Finite Group Databasebeta

← C2×#11722868 #13170647

Subgroups — C2×#11722868 #13170647

Order 1728.

1562 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89022C211yesmaximal, characteristic, complemented
2C2×C3×D3×D12C211yesmaximal, characteristic, complemented
3C2×#88811C211yesmaximal, characteristic, complemented
4C2×#88791C211yesmaximal, characteristic, complemented
5C2×#88790C211yesmaximal, characteristic, complemented
6C2×C3×#3716C211yesmaximal, characteristic, complemented
7C2×C3×#3711C211yesmaximal, characteristic, complemented
8#11722868C218yesmaximal, direct product factor
9C2×#63934—31nomaximal
10C2×#63830—31nomaximal
11C2×#63794—31nomaximal
12C22×C3×D32—21no—
13C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic, complemented
14C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
15C2×C3×#634C2211yescharacteristic, complemented
16C2×C32×D12C2211yescharacteristic
17C2×C32×C4×D3C2211yescharacteristic
18C2×#6291—21no—
19C2×#6289—21no—
20#89022—22no—
21#89022C2214yescomplemented
22C2×C3×#626—21no—
23C3×D3×D12—22no—
24C3×D3×D12C2214yescomplemented
25C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
26C2×C32×C3⋊C8C2211yescharacteristic, complemented
27#88811C2214yescomplemented
28#88791C2214yescomplemented
29#88790C2214yescomplemented
30C3×#3716C2214yescomplemented
31C3×#3711C2214yescomplemented
32C2×#3828—31no—
33C2×C3×D3×D4—31no—
34C22×C3×D12—31no—
35C2×D3×D12D311yescharacteristic, complemented
36C2×#3799—31no—
37C2×#3799—31no—
38C2×#3799—61no—
39C2×#3753—31no—
40C2×#3745—31no—
41C2×C3×#214—31no—
42C2×C3×#208—31no—
43C2×C3×#204—31no—
44C2×C3×ΓL(1,𝔽25)—31no—
45#63934—38no—
46C2×#3717—31no—
47#63830—38no—
48C2×#3716—31no—
49C2×#3716D311yescharacteristic, complemented
50C2×#3715—31no—
51C2×#3714—31no—
52C2×#3714—31no—
53C2×#3714—31no—
54C2×#3714—31no—
55C2×#3714—61no—
56C2×#3714—61no—
57C2×#3711D311yescharacteristic, complemented
58#63794—38no—
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
66C4⋊(C3⋊(C3⋊D3))—21no—
67C4⋊(C3⋊(C3⋊D3))C2312yescomplemented
68C2×C3×C3⋊Dic3—21no—
69C3×C4⋊(C3⋊D3)—21no—
70C3×C4⋊(C3⋊D3)C2312yes—
71C3×#634—21no—
72C3×#634C2312yescomplemented
73C2×C32×Dic3D411yescharacteristic
74C32×D12—21no—
75C32×D12C2312yes—
76C32×C4×D3D412yes—
77C32×C4×D3C2312yes—
78#6291—24no—
79#6289—24no—
80C3×#626—24no—
81C3×C3⋊(C3⋊C8)C2312yescomplemented
82C32×C3⋊C8C2312yescomplemented
83C2×#932—91no—
84C2×#914—91no—
85C2×#908—91no—
86C23×C3×D3—61no—
87C23×C3×D3—61no—
88C22×D32—21no—
89C2×C32×D4—31no—
90C22×C32×C4—31no—
91C2×#638—61no—
92#3828—34no—
93#3828—62no—
94C2×C4⋊(C3⋊D3)—31no—
95C2×C4⋊(C3⋊D3)—31no—
96C2×C4⋊(C3⋊D3)—31no—
97C2×C4⋊(C3⋊D3)—61no—
98C2×C4⋊(C3⋊D3)—61no—
99C2×C4⋊(C3⋊D3)—61no—
100C2×C4⋊(C3⋊D3)—121no—
101C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
102C2×C4×C3⋊D3—61no—
103C2×#634C2×D311yescharacteristic, complemented
