Finite Group Databasebeta

← #6395349

Subgroups — #6395349

Order 512.

1886 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3246C211yesmaximal, characteristic
2#34373C211yesmaximal, characteristic, complemented
3#34232C211yesmaximal, characteristic
4#23135C212yesmaximal, complemented
5#23131C212yesmaximal, complemented
6#23101C211yesmaximal, characteristic, complemented
7#23095C211yesmaximal, characteristic, complemented
8#23068C211yesmaximal, characteristic, complemented
9#23062C211yesmaximal, characteristic, complemented
10#23033C212yesmaximal, complemented
11#23023C212yesmaximal, complemented
12#23003C211yesmaximal, characteristic, complemented
13#22997C211yesmaximal, characteristic, complemented
14#22970C211yesmaximal, characteristic, complemented
15#22964C211yesmaximal, characteristic, complemented
16#22162C212yesmaximal, complemented
17#22123C212yesmaximal, complemented
18#21863C211yesmaximal, characteristic
19#21623C212yesmaximal, complemented
20#21514C212yesmaximal, complemented
21#21389C211yesmaximal, characteristic, complemented
22#21169C211yesmaximal, characteristic, complemented
23#20545C211yesmaximal, 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—
37C2×#431C2211yescharacteristic
38C2×#427C2212yes—
39C22×C4⋊C8C2211yescharacteristic
40#2378—22no—
41#2366C2211yescharacteristic
42#2366C2211yescharacteristic
43#2365C2211yescharacteristic
44#2365C2211yescharacteristic
45#2363C2212yes—
46#2363C2212yes—
47#2362C2212yes—
48#2362C2212yes—
49#2355—21no—
50#2355—21no—
51#2355C2211yescharacteristic
52#2355C2211yescharacteristic
53#2353—22no—
54Q8×C4⋊C4C2211yescharacteristic
55Q8×C4⋊C4C2211yescharacteristic
56#2341—21no—
57#2339—21no—
58#2336—22no—
59#2333—22no—
60#2331C2212yes—
61#2327C2212yes—
62#2319C2212yes—
63#2314—21no—
64#2314—21no—
65C4×#124—21no—
66C4×#124—21no—
67#2285C2211yescharacteristic
68#2283C2211yescharacteristic
69#2275C2212yes—
70C4×#117C2211yescharacteristic
71#1990C2211yescharacteristic
72#1990C2211yescharacteristic
73#1988C2211yescharacteristic
74#1988C2211yescharacteristic
75#1981C2211yescharacteristic
76#1981C2211yescharacteristic
77#1973C2212yes—
78#1968C2212yes—
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#1880C2212yes—
102#1880C2212yes—
103#1877C2212yes—
104#1877C2212yes—
105#1875C2212yes—
106#1875C2212yes—
107#1873C2211yescharacteristic
108#1873C2211yescharacteristic
109#1873C2211yescharacteristic
110#1873C2211yescharacteristic
111#1865C2212yes—
112#1864C2212yes—
113#1863C2212yes—
114#1862C2212yes—
115#1804C2212yes—
116#1804C2212yes—
117#1776C2212yes—
118C4×#106C2212yes—
119#1770C2211yescharacteristic
120#1770C2211yescharacteristic
121C8×C4⋊C4C2211yescharacteristic
122C8×C4⋊C4C2211yescharacteristic
123#1768C2212yes—
124#1768C2212yes—
125#1763C2212yes—
126#1762C2212yes—
127C4×#103C2212yes—
128C4×#103C2211yescharacteristic
129C4×#103C2211yescharacteristic
130C4×#103C2211yescharacteristic
131C4×#103C2211yescharacteristic
132C4×#102C2212yes—
133#1752C2212yes—
134C8×C22⋊C4C2212yes—
135#1735C2212yes—
136C22×#41—21no—
137C22×SD16C2312yes—
138C22×SD16C2312yes—
