Finite Group Databasebeta

← C2×#87022 #11703387

Subgroups — C2×#87022 #11703387

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×#557C211yesmaximal, characteristic, complemented
2#87022C2132yesmaximal, direct product factor
3C2×#5730C213yesmaximal, complemented
4C2×#5733C213yesmaximal, complemented
5C2×#5695C213yesmaximal, complemented
6C2×#5694C213yesmaximal, complemented
7C2×#5698C213yesmaximal, complemented
8C2×#5691C213yesmaximal, complemented
9C2×Q8×D12C211yesmaximal, characteristic, complemented
10C2×#5576C211yesmaximal, characteristic, complemented
11C2×#5576C211yesmaximal, characteristic, complemented
12C2×#5580C213yesmaximal, complemented
13C2×#5572C211yesmaximal, characteristic, complemented
14C2×C4×D3×Q8C211yesmaximal, characteristic, complemented
15C2×#5584C213yesmaximal, complemented
16C2×#5574C211yesmaximal, characteristic, complemented
17C2×#3516—31nomaximal, Sylow
18C22×#239C2211yescharacteristic
19C22×D3×Q8C2211yescharacteristic
20C22×D3×Q8C2211yescharacteristic
21C3×#557C22116yescomplemented
22C2×C3×C4⋊Q8C2213yes—
23C2×C3×#125C2213yes—
24C2×C3×#125C2213yes—
25C2×C3×C4×Q8C2211yescharacteristic
26C2×C3×C4×Q8C2213yes—
27C2×C3×C4×Q8C2211yescharacteristic
28C2×C3×C4×Q8C2211yescharacteristic
29C2×#947C2213yes—
30C2×#946C2216yes—
31C2×#946C2213yes—
32C2×Q8×Dic3C2211yescharacteristic
33#5733C22148yescomplemented
34#5730C22148yescomplemented
35#5698C22148yescomplemented
36#5695C22148yescomplemented
37#5694C22148yescomplemented
38#5691C22148yescomplemented
39#5584C22148yescomplemented
40#5580C22148yescomplemented
41#5576C22116yescomplemented
42#5576C22116yescomplemented
43Q8×D12C22116yescomplemented
44#5574C22116yescomplemented
45#5572C22116yescomplemented
46C4×D3×Q8C22116yescomplemented
47C2×#898C2213yes—
48C2×#898C2216yes—
49C2×#898C2213yes—
50C2×#898C2216yes—
51C2×#897C2213yes—
52C2×#897C2213yes—
53C2×#897C2213yes—
54C2×#897C2213yes—
55C2×#895C2213yes—
56C2×#895C2213yes—
57C2×#895C2213yes—
58C2×#894C2211yescharacteristic
59C2×#894C2213yes—
60C2×#894C2216yes—
61C2×#893C2213yes—
62C2×#893C2216yes—
63C2×#892C2216yes—
64C2×#892C2213yes—
65C2×D3×C4⋊C4C2213yes—
66C2×D3×C4⋊C4C2213yes—
67C2×#890C2213yes—
68C2×#890C2216yes—
69C2×#887C2213yes—
70C2×#887C2213yes—
71C2×#875C2213yes—
72C2×#875C2213yes—
73C2×C4×D12C2213yes—
74C2×C4×D12C2213yes—
75C2×C4×D12C2213yes—
76C2×C4×D12C2213yes—
77C2×#872C2213yes—
78C2×#872C2213yes—
79C2×C42×D3C2213yes—
80C2×#869C2213yes—
81C2×C4×Dic6C2213yes—
82C2×C4×Dic6C2213yes—
83#3516—332no—
84C2×#557D311yescharacteristic, complemented
85C2×#556—33no—
86C2×#554—33no—
87C2×#553—33no—
88C2×#552—33no—
89C2×D4×Q8—31no—
