Finite Group Databasebeta

← #370484

Subgroups — #370484

Order 512.

1880 conjugacy classes of subgroups.

The subgroup lattice has 925 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2440C211yesmaximal, characteristic
2C2×#1990C211yesmaximal, characteristic, complemented
3C2×C8×C22⋊C4C211yesmaximal, characteristic
4C22×#340C211yesmaximal, characteristic
5#13880C211yesmaximal, characteristic
6#11384C211yesmaximal, characteristic, complemented
7#11357C211yesmaximal, characteristic, complemented
8#11207C211yesmaximal, characteristic, complemented
9#11207C211yesmaximal, characteristic, complemented
10#10880C211yesmaximal, characteristic, complemented
11#10880C211yesmaximal, characteristic, complemented
12#10841C211yesmaximal, characteristic, complemented
13#10730C211yesmaximal, characteristic
14#10730C211yesmaximal, characteristic
15#10721C211yesmaximal, characteristic
16C24×C8C2211yescharacteristic
17C22×C4⋊Q8C2211yescharacteristic
18C22×C22⋊Q8—21no—
19C23×C4⋊C4C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic
21C22×C22⋊C8C2211yescharacteristic
22C22×C4×C8C2211yescharacteristic
23C22×C4×C8C2211yescharacteristic
24#2440—24no—
25#2440C418yescomplemented
26C2×#398—21no—
27C2×#395—21no—
28C2×#389C2211yescharacteristic
29C2×#389C2211yescharacteristic
30C2×#385—21no—
31C2×#385—21no—
32C2×#385—21no—
33C2×#384C2211yescharacteristic
34C2×#384C2211yescharacteristic
35C2×#384C2211yescharacteristic
36C2×#380C2211yescharacteristic
37C2×#380C2211yescharacteristic
38C2×C4×C22⋊C4C2211yescharacteristic
39#1990—24no—
40C8×C22⋊C4—24no—
41C2×#340—24no—
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
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#1444—21no—
61#1444—21no—
62C4⋊#95C2211yescharacteristic
63C4⋊#95C2211yescharacteristic
64C23×Q8—21no—
65C24×C4—21no—
66C24×C4—21no—
67C24×C4C2311yescharacteristic
68C23×C8—22no—
69C23×C8—22no—
70C23×C8—22no—
71C23×C8—22no—
72C23×C8—41no—
73C23×C8—41no—
74C23×C8Q814yescomplemented
75C23×C8C2311yescharacteristic
76C23×C8C2311yescharacteristic
77C23×C8C2311yescharacteristic
78C23×C8C2311yescharacteristic
79C2×C4⋊Q8—22no—
80C2×C4⋊Q8—22no—
81C2×C4⋊Q8—22no—
82C2×C4⋊Q8—41no—
83C2×C4⋊Q8—41no—
84C2×C4⋊Q8C2×C414yescomplemented
85C2×C22⋊Q8—28no—
86C2×C22⋊Q8—44no—
87C2×C22⋊Q8—44no—
88C22×C4⋊C4—22no—
89C22×C4⋊C4—22no—
90C22×C4⋊C4—22no—
91C22×C4⋊C4—22no—
92C22×C4⋊C4—22no—
93C22×C4⋊C4—21no—
94C22×C4⋊C4—21no—
95C22×C4⋊C4—21no—
96C22×C4⋊C4—21no—
97C22×C4⋊C4—21no—
98C22×C4⋊C4—22no—
99C22×C4⋊C4—21no—
100C22×C4⋊C4—22no—
101C22×C4⋊C4—21no—
102C22×C4⋊C4—21no—
103C22×C4⋊C4—21no—
104C22×C4⋊C4—21no—
105C22×C4⋊C4—21no—
106C22×C4⋊C4—41no—
107C22×C4⋊C4—41no—
108C22×C4⋊C4—41no—
109C22×C4⋊C4—41no—
110C22×C4⋊C4C2×C414yes—
111C22×C4⋊C4C2311yescharacteristic
112C22×C4⋊C4C2311yescharacteristic
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2311yescharacteristic
119C22×C22⋊C4—21no—
120C22×C22⋊C4—21no—
121C22×C22⋊C4D411yescharacteristic
122C22×C22⋊C4D411yescharacteristic