104C2×C3×#67—61no—
105C3×D3×D4—34no—
106C3×D3×D4—62no—
107C2×C3×D12—21no—
108C2×C3×D12—31no—
109C2×C3×D12—31no—
110C2×C3×D12—34no—
111C2×C3×D12—62no—
112C2×C3×D12—61no—
113C2×C3×D12—61no—
114C2×C3×D12C2×D311yescharacteristic
115C2×C3×D12C2×D311yescharacteristic
116C2×C3×C4×D3—21no—
117C2×C3×C4×D3C2×D311yescharacteristic
118C2×C3×C4×D3C2×D311yescharacteristic
119C2×C3×Dic6—31no—
120C2×C3×Dic6—31no—
121C2×C3×Dic6—61no—
122C2×#626—21no—
123C2×#626—62no—
124C2×#626—61no—
125C2×#626—61no—
126C2×#624—62no—
127C2×#624—61no—
128C2×#624—61no—
129D3×D12—22no—
130D3×D12C2×D314yescomplemented
131#3799—34no—
132#3799—34no—
133#3799—64no—
134#3799—64no—
135#3799—62no—
136#3799—62no—
137C2×C32×C8—31no—
138#3753—34no—
139C2×C3⋊(C3⋊C8)C2×D311yescharacteristic, complemented
140#3745—34no—
141C3×#214—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#3716—34no—
153#3716C2×D314yescomplemented
154#3715—34no—
155#3714—34no—
156#3714—34no—
157#3714—34no—
158#3714—34no—
159#3714—64no—
160#3714—64no—
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—42no—
167C2×C32×D3—22no—
168C2×C32×D3—22no—
169C2×C32×D3—42no—
170C2×C32×D3C2×D412yes—
171C3×D32—48no—
172C33×C4C2×D411yescharacteristic
173C33×C4C2411yescharacteristic
174C3×C3⋊Dic3—22no—
175C32×Dic3C2×D412yes—
176C22×C3×D4—91no—
177C2×#239—91no—
178C2×D3×D4—31no—
179C2×#235—91no—
180C2×#235—91no—
181C2×#235—181no—
182C22×D12—31no—
183C2×C3×SD16—91no—
184C2×C3×M16—91no—
185C2×#215—91no—
186C2×#214—31no—
187C2×#214—91no—
188#932—98no—
189C2×#213—91no—
190C2×#213—91no—
191C2×#213—91no—
192C2×#213—181no—
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—
204C23×C32—61no—
205C22×C3⋊D3—21no—
206C22×C3⋊D3—61no—
207C22×C3⋊D3—62no—
208C22×C3⋊D3—61no—
209C22×C3⋊D3—61no—
210C22×C3⋊D3—121no—
211C22×C3⋊D3—121no—
212C22×C3⋊D3—122no—
213C22×C3×D3—21no—
214C22×C3×D3—21no—
215C22×C3×D3—21no—
216C22×C3×D3—41no—
217C22×C3×D3—64no—
218C22×C3×D3—61no—
219C22×C3×D3—61no—
220C22×C3×D3—64no—
221C22×C3×D3—121no—
222C22×C3×D3—124no—
223C22×C3×D3—124no—
224C22×C3×D3D1211yescharacteristic
225C22×C3×D3#6711yescharacteristic
226C2×D32—24no—
227C2×D32—44no—
228C32×D4—32no—
229C32×D4—61no—
230C2×C32×C4—21no—
231C2×C32×C4—21no—
232C2×C32×C4—21no—
233C2×C32×C4—31no—
234C2×C32×C4—32no—
235C2×C32×C4—32no—
236C2×C32×C4—41no—
237C2×C32×C4C22×D311yescharacteristic
238C2×C32×C4C22×D311yescharacteristic
239C2×C32×C4C22×D311yescharacteristic
240#638—64no—
241C2×C3⋊Dic3—21no—
242C4⋊(C3⋊D3)—21no—
243C4⋊(C3⋊D3)—32no—
244C4⋊(C3⋊D3)—32no—
245C4⋊(C3⋊D3)—32no—
246C4⋊(C3⋊D3)—62no—
247C4⋊(C3⋊D3)—62no—
248C4⋊(C3⋊D3)—62no—
249C4⋊(C3⋊D3)—61no—
250C4⋊(C3⋊D3)—62no—
251C4⋊(C3⋊D3)—61no—
252C4⋊(C3⋊D3)—61no—
253C4⋊(C3⋊D3)—122no—
254C4⋊(C3⋊D3)—121no—
255C4⋊(C3⋊D3)—121no—
256C4⋊(C3⋊D3)—122no—
257C4⋊(C3⋊D3)C22×D312yes—
258C4×C3⋊D3—64no—
259#634—21no—
260#634C22×D312yescomplemented
