Finite Group Databasebeta

← C2×#78986 #11661817

Subgroups — C2×#78986 #11661817

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×#5822C211yesmaximal, characteristic, complemented
3C2×#5748C211yesmaximal, characteristic, complemented
4C2×#5477C211yesmaximal, characteristic, complemented
5C22×C3×#104C211yesmaximal, characteristic, complemented
6C2×#5132C211yesmaximal, characteristic, complemented
7C22×#805C211yesmaximal, characteristic, complemented
8C2×#4826C212yesmaximal, complemented
9C2×#4827C212yesmaximal, complemented
10#78986C2116yesmaximal, direct product factor
11C2×#4825C212yesmaximal, complemented
12C2×#4822C212yesmaximal, complemented
13C2×#3018—31nomaximal, Sylow
14C22×C3×#41C2211yescharacteristic
15#5964—24no—
16#5964—24no—
17#5964—24no—
18#5964C2218yescomplemented
19C2×#1010—21no—
20C2×#1010C2212yes—
21C2×#1009—21no—
22C2×#1009C2212yes—
23C2×D3×#41—22no—
24C2×D3×#41—22no—
25C2×#1007—21no—
26C2×#1004—21no—
27C2×#1004—22no—
28C22×#235—22no—
29C22×#235C2211yescharacteristic
30C22×#235C2211yescharacteristic
31C22×#235C2211yescharacteristic, complemented
32C22×C3×M16C2211yescharacteristic, complemented
33C22×C3×C42C2211yescharacteristic, complemented
34C2×#951C2212yescomplemented
35#5822—24no—
36#5822C2218yescomplemented
37C2×#950—22no—
38C2×#949C2212yescomplemented
39C2×#942—21no—
40C2×#932—21no—
41C2×#930—22no—
42C22×#208C2211yescharacteristic, complemented
43#5748—24no—
44#5748C2218yescomplemented
45C2×#909—21no—
46C2×#909C2212yescomplemented
47C2×#908—21no—
48C2×#908C2212yescomplemented
49C2×#904—22no—
50#5477—24no—
51#5477C2218yescomplemented
52C2×#875C2211yescharacteristic, complemented
53C2×#875C2211yescharacteristic, complemented
54C2×#874C2211yescharacteristic, complemented
55C2×C4×D12—22no—
56C2×#869C2211yescharacteristic, complemented
57C2×C3×#104C2212yescomplemented
58C2×C3×#104C2212yescomplemented
59C2×C3×#104C2218yescomplemented
60C2×#824C2212yescomplemented
61#5132C2218yescomplemented
62C2×#823C2212yescomplemented
63C2×#805C2212yescomplemented
64C2×#805C2212yescomplemented
65C2×#805C2218yescomplemented
66#4827C22116yescomplemented
67#4826C22116yescomplemented
68#4825C22116yescomplemented
69#4822C22116yescomplemented
70C2×#585—31no—
71C2×#575—31no—
72C2×#575—31no—
73C2×#532—31no—
74#3018—316no—
75C2×#456—32no—
76C2×#454—32no—
77C2×#455—32no—
78C2×#453—32no—
79C22×#104—31no—
80C22×#104D311yescharacteristic, complemented
81C2×#413—31no—
82C2×C3×#41—21no—
83C2×C3×#41—21no—
84C2×C3×#41—22no—
85C2×C3×#41—22no—
86C2×C3×#41D412yescomplemented
87C2×C3×#41D414yescomplemented
88C2×C3×#41C2312yes—
89C2×C3×#41C2314yes—
90C22×C3×Q8D411yescharacteristic, complemented
91C22×C3×D4—21no—
92C22×C3×D4D411yescharacteristic, complemented
93C23×C3×C4—21no—
94C23×C3×C4—21no—
95C23×C3×C4C2311yescharacteristic
96C22×#67—24no—
97C22×#67—21no—
98C22×#67—21no—
99C22×#67D412yes—
100#1010—28no—
101#1010—24no—
102#1010—24no—
103#1010—24no—
104#1010—28no—
