Finite Group Databasebeta

← #10800981

Subgroups — #10800981

Order 768.

1344 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#519C211yesmaximal, characteristic
2C2×#5228C211yesmaximal, characteristic
3C2×#5030C211yesmaximal, characteristic, complemented
4C2×C4×#216C211yesmaximal, characteristic, complemented
5#82235C211yesmaximal, characteristic
6#72132C211yesmaximal, characteristic
7#71632C211yesmaximal, characteristic, complemented
8#71632C211yesmaximal, characteristic, complemented
9#71631C211yesmaximal, characteristic, complemented
10C4×#835C211yesmaximal, characteristic, complemented
11#71629C211yesmaximal, characteristic, complemented
12#71628C211yesmaximal, characteristic, complemented
13#71585C211yesmaximal, characteristic
14#71582C211yesmaximal, characteristic
15#71576C211yesmaximal, characteristic
16#21463—31nomaximal, Sylow
17C23×C3×Q8C2211yescharacteristic
18C3×#519—24no—
19C3×#519—24no—
20C2×C3×C4×Q8—21no—
21C2×C3×C4×Q8—21no—
22C2×C3×C4×Q8C2211yescharacteristic
23C2×C3×C4×Q8C2211yescharacteristic
24C2×C3×C4×Q8C2211yescharacteristic
25C2×C3×C4×Q8C2211yescharacteristic
26C2×C3×#117—21no—
27C2×C3×#117—21no—
28C2×C3×#117C2211yescharacteristic
29C2×C3×#117C2211yescharacteristic
30C22×#216C2211yescharacteristic
31C22×#216C2211yescharacteristic
32C2×#924C2211yescharacteristic
33C2×C4×Dic6C2211yescharacteristic
34#5228C418yescomplemented
35C2×#835C2211yescharacteristic
36C2×#835C2211yescharacteristic
37C2×#835C2211yescharacteristic
38C2×#835C2211yescharacteristic
39C2×#835C2211yescharacteristic
40C2×#835C2211yescharacteristic
41#5212C2211yescharacteristic
42C2×#830C2211yescharacteristic
43C2×#830C2211yescharacteristic
44#5030—24no—
45C4×#216—24no—
46#4978—21no—
47#4976—21no—
48C2×#810C2211yescharacteristic
49C2×#810C2211yescharacteristic
50C2×#808C2211yescharacteristic
51C2×#807C2211yescharacteristic
52#4945—21no—
53#4944—21no—
54C4×C4⋊Dic3C2211yescharacteristic
55#4929C2211yescharacteristic
56#4928C2211yescharacteristic
57C2×#803C2211yescharacteristic
58C2×C4×C3⋊C8C2211yescharacteristic
59#4529C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4524C2211yescharacteristic
64#4524C2211yescharacteristic
65C2×#519D311yescharacteristic
66C2×#451—31no—
67C2×#441—31no—
68C2×C4×Q16—31no—
69#2323—31no—
70#1878—31no—
71#1878—31no—
72#1873—31no—
73#1865—31no—
74#1863—31no—
75#1854—31no—
76#1787—31no—
77#1763—31no—
78C4×#103—31no—
79#1750—31no—
80C22×C3×Q8—22no—
81C22×C3×Q8—22no—
82C22×C3×Q8—22no—
83C22×C3×Q8—22no—
84C22×C3×Q8—21no—
85C22×C3×Q8—22no—
86C22×C3×Q8C2×C414yes—
87C22×C3×Q8C2311yescharacteristic
88C22×C3×Q8C2311yescharacteristic
89C23×C3×C4—21no—
90C23×C3×C4C2311yescharacteristic
91C22×Dic6C2311yescharacteristic
92C3×C4×Q8—28no—
93C3×C4×Q8—28no—
94C3×C4×Q8—22no—
95C3×C4×Q8—22no—
96C3×C4×Q8—22no—
97C3×C4×Q8—22no—
98C3×C4×Q8—22no—
99C3×C4×Q8—22no—
100C3×C4×Q8D414yes—
101C3×C4×Q8D414yes—
102C3×#117—28no—
103C3×#117—28no—
104C3×#117—22no—
105C3×#117—22no—
106C3×#117—22no—
107C3×#117—22no—
