Finite Group Databasebeta

← #6611542

Subgroups — #6611542

Order 512.

1748 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36182C211yesmaximal, characteristic
2#36129C211yesmaximal, characteristic, complemented
3#33290C211yesmaximal, characteristic, complemented
4#33048C211yesmaximal, characteristic, complemented
5#33048C211yesmaximal, characteristic, complemented
6#29220C211yesmaximal, characteristic, complemented
7#28718C211yesmaximal, characteristic, complemented
8#27962C211yesmaximal, characteristic, complemented
9#27960C211yesmaximal, characteristic, complemented
10#27819C214yesmaximal, complemented
11#27710C214yesmaximal, complemented
12#27703C214yesmaximal, complemented
13#25905C211yesmaximal, characteristic, complemented
14#25903C211yesmaximal, characteristic, complemented
15#22501C214yesmaximal, complemented
16C4×#486C211yesmaximal, characteristic, complemented
17#21324C211yesmaximal, characteristic, complemented
18#21322C211yesmaximal, characteristic, complemented
19C4×#436C211yesmaximal, characteristic, complemented
20C2×#553C2212yes—
21C2×#533C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23C2×#486C2211yescharacteristic
24C2×#486C2211yescharacteristic
25C2×#486C2211yescharacteristic
26C2×#436C2212yes—
27C2×C4×M16C2211yescharacteristic
28C2×C4×M16C2211yescharacteristic
29#2862C2211yescharacteristic
30#2859C2211yescharacteristic
31#2857C2211yescharacteristic
32#2857C2211yescharacteristic
33#2856C2211yescharacteristic
34#2856C2211yescharacteristic
35#2566C2212yes—
36#2550C2212yes—
37#2512—21no—
38#2512—21no—
39#2504C2212yes—
40#2500C2212yes—
41#2492—21no—
42#2451—21no—
43#2446—21no—
44#2442C2212yes—
45#2439C2212yes—
46#2429—21no—
47#2422—21no—
48#2422—21no—
49#2417—21no—
50#2416—21no—
51#2416—21no—
52#2409—21no—
53#2361—21no—
54#2361—21no—
55#2360—21no—
56#2352C2212yes—
57Q8×C22⋊C4—21no—
58C4×C4⋊Q8C2211yescharacteristic
59C4×#127C2211yescharacteristic
60#2285C2211yescharacteristic
61C2×#384C2211yescharacteristic
62C42×D4C2211yescharacteristic
63#2101C2214yes—
64#2101C2214yes—
65#2099C2214yes—
66#2073C2214yes—
67#2025C2214yes—
68#2023C2214yes—
69#1993C2214yes—
70#1992C2214yes—
71#1991C2214yes—
72#1990C2211yescharacteristic
73#1990C2211yescharacteristic
74#1990C2211yescharacteristic
75#1990C2211yescharacteristic
76#1990C2211yescharacteristic
77#1990C2211yescharacteristic
78#1990C2211yescharacteristic
79#1990C2211yescharacteristic
80#1990C2211yescharacteristic
81#1989C2214yes—
82#1957C2211yescharacteristic
83#1936C2214yes—
84#1936C2214yes—
85#1934C2214yes—
86#1895C2214yes—
87#1895C2214yes—
88#1875C2214yes—
89#1874C2214yes—
90#1835C2214yes—
91#1834C2211yescharacteristic
92#1834C2211yescharacteristic
93#1834C2211yescharacteristic
94#1825C2214yes—
95#1823C2214yes—
96#1804C2214yes—
97#1770C2212yes—
98C4×C4⋊C8C2211yescharacteristic
99C4×#102C2214yes—
100#1753C2212yes—
101#1753C2212yes—
