Finite Group Databasebeta

← #26114571

Subgroups — #26114571

Order 12032.

446 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#20244181C211yesmaximal, characteristic
2#20244107C211yesmaximal, characteristic, complemented
3C4×#13093944C211yesmaximal, characteristic
4C2×#15688852C211yesmaximal, characteristic
5C2×#15688845C211yesmaximal, characteristic, complemented
6#20241222C211yesmaximal, characteristic, complemented
7C47×#1279C211yesmaximal, characteristic, complemented
8C2×C4×D188C2211yescharacteristic
9C2×C4⋊(C47⋊C8)—21no—
10C2×C4⋊(C47⋊C8)C2211yescharacteristic
11C2×#13093944C411yescharacteristic
12C2×#13093944C411yescharacteristic
13C2×(C2×D47)⋊C8—21no—
14C2×(C2×D47)⋊C8—21no—
15C2×C4×C47⋊C8C2211yescharacteristic
16C2×C4×C47⋊C8C2211yescharacteristic
17#15688885C411yescharacteristic
18#15688885C411yescharacteristic
19#15688878—21no—
20#15688852—22no—
21#15688845—22no—
22C2×C4⋊C8×C47C2211yescharacteristic
23C2×C4×C8×C47C2211yescharacteristic
24C4×C4⋊C4×C47C2211yescharacteristic
25C22×D188C2×C411yescharacteristic
26C22×C4×D47—21no—
27C22×C47⋊C8—21no—
28C22×C47⋊C8C2×C411yescharacteristic
29C22×C47⋊C8C2×C411yescharacteristic
30C22×C47⋊C8D411yescharacteristic
31C22×C47⋊C8D411yescharacteristic
32C4×D188—21no—
33C4×D188—21no—
34C4×D188—21no—
35C4×D188—21no—
36C2×C4⋊Dic47C2×C411yescharacteristic
37C2×(C2×D47)⋊C4—21no—
38C4⋊(C47⋊C8)—21no—
39C4⋊(C47⋊C8)—21no—
40C4⋊(C47⋊C8)—42no—
41#13093944—22no—
42#13093944—22no—
43(C2×D47)⋊C8—42no—
44(C2×D47)⋊C8—42no—
45C4×C47⋊C8—21no—
46C4×C47⋊C8—21no—
47C4×C47⋊C8—21no—
48C4×C47⋊C8—21no—
49C22×C8×C47—21no—
50C22×C8×C47—21no—
51C2×C4⋊C4×C47C2×C411yescharacteristic
52C2×C4⋊C4×C47C2×C411yescharacteristic
53C2×C42×C47—21no—
54C2×C42×C47C2311yescharacteristic
55C4⋊C8×C47—21no—
56C4⋊C8×C47—21no—
57C4×C8×C47—21no—
58C4×C8×C47D412yes—
59#95×C47—21no—
60C23×D47—21no—
61C22×C4×C47—21no—
62C22×C4×C47—21no—
63C22×C4×C47C22×C411yescharacteristic
64C22×C4×C47C2×D411yescharacteristic
65C22×C4×C47#4111yescharacteristic
66C22×Dic47—21no—
67C2×D188—21no—
68C2×D188—21no—
69C2×D188—21no—
70C2×D188—21no—
71C2×D188—21no—
72C2×D188M1612yes—
73C2×C4×D47—41no—
74C2×C4×D47—41no—
75C2×C4×D47—41no—
76C2×C4×D47—41no—
77C2×C4×D47—41no—
78C2×C4×D47—41no—
79C2×C8×C47—22no—
80C2×C8×C47—41no—
81C2×C8×C47—41no—
82C2×C8×C47—41no—
83C2×C8×C47—41no—
84C2×C8×C47—41no—
85C4⋊C4×C47—21no—
86C4⋊C4×C47—21no—
87C4⋊C4×C47—21no—
88C4⋊C4×C47M1612yes—
89C42×C47—41no—
90C42×C47—41no—
91C42×C47C2×D411yescharacteristic
92C42×C47#4111yescharacteristic
93C42×C47#4111yescharacteristic
94C42×C47#4111yescharacteristic
95(C2×D47)⋊C4—41no—
96(C2×D47)⋊C4—41no—
97C4⋊Dic47—21no—
98C4⋊Dic47—21no—
99C2×C47⋊C8—21no—
100C2×C47⋊C8—21no—
101C2×C47⋊C8—21no—
102C2×C47⋊C8—21no—
103C2×C47⋊C8—21no—
104C2×C47⋊C8—21no—
105C2×C47⋊C8—21no—
106C2×C47⋊C8—21no—
107C2×C47⋊C8—21no—
108C2×C47⋊C8—21no—
109C2×C47⋊C8—41no—
110C2×C47⋊C8—41no—
111C2×C47⋊C8—41no—
112C2×C47⋊C8D812yes—
113C2×C47⋊C8SD1612yes—
114C23×C47C4×D411yescharacteristic
115C22×D47—22no—
116C22×D47—41no—
117C22×D47—41no—
118C22×D47—41no—
119C22×D47—41no—
120C22×D47—41no—
121C22×D47—41no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47—22no—
125C2×C4×C47—41no—
126C2×C4×C47—41no—
127C2×C4×C47—41no—
128C2×C4×C47—41no—
129C2×C4×C47—41no—
130C2×C4×C47#11711yescharacteristic