105#1010C2318yes—
106#1009—28no—
107#1009—24no—
108#1009—24no—
109#1009—24no—
110#1009—28no—
111#1009C2318yes—
112D3×#41—216no—
113D3×#41—216no—
114D3×#41—216no—
115D3×#41—216no—
116#1007—28no—
117#1007—28no—
118C2×#239—22no—
119C2×#239—22no—
120C2×D3×Q8—22no—
121C2×D3×Q8—22no—
122#1004—216no—
123#1004—28no—
124#1004—28no—
125#1004—216no—
126C2×#237—24no—
127C2×#237—22no—
128C2×#237—22no—
129C2×#237—24no—
130C2×D3×D4—24no—
131C2×D3×D4—22no—
132C2×D3×D4—24no—
133C2×D3×D4—22no—
134C2×#235—24no—
135C2×#235—24no—
136C2×#235—216no—
137C2×#235—21no—
138C2×#235—21no—
139C2×#235—21no—
140C2×#235—21no—
141C2×#235—21no—
142C2×#235—21no—
143C2×#235—22no—
144C2×#235—22no—
145C2×#235—22no—
146C2×#235—22no—
147C2×#235—216no—
148C2×#235—22no—
149C2×#235—22no—
150C2×#235—21no—
151C2×#235—21no—
152C2×#235—22no—
153C2×#235—21no—
154C2×#235—21no—
155C2×#235—22no—
156C2×#235—22no—
157C2×#235D414yes—
158C2×#235D412yescomplemented
159C2×#235D414yescomplemented
160C2×#235C2312yes—
161C2×#235C2314yes—
162C2×#235C2314yes—
163C2×#235C2314yescomplemented
164C22×D12—22no—
165C22×D12—22no—
166C22×D12D411yescharacteristic, complemented
167C22×D12C2311yescharacteristic
168C22×D12C2311yescharacteristic
169C22×C4×D3—24no—
170C22×C4×D3—21no—
171C22×C4×D3—21no—
172C22×C4×D3D412yes—
173C22×Dic6—22no—
174C22×Dic6D411yescharacteristic, complemented
175C22×Dic6C2311yescharacteristic
176C22×Dic6C2311yescharacteristic
177C2×C3×M16—21no—
178C2×C3×M16—22no—
179C2×C3×M16C2312yes—
180C2×C3×M16C2314yescomplemented
181C22×C3×C8—21no—
182C2×C3×C42—21no—
183C2×C3×C42—22no—
184C2×C3×C42C2311yescharacteristic
185C2×C3×C42C2311yescharacteristic
186C2×C3×C42C2314yescomplemented
187#951—24no—
188#951C2318yescomplemented
189#950—216no—
190#949—24no—
191#949C2318yescomplemented
192C2×#216—22no—
193#942—28no—
194C2×#215—22no—
195C2×#214—22no—
196#932—28no—
197C2×#213—22no—
198#930—216no—
199C2×(C2×D3)⋊C4—22no—
200C2×(C2×D3)⋊C4—22no—
201C2×C4⋊Dic3—22no—
202C2×#208—21no—
203C2×#208—22no—
204C2×#208C2312yes—
205C2×#208C2314yescomplemented
206C22×C3⋊C8—21no—
207#909—24no—
208#909—28no—
209#909C2318yescomplemented
210#908—24no—
211#908—28no—
212#908C2318yescomplemented
213C2×Dic12—22no—
214#904—216no—
215C2×D24—22no—
216C2×#204—22no—
217C2×#204—22no—
218#875—22no—
219#875—22no—
220#875C2314yescomplemented
221#875C2314yescomplemented
222#874—22no—
223#874C2314yescomplemented
224C4×D12—216no—
225#869—22no—
226#869C2314yescomplemented
227C3×#104C2318yescomplemented
228C3×#104C2318yescomplemented
229#824C2318yescomplemented
230#823C2318yescomplemented
231#805C2318yescomplemented
232#805C2318yescomplemented
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—31no—
247C22×#41—62no—
248C22×#41—62no—
249C22×#41—62no—
250C22×#41C2×D311yescharacteristic
251#575—38no—
252#575—38no—
253#575—64no—
254#575—64no—
255C2×#137—32no—
256C2×#137—32no—
257C2×#137—61no—
258C2×#137—61no—
259C2×AGL(1,ℤ/8)—32no—
260C2×AGL(1,ℤ/8)—32no—
