Finite Group Databasebeta

← #7643327

Subgroups — #7643327

Order 512.

5758 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39736C214yesmaximal, complemented
2#39351C214yesmaximal, complemented
3#39147C214yesmaximal, complemented
4#38941C214yesmaximal, complemented
5#38054C218yesmaximal, complemented
6#37664C218yesmaximal, complemented
7#37292C218yesmaximal, complemented
8#36625C211yesmaximal, characteristic, complemented
9C2×#2856C211yesmaximal, characteristic
10#35584C212yesmaximal, complemented
11#35558C212yesmaximal, complemented
12#35540C212yesmaximal, complemented
13#35529C212yesmaximal, complemented
14#35288C214yesmaximal, complemented
15#35285C211yesmaximal, characteristic, complemented
16#35277C214yesmaximal, complemented
17#35275C211yesmaximal, characteristic, complemented
18#34214C211yesmaximal, characteristic, complemented
19#34210C211yesmaximal, characteristic, complemented
20#34012C211yesmaximal, characteristic, complemented
21C2×#544C2212yes—
22C2×#542C2218yescomplemented
23C2×#533C2211yescharacteristic
24C22×#127C2211yescharacteristic
25C22×#121C2212yes—
26C22×#121C2214yes—
27C2×#518C2212yes—
28C23×C42C2211yescharacteristic
29#2868C2212yescomplemented
30#2859C2212yescomplemented
31#2858C2214yescomplemented
32#2857C2212yescomplemented
33#2857C2212yescomplemented
34#2856C2214yes—
35#2856C2214yes—
36#2856C2214yes—
37#2856C2214yes—
38#2855C2214yes—
39#2851C2214yescomplemented
40#2848C2214yes—
41#2761C22116yescomplemented
42#2757C22116yescomplemented
43#2737C22116yescomplemented
44#2723C22116yescomplemented
45#2701C22116yescomplemented
46#2691C22116yescomplemented
47#2686C22116yescomplemented
48#2672C22116yescomplemented
49#2660C2214yescomplemented
50#2644C2218yescomplemented
51#2641C2214yescomplemented
52#2640C2218yescomplemented
53#2624C2218yescomplemented
54#2620C2218yescomplemented
55#2566C2214yescomplemented
56#2566C2214yescomplemented
57#2563C2214yescomplemented
58#2561C2218yes—
59#2552C2214yescomplemented
60#2551C2214yescomplemented
61#2548C2214yescomplemented
62#2548C2214yescomplemented
63#2542C2214yescomplemented
64#2513C2218yescomplemented
65#2513C2218yescomplemented
66#2512C2218yescomplemented
67#2512C2218yescomplemented
68#2512C2218yescomplemented
69#2491C2218yescomplemented
70#2491C2218yescomplemented
71#2491C2218yescomplemented
72#2490C2218yescomplemented
73#2490C2218yescomplemented
74#2483C2218yes—
75#2480C22116yes—
76#2454C2218yescomplemented
77#2452C2218yescomplemented
78#2452C2218yescomplemented
79#2448C2218yescomplemented
80#2447C2218yescomplemented
81#2440C2218yes—
82#2437C22116yes—
83#2435C2218yes—
84#2435C2218yes—
85#2427C2218yescomplemented
86#2426C2218yescomplemented
