Finite Group Databasebeta

← #368114

Subgroups — #368114

Order 512.

1934 conjugacy classes of subgroups.

The subgroup lattice has 973 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#440C211yesmaximal, characteristic
2C2×Q8×C4⋊C4C211yesmaximal, characteristic, complemented
3C2×#1880C211yesmaximal, characteristic
4C2×#1880C211yesmaximal, characteristic
5C2×#1863C211yesmaximal, characteristic, complemented
6C2×#1862C211yesmaximal, characteristic
7#14018C211yesmaximal, characteristic
8#11328C211yesmaximal, characteristic, complemented
9#11324C211yesmaximal, characteristic, complemented
10#11066C211yesmaximal, characteristic
11#11049C211yesmaximal, characteristic
12#10881C211yesmaximal, characteristic, complemented
13#10875C211yesmaximal, characteristic, complemented
14#10789C211yesmaximal, characteristic, complemented
15#10789C211yesmaximal, characteristic, complemented
16C23×SD16C2211yescharacteristic
17C22×C4×Q8C2211yescharacteristic
18C22×C4×Q8C2211yescharacteristic
19C22×C4×Q8C2211yescharacteristic
20C22×C4×D4C2211yescharacteristic
21C2×#440—24no—
22C2×#440—24no—
23C2×#440—24no—
24C22×#107C2211yescharacteristic
25C22×#107C2211yescharacteristic
26C22×#103C2211yescharacteristic
27C22×#103C2211yescharacteristic
28C22×#103C2211yescharacteristic
29C22×#102C2211yescharacteristic
30C22×#102C2211yescharacteristic
31C22×#102C2211yescharacteristic
32C22×#97C2211yescharacteristic
33Q8×C4⋊C4—24no—
34Q8×C4⋊C4—24no—
35C2×#390C2211yescharacteristic
36C2×#390C2211yescharacteristic
37C2×#389—21no—
38C2×#389—21no—
39C2×#389C2211yescharacteristic
40C2×#389C2211yescharacteristic
41C2×#389C2211yescharacteristic
42C2×#385—21no—
43C2×#384—21no—
44C2×#384C2211yescharacteristic
45C2×C4×C4⋊C4—21no—
46C2×C4×C4⋊C4C2211yescharacteristic
47#1880—24no—
48#1880C418yescomplemented
49#1863—24no—
50#1862—24no—
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56C2×#340C2211yescharacteristic
57C2×#340C2211yescharacteristic
58C2×#336C2211yescharacteristic
59C2×#336C2211yescharacteristic
60C2×#336C2211yescharacteristic
61C2×#336C2211yescharacteristic
62C2×#336C2211yescharacteristic
63#1439—21no—
64#1439—21no—
65C4⋊#95C2211yescharacteristic
66C4⋊#95C2211yescharacteristic
67C22⋊#95—21no—
68C23×Q8C2311yescharacteristic
69C23×D4C2311yescharacteristic
70C24×C4—21no—
71C22×SD16—22no—
72C22×SD16—22no—
73C22×SD16—22no—
74C22×SD16—22no—
75C22×SD16C2×C414yes—
76C22×SD16D414yes—
77C22×SD16Q814yes—
78C23×C8C2311yescharacteristic
79C23×C8C2311yescharacteristic
80C23×C8C2311yescharacteristic
81C23×C8C2311yescharacteristic
82C2×C4×Q8—22no—
83C2×C4×Q8—22no—
84C2×C4×Q8—22no—
85C2×C4×Q8—22no—
86C2×C4×Q8—22no—
87C2×C4×Q8—22no—
88C2×C4×Q8—22no—
89C2×C4×Q8—22no—
90C2×C4×Q8—22no—
91C2×C4×Q8—22no—
92C2×C4×Q8—22no—
93C2×C4×Q8—22no—
94C2×C4×Q8—41no—
95C2×C4×Q8—41no—
96C2×C4×Q8—41no—
