Finite Group Databasebeta

← #11860956

Subgroups — #11860956

Order 1152.

1115 conjugacy classes of subgroups.

The subgroup lattice has 625 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595975C211yesmaximal, characteristic, complemented
2#10594986C211yesmaximal, characteristic, complemented
3C2×#63829C211yesmaximal, characteristic
4C3×#4966C211yesmaximal, characteristic, complemented
5C2×C3×#808C211yesmaximal, characteristic, complemented
6#10591106C211yesmaximal, characteristic, complemented
7#10591059C211yesmaximal, characteristic, complemented
8#10590485C212yesmaximal, complemented
9#10590483C212yesmaximal, complemented
10#10590462C212yesmaximal, complemented
11#10590460C212yesmaximal, complemented
12#79106—31nomaximal
13#78869—31nomaximal
14C2×#3828C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C2×C32×C4⋊C4C2211yescharacteristic
17C4×#638—22no—
18#64135C2211yescharacteristic
19#64102C2212yes—
20#64101—21no—
21C4⋊C4×C3⋊D3—21no—
22#64096C2212yes—
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×#208C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26Dic3×#67—22no—
27#63898C2212yes—
28D3×C4⋊Dic3—21no—
29#63843C2212yes—
30#63841—21no—
31C2×#3719C2211yescharacteristic
32C2×#3717C2211yescharacteristic
33#63829C418yescomplemented
34C2×#3716C2211yescharacteristic
35C2×#3714C2211yescharacteristic
36C3×#810C2212yes—
37C3×#809C2212yes—
38C3×#808C2212yes—
39C3×#808C2212yes—
40#63567C2212yes—
41#63564C2212yes—
42#63555C2212yes—
43#63553C2212yes—
44#5827—31no—
45C2×#950—31no—
46C2×#904—31no—
47#5504—31no—
48#5504—31no—
49#5504—31no—
50#5504—61no—
51C2×C3×#106—31no—
52C3×#417—31no—
53#5133—31no—
54#5122—31no—
55#5101—31no—
56#4966—31no—
57#4966D311yescharacteristic, complemented
58C2×#808D311yescharacteristic, complemented
59#4869—32no—
60#4853—32no—
61#4852—32no—
62#4852—32no—
63#4789—32no—
64#4788—32no—
65#4785—32no—
66#4758—32no—
67C22×C32×C4—21no—
68C22×C32×C4C2311yescharacteristic
69C2×#638—21no—
70#3828—22no—
71#3828C2×C414yescomplemented
72C2×C4⋊(C3⋊D3)C2311yescharacteristic
73C2×C4×C3⋊D3—21no—
74C2×C4×C3⋊D3—22no—
75C2×#634C2311yescharacteristic
76C2×C3×#67—21no—
77C22×C3×Dic3—21no—
78C3×#235—22no—
79C3×#235C2×C414yescomplemented
80C2×C3×D12C2311yescharacteristic
81C2×C3×C4×D3—21no—
82C2×C3×Dic6C2311yescharacteristic
83C2×D3×Dic3—22no—
84C32×C4⋊C4—21no—
85C32×C4⋊C4C2312yes—
86#3757D412yes—
87#3752—22no—
88C4⋊(C3⋊Dic3)D411yescharacteristic
89C4⋊(C3⋊Dic3)D411yescharacteristic
90#3750—22no—
91C4×C3⋊Dic3—22no—
92C4×C3⋊Dic3C2312yes—
93C3×C4⋊Dic3—21no—
94C3×C4⋊Dic3C2312yes—
95C3×#208—22no—
96C2×C3×C3⋊C8C2×C414yescomplemented
97C2×C3×C3⋊C8C2312yes—
98C2×C3×C3⋊C8C2311yescharacteristic
99C2×C3×C3⋊C8C2311yescharacteristic
