Finite Group Databasebeta

← #26252503

Subgroups — #26252503

Order 12032.

1170 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257191C211yesmaximal, characteristic, complemented
2#20253185C212yesmaximal, complemented
3#20244733C212yesmaximal, complemented
4#20244544C212yesmaximal, complemented
5#20244365C212yesmaximal, complemented
6#20243787C212yesmaximal
7#20243597C212yesmaximal, complemented
8#20243380C211yesmaximal, characteristic, complemented
9C4×#127×C47C211yesmaximal, characteristic
10#15689832—24no—
11#15689830—22no—
12D4×Dic94—22no—
13#15689754C2212yes—
14#15689749—22no—
15#15689680C2212yes—
16C2×#13094003—22no—
17#15689598C2212yes—
18#15689423—24no—
19#15689413—22no—
20#15689403—22no—
21#15689163C2214yes—
22#15689147C2212yes—
23#15689128C2214yes—
24C2×#13093941C2212yes—
25#15688892C2212yes—
26#15688883C2214yes—
27#15688883C2214yes—
28C2×#127×C47C2211yescharacteristic
29C2×C4×D4×C47—22no—
30C2×C4×D4×C47C2211yescharacteristic
31C2×C4×D4×C47C2211yescharacteristic
32C47×#390—22no—
33C47×#390C2211yescharacteristic
34C47×#390C2211yescharacteristic
35C47×#384C2211yescharacteristic
36C43×C47C2211yescharacteristic
37C22×Dic94—22no—
38C2×#10625329C2314yes—
39#13094024D412yescomplemented
40#13094024D412yescomplemented
41#13094023—24no—
42#13094016D414yescomplemented
43#13094015—24no—
44#13094003—24no—
45#13094003—24no—
46#13094003—22no—
47#13094003—24no—
48#13094003—22no—
49#13094001—28no—
50#13094001—28no—
51C4×Dic94—22no—
52C4×Dic94—22no—
53D4×Dic47—24no—
54D4×Dic47—24no—
55#13093983C2314yes—
56C2×C4⋊Dic47—22no—
57C2×Dic47⋊C4—24no—
58C2×C22⋊Dic47—24no—
59#13093957—24no—
60#13093955—24no—
61C4⋊(C47⋊C8)—22no—
62C4⋊(C47⋊C8)—22no—
63#13093945—24no—
64#13093945—24no—
65#13093941—24no—
66C22×D4×C47—22no—
67C22×D4×C47C2311yescharacteristic
68C22×D4×C47C2311yescharacteristic
69C23×C4×C47—21no—
70C23×C4×C47D412yes—
71#127×C47—22no—
72#127×C47Q814yescomplemented
73C4×D4×C47—22no—
74C4×D4×C47—22no—
75C4×D4×C47—22no—
76C4×D4×C47—22no—
77C4×D4×C47—48no—
78C2×C4⋊C4×C47—22no—
79C2×C4⋊C4×C47C2311yescharacteristic
80C2×C4⋊C4×C47C2311yescharacteristic
81C2×C22⋊C4×C47—22no—
82C2×C22⋊C4×C47—22no—
83C2×C22⋊C4×C47—21no—
84C2×C22⋊C4×C47D412yes—
85C2×C42×C47—21no—
86C2×C42×C47—21no—
87C2×C42×C47C2311yescharacteristic
88C2×C42×C47C2311yescharacteristic
89C2×C42×C47C2311yescharacteristic
90C24×C47—21no—
91C24×C47C2×D412yes—
92C2×D4×C47—28no—
93C2×D4×C47—22no—
94C2×D4×C47—22no—
95C2×D4×C47—21no—
96C2×D4×C47—22no—
97C2×D4×C47—22no—
98C2×D4×C47—44no—
99C2×D4×C47—44no—
100C2×D4×C47C2×Q812yes—
101C2×D4×C47C2×Q812yescomplemented
102C2×D4×C47#4112yes—
103C22×C4×C47—21no—