87#2422C2218yescomplemented
88#2422C2218yescomplemented
89#2422C2218yescomplemented
90#2420C2218yescomplemented
91#2420C2218yescomplemented
92#2405C2218yes—
93#2366C2214yescomplemented
94#2366C2214yescomplemented
95#2360C2218yes—
96#2355C2214yescomplemented
97Q8×C4⋊C4C2214yescomplemented
98D4×C22⋊C4C2218yes—
99#2330C2214yescomplemented
100#2328C2214yescomplemented
101#2326C2218yescomplemented
102#2324C2218yescomplemented
103#2319C2218yescomplemented
104#2317C2212yes—
105#2317C2212yes—
106#2309C2212yes—
107#2309C2212yes—
108#2309C2212yes—
109C4×C4⋊Q8C2214yescomplemented
110C4×#127C2212yescomplemented
111C4×#127C2212yescomplemented
112C4×C22⋊Q8C2214yescomplemented
113C4×C22⋊Q8C2214yescomplemented
114#2296C2212yes—
115C2×#390C2214yes—
116C2×#390C2212yes—
117#2285C2211yescharacteristic
118#2285C2211yescharacteristic
119#2285C2211yescharacteristic
120#2285C2212yescomplemented
121#2285C2212yescomplemented
122C2×#384C2211yescharacteristic
123#2283C2214yes—
124#2283C2212yescomplemented
125#2283C2214yescomplemented
126#2283C2212yescomplemented
127#2280C2211yescharacteristic
128#2280C2212yes—
129#2280C2214yes—
130#2280C2211yescharacteristic
131#2274C2212yes—
132C4×#117C2211yescharacteristic
133C4×#117C2211yescharacteristic
134C4×#117C2214yescomplemented
135C23×D4C2312yes—
136C23×D4C2314yes—
137C23×D4C2314yes—
138C24×C4C2311yescharacteristic
139C24×C4C2312yes—
140#544—48no—
141#542—432no—
142#533—28no—
143C2×C4⋊Q8C2312yes—
144C2×C4⋊Q8C2314yes—
145C2×C4⋊Q8C2318yes—
146C2×C4⋊Q8C2314yes—
147C2×#127—28no—
148C2×#127C2312yes—
149C2×#127C2312yes—
150C2×#127C2314yes—
151C2×#126C23116yes—
152C2×#125C2312yes—
153C2×#125C2314yes—
154C2×#125C2314yes—
155C2×#124C2318yes—
156C2×#124C2318yes—
157C2×#124C23116yes—
158C2×#123C23116yes—
159C2×C22⋊Q8C2314yes—
160C2×C22⋊Q8C2314yes—
161C2×C22⋊Q8C2318yes—
162C2×C22⋊Q8C2314yes—
163C2×C22⋊Q8C23116yes—
164C2×#121—48no—
165C2×#121—416no—
166C2×#121C2318yes—
167C2×#121C2318yes—
168C2×#121C2318yes—
169C2×#121C2318yes—
170C2×#121C2318yes—
171C2×#121C2318yes—
172#518—48no—
173C2×C4×Q8C2314yes—
174C2×C4×Q8C2318yes—
175C2×C4×D4C2318yes—
176C2×C4×D4C2318yes—
177C2×C4×D4C2314yes—
178C2×C4×D4C2314yes—
179C2×C4×D4C2314yes—
180C2×C4×D4C2314yes—
181C2×#117C2311yescharacteristic
182C2×#117C2312yes—
183C2×#117C2311yescharacteristic
184C2×#117C2311yescharacteristic
185C2×#117C2312yes—
186C2×#117C2311yescharacteristic
187C2×#117C2314yes—
188C2×#117C2314yes—
189C22×C4⋊C4C2312yes—
190C22×C4⋊C4C2314yes—
191C22×C22⋊C4C2314yes—
192C22×C22⋊C4C2318yes—
193C22×C22⋊C4C2318yes—
194C22×C42—28no—
195C22×C42C2312yes—
196C22×C42C2312yes—
197C22×C42C2312yes—
198C22×C42C2312yes—
199C22×C42C2312yes—
200C22×C42C2311yescharacteristic
