Finite Group Databasebeta

← #11902848

Subgroups — #11902848

Order 1152.

3441 conjugacy classes of subgroups.

The subgroup lattice has 917 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×#41C211yesmaximal, characteristic, complemented
2C2×#64319C211yesmaximal, characteristic, complemented
3#10596302C211yesmaximal, characteristic, complemented
4C3×#5834C211yesmaximal, characteristic, complemented
5#10595409C211yesmaximal, characteristic, complemented
6Q8×#626C211yesmaximal, characteristic, complemented
7Dic3×#239C211yesmaximal, characteristic, complemented
8#10595301C213yesmaximal, complemented
9#10595293C213yesmaximal, complemented
10#10595228C213yesmaximal, complemented
11#10595152C213yesmaximal, complemented
12#10595070C213yesmaximal, complemented
13C4×D3×#67C213yesmaximal, complemented
14#10594892C213yesmaximal, complemented
15#10594887C213yesmaximal, complemented
16#41×#67—31nomaximal
17#86766—31nomaximal
18C2×C32×#41C2211yescharacteristic, complemented
19C2×Q8×C3⋊D3C2211yescharacteristic, complemented
20C3×D3×#41—28no—
21C2×C3×#239C2211yescharacteristic
22C2×C3×#239C2211yescharacteristic, complemented
23C2×C3×D3×Q8C2211yescharacteristic, complemented
24C2×C3×#237C2213yescomplemented
25C2×C3×D3×D4C2213yescomplemented
26C2×C3×#235C2213yescomplemented
27C22×C3×C4×D3C2213yescomplemented
28C2×D3×#67C2213yes—
29#64319—28no—
30C2×#3802C2213yescomplemented
31C2×C4×D32C2213yescomplemented
32C2×#3795C2213yescomplemented
33C2×#3795C2213yescomplemented
34Q8×C3⋊Dic3C2211yescharacteristic, complemented
35#64147C2213yescomplemented
36#64145C2213yescomplemented
37C4×#638C2213yescomplemented
38#64133C2213yescomplemented
39C3×Q8×Dic3C2211yescharacteristic, complemented
40C3×#940C2213yescomplemented
41C3×#938C2213yescomplemented
42C3×#930C2213yescomplemented
43C3×C4×#67C2213yescomplemented
44#63983C2216yescomplemented
45#63976C2216yescomplemented
46Dic3×#67C2216yescomplemented
47Dic3×#67C2213yescomplemented
48#63970C2216yescomplemented
49#63970C2216yescomplemented
50#63969C2216yescomplemented
51D3×#217C2213yescomplemented
52#63952C2213yescomplemented
53D3×(C2×D3)⋊C4C2213yescomplemented
54#63908C2213yescomplemented
55#63905C2216yescomplemented
56#63904C2211yescharacteristic
57C4×#626C2213yes—
58C4×#625C2213yescomplemented
59#63898C2213yescomplemented
60Dic3×D12C2213yescomplemented
61#63879C2213yescomplemented
62D3×Dic3⋊C4C2213yescomplemented
63C4×D3×Dic3C2213yescomplemented
64#63871C2213yescomplemented
65#63866C2213yescomplemented
66#63863C2213yescomplemented
67#63857C2213yescomplemented
68#63856C2213yescomplemented
69#63841C2213yescomplemented
70C22×C3×#41—31no—
71C2×D3×#41—31no—
