Finite Group Databasebeta

← C2×#14359 #520657

Subgroups — C2×#14359 #520657

Order 512.

7658 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#123C211yesmaximal, characteristic
2C22×#388C211yesmaximal, characteristic, complemented
3C22×#386C211yesmaximal, characteristic
4C22×#385C211yesmaximal, characteristic, complemented
5C22×#380C211yesmaximal, characteristic, complemented
6#14359C2116yesmaximal, direct product factor
7C2×#1445C211yesmaximal, characteristic, complemented
8C2×#1441C211yesmaximal, characteristic, complemented
9C2×#1441C211yesmaximal, characteristic, complemented
10C2×#1440C211yesmaximal, characteristic, complemented
11C2×#1439C211yesmaximal, characteristic, complemented
12C2×#1438C211yesmaximal, characteristic
13C2×#1437C211yesmaximal, characteristic, complemented
14C2×C4⋊#95C211yesmaximal, characteristic, complemented
15C2×C22⋊#95C211yesmaximal, characteristic, complemented
16C2×C22⋊#95C211yesmaximal, characteristic, complemented
17C24×D4C2211yescharacteristic
18C25×C4C2211yescharacteristic
19C25×C4C2211yescharacteristic
20C22×#123—28no—
21C22×#123—28no—
22C22×#123C4116yescomplemented
23C22×#123C2218yes—
24C23×C4⋊C4C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27C23×C4⋊C4C2211yescharacteristic
28C23×C4⋊C4C2211yescharacteristic
29C23×C22⋊C4C2211yescharacteristic
30C23×C22⋊C4C2211yescharacteristic
31C23×C22⋊C4C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C23×C22⋊C4C2211yescharacteristic
35C23×C22⋊C4C2211yescharacteristic
36C23×C22⋊C4C2211yescharacteristic
37C23×C22⋊C4C2211yescharacteristic
38C23×C22⋊C4C2211yescharacteristic
39C23×C42C2211yescharacteristic
40C2×#388—28no—
41C2×#388C2218yescomplemented
42C2×#386—28no—
43C2×#386C2218yes—
44C2×#385—28no—
45C2×#385C2218yescomplemented
46C2×#380—28no—
47C2×#380C2218yescomplemented
48C22×#95C2211yescharacteristic
49C22×#95C2211yescharacteristic
50C22×#95C2211yescharacteristic
51C22×#95C2211yescharacteristic
52C22×#95C2211yescharacteristic
53C22×#95C2211yescharacteristic
54C22×#95C2211yescharacteristic
55C22×#95C2211yescharacteristic
56C22×#95C2211yescharacteristic
57C22×#95C2211yescharacteristic
58C22×#95C2211yescharacteristic
59C22×#95C2211yescharacteristic
60C22×#95C2211yescharacteristic
61C22×#95C2211yescharacteristic
62C22×#95C2211yescharacteristic
63C22×#95C2211yescharacteristic
64#1445C2218yescomplemented
65#1441C2218yescomplemented
66#1441C2218yescomplemented
67#1440C2218yescomplemented
68#1439C2218yescomplemented
69#1438C2218yes—
70#1437C2218yescomplemented
71C4⋊#95C2218yescomplemented
72C22⋊#95C2218yescomplemented
73C22⋊#95C2218yescomplemented
74C26C2311yescharacteristic
75C26C2311yescharacteristic
76C23×D4—24no—
77C23×D4—24no—
78C23×D4—24no—
79C23×D4—24no—
80C23×D4—42no—
81C23×D4—42no—
