Finite Group Databasebeta

← #6446793

Subgroups — #6446793

Order 512.

1834 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#35627C211yesmaximal, characteristic, complemented
2#34248C211yesmaximal, characteristic
3#26125C212yesmaximal, complemented
4#26125C212yesmaximal, complemented
5#26119C212yesmaximal, complemented
6#26118C212yesmaximal, complemented
7#26117C212yesmaximal, complemented
8#26115C212yesmaximal, complemented
9#26111C212yesmaximal, complemented
10#26107C212yesmaximal, complemented
11#23748C211yesmaximal, characteristic, complemented
12#23746C211yesmaximal, characteristic, complemented
13#23671C211yesmaximal, characteristic, complemented
14#23666C211yesmaximal, characteristic, complemented
15#21175C211yesmaximal, characteristic, complemented
16#21147C211yesmaximal, characteristic, complemented
17#20879C211yesmaximal, characteristic
18#20873C211yesmaximal, characteristic
19#20763C211yesmaximal, characteristic, complemented
20#20650C211yesmaximal, characteristic
21#20650C211yesmaximal, characteristic
22C2×#1804C211yesmaximal, characteristic
23#20416C211yesmaximal, characteristic
24C2×#518C2211yescharacteristic
25C2×#518C2211yescharacteristic
26C22×C4×D4C2211yescharacteristic
27C2×#428C2211yescharacteristic
28C2×#427C2211yescharacteristic
29C2×#424C2211yescharacteristic
30C2×#424C2211yescharacteristic
31C22×C4⋊C8C2211yescharacteristic
32C2×#418C2211yescharacteristic
33C2×#418C2211yescharacteristic
34C22×#102C2211yescharacteristic
35C22×#102C2211yescharacteristic
36C2×#405C2211yescharacteristic
37#2571C2212yescomplemented
38#2571C2212yescomplemented
39#2570C2212yescomplemented
40#2570C2212yescomplemented
41#2509—21no—
42#2509—21no—
43#2508—21no—
44#2508—21no—
45#2505—22no—
46#2505—22no—
47#2349—21no—
48#2349—21no—
49#2349C2212yes—
50#2349C2212yes—
51D4×C4⋊C4—21no—
52D4×C4⋊C4—21no—
53D4×C4⋊C4C2212yes—
54D4×C4⋊C4C2212yes—
55#2317C2211yescharacteristic
56#2317C2211yescharacteristic
57#2317C2211yescharacteristic
58#2317C2211yescharacteristic
59#2316C2211yescharacteristic
60#2315—22no—
61#2296C2211yescharacteristic
62#2296C2211yescharacteristic
63#2296C2211yescharacteristic
64C2×#385—22no—
65C2×#382C2211yescharacteristic
66#2274C2211yescharacteristic
67#2101C2212yescomplemented
68#2101C2212yescomplemented
69#2101C2212yescomplemented
70#2101C2212yescomplemented
71#2101C2212yescomplemented
72#2101C2212yescomplemented
73#2100C2212yescomplemented
74#2099C2212yescomplemented
75#2088C2211yescharacteristic, complemented
76#2088C2212yescomplemented
77#2088C2211yescharacteristic, complemented
78#2088C2212yescomplemented
79#2088C2211yescharacteristic, complemented
80#2088C2211yescharacteristic, complemented
81#2087C2212yescomplemented
82#2087C2211yescharacteristic, complemented
83#2087C2211yescharacteristic, complemented
84#2086C2211yescharacteristic, complemented
85#2086C2212yescomplemented
86#2086C2211yescharacteristic, complemented
