Finite Group Databasebeta

← #26268395

Subgroups — #26268395

Order 12032.

664 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253935C211yesmaximal, characteristic, complemented
2#20253181C211yesmaximal, characteristic
3C2×#15689414C211yesmaximal, characteristic
4#20244898C212yesmaximal, complemented
5#20244747C212yesmaximal
6#20244377C211yesmaximal, characteristic, complemented
7#20244168C212yesmaximal, complemented
8#20244164C211yesmaximal, characteristic, complemented
9#20244050C212yesmaximal
10C4×#13093940C211yesmaximal, characteristic
11C47×#2962C211yesmaximal, characteristic, complemented
12C2×#13094024C2211yescharacteristic
13C2×C4×D188C2211yescharacteristic
14#15689533—22no—
15#15689526—21no—
16#15689519—21no—
17#15689420—22no—
18#15689414—21no—
19#15689414—21no—
20#15689414—22no—
21#15689410—21no—
22#15689400—21no—
23C2×#13093960C2212yes—
24#15689166C2212yes—
25#15689166C2212yes—
26#15689166C2212yes—
27C2×#13093956C2212yes—
28#15689147C2211yescharacteristic
29#15689127C2212yes—
30C2×#13093946C2212yes—
31C2×#13093940C2211yescharacteristic
32C2×#13093940C2211yescharacteristic
33C4×#10625329C2211yescharacteristic
34#15688891C2212yes—
35#15688891C2212yes—
36#15688891C2211yescharacteristic
37#15688891C2211yescharacteristic
38#15688888C2212yes—
39C47×#533C2211yescharacteristic
40C47×#446—22no—
41C47×#446—21no—
42C8×Q8×C47—21no—
43C47×#424C2212yes—
44C2×C4⋊C8×C47C2211yescharacteristic
45C47×#405C2212yes—
46C4×M16×C47C2211yescharacteristic
47C22×Dic94—21no—
48C22×D188C2311yescharacteristic
49C22×C4×D47—21no—
50C2×#10625329C2312yes—
51C2×#10625329C2311yescharacteristic
52C2×#10625329C2311yescharacteristic
53#13094024—21no—
54#13094024—21no—
55#13094024—21no—
56#13094024—21no—
57C4×D188—21no—
58C4×D188—21no—
59C4×D188—21no—
60C4×D188—21no—
61C2×C4⋊Dic47—21no—
62C2×C4⋊Dic47C2311yescharacteristic
63C2×C4⋊Dic47C2312yes—
64C2×(C2×D47)⋊C4—21no—
65#13093960—24no—
66#13093957—22no—
67#13093957—22no—
68#13093957—22no—
69#13093956—22no—
70#13093956—22no—
71#13093955—22no—
72#13093955—22no—
73#13093955—22no—
74C4⋊(C47⋊C8)—21no—
75C4⋊(C47⋊C8)—21no—
76#13093946—22no—
77#13093946—22no—
78#13093944—22no—
79#13093944—22no—
80#13093940—22no—
81#13093940Q814yescomplemented
82#13093935—21no—
83C4×C47⋊C8—21no—
84C2×M16×C47C2311yescharacteristic
85C2×M16×C47C2311yescharacteristic
86C22×C8×C47C2312yes—
87C4⋊Q8×C47D411yescharacteristic
88C4⋊Q8×C47D411yescharacteristic
89#125×C47D412yes—
90C22⋊Q8×C47—21no—
91C22⋊Q8×C47—21no—
92C4×Q8×C47—21no—
93C4×Q8×C47—21no—
94#117×C47C2312yes—
95C2×C42×C47C2311yescharacteristic
96C4⋊C8×C47—22no—
97C4⋊C8×C47—22no—
98C4⋊C8×C47D411yescharacteristic
99C4⋊C8×C47D411yescharacteristic
100C4⋊C8×C47D412yes—
101#97×C47—22no—
102#97×C47—21no—
