Finite Group Databasebeta

← C2×#11723706 #13178700

Subgroups — C2×#11723706 #13178700

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×D4×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×#89041C211yesmaximal, characteristic, complemented
3C2×C3×#3754C211yesmaximal, characteristic, complemented
4C2×C3×#3753C211yesmaximal, characteristic, complemented
5#11723706C218yesmaximal, direct product factor
6C2×#88811C211yesmaximal, characteristic, complemented
7C2×#88810C211yesmaximal, characteristic, complemented
8C2×#88809C211yesmaximal, characteristic, complemented
9C2×#63937—31nomaximal
10C2×#63934—31nomaximal
11C2×#63932—31nomaximal
12C23×C3×C3⋊D3—21no—
13C2×C33×D4C2211yescharacteristic
14C2×C3×#638—21no—
15C3×D4×C3⋊D3—22no—
16C3×D4×C3⋊D3C2214yescomplemented
17C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
18C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
19C2×C3×C4×C3⋊D3C2211yescharacteristic
20C2×C3×#634C2211yescharacteristic, complemented
21C2×#6295—21no—
22C2×#6294—21no—
23#89041—22no—
24#89041C2214yescomplemented
25C3×#3754C2214yescomplemented
26C3×#3753C2214yescomplemented
27C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
28C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
29#88811C2214yescomplemented
30#88810C2214yescomplemented
31#88809C2214yescomplemented
32C2×D4×C3⋊D3D311yescharacteristic, complemented
33C2×C3×D3×D4—31no—
34C2×C3×D3×D4—31no—
35C2×C3×D3×D4—61no—
36C2×#3799—31no—
37C2×#3796—31no—
38C2×#3795—31no—
39C2×#3754D311yescharacteristic, complemented
40C2×#3753D311yescharacteristic, complemented
41C2×C3×#214—31no—
42C2×C3×#214—31no—
43C2×C3×#214—61no—
44C2×C3×#213—31no—
45C2×C3×#213—31no—
46C2×C3×#213—61no—
47#63937—38no—
48#63934—38no—
49#63932—38no—
50C2×#3717—31no—
51C2×#3716—31no—
52C2×#3715—31no—
53C2×#3714—31no—
54C2×#3714—31no—
55C2×#3713—31no—
56C2×#3712—31no—
57C2×#3711—31no—
58C2×#3711—31no—
59C23×C33—21no—
60C22×C3×C3⋊D3—21no—
61C22×C3×C3⋊D3—21no—
62C22×C3×C3⋊D3—24no—
63C22×C3×C3⋊D3—44no—
64C22×C3×C3⋊D3D411yescharacteristic
65C33×D4—21no—
66C33×D4C2312yes—
67C2×C33×C4C2311yescharacteristic
68C3×#638—24no—
69C2×C3×C3⋊Dic3—21no—
70C2×C3×C3⋊Dic3D411yescharacteristic
71C3×C4⋊(C3⋊D3)—21no—
72C3×C4⋊(C3⋊D3)—21no—
73C3×C4⋊(C3⋊D3)C2312yes—
74C3×C4⋊(C3⋊D3)C2312yescomplemented
75C3×C4×C3⋊D3D412yes—
76C3×C4×C3⋊D3C2312yes—
77C3×#634—21no—
78C3×#634C2312yescomplemented
79#6295—24no—
80#6294—24no—
81C3×C3⋊(C3⋊C8)C2312yescomplemented
82C3×C3⋊(C3⋊C8)C2312yescomplemented
83C2×#932—91no—
84C2×#914—91no—
85C2×#911—91no—
86C23×C3⋊D3—21no—
87C23×C3×D3—61no—
88C23×C3×D3—61no—
89C23×C3×D3—62no—
90C2×C32×D4—21no—
91C2×C32×D4—21no—
92C2×C32×D4—21no—
93C2×C32×D4—41no—
94C2×C32×D4C2×D311yescharacteristic
95C2×C32×D4C2×D311yescharacteristic
96C2×C32×D4C2×D311yescharacteristic
97C2×#638—21no—
