Finite Group Databasebeta

← #11787652

Subgroups — #11787652

Order 1152.

751 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596219C211yesmaximal, characteristic
2#10594780C211yesmaximal, characteristic, complemented
3#10591113C211yesmaximal, characteristic, complemented
4#10591105C211yesmaximal, characteristic, complemented
5#10591073C211yesmaximal, characteristic, complemented
6C3×#4559C211yesmaximal, characteristic, complemented
7C3×#4558C211yesmaximal, characteristic, complemented
8#69035—31nomaximal
9#68947—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×#3828C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13#64118—21no—
14#64118C412yescomplemented
15#64117—21no—
16#64117C412yescomplemented
17#64113—22no—
18C3×#926C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22#63818—22no—
23#63817—22no—
24#63817—22no—
25#63570—22no—
26#63567—21no—
27#63564—21no—
28#63557—22no—
29#5748—31no—
30#5748—31no—
31#5748—61no—
32#5745—31no—
33#5745—31no—
34#5139—31no—
35#5129—31no—
36#5113—31no—
37#5110—31no—
38#5005—31no—
39#5002—31no—
40C3×#344—31no—
41C3×#341—31no—
42#4559D311yescharacteristic, complemented
43#4558D311yescharacteristic, complemented
44C22×C32×C4C2311yescharacteristic
45C2×#638—21no—
46C2×#638—21no—
47#3828—21no—
48#3828—21no—
49#3828—21no—
50#3828—21no—
51#3828—21no—
52#3828—21no—
53#3828C2×C412yes—
54#3828D412yes—
55C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
56C2×C4⋊(C3⋊D3)D411yescharacteristic
57C2×C4×C3⋊D3—21no—
58C2×C4×C3⋊D3—21no—
59C2×#634C2×C411yescharacteristic
60C2×#634D411yescharacteristic
61C32×M16—21no—
62C32×M16C2×C412yes—
63C2×C32×C8—21no—
64#3746—22no—
65#3745—22no—
66#3744—22no—
67#3744—22no—
68C3×#217—21no—
69C3×C4⋊Dic3—21no—
70C3×C4×Dic3—21no—
71C3×#208—21no—
72C3×#208—21no—
73C3×#208—21no—
74C3×#208D412yes—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8—21no—
78C2×C3×C3⋊C8—21no—
79C2×C3×C3⋊C8D412yes—
80#3712—24no—
81#3710—24no—
82#1881—91noSylow
83C2×#235—31no—
84C2×#235—31no—
85C2×#235—31no—
86C2×#235—31no—
87C2×#235—61no—
88C2×#235—61no—
89C2×C3×M16—21no—
90C2×C3×M16—31no—
91C2×C3×M16—31no—
92C2×C3×M16C2×D311yescharacteristic
93C2×C3×M16C2×D311yescharacteristic
94C22×C3×C8—31no—
95C3×#117—31no—
96#926C2×D311yescharacteristic
97C2×#208C2×D311yescharacteristic
98C2×#208C2×D311yescharacteristic
99C22×C3⋊C8C2×D311yescharacteristic
100#909—32no—
101#909—32no—
102#909—62no—
103#909—61no—
104#909—61no—
105#909—62no—
106#908—32no—
107#908—32no—
108#908—62no—
109#908—61no—
110#908—61no—
111#908—62no—
112#907—62no—
113#907—62no—
114D3×M16—62no—
115D3×M16—62no—
116#904—62no—
117#904—62no—
118#904—64no—
119#901—62no—
120#901—62no—
121#825—62no—
122#821—61no—
123(C2×D3)⋊C8—62no—
124(C2×D3)⋊C8—62no—
125#816—61no—
126#810—61no—
127#809—61no—
128#805—62no—
129C23×C32#4111yescharacteristic
