Finite Group Databasebeta

← #11785004

Subgroups — #11785004

Order 1152.

1147 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64298C211yesmaximal, characteristic
2#10592703C211yesmaximal, characteristic, complemented
3C3×#5006C211yesmaximal, characteristic, complemented
4C3×#5005C211yesmaximal, characteristic, complemented
5#10591111C211yesmaximal, characteristic, complemented
6#10591107C211yesmaximal, characteristic, complemented
7#10591076C211yesmaximal, characteristic, complemented
8#70415—31nomaximal
9#70051—31nomaximal
10C22×#634C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×C3×#235C2211yescharacteristic
13C2×#3805—22no—
14#64298—22no—
15#64298—22no—
16#64298—22no—
17#64298—22no—
18C2×#3795—21no—
19C2×#3795C412yescomplemented
20C2×D3×Dic6—21no—
21C2×D3×Dic6C412yescomplemented
22C32×#117C2211yescharacteristic
23C2×#3748C2211yescharacteristic
24C3×#926C2211yescharacteristic
25C2×C3×#208C2211yescharacteristic
26#63637—22no—
27C3×#806—22no—
28C3×#805—22no—
29#63569—22no—
30#63567—22no—
31#63560—21no—
32#63558—21no—
33C2×#1010—31no—
34C2×#1010—31no—
35C3×#421—31no—
36C3×#410—31no—
37#5237—31no—
38#5236—31no—
39#5132—31no—
40#5120—31no—
41#5006D311yescharacteristic, complemented
42#5005—31no—
43#5005D311yescharacteristic, complemented
44#5004—31no—
45#5004—31no—
46#5004—31no—
47#5004—61no—
48C22×C32×C4C2311yescharacteristic
49C22×C3⋊Dic3—21no—
50C2×#634—21no—
51C2×#634—21no—
52C2×#634—21no—
53C2×#634C2×C412yes—
54C2×#634D412yes—
55C2×#634D412yes—
56C2×C3×#67—21no—
57C2×C3×#67D412yes—
58C3×#235—21no—
59C3×#235—21no—
60C3×#235—21no—
61C3×#235—21no—
62C3×#235—21no—
63C3×#235—21no—
64C3×#235D412yes—
65C3×#235D412yes—
66C2×C3×D12C2×C411yescharacteristic
67C2×C3×D12D411yescharacteristic
68C2×C3×C4×D3—21no—
69C2×C3×C4×D3C2×C412yes—
70C2×C3×Dic6C2×C411yescharacteristic
71C2×C3×Dic6D411yescharacteristic
72C2×#627—22no—
73C2×#625—22no—
74#3805—28no—
75#3805—28no—
76C2×D3×Dic3—22no—
77C2×D3×Dic3—22no—
78#3795—24no—
79#3795—24no—
80#3795—24no—
81#3795—24no—
82D3×Dic6—24no—
83D3×Dic6—24no—
84D3×Dic6—24no—
85D3×Dic6—24no—
86C32×C4⋊C4—21no—
87C32×C22⋊C4—21no—
88C32×C42—21no—
89#3748—21no—
90#3748—21no—
91C2×C3⋊(C3⋊C8)—21no—
92C3×#217—21no—
93C3×C4⋊Dic3—21no—
94C3×C4×Dic3—21no—
95C3×#208—21no—
96C3×#208—21no—
97C2×C3×C3⋊C8—21no—
98#1796—91noSylow
99C2×C3×#41—31no—
100C2×C3×#41—31no—
101#1010—62no—
102#1010—62no—
103#1010—62no—
104#1010—62no—
105#1010—62no—
106#1010—62no—
107#1010—62no—
108#1010—62no—
109C2×D3×Q8—32no—
110C2×D3×Q8—61no—
111C2×#237—32no—
112C2×#237—61no—
113C2×#237—62no—
114C2×#237—62no—
115C2×#235—32no—
116C2×#235—61no—