72C2×D3×#41—31no—
73C2×D3×#41D311yescharacteristic, complemented
74C3×#550—31no—
75#5834D311yescharacteristic, complemented
76#5832—33no—
77#5831—31no—
78#5831—31no—
79#5831—31no—
80#5831—61no—
81#5829—33no—
82#5828—33no—
83Dic3×#41—31no—
84#5824—33no—
85#5817—31no—
86Q8×#67—31no—
87#5806—33no—
88D4×#67—33no—
89#5791—33no—
90C2×C4×#67—33no—
91#5717—33no—
92#5716—33no—
93#5612—33no—
94#5612—33no—
95#5606—33no—
96#5606—33no—
97Q8×D12—31no—
98C4×#239—31no—
99#5551—33no—
100C4×D3×D4—33no—
101C23×C3×D3C2313yes—
102C22×D32C2313yes—
103C32×#41—24no—
104C2×C32×Q8C2311yescharacteristic
105C2×C32×D4C2313yes—
106C22×C32×C4C2313yes—
107C2×#638C2313yes—
108Q8×C3⋊D3—24no—
109C2×C4×C3⋊D3C2313yes—
110C2×#634C2313yes—
111C2×C3×#67C2313yes—
112C2×C3×#67C2316yes—
113C2×C3×#67C2316yes—
114C22×C3×Dic3C2313yes—
115C3×#239—24no—
116C3×#239D418yescomplemented
117C3×D3×Q8—24no—
118C3×#237—212no—
119C3×D3×D4—212no—
120C3×#235—212no—
121C2×C3×D12C2313yes—
122C2×C3×D12C2313yes—
123C2×C3×C4×D3—212no—
124C2×C3×C4×D3C2313yes—
125C2×C3×C4×D3C2311yescharacteristic
126C2×C3×C4×D3C2313yes—
127C2×C3×C4×D3C2313yes—
128C2×C3×C4×D3C2313yes—
129C2×C3×Dic6C2313yes—
130D3×#67—212no—
131C2×#626C2311yescharacteristic
132C2×#625C2316yes—
133C2×#625C2313yes—
134C2×#624C2311yescharacteristic
135C2×D3×Dic3C2313yes—
136C2×D3×Dic3C2313yes—
137C2×D3×Dic3C2313yes—
138C2×D3×Dic3C2313yes—
139#3802—212no—
140C4×D32—212no—
141#3795—212no—
142#3795—212no—
143#3757C2316yes—
144#3757C2313yes—
145#3752C2311yescharacteristic
146C4⋊(C3⋊Dic3)C2313yes—
147#3750C2313yes—
148C4×C3⋊Dic3C2313yes—
149C3×#217C2313yes—
150C3×(C2×D3)⋊C4C2313yes—
151C3×C4⋊Dic3C2313yes—
152C3×Dic3⋊C4C2311yescharacteristic
153C3×C4×Dic3C2313yes—
154#3724C2313yes—
155Dic3⋊Dic3C2316yes—
156Dic3⋊Dic3C2313yes—
157#3722C2313yes—
158(C2×D3)⋊Dic3C2316yes—
159(C2×D3)⋊Dic3C2316yes—
160(C2×D3)⋊Dic3C2313yes—
161(C2×D3)⋊Dic3C2313yes—
162(C2×D3)⋊Dic3C2311yescharacteristic
163Dic32C2313yes—
164Dic32C2311yescharacteristic
165D4×#41—91noSylow
166C2×C3×#41—21no—
167C2×C3×#41—31no—
168C2×C3×#41—31no—
169C2×C3×#41—33no—
170C2×C3×#41—33no—
171C2×C3×#41—68no—
172C2×C3×#41C2×D311yescharacteristic, complemented
173C2×C3×#41C2×D311yescharacteristic, complemented
174C22×C3×Q8—31no—
175C22×C3×D4—33no—
176C23×C3×C4—33no—
177C22×#67—33no—
178D3×#41—28no—
179D3×#41—68no—
180D3×#41—68no—
181C2×#239C2×D311yescharacteristic
182C2×#239C2×D311yescharacteristic, complemented
183C2×D3×Q8—31no—
184C2×D3×Q8—31no—
185C2×D3×Q8—61no—
186C2×D3×Q8C2×D311yescharacteristic, complemented
187C2×#237—33no—
188C2×#237—33no—
189C2×#237C2×D313yescomplemented
190C2×D3×D4—33no—
191C2×D3×D4—33no—
192C2×D3×D4—33no—
