Finite Group Databasebeta

← #26112234

Subgroups — #26112234

Order 12032.

500 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
1#20252860C211yesmaximal, characteristic
2#20241947C211yesmaximal, characteristic
3#20241882C211yesmaximal, characteristic
4#20241783C211yesmaximal, characteristic, complemented
5#20241291C211yesmaximal, characteristic, complemented
6#20241246C211yesmaximal, characteristic, complemented
7C47×#2356C211yesmaximal, characteristic, complemented
8C2×#13094055—21no—
9#15689673C2211yescharacteristic
10#15689345—22no—
11#15689333C412yescomplemented
12#15689323C412yescomplemented
13#15689176C2211yescharacteristic
14#15689176C2211yescharacteristic
15#15689147C2211yescharacteristic
16#15689122—21no—
17#15688856—22no—
18#15688856—21no—
19#15688856—21no—
20Q8⋊(C47⋊C8)—22no—
21C2×C4×Q8×C47C2211yescharacteristic
22C47×#391—21no—
23C47×#387—22no—
24C47×#383—21no—
25C47×#382C2211yescharacteristic
26C4×C4⋊C4×C47—21no—
27C4×C4⋊C4×C47C2211yescharacteristic
28C47×#376—21no—
29C2×#10625350—21no—
30#13094055—42no—
31#13094055—42no—
32C2×#10625337—22no—
33C2×#10625336—22no—
34C2×#10625329—21no—
35#13094024C2×C411yescharacteristic
36#13094021C2×C411yescharacteristic
37#13094012—21no—
38#13093998—21no—
39#13093998—21no—
40C4×D188—21no—
41C4×D188—21no—
42C4⋊(C47⋊C8)—21no—
43C4⋊(C47⋊C8)—21no—
44C4⋊(C47⋊C8)—21no—
45C4⋊(C47⋊C8)C2×C412yes—
46#13093947—22no—
47#13093944—22no—
48C22⋊(C47⋊C8)—21no—
49C22⋊(C47⋊C8)—21no—
50C4×C47⋊C8—21no—
51C4×C47⋊C8—21no—
52C22×Q8×C47D411yescharacteristic
53C4×Q8×C47—21no—
54C4×Q8×C47—21no—
55C4×Q8×C47C2×C412yes—
56C4×Q8×C47D412yes—
57C2×C4⋊C4×C47—21no—
58C2×C4⋊C4×C47—21no—
59C2×C4⋊C4×C47—21no—
60C2×C4⋊C4×C47D411yescharacteristic
61C2×C42×C47—21no—
62C2×C42×C47—22no—
63C2×C42×C47—21no—
64C2×C42×C47C2311yescharacteristic
65#95×C47—22no—
66#95×C47—22no—
67#95×C47—22no—
68#95×C47—21no—
69#95×C47D411yescharacteristic
70#95×C47D411yescharacteristic
71#95×C47D412yes—
72C2×Q8×C47—21no—
73C2×Q8×C47—21no—
74C2×Q8×C47—21no—
75C2×Q8×C47—21no—
76C2×Q8×C47—21no—
77C2×Q8×C47C22⋊C412yes—
78C22×C4×C47—21no—
79C22×C4×C47—21no—
80C22×C4×C47—21no—
81C22×C4×C47—22no—
82C22×C4×C47—21no—
83C22×C4×C47C2×D411yescharacteristic
84C22×C4×C47C2×D411yescharacteristic
85C22×C4×C47C2×D411yescharacteristic
86C2×C22⋊D47—41no—
87#10625350—41no—
88#10625350—41no—
89#10625350—41no—
90#10625350—41no—
91C2×D188—21no—
92C2×D188—21no—
93C2×D188—21no—
94C2×C4×D47—41no—
95C2×Dic94—21no—
96C4⋊C4×C47—22no—
97C4⋊C4×C47—22no—
98C4⋊C4×C47—21no—
99C4⋊C4×C47—42no—
100C4⋊C4×C47—41no—
101C4⋊C4×C47—41no—
102C4⋊C4×C47C22⋊C412yes—
103C42×C47—22no—
104C42×C47—22no—
105C42×C47—44no—
106C42×C47—41no—
107C42×C47—41no—
108C42×C47C22×C411yescharacteristic
109C42×C47C2×D411yescharacteristic
110C42×C47#4111yescharacteristic
111C42×C47#4111yescharacteristic
112#10625337—44no—
113#10625336—44no—
114(C2×D47)⋊C4—41no—
115(C2×D47)⋊C4—41no—
116C4⋊Dic47—21no—
117C4⋊Dic47—21no—
118#10625329—41no—
119#10625329—41no—
120C2×C47⋊C8—22no—
121C2×C47⋊C8—41no—
122C2×C47⋊C8—41no—
123C23×C47#12011yescharacteristic
124C22×D47—41no—
