Finite Group Databasebeta

← #26119626

Subgroups — #26119626

Order 12032.

620 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20249502C211yesmaximal, characteristic
2#20243695C212yesmaximal
3C2×#15688859C212yesmaximal
4#20241231C211yesmaximal, characteristic
5C47×#1444C211yesmaximal, characteristic
6C2×#13094003C2212yes—
7C2×#13093947—22no—
8C2×C22⋊(C47⋊C8)C2212yes—
9#15689055—22no—
10#15689044—22no—
11#15688983—21no—
12#15688983—21no—
13#15688885—22no—
14#15688859—24no—
15C22×C4⋊C4×C47—21no—
16C22×C4⋊C4×C47C2211yescharacteristic
17C2×#95×C47—21no—
18C2×#95×C47C2211yescharacteristic
19C2×#95×C47C2211yescharacteristic
20C22×Dic94D412yes—
21C22×C47⋊C8—22no—
22#13094003—22no—
23#13094003—22no—
24#13094003—22no—
25#13094003—22no—
26C2×C4⋊Dic47—21no—
27C2×C4⋊Dic47—21no—
28C2×C4⋊Dic47—21no—
29C2×C4⋊Dic47—21no—
30C2×C4⋊Dic47D412yes—
31C2×Dic47⋊C4—22no—
32C2×C22⋊Dic47—22no—
33#13093947—44no—
34C22⋊(C47⋊C8)—22no—
35C22⋊(C47⋊C8)—22no—
36C47⋊#95—22no—
37C47⋊#95—22no—
38C23×C4×C47—21no—
39C23×C4×C47—21no—
40C23×C4×C47D411yescharacteristic
41C23×C4×C47D411yescharacteristic
42C23×C4×C47C2311yescharacteristic
43C2×C4⋊C4×C47—22no—
44C2×C4⋊C4×C47—42no—
45C2×C4⋊C4×C47—42no—
46C2×C4⋊C4×C47—42no—
47C2×C4⋊C4×C47—42no—
48#95×C47—22no—
49#95×C47—21no—
50#95×C47—42no—
51#95×C47D412yes—
52C24×C47C2×D411yescharacteristic
53C22×C4×C47—22no—
54C22×C4×C47—22no—
55C22×C4×C47—21no—
56C22×C4×C47—21no—
57C22×C4×C47—22no—
58C22×C4×C47—21no—
59C22×C4×C47—21no—
60C22×C4×C47—22no—
61C22×C4×C47—41no—
62C22×C4×C47—41no—
63C22×C4×C47—41no—
64C22×C4×C47—41no—
65C22×C4×C47—41no—
66C22×C4×C47—41no—
67C22×C4×C47—41no—
68C22×C4×C47—41no—
69C22×C4×C47—41no—
70C22×C4×C47—41no—
71C22×C4×C47—41no—
72C22×C4×C47—41no—
73C22×C4×C47—41no—
74C22×C4×C47—41no—
75C22×C4×C47—41no—
76C22×C4×C47—41no—
77C22×C4×C47SD1612yes—
78C22×C4×C47Q1612yes—
79C22×C4×C47C2×D412yes—
80C22×C4×C47C2×D411yescharacteristic
81C22×C4×C47#4112yes—
82C22×C4×C47#4111yescharacteristic
83C22×Dic47—22no—
84C22×Dic47—22no—
85C2×Dic94—22no—
86C2×Dic94—22no—
87C2×Dic94—42no—
88C2×Dic94—42no—
89C4⋊C4×C47—24no—
90C4⋊C4×C47—42no—
91C4⋊C4×C47—48no—
92C22⋊Dic47—42no—
93C22⋊Dic47—42no—
94C4⋊Dic47—22no—
95C4⋊Dic47—22no—
96C4⋊Dic47—81no—
97C4⋊Dic47—81no—
98C4⋊Dic47—81no—
99C4⋊Dic47—81no—
100Dic47⋊C4—42no—
101Dic47⋊C4—42no—
102C2×C47⋊C8—42no—
103C2×C47⋊C8—42no—
104C2×C47⋊C8—42no—
105C23×C47—21no—
106C23×C47—21no—
107C23×C47—21no—
108C23×C47—21no—
109C23×C47#12011yescharacteristic
110C23×C47#12111yescharacteristic
111C23×C47#12411yescharacteristic
112C23×C47C2×SD1611yescharacteristic
113C23×C47C2×Q1611yescharacteristic
114C23×C47#13711yescharacteristic
115C23×C47#13711yescharacteristic
116C2×C4×C47—22no—
117C2×C4×C47—22no—
118C2×C4×C47—24no—
119C2×C4×C47—22no—