130C22×C3⋊D3—21no—
131C22×C3⋊D3—21no—
132C2×C32×C4C22×C411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4#4111yescharacteristic
138#638—22no—
139#638—22no—
140#638—41no—
141#638—41no—
142C2×C3⋊Dic3—21no—
143C2×C3⋊Dic3—21no—
144C4⋊(C3⋊D3)—21no—
145C4⋊(C3⋊D3)—21no—
146C4⋊(C3⋊D3)—21no—
147C4⋊(C3⋊D3)C22⋊C412yes—
148C4×C3⋊D3—22no—
149C4×C3⋊D3—22no—
150C4×C3⋊D3—41no—
151C4×C3⋊D3—41no—
152#634—21no—
153#634—21no—
154#634—21no—
155#634C22⋊C412yes—
156C2×C3×Dic3—41no—
157C32×C8—22no—
158C3×C3⋊C8—22no—
159C3×C3⋊C8—22no—
160C3×C3⋊C8—41no—
161#575—91no—
162#568—91no—
163#421—91no—
164#416—91no—
165#408—91no—
166#344—31no—
167#341—31no—
168C22×C3×C4—21no—
169C22×C3×C4C22×D311yescharacteristic
170C22×C3×C4C22×D311yescharacteristic
171C2×#67—61no—
172C2×#67—61no—
173C2×#67—61no—
174C2×#67—61no—
175C2×#67—121no—
176C2×#67—121no—
177#235—32no—
178#235—32no—
179#235—32no—
180#235—32no—
181#235—62no—
182#235—62no—
183#235—61no—
184#235—61no—
185#235—61no—
186#235—61no—
187#235—62no—
188#235—62no—
189#235—61no—
190#235—61no—
191#235—61no—
192#235—61no—
193#235—61no—
194#235—61no—
195#235—61no—
196#235—61no—
197#235—121no—
198#235—121no—
199#235—121no—
200#235—121no—
201C2×D12—31no—
202C2×D12—31no—
203C2×D12—31no—
204C2×D12—31no—
205C2×D12—61no—
206C2×D12—61no—
207C2×C4×D3—61no—
208C2×C4×D3—61no—
209C2×C4×D3—61no—
210C2×C4×D3—61no—
211C2×C4×D3—121no—
212C2×C4×D3—121no—
213C2×Dic6—31no—
214C2×Dic6—31no—
215C2×Dic6—31no—
216C2×Dic6—31no—
217C2×Dic6—61no—
218C2×Dic6—61no—
219C3×M16—22no—
220C3×M16—21no—
221C3×M16—21no—
222C3×M16—22no—
223C3×M16—32no—
224C3×M16—61no—
225C3×M16—61no—
226C3×M16—61no—
227C3×M16C4×D312yes—
228C3×M16C4×D312yes—
229C2×C3×C8—22no—
230C2×C3×C8—21no—
231C2×C3×C8—21no—
232C2×C3×C8—32no—
233C2×C3×C8—61no—
234C2×C3×C8—61no—
235C2×C3×C8—61no—
236C2×C3×C8—61no—
237C3×C4⋊C4—61no—
238C3×C22⋊C4—61no—
239C3×C42—61no—
240#217—21no—
241C4⋊Dic3—21no—
242C4×Dic3—21no—
243#208—21no—
244#208—21no—
245#208—21no—
246#208D1212yes—
247C2×C3⋊C8—21no—
248C2×C3⋊C8—21no—
249C2×C3⋊C8—21no—
250C2×C3⋊C8—21no—
251C2×C3⋊C8D1212yes—
252Dic12—62no—
253Dic12—62no—
254Dic12—64no—
255D24—62no—
256D24—62no—
257D24—64no—
258#204—62no—
259#204—62no—
260#204—62no—
261#204—62no—
262#204—64no—
263#204—64no—
264ΓL(1,𝔽25)—64no—
265ΓL(1,𝔽25)—64no—
266D3×C8—64no—
267D3×C8—64no—
268C22×C32—41no—
269C22×C32C4×D411yescharacteristic
270C22×C32#12111yescharacteristic
271C22×C32#12311yescharacteristic
272C2×C3⋊D3—22no—
273C2×C3⋊D3—41no—
274C2×C3⋊D3—42no—
275C2×C3⋊D3—81no—
276C32×C4C2×C22⋊C411yescharacteristic
277C32×C4C4×D411yescharacteristic
278C32×C4#12011yescharacteristic
279C32×C4#12111yescharacteristic
280C3⋊Dic3—22no—
281C3⋊Dic3—41no—
282C3×Dic3—81no—
283C2×#41—91no—
284C2×#41—91no—
285#137—92no—
286#137—181no—
287AGL(1,ℤ/8)—92no—
288AGL(1,ℤ/8)—181no—
289#135—182no—
