Finite Group Databasebeta

← C2×#11722867 #13170645

Subgroups — C2×#11722867 #13170645

Order 1728.

1426 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×D12C211yesmaximal, characteristic, complemented
2C2×C3×#3799C211yesmaximal, characteristic, complemented
3C2×#88810C211yesmaximal, characteristic, complemented
4C2×#88793C211yesmaximal, characteristic, complemented
5C2×#88789C211yesmaximal, characteristic, complemented
6C2×#88786C211yesmaximal, characteristic, complemented
7C2×C3×#3715C211yesmaximal, characteristic, complemented
8#11722867C218yesmaximal, direct product factor
9C2×#63939—31nomaximal
10C2×#63934—31nomaximal
11C2×#63823—31nomaximal
12C22×C3×D32—21no—
13C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
14C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
15C2×C32×D12C2211yescharacteristic
16C2×C32×C4×D3C2211yescharacteristic
17C2×C32×Dic6C2211yescharacteristic, complemented
18C2×C3×#626—21no—
19C2×C3×#626—21no—
20C2×C3×#624—21no—
21C3×D3×D12—22no—
22C3×D3×D12C2214yescomplemented
23C3×#3799—22no—
24C3×#3799C2214yescomplemented
25C2×C3⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
26C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
27#88810C2214yescomplemented
28#88793C2214yescomplemented
29#88789C2214yescomplemented
30#88786C2214yescomplemented
31C3×#3715C2214yescomplemented
32C2×C3×#239—31no—
33C2×C3×D3×D4—31no—
34C2×C3×#235—31no—
35C22×C3×D12—31no—
36C2×D3×D12D311yescharacteristic, complemented
37C2×#3799D311yescharacteristic, complemented
38C2×#3755—31no—
39C2×#3753—31no—
40C2×#3748—31no—
41C2×C3×#215—31no—
42C2×C3×#214—31no—
43#63939—38no—
44#63934—38no—
45C2×#3715—31no—
46C2×#3715—31no—
47C2×#3715—61no—
48C2×#3715D311yescharacteristic, complemented
49C2×#3714—31no—
50C2×#3714—31no—
51#63823—38no—
52C2×#3713—31no—
53C2×#3713—31no—
54C2×#3713—31no—
55C2×#3713—61no—
56C2×#3711—31no—
57C2×#3711—31no—
58C2×#3711—61no—
59C22×C3×C3⋊D3—21no—
60C22×C3×C3⋊D3—21no—
61C22×C32×D3—21no—
62C22×C32×D3D411yescharacteristic
63C2×C3×D32—24no—
64C2×C3×D32—44no—
65C2×C33×C4C2311yescharacteristic
66C3×C4⋊(C3⋊D3)—21no—
67C3×C4⋊(C3⋊D3)—21no—
68C3×C4⋊(C3⋊D3)C2312yes—
69C3×C4⋊(C3⋊D3)C2312yescomplemented
70C2×C32×Dic3—21no—
71C2×C32×Dic3D411yescharacteristic
72C32×D12—21no—
73C32×D12C2312yes—
74C32×C4×D3D412yes—
75C32×C4×D3C2312yes—
76C32×Dic6—21no—
77C32×Dic6C2312yescomplemented
78C3×#626—24no—
79C3×#626—24no—
80C3×#624—24no—
81C3⋊(C3⋊(C3⋊C8))C2312yescomplemented
