Finite Group Databasebeta

← #26107348

Subgroups — #26107348

Order 12032.

482 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252100C211yesmaximal, characteristic
2#20243253C211yesmaximal, characteristic, complemented
3#20241883C211yesmaximal, characteristic
4#20241672C211yesmaximal, characteristic, complemented
5#20241290C211yesmaximal, characteristic, complemented
6#20241285C211yesmaximal, characteristic, complemented
7C47×#1540C211yesmaximal, characteristic
8C2×#13094031—21no—
9#15689201—21no—
10#15689201C412yescomplemented
11D4×C47⋊C8—21no—
12D4×C47⋊C8C412yescomplemented
13#15689176C2211yescharacteristic
14#15689147C2211yescharacteristic
15#15689090—21no—
16C2×C4×C47⋊C8C2211yescharacteristic
17C2×C8×Dic47—21no—
18C4×C4⋊Dic47C2211yescharacteristic
19#15688877—21no—
20#15688857C414yes—
21#15688845—21no—
22C8×C47⋊C8—21no—
23C47×#532C2211yescharacteristic
24C47×#431C2211yescharacteristic
25C2×C4⋊C8×C47C2211yescharacteristic
26C47×#332C412yescomplemented
27C47×#331C412yescomplemented
28#13094031—42no—
29#13094031—42no—
30C2×#10625329—21no—
31C2×#10625329—22no—
32C22×C47⋊C8—22no—
33C22×C47⋊C8D411yescharacteristic
34C22×C47⋊C8D411yescharacteristic
35C2×C4⋊Dic47—21no—
36C2×C4×Dic47—21no—
37C4⋊(C47⋊C8)—21no—
38C4⋊(C47⋊C8)—21no—
39C4⋊(C47⋊C8)C2×C412yes—
40C22⋊(C47⋊C8)—22no—
41C22⋊(C47⋊C8)—22no—
42C22⋊(C47⋊C8)C2×C412yes—
43C4×C47⋊C8—21no—
44C4×C47⋊C8C2×C411yescharacteristic
45C4×C47⋊C8C2×C411yescharacteristic
46C4×C47⋊C8D411yescharacteristic
47C4×C47⋊C8D411yescharacteristic
48C8×Dic47—42no—
49C47⋊#95C2×C412yes—
50C2×#41×C47—21no—
51C22×C8×C47—21no—
52C4⋊Q8×C47C2×C411yescharacteristic
53#127×C47C2×C411yescharacteristic
54#124×C47—21no—
55#121×C47—21no—
56#121×C47C2×C412yes—
57C4×D4×C47—21no—
58C4×D4×C47C2×C412yes—
59C2×C42×C47C2311yescharacteristic
60C4⋊C8×C47—21no—
61C4⋊C8×C47C2×C412yes—
62C4⋊C8×C47C2×C412yes—
63C22⋊C8×C47—21no—
64C4×C8×C47—21no—
65#41×C47—41no—
66#41×C47—41no—
67#41×C47—41no—
68#41×C47—41no—
69C2×Q8×C47—21no—
70C2×D4×C47—22no—
71C2×D4×C47—21no—
72C2×D4×C47—21no—
73C2×D4×C47C4212yes—
74C22×C4×C47—22no—
75C22×C4×C47C22×C411yescharacteristic
76C22×C4×C47C2×D411yescharacteristic
77C22×C4×C47#4111yescharacteristic
78C22×Dic47—22no—
79C2×C8×C47—22no—
80C2×C8×C47—22no—
81C2×C8×C47—41no—
82C2×C8×C47—41no—
83C4⋊C4×C47—21no—
84C4⋊C4×C47C4212yes—
85C22⋊C4×C47—22no—
86C22⋊C4×C47—22no—
87C42×C47C22×C411yescharacteristic
88C42×C47C22×C411yescharacteristic
89C42×C47C2×D411yescharacteristic
90C42×C47#4111yescharacteristic
91C4⋊Dic47—24no—
92C4×Dic47—41no—
93C4×Dic47—41no—
94#10625329—41no—
95#10625329—41no—
96#10625329—44no—
97C2×C47⋊C8—21no—
98C2×C47⋊C8—21no—
99C2×C47⋊C8—22no—
100C2×C47⋊C8—22no—
101C2×C47⋊C8—44no—
102C2×C47⋊C8C22⋊C411yescharacteristic
103C2×C47⋊C8C22⋊C411yescharacteristic
104C2×C47⋊C8C22⋊C411yescharacteristic
105C2×C47⋊C8C22⋊C411yescharacteristic
106C2×C47⋊C8D812yes—
