Finite Group Databasebeta

← #360176

Subgroups — #360176

Order 512.

2000 conjugacy classes of subgroups.

The subgroup lattice has 1031 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#424C211yesmaximal, characteristic, complemented
2C2×#2324C211yesmaximal, characteristic
3C2×#1895C211yesmaximal, characteristic
4C2×#1893C211yesmaximal, characteristic
5C2×#1804C211yesmaximal, characteristic, complemented
6C2×#1802C211yesmaximal, characteristic, complemented
7#14340C211yesmaximal, characteristic, complemented
8#11228C211yesmaximal, characteristic, complemented
9#11227C211yesmaximal, characteristic, complemented
10#11076C211yesmaximal, characteristic, complemented
11#11076C211yesmaximal, characteristic, complemented
12#10850C211yesmaximal, characteristic, complemented
13#10849C211yesmaximal, characteristic, complemented
14#10722C211yesmaximal, characteristic, complemented
15#10721C211yesmaximal, characteristic, complemented
16C23×M16C2211yescharacteristic
17C24×C8C2211yescharacteristic
18C22×#121C2211yescharacteristic
19C22×C4×D4C2211yescharacteristic
20C22×#117C2211yescharacteristic
21C2×#424—24no—
22C2×#424—24no—
23C2×#424—24no—
24C22×C4⋊C8C2211yescharacteristic
25C22×C4⋊C8C2211yescharacteristic
26C22×C4⋊C8C2211yescharacteristic
27C22×C4⋊C8C2211yescharacteristic
28C22×#102C2211yescharacteristic
29C22×#102C2211yescharacteristic
30C22×#102C2211yescharacteristic
31C22×#102C2211yescharacteristic
32#2324—24no—
33#2324C418yescomplemented
34C2×#390—21no—
35C2×#390C2211yescharacteristic
36C2×#389C2211yescharacteristic
37C2×#388—21no—
38C2×#386—21no—
39C2×#385—21no—
40C2×#384C2211yescharacteristic
41C2×#382C2211yescharacteristic
42C2×#380C2211yescharacteristic
43C2×#380C2211yescharacteristic
44C2×#380C2211yescharacteristic
45C2×C4×C4⋊C4C2211yescharacteristic
46#1895—24no—
47#1893—24no—
48#1804—24no—
49#1802—24no—
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56C2×#340C2211yescharacteristic
57C2×#340C2211yescharacteristic
58C2×#340C2211yescharacteristic
59C2×#340C2211yescharacteristic
60C2×#340C2211yescharacteristic
61C2×#340C2211yescharacteristic
62#1441—21no—
63#1441—21no—
64#1439—21no—
65#1439—21no—
66C4⋊#95C2211yescharacteristic
67C4⋊#95C2211yescharacteristic
68C23×D4—21no—
69C23×D4C2311yescharacteristic
70C24×C4—21no—
71C24×C4C2311yescharacteristic
72C22×M16—22no—
73C22×M16—22no—
74C22×M16—22no—
75C22×M16—22no—
76C22×M16—22no—
77C22×M16—41no—
78C22×M16—41no—
79C23×C8—22no—
80C23×C8—22no—
81C23×C8—22no—
82C23×C8—22no—
83C23×C8—22no—
84C23×C8—41no—
85C23×C8—41no—
86C23×C8C2311yescharacteristic
87C23×C8C2311yescharacteristic
88C23×C8C2311yescharacteristic
89C23×C8C2311yescharacteristic
90C2×#121—22no—
91C2×#121—22no—
92C2×#121—22no—
93C2×#121C2×C414yes—
94C2×#121D414yes—
95C2×#121Q814yes—
