Finite Group Databasebeta

← #26109603

Subgroups — #26109603

Order 12032.

598 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
1C2×#15688968C211yesmaximal, characteristic
2#20243454C212yesmaximal
3#20241231C211yesmaximal, characteristic
4#20241230C212yesmaximal
5C47×#1280C211yesmaximal, characteristic
6C22×C4×Dic47C411yescharacteristic
7C22×C4×Dic47C411yescharacteristic
8C22×C4×Dic47C2211yescharacteristic
9C2×C22⋊(C47⋊C8)C2212yes—
10#15688968—24no—
11C2×C47⋊#95C411yescharacteristic
12C2×C47⋊#95C411yescharacteristic
13C2×C47⋊#95C2211yescharacteristic
14#15688877—24no—
15C2×C22⋊C8×C47C2212yes—
16C2×#95×C47C2211yescharacteristic
17C23×Dic47C2×C411yescharacteristic
18C23×Dic47C2×C411yescharacteristic
19C23×Dic47C2×C411yescharacteristic
20C23×Dic47C2×C411yescharacteristic
21C22×C47⋊C8—22no—
22C2×C4×Dic47—22no—
23C2×C4×Dic47—22no—
24C2×C4×Dic47—21no—
25C2×C4×Dic47—21no—
26C2×C4×Dic47—22no—
27C2×C4×Dic47—22no—
28C2×C4×Dic47—22no—
29C2×C4×Dic47—22no—
30C2×C4×Dic47C814yescomplemented
31C2×C4×Dic47D414yes—
32C22⋊(C47⋊C8)—22no—
33C22⋊(C47⋊C8)—22no—
34C47⋊#95—22no—
35C47⋊#95—22no—
36C47⋊#95—22no—
37C23×C4×C47C2×C411yescharacteristic
38C23×C4×C47C2×C411yescharacteristic
39C23×C4×C47C2311yescharacteristic
40C22×C8×C47—22no—
41C22⋊C8×C47—22no—
42C22⋊C8×C47—22no—
43#95×C47—22no—
44C24×C47C22×C411yescharacteristic
45C22×C4×C47—21no—
46C22×C4×C47—21no—
47C22×C4×C47—21no—
48C22×C4×C47—21no—
49C22×C4×C47—41no—
50C22×C4×C47—41no—
51C22×C4×C47—41no—
52C22×C4×C47—41no—
53C22×C4×C47—41no—
54C22×C4×C47—41no—
55C22×C4×C47C2×C812yes—
56C22×C4×C47M1612yes—
57C22×C4×C47C2×D412yes—
58C22×C4×C47#4112yes—
59C22×C4×C47#4111yescharacteristic
60C22×C4×C47#4111yescharacteristic
61C22×Dic47—21no—
62C22×Dic47—21no—
63C22×Dic47—21no—
64C22×Dic47—21no—
65C22×Dic47—21no—
66C22×Dic47—21no—
67C22×Dic47—21no—
68C22×Dic47—21no—
69C22×Dic47—21no—
70C22×Dic47—21no—
71C22×Dic47—41no—
72C22×Dic47—41no—
73C22×Dic47—41no—
74C22×Dic47—41no—
75C22×Dic47—41no—
76C22×Dic47—41no—
77C22×Dic47C22⋊C412yes—
78C22×Dic47C22⋊C412yes—
79C22×Dic47C2×C812yes—
80C22×Dic47C2×C812yes—
81C22×Dic47M1612yes—
82C22×Dic47M1612yes—
83C2×C8×C47—42no—
84C2×C8×C47—42no—
85C2×C8×C47—42no—
86C4×Dic47—28no—
87C4×Dic47—24no—
88C4×Dic47—24no—
89C4×Dic47—28no—
90C2×C47⋊C8—42no—
91C2×C47⋊C8—42no—
92C2×C47⋊C8—42no—
93C23×C47—21no—
94C23×C47—21no—
95C23×C47—21no—
96C23×C47—21no—
97C23×C47C2×C22⋊C411yescharacteristic
98C23×C47#11711yescharacteristic
99C23×C47#11711yescharacteristic
100C23×C47C22×C811yescharacteristic
101C23×C47C2×M1611yescharacteristic
102C23×C47C2×M1611yescharacteristic
103C23×C47C2×M1611yescharacteristic
104C2×C4×C47—22no—
105C2×C4×C47—22no—
106C2×C4×C47—22no—
107C2×C4×C47—22no—
108C2×C4×C47—42no—
109C2×C4×C47—41no—
110C2×C4×C47—41no—
111C2×C4×C47—42no—