87#1949C2212yescomplemented
88#1949C2212yescomplemented
89#1948C2212yescomplemented
90#1947C2212yescomplemented
91#1940C2212yescomplemented
92#1940C2212yescomplemented
93#1939C2212yescomplemented
94#1939C2212yescomplemented
95#1864C2212yes—
96#1864C2212yes—
97#1864C2212yes—
98#1864C2212yes—
99#1862C2212yes—
100#1862C2212yes—
101#1862C2212yes—
102#1862C2212yes—
103#1836C2212yescomplemented
104#1836C2212yescomplemented
105#1835C2212yescomplemented
106#1834C2212yescomplemented
107#1804C2212yes—
108#1804C2212yes—
109#1804C2212yes—
110#1804C2212yes—
111#1804C2212yes—
112#1804C2212yes—
113#1804C2212yes—
114#1804C2212yes—
115#1802C2212yes—
116#1802C2212yes—
117#1802C2212yes—
118#1802C2212yes—
119#1762C2212yes—
120#1762C2212yes—
121C4×#102C2212yes—
122C4×#102C2212yes—
123#1736C2211yescharacteristic
124#1736C2211yescharacteristic
125#1736C2211yescharacteristic
126#1736C2211yescharacteristic
127#1736C2211yescharacteristic
128#1735C2211yescharacteristic
129#1735C2211yescharacteristic
130#1735C2211yescharacteristic
131C2×#340C2211yescharacteristic
132C2×#340C2211yescharacteristic
133#1729C2211yescharacteristic
134#1728C2211yescharacteristic
135C23×D4C2311yescharacteristic
136C24×C4—21no—
137C22×M16C2311yescharacteristic
138C22×M16C2311yescharacteristic
139C23×C8C2311yescharacteristic
140C23×C8C2311yescharacteristic
141#518—24no—
142#518—24no—
143#518—42no—
144#518Q818yes—
145C2×C4×D4—21no—
146C2×C4×D4—21no—
147C2×C4×D4—21no—
148C2×C4×D4—21no—
149C2×C4×D4—24no—
150C2×C4×D4—21no—
151C2×C4×D4—21no—
152C2×C4×D4—42no—
153C2×C4×D4C2312yes—
154C2×C4×D4C2312yes—
155C2×C4×D4C2312yes—
156C2×C4×D4C2312yes—
157C2×C4×D4C2312yes—
158C2×C4×D4C2312yes—
159C2×#117C2311yescharacteristic
160C2×#117C2311yescharacteristic
161C2×#117C2311yescharacteristic
162C2×#117C2311yescharacteristic
163C2×#117C2311yescharacteristic
164C2×#117C2311yescharacteristic
165C22×C4⋊C4—22no—
166C22×C4⋊C4—22no—
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2311yescharacteristic
170C22×C22⋊C4—22no—
171C22×C22⋊C4—21no—
172C22×C22⋊C4—22no—
173C22×C42C2311yescharacteristic
174#428—42no—
175#427—42no—
176C2×#107C2311yescharacteristic
177C2×#107C2312yes—
178C2×#107C2311yescharacteristic
179C2×#106C2311yescharacteristic
180C2×#106C2311yescharacteristic
181C2×#106C2312yes—
182#424—24no—
183#424—42no—
184C2×C4⋊C8—42no—
185C2×C4⋊C8C2312yes—
186C2×C4⋊C8C2312yes—
187C2×C4⋊C8C2312yes—
188C2×C4⋊C8C2312yes—
189C2×C4⋊C8C2311yescharacteristic
190C2×C4⋊C8C2311yescharacteristic
191C2×C4⋊C8C2311yescharacteristic
192C2×C4⋊C8C2311yescharacteristic
193#418—24no—
194#418—24no—
195C2×#102—24no—
196C2×#102—24no—
197C2×#102C2312yes—
198C2×#102C2312yes—
199C2×#102C2312yes—
200C2×#102C2312yes—
201C2×#102C2312yes—
202C2×#102C2312yes—
203C2×#102C2312yes—
204C2×#102C2312yes—
205#405—24no—
206C2×#97C2312yes—
207C2×C4×C8C2312yes—
208#400—22no—
209#400—22no—
210#400—22no—
211#400—22no—
212#400—22no—
213#400—22no—
214#398—22no—
