Finite Group Databasebeta

← C2×#87207 #11709026

Subgroups — C2×#87207 #11709026

Order 768.

11138 conjugacy classes of subgroups.

The subgroup lattice has 1120 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5968C211yesmaximal, characteristic, complemented
2C2×D3×H(5,𝔽2)C211yesmaximal, characteristic, complemented
3C2×C3×#577C211yesmaximal, characteristic, complemented
4C2×#5837C211yesmaximal, characteristic, complemented
5C2×#5835C211yesmaximal, characteristic, complemented
6#87207C2132yesmaximal, direct product factor
7C2×#5778C213yesmaximal, complemented
8C2×#5777C213yesmaximal, complemented
9C2×#5774C213yesmaximal, complemented
10C2×D3×AGL(1,ℤ/8)C213yesmaximal, complemented
11C2×#5769C213yesmaximal, complemented
12C2×#5768C213yesmaximal, complemented
13C2×#5762C213yesmaximal, complemented
14C22×#914C213yesmaximal, complemented
15C2×#5752C211yesmaximal, characteristic, complemented
16C2×#5750C211yesmaximal, characteristic, complemented
17C2×#3585—31nomaximal, Sylow
18C2×C3×2−1+4C2211yescharacteristic, complemented
19C2×C3×H(5,𝔽2)C2211yescharacteristic, complemented
20#5968—28no—
21#5968C22116yescomplemented
22D3×H(5,𝔽2)—28no—
23D3×H(5,𝔽2)C22116yescomplemented
24C2×#1009—21no—
25C2×#1009—23no—
26C2×#1009C2213yescomplemented
27C2×#1009C2213yescomplemented
28C2×#1009C2211yescharacteristic, complemented
29C2×#1009C2211yescharacteristic, complemented
30C2×D3×#41—21no—
31C2×D3×#41—23no—
32C2×D3×#41C2211yescharacteristic
33C2×D3×#41C2213yescomplemented
34C2×D3×#41C2213yescomplemented
35C2×#1007—21no—
36C2×#1007C2213yescomplemented
37C22×#239—21no—
38C22×#239C2213yescomplemented
39C2×#1004—23no—
40C2×#1004C2213yescomplemented
41C22×D3×D4—23no—
42C22×D3×D4C2213yescomplemented
43C3×#577C22116yescomplemented
44C2×C3×#137C2213yescomplemented
45C2×C3×AGL(1,ℤ/8)C2213yescomplemented
46C2×C3×#135C2213yescomplemented
47C22×C3×SD16C2213yescomplemented
48C2×C3×#131C2211yescharacteristic, complemented
49#5837C22116yescomplemented
50#5835C22116yescomplemented
51C2×#950C2213yescomplemented
52C2×#950C2213yescomplemented
53C2×#949C2213yescomplemented
54C2×#949C2213yescomplemented
55C2×#948C2211yescharacteristic, complemented
56C2×#942C2213yescomplemented
57C22×#215C2213yescomplemented
58C2×#932C2213yescomplemented
59C22×#213C2213yescomplemented
60#5778C22148yescomplemented
61#5777C22148yescomplemented
62#5774C22148yescomplemented
63D3×AGL(1,ℤ/8)C22148yescomplemented
64#5769C22148yescomplemented
65#5768C22148yescomplemented
66C2×#919C2216yescomplemented
67C2×#918C2213yescomplemented
68C2×#918C2213yescomplemented
69#5762C22148yescomplemented
70C2×#916C2216yescomplemented
71C2×#915C2211yescharacteristic, complemented
72C2×#915C2213yescomplemented
73C2×#914C2213yescomplemented
74C2×#914C2216yescomplemented
75C2×#914C2216yescomplemented
76C2×#914C2216yescomplemented
77C2×#914C2213yescomplemented
78C2×#914C22148yescomplemented
79C2×D3×SD16C2216yescomplemented
80C2×#911C2213yescomplemented
81C2×#911C2213yescomplemented
82C2×D3×D8C2216yescomplemented
83#5752C22116yescomplemented
84#5750C22116yescomplemented
85C2×#908C2213yescomplemented
86C2×#908C2213yescomplemented
87C2×#907C2213yescomplemented
88C2×D3×M16C2213yescomplemented
89C2×#904C2213yescomplemented
90C22×D24C2213yescomplemented
91C2×#901C2213yescomplemented
92C22×ΓL(1,𝔽25)C2213yescomplemented
93C2×#585—31no—
94C22×H(5,𝔽2)—31no—
95#3585—332no—
96C2×#577—31no—
97C2×#577—33no—
98C2×#577—33no—
99C2×#577D311yescharacteristic, complemented
100C2×#576—31no—
101C2×#576—33no—
102C2×#576—33no—
103C2×#576—31no—
104C2×#575—33no—
105C2×#575—33no—
106C22×AGL(1,ℤ/8)—33no—
107C22×AGL(1,ℤ/8)—33no—
108C2×#568—31no—
109C24×D3—23no—
110C3×2−1+4—24no—
111C3×2−1+4C2318yescomplemented
112C3×H(5,𝔽2)—24no—
113C3×H(5,𝔽2)C2318yescomplemented
