Finite Group Databasebeta

← C2×#11722871 #13170653

Subgroups — C2×#11722871 #13170653

Order 1728.

1626 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
2C2×C3×#3799C211yesmaximal, characteristic, complemented
3C2×#88810C211yesmaximal, characteristic, complemented
4C2×#88795C211yesmaximal, characteristic, complemented
5C2×#88791C211yesmaximal, characteristic, complemented
6C2×C3×#3717C211yesmaximal, characteristic, complemented
7C2×C3×#3711C211yesmaximal, characteristic, complemented
8#11722871C218yesmaximal, direct product factor
9C2×#63939—31nomaximal
10C2×#63825—31nomaximal
11C2×#63794—31nomaximal
12C22×D3×C3⋊D3—21no—
13C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
14C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
15C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
16C2×C32×C4×D3C2211yescharacteristic
17C2×C32×Dic6C2211yescharacteristic, complemented
18C2×#6292—21no—
19D3×C4⋊(C3⋊D3)—22no—
20D3×C4⋊(C3⋊D3)C2214yescomplemented
21C2×C3×#626—21no—
22C2×C3×#624—21no—
23C3×#3799—22no—
24C3×#3799C2214yescomplemented
25C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
26C2×C32×C3⋊C8C2211yescharacteristic, complemented
27#88810C2214yescomplemented
28#88795C2214yescomplemented
29#88791C2214yescomplemented
30C3×#3717C2214yescomplemented
31C3×#3711C2214yescomplemented
32C22×C4⋊(C3⋊D3)—31no—
33C2×C3×#239—31no—
34C2×C3×#235—31no—
35C2×D3×D12—31no—
36C2×D3×D12—31no—
37C2×D3×D12—61no—
38C2×#3799D311yescharacteristic, complemented
39C2×#3755—31no—
40C2×#3745—31no—
41C2×C3×#215—31no—
42C2×C3×#208—31no—
43C2×C3×#204—31no—
44C2×C3×ΓL(1,𝔽25)—31no—
45#63939—38no—
46C2×#3717—31no—
47C2×#3717—31no—
48C2×#3717—61no—
49C2×#3717D311yescharacteristic, complemented
50#63825—38no—
51C2×#3714—31no—
52C2×#3714—31no—
53C2×#3714—31no—
54C2×#3714—31no—
55C2×#3714—61no—
56C2×#3713—31no—
57C2×#3711D311yescharacteristic, complemented
58#63794—38no—
59C22×C3⋊(C3⋊D3)—21no—
60C22×C3×C3⋊D3—21no—
61C22×C3×C3⋊D3—21no—
62C22×C32×D3D411yescharacteristic
63C2×D3×C3⋊D3—24no—
64C2×D3×C3⋊D3—44no—
65C2×C33×C4C2311yescharacteristic
66C4⋊(C3⋊(C3⋊D3))—21no—
67C4⋊(C3⋊(C3⋊D3))C2312yes—
68C3×C4⋊(C3⋊D3)—21no—
69C3×C4⋊(C3⋊D3)—21no—
70C3×C4⋊(C3⋊D3)C2312yes—
71C3×C4⋊(C3⋊D3)C2312yescomplemented
72C2×C32×Dic3—21no—
73C2×C32×Dic3D411yescharacteristic
74C32×C4×D3D412yes—
75C32×C4×D3C2312yes—
76C32×Dic6—21no—
77C32×Dic6C2312yescomplemented
78#6292—24no—
79C3×#626—24no—
80C3×#624—24no—
81C3×C3⋊(C3⋊C8)C2312yescomplemented
82C32×C3⋊C8C2312yescomplemented
83C2×#949—91no—
84C2×#914—91no—
85C2×#908—91no—
86C23×C3⋊D3—61no—
87C22×D32—62no—
88C22×D32—61no—
