Finite Group Databasebeta

← #363123

Subgroups — #363123

Order 512.

1260 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#446C211yesmaximal, characteristic
2C2×#1949C211yesmaximal, characteristic
3C2×#1947C211yesmaximal, characteristic
4#13926C211yesmaximal, characteristic
5#13925C211yesmaximal, characteristic
6#11232C211yesmaximal, characteristic
7#11232C211yesmaximal, characteristic
8#11232C211yesmaximal, characteristic
9#11231C211yesmaximal, characteristic
10#10863C211yesmaximal, characteristic
11#10862C211yesmaximal, characteristic
12#10843C211yesmaximal, characteristic
13#10821C211yesmaximal, characteristic
14#10820C211yesmaximal, characteristic
15#10703C211yesmaximal, characteristic
16C22×C4×Q8C2211yescharacteristic
17C2×#446—24no—
18C2×#446—24no—
19C2×#446C418yescomplemented
20C22×#107C2211yescharacteristic
21C22×#107C2211yescharacteristic
22C22×#107C2211yescharacteristic
23C22×#106C2211yescharacteristic
24C22×C4⋊C8C2211yescharacteristic
25C22×C4⋊C8C2211yescharacteristic
26C22×C4⋊C8C2211yescharacteristic
27C22×#97C2211yescharacteristic
28C22×#97C2211yescharacteristic
29C22×C4×C8C2211yescharacteristic
30C2×#391—21no—
31C2×#384C2211yescharacteristic
32C2×#382C2211yescharacteristic
33C2×C4×C4⋊C4C2211yescharacteristic
34C2×C4×C4⋊C4C2211yescharacteristic
35#1949—24no—
36#1947—24no—
37C2×#340C2211yescharacteristic
38C2×#340C2211yescharacteristic
39C2×#340C2211yescharacteristic
40C2×#340C2211yescharacteristic
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49#1446—21no—
50#1445—21no—
51#1441—21no—
52#1441—21no—
53#1436—21no—
54#1436—21no—
55C4⋊#95—21no—
56C4⋊#95C2211yescharacteristic
57C4⋊#95C2211yescharacteristic
58C4⋊#95C2211yescharacteristic
59C4⋊#95C2211yescharacteristic
60C4⋊#95C2211yescharacteristic
61C4⋊#95C2211yescharacteristic
62C4⋊#95C2211yescharacteristic
63C4⋊#95C2211yescharacteristic
64C23×Q8D411yescharacteristic
65C23×C8C2311yescharacteristic
66C23×C8C2311yescharacteristic
67C23×C8C2311yescharacteristic
68C23×C8C2311yescharacteristic
69C2×C4×Q8—22no—
70C2×C4×Q8—22no—
71C2×C4×Q8—22no—
72C2×C4×Q8—22no—
73C2×C4×Q8C2×C414yes—
74C2×C4×Q8Q814yes—
75C22×C4⋊C4—21no—
76C22×C4⋊C4—21no—
77C22×C4⋊C4D411yescharacteristic
78C22×C4⋊C4D411yescharacteristic
79C22×C4⋊C4D411yescharacteristic
80C22×C4⋊C4C2311yescharacteristic
81C22×C4⋊C4C2311yescharacteristic
82C22×C4⋊C4C2311yescharacteristic
83C22×C4⋊C4C2311yescharacteristic
84C22×C4⋊C4C2311yescharacteristic
85C22×C4⋊C4C2311yescharacteristic
86C22×C4⋊C4C2311yescharacteristic
87C22×C4⋊C4C2311yescharacteristic
88C22×C42—21no—
89C22×C42—21no—
90C22×C42C2311yescharacteristic
91C22×C42C2311yescharacteristic
92C22×C42C2311yescharacteristic
93#446—232no—
94C2×#107—22no—
