Finite Group Databasebeta

← #26119409

Subgroups — #26119409

Order 12032.

416 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 95 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#20246682C211yesmaximal, characteristic
2#20244370C211yesmaximal, characteristic
3#20241887C211yesmaximal, characteristic
4#20241291C211yesmaximal, characteristic
5#20241290C211yesmaximal, characteristic
6#20241216C211yesmaximal, characteristic
7C47×#1503C211yesmaximal, characteristic
8C2×C4×Dic94—21no—
9#15689176C2211yescharacteristic
10#15689147C2211yescharacteristic
11#15689057—21no—
12#15689056—21no—
13#15689044—21no—
14#15689043—21no—
15C4×Dic47⋊C4—21no—
16C4×C4⋊Dic47C2211yescharacteristic
17#15688969C2211yescharacteristic
18#15688882—21no—
19#15688882—21no—
20#15688860—21no—
21#15688860—21no—
22C47×#533C2211yescharacteristic
23C47×#431C2211yescharacteristic
24C4×C4⋊C4×C47C2211yescharacteristic
25C47×#328—21no—
26C47×#328—21no—
27C22×Dic94—21no—
28C2×#10625329—21no—
29C4×Dic94—42no—
30C4×Dic94—42no—
31C2×C4⋊Dic47—21no—
32C2×C4⋊Dic47—21no—
33C2×Dic47⋊C4—21no—
34C2×Dic47⋊C4—21no—
35C2×Dic47⋊C4—21no—
36C2×Dic47⋊C4—21no—
37C2×C4×Dic47—21no—
38C2×C4×Dic47D411yescharacteristic
39C2×C4×Dic47D411yescharacteristic
40C4⋊(C47⋊C8)—21no—
41C4⋊(C47⋊C8)—21no—
42C4⋊(C47⋊C8)—21no—
43C22⋊(C47⋊C8)—21no—
44C4×C47⋊C8—21no—
45C47⋊#95—21no—
46C47⋊#95—21no—
47C47⋊#95—21no—
48C47⋊#95—21no—
49C47⋊#95D411yescharacteristic
50C47⋊#95D411yescharacteristic
51C4⋊Q8×C47Q811yescharacteristic, complemented
52C4⋊Q8×C47Q811yescharacteristic, complemented
53#125×C47—21no—
54C22⋊Q8×C47—21no—
55C22⋊Q8×C47—21no—
56C4×Q8×C47—21no—
57C4×Q8×C47—21no—
58#117×C47—21no—
59C2×C4⋊C4×C47—21no—
60C2×C42×C47—21no—
61C2×C42×C47C2311yescharacteristic
62C4⋊C8×C47—21no—
63C22⋊C8×C47—21no—
64C4×C8×C47—21no—
65#95×C47D411yescharacteristic
66#95×C47D411yescharacteristic
67C2×Q8×C47—21no—
68C2×Q8×C47—21no—
69C22×C4×C47—21no—
70C22×C4×C47—21no—
71C22×C4×C47C2×D411yescharacteristic
72C22×C4×C47C2×D411yescharacteristic
73C22×C4×C47C2×D411yescharacteristic
74C22×Dic47—21no—
75C22×Dic47—21no—
76C22×Dic47—21no—
77C22×Dic47—21no—
78C2×Dic94—42no—
79C2×Dic94—42no—
80C2×Dic94—42no—
81C2×C8×C47—41no—
82C4⋊C4×C47—21no—
83C4⋊C4×C47—21no—
84C4⋊C4×C47—21no—
85C4⋊C4×C47—21no—
86C4⋊C4×C47—42no—
87C4⋊C4×C47—41no—
88C4⋊C4×C47—41no—
89C22⋊C4×C47—41no—
90C42×C47—41no—
91C42×C47—41no—
92C42×C47—41no—
93C42×C47C2×Q811yescharacteristic
94C42×C47#4111yescharacteristic
95C42×C47#4111yescharacteristic
96C42×C47#4111yescharacteristic
97C4⋊Dic47—42no—
98C4⋊Dic47—42no—
99Dic47⋊C4—42no—
100Dic47⋊C4—42no—
101Dic47⋊C4—42no—
102Dic47⋊C4—42no—
103C4×Dic47—21no—
104C4×Dic47—21no—
105C4×Dic47—41no—
106C4×Dic47—41no—
107C4×Dic47SD1612yes—
108C4×Dic47Q1612yes—
109#10625329—41no—
110#10625329—41no—
111C2×C47⋊C8—41no—
112C2×C47⋊C8—41no—