90C2×#548—31no—
91C2×#548—31no—
92C2×#542—33no—
93C2×#541—33no—
94C2×#529—33no—
95C2×#529—33no—
96C2×#520—31no—
97C2×#519—31no—
98C22×C4×Q8—31no—
99C22×C3×Q8C2313yes—
100C22×C3×Q8C2311yescharacteristic
101C2×#239—28no—
102C2×#239C2318yes—
103C2×D3×Q8—28no—
104C2×D3×Q8—28no—
105C2×D3×Q8C2318yes—
106C2×D3×Q8C2318yes—
107C22×D12C2313yes—
108C22×D12C2311yescharacteristic
109C22×D12C2313yes—
110C22×D12C2313yes—
111C22×C4×D3C2313yes—
112C22×C4×D3C2313yes—
113C22×C4×D3C2313yes—
114C22×C4×D3C2311yescharacteristic
115C22×C4×D3C2313yes—
116C22×C4×D3C2316yes—
117C22×Dic6C2313yes—
118C22×Dic6C2313yes—
119C3×C4⋊Q8C23124yes—
120C3×#125C23124yes—
121C3×#125C23124yes—
122C3×C4×Q8C2318yes—
123C3×C4×Q8C2318yes—
124C3×C4×Q8C2318yes—
125C3×C4×Q8C23124yes—
126C2×C3×C4⋊C4C2313yes—
127C2×C3×C4⋊C4C2313yes—
128C2×C3×C4⋊C4C2316yes—
129C2×C3×C4⋊C4C2313yes—
130C2×C3×C4⋊C4C2313yes—
131C2×C3×C4⋊C4C2313yes—
132C2×C3×C4⋊C4C2311yescharacteristic
133C2×C3×C42C2313yes—
134C2×C3×C42C2313yes—
135C2×C3×C42C2313yes—
136#947C23124yes—
137#946C23124yes—
138#946C23148yes—
139Q8×Dic3C2318yes—
140C2×(C2×D3)⋊C4C2311yescharacteristic
141C2×(C2×D3)⋊C4C2313yes—
142C2×(C2×D3)⋊C4C2313yes—
143C2×(C2×D3)⋊C4C2313yes—
144C2×(C2×D3)⋊C4C2311yescharacteristic
145C2×(C2×D3)⋊C4C2311yescharacteristic
146C2×(C2×D3)⋊C4C2313yes—
147C2×(C2×D3)⋊C4C2313yes—
148C2×(C2×D3)⋊C4C2313yes—
149C2×(C2×D3)⋊C4C2313yes—
150C2×(C2×D3)⋊C4C2316yes—
151C2×(C2×D3)⋊C4C2316yes—
152C2×C4⋊Dic3C2313yes—
153C2×C4⋊Dic3C2313yes—
154C2×C4⋊Dic3C2316yes—
155C2×C4⋊Dic3C2313yes—
156C2×C4⋊Dic3C2313yes—
157C2×Dic3⋊C4C2313yes—
158C2×Dic3⋊C4C2316yes—
159C2×Dic3⋊C4C2311yescharacteristic
160C2×Dic3⋊C4C2313yes—
161C2×Dic3⋊C4C2313yes—
162C2×C4×Dic3C2313yes—
163C2×C4×Dic3C2316yes—
164C2×C4×Dic3C2313yes—
165C2×C4×Dic3C2313yes—
166#898C23148yes—
167#898C23124yes—
168#898C23148yes—
169#898C23124yes—
170#897C23124yes—
171#897C23124yes—
172#897C23124yes—
173#897C23124yes—
174#895C23124yes—
175#895C23124yes—
176#895C23124yes—
177#894C23124yes—
178#894C23148yes—
179#894C2318yes—
180#893C23148yes—
181#893C23124yes—
182#892C23148yes—
183#892C23124yes—
184D3×C4⋊C4C23124yes—
185D3×C4⋊C4C23124yes—
186#890C23148yes—
187#890C23124yes—
188#887C23124yes—
189#887C23124yes—
190#875C23124yes—
191#875C23124yes—
192C4×D12C23124yes—
193C4×D12C23124yes—
194C4×D12C23124yes—
195C4×D12C23124yes—
196#872C23124yes—
197#872C23124yes—
198C42×D3C23124yes—
199#869C23124yes—
200C4×Dic6C23124yes—
201C4×Dic6C23124yes—
202C22×#41—31no—
203C23×Q8—31no—
204C23×Q8—31no—
205#557C2×D3116yescomplemented
206#556—348no—
207#554—348no—
208#553—348no—
209#552—348no—
210D4×Q8—316no—
211#548—316no—
212#548—316no—
