Finite Group Databasebeta

← C2×#84004 #11661812

Subgroups — C2×#84004 #11661812

Order 768.

4850 conjugacy classes of subgroups.

The subgroup lattice has 1156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5964C211yesmaximal, characteristic, complemented
2C2×C3×#575C211yesmaximal, characteristic, complemented
3C2×#5832C211yesmaximal, characteristic, complemented
4C2×#5822C211yesmaximal, characteristic, complemented
5C22×#837C211yesmaximal, characteristic, complemented
6#84004C2116yesmaximal, direct product factor
7C2×#5205C212yesmaximal, complemented
8C2×#5202C212yesmaximal, complemented
9C2×#5201C212yesmaximal, complemented
10C2×#5198C212yesmaximal, complemented
11C22×#825C211yesmaximal, characteristic, complemented
12C2×#5132C211yesmaximal, characteristic, complemented
13C2×#3018—31nomaximal, Sylow
14C22×C3×#41C2211yescharacteristic
15C22×C3×#41C2211yescharacteristic, complemented
16#5964—24no—
17#5964—24no—
18#5964—24no—
19#5964C2218yescomplemented
20C2×#1010—21no—
21C2×#1010C2212yes—
22C2×#1009—21no—
23C2×#1009C2212yes—
24C2×D3×#41—22no—
25C2×D3×#41—22no—
26C2×#1007—21no—
27C2×#1004—21no—
28C2×#1004—22no—
29C22×#235—22no—
30C22×#235C2211yescharacteristic
31C22×#235C2211yescharacteristic
32C3×#575—24no—
33C3×#575C2218yescomplemented
34C2×C3×#137—21no—
35C2×C3×#137C2212yescomplemented
36C2×C3×AGL(1,ℤ/8)—21no—
37C2×C3×AGL(1,ℤ/8)C2212yescomplemented
38C2×C3×#135—22no—
39C22×C3×M16C2211yescharacteristic, complemented
40#5832—24no—
41#5832C2218yescomplemented
42C2×#951—21no—
43#5822—24no—
44#5822C2218yescomplemented
45C2×#950—22no—
46C2×#949—21no—
47C2×#947C2211yescharacteristic, complemented
48C2×#944C2211yescharacteristic, complemented
49C2×#942C2212yescomplemented
50C2×#940C2211yescharacteristic, complemented
51C2×#939—22no—
52C2×#936C2211yescharacteristic, complemented
53C2×#932C2212yescomplemented
54C2×C4×#67—22no—
55C22×C4×Dic3C2211yescharacteristic, complemented
56C22×#208C2211yescharacteristic, complemented
57C2×#837C2212yescomplemented
58C2×#837C2212yescomplemented
59C2×#837C2218yescomplemented
60#5205C22116yescomplemented
61#5202C22116yescomplemented
62#5201C22116yescomplemented
63#5198C22116yescomplemented
64C2×#825C2212yescomplemented
65C2×#825C2212yescomplemented
66C2×#825C2218yescomplemented
67C2×#824C2212yescomplemented
68#5132C2218yescomplemented
69C2×#823C2212yescomplemented
70C2×#585—31no—
71C2×#575—31no—
72C2×#575D311yescharacteristic, complemented
73C2×#532—31no—
74#3018—316no—
75C2×#456—32no—
76C2×#454—32no—
77C2×#455—32no—
78C2×#453—32no—
79C22×#104—31no—
80C22×#104—31no—
81C2×#413—31no—
82C2×C3×#41—21no—
83C2×C3×#41—21no—
84C2×C3×#41—22no—
85C2×C3×#41—22no—
86C2×C3×#41—22no—
87C2×C3×#41—21no—
88C2×C3×#41—21no—
89C2×C3×#41—22no—
90C2×C3×#41—21no—
91C2×C3×#41—21no—
92C2×C3×#41—22no—
93C2×C3×#41D412yescomplemented
94C2×C3×#41D414yescomplemented
95C2×C3×#41C2312yes—
96C2×C3×#41C2314yes—
97C2×C3×#41C2314yescomplemented
98C22×C3×Q8D411yescharacteristic, complemented
99C22×C3×Q8C2311yescharacteristic
100C22×C3×D4—21no—
101C22×C3×D4—21no—
102C22×C3×D4D411yescharacteristic, complemented
103C22×C3×D4C2311yescharacteristic
