Finite Group Databasebeta

← C2×#20242843 #26198675

Subgroups — C2×#20242843 #26198675

Order 12032.

638 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689415C211yesmaximal, characteristic
2C2×#15689405C211yesmaximal, characteristic
3C2×C8×Dic94C211yesmaximal, characteristic
4#20242843C218yesmaximal, direct product factor
5C2×#15688876C211yesmaximal, characteristic
6C2×#15688872C211yesmaximal, characteristic
7C2×#15688869C211yesmaximal, characteristic
8C2×C47×#487C211yesmaximal, characteristic
9C2×C4×Dic94C2211yescharacteristic
10#15689415—22no—
11#15689415C2214yes—
12#15689405—22no—
13#15689405C2214yes—
14C8×Dic94—22no—
15C8×Dic94C2214yes—
16C2×#13093957—21no—
17C2×#13093955—21no—
18C2×C4⋊(C47⋊C8)C2211yescharacteristic
19C2×C4⋊(C47⋊C8)C2211yescharacteristic
20C2×C4⋊(C47⋊C8)C2211yescharacteristic
21C2×Dic47⋊C8—21no—
22C2×#13093947—21no—
23C2×#13093947—21no—
24C2×C8×Dic47—21no—
25#15688876C2214yes—
26#15688872C2214yes—
27#15688869C2214yes—
28C2×C4⋊Q8×C47C2211yescharacteristic
29C2×C4⋊Q8×C47C2211yescharacteristic
30C47×#487—22no—
31C47×#487C2214yes—
32C2×#103×C47—21no—
33C2×#103×C47—21no—
34C2×C4×C8×C47C2211yescharacteristic
35C22×Dic94D411yescharacteristic
36C22×C47⋊C8—21no—
37C22×C47⋊C8—21no—
38C22×C47⋊C8—21no—
39C4×Dic94—21no—
40C4×Dic94—21no—
41C4×Dic94D412yes—
42C4×Dic94C2312yes—
43C2×C4⋊Dic47D411yescharacteristic
44C2×Dic47⋊C4—21no—
45C2×C4×Dic47—21no—
46#13093957—24no—
47#13093955—24no—
48C4⋊(C47⋊C8)—21no—
49C4⋊(C47⋊C8)—21no—
50C4⋊(C47⋊C8)—21no—
51C4⋊(C47⋊C8)C2312yes—
52C4⋊(C47⋊C8)C2312yes—
53C4⋊(C47⋊C8)C2312yes—
54Dic47⋊C8—24no—
55#13093947—24no—
56#13093947—24no—
57C8×Dic47—24no—
58C22×Q8×C47—21no—
59C22×Q8×C47—21no—
60C22×C8×C47D411yescharacteristic
61C22×C8×C47D411yescharacteristic
62C4⋊Q8×C47—21no—
63C4⋊Q8×C47—21no—
64C4⋊Q8×C47—21no—
65C4⋊Q8×C47—21no—
66C4⋊Q8×C47—21no—
67C4⋊Q8×C47—21no—
68C4⋊Q8×C47C2312yes—
69C4⋊Q8×C47C2312yes—
70C2×C4⋊C4×C47—21no—
71C2×C4⋊C4×C47—21no—
72C2×C4⋊C4×C47—21no—
73C2×C4⋊C4×C47—21no—
74C2×C42×C47C2311yescharacteristic
75#103×C47—24no—
76#103×C47—24no—
77C4×C8×C47D412yes—
78C4×C8×C47C2312yes—
79C2×Q8×C47—22no—
80C2×Q8×C47—22no—
81C2×Q8×C47—41no—
82C2×Q8×C47—41no—
83C2×Q8×C47—42no—
84C2×Q8×C47—42no—
85C2×Q8×C47—82no—
86C22×C4×C47—41no—
87C22×C4×C47—41no—
88C22×C4×C47C2×D411yescharacteristic
89C22×C4×C47C2×D411yescharacteristic
90C22×C4×C47#4111yescharacteristic
91C22×Dic47—21no—
92C22×Dic47—21no—
93C2×Dic94—21no—
94C2×Dic94—22no—
95C2×Dic94Q1614yes—
96C2×Dic94C2×D412yes—
97C2×C8×C47—22no—
98C2×C8×C47—22no—
99C2×C8×C47C2×D412yes—
100C2×C8×C47C2×D412yes—
101C4⋊C4×C47—22no—
102C4⋊C4×C47—22no—
103C4⋊C4×C47—22no—
104C4⋊C4×C47—22no—
105C4⋊C4×C47—41no—
106C4⋊C4×C47—41no—
107C4⋊C4×C47—41no—
108C4⋊C4×C47—41no—
109C42×C47C2×D411yescharacteristic
110C42×C47C2×D411yescharacteristic
111C42×C47#4111yescharacteristic
112C42×C47C2411yescharacteristic
