Finite Group Databasebeta

← #26108956

Subgroups — #26108956

Order 12032.

570 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20243368C211yesmaximal, characteristic
2#20243368C211yesmaximal, characteristic
3C2×#15688849C212yesmaximal
4#20241231C212yesmaximal
5C2×C47×#387C211yesmaximal, characteristic
6C2×C4⋊(C47⋊C8)—21no—
7C2×C4⋊(C47⋊C8)—21no—
8C2×C22⋊(C47⋊C8)C2212yes—
9C2×C22⋊(C47⋊C8)C2212yes—
10#15688878—21no—
11#15688878—21no—
12#15688849—24no—
13C22×C4⋊C4×C47C411yescharacteristic
14C22×C4⋊C4×C47C2211yescharacteristic
15C22×C42×C47C2211yescharacteristic
16C47×#387—21no—
17C47×#387—21no—
18C47×#387—21no—
19C47×#387—21no—
20C2×#95×C47C411yescharacteristic
21C2×#95×C47C411yescharacteristic
22C2×#95×C47C411yescharacteristic
23C2×#95×C47C2211yescharacteristic
24C22×C47⋊C8—22no—
25C22×C47⋊C8—22no—
26C4⋊(C47⋊C8)—42no—
27C4⋊(C47⋊C8)—42no—
28C22⋊(C47⋊C8)—22no—
29C22⋊(C47⋊C8)—22no—
30C22⋊(C47⋊C8)—22no—
31C22⋊(C47⋊C8)—22no—
32C23×C4×C47C2×C411yescharacteristic
33C23×C4×C47C2×C411yescharacteristic
34C23×C4×C47C2×C411yescharacteristic
35C23×C4×C47C2×C411yescharacteristic
36C23×C4×C47C2×C411yescharacteristic
37C23×C4×C47C2×C411yescharacteristic
38C23×C4×C47C2311yescharacteristic
39C2×C4⋊C4×C47—21no—
40C2×C4⋊C4×C47—21no—
41C2×C4⋊C4×C47—21no—
42C2×C4⋊C4×C47—21no—
43C2×C4⋊C4×C47—21no—
44C2×C4⋊C4×C47—21no—
45C2×C4⋊C4×C47—42no—
46C2×C4⋊C4×C47D412yes—
47C2×C4⋊C4×C47Q812yes—
48C2×C42×C47—42no—
49C2×C42×C47D411yescharacteristic
50C2×C42×C47D411yescharacteristic
51C2×C42×C47D411yescharacteristic
52C2×C42×C47D411yescharacteristic
53#95×C47—21no—
54#95×C47—21no—
55#95×C47—21no—
56#95×C47—21no—
57#95×C47—21no—
58#95×C47—21no—
59#95×C47—21no—
60#95×C47—21no—
61C24×C47C22×C411yescharacteristic
62C22×C4×C47—21no—
63C22×C4×C47—21no—
64C22×C4×C47—21no—
65C22×C4×C47—21no—
66C22×C4×C47—22no—
67C22×C4×C47—22no—
68C22×C4×C47—22no—
69C22×C4×C47—22no—
70C22×C4×C47—22no—
71C22×C4×C47—22no—
72C22×C4×C47—21no—
73C22×C4×C47—21no—
74C22×C4×C47—22no—
75C22×C4×C47—22no—
76C22×C4×C47—41no—
77C22×C4×C47—41no—
78C22×C4×C47—41no—
79C22×C4×C47—41no—
80C22×C4×C47—41no—
81C22×C4×C47—41no—
82C22×C4×C47—41no—
83C22×C4×C47—41no—
84C22×C4×C47—41no—
85C22×C4×C47—41no—
86C22×C4×C47C22⋊C411yescharacteristic
87C22×C4×C47C22⋊C411yescharacteristic
88C22×C4×C47C22⋊C411yescharacteristic
89C22×C4×C47C22⋊C411yescharacteristic
90C22×C4×C47C4⋊C412yes—
91C22×C4×C47C4⋊C412yes—
92C22×C4×C47C2×D411yescharacteristic
93C22×C4×C47C2×D411yescharacteristic
94C22×C4×C47C2×D411yescharacteristic
95C22×C4×C47C2×Q811yescharacteristic
96C22×C4×C47#4111yescharacteristic
97C22×C4×C47#4111yescharacteristic
98C4⋊C4×C47—22no—
99C4⋊C4×C47—22no—
100C4⋊C4×C47—22no—
101C4⋊C4×C47—22no—
102C4⋊C4×C47—42no—
103C4⋊C4×C47—42no—
104C42×C47—22no—
105C42×C47—22no—
106C42×C47—41no—
107C42×C47—41no—
108C2×C47⋊C8—42no—
109C2×C47⋊C8—42no—
110C2×C47⋊C8—42no—
111C2×C47⋊C8—42no—
112C2×C47⋊C8—42no—
113C2×C47⋊C8—42no—
114C23×C47—21no—
115C23×C47—21no—
116C23×C47—21no—
117C23×C47—21no—