201C22×C42C2311yescharacteristic
202#399C23116yes—
203#398C23116yes—
204#397C23116yes—
205#397C23116yes—
206#397C23116yes—
207#397C23116yes—
208#397C23116yes—
209#397C23116yes—
210#396C23116yes—
211#396C23116yes—
212#396C23116yes—
213#395C23116yes—
214#394C23116yes—
215#394C23116yes—
216#394C23116yes—
217#394C23116yes—
218#394C23116yes—
219#394C23116yes—
220#393C23116yes—
221#393C23116yes—
222#391C2318yes—
223#391C2314yes—
224#391C2314yes—
225#390C2314yes—
226#390C2314yes—
227#390C2318yes—
228#390C2318yes—
229#390C2314yes—
230#390C2314yes—
231#390C2314yes—
232#390C2318yes—
233#390C2318yes—
234#390C2318yes—
235#390C2318yes—
236#390C2314yes—
237#390C2318yes—
238#390C2318yes—
239#390C2318yes—
240#390C23116yes—
241#390C2318yes—
242#390C2318yes—
243#390C2318yes—
244#390C2318yes—
245#389C2318yes—
246#389C2318yes—
247#389C2318yes—
248#389C2314yes—
249#389C2318yes—
250#389C2318yes—
251#389C23116yes—
252#389C2314yes—
253#389C2314yes—
254#389C2314yes—
255#388C23116yes—
256#388C23116yes—
257#388C23116yes—
258#388C23116yes—
259#388C23116yes—
260#387C23116yes—
261#387C2318yes—
262#387C2318yes—
263#386C23116yes—
264#386C23116yes—
265#386C23116yes—
266#385C23116yes—
267#385C23116yes—
268#385C2318yes—
269#385C2318yes—
270#385C23116yes—
271#385C2318yes—
272#385C2318yes—
273#385C2318yes—
274#384C2311yescharacteristic
275#384C2311yescharacteristic
276#384C2312yes—
277#384C2311yescharacteristic
278#384C2314yes—
279#384C2314yes—
280#384C2318yes—
281#384C2312yes—
282#384C2314yes—
283#384C2312yes—
284#384C2311yescharacteristic
285#383C2314yes—
286#383C2314yes—
287#382C2311yescharacteristic
288#382C2314yes—
289#382C2311yescharacteristic
290#382C2314yes—
291#382C2312yes—
292#382C2314yes—
293#382C2314yes—
294#382C2312yes—
295#381C2312yes—
296#381C2314yes—
297#381C23116yes—
298#381C2314yes—
299#381C2314yes—
300#381C2312yes—
301#380C23116yes—
302#380C2314yes—
303#380C2314yes—
304#380C2314yes—
305#380C2314yes—
306#380C2314yes—
307#380C2314yes—
308#380C2312yes—
309#380C2312yes—
310#380C2314yes—
311#380C2314yes—
312#380C2314yes—
313#380C2312yes—
314#380C2312yes—
315#379C2318yes—
316#379C2318yes—
317#379C2318yes—
318#379C2314yes—
319#379C2312yes—
320#379C2312yes—
321C4×C4⋊C4C2318yes—
322C4×C4⋊C4C2318yes—
323C4×C4⋊C4C2314yes—
324C4×C4⋊C4C2314yes—
325C4×C4⋊C4C2312yes—
326C4×C4⋊C4C2318yes—
327C4×C4⋊C4C2312yes—
328C4×C4⋊C4C2314yes—
329C4×C4⋊C4C2314yes—
330C4×C4⋊C4C2314yes—
331C4×C4⋊C4C2314yes—
332C4×C4⋊C4C2314yes—
333C4×C4⋊C4C2312yes—
334C4×C4⋊C4C2312yes—
335C4×C22⋊C4C2318yes—
336C4×C22⋊C4C2314yes—
337C4×C22⋊C4C2314yes—
338C4×C22⋊C4C2318yes—
339C4×C22⋊C4C2314yes—
340C4×C22⋊C4C2314yes—
341C4×C22⋊C4C2314yes—
342C4×C22⋊C4C2314yes—
343#376C2314yes—
344#376C2314yes—
