Finite Group Databasebeta

← #11788575

Subgroups — #11788575

Order 1152.

743 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Dic3×#235C211yesmaximal, characteristic, complemented
2#10594795C211yesmaximal, characteristic
3#10592705C211yesmaximal, characteristic, complemented
4C3×#5005C211yesmaximal, characteristic, complemented
5C2×#63570C211yesmaximal, characteristic, complemented
6C3×#4532C211yesmaximal, characteristic, complemented
7#10589171C211yesmaximal, characteristic, complemented
8#70395—31nomaximal
9#68778—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C32×#117C2211yescharacteristic
13#64135C2211yescharacteristic
14C2×C3×C4×Dic3C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17Dic3×#67—22no—
18Dic3×D12—21no—
19C4×D3×Dic3—21no—
20#63855—21no—
21Dic3×Dic6—21no—
22#63833—21no—
23#63831C412yescomplemented
24#63830—21no—
25#63829—22no—
26#63825C412yescomplemented
27#63633—22no—
28C3×#805—22no—
29#63570—21no—
30#63570—21no—
31Dic3×#41—31no—
32#5822—31no—
33#5748—31no—
34C4×#235—31no—
35C3×#421—31no—
36C2×#825—31no—
37#5006—31no—
38#5006—31no—
39#5006—61no—
40#5005D311yescharacteristic, complemented
41C2×#805—31no—
42C3×#339—31no—
43#4559—31no—
44#4556—31no—
45#4532D311yescharacteristic, complemented
46C22×C32×C4C2311yescharacteristic
47C2×#638—21no—
48#3828—21no—
49#3828—21no—
50#3828—21no—
51#3828—21no—
52C2×C4⋊(C3⋊D3)C2×C411yescharacteristic, complemented
53C2×C4×C3⋊D3—21no—
54C2×#634C2×C411yescharacteristic, complemented
55C2×C3×#67—21no—
56C22×C3×Dic3—21no—
57C3×#235—21no—
58C3×#235—21no—
59C3×#235C2×C412yes—
60C3×#235D412yes—
61C2×C3×D12D411yescharacteristic
62C2×C3×C4×D3—21no—
63C2×C3×Dic6D411yescharacteristic
64C2×D3×Dic3—22no—
65C32×C4⋊C4—21no—
66C32×C22⋊C4—21no—
67C32×C42—21no—
68#3757D412yes—
69C4⋊(C3⋊Dic3)—21no—
70C4×C3⋊Dic3—21no—
71C3×C4×Dic3—21no—
72C3×C4×Dic3D411yescharacteristic
73C3×C4×Dic3D411yescharacteristic
74C3×#208—21no—
75C3×#208—21no—
76C3×#208—21no—
77C3×#208C2×C412yescomplemented
78C2×C3×C3⋊C8—21no—
79C2×C3×C3⋊C8—21no—
80Dic3⋊Dic3—22no—
81(C2×D3)⋊Dic3—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—
94C2×C3×M16—31no—
95C3×#117—21no—
96C3×#117C2×D311yescharacteristic
97C3×#117C2×D311yescharacteristic
98C2×C3×C42—31no—
99#951—32no—
100#950—62no—
101#949—32no—
102Q8×Dic3—61no—
103#942—61no—
104D4×Dic3—61no—
105D4×Dic3—62no—
106#932—61no—
107C4×#67—62no—
108#926—31no—
109#926—31no—
110#926—61no—
111#926—61no—
112C2×C4×Dic3—61no—
113C2×C4×Dic3C2×D311yescharacteristic
114C2×#208C2×D311yescharacteristic
115C2×#208C2×D311yescharacteristic
116#909—32no—
117#909—61no—
118#908—32no—
119#908—61no—
120#904—62no—
121C4×D12—61no—
122#872—61no—
123C42×D3—61no—
124C4×Dic6—61no—
