Finite Group Databasebeta

← #26371353

Subgroups — #26371353

Order 12032.

592 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253967C211yesmaximal, characteristic, complemented
2#20245579C212yesmaximal, complemented
3#20245530C211yesmaximal, characteristic, complemented
4#20245525C211yesmaximal, characteristic, complemented
5#20245428C211yesmaximal, characteristic, complemented
6#20245423C211yesmaximal, characteristic, complemented
7#20245311C212yesmaximal, complemented
8#20245262C212yesmaximal, complemented
9#20245250C212yesmaximal, complemented
10#20245191C211yesmaximal, characteristic, complemented
11C4×#135×C47C211yesmaximal, characteristic, complemented
12#15689673—21no—
13C2×#13093967C2212yes—
14C2×#13093965C2212yes—
15#15689528C2211yescharacteristic
16#15689500C2211yescharacteristic
17#15689470—21no—
18#15689359—21no—
19#15689359C2212yes—
20C4×D376—21no—
21C4×D376C2212yes—
22#15688950C2212yes—
23#15688948C2212yes—
24C4⋊(C47⋊C16)C2211yescharacteristic
25C4⋊(C47⋊C16)C2211yescharacteristic
26#15688927C2212yes—
27#15688924C2212yes—
28#15688923C2212yes—
29#15688923C2212yes—
30C22⋊(C47⋊C16)C2212yes—
31#15688899C2212yes—
32C2×#135×C47C2211yescharacteristic
33C4×#41×C47—21no—
34C4×Q16×C47C2211yescharacteristic
35C4×Q16×C47C2211yescharacteristic
36C4×SD16×C47—21no—
37C4×SD16×C47—21no—
38C4×D8×C47C2211yescharacteristic
39C4×D8×C47C2211yescharacteristic
40C47×#427C2211yescharacteristic
41C47×#416—21no—
42C2×C4×C8×C47C2211yescharacteristic
43C2×#10625350—41no—
44C2×D376—21no—
45C2×D376C2312yes—
46#13094024—21no—
47#13094021—21no—
48#13094012—41no—
49#13093998—22no—
50#13093998—41no—
51C4×D188—22no—
52C4×D188—41no—
53#13093967—24no—
54#13093965—24no—
55C2×C47⋊C16C2312yes—
56C2×C47⋊C16C2312yes—
57#13093958—21no—
58#13093958C2312yes—
59#13093946—22no—
60#13093946—22no—
61C2×#41×C47—21no—
62#135×C47—22no—
63#135×C47—22no—
64C2×Q16×C47C2311yescharacteristic
65C2×SD16×C47—21no—
66C2×D8×C47C2311yescharacteristic
67C22×C8×C47D411yescharacteristic
68C22×C8×C47C2311yescharacteristic
69C4×Q8×C47—21no—
70C4×Q8×C47—21no—
71C4×D4×C47—21no—
72C4×D4×C47—21no—
73C4×D4×C47—41no—
74C4×D4×C47—41no—
75#117×C47—21no—
76#117×C47—41no—
77C2×C42×C47—41no—
78C2×C42×C47D411yescharacteristic
79#107×C47C2311yescharacteristic
80#107×C47C2311yescharacteristic
81#106×C47—21no—
82#103×C47—21no—
83#103×C47—21no—
84#102×C47—21no—
85#102×C47—21no—
86C4×C8×C47D411yescharacteristic
87C4×C8×C47D411yescharacteristic
88C4×C8×C47C2311yescharacteristic
89C4×C8×C47C2311yescharacteristic
90#41×C47—24no—
91#41×C47—42no—
92C2×Q8×C47—21no—
93C2×D4×C47—21no—
94C2×D4×C47—41no—
95C22×C4×C47—41no—
96C22×C4×C47—41no—
97C22×C4×C47—41no—
98C22×C4×C47D811yescharacteristic
99C22×C4×C47D811yescharacteristic
100C22×C4×C47C2×D411yescharacteristic
101C2×C22⋊D47—42no—
102#10625350—84no—
103C2×D188—22no—
104C2×D188—41no—
105C2×D188—41no—
106C2×C4×D47—42no—
107C2×Dic94—41no—
108Q16×C47—21no—
109Q16×C47#4112yescomplemented
110SD16×C47—24no—
111D8×C47—21no—
112D8×C47#4112yescomplemented
113C2×C8×C47—21no—
114C2×C8×C47—21no—
115C2×C8×C47—41no—
116C2×C8×C47C2×D411yescharacteristic
117C2×C8×C47C2×D411yescharacteristic
118C2×C8×C47C2×D411yescharacteristic
119C2×C8×C47C2411yescharacteristic
120C4⋊C4×C47—21no—
121C4⋊C4×C47—21no—
122C4⋊C4×C47—41no—
123C4⋊C4×C47—41no—
124C22⋊C4×C47—41no—
125C22⋊C4×C47—41no—
126C22⋊C4×C47—41no—
127C42×C47—41no—
128C42×C47—41no—
129C42×C47—41no—
