Finite Group Databasebeta

← #26110594

Subgroups — #26110594

Order 12032.

438 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20251956C211yesmaximal, characteristic
2#20243408C211yesmaximal, characteristic
3#20242159C211yesmaximal, characteristic, complemented
4#20242144C211yesmaximal, characteristic, complemented
5#20241290C211yesmaximal, characteristic, complemented
6#20241228C211yesmaximal, characteristic, complemented
7C47×#1476C211yesmaximal, characteristic
8C2×#13094031—21no—
9#15689150—22no—
10#15689150—21no—
11#15689147—21no—
12#15689147C2211yescharacteristic
13#15689147C2211yescharacteristic
14C2×C4⋊(C47⋊C8)—21no—
15C2×C4⋊(C47⋊C8)C2211yescharacteristic
16C2×#13093951—21no—
17C4×C4⋊Dic47C2211yescharacteristic
18#15688882—21no—
19#15688874—22no—
20#15688874—21no—
21#15688874—21no—
22C4×#41×C47C2211yescharacteristic
23C47×#431C2211yescharacteristic
24C2×C4×C8×C47C2211yescharacteristic
25C47×Q8⋊C8C411yescharacteristic, complemented
26C47×Q8⋊C8C411yescharacteristic, complemented
27C47×D4⋊C8C411yescharacteristic, complemented
28C47×D4⋊C8C411yescharacteristic, complemented
29#13094031—42no—
30#13094031—42no—
31C2×#10625329—22no—
32C2×#10625329—21no—
33C2×#10625329—21no—
34C22×C47⋊C8—22no—
35C22×C47⋊C8—21no—
36C2×C4⋊Dic47—21no—
37C2×C4×Dic47—21no—
38C4⋊(C47⋊C8)—22no—
39C4⋊(C47⋊C8)—22no—
40C4⋊(C47⋊C8)—21no—
41C4⋊(C47⋊C8)—21no—
42C4⋊(C47⋊C8)—21no—
43C4⋊(C47⋊C8)—21no—
44C4⋊(C47⋊C8)D411yescharacteristic
45C4⋊(C47⋊C8)D411yescharacteristic
46C4⋊(C47⋊C8)D412yes—
47#13093951—42no—
48C47⋊#95—21no—
49C2×#41×C47D411yescharacteristic
50C22×C8×C47—21no—
51C4×Q8×C47C2×C411yescharacteristic
52C4×Q8×C47Q811yescharacteristic
53C4×D4×C47—21no—
54C4×D4×C47—21no—
55C4×D4×C47C2×C411yescharacteristic
56C4×D4×C47Q811yescharacteristic
57#117×C47—21no—
58#117×C47D411yescharacteristic
59C2×C42×C47—21no—
60C2×C42×C47C2311yescharacteristic
61C4⋊C8×C47C2×C411yescharacteristic
62C4⋊C8×C47C2×C411yescharacteristic
63C22⋊C8×C47—21no—
64C4×C8×C47—21no—
65C4×C8×C47—21no—
66C4×C8×C47C2×C411yescharacteristic
67C4×C8×C47C2×C411yescharacteristic
68#41×C47—21no—
69#41×C47—21no—
70#41×C47SD1612yes—
71#41×C47SD1612yes—
72C2×Q8×C47C4⋊C411yescharacteristic
73C2×D4×C47—21no—
74C2×D4×C47C4⋊C411yescharacteristic
75C22×C4×C47—21no—
76C22×C4×C47—21no—
77C22×C4×C47—21no—
78C22×C4×C47C2×D411yescharacteristic
79C22×C4×C47#4111yescharacteristic
80C22×C4×C47#4111yescharacteristic
81C22×Dic47—41no—
82C2×C8×C47—21no—
83C2×C8×C47—21no—
84C2×C8×C47—21no—
85C2×C8×C47—21no—
86C2×C8×C47—42no—
87C4⋊C4×C47—21no—
88C4⋊C4×C47—21no—
89C4⋊C4×C47C4⋊C411yescharacteristic
90C4⋊C4×C47C4⋊C411yescharacteristic
91C22⋊C4×C47—21no—
92C22⋊C4×C47—21no—
93C22⋊C4×C47—21no—
94C42×C47—21no—
95C42×C47—21no—
96C42×C47—21no—
97C42×C47C22×C411yescharacteristic
98C42×C47C2×D411yescharacteristic
99C42×C47C2×D411yescharacteristic
100C42×C47C2×Q811yescharacteristic
101C4⋊Dic47—22no—
102C4⋊Dic47—41no—
103C4×Dic47—41no—
104C4×Dic47—41no—
105#10625329—44no—
106#10625329—41no—
107#10625329—41no—
108#10625329—41no—
109#10625329—41no—
110C2×C47⋊C8—21no—
111C2×C47⋊C8—22no—
112C2×C47⋊C8—21no—
113C2×C47⋊C8—44no—
114C2×C47⋊C8—41no—
115C2×C47⋊C8—41no—
116C2×C47⋊C8—41no—
