Finite Group Databasebeta

← #26116331

Subgroups — #26116331

Order 12032.

556 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689007C211yesmaximal, characteristic
2#20243368C211yesmaximal, characteristic
3#20241230C212yesmaximal
4#20241230C212yesmaximal
5C47×#1749C211yesmaximal, characteristic
6C22×Dic47⋊C4C411yescharacteristic
7C22×Dic47⋊C4C411yescharacteristic
8C2×C4⋊(C47⋊C8)—21no—
9C2×C22⋊(C47⋊C8)C2212yes—
10#15689007—21no—
11#15689007—21no—
12#15689007—21no—
13#15689007—21no—
14C2×C47⋊#95C411yescharacteristic
15C2×C47⋊#95C411yescharacteristic
16C2×C47⋊#95C2211yescharacteristic
17C2×C47⋊#95C2211yescharacteristic
18#15688878—21no—
19C22×C42×C47C2211yescharacteristic
20C2×C22⋊C8×C47C2212yes—
21C2×#97×C47—21no—
22C47×#336—21no—
23C23×Dic47C2×C411yescharacteristic
24C23×Dic47C2×C411yescharacteristic
25C23×Dic47C2×C411yescharacteristic
26C23×Dic47C2×C411yescharacteristic
27C22×C47⋊C8—22no—
28C2×Dic47⋊C4—21no—
29C2×Dic47⋊C4—21no—
30C2×Dic47⋊C4—22no—
31C2×Dic47⋊C4—22no—
32C2×Dic47⋊C4—21no—
33C2×Dic47⋊C4—21no—
34C2×Dic47⋊C4—42no—
35C4⋊(C47⋊C8)—42no—
36C22⋊(C47⋊C8)—24no—
37C47⋊#95—21no—
38C47⋊#95—21no—
39C47⋊#95—21no—
40C47⋊#95—21no—
41C47⋊#95—21no—
42C47⋊#95—21no—
43C47⋊#95—21no—
44C47⋊#95—21no—
45C23×C4×C47C2×C411yescharacteristic
46C23×C4×C47C2×C411yescharacteristic
47C23×C4×C47C2311yescharacteristic
48C22×C8×C47—22no—
49C2×C42×C47—42no—
50C2×C42×C47D411yescharacteristic
51C2×C42×C47D411yescharacteristic
52C2×C42×C47D411yescharacteristic
53C2×C42×C47D411yescharacteristic
54C22⋊C8×C47—22no—
55C22⋊C8×C47Q814yes—
56#97×C47—42no—
57C24×C47C22×C411yescharacteristic
58C22×C4×C47—21no—
59C22×C4×C47—21no—
60C22×C4×C47—22no—
61C22×C4×C47—22no—
62C22×C4×C47—41no—
63C22×C4×C47—41no—
64C22×C4×C47—41no—
65C22×C4×C47—41no—
66C22×C4×C47—41no—
67C22×C4×C47C22⋊C411yescharacteristic
68C22×C4×C47C22⋊C411yescharacteristic
69C22×C4×C47C22⋊C411yescharacteristic
70C22×C4×C47C22⋊C411yescharacteristic
71C22×C4×C47C2×D411yescharacteristic
72C22×C4×C47C2×D411yescharacteristic
73C22×C4×C47C2×Q812yes—
74C22×C4×C47#4112yes—
75C22×Dic47—21no—
76C22×Dic47—21no—
77C22×Dic47—21no—
78C22×Dic47—21no—
79C22×Dic47—21no—
80C22×Dic47—21no—
81C22×Dic47—22no—
82C22×Dic47—22no—
83C22×Dic47—41no—
84C22×Dic47—41no—
85C22×Dic47—41no—
86C22×Dic47—41no—
87C22×Dic47—41no—
88C22×Dic47—41no—
89C22×Dic47—41no—
90C22×Dic47—41no—
91C22×Dic47M1612yes—
92C22×Dic47M1612yes—
93C2×C8×C47—24no—
94C2×C8×C47—42no—
95C2×C8×C47—42no—
96C42×C47—22no—
97C42×C47—22no—
98C42×C47—41no—
99C42×C47—41no—
100Dic47⋊C4—24no—
101Dic47⋊C4—24no—
102Dic47⋊C4—42no—
103Dic47⋊C4—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×C47C4×Q812yes—
113C23×C47C2×M1611yescharacteristic
114C23×C47C2×M1611yescharacteristic
115C23×C47#13112yes—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