345#376C2312yes—
346#376C2312yes—
347C43C2312yes—
348C43C2312yes—
349C25C2411yescharacteristic
350C25C2414yes—
351C22×Q8C2414yes—
352C22×Q8C2418yes—
353C22×D4—28no—
354C22×D4—216no—
355C22×D4—28no—
356C22×D4—28no—
357C22×D4—48no—
358C22×D4—48no—
359C22×D4—48no—
360C22×D4—416no—
361C22×D4C2418yes—
362C22×D4C2414yes—
363C22×D4C2414yes—
364C22×D4C24116yes—
365C22×D4C2418yes—
366C23×C4—28no—
367C23×C4—24no—
368C23×C4—28no—
369C23×C4—24no—
370C23×C4—24no—
371C23×C4—44no—
372C23×C4C2411yescharacteristic
373C23×C4C2412yes—
374C23×C4C2412yes—
375C23×C4C2412yes—
376C23×C4C2412yes—
377C23×C4C2412yes—
378C23×C4C2412yes—
379C23×C4C2412yes—
380C23×C4C2412yes—
381C23×C4C2414yes—
382C23×C4C2418yes—
383C23×C4C2418yes—
384C23×C4C2411yescharacteristic
385C4⋊Q8—28no—
386C4⋊Q8—416no—
387C4⋊Q8—48no—
388C4⋊Q8—48no—
389#127—216no—
390#127—28no—
391#127—28no—
392#126—432no—
393#125—28no—
394#125—48no—
395#125—48no—
396#124—416no—
397#124—416no—
398#124—432no—
399#123—432no—
400C22⋊Q8—216no—
401C22⋊Q8—216no—
402C22⋊Q8—416no—
403C22⋊Q8—432no—
404C22⋊Q8—48no—
405#121—232no—
406#121—416no—
407#121—416no—
408#121—416no—
409#121—416no—
410#121—416no—
411C4×Q8—216no—
412C4×Q8—416no—
413C4×D4—416no—
414C4×D4—48no—
415C4×D4—48no—
416C4×D4—48no—
417C4×D4—48no—
418C4×D4—416no—
419#117—28no—
420#117—24no—
421#117—28no—
422#117—216no—
423#117—24no—
424#117—24no—
425#117—24no—
426#117—48no—
427C2×C4⋊C4—28no—
428C2×C4⋊C4—48no—
429C2×C4⋊C4C2418yes—
430C2×C4⋊C4C2414yes—
431C2×C4⋊C4C2414yes—
432C2×C4⋊C4C2411yescharacteristic
433C2×C4⋊C4C2411yescharacteristic
434C2×C4⋊C4C2412yes—
435C2×C4⋊C4C2412yes—
436C2×C4⋊C4C2414yes—
437C2×C4⋊C4C2411yescharacteristic
438C2×C4⋊C4C2414yes—
439C2×C4⋊C4C2414yes—
440C2×C4⋊C4C2411yescharacteristic
441C2×C4⋊C4C2412yes—
442C2×C4⋊C4C2412yes—
443C2×C4⋊C4C2414yes—
444C2×C4⋊C4C2414yes—
445C2×C4⋊C4C2418yes—
446C2×C4⋊C4C2414yes—
447C2×C4⋊C4C2418yes—
448C2×C4⋊C4C2418yes—
449C2×C4⋊C4C2414yes—
450C2×C4⋊C4C2414yes—
451C2×C4⋊C4C24116yes—
452C2×C4⋊C4C2418yes—
453C2×C4⋊C4C2418yes—
454C2×C4⋊C4C2418yes—
455C2×C4⋊C4C2418yes—
456C2×C4⋊C4C24116yes—
457C2×C22⋊C4—416no—
458C2×C22⋊C4—416no—
459C2×C22⋊C4—48no—
460C2×C22⋊C4C2412yes—
461C2×C22⋊C4C2414yes—
462C2×C22⋊C4C24116yes—
463C2×C22⋊C4C2412yes—
464C2×C22⋊C4C2414yes—
465C2×C22⋊C4C2414yes—
466C2×C22⋊C4C2414yes—
467C2×C22⋊C4C2412yes—
468C2×C22⋊C4C2412yes—
469C2×C22⋊C4C2418yes—
470C2×C22⋊C4C2418yes—
471C2×C22⋊C4C2418yes—
472C2×C22⋊C4C24116yes—
473C2×C22⋊C4C24116yes—
474C2×C22⋊C4C2414yes—
475C2×C22⋊C4C2414yes—
476C2×C22⋊C4C24116yes—
477C2×C22⋊C4C24116yes—
478C2×C22⋊C4C24116yes—
479C2×C22⋊C4C2418yes—
480C2×C22⋊C4C24116yes—
481C2×C22⋊C4C24116yes—
482C2×C22⋊C4C24116yes—
483C2×C42—28no—
484C2×C42—24no—
