Finite Group Databasebeta

← C2×#11715661 #72341506

Subgroups — C2×#11715661 #72341506

Order 1536.

7312 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 7312 conjugacy classes of subgroups — too many to draw. Only its 110 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
1#11715661C214yesmaximal, direct product factor
2C2×#85566C212yesmaximal, complemented
3C22×#5950C211yesmaximal, characteristic
4C2×#20612—31nomaximal, Sylow
5C2×#5950C411yescharacteristic
6C2×#5950C412yes—
7C2×#5950C2211yescharacteristic
8C2×#5950C2212yes—
9C22×#997C411yescharacteristic
10#85566C2214yescomplemented
11C2×#5409—43nomaximal
12C22×#585D311yescharacteristic
13C22×#413—33no—
14C2×#2879—33no—
15#20612—312no—
16#20612—34no—
17C2×#1791—36no—
18C2×#1791—32no—
19#5950C2×C411yescharacteristic
20#5950C2×C412yes—
21#5950C2311yescharacteristic
22C2×#997C2×C411yescharacteristic
23C2×#997C2×C412yes—
24C22×#41⋊C3—81no—
25C22×C4×A4—43no—
26#5409—412no—
27C2×A4⋊C8—46no—
28C2×#585—33no—
29C2×#585—36no—
30C2×#585—33no—
31C2×#585—36no—
32C2×#585—61no—
33C2×#585—62no—
34C2×#585—61no—
35C2×#585—62no—
36C2×#585Dic311yescharacteristic
37C2×#585Dic312yes—
38C2×#585C2×D311yescharacteristic
39C2×#585C2×D312yes—
40C22×2−1+4—61no—
41C22×H(5,𝔽2)—33no—
42C22×H(5,𝔽2)Dic311yescharacteristic
43C23×#41—33no—
44C23×#41—61no—
45C23×M16—31no—
46C23×M16—33no—
47C2×#413—36no—
48C2×#413—36no—
49C2×#413—312no—
50C2×#413—312no—
51C2×#413—63no—
52C2×#413—66no—
53C2×#413—63no—
54C2×#413—66no—
55C22×#101—63no—
56C22×#100—63no—
57#2879—312no—
58#2879—312no—
59#2879—66no—
60#2879—66no—
61C2×#408—36no—
62C2×#408—36no—
63C2×#408—63no—
64C2×#408—63no—
65C2×#407—63no—
66C2×#407—63no—
67#1791—324no—
68#1791—312no—
69#1791—324no—
70#1791—34no—
71C23×A4—43no—
72#997C22×C411yescharacteristic
73C2×#41⋊C3—81no—
74C2×#41⋊C3—82no—
75C2×#41⋊C3—82no—
76C2×#41⋊C3—81no—
77C22×SL(2,𝔽3)—81no—
78C2×C4×A4—43no—
79C2×C4×A4—46no—
80C2×C4×A4—43no—
81C2×C4×A4—46no—
82C2×#208—161no—
83A4⋊C8—412no—
84#585—36no—
85#585—36no—
86#585—36no—
87#585—33no—
88#585—36no—
89#585—36no—
90#585—33no—
91#585—36no—
92#585—312no—
93#585—36no—
94#585—63no—
95#585—66no—
96#585—63no—
97#585—62no—
98#585—62no—
99#585—62no—
100#585—61no—
101#585—62no—
102#585—61no—
103#585—62no—
104#585—66no—
105#585—612no—
106#585—612no—
107#585—612no—
108#585—612no—
109#585—612no—
110#585—66no—
111#585—66no—
112#585—66no—
113#585—66no—
114#585—63no—
115#585—66no—
116#585—63no—
117#585—66no—
118#585—62no—
119#585—62no—
120#585—64no—
121#585C2×Dic311yescharacteristic
122#585C2×Dic312yes—
123#585C22×D311yescharacteristic
124C2×2−1+4—61no—
125C2×2−1+4—62no—
126C2×2−1+4—61no—
127C2×2−1+4—62no—
128C2×2−1+4—66no—