114C2×C3×#41—21no—
115C2×C3×#41—23no—
116C2×C3×#41C2313yes—
117C2×C3×#41C2311yescharacteristic
118C2×C3×#41C2313yescomplemented
119C22×C3×Q8—21no—
120C22×C3×Q8C2313yescomplemented
121C22×C3×D4—23no—
122C22×C3×D4C2313yes—
123C22×#67—26no—
124C22×#67—23no—
125#1009—24no—
126#1009—24no—
127#1009—216no—
128#1009—248no—
129#1009—212no—
130#1009—212no—
131#1009C23124yescomplemented
132#1009C23124yescomplemented
133#1009C2318yescomplemented
134#1009C2318yescomplemented
135D3×#41—216no—
136D3×#41—248no—
137D3×#41—212no—
138D3×#41—212no—
139D3×#41D418yes—
140D3×#41C2318yes—
141D3×#41C23124yescomplemented
142D3×#41C23124yescomplemented
143#1007—216no—
144#1007—212no—
145#1007C23124yescomplemented
146C2×#239—21no—
147C2×#239—21no—
148C2×#239—216no—
149C2×#239—23no—
150C2×#239—23no—
151C2×#239—23no—
152C2×#239—212no—
153C2×#239D411yescharacteristic
154C2×#239C2313yes—
155C2×#239C2313yes—
156C2×#239C2316yescomplemented
157C2×#239C23124yescomplemented
158C2×D3×Q8—23no—
159C2×D3×Q8D411yescharacteristic
160C2×D3×Q8C2311yescharacteristic
161C2×D3×Q8C2313yescomplemented
162#1004—248no—
163#1004—212no—
164#1004C23124yescomplemented
165C2×#237—23no—
166C2×#237—23no—
167C2×#237—23no—
168C2×#237D413yes—
169C2×#237C2313yes—
170C2×#237C2311yescharacteristic
171C2×D3×D4—23no—
172C2×D3×D4—23no—
173C2×D3×D4—23no—
174C2×D3×D4—23no—
175C2×D3×D4—26no—
176C2×D3×D4—26no—
177C2×D3×D4—248no—
178C2×D3×D4—23no—
179C2×D3×D4—23no—
180C2×D3×D4—23no—
181C2×D3×D4—212no—
182C2×D3×D4D413yes—
183C2×D3×D4C2313yes—
184C2×D3×D4C2316yes—
185C2×D3×D4C23124yescomplemented
186C2×D3×D4C2313yescomplemented
187C2×#235—26no—
188C2×#235—23no—
189C2×#235—23no—
190C2×#235—23no—
191C2×#235—23no—
192C2×#235C2313yes—
193C2×#235C2313yes—
194C2×#235C2313yescomplemented
195C22×D12—23no—
196C22×D12—23no—
197C22×D12—23no—
198C22×D12C2313yes—
199C22×D12C2313yescomplemented
200C22×C4×D3—23no—
201C22×C4×D3—23no—
202C22×C4×D3—23no—
203C22×C4×D3C2313yes—
204C3×#137C23124yescomplemented
205C3×AGL(1,ℤ/8)C23124yescomplemented
206C3×#135C23124yescomplemented
207C2×C3×Q16C2313yescomplemented
208C2×C3×SD16C2313yescomplemented
209C2×C3×SD16C2316yescomplemented
210C2×C3×SD16C2311yescharacteristic, complemented
211C2×C3×SD16C23124yescomplemented
212C2×C3×D8C2313yescomplemented
213C3×#131C2318yescomplemented
214C2×C3×M16C2313yescomplemented
215C22×C3×C8C2313yescomplemented
216#950C23124yescomplemented
217#950C23124yescomplemented
218#949C23124yescomplemented
219#949C23124yescomplemented
220#948C2318yescomplemented
221C2×#216C2313yescomplemented
222C2×#216C2311yescharacteristic, complemented
223#942C23124yescomplemented
224C2×#215C2316yescomplemented
225C2×#215C2313yescomplemented
226C2×#215C2313yescomplemented
227C2×#215C23124yescomplemented
228C2×#214C2311yescharacteristic, complemented
229C2×#214C2313yescomplemented
230#932C23124yescomplemented
231C2×#213C2313yescomplemented
232C2×#213C2316yescomplemented
233C2×#213C2313yescomplemented
234C2×#213C23124yescomplemented
235C2×#208C2313yescomplemented
236C22×C3⋊C8C2313yescomplemented
237#919C23148yescomplemented
238#918C23124yescomplemented
239#918C23124yescomplemented
240#916C23148yescomplemented
241#915C2318yescomplemented
242#915C23124yescomplemented
243#914C23124yescomplemented
244#914C23148yescomplemented
245#914C23148yescomplemented
246#914C23148yescomplemented
247#914C23124yescomplemented
248D3×SD16C23148yescomplemented
249#911C23124yescomplemented
250#911C23124yescomplemented
251D3×D8C23148yescomplemented
252#908C23124yescomplemented
253#908C23124yescomplemented
254#907C23124yescomplemented
255D3×M16C23124yescomplemented
256C2×Dic12C2311yescharacteristic, complemented
257#904C23124yescomplemented
258C2×D24C2313yescomplemented
259C2×D24C2316yescomplemented
260C2×D24C23124yescomplemented
