Finite Group Databasebeta

← C2×#20242398 #26188509

Subgroups — C2×#20242398 #26188509

Order 12032.

1028 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 1028 conjugacy classes of subgroups — too many to draw. Only its 203 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×#15689754C211yesmaximal, characteristic
2C2×#15689454C212yesmaximal
3C2×#15689053C211yesmaximal, characteristic
4#20242398C218yesmaximal, direct product factor
5C2×#15688861C212yesmaximal
6C2×C47×#324C211yesmaximal, characteristic
7#15689754—24no—
8#15689754—22no—
9#15689754C2214yes—
10C2×#13094023—22no—
11C2×#13094015—22no—
12C2×#13094003—21no—
13C2×#13094003C2212yes—
14C2×#13093983—21no—
15C22×C4⋊Dic47C2211yescharacteristic
16C22×Dic47⋊C4—21no—
17#15689454—24no—
18#15689454C2218yes—
19C2×#13093956—22no—
20C2×#13093949—22no—
21#15689053—22no—
22#15689053C2214yes—
23C2×C47⋊#95—21no—
24C2×C47⋊#95C2211yescharacteristic
25#15688861C2218yes—
26C22×C4⋊C4×C47C2211yescharacteristic
27C2×C22⋊C8×C47C2212yes—
28C47×#324C2214yes—
29C22×Dic94—21no—
30C22×Dic94D412yes—
31C23×Dic47—21no—
32C23×Dic47—21no—
33#13094023—28no—
34#13094023—28no—
35#13094015—28no—
36#13094015—28no—
37#13094003—24no—
38#13094003—22no—
39#13094003—22no—
40#13094003—24no—
41#13094003D414yes—
42#13094003C2314yes—
43#13093983—24no—
44#13093983—24no—
45C2×C4⋊Dic47—21no—
46C2×C4⋊Dic47—21no—
47C2×C4⋊Dic47—21no—
48C2×C4⋊Dic47—22no—
49C2×C4⋊Dic47—22no—
50C2×C4⋊Dic47—21no—
51C2×C4⋊Dic47D412yes—
52C2×C4⋊Dic47C2312yes—
53C2×Dic47⋊C4—22no—
54C2×Dic47⋊C4—22no—
55C2×Dic47⋊C4—24no—
56C2×Dic47⋊C4—44no—
57C2×C22⋊Dic47—22no—
58C2×C4×Dic47—22no—
59#13093956—28no—
60#13093949—28no—
61C47⋊#95—24no—
62C47⋊#95—21no—
63C47⋊#95C2312yes—
64C23×C4×C47D411yescharacteristic
65C23×C4×C47D411yescharacteristic
66C23×C4×C47C2311yescharacteristic
67C22×C8×C47—22no—
68C2×C4⋊C4×C47—22no—
69C2×C4⋊C4×C47—22no—
70C2×C4⋊C4×C47D412yes—
71C2×C4⋊C4×C47C2312yes—
72C22⋊C8×C47—22no—
73C22⋊C8×C47C2314yes—
74C24×C47C2×D411yescharacteristic
75C22×C4×C47—21no—
76C22×C4×C47—21no—
77C22×C4×C47—22no—
78C22×C4×C47—21no—
79C22×C4×C47—21no—
80C22×C4×C47—42no—
81C22×C4×C47—42no—
82C22×C4×C47SD1614yes—
83C22×C4×C47C2×D412yes—
84C22×C4×C47C2×D412yes—
85C22×C4×C47C2×D412yes—
86C22×C4×C47C2×D411yescharacteristic
87C22×C4×C47C2×D412yes—
88C22×C4×C47C2411yescharacteristic
89C22×Dic47—24no—
90C22×Dic47—22no—
91C22×Dic47—22no—
92C22×Dic47—22no—
93C22×Dic47—22no—
94C22×Dic47—42no—
95C22×Dic47—42no—
96C22×Dic47—41no—
97C22×Dic47—41no—
98C22×Dic47—42no—
99C22×Dic47—42no—
100C2×Dic94—24no—
101C2×Dic94—22no—
102C2×Dic94—44no—
103C2×Dic94—82no—
104C2×Dic94C2×D414yes—
105C2×C8×C47—24no—
106C2×C8×C47—44no—
107C4⋊C4×C47—24no—
108C4⋊C4×C47—24no—
109C22⋊Dic47—24no—
110C22⋊Dic47—24no—
111C4⋊Dic47—24no—
112C4⋊Dic47—24no—
113C4⋊Dic47—24no—
114C4⋊Dic47—22no—
115C4⋊Dic47—24no—
