Finite Group Databasebeta

← #6445867

Subgroups — #6445867

Order 512.

1787 conjugacy classes of subgroups.

The subgroup lattice has 883 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35174C211yesmaximal, characteristic
2#34272C211yesmaximal, characteristic, complemented
3#27027C212yesmaximal, complemented
4#27026C212yesmaximal, complemented
5#27015C212yesmaximal, complemented
6#27014C212yesmaximal, complemented
7#27007C212yesmaximal, complemented
8#27006C212yesmaximal, complemented
9#27003C212yesmaximal, complemented
10#27002C212yesmaximal, complemented
11#23612C211yesmaximal, characteristic
12#23557C211yesmaximal, characteristic, complemented
13#23556C211yesmaximal, characteristic, complemented
14#23456C211yesmaximal, characteristic
15#21315C211yesmaximal, characteristic, complemented
16#21159C211yesmaximal, characteristic, complemented
17#21063C211yesmaximal, characteristic
18#21063C211yesmaximal, characteristic
19#21038C211yesmaximal, characteristic, complemented
20#21032C211yesmaximal, characteristic, complemented
21#21022C211yesmaximal, characteristic, complemented
22C2×#1864C211yesmaximal, characteristic
23C4×#418C211yesmaximal, characteristic
24C2×#544C2211yescharacteristic
25C2×#544C2211yescharacteristic
26C22×C4×D4C2211yescharacteristic
27C2×#428C2211yescharacteristic
28C2×#428C2211yescharacteristic
29C2×#427C2211yescharacteristic
30C22×#106C2211yescharacteristic
31C2×#424C2211yescharacteristic
32C2×#418C2211yescharacteristic
33C2×#418C2211yescharacteristic
34C22×#102C2211yescharacteristic
35C22×#102C2211yescharacteristic
36C2×C4×M16C2211yescharacteristic
37#2848—22no—
38#2626—22no—
39#2454—21no—
40#2454—21no—
41#2454C2212yes—
42#2454C2212yes—
43#2452—21no—
44#2452—21no—
45#2452C2212yes—
46#2452C2212yes—
47#2370C2212yescomplemented
48#2370C2212yescomplemented
49#2369C2212yescomplemented
50#2368—22no—
51#2365C2212yescomplemented
52#2360—22no—
53#2331—21no—
54#2330—21no—
55#2317C2211yescharacteristic
56#2316C2211yescharacteristic
57#2309C2211yescharacteristic
58#2309C2211yescharacteristic
59C4×C4⋊Q8—21no—
60C4×#125—21no—
61#2296C2211yescharacteristic
62#2296C2211yescharacteristic
63C2×#389C2211yescharacteristic
64#2274C2211yescharacteristic
65#2274C2211yescharacteristic
66C4×#117C2211yescharacteristic
67#2067C2212yes—
68#2067C2212yes—
69#2065C2212yes—
70#2065C2212yes—
71#2059C2212yescomplemented
72#2059C2212yescomplemented
73#2059C2212yescomplemented
74#2059C2212yescomplemented
75#2058C2212yescomplemented
76#2058C2212yescomplemented
77#2058C2212yescomplemented
78#2057C2212yescomplemented
79#2025C2212yes—
80#2025C2212yes—
81#2023C2212yes—
82#2023C2212yes—
83#1989C2212yescomplemented
84#1989C2212yescomplemented
85#1988C2212yescomplemented
86#1987C2212yescomplemented
87#1944C2212yescomplemented
88#1943C2212yescomplemented
89#1942C2212yescomplemented
90#1941C2212yescomplemented
91#1926C2212yes—
92#1926C2212yes—
93#1926C2212yes—
94#1926C2212yes—
95#1925C2212yes—
96#1925C2212yes—
97#1925C2212yes—
98#1925C2212yes—
