Finite Group Databasebeta

← #6396348

Subgroups — #6396348

Order 512.

1902 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3246C211yesmaximal, characteristic
2#34393C211yesmaximal, characteristic
3#34374C211yesmaximal, characteristic, complemented
4#23112C212yesmaximal, complemented
5#23101C211yesmaximal, characteristic, complemented
6#23095C211yesmaximal, characteristic, complemented
7#23075C212yesmaximal, complemented
8#23068C211yesmaximal, characteristic, complemented
9#23062C211yesmaximal, characteristic, complemented
10#23012C212yesmaximal, complemented
11#23003C211yesmaximal, characteristic, complemented
12#22997C211yesmaximal, characteristic, complemented
13#22975C212yesmaximal, complemented
14#22970C211yesmaximal, characteristic, complemented
15#22964C211yesmaximal, characteristic, complemented
16#22195C212yesmaximal, complemented
17#22194C212yesmaximal, complemented
18#21962C211yesmaximal, characteristic, complemented
19#21531C212yesmaximal, complemented
20#21523C212yesmaximal, complemented
21#21410C211yesmaximal, characteristic
22#21404C211yesmaximal, characteristic, complemented
23#20441C211yesmaximal, characteristic, complemented
24C2×#533C2211yescharacteristic
25C2×#532C2211yescharacteristic
26#3246C4116yescomplemented
27C2×#475C2211yescharacteristic
28C2×#475C2211yescharacteristic
29C2×#476C2212yes—
30C2×#465C2212yes—
31C2×#465C2212yes—
32C2×#460C2211yescharacteristic
33C2×#460C2211yescharacteristic
34C2×#461C2212yes—
35C2×#440C2212yes—
36C2×C4×SD16C2212yes—
37C22×C4⋊C8C2211yescharacteristic
38C2×#405C2212yes—
39C2×C4×M16C2211yescharacteristic
40#2382—22no—
41#2377—22no—
42#2366C2211yescharacteristic
43#2366C2211yescharacteristic
44#2365C2211yescharacteristic
45#2365C2211yescharacteristic
46#2365C2212yes—
47#2365C2212yes—
48#2357C2212yes—
49#2355—21no—
50#2355C2211yescharacteristic
51#2355C2211yescharacteristic
52Q8×C4⋊C4—21no—
53Q8×C4⋊C4C2211yescharacteristic
54Q8×C4⋊C4C2211yescharacteristic
55#2349C2212yes—
56#2341—21no—
57#2339—21no—
58#2326—21no—
59#2326—21no—
60#2324C2212yes—
61#2324C2212yes—
62#2323—22no—
63#2323C2212yes—
64#2323C2212yes—
65#2318—22no—
66#2314—21no—
67#2314—21no—
68#2285C2211yescharacteristic
69#2285C2211yescharacteristic
70#2283C2211yescharacteristic
71#1993C2211yescharacteristic
72#1993C2211yescharacteristic
73#1990C2211yescharacteristic
74#1990C2211yescharacteristic
75#1973C2212yes—
76#1968C2212yes—
77#1960C2211yescharacteristic
78#1960C2211yescharacteristic
79#1957C2211yescharacteristic
80#1957C2211yescharacteristic
81#1949C2212yes—
82#1949C2212yes—
83#1948C2211yescharacteristic
84#1948C2211yescharacteristic
85#1947C2211yescharacteristic
86#1947C2211yescharacteristic
87#1944C2212yes—
88#1941C2212yes—
89#1936C2212yes—
90#1935C2212yes—
91#1934C2212yes—
92#1933C2212yes—
93#1928C2212yes—
94#1927C2212yes—
95#1926C2212yes—
96#1925C2212yes—
