Finite Group Databasebeta

← #7632687

Subgroups — #7632687

Order 512.

11520 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3500C211yesmaximal, characteristic, complemented
2C2×#3500C211yesmaximal, characteristic, complemented
3C2×#3498C211yesmaximal, characteristic, complemented
4C2×C4×H(5,𝔽2)C211yesmaximal, characteristic, complemented
5#36430C214yesmaximal, complemented
6#36214C2112yesmaximal, complemented
7#35831C214yesmaximal, complemented
8#35761C2112yesmaximal, complemented
9#35621C213yesmaximal, complemented
10#35617C213yesmaximal, complemented
11#35533C213yesmaximal, complemented
12#35528C213yesmaximal, complemented
13#35327C213yesmaximal, complemented
14#35165C213yesmaximal, complemented
15#34937C213yesmaximal, complemented
16C2×#2544C213yesmaximal, complemented
17#34259C211yesmaximal, characteristic, complemented
18#34258C211yesmaximal, characteristic, complemented
19C4⋊C4×#41C211yesmaximal, characteristic, complemented
20C22×2−1+4C2211yescharacteristic
21C22×H(5,𝔽2)C2211yescharacteristic
22C22×H(5,𝔽2)C2211yescharacteristic
23#3500—216no—
24#3500—216no—
25#3498—216no—
26C2×#550C2214yes—
27C2×#548C2212yescomplemented
28C2×#548C2214yescomplemented
29C2×#548C2212yescomplemented
30C2×#546C2216yescomplemented
31C2×#546C22112yescomplemented
32C2×#546C2216yescomplemented
33C2×D42C22112yes—
34C2×#536C2213yescomplemented
35C2×#536C2213yescomplemented
36C2×#535C2213yes—
37C2×#535C2213yes—
38C2×#535C2213yescomplemented
39C2×#535C2213yescomplemented
40C2×#532C2213yes—
41C2×#532C2213yescomplemented
42C2×#532C2213yescomplemented
43C22×#127C2213yes—
44C22×#124C2213yescomplemented
45C22×#124C2213yescomplemented
46C4×H(5,𝔽2)—216no—
47C2×#520C2211yescharacteristic
48C2×#520C2213yescomplemented
49C2×#520C2212yescomplemented
50C2×#518C2213yescomplemented
51C2×#518C2216yescomplemented
52C2×C4×#41C2211yescharacteristic
53C2×C4×#41C2211yescharacteristic
54C2×C4×#41C2211yescharacteristic
55C2×C4×#41C2212yescomplemented
56C2×C4×#41C2213yescomplemented
57C22×C4×D4C2213yescomplemented
58C22×C4×D4C2216yescomplemented
59#2850C22112yescomplemented
60#2847C22112yescomplemented
61#2620C22112yescomplemented
62#2617C22112yescomplemented
63#2548C2213yescomplemented
64#2547C2213yescomplemented
65#2547C2216yescomplemented
66#2546C2213yescomplemented
67#2545C2216yescomplemented
68#2545C2211yescharacteristic, complemented
69#2545C2213yescomplemented
70#2544C2216yescomplemented
71#2544C2216yescomplemented
72#2544C2216yescomplemented
73#2544C2213yescomplemented
74#2544C22112yescomplemented
75#2544C2216yescomplemented
76#2544C22112yescomplemented
77#2544C2213yescomplemented
78#2543C22112yescomplemented