112C2×C4×C47—42no—
113C2×C4×C47—41no—
114C2×C4×C47—41no—
115C2×C4×C47—41no—
116C2×C4×C47—41no—
117C2×C4×C47—42no—
118C2×C4×C47—42no—
119C2×C4×C47#12312yes—
120C2×C4×C47#12312yes—
121C2×Dic47—22no—
122C2×Dic47—22no—
123C2×Dic47—22no—
124C2×Dic47—22no—
125C2×Dic47—22no—
126C2×Dic47—22no—
127C2×Dic47—22no—
128C2×Dic47—22no—
129C2×Dic47—22no—
130C2×Dic47—22no—
131C2×Dic47—22no—
132C2×Dic47—42no—
133C2×Dic47—42no—
134C2×Dic47—42no—
135C2×Dic47—42no—
136C2×Dic47—41no—
137C2×Dic47—41no—
138C2×Dic47—41no—
139C2×Dic47—41no—
140C2×Dic47—42no—
141C2×Dic47—42no—
142C2×Dic47C22⋊C814yes—
143C8×C47—82no—
144C47⋊C8—82no—
145#8699—471nomaximal, Sylow
146C22×C47—21no—
147C22×C47—21no—
148C22×C47—21no—
149C22×C47—21no—
150C22×C47—21no—
151C22×C47—21no—
152C22×C47—21no—
153C22×C47—21no—
154C22×C47—21no—
155C22×C47—21no—
156C22×C47—21no—
157C22×C47—21no—
158C22×C47#38111yescharacteristic
159C22×C47C2×C22⋊C811yescharacteristic
160C22×C47#40711yescharacteristic
161C22×C47#41011yescharacteristic
162C22×C47#41011yescharacteristic
163C22×C47#41311yescharacteristic
164C22×C47#41311yescharacteristic
165C22×C47#43111yescharacteristic
166C22×C47#43111yescharacteristic
167C22×C47#43211yescharacteristic
168C22×C47#43211yescharacteristic
169C4×C47—22no—
170C4×C47—22no—
171C4×C47—42no—
172C4×C47—42no—
173Dic47—24no—
174Dic47—42no—
175Dic47—42no—
176Dic47—42no—
177C2×#376—471no—
178#1817—472no—
179#1280—472no—
180#1280—471no—
181#1280D4711yescharacteristic
182C2×C47—21no—
183C2×C47—21no—
184C2×C47—21no—
185C2×C47—21no—
186C2×C47#145811yescharacteristic
187C2×C47#145811yescharacteristic
188C2×C47#146411yescharacteristic
189C2×C47#146411yescharacteristic
190C2×C47#181711yescharacteristic
191C2×C47#182011yescharacteristic
192C2×C47#182211yescharacteristic
193C22×C42—471no—
194C22×C42—471no—
195C22×C42—471no—
196C2×C22⋊C8—472no—
197C2×C22⋊C8C2×D4712yes—
198#376—944no—
199C2×#95—471no—
200C2×#95—471no—
201C2×#95—471no—
202C2×#95C2×D4711yescharacteristic
203#336—944no—
204C47#869911yescharacteristic, complemented, Sylow
205C23×C4—471no—
206C23×C4—471no—
207C23×C4—471no—
208C23×C4—471no—
209C23×C4C4×D4711yescharacteristic
210C23×C4C4×D4711yescharacteristic
211C23×C4C22×D4711yescharacteristic
212C22×C8—22no—
213C22×C8—942no—
214C2×C42—474no—
215C2×C42—474no—
216C2×C42—942no—
217C2×C42—942no—
218C2×C42—942no—
219C2×C42—942no—
220C2×C42—942no—
221C2×C42—942no—
222C2×C42—941no—
223C2×C42—941no—
224C22⋊C8—22no—
225C22⋊C8—22no—
226C22⋊C8—942no—
227C22⋊C8—942no—
228#95—22no—
229#95—942no—
230#95—942no—
231#95—942no—
232C24C2×C4×D4711yescharacteristic
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—41no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4—472no—
244C22×C4—472no—
245C22×C4—472no—
246C22×C4—472no—
247C22×C4—472no—
