Finite Group Databasebeta

← #7506844

Subgroups — #7506844

Order 512.

1674 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35585C211yesmaximal, characteristic, complemented
2#35531C211yesmaximal, characteristic
3#31977C212yesmaximal, complemented
4#31976C212yesmaximal, complemented
5#31973C212yesmaximal, complemented
6#31972C212yesmaximal, complemented
7#31967C212yesmaximal, complemented
8#31966C212yesmaximal, complemented
9#31963C212yesmaximal, complemented
10#31962C212yesmaximal, complemented
11#23671C211yesmaximal, characteristic, complemented
12#23632C211yesmaximal, characteristic, complemented
13#23618C211yesmaximal, characteristic, complemented
14#23617C211yesmaximal, characteristic, complemented
15#23614C211yesmaximal, characteristic, complemented
16#23511C211yesmaximal, characteristic
17#21263C211yesmaximal, characteristic
18#21143C211yesmaximal, characteristic, complemented
19#21083C211yesmaximal, characteristic, complemented
20C2×#1934C211yesmaximal, characteristic, complemented
21#21035C211yesmaximal, characteristic, complemented
22#20878C211yesmaximal, characteristic, complemented
23#20652C211yesmaximal, characteristic, complemented
24C2×#535C2211yescharacteristic
25C2×#520C2211yescharacteristic
26C2×#428C2211yescharacteristic
27C2×#428C2211yescharacteristic
28C2×#424C2211yescharacteristic
29C2×#424C2211yescharacteristic
30C2×#423C2211yescharacteristic
31C2×#417C2211yescharacteristic
32C2×#417C2211yescharacteristic
33C2×#418C2211yescharacteristic
34C2×#418C2211yescharacteristic
35C2×#416C2211yescharacteristic
36C2×#416C2211yescharacteristic
37C22×#102C2211yescharacteristic
38C22×#102C2211yescharacteristic
39C22×C4×C8C2211yescharacteristic
40#2569—22no—
41#2509—21no—
42#2509C2212yescomplemented
43#2508—21no—
44#2508C2212yescomplemented
45#2507—21no—
46#2507C2212yescomplemented
47#2506—21no—
48#2506C2212yescomplemented
49#2504—21no—
50#2501—21no—
51#2500—21no—
52#2500—21no—
53#2448C2212yes—
54#2448C2212yes—
55#2445C2212yes—
56#2445C2212yes—
57#2442—22no—
58#2418—22no—
59#2418—22no—
60#2317C2211yescharacteristic
61#2317C2211yescharacteristic
62#2316C2211yescharacteristic
63#2316C2211yescharacteristic
64#2309C2211yescharacteristic
65#2297C2211yescharacteristic
66#2296C2211yescharacteristic
67C2×#390C2211yescharacteristic
68C2×#389C2211yescharacteristic
69#2285C2211yescharacteristic
70#2274C2211yescharacteristic
71#2088C2212yescomplemented
72#2088C2212yescomplemented
73#2087C2212yescomplemented
74#2086C2212yescomplemented
75#2073C2212yes—
76#2073C2212yes—
77#2071C2212yes—
78#2071C2212yes—
79#2068C2212yescomplemented
80#2067C2212yes—
81#2067C2212yes—
82#2067C2212yes—
83#2067C2212yes—
84#2067C2212yescomplemented
85#2066C2212yescomplemented
86#2065C2212yes—
87#2065C2212yes—
88#2065C2212yes—
89#2065C2212yes—
90#2065C2212yescomplemented
91#2042C2212yes—
92#2042C2212yes—
93#2041C2212yes—
94#2041C2212yes—
95#1983C2212yes—
96#1983C2212yes—
97#1982C2212yes—
98#1982C2212yes—
99#1939C2212yescomplemented
100#1939C2212yescomplemented
