Finite Group Databasebeta

← #6813499

Subgroups — #6813499

Order 512.

1574 conjugacy classes of subgroups.

The subgroup lattice has 923 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42923C212yesmaximal, complemented
2#32933C211yesmaximal, characteristic, complemented
3#32222C212yesmaximal, complemented
4#32019C212yesmaximal, complemented
5#31630C212yesmaximal, complemented
6#31349C212yesmaximal, complemented
7#29898C212yesmaximal, complemented
8#28705C211yesmaximal, characteristic, complemented
9#28227C211yesmaximal, characteristic, complemented
10#27840C211yesmaximal, characteristic, complemented
11#27839C211yesmaximal, characteristic, complemented
12#27791C211yesmaximal, characteristic, complemented
13#27660C211yesmaximal, characteristic, complemented
14#26427C212yesmaximal, complemented
15#26225C212yesmaximal, complemented
16#26065C211yesmaximal, characteristic, complemented
17#25034C211yesmaximal, characteristic, complemented
18#24780C211yesmaximal, characteristic, complemented
19#24778C211yesmaximal, characteristic, complemented
20#23027C211yesmaximal, characteristic, complemented
21#22658C211yesmaximal, characteristic, complemented
22#21442C211yesmaximal, characteristic, complemented
23#20663C211yesmaximal, characteristic, complemented
24C22×#131C2211yescharacteristic
25C2×#500C2211yescharacteristic
26C2×#466C2211yescharacteristic
27C2×#466C2211yescharacteristic
28C2×#466C2211yescharacteristic
29C2×#466C2211yescharacteristic
30C2×C4×D8C2211yescharacteristic
31C2×C8×D4C2211yescharacteristic
32C2×C8×D4C2211yescharacteristic
33C2×C8×D4C2211yescharacteristic
34C2×#427C2211yescharacteristic
35C2×#427C2211yescharacteristic
36C22×#107C2211yescharacteristic
37#2832—22no—
38#2753—22no—
39#2714—22no—
40#2696—22no—
41#2676—22no—
42#2662—22no—
43#2661—22no—
44#2615C2212yes—
45#2574—22no—
46#2563C2212yes—
47#2537C2212yes—
48#2497C2212yes—
49#2496C2212yes—
50#2491C2212yes—
51#2485C2212yes—
52#2440C2212yes—
53#2422C2212yes—
54#2416C2212yes—
55#2414C2212yes—
56#2388C2211yescharacteristic
57#2363C2212yes—
58#2354C2212yes—
59#2311C2212yes—
60#2100C2212yes—
61#2099C2212yes—
62#2088C2212yes—
63#2083C2212yes—
64#2077C2212yes—
65#2076C2212yes—
66#2076C2212yes—
67#2076C2212yes—
68#2075C2212yes—
69#2071C2212yes—
70#2067C2212yes—
71#2065C2212yes—
72#2057C2212yes—
73#2034C2212yes—
74#2033C2212yes—
75#2033C2212yes—
76#2033C2212yes—
77#2033C2212yes—
78#2033C2212yes—
79#2023C2212yes—
80#1987C2212yes—
81#1970C2211yescharacteristic
82#1970C2211yescharacteristic
83#1948C2212yes—
84#1942C2211yescharacteristic
85#1942C2211yescharacteristic
86#1942C2211yescharacteristic
87#1942C2211yescharacteristic
88#1926C2212yes—
89#1925C2212yes—
90#1921C2212yes—
91#1918C2212yes—
92#1895C2212yes—
93#1895C2212yes—
94#1895C2212yes—
95#1875C2212yes—
96#1875C2212yes—
97#1874C2212yes—
98#1870C2211yescharacteristic
99#1870C2211yescharacteristic
100#1870C2211yescharacteristic
101#1864C2212yes—
102#1862C2212yes—
103#1854C2212yes—
104#1854C2212yes—
105#1852C2212yes—
106#1851C2211yescharacteristic
107#1851C2211yescharacteristic
108#1851C2211yescharacteristic
109#1845C2211yescharacteristic
110#1845C2211yescharacteristic
111#1825C2212yes—
112#1809C2212yes—
113#1809C2212yes—
114#1808C2211yescharacteristic
115#1808C2211yescharacteristic
