Finite Group Databasebeta

← #10823531

Subgroups — #10823531

Order 768.

1186 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5535C211yesmaximal, characteristic
2C3×#2323C211yesmaximal, characteristic, complemented
3C2×#5026C211yesmaximal, characteristic, complemented
4C2×C4×#215C211yesmaximal, characteristic, complemented
5#71699C211yesmaximal, characteristic, complemented
6#71699C211yesmaximal, characteristic, complemented
7#71582C211yesmaximal, characteristic, complemented
8#69688C211yesmaximal, characteristic, complemented
9#69669C211yesmaximal, characteristic, complemented
10#69627C211yesmaximal, characteristic, complemented
11#69606C211yesmaximal, characteristic, complemented
12#69524C211yesmaximal, characteristic, complemented
13#69523C211yesmaximal, characteristic, complemented
14#69474C211yesmaximal, characteristic, complemented
15C4×#809C211yesmaximal, characteristic, complemented
16#23582—31nomaximal, Sylow
17C2×C3×C22⋊Q8C2211yescharacteristic
18C2×C3×C4×Q8C2211yescharacteristic
19C2×C3×#117C2211yescharacteristic
20C22×#215C2211yescharacteristic
21C22×#215C2211yescharacteristic
22C2×#930C2211yescharacteristic
23C2×#930C2211yescharacteristic
24#5535—24no—
25#5535—24no—
26C2×#894—21no—
27C2×#894—21no—
28C2×#884—21no—
29C2×#884—21no—
30C2×#874C2211yescharacteristic
31C2×C4×D12C2211yescharacteristic
32C2×C4×D12C2211yescharacteristic
33C2×#870C2211yescharacteristic
34C3×#391C2211yescharacteristic
35C3×#389—21no—
36C3×#389C2211yescharacteristic
37C3×#388—21no—
38C3×#388—21no—
39C3×#387—21no—
40C3×#380C2211yescharacteristic
41C3×C4×C4⋊C4C2211yescharacteristic
42C2×#835C2211yescharacteristic
43C2×#835C2211yescharacteristic
44C2×#830C2211yescharacteristic
45C2×#830C2211yescharacteristic
46#5026—24no—
47C4×#215—24no—
48C2×#809C2211yescharacteristic
49C2×#809C2211yescharacteristic
50C2×#809C2211yescharacteristic
51C2×#809C2211yescharacteristic
52C2×#809C2211yescharacteristic
53C2×#809C2211yescharacteristic
54C2×#808C2211yescharacteristic
55C2×#807C2211yescharacteristic
56C2×#803C2211yescharacteristic
57C2×C4×C3⋊C8C2211yescharacteristic
58#4529C2211yescharacteristic
59#4529C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4524C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#540—31no—
65C2×#440—31no—
66C2×C4×SD16—31no—
67#2323D311yescharacteristic, complemented
68#2059—31no—
69#2041—31no—
70#2034—31no—
71#2033—31no—
72#2026—31no—
73#2014—31no—
74#2000—31no—
75#2000—31no—
76#1762—31no—
77C4×#102—31no—
78#1750—31no—
79C22×C3×Q8C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C22×#67—21no—
82C22×#67—21no—
83C22×D12—21no—
84C22×D12—21no—
85C22×D12C2311yescharacteristic
86C22×D12C2311yescharacteristic
87C22×C4×D3—21no—
88C22×C4×D3—21no—
89C3×C22⋊Q8—22no—
90C3×C22⋊Q8—22no—
91C3×C4×Q8—22no—
92C3×C4×Q8—22no—
93C3×#117—22no—
94C3×#117—22no—
95C2×C3×C4⋊C4—21no—
96C2×C3×C4⋊C4—21no—
97C2×C3×C4⋊C4—21no—
98C2×C3×C4⋊C4D411yescharacteristic
99C2×C3×C4⋊C4D411yescharacteristic
100C2×C3×C4⋊C4C2311yescharacteristic
101C2×C3×C4⋊C4C2311yescharacteristic
102C2×C3×C4⋊C4C2311yescharacteristic