97#1920C2212yes—
98#1920C2212yes—
99#1919C2212yes—
100#1919C2212yes—
101#1895C2212yes—
102#1895C2212yes—
103#1894C2211yescharacteristic
104#1894C2211yescharacteristic
105#1894C2211yescharacteristic
106#1894C2211yescharacteristic
107#1880C2212yes—
108#1880C2212yes—
109#1877C2212yes—
110#1877C2212yes—
111#1865C2212yes—
112#1864C2212yes—
113#1863C2212yes—
114#1862C2212yes—
115#1808C2212yes—
116#1807C2212yes—
117#1776C2212yes—
118C4×#106C2212yes—
119#1771C2212yes—
120#1771C2212yes—
121#1770C2211yescharacteristic
122#1770C2211yescharacteristic
123C8×C4⋊C4C2211yescharacteristic
124C8×C4⋊C4C2211yescharacteristic
125#1763C2212yes—
126#1762C2212yes—
127#1762C2212yes—
128#1762C2212yes—
129C4×#103C2211yescharacteristic
130C4×#103C2212yes—
131C4×#103C2211yescharacteristic
132C4×#103C2211yescharacteristic
133C4×#103C2211yescharacteristic
134C4×#102C2212yes—
135#1729C2212yes—
136C22×#41—21no—
137C22×SD16C2312yes—
138C22×SD16C2312yes—
139C22×M16C2311yescharacteristic
140C22×M16C2311yescharacteristic
141C23×C8C2312yes—
142#533—24no—
143#533C2×C418yescomplemented
144#532—24no—
145#532C2×C418yes—
146C2×C4⋊Q8C2311yescharacteristic
147C2×C4⋊Q8C2311yescharacteristic
148C2×C4⋊Q8C2311yescharacteristic
149C2×#127C2311yescharacteristic
150C2×#125—21no—
151C2×#124—21no—
152C2×C22⋊Q8—21no—
153C2×C22⋊Q8C2311yescharacteristic
154C2×C22⋊Q8C2311yescharacteristic
155C2×#121—21no—
156C2×#121C2312yes—
157C2×C4×Q8—22no—
158C2×C4×Q8—21no—
159C2×C4×Q8—21no—
160C2×C4×Q8—21no—
161C2×C4×Q8C2311yescharacteristic
162C2×C4×Q8C2311yescharacteristic
163C2×C4×Q8C2312yes—
164C2×C4×Q8C2312yes—
165C2×C4×D4—21no—
166C2×C4×D4—21no—
167C2×C4×D4—21no—
168C2×C4×D4C2312yes—
169C2×C4×D4C2312yes—
170C2×C4×D4C2312yes—
171C2×#117—21no—
172C2×#117—21no—
173C2×#117C2312yes—
174C22×C42C2311yescharacteristic
175#476C2×C4116yescomplemented
176#475C2×C418yescomplemented
177#475C2×C418yescomplemented
178#465C2×C4116yescomplemented
179#465C2×C4116yescomplemented
180#461C2×C4116yescomplemented
181#460C2×C418yes—
182#460C2×C418yes—
183#440—44no—
184C4×SD16—44no—
185C2×#107C2312yes—
186C2×#107C2312yes—
187C2×#106C2312yes—
188C2×#106C2312yes—
189C2×#106C2312yes—
190C2×#106C2312yes—
191C2×C4⋊C8C2×C418yescomplemented
192C2×C4⋊C8C2311yescharacteristic
193C2×C4⋊C8C2311yescharacteristic
194C2×C4⋊C8C2312yes—
195C2×#103C2311yescharacteristic
196C2×#103C2311yescharacteristic
197C2×#103C2311yescharacteristic
198C2×#103C2311yescharacteristic
199C2×#103C2311yescharacteristic
200C2×#103C2311yescharacteristic
201C2×#103C2311yescharacteristic
202C2×#103C2311yescharacteristic
203C2×#103C2312yes—
204C2×#103C2312yes—
205C2×#102C2312yes—
206C2×#102C2312yes—
207C2×#102C2312yes—
208C2×#102C2312yes—
209C2×#102C2312yes—
210C2×#102C2312yes—
211#405—44no—
212C4×M16—24no—
213C2×#97C2311yescharacteristic
214C2×#97C2311yescharacteristic
215C2×#97C2312yes—
216C2×#97C2312yes—
