Finite Group Databasebeta

← #11904814

Subgroups — #11904814

Order 1152.

3184 conjugacy classes of subgroups.

The subgroup lattice has 893 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1007C211yesmaximal, characteristic, complemented
2C2×#64319C211yesmaximal, characteristic, complemented
3Q8×#638C211yesmaximal, characteristic, complemented
4C3×#5817C211yesmaximal, characteristic, complemented
5#10595428C213yesmaximal, complemented
6D3×#946C213yesmaximal, complemented
7#10595409C211yesmaximal, characteristic, complemented
8Q8×#626C211yesmaximal, characteristic, complemented
9#10595399C213yesmaximal, complemented
10#10595394C211yesmaximal, characteristic, complemented
11#10595357C213yesmaximal, complemented
12#10595070C213yesmaximal, complemented
13#10595060C213yesmaximal, complemented
14#10595004C213yesmaximal, complemented
15#10594887C213yesmaximal, complemented
16#87295—31nomaximal
17#86714—31nomaximal
18C22×C32×Q8C2211yescharacteristic, complemented
19C2×Q8×C3⋊D3C2211yescharacteristic
20C3×#1007—28no—
21C2×C3×#239C2211yescharacteristic
22C2×C3×#239C2211yescharacteristic
23C2×C3×#239C2213yescomplemented
24C2×C3×D3×Q8C2213yescomplemented
25C2×C3×D3×Q8C2211yescharacteristic, complemented
26C2×C3×#235C2213yescomplemented
27C2×C3×#235C2213yescomplemented
28#64319—28no—
29C2×#3802C2213yes—
30C2×C4×D32C2213yes—
31C2×#3795C2213yes—
32C2×#3795C2213yes—
33#64155C2213yes—
34Q8×C3⋊Dic3C2211yescharacteristic, complemented
35#64153C2213yescomplemented
36C4×#638C2213yes—
37#64133C2213yescomplemented
38C3×#947C2213yescomplemented
39C3×#946C2213yescomplemented
40C3×Q8×Dic3C2211yescharacteristic, complemented
41C3×#930C2213yescomplemented
42C3×C4×#67C2213yescomplemented
43#63983C2213yes—
44#63970C2216yescomplemented
45#63970C2213yescomplemented
46#63969C2213yescomplemented
47#63958C2211yescharacteristic
48#63922C2213yes—
49D3×(C2×D3)⋊C4C2216yes—
50#63908C2213yescomplemented
51#63905C2216yescomplemented
52#63905C2216yescomplemented
53C4×#626C2213yes—
54C4×#625C2213yescomplemented
55#63898C2213yescomplemented
56Dic3×D12C2213yescomplemented
57D3×C4⋊Dic3C2213yescomplemented
58#63888C2213yes—
59#63887C2213yescomplemented
60#63887C2216yescomplemented
61#63885C2216yescomplemented
62#63884C2213yescomplemented
63D3×Dic3⋊C4C2216yescomplemented
64#63871C2213yes—
65#63866C2213yescomplemented
66#63863C2213yescomplemented
67#63857C2213yescomplemented
68#63856C2213yescomplemented
69#63855C2213yescomplemented
