Finite Group Databasebeta

← C22×#3025⋊C3 #72341856

Subgroups — C22×#3025⋊C3 #72341856

Order 1536.

8336 conjugacy classes of subgroups; only the 228 normal subgroups are shown.

normal subgroups only

This group has 8336 conjugacy classes of subgroups — too many to draw. Only its 228 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#5950C211yesmaximal, characteristic, complemented
2C2×#3025⋊C3C2112yesmaximal, direct product factor
3C22×#458⋊C3C211yesmaximal, characteristic, complemented
4C22×B(4,𝔽2)⋊C3C211yesmaximal, characteristic, complemented
5C22×#3025C311yesmaximal, characteristic, complemented, Sylow
6C2×#5950C2216yescomplemented
7C22×#997C2211yescharacteristic
8C23×C4×A4—41nomaximal
9#3025⋊C3C22116yesdirect product factor
10C2×#458⋊C3C2216yescomplemented
11C2×B(4,𝔽2)⋊C3C2216yescomplemented
12C22×#585C2×C311yescharacteristic, complemented
13C22×#525—31no—
14C2×#3025—312no—
15C2×#3025C2×C3112yescomplemented
16C22×#458—31no—
17C22×#458C2×C311yescharacteristic, complemented
18C22×B(4,𝔽2)—31no—
19C22×B(4,𝔽2)C2×C311yescharacteristic
20C22×#410—31no—
21C24×A4—41no—
22#5950C2314yescomplemented
23C2×#997C2313yes—
24C22×#41⋊C3—81no—
25C22×C4×A4—41no—
26C22×C4×A4—41no—
27C22×C4×A4—412no—
28C22×C4×A4—81no—
29#458⋊C3C2314yescomplemented
30B(4,𝔽2)⋊C3C2314yescomplemented
31C2×#585—36no—
32C2×#585—66no—
33C2×#585—66no—
34C2×#585C22×C316yescomplemented
35C22×2−1+4—61no—
36C22×H(5,𝔽2)—31no—
37C22×H(5,𝔽2)—61no—
38C22×H(5,𝔽2)C22×C311yescharacteristic
39C23×#41—31no—
40C23×#41—61no—
41C23×#41—61no—
42C25×C4A411yescharacteristic, complemented
43C2×#525—312no—
44C2×#525—312no—
45C2×#525—66no—
46C2×#525—66no—
47C22×#123—31no—
48C22×#123—31no—
49C22×C22⋊Q8—61no—
50C22×#121—61no—
51C22×#120—31no—
52C22×#120—31no—
53C22×C4×D4—61no—
54C22×C4×D4—61no—
55C22×#117—31no—
56#3025—332no—
57#3025—348no—
58#3025C22×C3116yescomplemented
59C2×#458—312no—
60C2×#458—312no—
61C2×#458—36no—
62C2×#458C22×C316yescomplemented
63C2×B(4,𝔽2)—312no—
64C2×B(4,𝔽2)—312no—
65C2×B(4,𝔽2)—36no—
66C2×B(4,𝔽2)C22×C316yes—
67C2×#410—312no—
68C2×#410—312no—
69C22×#99—32no—
70C22×#99—31no—
71C22×#99—31no—
72C23×A4—48no—
73C23×A4—46no—
74C23×A4—41no—
75C23×A4—81no—
76C23×C3×C4—161no—
77#997C2411yescharacteristic
78C2×#41⋊C3—86no—
79C22×SL(2,𝔽3)—81no—
80C2×C4×A4—46no—
81C2×C4×A4—46no—
82C2×C4×A4—416no—
83C2×C4×A4—86no—
84C26C2×A411yescharacteristic
85#585—38no—
86#585—312no—
87#585—612no—
