Finite Group Databasebeta

← #11904816

Subgroups — #11904816

Order 1152.

3189 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×D3×#239C211yesmaximal, characteristic, complemented
3#10596288C211yesmaximal, characteristic, complemented
4C3×Q8×#67C211yesmaximal, characteristic, complemented
5#10595427C213yesmaximal, complemented
6D3×#946C213yesmaximal, complemented
7Q8×#625C211yesmaximal, characteristic, complemented
8#10595394C211yesmaximal, characteristic, complemented
9#10595358C213yesmaximal, complemented
10#10595342C211yesmaximal, characteristic, complemented
11#10595340C213yesmaximal, complemented
12#10595067C213yesmaximal, complemented
13#10595060C213yesmaximal, complemented
14#10594894C213yesmaximal, complemented
15#10594890C213yesmaximal, complemented
16#87295—31nomaximal
17#86745—31nomaximal
18C22×C32×Q8C2211yescharacteristic, complemented
19C2×#3832C2211yescharacteristic
20C3×#1007—28no—
21C2×C3×#239C2211yescharacteristic
22C2×C3×#239C2213yescomplemented
23C2×C3×D3×Q8C2211yescharacteristic
24C2×C3×D3×Q8C2213yescomplemented
25C2×C3×D3×Q8C2211yescharacteristic, complemented
26C2×C3×#235C2213yescomplemented
27C2×C3×#235C2213yescomplemented
28D3×#239—28no—
29C2×D3×D12C2213yes—
30C2×C4×D32C2213yes—
31C2×#3799C2213yes—
32C2×#3796C2213yes—
33#64156C2213yescomplemented
34#64155C2213yescomplemented
35Q8×C3⋊Dic3C2211yescharacteristic, complemented
36#64139C2213yescomplemented
37C4×#638C2213yescomplemented
38C3×#946C2213yes—
39C3×Q8×Dic3C2211yescharacteristic, complemented
40C3×#944C2213yescomplemented
41C3×C4×#67C2213yes—
42C3×#924C2213yescomplemented
43#63983C2213yes—
44#63971C2216yescomplemented
45#63970C2211yescharacteristic
46#63969C2213yescomplemented
47#63958C2213yescomplemented
48#63922C2213yes—
49D3×(C2×D3)⋊C4C2216yes—
50#63909C2213yescomplemented
51C4×#626C2213yescomplemented
52C4×#625C2213yes—
53#63898C2213yescomplemented
54Dic3×D12C2213yescomplemented
55D3×C4⋊Dic3C2213yescomplemented
56#63888C2213yescomplemented
57#63888C2216yescomplemented
58#63887C2213yes—
59#63886C2216yescomplemented
60#63884C2213yescomplemented
61D3×Dic3⋊C4C2216yescomplemented
62#63873C2213yescomplemented
63#63871C2213yescomplemented
64#63864C2213yescomplemented
65#63856C2213yes—
66#63856C2213yescomplemented
67#63855C2213yescomplemented
68#63850C2216yescomplemented
69#63850C2216yescomplemented
70C2×C3×2−1+4—31no—
71C2×D3×#41—31no—
72C2×#1007D311yescharacteristic, complemented
73C22×#239—31no—
74C3×D4×Q8—31no—
75#5833—33no—
76#5829—33no—
77#5829—33no—
78#5828—33no—
79#5827—31no—
80#5824—33no—