103C2×C3×C22⋊C4—21no—
104C2×C3×C22⋊C4—21no—
105C2×C3×C22⋊C4D411yescharacteristic
106C2×C3×C22⋊C4D411yescharacteristic
107C2×C3×C42—21no—
108C2×C3×C42—21no—
109C2×C3×C42C2311yescharacteristic
110C2×C3×C42C2311yescharacteristic
111C2×#215—22no—
112C2×#215—22no—
113C2×#215—22no—
114C2×#215—22no—
115C2×#215—22no—
116C2×#215—22no—
117#930—22no—
118#930—22no—
119#930—22no—
120#930—22no—
121C2×(C2×D3)⋊C4—21no—
122C2×(C2×D3)⋊C4—21no—
123C2×(C2×D3)⋊C4—21no—
124C2×(C2×D3)⋊C4—21no—
125C2×C4⋊Dic3C2311yescharacteristic
126C2×C4⋊Dic3C2311yescharacteristic
127C2×Dic3⋊C4—21no—
128C2×Dic3⋊C4—21no—
129C22×C3⋊C8C2311yescharacteristic
130C22×C3⋊C8C2311yescharacteristic
131C22×C3⋊C8C2311yescharacteristic
132C22×C3⋊C8C2311yescharacteristic
133#894—28no—
134#894—28no—
135#884—28no—
136#884—28no—
137#874—22no—
138#874—22no—
139C4×D12—22no—
140C4×D12—22no—
141C4×D12D414yes—
142C4×D12D414yes—
143#870—22no—
144#870—22no—
145C3×#95—21no—
146C3×#95—21no—
147C3×#95—21no—
148C3×#95—21no—
149C3×#95—21no—
150#835—22no—
151#835—22no—
152#830—22no—
153#830—22no—
154#809—22no—
155#809—22no—
156#809—22no—
157#809—22no—
158#809—22no—
159#809—22no—
160#808—22no—
161#807—22no—
162#803—22no—
163C4×C3⋊C8—22no—
164C22×SD16—31no—
165C22×SD16—31no—
166#540—64no—
167#540—64no—
168C2×#127—31no—
169C2×#125—31no—
170C2×#123—61no—
171C2×#123—61no—
172C2×C22⋊Q8C2×D311yescharacteristic
173C2×#121—31no—
174C2×#121—31no—
175C2×#121—61no—
176C2×#121—61no—
177C2×C4×Q8C2×D311yescharacteristic
178C2×C4×D4—31no—
179C2×C4×D4—31no—
180C2×#117C2×D311yescharacteristic
181#440—64no—
182C4×SD16—64no—
183C2×#107—31no—
184C2×#106—31no—
185C2×#103—31no—
186C2×#103—31no—
187C2×#102—31no—
188C2×#102—31no—
189C2×#102—31no—
190C2×#102—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×C22⋊C8—31no—
194C2×C22⋊C8—31no—
195C2×#97—31no—
196C2×C4×C8—31no—
197#391C2×D311yescharacteristic
198#389—21no—
199#389C2×D311yescharacteristic
200#388—21no—
201#388—21no—
202#387—21no—
203#380C2×D311yescharacteristic
204C4×C4⋊C4C2×D311yescharacteristic
205#340—31no—
206#340—31no—
207#340—31no—
208#340—31no—
209#336—31no—
210#336—31no—
211C24×C3C2×D411yescharacteristic
212C23×D3—21no—
213C23×D3—21no—
214C2×C3×Q8—21no—
215C2×C3×Q8—21no—
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8#4112yes—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4C2×D411yescharacteristic
231C22×C3×C4C2×D411yescharacteristic
232C22×C3×C4C2×D411yescharacteristic
233C22×C3×C4C2×D411yescharacteristic
234C22×C3×C4C2×D411yescharacteristic
235C22×C3×C4C2411yescharacteristic
236C2×#67—24no—
237C2×#67—24no—
238C2×#67—81no—
239C2×#67—81no—
240C2×#67—81no—
241C2×#67—81no—
242C22×Dic3—21no—
243C22×Dic3—21no—
244C2×D12—21no—
245C2×D12—21no—
246C2×D12—21no—
247C2×D12—21no—
248C2×D12—21no—
249C2×D12—21no—
250C2×D12—21no—
251C2×D12—21no—
252C2×D12—21no—
253C2×D12—21no—
254C2×D12—24no—
255C2×D12—24no—
256C2×D12—81no—
257C2×D12—81no—
258C2×D12—81no—
259C2×D12—81no—
260C2×D12C2×D412yes—
261C2×D12C2×D412yes—
262C2×C4×D3—24no—
263C2×C4×D3—24no—
264C2×C4×D3—81no—
265C2×C4×D3—81no—
266C2×C4×D3—81no—
