Finite Group Databasebeta

← #11895741

Subgroups — #11895741

Order 1152.

847 conjugacy classes of subgroups.

The subgroup lattice has 773 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5718C211yesmaximal, characteristic, complemented
2#10593929C211yesmaximal, characteristic, complemented
3#10592770C211yesmaximal, characteristic, complemented
4C3×#5072C211yesmaximal, characteristic, complemented
5#10591487C211yesmaximal, characteristic, complemented
6#10591477C211yesmaximal, characteristic, complemented
7#10591430C211yesmaximal, characteristic, complemented
8#10591428C211yesmaximal, characteristic, complemented
9#10591428C211yesmaximal, characteristic, complemented
10Dic3×#213C211yesmaximal, characteristic, complemented
11#10591411C211yesmaximal, characteristic, complemented
12#10591408C211yesmaximal, characteristic, complemented
13#10590344C211yesmaximal, characteristic, complemented
14#10590271C211yesmaximal, characteristic, complemented
15#10590252C211yesmaximal, characteristic, complemented
16#83581—31nomaximal
17#80321—31nomaximal
18C2×C3×#237—21no—
19C32×#127C2211yescharacteristic
20#64079C2211yescharacteristic
21C3×#940C2211yescharacteristic
22C3×#940C2211yescharacteristic
23C3×#939—21no—
24C3×#939—21no—
25C3×#938—21no—
26C3×D4×Dic3C2211yescharacteristic
27C3×D4×Dic3C2211yescharacteristic
28C2×C3×#213C2211yescharacteristic
29C2×C3×#213C2211yescharacteristic
30C3×C4×D12C2211yescharacteristic
31C3×C4×D12C2211yescharacteristic
32C3×C4×Dic6C2211yescharacteristic
33#63918C2211yescharacteristic
34#63899—21no—
35Dic3×D12C2211yescharacteristic
36Dic3×D12C2211yescharacteristic
37#63887—21no—
38D3×Dic3⋊C4—21no—
39#63869C2211yescharacteristic
40#63851—21no—
41C2×#3713C2211yescharacteristic
42#63659C2211yescharacteristic
43#63659C2211yescharacteristic
44#63659C2211yescharacteristic
45#63659C2211yescharacteristic
46#63630C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×C4⋊(C3⋊C8)C2211yescharacteristic
50#63575C2211yescharacteristic
51#63574C2211yescharacteristic
52#63573C2211yescharacteristic
53Dic3⋊(C3⋊C8)C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63563C2211yescharacteristic
56#63563C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59#63554C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#550—31no—
62#5718D311yescharacteristic, complemented
63#5579—31no—
64#5539—31no—
65C3×#459—31no—
66#5152—31no—
67#5150—31no—
68#5150—31no—
69Dic3×D8—31no—
70#5072—31no—
71#5072—31no—
72#5072D311yescharacteristic, complemented
73#5071—31no—
74#5071—31no—
75#5071—31no—
76#5071—61no—
77#5070—31no—
78#5024—31no—
79#5014—31no—
80#5014—31no—
81#5014—31no—
82C4×#213—31no—
83#5009—31no—
84#5009—31no—
85#5008—31no—
86#4847—31no—
87#4828—31no—
88#4766—31no—
89#4764—31no—
90#4761—31no—
91#4760—31no—
92C2×C32×D4—21no—
93C2×C32×D4—21no—
94C2×C32×D4C2311yescharacteristic
95C2×C32×D4C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C22×C3×Dic3—21no—
101C22×C3×Dic3—21no—
102C3×#237—44no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3—21no—
107C2×C3×Dic6D411yescharacteristic
108C2×#627—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111C32×C42C2311yescharacteristic
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114#3750—21no—
115#3750—21no—