108C2×C3×C4⋊C4—21no—
109C2×C3×C4⋊C4—21no—
110C2×C3×C4⋊C4—21no—
111C2×C3×C4⋊C4—21no—
112C2×C3×C4⋊C4D411yescharacteristic
113C2×C3×C4⋊C4D411yescharacteristic
114C2×C3×C4⋊C4C2311yescharacteristic
115C2×C3×C4⋊C4C2311yescharacteristic
116C2×C3×C22⋊C4—21no—
117C2×C3×C22⋊C4D411yescharacteristic
118C2×C3×C22⋊C4D411yescharacteristic
119C2×C3×C42—21no—
120C2×C3×C42—21no—
121C2×C3×C42—21no—
122C2×C3×C42—21no—
123C2×C3×C42—21no—
124C2×C3×C42C2311yescharacteristic
125C2×C3×C42C2311yescharacteristic
126C2×#217—21no—
127C2×#217—21no—
128C2×#216—22no—
129C2×#216—22no—
130C2×#216—22no—
131C2×#216—22no—
132C2×#216C2×C414yes—
133C2×#216C2×C414yes—
134C2×C4⋊Dic3C2311yescharacteristic
135C2×C4⋊Dic3C2311yescharacteristic
136C2×C4⋊Dic3C2311yescharacteristic
137#924—22no—
138#924C2×C414yes—
139C2×Dic3⋊C4—21no—
140C2×Dic3⋊C4—21no—
141C2×Dic3⋊C4—21no—
142C2×C4×Dic3—21no—
143C2×C4×Dic3—21no—
144C22×C3⋊C8C2311yescharacteristic
145C22×C3⋊C8C2311yescharacteristic
146C22×C3⋊C8C2311yescharacteristic
147C22×C3⋊C8C2311yescharacteristic
148C4×Dic6—22no—
149C4×Dic6—22no—
150#835—22no—
151#835—22no—
152#835—22no—
153#835—22no—
154#835C2×C414yes—
155#835C2×C414yes—
156C3⋊#95—21no—
157C3⋊#95—21no—
158C3⋊#95—21no—
159C3⋊#95—21no—
160C3⋊#95—21no—
161#830—22no—
162#830C2×C414yes—
163#810—22no—
164#810—22no—
165#808—22no—
166#807—22no—
167#803—22no—
168C4×C3⋊C8—22no—
169C23×Q8C2×D311yescharacteristic
170C22×Q16—31no—
171C22×Q16—31no—
172C2×C22⋊Q8—31no—
173#519—24no—
174#519—24no—
175C2×C4×Q8—21no—
176C2×C4×Q8—21no—
177C2×C4×Q8—31no—
178C2×C4×Q8C2×D311yescharacteristic
179C2×C4×Q8C2×D311yescharacteristic
180C2×C4×Q8C2×D311yescharacteristic
181C2×C4×Q8C2×D311yescharacteristic
182C2×#117—21no—
183C2×#117—21no—
184C2×#117C2×D311yescharacteristic
185C2×#117C2×D311yescharacteristic
186#451—38no—
187#441—64no—
188C4×Q16—64no—
189C2×#107—31no—
190C2×#106—31no—
191C2×#103—31no—
192C2×#103—31no—
193C2×#103—31no—
194C2×#103—31no—
195C2×#103—31no—
196C2×#103—31no—
197C2×#103—31no—
198C2×#103—31no—
199C2×C22⋊C8—31no—
200C2×C22⋊C8—31no—
201C2×#97—31no—
202C2×C4×C8—31no—
203#391—31no—
204#389—31no—
205#389—61no—
206#388—61no—
207#388—61no—
208#387—61no—
209#380—31no—
210C4×C4⋊C4—31no—
211#340—31no—
212#340—31no—
213#340—31no—
214#340—31no—
215#336—31no—
216#336—31no—
217C24×C3C2×D411yescharacteristic
218C2×C3×Q8—24no—
219C2×C3×Q8—28no—
220C2×C3×Q8—28no—
221C2×C3×Q8—24no—
222C2×C3×Q8—28no—
223C2×C3×Q8—28no—
224C2×C3×Q8—24no—
225C2×C3×Q8—21no—
226C2×C3×Q8—21no—
227C2×C3×Q8—21no—
228C2×C3×Q8—21no—
229C2×C3×Q8—21no—
230C2×C3×Q8—21no—
231C2×C3×Q8C22×C412yes—
232C2×C3×Q8C22×C412yes—
233C2×C3×Q8C2×D412yes—
234C2×C3×Q8C2×D412yes—
235C2×C3×Q8#4112yes—
236C2×C3×Q8#4112yes—
237C22×C3×C4—24no—
238C22×C3×C4—24no—
239C22×C3×C4—24no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4C22×C412yes—
249C22×C3×C4C2×D411yescharacteristic
250C22×C3×C4C2×D411yescharacteristic
251C22×C3×C4C2×D411yescharacteristic
252C22×C3×C4C2×D411yescharacteristic
253C22×C3×C4C2×D411yescharacteristic
