Finite Group Databasebeta

← C2×#14543713 #17958143

Subgroups — C2×#14543713 #17958143

Order 4352.

834 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 834 conjugacy classes of subgroups — too many to draw. Only its 120 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
1C2×#11763654C212yesmaximal, complemented
2#14543713C214yesmaximal, direct product factor
3C2×#11762711C211yesmaximal, characteristic
4C2×C22⋊#3624—22no—
5#11763654—22no—
6#11763654C2214yescomplemented
7C23×D68C411yescharacteristic
8C22×C4⋊Dic17C2211yescharacteristic
9C22×#63227—22no—
10#11762711—22no—
11#11762711C412yes—
12#11762711C2212yes—
13C22×C42×C17C411yescharacteristic
14C24×D17—21no—
15C23×C4×C17—21no—
16C23×C4×C17C2×C411yescharacteristic
17C23×Dic17D412yes—
18C22×D68—21no—
19C22×D68—22no—
20C22×D68—41no—
21C22×D68—41no—
22C22×D68—42no—
23C22×D68C814yescomplemented
24C22×D68C2×C412yes—
25C22×#3624—42no—
26C2×C42×C17—21no—
27C2×C42×C17—42no—
28C2×C42×C17C2×C412yes—
29C2×#63227—24no—
30C2×#63227—24no—
31C2×#63227—48no—
32C2×C4⋊Dic17—41no—
33C2×C4⋊Dic17—41no—
34C2×C4⋊Dic17C2×C411yescharacteristic
35C2×C4⋊Dic17D412yes—
36C2×C4⋊Dic17C2311yescharacteristic
37C22⋊#3624—24no—
38C22⋊#3624—42no—
39C24×C17C22⋊C411yescharacteristic
40C23×D17—24no—
41C23×D17—22no—
42C23×D17—44no—
43C23×D17—44no—
44C23×D17—41no—
45C23×D17—41no—
46C23×D17—42no—
47C22×C4×C17—21no—
48C22×C4×C17—21no—
49C22×C4×C17—22no—
50C22×C4×C17—24no—
51C22×C4×C17—22no—
52C22×C4×C17—42no—
53C22×C4×C17—42no—
54C22×C4×C17C22⋊C411yescharacteristic
55C22×C4×C17C2×C812yes—
56C22×C4×C17M1612yes—
57C22×C4×C17C22×C411yescharacteristic
58C22×Dic17—22no—
59C22×Dic17—22no—
60C22×Dic17—44no—
61C22×Dic17C22⋊C412yes—
62C22×Dic17C2×D412yes—
63C2×D68—24no—
64C2×D68—22no—
65C2×D68—44no—
66C2×D68—44no—
67C2×D68—42no—
68C2×D68—42no—
69C2×D68—44no—
70C2×D68—44no—
71C2×D68—42no—
72C2×D68—42no—
73C2×D68C2×C814yescomplemented
74C2×#3624—44no—
75C2×#3624—84no—
76C42×C17—42no—
77C42×C17—42no—
78#63227—48no—
79#63227—48no—
80C4⋊Dic17—41no—
81C4⋊Dic17—42no—
82C4⋊Dic17—41no—
83C2×#1318—171nomaximal, Sylow
84C23×C17—22no—
85C23×C17—22no—
86C23×C17C22⋊C812yes—
87C23×C17#9911yescharacteristic
88C23×C17#9911yescharacteristic
89C23×C17#10012yes—
90C23×C17C2×C22⋊C411yescharacteristic
91C22×D17—24no—
92C22×D17—416no—
93C22×D17—44no—
94C22×D17—44no—
95C22×D17—44no—
96C22×D17—44no—
97C22×D17—42no—
98C22×D17—42no—
99C22×D17—88no—
100C22×D17—82no—
101C22×D17—82no—
102C22×D17—82no—
103C22×D17—82no—
104C2×C4×C17—22no—
105C2×C4×C17—22no—
106C2×C4×C17—22no—
107C2×C4×C17—22no—
108C2×C4×C17—21no—
109C2×C4×C17—21no—
110C2×C4×C17—21no—
111C2×C4×C17—21no—
112C2×C4×C17—24no—
113C2×C4×C17—48no—
114C2×C4×C17—42no—
115C2×C4×C17—42no—
116C2×C4×C17C22⋊C812yes—
117C2×C4×C17C22×C811yescharacteristic
118C2×C4×C17C2×M1611yescharacteristic
119C2×Dic17—22no—
120C2×Dic17—22no—
121C2×Dic17—44no—
122C2×Dic17—42no—
123C2×Dic17—42no—
124C2×Dic17—82no—
125D68—44no—
126D68—48no—
127D68—44no—
128#3624—84no—
129C2×#390—171no—
130C2×#324—172no—
131#1318—174no—
132C22×C17—24no—
133C22×C17—24no—
134C22×C17—21no—
135C22×C17—21no—
136C22×C17—21no—
137C22×C17—21no—
138C22×C17#32312yes—
139C22×C17#32312yes—
140C22×C17#35312yes—
141C22×C17#35512yes—
142C22×C17C2×C22⋊C811yescharacteristic
143C22×C17C2×#9911yescharacteristic
144C22×C17C2×#10011yescharacteristic
145C2×D17—48no—
146C2×D17—44no—
147C2×D17—84no—
148C2×D17—88no—
149C2×D17—88no—
150C2×D17—82no—
151C2×D17—82no—
152C4×C17—22no—
153C4×C17—21no—
154C4×C17—21no—
155C4×C17—44no—
156Dic17—42no—
157Dic17—42no—
158C23×D4—171no—
159C22×C4⋊C4—171no—
160C22×C22⋊C4—342no—
161C22×C42#59511yescharacteristic
162C2×C22⋊C8—342no—
