Finite Group Databasebeta

← #6909552

Subgroups — #6909552

Order 512.

1854 conjugacy classes of subgroups.

The subgroup lattice has 897 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#38094C211yesmaximal, characteristic, complemented
2#37701C211yesmaximal, characteristic, complemented
3#32812C211yesmaximal, characteristic, complemented
4#32766C211yesmaximal, characteristic, complemented
5#31844C212yesmaximal, complemented
6#31643C212yesmaximal, complemented
7#30748C212yesmaximal, complemented
8#30448C212yesmaximal, complemented
9#30186C211yesmaximal, characteristic, complemented
10#30053C211yesmaximal, characteristic, complemented
11#30050C211yesmaximal, characteristic, complemented
12#29721C211yesmaximal, characteristic, complemented
13#29674C211yesmaximal, characteristic, complemented
14#29108C211yesmaximal, characteristic, complemented
15#28173C211yesmaximal, characteristic, complemented
16#25723C211yesmaximal, characteristic, complemented
17#24535C212yesmaximal, complemented
18#24363C212yesmaximal, complemented
19#23968C212yesmaximal, complemented
20#23942C211yesmaximal, characteristic, complemented
21#23850C212yesmaximal, complemented
22#23421C211yesmaximal, characteristic, complemented
23#21997C211yesmaximal, characteristic, complemented
24C22×#135C2212yes—
25C2×#556C2211yescharacteristic
26C2×#546C2211yescharacteristic
27C2×#541C2211yescharacteristic
28C2×#532C2211yescharacteristic, complemented
29C2×#495C2212yes—
30C2×#464C2212yes—
31C2×#462C2212yescomplemented
32C2×#452C2212yescomplemented
33C2×#449C2212yes—
34C2×#450C2212yes—
35C2×#447C2212yes—
36C2×#416C2212yescomplemented
37#2851C2211yescharacteristic, complemented
38#2850C2211yescharacteristic
39#2714—22no—
40#2711—22no—
41#2691—22no—
42#2684—22no—
43#2641C2211yescharacteristic, complemented
44#2640C2211yescharacteristic
45#2621C2211yescharacteristic
46#2619C2211yescharacteristic
47#2563C2211yescharacteristic
48#2545C2211yescharacteristic
49#2500C2211yescharacteristic
50#2499C2211yescharacteristic
51#2480—22no—
52#2467—22no—
53#2460—22no—
54#2458—22no—
55#2448C2212yescomplemented
56#2435C2211yescharacteristic
57#2432C2211yescharacteristic
58#2426C2212yes—
59#2407C2212yes—
60#2341C2212yescomplemented
61#2327C2211yescharacteristic, complemented
62#2326C2211yescharacteristic
63#2309C2211yescharacteristic
64#2297C2211yescharacteristic
65#2290C2211yescharacteristic
66#2101C2212yescomplemented
67#2074C2211yescharacteristic, complemented
68#2074C2211yescharacteristic, complemented
69#2073C2211yescharacteristic
70#2073C2211yescharacteristic
71#2073C2212yescomplemented
72#2071C2212yescomplemented
73#2055C2212yescomplemented
74#2054C2212yes—
75#2054C2212yes—
76#2054C2212yes—
77#2042C2212yes—
78#2026C2211yescharacteristic, complemented
79#2026C2211yescharacteristic, complemented
80#2025C2211yescharacteristic
81#2025C2211yescharacteristic
82#2024C2212yescomplemented
83#2023C2212yescomplemented