107C2×C47⋊C8SD1612yes—
108C23×C47—22no—
109C23×C47C4×D411yescharacteristic
110Q8×C47—41no—
111Q8×C47—41no—
112D4×C47—42no—
113D4×C47—42no—
114D4×C47—42no—
115D4×C47—41no—
116D4×C47—41no—
117D4×C47—42no—
118C2×C4×C47—22no—
119C2×C4×C47—22no—
120C2×C4×C47—41no—
121C2×C4×C47—42no—
122C2×C4×C47—42no—
123C2×C4×C47C2×C4211yescharacteristic
124C2×C4×C47C2×C22⋊C411yescharacteristic
125C2×C4×C47#11711yescharacteristic
126C2×C4×C47C4×D411yescharacteristic
127C2×C4×C47C4×D411yescharacteristic
128C2×C4×C47C4×D411yescharacteristic
129C2×C4×C47C2×D811yescharacteristic
130C2×C4×C47C2×SD1611yescharacteristic
131C2×C4×C47#13511yescharacteristic
132C2×C4×C47#13511yescharacteristic
133C2×Dic47—24no—
134C2×Dic47—42no—
135C2×Dic47—42no—
136C8×C47—42no—
137C8×C47—42no—
138C47⋊C8—21no—
139C47⋊C8—21no—
140C47⋊C8—42no—
141C47⋊C8—42no—
142C47⋊C8#10212yes—
143C47⋊C8#10212yes—
144#8251—471nomaximal, Sylow
145C22×C47—21no—
146C22×C47—21no—
147C22×C47—42no—
148C22×C47—42no—
149C22×C47—42no—
150C22×C47C4×C22⋊C411yescharacteristic
151C22×C47C4×D811yescharacteristic
152C22×C47C4×SD1611yescharacteristic
153C4×C47—21no—
154C4×C47—21no—
155C4×C47—21no—
156C4×C47—42no—
157C4×C47C2×#10211yescharacteristic
158C4×C47#41611yescharacteristic
159C4×C47C4×D811yescharacteristic
160C4×C47C4×SD1611yescharacteristic
161C4×C47#44312yes—
162Dic47—44no—
163#2931—471no—
164C8×C4⋊C4—471no—
165#1540D4711yescharacteristic
166#1502—471no—
167#1450—471no—
168#1303—471no—
169#1301—471no—
170C2×C47—21no—
171C2×C47—21no—
172C2×C47—82no—
173C2×C47#175711yescharacteristic
174C2×C47C4×#10211yescharacteristic
175C2×C47#176411yescharacteristic
176C2×#131—941no—
177#532C2×D4711yescharacteristic
178#436—472no—
179#436—941no—
180C8×D4—472no—
181C8×D4—941no—
182#431—471no—
183#431C2×D4711yescharacteristic
184#423—471no—
185C2×C4⋊C8C2×D4711yescharacteristic
186#408—941no—
187C2×C4×C8—471no—
188C2×C4×C8—941no—
189C4×C4⋊C4—471no—
190#336—941no—
191#332Dic4712yescomplemented
192#331Dic4712yescomplemented
193#327—474no—
194#322—941no—
195C82—941no—
196C47#825111yescharacteristic, complemented, Sylow
197C2×#41—21no—
198#131—1882no—
199#131—1882no—
200C2×M16—942no—
201C2×M16—941no—
202C22×C8—21no—
203C22×C8—471no—
204C22×C8—471no—
205C22×C8—942no—
206C4⋊Q8C2×Dic4711yescharacteristic
207#127C2×Dic4711yescharacteristic
208#124—21no—
209#121—21no—
210#121C4×D4712yes—
211C4×D4—21no—
212C4×D4C4×D4712yes—
213C2×C4⋊C4—941no—
214C2×C42—941no—
215C2×C42C22×D4711yescharacteristic
216C4⋊C8—21no—
217C4⋊C8—472no—
218C4⋊C8—941no—
219C4⋊C8—941no—
220C4⋊C8C2×Dic4712yes—
221C4⋊C8C2×Dic4712yes—
222C22⋊C8—21no—
223C22⋊C8—472no—
224C22⋊C8—942no—
225C22⋊C8—942no—
226C4×C8—21no—
227C4×C8—471no—
228C4×C8—471no—
229C4×C8—471no—
230C4×C8—471no—
231C4×C8—941no—
232C4×C8—1882no—
233#95—472no—
234#41—41no—
235#41—41no—
236#41—41no—
237#41—41no—
238C2×Q8—21no—
