Finite Group Databasebeta

← #11868747

Subgroups — #11868747

Order 1152.

863 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595988C211yesmaximal, characteristic
2C2×#63843C211yesmaximal, characteristic
3C3×#5004C211yesmaximal, characteristic
4C3×#4995C211yesmaximal, characteristic
5#10591130C211yesmaximal, characteristic
6#10591120C211yesmaximal, characteristic
7#10591100C211yesmaximal, characteristic
8#10590497C212yesmaximal, complemented
9#10590496C212yesmaximal, complemented
10#10590495C212yesmaximal, complemented
11#10590494C212yesmaximal, complemented
12#79245—31nomaximal
13#78949—31nomaximal
14C22×C3×Dic6C2211yescharacteristic
15C32×#117C2211yescharacteristic
16#64135C2211yescharacteristic
17C2×C4×C3⋊Dic3C2211yescharacteristic
18#64099C2211yescharacteristic
19#64099C2211yescharacteristic
20#64097C2211yescharacteristic
21#64097C2211yescharacteristic
22#64087—21no—
23#64087—21no—
24C4×#634—21no—
25C4×#634—21no—
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×#208C2211yescharacteristic
28C2×C3×#208C2211yescharacteristic
29C2×Dic3⋊Dic3—21no—
30C2×Dic32—21no—
31#63843—21no—
32#63843—21no—
33#63843C2212yes—
34#63843C2212yes—
35C3×#810C2212yes—
36C3×#810C2212yes—
37C3×#808C2212yes—
38C3×#807C2212yes—
39#63575C2212yes—
40#63573C2212yes—
41#63572C2212yes—
42#63572C2212yes—
43#63566C2212yes—
44#63566C2212yes—
45C2×Q8×Dic3—31no—
46#5517—31no—
47#5517—31no—
48#5517—61no—
49C2×#887—31no—
50C3×#428—31no—
51C3×#419—31no—
52#5225—31no—
53#5121—31no—
54#5120—31no—
55#5118—31no—
56#5118—31no—
57#5004D311yescharacteristic
58#4995D311yescharacteristic
59#4964—31no—
60#4877—32no—
61#4875—32no—
62#4857—32no—
63#4854—32no—
64#4799—32no—
65#4796—32no—
66#4793—32no—
67#4791—32no—
68C22×C32×C4C2311yescharacteristic
69C22×C3⋊Dic3D411yescharacteristic
70C22×C3⋊Dic3D411yescharacteristic
71C2×#634—21no—
72C2×#634—21no—
73C22×C3×Dic3—21no—
74C22×C3×Dic3—21no—
75C2×C3×Dic6—21no—
76C2×C3×Dic6—22no—
77C2×C3×Dic6Q814yescomplemented
78C2×C3×Dic6C2312yes—
79C32×C4⋊C4C2311yescharacteristic
80C32×C4⋊C4C2311yescharacteristic
81C32×C22⋊C4—21no—
82C32×C42—21no—
83#3757—21no—
84C4⋊(C3⋊Dic3)—21no—
85C4⋊(C3⋊Dic3)—21no—
86C4⋊(C3⋊Dic3)C2311yescharacteristic
87C4⋊(C3⋊Dic3)C2311yescharacteristic
88#3750—21no—
89#3750—21no—
90#3750—21no—
91#3750—21no—
92C4×C3⋊Dic3—21no—
93C4×C3⋊Dic3D411yescharacteristic
94C4×C3⋊Dic3D411yescharacteristic
95C4×C3⋊Dic3C2311yescharacteristic
96C4×C3⋊Dic3C2311yescharacteristic
97C3×C4⋊Dic3—21no—
98C3×C4⋊Dic3C2312yes—