123C22×C42C2311yescharacteristic
124C22×C42C2311yescharacteristic
125C2×C22⋊C8—22no—
126C2×C22⋊C8—22no—
127C2×C22⋊C8Q814yescomplemented
128C2×C4×C8—22no—
129C2×C4×C8—22no—
130C2×C4×C8—22no—
131C2×C4×C8—22no—
132C2×C4×C8—41no—
133C2×C4×C8—41no—
134#398—28no—
135#395—28no—
136#389—22no—
137#389—22no—
138#389C2×C414yescomplemented
139#389C2×C414yescomplemented
140#385—28no—
141#385—44no—
142#385—44no—
143#384—22no—
144#384—22no—
145#384—22no—
146#384—41no—
147#384—41no—
148#384C2×C414yescomplemented
149#380—22no—
150#380—22no—
151#380—22no—
152#380C2×C414yes—
153C4×C22⋊C4C2×C414yes—
154C4×C22⋊C4D414yes—
155C2×#95—21no—
156C2×#95—21no—
157C2×#95—21no—
158C2×#95—21no—
159C2×#95—21no—
160C2×#95—21no—
161C2×#95—21no—
162C2×#95—21no—
163C2×#95D411yescharacteristic
164C2×#95D411yescharacteristic
165#340—22no—
166#340—22no—
167#340—22no—
168#340—22no—
169#340—22no—
170#340—22no—
171#340—22no—
172#340—22no—
173#340—22no—
174#340—41no—
175#340—41no—
176#340—41no—
177#340—41no—
178#340—41no—
179#340—41no—
180#340D414yes—
181#336—22no—
182#336—22no—
183C25C2×D411yescharacteristic
184C22×Q8—24no—
185C22×Q8—42no—
186C22×Q8—42no—
187C22×Q8—42no—
188C22×Q8—42no—
189C22×Q8—81no—
190C22×Q8—81no—
191C23×C4—21no—
192C23×C4—21no—
193C23×C4—21no—
194C23×C4—21no—
195C23×C4—21no—
196C23×C4—21no—
197C23×C4—21no—
198C23×C4—21no—
199C23×C4—21no—
200C23×C4—21no—
201C23×C4—21no—
202C23×C4—21no—
203C23×C4—21no—
204C23×C4—21no—
205C23×C4—24no—
206C23×C4—21no—
207C23×C4—21no—
208C23×C4—42no—
209C23×C4—42no—
210C23×C4—42no—
211C23×C4—42no—
212C23×C4—42no—
213C23×C4—42no—
214C23×C4—42no—
215C23×C4—42no—
216C23×C4—42no—
217C23×C4—81no—
218C23×C4—81no—
219C23×C4—81no—
220C23×C4—81no—
221C23×C4C22×C412yes—
222C23×C4C2×D411yescharacteristic
223C23×C4C2×D411yescharacteristic
224C23×C4C2×D411yescharacteristic
225C23×C4C2×D411yescharacteristic
226C23×C4C2×D411yescharacteristic
227C23×C4C2×D412yes—
228C23×C4C2×Q812yes—
229C23×C4C2×Q812yes—
230C23×C4#4112yes—
231C23×C4#4112yes—
232C23×C4C2411yescharacteristic
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—28no—
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—28no—
257C22×C8—44no—
258C22×C8—44no—
259C22×C8—44no—
260C22×C8—44no—
261C22×C8—44no—
262C22×C8C2×D412yes—
263C22×C8C2×Q812yes—
264C22×C8C2×Q812yes—
265C22×C8C2×Q812yes—
266C22×C8C2×Q812yes—
267C22×C8#4112yes—
268C4⋊Q8—28no—
269C4⋊Q8—44no—
270C4⋊Q8—44no—
271C4⋊Q8—44no—
272C22⋊Q8—432no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—28no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
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—28no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
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—24no—
321C2×C4⋊C4—44no—
322C2×C4⋊C4—44no—
323C2×C4⋊C4—44no—
324C2×C4⋊C4—44no—
325C2×C4⋊C4—44no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—44no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—42no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4—42no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4—42no—