125Q8×C47—22no—
126Q8×C47—22no—
127Q8×C47—41no—
128Q8×C47—41no—
129C2×C4×C47—22no—
130C2×C4×C47—22no—
131C2×C4×C47—22no—
132C2×C4×C47—41no—
133C2×C4×C47—41no—
134C2×C4×C47—42no—
135C2×C4×C47—41no—
136C2×C4×C47—41no—
137C2×C4×C47—41no—
138C2×C4×C47—41no—
139C2×C4×C47—42no—
140C2×C4×C47—41no—
141C2×C4×C47—41no—
142C2×C4×C47—42no—
143C2×C4×C47—41no—
144C2×C4×C47—42no—
145C2×C4×C47C2×C22⋊C411yescharacteristic
146C2×C4×C47C4×D411yescharacteristic
147C2×C4×C47C4×D411yescharacteristic
148C2×C4×C47#12111yescharacteristic
149C2×C4×C47#12111yescharacteristic
150C2×C4×C47#12311yescharacteristic
151C2×C4×C47#13511yescharacteristic
152C2×C4×C47#13511yescharacteristic
153C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
155C22⋊D47—81no—
156C22⋊D47—81no—
157C2×Dic47—41no—
158D188—41no—
159D188—41no—
160D188—81no—
161D188—81no—
162C4×D47—81no—
163C4×D47—81no—
164Dic94—41no—
165Dic94—41no—
166C47⋊C8—42no—
167C47⋊C8—81no—
168C47⋊C8—81no—
169#9182—471nomaximal, Sylow
170C22×C47—21no—
171C22×C47—21no—
172C22×C47#38611yescharacteristic
173C22×C47#44911yescharacteristic
174C22×C47#44911yescharacteristic
175C2×D47—81no—
176C2×D47—81no—
177C2×D47—81no—
178C4×C47—21no—
179C4×C47—21no—
180C4×C47—21no—
181C4×C47—21no—
182C4×C47—42no—
183C4×C47—42no—
184C4×C47—42no—
185C4×C47—81no—
186C4×C47—82no—
187C4×C47#41611yescharacteristic
188C4×C47#41811yescharacteristic
189C4×C47#48211yescharacteristic
190C4×C47#48211yescharacteristic
191Dic47—81no—
192#3037—471no—
193#2356D4711yescharacteristic, complemented
194#1517—471no—
195#1502—471no—
196#1479—471no—
197#1303—471no—
198#1286—471no—
199C2×C47—21no—
200C2×C47—21no—
201C2×C47#187511yescharacteristic
202C2×C47#190511yescharacteristic
203C2×C47#190611yescharacteristic
204D47—161no—
205C2×#137—941no—
206#532—471no—
207C2×C4×Q8C2×D4711yescharacteristic
208#464—942no—
209#462—472no—
210#460—472no—
211#431—471no—
212#431—471no—
213#423—471no—
214#417—941no—
215#391—21no—
216#387—22no—
217#383—21no—
218#382C2×D4711yescharacteristic
219C4×C4⋊C4—21no—
220C4×C4⋊C4C2×D4711yescharacteristic
221#376—21no—
222#327—941no—
223#327—941no—
224#327—942no—
225Q8⋊C8—942no—
226C47#918211yescharacteristic, complemented, Sylow
227C2×#41—941no—
228C22×Q8C22⋊D4711yescharacteristic
229#137—1882no—
230#137—1882no—
231C2×Q16—942no—
232C2×SD16—942no—
233C2×M16—941no—
234C4⋊Q8—471no—
235#127—471no—
236#124—941no—
237#121—941no—
238#121—941no—
239C4×Q8—21no—
240C4×Q8—21no—
241C4×Q8C4×D4712yes—
242C4×Q8D18812yes—
243C4×D4—941no—
244C4×D4—941no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4C22⋊D4711yescharacteristic
249C2×C42—21no—
250C2×C42—22no—
251C2×C42—21no—
252C2×C42C22×D4711yescharacteristic
253C4⋊C8—472no—
254C4⋊C8—941no—
255C4⋊C8—941no—
256C4⋊C8—941no—
257#103—942no—
258#102—942no—
259C22⋊C8—941no—
260C22⋊C8—941no—
261C4×C8—941no—
262C4×C8—941no—
263#95—22no—
264#95—22no—
265#95—22no—
266#95—21no—
267#95C22⋊D4711yescharacteristic
268#95C22⋊D4711yescharacteristic
269#95C22⋊D4712yes—
270#41—1881no—
271#41—1881no—
272#41—1881no—
273#41—1881no—
274C2×Q8—21no—
275C2×Q8—21no—