89C22×D32—61no—
90C2×C32×Q8—31no—
91C22×C32×C4—31no—
92C2×C4⋊(C3⋊D3)—31no—
93C2×C4⋊(C3⋊D3)—31no—
94C2×C4⋊(C3⋊D3)—31no—
95C2×C4⋊(C3⋊D3)—34no—
96C2×C4⋊(C3⋊D3)—62no—
97C2×C4⋊(C3⋊D3)—61no—
98C2×C4⋊(C3⋊D3)—61no—
99C2×C4⋊(C3⋊D3)—61no—
100C2×C4⋊(C3⋊D3)—61no—
101C2×C4⋊(C3⋊D3)—121no—
102C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
103C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
104C2×C3×#67—61no—
105C3×#239—34no—
106C3×#239—62no—
107C3×#235—34no—
108C3×#235—62no—
109C2×C3×D12—31no—
110C2×C3×D12—31no—
111C2×C3×D12—31no—
112C2×C3×D12—31no—
113C2×C3×D12—61no—
114C2×C3×D12—61no—
115C2×C3×D12—61no—
116C2×C3×C4×D3—21no—
117C2×C3×C4×D3—61no—
118C2×C3×C4×D3—61no—
119C2×C3×C4×D3C2×D311yescharacteristic
120C2×C3×C4×D3C2×D311yescharacteristic
121C2×C3×Dic6—21no—
122C2×C3×Dic6C2×D311yescharacteristic, complemented
123C2×C3×Dic6C2×D311yescharacteristic, complemented
124C2×#626—21no—
125C2×#626—62no—
126C2×#626—61no—
127C2×#626—61no—
128C2×#624—21no—
129D3×D12—34no—
130D3×D12—34no—
131D3×D12—64no—
132D3×D12—64no—
133D3×D12—62no—
134D3×D12—62no—
135#3799—22no—
136#3799C2×D314yescomplemented
137C2×C32×C8—31no—
138#3755—34no—
139C2×C3⋊(C3⋊C8)C2×D311yescharacteristic, complemented
140#3745—34no—
141C3×#215—34no—
142C3×#208—34no—
143C2×C3×C3⋊C8—21no—
144C2×C3×C3⋊C8—31no—
145C2×C3×C3⋊C8—31no—
146C2×C3×C3⋊C8—61no—
147C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
148C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
149C3×#204—34no—
150C3×ΓL(1,𝔽25)—34no—
151#3717—34no—
152#3717—34no—
153#3717—64no—
154#3717C2×D314yescomplemented
155#3714—34no—
156#3714—34no—
157#3714—34no—
158#3714—34no—
159#3714—64no—
160#3713—34no—
161#3711C2×D314yescomplemented
162C22×C33C2×D411yescharacteristic
163C2×C3⋊(C3⋊D3)—22no—
164C2×C3⋊(C3⋊D3)—42no—
165C2×C3×C3⋊D3—22no—
166C2×C3×C3⋊D3—22no—
167C2×C3×C3⋊D3—42no—
168C2×C3×C3⋊D3—42no—
169C2×C32×D3—22no—
170C2×C32×D3C2×D412yes—
171D3×C3⋊D3—48no—
172C33×C4C2×D411yescharacteristic
173C33×C4C2411yescharacteristic
174C32×Dic3—22no—
175C32×Dic3C2×D412yes—
176C2×C3×#41—91no—
177C2×#239—31no—
178C2×D3×D4—91no—
179C2×#235—31no—
180C22×D12—91no—
181C22×D12—91no—
182C22×D12—181no—
183C2×C3×SD16—91no—
184C2×C3×M16—91no—
185#949—98no—
186C2×#215—31no—
187C2×#215—91no—
188C2×#215—91no—
189C2×#215—181no—
190C2×#213—91no—
191C2×#213—91no—
192C2×#213—91no—
193C2×#208—31no—
194#914—98no—
195#908—98no—
196C2×D24—91no—
197C2×D24—91no—
198C2×D24—91no—
199C2×D24—181no—
200C2×#204—31no—
201C2×#204—91no—
202C2×ΓL(1,𝔽25)—31no—
203C23×C32—31no—
204C22×C3⋊D3—21no—
205C22×C3⋊D3—21no—
206C22×C3⋊D3—64no—
