Finite Group Databasebeta

← #11870721

Subgroups — #11870721

Order 1152.

935 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594910C211yesmaximal, characteristic
2C2×#63844C211yesmaximal, characteristic, complemented
3#10592437C211yesmaximal, characteristic, complemented
4C3×#4735C211yesmaximal, characteristic, complemented
5C3×#4718C211yesmaximal, characteristic, complemented
6#10591181C211yesmaximal, characteristic, complemented
7#10591125C211yesmaximal, characteristic, complemented
8#10590879C212yesmaximal, complemented
9#10590802C212yesmaximal, complemented
10#10590758C212yesmaximal, complemented
11#10590744C212yesmaximal, complemented
12#81308—31nomaximal
13#79309—31nomaximal
14C22×#634C2211yescharacteristic
15C2×#3804—21no—
16#64139C2211yescharacteristic
17C2×#3744C2212yes—
18C3×#930C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×C4×Dic3C2211yescharacteristic
21#63978—21no—
22C2×#3724—21no—
23C2×Dic32—21no—
24#63918C2211yescharacteristic
25#63911C2211yescharacteristic
26#63894C2211yescharacteristic
27Dic3×D12C2211yescharacteristic
28#63880—21no—
29#63852—21no—
30#63844—21no—
31#63844—21no—
32#63844C2212yes—
33#63844C2212yes—
34C2×#3716C2212yes—
35C32×C22⋊C8C2211yescharacteristic
36#63643C2212yes—
37C3×#830C2211yescharacteristic
38C3×#821C2212yes—
39C3×#817C2212yes—
40C3×Dic3⋊C8C2212yes—
41C3×C8×Dic3C2212yes—
42#63573C2212yes—
43#63567C2212yes—
44#63564C2212yes—
45#5596—31no—
46C2×#887—31no—
47#5477—31no—
48C2×C4×Dic6—31no—
49C3×#481—31no—
50C3×#431—31no—
51#5040—31no—
52#4968—31no—
53#4854—32no—
54#4852—32no—
55#4851—32no—
56#4848—32no—
57#4762—32no—
58#4758—32no—
59#4738—31no—
60#4738—31no—
61#4738—31no—
62#4738—61no—
63#4735—31no—
64#4735D311yescharacteristic, complemented
65#4718D311yescharacteristic, complemented
66C4×#204—32no—
67C4×#204—32no—
68C22×C32×C4C2311yescharacteristic
69C2×#638—21no—
70C22×C3⋊Dic3—21no—
71C2×C4⋊(C3⋊D3)C2311yescharacteristic
72C2×#634—21no—
73C2×#634—24no—
74C2×#634C2312yes—
75C2×C3×#67—21no—
76C22×C3×Dic3—21no—
77C22×C3×Dic3D411yescharacteristic
78C22×C3×Dic3D411yescharacteristic
79C2×C3×D12C2311yescharacteristic
80C2×#627—21no—
81C2×#626—21no—
82C2×#626—21no—
83C2×#624—21no—
84#3804—44no—
85C2×D3×Dic3—21no—
86C2×C32×C8C2312yes—
87#3752—21no—
88C4⋊(C3⋊Dic3)C2311yescharacteristic
89#3744—24no—
90C3×(C2×D3)⋊C4—21no—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3C2312yes—
93C3×C4⋊Dic3C2311yescharacteristic
94C3×C4×Dic3D411yescharacteristic
95C3×C4×Dic3D411yescharacteristic
96C3×C4×Dic3C2311yescharacteristic
97C3×C4×Dic3C2311yescharacteristic
98C2×C3×C3⋊C8C2312yes—
