Finite Group Databasebeta

← #26133140

Subgroups — #26133140

Order 12032.

494 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×M32×D47C211yesmaximal, characteristic, complemented
2#20252080C211yesmaximal, characteristic
3C2×#15688907C211yesmaximal, characteristic, complemented
4C2×(C2×D47)⋊C16C211yesmaximal, characteristic, complemented
5#20241478C211yesmaximal, characteristic, complemented
6#20241476C211yesmaximal, characteristic, complemented
7C2×C47×#350C211yesmaximal, characteristic, complemented
8C22×C8×D47C2211yescharacteristic
9#15689630C411yescharacteristic
10C2×#13093964C2211yescharacteristic
11C2×#13093963—21no—
12M32×D47—22no—
13M32×D47—22no—
14C22×C47⋊C16C2211yescharacteristic
15C2×C16×D47—21no—
16#15689192—21no—
17#15689192—21no—
18C8×C22⋊D47—21no—
19C8×C22⋊D47—21no—
20#15689151C411yescharacteristic
21#15689090C411yescharacteristic
22#15689086C411yescharacteristic
23#15689078C2211yescharacteristic
24#15688907—22no—
25(C2×D47)⋊C16—21no—
26(C2×D47)⋊C16—21no—
27C2×#131×C47C2211yescharacteristic
28C2×M32×C47C2211yescharacteristic
29C22×C16×C47C2211yescharacteristic
30C47×#350—22no—
31C22×C4×D47C2×C411yescharacteristic
32C2×#10625329C2×C411yescharacteristic
33C22×C47⋊C8C2×C411yescharacteristic
34C2×C8×D47—21no—
35C2×C8×D47—21no—
36C2×C8×D47—21no—
37C2×C8×D47—21no—
38C2×C8×D47D411yescharacteristic
39C2×C8×D47D411yescharacteristic
40C2×C8×D47D411yescharacteristic
41C2×C8×D47D411yescharacteristic
42#13094005—21no—
43#13094000C811yescharacteristic
44#13094000C811yescharacteristic
45#13093995C811yescharacteristic
46#13093995C811yescharacteristic
47#13093992—21no—
48C4×C22⋊D47—21no—
49C4×C22⋊D47—21no—
50#13093983C2×C411yescharacteristic
51#13093964—21no—
52#13093964D412yescomplemented
53#13093963—24no—
54C2×C47⋊C16—21no—
55C2×C47⋊C16—21no—
56C2×C47⋊C16—21no—
57C2×C47⋊C16—21no—
58C16×D47—24no—
59Dic47⋊C8—21no—
60Dic47⋊C8—21no—
61C22⋊(C47⋊C8)—21no—
62C22⋊(C47⋊C8)—21no—
63(C2×D47)⋊C8—21no—
64(C2×D47)⋊C8—21no—
65#13093934—21no—
66C8×Dic47—21no—
67C2×#41×C47C2×C411yescharacteristic
68#131×C47—21no—
69#131×C47—21no—
70#131×C47—21no—
71#131×C47—21no—
72C2×M16×C47—21no—
73C2×M16×C47C2×C411yescharacteristic
74C22×C8×C47—21no—
75C22×C8×C47C2311yescharacteristic
76M32×C47—21no—
77M32×C47D412yescomplemented
78C2×C16×C47—21no—
79C2×C16×C47—21no—
80C2×C16×C47—21no—
81C2×C16×C47—21no—
82C23×D47M1611yescharacteristic
83#41×C47—21no—
84#41×C47—21no—
85#41×C47—21no—
86#41×C47—21no—
87C2×Q8×C47C2×C811yescharacteristic
88C2×D4×C47—21no—
89C2×D4×C47C2×C811yescharacteristic
90C22×C4×C47—21no—
91C22×C4×C47C22×C411yescharacteristic
92C2×C22⋊D47—21no—
93C2×C22⋊D47—21no—
94C22×Dic47M1611yescharacteristic
95C2×C4×D47—21no—
