Finite Group Databasebeta

← #7710939

Subgroups — #7710939

Order 512.

8466 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3543C212yesmaximal, complemented
2#59827C211yesmaximal, characteristic, complemented
3#59816C211yesmaximal, characteristic, complemented
4#59815C212yesmaximal, complemented
5#59420C212yesmaximal, complemented
6#59419C212yesmaximal, complemented
7#46328C214yesmaximal, complemented
8#46280C214yesmaximal, complemented
9#39416C218yesmaximal, complemented
10#39378C214yesmaximal, complemented
11#39362C214yesmaximal, complemented
12#38949C218yesmaximal, complemented
13#37620C212yesmaximal, complemented
14#37129C214yesmaximal, complemented
15#36631C212yesmaximal, complemented
16#36153C214yesmaximal, complemented
17D4×#121C214yesmaximal, complemented
18#35000C214yesmaximal, complemented
19C2×C4×#127C211yesmaximal, characteristic, complemented
20#3543—232no—
21C2×#560C2218yescomplemented
22C2×#559C2212yes—
23C2×#550C2214yescomplemented
24C2×#547C2214yescomplemented
25C2×#546C2218yescomplemented
26C2×D42C2212yes—
27C2×D42C2218yescomplemented
28C2×D42C2214yescomplemented
29C2×#540C2218yescomplemented
30C2×#535C2218yescomplemented
31C2×#534C2218yescomplemented
32C22×#127C2211yescharacteristic
33C2×#529C2214yescomplemented
34C22×#121C2214yescomplemented
35C22×C4×D4C2214yescomplemented
36C22×C4×D4C2212yescomplemented
37#2861C2214yescomplemented
38#2860C2214yescomplemented
39#2860C2214yescomplemented
40#2859C2212yescomplemented
41#2858C2212yescomplemented
42#2857C2212yescomplemented
43#2856C2212yes—
44#2854C2214yescomplemented
45#2854C2214yescomplemented
46#2850C2214yescomplemented
47#2847C2218yescomplemented
48#2823C2218yescomplemented
49#2724C2214yescomplemented
50#2701C22116yescomplemented
51#2701C22116yescomplemented
52#2699C2218yescomplemented
53#2699C22116yescomplemented
54#2697C2218yescomplemented
55#2697C22116yescomplemented
56#2682C2218yescomplemented
57#2679C2214yescomplemented
58#2678C22116yescomplemented
59#2678C22116yescomplemented
60#2629C2218yescomplemented
61#2620C2218yescomplemented
62#2618C2218yescomplemented
63#2617C2218yescomplemented
64#2582C2212yescomplemented
65#2547C2214yescomplemented
66#2543C2218yescomplemented
67#2543C2218yescomplemented
68#2541C2214yescomplemented
69#2538C2214yescomplemented
70#2537C2212yescomplemented
71#2537C2214yescomplemented
72#2537C2214yescomplemented
73#2534C2218yescomplemented
74#2534C2218yescomplemented
75#2486C2218yescomplemented
76#2486C2214yescomplemented
77#2486C2214yescomplemented
78#2447C2218yescomplemented
79#2445C2218yescomplemented
80#2435C2218yescomplemented
81#2431C2218yescomplemented
82#2428C2218yescomplemented
83#2427C2218yescomplemented
84#2425C22116yescomplemented
85#2424C22116yescomplemented
86#2420C2218yescomplemented
87#2420C2218yescomplemented
88#2417C2218yescomplemented
89#2416C2218yescomplemented
90#2416C2218yescomplemented
91#2416C2218yescomplemented