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×#217—21no—
119C3×#217—21no—
120C3×#213—22no—
121C3×#213—22no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×C4⋊Dic3D411yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4D411yescharacteristic
128C3×Dic3⋊C4D411yescharacteristic
129C3×C4×Dic3C2311yescharacteristic
130C3×C4×Dic3C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133#3724—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138#3713—22no—
139#3366—91noSylow
140C2×C3×#41—61no—
141C2×#237—21no—
142C2×C3×D8—31no—
143C2×C3×D8—31no—
144C3×#127—21no—
145C3×#127—31no—
146C3×#127—31no—
147C3×#127C2×D311yescharacteristic
148C3×#127C2×D311yescharacteristic
149C3×#121—61no—
150C3×#121—61no—
151C3×#121—61no—
152C3×C4×Q8—31no—
153C3×C4×D4—31no—
154C3×C4×D4—31no—
155C3×C4×D4—31no—
156C3×C4×D4—31no—
157#946—61no—
158#940C2×D311yescharacteristic
159#940C2×D311yescharacteristic
160#939—21no—
161#939—21no—
162#938—21no—
163D4×Dic3—31no—
164D4×Dic3—31no—
165D4×Dic3C2×D311yescharacteristic
166D4×Dic3C2×D311yescharacteristic
167C2×#213—31no—
168C2×#213—31no—
169C2×#213C2×D311yescharacteristic
170C2×#213C2×D311yescharacteristic
171#924—61no—
172C2×Dic3⋊C4—61no—
173#896—61no—
174#896—61no—
175D3×C4⋊C4—61no—
176#890—31no—
177#888—31no—
178#878—61no—
179#878—61no—
180C4×D12—31no—
181C4×D12—31no—
182C4×D12C2×D311yescharacteristic
183C4×D12C2×D311yescharacteristic
184#870—31no—
185#870—31no—
186#870—31no—
187#870—61no—
188#869—31no—
189C4×Dic6C2×D311yescharacteristic
190C3×C4⋊C8—31no—
191C3×#102—31no—
192C3×#102—31no—
193#832—31no—
194#832—31no—
195#832—31no—
196#832—31no—
197#832—31no—
198#832—31no—
199#832—31no—
200#832—31no—
201#832—31no—
202#832—31no—
203#832—31no—
204#832—31no—
205#832—61no—
206#832—61no—
207#832—61no—
208#832—61no—
209#832C2×D311yescharacteristic
210#832C2×D311yescharacteristic
211#821—31no—
212#821—31no—
213#818—31no—
214#817—31no—
215#815—31no—
216Dic3⋊C8—31no—
217Dic3⋊C8—31no—
218C8×Dic3—31no—
219#809—31no—
220#809—31no—
221#808—31no—
222#808—31no—
223#808—31no—
224#807—31no—
225C4⋊(C3⋊C8)—31no—
226C4⋊(C3⋊C8)—31no—
227C4⋊(C3⋊C8)C2×D311yescharacteristic
228#803—31no—
229#803—31no—
230#803—31no—
231#803—61no—
232C4×C3⋊C8—31no—
233C23×C32—21no—
234C23×C32—21no—
235C22×C3×D3—21no—
236C22×C3×D3—21no—
237C32×D4—21no—
238C32×D4—21no—
239C32×D4—21no—
240C32×D4—21no—
241C32×D4—42no—
242C32×D4—81no—
243C2×C32×C4C2×D411yescharacteristic
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2411yescharacteristic
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3—21no—
248C3×#67—42no—
249C3×#67—42no—
250C3×#67—81no—
251C3×#67—81no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—42no—
255C2×C3×Dic3—42no—
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C3×D12—21no—
261C3×D12—21no—
262C3×D12—21no—
263C3×D12#4112yescomplemented
264C3×C4×D3—42no—
265C3×C4×D3—81no—
266C3×Dic6—22no—
267#627—81no—
268D3×Dic3—42no—
269D3×Dic3—81no—
270C3⋊(C3⋊C8)—21no—
271C3⋊(C3⋊C8)—21no—
272C3×C3⋊C8—21no—
273C3×C3⋊C8—21no—
274#554—91no—
275#550—31no—
276#490—91no—
277#490—91no—
278#486—91no—
279#478—91no—
280#478—91no—
281#476—91no—
282#459—31no—
283#459—91no—
284#459—91no—
285#446—91no—
286#442—91no—
287#442—91no—
288C4×D8—91no—
289C3×#41—124no—
290C2×C3×Q8—31no—
