Finite Group Databasebeta

← C2×#11722874 #13170659

Subgroups — C2×#11722874 #13170659

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×C3⋊D3×D12C211yesmaximal, characteristic, complemented
2C2×C3×#3796C211yesmaximal, characteristic, complemented
3C2×#88809C211yesmaximal, characteristic, complemented
4C2×#88795C211yesmaximal, characteristic, complemented
5C2×#88790C211yesmaximal, characteristic, complemented
6C2×C3×#3715C211yesmaximal, characteristic, complemented
7C2×C3×#3713C211yesmaximal, characteristic, complemented
8#11722874C218yesmaximal, direct product factor
9C2×#63939—31nomaximal
10C2×#63937—31nomaximal
11C2×#63925—31nomaximal
12C22×D3×C3⋊D3—21no—
13C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
14C2×C3×C4×C3⋊D3C2211yescharacteristic
15C2×C32×D12C2211yescharacteristic
16C2×C32×D12C2211yescharacteristic, complemented
17C2×C32×Dic6C2211yescharacteristic, complemented
18C2×#6291—21no—
19C3⋊D3×D12—22no—
20C3⋊D3×D12C2214yescomplemented
21C2×C3×#626—21no—
22C2×C3×D3×Dic3—21no—
23C3×#3796—22no—
24C3×#3796C2214yescomplemented
25C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
26C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
27#88809C2214yescomplemented
28#88795C2214yescomplemented
29#88790C2214yescomplemented
30C3×#3715C2214yescomplemented
31C3×#3713C2214yescomplemented
32C2×D4×C3⋊D3—31no—
33C2×C3×#239—31no—
34C2×C3×#237—31no—
35C2×D3×D12—31no—
36C2×D3×D12—31no—
37C2×D3×D12—61no—
38C2×#3796D311yescharacteristic, complemented
39C2×#3755—31no—
40C2×#3753—31no—
41C2×C3×#215—31no—
42C2×C3×#214—31no—
43C2×C3×#213—31no—
44C2×C3×#213—31no—
45#63939—38no—
46#63937—38no—
47#63925—38no—
48C2×#3717—31no—
49C2×#3717—31no—
50C2×#3717—61no—
51C2×#3715D311yescharacteristic, complemented
52C2×#3714—31no—
53C2×#3714—31no—
54C2×#3714—61no—
55C2×#3713D311yescharacteristic, complemented
56C2×#3712—31no—
57C2×#3711—31no—
58C2×#3711—31no—
59C22×C3⋊(C3⋊D3)—21no—
60C22×C3×C3⋊D3D411yescharacteristic
61C22×C32×D3—21no—
62C22×C32×D3—21no—
63C2×D3×C3⋊D3—24no—
64C2×D3×C3⋊D3—44no—
65C2×C33×C4C2311yescharacteristic
66C4⋊(C3⋊(C3⋊D3))—21no—
67C4⋊(C3⋊(C3⋊D3))C2312yes—
68C2×C3×C3⋊Dic3D411yescharacteristic
69C3×C4×C3⋊D3D412yes—
70C3×C4×C3⋊D3C2312yes—
71C2×C32×Dic3—21no—
72C32×D12—21no—
73C32×D12—21no—
74C32×D12C2312yes—
75C32×D12C2312yescomplemented
76C32×Dic6—21no—
77C32×Dic6C2312yescomplemented
78#6291—24no—
79C3×#626—24no—
80C3×D3×Dic3—24no—
81C3×C3⋊(C3⋊C8)C2312yescomplemented
82C3×C3⋊(C3⋊C8)C2312yescomplemented
83C2×#949—91no—
