Finite Group Databasebeta

← #7631839

Subgroups — #7631839

Order 512.

22938 conjugacy classes of subgroups.

The subgroup lattice has 998 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#585C211yesmaximal, characteristic, complemented
2C2×#3485C211yesmaximal, characteristic, complemented
3C2×#3496C212yesmaximal, complemented
4#36213C218yesmaximal, complemented
5#36212C218yesmaximal, complemented
6#36085C214yesmaximal, complemented
7#36078C214yesmaximal, complemented
8#35750C214yesmaximal, complemented
9#35680C214yesmaximal, complemented
10#35660C214yesmaximal, complemented
11#35347C218yesmaximal, complemented
12#35251C212yesmaximal, complemented
13#35088C214yesmaximal, complemented
14#34738C212yesmaximal, complemented
15C2×#2430C214yesmaximal, complemented
16#34256C212yesmaximal, complemented
17C2×#2339C211yesmaximal, characteristic, complemented
18C2×#585—232no—
19C2×#585—216no—
20C22×2−1+4C2212yescomplemented
21C22×2−1+4C2214yescomplemented
22C22×H(5,𝔽2)C2212yes—
23C22×H(5,𝔽2)C2214yescomplemented
24C22×H(5,𝔽2)C2211yescharacteristic, complemented
25C22×H(5,𝔽2)C2214yescomplemented
26C23×#41C2211yescharacteristic
27C23×#41C2214yescomplemented
28C23×#41C2218yescomplemented
29C23×#41C2212yescomplemented
30#3496—232no—
31#3485—216no—
32C2×#547C2218yescomplemented
33C2×#547C2214yescomplemented
34C2×#547C2214yescomplemented
35C2×#546C2218yescomplemented
36C2×#546C2218yescomplemented
37C2×#546C2214yescomplemented
38C2×#546C2214yescomplemented
39C2×D42C2218yescomplemented
40C2×#537C2214yescomplemented
41C2×#536C2212yescomplemented
42C2×#534C2218yescomplemented
43C2×#534C2214yescomplemented
44C2×#532C2214yescomplemented
45C2×#525C2212yescomplemented
46C22×#123C2214yescomplemented
47C22×#121C2218yescomplemented
48C2×#518C2211yescharacteristic, complemented
49C22×C4×D4C2212yescomplemented
50#2849C22116yescomplemented
51#2848C2214yescomplemented
52#2847C2214yescomplemented
53#2616C2214yescomplemented
54#2615C2214yescomplemented
55#2614C2218yescomplemented
56#2613C2218yescomplemented
57#2436C2218yescomplemented
58#2436C2212yescomplemented
59#2435C2212yescomplemented
60#2434C2218yescomplemented
61#2434C2212yescomplemented
62#2433C2212yescomplemented
63#2432C2218yescomplemented
64#2432C2214yescomplemented
65#2431C2218yescomplemented
66#2431C2214yescomplemented
67#2430C2214yescomplemented
68#2430C22116yescomplemented
69#2430C2218yescomplemented
70#2430C22116yescomplemented
71#2430C22116yescomplemented
72#2430C22116yescomplemented
73#2430C2218yescomplemented
74#2430C22116yescomplemented
75#2430C2218yescomplemented
76#2430C2214yescomplemented
77#2410C2218yescomplemented
78#2410C2218yescomplemented
79#2410C22116yescomplemented
80#2410C22116yescomplemented
81#2409C2218yescomplemented
82#2409C2218yescomplemented
83#2409C2214yescomplemented
84#2408C2214yescomplemented
85#2407C2218yescomplemented
86#2407C2218yescomplemented
