Finite Group Databasebeta

← #7630548

Subgroups — #7630548

Order 512.

8198 conjugacy classes of subgroups.

The subgroup lattice has 879 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3460C211yesmaximal, characteristic, complemented
2C22×#520C211yesmaximal, characteristic, complemented
3#35654C218yesmaximal, complemented
4#35606C218yesmaximal, complemented
5#35601C218yesmaximal, complemented
6#35600C218yesmaximal, complemented
7#35224C211yesmaximal, characteristic, complemented
8#35223C211yesmaximal, characteristic, complemented
9#35154C211yesmaximal, characteristic, complemented
10#35153C211yesmaximal, characteristic, complemented
11#35152C212yesmaximal, complemented
12#35149C212yesmaximal, complemented
13#35093C214yesmaximal, complemented
14#35091C214yesmaximal, complemented
15#35057C214yesmaximal, complemented
16#35031C214yesmaximal, complemented
17C4×#536C212yesmaximal, complemented
18#34065C212yesmaximal, complemented
19#34058C211yesmaximal, characteristic, complemented
20C23×#41C2211yescharacteristic
21#3460—216no—
22C2×#544C2211yescharacteristic
23C2×#542C2214yescomplemented
24C2×#540C2214yescomplemented
25C2×#538C2214yes—
26C2×#537C2211yescharacteristic
27C2×#536C2212yes—
28C2×#535C2212yes—
29C2×#532C2214yescomplemented
30C2×#529C2214yescomplemented
31C2×#525C2212yes—
32C2×#525C2214yes—
33C2×#520—216no—
34C2×#520C2218yes—
35C2×#520C2218yes—
36C2×C4×#41C2212yes—
37C22×C4×Q8C2211yescharacteristic
38C22×C4×Q8C2211yescharacteristic
39C22×C4×D4C2212yes—
40C22×C4×D4C2211yescharacteristic
41C22×C4×D4C2212yes—
42C22×C4×D4C2211yescharacteristic
43C22×#117C2211yescharacteristic
44C22×#117C2212yes—
45C23×C4⋊C4C2211yescharacteristic
46C23×C4⋊C4C2212yes—
47#2855C2214yes—
48#2854C2214yes—
49#2849C2218yes—
50#2849C2218yes—
51#2848C2214yes—
52#2847C2214yes—
53#2627C2214yes—
54#2627C2214yes—
55#2622C2218yes—
56#2618C2214yes—
57#2618C2214yes—
58#2613C2218yes—
59#2602C22116yescomplemented
60#2600C22116yescomplemented
61#2591C2218yescomplemented
62#2583C2218yescomplemented
63#2579C22116yescomplemented
64#2485C2218yescomplemented
65#2484C2218yescomplemented
66#2478C22116yescomplemented
67#2476C22116yescomplemented
68#2474C22116yescomplemented
69#2470C22116yescomplemented
70#2468C22116yescomplemented
71#2464C22116yescomplemented
72#2461C22116yescomplemented
73#2457C22116yescomplemented
74#2453C2218yescomplemented
75#2451C2218yescomplemented
76#2447C2218yescomplemented
77#2445C2218yescomplemented
78#2442C2218yescomplemented
79#2440C2218yescomplemented
80#2432C2218yes—
81#2431C2218yes—
82#2429C2218yescomplemented
83#2426C2218yescomplemented
84#2422C2218yescomplemented
85#2420C2218yescomplemented
86#2417C2218yescomplemented
87#2416C2218yescomplemented
88#2415C2218yescomplemented
