Finite Group Databasebeta

← #26110133

Subgroups — #26110133

Order 12032.

476 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689179C211yesmaximal, characteristic
2#20243365C211yesmaximal, characteristic
3C4×(C2×D47)⋊C8C211yesmaximal, characteristic
4C2×#15688875C211yesmaximal, characteristic, complemented
5#20241223C211yesmaximal, characteristic, complemented
6#20241222C211yesmaximal, characteristic, complemented
7C2×C47×#334C211yesmaximal, characteristic, complemented
8C2×C42×D47C2211yescharacteristic
9#15689179—22no—
10#15689179—22no—
11C2×C4⋊(C47⋊C8)C2211yescharacteristic
12C2×C4⋊(C47⋊C8)C2211yescharacteristic
13C2×(C2×D47)⋊C8—21no—
14C2×(C2×D47)⋊C8—21no—
15C2×(C2×D47)⋊C8C411yescharacteristic
16C2×(C2×D47)⋊C8C411yescharacteristic
17C2×#13093934—21no—
18C2×C4×C47⋊C8C2211yescharacteristic
19#15688877—21no—
20#15688877C411yescharacteristic
21#15688877C411yescharacteristic
22#15688875—22no—
23C2×C4⋊C8×C47C2211yescharacteristic
24C2×C4⋊C8×C47C2211yescharacteristic
25C2×C4×C8×C47C2211yescharacteristic
26C47×#334—22no—
27C22×C4×D47C2×C411yescharacteristic
28C22×C4×D47D411yescharacteristic
29C22×C4×D47Q811yescharacteristic
30C22×C47⋊C8—21no—
31C22×C47⋊C8—21no—
32C22×C47⋊C8C2×C411yescharacteristic
33C22×C47⋊C8C2×C411yescharacteristic
34C2×C4×Dic47C2×C411yescharacteristic
35C2×C4×Dic47D411yescharacteristic
36C2×C4×Dic47Q811yescharacteristic
37C42×D47—21no—
38C42×D47—21no—
39C42×D47—21no—
40C42×D47—21no—
41C4⋊(C47⋊C8)—21no—
42C4⋊(C47⋊C8)—21no—
43C4⋊(C47⋊C8)—21no—
44C4⋊(C47⋊C8)D412yes—
45(C2×D47)⋊C8—24no—
46(C2×D47)⋊C8—22no—
47(C2×D47)⋊C8—22no—
48(C2×D47)⋊C8—42no—
49#13093934—24no—
50C4×C47⋊C8—21no—
51C4×C47⋊C8—21no—
52C22×C8×C47—21no—
53C22×C8×C47—21no—
54C22×C8×C47C2×C411yescharacteristic
55C22×C8×C47C2×C411yescharacteristic
56C2×C42×C47C2311yescharacteristic
57C4⋊C8×C47—21no—
58C4⋊C8×C47—21no—
59C4⋊C8×C47—21no—
60C4⋊C8×C47D412yes—
61C4×C8×C47—21no—
62C4×C8×C47—21no—
63C23×D47C4⋊C411yescharacteristic
64C22×C4×C47C22×C411yescharacteristic
65C22×C4×C47C2×D411yescharacteristic
66C22×C4×C47C2×Q811yescharacteristic
67C22×Dic47C4⋊C411yescharacteristic
68C22×Dic47C4⋊C411yescharacteristic
69C22×Dic47C4⋊C411yescharacteristic
70C2×C4×D47—22no—
71C2×C4×D47—21no—
72C2×C4×D47—21no—
73C2×C4×D47—21no—
74C2×C4×D47—21no—
75C2×C4×D47—21no—
76C2×C4×D47—21no—
77C2×C4×D47—21no—
78C2×C4×D47—21no—
79C2×C4×D47—21no—
80C2×C4×D47—21no—
81C2×C4×D47—21no—
82C2×C4×D47—21no—
83C2×C4×D47—21no—
84C2×C4×D47—21no—
85C2×C4×D47—41no—
86C2×C8×C47—21no—
87C2×C8×C47—21no—
88C2×C8×C47—21no—
89C2×C8×C47—22no—
90C2×C8×C47—21no—
91C2×C8×C47—21no—
92C2×C8×C47—41no—
93C2×C8×C47—41no—
94C2×C8×C47—41no—
95C2×C8×C47—41no—
96C2×C8×C47—41no—
97C2×C8×C47M1612yes—
98C42×C47C2×D411yescharacteristic
99C42×C47C2×D411yescharacteristic
100C42×C47#4111yescharacteristic
101C42×C47#4111yescharacteristic
102C4×Dic47—21no—
103C4×Dic47—21no—
104C4×Dic47—21no—
105C4×Dic47—21no—
106C4×Dic47—21no—
107C4×Dic47—21no—
108C2×C47⋊C8—21no—
109C2×C47⋊C8—21no—
110C2×C47⋊C8—21no—
111C2×C47⋊C8—22no—
112C2×C47⋊C8—21no—
113C2×C47⋊C8—21no—
114C2×C47⋊C8—41no—
115C2×C47⋊C8—41no—
116C2×C47⋊C8—41no—
117C2×C47⋊C8—41no—
118C2×C47⋊C8—41no—
119C2×C47⋊C8M1612yes—
120C23×C47C2×C4⋊C411yescharacteristic
121C22×D47—21no—
122C22×D47—21no—
123C22×D47—21no—
124C22×D47—21no—
125C22×D47—21no—
126C22×D47—21no—
127C22×D47#10812yes—
128C2×C4×C47—21no—
129C2×C4×C47—21no—
130C2×C4×C47C4×D411yescharacteristic
131C2×C4×C47C4×D411yescharacteristic
132C2×C4×C47#12011yescharacteristic