130C42×C47D811yescharacteristic
131C42×C47D811yescharacteristic
132C42×C47C2×D411yescharacteristic
133C42×C47C2×D411yescharacteristic
134(C2×D47)⋊C4—42no—
135(C2×D47)⋊C4—42no—
136C4⋊Dic47—22no—
137C4⋊Dic47—41no—
138D376—22no—
139D376—22no—
140D376—42no—
141C47⋊C16—22no—
142C47⋊C16—22no—
143C23×C47—41no—
144C23×C47C2×D811yescharacteristic
145C22×D47—42no—
146Q8×C47—22no—
147Q8×C47—41no—
148D4×C47—22no—
149D4×C47—44no—
150D4×C47—41no—
151C2×C4×C47—21no—
152C2×C4×C47—21no—
153C2×C4×C47—22no—
154C2×C4×C47—41no—
155C2×C4×C47—44no—
156C2×C4×C47—41no—
157C2×C4×C47—41no—
158C2×C4×C47—41no—
159C2×C4×C47—82no—
160C2×C4×C47—82no—
161C2×C4×C47C2×D811yescharacteristic
162C2×C4×C47C2×D811yescharacteristic
163C2×C4×C47C2×D811yescharacteristic
164C2×C4×C47C2×D811yescharacteristic
165C2×C4×C47C2×D811yescharacteristic
166C2×C4×C47C22×D411yescharacteristic
167C22⋊D47—84no—
168C2×Dic47—42no—
169D188—42no—
170D188—42no—
171D188—82no—
172D188—82no—
173C4×D47—84no—
174Dic94—82no—
175C8×C47—21no—
176C8×C47—21no—
177C8×C47—21no—
178C8×C47C2×#4111yescharacteristic
179C8×C47C2×#4111yescharacteristic
180#33675—471nomaximal, Sylow
181C22×C47—21no—
182C22×C47—21no—
183C22×C47—21no—
184C22×C47—42no—
185C22×C47—81no—
186C22×C47—81no—
187C22×C47C22×D811yescharacteristic
188C2×D47—82no—
189C2×D47—82no—
190C2×D47—82no—
191C4×C47—21no—
192C4×C47—21no—
193C4×C47—21no—
194C4×C47—21no—
195C4×C47—42no—
196C4×C47—81no—
197C4×C47—81no—
198C4×C47#50912yes—
199C4×C47#52511yescharacteristic
200C4×C47#57511yescharacteristic
201Dic47—82no—
202#3169—471no—
203C4×#135D4711yescharacteristic, complemented
204#2234—472no—
205#2225—471no—
206#2224—471no—
207#2207—471no—
208#2206—471no—
209#2186—472no—
210#2177—472no—
211#2175—472no—
212#2163—471no—
213C2×C47—41no—
214C2×C47—82no—
215C2×C47#310011yescharacteristic
216C2×C47C2×#50911yescharacteristic
217C2×C47#341411yescharacteristic
218D47—162no—
219C2×#135C2×D4711yescharacteristic
220#532—941no—
221C4×#41—21no—
222C2×SD32—472no—
223C2×D16—472no—
224#500—471no—
225#493—471no—
226#486—941no—
227#466—472no—
228#466—941no—
229C4×Q16C2×D4711yescharacteristic
230C4×Q16C2×D4711yescharacteristic
231C4×SD16—21no—
232C4×SD16—21no—
233C4×D8—472no—
234C4×D8—941no—
235C4×D8C2×D4711yescharacteristic
236C4×D8C2×D4711yescharacteristic
237#427C2×D4711yescharacteristic
238#416—21no—
239C2×C4×C8C2×D4711yescharacteristic
240#367—472no—
241#366—472no—
242C4⋊C16—471no—
243C4⋊C16—471no—
244#358—472no—
245#357—472no—
246#357—472no—
247#357—472no—
248C22⋊C16—472no—
249#346—472no—
250C47#3367511yescharacteristic, complemented, Sylow
251C2×#41—21no—
252C2×#41—1881no—
253#135—22no—
254#135—22no—
255C2×Q16C22×D4711yescharacteristic
256C2×SD16—21no—
257C2×D8—472no—
258C2×D8—941no—
259C2×D8C22×D4711yescharacteristic
260C22×C8C22⋊D4711yescharacteristic
261C22×C8C22×D4711yescharacteristic
262C4⋊Q8—941no—
263#127—941no—
264#124—1881no—
265#121—942no—
266#121—1881no—
267C4×Q8—21no—
268C4×Q8—21no—
269C4×D4—21no—
270C4×D4—21no—
271C4×D4—41no—
272C4×D4—41no—
273C4×D4—942no—
274C4×D4—1881no—
275#117—21no—
276#117—41no—
277C2×C42—41no—
278C2×C42C22⋊D4711yescharacteristic
279SD32—944no—
280D16—944no—
281C2×C16—472no—
282C2×C16—472no—
283#107—472no—
284#107—941no—
285#107C22×D4711yescharacteristic
286#107C22×D4711yescharacteristic
287#106—21no—
288#103—21no—
289#103—21no—
290#102—21no—
291#102—21no—
292#102—942no—
293#102—942no—
294C4×C8C22⋊D4711yescharacteristic