261C3×#67—64no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—62no—
264C2×C3×Dic3—61no—
265C2×C3×Dic3—61no—
266C2×C3×Dic3D1211yescharacteristic
267C2×C3×Dic3#6711yescharacteristic
268C3×D12—21no—
269C3×D12—21no—
270C3×D12—22no—
271C3×D12—32no—
272C3×D12—32no—
273C3×D12—41no—
274C3×D12—62no—
275C3×D12—64no—
276C3×D12—61no—
277C3×D12—61no—
278C3×D12—121no—
279C3×D12C22×D312yes—
280C3×D12C22×D312yes—
281C3×C4×D3—22no—
282C3×C4×D3—22no—
283C3×C4×D3D1212yes—
284C3×C4×D3#6712yes—
285C3×C4×D3C22×D312yes—
286C3×C4×D3C22×D312yes—
287C3×Dic6—32no—
288C3×Dic6—32no—
289C3×Dic6—62no—
290C3×Dic6—62no—
291C3×Dic6—61no—
292C3×Dic6—61no—
293#626—24no—
294#626—68no—
295#626—64no—
296#626—64no—
297#624—68no—
298#624—64no—
299#624—64no—
300C32×C8—32no—
301C3⋊(C3⋊C8)C22×D312yescomplemented
302C3×C3⋊C8—22no—
303C3×C3⋊C8—32no—
304C3×C3⋊C8—32no—
305C3×C3⋊C8—62no—
306C3×C3⋊C8C22×D312yescomplemented
307C3×C3⋊C8C22×D312yescomplemented
308C2×AGL(1,ℤ/8)—271noSylow
309C2×C33AGL(1,ℤ/8)12yescomplemented
310C2×C33C22×D411yescharacteristic
311C3⋊(C3⋊D3)—42no—
312C3×C3⋊D3—42no—
313C32×D3—22no—
314C32×D3—42no—
315C24×C3—181no—
316C23×D3—61no—
317C23×D3—61no—
318C2×C3×Q8—91no—
319C2×C3×D4—31no—
320C2×C3×D4—31no—
321C2×C3×D4—61no—
322C2×C3×D4—94no—
323C2×C3×D4—91no—
324C2×C3×D4—182no—
325C2×C3×D4—181no—
326C22×C3×C4—31no—
327C22×C3×C4—31no—
328C22×C3×C4—61no—
329C2×#67—61no—
330C2×#67—181no—
331C2×#67—181no—
332C2×#67—182no—
333#239—94no—
334#239—182no—
335D3×D4—34no—
336D3×D4—62no—
337#235—94no—
338#235—94no—
339#235—184no—
340#235—182no—
341#235—182no—
342#235—184no—
343C2×D12—31no—
344C2×D12—31no—
345C2×D12—34no—
346C2×D12—61no—
347C2×D12—62no—
348C2×D12—61no—
349C2×D12—91no—
350C2×D12—91no—
351C2×D12—91no—
352C2×D12—181no—
353C2×D12—181no—
354C2×D12—181no—
355C2×D12—181no—
356C2×D12—361no—
357C2×D12D3211yescharacteristic
358C2×C4×D3—181no—
359C2×C4×D3—181no—
360C2×C4×D3—182no—
361C2×C4×D3—181no—
362C2×C4×D3D3211yescharacteristic
363C2×Dic6—31no—
364C2×Dic6—31no—
365C2×Dic6—61no—
366C3×SD16—94no—
367C3×M16—94no—
368C2×C3×C8—31no—
369C2×C3×C8—31no—
370C2×C3×C8—61no—
371C2×C3×C8—91no—
372#215—94no—
373#214—34no—
374#214—94no—
375#213—94no—
376#213—94no—
377#213—94no—
378#213—184no—
379#208—34no—
380C2×C3⋊C8—31no—
381C2×C3⋊C8—31no—
382C2×C3⋊C8—61no—
383C2×C3⋊C8D3211yescharacteristic, complemented
384D24—94no—
385D24—94no—
386D24—94no—
387D24—184no—
388#204—34no—
389#204—94no—
390ΓL(1,𝔽25)—34no—
391C22×C32—21no—
392C22×C32—21no—
393C22×C32—21no—
394C22×C32—32no—
395C22×C32—41no—
396C22×C32—62no—
397C22×C32—62no—
398C22×C32—122no—
399C22×C32C2×D1211yescharacteristic
400C22×C32D3×D411yescharacteristic
401C22×C32C2×#6711yescharacteristic
402C2×C3⋊D3—22no—
403C2×C3⋊D3—42no—
404C2×C3⋊D3—62no—
405C2×C3⋊D3—64no—
406C2×C3⋊D3—62no—
407C2×C3⋊D3—62no—
408C2×C3⋊D3—122no—
409C2×C3⋊D3—122no—
410C2×C3⋊D3—124no—