82C3×C3⋊(C3⋊C8)C2312yescomplemented
83C2×#949—91no—
84C2×#932—91no—
85C2×#914—91no—
86C23×C3×D3—61no—
87C23×C3×D3—61no—
88C22×D32—21no—
89C2×C32×Q8—31no—
90C2×C32×D4—31no—
91C22×C32×C4—31no—
92C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
93C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
94C2×C3×#67—61no—
95C2×C3×#67—61no—
96C3×#239—34no—
97C3×#239—62no—
98C3×D3×D4—34no—
99C3×D3×D4—62no—
100C3×#235—34no—
101C3×#235—62no—
102C2×C3×D12—21no—
103C2×C3×D12—31no—
104C2×C3×D12—31no—
105C2×C3×D12—31no—
106C2×C3×D12—31no—
107C2×C3×D12—34no—
108C2×C3×D12—62no—
109C2×C3×D12—61no—
110C2×C3×D12—61no—
111C2×C3×D12—61no—
112C2×C3×D12—61no—
113C2×C3×D12C2×D311yescharacteristic
114C2×C3×D12C2×D311yescharacteristic
115C2×C3×C4×D3—21no—
116C2×C3×C4×D3—61no—
117C2×C3×C4×D3—61no—
118C2×C3×C4×D3C2×D311yescharacteristic
119C2×C3×C4×D3C2×D311yescharacteristic
120C2×C3×Dic6—21no—
121C2×C3×Dic6C2×D311yescharacteristic, complemented
122C2×C3×Dic6C2×D311yescharacteristic, complemented
123C2×#626—21no—
124C2×#626—21no—
125C2×#624—21no—
126D3×D12—22no—
127D3×D12C2×D314yescomplemented
128#3799—22no—
129#3799C2×D314yescomplemented
130#3755—34no—
131#3753—34no—
132#3748—34no—
133C2×C3⋊(C3⋊C8)—31no—
134C2×C3⋊(C3⋊C8)—31no—
135C2×C3⋊(C3⋊C8)—31no—
136C2×C3⋊(C3⋊C8)—61no—
137C2×C3⋊(C3⋊C8)—61no—
138C2×C3⋊(C3⋊C8)—61no—
139C2×C3⋊(C3⋊C8)—121no—
140C2×C3⋊(C3⋊C8)C2×D311yescharacteristic, complemented
141C3×#215—34no—
142C3×#214—34no—
143C2×C3×C3⋊C8—31no—
144C2×C3×C3⋊C8—31no—
145C2×C3×C3⋊C8—61no—
146#3715—34no—
147#3715—34no—
148#3715—64no—
149#3715C2×D314yescomplemented
150#3714—34no—
151#3714—34no—
152#3713—34no—
153#3713—34no—
154#3713—34no—
155#3713—64no—
156#3711—34no—
157#3711—34no—
158#3711—64no—
159C22×C33C2×D411yescharacteristic
160C2×C3×C3⋊D3—22no—
161C2×C3×C3⋊D3—22no—
162C2×C3×C3⋊D3—42no—
163C2×C3×C3⋊D3—42no—
164C2×C32×D3—22no—
165C2×C32×D3—22no—
166C2×C32×D3—42no—
167C2×C32×D3C2×D412yes—
168C3×D32—48no—
169C33×C4C2×D411yescharacteristic
170C33×C4C2411yescharacteristic
171C32×Dic3—22no—
172C32×Dic3C2×D412yes—
173C2×C3×#41—91no—
174C22×C3×D4—91no—
175C2×#239—31no—
176C2×D3×D4—31no—
177C2×#235—31no—
178C22×D12—31no—
179C2×C3×SD16—91no—
180#949—98no—
181C2×#215—31no—
182C2×#215—91no—
183C2×#215—91no—
184C2×#215—181no—
185C2×#214—31no—
186C2×#214—91no—
187#932—98no—
188C2×#213—91no—
189C2×#213—91no—
190C2×#213—91no—
191C2×#213—91no—
192C2×#213—91no—
193C2×#213—181no—
194C2×#208—91no—
195C2×#208—91no—
196C2×#208—181no—