81#5824—33no—
82#5817—31no—
83#5817—31no—
84#5817—31no—
85#5817—61no—
86#5816—33no—
87Q8×#67—31no—
88Q8×#67—31no—
89Q8×#67D311yescharacteristic, complemented
90C2×#946—33no—
91#5726—33no—
92#5724—33no—
93#5631—33no—
94#5630—33no—
95#5629—33no—
96D3×C22⋊Q8—33no—
97#5576—31no—
98#5574—31no—
99#5550—33no—
100#5547—33no—
101C22×D32C2313yes—
102C2×C32×Q8—24no—
103C2×C32×Q8C2313yes—
104C2×C32×Q8C2311yescharacteristic
105C22×C32×C4C2313yes—
106C2×#638C2313yes—
107#3832—24no—
108C2×C4⋊(C3⋊D3)C2313yes—
109C2×C4×C3⋊D3C2313yes—
110C2×C3×#67C2311yescharacteristic
111C2×C3×#67C2311yescharacteristic
112C2×C3×#67C2313yes—
113C3×#239—212no—
114C3×#239D418yescomplemented
115C3×D3×Q8—24no—
116C3×D3×Q8—24no—
117C3×D3×Q8—212no—
118C3×#235—212no—
119C3×#235—212no—
120C2×C3×D12C2313yes—
121C2×C3×D12C2313yes—
122C2×C3×C4×D3C2313yes—
123C2×C3×C4×D3C2316yes—
124C2×C3×C4×D3C2313yes—
125C2×C3×C4×D3C2313yes—
126C2×C3×Dic6C2313yes—
127C2×C3×Dic6C2313yes—
128C2×C3×Dic6C2313yes—
129C2×#626C2316yes—
130C2×#626C2313yes—
131C2×#625C2311yescharacteristic
132C2×#624C2313yes—
133C2×D3×Dic3C2313yes—
134C2×D3×Dic3C2311yescharacteristic
135C2×D3×Dic3C2316yes—
136D3×D12—212no—
137C4×D32—212no—
138#3799—212no—
139#3796—212no—
140#3757C2311yescharacteristic
141#3752C2313yes—
142#3752C2316yes—
143C4⋊(C3⋊Dic3)C2313yes—
144#3750C2313yes—
145C4×C3⋊Dic3C2313yes—
146C3×#217C2313yes—
147C3×(C2×D3)⋊C4C2313yes—
148C3×C4⋊Dic3C2313yes—
149C3×Dic3⋊C4C2316yes—
150C3×Dic3⋊C4C2313yes—
151C3×C4×Dic3C2313yes—
152#3724C2313yes—
153#3724C2316yes—
154Dic3⋊Dic3C2311yescharacteristic
155Dic3⋊Dic3C2313yes—
156Dic3⋊Dic3C2313yes—
157#3722C2313yes—
158#3722C2316yes—
159(C2×D3)⋊Dic3C2313yes—
160(C2×D3)⋊Dic3C2313yes—
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—33no—
168C2×C3×#41—33no—
169C2×C3×#41—33no—
170C22×C3×Q8—21no—
171C22×C3×Q8—31no—
172C22×C3×Q8—33no—
173C22×C3×Q8—31no—
174C22×C3×Q8C2×D311yescharacteristic, complemented
175C22×C3×Q8C2×D311yescharacteristic, complemented
176D3×#41—68no—
177#1007—28no—
178C2×#239—31no—
179C2×#239—31no—
180C2×#239—33no—
181C2×#239—33no—
182C2×#239—61no—
183C2×#239—68no—
184C2×#239C2×D311yescharacteristic
185C2×#239C2×D313yescomplemented
186C2×D3×Q8C2×D311yescharacteristic
187C2×D3×Q8C2×D313yescomplemented
188C2×D3×Q8C2×D311yescharacteristic, complemented
189C2×#237—33no—
190C2×D3×D4—33no—
191C2×#235—33no—
192C2×#235C2×D313yescomplemented
193C2×#235C2×D313yescomplemented
194C22×D12—33no—
195C22×C4×D3—33no—
196C22×C4×D3—33no—
197C3×C4⋊Q8—33no—
198C3×C22⋊Q8—33no—
199C3×C22⋊Q8—33no—
200C3×C4×Q8—31no—