261C2×#204C2313yescomplemented
262C2×#204C2313yescomplemented
263#901C23124yescomplemented
264C2×ΓL(1,𝔽25)C2311yescharacteristic
265C2×ΓL(1,𝔽25)C2313yes—
266C2×ΓL(1,𝔽25)C23124yescomplemented
267C2×ΓL(1,𝔽25)C2313yescomplemented
268C2×ΓL(1,𝔽25)C2313yescomplemented
269C2×D3×C8C2316yescomplemented
270#585—316no—
271#585—68no—
272C2×2−1+4—33no—
273C2×2−1+4—61no—
274C2×2−1+4C2×D311yescharacteristic, complemented
275C2×H(5,𝔽2)—316no—
276C2×H(5,𝔽2)—33no—
277C2×H(5,𝔽2)—31no—
278C2×H(5,𝔽2)—31no—
279C2×H(5,𝔽2)—33no—
280C2×H(5,𝔽2)—33no—
281C2×H(5,𝔽2)—63no—
282C2×H(5,𝔽2)—63no—
283C2×H(5,𝔽2)—61no—
284C2×H(5,𝔽2)—68no—
285C2×H(5,𝔽2)C2×D311yescharacteristic, complemented
286C22×#41—31no—
287C22×#41—33no—
288C22×#41—33no—
289C22×#41—33no—
290C22×#41—61no—
291C22×#41—61no—
292C22×#41—63no—
293C23×D4—33no—
294C23×D4—63no—
295#577—316no—
296#577—348no—
297#577—348no—
298#577C2×D3116yescomplemented
299#576—316no—
300#576—348no—
301#576—348no—
302#576—316no—
303#575—348no—
304#575—348no—
305C2×#137—33no—
306C2×#137—33no—
307C2×#137—33no—
308C2×#137—31no—
309C2×#137—33no—
310C2×#137C2×D313yescomplemented
311C2×AGL(1,ℤ/8)—33no—
312C2×AGL(1,ℤ/8)—33no—
313C2×AGL(1,ℤ/8)—33no—
314C2×AGL(1,ℤ/8)—348no—
315C2×AGL(1,ℤ/8)—348no—
316C2×AGL(1,ℤ/8)—36no—
317C2×AGL(1,ℤ/8)—33no—
318C2×AGL(1,ℤ/8)—36no—
319C2×AGL(1,ℤ/8)—36no—
320C2×AGL(1,ℤ/8)—33no—
321C2×AGL(1,ℤ/8)—33no—
322C2×AGL(1,ℤ/8)—33no—
323C2×AGL(1,ℤ/8)—33no—
324C2×AGL(1,ℤ/8)—33no—
325C2×AGL(1,ℤ/8)C2×D313yescomplemented
326C2×#135—33no—
327C2×#135—33no—
328C2×#135—36no—
329C2×#135—36no—
330C2×#135—33no—
331C2×#135C2×D313yescomplemented
332C22×SD16—33no—
333C22×SD16—36no—
334C22×SD16C2×D313yescomplemented
335C22×D8—33no—
336C22×D8—36no—
337C22×D8—33no—
338#568—316no—
339C2×#131—31no—
340C2×#131—33no—
341C2×#131—33no—
342C2×#131C2×D311yescharacteristic, complemented
343C22×M16—33no—
344C22×M16—33no—
345C24×C3—23no—
346C23×D3—23no—
347C23×D3—23no—
348C23×D3—23no—
349C23×D3—23no—
350C23×D3—26no—
351C23×D3—224no—
352C23×D3—812no—
353C23×D3C2×D413yes—
354C3×#41—28no—
355C3×#41—224no—
356C3×#41—26no—
357C3×#41—26no—
358C3×#41C2×D414yes—
359C3×#41C24112yes—
360C3×#41C2414yes—
361C3×#41C24112yescomplemented
362C2×C3×Q8—28no—
363C2×C3×Q8—23no—
364C2×C3×Q8—26no—
365C2×C3×Q8C2×D411yescharacteristic
366C2×C3×Q8C2413yes—
367C2×C3×Q8C2411yescharacteristic
368C2×C3×Q8C24112yescomplemented
369C2×C3×D4—23no—
370C2×C3×D4—23no—
371C2×C3×D4—224no—
372C2×C3×D4—23no—
373C2×C3×D4—26no—
374C2×C3×D4C2×D413yes—
375C2×C3×D4C2411yescharacteristic
376C2×C3×D4C2413yes—
377C2×C3×D4C24112yes—
378C22×C3×C4—23no—
379C22×C3×C4—23no—
380C22×C3×C4—23no—
381C22×C3×C4C2413yes—
382C2×#67—23no—
383C2×#67—23no—
384C2×#67—21no—
385C2×#67—23no—
386C2×#67—248no—
387C2×#67—23no—
388C2×#67—26no—
389C2×#67—23no—
390C2×#67—224no—
391C2×#67C2×D416yes—
392C22×Dic3—21no—
393C22×Dic3—23no—
394C22×Dic3C2×D413yes—
395#239—28no—
396#239—28no—
397#239—224no—
398#239—26no—
399#239—224no—
400#239—224no—
401#239—212no—
402#239—26no—
403#239C2×D418yes—
404#239C24112yes—
405#239C24112yes—
406#239C24124yescomplemented
407D3×Q8—22no—
408D3×Q8—26no—
409D3×Q8—224no—
410D3×Q8C2×D418yes—
411D3×Q8C2414yes—
412D3×Q8C24112yescomplemented
413#237—224no—
414#237—224no—
415#237—26no—
416#237—22no—
417#237—224no—
418#237C2×D4124yes—
419#237C2414yes—
420#237C24112yes—
421D3×D4—224no—
422D3×D4—224no—
423D3×D4—224no—
424D3×D4—224no—
425D3×D4—248no—
426D3×D4—248no—
427D3×D4—224no—
428D3×D4—26no—
429D3×D4—224no—
430D3×D4—212no—
431D3×D4—224no—
432D3×D4—26no—
433D3×D4C2×D4124yes—
434D3×D4C24124yes—
435D3×D4C24112yes—
436D3×D4C24112yescomplemented
437#235—26no—
438#235—26no—
439#235—248no—
440#235—224no—
441#235—224no—
442#235—224no—
443#235—224no—
444#235C2×D4112yes—
445#235C24112yes—
446#235C24112yes—
447#235C24112yescomplemented
