Finite Group Databasebeta

← C2×#11723707 #13178701

Subgroups — C2×#11723707 #13178701

Order 1728.

1426 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3830C211yesmaximal, characteristic, complemented
2C2×#89041C211yesmaximal, characteristic, complemented
3C2×C3×#3754C211yesmaximal, characteristic, complemented
4C2×C3×#3753C211yesmaximal, characteristic, complemented
5#11723707C218yesmaximal, direct product factor
6C2×#88812C211yesmaximal, characteristic, complemented
7C2×#88811C211yesmaximal, characteristic, complemented
8C2×#88808C211yesmaximal, characteristic, complemented
9C2×#63936—31nomaximal
10C2×#63935—31nomaximal
11C2×#63933—31nomaximal
12C2×C33×D4C2211yescharacteristic
13C2×C3×#638—21no—
14C22×C3×C3⋊Dic3—21no—
15C3×#3830—22no—
16C3×#3830C2214yescomplemented
17C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
18C2×C3×C4×C3⋊D3C2211yescharacteristic
19C2×C3×#634C2211yescharacteristic
20C2×C3×#634C2211yescharacteristic
21C2×#6295—21no—
22C2×#6294—21no—
23#89041—22no—
24#89041C2214yescomplemented
25C3×#3754C2214yescomplemented
26C3×#3753C2214yescomplemented
27C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
28C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
29#88812C2214yescomplemented
30#88811C2214yescomplemented
31#88808C2214yescomplemented
32C2×#3830D311yescharacteristic, complemented
33C2×C3×#237—31no—
34C2×C3×#237—31no—
35C2×C3×#237—61no—
36C2×#3799—31no—
37C2×#3796—31no—
38C2×#3795—31no—
39C2×#3754D311yescharacteristic, complemented
40C2×#3753D311yescharacteristic, complemented
41C2×C3×#214—31no—
42C2×C3×#214—31no—
43C2×C3×#214—61no—
44C2×C3×#213—31no—
45C2×C3×#213—31no—
46C2×C3×#213—61no—
47#63936—38no—
48#63935—38no—
49#63933—38no—
50C2×#3719—31no—
51C2×#3719—31no—
52C2×#3718—31no—
53C2×#3717—31no—
54C2×#3716—31no—
55C2×#3715—31no—
56C2×#3710—31no—
57C2×D3×C3⋊C8—31no—
58C2×D3×C3⋊C8—31no—
59C23×C33—21no—
60C22×C3×C3⋊D3—21no—
61C22×C3×C3⋊D3D411yescharacteristic
62C33×D4—21no—
63C33×D4C2312yes—
64C2×C33×C4C2311yescharacteristic
65C3×#638—24no—
66C2×C3×C3⋊Dic3—21no—
67C2×C3×C3⋊Dic3—21no—
68C2×C3×C3⋊Dic3—24no—
69C2×C3×C3⋊Dic3D411yescharacteristic
70C3×C4⋊(C3⋊D3)—21no—
71C3×C4⋊(C3⋊D3)C2312yes—
72C3×C4×C3⋊D3D412yes—
73C3×C4×C3⋊D3C2312yes—
74C3×#634—21no—
75C3×#634—21no—
76C3×#634C2312yes—
77C3×#634C2312yes—
78#6295—24no—
79#6294—24no—
80C3×C3⋊(C3⋊C8)C2312yes—
81C3×C3⋊(C3⋊C8)C2312yes—
82C2×#950—91no—
83C2×#916—91no—
84C2×#912—91no—
85C2×C32×D4—21no—
86C2×C32×D4—21no—
87C2×C32×D4—21no—
88C2×C32×D4—41no—
89C2×C32×D4C2×D311yescharacteristic
90C2×C32×D4C2×D311yescharacteristic
91C2×C32×D4C2×D311yescharacteristic
92C2×#638—21no—
93C22×C3⋊Dic3—21no—
94#3830—22no—
95#3830C2×D314yescomplemented
96C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