100Dic3⋊Dic3—22no—
101(C2×D3)⋊Dic3—22no—
102Dic32—22no—
103#3719C2×C414yescomplemented
104#3717C2×C414yescomplemented
105#3716C2×C414yescomplemented
106#3714C2×C414yescomplemented
107#2952—91noSylow
108C2×C3×#41—31no—
109C2×#235—31no—
110C2×#235—31no—
111C2×#235—61no—
112C2×#235C2×D311yescharacteristic
113C2×C3×M16—31no—
114C22×C3×C8—31no—
115C2×C3×C4⋊C4—21no—
116C2×C3×C4⋊C4—31no—
117C2×C3×C4⋊C4C2×D311yescharacteristic
118C2×C3×C4⋊C4C2×D311yescharacteristic
119#950—38no—
120Q8×Dic3—32no—
121C2×#216—31no—
122C2×#215—31no—
123D4×Dic3—32no—
124D4×Dic3—62no—
125C2×#214—31no—
126C2×#213—31no—
127C4×#67—62no—
128C4×#67—62no—
129C4×#67—62no—
130C4×#67—64no—
131#926—31no—
132#926—31no—
133#926—61no—
134#926—61no—
135C2×C4⋊Dic3—61no—
136C2×C4⋊Dic3C2×D311yescharacteristic
137C2×#208C2×D311yescharacteristic
138C22×C3⋊C8C2×D311yescharacteristic
139C2×Dic12—31no—
140#904—38no—
141C2×D24—31no—
142C2×#204—31no—
143C2×#204—31no—
144#893—32no—
145#893—32no—
146#893—32no—
147#893—62no—
148#892—61no—
149#892—61no—
150#892—61no—
151#892—62no—
152D3×C4⋊C4—61no—
153D3×C4⋊C4—61no—
154D3×C4⋊C4—61no—
155D3×C4⋊C4—62no—
156#887—32no—
157#887—32no—
158#887—32no—
159#887—62no—
160C3×#106—32no—
161C3×#106—32no—
162C3×#103—32no—
163C3×#102—32no—
164#821—32no—
165#816—32no—
166#815—32no—
167#815—32no—
168C8×Dic3—32no—
169C8×Dic3—32no—
170#810—32no—
171#810C2×D312yes—
172#809—32no—
173#809C2×D312yes—
174#808C2×D312yes—
175#808C2×D312yes—
176C23×C32C2×D411yescharacteristic
177C22×C3⋊D3—21no—
178C22×C3×D3—21no—
179C2×C32×C4—22no—
180C2×C32×C4—81no—
181C2×C32×C4C22×C412yes—
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4#4112yes—
184C2×C32×C4C2411yescharacteristic
185#638—24no—
186C2×C3⋊Dic3—21no—
187C2×C3⋊Dic3C2×D412yes—
188C2×C3⋊Dic3C2×D412yes—
189C4⋊(C3⋊D3)—21no—
190C4⋊(C3⋊D3)C22×C412yes—
191C4×C3⋊D3—24no—
192C4×C3⋊D3—82no—
193#634—21no—
194#634C22×C412yes—
195C3×#67—24no—
196C2×C3×Dic3—21no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3—81no—
199C3×D12—21no—
200C3×D12C22×C412yes—
201C3×C4×D3—24no—
202C3×Dic6—21no—
203C3×Dic6C22×C412yes—
204D3×Dic3—82no—
205C3×C3⋊C8—22no—
206C3×C3⋊C8C22×C412yes—
207C3×C3⋊C8C22×C412yes—
208C2×#135—91no—
209#520—91no—
210#520—91no—
211#442—92no—
212#441—92no—
213C4×SD16—92no—
214C4×SD16—92no—
215C2×#106—31no—
216#417—31no—
217#417—91no—
218#405—91no—
219C3×#41—34no—
220C3×#41—62no—
221C2×C3×Q8—31no—
222C2×C3×D4—31no—
223C2×C3×D4—61no—
224C22×C3×C4—22no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—61no—
229C22×C3×C4—61no—
230C22×C3×C4C22×D311yescharacteristic
231C22×C3×C4C22×D311yescharacteristic
232C2×#67—21no—
233C2×#67—62no—
234C2×#67—61no—
235C2×#67—61no—
236C22×Dic3—21no—
237C22×Dic3—62no—
238#235—22no—
239#235—34no—
