Finite Group Databasebeta

← #26220683

Subgroups — #26220683

Order 12032.

722 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13094044C211yesmaximal, characteristic
2#20252040C211yesmaximal, characteristic, complemented
3#20252039C211yesmaximal, characteristic, complemented
4#20244273C212yesmaximal
5#20244135C212yesmaximal, complemented
6#20244100C212yesmaximal, complemented
7#20244096C212yesmaximal, complemented
8C4×#13093959C211yesmaximal, characteristic, complemented
9#20243199C211yesmaximal, characteristic, complemented
10#20243075C211yesmaximal, characteristic, complemented
11C47×#1759C211yesmaximal, characteristic, complemented
12C2×#13094044C2211yescharacteristic
13C4×#10625350C2211yescharacteristic
14C4×#10625337C412yescomplemented
15C4×#10625336C412yescomplemented
16C4×#10625335C412yescomplemented
17C4×#10625334C412yescomplemented
18#15689184—22no—
19#15689182—22no—
20#15689180—22no—
21#15689178—22no—
22C2×#13093959C2212yes—
23#15689159C2211yescharacteristic
24#15689151C2212yes—
25#15689150C2212yes—
26C2×#13093952C2212yes—
27#15689119C2211yescharacteristic
28#15689117C2211yescharacteristic
29#15689091C2212yes—
30#15689090C2212yes—
31C4×#10625329C2211yescharacteristic
32C2×#13093935C2212yes—
33C2×#13093935C2211yescharacteristic
34C2×C4×C47⋊C8C2212yes—
35C2×C4×C47⋊C8C2211yescharacteristic
36#15688887C2212yes—
37#15688883C2212yes—
38C4×#41×C47C2211yescharacteristic
39C2×#104×C47C2212yes—
40C4×M16×C47C2211yescharacteristic
41C47×#376C2211yescharacteristic
42C47×#339C2212yes—
43C2×#10625350C2311yescharacteristic
44#13094044—24no—
45C2×#10625337C2×C411yescharacteristic
46C2×#10625335C2×C411yescharacteristic
47C2×#10625336C2×C411yescharacteristic
48C2×#10625334C2×C411yescharacteristic
49C2×#10625329C2312yes—
50C22×C47⋊C8C2311yescharacteristic
51C22×C47⋊C8C2312yes—
52C22×C47⋊C8C2311yescharacteristic
53C4×Dic94C2×C412yes—
54C4×D188C2×C412yes—
55C4×C22⋊D47—22no—
56#13093983C2311yescharacteristic
57#13093981—21no—
58C42×D47—21no—
59#13093959—24no—
60#13093957C2×C412yes—
61#13093955C2×C412yes—
62C4⋊(C47⋊C8)—24no—
63Dic47⋊C8—24no—
64#13093952—24no—
65#13093948C2×C412yes—
66#13093947C2×C412yes—
67#13093945C2×C412yes—
68#13093944C2×C412yes—
69C22⋊(C47⋊C8)—24no—
70(C2×D47)⋊C8—24no—
71#13093935—21no—
72#13093935—24no—
73#13093935D412yes—
74#13093935D412yes—
75C4×C47⋊C8—21no—
76C4×C47⋊C8—24no—
77C4×C47⋊C8C2×C412yes—
78C4×C47⋊C8C2×C412yes—
79C2×#41×C47C2311yescharacteristic
80C2×M16×C47C2312yes—
81C4×Q8×C47C2×C412yes—
82C4×D4×C47—22no—
83C4×D4×C47C2×C412yes—
84#117×C47—21no—
85#117×C47C2311yescharacteristic
86C2×C42×C47—21no—
87C2×C42×C47C2312yes—
88C2×C42×C47C2311yescharacteristic
89#104×C47—24no—
90#97×C47—21no—
91C4×C8×C47—21no—
92#95×C47—22no—
93#41×C47—22no—
94#41×C47—22no—
95C2×Q8×C47C22×C411yescharacteristic
96C2×D4×C47—21no—
97C2×D4×C47C22×C411yescharacteristic
98C22×C4×C47—22no—
99C22×C4×C47—21no—
100C22×C4×C47—22no—
101C22×C4×C47#4112yes—
102C22×C4×C47C2411yescharacteristic
103C2×C22⋊D47—21no—
104#10625350—22no—
105#10625350—22no—
106C2×D188C22×C411yescharacteristic
107C2×C4×D47—21no—
108C2×C4×D47—22no—
109C2×Dic94C22×C411yescharacteristic
110M16×C47—22no—
111M16×C47—22no—
112C2×C8×C47—22no—
113C4⋊C4×C47—22no—
114C4⋊C4×C47C22×C412yes—