261C2×AGL(1,ℤ/8)—61no—
262C2×AGL(1,ℤ/8)—61no—
263C2×#135—62no—
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×C42C2×D311yescharacteristic, complemented
276#456—316no—
277#455—316no—
278#454—316no—
279#453—316no—
280C2×#104—32no—
281C2×#104—32no—
282C2×#104—38no—
283C2×#104C2×D312yescomplemented
284C2×#104C2×D312yescomplemented
285C2×#104C2×D318yescomplemented
286#413—38no—
287C2×#101—32no—
288C2×#100—32no—
289C24×C3—21no—
290C24×C3C2×D411yescharacteristic
291C23×D3—24no—
292C23×D3—21no—
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×#41C2×D414yes—
303C3×#41C2×D418yescomplemented
304C3×#41C2414yes—
305C2×C3×Q8—21no—
306C2×C3×Q8—22no—
307C2×C3×Q8C2×D412yes—
308C2×C3×Q8C2×D414yescomplemented
309C2×C3×D4—22no—
310C2×C3×D4—24no—
311C2×C3×D4—22no—
312C2×C3×D4—24no—
313C2×C3×D4—21no—
314C2×C3×D4—22no—
315C2×C3×D4C2×D412yes—
316C2×C3×D4C2×D414yescomplemented
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4—22no—
320C22×C3×C4—24no—
321C22×C3×C4—22no—
322C22×C3×C4—24no—
323C22×C3×C4—21no—
324C22×C3×C4—24no—
325C22×C3×C4—44no—
326C22×C3×C4C2×D411yescharacteristic
327C22×C3×C4C2×D411yescharacteristic
328C22×C3×C4C2×D412yes—
329C22×C3×C4C2×D411yescharacteristic
330C22×C3×C4C2×D412yes—
331C22×C3×C4C2×D411yescharacteristic
332C22×C3×C4C2×D411yescharacteristic
333C22×C3×C4C2×D412yes—
334C22×C3×C4C2411yescharacteristic
335C22×C3×C4C2412yes—
336C2×#67—24no—
337C2×#67—24no—
338C2×#67—232no—
339C2×#67—22no—
340C2×#67—22no—
341C2×#67—22no—
342C2×#67—24no—
343C2×#67—24no—
344C2×#67—22no—
345C2×#67—24no—
346C2×#67—24no—
347C2×#67—41no—
348C2×#67—41no—
349C2×#67—42no—
350C2×#67C2×D418yes—
351C22×Dic3—24no—
352C22×Dic3—21no—
353C22×Dic3—21no—
354C22×Dic3C2×D412yes—
355#239—28no—
356#239—216no—
357#239—28no—
358D3×Q8—28no—
359D3×Q8—216no—
360D3×Q8—28no—
361#237—216no—
362#237—232no—
363#237—28no—
364#237—216no—
365#237—28no—
366#237—216no—
367D3×D4—232no—
368D3×D4—216no—
369D3×D4—28no—
370D3×D4—216no—
371D3×D4—216no—
372D3×D4—28no—
373#235—232no—
374#235—232no—
375#235—28no—
376#235—28no—
377#235—24no—
378#235—24no—
379#235—24no—
380#235—24no—
381#235—24no—
382#235—24no—
383#235—24no—
384#235—24no—
385#235—24no—
386#235—24no—
387#235—24no—
388#235—24no—
389#235—22no—
390#235—22no—
391#235—24no—
392#235—28no—
393#235—24no—
394#235—24no—
395#235—24no—
396#235—24no—
397#235—28no—
398#235—42no—
399#235—42no—
400#235—42no—
401#235—42no—
402#235C2×D414yes—
403#235C2×D418yescomplemented
404#235C2414yes—
405C2×D12—24no—
406C2×D12—28no—
407C2×D12—21no—
408C2×D12—22no—
409C2×D12—21no—
410C2×D12—21no—
411C2×D12—21no—
412C2×D12—21no—
413C2×D12—28no—
414C2×D12—21no—
415C2×D12—21no—
416C2×D12—21no—
417C2×D12—21no—
418C2×D12—28no—
419C2×D12—21no—
420C2×D12—48no—
421C2×D12C2×D412yes—
422C2×D12C2×D412yes—
423C2×D12C2×D414yescomplemented
424C2×D12C2412yes—
425C2×D12C2412yes—
426C2×C4×D3—24no—
427C2×C4×D3—24no—
428C2×C4×D3—232no—
429C2×C4×D3—22no—
430C2×C4×D3—22no—
431C2×C4×D3—24no—
