Finite Group Databasebeta

← #26370924

Subgroups — #26370924

Order 12032.

546 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253902C211yesmaximal, characteristic, complemented
2#20245552C212yesmaximal, complemented
3#20245545C212yesmaximal, complemented
4#20245540C211yesmaximal, characteristic, complemented
5#20245535C211yesmaximal, characteristic, complemented
6#20245530C211yesmaximal, characteristic, complemented
7#20245525C211yesmaximal, characteristic, complemented
8#20245170C212yesmaximal, complemented
9C2×C4⋊(C47⋊C16)C211yesmaximal, characteristic, complemented
10#20245095C212yesmaximal
11C4×#135×C47C211yesmaximal, characteristic
12#15689680—21no—
13C22×C47⋊C16C2212yes—
14#15689528C2211yescharacteristic
15#15689528C2211yescharacteristic
16#15689525—21no—
17#15689525C2212yes—
18#15689521—21no—
19#15689161—21no—
20#15689161C2212yes—
21#15688950C2212yes—
22#15688950C2212yes—
23#15688948C2212yes—
24#15688948C2212yes—
25C4⋊(C47⋊C16)C2211yescharacteristic
26C4⋊(C47⋊C16)C2211yescharacteristic
27C4⋊(C47⋊C16)C2212yes—
28#15688927C2212yes—
29#15688927C2212yes—
30#15688924C2212yes—
31#15688924C2212yes—
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
43#13094024—21no—
44#13094024—21no—
45#13094016—22no—
46#13094003—41no—
47#13094003—41no—
48C4×Dic94—41no—
49C4×Dic94—41no—
50#13093983—22no—
51C2×C47⋊C16—24no—
52C2×C47⋊C16C2312yes—
53C2×C47⋊C16C2312yes—
54#13093958—21no—
55#13093958—21no—
56#13093958C2312yes—
57#13093958C2312yes—
58#13093956—22no—
59#13093956—22no—
60C2×#41×C47—21no—
61#135×C47—22no—
62#135×C47Q814yescomplemented
63C2×Q16×C47C2311yescharacteristic
64C2×SD16×C47—21no—
65C2×D8×C47C2311yescharacteristic
66C22×C8×C47D411yescharacteristic
67C22×C8×C47C2311yescharacteristic
68C4×Q8×C47—21no—
69C4×Q8×C47—21no—
70C4×D4×C47—21no—
71C4×D4×C47—21no—
72C4×D4×C47—41no—
73C4×D4×C47—41no—
74#117×C47—21no—
75#117×C47—41no—
76C2×C42×C47—41no—
77C2×C42×C47D411yescharacteristic
78#107×C47C2311yescharacteristic
79#107×C47C2311yescharacteristic
80#106×C47—21no—
81#103×C47—21no—
82#103×C47—21no—
83#102×C47—21no—
84#102×C47—21no—
85C4×C8×C47D411yescharacteristic
86C4×C8×C47D411yescharacteristic
87C4×C8×C47C2311yescharacteristic
88C4×C8×C47C2311yescharacteristic
89#41×C47—24no—
90#41×C47—42no—
91C2×Q8×C47—21no—
92C2×D4×C47—21no—
93C2×D4×C47—41no—
94C22×C4×C47—41no—
95C22×C4×C47—41no—
96C22×C4×C47—41no—
97C22×C4×C47D811yescharacteristic
98C22×C4×C47D811yescharacteristic
99C22×C4×C47C2×D411yescharacteristic
100C2×Dic94—41no—
101C2×Dic94—41no—
102Q16×C47—21no—
103Q16×C47C2×Q812yes—
104SD16×C47—24no—
105D8×C47—21no—
106D8×C47C2×Q812yes—
107C2×C8×C47—22no—
108C2×C8×C47C2×D411yescharacteristic
109C2×C8×C47C2×D411yescharacteristic
110C2×C8×C47C2×D411yescharacteristic
111C2×C8×C47C2×Q812yes—
112C2×C8×C47#4112yes—
113C2×C8×C47C2411yescharacteristic
114C4⋊C4×C47—21no—
115C4⋊C4×C47—21no—
116C4⋊C4×C47—41no—
117C4⋊C4×C47—41no—
118C22⋊C4×C47—41no—
119C22⋊C4×C47—41no—
120C22⋊C4×C47—41no—
121C42×C47—41no—
122C42×C47—41no—
123C42×C47—41no—
124C42×C47D811yescharacteristic
125C42×C47D811yescharacteristic
126C42×C47C2×D411yescharacteristic
127C42×C47C2×D411yescharacteristic
128C22⋊Dic47—42no—
129C4⋊Dic47—22no—
