Finite Group Databasebeta

← C2×#15913 #609694

Subgroups — C2×#15913 #609694

Order 512.

6146 conjugacy classes of subgroups.

The subgroup lattice has 1152 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#126C211yesmaximal, characteristic, complemented
2C22×#397C211yesmaximal, characteristic, complemented
3C22×#396C211yesmaximal, characteristic, complemented
4C22×#390C211yesmaximal, characteristic
5#15913C2116yesmaximal, direct product factor
6C2×#1444C211yesmaximal, characteristic, complemented
7C2×#1440C211yesmaximal, characteristic, complemented
8C2×#1439C211yesmaximal, characteristic, complemented
9C2×#1439C211yesmaximal, characteristic, complemented
10C2×#1439C211yesmaximal, characteristic, complemented
11C2×#1438C211yesmaximal, characteristic
12C2×#1438C211yesmaximal, characteristic
13C2×#1437C211yesmaximal, characteristic, complemented
14C2×#1436C211yesmaximal, characteristic, complemented
15C2×#1436C211yesmaximal, characteristic, complemented
16C2×C4⋊#95C211yesmaximal, characteristic, complemented
17C24×D4C2211yescharacteristic
18C22×#126—28no—
19C22×#126—28no—
20C22×#126—28no—
21C22×#126C2218yescomplemented
22C23×C4⋊C4C2211yescharacteristic
23C23×C4⋊C4C2211yescharacteristic
24C23×C4⋊C4C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27C23×C4⋊C4C2211yescharacteristic
28C23×C22⋊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×C22⋊C4C2211yescharacteristic
40C23×C42C2211yescharacteristic
41C23×C42C2211yescharacteristic
42C2×#397—28no—
43C2×#397C2218yescomplemented
44C2×#396—28no—
45C2×#396C2218yescomplemented
46C2×#390—28no—
47C2×#390C2218yes—
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
62#1444C2218yescomplemented
63#1440C2218yescomplemented
64#1439C2218yescomplemented
65#1439C2218yescomplemented
66#1439C2218yescomplemented
67#1438C2218yes—
68#1438C2218yes—
69#1437C2218yescomplemented
70#1436C2218yescomplemented
71#1436C2218yescomplemented
72C4⋊#95C2218yescomplemented
73C26C2311yescharacteristic
74C26C2311yescharacteristic
75C23×D4—24no—
76C23×D4—24no—
77C23×D4—24no—
78C23×D4—24no—
79C23×D4—24no—
80C23×D4—42no—
81C23×D4—42no—
82C23×D4C2314yes—
83C24×C4C2311yescharacteristic
84C24×C4C2311yescharacteristic
85C24×C4C2311yescharacteristic
86C24×C4C2311yescharacteristic
87C24×C4C2311yescharacteristic
88C24×C4C2311yescharacteristic
89C24×C4C2311yescharacteristic
90C24×C4C2311yescharacteristic
91C24×C4C2311yescharacteristic
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C2×#126—2128no—
97C2×#126—232no—
98C2×#126—232no—
99C2×#126—232no—
100C22×C4⋊C4—24no—
101C22×C4⋊C4—24no—
102C22×C4⋊C4—24no—
103C22×C4⋊C4—24no—
104C22×C4⋊C4—24no—
105C22×C4⋊C4—24no—
106C22×C4⋊C4—24no—
107C22×C4⋊C4—24no—
108C22×C4⋊C4—24no—
109C22×C4⋊C4—24no—
110C22×C4⋊C4—24no—
111C22×C4⋊C4—24no—
112C22×C4⋊C4—42no—
113C22×C4⋊C4—42no—
114C22×C4⋊C4—42no—
115C22×C4⋊C4—42no—
116C22×C4⋊C4D418yescomplemented
117C22×C4⋊C4D418yescomplemented