98D4×C3⋊D3—22no—
99D4×C3⋊D3C2×D314yescomplemented
100C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
101C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
102C2×C4×C3⋊D3C2×D311yescharacteristic
103C2×#634C2×D311yescharacteristic, complemented
104C2×C3×#67—61no—
105C2×C3×#67—61no—
106C2×C3×#67—62no—
107C3×D3×D4—34no—
108C3×D3×D4—34no—
109C3×D3×D4—62no—
110C3×D3×D4—62no—
111C3×D3×D4—64no—
112C3×D3×D4—64no—
113C2×C3×D12—31no—
114C2×C3×D12—31no—
115C2×C3×D12—31no—
116C2×C3×D12—31no—
117C2×C3×D12—61no—
118C2×C3×D12—61no—
119C2×C3×C4×D3—31no—
120C2×C3×C4×D3—31no—
121C2×C3×C4×D3—61no—
122C2×C3×Dic6—31no—
123C2×C3×Dic6—31no—
124C2×C3×Dic6—61no—
125C2×#626—61no—
126C2×#626—61no—
127C2×#625—61no—
128C2×#624—61no—
129C2×D3×Dic3—61no—
130C2×D3×Dic3—61no—
131#3799—34no—
132#3799—62no—
133#3796—34no—
134#3796—62no—
135#3795—34no—
136#3795—62no—
137#3754C2×D314yescomplemented
138#3753C2×D314yescomplemented
139C2×C3⋊(C3⋊C8)C2×D311yescharacteristic, complemented
140C2×C3⋊(C3⋊C8)C2×D311yescharacteristic, complemented
141C3×#214—34no—
142C3×#214—34no—
143C3×#214—64no—
144C3×#213—34no—
145C3×#213—34no—
146C3×#213—64no—
147C2×C3×C3⋊C8—31no—
148C2×C3×C3⋊C8—31no—
149C2×C3×C3⋊C8—31no—
150C2×C3×C3⋊C8—31no—
151C2×C3×C3⋊C8—61no—
152C2×C3×C3⋊C8—61no—
153#3717—34no—
154#3716—34no—
155#3715—34no—
156#3714—34no—
157#3714—34no—
158#3713—34no—
159#3712—34no—
160#3711—34no—
161#3711—34no—
162C22×C33—22no—
163C22×C33—42no—
164C22×C33C2×D411yescharacteristic
165C2×C3×C3⋊D3—22no—
166C2×C3×C3⋊D3—22no—
167C2×C3×C3⋊D3—22no—
168C2×C3×C3⋊D3—48no—
169C2×C3×C3⋊D3—42no—
170C2×C3×C3⋊D3—42no—
171C2×C3×C3⋊D3C2×D412yes—
172C33×C4C2×D411yescharacteristic
173C33×C4C2411yescharacteristic
174C3×C3⋊Dic3—22no—
175C3×C3⋊Dic3C2×D412yes—
176C22×C3×D4—91no—
177C2×#239—91no—
178C2×#237—91no—
179C2×D3×D4—31no—
180C2×D3×D4—31no—
181C2×D3×D4—61no—
182C2×#235—91no—
183C2×C3×SD16—91no—
184C2×C3×D8—91no—
185C2×#215—91no—
186C2×#214—31no—
187C2×#214—31no—
188C2×#214—61no—
189C2×#214—91no—
190#932—98no—
191C2×#213—31no—
192C2×#213—31no—
193C2×#213—61no—
194C2×#213—91no—
195C2×#213—91no—
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—21no—
204C23×C32—22no—
205C23×C32—21no—
206C23×C32—21no—
207C23×C32—41no—
208C23×C32—41no—
209C23×C32—42no—
210C22×C3⋊D3—21no—
211C22×C3⋊D3—24no—
212C22×C3⋊D3—21no—
213C22×C3⋊D3—44no—
214C22×C3⋊D3#6711yescharacteristic
215C22×C3×D3—31no—
216C22×C3×D3—31no—
217C22×C3×D3—61no—
218C22×C3×D3—64no—
219C22×C3×D3—64no—
220C22×C3×D3—62no—
221C22×C3×D3—68no—
222C22×C3×D3—61no—
223C22×C3×D3—61no—
224C22×C3×D3—61no—
225C22×C3×D3—61no—
226C22×C3×D3—121no—
227C22×C3×D3—128no—
228C22×C3×D3—124no—
229C22×C3×D3—124no—
230C32×D4—21no—
231C32×D4—22no—
232C32×D4—21no—
233C32×D4—21no—
234C32×D4—22no—
235C32×D4—22no—
236C32×D4—22no—
237C32×D4—42no—
238C32×D4—41no—