131C2×C4×C47C4×D411yescharacteristic
132C2×C4×C47#12111yescharacteristic
133C2×C4×C47#12311yescharacteristic
134C2×C4×C47#12411yescharacteristic
135C2×C4×C47#12611yescharacteristic
136C2×C4×C47C2×M1611yescharacteristic
137C2×C4×C47C2×M1611yescharacteristic
138C2×C4×C47#13111yescharacteristic
139C2×C4×C47#13111yescharacteristic
140C2×C4×C47C2×D811yescharacteristic
141C2×C4×C47C2×SD1611yescharacteristic
142C2×C4×C47#13511yescharacteristic
143C2×C4×C47#13511yescharacteristic
144C2×Dic47—41no—
145C2×Dic47—41no—
146C2×Dic47—41no—
147D188—22no—
148D188—22no—
149D188—41no—
150D188—41no—
151C4×D47—81no—
152C4×D47—81no—
153C4×D47—81no—
154C4×D47—81no—
155C8×C47—42no—
156C8×C47—81no—
157C47⋊C8—22no—
158C47⋊C8—22no—
159C47⋊C8—41no—
160C47⋊C8—41no—
161C47⋊C8—81no—
162#9558—471nomaximal, Sylow
163C22×C47#38811yescharacteristic
164C22×C47#43511yescharacteristic
165C22×C47#43511yescharacteristic
166C22×C47C4×D811yescharacteristic
167C22×C47C4×SD1611yescharacteristic
168C22×C47#44411yescharacteristic
169C22×C47#44411yescharacteristic
170C2×D47—42no—
171C2×D47—42no—
172C2×D47—42no—
173C2×D47—81no—
174C2×D47—81no—
175C2×D47—81no—
176C2×D47—81no—
177C4×C47—21no—
178C4×C47—21no—
179C4×C47—42no—
180C4×C47—81no—
181C4×C47#43211yescharacteristic
182C4×C47#43311yescharacteristic
183C4×C47#43511yescharacteristic
184C4×C47#43611yescharacteristic
185C4×C47#46511yescharacteristic
186C4×C47#46611yescharacteristic
187C4×C47#48611yescharacteristic
188C4×C47#48811yescharacteristic
189Dic47—81no—
190#1954—471no—
191#1939—471no—
192C4×#102—471no—
193C2×D4⋊C8—471no—
194C2×#322—471no—
195#1279D4711yescharacteristic, complemented
196#1277—471no—
197C2×C47#158111yescharacteristic
198C2×C47#158111yescharacteristic
199C2×C47#158211yescharacteristic
200C2×C47#158311yescharacteristic
201C2×C47#192411yescharacteristic
202C2×C47#193411yescharacteristic
203C2×C47#193811yescharacteristic
204D47—82no—
205C2×C4×D4—471no—
206C2×C4⋊C8—471no—
207C2×C4⋊C8—941no—
208C2×C4⋊C8C2×D4711yescharacteristic
209C2×#102—471no—
210C2×#102—471no—
211C2×C22⋊C8—941no—
212C2×C22⋊C8—941no—
213C2×C4×C8—471no—
214C2×C4×C8—471no—
215C2×C4×C8C2×D4711yescharacteristic
216C4×C4⋊C4C2×D4711yescharacteristic
217#340—471no—
218#340—471no—
219#336—941no—
220D4⋊C8—942no—
221#322—942no—
222C47#955811yescharacteristic, complemented, Sylow
223C22×D4—471no—
224C23×C4—941no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—471no—
228C22×C8—471no—
229C22×C8—471no—
230C22×C8—471no—
231C22×C8—941no—
232C4×D4—941no—
233C4×D4—941no—
234C4×D4—941no—
235C4×D4—941no—
236C2×C4⋊C4—471no—
237C2×C4⋊C4C4×D4711yescharacteristic
238C2×C4⋊C4C4×D4711yescharacteristic
239C2×C22⋊C4—941no—
240C2×C42—21no—
241C2×C42C22×D4711yescharacteristic
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8—941no—
245C4⋊C8—941no—
246C4⋊C8—1882no—
247#102—942no—
248#102—942no—
249C22⋊C8—1882no—
250C22⋊C8—1882no—
251C4×C8—21no—
252C4×C8—941no—
253C4×C8—941no—
254C4×C8—941no—
255C4×C8—941no—
256C4×C8D18812yes—
257#95—21no—
258C24—941no—
259C2×D4—472no—
260C2×D4—941no—
261C2×D4—941no—
262C2×D4—941no—
263C2×D4—941no—
264C2×D4—941no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—941no—
268C22×C4—1881no—
269C22×C4—1881no—
270C22×C4—1881no—
271C22×C4—1881no—
272C22×C4—1881no—
273C22×C4—1881no—