215#398—22no—
216#389—22no—
217#389—22no—
218#389—21no—
219#389—21no—
220#389—21no—
221#389—21no—
222#389—21no—
223#389—21no—
224#389—21no—
225#389—21no—
226#389D411yescharacteristic
227#389D411yescharacteristic
228#389D411yescharacteristic
229#389D411yescharacteristic
230#389C2311yescharacteristic
231#389C2311yescharacteristic
232#389C2312yes—
233#389C2312yes—
234#389C2311yescharacteristic
235#389C2311yescharacteristic
236#389C2312yes—
237#389C2312yes—
238#389C2311yescharacteristic
239#389C2311yescharacteristic
240#389C2311yescharacteristic
241#389C2311yescharacteristic
242#387—22no—
243#387—22no—
244#387—22no—
245#387—22no—
246#385—21no—
247#385—21no—
248#385—21no—
249#385—21no—
250#385—22no—
251#385—22no—
252#385—22no—
253#385—22no—
254#385—22no—
255#385—22no—
256#385—22no—
257#385—22no—
258#385—22no—
259#385—22no—
260#385—22no—
261#385—22no—
262#385D412yes—
263#385D412yes—
264#384—21no—
265#384C2312yes—
266#384C2312yes—
267#384C2312yes—
268#382—22no—
269#382—22no—
270#382—21no—
271#382—21no—
272#382—21no—
273#382C2312yes—
274#382C2312yes—
275#382C2312yes—
276#382C2312yes—
277#382C2312yes—
278#380—22no—
279#380—22no—
280#380—22no—
281#380—22no—
282#380—22no—
283C4×C4⋊C4—21no—
284C4×C4⋊C4—21no—
285C4×C4⋊C4—21no—
286C4×C4⋊C4—21no—
287C4×C4⋊C4—21no—
288C4×C4⋊C4—21no—
289C4×C4⋊C4C2312yes—
290C4×C4⋊C4C2312yes—
291C4×C4⋊C4C2312yes—
292C4×C4⋊C4C2312yes—
293C4×C22⋊C4—22no—
294C2×#95—21no—
295C2×#95—21no—
296C2×#95—22no—
297C2×#95—22no—
298#340C2311yescharacteristic
299#340C2311yescharacteristic
300#340C2311yescharacteristic
301#340C2311yescharacteristic
302#340C2312yes—
303#340C2312yes—
304#340C2312yes—
305#340C2312yes—
306#340C2311yescharacteristic
307#340C2312yes—
308#340C2311yescharacteristic
309#340C2311yescharacteristic
310#340C2312yes—
311#340C2311yescharacteristic
312#340C2312yes—
313#340C2312yes—
314#340C2311yescharacteristic
315#340C2311yescharacteristic
316#340C2311yescharacteristic
317#340C2311yescharacteristic
318#340C2312yes—
319#340C2312yes—
320#340C2312yes—
321#340C2312yes—
322#340C2312yes—
323#340C2312yes—
324#336C2312yes—
325#336C2312yes—
326#336C2312yes—
327#336C2312yes—
328C25—21no—
329C22×D4—21no—
330C22×D4—22no—
331C22×D4—22no—
332C22×D4—22no—
333C22×D4C2×Q814yes—
334C22×D4#4114yes—
335C22×D4#4114yes—
336C22×D4C2412yes—
337C23×C4—22no—
338C23×C4—22no—
339C23×C4—21no—
340C23×C4—21no—
341C23×C4—21no—
342C23×C4—22no—
343C23×C4—22no—
344C23×C4—22no—
345C23×C4—22no—
346C23×C4—44no—
347C23×C4—82no—
348C23×C4—82no—
349C23×C4C2×D411yescharacteristic
350C23×C4C2×D411yescharacteristic
351C23×C4C2411yescharacteristic
352C2×M16—22no—
353C2×M16—22no—
354C2×M16—22no—
355C2×M16—22no—
356C2×M16—22no—
357C2×M16—22no—
358C22×C8—22no—
359C22×C8—22no—
360C22×C8—22no—
361C22×C8—22no—
362C22×C8—22no—
363C22×C8—22no—
364C22×C8C2411yescharacteristic
365C22×C8C2411yescharacteristic
366C22×C8C2411yescharacteristic
367C22×C8C2411yescharacteristic
368C22×C8C2412yes—
