Finite Group Databasebeta

← #11905993

Subgroups — #11905993

Order 1152.

3652 conjugacy classes of subgroups.

The subgroup lattice has 934 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1009C211yesmaximal, characteristic, complemented
2C2×#64320C211yesmaximal, characteristic, complemented
3#10596305C211yesmaximal, characteristic, complemented
4C3×#5834C211yesmaximal, characteristic, complemented
5#10595412C211yesmaximal, characteristic, complemented
6#10595410C211yesmaximal, characteristic, complemented
7Dic3×#239C211yesmaximal, characteristic, complemented
8#10595293C213yesmaximal, complemented
9#10595288C213yesmaximal, complemented
10D3×#940C213yesmaximal, complemented
11#10595231C213yesmaximal, complemented
12#10595069C213yesmaximal, complemented
13D12×#67C213yesmaximal, complemented
14#10595064C213yesmaximal, complemented
15#10595003C213yesmaximal, complemented
16#87282—31nomaximal
17#86770—31nomaximal
18C2×C32×#41C2211yescharacteristic, complemented
19C2×#3832C2211yescharacteristic, complemented
20C3×#1009—28no—
21C2×C3×#239C2211yescharacteristic
22C2×C3×#239C2211yescharacteristic, complemented
23C2×C3×#239C2211yescharacteristic, complemented
24C2×C3×D3×D4C2213yescomplemented
25C2×C3×D3×D4C2213yescomplemented
26C2×C3×#235C2213yescomplemented
27C22×C3×D12C2213yescomplemented
28C2×D3×#67C2216yescomplemented
29C2×D3×#67C2216yescomplemented
30#64320—28no—
31C2×#3802C2213yescomplemented
32C2×D3×D12C2213yescomplemented
33C2×D3×D12C2213yescomplemented
34C2×#3798C2213yescomplemented
35Q8×C3⋊Dic3C2211yescharacteristic, complemented
36#64149C2213yescomplemented
37#64147C2213yescomplemented
38#64139C2213yescomplemented
39C4×#638C2213yescomplemented
40C3×Q8×Dic3C2211yescharacteristic, complemented
41C3×#940C2213yescomplemented
42C3×#938C2213yescomplemented
43C3×#930C2213yescomplemented
44C3×C4×#67C2213yescomplemented
45#63983C2216yescomplemented
46#63979C2216yescomplemented
47#63979C2213yescomplemented
48#63977C2216yescomplemented
49#63976C2216yescomplemented
50#63971C2213yescomplemented
51#63970C2213yescomplemented
52#63959C2213yescomplemented
53#63922C2216yescomplemented
54#63916C2213yescomplemented
55#63914C2213yescomplemented
56#63911C2213yescomplemented
57#63909C2213yescomplemented
58#63908C2213yescomplemented
59#63908C2213yescomplemented
60#63907C2213yescomplemented
61C4×#626C2213yescomplemented
62C4×#625C2213yescomplemented
63#63898C2213yescomplemented
64Dic3×D12C2213yescomplemented
65#63886C2213yescomplemented
66#63885C2213yescomplemented
67C4×D3×Dic3C2213yescomplemented
68#63841C2213yescomplemented
69#63839C2211yescharacteristic, complemented
70C2×C3×H(5,𝔽2)—31no—