344C2×C4⋊C4—42no—
345C2×C4⋊C4—42no—
346C2×C4⋊C4—42no—
347C2×C4⋊C4—42no—
348C2×C4⋊C4—81no—
349C2×C4⋊C4—81no—
350C2×C4⋊C4—81no—
351C2×C4⋊C4—81no—
352C2×C4⋊C4—81no—
353C2×C4⋊C4—81no—
354C2×C4⋊C4C22×C412yes—
355C2×C4⋊C4C22×C412yes—
356C2×C4⋊C4C22×C412yes—
357C2×C4⋊C4C22×C412yes—
358C2×C4⋊C4C2×D412yes—
359C2×C4⋊C4C2×D412yes—
360C2×C4⋊C4#4112yes—
361C2×C4⋊C4#4112yes—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4C22⋊C414yes—
369C2×C22⋊C4C22⋊C414yes—
370C2×C22⋊C4D814yes—
371C2×C22⋊C4SD1614yes—
372C2×C22⋊C4SD1614yes—
373C2×C22⋊C4Q1614yes—
374C2×C42—21no—
375C2×C42—21no—
376C2×C42—21no—
377C2×C42—21no—
378C2×C42—21no—
379C2×C42—21no—
380C2×C42—21no—
381C2×C42—21no—
382C2×C42C22×C412yes—
383C2×C42C22×C412yes—
384C2×C42C2×D412yes—
385C2×C42C2×D412yes—
386C22⋊C8—28no—
387C4×C8—44no—
388C4×C8—44no—
389#95—24no—
390#95—24no—
391#95—24no—
392#95—42no—
393#95—42no—
394#95—42no—
395#95—42no—
396#95—42no—
397#95C22⋊C414yes—
398#95C22⋊C414yes—
399C24—21no—
400C24—21no—
401C24—21no—
402C24—21no—
403C24—21no—
404C24—21no—
405C24—21no—
406C24—21no—
407C24C2×C22⋊C412yes—
408C24#12412yes—
409C24C4⋊Q812yes—
410C24C2×D812yes—
411C24C2×SD1612yes—
412C24C2×SD1612yes—
413C24C2×Q1612yes—
414C24C22×D411yescharacteristic
415C2×Q8—48no—
416C2×Q8—48no—
417C2×Q8—84no—
418C2×Q8—84no—
419C2×Q8—84no—
420C2×Q8—84no—
421C2×Q8—84no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—48no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—48no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—41no—
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—48no—
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—84no—
526C22×C4—84no—
527C22×C4—84no—
528C22×C4—84no—
529C22×C4—84no—
530C22×C4—84no—
531C22×C4—84no—
532C22×C4—84no—
533C22×C4—84no—
534C22×C4—84no—
535C22×C4—84no—
536C22×C4C2×C22⋊C412yes—
537C22×C4C2×C22⋊C412yes—
538C22×C4C2×C22⋊C412yes—
539C22×C4C2×C22⋊C412yes—
540C22×C4C2×C22⋊C412yes—
541C22×C4C4×Q814yes—
542C22×C4C4×Q814yes—
543C22×C4C22⋊Q814yes—
544C22×C4C22⋊Q814yes—
545C22×C4#12412yes—
546C22×C4C4⋊Q812yes—
547C22×C4C2×D812yes—
548C22×C4C2×D812yes—
549C22×C4C2×SD1612yes—
550C22×C4C2×SD1612yes—
551C22×C4C2×SD1612yes—
552C22×C4C2×SD1612yes—
553C22×C4C2×Q1612yes—
554C22×C4C2×Q1612yes—
555C22×C4C23×C411yescharacteristic
556C22×C4C22×D411yescharacteristic
557C22×C4C22×D411yescharacteristic
558C22×C4C22×Q811yescharacteristic
559C22×C4C22×Q811yescharacteristic
560C22×C4C2×#4111yescharacteristic
561C22×C4C2×#4111yescharacteristic
562C22×C4C2×#4111yescharacteristic
563C22×C4C2×#4111yescharacteristic
564C22×C4C2×#4111yescharacteristic
565C22×C4H(5,𝔽2)11yescharacteristic
566C22×C4H(5,𝔽2)11yescharacteristic
567C22×C4H(5,𝔽2)11yescharacteristic
568C22×C42−1+411yescharacteristic
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—22no—
581C2×C8—22no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—416no—
