Finite Group Databasebeta

← C2×#80633 #11664906

Subgroups — C2×#80633 #11664906

Order 768.

2070 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5624C211yesmaximal, characteristic, complemented
2C2×#5600C211yesmaximal, characteristic, complemented
3C2×C3×#465C211yesmaximal, characteristic, complemented
4C2×#5168C211yesmaximal, characteristic, complemented
5C2×Dic3×SD16C211yesmaximal, characteristic, complemented
6C2×#5114C211yesmaximal, characteristic, complemented
7C22×C8×Dic3C211yesmaximal, characteristic, complemented
8C2×#5051C211yesmaximal, characteristic, complemented
9C2×#5038C211yesmaximal, characteristic
10#80633C2116yesmaximal, direct product factor
11C2×#4858C211yesmaximal, characteristic, complemented
12C2×#4852C211yesmaximal, characteristic, complemented
13C2×#4800C211yesmaximal, characteristic, complemented
14C2×#4790C211yesmaximal, characteristic, complemented
15C2×#4768C211yesmaximal, characteristic, complemented
16C2×#4756C211yesmaximal, characteristic, complemented
17C2×#3168—31nomaximal, Sylow
18C22×C3×SD16C2211yescharacteristic
19C23×C3×C8C2211yescharacteristic
20C2×C3×C22⋊Q8C2211yescharacteristic
21C2×C3×#121C2211yescharacteristic
22C2×#947C2211yescharacteristic
23C2×Q8×Dic3C2211yescharacteristic
24C22×#216C2211yescharacteristic
25C2×#936C2211yescharacteristic
26C2×#935—21no—
27C2×D4×Dic3—21no—
28C2×D4×Dic3C2211yescharacteristic
29C22×#213C2211yescharacteristic
30C2×#930C2211yescharacteristic
31C2×#924C2211yescharacteristic
32C22×C4×Dic3C2211yescharacteristic
33C23×C3⋊C8C2211yescharacteristic
34C22×#204C2211yescharacteristic
35#5624—24no—
36#5624C2218yescomplemented
37#5600—24no—
38#5600C2218yescomplemented
39C2×#898—21no—
40C2×#893C2211yescharacteristic
41C2×#892—21no—
42C2×#890C2211yescharacteristic
43C2×#890C2211yescharacteristic
44C2×#887C2211yescharacteristic
45C2×#886—21no—
46C2×#67⋊C4—21no—
47C2×#879—21no—
48C2×#877—21no—
49C3×#465C2218yescomplemented
50C2×C3×#106C2211yescharacteristic
51C2×C3×#103C2211yescharacteristic
52C2×C3×#102C2211yescharacteristic
53C2×#835C2211yescharacteristic
54C2×#832C2211yescharacteristic
55#5168C2218yescomplemented
56Dic3×SD16C2218yescomplemented
57#5114C2218yescomplemented
58C2×#821C2211yescharacteristic
59C2×#817C2211yescharacteristic
60C2×#816C2211yescharacteristic
61C2×C8×Dic3C2211yescharacteristic
62C2×C8×Dic3C2211yescharacteristic
63C2×C8×Dic3C2211yescharacteristic
64C2×C8×Dic3C2211yescharacteristic
65C2×C8×Dic3C2218yescomplemented
66#5051C2218yescomplemented
67#5038C2218yes—
68C2×#810C2211yescharacteristic
69C2×#809C2211yescharacteristic
70C2×#807C2211yescharacteristic
71C2×#807C2211yescharacteristic
72#4858C2218yescomplemented
73#4852C2218yescomplemented
74#4800C2218yescomplemented
75#4790C2218yescomplemented