130C4⋊Dic47—22no—
131C4⋊Dic47—41no—
132C4⋊Dic47—41no—
133Dic47⋊C4—42no—
134Dic47⋊C4—42no—
135C4×Dic47—42no—
136C47⋊C16—22no—
137C47⋊C16—22no—
138C23×C47—41no—
139C23×C47C2×D811yescharacteristic
140Q8×C47—22no—
141Q8×C47—41no—
142D4×C47—22no—
143D4×C47—44no—
144D4×C47—41no—
145C2×C4×C47—22no—
146C2×C4×C47—41no—
147C2×C4×C47—41no—
148C2×C4×C47—44no—
149C2×C4×C47—41no—
150C2×C4×C47—41no—
151C2×C4×C47—82no—
152C2×C4×C47—82no—
153C2×C4×C47C22⋊Q812yes—
154C2×C4×C47C2×D811yescharacteristic
155C2×C4×C47C2×D811yescharacteristic
156C2×C4×C47C2×D811yescharacteristic
157C2×C4×C47C2×D811yescharacteristic
158C2×C4×C47C2×D811yescharacteristic
159C2×C4×C47#13712yes—
160C2×C4×C47C22×D411yescharacteristic
161C2×Dic47—42no—
162C2×Dic47—42no—
163Dic94—82no—
164Dic94—82no—
165C8×C47—21no—
166C8×C47—21no—
167C8×C47C22⋊Q812yes—
168C8×C47C22×Q811yescharacteristic
169C8×C47C2×#4111yescharacteristic
170#33626—471nomaximal, Sylow
171C22×C47—21no—
172C22×C47—21no—
173C22×C47—42no—
174C22×C47—81no—
175C22×C47—81no—
176C22×C47#47412yes—
177C22×C47C22×D811yescharacteristic
178C4×C47—21no—
179C4×C47—21no—
180C4×C47—21no—
181C4×C47—42no—
182C4×C47—81no—
183C4×C47—81no—
184C4×C47#47412yes—
185C4×C47#50812yes—
186C4×C47C2×C22⋊Q811yescharacteristic
187C4×C47C2×#13711yescharacteristic
188Dic47—82no—
189Dic47—82no—
190#3160—471no—
191C4×#135D4711yescharacteristic
192#2229—472no—
193#2228—472no—
194#2227—471no—
195#2226—471no—
196#2225—471no—
197#2224—471no—
198#2158—472no—
199C2×C4⋊C16—471no—
200#2138—472no—
201C2×C47—22no—
202C2×C47—82no—
203C2×C47C2×#47411yescharacteristic
204C2×C47C2×#50811yescharacteristic
205C2×C47#341411yescharacteristic
206C2×#135C2×D4711yescharacteristic
207#533—941no—
208C4×#41—21no—
209C22×C16—472no—
210#500—471no—
211#500—471no—
212#499—472no—
213#499—941no—
214#498—941no—
215C4×Q16C2×D4711yescharacteristic
216C4×Q16C2×D4711yescharacteristic
217C4×SD16—21no—
218C4×SD16—21no—
219C4×D8C2×D4711yescharacteristic
220C4×D8C2×D4711yescharacteristic
221#427—472no—
222#427—941no—
223#427C2×D4711yescharacteristic
224#416—21no—
225C2×C4×C8C2×D4711yescharacteristic
226#367—472no—
227#367—472no—
228#366—472no—
229#366—472no—
230C4⋊C16—471no—
231C4⋊C16—471no—
232C4⋊C16—472no—
233#358—472no—
234#358—472no—
235#357—472no—
236#357—472no—
237C47#3362611yescharacteristic, complemented, Sylow
238C2×#41—21no—
239#135—22no—
240#135Dic9414yescomplemented
241C2×Q16C22×D4711yescharacteristic
242C2×SD16—21no—
243C2×D8C22×D4711yescharacteristic
244C22×C8C22⋊D4711yescharacteristic
245C22×C8C22×D4711yescharacteristic
246C4⋊Q8—941no—
247C4⋊Q8—941no—
248#125—942no—
249C22⋊Q8—1881no—
250C22⋊Q8—1881no—
251C4×Q8—21no—
252C4×Q8—21no—
253C4×Q8—1881no—
254C4×Q8—1881no—
255C4×D4—21no—
256C4×D4—21no—
257C4×D4—41no—
258C4×D4—41no—
259#117—21no—
260#117—41no—
261#117—942no—
262C2×C42—41no—
263C2×C42C22⋊D4711yescharacteristic
264C2×C16—472no—
265C2×C16—472no—
266C2×C16—944no—
267#107—472no—
268#107—472no—
269#107—941no—
270#107—941no—
271#107C22×D4711yescharacteristic
272#107C22×D4711yescharacteristic
273#106—21no—
274#106—942no—
275#106—942no—
276#103—21no—
277#103—21no—
278#102—21no—
279#102—21no—
280C4×C8C22⋊D4711yescharacteristic
281C4×C8C22⋊D4711yescharacteristic