70C2×C3×2−1+4—31no—
71C2×D3×#41—31no—
72C2×D3×#41—31no—
73C2×#1007D311yescharacteristic, complemented
74C3×#548—31no—
75#5833—33no—
76#5831—31no—
77#5829—33no—
78#5829—33no—
79#5828—33no—
80#5827—31no—
81#5824—33no—
82#5824—33no—
83#5817—31no—
84#5817D311yescharacteristic, complemented
85#5816—33no—
86Q8×#67—31no—
87Q8×#67—31no—
88Q8×#67—31no—
89Q8×#67—61no—
90C2×#946—33no—
91#5676—33no—
92#5675—33no—
93#5631—33no—
94D3×C22⋊Q8—33no—
95#5612—33no—
96#5608—33no—
97Q8×D12—31no—
98#5574—31no—
99#5551—33no—
100#5547—33no—
101C22×D32C2313yes—
102C2×C32×Q8—24no—
103C2×C32×Q8C2313yes—
104C2×C32×Q8C2311yescharacteristic
105C22×C32×C4C2313yes—
106C2×#638C2311yescharacteristic
107Q8×C3⋊D3—24no—
108C2×C4×C3⋊D3C2313yes—
109C2×#634C2313yes—
110C2×C3×#67C2311yescharacteristic
111C2×C3×#67C2313yes—
112C2×C3×#67C2313yes—
113C3×#239—24no—
114C3×#239—212no—
115C3×#239D418yescomplemented
116C3×D3×Q8—24no—
117C3×D3×Q8—212no—
118C3×#235—212no—
119C3×#235—212no—
120C2×C3×D12C2313yes—
121C2×C3×D12C2313yes—
122C2×C3×D12C2313yes—
123C2×C3×C4×D3C2313yes—
124C2×C3×C4×D3C2313yes—
125C2×C3×C4×D3C2316yes—
126C2×C3×C4×D3C2313yes—
127C2×C3×Dic6C2313yes—
128C2×C3×Dic6C2313yes—
129C2×#626C2311yescharacteristic
130C2×#625C2316yes—
131C2×#625C2313yes—
132C2×#624C2311yescharacteristic
133C2×D3×Dic3C2313yes—
134C2×D3×Dic3C2313yes—
135C2×D3×Dic3C2316yes—
136#3802—212no—
137C4×D32—212no—
138#3795—212no—
139#3795—212no—
140#3757C2313yes—
141#3752C2313yes—
142C4⋊(C3⋊Dic3)C2313yes—
143#3750C2316yes—
144#3750C2313yes—
145C4×C3⋊Dic3C2313yes—
146C3×#217C2311yescharacteristic
147C3×(C2×D3)⋊C4C2313yes—
148C3×(C2×D3)⋊C4C2316yes—
149C3×C4⋊Dic3C2313yes—
150C3×Dic3⋊C4C2313yes—
151C3×C4×Dic3C2313yes—
152#3724C2313yes—
153Dic3⋊Dic3C2311yescharacteristic
154Dic3⋊Dic3C2313yes—
155Dic3⋊Dic3C2316yes—
156Dic3⋊Dic3C2313yes—
157#3722C2313yes—
158(C2×D3)⋊Dic3C2313yes—
159(C2×D3)⋊Dic3C2313yes—
160(C2×D3)⋊Dic3C2316yes—
161(C2×D3)⋊Dic3C2313yes—
162(C2×D3)⋊Dic3C2313yes—
163(C2×D3)⋊Dic3C2311yescharacteristic
164#3489—91noSylow
165C3×2−1+4—68no—
166C2×C3×#41—31no—
167C2×C3×#41—31no—
168C2×C3×#41—33no—
169C2×C3×#41—33no—
170C2×C3×#41—33no—
171C22×C3×Q8—21no—
172C22×C3×Q8—33no—
173C22×C3×Q8—31no—
174C22×C3×Q8C2×D311yescharacteristic, complemented
175C22×C3×Q8C2×D311yescharacteristic, complemented
176D3×#41—68no—
177D3×#41—68no—
178#1007—28no—
179C2×#239C2×D311yescharacteristic
180C2×#239C2×D311yescharacteristic
181C2×#239C2×D313yescomplemented
182C2×D3×Q8—31no—
