Finite Group Databasebeta

← #7642012

Subgroups — #7642012

Order 512.

5534 conjugacy classes of subgroups.

The subgroup lattice has 825 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36985C218yesmaximal, complemented
2#36807C218yesmaximal, complemented
3#36780C218yesmaximal, complemented
4#36775C218yesmaximal, complemented
5#36757C218yesmaximal, complemented
6#36726C218yesmaximal, complemented
7#34995C212yesmaximal, complemented
8#34994C212yesmaximal, complemented
9#34992C212yesmaximal, complemented
10#34985C212yesmaximal, complemented
11#34983C212yesmaximal, complemented
12#34982C211yesmaximal, characteristic, complemented
13#34981C211yesmaximal, characteristic
14C2×#2321C212yesmaximal, complemented
15C2×#2315C211yesmaximal, characteristic, complemented
16C2×#543C2211yescharacteristic
17C2×#534C2211yescharacteristic
18C22×#120C2212yes—
19C22×C4×D4C2212yes—
20C23×C22⋊C4C2211yescharacteristic
21C23×C22⋊C4C2211yescharacteristic
22C23×C22⋊C4C2211yescharacteristic
23#2855C2214yescomplemented
24#2853C2214yescomplemented
25#2852C2218yescomplemented
26#2851C2218yescomplemented
27#2849C2218yescomplemented
28#2849C2214yescomplemented
29#2848C2214yescomplemented
30#2848C2214yescomplemented
31#2847C2214yes—
32#2796C2218yescomplemented
33#2787C2218yescomplemented
34#2786C2218yescomplemented
35#2782C2218yescomplemented
36#2770C2218yescomplemented
37#2757C2218yescomplemented
38#2750C2218yescomplemented
39#2747C2218yescomplemented
40#2746C2218yescomplemented
41#2746C2218yescomplemented
42#2745C2218yescomplemented
43#2744C2218yescomplemented
44#2743C2218yescomplemented
45#2740C2218yescomplemented
46#2739C2218yescomplemented
47#2738C2218yescomplemented
48#2737C2218yescomplemented
49#2728C2218yescomplemented
50#2723C2218yescomplemented
51#2711C2218yescomplemented
52#2708C2218yescomplemented
53#2707C2218yescomplemented
54#2706C2218yescomplemented
55#2705C2218yescomplemented
56#2696C2218yescomplemented
57#2695C2218yescomplemented
58#2694C2218yescomplemented
59#2693C2218yescomplemented
60#2691C2218yescomplemented
61#2690C2218yescomplemented
62#2687C2218yescomplemented
63#2681C2218yescomplemented
64#2646C2218yescomplemented
65#2643C2218yescomplemented
66#2627C2214yescomplemented
67#2626C2214yescomplemented
68#2626C2214yescomplemented
69#2623C2214yescomplemented
70#2622C2218yescomplemented
71#2622C2214yescomplemented
72#2617C2214yes—
73#2510C2218yescomplemented
74#2505C2218yescomplemented
75#2505C2218yescomplemented
76#2493C2218yescomplemented
77#2483C2218yescomplemented
78#2481C2218yescomplemented
79#2480C2218yescomplemented
80#2473C2218yescomplemented
81#2473C2218yescomplemented
82#2450C2218yescomplemented
83#2450C2218yescomplemented
84#2449C2218yescomplemented
85#2449C2218yescomplemented
86#2444C2218yescomplemented
87#2443C2218yescomplemented
88#2437C2218yescomplemented
89#2437C2218yescomplemented
