Finite Group Databasebeta

← #26109609

Subgroups — #26109609

Order 12032.

642 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15688974C211yesmaximal, characteristic
2#20243454C212yesmaximal
3#20241231C211yesmaximal, characteristic
4#20241230C212yesmaximal
5C47×#1280C211yesmaximal, characteristic
6C22×Dic47⋊C4C411yescharacteristic
7C22×Dic47⋊C4C411yescharacteristic
8C22×C4×Dic47C411yescharacteristic
9C22×C4×Dic47C411yescharacteristic
10C22×C4×Dic47C2211yescharacteristic
11C2×C22⋊(C47⋊C8)C2212yes—
12#15688974—22no—
13#15688974—22no—
14C2×C47⋊#95C2211yescharacteristic
15#15688877—22no—
16#15688877—22no—
17C2×C22⋊C8×C47C2212yes—
18C2×#95×C47C2211yescharacteristic
19C23×Dic47C2×C411yescharacteristic
20C23×Dic47C2×C411yescharacteristic
21C23×Dic47C2×C411yescharacteristic
22C23×Dic47C2×C411yescharacteristic
23C22×C47⋊C8—22no—
24C2×Dic47⋊C4—22no—
25C2×Dic47⋊C4—22no—
26C2×Dic47⋊C4—22no—
27C2×Dic47⋊C4—22no—
28C2×Dic47⋊C4—22no—
29C2×Dic47⋊C4C814yescomplemented
30C2×C4×Dic47—22no—
31C2×C4×Dic47—21no—
32C2×C4×Dic47—21no—
33C2×C4×Dic47—21no—
34C2×C4×Dic47—21no—
35C2×C4×Dic47—21no—
36C2×C4×Dic47—21no—
37C2×C4×Dic47—42no—
38C2×C4×Dic47—42no—
39C2×C4×Dic47D412yes—
40C2×C4×Dic47D412yes—
41C22⋊(C47⋊C8)—22no—
42C22⋊(C47⋊C8)—22no—
43C47⋊#95—22no—
44C23×C4×C47C2×C411yescharacteristic
45C23×C4×C47C2×C411yescharacteristic
46C23×C4×C47C2311yescharacteristic
47C22×C8×C47—22no—
48C22⋊C8×C47—22no—
49C22⋊C8×C47—22no—
50#95×C47—22no—
51C24×C47C22×C411yescharacteristic
52C22×C4×C47—21no—
53C22×C4×C47—21no—
54C22×C4×C47—21no—
55C22×C4×C47—21no—
56C22×C4×C47—41no—
57C22×C4×C47—41no—
58C22×C4×C47—41no—
59C22×C4×C47—41no—
60C22×C4×C47—41no—
61C22×C4×C47—41no—
62C22×C4×C47C2×C812yes—
63C22×C4×C47M1612yes—
64C22×C4×C47C2×D412yes—
65C22×C4×C47#4112yes—
66C22×C4×C47#4111yescharacteristic
67C22×C4×C47#4111yescharacteristic
68C22×Dic47—21no—
69C22×Dic47—21no—
70C22×Dic47—21no—
71C22×Dic47—21no—
72C22×Dic47—21no—
73C22×Dic47—21no—
74C22×Dic47—22no—
75C22×Dic47—22no—
76C22×Dic47—21no—
77C22×Dic47—21no—
78C22×Dic47—21no—
79C22×Dic47—21no—
80C22×Dic47—41no—
81C22×Dic47—41no—
82C22×Dic47—41no—
83C22×Dic47—41no—
84C22×Dic47C22⋊C412yes—
85C22×Dic47C22⋊C411yescharacteristic
86C22×Dic47C22⋊C411yescharacteristic
87C22×Dic47C2×C812yes—
88C22×Dic47C2×C812yes—
89C22×Dic47M1612yes—
90C22×Dic47M1612yes—
91C2×C8×C47—42no—
92C2×C8×C47—42no—
93C2×C8×C47—42no—
94Dic47⋊C4—28no—
95Dic47⋊C4—28no—
96C4×Dic47—22no—
97C4×Dic47—22no—
98C4×Dic47—22no—
99C4×Dic47—22no—
100C4×Dic47—42no—
101C4×Dic47—42no—
102C4×Dic47—42no—
103C4×Dic47—42no—
104C2×C47⋊C8—42no—
105C2×C47⋊C8—42no—
106C2×C47⋊C8—42no—
107C23×C47—21no—
108C23×C47—21no—
109C23×C47—21no—
110C23×C47—21no—
111C23×C47C2×C22⋊C411yescharacteristic
112C23×C47#11711yescharacteristic
113C23×C47#11711yescharacteristic
114C23×C47C22×C811yescharacteristic
115C23×C47C2×M1611yescharacteristic
116C23×C47C2×M1611yescharacteristic
117C23×C47C2×M1611yescharacteristic