96C2×C4×D47—21no—
97C2×C4×D47—21no—
98C2×C4×D47—21no—
99C2×C4×D47C22⋊C411yescharacteristic
100C2×C4×D47C22⋊C411yescharacteristic
101C2×C4×D47C2×C811yescharacteristic
102C2×C4×D47C2×C811yescharacteristic
103M16×C47—21no—
104M16×C47—21no—
105M16×C47—41no—
106M16×C47—41no—
107C2×C8×C47—21no—
108C2×C8×C47—41no—
109C2×C8×C47—41no—
110C2×C8×C47C2×D411yescharacteristic
111C2×C8×C47C2×D411yescharacteristic
112C2×C8×C47C2×D411yescharacteristic
113C2×C8×C47C2×D411yescharacteristic
114C2×C8×C47#4111yescharacteristic
115C2×C8×C47#4111yescharacteristic
116C22⋊Dic47—21no—
117C22⋊Dic47—21no—
118C22⋊Dic47—21no—
119(C2×D47)⋊C4—21no—
120(C2×D47)⋊C4—21no—
121C4⋊Dic47C2×C811yescharacteristic
122C4⋊Dic47C2×C811yescharacteristic
123Dic47⋊C4—21no—
124Dic47⋊C4—21no—
125C4×Dic47—21no—
126#10625329—21no—
127#10625329—21no—
128C2×C47⋊C8—21no—
129C2×C47⋊C8—21no—
130C2×C47⋊C8—21no—
131C2×C47⋊C8C22⋊C411yescharacteristic
132C2×C47⋊C8C22⋊C411yescharacteristic
133C8×D47—21no—
134C8×D47—21no—
135C8×D47—21no—
136C8×D47—21no—
137C8×D47—21no—
138C8×D47—21no—
139C8×D47—21no—
140C8×D47—21no—
141C16×C47—22no—
142C16×C47—41no—
143C47⋊C16—22no—
144C47⋊C16—41no—
145C23×C47—21no—
146C23×C47C2×M1611yescharacteristic
147C22×D47—21no—
148C22×D47—21no—
149C22×D47—22no—
150C22×D47—41no—
151C22×D47C22⋊C811yescharacteristic
152C22×D47C22⋊C811yescharacteristic
153Q8×C47—21no—
154Q8×C47—21no—
155D4×C47—21no—
156D4×C47—21no—
157D4×C47—41no—
158D4×C47—41no—
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×C47C22×C811yescharacteristic
166C2×C4×C47#13111yescharacteristic
167C2×C4×C47#13111yescharacteristic
168C22⋊D47—42no—
169C22⋊D47—42no—
170C2×Dic47—21no—
171C2×Dic47—21no—
172C2×Dic47—21no—
173C2×Dic47—21no—
174C2×Dic47C22⋊C811yescharacteristic
175C2×Dic47C22⋊C811yescharacteristic
176C4×D47—21no—
177C4×D47—21no—
178C4×D47—21no—
179C4×D47—21no—
180C4×D47—21no—
181C4×D47—21no—
182C4×D47—21no—
183C4×D47—21no—
184C8×C47—41no—
185C8×C47#12011yescharacteristic
186C8×C47#12111yescharacteristic
187C8×C47#12111yescharacteristic
188C8×C47#12311yescharacteristic
189C47⋊C8—21no—
190C47⋊C8—21no—
191C47⋊C8—41no—
192#12978—471nomaximal, Sylow
193C22×C47—21no—
194C22×C47—21no—
195C22×C47—41no—
196C22×C47—41no—
197C22×C47—41no—
198C22×C47C2×C22⋊C811yescharacteristic
199C22×C47#43511yescharacteristic
200C22×C47#43511yescharacteristic
201C2×D47—21no—
202C2×D47—21no—
203C2×D47—21no—
204C2×D47—21no—
205C2×D47—21no—
206C2×D47—42no—
207C2×D47—42no—
208C2×D47#35012yescomplemented
209C4×C47—41no—
210C4×C47#38611yescharacteristic
211C4×C47#40811yescharacteristic
212C4×C47C8×D411yescharacteristic
213C4×C47C8×D411yescharacteristic
214Dic47—21no—
215Dic47—21no—
216Dic47—41no—
