Finite Group Databasebeta

← C2×#20243065 #26204076

Subgroups — C2×#20243065 #26204076

Order 12032.

798 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689528C211yesmaximal, characteristic
2C2×#15689528C211yesmaximal, characteristic
3C2×#15689521C211yesmaximal, characteristic
4C2×#15689503C211yesmaximal, characteristic
5C2×#15689474C211yesmaximal, characteristic
6C2×#15689474C211yesmaximal, characteristic
7#20243065C218yesmaximal, direct product factor
8C2×C47×#322C211yesmaximal, characteristic
9C22×Dic188—22no—
10C2×#13094024C2211yescharacteristic
11C2×#13094024C2211yescharacteristic
12C2×#13094024C2211yescharacteristic
13C2×#13094024C2211yescharacteristic
14#15689528—22no—
15#15689528—22no—
16#15689528C2214yes—
17#15689528C2214yes—
18#15689521—22no—
19#15689521C2214yes—
20#15689503—22no—
21#15689503C2214yes—
22#15689474—22no—
23#15689474—22no—
24#15689474C2214yes—
25#15689474C2214yes—
26C2×#13093958—22no—
27C2×#13093958—22no—
28C2×#13093956—22no—
29C2×#13093949—22no—
30C2×#13093949—22no—
31C2×C4×C8×C47C2211yescharacteristic
32C2×C4×C8×C47C2211yescharacteristic
33C2×C4×C8×C47C2211yescharacteristic
34C47×#322C2214yes—
35C22×Dic94—21no—
36C22×Dic94—21no—
37C22×Dic94—21no—
38C22×Dic94—21no—
39C2×Dic188—28no—
40C2×Dic188—48no—
41#13094024—21no—
42#13094024—21no—
43#13094024—21no—
44#13094024—21no—
45#13094024—21no—
46#13094024—21no—
47#13094024—21no—
48#13094024—21no—
49#13094024—21no—
50#13094024—21no—
51#13094024—21no—
52#13094024—21no—
53#13094024C2312yes—
54#13094024C2312yes—
55#13094024C2312yes—
56#13094024C2312yes—
57C2×C4⋊Dic47—21no—
58C2×C4⋊Dic47—21no—
59C2×C4⋊Dic47—21no—
60C2×C4⋊Dic47—21no—
61C2×C4⋊Dic47—21no—
62C2×C4⋊Dic47—21no—
63C2×C4⋊Dic47—21no—
64C2×C4⋊Dic47—21no—
65#13093958—28no—
66#13093958—28no—
67#13093956—28no—
68#13093949—28no—
69#13093949—28no—
70C22×C8×C47D412yes—
71C22×C8×C47D412yes—
72C22×C8×C47D412yes—
73C2×C42×C47C2311yescharacteristic
74C4×C8×C47D412yes—
75C4×C8×C47D412yes—
76C4×C8×C47D412yes—
77C4×C8×C47C2312yes—
78C4×C8×C47C2312yes—
79C4×C8×C47C2312yes—
80C22×C4×C47C2×D411yescharacteristic
81C22×C4×C47C2×D411yescharacteristic
82C22×C4×C47C2×D411yescharacteristic
83C22×Dic47—41no—
84C22×Dic47—41no—
85C22×Dic47—41no—
86C22×Dic47—41no—
87C2×Dic94—22no—
88C2×Dic94—22no—
89C2×Dic94—22no—
90C2×Dic94—22no—
91C2×Dic94—44no—
92C2×Dic94—44no—
93C2×Dic94—44no—
94C2×Dic94—44no—
95C2×Dic94—41no—
96C2×Dic94—41no—
97C2×Dic94—41no—
98C2×Dic94—41no—
99C2×C8×C47—24no—
100C2×C8×C47—24no—
101C2×C8×C47Q1618yescomplemented
102C2×C8×C47C2×D414yes—
103C2×C8×C47C2×D414yes—
104C2×C8×C47C2×D414yes—
105C42×C47C2×D411yescharacteristic
106C42×C47C2×D411yescharacteristic
107C42×C47C2×D411yescharacteristic
108C42×C47C2411yescharacteristic
109C4⋊Dic47—22no—
110C4⋊Dic47—22no—
111C4⋊Dic47—22no—
112C4⋊Dic47—22no—