369C22×C8C2412yes—
370C4×D4—28no—
371C4×D4—28no—
372C4×D4—24no—
373C4×D4—24no—
374C4×D4—24no—
375C4×D4—24no—
376C4×D4—24no—
377C4×D4—24no—
378C4×D4—42no—
379C4×D4—42no—
380C4×D4—42no—
381C4×D4—42no—
382C4×D4—44no—
383C4×D4—44no—
384C4×D4—44no—
385C4×D4—44no—
386C4×D4C2×Q818yes—
387C4×D4C2×Q818yes—
388#117—22no—
389#117—22no—
390#117—22no—
391#117—22no—
392#117—22no—
393#117—22no—
394#117—22no—
395#117—22no—
396#117—22no—
397#117C2×Q814yes—
398#117C2×Q814yes—
399#117#4114yes—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—84no—
428C2×C4⋊C4—84no—
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⋊C4C2×D411yescharacteristic
436C2×C4⋊C4C2×D411yescharacteristic
437C2×C4⋊C4C2412yes—
438C2×C4⋊C4C2412yes—
439C2×C4⋊C4C2412yes—
440C2×C4⋊C4C2411yescharacteristic
441C2×C4⋊C4C2411yescharacteristic
442C2×C4⋊C4C2411yescharacteristic
443C2×C4⋊C4C2411yescharacteristic
444C2×C4⋊C4C2411yescharacteristic
445C2×C4⋊C4C2411yescharacteristic
446C2×C4⋊C4C2411yescharacteristic
447C2×C4⋊C4C2411yescharacteristic
448C2×C22⋊C4—21no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—216no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—48no—
460C2×C22⋊C4—44no—
461C2×C22⋊C4C2×D412yes—
462C2×C22⋊C4C2×D412yes—
463C2×C42—21no—
464C2×C42—22no—
465C2×C42—22no—
466C2×C42—21no—
467C2×C42—21no—
468C2×C42—21no—
469C2×C42—22no—
470C2×C42—22no—
471C2×C42C2×D411yescharacteristic
472C2×C42C2×D411yescharacteristic
473C2×C42C2412yes—
474C2×C42C2411yescharacteristic
475C2×C42C2411yescharacteristic
476C2×C42C2412yes—
477#107—41no—
478#107—41no—
479#107—42no—
480#106—41no—
481#106—41no—
482#106—42no—
483C4⋊C8—24no—
484C4⋊C8—24no—
485C4⋊C8—41no—
486C4⋊C8—41no—
487C4⋊C8—41no—
488C4⋊C8—41no—
489C4⋊C8—42no—
490C4⋊C8—42no—
491#102—24no—
492#102—24no—
493#102—24no—
494#102—24no—
495#102—24no—
496#102—24no—
497#102—24no—
498#102—24no—
499#97—24no—
500C4×C8—24no—
501#95—21no—
502#95—21no—
503#95—22no—
504#95—22no—
505#95—22no—
506#95—22no—
507#95—22no—
508#95—22no—
509#95—22no—
510#95—22no—
511#95—22no—
512#95—22no—
513#95—21no—
514#95—21no—
515#95—21no—
516#95—21no—
517#95—21no—
518#95—21no—
519#95—22no—
520#95—22no—
521#95—22no—
522#95—22no—
523#95—22no—
524#95—22no—
525#95C2×D412yes—
526#95C2×D412yes—
527#95C2×D412yes—
528#95C2×D412yes—
529C24—22no—
530C24—24no—
531C24—24no—
532C24—24no—
533C24—81no—
534C24—81no—
535C24—81no—
536C24—81no—
537C24C22×D411yescharacteristic
538C2×D4—24no—
539C2×D4—28no—
540C2×D4—24no—
541C2×D4—24no—
542C2×D4—28no—
543C2×D4—28no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4#125116yes—
548C2×D4C22×Q814yes—
549C2×D4C2×#4114yes—
550C2×D4C2×#4114yes—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—28no—
556C22×C4—28no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4—41no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—44no—
574C22×C4—44no—
575C22×C4—44no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—82no—
580C22×C4—82no—
