Finite Group Databasebeta

← #26110183

Subgroups — #26110183

Order 12032.

420 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252501C211yesmaximal, characteristic
2#20243505C211yesmaximal, characteristic, complemented
3C4×#13093952C211yesmaximal, characteristic
4#20242141C211yesmaximal, characteristic, complemented
5#20241776C211yesmaximal, characteristic
6#20241237C211yesmaximal, characteristic, complemented
7C47×#1276C211yesmaximal, characteristic, complemented
8C4×#10625350C2211yescharacteristic
9#15689253—21no—
10#15689202—21no—
11#15689191—22no—
12#15689179—21no—
13#15689145—21no—
14C2×C4⋊(C47⋊C8)C2211yescharacteristic
15C2×C4⋊(C47⋊C8)C2211yescharacteristic
16C2×#13093952C411yescharacteristic
17C2×#13093952C411yescharacteristic
18C4×#10625329C2211yescharacteristic
19#15688883C411yescharacteristic
20#15688883C411yescharacteristic
21#15688878—22no—
22#15688875—21no—
23#15688873—21no—
24#15688855—21no—
25#15688852—21no—
26C47×#431C2211yescharacteristic
27C47×#431C2211yescharacteristic
28C43×C47C2211yescharacteristic
29C2×#10625350C2×C411yescharacteristic
30C2×#10625329C2×C411yescharacteristic
31C2×#10625329C2×C411yescharacteristic
32C2×#10625324—22no—
33C22×C47⋊C8—21no—
34C22×C47⋊C8D412yes—
35C4×Dic94D411yescharacteristic
36C4×Dic94Q811yescharacteristic
37C4×D188D411yescharacteristic
38C4×D188Q811yescharacteristic
39C4×C22⋊D47—21no—
40C4×C22⋊D47—21no—
41#13093983C2×C411yescharacteristic
42#13093981—21no—
43C42×D47—21no—
44C4⋊(C47⋊C8)—21no—
45C4⋊(C47⋊C8)—21no—
46C4⋊(C47⋊C8)—21no—
47C4⋊(C47⋊C8)—21no—
48Dic47⋊C8—22no—
49#13093952—22no—
50#13093952—22no—
51(C2×D47)⋊C8—22no—
52#13093935—21no—
53#13093934—22no—
54C4×C47⋊C8—21no—
55C2×C42×C47—21no—
56C2×C42×C47—21no—
57C2×C42×C47C2×C411yescharacteristic
58C2×C42×C47C2×C411yescharacteristic
59C2×C42×C47C2311yescharacteristic
60C4⋊C8×C47—21no—
61C4⋊C8×C47D411yescharacteristic
62C4⋊C8×C47D411yescharacteristic
63C22⋊C8×C47—21no—
64C22⋊C8×C47—21no—
65C4×C8×C47—21no—
66C4×C8×C47—21no—
67C22×C4×C47—21no—
68C22×C4×C47—21no—
69C22×C4×C47C22×C411yescharacteristic
70C22×C4×C47C2×D411yescharacteristic
71C22×C4×C47#4111yescharacteristic
72C2×C22⋊D47—21no—
73#10625350—21no—
74#10625350—21no—
75#10625350—21no—
76#10625350—21no—
77C2×D188C4⋊C411yescharacteristic
78C2×C4×D47—21no—
79C2×C4×D47—21no—
80C2×C4×D47—21no—
81C2×Dic94C4⋊C411yescharacteristic
82C2×C8×C47—21no—
83C2×C8×C47—21no—
84C2×C8×C47—41no—
85C42×C47—21no—
86C42×C47—21no—
87C42×C47—21no—
88C42×C47—41no—
89C42×C47—41no—
90C42×C47—42no—
91C42×C47M1612yescomplemented
92C42×C47C2×D411yescharacteristic
93C42×C47C2×D411yescharacteristic
94C42×C47C2×Q811yescharacteristic
95C42×C47#4111yescharacteristic
96C22⋊Dic47—21no—
97(C2×D47)⋊C4—21no—
98(C2×D47)⋊C4—21no—
99C4⋊Dic47C4⋊C411yescharacteristic
100C4⋊Dic47C4⋊C411yescharacteristic
101Dic47⋊C4—21no—
102Dic47⋊C4—21no—
103C4×Dic47—21no—
104C4×Dic47—21no—
105C4×Dic47—21no—
106#10625329—21no—
107#10625329—21no—
108#10625329—21no—
109#10625329M1612yescomplemented
110C2×C47⋊C8—21no—
111C2×C47⋊C8—21no—
112C2×C47⋊C8—22no—