267C2×C4×D3—81no—
268C3×C4⋊C4—24no—
269C3×C4⋊C4—22no—
270C3×C4⋊C4—22no—
271C3×C4⋊C4—21no—
272C3×C4⋊C4—21no—
273C3×C4⋊C4—21no—
274C3×C4⋊C4—21no—
275C3×C4⋊C4—21no—
276C3×C4⋊C4—42no—
277C3×C4⋊C4—81no—
278C3×C4⋊C4#4112yes—
279C3×C22⋊C4—24no—
280C3×C22⋊C4—22no—
281C3×C22⋊C4—22no—
282C3×C22⋊C4—81no—
283C3×C42—21no—
284C3×C42—21no—
285C3×C42—42no—
286C3×C42—81no—
287C3×C42C2×D412yes—
288C3×C42C2×D412yes—
289#215—28no—
290#215—28no—
291(C2×D3)⋊C4—24no—
292(C2×D3)⋊C4—24no—
293(C2×D3)⋊C4—24no—
294(C2×D3)⋊C4—24no—
295C4⋊Dic3—21no—
296C4⋊Dic3—21no—
297C4⋊Dic3C2×D412yes—
298C4⋊Dic3C2×D412yes—
299Dic3⋊C4—24no—
300Dic3⋊C4—24no—
301C2×C3⋊C8—21no—
302C2×C3⋊C8—21no—
303C2×C3⋊C8—21no—
304C2×C3⋊C8—21no—
305C2×C3⋊C8—21no—
306C2×C3⋊C8—21no—
307C2×C3⋊C8—21no—
308C2×C3⋊C8—21no—
309C2×C3⋊C8—21no—
310C2×C3⋊C8—21no—
311C2×C3⋊C8#4112yes—
312C2×C3⋊C8#4112yes—
313C22×Q8C22×D311yescharacteristic
314C22×D4—31no—
315C22×D4—31no—
316C22×D4—61no—
317C22×D4—61no—
318C22×D4—61no—
319C22×D4—61no—
320C23×C4—61no—
321C23×C4—61no—
322C23×C4C22×D311yescharacteristic
323C2×SD16—62no—
324C2×SD16—62no—
325C2×SD16—62no—
326C2×SD16—62no—
327C2×SD16—62no—
328C2×SD16—62no—
329C22×C8—31no—
330C22×C8—31no—
331C22×C8—31no—
332C22×C8—31no—
333#127—62no—
334#127—62no—
335#125—62no—
336#125—62no—
337#123—68no—
338#123—68no—
339C22⋊Q8—22no—
340C22⋊Q8—22no—
341#121—68no—
342#121—68no—
343#121—62no—
344#121—62no—
345#121—62no—
346#121—62no—
347C4×Q8—22no—
348C4×Q8—22no—
349C4×D4—34no—
350C4×D4—34no—
351C4×D4—62no—
352C4×D4—62no—
353#117—22no—
354#117—22no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—31no—
359C2×C4⋊C4—31no—
360C2×C4⋊C4—61no—
361C2×C4⋊C4—61no—
362C2×C4⋊C4#6711yescharacteristic
363C2×C4⋊C4#6711yescharacteristic
364C2×C4⋊C4C22×D311yescharacteristic
365C2×C4⋊C4C22×D311yescharacteristic
366C2×C4⋊C4C22×D311yescharacteristic
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—61no—
370C2×C22⋊C4—61no—
371C2×C22⋊C4—61no—
372C2×C22⋊C4—61no—
373C2×C22⋊C4#6711yescharacteristic
374C2×C22⋊C4#6711yescharacteristic
375C2×C42—21no—
376C2×C42—21no—
377C2×C42C22×D311yescharacteristic
378C2×C42C22×D311yescharacteristic
379#107—62no—
380#106—62no—
381#103—62no—
382#103—62no—
383#102—62no—
384#102—62no—
385#102—62no—
386#102—62no—
387#102—62no—
388#102—62no—
389C22⋊C8—62no—
390C22⋊C8—62no—
391#97—62no—
392C4×C8—62no—
393#95—21no—
394#95—21no—
395#95—21no—
396#95—21no—
397#95—21no—
398C23×C3—21no—
399C23×C3—21no—
400C23×C3—21no—
401C23×C3—21no—
402C23×C3—21no—
403C23×C3—21no—
404C23×C3—21no—
405C23×C3C22×D411yescharacteristic
406C22×D3—22no—
407C22×D3—22no—
408C22×D3—41no—
409C22×D3—41no—
410C22×D3—41no—
411C22×D3—41no—
412C22×D3—41no—
413C22×D3—41no—
414C22×D3—41no—
415C22×D3—41no—
416C22×D3—41no—
417C22×D3—41no—
418C22×D3—41no—
419C22×D3—41no—
420C3×Q8—22no—
421C3×Q8—22no—
422C3×Q8—41no—
423C3×Q8—41no—
424C2×C3×C4—21no—
425C2×C3×C4—21no—
426C2×C3×C4—21no—
427C2×C3×C4—21no—
428C2×C3×C4—21no—
429C2×C3×C4—21no—
430C2×C3×C4—21no—
431C2×C3×C4—22no—
432C2×C3×C4—22no—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—41no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4#12012yes—