193C2×D3×D4C2×D313yescomplemented
194C2×#235—33no—
195C2×#235—33no—
196C2×#235C2×D313yescomplemented
197C22×C4×D3—33no—
198C22×C4×D3—33no—
199C22×C4×D3C2×D313yescomplemented
200C3×#127—33no—
201C3×#121—33no—
202C3×#121—33no—
203C3×C4×Q8—31no—
204C3×C4×D4—33no—
205#953—36no—
206C2×#217—33no—
207#947—33no—
208#946—33no—
209#946—33no—
210Q8×Dic3—31no—
211Q8×Dic3—31no—
212Q8×Dic3—61no—
213Q8×Dic3C2×D311yescharacteristic, complemented
214#944—33no—
215#940C2×D313yescomplemented
216#939—36no—
217#939—36no—
218#938—33no—
219#938—33no—
220#938—36no—
221#938—36no—
222#938—33no—
223#938—63no—
224#938C2×D313yescomplemented
225#937—36no—
226#937—36no—
227#937—36no—
228#936—33no—
229#936—33no—
230#936—33no—
231#936—63no—
232#935—36no—
233D4×Dic3—33no—
234D4×Dic3—36no—
235D4×Dic3—33no—
236D4×Dic3—33no—
237#930—33no—
238#930C2×D313yescomplemented
239#929—36no—
240C4×#67—33no—
241C4×#67—33no—
242C4×#67—33no—
243C4×#67—36no—
244C4×#67—33no—
245C4×#67—33no—
246C4×#67—33no—
247C4×#67—33no—
248C4×#67—31no—
249C4×#67—33no—
250C4×#67—63no—
251C4×#67C2×D313yescomplemented
252C2×(C2×D3)⋊C4—33no—
253#926—33no—
254#924—33no—
255#924—33no—
256#924—33no—
257#924—33no—
258#924—63no—
259C2×Dic3⋊C4—33no—
260C2×C4×Dic3—33no—
261#897—33no—
262#897—33no—
263#893—33no—
264#893—31no—
265#892—33no—
266D3×C4⋊C4—33no—
267#883—36no—
268#883—36no—
269#67⋊C4—33no—
270#67⋊C4—33no—
271D3×C22⋊C4—33no—
272D3×C22⋊C4—33no—
273C4×D12—33no—
274C4×D12—33no—
275C42×D3—33no—
276#869—33no—
277C23×C32C2413yes—
278C22×C3⋊D3C2411yescharacteristic
279C22×C3×D3—26no—
280C22×C3×D3—26no—
281C22×C3×D3—43no—
282C22×C3×D3C2413yes—
283C22×C3×D3C2413yes—
284C22×C3×D3C2411yescharacteristic
285C2×D32—26no—
286C2×D32—26no—
287C2×D32—43no—
288C32×Q8C2×D414yescomplemented
289C32×D4—26no—
290C2×C32×C4—26no—
291C2×C32×C4C2411yescharacteristic
292C2×C32×C4C2413yes—
293#638—26no—
294C2×C3⋊Dic3C2413yes—
295C2×C3⋊Dic3C2411yescharacteristic
296C2×C3⋊Dic3C2413yes—
297C4×C3⋊D3—26no—
298#634—26no—
299C3×#67—212no—
300C3×#67—26no—
301C3×#67—46no—
302C2×C3×Dic3—26no—
303C2×C3×Dic3C2413yes—
304C2×C3×Dic3C2413yes—
305C2×C3×Dic3C2411yescharacteristic
306C2×C3×Dic3C2411yescharacteristic
307C2×C3×Dic3C2411yescharacteristic
308C3×D12—26no—
309C3×D12C2×D4112yescomplemented
310C3×C4×D3—26no—
311C3×C4×D3—26no—
312C3×C4×D3—26no—
313C3×C4×D3—22no—
314C3×C4×D3C2×D4112yescomplemented
315C3×Dic6—26no—
316#626#4114yescomplemented
317#625—212no—
318#625—26no—
319#624—22no—
320D3×Dic3—26no—
321D3×Dic3—26no—
322D3×Dic3—26no—
323D3×Dic3—43no—
324C22×#41—31no—
325C22×#41—91no—
326#550—31no—
327D4×Q8—91no—
328#548—91no—
329#548—91no—
330#547—93no—
331#546—93no—