82C23×D4C2×C418yes—
83C23×D4C2314yes—
84C24×C4—24no—
85C24×C4—24no—
86C24×C4—24no—
87C24×C4—24no—
88C24×C4—24no—
89C24×C4—24no—
90C24×C4—24no—
91C24×C4—42no—
92C24×C4—42no—
93C24×C4—42no—
94C24×C4—42no—
95C24×C4—42no—
96C24×C4—42no—
97C24×C4C2×C418yescomplemented
98C24×C4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C24×C4C2311yescharacteristic
103C24×C4C2311yescharacteristic
104C24×C4C2311yescharacteristic
105C24×C4C2311yescharacteristic
106C24×C4C2311yescharacteristic
107C24×C4C2311yescharacteristic
108C24×C4C2311yescharacteristic
109C24×C4C2314yes—
110C24×C4C2311yescharacteristic
111C24×C4C2311yescharacteristic
112C24×C4C2314yes—
113C2×#123—2128no—
114C2×#123—232no—
115C2×#123—232no—
116C2×#123C2×C4164yescomplemented
117C22×C4⋊C4—24no—
118C22×C4⋊C4—24no—
119C22×C4⋊C4—24no—
120C22×C4⋊C4—24no—
121C22×C4⋊C4—24no—
122C22×C4⋊C4—24no—
123C22×C4⋊C4—24no—
124C22×C4⋊C4—24no—
125C22×C4⋊C4—24no—
126C22×C4⋊C4—24no—
127C22×C4⋊C4—42no—
128C22×C4⋊C4—42no—
129C22×C4⋊C4—42no—
130C22×C4⋊C4C2×C418yescomplemented
131C22×C4⋊C4C2×C418yescomplemented
132C22×C4⋊C4C2314yes—
133C22×C4⋊C4C2314yes—
134C22×C4⋊C4C2314yes—
135C22×C4⋊C4C2314yes—
136C22×C4⋊C4C2314yes—
137C22×C22⋊C4—24no—
138C22×C22⋊C4—24no—
139C22×C22⋊C4—24no—
140C22×C22⋊C4—24no—
141C22×C22⋊C4—24no—
142C22×C22⋊C4—24no—
143C22×C22⋊C4—24no—
144C22×C22⋊C4—24no—
145C22×C22⋊C4—24no—
146C22×C22⋊C4—24no—
147C22×C22⋊C4—24no—
148C22×C22⋊C4—24no—
149C22×C22⋊C4—24no—
150C22×C22⋊C4—24no—
151C22×C22⋊C4—42no—
152C22×C22⋊C4—42no—
153C22×C22⋊C4—42no—
154C22×C22⋊C4—42no—
155C22×C22⋊C4—42no—
156C22×C22⋊C4—42no—
157C22×C22⋊C4—42no—
158C22×C22⋊C4—42no—
159C22×C22⋊C4—42no—
160C22×C22⋊C4—42no—
161C22×C22⋊C4C2×C418yes—
162C22×C22⋊C4C2×C418yes—
163C22×C22⋊C4C2×C418yescomplemented
164C22×C22⋊C4D418yes—
165C22×C22⋊C4D418yes—
166C22×C22⋊C4D418yes—
167C22×C22⋊C4C2314yes—
168C22×C22⋊C4C2314yes—
169C22×C22⋊C4C2314yes—
170C22×C22⋊C4C2314yes—
171C22×C22⋊C4C2314yes—
172C22×C22⋊C4C2314yes—
173C22×C22⋊C4C2314yes—
174C22×C22⋊C4C2314yes—
175C22×C22⋊C4C2314yes—
176C22×C22⋊C4C2314yes—
177C22×C42—24no—
178C22×C42—24no—
179C22×C42—42no—
180C22×C42C2314yes—
181#388—232no—
182#386—232no—
183#385—232no—
184#380—232no—
185C2×#95—24no—
186C2×#95—24no—
187C2×#95—24no—
188C2×#95—24no—
189C2×#95—24no—
190C2×#95—24no—
191C2×#95—24no—
192C2×#95—24no—
193C2×#95—42no—
194C2×#95—42no—
195C2×#95—42no—
196C2×#95—42no—
197C2×#95—42no—
198C2×#95—42no—
199C2×#95—42no—
200C2×#95—42no—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2314yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C25—22no—
218C25—22no—
219C25—22no—
220C25—22no—
221C25—22no—
222C25—22no—
223C25—22no—
224C25—22no—
225C25—22no—
226C25—22no—
227C25—22no—
228C25—22no—
229C25—22no—
230C25—22no—
231C25—22no—
232C25—22no—
233C25—22no—