71C2×#1009—31no—
72C2×#1009—31no—
73C2×#1009D311yescharacteristic, complemented
74C3×#550—31no—
75#5834—31no—
76#5834—31no—
77#5834—31no—
78#5834—31no—
79#5834—31no—
80#5834—61no—
81#5834D311yescharacteristic, complemented
82#5832—33no—
83#5830—33no—
84Dic3×#41—31no—
85#5805—33no—
86C2×#940—33no—
87D4×#67—33no—
88D4×#67—33no—
89D4×#67—33no—
90D4×#67—33no—
91#5717—33no—
92D3×#127—33no—
93#5609—33no—
94#5609—33no—
95#5607—33no—
96#5607—33no—
97#5577—31no—
98C4×#239—31no—
99D4×D12—33no—
100#5548—33no—
101C23×C3×D3C2316yes—
102C22×D32C2316yes—
103C32×#41—24no—
104C2×C32×Q8C2311yescharacteristic
105C2×C32×D4C2313yes—
106C22×C32×C4C2313yes—
107C2×#638C2313yes—
108C2×#638C2316yes—
109#3832—24no—
110C2×C4⋊(C3⋊D3)C2313yes—
111C2×C4×C3⋊D3C2313yes—
112C2×C3×#67C2313yes—
113C2×C3×#67C2313yes—
114C2×C3×#67C2313yes—
115C2×C3×#67C2316yes—
116C3×#239—24no—
117C3×#239—24no—
118C3×#239D418yescomplemented
119C3×D3×D4—212no—
120C3×D3×D4—212no—
121C3×#235—212no—
122C2×C3×D12—212no—
123C2×C3×D12C2313yes—
124C2×C3×D12C2313yes—
125C2×C3×D12C2313yes—
126C2×C3×D12C2313yes—
127C2×C3×C4×D3C2313yes—
128C2×C3×C4×D3C2313yes—
129C2×C3×C4×D3C2313yes—
130C2×C3×Dic6C2311yescharacteristic
131D3×#67—412no—
132D3×#67—412no—
133C2×#627C2311yescharacteristic
134C2×#626C2313yes—
135C2×#626C2313yes—
136C2×#626C2313yes—
137C2×#626C2316yes—
138C2×#625C2313yes—
139C2×#625C2313yes—
140C2×#625C2316yes—
141C2×D3×Dic3C2313yes—
142C2×D3×Dic3C2313yes—
143#3802—212no—
144D3×D12—212no—
145D3×D12—212no—
146#3798—212no—
147#3757C2313yes—
148#3752C2313yes—
149C4⋊(C3⋊Dic3)C2313yes—
150#3750C2311yescharacteristic
151C4×C3⋊Dic3C2313yes—
152C3×#217C2313yes—
153C3×(C2×D3)⋊C4C2313yes—
154C3×C4⋊Dic3C2313yes—
155C3×Dic3⋊C4C2311yescharacteristic
156C3×C4×Dic3C2313yes—
157#3724C2311yescharacteristic
158Dic3⋊Dic3C2311yescharacteristic
159#3722C2313yes—
160(C2×D3)⋊Dic3C2316yes—
161(C2×D3)⋊Dic3C2313yes—
162(C2×D3)⋊Dic3C2313yes—
163(C2×D3)⋊Dic3C2313yes—
164Dic32C2311yescharacteristic
165Dic32C2313yes—
166#3498—91noSylow
167C3×H(5,𝔽2)—68no—
168C2×C3×#41—21no—
169C2×C3×#41—31no—
170C2×C3×#41—31no—
171C2×C3×#41—31no—
172C2×C3×#41—33no—
173C2×C3×#41C2×D311yescharacteristic, complemented
174C2×C3×#41C2×D311yescharacteristic, complemented
175C22×C3×D4—33no—
176C22×C3×D4—33no—
177C22×C3×D4—33no—
178C22×#67—36no—
179C22×#67—36no—
180#1009—28no—
181#1009—68no—
182#1009—68no—
183C2×#239—31no—
184C2×#239—31no—
185C2×#239—61no—
186C2×#239C2×D311yescharacteristic
187C2×#239C2×D311yescharacteristic, complemented
188C2×#239C2×D311yescharacteristic, complemented
189C2×D3×D4—36no—
190C2×D3×D4—36no—
191C2×D3×D4—33no—
192C2×D3×D4—33no—
193C2×D3×D4—33no—
