Finite Group Databasebeta

← #356198

Subgroups — #356198

Order 512.

1996 conjugacy classes of subgroups.

The subgroup lattice has 917 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C4⋊C4C211yesmaximal, characteristic
2C2×#1804C211yesmaximal, characteristic
3C2×#1771C211yesmaximal, characteristic, complemented
4C2×#1762C211yesmaximal, characteristic
5C2×#1762C211yesmaximal, characteristic
6C2×C4×#102C211yesmaximal, characteristic
7#13804C211yesmaximal, characteristic, complemented
8#10885C211yesmaximal, characteristic, complemented
9#10884C211yesmaximal, characteristic, complemented
10#10881C211yesmaximal, characteristic, complemented
11#10880C211yesmaximal, characteristic, complemented
12#10849C211yesmaximal, characteristic, complemented
13#10843C211yesmaximal, characteristic, complemented
14#10788C211yesmaximal, characteristic
15#10788C211yesmaximal, characteristic
16C22×C4×D4C2211yescharacteristic
17C22×C4×D4C2211yescharacteristic
18C22×C4×D4C2211yescharacteristic
19C23×C4⋊C4—21no—
20C22×C4⋊C8C2211yescharacteristic
21C22×#102C2211yescharacteristic
22C22×#102C2211yescharacteristic
23C22×#102C2211yescharacteristic
24C22×#102C2211yescharacteristic
25C22×#97C2211yescharacteristic
26C22×#97C2211yescharacteristic
27C22×C4×C8C2211yescharacteristic
28D4×C4⋊C4—24no—
29D4×C4⋊C4C418yescomplemented
30C2×#389C2211yescharacteristic
31C2×#389C2211yescharacteristic
32C2×#385—21no—
33C2×#385—21no—
34C2×#384C2211yescharacteristic
35C2×#382C2211yescharacteristic
36C2×#380—21no—
37C2×C4×C4⋊C4C2211yescharacteristic
38C2×C4×C4⋊C4C2211yescharacteristic
39C2×C4×C4⋊C4C2211yescharacteristic
40C2×C4×C4⋊C4C2211yescharacteristic
41#1804C418yescomplemented
42#1771—24no—
43#1762—24no—
44#1762C418yescomplemented
45C4×#102—24no—
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56C2×#340C2211yescharacteristic
57C2×#340C2211yescharacteristic
58C2×#336C2211yescharacteristic
59C2×#336C2211yescharacteristic
60#1436—21no—
61#1436—21no—
62C4⋊#95C2211yescharacteristic
63C4⋊#95C2211yescharacteristic
64#1434—21no—
65C4×#95—21no—
66C23×D4C2311yescharacteristic
67C24×C4—21no—
68C24×C4—21no—
69C24×C4—21no—
70C23×C8C2311yescharacteristic
71C23×C8C2311yescharacteristic
72C23×C8C2311yescharacteristic
73C23×C8C2311yescharacteristic
74C2×C4×D4—22no—
75C2×C4×D4—22no—
76C2×C4×D4—22no—
77C2×C4×D4—22no—
78C2×C4×D4—22no—
79C2×C4×D4—22no—
80C2×C4×D4—22no—
81C2×C4×D4—22no—
82C2×C4×D4—22no—
83C2×C4×D4—41no—
84C2×C4×D4—41no—
85C2×C4×D4—41no—
86C2×C4×D4—41no—
87C2×C4×D4C2×C414yes—
88C2×C4×D4C2×C414yes—
89C2×C4×D4C2×C414yes—
90C2×C4×D4C2×C414yes—
91C2×C4×D4C2×C414yes—
92C22×C4⋊C4—21no—
93C22×C4⋊C4—21no—
94C22×C4⋊C4—21no—
95C22×C4⋊C4—21no—
96C22×C4⋊C4—28no—
97C22×C4⋊C4—44no—
98C22×C4⋊C4—44no—
99C22×C4⋊C4D411yescharacteristic
100C22×C4⋊C4D411yescharacteristic
101C22×C4⋊C4C2311yescharacteristic
102C22×C4⋊C4C2311yescharacteristic
103C22×C4⋊C4C2311yescharacteristic
104C22×C4⋊C4C2311yescharacteristic
105C22×C4⋊C4C2311yescharacteristic
106C22×C4⋊C4C2311yescharacteristic
107C22×C4⋊C4C2311yescharacteristic
108C22×C22⋊C4—21no—
109C22×C22⋊C4—21no—
110C22×C22⋊C4—21no—
111C22×C42—21no—
112C22×C42—21no—
113C22×C42—21no—