99#1921C2211yescharacteristic, complemented
100#1921C2211yescharacteristic, complemented
101#1920C2211yescharacteristic, complemented
102#1920C2211yescharacteristic, complemented
103#1920C2212yescomplemented
104#1920C2212yescomplemented
105#1919C2211yescharacteristic, complemented
106#1919C2211yescharacteristic, complemented
107#1919C2212yescomplemented
108#1919C2212yescomplemented
109#1918C2211yescharacteristic, complemented
110#1918C2211yescharacteristic, complemented
111#1917C2212yescomplemented
112#1917C2212yescomplemented
113#1916C2212yescomplemented
114#1916C2212yescomplemented
115#1864C2212yes—
116#1864C2212yes—
117#1864C2212yes—
118#1864C2212yes—
119#1762C2212yes—
120#1762C2212yes—
121C4×#102C2212yes—
122C4×#102C2212yes—
123#1736C2211yescharacteristic
124#1736C2211yescharacteristic
125#1736C2211yescharacteristic
126#1736C2211yescharacteristic
127#1735C2211yescharacteristic
128#1735C2211yescharacteristic
129#1735C2211yescharacteristic
130C2×#340C2211yescharacteristic
131#1729C2211yescharacteristic
132#1729C2211yescharacteristic
133#1729C2211yescharacteristic
134C2×#336C2211yescharacteristic
135C23×D4C2311yescharacteristic
136C24×C4—21no—
137C22×M16C2311yescharacteristic
138C22×M16C2311yescharacteristic
139C23×C8C2311yescharacteristic
140C23×C8C2311yescharacteristic
141#544—24no—
142#544—24no—
143#544—24no—
144#544—42no—
145C2×C4⋊Q8—21no—
146C2×C4⋊Q8—21no—
147C2×C4⋊Q8C2312yes—
148C2×C4⋊Q8C2312yes—
149C2×#125—21no—
150C2×#125—21no—
151C2×#125C2312yes—
152C2×#125C2312yes—
153C2×C22⋊Q8—22no—
154C2×C22⋊Q8—22no—
155C2×C22⋊Q8—22no—
156C2×C22⋊Q8—22no—
157C2×C4×Q8—22no—
158C2×C4×D4—24no—
159C2×C4×D4—21no—
160C2×C4×D4—21no—
161C2×C4×D4—42no—
162C2×C4×D4C2312yes—
163C2×C4×D4C2312yes—
164C2×#117C2311yescharacteristic
165C2×#117C2311yescharacteristic
166C2×#117C2311yescharacteristic
167C2×#117C2311yescharacteristic
168C2×#117C2311yescharacteristic
169C2×#117C2311yescharacteristic
170C22×C4⋊C4—21no—
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2311yescharacteristic
174C22×C22⋊C4—21no—
175C22×C42C2311yescharacteristic
176#428—24no—
177#428—42no—
178#427—24no—
179C2×#107C2311yescharacteristic
180C2×#107C2312yes—
181C2×#107C2311yescharacteristic
182C2×#107C2312yes—
183C2×#106—24no—
184C2×#106C2311yescharacteristic
185C2×#106C2312yes—
186C2×#106C2312yes—
187C2×#106C2312yes—
188C2×#106C2311yescharacteristic
189C2×#106C2312yes—
190#424—42no—
191C2×C4⋊C8C2312yes—
192C2×C4⋊C8C2312yes—
193#418—24no—
194#418Q818yescomplemented
195C2×#102—24no—
196C2×#102—42no—
197C2×#102C2312yes—
198C2×#102C2312yes—
199C2×#102C2312yes—
200C2×#102C2312yes—
201C2×#102C2312yes—
202C2×#102C2312yes—
203C2×#102C2312yes—
204C2×#102C2312yes—
205C4×M16—42no—
206C2×#97C2312yes—
207C2×C4×C8C2312yes—
208#399—22no—
209#399—22no—
210#396—22no—
211#396—22no—
212#396—22no—
213#396—22no—
214#393—22no—
215#393—22no—
216#391—22no—
217#391—22no—
218#391—22no—
219#390—21no—
220#390—21no—
221#390—21no—
222#390—21no—
223#390C2312yes—
224#390C2312yes—
225#390C2312yes—