183C2×D3×Q8—31no—
184C2×D3×Q8—61no—
185C2×D3×Q8C2×D313yescomplemented
186C2×D3×Q8C2×D311yescharacteristic, complemented
187C2×#237—33no—
188C2×#237—33no—
189C2×D3×D4—33no—
190C2×D3×D4—33no—
191C2×#235—33no—
192C2×#235—33no—
193C2×#235C2×D313yescomplemented
194C2×#235C2×D313yescomplemented
195C22×C4×D3—33no—
196C22×C4×D3—33no—
197C3×#124—33no—
198C3×C22⋊Q8—33no—
199C3×#121—33no—
200C3×C4×Q8—31no—
201C3×C4×D4—33no—
202#947—33no—
203#947C2×D313yescomplemented
204#946—33no—
205#946—33no—
206#946—33no—
207#946—36no—
208#946—33no—
209#946—33no—
210#946—33no—
211#946—63no—
212#946C2×D313yescomplemented
213Q8×Dic3—31no—
214Q8×Dic3—31no—
215Q8×Dic3—61no—
216Q8×Dic3C2×D311yescharacteristic, complemented
217#944—33no—
218#944—33no—
219#944—33no—
220#944—63no—
221#939—33no—
222#939—36no—
223#939—36no—
224#938—36no—
225#938—33no—
226#938—33no—
227#938—31no—
228#937—33no—
229#937—33no—
230#937—33no—
231#936—33no—
232#935—33no—
233#935—33no—
234D4×Dic3—33no—
235D4×Dic3—33no—
236#930—33no—
237#930C2×D313yescomplemented
238#929—36no—
239#929—36no—
240C4×#67—33no—
241C4×#67—33no—
242C4×#67—33no—
243C4×#67—33no—
244C4×#67—33no—
245C4×#67—63no—
246C4×#67C2×D313yescomplemented
247C2×(C2×D3)⋊C4—36no—
248#926—33no—
249C2×C4⋊Dic3—33no—
250#924—33no—
251#924—33no—
252#924—33no—
253#924—33no—
254#924—63no—
255C2×Dic3⋊C4—36no—
256#897—33no—
257#897—33no—
258#896—33no—
259#894—33no—
260#893—33no—
261D3×C4⋊C4—36no—
262D3×C4⋊C4—33no—
263#884—31no—
264#884—36no—
265#883—33no—
266#883—36no—
267#883—36no—
268#882—33no—
269D3×C22⋊C4—36no—
270#878—33no—
271#878—36no—
272C4×D12—33no—
273C4×D12—33no—
274#872—33no—
275#869—33no—
276C23×C32C2411yescharacteristic
277C22×C3⋊D3C2411yescharacteristic
278C22×C3×D3C2413yes—
279C22×C3×D3C2411yescharacteristic
280C22×C3×D3C2413yes—
281C2×D32—26no—
282C2×D32—26no—
283C2×D32—43no—
284C32×Q8—26no—
285C32×Q8C2×D414yes—
286C2×C32×C4—26no—
287C2×C32×C4C2413yes—
288C2×C32×C4C2413yes—
289#638—22no—
290C2×C3⋊Dic3C2411yescharacteristic
291C2×C3⋊Dic3C2413yes—
292C2×C3⋊Dic3C2413yes—
293C4×C3⋊D3—26no—
294#634—26no—
295C3×#67—26no—
296C3×#67—22no—
297C3×#67—43no—
298C2×C3×Dic3C2413yes—
299C2×C3×Dic3C2411yescharacteristic
300C2×C3×Dic3C2413yes—
301C2×C3×Dic3C2411yescharacteristic
302C2×C3×Dic3C2411yescharacteristic
303C3×D12—26no—
304C3×D12—26no—
305C3×D12C2×D4112yes—
306C3×C4×D3—212no—
307C3×C4×D3—26no—
308C3×C4×D3—26no—
309C3×C4×D3C2×D4112yes—
310C3×Dic6—26no—
311C3×Dic6—26no—
312#626—22no—