113C4⋊Dic47—22no—
114C4⋊Dic47—22no—
115C4⋊Dic47—22no—
116C4⋊Dic47—22no—
117C4⋊Dic47—41no—
118C4⋊Dic47—41no—
119C4⋊Dic47—41no—
120C4⋊Dic47—41no—
121C4⋊Dic47—41no—
122C4⋊Dic47—41no—
123C4⋊Dic47—41no—
124C4⋊Dic47—41no—
125Dic188—416no—
126C23×C47#12711yescharacteristic
127C2×C4×C47#12711yescharacteristic
128C2×C4×C47#12711yescharacteristic
129C2×C4×C47#12711yescharacteristic
130C2×C4×C47C2×Q1614yes—
131C2×C4×C47AGL(1,ℤ/8)14yes—
132C2×C4×C47#13714yes—
133C2×C4×C47C22×D411yescharacteristic
134C2×C4×C47C22×D411yescharacteristic
135C2×C4×C47C22×D411yescharacteristic
136C2×Dic47—42no—
137C2×Dic47—42no—
138C2×Dic47—42no—
139C2×Dic47—42no—
140C2×Dic47—82no—
141C2×Dic47—82no—
142C2×Dic47—82no—
143C2×Dic47—82no—
144Dic94—44no—
145Dic94—44no—
146Dic94—44no—
147Dic94—44no—
148Dic94—82no—
149Dic94—82no—
150Dic94—82no—
151Dic94—82no—
152C8×C47—24no—
153C8×C47—24no—
154C8×C47C2×Q1618yescomplemented
155C2×#1723—471nomaximal, Sylow
156C22×C47#49412yes—
157C22×C47#49612yes—
158C22×C47#49712yes—
159C22×C47C2×#12711yescharacteristic
160C4×C47#49412yes—
161C4×C47#49612yes—
162C4×C47#49712yes—
163C4×C47C22×Q1612yes—
164C4×C47C2×AGL(1,ℤ/8)12yes—
165C4×C47C2×#13712yes—
166Dic47—82no—
167Dic47—82no—
168Dic47—82no—
169Dic47—82no—
170C2×#500—471no—
171C2×#500—471no—
172C2×#498—471no—
173C2×#494—471no—
174C2×#487—471no—
175C2×#487—471no—
176#1723—478no—
177C2×#322D4711yescharacteristic
178C2×C47#172314yescomplemented
179C2×C47C2×#49411yescharacteristic
180C2×C47C2×#49611yescharacteristic
181C2×C47C2×#49711yescharacteristic
182C22×Q16—942no—
183C2×C4⋊Q8—471no—
184C2×C4⋊Q8—471no—
185C2×C4⋊Q8—471no—
186C2×C4⋊Q8—471no—
187#500—474no—
188#500—474no—
189#500—942no—
190#500—942no—
191#498—474no—
192#498—942no—
193#494—474no—
194#494—942no—
195#487—474no—
196#487—474no—
197#487—942no—
198#487—942no—
199C2×#107—942no—
200C2×#107—942no—
201C2×#106—942no—
202C2×#103—942no—
203C2×#103—942no—
204C2×C4×C8C2×D4711yescharacteristic
205C2×C4×C8C2×D4711yescharacteristic
206C2×C4×C8C2×D4711yescharacteristic
207#322C2×D4714yes—
208C47C2×#172311yescharacteristic, complemented, Sylow
209C22×Q8—941no—
210C22×Q8—941no—
211C22×Q8—941no—
212C22×Q8—941no—
213C2×Q16—948no—
214C2×Q16—1888no—
215C22×C8D18812yes—
216C22×C8D18812yes—
217C22×C8D18812yes—
218C4⋊Q8—472no—
219C4⋊Q8—472no—
220C4⋊Q8—472no—
221C4⋊Q8—472no—
222C4⋊Q8—941no—
223C4⋊Q8—941no—
224C4⋊Q8—941no—
225C4⋊Q8—941no—
226C4⋊Q8—941no—
227C4⋊Q8—941no—
228C4⋊Q8—941no—
229C4⋊Q8—941no—
230C4⋊Q8—941no—
231C4⋊Q8—941no—
232C4⋊Q8—941no—
233C4⋊Q8—941no—
234C2×C4⋊C4—941no—
235C2×C4⋊C4—941no—
236C2×C4⋊C4—941no—
237C2×C4⋊C4—941no—
238C2×C4⋊C4—941no—
239C2×C4⋊C4—941no—
240C2×C4⋊C4—941no—
241C2×C4⋊C4—941no—
242C2×C42C22×D4711yescharacteristic
243#107—948no—
244#107—948no—
245#106—948no—
246#103—948no—
247#103—948no—
248C4×C8D18812yes—