194C2×D3×D4—33no—
195C2×D3×D4C2×D313yescomplemented
196C2×D3×D4C2×D313yescomplemented
197C2×#235—33no—
198C2×#235—33no—
199C2×#235C2×D313yescomplemented
200C22×D12—33no—
201C22×D12—33no—
202C22×D12C2×D313yescomplemented
203C3×#127—33no—
204C3×#121—33no—
205C3×#121—33no—
206C3×C4×Q8—31no—
207C3×C4×D4—33no—
208#953—36no—
209#953—36no—
210#947—33no—
211Q8×Dic3—31no—
212Q8×Dic3—31no—
213Q8×Dic3—61no—
214Q8×Dic3C2×D311yescharacteristic, complemented
215#944—31no—
216#940—33no—
217#940—33no—
218#940—33no—
219#940—36no—
220#940—33no—
221#940—36no—
222#940—33no—
223#940—33no—
224#940—33no—
225#940—63no—
226#940C2×D313yescomplemented
227#939—33no—
228#939—33no—
229#939—33no—
230#939—33no—
231#938—33no—
232#938—33no—
233#938—33no—
234#938—33no—
235#938—33no—
236#938—33no—
237#938—63no—
238#938C2×D313yescomplemented
239#937—36no—
240#937—36no—
241#937—36no—
242#937—36no—
243#936—33no—
244D4×Dic3—33no—
245D4×Dic3—33no—
246#930—33no—
247#930—33no—
248#930—33no—
249#930—33no—
250#930—33no—
251#930—63no—
252#930C2×D313yescomplemented
253C4×#67—33no—
254C4×#67—33no—
255C4×#67—33no—
256C4×#67—33no—
257C4×#67—33no—
258C4×#67—63no—
259C4×#67C2×D313yescomplemented
260#926—33no—
261C2×C4×Dic3—33no—
262#895—33no—
263#895—33no—
264#895—33no—
265#893—33no—
266#892—33no—
267#888—31no—
268#885—33no—
269#885—33no—
270#884—33no—
271#884—33no—
272#882—36no—
273#882—36no—
274#874—33no—
275C4×D12—33no—
276C4×D12—33no—
277C42×D3—33no—
278C23×C32C2413yes—
279C22×C3⋊D3C2413yes—
280C22×C3×D3—212no—
281C22×C3×D3—46no—
282C22×C3×D3—46no—
283C22×C3×D3C2413yes—
284C22×C3×D3C2413yes—
285C22×C3×D3C2413yes—
286C2×D32—212no—
287C2×D32—46no—
288C2×D32—46no—
289C32×Q8C2×D414yescomplemented
290C32×D4—26no—
291C2×C32×C4—26no—
292C2×C32×C4C2411yescharacteristic
293C2×C32×C4C2413yes—
294#638—26no—
295#638—46no—
296C2×C3⋊Dic3C2413yes—
297C2×C3⋊Dic3C2411yescharacteristic
298C2×C3⋊Dic3C2411yescharacteristic
299C4⋊(C3⋊D3)—26no—
300C4×C3⋊D3—26no—
301C3×#67—26no—
302C3×#67—26no—
303C3×#67—26no—
304C3×#67—46no—
305C2×C3×Dic3C2413yes—
306C2×C3×Dic3C2411yescharacteristic
307C2×C3×Dic3C2411yescharacteristic
308C2×C3×Dic3C2411yescharacteristic
309C2×C3×Dic3C2411yescharacteristic
310C3×D12—26no—
311C3×D12—26no—
312C3×D12—26no—
313C3×D12C2×D4112yescomplemented
314C3×C4×D3—26no—
315C3×C4×D3—26no—
316C3×C4×D3C2×D4112yescomplemented
317C3×Dic6—22no—
318#627—22no—
319#626—26no—
320#626—26no—
321#626—26no—
322#626—46no—
323#625—26no—
324#625—26no—
325#625—46no—
326D3×Dic3—26no—
327D3×Dic3—26no—
328C2×H(5,𝔽2)—31no—
329C2×H(5,𝔽2)—91no—
330#550—31no—
331#550—91no—
332#550—91no—
333#550—91no—
334D42—93no—
335D42—93no—
336D42—93no—
337D42—93no—