118C22×C4⋊C4C2314yes—
119C22×C4⋊C4C2314yes—
120C22×C4⋊C4C2314yes—
121C22×C4⋊C4C2314yes—
122C22×C4⋊C4C2314yes—
123C22×C4⋊C4C2314yes—
124C22×C22⋊C4—24no—
125C22×C22⋊C4—24no—
126C22×C22⋊C4—24no—
127C22×C22⋊C4—24no—
128C22×C22⋊C4—24no—
129C22×C22⋊C4—24no—
130C22×C22⋊C4—24no—
131C22×C22⋊C4—24no—
132C22×C22⋊C4—24no—
133C22×C22⋊C4—24no—
134C22×C22⋊C4—24no—
135C22×C22⋊C4—24no—
136C22×C22⋊C4—24no—
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—42no—
148C22×C22⋊C4—42no—
149C22×C22⋊C4—42no—
150C22×C22⋊C4—42no—
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⋊C4D418yes—
160C22×C22⋊C4C2314yes—
161C22×C22⋊C4C2314yes—
162C22×C22⋊C4C2314yes—
163C22×C22⋊C4C2314yes—
164C22×C22⋊C4C2314yes—
165C22×C22⋊C4C2314yes—
166C22×C22⋊C4C2314yes—
167C22×C22⋊C4C2314yes—
168C22×C22⋊C4C2314yes—
169C22×C22⋊C4C2314yes—
170C22×C22⋊C4C2314yes—
171C22×C22⋊C4C2314yes—
172C22×C42—24no—
173C22×C42—24no—
174C22×C42—24no—
175C22×C42—24no—
176C22×C42—24no—
177C22×C42—42no—
178C22×C42C2314yes—
179C22×C42C2314yes—
180#397—232no—
181#396—232no—
182#390—232no—
183C2×#95—24no—
184C2×#95—24no—
185C2×#95—24no—
186C2×#95—24no—
187C2×#95—24no—
188C2×#95—24no—
189C2×#95—24no—
190C2×#95—24no—
191C2×#95—24no—
192C2×#95—42no—
193C2×#95—42no—
194C2×#95—42no—
195C2×#95—42no—
196C2×#95—42no—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C25—22no—
212C25—22no—
213C25—22no—
214C25—22no—
215C25—22no—
216C25—22no—
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—
239C25C2×D414yes—
240C25#4114yes—
241C25C2412yes—
242C25C2412yes—
243C25C2411yescharacteristic
244C22×D4—232no—
245C22×D4—28no—
246C22×D4—28no—
247C22×D4—28no—
248C22×D4—28no—
249C22×D4—28no—
250C22×D4—44no—
251C22×D4—44no—
252C22×D4—416no—
253C22×D4—416no—
254C22×D4—416no—
255C22×D4—416no—
256C22×D4—416no—
257C22×D4—416no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
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—22no—
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—22no—
286C23×C4—22no—
287C23×C4—22no—
288C23×C4—22no—
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—22no—
318C23×C4—22no—
319C23×C4—22no—
320C23×C4—22no—
321C23×C4—22no—
322C23×C4—22no—
323C23×C4—22no—
324C23×C4—22no—
325C23×C4—22no—
326C23×C4—22no—
327C23×C4—22no—
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×C4C2×D414yes—
337C23×C4C2×D414yes—
338C23×C4C2×D414yes—
339C23×C4C2×D414yes—
340C23×C4C2×D414yes—
341C23×C4C2×D414yes—
342C23×C4C2×D414yes—
343C23×C4C2×D414yes—
344C23×C4#4114yes—
345C23×C4#4114yes—
346C23×C4#4114yes—
347C23×C4#4114yes—
348C23×C4#4114yes—
349C23×C4C2412yes—
350C23×C4C2412yes—
351C23×C4C2412yes—
352C23×C4C2412yes—
353C23×C4C2412yes—
354C23×C4C2412yes—
355C23×C4C2412yes—
356C23×C4C2412yes—
357C23×C4C2412yes—
358C23×C4C2412yes—
359C23×C4C2412yes—
360C23×C4C2412yes—
361C23×C4C2412yes—
362#126—2256no—
363C2×C4⋊C4—232no—
364C2×C4⋊C4—232no—
365C2×C4⋊C4—232no—
