Finite Group Databasebeta

← #11788576

Subgroups — #11788576

Order 1152.

741 conjugacy classes of subgroups.

The subgroup lattice has 577 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594954C211yesmaximal, characteristic, complemented
2#10594795C211yesmaximal, characteristic
3#10592704C211yesmaximal, characteristic, complemented
4C3×#5006C211yesmaximal, characteristic, complemented
5C2×#63569C211yesmaximal, characteristic, complemented
6C3×#4532C211yesmaximal, characteristic, complemented
7#10589170C211yesmaximal, characteristic, complemented
8#70055—31nomaximal
9#68778—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C32×#117C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63952—22no—
18#63894—21no—
19C4×#624—21no—
20#63874—21no—
21#63844—21no—
22#63833C412yescomplemented
23#63831—21no—
24#63830C412yescomplemented
25#63829—22no—
26#63825—21no—
27#63632—22no—
28C3×#806—22no—
29#63569—21no—
30#63569—21no—
31#5822—31no—
32#5748—31no—
33#5522—31no—
34C4×#235—31no—
35C3×#410—31no—
36C2×#837—31no—
37#5006D311yescharacteristic, complemented
38#5005—31no—
39#5005—31no—
40#5005—61no—
41C2×#805—31no—
42C3×#339—31no—
43#4559—31no—
44#4533—31no—
45#4532D311yescharacteristic, complemented
46C22×C32×C4C2311yescharacteristic
47C2×#638—21no—
48#3828—21no—
49#3828—21no—
50#3828C2×C412yes—
51#3828D412yes—
52C2×C4⋊(C3⋊D3)D411yescharacteristic
53C2×C4×C3⋊D3—21no—
54C2×#634D411yescharacteristic
55C2×C3×#67—21no—
56C22×C3×Dic3—21no—
57C3×#235—21no—
58C3×#235—21no—
59C3×#235—21no—
60C3×#235—21no—
61C2×C3×D12C2×C411yescharacteristic, complemented
62C2×C3×C4×D3—21no—
63C2×C3×Dic6C2×C411yescharacteristic, complemented
64C2×#624—22no—
65C32×C4⋊C4—21no—
66C32×C22⋊C4—21no—
67C32×C42—21no—
68#3748—21no—
69#3748—21no—
70C2×C3⋊(C3⋊C8)—21no—
71C3×#217D412yes—
72C3×C4⋊Dic3—21no—
73C3×C4×Dic3—21no—
74C3×C4×Dic3—21no—
75C3×C4×Dic3D411yescharacteristic
76C3×C4×Dic3D411yescharacteristic
77C3×#208—21no—
78C3×#208C2×C412yescomplemented
79C2×C3×C3⋊C8—21no—
80#3724—22no—
81#3722—22no—
82Dic32—22no—
83#3719—22no—
84#3717—22no—
85#3716—22no—
86#3714—22no—
87#1906—91noSylow
88C2×C3×#41—31no—
89C2×#235—31no—
90C2×#235—31no—
91C2×#235—61no—
92C2×#235C2×D311yescharacteristic
93C2×C3×M16—31no—
94C3×#117—21no—
95C3×#117—31no—
96C3×#117C2×D311yescharacteristic
97C3×#117C2×D311yescharacteristic
98C2×C3×C42—31no—
99#951—61no—
100#950—62no—
101#949—61no—
102#942—32no—
103#932—32no—
104C4×#67—62no—
105#926C2×D311yescharacteristic
106C2×C4×Dic3C2×D311yescharacteristic
107C2×#208—31no—
108C2×#208—31no—
109C2×#208—61no—
110C2×#208C2×D311yescharacteristic
111#909—32no—
112#909—61no—
113#908—32no—
114#908—61no—
115#904—62no—
116#893—61no—
117#887—61no—
118#67⋊C4—62no—
119C4×D12—61no—
120#872—61no—
121#872—61no—
122C42×D3—61no—
123C42×D3—61no—
124C4×Dic6—61no—
125C3×#99—62no—
126#837—61no—
127#837—61no—
128#806—22no—
129#805—62no—
130#805—62no—
131#805—64no—
132#805—61no—
133#805—61no—
134C23×C32C2×D411yescharacteristic
135C22×C3⋊D3—21no—
136C22×C3×D3—21no—
