Finite Group Databasebeta

← C2×#86718 #11703373

Subgroups — C2×#86718 #11703373

Order 768.

7130 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#548C211yesmaximal, characteristic, complemented
2C2×#5831C211yesmaximal, characteristic, complemented
3C2×#5827C211yesmaximal, characteristic, complemented
4C2×Q8×#67C211yesmaximal, characteristic, complemented
5C22×Q8×Dic3C211yesmaximal, characteristic, complemented
6#86718C2132yesmaximal, direct product factor
7C2×#5682C213yesmaximal, complemented
8C2×#5671C213yesmaximal, complemented
9C2×#5642C213yesmaximal, complemented
10C2×#5625C213yesmaximal, complemented
11C2×#5618C213yesmaximal, complemented
12C2×#5600C213yesmaximal, complemented
13C2×#5572C211yesmaximal, characteristic, complemented
14C2×#5570C211yesmaximal, characteristic, complemented
15C2×#5543C213yesmaximal, complemented
16C2×#5538C213yesmaximal, complemented
17C2×#3516—31nomaximal, Sylow
18C22×C3×#41C2211yescharacteristic
19C23×C3×Q8C2211yescharacteristic
20C22×D3×Q8C2211yescharacteristic
21C3×#548C22116yescomplemented
22C2×C3×#124C2213yes—
23C2×C3×C22⋊Q8C2213yes—
24C2×C3×#121C2213yes—
25C2×C3×C4×Q8C2211yescharacteristic
26C2×C3×C4×D4C2213yes—
27#5831C22116yescomplemented
28#5827C22116yescomplemented
29Q8×#67C22116yescomplemented
30C2×#946C2213yes—
31C2×Q8×Dic3C2211yescharacteristic
32C2×Q8×Dic3C2211yescharacteristic
33C2×Q8×Dic3C2211yescharacteristic
34C2×Q8×Dic3C2213yes—
35C2×Q8×Dic3C2213yes—
36C2×Q8×Dic3C22116yescomplemented
37C2×#944C2213yes—
38C2×#939C2213yes—
39C2×#938C2213yes—
40C2×#936C2213yes—
41C2×#935C2213yes—
42C2×D4×Dic3C2216yes—
43C2×D4×Dic3C2213yes—
44C2×D4×Dic3C2213yes—
45C2×C4×#67C2213yes—
46C2×C4×#67C2213yes—
47C2×#926C2213yes—
48C22×C4⋊Dic3C2213yes—
49C22×C4⋊Dic3C2213yes—
50C2×#924C2213yes—
51C2×#924C2213yes—
52C22×C4×Dic3C2213yes—
53#5682C22148yescomplemented
54#5671C22148yescomplemented
55#5642C22148yescomplemented
56#5625C22148yescomplemented
57#5618C22148yescomplemented
58#5600C22148yescomplemented
59#5572C22116yescomplemented
60#5570C22116yescomplemented
61#5543C22148yescomplemented
62#5538C22148yescomplemented
63C2×#898C2213yes—
64C2×#892C2213yes—
65C2×#890C2216yes—
66C2×#890C2213yes—
67C2×#890C2213yes—
68C2×#889C2213yes—
69C2×#887C2213yes—
70C2×#886C2216yes—
71C2×#886C2211yescharacteristic
72C2×#885C2213yes—
73C2×#879C2213yes—
74C2×#879C2216yes—
75C2×#879C2216yes—
76C2×#878C2213yes—
77C2×#878C2216yes—
78C2×#877C2216yes—
79C2×#872C2213yes—
80C2×#869C2213yes—
81C2×C4×Dic6C2213yes—
82C2×C4×Dic6C2213yes—
83#3516—332no—
84C2×#557—31no—
85C2×#556—33no—
86C2×#554—33no—
87C2×#553—33no—
88C2×#552—33no—
89C2×D4×Q8—31no—
90C2×#548—31no—