217C2×C4×C8C2311yescharacteristic
218C2×C4×C8C2311yescharacteristic
219C2×C4×C8C2312yes—
220C2×C4×C8C2312yes—
221#391—22no—
222#391—21no—
223#391—21no—
224#391C2312yes—
225#391C2312yes—
226#390—21no—
227#390—21no—
228#390—22no—
229#390—22no—
230#390C2312yes—
231#390C2312yes—
232#389—22no—
233#389—22no—
234#389—22no—
235#389—22no—
236#389—22no—
237#389C2312yes—
238#389C2312yes—
239#389C2312yes—
240#389C2312yes—
241#388—22no—
242#388—22no—
243#388—22no—
244#388—22no—
245#388—22no—
246#388—22no—
247#388—22no—
248#388—22no—
249#387—22no—
250#387—22no—
251#387—22no—
252#387—22no—
253#387—22no—
254#387—22no—
255#387—22no—
256#387—22no—
257#387—22no—
258#387—22no—
259#386—22no—
260#386—22no—
261#386—22no—
262#386—22no—
263#385—22no—
264#385—22no—
265#385—22no—
266#385—22no—
267#384—21no—
268#384—21no—
269#384D411yescharacteristic
270#384D411yescharacteristic
271#384C2311yescharacteristic
272#384C2311yescharacteristic
273#383—21no—
274#382—21no—
275#382—21no—
276#382—21no—
277#382D412yes—
278#382C2311yescharacteristic
279#382C2311yescharacteristic
280#381—21no—
281#381—22no—
282#380—21no—
283#380—22no—
284#380D411yescharacteristic
285#380D411yescharacteristic
286#380D412yes—
287#380C2311yescharacteristic
288#380C2312yes—
289#380C2311yescharacteristic
290C4×C4⋊C4—21no—
291C4×C4⋊C4—21no—
292C4×C4⋊C4—21no—
293C4×C4⋊C4—21no—
294C4×C4⋊C4—22no—
295C4×C4⋊C4—21no—
296C4×C4⋊C4C2312yes—
297C4×C4⋊C4C2312yes—
298C4×C4⋊C4C2312yes—
299C4×C4⋊C4C2312yes—
300C4×C4⋊C4C2312yes—
301C4×C4⋊C4C2311yescharacteristic
302C4×C4⋊C4C2311yescharacteristic
303C4×C4⋊C4C2312yes—
304C4×C4⋊C4C2311yescharacteristic
305C4×C4⋊C4C2311yescharacteristic
306C4×C22⋊C4—21no—
307C4×C22⋊C4—22no—
308#376—21no—
309C2×#95—22no—
310#340C2312yes—
311#340C2312yes—
312#340C2312yes—
313#340C2312yes—
314#340C2311yescharacteristic
315#340C2312yes—
316#340C2311yescharacteristic
317#340C2311yescharacteristic
318#340C2311yescharacteristic
319#340C2311yescharacteristic
320#340C2311yescharacteristic
321#340C2311yescharacteristic
322#340C2311yescharacteristic
323#340C2312yes—
324#340C2312yes—
325#340C2312yes—
326#336C2312yes—
327#336C2312yes—
328#336C2312yes—
329#336C2312yes—
330C2×#41—28no—
331C2×#41—82no—
332C2×#41—82no—
333C22×Q8—21no—
334C22×Q8—21no—
335C22×Q8C2411yescharacteristic
336C22×Q8C2411yescharacteristic
337C22×D4—22no—
338C22×D4—21no—
339C22×D4—21no—
340C22×D4C2412yes—
341C23×C4—22no—
342C23×C4—22no—
343C23×C4—22no—
344C23×C4C2×D411yescharacteristic
345C23×C4C2×D411yescharacteristic
346C23×C4C2411yescharacteristic
347C2×SD16—42no—
348C2×SD16—42no—
349C2×SD16—42no—
350C2×SD16—42no—
351C2×SD16C22×C418yes—
352C2×SD16C22×C418yes—
353C2×M16—22no—
354C2×M16—22no—
355C2×M16—22no—
356C2×M16—22no—
357C2×M16—41no—
358C2×M16—41no—
359C22×C8—42no—
360C22×C8—42no—
361C22×C8C22×C418yes—
362C22×C8C2411yescharacteristic
363C22×C8C2411yescharacteristic