585C2×C8—41no—
586C2×C8—41no—
587C2×C8—41no—
588C2×C8—41no—
589C2×C8—41no—
590C2×C8—41no—
591C2×C8—41no—
592C2×C8—41no—
593C2×C8—41no—
594C2×C8—41no—
595C2×C8—41no—
596C2×C8—41no—
597C2×C8C22⋊Q814yescomplemented
598C4⋊C4—22no—
599C4⋊C4—22no—
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—22no—
611C4⋊C4—48no—
612C4⋊C4—48no—
613C4⋊C4—48no—
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—41no—
624C4⋊C4—48no—
625C4⋊C4—48no—
626C4⋊C4—48no—
627C4⋊C4—41no—
628C4⋊C4—41no—
629C4⋊C4—41no—
630C4⋊C4—41no—
631C4⋊C4—41no—
632C4⋊C4—41no—
633C4⋊C4—41no—
634C4⋊C4—41no—
635C4⋊C4—84no—
636C4⋊C4—84no—
637C4⋊C4—84no—
638C4⋊C4—84no—
639C4⋊C4—84no—
640C4⋊C4C4×D414yes—
641C22⋊C4—48no—
642C22⋊C4—84no—
643C22⋊C4#102116yes—
644C22⋊C4#103116yes—
645C42—22no—
646C42—22no—
647C42—22no—
648C42—22no—
649C42—22no—
650C42—22no—
651C42—22no—
652C42—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23#39114yes—
682C23C2×#10214yes—
683C23C2×#10314yes—
684C23#48614yes—
685C23#48714yes—
686C23#49814yes—
687C23#50014yes—
688C23C22×C22⋊C411yescharacteristic
689C23C2×#12411yescharacteristic
690C23C2×C4⋊Q811yescharacteristic
691C23D4211yescharacteristic
692C23#54611yescharacteristic
693C23#54611yescharacteristic
694C23#54711yescharacteristic
695C23C22×D811yescharacteristic
696C23C22×SD1611yescharacteristic
697C23C22×SD1611yescharacteristic
698C23C22×Q1611yescharacteristic
699C23#57611yescharacteristic
700C23#57711yescharacteristic
701C23#57711yescharacteristic
702C23#57811yescharacteristic
703Q8—816no—
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—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—816no—
765C2×C4—816no—
766C2×C4—81no—
767C2×C4—81no—
768C2×C4—81no—
769C2×C4—81no—
770C2×C4—81no—
771C2×C4—81no—
772C2×C4—81no—
773C2×C4—81no—
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×C4—81no—
795C2×C4—81no—
796C2×C4—81no—
797C2×C4—81no—
798C2×C4—81no—
799C2×C4—81no—
800C2×C4#39114yes—
801C2×C4C2×#10214yes—
802C2×C4C2×#10214yes—
803C2×C4C2×#10314yes—
804C2×C4C2×#10314yes—
805C2×C4C2×C4×D411yescharacteristic
806C2×C4C2×C4×Q811yescharacteristic
807C2×C4C2×C4×Q811yescharacteristic
808C2×C4C4×#4111yescharacteristic
809C2×C4#51811yescharacteristic
810C2×C4#52011yescharacteristic
811C2×C4C2×C22⋊Q811yescharacteristic
812C2×C4C2×C22⋊Q811yescharacteristic
813C2×C4C2×C22⋊Q811yescharacteristic
814C2×C4#52511yescharacteristic
815C2×C4#52911yescharacteristic
816C2×C4#53311yescharacteristic
817C2×C4#53811yescharacteristic
818C2×C4#53911yescharacteristic
819C2×C4#54311yescharacteristic
820C2×C4#54411yescharacteristic
821C2×C4D4211yescharacteristic
822C2×C4#54611yescharacteristic
823C2×C4#54611yescharacteristic
824C2×C4#54611yescharacteristic
825C2×C4#54711yescharacteristic
826C2×C4D4×Q811yescharacteristic
827C2×C4#55111yescharacteristic
828C2×C4#55111yescharacteristic
829C2×C4#55211yescharacteristic
830C2×C4#55411yescharacteristic
831C2×C4#55411yescharacteristic
832C2×C4#55411yescharacteristic
833C8—24no—