96C2×C4×D4—22no—
97C2×C4×D4—22no—
98C2×C4×D4—22no—
99C2×C4×D4—22no—
100C2×C4×D4—22no—
101C2×C4×D4C2×C414yes—
102C2×#117—22no—
103C2×#117—22no—
104C2×#117—22no—
105C2×#117—22no—
106C2×#117C2×C414yes—
107C2×#117D414yes—
108C22×C4⋊C4—21no—
109C22×C4⋊C4—21no—
110C22×C4⋊C4—21no—
111C22×C4⋊C4D411yescharacteristic
112C22×C4⋊C4D411yescharacteristic
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2311yescharacteristic
120C22×C22⋊C4—21no—
121C22×C22⋊C4—21no—
122C22×C22⋊C4—21no—
123C22×C22⋊C4—21no—
124C22×C22⋊C4—21no—
125C22×C22⋊C4—21no—
126C22×C22⋊C4—21no—
127C22×C22⋊C4D411yescharacteristic
128C22×C22⋊C4D411yescharacteristic
129C22×C42—21no—
130C22×C42C2311yescharacteristic
131C22×C42C2311yescharacteristic
132#424—232no—
133C2×C4⋊C8—22no—
134C2×C4⋊C8—22no—
135C2×C4⋊C8—22no—
136C2×C4⋊C8—22no—
137C2×C4⋊C8—22no—
138C2×C4⋊C8—22no—
139C2×C4⋊C8—22no—
140C2×C4⋊C8—22no—
141C2×C4⋊C8—22no—
142C2×C4⋊C8—22no—
143C2×C4⋊C8D414yescomplemented
144C2×C4⋊C8D414yescomplemented
145C2×#102—22no—
146C2×#102—22no—
147C2×#102—22no—
148C2×#102—22no—
149C2×#102—22no—
150C2×#102—22no—
151C2×#102—22no—
152C2×#102—22no—
153C2×#102—41no—
154C2×#102—41no—
155C2×#102—41no—
156C2×#102—41no—
157#390—28no—
158#390—22no—
159#390C2×C414yes—
160#389—22no—
161#389C2×C414yes—
162#388—28no—
163#386—28no—
164#385—28no—
165#384—22no—
166#384—22no—
167#382—22no—
168#382—22no—
169#380—22no—
170#380—22no—
171#380—22no—
172#380—22no—
173#380—22no—
174#380C2×C414yes—
175C4×C4⋊C4—22no—
176C4×C4⋊C4C2×C414yes—
177C2×#95—21no—
178C2×#95—21no—
179C2×#95—21no—
180C2×#95—21no—
181C2×#95—21no—
182C2×#95—21no—
183C2×#95—21no—
184C2×#95—21no—
185C2×#95—21no—
186C2×#95—21no—
187C2×#95—21no—
188#340—22no—
189#340—22no—
190#340—22no—
191#340—22no—
192#340—22no—
193#340—22no—
194#340—22no—
195#340—22no—
196#340—41no—
197#340—41no—
198#340—41no—
199#340—41no—
200C25—21no—
201C25C2×D411yescharacteristic
202C22×D4—24no—
203C22×D4—24no—
204C22×D4—24no—
205C22×D4—21no—
206C22×D4—21no—
207C22×D4—21no—
208C22×D4—21no—
209C22×D4—21no—
210C22×D4—21no—
211C22×D4—21no—
212C22×D4—21no—
213C22×D4—21no—
214C22×D4—21no—
215C22×D4—21no—
216C22×D4—81no—
217C22×D4—81no—
218C22×D4—81no—
219C22×D4—81no—
220C22×D4C22×C412yes—
221C22×D4C2×D412yes—
222C22×D4C2×Q812yes—
223C23×C4—21no—
224C23×C4—21no—
225C23×C4—21no—
226C23×C4—21no—
227C23×C4—21no—
228C23×C4—21no—
229C23×C4—21no—
230C23×C4—21no—
231C23×C4—21no—
232C23×C4—21no—
233C23×C4—21no—
234C23×C4—24no—
235C23×C4—21no—
236C23×C4—21no—
237C23×C4—21no—
238C23×C4—21no—
239C23×C4—42no—
240C23×C4—42no—
241C23×C4—81no—
242C23×C4—81no—
243C23×C4—81no—
244C23×C4—81no—
245C23×C4C22×C412yes—
246C23×C4C2×D411yescharacteristic
247C23×C4C2×D411yescharacteristic
248C23×C4C2×D411yescharacteristic
249C23×C4C2×D411yescharacteristic
250C23×C4C2×D411yescharacteristic