84C2×#914—91no—
85C2×#911—91no—
86C23×C3⋊D3—61no—
87C22×D32—61no—
88C22×D32—61no—
89C22×D32—62no—
90C2×C32×Q8—31no—
91C2×C32×D4—31no—
92C2×C32×D4—31no—
93C2×#638—61no—
94D4×C3⋊D3—34no—
95D4×C3⋊D3—62no—
96C2×C4⋊(C3⋊D3)—31no—
97C2×C4⋊(C3⋊D3)—31no—
98C2×C4⋊(C3⋊D3)—31no—
99C2×C4⋊(C3⋊D3)—61no—
100C2×C4⋊(C3⋊D3)—61no—
101C2×C4⋊(C3⋊D3)—61no—
102C2×C4⋊(C3⋊D3)—121no—
103C2×C4×C3⋊D3C2×D311yescharacteristic
104C2×C3×#67—61no—
105C22×C3×Dic3—61no—
106C3×#239—34no—
107C3×#239—62no—
108C3×#237—34no—
109C3×#237—62no—
110C2×C3×D12—21no—
111C2×C3×D12—21no—
112C2×C3×D12—61no—
113C2×C3×D12C2×D311yescharacteristic
114C2×C3×D12C2×D311yescharacteristic
115C2×C3×D12C2×D311yescharacteristic, complemented
116C2×C3×D12C2×D311yescharacteristic, complemented
117C2×C3×C4×D3—31no—
118C2×C3×C4×D3—31no—
119C2×C3×C4×D3—61no—
120C2×C3×C4×D3—61no—
121C2×C3×Dic6—21no—
122C2×C3×Dic6C2×D311yescharacteristic, complemented
123C2×C3×Dic6C2×D311yescharacteristic, complemented
124C2×#626—21no—
125C2×#626—61no—
126C2×#626—61no—
127C2×#626—62no—
128C2×D3×Dic3—21no—
129D3×D12—34no—
130D3×D12—34no—
131D3×D12—62no—
132D3×D12—62no—
133D3×D12—64no—
134D3×D12—64no—
135#3796—22no—
136#3796C2×D314yescomplemented
137#3755—34no—
138#3753—34no—
139C2×C3⋊(C3⋊C8)C2×D311yescharacteristic, complemented
140C2×C3⋊(C3⋊C8)C2×D311yescharacteristic, complemented
141C3×#215—34no—
142C3×#214—34no—
143C3×#213—34no—
144C3×#213—34no—
145C2×C3×C3⋊C8—31no—
146C2×C3×C3⋊C8—31no—
147C2×C3×C3⋊C8—31no—
148C2×C3×C3⋊C8—31no—
149C2×C3×C3⋊C8—61no—
150C2×C3×C3⋊C8—61no—
151#3717—34no—
152#3717—34no—
153#3717—64no—
154#3715C2×D314yescomplemented
155#3714—34no—
156#3714—34no—
157#3714—64no—
158#3713C2×D314yescomplemented
159#3712—34no—
160#3711—34no—
161#3711—34no—
162C22×C33C2×D411yescharacteristic
163C2×C3⋊(C3⋊D3)—22no—
164C2×C3⋊(C3⋊D3)—42no—
165C2×C3×C3⋊D3—22no—
166C2×C3×C3⋊D3C2×D412yes—
167C2×C32×D3—22no—
168C2×C32×D3—22no—
169C2×C32×D3—42no—
170C2×C32×D3—42no—
171D3×C3⋊D3—48no—
172C33×C4C2×D411yescharacteristic
173C33×C4C2411yescharacteristic
174C3×C3⋊Dic3C2×D412yes—
175C32×Dic3—22no—
176C2×C3×#41—91no—
177C2×#239—31no—
178C2×#237—31no—
179C2×D3×D4—91no—
180C2×D3×D4—91no—
181C2×D3×D4—181no—
182C22×D12—91no—
183C2×C3×SD16—91no—
184C2×C3×D8—91no—
185#949—98no—
186C2×#215—31no—
187C2×#215—91no—
188C2×#215—91no—
189C2×#215—181no—
190C2×#214—31no—
191C2×#213—31no—
192C2×#213—31no—
193C2×#213—91no—
194C2×#213—91no—
195C2×#213—181no—
196C2×#208—91no—
197#914—98no—
198#911—98no—
199C2×D24—91no—