117C23×C47—21no—
118C23×C47#12311yescharacteristic
119Q8×C47—21no—
120Q8×C47#10612yes—
121D4×C47—22no—
122D4×C47—22no—
123D4×C47—21no—
124D4×C47#10612yes—
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47—22no—
129C2×C4×C47—22no—
130C2×C4×C47—21no—
131C2×C4×C47—21no—
132C2×C4×C47—41no—
133C2×C4×C47—41no—
134C2×C4×C47—41no—
135C2×C4×C47—81no—
136C2×C4×C47C2×C4⋊C411yescharacteristic
137C2×C4×C47C4×D411yescharacteristic
138C2×C4×C47C4×D411yescharacteristic
139C2×C4×C47#12011yescharacteristic
140C2×C4×C47C22⋊Q811yescharacteristic
141C2×C4×C47C22⋊Q811yescharacteristic
142C2×C4×C47C2×SD1611yescharacteristic
143C2×C4×C47C2×SD1611yescharacteristic
144C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C47#13711yescharacteristic
146C2×Dic47—42no—
147C2×Dic47—81no—
148C2×Dic47—81no—
149C8×C47—22no—
150C8×C47—41no—
151C8×C47—41no—
152C8×C47—41no—
153C47⋊C8—41no—
154C47⋊C8—42no—
155C47⋊C8—41no—
156C47⋊C8—81no—
157#8904—471nomaximal, Sylow
158C22×C47—21no—
159C22×C47—21no—
160C22×C47—22no—
161C22×C47—41no—
162C22×C47—41no—
163C22×C47#38511yescharacteristic
164C22×C47#48111yescharacteristic
165C22×C47#48311yescharacteristic
166C4×C47—22no—
167C4×C47—21no—
168C4×C47—21no—
169C4×C47—21no—
170C4×C47—41no—
171C4×C47—41no—
172C4×C47C2×#10611yescharacteristic
173C4×C47#42811yescharacteristic
174C4×C47#44311yescharacteristic
175C4×C47#44411yescharacteristic
176C4×C47#44811yescharacteristic
177C4×C47#45011yescharacteristic
178Dic47—82no—
179#2906—471no—
180#1806—471no—
181#1570—471no—
182#1566—471no—
183#1476D4711yescharacteristic
184#1303—471no—
185#1279—471no—
186C2×C47—21no—
187C2×C47—21no—
188C2×C47—42no—
189C2×C47#185311yescharacteristic
190C2×C47#186111yescharacteristic
191C2×C47#186611yescharacteristic
192C2×#131—941no—
193C4×#41C2×D4711yescharacteristic
194#431C2×D4711yescharacteristic
195#424—942no—
196#424—941no—
197#423—471no—
198#423—471no—
199#423—941no—
200C2×C4⋊C8—471no—
201C2×C4⋊C8—941no—
202C2×#104—941no—
203C2×C4×C8C2×D4711yescharacteristic
204C4×C4⋊C4—471no—
205#339—941no—
206#334—942no—
207#334—941no—
208#334—941no—
209Q8⋊C8Dic4711yescharacteristic, complemented
210Q8⋊C8Dic4711yescharacteristic, complemented
211D4⋊C8Dic4711yescharacteristic, complemented
212D4⋊C8Dic4711yescharacteristic, complemented
213C47#890411yescharacteristic, complemented, Sylow
214C2×#41D18811yescharacteristic
215#131—1882no—
216#131—1882no—
217C2×M16—942no—
218C2×M16—941no—
219C2×M16—941no—
220C22×C8—21no—
221C22×C8—942no—
222C22×C8—941no—
223C4×Q8Dic9411yescharacteristic
224C4×Q8C2×Dic4711yescharacteristic
225C4×D4—21no—
226C4×D4—21no—
227C4×D4Dic9411yescharacteristic
228C4×D4C2×Dic4711yescharacteristic
229#117—21no—
230#117D18811yescharacteristic
231C2×C4⋊C4—941no—
232C2×C42—21no—
233C2×C42—941no—
234C2×C42C22×D4711yescharacteristic
235C4⋊C8—471no—
236C4⋊C8—471no—
237C4⋊C8—472no—
238C4⋊C8—942no—
239C4⋊C8—942no—
240C4⋊C8—941no—
241C4⋊C8—941no—
242C4⋊C8—941no—
243C4⋊C8—941no—
244C4⋊C8C2×Dic4711yescharacteristic
245C4⋊C8C2×Dic4711yescharacteristic
246#104—1882no—
247C22⋊C8—21no—
248C4×C8—21no—
249C4×C8—21no—
250C4×C8C2×Dic4711yescharacteristic
251C4×C8C2×Dic4711yescharacteristic
252#95—941no—