76#4768C2218yescomplemented
77#4756C2218yescomplemented
78C2×#529—31no—
79C2×#529—31no—
80#3168—316no—
81C2×#499—31no—
82C2×#495—31no—
83C2×#488—31no—
84C2×#488—31no—
85C2×#467—31no—
86C2×#466—31no—
87C2×#465—31no—
88C2×#465D311yescharacteristic, complemented
89C2×C4×Q16—31no—
90C2×C4×SD16—31no—
91C2×C4×SD16—31no—
92C2×C4×D8—31no—
93C22×C4×C8—31no—
94C22×C3×Q8C2311yescharacteristic
95C22×C3×D4—21no—
96C22×C3×D4C2311yescharacteristic
97C23×C3×C4C2311yescharacteristic
98C22×#67—21no—
99C23×Dic3—21no—
100C23×Dic3D411yescharacteristic
101C23×Dic3D411yescharacteristic
102C22×D12C2311yescharacteristic
103C22×C4×D3—21no—
104C22×Dic6C2311yescharacteristic
105C2×C3×SD16—24no—
106C2×C3×SD16C2314yes—
107C22×C3×C8—24no—
108C22×C3×C8C2311yescharacteristic
109C22×C3×C8C2314yes—
110C22×C3×C8C2311yescharacteristic
111C3×C22⋊Q8—22no—
112C3×C22⋊Q8C2314yes—
113C3×#121—22no—
114C3×#121C2314yes—
115C2×C3×C4⋊C4—21no—
116C2×C3×C4⋊C4C2311yescharacteristic
117C2×C3×C4⋊C4C2311yescharacteristic
118C2×C3×C22⋊C4—21no—
119C2×C3×C22⋊C4—21no—
120C2×#217—21no—
121C2×#217—21no—
122C2×#217—21no—
123C2×#217—21no—
124#947—22no—
125#947C2314yes—
126Q8×Dic3—22no—
127Q8×Dic3C2314yes—
128C2×#216—24no—
129C2×#216C2314yes—
130#936—22no—
131#936C2314yes—
132#935—28no—
133D4×Dic3—28no—
134D4×Dic3—22no—
135D4×Dic3C2314yes—
136C2×#213—24no—
137C2×#213C2314yes—
138#930—22no—
139#930C2314yes—
140C2×(C2×D3)⋊C4—21no—
141C2×(C2×D3)⋊C4—21no—
142C2×(C2×D3)⋊C4—21no—
143C2×(C2×D3)⋊C4—21no—
144C2×C4⋊Dic3—21no—
145C2×C4⋊Dic3—21no—
146C2×C4⋊Dic3—21no—
147C2×C4⋊Dic3C2311yescharacteristic
148C2×C4⋊Dic3C2311yescharacteristic
149#924—22no—
150#924C2314yes—
151C2×Dic3⋊C4—21no—
152C2×Dic3⋊C4—21no—
153C2×Dic3⋊C4—21no—
154C2×Dic3⋊C4—21no—
155C2×C4×Dic3—21no—
156C2×C4×Dic3—21no—
157C2×C4×Dic3D411yescharacteristic
158C2×C4×Dic3D411yescharacteristic
159C2×C4×Dic3D414yes—
160C2×C4×Dic3C2311yescharacteristic
161C2×C4×Dic3C2311yescharacteristic
162C2×C4×Dic3C2314yes—
163C22×C3⋊C8—24no—
164C22×C3⋊C8C2311yescharacteristic
165C22×C3⋊C8C2314yes—
166C22×C3⋊C8C2311yescharacteristic
167C2×#204—24no—
168C2×#204C2314yes—
169#898—28no—
170#893—22no—
171#893C2314yes—
172#892—28no—
173#890—22no—
174#890—22no—
175#890C2314yes—
176#890C2314yes—
177#887—22no—
178#887C2314yes—
179#886—28no—
180#67⋊C4—28no—
181#879—28no—
182#877—28no—
183C3×#106C2314yes—
184C3×#103C2314yes—
185C3×#102C2314yes—
186#835C2314yes—
187#832C2314yes—
188#821C2314yes—
189#817C2314yes—
190#816C2314yes—
191C8×Dic3C2314yes—
192C8×Dic3C2314yes—
193C8×Dic3C2314yes—
194C8×Dic3C2314yes—
195#810C2314yes—
196#809C2314yes—
197#807C2314yes—
198#807C2314yes—
199C22×Q16—31no—
200C22×SD16—31no—
201C22×SD16C2×D311yescharacteristic
202C22×D8—31no—
203C23×C8—31no—
204C23×C8C2×D311yescharacteristic
205#529—38no—
206#529—38no—
