Finite Group Databasebeta

← #7643429

Subgroups — #7643429

Order 512.

5258 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39606C214yesmaximal, complemented
2#39481C214yesmaximal, complemented
3#39156C214yesmaximal, complemented
4#38930C214yesmaximal, complemented
5#38067C218yesmaximal, complemented
6#37851C218yesmaximal, complemented
7#37384C218yesmaximal, complemented
8#36624C211yesmaximal, characteristic
9C2×#2857C211yesmaximal, characteristic, complemented
10#35673C212yesmaximal, complemented
11#35661C212yesmaximal, complemented
12#35633C212yesmaximal, complemented
13#35619C212yesmaximal, complemented
14#35317C211yesmaximal, characteristic, complemented
15#35288C214yesmaximal, complemented
16#35286C211yesmaximal, characteristic, complemented
17#35284C214yesmaximal, complemented
18#34209C211yesmaximal, characteristic, complemented
19#34207C211yesmaximal, characteristic, complemented
20#34012C211yesmaximal, characteristic, complemented
21C2×#536C2212yes—
22C2×#536C2212yes—
23C2×#532C2211yescharacteristic
24C22×C4⋊Q8C2211yescharacteristic
25C2×#525C2212yes—
26C22×C22⋊Q8C2212yes—
27C2×#520C2212yes—
28C2×#519C2212yes—
29C23×C42C2211yescharacteristic
30#2868C2212yescomplemented
31#2859C2214yescomplemented
32#2858C2212yescomplemented
33#2857C2214yes—
34#2857C2214yes—
35#2857C2214yes—
36#2857C2214yes—
37#2857C2212yes—
38#2856C2212yes—
39#2854C2214yes—
40#2850C2214yes—
41#2847C2214yes—
42#2777C22116yescomplemented
43#2773C22116yescomplemented
44#2768C22116yescomplemented
45#2748C22116yes—
46#2743C22116yes—
47#2741C22116yes—
48#2740C22116yes—
49#2738C22116yescomplemented
50#2658C2214yescomplemented
51#2647C2214yescomplemented
52#2647C2218yescomplemented
53#2644C2218yescomplemented
54#2629C2218yes—
55#2624C2218yes—
56#2571C2214yescomplemented
57#2552C2214yescomplemented
58#2542C2214yescomplemented
59#2542C2214yescomplemented
60#2538C2218yes—
61#2536C2218yes—
62#2534C2218yes—
63#2513C2218yescomplemented
64#2507C2218yescomplemented
65#2507C2218yescomplemented
66#2503C2214yescomplemented
67#2502C2214yescomplemented
68#2501C2218yes—
69#2499C2214yescomplemented
70#2499C2214yescomplemented
71#2498C22116yes—
72#2497C2218yes—
73#2497C2218yes—
74#2490C2218yes—
75#2486C2218yes—
76#2454C2218yescomplemented
77#2448C2218yescomplemented
78#2447C2218yescomplemented
79#2446C2218yescomplemented
80#2446C2218yescomplemented
81#2442C2218yes—
82#2429C2218yes—
83#2429C2218yes—
84#2427C2218yes—
85#2426C2218yes—
86#2423C2218yescomplemented
87#2421C2218yescomplemented
88#2420C2218yes—
89#2419C22116yes—
90#2417C2218yes—
91#2415C2218yes—
92#2413C2218yes—
93#2411C2218yes—
94#2365C2214yescomplemented
95#2365C2214yescomplemented
96#2361C2218yes—
97#2354C2214yescomplemented
98D4×C4⋊C4C2214yescomplemented
99#2344C2218yes—
100#2330C2218yescomplemented
101#2327C2214yescomplemented
102#2326C2214yescomplemented
103#2324C2218yes—
104#2319C2218yescomplemented
105#2317C2212yes—