89#2414C2218yescomplemented
90#2413C22116yescomplemented
91#2407C2218yes—
92#2407C2218yes—
93#2407C2218yescomplemented
94#2406C2218yescomplemented
95#2327C2214yescomplemented
96#2326C2214yescomplemented
97#2324C2214yescomplemented
98#2324C2214yescomplemented
99#2323C2214yescomplemented
100#2323C2214yescomplemented
101#2323C2218yescomplemented
102#2322C2214yes—
103#2322C2214yes—
104#2322C2218yes—
105#2321C2214yes—
106#2321C2214yes—
107#2319C2218yescomplemented
108#2317C2212yes—
109#2316C2211yescharacteristic
110#2316C2211yescharacteristic
111#2312C2214yes—
112#2311C2212yes—
113#2310C2212yes—
114#2309C2212yes—
115C4×C4⋊Q8C2214yescomplemented
116C4×#124C2214yescomplemented
117C4×C22⋊Q8C2218yescomplemented
118C4×#123C2218yes—
119#2297C2212yes—
120#2296C2212yes—
121#2293C2218yescomplemented
122#2293C2218yescomplemented
123#2290C2218yescomplemented
124#2280C2214yes—
125#2280C2212yes—
126C4×#117C2212yes—
127C22×#41—28no—
128C22×#41—28no—
129C22×#41—28no—
130C22×#41C2318yes—
131C22×#41C2312yes—
132C22×#41C2314yes—
133C23×Q8C2311yescharacteristic
134C23×D4C2312yes—
135C23×D4C2311yescharacteristic
136C24×C4C2312yes—
137C24×C4C2311yescharacteristic
138C24×C4C2312yes—
139C24×C4C2312yes—
140C24×C4C2312yes—
141#544—28no—
142#542—232no—
143#540—232no—
144#538—232no—
145#537—28no—
146#536—216no—
147#535—216no—
148#532—232no—
149C2×C4⋊Q8C2314yes—
150C2×C4⋊Q8C2314yes—
151C2×#127C2314yes—
152#529—232no—
153C2×#126C2318yes—
154C2×#125C2314yes—
155C2×#124C2314yes—
156C2×#124C2314yes—
157C2×#124C2318yes—
158#525—232no—
159#525—216no—
160C2×#123C2314yes—
161C2×#123C2318yes—
162C2×#123C2318yes—
163C2×#123C2318yes—
164C2×#123C23116yes—
165C2×C22⋊Q8C2314yes—
166C2×C22⋊Q8C2318yes—
167C2×C22⋊Q8C2314yes—
168C2×C22⋊Q8C2314yes—
169C2×C22⋊Q8C2314yes—
170C2×C22⋊Q8C2318yes—
171C2×#121C2314yes—
172C2×#121C2314yes—
173C2×#121C2314yes—
174C2×#121C2314yes—
175C2×#121C2314yes—
176C2×#121C2314yes—
177C2×#121C2318yes—
178C2×#121C2318yes—
179C2×#120C2314yes—
180C2×#120C2318yes—
181#520—264no—
182#520—264no—
183C4×#41—216no—
184C2×C4×Q8—28no—
185C2×C4×Q8—28no—
186C2×C4×Q8C2312yes—
187C2×C4×Q8C2314yes—
188C2×C4×Q8C2312yes—
189C2×C4×Q8C2314yes—
190C2×C4×Q8C2318yes—
191C2×C4×D4—28no—
192C2×C4×D4—216no—
193C2×C4×D4—216no—
194C2×C4×D4D4116yescomplemented
195C2×C4×D4C2314yes—
196C2×C4×D4C2314yes—
197C2×C4×D4C2318yes—
198C2×C4×D4C2312yes—
199C2×C4×D4C2312yes—
200C2×C4×D4C2318yes—
201C2×C4×D4C2318yes—
202C2×C4×D4C2318yes—
203C2×C4×D4C23116yes—
204C2×C4×D4C2318yes—
205C2×C4×D4C2314yes—
206C2×C4×D4C2314yes—
207C2×#117—216no—
208C2×#117—28no—
209C2×#117C2312yes—
210C2×#117C2312yes—
211C2×#117C2312yes—
212C2×#117C2314yes—
213C2×#117C2314yes—
214C2×#117C2314yes—
215C2×#117C23116yes—
216C2×#117C2314yes—
