Finite Group Databasebeta

← C2×#86018 #11701895

Subgroups — C2×#86018 #11701895

Order 768.

8518 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#525C211yesmaximal, characteristic, complemented
2C2×#5832C211yesmaximal, characteristic, complemented
3C2×Dic3×#41C211yesmaximal, characteristic, complemented
4C2×#5791C211yesmaximal, characteristic, complemented
5C23×C4×Dic3C211yesmaximal, characteristic, complemented
6#86018C2132yesmaximal, direct product factor
7C2×#5649C214yesmaximal, complemented
8C2×#5622C212yesmaximal, complemented
9C2×#5624C212yesmaximal, complemented
10C2×#5596C212yesmaximal, complemented
11C2×#5600C212yesmaximal, complemented
12C2×#5586C214yesmaximal, complemented
13C2×#5538C214yesmaximal, complemented
14C2×C4×#237C214yesmaximal, complemented
15C2×#5517C211yesmaximal, characteristic, complemented
16C2×#5522C211yesmaximal, characteristic, complemented
17C2×#3444—31nomaximal, Sylow
18C22×C3×#41C2211yescharacteristic
19C24×C3×C4C2211yescharacteristic
20C24×Dic3C2212yes—
21C22×#237C2214yes—
22C22×#235C2211yescharacteristic
23C3×#525C22116yescomplemented
24C2×C3×#123C2212yes—
25C2×C3×C22⋊Q8C2212yes—
26C2×C3×#121C2212yes—
27C2×C3×#120C2212yes—
28C2×C3×C4×D4C2214yes—
29C2×C3×#117C2211yescharacteristic
30C2×#953C2212yes—
31#5832C22116yescomplemented
32Dic3×#41C22116yescomplemented
33C2×#947C2211yescharacteristic, complemented
34C2×Q8×Dic3C2212yescomplemented
35C2×#944C2211yescharacteristic, complemented
36C2×#940C2211yescharacteristic, complemented
37C2×#939C2214yes—
38C2×#939C2214yes—
39C2×#936C2211yescharacteristic, complemented
40C2×#935C2214yes—
41C2×D4×Dic3C2214yes—
42C2×D4×Dic3C2214yes—
43C2×D4×Dic3C2212yescomplemented
44#5791C22116yescomplemented
45C2×#930C2212yes—
46C2×#929C2212yes—
47C2×C4×#67C2214yes—
48C2×C4×#67C2214yescomplemented
49C2×#926C2211yescharacteristic
50C2×#926C2212yescomplemented
51C2×#924C2212yes—
52C22×C4×Dic3C2212yes—
53C22×C4×Dic3C2212yes—
54C22×C4×Dic3C2211yescharacteristic
55C22×C4×Dic3C2211yescharacteristic
56C22×C4×Dic3C2212yes—
57C22×C4×Dic3C2212yes—
58C22×C4×Dic3C2212yes—
59C22×C4×Dic3C22116yescomplemented
60C22×C4×Dic3C2212yescomplemented
61#5649C22164yescomplemented
62#5624C22132yescomplemented
63#5622C22132yescomplemented
64#5600C22132yescomplemented
65#5596C22132yescomplemented
66#5586C22164yescomplemented
67#5538C22164yescomplemented
68C4×#237C22164yescomplemented
69#5522C22116yescomplemented
70#5517C22116yescomplemented
71C2×#898C2214yescomplemented
72C2×#893C2212yescomplemented