84#2016C2211yescharacteristic, complemented
85#2016C2211yescharacteristic, complemented
86#2015C2212yes—
87#2015C2212yescomplemented
88#2014C2211yescharacteristic, complemented
89#2014C2211yescharacteristic, complemented
90#2013C2211yescharacteristic
91#2013C2211yescharacteristic
92#2013C2212yescomplemented
93#2012C2212yes—
94#2012C2212yes—
95#2012C2212yes—
96#2011C2211yescharacteristic
97#2011C2211yescharacteristic
98#2001C2212yes—
99#2001C2212yes—
100#2000C2212yes—
101#2000C2212yes—
102#1958C2212yescomplemented
103#1934C2212yes—
104#1933C2212yescomplemented
105#1923C2212yes—
106#1916C2212yescomplemented
107#1893C2212yes—
108#1892C2212yescomplemented
109#1880C2212yes—
110#1880C2212yes—
111#1880C2212yes—
112#1880C2212yescomplemented
113#1879C2212yes—
114#1878C2212yescomplemented
115#1878C2212yescomplemented
116#1877C2212yes—
117#1875C2212yes—
118#1873C2212yes—
119#1869C2212yes—
120#1850C2212yescomplemented
121#1840C2211yescharacteristic, complemented
122#1832C2211yescharacteristic, complemented
123#1825C2212yescomplemented
124#1818C2211yescharacteristic
125#1805C2212yescomplemented
126#1803C2212yescomplemented
127#1798C2211yescharacteristic
128#1788C2212yes—
129C4×C22⋊C8C2211yescharacteristic, complemented
130C2×#336C2211yescharacteristic, complemented
131C22×#41C2312yes—
132C22×#41C2311yescharacteristic
133C23×D4C2311yescharacteristic
134C2×#135—44no—
135C2×#135—44no—
136C2×#135—44no—
137C22×Q16C2312yes—
138C22×Q16C2312yes—
139C22×SD16C2312yes—
140C22×SD16C2312yes—
141C22×SD16C2312yes—
142C22×SD16C2312yes—
143C22×D8C2312yes—
144C22×D8C2312yes—
145C23×C8C2312yes—
146#556—44no—
147#546—44no—
148#541—44no—
149#532—44no—
150C2×C4⋊Q8C2311yescharacteristic
151C2×C4⋊Q8C2311yescharacteristic
152C2×C4⋊Q8C2311yescharacteristic
153C2×#127C2311yescharacteristic
154C2×#126—22no—
155C2×#126—21no—
156C2×#126—21no—
157C2×#125—22no—
158C2×#125C2311yescharacteristic
159C2×#124—21no—
160C2×#124C2311yescharacteristic
161C2×#124C2312yes—
162C2×#124C2311yescharacteristic
163C2×#124C2311yescharacteristic
164C2×#123—21no—
165C2×C22⋊Q8C2311yescharacteristic
166C2×C22⋊Q8C2312yes—
167C2×C22⋊Q8C2311yescharacteristic
168C2×C22⋊Q8C2311yescharacteristic
169C2×#121—22no—
170C2×#121—21no—
171C2×#121C2311yescharacteristic
172C2×#121C2312yes—
173C2×#120—21no—
174C2×C4×Q8—21no—
175C2×C4×Q8C2312yes—
176C2×C4×Q8C2312yes—
177C2×C4×Q8C2311yescharacteristic
178C2×C4×D4—22no—
179C2×C4×D4C2311yescharacteristic
180C2×C4×D4C2311yescharacteristic
181C2×#117C2311yescharacteristic
182C2×#117C2311yescharacteristic
183C2×#117C2311yescharacteristic
184C22×C22⋊C4—21no—
185C22×C42C2311yescharacteristic
186#495—44no—
187#464—44no—
188#462—44no—
189#452—44no—
190#450—44no—
191#449—44no—
192#447—44no—
193C2×C4⋊C8C2312yes—
194C2×C4⋊C8C2312yes—
195#416—44no—
196C2×#103C2312yes—
197C2×#103C2312yes—
198C2×#103C2312yes—
199C2×#103C2312yes—
200C2×#103C2312yes—
201C2×#103C2312yes—
202C2×#103C2312yes—