92#2416C2218yescomplemented
93#2416C2218yescomplemented
94#2412C22116yescomplemented
95#2410C22116yescomplemented
96#2408C2218yescomplemented
97#2408C2214yescomplemented
98#2408C2214yescomplemented
99#2408C2218yescomplemented
100#2407C2218yescomplemented
101D4×C4⋊C4C2214yescomplemented
102D4×C4⋊C4C2214yescomplemented
103#2339C2218yescomplemented
104D4×C22⋊C4C2218yescomplemented
105#2308C2218yescomplemented
106C4×C4⋊Q8C2212yescomplemented
107C4×#127C2211yescharacteristic
108C4×#127C2211yescharacteristic
109C4×#127C2212yescomplemented
110C4×#127C2211yescharacteristic, complemented
111C4×#127C2211yescharacteristic, complemented
112C4×#127C2214yescomplemented
113C4×#127C2212yescomplemented
114C4×#127C2214yescomplemented
115C4×#127C2212yescomplemented
116C4×#124C2214yescomplemented
117C4×#121C2214yescomplemented
118C4×#121C2214yescomplemented
119#2293C2214yescomplemented
120#2293C2214yescomplemented
121C2×#390C2212yescomplemented
122C2×#390C2214yescomplemented
123C2×#384C2211yescharacteristic, complemented
124C2×#380C2214yescomplemented
125C2×C43C2211yescharacteristic, complemented
126C22×#41C2318yes—
127C23×D4C2318yes—
128C23×D4C2318yes—
129C23×D4C2314yes—
130C23×D4C2312yes—
131C23×D4C2314yes—
132C24×C4C2314yes—
133#560—264no—
134#559—216no—
135#550—232no—
136#547—416no—
137#546—264no—
138D42—264no—
139D42—216no—
140D42—416no—
141#540—264no—
142#535—264no—
143#534—264no—
144C2×C4⋊Q8C2312yes—
145C2×#127D4116yescomplemented
146C2×#127C2312yes—
147C2×#127C2318yes—
148C2×#127C2311yescharacteristic
149C2×#127C2314yes—
150C2×#127C2311yescharacteristic
151C2×#127C2312yes—
152#529—232no—
153C2×#126C2318yes—
154C2×#125C2314yes—
155C2×#124C2314yes—
156C2×#124C2318yes—
157C2×#124C2314yes—
158C2×#123C2318yes—
159C2×#123C2318yes—
160C2×#123C2318yes—
161C2×#123C23116yes—
162C2×#123C23116yes—
163C2×C22⋊Q8C2314yes—
164C2×C22⋊Q8C2318yes—
165C2×#121—416no—
166C2×#121C2314yes—
167C2×#121C2314yes—
168C2×#121C2318yes—
169C2×#121C2318yes—
170C2×#121C23116yes—
171C2×#121C23116yes—
172C2×#121C23116yes—
173C2×#121C23116yes—
174C2×#121C2318yes—
175C2×#121C2318yes—
176C2×#121C2314yes—
177C2×#121C2318yes—
178C2×#121C2318yes—
179C2×#121C2318yes—
180C2×#121C2318yes—
181C2×#120C23116yes—
182C2×#120C2318yes—
183C2×#120C2318yes—
184C2×#120C23116yes—
185C2×#120C23116yes—
186C2×C4×Q8C2314yes—
187C2×C4×D4—416no—
188C2×C4×D4—48no—
189C2×C4×D4C2314yes—
190C2×C4×D4C2314yes—
191C2×C4×D4C2314yes—
192C2×C4×D4C2314yes—
193C2×C4×D4C2318yes—
194C2×C4×D4C2318yes—
195C2×C4×D4C2318yes—
196C2×C4×D4C2314yes—
197C2×C4×D4C2312yes—
198C2×C4×D4C2312yes—
199C2×C4×D4C2314yes—
200C2×C4×D4C2314yes—
201C2×C4×D4C2318yes—
202C2×C4×D4C2312yes—
203C2×C4×D4C2318yes—
204C2×C4×D4C2314yes—
205C2×C4×D4C2312yes—
206C2×C4×D4C2314yes—
207C2×#117C2318yes—
208C22×C4⋊C4C2314yes—
209C22×C4⋊C4C2318yes—
210C22×C4⋊C4C2312yes—
211C22×C4⋊C4C2314yes—
212C22×C22⋊C4C2318yes—
213C22×C22⋊C4C2314yes—
214C22×C22⋊C4C2318yes—
215C22×C22⋊C4C2318yes—
