Finite Group Databasebeta

← C2×#11723713 #13178757

Subgroups — C2×#11723713 #13178757

Order 1728.

1394 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3832C211yesmaximal, characteristic, complemented
2C2×#89041C211yesmaximal, characteristic, complemented
3C2×C3×#3756C211yesmaximal, characteristic, complemented
4C2×C3×#3755C211yesmaximal, characteristic, complemented
5#11723713C218yesmaximal, direct product factor
6C2×#88811C211yesmaximal, characteristic, complemented
7C2×#88810C211yesmaximal, characteristic, complemented
8C2×#88808C211yesmaximal, characteristic, complemented
9C2×#63950—31nomaximal
10C2×#63949—31nomaximal
11C2×#63947—31nomaximal
12C2×C33×Q8C2211yescharacteristic
13C3×#3832—22no—
14C3×#3832C2214yescomplemented
15C2×C3×C4⋊(C3⋊D3)—21no—
16C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
17C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
18C2×C3×C4×C3⋊D3—21no—
19C2×C3×C4×C3⋊D3C2211yescharacteristic
20C2×C3×#634C2211yescharacteristic
21C2×#6295—21no—
22C2×#6294—21no—
23#89041—22no—
24#89041C2214yescomplemented
25C3×#3756C2214yescomplemented
26C3×#3755C2214yescomplemented
27C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
28C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
29#88811C2214yescomplemented
30#88810C2214yescomplemented
31#88808C2214yescomplemented
32C2×#3832D311yescharacteristic, complemented
33C2×C3×#239—31no—
34C2×C3×#239—31no—
35C2×C3×#239—61no—
36C2×#3799—31no—
37C2×#3796—31no—
38C2×#3795—31no—
39C2×#3756D311yescharacteristic, complemented
40C2×#3755D311yescharacteristic, complemented
41C2×C3×#216—31no—
42C2×C3×#216—31no—
43C2×C3×#216—61no—
44C2×C3×#215—31no—
45C2×C3×#215—31no—
46C2×C3×#215—61no—
47#63950—38no—
48#63949—38no—
49#63947—38no—
50C2×#3717—31no—
51C2×#3716—31no—
52C2×#3715—31no—
53C2×#3714—31no—
54C2×#3714—31no—
55C2×#3713—31no—
56C2×#3710—31no—
57C2×D3×C3⋊C8—31no—
58C2×D3×C3⋊C8—31no—
59C22×C3×C3⋊D3—21no—
60C22×C3×C3⋊D3—21no—
61C22×C3×C3⋊D3D411yescharacteristic
62C33×Q8—21no—
63C33×Q8C2312yes—
64C2×C33×C4—21no—
65C2×C33×C4C2311yescharacteristic
66C2×C3×C3⋊Dic3—21no—
67C2×C3×C3⋊Dic3D411yescharacteristic
68C3×C4⋊(C3⋊D3)—24no—
69C3×C4⋊(C3⋊D3)—21no—
70C3×C4⋊(C3⋊D3)—21no—
71C3×C4⋊(C3⋊D3)C2312yes—
72C3×C4⋊(C3⋊D3)C2312yes—
73C3×C4×C3⋊D3—24no—
74C3×C4×C3⋊D3D412yes—
75C3×C4×C3⋊D3C2312yes—
76C3×#634—21no—
77C3×#634C2312yes—
78#6295—24no—
79#6294—24no—
80C3×C3⋊(C3⋊C8)C2312yes—
81C3×C3⋊(C3⋊C8)C2312yes—
82C2×#950—91no—
83C2×#919—91no—
84C2×#916—91no—
85C2×C32×Q8—21no—
86C2×C32×Q8—21no—
87C2×C32×Q8—21no—
88C2×C32×Q8—41no—
89C2×C32×Q8C2×D311yescharacteristic