313#625—212no—
314#625—43no—
315#624—22no—
316D3×Dic3—26no—
317D3×Dic3—26no—
318D3×Dic3—46no—
319C2×2−1+4—31no—
320C22×#41—91no—
321D4×Q8—91no—
322D4×Q8—91no—
323#548—31no—
324#548—91no—
325#547—93no—
326#547—93no—
327#546—93no—
328#546—93no—
329#537—93no—
330#536—93no—
331#525—93no—
332C2×C22⋊Q8—93no—
333#520—91no—
334C23×D3—33no—
335C23×D3—33no—
336C3×#41—38no—
337C3×#41—612no—
338C3×#41—612no—
339C3×#41—612no—
340C3×#41—64no—
341C2×C3×Q8—24no—
342C2×C3×Q8—24no—
343C2×C3×Q8—21no—
344C2×C3×Q8—23no—
345C2×C3×Q8—33no—
346C2×C3×Q8—33no—
347C2×C3×Q8—44no—
348C2×C3×Q8—612no—
349C2×C3×Q8—64no—
350C2×C3×Q8C22×D313yes—
351C2×C3×Q8C22×D313yes—
352C2×C3×Q8C22×D311yescharacteristic
353C2×C3×Q8C22×D311yescharacteristic
354C2×C3×D4—33no—
355C2×C3×D4—31no—
356C2×C3×D4—33no—
357C2×C3×D4—33no—
358C2×C3×D4—33no—
359C2×C3×D4—33no—
360C22×C3×C4—23no—
361C22×C3×C4—33no—
362C22×C3×C4—36no—
363C22×C3×C4—33no—
364C22×C3×C4—33no—
365C22×C3×C4C22×D313yes—
366C22×C3×C4C22×D313yes—
367C2×#67—31no—
368C2×#67—31no—
369C2×#67—36no—
370C2×#67—36no—
371C2×#67—33no—
372C2×#67—33no—
373C2×#67—31no—
374C2×#67—61no—
375C2×#67C22×D313yes—
376C2×#67C22×D311yescharacteristic
377C2×#67C22×D313yes—
378C22×Dic3—33no—
379C22×Dic3—33no—
380C22×Dic3—36no—
381#239—24no—
382#239—212no—
383#239#6718yescomplemented
384D3×Q8—24no—
385D3×Q8—212no—
386D3×Q8—64no—
387D3×Q8—64no—
388D3×Q8—124no—
389#237—612no—
390#237—612no—
391D3×D4—612no—
392D3×D4—612no—
393#235—212no—
394#235—212no—
395#235—612no—
396#235—612no—
397C2×D12—31no—
398C2×D12C22×D313yes—
399C2×D12C22×D313yes—
400C2×D12C22×D313yes—
401C2×C4×D3—33no—
402C2×C4×D3—33no—
403C2×C4×D3—33no—
404C2×C4×D3—33no—
405C2×C4×D3—31no—
406C2×C4×D3—31no—
407C2×C4×D3—36no—
408C2×C4×D3—63no—
409C2×C4×D3—612no—
410C2×C4×D3—612no—
411C2×C4×D3C22×D313yes—
412C2×C4×D3C22×D316yes—
413C2×C4×D3C22×D313yes—
414C2×C4×D3C22×D313yes—
415C2×Dic6—33no—
416C2×Dic6—33no—
417C2×Dic6—63no—
418C2×Dic6C22×D313yes—
419C2×Dic6C22×D313yes—
420C3×C4⋊C4—33no—
421C3×C4⋊C4—33no—
422C3×C22⋊C4—31no—
423C3×C22⋊C4—36no—
424C3×C22⋊C4—33no—
425C3×C42—33no—
426#217—33no—
427#217—33no—
428#217—36no—
429#217—33no—
430#217—33no—
431#217—33no—
432#217—33no—
433#217—31no—
434#217—63no—
435#217C22×D311yescharacteristic
436(C2×D3)⋊C4—33no—
437(C2×D3)⋊C4—33no—
438(C2×D3)⋊C4—33no—
439(C2×D3)⋊C4—31no—
440(C2×D3)⋊C4—36no—
441(C2×D3)⋊C4—33no—
442(C2×D3)⋊C4—33no—
443(C2×D3)⋊C4—33no—
444(C2×D3)⋊C4—33no—
445(C2×D3)⋊C4—33no—
446(C2×D3)⋊C4—63no—