101#1939C2212yescomplemented
102#1939C2212yescomplemented
103#1934C2212yes—
104#1934C2212yes—
105#1934C2212yes—
106#1934C2212yes—
107#1934C2211yescharacteristic, complemented
108#1934C2211yescharacteristic, complemented
109#1934C2211yescharacteristic, complemented
110#1934C2211yescharacteristic, complemented
111#1933C2211yescharacteristic, complemented
112#1933C2211yescharacteristic, complemented
113#1933C2211yescharacteristic, complemented
114#1933C2211yescharacteristic, complemented
115#1921C2212yescomplemented
116#1920C2212yescomplemented
117#1919C2212yescomplemented
118#1918C2212yescomplemented
119#1865C2212yescomplemented
120#1864C2212yescomplemented
121#1863C2212yescomplemented
122#1862C2212yescomplemented
123#1805C2212yescomplemented
124#1804C2212yescomplemented
125#1803C2212yescomplemented
126#1802C2212yescomplemented
127#1736C2211yescharacteristic
128#1736C2211yescharacteristic
129#1735C2211yescharacteristic
130#1735C2211yescharacteristic
131C2×#340C2211yescharacteristic
132C2×#340C2211yescharacteristic
133#1729C2211yescharacteristic
134#1729C2211yescharacteristic
135C22×#41C2311yescharacteristic
136C23×D4C2311yescharacteristic
137C22×M16C2311yescharacteristic
138C22×M16C2311yescharacteristic
139C23×C8C2311yescharacteristic
140C23×C8C2311yescharacteristic
141#535—24no—
142#535—42no—
143C2×#127C2312yes—
144C2×#125—22no—
145C2×#124C2312yes—
146C2×#123—22no—
147C2×#123—22no—
148C2×#121—21no—
149C2×#121—21no—
150C2×#120—22no—
151#520—24no—
152#520—42no—
153C2×C4×Q8C2312yes—
154C2×C4×D4—22no—
155C2×C4×D4C2312yes—
156C2×#117—21no—
157C2×#117C2311yescharacteristic
158C2×#117C2311yescharacteristic
159C2×#117C2311yescharacteristic
160C2×#117C2311yescharacteristic
161C2×#117C2311yescharacteristic
162C22×C4⋊C4—21no—
163C22×C4⋊C4—21no—
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2311yescharacteristic
167C22×C22⋊C4—21no—
168C22×C22⋊C4—21no—
169C22×C42C2311yescharacteristic
170#428—24no—
171#428—42no—
172C2×#107C2312yes—
173C2×#107C2312yes—
174C2×#106C2312yes—
175C2×#106C2312yes—
176#424—42no—
177#424—42no—
178#423—42no—
179C2×C4⋊C8C2312yes—
180C2×C4⋊C8C2312yes—
181C2×C4⋊C8C2312yes—
182C2×C4⋊C8C2312yes—
183C2×C4⋊C8C2312yes—
184C2×C4⋊C8C2312yes—
185#418—42no—
186#418—42no—
187#417—24no—
188#417—42no—
189#416—24no—
190#416—42no—
191C2×#103C2312yes—
192C2×#103C2311yescharacteristic
193C2×#103C2311yescharacteristic
194C2×#103C2311yescharacteristic
195C2×#103C2312yes—
196C2×#103C2311yescharacteristic
197C2×#102—24no—
198C2×#102—42no—
199C2×#102C2312yes—
200C2×#102C2312yes—
201C2×#102C2312yes—
202C2×#102C2311yescharacteristic
203C2×#102C2311yescharacteristic
204C2×#102C2311yescharacteristic
205C2×#102C2312yes—
206C2×#102C2311yescharacteristic
207C2×#102C2312yes—
208C2×#102C2312yes—
209C2×#102C2312yes—
210C2×#102C2312yes—
211C2×#102C2312yes—
212C2×#102C2312yes—
213C2×C4×C8—42no—
214C2×C4×C8C2311yescharacteristic
215C2×C4×C8C2311yescharacteristic
216C2×C4×C8C2311yescharacteristic
217C2×C4×C8C2311yescharacteristic