116#1808C2211yescharacteristic
117#1808C2211yescharacteristic
118#1808C2211yescharacteristic
119#1808C2211yescharacteristic
120#1808C2211yescharacteristic
121#1808C2211yescharacteristic
122#1808C2211yescharacteristic
123#1802C2212yes—
124#1780C2211yescharacteristic
125C4×#107C2211yescharacteristic
126C4×#107C2211yescharacteristic
127C8×C22⋊C4C2211yescharacteristic
128C8×C22⋊C4C2211yescharacteristic
129C8×C22⋊C4C2211yescharacteristic
130#1736C2212yes—
131C22×#41C2311yescharacteristic
132C22×D8C2311yescharacteristic
133C2×#131—24no—
134C2×#131—42no—
135C2×#131—42no—
136C22×M16C2311yescharacteristic
137C22×M16C2311yescharacteristic
138C22×M16C2311yescharacteristic
139C23×C8C2311yescharacteristic
140C23×C8C2311yescharacteristic
141C23×C8C2311yescharacteristic
142C23×C8C2311yescharacteristic
143C2×C4⋊Q8C2312yes—
144C2×#126—22no—
145C2×#124—22no—
146C2×#123—22no—
147C2×C22⋊Q8—22no—
148C2×#121—22no—
149C2×#121—22no—
150C2×#121C2312yes—
151C2×#121C2312yes—
152C2×#121C2312yes—
153C2×#121C2312yes—
154C2×C4×D4C2312yes—
155C2×C4×D4C2311yescharacteristic
156C2×C4×D4C2311yescharacteristic
157C2×C4×D4C2311yescharacteristic
158C2×#117C2312yes—
159C2×#117C2312yes—
160C22×C4⋊C4C2312yes—
161#500—42no—
162#466—24no—
163#466—42no—
164#466—42no—
165#466—42no—
166C4×D8—42no—
167C8×D4—24no—
168C8×D4—42no—
169C8×D4—42no—
170#427—42no—
171#427—42no—
172C2×#107—42no—
173C2×#107C2311yescharacteristic
174C2×#107C2311yescharacteristic
175C2×#107C2311yescharacteristic
176C2×#107C2311yescharacteristic
177C2×#107C2311yescharacteristic
178C2×#107C2311yescharacteristic
179C2×#107C2311yescharacteristic
180C2×#107C2312yes—
181C2×#107C2312yes—
182C2×#107C2312yes—
183C2×#107C2312yes—
184C2×#106C2312yes—
185C2×#106C2312yes—
186C2×C4⋊C8C2311yescharacteristic
187C2×C4⋊C8C2311yescharacteristic
188C2×C4⋊C8C2311yescharacteristic
189C2×#102C2312yes—
190C2×#102C2312yes—
191C2×#102C2312yes—
192C2×#102C2312yes—
193C2×#102C2312yes—
194C2×#102C2312yes—
195C2×#102C2312yes—
196C2×C22⋊C8C2311yescharacteristic
197C2×C22⋊C8C2311yescharacteristic
198C2×C22⋊C8C2311yescharacteristic
199C2×C22⋊C8C2311yescharacteristic
200C2×C22⋊C8C2311yescharacteristic
201C2×C22⋊C8C2311yescharacteristic
202C2×C22⋊C8C2311yescharacteristic
203C2×C22⋊C8C2311yescharacteristic
204C2×C22⋊C8C2311yescharacteristic
205C2×C4×C8C2311yescharacteristic
206C2×C4×C8C2311yescharacteristic
207C2×C4×C8C2311yescharacteristic
208#400—22no—
209#400—22no—
210#398—22no—
211#397—22no—
212#397—22no—
213#397—22no—
214#396—22no—
215#396—22no—
216#395—22no—
217#395D411yescharacteristic
218#394—22no—
219#394—22no—
220#394—22no—
221#394—22no—
222#394—22no—
223#394—22no—
224#394—22no—
225#394D411yescharacteristic
226#394D411yescharacteristic
227#394D411yescharacteristic
228#393—22no—
229#393—22no—
230#393—22no—
231#393—22no—
232#393D411yescharacteristic
233#392—22no—
234#392—22no—
235#392—22no—
236#392—22no—
237#392D411yescharacteristic
238#392D411yescharacteristic
239#392D411yescharacteristic
240#391—22no—
241#390—22no—
242#390—22no—
243#390—22no—
244#390—22no—
245#390—22no—
246#390C2312yes—
247#390C2312yes—
248#389C2312yes—
249#389C2312yes—
250#389C2312yes—
251#389C2312yes—
252#388—22no—
253#388—22no—
254#388—22no—
255#388—22no—
256#388—22no—
257#388—22no—
258#388—22no—
