Finite Group Databasebeta

← #67×#239 #11902845

Subgroups — #67×#239 #11902845

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
1C22×C3×#239C211yesmaximal, characteristic, complemented
2C2×D3×#239C211yesmaximal, characteristic, complemented
3#10596288C211yesmaximal, characteristic, complemented
4C3×Q8×#67C211yesmaximal, characteristic, complemented
5#10595427C213yesmaximal, complemented
6#10595424C213yesmaximal, complemented
7#10595410C211yesmaximal, characteristic, complemented
8#10595409C211yesmaximal, characteristic, complemented
9Dic3×#239C211yesmaximal, characteristic, complemented
10#10595360C213yesmaximal, complemented
11#10595358C213yesmaximal, complemented
12D12×#67C213yesmaximal, complemented
13C4×D3×#67C213yesmaximal, complemented
14#10595005C213yesmaximal, complemented
15#10594889C213yesmaximal, complemented
16#41×#67—31nomaximal
17D4×#239—31nomaximal
18C22×C32×Q8C2211yescharacteristic, complemented
19C2×#3832C2211yescharacteristic, complemented
20C2×C3×#239—28no—
21C2×C3×#239C2211yescharacteristic
22C2×C3×#239C2213yescomplemented
23C2×C3×#239C2213yescomplemented
24C2×C3×#239C2211yescharacteristic, complemented
25C2×C3×D3×Q8C2211yescharacteristic, complemented
26C22×C3×D12C2213yescomplemented
27C22×C3×C4×D3C2213yescomplemented
28C2×D3×#67C2213yes—
29D3×#239—28no—
30C2×D3×D12C2213yescomplemented
31C2×C4×D32C2213yescomplemented
32C2×#3799C2213yescomplemented
33C2×#3796C2213yescomplemented
34#64156C2213yescomplemented
35#64155C2213yescomplemented
36Q8×C3⋊Dic3C2211yescharacteristic, complemented
37#64139C2213yescomplemented
38C4×#638C2213yescomplemented
39C3×#946C2213yescomplemented
40C3×Q8×Dic3C2211yescharacteristic, complemented
41C3×#944C2213yescomplemented
42C3×C4×#67C2213yes—
43C3×#924C2213yescomplemented
44#63977C2216yescomplemented
45Dic3×#67C2211yescharacteristic
46D3×#217C2213yescomplemented
47#63952C2213yescomplemented
48#63922C2216yescomplemented
49D3×(C2×D3)⋊C4C2213yescomplemented
50#63916C2213yescomplemented
51#63911C2213yescomplemented
52#63909C2213yescomplemented
53#63908C2213yescomplemented
54#63904C2213yescomplemented
55#63904C2216yescomplemented
56C4×#626C2213yescomplemented
57C4×#625C2213yescomplemented
58#63898C2213yescomplemented
59Dic3×D12C2213yescomplemented
60#63886C2216yescomplemented
61#63886C2216yescomplemented
62#63884C2216yescomplemented
63#63879C2213yescomplemented
64D3×Dic3⋊C4C2213yescomplemented
65C4×D3×Dic3C2213yescomplemented
66#63863C2213yescomplemented
67#63856C2213yescomplemented