581C22×C4—82no—
582C22×C4—82no—
583C22×C4—82no—
584C22×C4—82no—
585C22×C4—82no—
586C22×C4—82no—
587C22×C4—82no—
588C22×C4—82no—
589C22×C4—81no—
590C22×C4—81no—
591C22×C4—81no—
592C22×C4—81no—
593C22×C4—81no—
594C22×C4—81no—
595C22×C4—816no—
596C22×C4C22×D411yescharacteristic
597C22×C4C22×D411yescharacteristic
598C22×C4C22×D411yescharacteristic
599C22×C4C22×D411yescharacteristic
600C22×C4C22×D412yes—
601C22×C4C22×D412yes—
602C22×C4C22×D412yes—
603C22×C4C22×D412yes—
604C22×C4C22×D411yescharacteristic
605C22×C4C22×Q812yes—
606C22×C4C2×#4112yes—
607C22×C4C2×#4112yes—
608C22×C4C2×#4112yes—
609C22×C4H(5,𝔽2)12yes—
610C22×C42−1+412yes—
611C22×C4C2511yescharacteristic
612M16—44no—
613M16—44no—
614C2×C8—21no—
615C2×C8—22no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—22no—
622C2×C8—22no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—22no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—22no—
630C2×C8—21no—
631C2×C8—22no—
632C2×C8—44no—
633C2×C8—44no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—22no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—22no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—22no—
653C4⋊C4—22no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—42no—
657C4⋊C4—42no—
658C4⋊C4—42no—
659C4⋊C4—42no—
660C4⋊C4—42no—
661C4⋊C4—42no—
662C4⋊C4—42no—
663C4⋊C4—42no—
664C4⋊C4—42no—
665C4⋊C4—82no—
666C4⋊C4—82no—
667C4⋊C4—82no—
668C4⋊C4—82no—
669C4⋊C4—81no—
670C4⋊C4—81no—
671C4⋊C4—81no—
672C4⋊C4—81no—
673C4⋊C4—82no—
674C4⋊C4—82no—
675C4⋊C4—81no—
676C4⋊C4—81no—
677C4⋊C4—82no—
678C4⋊C4—82no—
679C4⋊C4—82no—
680C4⋊C4—82no—
681C4⋊C4C22⋊Q814yes—
682C4⋊C4C22⋊Q814yes—
683C4⋊C4C22×Q812yes—
684C4⋊C4C22×Q812yes—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—28no—
688C22⋊C4—28no—
689C22⋊C4—44no—
690C22⋊C4—44no—
691C22⋊C4—44no—
692C22⋊C4—44no—
693C22⋊C4—42no—
694C22⋊C4—42no—
695C22⋊C4—42no—
696C22⋊C4C22⋊Q818yes—
697C42—24no—
698C42—22no—
699C42—22no—
700C42—21no—
701C42—21no—
702C42—22no—
703C42—21no—
704C42—21no—
705C42—22no—
706C42—42no—
707C42—42no—
708C42—42no—
709C42—82no—
710C42—82no—
711C42C22×Q814yes—
712C42C2×#4114yes—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—24no—
718C23—24no—
719C23—24no—
720C23—216no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—84no—
726C23—84no—
727C23—84no—
728C23—84no—
729C23—84no—
730C23—84no—
731C23C2×C22⋊Q812yes—
732C23#54612yes—
733C23#54812yes—
734C23C23×D411yescharacteristic
735D4—24no—
736D4—216no—
737D4—24no—
738D4—24no—
739D4C2×#12518yes—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—42no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—42no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—88no—
798C2×C4—88no—
799C2×C4—88no—
800C2×C4—88no—
801C2×C4—84no—
802C2×C4—164no—
803C2×C4—164no—
804C2×C4—162no—
805C2×C4—162no—
806C2×C4C2×C22⋊Q814yes—
807C2×C4C2×C22⋊Q814yes—
808C2×C4C2×C22⋊Q812yes—
809C2×C4C2×#12514yes—
810C2×C4#54414yes—
811C2×C4#54612yes—