338#535—93no—
339#535—93no—
340#532—93no—
341C2×#127—93no—
342C4×#41—91no—
343C24×C3—36no—
344C23×D3—36no—
345C23×D3—36no—
346C23×D3C22×D316yes—
347C3×#41—24no—
348C3×#41—24no—
349C3×#41—38no—
350C3×#41—44no—
351C3×#41—612no—
352C3×#41—64no—
353C3×#41—64no—
354C2×C3×Q8—21no—
355C2×C3×Q8—31no—
356C2×C3×Q8C22×D311yescharacteristic
357C2×C3×Q8C22×D311yescharacteristic
358C2×C3×D4—23no—
359C2×C3×D4—33no—
360C2×C3×D4—33no—
361C2×C3×D4—33no—
362C2×C3×D4—36no—
363C2×C3×D4—33no—
364C2×C3×D4—33no—
365C2×C3×D4—33no—
366C2×C3×D4—33no—
367C2×C3×D4—612no—
368C2×C3×D4—612no—
369C2×C3×D4—612no—
370C2×C3×D4C22×D313yes—
371C2×C3×D4C22×D313yes—
372C22×C3×C4—23no—
373C22×C3×C4—33no—
374C22×C3×C4—33no—
375C22×C3×C4—33no—
376C22×C3×C4C22×D313yes—
377C22×C3×C4C22×D313yes—
378C2×#67—33no—
379C2×#67—33no—
380C2×#67—33no—
381C2×#67—33no—
382C2×#67—33no—
383C2×#67—33no—
384C2×#67—36no—
385C2×#67—36no—
386C2×#67—36no—
387C2×#67—36no—
388C2×#67—33no—
389C2×#67—33no—
390C2×#67—33no—
391C2×#67—36no—
392C2×#67—63no—
393C2×#67—66no—
394C2×#67—1212no—
395C2×#67—1212no—
396C2×#67C22×D313yes—
397C2×#67C22×D313yes—
398C2×#67C22×D313yes—
399C2×#67C22×D316yes—
400C22×Dic3—33no—
401C22×Dic3—33no—
402#239—24no—
403#239—24no—
404#239—64no—
405#239—64no—
406#239—124no—
407#239#6718yescomplemented
408D3×D4—212no—
409D3×D4—212no—
410D3×D4—612no—
411D3×D4—612no—
412D3×D4—612no—
413D3×D4—612no—
414D3×D4—1212no—
415D3×D4—1212no—
416#235—212no—
417#235—612no—
418#235—612no—
419C2×D12—212no—
420C2×D12—33no—
421C2×D12—33no—
422C2×D12—33no—
423C2×D12—33no—
424C2×D12—33no—
425C2×D12—36no—
426C2×D12—63no—
427C2×D12—612no—
428C2×D12—612no—
429C2×D12C22×D313yes—
430C2×D12C22×D313yes—
431C2×D12C22×D313yes—
432C2×D12C22×D313yes—
433C2×C4×D3—33no—
434C2×C4×D3—33no—
435C2×C4×D3—33no—
436C2×C4×D3—33no—
437C2×C4×D3—63no—
438C2×C4×D3C22×D313yes—
439C2×C4×D3C22×D313yes—
440C2×C4×D3C22×D313yes—
441C2×Dic6—31no—
442C2×Dic6—31no—
443C2×Dic6C22×D311yescharacteristic
444C3×C4⋊C4—31no—
445C3×C4⋊C4—33no—
446C3×C22⋊C4—33no—
447C3×C22⋊C4—33no—
448C3×C42—33no—
449#217—33no—
450#217—33no—
451#217—33no—
452#217—36no—
453#217—33no—
454#217—33no—
455#217—63no—
456#217C22×D313yes—
457(C2×D3)⋊C4—36no—
458(C2×D3)⋊C4—33no—
459(C2×D3)⋊C4—33no—
460(C2×D3)⋊C4—33no—
461(C2×D3)⋊C4—33no—
462(C2×D3)⋊C4—33no—
463(C2×D3)⋊C4—33no—
464(C2×D3)⋊C4—33no—
465(C2×D3)⋊C4—63no—
466(C2×D3)⋊C4C22×D313yes—
467C4⋊Dic3—33no—
468C4⋊Dic3—33no—
469C4⋊Dic3—31no—
470C4⋊Dic3—63no—
471C4⋊Dic3C22×D313yes—
472Dic3⋊C4—31no—
473Dic3⋊C4—31no—
474Dic3⋊C4—31no—
475Dic3⋊C4—31no—
476Dic3⋊C4—31no—
477Dic3⋊C4—61no—
478Dic3⋊C4C22×D311yescharacteristic
479C4×Dic3—33no—
480C4×Dic3—33no—
481C4×Dic3—31no—