254C22×C3×C4#4112yes—
255C22×C3×C4C2411yescharacteristic
256C22×Dic3—21no—
257C22×Dic3—21no—
258C22×Dic3—21no—
259C22×Dic3—21no—
260C2×Dic6—21no—
261C2×Dic6—21no—
262C2×Dic6—21no—
263C2×Dic6—21no—
264C2×Dic6—21no—
265C2×Dic6C22×C412yes—
266C3×C4⋊C4—24no—
267C3×C4⋊C4—24no—
268C3×C4⋊C4—24no—
269C3×C4⋊C4—24no—
270C3×C4⋊C4—22no—
271C3×C4⋊C4—22no—
272C3×C4⋊C4—21no—
273C3×C4⋊C4—21no—
274C3×C4⋊C4C2×D412yes—
275C3×C4⋊C4C2×D412yes—
276C3×C22⋊C4—24no—
277C3×C22⋊C4—22no—
278C3×C22⋊C4—22no—
279C3×C42—24no—
280C3×C42—24no—
281C3×C42—24no—
282C3×C42—24no—
283C3×C42—24no—
284C3×C42—21no—
285C3×C42—21no—
286C3×C42C2×D412yes—
287C3×C42C2×D412yes—
288#217—24no—
289#217—81no—
290#216—28no—
291#216—28no—
292C4⋊Dic3—21no—
293C4⋊Dic3—21no—
294C4⋊Dic3—21no—
295C4⋊Dic3—21no—
296C4⋊Dic3—21no—
297C4⋊Dic3C22×C412yes—
298Dic3⋊C4—24no—
299Dic3⋊C4—42no—
300Dic3⋊C4—81no—
301C4×Dic3—42no—
302C4×Dic3—81no—
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—21no—
312C2×C3⋊C8—21no—
313C2×C3⋊C8C22×C412yes—
314C2×C3⋊C8C22×C412yes—
315C22×Q8—22no—
316C22×Q8—22no—
317C22×Q8—22no—
318C22×Q8—22no—
319C22×Q8—22no—
320C22×Q8—21no—
321C22×Q8—31no—
322C22×Q8C4×D314yes—
323C22×Q8C22×D311yescharacteristic
324C22×Q8C22×D311yescharacteristic
325C23×C4—21no—
326C23×C4C22×D311yescharacteristic
327C2×Q16—34no—
328C2×Q16—34no—
329C2×Q16—62no—
330C2×Q16—62no—
331C2×Q16—62no—
332C2×Q16—62no—
333C22×C8—31no—
334C22×C8—31no—
335C22×C8—31no—
336C22×C8—31no—
337C22⋊Q8—34no—
338C22⋊Q8—62no—
339C4×Q8—28no—
340C4×Q8—28no—
341C4×Q8—22no—
342C4×Q8—22no—
343C4×Q8—22no—
344C4×Q8—22no—
345C4×Q8—22no—
346C4×Q8—22no—
347C4×Q8—62no—
348C4×Q8—62no—
349C4×Q8#6714yes—
350C4×Q8#6714yes—
351#117—28no—
352#117—28no—
353#117—22no—
354#117—22no—
355#117—22no—
356#117—22no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—31no—
362C2×C4⋊C4—31no—
363C2×C4⋊C4—31no—
364C2×C4⋊C4—61no—
365C2×C4⋊C4—61no—
366C2×C4⋊C4—61no—
367C2×C4⋊C4#6711yescharacteristic
368C2×C4⋊C4#6711yescharacteristic
369C2×C4⋊C4C22×D311yescharacteristic
370C2×C4⋊C4C22×D311yescharacteristic
371C2×C22⋊C4—21no—
372C2×C22⋊C4—61no—
373C2×C22⋊C4—61no—
374C2×C22⋊C4#6711yescharacteristic
375C2×C22⋊C4#6711yescharacteristic
376C2×C42—21no—
377C2×C42—21no—
378C2×C42—21no—
379C2×C42—21no—
380C2×C42—21no—
381C2×C42—61no—
382C2×C42—61no—
383C2×C42C22×D311yescharacteristic
384C2×C42C22×D311yescharacteristic
385#107—62no—
386#106—62no—
387#103—34no—
388#103—34no—
389#103—62no—
390#103—62no—
391#103—62no—
392#103—62no—
393#103—62no—
394#103—62no—
395C22⋊C8—34no—
396C22⋊C8—62no—
397#97—62no—
398C4×C8—62no—
399#95—61no—
400#95—61no—
401#95—61no—
402#95—61no—
403#95—61no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3—21no—
407C23×C3—21no—
408C23×C3—21no—
409C23×C3—21no—
410C23×C3C4×D412yes—
411C23×C3C22×D411yescharacteristic
412C3×Q8—216no—
413C3×Q8—22no—
414C3×Q8—22no—
415C3×Q8—22no—
416C3×Q8—22no—
417C3×Q8—22no—
418C3×Q8—22no—
419C3×Q8C4×D414yes—
420C3×Q8C4×D414yes—
421C2×C3×C4—216no—
422C2×C3×C4—22no—