216C22×C42C2311yescharacteristic
217C22×C42C2312yes—
218C22×C42C2312yes—
219C22×C42C2311yescharacteristic
220C22×C42C2311yescharacteristic
221#398C2318yes—
222#398C23116yes—
223#398C2318yes—
224#397C2318yes—
225#397C2318yes—
226#397C23116yes—
227#397C23116yes—
228#396C23116yes—
229#396C23116yes—
230#396C23116yes—
231#396C23116yes—
232#394C2318yes—
233#394C23116yes—
234#394C23116yes—
235#394C23116yes—
236#394C2318yes—
237#394C23116yes—
238#394C23116yes—
239#394C23116yes—
240#394C23116yes—
241#392C2318yes—
242#392C2318yes—
243#392C23116yes—
244#392C23116yes—
245#391C2314yes—
246#391C2318yes—
247#391C2314yes—
248#390C2314yes—
249#390C2314yes—
250#390C2312yes—
251#390C2312yes—
252#390C2314yes—
253#390C2314yes—
254#390C2318yes—
255#390C2318yes—
256#390C2312yes—
257#390C2318yes—
258#390C2312yes—
259#390C2314yes—
260#390C2314yes—
261#390C2314yes—
262#390C2314yes—
263#390C2318yes—
264#390C2314yes—
265#390C2314yes—
266#390C2314yes—
267#390C2314yes—
268#390C2314yes—
269#390C2314yes—
270#389C2314yes—
271#389C2314yes—
272#389C2318yes—
273#389C2314yes—
274#389C2314yes—
275#389C2314yes—
276#389C2314yes—
277#389C2314yes—
278#389C2314yes—
279#389C2318yes—
280#388C2318yes—
281#388C2318yes—
282#388C2318yes—
283#388C2318yes—
284#388C2318yes—
285#388C2318yes—
286#388C2318yes—
287#388C2318yes—
288#386C2318yes—
289#386C23116yes—
290#386C23116yes—
291#386C23116yes—
292#386C23116yes—
293#386C23116yes—
294#386C23116yes—
295#386C2318yes—
296#386C23116yes—
297#385C23116yes—
298#385C23116yes—
299#384C2311yescharacteristic
300#384C2311yescharacteristic
301#384C2312yes—
302#384C2314yes—
303#384C2312yes—
304#384C2312yes—
305#382C2314yes—
306#381C2318yes—
307#381C2318yes—
308#381C23116yes—
309#380C2314yes—
310#380C2318yes—
311#380C2318yes—
312#380C2318yes—
313#380C2318yes—
314#380C2314yes—
315#380C2318yes—
316#380C2314yes—
317#380C2314yes—
318#380C2318yes—
319#379C2318yes—
320#379C2318yes—
321#379C23116yes—
322C4×C4⋊C4C2314yes—
323C4×C4⋊C4C2314yes—
324C4×C22⋊C4C2318yes—
325C4×C22⋊C4C2318yes—
326C2×#95C2318yes—
327C43C2311yescharacteristic
328C43C2311yescharacteristic
329C43C2312yes—
330C43C2311yescharacteristic
331C43C2311yescharacteristic
332C43C2312yes—
333C25C2414yes—
334C25C2418yes—
335C2×#41—232no—
336C2×#41—416no—
337C2×#41—416no—
338C22×Q8C2414yes—
339C22×D4—232no—
340C22×D4—232no—
341C22×D4—48no—
342C22×D4—48no—
343C22×D4—48no—
344C22×D4—416no—
345C22×D4—416no—
346C22×D4—416no—
347C22×D4—44no—
348C22×D4—44no—
349C22×D4—416no—
350C22×D4—416no—
351C22×D4C2×D4116yescomplemented
352C22×D4C2×D4132yescomplemented
353C22×D4C2418yes—
354C22×D4C2414yes—
355C22×D4C2414yes—
356C22×D4C2414yes—
357C22×D4C2414yes—
358C22×D4C2414yes—
359C22×D4C24116yes—
360C22×D4C24116yes—
361C22×D4C24116yes—
362C22×D4C2418yes—
363C22×D4C2412yes—
364C22×D4C2418yes—
365C22×D4C2414yes—
366C22×D4C2412yes—
367C23×C4—216no—
368C23×C4—416no—
369C23×C4C2414yes—
370C23×C4C2414yes—
371C23×C4C2418yes—
372C23×C4C2412yes—