104C23×C3×C4—21no—
105C23×C3×C4—21no—
106C23×C3×C4C2311yescharacteristic
107C22×#67—24no—
108C22×#67—21no—
109C22×#67—22no—
110C22×#67D412yes—
111C23×Dic3—21no—
112#1010—28no—
113#1010—24no—
114#1010—24no—
115#1010—24no—
116#1010—28no—
117#1010C2318yes—
118#1009—28no—
119#1009—24no—
120#1009—24no—
121#1009—24no—
122#1009—28no—
123#1009C2318yes—
124D3×#41—216no—
125D3×#41—216no—
126D3×#41—216no—
127D3×#41—216no—
128#1007—28no—
129#1007—28no—
130C2×#239—22no—
131C2×#239—22no—
132C2×D3×Q8—22no—
133C2×D3×Q8—22no—
134#1004—216no—
135#1004—28no—
136#1004—28no—
137#1004—216no—
138C2×#237—24no—
139C2×#237—22no—
140C2×#237—22no—
141C2×#237—24no—
142C2×D3×D4—24no—
143C2×D3×D4—22no—
144C2×D3×D4—24no—
145C2×D3×D4—22no—
146C2×#235—24no—
147C2×#235—24no—
148C2×#235—216no—
149C2×#235—21no—
150C2×#235—21no—
151C2×#235—21no—
152C2×#235—21no—
153C2×#235—21no—
154C2×#235—21no—
155C2×#235—22no—
156C2×#235—22no—
157C2×#235—22no—
158C2×#235—22no—
159C2×#235—216no—
160C2×#235—22no—
161C2×#235—22no—
162C2×#235D414yes—
163C2×#235D412yescomplemented
164C2×#235D414yescomplemented
165C2×#235C2312yes—
166C2×#235C2314yes—
167C2×#235C2314yes—
168C22×D12—22no—
169C22×D12D411yescharacteristic, complemented
170C22×D12C2311yescharacteristic
171C22×C4×D3—24no—
172C22×C4×D3—21no—
173C22×C4×D3D412yes—
174C22×Dic6—22no—
175C22×Dic6D411yescharacteristic, complemented
176C22×Dic6C2311yescharacteristic
177C3×#137—24no—
178C3×#137—28no—
179C3×#137C2318yescomplemented
180C3×AGL(1,ℤ/8)—24no—
181C3×AGL(1,ℤ/8)—28no—
182C3×AGL(1,ℤ/8)C2318yescomplemented
183C3×#135—216no—
184C2×C3×Q16—22no—
185C2×C3×SD16—22no—
186C2×C3×SD16—22no—
187C2×C3×D8—22no—
188C2×C3×M16—21no—
189C2×C3×M16—22no—
190C2×C3×M16C2312yes—
191C2×C3×M16C2314yescomplemented
192C22×C3×C8—21no—
193C2×#217—22no—
194#951—28no—
195#950—216no—
196#949—28no—
197#947—22no—
198#947C2314yescomplemented
199#944—22no—
200#944C2314yescomplemented
201C2×#216—22no—
202#942—24no—
203#942C2318yescomplemented
204C2×#215—22no—
205#940—22no—
206#940C2314yescomplemented
207#939—216no—
208#936—22no—
209#936C2314yescomplemented
210C2×#214—22no—
211#932—24no—
212#932C2318yescomplemented
213C2×#213—22no—
214C4×#67—216no—
215C2×(C2×D3)⋊C4—22no—
216C2×Dic3⋊C4—22no—
217C2×C4×Dic3—21no—
218C2×C4×Dic3—22no—
219C2×C4×Dic3C2311yescharacteristic
220C2×C4×Dic3C2311yescharacteristic
221C2×C4×Dic3C2314yescomplemented
222C2×#208—21no—
223C2×#208—22no—
224C2×#208C2312yes—
225C2×#208C2314yescomplemented
226C22×C3⋊C8—21no—
227#837C2318yescomplemented
228#837C2318yescomplemented
229#825C2318yescomplemented
230#825C2318yescomplemented
231#824C2318yescomplemented
232#823C2318yescomplemented
233#585—38no—
234#585—64no—
235#585—64no—
236#585—64no—
237C2×2−1+4—32no—
238C2×2−1+4—61no—
239C2×2−1+4—61no—
240C2×H(5,𝔽2)—32no—
241C2×H(5,𝔽2)—62no—
242C2×H(5,𝔽2)—61no—
243C2×H(5,𝔽2)—61no—
244C22×#41—31no—
245C22×#41—31no—
246C22×#41—62no—
247C22×#41—62no—
248C22×#41—62no—
249C22×#41C2×D311yescharacteristic
250C22×#41C2×D311yescharacteristic, complemented
251#575—24no—
252#575—38no—
253#575—64no—
254#575C2×D318yescomplemented
255C2×#137—21no—
256C2×#137—32no—
257C2×#137—61no—
