Finite Group Databasebeta

← #26103240

Subgroups — #26103240

Order 12032.

462 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15688849C211yesmaximal, characteristic
2#20241617C211yesmaximal, characteristic
3C2×C47×#324C211yesmaximal, characteristic
4C22×C4⋊Dic47C411yescharacteristic
5C22×C4×Dic47C411yescharacteristic
6C2×C22⋊(C47⋊C8)—21no—
7C2×C47⋊#95—21no—
8C2×C47⋊#95—21no—
9#15688849—21no—
10#15688849C412yescomplemented
11C22×C4⋊C4×C47C2211yescharacteristic
12C2×C22⋊C8×C47—21no—
13C47×#324—21no—
14C47×#324C412yescomplemented
15C23×Dic47—21no—
16C23×Dic47—21no—
17C22×C47⋊C8—41no—
18C2×C4⋊Dic47—21no—
19C2×C4⋊Dic47—41no—
20C2×C4⋊Dic47—41no—
21C2×C4⋊Dic47C812yescomplemented
22C2×C4×Dic47—21no—
23C2×C4×Dic47—41no—
24C2×C4×Dic47—41no—
25C2×C4×Dic47C812yescomplemented
26C22⋊(C47⋊C8)—22no—
27C22⋊(C47⋊C8)—41no—
28C47⋊#95—42no—
29C47⋊#95—42no—
30C23×C4×C47C2×C411yescharacteristic
31C23×C4×C47D411yescharacteristic
32C23×C4×C47D411yescharacteristic
33C22×C8×C47—41no—
34C2×C4⋊C4×C47—41no—
35C2×C4⋊C4×C47—41no—
36C2×C4⋊C4×C47C2×C411yescharacteristic
37C2×C4⋊C4×C47C2×C411yescharacteristic
38C2×C4⋊C4×C47D411yescharacteristic
39C2×C4⋊C4×C47Q811yescharacteristic
40C22⋊C8×C47—22no—
41C22⋊C8×C47—41no—
42C24×C47C22⋊C411yescharacteristic
43C22×C4×C47—21no—
44C22×C4×C47—21no—
45C22×C4×C47—21no—
46C22×C4×C47—21no—
47C22×C4×C47—21no—
48C22×C4×C47—21no—
49C22×C4×C47—21no—
50C22×C4×C47—21no—
51C22×C4×C47—41no—
52C22×C4×C47—41no—
53C22×C4×C47—41no—
54C22×C4×C47—41no—
55C22×C4×C47C4211yescharacteristic
56C22×C4×C47C22⋊C411yescharacteristic
57C22×C4×C47C22⋊C411yescharacteristic
58C22×C4×C47C4⋊C411yescharacteristic
59C22×C4×C47C4⋊C411yescharacteristic
60C22×C4×C47C4⋊C411yescharacteristic
61C22×C4×C47C2×C811yescharacteristic
62C22×C4×C47C2×C811yescharacteristic
63C22×C4×C47M1611yescharacteristic
64C22×C4×C47M1611yescharacteristic
65C22×Dic47—22no—
66C22×Dic47—22no—
67C22×Dic47—22no—
68C22×Dic47—22no—
69C22×Dic47—41no—
70C22×Dic47—41no—
71C22×Dic47—41no—
72C22×Dic47—41no—
73C22×Dic47—41no—
74C22×Dic47—41no—
75C22×Dic47—41no—
76C22×Dic47—41no—
77C22×Dic47—41no—
78C22×Dic47—41no—
79C2×C8×C47—42no—
80C2×C8×C47—81no—
81C2×C8×C47—81no—
82C4⋊C4×C47—41no—
83C4⋊C4×C47—41no—
84C4⋊C4×C47—41no—
85C4⋊C4×C47—41no—
86C4⋊Dic47—42no—
87C4⋊Dic47—42no—
88C4×Dic47—42no—
89C4×Dic47—42no—
90C2×C47⋊C8—42no—
91C2×C47⋊C8—81no—
92C2×C47⋊C8—81no—
93C23×C47—21no—
94C23×C47—21no—
95C23×C47—21no—
96C23×C47—21no—
97C23×C47#9511yescharacteristic
98C23×C47C22⋊C811yescharacteristic
99C23×C47C22⋊C811yescharacteristic
100C23×C47#9911yescharacteristic
101C23×C47#9911yescharacteristic
102C23×C47#10011yescharacteristic
103C23×C47#10111yescharacteristic
104C2×C4×C47—21no—
105C2×C4×C47—21no—
106C2×C4×C47—21no—
107C2×C4×C47—21no—
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—41no—
121C2×C4×C47—41no—
122C2×C4×C47—41no—
123C2×C4×C47—41no—