79#2541C2216yescomplemented
80#2541C2213yescomplemented
81#2537C22112yescomplemented
82#2535C22112yescomplemented
83#2534C22112yescomplemented
84#2534C22112yescomplemented
85#2428C22112yescomplemented
86#2428C22112yescomplemented
87#2427C22112yescomplemented
88#2427C22112yescomplemented
89#2425C22124yescomplemented
90#2424C22124yescomplemented
91#2417C22112yescomplemented
92#2416C22112yescomplemented
93#2416C22112yescomplemented
94#2415C22112yescomplemented
95#2414C22112yescomplemented
96#2412C22124yescomplemented
97#2410C22124yescomplemented
98#2392C22112yescomplemented
99C2×#394C22112yescomplemented
100#2351C2212yescomplemented
101Q8×C4⋊C4C2212yescomplemented
102#2349C2216yescomplemented
103D4×C4⋊C4C2216yescomplemented
104#2341C2214yescomplemented
105Q8×C22⋊C4C2214yescomplemented
106#2339C22112yescomplemented
107D4×C22⋊C4C22112yescomplemented
108#2311C2213yescomplemented
109#2311C2213yescomplemented
110#2310C2213yescomplemented
111#2309C2213yescomplemented
112C4×#121C22112yescomplemented
113#2297C2213yescomplemented
114#2297C2213yescomplemented
115#2296C2213yescomplemented
116#2296C2213yescomplemented
117C2×#391C2213yescomplemented
118C2×#390C2213yescomplemented
119C2×#386C22112yescomplemented
120#2285C2213yescomplemented
121C2×C4×C4⋊C4C2213yescomplemented
122C2×2−1+4—28no—
123C2×2−1+4—28no—
124C2×2−1+4—28no—
125C2×H(5,𝔽2)—28no—
126C2×H(5,𝔽2)—28no—
127C2×H(5,𝔽2)—28no—
128C2×H(5,𝔽2)—28no—
129C2×H(5,𝔽2)—28no—
130C2×H(5,𝔽2)D4116yescomplemented
131C22×#41C2313yes—
132C22×#41C2313yes—
133C22×#41C2312yes—
134C22×#41C2316yes—
135C22×#41C2313yes—
136C22×#41C2312yes—
137C22×#41C2311yescharacteristic
138C23×Q8C2313yes—
139C23×Q8C2312yes—
140C23×D4C2313yes—
141C23×D4C2316yes—
142C23×D4C2313yes—
143C23×D4C2316yes—
144C23×D4C23112yes—
145C24×C4C2316yes—
146#550—232no—
147#548—232no—
148#548—216no—
149#548—216no—
150#546—296no—
151#546—248no—
152#546—248no—
153D42—296no—
154#536—224no—
155#536—224no—
156#535—224no—
157#535—224no—
158#535—224no—
159#535—224no—
160#532—224no—
161#532—224no—
162#532—224no—
163C2×C4⋊Q8C2311yescharacteristic
164C2×C4⋊Q8C2313yes—
165C2×C4⋊Q8C2313yes—
166C2×#127—224no—
167C2×#127C2313yes—
168C2×#127C2316yes—
169C2×#127C23112yes—
170C2×#127C2313yes—
171C2×#127C2313yes—
172C2×#124—224no—
173C2×#124—224no—
174C2×#124C2316yes—
175C2×#124C2316yes—
176C2×#124C2313yes—
177C2×#124C2313yes—
178C2×#124C2316yes—
179C2×#124C2316yes—
180C2×#124C23112yes—
181C2×#124C2313yes—
182C2×#124C2313yes—
183C2×#124C2311yescharacteristic
184C2×#124C2311yescharacteristic
185C2×#123C23112yes—
186C2×#123C23112yes—
187C2×C22⋊Q8C23112yes—
188C2×C22⋊Q8C2316yes—
189C2×C22⋊Q8C2316yes—
190C2×#121C2316yes—