432C2×C4×D3—22no—
433C2×C4×D3—24no—
434C2×C4×D3—22no—
435C2×C4×D3—24no—
436C2×C4×D3—24no—
437C2×C4×D3—41no—
438C2×C4×D3—42no—
439C2×C4×D3—41no—
440C2×C4×D3C2×D418yes—
441C2×Dic6—24no—
442C2×Dic6—28no—
443C2×Dic6—21no—
444C2×Dic6—22no—
445C2×Dic6—21no—
446C2×Dic6—21no—
447C2×Dic6—21no—
448C2×Dic6—21no—
449C2×Dic6—28no—
450C2×Dic6—21no—
451C2×Dic6—21no—
452C2×Dic6—21no—
453C2×Dic6—21no—
454C2×Dic6—21no—
455C2×Dic6C2×D412yes—
456C2×Dic6C2×D412yes—
457C2×Dic6C2×D414yescomplemented
458C2×Dic6C2412yes—
459C2×Dic6C2412yes—
460C3×M16—22no—
461C3×M16—24no—
462C3×M16C2414yes—
463C2×C3×C8—22no—
464C2×C3×C8—24no—
465C3×C42—21no—
466C3×C42—24no—
467C3×C42—21no—
468C3×C42C2412yes—
469C3×C42C2412yes—
470#216—28no—
471#215—28no—
472#214—28no—
473#213—28no—
474(C2×D3)⋊C4—28no—
475(C2×D3)⋊C4—28no—
476C4⋊Dic3—28no—
477#208—22no—
478#208—24no—
479#208C2414yes—
480C2×C3⋊C8—22no—
481C2×C3⋊C8—24no—
482Dic12—28no—
483D24—28no—
484#204—28no—
485#204—28no—
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—34no—
509C2×#41—34no—
510C2×#41—32no—
511C2×#41—34no—
512C2×#41—32no—
513C2×#41—34no—
514C2×#41—34no—
515C2×#41—62no—
516C2×#41—62no—
517C2×#41—616no—
518C2×#41—64no—
519C2×#41—64no—
520C2×#41—616no—
521C2×#41—64no—
522C2×#41—616no—
523C2×#41—64no—
524C2×#41—62no—
525C2×#41—62no—
526C2×#41—616no—
527C2×#41—616no—
528C2×#41—616no—
529C2×#41—62no—
530C2×#41—62no—
531C2×#41—61no—
532C2×#41—61no—
533C2×#41—61no—
534C2×#41—62no—
535C2×#41—62no—
536C2×#41—61no—
537C2×#41—61no—
538C2×#41—61no—
539C2×#41—62no—
540C2×#41—62no—
541C2×#41—62no—
542C2×#41—61no—
543C2×#41—61no—
544C2×#41—62no—
545C2×#41—61no—
546C2×#41—61no—
547C2×#41—62no—
548C2×#41D1212yescomplemented
549C2×#41D1214yescomplemented
550C2×#41C22×D312yes—
551C2×#41C22×D314yes—
552C22×Q8—31no—
553C22×Q8—31no—
554C22×Q8—31no—
555C22×Q8—62no—
556C22×Q8—62no—
557C22×Q8—62no—
558C22×Q8D1211yescharacteristic, complemented
559C22×D4—21no—
560C22×D4—32no—
561C22×D4—31no—
562C22×D4—31no—
563C22×D4—31no—
564C22×D4—62no—
565C22×D4—62no—
566C22×D4—64no—
567C22×D4—64no—
568C22×D4—62no—
569C22×D4—64no—
570C22×D4—61no—
571C22×D4—62no—
572C22×D4—61no—
573C22×D4D1211yescharacteristic, complemented
574C23×C4—21no—
575C23×C4—21no—
576C23×C4—32no—
577C23×C4—64no—
578C23×C4—61no—
579C23×C4—61no—
580C23×C4C22×D311yescharacteristic
581#137—38no—
582#137—38no—
583#137—68no—
584#137—64no—
585#137—64no—
586#137—68no—
587AGL(1,ℤ/8)—38no—
588AGL(1,ℤ/8)—38no—
589AGL(1,ℤ/8)—68no—
590AGL(1,ℤ/8)—64no—
591AGL(1,ℤ/8)—64no—
592AGL(1,ℤ/8)—68no—
593#135—616no—
594#135—616no—
595C2×Q16—62no—
596C2×Q16—62no—
597C2×SD16—62no—
598C2×SD16—62no—
599C2×SD16—62no—
600C2×SD16—62no—
601C2×D8—62no—
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—21no—
627C2×C42—22no—
628C2×C42C22×D311yescharacteristic
629C2×C42C22×D311yescharacteristic
630C2×C42C22×D314yescomplemented
631#104—38no—
632#104—38no—
633#104C22×D318yescomplemented
634#104C22×D318yescomplemented
635#101—38no—