104C22×C4×C47—21no—
105C22×C4×C47—22no—
106C22×C4×C47—22no—
107C22×C4×C47—21no—
108C22×C4×C47—44no—
109C22×C4×C47—44no—
110C22×C4×C47—41no—
111C22×C4×C47—41no—
112C22×C4×C47C2×D411yescharacteristic
113C22×C4×C47C2×D412yes—
114C22×C4×C47C2×D411yescharacteristic
115C22×C4×C47C2411yescharacteristic
116C22×Dic47—24no—
117C22×Dic47—24no—
118C2×Dic94—22no—
119C2×Dic94—24no—
120C2×Dic94—22no—
121C2×Dic94—84no—
122C4⋊C4×C47—22no—
123C4⋊C4×C47—22no—
124C4⋊C4×C47—44no—
125C22⋊C4×C47—24no—
126C22⋊C4×C47—44no—
127C22⋊C4×C47—44no—
128C22⋊C4×C47—42no—
129C42×C47—24no—
130C42×C47—21no—
131C42×C47—22no—
132C42×C47—42no—
133C42×C47C2×D412yes—
134C42×C47C2×D412yes—
135C42×C47C2×Q812yescomplemented
136C22⋊Dic47—28no—
137C22⋊Dic47—24no—
138C4⋊Dic47—24no—
139C4⋊Dic47—22no—
140C4⋊Dic47—22no—
141C4⋊Dic47C2×D414yes—
142C4⋊Dic47C2×D414yes—
143Dic47⋊C4—28no—
144Dic47⋊C4—24no—
145Dic47⋊C4—24no—
146C4×Dic47—24no—
147#10625329—24no—
148#10625329—24no—
149C2×C47⋊C8—24no—
150C23×C47—22no—
151C23×C47—22no—
152C23×C47—22no—
153C23×C47—42no—
154C23×C47—42no—
155C23×C47—42no—
156C23×C47—42no—
157C23×C47—41no—
158C23×C47—41no—
159C23×C47C22⋊Q814yes—
160C23×C47C22×D411yescharacteristic
161D4×C47—24no—
162D4×C47—24no—
163D4×C47—24no—
164D4×C47—416no—
165D4×C47—42no—
166C2×C4×C47—22no—
167C2×C4×C47—22no—
168C2×C4×C47—22no—
169C2×C4×C47—22no—
170C2×C4×C47—22no—
171C2×C4×C47—22no—
172C2×C4×C47—41no—
173C2×C4×C47—41no—
174C2×C4×C47—41no—
175C2×C4×C47—44no—
176C2×C4×C47—42no—
177C2×C4×C47—42no—
178C2×C4×C47—41no—
179C2×C4×C47—82no—
180C2×C4×C47—82no—
181C2×C4×C47—82no—
182C2×C4×C47#12011yescharacteristic
183C2×C4×C47#12012yes—
184C2×C4×C47#12011yescharacteristic
185C2×C4×C47C22×D412yes—
186C2×C4×C47C22×Q811yescharacteristic
187C2×C4×C47C2×#4111yescharacteristic
188C2×C4×C472−1+412yes—
189C2×Dic47—24no—
190C2×Dic47—24no—
191C2×Dic47—84no—
192C2×Dic47—84no—
193Dic94—44no—
194Dic94—82no—
195Dic94—84no—
196C47⋊C8—44no—
197#24312—471nomaximal, Sylow
198C22×C47—21no—
199C22×C47—21no—
200C22×C47—24no—
201C22×C47—44no—
202C22×C47—44no—
203C22×C47—42no—
204C22×C47—42no—
205C22×C47—42no—
206C22×C47—82no—
207C22×C47—82no—
208C22×C47—81no—
209C22×C47—81no—
210C22×C47C2×#12011yescharacteristic
211C22×C47C2×C22⋊Q811yescharacteristic
212C22×C47#53611yescharacteristic
213C4×C47—24no—
214C4×C47—21no—
215C4×C47—22no—
216C4×C47—42no—
217C4×C47—42no—
218C4×C47—81no—
219C4×C47#45312yes—
220C4×C47#54812yes—
221C4×C47D4×Q812yes—
222Dic47—44no—
223Dic47—44no—
224#3501—471no—
225#3077—472no—
226C4×#127D4711yescharacteristic
227#2060—472no—
228#2027—472no—
229#1994—472no—
230#1887—472no—
231#1856—472no—
232#1800—471no—