201C3×C4×D4—33no—
202#947—33no—
203#947—33no—
204#947—33no—
205#947—63no—
206#946—33no—
207#946—33no—
208#946—33no—
209#946—33no—
210#946—33no—
211#946—33no—
212#946—36no—
213#946—33no—
214#946—63no—
215#946C2×D313yes—
216Q8×Dic3—31no—
217Q8×Dic3—31no—
218Q8×Dic3—61no—
219Q8×Dic3C2×D311yescharacteristic, complemented
220#944—33no—
221#944—33no—
222#944C2×D313yescomplemented
223#939—31no—
224#939—36no—
225#939—36no—
226#938—31no—
227#938—33no—
228#937—33no—
229#937—33no—
230#937—33no—
231#935—33no—
232#935—33no—
233D4×Dic3—33no—
234D4×Dic3—33no—
235#930—33no—
236#930—33no—
237#930—33no—
238#930—63no—
239#929—36no—
240#929—36no—
241C4×#67—33no—
242C4×#67—33no—
243C4×#67—33no—
244C4×#67—33no—
245C4×#67—33no—
246C4×#67—63no—
247C4×#67C2×D313yes—
248C2×(C2×D3)⋊C4—36no—
249#926—33no—
250C2×C4⋊Dic3—33no—
251#924—33no—
252#924—33no—
253#924C2×D313yescomplemented
254C2×Dic3⋊C4—36no—
255#897—33no—
256#896—33no—
257#896—36no—
258#895—36no—
259#895—33no—
260#894—33no—
261#894—36no—
262#894—36no—
263#893—33no—
264D3×C4⋊C4—36no—
265D3×C4⋊C4—33no—
266#884—33no—
267#884—36no—
268#883—33no—
269#882—33no—
270D3×C22⋊C4—36no—
271#878—33no—
272#875—33no—
273C4×D12—33no—
274C4×D12—33no—
275#872—33no—
276C23×C32C2411yescharacteristic
277C22×C3⋊D3C2413yes—
278C22×C3×D3C2411yescharacteristic
279C22×C3×D3C2413yes—
280C22×C3×D3C2411yescharacteristic
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—43no—
290C2×C3⋊Dic3C2411yescharacteristic
291C2×C3⋊Dic3C2413yes—
292C2×C3⋊Dic3C2411yescharacteristic
293C4⋊(C3⋊D3)—26no—
294C4×C3⋊D3—26no—
295C3×#67—26no—
296C3×#67—22no—
297C3×#67—22no—
298C2×C3×Dic3C2411yescharacteristic
299C2×C3×Dic3C2413yes—
300C2×C3×Dic3C2413yes—
301C2×C3×Dic3C2413yes—
302C2×C3×Dic3C2411yescharacteristic
303C3×D12—26no—
304C3×D12C2×D4112yes—
305C3×C4×D3—212no—
306C3×C4×D3—26no—
307C3×C4×D3—26no—
308C3×C4×D3C2×D4112yes—
309C3×Dic6—26no—
310C3×Dic6—26no—
311C3×Dic6—26no—
312#626—212no—
313#626—43no—
314#625—22no—
315#624—26no—
316D3×Dic3—26no—
317D3×Dic3—22no—
318D3×Dic3—46no—
319C2×2−1+4—31no—
320C22×#41—91no—
321D4×Q8—31no—
322D4×Q8—91no—
323#548—91no—
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—
340C2×C3×Q8—24no—
341C2×C3×Q8—24no—
342C2×C3×Q8—21no—
343C2×C3×Q8—23no—
344C2×C3×Q8—33no—
345C2×C3×Q8—33no—
346C2×C3×Q8—33no—
347C2×C3×Q8—44no—
348C2×C3×Q8—612no—
349C2×C3×Q8—64no—
350C2×C3×Q8—64no—
351C2×C3×Q8C22×D313yes—
352C2×C3×Q8C22×D313yes—
353C2×C3×Q8C22×D311yescharacteristic
354C2×C3×Q8C22×D311yescharacteristic
355C2×C3×D4—33no—
356C2×C3×D4—31no—
357C2×C3×D4—31no—