217C2×#117C2318yes—
218C22×C4⋊C4—216no—
219C22×C4⋊C4—28no—
220C22×C4⋊C4C2311yescharacteristic
221C22×C4⋊C4C2311yescharacteristic
222C22×C4⋊C4C2312yes—
223C22×C4⋊C4C2311yescharacteristic
224C22×C4⋊C4C2318yes—
225C22×C4⋊C4C2318yes—
226C22×C4⋊C4C2312yes—
227C22×C4⋊C4C2312yes—
228C22×C4⋊C4C2318yes—
229C22×C4⋊C4C2311yescharacteristic
230C22×C22⋊C4C2311yescharacteristic
231C22×C22⋊C4C2311yescharacteristic
232C22×C22⋊C4C2312yes—
233C22×C22⋊C4C2312yes—
234C22×C42C2312yes—
235C22×C42C2311yescharacteristic
236C22×C42C2312yes—
237C22×C42C2314yes—
238C22×C42C2311yescharacteristic
239#400C2318yes—
240#400C2318yes—
241#398C23116yes—
242#398C23116yes—
243#398C2318yes—
244#398C2318yes—
245#397C23116yes—
246#397C23116yes—
247#396C23116yes—
248#396C23116yes—
249#395C2318yes—
250#395C2318yes—
251#394C2318yes—
252#394C2318yes—
253#394C23116yes—
254#394C23116yes—
255#394C23116yes—
256#394C23116yes—
257#392C23116yes—
258#392C23116yes—
259#391C2314yes—
260#391C2314yes—
261#391C2318yes—
262#391C2314yes—
263#391C2314yes—
264#391C2318yes—
265#390C2318yes—
266#390C2318yes—
267#390C2314yes—
268#390C2318yes—
269#390C2318yes—
270#390C2314yes—
271#390C2318yes—
272#389C23116yes—
273#389C2318yes—
274#389C2318yes—
275#389C2318yes—
276#389C2318yes—
277#389C2318yes—
278#389C2314yes—
279#389C2314yes—
280#389C2318yes—
281#389C2318yes—
282#388C23116yes—
283#388C23116yes—
284#388C2318yes—
285#388C2318yes—
286#388C2318yes—
287#388C2318yes—
288#388C23116yes—
289#388C2318yes—
290#388C2318yes—
291#388C23116yes—
292#388C23116yes—
293#387C2318yes—
294#387C2318yes—
295#387C23116yes—
296#387C23116yes—
297#387C23116yes—
298#386C2318yes—
299#386C2314yes—
300#386C2314yes—
301#386C2318yes—
302#386C2318yes—
303#386C23116yes—
304#386C23116yes—
305#386C23116yes—
306#386C23116yes—
307#385C2318yes—
308#385C2314yes—
309#385C2314yes—
310#385C2318yes—
311#385C23116yes—
312#385C2318yes—
313#385C23116yes—
314#385C23116yes—
315#385C23116yes—
316#385C23116yes—
317#384C2314yes—
318#382C2314yes—
319#381C2318yes—
320#381C2318yes—
321#381C2314yes—
322#381C23116yes—
323#380C2318yes—
324#380C2314yes—
325#380C2314yes—
326#380C2318yes—
327#380C2314yes—
328#380C2314yes—
329#380C2318yes—
330#380C2318yes—
331#379C2318yes—
332#379C2314yes—
333C4×C4⋊C4C23116yes—
334C4×C4⋊C4C2314yes—
335C4×C4⋊C4C2314yes—
336C4×C4⋊C4C2318yes—
337C4×C22⋊C4C2314yes—
338C4×C22⋊C4C2314yes—
339C4×C22⋊C4C2318yes—
340C4×C22⋊C4C2318yes—
341C4×C22⋊C4C2318yes—
342C4×C22⋊C4C23116yes—
343#376C2314yes—
344C43C2314yes—
345C25C2412yes—
346C25C2411yescharacteristic
347C2×#41—2128no—
348C2×#41—232no—
349C2×#41—232no—
350C2×#41—28no—
351C2×#41—216no—
352C2×#41—232no—
353C2×#41—28no—
354C2×#41—28no—
355C2×#41—88no—
356C22×Q8—24no—
357C22×Q8—24no—
358C22×Q8#4118yescomplemented