197#914—98no—
198C2×D24—91no—
199C2×ΓL(1,𝔽25)—91no—
200C23×C32—31no—
201C23×C32—61no—
202C22×C3⋊D3—21no—
203C22×C3⋊D3—21no—
204C22×C3×D3—21no—
205C22×C3×D3—21no—
206C22×C3×D3—21no—
207C22×C3×D3—41no—
208C22×C3×D3—64no—
209C22×C3×D3—61no—
210C22×C3×D3—61no—
211C22×C3×D3—61no—
212C22×C3×D3—61no—
213C22×C3×D3—64no—
214C22×C3×D3—121no—
215C22×C3×D3—121no—
216C22×C3×D3—124no—
217C22×C3×D3—124no—
218C22×C3×D3#6711yescharacteristic
219C22×C3×D3#6711yescharacteristic
220C2×D32—24no—
221C2×D32—44no—
222C32×Q8—32no—
223C32×Q8—61no—
224C32×D4—32no—
225C32×D4—61no—
226C2×C32×C4—21no—
227C2×C32×C4—21no—
228C2×C32×C4—21no—
229C2×C32×C4—31no—
230C2×C32×C4—32no—
231C2×C32×C4—32no—
232C2×C32×C4—41no—
233C2×C32×C4—61no—
234C2×C32×C4C22×D311yescharacteristic
235C2×C32×C4C22×D311yescharacteristic
236C2×C32×C4C22×D311yescharacteristic
237C4⋊(C3⋊D3)—21no—
238C4⋊(C3⋊D3)—21no—
239C4⋊(C3⋊D3)C22×D312yes—
240C4⋊(C3⋊D3)C22×D312yescomplemented
241C3×#67—64no—
242C3×#67—64no—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—41no—
247C2×C3×Dic3#6711yescharacteristic
248C2×C3×Dic3#6711yescharacteristic
249C3×D12—21no—
250C3×D12—21no—
251C3×D12—22no—
252C3×D12—32no—
253C3×D12—32no—
254C3×D12—32no—
255C3×D12—32no—
256C3×D12—41no—
257C3×D12—62no—
258C3×D12—62no—
259C3×D12—64no—
260C3×D12—64no—
261C3×D12—61no—
262C3×D12—61no—
263C3×D12—61no—
264C3×D12—61no—
265C3×D12—121no—
266C3×D12—121no—
267C3×D12C22×D312yes—
268C3×D12C22×D312yes—
269C3×C4×D3—22no—
270C3×C4×D3—22no—
271C3×C4×D3—64no—
272C3×C4×D3—64no—
273C3×C4×D3#6712yes—
274C3×C4×D3#6712yes—
275C3×C4×D3C22×D312yes—
276C3×C4×D3C22×D312yes—
277C3×Dic6—21no—
278C3×Dic6—21no—
279C3×Dic6—22no—
280C3×Dic6—41no—
281C3×Dic6C22×D312yescomplemented
282C3×Dic6C22×D312yescomplemented
283#626—24no—
284#626—24no—
285#624—24no—
286C3⋊(C3⋊C8)—32no—
287C3⋊(C3⋊C8)—32no—
288C3⋊(C3⋊C8)—32no—
289C3⋊(C3⋊C8)—62no—
290C3⋊(C3⋊C8)—62no—
291C3⋊(C3⋊C8)—62no—
292C3⋊(C3⋊C8)—122no—
293C3⋊(C3⋊C8)C22×D312yescomplemented
294C3×C3⋊C8—32no—
295C3×C3⋊C8—32no—
296C3×C3⋊C8—62no—
297C2×AGL(1,ℤ/8)—271noSylow
298C2×C33AGL(1,ℤ/8)12yescomplemented
299C2×C33C22×D411yescharacteristic
300C3×C3⋊D3—42no—
301C3×C3⋊D3—42no—
302C32×D3—22no—
303C32×D3—42no—
304C24×C3—181no—
305C23×D3—61no—
306C23×D3—61no—
307C3×#41—94no—
308C3×#41—182no—
309C2×C3×Q8—31no—
310C2×C3×Q8—31no—
311C2×C3×Q8—61no—
312C2×C3×D4—31no—
313C2×C3×D4—31no—
314C2×C3×D4—61no—
315C2×C3×D4—94no—
316C2×C3×D4—91no—
317C2×C3×D4—91no—
318C2×C3×D4—182no—