137C2×C32×C4—41no—
138C2×C32×C4C22×C411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4#4111yescharacteristic
143C2×C32×C4#4111yescharacteristic
144#638—22no—
145#638—22no—
146C2×C3⋊Dic3—21no—
147C4⋊(C3⋊D3)—21no—
148C4⋊(C3⋊D3)C22⋊C412yes—
149C4×C3⋊D3—22no—
150C4×C3⋊D3—22no—
151#634—21no—
152#634C22⋊C412yes—
153C3×#67—41no—
154C3×#67—41no—
155C2×C3×Dic3—21no—
156C2×C3×Dic3—21no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—21no—
159C2×C3×Dic3—42no—
160C3×D12—21no—
161C3×D12—21no—
162C3×C4×D3—41no—
163C3×C4×D3—41no—
164C3×Dic6—21no—
165C3×Dic6—21no—
166#624—44no—
167C3⋊(C3⋊C8)—41no—
168C3×C3⋊C8—22no—
169#575—91no—
170C4×#41—91no—
171#421—91no—
172C2×#104—91no—
173#410—31no—
174#344—91no—
175#339—31no—
176C3×#41—61no—
177C3×#41—61no—
178C3×#41—61no—
179C3×#41—61no—
180C2×C3×Q8—31no—
181C2×C3×D4—31no—
182C2×C3×D4—61no—
183C22×C3×C4—21no—
184C22×C3×C4—61no—
185C22×C3×C4—61no—
186C22×C3×C4C22×D311yescharacteristic
187C22×C3×C4C22×D311yescharacteristic
188C2×#67—21no—
189C2×#67—61no—
190C2×#67—61no—
191C2×#67—121no—
192C22×Dic3—21no—
193#235—21no—
194#235—21no—
195#235—21no—
196#235—21no—
197#235—32no—
198#235—32no—
199#235—32no—
200#235—32no—
201#235—62no—
202#235—62no—
203#235—61no—
204#235—61no—
205#235—61no—
206#235—61no—
207#235—121no—
208#235—121no—
209C2×D12—31no—
210C2×D12—31no—
211C2×D12—61no—
212C2×D12C4×D311yescharacteristic, complemented
213C2×C4×D3—21no—
214C2×C4×D3—61no—
215C2×C4×D3—61no—
216C2×C4×D3—62no—
217C2×C4×D3—62no—
218C2×C4×D3—121no—
219C2×Dic6—31no—
220C2×Dic6—31no—
221C2×Dic6—61no—
222C2×Dic6C4×D311yescharacteristic, complemented
223C3×M16—32no—
224C3×M16—61no—
225C2×C3×C8—61no—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—21no—
228C3×C4⋊C4—41no—
229C3×C4⋊C4—61no—
230C3×C22⋊C4—21no—
231C3×C22⋊C4—21no—
232C3×C22⋊C4—32no—
233C3×C22⋊C4—41no—
234C3×C42—22no—
235C3×C42—21no—
236C3×C42—21no—
237C3×C42—31no—
238C3×C42—31no—
239C3×C42—61no—
240C3×C42—61no—
241#217#6712yes—
242#216—62no—
243#215—62no—
244#214—62no—
245#213—62no—
246(C2×D3)⋊C4—62no—
247(C2×D3)⋊C4—62no—
248C4⋊Dic3—21no—
249Dic3⋊C4—62no—
250Dic3⋊C4—62no—
251C4×Dic3—21no—
252C4×Dic3—21no—
253C4×Dic3—62no—
254C4×Dic3—62no—
255C4×Dic3D1211yescharacteristic
256C4×Dic3D1211yescharacteristic
257#208—21no—
258#208—62no—
259#208—61no—
260#208—61no—
261#208—61no—
262#208—61no—
263#208—121no—
264#208C4×D312yescomplemented
265C2×C3⋊C8—21no—
266C2×C3⋊C8—61no—
267C2×C3⋊C8—61no—
268C2×C3⋊C8—121no—
269Dic12—62no—
270D24—62no—
271#204—62no—
272#204—62no—
273C22×C32—41no—
274C22×C32C4×D411yescharacteristic
275C22×C32#12011yescharacteristic
276C22×C32#12111yescharacteristic
277C2×C3⋊D3—22no—
278C2×C3⋊D3—42no—
279C2×C3×D3—41no—
280C2×C3×D3—81no—
281C32×C4—81no—
282C32×C4C2×C22⋊C411yescharacteristic
283C32×C4C4×D411yescharacteristic
284C32×C4#12111yescharacteristic
285C32×C4#12311yescharacteristic
286C3⋊Dic3—22no—
287C3×Dic3—22no—
288C3×Dic3—42no—
289C3×Dic3—41no—
290C3×Dic3—41no—
291C2×#41—31no—
292C2×#41—91no—
293#137—92no—
294#137—181no—
295AGL(1,ℤ/8)—92no—