239C2×D4—22no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4C4×Dic4712yes—
243C22×C4—22no—
244C22×C4—942no—
245C22×C4C2×C4×D4711yescharacteristic
246C22×C4D4×D4711yescharacteristic
247C22×C4#1062535211yescharacteristic
248M16—1884no—
249M16—1881no—
250M16—1881no—
251C2×C8—22no—
252C2×C8—22no—
253C2×C8—41no—
254C2×C8—41no—
255C2×C8—471no—
256C2×C8—471no—
257C2×C8—472no—
258C2×C8—472no—
259C2×C8—471no—
260C2×C8—471no—
261C2×C8—941no—
262C2×C8—941no—
263C2×C8—942no—
264C2×C8—942no—
265C2×C8—1884no—
266C4⋊C4—21no—
267C4⋊C4—944no—
268C4⋊C4C4×Dic4712yes—
269C22⋊C4—22no—
270C22⋊C4—22no—
271C42—1881no—
272C42—1881no—
273C42C2×C4×D4711yescharacteristic
274C42D4×D4711yescharacteristic
275C42#1062535211yescharacteristic
276C42C22×Dic4711yescharacteristic
277C23—22no—
278C23(C22⋊D47)⋊C411yescharacteristic
279Q8—41no—
280Q8—41no—
281D4—42no—
282D4—42no—
283D4—42no—
284D4—42no—
285D4—41no—
286D4—41no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—41no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—944no—
293C2×C4—1882no—
294C2×C4—1882no—
295C2×C4C2×C4×Dic4711yescharacteristic
296C2×C4C22⋊C4×D4711yescharacteristic
297C2×C4#1309398011yescharacteristic
298C2×C4(C22⋊D47)⋊C411yescharacteristic
299C2×C4D4×Dic4711yescharacteristic
300C2×C4D4×Dic4711yescharacteristic
301C2×C4D8×D4711yescharacteristic
302C2×C4SD16×D4711yescharacteristic
303C2×C4#1309404311yescharacteristic
304C2×C4#1309404511yescharacteristic
305C8—42no—
306C8—42no—
307C8—472no—
308C8—472no—
309C8—941no—
310C8—941no—
311C8—1882no—
312C8—1882no—
313C22—21no—
314C22—21no—
315C22—42no—
316C22—42no—
317C22—42no—
318C22C22⋊C4×Dic4711yescharacteristic
319C22#1568920311yescharacteristic
320C22#1568921411yescharacteristic
321C4—21no—
322C4—21no—
323C4—21no—
324C4—42no—
325C4—1884no—
326C4#102×D4711yescharacteristic
327C4#1568911611yescharacteristic
328C4D8×Dic4711yescharacteristic
329C4SD16×Dic4711yescharacteristic
330C4#1568924012yes—
331C2—21no—
332C2—21no—
333C2—82no—
334C2#2024319111yescharacteristic
335C2#102×Dic4711yescharacteristic
336C2#2024322811yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D47
commutatorC2×C4×C47C2×C42
FrattiniC2×C42C22×D47
FittingC47×#1540C2
socleC22×C47C4×C22⋊C4
prime radicalC47×#532C22
cosocleC2×C42×C47C23
hypercenter#1540D47
hypocenterC47#8251
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1540

Complements

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

NH ≅ G/Ntype
2. #20243253C2semidirect
4. #20241672C2semidirect
5. #20241290C2semidirect
6. #20241285C2semidirect
10. #15689201C4semidirect
12. D4×C47⋊C8C4semidirect
26. C47×#332C4semidirect
27. C47×#331C4semidirect
191. #332Dic47semidirect
192. #331Dic47semidirect
196. C47#8251semidirect

Maximal subgroups

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

subgroupindex
#202521002
#202432532
#202418832
#202416722
#202412902
#202412852
C47×#15402
#825147