90#2419C2218yescomplemented
91#2418C2218yescomplemented
92#2412C2218yes—
93#2412C2218yes—
94#2412C2218yes—
95#2410C2218yes—
96#2405C2218yescomplemented
97#2321C2218yes—
98#2321C2218yes—
99#2321C2218yescomplemented
100#2321C2218yescomplemented
101#2315C2211yescharacteristic
102#2315C2212yes—
103#2315C2211yescharacteristic
104#2315C2212yes—
105#2315C2212yes—
106#2315C2218yescomplemented
107#2315C2218yescomplemented
108#2308C2212yes—
109#2308C2212yes—
110#2308C2212yes—
111C2×#390C2214yescomplemented
112C2×#388C2214yescomplemented
113C2×#388C2214yescomplemented
114C2×#386C2212yes—
115C2×#386C2214yescomplemented
116C2×#385C2212yes—
117C2×#385C2212yes—
118C2×#385C2212yes—
119C2×#385C2214yescomplemented
120C2×#380C2214yescomplemented
121C2×#379C2212yes—
122C2×C4×C22⋊C4C2212yes—
123C26C2311yescharacteristic
124C23×D4C2312yes—
125C23×D4C2314yes—
126C24×C4C2312yes—
127C24×C4C2312yes—
128C24×C4C2312yes—
129C24×C4C2312yes—
130#543—44no—
131#534—44no—
132C2×#126C2318yescomplemented
133C2×#125C2318yescomplemented
134C2×#123C2314yes—
135C2×#123C2318yes—
136C2×#123C2318yes—
137C2×#123C2318yescomplemented
138C2×C22⋊Q8C2314yes—
139C2×C22⋊Q8C2314yes—
140C2×C22⋊Q8C2314yes—
141C2×C22⋊Q8C2318yes—
142C2×C22⋊Q8C2318yescomplemented
143C2×#121C2314yes—
144C2×#121C2318yes—
145C2×#120—216no—
146C2×#120C2318yes—
147C2×#120C2314yes—
148C2×#120C2314yes—
149C2×#120C2314yes—
150C2×C4×D4—48no—
151C2×C4×D4C2318yes—
152C2×C4×D4C2318yes—
153C22×C4⋊C4C2312yes—
154C22×C4⋊C4C2314yes—
155C22×C4⋊C4C2314yes—
156C22×C4⋊C4C2314yes—
157C22×C22⋊C4—28no—
158C22×C22⋊C4—44no—
159C22×C22⋊C4—44no—
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2311yescharacteristic
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2312yes—
164C22×C22⋊C4C2312yes—
165C22×C22⋊C4C2311yescharacteristic
166C22×C22⋊C4C2318yes—
167C22×C22⋊C4C2312yes—
168C22×C22⋊C4C2314yes—
169C22×C22⋊C4C2314yes—
170C22×C22⋊C4C2314yes—
171C22×C22⋊C4C2318yes—
172C22×C22⋊C4C2312yes—
173C22×C22⋊C4C2312yes—
174C22×C22⋊C4C2312yes—
175C22×C22⋊C4C2312yes—
176C22×C22⋊C4C2314yes—
177C22×C22⋊C4C2314yes—
178C22×C22⋊C4C2314yes—
179C22×C42C2312yes—
180C22×C42C2314yes—
181#401C2318yescomplemented
182#400C2318yescomplemented
183#400C2318yescomplemented
184#400C2318yescomplemented
185#400C2318yescomplemented
186#400C2318yescomplemented
187#400C2318yescomplemented
188#400C2318yescomplemented
189#400C2318yescomplemented
190#400C2318yescomplemented
191#399C2318yes—
192#399C2318yescomplemented
193#399C2318yescomplemented
194#398C2318yescomplemented
195#398C2318yescomplemented
196#398C2318yescomplemented
197#398C2318yescomplemented
198#398C2318yescomplemented
199#398C2318yescomplemented
200#398C2318yescomplemented
201#397C2318yes—
202#397C2318yes—
203#397C2318yes—
204#397C2318yes—
205#397C2318yes—
206#397C2318yescomplemented
207#397C2318yescomplemented
208#397C2318yescomplemented
209#397C2318yescomplemented