274C22×C4C2×C4×D4711yescharacteristic
275C22×C4D4×D4711yescharacteristic
276C22×C4#1062535211yescharacteristic
277C2×C8—22no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—472no—
284C2×C8—472no—
285C2×C8—941no—
286C2×C8—941no—
287C2×C8—941no—
288C2×C8—941no—
289C2×C8—941no—
290C2×C8—941no—
291C2×C8—941no—
292C2×C8—941no—
293C2×C8—941no—
294C2×C8—941no—
295C2×C8—1881no—
296C2×C8—1881no—
297C2×C8—1881no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—941no—
302C4⋊C4—941no—
303C4⋊C4#1062532412yes—
304C22⋊C4—1881no—
305C22⋊C4—1881no—
306C42—41no—
307C42—41no—
308C42C2×D18811yescharacteristic
309C42#1062535011yescharacteristic
310C42#1062535211yescharacteristic
311C42#1062535411yescharacteristic
312C23—942no—
313C23—1881no—
314C23—1881no—
315C23—1881no—
316C23—1881no—
317C23—1881no—
318C23—1881no—
319C23(C22⋊D47)⋊C411yescharacteristic
320D4—942no—
321D4—942no—
322D4—1881no—
323D4—1881no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—22no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—3761no—
333C2×C4—3761no—
334C2×C4—3761no—
335C2×C4—3761no—
336C2×C4—1881no—
337C2×C4—1881no—
338C2×C4—1881no—
339C2×C4#1309398211yescharacteristic
340C2×C4C4×D18811yescharacteristic
341C2×C4#1309399911yescharacteristic
342C2×C4#1309400811yescharacteristic
343C2×C4#1309401011yescharacteristic
344C2×C4#1309401911yescharacteristic
345C2×C4M16×D4711yescharacteristic
346C2×C4C2×#1062532411yescharacteristic
347C2×C4#1309403011yescharacteristic
348C2×C4#1309403211yescharacteristic
349C2×C4D8×D4711yescharacteristic
350C2×C4SD16×D4711yescharacteristic
351C2×C4#1309404511yescharacteristic
352C2×C4#1309404711yescharacteristic
353C8—42no—
354C8—81no—
355C8—942no—
356C8—942no—
357C8—3761no—
358C8—1881no—
359C8—1881no—
360C22—3761no—
361C22—3761no—
362C22—3761no—
363C22—3761no—
364C22—1882no—
365C22—1882no—
366C22—1882no—
367C22#1568901511yescharacteristic
368C22#1568919111yescharacteristic
369C22#1568919711yescharacteristic
370C22#1568920311yescharacteristic
371C22#1568920811yescharacteristic
372C22#1568924211yescharacteristic
373C22#1568924211yescharacteristic
374C4—21no—
375C4—21no—
376C4—42no—
377C4—81no—
378C4—3761no—
379C4#1568917911yescharacteristic
380C4#1568918311yescharacteristic
381C4#1568919611yescharacteristic
382C4#1568920211yescharacteristic
383C4#1568935311yescharacteristic
384C4#1568936011yescharacteristic
385C4#1568946811yescharacteristic
386C4#1568947911yescharacteristic
387C2—3762no—
388C2#2024221411yescharacteristic
389C2#2024222011yescharacteristic
390C2#2024222711yescharacteristic
391C2#2024222811yescharacteristic
392C2#2024400211yescharacteristic
393C2#2024407211yescharacteristic
394C2#2024410011yescharacteristic
subgroupG/H
centerC22×C4D4×D47
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1279C2
socleC23×C47C4×D4
prime radicalC22×D188C2×C4
cosocleC2×C42×C47C23
hypercenter#1279D47
hypocenterC47#9558
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
2. #20244107C2semidirect
5. C2×#15688845C2semidirect
6. #20241222C2semidirect
7. C47×#1279C2semidirect
195. #1279D47semidirect
222. C47#9558semidirect

Maximal subgroups

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

subgroupindex
#202441812
#202441072
C4×#130939442
C2×#156888522
C2×#156888452
#202412222
C47×#12792
#955847