207#529—64no—
208#529—64no—
209C2×#126—61no—
210C2×#126—61no—
211C2×#125—31no—
212C2×#125—31no—
213C2×#124—31no—
214C2×#124—31no—
215C2×#123—61no—
216C2×#123—61no—
217C2×C22⋊Q8—31no—
218C2×C22⋊Q8C2×D311yescharacteristic
219C2×#121—31no—
220C2×#121C2×D311yescharacteristic
221C2×C4×Q8—31no—
222C2×C4×Q8—31no—
223C2×C4×D4—31no—
224C2×C4×D4—31no—
225C2×C4×D4—61no—
226C2×C4×D4—61no—
227C2×#117—61no—
228C2×#117—61no—
229C22×C42—31no—
230#499—38no—
231#495—38no—
232#488—38no—
233#488—38no—
234#467—38no—
235#466—38no—
236#465—38no—
237#465C2×D318yescomplemented
238C4×Q16—38no—
239C4×SD16—38no—
240C4×SD16—38no—
241C4×D8—38no—
242C2×#107—31no—
243C2×#107—31no—
244C2×#106—31no—
245C2×#106C2×D311yescharacteristic
246C2×#103—31no—
247C2×#103—31no—
248C2×#103—31no—
249C2×#103C2×D311yescharacteristic
250C2×#102—31no—
251C2×#102—31no—
252C2×#102—31no—
253C2×#102C2×D311yescharacteristic
254C2×C4×C8—31no—
255C2×C4×C8—31no—
256C2×C4×C8—38no—
257C2×C4×C8—31no—
258C2×C4×C8—31no—
259C24×C3—21no—
260C24×C3C2×D411yescharacteristic
261C23×D3—21no—
262C2×C3×Q8—21no—
263C2×C3×Q8—22no—
264C2×C3×Q8—22no—
265C2×C3×Q8C2412yes—
266C2×C3×D4—24no—
267C2×C3×D4—21no—
268C2×C3×D4—22no—
269C2×C3×D4—22no—
270C2×C3×D4—44no—
271C2×C3×D4C2412yes—
272C22×C3×C4—22no—
273C22×C3×C4—22no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4C2×D411yescharacteristic
278C22×C3×C4C2×D412yes—
279C22×C3×C4C2412yes—
280C22×C3×C4C2411yescharacteristic
281C2×#67—24no—
282C2×#67—44no—
283C22×Dic3—24no—
284C22×Dic3—24no—
285C22×Dic3—21no—
286C22×Dic3—21no—
287C22×Dic3—21no—
288C22×Dic3—24no—
289C22×Dic3—44no—
290C22×Dic3C2×D414yes—
291C22×Dic3C2×D414yes—
292C22×Dic3C2×D411yescharacteristic
293C22×Dic3C2×D411yescharacteristic
294C22×Dic3C2×D411yescharacteristic
295C22×Dic3C2×D411yescharacteristic
296C2×D12—22no—
297C2×D12—22no—
298C2×D12—21no—
299C2×D12C2412yes—
300C2×C4×D3—24no—
301C2×C4×D3—44no—
302C2×Dic6—22no—
303C2×Dic6—22no—
304C2×Dic6—21no—
305C2×Dic6C2412yes—
306C3×SD16—28no—
307C2×C3×C8—22no—
308C2×C3×C8—28no—
309C2×C3×C8#4114yes—
310C2×C3×C8C2412yes—
311C2×C3×C8C2412yes—
312C3×C4⋊C4—21no—
313C3×C4⋊C4—21no—
314C3×C4⋊C4—24no—
315C3×C4⋊C4C2412yes—
316C3×C4⋊C4C2412yes—
317C3×C22⋊C4—24no—
318C3×C22⋊C4—24no—
319#217—24no—
320#217—24no—
321#217—24no—
322#217—24no—
323#216—28no—
324#213—28no—
325(C2×D3)⋊C4—24no—
326(C2×D3)⋊C4—24no—
327(C2×D3)⋊C4—24no—
328(C2×D3)⋊C4—24no—
329C4⋊Dic3—21no—
330C4⋊Dic3—21no—
331C4⋊Dic3—24no—
332C4⋊Dic3—24no—
333C4⋊Dic3—24no—
334C4⋊Dic3C2412yes—
335C4⋊Dic3C2412yes—
336Dic3⋊C4—24no—
337Dic3⋊C4—24no—
338Dic3⋊C4—24no—
339Dic3⋊C4—24no—
340C4×Dic3—24no—
341C4×Dic3—24no—
342C4×Dic3C2×D414yes—
343C4×Dic3C2×D414yes—
344C4×Dic3C2×D412yes—
345C4×Dic3C2×D412yes—
346C4×Dic3C2412yes—
347C4×Dic3C2412yes—
348C2×C3⋊C8—22no—