258C2×#137C2×D312yescomplemented
259C2×AGL(1,ℤ/8)—21no—
260C2×AGL(1,ℤ/8)—32no—
261C2×AGL(1,ℤ/8)—61no—
262C2×AGL(1,ℤ/8)C2×D312yescomplemented
263C2×#135—22no—
264C2×#135—62no—
265C22×M16—31no—
266C22×M16C2×D311yescharacteristic, complemented
267#532—38no—
268#532—64no—
269C2×C4⋊Q8—31no—
270C2×#127—31no—
271C2×#124—31no—
272C2×#124—31no—
273C2×#121—62no—
274C2×C4×D4—62no—
275C22×C42—31no—
276#456—316no—
277#455—316no—
278#454—316no—
279#453—316no—
280C2×#104—32no—
281C2×#104—32no—
282C2×#104—38no—
283C2×#104—32no—
284C2×#104—32no—
285C2×#104—38no—
286#413—38no—
287C2×#101—32no—
288C2×#100—32no—
289C24×C3—21no—
290C24×C3—21no—
291C24×C3C2×D411yescharacteristic
292C23×D3—24no—
293C23×D3—21no—
294C23×D3C2×D412yes—
295C3×#41—24no—
296C3×#41—24no—
297C3×#41—24no—
298C3×#41—24no—
299C3×#41—22no—
300C3×#41—22no—
301C3×#41—24no—
302C3×#41—24no—
303C3×#41—24no—
304C3×#41—24no—
305C3×#41—24no—
306C3×#41—42no—
307C3×#41—42no—
308C3×#41—42no—
309C3×#41—42no—
310C3×#41C2×D414yes—
311C3×#41C2×D418yescomplemented
312C3×#41C2414yes—
313C2×C3×Q8—21no—
314C2×C3×Q8—22no—
315C2×C3×Q8—21no—
316C2×C3×Q8—21no—
317C2×C3×Q8—21no—
318C2×C3×Q8—21no—
319C2×C3×Q8—21no—
320C2×C3×Q8C2×D412yes—
321C2×C3×Q8C2×D414yescomplemented
322C2×C3×Q8C2412yes—
323C2×C3×D4—22no—
324C2×C3×D4—24no—
325C2×C3×D4—22no—
326C2×C3×D4—24no—
327C2×C3×D4—24no—
328C2×C3×D4—21no—
329C2×C3×D4—22no—
330C2×C3×D4—21no—
331C2×C3×D4—21no—
332C2×C3×D4—21no—
333C2×C3×D4—21no—
334C2×C3×D4—21no—
335C2×C3×D4—41no—
336C2×C3×D4—41no—
337C2×C3×D4—42no—
338C2×C3×D4C2×D412yes—
339C2×C3×D4C2×D414yescomplemented
340C2×C3×D4C2412yes—
341C22×C3×C4—21no—
342C22×C3×C4—22no—
343C22×C3×C4—24no—
344C22×C3×C4—22no—
345C22×C3×C4—24no—
346C22×C3×C4—21no—
347C22×C3×C4—24no—
348C22×C3×C4—41no—
349C22×C3×C4—42no—
350C22×C3×C4—41no—
351C22×C3×C4C2×D411yescharacteristic
352C22×C3×C4C2×D412yes—
353C22×C3×C4C2×D411yescharacteristic
354C22×C3×C4C2×D411yescharacteristic
355C22×C3×C4C2×D412yes—
356C22×C3×C4C2×D411yescharacteristic
357C22×C3×C4C2×D411yescharacteristic
358C22×C3×C4C2×D412yes—
359C22×C3×C4C2411yescharacteristic
360C22×C3×C4C2412yes—
361C2×#67—24no—
362C2×#67—24no—
363C2×#67—232no—
364C2×#67—22no—
365C2×#67—22no—
366C2×#67—22no—
367C2×#67—24no—
368C2×#67—24no—
369C2×#67—22no—
370C2×#67—24no—
371C2×#67—28no—
372C2×#67—48no—
373C2×#67C2×D418yes—
374C22×Dic3—24no—
375C22×Dic3—21no—
376C22×Dic3—21no—
377C22×Dic3—21no—
378C22×Dic3—24no—
379C22×Dic3—44no—
380C22×Dic3C2×D412yes—
381#239—28no—
382#239—216no—
383#239—28no—
384D3×Q8—28no—
385D3×Q8—216no—
386D3×Q8—28no—
387#237—216no—
388#237—232no—
389#237—28no—
390#237—216no—
391#237—28no—
392#237—216no—
393D3×D4—232no—
394D3×D4—216no—
395D3×D4—28no—
396D3×D4—216no—
397D3×D4—216no—
398D3×D4—28no—
399#235—232no—
400#235—232no—
401#235—28no—
402#235—28no—
403#235—24no—
404#235—24no—
405#235—24no—
406#235—24no—
407#235—24no—
408#235—24no—
409#235—24no—
410#235—24no—
411#235—24no—
412#235—24no—
413#235—24no—
414#235—24no—
415#235—22no—
416#235—24no—
417#235—22no—
418#235—28no—
419#235—28no—
420#235C2×D414yes—
421#235C2×D418yescomplemented
422#235C2414yes—
423C2×D12—24no—
424C2×D12—28no—
425C2×D12—21no—