73C2×#892C2214yescomplemented
74C2×#890C2212yescomplemented
75C2×#889C2214yescomplemented
76C2×#888C2212yescomplemented
77C2×#887C2212yescomplemented
78C2×#887C2214yescomplemented
79C2×#886C2214yes—
80C2×#885C2214yescomplemented
81C2×#67⋊C4C2214yes—
82C2×#67⋊C4C2214yes—
83C2×#67⋊C4C2214yescomplemented
84C2×#879C2214yescomplemented
85C2×#878C2214yes—
86C2×#878C2214yes—
87C2×#877C2214yes—
88C2×#877C2214yescomplemented
89C2×#872C2212yescomplemented
90C2×C42×D3C2212yescomplemented
91C2×C4×Dic6C2214yescomplemented
92#3444—332no—
93C2×#533—32no—
94C2×#533—31no—
95C2×#532—31no—
96C2×#532—32no—
97C2×#529—34no—
98C2×#529—32no—
99C2×#529—32no—
100C2×#529—34no—
101C2×#525—31no—
102C2×#525—34no—
103C2×#525D311yescharacteristic, complemented
104C2×C4×#41—31no—
105C2×C4×#41—34no—
106C2×C4×#41—31no—
107C23×C42—31no—
108C25×C3C2311yescharacteristic
109C2×C3×#41—28no—
110C2×C3×#41C2318yes—
111C22×C3×Q8C2311yescharacteristic
112C22×C3×D4C2314yes—
113C22×C3×D4C2312yes—
114C22×C3×D4C2311yescharacteristic
115C23×C3×C4—28no—
116C23×C3×C4C2312yes—
117C23×C3×C4C2312yes—
118C23×C3×C4C2311yescharacteristic
119C23×C3×C4C2318yes—
120C23×C3×C4C2312yes—
121C23×C3×C4C2311yescharacteristic
122C22×#67C2312yes—
123C22×#67C2314yes—
124C22×#67C2314yes—
125C23×Dic3—216no—
126C23×Dic3C2314yes—
127C23×Dic3C2312yes—
128C23×Dic3C2312yes—
129C23×Dic3C2312yes—
130C23×Dic3C2312yes—
131C23×Dic3C2312yes—
132C23×Dic3C23116yes—
133C23×Dic3C2312yes—
134C2×#237—232no—
135C2×#237C23132yes—
136C2×#235—28no—
137C2×#235C2318yes—
138C22×D12C2311yescharacteristic
139C22×C4×D3C2312yes—
140C22×C4×D3C2314yes—
141C22×Dic6C2311yescharacteristic
142C22×Dic6C2314yes—
143C3×#123C23116yes—
144C3×C22⋊Q8C23116yes—
145C3×#121C23116yes—
146C3×#120C23116yes—
147C3×C4×D4C23132yes—
148C3×#117C2318yes—
149C2×C3×C4⋊C4C2312yes—
150C2×C3×C4⋊C4C2314yes—
151C2×C3×C22⋊C4C2314yes—
152C2×C3×C22⋊C4C2314yes—
153C2×C3×C22⋊C4C2312yes—
154C2×C3×C42C2312yes—
155#953C23116yes—
156C2×#217C2314yes—
157C2×#217C2314yes—
158C2×#217C2312yes—
159C2×#217C2314yes—
160#947C2318yescomplemented
161Q8×Dic3C23116yescomplemented
162#944C2318yescomplemented
163#940C2318yescomplemented
164#939C23132yes—
165#939C23132yes—
166#936C2318yescomplemented
167#935C23132yes—
168D4×Dic3C23132yes—
169D4×Dic3C23132yes—
170D4×Dic3C23116yescomplemented
171#930C23116yes—
172#929C23116yes—
173C4×#67C23132yes—
174C4×#67C23132yescomplemented
175C2×(C2×D3)⋊C4C2314yes—
176C2×(C2×D3)⋊C4C2314yes—
177C2×(C2×D3)⋊C4C2314yes—
178#926C2318yes—
179#926C23116yescomplemented
180C2×C4⋊Dic3C2314yes—