332#546—93no—
333D42—93no—
334#532—93no—
335#525—93no—
336#525—93no—
337C4×#41—91no—
338C2×C4×D4—93no—
339C24×C3—33no—
340C23×D3—33no—
341C23×D3—33no—
342C23×D3C22×D313yes—
343C3×#41—24no—
344C3×#41—24no—
345C3×#41—38no—
346C3×#41—44no—
347C3×#41—612no—
348C3×#41—612no—
349C3×#41—64no—
350C2×C3×Q8—21no—
351C2×C3×Q8—33no—
352C2×C3×Q8—64no—
353C2×C3×Q8C22×D311yescharacteristic
354C2×C3×Q8C22×D311yescharacteristic
355C2×C3×D4—23no—
356C2×C3×D4—33no—
357C2×C3×D4—36no—
358C2×C3×D4—36no—
359C2×C3×D4—33no—
360C2×C3×D4—33no—
361C2×C3×D4—612no—
362C2×C3×D4C22×D313yes—
363C2×C3×D4C22×D313yes—
364C22×C3×C4—23no—
365C22×C3×C4—33no—
366C22×C3×C4—33no—
367C22×C3×C4—33no—
368C22×C3×C4—33no—
369C22×C3×C4—33no—
370C22×C3×C4—31no—
371C22×C3×C4—612no—
372C22×C3×C4C22×D313yes—
373C22×C3×C4C22×D313yes—
374C2×#67—33no—
375C2×#67—33no—
376C2×#67—33no—
377C2×#67—36no—
378C2×#67—33no—
379C2×#67—36no—
380C2×#67—31no—
381C2×#67—63no—
382C2×#67—612no—
383C2×#67C22×D316yes—
384C2×#67C22×D313yes—
385C2×#67C22×D316yes—
386C22×Dic3—33no—
387C22×Dic3—33no—
388C22×Dic3—33no—
389C22×Dic3—33no—
390C22×Dic3C22×D313yes—
391#239—24no—
392#239#6718yescomplemented
393D3×Q8—24no—
394D3×Q8—64no—
395D3×Q8—64no—
396D3×Q8—124no—
397#237—212no—
398#237—612no—
399#237—612no—
400D3×D4—212no—
401D3×D4—612no—
402D3×D4—612no—
403D3×D4—612no—
404#235—212no—
405#235—612no—
406#235—612no—
407C2×D12—31no—
408C2×D12C22×D313yes—
409C2×D12C22×D313yes—
410C2×C4×D3—212no—
411C2×C4×D3—33no—
412C2×C4×D3—33no—
413C2×C4×D3—33no—
414C2×C4×D3—33no—
415C2×C4×D3—33no—
416C2×C4×D3—31no—
417C2×C4×D3—31no—
418C2×C4×D3—33no—
419C2×C4×D3—63no—
420C2×C4×D3—612no—
421C2×C4×D3—612no—
422C2×C4×D3C22×D313yes—
423C2×C4×D3C22×D313yes—
424C2×C4×D3C22×D311yescharacteristic
425C2×C4×D3C22×D313yes—
426C2×C4×D3C22×D313yes—
427C2×Dic6—33no—
428C2×Dic6—33no—
429C2×Dic6—63no—
430C2×Dic6C22×D313yes—
431C3×C4⋊C4—31no—
432C3×C4⋊C4—33no—
433C3×C22⋊C4—33no—
434C3×C22⋊C4—33no—
435C3×C42—33no—
436#217—33no—
437#217—36no—
438#217—36no—
439#217—33no—
440#217—33no—
441#217—36no—
442#217—33no—
443#217—36no—
444#217—31no—
445#217—66no—
446#217—63no—
447#217C22×D313yes—
448(C2×D3)⋊C4—33no—
449(C2×D3)⋊C4—36no—
450(C2×D3)⋊C4—31no—
451(C2×D3)⋊C4—33no—
452(C2×D3)⋊C4—36no—
453(C2×D3)⋊C4—31no—
454(C2×D3)⋊C4—31no—
455(C2×D3)⋊C4—33no—
456(C2×D3)⋊C4—33no—
457(C2×D3)⋊C4—61no—
458(C2×D3)⋊C4C22×D313yes—
459C4⋊Dic3—33no—
460C4⋊Dic3—33no—
461C4⋊Dic3—33no—
462C4⋊Dic3—36no—
463C4⋊Dic3—63no—
464C4⋊Dic3C22×D313yes—
465Dic3⋊C4—33no—
466Dic3⋊C4—33no—
467Dic3⋊C4—33no—
468Dic3⋊C4—33no—
469Dic3⋊C4—36no—
470Dic3⋊C4—33no—
471Dic3⋊C4—63no—
472Dic3⋊C4C22×D311yescharacteristic
473C4×Dic3—33no—
474C4×Dic3—33no—