68#63850C2216yescomplemented
69#63841C2213yescomplemented
70C22×C3×#41—31no—
71C2×D3×#41—31no—
72C22×#239—31no—
73C22×#239D311yescharacteristic, complemented
74C3×D4×Q8—31no—
75#5834—31no—
76#5832—33no—
77#5831—31no—
78#5829—33no—
79#5828—33no—
80Dic3×#41—31no—
81#5824—33no—
82#5817—31no—
83#5817—31no—
84#5817—31no—
85#5817—61no—
86Q8×#67D311yescharacteristic, complemented
87#5806—33no—
88D4×#67—33no—
89#5791—33no—
90C2×C4×#67—33no—
91#5726—33no—
92#5725—33no—
93#5630—33no—
94#5630—33no—
95#5627—33no—
96#5627—33no—
97#5577—31no—
98C4×#239—31no—
99D4×D12—33no—
100C4×D3×D4—33no—
101C23×C3×D3C2313yes—
102C22×D32C2313yes—
103C2×C32×Q8—24no—
104C2×C32×Q8C2313yes—
105C2×C32×Q8C2311yescharacteristic
106C22×C32×C4C2313yes—
107C2×#638C2313yes—
108#3832—24no—
109C2×C4⋊(C3⋊D3)C2313yes—
110C2×C4×C3⋊D3C2313yes—
111C2×C3×#67C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C3×#239—24no—
114C3×#239—212no—
115C3×#239—212no—
116C3×#239D418yescomplemented
117C3×D3×Q8—24no—
118C2×C3×D12—212no—
119C2×C3×D12C2313yes—
120C2×C3×D12C2316yes—
121C2×C3×D12C2313yes—
122C2×C3×C4×D3—212no—
123C2×C3×C4×D3C2313yes—
124C2×C3×C4×D3C2313yes—
125C2×C3×C4×D3C2313yes—
126C2×C3×C4×D3C2313yes—
127C2×C3×C4×D3C2313yes—
128C2×C3×Dic6C2313yes—
129D3×#67—212no—
130C2×#626C2316yes—
131C2×#626C2313yes—
132C2×#626C2316yes—
133C2×#625C2313yes—
134C2×#624C2313yes—
135C2×D3×Dic3C2313yes—
136C2×D3×Dic3C2311yescharacteristic
137C2×D3×Dic3C2313yes—
138C2×D3×Dic3C2313yes—
139D3×D12—212no—
140C4×D32—212no—
141#3799—212no—
142#3796—212no—
143#3757C2311yescharacteristic
144#3752C2316yes—
145#3752C2313yes—
146C4⋊(C3⋊Dic3)C2313yes—
147#3750C2313yes—
148C4×C3⋊Dic3C2313yes—
149C3×#217C2313yes—
150C3×(C2×D3)⋊C4C2313yes—
151C3×C4⋊Dic3C2313yes—
152C3×Dic3⋊C4C2316yes—
153C3×Dic3⋊C4C2313yes—
154C3×C4×Dic3C2313yes—
155#3724C2313yes—
156Dic3⋊Dic3C2311yescharacteristic
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—31no—
167C2×C3×#41—33no—
168C2×C3×#41—33no—
169C2×C3×#41—31no—
170C2×C3×#41—68no—
171C22×C3×Q8—21no—
172C22×C3×Q8—31no—
173C22×C3×Q8C2×D311yescharacteristic, complemented
174C22×C3×Q8C2×D311yescharacteristic, complemented
175C22×C3×D4—33no—
176C23×C3×C4—33no—
177C22×#67—33no—
178D3×#41—68no—
179C2×#239—28no—
180C2×#239—31no—
181C2×#239—31no—
182C2×#239—33no—
183C2×#239—33no—
184C2×#239—61no—
185C2×#239—68no—
186C2×#239C2×D311yescharacteristic
187C2×#239C2×D313yescomplemented
188C2×#239C2×D313yescomplemented
189C2×#239C2×D311yescharacteristic, complemented
190C2×D3×Q8C2×D311yescharacteristic, complemented
