Finite Group Databasebeta

← #11904218

Subgroups — #11904218

Order 1152.

2288 conjugacy classes of subgroups.

The subgroup lattice has 765 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596040C211yesmaximal, characteristic, complemented
2C3×#5576C211yesmaximal, characteristic, complemented
3C3×C4×D3×Q8C211yesmaximal, characteristic, complemented
4#10595409C211yesmaximal, characteristic, complemented
5Q8×#625C211yesmaximal, characteristic, complemented
6Dic3×#239C211yesmaximal, characteristic, complemented
7D3×Q8×Dic3C211yesmaximal, characteristic, complemented
8#10594551C213yesmaximal, complemented
9#10594426C213yesmaximal, complemented
10#10594385C213yesmaximal, complemented
11#10594370C213yesmaximal, complemented
12#10593942C213yesmaximal, complemented
13#10593921C213yesmaximal, complemented
14#10593917C213yesmaximal, complemented
15C4×#3795C213yesmaximal, complemented
16#86712—31nomaximal
17#85817—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C2×C3×D3×Q8C2211yescharacteristic
21C2×#3795C2213yes—
22C32×C4×Q8C2211yescharacteristic
23Q8×C3⋊Dic3C2211yescharacteristic
24Q8×C3⋊Dic3C2211yescharacteristic
25#64099C2213yes—
26#64097C2213yes—
27#64079C2213yes—
28C4×#634C2213yes—
29C3×Q8×Dic3C2211yescharacteristic
30C3×#897C2213yes—
31C3×#895C2213yes—
32C3×D3×C4⋊C4C2213yes—
33C3×#887C2213yes—
34C3×#875C2213yes—
35C3×C4×D12C2213yes—
36C3×C42×D3C2213yes—
37C3×C4×Dic6C2213yes—
38#63908C2213yes—
39#63905C2216yes—
40C4×#625C2213yes—
41C4×#625C2213yes—
42#63898C2213yes—
43#63896C2216yes—
44Dic3×D12C2213yes—
45Dic3×D12C2213yes—
46D3×C4⋊Dic3C2213yes—
47#63884C2216yes—
48#63879C2211yescharacteristic
49#63879C2213yes—
50#63877C2216yes—
51#63877C2213yes—
52#63877C2213yes—
53C4×D3×Dic3C2213yes—
54C4×D3×Dic3C2213yes—
55#63873C2213yes—
56#63863C2213yes—
57#63861C2216yes—
58#63859C2216yes—
59#63856C2213yes—
60#63856C2213yes—
61#63856C2213yes—
62#63847C2216yes—
63#63844C2213yes—
64#63843C2213yes—
65Dic3×Dic6C2213yes—
66#63841C2213yes—
67#63841C2213yes—
68C3×#548—31no—
69C2×C3×C4×Q8—31no—
70#5831—31no—
71Dic3×#41—31no—
72#5817—31no—
73Q8×#67—31no—
74Q8×#67—31no—
75C2×Q8×Dic3—31no—
76#5680—33no—
77#5671—33no—
78#5639—33no—
79#5622—33no—
80#5611—33no—
81#5600—33no—
82#5581—33no—
83#5580—33no—
84#5578—33no—
85#5576D311yescharacteristic, complemented
86C4×#239—31no—
87C4×D3×Q8—31no—
88C4×D3×Q8D311yescharacteristic, complemented
89#5569—31no—
90#5569—31no—
91#5569—61no—
92#5568—33no—
93#5541—33no—
94C4×#237—33no—
95#5513—33no—
96#5507—33no—
97#5479—33no—
98C4×#235—33no—
99C2×C32×Q8C2311yescharacteristic
100C2×#634C2313yes—
101C3×#239—24no—
102C3×D3×Q8—24no—
103C3×D3×Q8—24no—
104C2×C3×D12C2313yes—