117C2×#235C2×D311yescharacteristic
118C2×#235C2×D311yescharacteristic
119C22×Dic6—31no—
120C22×Dic6—31no—
121C22×Dic6—32no—
122C22×Dic6—61no—
123C22×Dic6—61no—
124C2×C3×M16—31no—
125C3×#117—21no—
126C3×#117—31no—
127C3×#117C2×D311yescharacteristic
128C3×#117C2×D311yescharacteristic
129#926C2×D311yescharacteristic
130C2×#208—31no—
131C2×#208—31no—
132C2×#208—61no—
133C2×#208C2×D311yescharacteristic
134C3×#104—62no—
135C3×#99—62no—
136#837—62no—
137#836—61no—
138#833—61no—
139#824—61no—
140#823—61no—
141#816—62no—
142#810—62no—
143#810—62no—
144#810—62no—
145#810—64no—
146#806—22no—
147#805—22no—
148#805—62no—
149C23×C32C2×D411yescharacteristic
150C22×C3×D3—21no—
151C22×C3×D3C22⋊C412yes—
152C2×C32×C4—41no—
153C2×C32×C4C22×C411yescharacteristic
154C2×C32×C4C2×D411yescharacteristic
155C2×C32×C4C2×D411yescharacteristic
156C2×C32×C4C2×D411yescharacteristic
157C2×C32×C4C2×D411yescharacteristic
158C2×C32×C4C2×D411yescharacteristic
159C2×C3⋊Dic3—22no—
160C2×C3⋊Dic3—22no—
161C2×C3⋊Dic3—22no—
162#634—22no—
163#634—22no—
164#634—22no—
165#634C22⋊C414yes—
166C3×#67—22no—
167C3×#67—22no—
168C3×#67—22no—
169C3×#67—22no—
170C2×C3×Dic3—21no—
171C2×C3×Dic3—41no—
172C2×C3×Dic3C22⋊C412yes—
173C3×D12—21no—
174C3×D12—21no—
175C3×D12—21no—
176C3×D12C22⋊C412yes—
177C3×C4×D3—22no—
178C3×C4×D3—22no—
179C3×C4×D3—22no—
180C3×C4×D3—22no—
181C3×Dic6—21no—
182C3×Dic6—21no—
183C3×Dic6—21no—
184C3×Dic6C22⋊C412yes—
185#627—28no—
186#625—28no—
187D3×Dic3—28no—
188D3×Dic3—28no—
189C3⋊(C3⋊C8)—41no—
190C3×C3⋊C8—41no—
191C2×2−1+4—91no—
192#421—31no—
193#421—91no—
194#419—91no—
195#419—91no—
196#413—91no—
197#410—31no—
198C3×#41—32no—
199C3×#41—32no—
200C3×#41—61no—
201C3×#41—61no—
202C3×#41—61no—
203C3×#41—61no—
204C3×#41—61no—
205C3×#41—61no—
206C2×C3×Q8—31no—
207C2×C3×Q8—31no—
208C2×C3×D4—32no—
209C2×C3×D4—31no—
210C2×C3×D4—31no—
211C2×C3×D4—61no—
212C22×C3×C4—21no—
213C22×C3×C4—32no—
214C22×C3×C4—61no—
215C22×C3×C4C22×D311yescharacteristic
216C22×C3×C4C22×D311yescharacteristic
217C2×#67—21no—
218C2×#67—62no—
219C2×#67—62no—
220C2×#67#6712yes—
221C22×Dic3—62no—
222C22×Dic3—61no—
223C22×Dic3—61no—
224C22×Dic3—62no—
225C22×Dic3—121no—
226D3×Q8—64no—
227D3×Q8—64no—
228D3×Q8—64no—
229D3×Q8—64no—
230#237—64no—
231#237—64no—
232#237—64no—
233#237—64no—
234#237—68no—
235#237—68no—
236#237—68no—
237#237—68no—
238#235—21no—
239#235—21no—
240#235—21no—
241#235—21no—
242#235—21no—
243#235—21no—
244#235—64no—
245#235—64no—
246#235—64no—
247#235—64no—
248#235D1212yes—
249#235#6712yes—
250C2×D12C4×D311yescharacteristic
251C2×D12D1211yescharacteristic
252C2×C4×D3—21no—
253C2×C4×D3—62no—
254C2×C4×D3—62no—