448C2×D12—23no—
449C2×D12—23no—
450C2×D12—26no—
451C2×D12—224no—
452C2×D12—23no—
453C2×D12—23no—
454C2×D12—26no—
455C2×D12—26no—
456C2×D12—224no—
457C2×D12—224no—
458C2×D12C2×D413yes—
459C2×D12C2413yes—
460C2×D12C2413yes—
461C2×D12C24112yes—
462C2×D12C24112yescomplemented
463C2×C4×D3—21no—
464C2×C4×D3—23no—
465C2×C4×D3—23no—
466C2×C4×D3—23no—
467C2×C4×D3—23no—
468C2×C4×D3—23no—
469C2×C4×D3—26no—
470C2×C4×D3—224no—
471C2×C4×D3—224no—
472C2×C4×D3—224no—
473C2×C4×D3C2×D413yes—
474C2×C4×D3C2×D413yes—
475C2×C4×D3C2×D4112yes—
476C2×C4×D3C2413yes—
477C2×C4×D3C2411yescharacteristic
478C2×C4×D3C24112yes—
479C2×Dic6—21no—
480C2×Dic6—23no—
481C2×Dic6C2×D413yes—
482C2×Dic6C2411yescharacteristic
483C2×Dic6C2411yescharacteristic
484C3×Q16C24112yescomplemented
485C3×SD16C24124yescomplemented
486C3×SD16C24112yescomplemented
487C3×SD16C2414yescomplemented
488C3×D8C24112yescomplemented
489C3×M16C24112yescomplemented
490C2×C3×C8C2413yes—
491C2×C3×C8C2411yescharacteristic
492C2×C3×C8C24112yescomplemented
493#216C24112yescomplemented
494#216C2414yescomplemented
495#215C24124yescomplemented
496#215C24112yescomplemented
497#215C24112yescomplemented
498#214C2414yescomplemented
499#214C24112yescomplemented
500#213C24112yescomplemented
501#213C24124yescomplemented
502#213C24112yescomplemented
503#208C24112yescomplemented
504C2×C3⋊C8C2413yes—
505C2×C3⋊C8C2411yescharacteristic
506C2×C3⋊C8C24112yescomplemented
507Dic12C2414yescomplemented
508D24C24112yescomplemented
509D24C24124yescomplemented
510#204C24112yescomplemented
511#204C24112yescomplemented
512ΓL(1,𝔽25)C2414yes—
513ΓL(1,𝔽25)C24112yes—
514ΓL(1,𝔽25)C24112yescomplemented
515ΓL(1,𝔽25)C24112yescomplemented
516D3×C8C24124yescomplemented
517C25—63no—
5182−1+4—24no—
5192−1+4—324no—
5202−1+4—616no—
5212−1+4—612no—
5222−1+4C22×D318yescomplemented
523H(5,𝔽2)—24no—
524H(5,𝔽2)—38no—
525H(5,𝔽2)—324no—
526H(5,𝔽2)—38no—
527H(5,𝔽2)—324no—
528H(5,𝔽2)—324no—
529H(5,𝔽2)—648no—
530H(5,𝔽2)—612no—
531H(5,𝔽2)—648no—
532H(5,𝔽2)—616no—
533H(5,𝔽2)—612no—
534H(5,𝔽2)—612no—
535H(5,𝔽2)—64no—
536H(5,𝔽2)—64no—
537H(5,𝔽2)C22×D318yescomplemented
538C2×#41—21no—
539C2×#41—23no—
540C2×#41—38no—
541C2×#41—38no—
542C2×#41—31no—
543C2×#41—33no—
544C2×#41—33no—
545C2×#41—324no—
546C2×#41—324no—
547C2×#41—36no—
548C2×#41—33no—
549C2×#41—33no—
550C2×#41—324no—
551C2×#41—33no—
552C2×#41—31no—
553C2×#41—33no—
554C2×#41—33no—
555C2×#41—63no—
556C2×#41—63no—
557C2×#41—66no—
558C2×#41—63no—
559C2×#41—63no—
560C2×#41—63no—
561C2×#41—63no—
562C2×#41—63no—
563C2×#41—63no—
564C2×#41—612no—
565C2×#41—612no—
566C2×#41—612no—
567C2×#41—63no—
568C2×#41—63no—
569C2×#41—616no—
570C2×#41—616no—
571C2×#41—648no—
572C2×#41—61no—
573C2×#41—61no—
574C2×#41C22×D313yes—
575C2×#41C22×D311yescharacteristic
576C2×#41C22×D313yescomplemented
577C22×Q8—21no—
578C22×Q8—31no—
579C22×Q8—33no—
580C22×Q8—31no—
581C22×Q8—63no—
582C22×Q8C22×D313yescomplemented
583C22×D4—23no—
584C22×D4—33no—
585C22×D4—33no—
586C22×D4—36no—
587C22×D4—33no—
588C22×D4—324no—
589C22×D4—33no—
590C22×D4—33no—
591C22×D4—63no—
592C22×D4—63no—
593C22×D4—63no—
594C22×D4—63no—
595C22×D4—63no—
596C22×D4—612no—
597C22×D4—63no—
598C22×D4—66no—
599C22×D4—648no—
600C22×D4—63no—
601C22×D4—66no—
602C22×D4—63no—
603C22×D4—63no—
604C22×D4—66no—
605C22×D4—63no—
606C22×D4—63no—
607C22×D4C22×D313yes—
608C23×C4—33no—
609C23×C4—63no—
610C23×C4—63no—
611C23×C4—63no—
612#137—324no—
613#137—324no—
614#137—324no—
615#137—38no—
616#137—324no—
617#137C22×D3124yescomplemented
618AGL(1,ℤ/8)—324no—
619AGL(1,ℤ/8)—324no—
620AGL(1,ℤ/8)—324no—
621AGL(1,ℤ/8)—348no—
622AGL(1,ℤ/8)—324no—
623AGL(1,ℤ/8)—348no—
624AGL(1,ℤ/8)—348no—
625AGL(1,ℤ/8)—324no—
626AGL(1,ℤ/8)—324no—
627AGL(1,ℤ/8)—324no—
628AGL(1,ℤ/8)—324no—
629AGL(1,ℤ/8)—324no—
