Finite Group Databasebeta

← C2×#86127 #11703451

Subgroups — C2×#86127 #11703451

Order 768.

7118 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#529C211yesmaximal, characteristic, complemented
2#86127C2132yesmaximal, direct product factor
3C2×#5702C214yesmaximal, complemented
4C2×#5688C212yesmaximal, complemented
5C2×#5680C212yesmaximal, complemented
6C2×#5662C214yesmaximal, complemented
7C2×#5641C212yesmaximal, complemented
8C2×#5616C212yesmaximal, complemented
9C2×Q8×Dic6C211yesmaximal, characteristic, complemented
10C2×#5584C211yesmaximal, characteristic, complemented
11C2×#5542C212yesmaximal, complemented
12C2×#5563C211yesmaximal, characteristic, complemented
13C2×D4×Dic6C211yesmaximal, characteristic, complemented
14C2×#5552C212yesmaximal, complemented
15C2×#5534C212yesmaximal, complemented
16C2×#5516C212yesmaximal, complemented
17C2×#5470C211yesmaximal, characteristic, complemented
18C2×C4×#235C211yesmaximal, characteristic, complemented
19C2×#3518—31nomaximal, Sylow
20C22×#235C2211yescharacteristic
21C23×Dic6C2212yes—
22C3×#529C22116yescomplemented
23C2×C3×#126C2212yes—
24C2×C3×#125C2211yescharacteristic
25C2×C3×#124C2211yescharacteristic
26C2×C3×#123C2212yes—
27C2×C3×C22⋊Q8C2211yescharacteristic
28C2×C3×#121C2211yescharacteristic
29C2×C3×C4×Q8C2211yescharacteristic
30C2×C3×C4×D4C2211yescharacteristic
31C2×C3×C4×D4C2212yes—
32C2×C3×#117C2212yes—
33C22×C3×C42C2211yescharacteristic
34C2×#946C2212yes—
35C2×Q8×Dic3C2212yes—
36C2×#939C2214yes—
37C2×#938C2212yes—
38C2×#936C2214yes—
39C2×D4×Dic3C2212yes—
40C2×#930C2212yes—
41C2×C4×#67C2212yes—
42C2×C4×#67C2212yes—
43C2×#926C2212yes—
44C2×#926C2211yescharacteristic
45C2×#926C2212yes—
46C2×#924C2212yes—
47C2×#924C2212yes—
48C2×#924C2212yes—
49#5702C22164yescomplemented
50#5688C22132yescomplemented
51#5680C22132yescomplemented
52#5662C22164yescomplemented
53#5641C22132yescomplemented
54#5616C22132yescomplemented
55#5584C22116yescomplemented
56Q8×Dic6C22116yescomplemented
57#5563C22116yescomplemented
58#5552C22132yescomplemented
59#5542C22132yescomplemented
60D4×Dic6C22116yescomplemented
61#5534C22132yescomplemented
62#5516C22132yescomplemented
63C2×#898C2214yes—
64C2×#898C2214yes—
65C2×#896C2214yes—
66C2×#896C2214yes—
67C2×#892C2212yes—
68C2×#892C2212yes—
69C2×#888C2212yes—
70C2×#888C2214yes—
71C2×#888C2212yes—
72C2×#887C2214yes—
73C2×#887C2214yes—
74C2×#887C2214yes—
75C2×#885C2214yes—
76C2×#885C2214yes—