87#2407C2218yescomplemented
88#2406C2218yescomplemented
89#2406C2218yescomplemented
90#2406C22116yescomplemented
91#2405C22116yescomplemented
92#2404C2218yescomplemented
93#2404C2218yescomplemented
94#2404C22116yescomplemented
95#2403C22116yescomplemented
96#2388C2214yescomplemented
97#2388C2214yescomplemented
98C2×#395C2214yescomplemented
99C2×#394C2214yescomplemented
100C2×#393C2214yescomplemented
101C2×#392C2214yescomplemented
102#2339C2214yescomplemented
103#2339C2218yescomplemented
104#2339C2214yescomplemented
105#2339C2218yescomplemented
106#2339C2218yescomplemented
107D4×C22⋊C4C2218yescomplemented
108D4×C22⋊C4C2218yescomplemented
109#2311C2214yescomplemented
110#2308C2218yescomplemented
111C4×#120C2218yescomplemented
112#2297C2214yescomplemented
113C2×#391C2212yescomplemented
114C2×#386C2214yescomplemented
115C2×#386C2218yescomplemented
116C2×#386C2218yescomplemented
117C2×#385C2218yescomplemented
118C2×#381C2212yescomplemented
119C2×#380C2211yescharacteristic, complemented
120C2×C4×C22⋊C4C2211yescharacteristic, complemented
121C22×#95C2212yescomplemented
122#585—2512no—
123C2×2−1+4—232no—
124C2×2−1+4—264no—
125C2×2−1+4—232no—
126C2×2−1+4—216no—
127C2×H(5,𝔽2)—232no—
128C2×H(5,𝔽2)—216no—
129C2×H(5,𝔽2)—216no—
130C2×H(5,𝔽2)—28no—
131C2×H(5,𝔽2)—216no—
132C2×H(5,𝔽2)—264no—
133C2×H(5,𝔽2)—232no—
134C2×H(5,𝔽2)—264no—
135C2×H(5,𝔽2)D4132yescomplemented
136C22×#41—232no—
137C22×#41—264no—
138C22×#41—264no—
139C22×#41—216no—
140C22×#41—264no—
141C22×#41—264no—
142C22×#41—232no—
143C22×#41—216no—
144C22×#41D4116yescomplemented
145C22×#41C2318yes—
146C22×#41C2314yes—
147C22×#41C2314yes—
148C22×#41C2314yes—
149C22×#41C2318yes—
150C22×#41C23116yes—
151C22×#41C2318yes—
152C22×#41C2318yes—
153C22×#41C2312yes—
154C22×#41C2314yes—
155C22×#41C2314yes—
156C22×#41C2314yes—
157C22×#41C2314yes—
158C22×#41C2318yes—
159C23×Q8C2314yes—
160C23×Q8C2318yes—
161C23×Q8C2312yes—
162C23×Q8C2311yescharacteristic
163C23×D4C2314yes—
164C23×D4C23116yes—
165C23×D4C2312yes—
166C23×D4C2314yes—
167C23×D4C2314yes—
168C23×D4C2314yes—
169C23×D4C2318yes—
170C23×D4C2312yes—
171C23×D4C2318yes—
172C23×D4C2318yes—
173C23×D4C2311yescharacteristic
174C24×C4C2314yes—
175C24×C4C2318yes—
176C24×C4C2312yes—
177C24×C4C2311yescharacteristic
178C24×C4C2314yes—
179#547—232no—
180#547—232no—
181#547—264no—
182#546—232no—
183#546—232no—
184#546—264no—
185#546—264no—
186D42—264no—
187#537—232no—
188#536—216no—
189#534—232no—
190#534—264no—
191#532—232no—
192C2×C4⋊Q8C2314yes—
193C2×C4⋊Q8C2314yes—
194C2×#127C2314yes—
195C2×#124C2314yes—
196C2×#124C2314yes—
197C2×#124C2314yes—
198#525—216no—
199C2×#123—232no—
200C2×#123C2318yes—
201C2×#123C23116yes—
202C2×#123C2318yes—
203C2×#123C2318yes—
204C2×#123C23116yes—
205C2×#123C2314yes—
206C2×#123C2318yes—
207C2×C22⋊Q8C2312yes—
208C2×C22⋊Q8C2318yes—
209C2×C22⋊Q8C2312yes—
210C2×C22⋊Q8C2314yes—
211C2×C22⋊Q8C2314yes—