630AGL(1,ℤ/8)C22×D3124yescomplemented
631#135—324no—
632#135—324no—
633#135—348no—
634#135—348no—
635#135—324no—
636#135C22×D3124yescomplemented
637C2×Q16—31no—
638C2×Q16—33no—
639C2×Q16—31no—
640C2×Q16C22×D313yescomplemented
641C2×SD16—33no—
642C2×SD16—36no—
643C2×SD16—33no—
644C2×SD16—324no—
645C2×SD16—33no—
646C2×SD16—31no—
647C2×SD16—348no—
648C2×SD16—33no—
649C2×SD16—33no—
650C2×SD16C22×D316yescomplemented
651C2×SD16C22×D313yescomplemented
652C2×SD16C22×D311yescharacteristic, complemented
653C2×SD16C22×D3124yescomplemented
654C2×D8—33no—
655C2×D8—36no—
656C2×D8—33no—
657C2×D8—324no—
658C2×D8—348no—
659C2×D8—36no—
660C2×D8—33no—
661C2×D8—324no—
662C2×D8C22×D313yescomplemented
663#131—38no—
664#131—324no—
665#131—324no—
666#131C22×D318yescomplemented
667C2×M16—33no—
668C2×M16—324no—
669C2×M16—33no—
670C2×M16—31no—
671C2×M16—33no—
672C2×M16—33no—
673C2×M16—324no—
674C2×M16C22×D313yescomplemented
675C22×C8—33no—
676C22×C8—36no—
677C22×C8C22×D313yescomplemented
678C23×C3—21no—
679C23×C3—23no—
680C23×C3—212no—
681C23×C3—86no—
682C23×C3C22×D413yes—
683C22×D3—23no—
684C22×D3—23no—
685C22×D3—212no—
686C22×D3—212no—
687C22×D3—212no—
688C22×D3—212no—
689C22×D3—224no—
690C22×D3—46no—
691C22×D3—412no—
692C22×D3—86no—
693C22×D3—812no—
694C22×D3—848no—
695C22×D3—86no—
696C22×D3—86no—
697C22×D3C22×D411yescharacteristic
698C22×D3C22×D413yes—
699C22×D3C22×D4112yes—
700C3×Q8—23no—
701C3×Q8—212no—
702C3×Q8—21no—
703C3×Q8C22×D414yes—
704C3×Q8C2516yes—
705C3×Q8C2512yes—
706C3×D4—212no—
707C3×D4—212no—
708C3×D4—23no—
709C3×D4—212no—
710C3×D4—21no—
711C3×D4C22×D4112yes—
712C3×D4C2512yes—
713C3×D4C2516yes—
714C2×C3×C4—21no—
715C2×C3×C4—23no—
716C2×C3×C4—212no—
717C2×C3×C4—212no—
718C2×C3×C4—212no—
719C2×C3×C4C22×D413yes—
720C2×C3×C4C22×D416yes—
721C2×C3×C4C2511yescharacteristic
722C2×C3×C4C2516yes—
723#67—212no—
724#67—212no—
725#67—24no—
726#67—212no—
727#67—212no—
728#67—224no—
729#67—212no—
730#67C22×D4124yes—
731C2×Dic3—21no—
732C2×Dic3—21no—
733C2×Dic3—24no—
734C2×Dic3—212no—
735C2×Dic3C22×D413yes—
736C2×Dic3C22×D411yescharacteristic
737C2×Dic3C22×D4112yes—
738D12—212no—
739D12—212no—
740D12—224no—
741D12—23no—
742D12—212no—
743D12—23no—
744D12—212no—
745D12C22×D4112yes—
746D12C2516yes—
747D12C2516yes—
748C4×D3—24no—
749C4×D3—212no—
750C4×D3—212no—
751C4×D3—212no—
752C4×D3—212no—
753C4×D3—212no—
754C4×D3—224no—
755C4×D3C22×D4112yes—
756C4×D3C22×D4112yes—
757C4×D3C22×D412yes—
758C4×D3C22×D416yes—
759C4×D3C2516yes—
760C4×D3C2512yes—
761Dic6—21no—
762Dic6—21no—
763Dic6—24no—
764Dic6—212no—
765Dic6C22×D4112yes—
766Dic6C2512yes—
767Dic6C2512yes—
768C3×C8C2516yes—
769C3×C8C2512yes—
770C3⋊C8C2516yes—
771C3⋊C8C2512yes—
772C24—23no—
773C24—33no—
774C24—63no—
775C24—63no—
776C24—66no—
777C24—624no—
778C24—63no—
779C24—63no—
780C24—2412no—
781#41—28no—
782#41—224no—
783#41—26no—
784#41—26no—
785#41—38no—
786#41—324no—
787#41—312no—
788#41—312no—
789#41—324no—
790#41—312no—
791#41—312no—
792#41—312no—
793#41—34no—
794#41—312no—
795#41—312no—
796#41—624no—
797#41—624no—
798#41—648no—
799#41—624no—
800#41—624no—
801#41—624no—
802#41—62no—
803#41—624no—
804#41—66no—
805#41—66no—
806#41—624no—
807#41—66no—
808#41—624no—
809#41—612no—
810#41—624no—
811#41—624no—
812#41—68no—
813#41—68no—
814#41—66no—
815#41—66no—
816#41D3×D414yes—
817#41C23×D3112yes—
818#41C23×D314yes—
819#41C23×D3112yescomplemented
820C2×Q8—28no—
821C2×Q8—23no—
822C2×Q8—26no—
823C2×Q8—38no—
824C2×Q8—33no—
825C2×Q8—312no—
826C2×Q8—34no—
827C2×Q8—31no—
828C2×Q8—31no—
829C2×Q8—63no—
830C2×Q8—61no—
831C2×Q8—62no—
832C2×Q8—66no—
833C2×Q8—624no—
834C2×Q8D3×D411yescharacteristic
835C2×Q8C23×D313yes—
836C2×Q8C23×D311yescharacteristic
837C2×Q8C23×D3112yescomplemented
838C2×D4—23no—
839C2×D4—23no—
840C2×D4—224no—
841C2×D4—23no—
842C2×D4—26no—
