Finite Group Databasebeta

← #366136

Subgroups — #366136

Order 512.

1684 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1924C211yesmaximal, characteristic, complemented
2C2×#1870C211yesmaximal, characteristic
3C2×#1851C211yesmaximal, characteristic, complemented
4C2×#1797C211yesmaximal, characteristic, complemented
5C2×#1753C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊C8C211yesmaximal, characteristic, complemented
7C4×#386C211yesmaximal, characteristic
8#11255C211yesmaximal, characteristic, complemented
9#11147C211yesmaximal, characteristic, complemented
10#11042C211yesmaximal, characteristic, complemented
11#10964C211yesmaximal, characteristic
12#10921C211yesmaximal, characteristic, complemented
13#10877C211yesmaximal, characteristic, complemented
14#10876C211yesmaximal, characteristic, complemented
15#10797C211yesmaximal, characteristic, complemented
16C23×M16C2211yescharacteristic
17C22×C4×D4C2211yescharacteristic
18C23×C42C2211yescharacteristic
19C22×C4⋊C8C2211yescharacteristic
20C22×C4⋊C8C2211yescharacteristic
21C22×C4⋊C8C2211yescharacteristic
22C22×C22⋊C8C2211yescharacteristic
23C22×C22⋊C8C2211yescharacteristic
24C22×C22⋊C8C2211yescharacteristic
25C22×C22⋊C8C2211yescharacteristic
26C22×C22⋊C8C2211yescharacteristic
27C22×C22⋊C8C2211yescharacteristic
28C22×C22⋊C8C2211yescharacteristic
29C22×#97C2211yescharacteristic
30C22×C4×C8C2211yescharacteristic
31C22×C4×C8C2211yescharacteristic
32C2×#386C411yescharacteristic
33C2×#386C411yescharacteristic
34C2×C4×C22⋊C4C2211yescharacteristic
35C2×C4×C22⋊C4C2211yescharacteristic
36C2×C4×C22⋊C4C2211yescharacteristic
37#1924—24no—
38#1870—24no—
39#1851—24no—
40#1797—24no—
41#1753—24no—
42C4×C22⋊C8—24no—
43C2×#336C2211yescharacteristic
44C2×#336C2211yescharacteristic
45C2×#336C2211yescharacteristic
46C2×#336C2211yescharacteristic
47C2×#336C2211yescharacteristic
48C2×#336C2211yescharacteristic
49C2×#336C2211yescharacteristic
50C2×#336C2211yescharacteristic
51C2×#336C2211yescharacteristic
52C2×#336C2211yescharacteristic
53C2×#336C2211yescharacteristic
54C2×#336C2211yescharacteristic
55C2×#336C2211yescharacteristic
56C2×#336C2211yescharacteristic
57#1437C411yescharacteristic
58#1437C411yescharacteristic
59#1436C411yescharacteristic
60#1436C411yescharacteristic
61C22⋊#95C411yescharacteristic
62C22⋊#95C411yescharacteristic
63C4×#95C2211yescharacteristic
64C4×#95C2211yescharacteristic
65C23×D4C2×C411yescharacteristic
66C24×C4C2×C411yescharacteristic
67C24×C4C2×C411yescharacteristic
68C24×C4C2311yescharacteristic
69C24×C4C2311yescharacteristic
70C22×M16—22no—
71C22×M16—22no—
72C22×M16—22no—
73C22×M16—22no—
74C22×M16—22no—
75C22×M16—41no—
76C22×M16—41no—
77C23×C8C2311yescharacteristic
78C23×C8C2311yescharacteristic
79C23×C8C2311yescharacteristic
80C23×C8C2311yescharacteristic
81C23×C8C2311yescharacteristic
82C23×C8C2311yescharacteristic
83C23×C8C2311yescharacteristic
84C23×C8C2311yescharacteristic
85C2×C4×D4—22no—
86C2×C4×D4—22no—
87C2×C4×D4—22no—
88C2×C4×D4—22no—
89C2×C4×D4—41no—
90C2×C4×D4—41no—
91C22×C4⋊C4C2×C411yescharacteristic
92C22×C22⋊C4C2×C411yescharacteristic
93C22×C22⋊C4C2×C411yescharacteristic
94C22×C22⋊C4C2×C411yescharacteristic
95C22×C22⋊C4C2×C411yescharacteristic
96C22×C22⋊C4C2×C411yescharacteristic
97C22×C22⋊C4C2×C411yescharacteristic
98C22×C22⋊C4C2×C411yescharacteristic