482C4×Dic3—33no—
483C4×Dic3—31no—
484C4×Dic3—33no—
485C4×Dic3—63no—
486C4×Dic3C22×D313yes—
487C22×C32—23no—
488C22×C32—23no—
489C22×C32—23no—
490C22×C32C2511yescharacteristic
491C2×C3⋊D3—23no—
492C2×C3⋊D3—23no—
493C2×C3⋊D3—23no—
494C2×C3×D3—23no—
495C2×C3×D3—23no—
496C2×C3×D3—23no—
497C2×C3×D3—23no—
498C2×C3×D3—23no—
499C2×C3×D3—23no—
500C2×C3×D3—23no—
501C2×C3×D3—23no—
502C2×C3×D3—812no—
503C2×C3×D3C22×D416yes—
504D32—812no—
505C32×C4—21no—
506C32×C4C22×D416yes—
507C3⋊Dic3—21no—
508C3⋊Dic3—23no—
509C3⋊Dic3H(5,𝔽2)12yescomplemented
510C3×Dic3—21no—
511C3×Dic3—21no—
512C3×Dic3—23no—
513C3×Dic3C22×D412yes—
514C3×Dic3H(5,𝔽2)12yescomplemented
515H(5,𝔽2)—68no—
516H(5,𝔽2)—188no—
517C2×#41—31no—
518C2×#41—31no—
519C2×#41—31no—
520C2×#41—33no—
521C2×#41—93no—
522C2×#41—91no—
523C2×#41D3211yescharacteristic, complemented
524C22×D4—33no—
525C22×D4—33no—
526C22×D4—33no—
527C22×D4—93no—
528C22×D4—93no—
529C22×D4—93no—
530C22×D4—96no—
531C22×D4—96no—
532C4⋊Q8—91no—
533#127—33no—
534#127—93no—
535#127—93no—
536#127—96no—
537#127—93no—
538#127—93no—
539#124—93no—
540#124—93no—
541#121—33no—
542#121—33no—
543#121—93no—
544#121—93no—
545#121—93no—
546#121—93no—
547#121—93no—
548#121—93no—
549#121—93no—
550#121—93no—
551#121—93no—
552#121—93no—
553#120—96no—
554#120—96no—
555#120—96no—
556#120—96no—
557C4×Q8—31no—
558C4×Q8—91no—
559C4×D4—33no—
560C4×D4—93no—
561C4×D4—93no—
562C4×D4—93no—
563C4×D4—93no—
564C4×D4—93no—
565#117—93no—
566C2×C42—93no—
567C23×C3—23no—
568C23×C3—33no—
569C23×C3—33no—
570C23×C3—33no—
571C23×C3—612no—
572C23×C3—126no—
573C23×C3—126no—
574C23×C3C23×D313yes—
575C23×C3C23×D313yes—
576C22×D3—212no—
577C22×D3—33no—
578C22×D3—33no—
579C22×D3—46no—
580C22×D3—46no—
581C22×D3—63no—
582C22×D3—612no—
583C22×D3—612no—
584C22×D3—126no—
585C22×D3—126no—
586C22×D3—126no—
587C22×D3—126no—
588C22×D3C23×D313yes—
589C22×D3C23×D313yes—
590C22×D3C23×D313yes—
591C3×Q8—24no—
592C3×Q8—62no—
593C3×Q8D3×D414yescomplemented
594C3×Q8C2×#6714yescomplemented
595C3×D4—26no—
596C3×D4—26no—
597C3×D4—312no—
598C3×D4—46no—
599C3×D4—66no—
600C3×D4—66no—
601C3×D4—66no—
602C3×D4—66no—
603C3×D4—66no—
604C3×D4—66no—
605C3×D4—126no—
606C2×C3×C4—26no—
607C2×C3×C4—26no—
608C2×C3×C4—23no—
609C2×C3×C4—21no—
610C2×C3×C4—31no—
611C2×C3×C4—31no—
612C2×C3×C4—312no—
613C2×C3×C4—33no—
614C2×C3×C4—31no—
615C2×C3×C4—31no—
616C2×C3×C4—46no—
617C2×C3×C4—66no—
618C2×C3×C4—66no—
619C2×C3×C4C23×D311yescharacteristic
620C2×C3×C4C23×D311yescharacteristic
621C2×C3×C4C23×D313yes—
622C2×C3×C4C23×D313yes—
623#67—26no—
624#67—26no—
625#67—26no—
626#67—46no—
627#67—66no—
628#67—66no—
629#67—66no—
630#67—66no—
631#67—66no—
