Finite Group Databasebeta

← C2×#14543773 #17959082

Subgroups — C2×#14543773 #17959082

Order 4352.

506 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 112 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×#11763704C211yesmaximal, characteristic
2C2×#11763683C211yesmaximal, characteristic
3#14543773C214yesmaximal, direct product factor
4C2×#11763051C211yesmaximal, characteristic
5C22×C4⋊#595—21no—
6C22×#63216—21no—
7#11763704—21no—
8#11763704C2212yes—
9#11763683—21no—
10#11763683C2212yes—
11C22×Dic68C411yescharacteristic, complemented
12C22×C8×D17C2211yescharacteristic
13C2×#10587583—21no—
14#11763051—21no—
15#11763051—21no—
16#11763051C412yescomplemented
17#11763051C2212yes—
18C2×#10587481—21no—
19C2×C17×#107C411yescharacteristic, complemented
20C23×#595—41no—
21C22×C4×D17D411yescharacteristic
22C22×Dic34—21no—
23C2×C4⋊#595—24no—
24C2×C4⋊#595—22no—
25C2×C4⋊#595—42no—
26C2×C4⋊#595—41no—
27C22×C8×C17C2×C411yescharacteristic
28C2×C4⋊C4×C17—21no—
29C2×#63227—41no—
30C2×C4⋊Dic17—41no—
31C22×#3622D411yescharacteristic
32C2×Dic68—21no—
33C2×Dic68—42no—
34C2×Dic68C2×C412yescomplemented
35C2×C8×D17—42no—
36C2×C8×D17C2×C411yescharacteristic
37C2×C8×D17D411yescharacteristic
38C2×C8×D17D411yescharacteristic
39C2×C8×D17C2311yescharacteristic
40#10587583—22no—
41#10587583—22no—
42#10587583—41no—
43#10587583—41no—
44C2×#63216—22no—
45C2×#63216—42no—
46C17×#107—21no—
47C17×#107C2×C412yescomplemented
48#10587481—22no—
49#10587481—22no—
50C23×D17D811yescharacteristic
51C22×#595—44no—
52C22×#595—42no—
53C22×#595—82no—
54C22×#595—82no—
55C22×C4×C17—41no—
56C22×C4×C17C22⋊C411yescharacteristic
57C22×Dic17—41no—
58C22×Dic17SD1611yescharacteristic
59C2×C4×D17—22no—
60C2×C4×D17—22no—
61C2×C4×D17C22⋊C411yescharacteristic
62C2×C4×D17D811yescharacteristic
63C2×C4×D17SD1611yescharacteristic
64C2×C4×D17C2×D411yescharacteristic
65C2×Dic34—22no—
66C2×Dic34—42no—
67C2×Dic34—42no—
68C2×Dic34—41no—
69C4⋊#595—24no—
70C4⋊#595—44no—
71C4⋊#595—42no—
72C2×C8×C17—22no—
73C2×C8×C17C22⋊C411yescharacteristic
74C2×C8×C17C22×C411yescharacteristic
75C4⋊C4×C17—22no—
76C4⋊C4×C17—41no—
77#63227—42no—
78#63227—42no—
79C4⋊Dic17—42no—
80C4⋊Dic17—42no—
81C2×#3622—22no—
82C2×#3622C22⋊C411yescharacteristic
83C2×#3622C2×D411yescharacteristic
84Dic68—42no—
85Dic68—42no—
86C8×D17—41no—
87C8×D17—41no—
88C8×D17—41no—
89C8×D17—41no—
90#63216—42no—
91C2×#1348—171nomaximal, Sylow
92C23×C17#10211yescharacteristic
93C22×D17—22no—
94C22×D17—22no—
95C22×D17#10211yescharacteristic
96C22×D17SD3212yes—
97C22×D17Q3212yes—
98C22×D17C2×D811yescharacteristic
99C2×#595—44no—
100C2×#595—88no—
101C2×#595—82no—
102C2×#595—82no—
103C2×C4×C17—42no—
104C2×C4×C17—82no—
105C2×C4×C17#9912yes—
106C2×C4×C17#10211yescharacteristic
107C2×C4×C17#10412yes—
108C2×C4×C17C2×C22⋊C411yescharacteristic
109C2×Dic17—22no—
110C2×Dic17—42no—
111C2×Dic17—82no—
112C2×Dic17#10211yescharacteristic
113C2×Dic17C2×SD1611yescharacteristic
114C4×D17—22no—
115C4×D17—22no—
116C4×D17—21no—
117C4×D17—21no—
118C4×D17—21no—
119C4×D17—21no—
120Dic34—42no—
121Dic34—42no—
122Dic34—82no—
123C8×C17—21no—
124C8×C17—21no—
125#3622—21no—
126#3622—21no—
127C2×#467—171no—
128C2×C22⋊C16—171no—
129C2×#340—171no—
130#1348—174no—
131C22×C17#32712yes—
132C22×C17#35812yes—
133C22×C17#36012yes—
134C22×C17C2×#10211yescharacteristic
135C2×D17—24no—
136C2×D17—24no—
137C2×D17—21no—
138C2×D17—21no—
139C2×D17—21no—
140C2×D17—21no—
141C2×D17#35812yes—
142C2×D17C2×SD3211yescharacteristic
143C2×D17C2×Q3211yescharacteristic
144#595—84no—
145C4×C17—82no—
146C4×C17#32712yes—
147C4×C17C2×#9911yescharacteristic
148C4×C17C2×#10411yescharacteristic
149Dic17—21no—
150Dic17—21no—
151Dic17—82no—
152C22×Q16—171no—
153C23×C8—171no—