636#100—38no—
637C23×C3—22no—
638C23×C3—24no—
639C23×C3—42no—
640C23×C3—82no—
641C23×C3#12011yescharacteristic
642C23×C3#12011yescharacteristic
643C23×C3#12012yes—
644C23×C3C22×D411yescharacteristic
645C23×C3C22×D412yes—
646C22×D3—22no—
647C22×D3—22no—
648C22×D3—216no—
649C22×D3—22no—
650C22×D3—24no—
651C22×D3—22no—
652C22×D3—44no—
653C22×D3—44no—
654C22×D3—41no—
655C22×D3—41no—
656C22×D3—82no—
657C22×D3—88no—
658C22×D3C22×D414yes—
659C3×Q8—22no—
660C3×Q8—24no—
661C3×Q8C22×D414yes—
662C3×D4—24no—
663C3×D4—28no—
664C3×D4—24no—
665C3×D4—22no—
666C3×D4—24no—
667C3×D4C22×D414yes—
668C2×C3×C4—24no—
669C2×C3×C4—22no—
670C2×C3×C4—24no—
671C2×C3×C4—22no—
672C2×C3×C4—24no—
673C2×C3×C4—28no—
674C2×C3×C4—24no—
675C2×C3×C4—22no—
676C2×C3×C4—48no—
677C2×C3×C4—42no—
678C2×C3×C4#12011yescharacteristic
679C2×C3×C4#12012yes—
680C2×C3×C4#12012yes—
681C2×C3×C4#12012yes—
682C2×C3×C4#12012yes—
683C2×C3×C4#12012yes—
684C2×C3×C4#12011yescharacteristic
685C2×C3×C4C22×D411yescharacteristic
686C2×C3×C4C22×D412yes—
687C2×C3×C4C22×D411yescharacteristic
688C2×C3×C4C22×D412yes—
689C2×C3×C4C22×D411yescharacteristic
690C2×C3×C4C22×D412yes—
691C2×C3×C4C22×D411yescharacteristic
692C2×C3×C4C22×D412yes—
693C2×C3×C4C22×D411yescharacteristic
694C2×C3×C4C22×D412yes—
695C2×C3×C4C2511yescharacteristic
696#67—216no—
697#67—216no—
698#67—28no—
699#67—28no—
700#67—28no—
701#67—24no—
702#67—24no—
703#67—44no—
704#67—44no—
705C2×Dic3—216no—
706C2×Dic3—22no—
707C2×Dic3—22no—
708C2×Dic3—22no—
709C2×Dic3—24no—
710C2×Dic3—22no—
711C2×Dic3—41no—
712C2×Dic3—41no—
713C2×Dic3C22×D414yes—
714D12—216no—
715D12—22no—
716D12—22no—
717D12—22no—
718D12—24no—
719D12—22no—
720D12—22no—
721D12—22no—
722D12—22no—
723D12—416no—
724D12—41no—
725D12—41no—
726D12C22×D414yes—
727C4×D3—216no—
728C4×D3—216no—
729C4×D3—28no—
730C4×D3—28no—
731C4×D3—24no—
732C4×D3—28no—
733C4×D3—24no—
734C4×D3—44no—
735C4×D3—44no—
736Dic6—216no—
737Dic6—22no—
738Dic6—22no—
739Dic6—22no—
740Dic6—24no—
741Dic6—22no—
742Dic6—22no—
743Dic6—22no—
744Dic6—22no—
745Dic6—41no—
746Dic6—41no—
747Dic6C22×D414yes—
748C3×C8—24no—
749C3⋊C8—24no—
750C24—21no—
751C24—32no—
752C24—64no—
753C24—61no—
754C24—61no—
755C24D3×D411yescharacteristic
756#41—24no—
757#41—24no—
758#41—24no—
759#41—24no—
760#41—24no—
761#41—22no—
762#41—22no—
763#41—38no—
764#41—34no—
765#41—34no—
766#41—68no—
767#41—68no—
768#41—632no—
769#41—632no—
770#41—68no—
771#41—68no—
772#41—616no—
773#41—616no—
774#41—632no—
775#41—616no—
776#41—68no—
777#41—616no—
778#41—68no—
779#41—68no—
780#41—68no—
781#41—64no—
782#41—64no—
783#41—64no—
784#41—64no—
785#41—64no—
786#41—64no—
787#41—64no—
788#41—64no—
789#41—62no—
790#41—64no—
791#41—64no—
792#41—64no—
793#41—64no—
794#41—64no—
795#41—62no—
796#41—64no—
797#41—64no—
798#41—64no—
799#41—64no—
800#41—122no—
801#41—122no—
802#41—122no—
803#41—122no—
804#41C2×D1214yes—
805#41C2×D1218yescomplemented
806#41C23×D314yes—
807C2×Q8—21no—
808C2×Q8—22no—