411C2×C3⋊D3—122no—
412C2×C3⋊D3—124no—
413C2×C3⋊D3—122no—
414C2×C3⋊D3—122no—
415C2×C3⋊D3—242no—
416C2×C3⋊D3—242no—
417C2×C3⋊D3—244no—
418C2×C3×D3—22no—
419C2×C3×D3—22no—
420C2×C3×D3—22no—
421C2×C3×D3—22no—
422C2×C3×D3—22no—
423C2×C3×D3—42no—
424C2×C3×D3—42no—
425C2×C3×D3—42no—
426C2×C3×D3—42no—
427C2×C3×D3—62no—
428C2×C3×D3—62no—
429C2×C3×D3—82no—
430C2×C3×D3—122no—
431C2×C3×D3—128no—
432C2×C3×D3—128no—
433C2×C3×D3—122no—
434C2×C3×D3—122no—
435C2×C3×D3—242no—
436C2×C3×D3C2×D1212yes—
437C2×C3×D3C2×#6712yes—
438D32—48no—
439C32×C4—21no—
440C32×C4—21no—
441C32×C4—21no—
442C32×C4—21no—
443C32×C4—21no—
444C32×C4—21no—
445C32×C4—32no—
446C32×C4—41no—
447C32×C4—41no—
448C32×C4C2×D1211yescharacteristic
449C32×C4D3×D411yescharacteristic
450C32×C4C2×#6711yescharacteristic
451C32×C4C23×D311yescharacteristic
452C32×C4C23×D311yescharacteristic
453C32×C4C23×D311yescharacteristic
454C3⋊Dic3—22no—
455C3×Dic3—22no—
456C3×Dic3—64no—
457C3×Dic3—62no—
458C3×Dic3—62no—
459C3×Dic3C2×D1212yes—
460C3×Dic3C2×#6712yes—
461C2×#41—271no—
462C22×D4—91no—
463AGL(1,ℤ/8)—278no—
464C2×SD16—91no—
465C2×SD16—271no—
466C2×D8—271no—
467C2×D8—271no—
468C2×M16—91no—
469C33C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
470C23×C3—31no—
471C23×C3—31no—
472C23×C3—61no—
473C23×C3—61no—
474C23×C3—61no—
475C23×C3—121no—
476C23×C3—184no—
477C23×C3—181no—
478C23×C3—364no—
479C22×D3—21no—
480C22×D3—64no—
481C22×D3—61no—
482C22×D3—61no—
483C22×D3—64no—
484C22×D3—121no—
485C22×D3—124no—
486C22×D3—124no—
487C22×D3—182no—
488C22×D3—181no—
489C22×D3—181no—
490C22×D3—181no—
491C22×D3—361no—
492C22×D3—361no—
493C22×D3—362no—
494C22×D3#62611yescharacteristic
495C3×Q8—92no—
496C3×Q8—181no—
497C3×D4—32no—
498C3×D4—32no—
499C3×D4—62no—
500C3×D4—61no—
501C3×D4—61no—
502C3×D4—92no—
503C3×D4—121no—
504C3×D4—184no—
505C3×D4—181no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—31no—
510C2×C3×C4—31no—
511C2×C3×C4—32no—
512C2×C3×C4—32no—
513C2×C3×C4—32no—
514C2×C3×C4—32no—
515C2×C3×C4—41no—
516C2×C3×C4—62no—
517C2×C3×C4—62no—
518C2×C3×C4—61no—
519C2×C3×C4—181no—
520C2×C3×C4C2×D3211yescharacteristic
521C2×C3×C4C2×D3211yescharacteristic
522C2×C3×C4C2×D3211yescharacteristic
523#67—64no—
524#67—184no—
525#67—184no—
526#67—188no—
527C2×Dic3—62no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3#62611yescharacteristic
531D12—21no—
532D12—32no—
533D12—32no—
534D12—62no—
535D12—64no—
536D12—61no—
537D12—61no—
538D12—92no—
539D12—92no—
540D12—92no—
541D12—121no—
542D12—182no—
543D12—182no—
544D12—182no—
545D12—182no—
546D12—184no—
547D12—181no—
548D12—181no—
549D12—181no—
550D12—362no—
551D12—361no—
552D12—361no—
553D12—362no—
554D12C2×D3212yes—
555C4×D3—184no—
556C4×D3—184no—
557C4×D3—188no—
558C4×D3—184no—
559C4×D3#62612yes—
560C4×D3C2×D3212yes—
561Dic6—32no—
562Dic6—32no—
563Dic6—62no—
564Dic6—62no—
565Dic6—61no—