426C2×D12—22no—
427C2×D12—21no—
428C2×D12—21no—
429C2×D12—21no—
430C2×D12—21no—
431C2×D12—28no—
432C2×D12C2×D412yes—
433C2×D12C2×D412yes—
434C2×D12C2×D414yescomplemented
435C2×D12C2412yes—
436C2×C4×D3—24no—
437C2×C4×D3—24no—
438C2×C4×D3—232no—
439C2×C4×D3—22no—
440C2×C4×D3—22no—
441C2×C4×D3—24no—
442C2×C4×D3—22no—
443C2×C4×D3—24no—
444C2×C4×D3—22no—
445C2×C4×D3—24no—
446C2×C4×D3C2×D418yes—
447C2×Dic6—24no—
448C2×Dic6—28no—
449C2×Dic6—21no—
450C2×Dic6—22no—
451C2×Dic6—21no—
452C2×Dic6—21no—
453C2×Dic6—21no—
454C2×Dic6—21no—
455C2×Dic6—28no—
456C2×Dic6C2×D412yes—
457C2×Dic6C2×D412yes—
458C2×Dic6C2×D414yescomplemented
459C2×Dic6C2412yes—
460C3×Q16—28no—
461C3×SD16—28no—
462C3×SD16—28no—
463C3×D8—28no—
464C3×M16—22no—
465C3×M16—24no—
466C3×M16C2414yes—
467C2×C3×C8—22no—
468C2×C3×C8—24no—
469#217—28no—
470#216—28no—
471#215—28no—
472#214—28no—
473#213—28no—
474(C2×D3)⋊C4—28no—
475Dic3⋊C4—28no—
476C4×Dic3—21no—
477C4×Dic3—21no—
478C4×Dic3—24no—
479C4×Dic3C2412yes—
480C4×Dic3C2412yes—
481#208—22no—
482#208—24no—
483#208C2414yes—
484C2×C3⋊C8—22no—
485C2×C3⋊C8—24no—
4862−1+4—38no—
4872−1+4—68no—
4882−1+4—64no—
4892−1+4—68no—
4902−1+4—64no—
4912−1+4—68no—
4922−1+4—64no—
4932−1+4—68no—
494H(5,𝔽2)—38no—
495H(5,𝔽2)—616no—
496H(5,𝔽2)—616no—
497H(5,𝔽2)—68no—
498H(5,𝔽2)—64no—
499H(5,𝔽2)—68no—
500H(5,𝔽2)—64no—
501H(5,𝔽2)—68no—
502H(5,𝔽2)—64no—
503H(5,𝔽2)—68no—
504C2×#41—21no—
505C2×#41—21no—
506C2×#41—22no—
507C2×#41—22no—
508C2×#41—22no—
509C2×#41—21no—
510C2×#41—21no—
511C2×#41—22no—
512C2×#41—21no—
513C2×#41—21no—
514C2×#41—22no—
515C2×#41—34no—
516C2×#41—34no—
517C2×#41—32no—
518C2×#41—34no—
519C2×#41—32no—
520C2×#41—34no—
521C2×#41—62no—
522C2×#41—62no—
523C2×#41—616no—
524C2×#41—64no—
525C2×#41—64no—
526C2×#41—616no—
527C2×#41—64no—
528C2×#41—616no—
529C2×#41—64no—
530C2×#41—62no—
531C2×#41—62no—
532C2×#41—616no—
533C2×#41—616no—
534C2×#41—616no—
535C2×#41—62no—
536C2×#41—62no—
537C2×#41—61no—
538C2×#41—61no—
539C2×#41—61no—
540C2×#41—62no—
541C2×#41—62no—
542C2×#41—61no—
543C2×#41—61no—
544C2×#41—61no—
545C2×#41—62no—
546C2×#41—62no—
547C2×#41#6712yescomplemented
548C2×#41#6714yescomplemented
549C2×#41C22×D312yes—
550C2×#41C22×D314yes—
551C2×#41C22×D314yescomplemented
552C22×Q8—31no—
553C22×Q8—31no—
554C22×Q8—62no—
555C22×Q8—62no—
556C22×Q8—62no—
557C22×Q8#6711yescharacteristic, complemented
558C22×Q8C22×D311yescharacteristic
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—32no—
562C22×D4—31no—
563C22×D4—31no—
564C22×D4—62no—
565C22×D4—64no—
566C22×D4—64no—
567C22×D4—62no—
568C22×D4—64no—
569C22×D4—61no—
570C22×D4—62no—
571C22×D4—62no—
572C22×D4#6711yescharacteristic, complemented
573C22×D4C22×D311yescharacteristic
574C23×C4—21no—
575C23×C4—21no—
576C23×C4—32no—
577C23×C4—64no—
578C23×C4—61no—
579C23×C4—61no—
580C23×C4C22×D311yescharacteristic
581#137—24no—
582#137—28no—
583#137—38no—
584#137—64no—
585#137—68no—
586#137C22×D318yescomplemented
587AGL(1,ℤ/8)—24no—
588AGL(1,ℤ/8)—28no—
589AGL(1,ℤ/8)—38no—
590AGL(1,ℤ/8)—64no—
591AGL(1,ℤ/8)—68no—
592AGL(1,ℤ/8)C22×D318yescomplemented
593#135—216no—
594#135—616no—
595C2×Q16—22no—
596C2×Q16—62no—
597C2×SD16—22no—