213#542—348no—
214#541—348no—
215C2×C4⋊Q8—33no—
216C2×C4⋊Q8C2×D313yes—
217#529—348no—
218#529—348no—
219C2×#126—36no—
220C2×#126—33no—
221C2×#126—33no—
222C2×#126—36no—
223C2×#125—33no—
224C2×#125—36no—
225C2×#125C2×D313yes—
226C2×#125C2×D313yes—
227C2×#124—33no—
228C2×#124—33no—
229C2×#124—33no—
230C2×#123—31no—
231C2×#123—33no—
232C2×#123—36no—
233C2×C22⋊Q8—33no—
234C2×C22⋊Q8—36no—
235C2×C22⋊Q8—33no—
236C2×C22⋊Q8—33no—
237C2×C22⋊Q8—33no—
238C2×C22⋊Q8—33no—
239C2×#121—33no—
240C2×#121—33no—
241C2×#121—33no—
242#520—316no—
243#519—316no—
244C2×C4×Q8—31no—
245C2×C4×Q8—316no—
246C2×C4×Q8—33no—
247C2×C4×Q8—33no—
248C2×C4×Q8—33no—
249C2×C4×Q8—33no—
250C2×C4×Q8C2×D311yescharacteristic
251C2×C4×Q8C2×D311yescharacteristic
252C2×C4×Q8C2×D311yescharacteristic
253C2×C4×Q8C2×D313yes—
254C2×C4×D4—33no—
255C2×C4×D4—36no—
256C2×C4×D4—33no—
257C2×C4×D4—33no—
258C2×C4×D4—33no—
259C2×C4×D4—33no—
260C2×#117—33no—
261C2×#117—36no—
262C2×#117—33no—
263C2×#117—33no—
264C22×C4⋊C4—33no—
265C22×C4⋊C4—33no—
266C22×C42—33no—
267C23×D3C2411yescharacteristic
268C23×D3C2413yes—
269C23×D3C2411yescharacteristic
270C2×C3×Q8—46no—
271C2×C3×Q8#4118yes—
272C2×C3×Q8C24112yes—
273C2×C3×Q8C2414yes—
274C22×C3×C4C2411yescharacteristic
275C22×C3×C4C2413yes—
276C22×C3×C4C2413yes—
277C22×C3×C4C2411yescharacteristic
278C22×C3×C4C2411yescharacteristic
279C22×C3×C4C2413yes—
280C22×C3×C4C2413yes—
281C22×Dic3C2411yescharacteristic
282C22×Dic3C2413yes—
283C22×Dic3C2413yes—
284C22×Dic3C2413yes—
285C22×Dic3C2411yescharacteristic
286#239—232no—
287D3×Q8—232no—
288D3×Q8—232no—
289C2×D12—24no—
290C2×D12—212no—
291C2×D12—212no—
292C2×D12—46no—
293C2×D12C2414yes—
294C2×D12C24112yes—
295C2×D12C24112yes—
296C2×D12C24112yes—
297C2×C4×D3—24no—
298C2×C4×D3—212no—
299C2×C4×D3—212no—
300C2×C4×D3—212no—
301C2×C4×D3—412no—
302C2×C4×D3—46no—
303C2×C4×D3C2414yes—
304C2×C4×D3C24112yes—
305C2×C4×D3C24112yes—
306C2×C4×D3C24112yes—
307C2×C4×D3C24112yes—
308C2×C4×D3C24124yes—
309C2×Dic6—212no—
310C2×Dic6—212no—
311C2×Dic6C24112yes—
312C2×Dic6C24112yes—
313C3×C4⋊C4C24112yes—
314C3×C4⋊C4C24112yes—
315C3×C4⋊C4C24124yes—
316C3×C4⋊C4C24112yes—
317C3×C4⋊C4C24112yes—
318C3×C4⋊C4C24112yes—
319C3×C4⋊C4C2414yes—
320C3×C42C24112yes—
321C3×C42C24112yes—
322C3×C42C24112yes—
323(C2×D3)⋊C4C2414yes—
324(C2×D3)⋊C4C24112yes—
325(C2×D3)⋊C4C24112yes—
326(C2×D3)⋊C4C24112yes—
327(C2×D3)⋊C4C2414yes—
328(C2×D3)⋊C4C2414yes—
329(C2×D3)⋊C4C24112yes—
330(C2×D3)⋊C4C24112yes—
331(C2×D3)⋊C4C24112yes—
332(C2×D3)⋊C4C24112yes—
333(C2×D3)⋊C4C24124yes—
334(C2×D3)⋊C4C24124yes—
335C4⋊Dic3C24112yes—
336C4⋊Dic3C24112yes—
337C4⋊Dic3C24124yes—
338C4⋊Dic3C24112yes—