139C23×C8C2312yes—
140#533—24no—
141#533C2×C418yescomplemented
142#532—24no—
143#532C2×C418yes—
144C2×C4⋊Q8C2311yescharacteristic
145C2×C4⋊Q8C2311yescharacteristic
146C2×C4⋊Q8C2311yescharacteristic
147C2×#127C2311yescharacteristic
148C2×#125—21no—
149C2×#124—21no—
150C2×C22⋊Q8—21no—
151C2×C22⋊Q8C2311yescharacteristic
152C2×C22⋊Q8C2311yescharacteristic
153C2×#121—21no—
154C2×#121C2312yes—
155C2×C4×Q8—21no—
156C2×C4×Q8—21no—
157C2×C4×Q8—21no—
158C2×C4×Q8C2311yescharacteristic
159C2×C4×Q8C2311yescharacteristic
160C2×C4×Q8C2312yes—
161C2×C4×Q8C2312yes—
162C2×C4×D4—21no—
163C2×C4×D4—21no—
164C2×C4×D4—21no—
165C2×C4×D4C2312yes—
166C2×C4×D4C2312yes—
167C2×C4×D4C2312yes—
168C2×#117—21no—
169C2×#117C2311yescharacteristic
170C2×#117C2311yescharacteristic
171C2×#117C2312yes—
172C22×C42C2311yescharacteristic
173#476C2×C4116yescomplemented
174#475C2×C418yescomplemented
175#475C2×C418yescomplemented
176#465C2×C4116yescomplemented
177#465C2×C4116yescomplemented
178#461C2×C4116yescomplemented
179#460C2×C418yes—
180#460C2×C418yes—
181#440—44no—
182C4×SD16—44no—
183#431—24no—
184#427—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⋊C8C2311yescharacteristic
195C2×C4⋊C8C2311yescharacteristic
196C2×C4⋊C8C2312yes—
197C2×#103C2311yescharacteristic
198C2×#103C2311yescharacteristic
199C2×#103C2311yescharacteristic
200C2×#103C2311yescharacteristic
201C2×#103C2311yescharacteristic
202C2×#103C2311yescharacteristic
203C2×#103C2311yescharacteristic
204C2×#103C2311yescharacteristic
205C2×#103C2312yes—
206C2×#103C2312yes—
207C2×#102C2312yes—
208C2×#102C2312yes—
209C2×#102C2312yes—
210C2×#102C2312yes—
211C2×#102C2312yes—
212C2×#102C2312yes—
213C2×C22⋊C8C2311yescharacteristic
214C2×C22⋊C8C2311yescharacteristic
215C2×#97C2312yes—
216C2×#97C2312yes—
217C2×C4×C8C2311yescharacteristic
218C2×C4×C8C2311yescharacteristic
219C2×C4×C8C2312yes—
220C2×C4×C8C2312yes—
221#391—21no—
222#391—21no—
223#391—22no—
224#391—22no—
225#391C2312yes—
226#391C2312yes—
227#390—21no—
228#390—21no—
229#390—22no—
230#390—22no—
231#390C2312yes—
232#390C2312yes—
233#389—22no—
234#389—22no—
235#389C2312yes—
236#389C2312yes—
237#389C2312yes—
238#389C2312yes—
239#388—22no—
240#388—22no—
241#388—22no—
242#388—22no—
243#388—22no—
244#388—22no—
245#388—22no—
246#388—22no—
247#387—22no—
248#387—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#384—21no—
264#384—21no—
265#384C2311yescharacteristic
266#384C2311yescharacteristic
267#383D412yes—
268#382—21no—
269#382—21no—
270#382D411yescharacteristic
271#382D411yescharacteristic
272#382C2312yes—
273#381—22no—
274#381D412yes—
275#380—21no—
276#380—21no—
277#380—22no—
278#380D411yescharacteristic
279#380D411yescharacteristic
280C4×C4⋊C4—21no—
281C4×C4⋊C4—21no—
282C4×C4⋊C4—21no—
283C4×C4⋊C4—21no—
284C4×C4⋊C4—21no—
285C4×C4⋊C4—21no—
286C4×C4⋊C4—22no—
287C4×C4⋊C4—22no—
288C4×C4⋊C4C2311yescharacteristic
289C4×C4⋊C4C2312yes—
290C4×C4⋊C4C2312yes—
291C4×C4⋊C4C2312yes—
292C4×C4⋊C4C2312yes—
293C4×C4⋊C4C2311yescharacteristic
294C4×C4⋊C4C2311yescharacteristic
295C4×C4⋊C4C2311yescharacteristic
296C4×C4⋊C4C2311yescharacteristic