210#397C2318yescomplemented
211#397C2318yescomplemented
212#396C2318yes—
213#396C2318yes—
214#396C2318yescomplemented
215#396C2318yescomplemented
216#396C2318yescomplemented
217#395C2318yescomplemented
218#394C2318yes—
219#394C2318yes—
220#394C2318yes—
221#394C2318yes—
222#394C2318yes—
223#394C2318yes—
224#394C2318yescomplemented
225#394C2318yescomplemented
226#393C2318yes—
227#393C2318yescomplemented
228#392C2318yes—
229#391C2318yescomplemented
230#390C2318yes—
231#390C2318yes—
232#390C2318yes—
233#390C2318yes—
234#389C2318yescomplemented
235#389C2318yescomplemented
236#389C2318yescomplemented
237#388C2318yes—
238#388C2318yes—
239#388C2318yes—
240#388C2318yes—
241#388C2318yes—
242#388C2318yes—
243#388C2318yes—
244#388C2318yes—
245#388C2318yescomplemented
246#388C2318yescomplemented
247#388C2318yescomplemented
248#388C2318yescomplemented
249#388C2318yescomplemented
250#387C2318yescomplemented
251#387C2318yescomplemented
252#387C2318yescomplemented
253#387C2318yescomplemented
254#387C2318yescomplemented
255#387C2318yescomplemented
256#387C2318yescomplemented
257#387C2318yescomplemented
258#387C2318yescomplemented
259#387C2318yescomplemented
260#387C2318yescomplemented
261#386C2314yes—
262#386C2314yes—
263#386C2318yes—
264#386C2318yes—
265#386C2314yes—
266#386C2318yes—
267#386C2318yes—
268#386C2314yes—
269#386C2314yes—
270#386C2314yes—
271#386C2318yes—
272#386C2318yes—
273#386C2318yes—
274#386C2318yes—
275#386C2318yes—
276#386C2318yes—
277#386C2318yes—
278#386C2318yes—
279#386C2318yes—
280#386C2318yescomplemented
281#385C2314yes—
282#385C2314yes—
283#385C2318yes—
284#385C2318yes—
285#385C2314yes—
286#385C2318yes—
287#385C2318yes—
288#385C2318yes—
289#385C2318yes—
290#385C2314yes—
291#385C2314yes—
292#385C2314yes—
293#385C2314yes—
294#385C2314yes—
295#385C2318yes—
296#385C2318yes—
297#385C2318yes—
298#385C2318yes—
299#385C2318yes—
300#385C2318yes—
301#385C2314yes—
302#385C2314yes—
303#385C2318yes—
304#385C2318yes—
305#385C2318yes—
306#385C2318yes—
307#385C2318yes—
308#385C2318yescomplemented
309#385C2318yescomplemented
310#385C2318yescomplemented
311#383C2318yescomplemented
312#382C2318yescomplemented
313#381C2314yes—
314#381C2314yes—
315#381C2314yes—
316#381C2318yes—
317#381C2318yes—
318#381C2318yescomplemented
319#380C2314yes—
320#380C2314yes—
321#380C2314yes—
322#380C2318yes—
323#380C2318yes—
324#380C2314yes—
325#380C2318yes—
326#380C2318yes—
327#380C2318yes—
328#380C2318yes—
329#380C2318yes—
330#380C2318yes—
331#380C2318yescomplemented
332#379C2314yes—
333#379C2314yes—
334#379C2314yes—
335#379C2318yes—
336#379C2314yes—
337#379C2314yes—
338C4×C22⋊C4C2318yes—
339C4×C22⋊C4C2318yes—
340C2×#95C2314yes—
341C2×#95C2314yes—
342C2×#95C2314yes—
343C2×#95C2314yes—
344C2×#95C2314yes—
345C25—24no—
346C25—24no—
347C25—84no—
348C25#4118yes—
349C25C2412yes—
350C25C2414yes—
351C25C2411yescharacteristic
352C25C2411yescharacteristic
