Finite Group Databasebeta

← #26133185

Subgroups — #26133185

Order 12032.

456 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20256491C211yesmaximal, characteristic, complemented
2C2×#15689243C211yesmaximal, characteristic
3#20245017C211yesmaximal, characteristic, complemented
4#20245008C211yesmaximal, characteristic, complemented
5#20241471C211yesmaximal, characteristic, complemented
6#20241467C211yesmaximal, characteristic, complemented
7C47×#2117C211yesmaximal, characteristic, complemented
8C2×#13094044C411yescharacteristic
9C2×#13094030C2211yescharacteristic
10#15689540—22no—
11#15689540—22no—
12C2×#13093964—22no—
13C2×#13093964C2211yescharacteristic
14C2×#13093964C2211yescharacteristic
15#15689243—22no—
16#15689243—22no—
17C2×#13093959C411yescharacteristic
18C2×#13093951C411yescharacteristic
19C2×#13093950C411yescharacteristic
20C2×#13093934C2211yescharacteristic
21#15688908—22no—
22#15688904—22no—
23C2×#131×C47C2211yescharacteristic
24C2×M32×C47C2211yescharacteristic
25C2×M32×C47C2211yescharacteristic
26C47×#350—22no—
27C2×#10625350C2×C411yescharacteristic
28#13094044—22no—
29#13094044—22no—
30C2×#10625337C811yescharacteristic
31C2×#10625335C811yescharacteristic
32C2×#10625336C811yescharacteristic
33C2×#10625334C811yescharacteristic
34#13094030—21no—
35#13094030—21no—
36#13094030—21no—
37#13094030—21no—
38C2×#10625329C2×C411yescharacteristic
39C2×#10625324—21no—
40C22×C47⋊C8C2×C411yescharacteristic
41C2×C8×D47—21no—
42C2×C4×Dic47C2×C411yescharacteristic
43#13093964—24no—
44#13093964—21no—
45#13093964—21no—
46#13093964—21no—
47#13093964D412yes—
48C2×C47⋊C16—24no—
49C2×C47⋊C16—21no—
50C2×C47⋊C16D412yes—
51#13093959—22no—
52#13093951—22no—
53#13093950—22no—
54#13093934—21no—
55#13093934—21no—
56C2×#41×C47C2×C411yescharacteristic
57#131×C47—21no—
58#131×C47—21no—
59#131×C47D412yes—
60#131×C47D412yes—
61C2×M16×C47—21no—
62C2×M16×C47C2×C411yescharacteristic
63C22×C8×C47—21no—
64C22×C8×C47C2311yescharacteristic
65M32×C47—21no—
66M32×C47—21no—
67M32×C47—21no—
68M32×C47—21no—
69C2×C16×C47—21no—
70C2×C16×C47—21no—
71#41×C47—21no—
72#41×C47—21no—
73#41×C47C22⋊C412yes—
74#41×C47M1612yes—
75C2×Q8×C47C2×C811yescharacteristic
76C2×D4×C47—21no—
77C2×D4×C47C2×C811yescharacteristic
78C22×C4×C47—21no—
79C22×C4×C47C22×C411yescharacteristic
80C2×C22⋊D47—21no—
81C22×Dic47—21no—
82#10625350—21no—
83#10625350—21no—
84#10625350—21no—
85#10625350—21no—
86C2×D188C2×C811yescharacteristic
87C2×C4×D47—21no—
88C2×Dic94C2×C811yescharacteristic
89M16×C47—21no—
90M16×C47—22no—
91M16×C47—22no—
92M16×C47C22⋊C412yes—
93C2×C8×C47—21no—
94C2×C8×C47—22no—
95C2×C8×C47—22no—
96C2×C8×C47C2×D411yescharacteristic
97C2×C8×C47C2×D411yescharacteristic
98C2×C8×C47C2×D411yescharacteristic
99C2×C8×C47C2×D411yescharacteristic
100C2×C8×C47#4111yescharacteristic
101C2×C8×C47#4111yescharacteristic
102#10625337—22no—
103#10625336—22no—
104#10625335—22no—
105#10625334—22no—
106C4×Dic47—21no—
107C4×Dic47—21no—
108#10625329—21no—