129C2×2−1+4—612no—
130C2×2−1+4—63no—
131C2×2−1+4—66no—
132C2×2−1+4—63no—
133C2×2−1+4—66no—
134C2×2−1+4—62no—
135C2×2−1+4—64no—
136C2×H(5,𝔽2)—33no—
137C2×H(5,𝔽2)—36no—
138C2×H(5,𝔽2)—33no—
139C2×H(5,𝔽2)—36no—
140C2×H(5,𝔽2)—33no—
141C2×H(5,𝔽2)—36no—
142C2×H(5,𝔽2)—36no—
143C2×H(5,𝔽2)—312no—
144C2×H(5,𝔽2)—63no—
145C2×H(5,𝔽2)—66no—
146C2×H(5,𝔽2)—61no—
147C2×H(5,𝔽2)—62no—
148C2×H(5,𝔽2)—66no—
149C2×H(5,𝔽2)—612no—
150C2×H(5,𝔽2)—66no—
151C2×H(5,𝔽2)—612no—
152C2×H(5,𝔽2)—63no—
153C2×H(5,𝔽2)—66no—
154C2×H(5,𝔽2)C2×Dic311yescharacteristic
155C2×H(5,𝔽2)C2×Dic312yes—
156C22×#41—21no—
157C22×#41—33no—
158C22×#41—36no—
159C22×#41—33no—
160C22×#41—36no—
161C22×#41—33no—
162C22×#41—36no—
163C22×#41—33no—
164C22×#41—36no—
165C22×#41—33no—
166C22×#41—36no—
167C22×#41—33no—
168C22×#41—36no—
169C22×#41—33no—
170C22×#41—36no—
171C22×#41—33no—
172C22×#41—36no—
173C22×#41—61no—
174C22×#41—61no—
175C22×#41—62no—
176C22×#41—61no—
177C22×#41—62no—
178C22×#41—63no—
179C22×#41—66no—
180C22×#41—66no—
181C22×#41—66no—
182C22×#41—612no—
183C22×#41—612no—
184C22×#41—63no—
185C22×#41—66no—
186C22×#41—63no—
187C22×#41—66no—
188C22×#41—63no—
189C22×#41—63no—
190C22×#41—66no—
191C22×#41—63no—
192C22×#41—66no—
193C22×#41—61no—
194C22×#41—62no—
195C22×#41—62no—
196C22×#41—61no—
197C23×Q8—33no—
198C23×Q8—61no—
199C23×D4—33no—
200C23×D4—33no—
201C23×D4—33no—
202C23×D4—63no—
203C24×C4—31no—
204C24×C4—33no—
205C24×C4S413yes—
206C22×M16—34no—
207C22×M16—36no—
208C22×M16—312no—
209C22×M16—63no—
210C22×M16—63no—
211C22×M16—63no—
212C22×M16—66no—
213C22×M16—66no—
214C22×M16—66no—
215C22×M16—66no—
216C22×M16—612no—
217C23×C8—32no—
218C23×C8—63no—
219#413—324no—
220#413—312no—
221#413—312no—
222#413—612no—
223#413—66no—
224#413—612no—
225#413—612no—
226#413—612no—
227#413—66no—
228#413—612no—
229C2×#101—66no—
230C2×#101—66no—
231C2×#101—612no—
232C2×#101—612no—
233C2×#100—66no—
234C2×#100—612no—
235C2×#100—66no—
236C2×#100—612no—
237#408—324no—
238#408—312no—
239#408—312no—
240#408—612no—
241#408—66no—
242#408—66no—
243#408—612no—
244#408—612no—
245#408—612no—
246#408—612no—
247#407—612no—
248#407—612no—
249#407—612no—
250#407—612no—
251C2×C22⋊C8—66no—
252C2×C22⋊C8—66no—
253C2×C22⋊C8—66no—
254C2×C22⋊C8—66no—
255C22×A4—43no—
256C22×A4—46no—
257C22×A4—86no—
258C22×C3×C4—161no—
259#41⋊C3—82no—
260#41⋊C3—81no—
261#41⋊C3—81no—
262C2×SL(2,𝔽3)—81no—
263C2×SL(2,𝔽3)—82no—
264C4×A4—43no—
265C4×A4—46no—
266C4×A4—43no—
267#208—164no—
268C2×C3⋊C8—162no—
269C25—31no—
270C25—33no—
271C25SL(2,ℤ/4)13yes—
2722−1+4—61no—
2732−1+4—62no—
2742−1+4—61no—
2752−1+4—612no—
2762−1+4—66no—
2772−1+4—612no—
2782−1+4—66no—
2792−1+4—66no—
2802−1+4—63no—
2812−1+4—612no—
2822−1+4—66no—
