Finite Group Databasebeta

← #383281

Subgroups — #383281

Order 512.

1394 conjugacy classes of subgroups.

The subgroup lattice has 909 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#485C211yesmaximal, characteristic
2C2×#1935C211yesmaximal, characteristic, complemented
3C2×#1863C211yesmaximal, characteristic, complemented
4#13969C211yesmaximal, characteristic
5#13951C211yesmaximal, characteristic
6#11378C211yesmaximal, characteristic, complemented
7#11219C211yesmaximal, characteristic, complemented
8#11219C211yesmaximal, characteristic, complemented
9#11190C211yesmaximal, characteristic, complemented
10#11096C211yesmaximal, characteristic
11#10970C211yesmaximal, characteristic
12#10922C211yesmaximal, characteristic
13#10863C211yesmaximal, characteristic, complemented
14#10789C211yesmaximal, characteristic, complemented
15#10731C211yesmaximal, characteristic
16C22×C22⋊Q8C2211yescharacteristic
17C22×C4×Q8C2211yescharacteristic
18C22×#117C2211yescharacteristic
19C2×#485—24no—
20C2×#485—24no—
21C2×#485C418yescomplemented
22C22×#107C2211yescharacteristic
23C22×#107C2211yescharacteristic
24C22×#106C2211yescharacteristic
25C22×#103C2211yescharacteristic
26C22×#103C2211yescharacteristic
27C22×#103C2211yescharacteristic
28C22×#103C2211yescharacteristic
29C22×C22⋊C8C2211yescharacteristic
30C22×C22⋊C8C2211yescharacteristic
31C22×#97C2211yescharacteristic
32C2×#391C2211yescharacteristic
33C2×#389C2211yescharacteristic
34C2×#389C2211yescharacteristic
35C2×#380C2211yescharacteristic
36C2×#380C2211yescharacteristic
37C2×C4×C22⋊C4C2211yescharacteristic
38#1935—24no—
39#1863—24no—
40C2×#340C2211yescharacteristic
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#336C2211yescharacteristic
50C2×#336C2211yescharacteristic
51C2×#336C2211yescharacteristic
52#1441—21no—
53#1439—21no—
54#1439—21no—
55#1439—21no—
56#1437—21no—
57#1436—21no—
58C4⋊#95—21no—
59C4⋊#95C2211yescharacteristic
60C4⋊#95C2211yescharacteristic
61C4⋊#95C2211yescharacteristic
62C4⋊#95C2211yescharacteristic
63#1434—21no—
64C23×Q8C2311yescharacteristic
65C24×C4C2311yescharacteristic
66C23×C8C2311yescharacteristic
67C23×C8C2311yescharacteristic
68C23×C8C2311yescharacteristic
69C23×C8C2311yescharacteristic
70C2×C22⋊Q8—22no—
71C2×C22⋊Q8—22no—
72C2×C22⋊Q8—22no—
73C2×C22⋊Q8—41no—
74C2×C22⋊Q8—41no—
75C2×C22⋊Q8C2×C414yes—
76C2×C4×Q8—22no—
77C2×C4×Q8—22no—
78C2×C4×Q8—41no—
79C2×C4×Q8—41no—
80C2×C4×Q8—41no—
81C2×C4×Q8—41no—
82C2×#117—22no—
83C2×#117—22no—
84C2×#117—22no—
85C2×#117—41no—
86C2×#117—41no—
87C2×#117C2×C414yes—
88C22×C4⋊C4—21no—
89C22×C4⋊C4—21no—
90C22×C4⋊C4—21no—
91C22×C4⋊C4—21no—
92C22×C4⋊C4C2311yescharacteristic
93C22×C4⋊C4C2311yescharacteristic
94C22×C4⋊C4C2311yescharacteristic
95C22×C4⋊C4C2311yescharacteristic
96C22×C4⋊C4C2311yescharacteristic
97C22×C4⋊C4C2311yescharacteristic
98C22×C4⋊C4C2311yescharacteristic
99C22×C22⋊C4—21no—
100C22×C22⋊C4—21no—
101C22×C22⋊C4—21no—
102C22×C22⋊C4—21no—
103C22×C22⋊C4D411yescharacteristic
104C22×C22⋊C4D411yescharacteristic
105C22×C42—21no—
106C22×C42—21no—
107C22×C42C2311yescharacteristic
108C22×C42C2311yescharacteristic
109#485—232no—
110C2×#107—22no—
111C2×#107—22no—
112C2×#107—22no—
113C2×#107—22no—
114C2×#107—41no—
115C2×#107C2×C414yes—
116C2×#106—22no—
117C2×#106—22no—
118C2×#106C2×C414yes—
119C2×#103—22no—
120C2×#103—22no—
121C2×#103—22no—
122C2×#103—22no—
123C2×#103—22no—
124C2×#103—41no—
125C2×#103—41no—
126C2×#103—41no—
127C2×#103C2×C414yes—
128C2×#103C2×C414yes—
129C2×#103D414yes—
130C2×#103D414yes—
131C2×C22⋊C8—22no—
132C2×C22⋊C8—22no—
133C2×C22⋊C8—22no—
134C2×C22⋊C8—22no—