191C2×#237—33no—
192C2×D3×D4—33no—
193C2×D3×D4—33no—
194C2×#235—33no—
195C22×D12—33no—
196C22×D12C2×D313yescomplemented
197C22×C4×D3—33no—
198C22×C4×D3—33no—
199C22×C4×D3C2×D313yescomplemented
200C3×C4⋊Q8—33no—
201C3×C22⋊Q8—33no—
202C3×C22⋊Q8—33no—
203C3×C4×Q8—31no—
204C3×C4×D4—33no—
205#953—36no—
206C2×#217—33no—
207#947—33no—
208#947—33no—
209#947—33no—
210#947—63no—
211#946—33no—
212#946—33no—
213#946—33no—
214#946—63no—
215#946C2×D313yescomplemented
216Q8×Dic3—31no—
217Q8×Dic3—31no—
218Q8×Dic3—61no—
219Q8×Dic3C2×D311yescharacteristic, complemented
220#944C2×D313yescomplemented
221#940—33no—
222#939—36no—
223#939—36no—
224#938—33no—
225#938—33no—
226#937—36no—
227#936—33no—
228#935—36no—
229D4×Dic3—31no—
230D4×Dic3—33no—
231D4×Dic3—33no—
232#930—33no—
233#930—33no—
234#930—33no—
235#930—33no—
236#930—63no—
237#929—36no—
238C4×#67—33no—
239C4×#67—33no—
240C4×#67—31no—
241C4×#67—33no—
242C4×#67—33no—
243C4×#67—33no—
244C4×#67—33no—
245C4×#67—33no—
246C4×#67—36no—
247C4×#67—33no—
248C4×#67—63no—
249C4×#67C2×D313yes—
250C2×(C2×D3)⋊C4—33no—
251#926—33no—
252#924—33no—
253#924C2×D313yescomplemented
254C2×Dic3⋊C4—33no—
255C2×C4×Dic3—33no—
256#895—36no—
257#895—36no—
258#895—33no—
259#895—33no—
260#894—36no—
261#894—36no—
262#893—33no—
263#893—33no—
264#893—36no—
265#892—33no—
266D3×C4⋊C4—33no—
267#882—36no—
268#882—36no—
269#67⋊C4—33no—
270#67⋊C4—33no—
271D3×C22⋊C4—33no—
272D3×C22⋊C4—33no—
273#874—33no—
274C4×D12—33no—
275C4×D12—33no—
276C42×D3—33no—
277C23×C32C2411yescharacteristic
278C22×C3⋊D3C2413yes—
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×Q8—26no—
289C32×Q8C2×D414yescomplemented
290C2×C32×C4—26no—
291C2×C32×C4C2413yes—
292C2×C32×C4C2413yes—
293#638—26no—
294C2×C3⋊Dic3C2413yes—
295C2×C3⋊Dic3C2411yescharacteristic
296C2×C3⋊Dic3C2411yescharacteristic
297C4⋊(C3⋊D3)—26no—
298C4×C3⋊D3—26no—
299C3×#67#4114yescomplemented
300C2×C3×Dic3—22no—
301C2×C3×Dic3C2413yes—
302C2×C3×Dic3C2413yes—
303C2×C3×Dic3C2411yescharacteristic
304C2×C3×Dic3C2411yescharacteristic
305C2×C3×Dic3C2411yescharacteristic
306C3×D12—212no—
307C3×D12—26no—
308C3×D12C2×D4112yescomplemented
309C3×C4×D3—26no—
310C3×C4×D3—26no—
311C3×C4×D3—26no—
312C3×C4×D3—26no—
313C3×C4×D3C2×D4112yescomplemented
314C3×Dic6—26no—
315#626—212no—
316#626—26no—
317#626—46no—
318#625—26no—
319#624—26no—
320D3×Dic3—26no—
321D3×Dic3—22no—
322D3×Dic3—26no—
323D3×Dic3—43no—
324C22×#41—31no—
325C22×#41—91no—
326#550—91no—
327D4×Q8—31no—
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—38no—