99C3×#208—22no—
100C3×#208—22no—
101C2×C3×C3⋊C8C2312yes—
102C2×C3×C3⋊C8C2312yes—
103Dic3⋊Dic3—22no—
104Dic3⋊Dic3—22no—
105Dic32—22no—
106Dic32—22no—
107#3078—91noSylow
108C22×C3×Q8—31no—
109C22×Dic6C2×D311yescharacteristic
110C2×C3×M16—31no—
111C2×C3×M16—31no—
112C3×#117—21no—
113C3×#117C2×D311yescharacteristic
114C3×#117C2×D311yescharacteristic
115C2×C3×C4⋊C4—31no—
116Q8×Dic3—32no—
117Q8×Dic3—32no—
118Q8×Dic3—61no—
119Q8×Dic3—61no—
120#926—31no—
121#926—31no—
122#926—61no—
123C2×C4⋊Dic3—61no—
124C2×C4⋊Dic3C2×D311yescharacteristic
125C2×Dic3⋊C4—61no—
126C2×C4×Dic3—31no—
127C2×C4×Dic3—31no—
128C2×C4×Dic3—61no—
129C2×C4×Dic3—61no—
130C2×C4×Dic3—61no—
131C2×#208C2×D311yescharacteristic
132C2×#208C2×D311yescharacteristic
133#890—31no—
134#890—31no—
135#890—31no—
136#890—31no—
137#890—61no—
138#890—61no—
139#888—31no—
140#888—31no—
141#888—31no—
142#888—31no—
143#888—61no—
144#888—61no—
145#887—32no—
146#887—32no—
147#887—61no—
148#887—61no—
149#878—61no—
150#878—61no—
151#878—61no—
152#878—61no—
153#878—62no—
154#878—62no—
155C4×Dic6—61no—
156C4×Dic6—61no—
157C4×Dic6—61no—
158C4×Dic6—61no—
159C4×Dic6—62no—
160C4×Dic6—62no—
161C3×#107—32no—
162C3×#106—32no—
163C3×#103—32no—
164C3×#103—32no—
165#835—32no—
166#835—32no—
167#818—32no—
168#817—32no—
169#816—32no—
170#816—32no—
171Dic3⋊C8—32no—
172Dic3⋊C8—32no—
173Dic3⋊C8—32no—
174Dic3⋊C8—32no—
175#810C2×D312yes—
176#810C2×D312yes—
177#808—32no—
178#808C2×D312yes—
179#807—32no—
180#807C2×D312yes—
181C23×C32C2×D411yescharacteristic
182C2×C32×C4—21no—
183C2×C32×C4—21no—
184C2×C32×C4C2×D411yescharacteristic
185C2×C32×C4C2×Q812yes—
186C2×C32×C4#4112yes—
187C2×C32×C4C2411yescharacteristic
188C2×C3⋊Dic3—21no—
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3—22no—
191C2×C3⋊Dic3—41no—
192C2×C3⋊Dic3C2×D411yescharacteristic
193C2×C3⋊Dic3C2×D411yescharacteristic
194C2×C3⋊Dic3C2×D411yescharacteristic
195C2×C3⋊Dic3C2×D411yescharacteristic
196#634—42no—
197#634—42no—
198C2×C3×Dic3—24no—
199C2×C3×Dic3—22no—
200C2×C3×Dic3—22no—
201C2×C3×Dic3—42no—
202C3×Dic6—24no—
203C3×Dic6—22no—
204C3×Dic6C2×Q814yes—
205C3×C3⋊C8—22no—
206C3×C3⋊C8—22no—
207#533—91no—
208C2×C4×Q8—91no—
209#479—92no—
210#479—92no—
211#477—92no—
212#475—92no—
213#428—31no—
214#428—91no—
215#423—91no—
216#419—31no—
217#419—91no—
218C2×C3×Q8—34no—
219C2×C3×Q8—32no—
220C2×C3×Q8—62no—
221C2×C3×Q8—61no—
222C22×C3×C4—21no—
223C22×C3×C4—61no—
224C22×C3×C4—61no—
225C22×C3×C4C22×D311yescharacteristic
226C22×C3×C4C22×D311yescharacteristic