373C23×C4C2412yes—
374C23×C4C2411yescharacteristic
375C23×C4C2411yescharacteristic
376C23×C4C2411yescharacteristic
377C23×C4C2414yes—
378C23×C4C2414yes—
379C23×C4C2418yes—
380C23×C4C24116yes—
381C23×C4C2414yes—
382C4⋊Q8—28no—
383#127—232no—
384#127—28no—
385#127C2×D418yes—
386#127C2×D4132yescomplemented
387#127C2×D418yescomplemented
388#127C2×D4116yescomplemented
389#126—232no—
390#125—216no—
391#124—232no—
392#124—216no—
393#124—48no—
394#123—232no—
395#123—232no—
396#123—264no—
397#123—232no—
398#123—432no—
399C22⋊Q8—216no—
400C22⋊Q8—416no—
401#121—264no—
402#121—264no—
403#121—264no—
404#121—232no—
405#121—232no—
406#121—264no—
407#121—216no—
408#121—216no—
409#121—416no—
410#121—416no—
411#121—416no—
412#121—416no—
413#121—416no—
414#121—416no—
415#121—48no—
416#120—264no—
417#120—232no—
418#120—232no—
419#120—264no—
420#120—432no—
421C4×Q8—216no—
422C4×D4—232no—
423C4×D4—232no—
424C4×D4—232no—
425C4×D4—216no—
426C4×D4—216no—
427C4×D4—216no—
428C4×D4—216no—
429C4×D4—416no—
430C4×D4—48no—
431C4×D4—48no—
432C4×D4—416no—
433C4×D4—44no—
434C4×D4—48no—
435C4×D4—44no—
436C4×D4—44no—
437C4×D4—48no—
438C4×D4—44no—
439C4×D4—48no—
440#117—232no—
441C2×C4⋊C4—48no—
442C2×C4⋊C4—48no—
443C2×C4⋊C4—416no—
444C2×C4⋊C4—44no—
445C2×C4⋊C4C2414yes—
446C2×C4⋊C4C2414yes—
447C2×C4⋊C4C2414yes—
448C2×C4⋊C4C2414yes—
449C2×C4⋊C4C2414yes—
450C2×C4⋊C4C2418yes—
451C2×C4⋊C4C2418yes—
452C2×C4⋊C4C2414yes—
453C2×C4⋊C4C2414yes—
454C2×C4⋊C4C2418yes—
455C2×C4⋊C4C2418yes—
456C2×C4⋊C4C2414yes—
457C2×C4⋊C4C2412yes—
458C2×C4⋊C4C2414yes—
459C2×C4⋊C4C2418yes—
460C2×C4⋊C4C2412yes—
461C2×C4⋊C4C2418yes—
462C2×C4⋊C4C24116yes—
463C2×C4⋊C4C2414yes—
464C2×C4⋊C4C2414yes—
465C2×C22⋊C4—232no—
466C2×C22⋊C4—416no—
467C2×C22⋊C4—416no—
468C2×C22⋊C4—48no—
469C2×C22⋊C4C2418yes—
470C2×C22⋊C4C2418yes—
471C2×C22⋊C4C2418yes—
472C2×C22⋊C4C2418yes—
473C2×C22⋊C4C2418yes—
474C2×C22⋊C4C2418yes—
475C2×C22⋊C4C2418yes—
476C2×C22⋊C4C2418yes—
477C2×C22⋊C4C2418yes—
478C2×C22⋊C4C2418yes—
479C2×C22⋊C4C24116yes—
480C2×C22⋊C4C2418yes—
481C2×C22⋊C4C24116yes—
482C2×C22⋊C4C2414yes—
483C2×C22⋊C4C2414yes—
484C2×C22⋊C4C2418yes—
485C2×C22⋊C4C2418yes—
486C2×C22⋊C4C2414yes—
487C2×C22⋊C4C2414yes—
488C2×C22⋊C4C24116yes—
489C2×C22⋊C4C2418yes—
490C2×C22⋊C4C24116yes—
491C2×C22⋊C4C24116yes—
492C2×C22⋊C4C2418yes—
493C2×C22⋊C4C2418yes—
494C2×C22⋊C4C2418yes—
495C2×C42—24no—
496C2×C42—28no—
497C2×C42—44no—
498C2×C42—42no—
499C2×C42C2×D418yescomplemented
500C2×C42C2418yes—
501C2×C42C2412yes—
502C2×C42C2411yescharacteristic
503C2×C42C2411yescharacteristic
504C2×C42C2412yes—
505C2×C42C2411yescharacteristic
506C2×C42C2411yescharacteristic
507C2×C42C2412yes—
508C2×C42C2412yes—
509C2×C42C2412yes—
510C2×C42C2411yescharacteristic
511C2×C42C2412yes—
512C2×C42C2412yes—
513C2×C42C2412yes—
514C2×C42C2411yescharacteristic
515C2×C42C2412yes—
516C2×C42C2411yescharacteristic
517C2×C42C2411yescharacteristic
518C2×C42C2412yes—
519#95C2418yes—
520#95C2418yes—