218#400—22no—
219#400—22no—
220#400—22no—
221#400—22no—
222#399—22no—
223#399—22no—
224#398—22no—
225#398—22no—
226#398—22no—
227#398—22no—
228#397—22no—
229#397—22no—
230#394—22no—
231#394—22no—
232#394—22no—
233#394—22no—
234#391C2311yescharacteristic
235#391C2311yescharacteristic
236#390—21no—
237#390—21no—
238#390—21no—
239#390—21no—
240#390C2312yes—
241#390C2312yes—
242#390C2312yes—
243#390C2312yes—
244#390C2311yescharacteristic
245#390C2311yescharacteristic
246#389—21no—
247#389—21no—
248#389—21no—
249#389—21no—
250#389—21no—
251#389—21no—
252#389—22no—
253#389—21no—
254#389—21no—
255#389—22no—
256#389C2312yes—
257#389C2312yes—
258#389C2312yes—
259#389C2312yes—
260#389C2312yes—
261#389C2312yes—
262#389C2311yescharacteristic
263#389C2311yescharacteristic
264#389C2312yes—
265#389C2312yes—
266#389C2311yescharacteristic
267#389C2311yescharacteristic
268#388—22no—
269#388—22no—
270#388—22no—
271#388—22no—
272#387—22no—
273#387—22no—
274#387—22no—
275#387—22no—
276#386—21no—
277#386—21no—
278#386—22no—
279#386—22no—
280#385—21no—
281#385—21no—
282#385—22no—
283#385—22no—
284#384—21no—
285#384D411yescharacteristic
286#384D411yescharacteristic
287#384C2312yes—
288#382—21no—
289#382—22no—
290#382D411yescharacteristic
291#382D411yescharacteristic
292#382C2312yes—
293#380—22no—
294#380—22no—
295#380D412yes—
296#380D412yes—
297#379—22no—
298C4×C4⋊C4—21no—
299C4×C4⋊C4—21no—
300C4×C4⋊C4—21no—
301C4×C4⋊C4—21no—
302C4×C4⋊C4C2312yes—
303C4×C4⋊C4C2312yes—
304C4×C4⋊C4C2312yes—
305C4×C4⋊C4C2312yes—
306C4×C22⋊C4—22no—
307C4×C22⋊C4—21no—
308C4×C22⋊C4—21no—
309C2×#95—21no—
310#340C2312yes—
311#340C2312yes—
312#340C2312yes—
313#340C2312yes—
314#340C2311yescharacteristic
315#340C2311yescharacteristic
316#340C2312yes—
317#340C2311yescharacteristic
318#340C2311yescharacteristic
319#340C2312yes—
320#340C2311yescharacteristic
321#340C2311yescharacteristic
322#340C2311yescharacteristic
323#340C2311yescharacteristic
324#340C2312yes—
325#340C2312yes—
326#336C2312yes—
327#336C2312yes—
328#336C2312yes—
329#336C2312yes—
330C25—21no—
331C2×#41—22no—
332C2×#41—22no—
333C2×#41—22no—
334C2×#41—22no—
335C2×#41—22no—
336C2×#41#4114yes—
337C22×Q8C2411yescharacteristic
338C22×D4—21no—
339C22×D4—21no—
340C22×D4—22no—
341C22×D4—22no—
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4—22no—
346C22×D4—22no—
347C22×D4—22no—
348C22×D4C2412yes—
349C22×D4C2411yescharacteristic
350C23×C4—21no—
351C23×C4—21no—
352C23×C4—21no—
353C23×C4—21no—
354C23×C4—22no—
355C23×C4C2×D411yescharacteristic
356C23×C4C2×D411yescharacteristic
357C23×C4C2411yescharacteristic
358C2×M16—22no—
359C2×M16—22no—
360C2×M16—22no—
361C2×M16—22no—
362C2×M16—22no—
363C2×M16—22no—
364C22×C8—22no—
365C22×C8—22no—
366C22×C8—22no—
367C22×C8—22no—
368C22×C8—22no—
369C22×C8—22no—
370C22×C8C2411yescharacteristic
371C22×C8C2411yescharacteristic
372C22×C8C2411yescharacteristic
373C22×C8C2411yescharacteristic
374C22×C8C2412yes—
375C22×C8C2412yes—
376#127—24no—
377#127—42no—
378#125—84no—
379#124—24no—
380#124—42no—