116C4⋊Dic47—42no—
117C4⋊Dic47C2×D414yes—
118Dic47⋊C4—28no—
119Dic47⋊C4—24no—
120Dic47⋊C4—24no—
121Dic47⋊C4—48no—
122C4×Dic47—28no—
123C23×C47—22no—
124C23×C47—22no—
125C23×C47#12011yescharacteristic
126C23×C47#12011yescharacteristic
127C23×C47C2×SD1612yes—
128C23×C47#13712yes—
129C23×C47C22×D411yescharacteristic
130C2×C4×C47—22no—
131C2×C4×C47—22no—
132C2×C4×C47—24no—
133C2×C4×C47—24no—
134C2×C4×C47—24no—
135C2×C4×C47—22no—
136C2×C4×C47—41no—
137C2×C4×C47—42no—
138C2×C4×C47—41no—
139C2×C4×C47—42no—
140C2×C4×C47—42no—
141C2×C4×C47—81no—
142C2×C4×C47#12012yes—
143C2×C4×C47C2×SD1614yes—
144C2×C4×C47C22×D412yes—
145C2×Dic47—24no—
146C2×Dic47—24no—
147C2×Dic47—24no—
148C2×Dic47—48no—
149C2×Dic47—42no—
150C2×Dic47—42no—
151C2×Dic47—44no—
152C2×Dic47—44no—
153C2×Dic47—42no—
154C2×Dic47—42no—
155C2×Dic47—42no—
156C2×Dic47—82no—
157C2×Dic47—82no—
158Dic94—44no—
159Dic94—82no—
160Dic94—84no—
161C8×C47—44no—
162C2×#1611—471nomaximal, Sylow
163C22×C47—24no—
164C22×C47—24no—
165C22×C47—21no—
166C22×C47—21no—
167C22×C47—21no—
168C22×C47—21no—
169C22×C47#44812yes—
170C22×C47#44812yes—
171C22×C47#45612yes—
172C22×C47#45812yes—
173C22×C47C2×#12011yescharacteristic
174C22×C47C22×SD1611yescharacteristic
175C22×C47C2×#13711yescharacteristic
176C4×C47—24no—
177C4×C47—22no—
178C4×C47—22no—
179C4×C47—42no—
180Dic47—44no—
181Dic47—44no—
182Dic47—44no—
183Dic47—82no—
184C2×#544—471no—
185C2×#483—472no—
186C2×#398—471no—
187#1611—478no—
188C2×#328—472no—
189C2×#324D4711yescharacteristic
190C2×C47—21no—
191C2×C47—21no—
192C2×C47—22no—
193C2×C47#161114yescomplemented
194C2×C47C2×#44811yescharacteristic
195C2×C47C2×#45611yescharacteristic
196C2×C47C2×#45811yescharacteristic
197#544—474no—
198#544—944no—
199#544—942no—
200C2×C4⋊Q8—942no—
201C2×#125—942no—
202C2×C22⋊Q8—472no—
203C2×C22⋊Q8—941no—
204C2×#117—941no—
205C22×C4⋊C4—471no—
206C22×C4⋊C4—941no—
207C22×C4⋊C4C2×D4711yescharacteristic
208#483—478no—
209#483—944no—
210C2×#106—942no—
211C2×#103—942no—
212C2×C22⋊C8C2×D4712yes—
213#398—474no—
214#398—942no—
215C2×#95—471no—
216C2×#95—941no—
217#328—478no—
218#324C2×D4714yes—
219C47C2×#161111yescharacteristic, complemented, Sylow
220C22×Q8—472no—
221C22×Q8—941no—
222C23×C4—941no—
223C23×C4—941no—
224C23×C4D18811yescharacteristic
225C23×C4D18811yescharacteristic
226C23×C4C22×D4711yescharacteristic
227C22×C8—22no—
228C4⋊Q8—948no—
229C4⋊Q8—948no—
230#125—948no—
231#125—948no—
232C22⋊Q8—474no—
233C22⋊Q8—474no—
234C22⋊Q8—944no—
235C22⋊Q8—942no—
236C22⋊Q8—944no—
237C22⋊Q8—942no—
238#117—944no—
239#117—944no—
240C2×C4⋊C4—22no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4—472no—
243C2×C4⋊C4—472no—
244C2×C4⋊C4—941no—
245C2×C4⋊C4—941no—
246C2×C4⋊C4—941no—
247C2×C4⋊C4—942no—
248C2×C4⋊C4—942no—
249C2×C4⋊C4—942no—
250C2×C4⋊C4—942no—
251C2×C4⋊C4—941no—
252C2×C4⋊C4—944no—