234C25—22no—
235C25—22no—
236C25—22no—
237C25—22no—
238C25—22no—
239C25—22no—
240C25—22no—
241C25C22×C414yes—
242C25C22×C414yes—
243C25C2×D414yes—
244C25C2×D414yes—
245C25C2×D414yes—
246C25#4114yes—
247C25C2412yes—
248C25C2412yes—
249C25C2411yescharacteristic
250C22×D4—232no—
251C22×D4—232no—
252C22×D4—28no—
253C22×D4—28no—
254C22×D4—28no—
255C22×D4—28no—
256C22×D4—416no—
257C22×D4—44no—
258C22×D4—44no—
259C22×D4—416no—
260C22×D4—416no—
261C22×D4—416no—
262C22×D4—416no—
263C22×D4C22×C4116yes—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—232no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—28no—
286C23×C4—22no—
287C23×C4—22no—
288C23×C4—28no—
289C23×C4—22no—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4—22no—
293C23×C4—22no—
294C23×C4—22no—
295C23×C4—22no—
296C23×C4—22no—
297C23×C4—22no—
298C23×C4—22no—
299C23×C4—22no—
300C23×C4—22no—
301C23×C4—22no—
302C23×C4—22no—
303C23×C4—22no—
304C23×C4—22no—
305C23×C4—22no—
306C23×C4—22no—
307C23×C4—22no—
308C23×C4—22no—
309C23×C4—22no—
310C23×C4—22no—
311C23×C4—22no—
312C23×C4—22no—
313C23×C4—22no—
314C23×C4—22no—
315C23×C4—22no—
316C23×C4—22no—
317C23×C4—232no—
318C23×C4—28no—
319C23×C4—28no—
320C23×C4—22no—
321C23×C4—22no—
322C23×C4—22no—
323C23×C4—22no—
324C23×C4—22no—
325C23×C4—22no—
326C23×C4—22no—
327C23×C4—28no—
328C23×C4—22no—
329C23×C4—22no—
330C23×C4—22no—
331C23×C4—22no—
332C23×C4—22no—
333C23×C4—22no—
334C23×C4—22no—
335C23×C4—22no—
336C23×C4—22no—
337C23×C4—22no—
338C23×C4—22no—
339C23×C4—22no—
340C23×C4—22no—
341C23×C4—22no—
342C23×C4—22no—
343C23×C4—22no—
344C23×C4—22no—
345C23×C4—22no—
346C23×C4—22no—
347C23×C4—22no—
348C23×C4—22no—
349C23×C4—28no—
350C23×C4—28no—
351C23×C4—416no—
352C23×C4—44no—
353C23×C4—44no—
354C23×C4—44no—
355C23×C4—44no—
356C23×C4—44no—
357C23×C4—44no—
358C23×C4—416no—
359C23×C4—416no—
360C23×C4—416no—
361C23×C4—416no—
362C23×C4—416no—
363C23×C4—416no—
364C23×C4—416no—
365C23×C4—416no—
366C23×C4—416no—
367C23×C4—416no—
368C23×C4—416no—
369C23×C4C22×C414yes—
370C23×C4C22×C414yes—
371C23×C4C22×C414yes—
372C23×C4C22×C414yes—
373C23×C4C22×C414yes—
374C23×C4C22×C4116yescomplemented
375C23×C4C2×D414yes—
376C23×C4C2×D414yes—
377C23×C4C2×D414yes—
378C23×C4C2×D414yes—
379C23×C4C2×D414yes—
380C23×C4C2×D414yes—
381C23×C4#4114yes—
382C23×C4#4114yes—
383C23×C4C2412yes—
384C23×C4C2412yes—
385C23×C4C2412yes—
386C23×C4C2412yes—
387C23×C4C2412yes—
388C23×C4C2412yes—
389C23×C4C2412yes—
390C23×C4C2412yes—
391C23×C4C2412yes—
392C23×C4C2412yes—
393C23×C4C2412yes—
394C23×C4C2412yes—
395C23×C4C2412yes—
396#123—2256no—
397C2×C4⋊C4—232no—
398C2×C4⋊C4—232no—
399C2×C4⋊C4—28no—
400C2×C4⋊C4—28no—
401C2×C4⋊C4—28no—
402C2×C4⋊C4—28no—
403C2×C4⋊C4—28no—
404C2×C4⋊C4—28no—
405C2×C4⋊C4—28no—
406C2×C4⋊C4—28no—
407C2×C4⋊C4—28no—