212C2×C22⋊Q8C2318yes—
213C2×#121—264no—
214C2×#121C2312yes—
215C2×#121C2318yes—
216C2×#121C2312yes—
217C2×#121C2318yes—
218C2×#121C2318yes—
219C2×#121C23116yes—
220C2×#121C23116yes—
221C2×#121C23116yes—
222C2×#121C2318yes—
223C2×#121C2318yes—
224C2×#121C2318yes—
225C2×#120C23116yes—
226C2×#120C2318yes—
227C2×#120C23116yes—
228C2×#120C2314yes—
229C2×#120C2318yes—
230C2×#120C2318yes—
231#518—28no—
232C2×C4×D4—216no—
233C2×C4×D4C2314yes—
234C2×C4×D4C2314yes—
235C2×C4×D4C2318yes—
236C2×C4×D4C2318yes—
237C2×C4×D4C2314yes—
238C2×C4×D4C2318yes—
239C2×C4×D4C2318yes—
240C2×C4×D4C2314yes—
241C2×#117C2312yes—
242C22×C4⋊C4C2312yes—
243C22×C4⋊C4C2314yes—
244C22×C4⋊C4C2318yes—
245C22×C4⋊C4C2314yes—
246C22×C22⋊C4C2314yes—
247C22×C22⋊C4C2314yes—
248C22×C22⋊C4C2314yes—
249C22×C22⋊C4C2318yes—
250C22×C22⋊C4C2318yes—
251C22×C22⋊C4C2314yes—
252C22×C22⋊C4C2318yes—
253C22×C22⋊C4C2312yes—
254C22×C22⋊C4C2318yes—
255C22×C22⋊C4C2312yes—
256C22×C42C2312yes—
257#395C2314yes—
258#395C2318yes—
259#395C23116yes—
260#395C2314yes—
261#395C23116yes—
262#394C2314yes—
263#394C2318yes—
264#394C23116yes—
265#394C23116yes—
266#394C2314yes—
267#394C23116yes—
268#394C2318yes—
269#394C2318yes—
270#393C2314yes—
271#393C2318yes—
272#393C23116yes—
273#393C2314yes—
274#393C23116yes—
275#392C2314yes—
276#392C2318yes—
277#392C23116yes—
278#392C23116yes—
279#392C2314yes—
280#392C23116yes—
281#392C2318yes—
282#392C2318yes—
283#391C2318yes—
284#391C2318yes—
285#391C2318yes—
286#391C2314yes—
287#391C2314yes—
288#390C2318yes—
289#390C2314yes—
290#390C2314yes—
291#386C2318yes—
292#386C23116yes—
293#386C23116yes—
294#386C23116yes—
295#386C23116yes—
296#386C2318yes—
297#386C2318yes—
298#386C23116yes—
299#386C23116yes—
300#386C23116yes—
301#386C23116yes—
302#386C23116yes—
303#386C23116yes—
304#386C23116yes—
305#386C2318yes—
306#386C23116yes—
307#386C2318yes—
308#386C2318yes—
309#385C23116yes—
310#385C2318yes—
311#385C2318yes—
312#385C23116yes—
313#385C23116yes—
314#385C23116yes—
315#385C2318yes—
316#385C23116yes—
317#385C2318yes—
318#381C23116yes—
319#381C2318yes—
320#381C2318yes—
321#380C2318yes—
322#380C2318yes—
323#380C2314yes—
324#380C2314yes—
325#379C23116yes—
326#379C2318yes—
327#379C2318yes—
328C4×C22⋊C4C2318yes—
329C4×C22⋊C4C2318yes—
330C4×C22⋊C4C2312yes—
331C4×C22⋊C4C2312yes—
332C4×C22⋊C4C2314yes—
333C2×#95C2314yes—
334C2×#95C2314yes—
335C2×#95C2318yes—
336C2×#95C2318yes—
337C2×#95C2318yes—
338C2×#95C2311yescharacteristic
339C2×#95C2312yes—
340C2×#95C2314yes—
341C2×#95C2311yescharacteristic
342C2×#95C2314yes—
343C25C2414yes—
344C25C2414yes—
345C25C2411yescharacteristic
346C25C2418yes—
347C25C2412yes—
3482−1+4—2512no—
3492−1+4—2256no—
350H(5,𝔽2)—2512no—
351H(5,𝔽2)—2512no—
352H(5,𝔽2)—2256no—
353H(5,𝔽2)—464no—
354C2×#41—21024no—
355C2×#41—2512no—
356C2×#41—2256no—
357C2×#41—216no—
358C2×#41—232no—
359C2×#41—2128no—
360C2×#41—264no—
361C2×#41—232no—