566Dic6—61no—
567C3×C8—32no—
568C3×C8—32no—
569C3×C8—62no—
570C3×C8—92no—
571C3⋊C8—32no—
572C3⋊C8—32no—
573C3⋊C8—62no—
574C3⋊C8C2×D3212yescomplemented
575C2×C32—21no—
576C2×C32—22no—
577C2×C32—21no—
578C2×C32—21no—
579C2×C32—22no—
580C2×C32—22no—
581C2×C32—42no—
582C2×C32—41no—
583C2×C32—62no—
584C2×C32—122no—
585C2×C32#90812yescomplemented
586C2×C32#91412yescomplemented
587C2×C32#93212yescomplemented
588C2×C32C22×D1211yescharacteristic
589C2×C32C2×D3×D411yescharacteristic
590C2×C32C22×#6711yescharacteristic
591C3⋊D3—42no—
592C3⋊D3—122no—
593C3⋊D3—124no—
594C3⋊D3—122no—
595C3⋊D3—122no—
596C3⋊D3—242no—
597C3⋊D3—242no—
598C3⋊D3—244no—
599C3×D3—22no—
600C3×D3—22no—
601C3×D3—42no—
602C3×D3—42no—
603C3×D3—42no—
604C3×D3—82no—
605C3×D3—122no—
606C3×D3—122no—
607C3×D3—242no—
608C24—181no—
609#41—274no—
610#41—542no—
611C2×Q8—91no—
612C2×D4—31no—
613C2×D4—94no—
614C2×D4—91no—
615C2×D4—182no—
616C2×D4—181no—
617C2×D4—271no—
618C2×D4—541no—
619C22×C4—31no—
620C22×C4—541no—
621SD16—94no—
622SD16—274no—
623D8—274no—
624D8—274no—
625M16—94no—
626C2×C8—31no—
627C2×C8—91no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—32no—
632C22×C3—32no—
633C22×C3—41no—
634C22×C3—62no—
635C22×C3—62no—
636C22×C3—62no—
637C22×C3—62no—
638C22×C3—62no—
639C22×C3—122no—
640C22×C3—122no—
641C22×C3—122no—
642C22×C3—122no—
643C22×C3—182no—
644C22×C3—242no—
645C22×C3—368no—
646C22×C3—362no—
647C22×C3D3×D1211yescharacteristic
648C22×C3C2×#62611yescharacteristic
649C22×C3D3×#6711yescharacteristic
650C2×D3—22no—
651C2×D3—22no—
652C2×D3—42no—
653C2×D3—62no—
654C2×D3—62no—
655C2×D3—122no—
656C2×D3—128no—
657C2×D3—128no—
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—364no—
669C2×D3—362no—
670C2×D3—362no—
671C2×D3—362no—
672C2×D3—722no—
673C2×D3—722no—
674C2×D3—724no—
675C2×D3C2×#62612yes—
676C3×C4—21no—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—21no—
680C3×C4—21no—
681C3×C4—21no—
682C3×C4—32no—
683C3×C4—32no—
684C3×C4—41no—
685C3×C4—41no—
686C3×C4—62no—
687C3×C4—182no—
688C3×C4D3×D1211yescharacteristic
689C3×C4C2×#62611yescharacteristic
690C3×C4D3×#6711yescharacteristic
691C3×C4C22×D3211yescharacteristic
692C3×C4C22×D3211yescharacteristic
693C3×C4C22×D3211yescharacteristic
694Dic3—64no—
695Dic3—62no—
696Dic3—62no—
697Dic3C2×#62612yes—
698C32—21no—
699C32—21no—
700C32—21no—
701C32—41no—
702C32C2×#90811yescharacteristic, complemented
703C32C2×#91411yescharacteristic, complemented
704C32C2×#93211yescharacteristic, complemented
705C23—31no—
706C23—61no—
707C23—184no—
708C23—181no—
709C23—364no—
710C23—541no—
711Q8—92no—
712Q8—181no—
713D4—32no—
714D4—61no—
715D4—92no—
716D4—184no—
717D4—181no—
718D4—272no—
719D4—544no—
720D4—541no—
721C2×C4—31no—
722C2×C4—32no—
723C2×C4—32no—
724C2×C4—181no—
725C2×C4—544no—
726C2×C4D3311yescharacteristic
727C8—32no—
728C8—92no—
729C2×C3—22no—
730C2×C3—22no—