118C23×C47C2×C22⋊C411yescharacteristic
119C23×C47C2×C4⋊C411yescharacteristic
120C23×C47#11711yescharacteristic
121C23×C47#13112yes—
122C23×C47#13112yes—
123C2×C4×C47—21no—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47—21no—
129C2×C4×C47—21no—
130C2×C4×C47—21no—
131C2×C4×C47—22no—
132C2×C4×C47—22no—
133C2×C4×C47—21no—
134C2×C4×C47—21no—
135C2×C4×C47—21no—
136C2×C4×C47—21no—
137C2×C4×C47—21no—
138C2×C4×C47—21no—
139C2×C4×C47—24no—
140C2×C4×C47—41no—
141C2×C4×C47—41no—
142C2×C4×C47—41no—
143C2×C4×C47—41no—
144C2×C4×C47—44no—
145C2×C4×C47—44no—
146C2×C4×C47—42no—
147C2×C4×C47—41no—
148C2×C4×C47—41no—
149C2×C4×C47—41no—
150C2×C4×C47—41no—
151C2×C4×C47—42no—
152C2×C4×C47—42no—
153C2×C4×C47—41no—
154C2×C4×C47—41no—
155C2×C4×C47—41no—
156C2×C4×C47—41no—
157C2×C4×C47—41no—
158C2×C4×C47—41no—
159C2×C4×C47—82no—
160C2×C4×C47—82no—
161C2×C4×C47#9912yes—
162C2×C4×C47#10112yes—
163C2×C4×C47#12111yescharacteristic
164C2×C4×C47#12111yescharacteristic
165C2×C4×C47C22⋊Q811yescharacteristic
166C2×C4×C47C22⋊Q811yescharacteristic
167C47⋊C8—82no—
168C47⋊C8—82no—
169#8562—471nomaximal, Sylow
170C22×C47—21no—
171C22×C47—21no—
172C22×C47—21no—
173C22×C47—21no—
174C22×C47—22no—
175C22×C47—22no—
176C22×C47—22no—
177C22×C47—22no—
178C22×C47#38011yescharacteristic
179C22×C47#40811yescharacteristic
180C22×C47#40811yescharacteristic
181C22×C47C2×#9911yescharacteristic
182C22×C47#41011yescharacteristic
183C22×C47C2×#10111yescharacteristic
184C22×C47#41311yescharacteristic
185C22×C47#42412yes—
186C22×C47#43312yes—
187C4×C47—21no—
188C4×C47—21no—
189C4×C47—21no—
190C4×C47—21no—
191C4×C47—22no—
192C4×C47—22no—
193C4×C47—42no—
194C4×C47—42no—
195C4×C47—41no—
196C4×C47—41no—
197C4×C47—81no—
198C4×C47—81no—
199C2×#387D4711yescharacteristic
200#1797—471no—
201#1797—471no—
202C2×#324—472no—
203#1280—472no—
204C2×C47—22no—
205C2×C47—22no—
206C2×C47#146811yescharacteristic
207C2×C47#147011yescharacteristic
208C2×C47#147211yescharacteristic
209C2×C47#147311yescharacteristic
210C2×C47#179811yescharacteristic
211C2×C47#179911yescharacteristic
212C2×C47#180111yescharacteristic
213C22×C4⋊C4Dic4711yescharacteristic
214C22×C4⋊C4C2×D4711yescharacteristic
215C22×C42C2×D4711yescharacteristic
216C2×C4⋊C8—941no—
217C2×C4⋊C8—941no—
218C2×C22⋊C8—472no—
219C2×C22⋊C8—472no—
220#387—21no—
221#387—21no—
222#387—21no—
223#387—21no—
224C2×#95Dic4711yescharacteristic
225C2×#95Dic4711yescharacteristic
226C2×#95Dic4711yescharacteristic
227C2×#95C2×D4711yescharacteristic
228#336—941no—
229#336—941no—
230#324—944no—
231C47#856211yescharacteristic, complemented, Sylow
232C23×C4C2×Dic4711yescharacteristic
233C23×C4C2×Dic4711yescharacteristic
234C23×C4C2×Dic4711yescharacteristic
235C23×C4C2×Dic4711yescharacteristic
236C23×C4C2×Dic4711yescharacteristic
237C23×C4C2×Dic4711yescharacteristic
238C23×C4C22×D4711yescharacteristic
239C22×C8—942no—
240C22×C8—942no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—42no—
248C2×C4⋊C4Dic9412yes—
249C2×C4⋊C4D18812yes—
250C2×C42—42no—