207C22×C3⋊D3—61no—
208C22×C3⋊D3—62no—
209C22×C3⋊D3—61no—
210C22×C3⋊D3—61no—
211C22×C3⋊D3—121no—
212C22×C3⋊D3—121no—
213C22×C3⋊D3—122no—
214C22×C3⋊D3—124no—
215C22×C3×D3—21no—
216C22×C3×D3—62no—
217C22×C3×D3—61no—
218C22×C3×D3—61no—
219C22×C3×D3—61no—
220C22×C3×D3—61no—
221C22×C3×D3—121no—
222C22×C3×D3D1211yescharacteristic
223C22×C3×D3#6711yescharacteristic
224C2×D32—68no—
225C2×D32—64no—
226C2×D32—64no—
227C2×D32—128no—
228C2×D32—124no—
229C2×D32—124no—
230C32×Q8—32no—
231C32×Q8—61no—
232C2×C32×C4—21no—
233C2×C32×C4—21no—
234C2×C32×C4—21no—
235C2×C32×C4—31no—
236C2×C32×C4—32no—
237C2×C32×C4—32no—
238C2×C32×C4—41no—
239C2×C32×C4—61no—
240C2×C32×C4C22×D311yescharacteristic
241C2×C32×C4C22×D311yescharacteristic
242C2×C32×C4C22×D311yescharacteristic
243C4⋊(C3⋊D3)—21no—
244C4⋊(C3⋊D3)—21no—
245C4⋊(C3⋊D3)—32no—
246C4⋊(C3⋊D3)—32no—
247C4⋊(C3⋊D3)—32no—
248C4⋊(C3⋊D3)—62no—
249C4⋊(C3⋊D3)—62no—
250C4⋊(C3⋊D3)—62no—
251C4⋊(C3⋊D3)—64no—
252C4⋊(C3⋊D3)—61no—
253C4⋊(C3⋊D3)—62no—
254C4⋊(C3⋊D3)—61no—
255C4⋊(C3⋊D3)—61no—
256C4⋊(C3⋊D3)—122no—
257C4⋊(C3⋊D3)—121no—
258C4⋊(C3⋊D3)—121no—
259C4⋊(C3⋊D3)—122no—
260C4⋊(C3⋊D3)C22×D312yes—
261C4⋊(C3⋊D3)C22×D312yescomplemented
262C3×#67—64no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—41no—
267C2×C3×Dic3D1211yescharacteristic
268C2×C3×Dic3#6711yescharacteristic
269C3×D12—32no—
270C3×D12—32no—
271C3×D12—32no—
272C3×D12—32no—
273C3×D12—62no—
274C3×D12—62no—
275C3×D12—62no—
276C3×D12—64no—
277C3×D12—61no—
278C3×D12—61no—
279C3×D12—61no—
280C3×D12—61no—
281C3×D12—121no—
282C3×C4×D3—22no—
283C3×C4×D3—22no—
284C3×C4×D3—64no—
285C3×C4×D3—64no—
286C3×C4×D3D1212yes—
287C3×C4×D3#6712yes—
288C3×C4×D3C22×D312yes—
289C3×C4×D3C22×D312yes—
290C3×Dic6—21no—
291C3×Dic6—21no—
292C3×Dic6—22no—
293C3×Dic6—41no—
294C3×Dic6C22×D312yescomplemented
295C3×Dic6C22×D312yescomplemented
296#626—24no—
297#626—68no—
298#626—64no—
299#626—64no—
300#624—24no—
301C32×C8—32no—
302C3⋊(C3⋊C8)C22×D312yescomplemented
303C3×C3⋊C8—22no—
304C3×C3⋊C8—32no—
305C3×C3⋊C8—32no—
306C3×C3⋊C8—62no—
307C3×C3⋊C8C22×D312yescomplemented
308C3×C3⋊C8C22×D312yescomplemented
309C2×AGL(1,ℤ/8)—271noSylow
310C2×C33AGL(1,ℤ/8)12yescomplemented
311C2×C33C22×D411yescharacteristic
312C3⋊(C3⋊D3)—42no—
313C3×C3⋊D3—42no—
314C3×C3⋊D3—42no—
315C32×D3—22no—
316C23×D3—181no—
317C23×D3—181no—
318C23×D3—182no—
319C23×D3—181no—
320C3×#41—94no—
321C3×#41—182no—
322C2×C3×Q8—31no—
323C2×C3×Q8—31no—
324C2×C3×Q8—61no—
325C2×C3×D4—91no—
326C2×C3×D4—91no—
327C2×C3×D4—181no—
328C22×C3×C4—31no—
329C22×C3×C4—31no—
330C22×C3×C4—61no—
331C22×C3×C4—181no—
332C2×#67—61no—
333C2×#67—181no—