181C2×C4⋊Dic3C2314yes—
182C2×C4⋊Dic3C2312yes—
183#924C23116yes—
184C2×Dic3⋊C4C2314yes—
185C2×Dic3⋊C4C2314yes—
186C2×Dic3⋊C4C2314yes—
187C2×Dic3⋊C4C2314yes—
188C2×Dic3⋊C4C2314yes—
189C2×C4×Dic3C23116yes—
190C2×C4×Dic3C2312yes—
191C2×C4×Dic3C2312yes—
192C2×C4×Dic3C2311yescharacteristic
193C2×C4×Dic3C2314yes—
194C2×C4×Dic3C2311yescharacteristic
195C2×C4×Dic3C2314yes—
196C2×C4×Dic3C2312yes—
197C2×C4×Dic3C2312yes—
198C2×C4×Dic3C2312yes—
199C2×C4×Dic3C2312yes—
200C2×C4×Dic3C2312yes—
201C2×C4×Dic3C2311yescharacteristic
202C2×C4×Dic3C2311yescharacteristic
203C2×C4×Dic3C2318yes—
204C2×C4×Dic3C2318yes—
205C2×C4×Dic3C23116yes—
206C2×C4×Dic3C23116yes—
207C2×C4×Dic3C23116yes—
208C2×C4×Dic3C23116yes—
209C2×C4×Dic3C23116yescomplemented
210#898C23132yescomplemented
211#893C23116yescomplemented
212#892C23132yescomplemented
213#890C23116yescomplemented
214#889C23132yescomplemented
215#888C23116yescomplemented
216#887C23132yescomplemented
217#887C23116yescomplemented
218#886C23132yes—
219#885C23132yescomplemented
220#67⋊C4C23132yes—
221#67⋊C4C23132yes—
222#67⋊C4C23132yescomplemented
223#879C23132yescomplemented
224#878C23132yes—
225#878C23132yes—
226#877C23132yes—
227#877C23132yescomplemented
228#872C23116yescomplemented
229C42×D3C23116yescomplemented
230C4×Dic6C23132yescomplemented
231C22×#41—34no—
232C22×#41—31no—
233C22×#41C2×D311yescharacteristic
234C24×C4—32no—
235C24×C4C2×D311yescharacteristic
236#533—332no—
237#533—316no—
238#532—316no—
239#532—332no—
240C2×C4⋊Q8—31no—
241C2×C4⋊Q8—32no—
242C2×#127—31no—
243#529—364no—
244#529—332no—
245#529—332no—
246#529—364no—
247C2×#126—34no—
248C2×#126—34no—
249C2×#125—34no—
250C2×#125—32no—
251C2×#124—31no—
252C2×#124—31no—
253C2×#124—34no—
254#525—316no—
255#525—364no—
256#525C2×D3116yescomplemented
257C2×#123—34no—
258C2×#123—32no—
259C2×#123—34no—
260C2×#123C2×D312yes—
261C2×C22⋊Q8—32no—
262C2×C22⋊Q8—34no—
263C2×C22⋊Q8—34no—
264C2×C22⋊Q8C2×D312yes—
265C2×#121—34no—
266C2×#121—34no—
267C2×#121—32no—
268C2×#121C2×D312yes—
269C2×#120—32no—
270C2×#120C2×D312yes—
271C4×#41—316no—
272C4×#41—364no—
273C4×#41—316no—
274C2×C4×Q8—32no—
275C2×C4×Q8—34no—
276C2×C4×Q8—32no—
277C2×C4×Q8—34no—
278C2×C4×D4—34no—
279C2×C4×D4—34no—
280C2×C4×D4—32no—
281C2×C4×D4—34no—
282C2×C4×D4—34no—
283C2×C4×D4—32no—
284C2×C4×D4—34no—
285C2×C4×D4—34no—
286C2×C4×D4—34no—
287C2×C4×D4C2×D314yes—
288C2×#117—31no—
289C2×#117—32no—
290C2×#117—34no—
291C2×#117—34no—
292C2×#117—34no—
293C2×#117—32no—
294C2×#117C2×D311yescharacteristic
295C22×C42—32no—