319C2×C3×D4—181no—
320C2×C3×D4—181no—
321C22×C3×C4—31no—
322C22×C3×C4—31no—
323C22×C3×C4—61no—
324C22×C3×C4—181no—
325C2×#67—61no—
326C2×#67—61no—
327#239—34no—
328#239—62no—
329D3×D4—34no—
330D3×D4—62no—
331#235—34no—
332#235—62no—
333C2×D12—31no—
334C2×D12—31no—
335C2×D12—31no—
336C2×D12—31no—
337C2×D12—34no—
338C2×D12—61no—
339C2×D12—61no—
340C2×D12—62no—
341C2×D12—61no—
342C2×D12—61no—
343C2×D12D3211yescharacteristic
344C2×C4×D3—61no—
345C2×C4×D3—61no—
346C2×C4×D3D3211yescharacteristic
347C2×Dic6D3211yescharacteristic, complemented
348C3×SD16—94no—
349C2×C3×C8—91no—
350#215—34no—
351#215—94no—
352#215—94no—
353#215—184no—
354#214—34no—
355#214—94no—
356#213—94no—
357#213—94no—
358#213—94no—
359#213—94no—
360#213—94no—
361#213—184no—
362#208—94no—
363#208—94no—
364#208—184no—
365C2×C3⋊C8—31no—
366C2×C3⋊C8—31no—
367C2×C3⋊C8—61no—
368C2×C3⋊C8—91no—
369C2×C3⋊C8—91no—
370C2×C3⋊C8—91no—
371C2×C3⋊C8—181no—
372C2×C3⋊C8—181no—
373C2×C3⋊C8—181no—
374C2×C3⋊C8—361no—
375D24—94no—
376ΓL(1,𝔽25)—94no—
377C22×C32—21no—
378C22×C32—21no—
379C22×C32—21no—
380C22×C32—32no—
381C22×C32—41no—
382C22×C32—62no—
383C22×C32—62no—
384C22×C32—122no—
385C22×C32D3×D411yescharacteristic
386C22×C32C2×#6711yescharacteristic
387C22×C32C2×#6711yescharacteristic
388C2×C3⋊D3—22no—
389C2×C3⋊D3—22no—
390C2×C3⋊D3—42no—
391C2×C3⋊D3—42no—
392C2×C3×D3—22no—
393C2×C3×D3—22no—
394C2×C3×D3—22no—
395C2×C3×D3—22no—
396C2×C3×D3—22no—
397C2×C3×D3—42no—
398C2×C3×D3—42no—
399C2×C3×D3—42no—
400C2×C3×D3—42no—
401C2×C3×D3—62no—
402C2×C3×D3—62no—
403C2×C3×D3—62no—
404C2×C3×D3—62no—
405C2×C3×D3—82no—
406C2×C3×D3—122no—
407C2×C3×D3—122no—
408C2×C3×D3—128no—
409C2×C3×D3—128no—
410C2×C3×D3—122no—
411C2×C3×D3—122no—
412C2×C3×D3—122no—
413C2×C3×D3—122no—
414C2×C3×D3—242no—
415C2×C3×D3—242no—
416C2×C3×D3C2×#6712yes—
417C2×C3×D3C2×#6712yes—
418D32—48no—
419C32×C4—21no—
420C32×C4—21no—
421C32×C4—21no—
422C32×C4—21no—
423C32×C4—21no—
424C32×C4—21no—
425C32×C4—32no—
426C32×C4—41no—
427C32×C4—41no—
428C32×C4—62no—
429C32×C4D3×D411yescharacteristic
430C32×C4C2×#6711yescharacteristic
431C32×C4C2×#6711yescharacteristic
432C32×C4C23×D311yescharacteristic
433C32×C4C23×D311yescharacteristic
434C32×C4C23×D311yescharacteristic
435C3×Dic3—22no—
436C3×Dic3—22no—
437C3×Dic3—22no—
438C3×Dic3—42no—
439C3×Dic3C2×#6712yes—
440C3×Dic3C2×#6712yes—
441C2×#41—91no—
442C22×D4—91no—
443AGL(1,ℤ/8)—278no—
444C2×SD16—91no—
445C2×SD16—271no—
446C2×D8—271no—
447C2×D8—271no—
