C22×#595—42no—
41C22×C4×C17C4211yescharacteristic
42C22×C4×C17C22⋊C411yescharacteristic
43C22×C4×C17C4⋊C411yescharacteristic
44C22×Dic17C22⋊C411yescharacteristic
45C22×Dic17C4⋊C411yescharacteristic
46C2×D68—41no—
47C2×D68—41no—
48C2×D68C2×C812yes—
49C2×D68M1612yes—
50C2×C4×D17—21no—
51C2×C4×D17—21no—
52C2×C4×D17—21no—
53C2×C4×D17—21no—
54C2×C4×D17—41no—
55C2×C4×D17—41no—
56C2×C4×D17—41no—
57C2×C4×D17—41no—
58C22⋊#595—24no—
59C22⋊#595—42no—
60C2×#3624—42no—
61C4×#595—81no—
62C4×#595—81no—
63#63242—81no—
64#63242—81no—
65C2×C8×C17—41no—
66C2×C8×C17—41no—
67C2×C8×C17—41no—
68C42×C17—21no—
69C42×C17—21no—
70#63227—41no—
71#63227—41no—
72C4⋊Dic17—41no—
73C2×#3622—22no—
74C2×#3622—41no—
75C2×#3622—41no—
76#7205—171nomaximal, Sylow
77C23×C17#9511yescharacteristic
78C22×D17—21no—
79C22×D17—21no—
80C22×D17—21no—
81C22×D17—21no—
82C22×D17—41no—
83C22×D17—41no—
84C22×D17—41no—
85C22×D17—41no—
86C22×D17C22⋊C812yes—
87C22×D17C4⋊C812yes—
88C2×#595—44no—
89C2×#595—82no—
90C2×#595—82no—
91C2×C4×C17—21no—
92C2×C4×C17—21no—
93C2×C4×C17—21no—
94C2×C4×C17—21no—
95C2×C4×C17—21no—
96C2×C4×C17—41no—
97C2×C4×C17C4×C811yescharacteristic
98C2×C4×C17#9711yescharacteristic
99C2×C4×C17#9911yescharacteristic
100C2×C4×C17#9911yescharacteristic
101C2×Dic17—21no—
102C2×Dic17—21no—
103C2×Dic17—41no—
104C2×Dic17—41no—
105D68—42no—
106D68—42no—
107C4×D17—41no—
108C4×D17—41no—
109C4×D17—41no—
110C4×D17—41no—
111C4×D17—81no—
112C4×D17—81no—
113#3624—82no—
114C8×C17—81no—
115#3622—42no—
116#1954—171no—
117C4×#99—171no—
118#1459—171no—
119C22×C17—21no—
120C22×C17—21no—
121C22×C17#33611yescharacteristic
122C22×C17#34211yescharacteristic
123C22×C17#34411yescharacteristic
124C2×D17—22no—
125C2×D17—22no—
126C2×D17—41no—
127C2×D17—41no—
128C2×D17—41no—
129C2×D17—41no—
130C2×D17—42no—
131C2×D17—42no—
132C2×D17—81no—
133C2×D17—81no—
134#595—84no—
135C4×C17—21no—
136C4×C17—21no—
137C4×C17—21no—
138C4×C17—41no—
139C4×C17#35311yescharacteristic
140C4×C17#35411yescharacteristic
141Dic17—41no—
142Dic17—41no—
143C2×C4×D4—171no—
144C2×C4⋊C8#59511yescharacteristic, complemented
145C2×#99—172no—
146C2×C22⋊C8—341no—
147C2×C22⋊C8—341no—
148C2×C22⋊C8—341no—
149C2×C4×C8—171no—
150C4×C22⋊C4—341no—
151#342—341no—
152#324—172no—
153#323—341no—
154C2×C17—21no—
155C2×C17—21no—
156C2×C17#128211yescharacteristic
157C2×C17#139311yescharacteristic
158C2×C17#139511yescharacteristic
159D17—42no—
160D17—42no—
161C22×D4—171no—
162C23×C4—171no—
163C23×C4—171no—
164C22×C8—21no—
165C22×C8—341no—
166C22×C8—681no—
167C4×D4—681no—
168C4×D4—681no—
169C2×C4⋊C4—171no—
170C2×C22⋊C4—171no—
171C2×C22⋊C4—171no—
172C2×C22⋊C4—342no—
173C2×C42—681no—
174C2×C42C2×#59511yescharacteristic