255C2×C4×D3C4×D312yes—
256C2×Dic6—32no—
257C2×Dic6—32no—
258C2×Dic6—32no—
259C2×Dic6—32no—
260C2×Dic6—32no—
261C2×Dic6—32no—
262C2×Dic6—62no—
263C2×Dic6—62no—
264C2×Dic6—62no—
265C2×Dic6—64no—
266C2×Dic6—64no—
267C2×Dic6—64no—
268C2×Dic6—62no—
269C2×Dic6—61no—
270C2×Dic6—61no—
271C2×Dic6—61no—
272C2×Dic6—61no—
273C2×Dic6—61no—
274C2×Dic6—61no—
275C2×Dic6—62no—
276C2×Dic6—64no—
277C2×Dic6—121no—
278C2×Dic6—121no—
279C2×Dic6—121no—
280C2×Dic6C4×D311yescharacteristic
281C2×Dic6D1211yescharacteristic
282C3×M16—61no—
283C3×M16—61no—
284C2×C3×C8—61no—
285C3×C4⋊C4—22no—
286C3×C4⋊C4—21no—
287C3×C4⋊C4—21no—
288C3×C4⋊C4—61no—
289C3×C22⋊C4—21no—
290C3×C22⋊C4—21no—
291C3×C22⋊C4—41no—
292C3×C22⋊C4—61no—
293C3×C42—21no—
294C3×C42—21no—
295C3×C42—41no—
296C3×C42—61no—
297#217—21no—
298C4⋊Dic3—21no—
299C4×Dic3—21no—
300#208—21no—
301#208—21no—
302#208—61no—
303#208—61no—
304#208—61no—
305#208—61no—
306#208—121no—
307#208—121no—
308C2×C3⋊C8—21no—
309C2×C3⋊C8—62no—
310C2×C3⋊C8—61no—
311C2×C3⋊C8—61no—
312C22×C32—41no—
313C22×C32C2×C22⋊C411yescharacteristic
314C22×C32#12011yescharacteristic
315C22×C32#12011yescharacteristic
316C2×C3×D3—22no—
317C2×C3×D3—22no—
318C2×C3×D3—42no—
319C2×C3×D3—42no—
320C32×C4—81no—
321C32×C4C2×C22⋊C411yescharacteristic
322C32×C4C2×C22⋊C411yescharacteristic
323C32×C4#12011yescharacteristic
324C32×C4#12011yescharacteristic
325C3⋊Dic3—24no—
326C3×Dic3—22no—
327C3×Dic3—22no—
328C3×Dic3—81no—
3292−1+4—182no—
3302−1+4—182no—
3312−1+4—182no—
3322−1+4—182no—
333C2×#41—31no—
334C2×#41—31no—
335C2×#41—92no—
336C2×#41—181no—
337C2×#41—182no—
338C22×Q8—92no—
339C22×Q8—91no—
340C22×Q8—181no—
341C2×M16—31no—
342C2×M16—91no—
343#117—31no—
344#117D3211yescharacteristic
345#104—62no—
346#104—182no—
347#103—182no—
348#103—182no—
349#101—181no—
350#100—181no—
351#99—62no—
352C23×C3—21no—
353C23×C3—32no—
354C23×C3—61no—
355C23×C3D3×D411yescharacteristic
356C23×C3C2×#6711yescharacteristic
357C22×D3—21no—
358C22×D3(C2×D3)⋊C412yes—
359C3×Q8—32no—
360C3×Q8—61no—
361C3×Q8—61no—
362C3×Q8—61no—
363C3×D4—32no—
364C3×D4—62no—
365C3×D4—62no—
366C3×D4—62no—
367C3×D4—62no—
368C3×D4—61no—
369C3×D4—61no—
370C3×D4—61no—
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—21no—
377C2×C3×C4—32no—
378C2×C3×C4—42no—
379C2×C3×C4—41no—
380C2×C3×C4—41no—
381C2×C3×C4—61no—
382C2×C3×C4—62no—
383C2×C3×C4—62no—
384C2×C3×C4—62no—
385C2×C3×C4—62no—
386C2×C3×C4—121no—
387C2×C3×C4C2×C4×D311yescharacteristic
388C2×C3×C4C2×C4×D311yescharacteristic
389C2×C3×C4C2×D1211yescharacteristic
390C2×C3×C4C2×D1211yescharacteristic
391C2×C3×C4D3×D411yescharacteristic
392C2×C3×C4D3×D411yescharacteristic