251C2×C42C22⋊D4711yescharacteristic
252C2×C42C22⋊D4711yescharacteristic
253C2×C42C22⋊D4711yescharacteristic
254C2×C42C22⋊D4711yescharacteristic
255C4⋊C8—1882no—
256C4⋊C8—1882no—
257C22⋊C8—942no—
258C22⋊C8—942no—
259C22⋊C8—942no—
260C22⋊C8—942no—
261#95—21no—
262#95—21no—
263#95—21no—
264#95—21no—
265#95—21no—
266#95—21no—
267#95—21no—
268#95—21no—
269C24C22×Dic4711yescharacteristic
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4C4⋊Dic4712yes—
295C22×C4C4⋊Dic4712yes—
296C22×C4C22⋊Dic4711yescharacteristic
297C22×C4C22⋊Dic4711yescharacteristic
298C22×C4C22⋊Dic4711yescharacteristic
299C22×C4C22⋊Dic4711yescharacteristic
300C22×C4C2×Dic9411yescharacteristic
301C22×C4C2×D18811yescharacteristic
302C22×C4#1062535011yescharacteristic
303C22×C4#1062535011yescharacteristic
304C22×C4C2×C22⋊D4711yescharacteristic
305C22×C4C2×C22⋊D4711yescharacteristic
306C2×C8—1882no—
307C2×C8—1882no—
308C2×C8—1882no—
309C2×C8—1882no—
310C2×C8—1882no—
311C2×C8—1882no—
312C4⋊C4—22no—
313C4⋊C4—22no—
314C4⋊C4—22no—
315C4⋊C4—22no—
316C4⋊C4—42no—
317C4⋊C4—42no—
318C42—22no—
319C42—22no—
320C42—41no—
321C42—41no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23C2×C22⋊Dic4711yescharacteristic
327C23C2×C4⋊Dic4711yescharacteristic
328C23#1309398311yescharacteristic
329C23#1309403112yes—
330C23#1309403112yes—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—24no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—44no—
353C2×C4—44no—
354C2×C4—42no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—82no—
368C2×C4—82no—
369C2×C4#1309393912yes—
370C2×C4#1309394312yes—
371C2×C4#1309399811yescharacteristic
372C2×C4#1309399811yescharacteristic
373C2×C4#1309400311yescharacteristic
374C2×C4#1309400311yescharacteristic
375C8—3762no—
376C8—3762no—
377C22—22no—
378C22—22no—
379C22—22no—
380C22—22no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22#1568898311yescharacteristic
386C22#1568909011yescharacteristic
387C22#1568909011yescharacteristic
388C22C2×#1309393911yescharacteristic
389C22#1568909711yescharacteristic
390C22C2×#1309394311yescharacteristic
391C22#1568910711yescharacteristic
392C22#1568915012yes—
393C22#1568918412yes—
394C4—22no—
395C4—22no—
396C4—21no—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—42no—
403C4—42no—
404C4—81no—
405C4—81no—
406C2—22no—
407C2—22no—
408C2#2024173611yescharacteristic
409C2#2024174411yescharacteristic
410C2#2024175211yescharacteristic
411C2#2024175711yescharacteristic
412C2#2024337211yescharacteristic
413C2#2024337611yescharacteristic
414C2#2024338411yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic47
commutator, prime radicalC24×C47C22×C4
FrattiniC23×C4C22×D47
FittingC2×C47×#387C2
socleC23×C47C2×C22⋊C4
cosocleC23×C4×C47C23
hypercenterC2×#387D47
hypocenterC47#8562
LCSG ▷ C24×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
231. C47#8562semidirect

Maximal subgroups

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

subgroupindex
#202433682
C2×#156888492
#202412312
C2×C47×#3872
#856247