731C2×C3—22no—
732C2×C3—21no—
733C2×C3—21no—
734C2×C3—21no—
735C2×C3—42no—
736C2×C3—41no—
737C2×C3—62no—
738C2×C3—62no—
739C2×C3—122no—
740C2×C3—122no—
741C2×C3—122no—
742C2×C3—242no—
743C2×C3—362no—
744C2×C3#6379412yescomplemented
745C2×C3#6383012yescomplemented
746C2×C3#6393412yescomplemented
747C2×C3C2×D3×D1211yescharacteristic
748C2×C3C22×#62611yescharacteristic
749C2×C3C2×D3×#6711yescharacteristic
750D3—22no—
751D3—42no—
752D3—122no—
753D3—122no—
754D3—242no—
755D3—364no—
756D3—362no—
757D3—362no—
758D3—362no—
759D3—722no—
760D3—722no—
761D3—724no—
762C22—32no—
763C22—62no—
764C22—62no—
765C22—122no—
766C22—182no—
767C22—368no—
768C22—362no—
769C22—542no—
770C22—1082no—
771C22D3×#62611yescharacteristic
772C4—32no—
773C4—182no—
774C4D3×#62611yescharacteristic
775C4C2×D3311yescharacteristic
776C3—21no—
777C3—21no—
778C3—21no—
779C3—41no—
780C3C2×#6379411yescharacteristic, complemented
781C3C2×#6383011yescharacteristic, complemented
782C3C2×#6393411yescharacteristic, complemented
783C2—62no—
784C2—122no—
785C2—362no—
786C2—1082no—
787C2#1172286812yesdirect product factor
788C2C2×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×#89022C2semidirect
2. C2×C3×D3×D12C2semidirect
3. C2×#88811C2semidirect
4. C2×#88791C2semidirect
5. C2×#88790C2semidirect
6. C2×C3×#3716C2semidirect
7. C2×C3×#3711C2semidirect
8. #11722868C2direct (N × H)
13. C2×C4⋊(C3⋊(C3⋊D3))C22semidirect
15. C2×C3×#634C22semidirect
21. #89022C22semidirect
24. C3×D3×D12C22semidirect
25. C2×C3×C3⋊(C3⋊C8)C22semidirect
26. C2×C32×C3⋊C8C22semidirect
27. #88811C22semidirect
28. #88791C22semidirect
29. #88790C22semidirect
30. C3×#3716C22semidirect
31. C3×#3711C22semidirect
35. C2×D3×D12D3semidirect
49. C2×#3716D3semidirect
57. C2×#3711D3semidirect
67. C4⋊(C3⋊(C3⋊D3))C23semidirect
72. C3×#634C23semidirect
81. C3×C3⋊(C3⋊C8)C23semidirect
82. C32×C3⋊C8C23semidirect
103. C2×#634C2×D3semidirect
130. D3×D12C2×D3semidirect
139. C2×C3⋊(C3⋊C8)C2×D3semidirect
147. C2×C3×C3⋊C8C2×D3semidirect
148. C2×C3×C3⋊C8C2×D3semidirect
153. #3716C2×D3semidirect
161. #3711C2×D3semidirect
260. #634C22×D3semidirect
301. C3⋊(C3⋊C8)C22×D3semidirect
306. C3×C3⋊C8C22×D3semidirect
307. C3×C3⋊C8C22×D3semidirect
309. C2×C33AGL(1,ℤ/8)semidirect
383. C2×C3⋊C8D32semidirect
469. C33C2×AGL(1,ℤ/8)semidirect
574. C3⋊C8C2×D32semidirect
585. C2×C32#908semidirect
586. C2×C32#914semidirect
587. C2×C32#932semidirect
702. C32C2×#908semidirect
703. C32C2×#914semidirect
704. C32C2×#932semidirect
744. C2×C3#63794semidirect
745. C2×C3#63830semidirect
746. C2×C3#63934semidirect
780. C3C2×#63794semidirect
781. C3C2×#63830semidirect
782. C3C2×#63934semidirect
787. C2#11722868direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#890222
C2×C3×D3×D122
C2×#888112
C2×#887912
C2×#887902
C2×C3×#37162
C2×C3×#37112
#117228682
C2×#639343
C2×#638303
C2×#637943