191C2×#121C23112yes—
192C2×#121C2316yes—
193C2×#121C2316yes—
194C2×#121C2316yes—
195C2×#121C23112yes—
196C2×#121C23112yes—
197C2×#121C23112yes—
198C2×#121C23112yes—
199C2×#121C23112yes—
200C2×#121C23124yes—
201C2×#120C23112yes—
202C2×#120C23112yes—
203C2×#120C23112yes—
204C2×#120C23112yes—
205#520—28no—
206#520—216no—
207#520—224no—
208#518—248no—
209#518—224no—
210C4×#41—28no—
211C4×#41—28no—
212C4×#41—216no—
213C4×#41—224no—
214C4×#41D4116yescomplemented
215C2×C4×Q8C2312yes—
216C2×C4×Q8C2312yes—
217C2×C4×Q8C2312yes—
218C2×C4×Q8C2311yescharacteristic
219C2×C4×Q8C2313yes—
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×D4—248no—
223C2×C4×D4—224no—
224C2×C4×D4C2316yes—
225C2×C4×D4C2316yes—
226C2×C4×D4C2316yes—
227C2×C4×D4C2316yes—
228C2×C4×D4C23112yes—
229C2×C4×D4C23112yes—
230C2×C4×D4C2316yes—
231C2×C4×D4C2316yes—
232C2×C4×D4C2313yes—
233C2×C4×D4C23112yes—
234C2×C4×D4C2316yes—
235C2×C4×D4C2316yes—
236C2×C4×D4C2316yes—
237C2×C4×D4C2316yes—
238C2×C4×D4C2316yes—
239C2×C4×D4C2313yes—
240C2×C4×D4C2316yes—
241C2×C4×D4C2313yes—
242C2×C4×D4C2313yes—
243C2×#117C2313yes—
244C2×#117C2313yes—
245C2×#117C2313yes—
246C2×#117C2316yes—
247C2×#117C2316yes—
248C2×#117C2313yes—
249C22×C4⋊C4C2313yes—
250C22×C4⋊C4C2316yes—
251C22×C4⋊C4C2316yes—
252C22×C22⋊C4C2316yes—
253C22×C22⋊C4C2316yes—
254C22×C22⋊C4C23112yes—
255C22×C22⋊C4C23112yes—
256C22×C22⋊C4C2316yes—
257C22×C22⋊C4C23112yes—
258C22×C42C2316yes—
259C22×C42C2313yes—
260C22×C42C2313yes—
261C22×C42C2313yes—
262#398C23112yes—
263#397C23124yes—
264#397C23112yes—
265#396C23112yes—
266#396C23124yes—
267#396C2314yes—
268#394C23112yes—
269#394C23124yes—
270#394C23124yes—
271#394C23112yes—
272#394C23124yes—
273#394C23124yes—
274#394C23112yes—
275#392C23124yes—
276#392C23112yes—
277#391C2313yes—
278#391C2316yes—
279#391C23112yes—
280#391C2313yes—
281#391C23112yes—
282#391C2313yes—
283#391C2311yescharacteristic
284#390C2313yes—
285#390C2316yes—
286#390C23112yes—
287#390C2313yes—
288#390C23112yes—
289#390C23112yes—
290#390C2311yescharacteristic
291#390C2313yes—
292#389C2316yes—
293#389C2316yes—
294#389C2316yes—
295#389C2316yes—
296#389C23112yes—
297#388C23112yes—
298#388C23124yes—
299#388C2314yes—
300#386C23112yes—
301#386C23112yes—
302#386C23112yes—
303#386C23124yes—
304#386C23112yes—
305#386C23124yes—
306#386C23112yes—
307#386C23124yes—
308#386C23124yes—
309#386C23112yes—
310#385C23112yes—
311#385C23112yes—
312#384C2316yes—
313#382C2316yes—
314#381C23112yes—
315#380C23112yes—
316#380C23112yes—
317#380C2316yes—
318#380C23124yes—
319#380C2316yes—
320#380C23112yes—
321#379C23112yes—
322C4×C4⋊C4C2316yes—
323C4×C4⋊C4C2316yes—
324C4×C4⋊C4C2311yescharacteristic