77C2×#885C2214yes—
78C2×#883C2214yes—
79C2×#67⋊C4C2214yes—
80C2×#879C2214yes—
81C2×#879C2214yes—
82C2×#878C2214yes—
83C2×#877C2214yes—
84C2×#877C2214yes—
85C2×#875C2212yes—
86C4×#235C22116yescomplemented
87C2×C4×D12C2211yescharacteristic
88C2×C4×D12C2211yescharacteristic
89C2×#872C2212yes—
90C2×C42×D3C2212yes—
91#5470C22116yescomplemented
92C2×#870C2212yes—
93C2×#869C2211yescharacteristic
94C2×#869C2212yes—
95C2×#869C2211yescharacteristic
96C2×C4×Dic6C2212yes—
97C2×C4×Dic6C2211yescharacteristic
98C2×C4×Dic6C2212yes—
99C2×C4×Dic6C2212yes—
100C2×C4×Dic6C2211yescharacteristic
101C2×C4×Dic6C2212yes—
102#3518—332no—
103C2×Q82—31no—
104C2×#556—34no—
105C2×#556—32no—
106C2×#556—31no—
107C2×#556—32no—
108C2×#555—32no—
109C2×#555—31no—
110C2×D4×Q8—31no—
111C2×#548—32no—
112C2×#542—34no—
113C2×#542—32no—
114C2×#533—31no—
115C2×#533—32no—
116C2×#529—32no—
117C2×#529D311yescharacteristic, complemented
118C2×#519—32no—
119C2×C4×#41—31no—
120C22×C3×Q8C2311yescharacteristic
121C22×C3×D4C2311yescharacteristic
122C22×C3×D4C2312yes—
123C23×C3×C4C2312yes—
124C23×C3×C4C2311yescharacteristic
125C23×C3×C4C2311yescharacteristic
126C23×C3×C4C2311yescharacteristic
127C22×#67C2312yes—
128C22×#67C2314yes—
129C23×Dic3C2314yes—
130C2×#235—28no—
131C2×#235C2318yes—
132C22×D12C2311yescharacteristic
133C22×C4×D3C2312yes—
134C22×C4×D3C2312yes—
135C22×C4×D3C2312yes—
136C22×Dic6—216no—
137C22×Dic6C2312yes—
138C22×Dic6C2314yes—
139C22×Dic6C23116yes—
140C22×Dic6C2312yes—
141C22×Dic6C2314yes—
142C22×Dic6C2311yescharacteristic
143C3×#126C23116yes—
144C3×#125C2318yes—
145C3×#124C2318yes—
146C3×#123C23116yes—
147C3×C22⋊Q8C2318yes—
148C3×#121C2318yes—
149C3×C4×Q8C2318yes—
150C3×C4×D4C2318yes—
151C3×C4×D4C23116yes—
152C3×#117C23116yes—
153C2×C3×C4⋊C4C2312yes—
154C2×C3×C4⋊C4C2312yes—
155C2×C3×C4⋊C4C2312yes—
156C2×C3×C4⋊C4C2311yescharacteristic
157C2×C3×C4⋊C4C2311yescharacteristic
158C2×C3×C4⋊C4C2312yes—
159C2×C3×C22⋊C4C2312yes—
160C2×C3×C22⋊C4C2312yes—
161C2×C3×C22⋊C4C2312yes—
162C2×C3×C22⋊C4C2312yes—
163C2×C3×C22⋊C4C2312yes—
164C2×C3×C42C2311yescharacteristic
165C2×C3×C42C2312yes—
166C2×C3×C42C2311yescharacteristic
167C2×C3×C42C2311yescharacteristic
168C2×C3×C42C2311yescharacteristic
169C2×C3×C42C2318yes—
170C2×#217C2314yes—
171C2×#217C2314yes—
172C2×#217C2312yes—
173C2×#217C2314yes—
174#946C23116yes—
175Q8×Dic3C23116yes—
176#939C23132yes—
177#938C23116yes—
178#936C23132yes—
179D4×Dic3C23116yes—
180#930C23116yes—