99#3724—22no—
100#3724—22no—
101Dic3⋊Dic3—21no—
102#3722—21no—
103(C2×D3)⋊Dic3—21no—
104Dic32—22no—
105Dic32—22no—
106#3716—24no—
107#3103—91noSylow
108C2×#237—61no—
109C2×#235—61no—
110C22×Dic6—31no—
111C22×Dic6—31no—
112C22×Dic6—61no—
113C3×#121—31no—
114C2×C3×C4⋊C4—31no—
115C2×C3×C42—31no—
116#940—31no—
117#939—61no—
118D4×Dic3—31no—
119C2×#214—32no—
120#930—31no—
121#930—31no—
122#930—61no—
123#930—61no—
124#930C2×D311yescharacteristic
125C2×C4⋊Dic3C2×D311yescharacteristic
126C2×Dic3⋊C4—61no—
127C2×Dic3⋊C4—61no—
128C2×C4×Dic3—61no—
129C2×C4×Dic3—61no—
130C2×C4×Dic3C2×D311yescharacteristic
131C2×#204—32no—
132C2×#204—32no—
133C2×#204—32no—
134C2×#204—62no—
135#893—31no—
136#888—31no—
137#887—32no—
138#887—32no—
139#887—61no—
140#887—61no—
141#885—61no—
142#67⋊C4—61no—
143#875—61no—
144#874—31no—
145C4×D12—31no—
146C4×D12—31no—
147C4×D12—61no—
148#869—31no—
149C4×Dic6—32no—
150C4×Dic6—32no—
151C4×Dic6—61no—
152C4×Dic6—61no—
153C3×#106—32no—
154C3×C4⋊C8—32no—
155C3×#102—32no—
156C3×C22⋊C8—21no—
157C3×C22⋊C8—31no—
158C3×C22⋊C8C2×D311yescharacteristic
159C3×C22⋊C8C2×D311yescharacteristic
160C3×C4×C8—32no—
161#830C2×D311yescharacteristic
162#821—32no—
163#821C2×D312yes—
164#817—32no—
165#817C2×D312yes—
166#816—32no—
167#816—32no—
168#816—32no—
169#816—62no—
170Dic3⋊C8C2×D312yes—
171C8×Dic3C2×D312yes—
172#810—32no—
173#809—32no—
174#808—32no—
175C23×C32C2×D411yescharacteristic
176C22×C3⋊D3—21no—
177C22×C3×D3—21no—
178C2×C32×C4—22no—
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4C2411yescharacteristic
181#638—42no—
182C2×C3⋊Dic3—24no—
183C2×C3⋊Dic3—22no—
184C2×C3⋊Dic3—21no—
185C4⋊(C3⋊D3)—22no—
186#634—24no—
187#634—22no—
188#634#4114yescomplemented
189C3×#67—42no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—41no—
193C2×C3×Dic3—42no—
194C2×C3×Dic3SD1614yescomplemented
195C2×C3×Dic3C2×D411yescharacteristic
196C2×C3×Dic3C2×D411yescharacteristic
197C2×C3×Dic3C2×D411yescharacteristic
198C2×C3×Dic3C2×D411yescharacteristic
199C3×D12—22no—
200#627—42no—
201#626—42no—
202#626—42no—
203#624—42no—
204D3×Dic3—42no—
205C32×C8—22no—
206C3×C3⋊C8—22no—
207#532—91no—
208C2×C4×Q8—91no—
209#481—31no—
210#481—91no—
211#475—92no—
212#460—92no—
213#448—91no—
214#448—91no—
215C4×SD16—92no—
216C4×SD16—92no—
217#431—31no—
218C2×C3×D4—31no—
219C2×C3×D4—61no—
220C22×C3×C4—21no—
221C22×C3×C4—31no—
222C22×C3×C4—31no—
223C22×C3×C4—61no—
224C22×C3×C4C22×D311yescharacteristic
225C22×C3×C4C22×D311yescharacteristic
226C2×#67—21no—
227C2×#67—61no—
228C2×#67—61no—
229C2×#67—61no—
230C2×#67—61no—
231C2×#67—121no—
232C22×Dic3—21no—
233C22×Dic3—61no—