448C2×M16—271no—
449C33C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
450C23×C3—31no—
451C23×C3—31no—
452C23×C3—61no—
453C23×C3—61no—
454C23×C3—61no—
455C23×C3—121no—
456C23×C3—184no—
457C23×C3—181no—
458C23×C3—181no—
459C23×C3—364no—
460C22×D3—21no—
461C22×D3—64no—
462C22×D3—61no—
463C22×D3—61no—
464C22×D3—61no—
465C22×D3—61no—
466C22×D3—64no—
467C22×D3—121no—
468C22×D3—121no—
469C22×D3—124no—
470C22×D3—124no—
471C22×D3#62511yescharacteristic
472C3×Q8—32no—
473C3×Q8—32no—
474C3×Q8—62no—
475C3×Q8—61no—
476C3×Q8—61no—
477C3×Q8—121no—
478C3×D4—32no—
479C3×D4—32no—
480C3×D4—62no—
481C3×D4—61no—
482C3×D4—61no—
483C3×D4—92no—
484C3×D4—92no—
485C3×D4—121no—
486C3×D4—184no—
487C3×D4—184no—
488C3×D4—181no—
489C3×D4—181no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—31no—
494C2×C3×C4—31no—
495C2×C3×C4—32no—
496C2×C3×C4—32no—
497C2×C3×C4—32no—
498C2×C3×C4—32no—
499C2×C3×C4—41no—
500C2×C3×C4—62no—
501C2×C3×C4—62no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—121no—
506C2×C3×C4—184no—
507C2×C3×C4C2×D3211yescharacteristic
508C2×C3×C4C2×D3211yescharacteristic
509C2×C3×C4C2×D3211yescharacteristic
510#67—64no—
511#67—64no—
512C2×Dic3—21no—
513C2×Dic3#62511yescharacteristic
514D12—21no—
515D12—32no—
516D12—32no—
517D12—32no—
518D12—32no—
519D12—62no—
520D12—62no—
521D12—64no—
522D12—64no—
523D12—61no—
524D12—61no—
525D12—61no—
526D12—61no—
527D12—121no—
528D12—121no—
529D12C2×D3212yes—
530C4×D3—64no—
531C4×D3—64no—
532C4×D3#62512yes—
533C4×D3C2×D3212yes—
534Dic6—21no—
535Dic6C2×D3212yescomplemented
536C3×C8—92no—
537C3⋊C8—32no—
538C3⋊C8—32no—
539C3⋊C8—62no—
540C3⋊C8—92no—
541C3⋊C8—92no—
542C3⋊C8—92no—
543C3⋊C8—182no—
544C3⋊C8—182no—
545C3⋊C8—182no—
546C3⋊C8—362no—
547C2×C32—21no—
548C2×C32—21no—
549C2×C32—21no—
550C2×C32—22no—
551C2×C32—22no—
552C2×C32—22no—
553C2×C32—42no—
554C2×C32—41no—
555C2×C32—62no—
556C2×C32—122no—
557C2×C32#91412yescomplemented
558C2×C32#93212yescomplemented
559C2×C32#94912yescomplemented
560C2×C32C2×D3×D411yescharacteristic
561C2×C32C22×#6711yescharacteristic
562C2×C32C22×#6711yescharacteristic
563C3⋊D3—42no—
564C3⋊D3—42no—
565C3×D3—22no—
566C3×D3—22no—
567C3×D3—42no—
568C3×D3—42no—
569C3×D3—42no—
570C3×D3—82no—
571C3×D3—122no—
572C3×D3—122no—
573C3×D3—122no—
574C3×D3—122no—
575C3×D3—242no—
576C3×D3—242no—
577C24—181no—
578#41—94no—
579#41—182no—
580C2×Q8—31no—
581C2×D4—31no—
582C2×D4—94no—
583C2×D4—91no—
584C2×D4—91no—
585C2×D4—182no—
586C2×D4—181no—
587C2×D4—181no—