203C2×#103C2312yes—
204C2×#102C2312yes—
205C2×#102C2312yes—
206C2×#102C2312yes—
207C2×#102C2312yes—
208C2×#102C2312yes—
209C2×#102C2312yes—
210C2×#102C2312yes—
211C2×#102C2312yes—
212C2×C22⋊C8C2312yes—
213C2×C22⋊C8C2312yes—
214C2×C22⋊C8C2312yes—
215C2×C4×C8C2312yes—
216#399—22no—
217#398—22no—
218#397—22no—
219#397—22no—
220#397—22no—
221#397—22no—
222#396—22no—
223#396—22no—
224#394—22no—
225#394—22no—
226#394—22no—
227#394—22no—
228#394—22no—
229#394—22no—
230#394—22no—
231#394—22no—
232#393—22no—
233#393—22no—
234#392—22no—
235#392—22no—
236#391C2311yescharacteristic
237#391C2311yescharacteristic
238#391C2312yes—
239#391C2311yescharacteristic
240#391C2311yescharacteristic
241#390—22no—
242#390—22no—
243#390—22no—
244#390—22no—
245#390C2311yescharacteristic
246#390C2311yescharacteristic
247#390C2311yescharacteristic
248#390C2311yescharacteristic
249#390C2311yescharacteristic
250#390C2312yes—
251#390C2311yescharacteristic
252#390C2312yes—
253#390C2312yes—
254#389C2312yes—
255#388—22no—
256#388—22no—
257#388—22no—
258#388—22no—
259#388—22no—
260#388—22no—
261#388—22no—
262#388D412yes—
263#387—22no—
264#387—22no—
265#387—22no—
266#387—22no—
267#387D412yes—
268#386—22no—
269#386—22no—
270#386—22no—
271#386D412yes—
272#385—22no—
273#385—22no—
274#385—22no—
275#385—22no—
276#385D412yes—
277#384C2311yescharacteristic
278#382C2311yescharacteristic
279#382C2311yescharacteristic
280#382C2311yescharacteristic
281#380—22no—
282#380—22no—
283#380C2312yes—
284#379—22no—
285#379—22no—
286C4×C4⋊C4C2311yescharacteristic
287C4×C22⋊C4—22no—
288C4×C22⋊C4—22no—
289C4×C22⋊C4C2311yescharacteristic
290C4×C22⋊C4C2311yescharacteristic
291#376C2311yescharacteristic
292#340C2312yes—
293#340C2312yes—
294#340C2312yes—
295#340C2312yes—
296#340C2312yes—
297#340C2312yes—
298#340C2312yes—
299#340C2312yes—
300#336C2311yescharacteristic
301#336C2311yescharacteristic
302#336C2312yes—
303#336C2312yes—
304#336C2311yescharacteristic
305#336C2311yescharacteristic
306#336C2312yes—
307#336C2312yes—
308#336C2312yes—
309C25—21no—
310C2×#41—24no—
311C2×#41—22no—
312C2×#41—24no—
313C2×#41—24no—
314C2×#41—24no—
315C2×#41—42no—
316C2×#41—41no—
317C2×#41—42no—
318C2×#41—42no—
319C2×#41—42no—
320C22×Q8—21no—
321C22×Q8C2411yescharacteristic
322C22×Q8C2411yescharacteristic
323C22×Q8C2412yes—
324C22×D4—22no—
325C22×D4—21no—
326C22×D4—22no—
327C22×D4—21no—
328C22×D4—22no—
329C22×D4—21no—
330C22×D4—22no—
331C22×D4—42no—
332C22×D4—41no—
333C22×D4—42no—
334C22×D4C2×D411yescharacteristic
335C22×D4C2411yescharacteristic
336C22×D4C2412yes—
337C22×D4C2411yescharacteristic
338C23×C4—21no—
339C23×C4—22no—
340C23×C4—21no—
341C23×C4C2×D412yes—
342C23×C4C2411yescharacteristic
343C23×C4C2411yescharacteristic
344#135—432no—
345C2×Q16—24no—
346C2×Q16—24no—
347C2×Q16—42no—
348C2×Q16—42no—
349C2×Q16—42no—
350C2×Q16—42no—
351C2×SD16—24no—
352C2×SD16—24no—
353C2×SD16—24no—
354C2×SD16—42no—
355C2×SD16—42no—
356C2×SD16—42no—