381#123—84no—
382#123—84no—
383#121—44no—
384#121—44no—
385#120—48no—
386C4×Q8—24no—
387C4×Q8—42no—
388C4×D4—24no—
389C4×D4—42no—
390C4×D4—48no—
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#117—44no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—44no—
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⋊C4C2412yes—
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×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—22no—
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—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—82no—
464C2×C22⋊C4—82no—
465C2×C22⋊C4C2×D412yes—
466C2×C22⋊C4C2×D412yes—
467C2×C42—22no—
468C2×C42—22no—
469C2×C42—22no—
470C2×C42—21no—
471C2×C42—21no—
472C2×C42—21no—
473C2×C42—22no—
474C2×C42—22no—
475C2×C42C2×D411yescharacteristic
476C2×C42C2×D411yescharacteristic
477C2×C42C2412yes—
478C2×C42C2412yes—
479C2×C42C2411yescharacteristic
480C2×C42C2411yescharacteristic
481#107—24no—
482#107—42no—
483#106—24no—
484#106—42no—
485C4⋊C8—42no—
486C4⋊C8—42no—
487C4⋊C8—42no—
488C4⋊C8—42no—
489C4⋊C8—42no—
490C4⋊C8—42no—
491#103—22no—
492#103—22no—
493#103—24no—
494#103—41no—
495#103—41no—
496#103—42no—
497#102—22no—
498#102—22no—
499#102—24no—
500#102—24no—
501#102—24no—
502#102—42no—
503#102—42no—
504#102—41no—
505#102—41no—
506#102—42no—
507#102—42no—
508#102—42no—
509#102—42no—
510#102—42no—
511C4×C8—41no—
512C4×C8—41no—
513C4×C8—41no—
514C4×C8—41no—
515#95—22no—
516#95—22no—
517#95—22no—
518#95—22no—
519#95—21no—
520#95—21no—
521#95—21no—
522#95—21no—
523#95—21no—
524#95—21no—
525#95—21no—
526#95—21no—
527#95—22no—
528#95—22no—
529#95—22no—
530#95—22no—
531#95—22no—
532#95—22no—
533#95—22no—
534#95—22no—
535#95C2×D412yes—
536#95C2×D412yes—
537#95C2×D412yes—
538#95C2×D412yes—
539C24—21no—
540C24—22no—
541C24—42no—
542C24—42no—
543C24—42no—
544C24—81no—
545C24—81no—
546C24—81no—
547C24—81no—
548C24C22×D411yescharacteristic
549#41—28no—
550#41—28no—
551#41—44no—
552#41—44no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8C2×#4112yes—
559C2×D4—24no—
560C2×D4—21no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—44no—
572C2×D4—44no—
573C2×D4—42no—
574C2×D4—42no—
575C2×D4—42no—
576C2×D4—44no—
577C2×D4—44no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—44no—
581C2×D4—44no—
582C2×D4—82no—
583C2×D4—82no—
584C2×D4—82no—
585C2×D4—82no—
586C2×D4C2×#4112yes—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—24no—
592C22×C4—24no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—22no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—22no—
603C22×C4—41no—
604C22×C4—41no—
605C22×C4—44no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—82no—
611C22×C4—82no—
612C22×C4—81no—
613C22×C4—81no—
614C22×C4—81no—
615C22×C4—81no—
616C22×C4—81no—
617C22×C4—81no—
618C22×C4C22×D411yescharacteristic
619C22×C4C22×D412yes—
620C22×C4C22×D411yescharacteristic
621C22×C4C22×D412yes—
622C22×C4C22×D412yes—
623C22×C4C22×D412yes—
624C22×C4C22×D411yescharacteristic
625C22×C4C22×D411yescharacteristic