124C2×C4×C47—41no—
125C2×C4×C47—41no—
126C2×C4×C47—41no—
127C2×C4×C47—41no—
128C2×C4×C47—81no—
129C2×C4×C47—81no—
130C2×C4×C47C4×C811yescharacteristic
131C2×C4×C47#9711yescharacteristic
132C2×C4×C47C4⋊C811yescharacteristic
133C2×C4×C47C4⋊C811yescharacteristic
134C2×Dic47—24no—
135C2×Dic47—42no—
136C2×Dic47—42no—
137C2×Dic47—42no—
138C2×Dic47—42no—
139C2×Dic47—42no—
140C2×Dic47—42no—
141C2×Dic47—42no—
142C2×Dic47—42no—
143C2×Dic47—42no—
144C2×Dic47—81no—
145C2×Dic47—81no—
146C2×Dic47—81no—
147C2×Dic47—81no—
148C8×C47—82no—
149C47⋊C8—82no—
150#7189—471nomaximal, Sylow
151C22×C47—21no—
152C22×C47—21no—
153C22×C47—21no—
154C22×C47—21no—
155C22×C47—21no—
156C22×C47—21no—
157C22×C47—21no—
158C22×C47—21no—
159C22×C47—21no—
160C22×C47—21no—
161C22×C47—21no—
162C22×C47—21no—
163C22×C47#32311yescharacteristic
164C22×C47#32311yescharacteristic
165C22×C47#32411yescharacteristic
166C22×C47#32411yescharacteristic
167C22×C47#33611yescharacteristic
168C22×C47#34211yescharacteristic
169C22×C47#34311yescharacteristic
170C22×C47#35311yescharacteristic
171C22×C47#35411yescharacteristic
172C22×C47#35511yescharacteristic
173C22×C47#35611yescharacteristic
174C4×C47—21no—
175C4×C47—21no—
176C4×C47—21no—
177C4×C47—21no—
178C4×C47—41no—
179C4×C47—41no—
180C4×C47—41no—
181C4×C47—41no—
182Dic47—44no—
183Dic47—82no—
184C2×#324—471no—
185C2×#324D4711yescharacteristic
186C4⋊#95—471no—
187C2×C47—21no—
188C2×C47—21no—
189C2×C47—21no—
190C2×C47—21no—
191C2×C47#128011yescharacteristic
192C2×C47#131811yescharacteristic
193C2×C47#131911yescharacteristic
194C2×C47#132411yescharacteristic
195C2×C47#132511yescharacteristic
196C2×C47#139311yescharacteristic
197C2×C47#139411yescharacteristic
198C22×C4⋊C4—471no—
199C22×C4⋊C4C2×D4711yescharacteristic
200C22×C42—471no—
201C2×C22⋊C8—21no—
202C2×C22⋊C8—941no—
203C2×#95—941no—
204C2×#95—941no—
205#324—21no—
206#324—472no—
207#324—941no—
208#324Dic4712yescomplemented
209C47#718911yescharacteristic, complemented, Sylow
210C23×C4—941no—
211C23×C4—941no—
212C23×C4C4×D4711yescharacteristic
213C23×C4D18811yescharacteristic
214C23×C4C22⋊D4711yescharacteristic
215C22×C8—41no—
216C22×C8—1881no—
217C2×C4⋊C4—41no—
218C2×C4⋊C4—41no—
219C2×C4⋊C4—472no—
220C2×C4⋊C4—941no—
221C2×C4⋊C4—1881no—
222C2×C4⋊C4—1881no—
223C2×C4⋊C4Dic9411yescharacteristic
224C2×C4⋊C4C4×D4711yescharacteristic
225C2×C4⋊C4C2×Dic4711yescharacteristic
226C2×C4⋊C4C22⋊D4711yescharacteristic
227C2×C42—472no—
228C2×C42—941no—
229C2×C42—1881no—
230C2×C42—1881no—
231C22⋊C8—22no—
232C22⋊C8—41no—
233C22⋊C8—942no—
234C22⋊C8—1881no—
235#95—1882no—
236#95—1882no—
237C24(C2×D47)⋊C411yescharacteristic
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—942no—
251C22×C4—942no—
252C22×C4—942no—
253C22×C4—942no—
254C22×C4—1881no—
255C22×C4—1881no—
256C22×C4—1881no—
257C22×C4—1881no—
258C22×C4—1881no—
259C22×C4—1881no—
260C22×C4—1881no—