408C2×C4⋊C4—28no—
409C2×C4⋊C4—44no—
410C2×C4⋊C4—44no—
411C2×C4⋊C4—44no—
412C2×C4⋊C4—416no—
413C2×C4⋊C4—416no—
414C2×C4⋊C4—416no—
415C2×C4⋊C4C22×C4116yescomplemented
416C2×C4⋊C4C22×C4116yescomplemented
417C2×C22⋊C4—232no—
418C2×C22⋊C4—28no—
419C2×C22⋊C4—28no—
420C2×C22⋊C4—232no—
421C2×C22⋊C4—28no—
422C2×C22⋊C4—28no—
423C2×C22⋊C4—28no—
424C2×C22⋊C4—28no—
425C2×C22⋊C4—28no—
426C2×C22⋊C4—28no—
427C2×C22⋊C4—28no—
428C2×C22⋊C4—28no—
429C2×C22⋊C4—28no—
430C2×C22⋊C4—28no—
431C2×C22⋊C4—28no—
432C2×C22⋊C4—28no—
433C2×C22⋊C4—416no—
434C2×C22⋊C4—44no—
435C2×C22⋊C4—44no—
436C2×C22⋊C4—44no—
437C2×C22⋊C4—44no—
438C2×C22⋊C4—44no—
439C2×C22⋊C4—44no—
440C2×C22⋊C4—44no—
441C2×C22⋊C4—44no—
442C2×C22⋊C4—44no—
443C2×C22⋊C4—44no—
444C2×C22⋊C4—416no—
445C2×C22⋊C4—416no—
446C2×C22⋊C4—416no—
447C2×C22⋊C4—416no—
448C2×C22⋊C4—416no—
449C2×C22⋊C4—416no—
450C2×C22⋊C4C22⋊C4164yescomplemented
451C2×C22⋊C4C22×C4116yes—
452C2×C22⋊C4C22×C4116yes—
453C2×C22⋊C4C22×C4116yescomplemented
454C2×C22⋊C4C2×D4116yes—
455C2×C22⋊C4C2×D4116yes—
456C2×C22⋊C4C2×D4116yes—
457C2×C42—28no—
458C2×C42—28no—
459C2×C42—44no—
460C2×C42—416no—
461#95—28no—
462#95—28no—
463#95—28no—
464#95—28no—
465#95—28no—
466#95—28no—
467#95—28no—
468#95—28no—
469#95—44no—
470#95—44no—
471#95—44no—
472#95—44no—
473#95—44no—
474#95—44no—
475#95—44no—
476#95—44no—
477C24—28no—
478C24—28no—
479C24—28no—
480C24—28no—
481C24—28no—
482C24—28no—
483C24—28no—
484C24—28no—
485C24—28no—
486C24—28no—
487C24—28no—
488C24—28no—
489C24—28no—
490C24—28no—
491C24—28no—
492C24—28no—
493C24—28no—
494C24—28no—
495C24—28no—
496C24—28no—
497C24—28no—
498C24—28no—
499C24—28no—
500C24—28no—
501C24—28no—
502C24—28no—
503C24—28no—
504C24—28no—
505C24—28no—
506C24—28no—
507C24—28no—
508C24—28no—
509C24—28no—
510C24—28no—
511C24—28no—
512C24—28no—
513C24—22no—
514C24—22no—
515C24—22no—
516C24—22no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—44no—
538C24—44no—
539C24—44no—
540C24—44no—
541C24—44no—
542C24—44no—
543C24—44no—
544C24—44no—
545C24—44no—
546C24—44no—
547C24—44no—
548C24—44no—
549C24—44no—
550C24—44no—
551C24—44no—
552C24—44no—
553C24—44no—
554C24—44no—
555C24—44no—
556C24—44no—
557C24—44no—
558C24—44no—
559C24—44no—
560C24—44no—
561C24—44no—
562C24—44no—
563C24—44no—
564C24—44no—
565C24—44no—
566C24—44no—
567C24—44no—
568C24—44no—
569C24C2×C22⋊C4116yes—
570C24C4×D4116yes—
571C24C23×C414yes—
572C24C23×C414yes—
573C24C23×C412yes—
574C24C22×D414yes—
575C24C22×D414yes—
576C24C22×D414yes—
577C24C22×D412yes—
578C24C22×D412yes—
579C24C22×D412yes—
580C24C2×#4114yes—
581C24C2×#4112yes—
582C24C2×#4112yes—
583C24C2×#4112yes—
584C24H(5,𝔽2)12yes—
585C24H(5,𝔽2)12yes—
586C24H(5,𝔽2)12yes—
587C24H(5,𝔽2)12yes—
588C24H(5,𝔽2)12yes—
589C242−1+412yes—
590C242−1+412yes—
591C242−1+412yes—