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—42no—
132C2×C4×C47—42no—
133C2×C4×C47—44no—
134C2×C4×C47—42no—
135C2×C4×C47—42no—
136C2×C4×C47#9912yes—
137C2×C4×C47C22⋊Q812yes—
138C2×C4×C47#12411yescharacteristic
139C2×C4×C47C4⋊Q811yescharacteristic
140C2×Dic47—22no—
141C2×Dic47—22no—
142C2×Dic47—42no—
143C2×Dic47—42no—
144C2×Dic47—41no—
145C2×Dic47—41no—
146C2×Dic47—41no—
147C2×Dic47—41no—
148C2×Dic47—42no—
149C2×Dic47—42no—
150C2×Dic47—41no—
151C2×Dic47—41no—
152C2×Dic47—41no—
153C2×Dic47—41no—
154C2×Dic47—41no—
155C2×Dic47—41no—
156C2×Dic47—82no—
157C2×Dic47—82no—
158C8×C47—44no—
159C47⋊C8—82no—
160#9881—471nomaximal, Sylow
161C22×C47—21no—
162C22×C47—21no—
163C22×C47—21no—
164C22×C47—21no—
165C22×C47—22no—
166C22×C47—22no—
167C22×C47—22no—
168C22×C47—22no—
169C22×C47#39111yescharacteristic
170C22×C47#40711yescharacteristic
171C22×C47#40811yescharacteristic
172C22×C47C2×#9911yescharacteristic
173C22×C47#41011yescharacteristic
174C22×C47#41311yescharacteristic
175C22×C47#41311yescharacteristic
176C22×C47#44612yes—
177C22×C47#44612yes—
178C4×C47—22no—
179C4×C47—21no—
180C4×C47—22no—
181C4×C47—21no—
182C4×C47—41no—
183C4×C47—41no—
184C4×C47—41no—
185Dic47—42no—
186Dic47—42no—
187Dic47—81no—
188Dic47—81no—
189C2×#387—471no—
190#1797—471no—
191#1749D4711yescharacteristic
192#1280—472no—
193#1280—472no—
194C2×C47—22no—
195C2×C47—22no—
196C2×C47#146411yescharacteristic
197C2×C47#146511yescharacteristic
198C2×C47#146811yescharacteristic
199C2×C47#147311yescharacteristic
200C2×C47#198511yescharacteristic
201C2×C47#199611yescharacteristic
202C2×C47#199811yescharacteristic
203C22×C4⋊C4—471no—
204C22×C4⋊C4—471no—
205C22×C42C2×D4711yescharacteristic
206C2×C4⋊C8—941no—
207C2×C22⋊C8—472no—
208C2×C22⋊C8C2×D4712yes—
209C2×#97—21no—
210#387—941no—
211#387—941no—
212#387—941no—
213#387—941no—
214C2×#95—471no—
215C2×#95—471no—
216C2×#95—471no—
217C2×#95—471no—
218#336—21no—
219#336—941no—
220C47#988111yescharacteristic, complemented, Sylow
221C23×C4—471no—
222C23×C4—471no—
223C23×C4—471no—
224C23×C4—471no—
225C23×C4C4×D4711yescharacteristic
226C23×C4C4×D4711yescharacteristic
227C23×C4C22×D4711yescharacteristic
228C22×C8—22no—
229C22×C8—942no—
230C2×C4⋊C4—942no—
231C2×C4⋊C4—942no—
232C2×C4⋊C4—941no—
233C2×C4⋊C4—941no—
234C2×C4⋊C4—941no—
235C2×C4⋊C4—941no—
236C2×C4⋊C4—1882no—
237C2×C42—42no—
238C2×C42D18811yescharacteristic
239C2×C42D18811yescharacteristic
240C2×C42C22⋊D4711yescharacteristic
241C2×C42C22⋊D4711yescharacteristic
242C4⋊C8—1882no—
243C22⋊C8—22no—
244C22⋊C8—944no—
245C22⋊C8Dic9414yes—
246#97—42no—
247#95—941no—
248#95—941no—
249#95—941no—
250#95—941no—
251#95—941no—
252#95—941no—
253#95—941no—
254#95—941no—
255C24C2×C4×D4711yescharacteristic
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—472no—
266C22×C4—472no—
267C22×C4—941no—
268C22×C4—941no—
269C22×C4—941no—