325C4×C4⋊C4C2313yes—
326C4×C4⋊C4C2313yes—
327C4×C4⋊C4C2313yes—
328C4×C4⋊C4C2316yes—
329C4×C22⋊C4C23112yes—
330C4×C22⋊C4C23112yes—
331C2×#95C23112yes—
332C2×#95C2316yes—
333C25C2416yes—
334C25C2416yes—
3352−1+4—464no—
336H(5,𝔽2)—2128no—
337H(5,𝔽2)—464no—
338C2×#41—28no—
339C2×#41—28no—
340C2×#41—28no—
341C2×#41—28no—
342C2×#41—28no—
343C2×#41—224no—
344C2×#41—224no—
345C2×#41—224no—
346C2×#41—212no—
347C2×#41—212no—
348C2×#41—212no—
349C2×#41—212no—
350C2×#41—212no—
351C2×#41—212no—
352C2×#41—212no—
353C2×#41—212no—
354C2×#41C2×D4124yes—
355C2×#41C2×D4116yes—
356C2×#41C2×D418yes—
357C2×#41C2×D418yes—
358C2×#41#4118yes—
359C22×Q8—28no—
360C22×Q8—28no—
361C22×Q8—28no—
362C22×Q8—212no—
363C22×Q8—212no—
364C22×Q8—212no—
365C22×Q8C2416yes—
366C22×Q8C2413yes—
367C22×Q8C2411yescharacteristic
368C22×Q8C2411yescharacteristic
369C22×Q8C2411yescharacteristic
370C22×D4—224no—
371C22×D4—224no—
372C22×D4—248no—
373C22×D4—224no—
374C22×D4—224no—
375C22×D4—224no—
376C22×D4—212no—
377C22×D4—212no—
378C22×D4—212no—
379C22×D4—212no—
380C22×D4—212no—
381C22×D4—424no—
382C22×D4—812no—
383C22×D4C2×D4124yes—
384C22×D4C2×D4148yes—
385C22×D4C2416yes—
386C22×D4C2416yes—
387C22×D4C2416yes—
388C22×D4C2413yes—
389C22×D4C2411yescharacteristic
390C22×D4C24112yes—
391C22×D4C2416yes—
392C22×D4C2416yes—
393C22×D4C2413yes—
394C22×D4C2416yes—
395C22×D4C24112yes—
396C22×D4C2416yes—
397C22×D4C24124yes—
398C22×D4C2413yes—
399C23×C4—224no—
400C23×C4—812no—
401C23×C4C2416yes—
402C23×C4C2416yes—
403C23×C4C2416yes—
404C23×C4C2416yes—
405C23×C4C2416yes—
406C23×C4C2416yes—
407C23×C4C2416yes—
408C23×C4C2416yes—
409C23×C4C24112yes—
410C23×C4C2416yes—
411C23×C4C2413yes—
412C23×C4C2413yes—
413C23×C4C2413yes—
414C4⋊Q8—24no—
415C4⋊Q8—212no—
416C4⋊Q8—212no—
417#127—212no—
418#127—224no—
419#127—248no—
420#127—212no—
421#127—212no—
422#124—24no—
423#124—212no—
424#124—212no—
425#124—224no—
426#124—248no—
427#124—212no—
428#124—212no—
429#124—224no—
430#124—224no—
431#124—224no—
432#124—24no—
433#123—248no—
434#123—248no—
435C22⋊Q8—248no—
436C22⋊Q8—224no—
437C22⋊Q8—224no—
438#121—248no—
439#121—248no—
440#121—248no—
441#121—248no—
442#121—224no—
443#121—224no—
444#121—248no—
445#121—224no—
446#121—224no—
447#121—424no—
448#121—824no—
449#120—248no—
450#120—248no—
451#120—248no—
452#120—248no—
453C4×Q8—28no—
454C4×Q8—28no—
455C4×Q8—28no—
456C4×Q8—24no—
457C4×Q8—212no—
458C4×Q8C2×D418yescomplemented
459C4×Q8C2×D418yescomplemented
460C4×D4—224no—
461C4×D4—224no—
462C4×D4—224no—
463C4×D4—224no—
464C4×D4—224no—
465C4×D4—248no—
466C4×D4—248no—
467C4×D4—224no—
468C4×D4—224no—
469C4×D4—248no—
470C4×D4—224no—
471C4×D4—212no—