103C4×C8×C47—22no—
104C4×C8×C47—21no—
105C23×D47—21no—
106C2×Q8×C47—21no—
107C2×Q8×C47—21no—
108C22×C4×C47#4111yescharacteristic
109C22×C4×C47#4111yescharacteristic
110C22×C4×C47C2411yescharacteristic
111C22×Dic47—21no—
112C22×Dic47—22no—
113C2×D188—21no—
114C2×D188—21no—
115C2×D188—21no—
116C2×D188—21no—
117C2×D188—21no—
118C2×D188C2×Q812yes—
119C2×C4×D47—41no—
120C2×C4×D47—41no—
121C2×C4×D47—82no—
122C2×Dic94—41no—
123C2×Dic94—41no—
124C2×Dic94—82no—
125M16×C47—21no—
126M16×C47—21no—
127M16×C47—21no—
128M16×C47C2×Q812yes—
129C2×C8×C47—21no—
130C2×C8×C47—22no—
131C2×C8×C47—22no—
132C2×C8×C47—21no—
133C2×C8×C47C2×D412yes—
134C2×C8×C47C2×D412yes—
135C4⋊C4×C47—22no—
136C4⋊C4×C47—22no—
137C4⋊C4×C47—21no—
138C4⋊C4×C47—21no—
139C4⋊C4×C47C2×D412yes—
140C4⋊C4×C47C2×D412yes—
141C22⋊C4×C47—22no—
142C42×C47—22no—
143C42×C47C2×D411yescharacteristic
144C42×C47C2×D411yescharacteristic
145C42×C47C2×D411yescharacteristic
146C42×C47C2×D411yescharacteristic
147(C2×D47)⋊C4—41no—
148(C2×D47)⋊C4—41no—
149C4⋊Dic47—22no—
150C4⋊Dic47—21no—
151C4⋊Dic47—22no—
152C4⋊Dic47—21no—
153C4⋊Dic47—41no—
154C4⋊Dic47—41no—
155#10625329—21no—
156#10625329—21no—
157#10625329—22no—
158#10625329—22no—
159#10625329C2×Q812yes—
160#10625329#4112yes—
161C2×C47⋊C8—21no—
162C2×C47⋊C8—21no—
163C2×C47⋊C8—22no—
164C23×C47C2×#4111yescharacteristic
165C22×D47—22no—
166C22×D47—41no—
167C22×D47—41no—
168C22×D47—81no—
169C22×D47—81no—
170Q8×C47—42no—
171Q8×C47—81no—
172C2×C4×C47—22no—
173C2×C4×C47—22no—
174C2×C4×C47—22no—
175C2×C4×C47—41no—
176C2×C4×C47#12111yescharacteristic
177C2×C4×C47#12111yescharacteristic
178C2×C4×C47#12111yescharacteristic
179C2×C4×C47#12111yescharacteristic
180C2×C4×C47C22×D411yescharacteristic
181C2×C4×C47C22×D411yescharacteristic
182C2×C4×C47C22×Q811yescharacteristic
183C2×C4×C47C2×#4111yescharacteristic
184C2×C4×C472−1+411yescharacteristic
185C2×C4×C472−1+411yescharacteristic
186C2×Dic47—42no—
187C2×Dic47—41no—
188C2×Dic47—82no—
189C2×Dic47—81no—
190D188—22no—
191D188—22no—
192D188—41no—
193D188—41no—
194C4×D47—82no—
195C4×D47—82no—
196Dic94—82no—
197Dic94—82no—
198C8×C47—22no—
199C8×C47—22no—
200C8×C47—22no—
201C8×C47—41no—
202C47⋊C8—22no—
203C47⋊C8—22no—
204C47⋊C8—42no—
205#25490—471nomaximal, Sylow
206C22×C47—21no—
207C22×C47—21no—
208C22×C47C2×#12111yescharacteristic
209C22×C47#53311yescharacteristic
210C22×C47#54111yescharacteristic
211C2×D47—42no—
212C2×D47—82no—
213C2×D47—81no—
214C2×D47—81no—
215C2×D47—82no—
216C4×C47—21no—
217C4×C47—21no—
218C4×C47—21no—
219C4×C47—42no—
220C4×C47—42no—
221C4×C47#47112yes—
222C4×C47#54711yescharacteristic
223C4×C47#54811yescharacteristic
224C4×C47D4×Q811yescharacteristic
225C4×C47D4×Q811yescharacteristic
226Dic47—81no—
227Dic47—82no—