359C22×Q8C2412yes—
360C22×Q8C2414yes—
361C22×Q8C2414yes—
362C22×D4—28no—
363C22×D4—28no—
364C22×D4—28no—
365C22×D4—24no—
366C22×D4—24no—
367C22×D4C2×D418yes—
368C22×D4C2418yes—
369C22×D4C2414yes—
370C22×D4C2412yes—
371C22×D4C2414yes—
372C22×D4C2418yes—
373C22×D4C2418yes—
374C22×D4C2418yes—
375C22×D4C2414yes—
376C23×C4—28no—
377C23×C4—24no—
378C23×C4—28no—
379C23×C4—28no—
380C23×C4—24no—
381C23×C4—28no—
382C23×C4—28no—
383C23×C4—84no—
384C23×C4—84no—
385C23×C4—84no—
386C23×C4C2×D4116yes—
387C23×C4#4118yescomplemented
388C23×C4C2418yes—
389C23×C4C2414yes—
390C23×C4C2411yescharacteristic
391C23×C4C2414yes—
392C23×C4C2412yes—
393C23×C4C2411yescharacteristic
394C23×C4C2411yescharacteristic
395C23×C4C2412yes—
396C23×C4C2418yes—
397C23×C4C2418yes—
398C23×C4C2414yes—
399C23×C4C2414yes—
400C23×C4C2411yescharacteristic
401C23×C4C2411yescharacteristic
402C23×C4C2412yes—
403C23×C4C2414yes—
404C23×C4C2414yes—
405C23×C4C2411yescharacteristic
406C4⋊Q8—216no—
407C4⋊Q8—216no—
408#127—216no—
409#126—232no—
410#125—216no—
411#124—216no—
412#124—216no—
413#124—232no—
414#123—232no—
415#123—216no—
416#123—232no—
417#123—232no—
418#123—816no—
419C22⋊Q8—232no—
420C22⋊Q8—216no—
421C22⋊Q8—216no—
422C22⋊Q8—216no—
423C22⋊Q8—216no—
424C22⋊Q8—88no—
425#121—216no—
426#121—216no—
427#121—216no—
428#121—216no—
429#121—216no—
430#121—216no—
431#121—232no—
432#121—88no—
433#120—232no—
434#120—216no—
435C4×Q8—232no—
436C4×Q8—216no—
437C4×Q8—216no—
438C4×Q8—28no—
439C4×Q8—28no—
440C4×D4—232no—
441C4×D4—232no—
442C4×D4—232no—
443C4×D4—216no—
444C4×D4—216no—
445C4×D4—232no—
446C4×D4—232no—
447C4×D4—264no—
448C4×D4—28no—
449C4×D4—28no—
450C4×D4C2×D4132yes—
451C4×D4C2×D4132yes—
452#117—28no—
453#117—216no—
454#117—28no—
455#117—28no—
456#117—264no—
457#117—216no—
458#117—216no—
459#117—216no—
460#117—88no—
461C2×C4⋊C4—28no—
462C2×C4⋊C4—24no—
463C2×C4⋊C4—28no—
464C2×C4⋊C4—28no—
465C2×C4⋊C4—24no—
466C2×C4⋊C4—232no—
467C2×C4⋊C4—232no—
468C2×C4⋊C4—24no—
469C2×C4⋊C4—232no—
470C2×C4⋊C4C2×D418yes—
471C2×C4⋊C4C2412yes—
472C2×C4⋊C4C2412yes—
473C2×C4⋊C4C2418yes—
474C2×C4⋊C4C2414yes—
475C2×C4⋊C4C2414yes—
476C2×C4⋊C4C2414yes—
477C2×C4⋊C4C2418yes—
478C2×C4⋊C4C2414yes—
479C2×C4⋊C4C2412yes—
480C2×C4⋊C4C2412yes—
481C2×C4⋊C4C2414yes—
482C2×C4⋊C4C2414yes—
483C2×C4⋊C4C2414yes—
484C2×C4⋊C4C2414yes—
485C2×C4⋊C4C2414yes—
486C2×C4⋊C4C2414yes—
487C2×C4⋊C4C2418yes—
488C2×C4⋊C4C2418yes—
489C2×C4⋊C4C24116yes—
490C2×C4⋊C4C2418yes—
491C2×C4⋊C4C2418yes—
492C2×C4⋊C4C24116yes—
493C2×C4⋊C4C2418yes—
494C2×C4⋊C4C2418yes—
495C2×C4⋊C4C2414yes—
496C2×C22⋊C4—28no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4C2×D4116yes—
500C2×C22⋊C4C2412yes—
501C2×C22⋊C4C2414yes—
502C2×C22⋊C4C2412yes—
503C2×C22⋊C4C2418yes—
504C2×C22⋊C4C2414yes—
505C2×C22⋊C4C2414yes—