344C3×#41—612no—
345C3×#41—612no—
346C3×#41—64no—
347C2×C3×Q8—24no—
348C2×C3×Q8—24no—
349C2×C3×Q8—21no—
350C2×C3×Q8—23no—
351C2×C3×Q8—33no—
352C2×C3×Q8—44no—
353C2×C3×Q8—64no—
354C2×C3×Q8C22×D313yes—
355C2×C3×Q8C22×D313yes—
356C2×C3×Q8C22×D311yescharacteristic
357C2×C3×Q8C22×D311yescharacteristic
358C2×C3×D4—31no—
359C2×C3×D4—33no—
360C2×C3×D4—36no—
361C2×C3×D4—33no—
362C2×C3×D4—612no—
363C22×C3×C4—23no—
364C22×C3×C4—33no—
365C22×C3×C4—31no—
366C22×C3×C4—33no—
367C22×C3×C4—33no—
368C22×C3×C4—33no—
369C22×C3×C4—33no—
370C22×C3×C4—612no—
371C22×C3×C4C22×D313yes—
372C22×C3×C4C22×D313yes—
373C2×#67—33no—
374C2×#67—33no—
375C2×#67—33no—
376C2×#67—33no—
377C2×#67—33no—
378C2×#67—36no—
379C2×#67—36no—
380C2×#67—63no—
381C2×#67—612no—
382C2×#67C22×D311yescharacteristic
383C22×Dic3—31no—
384C22×Dic3—33no—
385C22×Dic3—33no—
386C22×Dic3—33no—
387C22×Dic3C22×D311yescharacteristic
388#239—24no—
389#239—212no—
390#239—212no—
391#239—64no—
392#239—64no—
393#239—612no—
394#239—612no—
395#239—124no—
396#239#6718yesdirect product factor
397D3×Q8—24no—
398#237—612no—
399D3×D4—612no—
400D3×D4—612no—
401#235—612no—
402C2×D12—212no—
403C2×D12—33no—
404C2×D12—36no—
405C2×D12—33no—
406C2×D12—33no—
407C2×D12—36no—
408C2×D12—63no—
409C2×D12—612no—
410C2×D12C22×D313yes—
411C2×D12C22×D316yes—
412C2×D12C22×D313yes—
413C2×C4×D3—212no—
414C2×C4×D3—33no—
415C2×C4×D3—33no—
416C2×C4×D3—31no—
417C2×C4×D3—33no—
418C2×C4×D3—33no—
419C2×C4×D3—33no—
420C2×C4×D3—33no—
421C2×C4×D3—33no—
422C2×C4×D3—63no—
423C2×C4×D3—612no—
424C2×C4×D3—612no—
425C2×C4×D3C22×D313yes—
426C2×C4×D3C22×D313yes—
427C2×C4×D3C22×D313yes—
428C2×C4×D3C22×D313yes—
429C2×C4×D3C22×D313yes—
430C2×Dic6C22×D313yes—
431C3×C4⋊C4—33no—
432C3×C4⋊C4—33no—
433C3×C4⋊C4—36no—
434C3×C22⋊C4—33no—
435C3×C22⋊C4—33no—
436C3×C42—33no—
437#217—31no—
438#217—31no—
439#217—31no—
440#217—36no—
441#217—36no—
442#217—33no—
443#217—33no—
444#217—61no—
445#217C22×D313yes—
446(C2×D3)⋊C4—33no—
447(C2×D3)⋊C4—36no—
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—33no—
454(C2×D3)⋊C4—36no—
455(C2×D3)⋊C4—33no—
456(C2×D3)⋊C4—33no—
457(C2×D3)⋊C4—63no—
458(C2×D3)⋊C4—66no—
459(C2×D3)⋊C4C22×D313yes—
460C4⋊Dic3—33no—
461C4⋊Dic3—33no—
462C4⋊Dic3—31no—
463C4⋊Dic3—63no—
464C4⋊Dic3C22×D313yes—
465Dic3⋊C4—33no—
466Dic3⋊C4—33no—
467Dic3⋊C4—33no—
468Dic3⋊C4—31no—
469Dic3⋊C4—33no—
470Dic3⋊C4—63no—
471Dic3⋊C4C22×D313yes—
472Dic3⋊C4C22×D316yes—
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—21no—
482C22×C32—21no—
483C22×C32C2×#4112yescomplemented
