Finite Group Databasebeta

← #26133236

Subgroups — #26133236

Order 12032.

476 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253108C211yesmaximal, characteristic
2#20245115C211yesmaximal, characteristic, complemented
3C2×#15688929C211yesmaximal, characteristic, complemented
4C2×#15688907C211yesmaximal, characteristic, complemented
5#20241499C211yesmaximal, characteristic, complemented
6#20241481C211yesmaximal, characteristic, complemented
7C47×#2916C211yesmaximal, characteristic, complemented
8#15689921—21no—
9C2×#13094046C2211yescharacteristic
10C2×#13093964C2211yescharacteristic
11C22×C47⋊C16C2211yescharacteristic
12#15689398C412yes—
13#15689393C412yes—
14#15689386—22no—
15C2×#13093960C2211yescharacteristic
16#15689105—21no—
17#15688929—22no—
18#15688929—22no—
19#15688907—22no—
20C47×#568—21no—
21C2×#131×C47C2211yescharacteristic
22C47×#430—21no—
23C47×#430—22no—
24C2×#108×C47—22no—
25C2×#108×C47C2211yescharacteristic
26C2×#108×C47C2211yescharacteristic
27C2×#10625350—21no—
28#13094055—41no—
29#13094054—22no—
30#13094050—41no—
31#13094049—22no—
32#13094046—21no—
33#13094046—21no—
34#13094046—21no—
35#13094046—21no—
36#13094044—42no—
37C2×Dic188C2×C411yescharacteristic
38C2×#10625325—21no—
39C2×D376C2×C411yescharacteristic
40C2×#10625329—21no—
41#13093964—21no—
42#13093964—21no—
43C2×C47⋊C16—21no—
44C2×C47⋊C16—21no—
45C2×C47⋊C16—21no—
46C2×C47⋊C16—21no—
47#13093960—21no—
48#13093960C2×C412yes—
49#13093942—22no—
50#13093940—22no—
51C2×#41×C47D411yescharacteristic
52#131×C47—21no—
53#131×C47—21no—
54#131×C47—42no—
55#131×C47—42no—
56#131×C47C2×C412yes—
57#131×C47D412yes—
58C2×M16×C47—21no—
59C2×M16×C47—24no—
60C2×M16×C47—21no—
61C2×M16×C47—21no—
62C2×M16×C47D411yescharacteristic
63C22×C8×C47—21no—
64C22×C8×C47C2311yescharacteristic
65#108×C47—24no—
66#108×C47—21no—
67#108×C47—21no—
68#108×C47D412yes—
69#108×C47D412yes—
70#41×C47—21no—
71#41×C47—21no—
72#41×C47C22⋊C412yes—
73#41×C47D812yes—
74C2×Q8×C47SD1611yescharacteristic
75C2×D4×C47—21no—
76C2×D4×C47SD1611yescharacteristic
77C22×C4×C47—21no—
78C22×C4×C47C2×D411yescharacteristic
79C2×C22⋊D47—41no—
80#10625350—41no—
81#10625350—41no—
82#10625350—41no—
83#10625350—41no—
84C2×D188—21no—
85C2×C4×D47—41no—
86C2×Dic94—21no—
87M16×C47—21no—
88M16×C47—22no—
89M16×C47—22no—
90M16×C47—22no—
91M16×C47—22no—
92M16×C47—44no—
93M16×C47—41no—
94M16×C47—41no—
95M16×C47C22⋊C412yes—
96C2×C8×C47—21no—
97C2×C8×C47—22no—
98C2×C8×C47—22no—
99C2×C8×C47—44no—
100C2×C8×C47—41no—
101C2×C8×C47—41no—
102C2×C8×C47C22×C411yescharacteristic
103C2×C8×C47C2×D411yescharacteristic
104C2×C8×C47C2×D411yescharacteristic
105C2×C8×C47C2×D411yescharacteristic
106C2×C8×C47#4111yescharacteristic
107C2×C8×C47#4111yescharacteristic
108#10625337—42no—
109#10625336—42no—
110#10625335—42no—
111#10625334—42no—
112#10625329—22no—
113#10625329—41no—
114C2×C47⋊C8—41no—
115Dic188—21no—