99C22×C22⋊C4C2×C411yescharacteristic
100C22×C42—22no—
101C22×C42—22no—
102C22×C42—22no—
103C22×C42—22no—
104C22×C42—41no—
105C22×C42—41no—
106C22×C42C2×C411yescharacteristic
107C22×C42C2×C411yescharacteristic
108C22×C42C2311yescharacteristic
109C22×C42C2311yescharacteristic
110C22×C42C2311yescharacteristic
111C22×C42C2311yescharacteristic
112C22×C42C2311yescharacteristic
113C2×C4⋊C8—22no—
114C2×C4⋊C8—22no—
115C2×C4⋊C8—22no—
116C2×C4⋊C8—22no—
117C2×C4⋊C8—22no—
118C2×C4⋊C8—22no—
119C2×C4⋊C8—22no—
120C2×C4⋊C8—41no—
121C2×C4⋊C8—41no—
122C2×C22⋊C8—22no—
123C2×C22⋊C8—22no—
124C2×C22⋊C8—22no—
125C2×C22⋊C8—22no—
126C2×C22⋊C8—22no—
127C2×C22⋊C8—22no—
128C2×C22⋊C8—22no—
129C2×C22⋊C8—22no—
130C2×C22⋊C8—22no—
131C2×C22⋊C8—22no—
132C2×C22⋊C8—22no—
133C2×C22⋊C8—22no—
134C2×C22⋊C8—22no—
135C2×C22⋊C8—22no—
136C2×C22⋊C8—22no—
137C2×C22⋊C8—22no—
138C2×C22⋊C8—41no—
139C2×C22⋊C8—41no—
140C2×C22⋊C8—41no—
141C2×C22⋊C8—41no—
142C2×C22⋊C8D414yes—
143C2×#97—22no—
144C2×#97—22no—
145C2×#97—41no—
146C2×C4×C8—22no—
147C2×C4×C8—22no—
148C2×C4×C8—22no—
149C2×C4×C8—22no—
150C2×C4×C8—41no—
151C2×C4×C8—41no—
152#386—24no—
153#386—24no—
154C4×C22⋊C4—22no—
155C4×C22⋊C4—22no—
156C4×C22⋊C4—22no—
157C4×C22⋊C4—22no—
158C4×C22⋊C4—22no—
159C4×C22⋊C4—22no—
160C2×#95C2×C411yescharacteristic
161C2×#95C2×C411yescharacteristic
162C2×#95C2×C411yescharacteristic
163C2×#95C2×C411yescharacteristic
164C2×#95C2×C411yescharacteristic
165C2×#95C2×C411yescharacteristic
166C2×#95C2×C411yescharacteristic
167C2×#95C2×C411yescharacteristic
168C2×#95C2×C411yescharacteristic
169C2×#95C2×C411yescharacteristic
170C2×#95C2×C411yescharacteristic
171C2×#95C2×C411yescharacteristic
172C2×#95C2×C411yescharacteristic
173C2×#95C2×C411yescharacteristic
174#336—22no—
175#336—22no—
176#336—22no—
177#336—22no—
178#336—22no—
179#336—22no—
180#336—22no—
181#336—22no—
182#336—22no—
183#336—41no—
184#336—41no—
185#336—41no—
186#336D414yescomplemented
187#336D414yescomplemented
188C25C22×C411yescharacteristic
189C25C22×C411yescharacteristic
190C22×D4—22no—
191C22×D4—22no—
192C22×D4—22no—
193C22×D4—22no—
194C22×D4—22no—
195C22×D4—41no—
196C22×D4—41no—
197C23×C4—22no—
198C23×C4—22no—
199C23×C4—22no—
200C23×C4—22no—
201C23×C4—22no—
202C23×C4—22no—
203C23×C4—22no—
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×C4—21no—
216C23×C4—21no—
217C23×C4—21no—
218C23×C4—21no—
219C23×C4—21no—
220C23×C4—21no—
221C23×C4—21no—
222C23×C4—21no—
223C23×C4—21no—
224C23×C4—21no—
225C23×C4—21no—
226C23×C4—21no—
227C23×C4—21no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—41no—
231C23×C4—41no—
232C23×C4—41no—
233C23×C4—41no—
234C23×C4M1614yescomplemented
235C23×C4C22×C411yescharacteristic
236C23×C4C22×C411yescharacteristic
237C23×C4C22×C411yescharacteristic
238C23×C4C22×C411yescharacteristic
239C23×C4C22×C411yescharacteristic
240C23×C4C22×C411yescharacteristic
241C23×C4C22×C411yescharacteristic
242C23×C4C22×C411yescharacteristic
243C23×C4C22×C411yescharacteristic
244C23×C4C22×C411yescharacteristic
245C23×C4C22×C411yescharacteristic
246C23×C4C22×C411yescharacteristic
247C23×C4C2×D412yes—
248C23×C4#4112yes—
249C23×C4#4112yes—
250C23×C4#4112yes—
251C23×C4C2411yescharacteristic
252C2×M16—28no—
253C2×M16—44no—
254C2×M16—44no—
255C2×M16—44no—
256C2×M16—44no—
257C2×M16—44no—
258C2×M16—44no—