339C4⋊Dic3C24112yes—
340Dic3⋊C4C24112yes—
341Dic3⋊C4C24124yes—
342Dic3⋊C4C2414yes—
343Dic3⋊C4C24112yes—
344Dic3⋊C4C24112yes—
345C4×Dic3C24112yes—
346C4×Dic3C24124yes—
347C4×Dic3C24112yes—
348C4×Dic3C24112yes—
349C2×#41—38no—
350C2×#41—68no—
351C22×Q8—38no—
352C22×Q8—38no—
353C22×Q8—33no—
354C22×Q8—33no—
355C22×Q8—68no—
356C22×Q8—68no—
357C22×Q8C22×D313yes—
358C22×Q8C22×D311yescharacteristic
359C22×D4—33no—
360C22×D4—31no—
361C22×D4—33no—
362C22×D4—33no—
363C23×C4—33no—
364C23×C4—33no—
365C23×C4—33no—
366C23×C4—31no—
367C23×C4—33no—
368C23×C4—36no—
369C4⋊Q8—324no—
370C4⋊Q8C22×D3124yes—
371#126—348no—
372#126—324no—
373#126—324no—
374#126—348no—
375#125—324no—
376#125—348no—
377#125C22×D3124yes—
378#125C22×D3124yes—
379#124—324no—
380#124—324no—
381#124—324no—
382#123—38no—
383#123—324no—
384#123—348no—
385C22⋊Q8—324no—
386C22⋊Q8—348no—
387C22⋊Q8—324no—
388C22⋊Q8—324no—
389C22⋊Q8—324no—
390C22⋊Q8—324no—
391#121—324no—
392#121—324no—
393#121—324no—
394C4×Q8—38no—
395C4×Q8—324no—
396C4×Q8—324no—
397C4×Q8—324no—
398C4×Q8—324no—
399C4×Q8C22×D318yes—
400C4×Q8C22×D318yes—
401C4×Q8C22×D318yes—
402C4×Q8C22×D3124yes—
403C4×D4—324no—
404C4×D4—348no—
405C4×D4—324no—
406C4×D4—324no—
407C4×D4—324no—
408C4×D4—324no—
409#117—324no—
410#117—348no—
411#117—324no—
412#117—324no—
413C2×C4⋊C4—33no—
414C2×C4⋊C4—33no—
415C2×C4⋊C4—36no—
416C2×C4⋊C4—31no—
417C2×C4⋊C4—33no—
418C2×C4⋊C4—33no—
419C2×C4⋊C4—36no—
420C2×C4⋊C4—33no—
421C2×C4⋊C4—33no—
422C2×C4⋊C4—33no—
423C2×C4⋊C4—324no—
424C2×C4⋊C4—324no—
425C2×C4⋊C4C22×D313yes—
426C2×C4⋊C4C22×D313yes—
427C2×C4⋊C4C22×D313yes—
428C2×C4⋊C4C22×D313yes—
429C2×C4⋊C4C22×D316yes—
430C2×C4⋊C4C22×D311yescharacteristic
431C2×C4⋊C4C22×D313yes—
432C2×C22⋊C4—33no—
433C2×C22⋊C4—31no—
434C2×C22⋊C4—33no—
435C2×C22⋊C4—33no—
436C2×C22⋊C4—33no—
437C2×C22⋊C4—36no—
438C2×C22⋊C4—33no—
439C2×C22⋊C4—31no—
440C2×C22⋊C4—31no—
441C2×C22⋊C4—36no—
442C2×C22⋊C4—33no—
443C2×C22⋊C4—33no—
444C2×C42—33no—
445C2×C42—36no—
446C2×C42—33no—
447C2×C42—33no—
448C2×C42—324no—
449C2×C42C22×D313yes—
450C2×C42C22×D313yes—
451C2×C42C22×D313yes—
452C23×C3C2511yescharacteristic
453C22×D3—22no—
454C22×D3—22no—
455C22×D3—22no—
456C22×D3—26no—
457C22×D3—22no—
458C22×D3—26no—
459C22×D3—26no—
460C22×D3—22no—
461C22×D32−1+414yes—
462C22×D3C2512yes—
463C22×D3C2516yes—
464C22×D3C2512yes—
465C3×Q8—412no—
466C3×Q8C2×#41116yes—
467C2×C3×C4—22no—
468C2×C3×C4—26no—
469C2×C3×C4—22no—
470C2×C3×C4—26no—
471C2×C3×C4—26no—
472C2×C3×C4—22no—
473C2×C3×C4C2×#41112yes—
474C2×C3×C4C2512yes—
475C2×C3×C4C2516yes—
476C2×C3×C4C2516yes—
477C2×C3×C4C2512yes—
478C2×C3×C4C2512yes—
479C2×C3×C4C2516yes—
480C2×C3×C4C2516yes—