2832−1+4—66no—
2842−1+4—66no—
2852−1+4—66no—
2862−1+4—66no—
2872−1+4—63no—
2882−1+4—612no—
2892−1+4—612no—
2902−1+4—612no—
2912−1+4—66no—
2922−1+4—612no—
2932−1+4—64no—
2942−1+4—62no—
2952−1+4—64no—
2962−1+4—62no—
2972−1+4—612no—
2982−1+4—612no—
2992−1+4—612no—
3002−1+4—612no—
3012−1+4—612no—
3022−1+4—612no—
3032−1+4—66no—
3042−1+4—612no—
3052−1+4—66no—
306H(5,𝔽2)—36no—
307H(5,𝔽2)—33no—
308H(5,𝔽2)—33no—
309H(5,𝔽2)—36no—
310H(5,𝔽2)—33no—
311H(5,𝔽2)—36no—
312H(5,𝔽2)—312no—
313H(5,𝔽2)—312no—
314H(5,𝔽2)—36no—
315H(5,𝔽2)—36no—
316H(5,𝔽2)—61no—
317H(5,𝔽2)—62no—
318H(5,𝔽2)—63no—
319H(5,𝔽2)—63no—
320H(5,𝔽2)—66no—
321H(5,𝔽2)—63no—
322H(5,𝔽2)—66no—
323H(5,𝔽2)—612no—
324H(5,𝔽2)—66no—
325H(5,𝔽2)—612no—
326H(5,𝔽2)—66no—
327H(5,𝔽2)—612no—
328H(5,𝔽2)—612no—
329H(5,𝔽2)—612no—
330H(5,𝔽2)—612no—
331H(5,𝔽2)—66no—
332H(5,𝔽2)—63no—
333H(5,𝔽2)—66no—
334H(5,𝔽2)—66no—
335H(5,𝔽2)—63no—
336H(5,𝔽2)—612no—
337H(5,𝔽2)—612no—
338H(5,𝔽2)—612no—
339H(5,𝔽2)—66no—
340H(5,𝔽2)—612no—
341H(5,𝔽2)—612no—
342H(5,𝔽2)—612no—
343H(5,𝔽2)—612no—
344H(5,𝔽2)—66no—
345H(5,𝔽2)—612no—
346H(5,𝔽2)—63no—
347H(5,𝔽2)—66no—
348H(5,𝔽2)—66no—
349H(5,𝔽2)—612no—
350H(5,𝔽2)—66no—
351H(5,𝔽2)—612no—
352H(5,𝔽2)—612no—
353H(5,𝔽2)—612no—
354H(5,𝔽2)—612no—
355H(5,𝔽2)—66no—
356H(5,𝔽2)—612no—
357H(5,𝔽2)—612no—
358H(5,𝔽2)—612no—
359H(5,𝔽2)—612no—
360H(5,𝔽2)—66no—
361H(5,𝔽2)—612no—
362H(5,𝔽2)—62no—
363H(5,𝔽2)C22×Dic311yescharacteristic
364C2×#41—22no—
365C2×#41—21no—
366C2×#41—22no—
367C2×#41—21no—
368C2×#41—36no—
369C2×#41—36no—
370C2×#41—36no—
371C2×#41—33no—
372C2×#41—36no—
373C2×#41—36no—
374C2×#41—33no—
375C2×#41—36no—
376C2×#41—36no—
377C2×#41—36no—
378C2×#41—36no—
379C2×#41—36no—
380C2×#41—36no—
381C2×#41—36no—
382C2×#41—36no—
383C2×#41—36no—
384C2×#41—36no—
385C2×#41—36no—
386C2×#41—36no—
387C2×#41—36no—
388C2×#41—33no—
389C2×#41—36no—
390C2×#41—36no—
391C2×#41—36no—
392C2×#41—33no—
393C2×#41—36no—
394C2×#41—33no—
395C2×#41—36no—
396C2×#41—36no—
397C2×#41—36no—
398C2×#41—36no—
399C2×#41—33no—
400C2×#41—36no—
401C2×#41—33no—
402C2×#41—33no—
403C2×#41—36no—
404C2×#41—61no—
405C2×#41—62no—
406C2×#41—61no—
407C2×#41—62no—
408C2×#41—61no—
409C2×#41—63no—
410C2×#41—66no—
411C2×#41—66no—
412C2×#41—612no—
413C2×#41—63no—
414C2×#41—66no—
415C2×#41—66no—
416C2×#41—612no—
417C2×#41—66no—
418C2×#41—63no—
419C2×#41—66no—
420C2×#41—63no—
421C2×#41—66no—
422C2×#41—66no—
423C2×#41—66no—
424C2×#41—612no—
425C2×#41—612no—
426C2×#41—612no—
427C2×#41—66no—
428C2×#41—612no—
429C2×#41—66no—
430C2×#41—612no—
431C2×#41—612no—
432C2×#41—66no—
433C2×#41—66no—
434C2×#41—612no—
435C2×#41—66no—
436C2×#41—612no—
437C2×#41—612no—
438C2×#41—612no—
439C2×#41—612no—
440C2×#41—612no—
441C2×#41—612no—