632#67—66no—
633#67—66no—
634#67—66no—
635#67—66no—
636#67—126no—
637#67—126no—
638#67—126no—
639#67—126no—
640#67—126no—
641#67—126no—
642#67—246no—
643C2×Dic3—31no—
644C2×Dic3—31no—
645C2×Dic3—33no—
646C2×Dic3—33no—
647C2×Dic3—31no—
648C2×Dic3—31no—
649C2×Dic3—61no—
650C2×Dic3—63no—
651C2×Dic3—61no—
652C2×Dic3—66no—
653C2×Dic3—66no—
654C2×Dic3C23×D313yes—
655C2×Dic3C23×D311yescharacteristic
656C2×Dic3C23×D311yescharacteristic
657C2×Dic3C23×D311yescharacteristic
658C2×Dic3C23×D311yescharacteristic
659D12—26no—
660D12—26no—
661D12—26no—
662D12—66no—
663D12—66no—
664D12—66no—
665D12—66no—
666D12—66no—
667D12—126no—
668D12—126no—
669D12C2×#67112yescomplemented
670C4×D3—26no—
671C4×D3—26no—
672C4×D3—66no—
673C4×D3—66no—
674C4×D3—66no—
675C4×D3—66no—
676C4×D3—126no—
677C4×D3C2×#67112yescomplemented
678Dic6—22no—
679Dic6—62no—
680Dic6—62no—
681C2×C32—43no—
682C2×C32C23×D411yescharacteristic
683C2×C32C2×H(5,𝔽2)11yescharacteristic
684C2×C32C2×H(5,𝔽2)11yescharacteristic
685C3⋊D3—43no—
686C3×D3—26no—
687C3×D3—43no—
688C3×D3—43no—
689C24—36no—
690C24—96no—
691#41—24no—
692#41—38no—
693#41—612no—
694#41—64no—
695#41—64no—
696#41—1812no—
697#41—184no—
698C2×Q8—31no—
699C2×Q8—91no—
700C2×Q8C2×D3211yescharacteristic
701C2×D4—33no—
702C2×D4—33no—
703C2×D4—33no—
704C2×D4—36no—
705C2×D4—33no—
706C2×D4—33no—
707C2×D4—33no—
708C2×D4—33no—
709C2×D4—612no—
710C2×D4—612no—
711C2×D4—612no—
712C2×D4—93no—
713C2×D4—93no—
714C2×D4—93no—
715C2×D4—96no—
716C2×D4—93no—
717C2×D4—93no—
718C2×D4—93no—
719C2×D4—96no—
720C2×D4—96no—
721C2×D4—93no—
722C2×D4—1812no—
723C2×D4—1812no—
724C2×D4—1812no—
725C2×D4—3612no—
726C2×D4—3612no—
727C2×D4C2×D3213yes—
728C22×C4—33no—
729C22×C4—33no—
730C22×C4—33no—
731C22×C4—93no—
732C22×C4—93no—
733C22×C4—93no—
734C22×C4C2×D3213yes—
735C4⋊C4—33no—
736C4⋊C4—31no—
737C4⋊C4—91no—
738C4⋊C4—91no—
739C4⋊C4—93no—
740C4⋊C4—91no—
741C22⋊C4—33no—
742C22⋊C4—33no—
743C22⋊C4—93no—
744C22⋊C4—96no—
745C22⋊C4—93no—
746C22⋊C4—93no—
747C22⋊C4—93no—
748C22⋊C4—93no—
749C22⋊C4—93no—
750C42—33no—
751C42—91no—
752C42—93no—
753C42—93no—
754C22×C3—23no—
755C22×C3—23no—
756C22×C3—23no—
757C22×C3—23no—
758C22×C3—23no—
759C22×C3—23no—
760C22×C3—21no—
761C22×C3—36no—
762C22×C3—43no—
763C22×C3—43no—
764C22×C3—43no—
765C22×C3—63no—
766C22×C3—63no—
767C22×C3—63no—
768C22×C3—63no—
769C22×C3—63no—
770C22×C3—63no—
771C22×C3—63no—
772C22×C3—63no—
773C22×C3—2412no—
774C22×C3C24×D311yescharacteristic
775C22×C3C24×D311yescharacteristic
776C2×D3—23no—
777C2×D3—23no—
778C2×D3—23no—
779C2×D3—23no—
780C2×D3—23no—
781C2×D3—23no—
782C2×D3—23no—
783C2×D3—23no—
784C2×D3—63no—
785C2×D3—63no—
786C2×D3—63no—
787C2×D3—63no—