88#585—612no—
89#585—648no—
90#585—612no—
91#585—612no—
92#585—68no—
93#585—68no—
94#585—624no—
95#585—624no—
96#585C23×C314yescomplemented
97C2×2−1+4—66no—
98C2×2−1+4—612no—
99C2×2−1+4—66no—
100C2×2−1+4—66no—
101C2×2−1+4—612no—
102C2×2−1+4—66no—
103C2×H(5,𝔽2)—36no—
104C2×H(5,𝔽2)—36no—
105C2×H(5,𝔽2)—33no—
106C2×H(5,𝔽2)—63no—
107C2×H(5,𝔽2)—63no—
108C2×H(5,𝔽2)—612no—
109C2×H(5,𝔽2)—66no—
110C2×H(5,𝔽2)—612no—
111C2×H(5,𝔽2)—63no—
112C2×H(5,𝔽2)—63no—
113C2×H(5,𝔽2)—66no—
114C2×H(5,𝔽2)—66no—
115C2×H(5,𝔽2)—612no—
116C2×H(5,𝔽2)—66no—
117C2×H(5,𝔽2)C23×C313yes—
118C22×#41—21no—
119C22×#41—36no—
120C22×#41—36no—
121C22×#41—36no—
122C22×#41—36no—
123C22×#41—66no—
124C22×#41—66no—
125C22×#41—62no—
126C22×#41—62no—
127C22×#41—612no—
128C22×#41—61no—
129C22×#41—62no—
130C22×#41—66no—
131C22×#41—612no—
132C22×#41—612no—
133C22×#41—66no—
134C22×#41—61no—
135C22×#41—66no—
136C22×#41—66no—
137C22×#41—66no—
138C22×#41—62no—
139C22×#41—62no—
140C22×#41—612no—
141C22×#41—612no—
142C22×#41—61no—
143C22×#41—66no—
144C23×Q8—31no—
145C23×Q8—61no—
146C23×Q8—61no—
147C23×D4—31no—
148C23×D4—31no—
149C23×D4—31no—
150C23×D4—61no—
151C23×D4—62no—
152C23×D4—61no—
153C23×D4—61no—
154C23×D4—61no—
155C23×D4—61no—
156C23×D4—61no—
157C24×C4—21no—
158C24×C4—31no—
159C24×C4—31no—
160C24×C4—61no—
161C24×C4—61no—
162C24×C4—66no—
163C24×C4—61no—
164C24×C4C2×A411yescharacteristic
165C24×C4C2×A411yescharacteristic
166C24×C4C2×A4112yescomplemented
167#525—348no—
168#525—316no—
169#525—648no—
170#525—624no—
171#525—624no—
172C2×#123—312no—
173C2×#123—36no—
174C2×#123—36no—
175C2×#123—66no—
176C2×#123—63no—
177C2×#123—63no—
178C2×C22⋊Q8—612no—
179C2×C22⋊Q8—612no—
180C2×#121—612no—
181C2×#121—612no—
182C2×#120—312no—
183C2×#120—36no—
184C2×#120—36no—
185C2×#120—66no—
186C2×#120—63no—
187C2×#120—63no—
188C2×C4×D4—612no—
189C2×C4×D4—612no—
190C2×C4×D4—612no—
191C2×C4×D4—612no—
192C2×#117—312no—
193C2×#117—66no—
194C22×C4⋊C4—61no—
195C22×C4⋊C4—61no—
196C22×C4⋊C4—61no—
197C22×C22⋊C4—31no—
198C22×C22⋊C4—31no—
199C22×C22⋊C4—61no—
200C22×C22⋊C4—61no—
201C22×C22⋊C4—61no—
202C22×C22⋊C4—61no—
203C22×C42—61no—
204#458—348no—
205#458—38no—
206#458—316no—
207#458—312no—
208#458C23×C314yescomplemented
209B(4,𝔽2)—348no—
210B(4,𝔽2)—38no—
211B(4,𝔽2)—316no—
212B(4,𝔽2)—312no—
213B(4,𝔽2)C23×C314yes—
214#410—348no—
215#410—316no—
216C2×#99—324no—
217C2×#99—36no—
218C2×#99—36no—
219C2×#99—36no—
220C2×#99—36no—