95C2×#107—22no—
96C2×#107—22no—
97C2×#107—22no—
98C2×#107—22no—
99C2×#107—22no—
100C2×#107—41no—
101C2×#107—41no—
102C2×#107—41no—
103C2×#106—22no—
104C2×#106—22no—
105C2×#106—41no—
106C2×C4⋊C8—22no—
107C2×C4⋊C8—22no—
108C2×C4⋊C8—22no—
109C2×C4⋊C8—22no—
110C2×C4⋊C8C2×C414yes—
111C2×C4⋊C8C2×C414yes—
112C2×C4⋊C8C2×C414yes—
113C2×C4⋊C8D414yes—
114C2×C4⋊C8D414yes—
115C2×#97—22no—
116C2×#97—22no—
117C2×#97—22no—
118C2×#97—22no—
119C2×#97C2×C414yes—
120C2×#97C2×C414yes—
121C2×C4×C8—22no—
122C2×C4×C8—22no—
123C2×C4×C8C2×C414yes—
124#391—44no—
125#384—22no—
126#384—22no—
127#382—22no—
128#382—22no—
129C4×C4⋊C4—22no—
130C4×C4⋊C4—22no—
131C4×C4⋊C4—22no—
132C4×C4⋊C4—22no—
133C2×#95—21no—
134C2×#95—21no—
135C2×#95—21no—
136C2×#95—21no—
137C2×#95—21no—
138C2×#95—21no—
139C2×#95—21no—
140C2×#95—21no—
141C2×#95—21no—
142C2×#95—21no—
143C2×#95—21no—
144C2×#95—21no—
145C2×#95—21no—
146C2×#95—21no—
147C2×#95—21no—
148C2×#95—21no—
149C2×#95—21no—
150C2×#95—21no—
151C2×#95—21no—
152C2×#95—21no—
153#340—22no—
154#340—22no—
155#340—22no—
156#340—22no—
157#340—22no—
158#340—22no—
159#340—22no—
160#340—22no—
161#340—22no—
162#340—41no—
163#340—41no—
164#340Q814yescomplemented
165C22×Q8—22no—
166C22×Q8—22no—
167C22×Q8—22no—
168C22×Q8—22no—
169C22×Q8—41no—
170C22×Q8—41no—
171C22×Q8C4⋊C414yes—
172C23×C4—21no—
173C23×C4—21no—
174C23×C4—21no—
175C23×C4—21no—
176C23×C4—21no—
177C23×C4—21no—
178C23×C4—21no—
179C23×C4—21no—
180C23×C4C2×D411yescharacteristic
181C23×C4C2×D411yescharacteristic
182C23×C4C2×D411yescharacteristic
183C23×C4C2×D411yescharacteristic
184C23×C4C2×D411yescharacteristic
185C23×C4C2×D411yescharacteristic
186C23×C4C2411yescharacteristic
187C22×C8—21no—
188C22×C8—21no—
189C22×C8—21no—
190C22×C8—21no—
191C22×C8—21no—
192C22×C8—21no—
193C22×C8—21no—
194C22×C8—21no—
195C22×C8—21no—
196C22×C8—21no—
197C22×C8—21no—
198C22×C8—21no—
199C22×C8—21no—
200C22×C8—21no—
201C22×C8—21no—
202C22×C8—21no—
203C22×C8—21no—
204C22×C8—21no—
205C22×C8C22×C412yes—
206C22×C8C22×C412yes—
207C22×C8C22×C412yes—
208C22×C8C22×C412yes—
209C22×C8C2×D412yes—
210C22×C8C2×D412yes—
211C22×C8C2×D412yes—
212C22×C8C2×D412yes—
213C22×C8C2×Q812yes—
214C22×C8#4112yes—
215C4×Q8—28no—
216C4×Q8—28no—
217C4×Q8—28no—
218C4×Q8—28no—
219C2×C4⋊C4—22no—
220C2×C4⋊C4—22no—
221C2×C4⋊C4—22no—
222C2×C4⋊C4—22no—
223C2×C4⋊C4—22no—
224C2×C4⋊C4—22no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—42no—
270C2×C4⋊C4—42no—
271C2×C4⋊C4—42no—
272C2×C4⋊C4—42no—
273C2×C4⋊C4—81no—
274C2×C4⋊C4—81no—
275C2×C4⋊C4C4⋊C414yes—
276C2×C4⋊C4C4⋊C414yes—
277C2×C4⋊C4C4⋊C414yes—
278C2×C4⋊C4C2×Q812yes—
279C2×C4⋊C4C2×Q812yes—
280C2×C4⋊C4#4112yes—
281C2×C4⋊C4#4112yes—
282C2×C42—21no—
283C2×C42—21no—