226#390C2312yes—
227#389—22no—
228#389—21no—
229#389—21no—
230#389—22no—
231#389—22no—
232#389—21no—
233#389—21no—
234#389D411yescharacteristic
235#389D411yescharacteristic
236#389D411yescharacteristic
237#389D411yescharacteristic
238#389C2312yes—
239#389C2312yes—
240#389C2312yes—
241#389C2312yes—
242#389C2312yes—
243#389C2312yes—
244#389C2311yescharacteristic
245#389C2311yescharacteristic
246#389C2311yescharacteristic
247#389C2311yescharacteristic
248#387—22no—
249#387—22no—
250#387—22no—
251#387—22no—
252#387—22no—
253#387—22no—
254#385—21no—
255#385—21no—
256#385—22no—
257#385—22no—
258#385—22no—
259#385—22no—
260#385—22no—
261#385D412yes—
262#385D412yes—
263#384—21no—
264#382—21no—
265#380—22no—
266#380—22no—
267#380—22no—
268#379—22no—
269#379—22no—
270C4×C4⋊C4—21no—
271C4×C4⋊C4—21no—
272C4×C4⋊C4—22no—
273C4×C4⋊C4—21no—
274C4×C4⋊C4—21no—
275C4×C4⋊C4—21no—
276C4×C4⋊C4—21no—
277C4×C4⋊C4—22no—
278C4×C4⋊C4—22no—
279C4×C4⋊C4C2311yescharacteristic
280C4×C4⋊C4C2312yes—
281C4×C4⋊C4C2312yes—
282C4×C4⋊C4C2311yescharacteristic
283C4×C4⋊C4C2312yes—
284C4×C4⋊C4C2312yes—
285C4×C4⋊C4C2311yescharacteristic
286C4×C4⋊C4C2311yescharacteristic
287C4×C4⋊C4C2312yes—
288C4×C4⋊C4C2312yes—
289C4×C22⋊C4—21no—
290C4×C22⋊C4—21no—
291C4×C22⋊C4—22no—
292C4×C22⋊C4—22no—
293#376—21no—
294C2×#95—21no—
295C43—21no—
296#340C2312yes—
297#340C2312yes—
298#340C2311yescharacteristic
299#340C2311yescharacteristic
300#340C2312yes—
301#340C2312yes—
302#340C2311yescharacteristic
303#340C2311yescharacteristic
304#340C2312yes—
305#340C2312yes—
306#340C2311yescharacteristic
307#340C2311yescharacteristic
308#340C2311yescharacteristic
309#340C2311yescharacteristic
310#340C2311yescharacteristic
311#340C2311yescharacteristic
312#340C2311yescharacteristic
313#340C2312yes—
314#340C2312yes—
315#340C2311yescharacteristic
316#340C2312yes—
317#340C2312yes—
318#336C2312yes—
319#336C2312yes—
320#336C2312yes—
321#336C2312yes—
322#336C2311yescharacteristic
323#336C2311yescharacteristic
324#336C2311yescharacteristic
325#336C2311yescharacteristic
326#336C2312yes—
327#336C2312yes—
328C25—21no—
329C22×Q8—22no—
330C22×Q8—22no—
331C22×D4—21no—
332C22×D4—22no—
333C22×D4—22no—
334C22×D4—22no—
335C22×D4—22no—
336C22×D4—22no—
337C22×D4C2×Q814yes—
338C22×D4C2412yes—
339C23×C4—21no—
340C23×C4—21no—
341C23×C4—21no—
342C23×C4—22no—
343C23×C4—22no—
344C23×C4—44no—
345C23×C4—82no—
346C23×C4—82no—
347C23×C4C2×D411yescharacteristic
348C23×C4C2×D411yescharacteristic
349C23×C4C2411yescharacteristic
350C2×M16—22no—
351C2×M16—22no—
352C2×M16—22no—
353C2×M16—22no—
354C2×M16—22no—
355C2×M16C2×Q814yes—
356C22×C8—22no—
357C22×C8—22no—
358C22×C8—22no—
359C22×C8—22no—
360C22×C8—22no—
361C22×C8—22no—
362C22×C8C2411yescharacteristic
363C22×C8C2411yescharacteristic
364C22×C8C2411yescharacteristic
365C22×C8C2411yescharacteristic
366C22×C8C2412yes—
367C22×C8C2412yes—
368C4⋊Q8—28no—
369C4⋊Q8—24no—
370C4⋊Q8—24no—
371C4⋊Q8—24no—
372C4⋊Q8—42no—
373C4⋊Q8—44no—
374#125—28no—
375#125—24no—
376#125—24no—
377#125—24no—