91C2×#548D311yescharacteristic, complemented
92C2×#542—33no—
93C2×#541—33no—
94C2×#529—33no—
95C2×#529—33no—
96C2×#520—31no—
97C2×#519—31no—
98C22×C4×Q8—31no—
99C2×C3×#41—28no—
100C2×C3×#41C2318yes—
101C22×C3×Q8—28no—
102C22×C3×Q8C2313yes—
103C22×C3×Q8C2318yes—
104C22×C3×Q8C2311yescharacteristic
105C22×C3×D4C2313yes—
106C22×C3×D4C2313yes—
107C23×C3×C4C2313yes—
108C23×C3×C4C2313yes—
109C22×#67C2311yescharacteristic
110C22×#67C2313yes—
111C23×Dic3C2311yescharacteristic
112C23×Dic3C2316yes—
113C23×Dic3C2313yes—
114C2×D3×Q8—28no—
115C2×D3×Q8C2318yes—
116C22×C4×D3C2313yes—
117C22×Dic6C2313yes—
118C22×Dic6C2313yes—
119C3×#124C23124yes—
120C3×C22⋊Q8C23124yes—
121C3×#121C23124yes—
122C3×C4×Q8C2318yes—
123C3×C4×D4C23124yes—
124C2×C3×C4⋊C4C2313yes—
125C2×C3×C4⋊C4C2313yes—
126C2×C3×C22⋊C4C2316yes—
127C2×C3×C22⋊C4C2311yescharacteristic
128C2×C3×C22⋊C4C2313yes—
129C2×C3×C42C2313yes—
130C2×#217C2313yes—
131C2×#217C2316yes—
132C2×#217C2313yes—
133C2×#217C2313yes—
134C2×#217C2313yes—
135#946C23124yes—
136Q8×Dic3C23124yes—
137Q8×Dic3C23124yes—
138Q8×Dic3C2318yes—
139Q8×Dic3C2318yes—
140Q8×Dic3C2318yes—
141#944C23124yes—
142#939C23124yes—
143#938C23124yes—
144#936C23124yes—
145#935C23124yes—
146D4×Dic3C23124yes—
147D4×Dic3C23124yes—
148D4×Dic3C23148yes—
149C4×#67C23124yes—
150C4×#67C23124yes—
151C2×(C2×D3)⋊C4C2311yescharacteristic
152C2×(C2×D3)⋊C4C2313yes—
153C2×(C2×D3)⋊C4C2313yes—
154C2×(C2×D3)⋊C4C2311yescharacteristic
155#926C23124yes—
156C2×C4⋊Dic3C23124yes—
157C2×C4⋊Dic3C2311yescharacteristic
158C2×C4⋊Dic3C2313yes—
159C2×C4⋊Dic3C2316yes—
160C2×C4⋊Dic3C2313yes—
161C2×C4⋊Dic3C2313yes—
162C2×C4⋊Dic3C2316yes—
163C2×C4⋊Dic3C2313yes—
164C2×C4⋊Dic3C2311yescharacteristic
165C2×C4⋊Dic3C23124yes—
166#924C23124yes—
167#924C23124yes—
168C2×Dic3⋊C4C2313yes—
169C2×Dic3⋊C4C2313yes—
170C2×Dic3⋊C4C2313yes—
171C2×Dic3⋊C4C2313yes—
172C2×Dic3⋊C4C2316yes—
173C2×Dic3⋊C4C2313yes—
174C2×Dic3⋊C4C2313yes—
175C2×C4×Dic3C2316yes—
176C2×C4×Dic3C2313yes—
177C2×C4×Dic3C2313yes—
178C2×C4×Dic3C2313yes—
179C2×C4×Dic3C2313yes—
180C2×C4×Dic3C2313yes—
181C2×C4×Dic3C23124yes—
182#898C23124yes—
183#892C23124yes—
184#890C23148yes—
185#890C23124yes—
186#890C23124yes—
187#889C23124yes—
188#887C23124yes—
189#886C23148yes—
190#886C2318yes—
191#885C23124yes—
192#879C23124yes—
193#879C23148yes—
194#879C23148yes—
195#878C23148yes—
196#878C23124yes—
197#877C23148yes—
198#872C23124yes—
199#869C23124yes—
200C4×Dic6C23124yes—
201C4×Dic6C23124yes—
202C22×#41C2×D311yescharacteristic
203C23×Q8—31no—
204C23×Q8C2×D311yescharacteristic
205#557—316no—
206#556—348no—
207#554—348no—
208#553—348no—
209#552—348no—
210D4×Q8—316no—
