Finite Group Databasebeta

← #26133400

Subgroups — #26133400

Order 12032.

462 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252305C211yesmaximal, characteristic, complemented
2C2×#15688930C211yesmaximal, characteristic, complemented
3#20245095C211yesmaximal, characteristic, complemented
4#20244287C211yesmaximal, characteristic, complemented
5#20241503C211yesmaximal, characteristic, complemented
6#20241478C211yesmaximal, characteristic, complemented
7C47×#3414C211yesmaximal, characteristic
8#15689890—21no—
9C22×C47⋊C16C2211yescharacteristic
10#15689245—22no—
11#15689240—22no—
12C2×#13093960C2211yescharacteristic
13#15689161C2211yescharacteristic
14#15689140—21no—
15#15689140—21no—
16#15689097—21no—
17#15689078C2211yescharacteristic
18#15688930—22no—
19#15688927—21no—
20#15688924—21no—
21C2×#135×C47C2211yescharacteristic
22C2×#135×C47C2211yescharacteristic
23C47×#510—21no—
24C47×#510C412yescomplemented
25C47×#509—21no—
26C47×#509C412yescomplemented
27C47×#508—22no—
28C2×M32×C47C2211yescharacteristic
29#13094031—24no—
30#13094031—42no—
31C2×#10625329—21no—
32C2×#10625329—42no—
33C2×#10625329D411yescharacteristic
34#13093983—21no—
35#13093983D411yescharacteristic
36C2×C47⋊C16—21no—
37C2×C47⋊C16—21no—
38C2×C47⋊C16—21no—
39#13093960—21no—
40#13093960D412yes—
41#13093958—21no—
42#13093956—21no—
43#13093951—24no—
44#13093951—42no—
45#13093939—42no—
46#13093934—21no—
47C8×Dic47—21no—
48C2×#41×C47—21no—
49C2×#41×C47—21no—
50#135×C47—21no—
51#135×C47—21no—
52#135×C47—21no—
53#135×C47—21no—
54#135×C47—21no—
55#135×C47—21no—
56#135×C47C2×C412yes—
57#135×C47D412yes—
58C2×Q16×C47C2×C411yescharacteristic
59C2×Q16×C47D411yescharacteristic
60C2×SD16×C47—21no—
61C2×SD16×C47—21no—
62C2×D8×C47C2×C411yescharacteristic
63C2×D8×C47D411yescharacteristic
64C22×C8×C47C2311yescharacteristic
65Q32×C47—22no—
66SD32×C47—22no—
67SD32×C47—22no—
68D16×C47—22no—
69M32×C47—21no—
70M32×C47C2×C412yes—
71C2×C16×C47—21no—
72#41×C47—22no—
73#41×C47—22no—
74#41×C47—41no—
75#41×C47—41no—
76#41×C47—41no—
77#41×C47—41no—
78#41×C47—41no—
79#41×C47—41no—
80C2×Q8×C47—21no—
81C2×Q8×C47—21no—
82C2×D4×C47—21no—
83C2×D4×C47—21no—
84C2×D4×C47—41no—
85C2×D4×C47—41no—
86C22×C4×C47—41no—
87C22×C4×C47—41no—
88C22×C4×C47C2×D411yescharacteristic
89Q16×C47—21no—
90Q16×C47—21no—
91Q16×C47—21no—
92Q16×C47C22⋊C412yes—
93SD16×C47—22no—
94SD16×C47—22no—
95SD16×C47—41no—
96SD16×C47—41no—
97D8×C47—21no—
98D8×C47—21no—
99D8×C47—21no—
100D8×C47C22⋊C412yes—
101C2×C8×C47C22×C411yescharacteristic
102C2×C8×C47C2×D411yescharacteristic
103C2×C8×C47C2×D411yescharacteristic
104C2×C8×C47C2×D411yescharacteristic
105C2×C8×C47#4111yescharacteristic
106C2×C8×C47#4111yescharacteristic
107C22⋊Dic47—21no—
108C22⋊Dic47—41no—
109C4⋊Dic47—21no—
110C4⋊Dic47—41no—
111C4×Dic47—21no—
112C4×Dic47—41no—
113#10625329—21no—
114#10625329—22no—
115#10625329—44no—
116#10625329—41no—
117#10625329D812yes—