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×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—21no—
290C22×C8—21no—
291C22×C8—21no—
292C22×C8—21no—
293C22×C8—21no—
294C22×C8—21no—
295C22×C8—21no—
296C22×C8—21no—
297C22×C8—21no—
298C22×C8—21no—
299C22×C8—21no—
300C22×C8—21no—
301C22×C8—21no—
302C22×C8—21no—
303C22×C8—21no—
304C22×C8—21no—
305C22×C8—21no—
306C22×C8—21no—
307C22×C8C2×D412yes—
308C22×C8C2×D412yes—
309C22×C8C2×D412yes—
310C22×C8C2×D412yes—
311C22×C8C2×D412yes—
312C22×C8C2×D412yes—
313C22×C8#4112yes—
314C22×C8#4112yes—
315C4×D4—44no—
316C4×D4—44no—
317C4×D4—44no—
318C4×D4—44no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—41no—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—22no—
329C2×C22⋊C4—22no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—22no—
340C2×C22⋊C4—22no—
341C2×C22⋊C4—22no—
342C2×C22⋊C4—41no—
343C2×C22⋊C4—41no—
344C2×C22⋊C4—41no—
345C2×C22⋊C4—41no—
346C2×C42—21no—
347C2×C42—21no—
348C2×C42—21no—
349C2×C42—21no—
350C2×C42—21no—
351C2×C42—21no—
352C2×C42—21no—
353C2×C42—21no—
354C2×C42—22no—
355C2×C42—22no—
356C2×C42—22no—
357C2×C42—22no—
358C2×C42—21no—
359C2×C42—21no—
360C2×C42—21no—
361C2×C42—21no—
362C2×C42—21no—
363C2×C42—21no—
364C2×C42—21no—
365C2×C42—21no—
366C2×C42—21no—
367C2×C42—21no—
368C2×C42—21no—
369C2×C42—21no—
370C2×C42—21no—
371C2×C42—21no—
372C2×C42—21no—
373C2×C42—21no—
374C2×C42—21no—
375C2×C42—21no—
376C2×C42—44no—
377C2×C42—44no—
378C2×C42—44no—
379C2×C42—44no—
380C2×C42—41no—
381C2×C42—41no—
382C2×C42C2×D412yes—
383C2×C42C2×D412yes—
384C2×C42#4112yes—
385C2×C42#4112yes—
386C4⋊C8—44no—
387C4⋊C8—44no—
388C4⋊C8—44no—
389C22⋊C8—28no—
390C22⋊C8—28no—
391C22⋊C8—28no—
392C22⋊C8—44no—
393C22⋊C8—44no—
394C22⋊C8—44no—
395C22⋊C8—44no—
396#97—44no—
397C4×C8—44no—
398C4×C8—44no—
399#95—22no—
400#95—22no—
401#95—22no—
402#95—22no—
403#95—22no—
404#95—22no—
405#95—22no—
406#95—22no—
407#95—22no—
408#95—22no—
409#95—22no—
410#95—22no—
411#95—41no—
412#95M1614yescomplemented
413C24—21no—
414C24—21no—
415C24—21no—
416C24—21no—
417C24—21no—
418C24—21no—
419C24—21no—
420C24—21no—
421C24—21no—
422C24—21no—
423C24—21no—
424C24—21no—
425C24—21no—
426C24—21no—
427C24—21no—
428C24—21no—
429C24—21no—
430C24—21no—
431C24—21no—
432C24—21no—
433C24—21no—
434C24—21no—
435C24—21no—
436C24—21no—
437C24—21no—
438C24—21no—
439C24#11712yes—
440C24C4×D412yes—
441C24C2×M1612yes—
442C24#13112yes—
443C24C23×C411yescharacteristic
444C2×D4—28no—
445C2×D4—44no—
446C2×D4—44no—
447C2×D4—44no—
448C2×D4—44no—
449C2×D4—44no—
450C2×D4—44no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—28no—
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—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
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—28no—
519C22×C4—28no—
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—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—44no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—44no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4—44no—
557C22×C4—44no—
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—41no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—44no—
591C22×C4#11712yes—
592C22×C4C4×D412yes—
593C22×C4C4×D412yes—
594C22×C4C4×D412yes—
595C22×C4C4×D412yes—
596C22×C4C4×D412yes—
597C22×C4C2×M1612yes—
598C22×C4C2×M1612yes—
599C22×C4C2×M1612yes—
600C22×C4C2×M1612yes—