233C2×C47—21no—
234C2×C47—21no—
235C2×C47—44no—
236C2×C47—82no—
237C2×C47#240911yescharacteristic
238C2×C47C2×#45311yescharacteristic
239C2×C47#301811yescharacteristic
240#554—944no—
241#554—942no—
242D4×Q8—942no—
243#544—472no—
244#543—942no—
245#533—472no—
246C2×#127C2×D4711yescharacteristic
247C2×C22⋊Q8—942no—
248#518—472no—
249C2×C4×D4—22no—
250C2×C4×D4C2×D4711yescharacteristic
251C2×C4×D4C2×D4711yescharacteristic
252#478—944no—
253#476—942no—
254#474—942no—
255#428—474no—
256#423—472no—
257#418—474no—
258C2×#100—472no—
259#390—22no—
260#390C2×D4711yescharacteristic
261#390C2×D4711yescharacteristic
262#384C2×D4711yescharacteristic
263C43C2×D4711yescharacteristic
264#343—472no—
265#339—474no—
266#339—474no—
267C47#2431211yescharacteristic, complemented, Sylow
268C22×Q8—942no—
269C22×D4—22no—
270C22×D4C22×D4711yescharacteristic
271C22×D4C22×D4711yescharacteristic
272C23×C4—21no—
273C23×C4C22⋊D4712yes—
274C2×M16—474no—
275C4⋊Q8—472no—
276C4⋊Q8—472no—
277C4⋊Q8—944no—
278#127—22no—
279#127Dic9414yescomplemented
280#125—474no—
281#125—944no—
282C22⋊Q8—948no—
283C22⋊Q8—948no—
284C22⋊Q8—944no—
285C22⋊Q8—944no—
286C22⋊Q8—942no—
287C22⋊Q8—944no—
288C22⋊Q8—942no—
289C4×Q8—942no—
290C4×Q8—942no—
291C4×D4—22no—
292C4×D4—22no—
293C4×D4—22no—
294C4×D4—22no—
295C4×D4—48no—
296C4×D4—944no—
297C4×D4—944no—
298#117—474no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—944no—
301C2×C4⋊C4—942no—
302C2×C4⋊C4C22×D4711yescharacteristic
303C2×C4⋊C4C22×D4711yescharacteristic
304C2×C22⋊C4—22no—
305C2×C22⋊C4—22no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—944no—
308C2×C22⋊C4C22⋊D4712yes—
309C2×C42—21no—
310C2×C42—21no—
311C2×C42C22×D4711yescharacteristic
312C2×C42C22×D4711yescharacteristic
313C2×C42C22×D4711yescharacteristic
314#107—944no—
315#106—944no—
316C4⋊C8—942no—
317C4⋊C8—942no—
318#102—944no—
319#102—944no—
320#100—944no—
321C24—21no—
322C24C2×C22⋊D4712yes—
323C2×Q8—944no—
324C2×Q8—942no—
325C2×Q8—942no—
326C2×Q8—3764no—
327C2×D4—28no—
328C2×D4—22no—
329C2×D4—22no—
330C2×D4—21no—
331C2×D4—22no—
332C2×D4—22no—
333C2×D4—44no—
334C2×D4—44no—
335C2×D4C2×Dic9412yes—
336C2×D4C2×Dic9412yescomplemented
337C2×D4#1062535012yes—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—21no—
343C22×C4—44no—
344C22×C4—44no—
345C22×C4—41no—
346C22×C4—41no—
347C22×C4—944no—
348C22×C4—944no—
349C22×C4C2×C22⋊D4711yescharacteristic
350C22×C4C2×C22⋊D4712yes—
351C22×C4C2×C22⋊D4711yescharacteristic
352C22×C4C23×D4711yescharacteristic
353M16—944no—
354M16—944no—
355C2×C8—944no—
356C4⋊C4—22no—
357C4⋊C4—22no—
358C4⋊C4—44no—
359C4⋊C4—474no—
360C4⋊C4—474no—
361C4⋊C4—948no—
362C4⋊C4—944no—