334#239—34no—
335#239—62no—
336D3×D4—94no—
337D3×D4—182no—
338#235—34no—
339#235—62no—
340C2×D12—31no—
341C2×D12—31no—
342C2×D12—31no—
343C2×D12—31no—
344C2×D12—61no—
345C2×D12—61no—
346C2×D12—61no—
347C2×D12—94no—
348C2×D12—94no—
349C2×D12—91no—
350C2×D12—91no—
351C2×D12—91no—
352C2×D12—184no—
353C2×D12—181no—
354C2×D12—181no—
355C2×D12—181no—
356C2×D12—182no—
357C2×D12—182no—
358C2×D12—184no—
359C2×D12—181no—
360C2×D12—181no—
361C2×D12—182no—
362C2×D12—361no—
363C2×C4×D3—61no—
364C2×C4×D3—61no—
365C2×C4×D3D3211yescharacteristic
366C2×Dic6D3211yescharacteristic, complemented
367C3×SD16—94no—
368C3×M16—94no—
369C2×C3×C8—31no—
370C2×C3×C8—31no—
371C2×C3×C8—61no—
372C2×C3×C8—91no—
373#215—34no—
374#215—94no—
375#215—94no—
376#215—184no—
377#213—94no—
378#213—94no—
379#213—94no—
380#208—34no—
381C2×C3⋊C8—31no—
382C2×C3⋊C8—31no—
383C2×C3⋊C8—61no—
384C2×C3⋊C8D3211yescharacteristic, complemented
385D24—94no—
386D24—94no—
387D24—94no—
388D24—184no—
389#204—34no—
390#204—94no—
391ΓL(1,𝔽25)—34no—
392C22×C32—21no—
393C22×C32—21no—
394C22×C32—21no—
395C22×C32—32no—
396C22×C32—41no—
397C22×C32—62no—
398C22×C32C2×D1211yescharacteristic
399C22×C32D3×D411yescharacteristic
400C22×C32C2×#6711yescharacteristic
401C2×C3⋊D3—22no—
402C2×C3⋊D3—22no—
403C2×C3⋊D3—42no—
404C2×C3⋊D3—42no—
405C2×C3⋊D3—62no—
406C2×C3⋊D3—64no—
407C2×C3⋊D3—62no—
408C2×C3⋊D3—62no—
409C2×C3⋊D3—122no—
410C2×C3⋊D3—122no—
411C2×C3⋊D3—124no—
412C2×C3⋊D3—128no—
413C2×C3⋊D3—122no—
414C2×C3⋊D3—124no—
415C2×C3⋊D3—122no—
416C2×C3⋊D3—122no—
417C2×C3⋊D3—242no—
418C2×C3⋊D3—242no—
419C2×C3⋊D3—244no—
420C2×C3×D3—24no—
421C2×C3×D3—22no—
422C2×C3×D3—22no—
423C2×C3×D3—22no—
424C2×C3×D3—64no—
425C2×C3×D3—62no—
426C2×C3×D3—62no—
427C2×C3×D3—62no—
428C2×C3×D3—62no—
429C2×C3×D3—122no—
430C2×C3×D3—124no—
431C2×C3×D3—122no—
432C2×C3×D3—122no—
433C2×C3×D3—122no—
434C2×C3×D3—122no—
435C2×C3×D3—242no—
436C2×C3×D3C2×D1212yes—
437C2×C3×D3C2×#6712yes—
438D32—1216no—
439D32—128no—
440D32—128no—
441C32×C4—21no—
442C32×C4—21no—
443C32×C4—21no—
444C32×C4—21no—
445C32×C4—21no—
446C32×C4—21no—
447C32×C4—32no—
448C32×C4—41no—
449C32×C4—41no—
450C32×C4—62no—
451C32×C4C2×D1211yescharacteristic
452C32×C4D3×D411yescharacteristic
453C32×C4C2×#6711yescharacteristic
454C32×C4C23×D311yescharacteristic
455C32×C4C23×D311yescharacteristic
456C32×C4C23×D311yescharacteristic
457C3×Dic3—22no—
458C3×Dic3—22no—
459C3×Dic3—22no—
460C3×Dic3—42no—
461C3×Dic3C2×D1212yes—
462C3×Dic3C2×#6712yes—
463C2×#41—91no—
464C22×D4—271no—
465AGL(1,ℤ/8)—278no—
466C2×SD16—91no—
467C2×SD16—271no—
468C2×D8—271no—
469C2×D8—271no—