181C4×#67C23116yes—
182C4×#67C23116yes—
183C2×(C2×D3)⋊C4C2312yes—
184C2×(C2×D3)⋊C4C2312yes—
185C2×(C2×D3)⋊C4C2314yes—
186C2×(C2×D3)⋊C4C2314yes—
187C2×(C2×D3)⋊C4C2314yes—
188#926C23116yes—
189#926C2318yes—
190#926C23116yes—
191C2×C4⋊Dic3C2311yescharacteristic
192C2×C4⋊Dic3C2312yes—
193C2×C4⋊Dic3C2311yescharacteristic
194C2×C4⋊Dic3C2312yes—
195C2×C4⋊Dic3C2312yes—
196C2×C4⋊Dic3C2312yes—
197C2×C4⋊Dic3C2314yes—
198#924C23116yes—
199#924C23116yes—
200#924C23116yes—
201C2×Dic3⋊C4C2314yes—
202C2×Dic3⋊C4C2314yes—
203C2×Dic3⋊C4C2312yes—
204C2×Dic3⋊C4C2312yes—
205C2×Dic3⋊C4C2314yes—
206C2×Dic3⋊C4C2314yes—
207C2×Dic3⋊C4C2314yes—
208C2×C4×Dic3C2314yes—
209C2×C4×Dic3C2312yes—
210C2×C4×Dic3C2312yes—
211C2×C4×Dic3C2314yes—
212C2×C4×Dic3C2314yes—
213C2×C4×Dic3C2312yes—
214C2×C4×Dic3C2314yes—
215#898C23132yes—
216#898C23132yes—
217#896C23132yes—
218#896C23132yes—
219#892C23116yes—
220#892C23116yes—
221#888C23116yes—
222#888C23132yes—
223#888C23116yes—
224#887C23132yes—
225#887C23132yes—
226#887C23132yes—
227#885C23132yes—
228#885C23132yes—
229#885C23132yes—
230#883C23132yes—
231#67⋊C4C23132yes—
232#879C23132yes—
233#879C23132yes—
234#878C23132yes—
235#877C23132yes—
236#877C23132yes—
237#875C23116yes—
238C4×D12C2318yes—
239C4×D12C2318yes—
240#872C23116yes—
241C42×D3C23116yes—
242#870C23116yes—
243#869C2318yes—
244#869C2318yes—
245#869C23116yes—
246C4×Dic6C23116yes—
247C4×Dic6C23116yes—
248C4×Dic6C2318yes—
249C4×Dic6C2318yes—
250C4×Dic6C23116yes—
251C4×Dic6C23116yes—
252C22×#41—31no—
253C23×Q8—32no—
254Q82—316no—
255#556—364no—
256#556—332no—
257#556—316no—
258#556—332no—
259#555—332no—
260#555—316no—
261D4×Q8—316no—
262#548—332no—
263#542—364no—
264#542—332no—
265#533—332no—
266#533—316no—
267C2×C4⋊Q8—32no—
268C2×C4⋊Q8—32no—
269C2×C4⋊Q8—34no—
270C2×C4⋊Q8—31no—
271C2×C4⋊Q8—31no—
272C2×C4⋊Q8—32no—
273#529—332no—
274#529C2×D3116yescomplemented
275C2×#126—34no—
276C2×#126—34no—
277C2×#126—34no—
278C2×#126—34no—
279C2×#126C2×D312yes—
280C2×#125—32no—
281C2×#125C2×D311yescharacteristic
282C2×#124—34no—
283C2×#124—34no—
284C2×#124—34no—
285C2×#124—34no—
286C2×#124—32no—
287C2×#124C2×D311yescharacteristic
288C2×#123—34no—
289C2×#123C2×D312yes—
290C2×C22⋊Q8—32no—
291C2×C22⋊Q8—32no—
292C2×C22⋊Q8—32no—
293C2×C22⋊Q8—32no—
294C2×C22⋊Q8—34no—
295C2×C22⋊Q8—34no—
296C2×C22⋊Q8—34no—
297C2×C22⋊Q8C2×D311yescharacteristic
298C2×#121—32no—
299C2×#121—34no—
300C2×#121—32no—
301C2×#121C2×D311yescharacteristic