592C24C2511yescharacteristic
593C2×D4—232no—
594C2×D4—232no—
595C2×D4—416no—
596C2×D4—4128no—
597C2×D4—416no—
598C2×D4—416no—
599C2×D4—416no—
600C2×D4—416no—
601C22×C4—28no—
602C22×C4—28no—
603C22×C4—28no—
604C22×C4—28no—
605C22×C4—28no—
606C22×C4—28no—
607C22×C4—28no—
608C22×C4—28no—
609C22×C4—28no—
610C22×C4—28no—
611C22×C4—28no—
612C22×C4—28no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—28no—
622C22×C4—28no—
623C22×C4—28no—
624C22×C4—28no—
625C22×C4—232no—
626C22×C4—28no—
627C22×C4—28no—
628C22×C4—28no—
629C22×C4—28no—
630C22×C4—28no—
631C22×C4—28no—
632C22×C4—28no—
633C22×C4—28no—
634C22×C4—28no—
635C22×C4—28no—
636C22×C4—28no—
637C22×C4—28no—
638C22×C4—28no—
639C22×C4—28no—
640C22×C4—28no—
641C22×C4—28no—
642C22×C4—28no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—232no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—22no—
706C22×C4—22no—
707C22×C4—22no—
708C22×C4—22no—
709C22×C4—22no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—416no—
715C22×C4—416no—
716C22×C4—4128no—
717C22×C4—416no—
718C22×C4—416no—
719C22×C4—416no—
720C22×C4—416no—
721C22×C4—416no—
722C22×C4—416no—
723C22×C4—416no—
724C22×C4—416no—
725C22×C4—416no—
726C22×C4—4128no—
727C22×C4—416no—
728C22×C4—44no—
729C22×C4—44no—
730C22×C4—44no—
731C22×C4—44no—
732C22×C4—44no—
733C22×C4—44no—
734C22×C4—44no—
735C22×C4—44no—
736C22×C4—44no—
737C22×C4—44no—
738C22×C4—44no—
739C22×C4—44no—
740C22×C4—44no—
741C22×C4—44no—
742C22×C4—44no—
743C22×C4—44no—
744C22×C4—44no—
745C22×C4—44no—
746C22×C4—44no—
747C22×C4—44no—
748C22×C4—44no—
749C22×C4—44no—
750C22×C4—44no—
751C22×C4—44no—
752C22×C4—44no—
753C22×C4—44no—
754C22×C4—44no—
755C22×C4—44no—
756C22×C4—44no—
757C22×C4—44no—
758C22×C4—44no—
759C22×C4—44no—
760C22×C4—44no—
761C22×C4—44no—
762C22×C4—44no—
763C22×C4—44no—
764C22×C4—44no—
765C22×C4—44no—
766C22×C4—44no—
767C22×C4—44no—
768C22×C4—44no—
769C22×C4—44no—
770C22×C4—44no—
771C22×C4—44no—
772C22×C4—44no—
773C22×C4—44no—
774C22×C4—44no—
775C22×C4—44no—
776C22×C4—44no—
777C22×C4—44no—
778C22×C4—44no—
779C22×C4—44no—
780C22×C4—44no—
781C22×C4—44no—
782C22×C4—44no—
783C22×C4—44no—
784C22×C4C2×C22⋊C4116yes—
785C22×C4C2×C22⋊C4116yes—
786C22×C4C23×C414yes—
787C22×C4C23×C414yes—
788C22×C4C23×C414yes—
789C22×C4C23×C414yes—
790C22×C4C23×C414yes—
791C22×C4C22×D414yes—
792C22×C4C22×D414yes—
793C22×C4C22×D414yes—
794C22×C4C22×D414yes—
795C22×C4C22×D414yes—
796C22×C4C22×D414yes—
797C22×C4C2×#4114yes—
798C22×C4C2×#4114yes—
799C4⋊C4—232no—
800C4⋊C4—232no—
801C4⋊C4—416no—
802C4⋊C4—416no—
803C4⋊C4—416no—
804C22⋊C4—232no—
805C22⋊C4—232no—
806C22⋊C4—416no—
807C22⋊C4—416no—
808C22⋊C4—416no—
809C22⋊C4—416no—
810C22⋊C4—416no—
811C22⋊C4—416no—
812C22⋊C4—416no—
813C22⋊C4C2×C22⋊C4164yescomplemented
814C42—416no—
815C23—232no—