366C2×C4⋊C4—28no—
367C2×C4⋊C4—28no—
368C2×C4⋊C4—28no—
369C2×C4⋊C4—28no—
370C2×C4⋊C4—28no—
371C2×C4⋊C4—28no—
372C2×C4⋊C4—28no—
373C2×C4⋊C4—28no—
374C2×C4⋊C4—28no—
375C2×C4⋊C4—28no—
376C2×C4⋊C4—28no—
377C2×C4⋊C4—28no—
378C2×C4⋊C4—44no—
379C2×C4⋊C4—44no—
380C2×C4⋊C4—44no—
381C2×C4⋊C4—44no—
382C2×C4⋊C4—416no—
383C2×C4⋊C4—416no—
384C2×C4⋊C4—416no—
385C2×C4⋊C4C2×D4116yescomplemented
386C2×C4⋊C4C2×D4116yescomplemented
387C2×C22⋊C4—232no—
388C2×C22⋊C4—232no—
389C2×C22⋊C4—28no—
390C2×C22⋊C4—28no—
391C2×C22⋊C4—232no—
392C2×C22⋊C4—28no—
393C2×C22⋊C4—28no—
394C2×C22⋊C4—28no—
395C2×C22⋊C4—28no—
396C2×C22⋊C4—28no—
397C2×C22⋊C4—28no—
398C2×C22⋊C4—28no—
399C2×C22⋊C4—28no—
400C2×C22⋊C4—28no—
401C2×C22⋊C4—28no—
402C2×C22⋊C4—28no—
403C2×C22⋊C4—28no—
404C2×C22⋊C4—28no—
405C2×C22⋊C4—28no—
406C2×C22⋊C4—28no—
407C2×C22⋊C4—28no—
408C2×C22⋊C4—28no—
409C2×C22⋊C4—28no—
410C2×C22⋊C4—28no—
411C2×C22⋊C4—28no—
412C2×C22⋊C4—28no—
413C2×C22⋊C4—44no—
414C2×C22⋊C4—44no—
415C2×C22⋊C4—44no—
416C2×C22⋊C4—44no—
417C2×C22⋊C4—44no—
418C2×C22⋊C4—44no—
419C2×C22⋊C4—44no—
420C2×C22⋊C4—44no—
421C2×C22⋊C4—44no—
422C2×C22⋊C4—44no—
423C2×C22⋊C4—44no—
424C2×C22⋊C4—44no—
425C2×C22⋊C4—416no—
426C2×C22⋊C4—416no—
427C2×C22⋊C4—416no—
428C2×C22⋊C4—416no—
429C2×C22⋊C4—416no—
430C2×C22⋊C4—416no—
431C2×C22⋊C4—416no—
432C2×C22⋊C4—416no—
433C2×C22⋊C4—416no—
434C2×C22⋊C4C2×D4116yes—
435C2×C42—232no—
436C2×C42—28no—
437C2×C42—28no—
438C2×C42—28no—
439C2×C42—28no—
440C2×C42—28no—
441C2×C42—44no—
442C2×C42—416no—
443#95—28no—
444#95—28no—
445#95—28no—
446#95—28no—
447#95—28no—
448#95—28no—
449#95—28no—
450#95—28no—
451#95—28no—
452#95—44no—
453#95—44no—
454#95—44no—
455#95—44no—
456#95—44no—
457C24—28no—
458C24—28no—
459C24—28no—
460C24—28no—
461C24—28no—
462C24—28no—
463C24—28no—
464C24—28no—
465C24—28no—
466C24—28no—
467C24—28no—
468C24—28no—
469C24—28no—
470C24—28no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—22no—
475C24—22no—
476C24—22no—
477C24—22no—
478C24—22no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24—22no—
486C24—22no—
487C24—22no—
488C24—22no—
489C24—22no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24—22no—
494C24—22no—
495C24—22no—
496C24—22no—
497C24—22no—
498C24—22no—
499C24—44no—
500C24—44no—
501C24—44no—
502C24—44no—
503C24—44no—
504C24—44no—
505C24—44no—
506C24—44no—
507C24—44no—
508C24—44no—
509C24—44no—
510C24—44no—
511C24—44no—
512C24—44no—
513C24—44no—
514C24—44no—
515C24—44no—
516C24—44no—
517C24—44no—
518C24—44no—
519C24—44no—
520C24—44no—
521C24—44no—
522C24—44no—
523C24—44no—
524C24—44no—
525C24—44no—
526C24—44no—
527C24—44no—
528C24—44no—
529C24—44no—
530C24—44no—
531C24—44no—
532C24—44no—
533C24—44no—
534C24—44no—
535C24—44no—
536C24—44no—
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—
555C24C22×D414yes—
556C24C22×D412yes—
557C24C22×D412yes—
558C24C22×D412yes—
559C24C2×#4114yes—
560C24C2×#4112yes—
561C24C2×#4112yes—