302#519—332no—
303C4×#41—316no—
304C2×C4×Q8—32no—
305C2×C4×Q8—34no—
306C2×C4×Q8—34no—
307C2×C4×Q8—34no—
308C2×C4×Q8—31no—
309C2×C4×Q8—31no—
310C2×C4×Q8—32no—
311C2×C4×Q8—32no—
312C2×C4×Q8—32no—
313C2×C4×Q8—32no—
314C2×C4×Q8C2×D311yescharacteristic
315C2×C4×D4—32no—
316C2×C4×D4—32no—
317C2×C4×D4—32no—
318C2×C4×D4—34no—
319C2×C4×D4—31no—
320C2×C4×D4—31no—
321C2×C4×D4C2×D312yes—
322C2×C4×D4C2×D311yescharacteristic
323C2×#117—31no—
324C2×#117—32no—
325C2×#117—32no—
326C2×#117—32no—
327C2×#117—32no—
328C2×#117—34no—
329C2×#117—34no—
330C2×#117—32no—
331C2×#117C2×D312yes—
332C22×C42—32no—
333C22×C42C2×D311yescharacteristic
334C24×C3C2411yescharacteristic
335C24×C3C2412yes—
336C23×D3C2412yes—
337C2×C3×Q8—24no—
338C2×C3×Q8C2414yes—
339C2×C3×D4—24no—
340C2×C3×D4—44no—
341C2×C3×D4C2414yes—
342C2×C3×D4C2418yes—
343C22×C3×C4—28no—
344C22×C3×C4—24no—
345C22×C3×C4—24no—
346C22×C3×C4—42no—
347C22×C3×C4C2411yescharacteristic
348C22×C3×C4C2411yescharacteristic
349C22×C3×C4C2411yescharacteristic
350C22×C3×C4C2412yes—
351C22×C3×C4C2412yes—
352C22×C3×C4C2412yes—
353C22×C3×C4C2411yescharacteristic
354C22×C3×C4C2414yes—
355C22×C3×C4C2418yes—
356C22×C3×C4C2414yes—
357C22×C3×C4C2414yes—
358C22×C3×C4C2411yescharacteristic
359C22×C3×C4C2411yescharacteristic
360C2×#67—28no—
361C2×#67—48no—
362C2×#67C2418yes—
363C2×#67C24116yes—
364C22×Dic3—216no—
365C22×Dic3C24116yes—
366C22×Dic3C2412yes—
367C22×Dic3C2414yes—
368C22×Dic3C2414yes—
369C22×Dic3C2412yes—
370C22×Dic3C2412yes—
371#235—232no—
372C2×D12—24no—
373C2×D12C2414yes—
374C2×C4×D3—28no—
375C2×C4×D3—28no—
376C2×C4×D3—44no—
377C2×C4×D3C2418yes—
378C2×C4×D3C2418yes—
379C2×C4×D3C2418yes—
380C2×Dic6—28no—
381C2×Dic6—216no—
382C2×Dic6—264no—
383C2×Dic6—48no—
384C2×Dic6—44no—
385C2×Dic6#4118yes—
386C2×Dic6C2418yes—
387C2×Dic6C24116yes—
388C2×Dic6C2418yes—
389C2×Dic6C24116yes—
390C2×Dic6C2414yes—
391C3×C4⋊C4C2418yes—
392C3×C4⋊C4C2418yes—
393C3×C4⋊C4C2418yes—
394C3×C4⋊C4C2414yes—
395C3×C4⋊C4C2414yes—
396C3×C4⋊C4C2418yes—
397C3×C22⋊C4C2418yes—
398C3×C22⋊C4C2418yes—
399C3×C22⋊C4C2418yes—
400C3×C22⋊C4C2418yes—
401C3×C22⋊C4C2418yes—
402C3×C42C2414yes—
403C3×C42C2418yes—
404C3×C42C2414yes—
405C3×C42C2414yes—
406C3×C42C2414yes—
407#217C24116yes—
408#217C24116yes—
409#217C2418yes—
410#217C24116yes—
411(C2×D3)⋊C4C2418yes—
412(C2×D3)⋊C4C2418yes—
413(C2×D3)⋊C4C24116yes—
414(C2×D3)⋊C4C24116yes—
415(C2×D3)⋊C4C24116yes—
416C4⋊Dic3C2414yes—
