Finite Group Databasebeta

← #6432549

Subgroups — #6432549

Order 512.

2102 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#533C211yesmaximal, characteristic, complemented
2C2×#2293C211yesmaximal, characteristic
3#23784C214yesmaximal, complemented
4#23781C212yesmaximal, complemented
5#23780C212yesmaximal, complemented
6#23778C214yesmaximal, complemented
7#23775C212yesmaximal, complemented
8#23774C212yesmaximal, complemented
9#23747C211yesmaximal, characteristic, complemented
10#23731C211yesmaximal, characteristic
11#23670C212yesmaximal, complemented
12#23618C212yesmaximal
13#23554C211yesmaximal, characteristic, complemented
14#23454C211yesmaximal, characteristic
15C4×#428C212yesmaximal, complemented
16C4×#423C211yesmaximal, characteristic, complemented
17C4×#418C212yesmaximal
18C2×#533C2211yescharacteristic
19C22×C4×D4C2211yescharacteristic
20C22×#117—21no—
21C2×#428C2212yes—
22C2×#428C2212yes—
23C2×#423C2212yes—
24C2×#418C2212yes—
25C2×#418C2212yes—
26C2×C4×M16C2212yes—
27C4×C4⋊Q8C2211yescharacteristic, complemented
28C4×C4⋊Q8C2211yescharacteristic, complemented
29C4×C4⋊Q8C2211yescharacteristic, complemented
30C4×C4⋊Q8C2211yescharacteristic, complemented
31C4×#125C2212yescomplemented
32C4×#125C2212yescomplemented
33C4×C22⋊Q8—21no—
34C4×C22⋊Q8—21no—
35C4×C22⋊Q8—21no—
36C4×C22⋊Q8—21no—
37#2296C2212yes—
38#2295—21no—
39#2295—21no—
40#2293—21no—
41#2293—21no—
42#2293—21no—
43#2293—21no—
44#2293C2212yes—
45#2293C2212yes—
46#2293C2212yes—
47#2293C2212yes—
48C2×#390C2211yescharacteristic
49C2×#390C2211yescharacteristic
50C2×#389C2211yescharacteristic
51C2×#389C2211yescharacteristic
52C2×#388—21no—
53C2×#388—21no—
54#2285C2211yescharacteristic
55C42×Q8—21no—
56C42×Q8—21no—
57C4×#117C2212yes—
58C2×C4×C4⋊C4C2211yescharacteristic
59C2×C4×C22⋊C4—21no—
60C2×C43C2211yescharacteristic
61#2101C2214yescomplemented
62#2100C2212yescomplemented
63#2099C2212yescomplemented
64#2094C2212yes—
65#2093C2212yes—
66#2092C2214yes—
67#2088C2214yescomplemented
68#2088C2214yescomplemented
69#2087C2214yescomplemented
70#2086C2214yescomplemented
71#2067C2214yes—
72#2067C2214yes—
73#2065C2214yes—
74#2065C2214yes—
75#2059C2214yescomplemented
76#2058C2212yescomplemented
77#2057C2212yescomplemented
78#2025C2214yes—
79#2023C2212yes—
80#2023C2212yes—
81#1776C2214yescomplemented
82#1776C2214yescomplemented
83C4×#107C2214yescomplemented
84C4×#106C2214yescomplemented
85#1767C2212yescomplemented
86#1767C2212yescomplemented
87C4×C4⋊C8C2212yescomplemented
88C4×C4⋊C8C2212yescomplemented
89#1762C2214yes—
90#1762C2214yes—
91C4×#102C2214yes—
92C4×#102C2214yes—
93#1736C2212yes—
94#1736C2212yes—
95#1736C2212yes—
96#1736C2212yes—
97#1728C2211yescharacteristic
98#1728C2211yescharacteristic
99C23×D4C2311yescharacteristic
100C24×C4—21no—
101C22×M16C2312yes—
102C22×M16C2312yes—
103#533—28no—
104C2×C4⋊Q8C2311yescharacteristic
105C2×C4⋊Q8C2311yescharacteristic
106C2×#125C2312yes—
107C2×C22⋊Q8—21no—
108C2×C22⋊Q8—21no—
109C2×C4×Q8—21no—
110C2×C4×Q8—21no—
111C2×C4×Q8—21no—
112C2×C4×Q8—21no—