154C2×C22⋊Q8—341no—
155C22×C4⋊C4—341no—
156C22×C16—341no—
157#467—172no—
158#467—172no—
159#467—341no—
160#467—341no—
161C2×#107#59511yescharacteristic, complemented
162C2×#103—341no—
163C22⋊C16—172no—
164C22⋊C16—341no—
165#340—172no—
166#340—341no—
167C2×C17#134814yescomplemented
168C2×C17C2×#32711yescharacteristic
169C2×C17C2×#35811yescharacteristic
170C2×C17C2×#36011yescharacteristic
171D17—21no—
172D17—22no—
173D17—21no—
174C22×Q8—341no—
175C23×C4—171no—
176C23×C4—681no—
177C2×Q16—172no—
178C2×Q16—341no—
179C2×Q16—682no—
180C22×C8—171no—
181C22×C8—171no—
182C22×C8—171no—
183C22×C8—171no—
184C22×C8—171no—
185C22×C8—682no—
186C22×C8C2×#59511yescharacteristic
187C22⋊Q8—342no—
188C22⋊Q8—342no—
189C22⋊Q8—681no—
190C22⋊Q8—681no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—342no—
193C2×C4⋊C4—344no—
194C2×C4⋊C4—681no—
195C2×C4⋊C4—681no—
196C2×C4⋊C4—682no—
197C2×C22⋊C4—681no—
198C2×C16—342no—
199C2×C16—682no—
200#107—21no—
201#107C2×#59512yescomplemented
202#103—342no—
203#103—342no—
204C17C2×#134811yescharacteristic, complemented, Sylow
205C24—171no—
206C2×Q8—342no—
207C2×Q8—681no—
208C2×Q8—682no—
209C2×Q8—682no—
210C22×C4—41no—
211C22×C4—171no—
212C22×C4—171no—
213C22×C4—171no—
214C22×C4—171no—
215C22×C4—171no—
216C22×C4—342no—
217C22×C4—342no—
218C22×C4—682no—
219C22×C4—684no—
220C22×C4—681no—
221C22×C4—1362no—
222C22×C4—1362no—
223C22×C4C22⋊#59511yescharacteristic
224Q16—682no—
225Q16—682no—
226C2×C8—22no—
227C2×C8—171no—
228C2×C8—171no—
229C2×C8—342no—
230C2×C8—681no—
231C2×C8—681no—
232C2×C8—681no—
233C2×C8—681no—
234C2×C8C22⋊#59511yescharacteristic
235C2×C8C22×#59511yescharacteristic
236C4⋊C4—22no—
237C4⋊C4—41no—
238C4⋊C4—344no—
239C4⋊C4—682no—
240C4⋊C4—682no—
241C4⋊C4—682no—
242C4⋊C4—684no—
243C22⋊C4—682no—
244C22⋊C4—682no—
245C16—682no—
246C23—172no—
247C23—172no—
248C23—171no—
249C23—171no—
250C23—342no—
251C23—342no—
252C23#1058754711yescharacteristic
253Q8—682no—
254Q8—682no—
255Q8—1362no—
256C2×C4—42no—
257C2×C4—82no—
258C2×C4—171no—
259C2×C4—171no—
260C2×C4—342no—
261C2×C4—341no—
262C2×C4—341no—
263C2×C4—341no—
264C2×C4—341no—
265C2×C4—342no—
266C2×C4—342no—
267C2×C4—684no—
268C2×C4—682no—
269C2×C4—1362no—
270C2×C4—1368no—
271C2×C4—1362no—
272C2×C4—1362no—
273C2×C4#1058753912yes—
274C2×C4#1058754711yescharacteristic
275C2×C4#1058755012yes—
276C2×C4C2×C22⋊#59511yescharacteristic
277C8—21no—
278C8—21no—
279C8—341no—
280C8—341no—
281C22—171no—
282C22—172no—
283C22—171no—
284C22—341no—
285C22—341no—
286C22—344no—
287C22—344no—
288C22—341no—
289C22—341no—
290C22#1176366112yes—
291C22#1176372212yes—
292C22#1176372512yes—
293C22C2×#1058754711yescharacteristic
294C4—82no—
295C4—341no—
296C4—341no—
297C4—1364no—
298C4—1362no—
299C4#1176366112yes—
300C4C2×#1058753911yescharacteristic
301C4C2×#1058755011yescharacteristic
302C2—341no—
303C2—342no—
304C2—341no—
305C2#1454377314yesdirect product factor
306C2C2×#1176366111yescharacteristic
307C2C2×#1176372211yescharacteristic
308C2C2×#1176372511yescharacteristic
subgroupG/H
centerC23#10587547
commutatorC2×C8×C17C22×C4
FrattiniC2×C8C22×#595
FittingC2×C17×#107C4
socleC23×C17#102
prime radicalC23×D17D8
cosocleC2×C8×D17C23
hypercenterC2×#107#595
hypocenterC17C2×#1348
LCSG ▷ C2×C8×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
3. #14543773C2direct (N × H)
11. C22×Dic68C4semidirect
16. #11763051C4semidirect
19. C2×C17×#107C4semidirect
34. C2×Dic68C2×C4semidirect
47. C17×#107C2×C4semidirect
161. C2×#107#595semidirect
167. C2×C17#1348semidirect
201. #107C2×#595semidirect
204. C17C2×#1348semidirect
305. C2#14543773direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117637042
C2×#117636832
#145437732
C2×#117630512
C2×#134817