200C2×#204—91no—
201C2×ΓL(1,𝔽25)—91no—
202C2×ΓL(1,𝔽25)—91no—
203C23×C32—61no—
204C23×C32—61no—
205C22×C3⋊D3—61no—
206C22×C3⋊D3—64no—
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—124no—
214C22×C3⋊D3#6711yescharacteristic
215C22×C3×D3—22no—
216C22×C3×D3—21no—
217C22×C3×D3—21no—
218C22×C3×D3—21no—
219C22×C3×D3—21no—
220C22×C3×D3—31no—
221C22×C3×D3—31no—
222C22×C3×D3—41no—
223C22×C3×D3—61no—
224C2×D32—64no—
225C2×D32—64no—
226C2×D32—68no—
227C2×D32—128no—
228C2×D32—124no—
229C2×D32—124no—
230C32×Q8—32no—
231C32×Q8—61no—
232C32×D4—32no—
233C32×D4—32no—
234C32×D4—61no—
235C32×D4—61no—
236C2×C32×C4—21no—
237C2×C32×C4—21no—
238C2×C32×C4—21no—
239C2×C32×C4—41no—
240C2×C32×C4—61no—
241C2×C32×C4C22×D311yescharacteristic
242C2×C32×C4C22×D311yescharacteristic
243C2×C32×C4C22×D311yescharacteristic
244#638—64no—
245C2×C3⋊Dic3#6711yescharacteristic
246C4⋊(C3⋊D3)—32no—
247C4⋊(C3⋊D3)—32no—
248C4⋊(C3⋊D3)—32no—
249C4⋊(C3⋊D3)—62no—
250C4⋊(C3⋊D3)—62no—
251C4⋊(C3⋊D3)—62no—
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#6712yes—
261C4×C3⋊D3C22×D312yes—
262C3×#67—64no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—31no—
266C2×C3×Dic3—31no—
267C2×C3×Dic3—41no—
268C2×C3×Dic3—61no—
269C2×C3×Dic3—64no—
270C3×D12—22no—
271C3×D12—21no—
272C3×D12—21no—
273C3×D12—21no—
274C3×D12—21no—
275C3×D12—22no—
276C3×D12—22no—
277C3×D12—41no—
278C3×D12—64no—
279C3×D12C22×D312yes—
280C3×D12C22×D312yes—
281C3×D12C22×D312yescomplemented
282C3×D12C22×D312yescomplemented
283C3×C4×D3—32no—
284C3×C4×D3—32no—
285C3×C4×D3—32no—
286C3×C4×D3—32no—
287C3×C4×D3—62no—
288C3×C4×D3—62no—
289C3×C4×D3—64no—
290C3×Dic6—21no—
291C3×Dic6—21no—
292C3×Dic6—22no—
293C3×Dic6—41no—
294C3×Dic6C22×D312yescomplemented
295C3×Dic6C22×D312yescomplemented
296#626—24no—
297#626—64no—
298#626—64no—
299#626—68no—
300D3×Dic3—24no—
301C3⋊(C3⋊C8)C22×D312yescomplemented
302C3⋊(C3⋊C8)C22×D312yescomplemented
303C3×C3⋊C8—32no—
304C3×C3⋊C8—32no—
305C3×C3⋊C8—32no—
306C3×C3⋊C8—32no—
307C3×C3⋊C8—62no—
308C3×C3⋊C8—62no—
309C2×AGL(1,ℤ/8)—271noSylow
310C2×C33AGL(1,ℤ/8)12yescomplemented
311C2×C33C22×D411yescharacteristic
312C3⋊(C3⋊D3)—42no—
313C3×C3⋊D3—22no—
314C32×D3—42no—
315C32×D3—42no—
316C23×D3—181no—
317C23×D3—181no—
318C23×D3—181no—
319C23×D3—182no—
320C3×#41—94no—
321C3×#41—182no—
322C2×C3×Q8—31no—
323C2×C3×Q8—31no—
324C2×C3×Q8—61no—
325C2×C3×D4—31no—
326C2×C3×D4—31no—
327C2×C3×D4—31no—
328C2×C3×D4—31no—
329C2×C3×D4—61no—
330C2×C3×D4—61no—
331C2×C3×D4—181no—
332C22×C3×C4—91no—
333C22×C3×C4—181no—