239C32×D4—41no—
240C32×D4—42no—
241C32×D4C22×D312yes—
242C32×D4C22×D312yes—
243C32×D4C22×D312yes—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—41no—
248C2×C32×C4C22×D311yescharacteristic
249C2×C32×C4C22×D311yescharacteristic
250C2×C32×C4C22×D311yescharacteristic
251#638—24no—
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3#6711yescharacteristic
254C4⋊(C3⋊D3)—21no—
255C4⋊(C3⋊D3)—21no—
256C4⋊(C3⋊D3)C22×D312yes—
257C4⋊(C3⋊D3)C22×D312yescomplemented
258C4×C3⋊D3#6712yes—
259C4×C3⋊D3C22×D312yes—
260#634—21no—
261#634C22×D312yescomplemented
262C3×#67—64no—
263C3×#67—64no—
264C3×#67—68no—
265C2×C3×Dic3—31no—
266C2×C3×Dic3—31no—
267C2×C3×Dic3—61no—
268C2×C3×Dic3—61no—
269C2×C3×Dic3—61no—
270C2×C3×Dic3—121no—
271C3×D12—32no—
272C3×D12—32no—
273C3×D12—32no—
274C3×D12—32no—
275C3×D12—62no—
276C3×D12—62no—
277C3×D12—62no—
278C3×D12—61no—
279C3×D12—61no—
280C3×D12—61no—
281C3×D12—61no—
282C3×D12—121no—
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×Dic6—32no—
290C3×Dic6—32no—
291C3×Dic6—62no—
292C3×Dic6—61no—
293C3×Dic6—61no—
294C3×Dic6—121no—
295#626—64no—
296#626—64no—
297#625—64no—
298#624—64no—
299D3×Dic3—64no—
300D3×Dic3—64no—
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×C33—42no—
311C2×C33AGL(1,ℤ/8)12yescomplemented
312C2×C33C22×D411yescharacteristic
313C3×C3⋊D3—22no—
314C3×C3⋊D3—42no—
315C3×C3⋊D3—42no—
316C24×C3—181no—
317C23×D3—61no—
318C23×D3—61no—
319C23×D3—62no—
320C2×C3×Q8—91no—
321C2×C3×D4—21no—
322C2×C3×D4—21no—
323C2×C3×D4—21no—
324C2×C3×D4—41no—
325C2×C3×D4—94no—
326C2×C3×D4—91no—
327C2×C3×D4—91no—
328C2×C3×D4—182no—
329C2×C3×D4—181no—
330C2×C3×D4D3211yescharacteristic
331C2×C3×D4D3211yescharacteristic
332C2×C3×D4D3211yescharacteristic
333C22×C3×C4—91no—
334C2×#67—61no—
335C2×#67—61no—
336C2×#67—62no—
337C2×#67—181no—
338C2×#67—181no—
339C22×Dic3—181no—
340#239—94no—
341#239—182no—
342#237—94no—
343#237—182no—
344D3×D4—34no—
345D3×D4—34no—
346D3×D4—64no—
347D3×D4—62no—
348D3×D4—62no—
349D3×D4—64no—
350#235—94no—
351#235—182no—
352C2×D12—31no—
353C2×D12—31no—
354C2×D12—31no—
355C2×D12—31no—
356C2×D12—61no—
357C2×D12—61no—
358C2×D12—181no—
359C2×C4×D3—31no—
360C2×C4×D3—31no—
361C2×C4×D3—61no—
362C2×C4×D3—181no—
363C2×C4×D3—181no—
364C2×Dic6—31no—
365C2×Dic6—31no—
366C2×Dic6—61no—
367C3×SD16—94no—
368C3×D8—94no—
369C2×C3×C8—91no—
370C2×C3×C8—91no—
371#215—94no—
372#214—34no—
373#214—34no—
374#214—64no—
375#214—94no—
376#213—34no—
377#213—34no—
378#213—64no—
379#213—94no—
380#213—94no—
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—22no—
393C22×C32—24no—
394C22×C32—22no—
395C22×C32—22no—
396C22×C32—21no—
397C22×C32—21no—
398C22×C32—21no—
399C22×C32—41no—
400C22×C32—42no—
401C22×C32—42no—
402C22×C32—44no—
403C22×C32—42no—
404C22×C32—44no—
405C22×C32—42no—
406C22×C32—42no—
407C22×C32—82no—