106#2316C2212yes—
107#2314C2218yes—
108#2311C2212yes—
109#2310C2212yes—
110C4×C4⋊Q8C2212yescomplemented
111C4×C4⋊Q8C2214yescomplemented
112C4×#127C2212yescomplemented
113C4×#121C2214yes—
114C4×#121C2214yes—
115#2297C2212yes—
116C2×#391C2212yes—
117C2×#389C2214yes—
118#2285C2211yescharacteristic
119#2285C2211yescharacteristic
120#2285C2212yes—
121#2285C2211yescharacteristic
122#2285C2212yes—
123C2×#384C2211yescharacteristic
124#2283C2214yes—
125#2283C2212yes—
126#2283C2214yes—
127#2283C2212yes—
128#2280C2211yescharacteristic
129#2280C2211yescharacteristic
130#2280C2214yes—
131C2×#380C2214yes—
132C4×#117C2211yescharacteristic
133C4×#117C2214yes—
134C4×#117C2211yescharacteristic
135C22×#41C2312yes—
136C23×Q8C2312yes—
137C24×C4C2311yescharacteristic
138C24×C4C2312yes—
139#536—48no—
140#536—48no—
141#532—28no—
142C2×C4⋊Q8—28no—
143C2×C4⋊Q8C2312yes—
144C2×C4⋊Q8C2311yescharacteristic
145C2×C4⋊Q8C2312yes—
146C2×C4⋊Q8C2314yes—
147C2×C4⋊Q8C2314yes—
148C2×C4⋊Q8C2314yes—
149C2×#127C2311yescharacteristic
150C2×#125C2318yes—
151C2×#124C2312yes—
152C2×#124C2314yes—
153C2×#124C2314yes—
154#525—48no—
155C2×#123C2314yes—
156C2×#123C2318yes—
157C2×#123C2318yes—
158C2×C22⋊Q8—48no—
159C2×C22⋊Q8C2314yes—
160C2×C22⋊Q8C2318yes—
161C2×C22⋊Q8C2318yes—
162C2×C22⋊Q8C2318yes—
163C2×C22⋊Q8C2314yes—
164C2×C22⋊Q8C2314yes—
165C2×#121C2314yes—
166C2×#121C2314yes—
167C2×#121C2314yes—
168C2×#121C2314yes—
169C2×#120C2314yes—
170#520—48no—
171#519—48no—
172C2×C4×Q8C2314yes—
173C2×C4×Q8C2318yes—
174C2×C4×Q8C2318yes—
175C2×C4×D4C2314yes—
176C2×C4×D4C2318yes—
177C2×C4×D4C2314yes—
178C2×C4×D4C2318yes—
179C2×C4×D4C2318yes—
180C2×#117C2311yescharacteristic
181C2×#117C2312yes—
182C2×#117C2311yescharacteristic
183C2×#117C2314yes—
184C2×#117C2311yescharacteristic
185C2×#117C2311yescharacteristic
186C2×#117C2314yes—
187C2×#117C2318yes—
188C2×#117C2314yes—
189C22×C4⋊C4C2312yes—
190C22×C4⋊C4C2314yes—
191C22×C4⋊C4C2314yes—
192C22×C4⋊C4C2314yes—
193C22×C4⋊C4C2314yes—
194C22×C22⋊C4C2314yes—
195C22×C42—28no—
196C22×C42C2312yes—
197C22×C42C2312yes—
198C22×C42C2312yes—
199C22×C42C2312yes—
200C22×C42C2312yes—
201C22×C42C2311yescharacteristic
202C22×C42C2311yescharacteristic
203#400C23116yes—
204#400C23116yes—
205#400C23116yes—
206#399C23116yes—
207#399C23116yes—
208#399C23116yes—
209#398C23116yes—
210#398C23116yes—
211#398C23116yes—
212#398C23116yes—
213#398C23116yes—
214#397C23116yes—
215#397C23116yes—
216#397C23116yes—
217#397C23116yes—
218#396C23116yes—
219#396C23116yes—
220#396C23116yes—
221#394C23116yes—
222#394C23116yes—
223#391C2318yes—
224#391C2314yes—
225#391C2314yes—
226#391C2314yes—
227#391C2314yes—
228#391C2314yes—
229#391C2314yes—
230#391C2318yes—
231#390C2314yes—
232#390C2318yes—
233#390C2314yes—
234#390C2318yes—
235#390C2318yes—
236#390C23116yes—
237#390C2314yes—
238#390C2314yes—
239#389C2318yes—
240#389C2318yes—
241#389C2318yes—
242#389C2318yes—
243#389C2318yes—
244#389C2318yes—
