Finite Group Databasebeta

← #356646

Subgroups — #356646

Order 512.

1818 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34136C211yesmaximal, characteristic
2C2×#1897C211yesmaximal, characteristic
3C2×#1871C211yesmaximal, characteristic
4C2×C4×#104C211yesmaximal, characteristic, complemented
5C22⋊C4×M16C211yesmaximal, characteristic, complemented
6C2×#1733C211yesmaximal, characteristic, complemented
7#13761C211yesmaximal, characteristic, complemented
8#10933C211yesmaximal, characteristic, complemented
9#10924C211yesmaximal, characteristic, complemented
10#10886C211yesmaximal, characteristic, complemented
11#10878C211yesmaximal, characteristic, complemented
12#10808C211yesmaximal, characteristic, complemented
13#10790C211yesmaximal, characteristic, complemented
14#10733C211yesmaximal, characteristic, complemented
15#10701C211yesmaximal, characteristic, complemented
16C23×M16C2211yescharacteristic
17C2×#525C2211yescharacteristic
18C2×C4×#41C2211yescharacteristic
19C22×#117C2211yescharacteristic
20C22×#117C2211yescharacteristic
21C22×#104C2211yescharacteristic
22C22×#104C2211yescharacteristic
23C22×#104C2211yescharacteristic
24C22×#104C2211yescharacteristic
25C2×#407C2211yescharacteristic
26C2×C4×M16C2211yescharacteristic
27C2×C4×M16C2211yescharacteristic
28#2363C412yescomplemented
29#2362C412yescomplemented
30#2361C412yescomplemented
31#2360C412yescomplemented
32#2359—22no—
33#2358—22no—
34#2297C2211yescharacteristic
35#2296C2211yescharacteristic
36#2293—21no—
37#2290—21no—
38#2290—21no—
39C42×D4—21no—
40C4×#117C2211yescharacteristic
41C2×C4×C22⋊C4C2211yescharacteristic
42C2×C4×C22⋊C4C2211yescharacteristic
43C2×#376C2211yescharacteristic
44C2×C43C2211yescharacteristic
45#1897C418yescomplemented
46#1871C418yescomplemented
47C4×#104—24no—
48#1753—21no—
49#1753—21no—
50#1752—21no—
51C8×C22⋊C4—21no—
52#1733—24no—
53C2×#339C2211yescharacteristic
54C2×#339C2211yescharacteristic
55C2×#339C2211yescharacteristic
56C2×#339C2211yescharacteristic
57C2×#339C2211yescharacteristic
58C2×#339C2211yescharacteristic
59C2×#339C2211yescharacteristic
60C2×#339C2211yescharacteristic
61C2×#339C2211yescharacteristic
62C2×#339C2211yescharacteristic
63C2×#339C2211yescharacteristic
64C2×#339C2211yescharacteristic
65#1728C2211yescharacteristic
66#1728C2211yescharacteristic
67#1437—22no—
68#1436—22no—
69C4×#95C2211yescharacteristic
70C4×#95C2211yescharacteristic
71C22×#41C2311yescharacteristic
72C24×C4C2311yescharacteristic
73C22×M16—21no—
74C22×M16—22no—
75C22×M16—22no—
76C22×M16—22no—
77C22×M16—41no—
78C22×M16—41no—
79C22×M16C2×C414yescomplemented
80C22×M16C2311yescharacteristic
81C22×M16C2311yescharacteristic
82C22×M16C2311yescharacteristic
83C22×M16C2311yescharacteristic
84C23×C8—21no—
85#525—22no—
86#525—22no—
87#525C2×C414yes—
88#525C2×C414yes—
89C2×#123—21no—
90C2×C22⋊Q8C2×C411yescharacteristic
91C2×C22⋊Q8C2×C411yescharacteristic
92C2×#121C2×C411yescharacteristic
93C2×#121C2×C411yescharacteristic
94C2×#120—21no—
95C4×#41—22no—
96C4×#41—22no—