133C2×C4×C47C22⋊Q811yescharacteristic
134C2×C4×C47C22⋊Q811yescharacteristic
135C2×C4×C47#12311yescharacteristic
136C2×C4×C47C2×M1611yescharacteristic
137C2×C4×C47C2×M1611yescharacteristic
138C2×C4×C47#13111yescharacteristic
139C2×C4×C47#13111yescharacteristic
140C2×C4×C47#13511yescharacteristic
141C2×C4×C47#13511yescharacteristic
142C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C47#13711yescharacteristic
144C2×Dic47—21no—
145C2×Dic47—21no—
146C2×Dic47—21no—
147C2×Dic47—21no—
148C2×Dic47—21no—
149C2×Dic47—21no—
150C2×Dic47—21no—
151C2×Dic47—21no—
152C2×Dic47—21no—
153C4×D47—42no—
154C4×D47—42no—
155C4×D47—41no—
156C4×D47—41no—
157C4×D47—41no—
158C4×D47—41no—
159C4×D47—41no—
160C4×D47—41no—
161C4×D47—41no—
162C4×D47—41no—
163C8×C47—22no—
164C8×C47—41no—
165C8×C47—42no—
166C8×C47—81no—
167C47⋊C8—22no—
168C47⋊C8—41no—
169C47⋊C8—42no—
170C47⋊C8—81no—
171#8834—471nomaximal, Sylow
172C22×C47#38511yescharacteristic
173C22×C47#42311yescharacteristic
174C22×C47#42411yescharacteristic
175C22×C47#42711yescharacteristic
176C22×C47#42811yescharacteristic
177C22×C47C2×#10811yescharacteristic
178C22×C47#43011yescharacteristic
179C2×D47—22no—
180C2×D47—22no—
181C2×D47—22no—
182C2×D47—41no—
183C2×D47—41no—
184C2×D47—41no—
185C2×D47—41no—
186C4×C47—21no—
187C4×C47—21no—
188C4×C47#43511yescharacteristic
189C4×C47#43511yescharacteristic
190C4×C47#43611yescharacteristic
191C4×C47#43611yescharacteristic
192C4×C47#44911yescharacteristic
193C4×C47#45211yescharacteristic
194C4×C47#48211yescharacteristic
195C4×C47#48511yescharacteristic
196Dic47—41no—
197Dic47—41no—
198Dic47—41no—
199C2×#432—471no—
200#1797—471no—
201C4×C22⋊C8—471no—
202C2×#335—471no—
203C2×#334D4711yescharacteristic, complemented
204#1277—471no—
205#1277—471no—
206C2×C47#156811yescharacteristic
207C2×C47#156911yescharacteristic
208C2×C47#157211yescharacteristic
209C2×C47#157311yescharacteristic
210C2×C47#185111yescharacteristic
211C2×C47#185411yescharacteristic
212C2×C47#185511yescharacteristic
213D47—42no—
214C22×C42—471no—
215#432—942no—
216#432—942no—
217C2×C4⋊C8—471no—
218C2×C4⋊C8—471no—
219C2×C4⋊C8C2×D4711yescharacteristic
220C2×C4⋊C8C2×D4711yescharacteristic
221C2×C22⋊C8—471no—
222C2×C22⋊C8—471no—
223C2×C22⋊C8—941no—
224C2×C22⋊C8—941no—
225C2×#97—941no—
226C2×C4×C8—471no—
227C2×C4×C8C2×D4711yescharacteristic
228#336—471no—
229#336—471no—
230#336—941no—
231#335—942no—
232#334—22no—
233C47#883411yescharacteristic, complemented, Sylow
234C23×C4—471no—
235C23×C4—471no—
236C23×C4—471no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—471no—
240C22×C8—471no—
241C22×C8—941no—
242C22×C8—941no—
243C22×C8C4×D4711yescharacteristic
244C22×C8C4×D4711yescharacteristic
245C2×C42—471no—
246C2×C42—471no—
247C2×C42—471no—
248C2×C42—941no—
249C2×C42—941no—
250C2×C42—941no—
251C2×C42—941no—
252C2×C42C22×D4711yescharacteristic
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—21no—
256C4⋊C8—472no—
257C4⋊C8—941no—
258C4⋊C8—941no—
259C4⋊C8—941no—
260C4⋊C8C22⋊D4712yes—
261C22⋊C8—942no—
262C22⋊C8—944no—
263C22⋊C8—942no—
264C22⋊C8—1882no—
265#97—944no—
266C4×C8—21no—
267C4×C8—21no—
268C4×C8—941no—
269C4×C8—941no—
270C24—471no—
271C22×C4—471no—
272C22×C4—471no—
273C22×C4—471no—
274C22×C4—942no—
275C22×C4—941no—
276C22×C4—941no—
277C22×C4—941no—
278C22×C4—941no—
279C22×C4—941no—
280C22×C4—941no—
281C22×C4—941no—
282C22×C4—941no—
283C22×C4—941no—
284C22×C4—941no—
285C22×C4—941no—
286C22×C4—941no—
287C22×C4—941no—
288C22×C4—941no—
289C22×C4—1881no—