251C23×C4C2×D412yes—
252C23×C4C2×D412yes—
253C23×C4C2×Q812yes—
254C23×C4#4112yes—
255C23×C4#4112yes—
256C23×C4C2411yescharacteristic
257C2×M16—28no—
258C2×M16—44no—
259C2×M16—44no—
260C2×M16—44no—
261C2×M16—44no—
262C2×M16—44no—
263C2×M16—44no—
264C22×C8—28no—
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×C8—21no—
282C22×C8—21no—
283C22×C8—21no—
284C22×C8—21no—
285C22×C8—21no—
286C22×C8—21no—
287C22×C8—21no—
288C22×C8—21no—
289C22×C8—44no—
290C22×C8—44no—
291C22×C8—44no—
292C22×C8—44no—
293C22×C8—44no—
294C22×C8—44no—
295C22×C8C2×D412yes—
296C22×C8C2×D412yes—
297C22×C8C2×D412yes—
298C22×C8C2×D412yes—
299#121—28no—
300#121—28no—
301#121—28no—
302#121C4⋊C4116yescomplemented
303C4×D4—28no—
304C4×D4—28no—
305C4×D4—44no—
306C4×D4—44no—
307#117—28no—
308#117—28no—
309#117—28no—
310#117—28no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
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—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
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—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4—42no—
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⋊C414yes—
362C2×C4⋊C4C22⋊C414yes—
363C2×C4⋊C4C22×C412yes—
364C2×C4⋊C4C22×C412yes—
365C2×C4⋊C4C22×C412yes—
366C2×C4⋊C4C2×D412yes—
367C2×C4⋊C4C2×Q812yes—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—81no—
384C2×C22⋊C4—81no—
385C2×C22⋊C4—81no—
386C2×C22⋊C4—81no—
387C2×C22⋊C4—81no—
388C2×C22⋊C4—81no—
389C2×C22⋊C4—81no—
390C2×C22⋊C4—81no—
391C2×C22⋊C4—81no—
392C2×C22⋊C4—81no—
393C2×C22⋊C4C22⋊C414yes—
394C2×C22⋊C4C22⋊C414yes—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—21no—
398C2×C42—21no—
399C2×C42—24no—
400C2×C42—81no—
401C2×C42—81no—
402C2×C42C22×C412yes—
403C2×C42C22×C412yes—
404C2×C42C2×D412yes—
405C2×C42C2×D412yes—
406C2×C42C2×D412yes—
407C2×C42C2×D412yes—
408C2×C42#4112yes—
409C2×C42#4112yes—
410C4⋊C8—28no—
411C4⋊C8—28no—
412C4⋊C8—28no—
413C4⋊C8—28no—
414#102—44no—
415#102—44no—
416#102—44no—
417#102—44no—
418#95—24no—
419#95—24no—
420#95—24no—
421#95—42no—
422#95—42no—
423#95—42no—
424#95—42no—
425#95—81no—
426#95—81no—
427#95—81no—
428#95—81no—
429C24—21no—
430C24—21no—
431C24—21no—
432C24—21no—
433C24—21no—
434C24—21no—
435C24—21no—
436C24—21no—
437C24—21no—
438C24—21no—
439C24—21no—
440C24—21no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—41no—
445C24—41no—
446C24—41no—
447C24—41no—
448C24—41no—
449C24—41no—
450C24—41no—
451C24—41no—
452C24—41no—
453C24—41no—
454C24—41no—
455C24—41no—
456C24C2×C22⋊C412yes—
457C24#12112yes—
458C24C22⋊Q812yes—
459C24C22×D411yescharacteristic
460C2×D4—216no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—41no—
477C2×D4—41no—
478C2×D4—41no—
479C2×D4—41no—
480C2×D4—41no—
481C2×D4—41no—
482C2×D4—41no—
483C2×D4—41no—