227C22×Dic3—21no—
228C22×Dic3—21no—
229C22×Dic3—31no—
230C22×Dic3—31no—
231C22×Dic3—31no—
232C22×Dic3—31no—
233C22×Dic3—61no—
234C22×Dic3—61no—
235C2×Dic6—21no—
236C2×Dic6—22no—
237C2×Dic6—61no—
238C2×Dic6—61no—
239C2×Dic6—61no—
240C2×Dic6—61no—
241C2×Dic6—62no—
242C2×Dic6—62no—
243C2×Dic6Dic614yescomplemented
244C2×Dic6C22×D312yes—
245C3×M16—62no—
246C3×M16—62no—
247C2×C3×C8—32no—
248C2×C3×C8—32no—
249C3×C4⋊C4—21no—
250C3×C4⋊C4—21no—
251C3×C4⋊C4—32no—
252C3×C4⋊C4—61no—
253C3×C4⋊C4C22×D311yescharacteristic
254C3×C4⋊C4C22×D311yescharacteristic
255C3×C4⋊C4C22×D311yescharacteristic
256C3×C4⋊C4C22×D311yescharacteristic
257C3×C22⋊C4—22no—
258C3×C22⋊C4—21no—
259C3×C22⋊C4—21no—
260C3×C42—22no—
261C3×C42—21no—
262C3×C42—21no—
263#217—62no—
264#217—61no—
265#217—61no—
266C4⋊Dic3—21no—
267C4⋊Dic3—31no—
268C4⋊Dic3—31no—
269C4⋊Dic3—31no—
270C4⋊Dic3—31no—
271C4⋊Dic3—61no—
272C4⋊Dic3—61no—
273C4⋊Dic3—62no—
274C4⋊Dic3—62no—
275C4⋊Dic3—61no—
276C4⋊Dic3—61no—
277C4⋊Dic3—61no—
278C4⋊Dic3—61no—
279C4⋊Dic3—62no—
280C4⋊Dic3—62no—
281C4⋊Dic3C22×D312yes—
282Dic3⋊C4—62no—
283Dic3⋊C4—62no—
284Dic3⋊C4—61no—
285Dic3⋊C4—61no—
286Dic3⋊C4—61no—
287Dic3⋊C4—61no—
288Dic3⋊C4—61no—
289Dic3⋊C4—61no—
290Dic3⋊C4—61no—
291Dic3⋊C4—61no—
292Dic3⋊C4—62no—
293Dic3⋊C4—62no—
294Dic3⋊C4—62no—
295Dic3⋊C4—62no—
296C4×Dic3—31no—
297C4×Dic3—31no—
298C4×Dic3—31no—
299C4×Dic3—31no—
300C4×Dic3—31no—
301C4×Dic3—31no—
302C4×Dic3—31no—
303C4×Dic3—31no—
304C4×Dic3—61no—
305C4×Dic3—61no—
306C4×Dic3—61no—
307C4×Dic3—61no—
308C4×Dic3—62no—
309C4×Dic3—62no—
310C4×Dic3—62no—
311C4×Dic3—62no—
312C4×Dic3—62no—
313C4×Dic3—61no—
314C4×Dic3—61no—
315#208—22no—
316#208—22no—
317C2×C3⋊C8C22×D312yes—
318C2×C3⋊C8C22×D312yes—
319C22×C32—21no—
320C22×C32—21no—
321C22×C32C22⋊Q812yes—
322C22×C32C22×D411yescharacteristic
323C32×C4—41no—
324C32×C4—41no—
325C32×C4C22⋊Q812yes—
326C32×C4C22×Q811yescharacteristic
327C32×C4C2×#4111yescharacteristic
328C3⋊Dic3—21no—
329C3⋊Dic3—21no—
330C3⋊Dic3—21no—
331C3⋊Dic3—41no—
332C3⋊Dic3—41no—
333C3⋊Dic3#13712yes—
334C3×Dic3—24no—
335C3×Dic3—42no—
336C22×Q8—31no—
337C2×M16—31no—
338C2×M16—31no—
339C4⋊Q8—91no—
340C4⋊Q8—91no—
341#125—91no—
342#125—91no—
343C22⋊Q8—181no—
344C22⋊Q8—181no—
345C4×Q8—92no—
346C4×Q8—92no—
347C4×Q8—181no—
348C4×Q8—181no—
349C4×Q8—181no—
350C4×Q8—181no—
351#117—91no—
352#117D3211yescharacteristic
353C2×C4⋊C4—31no—
354C2×C4⋊C4—181no—
355C2×C42—91no—
356C2×C42—181no—
357#107—32no—
358#107—92no—
359#106—32no—
