Finite Group Databasebeta

← C2×#22608983 #33061586

Subgroups — C2×#22608983 #33061586

Order 18688.

1838 conjugacy classes of subgroups; only the 219 normal subgroups are shown.

normal subgroups only

This group has 1838 conjugacy classes of subgroups — too many to draw. Only its 219 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×#17989222C211yesmaximal, characteristic, complemented
2C2×#17988779C212yesmaximal, complemented
3#22608983C218yesmaximal, direct product factor
4C2×#17988331C211yesmaximal, characteristic, complemented
5C2×#17988316C212yesmaximal, complemented
6C2×#493×C73C211yesmaximal, characteristic, complemented
7C22×D4×D73—22no—
8C22×#11924013—22no—
9#17989222—24no—
10#17989222—22no—
11#17989222C2214yescomplemented
12C2×#14556562—22no—
13C2×#14556559—22no—
14C2×C4×D292C2212yes—
15#17988779—24no—
16#17988779C2218yescomplemented
17C2×C4⋊#10596831C2212yescomplemented
18C2×#14556512—22no—
19#17988331C2214yescomplemented
20#17988316C2218yescomplemented
21C22×D8×C73—22no—
22C2×#127×C73C2211yescharacteristic
23C2×#127×C73C2211yescharacteristic, complemented
24#493×C73—22no—
25#493×C73C2214yescomplemented
26C2×C4×C8×C73C2211yescharacteristic, complemented
27C24×D73—22no—
28C22×D292D412yes—
29C22×C22⋊D73—24no—
30C2×D4×D73—28no—
31C2×D4×D73—28no—
32C2×D4×D73—48no—
33C2×D4×D73—48no—
34C22×C4×D73—22no—
35C2×#11924013—28no—
36C2×#11924013—48no—
37C22×#10596831—22no—
38#14556562—28no—
39#14556562—28no—
40#14556559—28no—
41#14556559—28no—
42C4×D292—22no—
43C4×D292—22no—
44C4×D292D414yes—
45C4×D292C2314yes—
46C2×C4⋊Dic73D412yes—
47C2×C22⋊Dic73—22no—
48C2×#11924005—22no—
49C4⋊#10596831—22no—
50C4⋊#10596831C2314yescomplemented
51#14556512—28no—
52C22×D4×C73—22no—
53C22×D4×C73—21no—
54C22×D4×C73—22no—
55C22×D4×C73D412yes—
56C2×D8×C73—28no—
57C2×D8×C73—48no—
58C22×C8×C73—21no—
59#127×C73—22no—
60#127×C73—21no—
61#127×C73—22no—
62#127×C73D412yes—
63#127×C73C2312yes—
64#127×C73C2312yescomplemented
65C2×C42×C73C2311yescharacteristic
66C4×C8×C73—21no—
67C4×C8×C73C2312yescomplemented
68C23×D73—22no—
69C23×D73—28no—
70C23×D73—416no—
71C23×D73—84no—
72C2×D292—22no—
73C2×D292—24no—
74C2×D292D818yescomplemented
75C2×D292C2×D414yes—
76C2×C22⋊D73—216no—
77C2×C22⋊D73—416no—
78D4×D73—416no—
79D4×D73—432no—
80D4×D73—416no—
81C22×Dic73—22no—
82C2×C4×D73—24no—
83C2×C4×D73—24no—
84C2×C4×D73—44no—
85C2×C4×D73—44no—
86#11924013—416no—
87C2×#10596831—24no—
88C2×#10596831—44no—
89C4⋊Dic73—22no—
90C4⋊Dic73C2×D414yes—
91C22⋊Dic73—28no—
92#11924005—24no—
93#11924005—24no—
94C24×C73—22no—
95C24×C73—41no—
96C2×D4×C73—24no—
97C2×D4×C73—22no—
98C2×D4×C73—24no—
99C2×D4×C73—22no—
100C2×D4×C73—24no—
101C2×D4×C73—44no—
102C2×D4×C73—44no—
103C2×D4×C73—41no—
104C2×D4×C73—42no—
105C2×D4×C73—44no—
106C2×D4×C73—44no—
107C2×D4×C73—44no—
108C2×D4×C73—44no—
109C2×D4×C73C2×D414yes—
110C22×C4×C73C2×D412yes—
111C22×C4×C73C2×D411yescharacteristic
112D8×C73—416no—
113C2×C8×C73—24no—
114C2×C8×C73—22no—
115C42×C73C2×D412yes—
116C42×C73C2×D411yescharacteristic
117C42×C73C2411yescharacteristic