562C24C2×#4112yes—
563C24C2×#4112yes—
564C24C2×#4112yes—
565C24C2×#4112yes—
566C24H(5,𝔽2)12yes—
567C24H(5,𝔽2)12yes—
568C24H(5,𝔽2)12yes—
569C24H(5,𝔽2)12yes—
570C242−1+412yes—
571C242−1+412yes—
572C24C2511yescharacteristic
573C2×D4—232no—
574C2×D4—416no—
575C2×D4—416no—
576C2×D4—416no—
577C2×D4—416no—
578C2×D4—416no—
579C2×D4—4128no—
580C2×D4—416no—
581C22×C4—28no—
582C22×C4—28no—
583C22×C4—28no—
584C22×C4—28no—
585C22×C4—28no—
586C22×C4—28no—
587C22×C4—28no—
588C22×C4—28no—
589C22×C4—28no—
590C22×C4—28no—
591C22×C4—28no—
592C22×C4—28no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
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—28no—
614C22×C4—28no—
615C22×C4—28no—
616C22×C4—28no—
617C22×C4—28no—
618C22×C4—28no—
619C22×C4—28no—
620C22×C4—28no—
621C22×C4—28no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
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—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—44no—
693C22×C4—44no—
694C22×C4—44no—
695C22×C4—44no—
696C22×C4—44no—
697C22×C4—44no—
698C22×C4—44no—
699C22×C4—44no—
700C22×C4—44no—
701C22×C4—44no—
702C22×C4—44no—
703C22×C4—44no—
704C22×C4—44no—
705C22×C4—44no—
706C22×C4—44no—
707C22×C4—44no—
708C22×C4—44no—
709C22×C4—44no—
710C22×C4—44no—
711C22×C4—44no—
712C22×C4—44no—
713C22×C4—44no—
714C22×C4—44no—
715C22×C4—44no—
716C22×C4—44no—
717C22×C4—44no—
718C22×C4—44no—
719C22×C4—44no—
720C22×C4—44no—
721C22×C4—44no—
722C22×C4—44no—
723C22×C4—44no—
724C22×C4—44no—
725C22×C4—44no—
726C22×C4—44no—
727C22×C4—44no—
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#120116yes—
749C22×C4#126116yescomplemented
750C22×C4C22×D414yes—
751C22×C4C22×D414yes—
752C22×C4C22×D414yes—
753C22×C4C22×D414yes—
754C22×C4C22×D414yes—
755C22×C4C22×D414yes—
756C22×C4C22×D414yes—
757C22×C4C22×D414yes—
758C22×C4C2×#4114yes—
759C22×C4C2×#4114yes—
760C22×C4C2×#4114yes—
761C22×C4C2×#4114yes—
762C22×C4C2×#4114yes—
763C4⋊C4—232no—
764C4⋊C4—232no—
765C4⋊C4—232no—
766C4⋊C4—416no—
767C4⋊C4—416no—
768C4⋊C4—416no—
769C22⋊C4—232no—
770C22⋊C4—232no—
771C22⋊C4—232no—
772C22⋊C4—416no—
773C22⋊C4—416no—
774C22⋊C4—416no—
775C22⋊C4—416no—
776C22⋊C4—416no—
777C22⋊C4—416no—
778C22⋊C4—416no—
779C22⋊C4—416no—
780C22⋊C4—416no—
781C42—232no—
782C42—416no—
783C23—24no—
784C23—24no—
785C23—24no—
786C23—24no—
787C23—24no—
788C23—24no—
789C23—24no—
790C23—24no—
791C23—24no—
792C23—24no—
793C23—24no—
794C23—24no—
795C23—24no—
796C23—24no—
797C23—416no—
798C23—416no—
799C23—416no—
800C23—42no—
801C23—42no—
802C23—42no—
803C23—42no—
804C23—42no—
805C23—42no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23—42no—
815C23—42no—
816C23—42no—
817C23—42no—
818C23—42no—
819C23—42no—
820C23—416no—
821C23—42no—
822C23—42no—
823C23—42no—
824C23—42no—
825C23—416no—
826C23—416no—
827C23—42no—
828C23—42no—
829C23—42no—
830C23—42no—
831C23—42no—
832C23—42no—
833C23—42no—
834C23—42no—
835C23—42no—
836C23—42no—