175C4⋊C8—41no—
176#99—174no—
177#99—342no—
178C22⋊C8—342no—
179C22⋊C8—682no—
180C22⋊C8—682no—
181C22⋊C8—681no—
182C4×C8—681no—
183#95—681no—
184C17#720511yescharacteristic, complemented, Sylow
185C24—171no—
186C24—171no—
187C2×D4—172no—
188C2×D4—172no—
189C2×D4—681no—
190C2×D4—681no—
191C22×C4—171no—
192C22×C4—171no—
193C22×C4—341no—
194C22×C4—341no—
195C22×C4—341no—
196C22×C4—341no—
197C22×C4—681no—
198C22×C4—681no—
199C22×C4—681no—
200C22×C4—681no—
201C22×C4—682no—
202C22×C4C4×#59511yescharacteristic
203C22×C4C4⋊#59511yescharacteristic
204C22×C4C22⋊#59511yescharacteristic
205C2×C8—41no—
206C2×C8—41no—
207C2×C8—41no—
208C2×C8—342no—
209C2×C8—681no—
210C2×C8—681no—
211C2×C8—682no—
212C2×C8—1361no—
213C2×C8—1361no—
214C4⋊C4—681no—
215C22⋊C4—344no—
216C22⋊C4—681no—
217C22⋊C4—681no—
218C22⋊C4—682no—
219C42—21no—
220C42—21no—
221C42—1361no—
222C42—1361no—
223C23—172no—
224C23—172no—
225C23—341no—
226C23—341no—
227C23—341no—
228C23—341no—
229C23—681no—
230C23—681no—
231C23—681no—
232C23—681no—
233C23(C2×#595)⋊C411yescharacteristic
234D4—682no—
235D4—682no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—41no—
242C2×C4—341no—
243C2×C4—341no—
244C2×C4—681no—
245C2×C4—681no—
246C2×C4—681no—
247C2×C4—681no—
248C2×C4—681no—
249C2×C4—681no—
250C2×C4—684no—
251C2×C4—1361no—
252C2×C4—1361no—
253C2×C4—1362no—
254C2×C4—1362no—
255C2×C4C8×#59511yescharacteristic
256C2×C4#1058753211yescharacteristic
257C2×C4#1058753911yescharacteristic
258C2×C4#1058755111yescharacteristic
259C8—81no—
260C8—682no—
261C8—1362no—
262C22—21no—
263C22—21no—
264C22—342no—
265C22—342no—
266C22—682no—
267C22—682no—
268C22—681no—
269C22—681no—
270C22—681no—
271C22—681no—
272C22—1361no—
273C22—1361no—
274C22#1176367411yescharacteristic
275C22#1176368711yescharacteristic
276C22#1176369111yescharacteristic
277C4—21no—
278C4—21no—
279C4—21no—
280C4—41no—
281C4—681no—
282C4—681no—
283C4—1364no—
284C4#1176371311yescharacteristic
285C4#1176371511yescharacteristic
286C2—21no—
287C2—21no—
288C2—682no—
289C2—682no—
290C2#1454362611yescharacteristic
291C2#1454387911yescharacteristic
292C2#1454388511yescharacteristic
subgroupG/H
centerC2×C4#10587551
commutatorC2×C4×C17C4×C8
FrattiniC2×C42C2×#595
FittingC2×C17×C4⋊C8C4
socleC22×C17#342
prime radicalC22×D68C2×C4
cosocleC2×C4×D68C22
hypercenterC2×C4⋊C8#595
hypocenterC17#7205
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
8. #11763654C4semidirect
13. C2×C4×#3622C4semidirect
14. C2×C17×C4⋊C8C4semidirect
33. #10587539C8semidirect
144. C2×C4⋊C8#595semidirect
184. C17#7205semidirect

Maximal subgroups

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

subgroupindex
C4×#105875392
#145440212
#145295772
#720517