378#125—42no—
379#125—44no—
380C22⋊Q8—216no—
381C22⋊Q8—48no—
382C22⋊Q8—84no—
383C22⋊Q8—84no—
384C4×Q8—84no—
385C4×D4—24no—
386C4×D4—24no—
387C4×D4—42no—
388C4×D4—42no—
389C4×D4—44no—
390C4×D4—44no—
391#117—22no—
392#117—22no—
393#117—22no—
394#117—22no—
395#117—22no—
396#117—22no—
397#117—22no—
398#117—22no—
399#117—22no—
400#117—22no—
401#117C2×Q814yes—
402#117#4114yes—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—82no—
427C2×C4⋊C4C2×D411yescharacteristic
428C2×C4⋊C4C2×D411yescharacteristic
429C2×C4⋊C4C2×D411yescharacteristic
430C2×C4⋊C4C2×D411yescharacteristic
431C2×C4⋊C4C2×D412yes—
432C2×C4⋊C4C2×D412yes—
433C2×C4⋊C4C2×D412yes—
434C2×C4⋊C4C2×D412yes—
435C2×C4⋊C4#4114yes—
436C2×C4⋊C4#4114yes—
437C2×C4⋊C4C2412yes—
438C2×C4⋊C4C2411yescharacteristic
439C2×C4⋊C4C2411yescharacteristic
440C2×C4⋊C4C2411yescharacteristic
441C2×C4⋊C4C2411yescharacteristic
442C2×C4⋊C4C2411yescharacteristic
443C2×C4⋊C4C2411yescharacteristic
444C2×C4⋊C4C2412yes—
445C2×C4⋊C4C2412yes—
446C2×C4⋊C4C2411yescharacteristic
447C2×C4⋊C4C2411yescharacteristic
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—44no—
463C2×C22⋊C4C2×D412yes—
464C2×C22⋊C4C2×D412yes—
465C2×C42—21no—
466C2×C42—21no—
467C2×C42—22no—
468C2×C42—22no—
469C2×C42—21no—
470C2×C42—21no—
471C2×C42—21no—
472C2×C42—21no—
473C2×C42—22no—
474C2×C42—22no—
475C2×C42—21no—
476C2×C42—21no—
477C2×C42—22no—
478C2×C42—22no—
479C2×C42C2×D411yescharacteristic
480C2×C42C2×D411yescharacteristic
481C2×C42C2412yes—
482C2×C42C2412yes—
483C2×C42C2411yescharacteristic
484C2×C42C2411yescharacteristic
485#107—22no—
486#107—22no—
487#107—24no—
488#107—42no—
489#106—24no—
490#106—24no—
491#106—22no—
492#106—22no—
493#106—24no—
494#106—42no—
495C4⋊C8—42no—
496C4⋊C8—42no—
497#102—24no—
498#102—24no—
499#102—24no—
500#102—24no—
501#102—42no—
502#102—42no—
503#102C2×Q818yes—
504#102C2×Q818yes—
505#97—42no—
506C4×C8—42no—
507#95—22no—
508#95—22no—
509#95—21no—
510#95—21no—
511#95—21no—
512#95—21no—
513#95—22no—
514#95—22no—
515#95—22no—
516#95—22no—
517#95—21no—
518#95—21no—
519#95—22no—
520#95—22no—
521#95—21no—
522#95—21no—
523#95—22no—
524#95—22no—
525#95C2×D412yes—
526#95C2×D412yes—
527#95C2×D412yes—
528#95C2×D412yes—
529C24—22no—
530C24—24no—
531C24—42no—
532C24—42no—
533C24—81no—
534C24—81no—
535C24—81no—
536C24—81no—
537C24C22×D411yescharacteristic
538C2×Q8—28no—
539C2×Q8—44no—
540C2×Q8—82no—
541C2×Q8—82no—
542C2×Q8—82no—
543C2×Q8—82no—
544C2×D4—28no—
545C2×D4—24no—
546C2×D4—28no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—42no—
553C2×D4—44no—
554C2×D4—42no—
555C2×D4—44no—
556C2×D4C22×Q814yes—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—24no—
565C22×C4—22no—
566C22×C4—24no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—41no—
574C22×C4—41no—
575C22×C4—41no—
576C22×C4—44no—
577C22×C4—44no—
578C22×C4—44no—
579C22×C4—42no—
580C22×C4—44no—
581C22×C4—82no—
582C22×C4—82no—
583C22×C4—81no—
584C22×C4—81no—
585C22×C4—81no—
586C22×C4—81no—
587C22×C4—81no—
588C22×C4—81no—
589C22×C4—816no—