521#95C2418yes—
522#95C2418yes—
523#95C2418yes—
524#95C2418yes—
525#95C2418yes—
526#95C2418yes—
527#95C24116yes—
528#95C24116yes—
529C24—28no—
530C24—28no—
531C24—216no—
532C24—48no—
533C24—48no—
534C24—48no—
535C24—416no—
536C24—416no—
537C24—48no—
538C24C22×D4116yes—
539C24C2518yes—
540C24C2514yes—
541C24C2514yes—
542C24C2511yescharacteristic
543#41—864no—
544C2×Q8—28no—
545C2×Q8—28no—
546C2×Q8—28no—
547C2×D4—216no—
548C2×D4—216no—
549C2×D4—216no—
550C2×D4—232no—
551C2×D4—232no—
552C2×D4—232no—
553C2×D4—28no—
554C2×D4—28no—
555C2×D4—28no—
556C2×D4—28no—
557C2×D4—28no—
558C2×D4—28no—
559C2×D4—28no—
560C2×D4—28no—
561C2×D4—28no—
562C2×D4—28no—
563C2×D4—28no—
564C2×D4—464no—
565C2×D4—48no—
566C2×D4—42no—
567C2×D4—44no—
568C2×D4—42no—
569C2×D4—432no—
570C2×D4—48no—
571C2×D4—42no—
572C2×D4—44no—
573C2×D4—42no—
574C2×D4—44no—
575C2×D4—416no—
576C2×D4—416no—
577C2×D4—416no—
578C2×D4—48no—
579C2×D4—416no—
580C2×D4—44no—
581C2×D4—416no—
582C2×D4—416no—
583C2×D4—416no—
584C2×D4—864no—
585C2×D4—832no—
586C2×D4—864no—
587C2×D4C22×D4116yes—
588C2×D4C22×D4116yes—
589C2×D4C22×D418yes—
590C2×D4C22×D4116yes—
591C2×D4C22×D4132yes—
592C2×D4C22×D418yes—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—24no—
596C22×C4—24no—
597C22×C4—24no—
598C22×C4—22no—
599C22×C4—24no—
600C22×C4—232no—
601C22×C4—216no—
602C22×C4—28no—
603C22×C4—216no—
604C22×C4—24no—
605C22×C4—216no—
606C22×C4—28no—
607C22×C4—216no—
608C22×C4—216no—
609C22×C4—28no—
610C22×C4—216no—
611C22×C4—28no—
612C22×C4—28no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—48no—
616C22×C4—48no—
617C22×C4—416no—
618C22×C4—48no—
619C22×C4—48no—
620C22×C4—48no—
621C22×C4—416no—
622C22×C4—832no—
623C22×C4C22×D418yes—
624C22×C4C22×D414yes—
625C22×C4H(5,𝔽2)14yes—
626C22×C4C2511yescharacteristic
627C22×C4C2511yescharacteristic
628C22×C4C2512yes—
629C22×C4C2518yes—
630C22×C4C2518yes—
631C22×C4C2518yes—
632C22×C4C2514yes—
633C22×C4C2514yes—
634C22×C4C2511yescharacteristic
635C22×C4C2511yescharacteristic
636C22×C4C2512yes—
637C22×C4C2511yescharacteristic
638C22×C4C2512yes—
639C22×C4C2512yes—
640C22×C4C2511yescharacteristic
641C4⋊C4—216no—
642C4⋊C4—216no—
643C4⋊C4—28no—
644C4⋊C4—28no—
645C4⋊C4—216no—
646C4⋊C4—216no—
647C4⋊C4—28no—
648C4⋊C4—28no—
649C4⋊C4—28no—
650C4⋊C4—28no—
651C4⋊C4—28no—
652C4⋊C4—28no—
653C4⋊C4—48no—
654C4⋊C4—42no—
655C4⋊C4—44no—
656C4⋊C4—42no—
657C4⋊C4—48no—
658C4⋊C4—416no—
659C4⋊C4—44no—
660C4⋊C4—44no—
661C22⋊C4—216no—
662C22⋊C4—216no—
663C22⋊C4—216no—
664C22⋊C4—232no—
665C22⋊C4—232no—
666C22⋊C4—216no—
667C22⋊C4—216no—
668C22⋊C4—216no—
669C22⋊C4—216no—
670C22⋊C4—216no—
671C22⋊C4—216no—
672C22⋊C4—216no—
673C22⋊C4—216no—
674C22⋊C4—48no—
675C22⋊C4—48no—
676C22⋊C4—44no—
677C22⋊C4—44no—
678C22⋊C4—44no—
679C22⋊C4—44no—
680C22⋊C4—416no—
681C22⋊C4—48no—
682C22⋊C4—416no—
683C22⋊C4—48no—
684C22⋊C4—416no—
685C22⋊C4—48no—
686C22⋊C4—48no—
687C42—216no—
688C42—24no—
689C42—22no—
690C42—22no—
691C42—22no—