295C4×C8C22⋊D4711yescharacteristic
296C4×C8C22×D4711yescharacteristic
297C4×C8C22×D4711yescharacteristic
298#41—24no—
299#41—42no—
300#41—3764no—
301C2×Q8—21no—
302C2×Q8—1881no—
303C2×D4—21no—
304C2×D4—41no—
305C2×D4—942no—
306C2×D4—1882no—
307C2×D4—1881no—
308C2×D4—1881no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—1882no—
313C22×C4#1062533411yescharacteristic
314C22×C4#1062533411yescharacteristic
315C22×C4C2×C22⋊D4711yescharacteristic
316Q16—21no—
317Q16#1062535012yescomplemented
318SD16—24no—
319D8—21no—
320D8—942no—
321D8—942no—
322D8—1882no—
323D8#1062535012yescomplemented
324C2×C8—21no—
325C2×C8—21no—
326C2×C8—41no—
327C2×C8C2×C22⋊D4711yescharacteristic
328C2×C8C2×C22⋊D4711yescharacteristic
329C2×C8C2×C22⋊D4711yescharacteristic
330C2×C8C23×D4711yescharacteristic
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4—942no—
336C4⋊C4—1881no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—1882no—
341C22⋊C4—1882no—
342C42—41no—
343C42—41no—
344C42—41no—
345C42#1062533411yescharacteristic
346C42#1062533411yescharacteristic
347C42C2×C22⋊D4711yescharacteristic
348C42C2×C22⋊D4711yescharacteristic
349C16—942no—
350C16—942no—
351C23—41no—
352C23—1882no—
353C23C2×#1062533411yescharacteristic
354Q8—22no—
355Q8—41no—
356Q8—3762no—
357D4—22no—
358D4—44no—
359D4—41no—
360D4—3762no—
361D4—3764no—
362D4—3762no—
363D4—1882no—
364D4—1882no—
365C2×C4—22no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—41no—
369C2×C4—44no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—82no—
374C2×C4—82no—
375C2×C4—3764no—
376C2×C4—1882no—
377C2×C4C2×#1062533411yescharacteristic
378C2×C4C2×#1062533411yescharacteristic
379C2×C4C2×#1062533411yescharacteristic
380C2×C4C2×#1062533411yescharacteristic
381C2×C4C2×#1062533411yescharacteristic
382C2×C4C22×C22⋊D4711yescharacteristic
383C8—21no—
384C8—21no—
385C8—21no—
386C8C2×#1062535011yescharacteristic
387C8C2×#1062535011yescharacteristic
388C22—21no—
389C22—21no—
390C22—21no—
391C22—42no—
392C22—81no—
393C22—81no—
394C22—3762no—
395C22—3762no—
396C22—3762no—
397C22C22×#1062533411yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—42no—
403C4—81no—
404C4—81no—
405C4—3762no—
406C4#1568955812yes—
407C4#1568963411yescharacteristic
408C4#1568992111yescharacteristic
409C2—41no—
410C2—82no—
411C2—7522no—
412C2#2025338811yescharacteristic
413C2C2×#1568955811yescharacteristic
414C2#2025652211yescharacteristic
subgroupG/H
centerC22C22×#10625334
commutator, cosocleC2×C8×C47C24
FrattiniC2×C8C23×D47
FittingC4×#135×C47C2
socleC22×C47C22×D8
hypercenterC4×#135D47
hypocenterC47#33675
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ C4×#135

Complements

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

NH ≅ G/Ntype
1. #20253967C2semidirect
2. #20245579C2semidirect
3. #20245530C2semidirect
4. #20245525C2semidirect
5. #20245428C2semidirect
6. #20245423C2semidirect
7. #20245311C2semidirect
8. #20245262C2semidirect
9. #20245250C2semidirect
10. #20245191C2semidirect
11. C4×#135×C47C2semidirect
109. Q16×C47#41semidirect
112. D8×C47#41semidirect
203. C4×#135D47semidirect
250. C47#33675semidirect
317. Q16#10625350semidirect
323. D8#10625350semidirect

Maximal subgroups

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

subgroupindex
#202539672
#202455792
#202455302
#202455252
#202454282
#202454232
#202453112
#202452622
#202452502
#202451912
C4×#135×C472
#3367547