296AGL(1,ℤ/8)—181no—
297#135—182no—
298C2×M16—31no—
299C2×M16—91no—
300C4×Q8—181no—
301C4×D4—181no—
302C4×D4—182no—
303#117—31no—
304#117—181no—
305#117D3211yescharacteristic
306C2×C42—31no—
307C2×C42—181no—
308#104—182no—
309#104—181no—
310#104—181no—
311#99—62no—
312C23×C3—21no—
313C23×C3—61no—
314C23×C3D3×D411yescharacteristic
315C23×C3C2×#6711yescharacteristic
316C22×D3—21no—
317C22×D3—61no—
318C22×D3—61no—
319C22×D3—121no—
320C3×Q8—61no—
321C3×Q8—61no—
322C3×D4—61no—
323C3×D4—61no—
324C3×D4—121no—
325C3×D4—121no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—42no—
333C2×C3×C4—41no—
334C2×C3×C4—41no—
335C2×C3×C4—61no—
336C2×C3×C4—62no—
337C2×C3×C4—61no—
338C2×C3×C4—61no—
339C2×C3×C4—122no—
340C2×C3×C4—121no—
341C2×C3×C4—121no—
342C2×C3×C4C2×C4×D311yescharacteristic
343C2×C3×C4C2×C4×D311yescharacteristic
344C2×C3×C4C2×D1211yescharacteristic
345C2×C3×C4#23511yescharacteristic
346C2×C3×C4#23511yescharacteristic
347C2×C3×C4D3×D411yescharacteristic
348C2×C3×C4D3×D411yescharacteristic
349C2×C3×C4D3×D411yescharacteristic
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4#23711yescharacteristic
353C2×C3×C4#23911yescharacteristic
354#67—41no—
355#67—41no—
356#67—62no—
357#67—62no—
358#67—62no—
359#67—62no—
360#67—122no—
361#67—122no—
362C2×Dic3—21no—
363C2×Dic3—21no—
364C2×Dic3—21no—
365C2×Dic3—22no—
366C2×Dic3—42no—
367C2×Dic3—61no—
368C2×Dic3—61no—
369C2×Dic3—121no—
370D12—21no—
371D12—21no—
372D12—32no—
373D12—32no—
374D12—62no—
375D12—61no—
376D12—61no—
377D12—121no—
378C4×D3—41no—
379C4×D3—41no—
380C4×D3—62no—
381C4×D3—62no—
382C4×D3—62no—
383C4×D3—62no—
384C4×D3—122no—
385C4×D3—122no—
386C4×D3—124no—
387C4×D3—124no—
388Dic6—21no—
389Dic6—21no—
390Dic6—32no—
391Dic6—32no—
392Dic6—62no—
393Dic6—61no—
394Dic6—61no—
395Dic6—121no—
396C3×C8—62no—
397C3⋊C8—22no—
398C3⋊C8—122no—
399C3⋊C8—121no—
400C3⋊C8—121no—
401C2×C32—21no—
402C2×C32—21no—
403C2×C32—21no—
404C2×C32#38611yescharacteristic
405C3⋊D3—42no—
406C3×D3—81no—
407#41—61no—
408#41—61no—
409#41—61no—
410#41—61no—
411#41—92no—
412#41—92no—
413#41—181no—
414#41—181no—
415C2×Q8—31no—
416C2×Q8—91no—
417C2×D4—31no—
418C2×D4—61no—
419C2×D4—91no—
420C2×D4—181no—
421C22×C4—61no—
422C22×C4—61no—
423C22×C4—182no—
424C22×C4—181no—
425C22×C4C2×D3211yescharacteristic
426Q16—182no—
427SD16—182no—
428SD16—182no—
429D8—182no—
430M16—32no—
431M16—61no—
432M16—181no—
433M16—181no—
434C2×C8—61no—
435C2×C8—181no—
436C4⋊C4—21no—
437C4⋊C4—61no—
438C4⋊C4—182no—
439C22⋊C4—21no—
440C22⋊C4—32no—
441C22⋊C4—182no—
442C42—21no—
443C42—31no—
444C42—31no—
445C42—61no—
446C42—61no—
447C42—182no—
448C22×C3—21no—
449C22×C3—21no—
450C22×C3—21no—
451C22×C3—41no—
452C22×C3—41no—
453C22×C3—81no—
454C22×C3—121no—
455C22×C3—241no—
456C22×C3#88211yescharacteristic
457C22×C3#88411yescharacteristic
458C22×C3#89311yescharacteristic
459C22×C3C4×#6711yescharacteristic
460C22×C3#93711yescharacteristic
461C22×C3#93811yescharacteristic
462C2×D3—41no—
463C2×D3—62no—
464C2×D3—62no—
465C2×D3—81no—
466C2×D3—122no—