261C22×C4—1881no—
262C22×C4—1881no—
263C22×C4—1881no—
264C22×C4C8×D4711yescharacteristic
265C22×C4C8×D4711yescharacteristic
266C22×C4#1062532411yescharacteristic
267C22×C4#1062532411yescharacteristic
268C22×C4C4×Dic4711yescharacteristic
269C22×C4Dic47⋊C411yescharacteristic
270C22×C4Dic47⋊C411yescharacteristic
271C22×C4C4⋊Dic4711yescharacteristic
272C22×C4(C2×D47)⋊C411yescharacteristic
273C22×C4C22⋊Dic4711yescharacteristic
274C2×C8—42no—
275C2×C8—81no—
276C2×C8—81no—
277C2×C8—3761no—
278C2×C8—3761no—
279C2×C8—1882no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—1882no—
285C4⋊C4—1882no—
286C42—1882no—
287C42—1882no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23C47⋊#9511yescharacteristic
293C23(C2×D47)⋊C811yescharacteristic
294C23(C2×D47)⋊C811yescharacteristic
295C23#1309393811yescharacteristic
296C23#1309393811yescharacteristic
297C23#1309394011yescharacteristic
298C23#1309394211yescharacteristic
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—944no—
326C2×C4—3761no—
327C2×C4—3761no—
328C2×C4—3761no—
329C2×C4—3761no—
330C2×C4—1882no—
331C2×C4—1882no—
332C2×C4—1882no—
333C2×C4—1882no—
334C2×C4—1882no—
335C2×C4—1882no—
336C2×C4—1882no—
337C2×C4—1882no—
338C2×C4—1882no—
339C2×C4C8×Dic4711yescharacteristic
340C2×C4#1309393411yescharacteristic
341C2×C4Dic47⋊C811yescharacteristic
342C2×C4Dic47⋊C811yescharacteristic
343C8—82no—
344C8—3762no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22#1568884611yescharacteristic
358C22#1568884611yescharacteristic
359C22#1568884811yescharacteristic
360C22#1568884811yescharacteristic
361C22#1568887711yescharacteristic
362C22#1568888911yescharacteristic
363C22#1568889111yescharacteristic
364C22#1568891511yescharacteristic
365C22#1568891711yescharacteristic
366C22#1568891911yescharacteristic
367C22#1568892111yescharacteristic
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—41no—
373C4—41no—
374C4—41no—
375C4—41no—
376C4—3762no—
377C4—1884no—
378C2—21no—
379C2—21no—
380C2—21no—
381C2—21no—
382C2#2024123011yescharacteristic
383C2#2024131911yescharacteristic
384C2#2024132111yescharacteristic
385C2#2024133111yescharacteristic
386C2#2024133311yescharacteristic
387C2#2024151211yescharacteristic
388C2#2024151411yescharacteristic
subgroupG/H
centerC23#13093938
commutatorC2×C4×C47C4×C8
FrattiniC22×C4⋊C4C2×D47
FittingC2×C47×#324C2
socleC23×C47#99
prime radicalC24×C47C22⋊C4
cosocleC22×C4⋊C4×C47C22
hypercenterC2×#324D47
hypocenterC47#7189
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C24 ◁ C22×C4⋊C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
10. #15688849C4semidirect
14. C47×#324C4semidirect
21. C2×C4⋊Dic47C8semidirect
25. C2×C4×Dic47C8semidirect
208. #324Dic47semidirect
209. C47#7189semidirect

Maximal subgroups

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

subgroupindex
C2×#156888492
#202416172
C2×C47×#3242
#718947