362C2×#41—216no—
363C2×#41—232no—
364C2×#41—264no—
365C2×#41—264no—
366C2×#41—264no—
367C2×#41—264no—
368C2×#41—232no—
369C2×#41—232no—
370C2×#41—232no—
371C2×#41—232no—
372C2×#41—232no—
373C2×#41—216no—
374C2×#41—232no—
375C2×#41—216no—
376C2×#41—216no—
377C2×#41—264no—
378C2×#41—232no—
379C2×#41—232no—
380C2×#41—232no—
381C2×#41—216no—
382C2×#41—232no—
383C2×#41—216no—
384C2×#41—216no—
385C2×#41—28no—
386C2×#41—216no—
387C2×#41C2×D4132yescomplemented
388C2×#41C2×D4132yescomplemented
389C2×#41C2×D4164yescomplemented
390C2×#41C2×D4132yescomplemented
391C22×Q8—232no—
392C22×Q8—216no—
393C22×Q8—232no—
394C22×Q8—232no—
395C22×Q8—216no—
396C22×Q8—232no—
397C22×Q8—28no—
398C22×Q8—28no—
399C22×Q8C2×D418yescomplemented
400C22×Q8C2412yes—
401C22×Q8C2414yes—
402C22×Q8C2418yes—
403C22×Q8C2414yes—
404C22×Q8C2414yes—
405C22×D4—232no—
406C22×D4—264no—
407C22×D4—216no—
408C22×D4—232no—
409C22×D4—232no—
410C22×D4—216no—
411C22×D4—264no—
412C22×D4—264no—
413C22×D4—232no—
414C22×D4—216no—
415C22×D4—232no—
416C22×D4—232no—
417C22×D4—232no—
418C22×D4—216no—
419C22×D4—232no—
420C22×D4—232no—
421C22×D4—216no—
422C22×D4—216no—
423C22×D4—28no—
424C22×D4—416no—
425C22×D4—88no—
426C22×D4C2×D4116yes—
427C22×D4C2×D418yes—
428C22×D4C2×D4164yescomplemented
429C22×D4C2×D4116yescomplemented
430C22×D4C2×D4164yescomplemented
431C22×D4C2418yes—
432C22×D4C2414yes—
433C22×D4C2412yes—
434C22×D4C2414yes—
435C22×D4C2418yes—
436C22×D4C2418yes—
437C22×D4C2418yes—
438C22×D4C2418yes—
439C22×D4C24116yes—
440C22×D4C2418yes—
441C22×D4C2414yes—
442C22×D4C2414yes—
443C22×D4C2414yes—
444C22×D4C2418yes—
445C22×D4C24116yes—
446C22×D4C2414yes—
447C23×C4—232no—
448C23×C4—216no—
449C23×C4—232no—
450C23×C4—232no—
451C23×C4—232no—
452C23×C4—216no—
453C23×C4—28no—
454C23×C4—216no—
455C23×C4—48no—
456C23×C4—84no—
457C23×C4C2×D4116yescomplemented
458C23×C4C2×D418yescomplemented
459C23×C4C2414yes—
460C23×C4C2414yes—
461C23×C4C2418yes—
462C23×C4C2414yes—
463C23×C4C24116yes—
464C23×C4C2418yes—
465C23×C4C2412yes—
466C23×C4C2414yes—
467C23×C4C2418yes—
468C23×C4C2414yes—
469C23×C4C2412yes—
470C23×C4C2418yes—
471C23×C4C2412yes—
472C23×C4C2411yescharacteristic
473C23×C4C2412yes—
474C23×C4C2414yes—
475C23×C4C2414yes—
476C23×C4C2418yes—
477C23×C4C2412yes—
478C23×C4C2414yes—
479C23×C4C2411yescharacteristic
480C4⋊Q8—216no—
481C4⋊Q8—216no—
482#127—216no—
483#124—216no—
484#124—216no—
485#124—216no—
486#123—264no—
487#123—232no—
488#123—216no—
489#123—232no—
490#123—232no—
491#123—232no—
492#123—264no—
493C22⋊Q8—216no—
494C22⋊Q8—216no—
495C22⋊Q8—232no—
496C22⋊Q8—28no—
497C22⋊Q8—28no—
498C22⋊Q8—232no—
499#121—232no—
500#121—264no—
501#121—264no—
502#121—264no—
503#121—232no—
504#121—232no—
505#121—232no—
506#121—232no—
507#121—28no—
508#121—28no—
509#121—232no—
510#120—216no—
511#120—264no—
512#120—264no—
513#120—232no—
514#120—416no—
515#120—88no—
516C4×D4—232no—
517C4×D4—232no—