270C22×C4—941no—
271C22×C4—942no—
272C22×C4—942no—
273C22×C4—941no—
274C22×C4—941no—
275C22×C4—1881no—
276C22×C4—1881no—
277C22×C4—1881no—
278C22×C4—1881no—
279C22×C4—1881no—
280C22×C4—1881no—
281C22×C4—1881no—
282C22×C4—1881no—
283C22×C4(C2×D47)⋊C411yescharacteristic
284C22×C4(C2×D47)⋊C411yescharacteristic
285C22×C4(C2×D47)⋊C411yescharacteristic
286C22×C4(C2×D47)⋊C411yescharacteristic
287C22×C4C2×Dic9412yes—
288C22×C4C2×D18811yescharacteristic
289C22×C4#1062535012yes—
290C22×C4C2×C22⋊D4711yescharacteristic
291C2×C8—24no—
292C2×C8—42no—
293C2×C8—42no—
294C2×C8—1882no—
295C2×C8—1882no—
296C2×C8—1882no—
297C4⋊C4—944no—
298C4⋊C4—944no—
299C4⋊C4—1882no—
300C4⋊C4—1882no—
301C42—22no—
302C42—22no—
303C42—41no—
304C42—41no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23C2×(C2×D47)⋊C411yescharacteristic
310C23C4×Dic9412yes—
311C23M16×D4711yescharacteristic
312C23M16×D4711yescharacteristic
313C23#1309403212yes—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—44no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—942no—
335C2×C4—942no—
336C2×C4—3762no—
337C2×C4—3762no—
338C2×C4—1881no—
339C2×C4—1881no—
340C2×C4—1881no—
341C2×C4—1881no—
342C2×C4—1881no—
343C2×C4—1881no—
344C2×C4—1882no—
345C2×C4—1882no—
346C2×C4—1881no—
347C2×C4—1881no—
348C2×C4—1881no—
349C2×C4—1881no—
350C2×C4—1882no—
351C2×C4—1882no—
352C2×C4#1309393812yes—
353C2×C4#1309400312yes—
354C2×C4#1309401211yescharacteristic
355C2×C4#1309402411yescharacteristic
356C8—44no—
357C8—3762no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—22no—
363C22—22no—
364C22—22no—
365C22—22no—
366C22#1568902911yescharacteristic
367C22#1568908611yescharacteristic
368C22#1568909111yescharacteristic
369C22C2×#1309393811yescharacteristic
370C22#1568909611yescharacteristic
371C22#1568910511yescharacteristic
372C22#1568910511yescharacteristic
373C22#1568925112yes—
374C22#1568925112yes—
375C4—22no—
376C4—22no—
377C4—21no—
378C4—21no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—3761no—
383C4—3761no—
384C4—1882no—
385C4—1882no—
386C2—22no—
387C2—22no—
388C2#2024172011yescharacteristic
389C2#2024172411yescharacteristic
390C2#2024173711yescharacteristic
391C2#2024175811yescharacteristic
392C2#2024432811yescharacteristic
393C2#2024437311yescharacteristic
394C2#2024438111yescharacteristic
subgroupG/H
centerC23C2×(C2×D47)⋊C4
commutator, prime radicalC24×C47C22×C4
FrattiniC23×C4C22×D47
FittingC47×#1749C2
socleC23×C47C2×C22⋊C4
cosocleC23×C4×C47C23
hypercenter#1749D47
hypocenterC47#9881
LCSG ▷ C24×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1749

Complements

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

NH ≅ G/Ntype
220. C47#9881semidirect

Maximal subgroups

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

subgroupindex
C2×#156890072
#202433682
#202412302
C47×#17492
#988147