97C2×C4×C3⋊D3C2×D311yescharacteristic
98C2×#634C2×D311yescharacteristic
99C2×#634C2×D311yescharacteristic
100C2×C3×#67—61no—
101C2×C3×#67—61no—
102C2×C3×#67—62no—
103C22×C3×Dic3—61no—
104C22×C3×Dic3—61no—
105C22×C3×Dic3—62no—
106C3×#237—34no—
107C3×#237—34no—
108C3×#237—62no—
109C3×#237—62no—
110C3×#237—64no—
111C3×#237—64no—
112C2×C3×D12—31no—
113C2×C3×D12—31no—
114C2×C3×D12—61no—
115C2×C3×C4×D3—31no—
116C2×C3×C4×D3—31no—
117C2×C3×C4×D3—61no—
118C2×C3×Dic6—31no—
119C2×C3×Dic6—31no—
120C2×C3×Dic6—31no—
121C2×C3×Dic6—31no—
122C2×C3×Dic6—61no—
123C2×C3×Dic6—61no—
124C2×#626—61no—
125C2×#626—61no—
126C2×#625—61no—
127C2×#624—61no—
128C2×D3×Dic3—61no—
129C2×D3×Dic3—61no—
130#3799—34no—
131#3799—62no—
132#3796—34no—
133#3796—62no—
134#3795—34no—
135#3795—62no—
136#3754C2×D314yescomplemented
137#3753C2×D314yescomplemented
138C2×C3⋊(C3⋊C8)C2×D311yescharacteristic
139C2×C3⋊(C3⋊C8)C2×D311yescharacteristic
140C3×#214—34no—
141C3×#214—34no—
142C3×#214—64no—
143C3×#213—34no—
144C3×#213—34no—
145C3×#213—64no—
146C2×C3×C3⋊C8—31no—
147C2×C3×C3⋊C8—31no—
148C2×C3×C3⋊C8—31no—
149C2×C3×C3⋊C8—31no—
150C2×C3×C3⋊C8—61no—
151C2×C3×C3⋊C8—61no—
152#3719—34no—
153#3719—34no—
154#3718—34no—
155#3717—34no—
156#3716—34no—
157#3715—34no—
158#3710—34no—
159D3×C3⋊C8—34no—
160D3×C3⋊C8—34no—
161C22×C33—22no—
162C22×C33—42no—
163C22×C33C2×D411yescharacteristic
164C2×C3×C3⋊D3—22no—
165C2×C3×C3⋊D3—22no—
166C2×C3×C3⋊D3—42no—
167C2×C3×C3⋊D3C2×D412yes—
168C33×C4C2×D411yescharacteristic
169C33×C4C2411yescharacteristic
170C3×C3⋊Dic3—22no—
171C3×C3⋊Dic3—22no—
172C3×C3⋊Dic3C2×D412yes—
173C2×C3×#41—91no—
174C2×#239—91no—
175C2×#237—31no—
176C2×#237—31no—
177C2×#237—61no—
178C2×#237—91no—
179C2×#235—91no—
180C2×C3×SD16—91no—
181C2×C3×D8—91no—
182#950—98no—
183C2×#216—91no—
184C2×#216—91no—
185C2×#215—91no—
186C2×#214—31no—
187C2×#214—31no—
188C2×#214—61no—
189C2×#214—91no—
190C2×#213—31no—
191C2×#213—31no—
192C2×#213—61no—
193C22×C3⋊C8—91no—
194#916—98no—
195#912—98no—
196C2×Dic12—91no—
197C2×#204—91no—
198C2×D3×C8—91no—
199C2×D3×C8—91no—
200C23×C32—21no—
201C23×C32—22no—
202C23×C32—21no—
203C23×C32—21no—
204C23×C32—41no—
205C23×C32—41no—
206C23×C32—42no—
207C22×C3⋊D3—21no—
208C22×C3⋊D3#6711yescharacteristic
209C22×C3×D3—31no—
210C22×C3×D3—31no—
211C22×C3×D3—61no—
212C22×C3×D3—61no—
213C22×C3×D3—61no—
214C22×C3×D3—121no—
215C32×D4—21no—
216C32×D4—22no—
217C32×D4—21no—
218C32×D4—21no—
219C32×D4—22no—
220C32×D4—22no—
221C32×D4—22no—
222C32×D4—42no—
223C32×D4—41no—
224C32×D4—41no—
225C32×D4—42no—
226C32×D4C22×D312yes—
227C32×D4C22×D312yes—
228C32×D4C22×D312yes—
229C2×C32×C4—21no—
230C2×C32×C4—21no—
231C2×C32×C4—21no—
232C2×C32×C4—41no—
233C2×C32×C4C22×D311yescharacteristic