118C2×C4×C47—22no—
119C2×C4×C47—22no—
120C2×C4×C47—22no—
121C2×C4×C47—22no—
122C2×C4×C47—42no—
123C2×C4×C47—41no—
124C2×C4×C47—41no—
125C2×C4×C47—42no—
126C2×C4×C47—42no—
127C2×C4×C47—41no—
128C2×C4×C47—41no—
129C2×C4×C47—41no—
130C2×C4×C47—41no—
131C2×C4×C47—42no—
132C2×C4×C47—42no—
133C2×C4×C47#12312yes—
134C2×C4×C47#12312yes—
135C2×Dic47—24no—
136C2×Dic47—24no—
137C2×Dic47—22no—
138C2×Dic47—21no—
139C2×Dic47—21no—
140C2×Dic47—22no—
141C2×Dic47—21no—
142C2×Dic47—21no—
143C2×Dic47—22no—
144C2×Dic47—22no—
145C2×Dic47—22no—
146C2×Dic47—22no—
147C2×Dic47—22no—
148C2×Dic47—22no—
149C2×Dic47—42no—
150C2×Dic47—42no—
151C2×Dic47—41no—
152C2×Dic47—41no—
153C2×Dic47—41no—
154C2×Dic47—41no—
155C2×Dic47—42no—
156C2×Dic47—42no—
157C2×Dic47C22⋊C814yes—
158C2×Dic47#10012yes—
159C2×Dic47#10112yes—
160C8×C47—82no—
161C47⋊C8—82no—
162#8701—471nomaximal, Sylow
163C22×C47—21no—
164C22×C47—21no—
165C22×C47—21no—
166C22×C47—21no—
167C22×C47—21no—
168C22×C47—21no—
169C22×C47—21no—
170C22×C47—21no—
171C22×C47—21no—
172C22×C47—21no—
173C22×C47—21no—
174C22×C47—21no—
175C22×C47#38111yescharacteristic
176C22×C47C2×C22⋊C811yescharacteristic
177C22×C47#40711yescharacteristic
178C22×C47#41011yescharacteristic
179C22×C47#41011yescharacteristic
180C22×C47C2×#10011yescharacteristic
181C22×C47C2×#10111yescharacteristic
182C22×C47#43111yescharacteristic
183C22×C47#43111yescharacteristic
184C22×C47#43211yescharacteristic
185C22×C47#43211yescharacteristic
186C4×C47—22no—
187C4×C47—22no—
188C4×C47—42no—
189C4×C47—42no—
190Dic47—24no—
191Dic47—22no—
192Dic47—22no—
193Dic47—42no—
194Dic47—42no—
195C2×C4×C4⋊C4—471no—
196#1817—472no—
197#1280—472no—
198#1280—471no—
199#1280D4711yescharacteristic
200C2×C47—21no—
201C2×C47—21no—
202C2×C47—21no—
203C2×C47—21no—
204C2×C47#146011yescharacteristic
205C2×C47#146111yescharacteristic
206C2×C47#146611yescharacteristic
207C2×C47#146711yescharacteristic
208C2×C47#181711yescharacteristic
209C2×C47#182011yescharacteristic
210C2×C47#182111yescharacteristic
211C22×C4⋊C4—471no—
212C22×C4⋊C4—471no—
213C22×C42—471no—
214C22×C42—471no—
215C22×C42—471no—
216C2×C22⋊C8—472no—
217C2×C22⋊C8C2×D4712yes—
218C4×C4⋊C4—942no—
219C4×C4⋊C4—942no—
220C2×#95—471no—
221C2×#95C2×D4711yescharacteristic
222#336—942no—
223#336—942no—
224C47#870111yescharacteristic, complemented, Sylow
225C23×C4—471no—
226C23×C4—471no—
227C23×C4—471no—
228C23×C4—471no—
229C23×C4C4×D4711yescharacteristic
230C23×C4C4×D4711yescharacteristic
231C23×C4C22×D4711yescharacteristic
232C22×C8—22no—
233C22×C8—942no—
234C2×C4⋊C4—474no—
235C2×C4⋊C4—942no—
236C2×C4⋊C4—942no—
237C2×C4⋊C4—942no—
238C2×C4⋊C4—942no—
239C2×C4⋊C4—942no—
240C2×C42—472no—
241C2×C42—472no—
242C2×C42—942no—
243C2×C42—941no—
244C2×C42—941no—
245C2×C42—941no—
246C2×C42—941no—
247C2×C42—941no—
248C2×C42—941no—
249C2×C42—1882no—
250C2×C42—1882no—
251C22⋊C8—22no—
252C22⋊C8—22no—
253C22⋊C8—942no—
254C22⋊C8—942no—