588C22×C4—31no—
589C22×C4—181no—
590SD16—94no—
591SD16—274no—
592D8—274no—
593D8—274no—
594M16—274no—
595C2×C8—91no—
596C2×C8—271no—
597C22×C3—21no—
598C22×C3—21no—
599C22×C3—21no—
600C22×C3—32no—
601C22×C3—32no—
602C22×C3—41no—
603C22×C3—62no—
604C22×C3—62no—
605C22×C3—62no—
606C22×C3—62no—
607C22×C3—62no—
608C22×C3—122no—
609C22×C3—122no—
610C22×C3—122no—
611C22×C3—122no—
612C22×C3—182no—
613C22×C3—182no—
614C22×C3—242no—
615C22×C3—368no—
616C22×C3—362no—
617C22×C3—362no—
618C22×C3C2×#62511yescharacteristic
619C22×C3D3×#6711yescharacteristic
620C22×C3D3×#6711yescharacteristic
621C2×D3—22no—
622C2×D3—22no—
623C2×D3—42no—
624C2×D3—62no—
625C2×D3—62no—
626C2×D3—62no—
627C2×D3—62no—
628C2×D3—122no—
629C2×D3—122no—
630C2×D3—128no—
631C2×D3—128no—
632C2×D3—122no—
633C2×D3—122no—
634C2×D3—122no—
635C2×D3—122no—
636C2×D3—242no—
637C2×D3—242no—
638C2×D3C2×#62512yes—
639C3×C4—21no—
640C3×C4—21no—
641C3×C4—21no—
642C3×C4—21no—
643C3×C4—21no—
644C3×C4—21no—
645C3×C4—32no—
646C3×C4—32no—
647C3×C4—41no—
648C3×C4—41no—
649C3×C4—62no—
650C3×C4—62no—
651C3×C4—62no—
652C3×C4—122no—
653C3×C4C2×#62511yescharacteristic
654C3×C4D3×#6711yescharacteristic
655C3×C4D3×#6711yescharacteristic
656C3×C4C22×D3211yescharacteristic
657C3×C4C22×D3211yescharacteristic
658C3×C4C22×D3211yescharacteristic
659Dic3—22no—
660Dic3C2×#62512yes—
661C32—21no—
662C32—21no—
663C32—21no—
664C32—41no—
665C32C2×#91411yescharacteristic, complemented
666C32C2×#93211yescharacteristic, complemented
667C32C2×#94911yescharacteristic, complemented
668C23—31no—
669C23—61no—
670C23—184no—
671C23—181no—
672C23—181no—
673C23—364no—
674Q8—32no—
675Q8—61no—
676D4—32no—
677D4—61no—
678D4—92no—
679D4—92no—
680D4—184no—
681D4—184no—
682D4—181no—
683D4—181no—
684C2×C4—31no—
685C2×C4—32no—
686C2×C4—32no—
687C2×C4—61no—
688C2×C4—184no—
689C2×C4D3311yescharacteristic
690C8—92no—
691C8—272no—
692C2×C3—22no—
693C2×C3—22no—
694C2×C3—22no—
695C2×C3—21no—
696C2×C3—21no—
697C2×C3—21no—
698C2×C3—42no—
699C2×C3—41no—
700C2×C3—62no—
701C2×C3—62no—
702C2×C3—122no—
703C2×C3—122no—
704C2×C3—122no—
705C2×C3—242no—
706C2×C3—362no—
707C2×C3—362no—
708C2×C3#6382312yescomplemented
709C2×C3#6393412yescomplemented
710C2×C3#6393912yescomplemented
711C2×C3C22×#62511yescharacteristic
712C2×C3C2×D3×#6711yescharacteristic
713C2×C3C2×D3×#6711yescharacteristic
714D3—22no—
715D3—42no—
716D3—122no—
717D3—122no—
718D3—122no—
719D3—122no—
720D3—242no—
721D3—242no—
722C22—32no—