442C2×#41—612no—
443C2×#41—63no—
444C2×#41—66no—
445C2×#41—63no—
446C2×#41—66no—
447C2×#41—66no—
448C2×#41—66no—
449C2×#41—66no—
450C2×#41—63no—
451C2×#41—66no—
452C2×#41—66no—
453C2×#41—66no—
454C2×#41—66no—
455C2×#41—612no—
456C2×#41—612no—
457C2×#41—612no—
458C2×#41—66no—
459C2×#41—612no—
460C2×#41—66no—
461C2×#41—612no—
462C2×#41—66no—
463C2×#41—612no—
464C2×#41—66no—
465C2×#41—612no—
466C2×#41—66no—
467C2×#41—612no—
468C2×#41—612no—
469C2×#41—612no—
470C2×#41—612no—
471C2×#41—612no—
472C2×#41—612no—
473C2×#41—612no—
474C2×#41—63no—
475C2×#41—66no—
476C2×#41—63no—
477C2×#41—66no—
478C2×#41—66no—
479C2×#41—612no—
480C2×#41—63no—
481C2×#41—66no—
482C2×#41—612no—
483C2×#41—66no—
484C2×#41—63no—
485C2×#41—66no—
486C2×#41—66no—
487C2×#41—612no—
488C2×#41—612no—
489C2×#41—612no—
490C2×#41—612no—
491C2×#41—66no—
492C2×#41—66no—
493C2×#41—66no—
494C2×#41—63no—
495C2×#41—66no—
496C2×#41—61no—
497C2×#41—62no—
498C2×#41—62no—
499C2×#41—62no—
500C2×#41—62no—
501C2×#41—61no—
502C2×#41—62no—
503C2×#41—61no—
504C2×#41—62no—
505C2×#41—63no—
506C2×#41—66no—
507C2×#41—63no—
508C2×#41—66no—
509C2×#41—66no—
510C2×#41—612no—
511C2×#41—66no—
512C2×#41—66no—
513C2×#41—612no—
514C2×#41—66no—
515C2×#41—66no—
516C2×#41—66no—
517C2×#41—66no—
518C2×#41—66no—
519C2×#41—66no—
520C2×#41—66no—
521C2×#41—66no—
522C2×#41—66no—
523C2×#41—66no—
524C2×#41—66no—
525C2×#41—66no—
526C2×#41—62no—
527C2×#41—61no—
528C2×#41—62no—
529C2×#41—61no—
530C22×Q8—21no—
531C22×Q8—33no—
532C22×Q8—36no—
533C22×Q8—33no—
534C22×Q8—36no—
535C22×Q8—33no—
536C22×Q8—36no—
537C22×Q8—33no—
538C22×Q8—36no—
539C22×Q8—63no—
540C22×Q8—66no—
541C22×Q8—612no—
542C22×Q8—62no—
543C22×Q8—61no—
544C22×Q8—61no—
545C22×Q8—62no—
546C22×Q8—63no—
547C22×Q8—63no—
548C22×Q8—66no—
549C22×Q8—66no—
550C22×D4—33no—
551C22×D4—36no—
552C22×D4—33no—
553C22×D4—36no—
554C22×D4—33no—
555C22×D4—36no—
556C22×D4—33no—
557C22×D4—36no—
558C22×D4—33no—
559C22×D4—36no—
560C22×D4—33no—
561C22×D4—36no—
562C22×D4—33no—
563C22×D4—36no—
564C22×D4—33no—
565C22×D4—36no—
566C22×D4—33no—
567C22×D4—36no—
568C22×D4—33no—
569C22×D4—36no—
570C22×D4—33no—
571C22×D4—36no—
572C22×D4—33no—
573C22×D4—36no—
574C22×D4—66no—
575C22×D4—66no—
576C22×D4—612no—
577C22×D4—63no—
578C22×D4—66no—
579C22×D4—612no—
580C22×D4—63no—
581C22×D4—63no—
582C22×D4—66no—
583C22×D4—66no—
584C22×D4—66no—
585C22×D4—612no—
586C22×D4—66no—
587C22×D4—66no—
588C22×D4—612no—
589C22×D4—612no—
590C22×D4—61no—
591C22×D4—63no—
592C22×D4—66no—
593C22×D4—63no—
594C22×D4—66no—
595C23×C4—31no—
596C23×C4—33no—
597C23×C4—32no—
598C23×C4—33no—
599C23×C4—36no—
600C23×C4—33no—
601C23×C4—36no—
602C23×C4—31no—
603C23×C4—32no—
604C23×C4—33no—