408C22×C32—82no—
409C22×C32—84no—
410C22×C32D3×D411yescharacteristic
411C22×C32D3×D411yescharacteristic
412C22×C32C2×#6711yescharacteristic
413C2×C3⋊D3—22no—
414C2×C3⋊D3—22no—
415C2×C3⋊D3—22no—
416C2×C3⋊D3—48no—
417C2×C3⋊D3—42no—
418C2×C3⋊D3—42no—
419C2×C3⋊D3C2×#6712yes—
420C2×C3×D3—32no—
421C2×C3×D3—32no—
422C2×C3×D3—62no—
423C2×C3×D3—64no—
424C2×C3×D3—62no—
425C2×C3×D3—62no—
426C2×C3×D3—64no—
427C2×C3×D3—62no—
428C2×C3×D3—62no—
429C2×C3×D3—62no—
430C2×C3×D3—62no—
431C2×C3×D3—122no—
432C2×C3×D3—1216no—
433C2×C3×D3—128no—
434C2×C3×D3—128no—
435C2×C3×D3—124no—
436C2×C3×D3—122no—
437C2×C3×D3—122no—
438C2×C3×D3—122no—
439C2×C3×D3—122no—
440C2×C3×D3—242no—
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×C4D3×D411yescharacteristic
450C32×C4D3×D411yescharacteristic
451C32×C4C2×#6711yescharacteristic
452C32×C4C23×D311yescharacteristic
453C32×C4C23×D311yescharacteristic
454C32×C4C23×D311yescharacteristic
455C3⋊Dic3—22no—
456C3⋊Dic3C2×#6712yes—
457C3×Dic3—32no—
458C3×Dic3—32no—
459C3×Dic3—62no—
460C3×Dic3—62no—
461C3×Dic3—62no—
462C3×Dic3—122no—
463C2×#41—271no—
464C22×D4—91no—
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—22no—
473C23×C3—21no—
474C23×C3—21no—
475C23×C3—21no—
476C23×C3—41no—
477C23×C3—41no—
478C23×C3—42no—
479C23×C3—91no—
480C23×C3—184no—
481C23×C3—181no—
482C23×C3—181no—
483C23×C3—364no—
484C22×D3—31no—
485C22×D3—31no—
486C22×D3—61no—
487C22×D3—64no—
488C22×D3—64no—
489C22×D3—62no—
490C22×D3—68no—
491C22×D3—61no—
492C22×D3—61no—
493C22×D3—61no—
494C22×D3—61no—
495C22×D3—121no—
496C22×D3—128no—
497C22×D3—124no—
498C22×D3—124no—
499C3×Q8—92no—
500C3×Q8—181no—
501C3×D4—22no—
502C3×D4—21no—
503C3×D4—21no—
504C3×D4—21no—
505C3×D4—22no—
506C3×D4—22no—
507C3×D4—22no—
508C3×D4—41no—
509C3×D4—41no—
510C3×D4—42no—
511C3×D4—42no—
512C3×D4—92no—
513C3×D4—92no—
514C3×D4—184no—
515C3×D4—181no—
516C3×D4—181no—
517C3×D4C2×D3212yes—
518C3×D4C2×D3212yes—
519C3×D4C2×D3212yes—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—41no—
524C2×C3×C4—91no—
525C2×C3×C4—92no—
526C2×C3×C4—92no—
527C2×C3×C4—181no—
528C2×C3×C4C2×D3211yescharacteristic
529C2×C3×C4C2×D3211yescharacteristic
530C2×C3×C4C2×D3211yescharacteristic
531#67—64no—
532#67—64no—
533#67—68no—
534#67—184no—
535#67—184no—
536C2×Dic3—31no—
537C2×Dic3—31no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—121no—
542C2×Dic3—184no—
543D12—32no—
544D12—32no—
545D12—32no—
546D12—32no—
547D12—62no—
548D12—62no—
549D12—62no—
550D12—61no—
551D12—61no—
552D12—61no—
553D12—61no—
554D12—121no—
555D12—184no—
556C4×D3—32no—
557C4×D3—32no—
558C4×D3—32no—
559C4×D3—32no—
560C4×D3—62no—
561C4×D3—62no—
562C4×D3—184no—
563C4×D3—184no—
564Dic6—32no—
565Dic6—32no—
566Dic6—62no—
567Dic6—61no—
568Dic6—61no—
569Dic6—121no—
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—42no—
587C2×C32—44no—