113C2×C4×Q8—21no—
114C2×C4×Q8—21no—
115C2×C4×D4—21no—
116C2×C4×D4—21no—
117C2×C4×D4—24no—
118C2×C4×D4Q818yescomplemented
119C2×C4×D4C2312yes—
120C2×C4×D4C2312yes—
121C2×#117—22no—
122C2×#117—22no—
123C2×#117—22no—
124C2×#117—22no—
125C2×#117—48no—
126C2×#117C2312yes—
127C2×#117C2312yes—
128C22×C4⋊C4—21no—
129C22×C4⋊C4—21no—
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C22⋊C4—21no—
134C22×C22⋊C4—21no—
135C22×C22⋊C4—21no—
136C22×C22⋊C4—21no—
137C22×C22⋊C4—21no—
138C22×C42—21no—
139C22×C42D411yescharacteristic
140C22×C42D411yescharacteristic
141C22×C42D411yescharacteristic
142C22×C42D411yescharacteristic
143C22×C42C2311yescharacteristic
144C22×C42C2311yescharacteristic
145C22×C42C2311yescharacteristic
146#428—28no—
147#428—28no—
148C2×#107C2314yes—
149C2×#107C2314yes—
150C2×#106C2314yes—
151C2×#106C2314yes—
152#423—28no—
153C2×C4⋊C8C2314yes—
154C2×C4⋊C8C2314yes—
155#418—28no—
156#418—28no—
157C2×#102C2314yes—
158C2×#102C2314yes—
159C2×#102C2314yes—
160C2×#102C2314yes—
161C4×M16—28no—
162C2×#97C2314yes—
163C2×C4×C8C2314yes—
164#391—21no—
165#391—21no—
166#391—21no—
167#391—21no—
168#390—21no—
169#390—21no—
170#390—21no—
171#390—21no—
172#390C2312yes—
173#390C2312yes—
174#390C2312yes—
175#390C2312yes—
176#389—21no—
177#389—21no—
178#389—21no—
179#389—21no—
180#389—21no—
181#389—21no—
182#389—21no—
183#389—21no—
184#389C2312yes—
185#389C2312yes—
186#389C2312yes—
187#389C2312yes—
188#389C2312yes—
189#389C2312yes—
190#389C2312yes—
191#389C2312yes—
192#388—22no—
193#388—22no—
194#388—22no—
195#388—22no—
196#388—22no—
197#388—22no—
198#388—22no—
199#388—22no—
200#387—22no—
201#387—22no—
202#387—22no—
203#387—22no—
204#385—22no—
205#385—22no—
206#384C2311yescharacteristic
207#384C2311yescharacteristic
208#382C2312yes—
209#380—21no—
210#380—21no—
211C4×C4⋊C4—22no—
212C4×C4⋊C4—22no—
213C4×C4⋊C4—22no—
214C4×C4⋊C4—22no—
215C4×C4⋊C4—21no—
216C4×C4⋊C4—21no—
217C4×C4⋊C4—21no—
218C4×C4⋊C4—21no—
219C4×C4⋊C4—21no—
220C4×C4⋊C4—21no—
221C4×C4⋊C4—21no—
222C4×C4⋊C4—21no—
223C4×C4⋊C4—22no—
224C4×C4⋊C4—22no—
225C4×C4⋊C4C2312yes—
226C4×C4⋊C4C2312yes—
227C4×C4⋊C4C2312yes—
228C4×C4⋊C4C2312yes—
229C4×C4⋊C4C2312yes—
230C4×C4⋊C4C2312yes—
231C4×C22⋊C4—22no—
232C4×C22⋊C4—22no—
233C4×C22⋊C4—22no—
234C4×C22⋊C4—22no—
235C4×C22⋊C4—22no—
236C4×C22⋊C4—22no—
237#376—22no—
238C2×#95—21no—
239C2×#95—21no—
240C2×#95—21no—
241C43—22no—
242C43D411yescharacteristic
243C43D411yescharacteristic
244C43D411yescharacteristic
245C43D411yescharacteristic
246C43C2311yescharacteristic
247C43C2311yescharacteristic
248C43C2311yescharacteristic
249C43C2311yescharacteristic
250#340C2314yes—
251#340C2314yes—
252#340C2314yes—
253#340C2314yes—
254#340C2314yes—
255#340C2314yes—
256#340C2314yes—
257#340C2314yes—
258#336C2312yes—
259#336C2312yes—
260#336C2312yes—
261#336C2312yes—
262C25—21no—
263C22×Q8—21no—
264C22×Q8—21no—
265C22×D4—21no—
266C22×D4—24no—
267C22×D4—24no—
268C22×D4—22no—
269C22×D4C2×Q814yes—
270C22×D4C2412yes—
271C23×C4—21no—
272C23×C4—28no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—21no—