211#548—316no—
212#548C2×D3116yescomplemented
213#542—348no—
214#541—348no—
215C2×C4⋊Q8—33no—
216C2×C4⋊Q8—33no—
217#529—348no—
218#529—348no—
219C2×#126—33no—
220C2×#126—36no—
221C2×#126—33no—
222C2×#126—36no—
223C2×#125—33no—
224C2×#125—33no—
225C2×#125—36no—
226C2×#125—33no—
227C2×#124—33no—
228C2×#124—33no—
229C2×#124C2×D313yes—
230C2×#123—33no—
231C2×#123—31no—
232C2×#123—36no—
233C2×C22⋊Q8—33no—
234C2×C22⋊Q8—33no—
235C2×C22⋊Q8—33no—
236C2×C22⋊Q8—33no—
237C2×C22⋊Q8—36no—
238C2×C22⋊Q8C2×D313yes—
239C2×#121—33no—
240C2×#121—33no—
241C2×#121C2×D313yes—
242#520—316no—
243#519—316no—
244C2×C4×Q8—31no—
245C2×C4×Q8—33no—
246C2×C4×Q8—31no—
247C2×C4×Q8—33no—
248C2×C4×Q8—316no—
249C2×C4×Q8—31no—
250C2×C4×Q8—33no—
251C2×C4×Q8—33no—
252C2×C4×Q8—33no—
253C2×C4×Q8C2×D311yescharacteristic
254C2×C4×D4—33no—
255C2×C4×D4—33no—
256C2×C4×D4—36no—
257C2×C4×D4—33no—
258C2×C4×D4—33no—
259C2×C4×D4C2×D313yes—
260C2×#117—33no—
261C2×#117—33no—
262C2×#117—36no—
263C2×#117—33no—
264C22×C4⋊C4—33no—
265C22×C4⋊C4—33no—
266C22×C42—33no—
267C24×C3C2413yes—
268C24×C3C2411yescharacteristic
269C23×D3C2411yescharacteristic
270C3×#41—232no—
271C2×C3×Q8—232no—
272C2×C3×Q8—212no—
273C2×C3×Q8#4118yes—
274C2×C3×Q8C24112yes—
275C2×C3×Q8C2414yes—
276C2×C3×D4—212no—
277C2×C3×D4—212no—
278C2×C3×D4C24112yes—
279C2×C3×D4C24112yes—
280C22×C3×C4—212no—
281C22×C3×C4—212no—
282C22×C3×C4C2413yes—
283C22×C3×C4C2413yes—
284C22×C3×C4C24112yes—
285C22×C3×C4C2411yescharacteristic
286C22×C3×C4C2411yescharacteristic
287C22×C3×C4C24112yes—
288C22×C3×C4C2413yes—
289C2×#67—24no—
290C2×#67—46no—
291C2×#67C2414yes—
292C2×#67C24112yes—
293C22×Dic3—24no—
294C22×Dic3—412no—
295C22×Dic3—46no—
296C22×Dic3C2414yes—
297C22×Dic3C2411yescharacteristic
298C22×Dic3C2411yescharacteristic
299C22×Dic3C2413yes—
300C22×Dic3C2411yescharacteristic
301C22×Dic3C2413yes—
302C22×Dic3C2413yes—
303C22×Dic3C2413yes—
304C22×Dic3C24124yes—
305C22×Dic3C24112yes—
306D3×Q8—232no—
307C2×C4×D3—212no—
308C2×C4×D3C24112yes—
309C2×Dic6—212no—
310C2×Dic6—46no—
311C2×Dic6C24112yes—
312C2×Dic6C24112yes—
313C3×C4⋊C4C24112yes—
314C3×C4⋊C4C24112yes—
315C3×C22⋊C4C24124yes—
316C3×C22⋊C4C2414yes—
317C3×C22⋊C4C24112yes—
318C3×C42C24112yes—
319#217C24112yes—
320#217C24124yes—
321#217C24112yes—
322#217C24112yes—
323#217C24112yes—
324(C2×D3)⋊C4C2414yes—
325(C2×D3)⋊C4C24112yes—
326(C2×D3)⋊C4C24112yes—
327(C2×D3)⋊C4C2414yes—
328C4⋊Dic3C2414yes—
329C4⋊Dic3C24112yes—
330C4⋊Dic3C24124yes—
331C4⋊Dic3C24112yes—
332C4⋊Dic3C24112yes—
333C4⋊Dic3C24124yes—
334C4⋊Dic3C24112yes—
335C4⋊Dic3C2414yes—
336Dic3⋊C4C24112yes—
337Dic3⋊C4C24112yes—
338Dic3⋊C4C24112yes—
339Dic3⋊C4C24112yes—