118C2×C47⋊C8—21no—
119C2×C47⋊C8—44no—
120C2×C47⋊C8—41no—
121C16×C47—22no—
122C47⋊C16—41no—
123C23×C47—41no—
124C23×C47—41no—
125C23×C47AGL(1,ℤ/8)11yescharacteristic
126Q8×C47—22no—
127Q8×C47—41no—
128Q8×C47—41no—
129Q8×C47—41no—
130D4×C47—22no—
131D4×C47—42no—
132D4×C47—42no—
133D4×C47—41no—
134D4×C47—41no—
135D4×C47—41no—
136D4×C47—81no—
137D4×C47—81no—
138C2×C4×C47—41no—
139C2×C4×C47—42no—
140C2×C4×C47—42no—
141C2×C4×C47—41no—
142C2×C4×C47—81no—
143C2×C4×C47—81no—
144C2×C4×C47C4×D411yescharacteristic
145C2×C4×C47#12011yescharacteristic
146C2×C4×C47#12111yescharacteristic
147C2×C4×C47C2×D811yescharacteristic
148C2×C4×C47#13511yescharacteristic
149C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
150C2×Dic47—41no—
151C2×Dic47—81no—
152C8×C47C2×C22⋊C411yescharacteristic
153C8×C47C4×D411yescharacteristic
154C8×C47#12111yescharacteristic
155C8×C47#12311yescharacteristic
156C47⋊C8—22no—
157C47⋊C8—42no—
158#13021—471nomaximal, Sylow
159C22×C47—41no—
160C22×C47—42no—
161C22×C47—81no—
162C22×C47—161no—
163C22×C47—161no—
164C22×C47#44211yescharacteristic
165C22×C47#44911yescharacteristic
166C22×C47#45911yescharacteristic
167C4×C47—42no—
168C4×C47—81no—
169C4×C47#38611yescharacteristic
170C4×C47C4×D811yescharacteristic
171C4×C47#44711yescharacteristic
172C4×C47#46311yescharacteristic
173Dic47—81no—
174Dic47—161no—
175#3414D4711yescharacteristic
176#2957—471no—
177C2×#359—471no—
178#2138—471no—
179#1976—471no—
180#1389—471no—
181#1379—471no—
182C2×C47—21no—
183C2×C47—21no—
184C2×C47—21no—
185C2×C47—82no—
186C2×C47—161no—
187C2×C47#187911yescharacteristic
188C2×#135C2×D4711yescharacteristic
189C2×#135C2×D4711yescharacteristic
190#568—941no—
191#510—21no—
192#510Dic4712yescomplemented
193#509—21no—
194#509Dic4712yescomplemented
195#508—22no—
196C2×M32C2×D4711yescharacteristic
197C22×C16—471no—
198#444—942no—
199#443—942no—
200C2×#108—471no—
201#427—471no—
202#421—941no—
203#421—941no—
204#410—941no—
205#405—471no—
206#359—942no—
207#358—941no—
208#357—941no—
209C47#1302111yescharacteristic, complemented, Sylow
210C2×#41—21no—
211C2×#41—21no—
212#135—21no—
213#135—21no—
214#135—21no—
215#135—21no—
216#135—21no—
217#135—21no—
218#135C2×Dic4712yes—
219#135C22⋊D4712yes—
220C2×Q16C2×Dic4711yescharacteristic
221C2×Q16C22⋊D4711yescharacteristic
222C2×SD16—21no—
223C2×SD16—21no—
224C2×D8C2×Dic4711yescharacteristic
225C2×D8C22⋊D4711yescharacteristic
226#131—944no—
227#131—1882no—
228C2×M16—471no—
229C2×M16—941no—
230C2×M16—1882no—
231C22×C8C22×D4711yescharacteristic
232#117—471no—
233#117—941no—
234Q32—22no—
235SD32—22no—
236SD32—22no—
237D16—22no—
238M32—21no—
239M32C2×Dic4712yes—
240C2×C16—21no—
241C2×C16—941no—
242C2×C16—941no—
243C2×C16—941no—
244#108—472no—
245#108—941no—
246#107—941no—
247#106—941no—
248#104—944no—
249#104—1882no—
250#99—1882no—
251#97—941no—
252C4×C8—941no—
253#41—22no—
254#41—22no—
255#41—41no—