360#106—92no—
361C4⋊C8—92no—
362C4⋊C8—92no—
363#103—32no—
364#103—32no—
365#103—92no—
366#103—92no—
367C23×C3—21no—
368C23×C3D3×D411yescharacteristic
369C23×C3D3×D411yescharacteristic
370C3×Q8—34no—
371C3×Q8—64no—
372C3×Q8—62no—
373C2×C3×C4—22no—
374C2×C3×C4—22no—
375C2×C3×C4—21no—
376C2×C3×C4—21no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—22no—
381C2×C3×C4—22no—
382C2×C3×C4—21no—
383C2×C3×C4—64no—
384C2×C3×C4—62no—
385C2×C3×C4—62no—
386C2×C3×C4—122no—
387C2×C3×C4C2×Dic612yes—
388C2×C3×C4#23512yes—
389C2×C3×C4D3×D411yescharacteristic
390C2×C3×C4D3×D411yescharacteristic
391C2×C3×C4#23712yes—
392C2×C3×C4D3×Q812yes—
393C2×C3×C4C23×D311yescharacteristic
394C2×C3×C4C23×D311yescharacteristic
395C2×Dic3—24no—
396C2×Dic3—22no—
397C2×Dic3—22no—
398C2×Dic3—31no—
399C2×Dic3—31no—
400C2×Dic3—31no—
401C2×Dic3—31no—
402C2×Dic3—31no—
403C2×Dic3—31no—
404C2×Dic3—31no—
405C2×Dic3—31no—
406C2×Dic3—42no—
407C2×Dic3—61no—
408C2×Dic3—61no—
409C2×Dic3—61no—
410C2×Dic3—61no—
411C2×Dic3—62no—
412C2×Dic3—62no—
413C2×Dic3—62no—
414C2×Dic3—62no—
415C2×Dic3—61no—
416C2×Dic3—61no—
417C2×Dic3—61no—
418C2×Dic3—61no—
419C2×Dic3—122no—
420C2×Dic3—121no—
421C2×Dic3—121no—
422C2×Dic3—122no—
423Dic6—24no—
424Dic6—22no—
425Dic6—122no—
426Dic6—122no—
427Dic6—124no—
428Dic6—124no—
429Dic6—122no—
430Dic6—122no—
431Dic6C2×Dic614yes—
432C3×C8—62no—
433C3×C8—62no—
434C3⋊C8—22no—
435C3⋊C8—22no—
436C2×C32—22no—
437C2×C32C2×C22⋊Q811yescharacteristic
438C2×C32C2×#13711yescharacteristic
439C2×C32#57511yescharacteristic
440C2×Q8—32no—
441C2×Q8—34no—
442C2×Q8—62no—
443C2×Q8—61no—
444C2×Q8—181no—
445C2×Q8—181no—
446C22×C4—61no—
447C22×C4—61no—
448C22×C4—91no—
449C22×C4—91no—
450C22×C4C2×D3211yescharacteristic
451M16—62no—
452M16—62no—
453C2×C8—32no—
454C2×C8—32no—
455C4⋊C4—32no—
456C4⋊C4—61no—
457C4⋊C4—91no—
458C4⋊C4—91no—
459C4⋊C4—181no—
460C4⋊C4—181no—
461C4⋊C4—181no—
462C4⋊C4—181no—
463C4⋊C4—181no—
464C4⋊C4—181no—
465C4⋊C4—182no—
466C4⋊C4—182no—
467C4⋊C4C2×D3211yescharacteristic
468C4⋊C4C2×D3211yescharacteristic
469C22⋊C4—21no—
470C22⋊C4—181no—
471C42—21no—
472C42—91no—
473C42—91no—
474C42—91no—
475C42—91no—
476C42—182no—
477C42—182no—
478C42—181no—
479C22×C3—21no—
480C22×C3—21no—
481C22×C3—21no—
482C22×C3—21no—
483C22×C3—21no—
484C22×C3—22no—
485C22×C3—41no—
486C22×C3—41no—
487C22×C3#87812yes—
488C22×C3#89612yes—
489C22×C3C2×D3×D411yescharacteristic
490C22×C3C2×D3×D411yescharacteristic
491C3×C4—21no—
492C3×C4—21no—
493C3×C4—22no—
494C3×C4—42no—
495C3×C4—42no—