97C4×#41—41no—
98C4×#41—41no—
99C2×C4×Q8C2×C412yes—
100C2×C4×D4—21no—
101C2×C4×D4—21no—
102C2×C4×D4—22no—
103C2×C4×D4—22no—
104C2×C4×D4C2×C412yes—
105C2×#117—21no—
106C2×#117—21no—
107C2×#117—22no—
108C2×#117—21no—
109C2×#117—22no—
110C2×#117—22no—
111C2×#117—22no—
112C2×#117—22no—
113C2×#117—41no—
114C2×#117—41no—
115C2×#117—41no—
116C2×#117—41no—
117C2×#117C2×C412yes—
118C2×#117C2×C414yescomplemented
119C2×#117C2311yescharacteristic
120C2×#117C2311yescharacteristic
121C2×#117C2311yescharacteristic
122C22×C4⋊C4—21no—
123C22×C4⋊C4C2×C412yes—
124C22×C22⋊C4—21no—
125C22×C22⋊C4—21no—
126C22×C22⋊C4—21no—
127C22×C22⋊C4D412yes—
128C22×C42—21no—
129C22×C42—21no—
130C22×C42—22no—
131C22×C42C2311yescharacteristic
132C22×C42C2311yescharacteristic
133C22×C42C2311yescharacteristic
134C22×C42C2311yescharacteristic
135C22×C42C2311yescharacteristic
136C22×C42C2311yescharacteristic
137C2×#104—22no—
138C2×#104—22no—
139C2×#104—22no—
140C2×#104—22no—
141C2×#104—41no—
142C2×#104—41no—
143C2×#104—41no—
144C2×#104—41no—
145C2×#104C2×C414yescomplemented
146C2×#104C2×C414yescomplemented
147C2×#104C2×C414yescomplemented
148C2×#104C2×C414yescomplemented
149#407—22no—
150#407C2×C414yescomplemented
151C2×C22⋊C8—21no—
152C2×C22⋊C8—21no—
153C4×M16—22no—
154C4×M16—22no—
155C4×M16—41no—
156C4×M16—41no—
157C2×#97—21no—
158C2×#97—21no—
159C2×C4×C8—21no—
160C2×C4×C8—21no—
161#391C2×C412yes—
162#390—22no—
163#390C2×C412yes—
164#389—22no—
165#389C2×C412yes—
166#389C2×C412yes—
167#388—22no—
168#388—22no—
169#388—22no—
170#388—22no—
171#387—22no—
172#387—22no—
173#386—22no—
174#386—22no—
175#386—22no—
176#385—22no—
177#385—22no—
178#385—22no—
179C4×C4⋊C4—21no—
180C4×C4⋊C4—21no—
181C4×C4⋊C4—22no—
182C4×C4⋊C4C2×C412yes—
183C4×C4⋊C4C2×C412yes—
184C4×C22⋊C4—22no—
185C4×C22⋊C4—22no—
186C4×C22⋊C4—22no—
187C4×C22⋊C4—21no—
188C4×C22⋊C4—21no—
189C4×C22⋊C4—22no—
190C4×C22⋊C4C2×C412yes—
191C4×C22⋊C4C2×C412yes—
192C4×C22⋊C4C2×C414yescomplemented
193C4×C22⋊C4D411yescharacteristic
194C4×C22⋊C4D411yescharacteristic
195C4×C22⋊C4D411yescharacteristic
196C4×C22⋊C4D411yescharacteristic
197#376—21no—
198#376—22no—
199#376—41no—
200C2×#95—21no—
201C2×#95—22no—
202C2×#95—22no—
203C2×#95—22no—
204C2×#95D412yes—
205C43—21no—
206C43—22no—
207C43—41no—
208#339—22no—
209#339—22no—
210#339—22no—
211#339—22no—
212#339—22no—
213#339—41no—
214#339—41no—
215#339C2×C414yescomplemented
216#339C2×C414yescomplemented
217#339C2×C414yescomplemented
218#339C2×C414yescomplemented
219#339D414yescomplemented
220#336—21no—
221#336—21no—
222#336—21no—
223#336—21no—
224C25C2×D411yescharacteristic
225C2×#41—21no—
226C2×#41—21no—
227C2×#41—21no—
228C2×#41—21no—
229C2×#41—21no—
230C2×#41—21no—
231C2×#41—21no—
232C2×#41—21no—
233C2×#41—21no—
234C2×#41—21no—
235C2×#41C22×C412yes—
236C2×#41C22×C412yes—
237C22×Q8C22×C411yescharacteristic
238C22×D4—21no—
239C22×D4—21no—
240C22×D4—21no—
241C22×D4C22×C411yescharacteristic
242C23×C4—21no—
243C23×C4—21no—
244C23×C4—21no—
245C23×C4—21no—
246C23×C4—21no—