484C22×C32C2511yescharacteristic
485C2×C3⋊D3—23no—
486C2×C3⋊D3—23no—
487C2×C3⋊D3—23no—
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—23no—
500C32×C4C22×D416yes—
501C3⋊Dic3—21no—
502C3⋊Dic3—23no—
503C3⋊Dic3—21no—
504C3×Dic3—23no—
505C3×Dic3—21no—
506C3×Dic3—23no—
507C3×Dic3C22×D412yes—
508C3×Dic3C2×#4112yescomplemented
509C2×#41—31no—
510C2×#41—33no—
511C2×#41—33no—
512C2×#41—31no—
513C2×#41—68no—
514C2×#41—93no—
515C2×#41—93no—
516C2×#41—91no—
517C2×#41—188no—
518C22×Q8—31no—
519C22×Q8D3211yescharacteristic, complemented
520C22×D4—33no—
521C22×D4—93no—
522C22×D4—93no—
523C23×C4—33no—
524C23×C4—93no—
525C4⋊Q8—33no—
526#127—93no—
527#124—93no—
528#124—93no—
529#123—96no—
530#123—96no—
531C22⋊Q8—33no—
532C22⋊Q8—33no—
533C22⋊Q8—93no—
534C22⋊Q8—93no—
535#121—93no—
536#121—93no—
537#121—96no—
538#121—96no—
539#121—93no—
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—93no—
551C4×D4—96no—
552C4×D4—93no—
553C4×D4—93no—
554C4×D4—91no—
555C4×D4—93no—
556#117—93no—
557C2×C4⋊C4—93no—
558C2×C22⋊C4—93no—
559C2×C22⋊C4—93no—
560C2×C42—93no—
561C23×C3—21no—
562C23×C3—33no—
563C23×C3—31no—
564C23×C3—33no—
565C23×C3—66no—
566C23×C3—66no—
567C23×C3—123no—
568C23×C3C23×D311yescharacteristic
569C23×C3C23×D311yescharacteristic
570C22×D3—26no—
571C22×D3—26no—
572C22×D3—33no—
573C22×D3—33no—
574C22×D3—43no—
575C22×D3—63no—
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—26no—
586C3×Q8—26no—
587C3×Q8—24no—
588C3×Q8—46no—
589C3×Q8—66no—
590C3×Q8D3×D414yescomplemented
591C3×Q8C2×#6714yescomplemented
592C3×D4—34no—
593C3×D4—312no—
594C3×D4—612no—
595C3×D4—66no—
596C2×C3×C4—26no—
597C2×C3×C4—26no—
598C2×C3×C4—23no—
599C2×C3×C4—23no—
600C2×C3×C4—31no—
601C2×C3×C4—31no—
602C2×C3×C4—312no—
603C2×C3×C4—33no—
604C2×C3×C4—31no—
605C2×C3×C4—33no—
606C2×C3×C4—46no—
607C2×C3×C4—66no—
608C2×C3×C4—66no—
609C2×C3×C4—62no—
610C2×C3×C4—66no—
611C2×C3×C4—66no—
612C2×C3×C4C23×D313yes—
613C2×C3×C4C23×D313yes—
614C2×C3×C4C23×D313yes—
615C2×C3×C4C23×D313yes—
616#67—612no—
617#67—66no—
618#67—66no—
619#67—66no—
620#67—66no—
621#67—66no—
622#67—126no—
623#67—126no—
624#67#23914yesdirect product factor
625C2×Dic3—22no—
626C2×Dic3—31no—
627C2×Dic3—31no—
628C2×Dic3—33no—
629C2×Dic3—33no—
630C2×Dic3—31no—
631C2×Dic3—31no—
632C2×Dic3—61no—
633C2×Dic3—63no—
634C2×Dic3—61no—
635C2×Dic3—66no—
636C2×Dic3—66no—
637C2×Dic3—62no—
638C2×Dic3—123no—
639C2×Dic3C23×D313yes—
640C2×Dic3C23×D311yescharacteristic
641C2×Dic3C23×D313yes—
642C2×Dic3C23×D311yescharacteristic