114C22×C42C2311yescharacteristic
115C22×C42C2311yescharacteristic
116C22×C42C2311yescharacteristic
117C2×C4⋊C8—22no—
118C2×C4⋊C8—22no—
119C2×C4⋊C8C2×C414yescomplemented
120C2×#102—22no—
121C2×#102—22no—
122C2×#102—22no—
123C2×#102—22no—
124C2×#102—22no—
125C2×#102—22no—
126C2×#102C2×C414yes—
127C2×#102C2×C414yes—
128C2×#102C2×C414yes—
129C2×#102C2×C414yes—
130C2×#102D414yes—
131C2×#102Q814yes—
132C2×#97—22no—
133C2×#97—22no—
134C2×#97—22no—
135C2×#97—22no—
136C2×#97—41no—
137C2×#97C2×C414yescomplemented
138C2×C4×C8—22no—
139C2×C4×C8—22no—
140C2×C4×C8—41no—
141#389—22no—
142#389—22no—
143#389C2×C414yes—
144#389C2×C414yes—
145#385—28no—
146#385—28no—
147#384—22no—
148#384C2×C414yes—
149#382—22no—
150#382C2×C414yescomplemented
151#380—28no—
152C4×C4⋊C4—22no—
153C4×C4⋊C4—22no—
154C4×C4⋊C4—22no—
155C4×C4⋊C4—41no—
156C4×C4⋊C4—41no—
157C4×C4⋊C4C2×C414yes—
158C4×C4⋊C4C2×C414yescomplemented
159C4×C4⋊C4D414yes—
160C2×#95—21no—
161C2×#95—21no—
162C2×#95—21no—
163C2×#95—21no—
164C2×#95—21no—
165C2×#95—21no—
166C2×#95—21no—
167C2×#95—21no—
168C2×#95—21no—
169C2×#95—21no—
170C2×#95—21no—
171C2×#95D411yescharacteristic
172C2×#95D411yescharacteristic
173#340—22no—
174#340—22no—
175#340—22no—
176#340—22no—
177#340—41no—
178#340—41no—
179#340—41no—
180#340—41no—
181#340C2×C414yescomplemented
182#340C2×C414yescomplemented
183#340C2×C414yescomplemented
184#340C2×C414yescomplemented
185#336—22no—
186#336—22no—
187C25—21no—
188C22×D4—21no—
189C22×D4—21no—
190C22×D4—21no—
191C22×D4—21no—
192C22×D4—21no—
193C22×D4—21no—
194C22×D4—21no—
195C22×D4C22×C412yes—
196C22×D4C22×C412yes—
197C22×D4C22×C412yes—
198C22×D4C2×D412yes—
199C22×D4C2×Q812yes—
200C22×D4#4112yes—
201C22×D4#4112yes—
202C23×C4—21no—
203C23×C4—21no—
204C23×C4—24no—
205C23×C4—24no—
206C23×C4—24no—
207C23×C4—21no—
208C23×C4—21no—
209C23×C4—21no—
210C23×C4—21no—
211C23×C4—21no—
212C23×C4—24no—
213C23×C4—24no—
214C23×C4—42no—
215C23×C4—42no—
216C23×C4—42no—
217C23×C4—42no—
218C23×C4—42no—
219C23×C4—42no—
220C23×C4—42no—
221C23×C4—42no—
222C23×C4—42no—
223C23×C4—42no—
224C23×C4—42no—
225C23×C4—42no—
226C23×C4—81no—
227C23×C4—81no—
228C23×C4—81no—
229C23×C4—81no—
230C23×C4C2×D411yescharacteristic
231C23×C4C2×D411yescharacteristic
232C23×C4C2×D411yescharacteristic
233C23×C4C2×D411yescharacteristic
234C23×C4C2×D411yescharacteristic
235C23×C4C2×D411yescharacteristic
236C23×C4C2411yescharacteristic
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—21no—
242C22×C8—21no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—21no—
246C22×C8—21no—
247C22×C8—21no—
248C22×C8—21no—
249C22×C8—21no—
250C22×C8—21no—
251C22×C8—21no—
252C22×C8—21no—
253C22×C8—21no—
254C22×C8—21no—
255C22×C8—21no—
256C22×C8—21no—
257C22×C8—21no—
258C22×C8—21no—
259C22×C8C22×C412yes—
260C22×C8C22×C412yes—
261C22×C8C22×C412yes—
262C22×C8C22×C412yes—
263C22×C8C2×D412yes—
264C22×C8C2×Q812yes—
265C4×D4—28no—
266C4×D4—28no—
267C4×D4—28no—
268C4×D4—28no—
269C4×D4—28no—
270C4×D4—44no—
271C4×D4—44no—
272C4×D4—44no—
273C4×D4—44no—
274C4×D4—44no—
275C4×D4—44no—
276C4×D4C42116yescomplemented
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—432no—
315C2×C4⋊C4—41no—