353C25C2411yescharacteristic
354C22×Q8C2414yes—
355C22×D4—28no—
356C22×D4—28no—
357C22×D4—28no—
358C22×D4—216no—
359C22×D4—84no—
360C22×D4—84no—
361C22×D4C2414yes—
362C22×D4C2414yes—
363C22×D4C2418yes—
364C22×D4C2418yes—
365C22×D4C2414yes—
366C23×C4—28no—
367C23×C4—28no—
368C23×C4—44no—
369C23×C4—44no—
370C23×C4—84no—
371C23×C4—84no—
372C23×C4—84no—
373C23×C4—84no—
374C23×C4C2412yes—
375C23×C4C2412yes—
376C23×C4C2414yes—
377C23×C4C2414yes—
378C23×C4C2412yes—
379C23×C4C2412yes—
380C23×C4C2414yes—
381C23×C4C2412yes—
382C23×C4C2412yes—
383C23×C4C2414yes—
384C23×C4C2414yes—
385C23×C4C2418yes—
386C23×C4C2412yes—
387C23×C4C2418yes—
388C23×C4C2418yes—
389#126—88no—
390#125—88no—
391#123—48no—
392#123—88no—
393#123—88no—
394#123—88no—
395C22⋊Q8—48no—
396C22⋊Q8—48no—
397C22⋊Q8—48no—
398C22⋊Q8—88no—
399C22⋊Q8—88no—
400#121—48no—
401#121—88no—
402#120—232no—
403#120—216no—
404#120—216no—
405#120—48no—
406C4×D4—416no—
407C4×D4—416no—
408C2×C4⋊C4—44no—
409C2×C4⋊C4—84no—
410C2×C4⋊C4—84no—
411C2×C4⋊C4—84no—
412C2×C4⋊C4C2418yes—
413C2×C4⋊C4C2418yes—
414C2×C4⋊C4C2418yes—
415C2×C4⋊C4C2418yes—
416C2×C4⋊C4C2418yes—
417C2×C4⋊C4C2418yes—
418C2×C4⋊C4C2418yes—
419C2×C4⋊C4C2414yes—
420C2×C4⋊C4C2418yes—
421C2×C4⋊C4C2414yes—
422C2×C4⋊C4C2414yes—
423C2×C4⋊C4C2414yes—
424C2×C4⋊C4C2418yes—
425C2×C4⋊C4C2418yes—
426C2×C4⋊C4C2418yes—
427C2×C4⋊C4C2418yes—
428C2×C4⋊C4C2418yes—
429C2×C4⋊C4C2418yes—
430C2×C4⋊C4C2418yes—
431C2×C22⋊C4—28no—
432C2×C22⋊C4—28no—
433C2×C22⋊C4—232no—
434C2×C22⋊C4—216no—
435C2×C22⋊C4—28no—
436C2×C22⋊C4—24no—
437C2×C22⋊C4—24no—
438C2×C22⋊C4—28no—
439C2×C22⋊C4—28no—
440C2×C22⋊C4—416no—
441C2×C22⋊C4—48no—
442C2×C22⋊C4—48no—
443C2×C22⋊C4—44no—
444C2×C22⋊C4—44no—
445C2×C22⋊C4—44no—
446C2×C22⋊C4—44no—
447C2×C22⋊C4—84no—
448C2×C22⋊C4—84no—
449C2×C22⋊C4—84no—
450C2×C22⋊C4C2414yes—
451C2×C22⋊C4C2414yes—
452C2×C22⋊C4C2414yes—
453C2×C22⋊C4C2414yes—
454C2×C22⋊C4C2418yes—
455C2×C22⋊C4C2414yes—
456C2×C22⋊C4C2414yes—
457C2×C22⋊C4C2414yes—
458C2×C22⋊C4C2414yes—
459C2×C22⋊C4C2418yes—
460C2×C22⋊C4C2418yes—
461C2×C22⋊C4C2414yes—
462C2×C22⋊C4C2414yes—
463C2×C22⋊C4C2412yes—
464C2×C22⋊C4C2414yes—
465C2×C22⋊C4C2412yes—
466C2×C22⋊C4C2418yes—
467C2×C22⋊C4C2412yes—
468C2×C22⋊C4C2414yes—
469C2×C22⋊C4C2412yes—
470C2×C22⋊C4C2418yes—
471C2×C22⋊C4C2418yes—
472C2×C22⋊C4C2418yes—
473C2×C22⋊C4C2418yes—
474C2×C22⋊C4C2418yes—
475C2×C22⋊C4C2418yes—
476C2×C22⋊C4C2418yes—
477C2×C22⋊C4C2414yes—
478C2×C22⋊C4C2414yes—
479C2×C22⋊C4C2418yes—
480C2×C22⋊C4C2418yes—
481C2×C22⋊C4C2418yes—
482C2×C22⋊C4C2418yes—
483C2×C22⋊C4C2418yes—
484C2×C22⋊C4C2418yes—
485C2×C42—44no—
486C2×C42—84no—
487C2×C42C2418yes—
488C2×C42C2418yes—
489C2×C42C2418yes—
490#95C2418yes—
491#95C2418yes—
492#95C2418yes—
493#95C2418yes—
494#95C2418yes—
495#95C2418yes—
496#95C2418yes—
497#95C2418yes—
498#95C2418yes—
499#95C2418yes—
500#95C2418yes—
501#95C2418yes—
502#95C2418yes—
503#95C2418yes—