334C2×#67—61no—
335C2×#67—181no—
336C2×#67—181no—
337C2×#67—182no—
338C22×Dic3—61no—
339#239—34no—
340#239—62no—
341#237—34no—
342#237—62no—
343D3×D4—94no—
344D3×D4—94no—
345D3×D4—184no—
346D3×D4—182no—
347D3×D4—182no—
348D3×D4—184no—
349C2×D12—61no—
350C2×D12—91no—
351C2×D12—91no—
352C2×D12—91no—
353C2×D12—94no—
354C2×D12—181no—
355C2×D12—181no—
356C2×D12—181no—
357C2×D12—182no—
358C2×D12—181no—
359C2×D12—361no—
360C2×D12D3211yescharacteristic
361C2×D12D3211yescharacteristic, complemented
362C2×C4×D3—31no—
363C2×C4×D3—31no—
364C2×C4×D3—61no—
365C2×C4×D3—61no—
366C2×Dic6D3211yescharacteristic, complemented
367C3×SD16—94no—
368C3×D8—94no—
369C2×C3×C8—91no—
370C2×C3×C8—91no—
371#215—34no—
372#215—94no—
373#215—94no—
374#215—184no—
375#214—34no—
376#213—34no—
377#213—34no—
378#213—94no—
379#213—94no—
380#213—184no—
381#208—94no—
382C2×C3⋊C8—31no—
383C2×C3⋊C8—31no—
384C2×C3⋊C8—31no—
385C2×C3⋊C8—31no—
386C2×C3⋊C8—61no—
387C2×C3⋊C8—61no—
388D24—94no—
389#204—94no—
390ΓL(1,𝔽25)—94no—
391ΓL(1,𝔽25)—94no—
392C22×C32—21no—
393C22×C32—21no—
394C22×C32—21no—
395C22×C32—41no—
396C22×C32—62no—
397C22×C32—62no—
398C22×C32—122no—
399C22×C32—122no—
400C22×C32D3×D411yescharacteristic
401C22×C32D3×D411yescharacteristic
402C22×C32C2×#6711yescharacteristic
403C2×C3⋊D3—22no—
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—128no—
412C2×C3⋊D3—122no—
413C2×C3⋊D3—124no—
414C2×C3⋊D3—122no—
415C2×C3⋊D3—122no—
416C2×C3⋊D3—242no—
417C2×C3⋊D3—242no—
418C2×C3⋊D3—244no—
419C2×C3⋊D3C2×#6712yes—
420C2×C3×D3—24no—
421C2×C3×D3—22no—
422C2×C3×D3—22no—
423C2×C3×D3—22no—
424C2×C3×D3—22no—
425C2×C3×D3—32no—
426C2×C3×D3—32no—
427C2×C3×D3—42no—
428C2×C3×D3—44no—
429C2×C3×D3—42no—
430C2×C3×D3—42no—
431C2×C3×D3—42no—
432C2×C3×D3—42no—
433C2×C3×D3—62no—
434C2×C3×D3—64no—
435C2×C3×D3—62no—
436C2×C3×D3—62no—
437C2×C3×D3—82no—
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—41no—
448C32×C4—41no—
449C32×C4—62no—
450C32×C4D3×D411yescharacteristic
451C32×C4D3×D411yescharacteristic
452C32×C4C2×#6711yescharacteristic
453C32×C4C23×D311yescharacteristic
454C32×C4C23×D311yescharacteristic
455C32×C4C23×D311yescharacteristic
456C3⋊Dic3C2×#6712yes—
457C3×Dic3—22no—
458C3×Dic3—22no—
459C3×Dic3—32no—
460C3×Dic3—32no—
461C3×Dic3—42no—
462C3×Dic3—62no—
463C2×#41—91no—
464C22×D4—271no—
465AGL(1,ℤ/8)—278no—
466C2×SD16—91no—
467C2×SD16—271no—
468C2×D8—91no—
469C2×D8—271no—
470C2×M16—271no—
471C33C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
472C23×C3—62no—