221C24×C3—161no—
222C22×A4—424no—
223C22×A4—44no—
224C22×A4—44no—
225C22×A4—43no—
226C22×A4—83no—
227C22×A4—84no—
228C22×C3×C4—161no—
229C22×C3×C4—1612no—
230C22×C3×C4—161no—
231#41⋊C3—84no—
232C2×SL(2,𝔽3)—83no—
233C4×A4—44no—
234C4×A4—44no—
235C4×A4—84no—
236C25—21no—
237C25—31no—
238C25—31no—
239C25—48no—
240C25—61no—
241C25—63no—
242C25—61no—
243C25C22×A411yescharacteristic
244C25C22×A416yes—
2452−1+4—624no—
2462−1+4—612no—
2472−1+4—624no—
2482−1+4—64no—
2492−1+4—612no—
2502−1+4—624no—
2512−1+4—648no—
2522−1+4—624no—
2532−1+4—624no—
2542−1+4—648no—
2552−1+4—612no—
256H(5,𝔽2)—312no—
257H(5,𝔽2)—32no—
258H(5,𝔽2)—34no—
259H(5,𝔽2)—33no—
260H(5,𝔽2)—612no—
261H(5,𝔽2)—624no—
262H(5,𝔽2)—66no—
263H(5,𝔽2)—66no—
264H(5,𝔽2)—624no—
265H(5,𝔽2)—63no—
266H(5,𝔽2)—63no—
267H(5,𝔽2)—612no—
268H(5,𝔽2)—624no—
269H(5,𝔽2)—612no—
270H(5,𝔽2)—624no—
271H(5,𝔽2)—63no—
272H(5,𝔽2)—63no—
273H(5,𝔽2)—64no—
274H(5,𝔽2)—612no—
275H(5,𝔽2)—624no—
276H(5,𝔽2)—648no—
277H(5,𝔽2)—624no—
278H(5,𝔽2)—624no—
279H(5,𝔽2)—648no—
280H(5,𝔽2)—612no—
281H(5,𝔽2)—62no—
282H(5,𝔽2)—62no—
283H(5,𝔽2)—624no—
284H(5,𝔽2)—624no—
285H(5,𝔽2)—66no—
286H(5,𝔽2)—66no—
287H(5,𝔽2)C24×C311yescharacteristic
288C2×#41—26no—
289C2×#41—312no—
290C2×#41—312no—
291C2×#41—324no—
292C2×#41—34no—
293C2×#41—312no—
294C2×#41—64no—
295C2×#41—612no—
296C2×#41—612no—
297C2×#41—612no—
298C2×#41—612no—
299C2×#41—612no—
300C2×#41—612no—
301C2×#41—612no—
302C2×#41—612no—
303C2×#41—612no—
304C2×#41—624no—
305C2×#41—624no—
306C2×#41—624no—
307C2×#41—624no—
308C2×#41—66no—
309C2×#41—63no—
310C2×#41—66no—
311C2×#41—612no—
312C2×#41—612no—
313C2×#41—66no—
314C2×#41—624no—
315C2×#41—624no—
316C2×#41—612no—
317C2×#41—624no—
318C2×#41—624no—
319C2×#41—612no—
320C2×#41—63no—
321C2×#41—64no—
322C2×#41—63no—
323C2×#41—612no—
324C2×#41—612no—
325C2×#41—612no—
326C2×#41—612no—
327C2×#41—612no—
328C2×#41—612no—
329C2×#41—612no—
330C2×#41—612no—
331C2×#41—612no—
332C2×#41—612no—
333C2×#41—612no—
334C2×#41—66no—
335C2×#41—66no—
336C2×#41—612no—
337C2×#41—612no—
338C2×#41—66no—
339C2×#41—624no—
340C2×#41—624no—
341C2×#41—648no—
342C2×#41—648no—
343C2×#41—624no—
344C2×#41—648no—
345C2×#41—624no—
346C2×#41—648no—
347C2×#41—624no—
348C2×#41—624no—
349C2×#41—66no—
350C2×#41—66no—
351C2×#41—66no—
352C2×#41—63no—
353C2×#41—612no—
354C22×Q8—21no—
355C22×Q8—36no—
356C22×Q8—36no—
357C22×Q8—62no—
358C22×Q8—66no—
359C22×Q8—66no—
360C22×Q8—66no—