115C22⋊C4×C47—21no—
116C22⋊C4×C47—22no—
117C42×C47—22no—
118C42×C47—21no—
119C42×C47—22no—
120C42×C47C22×C412yes—
121C42×C47C2×D411yescharacteristic
122C42×C47C2×D411yescharacteristic
123C42×C47#4114yes—
124C22⋊Dic47—21no—
125#10625337—22no—
126#10625336—22no—
127#10625335—22no—
128#10625334—22no—
129(C2×D47)⋊C4—22no—
130C4⋊Dic47C22×C412yes—
131Dic47⋊C4—22no—
132C4×Dic47—22no—
133C4×Dic47—21no—
134#10625329—22no—
135#10625329—22no—
136C2×C47⋊C8—22no—
137C2×C47⋊C8—22no—
138C2×C47⋊C8—22no—
139C2×C47⋊C8—22no—
140C2×C47⋊C8C22×C412yes—
141C2×C47⋊C8C22×C411yescharacteristic
142C2×C47⋊C8C22×C411yescharacteristic
143C2×C47⋊C8C2×D414yes—
144C2×C47⋊C8#4114yes—
145C23×C47—21no—
146C23×C47C2×#4111yescharacteristic
147C22×D47—21no—
148Q8×C47—21no—
149Q8×C47—21no—
150D4×C47—21no—
151D4×C47—21no—
152D4×C47—42no—
153C2×C4×C47—22no—
154C2×C4×C47—21no—
155C2×C4×C47—24no—
156C2×C4×C47—42no—
157C2×C4×C47—44no—
158C2×C4×C47—42no—
159C2×C4×C47—82no—
160C2×C4×C47C4×D412yes—
161C2×C4×C47C4×D412yes—
162C2×C4×C47C23×C411yescharacteristic
163C2×C4×C47C22×D411yescharacteristic
164C2×C4×C47C2×#4112yes—
165C2×C4×C47C2×#4112yes—
166C22⋊D47—42no—
167C2×Dic47—21no—
168C2×Dic47—22no—
169D188—21no—
170D188—21no—
171C4×D47—42no—
172C4×D47—82no—
173Dic94—21no—
174Dic94—21no—
175C8×C47—42no—
176C47⋊C8—22no—
177C47⋊C8—24no—
178C47⋊C8—42no—
179C47⋊C8#11712yes—
180C47⋊C8#11712yes—
181#21294—471nomaximal, Sylow
182C22×C47—22no—
183C22×C47—42no—
184C22×C47—41no—
185C22×C47C2×C4×D411yescharacteristic
186C22×C47#52912yes—
187C2×D47—42no—
188C2×D47—41no—
189C4×C47—22no—
190C4×C47—22no—
191C4×C47—44no—
192C4×C47—42no—
193C4×C47—41no—
194C4×C47C2×#11711yescharacteristic
195C4×C47C4×#4111yescharacteristic
196C4×C47#53212yes—
197Dic47—42no—
198Dic47—41no—
199C4×#135—471no—
200#2923—471no—
201#2923—471no—
202#1974—472no—
203#1945—472no—
204#1938—472no—
205#1938—472no—
206C4×#108—471no—
207#1759—471no—
208#1759D4711yescharacteristic, complemented
209#1726—471no—
210C2×C47—22no—
211C2×C47—81no—
212C2×C47#229311yescharacteristic
213C2×C47#295712yes—
214D47—81no—
215C2×#135—471no—
216C4×#41—471no—
217C4×#41C2×D4711yescharacteristic
218C4×Q16—472no—
219C4×SD16—472no—
220C4×SD16—472no—
221C4×D8—472no—
222#433—942no—
223#433—942no—
224#432—942no—
225#432—942no—
226C2×#108—472no—
227#427—471no—
228#424—472no—
229#424—472no—
230C2×#104—472no—
231C2×#104C2×D4712yes—
232#416—471no—
233#416—471no—
234#408—472no—
235#408—472no—
236C4×M16—471no—
237C4×M16C2×D4711yescharacteristic
238C2×#97—471no—
239C2×#97—472no—
240C2×C4×C8—471no—
241C2×C4×C8—472no—
242#376C2×D4711yescharacteristic
243#341—472no—
244#339—472no—
245#339C2×D4712yes—
246C47#2129411yescharacteristic, complemented, Sylow
247C2×#41—471no—
248C2×#41C22×D4711yescharacteristic
249#135—944no—
250C2×Q16—471no—
251C2×SD16—471no—
252C2×SD16—471no—
253C2×D8—471no—
254C2×M16—472no—
255C2×M16C22×D4712yes—
256C22×C8—471no—
257C22×C8—471no—
258C22×C8—472no—
259C4×Q8—472no—
260C4×Q8C4×D4712yes—
261C4×D4—22no—
262C4×D4—472no—
263C4×D4—942no—
264C4×D4C4×D4712yes—
265#117—21no—
266#117—471no—
267#117—941no—
268#117C22×D4711yescharacteristic
269C2×C42—21no—
270C2×C42—941no—
271C2×C42C22×D4712yes—
272C2×C42C22×D4711yescharacteristic
273#108—944no—
274#107—472no—