475C4×Dic3—31no—
476C4×Dic3—33no—
477C4×Dic3—31no—
478C4×Dic3—33no—
479C4×Dic3—63no—
480C4×Dic3C22×D313yes—
481C22×C32—23no—
482C22×C32—23no—
483C22×C32—23no—
484C22×C32C2511yescharacteristic
485C2×C3⋊D3—21no—
486C2×C3⋊D3—21no—
487C2×C3⋊D3C2×#4112yescomplemented
488C2×C3×D3—21no—
489C2×C3×D3—23no—
490C2×C3×D3—23no—
491C2×C3×D3—21no—
492C2×C3×D3—23no—
493C2×C3×D3—23no—
494C2×C3×D3—23no—
495C2×C3×D3—412no—
496C2×C3×D3C22×D416yes—
497C2×C3×D3C2×#4112yescomplemented
498D32—412no—
499C32×C4—21no—
500C32×C4C22×D416yes—
501C3⋊Dic3—23no—
502C3⋊Dic3—23no—
503C3⋊Dic3—21no—
504C3×Dic3—21no—
505C3×Dic3—23no—
506C3×Dic3—23no—
507C3×Dic3C22×D412yes—
508C3×Dic3C2×#4112yescomplemented
509C2×#41—31no—
510C2×#41—31no—
511C2×#41—33no—
512C2×#41—33no—
513C2×#41—68no—
514C2×#41—93no—
515C2×#41—93no—
516C2×#41—188no—
517C2×#41D3211yescharacteristic, complemented
518C22×Q8—31no—
519C22×Q8—91no—
520C22×D4—33no—
521C22×D4—93no—
522C22×D4—93no—
523C23×C4—33no—
524C23×C4—93no—
525C4⋊Q8—93no—
526#127—33no—
527#124—93no—
528#124—93no—
529#123—96no—
530#123—96no—
531C22⋊Q8—93no—
532C22⋊Q8—93no—
533C22⋊Q8—93no—
534C22⋊Q8—93no—
535#121—33no—
536#121—33no—
537#121—93no—
538#121—96no—
539#121—96no—
540#121—93no—
541#120—96no—
542#120—96no—
543C4×Q8—31no—
544C4×Q8—91no—
545C4×D4—33no—
546C4×D4—93no—
547C4×D4—93no—
548C4×D4—93no—
549C4×D4—93no—
550C4×D4—91no—
551C4×D4—93no—
552C4×D4—93no—
553C4×D4—93no—
554C4×D4—96no—
555C4×D4—93no—
556#117—93no—
557C2×C4⋊C4—93no—
558C2×C22⋊C4—93no—
559C2×C22⋊C4—93no—
560C2×C42—93no—
561C23×C3—23no—
562C23×C3—31no—
563C23×C3—33no—
564C23×C3—33no—
565C23×C3—66no—
566C23×C3—66no—
567C23×C3—123no—
568C23×C3C23×D313yes—
569C23×C3C23×D313yes—
570C22×D3—26no—
571C22×D3—26no—
572C22×D3—31no—
573C22×D3—31no—
574C22×D3—43no—
575C22×D3—61no—
576C22×D3—66no—
577C22×D3—66no—
578C22×D3—66no—
579C22×D3—66no—
580C22×D3—123no—
581C22×D3—123no—
582C22×D3C23×D313yes—
583C22×D3C23×D311yescharacteristic
584C22×D3C23×D313yes—
585C3×Q8—24no—
586C3×Q8—66no—
587C3×Q8D3×D414yescomplemented
588C3×Q8C2×#6714yescomplemented
589C3×D4—26no—
590C3×D4—26no—
591C3×D4—312no—
592C3×D4—46no—
593C3×D4—66no—
594C3×D4—612no—
595C3×D4—66no—
596C3×D4—126no—
597C2×C3×C4—26no—
598C2×C3×C4—26no—
599C2×C3×C4—23no—
600C2×C3×C4—21no—
601C2×C3×C4—31no—
602C2×C3×C4—31no—
603C2×C3×C4—312no—
604C2×C3×C4—33no—
605C2×C3×C4—33no—
606C2×C3×C4—31no—
607C2×C3×C4—46no—
608C2×C3×C4—62no—
609C2×C3×C4—66no—
610C2×C3×C4—66no—
611C2×C3×C4—66no—
612C2×C3×C4—66no—
613C2×C3×C4C23×D311yescharacteristic
614C2×C3×C4C23×D311yescharacteristic
615C2×C3×C4C23×D313yes—
616C2×C3×C4C23×D313yes—
617#67—212no—
618#67—26no—
619#67—34no—
620#67—46no—