506C2×C22⋊C4C2414yes—
507C2×C22⋊C4C2418yes—
508C2×C22⋊C4C2414yes—
509C2×C22⋊C4C2414yes—
510C2×C22⋊C4C2418yes—
511C2×C22⋊C4C2418yes—
512C2×C22⋊C4C2418yes—
513C2×C22⋊C4C2418yes—
514C2×C22⋊C4C24116yes—
515C2×C22⋊C4C24116yes—
516C2×C22⋊C4C24116yes—
517C2×C22⋊C4C2418yes—
518C2×C22⋊C4C2418yes—
519C2×C22⋊C4C2418yes—
520C2×C22⋊C4C24116yes—
521C2×C22⋊C4C2418yes—
522C2×C22⋊C4C2418yes—
523C2×C42—28no—
524C2×C42—28no—
525C2×C42—24no—
526C2×C42—216no—
527C2×C42C2×D418yes—
528C2×C42C2414yes—
529C2×C42C2418yes—
530C2×C42C2414yes—
531C2×C42C2418yes—
532C2×C42C2414yes—
533C2×C42C2414yes—
534C2×C42C2414yes—
535C2×C42C2414yes—
536C2×C42C2418yes—
537C2×C42C2418yes—
538C2×C42C2412yes—
539C2×C42C2412yes—
540#95C2418yes—
541#95C2418yes—
542#95C24116yes—
543#95C2418yes—
544#95C2418yes—
545#95C2418yes—
546#95C2418yes—
547#95C2418yes—
548#95C24116yes—
549#95C2418yes—
550#95C24116yes—
551#95C2418yes—
552#95C24116yes—
553#95C2418yes—
554C24—22no—
555C24—24no—
556C24—24no—
557C24—22no—
558C24—42no—
559C24—44no—
560C24—42no—
561C24—44no—
562C24C22×D418yes—
563C24C2×#4114yes—
564C24C2514yes—
565C24C2514yes—
566C24C2512yes—
567C24C2511yescharacteristic
568#41—2256no—
569#41—432no—
570#41—832no—
571C2×Q8—232no—
572C2×Q8—28no—
573C2×Q8—24no—
574C2×Q8—28no—
575C2×Q8—28no—
576C2×Q8—24no—
577C2×Q8—24no—
578C2×Q8—48no—
579C2×Q8C2×#41116yes—
580C2×D4—264no—
581C2×D4—216no—
582C2×D4—216no—
583C2×D4—28no—
584C2×D4—28no—
585C2×D4—28no—
586C2×D4—216no—
587C2×D4—216no—
588C2×D4—216no—
589C2×D4—232no—
590C2×D4—24no—
591C2×D4—28no—
592C2×D4—216no—
593C2×D4—28no—
594C2×D4—28no—
595C2×D4—24no—
596C2×D4—24no—
597C2×D4—48no—
598C2×D4—48no—
599C2×D4—416no—
600C2×D4—48no—
601C2×D4—416no—
602C2×D4C22×D4116yes—
603C22×C4—264no—
604C22×C4—24no—
605C22×C4—22no—
606C22×C4—216no—
607C22×C4—22no—
608C22×C4—24no—
609C22×C4—232no—
610C22×C4—28no—
611C22×C4—216no—
612C22×C4—216no—
613C22×C4—28no—
614C22×C4—22no—
615C22×C4—24no—
616C22×C4—22no—
617C22×C4—216no—
618C22×C4—28no—
619C22×C4—28no—
620C22×C4—28no—
621C22×C4—28no—
622C22×C4—28no—
623C22×C4—216no—
624C22×C4—48no—
625C22×C4—42no—
626C22×C4—44no—
627C22×C4—44no—
628C22×C4—42no—
629C22×C4—48no—
630C22×C4—42no—
631C22×C4—42no—
632C22×C4—48no—
633C22×C4—48no—
634C22×C4—48no—
635C22×C4—416no—
636C22×C4—48no—
637C22×C4—816no—
638C22×C4—816no—
639C22×C4—816no—
640C22×C4C22×D414yes—
641C22×C4C22×D418yes—
642C22×C4C22×D414yes—
643C22×C4C22×D4116yes—
644C22×C4C22×D4116yes—
645C22×C4C22×D414yes—
646C22×C4C2×#41116yes—
647C22×C4C2×#4114yes—
648C22×C4C2×#4118yes—
649C22×C4C2×#4114yes—
650C22×C4C2×#4114yes—
651C22×C4C2518yes—
652C22×C4C2514yes—
653C22×C4C2518yes—
654C22×C4C2512yes—
655C22×C4C2514yes—
656C22×C4C2514yes—
657C22×C4C2512yes—
658C22×C4C2514yes—