135C2×C22⋊C8—41no—
136C2×C22⋊C8C2×C414yes—
137C2×#97—22no—
138C2×#97—22no—
139C2×#97—41no—
140#391—22no—
141#391—41no—
142#389—22no—
143#389—22no—
144#389—41no—
145#389—41no—
146#380—22no—
147#380—41no—
148#380—41no—
149#380—41no—
150C4×C22⋊C4—41no—
151C4×C22⋊C4—41no—
152C2×#95—21no—
153C2×#95—21no—
154C2×#95—21no—
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×#95—21no—
164C2×#95—21no—
165C2×#95—21no—
166C2×#95D411yescharacteristic
167C2×#95D411yescharacteristic
168#340—22no—
169#340—22no—
170#340—22no—
171#340—41no—
172#340—41no—
173#340—41no—
174#340—41no—
175#340—41no—
176#340—41no—
177#336—22no—
178#336—41no—
179#336—41no—
180C25C2×D411yescharacteristic
181C22×Q8—21no—
182C22×Q8—21no—
183C22×Q8—21no—
184C22×Q8—21no—
185C22×Q8—21no—
186C22×Q8—21no—
187C22×Q8—21no—
188C22×Q8—21no—
189C22×Q8—21no—
190C22×Q8—21no—
191C22×Q8—21no—
192C22×Q8C22×C412yes—
193C22×Q8C2×D412yes—
194C22×Q8C2×D412yes—
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—21no—
206C23×C4—21no—
207C23×C4—21no—
208C23×C4—21no—
209C23×C4—21no—
210C23×C4—21no—
211C23×C4—21no—
212C23×C4—21no—
213C23×C4—21no—
214C23×C4—21no—
215C23×C4C22×C412yes—
216C23×C4C2×D411yescharacteristic
217C23×C4C2×D411yescharacteristic
218C23×C4C2×D411yescharacteristic
219C23×C4C2×D411yescharacteristic
220C23×C4C2×D411yescharacteristic
221C23×C4#4112yes—
222C23×C4C2411yescharacteristic
223C22×C8—21no—
224C22×C8—21no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—21no—
228C22×C8—21no—
229C22×C8—21no—
230C22×C8—21no—
231C22×C8—21no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—21no—
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×C8C22×C412yes—
247C22×C8C22×C412yes—
248C22×C8C2×D412yes—
249C22×C8C2×D412yes—
250C22×C8#4112yes—
251C22⋊Q8—28no—
252C22⋊Q8—44no—
253C22⋊Q8—44no—
254C22⋊Q8—44no—
255C4×Q8—44no—
256C4×Q8—44no—
257C4×Q8—44no—
258C4×Q8—44no—
259#117—28no—
260#117—44no—
261#117—44no—
262#117—44no—
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—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—24no—
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—42no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—81no—
310C2×C4⋊C4—81no—
311C2×C4⋊C4C22×C412yes—
312C2×C4⋊C4C22×C412yes—
313C2×C4⋊C4C22×C412yes—
314C2×C4⋊C4C2×D412yes—
315C2×C4⋊C4C2×D412yes—
316C2×C4⋊C4#4112yes—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—41no—
321C2×C22⋊C4—41no—
322C2×C22⋊C4—41no—
323C2×C22⋊C4—41no—
324C2×C22⋊C4—41no—
325C2×C22⋊C4—42no—
326C2×C22⋊C4—42no—
327C2×C22⋊C4—42no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4—42no—
330C2×C22⋊C4—42no—
331C2×C22⋊C4—42no—
332C2×C22⋊C4—81no—
333C2×C22⋊C4—81no—
334C2×C22⋊C4—81no—
335C2×C42—24no—
336C2×C42—21no—
337C2×C42—21no—
338C2×C42—21no—
339C2×C42—21no—
340C2×C42—21no—
341C2×C42—21no—
342C2×C42—21no—
343C2×C42—21no—
344C2×C42—21no—
345C2×C42—21no—
346C2×C42—21no—
347C2×C42—21no—
348C2×C42—42no—
349C2×C42—42no—
350C2×C42—42no—
351C2×C42—42no—
352C2×C42—42no—
353#107—28no—
354#107—44no—
355#106—28no—
356#103—28no—
357#103—44no—
358#103—44no—
359#103C22⋊C4116yescomplemented
360C22⋊C8—28no—
361C22⋊C8—44no—
362#97—44no—
363#95—41no—
364#95—41no—
365#95—42no—
366#95—42no—
367#95—42no—
368#95—42no—
369#95—42no—
370#95—42no—
371#95—42no—
372#95—42no—
373#95—42no—
374#95—42no—
375#95—81no—
376#95—81no—
377#95—81no—
378#95—81no—
379C24—21no—
380C24—21no—
381C24—21no—
382C24—21no—
383C24—21no—
384C24—21no—
385C24—21no—
386C24—21no—
387C24—21no—
388C24—21no—
389C24—21no—
390C24—21no—
391C24—21no—
392C24—21no—
393C24C4×D412yes—
394C24C22×D411yescharacteristic
395C2×Q8—22no—