454C2×C3×C4#12012yes—
455C2×C3×C4C22×D411yescharacteristic
456C2×C3×C4C22×D411yescharacteristic
457C2×C3×C4C2×#4111yescharacteristic
458C2×C3×C4C2×#4111yescharacteristic
459C2×C3×C4C2×#4111yescharacteristic
460C2×C3×C4C2×#4111yescharacteristic
461#67—84no—
462#67—84no—
463C2×Dic3—22no—
464C2×Dic3—22no—
465C2×Dic3—41no—
466C2×Dic3—41no—
467C2×Dic3—41no—
468C2×Dic3—41no—
469D12—22no—
470D12—22no—
471D12—22no—
472D12—22no—
473D12—41no—
474D12—41no—
475D12—41no—
476D12—41no—
477D12—84no—
478D12—84no—
479C4×D3—84no—
480C4×D3—84no—
481C3⋊C8—22no—
482C3⋊C8—22no—
483C3⋊C8—41no—
484C3⋊C8—41no—
485C24—61no—
486C24—61no—
487C24C2×#6711yescharacteristic
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8#23512yes—
494C2×D4—32no—
495C2×D4—32no—
496C2×D4—64no—
497C2×D4—64no—
498C2×D4—64no—
499C2×D4—64no—
500C2×D4—61no—
501C2×D4—61no—
502C2×D4—61no—
503C2×D4—61no—
504C2×D4—61no—
505C2×D4—61no—
506C2×D4—61no—
507C2×D4—61no—
508C2×D4—61no—
509C2×D4—61no—
510C2×D4—241no—
511C2×D4—241no—
512C2×D4—241no—
513C2×D4—241no—
514C2×D4—241no—
515C2×D4—241no—
516C2×D4—241no—
517C2×D4—241no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—61no—
529C22×C4—61no—
530C22×C4—64no—
531C22×C4—64no—
532C22×C4—241no—
533C22×C4—241no—
534C22×C4—241no—
535C22×C4—241no—
536C22×C4C2×#6711yescharacteristic
537C22×C4C2×#6711yescharacteristic
538C22×C4C2×#6711yescharacteristic
539C22×C4C2×#6711yescharacteristic
540C22×C4C2×#6711yescharacteristic
541C22×C4C23×D311yescharacteristic
542SD16—68no—
543SD16—68no—
544C2×C8—32no—
545C2×C8—32no—
546C2×C8—61no—
547C2×C8—61no—
548C2×C8—61no—
549C2×C8—61no—
550C2×C8—61no—
551C2×C8—61no—
552C2×C8—61no—
553C2×C8—61no—
554C2×C8—61no—
555C2×C8—61no—
556C4⋊C4—24no—
557C4⋊C4—22no—
558C4⋊C4—22no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—32no—
565C4⋊C4—32no—
566C4⋊C4—42no—
567C4⋊C4—64no—
568C4⋊C4—64no—
569C4⋊C4—61no—
570C4⋊C4—61no—
571C4⋊C4—81no—
572C4⋊C4#23512yes—
573C22⋊C4—24no—
574C22⋊C4—22no—
575C22⋊C4—22no—
576C22⋊C4—64no—
577C22⋊C4—64no—
578C22⋊C4—64no—
579C22⋊C4—64no—
580C22⋊C4—81no—
581C42—21no—
582C42—21no—
583C42—42no—
584C42—81no—
585C42D3×D412yes—
586C42D3×D412yes—
587C22×C3—41no—
588C22×C3—41no—
589C22×C3—41no—
590C22×C3—41no—
591C22×C3—41no—
592C22×C3—41no—
593C22×C3—41no—
594C22×C3C2×#12011yescharacteristic
595C22×C3#52511yescharacteristic
596C22×C3#53211yescharacteristic
597C22×C3#57611yescharacteristic
598C22×C3#57711yescharacteristic
599C22×C3#57711yescharacteristic
600C22×C3#57711yescharacteristic
601C2×D3—42no—
602C2×D3—42no—
603C2×D3—42no—
604C2×D3—42no—
605C2×D3—42no—
606C2×D3—42no—
607C2×D3—81no—
608C2×D3—81no—
609C2×D3—81no—
610C2×D3—81no—
611C2×D3—81no—
612C2×D3—81no—
613C2×D3—81no—
614C2×D3—81no—
615C3×C4—22no—
616C3×C4—22no—
617C3×C4—42no—
618C3×C4—41no—
619C3×C4—42no—
620C3×C4—41no—
621C3×C4—41no—
622C3×C4—81no—
623C3×C4—81no—
624C3×C4#52511yescharacteristic
625C3×C4#52511yescharacteristic
626C3×C4#53211yescharacteristic
627C3×C4#53211yescharacteristic
628Dic3—42no—
629Dic3—42no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—62no—