659C22×C4C2511yescharacteristic
660C22×C4C2512yes—
661C22×C4C2514yes—
662C22×C4C2511yescharacteristic
663C22×C4C2514yes—
664C22×C4C2512yes—
665C22×C4C2512yes—
666C4⋊C4—24no—
667C4⋊C4—216no—
668C4⋊C4—24no—
669C4⋊C4—28no—
670C4⋊C4—216no—
671C4⋊C4—28no—
672C4⋊C4—28no—
673C4⋊C4—28no—
674C4⋊C4—24no—
675C4⋊C4—24no—
676C4⋊C4—28no—
677C4⋊C4—28no—
678C4⋊C4—28no—
679C4⋊C4—28no—
680C4⋊C4—216no—
681C4⋊C4—28no—
682C4⋊C4—28no—
683C4⋊C4—216no—
684C4⋊C4—232no—
685C4⋊C4—48no—
686C4⋊C4—48no—
687C4⋊C4—48no—
688C4⋊C4—416no—
689C4⋊C4—48no—
690C4⋊C4C22×D4116yes—
691C22⋊C4—216no—
692C22⋊C4—28no—
693C22⋊C4—216no—
694C22⋊C4—216no—
695C22⋊C4—28no—
696C22⋊C4—28no—
697C22⋊C4—216no—
698C22⋊C4—24no—
699C22⋊C4—24no—
700C22⋊C4—28no—
701C22⋊C4—28no—
702C22⋊C4—28no—
703C22⋊C4—216no—
704C22⋊C4—216no—
705C22⋊C4—232no—
706C22⋊C4—416no—
707C22⋊C4—48no—
708C22⋊C4—48no—
709C22⋊C4—416no—
710C22⋊C4—416no—
711C22⋊C4—48no—
712C22⋊C4—48no—
713C22⋊C4C22×D4132yes—
714C42—28no—
715C42—216no—
716C42—216no—
717C42—28no—
718C42—28no—
719C42—28no—
720C42—28no—
721C42—28no—
722C42—48no—
723C42—48no—
724C42C22×D418yes—
725C42C22×D418yes—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—24no—
730C23—24no—
731C23—22no—
732C23—22no—
733C23—28no—
734C23—22no—
735C23—22no—
736C23—28no—
737C23—22no—
738C23—216no—
739C23—28no—
740C23—24no—
741C23—24no—
742C23—24no—
743C23—28no—
744C23—28no—
745C23—48no—
746C23—48no—
747C23—48no—
748C23—44no—
749C23—416no—
750C23—48no—
751C23—416no—
752C23—44no—
753C23C23×D418yes—
754C23C23×D412yes—
755C23C22×#4114yes—
756C23C22×#4112yes—
757C23C22×#4112yes—
758C23C2611yescharacteristic
759Q8—232no—
760Q8—48no—
761Q8—88no—
762D4—264no—
763D4—232no—
764D4—416no—
765D4—48no—
766D4—88no—
767D4—816no—
768D4—816no—
769D4—816no—
770C2×C4—264no—
771C2×C4—24no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—24no—
775C2×C4—22no—
776C2×C4—28no—
777C2×C4—22no—
778C2×C4—24no—
779C2×C4—28no—
780C2×C4—216no—
781C2×C4—232no—
782C2×C4—22no—
783C2×C4—24no—
784C2×C4—24no—
785C2×C4—24no—
786C2×C4—24no—
787C2×C4—22no—
788C2×C4—28no—
789C2×C4—28no—
790C2×C4—24no—
791C2×C4—24no—
792C2×C4—28no—
793C2×C4—28no—
794C2×C4—28no—
795C2×C4—24no—
796C2×C4—28no—
797C2×C4—28no—
798C2×C4—28no—
799C2×C4—22no—
800C2×C4—28no—
801C2×C4—22no—
802C2×C4—44no—
803C2×C4—48no—
804C2×C4—416no—
805C2×C4—416no—
806C2×C4—44no—
807C2×C4—416no—
808C2×C4—44no—
809C2×C4—48no—
810C2×C4—44no—
811C2×C4—416no—
812C2×C4—88no—
813C2×C4—816no—
814C2×C4—816no—
815C2×C4#525116yes—
816C2×C4C23×D414yes—
817C2×C4C23×D412yes—
818C2×C4C23×D418yes—
819C2×C4C23×D412yes—
820C2×C4C23×D414yes—
821C2×C4C22×#4114yes—
822C2×C4C22×#4118yes—
823C2×C4C22×#4114yes—
824C2×C4C22×#4114yes—
825C22—22no—
826C22—24no—
827C22—24no—
828C22—22no—
829C22—28no—
830C22—24no—
831C22—24no—