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—33no—
370C2×#67—33no—
371C2×#67—36no—
372C2×#67—33no—
373C2×#67—63no—
374C2×#67C22×D313yes—
375C2×#67C22×D311yescharacteristic
376C2×#67C22×D311yescharacteristic
377C22×Dic3—31no—
378C22×Dic3—33no—
379C22×Dic3—36no—
380#239—212no—
381#239—64no—
382#239—64no—
383#239—612no—
384#239—612no—
385#239—124no—
386#239#6718yescomplemented
387D3×Q8—24no—
388D3×Q8—24no—
389D3×Q8—212no—
390#237—612no—
391D3×D4—612no—
392#235—212no—
393#235—212no—
394#235—612no—
395C2×D12—36no—
396C2×D12—33no—
397C2×D12—33no—
398C2×D12—33no—
399C2×D12—63no—
400C2×D12—612no—
401C2×D12C22×D313yes—
402C2×D12C22×D313yes—
403C2×C4×D3—33no—
404C2×C4×D3—31no—
405C2×C4×D3—33no—
406C2×C4×D3—33no—
407C2×C4×D3—33no—
408C2×C4×D3—33no—
409C2×C4×D3—36no—
410C2×C4×D3—63no—
411C2×C4×D3—612no—
412C2×C4×D3—612no—
413C2×C4×D3C22×D313yes—
414C2×C4×D3C22×D316yes—
415C2×C4×D3C22×D313yes—
416C2×C4×D3C22×D313yes—
417C2×Dic6C22×D313yes—
418C2×Dic6C22×D313yes—
419C2×Dic6C22×D313yes—
420C3×C4⋊C4—33no—
421C3×C4⋊C4—36no—
422C3×C4⋊C4—33no—
423C3×C22⋊C4—33no—
424C3×C22⋊C4—33no—
425C3×C42—33no—
426#217—31no—
427#217—31no—
428#217—33no—
429#217—33no—
430#217—33no—
431#217—33no—
432#217—31no—
433#217—61no—
434#217C22×D313yes—
435(C2×D3)⋊C4—33no—
436(C2×D3)⋊C4—33no—
437(C2×D3)⋊C4—31no—
438(C2×D3)⋊C4—33no—
439(C2×D3)⋊C4—33no—
440(C2×D3)⋊C4—36no—
441(C2×D3)⋊C4—33no—
442(C2×D3)⋊C4—36no—
443(C2×D3)⋊C4—33no—
444(C2×D3)⋊C4—33no—
445(C2×D3)⋊C4—36no—
446(C2×D3)⋊C4—36no—
447(C2×D3)⋊C4—33no—
448(C2×D3)⋊C4—63no—
449(C2×D3)⋊C4—66no—
450(C2×D3)⋊C4C22×D313yes—
451C4⋊Dic3—33no—
452C4⋊Dic3—33no—
453C4⋊Dic3—33no—
454C4⋊Dic3—33no—
455C4⋊Dic3—31no—
456C4⋊Dic3—63no—
457C4⋊Dic3C22×D313yes—
458Dic3⋊C4—33no—
459Dic3⋊C4—33no—
460Dic3⋊C4—31no—
461Dic3⋊C4—33no—
462Dic3⋊C4—33no—
463Dic3⋊C4—36no—
464Dic3⋊C4—33no—
465Dic3⋊C4—36no—
466Dic3⋊C4—33no—
467Dic3⋊C4—63no—
468Dic3⋊C4C22×D316yes—
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—23no—
479C2×C3⋊D3—23no—
480C2×C3⋊D3—23no—
481C2×C3×D3—21no—
482C2×C3×D3—23no—
483C2×C3×D3—23no—
484C2×C3×D3—21no—
485C2×C3×D3—21no—
486C2×C3×D3—21no—
487C2×C3×D3—21no—
488C2×C3×D3C22×D416yes—
489C2×C3×D32−1+412yescomplemented
490D32—412no—
491C32×C4—23no—
492C32×C4C22×D416yes—
493C3⋊Dic3—21no—
494C3⋊Dic3—21no—
495C3⋊Dic3—23no—
496C3×Dic3—23no—
497C3×Dic3—23no—
498C3×Dic3—21no—
499C3×Dic3—23no—
500C3×Dic3C22×D412yes—
5012−1+4—68no—
502C2×#41—31no—
503C2×#41—33no—
504C2×#41—33no—
505C2×#41—33no—
506C2×#41—93no—
507C2×#41—93no—
508C2×#41—91no—
509C2×#41—188no—
510C22×Q8—33no—
511C22×Q8—31no—
512C22×Q8—31no—