90C2×C32×Q8C2×D311yescharacteristic
91C2×C32×Q8C2×D311yescharacteristic
92#3832—22no—
93#3832C2×D314yescomplemented
94C2×C4⋊(C3⋊D3)—21no—
95C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
96C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
97C2×C4×C3⋊D3—21no—
98C2×C4×C3⋊D3C2×D311yescharacteristic
99C2×#634C2×D311yescharacteristic
100C3×#239—34no—
101C3×#239—34no—
102C3×#239—62no—
103C3×#239—62no—
104C3×#239—64no—
105C3×#239—64no—
106C2×C3×D12—31no—
107C2×C3×D12—31no—
108C2×C3×D12—31no—
109C2×C3×D12—31no—
110C2×C3×D12—61no—
111C2×C3×D12—61no—
112C2×C3×D12—61no—
113C2×C3×D12—62no—
114C2×C3×D12—61no—
115C2×C3×C4×D3—31no—
116C2×C3×C4×D3—31no—
117C2×C3×C4×D3—61no—
118C2×C3×C4×D3—61no—
119C2×C3×C4×D3—61no—
120C2×C3×C4×D3—62no—
121C2×C3×Dic6—31no—
122C2×C3×Dic6—31no—
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#3756C2×D314yescomplemented
137#3755C2×D314yescomplemented
138C2×C3⋊(C3⋊C8)C2×D311yescharacteristic
139C2×C3⋊(C3⋊C8)C2×D311yescharacteristic
140C3×#216—34no—
141C3×#216—34no—
142C3×#216—64no—
143C3×#215—34no—
144C3×#215—34no—
145C3×#215—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#3717—34no—
153#3716—34no—
154#3715—34no—
155#3714—34no—
156#3714—34no—
157#3713—34no—
158#3710—34no—
159D3×C3⋊C8—34no—
160D3×C3⋊C8—34no—
161C22×C33C2×D411yescharacteristic
162C2×C3×C3⋊D3—22no—
163C2×C3×C3⋊D3—22no—
164C2×C3×C3⋊D3—22no—
165C2×C3×C3⋊D3—42no—
166C2×C3×C3⋊D3—42no—
167C2×C3×C3⋊D3C2×D412yes—
168C33×C4—22no—
169C33×C4C2×D411yescharacteristic
170C33×C4C2411yescharacteristic
171C3×C3⋊Dic3—22no—
172C3×C3⋊Dic3C2×D412yes—
173C2×C3×#41—91no—
174C2×#239—31no—
175C2×#239—31no—
176C2×#239—61no—
177C2×#239—91no—
178C2×#237—91no—
179C2×#235—91no—
180C2×C3×Q16—91no—
181C2×C3×SD16—91no—
182#950—98no—
183C2×#216—31no—
184C2×#216—31no—
185C2×#216—61no—
186C2×#215—31no—
187C2×#215—31no—
188C2×#215—61no—
189C2×#215—91no—
190C2×#214—91no—
191C2×#213—91no—
192C2×#213—91no—
193C22×C3⋊C8—91no—
194#919—98no—
195#916—98no—
196C2×D24—91no—
197C2×#204—91no—
198C2×D3×C8—91no—
199C2×D3×C8—91no—
200C22×C3⋊D3—21no—
201C22×C3⋊D3—21no—
202C22×C3⋊D3#6711yescharacteristic
203C22×C3×D3—31no—
204C22×C3×D3—31no—
205C22×C3×D3—61no—
206C22×C3×D3—62no—
207C22×C3×D3—61no—
208C22×C3×D3—61no—
209C22×C3×D3—61no—
210C22×C3×D3—61no—
211C22×C3×D3—121no—
212C32×Q8—21no—
213C32×Q8—22no—
214C32×Q8—21no—
215C32×Q8—21no—
216C32×Q8—22no—
217C32×Q8—22no—
218C32×Q8—22no—
219C32×Q8—42no—
220C32×Q8—41no—
221C32×Q8—41no—
222C32×Q8—42no—
223C32×Q8C22×D312yes—
224C32×Q8C22×D312yes—
225C32×Q8C22×D312yes—
226C2×C32×C4—21no—
227C2×C32×C4—22no—