417C4⋊Dic3C2418yes—
418C4⋊Dic3C2414yes—
419C4⋊Dic3C2418yes—
420C4⋊Dic3C2418yes—
421C4⋊Dic3C2418yes—
422C4⋊Dic3C24116yes—
423Dic3⋊C4C24116yes—
424Dic3⋊C4C24116yes—
425Dic3⋊C4C2418yes—
426Dic3⋊C4C2418yes—
427Dic3⋊C4C24116yes—
428Dic3⋊C4C24116yes—
429Dic3⋊C4C24116yes—
430C4×Dic3C24116yes—
431C4×Dic3C2418yes—
432C4×Dic3C2418yes—
433C4×Dic3C24116yes—
434C4×Dic3C24116yes—
435C4×Dic3C2418yes—
436C4×Dic3C24116yes—
437C2×#41—38no—
438C2×#41—68no—
439C22×Q8—31no—
440C22×Q8—34no—
441C22×Q8—32no—
442C22×Q8—316no—
443C22×Q8—32no—
444C22×Q8—34no—
445C22×Q8—616no—
446C22×Q8C22×D311yescharacteristic
447C22×D4—32no—
448C22×D4—34no—
449C22×D4—31no—
450C22×D4C22×D311yescharacteristic
451C22×D4C22×D312yes—
452C23×C4—34no—
453C23×C4—32no—
454C23×C4—32no—
455C23×C4—32no—
456C23×C4C22×D311yescharacteristic
457C23×C4C22×D312yes—
458C23×C4C22×D311yescharacteristic
459C23×C4C22×D311yescharacteristic
460C4⋊Q8—316no—
461C4⋊Q8—316no—
462C4⋊Q8—332no—
463C4⋊Q8—38no—
464C4⋊Q8—38no—
465C4⋊Q8—316no—
466#126—332no—
467#126—332no—
468#126—332no—
469#126—332no—
470#126C22×D3116yes—
471#125—316no—
472#125C22×D318yes—
473#124—332no—
474#124—332no—
475#124—332no—
476#124—332no—
477#124—316no—
478#124C22×D318yes—
479#123—332no—
480#123C22×D3116yes—
481C22⋊Q8—316no—
482C22⋊Q8—316no—
483C22⋊Q8—316no—
484C22⋊Q8—316no—
485C22⋊Q8—332no—
486C22⋊Q8—332no—
487C22⋊Q8—332no—
488C22⋊Q8C22×D318yes—
489#121—316no—
490#121—332no—
491#121—316no—
492#121C22×D318yes—
493C4×Q8—316no—
494C4×Q8—332no—
495C4×Q8—332no—
496C4×Q8—332no—
497C4×Q8—38no—
498C4×Q8—38no—
499C4×Q8—316no—
500C4×Q8—316no—
501C4×Q8—316no—
502C4×Q8—316no—
503C4×Q8C22×D318yes—
504C4×D4—316no—
505C4×D4—316no—
506C4×D4—316no—
507C4×D4—332no—
508C4×D4—38no—
509C4×D4—38no—
510C4×D4C22×D3116yes—
511C4×D4C22×D318yes—
512#117—38no—
513#117—316no—
514#117—316no—
515#117—316no—
516#117—316no—
517#117—332no—
518#117—332no—
519#117—316no—
520#117C22×D3116yes—
521C2×C4⋊C4—32no—
522C2×C4⋊C4—31no—
523C2×C4⋊C4—32no—
524C2×C4⋊C4—32no—
525C2×C4⋊C4—32no—
526C2×C4⋊C4—31no—
527C2×C4⋊C4—34no—
528C2×C4⋊C4—32no—
529C2×C4⋊C4—34no—
530C2×C4⋊C4—34no—
531C2×C4⋊C4—34no—
532C2×C4⋊C4—34no—
533C2×C4⋊C4—32no—
534C2×C4⋊C4—34no—
535C2×C4⋊C4C22×D311yescharacteristic
536C2×C4⋊C4C22×D311yescharacteristic
537C2×C4⋊C4C22×D312yes—
538C2×C4⋊C4C22×D312yes—
539C2×C4⋊C4C22×D312yes—
540C2×C4⋊C4C22×D312yes—
541C2×C22⋊C4—34no—
542C2×C22⋊C4—32no—
543C2×C22⋊C4—34no—
544C2×C22⋊C4—34no—
545C2×C22⋊C4—32no—