513C22×Q8D3211yescharacteristic, complemented
514C22×D4—93no—
515C23×C4—93no—
516C4⋊Q8—33no—
517C4⋊Q8—93no—
518#124—93no—
519#124—93no—
520#123—93no—
521#123—96no—
522#123—96no—
523#123—93no—
524C22⋊Q8—33no—
525C22⋊Q8—33no—
526C22⋊Q8—93no—
527C22⋊Q8—96no—
528C22⋊Q8—93no—
529C22⋊Q8—93no—
530C22⋊Q8—93no—
531C22⋊Q8—93no—
532C22⋊Q8—93no—
533#121—93no—
534#121—96no—
535#121—93no—
536#121—96no—
537#121—91no—
538#121—93no—
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—31no—
555C23×C3—33no—
556C23×C3—31no—
557C23×C3C23×D311yescharacteristic
558C23×C3C23×D311yescharacteristic
559C22×D3—33no—
560C22×D3—33no—
561C22×D3—63no—
562C22×D3—66no—
563C22×D3—66no—
564C22×D3—66no—
565C22×D3—66no—
566C22×D3—123no—
567C22×D3—123no—
568C22×D3C23×D311yescharacteristic
569C22×D3C23×D311yescharacteristic
570C22×D3C23×D313yes—
571C3×Q8—26no—
572C3×Q8—26no—
573C3×Q8—24no—
574C3×Q8—46no—
575C3×Q8—66no—
576C3×Q8—66no—
577C3×Q8—66no—
578C3×Q8D3×D414yes—
579C3×Q8C2×#6714yes—
580C3×D4—312no—
581C3×D4—66no—
582C3×D4—62no—
583C3×D4—62no—
584C3×D4—66no—
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—33no—
593C2×C3×C4—33no—
594C2×C3×C4—31no—
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—22no—
604#67—26no—
605#67—22no—
606#67—612no—
607#67—62no—
608#67—62no—
609#67—123no—
610#67—123no—
611#67—123no—
612#67—126no—
613C2×Dic3—31no—
614C2×Dic3—31no—
615C2×Dic3—33no—
616C2×Dic3—33no—
617C2×Dic3—31no—
618C2×Dic3—31no—
619C2×Dic3—61no—
620C2×Dic3—63no—
621C2×Dic3—61no—
622C2×Dic3—66no—
623C2×Dic3—62no—
624C2×Dic3—126no—
625C2×Dic3C23×D311yescharacteristic
626C2×Dic3C23×D313yes—
627C2×Dic3C23×D313yes—
628C2×Dic3C23×D313yes—
629C2×Dic3C23×D311yescharacteristic
630D12—26no—
631D12—612no—
632D12—66no—
633D12—66no—
634D12—126no—
635D12—123no—
636D12C2×#67112yes—
637C4×D3—212no—
638C4×D3—26no—
639C4×D3—26no—
640C4×D3—66no—
641C4×D3—62no—
642C4×D3—66no—
643C4×D3—66no—
644C4×D3—66no—
645C4×D3—66no—
646C4×D3—126no—
647C4×D3—126no—
648C4×D3C2×#67112yes—
649Dic6—26no—
650Dic6—26no—
651Dic6—26no—
652C2×C32—41no—
653C2×C32C23×D411yescharacteristic
654C2×C32C2×2−1+411yescharacteristic
655C2×C32#58511yescharacteristic
656C3⋊D3—43no—
657C3×D3—22no—
658C3×D3—26no—
659C3×D3—41no—
660C24—93no—
661#41—38no—
662#41—612no—
663#41—612no—
664#41—612no—
665#41—1812no—
666#41—1812no—
667#41—184no—
668C2×Q8—24no—
669C2×Q8—33no—
670C2×Q8—33no—
671C2×Q8—33no—
672C2×Q8—612no—
673C2×Q8—64no—
674C2×Q8—64no—
675C2×Q8C2×D3213yes—
676C2×Q8C2×D3211yescharacteristic
677C2×D4—31no—
678C2×D4—33no—
679C2×D4—31no—
680C2×D4—33no—
681C2×D4—33no—