447(C2×D3)⋊C4C22×D316yes—
448(C2×D3)⋊C4C22×D313yes—
449C4⋊Dic3—33no—
450C4⋊Dic3—33no—
451C4⋊Dic3—33no—
452C4⋊Dic3—36no—
453C4⋊Dic3—33no—
454C4⋊Dic3—31no—
455C4⋊Dic3—63no—
456C4⋊Dic3C22×D313yes—
457Dic3⋊C4—33no—
458Dic3⋊C4—36no—
459Dic3⋊C4—36no—
460Dic3⋊C4—33no—
461Dic3⋊C4—31no—
462Dic3⋊C4—33no—
463Dic3⋊C4—33no—
464Dic3⋊C4—36no—
465Dic3⋊C4—33no—
466Dic3⋊C4—33no—
467Dic3⋊C4—66no—
468Dic3⋊C4—63no—
469Dic3⋊C4C22×D313yes—
470C4×Dic3—33no—
471C4×Dic3—33no—
472C4×Dic3—63no—
473C4×Dic3C22×D313yes—
474C22×C32—21no—
475C22×C32—21no—
476C22×C32—21no—
477C22×C32C2511yescharacteristic
478C2×C3⋊D3—21no—
479C2×C3⋊D3—21no—
480C2×C3⋊D32−1+412yescomplemented
481C2×C3×D3—23no—
482C2×C3×D3—23no—
483C2×C3×D3—23no—
484C2×C3×D3—21no—
485C2×C3×D3—21no—
486C2×C3×D3—23no—
487C2×C3×D3—21no—
488C2×C3×D3—23no—
489C2×C3×D3C22×D416yes—
490D32—412no—
491C32×C4—23no—
492C32×C4C22×D416yes—
493C3⋊Dic3—21no—
494C3⋊Dic3—23no—
495C3⋊Dic3—23no—
496C3×Dic3—21no—
497C3×Dic3—23no—
498C3×Dic3—21no—
499C3×Dic3—23no—
500C3×Dic3C22×D412yes—
5012−1+4—68no—
502C2×#41—31no—
503C2×#41—33no—
504C2×#41—31no—
505C2×#41—33no—
506C2×#41—33no—
507C2×#41—93no—
508C2×#41—93no—
509C2×#41—188no—
510C22×Q8—33no—
511C22×Q8—31no—
512C22×Q8—91no—
513C22×Q8D3211yescharacteristic, complemented
514C22×D4—93no—
515C23×C4—93no—
516C4⋊Q8—93no—
517C4⋊Q8—93no—
518#124—33no—
519#124—93no—
520#123—96no—
521#123—96no—
522#123—93no—
523#123—93no—
524C22⋊Q8—33no—
525C22⋊Q8—96no—
526C22⋊Q8—93no—
527C22⋊Q8—93no—
528C22⋊Q8—93no—
529C22⋊Q8—93no—
530C22⋊Q8—93no—
531C22⋊Q8—93no—
532C22⋊Q8—93no—
533#121—33no—
534#121—91no—
535#121—96no—
536#121—93no—
537#121—93no—
538#121—96no—
539#120—93no—
540#120—93no—
541C4×Q8—31no—
542C4×Q8—91no—
543C4×D4—33no—
544C4×D4—93no—
545C4×D4—93no—
546C4×D4—93no—
547C4×D4—93no—
548C4×D4—93no—
549#117—93no—
550C2×C4⋊C4—93no—
551C2×C4⋊C4—96no—
552C2×C22⋊C4—96no—
553C23×C3—21no—
554C23×C3—33no—
555C23×C3—31no—
556C23×C3—33no—
557C23×C3C23×D311yescharacteristic
558C23×C3C23×D311yescharacteristic
559C22×D3—31no—
560C22×D3—31no—
561C22×D3—61no—
562C22×D3—66no—
563C22×D3—66no—
564C22×D3—66no—
565C22×D3—66no—
566C22×D3—123no—
567C22×D3—123no—
568C22×D3C23×D311yescharacteristic
569C22×D3C23×D313yes—
570C22×D3C23×D313yes—
571C3×Q8—26no—
572C3×Q8—26no—
573C3×Q8—24no—
574C3×Q8—46no—
575C3×Q8—66no—
576C3×Q8—66no—
577C3×Q8D3×D414yes—
578C3×Q8C2×#6714yes—
579C3×D4—312no—
580C3×D4—66no—
581C3×D4—62no—
582C3×D4—66no—
583C3×D4—66no—
584C3×D4—123no—
585C2×C3×C4—26no—
