Finite Group Databasebeta

← #26133181

Subgroups — #26133181

Order 12032.

510 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×M32×D47C211yesmaximal, characteristic, complemented
2C2×#15689196C211yesmaximal, characteristic
3C2×#15688904C211yesmaximal, characteristic, complemented
4C2×#15688904C211yesmaximal, characteristic, complemented
5#20244998C211yesmaximal, characteristic, complemented
6#20241472C211yesmaximal, characteristic, complemented
7C47×#1377C211yesmaximal, characteristic, complemented
8C22×#10625324C2211yescharacteristic
9C22×C8×D47C2211yescharacteristic
10C2×C4×D188C411yescharacteristic
11C2×#13093964C2211yescharacteristic
12C2×#13093964C2211yescharacteristic
13C2×#13093963—21no—
14M32×D47—22no—
15M32×D47—22no—
16C2×C16×D47—21no—
17#15689196—21no—
18#15689196—21no—
19#15689196—21no—
20#15689196—21no—
21C2×C4⋊(C47⋊C8)C411yescharacteristic
22C2×(C2×D47)⋊C8C411yescharacteristic
23C2×(C2×D47)⋊C8C411yescharacteristic
24#15688904—22no—
25#15688904—22no—
26(C2×D47)⋊C16—21no—
27(C2×D47)⋊C16—21no—
28C2×M32×C47C2211yescharacteristic
29C2×M32×C47C2211yescharacteristic
30C2×#97×C47C2211yescharacteristic
31C22×D188C811yescharacteristic
32C22×C4×D47C2×C411yescharacteristic
33C22×C4×D47C2×C411yescharacteristic
34C2×#10625324—21no—
35C2×#10625324—21no—
36C2×#10625324—21no—
37C2×#10625324—21no—
38C2×#10625324—21no—
39C2×#10625324—21no—
40C22×C47⋊C8C2×C411yescharacteristic
41C22×C47⋊C8C2×C411yescharacteristic
42C2×C8×D47—21no—
43C2×C8×D47—21no—
44C2×C8×D47—21no—
45C2×C8×D47—21no—
46C2×C8×D47D411yescharacteristic
47C2×C8×D47D411yescharacteristic
48C2×C8×D47D411yescharacteristic
49C2×C8×D47D411yescharacteristic
50C4×D188—21no—
51C4×D188—21no—
52C4×D188—21no—
53C4×D188—21no—
54C2×C4⋊Dic47C811yescharacteristic
55C2×(C2×D47)⋊C4C811yescharacteristic
56C2×(C2×D47)⋊C4C811yescharacteristic
57#13093964—21no—
58#13093964—21no—
59#13093964—21no—
60#13093964D412yescomplemented
61#13093963—24no—
62C2×C47⋊C16—21no—
63C2×C47⋊C16—21no—
64C16×D47—24no—
65C4⋊(C47⋊C8)—21no—
66C4⋊(C47⋊C8)—21no—
67(C2×D47)⋊C8—21no—
68(C2×D47)⋊C8—21no—
69(C2×D47)⋊C8—21no—
70(C2×D47)⋊C8—21no—
71C22×C8×C47C2×C411yescharacteristic
72C22×C8×C47C2311yescharacteristic
73C2×C42×C47C2×C411yescharacteristic
74M32×C47—21no—
75M32×C47—21no—
76M32×C47—21no—
77M32×C47D412yescomplemented
78C2×C16×C47—21no—
79C2×C16×C47—21no—
80#97×C47—21no—
81#97×C47—21no—
82C23×D47C2×C811yescharacteristic
83C23×D47C2×C811yescharacteristic
84C22×C4×C47C2×C811yescharacteristic
85C22×C4×C47C2×C811yescharacteristic
86C22×C4×C47C22×C411yescharacteristic
87C22×Dic47C2×C811yescharacteristic
88C22×Dic47C2×C811yescharacteristic
89C2×D188—21no—
90C2×D188—21no—
91C2×D188—42no—
92C2×C4×D47—21no—
93C2×C4×D47—21no—
94C2×C4×D47—21no—
95C2×C4×D47—21no—
96C2×C4×D47—21no—
97C2×C4×D47—21no—