682C2×D4—96no—
683C2×D4—93no—
684C2×D4—91no—
685C2×D4—93no—
686C2×D4—93no—
687C2×D4—1812no—
688C22×C4—33no—
689C22×C4—36no—
690C22×C4—33no—
691C22×C4—33no—
692C22×C4—93no—
693C22×C4—93no—
694C22×C4—91no—
695C22×C4—96no—
696C22×C4—93no—
697C22×C4—1812no—
698C22×C4C2×D3213yes—
699C4⋊C4—33no—
700C4⋊C4—36no—
701C4⋊C4—33no—
702C4⋊C4—93no—
703C4⋊C4—93no—
704C4⋊C4—96no—
705C4⋊C4—91no—
706C4⋊C4—93no—
707C4⋊C4—93no—
708C4⋊C4—93no—
709C22⋊C4—33no—
710C22⋊C4—33no—
711C22⋊C4—96no—
712C22⋊C4—93no—
713C22⋊C4—93no—
714C22⋊C4—93no—
715C22⋊C4—93no—
716C22⋊C4—91no—
717C22⋊C4—93no—
718C22⋊C4—91no—
719C22⋊C4—96no—
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—32no—
733C22×C3—41no—
734C22×C3—41no—
735C22×C3—63no—
736C22×C3—63no—
737C22×C3—61no—
738C22×C3—61no—
739C22×C3—61no—
740C22×C3—61no—
741C22×C3—61no—
742C22×C3C24×D311yescharacteristic
743C22×C3C24×D311yescharacteristic
744C2×D3—21no—
745C2×D3—23no—
746C2×D3—23no—
747C2×D3—21no—
748C2×D3—21no—
749C2×D3—21no—
750C2×D3—21no—
751C2×D3—63no—
752C2×D3—63no—
753C2×D3—63no—
754C2×D3—63no—
755C2×D3—63no—
756C2×D3—63no—
757C2×D3—123no—
758C2×D3—123no—
759C2×D3—123no—
760C2×D3—1212no—
761C2×D3—1212no—
762C2×D3#100712yescomplemented
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—63no—
773C3×C4C2×D3×D416yes—
774C3×C4C22×#6716yes—
775Dic3—23no—
776Dic3—21no—
777Dic3—23no—
778Dic3—23no—
779Dic3—61no—
780Dic3—61no—
781Dic3—61no—
782Dic3—63no—
783Dic3—63no—
784Dic3—61no—
785Dic3—121no—
786Dic3—123no—
787Dic3—121no—
788Dic3C22×#6712yes—
789C32#348911yescharacteristic, complemented, Sylow
790C23—31no—
791C23—33no—
792C23—31no—
793C23—93no—
794C23—186no—
795C23—186no—
796C23—363no—
797C23C22×D3211yescharacteristic
798Q8—26no—
799Q8—66no—
800Q8—66no—
801Q8—66no—
802Q8D3×#6714yes—
803D4—312no—
804D4—66no—
805D4—62no—
806D4—66no—
807D4—62no—
808D4—1812no—
809D4—182no—
810D4—186no—
811D4—363no—
812D4—363no—
813C2×C4—26no—
814C2×C4—31no—
815C2×C4—312no—
816C2×C4—31no—
817C2×C4—33no—
818C2×C4—33no—
819C2×C4—33no—
820C2×C4—612no—
821C2×C4—66no—
822C2×C4—66no—
823C2×C4—91no—
824C2×C4—93no—
825C2×C4—91no—
826C2×C4—186no—
827C2×C4—182no—
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—62no—
841C2×C3—121no—
842C2×C3C22×D3×D411yescharacteristic
843C2×C3C2×#100711yescharacteristic
844C2×C3D3×2−1+411yescharacteristic
845C2×C3#596811yescharacteristic
846C2×C3#596811yescharacteristic
847C2×C3C23×#6711yescharacteristic
848D3—22no—
849D3—26no—
850D3—41no—
851D3—123no—
852D3—123no—
853D3—243no—
854C22—21no—
855C22—21no—
856C22—21no—
857C22—32no—
858C22—36no—