253C2×C4⋊C4—1884no—
254C2×C4⋊C4D18812yes—
255C2×C4⋊C4C22×D4712yes—
256C2×C22⋊C4—942no—
257C2×C42—942no—
258#106—948no—
259#103—948no—
260C22⋊C8—22no—
261C22⋊C8C22×D4714yes—
262#95—472no—
263#95—941no—
264#95—944no—
265C24C2×D18811yescharacteristic
266C2×Q8—474no—
267C2×Q8—944no—
268C2×Q8—942no—
269C2×Q8—3762no—
270C2×Q8—1884no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—22no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—42no—
277C22×C4—42no—
278C22×C4—944no—
279C22×C4—942no—
280C22×C4—942no—
281C22×C4—942no—
282C22×C4—942no—
283C22×C4—1881no—
284C22×C4—1881no—
285C22×C4—1882no—
286C22×C4—1882no—
287C22×C4—1882no—
288C22×C4—1882no—
289C22×C4#1062532514yes—
290C22×C4C2×D18812yes—
291C22×C4C2×D18812yes—
292C22×C4C2×D18811yescharacteristic
293C22×C4D4×D4712yes—
294C22×C4D4×D4712yes—
295C22×C4C23×D4711yescharacteristic
296C2×C8—24no—
297C2×C8—44no—
298C4⋊C4—24no—
299C4⋊C4—24no—
300C4⋊C4—474no—
301C4⋊C4—948no—
302C4⋊C4—944no—
303C4⋊C4—944no—
304C4⋊C4—944no—
305C4⋊C4—944no—
306C4⋊C4—942no—
307C4⋊C4—944no—
308C4⋊C4—944no—
309C4⋊C4—1882no—
310C4⋊C4—1888no—
311C22⋊C4—944no—
312C22⋊C4—944no—
313C42—948no—
314C23—22no—
315C23—22no—
316C23#1309399411yescharacteristic
317C23#1309399411yescharacteristic
318C23C2×#1062532512yes—
319C23#1309405712yes—
320C23C22×D18811yescharacteristic
321Q8—3762no—
322Q8—3764no—
323Q8—1884no—
324C2×C4—24no—
325C2×C4—24no—
326C2×C4—24no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—81no—
336C2×C4—944no—
337C2×C4—944no—
338C2×C4—944no—
339C2×C4—3762no—
340C2×C4—3762no—
341C2×C4—1882no—
342C2×C4—1882no—
343C2×C4—1882no—
344C2×C4—1882no—
345C2×C4—1888no—
346C2×C4—1884no—
347C2×C4—1884no—
348C2×C4—1882no—
349C2×C4#1309399412yes—
350C2×C4C2×#1062532514yes—
351C2×C4C2×D4×D4712yes—
352C8—44no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—24no—
358C22—24no—
359C22#1568926412yes—
360C22#1568926412yes—
361C22#1568930812yes—
362C22#1568931412yes—
363C22C2×#1309399411yescharacteristic
364C22C22×#1062532511yescharacteristic
365C22C2×#1309405711yescharacteristic
366C4—22no—
367C4—22no—
368C4—24no—
369C4—42no—
370C4—3762no—
371C4—1884no—
372C4—1884no—
373C4—1884no—
374C2—21no—
375C2—22no—
376C2—21no—
377C2#2024239814yesdirect product factor
378C2C2×#1568926411yescharacteristic
379C2C2×#1568930811yescharacteristic
380C2C2×#1568931411yescharacteristic
subgroupG/H
centerC23#13093994
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC2×C47×#324C2
socleC23×C47#120
prime radicalC24×C47C2×D4
hypercenterC2×#324D47
hypocenterC47C2×#1611
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
4. #20242398C2direct (N × H)
193. C2×C47#1611semidirect
219. C47C2×#1611semidirect
377. C2#20242398direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897542
C2×#156894542
C2×#156890532
#202423982
C2×#156888612
C2×C47×#3242
C2×#161147