643C2×Dic3C23×D311yescharacteristic
644D12—212no—
645D12—26no—
646D12—66no—
647D12—612no—
648D12—66no—
649D12—66no—
650D12—126no—
651D12—126no—
652D12C2×#67112yescomplemented
653C4×D3—26no—
654C4×D3—26no—
655C4×D3—26no—
656C4×D3—26no—
657C4×D3—66no—
658C4×D3—62no—
659C4×D3—66no—
660C4×D3—66no—
661C4×D3—66no—
662C4×D3—66no—
663C4×D3—66no—
664C4×D3—126no—
665C4×D3—123no—
666C4×D3C2×#67112yescomplemented
667Dic6—26no—
668C2×C32—22no—
669C2×C32C23×D411yescharacteristic
670C2×C32C22×#4111yescharacteristic
671C2×C32#58511yescharacteristic
672C3⋊D3—43no—
673C3×D3—22no—
674C3×D3—26no—
675C3×D3—43no—
676C24—33no—
677C24—93no—
678#41—38no—
679#41—612no—
680#41—612no—
681#41—64no—
682#41—1812no—
683#41—1812no—
684#41—184no—
685C2×Q8—24no—
686C2×Q8—33no—
687C2×Q8—64no—
688C2×Q8C2×D3213yes—
689C2×Q8C2×D3211yescharacteristic
690C2×D4—31no—
691C2×D4—33no—
692C2×D4—36no—
693C2×D4—33no—
694C2×D4—612no—
695C2×D4—93no—
696C2×D4—96no—
697C2×D4—96no—
698C2×D4—93no—
699C2×D4—93no—
700C2×D4—93no—
701C2×D4—1812no—
702C2×D4—1812no—
703C22×C4—33no—
704C22×C4—31no—
705C22×C4—33no—
706C22×C4—33no—
707C22×C4—33no—
708C22×C4—33no—
709C22×C4—612no—
710C22×C4—93no—
711C22×C4—93no—
712C22×C4—93no—
713C22×C4—91no—
714C22×C4—93no—
715C22×C4—93no—
716C22×C4—1812no—
717C22×C4C2×D3213yes—
718C4⋊C4—33no—
719C4⋊C4—33no—
720C4⋊C4—36no—
721C4⋊C4—91no—
722C4⋊C4—93no—
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—91no—
734C22⋊C4—93no—
735C22⋊C4—96no—
736C42—33no—
737C42—91no—
738C42—93no—
739C42—93no—
740C22×C3—21no—
741C22×C3—21no—
742C22×C3—21no—
743C22×C3—21no—
744C22×C3—22no—
745C22×C3—21no—
746C22×C3—36no—
747C22×C3—32no—
748C22×C3—41no—
749C22×C3—41no—
750C22×C3—63no—
751C22×C3—61no—
752C22×C3—63no—
753C22×C3—61no—
754C22×C3—63no—
755C22×C3—63no—
756C22×C3—63no—
757C22×C3—1212no—
758C22×C3C2×#23912yescomplemented
759C22×C3D3×#4112yescomplemented
760C22×C3C24×D311yescharacteristic
761C22×C3C24×D311yescharacteristic
762C2×D3—21no—
763C2×D3—23no—
764C2×D3—23no—
765C2×D3—21no—
766C2×D3—23no—
767C2×D3—23no—
768C2×D3—23no—
769C2×D3—412no—
770C2×D3—63no—
771C2×D3—63no—
772C2×D3—63no—
773C2×D3—63no—
774C2×D3—63no—
775C2×D3—63no—
776C2×D3—123no—
777C2×D3—123no—
778C2×D3—123no—
779C2×D3—1212no—
780C2×D3—1212no—
781C2×D3C2×#23912yescomplemented
782C2×D3C22×#6716yes—
783C3×C4—23no—
784C3×C4—23no—
785C3×C4—26no—
786C3×C4—32no—
787C3×C4—32no—
788C3×C4—43no—
789C3×C4—61no—
790C3×C4—63no—
791C3×C4—63no—
792C3×C4C2×D3×D416yes—
793C3×C4C22×#6716yes—
794Dic3—23no—
795Dic3—23no—
796Dic3—21no—
797Dic3—61no—