788C2×D3—63no—
789C2×D3—63no—
790C2×D3—812no—
791C2×D3—123no—
792C2×D3—123no—
793C2×D3—123no—
794C2×D3—2412no—
795C2×D3—2412no—
796C2×D3C22×#6716yes—
797C3×C4—21no—
798C3×C4—21no—
799C3×C4—26no—
800C3×C4—32no—
801C3×C4—32no—
802C3×C4—41no—
803C3×C4—61no—
804C3×C4—63no—
805C3×C4—61no—
806C3×C4C2×D3×D416yes—
807C3×C4C22×#6716yes—
808Dic3—21no—
809Dic3—23no—
810Dic3—21no—
811Dic3—32no—
812Dic3—32no—
813Dic3—62no—
814Dic3—61no—
815Dic3—63no—
816Dic3—63no—
817Dic3—61no—
818Dic3—121no—
819Dic3—123no—
820Dic3#100912yescomplemented
821Dic3C22×#6712yes—
822C32#349811yescharacteristic, complemented, Sylow
823C23—33no—
824C23—33no—
825C23—33no—
826C23—612no—
827C23—93no—
828C23—126no—
829C23—126no—
830C23—1812no—
831C23—366no—
832C23—366no—
833C23C22×D3213yes—
834Q8—62no—
835Q8—182no—
836Q8D3×#6714yescomplemented
837D4—26no—
838D4—312no—
839D4—66no—
840D4—66no—
841D4—66no—
842D4—66no—
843D4—66no—
844D4—66no—
845D4—126no—
846D4—186no—
847D4—186no—
848D4—186no—
849D4—186no—
850D4—186no—
851D4—186no—
852D4—186no—
853D4—366no—
854D4—366no—
855D4—366no—
856C2×C4—26no—
857C2×C4—31no—
858C2×C4—31no—
859C2×C4—312no—
860C2×C4—33no—
861C2×C4—31no—
862C2×C4—31no—
863C2×C4—66no—
864C2×C4—66no—
865C2×C4—91no—
866C2×C4—93no—
867C2×C4—91no—
868C2×C4—186no—
869C2×C4—186no—
870C2×C4—186no—
871C2×C4C22×D3211yescharacteristic
872C2×C4C22×D3213yes—
873C2×C3—21no—
874C2×C3—21no—
875C2×C3—21no—
876C2×C3—43no—
877C2×C3—43no—
878C2×C3—66no—
879C2×C3—83no—
880C2×C3—123no—
881C2×C3—123no—
882C2×C3C22×D3×D411yescharacteristic
883C2×C3C2×#100911yescharacteristic
884C2×C3D3×H(5,𝔽2)11yescharacteristic
885C2×C3D3×H(5,𝔽2)11yescharacteristic
886C2×C3D3×H(5,𝔽2)11yescharacteristic
887C2×C3C23×#6711yescharacteristic
888D3—26no—
889D3—43no—
890D3—43no—
891D3—123no—
892D3—123no—
893D3—243no—
894C22—23no—
895C22—23no—
896C22—23no—
897C22—36no—
898C22—63no—
899C22—63no—
900C22—63no—
901C22—63no—
902C22—63no—
903C22—63no—
904C22—63no—
905C22—63no—
906C22—183no—
907C22—183no—
908C22—183no—
909C22—2412no—
910C22—7212no—
911C22C23×D3211yescharacteristic
912C4—21no—
913C4—32no—
914C4—32no—
915C4—63no—
916C4—61no—
917C4—61no—
918C4—92no—
919C4—183no—
920C4—181no—
921C4C2×D3×#6716yes—
922C3—21no—
923C3#8677011yescharacteristic, complemented
924C3#8728211yescharacteristic, complemented
925C2—43no—
926C2—66no—
927C2—123no—
928C2—123no—
929C2—363no—
930C2D3×#100911yescharacteristic
931C2#1059669211yescharacteristic
932C2C22×D3×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×#41C22
hypercenterC2×#41D32
hypocenterC32#3498
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1009C2semidirect
2. C2×#64320C2semidirect
3. #10596305C2semidirect
