Finite Group Databasebeta

← #11787643

Subgroups — #11787643

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#10596293C211yesmaximal, characteristic
2#10594780C211yesmaximal, characteristic, complemented
3C3×#5236C211yesmaximal, characteristic, complemented
4C3×#5234C211yesmaximal, characteristic, complemented
5#10591105C211yesmaximal, characteristic, complemented
6#10589169C211yesmaximal, characteristic, complemented
7#10589166C211yesmaximal, characteristic, complemented
8#70416—31nomaximal
9#70012—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C2×#3828C2211yescharacteristic
12#64160—21no—
13#64159—22no—
14#64158—21no—
15#64151C412yescomplemented
16#64141C412yescomplemented
17C2×#3748C2211yescharacteristic
18C3×#926C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22#63818—22no—
23#63817—22no—
24#63817—22no—
25C3×#837—22no—
26C3×#830—22no—
27#63567—21no—
28#63564—21no—
29#5822—31no—
30#5822—31no—
31#5822—61no—
32#5745—31no—
33#5745—31no—
34C3×#421—31no—
35C3×#408—31no—
36#5236D311yescharacteristic, complemented
37#5234D311yescharacteristic, complemented
38#5113—31no—
39#5002—31no—
40#4558—31no—
41#4556—31no—
42#4552—31no—
43#4533—31no—
44C32×#41—21no—
45C32×#41—21no—
46C32×#41—21no—
47C32×#41—21no—
48C2×C32×Q8C2×C411yescharacteristic
49C2×C32×D4—21no—
50C2×C32×D4C2×C411yescharacteristic
51C22×C32×C4—21no—
52C22×C32×C4C2311yescharacteristic
53C2×#638—21no—
54#3828—21no—
55#3828—21no—
56#3828C2×C412yes—
57#3828D412yes—
58C2×C4⋊(C3⋊D3)D411yescharacteristic
59C2×C4×C3⋊D3—21no—
60C2×#634D411yescharacteristic
61#3756—22no—
62#3755—22no—
63#3754—22no—
64#3753—22no—
65#3748—21no—
66#3748C2×C412yes—
67C2×C3⋊(C3⋊C8)—21no—
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×C3×#41—21no—
84C2×C3×#41C2×D311yescharacteristic
85C2×C3×#41C2×D311yescharacteristic
86C2×#235—31no—
87C2×#235—31no—
88C2×#235—61no—
89C2×C3×M16—31no—
90C2×C3×M16—31no—
91C22×C3×C8—31no—
92C3×#117—31no—
93#951—61no—
94#951—61no—
95#951—62no—
96#950—62no—
97#950—62no—
98#950—64no—
99#949—61no—
100#949—61no—
101#949—62no—
102#942—32no—
103#942—32no—
104#942—62no—
105#932—32no—
106#932—32no—
107#932—62no—
108#926C2×D311yescharacteristic
109C2×#208—31no—
110C2×#208—31no—
111C2×#208—61no—
112C2×#208C2×D311yescharacteristic
113C2×#208C2×D311yescharacteristic
114C22×C3⋊C8C2×D311yescharacteristic
115#907—62no—
116#907—62no—
117D3×M16—62no—
118D3×M16—62no—
119#901—62no—
120#901—62no—
121C3×#104—62no—
122C3×C22⋊C8—62no—
123#837—22no—
124#830—22no—
125#821—61no—
126#816—61no—
127#810—61no—
128#809—61no—
129C23×C32—21no—
130C23×C32#4111yescharacteristic
131C22×C3⋊D3—21no—
132C32×Q8—21no—
133C32×Q8—21no—
134C32×D4—21no—
135C32×D4—21no—
136C32×D4—41no—
137C32×D4—41no—