485C2×C42—28no—
486C2×C42—28no—
487C2×C42—28no—
488C2×C42—28no—
489C2×C42#4118yes—
490C2×C42C2412yes—
491C2×C42C2414yes—
492C2×C42C2414yes—
493C2×C42C2414yes—
494C2×C42C2414yes—
495C2×C42C2414yes—
496C2×C42C2414yes—
497C2×C42C2412yes—
498C2×C42C2412yes—
499C2×C42C2412yes—
500C2×C42C2412yes—
501C2×C42C2411yescharacteristic
502C2×C42C2411yescharacteristic
503C2×C42C2412yes—
504C2×C42C2412yes—
505C2×C42C2412yes—
506C2×C42C2412yes—
507C2×C42C24116yes—
508C2×C42C2412yes—
509C2×C42C2411yescharacteristic
510C2×C42C2411yescharacteristic
511#95C2414yes—
512#95C2414yes—
513#95C2414yes—
514#95C2414yes—
515#95C2414yes—
516#95C2414yes—
517#95C2414yes—
518#95C2414yes—
519#95C2414yes—
520#95C2414yes—
521#95C2414yes—
522#95C2414yes—
523#95C24116yes—
524#95C2418yes—
525#95C2418yes—
526#95C24116yes—
527#95C2418yes—
528#95C2418yes—
529#95C2418yes—
530#95C24116yes—
531C24—24no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—28no—
536C24—28no—
537C24—28no—
538C24—42no—
539C24—48no—
540C24—48no—
541C24C2518yes—
542C24C2512yes—
543C24C2511yescharacteristic
544C2×Q8—28no—
545C2×Q8—28no—
546C2×Q8—28no—
547C2×Q8—416no—
548C2×Q8—48no—
549C2×D4—232no—
550C2×D4—28no—
551C2×D4—28no—
552C2×D4—216no—
553C2×D4—216no—
554C2×D4—28no—
555C2×D4—28no—
556C2×D4—216no—
557C2×D4—28no—
558C2×D4—28no—
559C2×D4—216no—
560C2×D4—48no—
561C2×D4—416no—
562C2×D4—416no—
563C2×D4—48no—
564C2×D4—432no—
565C2×D4—832no—
566C2×D4—832no—
567C22×C4—24no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—24no—
575C22×C4—22no—
576C22×C4—28no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—24no—
581C22×C4—24no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—24no—
589C22×C4—24no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—432no—
594C22×C4—48no—
595C22×C4—48no—
596C22×C4—48no—
597C22×C4—416no—
598C22×C4—416no—
599C22×C4—416no—
600C22×C4C2×#4118yes—
601C22×C4C2×#4114yes—
602C22×C4H(5,𝔽2)18yes—
603C22×C4H(5,𝔽2)14yes—
604C22×C42−1+414yes—
605C22×C4C2512yes—
606C22×C4C2512yes—
607C22×C4C2512yes—
608C22×C4C2514yes—
609C22×C4C2514yes—
610C22×C4C2514yes—
611C22×C4C2518yes—
612C22×C4C2512yes—
613C22×C4C2512yes—
614C22×C4C2512yes—
615C22×C4C2518yes—
616C22×C4C2514yes—
617C22×C4C2512yes—
618C22×C4C2512yes—
619C22×C4C2511yescharacteristic
620C22×C4C2511yescharacteristic
621C22×C4C2512yes—
622C4⋊C4—28no—
623C4⋊C4—216no—
624C4⋊C4—28no—
625C4⋊C4—28no—
626C4⋊C4—28no—
627C4⋊C4—216no—
628C4⋊C4—22no—
629C4⋊C4—22no—
630C4⋊C4—24no—
631C4⋊C4—24no—
632C4⋊C4—28no—
633C4⋊C4—22no—
634C4⋊C4—28no—
635C4⋊C4—22no—
636C4⋊C4—28no—
637C4⋊C4—216no—
638C4⋊C4—24no—
639C4⋊C4—24no—
640C4⋊C4—28no—
641C4⋊C4—48no—
642C4⋊C4—44no—
643C4⋊C4—44no—
644C4⋊C4—416no—
645C4⋊C4—48no—
646C4⋊C4—48no—