843C2×D4—36no—
844C2×D4—324no—
845C2×D4—312no—
846C2×D4—324no—
847C2×D4—312no—
848C2×D4—33no—
849C2×D4—33no—
850C2×D4—33no—
851C2×D4—312no—
852C2×D4—312no—
853C2×D4—624no—
854C2×D4—624no—
855C2×D4—63no—
856C2×D4—63no—
857C2×D4—66no—
858C2×D4—624no—
859C2×D4—66no—
860C2×D4—624no—
861C2×D4—624no—
862C2×D4—612no—
863C2×D4—66no—
864C2×D4—63no—
865C2×D4—66no—
866C2×D4—63no—
867C2×D4—624no—
868C2×D4—648no—
869C2×D4—624no—
870C2×D4—648no—
871C2×D4—624no—
872C2×D4—624no—
873C2×D4—648no—
874C2×D4—63no—
875C2×D4—61no—
876C2×D4—63no—
877C2×D4—63no—
878C2×D4—624no—
879C2×D4—624no—
880C2×D4—63no—
881C2×D4—63no—
882C2×D4—66no—
883C2×D4—66no—
884C2×D4D3×D413yes—
885C2×D4C23×D311yescharacteristic
886C2×D4C23×D313yes—
887C2×D4C23×D3112yes—
888C22×C4—23no—
889C22×C4—23no—
890C22×C4—23no—
891C22×C4—33no—
892C22×C4—33no—
893C22×C4—33no—
894C22×C4—312no—
895C22×C4—33no—
896C22×C4—31no—
897C22×C4—312no—
898C22×C4—63no—
899C22×C4—63no—
900C22×C4—624no—
901C22×C4—66no—
902C22×C4—624no—
903C22×C4—624no—
904C22×C4—61no—
905C22×C4—63no—
906C22×C4—61no—
907C22×C4—63no—
908C22×C4—63no—
909C22×C4—63no—
910C22×C4C23×D313yes—
911Q16—34no—
912Q16—312no—
913Q16—34no—
914Q16C23×D3112yescomplemented
915SD16—312no—
916SD16—324no—
917SD16—312no—
918SD16—312no—
919SD16—34no—
920SD16—312no—
921SD16—312no—
922SD16C23×D3124yescomplemented
923SD16C23×D3112yescomplemented
924SD16C23×D314yescomplemented
925D8—312no—
926D8—324no—
927D8—312no—
928D8—324no—
929D8—312no—
930D8C23×D3112yescomplemented
931M16—312no—
932M16—312no—
933M16—34no—
934M16—312no—
935M16—312no—
936M16C23×D3112yescomplemented
937C2×C8—31no—
938C2×C8—33no—
939C2×C8—312no—
940C2×C8—324no—
941C2×C8C23×D313yes—
942C2×C8C23×D311yescharacteristic
943C2×C8C23×D3112yescomplemented
944C22×C3—26no—
945C22×C3—22no—
946C22×C3—26no—
947C22×C3—46no—
948C22×C3—42no—
949C22×C3—812no—
950C22×C3C23×D416yes—
951C22×C3C23×D411yescharacteristic
952C2×D3—22no—
953C2×D3—26no—
954C2×D3—26no—
955C2×D3—26no—
956C2×D3—412no—
957C2×D3—424no—
958C2×D3—46no—
959C2×D3—46no—
960C2×D3—812no—
961C2×D3—824no—
962C2×D3—812no—
963C2×D3—812no—
964C2×D3C23×D412yes—
965C2×D3C23×D416yes—
966C3×C4—22no—
967C3×C4—26no—
968C3×C4C23×D411yescharacteristic
969C3×C4C23×D416yes—
970C3×C4C2611yescharacteristic
971Dic3—22no—
972Dic3—22no—
973Dic3C23×D416yes—
974Dic3C23×D412yes—
975C23—21no—
976C23—23no—
977C23—212no—
978C23—31no—
979C23—33no—
980C23—312no—
981C23—612no—
982C23—612no—
983C23—624no—
984C23—63no—
985C23—63no—
986C23—612no—
987C23—612no—
988C23—86no—
989C23—126no—
990C23—1212no—
991C23—246no—
992C23—246no—
993C23—2412no—
994C23—246no—
995C23—2448no—
996C23C2×D3×D413yes—
997Q8—23no—
998Q8—212no—
999Q8—21no—
1000Q8—312no—
1001Q8—32no—
1002Q8—32no—
1003Q8—612no—
1004Q8—64no—
1005Q8—61no—
1006Q8—61no—
1007Q8C2×D3×D414yes—
1008Q8C24×D316yes—
1009Q8C24×D312yes—
1010D4—212no—
1011D4—212no—
1012D4—212no—
1013D4—23no—
1014D4—21no—
1015D4—324no—
1016D4—312no—
1017D4—36no—
1018D4—36no—
1019D4—612no—
1020D4—612no—
1021D4—624no—
1022D4—612no—
1023D4—624no—
1024D4—612no—
1025D4—612no—
1026D4—64no—
1027D4—612no—
1028D4—612no—
1029D4—612no—
1030D4—63no—
1031D4—612no—
1032D4—63no—
1033D4C2×D3×D4112yes—
1034D4C24×D312yes—
1035D4C24×D316yes—
1036C2×C4—212no—
1037C2×C4—21no—
1038C2×C4—23no—
1039C2×C4—212no—
1040C2×C4—212no—
1041C2×C4—312no—
1042C2×C4—31no—
1043C2×C4—33no—
1044C2×C4—32no—
1045C2×C4—312no—
1046C2×C4—312no—
1047C2×C4—36no—
1048C2×C4—36no—
1049C2×C4—32no—
1050C2×C4—612no—
1051C2×C4—612no—
1052C2×C4—624no—
1053C2×C4—64no—
1054C2×C4—612no—
1055C2×C4—64no—
1056C2×C4—612no—
1057C2×C4—61no—
1058C2×C4—61no—
1059C2×C4—612no—
1060C2×C4—612no—
1061C2×C4C2×D3×D416yes—
1062C2×C4C2×D3×D413yes—
1063C2×C4C24×D316yes—
1064C2×C4C24×D311yescharacteristic
1065C8—32no—
1066C8—36no—
1067C8C24×D316yes—