598C2×SD16—22no—
599C2×SD16—62no—
600C2×SD16—62no—
601C2×D8—22no—
602C2×D8—62no—
603C2×M16—21no—
604C2×M16—22no—
605C2×M16—32no—
606C2×M16—34no—
607C2×M16—61no—
608C2×M16—62no—
609C2×M16C22×D312yes—
610C2×M16C22×D314yescomplemented
611C22×C8—21no—
612C22×C8—61no—
613C4⋊Q8—34no—
614C4⋊Q8—62no—
615#127—34no—
616#127—62no—
617#124—34no—
618#124—34no—
619#124—62no—
620#124—62no—
621#121—616no—
622C4×D4—616no—
623C2×C4⋊C4—62no—
624C2×C22⋊C4—62no—
625C2×C22⋊C4—62no—
626C2×C42—31no—
627C2×C42—31no—
628C2×C42—34no—
629C2×C42—61no—
630C2×C42—62no—
631#104—38no—
632#104—38no—
633#104—38no—
634#104—38no—
635#101—38no—
636#100—38no—
637C23×C3—22no—
638C23×C3—24no—
639C23×C3—22no—
640C23×C3—42no—
641C23×C3—44no—
642C23×C3—41no—
643C23×C3—41no—
644C23×C3—82no—
645C23×C3#12011yescharacteristic
646C23×C3#12011yescharacteristic
647C23×C3#12012yes—
648C23×C3C22×D411yescharacteristic
649C23×C3C22×D412yes—
650C22×D3—22no—
651C22×D3—22no—
652C22×D3—216no—
653C22×D3—22no—
654C22×D3—24no—
655C22×D3—44no—
656C22×D3—82no—
657C22×D3—88no—
658C22×D3C22×D414yes—
659C3×Q8—22no—
660C3×Q8—24no—
661C3×Q8—22no—
662C3×Q8—22no—
663C3×Q8—41no—
664C3×Q8—41no—
665C3×Q8C22×D414yes—
666C3×D4—24no—
667C3×D4—28no—
668C3×D4—24no—
669C3×D4—22no—
670C3×D4—24no—
671C3×D4—22no—
672C3×D4—22no—
673C3×D4—44no—
674C3×D4—44no—
675C3×D4—41no—
676C3×D4—41no—
677C3×D4C22×D414yes—
678C2×C3×C4—22no—
679C2×C3×C4—24no—
680C2×C3×C4—24no—
681C2×C3×C4—28no—
682C2×C3×C4—24no—
683C2×C3×C4—22no—
684C2×C3×C4—41no—
685C2×C3×C4—41no—
686C2×C3×C4—44no—
687C2×C3×C4—44no—
688C2×C3×C4#12011yescharacteristic
689C2×C3×C4#12012yes—
690C2×C3×C4#12012yes—
691C2×C3×C4#12012yes—
692C2×C3×C4#12012yes—
693C2×C3×C4#12012yes—
694C2×C3×C4#12011yescharacteristic
695C2×C3×C4C22×D411yescharacteristic
696C2×C3×C4C22×D412yes—
697C2×C3×C4C22×D411yescharacteristic
698C2×C3×C4C22×D412yes—
699C2×C3×C4C22×D411yescharacteristic
700C2×C3×C4C22×D412yes—
701C2×C3×C4C22×D411yescharacteristic
702C2×C3×C4C22×D412yes—
703C2×C3×C4C22×D411yescharacteristic
704C2×C3×C4C22×D412yes—
705C2×C3×C4C2511yescharacteristic
706#67—216no—
707#67—216no—
708#67—28no—
709#67—28no—
710#67—28no—
711#67—24no—
712#67—24no—
713#67—416no—
714C2×Dic3—216no—
715C2×Dic3—24no—
716C2×Dic3—22no—
717C2×Dic3—22no—
718C2×Dic3—22no—
719C2×Dic3—24no—
720C2×Dic3—22no—
721C2×Dic3—22no—
722C2×Dic3—48no—
723C2×Dic3—42no—
724C2×Dic3C22×D414yes—
725D12—216no—
726D12—22no—
727D12—22no—
728D12—22no—
729D12—24no—
730D12—22no—
731D12—22no—
732D12C22×D414yes—
733C4×D3—216no—
734C4×D3—216no—
735C4×D3—28no—
736C4×D3—28no—
737C4×D3—24no—
738C4×D3—28no—
739C4×D3—24no—
740Dic6—216no—
741Dic6—22no—
742Dic6—22no—
743Dic6—22no—
744Dic6—24no—
745Dic6—22no—
746Dic6—22no—
747Dic6C22×D414yes—
748C3×C8—24no—
749C3⋊C8—24no—
750C24—21no—
751C24—21no—
752C24—32no—
753C24—64no—
754C24—61no—
755C24D3×D411yescharacteristic
756#41—24no—
757#41—24no—
758#41—24no—
759#41—24no—
760#41—22no—
761#41—24no—
762#41—22no—
763#41—24no—
764#41—24no—
765#41—24no—
766#41—24no—
767#41—38no—
768#41—34no—
769#41—34no—
770#41—42no—
771#41—42no—
772#41—42no—
773#41—42no—
774#41—68no—
775#41—68no—
776#41—632no—
777#41—632no—