364C22×C8C2412yes—
365C22×C8C2412yes—
366C22×C8C2411yescharacteristic
367C22×C8C2411yescharacteristic
368C4⋊Q8—22no—
369C4⋊Q8—22no—
370C4⋊Q8—22no—
371C4⋊Q8C22×C414yes—
372C4⋊Q8C22×C414yes—
373C4⋊Q8C22×C414yes—
374#127—22no—
375#127C22×C414yes—
376#125—28no—
377#124—28no—
378C22⋊Q8—28no—
379C22⋊Q8—22no—
380C22⋊Q8—22no—
381C22⋊Q8C22×C414yes—
382C22⋊Q8C22×C414yes—
383#121—28no—
384#121—24no—
385#121C22×C418yes—
386C4×Q8—28no—
387C4×Q8—22no—
388C4×Q8—22no—
389C4×Q8—42no—
390C4×Q8—42no—
391C4×Q8—42no—
392C4×Q8—42no—
393C4×Q8—82no—
394C4×Q8—82no—
395C4×Q8—84no—
396C4×Q8C22×C414yes—
397C4×Q8C22×C414yes—
398C4×D4—28no—
399C4×D4—24no—
400C4×D4—42no—
401C4×D4—42no—
402C4×D4—42no—
403C4×D4—42no—
404C4×D4—82no—
405C4×D4—82no—
406C4×D4C22×C418yes—
407#117—28no—
408#117—42no—
409#117—42no—
410#117—82no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
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—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4C2×D411yescharacteristic
430C2×C4⋊C4C2×D411yescharacteristic
431C2×C4⋊C4C2×D411yescharacteristic
432C2×C4⋊C4C2×D411yescharacteristic
433C2×C4⋊C4C2×D412yes—
434C2×C4⋊C4C2×D412yes—
435C2×C4⋊C4C2×D412yes—
436C2×C4⋊C4C2×D412yes—
437C2×C4⋊C4C2411yescharacteristic
438C2×C4⋊C4C2411yescharacteristic
439C2×C4⋊C4C2412yes—
440C2×C4⋊C4C2411yescharacteristic
441C2×C4⋊C4C2411yescharacteristic
442C2×C4⋊C4C2412yes—
443C2×C4⋊C4C2412yes—
444C2×C4⋊C4C2411yescharacteristic
445C2×C4⋊C4C2411yescharacteristic
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
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⋊C4C2×D412yes—
460C2×C22⋊C4C2×D412yes—
461C2×C42—21no—
462C2×C42—21no—
463C2×C42—22no—
464C2×C42—21no—
465C2×C42—21no—
466C2×C42—22no—
467C2×C42—22no—
468C2×C42—22no—
469C2×C42—22no—
470C2×C42—22no—
471C2×C42—22no—
472C2×C42C22×C414yes—
473C2×C42C2×D411yescharacteristic
474C2×C42C2×D411yescharacteristic
475C2×C42#4114yes—
476C2×C42C2412yes—
477C2×C42C2412yes—
478C2×C42C2411yescharacteristic
479C2×C42C2411yescharacteristic
480#107—42no—
481#107—42no—
482#106—42no—
483#106—42no—
484#106C22×C418yes—
485#106C22×C418yes—
486C4⋊C8C22×C414yes—
487C4⋊C8C22×C414yes—
488C4⋊C8C22×C418yes—
489#103—22no—
490#103—22no—
491#103—22no—
492#103—22no—
493#103—41no—
494#103—41no—
495#103—41no—
496#103—41no—
497#103C22×C418yes—
498#103C22×C418yes—
499#102—24no—
500#102—24no—
501#102—42no—
502#102—42no—
503#102C22×C418yes—
504#102C22×C418yes—
505#97—24no—
506#97—22no—
507#97—22no—
508#97—42no—
509C4×C8—24no—
510C4×C8—22no—
511C4×C8—22no—
512C4×C8—42no—
513#95—21no—
514#95—22no—
515#95—22no—
516#95—21no—
517#95—21no—
518#95—21no—
519#95—21no—
520#95—21no—
521#95—22no—
522#95—22no—
523#95—22no—
524#95—22no—
525#95—22no—
526#95—22no—
527#95—22no—
528#95—22no—
529#95—21no—
530#95—21no—
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—22no—
540C24C22×D411yescharacteristic