316C2×C4⋊C4—41no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—81no—
324C2×C4⋊C4—81no—
325C2×C4⋊C4C22⋊C414yes—
326C2×C4⋊C4C22⋊C414yes—
327C2×C4⋊C4C22×C412yes—
328C2×C4⋊C4C22×C412yes—
329C2×C4⋊C4C22×C412yes—
330C2×C4⋊C4C22×C412yes—
331C2×C4⋊C4C22×C412yes—
332C2×C4⋊C4C22×C412yes—
333C2×C4⋊C4C22×C412yes—
334C2×C4⋊C4C22×C412yes—
335C2×C4⋊C4C22×C412yes—
336C2×C4⋊C4C2×D412yes—
337C2×C4⋊C4C2×Q812yes—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—42no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—42no—
347C2×C42—21no—
348C2×C42—21no—
349C2×C42—21no—
350C2×C42—21no—
351C2×C42—21no—
352C2×C42—21no—
353C2×C42—21no—
354C2×C42—21no—
355C2×C42—24no—
356C2×C42—42no—
357C2×C42—42no—
358C2×C42—42no—
359C2×C42—42no—
360C2×C42—81no—
361C2×C42—81no—
362C2×C42—81no—
363C2×C42—81no—
364C2×C42C22×C412yes—
365C2×C42C22×C412yes—
366C2×C42C22×C412yes—
367C2×C42C22×C412yes—
368C2×C42C22×C412yes—
369C2×C42C2×D412yes—
370C2×C42C2×D412yes—
371C2×C42C2×D412yes—
372C2×C42#4112yes—
373C2×C42#4112yes—
374C4⋊C8—28no—
375#102—28no—
376#102—28no—
377#102—28no—
378#102C4⋊C4116yescomplemented
379#97—28no—
380#97—44no—
381C4×C8—44no—
382#95—24no—
383#95—24no—
384#95—24no—
385#95—24no—
386#95—24no—
387#95—42no—
388#95—42no—
389#95—42no—
390#95—42no—
391#95—81no—
392#95—81no—
393#95C22⋊C414yes—
394#95C22⋊C414yes—
395C24—22no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—41no—
403C24—41no—
404C24—41no—
405C24—41no—
406C24—41no—
407C24—41no—
408C24—41no—
409C24—41no—
410C24C22×D411yescharacteristic
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4C2×C4214yes—
433C2×D4C2×C4⋊C414yes—
434C2×D4#11714yes—
435C2×D4C4×D414yes—
436C2×D4C4×D414yes—
437C2×D4C4×Q814yes—
438C2×D4C4×Q814yes—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—216no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—48no—
482C22×C4—48no—
483C22×C4—48no—
484C22×C4—48no—
485C22×C4—48no—
486C22×C4—48no—
487C22×C4—48no—
488C22×C4—48no—
489C22×C4—48no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—41no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—41no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—41no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—48no—
529C22×C4—84no—
530C22×C4—84no—
531C22×C4—84no—
532C22×C4—84no—
533C22×C4—84no—
534C22×C4—84no—
535C22×C4—84no—
536C22×C4—84no—
537C22×C4—84no—
538C22×C4—84no—
539C22×C4C2×C22⋊C412yes—
540C22×C4C2×C22⋊C412yes—
541C22×C4C2×C22⋊C412yes—
542C22×C4C2×C22⋊C412yes—
543C22×C4C2×C22⋊C412yes—
544C22×C4C2×C22⋊C412yes—
545C22×C4C4×D412yes—
546C22×C4C4×D412yes—
547C22×C4C4×D412yes—
548C22×C4C4×D412yes—
549C22×C4AGL(1,ℤ/8)12yes—
550C22×C4AGL(1,ℤ/8)12yes—
551C22×C4C23×C411yescharacteristic
552C22×C4C23×C411yescharacteristic
553C22×C4C23×C411yescharacteristic
554C22×C4C22×D411yescharacteristic
555C22×C4C22×D411yescharacteristic
556C22×C4C22×Q811yescharacteristic
557C22×C4C2×#4111yescharacteristic
558C22×C4C2×#4111yescharacteristic
559C22×C4C2×#4111yescharacteristic
560C22×C4C2×#4111yescharacteristic
561C22×C4H(5,𝔽2)11yescharacteristic
562C22×C4H(5,𝔽2)11yescharacteristic
563C22×C42−1+411yescharacteristic
564C22×C42−1+411yescharacteristic