291C2×C3×D4—21no—
292C2×C3×D4—21no—
293C2×C3×D4—21no—
294C2×C3×D4—21no—
295C2×C3×D4—21no—
296C2×C3×D4—21no—
297C2×C3×D4—31no—
298C2×C3×D4—31no—
299C2×C3×D4—41no—
300C2×C3×D4—41no—
301C2×C3×D4—61no—
302C2×C3×D4—61no—
303C2×C3×D4—61no—
304C2×C3×D4—61no—
305C2×C3×D4C22×D311yescharacteristic
306C2×C3×D4C22×D311yescharacteristic
307C2×C3×D4C22×D311yescharacteristic
308C2×C3×D4C22×D311yescharacteristic
309C22×C3×C4—61no—
310C22×C3×C4—61no—
311C22×C3×C4—61no—
312C22×C3×C4—61no—
313C2×#67—21no—
314C2×#67—21no—
315C2×#67—21no—
316C2×#67—21no—
317C22×Dic3—21no—
318C22×Dic3—21no—
319C22×Dic3—61no—
320C22×Dic3—61no—
321#237—44no—
322C2×D12C22×D311yescharacteristic
323C2×D12C22×D311yescharacteristic
324C2×C4×D3—21no—
325C2×C4×D3—21no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×Dic6—61no—
329C2×Dic6—61no—
330C2×Dic6#6711yescharacteristic
331C3×D8—62no—
332C3×D8—62no—
333C2×C3×C8—31no—
334C2×C3×C8—31no—
335C3×C4⋊C4—31no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—31no—
340C3×C22⋊C4—61no—
341C3×C22⋊C4—61no—
342C3×C22⋊C4—61no—
343C3×C22⋊C4—61no—
344C3×C42—21no—
345C3×C42—31no—
346C3×C42—31no—
347C3×C42C22×D311yescharacteristic
348C3×C42C22×D311yescharacteristic
349#217—21no—
350#217—21no—
351#217—61no—
352#217—61no—
353#213—22no—
354#213—22no—
355#213—62no—
356#213—62no—
357(C2×D3)⋊C4—21no—
358(C2×D3)⋊C4—21no—
359(C2×D3)⋊C4—61no—
360(C2×D3)⋊C4—61no—
361C4⋊Dic3—31no—
362C4⋊Dic3—31no—
363C4⋊Dic3—31no—
364C4⋊Dic3—31no—
365C4⋊Dic3—61no—
366C4⋊Dic3—61no—
367C4⋊Dic3—61no—
368C4⋊Dic3—61no—
369C4⋊Dic3#6711yescharacteristic
370C4⋊Dic3C22×D311yescharacteristic
371C4⋊Dic3C22×D311yescharacteristic
372Dic3⋊C4—61no—
373Dic3⋊C4—61no—
374Dic3⋊C4—61no—
375Dic3⋊C4—61no—
376Dic3⋊C4—61no—
377Dic3⋊C4—61no—
378Dic3⋊C4—61no—
379Dic3⋊C4—61no—
380Dic3⋊C4—121no—
381Dic3⋊C4—121no—
382Dic3⋊C4#6711yescharacteristic
383Dic3⋊C4#6711yescharacteristic
384C4×Dic3C22×D311yescharacteristic
385C4×Dic3C22×D311yescharacteristic
386C2×C3⋊C8—31no—
387C2×C3⋊C8—31no—
388C2×C3⋊C8—31no—
389C2×C3⋊C8—31no—
390C2×C3⋊C8—61no—
391C2×C3⋊C8—61no—
392C2×C3⋊C8C22×D311yescharacteristic
393C2×C3⋊C8C22×D311yescharacteristic
394C22×C32—41no—
395C22×C32—41no—
396C22×C32—41no—
397C22×C32—41no—
398C22×C32—41no—
399C22×C32—41no—
400C22×C32C22×D411yescharacteristic
401C2×C3×D3—22no—
402C2×C3×D3—41no—
403C2×C3×D3—41no—
404C2×C3×D3—41no—
405C2×C3×D3—41no—
406C2×C3×D3—41no—
407C32×C4—21no—
408C32×C4—21no—
409C32×C4C2×#4111yescharacteristic
410C32×C42−1+411yescharacteristic
411C3⋊Dic3—41no—
412C3⋊Dic3—41no—
413C3×Dic3—21no—
414C3×Dic3—21no—
415C3×Dic3—21no—
416C3×Dic3—41no—
417C3×Dic3—41no—
418C3×Dic3AGL(1,ℤ/8)12yes—
419C2×#41—61no—
420C2×D8—31no—
421C2×D8—31no—
422C2×D8—91no—
423C4⋊Q8—91no—
424#127—31no—
425#127—31no—
426#127D3211yescharacteristic
427#125—91no—
428#125—91no—
429C22⋊Q8—181no—
430C22⋊Q8—181no—
431C22⋊Q8—181no—
432#121—61no—
433#121—61no—
434#121—61no—
435C4×Q8—31no—
436C4×D4—31no—
437C4×D4—31no—
438C4×D4—31no—
439C4×D4—31no—
440C4×D4—91no—
441C4×D4—91no—
442C2×C4⋊C4—181no—
443#107—91no—
444#106—91no—
445#106—91no—
446C4⋊C8—31no—
447C4⋊C8—91no—
448C4⋊C8—91no—
449#102—31no—
450#102—31no—
451#102—91no—
452#102—91no—
453#102—91no—
454#102—91no—
455#102—91no—
456#102—91no—
457#102—91no—
458#102—91no—
459#97—91no—
460#97—91no—