586C2×C3×C4—26no—
587C2×C3×C4—23no—
588C2×C3×C4—23no—
589C2×C3×C4—31no—
590C2×C3×C4—312no—
591C2×C3×C4—33no—
592C2×C3×C4—31no—
593C2×C3×C4—31no—
594C2×C3×C4—33no—
595C2×C3×C4—46no—
596C2×C3×C4—612no—
597C2×C3×C4—66no—
598C2×C3×C4—66no—
599C2×C3×C4C23×D313yes—
600C2×C3×C4C23×D313yes—
601C2×C3×C4C23×D313yes—
602C2×C3×C4C23×D313yes—
603#67—26no—
604#67—22no—
605#67—43no—
606#67—62no—
607#67—612no—
608#67—62no—
609#67—62no—
610#67—64no—
611#67—612no—
612#67—123no—
613#67—123no—
614C2×Dic3—31no—
615C2×Dic3—31no—
616C2×Dic3—33no—
617C2×Dic3—33no—
618C2×Dic3—33no—
619C2×Dic3—33no—
620C2×Dic3—61no—
621C2×Dic3—63no—
622C2×Dic3—63no—
623C2×Dic3—66no—
624C2×Dic3—66no—
625C2×Dic3—126no—
626C2×Dic3C23×D311yescharacteristic
627C2×Dic3C23×D313yes—
628C2×Dic3C23×D311yescharacteristic
629C2×Dic3C23×D313yes—
630C2×Dic3C23×D311yescharacteristic
631D12—26no—
632D12—26no—
633D12—62no—
634D12C2×#67112yes—
635C4×D3—212no—
636C4×D3—26no—
637C4×D3—26no—
638C4×D3—62no—
639C4×D3—66no—
640C4×D3—66no—
641C4×D3—66no—
642C4×D3—66no—
643C4×D3—62no—
644C4×D3—126no—
645C4×D3—126no—
646C4×D3C2×#67112yes—
647Dic6—26no—
648Dic6—26no—
649Dic6—66no—
650Dic6—66no—
651Dic6—126no—
652C2×C32—41no—
653C2×C32C23×D411yescharacteristic
654C2×C32C2×2−1+411yescharacteristic
655C2×C32#58511yescharacteristic
656C3⋊D3—22no—
657C3×D3—26no—
658C3×D3—43no—
659C3×D3—41no—
660C24—93no—
661#41—38no—
662#41—612no—
663#41—612no—
664#41—612no—
665#41—64no—
666#41—1812no—
667#41—1812no—
668C2×Q8—24no—
669C2×Q8—33no—
670C2×Q8—33no—
671C2×Q8—612no—
672C2×Q8—64no—
673C2×Q8—93no—
674C2×Q8—184no—
675C2×Q8C2×D3213yes—
676C2×Q8C2×D3211yescharacteristic
677C2×D4—33no—
678C2×D4—31no—
679C2×D4—33no—
680C2×D4—33no—
681C2×D4—33no—
682C2×D4—33no—
683C2×D4—91no—
684C2×D4—96no—
685C2×D4—91no—
686C2×D4—93no—
687C2×D4—1812no—
688C22×C4—33no—
689C22×C4—36no—
690C22×C4—33no—
691C22×C4—33no—
692C22×C4—91no—
693C22×C4—93no—
694C22×C4—93no—
695C22×C4—96no—
696C22×C4—93no—
697C22×C4—1812no—
698C22×C4C2×D3213yes—
699C4⋊C4—33no—
700C4⋊C4—33no—
701C4⋊C4—93no—
702C4⋊C4—93no—
703C4⋊C4—96no—
704C4⋊C4—91no—
705C4⋊C4—93no—
706C4⋊C4—93no—
707C4⋊C4—96no—
708C4⋊C4—93no—
709C22⋊C4—31no—
710C22⋊C4—36no—
711C22⋊C4—33no—
712C22⋊C4—93no—
713C22⋊C4—96no—
714C22⋊C4—93no—
715C22⋊C4—93no—
716C22⋊C4—91no—
717C22⋊C4—93no—
718C22⋊C4—93no—
719C22⋊C4—93no—
720C22⋊C4—93no—
721C42—33no—
722C42—93no—
723C22×C3—22no—
724C22×C3—21no—
725C22×C3—21no—
726C22×C3—21no—
727C22×C3—21no—
728C22×C3—21no—