340Dic3⋊C4C24124yes—
341Dic3⋊C4C24112yes—
342Dic3⋊C4C24112yes—
343C4×Dic3C24124yes—
344C4×Dic3C24112yes—
345C4×Dic3C24112yes—
346C4×Dic3C24112yes—
347C4×Dic3C24112yes—
348C4×Dic3C24112yes—
349C2×#41—28no—
350C2×#41C22×D318yes—
351C22×Q8—28no—
352C22×Q8—38no—
353C22×Q8—33no—
354C22×Q8—33no—
355C22×Q8—68no—
356C22×Q8C22×D313yes—
357C22×Q8C22×D318yes—
358C22×Q8C22×D311yescharacteristic
359C22×D4—31no—
360C22×D4—33no—
361C22×D4C22×D313yes—
362C22×D4C22×D313yes—
363C23×C4—31no—
364C23×C4—33no—
365C23×C4—36no—
366C23×C4—33no—
367C23×C4C22×D313yes—
368C23×C4C22×D313yes—
369C4⋊Q8—324no—
370C4⋊Q8—324no—
371#126—324no—
372#126—348no—
373#126—324no—
374#126—348no—
375#125—324no—
376#125—324no—
377#125—348no—
378#125—324no—
379#124—324no—
380#124—324no—
381#124C22×D3124yes—
382#123—324no—
383#123—38no—
384#123—348no—
385C22⋊Q8—324no—
386C22⋊Q8—324no—
387C22⋊Q8—324no—
388C22⋊Q8—324no—
389C22⋊Q8—348no—
390C22⋊Q8C22×D3124yes—
391#121—324no—
392#121—324no—
393#121C22×D3124yes—
394C4×Q8—38no—
395C4×Q8—324no—
396C4×Q8—38no—
397C4×Q8—324no—
398C4×Q8—38no—
399C4×Q8—324no—
400C4×Q8—324no—
401C4×Q8—324no—
402C4×Q8C22×D318yes—
403C4×D4—324no—
404C4×D4—324no—
405C4×D4—348no—
406C4×D4—324no—
407C4×D4—324no—
408C4×D4C22×D3124yes—
409#117—324no—
410#117—324no—
411#117—348no—
412#117—324no—
413C2×C4⋊C4—33no—
414C2×C4⋊C4—33no—
415C2×C4⋊C4—33no—
416C2×C4⋊C4—33no—
417C2×C4⋊C4—36no—
418C2×C4⋊C4—324no—
419C2×C4⋊C4—324no—
420C2×C4⋊C4—31no—
421C2×C4⋊C4—33no—
422C2×C4⋊C4—33no—
423C2×C4⋊C4—33no—
424C2×C4⋊C4—36no—
425C2×C4⋊C4—33no—
426C2×C4⋊C4—36no—
427C2×C4⋊C4—33no—
428C2×C4⋊C4—31no—
429C2×C4⋊C4—33no—
430C2×C4⋊C4C22×D313yes—
431C2×C4⋊C4C22×D313yes—
432C2×C22⋊C4—33no—
433C2×C22⋊C4—33no—
434C2×C22⋊C4—33no—
435C2×C22⋊C4—33no—
436C2×C22⋊C4—36no—
437C2×C22⋊C4—33no—
438C2×C22⋊C4—31no—
439C2×C22⋊C4—31no—
440C2×C22⋊C4—33no—
441C2×C22⋊C4C22×D316yes—
442C2×C22⋊C4C22×D311yescharacteristic
443C2×C22⋊C4C22×D313yes—
444C2×C42—33no—
445C2×C42—36no—
446C2×C42—33no—
447C2×C42—33no—
448C2×C42—33no—
449C2×C42—33no—
450C2×C42—324no—
451C2×C42C22×D313yes—
452C23×C3—22no—
453C23×C3—22no—
454C23×C3—26no—
455C23×C3—26no—
456C23×C3—26no—
457C23×C32−1+414yes—
458C23×C3C2516yes—
459C23×C3C2512yes—
460C23×C3C2511yescharacteristic
461C22×D3—22no—
462C22×D3—22no—
463C22×D3—22no—
464C22×D3C2512yes—
465C3×Q8—224no—
466C3×Q8C2×#41116yes—
467C3×D4—224no—
468C3×D4—224no—
469C2×C3×C4—22no—
470C2×C3×C4—26no—
471C2×C3×C4—26no—
472C2×C3×C4—22no—
473C2×C3×C4—224no—
474C2×C3×C4—224no—
475C2×C3×C4C2×#41112yes—
476C2×C3×C4C2516yes—
477C2×C3×C4C2516yes—
478C2×C3×C4C2512yes—
479C2×C3×C4C2512yes—
480C2×C3×C4C2516yes—
481#67—28no—
482#67—412no—