97C2×C4×Q8—41no—
98C2×C4×Q8C2×C414yescomplemented
99C2×C4×Q8D414yes—
100C2×C4×D4—22no—
101C2×C4×D4—22no—
102C2×C4×D4—22no—
103C2×C4×D4—22no—
104C2×C4×D4—41no—
105C2×C4×D4—41no—
106C22×C4⋊C4—21no—
107C22×C4⋊C4—21no—
108C22×C4⋊C4—21no—
109C22×C4⋊C4—21no—
110C22×C4⋊C4—21no—
111C22×C4⋊C4—21no—
112C22×C4⋊C4—21no—
113C22×C4⋊C4—21no—
114C22×C4⋊C4D411yescharacteristic
115C22×C4⋊C4D411yescharacteristic
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2311yescharacteristic
122C22×C22⋊C4—21no—
123C22×C22⋊C4—21no—
124C22×C22⋊C4—21no—
125C22×C22⋊C4—21no—
126C22×C22⋊C4—21no—
127C22×C42—21no—
128C22×C42—21no—
129C22×C42—21no—
130C22×C42C2311yescharacteristic
131C22×C42C2311yescharacteristic
132C22×C42C2311yescharacteristic
133#440—232no—
134C2×#107—22no—
135C2×#107—22no—
136C2×#107—22no—
137C2×#107—22no—
138C2×#107—22no—
139C2×#107—41no—
140C2×#103—22no—
141C2×#103—22no—
142C2×#103—22no—
143C2×#103—22no—
144C2×#103—22no—
145C2×#103—22no—
146C2×#103—22no—
147C2×#103C2×C414yescomplemented
148C2×#103D414yes—
149C2×#102—22no—
150C2×#102—22no—
151C2×#102—22no—
152C2×#102—22no—
153C2×#102—22no—
154C2×#102—22no—
155C2×#102—22no—
156C2×#102—41no—
157C2×#102C2×C414yes—
158C2×#97—22no—
159C2×#97—22no—
160C2×#97—22no—
161#390—22no—
162#390—22no—
163#390—41no—
164#390C2×C414yes—
165#389—28no—
166#389—28no—
167#389—22no—
168#389—22no—
169#389—22no—
170#389—22no—
171#389—41no—
172#389D414yes—
173#385—44no—
174#384—28no—
175#384—22no—
176#384—22no—
177C4×C4⋊C4—28no—
178C4×C4⋊C4—22no—
179C4×C4⋊C4—22no—
180C2×#95—21no—
181C2×#95—21no—
182C2×#95—21no—
183C2×#95—21no—
184C2×#95—21no—
185C2×#95—21no—
186C2×#95—21no—
187C2×#95D411yescharacteristic
188C2×#95D411yescharacteristic
189#340—22no—
190#340—22no—
191#340—22no—
192#340—22no—
193#340—41no—
194#340—41no—
195#340C2×C414yescomplemented
196#336—22no—
197#336—22no—
198#336—22no—
199#336—22no—
200#336C2×C414yescomplemented
201C25—21no—
202C22×Q8—21no—
203C22×Q8—21no—
204C22×Q8—21no—
205C22×Q8—21no—
206C22×Q8—21no—
207C22×Q8—21no—
208C22×Q8—21no—
209C22×Q8C22×C412yes—
210C22×Q8C2×D412yes—
211C22×Q8C2×D412yes—
212C22×Q8C2×D412yes—
213C22×Q8C2×Q812yes—
214C22×Q8#4112yes—
215C22×Q8#4112yes—
216C22×D4—21no—
217C22×D4—21no—
218C22×D4—21no—
219C22×D4—21no—
220C22×D4—21no—
221C22×D4—21no—
222C22×D4—21no—
223C22×D4—21no—
224C22×D4—21no—
225C22×D4—21no—
226C22×D4—21no—
227C22×D4C22×C412yes—
228C22×D4C2×D412yes—
229C22×D4C2×Q812yes—
230C23×C4—21no—
231C23×C4—21no—
232C23×C4—21no—
233C23×C4—21no—
234C23×C4—21no—
235C23×C4—21no—
236C23×C4—21no—
237C23×C4—42no—
238C23×C4—42no—
239C23×C4—42no—
240C23×C4—42no—
241C23×C4—42no—
242C23×C4—81no—
243C23×C4—81no—
244C23×C4C2×D411yescharacteristic
245C23×C4C2×D411yescharacteristic
246C23×C4C2×D411yescharacteristic
247C23×C4C2×D411yescharacteristic
248C23×C4C2×D411yescharacteristic