473C23×C3—61no—
474C23×C3—61no—
475C23×C3—61no—
476C23×C3—61no—
477C23×C3—91no—
478C23×C3—121no—
479C22×D3—21no—
480C22×D3—21no—
481C22×D3—31no—
482C22×D3—31no—
483C22×D3—61no—
484C22×D3—184no—
485C22×D3—184no—
486C22×D3—184no—
487C22×D3—188no—
488C22×D3—182no—
489C22×D3—181no—
490C22×D3—181no—
491C22×D3—181no—
492C22×D3—361no—
493C22×D3—361no—
494C22×D3—362no—
495C22×D3—364no—
496C22×D3—368no—
497C22×D3—364no—
498C22×D3—364no—
499C3×Q8—32no—
500C3×Q8—32no—
501C3×Q8—62no—
502C3×Q8—61no—
503C3×Q8—61no—
504C3×Q8—121no—
505C3×D4—32no—
506C3×D4—32no—
507C3×D4—32no—
508C3×D4—32no—
509C3×D4—62no—
510C3×D4—62no—
511C3×D4—62no—
512C3×D4—61no—
513C3×D4—61no—
514C3×D4—61no—
515C3×D4—61no—
516C3×D4—121no—
517C3×D4—184no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—41no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—91no—
525C2×C3×C4—92no—
526C2×C3×C4—92no—
527C2×C3×C4—121no—
528C2×C3×C4—184no—
529C2×C3×C4C2×D3211yescharacteristic
530C2×C3×C4C2×D3211yescharacteristic
531C2×C3×C4C2×D3211yescharacteristic
532#67—64no—
533#67—184no—
534#67—184no—
535#67—188no—
536C2×Dic3—21no—
537C2×Dic3—31no—
538C2×Dic3—31no—
539C2×Dic3—61no—
540C2×Dic3—64no—
541D12—21no—
542D12—21no—
543D12—64no—
544D12—92no—
545D12—92no—
546D12—92no—
547D12—182no—
548D12—182no—
549D12—182no—
550D12—182no—
551D12—184no—
552D12—181no—
553D12—181no—
554D12—181no—
555D12—362no—
556D12—361no—
557D12—361no—
558D12—362no—
559D12C2×D3212yes—
560D12C2×D3212yescomplemented
561C4×D3—32no—
562C4×D3—32no—
563C4×D3—32no—
564C4×D3—32no—
565C4×D3—62no—
566C4×D3—62no—
567C4×D3—64no—
568Dic6—21no—
569Dic6C2×D3212yescomplemented
570C3×C8—92no—
571C3×C8—92no—
572C3⋊C8—32no—
573C3⋊C8—32no—
574C3⋊C8—32no—
575C3⋊C8—32no—
576C3⋊C8—62no—
577C3⋊C8—62no—
578C2×C32—21no—
579C2×C32—21no—
580C2×C32—21no—
581C2×C32—22no—
582C2×C32—22no—
583C2×C32—22no—
584C2×C32—42no—
585C2×C32—41no—
586C2×C32—122no—
587C2×C32—122no—
588C2×C32#91112yescomplemented
589C2×C32#91412yescomplemented
590C2×C32#94912yescomplemented
591C2×C32C2×D3×D411yescharacteristic
592C2×C32C2×D3×D411yescharacteristic
593C2×C32C22×#6711yescharacteristic
594C3⋊D3—22no—
595C3⋊D3—122no—
596C3⋊D3—124no—
597C3⋊D3—122no—
598C3⋊D3—122no—
599C3⋊D3—242no—
600C3⋊D3—242no—
601C3⋊D3—244no—
602C3×D3—44no—
603C3×D3—42no—
604C3×D3—42no—
605C3×D3—42no—
606C3×D3—42no—
607C3×D3—64no—
608C3×D3—62no—
609C3×D3—62no—
610C3×D3—82no—
611C24—541no—
612#41—94no—
613#41—182no—
614C2×Q8—31no—
615C2×D4—31no—
616C2×D4—31no—
617C2×D4—181no—