363C4⋊C4—944no—
364C4⋊C4—944no—
365C4⋊C4—942no—
366C4⋊C4—942no—
367C22⋊C4—24no—
368C22⋊C4—44no—
369C22⋊C4—44no—
370C22⋊C4—42no—
371C22⋊C4—948no—
372C22⋊C4—944no—
373C42—24no—
374C42—21no—
375C42—22no—
376C42—42no—
377C42—944no—
378C42C2×Dic9412yescomplemented
379C42D4×D4712yes—
380C42D4×D4712yes—
381C23—22no—
382C23—22no—
383C23—22no—
384C23—42no—
385C23—42no—
386C23—42no—
387C23—42no—
388C23—41no—
389C23—41no—
390C23#1309400314yes—
391C23C22×C22⋊D4711yescharacteristic
392Q8—3762no—
393Q8—3764no—
394Q8—1884no—
395D4—24no—
396D4—24no—
397D4—24no—
398D4—416no—
399D4—42no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—44no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—41no—
413C2×C4—82no—
414C2×C4—82no—
415C2×C4—82no—
416C2×C4—944no—
417C2×C4—944no—
418C2×C4—3764no—
419C2×C4—3764no—
420C2×C4#1309399212yes—
421C2×C4#1309399211yescharacteristic
422C2×C4#1309399211yescharacteristic
423C2×C4C2×D4×D4712yes—
424C2×C4C22×Dic9411yescharacteristic
425C2×C4C2×#1062535011yescharacteristic
426C2×C4#1309407112yes—
427C8—1884no—
428C22—21no—
429C22—21no—
430C22—24no—
431C22—44no—
432C22—44no—
433C22—42no—
434C22—42no—
435C22—42no—
436C22—82no—
437C22—82no—
438C22—81no—
439C22—81no—
440C22C2×#1309399211yescharacteristic
441C22C2×#1309400311yescharacteristic
442C22#1568969411yescharacteristic
443C4—24no—
444C4—21no—
445C4—22no—
446C4—42no—
447C4—42no—
448C4—81no—
449C4—1884no—
450C4—1884no—
451C4#1568929012yes—
452C4#1568978212yes—
453C4D4×Dic9412yes—
454C2—21no—
455C2—21no—
456C2—44no—
457C2—82no—
458C2#2024675311yescharacteristic
459C2C2×#1568929011yescharacteristic
460C2#2025273611yescharacteristic
subgroupG/H
centerC22C2×#13093992
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC4×#127×C47C2
socleC22×C47C2×#120
prime radicalC2×#127×C47C22
hypercenterC4×#127D47
hypocenterC47#24312
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#127

Complements

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

NH ≅ G/Ntype
1. #20257191C2semidirect
2. #20253185C2semidirect
3. #20244733C2semidirect
4. #20244544C2semidirect
5. #20244365C2semidirect
7. #20243597C2semidirect
8. #20243380C2semidirect
39. #13094024D4semidirect
40. #13094024D4semidirect
42. #13094016D4semidirect
72. #127×C47Q8semidirect
101. C2×D4×C47C2×Q8semidirect
135. C42×C47C2×Q8semidirect
267. C47#24312semidirect
279. #127Dic94semidirect
336. C2×D4C2×Dic94semidirect
378. C42C2×Dic94semidirect

Maximal subgroups

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

subgroupindex
#202571912
#202531852
#202447332
#202445442
#202443652
#202437872
#202435972
#202433802
C4×#127×C472
#2431247