247C23×C4—21no—
248C23×C4—21no—
249C23×C4—21no—
250C23×C4—21no—
251C23×C4—21no—
252C23×C4—21no—
253C23×C4—21no—
254C23×C4—21no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4C22×C411yescharacteristic
258C23×C4C22×C411yescharacteristic
259C23×C4C22×C412yes—
260C23×C4C22×C412yes—
261C23×C4C2×D412yes—
262C23×C4C2×D411yescharacteristic
263C23×C4C2×D411yescharacteristic
264C23×C4C2×D411yescharacteristic
265C23×C4C2×D412yes—
266C23×C4#4112yes—
267C23×C4#4112yes—
268C23×C4C2411yescharacteristic
269C2×M16—21no—
270C2×M16—21no—
271C2×M16—21no—
272C2×M16—24no—
273C2×M16—21no—
274C2×M16—21no—
275C2×M16—21no—
276C2×M16—21no—
277C2×M16—21no—
278C2×M16—21no—
279C2×M16—21no—
280C2×M16—21no—
281C2×M16—21no—
282C2×M16—21no—
283C2×M16—21no—
284C2×M16—21no—
285C2×M16—21no—
286C2×M16—21no—
287C2×M16—21no—
288C2×M16—28no—
289C2×M16—42no—
290C2×M16—42no—
291C2×M16—44no—
292C2×M16—44no—
293C2×M16—44no—
294C2×M16C22×C412yes—
295C2×M16C22×C412yes—
296C2×M16C22×C412yes—
297C2×M16C22×C412yes—
298C2×M16C2×D412yes—
299C2×M16#4112yes—
300C22×C8—21no—
301C22×C8—24no—
302C22×C8—21no—
303C22×C8—21no—
304C22×C8—21no—
305C22×C8—42no—
306C22×C8—42no—
307#123—24no—
308#123—24no—
309C22⋊Q8—22no—
310C22⋊Q8—22no—
311C22⋊Q8C4214yescomplemented
312C22⋊Q8C4214yescomplemented
313#121—22no—
314#121—22no—
315#121C4214yescomplemented
316#121C4214yescomplemented
317#120—24no—
318#120—24no—
319C4×Q8—24no—
320C4×Q8—42no—
321C4×D4—24no—
322C4×D4—24no—
323C4×D4—24no—
324C4×D4—24no—
325C4×D4—24no—
326C4×D4—42no—
327C4×D4—44no—
328C4×D4—44no—
329C4×D4—48no—
330#117—21no—
331#117—21no—
332#117—21no—
333#117—21no—
334#117—28no—
335#117—21no—
336#117—21no—
337#117—21no—
338#117—21no—
339#117—24no—
340#117—44no—
341#117—42no—
342#117—42no—
343#117—42no—
344#117—44no—
345#117—42no—
346#117—44no—
347#117—42no—
348#117—42no—
349#117—42no—
350#117C22×C412yes—
351#117C22×C412yes—
352#117C2×D412yes—
353#117#4112yes—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—42no—
363C2×C4⋊C4—42no—
364C2×C4⋊C4—42no—
365C2×C4⋊C4C22×C412yes—
366C2×C4⋊C4C22×C411yescharacteristic
367C2×C4⋊C4C22×C411yescharacteristic
368C2×C4⋊C4C22×C412yes—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—44no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—44no—
388C2×C22⋊C4C22⋊C412yes—
389C2×C22⋊C4C22⋊C412yes—
390C2×C22⋊C4C22⋊C412yes—
391C2×C22⋊C4C22⋊C412yes—
392C2×C42—21no—
393C2×C42—21no—
394C2×C42—21no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—21no—
398C2×C42—21no—
399C2×C42—21no—
400C2×C42—21no—
401C2×C42—21no—
402C2×C42—21no—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42—21no—
406C2×C42—21no—
407C2×C42—21no—
408C2×C42—21no—
409C2×C42—21no—
410C2×C42—21no—
411C2×C42—21no—
412C2×C42—21no—
413C2×C42—21no—
414C2×C42—21no—
415C2×C42—21no—
416C2×C42—21no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—21no—
421C2×C42—21no—
422C2×C42—21no—
423C2×C42—21no—
424C2×C42—22no—
425C2×C42—42no—
426C2×C42—42no—
427C2×C42—42no—
428C2×C42—42no—
429C2×C42—44no—
430C2×C42—44no—
