Finite Group Databasebeta

← C2×#20247677 #26386099

Subgroups — C2×#20247677 #26386099

Order 12032.

2918 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093983C211yesmaximal, characteristic
2C23×Dic47⋊C4C211yesmaximal, characteristic
3#20247677C2116yesmaximal, direct product factor
4C2×#15689063C212yesmaximal, complemented
5C2×#15689055C212yesmaximal, complemented
6C2×#15689008C214yesmaximal, complemented
7C2×#15688998C212yesmaximal
8C2×#15688984C212yesmaximal
9C2×C47×#381C211yesmaximal, characteristic
10C24×Dic47C2211yescharacteristic
11C24×Dic47C2211yescharacteristic
12C2×#13093983—28no—
13C2×#13093983C2218yes—
14C22×C4⋊Dic47C2214yes—
15C22×C4⋊Dic47C2211yescharacteristic
16C22×C4⋊Dic47C2211yescharacteristic
17C22×Dic47⋊C4—28no—
18C22×Dic47⋊C4C2212yes—
19C22×Dic47⋊C4C2212yes—
20C22×Dic47⋊C4C2218yes—
21C22×C22⋊Dic47C2212yes—
22C22×C4×Dic47C2212yes—
23#15689063C22116yescomplemented
24#15689055C22116yescomplemented
25#15689008C22132yescomplemented
26#15688998C22116yes—
27#15688984C22116yes—
28C2×C47⋊#95C2214yes—
29C2×C47⋊#95C2214yes—
30C2×C47⋊#95C2214yes—
31C24×C4×C47C2211yescharacteristic
32C22×C22⋊C4×C47C2212yes—
33C47×#381C2218yes—
34C2×#95×C47C2212yes—
35C2×#95×C47C2212yes—
36C23×Dic47—24no—
37C23×Dic47—28no—
38C23×Dic47—24no—
39C23×Dic47—28no—
40C23×Dic47C2312yes—
41C23×Dic47C2312yes—
42C23×Dic47C2312yes—
43C23×Dic47C2314yes—
44C23×Dic47C2314yes—
45C23×Dic47C2312yes—
46#13093983—232no—
47C2×C4⋊Dic47—24no—
48C2×C4⋊Dic47—24no—
49C2×C4⋊Dic47—216no—
50C2×C4⋊Dic47C23116yes—
51C2×C4⋊Dic47C2314yes—
52C2×C4⋊Dic47C2314yes—
53C2×Dic47⋊C4—28no—
54C2×Dic47⋊C4—28no—
55C2×Dic47⋊C4—232no—
56C2×Dic47⋊C4C2318yes—
57C2×Dic47⋊C4C2318yes—
58C2×C22⋊Dic47—28no—
59C2×C22⋊Dic47C2318yes—
60C2×C4×Dic47—28no—
61C2×C4×Dic47C2318yes—
62C47⋊#95C23116yes—
63C47⋊#95C23116yes—
64C47⋊#95C23116yes—
65C25×C47C2311yescharacteristic
66C23×C4×C47—28no—
67C23×C4×C47D418yes—
68C23×C4×C47C2314yes—
69C23×C4×C47C2311yescharacteristic
70C23×C4×C47C2311yescharacteristic
71C23×C4×C47C2314yes—
72C2×C22⋊C4×C47—28no—
73C2×C22⋊C4×C47C2318yes—
74#95×C47C2318yes—
75#95×C47C2318yes—
76C24×C47—24no—
77C24×C47—24no—
78C24×C47C2×D414yes—
79C24×C47#4118yes—
80C24×C47C2412yes—
81C24×C47C2411yescharacteristic
82C22×C4×C47—232no—
83C22×C4×C47—216no—
84C22×C4×C47—24no—
85C22×C4×C47—24no—
86C22×C4×C47—28no—
87C22×C4×C47—28no—
88C22×C4×C47—28no—
89C22×C4×C47C2×D414yes—
90C22×C4×C47C2×D414yes—
91C22×C4×C47C2×D4116yes—
92C22×C4×C47C2418yes—
93C22×C4×C47C2412yes—
94C22×C4×C47C2412yes—
95C22×Dic47—232no—
96C22×Dic47—28no—
97C22×Dic47—24no—
98C22×Dic47—24no—
99C22×Dic47—216no—
100C22×Dic47—24no—
101C22×Dic47—24no—
102C22×Dic47—28no—
103C22×Dic47—24no—
104C22×Dic47—28no—
105C22×Dic47—216no—
106C22×Dic47—28no—
107C22×Dic47—28no—
108C22×Dic47—416no—
109C22×Dic47#4118yes—
110C22×Dic47C2414yes—
111C22×Dic47C2414yes—
112C22×Dic47C2414yes—
113C22×Dic47C2414yes—
114C22⋊C4×C47—216no—
115C22⋊Dic47—216no—