163#390—172no—
164#390—172no—
165#390—342no—
166#324—174no—
167#324—342no—
168C2×C17—21no—
169C2×C17—21no—
170C2×C17—22no—
171C2×C17#131814yescomplemented
172C2×C17C2×#32311yescharacteristic
173C2×C17C2×#35311yescharacteristic
174C2×C17C2×#35511yescharacteristic
175D17—84no—
176C25—341no—
177C22×D4—174no—
178C22×D4—172no—
179C22×D4—342no—
180C22×D4—341no—
181C22×D4—681no—
182C22×D4—681no—
183C22×D4—682no—
184C23×C4—21no—
185C23×C4—172no—
186C23×C4C2×#59511yescharacteristic
187C22×C8—682no—
188C2×C4⋊C4—172no—
189C2×C4⋊C4—171no—
190C2×C4⋊C4—171no—
191C2×C4⋊C4—681no—
192C2×C4⋊C4—681no—
193C2×C22⋊C4—344no—
194C2×C22⋊C4—344no—
195C2×C22⋊C4—688no—
196C2×C42—21no—
197C2×C42—42no—
198C2×C42C2×#59512yes—
199C22⋊C8—344no—
200C22⋊C8—682no—
201C17C2×#131811yescharacteristic, complemented, Sylow
202C24—342no—
203C24—344no—
204C24—684no—
205C24—684no—
206C24—681no—
207C24—681no—
208C24—682no—
209C24C22⋊#59511yescharacteristic
210C2×D4—174no—
211C2×D4—342no—
212C2×D4—344no—
213C2×D4—682no—
214C2×D4—682no—
215C2×D4—684no—
216C2×D4—684no—
217C2×D4—682no—
218C2×D4—682no—
219C2×D4—684no—
220C2×D4—684no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—22no—
224C22×C4—24no—
225C22×C4—22no—
226C22×C4—42no—
227C22×C4—42no—
228C22×C4—172no—
229C22×C4—172no—
230C22×C4—342no—
231C22×C4—342no—
232C22×C4—684no—
233C22×C4#6324212yes—
234C22×C4#6324312yes—
235C22×C4C22⋊#59511yescharacteristic
236C22×C4C22×#59511yescharacteristic
237C2×C8—684no—
238C2×C8—1364no—
239C4⋊C4—682no—
240C4⋊C4—681no—
241C4⋊C4—681no—
242C22⋊C4—688no—
243C22⋊C4—688no—
244C42—42no—
245C42—42no—
246C23—22no—
247C23—22no—
248C23—344no—
249C23—684no—
250C23—6816no—
251C23—684no—
252C23—682no—
253C23—682no—
254C23—684no—
255C23—684no—
256C23—1368no—
257C23—1362no—
258C23—1362no—
259C23—1362no—
260C23—1362no—
261C23#1058753911yescharacteristic
262C23#1058753911yescharacteristic
263C23#1058754312yes—
264C23#1058755312yes—
265C23C2×C22⋊#59511yescharacteristic
266D4—684no—
267D4—684no—
268D4—688no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—24no—
278C2×C4—48no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—342no—
282C2×C4—342no—
283C2×C4—684no—
284C2×C4—682no—
285C2×C4—682no—
286C2×C4—1362no—
287C2×C4#1058754312yes—
288C2×C4C2×#6324211yescharacteristic
289C2×C4C2×#6324311yescharacteristic
290C8—1364no—
291C22—24no—
292C22—24no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—21no—
297C22—688no—
298C22—684no—
299C22—1364no—
300C22—1368no—
301C22—1368no—
302C22—1362no—
303C22—1362no—
304C22#1176365312yes—
305C22#1176365312yes—
306C22#1176371412yes—
307C22#1176371812yes—
308C22C2×#1058754311yescharacteristic
309C22C2×#1058753911yescharacteristic
310C22C2×#1058755311yescharacteristic
311C4—21no—
312C4—21no—
313C4—22no—
314C4—44no—
315C4—682no—
316C4—682no—
317C2—21no—
318C2—21no—
319C2—22no—
320C2—1364no—
321C2#1454371314yesdirect product factor
322C2C2×#1176365311yescharacteristic
323C2C2×#1176371411yescharacteristic
324C2C2×#1176371811yescharacteristic
subgroupG/H
centerC23#10587539
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC22×C42×C17C4
socleC23×C17#99
prime radicalC23×D68C4
cosocleC2×C4⋊Dic17C23
hypercenterC22×C42#595
hypocenterC17C2×#1318
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C24 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
1. C2×#11763654C2semidirect
2. #14543713C2direct (N × H)
6. #11763654C22semidirect
23. C22×D68C8semidirect
73. C2×D68C2×C8semidirect
171. C2×C17#1318semidirect
201. C17C2×#1318semidirect
321. C2#14543713direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117636542
#145437132
C2×#117627112
C2×#131817