120C2×C4×C47—22no—
121C2×C4×C47—41no—
122C2×C4×C47—41no—
123C2×C4×C47—42no—
124C2×C4×C47—42no—
125C2×C4×C47—42no—
126C2×C4×C47—42no—
127C2×C4×C47—42no—
128C2×C4×C47—42no—
129C2×C4×C47—41no—
130C2×C4×C47—41no—
131C2×C4×C47—41no—
132C2×C4×C47—41no—
133C2×C4×C47—42no—
134C2×C4×C47—42no—
135C2×C4×C47—42no—
136C2×C4×C47—42no—
137C2×C4×C47—42no—
138C2×C4×C47—42no—
139C2×C4×C47—81no—
140C2×C4×C47—81no—
141C2×C4×C47—81no—
142C2×C4×C47—81no—
143C2×C4×C47—81no—
144C2×C4×C47—81no—
145C2×C4×C47#12112yes—
146C2×C4×C47#12312yes—
147C2×Dic47—42no—
148C2×Dic47—42no—
149C2×Dic47—42no—
150C2×Dic47—42no—
151C2×Dic47—42no—
152C2×Dic47—42no—
153Dic94—44no—
154Dic94—82no—
155C47⋊C8—82no—
156#10406—471nomaximal, Sylow
157C22×C47—21no—
158C22×C47—21no—
159C22×C47—21no—
160C22×C47—21no—
161C22×C47—21no—
162C22×C47—21no—
163C22×C47—21no—
164C22×C47—21no—
165C22×C47—21no—
166C22×C47—21no—
167C22×C47—21no—
168C22×C47—21no—
169C22×C47#39411yescharacteristic
170C22×C47#44811yescharacteristic
171C22×C47#45111yescharacteristic
172C22×C47#45311yescharacteristic
173C22×C47#45611yescharacteristic
174C22×C47B(4,𝔽2)11yescharacteristic
175C22×C47#45811yescharacteristic
176C22×C47#46111yescharacteristic
177C22×C47#46211yescharacteristic
178C22×C47#48711yescharacteristic
179C22×C47#49111yescharacteristic
180C4×C47—22no—
181C4×C47—22no—
182C4×C47—44no—
183C4×C47—42no—
184C4×C47—42no—
185C4×C47—82no—
186Dic47—82no—
187Dic47—82no—
188#2659—471no—
189#1872—472no—
190C2×#328—472no—
191#1444D4711yescharacteristic
192#1280—471no—
193C2×C47—21no—
194C2×C47—21no—
195C2×C47—21no—
196C2×C47—21no—
197C2×C47#159611yescharacteristic
198C2×C47#160511yescharacteristic
199C2×C47#161111yescharacteristic
200C2×C47#161411yescharacteristic
201C2×C47#203911yescharacteristic
202C2×C47#204311yescharacteristic
203C2×C47#204411yescharacteristic
204C2×C22⋊Q8—472no—
205C22×C4⋊C4—21no—
206C22×C4⋊C4C2×D4711yescharacteristic
207C2×#103—942no—
208C2×C22⋊C8—472no—
209#398—942no—
210#395—942no—
211#380—941no—
212#380—941no—
213C2×#95—21no—
214C2×#95C2×D4711yescharacteristic
215C2×#95C2×D4711yescharacteristic
216#340—942no—
217#328—944no—
218C47#1040611yescharacteristic, complemented, Sylow
219C22×Q8—472no—
220C23×C4—21no—
221C23×C4—21no—
222C23×C4C22⋊D4711yescharacteristic
223C23×C4C22⋊D4711yescharacteristic
224C23×C4C22×D4711yescharacteristic
225C22×C8—942no—
226C22⋊Q8—942no—
227C22⋊Q8—942no—
228C22⋊Q8—942no—
229C22⋊Q8—942no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—42no—
232C2×C4⋊C4—42no—
233C2×C4⋊C4—42no—
234C2×C4⋊C4—42no—
235C2×C4⋊C4—472no—
236C2×C4⋊C4—941no—
237C2×C4⋊C4—941no—
238C2×C4⋊C4—941no—
239C2×C4⋊C4—941no—
240C2×C4⋊C4—942no—
241C2×C22⋊C4—942no—
242#103—1884no—
243C22⋊C8—942no—
244C22⋊C8—942no—
245#95—21no—
246#95—22no—