98C2×C4×D47—21no—
99C2×C4×D47—21no—
100C2×C4×D47—21no—
101C2×C4×D47—21no—
102C2×C4×D47C22⋊C411yescharacteristic
103C2×C4×D47C22⋊C411yescharacteristic
104C2×C4×D47M1611yescharacteristic
105C2×C4×D47M1611yescharacteristic
106C2×C8×C47—21no—
107C2×C8×C47—21no—
108C2×C8×C47—21no—
109C2×C8×C47C2×D411yescharacteristic
110C2×C8×C47C2×D411yescharacteristic
111C2×C8×C47C2×D411yescharacteristic
112C2×C8×C47C2×D411yescharacteristic
113C2×C8×C47#4111yescharacteristic
114C2×C8×C47#4111yescharacteristic
115C42×C47—21no—
116C42×C47—21no—
117(C2×D47)⋊C4—21no—
118(C2×D47)⋊C4—21no—
119(C2×D47)⋊C4—21no—
120(C2×D47)⋊C4—21no—
121C4⋊Dic47—21no—
122C4⋊Dic47—21no—
123C2×C47⋊C8—21no—
124C2×C47⋊C8—21no—
125C2×C47⋊C8—21no—
126C2×C47⋊C8—21no—
127C2×C47⋊C8—21no—
128C2×C47⋊C8C22⋊C411yescharacteristic
129C2×C47⋊C8C22⋊C411yescharacteristic
130#10625324—41no—
131#10625324—41no—
132#10625324—41no—
133#10625324—41no—
134C8×D47—21no—
135C8×D47—21no—
136C8×D47—21no—
137C8×D47—21no—
138C8×D47—21no—
139C8×D47—21no—
140C8×D47—21no—
141C8×D47—21no—
142C16×C47—22no—
143C16×C47—41no—
144C47⋊C16—22no—
145C47⋊C16—41no—
146C23×C47C22×C811yescharacteristic
147C22×D47—21no—
148C22×D47—21no—
149C22×D47—22no—
150C22×D47—21no—
151C22×D47—21no—
152C22×D47—21no—
153C22×D47—41no—
154C22×D47—41no—
155C22×D47—41no—
156C22×D47C22⋊C811yescharacteristic
157C22×D47C22⋊C811yescharacteristic
158C2×C4×C47—21no—
159C2×C4×C47—21no—
160C2×C4×C47—41no—
161C2×C4×C47—41no—
162C2×C4×C47C2×C22⋊C411yescharacteristic
163C2×C4×C47C4×D411yescharacteristic
164C2×C4×C47C4×D411yescharacteristic
165C2×C4×C47C2×M1611yescharacteristic
166C2×C4×C47#13111yescharacteristic
167C2×C4×C47#13111yescharacteristic
168C2×Dic47—21no—
169C2×Dic47—21no—
170C2×Dic47—21no—
171C2×Dic47—21no—
172C2×Dic47—21no—
173C2×Dic47C22⋊C811yescharacteristic
174C2×Dic47C22⋊C811yescharacteristic
175D188—42no—
176D188—42no—
177C4×D47—21no—
178C4×D47—21no—
179C4×D47—21no—
180C4×D47—21no—
181C4×D47—21no—
182C4×D47—21no—
183C4×D47—21no—
184C4×D47—21no—
185C4×D47—41no—
186C4×D47—41no—
187C4×D47—41no—
188C4×D47—41no—
189C8×C47—41no—
190C8×C47#12011yescharacteristic
191C8×C47#12111yescharacteristic
192C8×C47#12111yescharacteristic
193C8×C47#12311yescharacteristic
194C47⋊C8—21no—
195C47⋊C8—21no—
196C47⋊C8—41no—
197#12985—471nomaximal, Sylow
198C22×C47—21no—
199C22×C47—21no—
200C22×C47C2×C22⋊C811yescharacteristic
201C22×C47C8×D411yescharacteristic
202C22×C47C8×D411yescharacteristic
203C2×D47—21no—
204C2×D47—21no—
205C2×D47—21no—
206C2×D47—21no—
207C2×D47—21no—
208C2×D47—42no—
209C2×D47—42no—
210C2×D47—41no—
211C2×D47—41no—
212C2×D47—41no—
213C2×D47—81no—
214C2×D47—81no—
215C2×D47#34912yescomplemented
216C4×C47—41no—
217C4×C47—41no—
218C4×C47#38611yescharacteristic
219C4×C47#40811yescharacteristic