105C2×C3×D12C2313yes—
106C2×C3×C4×D3C2313yes—
107C2×C3×C4×D3C2313yes—
108C2×C3×C4×D3C2313yes—
109C2×C3×C4×D3C2313yes—
110C2×C3×C4×D3C2311yescharacteristic
111C2×C3×Dic6C2313yes—
112C2×C3×Dic6C2313yes—
113C2×#625C2313yes—
114C2×#625C2311yescharacteristic
115C2×D3×Dic3C2313yes—
116C2×D3×Dic3C2313yes—
117C2×D3×Dic3C2311yescharacteristic
118C2×D3×Dic3C2313yes—
119#3795—212no—
120C32×C4⋊C4C2313yes—
121C32×C42C2313yes—
122C4⋊(C3⋊Dic3)C2313yes—
123C4⋊(C3⋊Dic3)C2313yes—
124C4⋊(C3⋊Dic3)C2313yes—
125#3750C2311yescharacteristic
126#3750C2313yes—
127#3750C2316yes—
128C4×C3⋊Dic3C2313yes—
129C4×C3⋊Dic3C2313yes—
130C3×(C2×D3)⋊C4C2316yes—
131C3×(C2×D3)⋊C4C2313yes—
132C3×(C2×D3)⋊C4C2311yescharacteristic
133C3×C4⋊Dic3C2313yes—
134C3×C4⋊Dic3C2313yes—
135C3×Dic3⋊C4C2316yes—
136C3×C4×Dic3C2313yes—
137C3×C4×Dic3C2313yes—
138C3×C4×Dic3C2313yes—
139#3724C2313yes—
140#3724C2313yes—
141#3724C2316yes—
142Dic3⋊Dic3C2316yes—
143(C2×D3)⋊Dic3C2311yescharacteristic
144(C2×D3)⋊Dic3C2313yes—
145(C2×D3)⋊Dic3C2316yes—
146(C2×D3)⋊Dic3C2313yes—
147(C2×D3)⋊Dic3C2316yes—
148(C2×D3)⋊Dic3C2313yes—
149Dic32C2313yes—
150Dic32C2313yes—
151Dic32C2313yes—
152Dic32C2311yescharacteristic
153#3482—91noSylow
154C2×C3×#41—31no—
155C22×C3×Q8—31no—
156C22×C3×Q8—31no—
157C2×#239C2×D311yescharacteristic
158C2×D3×Q8C2×D311yescharacteristic
159C2×D3×Q8C2×D311yescharacteristic
160C2×#237—33no—
161C2×#235—33no—
162C3×#124—33no—
163C3×C22⋊Q8—33no—
164C3×#121—33no—
165C3×C4×Q8—21no—
166C3×C4×Q8—31no—
167C3×C4×Q8—33no—
168C3×C4×Q8—33no—
169C3×C4×Q8C2×D311yescharacteristic
170C3×C4×Q8C2×D311yescharacteristic
171C3×C4×D4—33no—
172C2×C3×C4⋊C4—33no—
173C2×C3×C42—33no—
174#947—33no—
175#946—33no—
176#946—33no—
177#946—33no—
178Q8×Dic3—31no—
179Q8×Dic3—31no—
180Q8×Dic3—31no—
181Q8×Dic3—31no—
182Q8×Dic3—33no—
183Q8×Dic3—33no—
184Q8×Dic3—61no—
185Q8×Dic3—61no—
186Q8×Dic3C2×D311yescharacteristic
187#944—33no—
188#944—33no—
189#938—33no—
190#936—33no—
191#935—36no—
192D4×Dic3—33no—
193D4×Dic3—33no—
194D4×Dic3—33no—
195#930—33no—
196#929—36no—
197C4×#67—33no—
198C4×#67—33no—
199C4×#67—33no—
200C4×#67—33no—
201C4×#67—31no—
202C4×#67—33no—
203#926—33no—
204#926—33no—
205C2×C4⋊Dic3—33no—
206#924—33no—
207#924—33no—
208#924—33no—
209C2×C4×Dic3—33no—
210C2×C4×Dic3—33no—
211#898—36no—
212#897C2×D313yes—
213#896—36no—
214#895C2×D313yes—
215#894—36no—
216#893—33no—
217#892—33no—
218#892—33no—
219D3×C4⋊C4—33no—
220D3×C4⋊C4C2×D313yes—
221#890—33no—
222#890—33no—
223#890—63no—
224#889—36no—
225#889—36no—
226#888—33no—
227#888—33no—
228#888—63no—
229#887—33no—
230#887—33no—
231#887C2×D313yes—
232#883—36no—
233#67⋊C4—33no—
234#67⋊C4—31no—
235#879—36no—
236#879—36no—