483C2×Dic3—26no—
484C2×Dic3—28no—
485C2×Dic3—22no—
486C2×Dic3—22no—
487C2×Dic3—22no—
488C2×Dic3—26no—
489C2×Dic3—26no—
490C2×Dic3—26no—
491C2×Dic3—424no—
492C2×Dic3—412no—
493C2×Dic3C2512yes—
494C2×Dic3C2512yes—
495C2×Dic3C2516yes—
496C2×Dic3C2512yes—
497C2×Dic3C2516yes—
498C2×Dic3C2516yes—
499C2×Dic3C2516yes—
500C4×D3—224no—
501Dic6—224no—
502Dic6—412no—
503C24—31no—
504C24C23×D313yes—
505C24C23×D311yescharacteristic
506#41—232no—
507C2×Q8—232no—
508C2×Q8—212no—
509C2×Q8—312no—
510C2×Q8—312no—
511C2×Q8—632no—
512C2×Q8—612no—
513C2×Q8—126no—
514C2×Q8#23718yes—
515C2×Q8C23×D3112yes—
516C2×Q8C23×D314yes—
517C2×D4—212no—
518C2×D4—212no—
519C2×D4—34no—
520C2×D4—312no—
521C2×D4—64no—
522C2×D4—126no—
523C2×D4C23×D3112yes—
524C2×D4C23×D3112yes—
525C22×C4—212no—
526C22×C4—212no—
527C22×C4—34no—
528C22×C4—31no—
529C22×C4—31no—
530C22×C4—33no—
531C22×C4—31no—
532C22×C4—33no—
533C22×C4—33no—
534C22×C4—33no—
535C22×C4—312no—
536C22×C4—324no—
537C22×C4—312no—
538C22×C4—64no—
539C22×C4—612no—
540C22×C4—1212no—
541C22×C4—126no—
542C22×C4C23×D3112yes—
543C22×C4C23×D3112yes—
544C22×C4C23×D313yes—
545C22×C4C23×D313yes—
546C22×C4C23×D311yescharacteristic
547C22×C4C23×D311yescharacteristic
548C22×C4C23×D313yes—
549C4⋊C4—312no—
550C4⋊C4—312no—
551C4⋊C4—312no—
552C4⋊C4—312no—
553C4⋊C4—324no—
554C4⋊C4—34no—
555C4⋊C4—312no—
556C4⋊C4—312no—
557C4⋊C4—312no—
558C4⋊C4—324no—
559C4⋊C4—312no—
560C4⋊C4—324no—
561C4⋊C4—312no—
562C4⋊C4—34no—
563C4⋊C4—312no—
564C4⋊C4C23×D3112yes—
565C4⋊C4C23×D3112yes—
566C22⋊C4—312no—
567C22⋊C4—312no—
568C22⋊C4—312no—
569C22⋊C4—312no—
570C22⋊C4—324no—
571C22⋊C4—312no—
572C22⋊C4—34no—
573C22⋊C4—34no—
574C22⋊C4—312no—
575C22⋊C4C23×D3124yes—
576C22⋊C4C23×D314yes—
577C22⋊C4C23×D3112yes—
578C42—312no—
579C42—312no—
580C42—312no—
581C42—312no—
582C42—324no—
583C42—312no—
584C42C23×D3112yes—
585C22×C3—22no—
586C22×C3—22no—
587C22×C3—28no—
588C22×C3—26no—
589C22×C3—26no—
590C22×C3—26no—
591C22×C3—412no—
592C22×C3C22×#4112yes—
593C22×C3C2×2−1+414yes—
594C22×C3C2×2−1+412yes—
595C22×C3#58512yes—
596C22×C3C2611yescharacteristic
597C2×D3—22no—
598C2×D3—22no—
599C2×D3—22no—
600C2×D3—44no—
601C3×C4—22no—
602C3×C4—26no—
603C3×C4—26no—
604C3×C4—22no—
605C3×C4C22×#41112yes—
606Dic3—26no—
607Dic3—22no—
608Dic3—22no—
609Dic3—22no—
610Dic3—26no—
611Dic3—26no—
612Dic3—26no—
613C23—22no—
614C23—22no—
615C23—26no—
616C23—26no—
617C23—26no—
618C23—32no—
619C23—62no—
620C23—62no—
621C23—62no—
622C23#101014yes—
623C23C24×D316yes—
624C23C24×D312yes—
625C23C24×D311yescharacteristic
626Q8—224no—
627Q8—624no—
628Q8—1212no—
629Q8C2×#237116yes—
630D4—224no—
631D4—224no—
632D4—68no—
633D4—1212no—