588C2×C32—42no—
589C2×C32—42no—
590C2×C32—82no—
591C2×C32—82no—
592C2×C32—84no—
593C2×C32#91112yescomplemented
594C2×C32#91412yescomplemented
595C2×C32#93212yescomplemented
596C2×C32C2×D3×D411yescharacteristic
597C2×C32C2×D3×D411yescharacteristic
598C2×C32C22×#6711yescharacteristic
599C3⋊D3—22no—
600C3⋊D3—42no—
601C3⋊D3—42no—
602C3×D3—64no—
603C3×D3—62no—
604C3×D3—62no—
605C3×D3—124no—
606C3×D3—122no—
607C3×D3—122no—
608C3×D3—122no—
609C3×D3—122no—
610C3×D3—242no—
611C24—181no—
612#41—274no—
613#41—542no—
614C2×Q8—91no—
615C2×D4—94no—
616C2×D4—91no—
617C2×D4—91no—
618C2×D4—182no—
619C2×D4—181no—
620C2×D4—541no—
621C2×D4#111311yescharacteristic
622C22×C4—91no—
623C22×C4—541no—
624SD16—94no—
625SD16—274no—
626D8—94no—
627D8—274no—
628M16—274no—
629C2×C8—91no—
630C2×C8—91no—
631C22×C3—24no—
632C22×C3—22no—
633C22×C3—22no—
634C22×C3—22no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—42no—
639C22×C3—42no—
640C22×C3—44no—
641C22×C3—44no—
642C22×C3—42no—
643C22×C3—42no—
644C22×C3—42no—
645C22×C3—41no—
646C22×C3—82no—
647C22×C3—82no—
648C22×C3—84no—
649C22×C3—92no—
650C22×C3—182no—
651C22×C3—182no—
652C22×C3—182no—
653C22×C3—368no—
654C22×C3—362no—
655C22×C3—362no—
656C22×C3D3×#6711yescharacteristic
657C22×C3D3×#6711yescharacteristic
658C22×C3#381111yescharacteristic
659C2×D3—32no—
660C2×D3—32no—
661C2×D3—62no—
662C2×D3—64no—
663C2×D3—62no—
664C2×D3—62no—
665C2×D3—64no—
666C2×D3—62no—
667C2×D3—62no—
668C2×D3—62no—
669C2×D3—62no—
670C2×D3—122no—
671C2×D3—1216no—
672C2×D3—128no—
673C2×D3—128no—
674C2×D3—124no—
675C2×D3—122no—
676C2×D3—122no—
677C2×D3—122no—
678C2×D3—122no—
679C2×D3—242no—
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—92no—
689C3×C4—182no—
690C3×C4D3×#6711yescharacteristic
691C3×C4D3×#6711yescharacteristic
692C3×C4#381111yescharacteristic
693C3×C4C22×D3211yescharacteristic
694C3×C4C22×D3211yescharacteristic
695C3×C4C22×D3211yescharacteristic
696Dic3—32no—
697Dic3—32no—
698Dic3—62no—
699Dic3—62no—
700Dic3—62no—
701Dic3—122no—
702C32—21no—
703C32—21no—
704C32—21no—
705C32—41no—
706C32C2×#91111yescharacteristic, complemented
707C32C2×#91411yescharacteristic, complemented
708C32C2×#93211yescharacteristic, complemented
709C23—21no—
710C23—91no—
711C23—184no—
712C23—181no—
713C23—181no—
714C23—364no—
715Q8—92no—
716Q8—181no—
717D4—21no—
718D4—92no—
719D4—92no—
720D4—184no—
721D4—181no—
722D4—181no—
723D4—544no—
724D4C2×#111312yes—
725C2×C4—91no—
726C2×C4—92no—
727C2×C4—92no—
728C2×C4—181no—
729C2×C4—544no—
730C2×C4C2×#111311yescharacteristic
731C8—92no—
732C8—92no—
733C2×C3—21no—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—22no—
737C2×C3—22no—
738C2×C3—22no—
739C2×C3—44no—
740C2×C3—42no—
741C2×C3—42no—
742C2×C3—42no—
743C2×C3—41no—
744C2×C3—42no—
745C2×C3—82no—
746C2×C3—82no—
747C2×C3—84no—