249C4×C8D18812yes—
250C4×C8D18812yes—
251C4×C8C22×D4712yes—
252C4×C8C22×D4712yes—
253C4×C8C22×D4712yes—
254C2×Q8—942no—
255C2×Q8—942no—
256C2×Q8—942no—
257C2×Q8—942no—
258C2×Q8—1884no—
259C2×Q8—1884no—
260C2×Q8—1884no—
261C2×Q8—1884no—
262C2×Q8—1881no—
263C2×Q8—1881no—
264C2×Q8—1881no—
265C2×Q8—1881no—
266C22×C4—1881no—
267C22×C4—1881no—
268C22×C4—1881no—
269C22×C4—1881no—
270C22×C4C2×D18811yescharacteristic
271C22×C4C2×D18811yescharacteristic
272C22×C4C2×D18811yescharacteristic
273Q16—18816no—
274C2×C8—24no—
275C2×C8—24no—
276C2×C8Dic18818yescomplemented
277C2×C8C2×D18814yes—
278C2×C8C2×D18814yes—
279C2×C8C2×D18814yes—
280C4⋊C4—942no—
281C4⋊C4—942no—
282C4⋊C4—942no—
283C4⋊C4—942no—
284C4⋊C4—942no—
285C4⋊C4—942no—
286C4⋊C4—942no—
287C4⋊C4—942no—
288C4⋊C4—1881no—
289C4⋊C4—1881no—
290C4⋊C4—1881no—
291C4⋊C4—1881no—
292C4⋊C4—1881no—
293C4⋊C4—1881no—
294C4⋊C4—1881no—
295C4⋊C4—1881no—
296C42C2×D18811yescharacteristic
297C42C2×D18811yescharacteristic
298C42C2×D18811yescharacteristic
299C42C23×D4711yescharacteristic
300C23#1309402111yescharacteristic
301Q8—3762no—
302Q8—3762no—
303Q8—3762no—
304Q8—3762no—
305Q8—1884no—
306Q8—1884no—
307Q8—1884no—
308Q8—1884no—
309C2×C4—3762no—
310C2×C4—3762no—
311C2×C4—3762no—
312C2×C4—3762no—
313C2×C4—1882no—
314C2×C4—1882no—
315C2×C4—1882no—
316C2×C4—1882no—
317C2×C4#1309402111yescharacteristic
318C2×C4#1309402111yescharacteristic
319C2×C4#1309402111yescharacteristic
320C2×C4C2×Dic18814yes—
321C2×C4#1309405214yes—
322C2×C4#1309405714yes—
323C2×C4C22×D18811yescharacteristic
324C2×C4C22×D18811yescharacteristic
325C2×C4C22×D18811yescharacteristic
326C8—24no—
327C8—24no—
328C8C2×Dic18818yescomplemented
329C22#1568950312yes—
330C22#1568951212yes—
331C22#1568951712yes—
332C22C2×#1309402111yescharacteristic
333C4—3762no—
334C4—3762no—
335C4—3762no—
336C4—3762no—
337C4#1568950312yes—
338C4#1568951212yes—
339C4#1568951712yes—
340C4C22×Dic18812yes—
341C4C2×#1309405212yes—
342C4C2×#1309405712yes—
343C2#2024306514yesdirect product factor
344C2C2×#1568950311yescharacteristic
345C2C2×#1568951211yescharacteristic
346C2C2×#1568951711yescharacteristic
subgroupG/H
centerC23#13094021
commutator, cosocleC42×C47C24
FrattiniC42C23×D47
FittingC2×C47×#322C2
socle, prime radicalC23×C47#127
hypercenterC2×#322D47
hypocenterC47C2×#1723
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#322

Complements

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

NH ≅ G/Ntype
7. #20243065C2direct (N × H)
101. C2×C8×C47Q16semidirect
154. C8×C47C2×Q16semidirect
178. C2×C47#1723semidirect
208. C47C2×#1723semidirect
276. C2×C8Dic188semidirect
328. C8C2×Dic188semidirect
343. C2#20243065direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156895282
C2×#156895212
C2×#156895032
C2×#156894742
#202430652
C2×C47×#3222
C2×#172347