723C22—62no—
724C22—62no—
725C22—122no—
726C22—182no—
727C22—182no—
728C22—368no—
729C22—362no—
730C22—362no—
731C22D3×#62511yescharacteristic
732C4—32no—
733C4—62no—
734C4D3×#62511yescharacteristic
735C4C2×D3311yescharacteristic
736C3—21no—
737C3—21no—
738C3—21no—
739C3—41no—
740C3C2×#6382311yescharacteristic, complemented
741C3C2×#6393411yescharacteristic, complemented
742C3C2×#6393911yescharacteristic, complemented
743C2—62no—
744C2—122no—
745C2—362no—
746C2—362no—
747C2#1172286712yesdirect product factor
748C2C2×D3×#62511yescharacteristic
subgroupG/H
centerC22D3×#625
commutator, cosocleC33×C4C24
FrattiniC4C2×D33
FittingC2×C33×C4C23
socleC22×C33C2×D4
hypercenterC2×C4D33
hypocenterC33C2×AGL(1,ℤ/8)
LCSG ▷ C33×C4 ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×D12C2semidirect
2. C2×C3×#3799C2semidirect
3. C2×#88810C2semidirect
4. C2×#88793C2semidirect
5. C2×#88789C2semidirect
6. C2×#88786C2semidirect
7. C2×C3×#3715C2semidirect
8. #11722867C2direct (N × H)
14. C2×C3×C4⋊(C3⋊D3)C22semidirect
17. C2×C32×Dic6C22semidirect
22. C3×D3×D12C22semidirect
24. C3×#3799C22semidirect
25. C2×C3⋊(C3⋊(C3⋊C8))C22semidirect
26. C2×C3×C3⋊(C3⋊C8)C22semidirect
27. #88810C22semidirect
28. #88793C22semidirect
29. #88789C22semidirect
30. #88786C22semidirect
31. C3×#3715C22semidirect
36. C2×D3×D12D3semidirect
37. C2×#3799D3semidirect
48. C2×#3715D3semidirect
69. C3×C4⋊(C3⋊D3)C23semidirect
77. C32×Dic6C23semidirect
81. C3⋊(C3⋊(C3⋊C8))C23semidirect
82. C3×C3⋊(C3⋊C8)C23semidirect
93. C2×C4⋊(C3⋊D3)C2×D3semidirect
121. C2×C3×Dic6C2×D3semidirect
122. C2×C3×Dic6C2×D3semidirect
127. D3×D12C2×D3semidirect
129. #3799C2×D3semidirect
140. C2×C3⋊(C3⋊C8)C2×D3semidirect
149. #3715C2×D3semidirect
240. C4⋊(C3⋊D3)C22×D3semidirect
281. C3×Dic6C22×D3semidirect
282. C3×Dic6C22×D3semidirect
293. C3⋊(C3⋊C8)C22×D3semidirect
298. C2×C33AGL(1,ℤ/8)semidirect
347. C2×Dic6D32semidirect
449. C33C2×AGL(1,ℤ/8)semidirect
535. Dic6C2×D32semidirect
557. C2×C32#914semidirect
558. C2×C32#932semidirect
559. C2×C32#949semidirect
665. C32C2×#914semidirect
666. C32C2×#932semidirect
667. C32C2×#949semidirect
708. C2×C3#63823semidirect
709. C2×C3#63934semidirect
710. C2×C3#63939semidirect
740. C3C2×#63823semidirect
741. C3C2×#63934semidirect
742. C3C2×#63939semidirect
747. C2#11722867direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D3×D122
C2×C3×#37992
C2×#888102
C2×#887932
C2×#887892
C2×#887862
C2×C3×#37152
#117228672
C2×#639393
C2×#639343
C2×#638233