102C4×C22⋊C8C2211yescharacteristic
103C4×C22⋊C8C2211yescharacteristic
104#1736C2214yes—
105#1736C2214yes—
106C42×C8C2211yescharacteristic
107C23×Q8—21no—
108C22×M16C2312yes—
109C22×M16C2312yes—
110#553—216no—
111#533—24no—
112#533—42no—
113C2×C4⋊Q8—24no—
114C2×C4⋊Q8—21no—
115C2×C4⋊Q8—21no—
116C2×C4⋊Q8—42no—
117C2×C4⋊Q8C2311yescharacteristic
118C2×C4⋊Q8C2311yescharacteristic
119C2×C4⋊Q8C2312yes—
120C2×C4⋊Q8C2311yescharacteristic
121C2×#127C2311yescharacteristic
122C2×#126—22no—
123C2×#125C2312yes—
124C2×#125C2312yes—
125C2×#123—22no—
126C2×C22⋊Q8—21no—
127C2×C22⋊Q8—21no—
128C2×C22⋊Q8—21no—
129C2×C22⋊Q8—21no—
130C2×#121—22no—
131C2×#121—21no—
132C2×#121—21no—
133C2×#121—21no—
134C2×#121—21no—
135C2×#121C2312yes—
136C2×#121C2312yes—
137C2×C4×Q8—21no—
138C2×C4×Q8—21no—
139C2×C4×Q8—21no—
140C2×C4×D4—22no—
141C2×C4×D4—21no—
142C2×C4×D4—21no—
143C2×C4×D4D411yescharacteristic
144C2×C4×D4D411yescharacteristic
145C2×C4×D4C2312yes—
146C2×C4×D4C2311yescharacteristic
147C2×#117C2312yes—
148C2×#117C2312yes—
149C22×C4⋊C4—21no—
150C22×C4⋊C4—21no—
151C22×C4⋊C4—21no—
152C22×C4⋊C4C2312yes—
153C22×C4⋊C4C2312yes—
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156#486—24no—
157#486—42no—
158#486—42no—
159#436—28no—
160C2×C4⋊C8C2312yes—
161C2×#102C2314yes—
162C2×#102C2314yes—
163C2×#102C2314yes—
164C2×#102C2314yes—
165C2×C22⋊C8C2312yes—
166C2×C22⋊C8C2312yes—
167C4×M16—42no—
168C4×M16—42no—
169C2×#97C2312yes—
170C2×#97C2312yes—
171C2×C4×C8C2311yescharacteristic
172C2×C4×C8C2311yescharacteristic
173C2×C4×C8C2311yescharacteristic
174C2×C4×C8C2312yes—
175C2×C4×C8C2311yescharacteristic
176C2×C4×C8C2312yes—
177#400—22no—
178#398—22no—
179#398—22no—
180#397—22no—
181#397—22no—
182#396—22no—
183#396—22no—
184#396—22no—
185#395—22no—
186#394—22no—
187#394—22no—
188#393—22no—
189#391—21no—
190#391—21no—
191#391—21no—
192#391—21no—
193#391—21no—
194#391—21no—
195#391—21no—
196#391—22no—
197#391—22no—
198#390—21no—
199#390—21no—
200#390—21no—
201#390—21no—
202#390—21no—
203#390—21no—
204#390C2312yes—
205#390C2312yes—
206#390C2312yes—
207#389—21no—
208#389—21no—
209#389—21no—
210#389—21no—
211#389—21no—
212#389—21no—
213#389—21no—
214#389—22no—
215#389C2312yes—
216#389C2312yes—
217#389C2312yes—
218#388—22no—
219#388—22no—
220#388—22no—
221#387—22no—
222#387—22no—
223#386—22no—
224#386—22no—
225#386—22no—
226#385—22no—
227#385—22no—
228#385—22no—
229#384—21no—
230#384—21no—
231#384C2311yescharacteristic
232#384C2311yescharacteristic
233#384C2312yes—
234#384C2311yescharacteristic
235#384C2311yescharacteristic
236#382C2312yes—
237#382C2312yes—
238#382C2312yes—
239#382C2312yes—
240#380—21no—
241#380—21no—
242#380—21no—
243#380—21no—
244#380—22no—
245#380C2312yes—
246#380C2312yes—
247C4×C4⋊C4—21no—
248C4×C4⋊C4—21no—
249C4×C4⋊C4—21no—
250C4×C4⋊C4D411yescharacteristic
251C4×C4⋊C4D411yescharacteristic
252C4×C4⋊C4C2312yes—
253C4×C4⋊C4C2311yescharacteristic