228C2×C32×C4—21no—
229C2×C32×C4—21no—
230C2×C32×C4—21no—
231C2×C32×C4—21no—
232C2×C32×C4—21no—
233C2×C32×C4—41no—
234C2×C32×C4—41no—
235C2×C32×C4—41no—
236C2×C32×C4—42no—
237C2×C32×C4C22×D311yescharacteristic
238C2×C32×C4C22×D311yescharacteristic
239C2×C32×C4C22×D311yescharacteristic
240C2×C3⋊Dic3—21no—
241C2×C3⋊Dic3#6711yescharacteristic
242C4⋊(C3⋊D3)—24no—
243C4⋊(C3⋊D3)—21no—
244C4⋊(C3⋊D3)—21no—
245C4⋊(C3⋊D3)C22×D312yes—
246C4⋊(C3⋊D3)C22×D312yes—
247C4×C3⋊D3—24no—
248C4×C3⋊D3#6712yes—
249C4×C3⋊D3C22×D312yes—
250#634—21no—
251#634C22×D312yes—
252C2×C3×Dic3—31no—
253C2×C3×Dic3—31no—
254C2×C3×Dic3—61no—
255C2×C3×Dic3—61no—
256C2×C3×Dic3—61no—
257C2×C3×Dic3—121no—
258C3×D12—32no—
259C3×D12—32no—
260C3×D12—32no—
261C3×D12—32no—
262C3×D12—62no—
263C3×D12—62no—
264C3×D12—64no—
265C3×D12—64no—
266C3×D12—68no—
267C3×D12—62no—
268C3×D12—61no—
269C3×D12—61no—
270C3×D12—61no—
271C3×D12—61no—
272C3×D12—121no—
273C3×C4×D3—32no—
274C3×C4×D3—32no—
275C3×C4×D3—32no—
276C3×C4×D3—32no—
277C3×C4×D3—62no—
278C3×C4×D3—62no—
279C3×C4×D3—64no—
280C3×C4×D3—64no—
281C3×C4×D3—68no—
282C3×Dic6—32no—
283C3×Dic6—32no—
284C3×Dic6—62no—
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#13512yescomplemented
304C2×C33C22×D411yescharacteristic
305C3×C3⋊D3—22no—
306C3×C3⋊D3—42no—
307C3×C3⋊D3—42no—
308C3×#41—94no—
309C3×#41—182no—
310C2×C3×Q8—21no—
311C2×C3×Q8—21no—
312C2×C3×Q8—21no—
313C2×C3×Q8—41no—
314C2×C3×Q8—91no—
315C2×C3×Q8D3211yescharacteristic
316C2×C3×Q8D3211yescharacteristic
317C2×C3×Q8D3211yescharacteristic
318C2×C3×D4—91no—
319C2×C3×D4—91no—
320C2×C3×D4—181no—
321C22×C3×C4—91no—
322C22×C3×C4—181no—
323C2×#67—181no—
324C2×#67—181no—
325C22×Dic3—181no—
326#239—34no—
327#239—34no—
328#239—64no—
329#239—62no—
330#239—62no—
331#239—64no—
332#239—94no—
333#239—182no—
334#237—94no—
335#237—182no—
336#235—94no—
337#235—182no—
338C2×D12—31no—
339C2×D12—31no—
340C2×D12—31no—
341C2×D12—31no—
342C2×D12—61no—
343C2×D12—61no—
344C2×D12—61no—
345C2×D12—61no—
346C2×D12—62no—
347C2×D12—181no—
348C2×C4×D3—31no—
349C2×C4×D3—31no—
350C2×C4×D3—61no—
351C2×C4×D3—61no—
352C2×C4×D3—61no—
353C2×C4×D3—62no—
354C2×C4×D3—181no—
355C2×C4×D3—181no—
356C2×Dic6—31no—
357C2×Dic6—31no—
358C2×Dic6—61no—
359C3×Q16—94no—
360C3×SD16—94no—
361C2×C3×C8—91no—
362C2×C3×C8—91no—
363#216—34no—
364#216—34no—
365#216—64no—
366#215—34no—
367#215—34no—
368#215—64no—
369#215—94no—
370#214—94no—
371#213—94no—
372#213—94no—
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—
380D24—94no—
381#204—94no—
382D3×C8—94no—
383D3×C8—94no—
384C22×C32—21no—