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—22no—
572C2×C8—22no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—22no—
580C2×C8—41no—
581C2×C8—41no—
582C2×C8—41no—
583C2×C8—41no—
584C2×C8—41no—
585C2×C8—41no—
586C2×C8—41no—
587C2×C8—41no—
588C2×C8—41no—
589C2×C8—41no—
590C2×C8—41no—
591C2×C8—41no—
592C2×C8C2×C4⋊C414yescomplemented
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—28no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—44no—
611C4⋊C4—48no—
612C4⋊C4—48no—
613C4⋊C4—41no—
614C4⋊C4—41no—
615C4⋊C4—41no—
616C4⋊C4—41no—
617C4⋊C4—41no—
618C4⋊C4—41no—
619C4⋊C4—41no—
620C4⋊C4—41no—
621C4⋊C4—41no—
622C4⋊C4—41no—
623C4⋊C4—48no—
624C4⋊C4—84no—
625C4⋊C4C2×C4214yes—
626C4⋊C4C2×C4⋊C414yescomplemented
627C22⋊C4—216no—
628C22⋊C4—48no—
629C22⋊C4—48no—
630C42—22no—
631C42—22no—
632C42—22no—
633C42—22no—
634C42—22no—
635C42—22no—
636C42—22no—
637C42—22no—
638C42—84no—
639C42—84no—
640C42—84no—
641C42C2×C4214yes—
642C42#11714yes—
643C42C4×D414yes—
644C42C4×D414yes—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23C22×C22⋊C411yescharacteristic
681C23C2×C4×D411yescharacteristic
682C23C2×C4×D411yescharacteristic
683C23D4211yescharacteristic
684C23#54611yescharacteristic
685C23#54811yescharacteristic
686C23D4×Q811yescharacteristic
687C23C2×AGL(1,ℤ/8)11yescharacteristic
688C23C2×AGL(1,ℤ/8)11yescharacteristic
689C23#57511yescharacteristic
690C23#57511yescharacteristic
691C23#57611yescharacteristic
692C23#57711yescharacteristic
693C23#57711yescharacteristic
694C23#57811yescharacteristic
695D4—24no—
696D4—24no—
697D4—24no—
698D4—24no—
699D4—24no—
700D4—24no—
701D4—24no—
702D4C4×C4⋊C418yes—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—24no—
732C2×C4—432no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—42no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—816no—
773C2×C4—816no—
774C2×C4—81no—
775C2×C4—81no—
776C2×C4—81no—
777C2×C4—81no—
778C2×C4—81no—
779C2×C4—81no—
780C2×C4—81no—
781C2×C4—81no—
782C2×C4—81no—
783C2×C4—81no—
784C2×C4—81no—
785C2×C4—81no—
786C2×C4—81no—
787C2×C4—81no—
788C2×C4—81no—
789C2×C4—81no—
790C2×C4—81no—
791C2×C4—81no—
792C2×C4—81no—
793C2×C4—81no—
794C2×C4C4×C22⋊C414yes—
795C2×C4C4×C22⋊C414yes—
796C2×C4#41814yes—
797C2×C4C22×C4211yescharacteristic
798C2×C4C22×C4⋊C411yescharacteristic
799C2×C4C2×#11711yescharacteristic
800C2×C4C2×#11711yescharacteristic
801C2×C4C2×C4×D411yescharacteristic
802C2×C4C2×C4×D411yescharacteristic
803C2×C4C2×C4×D411yescharacteristic
804C2×C4C2×C4×D411yescharacteristic
805C2×C4C2×C4×Q811yescharacteristic
806C2×C4C2×C4×Q811yescharacteristic
807C2×C4#51811yescharacteristic
808C2×C4#51911yescharacteristic
809C2×C4#52011yescharacteristic
810C2×C4#52011yescharacteristic
811C2×C4#52011yescharacteristic
812C2×C4#52011yescharacteristic
813C2×C4D4211yescharacteristic
814C2×C4#54611yescharacteristic
815C2×C4#54711yescharacteristic
816C2×C4#54711yescharacteristic
817C2×C4#54811yescharacteristic
818C2×C4D4×Q811yescharacteristic
819C2×C4#55211yescharacteristic
820C2×C4#55211yescharacteristic
821C2×C4#55311yescharacteristic
822C2×C4#55311yescharacteristic
823C2×C4#55411yescharacteristic
824C2×C4#55411yescharacteristic
825C8—24no—