125C3×#104—62no—
126#825—61no—
127#825—61no—
128#806—62no—
129#806—62no—
130#806—64no—
131#805—22no—
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—41no—
145#638—41no—
146C2×C3⋊Dic3—21no—
147C2×C3⋊Dic3—22no—
148C4⋊(C3⋊D3)—21no—
149C4⋊(C3⋊D3)—21no—
150C4×C3⋊D3—41no—
151C4×C3⋊D3—41no—
152#634—21no—
153#634—21no—
154C3×#67—22no—
155C3×#67—22no—
156C2×C3×Dic3—21no—
157C2×C3×Dic3—21no—
158C2×C3×Dic3—21no—
159C2×C3×Dic3—42no—
160C3×D12—21no—
161C3×D12C22⋊C412yes—
162C3×C4×D3—22no—
163C3×C4×D3—22no—
164C3×Dic6—21no—
165C3×Dic6C22⋊C412yes—
166D3×Dic3—44no—
167C3×C3⋊C8—22no—
168C3×C3⋊C8—41no—
169#575—91no—
170C4×#41—91no—
171#421—31no—
172C2×#104—91no—
173#410—91no—
174#344—91no—
175#339—31no—
176C3×#41—32no—
177C3×#41—32no—
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—62no—
190C2×#67—61no—
191C2×#67—61no—
192C22×Dic3—21no—
193C22×Dic3—62no—
194#235—21no—
195#235—21no—
196#235—61no—
197#235—61no—
198#235—61no—
199#235—61no—
200#235—61no—
201#235—61no—
202#235—61no—
203#235—61no—
204#235—121no—
205#235—121no—
206#235—121no—
207#235—121no—
208#235C4×D312yes—
209#235#6712yes—
210C2×D12—31no—
211C2×D12—31no—
212C2×D12—61no—
213C2×D12D1211yescharacteristic
214C2×C4×D3—21no—
215C2×C4×D3—62no—
216C2×C4×D3—62no—
217C2×C4×D3—61no—
218C2×C4×D3—61no—
219C2×Dic6—31no—
220C2×Dic6—31no—
221C2×Dic6—61no—
222C2×Dic6D1211yescharacteristic
223C3×M16—32no—
224C3×M16—61no—
225C3×M16—61no—
226C3×M16—61no—
227C2×C3×C8—61no—
228C2×C3×C8—61no—
229C3×C4⋊C4—21no—
230C3×C4⋊C4—21no—
231C3×C4⋊C4—41no—
232C3×C22⋊C4—22no—
233C3×C22⋊C4—21no—
234C3×C22⋊C4—21no—
235C3×C42—21no—
236C3×C42—21no—
237C3×C42—31no—
238C3×C42—31no—
239C3×C42—41no—
240C3×C42—61no—
241#217—32no—
242#217—32no—
243#217—62no—
244#217—62no—
245#216—62no—
246#215—62no—
247#214—62no—
248#213—62no—
249(C2×D3)⋊C4—62no—
250C4⋊Dic3—62no—
251C4⋊Dic3—61no—
252C4⋊Dic3—61no—
253C4⋊Dic3—121no—
254Dic3⋊C4—62no—
255C4×Dic3—21no—
256C4×Dic3—62no—
257C4×Dic3—62no—
258C4×Dic3—61no—
259C4×Dic3—61no—
260C4×Dic3—121no—
261C4×Dic3D1211yescharacteristic
262C4×Dic3D1211yescharacteristic
263#208—21no—
264#208—21no—
265#208—21no—
266#208C4×D312yescomplemented
267C2×C3⋊C8—21no—
268C2×C3⋊C8—21no—
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—41no—
278C2×C3⋊D3—81no—
279C2×C3×D3—22no—
280C2×C3×D3—42no—
281C32×C4—81no—
282C32×C4C2×C22⋊C411yescharacteristic
283C32×C4C4×D411yescharacteristic
284C32×C4#12111yescharacteristic
285C32×C4#12311yescharacteristic
286C3⋊Dic3—41no—
287C3⋊Dic3—42no—
288C3×Dic3—22no—
289C3×Dic3—22no—
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—31no—
300C4×Q8—181no—
301C4×D4—181no—
302C4×D4—182no—
303#117—91no—
304#117—181no—
305#117D3211yescharacteristic
306C2×C42—31no—