245#389C2318yes—
246#389C2318yes—
247#389C2318yes—
248#389C2314yes—
249#389C23116yes—
250#389C23116yes—
251#389C2314yes—
252#389C2318yes—
253#389C2318yes—
254#389C2318yes—
255#388C23116yes—
256#388C23116yes—
257#388C23116yes—
258#388C23116yes—
259#388C23116yes—
260#388C23116yes—
261#388C2318yes—
262#388C2318yes—
263#387C23116yes—
264#387C23116yes—
265#387C23116yes—
266#387C23116yes—
267#387C23116yes—
268#387C23116yes—
269#386C2318yes—
270#386C23116yes—
271#386C2318yes—
272#386C2318yes—
273#386C2318yes—
274#385C2318yes—
275#385C23116yes—
276#385C23116yes—
277#384C2312yes—
278#384C2312yes—
279#384C2318yes—
280#384C2314yes—
281#384C2314yes—
282#384C2312yes—
283#384C2318yes—
284#384C2312yes—
285#384C2311yescharacteristic
286#384C2311yescharacteristic
287#383C2314yes—
288#383C2314yes—
289#382C2318yes—
290#382C2314yes—
291#382C2312yes—
292#382C2312yes—
293#382C2311yescharacteristic
294#382C2311yescharacteristic
295#382C2314yes—
296#382C2314yes—
297#381C2318yes—
298#381C23116yes—
299#381C2312yes—
300#381C2314yes—
301#381C2312yes—
302#381C2314yes—
303#380C2318yes—
304#380C2314yes—
305#380C2318yes—
306#380C2318yes—
307#380C23116yes—
308#380C2314yes—
309#380C2314yes—
310#380C2318yes—
311#380C2318yes—
312#380C2318yes—
313#380C2312yes—
314#380C2312yes—
315#380C2314yes—
316#380C2314yes—
317#380C2314yes—
318#380C2314yes—
319#380C2312yes—
320#380C2312yes—
321#379C2312yes—
322#379C2312yes—
323C4×C4⋊C4C2318yes—
324C4×C4⋊C4C2318yes—
325C4×C4⋊C4C2318yes—
326C4×C4⋊C4C2312yes—
327C4×C4⋊C4C2314yes—
328C4×C4⋊C4C2312yes—
329C4×C4⋊C4C2312yes—
330C4×C4⋊C4C2314yes—
331C4×C4⋊C4C2314yes—
332C4×C4⋊C4C2314yes—
333C4×C4⋊C4C2314yes—
334C4×C4⋊C4C2312yes—
335C4×C22⋊C4C2314yes—
336C4×C22⋊C4C2314yes—
337C4×C22⋊C4C2314yes—
338C4×C22⋊C4C2314yes—
339C4×C22⋊C4C2314yes—
340C4×C22⋊C4C2314yes—
341C4×C22⋊C4C2314yes—
342C4×C22⋊C4C2314yes—
343#376C2314yes—
344#376C2312yes—
345#376C2314yes—
346#376C2312yes—
347C2×#95C2318yes—
348C43C2312yes—
349C43C2312yes—
350C25C2411yescharacteristic
351C2×#41—28no—
352C2×#41—28no—
353C2×#41—28no—
354C22×Q8—28no—
355C22×Q8—28no—
356C22×Q8—28no—
357C22×Q8C2414yes—
358C22×Q8C2414yes—
359C22×Q8C2412yes—
360C22×D4C2414yes—
361C22×D4C2414yes—
362C22×D4C2412yes—
363C22×D4C2418yes—
364C23×C4—28no—
365C23×C4—24no—
366C23×C4—24no—
367C23×C4—24no—
368C23×C4—28no—
369C23×C4—44no—
370C23×C4C2414yes—
371C23×C4C2411yescharacteristic
372C23×C4C2414yes—
373C23×C4C2412yes—
374C23×C4C2412yes—
375C23×C4C2412yes—
376C23×C4C2412yes—
377C23×C4C2412yes—
378C23×C4C2412yes—
379C23×C4C2412yes—
380C23×C4C2412yes—
381C23×C4C2414yes—
382C23×C4C2418yes—
383C23×C4C2411yescharacteristic
384C4⋊Q8—216no—
385C4⋊Q8—28no—
386C4⋊Q8—28no—
387C4⋊Q8—24no—
388C4⋊Q8—48no—
389C4⋊Q8—48no—
390#127—24no—
391#125—416no—
392#124—28no—
393#124—48no—
394#124—48no—
395#123—48no—
396#123—416no—
397#123—416no—
398C22⋊Q8—416no—
399C22⋊Q8—416no—
400C22⋊Q8—48no—
401C22⋊Q8—48no—
402C22⋊Q8—48no—
403C22⋊Q8—416no—