396C2×Q8—22no—
397C2×Q8—22no—
398C2×Q8—22no—
399C2×Q8—22no—
400C2×Q8—22no—
401C2×Q8—22no—
402C2×Q8—22no—
403C2×Q8—22no—
404C2×Q8—22no—
405C2×Q8—22no—
406C2×Q8—22no—
407C2×Q8—22no—
408C2×Q8—22no—
409C2×Q8—22no—
410C2×Q8—41no—
411C2×Q8—41no—
412C2×Q8—41no—
413C2×Q8—41no—
414C2×Q8—41no—
415C2×Q8—41no—
416C2×Q8—41no—
417C2×Q8—41no—
418C2×Q8—41no—
419C2×Q8—41no—
420C2×Q8—41no—
421C2×Q8—41no—
422C2×Q8C2×C22⋊C414yes—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—22no—
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—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—21no—
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—21no—
476C22×C4—21no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—41no—
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—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—41no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4C4×D412yes—
541C22×C4#13712yes—
542C22×C4C23×C411yescharacteristic
543C22×C4C22×D411yescharacteristic
544C22×C4C22×D411yescharacteristic
545C22×C4C2×#4111yescharacteristic
546C22×C4C2×#4111yescharacteristic
547C22×C4C2×#4111yescharacteristic
548C22×C4H(5,𝔽2)11yescharacteristic
549C22×C4H(5,𝔽2)11yescharacteristic
550C22×C4H(5,𝔽2)11yescharacteristic
551C22×C4H(5,𝔽2)11yescharacteristic
552C22×C4H(5,𝔽2)11yescharacteristic
553C22×C42−1+411yescharacteristic
554C22×C42−1+411yescharacteristic
555C22×C42−1+411yescharacteristic
556C2×C8—22no—
557C2×C8—22no—
558C2×C8—22no—
559C2×C8—22no—
560C2×C8—22no—
561C2×C8—22no—
562C2×C8—22no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—41no—
569C2×C8—41no—
570C2×C8—41no—
571C2×C8—41no—
572C2×C8—41no—
573C2×C8—41no—
574C2×C8—41no—
575C2×C8—41no—
576C2×C8—41no—
577C2×C8—41no—
578C2×C8—41no—
579C2×C8—41no—
580C2×C8—41no—
581C2×C8—41no—
582C2×C8—41no—
583C2×C8C2×C22⋊C414yes—
584C4⋊C4—22no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—48no—
594C4⋊C4—48no—
595C4⋊C4—41no—
596C4⋊C4—41no—
597C4⋊C4—41no—
598C4⋊C4—41no—
599C4⋊C4—41no—
600C4⋊C4—41no—
601C4⋊C4—41no—
602C4⋊C4—41no—
603C4⋊C4—41no—
604C4⋊C4—41no—
605C4⋊C4—41no—
606C4⋊C4—41no—
607C4⋊C4—41no—
608C4⋊C4—41no—
609C4⋊C4—41no—
610C4⋊C4—41no—
611C4⋊C4—41no—
612C4⋊C4—41no—
613C4⋊C4—84no—
614C4⋊C4—84no—
615C4⋊C4C2×C22⋊C414yes—
616C22⋊C4—48no—
617C22⋊C4—48no—
618C22⋊C4—44no—
619C22⋊C4—44no—
620C22⋊C4—84no—
621C22⋊C4—84no—
622C42—48no—
623C42—48no—
624C42—41no—
625C42—41no—
626C42—41no—
627C42—41no—
628C42—41no—
629C42—41no—
630C42—41no—
631C42—41no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23C2×C4×D411yescharacteristic
668C23#53411yescharacteristic
669C23#53611yescharacteristic
670C23D4211yescharacteristic
671C23D4211yescharacteristic
672C23#54611yescharacteristic
673C23#54711yescharacteristic
674C23C2×#13711yescharacteristic
675C23#57511yescharacteristic
676C23#57511yescharacteristic
677C23#57511yescharacteristic
678C23#57611yescharacteristic
679C23#57711yescharacteristic
680C23#57811yescharacteristic
681C23#57811yescharacteristic
682Q8—24no—
683Q8—24no—
684Q8—42no—
685Q8—42no—
686Q8—42no—
687Q8—42no—
688Q8—42no—
689Q8—42no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—41no—
701C2×C4—42no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—41no—
705C2×C4—42no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—41no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—42no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—41no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—41no—
756C2×C4—81no—
757C2×C4—81no—
758C2×C4—81no—
759C2×C4—81no—
760C2×C4—81no—
761C2×C4—81no—
762C2×C4—81no—
763C2×C4—81no—