590C22×C4C22×D411yescharacteristic
591C22×C4C22×D412yes—
592C22×C4C22×D411yescharacteristic
593C22×C4C22×D412yes—
594C22×C4C22×D412yes—
595C22×C4C22×D411yescharacteristic
596C22×C4C22×D412yes—
597C22×C4C22×D411yescharacteristic
598C22×C4C22×D411yescharacteristic
599C22×C4C22×Q812yes—
600C22×C4C2×#4112yes—
601C22×C4C2×#4112yes—
602C22×C4C2×#4112yes—
603C22×C4H(5,𝔽2)12yes—
604C22×C42−1+412yes—
605C22×C4C2511yescharacteristic
606M16—28no—
607M16—44no—
608C2×C8—22no—
609C2×C8—22no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—22no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—22no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—22no—
625C2×C8—44no—
626C2×C8—44no—
627C2×C8C22×Q814yes—
628C4⋊C4—28no—
629C4⋊C4—28no—
630C4⋊C4—28no—
631C4⋊C4—24no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—24no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—24no—
638C4⋊C4—22no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—22no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—22no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—22no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—42no—
655C4⋊C4—42no—
656C4⋊C4—42no—
657C4⋊C4—44no—
658C4⋊C4—44no—
659C4⋊C4—44no—
660C4⋊C4—44no—
661C4⋊C4—42no—
662C4⋊C4—42no—
663C4⋊C4—42no—
664C4⋊C4—81no—
665C4⋊C4—82no—
666C4⋊C4—81no—
667C4⋊C4—82no—
668C4⋊C4—82no—
669C4⋊C4—82no—
670C4⋊C4—82no—
671C4⋊C4C22×Q812yes—
672C4⋊C4C22×Q812yes—
673C4⋊C4C2×#4114yes—
674C4⋊C4C2×#4112yes—
675C4⋊C4C2×#4112yes—
676C4⋊C4C2×#4114yes—
677C22⋊C4—24no—
678C22⋊C4—24no—
679C22⋊C4—24no—
680C22⋊C4—24no—
681C22⋊C4—44no—
682C22⋊C4—44no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—82no—
686C22⋊C4—82no—
687C22⋊C4—82no—
688C22⋊C4—82no—
689C22⋊C4—82no—
690C22⋊C4—82no—
691C22⋊C4—82no—
692C22⋊C4—82no—
693C42—24no—
694C42—22no—
695C42—22no—
696C42—24no—
697C42—21no—
698C42—21no—
699C42—22no—
700C42—22no—
701C42—22no—
702C42—21no—
703C42—21no—
704C42—22no—
705C42—42no—
706C42—42no—
707C42—42no—
708C42—42no—
709C42—81no—
710C42—82no—
711C42—81no—
712C42—82no—
713C42—82no—
714C42—82no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—24no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—48no—
726C23—42no—
727C23—84no—
728C23—84no—
729C23—84no—
730C23—84no—
731C23—84no—
732C23—84no—
733C23#52512yes—
734C23#54612yes—
735C23D4×Q812yes—
736C23C23×D411yescharacteristic
737Q8—88no—
738Q8—164no—
739D4—24no—
740D4—24no—
741D4—42no—
742D4—42no—
743D4—48no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—22no—
747C2×C4—21no—
748C2×C4—22no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—24no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—44no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—41no—
782C2×C4—42no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—42no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—88no—
802C2×C4—82no—
803C2×C4—84no—
804C2×C4—84no—
805C2×C4—88no—
806C2×C4—162no—
807C2×C4#52512yes—
808C2×C4#53314yes—
809C2×C4#54214yes—
810C2×C4#54612yes—
811C2×C4D4×Q812yes—