256#41—41no—
257#41—41no—
258#41—41no—
259#41—41no—
260#41—41no—
261C2×Q8—21no—
262C2×Q8—21no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—41no—
266C2×D4—41no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4D4×D4711yescharacteristic
270Q16—21no—
271Q16—21no—
272Q16—21no—
273Q16C22⋊Dic4712yes—
274SD16—22no—
275SD16—22no—
276SD16—41no—
277SD16—41no—
278D8—21no—
279D8—21no—
280D8—21no—
281D8C22⋊Dic4712yes—
282M16—472no—
283M16—941no—
284M16—942no—
285M16—1884no—
286M16—1881no—
287C2×C8—941no—
288C2×C8—1884no—
289C2×C8—1881no—
290C2×C8D4×D4711yescharacteristic
291C2×C8#1062535211yescharacteristic
292C2×C8#1062535211yescharacteristic
293C2×C8C22×Dic4711yescharacteristic
294C2×C8C2×C22⋊D4711yescharacteristic
295C2×C8C2×C22⋊D4711yescharacteristic
296C4⋊C4—941no—
297C4⋊C4—1881no—
298C22⋊C4—941no—
299C22⋊C4—1881no—
300C42—941no—
301C42—1881no—
302C16—22no—
303C16—1881no—
304C23—41no—
305C23—41no—
306C23#1309404811yescharacteristic
307Q8—22no—
308Q8—41no—
309Q8—41no—
310Q8—41no—
311D4—22no—
312D4—42no—
313D4—42no—
314D4—41no—
315D4—41no—
316D4—41no—
317D4—81no—
318D4—81no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—41no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—3761no—
326C2×C4—1881no—
327C2×C4D4×Dic4711yescharacteristic
328C2×C4#1309399211yescharacteristic
329C2×C4#1309399611yescharacteristic
330C2×C4D8×D4711yescharacteristic
331C2×C4#1309404311yescharacteristic
332C2×C4#1309404811yescharacteristic
333C8—942no—
334C8—1882no—
335C8C2×C22⋊Dic4711yescharacteristic
336C8D4×Dic4711yescharacteristic
337C8#1309399611yescharacteristic
338C8#1309400511yescharacteristic
339C22—41no—
340C22—42no—
341C22—81no—
342C22—161no—
343C22—161no—
344C22#1568923511yescharacteristic
345C22#1568926511yescharacteristic
346C22#1568931611yescharacteristic
347C4—42no—
348C4—81no—
349C4—3761no—
350C4—7521no—
351C4#1568900311yescharacteristic
352C4D8×Dic4711yescharacteristic
353C4#1568925511yescharacteristic
354C4#1568933611yescharacteristic
355C2—21no—
356C2—21no—
357C2—21no—
358C2—82no—
359C2—161no—
360C2#2024373811yescharacteristic
subgroupG/H
centerC4#15689255
commutatorC2×C8×C47C22×C4
FrattiniC22×C8C22×D47
Fitting, prime radicalC47×#3414C2
socleC2×C47#1879
cosocleC22×C8×C47C23
hypercenter#3414D47
hypocenterC47#13021
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ #3414

Complements

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

NH ≅ G/Ntype
1. #20252305C2semidirect
2. C2×#15688930C2semidirect
3. #20245095C2semidirect
4. #20244287C2semidirect
5. #20241503C2semidirect
6. #20241478C2semidirect
24. C47×#510C4semidirect
26. C47×#509C4semidirect
192. #510Dic47semidirect
194. #509Dic47semidirect
209. C47#13021semidirect

Maximal subgroups

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

subgroupindex
#202523052
C2×#156889302
#202450952
#202442872
#202415032
#202414782
C47×#34142
#1302147