634C2×C4—22no—
635C2×C4—26no—
636C2×C4—26no—
637C2×C4—22no—
638C2×C4—224no—
639C2×C4—224no—
640C2×C4—32no—
641C2×C4—32no—
642C2×C4—36no—
643C2×C4—32no—
644C2×C4—36no—
645C2×C4—36no—
646C2×C4—36no—
647C2×C4—66no—
648C2×C4—68no—
649C2×C4—62no—
650C2×C4—62no—
651C2×C4—62no—
652C2×C4—66no—
653C2×C4—66no—
654C2×C4—66no—
655C2×C4—624no—
656C2×C4—1224no—
657C2×C4—1212no—
658C2×C4C2×#237112yes—
659C2×C4C24×D316yes—
660C2×C4C24×D316yes—
661C2×C4C24×D312yes—
662C2×C4C24×D312yes—
663C2×C4C24×D316yes—
664C2×C3—24no—
665C2×C3—46no—
666C2×C3#351614yescomplemented
667C2×C3C23×#4111yescharacteristic
668C2×C3C22×2−1+411yescharacteristic
669C2×C3C2×#58511yescharacteristic
670D3—42no—
671C22—22no—
672C22—22no—
673C22—28no—
674C22—26no—
675C22—26no—
676C22—26no—
677C22—412no—
678C22—62no—
679C22—62no—
680C22—62no—
681C22—124no—
682C22C22×#23712yes—
683C22C2×#101014yes—
684C22C2×#101012yes—
685C22#596812yes—
686C22C25×D311yescharacteristic
687C4—22no—
688C4—26no—
689C4—26no—
690C4—22no—
691C4—66no—
692C4—62no—
693C4—62no—
694C4—62no—
695C4—66no—
696C4—66no—
697C4—66no—
698C4C22×#237112yes—
699C3C2×#351611yescharacteristic, complemented, Sylow
700C2—24no—
701C2—46no—
702C2—122no—
703C2#8671814yesdirect product factor
704C2C23×#23711yescharacteristic
705C2C22×#101011yescharacteristic
706C2C2×#596811yescharacteristic
subgroupG/H
centerC23C24×D3
commutator, cosocleC22×C3C26
FrattiniC22C25×D3
FittingC2×C3×#548C2
socleC23×C3C25
hypercenterC2×#548D3
hypocenterC3C2×#3516
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C2×C3×#548C2semidirect
2. C2×#5831C2semidirect
3. C2×#5827C2semidirect
4. C2×Q8×#67C2semidirect
5. C22×Q8×Dic3C2semidirect
6. #86718C2direct (N × H)
7. C2×#5682C2semidirect
8. C2×#5671C2semidirect
9. C2×#5642C2semidirect
10. C2×#5625C2semidirect
11. C2×#5618C2semidirect
12. C2×#5600C2semidirect
13. C2×#5572C2semidirect
14. C2×#5570C2semidirect
15. C2×#5543C2semidirect
16. C2×#5538C2semidirect
21. C3×#548C22semidirect
27. #5831C22semidirect
28. #5827C22semidirect
29. Q8×#67C22semidirect
36. C2×Q8×Dic3C22semidirect
53. #5682C22semidirect
54. #5671C22semidirect
55. #5642C22semidirect
56. #5625C22semidirect
57. #5618C22semidirect
58. #5600C22semidirect
59. #5572C22semidirect
60. #5570C22semidirect
61. #5543C22semidirect
62. #5538C22semidirect
91. C2×#548D3semidirect
212. #548C2×D3semidirect
666. C2×C3#3516semidirect
699. C3C2×#3516semidirect
703. C2#86718direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5482
C2×#58312
C2×#58272
C2×Q8×#672
C22×Q8×Dic32
#867182
C2×#56822
C2×#56712
C2×#56422
C2×#56252
C2×#56182
C2×#56002
C2×#55722
C2×#55702
C2×#55432
C2×#55382
C2×#35163