276C2×Q8—21no—
277C2×Q8—21no—
278C2×Q8—21no—
279C2×Q8—941no—
280C2×Q8(C2×D47)⋊C412yes—
281C2×D4—941no—
282C2×D4—941no—
283C2×D4—941no—
284C2×D4—1881no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—22no—
289C22×C4—21no—
290C22×C4—1881no—
291C22×C4C2×C22⋊D4711yescharacteristic
292C22×C4C2×C22⋊D4711yescharacteristic
293C22×C4C2×C22⋊D4711yescharacteristic
294Q16—1884no—
295SD16—1884no—
296M16—1881no—
297M16—1881no—
298C2×C8—942no—
299C2×C8—1881no—
300C2×C8—1881no—
301C4⋊C4—22no—
302C4⋊C4—22no—
303C4⋊C4—21no—
304C4⋊C4—42no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—941no—
308C4⋊C4—941no—
309C4⋊C4(C2×D47)⋊C412yes—
310C22⋊C4—1881no—
311C22⋊C4—1881no—
312C42—22no—
313C42—22no—
314C42—44no—
315C42—41no—
316C42—41no—
317C42C2×C4×D4711yescharacteristic
318C42C2×D18811yescharacteristic
319C42#1062535011yescharacteristic
320C42#1062535011yescharacteristic
321C23—1881no—
322C23#1309399311yescharacteristic
323Q8—22no—
324Q8—22no—
325Q8—41no—
326Q8—41no—
327Q8—1881no—
328Q8—1881no—
329D4—3761no—
330D4—3761no—
331D4—3761no—
332D4—3761no—
333D4—1881no—
334D4—1881no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—42no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—42no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—42no—
349C2×C4—41no—
350C2×C4—42no—
351C2×C4—3761no—
352C2×C4—3761no—
353C2×C4—1881no—
354C2×C4C2×(C2×D47)⋊C411yescharacteristic
355C2×C4C4×C22⋊D4711yescharacteristic
356C2×C4C4×C22⋊D4711yescharacteristic
357C2×C4#1309399811yescharacteristic
358C2×C4#1309399811yescharacteristic
359C2×C4#1309400711yescharacteristic
360C2×C4#1309404411yescharacteristic
361C2×C4#1309404411yescharacteristic
362C2×C4#1309404911yescharacteristic
363C2×C4#1309404911yescharacteristic
364C8—3761no—
365C8—3761no—
366C8—1882no—
367C22—21no—
368C22—21no—
369C22—3761no—
370C22—3761no—
371C22—3761no—
372C22#1568900211yescharacteristic
373C22#1568926811yescharacteristic
374C22#1568926811yescharacteristic
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—42no—
380C4—42no—
381C4—42no—
382C4—81no—
383C4—82no—
384C4—3761no—
385C4#1568911711yescharacteristic
386C4#1568912711yescharacteristic
387C4#1568944711yescharacteristic
388C4#1568944711yescharacteristic
389C2—21no—
390C2—21no—
391C2—7521no—
392C2#2024371011yescharacteristic
393C2#2024388211yescharacteristic
394C2#2024388911yescharacteristic
subgroupG/H
centerC22#15689002
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#2356C2
socleC22×C47#386
prime radical#15689673C22
cosocleC2×C42×C47C23
hypercenter#2356D47
hypocenterC47#9182
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2356

Complements

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

NH ≅ G/Ntype
4. #20241783C2semidirect
5. #20241291C2semidirect
6. #20241246C2semidirect
7. C47×#2356C2semidirect
11. #15689333C4semidirect
12. #15689323C4semidirect
193. #2356D47semidirect
226. C47#9182semidirect

Maximal subgroups

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

subgroupindex
#202528602
#202419472
#202418822
#202417832
#202412912
#202412462
C47×#23562
#918247