518C4×D4—216no—
519C4×D4—216no—
520C4×D4—216no—
521C4×D4—216no—
522C4×D4—232no—
523C4×D4—232no—
524#117—28no—
525C2×C4⋊C4—28no—
526C2×C4⋊C4—232no—
527C2×C4⋊C4—216no—
528C2×C4⋊C4—216no—
529C2×C4⋊C4C2418yes—
530C2×C4⋊C4C2414yes—
531C2×C4⋊C4C2414yes—
532C2×C4⋊C4C2418yes—
533C2×C4⋊C4C24116yes—
534C2×C4⋊C4C2418yes—
535C2×C4⋊C4C2418yes—
536C2×C4⋊C4C2412yes—
537C2×C4⋊C4C2412yes—
538C2×C4⋊C4C2418yes—
539C2×C22⋊C4—216no—
540C2×C22⋊C4—216no—
541C2×C22⋊C4—232no—
542C2×C22⋊C4—232no—
543C2×C22⋊C4—216no—
544C2×C22⋊C4—216no—
545C2×C22⋊C4—416no—
546C2×C22⋊C4—44no—
547C2×C22⋊C4—88no—
548C2×C22⋊C4—82no—
549C2×C22⋊C4C2414yes—
550C2×C22⋊C4C2418yes—
551C2×C22⋊C4C2418yes—
552C2×C22⋊C4C2414yes—
553C2×C22⋊C4C2414yes—
554C2×C22⋊C4C2418yes—
555C2×C22⋊C4C24116yes—
556C2×C22⋊C4C2418yes—
557C2×C22⋊C4C2414yes—
558C2×C22⋊C4C24116yes—
559C2×C22⋊C4C24116yes—
560C2×C22⋊C4C2418yes—
561C2×C22⋊C4C2418yes—
562C2×C22⋊C4C2418yes—
563C2×C22⋊C4C2418yes—
564C2×C22⋊C4C2414yes—
565C2×C22⋊C4C2414yes—
566C2×C22⋊C4C2418yes—
567C2×C22⋊C4C2418yes—
568C2×C22⋊C4C24116yes—
569C2×C22⋊C4C2414yes—
570C2×C22⋊C4C24116yes—
571C2×C22⋊C4C2418yes—
572C2×C22⋊C4C2418yes—
573C2×C42—28no—
574C2×C42C2414yes—
575C2×C42C2414yes—
576C2×C42C2414yes—
577#95C2412yes—
578#95C2411yescharacteristic
579#95C2411yescharacteristic
580#95C2414yes—
581#95C2414yes—
582#95C2418yes—
583#95C2418yes—
584#95C2418yes—
585#95C2418yes—
586#95C2412yes—
587#95C2412yes—
588#95C24116yes—
589#95C24116yes—
590#95C24116yes—
591#95C2418yes—
592#95C2418yes—
593C24—216no—
594C24—28no—
595C24—216no—
596C24—216no—
597C24—24no—
598C24—28no—
599C24—216no—
600C24—44no—
601C24—42no—
602C24—42no—
603C24—42no—
604C24—48no—
605C24—41no—
606C24—48no—
607C24—48no—
608C24—41no—
609C24—48no—
610C24—48no—
611C24—44no—
612C24—48no—
613C24—44no—
614C24—44no—
615C24—44no—
616C24C22×D4132yes—
617C24C22×D414yes—
618C24C22×D418yes—
619C24C22×D4116yes—
620C24C2514yes—
621C24C2518yes—
622C24C2512yes—
623C24C2514yes—
624C24C2511yescharacteristic
625#41—2256no—
626#41—2128no—
627#41—2128no—
628#41—2512no—
629#41—2256no—
630#41—2256no—
631#41—2256no—
632#41—2128no—
633#41—2128no—
634#41—2256no—
635#41—2128no—
636#41—2128no—
637#41—464no—
638#41—432no—
639C2×Q8—2256no—
640C2×Q8—264no—
641C2×Q8—2128no—
642C2×Q8—232no—
643C2×Q8—216no—
644C2×Q8—216no—
645C2×Q8—232no—
646C2×Q8—28no—
647C2×Q8—28no—
648C2×Q8—28no—
649C2×Q8—216no—
650C2×Q8—28no—
651C2×Q8—24no—
652C2×Q8C22×D4116yes—
653C2×Q8C22×D4116yes—
654C2×D4—2512no—
655C2×D4—2128no—
656C2×D4—2128no—
657C2×D4—264no—
658C2×D4—2256no—
659C2×D4—264no—
660C2×D4—216no—
661C2×D4—232no—
662C2×D4—216no—
663C2×D4—216no—
664C2×D4—216no—
665C2×D4—232no—
666C2×D4—232no—
667C2×D4—232no—
668C2×D4—216no—
669C2×D4—2256no—
670C2×D4—216no—
671C2×D4—232no—
672C2×D4—28no—
673C2×D4—216no—
674C2×D4—216no—
675C2×D4—216no—
676C2×D4—28no—
677C2×D4—28no—
678C2×D4—232no—
679C2×D4—216no—
680C2×D4—216no—