249C23×C4C2×D411yescharacteristic
250C23×C4C2411yescharacteristic
251C2×SD16—28no—
252C2×SD16—28no—
253C2×SD16—28no—
254C2×SD16—28no—
255C2×SD16—28no—
256C2×SD16—28no—
257C2×SD16C4⋊C4116yescomplemented
258C22×C8—21no—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—21no—
264C22×C8—21no—
265C22×C8—21no—
266C22×C8—21no—
267C22×C8—21no—
268C22×C8—21no—
269C22×C8—21no—
270C22×C8—21no—
271C22×C8—21no—
272C22×C8—21no—
273C22×C8—21no—
274C22×C8—21no—
275C22×C8—21no—
276C22×C8—21no—
277C22×C8—21no—
278C22×C8—21no—
279C22×C8—21no—
280C22×C8—21no—
281C22×C8C22×C412yes—
282C22×C8C22×C412yes—
283C22×C8C2×D412yes—
284C22×C8C2×D412yes—
285C22×C8C2×Q812yes—
286C4×Q8—28no—
287C4×Q8—28no—
288C4×Q8—28no—
289C4×Q8—28no—
290C4×Q8—28no—
291C4×Q8—44no—
292C4×Q8—44no—
293C4×Q8—44no—
294C4×Q8—44no—
295C4×Q8—44no—
296C4×Q8—44no—
297C4×Q8—44no—
298C4×D4—28no—
299C4×D4—44no—
300C4×D4—44no—
301C4×D4—44no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
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—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—41no—
346C2×C4⋊C4—42no—
347C2×C4⋊C4—42no—
348C2×C4⋊C4—42no—
349C2×C4⋊C4—42no—
350C2×C4⋊C4—42no—
351C2×C4⋊C4—42no—
352C2×C4⋊C4—42no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4—81no—
355C2×C4⋊C4—81no—
356C2×C4⋊C4—81no—
357C2×C4⋊C4—81no—
358C2×C4⋊C4—81no—
359C2×C4⋊C4—81no—
360C2×C4⋊C4—81no—
361C2×C4⋊C4C22×C412yes—
362C2×C4⋊C4C22×C412yes—
363C2×C4⋊C4C2×D412yes—
364C2×C4⋊C4C2×D412yes—
365C2×C4⋊C4C2×D412yes—
366C2×C4⋊C4C2×D412yes—
367C2×C4⋊C4#4112yes—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—81no—
380C2×C22⋊C4—81no—
381C2×C22⋊C4—81no—
382C2×C22⋊C4—81no—
383C2×C42—24no—
384C2×C42—24no—
385C2×C42—24no—
386C2×C42—21no—
387C2×C42—21no—
388C2×C42—21no—
389C2×C42—21no—
390C2×C42—21no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42—21no—
394C2×C42—24no—
395C2×C42—24no—
396C2×C42—21no—
397C2×C42—21no—
398C2×C42—21no—
399C2×C42—21no—
400C2×C42—21no—
401C2×C42—21no—
402C2×C42—42no—
403C2×C42—42no—
404C2×C42—42no—
405C2×C42—42no—
406C2×C42C22×C412yes—
407C2×C42C2×D412yes—
408C2×C42C2×D412yes—
409C2×C42#4112yes—
410#107—28no—
411#107—44no—
412#103—28no—
413#103—28no—
414#103—44no—
415#102—28no—
416#102—28no—
417#102—44no—
418#97—28no—
419#95—24no—
420#95—24no—
421#95—22no—
422#95—22no—
423#95—42no—
424#95—42no—
425#95—42no—
426#95—81no—
427#95—81no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—41no—
432C24—41no—
433C24—41no—
434C24—41no—
435C24—41no—
436C24—41no—
437C24—41no—
438C24—41no—
439C24—41no—
440C24—41no—
441C24—41no—
442C24—41no—
443C24C22×D411yescharacteristic
444C2×Q8—22no—
445C2×Q8—22no—
446C2×Q8—22no—
447C2×Q8—22no—
448C2×Q8—22no—
449C2×Q8—22no—
450C2×Q8—22no—
451C2×Q8—22no—
452C2×Q8—22no—
453C2×Q8—22no—
454C2×Q8—22no—
455C2×Q8—22no—
456C2×Q8—22no—
457C2×Q8—22no—
458C2×Q8—22no—
459C2×Q8—22no—