240#235—34no—
241#235—64no—
242#235—64no—
243#235—62no—
244#235—62no—
245#235C4×D314yescomplemented
246C2×D12—31no—
247C2×D12—31no—
248C2×D12—61no—
249C2×D12C22×D311yescharacteristic
250C2×C4×D3—21no—
251C2×C4×D3—62no—
252C2×C4×D3—61no—
253C2×C4×D3—61no—
254C2×C4×D3—62no—
255C2×C4×D3—62no—
256C2×C4×D3—62no—
257C2×C4×D3—64no—
258C2×Dic6—31no—
259C2×Dic6—31no—
260C2×Dic6—61no—
261C2×Dic6C22×D311yescharacteristic
262C3×M16—62no—
263C2×C3×C8—34no—
264C2×C3×C8—31no—
265C2×C3×C8—31no—
266C2×C3×C8—32no—
267C3×C4⋊C4—22no—
268C3×C4⋊C4—21no—
269C3×C4⋊C4—21no—
270C3×C4⋊C4—22no—
271C3×C4⋊C4—32no—
272C3×C4⋊C4—61no—
273C3×C4⋊C4C22×D312yes—
274C3×C4⋊C4C22×D312yes—
275#217—32no—
276#217—32no—
277#217—62no—
278#217—62no—
279#216—34no—
280#215—34no—
281#214—34no—
282#213—34no—
283(C2×D3)⋊C4—62no—
284(C2×D3)⋊C4—62no—
285(C2×D3)⋊C4—62no—
286(C2×D3)⋊C4—64no—
287C4⋊Dic3—21no—
288C4⋊Dic3—31no—
289C4⋊Dic3—31no—
290C4⋊Dic3—31no—
291C4⋊Dic3—31no—
292C4⋊Dic3—61no—
293C4⋊Dic3—61no—
294C4⋊Dic3—62no—
295C4⋊Dic3C22×D312yes—
296Dic3⋊C4—62no—
297Dic3⋊C4—62no—
298Dic3⋊C4—62no—
299Dic3⋊C4—64no—
300C4×Dic3—32no—
301C4×Dic3—32no—
302C4×Dic3—62no—
303C4×Dic3—62no—
304C4×Dic3—62no—
305C4×Dic3—62no—
306C4×Dic3—62no—
307C4×Dic3—64no—
308#208—22no—
309C2×C3⋊C8C4×D314yescomplemented
310C2×C3⋊C8C22×D312yes—
311C2×C3⋊C8C22×D311yescharacteristic
312C2×C3⋊C8C22×D311yescharacteristic
313Dic12—34no—
314D24—34no—
315#204—34no—
316#204—34no—
317C22×C32—21no—
318C22×C32—21no—
319C22×C32C4×D412yes—
320C22×C32C22×D411yescharacteristic
321C2×C3⋊D3—22no—
322C2×C3⋊D3—41no—
323C2×C3⋊D3—41no—
324C2×C3×D3—22no—
325C2×C3×D3—41no—
326C2×C3×D3—41no—
327C32×C4—42no—
328C32×C4C4×D412yes—
329C32×C4C23×C411yescharacteristic
330C32×C4C2×#4111yescharacteristic
331C3⋊Dic3—22no—
332C3⋊Dic3—22no—
333C3⋊Dic3—22no—
334C3×Dic3—22no—
335C3×Dic3—42no—
336C2×#41—31no—
337C2×#41—91no—
338#135—98no—
339C2×Q16—91no—
340C2×SD16—91no—
341C2×SD16—91no—
342C2×D8—91no—
343C2×M16—31no—
344C22×C8—31no—
345C4×Q8—92no—
346C4×Q8—92no—
347C4×D4—92no—
348C4×D4—92no—
349C4×D4—182no—
350C4×D4—182no—
351#117—91no—
352#117—181no—
353#117—181no—
354C2×C4⋊C4—31no—
355C2×C4⋊C4—181no—
356C2×C4⋊C4—181no—
357C2×C4⋊C4D3211yescharacteristic
358#106—32no—
359#106—32no—
360#103—32no—
361#103—92no—
362#102—32no—
363#102—92no—
364#97—92no—
365C4×C8—92no—
366C23×C3—21no—
367C23×C3—61no—
368C23×C3D3×D411yescharacteristic
369C23×C3D3×D411yescharacteristic
370C22×D3—21no—
371C22×D3—62no—
372C22×D3—61no—
373C22×D3—61no—
374C3×Q8—32no—
375C3×Q8—61no—
376C3×D4—32no—
377C3×D4—64no—
378C3×D4—61no—
379C2×C3×C4—24no—
380C2×C3×C4—22no—
381C2×C3×C4—22no—
382C2×C3×C4—21no—
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—21no—
386C2×C3×C4—61no—
