Finite Group Databasebeta

← #17981671

Subgroups — #17981671

Order 4352.

642 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 642 conjugacy classes of subgroups — too many to draw. Only its 109 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#14545925C212yesmaximal
2#14545793C214yesmaximal
3C2×C4⋊C4×#595C211yesmaximal, characteristic
4C2×C22⋊#3633C2214yes—
5(C2×#3633)⋊C4—22no—
6(C2×#3633)⋊C4—22no—
7C22×C4⋊#595C411yescharacteristic
8C22×C4×#595C412yes—
9C22×C4×#595C2211yescharacteristic
10C4⋊C4×#595—22no—
11C4⋊C4×#595—22no—
12C2×(C2×#595)⋊C4C2212yes—
13C2×C4⋊C4×D17C411yescharacteristic
14C23×#595C2×C411yescharacteristic
15C23×#595C2×C412yes—
16C23×#595C2311yescharacteristic
17C22×#3633—24no—
18C22×C4×D17C2×C411yescharacteristic
19C22×C4×D17C2×C412yes—
20C2×C4⋊#595—24no—
21C2×C4⋊#595—22no—
22C2×C4×#595—24no—
23C2×C4×#595—22no—
24C2×C4×#595—22no—
25C2×C4×#595—44no—
26C2×C4×#595D412yes—
27C2×C4×#595D412yes—
28C22⋊#3633—28no—
29C2×C4⋊C4×C17C811yescharacteristic, complemented
30C2×C4⋊Dic17C811yescharacteristic, complemented
31C2×#63225C812yescomplemented
32C4⋊C4×D17—22no—
33C4⋊C4×D17—22no—
34(C2×#595)⋊C4—24no—
35C23×D17C22×C411yescharacteristic
36C22×#595—22no—
37C22×#595—22no—
38C22×#595—22no—
39C22×#595—22no—
40C22×#595—22no—
41C22×#595—41no—
42C22×#595—41no—
43C22×#595—42no—
44C22×#595—42no—
45C22×#595C22⋊C411yescharacteristic
46C22×#595C22⋊C411yescharacteristic
47C22×#595M1614yes—
48C22×#595C2×D412yes—
49C22×#595#4114yes—
50C2×#3633—44no—
51C2×#3633—44no—
52C2×#3633—44no—
53C22×C4×C17C2×C812yes—
54C22×C4×C17C2×C811yescharacteristic
55C22×Dic17C2×C811yescharacteristic
56C22×Dic17C2×C812yes—
57C2×C4×D17—22no—
58C2×C4×D17—22no—
59C2×C4×D17—22no—
60C2×C4×D17—22no—
61C2×C4×D17—42no—
62C2×C4×D17—42no—
63C2×C4×D17C22⋊C412yes—
64C2×C4×D17M1612yes—
65C4⋊#595—28no—
66C4×#595—24no—
67C4×#595—24no—
68C4×#595—44no—
69C4×#595—44no—
70C4⋊C4×C17—22no—
71C4⋊Dic17—22no—
72#63225—24no—
73#8701—171nomaximal, Sylow
74C23×C17C22×C811yescharacteristic
75C22×D17—21no—
76C22×D17—21no—
77C22×D17—21no—
78C22×D17—21no—
79C22×D17C2×C22⋊C411yescharacteristic
80C22×D17#11712yes—
81C22×D17C2×M1612yes—
82C22×D17C2×M1611yescharacteristic
83C2×#595—28no—
84C2×#595—21no—
85C2×#595—21no—
86C2×#595—22no—
87C2×#595—22no—
88C2×#595—21no—
89C2×#595—21no—
90C2×#595—24no—
91C2×#595—44no—
92C2×#595—44no—
93C2×#595—42no—
94C2×#595—42no—
95C2×#595—44no—
96C2×#595#10012yes—
97C2×#595#10112yes—
98C2×#595#12314yes—
99#3633—84no—
100C2×C4×C17—22no—
101C2×C4×C17—22no—
102C2×C4×C17—42no—
103C2×C4×C17C22⋊C812yes—
104C2×Dic17—22no—
105C2×Dic17—22no—
106C2×Dic17—42no—
107C2×Dic17C22⋊C812yes—
108C4×D17—22no—
109C4×D17—22no—
110C4×D17—24no—
111C4×D17—44no—
112C4×D17—42no—
113C4×D17—42no—
114C2×C4×C4⋊C4—171no—
115#1817—172no—
116#1280—174no—
117C22×C17—21no—
118C22×C17—21no—
119C22×C17C2×C22⋊C811yescharacteristic
120C22×C17#43112yes—
121C2×D17—21no—
122C2×D17—21no—
123C2×D17—22no—
124C2×D17—22no—
125C2×D17—22no—
126C2×D17—22no—
127C2×D17#38111yescharacteristic
128C2×D17#40711yescharacteristic
129C2×D17#41011yescharacteristic
130C2×D17#41011yescharacteristic
131C2×D17C2×#10011yescharacteristic
132C2×D17C2×#10111yescharacteristic
133C2×D17#43212yes—
134#595—24no—
135#595—22no—
136#595—22no—
137#595—44no—
138C4×C17—22no—
139C4×C17—42no—
140Dic17—22no—
141Dic17—42no—