816C23—232no—
817C23—232no—
818C23—232no—
819C23—232no—
820C23—232no—
821C23—24no—
822C23—24no—
823C23—24no—
824C23—24no—
825C23—24no—
826C23—24no—
827C23—24no—
828C23—24no—
829C23—24no—
830C23—24no—
831C23—24no—
832C23—24no—
833C23—24no—
834C23—24no—
835C23—24no—
836C23—24no—
837C23—24no—
838C23—24no—
839C23—24no—
840C23—24no—
841C23—24no—
842C23—24no—
843C23—24no—
844C23—24no—
845C23—24no—
846C23—24no—
847C23—24no—
848C23—24no—
849C23—24no—
850C23—24no—
851C23—24no—
852C23—24no—
853C23—24no—
854C23—24no—
855C23—24no—
856C23—24no—
857C23—416no—
858C23—416no—
859C23—416no—
860C23—416no—
861C23—416no—
862C23—416no—
863C23—416no—
864C23—416no—
865C23—416no—
866C23—416no—
867C23—416no—
868C23—416no—
869C23—42no—
870C23—416no—
871C23—416no—
872C23—42no—
873C23—42no—
874C23—42no—
875C23—416no—
876C23—416no—
877C23—42no—
878C23—42no—
879C23—42no—
880C23—42no—
881C23—42no—
882C23—42no—
883C23—42no—
884C23—42no—
885C23—42no—
886C23—42no—
887C23—42no—
888C23—42no—
889C23—416no—
890C23—416no—
891C23—416no—
892C23—416no—
893C23—416no—
894C23—416no—
895C23—42no—
896C23—42no—
897C23—42no—
898C23—42no—
899C23—42no—
900C23—42no—
901C23—42no—
902C23—42no—
903C23—416no—
904C23—416no—
905C23—42no—
906C23—42no—
907C23—42no—
908C23—42no—
909C23—42no—
910C23—42no—
911C23—42no—
912C23—42no—
913C23C22×C22⋊C418yes—
914C23C22×C22⋊C414yes—
915C23C2×C4×D418yes—
916C23C2×C4×D414yes—
917C23C4×#4114yes—
918C23#51814yes—
919C23#52014yes—
920C23#52014yes—
921C23#52014yes—
922C23#53414yes—
923C23#53514yes—
924C23#53614yes—
925C23#53614yes—
926C23#53714yes—
927C23#53714yes—
928C23#53814yes—
929C23#53914yes—
930C23#53914yes—
931C23#53914yes—
932C23#54014yes—
933C23#54214yes—
934C23D4214yes—
935C23D4214yes—
936C23#54614yes—
937C23#54614yes—
938C23#54614yes—
939C23#54614yes—
940C23#54614yes—
941C23#54714yes—
942C23#54714yes—
943C23#54714yes—
944C23#55114yes—
945C23#55214yes—
946C23#56014yes—
947C23#56214yes—
948C23#56214yes—
949C23#56314yes—
950C23C24×C411yescharacteristic
951C23C23×D411yescharacteristic
952C23C23×D411yescharacteristic
953C23C23×D411yescharacteristic
954C23C22×#4111yescharacteristic
955C23C22×#4111yescharacteristic
956C23C22×#4111yescharacteristic
957C23C2×H(5,𝔽2)11yescharacteristic
958C23C2×H(5,𝔽2)11yescharacteristic
959C23C2×H(5,𝔽2)11yescharacteristic
960C23C2×H(5,𝔽2)11yescharacteristic
961C23C2×H(5,𝔽2)11yescharacteristic
962C23C2×2−1+411yescharacteristic
963C23C2×2−1+411yescharacteristic
964C23C2×2−1+411yescharacteristic
965D4—464no—
966C2×C4—232no—
967C2×C4—232no—
968C2×C4—24no—
969C2×C4—24no—
970C2×C4—24no—
971C2×C4—24no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—24no—
975C2×C4—24no—
976C2×C4—24no—
977C2×C4—24no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—24no—
981C2×C4—24no—