357C2×SD16—42no—
358C2×SD16—42no—
359C2×SD16—42no—
360C2×SD16—42no—
361C2×SD16—42no—
362C2×SD16—42no—
363C2×D8—24no—
364C2×D8—42no—
365C2×D8—42no—
366C2×D8—42no—
367C2×D8—42no—
368C2×D8—42no—
369C22×C8—24no—
370C22×C8—42no—
371C22×C8—42no—
372C22×C8C2412yes—
373C22×C8C2412yes—
374C22×C8C2412yes—
375C22×C8C2412yes—
376C4⋊Q8—24no—
377C4⋊Q8—42no—
378C4⋊Q8—42no—
379#127—42no—
380#126—44no—
381#126—44no—
382#126—48no—
383#125—42no—
384#125—48no—
385#124—24no—
386#124—22no—
387#124—41no—
388#124—42no—
389#124—42no—
390#124—42no—
391#124—44no—
392#123—44no—
393C22⋊Q8—24no—
394C22⋊Q8—24no—
395C22⋊Q8—42no—
396C22⋊Q8—42no—
397C22⋊Q8—42no—
398#121—24no—
399#121—44no—
400#121—48no—
401#121—42no—
402#121—42no—
403#120—44no—
404C4×Q8—24no—
405C4×Q8—42no—
406C4×Q8—42no—
407C4×Q8—42no—
408C4×Q8—42no—
409C4×Q8—44no—
410C4×D4—24no—
411C4×D4—42no—
412C4×D4—48no—
413#117—24no—
414#117—42no—
415#117—42no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4C2×D411yescharacteristic
430C2×C4⋊C4C2×D412yes—
431C2×C4⋊C4C2×D412yes—
432C2×C4⋊C4C2411yescharacteristic
433C2×C4⋊C4C2411yescharacteristic
434C2×C4⋊C4C2411yescharacteristic
435C2×C4⋊C4C2411yescharacteristic
436C2×C4⋊C4C2412yes—
437C2×C4⋊C4C2412yes—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—22no—
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—22no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—44no—
467C2×C22⋊C4C2×D411yescharacteristic
468C2×C22⋊C4C2×D411yescharacteristic
469C2×C22⋊C4C2×D412yes—
470C2×C22⋊C4C2×D412yes—
471C2×C22⋊C4C2×D412yes—
472C2×C42—21no—
473C2×C42—21no—
474C2×C42—21no—
475C2×C42—22no—
476C2×C42—22no—
477C2×C42—42no—
478C2×C42C2×D412yes—
479C2×C42C2411yescharacteristic
480C2×C42C2411yescharacteristic
481C2×C42C2411yescharacteristic
482C2×C42C2411yescharacteristic
483C2×C42C2411yescharacteristic
484C4⋊C8—42no—
485C4⋊C8—42no—
486#103—42no—
487#103—42no—
488#103—42no—
489#103—42no—
490#103—42no—
491#103—42no—
492#103—42no—
493#103—42no—
494#102—24no—
495#102—42no—
496#102—42no—
497#102—42no—
498#102—42no—
499#102—42no—
500#102—42no—
501#102—42no—
502C22⋊C8—24no—
503C22⋊C8—42no—
504C22⋊C8—42no—
505C4×C8—42no—
506#95—22no—
507#95—22no—
508#95—22no—
509#95—22no—
510#95—22no—
511#95—22no—
512#95—22no—
513#95—22no—
514#95—22no—
515#95—22no—
516#95—22no—
517#95C2×D412yes—
518#95C2×D412yes—
519#95C2×D412yes—
520#95C2×D412yes—
521#95C2×D412yes—
522C24—21no—
523C24—21no—
524C24—22no—
525C24—42no—
526C24—42no—
527C24—81no—
528C24—82no—
529C24—82no—
530C24C22×D411yescharacteristic
531C24C22×D411yescharacteristic
532#41—48no—
533#41—48no—
534#41—48no—
535#41—84no—
536#41—84no—
537#41—84no—
538C2×Q8—22no—
539C2×Q8—22no—
540C2×Q8—22no—
541C2×Q8—22no—
542C2×Q8—21no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—21no—
548C2×Q8—22no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—42no—
552C2×Q8—82no—
553C2×Q8H(5,𝔽2)14yes—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—21no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—21no—