113C4⋊Dic47—21no—
114C4⋊Dic47C2×D412yes—
115Dic47⋊C4—22no—
116Dic47⋊C4—22no—
117C4×Dic47—22no—
118C4×Dic47—22no—
119C2×C47⋊C8—22no—
120C2×C47⋊C8—22no—
121C2×C47⋊C8—22no—
122C2×C47⋊C8—42no—
123C2×C47⋊C8—42no—
124C2×C47⋊C8—42no—
125C23×C47#12111yescharacteristic
126Q8×C47—42no—
127Q8×C47—42no—
128Q8×C47—82no—
129Q8×C47—82no—
130Q8×C47—82no—
131C2×C4×C47—22no—
132C2×C4×C47—42no—
133C2×C4×C47—42no—
134C2×C4×C47—82no—
135C2×C4×C47—82no—
136C2×C4×C47#12111yescharacteristic
137C2×C4×C47#12111yescharacteristic
138C2×C4×C47#12111yescharacteristic
139C2×C4×C47C2×Q1612yes—
140C2×C4×C47#13512yes—
141C2×C4×C47#13512yes—
142C2×C4×C47#13712yes—
143C2×C4×C47C22×D411yescharacteristic
144C2×C4×C47C22×D411yescharacteristic
145C2×C4×C47C2×#4111yescharacteristic
146C2×Dic47—22no—
147C2×Dic47—24no—
148C2×Dic47—22no—
149C2×Dic47—42no—
150Dic94—22no—
151Dic94—24no—
152Dic94C2×Q1614yes—
153C8×C47—22no—
154C8×C47—22no—
155C47⋊C8—42no—
156C47⋊C8—42no—
157C47⋊C8—42no—
158C2×#1684—471nomaximal, Sylow
159C22×C47#46412yes—
160C22×C47#46712yes—
161C22×C47#47112yes—
162C22×C47C2×#12111yescharacteristic
163C4×C47—21no—
164C4×C47—21no—
165C4×C47—82no—
166C4×C47—82no—
167C4×C47#46412yes—
168C4×C47#46712yes—
169C4×C47C22×Q1611yescharacteristic
170C4×C47C2×#13511yescharacteristic
171C4×C47C2×#13511yescharacteristic
172C4×C47C2×#13711yescharacteristic
173Dic47—24no—
174Dic47—42no—
175C2×#487D4711yescharacteristic
176C2×#477—471no—
177C2×#475—471no—
178C2×C8×Q8—471no—
179#1684—478no—
180C2×#335—471no—
181C2×#333—471no—
182C2×#332—471no—
183C2×C47#168414yescomplemented
184C2×C47C2×#46411yescharacteristic
185C2×C47C2×#46711yescharacteristic
186C2×C47C2×#47111yescharacteristic
187C2×C4⋊Q8C2×D4711yescharacteristic
188C2×C4⋊Q8C2×D4711yescharacteristic
189C2×C4×Q8—471no—
190#487—22no—
191#487C2×D4714yes—
192#477—474no—
193#477—942no—
194#475—474no—
195#475—942no—
196C8×Q8—474no—
197C8×Q8—942no—
198C2×#107—941no—
199C2×#106—941no—
200C2×C4⋊C8—471no—
201C2×C4⋊C8—471no—
202C2×C4⋊C8—471no—
203C2×C4⋊C8—941no—
204C2×#103—21no—
205C2×#103—21no—
206C2×#103—941no—
207C2×#103—941no—
208C2×C4×C8—941no—
209C2×C4×C8C2×D4711yescharacteristic
210#335—474no—
211#333—474no—
212#332—474no—
213C47C2×#168411yescharacteristic, complemented, Sylow
214C22×Q8—21no—
215C22×Q8—21no—
216C22×Q8—471no—
217C22×C8—941no—
218C22×C8—941no—
219C22×C8—941no—
220C22×C8C22⋊D4711yescharacteristic
221C22×C8C22⋊D4711yescharacteristic
222C4⋊Q8—21no—
223C4⋊Q8—21no—
224C4⋊Q8—21no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8C22×D4712yes—
229C4⋊Q8C22×D4712yes—
230C4×Q8—472no—
231C4×Q8—472no—
232C4×Q8—941no—
233C4×Q8—941no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—471no—
239C2×C4⋊C4—941no—
240C2×C42—941no—
241C2×C42C22×D4711yescharacteristic
242#107—944no—
243#106—944no—
244C4⋊C8—472no—
245C4⋊C8—472no—
246C4⋊C8—472no—
247C4⋊C8—944no—