349C2×C3⋊C8—28no—
350C2×C3⋊C8#4114yes—
351C2×C3⋊C8C2412yes—
352C2×C3⋊C8C2412yes—
353#204—28no—
354C22×Q8—31no—
355C22×Q8C22×D311yescharacteristic
356C22×D4—21no—
357C22×D4—31no—
358C22×D4—61no—
359C22×D4C22×D311yescharacteristic
360C23×C4—31no—
361C23×C4—31no—
362C23×C4—61no—
363C23×C4—61no—
364C23×C4C22×D311yescharacteristic
365C2×Q16—34no—
366C2×Q16—64no—
367C2×SD16—24no—
368C2×SD16—34no—
369C2×SD16—64no—
370C2×SD16C22×D314yes—
371C2×D8—34no—
372C2×D8—64no—
373C22×C8—24no—
374C22×C8—31no—
375C22×C8—31no—
376C22×C8—34no—
377C22×C8—64no—
378C22×C8C22×D311yescharacteristic
379C22×C8C22×D314yes—
380C22×C8C22×D311yescharacteristic
381#126—68no—
382#126—68no—
383#125—34no—
384#125—34no—
385#125—62no—
386#125—62no—
387#124—34no—
388#124—34no—
389#124—62no—
390#124—62no—
391#123—68no—
392#123—68no—
393C22⋊Q8—22no—
394C22⋊Q8—34no—
395C22⋊Q8—62no—
396C22⋊Q8C22×D314yes—
397#121—22no—
398#121—34no—
399#121—62no—
400#121C22×D314yes—
401C4×Q8—34no—
402C4×Q8—34no—
403C4×Q8—62no—
404C4×Q8—62no—
405C4×D4—34no—
406C4×D4—34no—
407C4×D4—62no—
408C4×D4—62no—
409C4×D4—68no—
410C4×D4—68no—
411#117—68no—
412#117—68no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—31no—
415C2×C4⋊C4—31no—
416C2×C4⋊C4—61no—
417C2×C4⋊C4—61no—
418C2×C4⋊C4—61no—
419C2×C4⋊C4—61no—
420C2×C4⋊C4—61no—
421C2×C4⋊C4—61no—
422C2×C4⋊C4—61no—
423C2×C4⋊C4C22×D311yescharacteristic
424C2×C4⋊C4C22×D311yescharacteristic
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—61no—
428C2×C22⋊C4—61no—
429C2×C22⋊C4—61no—
430C2×C22⋊C4—61no—
431C2×C22⋊C4—61no—
432C2×C22⋊C4—61no—
433C2×C22⋊C4—61no—
434C2×C22⋊C4—61no—
435C2×C42—31no—
436C2×C42—31no—
437C2×C42—34no—
438C2×C42—31no—
439C2×C42—31no—
440C2×C42—34no—
441C2×C42—61no—
442C2×C42—61no—
443#107—34no—
444#107—34no—
445#106—34no—
446#106C22×D314yes—
447#103—34no—
448#103—34no—
449#103—34no—
450#103C22×D314yes—
451#102—34no—
452#102—34no—
453#102—34no—
454#102C22×D314yes—
455C4×C8—34no—
456C4×C8—34no—
457C4×C8—34no—
458C4×C8—34no—
459C23×C3—22no—
460C23×C3—22no—
461C23×C3—22no—
462C23×C3—42no—
463C23×C3—42no—
464C23×C3—42no—
465C23×C3#13514yes—
466C23×C3C22×D412yes—
467C23×C3C22×D411yescharacteristic
468C22×D3—22no—
469C22×D3—42no—
470C22×D3—42no—
471C22×D3—42no—
472C3×Q8—22no—
473C3×Q8—22no—
474C3×Q8—42no—
475C3×D4—22no—
476C3×D4—22no—
477C3×D4—48no—
478C3×D4—42no—
479C2×C3×C4—22no—
480C2×C3×C4—24no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—22no—
484C2×C3×C4—22no—
485C2×C3×C4—22no—
486C2×C3×C4—42no—
487C2×C3×C4—42no—
488C2×C3×C4—42no—
489C2×C3×C4C22×D412yes—
490C2×C3×C4C22×D411yescharacteristic
491C2×C3×C4C2×#4112yes—
492C2×C3×C4C2×#4112yes—
493C2×C3×C4C2511yescharacteristic
494#67—48no—
495C2×Dic3—28no—
496C2×Dic3—22no—
497C2×Dic3—22no—
498C2×Dic3—22no—
499C2×Dic3—28no—
500C2×Dic3—22no—