234C22×Dic3—61no—
235C22×Dic3—61no—
236C22×Dic3—121no—
237C22×Dic3D1211yescharacteristic
238C22×Dic3D1211yescharacteristic
239#237—124no—
240#235—124no—
241C2×D12—31no—
242C2×D12—31no—
243C2×D12—61no—
244C2×D12—61no—
245C2×D12—61no—
246C2×D12C22×D311yescharacteristic
247C2×C4×D3—61no—
248C2×C4×D3—61no—
249C2×C4×D3—61no—
250C2×Dic6—32no—
251C2×Dic6—32no—
252C2×Dic6—62no—
253C2×Dic6—64no—
254C2×Dic6—64no—
255C2×Dic6—61no—
256C2×Dic6—61no—
257C2×Dic6—61no—
258C2×Dic6—61no—
259C2×Dic6—124no—
260C2×Dic6—121no—
261C2×C3×C8—22no—
262C2×C3×C8—32no—
263C2×C3×C8C22×D312yes—
264C2×C3×C8C22×D312yes—
265C3×C4⋊C4—32no—
266C3×C4⋊C4—31no—
267C3×C4⋊C4—61no—
268C3×C22⋊C4—61no—
269C3×C42—31no—
270C3×C42—31no—
271C3×C42—31no—
272C3×C42—31no—
273#217—61no—
274#214—64no—
275(C2×D3)⋊C4—21no—
276(C2×D3)⋊C4—61no—
277(C2×D3)⋊C4—61no—
278(C2×D3)⋊C4—61no—
279(C2×D3)⋊C4—61no—
280(C2×D3)⋊C4—61no—
281(C2×D3)⋊C4—121no—
282C4⋊Dic3—21no—
283C4⋊Dic3—31no—
284C4⋊Dic3—31no—
285C4⋊Dic3—61no—
286C4⋊Dic3—61no—
287C4⋊Dic3C22×D311yescharacteristic
288C4⋊Dic3C22×D312yes—
289Dic3⋊C4—62no—
290Dic3⋊C4—62no—
291Dic3⋊C4—61no—
292Dic3⋊C4—62no—
293Dic3⋊C4—62no—
294C4×Dic3—62no—
295C4×Dic3—62no—
296C4×Dic3—62no—
297C4×Dic3—62no—
298C4×Dic3D1211yescharacteristic
299C4×Dic3D1211yescharacteristic
300C4×Dic3C22×D311yescharacteristic
301C4×Dic3C22×D311yescharacteristic
302C2×C3⋊C8C22×D312yes—
303#204—64no—
304#204—64no—
305#204—64no—
306#204—124no—
307C22×C32—21no—
308C22×C32—21no—
309C22×C32C2×SD1612yes—
310C22×C32C22×D411yescharacteristic
311C2×C3⋊D3—41no—
312C2×C3⋊D3—41no—
313C2×C3⋊D3—41no—
314C2×C3×D3—41no—
315C2×C3×D3—41no—
316C2×C3×D3—41no—
317C32×C4—21no—
318C32×C4C2×#4112yes—
319C3⋊Dic3—24no—
320C3⋊Dic3—41no—
321C3×Dic3—21no—
322C3×Dic3—21no—
323C3×Dic3—41no—
324C3×Dic3—42no—
325C3×Dic3C2×SD1612yes—
326C3×Dic3C2×SD1612yes—
327C2×#41—181no—
328C22×Q8—91no—
329C2×SD16—92no—
330C2×SD16—92no—
331C4⋊Q8—91no—
332#127—91no—
333#124—181no—
334#121—31no—
335#121—91no—
336#121—181no—
337C4×Q8—92no—
338C4×Q8—92no—
339C4×Q8—181no—
340C4×Q8—181no—
341C4×D4—91no—
342C4×D4—91no—
343C4×D4—181no—
344C2×C4⋊C4—31no—
345C2×C4⋊C4—181no—
346C2×C42—31no—
347C2×C42—181no—
348#106—32no—
349#106—92no—
350C4⋊C8—32no—
351#103—92no—
352#103—92no—
353#102—32no—
354#102—92no—
355C22⋊C8—31no—
356C22⋊C8D3211yescharacteristic
357C4×C8—32no—
358C23×C3—21no—
359C23×C3—61no—
360C23×C3C2×D1211yescharacteristic
361C23×C3D3×D411yescharacteristic
362C22×D3—21no—
363C22×D3—61no—
364C22×D3—61no—
365C22×D3—121no—
366C3×D4—62no—
367C3×D4—122no—
368C2×C3×C4—22no—
369C2×C3×C4—22no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4—34no—