385C22×C32—21no—
386C22×C32—21no—
387C22×C32—41no—
388C22×C32D3×D411yescharacteristic
389C22×C32D3×D411yescharacteristic
390C22×C32C2×#6711yescharacteristic
391C2×C3⋊D3—22no—
392C2×C3⋊D3—22no—
393C2×C3⋊D3—22no—
394C2×C3⋊D3—42no—
395C2×C3⋊D3—42no—
396C2×C3⋊D3C2×#6712yes—
397C2×C3×D3—32no—
398C2×C3×D3—32no—
399C2×C3×D3—62no—
400C2×C3×D3—62no—
401C2×C3×D3—62no—
402C2×C3×D3—64no—
403C2×C3×D3—62no—
404C2×C3×D3—62no—
405C2×C3×D3—62no—
406C2×C3×D3—62no—
407C2×C3×D3—122no—
408C2×C3×D3—122no—
409C2×C3×D3—124no—
410C2×C3×D3—122no—
411C2×C3×D3—122no—
412C2×C3×D3—122no—
413C2×C3×D3—122no—
414C2×C3×D3—242no—
415C32×C4—22no—
416C32×C4—24no—
417C32×C4—22no—
418C32×C4—22no—
419C32×C4—21no—
420C32×C4—21no—
421C32×C4—21no—
422C32×C4—21no—
423C32×C4—21no—
424C32×C4—21no—
425C32×C4—41no—
426C32×C4—41no—
427C32×C4—42no—
428C32×C4—42no—
429C32×C4—44no—
430C32×C4D3×D411yescharacteristic
431C32×C4D3×D411yescharacteristic
432C32×C4C2×#6711yescharacteristic
433C32×C4C23×D311yescharacteristic
434C32×C4C23×D311yescharacteristic
435C32×C4C23×D311yescharacteristic
436C3⋊Dic3—22no—
437C3⋊Dic3C2×#6712yes—
438C3×Dic3—32no—
439C3×Dic3—32no—
440C3×Dic3—62no—
441C3×Dic3—62no—
442C3×Dic3—62no—
443C3×Dic3—122no—
444C2×#41—91no—
445C2×#41—271no—
446#135—278no—
447C2×Q16—91no—
448C2×SD16—91no—
449C2×SD16—271no—
450C2×D8—271no—
451C22×C8—271no—
452C33C2×#13511yescharacteristic, complemented, Sylow
453C23×C3—91no—
454C23×C3—181no—
455C23×C3—181no—
456C22×D3—31no—
457C22×D3—31no—
458C22×D3—61no—
459C22×D3—62no—
460C22×D3—61no—
461C22×D3—61no—
462C22×D3—61no—
463C22×D3—61no—
464C22×D3—121no—
465C3×Q8—22no—
466C3×Q8—21no—
467C3×Q8—21no—
468C3×Q8—21no—
469C3×Q8—22no—
470C3×Q8—22no—
471C3×Q8—22no—
472C3×Q8—41no—
473C3×Q8—41no—
474C3×Q8—42no—
475C3×Q8—42no—
476C3×Q8—92no—
477C3×Q8—181no—
478C3×Q8C2×D3212yes—
479C3×Q8C2×D3212yes—
480C3×Q8C2×D3212yes—
481C3×D4—92no—
482C3×D4—92no—
483C3×D4—184no—
484C3×D4—181no—
485C3×D4—181no—
486C2×C3×C4—22no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
495C2×C3×C4—42no—
496C2×C3×C4—41no—
497C2×C3×C4—91no—
498C2×C3×C4—92no—
499C2×C3×C4—92no—
500C2×C3×C4—184no—
501C2×C3×C4—181no—
502C2×C3×C4C2×D3211yescharacteristic
503C2×C3×C4C2×D3211yescharacteristic
504C2×C3×C4C2×D3211yescharacteristic
505#67—184no—
506#67—184no—
507C2×Dic3—31no—
508C2×Dic3—31no—
509C2×Dic3—61no—
510C2×Dic3—61no—
511C2×Dic3—61no—
512C2×Dic3—121no—
513C2×Dic3—184no—
514D12—32no—
515D12—32no—
516D12—32no—
517D12—32no—
518D12—62no—
519D12—62no—
520D12—64no—
521D12—64no—
522D12—68no—
523D12—62no—
524D12—61no—
525D12—61no—