729C22×C3—21no—
730C22×C3—21no—
731C22×C3—36no—
732C22×C3—41no—
733C22×C3—41no—
734C22×C3—63no—
735C22×C3—63no—
736C22×C3—61no—
737C22×C3—61no—
738C22×C3—61no—
739C22×C3—63no—
740C22×C3—63no—
741C22×C3—63no—
742C22×C3C24×D311yescharacteristic
743C22×C3C24×D311yescharacteristic
744C2×D3—23no—
745C2×D3—23no—
746C2×D3—23no—
747C2×D3—23no—
748C2×D3—21no—
749C2×D3—23no—
750C2×D3—21no—
751C2×D3—21no—
752C2×D3—32no—
753C2×D3—32no—
754C2×D3—62no—
755C2×D3—61no—
756C2×D3—61no—
757C2×D3—61no—
758C2×D3—61no—
759C2×D3—121no—
760C2×D3—121no—
761C2×D3—1212no—
762C2×D3—1212no—
763C2×D3C22×#6716yes—
764C3×C4—23no—
765C3×C4—23no—
766C3×C4—26no—
767C3×C4—32no—
768C3×C4—43no—
769C3×C4—63no—
770C3×C4—61no—
771C3×C4—63no—
772C3×C4—61no—
773C3×C4C2×D3×D416yes—
774C3×C4C22×#6716yes—
775Dic3—21no—
776Dic3—23no—
777Dic3—21no—
778Dic3—23no—
779Dic3—62no—
780Dic3—63no—
781Dic3—63no—
782Dic3—61no—
783Dic3—61no—
784Dic3—63no—
785Dic3—63no—
786Dic3—123no—
787Dic3—123no—
788Dic3C22×#6712yes—
789C32#348911yescharacteristic, complemented, Sylow
790C23—33no—
791C23—33no—
792C23—31no—
793C23—91no—
794C23—186no—
795C23—186no—
796C23—363no—
797C23C22×D3211yescharacteristic
798Q8—26no—
799Q8—66no—
800Q8—66no—
801Q8—186no—
802Q8D3×#6714yes—
803D4—312no—
804D4—66no—
805D4—62no—
806D4—66no—
807D4—66no—
808D4—123no—
809D4—182no—
810D4—182no—
811D4—1812no—
812D4—363no—
813C2×C4—26no—
814C2×C4—31no—
815C2×C4—312no—
816C2×C4—31no—
817C2×C4—33no—
818C2×C4—31no—
819C2×C4—33no—
820C2×C4—612no—
821C2×C4—66no—
822C2×C4—66no—
823C2×C4—91no—
824C2×C4—93no—
825C2×C4—93no—
826C2×C4—182no—
827C2×C4—186no—
828C2×C4—186no—
829C2×C4—186no—
830C2×C4—366no—
831C2×C4C22×D3213yes—
832C2×C4C22×D3213yes—
833C2×C3—21no—
834C2×C3—21no—
835C2×C3—21no—
836C2×C3—42no—
837C2×C3—41no—
838C2×C3—41no—
839C2×C3—66no—
840C2×C3—121no—
841C2×C3—123no—
842C2×C3C22×D3×D411yescharacteristic
843C2×C3#596411yescharacteristic
844C2×C3D3×2−1+411yescharacteristic
845C2×C3D3×2−1+411yescharacteristic
846C2×C3#596811yescharacteristic
847C2×C3C23×#6711yescharacteristic
848D3—26no—
849D3—43no—
850D3—41no—
851D3—62no—
852D3—62no—
853D3—122no—
854C22—21no—
855C22—21no—
856C22—21no—
857C22—36no—
858C22—63no—
859C22—63no—
860C22—61no—
861C22—63no—
862C22—63no—
863C22—61no—
864C22—61no—
865C22—63no—
866C22—92no—
867C22—181no—
868C22—181no—
869C22—3612no—
870C22C23×D3211yescharacteristic
871C4—23no—
872C4—32no—
873C4—61no—
874C4—63no—
875C4—61no—
876C4—63no—
877C4—181no—
878C4—183no—