601C22×C4C2×M1612yes—
602C22×C4#13112yes—
603C22×C4#13112yes—
604C22×C4#13112yes—
605C22×C4C22×D411yescharacteristic
606C22×C4C22×D411yescharacteristic
607C22×C4C22×D411yescharacteristic
608C22×C4C2×#4111yescharacteristic
609C22×C4C2×#4111yescharacteristic
610C22×C4C2×#4111yescharacteristic
611C22×C4C2×#4111yescharacteristic
612C22×C4C2×#4111yescharacteristic
613C22×C4C2×#4111yescharacteristic
614C22×C4C2×#4111yescharacteristic
615C22×C4H(5,𝔽2)11yescharacteristic
616C22×C4H(5,𝔽2)11yescharacteristic
617C22×C4H(5,𝔽2)11yescharacteristic
618C22×C42−1+411yescharacteristic
619M16—416no—
620C2×C8—22no—
621C2×C8—22no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8—22no—
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—41no—
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—
658C2×C8—41no—
659C2×C8—41no—
660C2×C8—41no—
661C2×C8—41no—
662C2×C8—41no—
663C2×C8—41no—
664C2×C8—41no—
665C2×C8—41no—
666C2×C8—41no—
667C2×C8—41no—
668C2×C8—41no—
669C2×C8—41no—
670C2×C8—41no—
671C2×C8—41no—
672C2×C8—41no—
673C2×C8—41no—
674C2×C8—41no—
675C2×C8#12114yes—
676C4⋊C4—44no—
677C22⋊C4—44no—
678C22⋊C4—44no—
679C22⋊C4—44no—
680C22⋊C4—44no—
681C22⋊C4—44no—
682C22⋊C4—44no—
683C22⋊C4—44no—
684C22⋊C4—44no—
685C42—22no—
686C42—22no—
687C42—22no—
688C42—22no—
689C42—22no—
690C42—22no—
691C42—22no—
692C42—22no—
693C42—44no—
694C42—44no—
695C42—41no—
696C42—41no—
697C42—41no—
698C42—41no—
699C42—41no—
700C42—41no—
701C42—41no—
702C42—41no—
703C42—41no—
704C42—41no—
705C42—41no—
706C42—41no—
707C23—22no—
708C23—22no—
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—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—22no—
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—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23#43614yes—
777C23C2×#11711yescharacteristic
778C23C2×C4×D411yescharacteristic
779C23C2×C4×D411yescharacteristic
780C23C2×C4×D411yescharacteristic
781C23C4×#4111yescharacteristic
782C23#51811yescharacteristic
783C23#52011yescharacteristic
784C23C22×M1611yescharacteristic
785C23C22×M1611yescharacteristic
786C23C2×#13111yescharacteristic
787C23C2×#13111yescharacteristic
788C23C2×#13111yescharacteristic
789C23C2×#13111yescharacteristic
790C23#56811yescharacteristic
791C23#56811yescharacteristic
792D4—416no—
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—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—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—416no—
827C2×C4—416no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—42no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4#43514yes—
893C2×C4#43514yes—
894C2×C4#43614yes—
895C2×C4C2×#12111yescharacteristic
896C2×C4#52511yescharacteristic
897C2×C4#52511yescharacteristic
898C2×C4#52511yescharacteristic
899C2×C4#52911yescharacteristic
900C2×C4#52911yescharacteristic
901C2×C4#52911yescharacteristic
902C2×C4#53211yescharacteristic
903C2×C4#53811yescharacteristic
904C2×C4#53911yescharacteristic
905C2×C4#54011yescharacteristic
906C2×C4#54211yescharacteristic
907C2×C4D4211yescharacteristic
908C2×C4D4211yescharacteristic
909C2×C4#54611yescharacteristic
910C2×C4#54611yescharacteristic
911C2×C4#54611yescharacteristic
912C2×C4#54611yescharacteristic
913C2×C4#54611yescharacteristic
914C2×C4#54711yescharacteristic
915C2×C4#54811yescharacteristic
916C2×C4#54811yescharacteristic
