Finite Group Databasebeta

← #17952145

Subgroups — #17952145

Order 4352.

510 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 104 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#14544520C212yesmaximal, complemented
2#14544161C212yesmaximal
3#14543666C211yesmaximal, characteristic, complemented
4#14543664C211yesmaximal, characteristic, complemented
5#14537477C211yesmaximal, characteristic
6#11763777C2212yes—
7C2×#10587532—22no—
8C4×C22⋊#595C2212yes—
9#11763674—22no—
10#11763662C414yescomplemented
11#11763661C414yescomplemented
12C2×#10587593C411yescharacteristic, complemented
13C22×C8×D17C2211yescharacteristic
14#11763321C2211yescharacteristic
15#11762879—22no—
16#11762874—22no—
17#11762775C411yescharacteristic, complemented
18#11762772C2211yescharacteristic
19#11762765C411yescharacteristic, complemented
20C17×#424C411yescharacteristic, complemented
21C2×#63252C2×C411yescharacteristic
22C22×C4×D17C2311yescharacteristic
23C2×C22⋊#595—22no—
24C2×C4×#595—22no—
25C2×#63242—22no—
26C2×M16×C17C2×C411yescharacteristic
27C22×C8×C17C2×C411yescharacteristic
28C17×#117C2×C411yescharacteristic
29C2×#63223C2×C411yescharacteristic
30C22×#3622C2×C411yescharacteristic
31#10587593—42no—
32C2×#63218—21no—
33C2×C8×D17—21no—
34C2×C8×D17—42no—
35C2×C8×D17D412yes—
36C2×C8×D17D412yes—
37#10587583C2×C412yes—
38#10587581C2×C412yes—
39#10587572—21no—
40#10587568—21no—
41C4×D68—22no—
42C22⋊#3624—22no—
43(C2×#595)⋊C4C2×C414yes—
44#10587543C2×C414yes—
45#10587532—44no—
46C17×C4⋊C8—22no—
47#10587491—22no—
48#10587491—22no—
49#10587474—21no—
50C4×#3622—21no—
51C23×D17#4111yescharacteristic
52C22×#595—24no—
53C22×C4×C17C22×C411yescharacteristic
54C2×C22⋊D17—21no—
55C22×Dic17#4111yescharacteristic
56#63252—41no—
57#63252—41no—
58C2×D68—22no—
59C2×D68C4211yescharacteristic
60C2×C4×D17—21no—
61C2×C4×D17—41no—
62C2×C4×D17—41no—
63C2×C4×D17C22×C412yes—
64C2×C4×D17C2×D412yes—
65C2×Dic34C4211yescharacteristic
66C22⋊#595—44no—
67C2×#3624—24no—
68C4×#595—42no—
69C4×#595—42no—
70#63242—42no—
71#63242—42no—
72M16×C17—41no—
73C2×C8×C17—21no—
74C2×C8×C17—41no—
75C2×C8×C17C22⋊C412yes—
76C4⋊C4×C17C4212yes—
77C22⋊C4×C17—21no—
78C42×C17—21no—
79#63227—22no—
80#63227—22no—
81C4⋊Dic17—22no—
82#63223—41no—
83C2×#3622—22no—
84C2×#3622—21no—
85C2×#3622C22⋊C411yescharacteristic
86C2×#3622C22⋊C411yescharacteristic
87#63218—42no—
88C8×D17—24no—
89C8×D17—42no—
90C8×D17—42no—
91#8239—171nomaximal, Sylow
92C23×C17#11711yescharacteristic
93C22×D17—24no—
94C22×D17—21no—
95C22×D17—41no—
96C22×D17C4×D412yes—
97C2×#595—44no—
98C2×#595—44no—
99C2×#595—44no—
100C2×C4×C17—21no—
101C2×C4×C17—21no—
102C2×C4×C17—22no—
103C2×C4×C17C2×C4211yescharacteristic
104C2×C4×C17C2×C22⋊C411yescharacteristic
105C22⋊D17—42no—
106C2×Dic17—21no—
107C2×Dic17—41no—
108C2×Dic17C4×D412yes—
109D68—41no—
110D68—44no—
111C4×D17—22no—
112C4×D17—22no—
113C4×D17—42no—
114C4×D17—41no—
115C4×D17—41no—
116Dic34—41no—
117#3624—44no—
118C8×C17—22no—
119C8×C17—41no—
120#3622—21no—
121#3622—41no—
122#3622#9912yes—
123#2929—171no—
124#1752—172no—
125#1501—172no—
126#1298—171no—
127#1297—171no—
128C22×C17—21no—
129C22×C17—22no—
130C22×C17C4×C22⋊C411yescharacteristic
131C2×D17—22no—
132C2×D17—22no—
133C2×D17—44no—
134C2×D17—41no—
135C2×D17—42no—
136C2×D17#44414yes—
137#595—84no—
138C4×C17—21no—
139C4×C17—42no—
140C4×C17C2×#9911yescharacteristic
141C4×C17#41011yescharacteristic