296C22×C42—31no—
297C22×C42—32no—
298C22×C42—32no—
299C22×C42—32no—
300C22×C42—32no—
301C22×C42—31no—
302C22×C42—316no—
303C22×C42—32no—
304C22×C42—32no—
305C24×C3—28no—
306C24×C3—24no—
307C24×C3C2414yes—
308C24×C3C2412yes—
309C24×C3C2411yescharacteristic
310C24×C3C2412yes—
311C23×D3C2412yes—
312C3×#41—232no—
313C2×C3×Q8—24no—
314C2×C3×Q8C2414yes—
315C2×C3×D4—216no—
316C2×C3×D4—28no—
317C2×C3×D4—24no—
318C2×C3×D4C2418yes—
319C2×C3×D4C24116yes—
320C2×C3×D4C2414yes—
321C22×C3×C4—24no—
322C22×C3×C4—28no—
323C22×C3×C4—28no—
324C22×C3×C4—28no—
325C22×C3×C4—232no—
326C22×C3×C4#4118yescomplemented
327C22×C3×C4C2412yes—
328C22×C3×C4C2418yes—
329C22×C3×C4C2418yes—
330C22×C3×C4C2414yes—
331C22×C3×C4C2412yes—
332C22×C3×C4C2414yes—
333C22×C3×C4C2418yes—
334C22×C3×C4C2411yescharacteristic
335C22×C3×C4C2414yes—
336C22×C3×C4C2411yescharacteristic
337C2×#67—28no—
338C2×#67—216no—
339C2×#67—216no—
340C2×#67C2418yes—
341C2×#67C24116yes—
342C2×#67C24116yes—
343C22×Dic3—28no—
344C22×Dic3—216no—
345C22×Dic3—28no—
346C22×Dic3—28no—
347C22×Dic3—28no—
348C22×Dic3—28no—
349C22×Dic3—264no—
350C22×Dic3#41116yescomplemented
351C22×Dic3C24116yes—
352C22×Dic3C2418yes—
353C22×Dic3C2418yes—
354C22×Dic3C2418yes—
355C22×Dic3C2418yes—
356C22×Dic3C2418yes—
357C22×Dic3C2412yes—
358C22×Dic3C2412yes—
359C22×Dic3C2412yes—
360C22×Dic3C2414yes—
361C22×Dic3C2412yes—
362C22×Dic3C2412yes—
363C22×Dic3C2418yes—
364#237—2128no—
365#235—232no—
366C2×D12—24no—
367C2×D12C2414yes—
368C2×C4×D3—28no—
369C2×C4×D3—216no—
370C2×C4×D3C2418yes—
371C2×C4×D3C24116yes—
372C2×Dic6—24no—
373C2×Dic6—216no—
374C2×Dic6C24116yes—
375C2×Dic6C2414yes—
376C3×C4⋊C4C2418yes—
377C3×C4⋊C4C24116yes—
378C3×C22⋊C4C24116yes—
379C3×C22⋊C4C24116yes—
380C3×C22⋊C4C2418yes—
381C3×C42C2418yes—
382#217C24116yes—
383#217C24116yes—
384#217C2418yes—
385#217C24116yes—
386(C2×D3)⋊C4C24116yes—
387(C2×D3)⋊C4C24116yes—
388(C2×D3)⋊C4C24116yes—
389C4⋊Dic3C24116yes—
390C4⋊Dic3C24116yes—
391C4⋊Dic3C2418yes—
392Dic3⋊C4C24116yes—
393Dic3⋊C4C24116yes—
394Dic3⋊C4C24116yes—
395Dic3⋊C4C24116yes—
396Dic3⋊C4C24116yes—
397C4×Dic3C2418yes—
398C4×Dic3C2418yes—
399C4×Dic3C2414yes—
400C4×Dic3C24116yes—
401C4×Dic3C2414yes—
402C4×Dic3C24116yes—
403C4×Dic3C2418yes—
404C4×Dic3C2418yes—
405C4×Dic3C2418yes—
406C4×Dic3C2418yes—
407C4×Dic3C2418yes—
408C4×Dic3C2414yes—
409C4×Dic3C2414yes—
410C25C22×D311yescharacteristic
411C2×#41—28no—
412C2×#41—332no—
413C2×#41—38no—
414C2×#41—632no—
415C2×#41—68no—
416C2×#41C22×D318yes—
417C22×Q8—34no—
418C22×Q8—31no—
419C22×Q8C22×D311yescharacteristic