118C23×C73—24no—
119C23×C73—48no—
120C23×C73—44no—
121C23×C73—42no—
122C23×C73—84no—
123C23×C73—82no—
124C23×C73#12011yescharacteristic
125C22×D73—24no—
126C22×D73—28no—
127C22×D73—432no—
128C22×D73—44no—
129C22×D73—44no—
130C22×D73—88no—
131C22×D73—832no—
132D4×C73—44no—
133D4×C73—44no—
134D4×C73—44no—
135D4×C73—44no—
136D4×C73—44no—
137D4×C73—44no—
138D4×C73—48no—
139D4×C73—82no—
140D4×C73—82no—
141D4×C73—84no—
142C2×C4×C73—22no—
143C2×C4×C73#12011yescharacteristic
144C2×C4×C73#12012yes—
145C2×C4×C73C2×D814yes—
146C2×C4×C73AGL(1,ℤ/8)14yes—
147C2×C4×C73C22×D412yes—
148C2×C4×C73C22×D411yescharacteristic
149C22⋊D73—432no—
150C2×Dic73—24no—
151C2×Dic73—44no—
152D292—24no—
153D292—28no—
154D292C2×D818yescomplemented
155C4×D73—44no—
156C4×D73—44no—
157C4×D73—48no—
158C8×C73—24no—
159#10596831—44no—
160C22×C73—48no—
161C22×C73—44no—
162C22×C73—88no—
163C22×C73—84no—
164C22×C73—82no—
165C22×C73—164no—
166C22×C73#44714yes—
167C22×C73#45312yes—
168C22×C73C2×#12011yescharacteristic
169C2×D73—28no—
170C2×D73—416no—
171C2×D73—44no—
172C2×D73—44no—
173C2×D73—832no—
174C4×C73—21no—
175C4×C73—21no—
176C4×C73#44714yes—
177C4×C73C22×D812yes—
178C4×C73C2×AGL(1,ℤ/8)12yes—
179Dic73—44no—
180C2×#1619—731nomaximal, Sylow
181C2×C73—84no—
182C2×C73—162no—
183C2×C73#161914yescomplemented
184C2×C73C2×#44712yes—
185C2×C73C2×#45311yescharacteristic
186D73—48no—
187C2×D42—731no—
188C2×#493D7311yescharacteristic, complemented
189C2×#459—732no—
190#1619—738no—
191C2×#331—731no—
192C2×D4⋊C8—732no—
193C73C2×#161911yescharacteristic, complemented, Sylow
194C23×D4—1462no—
195C22×D8—22no—
196C22×D8—1462no—
197D42—734no—
198D42—1464no—
199D42—1462no—
200C2×#127C2×D7311yescharacteristic
201C2×#127C2×D7311yescharacteristic, complemented
202C2×#121—1462no—
203C2×#120—1462no—
204C2×C4×D4—732no—
205#493—22no—
206#493C2×D7314yescomplemented
207#459—738no—
208#459—1464no—
209C2×C4⋊C8—732no—
210C2×#102—1462no—
211C2×C4×C8C2×D7311yescharacteristic, complemented
212#331—734no—
213D4⋊C8—738no—
214C25—1462no—
215C22×D4—22no—
216C22×D4—22no—
217C22×D4—21no—
218C22×D4—2928no—
219C22×D4—2928no—
220C22×D4—732no—
221C22×D4—1468no—
222C22×D4—1468no—
223C22×D4—1464no—
224C22×D4C22⋊D7312yes—
225C23×C4—1462no—
226C2×D8—28no—
227C2×D8—48no—
228C2×D8—2928no—
229C2×D8—1468no—
230C22×C8—21no—
231C22×C8—1462no—
232#127—22no—
233#127—22no—
234#127—21no—
235#127C22⋊D7312yes—
236#127C22×D7312yes—
237#127C22×D7312yescomplemented
238#121—1468no—
239#121—1468no—
240#120—1468no—
241#120—1468no—
242C4×D4—734no—
243C4×D4—734no—
244C4×D4—1462no—
245C4×D4—1462no—
246C2×C4⋊C4—732no—
247C2×C22⋊C4—1462no—
248C2×C22⋊C4—1462no—
249C2×C42C22×D7311yescharacteristic
250C4⋊C8—734no—
251C4⋊C8—1462no—
252#102—1468no—
253C4×C8—21no—
254C4×C8C22×D7312yescomplemented
255C24—22no—
256C24—41no—
257C24—29216no—
258C24—5844no—
259C24—1468no—
260C24—1462no—
261C2×D4—24no—
262C2×D4—22no—
263C2×D4—24no—
264C2×D4—24no—
265C2×D4—22no—
266C2×D4—44no—
267C2×D4—44no—
268C2×D4—41no—
269C2×D4—42no—
270C2×D4—44no—
271C2×D4—44no—
272C2×D4—44no—