859C22—63no—
860C22—63no—
861C22—61no—
862C22—61no—
863C22—61no—
864C22—61no—
865C22—61no—
866C22—183no—
867C22—183no—
868C22—183no—
869C22—3612no—
870C22C23×D3211yescharacteristic
871C4—23no—
872C4—32no—
873C4—61no—
874C4—63no—
875C4—63no—
876C4—63no—
877C4—181no—
878C4—183no—
879C4—181no—
880C4C2×D3×#6716yes—
881C3—21no—
882C3#8674511yescharacteristic, complemented
883C3#8729511yescharacteristic, complemented
884C2—41no—
885C2—62no—
886C2—66no—
887C2—121no—
888C2—363no—
889C2D3×#100711yescharacteristic
890C2#1059668911yescharacteristic
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×D3×#239C2semidirect
3. #10596288C2semidirect
4. C3×Q8×#67C2semidirect
5. #10595427C2semidirect
6. D3×#946C2semidirect
7. Q8×#625C2semidirect
8. #10595394C2semidirect
9. #10595358C2semidirect
10. #10595342C2semidirect
11. #10595340C2semidirect
12. #10595067C2semidirect
13. #10595060C2semidirect
14. #10594894C2semidirect
15. #10594890C2semidirect
18. C22×C32×Q8C22semidirect
22. C2×C3×#239C22semidirect
24. C2×C3×D3×Q8C22semidirect
25. C2×C3×D3×Q8C22semidirect
26. C2×C3×#235C22semidirect
27. C2×C3×#235C22semidirect
33. #64156C22semidirect
34. #64155C22semidirect
35. Q8×C3⋊Dic3C22semidirect
36. #64139C22semidirect
37. C4×#638C22semidirect
39. C3×Q8×Dic3C22semidirect
40. C3×#944C22semidirect
42. C3×#924C22semidirect
44. #63971C22semidirect
46. #63969C22semidirect
47. #63958C22semidirect
50. #63909C22semidirect
51. C4×#626C22semidirect
53. #63898C22semidirect
54. Dic3×D12C22semidirect
55. D3×C4⋊Dic3C22semidirect
56. #63888C22semidirect
57. #63888C22semidirect
59. #63886C22semidirect
60. #63884C22semidirect
61. D3×Dic3⋊C4C22semidirect
62. #63873C22semidirect
63. #63871C22semidirect
64. #63864C22semidirect
66. #63856C22semidirect
67. #63855C22semidirect
68. #63850C22semidirect
69. #63850C22semidirect
72. C2×#1007D3semidirect
89. Q8×#67D3semidirect
114. C3×#239D4semidirect
174. C22×C3×Q8C2×D3semidirect
175. C22×C3×Q8C2×D3semidirect
185. C2×#239C2×D3semidirect
187. C2×D3×Q8C2×D3semidirect
188. C2×D3×Q8C2×D3semidirect
192. C2×#235C2×D3semidirect
193. C2×#235C2×D3semidirect
219. Q8×Dic3C2×D3semidirect
222. #944C2×D3semidirect
253. #924C2×D3semidirect
386. #239#67semidirect
489. C2×C3×D32−1+4semidirect
513. C22×Q8D32semidirect
762. C2×D3#1007semidirect
789. C32#3489semidirect
882. C3#86745semidirect
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×D3×#2392
#105962882
C3×Q8×#672
#105954272
D3×#9462
Q8×#6252
#105953942
#105953582
#105953422
#105953402
#105950672
#105950602
#105948942
#105948902
#872953
#867453