812C2×C4#55414yes—
813C2×C4#55614yes—
814C2×C4#57712yes—
815C2×C4C23×Q811yescharacteristic
816C2×C4C22×#4111yescharacteristic
817C2×C4C22×#4111yescharacteristic
818C2×C4C22×#4111yescharacteristic
819C2×C4C2×H(5,𝔽2)11yescharacteristic
820C2×C4C2×2−1+411yescharacteristic
821C8—24no—
822C8—41no—
823C8—41no—
824C8—42no—
825C8—41no—
826C8—41no—
827C22—22no—
828C22—22no—
829C22—22no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—44no—
834C22—44no—
835C22—44no—
836C22—816no—
837C22—82no—
838C22—82no—
839C22—82no—
840C22—82no—
841C22#246514yes—
842C22C2×#52511yescharacteristic
843C22C2×#54611yescharacteristic
844C22C2×D4×Q811yescharacteristic
845C22C2×#57711yescharacteristic
846C22#358411yescharacteristic
847C22#358511yescharacteristic
848C22#358511yescharacteristic
849C4—22no—
850C4—41no—
851C4—42no—
852C4—44no—
853C4—42no—
854C4—41no—
855C4—41no—
856C4—42no—
857C4—42no—
858C4—42no—
859C4—44no—
860C4—42no—
861C4—42no—
862C4—42no—
863C4—81no—
864C4—81no—
865C4—82no—
866C4—81no—
867C4—81no—
868C4#246514yes—
869C4C2×#53311yescharacteristic
870C4C2×#54211yescharacteristic
871C4C2×#55411yescharacteristic
872C4C2×#55611yescharacteristic
873C2—24no—
874C2—84no—
875C2C2×#246511yescharacteristic
876C2#6057211yescharacteristic
877C2#6057411yescharacteristic
878C2#6118411yescharacteristic
879C2#6118911yescharacteristic
880C2#6138211yescharacteristic
881C2#6138511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2296 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34272C2semidirect
3. #27027C2semidirect
4. #27026C2semidirect
5. #27015C2semidirect
6. #27014C2semidirect
7. #27007C2semidirect
8. #27006C2semidirect
9. #27003C2semidirect
10. #27002C2semidirect
12. #23557C2semidirect
13. #23556C2semidirect
15. #21315C2semidirect
16. #21159C2semidirect
19. #21038C2semidirect
20. #21032C2semidirect
21. #21022C2semidirect
47. #2370C22semidirect
48. #2370C22semidirect
49. #2369C22semidirect
51. #2365C22semidirect
71. #2059C22semidirect
72. #2059C22semidirect
73. #2059C22semidirect
74. #2059C22semidirect
75. #2058C22semidirect
76. #2058C22semidirect
77. #2058C22semidirect
78. #2057C22semidirect
83. #1989C22semidirect
84. #1989C22semidirect
85. #1988C22semidirect
86. #1987C22semidirect
87. #1944C22semidirect
88. #1943C22semidirect
89. #1942C22semidirect
90. #1941C22semidirect
99. #1921C22semidirect
100. #1921C22semidirect
101. #1920C22semidirect
102. #1920C22semidirect
103. #1920C22semidirect
104. #1920C22semidirect
105. #1919C22semidirect
106. #1919C22semidirect
107. #1919C22semidirect
108. #1919C22semidirect
109. #1918C22semidirect
110. #1918C22semidirect
111. #1917C22semidirect
112. #1917C22semidirect
113. #1916C22semidirect
114. #1916C22semidirect
194. #418Q8semidirect

Maximal subgroups

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

subgroupindex
#351742
#342722
#270272
#270262
#270152
#270142
#270072
#270062
#270032
#270022
#236122
#235572
#235562
#234562
#213152
#211592
#210632
#210382
#210322
#210222
C2×#18642
C4×#4182