393C2×C3×C4D3×D411yescharacteristic
394C2×C3×C4D3×D411yescharacteristic
395C2×C3×C4D3×D411yescharacteristic
396C2×C3×C4D3×D411yescharacteristic
397C2×C3×C4D3×D411yescharacteristic
398C2×C3×C4C2×#6711yescharacteristic
399#67—22no—
400#67—22no—
401#67—22no—
402#67—22no—
403#67—68no—
404#67—68no—
405C2×Dic3—21no—
406C2×Dic3—41no—
407C2×Dic3—68no—
408C2×Dic3—68no—
409C2×Dic3—62no—
410C2×Dic3—62no—
411C2×Dic3—62no—
412C2×Dic3—62no—
413C2×Dic3—62no—
414C2×Dic3—62no—
415C2×Dic3—122no—
416C2×Dic3—122no—
417C2×Dic3—122no—
418C2×Dic3(C2×D3)⋊C412yes—
419D12—21no—
420D12—21no—
421D12—21no—
422D12(C2×D3)⋊C412yes—
423C4×D3—22no—
424C4×D3—22no—
425C4×D3—22no—
426C4×D3—22no—
427C4×D3—68no—
428C4×D3—68no—
429Dic6—21no—
430Dic6—21no—
431Dic6—21no—
432Dic6—34no—
433Dic6—34no—
434Dic6—64no—
435Dic6—68no—
436Dic6—68no—
437Dic6—62no—
438Dic6—62no—
439Dic6—62no—
440Dic6—62no—
441Dic6—62no—
442Dic6—62no—
443Dic6—122no—
444Dic6—122no—
445Dic6—122no—
446Dic6(C2×D3)⋊C412yes—
447C3×C8—121no—
448C3⋊C8—41no—
449C3⋊C8—122no—
450C3⋊C8—121no—
451C3⋊C8—121no—
452C2×C32—21no—
453C2×C32—21no—
454C2×C32—21no—
455C2×C32#37911yescharacteristic
456C3×D3—42no—
457C3×D3—42no—
458#41—32no—
459#41—32no—
460#41—61no—
461#41—61no—
462#41—61no—
463#41—61no—
464#41—61no—
465#41—61no—
466#41—184no—
467#41—184no—
468#41—184no—
469#41—184no—
470#41—188no—
471#41—188no—
472C2×Q8—31no—
473C2×Q8—31no—
474C2×Q8—92no—
475C2×Q8—92no—
476C2×Q8—92no—
477C2×Q8—182no—
478C2×Q8—184no—
479C2×Q8—184no—
480C2×Q8—184no—
481C2×Q8—184no—
482C2×Q8—181no—
483C2×Q8—181no—
484C2×Q8—181no—
485C2×D4—32no—
486C2×D4—31no—
487C2×D4—31no—
488C2×D4—61no—
489C2×D4—182no—
490C22×C4—32no—
491C22×C4—61no—
492C22×C4—182no—
493C22×C4—182no—
494C22×C4—181no—
495C22×C4C2×D3211yescharacteristic
496M16—61no—
497M16—61no—
498M16—181no—
499M16—181no—
500C2×C8—61no—
501C2×C8—181no—
502C4⋊C4—21no—
503C4⋊C4—61no—
504C22⋊C4—21no—
505C22⋊C4—61no—
506C42—21no—
507C42—61no—
508C22×C3—21no—
509C22×C3—21no—
510C22×C3—21no—
511C22×C3—41no—
512C22×C3—41no—
513C22×C3—42no—
514C22×C3—62no—
515C22×C3—62no—
516C22×C3—122no—
517C22×C3—122no—
518C22×C3D3×C22⋊C411yescharacteristic
519C22×C3#88211yescharacteristic
520C22×C3C2×(C2×D3)⋊C411yescharacteristic
521C22×C3#93711yescharacteristic
522C22×C3#93711yescharacteristic
523C22×C3#93711yescharacteristic
524C2×D3—22no—
525C2×D3—22no—
526C2×D3—42no—
527C2×D3—42no—
528C3×C4—21no—
529C3×C4—21no—
530C3×C4—21no—
531C3×C4—21no—
532C3×C4—62no—
533C3×C4—62no—
534C3×C4—82no—
535C3×C4—81no—
536C3×C4—81no—
537C3×C4—241no—
538C3×C4D3×C22⋊C411yescharacteristic
539C3×C4D3×C22⋊C411yescharacteristic