290#131—182no—
291#131—182no—
292C2×M16—31no—
293C2×M16—31no—
294C2×M16—182no—
295C2×M16D3211yescharacteristic
296C22×C8—31no—
297#117—31no—
298#104—182no—
299#103—181no—
300#102—181no—
301C22⋊C8—182no—
302C23×C3—21no—
303C23×C3#23511yescharacteristic
304C23×C3#23911yescharacteristic
305C22×D3—61no—
306C22×D3—61no—
307C22×D3—61no—
308C22×D3—61no—
309C22×D3—121no—
310C22×D3—121no—
311C2×C3×C4—21no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—121no—
318C2×C3×C4C2×C4×D311yescharacteristic
319C2×C3×C4C2×C4×D311yescharacteristic
320C2×C3×C4C2×D1211yescharacteristic
321C2×C3×C4C2×D1211yescharacteristic
322C2×C3×C4#23511yescharacteristic
323C2×C3×C4D3×D411yescharacteristic
324C2×C3×C4D3×D411yescharacteristic
325C2×C3×C4D3×D411yescharacteristic
326C2×C3×C4D3×D411yescharacteristic
327C2×C3×C4D3×D411yescharacteristic
328C2×C3×C4D3×D411yescharacteristic
329C2×C3×C4#23911yescharacteristic
330#67—62no—
331#67—62no—
332#67—62no—
333#67—62no—
334#67—122no—
335#67—122no—
336#67—122no—
337#67—122no—
338#67—121no—
339#67—121no—
340#67—121no—
341#67—121no—
342C2×Dic3—41no—
343C2×Dic3—61no—
344C2×Dic3—61no—
345C2×Dic3—61no—
346C2×Dic3—61no—
347C2×Dic3—121no—
348C2×Dic3—121no—
349D12—32no—
350D12—32no—
351D12—62no—
352D12—62no—
353D12—61no—
354D12—61no—
355D12—61no—
356D12—61no—
357D12—61no—
358D12—61no—
359D12—121no—
360D12—121no—
361C4×D3—62no—
362C4×D3—62no—
363C4×D3—62no—
364C4×D3—62no—
365C4×D3—122no—
366C4×D3—122no—
367C4×D3—122no—
368C4×D3—122no—
369C4×D3—121no—
370C4×D3—121no—
371C4×D3—121no—
372C4×D3—121no—
373Dic6—32no—
374Dic6—32no—
375Dic6—62no—
376Dic6—61no—
377Dic6—61no—
378Dic6—62no—
379Dic6—61no—
380Dic6—61no—
381Dic6—61no—
382Dic6—61no—
383Dic6—121no—
384Dic6—121no—
385C3×C8—24no—
386C3×C8—22no—
387C3×C8—22no—
388C3×C8—62no—
389C3×C8—62no—
390C3×C8—121no—
391C3⋊C8—22no—
392C3⋊C8—22no—
393C3⋊C8—41no—
394C2×C32—21no—
395C2×C32—21no—
396C2×C32—21no—
397C2×C32#38611yescharacteristic
398C3⋊D3—42no—
399C3⋊D3—81no—
400#41—92no—
401#41—92no—
402#41—181no—
403#41—181no—
404#41—181no—
405#41—181no—
406#41—181no—
407#41—181no—
408C2×Q8—91no—
409C2×Q8—91no—
410C2×D4—91no—
411C2×D4—91no—
412C2×D4—181no—
413C2×D4—181no—
414C22×C4—181no—
415C22×C4—181no—
416C22×C4C2×D3211yescharacteristic
417Q16—182no—
418SD16—182no—
419SD16—182no—
420D8—182no—
421M16—21no—
422M16—32no—
423M16—61no—
424M16—61no—
425M16—61no—
426M16—184no—
427M16#62412yes—
428C2×C8—21no—
429C2×C8—32no—
430C2×C8—61no—
431C2×C8—61no—
432C2×C8—61no—
433C2×C8—61no—
434C2×C8—184no—
435C4⋊C4—61no—
436C22⋊C4—61no—
437C42—61no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—21no—
441C22×C3—41no—
442C22×C3—41no—
443C22×C3—81no—
444C22×C3C4×D1211yescharacteristic
445C22×C3#88411yescharacteristic
446C22×C3#89311yescharacteristic
447C22×C3#89411yescharacteristic
448C22×C3#89411yescharacteristic