284C2×C42—21no—
285C2×C42—21no—
286C2×C42—21no—
287C2×C42—21no—
288C2×C42—21no—
289C2×C42—21no—
290C2×C42—42no—
291C2×C42—42no—
292C2×C42—42no—
293C2×C42—42no—
294C2×C42—81no—
295C2×C42—81no—
296C2×C42C22×C412yes—
297C2×C42C22×C412yes—
298C2×C42C22×C412yes—
299C2×C42C2×D412yes—
300C2×C42C2×D412yes—
301C2×C42C2×Q812yes—
302C2×C42C2×Q812yes—
303C2×C42C2×Q812yes—
304C2×C42#4112yes—
305C2×C42#4112yes—
306#107—44no—
307#107—44no—
308#107—44no—
309#106—44no—
310C4⋊C8—28no—
311C4⋊C8—28no—
312C4⋊C8C22⋊C4116yes—
313#97—28no—
314#97—28no—
315C4×C8—28no—
316#95—42no—
317#95—42no—
318#95—42no—
319#95—42no—
320#95—42no—
321#95—42no—
322#95—42no—
323#95—42no—
324#95—42no—
325#95—42no—
326#95—42no—
327#95—42no—
328#95—81no—
329#95—81no—
330#95—81no—
331#95—81no—
332#95—81no—
333#95—81no—
334#95—81no—
335#95—81no—
336C24C22×D411yescharacteristic
337C2×Q8—28no—
338C2×Q8—28no—
339C2×Q8—44no—
340C2×Q8—44no—
341C2×Q8—44no—
342C2×Q8—44no—
343C2×Q8—44no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4—41no—
385C22×C4—41no—
386C22×C4—41no—
387C22×C4—41no—
388C22×C4—41no—
389C22×C4—41no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4—41no—
393C22×C4—41no—
394C22×C4—41no—
395C22×C4—41no—
396C22×C4—41no—
397C22×C4—41no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4—41no—
402C22×C4—41no—
403C22×C4—41no—
404C22×C4—41no—
405C22×C4—41no—
406C22×C4—41no—
407C22×C4—41no—
408C22×C4—41no—
409C22×C4—41no—
410C22×C4—41no—
411C22×C4—41no—
412C22×C4—41no—
413C22×C4—41no—
414C22×C4—41no—
415C22×C4—41no—
416C22×C4—41no—
417C22×C4—41no—
418C22×C4—41no—
419C22×C4—41no—
420C22×C4—41no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4C2×C4⋊C412yes—
431C22×C4C2×C4⋊C412yes—
432C22×C4C2×C4⋊C412yes—
433C22×C4C2×C4⋊C412yes—
434C22×C4C2×C4⋊C412yes—
435C22×C4C2×C4⋊C412yes—
436C22×C4#12112yes—
437C22×C4#12112yes—
438C22×C4#12112yes—
439C22×C4#12112yes—
440C22×C4AGL(1,ℤ/8)12yes—
441C22×C4#13712yes—
442C22×C4C23×C411yescharacteristic
443C22×C4C22×D411yescharacteristic
444C22×C4C22×D411yescharacteristic
445C22×C4C22×Q811yescharacteristic
446C22×C4C22×Q811yescharacteristic
447C22×C4C2×#4111yescharacteristic
448C22×C4C2×#4111yescharacteristic
449C22×C4C2×#4111yescharacteristic
450C22×C4C2×#4111yescharacteristic
451C22×C4C2×#4111yescharacteristic
452C22×C4H(5,𝔽2)11yescharacteristic
453C22×C42−1+411yescharacteristic
454C22×C42−1+411yescharacteristic
455C22×C42−1+411yescharacteristic
456C2×C8—22no—
457C2×C8—22no—
458C2×C8—22no—
459C2×C8—22no—
460C2×C8—22no—
461C2×C8—22no—
462C2×C8—22no—
463C2×C8—22no—
464C2×C8—22no—
465C2×C8—22no—
466C2×C8—22no—
467C2×C8—22no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—41no—
478C2×C8—41no—
479C2×C8—41no—