276C23×C4—21no—
277C23×C4—44no—
278C23×C4—44no—
279C23×C4C2×D411yescharacteristic
280C23×C4C2×D411yescharacteristic
281C23×C4C2×D411yescharacteristic
282C23×C4C2×D411yescharacteristic
283C23×C4C2×D411yescharacteristic
284C23×C4C2×D411yescharacteristic
285C23×C4C2411yescharacteristic
286C2×M16—24no—
287C2×M16—24no—
288C2×M16—24no—
289C2×M16—24no—
290C2×M16—24no—
291C2×M16#4118yes—
292C22×C8C2414yes—
293C22×C8C2414yes—
294C4⋊Q8—24no—
295C4⋊Q8—24no—
296#125—24no—
297#125—24no—
298C22⋊Q8—28no—
299C22⋊Q8—28no—
300C4×Q8—28no—
301C4×Q8—28no—
302C4×Q8—44no—
303C4×Q8—44no—
304C4×Q8—44no—
305C4×Q8—44no—
306C4×D4—28no—
307C4×D4—28no—
308C4×D4—24no—
309C4×D4—24no—
310C4×D4C2×Q818yes—
311C4×D4C2×Q818yes—
312#117—24no—
313#117—24no—
314#117—24no—
315#117—48no—
316#117—48no—
317#117—48no—
318#117—48no—
319#117#4118yes—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—44no—
343C2×C4⋊C4—44no—
344C2×C4⋊C4C2×Q814yes—
345C2×C4⋊C4C2412yes—
346C2×C4⋊C4C2412yes—
347C2×C4⋊C4C2412yes—
348C2×C4⋊C4C2412yes—
349C2×C4⋊C4C2412yes—
350C2×C4⋊C4C2412yes—
351C2×C4⋊C4C2412yes—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—28no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—44no—
366C2×C22⋊C4—44no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—44no—
369C2×C42—22no—
370C2×C42—24no—
371C2×C42—24no—
372C2×C42—24no—
373C2×C42—22no—
374C2×C42—22no—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42—22no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—42no—
381C2×C42—42no—
382C2×C42—42no—
383C2×C42—44no—
384C2×C42C2×D411yescharacteristic
385C2×C42C2×D411yescharacteristic
386C2×C42C2×D411yescharacteristic
387C2×C42C2×D411yescharacteristic
388C2×C42C2×D411yescharacteristic
389C2×C42C2×D411yescharacteristic
390C2×C42C2×D411yescharacteristic
391C2×C42C2×D411yescharacteristic
392C2×C42C2×D411yescharacteristic
393C2×C42C2×D411yescharacteristic
394C2×C42C2×D411yescharacteristic
395C2×C42C2×D411yescharacteristic
396C2×C42C2×D411yescharacteristic
397C2×C42C2×D411yescharacteristic
398C2×C42C2×D411yescharacteristic
399C2×C42C2×D411yescharacteristic
400C2×C42C2×D411yescharacteristic
401C2×C42C2×D411yescharacteristic
402C2×C42C2×D411yescharacteristic
403C2×C42C2×D411yescharacteristic
404C2×C42C2×D411yescharacteristic
405C2×C42C2×D411yescharacteristic
406C2×C42C2×Q814yes—
407C2×C42#4114yes—
408C2×C42C2411yescharacteristic
409C2×C42C2411yescharacteristic
410C2×C42C2411yescharacteristic
411C2×C42C2411yescharacteristic
412C2×C42C2411yescharacteristic
413C2×C42C2411yescharacteristic
414#107—28no—
415#107—28no—
416#106—28no—
417#106—28no—
418C4⋊C8—28no—
419C4⋊C8—28no—
420#102—28no—
421#102—28no—
422#102—28no—
423#102—28no—
424#97—28no—
425C4×C8—28no—
426#95—22no—
427#95—22no—
428#95—22no—
429#95—22no—
430#95—22no—
431#95—22no—
432#95—22no—
433#95—22no—
434#95—22no—
435#95—22no—
436#95—22no—
437#95—22no—
438#95—22no—
439#95—22no—
440#95—22no—
441#95—22no—
442C24—24no—
443C24—22no—
444C24—42no—
445C24—42no—
446C24—42no—
447C24—42no—
448C24—42no—