837C23—42no—
838C23—42no—
839C23—42no—
840C23—42no—
841C23—42no—
842C23—42no—
843C23—42no—
844C23—42no—
845C23—42no—
846C23—42no—
847C23—42no—
848C23—42no—
849C23—42no—
850C23—42no—
851C23—416no—
852C23—42no—
853C23—42no—
854C23—42no—
855C23—42no—
856C23—416no—
857C23—416no—
858C23—416no—
859C23—416no—
860C23—416no—
861C23—416no—
862C23—42no—
863C23—42no—
864C23—42no—
865C23—42no—
866C23—416no—
867C23—88no—
868C23—88no—
869C23—88no—
870C23—88no—
871C23—88no—
872C23—88no—
873C23—88no—
874C23—88no—
875C23—88no—
876C23—88no—
877C23—88no—
878C23—88no—
879C23—88no—
880C23—88no—
881C23—88no—
882C23—88no—
883C23C2×#12014yes—
884C23#52514yes—
885C23C2×#12614yes—
886C23#52914yes—
887C23#53214yes—
888C23#53214yes—
889C23#53514yes—
890C23#53714yes—
891C23#53714yes—
892C23#53814yes—
893C23#53814yes—
894C23#53914yes—
895C23#53914yes—
896C23#54214yes—
897C23#54214yes—
898C23#54614yes—
899C23#54614yes—
900C23#54614yes—
901C23#54614yes—
902C23#54614yes—
903C23#54714yes—
904C23#54714yes—
905C23#54714yes—
906C23#54814yes—
907C23#55014yes—
908C23#55014yes—
909C23#55014yes—
910C23#55114yes—
911C23#55114yes—
912C23#55314yes—
913C23#55314yes—
914C23#55614yes—
915C23#55614yes—
916C23#56014yes—
917C23#56314yes—
918C23C23×D411yescharacteristic
919C23C23×D411yescharacteristic
920C23C23×D411yescharacteristic
921C23C22×#4111yescharacteristic
922C23C22×#4111yescharacteristic
923C23C22×#4111yescharacteristic
924C23C22×#4111yescharacteristic
925C23C22×#4111yescharacteristic
926C23C22×#4111yescharacteristic
927C23C2×H(5,𝔽2)11yescharacteristic
928C23C2×H(5,𝔽2)11yescharacteristic
929C23C2×H(5,𝔽2)11yescharacteristic
930C23C2×H(5,𝔽2)11yescharacteristic
931C23C2×2−1+411yescharacteristic
932C23C2×2−1+411yescharacteristic
933D4—464no—
934C2×C4—24no—
935C2×C4—24no—
936C2×C4—24no—
937C2×C4—24no—
938C2×C4—232no—
939C2×C4—24no—
940C2×C4—24no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—24no—
945C2×C4—24no—
946C2×C4—24no—
947C2×C4—232no—
948C2×C4—24no—
949C2×C4—24no—
950C2×C4—24no—
951C2×C4—24no—
952C2×C4—24no—
953C2×C4—24no—
954C2×C4—24no—
955C2×C4—24no—
956C2×C4—24no—
957C2×C4—24no—
958C2×C4—24no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—24no—
969C2×C4—416no—
970C2×C4—416no—
971C2×C4—42no—
972C2×C4—42no—
973C2×C4—42no—
974C2×C4—42no—
975C2×C4—42no—
976C2×C4—42no—
977C2×C4—42no—
978C2×C4—42no—
979C2×C4—42no—
980C2×C4—42no—
981C2×C4—42no—
982C2×C4—416no—
983C2×C4—42no—
984C2×C4—416no—
985C2×C4—416no—
986C2×C4—416no—
987C2×C4—42no—
988C2×C4—42no—
989C2×C4—42no—
990C2×C4—42no—
991C2×C4—42no—
992C2×C4—42no—
993C2×C4—42no—
994C2×C4—42no—
995C2×C4—42no—
996C2×C4—42no—
997C2×C4—42no—
998C2×C4—42no—
999C2×C4—42no—
1000C2×C4—42no—
1001C2×C4—416no—
1002C2×C4—42no—
1003C2×C4—42no—
1004C2×C4—42no—
1005C2×C4—42no—
1006C2×C4—42no—
1007C2×C4—42no—
1008C2×C4—42no—
1009C2×C4—42no—
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—42no—