113C2×C47⋊C8—42no—
114C2×C47⋊C8—42no—
115C2×C47⋊C8—41no—
116#10625324—82no—
117C23×C47C4×D411yescharacteristic
118C22×D47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—22no—
122C2×C4×C47—22no—
123C2×C4×C47—41no—
124C2×C4×C47—41no—
125C2×C4×C47—41no—
126C2×C4×C47—41no—
127C2×C4×C47—41no—
128C2×C4×C47C2×C4⋊C411yescharacteristic
129C2×C4×C47C4×D411yescharacteristic
130C2×C4×C47#12011yescharacteristic
131C2×C4×C47C22⋊Q811yescharacteristic
132C2×C4×C47C22⋊Q811yescharacteristic
133C2×C4×C47#12311yescharacteristic
134C2×C4×C47C2×M1611yescharacteristic
135C2×C4×C47C2×M1611yescharacteristic
136C2×C4×C47#13111yescharacteristic
137C2×C4×C47#13111yescharacteristic
138C22⋊D47—41no—
139C22⋊D47—41no—
140C2×Dic47—21no—
141C2×Dic47—21no—
142C2×Dic47—21no—
143D188—21no—
144D188—21no—
145C4×D47—41no—
146C4×D47—41no—
147C4×D47—41no—
148C4×D47—41no—
149C4×D47—81no—
150Dic94—21no—
151Dic94—21no—
152C8×C47—41no—
153C8×C47—41no—
154C8×C47—81no—
155C47⋊C8—22no—
156C47⋊C8—41no—
157C47⋊C8—42no—
158C47⋊C8—81no—
159#8842—471nomaximal, Sylow
160C22×C47—21no—
161C22×C47—21no—
162C22×C47#38511yescharacteristic
163C22×C47#43511yescharacteristic
164C22×C47#43611yescharacteristic
165C2×D47—41no—
166C2×D47—41no—
167C2×D47—41no—
168C4×C47—21no—
169C4×C47—21no—
170C4×C47—21no—
171C4×C47—42no—
172C4×C47—42no—
173C4×C47#42311yescharacteristic
174C4×C47#42411yescharacteristic
175C4×C47#43511yescharacteristic
176C4×C47#43611yescharacteristic
177C4×C47#45411yescharacteristic
178C4×C47#45511yescharacteristic
179Dic47—41no—
180Dic47—41no—
181Dic47—41no—
182#2989—471no—
183#1831—471no—
184C4×#104—471no—
185#1565—471no—
186#1477—471no—
187#1283—471no—
188#1276D4711yescharacteristic, complemented
189C2×C47—21no—
190C2×C47—21no—
191C2×C47#185111yescharacteristic
192C2×C47#186011yescharacteristic
193C2×C47#186111yescharacteristic
194D47—81no—
195C4×#41—471no—
196#446—941no—
197#436—941no—
198#435—942no—
199#432—941no—
200#431C2×D4711yescharacteristic
201#431C2×D4711yescharacteristic
202#423—941no—
203C2×C4⋊C8—471no—
204C2×C4⋊C8—471no—
205C2×#104—471no—
206C2×#104—471no—
207C4×M16—471no—
208C43C2×D4711yescharacteristic
209#339—471no—
210#339—471no—
211#336—942no—
212#335—941no—
213#334—941no—
214Q8⋊C8—941no—
215D4⋊C8—941no—
216C47#884211yescharacteristic, complemented, Sylow
217C2×#41—471no—
218C2×M16—471no—
219C2×M16—471no—
220C2×M16—942no—
221C22×C8—472no—
222C22×C8—941no—
223C4×Q8—471no—
224C4×Q8—471no—
225C4×D4—471no—
226C4×D4—471no—
227C4×D4—941no—
228C4×D4—941no—
229#117—471no—
230#117—941no—
231C2×C42—21no—
232C2×C42—21no—
233C2×C42—941no—
234C2×C42C4×D4711yescharacteristic
235C2×C42C4×D4711yescharacteristic
236C2×C42C22×D4711yescharacteristic
237C4⋊C8—21no—
238C4⋊C8—942no—
239C4⋊C8—941no—
240C4⋊C8—941no—
241C4⋊C8—941no—
242C4⋊C8—941no—
243C4⋊C8D18811yescharacteristic
244C4⋊C8D18811yescharacteristic
245#104—942no—
246#104—942no—
247C22⋊C8—21no—
248C22⋊C8—21no—
249C22⋊C8—942no—
250#97—942no—
251#97—941no—
252C4×C8—21no—
253C4×C8—21no—
254C4×C8—941no—
255#41—941no—
256#41—941no—
257#41—941no—