431C2×C42—44no—
432C2×C42C22×C412yes—
433C2×C42C22×C412yes—
434C2×C42C22×C412yes—
435C2×C42C22×C412yes—
436C2×C42C22×C412yes—
437C2×C42C22×C412yes—
438C2×C42C2×D411yescharacteristic
439C2×C42C2×D411yescharacteristic
440C2×C42C2×D411yescharacteristic
441C2×C42C2×D411yescharacteristic
442C2×C42C2×D412yes—
443C2×C42#4112yes—
444#104—28no—
445#104—28no—
446#104—44no—
447#104—44no—
448C22⋊C8—24no—
449C22⋊C8—24no—
450#97—42no—
451#97—42no—
452C4×C8—42no—
453C4×C8—42no—
454#95—22no—
455#95—22no—
456#95—22no—
457#95—22no—
458#95—22no—
459#95—22no—
460#95—24no—
461#95—44no—
462#95—44no—
463#95—44no—
464#95C22⋊C412yes—
465#95C22⋊C412yes—
466#95C22⋊C412yes—
467#95C22⋊C412yes—
468C24—21no—
469C24—21no—
470C24—21no—
471C24—21no—
472C24—21no—
473C24—42no—
474C24—42no—
475C24C2×C22⋊C411yescharacteristic
476C24C2×C22⋊C411yescharacteristic
477C24C4×D412yes—
478C24C4×D412yes—
479C24C22×D411yescharacteristic
480#41—22no—
481#41—22no—
482#41—22no—
483#41—22no—
484#41—22no—
485#41—22no—
486#41—22no—
487#41—22no—
488#41—41no—
489#41—41no—
490#41—41no—
491#41—41no—
492#41—41no—
493#41—41no—
494#41—41no—
495#41—41no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8C2×C4212yes—
502C2×D4—22no—
503C2×D4—22no—
504C2×D4—24no—
505C2×D4—24no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—44no—
512C2×D4—41no—
513C2×D4—41no—
514C2×D4—41no—
515C2×D4—41no—
516C2×D4—82no—
517C2×D4C2×C4212yes—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—22no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—24no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—24no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—44no—
577C22×C4—44no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—44no—
592C22×C4—41no—
593C22×C4—41no—
594C22×C4—41no—
595C22×C4—41no—
596C22×C4—44no—
597C22×C4—82no—
598C22×C4—82no—
599C22×C4C2×C4212yes—
600C22×C4C2×C4212yes—
601C22×C4C2×C22⋊C412yes—
602C22×C4C2×C22⋊C412yes—
603C22×C4C2×C22⋊C412yes—
604C22×C4C2×C22⋊C411yescharacteristic
605C22×C4C2×C22⋊C411yescharacteristic
606C22×C4C2×C22⋊C412yes—
607C22×C4#11712yes—
608C22×C4#11712yes—
609C22×C4C4×D412yes—
610C22×C4C4×D412yes—
611C22×C4C4×D412yes—
612C22×C4C4×D412yes—
613C22×C4C4×D412yes—
614C22×C4C4×D412yes—
615C22×C4C23×C411yescharacteristic
616C22×C4C23×C411yescharacteristic
617C22×C4C23×C411yescharacteristic
618C22×C4C22×D411yescharacteristic
619C22×C4C22×D411yescharacteristic
620C22×C4C2×#4111yescharacteristic
621C22×C4C2×#4111yescharacteristic
622C22×C4C2×#4111yescharacteristic
623C22×C4C2×#4111yescharacteristic
624C22×C4C2×#4111yescharacteristic
625C22×C4H(5,𝔽2)11yescharacteristic
626C22×C4H(5,𝔽2)11yescharacteristic
627C22×C4H(5,𝔽2)11yescharacteristic
628C22×C42−1+411yescharacteristic
629M16—22no—
630M16—22no—
631M16—22no—
632M16—22no—
633M16—22no—
634M16—22no—
635M16—22no—
636M16—22no—
637M16—22no—
638M16—48no—
639M16—41no—
640M16—41no—
641M16—41no—
642M16—41no—
643M16—41no—
644M16—41no—
645M16C4×D414yescomplemented
646C2×C8—22no—
647C2×C8—22no—
648C2×C8—22no—