237#878—36no—
238#877—33no—
239#877—36no—
240#877—33no—
241#876—36no—
242#875C2×D313yes—
243C4×D12—33no—
244C4×D12—33no—
245C4×D12C2×D313yes—
246#872—33no—
247#872—33no—
248#872—36no—
249C42×D3—33no—
250C42×D3—33no—
251C42×D3C2×D313yes—
252#870—33no—
253#870—33no—
254#870—63no—
255C4×Dic6—33no—
256C4×Dic6—33no—
257C4×Dic6—33no—
258C4×Dic6—33no—
259C4×Dic6—63no—
260C4×Dic6C2×D313yes—
261C22×C3×D3C2413yes—
262C22×C3×D3C2411yescharacteristic
263C22×C3×D3C2411yescharacteristic
264C32×Q8#4114yescomplemented
265C2×C32×C4C2411yescharacteristic
266C2×C32×C4C2413yes—
267C2×C32×C4C2413yes—
268C2×C3⋊Dic3C2411yescharacteristic
269C2×C3⋊Dic3C2413yes—
270C2×C3⋊Dic3C2413yes—
271C2×C3⋊Dic3C2411yescharacteristic
272#634—26no—
273C2×C3×Dic3C2411yescharacteristic
274C2×C3×Dic3C2413yes—
275C2×C3×Dic3C2413yes—
276C2×C3×Dic3C2413yes—
277C2×C3×Dic3C2411yescharacteristic
278C3×D12—26no—
279C3×D12—26no—
280C3×C4×D3—26no—
281C3×C4×D3—26no—
282C3×C4×D3—26no—
283C3×C4×D3—26no—
284C3×C4×D3—22no—
285C3×Dic6—26no—
286C3×Dic6—26no—
287#625—26no—
288#625#4114yescomplemented
289D3×Dic3—26no—
290D3×Dic3—26no—
291D3×Dic3—22no—
292D3×Dic3—26no—
293#557—91no—
294#556—93no—
295#552—93no—
296#552—93no—
297D4×Q8—91no—
298#548—31no—
299#548—91no—
300#547—93no—
301#533—93no—
302#529—93no—
303#529—93no—
304C4×#41—93no—
305C4×#41—91no—
306C2×C4×Q8—31no—
307C2×C4×Q8—91no—
308C3×#41—64no—
309C2×C3×Q8—21no—
310C2×C3×Q8—33no—
311C2×C3×Q8—33no—
312C2×C3×Q8—64no—
313C2×C3×Q8—64no—
314C2×C3×Q8C22×D311yescharacteristic
315C2×C3×Q8C22×D311yescharacteristic
316C2×C3×D4—33no—
317C2×C3×D4—33no—
318C22×C3×C4—33no—
319C22×C3×C4—33no—
320C22×C3×C4—33no—
321C22×C3×C4—33no—
322C22×C3×C4—31no—
323C2×#67—31no—
324C2×#67—31no—
325C2×#67—33no—
326C2×#67—33no—
327C22×Dic3—33no—
328C22×Dic3—33no—
329C22×Dic3—33no—
330C22×Dic3—31no—
331#239—24no—
332D3×Q8—24no—
333D3×Q8—24no—
334#237—612no—
335#235—612no—
336C2×D12C22×D313yes—
337C2×D12C22×D313yes—
338C2×C4×D3—31no—
339C2×C4×D3—33no—
340C2×C4×D3—33no—
341C2×C4×D3—33no—
342C2×C4×D3C22×D313yes—
343C2×C4×D3C22×D313yes—
344C2×C4×D3C22×D311yescharacteristic
345C2×C4×D3C22×D313yes—
346C2×C4×D3C22×D313yes—
347C2×Dic6—33no—
348C2×Dic6—33no—
349C2×Dic6—63no—
350C2×Dic6C22×D313yes—
351C2×Dic6C22×D313yes—
352C3×C4⋊C4—23no—
353C3×C4⋊C4—33no—
354C3×C4⋊C4—33no—
355C3×C4⋊C4—36no—
356C3×C4⋊C4C22×D313yes—
357C3×C4⋊C4C22×D313yes—
358C3×C22⋊C4—31no—
359C3×C22⋊C4—36no—
360C3×C22⋊C4—33no—
361C3×C42—23no—
362C3×C42—33no—
363C3×C42—33no—
364C3×C42—33no—
365C3×C42C22×D313yes—
366C3×C42C22×D313yes—
367#217—36no—
368#217—33no—
369#217—33no—
370#217—36no—
371#217—33no—
372#217—31no—
373(C2×D3)⋊C4—33no—
374(C2×D3)⋊C4—33no—