116Dic188—21no—
117D376—21no—
118D376—21no—
119#10625325—41no—
120#10625325—41no—
121C47⋊C16—41no—
122C47⋊C16—41no—
123C23×C47—21no—
124C23×C47#13711yescharacteristic
125C22×D47—41no—
126Q8×C47—21no—
127Q8×C47#10212yes—
128D4×C47—22no—
129D4×C47—22no—
130D4×C47—21no—
131D4×C47#10212yes—
132C2×C4×C47—21no—
133C2×C4×C47—22no—
134C2×C4×C47—22no—
135C2×C4×C47C2×C22⋊C411yescharacteristic
136C2×C4×C47#12011yescharacteristic
137C2×C4×C47#12311yescharacteristic
138C2×C4×C47C2×D811yescharacteristic
139C2×C4×C47C2×SD1611yescharacteristic
140C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
141C22⋊D47—81no—
142C22⋊D47—81no—
143C2×Dic47—41no—
144D188—41no—
145D188—41no—
146C4×D47—81no—
147C4×D47—81no—
148Dic94—41no—
149Dic94—41no—
150C8×C47—22no—
151C8×C47—42no—
152C8×C47—42no—
153C8×C47C4×D411yescharacteristic
154C8×C47C4×D411yescharacteristic
155C8×C47#12111yescharacteristic
156C8×C47#12111yescharacteristic
157C47⋊C8—42no—
158#12995—471nomaximal, Sylow
159C22×C47—22no—
160C22×C47—41no—
161C22×C47—81no—
162C22×C47#41711yescharacteristic
163C22×C47#44811yescharacteristic
164C22×C47#48011yescharacteristic
165C2×D47—81no—
166C2×D47—161no—
167C4×C47—22no—
168C4×C47#38611yescharacteristic
169C4×C47C2×#10211yescharacteristic
170C4×C47#44711yescharacteristic
171C4×C47#48111yescharacteristic
172Dic47—81no—
173#3067—471no—
174#2916D4711yescharacteristic, complemented
175#2143—471no—
176C2×#359—471no—
177C2×#350—471no—
178#1388—471no—
179#1381—471no—
180C2×C47—21no—
181C2×C47—21no—
182C2×C47—21no—
183C2×C47—42no—
184C2×C47#187411yescharacteristic
185D47—161no—
186#575—941no—
187C2×#135—471no—
188#568—21no—
189C2×#131C2×D4711yescharacteristic
190C2×M32—471no—
191C22×C16—471no—
192#473—472no—
193#472—472no—
194#471—942no—
195#430—21no—
196#430—22no—
197C2×#108—22no—
198C2×#108—471no—
199C2×#108C2×D4711yescharacteristic
200C2×#108C2×D4711yescharacteristic
201#413—941no—
202#359—942no—
203#359—942no—
204#350—942no—
205C47#1299511yescharacteristic, complemented, Sylow
206C2×#41—941no—
207C2×#41C22⋊D4711yescharacteristic
208#137—942no—
209#137—1881no—
210AGL(1,ℤ/8)—942no—
211AGL(1,ℤ/8)—1881no—
212#135—941no—
213#135—941no—
214#135—941no—
215#135—941no—
216#135—1882no—
217C2×Q16—471no—
218C2×SD16—941no—
219C2×D8—471no—
220#131—21no—
221#131—21no—
222#131—42no—
223#131—42no—
224#131C4×D4712yes—
225#131D18812yes—
226C2×M16—21no—
227C2×M16—24no—
228C2×M16—21no—
229C2×M16—21no—
230C2×M16—941no—
231C2×M16C22⋊D4711yescharacteristic
232C22×C8—21no—
233C22×C8C22×D4711yescharacteristic
234M32—941no—
235M32—941no—
236C2×C16—941no—
237C2×C16—941no—
238C2×C16—941no—
239C2×C16—941no—
240#108—24no—
241#108—21no—
242#108—21no—
243#108—472no—
244#108—941no—
245#108C22⋊D4712yes—
246#108C22⋊D4712yes—
247#101—942no—
248#100—942no—
249#41—21no—
250#41—21no—
251#41—1881no—
252#41—1881no—
253#41—1881no—
254#41—1881no—
255#41(C2×D47)⋊C412yes—