484C2×D4—41no—
485C2×D4—41no—
486C2×D4—41no—
487C2×D4—41no—
488C2×D4—84no—
489C2×D4—84no—
490C2×D4—84no—
491C2×D4—84no—
492C2×D4—84no—
493C2×D4—84no—
494C2×D4C2×C4⋊C414yes—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—41no—
549C22×C4—41no—
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—48no—
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—41no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—41no—
593C22×C4—84no—
594C22×C4—84no—
595C22×C4—84no—
596C22×C4—84no—
597C22×C4—84no—
598C22×C4—84no—
599C22×C4C2×C22⋊C412yes—
600C22×C4C2×C22⋊C412yes—
601C22×C4C2×C22⋊C412yes—
602C22×C4C2×C22⋊C412yes—
603C22×C4C2×C22⋊C412yes—
604C22×C4C2×C4⋊C414yes—
605C22×C4#11714yes—
606C22×C4#12114yes—
607C22×C4#12112yes—
608C22×C4#12112yes—
609C22×C4#12112yes—
610C22×C4#12112yes—
611C22×C4#12112yes—
612C22×C4C22⋊Q814yes—
613C22×C4C22⋊Q812yes—
614C22×C4C23×C411yescharacteristic
615C22×C4C22×D411yescharacteristic
616C22×C4C22×D411yescharacteristic
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D411yescharacteristic
619C22×C4C22×Q811yescharacteristic
620C22×C4C2×#4111yescharacteristic
621C22×C4C2×#4111yescharacteristic
622C22×C4C2×#4111yescharacteristic
623C22×C4C2×#4111yescharacteristic
624C22×C4H(5,𝔽2)11yescharacteristic
625C22×C4H(5,𝔽2)11yescharacteristic
626C22×C42−1+411yescharacteristic
627C22×C42−1+411yescharacteristic
628M16—416no—
629C2×C8—22no—
630C2×C8—22no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—416no—
642C2×C8—41no—
643C2×C8—41no—
644C2×C8—41no—
645C2×C8—41no—
646C2×C8—41no—
647C2×C8—41no—
648C2×C8—41no—
649C2×C8—41no—
650C2×C8—41no—
651C2×C8—41no—
652C2×C8—41no—
653C2×C8—41no—
654C2×C8—41no—
655C2×C8—41no—
656C2×C8—41no—
657C2×C8—41no—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C4⋊C4—22no—
661C4⋊C4—28no—
662C4⋊C4—28no—
663C4⋊C4—22no—
664C4⋊C4—22no—
665C4⋊C4—22no—
666C4⋊C4—22no—
667C4⋊C4—41no—
668C4⋊C4—41no—
669C4⋊C4—41no—
670C4⋊C4—41no—
671C4⋊C4—41no—
672C4⋊C4—41no—
673C4⋊C4—41no—
674C4⋊C4—41no—
675C4⋊C4—41no—
676C4⋊C4—41no—
677C4⋊C4—41no—
678C4⋊C4—41no—
679C4⋊C4—41no—
680C4⋊C4—41no—
681C4⋊C4—41no—
682C4⋊C4—41no—
683C4⋊C4—41no—
684C4⋊C4—41no—
685C4⋊C4—41no—
686C4⋊C4—41no—
687C4⋊C4—84no—
688C4⋊C4—84no—
689C4⋊C4—84no—
690C4⋊C4C2×C4⋊C414yes—
691C22⋊C4—216no—
692C22⋊C4—28no—
693C22⋊C4—28no—
694C22⋊C4—48no—
695C22⋊C4—84no—
696C22⋊C4—84no—
697C22⋊C4—84no—
698C22⋊C4—84no—
699C22⋊C4—84no—
700C42—22no—
701C42—22no—
702C42—22no—
703C42—22no—
704C42—84no—
705C42C4×D414yes—
706C42C4×D414yes—
707C42#12014yes—
708C42#12314yes—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—24no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—42no—
757C23—42no—
758C23—42no—
759C23—42no—
760C23—42no—
761C23—42no—
762C23—81no—
763C23—81no—
764C23—81no—
765C23—81no—
766C23—81no—
767C23—81no—