387C2×C3×C4—64no—
388C2×C3×C4—62no—
389C2×C3×C4—81no—
390C2×C3×C4—81no—
391C2×C3×C4—82no—
392C2×C3×C4—241no—
393C2×C3×C4C2×C4×D312yes—
394C2×C3×C4C2×C4×D312yes—
395C2×C3×C4D3×D411yescharacteristic
396C2×C3×C4D3×D411yescharacteristic
397C2×C3×C4#23712yes—
398C2×C3×C4#23912yes—
399C2×C3×C4C23×D311yescharacteristic
400C2×C3×C4C23×D311yescharacteristic
401#67—24no—
402#67—68no—
403#67—64no—
404#67—64no—
405C2×Dic3—21no—
406C2×Dic3—22no—
407C2×Dic3—32no—
408C2×Dic3—32no—
409C2×Dic3—32no—
410C2×Dic3—32no—
411C2×Dic3—62no—
412C2×Dic3—62no—
413C2×Dic3—62no—
414C2×Dic3—61no—
415C2×Dic3—61no—
416C2×Dic3—81no—
417C2×Dic3—242no—
418D12—21no—
419D12—32no—
420D12—32no—
421D12—62no—
422D12—62no—
423D12—61no—
424D12—61no—
425D12C2×C4×D312yes—
426C4×D3—24no—
427C4×D3—68no—
428C4×D3—64no—
429C4×D3—64no—
430C4×D3—242no—
431C4×D3—242no—
432C4×D3—242no—
433C4×D3—244no—
434Dic6—21no—
435Dic6—32no—
436Dic6—32no—
437Dic6—62no—
438Dic6—62no—
439Dic6—61no—
440Dic6—61no—
441Dic6C2×C4×D312yes—
442C3×C8—32no—
443C3×C8—32no—
444C3×C8—62no—
445C3⋊C8—22no—
446C3⋊C8C2×C4×D312yes—
447C3⋊C8C2×C4×D312yes—
448C2×C32—22no—
449C2×C32C2×C4×D411yescharacteristic
450C2×C32#57711yescharacteristic
451C2×C32#57711yescharacteristic
452C3⋊D3—42no—
453C3×D3—42no—
454#41—34no—
455#41—62no—
456#41—94no—
457#41—182no—
458C2×Q8—31no—
459C2×Q8—91no—
460C2×D4—31no—
461C2×D4—61no—
462C2×D4—91no—
463C2×D4—181no—
464C22×C4—21no—
465C22×C4—61no—
466C22×C4—61no—
467C22×C4—182no—
468C22×C4—182no—
469C22×C4—181no—
470C22×C4C2×D3211yescharacteristic
471Q16—94no—
472SD16—94no—
473SD16—94no—
474D8—94no—
475M16—62no—
476C2×C8—31no—
477C2×C8—31no—
478C2×C8—34no—
479C2×C8—32no—
480C4⋊C4—21no—
481C4⋊C4—32no—
482C4⋊C4—61no—
483C4⋊C4—91no—
484C4⋊C4—91no—
485C4⋊C4—182no—
486C4⋊C4—182no—
487C4⋊C4C2×D3212yes—
488C22⋊C4—92no—
489C22⋊C4—182no—
490C22⋊C4—182no—
491C42—92no—
492C42—182no—
493C42—182no—
494C22×C3—21no—
495C22×C3—21no—
496C22×C3—21no—
497C22×C3—21no—
498C22×C3—21no—
499C22×C3—22no—
500C22×C3—41no—
501C22×C3—41no—
502C22×C3—62no—
503C22×C3—121no—
504C22×C3—121no—
505C22×C3#67⋊C412yes—
506C22×C3#89312yes—
507C22×C3C2×D3×D411yescharacteristic
508C22×C3C2×D3×D411yescharacteristic
509C2×D3—22no—
510C2×D3—41no—
511C2×D3—41no—
512C2×D3—64no—
513C2×D3—62no—
514C2×D3—62no—
515C2×D3—122no—
516C2×D3—122no—
517C2×D3—121no—
518C2×D3—121no—
519C2×D3—121no—
520C2×D3—121no—
521C3×C4—21no—
522C3×C4—21no—
523C3×C4—22no—
524C3×C4—44no—
525C3×C4—42no—
526C3×C4—42no—
527C3×C4—62no—
528C3×C4—122no—
529C3×C4#67⋊C412yes—
530C3×C4#89312yes—
531C3×C4C22×C4×D311yescharacteristic
532C3×C4C22×C4×D311yescharacteristic
533C3×C4C2×#23711yescharacteristic
534C3×C4C2×#23911yescharacteristic
535Dic3—22no—
536Dic3—42no—
537Dic3—64no—