220C4×C47#43511yescharacteristic
221C4×C47#43511yescharacteristic
222Dic47—21no—
223Dic47—21no—
224Dic47—41no—
225C22×M32—471no—
226C2×#435—471no—
227C2×#349—471no—
228C2×#349—471no—
229#2112—471no—
230#1377—471no—
231#1377D4711yescharacteristic, complemented
232C2×C47—21no—
233C2×C47—21no—
234C2×C47#186911yescharacteristic
235C2×C47C2×#34911yescharacteristic
236C2×C47#211511yescharacteristic
237D47—22no—
238D47—41no—
239D47—81no—
240C22×M16—471no—
241C23×C8—471no—
242C2×C4×D4—471no—
243C2×M32—471no—
244C2×M32—471no—
245C2×M32—941no—
246C2×M32—942no—
247C2×M32—942no—
248C2×M32C2×D4711yescharacteristic
249C2×M32C2×D4711yescharacteristic
250C22×C16—941no—
251#435—941no—
252#435—941no—
253#435—941no—
254#435—941no—
255C2×C4⋊C8—471no—
256C2×C22⋊C8—471no—
257C2×C22⋊C8—471no—
258C2×#97C2×D4711yescharacteristic
259#349—942no—
260#349—942no—
261C22⋊C16—941no—
262C22⋊C16—941no—
263C47#1298511yescharacteristic, complemented, Sylow
264C22×D4—471no—
265C23×C4—471no—
266C23×C4—471no—
267C2×M16—941no—
268C2×M16—941no—
269C2×M16—941no—
270C2×M16—941no—
271C2×M16—941no—
272C2×M16—941no—
273C22×C8—471no—
274C22×C8—471no—
275C22×C8—471no—
276C22×C8—471no—
277C22×C8—471no—
278C22×C8—471no—
279C22×C8—941no—
280C22×C8—941no—
281C22×C8—941no—
282C22×C8—941no—
283C22×C8C4×D4711yescharacteristic
284C22×C8C22×D4711yescharacteristic
285C4×D4—941no—
286C4×D4—941no—
287C4×D4—941no—
288C4×D4—941no—
289C2×C4⋊C4—471no—
290C2×C22⋊C4—471no—
291C2×C22⋊C4—471no—
292C2×C42C4×D4711yescharacteristic
293M32—21no—
294M32—21no—
295M32—21no—
296M32—472no—
297M32—944no—
298M32—941no—
299M32—941no—
300M32—941no—
301M32D18812yescomplemented
302C2×C16—21no—
303C2×C16—21no—
304C2×C16—944no—
305C2×C16—941no—
306C2×C16—941no—
307C4⋊C8—941no—
308C4⋊C8—941no—
309C22⋊C8—941no—
310C22⋊C8—941no—
311C22⋊C8—941no—
312C22⋊C8—941no—
313#97—21no—
314#97—21no—
315C24—471no—
316C24—471no—
317C2×D4—941no—
318C2×D4—941no—
319C2×D4—1882no—
320C22×C4—471no—
321C22×C4—471no—
322C22×C4—471no—
323C22×C4—471no—
324C22×C4—471no—
325C22×C4—471no—
326C22×C4—941no—
327C22×C4—941no—
328C22×C4—941no—
329C22×C4—941no—
330C22×C4—941no—
331C22×C4—941no—
332C22×C4—941no—
333C22×C4—941no—
334C22×C4—941no—
335C22×C4—941no—
336C22×C4C8×D4711yescharacteristic
337C22×C4C8×D4711yescharacteristic
338C22×C4C2×C4×D4711yescharacteristic
339M16—1881no—
340M16—1881no—
341M16—1881no—
342M16—1881no—
343C2×C8—21no—
344C2×C8—21no—
345C2×C8—21no—
346C2×C8—471no—
347C2×C8—471no—
348C2×C8—941no—
349C2×C8—941no—
350C2×C8—941no—
351C2×C8—941no—
352C2×C8—941no—
353C2×C8—941no—
354C2×C8—941no—
355C2×C8—941no—
356C2×C8—941no—
357C2×C8—941no—
358C2×C8—941no—
359C2×C8—941no—
360C2×C8—941no—
361C2×C8C2×D18811yescharacteristic
362C2×C8#1062535011yescharacteristic
363C2×C8D4×D4711yescharacteristic
364C2×C8D4×D4711yescharacteristic