764C2×C4—81no—
765C2×C4—81no—
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×C4C22×C22⋊C411yescharacteristic
790C2×C4C4×#4111yescharacteristic
791C2×C4#51811yescharacteristic
792C2×C4#52011yescharacteristic
793C2×C4#52011yescharacteristic
794C2×C4#52011yescharacteristic
795C2×C4#53511yescharacteristic
796C2×C4#53611yescharacteristic
797C2×C4#53711yescharacteristic
798C2×C4#53711yescharacteristic
799C2×C4#53811yescharacteristic
800C2×C4#53911yescharacteristic
801C2×C4#53911yescharacteristic
802C2×C4#53911yescharacteristic
803C2×C4#54011yescharacteristic
804C2×C4#54211yescharacteristic
805C2×C4#54611yescharacteristic
806C2×C4#54611yescharacteristic
807C2×C4#54611yescharacteristic
808C2×C4#54611yescharacteristic
809C2×C4#54711yescharacteristic
810C2×C4#54711yescharacteristic
811C2×C4#55111yescharacteristic
812C2×C4#55211yescharacteristic
813C2×C4#56011yescharacteristic
814C2×C4#56211yescharacteristic
815C2×C4#56211yescharacteristic
816C2×C4#56311yescharacteristic
817C8—24no—
818C8—42no—
819C8—42no—
820C8—81no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22—81no—
832C22—81no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22#232211yescharacteristic
837C22D4×C22⋊C411yescharacteristic
838C22#235911yescharacteristic
839C22#267111yescharacteristic
840C22#267211yescharacteristic
841C22#267811yescharacteristic
842C22#268011yescharacteristic
843C22#294311yescharacteristic
844C22C4×#13711yescharacteristic
845C22#294711yescharacteristic
846C22#295111yescharacteristic
847C22#319611yescharacteristic
848C22#319711yescharacteristic
849C22#319811yescharacteristic
850C22#320211yescharacteristic
851C22#323711yescharacteristic
852C22#324011yescharacteristic
853C22#324211yescharacteristic
854C22#324311yescharacteristic
855C22#326811yescharacteristic
856C22#326811yescharacteristic
857C22#326911yescharacteristic
858C22#326911yescharacteristic
859C22#327011yescharacteristic
860C22#327111yescharacteristic
861C22#327711yescharacteristic
862C22#327811yescharacteristic
863C22#330711yescharacteristic
864C22#331211yescharacteristic
865C22#331311yescharacteristic
866C22#331911yescharacteristic
867C22#334911yescharacteristic
868C22#335011yescharacteristic
869C22#335211yescharacteristic
870C22#335711yescharacteristic
871C4—42no—
872C4—44no—
873C4—42no—
874C4—44no—
875C4—81no—
876C4—82no—
877C4—81no—
878C4—81no—
879C4—82no—
880C4—82no—
881C4—161no—
882C4—161no—
883C4—161no—
884C4#231111yescharacteristic
885C4#233511yescharacteristic
886C4#233911yescharacteristic
887C4#237611yescharacteristic
888C4#268711yescharacteristic
889C4#269311yescharacteristic
890C4#269511yescharacteristic
891C4#270611yescharacteristic
892C2—82no—
893C2#1435911yescharacteristic
894C2#2208311yescharacteristic
895C2#2209411yescharacteristic
896C2#2243911yescharacteristic
897C2#2244511yescharacteristic
898C2#2292811yescharacteristic
899C2#2293711yescharacteristic
900C2#3058011yescharacteristic
901C2#3058811yescharacteristic
902C2#3065211yescharacteristic
903C2#3066011yescharacteristic
904C2#3103711yescharacteristic
905C2#3103911yescharacteristic
906C2#3109911yescharacteristic
907C2#3110111yescharacteristic
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×#1935C2semidirect
3. C2×#1863C2semidirect
6. #11378C2semidirect
7. #11219C2semidirect
8. #11219C2semidirect
9. #11190C2semidirect
13. #10863C2semidirect
14. #10789C2semidirect
21. C2×#485C4semidirect
359. #103C22⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#4852
C2×#19352
C2×#18632
#139692
#139512
#113782
#112192
#111902
#110962
#109702
#109222
#108632
#107892
#107312