692C42—22no—
693C42—24no—
694C42—24no—
695C42—24no—
696C42—24no—
697C42—42no—
698C42—41no—
699C42—42no—
700C42—42no—
701C42—41no—
702C42C22×D418yes—
703C42C22×D414yes—
704C42C22×D414yes—
705C42H(5,𝔽2)18yes—
706C23—22no—
707C23—22no—
708C23—28no—
709C23—28no—
710C23—24no—
711C23—24no—
712C23—28no—
713C23—24no—
714C23—28no—
715C23—24no—
716C23—232no—
717C23—28no—
718C23—28no—
719C23—28no—
720C23—28no—
721C23—28no—
722C23—28no—
723C23—28no—
724C23—432no—
725C23—88no—
726C23—88no—
727C23—816no—
728C23—816no—
729C23—832no—
730C23—816no—
731C23—816no—
732C23—1616no—
733C23C23×D418yes—
734C23C23×D418yes—
735C23C23×D412yes—
736C23C2×H(5,𝔽2)12yes—
737C23#58512yes—
738C23C2611yescharacteristic
739Q8—416no—
740D4—232no—
741D4—232no—
742D4—432no—
743D4—48no—
744D4—416no—
745D4—48no—
746D4—432no—
747D4—416no—
748D4—416no—
749D4—88no—
750D4—832no—
751D4—832no—
752D4—832no—
753D4—816no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—28no—
764C2×C4—216no—
765C2×C4—28no—
766C2×C4—28no—
767C2×C4—28no—
768C2×C4—28no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—28no—
773C2×C4—28no—
774C2×C4—28no—
775C2×C4—28no—
776C2×C4—24no—
777C2×C4—28no—
778C2×C4—24no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—28no—
784C2×C4—28no—
785C2×C4—28no—
786C2×C4—48no—
787C2×C4—44no—
788C2×C4—432no—
789C2×C4—416no—
790C2×C4—416no—
791C2×C4—88no—
792C2×C4—88no—
793C2×C4—88no—
794C2×C4—816no—
795C2×C4—832no—
796C2×C4C23×D412yes—
797C2×C4C23×D414yes—
798C2×C4C23×D412yes—
799C2×C4C23×D414yes—
800C2×C4C2×H(5,𝔽2)12yes—
801C2×C4C2×H(5,𝔽2)14yes—
802C2×C4C2×H(5,𝔽2)14yes—
803C2×C4C2×H(5,𝔽2)12yes—
804C2×C4C2×H(5,𝔽2)14yes—
805C2×C4#58514yes—
806C22—22no—
807C22—22no—
808C22—24no—
809C22—24no—
810C22—216no—
811C22—28no—
812C22—216no—
813C22—28no—
814C22—44no—
815C22—44no—
816C22—44no—
817C22—44no—
818C22—48no—
819C22—48no—
820C22—48no—
821C22—48no—
822C22—48no—
823C22—48no—
824C22—48no—
825C22—48no—
826C22—48no—
827C22—832no—
828C22—1632no—
829C22#349614yes—
830C22C24×D411yescharacteristic
831C22C22×H(5,𝔽2)11yescharacteristic
832C22C22×H(5,𝔽2)12yes—
833C22C2×#58512yes—
834C22C2×#58511yescharacteristic
835C4—22no—
836C4—22no—
837C4—22no—
838C4—24no—
839C4—24no—
840C4—44no—
841C4—44no—
842C4—41no—
843C4—41no—
844C4—48no—
845C4—48no—
846C4—48no—
847C4—42no—
848C4#349618yes—
849C4#354314yescomplemented
850C2—24no—
851C2—48no—
852C2—48no—
853C2—88no—
854C2C2×#354311yescharacteristic
855C2#6275911yescharacteristic
856C2C2×#349611yescharacteristic
857C2C2×#349612yes—
858C2#6283012yes—
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×#3543C2semidirect
2. #59827C2semidirect
3. #59816C2semidirect
4. #59815C2semidirect
5. #59420C2semidirect
6. #59419C2semidirect
7. #46328C2semidirect
8. #46280C2semidirect
9. #39416C2semidirect
10. #39378C2semidirect
11. #39362C2semidirect
12. #38949C2semidirect
13. #37620C2semidirect
14. #37129C2semidirect
15. #36631C2semidirect
16. #36153C2semidirect