566C2×D4—22no—
567C2×D4—21no—
568C2×D4—42no—
569C2×D4—44no—
570C2×D4—42no—
571C2×D4—44no—
572C2×D4—42no—
573C2×D4—42no—
574C2×D4—42no—
575C2×D4—44no—
576C2×D4—42no—
577C2×D4—82no—
578C2×D4—82no—
579C2×D4—81no—
580C2×D4—84no—
581C2×D4—84no—
582C2×D4—82no—
583C2×D4—81no—
584C2×D4—82no—
585C2×D4—82no—
586C2×D4—82no—
587C2×D4—82no—
588C2×D4H(5,𝔽2)12yes—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—21no—
597C22×C4—22no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—22no—
604C22×C4—21no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—44no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—44no—
613C22×C4—81no—
614C22×C4—82no—
615C22×C4—82no—
616C22×C4C22×D412yes—
617C22×C4C22×D412yes—
618C22×C4C22×D411yescharacteristic
619C22×C4C22×D411yescharacteristic
620C22×C4C22×D412yes—
621C22×C4C22×D412yes—
622C22×C4C22×D411yescharacteristic
623C22×C4C22×D411yescharacteristic
624C22×C4H(5,𝔽2)14yes—
625C22×C4C2511yescharacteristic
626Q16—48no—
627Q16—84no—
628SD16—48no—
629SD16—48no—
630SD16—84no—
631SD16—84no—
632D8—48no—
633D8—84no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8—48no—
647C4⋊C4—28no—
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—42no—
658C4⋊C4—42no—
659C4⋊C4—44no—
660C4⋊C4—44no—
661C4⋊C4—42no—
662C4⋊C4—42no—
663C4⋊C4—42no—
664C4⋊C4—44no—
665C4⋊C4—42no—
666C4⋊C4—42no—
667C4⋊C4—82no—
668C4⋊C4—82no—
669C4⋊C4—82no—
670C4⋊C4—82no—
671C22⋊C4—22no—
672C22⋊C4—22no—
673C22⋊C4—42no—
674C22⋊C4—42no—
675C22⋊C4—42no—
676C22⋊C4—44no—
677C22⋊C4—44no—
678C22⋊C4—44no—
679C22⋊C4—44no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—42no—
687C22⋊C4—42no—
688C22⋊C4—42no—
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—
702C22⋊C4—82no—
703C22⋊C4—82no—
704C42—22no—
705C42—21no—
706C42—22no—
707C42—22no—
708C42—22no—
709C42—21no—
710C42—42no—
711C42—44no—
712C42—42no—
713C42—42no—
714C42—42no—
715C42—82no—
716C23—22no—
717C23—22no—
718C23—21no—
719C23—21no—
720C23—22no—
721C23—22no—
722C23—21no—
723C23—21no—
724C23—22no—
725C23—21no—
726C23—42no—
727C23—42no—
728C23—41no—
729C23—41no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—41no—
737C23—42no—
738C23—42no—
739C23—41no—
740C23—42no—
741C23—41no—
742C23—84no—
743C23—84no—
744C23—164no—
745C23—162no—
746C23—164no—
747C23#53512yes—
748C23C23×D411yescharacteristic
749Q8—24no—
750Q8—24no—
751Q8—42no—
752Q8—42no—
753Q8—42no—
754Q8—42no—
755Q8—42no—
756Q8—42no—
757Q8—84no—
758D4—24no—
759D4—42no—
760D4—42no—
761D4—42no—
762D4—42no—
763D4—42no—
764D4—42no—
765D4—42no—
766D4—82no—
767D4—88no—
768D4—84no—
769D4—88no—
770D4—84no—
771D4—162no—
772D4—164no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—24no—
794C2×C4—21no—
795C2×C4—22no—
796C2×C4—21no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—42no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—42no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—88no—
822C2×C4—84no—