681C2×D4—28no—
682C2×D4—28no—
683C2×D4—28no—
684C2×D4—24no—
685C2×D4—28no—
686C2×D4—216no—
687C2×D4—48no—
688C2×D4—48no—
689C2×D4—48no—
690C2×D4—44no—
691C2×D4—416no—
692C2×D4—416no—
693C2×D4—44no—
694C2×D4—48no—
695C2×D4—464no—
696C2×D4—464no—
697C2×D4—864no—
698C2×D4#120164yescomplemented
699C2×D4C22×D4132yes—
700C2×D4C22×D4164yes—
701C2×D4C22×D4132yes—
702C2×D4C22×D4116yes—
703C2×D4C22×D4116yes—
704C2×D4C22×D4132yes—
705C22×C4—2256no—
706C22×C4—2128no—
707C22×C4—264no—
708C22×C4—216no—
709C22×C4—216no—
710C22×C4—24no—
711C22×C4—232no—
712C22×C4—28no—
713C22×C4—216no—
714C22×C4—216no—
715C22×C4—216no—
716C22×C4—28no—
717C22×C4—232no—
718C22×C4—216no—
719C22×C4—216no—
720C22×C4—28no—
721C22×C4—232no—
722C22×C4—232no—
723C22×C4—216no—
724C22×C4—216no—
725C22×C4—216no—
726C22×C4—28no—
727C22×C4—24no—
728C22×C4—216no—
729C22×C4—28no—
730C22×C4—216no—
731C22×C4—24no—
732C22×C4—28no—
733C22×C4—28no—
734C22×C4—216no—
735C22×C4—28no—
736C22×C4—216no—
737C22×C4—28no—
738C22×C4—24no—
739C22×C4—216no—
740C22×C4—42no—
741C22×C4—48no—
742C22×C4—48no—
743C22×C4—42no—
744C22×C4—44no—
745C22×C4—48no—
746C22×C4—44no—
747C22×C4—48no—
748C22×C4—44no—
749C22×C4—44no—
750C22×C4—42no—
751C22×C4—832no—
752C22×C4C22×D4116yes—
753C22×C4C22×D4132yes—
754C22×C4C22×D4116yes—
755C22×C4C22×D418yes—
756C22×C4C22×D4132yes—
757C22×C4C22×D418yes—
758C22×C4C22×D414yes—
759C22×C4C22×D418yes—
760C22×C4C22×D418yes—
761C22×C4C22×D414yes—
762C22×C4C2514yes—
763C22×C4C2512yes—
764C22×C4C2518yes—
765C22×C4C2514yes—
766C22×C4C2514yes—
767C22×C4C2514yes—
768C22×C4C2511yescharacteristic
769C22×C4C2514yes—
770C22×C4C2518yes—
771C22×C4C2511yescharacteristic
772C22×C4C2512yes—
773C22×C4C2512yes—
774C4⋊C4—216no—
775C4⋊C4—28no—
776C4⋊C4—28no—
777C4⋊C4—216no—
778C4⋊C4—232no—
779C4⋊C4—216no—
780C4⋊C4—216no—
781C4⋊C4—24no—
782C4⋊C4—24no—
783C4⋊C4—216no—
784C22⋊C4—28no—
785C22⋊C4—216no—
786C22⋊C4—232no—
787C22⋊C4—216no—
788C22⋊C4—232no—
789C22⋊C4—216no—
790C22⋊C4—28no—
791C22⋊C4—28no—
792C22⋊C4—216no—
793C22⋊C4—28no—
794C22⋊C4—28no—
795C22⋊C4—232no—
796C22⋊C4—216no—
797C22⋊C4—216no—
798C22⋊C4—216no—
799C22⋊C4—216no—
800C22⋊C4—28no—
801C22⋊C4—416no—
802C22⋊C4—44no—
803C22⋊C4—48no—
804C22⋊C4—416no—
805C22⋊C4—48no—
806C22⋊C4—48no—
807C22⋊C4—48no—
808C42—28no—
809C42—28no—
810C42—28no—
811C23—22no—
812C23—28no—
813C23—21no—
814C23—24no—
815C23—21no—
816C23—24no—
817C23—232no—
818C23—28no—
819C23—24no—
820C23—28no—
821C23—28no—
822C23—24no—
823C23—28no—
824C23—22no—
825C23—28no—
826C23—28no—
827C23—22no—
828C23—264no—
829C23—28no—
830C23—24no—
831C23—28no—
832C23—28no—
833C23—24no—
834C23—24no—
835C23—416no—
836C23—416no—
837C23—48no—
838C23—48no—
839C23—432no—
840C23—432no—
841C23—44no—
842C23—44no—
843C23—416no—
844C23—84no—
845C23—816no—
846C23—84no—
847C23—816no—
848C23—816no—
849C23—816no—
850C23—816no—
851C23—816no—
852C23—88no—
853C23—88no—
854C23—816no—