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—64no—
537C4×D3—64no—
538C4×D3—68no—
539C4×D3—184no—
540C4×D3—184no—
541Dic6—32no—
542Dic6—32no—
543Dic6—62no—
544Dic6—61no—
545Dic6—61no—
546Dic6—121no—
547C3×C8—92no—
548C3×C8—92no—
549C3⋊C8—32no—
550C3⋊C8—32no—
551C3⋊C8—32no—
552C3⋊C8—32no—
553C3⋊C8—62no—
554C3⋊C8—62no—
555C2×C32—21no—
556C2×C32—21no—
557C2×C32—21no—
558C2×C32—22no—
559C2×C32—22no—
560C2×C32—22no—
561C2×C32—42no—
562C2×C32—41no—
563C2×C32#91612yescomplemented
564C2×C32#91912yescomplemented
565C2×C32#95012yescomplemented
566C2×C32C2×D3×D411yescharacteristic
567C2×C32C2×D3×D411yescharacteristic
568C2×C32C22×#6711yescharacteristic
569C3⋊D3—22no—
570C3⋊D3—42no—
571C3⋊D3—42no—
572C3×D3—62no—
573C3×D3—62no—
574C3×D3—122no—
575C3×D3—124no—
576C3×D3—122no—
577C3×D3—122no—
578C3×D3—122no—
579C3×D3—122no—
580C3×D3—242no—
581#41—94no—
582#41—182no—
583#41—274no—
584#41—542no—
585C2×Q8—91no—
586C2×Q8#111311yescharacteristic
587C2×D4—91no—
588C2×D4—91no—
589C2×D4—181no—
590C2×D4—541no—
591C22×C4—91no—
592C22×C4—181no—
593C22×C4—541no—
594Q16—94no—
595SD16—94no—
596SD16—274no—
597D8—274no—
598C2×C8—91no—
599C2×C8—91no—
600C2×C8—274no—
601C22×C3—21no—
602C22×C3—21no—
603C22×C3—21no—
604C22×C3—41no—
605C22×C3—92no—
606C22×C3—182no—
607C22×C3—182no—
608C22×C3—182no—
609C22×C3—362no—
610C22×C3—362no—
611C22×C3D3×#6711yescharacteristic
612C22×C3D3×#6711yescharacteristic
613C22×C3#381111yescharacteristic
614C2×D3—32no—
615C2×D3—32no—
616C2×D3—62no—
617C2×D3—62no—
618C2×D3—62no—
619C2×D3—64no—
620C2×D3—62no—
621C2×D3—62no—
622C2×D3—62no—
623C2×D3—62no—
624C2×D3—122no—
625C2×D3—122no—
626C2×D3—124no—
627C2×D3—122no—
628C2×D3—122no—
629C2×D3—122no—
630C2×D3—122no—
631C2×D3—242no—
632C3×C4—24no—
633C3×C4—22no—
634C3×C4—22no—
635C3×C4—22no—
636C3×C4—21no—
637C3×C4—21no—
638C3×C4—21no—
639C3×C4—21no—
640C3×C4—21no—
641C3×C4—21no—
642C3×C4—42no—
643C3×C4—42no—
644C3×C4—44no—
645C3×C4—41no—
646C3×C4—41no—
647C3×C4—92no—
648C3×C4—182no—
649C3×C4D3×#6711yescharacteristic
650C3×C4D3×#6711yescharacteristic
651C3×C4#381111yescharacteristic
652C3×C4C22×D3211yescharacteristic
653C3×C4C22×D3211yescharacteristic
654C3×C4C22×D3211yescharacteristic
655Dic3—32no—
656Dic3—32no—
657Dic3—62no—
658Dic3—62no—
659Dic3—62no—
660Dic3—122no—
661C32—21no—
662C32—21no—
663C32—21no—
664C32—41no—
665C32C2×#91611yescharacteristic, complemented
666C32C2×#91911yescharacteristic, complemented
667C32C2×#95011yescharacteristic, complemented
668C23—91no—
669C23—181no—
670C23—181no—
671Q8—21no—
672Q8—92no—
673Q8—181no—
674Q8C2×#111312yes—
675D4—92no—
676D4—92no—