142C22×C4⋊C4—171no—
143C22×C4⋊C4—171no—
144C22×C42—171no—
145C22×C42—172no—
146C2×C22⋊C8—174no—
147C4×C4⋊C4—342no—
148C4×C4⋊C4—342no—
149C2×#95—172no—
150#336—342no—
151#336—342no—
152C2×C17—22no—
153C2×C17#146011yescharacteristic
154C2×C17#146111yescharacteristic
155C2×C17#181711yescharacteristic
156D17—22no—
157D17#146611yescharacteristic
158D17#146711yescharacteristic
159D17#182011yescharacteristic
160D17#182111yescharacteristic
161C23×C4—171no—
162C23×C4—171no—
163C23×C4—171no—
164C23×C4—172no—
165C23×C4—172no—
166C22×C8—344no—
167C2×C4⋊C4—172no—
168C2×C4⋊C4—171no—
169C2×C4⋊C4—342no—
170C2×C4⋊C4—342no—
171C2×C4⋊C4—344no—
172C2×C4⋊C4—342no—
173C2×C4⋊C4#363311yescharacteristic, complemented
174C2×C42—172no—
175C2×C42—172no—
176C2×C42—344no—
177C2×C42—342no—
178C2×C42—342no—
179C2×C42—684no—
180C22⋊C8—348no—
181#95—344no—
182C17#870111yescharacteristic, complemented, Sylow
183C24—171no—
184C22×C4—171no—
185C22×C4—171no—
186C22×C4—172no—
187C22×C4—171no—
188C22×C4—174no—
189C22×C4—172no—
190C22×C4—172no—
191C22×C4—174no—
192C22×C4—172no—
193C22×C4—342no—
194C22×C4—342no—
195C22×C4—342no—
196C22×C4—342no—
197C22×C4—342no—
198C22×C4—342no—
199C22×C4—342no—
200C22×C4—342no—
201C22×C4—342no—
202C22×C4—682no—
203C22×C4—682no—
204C22×C4—681no—
205C22×C4—681no—
206C22×C4—682no—
207C22×C4—682no—
208C22×C4C2×#363312yes—
209C22×C4C2×#363311yescharacteristic
210C2×C8—684no—
211C2×C8—684no—
212C2×C8—684no—
213C4⋊C4—22no—
214C4⋊C4—344no—
215C4⋊C4—348no—
216C4⋊C4—342no—
217C42—344no—
218C42—344no—
219C42—684no—
220C42—684no—
221C23—171no—
222C23—171no—
223C23—172no—
224C23—172no—
225C23—341no—
226C23—341no—
227C23—341no—
228C23—341no—
229C23C22×#363311yescharacteristic
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—42no—
233C2×C4—174no—
234C2×C4—172no—
235C2×C4—172no—
236C2×C4—172no—
237C2×C4—342no—
238C2×C4—342no—
239C2×C4—344no—
240C2×C4—341no—
241C2×C4—341no—
242C2×C4—341no—
243C2×C4—342no—
244C2×C4—342no—
245C2×C4—341no—
246C2×C4—348no—
247C2×C4—342no—
248C2×C4—344no—
249C2×C4—342no—
250C2×C4—682no—
251C2×C4—682no—
252C2×C4—684no—
253C2×C4—684no—
254C2×C4—682no—
255C2×C4—682no—
256C2×C4—684no—
257C2×C4—682no—
258C2×C4—684no—
259C2×C4C22⋊#363312yes—
260C8—1364no—
261C22—21no—
262C22—21no—
263C22—171no—
264C22—171no—
265C22—171no—
266C22—171no—
267C22—171no—
268C22—171no—
269C22—172no—
270C22—342no—
271C22—342no—
272C22—342no—
273C22—342no—
274C22—341no—
275C22—341no—
276C22C2×C22⋊#363311yescharacteristic
277C22#1176392212yes—
278C4—22no—
279C4—42no—
280C4—344no—
281C4—342no—
282C4—342no—
283C4—342no—
284C4—684no—
285C4—682no—
286C2—22no—
287C2—171no—
288C2—171no—
289C2—171no—
290C2—171no—
291C2—342no—
292C2#1454589811yescharacteristic
293C2#1454589911yescharacteristic
294C2#1454592511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3633
commutatorC23×C17C22×C8
FrattiniC23C22×#3633
FittingC2×C4⋊C4×C17C8
socleC22×C17C2×C22⋊C8
prime radicalC23×D17C22×C4
cosocleC23×#595C23
hypercenterC2×C4⋊C4#3633
hypocenterC17#8701
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
29. C2×C4⋊C4×C17C8semidirect
30. C2×C4⋊Dic17C8semidirect
31. C2×#63225C8semidirect
173. C2×C4⋊C4#3633semidirect
182. C17#8701semidirect

Maximal subgroups

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

subgroupindex
#145459252
#145457932
C2×C4⋊C4×#5952
#870117