116C4⋊Dic47—28no—
117C4⋊Dic47—28no—
118C4⋊Dic47—232no—
119Dic47⋊C4—216no—
120Dic47⋊C4—216no—
121C4×Dic47—216no—
122C23×C47—28no—
123C23×C47—28no—
124C23×C47—232no—
125C23×C47—24no—
126C23×C47—24no—
127C23×C47#123116yes—
128C23×C47C22×D414yes—
129C23×C47C22×D412yes—
130C23×C47C2×#4114yes—
131C23×C47C2×#4118yes—
132C23×C47C2×#4114yes—
133C23×C472−1+414yes—
134C23×C47C2511yescharacteristic
135C2×C4×C47—232no—
136C2×C4×C47—28no—
137C2×C4×C47—28no—
138C2×C4×C47—24no—
139C2×C4×C47—24no—
140C2×C4×C47—28no—
141C2×C4×C47—28no—
142C2×C4×C47—28no—
143C2×C4×C47—416no—
144C2×C4×C47C22×D414yes—
145C2×C4×C47C22×D414yes—
146C2×Dic47—232no—
147C2×Dic47—216no—
148C2×Dic47—24no—
149C2×Dic47—24no—
150C2×Dic47—24no—
151C2×Dic47—24no—
152C2×Dic47—24no—
153C2×Dic47—28no—
154C2×Dic47—28no—
155C2×Dic47—28no—
156C2×Dic47—416no—
157C2×Dic47—48no—
158C2×Dic47—48no—
159C2×Dic47—48no—
160C2×Dic47C2×#4118yes—
161C2×#2484—471nomaximal, Sylow
162C22×C47—24no—
163C22×C47—24no—
164C22×C47—216no—
165C22×C47—232no—
166C22×C47C2×#12318yes—
167C22×C47C2×#12314yes—
168C22×C47#52514yes—
169C22×C47#53614yes—
170C22×C47#552116yes—
171C22×C47C23×D411yescharacteristic
172C22×C47C22×#4112yes—
173C22×C47C22×#4112yes—
174C22×C47C2×2−1+412yes—
175C4×C47—24no—
176C4×C47—24no—
177C4×C47—48no—
178Dic47—28no—
179Dic47—44no—
180Dic47—44no—
181Dic47—44no—
182C22×#117—471no—
183C23×C4⋊C4—471no—
184#2484—4716no—
185C2×#400—472no—
186C2×#398—472no—
187C2×#387—474no—
188C2×#385—472no—
189C2×#381—472no—
190C2×#381D4711yescharacteristic
191C2×C47—28no—
192C2×C47#248418yescomplemented
193C2×C47C22×#12311yescharacteristic
194C2×C47C2×#52511yescharacteristic
195C2×C47C2×#53611yescharacteristic
196C2×C47C2×#55214yes—
197C24×C4—471no—
198C24×C4—471no—
199C24×C4C2×D4711yescharacteristic
200C2×#117—478no—
201C2×#117—948no—
202C22×C4⋊C4—471no—
203C22×C4⋊C4—472no—
204C22×C4⋊C4—474no—
205C22×C4⋊C4—471no—
206C22×C4⋊C4—478no—
207C22×C4⋊C4—472no—
208C22×C4⋊C4—948no—
209C22×C22⋊C4—472no—
210C22×C22⋊C4C2×D4712yes—
211C22×C42—472no—
212#400—4716no—
213#398—4716no—
214#387—4732no—
215#385—4716no—
216#381—4716no—
217#381C2×D4718yes—
218C2×#95—474no—
219C2×#95—474no—
220C2×#95—474no—
221C2×#95C2×D4712yes—
222C2×#95C2×D4712yes—
223C47C2×#248411yescharacteristic, complemented, Sylow
224C25C22×D4711yescharacteristic
225C23×C4—28no—
226C23×C4—472no—
227C23×C4—474no—
228C23×C4—474no—
229C23×C4—472no—
230C23×C4—472no—
231C23×C4—472no—
232C23×C4—948no—
233C23×C4—944no—
234C23×C4—944no—
235C23×C4—948no—
236C23×C4D18818yes—
237C23×C4C22×D4714yes—
238C23×C4C22×D4714yes—
239C23×C4C22×D4711yescharacteristic
240C23×C4C22×D4711yescharacteristic
241#117—9432no—
242C2×C4⋊C4—478no—
243C2×C4⋊C4—478no—
244C2×C4⋊C4—474no—
245C2×C4⋊C4—474no—
246C2×C4⋊C4—4716no—
247C2×C4⋊C4—9416no—
248C2×C4⋊C4—948no—
249C2×C4⋊C4—948no—
250C2×C4⋊C4—9432no—
251C2×C4⋊C4—944no—
252C2×C4⋊C4—944no—
253C2×C22⋊C4—28no—
254C2×C22⋊C4—478no—