618C2×D4—274no—
619C2×D4—271no—
620C2×D4—542no—
621C2×D4—541no—
622C22×C4—91no—
623C22×C4—181no—
624SD16—94no—
625SD16—274no—
626D8—94no—
627D8—274no—
628M16—274no—
629C2×C8—91no—
630C2×C8—91no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—41no—
635C22×C3—64no—
636C22×C3—62no—
637C22×C3—62no—
638C22×C3—62no—
639C22×C3—62no—
640C22×C3—92no—
641C22×C3—122no—
642C22×C3—124no—
643C22×C3—122no—
644C22×C3—122no—
645C22×C3—122no—
646C22×C3—122no—
647C22×C3—182no—
648C22×C3—242no—
649C22×C3D3×#6711yescharacteristic
650C22×C3D3×#6711yescharacteristic
651C22×C3#381111yescharacteristic
652C2×D3—22no—
653C2×D3—22no—
654C2×D3—32no—
655C2×D3—32no—
656C2×D3—42no—
657C2×D3—42no—
658C2×D3—62no—
659C2×D3—64no—
660C2×D3—62no—
661C2×D3—62no—
662C2×D3—184no—
663C2×D3—182no—
664C2×D3—182no—
665C2×D3—182no—
666C2×D3—362no—
667C2×D3—362no—
668C2×D3—364no—
669C2×D3—368no—
670C2×D3—3616no—
671C2×D3—368no—
672C2×D3—368no—
673C2×D3—364no—
674C2×D3—362no—
675C2×D3—362no—
676C2×D3—362no—
677C2×D3—722no—
678C2×D3—722no—
679C2×D3—724no—
680C3×C4—21no—
681C3×C4—21no—
682C3×C4—21no—
683C3×C4—21no—
684C3×C4—21no—
685C3×C4—21no—
686C3×C4—41no—
687C3×C4—41no—
688C3×C4—62no—
689C3×C4—62no—
690C3×C4—92no—
691C3×C4—122no—
692C3×C4D3×#6711yescharacteristic
693C3×C4D3×#6711yescharacteristic
694C3×C4#381111yescharacteristic
695C3×C4C22×D3211yescharacteristic
696C3×C4C22×D3211yescharacteristic
697C3×C4C22×D3211yescharacteristic
698Dic3—22no—
699Dic3—32no—
700Dic3—32no—
701Dic3—62no—
702C32—21no—
703C32—21no—
704C32—21no—
705C32—41no—
706C32C2×#91111yescharacteristic, complemented
707C32C2×#91411yescharacteristic, complemented
708C32C2×#94911yescharacteristic, complemented
709C23—61no—
710C23—61no—
711C23—91no—
712C23—544no—
713C23—541no—
714C23—1084no—
715Q8—32no—
716Q8—61no—
717D4—32no—
718D4—32no—
719D4—61no—
720D4—61no—
721D4—184no—
722D4—272no—
723D4—544no—
724D4—541no—
725C2×C4—61no—
726C2×C4—91no—
727C2×C4—92no—
728C2×C4—92no—
729C2×C4—184no—
730C2×C4D3311yescharacteristic
731C8—92no—
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—124no—
742C2×C3—122no—
743C2×C3—122no—
744C2×C3—122no—
745C2×C3—122no—
746C2×C3—182no—
747C2×C3—242no—
748C2×C3#6392512yescomplemented
749C2×C3#6393712yescomplemented
750C2×C3#6393912yescomplemented
751C2×C3C2×D3×#6711yescharacteristic
752C2×C3C2×D3×#6711yescharacteristic
753C2×C3C2×#381111yescharacteristic
754D3—42no—
755D3—42no—
756D3—64no—
757D3—62no—
758D3—62no—
759D3—364no—
760D3—362no—
761D3—362no—
762D3—362no—