138C2×C32×C4—21no—
139C2×C32×C4—41no—
140C2×C32×C4—41no—
141C2×C32×C4C22×C411yescharacteristic
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4#4111yescharacteristic
147#638—22no—
148#638—22no—
149C2×C3⋊Dic3—21no—
150C4⋊(C3⋊D3)—21no—
151C4⋊(C3⋊D3)C22⋊C412yes—
152C4×C3⋊D3—22no—
153C4×C3⋊D3—22no—
154#634—21no—
155#634C22⋊C412yes—
156C2×C3×Dic3—41no—
157C3⋊(C3⋊C8)—22no—
158C3×C3⋊C8—22no—
159C3×C3⋊C8—22no—
160C3×C3⋊C8—41no—
161#575—91no—
162#568—91no—
163#421—31no—
164#416—91no—
165#408—31no—
166#344—91no—
167#341—91no—
168C3×#41—22no—
169C3×#41—22no—
170C3×#41—21no—
171C3×#41—21no—
172C3×#41—21no—
173C3×#41—21no—
174C3×#41—21no—
175C3×#41—21no—
176C3×#41—21no—
177C3×#41—21no—
178C3×#41—41no—
179C3×#41—41no—
180C2×C3×Q8—21no—
181C2×C3×Q8C4×D311yescharacteristic
182C2×C3×Q8C4×D311yescharacteristic
183C2×C3×D4—21no—
184C2×C3×D4—21no—
185C2×C3×D4—21no—
186C2×C3×D4—41no—
187C2×C3×D4C4×D311yescharacteristic
188C2×C3×D4C4×D311yescharacteristic
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—41no—
193C22×C3×C4C22×D311yescharacteristic
194C22×C3×C4C22×D311yescharacteristic
195C2×#67—61no—
196C2×#67—61no—
197C2×#67—121no—
198#235—32no—
199#235—32no—
200#235—32no—
201#235—32no—
202#235—62no—
203#235—62no—
204#235—61no—
205#235—61no—
206#235—61no—
207#235—61no—
208#235—121no—
209#235—121no—
210C2×D12—31no—
211C2×D12—31no—
212C2×D12—61no—
213C2×C4×D3—61no—
214C2×C4×D3—61no—
215C2×C4×D3—121no—
216C2×Dic6—31no—
217C2×Dic6—31no—
218C2×Dic6—61no—
219C3×M16—32no—
220C3×M16—61no—
221C3×M16—61no—
222C3×M16—61no—
223C2×C3×C8—32no—
224C2×C3×C8—61no—
225C2×C3×C8—61no—
226C2×C3×C8—61no—
227C2×C3×C8—61no—
228C3×C4⋊C4—61no—
229C3×C22⋊C4—61no—
230C3×C42—61no—
231#217—21no—
232#216—62no—
233#216—62no—
234#216—64no—
235#215—62no—
236#215—62no—
237#215—64no—
238#214—62no—
239#214—62no—
240#214—64no—
241#213—62no—
242#213—62no—
243#213—64no—
244C4⋊Dic3—21no—
245C4×Dic3—21no—
246#208—21no—
247#208—21no—
248#208—21no—
249#208—32no—
250#208—32no—
251#208—62no—
252#208—62no—
253#208—61no—
254#208—61no—
255#208#6712yes—
256C2×C3⋊C8—21no—
257C2×C3⋊C8—21no—
258C2×C3⋊C8—21no—
259C2×C3⋊C8—21no—
260C2×C3⋊C8—62no—
261C2×C3⋊C8—61no—
262C2×C3⋊C8—61no—
263C2×C3⋊C8#6712yes—
264ΓL(1,𝔽25)—64no—
265ΓL(1,𝔽25)—64no—
266D3×C8—64no—
267D3×C8—64no—
268C22×C32—41no—
269C22×C32—41no—
270C22×C32—42no—
271C22×C32C4×D411yescharacteristic
272C22×C32#12111yescharacteristic
273C22×C32#12311yescharacteristic
274C2×C3⋊D3—22no—
275C2×C3⋊D3—81no—
276C32×C4—41no—
277C32×C4C2×C22⋊C411yescharacteristic
278C32×C4C4×D411yescharacteristic
279C32×C4#12011yescharacteristic
280C32×C4#12111yescharacteristic
281C3⋊Dic3—22no—
282C3×Dic3—81no—
283C2×#41—91no—
284C2×#41D3211yescharacteristic