361C22×Q8—612no—
362C22×Q8—612no—
363C22×Q8—66no—
364C22×Q8—66no—
365C22×Q8—61no—
366C22×D4—33no—
367C22×D4—33no—
368C22×D4—36no—
369C22×D4—36no—
370C22×D4—36no—
371C22×D4—33no—
372C22×D4—33no—
373C22×D4—36no—
374C22×D4—62no—
375C22×D4—66no—
376C22×D4—66no—
377C22×D4—63no—
378C22×D4—62no—
379C22×D4—62no—
380C22×D4—66no—
381C22×D4—66no—
382C22×D4—612no—
383C22×D4—66no—
384C22×D4—612no—
385C22×D4—66no—
386C22×D4—66no—
387C22×D4—63no—
388C22×D4—61no—
389C22×D4—61no—
390C22×D4—66no—
391C22×D4—62no—
392C22×D4—66no—
393C22×D4—612no—
394C22×D4—612no—
395C22×D4—66no—
396C22×D4—612no—
397C22×D4—66no—
398C22×D4—66no—
399C22×D4—612no—
400C22×D4—66no—
401C22×D4—63no—
402C22×D4—63no—
403C22×D4—66no—
404C22×D4—612no—
405C22×D4—66no—
406C22×D4—128no—
407C22×D4—128no—
408C23×C4—26no—
409C23×C4—31no—
410C23×C4—31no—
411C23×C4—36no—
412C23×C4—31no—
413C23×C4—31no—
414C23×C4—36no—
415C23×C4—36no—
416C23×C4—36no—
417C23×C4—36no—
418C23×C4—41no—
419C23×C4—612no—
420C23×C4—61no—
421C23×C4—61no—
422C23×C4—66no—
423C23×C4—66no—
424C23×C4—612no—
425C23×C4—624no—
426C23×C4—61no—
427C23×C4—62no—
428C23×C4—612no—
429C23×C4—61no—
430C23×C4—61no—
431C23×C4—61no—
432C23×C4—66no—
433C23×C4—61no—
434C23×C4—66no—
435C23×C4—66no—
436C23×C4—61no—
437C23×C4—61no—
438C23×C4—63no—
439C23×C4—126no—
440C23×C4—121no—
441C23×C4—126no—
442C23×C4—128no—
443C23×C4C22×A416yes—
444C23×C4C22×A416yes—
445C23×C4C22×A4116yescomplemented
446#123—316no—
447#123—312no—
448#123—34no—
449#123—624no—
450#123—612no—
451#123—66no—
452#123—66no—
453C22⋊Q8—648no—
454C22⋊Q8—616no—
455#121—648no—
456#121—616no—
457#120—316no—
458#120—312no—
459#120—34no—
460#120—624no—
461#120—612no—
462#120—66no—
463#120—66no—
464C4×D4—648no—
465C4×D4—648no—
466C4×D4—616no—
467C4×D4—616no—
468#117—316no—
469#117—624no—
470C2×C4⋊C4—612no—
471C2×C4⋊C4—612no—
472C2×C4⋊C4—66no—
473C2×C4⋊C4—66no—
474C2×C22⋊C4—36no—
475C2×C22⋊C4—36no—
476C2×C22⋊C4—612no—
477C2×C22⋊C4—66no—
478C2×C22⋊C4—66no—
479C2×C22⋊C4—63no—
480C2×C22⋊C4—63no—
481C2×C22⋊C4—612no—
482C2×C22⋊C4—66no—
483C2×C22⋊C4—66no—
484C2×C42—612no—
485#99—332no—
486#99—312no—
487#99—312no—
488#99—34no—
489#99—34no—
490C23×C3—166no—
491C23×C3—168no—
492C23×C3—161no—
493C2×A4—48no—
494C2×A4—46no—
495C2×A4—41no—
496C2×A4—81no—
497C2×A4—86no—
498C2×C3×C4—166no—
499C2×C3×C4—1616no—
500C2×C3×C4—166no—
501SL(2,𝔽3)—81no—
502C24—23no—
503C24—31no—
504C24—33no—
505C24—33no—