297C4×C4⋊C4C2311yescharacteristic
298C4×C22⋊C4—21no—
299C4×C22⋊C4—21no—
300C4×C22⋊C4—22no—
301C4×C22⋊C4—22no—
302C4×C22⋊C4—22no—
303C4×C22⋊C4—22no—
304C4×C22⋊C4—22no—
305C4×C22⋊C4C2312yes—
306#376—21no—
307#376C2312yes—
308C2×#95—22no—
309C43—21no—
310#340C2312yes—
311#340C2312yes—
312#340C2312yes—
313#340C2312yes—
314#340C2311yescharacteristic
315#340C2311yescharacteristic
316#340C2311yescharacteristic
317#340C2311yescharacteristic
318#340C2311yescharacteristic
319#340C2311yescharacteristic
320#340C2311yescharacteristic
321#340C2311yescharacteristic
322#340C2312yes—
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—
353C22×C8—42no—
354C22×C8—42no—
355C22×C8C22×C418yes—
356C22×C8C2411yescharacteristic
357C22×C8C2411yescharacteristic
358C22×C8C2411yescharacteristic
359C22×C8C2411yescharacteristic
360C22×C8C2412yes—
361C22×C8C2412yes—
362C4⋊Q8—22no—
363C4⋊Q8—22no—
364C4⋊Q8—22no—
365C4⋊Q8C22×C414yes—
366C4⋊Q8C22×C414yes—
367C4⋊Q8C22×C414yes—
368#127—22no—
369#127C22×C414yes—
370#125—28no—
371#124—28no—
372C22⋊Q8—28no—
373C22⋊Q8—22no—
374C22⋊Q8—22no—
375C22⋊Q8C22×C414yes—
376C22⋊Q8C22×C414yes—
377#121—28no—
378#121—24no—
379#121C22×C418yes—
380C4×Q8—28no—
381C4×Q8—22no—
382C4×Q8—22no—
383C4×Q8—42no—
384C4×Q8—42no—
385C4×Q8—42no—
386C4×Q8—42no—
387C4×Q8—82no—
388C4×Q8—82no—
389C4×Q8C22×C414yes—
390C4×Q8C22×C414yes—
391C4×D4—24no—
392C4×D4—24no—
393C4×D4—28no—
394C4×D4—24no—
395C4×D4—42no—
396C4×D4—42no—
397C4×D4—82no—
398C4×D4—82no—
399C4×D4C22×C418yes—
400#117—28no—
401#117—22no—
402#117—22no—
403#117—41no—
404#117—41no—
405#117—42no—
406#117—42no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
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—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4C2×D411yescharacteristic
426C2×C4⋊C4C2×D411yescharacteristic
427C2×C4⋊C4C2×D411yescharacteristic
428C2×C4⋊C4C2×D411yescharacteristic
429C2×C4⋊C4C2412yes—
430C2×C4⋊C4C2412yes—
431C2×C4⋊C4C2411yescharacteristic
432C2×C4⋊C4C2411yescharacteristic
433C2×C4⋊C4C2412yes—
434C2×C4⋊C4C2411yescharacteristic
435C2×C4⋊C4C2411yescharacteristic
436C2×C4⋊C4C2411yescharacteristic
437C2×C4⋊C4C2411yescharacteristic
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4C2×D412yes—
452C2×C22⋊C4C2×D412yes—
453C2×C42—21no—
454C2×C42—21no—
455C2×C42—21no—
456C2×C42—21no—
457C2×C42—21no—
458C2×C42—21no—
459C2×C42—22no—
460C2×C42—22no—
461C2×C42—22no—
462C2×C42—22no—
463C2×C42—22no—
464C2×C42—21no—
465C2×C42—21no—
466C2×C42—22no—
467C2×C42—22no—
468C2×C42C22×C414yes—
469C2×C42C2×D411yescharacteristic
470C2×C42C2×D411yescharacteristic
471C2×C42#4114yes—
472C2×C42C2412yes—
473C2×C42C2412yes—
474C2×C42C2411yescharacteristic
475C2×C42C2411yescharacteristic
476#107—24no—
477#107—42no—
478#106—24no—
479#106—42no—
480#106C22×C418yes—
481#106C22×C418yes—
482C4⋊C8—22no—
483C4⋊C8—22no—
484C4⋊C8C22×C414yes—
485C4⋊C8C22×C414yes—
486C4⋊C8C22×C418yes—
487#103—22no—
488#103—22no—
489#103—22no—
490#103—22no—
491#103—41no—
492#103—41no—
493#103—41no—
494#103—41no—
495#103C22×C418yes—
496#103C22×C418yes—
497#102—42no—
498#102—42no—