365C2×C8D4×D4711yescharacteristic
366C2×C8#1062535411yescharacteristic
367C4⋊C4—941no—
368C4⋊C4—941no—
369C22⋊C4—941no—
370C22⋊C4—941no—
371C22⋊C4—941no—
372C22⋊C4—941no—
373C42—21no—
374C42—21no—
375C16—22no—
376C16—41no—
377C16—942no—
378C16—1881no—
379C23—471no—
380C23—471no—
381C23—942no—
382C23—941no—
383C23—941no—
384C23—941no—
385C23—941no—
386C23—941no—
387C23—1881no—
388C23—1881no—
389C23—1881no—
390C23C2×C8×D4711yescharacteristic
391D4—1882no—
392D4—1882no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—471no—
398C2×C4—471no—
399C2×C4—941no—
400C2×C4—941no—
401C2×C4—941no—
402C2×C4—941no—
403C2×C4—941no—
404C2×C4—941no—
405C2×C4—941no—
406C2×C4—941no—
407C2×C4—941no—
408C2×C4—941no—
409C2×C4—941no—
410C2×C4—941no—
411C2×C4—941no—
412C2×C4—1881no—
413C2×C4—1881no—
414C2×C4—1881no—
415C2×C4—1881no—
416C2×C4C22⋊C4×D4711yescharacteristic
417C2×C4#1309398611yescharacteristic
418C2×C4C4×D18811yescharacteristic
419C2×C4M16×D4711yescharacteristic
420C2×C4#1309403011yescharacteristic
421C2×C4#1309403211yescharacteristic
422C8—41no—
423C8—941no—
424C8—941no—
425C8—1881no—
426C8#1309399411yescharacteristic
427C8#1309399711yescharacteristic
428C8#1309399911yescharacteristic
429C8#1309400911yescharacteristic
430C22—21no—
431C22—21no—
432C22—472no—
433C22—941no—
434C22—941no—
435C22—941no—
436C22—941no—
437C22—941no—
438C22—3761no—
439C22—3761no—
440C22—1882no—
441C22—1882no—
442C22—1881no—
443C22—1881no—
444C22—1881no—
445C22C22⋊C8×D4711yescharacteristic
446C22#1568918811yescharacteristic
447C22C8×D18811yescharacteristic
448C4—41no—
449C4—41no—
450C4—941no—
451C4—941no—
452C4—1881no—
453C4#1568900111yescharacteristic
454C4#1568908811yescharacteristic
455C4#1568919311yescharacteristic
456C4#1568919611yescharacteristic
457C2—21no—
458C2—21no—
459C2—942no—
460C2—3761no—
461C2—1881no—
462C2#2024367911yescharacteristic
463C2#349×D4711yescharacteristic
464C2#2024500711yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D47
commutatorC23×C47C22×C8
FrattiniC22×C8C22×D47
FittingC47×#1377C2
socleC22×C47C2×C22⋊C8
prime radicalC22×D188C8
cosocleC22×C8×C47C23
hypercenter#1377D47
hypocenterC47#12985
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1377

Complements

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

NH ≅ G/Ntype
1. C2×M32×D47C2semidirect
3. C2×#15688904C2semidirect
4. C2×#15688904C2semidirect
5. #20244998C2semidirect
6. #20241472C2semidirect
7. C47×#1377C2semidirect
60. #13093964D4semidirect
77. M32×C47D4semidirect
215. C2×D47#349semidirect
231. #1377D47semidirect
263. C47#12985semidirect
301. M32D188semidirect

Maximal subgroups

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

subgroupindex
C2×M32×D472
C2×#156891962
C2×#156889042
#202449982
#202414722
C47×#13772
#1298547