290C22×C4C2×C4×D4711yescharacteristic
291C22×C4D4×D4711yescharacteristic
292C22×C4Q8×D4711yescharacteristic
293C2×C8—21no—
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—22no—
297C2×C8—21no—
298C2×C8—21no—
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—472no—
305C2×C8—941no—
306C2×C8—941no—
307C2×C8—941no—
308C2×C8—942no—
309C2×C8—941no—
310C2×C8—941no—
311C2×C8—1881no—
312C2×C8—1881no—
313C2×C8—1881no—
314C2×C8—1881no—
315C2×C8—1881no—
316C2×C8#1062532412yes—
317C42—941no—
318C42—941no—
319C42—941no—
320C42—941no—
321C42—941no—
322C42—941no—
323C42#1062535011yescharacteristic
324C42D4×D4711yescharacteristic
325C42#1062535411yescharacteristic
326C42C2×C22⋊D4711yescharacteristic
327C23—472no—
328C23—941no—
329C23—941no—
330C23—941no—
331C23—941no—
332C23—941no—
333C23—941no—
334C23C4⋊C4×D4711yescharacteristic
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—941no—
338C2×C4—941no—
339C2×C4—941no—
340C2×C4—941no—
341C2×C4—941no—
342C2×C4—941no—
343C2×C4—941no—
344C2×C4—941no—
345C2×C4—941no—
346C2×C4—1882no—
347C2×C4—1882no—
348C2×C4—1881no—
349C2×C4—1881no—
350C2×C4—1881no—
351C2×C4—1881no—
352C2×C4—1881no—
353C2×C4—1881no—
354C2×C4—1881no—
355C2×C4—1881no—
356C2×C4C4×C22⋊D4711yescharacteristic
357C2×C4#1309398611yescharacteristic
358C2×C4#1309399211yescharacteristic
359C2×C4#1309400011yescharacteristic
360C2×C4#1309400211yescharacteristic
361C2×C4#1309400911yescharacteristic
362C2×C4M16×D4711yescharacteristic
363C2×C4C2×#1062532411yescharacteristic
364C2×C4#1309403011yescharacteristic
365C2×C4#1309403211yescharacteristic
366C2×C4#1309404511yescharacteristic
367C2×C4#1309404511yescharacteristic
368C2×C4#1309405111yescharacteristic
369C2×C4#1309405311yescharacteristic
370C8—22no—
371C8—42no—
372C8—41no—
373C8—81no—
374C8—942no—
375C8—3761no—
376C8—1882no—
377C8—1881no—
378C22—942no—
379C22—942no—
380C22—942no—
381C22—1881no—
382C22—1881no—
383C22—1881no—
384C22—1881no—
385C22#1568899411yescharacteristic
386C22#1568914511yescharacteristic
387C22#1568914811yescharacteristic
388C22#1568915811yescharacteristic
389C22#1568916211yescharacteristic
390C22#108×D4711yescharacteristic
391C22#1568917011yescharacteristic
392C4—21no—
393C4—21no—
394C4—1881no—
395C4—1881no—
396C4—1881no—
397C4#1568919311yescharacteristic
398C4#1568919411yescharacteristic
399C4#1568919911yescharacteristic
400C4#1568920011yescharacteristic
401C4#1568926711yescharacteristic
402C4#1568928211yescharacteristic
403C4#1568944911yescharacteristic
404C4#1568946711yescharacteristic
405C2—1882no—
406C2#2024214811yescharacteristic
407C2#2024215211yescharacteristic
408C2#2024216511yescharacteristic
409C2#2024217011yescharacteristic
410C2#2024356911yescharacteristic
411C2#2024358611yescharacteristic
412C2#2024359111yescharacteristic
subgroupG/H
centerC22×C4D4×D47
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC2×C47×#334C2
socleC23×C47C2×C4⋊C4
prime radicalC23×D47C4⋊C4
cosocleC2×C42×C47C23
hypercenterC2×#334D47
hypocenterC47#8834
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×#334

Complements

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

NH ≅ G/Ntype
4. C2×#15688875C2semidirect
5. #20241223C2semidirect
6. #20241222C2semidirect
7. C2×C47×#334C2semidirect
203. C2×#334D47semidirect
233. C47#8834semidirect

Maximal subgroups

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

subgroupindex
C2×#156891792
#202433652
C4×(C2×D47)⋊C82
C2×#156888752
#202412232
#202412222
C2×C47×#3342
#883447