626C22×C4C22×D411yescharacteristic
627C22×C4C2×#4112yes—
628C22×C4C2×#4112yes—
629C22×C4H(5,𝔽2)12yes—
630C22×C4H(5,𝔽2)12yes—
631C22×C42−1+412yes—
632C22×C42−1+412yes—
633C22×C4C2511yescharacteristic
634M16—44no—
635M16—44no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—22no—
647C2×C8—22no—
648C2×C8—22no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—22no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—44no—
655C2×C8—44no—
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C4⋊C4—24no—
661C4⋊C4—24no—
662C4⋊C4—24no—
663C4⋊C4—22no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—22no—
675C4⋊C4—22no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—42no—
681C4⋊C4—42no—
682C4⋊C4—44no—
683C4⋊C4—42no—
684C4⋊C4—42no—
685C4⋊C4—44no—
686C4⋊C4—42no—
687C4⋊C4—42no—
688C4⋊C4—82no—
689C4⋊C4—82no—
690C4⋊C4—81no—
691C4⋊C4—81no—
692C4⋊C4—82no—
693C4⋊C4—82no—
694C4⋊C4—82no—
695C4⋊C4—82no—
696C4⋊C4—82no—
697C4⋊C4—82no—
698C4⋊C4—82no—
699C4⋊C4C2×#4114yes—
700C22⋊C4—24no—
701C22⋊C4—24no—
702C22⋊C4—44no—
703C22⋊C4—44no—
704C22⋊C4—44no—
705C22⋊C4—42no—
706C22⋊C4—42no—
707C22⋊C4—42no—
708C22⋊C4—44no—
709C22⋊C4—42no—
710C22⋊C4—44no—
711C22⋊C4—42no—
712C22⋊C4—82no—
713C22⋊C4—82no—
714C22⋊C4—81no—
715C22⋊C4—81no—
716C22⋊C4—82no—
717C22⋊C4—82no—
718C22⋊C4—82no—
719C22⋊C4—82no—
720C42—22no—
721C42—22no—
722C42—22no—
723C42—22no—
724C42—21no—
725C42—21no—
726C42—22no—
727C42—22no—
728C42—21no—
729C42—21no—
730C42—44no—
731C42—42no—
732C42—42no—
733C42—42no—
734C42—82no—
735C42—82no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—22no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—42no—
748C23—42no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—84no—
755C23—84no—
756C23—84no—
757C23—162no—
758C23—162no—
759C23—162no—
760C23—162no—
761C23#53712yes—
762C23#54612yes—
763C23#54812yes—
764C23C23×D411yescharacteristic
765Q8—22no—
766Q8—22no—
767Q8—41no—
768Q8—41no—
769D4—22no—
770D4—22no—
771D4—48no—
772D4—42no—
773D4—41no—
774D4—42no—
775D4—42no—
776D4—41no—
777D4—42no—
778D4—84no—
779D4—164no—
780D4—164no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—22no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—24no—
799C2×C4—22no—
800C2×C4—21no—
801C2×C4—22no—
802C2×C4—21no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—42no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—48no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—42no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—42no—
830C2×C4—41no—
831C2×C4—42no—
832C2×C4—41no—
833C2×C4—42no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—84no—
837C2×C4—164no—
838C2×C4—162no—
839C2×C4—162no—
840C2×C4#53712yes—
841C2×C4#53914yes—
842C2×C4#54014yes—
843C2×C4#54612yes—
844C2×C4#54812yes—
845C2×C4#55214yes—
846C2×C4#56314yes—
847C2×C4#57612yes—
848C2×C4#57712yes—
849C2×C4C22×#4111yescharacteristic
850C2×C4C22×#4111yescharacteristic
851C2×C4C2×H(5,𝔽2)11yescharacteristic
852C2×C4C2×H(5,𝔽2)11yescharacteristic
853C2×C4C2×2−1+411yescharacteristic