259#387—22no—
260#387—22no—
261#387—22no—
262#386—22no—
263#386—22no—
264#386—22no—
265#386—22no—
266#385—22no—
267#385—22no—
268#384C2312yes—
269#384C2312yes—
270#382—22no—
271#380—22no—
272#380C2312yes—
273#380C2312yes—
274#380C2312yes—
275#380C2312yes—
276#380C2312yes—
277#380C2312yes—
278#380C2312yes—
279#380C2312yes—
280#380C2312yes—
281C4×C4⋊C4—22no—
282C4×C4⋊C4C2312yes—
283C4×C4⋊C4C2312yes—
284C4×C22⋊C4—22no—
285C4×C22⋊C4C2311yescharacteristic
286C4×C22⋊C4C2311yescharacteristic
287C4×C22⋊C4C2311yescharacteristic
288#340C2312yes—
289#340C2312yes—
290#340C2312yes—
291#340C2312yes—
292#340C2312yes—
293#340C2312yes—
294#340C2312yes—
295#340C2312yes—
296#340C2312yes—
297#340C2312yes—
298#340C2312yes—
299#340C2312yes—
300#340C2312yes—
301#340C2312yes—
302#340C2312yes—
303#336C2311yescharacteristic
304#336C2311yescharacteristic
305#336C2311yescharacteristic
306#336C2311yescharacteristic
307#336C2311yescharacteristic
308#336C2311yescharacteristic
309C2×#41—22no—
310C2×#41—22no—
311C2×#41—41no—
312C2×#41—41no—
313C2×#41—41no—
314C2×#41—41no—
315C22×Q8—22no—
316C22×Q8C2×D411yescharacteristic
317C22×D4—22no—
318C22×D4—22no—
319C22×D4—22no—
320C22×D4—22no—
321C22×D4C2×D411yescharacteristic
322C22×D4C2×D411yescharacteristic
323C22×D4C2×D411yescharacteristic
324C22×D4C2×D411yescharacteristic
325C22×D4C2×D411yescharacteristic
326C22×D4C2×D411yescharacteristic
327C22×D4C2412yes—
328C23×C4—22no—
329C23×C4—22no—
330C23×C4C2411yescharacteristic
331C23×C4C2411yescharacteristic
332C23×C4C2411yescharacteristic
333C23×C4C2411yescharacteristic
334C2×D8—22no—
335C2×D8—22no—
336C2×D8—22no—
337#131—416no—
338C2×M16—22no—
339C2×M16—22no—
340C2×M16—22no—
341C2×M16—41no—
342C2×M16—41no—
343C2×M16—41no—
344C2×M16—41no—
345C2×M16—41no—
346C2×M16—41no—
347C22×C8—22no—
348C22×C8—22no—
349C22×C8—22no—
350C22×C8—22no—
351C22×C8—22no—
352C22×C8—22no—
353C22×C8—22no—
354C22×C8—22no—
355C22×C8—22no—
356C22×C8—22no—
357C22×C8—22no—
358C22×C8#4114yes—
359C22×C8C2411yescharacteristic
360C22×C8C2411yescharacteristic
361C22×C8C2411yescharacteristic
362C22×C8C2411yescharacteristic
363C22×C8C2411yescharacteristic
364C22×C8C2411yescharacteristic
365C22×C8C2411yescharacteristic
366C22×C8C2411yescharacteristic
367C4⋊Q8—42no—
368C4⋊Q8—42no—
369#126—84no—
370#124—84no—
371#123—84no—
372C22⋊Q8—84no—
373#121—24no—
374#121—24no—
375#121—42no—
376#121—42no—
377#121—42no—
378#121—42no—
379#121—42no—
380#121—42no—
381#121—84no—
382#121—84no—
383C4×D4—22no—
384C4×D4—22no—
385C4×D4—41no—
386C4×D4—41no—
387C4×D4—41no—
388C4×D4—41no—
389C4×D4—42no—
390C4×D4—42no—
391#117—42no—
392#117—42no—
393#117—42no—
394#117—42no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—42no—
406C2×C4⋊C4—42no—
407C2×C4⋊C4C2×D411yescharacteristic
408C2×C4⋊C4C2×D411yescharacteristic
409C2×C4⋊C4C2×D411yescharacteristic
410C2×C4⋊C4C2412yes—
411C2×C4⋊C4C2412yes—
412C2×C4⋊C4C2412yes—
413C2×C4⋊C4C2412yes—
414C2×C4⋊C4C2412yes—
415C2×C4⋊C4C2412yes—
416C2×C4⋊C4C2412yes—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4C2×D411yescharacteristic
438C2×C22⋊C4C2×D411yescharacteristic
439C2×C22⋊C4C2×D411yescharacteristic
440C2×C22⋊C4C2×D411yescharacteristic
441C2×C22⋊C4C2×D411yescharacteristic
442C2×C22⋊C4C2×D411yescharacteristic
443C2×C22⋊C4C2×D411yescharacteristic