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—91no—
295C2×M16—182no—
296C22×C8—31no—
297#117—31no—
298#104—62no—
299#103—181no—
300#102—181no—
301C22⋊C8—62no—
302C23×C3—21no—
303C23×C3—21no—
304C23×C3—21no—
305C23×C3—41no—
306C23×C3#23511yescharacteristic
307C23×C3#23711yescharacteristic
308C22×D3—61no—
309C22×D3—61no—
310C22×D3—121no—
311C3×Q8—22no—
312C3×Q8—21no—
313C3×Q8—21no—
314C3×Q8—21no—
315C3×Q8—21no—
316C3×Q8—41no—
317C3×D4—22no—
318C3×D4—21no—
319C3×D4—21no—
320C3×D4—21no—
321C3×D4—21no—
322C3×D4—41no—
323C3×D4—42no—
324C3×D4—42no—
325C3×D4—41no—
326C3×D4—41no—
327C3×D4—41no—
328C3×D4—41no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—41no—
338C2×C3×C4—42no—
339C2×C3×C4—42no—
340C2×C3×C4—41no—
341C2×C3×C4—41no—
342C2×C3×C4—41no—
343C2×C3×C4—41no—
344C2×C3×C4—121no—
345C2×C3×C4C2×C4×D311yescharacteristic
346C2×C3×C4C2×C4×D311yescharacteristic
347C2×C3×C4#23511yescharacteristic
348C2×C3×C4D3×D411yescharacteristic
349C2×C3×C4D3×D411yescharacteristic
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4D3×D411yescharacteristic
353C2×C3×C4D3×D411yescharacteristic
354C2×C3×C4#23711yescharacteristic
355C2×C3×C4C2×#6711yescharacteristic
356C2×C3×C4C2×#6711yescharacteristic
357#67—62no—
358#67—62no—
359#67—62no—
360#67—62no—
361#67—122no—
362#67—122no—
363C2×Dic3—41no—
364C2×Dic3—61no—
365C2×Dic3—61no—
366C2×Dic3—121no—
367D12—32no—
368D12—32no—
369D12—62no—
370D12—61no—
371D12—61no—
372D12—121no—
373C4×D3—62no—
374C4×D3—62no—
375C4×D3—62no—
376C4×D3—62no—
377C4×D3—122no—
378C4×D3—122no—
379Dic6—32no—
380Dic6—32no—
381Dic6—62no—
382Dic6—61no—
383Dic6—61no—
384Dic6—121no—
385C3×C8—62no—
386C3×C8—62no—
387C3×C8—121no—
388C3⋊C8—22no—
389C3⋊C8—22no—
390C3⋊C8—41no—
391C3⋊C8—64no—
392C3⋊C8—62no—
393C3⋊C8—62no—
394C2×C32—21no—
395C2×C32—21no—
396C2×C32—21no—
397C2×C32—81no—
398C2×C32#38611yescharacteristic
399C3⋊D3—42no—
400#41—21no—
401#41—21no—
402#41—21no—
403#41—21no—
404#41—92no—
405#41—92no—
406#41—181no—
407#41—181no—
408C2×Q8—91no—
409C2×Q8#62411yescharacteristic
410C2×D4—21no—
411C2×D4—91no—
412C2×D4—181no—
413C2×D4#62411yescharacteristic
414C22×C4—21no—
415C22×C4—181no—
416C22×C4C2×D3211yescharacteristic
417Q16—182no—
418SD16—182no—
419SD16—182no—
420D8—182no—
421M16—32no—
422M16—61no—
423M16—61no—
424M16—61no—
425M16—92no—
426M16—184no—
427M16—181no—
428C2×C8—32no—
429C2×C8—61no—
430C2×C8—61no—
431C2×C8—61no—
432C2×C8—61no—
433C2×C8—184no—
434C2×C8—181no—
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—42no—
444C22×C3—42no—
445C22×C3—42no—
446C22×C3—41no—
447C22×C3—41no—
448C22×C3—81no—
449C22×C3—82no—
450C22×C3#67⋊C411yescharacteristic
451C22×C3#88311yescharacteristic
452C22×C3#88311yescharacteristic
453C22×C3#88411yescharacteristic