375(C2×D3)⋊C4—36no—
376(C2×D3)⋊C4—36no—
377(C2×D3)⋊C4—33no—
378(C2×D3)⋊C4—31no—
379(C2×D3)⋊C4C22×D311yescharacteristic
380(C2×D3)⋊C4C22×D313yes—
381(C2×D3)⋊C4C22×D316yes—
382C4⋊Dic3—33no—
383C4⋊Dic3—33no—
384C4⋊Dic3—33no—
385C4⋊Dic3—33no—
386C4⋊Dic3—33no—
387C4⋊Dic3—33no—
388C4⋊Dic3—36no—
389C4⋊Dic3—63no—
390C4⋊Dic3—63no—
391C4⋊Dic3—63no—
392C4⋊Dic3C22×D313yes—
393C4⋊Dic3C22×D313yes—
394Dic3⋊C4—31no—
395Dic3⋊C4—31no—
396Dic3⋊C4—33no—
397Dic3⋊C4—33no—
398Dic3⋊C4—36no—
399Dic3⋊C4—36no—
400Dic3⋊C4—33no—
401Dic3⋊C4—33no—
402Dic3⋊C4—36no—
403Dic3⋊C4—36no—
404Dic3⋊C4—33no—
405Dic3⋊C4—36no—
406Dic3⋊C4—33no—
407Dic3⋊C4—61no—
408Dic3⋊C4—63no—
409Dic3⋊C4—66no—
410Dic3⋊C4C22×D316yes—
411C4×Dic3—33no—
412C4×Dic3—33no—
413C4×Dic3—33no—
414C4×Dic3—33no—
415C4×Dic3—31no—
416C4×Dic3—33no—
417C4×Dic3—33no—
418C4×Dic3—33no—
419C4×Dic3—33no—
420C4×Dic3—33no—
421C4×Dic3—33no—
422C4×Dic3—31no—
423C4×Dic3—63no—
424C4×Dic3—63no—
425C4×Dic3C22×D313yes—
426C4×Dic3C22×D313yes—
427C4×Dic3C22×D313yes—
428C22×C32C2511yescharacteristic
429C2×C3×D3—21no—
430C2×C3×D3—21no—
431C2×C3×D3—21no—
432C2×C3×D3—21no—
433C2×C3×D3—23no—
434C2×C3×D3—23no—
435C2×C3×D3—23no—
436C2×C3×D3C2×#4112yes—
437C2×C3×D3C2×#4112yes—
438C32×C4—23no—
439C32×C4—21no—
440C32×C4C2×#4116yes—
441C3⋊Dic3—23no—
442C3⋊Dic3—21no—
443C3⋊Dic3—23no—
444C3⋊Dic3C2×#4112yes—
445C3×Dic3—23no—
446C3×Dic3—23no—
447C3×Dic3—23no—
448C3×Dic3—21no—
449C3×Dic32−1+412yes—
450C2×#41—31no—
451C2×#41—93no—
452C22×Q8—31no—
453C22×Q8—31no—
454C4⋊Q8—93no—
455C4⋊Q8—93no—
456#126—96no—
457#126—96no—
458#125—96no—
459#125—93no—
460#125—93no—
461#124—33no—
462#124—93no—
463#123—96no—
464#123—96no—
465C22⋊Q8—33no—
466C22⋊Q8—96no—
467C22⋊Q8—93no—
468C22⋊Q8—93no—
469C22⋊Q8—93no—
470#121—33no—
471#121—93no—
472C4×Q8—31no—
473C4×Q8—33no—
474C4×Q8—33no—
475C4×Q8—93no—
476C4×Q8—93no—
477C4×Q8—93no—
478C4×Q8—91no—
479C4×Q8—91no—
480C4×Q8—93no—
481C4×Q8D3211yescharacteristic
482C4×D4—33no—
483C4×D4—93no—
484C4×D4—93no—
485C4×D4—91no—
486C4×D4—93no—
487C4×D4—93no—
488C4×D4—93no—
489C4×D4—93no—
490#117—93no—
491#117—93no—
492#117—96no—
493#117—93no—
494#117—93no—
495C2×C4⋊C4—33no—
496C2×C4⋊C4—93no—
497C2×C42—33no—
498C2×C42—93no—
499C2×C42—93no—
500C23×C3—31no—
501C23×C3—31no—
502C23×C3—33no—
503C22×D3C23×D313yes—
504C22×D3C23×D311yescharacteristic
505C22×D3C23×D311yescharacteristic
506C3×Q8—24no—
507C3×Q8—66no—
508C3×Q8—66no—
509C3×Q8#23514yescomplemented
510C3×Q8#23714yescomplemented
511C3×D4—66no—
512C3×D4—66no—
513C2×C3×C4—23no—
514C2×C3×C4—21no—
515C2×C3×C4—23no—
516C2×C3×C4—31no—
517C2×C3×C4—31no—
518C2×C3×C4—33no—
519C2×C3×C4—33no—
520C2×C3×C4—33no—
521C2×C3×C4—62no—