404#121—216no—
405#121—216no—
406#121—48no—
407#121—48no—
408#120—48no—
409C4×Q8—416no—
410C4×Q8—416no—
411C4×Q8—48no—
412C4×D4—216no—
413C4×D4—416no—
414C4×D4—48no—
415C4×D4—416no—
416C4×D4—416no—
417#117—24no—
418#117—28no—
419#117—24no—
420#117—24no—
421#117—24no—
422#117—216no—
423#117—48no—
424#117—416no—
425#117—48no—
426C2×C4⋊C4—216no—
427C2×C4⋊C4—28no—
428C2×C4⋊C4—48no—
429C2×C4⋊C4—48no—
430C2×C4⋊C4—48no—
431C2×C4⋊C4C2411yescharacteristic
432C2×C4⋊C4C2414yes—
433C2×C4⋊C4C2414yes—
434C2×C4⋊C4C2418yes—
435C2×C4⋊C4C2418yes—
436C2×C4⋊C4C2418yes—
437C2×C4⋊C4C2411yescharacteristic
438C2×C4⋊C4C2412yes—
439C2×C4⋊C4C2414yes—
440C2×C4⋊C4C2411yescharacteristic
441C2×C4⋊C4C2411yescharacteristic
442C2×C4⋊C4C2412yes—
443C2×C4⋊C4C2414yes—
444C2×C4⋊C4C2414yes—
445C2×C4⋊C4C2414yes—
446C2×C4⋊C4C2414yes—
447C2×C4⋊C4C2414yes—
448C2×C4⋊C4C2418yes—
449C2×C4⋊C4C24116yes—
450C2×C4⋊C4C2418yes—
451C2×C4⋊C4C24116yes—
452C2×C4⋊C4C2414yes—
453C2×C4⋊C4C2414yes—
454C2×C4⋊C4C2418yes—
455C2×C4⋊C4C2418yes—
456C2×C4⋊C4C24116yes—
457C2×C4⋊C4C2418yes—
458C2×C4⋊C4C24116yes—
459C2×C4⋊C4C24116yes—
460C2×C22⋊C4—48no—
461C2×C22⋊C4C2412yes—
462C2×C22⋊C4C2414yes—
463C2×C22⋊C4C2412yes—
464C2×C22⋊C4C2412yes—
465C2×C22⋊C4C2412yes—
466C2×C22⋊C4C2414yes—
467C2×C22⋊C4C2414yes—
468C2×C22⋊C4C2418yes—
469C2×C22⋊C4C2418yes—
470C2×C22⋊C4C24116yes—
471C2×C22⋊C4C2418yes—
472C2×C22⋊C4C2414yes—
473C2×C22⋊C4C2414yes—
474C2×C22⋊C4C2418yes—
475C2×C22⋊C4C2418yes—
476C2×C22⋊C4C24116yes—
477C2×C22⋊C4C2418yes—
478C2×C22⋊C4C24116yes—
479C2×C22⋊C4C2418yes—
480C2×C22⋊C4C2418yes—
481C2×C42—28no—
482C2×C42—24no—
483C2×C42—28no—
484C2×C42—28no—
485C2×C42—28no—
486C2×C42—28no—
487C2×C42#4118yes—
488C2×C42C2412yes—
489C2×C42C2414yes—
490C2×C42C2414yes—
491C2×C42C2412yes—
492C2×C42C2412yes—
493C2×C42C2412yes—
494C2×C42C2414yes—
495C2×C42C2414yes—
496C2×C42C2414yes—
497C2×C42C2412yes—
498C2×C42C2411yescharacteristic
499C2×C42C2411yescharacteristic
500C2×C42C2412yes—
501C2×C42C2412yes—
502C2×C42C2412yes—
503C2×C42C2412yes—
504C2×C42C2418yes—
505C2×C42C24116yes—
506C2×C42C2412yes—
507C2×C42C2411yescharacteristic
508C2×C42C2411yescharacteristic
509#95C24116yes—
510#95C24116yes—
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#95C2418yes—
524#95C2418yes—
525#95C24116yes—
526#95C2418yes—
527#95C24116yes—
528#95C24116yes—
529#95C24116yes—
530#95C24116yes—
531C24—22no—
532C24—24no—
533C24—22no—
534C24—22no—
535C24—42no—
536C24C2514yes—
537C24C2512yes—
538C24C2511yescharacteristic
539#41—432no—
540C2×Q8—24no—
541C2×Q8—28no—
542C2×Q8—28no—
543C2×Q8—28no—
544C2×Q8—28no—
545C2×Q8—24no—
546C2×Q8—28no—
547C2×Q8—28no—
548C2×Q8—24no—
549C2×Q8—432no—
550C2×D4—28no—
551C2×D4—28no—
552C2×D4—28no—
553C2×D4—216no—
554C2×D4—28no—
555C2×D4—24no—
556C2×D4—24no—
557C2×D4—24no—
558C2×D4—28no—
559C2×D4—28no—
560C2×D4—48no—
561C2×D4—48no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—22no—
568C22×C4—28no—
569C22×C4—28no—