982C2×C4—24no—
983C2×C4—24no—
984C2×C4—24no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—24no—
988C2×C4—24no—
989C2×C4—24no—
990C2×C4—24no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—24no—
994C2×C4—24no—
995C2×C4—24no—
996C2×C4—24no—
997C2×C4—24no—
998C2×C4—24no—
999C2×C4—24no—
1000C2×C4—24no—
1001C2×C4—464no—
1002C2×C4—464no—
1003C2×C4—416no—
1004C2×C4—416no—
1005C2×C4—416no—
1006C2×C4—416no—
1007C2×C4—42no—
1008C2×C4—416no—
1009C2×C4—416no—
1010C2×C4—42no—
1011C2×C4—42no—
1012C2×C4—42no—
1013C2×C4—42no—
1014C2×C4—42no—
1015C2×C4—42no—
1016C2×C4—42no—
1017C2×C4—42no—
1018C2×C4—42no—
1019C2×C4—42no—
1020C2×C4—42no—
1021C2×C4—416no—
1022C2×C4—42no—
1023C2×C4—42no—
1024C2×C4—42no—
1025C2×C4—42no—
1026C2×C4—42no—
1027C2×C4—42no—
1028C2×C4—42no—
1029C2×C4—42no—
1030C2×C4—42no—
1031C2×C4—42no—
1032C2×C4—42no—
1033C2×C4—42no—
1034C2×C4—42no—
1035C2×C4—42no—
1036C2×C4—42no—
1037C2×C4—42no—
1038C2×C4—42no—
1039C2×C4—42no—
1040C2×C4—42no—
1041C2×C4—42no—
1042C2×C4—42no—
1043C2×C4—42no—
1044C2×C4—42no—
1045C2×C4—42no—
1046C2×C4—42no—
1047C2×C4—42no—
1048C2×C4—42no—
1049C2×C4—42no—
1050C2×C4—42no—
1051C2×C4—42no—
1052C2×C4—42no—
1053C2×C4—42no—
1054C2×C4—42no—
1055C2×C4—42no—
1056C2×C4—42no—
1057C2×C4—42no—
1058C2×C4—42no—
1059C2×C4—42no—
1060C2×C4—42no—
1061C2×C4—42no—
1062C2×C4—42no—
1063C2×C4—42no—
1064C2×C4—42no—
1065C2×C4—42no—
1066C2×C4—88no—
1067C2×C4—88no—
1068C2×C4—88no—
1069C2×C4—88no—
1070C2×C4C22×C22⋊C418yes—
1071C2×C4C22×C22⋊C418yes—
1072C22—28no—
1073C22—28no—
1074C22—28no—
1075C22—28no—
1076C22—28no—
1077C22—28no—
1078C22—44no—
1079C22—464no—
1080C22—464no—
1081C22—44no—
1082C22—44no—
1083C22—44no—
1084C22—44no—
1085C22—44no—
1086C22—44no—
1087C22—44no—
1088C22—44no—
1089C22—44no—
1090C22—44no—
1091C22—44no—
1092C22—44no—
1093C22—44no—
1094C22—44no—
1095C22—44no—
1096C22—44no—
1097C22—44no—
1098C22—44no—
1099C22—44no—
1100C22—44no—
1101C22—44no—
1102C22—44no—
1103C22—44no—
1104C22#231118yes—
1105C22#232218yes—
1106C22#233518yes—
1107C22D4×C22⋊C418yes—
1108C22#233918yes—
1109C22#235918yes—
1110C22#237618yes—
1111C22#267118yes—
1112C22#267218yes—
1113C22#267818yes—
1114C22#268018yes—
1115C22#268718yes—
1116C22#269318yes—
1117C22#269518yes—
1118C22#270618yes—
1119C22C23×C22⋊C411yescharacteristic
1120C22C22×C4×D411yescharacteristic
1121C22C2×C4×#4111yescharacteristic
1122C22C2×#51811yescharacteristic
1123C22C2×#52011yescharacteristic
1124C22C2×#52011yescharacteristic
1125C22C2×#52011yescharacteristic
1126C22C2×#53411yescharacteristic
1127C22C2×#53511yescharacteristic
1128C22C2×#53611yescharacteristic
1129C22C2×#53611yescharacteristic
1130C22C2×#53711yescharacteristic
1131C22C2×#53711yescharacteristic
1132C22C2×#53811yescharacteristic
1133C22C2×#53911yescharacteristic