470C2×M16—91no—
471C33C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
472C23×C3—31no—
473C23×C3—31no—
474C23×C3—61no—
475C23×C3—181no—
476C23×C3—181no—
477C22×D3—62no—
478C22×D3—61no—
479C22×D3—61no—
480C22×D3—61no—
481C22×D3—61no—
482C22×D3—121no—
483C22×D3—184no—
484C22×D3—184no—
485C22×D3—188no—
486C22×D3—182no—
487C22×D3—181no—
488C22×D3—181no—
489C22×D3—181no—
490C22×D3—184no—
491C22×D3—361no—
492C22×D3—361no—
493C22×D3—362no—
494C22×D3—364no—
495C22×D3—368no—
496C22×D3—364no—
497C22×D3—364no—
498C22×D3#62611yescharacteristic
499C3×Q8—32no—
500C3×Q8—32no—
501C3×Q8—62no—
502C3×Q8—61no—
503C3×Q8—61no—
504C3×Q8—121no—
505C3×D4—92no—
506C3×D4—92no—
507C3×D4—184no—
508C3×D4—181no—
509C3×D4—181no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—31no—
514C2×C3×C4—31no—
515C2×C3×C4—32no—
516C2×C3×C4—32no—
517C2×C3×C4—32no—
518C2×C3×C4—32no—
519C2×C3×C4—41no—
520C2×C3×C4—62no—
521C2×C3×C4—62no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—121no—
526C2×C3×C4—184no—
527C2×C3×C4C2×D3211yescharacteristic
528C2×C3×C4C2×D3211yescharacteristic
529C2×C3×C4C2×D3211yescharacteristic
530#67—64no—
531#67—184no—
532C2×Dic3—21no—
533C2×Dic3#62611yescharacteristic
534D12—32no—
535D12—32no—
536D12—32no—
537D12—32no—
538D12—62no—
539D12—62no—
540D12—62no—
541D12—64no—
542D12—61no—
543D12—61no—
544D12—61no—
545D12—61no—
546D12—92no—
547D12—92no—
548D12—92no—
549D12—121no—
550D12—182no—
551D12—182no—
552D12—182no—
553D12—182no—
554D12—184no—
555D12—184no—
556D12—188no—
557D12—181no—
558D12—181no—
559D12—181no—
560D12—362no—
561D12—361no—
562D12—361no—
563D12—362no—
564C4×D3—64no—
565C4×D3—64no—
566C4×D3#62612yes—
567C4×D3C2×D3212yes—
568Dic6—21no—
569Dic6C2×D3212yescomplemented
570C3×C8—32no—
571C3×C8—32no—
572C3×C8—62no—
573C3×C8—92no—
574C3⋊C8—32no—
575C3⋊C8—32no—
576C3⋊C8—62no—
577C3⋊C8C2×D3212yescomplemented
578C2×C32—21no—
579C2×C32—22no—
580C2×C32—21no—
581C2×C32—21no—
582C2×C32—22no—
583C2×C32—22no—
584C2×C32—42no—
585C2×C32—41no—
586C2×C32—62no—
587C2×C32#90812yescomplemented
588C2×C32#91412yescomplemented
589C2×C32#94912yescomplemented
590C2×C32C22×D1211yescharacteristic
591C2×C32C2×D3×D411yescharacteristic
592C2×C32C22×#6711yescharacteristic
593C3⋊D3—42no—
594C3⋊D3—42no—
595C3⋊D3—122no—
596C3⋊D3—124no—
597C3⋊D3—122no—
598C3⋊D3—122no—
599C3⋊D3—242no—
600C3⋊D3—242no—
601C3⋊D3—244no—
602C3×D3—24no—
603C3×D3—22no—
604C3×D3—22no—
605C3×D3—124no—
606C3×D3—122no—
607C3×D3—122no—
608C3×D3—122no—
609C3×D3—122no—
610C3×D3—242no—
611C24—541no—
612#41—94no—
613#41—182no—
614C2×Q8—31no—
615C2×D4—91no—
616C2×D4—91no—