254C4×C22⋊C4—22no—
255C4×C22⋊C4D411yescharacteristic
256C4×C22⋊C4D411yescharacteristic
257C4×C22⋊C4D411yescharacteristic
258C4×C22⋊C4D411yescharacteristic
259C4×C22⋊C4C2311yescharacteristic
260C4×C22⋊C4C2311yescharacteristic
261C43C2311yescharacteristic
262#340C2314yes—
263#340C2314yes—
264#340C2314yes—
265#340C2314yes—
266#340C2314yes—
267#340C2314yes—
268#340C2314yes—
269#340C2314yes—
270#340C2314yes—
271#340C2314yes—
272#340C2314yes—
273#340C2314yes—
274#336C2312yes—
275#336C2312yes—
276#336C2312yes—
277C22×Q8—21no—
278C22×Q8—21no—
279C22×Q8—21no—
280C22×Q8—22no—
281C22×Q8—44no—
282C22×Q8—44no—
283C22×Q8—82no—
284C22×D4—22no—
285C22×D4—22no—
286C22×D4—21no—
287C22×D4—21no—
288C22×D4C2×D411yescharacteristic
289C22×D4C2412yes—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4—22no—
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2411yescharacteristic
298C23×C4C2411yescharacteristic
299C2×M16—24no—
300C2×M16—24no—
301C2×M16—24no—
302C2×M16—24no—
303C2×M16—42no—
304C2×M16—42no—
305C22×C8C2412yes—
306C22×C8C2412yes—
307C22×C8C2412yes—
308C22×C8C2412yes—
309C4⋊Q8—24no—
310C4⋊Q8—22no—
311C4⋊Q8—22no—
312C4⋊Q8—22no—
313C4⋊Q8—22no—
314C4⋊Q8—22no—
315C4⋊Q8—42no—
316C4⋊Q8—44no—
317C4⋊Q8—44no—
318C4⋊Q8#4114yes—
319#127—22no—
320#127—22no—
321#126—48no—
322#125—24no—
323#125—28no—
324#125—42no—
325#123—48no—
326C22⋊Q8—44no—
327C22⋊Q8—44no—
328C22⋊Q8—44no—
329C22⋊Q8—82no—
330#121—28no—
331#121—28no—
332#121—44no—
333#121—44no—
334#121—48no—
335#121—82no—
336#121—82no—
337C4×Q8—44no—
338C4×Q8—44no—
339C4×Q8—82no—
340C4×D4—28no—
341C4×D4—42no—
342C4×D4—42no—
343C4×D4—48no—
344C4×D4—82no—
345C4×D4—82no—
346C4×D4#4118yes—
347#117—28no—
348#117—24no—
349#117—42no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—28no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—42no—
376C2×C4⋊C4—44no—
377C2×C4⋊C4—82no—
378C2×C4⋊C4—82no—
379C2×C4⋊C4C2×D411yescharacteristic
380C2×C4⋊C4C2×D411yescharacteristic
381C2×C4⋊C4C2×D411yescharacteristic
382C2×C4⋊C4C2412yes—
383C2×C4⋊C4C2412yes—
384C2×C4⋊C4C2412yes—
385C2×C4⋊C4C2412yes—
386C2×C4⋊C4C2412yes—
387C2×C4⋊C4C2412yes—
388C2×C4⋊C4C2412yes—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4C2×D411yescharacteristic
403C2×C22⋊C4C2×D411yescharacteristic
404C2×C22⋊C4C2×D411yescharacteristic
405C2×C22⋊C4C2×D411yescharacteristic
406C2×C22⋊C4C2×D411yescharacteristic
407C2×C22⋊C4C2×D411yescharacteristic
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42C2×D411yescharacteristic
416C2×C42C2×D411yescharacteristic
417C2×C42C2×D411yescharacteristic
418C2×C42C2×D411yescharacteristic
419C2×C42C2×D411yescharacteristic
420C2×C42C2×D411yescharacteristic
421C2×C42C2×D411yescharacteristic
422C2×C42C2×D411yescharacteristic
423C2×C42C2411yescharacteristic
424C2×C42C2411yescharacteristic
425C2×C42C2411yescharacteristic
426C2×C42C2411yescharacteristic
427C2×C42C2411yescharacteristic