621#67—612no—
622#67—66no—
623#67—66no—
624#67—66no—
625#67—66no—
626#67—612no—
627#67—126no—
628C2×Dic3—26no—
629C2×Dic3—31no—
630C2×Dic3—31no—
631C2×Dic3—33no—
632C2×Dic3—33no—
633C2×Dic3—33no—
634C2×Dic3—33no—
635C2×Dic3—61no—
636C2×Dic3—63no—
637C2×Dic3—63no—
638C2×Dic3—66no—
639C2×Dic3—66no—
640C2×Dic3—66no—
641C2×Dic3—123no—
642C2×Dic3C23×D313yes—
643C2×Dic3C23×D311yescharacteristic
644C2×Dic3C23×D313yes—
645C2×Dic3C23×D311yescharacteristic
646C2×Dic3C23×D311yescharacteristic
647D12—26no—
648D12—34no—
649D12C2×#67112yescomplemented
650C4×D3—26no—
651C4×D3—26no—
652C4×D3—26no—
653C4×D3—22no—
654C4×D3—62no—
655C4×D3—66no—
656C4×D3—66no—
657C4×D3—66no—
658C4×D3—66no—
659C4×D3—66no—
660C4×D3—62no—
661C4×D3—126no—
662C4×D3—123no—
663C4×D3C2×#67112yescomplemented
664Dic6—26no—
665Dic6—66no—
666Dic6—66no—
667Dic6—126no—
668C2×C32—43no—
669C2×C32C23×D411yescharacteristic
670C2×C32C22×#4111yescharacteristic
671C2×C32#58511yescharacteristic
672C3⋊D3—22no—
673C3×D3—26no—
674C3×D3—22no—
675C3×D3—43no—
676C24—33no—
677C24—93no—
678#41—24no—
679#41—38no—
680#41—612no—
681#41—612no—
682#41—64no—
683#41—1812no—
684#41—1812no—
685C2×Q8—33no—
686C2×Q8—64no—
687C2×Q8—93no—
688C2×Q8—184no—
689C2×Q8C2×D3211yescharacteristic
690C2×D4—33no—
691C2×D4—36no—
692C2×D4—36no—
693C2×D4—33no—
694C2×D4—33no—
695C2×D4—612no—
696C2×D4—91no—
697C2×D4—93no—
698C2×D4—96no—
699C2×D4—93no—
700C2×D4—1812no—
701C2×D4—1812no—
702C2×D4C2×D3213yes—
703C22×C4—33no—
704C22×C4—33no—
705C22×C4—33no—
706C22×C4—33no—
707C22×C4—31no—
708C22×C4—33no—
709C22×C4—612no—
710C22×C4—91no—
711C22×C4—93no—
712C22×C4—93no—
713C22×C4—93no—
714C22×C4—93no—
715C22×C4—93no—
716C22×C4—1812no—
717C22×C4C2×D3213yes—
718C4⋊C4—31no—
719C4⋊C4—33no—
720C4⋊C4—93no—
721C4⋊C4—93no—
722C4⋊C4—96no—
723C4⋊C4—93no—
724C4⋊C4—93no—
725C22⋊C4—33no—
726C22⋊C4—33no—
727C22⋊C4—93no—
728C22⋊C4—91no—
729C22⋊C4—93no—
730C22⋊C4—93no—
731C22⋊C4—96no—
732C22⋊C4—96no—
733C22⋊C4—93no—
734C22⋊C4—96no—
735C22⋊C4—91no—
736C42—33no—
737C42—91no—
738C42—93no—
739C42—93no—
740C22×C3—23no—
741C22×C3—23no—
742C22×C3—23no—
743C22×C3—23no—
744C22×C3—23no—
745C22×C3—23no—
746C22×C3—21no—
747C22×C3—36no—
748C22×C3—32no—
749C22×C3—43no—
750C22×C3—43no—
751C22×C3—43no—
752C22×C3—61no—
753C22×C3—63no—
754C22×C3—63no—
755C22×C3—61no—
756C22×C3—63no—
757C22×C3—63no—
758C22×C3—63no—
759C22×C3—1212no—
760C22×C3C24×D311yescharacteristic
761C22×C3C24×D311yescharacteristic
762C2×D3—23no—
763C2×D3—23no—
764C2×D3—21no—
765C2×D3—21no—
766C2×D3—23no—
767C2×D3—23no—
768C2×D3—23no—
769C2×D3—32no—
770C2×D3—32no—
771C2×D3—412no—
772C2×D3—62no—
773C2×D3—61no—
774C2×D3—61no—
775C2×D3—61no—