768C23—81no—
769C23—81no—
770C23—81no—
771C23—81no—
772C23—81no—
773C23—81no—
774C23—81no—
775C23—81no—
776C23—81no—
777C23—81no—
778C23#38014yes—
779C23C22×C22⋊C411yescharacteristic
780C23C2×#12111yescharacteristic
781C23C2×#12111yescharacteristic
782C23C2×#12111yescharacteristic
783C23C2×C22⋊Q811yescharacteristic
784C23#53711yescharacteristic
785C23#53711yescharacteristic
786C23#57611yescharacteristic
787C23#57611yescharacteristic
788C23#57611yescharacteristic
789C23#57711yescharacteristic
790C23#57711yescharacteristic
791C23#57711yescharacteristic
792C23#57711yescharacteristic
793C23#57811yescharacteristic
794D4—24no—
795D4—24no—
796D4—42no—
797D4—42no—
798D4—42no—
799D4—42no—
800D4—42no—
801D4—42no—
802D4—816no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—24no—
822C2×C4—24no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—24no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—24no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—816no—
857C2×C4—81no—
858C2×C4—81no—
859C2×C4—81no—
860C2×C4—81no—
861C2×C4—81no—
862C2×C4—81no—
863C2×C4—81no—
864C2×C4—81no—
865C2×C4—81no—
866C2×C4—81no—
867C2×C4—81no—
868C2×C4—81no—
869C2×C4—81no—
870C2×C4—81no—
871C2×C4—81no—
872C2×C4—81no—
873C2×C4—81no—
874C2×C4—81no—
875C2×C4—81no—
876C2×C4—81no—
877C2×C4—81no—
878C2×C4—81no—
879C2×C4—81no—
880C2×C4—81no—
881C2×C4—81no—
882C2×C4—81no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4—81no—
887C2×C4—81no—
888C2×C4—81no—
889C2×C4—81no—
890C2×C4—81no—
891C2×C4—81no—
892C2×C4—81no—
893C2×C4#38014yes—
894C2×C4#38614yes—
895C2×C4#38614yes—
896C2×C4C22×C4⋊C411yescharacteristic
897C2×C4C2×#11711yescharacteristic
898C2×C4C2×C4×D411yescharacteristic
899C2×C4C2×C4×D411yescharacteristic
900C2×C4#52011yescharacteristic
901C2×C4#52011yescharacteristic
902C2×C4C2×#12011yescharacteristic
903C2×C4C2×#12111yescharacteristic
904C2×C4C2×C22⋊Q811yescharacteristic
905C2×C4C2×#12311yescharacteristic
906C2×C4#53511yescharacteristic
907C2×C4#53611yescharacteristic
908C2×C4D4211yescharacteristic
909C2×C4D4211yescharacteristic
910C2×C4#54611yescharacteristic
911C2×C4#54611yescharacteristic
912C2×C4#54711yescharacteristic
913C2×C4#54711yescharacteristic
914C2×C4#54811yescharacteristic
915C2×C4#54811yescharacteristic
916C2×C4D4×Q811yescharacteristic
917C2×C4D4×Q811yescharacteristic
918C2×C4#55211yescharacteristic
919C2×C4#55211yescharacteristic
920C2×C4#55311yescharacteristic
921C2×C4#55311yescharacteristic
922C2×C4#55411yescharacteristic
923C2×C4#55411yescharacteristic
924C8—42no—
925C8—42no—
926C8—42no—
927C8—42no—
928C22—24no—
929C22—24no—
930C22—24no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—44no—
944C22—44no—
945C22—44no—
946C22—82no—
947C22—82no—
948C22—82no—
949C22—82no—
950C22—82no—
951C22—82no—
952C22—82no—