506C24—36no—
507C24—33no—
508C24—41no—
509C24—424no—
510C24—44no—
511C24—66no—
512C24—63no—
513C24—63no—
514C24—66no—
515C24—68no—
516C24—66no—
517C24—61no—
518C24—61no—
519C24—63no—
520C24—66no—
521C24—84no—
522C24—123no—
523C24—122no—
524C24—124no—
525C24—1224no—
526C24—124no—
527C24—124no—
528C24—244no—
529C24C23×A413yes—
530C24C23×A414yes—
531#41—24no—
532#41—68no—
533#41—624no—
534#41—624no—
535#41—624no—
536#41—648no—
537#41—624no—
538#41—624no—
539#41—648no—
540#41—68no—
541#41—624no—
542#41—64no—
543#41—63no—
544#41—612no—
545#41—624no—
546#41—66no—
547#41—68no—
548#41—66no—
549#41—61no—
550#41—63no—
551#41—624no—
552#41—624no—
553#41—68no—
554#41—624no—
555#41—624no—
556#41—624no—
557#41—624no—
558#41—648no—
559#41—648no—
560#41—68no—
561#41—624no—
562#41—68no—
563#41—624no—
564#41—612no—
565#41—66no—
566#41—612no—
567#41—624no—
568#41—612no—
569#41—66no—
570#41—624no—
571#41—648no—
572#41—624no—
573#41—66no—
574#41—612no—
575#41—612no—
576#41—64no—
577#41—612no—
578#41—63no—
579C2×Q8—23no—
580C2×Q8—34no—
581C2×Q8—312no—
582C2×Q8—612no—
583C2×Q8—612no—
584C2×Q8—612no—
585C2×Q8—612no—
586C2×Q8—64no—
587C2×Q8—64no—
588C2×Q8—66no—
589C2×Q8—612no—
590C2×Q8—624no—
591C2×Q8—624no—
592C2×Q8—624no—
593C2×Q8—624no—
594C2×Q8—612no—
595C2×Q8—63no—
596C2×Q8—66no—
597C2×D4—33no—
598C2×D4—33no—
599C2×D4—36no—
600C2×D4—312no—
601C2×D4—34no—
602C2×D4—312no—
603C2×D4—33no—
604C2×D4—34no—
605C2×D4—31no—
606C2×D4—612no—
607C2×D4—612no—
608C2×D4—612no—
609C2×D4—612no—
610C2×D4—64no—
611C2×D4—63no—
612C2×D4—66no—
613C2×D4—66no—
614C2×D4—66no—
615C2×D4—612no—
616C2×D4—66no—
617C2×D4—612no—
618C2×D4—66no—
619C2×D4—66no—
620C2×D4—612no—
621C2×D4—66no—
622C2×D4—66no—
623C2×D4—612no—
624C2×D4—68no—
625C2×D4—66no—
626C2×D4—624no—
627C2×D4—66no—
628C2×D4—612no—
629C2×D4—64no—
630C2×D4—63no—
631C2×D4—66no—
632C2×D4—63no—
633C2×D4—63no—
634C2×D4—64no—
635C2×D4—66no—
636C2×D4—612no—
637C2×D4—66no—
638C2×D4—612no—
639C2×D4—612no—
640C2×D4—624no—
641C2×D4—624no—
642C2×D4—624no—
643C2×D4—624no—
644C2×D4—612no—
645C2×D4—624no—
646C2×D4—612no—
647C2×D4—66no—
648C2×D4—648no—
649C2×D4—66no—
650C2×D4—612no—
651C2×D4—624no—
652C2×D4—612no—
653C2×D4—624no—
654C2×D4—612no—
655C2×D4—66no—
656C2×D4—61no—
657C2×D4—63no—
658C2×D4—612no—
659C2×D4—616no—
660C2×D4—64no—
661C2×D4—1224no—
662C2×D4—1224no—
663C2×D4—1248no—
664C22×C4—24no—
665C22×C4—36no—
666C22×C4—38no—
667C22×C4—31no—