540C3×C4D3×C22⋊C411yescharacteristic
541C3×C4#88211yescharacteristic
542C3×C4#88211yescharacteristic
543C3×C4#88211yescharacteristic
544C3×C4C2×(C2×D3)⋊C411yescharacteristic
545C3×C4#93711yescharacteristic
546Dic3—22no—
547Dic3—22no—
548Dic3—64no—
549Dic3—64no—
550Dic3—81no—
551Dic3—124no—
552C32#179611yescharacteristic, complemented, Sylow
553C23—32no—
554C23—61no—
555C23D3×#6711yescharacteristic
556Q8—32no—
557Q8—61no—
558Q8—61no—
559Q8—61no—
560Q8—94no—
561Q8—188no—
562Q8—182no—
563Q8—182no—
564Q8—182no—
565D4—32no—
566D4—62no—
567D4—62no—
568D4—62no—
569D4—62no—
570D4—61no—
571D4—61no—
572D4—61no—
573D4—188no—
574C2×C4—32no—
575C2×C4—41no—
576C2×C4—61no—
577C2×C4—62no—
578C2×C4—62no—
579C2×C4—62no—
580C2×C4—62no—
581C2×C4—121no—
582C2×C4—188no—
583C2×C4—188no—
584C2×C4—182no—
585C2×C4—182no—
586C2×C4—182no—
587C2×C4C4×D3211yescharacteristic
588C2×C4D3×D1211yescharacteristic
589C2×C4D3×D1211yescharacteristic
590C2×C4#380211yescharacteristic
591C2×C4D3×#6711yescharacteristic
592C2×C4#381111yescharacteristic
593C8—121no—
594C8—361no—
595C2×C3—22no—
596C2×C3—21no—
597C2×C3—21no—
598C2×C3—21no—
599C2×C3—21no—
600C2×C3—21no—
601C2×C3—21no—
602C2×C3—21no—
603C2×C3—41no—
604C2×C3—41no—
605C2×C3—122no—
606C2×C3—122no—
607C2×C3#495511yescharacteristic
608C2×C3#495511yescharacteristic
609D3—42no—
610D3—42no—
611C22—41no—
612C22—62no—
613C22—62no—
614C22—122no—
615C22—122no—
616C22D3×(C2×D3)⋊C411yescharacteristic
617C22#6392211yescharacteristic
618C22#6398311yescharacteristic
619C4—62no—
620C4—62no—
621C4—81no—
622C4—184no—
623C4—241no—
624C4D3×(C2×D3)⋊C411yescharacteristic
625C4#6392111yescharacteristic
626C4#6392211yescharacteristic
627C4#6392311yescharacteristic
628C3—21no—
629C3#7005111yescharacteristic, complemented
630C3#7041511yescharacteristic, complemented
631C2—21no—
632C2—21no—
633C2—21no—
634C2—122no—
635C2—122no—
636C2#1059139911yescharacteristic
subgroupG/H
centerC2#10591399
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC2×C32#379
prime radicalC2×#64298C2
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32#1796
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #10592703C2semidirect
3. C3×#5006C2semidirect
4. C3×#5005C2semidirect
5. #10591111C2semidirect
6. #10591107C2semidirect
7. #10591076C2semidirect
19. C2×#3795C4semidirect
21. C2×D3×Dic6C4semidirect
41. #5006D3semidirect
43. #5005D3semidirect
552. C32#1796semidirect
629. C3#70051semidirect
630. C3#70415semidirect

Maximal subgroups

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

subgroupindex
C2×#642982
#105927032
C3×#50062
C3×#50052
#105911112
#105911072
#105910762
#704153
#700513