953C22—82no—
954C22—82no—
955C22—82no—
956C22—82no—
957C22—82no—
958C22C2×#38011yescharacteristic
959C22C2×#38611yescharacteristic
960C22#231111yescharacteristic
961C22#241611yescharacteristic
962C22#241611yescharacteristic
963C22#241711yescharacteristic
964C22#241711yescharacteristic
965C22#289711yescharacteristic
966C22#289711yescharacteristic
967C22#289711yescharacteristic
968C22#289811yescharacteristic
969C22#304111yescharacteristic
970C22#304211yescharacteristic
971C22#304511yescharacteristic
972C22#304611yescharacteristic
973C22#305711yescharacteristic
974C22#305811yescharacteristic
975C22#306011yescharacteristic
976C22#306111yescharacteristic
977C22#306211yescharacteristic
978C22#306211yescharacteristic
979C22#306211yescharacteristic
980C22#306311yescharacteristic
981C22#308111yescharacteristic
982C22#308111yescharacteristic
983C22#308311yescharacteristic
984C22#308411yescharacteristic
985C22#325711yescharacteristic
986C22#325711yescharacteristic
987C22#325711yescharacteristic
988C22#325811yescharacteristic
989C22#325911yescharacteristic
990C22#326011yescharacteristic
991C22#326211yescharacteristic
992C22#326311yescharacteristic
993C4—24no—
994C4—24no—
995C4—24no—
996C4—44no—
997C4—42no—
998C4—42no—
999C4—82no—
1000C4—82no—
1001C4—161no—
1002C4—161no—
1003C4—161no—
1004C4—161no—
1005C4D4×C4⋊C411yescharacteristic
1006C4D4×C4⋊C411yescharacteristic
1007C4#235211yescharacteristic
1008C4#235211yescharacteristic
1009C4#240811yescharacteristic
1010C4#240911yescharacteristic
1011C4#248611yescharacteristic
1012C4#248711yescharacteristic
1013C2—44no—
1014C2—84no—
1015C2#1387211yescharacteristic
1016C2#2065011yescharacteristic
1017C2#2065211yescharacteristic
1018C2#2097511yescharacteristic
1019C2#2097611yescharacteristic
1020C2#2189611yescharacteristic
1021C2#2189711yescharacteristic
1022C2#2476211yescharacteristic
1023C2#2476311yescharacteristic
1024C2#2476611yescharacteristic
1025C2#2476711yescharacteristic
1026C2#2484711yescharacteristic
1027C2#2484811yescharacteristic
1028C2#2485111yescharacteristic
1029C2#2485211yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC22×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×#117 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#424C2semidirect
5. C2×#1804C2semidirect
6. C2×#1802C2semidirect
7. #14340C2semidirect
8. #11228C2semidirect
9. #11227C2semidirect
10. #11076C2semidirect
11. #11076C2semidirect
12. #10850C2semidirect
13. #10849C2semidirect
14. #10722C2semidirect
15. #10721C2semidirect
33. #2324C4semidirect
143. C2×C4⋊C8D4semidirect
144. C2×C4⋊C8D4semidirect
302. #121C4⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#4242
C2×#23242
C2×#18952
C2×#18932
C2×#18042
C2×#18022
#143402
#112282
#112272
#110762
#108502
#108492
#107222
#107212