248C22×C4—472no—
249C22×C4—941no—
250C22×C4—941no—
251C22×C4—941no—
252C22×C4—941no—
253C22×C4—941no—
254C22×C4—941no—
255C22×C4—941no—
256C22×C4—941no—
257C22×C4—941no—
258C22×C4—941no—
259C22×C4—1881no—
260C22×C4—1881no—
261C22×C4—1881no—
262C22×C4—1881no—
263C22×C4—1881no—
264C22×C4—1881no—
265C22×C4C8×D4712yes—
266C22×C4#1062532412yes—
267C22×C4#1062535012yes—
268C22×C4D4×D4712yes—
269C22×C4#1062535211yescharacteristic
270C22×C4#1062535411yescharacteristic
271C2×C8—42no—
272C2×C8—42no—
273C2×C8—42no—
274C2×C8—1882no—
275C2×C8—1882no—
276C2×C8—1882no—
277C42—948no—
278C42—948no—
279C42—944no—
280C42—944no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23C22⋊C4×D4711yescharacteristic
286C23#1309398111yescharacteristic
287C23#1309398211yescharacteristic
288C23C2×C8×D4711yescharacteristic
289C23M16×D4711yescharacteristic
290C23M16×D4711yescharacteristic
291C23C2×#1062532411yescharacteristic
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—42no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—474no—
308C2×C4—942no—
309C2×C4—942no—
310C2×C4—942no—
311C2×C4—942no—
312C2×C4—942no—
313C2×C4—942no—
314C2×C4—942no—
315C2×C4—942no—
316C2×C4—942no—
317C2×C4—942no—
318C2×C4—942no—
319C2×C4—1882no—
320C2×C4—1882no—
321C2×C4—1882no—
322C2×C4—1882no—
323C2×C4—1881no—
324C2×C4—1881no—
325C2×C4—1881no—
326C2×C4—1881no—
327C2×C4—1882no—
328C2×C4—1882no—
329C2×C4#1309400612yes—
330C2×C4#1309400912yes—
331C8—82no—
332C8—3762no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22#1568898511yescharacteristic
346C22C22⋊C8×D4711yescharacteristic
347C22#1568908511yescharacteristic
348C22#1568909511yescharacteristic
349C22#1568909511yescharacteristic
350C22#1568910411yescharacteristic
351C22#1568910611yescharacteristic
352C22#1568917411yescharacteristic
353C22#1568917511yescharacteristic
354C22#1568917811yescharacteristic
355C22#1568917911yescharacteristic
356C4—22no—
357C4—22no—
358C4—42no—
359C4—42no—
360C4—944no—
361C4—1882no—
362C4—1882no—
363C4—1882no—
364C2—21no—
365C2—21no—
366C2—21no—
367C2—21no—
368C2#2024169911yescharacteristic
369C2#2024170111yescharacteristic
370C2#2024171911yescharacteristic
371C2#2024172111yescharacteristic
372C2#2024345511yescharacteristic
373C2#2024346411yescharacteristic
374C2#2024347011yescharacteristic
subgroupG/H
centerC23C22⋊C4×D47
commutatorC23×C47C22×C8
FrattiniC23×C4C22×D47
FittingC47×#1280C2
socleC23×C47C2×C22⋊C4
prime radicalC24×C47C22×C4
cosocleC23×C4×C47C23
hypercenter#1280D47
hypocenterC47#8699
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
30. C2×C4×Dic47C8semidirect
204. C47#8699semidirect

Maximal subgroups

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

subgroupindex
C2×#156889682
#202434542
#202412312
#202412302
C47×#12802
#869947