879C4—183no—
880C4C2×D3×#6716yes—
881C3—21no—
882C3#8671411yescharacteristic, complemented
883C3#8729511yescharacteristic, complemented
884C2—41no—
885C2—66no—
886C2—123no—
887C2—121no—
888C2—182no—
889C2#1059668711yescharacteristic
890C2#1059668811yescharacteristic
891C2C22×D3×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC22×C32×Q8C22
hypercenterC22×Q8D32
hypocenterC32#3489
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1007C2semidirect
2. C2×#64319C2semidirect
3. Q8×#638C2semidirect
4. C3×#5817C2semidirect
5. #10595428C2semidirect
6. D3×#946C2semidirect
7. #10595409C2semidirect
8. Q8×#626C2semidirect
9. #10595399C2semidirect
10. #10595394C2semidirect
11. #10595357C2semidirect
12. #10595070C2semidirect
13. #10595060C2semidirect
14. #10595004C2semidirect
15. #10594887C2semidirect
18. C22×C32×Q8C22semidirect
23. C2×C3×#239C22semidirect
24. C2×C3×D3×Q8C22semidirect
25. C2×C3×D3×Q8C22semidirect
26. C2×C3×#235C22semidirect
27. C2×C3×#235C22semidirect
34. Q8×C3⋊Dic3C22semidirect
35. #64153C22semidirect
37. #64133C22semidirect
38. C3×#947C22semidirect
39. C3×#946C22semidirect
40. C3×Q8×Dic3C22semidirect
41. C3×#930C22semidirect
42. C3×C4×#67C22semidirect
44. #63970C22semidirect
45. #63970C22semidirect
46. #63969C22semidirect
50. #63908C22semidirect
51. #63905C22semidirect
52. #63905C22semidirect
54. C4×#625C22semidirect
55. #63898C22semidirect
56. Dic3×D12C22semidirect
57. D3×C4⋊Dic3C22semidirect
59. #63887C22semidirect
60. #63887C22semidirect
61. #63885C22semidirect
62. #63884C22semidirect
63. D3×Dic3⋊C4C22semidirect
65. #63866C22semidirect
66. #63863C22semidirect
67. #63857C22semidirect
68. #63856C22semidirect
69. #63855C22semidirect
73. C2×#1007D3semidirect
84. #5817D3semidirect
115. C3×#239D4semidirect
174. C22×C3×Q8C2×D3semidirect
175. C22×C3×Q8C2×D3semidirect
181. C2×#239C2×D3semidirect
185. C2×D3×Q8C2×D3semidirect
186. C2×D3×Q8C2×D3semidirect
193. C2×#235C2×D3semidirect
194. C2×#235C2×D3semidirect
203. #947C2×D3semidirect
212. #946C2×D3semidirect
216. Q8×Dic3C2×D3semidirect
237. #930C2×D3semidirect
246. C4×#67C2×D3semidirect
383. #239#67semidirect
480. C2×C3⋊D32−1+4semidirect
513. C22×Q8D32semidirect
789. C32#3489semidirect
882. C3#86714semidirect
883. C3#87295semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10072
C2×#643192
Q8×#6382
C3×#58172
#105954282
D3×#9462
#105954092
Q8×#6262
#105953992
#105953942
#105953572
#105950702
#105950602
#105950042
#105948872
#872953
#867143