449C22×C3#89511yescharacteristic
450C2×D3—62no—
451C2×D3—62no—
452C2×D3—122no—
453C2×D3—122no—
454C2×D3—122no—
455C2×D3—122no—
456C2×D3—121no—
457C2×D3—121no—
458C2×D3—242no—
459C2×D3—241no—
460C2×D3—241no—
461C2×D3—242no—
462C3×C4—21no—
463C3×C4—21no—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4—241no—
467C3×C4C4×D1211yescharacteristic
468C3×C4D3×C22⋊C411yescharacteristic
469C3×C4D3×C22⋊C411yescharacteristic
470C3×C4#88211yescharacteristic
471C3×C4#88211yescharacteristic
472C3×C4#88411yescharacteristic
473C3×C4#89311yescharacteristic
474C3×C4#89511yescharacteristic
475Dic3—62no—
476Dic3—62no—
477Dic3—81no—
478Dic3—122no—
479Dic3—122no—
480Dic3—121no—
481Dic3—121no—
482C32#188111yescharacteristic, complemented, Sylow
483C23—181no—
484C23—181no—
485C23#379911yescharacteristic
486Q8—92no—
487Q8—181no—
488Q8—181no—
489Q8—181no—
490D4—92no—
491D4—182no—
492D4—182no—
493D4—181no—
494D4—181no—
495D4—181no—
496D4—361no—
497D4—361no—
498C2×C4—121no—
499C2×C4—181no—
500C2×C4—182no—
501C2×C4—182no—
502C2×C4—181no—
503C2×C4—361no—
504C2×C4—361no—
505C2×C4#379911yescharacteristic
506C2×C4D3×D1211yescharacteristic
507C2×C4D3×D1211yescharacteristic
508C2×C4C2×#62411yescharacteristic
509C2×C4#381111yescharacteristic
510C2×C4#381111yescharacteristic
511C8—22no—
512C8—62no—
513C8—62no—
514C8—121no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—41no—
523C2×C3—41no—
524C2×C3—41no—
525C2×C3#466511yescharacteristic
526C2×C3#466511yescharacteristic
527D3—122no—
528D3—122no—
529D3—242no—
530D3—242no—
531D3—241no—
532D3—241no—
533C22—41no—
534C22—182no—
535C22—362no—
536C22—361no—
537C22—721no—
538C22#6389411yescharacteristic
539C22#6389711yescharacteristic
540C22#6391011yescharacteristic
541C4—182no—
542C4—241no—
543C4—361no—
544C4#6389411yescharacteristic
545C4#6391011yescharacteristic
546C4#6392311yescharacteristic
547C4#6397411yescharacteristic
548C3—21no—
549C3#6894711yescharacteristic, complemented
550C3#6903511yescharacteristic, complemented
551C2—21no—
552C2—21no—
553C2—21no—
554C2—362no—
555C2—721no—
556C2#1059138011yescharacteristic
subgroupG/H
centerC4#63923
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#386
prime radical#10596219C2
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1881
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. #10594780C2semidirect
3. #10591113C2semidirect
4. #10591105C2semidirect
5. #10591073C2semidirect
6. C3×#4559C2semidirect
7. C3×#4558C2semidirect
14. #64118C4semidirect
16. #64117C4semidirect
42. #4559D3semidirect
43. #4558D3semidirect
482. C32#1881semidirect
549. C3#68947semidirect
550. C3#69035semidirect

Maximal subgroups

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

subgroupindex
#105962192
#105947802
#105911132
#105911052
#105910732
C3×#45592
C3×#45582
#690353
#689473