428C4⋊C8—24no—
429#102—28no—
430#102—28no—
431#102—44no—
432#102—44no—
433C22⋊C8—24no—
434C22⋊C8—24no—
435#97—42no—
436#97—42no—
437C4×C8—24no—
438C4×C8—24no—
439C4×C8—22no—
440C4×C8—22no—
441C4×C8—22no—
442C4×C8—22no—
443#95—22no—
444#95—22no—
445#95—22no—
446#95—22no—
447#95—22no—
448#95—22no—
449#95—22no—
450#95—22no—
451#95—22no—
452#95—22no—
453#95—22no—
454#95—22no—
455#95—22no—
456#95—22no—
457#95C2×D411yescharacteristic
458#95C2×D411yescharacteristic
459#95C2×D411yescharacteristic
460#95C2×D411yescharacteristic
461#95C2×D411yescharacteristic
462#95C2×D411yescharacteristic
463C24—22no—
464C24C22×D411yescharacteristic
465C24C22×D411yescharacteristic
466C2×Q8—24no—
467C2×Q8—44no—
468C2×Q8—44no—
469C2×Q8—42no—
470C2×Q8—42no—
471C2×Q8—42no—
472C2×Q8—42no—
473C2×Q8—42no—
474C2×Q8—42no—
475C2×Q8—42no—
476C2×Q8—42no—
477C2×Q8—82no—
478C2×Q8—816no—
479C2×D4—22no—
480C2×D4—24no—
481C2×D4—22no—
482C2×D4—24no—
483C2×D4—41no—
484C2×D4—41no—
485C2×D4—44no—
486C2×D4—44no—
487C2×D4—44no—
488C2×D4—44no—
489C2×D4—42no—
490C2×D4—42no—
491C2×D4—42no—
492C2×D4—42no—
493C2×D4—42no—
494C2×D4—42no—
495C2×D4—82no—
496C2×D4—82no—
497C2×D4#12414yes—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—44no—
524C22×C4—44no—
525C22×C4—44no—
526C22×C4—44no—
527C22×C4—82no—
528C22×C4—82no—
529C22×C4—82no—
530C22×C4—82no—
531C22×C4—82no—
532C22×C4C22×D411yescharacteristic
533C22×C4C22×D411yescharacteristic
534C22×C4C22×D411yescharacteristic
535C22×C4C22×D411yescharacteristic
536C22×C4C22×D411yescharacteristic
537C22×C4C22×D411yescharacteristic
538C22×C4C22×D411yescharacteristic
539C22×C4C22×D411yescharacteristic
540C22×C4C22×D411yescharacteristic
541C22×C4C22×D411yescharacteristic
542C22×C4C22×D411yescharacteristic
543C22×C4C22×D411yescharacteristic
544C22×C4C2×#4114yes—
545C22×C4C2×#4114yes—
546C22×C4C2511yescharacteristic
547M16—48no—
548M16—48no—
549C2×C8—22no—
550C2×C8—22no—
551C2×C8—22no—
552C2×C8—22no—
553C2×C8—22no—
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—22no—
557C2×C8—22no—
558C2×C8—22no—
559C2×C8—22no—
560C2×C82−1+414yes—
561C4⋊C4—24no—
562C4⋊C4—22no—
563C4⋊C4—24no—
564C4⋊C4—24no—
565C4⋊C4—22no—
566C4⋊C4—24no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—24no—
571C4⋊C4—41no—
572C4⋊C4—41no—
573C4⋊C4—44no—
574C4⋊C4—44no—
575C4⋊C4—44no—
576C4⋊C4—44no—
577C4⋊C4—44no—
578C4⋊C4—44no—
579C4⋊C4—44no—
580C4⋊C4—44no—
581C4⋊C4—42no—
582C4⋊C4—42no—
583C4⋊C4—42no—
584C4⋊C4—42no—
585C4⋊C4—42no—
586C4⋊C4—42no—
587C4⋊C4—42no—
588C4⋊C4—42no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4—82no—
592C4⋊C4—82no—
593C4⋊C4—82no—
594C4⋊C4—82no—
595C4⋊C4#12414yes—
596C4⋊C4C2×#4114yes—
597C22⋊C4—41no—
598C22⋊C4—41no—
599C22⋊C4—41no—
600C22⋊C4—41no—
601C22⋊C4—44no—
602C22⋊C4—44no—
603C22⋊C4—44no—
604C22⋊C4—44no—
605C22⋊C4—44no—
606C22⋊C4—44no—
607C22⋊C4—44no—
608C22⋊C4—44no—
609C22⋊C4—82no—
610C22⋊C4—82no—