501C2×Dic3—22no—
502C2×Dic3—22no—
503C2×Dic3—42no—
504C2×Dic3—42no—
505C2×Dic3—42no—
506C2×Dic3—48no—
507C2×Dic3#13514yes—
508C2×Dic3C22×D412yes—
509C2×Dic3C22×D412yes—
510C2×Dic3C22×D412yes—
511C2×Dic3C22×D412yes—
512D12—22no—
513D12—22no—
514D12—42no—
515C4×D3—48no—
516Dic6—22no—
517Dic6—22no—
518Dic6—42no—
519C3×C8—22no—
520C3×C8C2×#4114yes—
521C3⋊C8—22no—
522C3⋊C8C2×#4114yes—
523C24—21no—
524C24—61no—
525C24D3×D411yescharacteristic
526C2×Q8—21no—
527C2×Q8—22no—
528C2×Q8—22no—
529C2×Q8—32no—
530C2×Q8—61no—
531C2×Q8—62no—
532C2×Q8—62no—
533C2×Q8C23×D312yes—
534C2×D4—24no—
535C2×D4—21no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—32no—
539C2×D4—44no—
540C2×D4—64no—
541C2×D4—61no—
542C2×D4—62no—
543C2×D4—62no—
544C2×D4—124no—
545C2×D4C23×D312yes—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—31no—
552C22×C4—34no—
553C22×C4—34no—
554C22×C4—31no—
555C22×C4—31no—
556C22×C4—31no—
557C22×C4—64no—
558C22×C4—64no—
559C22×C4—64no—
560C22×C4—64no—
561C22×C4—61no—
562C22×C4—61no—
563C22×C4—61no—
564C22×C4—124no—
565C22×C4—124no—
566C22×C4D3×D412yes—
567C22×C4D3×D411yescharacteristic
568C22×C4C23×D312yes—
569C22×C4C23×D311yescharacteristic
570Q16—68no—
571SD16—28no—
572SD16—68no—
573D8—68no—
574C2×C8—22no—
575C2×C8—28no—
576C2×C8—34no—
577C2×C8—32no—
578C2×C8—32no—
579C2×C8—68no—
580C2×C8—62no—
581C2×C8#23714yes—
582C2×C8C23×D312yes—
583C2×C8C23×D312yes—
584C4⋊C4—24no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—32no—
588C4⋊C4—32no—
589C4⋊C4—64no—
590C4⋊C4—64no—
591C4⋊C4—64no—
592C4⋊C4—64no—
593C4⋊C4—64no—
594C4⋊C4—64no—
595C4⋊C4—61no—
596C4⋊C4—61no—
597C4⋊C4—64no—
598C4⋊C4C23×D312yes—
599C4⋊C4C23×D312yes—
600C22⋊C4—24no—
601C22⋊C4—24no—
602C22⋊C4—64no—
603C22⋊C4—64no—
604C22⋊C4—64no—
605C22⋊C4—64no—
606C22⋊C4—64no—
607C22⋊C4—64no—
608C22⋊C4—64no—
609C22⋊C4—64no—
610C42—34no—
611C42—32no—
612C42—32no—
613C42—34no—
614C42—32no—
615C42—32no—
616C42—64no—
617C42—64no—
618C22×C3—28no—
619C22×C3—22no—
620C22×C3—22no—
621C22×C3—42no—
622C22×C3—42no—
623C22×C3—42no—
624C22×C3—84no—
625C22×C3#53212yes—
626C22×C3C2×#13514yes—
627C22×C3C2×#13512yes—
628C22×C3C2×#13512yes—
629C22×C3C23×D411yescharacteristic
630C2×D3—42no—
631C2×D3—42no—
632C2×D3—42no—
633C2×D3—84no—
634C3×C4—22no—
635C3×C4—42no—
636C3×C4—42no—
637C3×C4—42no—
638C3×C4#53212yes—
639C3×C4C22×#4111yescharacteristic
640C3×C4C22×#4111yescharacteristic
641Dic3—22no—
642Dic3—22no—
643Dic3—22no—
644Dic3—42no—
645Dic3—42no—
646Dic3—42no—
647Dic3C2×#13514yes—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—62no—
655C23—122no—
656C23—122no—
657C23—122no—
658C23#91614yes—
659C23C2×D3×D412yes—
660C23C2×D3×D411yescharacteristic
661Q8—22no—
662Q8—22no—
663Q8—42no—
664Q8—62no—
665Q8—62no—
666Q8—122no—
667D4—22no—
668D4—22no—
669D4—48no—