763D3—722no—
764D3—722no—
765D3—724no—
766C22—62no—
767C22—62no—
768C22—92no—
769C22—122no—
770C22—122no—
771C22—182no—
772C22—542no—
773C22—1088no—
774C22—1082no—
775C22#8895211yescharacteristic
776C4—62no—
777C4—92no—
778C4#8895211yescharacteristic
779C4C2×D3311yescharacteristic
780C3—21no—
781C3—21no—
782C3—21no—
783C3—41no—
784C3C2×#6392511yescharacteristic, complemented
785C3C2×#6393711yescharacteristic, complemented
786C3C2×#6393911yescharacteristic, complemented
787C2—122no—
788C2—122no—
789C2—182no—
790C2—1082no—
791C2#1172287412yesdirect product factor
792C2C2×#8895211yescharacteristic
subgroupG/H
centerC22#88952
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×#3796C2semidirect
3. C2×#88809C2semidirect
4. C2×#88795C2semidirect
5. C2×#88790C2semidirect
6. C2×C3×#3715C2semidirect
7. C2×C3×#3713C2semidirect
8. #11722874C2direct (N × H)
16. C2×C32×D12C22semidirect
17. C2×C32×Dic6C22semidirect
20. C3⋊D3×D12C22semidirect
24. C3×#3796C22semidirect
25. C2×C3×C3⋊(C3⋊C8)C22semidirect
26. C2×C3×C3⋊(C3⋊C8)C22semidirect
27. #88809C22semidirect
28. #88795C22semidirect
29. #88790C22semidirect
30. C3×#3715C22semidirect
31. C3×#3713C22semidirect
38. C2×#3796D3semidirect
51. C2×#3715D3semidirect
55. C2×#3713D3semidirect
75. C32×D12C23semidirect
77. C32×Dic6C23semidirect
81. C3×C3⋊(C3⋊C8)C23semidirect
82. C3×C3⋊(C3⋊C8)C23semidirect
115. C2×C3×D12C2×D3semidirect
116. C2×C3×D12C2×D3semidirect
122. C2×C3×Dic6C2×D3semidirect
123. C2×C3×Dic6C2×D3semidirect
136. #3796C2×D3semidirect
139. C2×C3⋊(C3⋊C8)C2×D3semidirect
140. C2×C3⋊(C3⋊C8)C2×D3semidirect
154. #3715C2×D3semidirect
158. #3713C2×D3semidirect
281. C3×D12C22×D3semidirect
282. C3×D12C22×D3semidirect
294. C3×Dic6C22×D3semidirect
295. C3×Dic6C22×D3semidirect
301. C3⋊(C3⋊C8)C22×D3semidirect
302. C3⋊(C3⋊C8)C22×D3semidirect
310. C2×C33AGL(1,ℤ/8)semidirect
361. C2×D12D32semidirect
366. C2×Dic6D32semidirect
471. C33C2×AGL(1,ℤ/8)semidirect
560. D12C2×D32semidirect
569. Dic6C2×D32semidirect
588. C2×C32#911semidirect
589. C2×C32#914semidirect
590. C2×C32#949semidirect
706. C32C2×#911semidirect
707. C32C2×#914semidirect
708. C32C2×#949semidirect
748. C2×C3#63925semidirect
749. C2×C3#63937semidirect
750. C2×C3#63939semidirect
784. C3C2×#63925semidirect
785. C3C2×#63937semidirect
786. C3C2×#63939semidirect
791. C2#11722874direct (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×#37962
C2×#888092
C2×#887952
C2×#887902
C2×C3×#37152
C2×C3×#37132
#117228742
C2×#639393
C2×#639373
C2×#639253