611C22⋊C4—82no—
612C22⋊C4—82no—
613C22⋊C4—82no—
614C22⋊C4#12414yes—
615C22⋊C4#12414yes—
616C42—22no—
617C42—22no—
618C42—22no—
619C42—22no—
620C42—22no—
621C42—22no—
622C42—22no—
623C42—22no—
624C42—21no—
625C42—21no—
626C42—21no—
627C42—21no—
628C42—22no—
629C42—44no—
630C42—44no—
631C42—82no—
632C42C2×#4114yes—
633C42C2×#4112yes—
634C42H(5,𝔽2)12yes—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23C2×#12412yes—
655C23C2×#12412yes—
656C23C23×D411yescharacteristic
657Q8—48no—
658Q8—88no—
659Q8—84no—
660Q8—84no—
661D4—44no—
662D4—44no—
663D4—44no—
664D4—88no—
665D4—84no—
666D4—84no—
667D4—164no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—24no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—44no—
702C2×C4—44no—
703C2×C4—44no—
704C2×C4—44no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—88no—
724C2×C4—164no—
725C2×C4—164no—
726C2×C4C2×#12412yes—
727C2×C4C2×#12412yes—
728C2×C4C2×#12412yes—
729C2×C4C2×#12412yes—
730C2×C4#54612yes—
731C2×C4#54612yes—
732C2×C4#57512yes—
733C2×C4#57512yes—
734C2×C4#57612yes—
735C2×C4#57712yes—
736C2×C4C22×#4111yescharacteristic
737C2×C4C22×#4112yes—
738C2×C4C2×H(5,𝔽2)11yescharacteristic
739C2×C4C2×2−1+412yes—
740C8—24no—
741C8—42no—
742C8—42no—
743C8—42no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—82no—
759C22—82no—
760C22—82no—
761C22—82no—
762C22—82no—
763C22—82no—
764C22—82no—
765C22C22×#12411yescharacteristic
766C22C2×#54611yescharacteristic
767C22#349911yescharacteristic
768C22C2×#57511yescharacteristic
769C22C2×#57511yescharacteristic
770C22C2×#57611yescharacteristic
771C22C2×#57711yescharacteristic
772C4—22no—
773C4—22no—
774C4—22no—
775C4—22no—
776C4—41no—
777C4—41no—
778C4—41no—
779C4—41no—
780C4—44no—
781C4—41no—
782C4—41no—
783C4—82no—
784C4—82no—
785C4—82no—
786C4—82no—
787C4—82no—
788C4—82no—
789C4#332214yes—
790C4#332614yes—
791C4#348212yes—
792C4#352012yes—
793C2—42no—
794C2—42no—
795C2—162no—
796C2#3630311yescharacteristic
797C2#6061811yescharacteristic
798C2#6062211yescharacteristic
799C2C2×#332211yescharacteristic
800C2C2×#332611yescharacteristic
801C2#6248111yescharacteristic
802C2#6248311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36182C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #36129C2semidirect
3. #33290C2semidirect
4. #33048C2semidirect
5. #33048C2semidirect
6. #29220C2semidirect
7. #28718C2semidirect
8. #27962C2semidirect
9. #27960C2semidirect
10. #27819C2semidirect
11. #27710C2semidirect
12. #27703C2semidirect
13. #25905C2semidirect
14. #25903C2semidirect
15. #22501C2semidirect
16. C4×#486C2semidirect
17. #21324C2semidirect
18. #21322C2semidirect
19. C4×#436C2semidirect

Maximal subgroups

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

subgroupindex
#361822
#361292
#332902
#330482
#292202
#287182
#279622
#279602
#278192
#277102
#277032
#259052
#259032
#225012
C4×#4862
#213242
#213222
C4×#4362