855C23—816no—
856C23—88no—
857C23—88no—
858C23C2×#120132yes—
859C23C23×D4116yes—
860C23C23×D414yes—
861C23C23×D412yes—
862C23C23×D4116yes—
863C23C23×D418yes—
864C23C23×D414yes—
865C23C2611yescharacteristic
866Q8—264no—
867Q8—232no—
868Q8—232no—
869Q8—232no—
870Q8—48no—
871D4—264no—
872D4—264no—
873D4—232no—
874D4—264no—
875D4—2128no—
876D4—264no—
877D4—232no—
878D4—432no—
879D4—432no—
880D4—416no—
881D4—48no—
882D4—816no—
883D4—88no—
884D4—88no—
885D4—832no—
886D4C2×#120164yes—
887C2×C4—264no—
888C2×C4—232no—
889C2×C4—2128no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—28no—
893C2×C4—28no—
894C2×C4—22no—
895C2×C4—28no—
896C2×C4—22no—
897C2×C4—232no—
898C2×C4—28no—
899C2×C4—264no—
900C2×C4—232no—
901C2×C4—216no—
902C2×C4—216no—
903C2×C4—264no—
904C2×C4—216no—
905C2×C4—24no—
906C2×C4—22no—
907C2×C4—24no—
908C2×C4—24no—
909C2×C4—28no—
910C2×C4—28no—
911C2×C4—24no—
912C2×C4—28no—
913C2×C4—24no—
914C2×C4—22no—
915C2×C4—28no—
916C2×C4—24no—
917C2×C4—22no—
918C2×C4—28no—
919C2×C4—24no—
920C2×C4—24no—
921C2×C4—48no—
922C2×C4—432no—
923C2×C4—416no—
924C2×C4—416no—
925C2×C4—84no—
926C2×C4—88no—
927C2×C4—88no—
928C2×C4—816no—
929C2×C4—88no—
930C2×C4C2×#120116yes—
931C2×C4C23×D412yes—
932C2×C4C23×D418yes—
933C2×C4C23×D4116yes—
934C2×C4C23×D412yes—
935C2×C4C23×D414yes—
936C2×C4C23×D418yes—
937C2×C4#58514yescomplemented
938C22—24no—
939C22—216no—
940C22—24no—
941C22—216no—
942C22—28no—
943C22—22no—
944C22—28no—
945C22—22no—
946C22—216no—
947C22—216no—
948C22—24no—
949C22—24no—
950C22—216no—
951C22—24no—
952C22—432no—
953C22—48no—
954C22—44no—
955C22—44no—
956C22—48no—
957C22—48no—
958C22—48no—
959C22—48no—
960C22—48no—
961C22—44no—
962C22—44no—
963C22—44no—
964C22—88no—
965C22—864no—
966C22—832no—
967C22—1616no—
968C22C22×#120116yes—
969C22C22×#12014yes—
970C22C24×D412yes—
971C22C24×D411yescharacteristic
972C22C2×#58512yes—
973C22H(7,𝔽2)11yescharacteristic
974C222−1+611yescharacteristic
975C4—24no—
976C4—22no—
977C4—216no—
978C4—28no—
979C4—22no—
980C4—42no—
981C4—48no—
982C4—44no—
983C4—44no—
984C4—44no—
985C4—44no—
986C4C22×#12018yes—
987C2—24no—
988C2—216no—
989C2—416no—
990C2—44no—
991C2—84no—
992C2C23×#12011yescharacteristic
993C2#6281211yescharacteristic
994C2#6285311yescharacteristic
995C2#6298712yes—
996C2#6298812yes—
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. C22×#585C2semidirect
2. C2×#3485C2semidirect
3. C2×#3496C2semidirect
4. #36213C2semidirect
5. #36212C2semidirect
6. #36085C2semidirect
7. #36078C2semidirect
8. #35750C2semidirect
9. #35680C2semidirect
10. #35660C2semidirect
11. #35347C2semidirect
12. #35251C2semidirect
13. #35088C2semidirect
14. #34738C2semidirect
15. C2×#2430C2semidirect
16. #34256C2semidirect
17. C2×#2339C2semidirect
20. C22×2−1+4C22semidirect
21. C22×2−1+4C22semidirect
23. C22×H(5,𝔽2)C22semidirect
24. C22×H(5,𝔽2)C22semidirect
25. C22×H(5,𝔽2)C22semidirect