504#95C2418yes—
505#95C2418yes—
506#95C2418yes—
507#95C2418yes—
508#95C2418yes—
509#95C2418yes—
510#95C2418yes—
511#95C2418yes—
512#95C2418yes—
513#95C2418yes—
514C24—22no—
515C24—22no—
516C24—22no—
517C24—22no—
518C24—232no—
519C24—28no—
520C24—28no—
521C24—24no—
522C24—24no—
523C24—24no—
524C24—44no—
525C24—44no—
526C24—44no—
527C24—44no—
528C24—44no—
529C24—44no—
530C24—44no—
531C24—44no—
532C24—44no—
533C24—816no—
534C24—816no—
535C24—816no—
536C24C2×#41116yes—
537C24C2×#4114yes—
538C24C2×#4114yes—
539C24C2×#4114yes—
540C24H(5,𝔽2)14yes—
541C242−1+414yes—
542C24C2514yes—
543C24C2512yes—
544C24C2512yes—
545C24C2512yes—
546C24C2511yescharacteristic
547C2×Q8—44no—
548C2×Q8—48no—
549C2×D4—28no—
550C2×D4—28no—
551C2×D4—28no—
552C2×D4—28no—
553C2×D4—28no—
554C2×D4—28no—
555C2×D4—216no—
556C2×D4—216no—
557C2×D4—48no—
558C2×D4—48no—
559C2×D4—48no—
560C2×D4—48no—
561C2×D4—44no—
562C2×D4—48no—
563C2×D4—432no—
564C2×D4—832no—
565C22×C4—28no—
566C22×C4—28no—
567C22×C4—24no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—216no—
573C22×C4—24no—
574C22×C4—24no—
575C22×C4—24no—
576C22×C4—24no—
577C22×C4—28no—
578C22×C4—28no—
579C22×C4—28no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—48no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—48no—
598C22×C4—48no—
599C22×C4—48no—
600C22×C4—48no—
601C22×C4—48no—
602C22×C4—48no—
603C22×C4—48no—
604C22×C4—816no—
605C22×C4—816no—
606C22×C4—816no—
607C22×C4—816no—
608C22×C4C2514yes—
609C22×C4C2518yes—
610C22×C4C2518yes—
611C22×C4C2514yes—
612C22×C4C2518yes—
613C22×C4C2514yes—
614C22×C4C2514yes—
615C22×C4C2514yes—
616C22×C4C2514yes—
617C22×C4C2514yes—
618C4⋊C4—48no—
619C4⋊C4—48no—
620C4⋊C4—48no—
621C4⋊C4—48no—
622C4⋊C4—48no—
623C4⋊C4—48no—
624C4⋊C4—48no—
625C4⋊C4—44no—
626C4⋊C4—48no—
627C4⋊C4—44no—
628C4⋊C4—44no—
629C4⋊C4—44no—
630C4⋊C4—48no—
631C4⋊C4—48no—
632C4⋊C4—48no—
633C4⋊C4—48no—
634C4⋊C4—48no—
635C4⋊C4—48no—
636C4⋊C4—48no—
637C22⋊C4—216no—
638C22⋊C4—28no—
639C22⋊C4—28no—
640C22⋊C4—216no—
641C22⋊C4—216no—
642C22⋊C4—28no—
643C22⋊C4—28no—
644C22⋊C4—28no—
645C22⋊C4—28no—
646C22⋊C4—28no—
647C22⋊C4—28no—
648C22⋊C4—28no—
649C22⋊C4—28no—
650C22⋊C4—42no—
651C22⋊C4—42no—
652C22⋊C4—44no—
653C22⋊C4—44no—
654C22⋊C4—48no—
655C22⋊C4—42no—
656C22⋊C4—42no—
657C22⋊C4—48no—
658C22⋊C4—48no—
659C22⋊C4—48no—
660C22⋊C4—48no—
661C22⋊C4—48no—
662C22⋊C4—48no—
663C22⋊C4—48no—
664C22⋊C4—44no—
665C22⋊C4—44no—
666C22⋊C4—48no—
667C22⋊C4—48no—
668C22⋊C4—48no—
669C22⋊C4—48no—
670C22⋊C4—48no—
671C22⋊C4—48no—
672C42—48no—
673C42—48no—
674C42—48no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—24no—
683C23—24no—
684C23—24no—
685C23—24no—
686C23—28no—
687C23—28no—
688C23—232no—
689C23—24no—
690C23—24no—
691C23—24no—
692C23—28no—
693C23—28no—
694C23—48no—
695C23—48no—
696C23—48no—
697C23—48no—
698C23—48no—
699C23—416no—
700C23—416no—
701C23—48no—
702C23—48no—
703C23—48no—