778#41—68no—
779#41—68no—
780#41—616no—
781#41—616no—
782#41—632no—
783#41—616no—
784#41—68no—
785#41—616no—
786#41—68no—
787#41—68no—
788#41—68no—
789#41—64no—
790#41—64no—
791#41—64no—
792#41—64no—
793#41—64no—
794#41—64no—
795#41—64no—
796#41—64no—
797#41—64no—
798#41—64no—
799#41—62no—
800#41—64no—
801#41—62no—
802#41—64no—
803#41—64no—
804#41C2×#6714yes—
805#41C2×#6718yescomplemented
806#41C23×D314yes—
807C2×Q8—21no—
808C2×Q8—22no—
809C2×Q8—21no—
810C2×Q8—21no—
811C2×Q8—21no—
812C2×Q8—21no—
813C2×Q8—21no—
814C2×Q8—32no—
815C2×Q8—32no—
816C2×Q8—32no—
817C2×Q8—34no—
818C2×Q8—68no—
819C2×Q8—64no—
820C2×Q8—68no—
821C2×Q8—616no—
822C2×Q8—68no—
823C2×Q8—68no—
824C2×Q8—61no—
825C2×Q8—62no—
826C2×Q8—61no—
827C2×Q8—61no—
828C2×Q8—61no—
829C2×Q8—61no—
830C2×Q8C2×#6712yes—
831C2×Q8C2×#6714yescomplemented
832C2×Q8C23×D312yes—
833C2×D4—22no—
834C2×D4—24no—
835C2×D4—22no—
836C2×D4—24no—
837C2×D4—24no—
838C2×D4—21no—
839C2×D4—22no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—38no—
846C2×D4—32no—
847C2×D4—34no—
848C2×D4—32no—
849C2×D4—32no—
850C2×D4—41no—
851C2×D4—41no—
852C2×D4—42no—
853C2×D4—68no—
854C2×D4—64no—
855C2×D4—68no—
856C2×D4—616no—
857C2×D4—616no—
858C2×D4—632no—
859C2×D4—616no—
860C2×D4—68no—
861C2×D4—64no—
862C2×D4—64no—
863C2×D4—632no—
864C2×D4—62no—
865C2×D4—62no—
866C2×D4—64no—
867C2×D4—62no—
868C2×D4—64no—
869C2×D4—62no—
870C2×D4—64no—
871C2×D4—68no—
872C2×D4—68no—
873C2×D4—61no—
874C2×D4—62no—
875C2×D4—61no—
876C2×D4—61no—
877C2×D4—61no—
878C2×D4—61no—
879C2×D4—128no—
880C2×D4C2×#6712yes—
881C2×D4C2×#6714yescomplemented
882C2×D4C23×D312yes—
883C22×C4—21no—
884C22×C4—24no—
885C22×C4—22no—
886C22×C4—22no—
887C22×C4—24no—
888C22×C4—21no—
889C22×C4—24no—
890C22×C4—32no—
891C22×C4—38no—
892C22×C4—41no—
893C22×C4—42no—
894C22×C4—41no—
895C22×C4—64no—
896C22×C4—64no—
897C22×C4—632no—
898C22×C4—64no—
899C22×C4—61no—
900C22×C4—61no—
901C22×C4—62no—
902C22×C4—64no—
903C22×C4—64no—
904C22×C4—62no—
905C22×C4—62no—
906C22×C4—62no—
907C22×C4—64no—
908C22×C4—61no—
909C22×C4—64no—
910C22×C4—124no—
911C22×C4D3×D412yes—
912C22×C4D3×D411yescharacteristic
913C22×C4D3×D411yescharacteristic
914C22×C4D3×D412yes—
915C22×C4D3×D411yescharacteristic
916C22×C4C2×#6711yescharacteristic
917C22×C4C2×#6712yes—
918C22×C4C2×#6711yescharacteristic
919C22×C4C23×D311yescharacteristic
920C22×C4C23×D312yes—
921Q16—28no—
922Q16—68no—
923SD16—28no—
924SD16—28no—
925SD16—68no—
926SD16—68no—
927D8—28no—
928D8—68no—
929M16—22no—
930M16—24no—
931M16—34no—
932M16—62no—
933M16—64no—
934M16C23×D314yes—
935C2×C8—22no—
936C2×C8—24no—
937C2×C8—62no—
938C2×C8—64no—
939C4⋊C4—68no—
940C22⋊C4—68no—
941C22⋊C4—68no—
942C42—32no—
943C42—32no—
944C42—64no—
945C42—61no—
946C42—61no—
947C22×C3—22no—
948C22×C3—22no—
949C22×C3—22no—
950C22×C3—24no—
951C22×C3—42no—
952C22×C3—42no—
953C22×C3—44no—
954C22×C3—44no—
955C22×C3—42no—
956C22×C3—84no—
957C22×C3—82no—
958C22×C3—82no—
959C22×C3C2×#12011yescharacteristic
960C22×C3C2×#12012yes—
961C22×C3C2×#12012yes—
962C22×C3C2×#12011yescharacteristic
963C22×C3C23×D411yescharacteristic
964C2×D3—24no—
965C2×D3—24no—
966C2×D3—44no—
967C2×D3—44no—
968C2×D3—44no—