541#41—816no—
542C2×Q8—24no—
543C2×Q8—24no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—42no—
555C2×Q8—42no—
556C2×Q8—42no—
557C2×Q8—42no—
558C2×Q8C23×C412yes—
559C2×Q8C23×C412yes—
560C2×D4—28no—
561C2×D4—24no—
562C2×D4—24no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—81no—
571C2×D4—81no—
572C2×D4—82no—
573C2×D4—82no—
574C2×D4C23×C414yes—
575C22×C4—22no—
576C22×C4—22no—
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—28no—
587C22×C4—22no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—22no—
593C22×C4—41no—
594C22×C4—41no—
595C22×C4—82no—
596C22×C4—82no—
597C22×C4—82no—
598C22×C4—82no—
599C22×C4—82no—
600C22×C4—82no—
601C22×C4—82no—
602C22×C4—82no—
603C22×C4C4×D414yes—
604C22×C4C4×D414yes—
605C22×C4C23×C412yes—
606C22×C4C22×D412yes—
607C22×C4C22×D412yes—
608C22×C4C22×D412yes—
609C22×C4C22×D412yes—
610C22×C4C22×D411yescharacteristic
611C22×C4C22×D411yescharacteristic
612C22×C4C22×D411yescharacteristic
613C22×C4C22×D411yescharacteristic
614C22×C4C22×D411yescharacteristic
615C22×C4C2×#4112yes—
616C22×C4C2511yescharacteristic
617SD16—48no—
618SD16—48no—
619M16—28no—
620M16—44no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—22no—
624C2×C8—21no—
625C2×C8—22no—
626C2×C8—21no—
627C2×C8—22no—
628C2×C8—22no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—48no—
636C2×C8C23×C414yes—
637C2×C8C23×C414yes—
638C2×C8H(5,𝔽2)12yes—
639C2×C82−1+412yes—
640C4⋊C4—24no—
641C4⋊C4—24no—
642C4⋊C4—24no—
643C4⋊C4—24no—
644C4⋊C4—24no—
645C4⋊C4—24no—
646C4⋊C4—24no—
647C4⋊C4—24no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—22no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—22no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—22no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—42no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4—42no—
673C4⋊C4—81no—
674C4⋊C4—81no—
675C4⋊C4—82no—
676C4⋊C4—82no—
677C4⋊C4—82no—
678C4⋊C4—82no—
679C4⋊C4—82no—
680C4⋊C4—82no—
681C4⋊C4C23×C412yes—
682C4⋊C4C23×C412yes—
683C4⋊C4C23×C414yes—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—28no—
687C22⋊C4—28no—
688C22⋊C4—42no—
689C22⋊C4—42no—
690C22⋊C4—82no—
691C22⋊C4—82no—
692C22⋊C4—82no—
693C22⋊C4—82no—
694C22⋊C4—82no—
695C22⋊C4—82no—
696C22⋊C4—81no—
697C22⋊C4—81no—
698C22⋊C4—82no—
699C42—24no—
700C42—24no—
701C42—22no—
702C42—22no—
703C42—22no—
704C42—22no—
705C42—44no—
706C42—42no—
707C42—42no—
708C42—82no—
709C42—82no—
710C42—82no—
711C42—82no—
712C42—82no—
713C42—82no—
714C42C4×D414yes—
715C42C4×D414yes—
716C42C23×C412yes—
717C42C23×C412yes—
718C42C2×#4112yes—
719C42C2×#4112yes—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—24no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23C2×C4×D412yes—
734C23C23×D411yescharacteristic
735Q8—22no—
736Q8—22no—
737Q8—22no—
738Q8—22no—
739Q8—48no—
740Q8—48no—
741Q8—41no—
742Q8—41no—
743Q8—41no—