809C2×Q8—32no—
810C2×Q8—32no—
811C2×Q8—32no—
812C2×Q8—34no—
813C2×Q8—32no—
814C2×Q8—68no—
815C2×Q8—64no—
816C2×Q8—68no—
817C2×Q8—616no—
818C2×Q8—68no—
819C2×Q8—68no—
820C2×Q8—61no—
821C2×Q8—62no—
822C2×Q8—61no—
823C2×Q8—61no—
824C2×Q8—61no—
825C2×Q8—61no—
826C2×Q8—61no—
827C2×Q8—61no—
828C2×Q8—61no—
829C2×Q8—61no—
830C2×Q8—61no—
831C2×Q8C2×D1212yes—
832C2×Q8C2×D1214yescomplemented
833C2×D4—22no—
834C2×D4—24no—
835C2×D4—22no—
836C2×D4—24no—
837C2×D4—21no—
838C2×D4—22no—
839C2×D4—38no—
840C2×D4—32no—
841C2×D4—34no—
842C2×D4—32no—
843C2×D4—32no—
844C2×D4—32no—
845C2×D4—68no—
846C2×D4—64no—
847C2×D4—68no—
848C2×D4—68no—
849C2×D4—616no—
850C2×D4—616no—
851C2×D4—632no—
852C2×D4—616no—
853C2×D4—68no—
854C2×D4—64no—
855C2×D4—64no—
856C2×D4—632no—
857C2×D4—62no—
858C2×D4—62no—
859C2×D4—64no—
860C2×D4—62no—
861C2×D4—64no—
862C2×D4—62no—
863C2×D4—64no—
864C2×D4—68no—
865C2×D4—64no—
866C2×D4—61no—
867C2×D4—62no—
868C2×D4—61no—
869C2×D4—61no—
870C2×D4—61no—
871C2×D4—61no—
872C2×D4—61no—
873C2×D4—61no—
874C2×D4—61no—
875C2×D4—61no—
876C2×D4—61no—
877C2×D4—128no—
878C2×D4—121no—
879C2×D4—121no—
880C2×D4—122no—
881C2×D4C2×D1212yes—
882C2×D4C2×D1214yescomplemented
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—24no—
886C22×C4—22no—
887C22×C4—22no—
888C22×C4—24no—
889C22×C4—21no—
890C22×C4—24no—
891C22×C4—32no—
892C22×C4—38no—
893C22×C4—44no—
894C22×C4—64no—
895C22×C4—64no—
896C22×C4—632no—
897C22×C4—64no—
898C22×C4—61no—
899C22×C4—62no—
900C22×C4—64no—
901C22×C4—64no—
902C22×C4—62no—
903C22×C4—62no—
904C22×C4—62no—
905C22×C4—64no—
906C22×C4—61no—
907C22×C4—64no—
908C22×C4—121no—
909C22×C4—122no—
910C22×C4—121no—
911C22×C4C2×D1211yescharacteristic
912C22×C4C2×D1212yes—
913C22×C4C2×D1211yescharacteristic
914C22×C4D3×D412yes—
915C22×C4D3×D411yescharacteristic
916C22×C4D3×D411yescharacteristic
917C22×C4D3×D412yes—
918C22×C4D3×D411yescharacteristic
919C22×C4C23×D311yescharacteristic
920C22×C4C23×D312yes—
921Q16—68no—
922Q16—68no—
923SD16—68no—
924SD16—68no—
925SD16—68no—
926SD16—68no—
927D8—68no—
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—21no—
943C42—21no—
944C42—24no—
945C42C23×D312yes—
946C42C23×D312yes—
947C22×C3—22no—
948C22×C3—22no—
949C22×C3—22no—
950C22×C3—24no—
951C22×C3—42no—
952C22×C3—42no—
953C22×C3—44no—
954C22×C3—84no—
955C22×C3C2×#12011yescharacteristic
956C22×C3C2×#12012yes—
957C22×C3C2×#12012yes—
958C22×C3C2×#12011yescharacteristic
959C22×C3C23×D411yescharacteristic
960C2×D3—24no—
961C2×D3—24no—
962C2×D3—44no—
963C2×D3—44no—
964C2×D3—44no—
965C2×D3—44no—
966C2×D3—42no—
967C2×D3—82no—
968C2×D3—84no—
969C2×D3—816no—
970C2×D3—82no—
971C2×D3—82no—
972C3×C4—24no—
973C3×C4—24no—
974C3×C4—42no—
975C3×C4C2×#12011yescharacteristic
976C3×C4C2×#12011yescharacteristic
977C3×C4C2×#12012yes—
978C3×C4C2×#12012yes—
979C3×C4C23×D411yescharacteristic
980C3×C4C23×D411yescharacteristic
981Dic3—24no—
982Dic3—24no—
983Dic3—42no—
984C23—22no—
985C23—24no—