255C2×C22⋊C4—948no—
256C2×C22⋊C4C22×D4718yes—
257C2×C42—478no—
258C2×C42—948no—
259#95—4716no—
260#95—4716no—
261#95—4716no—
262#95C22×D4718yes—
263#95C22×D4718yes—
264C24—24no—
265C24—24no—
266C24C2×D18814yes—
267C24#1062535218yes—
268C24C23×D4712yes—
269C24C23×D4711yescharacteristic
270C22×C4—232no—
271C22×C4—216no—
272C22×C4—24no—
273C22×C4—24no—
274C22×C4—28no—
275C22×C4—28no—
276C22×C4—28no—
277C22×C4—478no—
278C22×C4—474no—
279C22×C4—474no—
280C22×C4—474no—
281C22×C4—474no—
282C22×C4—9416no—
283C22×C4—9432no—
284C22×C4—948no—
285C22×C4—944no—
286C22×C4—944no—
287C22×C4—944no—
288C22×C4—944no—
289C22×C4—948no—
290C22×C4—944no—
291C22×C4—948no—
292C22×C4—9416no—
293C22×C4—948no—
294C22×C4—948no—
295C22×C4—18816no—
296C22×C4C2×D18814yes—
297C22×C4C2×D18814yes—
298C22×C4C2×D188116yes—
299C22×C4C23×D4718yes—
300C22×C4C23×D4712yes—
301C22×C4C23×D4712yes—
302C4⋊C4—9432no—
303C4⋊C4—9416no—
304C4⋊C4—9416no—
305C4⋊C4—948no—
306C4⋊C4—948no—
307C22⋊C4—216no—
308C22⋊C4—9416no—
309C42—9416no—
310C23—232no—
311C23—28no—
312C23—24no—
313C23—28no—
314C23—24no—
315C23#13094008116yes—
316C23C22×D18814yes—
317C23C22×D18812yes—
318C23#41×D4714yes—
319C23C2×#1062535218yes—
320C23C2×#1062535214yes—
321C23#1309407114yes—
322C23C24×D4711yescharacteristic
323C2×C4—232no—
324C2×C4—28no—
325C2×C4—28no—
326C2×C4—24no—
327C2×C4—24no—
328C2×C4—28no—
329C2×C4—28no—
330C2×C4—28no—
331C2×C4—416no—
332C2×C4—478no—
333C2×C4—9432no—
334C2×C4—9416no—
335C2×C4—944no—
336C2×C4—944no—
337C2×C4—944no—
338C2×C4—944no—
339C2×C4—944no—
340C2×C4—948no—
341C2×C4—948no—
342C2×C4—948no—
343C2×C4—18816no—
344C2×C4—1888no—
345C2×C4—1888no—
346C2×C4—1888no—
347C2×C4C22×D18814yes—
348C2×C4C22×D18814yes—
349C22—24no—
350C22—232no—
351C22—216no—
352C22—24no—
353C22C2×#1309400818yes—
354C22C2×#1309400814yes—
355C22#1568963514yes—
356C22#1568969914yes—
357C22#15689810116yes—
358C22C23×D18811yescharacteristic
359C22C2×#41×D4712yes—
360C22C22×#1062535212yes—
361C22C2×#1309407112yes—
362C4—24no—
363C4—24no—
364C4—48no—
365C4—948no—
366C4—1884no—
367C4—1884no—
368C4—1884no—
369C2—28no—
370C2#2024767718yesdirect product factor
371C2C22×#1309400811yescharacteristic
372C2C2×#1568963511yescharacteristic
373C2C2×#1568969911yescharacteristic
374C2C2×#1568981014yes—
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#381C2
socleC24×C47C24
prime radicalC25×C47C23
hypercenterC2×#381D47
hypocenterC47C2×#2484
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
3. #20247677C2direct (N × H)
4. C2×#15689063C2semidirect
5. C2×#15689055C2semidirect
6. C2×#15689008C2semidirect
23. #15689063C22semidirect
24. #15689055C22semidirect
25. #15689008C22semidirect
192. C2×C47#2484semidirect
223. C47C2×#2484semidirect
370. C2#20247677direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130939832
C23×Dic47⋊C42
#202476772
C2×#156890632
C2×#156890552
C2×#156890082
C2×#156889982
C2×#156889842
C2×C47×#3812
C2×#248447