969C2×D3—82no—
970C2×D3—84no—
971C2×D3—816no—
972C3×C4—24no—
973C3×C4—42no—
974C3×C4C2×#12011yescharacteristic
975C3×C4C2×#12012yes—
976C3×C4C2×#12011yescharacteristic
977C3×C4C2×#12012yes—
978C3×C4C23×D411yescharacteristic
979C3×C4C23×D411yescharacteristic
980Dic3—24no—
981Dic3—24no—
982Dic3—24no—
983Dic3—42no—
984C23—22no—
985C23—24no—
986C23—22no—
987C23—34no—
988C23—42no—
989C23—44no—
990C23—41no—
991C23—41no—
992C23—616no—
993C23—62no—
994C23—62no—
995C23—64no—
996C23—62no—
997C23—82no—
998C23—124no—
999C23—242no—
1000C23—248no—
1001C23#93711yescharacteristic
1002C23#93711yescharacteristic
1003C23#93712yes—
1004C23C2×D3×D411yescharacteristic
1005C23C2×D3×D412yes—
1006Q8—22no—
1007Q8—24no—
1008Q8—22no—
1009Q8—22no—
1010Q8—34no—
1011Q8—41no—
1012Q8—41no—
1013Q8—616no—
1014Q8—62no—
1015Q8—62no—
1016Q8—62no—
1017Q8—62no—
1018Q8—62no—
1019Q8—64no—
1020Q8C22×#6714yes—
1021D4—24no—
1022D4—24no—
1023D4—28no—
1024D4—22no—
1025D4—22no—
1026D4—22no—
1027D4—24no—
1028D4—34no—
1029D4—44no—
1030D4—44no—
1031D4—41no—
1032D4—41no—
1033D4—616no—
1034D4—616no—
1035D4—616no—
1036D4—64no—
1037D4—68no—
1038D4—68no—
1039D4—68no—
1040D4—64no—
1041D4—62no—
1042D4—62no—
1043D4—62no—
1044D4—62no—
1045D4—64no—
1046D4—62no—
1047D4—1216no—
1048D4C22×#6714yes—
1049C2×C4—22no—
1050C2×C4—24no—
1051C2×C4—24no—
1052C2×C4—28no—
1053C2×C4—24no—
1054C2×C4—22no—
1055C2×C4—34no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—44no—
1059C2×C4—44no—
1060C2×C4—616no—
1061C2×C4—616no—
1062C2×C4—616no—
1063C2×C4—64no—
1064C2×C4—62no—
1065C2×C4—62no—
1066C2×C4—62no—
1067C2×C4—62no—
1068C2×C4—64no—
1069C2×C4—64no—
1070C2×C4—68no—
1071C2×C4—68no—
1072C2×C4—68no—
1073C2×C4—64no—
1074C2×C4—62no—
1075C2×C4—128no—
1076C2×C4—122no—
1077C2×C4#93712yes—
1078C2×C4#93711yescharacteristic
1079C2×C4#93712yes—
1080C2×C4#93712yes—
1081C2×C4#93712yes—
1082C2×C4#93712yes—
1083C2×C4#93711yescharacteristic
1084C2×C4C2×D3×D411yescharacteristic
1085C2×C4C2×D3×D412yes—
1086C2×C4C2×D3×D411yescharacteristic
1087C2×C4C2×D3×D412yes—
1088C2×C4C2×D3×D412yes—
1089C2×C4C2×D3×D411yescharacteristic
1090C2×C4C22×#6711yescharacteristic
1091C2×C4C22×#6712yes—
1092C2×C4C22×#6711yescharacteristic
1093C2×C4C22×#6712yes—
1094C2×C4C24×D311yescharacteristic
1095C8—24no—
1096C8—64no—
1097C2×C3—21no—
1098C2×C3—21no—
1099C2×C3—22no—
1100C2×C3—22no—
1101C2×C3—44no—
1102C2×C3—82no—
1103C2×C3#301812yescomplemented
1104C2×C3C22×#12011yescharacteristic
1105D3—44no—
1106D3—44no—
1107C22—22no—
1108C22—22no—
1109C22—22no—
1110C22—24no—
1111C22—42no—
1112C22—42no—
1113C22—44no—
1114C22—44no—
1115C22—42no—
1116C22—64no—
1117C22—64no—
1118C22—84no—
1119C22—82no—
1120C22—82no—
1121C22—124no—
1122C22—124no—
1123C22—124no—
1124C22—242no—
1125C22—244no—
1126C22—2416no—
1127C22C2×#93712yes—
1128C22C2×#93711yescharacteristic
1129C22C2×#93712yes—
1130C22C2×#93711yescharacteristic
1131C22C22×D3×D411yescharacteristic
1132C4—24no—
1133C4—42no—
1134C4—64no—
1135C4—64no—
1136C4—64no—
1137C4—122no—
1138C4C2×#93712yes—
1139C4C2×#93711yescharacteristic
1140C4C2×#93712yes—
1141C4C2×#93711yescharacteristic
1142C4C22×D3×D411yescharacteristic