522C2×C3×C4—66no—
523C2×C3×C4—66no—
524C2×C3×C4—66no—
525C2×C3×C4—66no—
526C2×C3×C4C23×D311yescharacteristic
527C2×C3×C4C23×D313yes—
528C2×C3×C4C23×D311yescharacteristic
529C2×C3×C4C23×D313yes—
530C2×C3×C4C23×D313yes—
531C2×C3×C4C23×D313yes—
532#67—34no—
533#67—34no—
534#67—66no—
535#67—66no—
536C2×Dic3—31no—
537C2×Dic3—31no—
538C2×Dic3—31no—
539C2×Dic3—31no—
540C2×Dic3—33no—
541C2×Dic3—33no—
542C2×Dic3—33no—
543C2×Dic3—33no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—63no—
547C2×Dic3—63no—
548C2×Dic3—66no—
549C2×Dic3—66no—
550C2×Dic3—62no—
551C2×Dic3—66no—
552C2×Dic3C23×D311yescharacteristic
553C2×Dic3C23×D313yes—
554C2×Dic3C23×D313yes—
555C2×Dic3C23×D313yes—
556C2×Dic3C23×D311yescharacteristic
557D12—26no—
558D12—26no—
559C4×D3—26no—
560C4×D3—26no—
561C4×D3—26no—
562C4×D3—26no—
563C4×D3—22no—
564C4×D3—66no—
565C4×D3—62no—
566C4×D3—66no—
567C4×D3—66no—
568Dic6—26no—
569Dic6—26no—
570Dic6—66no—
571Dic6—66no—
572Dic6—126no—
573C2×C32C22×#4111yescharacteristic
574C2×C32C22×#4111yescharacteristic
575C2×C32C2×2−1+411yescharacteristic
576C3×D3—22no—
577C3×D3—22no—
578C3×D3—43no—
579#41—64no—
580#41—1812no—
581C2×Q8—33no—
582C2×Q8—33no—
583C2×Q8—64no—
584C2×Q8—64no—
585C2×Q8—93no—
586C2×Q8C2×D3211yescharacteristic
587C2×D4—33no—
588C2×D4—33no—
589C2×D4—91no—
590C2×D4—93no—
591C22×C4—31no—
592C22×C4—33no—
593C22×C4—33no—
594C22×C4—33no—
595C22×C4—33no—
596C22×C4—91no—
597C22×C4—93no—
598C22×C4—93no—
599C22×C4—93no—
600C4⋊C4—33no—
601C4⋊C4—36no—
602C4⋊C4—33no—
603C4⋊C4—96no—
604C4⋊C4—93no—
605C4⋊C4—93no—
606C4⋊C4—96no—
607C4⋊C4—93no—
608C4⋊C4—91no—
609C4⋊C4—93no—
610C4⋊C4—93no—
611C4⋊C4—93no—
612C4⋊C4—96no—
613C4⋊C4C2×D3213yes—
614C22⋊C4—31no—
615C22⋊C4—33no—
616C22⋊C4—36no—
617C22⋊C4—91no—
618C22⋊C4—93no—
619C22⋊C4—93no—
620C22⋊C4—96no—
621C22⋊C4—93no—
622C22⋊C4—96no—
623C42—33no—
624C42—33no—
625C42—33no—
626C42—91no—
627C42—93no—
628C42—93no—
629C42—93no—
630C42—93no—
631C42—93no—
632C42C2×D3213yes—
633C22×C3—21no—
634C22×C3—32no—
635C22×C3—32no—
636C22×C3—61no—
637C22×C3—61no—
638C22×C3—61no—
639C22×C3—61no—
640C22×C3—63no—
641C22×C3—63no—
642C22×C3—63no—
643C22×C3C24×D311yescharacteristic
644C22×C3C24×D311yescharacteristic
645C2×D3—21no—
646C2×D3—21no—
647C2×D3—21no—
648C2×D3—21no—
649C2×D3—23no—
650C2×D3—23no—
651C2×D3—23no—
652C2×D3D3×#4112yes—
653C2×D3D3×#4112yes—
654C3×C4—21no—
655C3×C4—23no—
656C3×C4—23no—
657C3×C4—21no—
658C3×C4—26no—
659C3×C4—32no—
660C3×C4—43no—
661C3×C4—41no—
662C3×C4—61no—
663C3×C4—63no—
664C3×C4—63no—
665C3×C4—63no—
666C3×C4C2×#23516yes—
667C3×C4C2×#23716yes—
668Dic3—23no—
669Dic3—23no—
670Dic3—21no—
671Dic3—23no—
672Dic3—32no—
673Dic3—32no—
674Dic3—62no—