255#95—22no—
256#95—942no—
257C24C2×C4×D4711yescharacteristic
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—471no—
269C22×C4—471no—
270C22×C4—472no—
271C22×C4—472no—
272C22×C4—472no—
273C22×C4—472no—
274C22×C4—472no—
275C22×C4—942no—
276C22×C4—942no—
277C22×C4—941no—
278C22×C4—941no—
279C22×C4—941no—
280C22×C4—941no—
281C22×C4—941no—
282C22×C4—941no—
283C22×C4—941no—
284C22×C4—941no—
285C22×C4—941no—
286C22×C4—941no—
287C22×C4—1881no—
288C22×C4—1881no—
289C22×C4—1881no—
290C22×C4—1881no—
291C22×C4C8×D4712yes—
292C22×C4#1062532412yes—
293C22×C4#1062535012yes—
294C22×C4D4×D4712yes—
295C22×C4#1062535211yescharacteristic
296C22×C4#1062535411yescharacteristic
297C2×C8—42no—
298C2×C8—42no—
299C2×C8—42no—
300C2×C8—1882no—
301C2×C8—1882no—
302C2×C8—1882no—
303C4⋊C4—948no—
304C4⋊C4—948no—
305C42—942no—
306C42—942no—
307C42—942no—
308C42—942no—
309C42—1882no—
310C42—1882no—
311C42—1882no—
312C42—1882no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23C22⋊C4×D4711yescharacteristic
318C23#1309398111yescharacteristic
319C23#1309398211yescharacteristic
320C23C2×C8×D4711yescharacteristic
321C23M16×D4711yescharacteristic
322C23M16×D4711yescharacteristic
323C23C2×#1062532411yescharacteristic
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—474no—
340C2×C4—472no—
341C2×C4—472no—
342C2×C4—944no—
343C2×C4—944no—
344C2×C4—941no—
345C2×C4—941no—
346C2×C4—942no—
347C2×C4—942no—
348C2×C4—941no—
349C2×C4—941no—
350C2×C4—942no—
351C2×C4—942no—
352C2×C4—942no—
353C2×C4—942no—
354C2×C4—942no—
355C2×C4—942no—
356C2×C4—1882no—
357C2×C4—1882no—
358C2×C4—1881no—
359C2×C4—1881no—
360C2×C4—1881no—
361C2×C4—1881no—
362C2×C4—1882no—
363C2×C4—1882no—
364C2×C4#1309400612yes—
365C2×C4#1309400912yes—
366C8—82no—
367C8—3762no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22#1568898511yescharacteristic
381C22C22⋊C8×D4711yescharacteristic
382C22#1568908511yescharacteristic
383C22#1568909511yescharacteristic
384C22#1568909511yescharacteristic
385C22#100×D4711yescharacteristic
386C22#101×D4711yescharacteristic
387C22#1568917411yescharacteristic
388C22#1568917511yescharacteristic
389C22#1568917811yescharacteristic
390C22#1568917911yescharacteristic
391C4—22no—
392C4—22no—
393C4—42no—
394C4—42no—
395C4—942no—
396C4—942no—
397C4—944no—
398C4—1882no—
399C4—1882no—
400C2—21no—
401C2—21no—
402C2—21no—
403C2—21no—
404C2#2024170711yescharacteristic
405C2#2024171011yescharacteristic
406C2#2024172711yescharacteristic
407C2#2024173011yescharacteristic
408C2#2024345511yescharacteristic
409C2#2024346411yescharacteristic
410C2#2024346711yescharacteristic
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#8701
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
29. C2×Dic47⋊C4C8semidirect
224. C47#8701semidirect

Maximal subgroups

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

subgroupindex
C2×#156889742
#202434542
#202412312
#202412302
C47×#12802
#870147