253#41—21no—
254#41—21no—
255#41#1062532512yes—
256#41#1062532512yes—
257C2×Q8C4⋊Dic4711yescharacteristic
258C2×D4—21no—
259C2×D4C4⋊Dic4711yescharacteristic
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—1881no—
264C22×C4C2×D18811yescharacteristic
265C22×C4#1062535211yescharacteristic
266C22×C4#1062535211yescharacteristic
267M16—1881no—
268M16—1881no—
269M16—1884no—
270M16—1881no—
271M16—1881no—
272C2×C8—21no—
273C2×C8—21no—
274C2×C8—21no—
275C2×C8—21no—
276C2×C8—42no—
277C2×C8—941no—
278C2×C8—941no—
279C2×C8—942no—
280C2×C8—1881no—
281C2×C8—1884no—
282C2×C8—1881no—
283C2×C8—1881no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—942no—
287C4⋊C4—1881no—
288C4⋊C4C4⋊Dic4711yescharacteristic
289C4⋊C4C4⋊Dic4711yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C42—21no—
294C42—21no—
295C42—21no—
296C42—1881no—
297C42—1881no—
298C42C2×Dic9411yescharacteristic
299C42D4×D4711yescharacteristic
300C42D4×D4711yescharacteristic
301C42C22×Dic4711yescharacteristic
302C23—21no—
303C23#1309400811yescharacteristic
304Q8—21no—
305Q8#1309395612yes—
306D4—22no—
307D4—22no—
308D4—21no—
309D4#1309395612yes—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—81no—
321C2×C4—3761no—
322C2×C4—3761no—
323C2×C4—1882no—
324C2×C4C2×C4⋊Dic4711yescharacteristic
325C2×C4D4×Dic4711yescharacteristic
326C2×C4D4×Dic4711yescharacteristic
327C2×C4#1309399411yescharacteristic
328C2×C4#1309400111yescharacteristic
329C2×C4#1309400111yescharacteristic
330C2×C4C2×#1062532511yescharacteristic
331C2×C4C2×#1062532511yescharacteristic
332C2×C4#1309405211yescharacteristic
333C2×C4#1309405711yescharacteristic
334C8—22no—
335C8—41no—
336C8—41no—
337C8—41no—
338C8—3761no—
339C8—1881no—
340C8—1882no—
341C8—1881no—
342C22—21no—
343C22—21no—
344C22—22no—
345C22—41no—
346C22—41no—
347C22#1568899811yescharacteristic
348C22#1568944211yescharacteristic
349C22#1568945411yescharacteristic
350C4—22no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—3762no—
357C4C2×#1309395611yescharacteristic
358C4#1568916511yescharacteristic
359C4#1568924011yescharacteristic
360C4#1568924511yescharacteristic
361C4#1568926411yescharacteristic
362C4#1568927611yescharacteristic
363C2—21no—
364C2—21no—
365C2—42no—
366C2#2024358311yescharacteristic
367C2#2024363011yescharacteristic
368C2#2024366511yescharacteristic
subgroupG/H
centerC2×C4#13093994
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1476C2
socleC22×C47#385
prime radicalC2×#41×C47D4
cosocleC2×C42×C47C23
hypercenter#1476D47
hypocenterC47#8904
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1476

Complements

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

NH ≅ G/Ntype
3. #20242159C2semidirect
4. #20242144C2semidirect
5. #20241290C2semidirect
6. #20241228C2semidirect
25. C47×Q8⋊C8C4semidirect
26. C47×Q8⋊C8C4semidirect
27. C47×D4⋊C8C4semidirect
28. C47×D4⋊C8C4semidirect
209. Q8⋊C8Dic47semidirect
210. Q8⋊C8Dic47semidirect
211. D4⋊C8Dic47semidirect
212. D4⋊C8Dic47semidirect
213. C47#8904semidirect

Maximal subgroups

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

subgroupindex
#202519562
#202434082
#202421592
#202421442
#202412902
#202412282
C47×#14762
#890447