675Dic3—61no—
676Dic3—63no—
677Dic3—63no—
678Dic3—63no—
679Dic3—61no—
680Dic3—63no—
681Dic3—123no—
682Dic3—121no—
683Dic3—123no—
684Dic3#100712yes—
685C32#348211yescharacteristic, complemented, Sylow
686C23—31no—
687C23—31no—
688C23—33no—
689Q8—66no—
690Q8—66no—
691Q8—186no—
692Q8#379514yescomplemented
693D4—66no—
694D4—66no—
695D4—94no—
696D4—186no—
697C2×C4—31no—
698C2×C4—33no—
699C2×C4—33no—
700C2×C4—31no—
701C2×C4—33no—
702C2×C4—62no—
703C2×C4—66no—
704C2×C4—66no—
705C2×C4—66no—
706C2×C4—66no—
707C2×C4—91no—
708C2×C4—91no—
709C2×C4—93no—
710C2×C4—93no—
711C2×C4—182no—
712C2×C4—186no—
713C2×C4—186no—
714C2×C4—186no—
715C2×C4C22×D3211yescharacteristic
716C2×C4C22×D3213yes—
717C2×C4C22×D3213yes—
718C2×C3—21no—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3—62no—
722C2×C3—62no—
723C2×C3—123no—
724C2×C3C22×#23511yescharacteristic
725C2×C3C22×#23711yescharacteristic
726C2×C3C2×#100711yescharacteristic
727C2×C3C2×D3×#4111yescharacteristic
728C2×C3C2×D3×#4111yescharacteristic
729C2×C3D3×2−1+411yescharacteristic
730D3—22no—
731D3—22no—
732D3—43no—
733C22—32no—
734C22—32no—
735C22—61no—
736C22—61no—
737C22—61no—
738C22—61no—
739C22—63no—
740C22—63no—
741C22—63no—
742C22C23×D3211yescharacteristic
743C4—21no—
744C4—23no—
745C4—32no—
746C4—61no—
747C4—63no—
748C4—63no—
749C4—63no—
750C4—92no—
751C4—181no—
752C4—183no—
753C4—183no—
754C4C2×#379516yes—
755C3—21no—
756C3#8581711yescharacteristic, complemented
757C3#8671211yescharacteristic, complemented
758C2—62no—
759C2—62no—
760C2—123no—
761C2C22×#379511yescharacteristic
762C2D3×#100711yescharacteristic
763C2D32×#4111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
hypercenterC4×Q8D32
hypocenterC32#3482
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #10596040C2semidirect
2. C3×#5576C2semidirect
3. C3×C4×D3×Q8C2semidirect
4. #10595409C2semidirect
5. Q8×#625C2semidirect
6. Dic3×#239C2semidirect
7. D3×Q8×Dic3C2semidirect
8. #10594551C2semidirect
9. #10594426C2semidirect
10. #10594385C2semidirect
11. #10594370C2semidirect
12. #10593942C2semidirect
13. #10593921C2semidirect
14. #10593917C2semidirect
15. C4×#3795C2semidirect
85. #5576D3semidirect
88. C4×D3×Q8D3semidirect
264. C32×Q8#41semidirect
288. #625#41semidirect
509. C3×Q8#235semidirect
510. C3×Q8#237semidirect
685. C32#3482semidirect
692. Q8#3795semidirect
756. C3#85817semidirect
757. C3#86712semidirect

Maximal subgroups

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

subgroupindex
#105960402
C3×#55762
C3×C4×D3×Q82
#105954092
Q8×#6252
Dic3×#2392
D3×Q8×Dic32
#105945512
#105944262
#105943852
#105943702
#105939422
#105939212
#105939172
C4×#37952
#867123
#858173