460C2×Q8—22no—
461C2×Q8—22no—
462C2×Q8—22no—
463C2×Q8—22no—
464C2×Q8—22no—
465C2×Q8C2×C4⋊C414yes—
466C2×Q8C4×D414yes—
467C2×Q8C4×D414yes—
468C2×Q8#12014yes—
469C2×Q8C22⋊Q814yes—
470C2×Q8C22⋊Q814yes—
471C2×Q8#12314yes—
472C2×D4—22no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—22no—
479C2×D4—22no—
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—22no—
487C2×D4—41no—
488C2×D4—41no—
489C2×D4—41no—
490C2×D4—41no—
491C2×D4—41no—
492C2×D4—41no—
493C2×D4—41no—
494C2×D4—41no—
495C2×D4—41no—
496C2×D4—41no—
497C2×D4—41no—
498C2×D4—41no—
499C2×D4C2×C4⋊C414yes—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—48no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4—41no—
574C22×C4—41no—
575C22×C4—41no—
576C22×C4—41no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—84no—
586C22×C4—84no—
587C22×C4—84no—
588C22×C4—84no—
589C22×C4—84no—
590C22×C4—84no—
591C22×C4C4×D412yes—
592C22×C4C4×D412yes—
593C22×C4#12012yes—
594C22×C4#12012yes—
595C22×C4AGL(1,ℤ/8)12yes—
596C22×C4#13712yes—
597C22×C4#13712yes—
598C22×C4C23×C411yescharacteristic
599C22×C4C22×D411yescharacteristic
600C22×C4C22×D411yescharacteristic
601C22×C4C22×D411yescharacteristic
602C22×C4C22×D411yescharacteristic
603C22×C4C22×Q811yescharacteristic
604C22×C4C2×#4111yescharacteristic
605C22×C4C2×#4111yescharacteristic
606C22×C4C2×#4111yescharacteristic
607C22×C4C2×#4111yescharacteristic
608C22×C4H(5,𝔽2)11yescharacteristic
609C22×C4H(5,𝔽2)11yescharacteristic
610C22×C42−1+411yescharacteristic
611C22×C42−1+411yescharacteristic
612SD16—232no—
613C2×C8—22no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8—22no—
621C2×C8—22no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—41no—
626C2×C8—41no—
627C2×C8—41no—
628C2×C8—41no—
629C2×C8—41no—
630C2×C8—41no—
631C2×C8—41no—
632C2×C8—41no—
633C2×C8—41no—
634C2×C8—41no—
635C2×C8—41no—
636C2×C8—41no—
637C2×C8—41no—
638C2×C8—41no—
639C2×C8—41no—
640C2×C8C2×C4⋊C414yes—
641C4⋊C4—28no—
642C4⋊C4—216no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—22no—
653C4⋊C4—22no—
654C4⋊C4—44no—
655C4⋊C4—48no—
656C4⋊C4—48no—
657C4⋊C4—48no—
658C4⋊C4—41no—
659C4⋊C4—41no—
660C4⋊C4—41no—
661C4⋊C4—41no—
662C4⋊C4—41no—
663C4⋊C4—41no—
664C4⋊C4—41no—
665C4⋊C4—41no—
666C4⋊C4—41no—
667C4⋊C4—41no—
668C4⋊C4—41no—
669C4⋊C4—41no—
670C4⋊C4—84no—
671C4⋊C4—84no—
672C4⋊C4—84no—
673C4⋊C4—84no—
674C4⋊C4C4×D414yes—
675C22⋊C4—48no—
676C22⋊C4—48no—
677C22⋊C4—84no—
678C22⋊C4—84no—
679C22⋊C4—84no—
680C42—216no—
681C42—22no—
682C42—22no—
683C42—22no—
684C42—22no—
685C42—22no—
686C42—22no—
687C42—22no—
688C42—22no—
689C42—48no—
690C42—48no—
691C42—41no—
692C42—41no—
693C42—41no—
694C42—41no—
695C23—24no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—81no—
715C23—81no—
716C23—81no—
717C23—81no—
718C23—81no—
719C23—81no—
720C23—81no—
721C23—81no—
722C23—81no—