834C8—42no—
835C8—42no—
836C8—42no—
837C22—24no—
838C22—24no—
839C22—24no—
840C22—24no—
841C22—24no—
842C22—24no—
843C22—24no—
844C22—24no—
845C22—24no—
846C22—24no—
847C22—24no—
848C22—24no—
849C22—24no—
850C22—24no—
851C22#199018yescomplemented
852C22C2×#39111yescharacteristic
853C22D4×C22⋊C411yescharacteristic
854C22#233911yescharacteristic
855C22#244011yescharacteristic
856C22#247211yescharacteristic
857C22#248811yescharacteristic
858C22#254911yescharacteristic
859C22C22×#10211yescharacteristic
860C22C22×#10311yescharacteristic
861C22#289711yescharacteristic
862C22#289811yescharacteristic
863C22C2×#48611yescharacteristic
864C22C2×#48711yescharacteristic
865C22#313611yescharacteristic
866C22#313711yescharacteristic
867C22C2×#49811yescharacteristic
868C22C2×#50011yescharacteristic
869C22#316311yescharacteristic
870C22#316411yescharacteristic
871C22D4×D811yescharacteristic
872C22D4×SD1611yescharacteristic
873C22D4×SD1611yescharacteristic
874C22D4×Q1611yescharacteristic
875C22#329411yescharacteristic
876C22#329411yescharacteristic
877C22#329511yescharacteristic
878C22#329511yescharacteristic
879C22#329811yescharacteristic
880C22#329811yescharacteristic
881C22#329911yescharacteristic
882C22#329911yescharacteristic
883C22#333411yescharacteristic
884C22#333511yescharacteristic
885C22#333511yescharacteristic
886C22#333811yescharacteristic
887C4—24no—
888C4—24no—
889C4—24no—
890C4—24no—
891C4—24no—
892C4—44no—
893C4—82no—
894C4—82no—
895C4—82no—
896C4—82no—
897C4—82no—
898C4—161no—
899C4—161no—
900C4C4×C22⋊Q811yescharacteristic
901C4#232911yescharacteristic
902C4#236011yescharacteristic
903C4#236811yescharacteristic
904C4#243711yescharacteristic
905C4#243811yescharacteristic
906C4#244911yescharacteristic
907C4#245011yescharacteristic
908C2—28no—
909C2#1405211yescharacteristic
910C2C2×#199011yescharacteristic
911C2#2132611yescharacteristic
912C2D4×#10211yescharacteristic
913C2D4×#10311yescharacteristic
914C2#2248511yescharacteristic
915C2#2248711yescharacteristic
916C2#2606011yescharacteristic
917C2#2606511yescharacteristic
918C2#2725411yescharacteristic
919C2#2725811yescharacteristic
920C2#2769511yescharacteristic
921C2#2769711yescharacteristic
922C2#2876911yescharacteristic
923C2#2877111yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC25C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#1990C2semidirect
6. #11384C2semidirect
7. #11357C2semidirect
8. #11207C2semidirect
9. #11207C2semidirect
10. #10880C2semidirect
11. #10880C2semidirect
12. #10841C2semidirect
25. #2440C4semidirect
74. C23×C8Q8semidirect
84. C2×C4⋊Q8C2×C4semidirect
127. C2×C22⋊C8Q8semidirect
138. #389C2×C4semidirect
139. #389C2×C4semidirect
148. #384C2×C4semidirect
597. C2×C8C22⋊Q8semidirect
851. C22#1990semidirect

Maximal subgroups

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

subgroupindex
C2×#24402
C2×#19902
C2×C8×C22⋊C42
C22×#3402
#138802
#113842
#113572
#112072
#108802
#108412
#107302
#107212