986C23—34no—
987C23—42no—
988C23—616no—
989C23—62no—
990C23—62no—
991C23—64no—
992C23—62no—
993C23—62no—
994C23—82no—
995C23—124no—
996C23—124no—
997C23—121no—
998C23—121no—
999C23—242no—
1000C23—248no—
1001C23#88211yescharacteristic
1002C23#88211yescharacteristic
1003C23#88212yes—
1004C23C2×D3×D411yescharacteristic
1005C23C2×D3×D412yes—
1006Q8—22no—
1007Q8—24no—
1008Q8—34no—
1009Q8—616no—
1010Q8—62no—
1011Q8—62no—
1012Q8—62no—
1013Q8—62no—
1014Q8—62no—
1015Q8—64no—
1016Q8—62no—
1017Q8—62no—
1018Q8—121no—
1019Q8—121no—
1020Q8C22×D1214yes—
1021D4—24no—
1022D4—24no—
1023D4—28no—
1024D4—22no—
1025D4—24no—
1026D4—34no—
1027D4—616no—
1028D4—616no—
1029D4—616no—
1030D4—64no—
1031D4—68no—
1032D4—68no—
1033D4—68no—
1034D4—64no—
1035D4—62no—
1036D4—62no—
1037D4—62no—
1038D4—62no—
1039D4—62no—
1040D4—62no—
1041D4—64no—
1042D4—62no—
1043D4—1216no—
1044D4—124no—
1045D4—124no—
1046D4—121no—
1047D4—121no—
1048D4C22×D1214yes—
1049C2×C4—24no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—28no—
1055C2×C4—24no—
1056C2×C4—22no—
1057C2×C4—34no—
1058C2×C4—48no—
1059C2×C4—42no—
1060C2×C4—616no—
1061C2×C4—616no—
1062C2×C4—616no—
1063C2×C4—62no—
1064C2×C4—62no—
1065C2×C4—62no—
1066C2×C4—64no—
1067C2×C4—64no—
1068C2×C4—68no—
1069C2×C4—68no—
1070C2×C4—68no—
1071C2×C4—64no—
1072C2×C4—62no—
1073C2×C4—121no—
1074C2×C4—121no—
1075C2×C4—124no—
1076C2×C4—124no—
1077C2×C4#88212yes—
1078C2×C4#88211yescharacteristic
1079C2×C4#88212yes—
1080C2×C4#88212yes—
1081C2×C4#88212yes—
1082C2×C4#88212yes—
1083C2×C4#88211yescharacteristic
1084C2×C4C22×D1211yescharacteristic
1085C2×C4C22×D1212yes—
1086C2×C4C22×D1211yescharacteristic
1087C2×C4C22×D1212yes—
1088C2×C4C2×D3×D411yescharacteristic
1089C2×C4C2×D3×D412yes—
1090C2×C4C2×D3×D412yes—
1091C2×C4C2×D3×D411yescharacteristic
1092C2×C4C2×D3×D412yes—
1093C2×C4C2×D3×D411yescharacteristic
1094C2×C4C24×D311yescharacteristic
1095C8—24no—
1096C8—64no—
1097C2×C3—21no—
1098C2×C3—21no—
1099C2×C3—22no—
1100C2×C3—22no—
1101C2×C3—44no—
1102C2×C3#301812yescomplemented
1103C2×C3C22×#12011yescharacteristic
1104D3—44no—
1105D3—44no—
1106D3—82no—
1107C22—22no—
1108C22—22no—
1109C22—22no—
1110C22—24no—
1111C22—42no—
1112C22—42no—
1113C22—44no—
1114C22—64no—
1115C22—64no—
1116C22—84no—
1117C22—124no—
1118C22—124no—
1119C22—124no—
1120C22—124no—
1121C22—122no—
1122C22—242no—
1123C22—244no—
1124C22—242no—
1125C22—2416no—
1126C22—242no—
1127C22C2×#88212yes—
1128C22C2×#88211yescharacteristic
1129C22C2×#88212yes—
1130C22C2×#88211yescharacteristic
1131C22C22×D3×D411yescharacteristic
1132C4—24no—
1133C4—24no—
1134C4—42no—
1135C4—64no—
1136C4—64no—
1137C4—122no—
1138C4C2×#88212yes—
1139C4C2×#88211yescharacteristic
1140C4C2×#88212yes—
1141C4C2×#88211yescharacteristic
1142C4C23×D1211yescharacteristic
1143C4C22×D3×D411yescharacteristic
1144C3C2×#301811yescharacteristic, complemented, Sylow
1145C2—21no—
1146C2—22no—
1147C2—21no—
1148C2—22no—
1149C2—44no—
1150C2—124no—
1151C2—124no—