826C8—42no—
827C8—42no—
828C8—42no—
829C22—28no—
830C22—44no—
831C22—44no—
832C22—44no—
833C22—44no—
834C22—44no—
835C22—44no—
836C22—44no—
837C22—44no—
838C22—44no—
839C22—44no—
840C22—44no—
841C22—44no—
842C22—44no—
843C22—44no—
844C22C2×C4×C22⋊C411yescharacteristic
845C22D4×C22⋊C411yescharacteristic
846C22Q8×C22⋊C411yescharacteristic
847C22D4×C4⋊C411yescharacteristic
848C22#235211yescharacteristic
849C22#236011yescharacteristic
850C22#236111yescharacteristic
851C22C2×#41811yescharacteristic
852C22#289611yescharacteristic
853C22#289711yescharacteristic
854C22#289811yescharacteristic
855C22C4×AGL(1,ℤ/8)11yescharacteristic
856C22C4×AGL(1,ℤ/8)11yescharacteristic
857C22C4×AGL(1,ℤ/8)11yescharacteristic
858C22C4×AGL(1,ℤ/8)11yescharacteristic
859C22#294611yescharacteristic
860C22#294711yescharacteristic
861C22#295111yescharacteristic
862C22#295211yescharacteristic
863C22#326411yescharacteristic
864C22#326511yescharacteristic
865C22#326711yescharacteristic
866C22#326911yescharacteristic
867C22#330711yescharacteristic
868C22#331011yescharacteristic
869C22#331511yescharacteristic
870C22#331811yescharacteristic
871C22#336711yescharacteristic
872C22#337011yescharacteristic
873C22#337311yescharacteristic
874C22#337611yescharacteristic
875C22#338411yescharacteristic
876C22#338611yescharacteristic
877C22#338811yescharacteristic
878C22#338911yescharacteristic
879C4—24no—
880C4—24no—
881C4—24no—
882C4—42no—
883C4—42no—
884C4—44no—
885C4—42no—
886C4—44no—
887C4—82no—
888C4—82no—
889C4—82no—
890C4—82no—
891C4—82no—
892C4C2×C4×C4⋊C411yescharacteristic
893C4#227411yescharacteristic
894C4#234411yescharacteristic
895C4#234511yescharacteristic
896C4D4×C4⋊C411yescharacteristic
897C4#235211yescharacteristic
898C4#236011yescharacteristic
899C4#236111yescharacteristic
900C2—48no—
901C2C22⋊C4×C4⋊C411yescharacteristic
902C2C4×#41811yescharacteristic
903C2#2041511yescharacteristic
904C2#2242011yescharacteristic
905C2#2242311yescharacteristic
906C2#2252311yescharacteristic
907C2#2252611yescharacteristic
908C2#2267611yescharacteristic
909C2#2267711yescharacteristic
910C2#2277411yescharacteristic
911C2#2277811yescharacteristic
912C2#2297411yescharacteristic
913C2#2297811yescharacteristic
914C2#2300711yescharacteristic
915C2#2301111yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC2×C4C22×C42
Frattini, cosocleC23×C4C24
prime radicalC23×D4C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C2×#1771C2semidirect
7. #13804C2semidirect
8. #10885C2semidirect
9. #10884C2semidirect
10. #10881C2semidirect
11. #10880C2semidirect
12. #10849C2semidirect
13. #10843C2semidirect
29. D4×C4⋊C4C4semidirect
41. #1804C4semidirect
44. #1762C4semidirect
119. C2×C4⋊C8C2×C4semidirect
137. C2×#97C2×C4semidirect
150. #382C2×C4semidirect
158. C4×C4⋊C4C2×C4semidirect
181. #340C2×C4semidirect
182. #340C2×C4semidirect
183. #340C2×C4semidirect
184. #340C2×C4semidirect
276. C4×D4C42semidirect
378. #102C4⋊C4semidirect
592. C2×C8C2×C4⋊C4semidirect
626. C4⋊C4C2×C4⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C4⋊C42
C2×#18042
C2×#17712
C2×#17622
C2×C4×#1022
#138042
#108852
#108842
#108812
#108802
#108492
#108432
#107882