668C22×C4—36no—
669C22×C4—36no—
670C22×C4—36no—
671C22×C4—312no—
672C22×C4—33no—
673C22×C4—33no—
674C22×C4—36no—
675C22×C4—34no—
676C22×C4—34no—
677C22×C4—312no—
678C22×C4—312no—
679C22×C4—41no—
680C22×C4—412no—
681C22×C4—616no—
682C22×C4—66no—
683C22×C4—66no—
684C22×C4—66no—
685C22×C4—66no—
686C22×C4—612no—
687C22×C4—612no—
688C22×C4—612no—
689C22×C4—612no—
690C22×C4—616no—
691C22×C4—66no—
692C22×C4—63no—
693C22×C4—63no—
694C22×C4—612no—
695C22×C4—66no—
696C22×C4—612no—
697C22×C4—66no—
698C22×C4—624no—
699C22×C4—624no—
700C22×C4—68no—
701C22×C4—61no—
702C22×C4—61no—
703C22×C4—66no—
704C22×C4—66no—
705C22×C4—66no—
706C22×C4—66no—
707C22×C4—66no—
708C22×C4—612no—
709C22×C4—63no—
710C22×C4—63no—
711C22×C4—64no—
712C22×C4—612no—
713C22×C4—66no—
714C22×C4—66no—
715C22×C4—66no—
716C22×C4—1224no—
717C22×C4—1212no—
718C22×C4—1224no—
719C22×C4—123no—
720C22×C4—122no—
721C22×C4—124no—
722C22×C4—124no—
723C22×C4#120⋊C311yescharacteristic
724C22×C4C23×A414yes—
725C22×C4C23×A414yes—
726C4⋊C4—616no—
727C4⋊C4—616no—
728C4⋊C4—612no—
729C4⋊C4—64no—
730C22⋊C4—34no—
731C22⋊C4—34no—
732C22⋊C4—616no—
733C22⋊C4—612no—
734C22⋊C4—64no—
735C22⋊C4—66no—
736C22⋊C4—66no—
737C22⋊C4—616no—
738C22⋊C4—612no—
739C22⋊C4—64no—
740C42—616no—
741C22×C3—164no—
742C22×C3—1624no—
743C22×C3—164no—
744C22×C3—163no—
745A4—41no—
746A4—81no—
747C3×C4—164no—
748C3×C4—164no—
749C23—21no—
750C23—32no—
751C23—33no—
752C23—33no—
753C23—33no—
754C23—31no—
755C23—34no—
756C23—33no—
757C23—48no—
758C23—46no—
759C23—48no—
760C23—46no—
761C23—64no—
762C23—63no—
763C23—66no—
764C23—63no—
765C23—624no—
766C23—64no—
767C23—612no—
768C23—62no—
769C23—63no—
770C23—66no—
771C23—63no—
772C23—63no—
773C23—64no—
774C23—86no—
775C23—126no—
776C23—1212no—
777C23—1224no—
778C23—126no—
779C23—1224no—
780C23—126no—
781C23—126no—
782C23—1212no—
783C23—1216no—
784C23—124no—
785C23—124no—
786C23—246no—
787C23—246no—
788C23—2412no—
789C23—246no—
790C23—2412no—
791C23C2×#120⋊C311yescharacteristic
792C23C24×A411yescharacteristic
793Q8—21no—
794Q8—68no—
795Q8—624no—
796Q8—63no—
797Q8—64no—
798Q8—612no—
799Q8—62no—
800D4—68no—
801D4—624no—
802D4—62no—
803D4—66no—
804D4—66no—
805D4—68no—
806D4—66no—
807D4—612no—
808D4—624no—
809D4—64no—
810D4—61no—
811D4—63no—
812D4—66no—
813D4—68no—
814D4—612no—
815D4—66no—
816D4—624no—
817D4—128no—
818D4—1224no—
819D4—1232no—
820C2×C4—312no—
821C2×C4—36no—
822C2×C4—34no—