449C24—42no—
450C24C22×D411yescharacteristic
451C2×Q8—24no—
452C2×Q8—24no—
453C2×Q8—42no—
454C2×Q8—42no—
455C2×Q8—42no—
456C2×Q8—42no—
457C2×D4—24no—
458C2×D4—216no—
459C2×D4—24no—
460C2×D4—24no—
461C2×D4—22no—
462C2×D4—42no—
463C2×D4—48no—
464C2×D4—42no—
465C2×D4C22×Q814yes—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—24no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—28no—
477C22×C4—28no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—44no—
493C22×C4—44no—
494C22×C4—432no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—44no—
498C22×C4—44no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4C22⋊Q814yes—
506C22×C4C22⋊Q814yes—
507C22×C4C22×D411yescharacteristic
508C22×C4C22×D411yescharacteristic
509C22×C4C22×D411yescharacteristic
510C22×C4C22×D411yescharacteristic
511C22×C4C22×D411yescharacteristic
512C22×C4C22×D411yescharacteristic
513C22×C4C22×D411yescharacteristic
514C22×C4C22×D411yescharacteristic
515C22×C4C22×D411yescharacteristic
516C22×C4C22×D411yescharacteristic
517C22×C4C22×D411yescharacteristic
518C22×C4C22×D411yescharacteristic
519C22×C4C22×D411yescharacteristic
520C22×C4C22×Q812yes—
521C22×C4C2×#4112yes—
522C22×C4C2×#4114yes—
523C22×C4C2×#4114yes—
524C22×C4C2511yescharacteristic
525M16—216no—
526M16—48no—
527C2×C8—24no—
528C2×C8—24no—
529C2×C8—24no—
530C2×C8—24no—
531C2×C8—24no—
532C2×C8C2×#4118yes—
533C4⋊C4—28no—
534C4⋊C4—28no—
535C4⋊C4—24no—
536C4⋊C4—24no—
537C4⋊C4—24no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—22no—
542C4⋊C4—22no—
543C4⋊C4—22no—
544C4⋊C4—24no—
545C4⋊C4—24no—
546C4⋊C4—22no—
547C4⋊C4—44no—
548C4⋊C4—44no—
549C4⋊C4—42no—
550C4⋊C4—42no—
551C4⋊C4—44no—
552C4⋊C4—44no—
553C4⋊C4—42no—
554C4⋊C4—42no—
555C4⋊C4—44no—
556C4⋊C4—44no—
557C4⋊C4—44no—
558C4⋊C4—42no—
559C4⋊C4—44no—
560C4⋊C4—42no—
561C4⋊C4C22×Q814yes—
562C4⋊C4C2×#4114yes—
563C4⋊C4C2×#4114yes—
564C22⋊C4—28no—
565C22⋊C4—28no—
566C22⋊C4—28no—
567C22⋊C4—44no—
568C22⋊C4—44no—
569C22⋊C4—44no—
570C22⋊C4—44no—
571C22⋊C4—44no—
572C22⋊C4—44no—
573C22⋊C4—44no—
574C22⋊C4—44no—
575C22⋊C4—44no—
576C42—22no—
577C42—22no—
578C42—28no—
579C42—22no—
580C42—22no—
581C42—22no—
582C42—22no—
583C42—22no—
584C42—22no—
585C42—22no—
586C42—22no—
587C42—22no—
588C42—22no—
589C42—22no—
590C42—22no—
591C42—22no—
592C42—22no—
593C42—22no—
594C42—41no—
595C42—41no—
596C42—41no—
597C42—41no—
598C42—41no—
599C42—41no—
600C42—44no—
601C42—44no—
602C42—44no—
603C42—44no—
604C42—44no—
605C42—44no—
606C42—44no—
607C42C22⋊Q814yes—
608C42C22⋊Q814yes—
609C42AGL(1,ℤ/8)14yes—
610C42C22×Q812yes—
611C42C22×Q812yes—
612C42C2×#4112yes—
613C42C2×#4112yes—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—24no—
619C23—48no—
620C23—48no—
621C23—48no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—84no—
629C23—84no—
630C23—84no—
631C23—84no—
632C23C2×C22⋊Q812yes—
633C23#52512yes—
634C23#53212yes—
635C23C23×D411yescharacteristic
636Q8—48no—
637Q8—48no—
638D4—28no—
639D4—48no—
640D4—44no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—28no—