113C23×C47#12011yescharacteristic
114Q8×C47—81no—
115Q8×C47—81no—
116C2×C4×C47—22no—
117C2×C4×C47—41no—
118C2×C4×C47—41no—
119C2×C4×C47—41no—
120C2×C4×C47—41no—
121C2×C4×C47—41no—
122C2×C4×C47—41no—
123C2×C4×C47—41no—
124C2×C4×C47—41no—
125C2×C4×C47—41no—
126C2×C4×C47C22⋊Q811yescharacteristic
127C2×C4×C47C22⋊Q811yescharacteristic
128C2×C4×C47C22⋊Q811yescharacteristic
129C2×C4×C47#12411yescharacteristic
130C2×C4×C47#12411yescharacteristic
131C2×C4×C47#12411yescharacteristic
132C2×C4×C47C2×SD1611yescharacteristic
133C2×C4×C47C2×Q1611yescharacteristic
134C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C47#13711yescharacteristic
136C2×Dic47—22no—
137C2×Dic47—22no—
138C2×Dic47—22no—
139C2×Dic47—41no—
140C2×Dic47—41no—
141C2×Dic47—41no—
142C2×Dic47—41no—
143C2×Dic47—41no—
144C2×Dic47—41no—
145C2×Dic47—41no—
146C2×Dic47—41no—
147C2×Dic47—41no—
148Dic94—48no—
149C8×C47—81no—
150C47⋊C8—81no—
151C47⋊C8—81no—
152#10371—471nomaximal, Sylow
153C22×C47—21no—
154C22×C47—21no—
155C22×C47#39311yescharacteristic
156C22×C47#45011yescharacteristic
157C22×C47#45111yescharacteristic
158C4×C47—21no—
159C4×C47—21no—
160C4×C47—21no—
161C4×C47—21no—
162C4×C47—42no—
163C4×C47—81no—
164C4×C47—81no—
165C4×C47—81no—
166C4×C47#47511yescharacteristic
167C4×C47#47711yescharacteristic
168C4×C47#48711yescharacteristic
169C4×C47#48911yescharacteristic
170Dic47—42no—
171Dic47—42no—
172Dic47—42no—
173Dic47—81no—
174#2399—471no—
175#1995—471no—
176#1503—471no—
177#1503D4711yescharacteristic
178#1303—471no—
179#1303—471no—
180#1274—471no—
181C2×C47—21no—
182C2×C47—21no—
183C2×C47#202411yescharacteristic
184C2×C47#203111yescharacteristic
185C2×C47#203111yescharacteristic
186#533C2×D4711yescharacteristic
187C2×C4×Q8—941no—
188#431—471no—
189#431C2×D4711yescharacteristic
190#423—471no—
191#398—941no—
192#398—941no—
193#395—941no—
194#395—941no—
195C4×C4⋊C4—471no—
196C4×C4⋊C4—941no—
197C4×C4⋊C4C2×D4711yescharacteristic
198#376—471no—
199#339—941no—
200#339—941no—
201#328—21no—
202#328—21no—
203#328—941no—
204#328—941no—
205C47#1037111yescharacteristic, complemented, Sylow
206C22×Q8—941no—
207C2×M16—941no—
208C4⋊Q8Dic9411yescharacteristic, complemented
209C4⋊Q8Dic9411yescharacteristic, complemented
210#125—21no—
211C22⋊Q8—21no—
212C22⋊Q8—21no—
213C4×Q8—21no—
214C4×Q8—21no—
215C4×Q8—1882no—
216C4×Q8—1882no—
217#117—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—941no—
220C2×C4⋊C4—941no—
221C2×C4⋊C4—941no—
222C2×C4⋊C4—941no—
223C2×C4⋊C4—941no—
224C2×C4⋊C4—941no—
225C2×C42—21no—
226C2×C42—471no—
227C2×C42—471no—
228C2×C42—941no—
229C2×C42C22×D4711yescharacteristic
230C4⋊C8—21no—
231C4⋊C8—941no—
232C4⋊C8—941no—
233C4⋊C8—941no—
234C22⋊C8—21no—
235C22⋊C8—941no—
236C4×C8—21no—
237C4×C8—941no—
238#95—471no—
239#95—471no—
240#95—941no—
241#95—941no—
242#95—941no—
243#95—941no—
244#95C22⋊D4711yescharacteristic