228#3165—471no—
229#3077—471no—
230C2×#476—471no—
231#2962D4711yescharacteristic, complemented
232#2090—472no—
233#2063—472no—
234#1997—471no—
235#1951—472no—
236#1950—471no—
237#1931—472no—
238C4×#100—471no—
239C2×C47—21no—
240C2×C47—21no—
241C2×C47#242911yescharacteristic
242C2×C47C2×#47111yescharacteristic
243C2×C47#306811yescharacteristic
244D47—82no—
245#533C2×D4711yescharacteristic
246C2×C4⋊Q8—471no—
247C2×C4×D4—471no—
248#501—942no—
249#500—941no—
250#498—941no—
251#478—942no—
252#476—941no—
253#476—941no—
254#476—942no—
255#476—941no—
256#474—941no—
257#446—22no—
258#446—21no—
259C8×Q8—21no—
260C2×#108—472no—
261#428—472no—
262#428—472no—
263#428—472no—
264C2×#106—472no—
265#424C2×D4712yes—
266#423—471no—
267C2×C4⋊C8C2×D4711yescharacteristic
268#418—472no—
269C2×#102—472no—
270C2×#100—471no—
271C2×#100—471no—
272#405C2×D4712yes—
273C4×M16—471no—
274C4×M16C2×D4711yescharacteristic
275#343—472no—
276#343—471no—
277#343—472no—
278#343—471no—
279#341—472no—
280C47#2549011yescharacteristic, complemented, Sylow
281C22×Q8—941no—
282C22×D4—471no—
283C23×C4—941no—
284C2×M16—471no—
285C2×M16—471no—
286C2×M16—472no—
287C2×M16C22×D4711yescharacteristic
288C2×M16C22×D4711yescharacteristic
289C22×C8C22×D4712yes—
290C4⋊Q8—941no—
291C4⋊Q8—941no—
292C4⋊Q8—941no—
293C4⋊Q8—941no—
294C4⋊Q8D18811yescharacteristic
295C4⋊Q8D18811yescharacteristic
296#125D18812yes—
297C22⋊Q8—21no—
298C22⋊Q8—21no—
299C4×Q8—21no—
300C4×Q8—21no—
301C4×D4—941no—
302C4×D4—941no—
303C4×D4—941no—
304C4×D4—941no—
305#117C22×D4712yes—
306C2×C4⋊C4—471no—
307C2×C4⋊C4—472no—
308C2×C4⋊C4—941no—
309C2×C22⋊C4—941no—
310C2×C42C22×D4711yescharacteristic
311#108—944no—
312#107—942no—
313#107—942no—
314#107—942no—
315#106—942no—
316#106—942no—
317#106—942no—
318#106—942no—
319#106—942no—
320C4⋊C8—22no—
321C4⋊C8—22no—
322C4⋊C8—941no—
323C4⋊C8—941no—
324C4⋊C8C22⋊D4711yescharacteristic
325C4⋊C8C22⋊D4711yescharacteristic
326C4⋊C8C22⋊D4712yes—
327#102—942no—
328#102—942no—
329#102—942no—
330#102—942no—
331#100—474no—
332#100—942no—
333#97—22no—
334#97—21no—
335#97—941no—
336C4×C8—22no—
337C4×C8—21no—
338C4×C8—941no—
339C24—941no—
340C2×Q8—21no—
341C2×Q8—21no—
342C2×Q8—3762no—
343C2×Q8—1881no—
344C2×Q8—1881no—
345C2×D4—472no—
346C2×D4—941no—
347C2×D4—941no—
348C2×D4—941no—
349C2×D4—941no—
350C2×D4—941no—
351C22×C4—941no—
352C22×C4—942no—
353C22×C4—3762no—
354C22×C4—1881no—
355C22×C4—1881no—
356C22×C4#1062535011yescharacteristic
357C22×C4#1062535011yescharacteristic
358C22×C4C23×D4711yescharacteristic
359M16—21no—
360M16—21no—
361M16—21no—
362M16—472no—
363M16—472no—
364M16—941no—
365M16—941no—
366M16—942no—
367M16—942no—
368M16Q8×D4712yes—
369C2×C8—21no—
370C2×C8—22no—
371C2×C8—22no—
372C2×C8—21no—
373C2×C8—941no—