307C2×C42—181no—
308#104—62no—
309#104—181no—
310#104—181no—
311#99—182no—
312C23×C3—21no—
313C23×C3—61no—
314C23×C3D3×D411yescharacteristic
315C23×C3D3×D411yescharacteristic
316C22×D3—21no—
317C22×D3—62no—
318C22×D3—61no—
319C22×D3—61no—
320C3×Q8—32no—
321C3×Q8—61no—
322C3×D4—32no—
323C3×D4—62no—
324C3×D4—62no—
325C3×D4—61no—
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—61no—
337C2×C3×C4—62no—
338C2×C3×C4—62no—
339C2×C3×C4—61no—
340C2×C3×C4—122no—
341C2×C3×C4C2×C4×D311yescharacteristic
342C2×C3×C4C2×C4×D311yescharacteristic
343C2×C3×C4C2×D1211yescharacteristic
344C2×C3×C4C2×D1211yescharacteristic
345C2×C3×C4#23511yescharacteristic
346C2×C3×C4D3×D411yescharacteristic
347C2×C3×C4D3×D411yescharacteristic
348C2×C3×C4D3×D411yescharacteristic
349C2×C3×C4#23711yescharacteristic
350C2×C3×C4#23711yescharacteristic
351C2×C3×C4#23911yescharacteristic
352C2×C3×C4C2×#6711yescharacteristic
353#67—22no—
354#67—22no—
355#67—122no—
356#67—122no—
357#67—121no—
358#67—121no—
359#67—121no—
360#67—121no—
361C2×Dic3—21no—
362C2×Dic3—21no—
363C2×Dic3—21no—
364C2×Dic3—42no—
365C2×Dic3—62no—
366C2×Dic3—61no—
367C2×Dic3—62no—
368C2×Dic3—62no—
369C2×Dic3—61no—
370C2×Dic3—122no—
371C2×Dic3—124no—
372D12—21no—
373D12—61no—
374D12—61no—
375D12—61no—
376D12—61no—
377D12—121no—
378D12—121no—
379D12(C2×D3)⋊C412yes—
380C4×D3—22no—
381C4×D3—22no—
382C4×D3—122no—
383C4×D3—122no—
384C4×D3—124no—
385C4×D3—121no—
386C4×D3—121no—
387C4×D3—121no—
388C4×D3—121no—
389Dic6—21no—
390Dic6—61no—
391Dic6—61no—
392Dic6—61no—
393Dic6—61no—
394Dic6—121no—
395Dic6—121no—
396Dic6(C2×D3)⋊C412yes—
397C3×C8—62no—
398C3×C8—121no—
399C3⋊C8—22no—
400C3⋊C8—41no—
401C2×C32—21no—
402C2×C32—21no—
403C2×C32—21no—
404C2×C32#38611yescharacteristic
405C3⋊D3—81no—
406C3×D3—42no—
407#41—32no—
408#41—32no—
409#41—61no—
410#41—61no—
411#41—181no—
412#41—181no—
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—61no—
433M16—61no—
434C2×C8—61no—
435C2×C8—61no—
436C4⋊C4—21no—
437C4⋊C4—182no—
438C4⋊C4—181no—
439C22⋊C4—21no—
440C22⋊C4—92no—
441C22⋊C4—182no—
442C42—21no—
443C42—31no—
444C42—31no—
445C42—61no—
446C42—182no—
447C42—181no—
448C22×C3—21no—
449C22×C3—21no—
450C22×C3—21no—
451C22×C3—41no—
452C22×C3—41no—
453C22×C3—62no—
454C22×C3—81no—
455C22×C3—122no—
456C22×C3#67⋊C411yescharacteristic
457C22×C3#88211yescharacteristic
458C22×C3#88211yescharacteristic
459C22×C3#88411yescharacteristic
460C22×C3#89311yescharacteristic
461C22×C3#93911yescharacteristic
462C2×D3—22no—
463C2×D3—42no—
464C2×D3—122no—
465C2×D3—121no—
466C2×D3—121no—
467C2×D3—241no—
468C2×D3—241no—
469C2×D3—242no—
470C3×C4—21no—
471C3×C4—21no—
472C3×C4—21no—
473C3×C4—21no—
474C3×C4—62no—
475C3×C4—62no—