247#95—42no—
248#95—942no—
249#95—942no—
250#95D18812yes—
251C24C2×C22⋊D4711yescharacteristic
252C2×Q8—942no—
253C2×Q8—942no—
254C2×Q8—1882no—
255C2×Q8—1882no—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—22no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—22no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—942no—
281C22×C4—942no—
282C22×C4#1062533512yes—
283C22×C4#1062533712yes—
284C22×C4C2×D18811yescharacteristic
285C22×C4#1062535011yescharacteristic
286C22×C4D4×D4712yes—
287C22×C4#1062535412yes—
288C2×C8—1882no—
289C2×C8—1882no—
290C2×C8—1882no—
291C4⋊C4—24no—
292C4⋊C4—42no—
293C4⋊C4—48no—
294C4⋊C4—942no—
295C4⋊C4—942no—
296C4⋊C4—3761no—
297C4⋊C4—3761no—
298C4⋊C4—3761no—
299C4⋊C4—3761no—
300C4⋊C4—1882no—
301C4⋊C4—1882no—
302C22⋊C4—1882no—
303C22⋊C4—1882no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23#1309399211yescharacteristic
309C23#1309399811yescharacteristic
310C23#1309401311yescharacteristic
311C23C2×#1062533511yescharacteristic
312C23C2×#1062533711yescharacteristic
313C23#1309405411yescharacteristic
314C23#1309405411yescharacteristic
315Q8—3762no—
316Q8—1884no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—24no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4—1882no—
347C2×C4—1882no—
348C2×C4—1882no—
349C2×C4—1882no—
350C2×C4—1882no—
351C2×C4—1882no—
352C2×C4#1309399912yes—
353C2×C4#1309400912yes—
354C8—3762no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22#1568904011yescharacteristic
368C22#1568926111yescharacteristic
369C22#1568927811yescharacteristic
370C22#1568929011yescharacteristic
371C22#1568930511yescharacteristic
372C22#1568930911yescharacteristic
373C22#1568931211yescharacteristic
374C22#1568932811yescharacteristic
375C22#1568933311yescharacteristic
376C22#1568947511yescharacteristic
377C22#1568949311yescharacteristic
378C4—22no—
379C4—22no—
380C4—44no—
381C4—42no—
382C4—42no—
383C4—82no—
384C4—3762no—
385C4—3762no—
386C2—21no—
387C2—21no—
388C2—21no—
389C2—21no—
390C2#2024231011yescharacteristic
391C2#2024236111yescharacteristic
392C2#2024239511yescharacteristic
393C2#2024241211yescharacteristic
394C2#2024461211yescharacteristic
395C2#2024463411yescharacteristic
396C2#2024463911yescharacteristic
subgroupG/H
centerC23#13093992
commutator, cosocleC23×C4×C47C23
FrattiniC23×C4C22×D47
FittingC47×#1444C2
socleC23×C47#120
prime radicalC24×C47C2×D4
hypercenter#1444D47
hypocenterC47#10406
LCSG ▷ C23×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1444

Complements

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

NH ≅ G/Ntype
218. C47#10406semidirect

Maximal subgroups

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

subgroupindex
#202495022
#202436952
C2×#156888592
#202412312
C47×#14442
#1040647