217Dic47—41no—
218C22×M32—471no—
219#2929—471no—
220C2×#350—471no—
221C2×#350D4711yescharacteristic, complemented
222C2×C22⋊C16—471no—
223#1379—471no—
224#1379—471no—
225C2×C47—21no—
226C2×C47—21no—
227C2×C47—81no—
228C2×C47#186911yescharacteristic
229C2×C47C2×#35011yescharacteristic
230C2×C47#211711yescharacteristic
231D47—22no—
232D47—41no—
233C2×#131C2×D4711yescharacteristic
234C23×C8—471no—
235#525—471no—
236C2×M32—471no—
237C2×M32—941no—
238C2×M32—942no—
239C2×M32—942no—
240C2×M32C2×D4711yescharacteristic
241C22×C16—471no—
242C22×C16—941no—
243C22×C16C2×D4711yescharacteristic
244#435—941no—
245#435—941no—
246C8×D4—941no—
247C8×D4—941no—
248#424—471no—
249#408—471no—
250#407—471no—
251#405—471no—
252#350—22no—
253#350—942no—
254C22⋊C16—941no—
255C22⋊C16—941no—
256C47#1297811yescharacteristic, complemented, Sylow
257C2×#41C4×D4711yescharacteristic
258C23×C4—471no—
259#131—21no—
260#131—21no—
261#131—21no—
262#131—21no—
263C2×M16—21no—
264C2×M16—471no—
265C2×M16C4×D4711yescharacteristic
266C22×C8—21no—
267C22×C8—471no—
268C22×C8—471no—
269C22×C8—471no—
270C22×C8—471no—
271C22×C8—471no—
272C22×C8—941no—
273C22×C8—941no—
274C22×C8—941no—
275C22×C8—941no—
276C22×C8C22×D4711yescharacteristic
277#123—941no—
278C22⋊Q8—471no—
279C22⋊Q8—471no—
280#121—471no—
281#121—471no—
282#120—941no—
283C4×D4—941no—
284C4×D4—941no—
285#117—471no—
286M32—21no—
287M32—472no—
288M32—944no—
289M32—941no—
290M32C22⋊D4712yescomplemented
291C2×C16—21no—
292C2×C16—21no—
293C2×C16—21no—
294C2×C16—21no—
295C2×C16—944no—
296C2×C16—941no—
297C2×C16—941no—
298C2×C16—941no—
299C2×C16—941no—
300C4⋊C8—941no—
301C4⋊C8—941no—
302C22⋊C8—941no—
303C22⋊C8—941no—
304C22⋊C8—941no—
305C22⋊C8—941no—
306#97—941no—
307C4×C8—941no—
308C24—471no—
309#41—21no—
310#41—21no—
311#41—21no—
312#41—21no—
313C2×Q8C8×D4711yescharacteristic
314C2×D4—21no—
315C2×D4—941no—
316C2×D4—941no—
317C2×D4C8×D4711yescharacteristic
318C22×C4—21no—
319C22×C4—471no—
320C22×C4—471no—
321C22×C4—471no—
322C22×C4—471no—
323C22×C4—471no—
324C22×C4—941no—
325C22×C4—941no—
326C22×C4—941no—
327C22×C4—941no—
328C22×C4C2×C4×D4711yescharacteristic
329M16—21no—
330M16—21no—
331M16—41no—
332M16—41no—
333M16—941no—
334M16—941no—
335C2×C8—21no—
336C2×C8—41no—
337C2×C8—41no—
338C2×C8—471no—
339C2×C8—471no—
340C2×C8—941no—
341C2×C8—941no—
342C2×C8—941no—
343C2×C8—941no—
344C2×C8—941no—
345C2×C8—941no—
346C2×C8—941no—
347C2×C8—941no—
348C2×C8—941no—
349C2×C8—941no—
350C2×C8—941no—
351C2×C8#1062535011yescharacteristic
352C2×C8D4×D4711yescharacteristic
353C2×C8D4×D4711yescharacteristic
354C2×C8D4×D4711yescharacteristic
355C2×C8#1062535211yescharacteristic
356C2×C8C2×C22⋊D4711yescharacteristic