1068C8C24×D312yes—
1069C2×C3—26no—
1070C2×C3—46no—
1071C2×C3—42no—
1072C2×C3#358512yescomplemented
1073C2×C3C24×D411yescharacteristic
1074D3—22no—
1075D3—26no—
1076D3—46no—
1077D3—46no—
1078C22—26no—
1079C22—22no—
1080C22—26no—
1081C22—32no—
1082C22—36no—
1083C22—46no—
1084C22—42no—
1085C22—62no—
1086C22—66no—
1087C22—66no—
1088C22—66no—
1089C22—812no—
1090C22—1212no—
1091C22—1224no—
1092C22—126no—
1093C22—126no—
1094C22—2412no—
1095C22—2412no—
1096C22—2424no—
1097C22—2412no—
1098C22C22×D3×D416yes—
1099C22C22×D3×D411yescharacteristic
1100C4—22no—
1101C4—26no—
1102C4—32no—
1103C4—36no—
1104C4—62no—
1105C4—62no—
1106C4C22×D3×D416yes—
1107C4C22×D3×D411yescharacteristic
1108C4C25×D311yescharacteristic
1109C3C2×#358511yescharacteristic, complemented, Sylow
1110C2—26no—
1111C2—46no—
1112C2—42no—
1113C2—62no—
1114C2—66no—
1115C2—126no—
1116C2—126no—
1117C2#8720712yesdirect product factor
1118C2C23×D3×D411yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC3×C4C26
FrattiniC4C25×D3
FittingC2×C3×#577C2
socleC22×C3C23×D4
hypercenterC2×#577D3
hypocenterC3C2×#3585
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#577

Complements

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

NH ≅ G/Ntype
1. C2×#5968C2semidirect
2. C2×D3×H(5,𝔽2)C2semidirect
3. C2×C3×#577C2semidirect
4. C2×#5837C2semidirect
5. C2×#5835C2semidirect
6. #87207C2direct (N × H)
7. C2×#5778C2semidirect
8. C2×#5777C2semidirect
9. C2×#5774C2semidirect
10. C2×D3×AGL(1,ℤ/8)C2semidirect
11. C2×#5769C2semidirect
12. C2×#5768C2semidirect
13. C2×#5762C2semidirect
14. C22×#914C2semidirect
15. C2×#5752C2semidirect
16. C2×#5750C2semidirect
18. C2×C3×2−1+4C22semidirect
19. C2×C3×H(5,𝔽2)C22semidirect
21. #5968C22semidirect
23. D3×H(5,𝔽2)C22semidirect
26. C2×#1009C22semidirect
27. C2×#1009C22semidirect
28. C2×#1009C22semidirect
29. C2×#1009C22semidirect
33. C2×D3×#41C22semidirect
34. C2×D3×#41C22semidirect
36. C2×#1007C22semidirect
38. C22×#239C22semidirect
40. C2×#1004C22semidirect
42. C22×D3×D4C22semidirect
43. C3×#577C22semidirect
44. C2×C3×#137C22semidirect
45. C2×C3×AGL(1,ℤ/8)C22semidirect
46. C2×C3×#135C22semidirect
47. C22×C3×SD16C22semidirect
48. C2×C3×#131C22semidirect
49. #5837C22semidirect
50. #5835C22semidirect
51. C2×#950C22semidirect
52. C2×#950C22semidirect
53. C2×#949C22semidirect
54. C2×#949C22semidirect
55. C2×#948C22semidirect
56. C2×#942C22semidirect
57. C22×#215C22semidirect
58. C2×#932C22semidirect
59. C22×#213C22semidirect
60. #5778C22semidirect
61. #5777C22semidirect
62. #5774C22semidirect
63. D3×AGL(1,ℤ/8)C22semidirect
64. #5769C22semidirect
65. #5768C22semidirect
66. C2×#919C22semidirect
67. C2×#918C22semidirect
68. C2×#918C22semidirect
69. #5762C22semidirect
70. C2×#916C22semidirect
71. C2×#915C22semidirect
72. C2×#915C22semidirect
73. C2×#914C22semidirect
74. C2×#914C22semidirect
75. C2×#914C22semidirect
76. C2×#914C22semidirect
77. C2×#914C22semidirect
78. C2×#914C22semidirect
79. C2×D3×SD16C22semidirect
80. C2×#911C22semidirect
81. C2×#911C22semidirect
82. C2×D3×D8C22semidirect
83. #5752C22semidirect
84. #5750C22semidirect
85. C2×#908C22semidirect
86. C2×#908C22semidirect
87. C2×#907C22semidirect
88. C2×D3×M16C22semidirect
89. C2×#904C22semidirect
90. C22×D24C22semidirect
91. C2×#901C22semidirect
92. C22×ΓL(1,𝔽25)C22semidirect
99. C2×#577D3semidirect
111. C3×2−1+4C23semidirect
113. C3×H(5,𝔽2)C23semidirect
118. C2×C3×#41C23semidirect
120. C22×C3×Q8C23semidirect
131. #1009C23semidirect
132. #1009C23semidirect
133. #1009C23semidirect
134. #1009C23semidirect
141. D3×#41C23semidirect
142. D3×#41C23semidirect
145. #1007C23semidirect
156. C2×#239C23semidirect
157. C2×#239C23semidirect
161. C2×D3×Q8C23semidirect
164. #1004C23semidirect
185. C2×D3×D4C23semidirect
186. C2×D3×D4C23semidirect