373C2×C3×C4—31no—
374C2×C3×C4—31no—
375C2×C3×C4—31no—
376C2×C3×C4—31no—
377C2×C3×C4—42no—
378C2×C3×C4—62no—
379C2×C3×C4—61no—
380C2×C3×C4—121no—
381C2×C3×C4—122no—
382C2×C3×C4C2×D1211yescharacteristic
383C2×C3×C4D3×D411yescharacteristic
384C2×C3×C4C23×D311yescharacteristic
385C2×C3×C4C23×D311yescharacteristic
386#67—42no—
387#67—122no—
388#67—122no—
389#67—122no—
390#67—122no—
391#67—242no—
392C2×Dic3—22no—
393C2×Dic3—21no—
394C2×Dic3—41no—
395C2×Dic3—42no—
396C2×Dic3—64no—
397C2×Dic3—64no—
398C2×Dic3—62no—
399C2×Dic3—62no—
400C2×Dic3—61no—
401C2×Dic3—61no—
402C2×Dic3—122no—
403C2×Dic3—124no—
404C2×Dic3—121no—
405C2×Dic3—122no—
406C2×Dic3#20414yescomplemented
407C2×Dic3C2×D1211yescharacteristic
408C2×Dic3C2×D1211yescharacteristic
409C2×Dic3C2×D1211yescharacteristic
410C2×Dic3C2×D1211yescharacteristic
411D12—22no—
412D12—62no—
413D12—62no—
414D12—122no—
415D12—122no—
416D12—122no—
417C4×D3—122no—
418C4×D3—122no—
419C4×D3—122no—
420Dic6—34no—
421Dic6—34no—
422Dic6—64no—
423Dic6—64no—
424Dic6—64no—
425Dic6—62no—
426Dic6—62no—
427Dic6—122no—
428Dic6—124no—
429Dic6—122no—
430Dic6—122no—
431C3×C8—22no—
432C3×C8—22no—
433C3×C8—42no—
434C3×C8—62no—
435C3⋊C8—22no—
436C2×C32—22no—
437C2×C32#52511yescharacteristic
438C2×C32C22×SD1611yescharacteristic
439C2×C32#57511yescharacteristic
440C3⋊D3—81no—
441C3×D3—81no—
442#41—364no—
443C2×Q8—92no—
444C2×Q8—184no—
445C2×Q8—181no—
446C2×Q8—181no—
447C2×D4—31no—
448C2×D4—61no—
449C2×D4—91no—
450C2×D4—181no—
451C2×D4—181no—
452C2×D4—181no—
453C22×C4—31no—
454C22×C4—31no—
455C22×C4—61no—
456C22×C4—181no—
457C22×C4—181no—
458C22×C4—181no—
459C22×C4C2×D3211yescharacteristic
460SD16—184no—
461SD16—184no—
462C2×C8—32no—
463C2×C8C2×D3212yes—
464C4⋊C4—32no—
465C4⋊C4—31no—
466C4⋊C4—61no—
467C4⋊C4—91no—
468C4⋊C4—182no—
469C4⋊C4—182no—
470C4⋊C4—181no—
471C22⋊C4—61no—
472C22⋊C4—181no—
473C22⋊C4—181no—
474C22⋊C4—181no—
475C42—31no—
476C42—31no—
477C42—31no—
478C42—31no—
479C42—182no—
480C42—182no—
481C22×C3—21no—
482C22×C3—21no—
483C22×C3—21no—
484C22×C3—21no—
485C22×C3—21no—
486C22×C3—22no—
487C22×C3—41no—
488C22×C3—41no—
489C22×C3—121no—
490C22×C3—121no—
491C22×C3—121no—
492C22×C3C2×#20412yes—
493C22×C3D3×SD1612yes—
494C22×C3C22×D1211yescharacteristic
495C22×C3C2×D3×D411yescharacteristic
496C2×D3—41no—
497C2×D3—41no—
498C2×D3—41no—
499C2×D3—121no—
500C2×D3—121no—
501C2×D3—121no—
502C2×D3—121no—
503C2×D3—121no—
504C2×D3—121no—
505C2×D3—241no—
506C2×D3—241no—
507C2×D3—241no—
508C3×C4—21no—
509C3×C4—21no—
510C3×C4—22no—
511C3×C4—32no—
512C3×C4—32no—
513C3×C4—41no—