832C22—28no—
833C22—28no—
834C22—24no—
835C22—432no—
836C22—416no—
837C22—42no—
838C22—42no—
839C22—48no—
840C22—42no—
841C22—48no—
842C22—42no—
843C22—44no—
844C22—48no—
845C22—48no—
846C22—44no—
847C22—44no—
848C22C2×#52514yes—
849C22C24×D411yescharacteristic
850C22C23×#4111yescharacteristic
851C22C23×#4111yescharacteristic
852C22H(7,𝔽2)12yes—
853C222−1+612yes—
854C4—22no—
855C4—22no—
856C4—28no—
857C4—24no—
858C4—24no—
859C4—28no—
860C4—44no—
861C4—42no—
862C4—44no—
863C4—48no—
864C4—48no—
865C4—42no—
866C4—44no—
867C4—44no—
868C4C2×#52518yes—
869C2—24no—
870C2—48no—
871C2—44no—
872C2—84no—
873C2C22×#52511yescharacteristic
874C2#6284211yescharacteristic
875C2#6285112yes—
876C2#6285612yes—
877C2#6285911yescharacteristic
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×#3460C2semidirect
2. C22×#520C2semidirect
3. #35654C2semidirect
4. #35606C2semidirect
5. #35601C2semidirect
6. #35600C2semidirect
7. #35224C2semidirect
8. #35223C2semidirect
9. #35154C2semidirect
10. #35153C2semidirect
11. #35152C2semidirect
12. #35149C2semidirect
13. #35093C2semidirect
14. #35091C2semidirect
15. #35057C2semidirect
16. #35031C2semidirect
17. C4×#536C2semidirect
18. #34065C2semidirect
19. #34058C2semidirect
23. C2×#542C22semidirect
24. C2×#540C22semidirect
29. C2×#532C22semidirect
30. C2×#529C22semidirect
59. #2602C22semidirect
60. #2600C22semidirect
61. #2591C22semidirect
62. #2583C22semidirect
63. #2579C22semidirect
64. #2485C22semidirect
65. #2484C22semidirect
66. #2478C22semidirect
67. #2476C22semidirect
68. #2474C22semidirect
69. #2470C22semidirect
70. #2468C22semidirect
71. #2464C22semidirect
72. #2461C22semidirect
73. #2457C22semidirect
74. #2453C22semidirect
75. #2451C22semidirect
76. #2447C22semidirect
77. #2445C22semidirect
78. #2442C22semidirect
79. #2440C22semidirect
82. #2429C22semidirect
83. #2426C22semidirect
84. #2422C22semidirect
85. #2420C22semidirect
86. #2417C22semidirect
87. #2416C22semidirect
88. #2415C22semidirect
89. #2414C22semidirect
90. #2413C22semidirect
93. #2407C22semidirect
94. #2406C22semidirect
95. #2327C22semidirect
96. #2326C22semidirect
97. #2324C22semidirect
98. #2324C22semidirect
99. #2323C22semidirect
100. #2323C22semidirect
101. #2323C22semidirect
107. #2319C22semidirect
115. C4×C4⋊Q8C22semidirect
116. C4×#124C22semidirect
117. C4×C22⋊Q8C22semidirect
121. #2293C22semidirect
122. #2293C22semidirect
123. #2290C22semidirect
194. C2×C4×D4D4semidirect
358. C22×Q8#41semidirect
387. C23×C4#41semidirect

Maximal subgroups

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

subgroupindex
C2×#34602
C22×#5202
#356542
#356062
#356012
#356002
#352242
#352232
#351542
#351532
#351522
#351492
#350932
#350912
#350572
#350312
C4×#5362
#340652
#340582