234C2×C32×C4C22×D311yescharacteristic
235C2×C32×C4C22×D311yescharacteristic
236#638—24no—
237C2×C3⋊Dic3—21no—
238C2×C3⋊Dic3—24no—
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3#6711yescharacteristic
241C4⋊(C3⋊D3)—21no—
242C4⋊(C3⋊D3)C22×D312yes—
243C4×C3⋊D3#6712yes—
244C4×C3⋊D3C22×D312yes—
245#634—21no—
246#634—21no—
247#634C22×D312yes—
248#634C22×D312yes—
249C3×#67—64no—
250C3×#67—64no—
251C3×#67—68no—
252C2×C3×Dic3—31no—
253C2×C3×Dic3—31no—
254C2×C3×Dic3—61no—
255C2×C3×Dic3—64no—
256C2×C3×Dic3—64no—
257C2×C3×Dic3—62no—
258C2×C3×Dic3—68no—
259C2×C3×Dic3—61no—
260C2×C3×Dic3—61no—
261C2×C3×Dic3—61no—
262C2×C3×Dic3—61no—
263C2×C3×Dic3—121no—
264C3×D12—32no—
265C3×D12—32no—
266C3×D12—62no—
267C3×D12—61no—
268C3×D12—61no—
269C3×D12—121no—
270C3×C4×D3—32no—
271C3×C4×D3—32no—
272C3×C4×D3—32no—
273C3×C4×D3—32no—
274C3×C4×D3—62no—
275C3×C4×D3—62no—
276C3×Dic6—32no—
277C3×Dic6—32no—
278C3×Dic6—32no—
279C3×Dic6—32no—
280C3×Dic6—62no—
281C3×Dic6—62no—
282C3×Dic6—62no—
283C3×Dic6—61no—
284C3×Dic6—61no—
285C3×Dic6—61no—
286C3×Dic6—61no—
287C3×Dic6—121no—
288#626—64no—
289#626—64no—
290#625—64no—
291#624—64no—
292D3×Dic3—64no—
293D3×Dic3—64no—
294C3⋊(C3⋊C8)C22×D312yes—
295C3⋊(C3⋊C8)C22×D312yes—
296C3×C3⋊C8—32no—
297C3×C3⋊C8—32no—
298C3×C3⋊C8—32no—
299C3×C3⋊C8—32no—
300C3×C3⋊C8—62no—
301C3×C3⋊C8—62no—
302C2×#135—271noSylow
303C2×C33—42no—
304C2×C33#13512yescomplemented
305C2×C33C22×D411yescharacteristic
306C3×C3⋊D3—22no—
307C3×C3⋊D3—42no—
308C3×#41—94no—
309C3×#41—182no—
310C2×C3×Q8—91no—
311C2×C3×Q8—91no—
312C2×C3×D4—21no—
313C2×C3×D4—21no—
314C2×C3×D4—21no—
315C2×C3×D4—41no—
316C2×C3×D4—91no—
317C2×C3×D4—181no—
318C2×C3×D4D3211yescharacteristic
319C2×C3×D4D3211yescharacteristic
320C2×C3×D4D3211yescharacteristic
321C22×C3×C4—91no—
322C22×C3×C4—181no—
323C2×#67—61no—
324C2×#67—61no—
325C2×#67—62no—
326C2×#67—181no—
327C2×#67—181no—
328C22×Dic3—61no—
329C22×Dic3—61no—
330C22×Dic3—62no—
331C22×Dic3—181no—
332#239—94no—
333#239—182no—
334#237—34no—
335#237—34no—
336#237—64no—
337#237—62no—
338#237—62no—
339#237—64no—
340#237—94no—
341#237—182no—
342#235—94no—
343#235—182no—
344C2×D12—31no—
345C2×D12—31no—
346C2×D12—61no—
347C2×D12—181no—
348C2×C4×D3—31no—
349C2×C4×D3—31no—
350C2×C4×D3—61no—
351C2×C4×D3—181no—
352C2×C4×D3—181no—
353C2×Dic6—31no—
354C2×Dic6—31no—
355C2×Dic6—31no—
356C2×Dic6—31no—
357C2×Dic6—61no—
358C2×Dic6—61no—
359C3×SD16—94no—
360C3×D8—94no—
361C2×C3×C8—91no—
362C2×C3×C8—91no—
363#216—94no—
364#216—94no—
365#215—94no—
366#214—34no—
367#214—34no—
368#214—64no—
369#214—94no—
370#213—34no—
371#213—34no—
372#213—64no—
373C2×C3⋊C8—31no—
374C2×C3⋊C8—31no—
375C2×C3⋊C8—31no—
376C2×C3⋊C8—31no—
377C2×C3⋊C8—61no—
378C2×C3⋊C8—61no—
379C2×C3⋊C8—94no—