917C2×C4#55111yescharacteristic
918C2×C4#55111yescharacteristic
919C2×C4#55111yescharacteristic
920C2×C4#55211yescharacteristic
921C2×C4#55311yescharacteristic
922C2×C4#55311yescharacteristic
923C8—24no—
924C8—42no—
925C8—42no—
926C8—42no—
927C8—42no—
928C8—42no—
929C8—81no—
930C8—81no—
931C22—24no—
932C22—24no—
933C22—24no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—81no—
954C22—81no—
955C22—81no—
956C22—81no—
957C22—81no—
958C22—81no—
959C22—81no—
960C22—81no—
961C22#229011yescharacteristic
962C22C4×#12111yescharacteristic
963C22#233511yescharacteristic
964C22#234211yescharacteristic
965C22#235211yescharacteristic
966C22#235811yescharacteristic
967C22#236111yescharacteristic
968C22#292011yescharacteristic
969C22#292211yescharacteristic
970C22#292411yescharacteristic
971C22#292511yescharacteristic
972C22C2×#43511yescharacteristic
973C22C2×#43511yescharacteristic
974C22C2×#43611yescharacteristic
975C22C2×#43611yescharacteristic
976C22#292911yescharacteristic
977C22#293111yescharacteristic
978C22#293311yescharacteristic
979C22#293311yescharacteristic
980C22#293311yescharacteristic
981C22D4×M1611yescharacteristic
982C22D4×M1611yescharacteristic
983C22#293511yescharacteristic
984C22#296511yescharacteristic
985C22#296511yescharacteristic
986C22#296611yescharacteristic
987C22#296711yescharacteristic
988C22#297311yescharacteristic
989C22#297411yescharacteristic
990C22#297611yescharacteristic
991C22#297711yescharacteristic
992C22#298911yescharacteristic
993C22#299111yescharacteristic
994C22#299311yescharacteristic
995C22#299411yescharacteristic
996C4—24no—
997C4—24no—
998C4—24no—
999C4—42no—
1000C4—42no—
1001C4—42no—
1002C4—42no—
1003C4—42no—
1004C4—81no—
1005C4—81no—
1006C4—81no—
1007C4—81no—
1008C4#242411yescharacteristic
1009C4#242711yescharacteristic
1010C4#245711yescharacteristic
1011C4#246311yescharacteristic
1012C4#246411yescharacteristic
1013C4#247711yescharacteristic
1014C4#255311yescharacteristic
1015C4#257811yescharacteristic
1016C2—44no—
1017C2—82no—
1018C2#1398811yescharacteristic
1019C2#2110211yescharacteristic
1020C2#2111211yescharacteristic
1021C2#2148711yescharacteristic
1022C2#2149011yescharacteristic
1023C2#2236511yescharacteristic
1024C2#2236911yescharacteristic
1025C2#2255511yescharacteristic
1026C2#2256011yescharacteristic
1027C2#2274911yescharacteristic
1028C2#2275211yescharacteristic
1029C2#2284411yescharacteristic
1030C2#2284811yescharacteristic
1031C2#2298911yescharacteristic
1032C2#2299011yescharacteristic
subgroupG/H
center, Frattini, cosocleC23×C4C24
commutator, socleC24C23×C4
prime radicalC23×D4C2×C4
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C23×C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#1924C2semidirect
3. C2×#1851C2semidirect
4. C2×#1797C2semidirect
5. C2×#1753C2semidirect
6. C2×C4×C22⋊C8C2semidirect
8. #11255C2semidirect
9. #11147C2semidirect
10. #11042C2semidirect
12. #10921C2semidirect
13. #10877C2semidirect
14. #10876C2semidirect
15. #10797C2semidirect
186. #336D4semidirect
187. #336D4semidirect
234. C23×C4M16semidirect
412. #95M16semidirect

Maximal subgroups

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

subgroupindex
C2×#19242
C2×#18702
C2×#18512
C2×#17972
C2×#17532
C2×C4×C22⋊C82
C4×#3862
#112552
#111472
#110422
#109642
#109212
#108772
#108762
#107972