605C23×C4—33no—
606C23×C4—33no—
607C23×C4—36no—
608C23×C4—33no—
609C23×C4—36no—
610C23×C4—33no—
611C23×C4—33no—
612C23×C4—36no—
613C23×C4—33no—
614C23×C4—36no—
615C23×C4—33no—
616C23×C4—33no—
617C23×C4—36no—
618C23×C4—36no—
619C23×C4—63no—
620C23×C4—63no—
621C23×C4—66no—
622C23×C4—66no—
623C23×C4—63no—
624C23×C4—61no—
625C23×C4SL(2,ℤ/4)13yes—
626C23×C4SL(2,ℤ/4)16yes—
627C23×C4C2×S413yes—
628C23×C4C2×S416yes—
629C2×M16—312no—
630C2×M16—612no—
631C2×M16—612no—
632C2×M16—612no—
633C2×M16—66no—
634C2×M16—612no—
635C2×M16—624no—
636C2×M16—612no—
637C2×M16—624no—
638C2×M16—126no—
639C2×M16—126no—
640C2×M16—1212no—
641C2×M16—1212no—
642C2×M16—123no—
643C2×M16—123no—
644C2×M16—126no—
645C2×M16—123no—
646C2×M16—121no—
647C22×C8—34no—
648C22×C8—66no—
649C22×C8—66no—
650C22×C8—66no—
651C22×C8—612no—
652C22×C8—126no—
653C22×C8—126no—
654#101—624no—
655#101—612no—
656#101—612no—
657#100—624no—
658#100—612no—
659#100—612no—
660C22⋊C8—624no—
661C22⋊C8—612no—
662C22⋊C8—612no—
663C22⋊C8—624no—
664C22⋊C8—612no—
665C22⋊C8—612no—
666C23×C3—161no—
667C2×A4—46no—
668C2×A4—43no—
669C2×A4—86no—
670C2×C3×C4—161no—
671C2×C3×C4—162no—
672C2×C3×C4—162no—
673C2×C3×C4—161no—
674SL(2,𝔽3)—81no—
675C3⋊C8—164no—
676C24—31no—
677C24—33no—
678C24—32no—
679C24—36no—
680C24—33no—
681C24—33no—
682C24—36no—
683C24—33no—
684C24—33no—
685C24—36no—
686C24—36no—
687C24—63no—
688C24—66no—
689C24—61no—
690C24—86no—
691C24—242no—
692C24—246no—
693C24C2×SL(2,ℤ/4)13yes—
694C24C2×SL(2,ℤ/4)16yes—
695#41—21no—
696#41—22no—
697#41—21no—
698#41—61no—
699#41—63no—
700#41—66no—
701#41—612no—
702#41—63no—
703#41—612no—
704#41—66no—
705#41—66no—
706#41—63no—
707#41—66no—
708#41—612no—
709#41—66no—
710#41—612no—
711#41—612no—
712#41—612no—
713#41—66no—
714#41—63no—
715#41—612no—
716#41—612no—
717#41—612no—
718#41—66no—
719#41—66no—
720#41—66no—
721#41—612no—
722#41—66no—
723#41—612no—
724#41—612no—
725#41—66no—
726#41—66no—
727#41—66no—
728#41—66no—
729#41—612no—
730#41—612no—
731#41—612no—
732#41—612no—
733#41—63no—
734#41—66no—
735#41—612no—
736#41—612no—
737#41—612no—
738#41—612no—
739#41—612no—
740#41—612no—
741#41—612no—
742#41—66no—
743#41—66no—
744#41—612no—
745#41—66no—
746#41—612no—
747#41—66no—
748#41—612no—
749#41—612no—
750#41—612no—
751#41—612no—
752#41—612no—
753#41—612no—
754#41—612no—
755#41—612no—
756#41—612no—
757#41—612no—
758#41—612no—
759#41—612no—
760#41—612no—
761#41—66no—
762#41—63no—
763#41—63no—
764#41—66no—
765#41—612no—
766#41—66no—
767#41—612no—
768#41—66no—
769#41—63no—
770#41—66no—
771#41—612no—
772#41—62no—
773#41—61no—
774#41—62no—
775#41—64no—
776#41—62no—
777#41—63no—
778#41—66no—
779#41—66no—
780#41—66no—
781#41—66no—