17. D4×#121C2semidirect
18. #35000C2semidirect
19. C2×C4×#127C2semidirect
21. C2×#560C22semidirect
23. C2×#550C22semidirect
24. C2×#547C22semidirect
25. C2×#546C22semidirect
27. C2×D42C22semidirect
28. C2×D42C22semidirect
29. C2×#540C22semidirect
30. C2×#535C22semidirect
31. C2×#534C22semidirect
33. C2×#529C22semidirect
34. C22×#121C22semidirect
35. C22×C4×D4C22semidirect
36. C22×C4×D4C22semidirect
37. #2861C22semidirect
38. #2860C22semidirect
39. #2860C22semidirect
40. #2859C22semidirect
41. #2858C22semidirect
42. #2857C22semidirect
44. #2854C22semidirect
45. #2854C22semidirect
46. #2850C22semidirect
47. #2847C22semidirect
48. #2823C22semidirect
49. #2724C22semidirect
50. #2701C22semidirect
51. #2701C22semidirect
52. #2699C22semidirect
53. #2699C22semidirect
54. #2697C22semidirect
55. #2697C22semidirect
56. #2682C22semidirect
57. #2679C22semidirect
58. #2678C22semidirect
59. #2678C22semidirect
60. #2629C22semidirect
61. #2620C22semidirect
62. #2618C22semidirect
63. #2617C22semidirect
64. #2582C22semidirect
65. #2547C22semidirect
66. #2543C22semidirect
67. #2543C22semidirect
68. #2541C22semidirect
69. #2538C22semidirect
70. #2537C22semidirect
71. #2537C22semidirect
72. #2537C22semidirect
73. #2534C22semidirect
74. #2534C22semidirect
75. #2486C22semidirect
76. #2486C22semidirect
77. #2486C22semidirect
78. #2447C22semidirect
79. #2445C22semidirect
80. #2435C22semidirect
81. #2431C22semidirect
82. #2428C22semidirect
83. #2427C22semidirect
84. #2425C22semidirect
85. #2424C22semidirect
86. #2420C22semidirect
87. #2420C22semidirect
88. #2417C22semidirect
89. #2416C22semidirect
90. #2416C22semidirect
91. #2416C22semidirect
92. #2416C22semidirect
93. #2416C22semidirect
94. #2412C22semidirect
95. #2410C22semidirect
96. #2408C22semidirect
97. #2408C22semidirect
98. #2408C22semidirect
99. #2408C22semidirect
100. #2407C22semidirect
101. D4×C4⋊C4C22semidirect
102. D4×C4⋊C4C22semidirect
103. #2339C22semidirect
104. D4×C22⋊C4C22semidirect
105. #2308C22semidirect
106. C4×C4⋊Q8C22semidirect
109. C4×#127C22semidirect
110. C4×#127C22semidirect
111. C4×#127C22semidirect
112. C4×#127C22semidirect
113. C4×#127C22semidirect
114. C4×#127C22semidirect
115. C4×#127C22semidirect
116. C4×#124C22semidirect
117. C4×#121C22semidirect
118. C4×#121C22semidirect
119. #2293C22semidirect
120. #2293C22semidirect
121. C2×#390C22semidirect
122. C2×#390C22semidirect
123. C2×#384C22semidirect
124. C2×#380C22semidirect
125. C2×C43C22semidirect
145. C2×#127D4semidirect
351. C22×D4C2×D4semidirect
352. C22×D4C2×D4semidirect
386. #127C2×D4semidirect
387. #127C2×D4semidirect
388. #127C2×D4semidirect
499. C2×C42C2×D4semidirect
849. C4#3543semidirect

Maximal subgroups

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

subgroupindex
C2×#35432
#598272
#598162
#598152
#594202
#594192
#463282
#462802
#394162
#393782
#393622
#389492
#376202
#371292
#366312
#361532
D4×#1212
#350002
C2×C4×#1272