1134C22C2×#53911yescharacteristic
1135C22C2×#53911yescharacteristic
1136C22C2×#54011yescharacteristic
1137C22C2×#54211yescharacteristic
1138C22C2×D4211yescharacteristic
1139C22C2×D4211yescharacteristic
1140C22C2×#54611yescharacteristic
1141C22C2×#54611yescharacteristic
1142C22C2×#54611yescharacteristic
1143C22C2×#54611yescharacteristic
1144C22C2×#54611yescharacteristic
1145C22C2×#54711yescharacteristic
1146C22C2×#54711yescharacteristic
1147C22C2×#54711yescharacteristic
1148C22C2×#55111yescharacteristic
1149C22C2×#55211yescharacteristic
1150C22C2×#56011yescharacteristic
1151C22C2×#56211yescharacteristic
1152C22C2×#56211yescharacteristic
1153C22C2×#56311yescharacteristic
1154C4—28no—
1155C4—28no—
1156C4—44no—
1157C4—44no—
1158C4—44no—
1159C4—44no—
1160C4—44no—
1161C4—44no—
1162C4—44no—
1163C4—82no—
1164C4—82no—
1165C4—82no—
1166C4—82no—
1167C2—48no—
1168C2—48no—
1169C2#14359116yesdirect product factor
1170C2C2×#231111yescharacteristic
1171C2C2×#232211yescharacteristic
1172C2C2×#233511yescharacteristic
1173C2C2×D4×C22⋊C411yescharacteristic
1174C2C2×#233911yescharacteristic
1175C2C2×#235911yescharacteristic
1176C2C2×#237611yescharacteristic
1177C2C2×#267111yescharacteristic
1178C2C2×#267211yescharacteristic
1179C2C2×#267811yescharacteristic
1180C2C2×#268011yescharacteristic
1181C2C2×#268711yescharacteristic
1182C2C2×#269311yescharacteristic
1183C2C2×#269511yescharacteristic
1184C2C2×#270611yescharacteristic
subgroupG/H
center, socleC25C24
commutatorC23C24×C4
Frattini, cosocleC24C25
prime radicalC24×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C22×#388C2semidirect
4. C22×#385C2semidirect
5. C22×#380C2semidirect
6. #14359C2direct (N × H)
7. C2×#1445C2semidirect
8. C2×#1441C2semidirect
9. C2×#1441C2semidirect
10. C2×#1440C2semidirect
11. C2×#1439C2semidirect
13. C2×#1437C2semidirect
14. C2×C4⋊#95C2semidirect
15. C2×C22⋊#95C2semidirect
16. C2×C22⋊#95C2semidirect
22. C22×#123C4semidirect
41. C2×#388C22semidirect
45. C2×#385C22semidirect
47. C2×#380C22semidirect
64. #1445C22semidirect
65. #1441C22semidirect
66. #1441C22semidirect
67. #1440C22semidirect
68. #1439C22semidirect
70. #1437C22semidirect
71. C4⋊#95C22semidirect
72. C22⋊#95C22semidirect
73. C22⋊#95C22semidirect
97. C24×C4C2×C4semidirect
116. C2×#123C2×C4semidirect
130. C22×C4⋊C4C2×C4semidirect
131. C22×C4⋊C4C2×C4semidirect
163. C22×C22⋊C4C2×C4semidirect
374. C23×C4C22×C4semidirect
415. C2×C4⋊C4C22×C4semidirect
416. C2×C4⋊C4C22×C4semidirect
450. C2×C22⋊C4C22⋊C4semidirect
453. C2×C22⋊C4C22×C4semidirect
813. C22⋊C4C2×C22⋊C4semidirect
1169. C2#14359direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#1232
C22×#3882
C22×#3862
C22×#3852
C22×#3802
#143592
C2×#14452
C2×#14412
C2×#14402
C2×#14392
C2×#14382
C2×#14372
C2×C4⋊#952
C2×C22⋊#952