461C4×C8—91no—
462C23×C3—21no—
463C23×C3—21no—
464C23×C3—21no—
465C23×C3—21no—
466C23×C3—41no—
467C23×C3—41no—
468C23×C3—61no—
469C23×C3—61no—
470C22×D3—21no—
471C22×D3—21no—
472C3×Q8—62no—
473C3×D4—21no—
474C3×D4—21no—
475C3×D4—21no—
476C3×D4—21no—
477C3×D4—21no—
478C3×D4—21no—
479C3×D4—21no—
480C3×D4—21no—
481C3×D4—32no—
482C3×D4—41no—
483C3×D4—41no—
484C3×D4—41no—
485C3×D4—41no—
486C3×D4—42no—
487C3×D4—42no—
488C3×D4—61no—
489C3×D4—61no—
490C3×D4—61no—
491C3×D4—82no—
492C3×D4—81no—
493C3×D4—81no—
494C3×D4—82no—
495C3×D4—122no—
496C3×D4—122no—
497C3×D4—241no—
498C3×D4—241no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—31no—
503C2×C3×C4—31no—
504C2×C3×C4—31no—
505C2×C3×C4—31no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—122no—
509C2×C3×C4—122no—
510C2×C3×C4—122no—
511C2×C3×C4—241no—
512C2×C3×C4D3×D411yescharacteristic
513C2×C3×C4D3×D411yescharacteristic
514C2×C3×C4C2×#6711yescharacteristic
515C2×C3×C4C2×#6711yescharacteristic
516C2×C3×C4C23×D311yescharacteristic
517C2×C3×C4C23×D311yescharacteristic
518#67—42no—
519#67—42no—
520#67—81no—
521#67—81no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—42no—
525C2×Dic3—42no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—121no—
531C2×Dic3—121no—
532C2×Dic3—122no—
533C2×Dic3—241no—
534C2×Dic3C2×#6711yescharacteristic
535C2×Dic3C2×#6711yescharacteristic
536C2×Dic3C2×#6711yescharacteristic
537C2×Dic3C2×#6711yescharacteristic
538D12—21no—
539D12—21no—
540D12—21no—
541D12#23712yescomplemented
542C4×D3—42no—
543C4×D3—81no—
544C4×D3—122no—
545C4×D3—241no—
546Dic6—22no—
547Dic6—241no—
548Dic6—241no—
549C3×C8—61no—
550C3×C8—61no—
551C3⋊C8—21no—
552C3⋊C8—21no—
553C3⋊C8—61no—
554C3⋊C8—61no—
555C3⋊C8—61no—
556C3⋊C8—61no—
557C3⋊C8—121no—
558C3⋊C8—121no—
559C2×C32—81no—
560C2×C32—81no—
561C2×C32#54811yescharacteristic
562C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
563C2×C32#57611yescharacteristic
564C3×D3—42no—
565C3×D3—81no—
566#41—124no—
567C2×Q8—31no—
568C2×Q8—181no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—31no—
572C2×D4—31no—
573C2×D4—61no—
574C2×D4—61no—
575C2×D4—61no—
576C2×D4—61no—
577C2×D4C2×D3211yescharacteristic
578C2×D4C2×D3211yescharacteristic
579C22×C4—61no—
580C22×C4—61no—
581C22×C4—61no—
582C22×C4—61no—
583C22×C4—181no—
584C22×C4—181no—
585D8—62no—
586D8—62no—
587D8—182no—
588C2×C8—31no—
589C2×C8—31no—
590C2×C8—91no—
591C2×C8—91no—
592C4⋊C4—31no—
593C4⋊C4—31no—
594C4⋊C4—31no—
595C4⋊C4—31no—
596C4⋊C4—31no—
597C4⋊C4—91no—
598C4⋊C4—91no—
599C4⋊C4—181no—
600C4⋊C4—181no—
601C4⋊C4—181no—
602C4⋊C4—181no—
603C4⋊C4—181no—
604C22⋊C4—61no—
605C22⋊C4—61no—
606C22⋊C4—61no—
607C22⋊C4—61no—
608C22⋊C4—181no—
609C22⋊C4—181no—
610C42—31no—
611C42—31no—
612C42C2×D3211yescharacteristic
613C22×C3—21no—
614C22×C3—41no—
615C22×C3—41no—
616C22×C3—41no—
617C22×C3—41no—
618C22×C3—41no—
619C22×C3—41no—
620C22×C3—41no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—62no—
627C22×C3—81no—
628C22×C3—81no—
629C22×C3—81no—
630C22×C3—81no—
631C22×C3—81no—
632C22×C3—81no—
633C22×C3—121no—
634C22×C3—121no—
635C22×C3—121no—
636C22×C3—121no—
637C22×C3—121no—
638C22×C3C2×D3×D411yescharacteristic
639C22×C3C22×#6711yescharacteristic
640C2×D3—22no—
641C2×D3—41no—
642C2×D3—41no—
643C2×D3—41no—
644C2×D3—41no—