194. C2×#235C23semidirect
199. C22×D12C23semidirect
204. C3×#137C23semidirect
205. C3×AGL(1,ℤ/8)C23semidirect
206. C3×#135C23semidirect
207. C2×C3×Q16C23semidirect
208. C2×C3×SD16C23semidirect
209. C2×C3×SD16C23semidirect
210. C2×C3×SD16C23semidirect
211. C2×C3×SD16C23semidirect
212. C2×C3×D8C23semidirect
213. C3×#131C23semidirect
214. C2×C3×M16C23semidirect
215. C22×C3×C8C23semidirect
216. #950C23semidirect
217. #950C23semidirect
218. #949C23semidirect
219. #949C23semidirect
220. #948C23semidirect
221. C2×#216C23semidirect
222. C2×#216C23semidirect
223. #942C23semidirect
224. C2×#215C23semidirect
225. C2×#215C23semidirect
226. C2×#215C23semidirect
227. C2×#215C23semidirect
228. C2×#214C23semidirect
229. C2×#214C23semidirect
230. #932C23semidirect
231. C2×#213C23semidirect
232. C2×#213C23semidirect
233. C2×#213C23semidirect
234. C2×#213C23semidirect
235. C2×#208C23semidirect
236. C22×C3⋊C8C23semidirect
237. #919C23semidirect
238. #918C23semidirect
239. #918C23semidirect
240. #916C23semidirect
241. #915C23semidirect
242. #915C23semidirect
243. #914C23semidirect
244. #914C23semidirect
245. #914C23semidirect
246. #914C23semidirect
247. #914C23semidirect
248. D3×SD16C23semidirect
249. #911C23semidirect
250. #911C23semidirect
251. D3×D8C23semidirect
252. #908C23semidirect
253. #908C23semidirect
254. #907C23semidirect
255. D3×M16C23semidirect
256. C2×Dic12C23semidirect
257. #904C23semidirect
258. C2×D24C23semidirect
259. C2×D24C23semidirect
260. C2×D24C23semidirect
261. C2×#204C23semidirect
262. C2×#204C23semidirect
263. #901C23semidirect
266. C2×ΓL(1,𝔽25)C23semidirect
267. C2×ΓL(1,𝔽25)C23semidirect
268. C2×ΓL(1,𝔽25)C23semidirect
269. C2×D3×C8C23semidirect
274. C2×2−1+4C2×D3semidirect
285. C2×H(5,𝔽2)C2×D3semidirect
298. #577C2×D3semidirect
310. C2×#137C2×D3semidirect
325. C2×AGL(1,ℤ/8)C2×D3semidirect
331. C2×#135C2×D3semidirect
334. C22×SD16C2×D3semidirect
342. C2×#131C2×D3semidirect
361. C3×#41C24semidirect
368. C2×C3×Q8C24semidirect
406. #239C24semidirect
412. D3×Q8C24semidirect
436. D3×D4C24semidirect
447. #235C24semidirect
462. C2×D12C24semidirect
484. C3×Q16C24semidirect
485. C3×SD16C24semidirect
486. C3×SD16C24semidirect
487. C3×SD16C24semidirect
488. C3×D8C24semidirect
489. C3×M16C24semidirect
492. C2×C3×C8C24semidirect
493. #216C24semidirect
494. #216C24semidirect
495. #215C24semidirect
496. #215C24semidirect
497. #215C24semidirect
498. #214C24semidirect
499. #214C24semidirect
500. #213C24semidirect
501. #213C24semidirect
502. #213C24semidirect
503. #208C24semidirect
506. C2×C3⋊C8C24semidirect
507. Dic12C24semidirect
508. D24C24semidirect
509. D24C24semidirect
510. #204C24semidirect
511. #204C24semidirect
514. ΓL(1,𝔽25)C24semidirect
515. ΓL(1,𝔽25)C24semidirect
516. D3×C8C24semidirect
522. 2−1+4C22×D3semidirect
537. H(5,𝔽2)C22×D3semidirect
576. C2×#41C22×D3semidirect
582. C22×Q8C22×D3semidirect
617. #137C22×D3semidirect
630. AGL(1,ℤ/8)C22×D3semidirect
636. #135C22×D3semidirect
640. C2×Q16C22×D3semidirect
650. C2×SD16C22×D3semidirect
651. C2×SD16C22×D3semidirect
652. C2×SD16C22×D3semidirect
653. C2×SD16C22×D3semidirect
662. C2×D8C22×D3semidirect
666. #131C22×D3semidirect
674. C2×M16C22×D3semidirect
677. C22×C8C22×D3semidirect
819. #41C23×D3semidirect
837. C2×Q8C23×D3semidirect
914. Q16C23×D3semidirect
922. SD16C23×D3semidirect
923. SD16C23×D3semidirect
924. SD16C23×D3semidirect
930. D8C23×D3semidirect
936. M16C23×D3semidirect
943. C2×C8C23×D3semidirect
1072. C2×C3#3585semidirect
1109. C3C2×#3585semidirect
1117. C2#87207direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#59682
C2×D3×H(5,𝔽2)2
C2×C3×#5772
C2×#58372
C2×#58352
#872072
C2×#57782
C2×#57772
C2×#57742
C2×D3×AGL(1,ℤ/8)2
C2×#57692
C2×#57682
C2×#57622
C22×#9142
C2×#57522
C2×#57502
C2×#35853