472C4×D4—224no—
473C4×D4—224no—
474C4×D4—212no—
475C4×D4—224no—
476C4×D4—224no—
477C4×D4C2×D4124yescomplemented
478C4×D4C2×D4124yescomplemented
479#117—212no—
480#117—212no—
481#117—212no—
482#117—224no—
483#117—224no—
484#117C2×D4124yescomplemented
485C2×C4⋊C4—212no—
486C2×C4⋊C4—224no—
487C2×C4⋊C4—412no—
488C2×C4⋊C4C2412yes—
489C2×C4⋊C4C2416yes—
490C2×C4⋊C4C2413yes—
491C2×C4⋊C4C2416yes—
492C2×C4⋊C4C2416yes—
493C2×C4⋊C4C2411yescharacteristic
494C2×C4⋊C4C2412yes—
495C2×C4⋊C4C2416yes—
496C2×C4⋊C4C2416yes—
497C2×C4⋊C4C2414yes—
498C2×C4⋊C4C2416yes—
499C2×C4⋊C4C2416yes—
500C2×C4⋊C4C24112yes—
501C2×C4⋊C4C2416yes—
502C2×C4⋊C4C2416yes—
503C2×C4⋊C4C24112yes—
504C2×C4⋊C4C2413yes—
505C2×C4⋊C4C2413yes—
506C2×C22⋊C4—248no—
507C2×C22⋊C4—224no—
508C2×C22⋊C4—224no—
509C2×C22⋊C4—224no—
510C2×C22⋊C4—248no—
511C2×C22⋊C4—812no—
512C2×C22⋊C4C2416yes—
513C2×C22⋊C4C2416yes—
514C2×C22⋊C4C24112yes—
515C2×C22⋊C4C2416yes—
516C2×C22⋊C4C24112yes—
517C2×C22⋊C4C2416yes—
518C2×C22⋊C4C2416yes—
519C2×C22⋊C4C24124yes—
520C2×C22⋊C4C24112yes—
521C2×C22⋊C4C24112yes—
522C2×C22⋊C4C2416yes—
523C2×C22⋊C4C2416yes—
524C2×C22⋊C4C2412yes—
525C2×C22⋊C4C2414yes—
526C2×C22⋊C4C2412yes—
527C2×C22⋊C4C24112yes—
528C2×C22⋊C4C24112yes—
529C2×C22⋊C4C2414yes—
530C2×C22⋊C4C24112yes—
531C2×C22⋊C4C24124yes—
532C2×C22⋊C4C24112yes—
533C2×C22⋊C4C24112yes—
534C2×C22⋊C4C2416yes—
535C2×C42—212no—
536C2×C42—212no—
537C2×C42—224no—
538C2×C42C2×D4124yescomplemented
539C2×C42C2416yes—
540C2×C42C2416yes—
541C2×C42C2413yes—
542C2×C42C2413yes—
543C2×C42C2416yes—
544C2×C42C2416yes—
545C2×C42C2412yes—
546C2×C42C2411yescharacteristic
547C2×C42C2411yescharacteristic
548C2×C42C2413yes—
549C2×C42C2413yes—
550C2×C42C2413yes—
551C2×C42C2411yescharacteristic
552#95C2412yes—
553#95C24112yes—
554#95C2416yes—
555#95C2416yes—
556#95C2416yes—
557#95C24124yes—
558#95C2414yes—
559#95C24112yes—
560#95C24112yes—
561#95C24112yes—
562C24—212no—
563C24—212no—
564C24—212no—
565C24—212no—
566C24—212no—
567C24—412no—
568C24—412no—
569C24—412no—
570C24—412no—
571C24C22×D4124yes—
572C24C2516yes—
573C24C2512yes—
574C24C2516yes—
575C24C2513yes—
576#41—264no—
577#41—296no—
578#41—432no—
579#41—496no—
580#41—448no—
581#41—448no—
582#41#121164yescomplemented
583C2×Q8—22no—
584C2×Q8—212no—
585C2×Q8—212no—
586C2×Q8—26no—
587C2×Q8—26no—
588C2×Q8—22no—
589C2×Q8—22no—
590C2×Q8—22no—
591C2×Q8—212no—
592C2×Q8—26no—
593C2×Q8—22no—
594C2×Q8—432no—
595C2×Q8—448no—
596C2×Q8C22×D414yes—
597C2×Q8C22×D414yes—
598C2×Q8C22×D414yes—
599C2×Q8C2×#4114yes—
600C2×D4—212no—
601C2×D4—212no—
602C2×D4—2192no—
603C2×D4—224no—
604C2×D4—212no—
605C2×D4—212no—
606C2×D4—212no—
607C2×D4—212no—
608C2×D4—212no—