248C4⋊C8—941no—
249C4⋊C8—941no—
250C4⋊C8—941no—
251#103—24no—
252#103—24no—
253#103—944no—
254#103—944no—
255C4×C8—944no—
256C4×C8C22⋊D4712yes—
257C4×C8C22×D4712yes—
258C2×Q8—22no—
259C2×Q8—22no—
260C2×Q8—41no—
261C2×Q8—41no—
262C2×Q8—42no—
263C2×Q8—42no—
264C2×Q8—82no—
265C2×Q8—474no—
266C2×Q8—472no—
267C2×Q8—941no—
268C2×Q8—942no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4—941no—
272C22×C4—941no—
273C22×C4D4×D4711yescharacteristic
274C22×C4#1062535211yescharacteristic
275C22×C4C2×C22⋊D4711yescharacteristic
276C2×C8—22no—
277C2×C8—22no—
278C2×C8—942no—
279C2×C8—942no—
280C2×C8—942no—
281C2×C8—1882no—
282C2×C8—1882no—
283C2×C8—1882no—
284C2×C8C2×C22⋊D4712yes—
285C2×C8C2×C22⋊D4712yes—
286C4⋊C4—22no—
287C4⋊C4—22no—
288C4⋊C4—22no—
289C4⋊C4—22no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—472no—
295C4⋊C4—942no—
296C4⋊C4—941no—
297C4⋊C4—942no—
298C42—942no—
299C42—942no—
300C42D4×D4711yescharacteristic
301C42#1062535211yescharacteristic
302C42C2×C22⋊D4711yescharacteristic
303C42C23×D4711yescharacteristic
304C23#1309399511yescharacteristic
305Q8—42no—
306Q8—42no—
307Q8—82no—
308Q8—82no—
309Q8—82no—
310Q8—474no—
311Q8—944no—
312Q8—942no—
313C2×C4—22no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—82no—
317C2×C4—82no—
318C2×C4—942no—
319C2×C4—944no—
320C2×C4—942no—
321C2×C4—1882no—
322C2×C4#1309399511yescharacteristic
323C2×C4#1309399511yescharacteristic
324C2×C4#1309399511yescharacteristic
325C2×C4Q16×D4712yes—
326C2×C4#1309404412yes—
327C2×C4#1309404712yes—
328C2×C4#1309405412yes—
329C2×C4C2×D4×D4711yescharacteristic
330C2×C4C22×C22⋊D4711yescharacteristic
331C2×C4C2×#1062535211yescharacteristic
332C8—22no—
333C8—22no—
334C8—1882no—
335C8—1882no—
336C8—1882no—
337C22#1568934212yes—
338C22#1568936112yes—
339C22#1568938312yes—
340C22C2×#1309399511yescharacteristic
341C4—21no—
342C4—21no—
343C4—82no—
344C4—82no—
345C4—944no—
346C4—1882no—
347C4#1568934212yes—
348C4#1568936112yes—
349C4C2×Q16×D4711yescharacteristic
350C4C2×#1309404411yescharacteristic
351C4C2×#1309404711yescharacteristic
352C4C2×#1309405411yescharacteristic
353C2#2024284314yesdirect product factor
354C2C2×#1568934211yescharacteristic
355C2C2×#1568936111yescharacteristic
356C2C2×#1568938311yescharacteristic
subgroupG/H
centerC23#13093995
commutator, cosocleC42×C47C24
FrattiniC42C23×D47
FittingC2×C47×#487C2
socle, prime radicalC23×C47#121
hypercenterC2×#487D47
hypocenterC47C2×#1684
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#487

Complements

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

NH ≅ G/Ntype
4. #20242843C2direct (N × H)
183. C2×C47#1684semidirect
213. C47C2×#1684semidirect
353. C2#20242843direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156894152
C2×#156894052
C2×C8×Dic942
#202428432
C2×#156888762
C2×#156888722
C2×#156888692
C2×C47×#4872
C2×#168447