748C2×C3—182no—
749C2×C3—362no—
750C2×C3—362no—
751C2×C3#6393212yescomplemented
752C2×C3#6393412yescomplemented
753C2×C3#6393712yescomplemented
754C2×C3C2×D3×#6711yescharacteristic
755C2×C3C2×D3×#6711yescharacteristic
756C2×C3C2×#381111yescharacteristic
757D3—64no—
758D3—62no—
759D3—62no—
760D3—124no—
761D3—122no—
762D3—122no—
763D3—122no—
764D3—122no—
765D3—242no—
766C22—22no—
767C22—42no—
768C22—92no—
769C22—182no—
770C22—182no—
771C22—182no—
772C22—368no—
773C22—362no—
774C22—362no—
775C22#8904911yescharacteristic
776C4—92no—
777C4—182no—
778C4#8904911yescharacteristic
779C4C22×#111311yescharacteristic
780C3—21no—
781C3—21no—
782C3—21no—
783C3—41no—
784C3C2×#6393211yescharacteristic, complemented
785C3C2×#6393411yescharacteristic, complemented
786C3C2×#6393711yescharacteristic, complemented
787C2—42no—
788C2—182no—
789C2—362no—
790C2—362no—
791C2#1172370612yesdirect product factor
792C2C2×#8904911yescharacteristic
subgroupG/H
centerC22#89049
commutator, cosocleC33×C4C24
FrattiniC4C22×#1113
FittingC2×C33×D4C22
socleC22×C33C2×D4
hypercenterC2×D4#1113
hypocenterC33C2×AGL(1,ℤ/8)
LCSG ▷ C33×C4 ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×D4×C3⋊D3C2semidirect
2. C2×#89041C2semidirect
3. C2×C3×#3754C2semidirect
4. C2×C3×#3753C2semidirect
5. #11723706C2direct (N × H)
6. C2×#88811C2semidirect
7. C2×#88810C2semidirect
8. C2×#88809C2semidirect
16. C3×D4×C3⋊D3C22semidirect
18. C2×C3×C4⋊(C3⋊D3)C22semidirect
20. C2×C3×#634C22semidirect
24. #89041C22semidirect
25. C3×#3754C22semidirect
26. C3×#3753C22semidirect
27. C2×C3×C3⋊(C3⋊C8)C22semidirect
28. C2×C3×C3⋊(C3⋊C8)C22semidirect
29. #88811C22semidirect
30. #88810C22semidirect
31. #88809C22semidirect
32. C2×D4×C3⋊D3D3semidirect
39. C2×#3754D3semidirect
40. C2×#3753D3semidirect
74. C3×C4⋊(C3⋊D3)C23semidirect
78. C3×#634C23semidirect
81. C3×C3⋊(C3⋊C8)C23semidirect
82. C3×C3⋊(C3⋊C8)C23semidirect
99. D4×C3⋊D3C2×D3semidirect
101. C2×C4⋊(C3⋊D3)C2×D3semidirect
103. C2×#634C2×D3semidirect
137. #3754C2×D3semidirect
138. #3753C2×D3semidirect
139. C2×C3⋊(C3⋊C8)C2×D3semidirect
140. C2×C3⋊(C3⋊C8)C2×D3semidirect
257. C4⋊(C3⋊D3)C22×D3semidirect
261. #634C22×D3semidirect
301. C3⋊(C3⋊C8)C22×D3semidirect
302. C3⋊(C3⋊C8)C22×D3semidirect
311. C2×C33AGL(1,ℤ/8)semidirect
471. C33C2×AGL(1,ℤ/8)semidirect
593. C2×C32#911semidirect
594. C2×C32#914semidirect
595. C2×C32#932semidirect
706. C32C2×#911semidirect
707. C32C2×#914semidirect
708. C32C2×#932semidirect
751. C2×C3#63932semidirect
752. C2×C3#63934semidirect
753. C2×C3#63937semidirect
784. C3C2×#63932semidirect
785. C3C2×#63934semidirect
786. C3C2×#63937semidirect
791. C2#11723706direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D4×C3⋊D32
C2×#890412
C2×C3×#37542
C2×C3×#37532
#117237062
C2×#888112
C2×#888102
C2×#888092
C2×#639373
C2×#639343
C2×#639323