454C22×C3C4×#6711yescharacteristic
455C22×C3#93811yescharacteristic
456C2×D3—62no—
457C2×D3—62no—
458C2×D3—122no—
459C2×D3—241no—
460C2×D3—241no—
461C2×D3—242no—
462C3×C4—21no—
463C3×C4—21no—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4—42no—
467C3×C4—41no—
468C3×C4—41no—
469C3×C4—241no—
470C3×C4D3×C22⋊C411yescharacteristic
471C3×C4D3×C22⋊C411yescharacteristic
472C3×C4#67⋊C411yescharacteristic
473C3×C4#88411yescharacteristic
474C3×C4C4×#6711yescharacteristic
475C3×C4#93711yescharacteristic
476C3×C4#93711yescharacteristic
477C3×C4#93811yescharacteristic
478Dic3—62no—
479Dic3—62no—
480Dic3—81no—
481Dic3—122no—
482C32#188111yescharacteristic, complemented, Sylow
483C23—21no—
484C23—181no—
485C23#380411yescharacteristic
486Q8—21no—
487Q8—21no—
488Q8—92no—
489Q8—181no—
490D4—21no—
491D4—21no—
492D4—41no—
493D4—41no—
494D4—92no—
495D4—182no—
496D4—182no—
497D4—181no—
498C2×C4—21no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—121no—
502C2×C4—181no—
503C2×C4—182no—
504C2×C4—182no—
505C2×C4#380411yescharacteristic
506C2×C4C2×#62411yescharacteristic
507C2×C4D3×#6711yescharacteristic
508C2×C4D3×#6711yescharacteristic
509C2×C4#381111yescharacteristic
510C2×C4#381111yescharacteristic
511C8—62no—
512C8—62no—
513C8—121no—
514C8—182no—
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—82no—
526C2×C3—81no—
527C2×C3—81no—
528C2×C3#495611yescharacteristic
529C2×C3#495611yescharacteristic
530D3—122no—
531D3—122no—
532D3—242no—
533C22—41no—
534C22—42no—
535C22—41no—
536C22—182no—
537C22—721no—
538C22#6395211yescharacteristic
539C22#6395811yescharacteristic
540C22#6397511yescharacteristic
541C4—41no—
542C4—182no—
543C4—241no—
544C4#6395211yescharacteristic
545C4#6395811yescharacteristic
546C4#6397411yescharacteristic
547C4#6398311yescharacteristic
548C3—21no—
549C3#7001211yescharacteristic, complemented
550C3#7041611yescharacteristic, complemented
551C2—21no—
552C2—21no—
553C2—21no—
554C2—81no—
555C2—362no—
556C2#1059172211yescharacteristic
subgroupG/H
centerC4#63983
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×#41C22
socleC2×C32#386
prime radical#10596293C2
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1881
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #10594780C2semidirect
3. C3×#5236C2semidirect
4. C3×#5234C2semidirect
5. #10591105C2semidirect
6. #10589169C2semidirect
7. #10589166C2semidirect
15. #64151C4semidirect
16. #64141C4semidirect
36. #5236D3semidirect
37. #5234D3semidirect
482. C32#1881semidirect
549. C3#70012semidirect
550. C3#70416semidirect

Maximal subgroups

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

subgroupindex
#105962932
#105947802
C3×#52362
C3×#52342
#105911052
#105891692
#105891662
#704163
#700123