782#41—66no—
783#41—63no—
784#41—612no—
785#41—66no—
786#41—66no—
787#41—612no—
788#41—612no—
789#41—612no—
790#41—612no—
791#41—612no—
792#41—612no—
793#41—612no—
794#41—66no—
795#41—66no—
796#41—66no—
797#41—66no—
798#41—62no—
799#41—61no—
800#41—62no—
801#41—62no—
802#41—62no—
803#41—62no—
804#41—61no—
805C2×Q8—22no—
806C2×Q8—21no—
807C2×Q8—36no—
808C2×Q8—33no—
809C2×Q8—33no—
810C2×Q8—36no—
811C2×Q8—36no—
812C2×Q8—36no—
813C2×Q8—36no—
814C2×Q8—33no—
815C2×Q8—36no—
816C2×Q8—33no—
817C2×Q8—63no—
818C2×Q8—66no—
819C2×Q8—66no—
820C2×Q8—612no—
821C2×Q8—66no—
822C2×Q8—63no—
823C2×Q8—612no—
824C2×Q8—612no—
825C2×Q8—66no—
826C2×Q8—66no—
827C2×Q8—612no—
828C2×Q8—66no—
829C2×Q8—612no—
830C2×Q8—66no—
831C2×Q8—62no—
832C2×Q8—61no—
833C2×Q8—61no—
834C2×Q8—66no—
835C2×Q8—63no—
836C2×Q8—63no—
837C2×Q8—66no—
838C2×Q8—66no—
839C2×Q8—66no—
840C2×Q8—66no—
841C2×Q8—66no—
842C2×Q8—612no—
843C2×Q8—66no—
844C2×Q8—62no—
845C2×Q8—61no—
846C2×D4—33no—
847C2×D4—36no—
848C2×D4—36no—
849C2×D4—33no—
850C2×D4—33no—
851C2×D4—33no—
852C2×D4—36no—
853C2×D4—33no—
854C2×D4—36no—
855C2×D4—36no—
856C2×D4—36no—
857C2×D4—36no—
858C2×D4—33no—
859C2×D4—36no—
860C2×D4—36no—
861C2×D4—36no—
862C2×D4—36no—
863C2×D4—33no—
864C2×D4—36no—
865C2×D4—36no—
866C2×D4—36no—
867C2×D4—36no—
868C2×D4—33no—
869C2×D4—36no—
870C2×D4—33no—
871C2×D4—33no—
872C2×D4—36no—
873C2×D4—33no—
874C2×D4—33no—
875C2×D4—36no—
876C2×D4—66no—
877C2×D4—66no—
878C2×D4—612no—
879C2×D4—612no—
880C2×D4—66no—
881C2×D4—66no—
882C2×D4—612no—
883C2×D4—612no—
884C2×D4—612no—
885C2×D4—66no—
886C2×D4—612no—
887C2×D4—66no—
888C2×D4—612no—
889C2×D4—66no—
890C2×D4—612no—
891C2×D4—66no—
892C2×D4—63no—
893C2×D4—63no—
894C2×D4—66no—
895C2×D4—66no—
896C2×D4—66no—
897C2×D4—612no—
898C2×D4—66no—
899C2×D4—612no—
900C2×D4—66no—
901C2×D4—612no—
902C2×D4—66no—
903C2×D4—63no—
904C2×D4—63no—
905C2×D4—66no—
906C2×D4—612no—
907C2×D4—66no—
908C2×D4—612no—
909C2×D4—66no—
910C2×D4—612no—
911C2×D4—66no—
912C2×D4—612no—
913C2×D4—66no—
914C2×D4—612no—
915C2×D4—66no—
916C2×D4—612no—
917C2×D4—66no—
918C2×D4—612no—
919C2×D4—612no—
920C2×D4—612no—
921C2×D4—612no—
922C2×D4—66no—
923C2×D4—612no—
924C2×D4—62no—
925C2×D4—62no—
926C2×D4—61no—
927C2×D4—61no—
928C2×D4—64no—
929C2×D4—62no—
930C2×D4—63no—
931C2×D4—66no—
932C2×D4—66no—
933C2×D4—63no—
934C2×D4—66no—
935C2×D4—66no—
936C2×D4—66no—
937C2×D4—612no—
938C2×D4—66no—
939C2×D4—612no—
940C2×D4—612no—
941C2×D4—612no—
942C2×D4—612no—
943C2×D4—66no—
944C22×C4—31no—
945C22×C4—36no—
946C22×C4—33no—
947C22×C4—36no—
948C22×C4—36no—
949C22×C4—36no—
950C22×C4—33no—
951C22×C4—36no—
952C22×C4—33no—
953C22×C4—312no—
954C22×C4—312no—
955C22×C4—36no—
956C22×C4—33no—
957C22×C4—36no—