374C2×C8—941no—
375C2×C8—942no—
376C2×C8C2×C22⋊D4712yes—
377C2×C8C2×C22⋊D4712yes—
378C4⋊C4—22no—
379C4⋊C4—22no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—942no—
383C4⋊C4—941no—
384C4⋊C4—941no—
385C4⋊C4—942no—
386C4⋊C4—1881no—
387C4⋊C4—1881no—
388C4⋊C4C2×D18812yes—
389C4⋊C4C2×D18812yes—
390C22⋊C4—22no—
391C22⋊C4—1881no—
392C22⋊C4—1881no—
393C42—22no—
394C42C2×D18811yescharacteristic
395C42C2×D18811yescharacteristic
396C42C2×C22⋊D4711yescharacteristic
397C42C2×C22⋊D4711yescharacteristic
398C23—942no—
399C23—3761no—
400C23—3761no—
401C23—1881no—
402C23—1881no—
403C23C2×#1062535011yescharacteristic
404Q8—42no—
405Q8—81no—
406Q8—3762no—
407Q8—3762no—
408D4—942no—
409D4—942no—
410D4—1881no—
411D4—1881no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—41no—
416C2×C4—3762no—
417C2×C4—3762no—
418C2×C4—3761no—
419C2×C4—3762no—
420C2×C4—1881no—
421C2×C4—1882no—
422C2×C4#1309399811yescharacteristic
423C2×C4#1309399811yescharacteristic
424C2×C4#1309399811yescharacteristic
425C2×C4#1309399811yescharacteristic
426C2×C4C22×C22⋊D4711yescharacteristic
427C2×C4C22×D18811yescharacteristic
428C2×C4C2×Q8×D4711yescharacteristic
429C2×C4#41×D4711yescharacteristic
430C2×C4#1309407111yescharacteristic
431C2×C4#1309407211yescharacteristic
432C8—22no—
433C8—22no—
434C8—22no—
435C8—41no—
436C8—942no—
437C8—942no—
438C8—1882no—
439C22—21no—
440C22—21no—
441C22—3762no—
442C22—3762no—
443C22—3761no—
444C22—3761no—
445C22—1882no—
446C22C2×#1309399811yescharacteristic
447C22#1568967711yescharacteristic
448C22#1568973111yescharacteristic
449C4—21no—
450C4—21no—
451C4—21no—
452C4—42no—
453C4—42no—
454C4—3761no—
455C4—3762no—
456C4#1568938612yes—
457C4#1568977211yescharacteristic
458C4#1568978511yescharacteristic
459C4Q8×C22⋊D4711yescharacteristic
460C4Q8×D18811yescharacteristic
461C2—21no—
462C2—21no—
463C2—3762no—
464C2#2024698111yescharacteristic
465C2C2×#1568938611yescharacteristic
466C2#2025311611yescharacteristic
subgroupG/H
centerC22C2×#13093998
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#2962C2
socleC22×C47C2×#121
prime radicalC22×D188C23
hypercenter#2962D47
hypocenterC47#25490
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2962

Complements

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

NH ≅ G/Ntype
1. #20253935C2semidirect
4. #20244898C2semidirect
6. #20244377C2semidirect
7. #20244168C2semidirect
8. #20244164C2semidirect
11. C47×#2962C2semidirect
81. #13093940Q8semidirect
231. #2962D47semidirect
280. C47#25490semidirect

Maximal subgroups

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

subgroupindex
#202539352
#202531812
C2×#156894142
#202448982
#202447472
#202443772
#202441682
#202441642
#202440502
C4×#130939402
C47×#29622
#2549047