444C2×C22⋊C4C2×D411yescharacteristic
445C2×C22⋊C4C2×D411yescharacteristic
446C2×C22⋊C4C2×D411yescharacteristic
447C2×C22⋊C4C2×D411yescharacteristic
448C2×C22⋊C4C2×D411yescharacteristic
449C2×C42—22no—
450C2×C42—22no—
451C2×C42—22no—
452C2×C42—22no—
453C2×C42C2411yescharacteristic
454C2×C42C2411yescharacteristic
455C2×C42C2411yescharacteristic
456#107—22no—
457#107—22no—
458#107—22no—
459#107—22no—
460#107—22no—
461#107—22no—
462#107—22no—
463#107—42no—
464#107—42no—
465#107—42no—
466#107—42no—
467#106—42no—
468#106—42no—
469C4⋊C8—22no—
470C4⋊C8—41no—
471C4⋊C8—41no—
472#102—24no—
473#102—42no—
474#102—42no—
475#102—42no—
476#102—42no—
477#102—42no—
478#102—42no—
479C22⋊C8—22no—
480C22⋊C8—22no—
481C22⋊C8—22no—
482C22⋊C8—41no—
483C22⋊C8—41no—
484C22⋊C8—41no—
485C22⋊C8—41no—
486C22⋊C8—41no—
487C22⋊C8—41no—
488C4×C8—22no—
489C4×C8—22no—
490C4×C8—22no—
491#95—22no—
492#95—22no—
493#95—22no—
494#95—22no—
495#95—22no—
496#95—22no—
497#95—22no—
498#95—22no—
499#95—22no—
500#95—22no—
501#95—22no—
502#95—22no—
503#95—22no—
504#95—22no—
505#95—22no—
506#95C2×D411yescharacteristic
507#95C2×D411yescharacteristic
508#95C2×D411yescharacteristic
509#95C2×D411yescharacteristic
510#95C2×D411yescharacteristic
511#95C2×D411yescharacteristic
512C24—22no—
513C24C22×D411yescharacteristic
514C24C22×D411yescharacteristic
515C24C22×D411yescharacteristic
516C24C22×D411yescharacteristic
517#41—44no—
518#41—44no—
519#41—44no—
520#41—44no—
521C2×Q8—22no—
522C2×Q8—41no—
523C2×Q8—41no—
524C2×Q8—82no—
525C2×Q8—82no—
526C2×Q8—82no—
527C2×D4—22no—
528C2×D4—22no—
529C2×D4—22no—
530C2×D4—22no—
531C2×D4—22no—
532C2×D4—22no—
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—41no—
541C2×D4—41no—
542C2×D4—41no—
543C2×D4—41no—
544C2×D4—41no—
545C2×D4—41no—
546C2×D4—41no—
547C2×D4—41no—
548C2×D4—41no—
549C2×D4—41no—
550C2×D4—41no—
551C2×D4—44no—
552C2×D4—82no—
553C2×D4—82no—
554C2×D4—82no—
555C2×D4—82no—
556C2×D4—82no—
557C2×D4—82no—
558C2×D4—82no—
559C2×D4—82no—
560C2×D4—82no—
561C2×D4—82no—
562C2×D4—82no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—44no—
593C22×C4—82no—
594C22×C4—82no—
595C22×C4—82no—
596C22×C4—82no—
597C22×C4—82no—
598C22×C4C22×D411yescharacteristic
599C22×C4C22×D411yescharacteristic
600C22×C4C22×D411yescharacteristic
601C22×C4C22×D411yescharacteristic
602C22×C4C22×D411yescharacteristic
603C22×C4C22×D411yescharacteristic
604C22×C4C22×D411yescharacteristic
605C22×C4C22×D411yescharacteristic
606C22×C4C22×D411yescharacteristic
607C22×C4C22×D411yescharacteristic
608C22×C4C2×#4112yes—
609C22×C42−1+412yes—
610C22×C4C2511yescharacteristic
611D8—44no—
612M16—44no—
613M16—44no—
614M16—44no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—28no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—44no—
637C2×C8—44no—
638C2×C8—44no—
639C2×C8C2×#4112yes—
640C2×C8C2×#4112yes—
641C2×C8H(5,𝔽2)12yes—
642C2×C8H(5,𝔽2)12yes—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—22no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—22no—
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—41no—
659C4⋊C4—41no—
660C4⋊C4—44no—
661C4⋊C4—44no—
662C4⋊C4—44no—
663C4⋊C4—82no—
664C4⋊C4—82no—
665C4⋊C4—82no—
666C4⋊C4—82no—
667C4⋊C4—82no—
668C4⋊C4—82no—