704C23—48no—
705C23—416no—
706C23—48no—
707C23—84no—
708C23—84no—
709C23—88no—
710C23—88no—
711C23—88no—
712C23—88no—
713C23—88no—
714C23—864no—
715C23#539116yes—
716C23C22×#4114yes—
717C23C22×#4114yes—
718C23C22×#4114yes—
719C23C22×#4112yes—
720C23C2×H(5,𝔽2)14yes—
721C23C2×H(5,𝔽2)12yes—
722C23C2×2−1+412yes—
723C23C2×2−1+414yes—
724C23C2611yescharacteristic
725Q8—164no—
726D4—416no—
727D4—416no—
728D4—816no—
729D4—816no—
730D4—164no—
731C2×C4—28no—
732C2×C4—28no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—28no—
742C2×C4—24no—
743C2×C4—28no—
744C2×C4—24no—
745C2×C4—28no—
746C2×C4—24no—
747C2×C4—28no—
748C2×C4—28no—
749C2×C4—28no—
750C2×C4—28no—
751C2×C4—28no—
752C2×C4—28no—
753C2×C4—24no—
754C2×C4—28no—
755C2×C4—28no—
756C2×C4—24no—
757C2×C4—416no—
758C2×C4—48no—
759C2×C4—48no—
760C2×C4—416no—
761C2×C4—48no—
762C2×C4—84no—
763C2×C4—88no—
764C2×C4—816no—
765C2×C4—88no—
766C2×C4—88no—
767C2×C4—84no—
768C2×C4—84no—
769C2×C4—84no—
770C2×C4—816no—
771C2×C4—816no—
772C22—24no—
773C22—28no—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—28no—
778C22—24no—
779C22—28no—
780C22—24no—
781C22—24no—
782C22—24no—
783C22—24no—
784C22—416no—
785C22—416no—
786C22—416no—
787C22—44no—
788C22—44no—
789C22—44no—
790C22—42no—
791C22—42no—
792C22—48no—
793C22—44no—
794C22—44no—
795C22—48no—
796C22—44no—
797C22—832no—
798C22—816no—
799C22C2×#53918yes—
800C22C2×#53914yes—
801C22C23×#4111yescharacteristic
802C22C22×H(5,𝔽2)11yescharacteristic
803C22C22×2−1+411yescharacteristic
804C22H(7,𝔽2)14yes—
805C4—48no—
806C4—48no—
807C4—44no—
808C4—44no—
809C4—44no—
810C4—44no—
811C4—44no—
812C4—44no—
813C4—48no—
814C4—44no—
815C2—24no—
816C2—28no—
817C2—44no—
818C2—44no—
819C2—84no—
820C2C22×#53911yescharacteristic
821C2#6284412yes—
822C2#6286212yes—
823C2#6286412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34981C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36985C2semidirect
2. #36807C2semidirect
3. #36780C2semidirect
4. #36775C2semidirect
5. #36757C2semidirect
6. #36726C2semidirect
7. #34995C2semidirect
8. #34994C2semidirect
9. #34992C2semidirect
10. #34985C2semidirect
11. #34983C2semidirect
12. #34982C2semidirect
14. C2×#2321C2semidirect
15. C2×#2315C2semidirect
23. #2855C22semidirect
24. #2853C22semidirect
25. #2852C22semidirect
26. #2851C22semidirect
27. #2849C22semidirect
28. #2849C22semidirect
29. #2848C22semidirect
30. #2848C22semidirect
32. #2796C22semidirect
33. #2787C22semidirect
34. #2786C22semidirect
35. #2782C22semidirect
36. #2770C22semidirect
37. #2757C22semidirect
38. #2750C22semidirect
39. #2747C22semidirect
40. #2746C22semidirect
41. #2746C22semidirect
42. #2745C22semidirect
43. #2744C22semidirect
44. #2743C22semidirect
45. #2740C22semidirect
46. #2739C22semidirect
47. #2738C22semidirect
48. #2737C22semidirect
49. #2728C22semidirect
50. #2723C22semidirect
51. #2711C22semidirect
52. #2708C22semidirect