142Dic17—22no—
143Dic17—41no—
144C2×#131—171no—
145C23×C8—171no—
146#525—171no—
147#435—342no—
148C8×D4—342no—
149#424#59511yescharacteristic, complemented
150#408—171no—
151#407—171no—
152C2×C22⋊C8—172no—
153#405—171no—
154C2×#97—342no—
155C4×C22⋊C4—172no—
156#336—342no—
157#328—174no—
158#327—174no—
159C2×C17—41no—
160C2×C17C4×#9911yescharacteristic
161C2×C17#176512yes—
162D17—24no—
163D17—81no—
164C2×#41—171no—
165C23×C4—171no—
166#131—682no—
167C2×M16—171no—
168C2×M16—341no—
169C2×M16C2×#59511yescharacteristic
170C22×C8—171no—
171C22×C8—172no—
172C22×C8—172no—
173C22×C8—341no—
174C22×C8—342no—
175C22×C8—682no—
176C22×C8C2×#59511yescharacteristic
177#123—341no—
178C22⋊Q8—172no—
179#121—172no—
180#120—341no—
181C4×D4—342no—
182#117C2×#59511yescharacteristic
183C2×C22⋊C4—342no—
184C2×C42—342no—
185C4⋊C8—22no—
186C22⋊C8—174no—
187C22⋊C8—342no—
188C22⋊C8—342no—
189C22⋊C8—342no—
190#97—341no—
191#97—684no—
192C4×C8—341no—
193#95—174no—
194C17#823911yescharacteristic, complemented, Sylow
195C24—171no—
196#41—681no—
197#41—681no—
198C2×Q8—171no—
199C2×D4—171no—
200C2×D4—342no—
201C2×D4—341no—
202C22×C4—171no—
203C22×C4—172no—
204C22×C4—172no—
205C22×C4—341no—
206C22×C4—344no—
207C22×C4—681no—
208C22×C4—681no—
209C22×C4C22×#59511yescharacteristic
210M16—41no—
211M16—682no—
212M16—681no—
213C2×C8—21no—
214C2×C8—41no—
215C2×C8—171no—
216C2×C8—171no—
217C2×C8—344no—
218C2×C8—342no—
219C2×C8—344no—
220C2×C8—341no—
221C2×C8—682no—
222C2×C8—682no—
223C2×C8—682no—
224C2×C8—682no—
225C2×C8C22⋊#59512yes—
226C4⋊C4—342no—
227C4⋊C4C4×#59512yes—
228C22⋊C4—21no—
229C22⋊C4—342no—
230C22⋊C4—342no—
231C22⋊C4—684no—
232C42—21no—
233C42—682no—
234C42—682no—
235C23—172no—
236C23—344no—
237C23—341no—
238C23—681no—
239C23#1058767711yescharacteristic
240Q8—681no—
241D4—681no—
242D4—684no—
243D4—682no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—172no—
248C2×C4—342no—
249C2×C4—342no—
250C2×C4—341no—
251C2×C4—682no—
252C2×C4—681no—
253C2×C4—681no—
254C2×C4—681no—
255C2×C4—684no—
256C2×C4—684no—
257C2×C4—684no—
258C2×C4C2×C4×#59511yescharacteristic
259C2×C4C2×C22⋊#59511yescharacteristic
260C8—22no—
261C8—41no—
262C8—172no—
263C8—341no—
264C8—684no—
265C8—681no—
266C22—21no—
267C22—22no—
268C22—174no—
269C22—342no—
270C22—342no—
271C22—684no—
272C22—681no—
273C22—682no—
274C22C4×C22⋊#59511yescharacteristic
275C4—21no—
276C4—42no—
277C4—342no—
278C4—681no—
279C4—1364no—
280C4D17⋊#9911yescharacteristic
281C4#1176379011yescharacteristic
282C2—41no—
283C2—344no—
284C2—1361no—
285C2#1454452911yescharacteristic
286C2#1454456212yes—
subgroupG/H
centerC2×C4C2×C22⋊#595
commutatorC2×C4×C17C2×C42
FrattiniC22×C4C22×#595
FittingC17×#424C4
socleC22×C17C4×C22⋊C4
prime radical#11763321C22
cosocleC22×C4×D17C23
hypercenter#424#595
hypocenterC17#8239
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #424

Complements

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

NH ≅ G/Ntype
1. #14544520C2semidirect
3. #14543666C2semidirect
4. #14543664C2semidirect
10. #11763662C4semidirect
11. #11763661C4semidirect
12. C2×#10587593C4semidirect
17. #11762775C4semidirect
19. #11762765C4semidirect
20. C17×#424C4semidirect
149. #424#595semidirect
194. C17#8239semidirect

Maximal subgroups

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

subgroupindex
#145445202
#145441612
#145436662
#145436642
#145374772
#823917