1152C2—242no—
1153C2#7898612yesdirect product factor
1154C2C22×#88211yescharacteristic
subgroupG/H
centerC2×C4#882
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC22×C3×#104C2
socleC22×C3C2×#120
hypercenterC22×#104D3
hypocenterC3C2×#3018
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×#104

Complements

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

NH ≅ G/Ntype
1. C2×#5964C2semidirect
2. C2×#5822C2semidirect
3. C2×#5748C2semidirect
4. C2×#5477C2semidirect
5. C22×C3×#104C2semidirect
6. C2×#5132C2semidirect
7. C22×#805C2semidirect
8. C2×#4826C2semidirect
9. C2×#4827C2semidirect
10. #78986C2direct (N × H)
11. C2×#4825C2semidirect
12. C2×#4822C2semidirect
18. #5964C22semidirect
31. C22×#235C22semidirect
32. C22×C3×M16C22semidirect
33. C22×C3×C42C22semidirect
34. C2×#951C22semidirect
36. #5822C22semidirect
38. C2×#949C22semidirect
42. C22×#208C22semidirect
44. #5748C22semidirect
46. C2×#909C22semidirect
48. C2×#908C22semidirect
51. #5477C22semidirect
52. C2×#875C22semidirect
53. C2×#875C22semidirect
54. C2×#874C22semidirect
56. C2×#869C22semidirect
57. C2×C3×#104C22semidirect
58. C2×C3×#104C22semidirect
59. C2×C3×#104C22semidirect
60. C2×#824C22semidirect
61. #5132C22semidirect
62. C2×#823C22semidirect
63. C2×#805C22semidirect
64. C2×#805C22semidirect
65. C2×#805C22semidirect
66. #4827C22semidirect
67. #4826C22semidirect
68. #4825C22semidirect
69. #4822C22semidirect
80. C22×#104D3semidirect
86. C2×C3×#41D4semidirect
87. C2×C3×#41D4semidirect
90. C22×C3×Q8D4semidirect
92. C22×C3×D4D4semidirect
158. C2×#235D4semidirect
159. C2×#235D4semidirect
163. C2×#235C23semidirect
166. C22×D12D4semidirect
174. C22×Dic6D4semidirect
180. C2×C3×M16C23semidirect
186. C2×C3×C42C23semidirect
188. #951C23semidirect
191. #949C23semidirect
205. C2×#208C23semidirect
209. #909C23semidirect
212. #908C23semidirect
220. #875C23semidirect
221. #875C23semidirect
223. #874C23semidirect
226. #869C23semidirect
227. C3×#104C23semidirect
228. C3×#104C23semidirect
229. #824C23semidirect
230. #823C23semidirect
231. #805C23semidirect
232. #805C23semidirect
266. C22×M16C2×D3semidirect
275. C22×C42C2×D3semidirect
283. C2×#104C2×D3semidirect
284. C2×#104C2×D3semidirect
285. C2×#104C2×D3semidirect
303. C3×#41C2×D4semidirect
308. C2×C3×Q8C2×D4semidirect
316. C2×C3×D4C2×D4semidirect
403. #235C2×D4semidirect
423. C2×D12C2×D4semidirect
457. C2×Dic6C2×D4semidirect
548. C2×#41D12semidirect
549. C2×#41D12semidirect
558. C22×Q8D12semidirect
573. C22×D4D12semidirect
610. C2×M16C22×D3semidirect
630. C2×C42C22×D3semidirect
633. #104C22×D3semidirect
634. #104C22×D3semidirect
805. #41C2×D12semidirect
832. C2×Q8C2×D12semidirect
882. C2×D4C2×D12semidirect
1102. C2×C3#3018semidirect
1144. C3C2×#3018semidirect
1153. C2#78986direct (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×#58222
C2×#57482
C2×#54772
C22×C3×#1042
C2×#51322
C22×#8052
C2×#48262
C2×#48272
#789862
C2×#48252
C2×#48222
C2×#30183