854C2×C4C2×2−1+411yescharacteristic
855C8—41no—
856C8—41no—
857C8—41no—
858C8—41no—
859C8—42no—
860C8—42no—
861C22—22no—
862C22—22no—
863C22—22no—
864C22—22no—
865C22—22no—
866C22—22no—
867C22—42no—
868C22—42no—
869C22—42no—
870C22—81no—
871C22—81no—
872C22—81no—
873C22—81no—
874C22—82no—
875C22—82no—
876C22—82no—
877C22—82no—
878C22—82no—
879C22—82no—
880C22—82no—
881C22—168no—
882C22#270714yes—
883C22C2×#53711yescharacteristic
884C22C2×#54611yescharacteristic
885C22C2×#54811yescharacteristic
886C22C2×#57611yescharacteristic
887C22C2×#57711yescharacteristic
888C22#358411yescharacteristic
889C22#358411yescharacteristic
890C4—22no—
891C4—22no—
892C4—41no—
893C4—41no—
894C4—42no—
895C4—42no—
896C4—42no—
897C4—42no—
898C4—44no—
899C4—42no—
900C4—81no—
901C4—82no—
902C4—81no—
903C4—81no—
904C4—82no—
905C4—81no—
906C4—81no—
907C4—81no—
908C4#270714yes—
909C4C2×#53911yescharacteristic
910C4C2×#54011yescharacteristic
911C4C2×#55211yescharacteristic
912C4C2×#56311yescharacteristic
913C2—24no—
914C2—82no—
915C2—162no—
916C2C2×#270711yescharacteristic
917C2#6093411yescharacteristic
918C2#6093511yescharacteristic
919C2#6121511yescharacteristic
920C2#6121611yescharacteristic
921C2#6132511yescharacteristic
922C2#6132711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#535C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2285 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #35585C2semidirect
3. #31977C2semidirect
4. #31976C2semidirect
5. #31973C2semidirect
6. #31972C2semidirect
7. #31967C2semidirect
8. #31966C2semidirect
9. #31963C2semidirect
10. #31962C2semidirect
11. #23671C2semidirect
12. #23632C2semidirect
13. #23618C2semidirect
14. #23617C2semidirect
15. #23614C2semidirect
18. #21143C2semidirect
19. #21083C2semidirect
20. C2×#1934C2semidirect
21. #21035C2semidirect
22. #20878C2semidirect
23. #20652C2semidirect
42. #2509C22semidirect
44. #2508C22semidirect
46. #2507C22semidirect
48. #2506C22semidirect
71. #2088C22semidirect
72. #2088C22semidirect
73. #2087C22semidirect
74. #2086C22semidirect
79. #2068C22semidirect
84. #2067C22semidirect
85. #2066C22semidirect
90. #2065C22semidirect
99. #1939C22semidirect
100. #1939C22semidirect
101. #1939C22semidirect
102. #1939C22semidirect
107. #1934C22semidirect
108. #1934C22semidirect
109. #1934C22semidirect
110. #1934C22semidirect
111. #1933C22semidirect
112. #1933C22semidirect
113. #1933C22semidirect
114. #1933C22semidirect
115. #1921C22semidirect
116. #1920C22semidirect
117. #1919C22semidirect
118. #1918C22semidirect
119. #1865C22semidirect
120. #1864C22semidirect
121. #1863C22semidirect
122. #1862C22semidirect
123. #1805C22semidirect
124. #1804C22semidirect
125. #1803C22semidirect
126. #1802C22semidirect

Maximal subgroups

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

subgroupindex
#355852
#355312
#319772
#319762
#319732
#319722
#319672
#319662
#319632
#319622
#236712
#236322
#236182
#236172
#236142
#235112
#212632
#211432
#210832
C2×#19342
#210352
#208782
#206522