282C4×C8C22×D4711yescharacteristic
283C4×C8C22×D4711yescharacteristic
284#41—24no—
285#41—42no—
286C2×Q8—21no—
287C2×Q8—1881no—
288C2×Q8—1881no—
289C2×D4—21no—
290C2×D4—41no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4#1062533411yescharacteristic
295C22×C4#1062533411yescharacteristic
296C22×C4C2×C22⋊D4711yescharacteristic
297Q16—21no—
298Q16C2×Dic9412yes—
299SD16—24no—
300D8—21no—
301D8C2×Dic9412yes—
302C2×C8—22no—
303C2×C8C2×Dic9412yes—
304C2×C8#1062535012yes—
305C2×C8C2×C22⋊D4711yescharacteristic
306C2×C8C2×C22⋊D4711yescharacteristic
307C2×C8C2×C22⋊D4711yescharacteristic
308C2×C8C23×D4711yescharacteristic
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—942no—
314C4⋊C4—942no—
315C4⋊C4—1882no—
316C4⋊C4—1882no—
317C4⋊C4—1881no—
318C4⋊C4—1881no—
319C22⋊C4—41no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C22⋊C4—1882no—
323C42—41no—
324C42—41no—
325C42—41no—
326C42—1882no—
327C42#1062533411yescharacteristic
328C42#1062533411yescharacteristic
329C42C2×C22⋊D4711yescharacteristic
330C42C2×C22⋊D4711yescharacteristic
331C16—942no—
332C16—942no—
333C23—41no—
334C23C2×#1062533411yescharacteristic
335Q8—22no—
336Q8—41no—
337Q8—3762no—
338Q8—3762no—
339D4—22no—
340D4—44no—
341D4—41no—
342C2×C4—22no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—44no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—82no—
349C2×C4—82no—
350C2×C4—1882no—
351C2×C4—1882no—
352C2×C4#1309400312yes—
353C2×C4C2×#1062533411yescharacteristic
354C2×C4C2×#1062533411yescharacteristic
355C2×C4C2×#1062533411yescharacteristic
356C2×C4C2×#1062533411yescharacteristic
357C2×C4C2×#1062533411yescharacteristic
358C2×C4#1309405412yes—
359C2×C4C22×C22⋊D4711yescharacteristic
360C8—21no—
361C8—21no—
362C8#1309400312yes—
363C8C22×Dic9411yescharacteristic
364C8C2×#1062535011yescharacteristic
365C22—21no—
366C22—21no—
367C22—42no—
368C22—81no—
369C22—81no—
370C22#1568940312yes—
371C22C22×#1062533411yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—42no—
376C4—81no—
377C4—81no—
378C4—3762no—
379C4—3762no—
380C4#1568940312yes—
381C4#1568955312yes—
382C4C2×#1309400311yescharacteristic
383C4C2×#1309405411yescharacteristic
384C2—22no—
385C2—82no—
386C2C2×#1568940311yescharacteristic
387C2C2×#1568955311yescharacteristic
388C2#2025652211yescharacteristic
subgroupG/H
centerC2×C4C2×#10625334
commutator, cosocleC2×C8×C47C24
FrattiniC2×C8C23×D47
FittingC4×#135×C47C2
socleC22×C47C22×D8
prime radicalC2×#135×C47C22
hypercenterC4×#135D47
hypocenterC47#33626
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C4×#135

Complements

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

NH ≅ G/Ntype
1. #20253902C2semidirect
2. #20245552C2semidirect
3. #20245545C2semidirect
4. #20245540C2semidirect
5. #20245535C2semidirect
6. #20245530C2semidirect
7. #20245525C2semidirect
8. #20245170C2semidirect
9. C2×C4⋊(C47⋊C16)C2semidirect
62. #135×C47Q8semidirect
237. C47#33626semidirect
240. #135Dic94semidirect

Maximal subgroups

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

subgroupindex
#202539022
#202455522
#202455452
#202455402
#202455352
#202455302
#202455252
#202451702
C2×C4⋊(C47⋊C16)2
#202450952
C4×#135×C472
#3362647