380Dic12—94no—
381#204—94no—
382D3×C8—94no—
383D3×C8—94no—
384C22×C32—22no—
385C22×C32—24no—
386C22×C32—22no—
387C22×C32—22no—
388C22×C32—21no—
389C22×C32—21no—
390C22×C32—21no—
391C22×C32—41no—
392C22×C32—42no—
393C22×C32—42no—
394C22×C32—44no—
395C22×C32—42no—
396C22×C32—44no—
397C22×C32—42no—
398C22×C32—42no—
399C22×C32—82no—
400C22×C32—82no—
401C22×C32—84no—
402C22×C32D3×D411yescharacteristic
403C22×C32D3×D411yescharacteristic
404C22×C32C2×#6711yescharacteristic
405C2×C3⋊D3—22no—
406C2×C3⋊D3—22no—
407C2×C3⋊D3—42no—
408C2×C3⋊D3C2×#6712yes—
409C2×C3×D3—32no—
410C2×C3×D3—32no—
411C2×C3×D3—62no—
412C2×C3×D3—62no—
413C2×C3×D3—62no—
414C2×C3×D3—62no—
415C2×C3×D3—62no—
416C2×C3×D3—122no—
417C2×C3×D3—122no—
418C2×C3×D3—122no—
419C2×C3×D3—122no—
420C2×C3×D3—242no—
421C32×C4—21no—
422C32×C4—21no—
423C32×C4—21no—
424C32×C4—21no—
425C32×C4—21no—
426C32×C4—21no—
427C32×C4—41no—
428C32×C4—41no—
429C32×C4D3×D411yescharacteristic
430C32×C4D3×D411yescharacteristic
431C32×C4C2×#6711yescharacteristic
432C32×C4C23×D311yescharacteristic
433C32×C4C23×D311yescharacteristic
434C32×C4C23×D311yescharacteristic
435C3⋊Dic3—22no—
436C3⋊Dic3—22no—
437C3⋊Dic3C2×#6712yes—
438C3×Dic3—32no—
439C3×Dic3—32no—
440C3×Dic3—62no—
441C3×Dic3—64no—
442C3×Dic3—62no—
443C3×Dic3—62no—
444C3×Dic3—62no—
445C3×Dic3—62no—
446C3×Dic3—122no—
447C2×#41—91no—
448C2×#41—271no—
449#135—278no—
450C2×Q16—271no—
451C2×SD16—91no—
452C2×SD16—271no—
453C2×D8—91no—
454C22×C8—271no—
455C33C2×#13511yescharacteristic, complemented, Sylow
456C23×C3—22no—
457C23×C3—21no—
458C23×C3—21no—
459C23×C3—21no—
460C23×C3—41no—
461C23×C3—41no—
462C23×C3—42no—
463C23×C3—91no—
464C23×C3—181no—
465C22×D3—31no—
466C22×D3—31no—
467C22×D3—61no—
468C22×D3—61no—
469C22×D3—61no—
470C22×D3—121no—
471C3×Q8—92no—
472C3×Q8—92no—
473C3×Q8—181no—
474C3×Q8—181no—
475C3×D4—22no—
476C3×D4—21no—
477C3×D4—21no—
478C3×D4—21no—
479C3×D4—22no—
480C3×D4—22no—
481C3×D4—22no—
482C3×D4—41no—
483C3×D4—41no—
484C3×D4—42no—
485C3×D4—42no—
486C3×D4—92no—
487C3×D4—184no—
488C3×D4—181no—
489C3×D4C2×D3212yes—
490C3×D4C2×D3212yes—
491C3×D4C2×D3212yes—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—41no—
496C2×C3×C4—91no—
497C2×C3×C4—92no—
498C2×C3×C4—92no—
499C2×C3×C4—184no—
500C2×C3×C4—181no—
501C2×C3×C4—181no—
502C2×C3×C4C2×D3211yescharacteristic
503C2×C3×C4C2×D3211yescharacteristic
504C2×C3×C4C2×D3211yescharacteristic
505#67—64no—
506#67—64no—
507#67—68no—
508#67—184no—
509#67—184no—
510C2×Dic3—31no—
511C2×Dic3—31no—
512C2×Dic3—61no—
513C2×Dic3—64no—
514C2×Dic3—64no—
515C2×Dic3—62no—
516C2×Dic3—68no—
517C2×Dic3—61no—
518C2×Dic3—61no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—121no—
522C2×Dic3—184no—
523D12—32no—
524D12—32no—
525D12—62no—