258#41—941no—
259C2×Q8—471no—
260C2×D4—471no—
261C2×D4—941no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—941no—
265C22×C4—941no—
266C22×C4—941no—
267C22×C4C2×C4×D4711yescharacteristic
268C22×C4D4×D4711yescharacteristic
269C22×C4#1062535211yescharacteristic
270M16—472no—
271M16—941no—
272M16—941no—
273M16—941no—
274M16—3762no—
275C2×C8—21no—
276C2×C8—21no—
277C2×C8—41no—
278C2×C8—941no—
279C2×C8—941no—
280C2×C8—942no—
281C2×C8—1882no—
282C2×C8—1881no—
283C2×C8—1882no—
284C4⋊C4—471no—
285C4⋊C4—471no—
286C4⋊C4—941no—
287C4⋊C4—941no—
288C22⋊C4—941no—
289C22⋊C4—941no—
290C22⋊C4—941no—
291C42—21no—
292C42—21no—
293C42—21no—
294C42—41no—
295C42—41no—
296C42—42no—
297C42—941no—
298C42—941no—
299C42—941no—
300C42#1062532412yescomplemented
301C42C2×D18811yescharacteristic
302C42#1062535011yescharacteristic
303C42D4×D4711yescharacteristic
304C42Q8×D4711yescharacteristic
305C23—941no—
306C23(C22⋊D47)⋊C411yescharacteristic
307Q8—941no—
308Q8—941no—
309D4—941no—
310D4—941no—
311D4—1881no—
312D4—1881no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—941no—
323C2×C4—941no—
324C2×C4—941no—
325C2×C4—3761no—
326C2×C4—1881no—
327C2×C4—1881no—
328C2×C4—1881no—
329C2×C4—1881no—
330C2×C4C4⋊C4×D4711yescharacteristic
331C2×C4C4×D18811yescharacteristic
332C2×C4#1309399411yescharacteristic
333C2×C4#1309400211yescharacteristic
334C2×C4#1309400411yescharacteristic
335C2×C4#1309400611yescharacteristic
336C2×C4M16×D4711yescharacteristic
337C2×C4C2×#1062532411yescharacteristic
338C2×C4#1309403011yescharacteristic
339C2×C4#1309403211yescharacteristic
340C8—41no—
341C8—41no—
342C8—81no—
343C8—942no—
344C8—3761no—
345C8—1882no—
346C8—1881no—
347C22—21no—
348C22—21no—
349C22—1881no—
350C22—1881no—
351C22—1881no—
352C22#1568899711yescharacteristic
353C22#1568919111yescharacteristic
354C22#1568919811yescharacteristic
355C4—21no—
356C4—21no—
357C4—21no—
358C4—42no—
359C4—42no—
360C4—1881no—
361C4—1881no—
362C4—1881no—
363C4#1568914511yescharacteristic
364C4#1568914811yescharacteristic
365C4#1568919611yescharacteristic
366C4#1568920211yescharacteristic
367C4#1568929711yescharacteristic
368C4#1568930211yescharacteristic
369C2—21no—
370C2—21no—
371C2—3761no—
372C2#2024357211yescharacteristic
373C2#2024362211yescharacteristic
374C2#2024362911yescharacteristic
subgroupG/H
centerC2×C4#13093994
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1276C2
socleC22×C47#385
prime radicalC2×#10625350C2×C4
cosocleC2×C42×C47C23
hypercenter#1276D47
hypocenterC47#8842
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1276

Complements

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

NH ≅ G/Ntype
2. #20243505C2semidirect
4. #20242141C2semidirect
6. #20241237C2semidirect
7. C47×#1276C2semidirect
91. C42×C47M16semidirect
109. #10625329M16semidirect
188. #1276D47semidirect
216. C47#8842semidirect
300. C42#10625324semidirect

Maximal subgroups

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

subgroupindex
#202525012
#202435052
C4×#130939522
#202421412
#202417762
#202412372
C47×#12762
#884247