723C23—81no—
724C23—81no—
725C23—81no—
726C23—81no—
727C23—81no—
728C23—81no—
729C23—81no—
730C23C2×C4×D411yescharacteristic
731C23C2×#12011yescharacteristic
732C23#52511yescharacteristic
733C23D4211yescharacteristic
734C23D4211yescharacteristic
735C23#54811yescharacteristic
736C23D4×Q811yescharacteristic
737C23C2×AGL(1,ℤ/8)11yescharacteristic
738C23C2×#13711yescharacteristic
739C23C2×#13711yescharacteristic
740C23#57511yescharacteristic
741C23#57611yescharacteristic
742C23#57611yescharacteristic
743C23#57711yescharacteristic
744C23#57811yescharacteristic
745Q8—24no—
746Q8—24no—
747Q8—24no—
748Q8—24no—
749Q8—24no—
750Q8—24no—
751Q8—24no—
752Q8#38518yescomplemented
753D4—24no—
754D4—24no—
755D4—42no—
756D4—42no—
757D4—42no—
758D4—42no—
759D4—42no—
760D4—42no—
761C2×C4—22no—
762C2×C4—24no—
763C2×C4—22no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—22no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—24no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—24no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—42no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—41no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—41no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—41no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—42no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—42no—
828C2×C4—816no—
829C2×C4—81no—
830C2×C4—81no—
831C2×C4—81no—
832C2×C4—81no—
833C2×C4—81no—
834C2×C4—81no—
835C2×C4—81no—
836C2×C4—81no—
837C2×C4—81no—
838C2×C4—81no—
839C2×C4—81no—
840C2×C4—81no—
841C2×C4—81no—
842C2×C4—81no—
843C2×C4—81no—
844C2×C4—81no—
845C2×C4—81no—
846C2×C4—81no—
847C2×C4—81no—
848C2×C4—81no—
849C2×C4—81no—
850C2×C4—81no—
851C2×C4—81no—
852C2×C4#44014yescomplemented
853C2×C4C22×C4⋊C411yescharacteristic
854C2×C4C2×C4×D411yescharacteristic
855C2×C4C2×C4×D411yescharacteristic
856C2×C4C2×C4×D411yescharacteristic
857C2×C4#52011yescharacteristic
858C2×C4#52011yescharacteristic
859C2×C4C2×#12011yescharacteristic
860C2×C4C2×C22⋊Q811yescharacteristic
861C2×C4C2×C22⋊Q811yescharacteristic
862C2×C4C2×#12311yescharacteristic
863C2×C4#52511yescharacteristic
864C2×C4#52511yescharacteristic
865C2×C4#53411yescharacteristic
866C2×C4#53611yescharacteristic
867C2×C4#53911yescharacteristic
868C2×C4#53911yescharacteristic
869C2×C4D4211yescharacteristic
870C2×C4D4211yescharacteristic
871C2×C4#54711yescharacteristic
872C2×C4#54711yescharacteristic
873C2×C4#54711yescharacteristic
874C2×C4#54711yescharacteristic
875C2×C4#54811yescharacteristic
876C2×C4D4×Q811yescharacteristic
877C2×C4#55311yescharacteristic
878C2×C4#55311yescharacteristic
879C2×C4#55411yescharacteristic
880C2×C4#55411yescharacteristic
881C8—24no—
882C8—42no—
883C8—42no—
884C8—81no—
885C22—44no—
886C22—44no—
887C22—44no—
888C22—82no—
889C22—82no—
890C22—82no—
891C22—82no—