27. C23×#41C22semidirect
28. C23×#41C22semidirect
29. C23×#41C22semidirect
32. C2×#547C22semidirect
33. C2×#547C22semidirect
34. C2×#547C22semidirect
35. C2×#546C22semidirect
36. C2×#546C22semidirect
37. C2×#546C22semidirect
38. C2×#546C22semidirect
39. C2×D42C22semidirect
40. C2×#537C22semidirect
41. C2×#536C22semidirect
42. C2×#534C22semidirect
43. C2×#534C22semidirect
44. C2×#532C22semidirect
45. C2×#525C22semidirect
46. C22×#123C22semidirect
47. C22×#121C22semidirect
48. C2×#518C22semidirect
49. C22×C4×D4C22semidirect
50. #2849C22semidirect
51. #2848C22semidirect
52. #2847C22semidirect
53. #2616C22semidirect
54. #2615C22semidirect
55. #2614C22semidirect
56. #2613C22semidirect
57. #2436C22semidirect
58. #2436C22semidirect
59. #2435C22semidirect
60. #2434C22semidirect
61. #2434C22semidirect
62. #2433C22semidirect
63. #2432C22semidirect
64. #2432C22semidirect
65. #2431C22semidirect
66. #2431C22semidirect
67. #2430C22semidirect
68. #2430C22semidirect
69. #2430C22semidirect
70. #2430C22semidirect
71. #2430C22semidirect
72. #2430C22semidirect
73. #2430C22semidirect
74. #2430C22semidirect
75. #2430C22semidirect
76. #2430C22semidirect
77. #2410C22semidirect
78. #2410C22semidirect
79. #2410C22semidirect
80. #2410C22semidirect
81. #2409C22semidirect
82. #2409C22semidirect
83. #2409C22semidirect
84. #2408C22semidirect
85. #2407C22semidirect
86. #2407C22semidirect
87. #2407C22semidirect
88. #2406C22semidirect
89. #2406C22semidirect
90. #2406C22semidirect
91. #2405C22semidirect
92. #2404C22semidirect
93. #2404C22semidirect
94. #2404C22semidirect
95. #2403C22semidirect
96. #2388C22semidirect
97. #2388C22semidirect
98. C2×#395C22semidirect
99. C2×#394C22semidirect
100. C2×#393C22semidirect
101. C2×#392C22semidirect
102. #2339C22semidirect
103. #2339C22semidirect
104. #2339C22semidirect
105. #2339C22semidirect
106. #2339C22semidirect
107. D4×C22⋊C4C22semidirect
108. D4×C22⋊C4C22semidirect
109. #2311C22semidirect
110. #2308C22semidirect
111. C4×#120C22semidirect
112. #2297C22semidirect
113. C2×#391C22semidirect
114. C2×#386C22semidirect
115. C2×#386C22semidirect
116. C2×#386C22semidirect
117. C2×#385C22semidirect
118. C2×#381C22semidirect
119. C2×#380C22semidirect
120. C2×C4×C22⋊C4C22semidirect
121. C22×#95C22semidirect
135. C2×H(5,𝔽2)D4semidirect
144. C22×#41D4semidirect
387. C2×#41C2×D4semidirect
388. C2×#41C2×D4semidirect
389. C2×#41C2×D4semidirect
390. C2×#41C2×D4semidirect
399. C22×Q8C2×D4semidirect
428. C22×D4C2×D4semidirect
429. C22×D4C2×D4semidirect
430. C22×D4C2×D4semidirect
457. C23×C4C2×D4semidirect
458. C23×C4C2×D4semidirect
698. C2×D4#120semidirect
937. C2×C4#585semidirect

Maximal subgroups

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

subgroupindex
C22×#5852
C2×#34852
C2×#34962
#362132
#362122
#360852
#360782
#357502
#356802
#356602
#353472
#352512
#350882
#347382
C2×#24302
#342562
C2×#23392