645C2×D3—41no—
646C3×C4—21no—
647C3×C4—21no—
648C3×C4—21no—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—21no—
652C3×C4—32no—
653C3×C4—41no—
654C3×C4—41no—
655C3×C4—61no—
656C3×C4—61no—
657C3×C4—61no—
658C3×C4—121no—
659C3×C4—121no—
660C3×C4C2×#23711yescharacteristic
661C3×C4D3×#4111yescharacteristic
662C3×C4#101011yescharacteristic
663C3×C4#101011yescharacteristic
664Dic3—21no—
665Dic3—21no—
666Dic3—21no—
667Dic3—41no—
668Dic3—41no—
669Dic3—121no—
670Dic3—121no—
671Dic3—121no—
672Dic3—121no—
673Dic3—241no—
674Dic3—241no—
675Dic3#93212yes—
676C32#336611yescharacteristic, complemented, Sylow
677C23—21no—
678C23—21no—
679C23—61no—
680C23—61no—
681Q8—62no—
682Q8—721no—
683D4—21no—
684D4—21no—
685D4—21no—
686D4—21no—
687D4—32no—
688D4—42no—
689D4—61no—
690D4—61no—
691D4—61no—
692D4—81no—
693D4—122no—
694D4—122no—
695D4—241no—
696D4—241no—
697C2×C4—31no—
698C2×C4—31no—
699C2×C4—31no—
700C2×C4—31no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—122no—
704C2×C4—122no—
705C2×C4—122no—
706C2×C4—181no—
707C2×C4—181no—
708C2×C4—241no—
709C2×C4—362no—
710C2×C4—721no—
711C2×C4D3×#6711yescharacteristic
712C2×C4D3×#6711yescharacteristic
713C2×C4C22×D3211yescharacteristic
714C8—61no—
715C8—61no—
716C8—181no—
717C8—181no—
718C2×C3—21no—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3—81no—
722C2×C3—81no—
723C2×C3—81no—
724C2×C3—81no—
725C2×C3—122no—
726C2×C3—161no—
727C2×C3—161no—
728C2×C3—241no—
729C2×C3#559811yescharacteristic
730C2×C3#575711yescharacteristic
731C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
732C2×C3C2×#93211yescharacteristic
733C2×C3#583111yescharacteristic
734C2×C3#583511yescharacteristic
735D3—42no—
736D3—81no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—62no—
744C22—121no—
745C22—121no—
746C22—121no—
747C22—121no—
748C22—121no—
749C22C2×D3×#6711yescharacteristic
750C4—21no—
751C4—21no—
752C4—32no—
753C4—61no—
754C4—61no—
755C4—61no—
756C4—121no—
757C4—121no—
758C4—361no—
759C4—361no—
760C4#6430911yescharacteristic
761C4D3×#23711yescharacteristic
762C3—21no—
763C3#8032111yescharacteristic, complemented
764C3#8358111yescharacteristic, complemented
765C2—81no—
766C2—81no—
767C2—122no—
768C2—241no—
769C2D3×#93211yescharacteristic
770C2#1059509611yescharacteristic
771C2#1059515711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#127C22
socleC22×C32C22×D4
hypercenter#127D32
hypocenterC32#3366
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. C3×#5718C2semidirect
2. #10593929C2semidirect
3. #10592770C2semidirect
4. C3×#5072C2semidirect
5. #10591487C2semidirect
6. #10591477C2semidirect
7. #10591430C2semidirect
8. #10591428C2semidirect
9. #10591428C2semidirect
10. Dic3×#213C2semidirect
11. #10591411C2semidirect
12. #10591408C2semidirect
13. #10590344C2semidirect
14. #10590271C2semidirect
15. #10590252C2semidirect
62. #5718D3semidirect
72. #5072D3semidirect
263. C3×D12#41semidirect
541. D12#237semidirect
676. C32#3366semidirect
763. C3#80321semidirect
764. C3#83581semidirect

Maximal subgroups

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

subgroupindex
C3×#57182
#105939292
#105927702
C3×#50722
#105914872
#105914772
#105914302
#105914282
Dic3×#2132
#105914112
#105914082
#105903442
#105902712
#105902522
#835813
#803213