245#95C22⋊D4711yescharacteristic
246C2×Q8—21no—
247C2×Q8—21no—
248C2×Q8—1882no—
249C2×Q8—1882no—
250C2×Q8—1882no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—941no—
254C22×C4—941no—
255C22×C4—941no—
256C22×C4—941no—
257C22×C4D4×D4711yescharacteristic
258C22×C4D4×D4711yescharacteristic
259C22×C4C2×C22⋊D4711yescharacteristic
260M16—1881no—
261M16—1881no—
262C2×C8—41no—
263C2×C8—1881no—
264C2×C8—1881no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—42no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—1882no—
273C4⋊C4—1882no—
274C4⋊C4—1882no—
275C4⋊C4—1882no—
276C4⋊C4—1882no—
277C4⋊C4—1882no—
278C22⋊C4—41no—
279C42—41no—
280C42—41no—
281C42—41no—
282C42—472no—
283C42—472no—
284C42—941no—
285C42—941no—
286C42—1881no—
287C42—1881no—
288C42C2×Dic9411yescharacteristic
289C42#1062535011yescharacteristic
290C42#1062535211yescharacteristic
291C42#1062535211yescharacteristic
292C23#1309399211yescharacteristic
293Q8—81no—
294Q8—81no—
295Q8—1888no—
296C2×C4—22no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—942no—
307C2×C4—942no—
308C2×C4—942no—
309C2×C4—1881no—
310C2×C4—1881no—
311C2×C4—1881no—
312C2×C4—1881no—
313C2×C4—1881no—
314C2×C4—1881no—
315C2×C4—1881no—
316C2×C4—1881no—
317C2×C4—1881no—
318C2×C4#1309400111yescharacteristic
319C2×C4#1309400111yescharacteristic
320C2×C4#1309400311yescharacteristic
321C2×C4#1309401011yescharacteristic
322C2×C4#1309401011yescharacteristic
323C2×C4#1309401111yescharacteristic
324C2×C4SD16×D4711yescharacteristic
325C2×C4Q16×D4711yescharacteristic
326C2×C4#1309405111yescharacteristic
327C2×C4#1309405611yescharacteristic
328C8—81no—
329C8—3761no—
330C8—3761no—
331C22—21no—
332C22—21no—
333C22#1568903511yescharacteristic
334C22#1568927211yescharacteristic
335C22#1568927711yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—42no—
341C4—81no—
342C4—81no—
343C4—81no—
344C4—3761no—
345C4—1882no—
346C4—1882no—
347C4—1882no—
348C4#1568940611yescharacteristic
349C4#1568941611yescharacteristic
350C4#1568947211yescharacteristic
351C4#1568948411yescharacteristic
352C2—21no—
353C2—21no—
354C2#2024452711yescharacteristic
355C2#2024456011yescharacteristic
356C2#2024456211yescharacteristic
subgroupG/H
centerC2×C4#13094010
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1503C2
socleC22×C47#393
prime radicalC23×C47#120
hypercenter#1503D47
hypocenterC47#10371
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1503

Complements

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

NH ≅ G/Ntype
51. C4⋊Q8×C47Q8semidirect
52. C4⋊Q8×C47Q8semidirect
205. C47#10371semidirect
208. C4⋊Q8Dic94semidirect
209. C4⋊Q8Dic94semidirect

Maximal subgroups

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

subgroupindex
#202466822
#202443702
#202418872
#202412912
#202412902
#202412162
C47×#15032
#1037147