481C2×Dic3—26no—
482C2×Dic3—26no—
483C2×Dic3—22no—
484C2×Dic3—22no—
485C2×Dic3—26no—
486C2×Dic3C2512yes—
487C2×Dic3C2516yes—
488C2×Dic3C2516yes—
489C2×Dic3C2516yes—
490C2×Dic3C2512yes—
491D12—28no—
492D12—224no—
493D12—224no—
494D12—412no—
495C4×D3—28no—
496C4×D3—224no—
497C4×D3—224no—
498C4×D3—224no—
499C4×D3—424no—
500C4×D3—412no—
501Dic6—224no—
502Dic6—224no—
503C24—31no—
504C24—31no—
505C24—33no—
506#41—632no—
507C2×Q8—312no—
508C2×Q8—312no—
509C2×Q8—46no—
510C2×Q8—632no—
511C2×Q8—632no—
512C2×Q8—612no—
513C2×Q8—612no—
514C2×Q8#23918yes—
515C2×Q8C23×D3112yes—
516C2×Q8C23×D314yes—
517C2×D4—312no—
518C2×D4—34no—
519C2×D4—312no—
520C2×D4—312no—
521C2×D4—612no—
522C2×D4—64no—
523C2×D4—612no—
524C2×D4—126no—
525C22×C4—31no—
526C22×C4—33no—
527C22×C4—33no—
528C22×C4—33no—
529C22×C4—31no—
530C22×C4—34no—
531C22×C4—312no—
532C22×C4—312no—
533C22×C4—312no—
534C22×C4—312no—
535C22×C4—324no—
536C22×C4—64no—
537C22×C4—612no—
538C22×C4—612no—
539C22×C4—612no—
540C22×C4—1212no—
541C22×C4—126no—
542C22×C4C23×D311yescharacteristic
543C22×C4C23×D313yes—
544C22×C4C23×D313yes—
545C22×C4C23×D311yescharacteristic
546C22×C4C23×D311yescharacteristic
547C22×C4C23×D313yes—
548C22×C4C23×D313yes—
549C4⋊C4—312no—
550C4⋊C4—312no—
551C4⋊C4—324no—
552C4⋊C4—34no—
553C4⋊C4—312no—
554C4⋊C4—312no—
555C4⋊C4—324no—
556C4⋊C4—312no—
557C4⋊C4—312no—
558C4⋊C4—312no—
559C4⋊C4C23×D3112yes—
560C4⋊C4C23×D3112yes—
561C4⋊C4C23×D3112yes—
562C4⋊C4C23×D3112yes—
563C4⋊C4C23×D3124yes—
564C4⋊C4C23×D314yes—
565C4⋊C4C23×D3112yes—
566C22⋊C4—312no—
567C22⋊C4—34no—
568C22⋊C4—312no—
569C22⋊C4—312no—
570C22⋊C4—312no—
571C22⋊C4—324no—
572C22⋊C4—312no—
573C22⋊C4—34no—
574C22⋊C4—34no—
575C22⋊C4—324no—
576C22⋊C4—312no—
577C22⋊C4—312no—
578C42—312no—
579C42—312no—
580C42—312no—
581C42—324no—
582C42C23×D3112yes—
583C42C23×D3112yes—
584C42C23×D3112yes—
585C22×C3C22×#4112yes—
586C22×C3C2×2−1+412yes—
587C22×C3#58512yes—
588C22×C3C2611yescharacteristic
589C2×D3—22no—
590C2×D3—22no—
591C2×D3—28no—
592C2×D3—22no—
593C2×D3—26no—
594C2×D3—22no—
595C2×D3—26no—
596C2×D3—26no—
597C2×D3—22no—
598C2×D3—44no—
599C2×D3—412no—
600C2×D3C2×2−1+414yes—
601C3×C4—22no—
602C3×C4—26no—
603C3×C4—22no—
604C3×C4—26no—
605C3×C4—26no—
606C3×C4—22no—
607C3×C4C22×#41112yes—
608Dic3—26no—
609Dic3—26no—
610Dic3—22no—
611Dic3—22no—
612Dic3—26no—
613C23—34no—
614C23—32no—
615C23—32no—
616C23—36no—
617C23—62no—
618C23—62no—
619C23—62no—
620C23—66no—
621C23—66no—
622C23—62no—
623C23—62no—
624C23—66no—
625C23C24×D311yescharacteristic
626Q8—412no—
627Q8—624no—
628Q8—624no—
629Q8C2×#239116yes—
630D4—624no—
631D4—68no—
632D4—624no—
633D4—1212no—
634C2×C4—26no—