958C22×C4—31no—
959C22×C4—32no—
960C22×C4—36no—
961C22×C4—36no—
962C22×C4—36no—
963C22×C4—33no—
964C22×C4—33no—
965C22×C4—36no—
966C22×C4—33no—
967C22×C4—36no—
968C22×C4—36no—
969C22×C4—36no—
970C22×C4—33no—
971C22×C4—33no—
972C22×C4—33no—
973C22×C4—36no—
974C22×C4—33no—
975C22×C4—36no—
976C22×C4—36no—
977C22×C4—36no—
978C22×C4—36no—
979C22×C4—33no—
980C22×C4—36no—
981C22×C4—33no—
982C22×C4—36no—
983C22×C4—33no—
984C22×C4—36no—
985C22×C4—33no—
986C22×C4—33no—
987C22×C4—36no—
988C22×C4—33no—
989C22×C4—36no—
990C22×C4—33no—
991C22×C4—36no—
992C22×C4—33no—
993C22×C4—36no—
994C22×C4—36no—
995C22×C4—36no—
996C22×C4—36no—
997C22×C4—63no—
998C22×C4—63no—
999C22×C4—66no—
1000C22×C4—63no—
1001C22×C4—66no—
1002C22×C4—63no—
1003C22×C4—63no—
1004C22×C4—66no—
1005C22×C4—66no—
1006C22×C4—66no—
1007C22×C4—63no—
1008C22×C4—66no—
1009C22×C4—63no—
1010C22×C4—63no—
1011C22×C4—63no—
1012C22×C4—66no—
1013C22×C4—66no—
1014C22×C4—63no—
1015C22×C4—63no—
1016C22×C4—66no—
1017C22×C4—66no—
1018C22×C4—66no—
1019C22×C4—66no—
1020C22×C4—66no—
1021C22×C4—66no—
1022C22×C4—66no—
1023C22×C4—66no—
1024C22×C4—63no—
1025C22×C4—66no—
1026C22×C4—61no—
1027C22×C4—62no—
1028C22×C4—61no—
1029C22×C4—62no—
1030C22×C4—61no—
1031C22×C4—62no—
1032C22×C4—62no—
1033C22×C4—61no—
1034C22×C4—61no—
1035C22×C4C2×SL(2,ℤ/4)13yes—
1036C22×C4C2×SL(2,ℤ/4)16yes—
1037C22×C4C22×S413yes—
1038C22×C4#102011yescharacteristic
1039M16—624no—
1040M16—1212no—
1041M16—1212no—
1042M16—1212no—
1043M16—1212no—
1044M16—124no—
1045C2×C8—612no—
1046C2×C8—612no—
1047C2×C8—126no—
1048C2×C8—1224no—
1049C2×C8—126no—
1050C2×C8—126no—
1051C2×C8—122no—
1052C22×C3—161no—
1053C22×C3—162no—
1054C22×C3—322no—
1055A4—43no—
1056C3×C4—161no—
1057C3×C4—162no—
1058C3×C4—161no—
1059C23—31no—
1060C23—33no—
1061C23—36no—
1062C23—36no—
1063C23—33no—
1064C23—33no—
1065C23—33no—
1066C23—36no—
1067C23—36no—
1068C23—36no—
1069C23—33no—
1070C23—36no—
1071C23—33no—
1072C23—46no—
1073C23—63no—
1074C23—63no—
1075C23—63no—
1076C23—66no—
1077C23—66no—
1078C23—62no—
1079C23—62no—
1080C23—61no—
1081C23—61no—
1082C23—86no—
1083C23—126no—
1084C23—124no—
1085C23—122no—
1086C23—126no—
1087C23—126no—
1088C23—126no—
1089C23—126no—
1090C23—246no—
1091C23—242no—
1092C23—246no—
1093C23—246no—
1094C23—246no—
1095C23—246no—
1096C23—2412no—
1097C23C22×SL(2,ℤ/4)13yes—
1098C23#593611yescharacteristic
1099Q8—21no—
1100Q8—63no—
1101Q8—612no—
1102Q8—66no—
1103Q8—66no—
1104Q8—63no—
1105Q8—66no—
1106Q8—612no—
1107Q8—62no—
1108Q8—61no—
1109Q8—62no—
1110D4—66no—
1111D4—612no—
1112D4—66no—
1113D4—612no—
1114D4—66no—
1115D4—612no—
1116D4—612no—
1117D4—612no—
1118D4—612no—
1119D4—66no—
1120D4—63no—
1121D4—66no—
1122D4—63no—