776C2×D3—61no—
777C2×D3—121no—
778C2×D3—121no—
779C2×D3—1212no—
780C2×D3—1212no—
781C2×D3D3×#4112yescomplemented
782C2×D3C22×#6716yes—
783C3×C4—21no—
784C3×C4—21no—
785C3×C4—26no—
786C3×C4—32no—
787C3×C4—32no—
788C3×C4—41no—
789C3×C4—63no—
790C3×C4—63no—
791C3×C4—61no—
792C3×C4C2×D3×D416yes—
793C3×C4C22×#6716yes—
794Dic3—21no—
795Dic3—23no—
796Dic3—23no—
797Dic3—63no—
798Dic3—63no—
799Dic3—63no—
800Dic3—61no—
801Dic3—61no—
802Dic3—63no—
803Dic3—123no—
804Dic3—123no—
805Dic3—121no—
806Dic3D3×#4112yescomplemented
807Dic3C22×#6712yes—
808C32D4×#4111yescharacteristic, complemented, Sylow
809C23—31no—
810C23—33no—
811C23—33no—
812C23—66no—
813C23—66no—
814C23—91no—
815C23—123no—
816C23—186no—
817C23—186no—
818C23—363no—
819C23C22×D3213yes—
820Q8—66no—
821Q8—186no—
822Q8D3×#6714yescomplemented
823D4—26no—
824D4—312no—
825D4—66no—
826D4—612no—
827D4—66no—
828D4—94no—
829D4—126no—
830D4—186no—
831D4—1812no—
832D4—186no—
833C2×C4—26no—
834C2×C4—31no—
835C2×C4—31no—
836C2×C4—312no—
837C2×C4—33no—
838C2×C4—31no—
839C2×C4—33no—
840C2×C4—62no—
841C2×C4—66no—
842C2×C4—66no—
843C2×C4—66no—
844C2×C4—66no—
845C2×C4—91no—
846C2×C4—93no—
847C2×C4—93no—
848C2×C4—182no—
849C2×C4—186no—
850C2×C4—186no—
851C2×C4—186no—
852C2×C4—186no—
853C2×C4—363no—
854C2×C4C22×D3211yescharacteristic
855C2×C4C22×D3213yes—
856C2×C3—21no—
857C2×C3—21no—
858C2×C3—21no—
859C2×C3—43no—
860C2×C3—43no—
861C2×C3—66no—
862C2×C3—62no—
863C2×C3—83no—
864C2×C3—123no—
865C2×C3C22×D3×D411yescharacteristic
866C2×C3C2×D3×#4111yescharacteristic
867C2×C3C2×D3×#4111yescharacteristic
868C2×C3#596411yescharacteristic
869C2×C3#596611yescharacteristic
870C2×C3C23×#6711yescharacteristic
871D3—22no—
872D3—26no—
873D3—43no—
874D3—62no—
875D3—62no—
876D3—122no—
877C22—23no—
878C22—23no—
879C22—23no—
880C22—32no—
881C22—36no—
882C22—63no—
883C22—63no—
884C22—61no—
885C22—61no—
886C22—63no—
887C22—63no—
888C22—63no—
889C22—92no—
890C22—1212no—
891C22—181no—
892C22—181no—
893C22—3612no—
894C22C23×D3211yescharacteristic
895C4—21no—
896C4—32no—
897C4—32no—
898C4—63no—
899C4—61no—
900C4—63no—
901C4—183no—
902C4—181no—
903C4—183no—
904C4C2×D3×#6716yes—
905C3—21no—
906C3#8676611yescharacteristic, complemented
907C3#41×#6711yescharacteristic, complemented
908C2—43no—
909C2—62no—
910C2—66no—
911C2—123no—
912C2—182no—
913C2D32×#4111yescharacteristic
914C2#1059669611yescharacteristic
915C2C22×D3×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×#41C22
hypercenterC2×#41D32
hypocenterC32D4×#41
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×D3×#41C2semidirect
2. C2×#64319C2semidirect
3. #10596302C2semidirect
4. C3×#5834C2semidirect