499#102—42no—
500#102—42no—
501#102C22×C418yes—
502#102C22×C418yes—
503C22⋊C8—22no—
504C22⋊C8—22no—
505#97—42no—
506#97—42no—
507C4×C8—22no—
508C4×C8—22no—
509C4×C8—42no—
510C4×C8—42no—
511#95—21no—
512#95—22no—
513#95—22no—
514#95—21no—
515#95—21no—
516#95—21no—
517#95—22no—
518#95—22no—
519#95—22no—
520#95—22no—
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#95C2×D412yes—
530#95C2×D412yes—
531#95C2×D412yes—
532#95C2×D412yes—
533#95C2×D412yes—
534#95C2×D412yes—
535#95C2×D412yes—
536#95C2×D412yes—
537C24—22no—
538C24C22×D411yescharacteristic
539#41—816no—
540C2×Q8—24no—
541C2×Q8—24no—
542C2×Q8—21no—
543C2×Q8—21no—
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—42no—
553C2×Q8—42no—
554C2×Q8—81no—
555C2×Q8—81no—
556C2×Q8C23×C412yes—
557C2×Q8C23×C412yes—
558C2×D4—28no—
559C2×D4—24no—
560C2×D4—24no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—81no—
569C2×D4—81no—
570C2×D4—82no—
571C2×D4—82no—
572C2×D4C23×C414yes—
573C22×C4—22no—
574C22×C4—22no—
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—28no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—41no—
592C22×C4—41no—
593C22×C4—44no—
594C22×C4—44no—
595C22×C4—82no—
596C22×C4—82no—
597C22×C4—82no—
598C22×C4—82no—
599C22×C4—82no—
600C22×C4—82no—
601C22×C4C4×D414yes—
602C22×C4C4×D414yes—
603C22×C4C23×C412yes—
604C22×C4C22×D412yes—
605C22×C4C22×D412yes—
606C22×C4C22×D412yes—
607C22×C4C22×D412yes—
608C22×C4C22×D411yescharacteristic
609C22×C4C22×D411yescharacteristic
610C22×C4C22×D411yescharacteristic
611C22×C4C22×D411yescharacteristic
612C22×C4C22×D411yescharacteristic
613C22×C4C2×#4112yes—
614C22×C4C2511yescharacteristic
615SD16—48no—
616SD16—48no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8—22no—
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—48no—
634C2×C8C23×C414yes—
635C2×C8C23×C414yes—
636C4⋊C4—24no—
637C4⋊C4—24no—
638C4⋊C4—24no—
639C4⋊C4—24no—
640C4⋊C4—24no—
641C4⋊C4—24no—
642C4⋊C4—24no—
643C4⋊C4—24no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—22no—
658C4⋊C4—22no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—42no—
662C4⋊C4—42no—
663C4⋊C4—81no—
664C4⋊C4—81no—
665C4⋊C4—82no—
666C4⋊C4—82no—
667C4⋊C4—82no—
668C4⋊C4—82no—
669C4⋊C4—82no—
670C4⋊C4—82no—
671C4⋊C4C23×C412yes—
672C4⋊C4C23×C412yes—
673C4⋊C4C23×C414yes—
674C4⋊C4H(5,𝔽2)12yes—
675C4⋊C42−1+412yes—
676C22⋊C4—24no—
677C22⋊C4—24no—
678C22⋊C4—28no—
679C22⋊C4—28no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—44no—
683C22⋊C4—44no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—82no—
687C22⋊C4—82no—
688C22⋊C4—82no—
689C22⋊C4—82no—
690C22⋊C4—82no—
691C42—24no—
692C42—24no—
693C42—22no—
694C42—22no—
695C42—22no—
696C42—22no—
697C42—42no—
698C42—42no—
699C42—42no—
700C42—42no—
701C42—81no—
702C42—81no—
703C42—82no—
704C42—82no—
705C42—82no—
706C42—82no—
707C42—82no—
708C42—82no—
709C42—82no—
710C42C4×D414yes—
711C42C4×D414yes—
712C42C23×C412yes—
713C42C23×C412yes—
714C42C2×#4112yes—
715C42C2×#4112yes—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—24no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23C2×C4×D412yes—