649C2×C8—22no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—48no—
653C2×C8—41no—
654C2×C8—41no—
655C2×C8—41no—
656C2×C8—41no—
657C2×C8—41no—
658C2×C8—41no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—22no—
662C4⋊C4—24no—
663C4⋊C4—24no—
664C4⋊C4—22no—
665C4⋊C4—22no—
666C4⋊C4—44no—
667C4⋊C4—48no—
668C4⋊C4—44no—
669C4⋊C4—44no—
670C4⋊C4—82no—
671C4⋊C4C2×C4212yes—
672C4⋊C4C2×C4212yes—
673C4⋊C4C4×D414yes—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—24no—
679C22⋊C4—24no—
680C22⋊C4—24no—
681C22⋊C4—24no—
682C22⋊C4—24no—
683C22⋊C4—24no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—44no—
687C22⋊C4—44no—
688C22⋊C4—48no—
689C22⋊C4—48no—
690C22⋊C4—44no—
691C22⋊C4—41no—
692C22⋊C4—41no—
693C22⋊C4—82no—
694C42—22no—
695C42—22no—
696C42—22no—
697C42—22no—
698C42—22no—
699C42—22no—
700C42—22no—
701C42—21no—
702C42—21no—
703C42—22no—
704C42—21no—
705C42—21no—
706C42—21no—
707C42—21no—
708C42—22no—
709C42—22no—
710C42—21no—
711C42—21no—
712C42—22no—
713C42—22no—
714C42—22no—
715C42—22no—
716C42—22no—
717C42—22no—
718C42—22no—
719C42—44no—
720C42—44no—
721C42—44no—
722C42—416no—
723C42—41no—
724C42—41no—
725C42—41no—
726C42—41no—
727C42—41no—
728C42—41no—
729C42—41no—
730C42—41no—
731C42—82no—
732C42C4×D414yescomplemented
733C23—22no—
734C23—22no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—42no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—41no—
753C23—41no—
754C23—42no—
755C23—42no—
756C23—82no—
757C23—82no—
758C23—82no—
759C23—82no—
760C23C4×C22⋊C412yes—
761C23C4×C22⋊C412yes—
762C23C22×C22⋊C411yescharacteristic
763C23C2×C4×D411yescharacteristic
764C23C2×C4×D411yescharacteristic
765C23D4211yescharacteristic
766C23#54611yescharacteristic
767C23#54611yescharacteristic
768C23#54711yescharacteristic
769Q8—22no—
770Q8—22no—
771Q8—41no—
772Q8—41no—
773D4—22no—
774D4—22no—
775D4—48no—
776D4—42no—
777D4—42no—
778D4—42no—
779D4—42no—
780D4—41no—
781D4—41no—
782D4—84no—
783C2×C4—22no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—24no—
810C2×C4—22no—
811C2×C4—24no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—24no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—44no—
825C2×C4—44no—
826C2×C4—44no—
827C2×C4—44no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—44no—
832C2×C4—44no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—88no—
854C2×C4—82no—
855C2×C4—82no—
856C2×C4—88no—
857C2×C4—82no—
858C2×C4—82no—
859C2×C4—82no—
860C2×C4—82no—
861C2×C4C4×C22⋊C412yes—
862C2×C4C4×C22⋊C412yes—
863C2×C4#42114yes—
864C2×C4C22×C4211yescharacteristic
865C2×C4C2×#11711yescharacteristic
866C2×C4C2×C4×D411yescharacteristic
867C2×C4C2×C4×D411yescharacteristic
868C2×C4C2×C4×D411yescharacteristic
869C2×C4C2×C4×D411yescharacteristic
870C2×C4C2×C4×D411yescharacteristic
871C2×C4C4×#4111yescharacteristic
872C2×C4C4×#4111yescharacteristic
873C2×C4C4×#4111yescharacteristic
874C2×C4#51811yescharacteristic
875C2×C4#51811yescharacteristic
876C2×C4#51811yescharacteristic
877C2×C4#52011yescharacteristic