546C2×C22⋊C4—32no—
547C2×C22⋊C4—34no—
548C2×C22⋊C4—34no—
549C2×C22⋊C4—34no—
550C2×C22⋊C4C22×D312yes—
551C2×C22⋊C4C22×D312yes—
552C2×C22⋊C4C22×D312yes—
553C2×C22⋊C4C22×D312yes—
554C2×C22⋊C4C22×D312yes—
555C2×C42—32no—
556C2×C42—34no—
557C2×C42—34no—
558C2×C42—34no—
559C2×C42—32no—
560C2×C42—34no—
561C2×C42—32no—
562C2×C42—316no—
563C2×C42C22×D311yescharacteristic
564C2×C42C22×D311yescharacteristic
565C2×C42C22×D312yes—
566C2×C42C22×D311yescharacteristic
567C2×C42C22×D318yes—
568C2×C42C22×D311yescharacteristic
569C23×C3—24no—
570C23×C3—22no—
571C23×C3—22no—
572C23×C3—24no—
573C23×C3—24no—
574C23×C3—22no—
575C23×C3C2512yes—
576C23×C3C2514yes—
577C23×C3C2511yescharacteristic
578C22×D3—24no—
579C22×D3—24no—
580C22×D3—24no—
581C22×D3C2514yes—
582C3×Q8—28no—
583C3×D4—28no—
584C3×D4—48no—
585C2×C3×C4—24no—
586C2×C3×C4—22no—
587C2×C3×C4—22no—
588C2×C3×C4—24no—
589C2×C3×C4—22no—
590C2×C3×C4—24no—
591C2×C3×C4—22no—
592C2×C3×C4—216no—
593C2×C3×C4—28no—
594C2×C3×C4—28no—
595C2×C3×C4—44no—
596C2×C3×C4C2×#4114yes—
597C2×C3×C42−1+414yes—
598C2×C3×C4C2512yes—
599C2×C3×C4C2512yes—
600C2×C3×C4C2512yes—
601C2×C3×C4C2514yes—
602C2×C3×C4C2514yes—
603C2×C3×C4C2514yes—
604C2×C3×C4C2512yes—
605C2×C3×C4C2512yes—
606C2×C3×C4C2512yes—
607#67—216no—
608#67—416no—
609C2×Dic3—28no—
610C2×Dic3—24no—
611C2×Dic3—24no—
612C2×Dic3—28no—
613C2×Dic3—232no—
614C2×Dic3C2×#4118yes—
615C2×Dic3C2514yes—
616C2×Dic3C2518yes—
617C2×Dic3C2518yes—
618C2×Dic3C2514yes—
619C2×Dic3C2514yes—
620D12—28no—
621C4×D3—216no—
622C4×D3—216no—
623C4×D3—48no—
624Dic6—216no—
625Dic6—232no—
626Dic6—416no—
627Dic6—48no—
628Dic6C2×#41116yes—
629C24—32no—
630C24C23×D311yescharacteristic
631C24C23×D312yes—
632#41—632no—
633C2×Q8—24no—
634C2×Q8—38no—
635C2×Q8—34no—
636C2×Q8—316no—
637C2×Q8—38no—
638C2×Q8—38no—
639C2×Q8—316no—
640C2×Q8—616no—
641C2×Q8—664no—
642C2×Q8—68no—
643C2×Q8—124no—
644C2×Q8—128no—
645C2×Q8C23×D314yes—
646C2×D4—24no—
647C2×D4—38no—
648C2×D4—316no—
649C2×D4—34no—
650C2×D4—44no—
651C2×D4—68no—
652C2×D4—64no—
653C2×D4—128no—
654C2×D4C23×D314yes—
655C2×D4C23×D318yes—
656C22×C4—28no—
657C22×C4—24no—
658C22×C4—24no—
659C22×C4—32no—
660C22×C4—316no—
661C22×C4—32no—
662C22×C4—34no—
663C22×C4—34no—
664C22×C4—32no—
665C22×C4—38no—
666C22×C4—38no—
667C22×C4—38no—
668C22×C4—42no—
669C22×C4—68no—
670C22×C4—616no—
671C22×C4—68no—
672C22×C4—124no—
673C22×C4C23×D314yes—
674C22×C4C23×D314yes—
675C22×C4C23×D318yes—