647C4⋊C4—48no—
648C4⋊C4—48no—
649C4⋊C4—416no—
650C22⋊C4—28no—
651C22⋊C4—24no—
652C22⋊C4—28no—
653C22⋊C4—24no—
654C22⋊C4—28no—
655C22⋊C4—28no—
656C22⋊C4—216no—
657C22⋊C4—24no—
658C22⋊C4—24no—
659C22⋊C4—232no—
660C22⋊C4—48no—
661C22⋊C4—48no—
662C22⋊C4—416no—
663C22⋊C4—416no—
664C22⋊C4—44no—
665C22⋊C4—44no—
666C22⋊C4—416no—
667C22⋊C4—416no—
668C22⋊C4—48no—
669C22⋊C4—416no—
670C22⋊C4—416no—
671C22⋊C4—416no—
672C22⋊C4—416no—
673C42—22no—
674C42—24no—
675C42—24no—
676C42—24no—
677C42—24no—
678C42—22no—
679C42—24no—
680C42—28no—
681C42—24no—
682C42—28no—
683C42—28no—
684C42—28no—
685C42—24no—
686C42—24no—
687C42—24no—
688C42—28no—
689C42—28no—
690C42—416no—
691C42C2×#4118yes—
692C42C2×#4114yes—
693C42C2×#4114yes—
694C23—22no—
695C23—22no—
696C23—28no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—28no—
704C23—216no—
705C23—28no—
706C23—28no—
707C23—216no—
708C23—48no—
709C23—48no—
710C23—44no—
711C23—44no—
712C23—416no—
713C23—816no—
714C23—88no—
715C23—816no—
716C23—88no—
717C23C22×#4112yes—
718C23C2×H(5,𝔽2)14yes—
719C23C2×H(5,𝔽2)12yes—
720C23C2×2−1+412yes—
721C23C2611yescharacteristic
722Q8—416no—
723Q8—168no—
724D4—416no—
725D4—416no—
726D4—432no—
727D4—816no—
728D4—832no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—216no—
734C2×C4—216no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—28no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—22no—
748C2×C4—28no—
749C2×C4—216no—
750C2×C4—28no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—28no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—22no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—28no—
762C2×C4—28no—
763C2×C4—22no—
764C2×C4—48no—
765C2×C4—48no—
766C2×C4—48no—
767C2×C4—44no—
768C2×C4—48no—
769C2×C4—48no—
770C2×C4—48no—
771C2×C4—88no—
772C2×C4—168no—
773C2×C4—168no—
774C2×C4#542116yescomplemented
775C2×C4C22×#4114yes—
776C2×C4C22×#4112yes—
777C2×C4C22×#4112yes—
778C2×C4C22×#4114yes—
779C2×C4C2×H(5,𝔽2)14yes—
780C2×C4C2×H(5,𝔽2)12yes—
781C2×C4C2×H(5,𝔽2)12yes—
782C2×C4C2×H(5,𝔽2)14yes—
783C2×C4C2×2−1+412yes—
784C2×C4C2×2−1+412yes—
785C2×C4#58514yes—
786C22—24no—
787C22—22no—
788C22—24no—
789C22—22no—
790C22—24no—
791C22—24no—
792C22—24no—
793C22—416no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—416no—
799C22—48no—
800C22—416no—
801C22—48no—
802C22—48no—
803C22—1616no—
804C22C2×#54214yes—
805C22C23×#4111yescharacteristic
806C22C22×H(5,𝔽2)12yes—
807C22C22×H(5,𝔽2)11yescharacteristic
808C22C22×2−1+411yescharacteristic
809C22C2×#58512yes—
810C4—24no—
811C4—24no—
812C4—42no—
813C4—48no—
814C4—48no—
815C4—42no—
816C4—44no—
817C4—42no—
818C4—44no—
819C4—44no—
820C4—42no—
821C4—44no—
822C4—42no—
823C4—42no—
824C4C2×#54214yes—