423C2×C3×C4—22no—
424C2×C3×C4—22no—
425C2×C3×C4—22no—
426C2×C3×C4—21no—
427C2×C3×C4—22no—
428C2×C3×C4—22no—
429C2×C3×C4—21no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—21no—
433C2×C3×C4—21no—
434C2×C3×C4—22no—
435C2×C3×C4—22no—
436C2×C3×C4—22no—
437C2×C3×C4—22no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—22no—
441C2×C3×C4—22no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4C4×D412yes—
451C2×C3×C4#12012yes—
452C2×C3×C4#12012yes—
453C2×C3×C4C23×C411yescharacteristic
454C2×C3×C4C22×D411yescharacteristic
455C2×C3×C4C22×D411yescharacteristic
456C2×C3×C4C2×#4111yescharacteristic
457C2×C3×C4C2×#4111yescharacteristic
458C2×C3×C4C2×#4111yescharacteristic
459C2×Dic3—22no—
460C2×Dic3—22no—
461C2×Dic3—41no—
462C2×Dic3—41no—
463C2×Dic3—41no—
464C2×Dic3—41no—
465C2×Dic3—41no—
466C2×Dic3—41no—
467C2×Dic3—41no—
468C2×Dic3—41no—
469C2×Dic3—41no—
470C2×Dic3—41no—
471Dic6—22no—
472Dic6—22no—
473Dic6—41no—
474Dic6—41no—
475C3⋊C8—22no—
476C3⋊C8—22no—
477C3⋊C8—41no—
478C3⋊C8—41no—
479C24C2×#6711yescharacteristic
480C2×Q8—24no—
481C2×Q8—28no—
482C2×Q8—28no—
483C2×Q8—24no—
484C2×Q8—28no—
485C2×Q8—28no—
486C2×Q8—24no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—32no—
494C2×Q8—61no—
495C2×Q8—61no—
496C2×Q8—61no—
497C2×Q8—61no—
498C2×Q8—61no—
499C2×Q8C2×C4×D312yes—
500C2×Q8C2×C4×D312yes—
501C2×Q8#23512yes—
502C2×Q8#23512yes—
503C2×Q8C2×#6712yes—
504C2×Q8C2×#6712yes—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—61no—
517C22×C4—61no—
518C22×C4—61no—
519C22×C4—61no—
520C22×C4C2×C4×D312yes—
521C22×C4#23512yes—
522C22×C4C2×#6711yescharacteristic
523C22×C4C2×#6711yescharacteristic
524C22×C4C2×#6711yescharacteristic
525C22×C4C2×#6711yescharacteristic
526C22×C4C2×#6711yescharacteristic
527C22×C4C23×D311yescharacteristic
528Q16—68no—
529Q16—68no—
530C2×C8—32no—
531C2×C8—32no—
532C2×C8—61no—
533C2×C8—61no—
534C2×C8—61no—
535C2×C8—61no—
536C2×C8—61no—
537C2×C8—61no—
538C2×C8—61no—
539C2×C8—61no—
540C2×C8—61no—
541C2×C8—61no—
542C4⋊C4—24no—
543C4⋊C4—24no—
544C4⋊C4—24no—
545C4⋊C4—24no—
546C4⋊C4—22no—
547C4⋊C4—22no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—32no—
551C4⋊C4—64no—
552C4⋊C4—61no—
553C4⋊C4—61no—
554C4⋊C4—61no—
555C4⋊C4—61no—
556C4⋊C4—61no—
557C4⋊C4—122no—
558C4⋊C4—241no—
559C4⋊C4C2×#6712yes—
560C4⋊C4C2×#6712yes—
561C22⋊C4—24no—
562C22⋊C4—22no—
563C22⋊C4—22no—
564C22⋊C4—64no—
565C22⋊C4—241no—
566C42—24no—
567C42—24no—
568C42—24no—
569C42—24no—
570C42—24no—
571C42—21no—
572C42—21no—
573C42—122no—
574C42—241no—
575C42C2×#6712yes—
576C42C2×#6712yes—
577C22×C3—22no—
578C22×C3—22no—
579C22×C3—22no—
580C22×C3—41no—
581C22×C3—41no—
582C22×C3—41no—
583C22×C3—41no—
584C22×C3C2×C4×D411yescharacteristic
585C22×C3C2×#12011yescharacteristic
586C22×C3#52511yescharacteristic
587C22×C3#57711yescharacteristic
588C22×C3#57811yescharacteristic
589C22×C3#57811yescharacteristic
590C22×C3#57811yescharacteristic
591C3×C4—22no—
592C3×C4—22no—
593C3×C4—24no—
594C3×C4—24no—
595C3×C4—22no—
596C3×C4—41no—