823C2×C4—84no—
824C2×C4—162no—
825C2×C4#53512yes—
826C2×C4C2×H(5,𝔽2)11yescharacteristic
827C2×C4C2×H(5,𝔽2)12yes—
828C2×C4C2×H(5,𝔽2)12yes—
829C2×C4#58511yescharacteristic
830C8—42no—
831C8—42no—
832C8—42no—
833C8—42no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—44no—
841C22—41no—
842C22—41no—
843C22—42no—
844C22—41no—
845C22—42no—
846C22—81no—
847C22—81no—
848C22—82no—
849C22—82no—
850C22—82no—
851C22—82no—
852C22—82no—
853C22—81no—
854C22—82no—
855C22—81no—
856C22—81no—
857C22—82no—
858C22—82no—
859C22—82no—
860C22—82no—
861C22—168no—
862C22C2×#53511yescharacteristic
863C22#348411yescharacteristic
864C22#348811yescharacteristic
865C22#358412yes—
866C22#358412yes—
867C4—22no—
868C4—42no—
869C4—41no—
870C4—41no—
871C4—44no—
872C4—41no—
873C4—42no—
874C4—42no—
875C4—42no—
876C4—82no—
877C4—81no—
878C4—81no—
879C4—81no—
880C4—81no—
881C4—81no—
882C4—81no—
883C4—82no—
884C4#353212yes—
885C4#353412yes—
886C2—42no—
887C2—81no—
888C2—82no—
889C2—162no—
890C2—161no—
891C2#4058811yescharacteristic
892C2#6079711yescharacteristic
893C2#6082311yescharacteristic
894C2#6163812yes—
895C2#6206012yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #38094C2semidirect
2. #37701C2semidirect
3. #32812C2semidirect
4. #32766C2semidirect
5. #31844C2semidirect
6. #31643C2semidirect
7. #30748C2semidirect
8. #30448C2semidirect
9. #30186C2semidirect
10. #30053C2semidirect
11. #30050C2semidirect
12. #29721C2semidirect
13. #29674C2semidirect
14. #29108C2semidirect
15. #28173C2semidirect
16. #25723C2semidirect
17. #24535C2semidirect
18. #24363C2semidirect
19. #23968C2semidirect
20. #23942C2semidirect
21. #23850C2semidirect
22. #23421C2semidirect
23. #21997C2semidirect
28. C2×#532C22semidirect
31. C2×#462C22semidirect
32. C2×#452C22semidirect
36. C2×#416C22semidirect
37. #2851C22semidirect
43. #2641C22semidirect
55. #2448C22semidirect
60. #2341C22semidirect
61. #2327C22semidirect
66. #2101C22semidirect
67. #2074C22semidirect
68. #2074C22semidirect
71. #2073C22semidirect
72. #2071C22semidirect
73. #2055C22semidirect
78. #2026C22semidirect
79. #2026C22semidirect
82. #2024C22semidirect
83. #2023C22semidirect
84. #2016C22semidirect
85. #2016C22semidirect
87. #2015C22semidirect
88. #2014C22semidirect
89. #2014C22semidirect
92. #2013C22semidirect
102. #1958C22semidirect
104. #1933C22semidirect
106. #1916C22semidirect
108. #1892C22semidirect
112. #1880C22semidirect
114. #1878C22semidirect
115. #1878C22semidirect
120. #1850C22semidirect
121. #1840C22semidirect
122. #1832C22semidirect
123. #1825C22semidirect
125. #1805C22semidirect
126. #1803C22semidirect
129. C4×C22⋊C8C22semidirect
130. C2×#336C22semidirect

Maximal subgroups

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

subgroupindex
#380942
#377012
#328122
#327662
#318442
#316432
#307482
#304482
#301862
#300532
#300502
#297212
#296742
#291082
#281732
#257232
#245352
#243632
#239682
#239422
#238502
#234212
#219972