798Dic3—63no—
799Dic3—63no—
800Dic3—61no—
801Dic3—61no—
802Dic3—61no—
803Dic3—121no—
804Dic3—123no—
805Dic3—121no—
806Dic3C2×#23912yescomplemented
807Dic3C22×#6712yes—
808C32D4×#4111yescharacteristic, complemented, Sylow
809C23—31no—
810C23—33no—
811C23—33no—
812C23—66no—
813C23—66no—
814C23—93no—
815C23—123no—
816C23—186no—
817C23—186no—
818C23—363no—
819C23C22×D3211yescharacteristic
820Q8—26no—
821Q8—66no—
822Q8D3×#6714yescomplemented
823D4—34no—
824D4—312no—
825D4—612no—
826D4—66no—
827D4—186no—
828D4—1812no—
829D4—186no—
830D4—186no—
831D4—186no—
832D4—366no—
833C2×C4—26no—
834C2×C4—31no—
835C2×C4—31no—
836C2×C4—312no—
837C2×C4—33no—
838C2×C4—33no—
839C2×C4—31no—
840C2×C4—66no—
841C2×C4—66no—
842C2×C4—62no—
843C2×C4—66no—
844C2×C4—66no—
845C2×C4—91no—
846C2×C4—93no—
847C2×C4—91no—
848C2×C4—186no—
849C2×C4—182no—
850C2×C4—186no—
851C2×C4—186no—
852C2×C4—186no—
853C2×C4—363no—
854C2×C4C22×D3213yes—
855C2×C4C22×D3213yes—
856C2×C3—22no—
857C2×C3—22no—
858C2×C3—21no—
859C2×C3—21no—
860C2×C3—21no—
861C2×C3—42no—
862C2×C3—66no—
863C2×C3—62no—
864C2×C3—123no—
865C2×C3C22×D3×D411yescharacteristic
866C2×C3C22×#23911yescharacteristic
867C2×C3C2×D3×#4111yescharacteristic
868C2×C3#596411yescharacteristic
869C2×C3#596811yescharacteristic
870C2×C3C23×#6711yescharacteristic
871D3—22no—
872D3—26no—
873D3—43no—
874D3—123no—
875D3—123no—
876D3—243no—
877C22—21no—
878C22—21no—
879C22—32no—
880C22—36no—
881C22—63no—
882C22—63no—
883C22—61no—
884C22—61no—
885C22—63no—
886C22—63no—
887C22—63no—
888C22—1212no—
889C22—183no—
890C22—183no—
891C22—183no—
892C22—3612no—
893C22D3×#23912yescomplemented
894C22C23×D3211yescharacteristic
895C4—23no—
896C4—32no—
897C4—32no—
898C4—63no—
899C4—61no—
900C4—63no—
901C4—183no—
902C4—181no—
903C4—181no—
904C4C2×D3×#6716yes—
905C3—21no—
906C3D4×#23911yescharacteristic, complemented
907C3#41×#6711yescharacteristic, complemented
908C2—22no—
909C2—66no—
910C2—62no—
911C2—123no—
912C2—363no—
913C2C2×D3×#23911yescharacteristic
914C2#1059668811yescharacteristic
915C2C22×D3×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC22×C32×Q8C22
hypercenterC22×Q8D32
hypocenterC32D4×#41
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×C3×#239C2semidirect
2. C2×D3×#239C2semidirect
3. #10596288C2semidirect
4. C3×Q8×#67C2semidirect
5. #10595427C2semidirect
6. #10595424C2semidirect
7. #10595410C2semidirect
8. #10595409C2semidirect
9. Dic3×#239C2semidirect
10. #10595360C2semidirect
11. #10595358C2semidirect
12. D12×#67C2semidirect
13. C4×D3×#67C2semidirect