878C2×C4#52011yescharacteristic
879C2×C4#52011yescharacteristic
880C2×C4D4211yescharacteristic
881C2×C4#54611yescharacteristic
882C2×C4#54611yescharacteristic
883C2×C4#54611yescharacteristic
884C2×C4#54711yescharacteristic
885C2×C4#54811yescharacteristic
886C2×C4#55111yescharacteristic
887C2×C4#55111yescharacteristic
888C2×C4#55211yescharacteristic
889C2×C4#55311yescharacteristic
890C2×C4#55311yescharacteristic
891C2×C4#55311yescharacteristic
892C8—24no—
893C8—42no—
894C8—42no—
895C8—42no—
896C22—22no—
897C22—22no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—22no—
903C22—22no—
904C22—22no—
905C22—22no—
906C22—22no—
907C22—22no—
908C22—22no—
909C22—22no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—82no—
918C22—82no—
919C22—82no—
920C22—82no—
921C22—82no—
922C22—82no—
923C22C2×C4×C22⋊C411yescharacteristic
924C22D4×C22⋊C411yescharacteristic
925C22#233911yescharacteristic
926C22#235811yescharacteristic
927C22#235911yescharacteristic
928C22#236111yescharacteristic
929C22#236411yescharacteristic
930C22C2×#42112yes—
931C22#290112yes—
932C4—24no—
933C4—22no—
934C4—22no—
935C4—44no—
936C4—44no—
937C4—42no—
938C4—44no—
939C4—42no—
940C4—42no—
941C4—42no—
942C4—42no—
943C4—42no—
944C4—82no—
945C4—82no—
946C4—82no—
947C4C42×D411yescharacteristic
948C4#227511yescharacteristic
949C4#235211yescharacteristic
950C4#235311yescharacteristic
951C4#235811yescharacteristic
952C4#235911yescharacteristic
953C4#236111yescharacteristic
954C4#236411yescharacteristic
955C2—21no—
956C2—21no—
957C2—21no—
958C2—21no—
959C2—42no—
960C2—42no—
961C2—82no—
962C2#1381311yescharacteristic
963C2C4×#42111yescharacteristic
964C2#2040511yescharacteristic
965C2#2243412yes—
966C2#2250712yes—
subgroupG/H
centerC22×C4C22×D4
commutatorC2×C4C22×C42
Frattini, cosocleC23×C4C24
socleC23C22×C22⋊C4
prime radicalC2×#525C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C2×C4×#104C2semidirect
5. C22⋊C4×M16C2semidirect
6. C2×#1733C2semidirect
7. #13761C2semidirect
8. #10933C2semidirect
9. #10924C2semidirect
10. #10886C2semidirect
11. #10878C2semidirect
12. #10808C2semidirect
13. #10790C2semidirect
14. #10733C2semidirect
15. #10701C2semidirect
28. #2363C4semidirect
29. #2362C4semidirect
30. #2361C4semidirect
31. #2360C4semidirect
45. #1897C4semidirect
46. #1871C4semidirect
79. C22×M16C2×C4semidirect
118. C2×#117C2×C4semidirect
145. C2×#104C2×C4semidirect
146. C2×#104C2×C4semidirect
147. C2×#104C2×C4semidirect
148. C2×#104C2×C4semidirect
150. #407C2×C4semidirect
192. C4×C22⋊C4C2×C4semidirect
215. #339C2×C4semidirect
216. #339C2×C4semidirect
217. #339C2×C4semidirect
218. #339C2×C4semidirect
219. #339D4semidirect
311. C22⋊Q8C42semidirect
312. C22⋊Q8C42semidirect
315. #121C42semidirect
316. #121C42semidirect
645. M16C4×D4semidirect
732. C42C4×D4semidirect

Maximal subgroups

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

subgroupindex
#341362
C2×#18972
C2×#18712
C2×C4×#1042
C22⋊C4×M162
C2×#17332
#137612
#109332
#109242
#108862
#108782
#108082
#107902
#107332
#107012