892C22—82no—
893C22—82no—
894C22—82no—
895C22—82no—
896C22—82no—
897C22—82no—
898C22—82no—
899C22—82no—
900C22C4×#12011yescharacteristic
901C22D4×C4⋊C411yescharacteristic
902C22#236111yescharacteristic
903C22#240311yescharacteristic
904C22#240911yescharacteristic
905C22#244311yescharacteristic
906C22#244911yescharacteristic
907C22C2×#44011yescharacteristic
908C22C4×#13711yescharacteristic
909C22#294611yescharacteristic
910C22#295111yescharacteristic
911C22#300411yescharacteristic
912C22#300611yescharacteristic
913C22#300811yescharacteristic
914C22#301311yescharacteristic
915C22#311211yescharacteristic
916C22#311711yescharacteristic
917C22#311911yescharacteristic
918C22#312411yescharacteristic
919C22#326611yescharacteristic
920C22#326811yescharacteristic
921C22#326811yescharacteristic
922C22#327011yescharacteristic
923C22#327411yescharacteristic
924C22#327411yescharacteristic
925C22#327611yescharacteristic
926C22#327811yescharacteristic
927C22#336811yescharacteristic
928C22#337511yescharacteristic
929C22#337511yescharacteristic
930C22#337711yescharacteristic
931C22#338511yescharacteristic
932C22#338511yescharacteristic
933C22#338611yescharacteristic
934C22#338811yescharacteristic
935C4—28no—
936C4—24no—
937C4—42no—
938C4—42no—
939C4—42no—
940C4—42no—
941C4—44no—
942C4—81no—
943C4—82no—
944C4—82no—
945C4—82no—
946C4—82no—
947C4—161no—
948C4C2×#38511yescharacteristic
949C4#232211yescharacteristic
950C4D4×C4⋊C411yescharacteristic
951C4#236111yescharacteristic
952C4#240611yescharacteristic
953C4#244311yescharacteristic
954C4#244911yescharacteristic
955C4#257911yescharacteristic
956C2—84no—
957C2#1401511yescharacteristic
958C2#2145411yescharacteristic
959C2#2146011yescharacteristic
960C2#2267111yescharacteristic
961C2#2267811yescharacteristic
962C2#2300311yescharacteristic
963C2#2300911yescharacteristic
964C2#2386811yescharacteristic
965C2#2386911yescharacteristic
966C2#2434111yescharacteristic
967C2#2434611yescharacteristic
968C2#2617711yescharacteristic
969C2#2617911yescharacteristic
970C2#2638711yescharacteristic
971C2#2639711yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC23×D4C23
LCSG ▷ C22×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
2. C2×Q8×C4⋊C4C2semidirect
5. C2×#1863C2semidirect
8. #11328C2semidirect
9. #11324C2semidirect
12. #10881C2semidirect
13. #10875C2semidirect
14. #10789C2semidirect
15. #10789C2semidirect
48. #1880C4semidirect
98. C2×C4×Q8C2×C4semidirect
147. C2×#103C2×C4semidirect
195. #340C2×C4semidirect
200. #336C2×C4semidirect
257. C2×SD16C4⋊C4semidirect
752. Q8#385semidirect
852. C2×C4#440semidirect

Maximal subgroups

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

subgroupindex
C22×#4402
C2×Q8×C4⋊C42
C2×#18802
C2×#18632
C2×#18622
#140182
#113282
#113242
#110662
#110492
#108812
#108752
#107892