570C22×C4—22no—
571C22×C4—28no—
572C22×C4—22no—
573C22×C4—24no—
574C22×C4—28no—
575C22×C4—24no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—28no—
581C22×C4—28no—
582C22×C4—24no—
583C22×C4—28no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—24no—
589C22×C4—24no—
590C22×C4—24no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—432no—
595C22×C4—48no—
596C22×C4—48no—
597C22×C4—416no—
598C22×C4—416no—
599C22×C4C2×#4118yes—
600C22×C4C2×#4114yes—
601C22×C4H(5,𝔽2)14yes—
602C22×C4H(5,𝔽2)14yes—
603C22×C42−1+418yes—
604C22×C4C2512yes—
605C22×C4C2512yes—
606C22×C4C2512yes—
607C22×C4C2512yes—
608C22×C4C2518yes—
609C22×C4C2514yes—
610C22×C4C2514yes—
611C22×C4C2518yes—
612C22×C4C2512yes—
613C22×C4C2518yes—
614C22×C4C2514yes—
615C22×C4C2512yes—
616C22×C4C2512yes—
617C22×C4C2512yes—
618C22×C4C2511yescharacteristic
619C22×C4C2511yescharacteristic
620C22×C4C2512yes—
621C4⋊C4—216no—
622C4⋊C4—216no—
623C4⋊C4—28no—
624C4⋊C4—28no—
625C4⋊C4—28no—
626C4⋊C4—22no—
627C4⋊C4—22no—
628C4⋊C4—24no—
629C4⋊C4—28no—
630C4⋊C4—24no—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—28no—
634C4⋊C4—28no—
635C4⋊C4—28no—
636C4⋊C4—216no—
637C4⋊C4—28no—
638C4⋊C4—48no—
639C4⋊C4—48no—
640C4⋊C4—416no—
641C4⋊C4—44no—
642C4⋊C4—44no—
643C4⋊C4—416no—
644C4⋊C4—48no—
645C4⋊C4—416no—
646C4⋊C4—48no—
647C4⋊C4—48no—
648C4⋊C4—416no—
649C4⋊C4—416no—
650C22⋊C4—24no—
651C22⋊C4—28no—
652C22⋊C4—24no—
653C22⋊C4—24no—
654C22⋊C4—24no—
655C22⋊C4—28no—
656C22⋊C4—28no—
657C22⋊C4—216no—
658C22⋊C4—216no—
659C22⋊C4—416no—
660C22⋊C4—44no—
661C22⋊C4—44no—
662C22⋊C4—48no—
663C22⋊C4—416no—
664C22⋊C4—48no—
665C22⋊C4—48no—
666C22⋊C4—48no—
667C22⋊C4—416no—
668C22⋊C4—48no—
669C22⋊C4—48no—
670C42—22no—
671C42—24no—
672C42—24no—
673C42—24no—
674C42—24no—
675C42—22no—
676C42—24no—
677C42—24no—
678C42—28no—
679C42—24no—
680C42—24no—
681C42—24no—
682C42—28no—
683C42—28no—
684C42—28no—
685C42—28no—
686C42—48no—
687C42—416no—
688C42C2×#4118yes—
689C42C2×#4114yes—
690C42C2×#4114yes—
691C23—22no—
692C23—22no—
693C23—28no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—24no—
701C23—24no—
702C23—24no—
703C23—28no—
704C23—28no—
705C23—48no—
706C23—48no—
707C23—44no—
708C23—44no—
709C23C22×#4112yes—
710C23C2×H(5,𝔽2)12yes—
711C23C2×H(5,𝔽2)12yes—
712C23C2×2−1+414yes—
713C23C2611yescharacteristic
714Q8—416no—
715Q8—416no—
716Q8—48no—
717D4—416no—
718D4—48no—
719D4—416no—
720D4—816no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—216no—
726C2×C4—216no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—24no—
730C2×C4—28no—
731C2×C4—22no—
732C2×C4—24no—
733C2×C4—28no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—28no—
739C2×C4—24no—
740C2×C4—28no—
741C2×C4—22no—
742C2×C4—28no—
743C2×C4—24no—
744C2×C4—22no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—28no—
750C2×C4—22no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—22no—
756C2×C4—28no—
757C2×C4—216no—
758C2×C4—48no—
759C2×C4—48no—