476C3×C4—81no—
477C3×C4—81no—
478C3×C4—82no—
479C3×C4—121no—
480C3×C4C4×D1211yescharacteristic
481C3×C4D3×C22⋊C411yescharacteristic
482C3×C4#67⋊C411yescharacteristic
483C3×C4#88611yescharacteristic
484C3×C4#89411yescharacteristic
485C3×C4#89511yescharacteristic
486C3×C4C2×(C2×D3)⋊C411yescharacteristic
487C3×C4#93911yescharacteristic
488Dic3—22no—
489Dic3—22no—
490Dic3—41no—
491Dic3—122no—
492Dic3—122no—
493Dic3—122no—
494Dic3—121no—
495Dic3—121no—
496Dic3—242no—
497C32#190611yescharacteristic, complemented, Sylow
498C23—61no—
499C23—181no—
500C23#381111yescharacteristic
501Q8—32no—
502Q8—61no—
503Q8—181no—
504Q8—181no—
505D4—32no—
506D4—62no—
507D4—62no—
508D4—61no—
509D4—181no—
510D4—181no—
511D4—361no—
512D4—361no—
513C2×C4—41no—
514C2×C4—61no—
515C2×C4—61no—
516C2×C4—62no—
517C2×C4—62no—
518C2×C4—61no—
519C2×C4—122no—
520C2×C4—181no—
521C2×C4—182no—
522C2×C4—364no—
523C2×C4—361no—
524C2×C4—361no—
525C2×C4#379611yescharacteristic
526C2×C4C4×D3211yescharacteristic
527C2×C4D3×D1211yescharacteristic
528C2×C4D3×D1211yescharacteristic
529C2×C4#380411yescharacteristic
530C2×C4D3×#6711yescharacteristic
531C8—62no—
532C8—121no—
533C2×C3—21no—
534C2×C3—21no—
535C2×C3—21no—
536C2×C3—21no—
537C2×C3—21no—
538C2×C3—21no—
539C2×C3—21no—
540C2×C3—41no—
541C2×C3—41no—
542C2×C3—41no—
543C2×C3—122no—
544C2×C3#466511yescharacteristic
545C2×C3#495811yescharacteristic
546D3—42no—
547D3—242no—
548D3—241no—
549D3—241no—
550C22—41no—
551C22—62no—
552C22—122no—
553C22—361no—
554C22—721no—
555C22#6388111yescharacteristic
556C22#6392311yescharacteristic
557C22#6397111yescharacteristic
558C4—62no—
559C4—62no—
560C4—81no—
561C4—121no—
562C4—362no—
563C4—361no—
564C4#6388011yescharacteristic
565C4#6388611yescharacteristic
566C4#6389011yescharacteristic
567C4D3×(C2×D3)⋊C411yescharacteristic
568C3—21no—
569C3#6877811yescharacteristic, complemented
570C3#7039511yescharacteristic, complemented
571C2—21no—
572C2—21no—
573C2—21no—
574C2—122no—
575C2—721no—
576C2#1059136411yescharacteristic
subgroupG/H
centerC4#63886
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. Dic3×#235C2semidirect
3. #10592705C2semidirect
4. C3×#5005C2semidirect
5. C2×#63570C2semidirect
6. C3×#4532C2semidirect
7. #10589171C2semidirect
23. #63831C4semidirect
26. #63825C4semidirect
40. #5005D3semidirect
45. #4532D3semidirect
52. C2×C4⋊(C3⋊D3)C2×C4semidirect
54. C2×#634C2×C4semidirect
77. C3×#208C2×C4semidirect
266. #208C4×D3semidirect
497. C32#1906semidirect
569. C3#68778semidirect
570. C3#70395semidirect

Maximal subgroups

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

subgroupindex
Dic3×#2352
#105947952
#105927052
C3×#50052
C2×#635702
C3×#45322
#105891712
#703953
#687783