514C3×C4—61no—
515C3×C4—61no—
516C3×C4—121no—
517C3×C4—122no—
518C3×C4D3×#4112yes—
519C3×C4D3×#4112yes—
520Dic3—21no—
521Dic3—21no—
522Dic3—41no—
523Dic3—42no—
524Dic3—64no—
525Dic3—64no—
526Dic3—124no—
527Dic3—121no—
528Dic3—121no—
529Dic3—241no—
530Dic3C2×#20412yes—
531Dic3C2×#20412yes—
532C32#310311yescharacteristic, complemented, Sylow
533C23—61no—
534C23—181no—
535C23D3×D1211yescharacteristic
536Q8—94no—
537Q8—184no—
538Q8—182no—
539Q8—362no—
540D4—62no—
541D4—122no—
542D4—182no—
543D4—362no—
544D4—362no—
545D4—362no—
546C2×C4—22no—
547C2×C4—31no—
548C2×C4—31no—
549C2×C4—34no—
550C2×C4—31no—
551C2×C4—31no—
552C2×C4—62no—
553C2×C4—61no—
554C2×C4—121no—
555C2×C4—122no—
556C2×C4—184no—
557C2×C4—182no—
558C2×C4—181no—
559C2×C4—362no—
560C2×C4—362no—
561C2×C4D3×D1211yescharacteristic
562C2×C4C22×D3211yescharacteristic
563C8—22no—
564C8—62no—
565C2×C3—22no—
566C2×C3—22no—
567C2×C3—21no—
568C2×C3—21no—
569C2×C3—21no—
570C2×C3—42no—
571C2×C3—241no—
572C2×C3#552411yescharacteristic
573C2×C3#565611yescharacteristic
574C2×C3C22×#20411yescharacteristic
575C2×C3#574811yescharacteristic
576C2×C3C2×D3×SD1611yescharacteristic
577C2×C3#577311yescharacteristic
578D3—81no—
579D3—241no—
580D3—241no—
581D3—481no—
582C22—21no—
583C22—21no—
584C22—121no—
585C22—121no—
586C22—121no—
587C22—361no—
588C22—361no—
589C22—361no—
590C22D3×#20412yes—
591C22C2×D3×D1211yescharacteristic
592C4—21no—
593C4—32no—
594C4—32no—
595C4—61no—
596C4—61no—
597C4—121no—
598C4—122no—
599C4—184no—
600C4—361no—
601C4#6431212yes—
602C3—21no—
603C3#7930911yescharacteristic, complemented
604C3#8130811yescharacteristic, complemented
605C2—22no—
606C2—241no—
607C2—721no—
608C2#1059407911yescharacteristic
609C2C2×D3×#20411yescharacteristic
610C2#1059471211yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radical#10594910C2
hypercenterC22⋊C8D32
hypocenterC32#3103
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#63844C2semidirect
3. #10592437C2semidirect
4. C3×#4735C2semidirect
5. C3×#4718C2semidirect
6. #10591181C2semidirect
7. #10591125C2semidirect
8. #10590879C2semidirect
9. #10590802C2semidirect
10. #10590758C2semidirect
11. #10590744C2semidirect
64. #4735D3semidirect
65. #4718D3semidirect
188. #634#41semidirect
194. C2×C3×Dic3SD16semidirect
406. C2×Dic3#204semidirect
532. C32#3103semidirect
603. C3#79309semidirect
604. C3#81308semidirect

Maximal subgroups

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

subgroupindex
#105949102
C2×#638442
#105924372
C3×#47352
C3×#47182
#105911812
#105911252
#105908792
#105908022
#105907582
#105907442
#813083
#793093