420C22×D4—32no—
421C22×D4—34no—
422C22×D4—34no—
423C22×D4—31no—
424C22×D4C22×D312yes—
425C22×D4C22×D311yescharacteristic
426C22×D4C22×D314yes—
427C23×C4—28no—
428C23×C4—32no—
429C23×C4—34no—
430C23×C4—32no—
431C23×C4—32no—
432C23×C4—32no—
433C23×C4—32no—
434C23×C4—32no—
435C23×C4—316no—
436C23×C4—34no—
437C23×C4—32no—
438C23×C4—616no—
439C23×C4C22×D312yes—
440C23×C4C22×D311yescharacteristic
441C23×C4C22×D318yes—
442C23×C4C22×D312yes—
443C23×C4C22×D312yes—
444C23×C4C22×D311yescharacteristic
445C4⋊Q8—38no—
446C4⋊Q8—316no—
447#127—38no—
448#126—332no—
449#126—332no—
450#125—332no—
451#125—316no—
452#124—38no—
453#124—38no—
454#124—332no—
455#123—332no—
456#123—316no—
457#123—332no—
458#123C22×D3116yes—
459C22⋊Q8—316no—
460C22⋊Q8—332no—
461C22⋊Q8—332no—
462C22⋊Q8C22×D3116yes—
463#121—332no—
464#121—332no—
465#121—316no—
466#121C22×D3116yes—
467#120—316no—
468#120C22×D3116yes—
469C4×Q8—316no—
470C4×Q8—332no—
471C4×Q8—316no—
472C4×Q8—332no—
473C4×D4—332no—
474C4×D4—332no—
475C4×D4—316no—
476C4×D4—332no—
477C4×D4—332no—
478C4×D4—316no—
479C4×D4—332no—
480C4×D4—332no—
481C4×D4—332no—
482C4×D4C22×D3132yes—
483#117—38no—
484#117—316no—
485#117—332no—
486#117—332no—
487#117—332no—
488#117—316no—
489#117C22×D318yes—
490C2×C4⋊C4—34no—
491C2×C4⋊C4—34no—
492C2×C4⋊C4—32no—
493C2×C4⋊C4—34no—
494C2×C4⋊C4—34no—
495C2×C4⋊C4—34no—
496C2×C4⋊C4—34no—
497C2×C4⋊C4—34no—
498C2×C4⋊C4C22×D314yes—
499C2×C4⋊C4C22×D312yes—
500C2×C22⋊C4—32no—
501C2×C22⋊C4—34no—
502C2×C22⋊C4—34no—
503C2×C22⋊C4—34no—
504C2×C22⋊C4—34no—
505C2×C22⋊C4—34no—
506C2×C22⋊C4—34no—
507C2×C22⋊C4C22×D314yes—
508C2×C22⋊C4C22×D314yes—
509C2×C22⋊C4C22×D312yes—
510C2×C42—32no—
511C2×C42—34no—
512C2×C42—34no—
513C2×C42—32no—
514C2×C42—32no—
515C2×C42—316no—
516C2×C42—316no—
517C2×C42—38no—
518C2×C42—32no—
519C2×C42—31no—
520C2×C42—32no—
521C2×C42—316no—
522C2×C42—316no—
523C2×C42—316no—
524C2×C42—31no—
525C2×C42—316no—
526C2×C42—38no—
527C2×C42—31no—
528C2×C42—32no—
529C2×C42—32no—
530C2×C42—31no—
531C2×C42—316no—
532C2×C42C22×D312yes—
533C23×C3—232no—
534C23×C3—216no—
535C23×C3—24no—
536C23×C3—24no—
537C23×C3—28no—
538C23×C3—24no—
539C23×C3—28no—
540C23×C3—24no—
541C23×C3C2×#4114yes—
542C23×C3C2×#4118yes—
543C23×C3C2514yes—
544C23×C3C2512yes—
545C23×C3C2514yes—
546C23×C3C2511yescharacteristic
547C22×D3—24no—
548C22×D3—28no—
549C22×D3C2514yes—
550C3×Q8—28no—
551C3×D4—232no—
552C3×D4—216no—
553C3×D4—28no—
554C2×C3×C4—28no—
555C2×C3×C4—28no—
556C2×C3×C4—24no—
557C2×C3×C4—24no—
558C2×C3×C4—216no—
559C2×C3×C4—216no—