480C2×C8—41no—
481C2×C8C2×C22⋊C414yes—
482C2×C8C2×C22⋊C414yes—
483C2×C8C4×Q814yes—
484C4⋊C4—28no—
485C4⋊C4—28no—
486C4⋊C4—28no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—41no—
496C4⋊C4—41no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C4⋊C4—41no—
500C4⋊C4—41no—
501C4⋊C4—41no—
502C4⋊C4—41no—
503C4⋊C4—41no—
504C4⋊C4—41no—
505C4⋊C4—41no—
506C4⋊C4—41no—
507C4⋊C4—41no—
508C4⋊C4—41no—
509C4⋊C4—41no—
510C4⋊C4—41no—
511C4⋊C4—41no—
512C4⋊C4—41no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4—41no—
516C4⋊C4—41no—
517C4⋊C4—41no—
518C4⋊C4—41no—
519C4⋊C4—84no—
520C4⋊C4—84no—
521C42—22no—
522C42—22no—
523C42—22no—
524C42—22no—
525C42—22no—
526C42—22no—
527C42—22no—
528C42—22no—
529C42—84no—
530C42—84no—
531C42C2×C22⋊C414yes—
532C42#11714yes—
533C42C22⋊Q814yes—
534C42C22⋊Q814yes—
535C23C22×C4⋊C411yescharacteristic
536C23C2×#12111yescharacteristic
537C23C2×#12111yescharacteristic
538C23#54811yescharacteristic
539C23#54811yescharacteristic
540C23D4×Q811yescharacteristic
541C23#55011yescharacteristic
542C23C2×AGL(1,ℤ/8)11yescharacteristic
543C23C2×#13711yescharacteristic
544C23#57511yescharacteristic
545C23#57511yescharacteristic
546C23#57611yescharacteristic
547C23#57611yescharacteristic
548C23#57811yescharacteristic
549C23#57811yescharacteristic
550Q8—416no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—81no—
603C2×C4—81no—
604C2×C4—81no—
605C2×C4—81no—
606C2×C4—81no—
607C2×C4—81no—
608C2×C4—81no—
609C2×C4—81no—
610C2×C4—81no—
611C2×C4—81no—
612C2×C4—81no—
613C2×C4—81no—
614C2×C4—81no—
615C2×C4—81no—
616C2×C4—81no—
617C2×C4—81no—
618C2×C4—81no—
619C2×C4—81no—
620C2×C4—81no—
621C2×C4—81no—
622C2×C4—81no—
623C2×C4—81no—
624C2×C4—81no—
625C2×C4—81no—
626C2×C4—81no—
627C2×C4—81no—
628C2×C4—81no—
629C2×C4—81no—
630C2×C4—81no—
631C2×C4—81no—
632C2×C4—81no—
633C2×C4—81no—
634C2×C4—81no—
635C2×C4—81no—
636C2×C4—81no—
637C2×C4—81no—
638C2×C4—81no—
639C2×C4—81no—
640C2×C4—81no—
641C2×C4—81no—
642C2×C4—81no—
643C2×C4—81no—
644C2×C4—81no—
645C2×C4—81no—
646C2×C4#38014yes—
647C2×C4#38014yes—
648C2×C4#42814yes—
649C2×C4C22×C22⋊C411yescharacteristic
650C2×C4C2×#11711yescharacteristic
651C2×C4C2×C4×Q811yescharacteristic
652C2×C4C4×#4111yescharacteristic
653C2×C4#51911yescharacteristic
654C2×C4#52011yescharacteristic
655C2×C4C2×C22⋊Q811yescharacteristic
656C2×C4C2×C22⋊Q811yescharacteristic
657C2×C4#52911yescharacteristic
658C2×C4#52911yescharacteristic
659C2×C4#53311yescharacteristic
660C2×C4#53311yescharacteristic
661C2×C4#54111yescharacteristic
662C2×C4#54111yescharacteristic
663C2×C4#54211yescharacteristic
664C2×C4#54211yescharacteristic
665C2×C4#54611yescharacteristic
666C2×C4#54611yescharacteristic
667C2×C4#54711yescharacteristic