656C2×C4—24no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—44no—
672C2×C4—44no—
673C2×C4—44no—
674C2×C4—44no—
675C2×C4—44no—
676C2×C4—416no—
677C2×C4—48no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—416no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—84no—
698C2×C4—84no—
699C2×C4C2×C22⋊Q812yes—
700C2×C4C2×C22⋊Q812yes—
701C2×C4C2×C22⋊Q812yes—
702C2×C4C2×C22⋊Q812yes—
703C2×C4C2×C22⋊Q812yes—
704C2×C4#52512yes—
705C2×C4#52918yes—
706C2×C4#53212yes—
707C2×C4#53318yes—
708C2×C4C2×AGL(1,ℤ/8)12yes—
709C2×C4C2×AGL(1,ℤ/8)12yes—
710C2×C4C2×AGL(1,ℤ/8)12yes—
711C2×C4#57512yes—
712C2×C4#57512yes—
713C2×C4#57512yes—
714C2×C4C23×Q811yescharacteristic
715C2×C4C22×#4111yescharacteristic
716C2×C4C22×#4112yes—
717C2×C4C22×#4112yes—
718C8—28no—
719C8—44no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—44no—
727C22—44no—
728C22—44no—
729C22—816no—
730C22—82no—
731C22—82no—
732C22—82no—
733C22—82no—
734C22#239614yes—
735C22C22×C22⋊Q811yescharacteristic
736C22C2×#52511yescharacteristic
737C22C2×#53211yescharacteristic
738C22C22×AGL(1,ℤ/8)11yescharacteristic
739C22C2×#57511yescharacteristic
740C22C2×#57511yescharacteristic
741C22C2×#57511yescharacteristic
742C4—22no—
743C4—22no—
744C4—22no—
745C4—22no—
746C4—22no—
747C4—22no—
748C4—22no—
749C4—41no—
750C4—41no—
751C4—44no—
752C4—41no—
753C4—44no—
754C4—41no—
755C4—44no—
756C4—82no—
757C4—82no—
758C4—82no—
759C4—82no—
760C4#239614yes—
761C4#307714yes—
762C4C2×#52912yes—
763C4C2×#53312yes—
764C2—24no—
765C2—84no—
766C2C2×#239611yescharacteristic
767C2C2×#307711yescharacteristic
768C2#6048411yescharacteristic
769C2#6056111yescharacteristic
770C2#6056311yescharacteristic
771C2#6070011yescharacteristic
772C2#6070211yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutator, Frattini, cosocleC22×C4C25
socleC23C23×D4
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C2×C43 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C4×#533C2semidirect
3. #23784C2semidirect
4. #23781C2semidirect
5. #23780C2semidirect
6. #23778C2semidirect
7. #23775C2semidirect
8. #23774C2semidirect
9. #23747C2semidirect
11. #23670C2semidirect
13. #23554C2semidirect
15. C4×#428C2semidirect
16. C4×#423C2semidirect
27. C4×C4⋊Q8C22semidirect
28. C4×C4⋊Q8C22semidirect
29. C4×C4⋊Q8C22semidirect
30. C4×C4⋊Q8C22semidirect
31. C4×#125C22semidirect
32. C4×#125C22semidirect
61. #2101C22semidirect
62. #2100C22semidirect
63. #2099C22semidirect
67. #2088C22semidirect
68. #2088C22semidirect
69. #2087C22semidirect
70. #2086C22semidirect
75. #2059C22semidirect
76. #2058C22semidirect
77. #2057C22semidirect
81. #1776C22semidirect
82. #1776C22semidirect
83. C4×#107C22semidirect
84. C4×#106C22semidirect
85. #1767C22semidirect
86. #1767C22semidirect
87. C4×C4⋊C8C22semidirect
88. C4×C4⋊C8C22semidirect
118. C2×C4×D4Q8semidirect

Maximal subgroups

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

subgroupindex
C4×#5332
C2×#22932
#237842
#237812
#237802
#237782
#237752
#237742
#237472
#237312
#236702
#236182
#235542
#234542
C4×#4282
C4×#4232
C4×#4182