617C2×D4—181no—
618C2×D4—274no—
619C2×D4—271no—
620C2×D4—542no—
621C2×D4—541no—
622C22×C4—31no—
623C22×C4—181no—
624SD16—94no—
625SD16—274no—
626D8—274no—
627D8—274no—
628M16—94no—
629C2×C8—31no—
630C2×C8—91no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—32no—
635C22×C3—32no—
636C22×C3—41no—
637C22×C3—62no—
638C22×C3—64no—
639C22×C3—62no—
640C22×C3—62no—
641C22×C3—182no—
642C22×C3—182no—
643C22×C3—362no—
644C22×C3—362no—
645C22×C3D3×D1211yescharacteristic
646C22×C3C2×#62611yescharacteristic
647C22×C3D3×#6711yescharacteristic
648C2×D3—22no—
649C2×D3—64no—
650C2×D3—62no—
651C2×D3—62no—
652C2×D3—62no—
653C2×D3—62no—
654C2×D3—122no—
655C2×D3—124no—
656C2×D3—122no—
657C2×D3—122no—
658C2×D3—122no—
659C2×D3—122no—
660C2×D3—184no—
661C2×D3—182no—
662C2×D3—182no—
663C2×D3—182no—
664C2×D3—242no—
665C2×D3—362no—
666C2×D3—362no—
667C2×D3—364no—
668C2×D3—368no—
669C2×D3—3616no—
670C2×D3—368no—
671C2×D3—368no—
672C2×D3—364no—
673C2×D3—362no—
674C2×D3—362no—
675C2×D3—362no—
676C2×D3—722no—
677C2×D3—722no—
678C2×D3—724no—
679C2×D3C2×#62612yes—
680C3×C4—21no—
681C3×C4—21no—
682C3×C4—21no—
683C3×C4—21no—
684C3×C4—21no—
685C3×C4—21no—
686C3×C4—32no—
687C3×C4—32no—
688C3×C4—41no—
689C3×C4—41no—
690C3×C4—62no—
691C3×C4—62no—
692C3×C4—62no—
693C3×C4—122no—
694C3×C4D3×D1211yescharacteristic
695C3×C4C2×#62611yescharacteristic
696C3×C4D3×#6711yescharacteristic
697C3×C4C22×D3211yescharacteristic
698C3×C4C22×D3211yescharacteristic
699C3×C4C22×D3211yescharacteristic
700Dic3—22no—
701Dic3C2×#62612yes—
702C32—21no—
703C32—21no—
704C32—21no—
705C32—41no—
706C32C2×#90811yescharacteristic, complemented
707C32C2×#91411yescharacteristic, complemented
708C32C2×#94911yescharacteristic, complemented
709C23—31no—
710C23—181no—
711C23—181no—
712C23—544no—
713C23—541no—
714C23—1084no—
715Q8—32no—
716Q8—61no—
717D4—92no—
718D4—92no—
719D4—184no—
720D4—181no—
721D4—181no—
722D4—272no—
723D4—544no—
724D4—541no—
725C2×C4—31no—
726C2×C4—32no—
727C2×C4—32no—
728C2×C4—61no—
729C2×C4—184no—
730C2×C4D3311yescharacteristic
731C8—32no—
732C8—92no—
733C2×C3—22no—
734C2×C3—22no—
735C2×C3—22no—
736C2×C3—21no—
737C2×C3—21no—
738C2×C3—21no—
739C2×C3—42no—
740C2×C3—41no—
741C2×C3—64no—
742C2×C3—62no—
743C2×C3—62no—
744C2×C3—362no—
745C2×C3—362no—
746C2×C3#6379412yescomplemented
747C2×C3#6382512yescomplemented
748C2×C3#6393912yescomplemented
749C2×C3C2×D3×D1211yescharacteristic
750C2×C3C22×#62611yescharacteristic
751C2×C3C2×D3×#6711yescharacteristic
752D3—22no—
753D3—124no—
754D3—122no—
755D3—122no—
756D3—122no—
757D3—122no—
758D3—242no—
759D3—364no—
760D3—362no—
761D3—362no—