609C2×D4—212no—
610C2×D4—224no—
611C2×D4—248no—
612C2×D4—296no—
613C2×D4—212no—
614C2×D4—26no—
615C2×D4—212no—
616C2×D4—212no—
617C2×D4—26no—
618C2×D4—26no—
619C2×D4—22no—
620C2×D4—22no—
621C2×D4—212no—
622C2×D4—212no—
623C2×D4—212no—
624C2×D4—26no—
625C2×D4—212no—
626C2×D4—26no—
627C2×D4—22no—
628C2×D4—224no—
629C2×D4—412no—
630C2×D4—412no—
631C2×D4—412no—
632C2×D4—412no—
633C2×D4—412no—
634C2×D4—424no—
635C2×D4—424no—
636C2×D4—496no—
637C2×D4—448no—
638C2×D4—896no—
639C2×D4C22×D4124yes—
640C2×D4C22×D4124yes—
641C2×D4C22×D4112yes—
642C2×D4C22×D4112yes—
643C2×D4C22×D4112yes—
644C2×D4C2×#41112yes—
645C22×C4—212no—
646C22×C4—212no—
647C22×C4—212no—
648C22×C4—212no—
649C22×C4—212no—
650C22×C4—212no—
651C22×C4—212no—
652C22×C4—212no—
653C22×C4—212no—
654C22×C4—212no—
655C22×C4—212no—
656C22×C4—212no—
657C22×C4—212no—
658C22×C4—212no—
659C22×C4—212no—
660C22×C4—212no—
661C22×C4—212no—
662C22×C4—224no—
663C22×C4—46no—
664C22×C4—46no—
665C22×C4—412no—
666C22×C4—46no—
667C22×C4—46no—
668C22×C4—412no—
669C22×C4—46no—
670C22×C4—412no—
671C22×C4—424no—
672C22×C4—848no—
673C22×C4C22×D4124yes—
674C22×C4C22×D4112yes—
675C22×C4C22×D4112yes—
676C22×C4C22×D4112yes—
677C22×C4C22×D4112yes—
678C22×C4C2×#41112yes—
679C22×C4C2516yes—
680C22×C4C2512yes—
681C22×C4C2516yes—
682C22×C4C2516yes—
683C22×C4C2512yes—
684C22×C4C2512yes—
685C22×C4C2516yes—
686C22×C4C2511yescharacteristic
687C22×C4C2513yes—
688C22×C4C2513yes—
689C22×C4C2511yescharacteristic
690C22×C4C2512yes—
691C22×C4C2512yes—
692C22×C4C2511yescharacteristic
693C22×C4C2513yes—
694C4⋊C4—212no—
695C4⋊C4—212no—
696C4⋊C4—26no—
697C4⋊C4—24no—
698C4⋊C4—22no—
699C4⋊C4—212no—
700C4⋊C4—212no—
701C4⋊C4—28no—
702C4⋊C4—224no—
703C4⋊C4—212no—
704C4⋊C4—212no—
705C4⋊C4—24no—
706C4⋊C4—212no—
707C4⋊C4—46no—
708C4⋊C4—46no—
709C4⋊C4—412no—
710C4⋊C4C22×D4112yes—
711C4⋊C4C22×D4112yes—
712C22⋊C4—212no—
713C22⋊C4—224no—
714C22⋊C4—248no—
715C22⋊C4—212no—
716C22⋊C4—212no—
717C22⋊C4—224no—
718C22⋊C4—212no—
719C22⋊C4—224no—
720C22⋊C4—212no—
721C22⋊C4—212no—
722C22⋊C4—212no—
723C22⋊C4—224no—
724C22⋊C4—224no—
725C22⋊C4—28no—
726C22⋊C4—24no—
727C22⋊C4—24no—
728C22⋊C4—224no—
729C22⋊C4—28no—
730C22⋊C4—412no—
731C22⋊C4—424no—
732C22⋊C4—412no—
733C22⋊C4—412no—
734C22⋊C4C22×D4124yes—
735C42—24no—
736C42—22no—
737C42—22no—
738C42—212no—
739C42—212no—
740C42—26no—
741C42—26no—
742C42—212no—
743C42—212no—
744C42C22×D4112yes—
745C42C22×D414yes—
746C42C22×D4112yes—
747C42C22×D4112yes—
748C23—26no—
749C23—26no—
750C23—26no—
751C23—26no—
752C23—212no—
753C23—212no—
754C23—248no—
755C23—26no—
756C23—22no—
757C23—22no—
758C23—26no—
759C23—22no—
760C23—26no—
761C23—24no—
762C23—212no—
763C23—24no—