538Dic3—62no—
539Dic3—62no—
540Dic3—62no—
541Dic3—62no—
542Dic3—62no—
543Dic3—62no—
544Dic3—122no—
545Dic3—122no—
546C32#295211yescharacteristic, complemented, Sylow
547C23—61no—
548C23—181no—
549C23#381111yescharacteristic
550Q8—32no—
551Q8—61no—
552Q8—92no—
553Q8—181no—
554D4—32no—
555D4—64no—
556D4—61no—
557D4—92no—
558D4—184no—
559D4—181no—
560C2×C4—22no—
561C2×C4—61no—
562C2×C4—64no—
563C2×C4—62no—
564C2×C4—81no—
565C2×C4—92no—
566C2×C4—92no—
567C2×C4—181no—
568C2×C4—184no—
569C2×C4—241no—
570C2×C4—722no—
571C2×C4—722no—
572C2×C4#379612yes—
573C2×C4C4×D3212yes—
574C2×C4#381111yescharacteristic
575C2×C4C22×D3211yescharacteristic
576C8—32no—
577C8—32no—
578C8—62no—
579C2×C3—22no—
580C2×C3—22no—
581C2×C3—21no—
582C2×C3—21no—
583C2×C3—21no—
584C2×C3—42no—
585C2×C3—122no—
586C2×C3C2×#67⋊C411yescharacteristic
587C2×C3C2×#89311yescharacteristic
588C2×C3#576211yescharacteristic
589C2×C3#576211yescharacteristic
590C2×C3#577511yescharacteristic
591C2×C3#577811yescharacteristic
592D3—42no—
593D3—124no—
594D3—122no—
595D3—122no—
596C22—21no—
597C22—21no—
598C22—62no—
599C22—121no—
600C22—121no—
601C22—182no—
602C22—361no—
603C22—361no—
604C22#6388112yes—
605C22C2×#381111yescharacteristic
606C4—42no—
607C4—62no—
608C4—122no—
609C4—182no—
610C4—182no—
611C4—182no—
612C4#6388112yes—
613C4C2×#379611yescharacteristic
614C4C2×C4×D3211yescharacteristic
615C3—21no—
616C3#7886911yescharacteristic, complemented
617C3#7910611yescharacteristic, complemented
618C2—22no—
619C2—122no—
620C2—362no—
621C2C2×#6388111yescharacteristic
622C2#1059511511yescharacteristic
623C2#1059532411yescharacteristic
subgroupG/H
centerC22C2×#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
prime radicalC2×#63829C2
cosocleC2×C32×C4C24
hypercenterC2×C4⋊C4D32
hypocenterC32#2952
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #10595975C2semidirect
2. #10594986C2semidirect
4. C3×#4966C2semidirect
5. C2×C3×#808C2semidirect
6. #10591106C2semidirect
7. #10591059C2semidirect
8. #10590485C2semidirect
9. #10590483C2semidirect
10. #10590462C2semidirect
11. #10590460C2semidirect
33. #63829C4semidirect
57. #4966D3semidirect
58. C2×#808D3semidirect
71. #3828C2×C4semidirect
79. C3×#235C2×C4semidirect
96. C2×C3×C3⋊C8C2×C4semidirect
103. #3719C2×C4semidirect
104. #3717C2×C4semidirect
105. #3716C2×C4semidirect
106. #3714C2×C4semidirect
245. #235C4×D3semidirect
309. C2×C3⋊C8C4×D3semidirect
546. C32#2952semidirect
616. C3#78869semidirect
617. C3#79106semidirect

Maximal subgroups

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

subgroupindex
#105959752
#105949862
C2×#638292
C3×#49662
C2×C3×#8082
#105911062
#105910592
#105904852
#105904832
#105904622
#105904602
#791063
#788693