14. #10595005C2semidirect
15. #10594889C2semidirect
18. C22×C32×Q8C22semidirect
19. C2×#3832C22semidirect
22. C2×C3×#239C22semidirect
23. C2×C3×#239C22semidirect
24. C2×C3×#239C22semidirect
25. C2×C3×D3×Q8C22semidirect
26. C22×C3×D12C22semidirect
27. C22×C3×C4×D3C22semidirect
30. C2×D3×D12C22semidirect
31. C2×C4×D32C22semidirect
32. C2×#3799C22semidirect
33. C2×#3796C22semidirect
34. #64156C22semidirect
35. #64155C22semidirect
36. Q8×C3⋊Dic3C22semidirect
37. #64139C22semidirect
38. C4×#638C22semidirect
39. C3×#946C22semidirect
40. C3×Q8×Dic3C22semidirect
41. C3×#944C22semidirect
43. C3×#924C22semidirect
44. #63977C22semidirect
46. D3×#217C22semidirect
47. #63952C22semidirect
48. #63922C22semidirect
49. D3×(C2×D3)⋊C4C22semidirect
50. #63916C22semidirect
51. #63911C22semidirect
52. #63909C22semidirect
53. #63908C22semidirect
54. #63904C22semidirect
55. #63904C22semidirect
56. C4×#626C22semidirect
57. C4×#625C22semidirect
58. #63898C22semidirect
59. Dic3×D12C22semidirect
60. #63886C22semidirect
61. #63886C22semidirect
62. #63884C22semidirect
63. #63879C22semidirect
64. D3×Dic3⋊C4C22semidirect
65. C4×D3×Dic3C22semidirect
66. #63863C22semidirect
67. #63856C22semidirect
68. #63850C22semidirect
69. #63841C22semidirect
73. C22×#239D3semidirect
86. Q8×#67D3semidirect
116. C3×#239D4semidirect
173. C22×C3×Q8C2×D3semidirect
174. C22×C3×Q8C2×D3semidirect
187. C2×#239C2×D3semidirect
188. C2×#239C2×D3semidirect
189. C2×#239C2×D3semidirect
190. C2×D3×Q8C2×D3semidirect
196. C22×D12C2×D3semidirect
199. C22×C4×D3C2×D3semidirect
215. #946C2×D3semidirect
219. Q8×Dic3C2×D3semidirect
220. #944C2×D3semidirect
253. #924C2×D3semidirect
289. C32×Q8C2×D4semidirect
299. C3×#67#41semidirect
308. C3×D12C2×D4semidirect
313. C3×C4×D3C2×D4semidirect
396. #239#67direct (N × H)
483. C22×C32C2×#41semidirect
497. C2×C3×D3C2×#41semidirect
508. C3×Dic3C2×#41semidirect
519. C22×Q8D32semidirect
590. C3×Q8D3×D4semidirect
591. C3×Q8C2×#67semidirect
624. #67#239direct (N × H)
652. D12C2×#67semidirect
666. C4×D3C2×#67semidirect
758. C22×C3C2×#239semidirect
759. C22×C3D3×#41semidirect
781. C2×D3C2×#239semidirect
806. Dic3C2×#239semidirect
808. C32D4×#41semidirect
822. Q8D3×#67semidirect
893. C22D3×#239semidirect
906. C3D4×#239semidirect
907. C3#41×#67semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2392
C2×D3×#2392
#105962882
C3×Q8×#672
#105954272
#105954242
#105954102
#105954092
Dic3×#2392
#105953602
#105953582
D12×#672
C4×D3×#672
#105950052
#105948892
#41×#673
D4×#2393