560C2×C3×C4—216no—
561C2×C3×C4C2×#4114yes—
562C2×C3×C4C2×#4114yes—
563C2×C3×C4C2×#41116yescomplemented
564C2×C3×C4C2514yes—
565C2×C3×C4C2514yes—
566C2×C3×C4C2518yes—
567C2×C3×C4C2512yes—
568C2×C3×C4C2512yes—
569#67—216no—
570#67—232no—
571#67—232no—
572C2×Dic3—24no—
573C2×Dic3—28no—
574C2×Dic3—216no—
575C2×Dic3—24no—
576C2×Dic3—24no—
577C2×Dic3—232no—
578C2×Dic3—216no—
579C2×Dic3—216no—
580C2×Dic3—216no—
581C2×Dic3—216no—
582C2×Dic3C2×#4118yes—
583C2×Dic3C2×#4118yes—
584C2×Dic3C2×#41132yescomplemented
585C2×Dic3C2514yes—
586C2×Dic3C2514yes—
587C2×Dic3C2514yes—
588C2×Dic3C2518yes—
589C2×Dic3C2514yes—
590C2×Dic3C2514yes—
591D12—28no—
592C4×D3—216no—
593C4×D3—232no—
594Dic6—28no—
595Dic6—232no—
596C24—24no—
597C24—28no—
598C24—32no—
599C24C23×D312yes—
600C24C23×D314yes—
601C24C23×D311yescharacteristic
602C24C23×D312yes—
603#41—232no—
604#41—6128no—
605#41—632no—
606C2×Q8—24no—
607C2×Q8—316no—
608C2×Q8—34no—
609C2×Q8—616no—
610C2×Q8—64no—
611C2×Q8C23×D314yes—
612C2×D4—28no—
613C2×D4—216no—
614C2×D4—24no—
615C2×D4—38no—
616C2×D4—316no—
617C2×D4—316no—
618C2×D4—34no—
619C2×D4—616no—
620C2×D4—68no—
621C2×D4—616no—
622C2×D4—64no—
623C2×D4C23×D318yes—
624C2×D4C23×D314yes—
625C2×D4C23×D3116yes—
626C22×C4—24no—
627C22×C4—28no—
628C22×C4—28no—
629C22×C4—28no—
630C22×C4—232no—
631C22×C4—316no—
632C22×C4—32no—
633C22×C4—32no—
634C22×C4—38no—
635C22×C4—32no—
636C22×C4—32no—
637C22×C4—38no—
638C22×C4—38no—
639C22×C4—38no—
640C22×C4—38no—
641C22×C4—38no—
642C22×C4—32no—
643C22×C4—34no—
644C22×C4—316no—
645C22×C4—316no—
646C22×C4—38no—
647C22×C4—616no—
648C22×C4—68no—
649C22×C4—68no—
650C22×C4—68no—
651C22×C4—68no—
652C22×C4—664no—
653C22×C4—616no—
654C22×C4—68no—
655C22×C4—68no—
656C22×C4#23718yescomplemented
657C22×C4C23×D312yes—
658C22×C4C23×D318yes—
659C22×C4C23×D318yes—
660C22×C4C23×D314yes—
661C22×C4C23×D312yes—
662C22×C4C23×D318yes—
663C22×C4C23×D314yes—
664C22×C4C23×D311yescharacteristic
665C22×C4C23×D314yes—
666C22×C4C23×D311yescharacteristic
667C4⋊C4—316no—
668C4⋊C4—316no—
669C4⋊C4—38no—
670C4⋊C4—316no—
671C4⋊C4—316no—
672C4⋊C4—316no—
673C4⋊C4—316no—
674C4⋊C4—316no—
675C4⋊C4C23×D3116yes—
676C4⋊C4C23×D318yes—
677C22⋊C4—38no—
678C22⋊C4—316no—
679C22⋊C4—316no—
680C22⋊C4—316no—
681C22⋊C4—316no—
682C22⋊C4—316no—
683C22⋊C4—316no—
684C22⋊C4C23×D3116yes—
685C22⋊C4C23×D3116yes—
686C22⋊C4C23×D318yes—
687C42—34no—
688C42—38no—
689C42—34no—
690C42—38no—
691C42—38no—
692C42—38no—
693C42—38no—
694C42—34no—
695C42—38no—
696C42—34no—
697C42—316no—
698C42—316no—