668C2×C4#54711yescharacteristic
669C2×C4#54811yescharacteristic
670C2×C4#54811yescharacteristic
671C2×C4D4×Q811yescharacteristic
672C2×C4D4×Q811yescharacteristic
673C2×C4#55711yescharacteristic
674C2×C4#55711yescharacteristic
675C2×C4#55711yescharacteristic
676C2×C4Q8211yescharacteristic
677C8—24no—
678C8—24no—
679C8—24no—
680C8—42no—
681C22C2×#38011yescharacteristic
682C22Q8×C4⋊C411yescharacteristic
683C22#235111yescharacteristic
684C22#242611yescharacteristic
685C22#242611yescharacteristic
686C22#242911yescharacteristic
687C22#242911yescharacteristic
688C22C2×#42811yescharacteristic
689C22#291111yescharacteristic
690C22#291311yescharacteristic
691C22#291311yescharacteristic
692C22#305511yescharacteristic
693C22#305511yescharacteristic
694C22#305611yescharacteristic
695C22#305611yescharacteristic
696C22#305811yescharacteristic
697C22#305911yescharacteristic
698C22#306111yescharacteristic
699C22#306111yescharacteristic
700C22#336611yescharacteristic
701C22#336711yescharacteristic
702C22#337011yescharacteristic
703C22#337011yescharacteristic
704C22#337411yescharacteristic
705C22#337511yescharacteristic
706C22#337711yescharacteristic
707C22#337711yescharacteristic
708C22#338511yescharacteristic
709C22#338611yescharacteristic
710C22#338911yescharacteristic
711C22#339011yescharacteristic
712C22#339811yescharacteristic
713C22#339911yescharacteristic
714C22#340211yescharacteristic
715C22#340311yescharacteristic
716C4—24no—
717C4—24no—
718C4—24no—
719C4—42no—
720C4—42no—
721C4—42no—
722C4—82no—
723C4—82no—
724C4—82no—
725C4—82no—
726C4—161no—
727C4—161no—
728C4—161no—
729C4—161no—
730C4#229511yescharacteristic
731C4#232011yescharacteristic
732C4#233911yescharacteristic
733C4Q8×C22⋊C411yescharacteristic
734C4#245111yescharacteristic
735C4#245111yescharacteristic
736C4#245311yescharacteristic
737C4#245311yescharacteristic
738C2#1393511yescharacteristic
739C2#2066111yescharacteristic
740C2#2066311yescharacteristic
741C2#2272811yescharacteristic
742C2#2273111yescharacteristic
743C2#2274311yescharacteristic
744C2#2274411yescharacteristic
745C2#2530411yescharacteristic
746C2#2530511yescharacteristic
747C2#2530611yescharacteristic
748C2#2530711yescharacteristic
749C2#2548111yescharacteristic
750C2#2548211yescharacteristic
751C2#2548311yescharacteristic
752C2#2548411yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×C4×Q8 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
19. C2×#446C4semidirect
164. #340Q8semidirect

Maximal subgroups

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

subgroupindex
C22×#4462
C2×#19492
C2×#19472
#139262
#139252
#112322
#112312
#108632
#108622
#108432
#108212
#108202
#107032