669C4⋊C4—82no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—22no—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—41no—
679C22⋊C4—41no—
680C22⋊C4—41no—
681C22⋊C4—41no—
682C22⋊C4—44no—
683C22⋊C4—44no—
684C22⋊C4—44no—
685C22⋊C4—82no—
686C22⋊C4—82no—
687C22⋊C4—82no—
688C22⋊C4—82no—
689C22⋊C4—82no—
690C22⋊C4—82no—
691C22⋊C4—82no—
692C22⋊C4—82no—
693C22⋊C4—82no—
694C22⋊C4—82no—
695C22⋊C4—82no—
696C22⋊C4—82no—
697C22⋊C4—82no—
698C22⋊C4—82no—
699C22⋊C4—82no—
700C22⋊C4—82no—
701C22⋊C4—82no—
702C42—21no—
703C42—21no—
704C42—21no—
705C42—21no—
706C42—21no—
707C42—21no—
708C42—44no—
709C42—82no—
710C42—82no—
711C42—82no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—42no—
746C23#54712yes—
747C23C23×D411yescharacteristic
748Q8—44no—
749Q8—164no—
750D4—44no—
751D4—44no—
752D4—44no—
753D4—44no—
754D4—44no—
755D4—44no—
756D4—42no—
757D4—42no—
758D4—42no—
759D4—42no—
760D4—164no—
761D4—164no—
762D4—164no—
763D4—164no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—164no—
828C2×C4—164no—
829C2×C4#54712yes—
830C2×C4#57612yes—
831C2×C4#57612yes—
832C2×C4#57812yes—
833C2×C4C22×#4111yescharacteristic
834C2×C4C2×H(5,𝔽2)11yescharacteristic
835C2×C4C2×H(5,𝔽2)11yescharacteristic
836C2×C4C2×2−1+411yescharacteristic
837C2×C4#58511yescharacteristic
838C2×C4#58511yescharacteristic
839C8—22no—
840C8—41no—
841C8—41no—
842C8—41no—
843C8—41no—
844C8—41no—
845C8—41no—
846C8#53814yes—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—41no—
872C22—41no—
873C22—41no—
874C22—41no—
875C22—82no—
876C22—82no—
877C22—82no—
878C22—82no—
879C22—82no—
880C22—82no—
881C22—82no—
882C22C2×#54711yescharacteristic
883C22#349611yescharacteristic
884C22#349611yescharacteristic
885C22C2×#57611yescharacteristic
886C22C2×#57611yescharacteristic
887C22C2×#57811yescharacteristic
888C22#358411yescharacteristic
889C4—22no—
890C4—22no—
891C4—22no—
892C4—22no—
893C4—41no—
894C4—41no—
895C4—41no—
896C4—41no—
897C4—41no—
898C4—41no—
899C4—82no—
900C4—82no—
901C4—82no—
902C4—82no—
903C4—82no—
904C4—82no—
905C4—82no—
906C4C2×#53811yescharacteristic
907C4#349311yescharacteristic
908C4#354111yescharacteristic
909C4#354111yescharacteristic
910C2—42no—
911C2—81no—
912C2—81no—
913C2—81no—
914C2—162no—
915C2#3934911yescharacteristic
916C2#6126211yescharacteristic
917C2#6128711yescharacteristic
918C2#6226611yescharacteristic
919C2#6226711yescharacteristic
920C2#6232811yescharacteristic
921C2#6233211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2388 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42923C2semidirect
2. #32933C2semidirect
3. #32222C2semidirect
4. #32019C2semidirect
5. #31630C2semidirect
6. #31349C2semidirect
7. #29898C2semidirect
8. #28705C2semidirect
9. #28227C2semidirect
10. #27840C2semidirect
11. #27839C2semidirect
12. #27791C2semidirect
13. #27660C2semidirect
14. #26427C2semidirect
15. #26225C2semidirect
16. #26065C2semidirect
17. #25034C2semidirect
18. #24780C2semidirect
19. #24778C2semidirect
20. #23027C2semidirect
21. #22658C2semidirect
22. #21442C2semidirect
23. #20663C2semidirect

Maximal subgroups

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

subgroupindex
#429232
#329332
#322222
#320192
#316302
#313492
#298982
#287052
#282272
#278402
#278392
#277912
#276602
#264272
#262252
#260652
#250342
#247802
#247782
#230272
#226582
#214422
#206632