764C23—212no—
765C23—448no—
766C23—424no—
767C23—812no—
768C23—824no—
769C23—812no—
770C23—824no—
771C23—824no—
772C23—812no—
773C23—812no—
774C23C23×D4112yes—
775C23C23×D416yes—
776C23C23×D416yes—
777C23C22×#4116yes—
778C23C2611yescharacteristic
779Q8—28no—
780Q8—424no—
781Q8—412no—
782Q8—44no—
783Q8C2×#121116yes—
784D4—248no—
785D4—248no—
786D4—224no—
787D4—448no—
788D4—424no—
789D4—424no—
790D4—424no—
791D4—412no—
792D4—44no—
793D4—812no—
794D4—812no—
795D4—824no—
796D4—848no—
797D4C2×#121148yes—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—26no—
803C2×C4—26no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—248no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—26no—
810C2×C4—26no—
811C2×C4—26no—
812C2×C4—22no—
813C2×C4—26no—
814C2×C4—26no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—26no—
818C2×C4—24no—
819C2×C4—26no—
820C2×C4—22no—
821C2×C4—26no—
822C2×C4—22no—
823C2×C4—26no—
824C2×C4—212no—
825C2×C4—26no—
826C2×C4—412no—
827C2×C4—412no—
828C2×C4—424no—
829C2×C4—424no—
830C2×C4—424no—
831C2×C4—424no—
832C2×C4—424no—
833C2×C4—812no—
834C2×C4—824no—
835C2×C4—812no—
836C2×C4—812no—
837C2×C4C2×#121148yes—
838C2×C4C23×D412yes—
839C2×C4C23×D416yes—
840C2×C4C23×D412yes—
841C2×C4C23×D416yes—
842C2×C4C23×D414yes—
843C2×C4C23×D412yes—
844C2×C4C23×D416yes—
845C2×C4C23×D416yes—
846C2×C4C23×D412yes—
847C2×C4C22×#4116yes—
848C2×C4C22×#4112yes—
849C2×C4#58514yes—
850C22—212no—
851C22—212no—
852C22—26no—
853C22—26no—
854C22—224no—
855C22—212no—
856C22—412no—
857C22—46no—
858C22—46no—
859C22—412no—
860C22—44no—
861C22—44no—
862C22—412no—
863C22—42no—
864C22—46no—
865C22—42no—
866C22—46no—
867C22—42no—
868C22—46no—
869C22—848no—
870C22—1624no—
871C22C22×#121112yes—
872C22C24×D411yescharacteristic
873C22C24×D411yescharacteristic
874C22C23×#4111yescharacteristic
875C22C2×#58512yes—
876C22H(7,𝔽2)12yes—
877C4—24no—
878C4—22no—
879C4—26no—
880C4—22no—
881C4—26no—
882C4—24no—
883C4—46no—
884C4—42no—
885C4—46no—
886C4—42no—
887C4—46no—
888C4—42no—
889C4—46no—
890C4C22×#121112yes—
891C4C22×#12114yes—
892C2—212no—
893C2—412no—
894C2—82no—
895C2—86no—
896C2C23×#12111yescharacteristic
897C2#6281211yescharacteristic
898C2#6285211yescharacteristic
899C2#6298712yes—
900C2#6301012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3500C2semidirect
2. C2×#3500C2semidirect
3. C2×#3498C2semidirect
4. C2×C4×H(5,𝔽2)C2semidirect
5. #36430C2semidirect
6. #36214C2semidirect
7. #35831C2semidirect
8. #35761C2semidirect
9. #35621C2semidirect
10. #35617C2semidirect
11. #35533C2semidirect
12. #35528C2semidirect
13. #35327C2semidirect
14. #35165C2semidirect
15. #34937C2semidirect