677D4—184no—
678D4—181no—
679D4—181no—
680D4—544no—
681C2×C4—21no—
682C2×C4—91no—
683C2×C4—92no—
684C2×C4—92no—
685C2×C4—184no—
686C2×C4—181no—
687C2×C4—544no—
688C2×C4C2×#111311yescharacteristic
689C8—92no—
690C8—92no—
691C2×C3—21no—
692C2×C3—21no—
693C2×C3—21no—
694C2×C3—22no—
695C2×C3—22no—
696C2×C3—22no—
697C2×C3—41no—
698C2×C3—42no—
699C2×C3—182no—
700C2×C3—362no—
701C2×C3—362no—
702C2×C3#6394712yescomplemented
703C2×C3#6394912yescomplemented
704C2×C3#6395012yescomplemented
705C2×C3C2×D3×#6711yescharacteristic
706C2×C3C2×D3×#6711yescharacteristic
707C2×C3C2×#381111yescharacteristic
708D3—62no—
709D3—62no—
710D3—122no—
711D3—124no—
712D3—122no—
713D3—122no—
714D3—122no—
715D3—122no—
716D3—242no—
717C22—92no—
718C22—182no—
719C22—182no—
720C22—182no—
721C22—362no—
722C22—362no—
723C22#8904911yescharacteristic
724C4—22no—
725C4—92no—
726C4—182no—
727C4#8904911yescharacteristic
728C4C22×#111311yescharacteristic
729C3—21no—
730C3—21no—
731C3—21no—
732C3—41no—
733C3C2×#6394711yescharacteristic, complemented
734C3C2×#6394911yescharacteristic, complemented
735C3C2×#6395011yescharacteristic, complemented
736C2—182no—
737C2—362no—
738C2—362no—
739C2#1172371312yesdirect product factor
740C2C2×#8904911yescharacteristic
subgroupG/H
centerC22#89049
commutator, cosocleC33×C4C24
FrattiniC4C22×#1113
FittingC2×C33×Q8C22
socleC22×C33C2×D4
hypercenterC2×Q8#1113
hypocenterC33C2×#135
LCSG ▷ C33×C4 ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3832C2semidirect
2. C2×#89041C2semidirect
3. C2×C3×#3756C2semidirect
4. C2×C3×#3755C2semidirect
5. #11723713C2direct (N × H)
6. C2×#88811C2semidirect
7. C2×#88810C2semidirect
8. C2×#88808C2semidirect
14. C3×#3832C22semidirect
24. #89041C22semidirect
25. C3×#3756C22semidirect
26. C3×#3755C22semidirect
29. #88811C22semidirect
30. #88810C22semidirect
31. #88808C22semidirect
32. C2×#3832D3semidirect
39. C2×#3756D3semidirect
40. C2×#3755D3semidirect
93. #3832C2×D3semidirect
136. #3756C2×D3semidirect
137. #3755C2×D3semidirect
303. C2×C33#135semidirect
452. C33C2×#135semidirect
563. C2×C32#916semidirect
564. C2×C32#919semidirect
565. C2×C32#950semidirect
665. C32C2×#916semidirect
666. C32C2×#919semidirect
667. C32C2×#950semidirect
702. C2×C3#63947semidirect
703. C2×C3#63949semidirect
704. C2×C3#63950semidirect
733. C3C2×#63947semidirect
734. C3C2×#63949semidirect
735. C3C2×#63950semidirect
739. C2#11723713direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#38322
C2×#890412
C2×C3×#37562
C2×C3×#37552
#117237132
C2×#888112
C2×#888102
C2×#888082
C2×#639503
C2×#639493
C2×#639473