676C22×C4C23×D311yescharacteristic
677C22×C4C23×D311yescharacteristic
678C22×C4C23×D311yescharacteristic
679C22×C4C23×D312yes—
680C22×C4C23×D312yes—
681C22×C4C23×D312yes—
682C22×C4C23×D311yescharacteristic
683C22×C4C23×D314yes—
684C22×C4C23×D311yescharacteristic
685C22×C4C23×D311yescharacteristic
686C4⋊C4—38no—
687C4⋊C4—34no—
688C4⋊C4—38no—
689C4⋊C4—38no—
690C4⋊C4—38no—
691C4⋊C4—34no—
692C4⋊C4—316no—
693C4⋊C4—38no—
694C4⋊C4—316no—
695C4⋊C4—316no—
696C4⋊C4—316no—
697C4⋊C4—316no—
698C4⋊C4—38no—
699C4⋊C4—316no—
700C4⋊C4C23×D314yes—
701C4⋊C4C23×D314yes—
702C4⋊C4C23×D318yes—
703C4⋊C4C23×D318yes—
704C4⋊C4C23×D318yes—
705C4⋊C4C23×D318yes—
706C22⋊C4—316no—
707C22⋊C4—38no—
708C22⋊C4—316no—
709C22⋊C4—316no—
710C22⋊C4—38no—
711C22⋊C4—38no—
712C22⋊C4—316no—
713C22⋊C4—316no—
714C22⋊C4—316no—
715C22⋊C4C23×D318yes—
716C22⋊C4C23×D318yes—
717C22⋊C4C23×D318yes—
718C22⋊C4C23×D318yes—
719C22⋊C4C23×D318yes—
720C42—38no—
721C42—38no—
722C42—38no—
723C42—316no—
724C42—316no—
725C42—316no—
726C42—316no—
727C42C23×D314yes—
728C42C23×D314yes—
729C42C23×D314yes—
730C42C23×D314yes—
731C42C23×D318yes—
732C22×C3—24no—
733C22×C3—22no—
734C22×C3—22no—
735C22×C3—24no—
736C22×C3—24no—
737C22×C3—22no—
738C22×C3—48no—
739C22×C3—44no—
740C22×C3C22×#4112yes—
741C22×C3C2×2−1+412yes—
742C22×C3#58512yes—
743C22×C3C2611yescharacteristic
744C2×D3—24no—
745C2×D3—24no—
746C2×D3—24no—
747C2×D3—48no—
748C3×C4—24no—
749C3×C4—22no—
750C3×C4—22no—
751C3×C4—24no—
752C3×C4—22no—
753C3×C4—24no—
754C3×C4—22no—
755C3×C4C22×#4114yes—
756C3×C4C2×2−1+414yes—
757Dic3—28no—
758Dic3—24no—
759Dic3—24no—
760Dic3—28no—
761Dic3C22×#4118yes—
762C23—24no—
763C23—22no—
764C23—22no—
765C23—24no—
766C23—22no—
767C23—24no—
768C23—34no—
769C23—64no—
770C23—64no—
771C23—64no—
772C23C24×D312yes—
773C23C24×D314yes—
774C23C24×D311yescharacteristic
775Q8—28no—
776Q8—316no—
777Q8—632no—
778Q8—616no—
779Q8—128no—
780Q8—1216no—
781D4—28no—
782D4—48no—
783D4—616no—
784D4—68no—
785D4—1216no—
786C2×C4—22no—
787C2×C4—24no—
788C2×C4—22no—
789C2×C4—24no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—24no—
793C2×C4—216no—
794C2×C4—28no—
795C2×C4—28no—
796C2×C4—38no—
797C2×C4—34no—
798C2×C4—34no—
799C2×C4—38no—
800C2×C4—38no—
801C2×C4—34no—
802C2×C4—44no—
803C2×C4—616no—
804C2×C4—632no—
805C2×C4—68no—
806C2×C4—64no—
807C2×C4—64no—
808C2×C4—68no—
809C2×C4—616no—
810C2×C4—128no—
811C2×C4D3×#4114yes—
812C2×C4#101014yes—
813C2×C4C24×D312yes—
814C2×C4C24×D312yes—