109#10625329—21no—
110C2×C47⋊C8—21no—
111C2×C47⋊C8—21no—
112C2×C47⋊C8—21no—
113C2×C47⋊C8C2×C811yescharacteristic
114C2×C47⋊C8C2×C811yescharacteristic
115#10625324—41no—
116#10625324—41no—
117C8×D47—41no—
118C8×D47—41no—
119C16×C47—41no—
120C16×C47—41no—
121C47⋊C16—22no—
122C47⋊C16—22no—
123C23×C47—21no—
124C23×C47#13111yescharacteristic
125C22×D47—21no—
126Q8×C47—21no—
127Q8×C47C22⋊C812yes—
128D4×C47—22no—
129D4×C47—22no—
130D4×C47—21no—
131D4×C47C22⋊C812yes—
132C2×C4×C47—21no—
133C2×C4×C47—22no—
134C2×C4×C47—22no—
135C2×C4×C47C2×C22⋊C411yescharacteristic
136C2×C4×C47C4×D411yescharacteristic
137C2×C4×C47C4×D411yescharacteristic
138C2×C4×C47C22×C811yescharacteristic
139C2×C4×C47C2×M1611yescharacteristic
140C2×C4×C47#13111yescharacteristic
141C22⋊D47—41no—
142C22⋊D47—41no—
143C2×Dic47—21no—
144C2×Dic47—41no—
145C2×Dic47—81no—
146D188—21no—
147D188—21no—
148C4×D47—41no—
149C4×D47—41no—
150Dic94—21no—
151Dic94—21no—
152C8×C47—22no—
153C8×C47#12011yescharacteristic
154C8×C47#12111yescharacteristic
155C8×C47#12111yescharacteristic
156C8×C47#12311yescharacteristic
157C47⋊C8—21no—
158C47⋊C8—21no—
159C47⋊C8—41no—
160#12986—471nomaximal, Sylow
161C22×C47—22no—
162C22×C47—41no—
163C22×C47—81no—
164C22×C47#40811yescharacteristic
165C22×C47C8×D411yescharacteristic
166C22×C47#43511yescharacteristic
167C2×D47—41no—
168C2×D47—81no—
169C4×C47—22no—
170C4×C47#38611yescharacteristic
171C4×C47C2×C22⋊C811yescharacteristic
172C4×C47C8×D411yescharacteristic
173C4×C47#43511yescharacteristic
174Dic47—41no—
175Dic47—81no—
176#3407—471no—
177C2×#444—471no—
178#2117—471no—
179#2117D4711yescharacteristic, complemented
180#2115—471no—
181#1377—471no—
182#1375—471no—
183C2×C47—21no—
184C2×C47—21no—
185C2×C47—21no—
186C2×C47—42no—
187C2×C47#186911yescharacteristic
188D47—81no—
189C2×#135—471no—
190C2×#131—471no—
191C2×#131C2×D4711yescharacteristic
192#504—942no—
193#504—942no—
194C2×M32—471no—
195C2×M32—471no—
196C2×M32—942no—
197C2×M32C2×D4711yescharacteristic
198C2×M32C2×D4711yescharacteristic
199#444—942no—
200#444—942no—
201C2×#108—471no—
202C2×#104—471no—
203C2×#104—471no—
204C2×#97—471no—
205#350—22no—
206#350—942no—
207#349—942no—
208C47#1298611yescharacteristic, complemented, Sylow
209C2×#41—471no—
210C2×#41C4×D4711yescharacteristic
211#135—942no—
212#135—942no—
213C2×Q16—471no—
214C2×SD16—471no—
215C2×SD16—471no—
216C2×D8—471no—
217#131—21no—
218#131—21no—
219#131—941no—
220#131—941no—
221#131—941no—
222#131—941no—
223#131D18812yes—
224#131C22⋊D4712yes—
225C2×M16—21no—
226C2×M16—471no—
227C2×M16—941no—
228C2×M16C4×D4711yescharacteristic
229C22×C8—21no—
230C22×C8—471no—
231C22×C8—941no—
232C22×C8C22×D4711yescharacteristic
233C2×C42—471no—
234M32—21no—
235M32—21no—
236M32—21no—
237M32—21no—
238M32—472no—
239M32—944no—
240M32—941no—
241M32—941no—
242M32—941no—
243C2×C16—21no—
244C2×C16—21no—
245C2×C16—472no—
246C2×C16—944no—
247C2×C16—941no—
248#108—942no—
249#104—942no—
250#104—942no—
251#97—941no—
252#97—941no—
253#41—21no—