526D12—61no—
527D12—61no—
528D12—121no—
529D12—184no—
530C4×D3—32no—
531C4×D3—32no—
532C4×D3—32no—
533C4×D3—32no—
534C4×D3—62no—
535C4×D3—62no—
536C4×D3—184no—
537C4×D3—184no—
538Dic6—32no—
539Dic6—32no—
540Dic6—32no—
541Dic6—32no—
542Dic6—62no—
543Dic6—62no—
544Dic6—62no—
545Dic6—61no—
546Dic6—61no—
547Dic6—61no—
548Dic6—61no—
549Dic6—121no—
550C3×C8—92no—
551C3×C8—92no—
552C3⋊C8—32no—
553C3⋊C8—32no—
554C3⋊C8—32no—
555C3⋊C8—32no—
556C3⋊C8—62no—
557C3⋊C8—62no—
558C2×C32—21no—
559C2×C32—21no—
560C2×C32—21no—
561C2×C32—22no—
562C2×C32—22no—
563C2×C32—22no—
564C2×C32—42no—
565C2×C32—41no—
566C2×C32—42no—
567C2×C32—44no—
568C2×C32—42no—
569C2×C32—42no—
570C2×C32—82no—
571C2×C32—82no—
572C2×C32—84no—
573C2×C32#91212yescomplemented
574C2×C32#91612yescomplemented
575C2×C32#95012yescomplemented
576C2×C32C2×D3×D411yescharacteristic
577C2×C32C2×D3×D411yescharacteristic
578C2×C32C22×#6711yescharacteristic
579C3⋊D3—22no—
580C3⋊D3—42no—
581C3×D3—62no—
582C3×D3—62no—
583C3×D3—122no—
584C3×D3—122no—
585C3×D3—122no—
586C3×D3—242no—
587#41—94no—
588#41—182no—
589#41—274no—
590#41—542no—
591C2×Q8—91no—
592C2×Q8—91no—
593C2×D4—91no—
594C2×D4—181no—
595C2×D4—541no—
596C2×D4#111311yescharacteristic
597C22×C4—91no—
598C22×C4—181no—
599C22×C4—541no—
600Q16—274no—
601SD16—94no—
602SD16—274no—
603D8—94no—
604C2×C8—91no—
605C2×C8—91no—
606C2×C8—274no—
607C22×C3—24no—
608C22×C3—22no—
609C22×C3—22no—
610C22×C3—22no—
611C22×C3—21no—
612C22×C3—21no—
613C22×C3—21no—
614C22×C3—42no—
615C22×C3—42no—
616C22×C3—44no—
617C22×C3—44no—
618C22×C3—42no—
619C22×C3—42no—
620C22×C3—42no—
621C22×C3—41no—
622C22×C3—82no—
623C22×C3—82no—
624C22×C3—84no—
625C22×C3—92no—
626C22×C3—182no—
627C22×C3—182no—
628C22×C3—362no—
629C22×C3D3×#6711yescharacteristic
630C22×C3D3×#6711yescharacteristic
631C22×C3#381111yescharacteristic
632C2×D3—32no—
633C2×D3—32no—
634C2×D3—62no—
635C2×D3—62no—
636C2×D3—62no—
637C2×D3—62no—
638C2×D3—62no—
639C2×D3—122no—
640C2×D3—122no—
641C2×D3—122no—
642C2×D3—122no—
643C2×D3—242no—
644C3×C4—21no—
645C3×C4—21no—
646C3×C4—21no—
647C3×C4—21no—
648C3×C4—21no—
649C3×C4—21no—
650C3×C4—41no—
651C3×C4—41no—
652C3×C4—92no—
653C3×C4—182no—
654C3×C4—182no—
655C3×C4D3×#6711yescharacteristic
656C3×C4D3×#6711yescharacteristic
657C3×C4#381111yescharacteristic
658C3×C4C22×D3211yescharacteristic
659C3×C4C22×D3211yescharacteristic
660C3×C4C22×D3211yescharacteristic
661Dic3—32no—
662Dic3—32no—
663Dic3—62no—
664Dic3—64no—
665Dic3—62no—
666Dic3—62no—
667Dic3—62no—
668Dic3—62no—
669Dic3—122no—
670C32—21no—
671C32—21no—
672C32—21no—
673C32—41no—
674C32C2×#91211yescharacteristic, complemented
675C32C2×#91611yescharacteristic, complemented
676C32C2×#95011yescharacteristic, complemented
677C23—21no—