635C2×C4—26no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—26no—
639C2×C4—22no—
640C2×C4—32no—
641C2×C4—36no—
642C2×C4—36no—
643C2×C4—36no—
644C2×C4—32no—
645C2×C4—68no—
646C2×C4—62no—
647C2×C4—66no—
648C2×C4—66no—
649C2×C4—66no—
650C2×C4—62no—
651C2×C4—624no—
652C2×C4—624no—
653C2×C4—624no—
654C2×C4—1224no—
655C2×C4—1212no—
656C2×C4C2×#239112yes—
657C2×C4C24×D312yes—
658C2×C4C24×D316yes—
659C2×C4C24×D316yes—
660C2×C4C24×D312yes—
661C2×C4C24×D312yes—
662C2×C4C24×D316yes—
663C2×C4C24×D316yes—
664C2×C3#351614yescomplemented
665C2×C3C23×#4111yescharacteristic
666C2×C3C22×2−1+411yescharacteristic
667C2×C3C2×#58511yescharacteristic
668D3—24no—
669D3—42no—
670D3—46no—
671C22—34no—
672C22—62no—
673C22—62no—
674C22—68no—
675C22—62no—
676C22—66no—
677C22—66no—
678C22—62no—
679C22—62no—
680C22—66no—
681C22—124no—
682C22—1212no—
683C22C22×#23912yes—
684C22#596412yes—
685C22D3×2−1+412yes—
686C22C25×D311yescharacteristic
687C4—26no—
688C4—26no—
689C4—22no—
690C4—22no—
691C4—26no—
692C4—22no—
693C4—62no—
694C4—66no—
695C4—66no—
696C4—66no—
697C4—62no—
698C4C22×#239112yes—
699C3C2×#351611yescharacteristic, complemented, Sylow
700C2—64no—
701C2—122no—
702C2—126no—
703C2#8702214yesdirect product factor
704C2C23×#23911yescharacteristic
705C2C2×#596411yescharacteristic
706C2C2×D3×2−1+411yescharacteristic
subgroupG/H
centerC23C24×D3
commutator, cosocleC22×C3C26
FrattiniC22C25×D3
FittingC2×C3×#557C2
socleC23×C3C25
hypercenterC2×#557D3
hypocenterC3C2×#3516
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. C2×C3×#557C2semidirect
2. #87022C2direct (N × H)
3. C2×#5730C2semidirect
4. C2×#5733C2semidirect
5. C2×#5695C2semidirect
6. C2×#5694C2semidirect
7. C2×#5698C2semidirect
8. C2×#5691C2semidirect
9. C2×Q8×D12C2semidirect
10. C2×#5576C2semidirect
11. C2×#5576C2semidirect
12. C2×#5580C2semidirect
13. C2×#5572C2semidirect
14. C2×C4×D3×Q8C2semidirect
15. C2×#5584C2semidirect
16. C2×#5574C2semidirect
21. C3×#557C22semidirect
33. #5733C22semidirect
34. #5730C22semidirect
35. #5698C22semidirect
36. #5695C22semidirect
37. #5694C22semidirect
38. #5691C22semidirect
39. #5584C22semidirect
40. #5580C22semidirect
41. #5576C22semidirect
42. #5576C22semidirect
43. Q8×D12C22semidirect
44. #5574C22semidirect
45. #5572C22semidirect
46. C4×D3×Q8C22semidirect
84. C2×#557D3semidirect
205. #557C2×D3semidirect
664. C2×C3#3516semidirect
699. C3C2×#3516semidirect
703. C2#87022direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5572
#870222
C2×#57302
C2×#57332
C2×#56952
C2×#56942
C2×#56982
C2×#56912
C2×Q8×D122
C2×#55762
C2×#55802
C2×#55722
C2×C4×D3×Q82
C2×#55842
C2×#55742
C2×#35163