467C2×D3—122no—
468C2×D3—122no—
469C2×D3—242no—
470C3×C4—21no—
471C3×C4—21no—
472C3×C4—21no—
473C3×C4—21no—
474C3×C4—62no—
475C3×C4—81no—
476C3×C4—81no—
477C3×C4—82no—
478C3×C4—122no—
479C3×C4—121no—
480C3×C4—121no—
481C3×C4C4×D1211yescharacteristic
482C3×C4D3×C22⋊C411yescharacteristic
483C3×C4D3×C22⋊C411yescharacteristic
484C3×C4#67⋊C411yescharacteristic
485C3×C4#88311yescharacteristic
486C3×C4#88411yescharacteristic
487C3×C4#89411yescharacteristic
488C3×C4#89511yescharacteristic
489Dic3—22no—
490Dic3—42no—
491Dic3—41no—
492Dic3—41no—
493Dic3—62no—
494Dic3—62no—
495Dic3—122no—
496C32#190611yescharacteristic, complemented, Sylow
497C23—61no—
498C23—181no—
499C23D3×#6711yescharacteristic
500Q8—61no—
501Q8—61no—
502Q8—92no—
503Q8—181no—
504D4—61no—
505D4—61no—
506D4—92no—
507D4—121no—
508D4—121no—
509D4—182no—
510D4—182no—
511D4—181no—
512C2×C4—41no—
513C2×C4—61no—
514C2×C4—61no—
515C2×C4—61no—
516C2×C4—62no—
517C2×C4—122no—
518C2×C4—121no—
519C2×C4—121no—
520C2×C4—181no—
521C2×C4—182no—
522C2×C4—182no—
523C2×C4—364no—
524C2×C4#379911yescharacteristic
525C2×C4C4×D3211yescharacteristic
526C2×C4D3×D1211yescharacteristic
527C2×C4#380211yescharacteristic
528C2×C4#380411yescharacteristic
529C2×C4#381111yescharacteristic
530C8—62no—
531C8—361no—
532C2×C3—21no—
533C2×C3—21no—
534C2×C3—21no—
535C2×C3—21no—
536C2×C3—21no—
537C2×C3—21no—
538C2×C3—21no—
539C2×C3—41no—
540C2×C3—41no—
541C2×C3—41no—
542C2×C3—241no—
543C2×C3#466511yescharacteristic
544C2×C3#495611yescharacteristic
545D3—81no—
546D3—122no—
547D3—122no—
548D3—242no—
549C22—41no—
550C22—121no—
551C22—182no—
552C22—241no—
553C22—362no—
554C22#6390411yescharacteristic
555C22#6392211yescharacteristic
556C22#6395811yescharacteristic
557C4—62no—
558C4—81no—
559C4—121no—
560C4—122no—
561C4—121no—
562C4—182no—
563C4#6385411yescharacteristic
564C4#6388011yescharacteristic
565C4#6391011yescharacteristic
566C4#6392111yescharacteristic
567C3—21no—
568C3#6877811yescharacteristic, complemented
569C3#7005511yescharacteristic, complemented
570C2—21no—
571C2—21no—
572C2—21no—
573C2—241no—
574C2—362no—
575C2#1059127511yescharacteristic
subgroupG/H
centerC4#63910
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC2×C32#386
prime radical#10594795C2
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32#1906
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #10594954C2semidirect
3. #10592704C2semidirect
4. C3×#5006C2semidirect
5. C2×#63569C2semidirect
6. C3×#4532C2semidirect
7. #10589170C2semidirect
22. #63833C4semidirect
24. #63830C4semidirect
37. #5006D3semidirect
45. #4532D3semidirect
61. C2×C3×D12C2×C4semidirect
63. C2×C3×Dic6C2×C4semidirect
78. C3×#208C2×C4semidirect
212. C2×D12C4×D3semidirect
222. C2×Dic6C4×D3semidirect
264. #208C4×D3semidirect
496. C32#1906semidirect
568. C3#68778semidirect
569. C3#70055semidirect

Maximal subgroups

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

subgroupindex
#105949542
#105947952
#105927042
C3×#50062
C2×#635692
C3×#45322
#105891702
#700553
#687783