53. #2707C22semidirect
54. #2706C22semidirect
55. #2705C22semidirect
56. #2696C22semidirect
57. #2695C22semidirect
58. #2694C22semidirect
59. #2693C22semidirect
60. #2691C22semidirect
61. #2690C22semidirect
62. #2687C22semidirect
63. #2681C22semidirect
64. #2646C22semidirect
65. #2643C22semidirect
66. #2627C22semidirect
67. #2626C22semidirect
68. #2626C22semidirect
69. #2623C22semidirect
70. #2622C22semidirect
71. #2622C22semidirect
73. #2510C22semidirect
74. #2505C22semidirect
75. #2505C22semidirect
76. #2493C22semidirect
77. #2483C22semidirect
78. #2481C22semidirect
79. #2480C22semidirect
80. #2473C22semidirect
81. #2473C22semidirect
82. #2450C22semidirect
83. #2450C22semidirect
84. #2449C22semidirect
85. #2449C22semidirect
86. #2444C22semidirect
87. #2443C22semidirect
88. #2437C22semidirect
89. #2437C22semidirect
90. #2419C22semidirect
91. #2418C22semidirect
96. #2405C22semidirect
99. #2321C22semidirect
100. #2321C22semidirect
106. #2315C22semidirect
107. #2315C22semidirect
111. C2×#390C22semidirect
112. C2×#388C22semidirect
113. C2×#388C22semidirect
115. C2×#386C22semidirect
119. C2×#385C22semidirect
120. C2×#380C22semidirect
132. C2×#126C23semidirect
133. C2×#125C23semidirect
137. C2×#123C23semidirect
142. C2×C22⋊Q8C23semidirect
181. #401C23semidirect
182. #400C23semidirect
183. #400C23semidirect
184. #400C23semidirect
185. #400C23semidirect
186. #400C23semidirect
187. #400C23semidirect
188. #400C23semidirect
189. #400C23semidirect
190. #400C23semidirect
192. #399C23semidirect
193. #399C23semidirect
194. #398C23semidirect
195. #398C23semidirect
196. #398C23semidirect
197. #398C23semidirect
198. #398C23semidirect
199. #398C23semidirect
200. #398C23semidirect
206. #397C23semidirect
207. #397C23semidirect
208. #397C23semidirect
209. #397C23semidirect
210. #397C23semidirect
211. #397C23semidirect
214. #396C23semidirect
215. #396C23semidirect
216. #396C23semidirect
217. #395C23semidirect
224. #394C23semidirect
225. #394C23semidirect
227. #393C23semidirect
229. #391C23semidirect
234. #389C23semidirect
235. #389C23semidirect
236. #389C23semidirect
245. #388C23semidirect
246. #388C23semidirect
247. #388C23semidirect
248. #388C23semidirect
249. #388C23semidirect
250. #387C23semidirect
251. #387C23semidirect
252. #387C23semidirect
253. #387C23semidirect
254. #387C23semidirect
255. #387C23semidirect
256. #387C23semidirect
257. #387C23semidirect
258. #387C23semidirect
259. #387C23semidirect
260. #387C23semidirect
280. #386C23semidirect
308. #385C23semidirect
309. #385C23semidirect
310. #385C23semidirect
311. #383C23semidirect
312. #382C23semidirect
318. #381C23semidirect
331. #380C23semidirect

Maximal subgroups

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

subgroupindex
#369852
#368072
#367802
#367752
#367572
#367262
#349952
#349942
#349922
#349852
#349832
#349822
#349812
C2×#23212
C2×#23152