496C3×C4—41no—
497C3×C4—41no—
498C3×C4—41no—
499C3×C4—41no—
500C3×C4—64no—
501C3×C4—122no—
502C3×C4#87812yes—
503C3×C4#89612yes—
504C3×C4C22×Dic611yescharacteristic
505C3×C4C2×#23511yescharacteristic
506C3×C4C2×#23711yescharacteristic
507C3×C4C2×D3×Q811yescharacteristic
508Dic3—24no—
509Dic3—32no—
510Dic3—32no—
511Dic3—42no—
512Dic3—62no—
513Dic3—62no—
514Dic3—61no—
515Dic3—61no—
516Dic3—61no—
517Dic3—61no—
518Dic3—61no—
519Dic3—61no—
520Dic3—121no—
521Dic3—121no—
522Dic3—122no—
523Dic3—122no—
524Dic3—121no—
525Dic3—121no—
526Dic3—121no—
527Dic3—121no—
528C32#307811yescharacteristic, complemented, Sylow
529C23#381111yescharacteristic
530Q8—34no—
531Q8—62no—
532Q8—64no—
533Q8—362no—
534Q8—362no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—62no—
538C2×C4—64no—
539C2×C4—62no—
540C2×C4—91no—
541C2×C4—91no—
542C2×C4—91no—
543C2×C4—91no—
544C2×C4—122no—
545C2×C4—182no—
546C2×C4—181no—
547C2×C4—181no—
548C2×C4—361no—
549C2×C4D3×Dic612yes—
550C2×C4#379512yes—
551C2×C4#381111yescharacteristic
552C2×C4C22×D3211yescharacteristic
553C8—62no—
554C8—62no—
555C2×C3—22no—
556C2×C3—22no—
557C2×C3—21no—
558C2×C3—21no—
559C2×C3—21no—
560C2×C3—42no—
561C2×C3C2×#87811yescharacteristic
562C2×C3C2×#89611yescharacteristic
563C2×C3#577311yescharacteristic
564C2×C3D3×#13711yescharacteristic
565C2×C3D3×#13711yescharacteristic
566C2×C3#577711yescharacteristic
567C22—21no—
568C22—21no—
569C22#6389612yes—
570C22C2×#381111yescharacteristic
571C4—41no—
572C4—41no—
573C4—64no—
574C4—92no—
575C4—122no—
576C4—181no—
577C4—181no—
578C4—181no—
579C4—361no—
580C4—361no—
581C4#6389612yes—
582C4C2×D3×Dic611yescharacteristic
583C4C2×#379511yescharacteristic
584C3—21no—
585C3#7894911yescharacteristic, complemented
586C3#7924511yescharacteristic, complemented
587C2—22no—
588C2C2×#6389611yescharacteristic
589C2#1059546811yescharacteristic
590C2#1059547111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radicalC23×C32C2×D4
hypercenter#117D32
hypocenterC32#3078
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
8. #10590497C2semidirect
9. #10590496C2semidirect
10. #10590495C2semidirect
11. #10590494C2semidirect
77. C2×C3×Dic6Q8semidirect
243. C2×Dic6Dic6semidirect
528. C32#3078semidirect
585. C3#78949semidirect
586. C3#79245semidirect

Maximal subgroups

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

subgroupindex
#105959882
C2×#638432
C3×#50042
C3×#49952
#105911302
#105911202
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