762D3—362no—
763D3—722no—
764D3—722no—
765D3—724no—
766C22—32no—
767C22—62no—
768C22—182no—
769C22—182no—
770C22—362no—
771C22—362no—
772C22—542no—
773C22—1088no—
774C22—1082no—
775C22D3×#62611yescharacteristic
776C4—32no—
777C4—62no—
778C4D3×#62611yescharacteristic
779C4C2×D3311yescharacteristic
780C3—21no—
781C3—21no—
782C3—21no—
783C3—41no—
784C3C2×#6379411yescharacteristic, complemented
785C3C2×#6382511yescharacteristic, complemented
786C3C2×#6393911yescharacteristic, complemented
787C2—62no—
788C2—362no—
789C2—362no—
790C2—1082no—
791C2#1172287112yesdirect product factor
792C2C2×D3×#62611yescharacteristic
subgroupG/H
centerC22D3×#626
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×D3×C4⋊(C3⋊D3)C2semidirect
2. C2×C3×#3799C2semidirect
3. C2×#88810C2semidirect
4. C2×#88795C2semidirect
5. C2×#88791C2semidirect
6. C2×C3×#3717C2semidirect
7. C2×C3×#3711C2semidirect
8. #11722871C2direct (N × H)
15. C2×C3×C4⋊(C3⋊D3)C22semidirect
17. C2×C32×Dic6C22semidirect
20. D3×C4⋊(C3⋊D3)C22semidirect
24. C3×#3799C22semidirect
25. C2×C3×C3⋊(C3⋊C8)C22semidirect
26. C2×C32×C3⋊C8C22semidirect
27. #88810C22semidirect
28. #88795C22semidirect
29. #88791C22semidirect
30. C3×#3717C22semidirect
31. C3×#3711C22semidirect
38. C2×#3799D3semidirect
49. C2×#3717D3semidirect
57. C2×#3711D3semidirect
71. C3×C4⋊(C3⋊D3)C23semidirect
77. C32×Dic6C23semidirect
81. C3×C3⋊(C3⋊C8)C23semidirect
82. C32×C3⋊C8C23semidirect
103. C2×C4⋊(C3⋊D3)C2×D3semidirect
122. C2×C3×Dic6C2×D3semidirect
123. C2×C3×Dic6C2×D3semidirect
136. #3799C2×D3semidirect
139. C2×C3⋊(C3⋊C8)C2×D3semidirect
147. C2×C3×C3⋊C8C2×D3semidirect
148. C2×C3×C3⋊C8C2×D3semidirect
154. #3717C2×D3semidirect
161. #3711C2×D3semidirect
261. C4⋊(C3⋊D3)C22×D3semidirect
294. C3×Dic6C22×D3semidirect
295. C3×Dic6C22×D3semidirect
302. C3⋊(C3⋊C8)C22×D3semidirect
307. C3×C3⋊C8C22×D3semidirect
308. C3×C3⋊C8C22×D3semidirect
310. C2×C33AGL(1,ℤ/8)semidirect
366. C2×Dic6D32semidirect
384. C2×C3⋊C8D32semidirect
471. C33C2×AGL(1,ℤ/8)semidirect
569. Dic6C2×D32semidirect
577. C3⋊C8C2×D32semidirect
587. C2×C32#908semidirect
588. C2×C32#914semidirect
589. C2×C32#949semidirect
706. C32C2×#908semidirect
707. C32C2×#914semidirect
708. C32C2×#949semidirect
746. C2×C3#63794semidirect
747. C2×C3#63825semidirect
748. C2×C3#63939semidirect
784. C3C2×#63794semidirect
785. C3C2×#63825semidirect
786. C3C2×#63939semidirect
791. C2#11722871direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D3×C4⋊(C3⋊D3)2
C2×C3×#37992
C2×#888102
C2×#887952
C2×#887912
C2×C3×#37172
C2×C3×#37112
#117228712
C2×#639393
C2×#638253
C2×#637943