357C4⋊C4—471no—
358C4⋊C4—471no—
359C4⋊C4—941no—
360C4⋊C4—941no—
361C22⋊C4—941no—
362C22⋊C4—941no—
363C22⋊C4—941no—
364C22⋊C4—941no—
365C22⋊C4—941no—
366C42—941no—
367C16—22no—
368C16—41no—
369C16—942no—
370C16—1881no—
371C23—21no—
372C23—471no—
373C23—471no—
374C23—942no—
375C23—941no—
376C23—941no—
377C23—1881no—
378C23M16×D4711yescharacteristic
379Q8—21no—
380Q8—21no—
381D4—21no—
382D4—21no—
383D4—41no—
384D4—41no—
385D4—1882no—
386D4—1882no—
387C2×C4—21no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—471no—
391C2×C4—471no—
392C2×C4—941no—
393C2×C4—941no—
394C2×C4—941no—
395C2×C4—941no—
396C2×C4—941no—
397C2×C4—941no—
398C2×C4—941no—
399C2×C4—941no—
400C2×C4—941no—
401C2×C4—941no—
402C2×C4—941no—
403C2×C4—941no—
404C2×C4C22⋊C4×D4711yescharacteristic
405C2×C4(C22⋊D47)⋊C411yescharacteristic
406C2×C4C4×C22⋊D4711yescharacteristic
407C2×C4C2×C8×D4711yescharacteristic
408C2×C4#1309403011yescharacteristic
409C2×C4#1309403211yescharacteristic
410C8—41no—
411C8—941no—
412C8—941no—
413C8—1881no—
414C8#1309399211yescharacteristic
415C8#1309399511yescharacteristic
416C8#1309399711yescharacteristic
417C8#1309400611yescharacteristic
418C22—21no—
419C22—21no—
420C22—41no—
421C22—41no—
422C22—41no—
423C22—472no—
424C22—941no—
425C22—941no—
426C22—941no—
427C22—941no—
428C22—941no—
429C22—1882no—
430C22—1882no—
431C22C22⋊C8×D4711yescharacteristic
432C22#1568919211yescharacteristic
433C22#1568919711yescharacteristic
434C4—41no—
435C4—941no—
436C4—941no—
437C4—1881no—
438C4—1881no—
439C4#1568899911yescharacteristic
440C4#1568908811yescharacteristic
441C4(C22⋊D47)⋊C811yescharacteristic
442C4C8×C22⋊D4711yescharacteristic
443C2—21no—
444C2—21no—
445C2—81no—
446C2—942no—
447C2—1881no—
448C2#2024367711yescharacteristic
449C2#350×D4711yescharacteristic
450C2#2024501411yescharacteristic
subgroupG/H
centerC2×C8D4×D47
commutatorC2×C4×C47C22×C8
FrattiniC22×C8C22×D47
FittingC2×C47×#350C2
socleC22×C47C2×C22⋊C8
prime radical#15689630C4
cosocleC22×C8×C47C23
hypercenterC2×#350D47
hypocenterC47#12978
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ C2×#350

Complements

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

NH ≅ G/Ntype
1. C2×M32×D47C2semidirect
3. C2×#15688907C2semidirect
4. C2×(C2×D47)⋊C16C2semidirect
5. #20241478C2semidirect
6. #20241476C2semidirect
7. C2×C47×#350C2semidirect
52. #13093964D4semidirect
77. M32×C47D4semidirect
208. C2×D47#350semidirect
221. C2×#350D47semidirect
256. C47#12978semidirect
290. M32C22⋊D47semidirect

Maximal subgroups

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

subgroupindex
C2×M32×D472
#202520802
C2×#156889072
C2×(C2×D47)⋊C162
#202414782
#202414762
C2×C47×#3502
#1297847