730C23C23×D411yescharacteristic
731Q8—22no—
732Q8—22no—
733Q8—22no—
734Q8—22no—
735Q8—48no—
736Q8—41no—
737Q8—41no—
738Q8—41no—
739Q8—41no—
740Q8—84no—
741D4—24no—
742D4—24no—
743D4—48no—
744D4—42no—
745D4—42no—
746D4—84no—
747D4—88no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—28no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—24no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—44no—
781C2×C4—41no—
782C2×C4—41no—
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—41no—
792C2×C4—41no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—88no—
808C2×C4—164no—
809C2×C4—164no—
810C2×C4C2×C4×D412yes—
811C2×C4C2×C4×D412yes—
812C2×C4C2×C4×D412yes—
813C2×C4C2×C4×D412yes—
814C2×C4C2×C4×D412yes—
815C2×C4#57712yes—
816C2×C4#57712yes—
817C2×C4C24×C411yescharacteristic
818C2×C4C22×#4111yescharacteristic
819C2×C4C2×H(5,𝔽2)11yescharacteristic
820C2×C4C2×2−1+411yescharacteristic
821C2×C4#58511yescharacteristic
822C2×C4#58511yescharacteristic
823C8—24no—
824C8—24no—
825C8—41no—
826C8—41no—
827C8—41no—
828C8—41no—
829C22—22no—
830C22—22no—
831C22—22no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—44no—
837C22—44no—
838C22—44no—
839C22—82no—
840C22—82no—
841C22—82no—
842C22—82no—
843C22C22×C4×D411yescharacteristic
844C22#348811yescharacteristic
845C22#348911yescharacteristic
846C22C2×#57711yescharacteristic
847C22C2×#57711yescharacteristic
848C22#358411yescharacteristic
849C22#358411yescharacteristic
850C4—22no—
851C4—22no—
852C4—22no—
853C4—22no—
854C4—42no—
855C4—42no—
856C4—44no—
857C4—42no—
858C4—42no—
859C4—42no—
860C4—42no—
861C4—42no—
862C4—42no—
863C4—42no—
864C4—42no—
865C4—81no—
866C4—82no—
867C4—81no—
868C4—82no—
869C4#294914yes—
870C4C4×H(5,𝔽2)11yescharacteristic
871C4C4×2−1+411yescharacteristic
872C4#351111yescharacteristic
873C4#351211yescharacteristic
874C2—42no—
875C2—84no—
876C2#3426711yescharacteristic
877C2#6016111yescharacteristic
878C2C2×#294911yescharacteristic
879C2#6206811yescharacteristic
880C2#6207311yescharacteristic
881C2#6221611yescharacteristic
882C2#6222111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#532C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2283 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34373C2semidirect
4. #23135C2semidirect
5. #23131C2semidirect
6. #23101C2semidirect
7. #23095C2semidirect
8. #23068C2semidirect
9. #23062C2semidirect
10. #23033C2semidirect
11. #23023C2semidirect
12. #23003C2semidirect
13. #22997C2semidirect
14. #22970C2semidirect
15. #22964C2semidirect
16. #22162C2semidirect
17. #22123C2semidirect
19. #21623C2semidirect
20. #21514C2semidirect
21. #21389C2semidirect
22. #21169C2semidirect
23. #20545C2semidirect
26. #3246C4semidirect
141. #533C2×C4semidirect
173. #476C2×C4semidirect
174. #475C2×C4semidirect
175. #475C2×C4semidirect
176. #465C2×C4semidirect
177. #465C2×C4semidirect
178. #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
#343732
#342322
#231352
#231312
#231012
#230952
#230682
#230622
#230332
#230232
#230032
#229972
#229702
#229642
#221622
#221232
#218632
#216232
#215142
#213892
#211692
#205452