16. C2×#2544C2semidirect
17. #34259C2semidirect
18. #34258C2semidirect
19. C4⋊C4×#41C2semidirect
27. C2×#548C22semidirect
28. C2×#548C22semidirect
29. C2×#548C22semidirect
30. C2×#546C22semidirect
31. C2×#546C22semidirect
32. C2×#546C22semidirect
34. C2×#536C22semidirect
35. C2×#536C22semidirect
38. C2×#535C22semidirect
39. C2×#535C22semidirect
41. C2×#532C22semidirect
42. C2×#532C22semidirect
44. C22×#124C22semidirect
45. C22×#124C22semidirect
48. C2×#520C22semidirect
49. C2×#520C22semidirect
50. C2×#518C22semidirect
51. C2×#518C22semidirect
55. C2×C4×#41C22semidirect
56. C2×C4×#41C22semidirect
57. C22×C4×D4C22semidirect
58. C22×C4×D4C22semidirect
59. #2850C22semidirect
60. #2847C22semidirect
61. #2620C22semidirect
62. #2617C22semidirect
63. #2548C22semidirect
64. #2547C22semidirect
65. #2547C22semidirect
66. #2546C22semidirect
67. #2545C22semidirect
68. #2545C22semidirect
69. #2545C22semidirect
70. #2544C22semidirect
71. #2544C22semidirect
72. #2544C22semidirect
73. #2544C22semidirect
74. #2544C22semidirect
75. #2544C22semidirect
76. #2544C22semidirect
77. #2544C22semidirect
78. #2543C22semidirect
79. #2541C22semidirect
80. #2541C22semidirect
81. #2537C22semidirect
82. #2535C22semidirect
83. #2534C22semidirect
84. #2534C22semidirect
85. #2428C22semidirect
86. #2428C22semidirect
87. #2427C22semidirect
88. #2427C22semidirect
89. #2425C22semidirect
90. #2424C22semidirect
91. #2417C22semidirect
92. #2416C22semidirect
93. #2416C22semidirect
94. #2415C22semidirect
95. #2414C22semidirect
96. #2412C22semidirect
97. #2410C22semidirect
98. #2392C22semidirect
99. C2×#394C22semidirect
100. #2351C22semidirect
101. Q8×C4⋊C4C22semidirect
102. #2349C22semidirect
103. D4×C4⋊C4C22semidirect
104. #2341C22semidirect
105. Q8×C22⋊C4C22semidirect
106. #2339C22semidirect
107. D4×C22⋊C4C22semidirect
108. #2311C22semidirect
109. #2311C22semidirect
110. #2310C22semidirect
111. #2309C22semidirect
112. C4×#121C22semidirect
113. #2297C22semidirect
114. #2297C22semidirect
115. #2296C22semidirect
116. #2296C22semidirect
117. C2×#391C22semidirect
118. C2×#390C22semidirect
119. C2×#386C22semidirect
120. #2285C22semidirect
121. C2×C4×C4⋊C4C22semidirect
130. C2×H(5,𝔽2)D4semidirect
214. C4×#41D4semidirect
458. C4×Q8C2×D4semidirect
459. C4×Q8C2×D4semidirect
477. C4×D4C2×D4semidirect
478. C4×D4C2×D4semidirect
484. #117C2×D4semidirect
538. C2×C42C2×D4semidirect
582. #41#121semidirect

Maximal subgroups

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

subgroupindex
C2×#35002
C2×#34982
C2×C4×H(5,𝔽2)2
#364302
#362142
#358312
#357612
#356212
#356172
#355332
#355282
#353272
#351652
#349372
C2×#25442
#342592
#342582
C4⋊C4×#412