638C23—62no—
639C23—121no—
640C23—121no—
641C23—121no—
642C23—121no—
643C23—121no—
644C23—121no—
645C23—121no—
646C23—121no—
647C23—121no—
648C23—121no—
649C23—121no—
650C23—121no—
651C23C22×#6711yescharacteristic
652Q8—22no—
653Q8—22no—
654Q8—41no—
655Q8—41no—
656D4—62no—
657D4—62no—
658D4—62no—
659D4—62no—
660D4—121no—
661D4—121no—
662D4—121no—
663D4—121no—
664D4—244no—
665D4—244no—
666D4—244no—
667D4—244no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—62no—
698C2×C4—62no—
699C2×C4—121no—
700C2×C4—121no—
701C2×C4—121no—
702C2×C4—121no—
703C2×C4—244no—
704C2×C4—244no—
705C2×C4#93712yes—
706C2×C4#93712yes—
707C2×C4C2×#23511yescharacteristic
708C2×C4C2×#23511yescharacteristic
709C2×C4C2×D3×D411yescharacteristic
710C2×C4C2×D3×D411yescharacteristic
711C2×C4D3×#4111yescharacteristic
712C2×C4D3×#4111yescharacteristic
713C8—62no—
714C8—62no—
715C8—121no—
716C8—121no—
717C2×C3—81no—
718C2×C3#238811yescharacteristic
719C2×C3#300911yescharacteristic
720C2×C3#301211yescharacteristic
721C2×C3#311911yescharacteristic
722C2×C3#312611yescharacteristic
723C2×C3#317411yescharacteristic
724C2×C3#317911yescharacteristic
725D3—82no—
726D3—82no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—122no—
735C22—122no—
736C22—122no—
737C22—122no—
738C22—122no—
739C22—122no—
740C22—241no—
741C22—241no—
742C22—241no—
743C22—241no—
744C22—241no—
745C22—241no—
746C22—241no—
747C22—241no—
748C22#579111yescharacteristic
749C22C2×#93711yescharacteristic
750C22#583211yescharacteristic
751C22#583511yescharacteristic
752C22#583711yescharacteristic
753C22#583711yescharacteristic
754C22#583711yescharacteristic
755C4—22no—
756C4—22no—
757C4—42no—
758C4—41no—
759C4—41no—
760C4—42no—
761C4—41no—
762C4—81no—
763C4—81no—
764C4—122no—
765C4—122no—
766C4#554711yescharacteristic
767C4#554711yescharacteristic
768C4#554811yescharacteristic
769C4#554811yescharacteristic
770C3#2358211yescharacteristic, complemented, Sylow
771C2—81no—
772C2—242no—
773C2—242no—
774C2#8240011yescharacteristic
775C2#8255311yescharacteristic
776C2#8256811yescharacteristic
777C2#8340411yescharacteristic
778C2#8342411yescharacteristic
779C2#8344311yescharacteristic
780C2#8345911yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2323C2
socleC23×C3C22×D4
prime radicalC2×#5535C2
hypercenter#2323D3
hypocenterC3#23582
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2323

Complements

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

NH ≅ G/Ntype
2. C3×#2323C2semidirect
3. C2×#5026C2semidirect
4. C2×C4×#215C2semidirect
5. #71699C2semidirect
6. #71699C2semidirect
7. #71582C2semidirect
8. #69688C2semidirect
9. #69669C2semidirect
10. #69627C2semidirect
11. #69606C2semidirect
12. #69524C2semidirect
13. #69523C2semidirect
14. #69474C2semidirect
15. C4×#809C2semidirect
67. #2323D3semidirect
770. C3#23582semidirect

Maximal subgroups

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

subgroupindex
C2×#55352
C3×#23232
C2×#50262
C2×C4×#2152
#716992
#715822
#696882
#696692
#696272
#696062
#695242
#695232
#694742
C4×#8092
#235823