699C42—38no—
700C42C23×D318yes—
701C22×C3—232no—
702C22×C3—24no—
703C22×C3—24no—
704C22×C3—24no—
705C22×C3—28no—
706C22×C3—216no—
707C22×C3—28no—
708C22×C3—24no—
709C22×C3—48no—
710C22×C3C22×#4114yes—
711C22×C3C22×#4112yes—
712C22×C3C22×#4118yes—
713C22×C3C22×#4114yes—
714C22×C3C2611yescharacteristic
715C2×D3—24no—
716C2×D3—28no—
717C2×D3—48no—
718C3×C4—28no—
719C3×C4—24no—
720C3×C4—24no—
721C3×C4C22×#4114yes—
722C3×C4C22×#4114yes—
723Dic3—24no—
724Dic3—28no—
725Dic3—24no—
726Dic3—24no—
727Dic3C22×#4118yes—
728Dic3C22×#4118yes—
729C23—232no—
730C23—28no—
731C23—24no—
732C23—216no—
733C23—24no—
734C23—24no—
735C23—24no—
736C23—28no—
737C23—34no—
738C23—64no—
739C23—68no—
740C23C2×#23714yes—
741C23D3×#4118yes—
742C23C24×D314yes—
743C23C24×D312yes—
744C23C24×D314yes—
745C23C24×D311yescharacteristic
746Q8—28no—
747Q8—632no—
748Q8—68no—
749D4—216no—
750D4—232no—
751D4—28no—
752D4—632no—
753D4—616no—
754D4—632no—
755D4—68no—
756C2×C4—28no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—28no—
760C2×C4—216no—
761C2×C4—216no—
762C2×C4—216no—
763C2×C4—38no—
764C2×C4—38no—
765C2×C4—332no—
766C2×C4—34no—
767C2×C4—34no—
768C2×C4—34no—
769C2×C4—34no—
770C2×C4—34no—
771C2×C4—38no—
772C2×C4—632no—
773C2×C4—616no—
774C2×C4—616no—
775C2×C4—616no—
776C2×C4—616no—
777C2×C4—632no—
778C2×C4—64no—
779C2×C4—616no—
780C2×C4—64no—
781C2×C4—64no—
782C2×C4—68no—
783C2×C4—616no—
784C2×C4C2×#23714yes—
785C2×C4C2×#23714yes—
786C2×C4C2×#237116yescomplemented
787C2×C4C24×D314yes—
788C2×C4C24×D314yes—
789C2×C4C24×D318yes—
790C2×C4C24×D312yes—
791C2×C4C24×D312yes—
792C2×C3—24no—
793C2×C3—28no—
794C2×C3—44no—
795C2×C3#344414yescomplemented
796C2×C3C23×#4111yescharacteristic
797C2×C3C23×#4112yes—
798D3—44no—
799C22—232no—
800C22—28no—
801C22—216no—
802C22—24no—
803C22—24no—
804C22—24no—
805C22—24no—
806C22—28no—
807C22—48no—
808C22—64no—
809C22—68no—
810C22—128no—
811C22C22×#23714yes—
812C22C22×#23712yes—
813C22C2×D3×#4118yes—
814C22C2×D3×#4114yes—
815C22C25×D311yescharacteristic
816C4—24no—
817C4—24no—
818C4—28no—
819C4—38no—
820C4—38no—
821C4—64no—
822C4—64no—
823C4—64no—
824C4—68no—
825C4C22×#23714yes—
826C4C22×#23714yes—
827C3C2×#344411yescharacteristic, complemented, Sylow
828C2—24no—
829C2—28no—
830C2—44no—
831C2—124no—
832C2#8601814yesdirect product factor
833C2C23×#23711yescharacteristic
834C2C22×D3×#4112yes—
subgroupG/H
centerC22×C4C23×D3
commutator, cosocleC22×C3C26
FrattiniC22C25×D3
FittingC2×C3×#525C2
socleC23×C3C25
hypercenterC2×#525D3
hypocenterC3C2×#3444