256#41#1062533412yes—
257C2×Q8—941no—
258C2×Q8#1062533611yescharacteristic
259C2×D4—21no—
260C2×D4—941no—
261C2×D4—1881no—
262C2×D4#1062533611yescharacteristic
263C22×C4—21no—
264C22×C4—1881no—
265C22×C4C2×C22⋊D4711yescharacteristic
266Q16—941no—
267Q16—941no—
268Q16—1882no—
269SD16—1882no—
270SD16—1882no—
271SD16—1881no—
272SD16—1881no—
273D8—941no—
274D8—941no—
275D8—1882no—
276M16—21no—
277M16—22no—
278M16—22no—
279M16—22no—
280M16—22no—
281M16—44no—
282M16—41no—
283M16—41no—
284M16—942no—
285M16—1881no—
286M16(C2×D47)⋊C412yes—
287C2×C8—21no—
288C2×C8—22no—
289C2×C8—22no—
290C2×C8—44no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—1881no—
294C2×C8C2×C4×D4711yescharacteristic
295C2×C8C2×D18811yescharacteristic
296C2×C8#1062535011yescharacteristic
297C2×C8#1062535011yescharacteristic
298C2×C8C2×C22⋊D4711yescharacteristic
299C2×C8C2×C22⋊D4711yescharacteristic
300C16—1881no—
301C16—1881no—
302C23—21no—
303C23—1881no—
304C23#1309405511yescharacteristic
305Q8—21no—
306Q8—1881no—
307Q8—1881no—
308Q8#1309394412yes—
309D4—22no—
310D4—22no—
311D4—21no—
312D4—3761no—
313D4—3761no—
314D4—1881no—
315D4—1881no—
316D4#1309394412yes—
317C2×C4—21no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—3761no—
321C2×C4—3761no—
322C2×C4—1881no—
323C2×C4C2×(C2×D47)⋊C411yescharacteristic
324C2×C4#1309399311yescharacteristic
325C2×C4#1309400711yescharacteristic
326C2×C4C2×#1062533411yescharacteristic
327C2×C4C2×#1062533611yescharacteristic
328C2×C4#1309405011yescharacteristic
329C8—22no—
330C8—42no—
331C8—42no—
332C8—1882no—
333C8C4×C22⋊D4711yescharacteristic
334C8C4×C22⋊D4711yescharacteristic
335C8#1309399811yescharacteristic
336C8#1309399811yescharacteristic
337C22—22no—
338C22—41no—
339C22—81no—
340C22—3761no—
341C22—7521no—
342C22#1568912211yescharacteristic
343C22#1568926211yescharacteristic
344C22#1568943611yescharacteristic
345C4—22no—
346C4—3761no—
347C4#1568900211yescharacteristic
348C4C2×#1309394411yescharacteristic
349C4#1568925711yescharacteristic
350C4#1568944111yescharacteristic
351C2—21no—
352C2—21no—
353C2—21no—
354C2—42no—
355C2—7521no—
356C2#2024370511yescharacteristic
subgroupG/H
centerC4#15689257
commutatorC2×C8×C47C22×C4
FrattiniC22×C8C22×D47
FittingC47×#2916C2
socleC2×C47#1874
prime radical#20253108C2
cosocleC22×C8×C47C23
hypercenter#2916D47
hypocenterC47#12995
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#131 ◁ #2916

Complements

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

NH ≅ G/Ntype
2. #20245115C2semidirect
3. C2×#15688929C2semidirect
4. C2×#15688907C2semidirect
5. #20241499C2semidirect
6. #20241481C2semidirect
7. C47×#2916C2semidirect
174. #2916D47semidirect
205. C47#12995semidirect

Maximal subgroups

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

subgroupindex
#202531082
#202451152
C2×#156889292
C2×#156889072
#202414992
#202414812
C47×#29162
#1299547