273C2×D4—44no—
274C2×D4—29216no—
275C2×D4—29232no—
276C2×D4—29216no—
277C2×D4—29216no—
278C2×D4—738no—
279C2×D4—734no—
280C2×D4—14616no—
281C2×D4—1462no—
282C2×D4—1464no—
283C2×D4C2×C22⋊D7314yes—
284C22×C4—2924no—
285C22×C4—2924no—
286C22×C4—1462no—
287C22×C4—1464no—
288C22×C4—1464no—
289C22×C4D4×D7312yes—
290C22×C4C2×C22⋊D7311yescharacteristic
291D8—416no—
292D8—29216no—
293C2×C8—24no—
294C2×C8—22no—
295C2×C8—2924no—
296C2×C8—1464no—
297C4⋊C4—734no—
298C4⋊C4—1462no—
299C22⋊C4—1468no—
300C22⋊C4—1464no—
301C22⋊C4—1464no—
302C42D4×D7312yes—
303C42C2×C22⋊D7311yescharacteristic
304C42C23×D7311yescharacteristic
305C23—24no—
306C23—48no—
307C23—44no—
308C23—42no—
309C23—84no—
310C23—82no—
311C23—29232no—
312C23—2924no—
313C23—2924no—
314C23—5848no—
315C23—58432no—
316C23—1468no—
317C23—1464no—
318C23#1455655911yescharacteristic
319D4—44no—
320D4—44no—
321D4—48no—
322D4—44no—
323D4—44no—
324D4—44no—
325D4—44no—
326D4—82no—
327D4—82no—
328D4—84no—
329D4—29232no—
330D4—738no—
331D4—1468no—
332D4—1464no—
333C2×C4—22no—
334C2×C4—2924no—
335C2×C4—2928no—
336C2×C4—2924no—
337C2×C4—2924no—
338C2×C4—1464no—
339C2×C4#1455655911yescharacteristic
340C2×C4#1455655912yes—
341C2×C4D8×D7314yes—
342C2×C4#1455661514yes—
343C2×C4C2×D4×D7312yes—
344C2×C4C22×C22⋊D7311yescharacteristic
345C8—24no—
346C8—2924no—
347C22—44no—
348C22—48no—
349C22—88no—
350C22—82no—
351C22—84no—
352C22—164no—
353C22—29216no—
354C22—2924no—
355C22—2924no—
356C22—58432no—
357C22—1468no—
358C22#1798871914yes—
359C22#1798875412yes—
360C22C2×#1455655911yescharacteristic
361C4—21no—
362C4—21no—
363C4—2924no—
364C4#1798871914yes—
365C4C2×D8×D7312yes—
366C4C2×#1455661512yes—
367C2—84no—
368C2—162no—
369C2—2928no—
370C2#2260898314yesdirect product factor
371C2C2×#1798871912yes—
372C2C2×#1798875411yescharacteristic
subgroupG/H
centerC23#14556559
commutator, cosocleC42×C73C24
FrattiniC42C23×D73
FittingC2×#493×C73C2
socleC23×C73#120
hypercenterC2×#493D73
hypocenterC73C2×#1619
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#493

Complements

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

NH ≅ G/Ntype
1. C2×#17989222C2semidirect
2. C2×#17988779C2semidirect
3. #22608983C2direct (N × H)
4. C2×#17988331C2semidirect
5. C2×#17988316C2semidirect
6. C2×#493×C73C2semidirect
11. #17989222C22semidirect
16. #17988779C22semidirect
17. C2×C4⋊#10596831C22semidirect
19. #17988331C22semidirect
20. #17988316C22semidirect
23. C2×#127×C73C22semidirect
25. #493×C73C22semidirect
26. C2×C4×C8×C73C22semidirect
50. C4⋊#10596831C23semidirect
64. #127×C73C23semidirect
67. C4×C8×C73C23semidirect
74. C2×D292D8semidirect
154. D292C2×D8semidirect
183. C2×C73#1619semidirect
188. C2×#493D73semidirect
193. C73C2×#1619semidirect
201. C2×#127C2×D73semidirect
206. #493C2×D73semidirect
211. C2×C4×C8C2×D73semidirect
237. #127C22×D73semidirect
254. C4×C8C22×D73semidirect
370. C2#22608983direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892222
C2×#179887792
#226089832
C2×#179883312
C2×#179883162
C2×#493×C732
C2×#161973