5. #10595409C2semidirect
6. Q8×#626C2semidirect
7. Dic3×#239C2semidirect
8. #10595301C2semidirect
9. #10595293C2semidirect
10. #10595228C2semidirect
11. #10595152C2semidirect
12. #10595070C2semidirect
13. C4×D3×#67C2semidirect
14. #10594892C2semidirect
15. #10594887C2semidirect
18. C2×C32×#41C22semidirect
19. C2×Q8×C3⋊D3C22semidirect
22. C2×C3×#239C22semidirect
23. C2×C3×D3×Q8C22semidirect
24. C2×C3×#237C22semidirect
25. C2×C3×D3×D4C22semidirect
26. C2×C3×#235C22semidirect
27. C22×C3×C4×D3C22semidirect
30. C2×#3802C22semidirect
31. C2×C4×D32C22semidirect
32. C2×#3795C22semidirect
33. C2×#3795C22semidirect
34. Q8×C3⋊Dic3C22semidirect
35. #64147C22semidirect
36. #64145C22semidirect
37. C4×#638C22semidirect
38. #64133C22semidirect
39. C3×Q8×Dic3C22semidirect
40. C3×#940C22semidirect
41. C3×#938C22semidirect
42. C3×#930C22semidirect
43. C3×C4×#67C22semidirect
44. #63983C22semidirect
45. #63976C22semidirect
46. Dic3×#67C22semidirect
47. Dic3×#67C22semidirect
48. #63970C22semidirect
49. #63970C22semidirect
50. #63969C22semidirect
51. D3×#217C22semidirect
52. #63952C22semidirect
53. D3×(C2×D3)⋊C4C22semidirect
54. #63908C22semidirect
55. #63905C22semidirect
58. C4×#625C22semidirect
59. #63898C22semidirect
60. Dic3×D12C22semidirect
61. #63879C22semidirect
62. D3×Dic3⋊C4C22semidirect
63. C4×D3×Dic3C22semidirect
64. #63871C22semidirect
65. #63866C22semidirect
66. #63863C22semidirect
67. #63857C22semidirect
68. #63856C22semidirect
69. #63841C22semidirect
73. C2×D3×#41D3semidirect
75. #5834D3semidirect
116. C3×#239D4semidirect
172. C2×C3×#41C2×D3semidirect
173. C2×C3×#41C2×D3semidirect
182. C2×#239C2×D3semidirect
186. C2×D3×Q8C2×D3semidirect
189. C2×#237C2×D3semidirect
193. C2×D3×D4C2×D3semidirect
196. C2×#235C2×D3semidirect
199. C22×C4×D3C2×D3semidirect
213. Q8×Dic3C2×D3semidirect
215. #940C2×D3semidirect
224. #938C2×D3semidirect
238. #930C2×D3semidirect
251. C4×#67C2×D3semidirect
288. C32×Q8C2×D4semidirect
309. C3×D12C2×D4semidirect
314. C3×C4×D3C2×D4semidirect
316. #626#41semidirect
392. #239#67semidirect
487. C2×C3⋊D3C2×#41semidirect
497. C2×C3×D3C2×#41semidirect
508. C3×Dic3C2×#41semidirect
517. C2×#41D32semidirect
587. C3×Q8D3×D4semidirect
588. C3×Q8C2×#67semidirect
649. D12C2×#67semidirect
663. C4×D3C2×#67semidirect
781. C2×D3D3×#41semidirect
806. Dic3D3×#41semidirect
808. C32D4×#41semidirect
822. Q8D3×#67semidirect
906. C3#86766semidirect
907. C3#41×#67semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×#412
C2×#643192
#105963022
C3×#58342
#105954092
Q8×#6262
Dic3×#2392
#105953012
#105952932
#105952282
#105951522
#105950702
C4×D3×#672
#105948922
#105948872
#41×#673
#867663