275#106—472no—
276C4⋊C8—944no—
277C4⋊C8—944no—
278#104—24no—
279#104—944no—
280#103—472no—
281#103—472no—
282#102—472no—
283#102—472no—
284C22⋊C8—944no—
285C22⋊C8—944no—
286#97—21no—
287#97—472no—
288#97—472no—
289#97—944no—
290#97—941no—
291C4×C8—21no—
292C4×C8—472no—
293C4×C8—472no—
294C4×C8—944no—
295C4×C8—941no—
296#95—22no—
297#41—22no—
298#41—22no—
299#41—942no—
300#41—942no—
301C2×Q8—471no—
302C2×Q8C2×C4×D4711yescharacteristic
303C2×D4—21no—
304C2×D4—471no—
305C2×D4—941no—
306C2×D4C2×C4×D4711yescharacteristic
307C22×C4—22no—
308C22×C4—21no—
309C22×C4—22no—
310C22×C4—942no—
311C22×C4—941no—
312C22×C4#1062535212yes—
313C22×C4C23×D4711yescharacteristic
314Q16—942no—
315SD16—942no—
316SD16—942no—
317D8—942no—
318M16—22no—
319M16—22no—
320M16—942no—
321M16—942no—
322C2×C8—22no—
323C2×C8—471no—
324C2×C8—471no—
325C2×C8—474no—
326C2×C8—472no—
327C2×C8—474no—
328C2×C8—942no—
329C2×C8—942no—
330C2×C8—942no—
331C2×C8—942no—
332C4⋊C4—22no—
333C4⋊C4—472no—
334C4⋊C4—942no—
335C4⋊C4C2×C4×D4712yes—
336C22⋊C4—21no—
337C22⋊C4—22no—
338C22⋊C4—941no—
339C22⋊C4—942no—
340C42—22no—
341C42—21no—
342C42—22no—
343C42—942no—
344C42—941no—
345C42C2×C4×D4712yes—
346C42#1062535014yes—
347C42D4×D4711yescharacteristic
348C42D4×D4711yescharacteristic
349C23—21no—
350C23—941no—
351C23C2×#1062535211yescharacteristic
352Q8—21no—
353Q8—21no—
354Q8—941no—
355Q8—941no—
356D4—21no—
357D4—21no—
358D4—42no—
359D4—941no—
360D4—941no—
361D4—1882no—
362C2×C4—22no—
363C2×C4—21no—
364C2×C4—24no—
365C2×C4—42no—
366C2×C4—44no—
367C2×C4—42no—
368C2×C4—82no—
369C2×C4—942no—
370C2×C4—941no—
371C2×C4—3762no—
372C2×C4—1882no—
373C2×C4(C22⋊D47)⋊C412yes—
374C2×C4(C22⋊D47)⋊C412yes—
375C2×C4C22×C4×D4711yescharacteristic
376C2×C4C2×D4×D4711yescharacteristic
377C2×C4#41×D4712yes—
378C2×C4C2×#1062535012yes—
379C8—42no—
380C8—472no—
381C8—472no—
382C8—942no—
383C8—944no—
384C8—1882no—
385C22—22no—
386C22—41no—
387C22—42no—
388C22—1881no—
389C22—1882no—
390C22C2×(C22⋊D47)⋊C411yescharacteristic
391C22#1568965312yes—
392C4—22no—
393C4—22no—
394C4—44no—
395C4—41no—
396C4—42no—
397C4—1881no—
398C4—1882no—
399C4#117×D4711yescharacteristic
400C4C4×#1062535011yescharacteristic
401C4#1568967012yes—
402C2—22no—
403C2—81no—
404C2—3761no—
405C2#2024585111yescharacteristic
406C2#2025230112yes—
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1759C2
socleC22×C47C2×C4×D4
prime radicalC2×#13094044C22
cosocleC22×C4×C47C24
hypercenter#1759D47
hypocenterC47#21294
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1759

Complements

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

NH ≅ G/Ntype
2. #20252040C2semidirect
3. #20252039C2semidirect
5. #20244135C2semidirect
6. #20244100C2semidirect
7. #20244096C2semidirect
8. C4×#13093959C2semidirect
9. #20243199C2semidirect
10. #20243075C2semidirect
11. C47×#1759C2semidirect
14. C4×#10625337C4semidirect
15. C4×#10625336C4semidirect
16. C4×#10625335C4semidirect
17. C4×#10625334C4semidirect
208. #1759D47semidirect
246. C47#21294semidirect

Maximal subgroups

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

subgroupindex
C4×#130940442
#202520402
#202520392
#202442732
#202441352
#202441002
#202440962
C4×#130939592
#202431992
#202430752
C47×#17592
#2129447