815C2×C4C24×D312yes—
816C2×C4C24×D314yes—
817C2×C4C24×D314yes—
818C2×C4C24×D314yes—
819C2×C4C24×D312yes—
820C2×C4C24×D312yes—
821C2×C4C24×D312yes—
822C2×C3—44no—
823C2×C3—42no—
824C2×C3#351814yescomplemented
825C2×C3C23×#4111yescharacteristic
826C2×C3C22×2−1+411yescharacteristic
827C2×C3C2×#58511yescharacteristic
828D3—44no—
829C22—22no—
830C22—24no—
831C22—24no—
832C22—22no—
833C22—22no—
834C22—24no—
835C22—48no—
836C22—44no—
837C22—64no—
838C22—64no—
839C22—64no—
840C22—128no—
841C22C2×D3×#4112yes—
842C22C2×#101012yes—
843C22#596412yes—
844C22C25×D311yescharacteristic
845C4—22no—
846C4—24no—
847C4—22no—
848C4—24no—
849C4—22no—
850C4—22no—
851C4—24no—
852C4—38no—
853C4—64no—
854C4—68no—
855C4—64no—
856C4—68no—
857C4C2×D3×#4114yes—
858C4C2×#101014yes—
859C3C2×#351811yescharacteristic, complemented, Sylow
860C2—42no—
861C2—44no—
862C2—124no—
863C2#8612714yesdirect product factor
864C2C22×#101011yescharacteristic
865C2C22×D3×#4111yescharacteristic
866C2C2×#596411yescharacteristic
subgroupG/H
centerC23C24×D3
commutator, cosocleC22×C3C26
FrattiniC22C25×D3
FittingC2×C3×#529C2
socleC23×C3C25
hypercenterC2×#529D3
hypocenterC3C2×#3518
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. C2×C3×#529C2semidirect
2. #86127C2direct (N × H)
3. C2×#5702C2semidirect
4. C2×#5688C2semidirect
5. C2×#5680C2semidirect
6. C2×#5662C2semidirect
7. C2×#5641C2semidirect
8. C2×#5616C2semidirect
9. C2×Q8×Dic6C2semidirect
10. C2×#5584C2semidirect
11. C2×#5542C2semidirect
12. C2×#5563C2semidirect
13. C2×D4×Dic6C2semidirect
14. C2×#5552C2semidirect
15. C2×#5534C2semidirect
16. C2×#5516C2semidirect
17. C2×#5470C2semidirect
18. C2×C4×#235C2semidirect
22. C3×#529C22semidirect
49. #5702C22semidirect
50. #5688C22semidirect
51. #5680C22semidirect
52. #5662C22semidirect
53. #5641C22semidirect
54. #5616C22semidirect
55. #5584C22semidirect
56. Q8×Dic6C22semidirect
57. #5563C22semidirect
58. #5552C22semidirect
59. #5542C22semidirect
60. D4×Dic6C22semidirect
61. #5534C22semidirect
62. #5516C22semidirect
86. C4×#235C22semidirect
91. #5470C22semidirect
117. C2×#529D3semidirect
274. #529C2×D3semidirect
824. C2×C3#3518semidirect
859. C3C2×#3518semidirect
863. C2#86127direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5292
#861272
C2×#57022
C2×#56882
C2×#56802
C2×#56622
C2×#56412
C2×#56162
C2×Q8×Dic62
C2×#55842
C2×#55422
C2×#55632
C2×D4×Dic62
C2×#55522
C2×#55342
C2×#55162
C2×#54702
C2×C4×#2352
C2×#35183