812C2×C4#54812yes—
813C2×C4#55214yes—
814C2×C4#55314yes—
815C2×C4C23×Q811yescharacteristic
816C2×C4C22×#4111yescharacteristic
817C2×C4C22×#4111yescharacteristic
818C2×C4C22×#4111yescharacteristic
819C2×C4C2×H(5,𝔽2)11yescharacteristic
820C2×C4C2×2−1+411yescharacteristic
821C8—42no—
822C8—41no—
823C8—41no—
824C8—41no—
825C8—41no—
826C8—42no—
827C22—22no—
828C22—22no—
829C22—22no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—28no—
834C22—44no—
835C22—44no—
836C22—44no—
837C22—44no—
838C22—44no—
839C22—44no—
840C22—816no—
841C22#244214yes—
842C22C22×C22⋊Q811yescharacteristic
843C22C2×#54611yescharacteristic
844C22C2×#54811yescharacteristic
845C22#358411yescharacteristic
846C22#358411yescharacteristic
847C22#358511yescharacteristic
848C22#358511yescharacteristic
849C4—24no—
850C4—24no—
851C4—42no—
852C4—42no—
853C4—41no—
854C4—41no—
855C4—42no—
856C4—41no—
857C4—41no—
858C4—42no—
859C4—81no—
860C4—81no—
861C4—82no—
862C4—82no—
863C4—81no—
864C4—81no—
865C4—81no—
866C4—82no—
867C4—81no—
868C4#244214yes—
869C4C22×#12511yescharacteristic
870C4C2×#54411yescharacteristic
871C4C2×#55211yescharacteristic
872C4C2×#55311yescharacteristic
873C2—24no—
874C2—48no—
875C2C2×#244211yescharacteristic
876C2#6049611yescharacteristic
877C2#6049611yescharacteristic
878C2#6116911yescharacteristic
879C2#6117511yescharacteristic
880C2#6134311yescharacteristic
881C2#6134311yescharacteristic
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
1. #35627C2semidirect
3. #26125C2semidirect
4. #26125C2semidirect
5. #26119C2semidirect
6. #26118C2semidirect
7. #26117C2semidirect
8. #26115C2semidirect
9. #26111C2semidirect
10. #26107C2semidirect
11. #23748C2semidirect
12. #23746C2semidirect
13. #23671C2semidirect
14. #23666C2semidirect
15. #21175C2semidirect
16. #21147C2semidirect
19. #20763C2semidirect
37. #2571C22semidirect
38. #2571C22semidirect
39. #2570C22semidirect
40. #2570C22semidirect
67. #2101C22semidirect
68. #2101C22semidirect
69. #2101C22semidirect
70. #2101C22semidirect
71. #2101C22semidirect
72. #2101C22semidirect
73. #2100C22semidirect
74. #2099C22semidirect
75. #2088C22semidirect
76. #2088C22semidirect
77. #2088C22semidirect
78. #2088C22semidirect
79. #2088C22semidirect
80. #2088C22semidirect
81. #2087C22semidirect
82. #2087C22semidirect
83. #2087C22semidirect
84. #2086C22semidirect
85. #2086C22semidirect
86. #2086C22semidirect
87. #1949C22semidirect
88. #1949C22semidirect
89. #1948C22semidirect
90. #1947C22semidirect
91. #1940C22semidirect
92. #1940C22semidirect
93. #1939C22semidirect
94. #1939C22semidirect
103. #1836C22semidirect
104. #1836C22semidirect
105. #1835C22semidirect
106. #1834C22semidirect

Maximal subgroups

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

subgroupindex
#356272
#342482
#261252
#261192
#261182
#261172
#261152
#261112
#261072
#237482
#237462
#236712
#236662
#211752
#211472
#208792
#208732
#207632
#206502
C2×#18042
#204162