760C2×C4—48no—
761C2×C4—44no—
762C2×C4—416no—
763C2×C4—48no—
764C2×C4—48no—
765C2×C4—416no—
766C2×C4—48no—
767C2×C4—88no—
768C2×C4—168no—
769C2×C4#540116yes—
770C2×C4C22×#4114yes—
771C2×C4C22×#4112yes—
772C2×C4C22×#4112yes—
773C2×C4C22×#4114yes—
774C2×C4C2×H(5,𝔽2)12yes—
775C2×C4C2×H(5,𝔽2)12yes—
776C2×C4C2×H(5,𝔽2)12yes—
777C2×C4C2×H(5,𝔽2)12yes—
778C2×C4C2×2−1+414yes—
779C2×C4C2×2−1+414yes—
780C2×C4#58514yes—
781C22—24no—
782C22—22no—
783C22—24no—
784C22—22no—
785C22—24no—
786C22—24no—
787C22—24no—
788C22—416no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—48no—
794C22—44no—
795C22—48no—
796C22—44no—
797C22—44no—
798C22C2×#54014yes—
799C22C23×#4111yescharacteristic
800C22C22×H(5,𝔽2)11yescharacteristic
801C22C22×H(5,𝔽2)11yescharacteristic
802C22C22×2−1+412yes—
803C22C2×#58512yes—
804C4—24no—
805C4—24no—
806C4—42no—
807C4—42no—
808C4—42no—
809C4—44no—
810C4—44no—
811C4—48no—
812C4—42no—
813C4—48no—
814C4—42no—
815C4—42no—
816C4—44no—
817C4—48no—
818C4C2×#54014yes—
819C4C2×#54014yes—
820C4#349518yes—
821C2—24no—
822C2—44no—
823C2—84no—
824C2C22×#54011yescharacteristic
825C2C2×#349512yes—
826C2#6283311yescharacteristic
827C2#6283512yes—
828C2#6283611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36624C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39606C2semidirect
2. #39481C2semidirect
3. #39156C2semidirect
4. #38930C2semidirect
5. #38067C2semidirect
6. #37851C2semidirect
7. #37384C2semidirect
9. C2×#2857C2semidirect
10. #35673C2semidirect
11. #35661C2semidirect
12. #35633C2semidirect
13. #35619C2semidirect
14. #35317C2semidirect
15. #35288C2semidirect
16. #35286C2semidirect
17. #35284C2semidirect
18. #34209C2semidirect
19. #34207C2semidirect
20. #34012C2semidirect
30. #2868C22semidirect
31. #2859C22semidirect
32. #2858C22semidirect
42. #2777C22semidirect
43. #2773C22semidirect
44. #2768C22semidirect
49. #2738C22semidirect
50. #2658C22semidirect
51. #2647C22semidirect
52. #2647C22semidirect
53. #2644C22semidirect
56. #2571C22semidirect
57. #2552C22semidirect
58. #2542C22semidirect
59. #2542C22semidirect
63. #2513C22semidirect
64. #2507C22semidirect
65. #2507C22semidirect
66. #2503C22semidirect
67. #2502C22semidirect
69. #2499C22semidirect
70. #2499C22semidirect
76. #2454C22semidirect
77. #2448C22semidirect
78. #2447C22semidirect
79. #2446C22semidirect
80. #2446C22semidirect
86. #2423C22semidirect
87. #2421C22semidirect
94. #2365C22semidirect
95. #2365C22semidirect
97. #2354C22semidirect
98. D4×C4⋊C4C22semidirect
100. #2330C22semidirect
101. #2327C22semidirect
102. #2326C22semidirect
104. #2319C22semidirect
110. C4×C4⋊Q8C22semidirect
111. C4×C4⋊Q8C22semidirect
112. C4×#127C22semidirect

Maximal subgroups

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

subgroupindex
#396062
#394812
#391562
#389302
#380672
#378512
#373842
#366242
C2×#28572
#356732
#356612
#356332
#356192
#353172
#352882
#352862
#352842
#342092
#342072
#340122