670D4—42no—
671D4—62no—
672D4—62no—
673D4—128no—
674D4—122no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—32no—
683C2×C4—34no—
684C2×C4—32no—
685C2×C4—32no—
686C2×C4—32no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—68no—
691C2×C4—68no—
692C2×C4—62no—
693C2×C4—62no—
694C2×C4—62no—
695C2×C4—62no—
696C2×C4—62no—
697C2×C4—62no—
698C2×C4—128no—
699C2×C4—128no—
700C2×C4—122no—
701C2×C4—122no—
702C2×C4—122no—
703C2×C4C2×D3×D412yes—
704C2×C4C2×D3×D411yescharacteristic
705C2×C4C2×#23712yes—
706C2×C4D3×#4112yes—
707C2×C4C24×D311yescharacteristic
708C8—22no—
709C8—34no—
710C8—62no—
711C8C2×#23714yes—
712C2×C3—24no—
713C2×C3—82no—
714C2×C3#316814yescomplemented
715C2×C3C2×#53211yescharacteristic
716C2×C3C22×#13511yescharacteristic
717C2×C3C22×#13511yescharacteristic
718D3—82no—
719C22—22no—
720C22—22no—
721C22—28no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—84no—
726C22—122no—
727C22—122no—
728C22—122no—
729C22—244no—
730C22#559612yes—
731C22C2×#91614yes—
732C22C2×#91612yes—
733C22D3×#13512yes—
734C22C22×D3×D411yescharacteristic
735C4—22no—
736C4—34no—
737C4—42no—
738C4—42no—
739C4—42no—
740C4—62no—
741C4—62no—
742C4—62no—
743C4—122no—
744C4—122no—
745C4—122no—
746C4#559612yes—
747C4C22×#23711yescharacteristic
748C4C2×D3×#4111yescharacteristic
749C3C2×#316811yescharacteristic, complemented, Sylow
750C2—24no—
751C2—82no—
752C2—242no—
753C2#8063314yesdirect product factor
754C2C2×#559611yescharacteristic
755C2C22×#91611yescharacteristic
756C2C2×D3×#13511yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#465C2
socleC23×C3C22×D4
prime radicalC2×#5038C2
hypercenterC2×#465D3
hypocenterC3C2×#3168
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×#5624C2semidirect
2. C2×#5600C2semidirect
3. C2×C3×#465C2semidirect
4. C2×#5168C2semidirect
5. C2×Dic3×SD16C2semidirect
6. C2×#5114C2semidirect
7. C22×C8×Dic3C2semidirect
8. C2×#5051C2semidirect
10. #80633C2direct (N × H)
11. C2×#4858C2semidirect
12. C2×#4852C2semidirect
13. C2×#4800C2semidirect
14. C2×#4790C2semidirect
15. C2×#4768C2semidirect
16. C2×#4756C2semidirect
36. #5624C22semidirect
38. #5600C22semidirect
49. C3×#465C22semidirect
55. #5168C22semidirect
56. Dic3×SD16C22semidirect
57. #5114C22semidirect
65. C2×C8×Dic3C22semidirect
66. #5051C22semidirect
72. #4858C22semidirect
73. #4852C22semidirect
74. #4800C22semidirect
75. #4790C22semidirect
76. #4768C22semidirect
77. #4756C22semidirect
88. C2×#465D3semidirect
237. #465C2×D3semidirect
714. C2×C3#3168semidirect
749. C3C2×#3168semidirect
753. C2#80633direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#56242
C2×#56002
C2×C3×#4652
C2×#51682
C2×Dic3×SD162
C2×#51142
C22×C8×Dic32
C2×#50512
C2×#50382
#806332
C2×#48582
C2×#48522
C2×#48002
C2×#47902
C2×#47682
C2×#47562
C2×#31683