4. C3×#5834C2semidirect
5. #10595412C2semidirect
6. #10595410C2semidirect
7. Dic3×#239C2semidirect
8. #10595293C2semidirect
9. #10595288C2semidirect
10. D3×#940C2semidirect
11. #10595231C2semidirect
12. #10595069C2semidirect
13. D12×#67C2semidirect
14. #10595064C2semidirect
15. #10595003C2semidirect
18. C2×C32×#41C22semidirect
19. C2×#3832C22semidirect
22. C2×C3×#239C22semidirect
23. C2×C3×#239C22semidirect
24. C2×C3×D3×D4C22semidirect
25. C2×C3×D3×D4C22semidirect
26. C2×C3×#235C22semidirect
27. C22×C3×D12C22semidirect
28. C2×D3×#67C22semidirect
29. C2×D3×#67C22semidirect
31. C2×#3802C22semidirect
32. C2×D3×D12C22semidirect
33. C2×D3×D12C22semidirect
34. C2×#3798C22semidirect
35. Q8×C3⋊Dic3C22semidirect
36. #64149C22semidirect
37. #64147C22semidirect
38. #64139C22semidirect
39. C4×#638C22semidirect
40. C3×Q8×Dic3C22semidirect
41. C3×#940C22semidirect
42. C3×#938C22semidirect
43. C3×#930C22semidirect
44. C3×C4×#67C22semidirect
45. #63983C22semidirect
46. #63979C22semidirect
47. #63979C22semidirect
48. #63977C22semidirect
49. #63976C22semidirect
50. #63971C22semidirect
51. #63970C22semidirect
52. #63959C22semidirect
53. #63922C22semidirect
54. #63916C22semidirect
55. #63914C22semidirect
56. #63911C22semidirect
57. #63909C22semidirect
58. #63908C22semidirect
59. #63908C22semidirect
60. #63907C22semidirect
61. C4×#626C22semidirect
62. C4×#625C22semidirect
63. #63898C22semidirect
64. Dic3×D12C22semidirect
65. #63886C22semidirect
66. #63885C22semidirect
67. C4×D3×Dic3C22semidirect
68. #63841C22semidirect
69. #63839C22semidirect
73. C2×#1009D3semidirect
81. #5834D3semidirect
118. C3×#239D4semidirect
173. C2×C3×#41C2×D3semidirect
174. C2×C3×#41C2×D3semidirect
187. C2×#239C2×D3semidirect
188. C2×#239C2×D3semidirect
195. C2×D3×D4C2×D3semidirect
196. C2×D3×D4C2×D3semidirect
199. C2×#235C2×D3semidirect
202. C22×D12C2×D3semidirect
214. Q8×Dic3C2×D3semidirect
226. #940C2×D3semidirect
238. #938C2×D3semidirect
252. #930C2×D3semidirect
259. C4×#67C2×D3semidirect
289. C32×Q8C2×D4semidirect
313. C3×D12C2×D4semidirect
316. C3×C4×D3C2×D4semidirect
407. #239#67semidirect
509. C3⋊Dic3H(5,𝔽2)semidirect
514. C3×Dic3H(5,𝔽2)semidirect
523. C2×#41D32semidirect
593. C3×Q8D3×D4semidirect
594. C3×Q8C2×#67semidirect
669. D12C2×#67semidirect
677. C4×D3C2×#67semidirect
820. Dic3#1009semidirect
822. C32#3498semidirect
836. Q8D3×#67semidirect
923. C3#86770semidirect
924. C3#87282semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10092
C2×#643202
#105963052
C3×#58342
#105954122
#105954102
Dic3×#2392
#105952932
#105952882
D3×#9402
#105952312
#105950692
D12×#672
#105950642
#105950032
#872823
#867703