823C2×C4—312no—
824C2×C4—34no—
825C2×C4—31no—
826C2×C4—33no—
827C2×C4—34no—
828C2×C4—46no—
829C2×C4—416no—
830C2×C4—64no—
831C2×C4—64no—
832C2×C4—612no—
833C2×C4—612no—
834C2×C4—64no—
835C2×C4—63no—
836C2×C4—63no—
837C2×C4—66no—
838C2×C4—68no—
839C2×C4—66no—
840C2×C4—624no—
841C2×C4—66no—
842C2×C4—612no—
843C2×C4—63no—
844C2×C4—63no—
845C2×C4—66no—
846C2×C4—64no—
847C2×C4—64no—
848C2×C4—612no—
849C2×C4—612no—
850C2×C4—64no—
851C2×C4—61no—
852C2×C4—63no—
853C2×C4—64no—
854C2×C4—64no—
855C2×C4—1216no—
856C2×C4—126no—
857C2×C4—1212no—
858C2×C4—1212no—
859C2×C4C2×#120⋊C316yes—
860C2×C3—168no—
861C2×C3—166no—
862C2×C3—161no—
863C22—31no—
864C22—33no—
865C22—424no—
866C22—44no—
867C22—41no—
868C22—68no—
869C22—66no—
870C22—66no—
871C22—61no—
872C22—64no—
873C22—63no—
874C22—81no—
875C22—124no—
876C22—1224no—
877C22—123no—
878C22—122no—
879C22—121no—
880C22—123no—
881C22—124no—
882C22—126no—
883C22—126no—
884C22—1212no—
885C22—243no—
886C22—243no—
887C22—246no—
888C22—243no—
889C22—244no—
890C22—2412no—
891C22—242no—
892C22#3025⋊C314yesdirect product factor
893C22C22×#120⋊C313yes—
894C4—34no—
895C4—44no—
896C4—61no—
897C4—63no—
898C4—64no—
899C4—124no—
900C4—124no—
901C4C22×#120⋊C314yes—
902C3—161noSylow
903C2—48no—
904C2—61no—
905C2—63no—
906C2—121no—
907C2—123no—
908C2—124no—
909C2C2×#3025⋊C316yesdirect product factor
910C2C23×#120⋊C311yescharacteristic
subgroupG/H
center, hypercenterC22×C4#120⋊C3
commutator, cosocle, hypocenterH(5,𝔽2)C24×C3
FrattiniC23C24×A4
FittingC22×#3025C3
socleC23C2×#120⋊C3
LCSG ▷ H(5,𝔽2)
UCSC1 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×#5950C2semidirect
2. C2×#3025⋊C3C2direct (N × H)
3. C22×#458⋊C3C2semidirect
4. C22×B(4,𝔽2)⋊C3C2semidirect
5. C22×#3025C3semidirect
6. C2×#5950C22semidirect
9. #3025⋊C3C22direct (N × H)
10. C2×#458⋊C3C22semidirect
11. C2×B(4,𝔽2)⋊C3C22semidirect
12. C22×#585C2×C3semidirect
15. C2×#3025C2×C3semidirect
17. C22×#458C2×C3semidirect
22. #5950C23semidirect
29. #458⋊C3C23semidirect
30. B(4,𝔽2)⋊C3C23semidirect
34. C2×#585C22×C3semidirect
42. C25×C4A4semidirect
58. #3025C22×C3semidirect
62. C2×#458C22×C3semidirect
96. #585C23×C3semidirect
166. C24×C4C2×A4semidirect
208. #458C23×C3semidirect
445. C23×C4C22×A4semidirect
892. C22#3025⋊C3direct (N × H)
909. C2C2×#3025⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#59502
C2×#3025⋊C32
C22×#458⋊C32
C22×B(4,𝔽2)⋊C32
C22×#30253
C23×C4×A44