597C3×C4—42no—
598C3×C4—41no—
599C3×C4—42no—
600C3×C4C2×C4×D411yescharacteristic
601C3×C4C2×C4×D411yescharacteristic
602C3×C4#52511yescharacteristic
603C3×C4#52511yescharacteristic
604Dic3—42no—
605Dic3—42no—
606Dic3—81no—
607Dic3—81no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23C4×#6712yes—
615C23C22×#6711yescharacteristic
616Q8—216no—
617Q8—22no—
618Q8—22no—
619Q8—22no—
620Q8—22no—
621Q8—22no—
622Q8—22no—
623Q8—62no—
624Q8—62no—
625Q8—121no—
626Q8—121no—
627Q8C4×#6714yes—
628Q8C4×#6714yes—
629C2×C4—216no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—62no—
659C2×C4—62no—
660C2×C4—121no—
661C2×C4—121no—
662C2×C4—121no—
663C2×C4—121no—
664C2×C4—121no—
665C2×C4—121no—
666C2×C4—121no—
667C2×C4—121no—
668C2×C4—121no—
669C2×C4—121no—
670C2×C4C4×#6712yes—
671C2×C4#95312yes—
672C2×C4#95312yes—
673C2×C4C22×C4×D311yescharacteristic
674C2×C4C2×#23511yescharacteristic
675C2×C4C2×#23511yescharacteristic
676C2×C4C2×#23511yescharacteristic
677C2×C4C22×#6711yescharacteristic
678C2×C4C22×#6711yescharacteristic
679C8—62no—
680C8—62no—
681C8—121no—
682C8—121no—
683C2×C3—42no—
684C2×C3C4×#12011yescharacteristic
685C2×C3#294711yescharacteristic
686C2×C3#295011yescharacteristic
687C2×C3#301111yescharacteristic
688C2×C3#301311yescharacteristic
689C2×C3#312111yescharacteristic
690C2×C3#312711yescharacteristic
691C22—22no—
692C22—22no—
693C22—22no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22C2×C4×#6711yescharacteristic
699C22#579111yescharacteristic
700C22#583711yescharacteristic
701C22#583811yescharacteristic
702C22#583811yescharacteristic
703C22#583811yescharacteristic
704C22C2×#95311yescharacteristic
705C4—24no—
706C4—24no—
707C4—22no—
708C4—22no—
709C4—22no—
710C4—41no—
711C4—42no—
712C4—41no—
713C4—42no—
714C4—122no—
715C4—122no—
716C4—241no—
717C4—241no—
718C4C2×C4×#6711yescharacteristic
719C4C2×C4×#6711yescharacteristic
720C4#579111yescharacteristic
721C4#579111yescharacteristic
722C3#2146311yescharacteristic, complemented, Sylow
723C2—42no—
724C2#8254711yescharacteristic
725C2#8254911yescharacteristic
726C2#8255211yescharacteristic
727C2#8255511yescharacteristic
728C2C4×#95311yescharacteristic
729C2#8411411yescharacteristic
730C2#8411711yescharacteristic
subgroupG/H
centerC23C22×#67
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC2×C3×#519C2
socleC23×C3C22×D4
prime radicalC24×C3C2×D4
cosocleC22×C3×C4C24
hypercenterC2×#519D3
hypocenterC3#21463
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#519

Complements

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

NH ≅ G/Ntype
3. C2×#5030C2semidirect
4. C2×C4×#216C2semidirect
7. #71632C2semidirect
8. #71632C2semidirect
9. #71631C2semidirect
10. C4×#835C2semidirect
11. #71629C2semidirect
12. #71628C2semidirect
34. #5228C4semidirect
722. C3#21463semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5192
C2×#52282
C2×#50302
C2×C4×#2162
#822352
#721322
#716322
#716312
C4×#8352
#716292
#716282
#715852
#715822
#715762
#214633