1143C4C23×#6711yescharacteristic
1144C3C2×#301811yescharacteristic, complemented, Sylow
1145C2—21no—
1146C2—21no—
1147C2—22no—
1148C2—22no—
1149C2—44no—
1150C2—82no—
1151C2—124no—
1152C2—124no—
1153C2#8400412yesdirect product factor
1154C2C22×#93711yescharacteristic
subgroupG/H
centerC2×C4#937
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#575C2
socleC22×C3C2×#120
hypercenterC2×#575D3
hypocenterC3C2×#3018
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#575

Complements

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

NH ≅ G/Ntype
1. C2×#5964C2semidirect
2. C2×C3×#575C2semidirect
3. C2×#5832C2semidirect
4. C2×#5822C2semidirect
5. C22×#837C2semidirect
6. #84004C2direct (N × H)
7. C2×#5205C2semidirect
8. C2×#5202C2semidirect
9. C2×#5201C2semidirect
10. C2×#5198C2semidirect
11. C22×#825C2semidirect
12. C2×#5132C2semidirect
15. C22×C3×#41C22semidirect
19. #5964C22semidirect
33. C3×#575C22semidirect
35. C2×C3×#137C22semidirect
37. C2×C3×AGL(1,ℤ/8)C22semidirect
39. C22×C3×M16C22semidirect
41. #5832C22semidirect
44. #5822C22semidirect
47. C2×#947C22semidirect
48. C2×#944C22semidirect
49. C2×#942C22semidirect
50. C2×#940C22semidirect
52. C2×#936C22semidirect
53. C2×#932C22semidirect
55. C22×C4×Dic3C22semidirect
56. C22×#208C22semidirect
57. C2×#837C22semidirect
58. C2×#837C22semidirect
59. C2×#837C22semidirect
60. #5205C22semidirect
61. #5202C22semidirect
62. #5201C22semidirect
63. #5198C22semidirect
64. C2×#825C22semidirect
65. C2×#825C22semidirect
66. C2×#825C22semidirect
67. C2×#824C22semidirect
68. #5132C22semidirect
69. C2×#823C22semidirect
72. C2×#575D3semidirect
93. C2×C3×#41D4semidirect
94. C2×C3×#41D4semidirect
97. C2×C3×#41C23semidirect
98. C22×C3×Q8D4semidirect
102. C22×C3×D4D4semidirect
163. C2×#235D4semidirect
164. C2×#235D4semidirect
169. C22×D12D4semidirect
175. C22×Dic6D4semidirect
179. C3×#137C23semidirect
182. C3×AGL(1,ℤ/8)C23semidirect
191. C2×C3×M16C23semidirect
198. #947C23semidirect
200. #944C23semidirect
203. #942C23semidirect
206. #940C23semidirect
209. #936C23semidirect
212. #932C23semidirect
221. C2×C4×Dic3C23semidirect
225. C2×#208C23semidirect
227. #837C23semidirect
228. #837C23semidirect
229. #825C23semidirect
230. #825C23semidirect
231. #824C23semidirect
232. #823C23semidirect
250. C22×#41C2×D3semidirect
254. #575C2×D3semidirect
258. C2×#137C2×D3semidirect
262. C2×AGL(1,ℤ/8)C2×D3semidirect
266. C22×M16C2×D3semidirect
311. C3×#41C2×D4semidirect
321. C2×C3×Q8C2×D4semidirect
339. C2×C3×D4C2×D4semidirect
421. #235C2×D4semidirect
434. C2×D12C2×D4semidirect
458. C2×Dic6C2×D4semidirect
547. C2×#41#67semidirect
548. C2×#41#67semidirect
551. C2×#41C22×D3semidirect
557. C22×Q8#67semidirect
572. C22×D4#67semidirect
586. #137C22×D3semidirect
592. AGL(1,ℤ/8)C22×D3semidirect
610. C2×M16C22×D3semidirect
805. #41C2×#67semidirect
831. C2×Q8C2×#67semidirect
881. C2×D4C2×#67semidirect
1103. C2×C3#3018semidirect
1144. C3C2×#3018semidirect
1153. C2#84004direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#59642
C2×C3×#5752
C2×#58322
C2×#58222
C22×#8372
#840042
C2×#52052
C2×#52022
C2×#52012
C2×#51982
C22×#8252
C2×#51322
C2×#30183