678C23—91no—
679C23—181no—
680Q8—92no—
681Q8—92no—
682Q8—181no—
683Q8—181no—
684D4—21no—
685D4—92no—
686D4—184no—
687D4—181no—
688D4—544no—
689D4C2×#111312yes—
690C2×C4—91no—
691C2×C4—92no—
692C2×C4—92no—
693C2×C4—184no—
694C2×C4—181no—
695C2×C4—181no—
696C2×C4—544no—
697C2×C4C2×#111311yescharacteristic
698C8—92no—
699C8—92no—
700C2×C3—21no—
701C2×C3—21no—
702C2×C3—21no—
703C2×C3—22no—
704C2×C3—22no—
705C2×C3—22no—
706C2×C3—44no—
707C2×C3—42no—
708C2×C3—42no—
709C2×C3—42no—
710C2×C3—41no—
711C2×C3—42no—
712C2×C3—82no—
713C2×C3—82no—
714C2×C3—84no—
715C2×C3—182no—
716C2×C3—362no—
717C2×C3#6393312yescomplemented
718C2×C3#6393512yescomplemented
719C2×C3#6393612yescomplemented
720C2×C3C2×D3×#6711yescharacteristic
721C2×C3C2×D3×#6711yescharacteristic
722C2×C3C2×#381111yescharacteristic
723D3—62no—
724D3—62no—
725D3—122no—
726D3—122no—
727D3—122no—
728D3—242no—
729C22—22no—
730C22—42no—
731C22—92no—
732C22—182no—
733C22—182no—
734C22—362no—
735C22#8904911yescharacteristic
736C4—92no—
737C4—182no—
738C4—182no—
739C4#8904911yescharacteristic
740C4C22×#111311yescharacteristic
741C3—21no—
742C3—21no—
743C3—21no—
744C3—41no—
745C3C2×#6393311yescharacteristic, complemented
746C3C2×#6393511yescharacteristic, complemented
747C3C2×#6393611yescharacteristic, complemented
748C2—42no—
749C2—182no—
750C2—362no—
751C2#1172370712yesdirect product factor
752C2C2×#8904911yescharacteristic
subgroupG/H
centerC22#89049
commutator, cosocleC33×C4C24
FrattiniC4C22×#1113
FittingC2×C33×D4C22
socleC22×C33C2×D4
hypercenterC2×D4#1113
hypocenterC33C2×#135
LCSG ▷ C33×C4 ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3830C2semidirect
2. C2×#89041C2semidirect
3. C2×C3×#3754C2semidirect
4. C2×C3×#3753C2semidirect
5. #11723707C2direct (N × H)
6. C2×#88812C2semidirect
7. C2×#88811C2semidirect
8. C2×#88808C2semidirect
16. C3×#3830C22semidirect
24. #89041C22semidirect
25. C3×#3754C22semidirect
26. C3×#3753C22semidirect
29. #88812C22semidirect
30. #88811C22semidirect
31. #88808C22semidirect
32. C2×#3830D3semidirect
39. C2×#3754D3semidirect
40. C2×#3753D3semidirect
95. #3830C2×D3semidirect
136. #3754C2×D3semidirect
137. #3753C2×D3semidirect
304. C2×C33#135semidirect
455. C33C2×#135semidirect
573. C2×C32#912semidirect
574. C2×C32#916semidirect
575. C2×C32#950semidirect
674. C32C2×#912semidirect
675. C32C2×#916semidirect
676. C32C2×#950semidirect
717. C2×C3#63933semidirect
718. C2×C3#63935semidirect
719. C2×C3#63936semidirect
745. C3C2×#63933semidirect
746. C3C2×#63935semidirect
747. C3C2×#63936semidirect
751. C2#11723707direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#38302
C2×#890412
C2×C3×#37542
C2×C3×#37532
#117237072
C2×#888122
C2×#888112
C2×#888082
C2×#639363
C2×#639353
C2×#639333