825C4C2×#54214yes—
826C4#349418yes—
827C2—24no—
828C2—44no—
829C2—88no—
830C2C22×#54211yescharacteristic
831C2C2×#349412yes—
832C2#6283211yescharacteristic
833C2#6283512yes—
834C2#6283611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#2856C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39736C2semidirect
2. #39351C2semidirect
3. #39147C2semidirect
4. #38941C2semidirect
5. #38054C2semidirect
6. #37664C2semidirect
7. #37292C2semidirect
8. #36625C2semidirect
10. #35584C2semidirect
11. #35558C2semidirect
12. #35540C2semidirect
13. #35529C2semidirect
14. #35288C2semidirect
15. #35285C2semidirect
16. #35277C2semidirect
17. #35275C2semidirect
18. #34214C2semidirect
19. #34210C2semidirect
20. #34012C2semidirect
22. C2×#542C22semidirect
29. #2868C22semidirect
30. #2859C22semidirect
31. #2858C22semidirect
32. #2857C22semidirect
33. #2857C22semidirect
39. #2851C22semidirect
41. #2761C22semidirect
42. #2757C22semidirect
43. #2737C22semidirect
44. #2723C22semidirect
45. #2701C22semidirect
46. #2691C22semidirect
47. #2686C22semidirect
48. #2672C22semidirect
49. #2660C22semidirect
50. #2644C22semidirect
51. #2641C22semidirect
52. #2640C22semidirect
53. #2624C22semidirect
54. #2620C22semidirect
55. #2566C22semidirect
56. #2566C22semidirect
57. #2563C22semidirect
59. #2552C22semidirect
60. #2551C22semidirect
61. #2548C22semidirect
62. #2548C22semidirect
63. #2542C22semidirect
64. #2513C22semidirect
65. #2513C22semidirect
66. #2512C22semidirect
67. #2512C22semidirect
68. #2512C22semidirect
69. #2491C22semidirect
70. #2491C22semidirect
71. #2491C22semidirect
72. #2490C22semidirect
73. #2490C22semidirect
76. #2454C22semidirect
77. #2452C22semidirect
78. #2452C22semidirect
79. #2448C22semidirect
80. #2447C22semidirect
85. #2427C22semidirect
86. #2426C22semidirect
87. #2422C22semidirect
88. #2422C22semidirect
89. #2422C22semidirect
90. #2420C22semidirect
91. #2420C22semidirect
93. #2366C22semidirect
94. #2366C22semidirect
96. #2355C22semidirect
97. Q8×C4⋊C4C22semidirect
99. #2330C22semidirect
100. #2328C22semidirect
101. #2326C22semidirect
102. #2324C22semidirect
103. #2319C22semidirect
109. C4×C4⋊Q8C22semidirect
110. C4×#127C22semidirect
111. C4×#127C22semidirect
112. C4×C22⋊Q8C22semidirect
113. C4×C22⋊Q8C22semidirect
120. #2285C22semidirect
121. #2285C22semidirect
124. #2283C22semidirect
125. #2283C22semidirect
126. #2283C22semidirect
134. C4×#117C22semidirect
774. C2×C4#542semidirect

Maximal subgroups

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

subgroupindex
#397362
#393512
#391472
#389412
#380542
#376642
#372922
#366252
C2×#28562
#355842
#355582
#355402
#355292
#352882
#352852
#352772
#352752
#342142
#342102
#340122