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C2×C3×#525C2semidirect
2. C2×#5832C2semidirect
3. C2×Dic3×#41C2semidirect
4. C2×#5791C2semidirect
5. C23×C4×Dic3C2semidirect
6. #86018C2direct (N × H)
7. C2×#5649C2semidirect
8. C2×#5622C2semidirect
9. C2×#5624C2semidirect
10. C2×#5596C2semidirect
11. C2×#5600C2semidirect
12. C2×#5586C2semidirect
13. C2×#5538C2semidirect
14. C2×C4×#237C2semidirect
15. C2×#5517C2semidirect
16. C2×#5522C2semidirect
23. C3×#525C22semidirect
31. #5832C22semidirect
32. Dic3×#41C22semidirect
33. C2×#947C22semidirect
34. C2×Q8×Dic3C22semidirect
35. C2×#944C22semidirect
36. C2×#940C22semidirect
39. C2×#936C22semidirect
43. C2×D4×Dic3C22semidirect
44. #5791C22semidirect
48. C2×C4×#67C22semidirect
50. C2×#926C22semidirect
59. C22×C4×Dic3C22semidirect
60. C22×C4×Dic3C22semidirect
61. #5649C22semidirect
62. #5624C22semidirect
63. #5622C22semidirect
64. #5600C22semidirect
65. #5596C22semidirect
66. #5586C22semidirect
67. #5538C22semidirect
68. C4×#237C22semidirect
69. #5522C22semidirect
70. #5517C22semidirect
71. C2×#898C22semidirect
72. C2×#893C22semidirect
73. C2×#892C22semidirect
74. C2×#890C22semidirect
75. C2×#889C22semidirect
76. C2×#888C22semidirect
77. C2×#887C22semidirect
78. C2×#887C22semidirect
80. C2×#885C22semidirect
83. C2×#67⋊C4C22semidirect
84. C2×#879C22semidirect
88. C2×#877C22semidirect
89. C2×#872C22semidirect
90. C2×C42×D3C22semidirect
91. C2×C4×Dic6C22semidirect
103. C2×#525D3semidirect
160. #947C23semidirect
161. Q8×Dic3C23semidirect
162. #944C23semidirect
163. #940C23semidirect
166. #936C23semidirect
170. D4×Dic3C23semidirect
174. C4×#67C23semidirect
179. #926C23semidirect
209. C2×C4×Dic3C23semidirect
210. #898C23semidirect
211. #893C23semidirect
212. #892C23semidirect
213. #890C23semidirect
214. #889C23semidirect
215. #888C23semidirect
216. #887C23semidirect
217. #887C23semidirect
219. #885C23semidirect
222. #67⋊C4C23semidirect
223. #879C23semidirect
227. #877C23semidirect
228. #872C23semidirect
229. C42×D3C23semidirect
230. C4×Dic6C23semidirect
256. #525C2×D3semidirect
326. C22×C3×C4#41semidirect
350. C22×Dic3#41semidirect
563. C2×C3×C4C2×#41semidirect
584. C2×Dic3C2×#41semidirect
656. C22×C4#237semidirect
786. C2×C4C2×#237semidirect
795. C2×C3#3444semidirect
827. C3C2×#3444semidirect
832. C2#86018direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5252
C2×#58322
C2×Dic3×#412
C2×#57912
C23×C4×Dic32
#860182
C2×#56492
C2×#56222
C2×#56242
C2×#55962
C2×#56002
C2×#55862
C2×#55382
C2×C4×#2372
C2×#55172
C2×#55222
C2×#34443