254#41—21no—
255#41—941no—
256#41—941no—
257#41—941no—
258#41—941no—
259#41#1062532412yes—
260#41(C2×D47)⋊C412yes—
261C2×Q8—471no—
262C2×Q8C8×D4711yescharacteristic
263C2×D4—21no—
264C2×D4—471no—
265C2×D4—941no—
266C2×D4C8×D4711yescharacteristic
267C22×C4—21no—
268C22×C4—941no—
269C22×C4—941no—
270C22×C4C2×C4×D4711yescharacteristic
271Q16—942no—
272SD16—942no—
273SD16—942no—
274D8—942no—
275M16—21no—
276M16—22no—
277M16—22no—
278M16—941no—
279M16—941no—
280M16—1881no—
281M16—1881no—
282M16(C2×D47)⋊C412yes—
283C2×C8—21no—
284C2×C8—22no—
285C2×C8—22no—
286C2×C8—471no—
287C2×C8—471no—
288C2×C8—941no—
289C2×C8—941no—
290C2×C8—941no—
291C2×C8—1881no—
292C2×C8—1881no—
293C2×C8C2×D18811yescharacteristic
294C2×C8D4×D4711yescharacteristic
295C2×C8D4×D4711yescharacteristic
296C2×C8#1062535211yescharacteristic
297C2×C8#1062535211yescharacteristic
298C2×C8C2×C22⋊D4711yescharacteristic
299C42—941no—
300C42—941no—
301C16—41no—
302C16—41no—
303C16—942no—
304C16—942no—
305C23—21no—
306C23—941no—
307C23#1309403211yescharacteristic
308Q8—21no—
309Q8—941no—
310Q8—941no—
311Q8(C2×D47)⋊C812yes—
312D4—22no—
313D4—22no—
314D4—21no—
315D4—941no—
316D4—941no—
317D4—1881no—
318D4—1881no—
319D4(C2×D47)⋊C812yes—
320C2×C4—21no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—941no—
324C2×C4—3761no—
325C2×C4—1881no—
326C2×C4—1881no—
327C2×C4—1881no—
328C2×C4C2×(C2×D47)⋊C411yescharacteristic
329C2×C4(C22⋊D47)⋊C411yescharacteristic
330C2×C4(C22⋊D47)⋊C411yescharacteristic
331C2×C4C2×C8×D4711yescharacteristic
332C2×C4C2×#1062532411yescharacteristic
333C2×C4#1309403211yescharacteristic
334C8—22no—
335C8—941no—
336C8—941no—
337C8—1881no—
338C8#1309399411yescharacteristic
339C8#1309399611yescharacteristic
340C8#1309399611yescharacteristic
341C8#1309400811yescharacteristic
342C22—22no—
343C22—41no—
344C22—81no—
345C22—3761no—
346C22—1881no—
347C22#1568909111yescharacteristic
348C22(C22⋊D47)⋊C811yescharacteristic
349C22#1568919111yescharacteristic
350C4—22no—
351C4—3761no—
352C4—1881no—
353C4#1568900011yescharacteristic
354C4C2×(C2×D47)⋊C811yescharacteristic
355C4(C22⋊D47)⋊C811yescharacteristic
356C4#1568919111yescharacteristic
357C2—21no—
358C2—21no—
359C2—21no—
360C2—42no—
361C2—3761no—
362C2#2024367811yescharacteristic
subgroupG/H
centerC4#15689000
commutatorC2×C4×C47C22×C8
FrattiniC22×C8C22×D47
FittingC47×#2117C2
socleC2×C47#1869
prime radicalC2×#13094044C4
cosocleC22×C8×C47C23
hypercenter#2117D47
hypocenterC47#12986
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C8 ◁ #2117

Complements

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

NH ≅ G/Ntype
1. #20256491C2semidirect
3. #20245017C2semidirect
4. #20245008C2semidirect
5. #20241471C2semidirect
6. #20241467C2semidirect
7. C47×#2117C2semidirect
179. #2117D47semidirect
208. C47#12986semidirect

Maximal subgroups

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

subgroupindex
#202564912
C2×#156892432
#202450172
#202450082
#202414712
#202414672
C47×#21172
#1298647