744Q8—41no—
745D4—24no—
746D4—24no—
747D4—48no—
748D4—42no—
749D4—42no—
750D4—84no—
751D4—88no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—28no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—24no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—44no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—42no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—88no—
812C2×C4—164no—
813C2×C4—164no—
814C2×C4C2×C4×D412yes—
815C2×C4C2×C4×D412yes—
816C2×C4C2×C4×D412yes—
817C2×C4C2×C4×D412yes—
818C2×C4C2×C4×D412yes—
819C2×C4#57712yes—
820C2×C4#57712yes—
821C2×C4C24×C411yescharacteristic
822C2×C4C22×#4111yescharacteristic
823C2×C4C2×H(5,𝔽2)11yescharacteristic
824C2×C4C2×2−1+411yescharacteristic
825C2×C4#58511yescharacteristic
826C2×C4#58511yescharacteristic
827C8—24no—
828C8—24no—
829C8—22no—
830C8—22no—
831C8—41no—
832C8—41no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—44no—
841C22—44no—
842C22—44no—
843C22—82no—
844C22—82no—
845C22—82no—
846C22—82no—
847C22C22×C4×D411yescharacteristic
848C22#349611yescharacteristic
849C22#349711yescharacteristic
850C22C2×#57711yescharacteristic
851C22C2×#57711yescharacteristic
852C22#358511yescharacteristic
853C22#358611yescharacteristic
854C4—22no—
855C4—22no—
856C4—22no—
857C4—22no—
858C4—44no—
859C4—42no—
860C4—42no—
861C4—42no—
862C4—42no—
863C4—42no—
864C4—42no—
865C4—42no—
866C4—42no—
867C4—81no—
868C4—82no—
869C4—81no—
870C4—81no—
871C4—82no—
872C4—81no—
873C4#294914yes—
874C4C4×H(5,𝔽2)11yescharacteristic
875C4C4×2−1+411yescharacteristic
876C4#349211yescharacteristic
877C4#349311yescharacteristic
878C2—42no—
879C2—84no—
880C2#3427411yescharacteristic
881C2C2×#294911yescharacteristic
882C2#6017011yescharacteristic
883C2#6234511yescharacteristic
884C2#6235511yescharacteristic
885C2#6240211yescharacteristic
886C2#6240811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#532C22
LCSG ▷ C2×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
3. #34374C2semidirect
4. #23112C2semidirect
5. #23101C2semidirect
6. #23095C2semidirect
7. #23075C2semidirect
8. #23068C2semidirect
9. #23062C2semidirect
10. #23012C2semidirect
11. #23003C2semidirect
12. #22997C2semidirect
13. #22975C2semidirect
14. #22970C2semidirect
15. #22964C2semidirect
16. #22195C2semidirect
17. #22194C2semidirect
18. #21962C2semidirect
19. #21531C2semidirect
20. #21523C2semidirect
22. #21404C2semidirect
23. #20441C2semidirect
26. #3246C4semidirect
143. #533C2×C4semidirect
175. #476C2×C4semidirect
176. #475C2×C4semidirect
177. #475C2×C4semidirect
178. #465C2×C4semidirect
179. #465C2×C4semidirect
180. #461C2×C4semidirect
191. C2×C4⋊C8C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#32462
#343932
#343742
#231122
#231012
#230952
#230752
#230682
#230622
#230122
#230032
#229972
#229752
#229702
#229642
#221952
#221942
#219622
#215312
#215232
#214102
#214042
#204412