1123D4—612no—
1124D4—66no—
1125D4—66no—
1126D4—612no—
1127D4—61no—
1128D4—62no—
1129D4—61no—
1130D4—64no—
1131D4—62no—
1132D4—64no—
1133D4—62no—
1134C2×C4—312no—
1135C2×C4—33no—
1136C2×C4—36no—
1137C2×C4—36no—
1138C2×C4—33no—
1139C2×C4—312no—
1140C2×C4—36no—
1141C2×C4—33no—
1142C2×C4—36no—
1143C2×C4—36no—
1144C2×C4—33no—
1145C2×C4—33no—
1146C2×C4—33no—
1147C2×C4—36no—
1148C2×C4—33no—
1149C2×C4—36no—
1150C2×C4—36no—
1151C2×C4—33no—
1152C2×C4—36no—
1153C2×C4—36no—
1154C2×C4—36no—
1155C2×C4—36no—
1156C2×C4—33no—
1157C2×C4—33no—
1158C2×C4—33no—
1159C2×C4—33no—
1160C2×C4—36no—
1161C2×C4—66no—
1162C2×C4—63no—
1163C2×C4—63no—
1164C2×C4—66no—
1165C2×C4—63no—
1166C2×C4—63no—
1167C2×C4—66no—
1168C2×C4—66no—
1169C2×C4—63no—
1170C2×C4—66no—
1171C2×C4—66no—
1172C2×C4—66no—
1173C2×C4—63no—
1174C2×C4—66no—
1175C2×C4—66no—
1176C2×C4—63no—
1177C2×C4—66no—
1178C2×C4—63no—
1179C2×C4—62no—
1180C2×C4—61no—
1181C2×C4—62no—
1182C2×C4—61no—
1183C2×C4—61no—
1184C2×C4—62no—
1185C2×C4—61no—
1186C2×C4—62no—
1187C2×C4—61no—
1188C2×C4—62no—
1189C2×C4—62no—
1190C2×C4—62no—
1191C2×C4—62no—
1192C2×C4—61no—
1193C2×C4#593611yescharacteristic
1194C2×C4#593612yes—
1195C2×C4C2×#102012yes—
1196C2×C4C2×#102011yescharacteristic
1197C8—1212no—
1198C8—124no—
1199C2×C3—162no—
1200C2×C3—161no—
1201C2×C3—322no—
1202C22—22no—
1203C22—33no—
1204C22—36no—
1205C22—33no—
1206C22—43no—
1207C22—66no—
1208C22—66no—
1209C22—61no—
1210C22—62no—
1211C22—61no—
1212C22—126no—
1213C22—126no—
1214C22—124no—
1215C22—124no—
1216C22—123no—
1217C22—126no—
1218C22—121no—
1219C22—123no—
1220C22—126no—
1221C22—126no—
1222C22—123no—
1223C22—126no—
1224C22—123no—
1225C22—122no—
1226C22—122no—
1227C22—243no—
1228C22—243no—
1229C22—243no—
1230C22—246no—
1231C22—246no—
1232C22C2×#593612yes—
1233C22C2×#593611yescharacteristic
1234C4—33no—
1235C4—36no—
1236C4—33no—
1237C4—61no—
1238C4—62no—
1239C4—61no—
1240C4C2×#593612yes—
1241C4C2×#593611yescharacteristic
1242C4C22×#102011yescharacteristic
1243C3—161noSylow
1244C2—22no—
1245C2—63no—
1246C2—63no—
1247C2—66no—
1248C2—121no—
1249C2—122no—
1250C2—121no—
1251C2#1171566112yesdirect product factor
1252C2C22×#593611yescharacteristic
subgroupG/H
centerC2×C4C2×#1020
commutator, hypocenter#997C22×C4
FrattiniC4C22×#1020
FittingC22×#585D3
socleC22C2×#5936
prime radicalC22×#5950C2
cosocle#5950C23
hypercenterC22×C4#1020
LCSG ▷ #997
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. #11715661C2direct (N × H)
2. C2×#85566C2semidirect
10. #85566C22semidirect
1251. C2#11715661direct (N × H)

Maximal subgroups

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

subgroupindex
#117156612
C2×#855662
C22×#59502
C2×#206123
C2×#54094