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—88no—
1033C2×C4—88no—
1034C2×C4—88no—
1035C2×C4—88no—
1036C2×C4C2×#12018yes—
1037C2×C4C2×#12618yescomplemented
1038C22—44no—
1039C22—44no—
1040C22—44no—
1041C22—44no—
1042C22—44no—
1043C22—44no—
1044C22—44no—
1045C22—44no—
1046C22—44no—
1047C22—44no—
1048C22—44no—
1049C22—44no—
1050C22—44no—
1051C22—44no—
1052C22—82no—
1053C22—82no—
1054C22—832no—
1055C22—832no—
1056C22—82no—
1057C22—82no—
1058C22—82no—
1059C22—82no—
1060C22—82no—
1061C22—82no—
1062C22—82no—
1063C22—82no—
1064C22—82no—
1065C22—82no—
1066C22—82no—
1067C22—82no—
1068C22—82no—
1069C22—82no—
1070C22#240718yes—
1071C22#243018yes—
1072C22#243118yes—
1073C22#246618yes—
1074C22#248018yes—
1075C22#251218yes—
1076C22#251218yes—
1077C22#255418yes—
1078C22#256018yes—
1079C22#269118yes—
1080C22#270518yes—
1081C22#271418yes—
1082C22#271518yes—
1083C22#272318yes—
1084C22#272718yes—
1085C22C22×#12011yescharacteristic
1086C22C2×#52511yescharacteristic
1087C22C22×#12611yescharacteristic
1088C22C2×#52911yescharacteristic
1089C22C2×#53211yescharacteristic
1090C22C2×#53211yescharacteristic
1091C22C2×#53511yescharacteristic
1092C22C2×#53711yescharacteristic
1093C22C2×#53711yescharacteristic
1094C22C2×#53811yescharacteristic
1095C22C2×#53811yescharacteristic
1096C22C2×#53911yescharacteristic
1097C22C2×#53911yescharacteristic
1098C22C2×#54211yescharacteristic
1099C22C2×#54211yescharacteristic
1100C22C2×#54611yescharacteristic
1101C22C2×#54611yescharacteristic
1102C22C2×#54611yescharacteristic
1103C22C2×#54611yescharacteristic
1104C22C2×#54611yescharacteristic
1105C22C2×#54711yescharacteristic
1106C22C2×#54711yescharacteristic
1107C22C2×#54711yescharacteristic
1108C22C2×#54811yescharacteristic
1109C22C2×#55011yescharacteristic
1110C22C2×#55011yescharacteristic
1111C22C2×#55011yescharacteristic
1112C22C2×#55111yescharacteristic
1113C22C2×#55111yescharacteristic
1114C22C2×#55311yescharacteristic
1115C22C2×#55311yescharacteristic
1116C22C2×#55611yescharacteristic
1117C22C2×#55611yescharacteristic
1118C22C2×#56011yescharacteristic
1119C22C2×#56311yescharacteristic
1120C4—28no—
1121C4—28no—
1122C4—44no—
1123C4—44no—
1124C4—44no—
1125C4—44no—
1126C4—44no—
1127C4—44no—
1128C4—44no—
1129C4—82no—
1130C4—82no—
1131C4—82no—
1132C4—82no—
1133C2—84no—
1134C2—84no—
1135C2#15913116yesdirect product factor
1136C2C2×#248011yescharacteristic
1137C2C2×#246611yescharacteristic
1138C2C2×#240711yescharacteristic
1139C2C2×#243111yescharacteristic
1140C2C2×#243011yescharacteristic
1141C2C2×#251211yescharacteristic
1142C2C2×#251211yescharacteristic
1143C2C2×#255411yescharacteristic
1144C2C2×#256011yescharacteristic
1145C2C2×#269111yescharacteristic
1146C2C2×#270511yescharacteristic
1147C2C2×#271411yescharacteristic
1148C2C2×#271511yescharacteristic
1149C2C2×#272311yescharacteristic
1150C2C2×#272711yescharacteristic
subgroupG/H
center, socleC25C24
commutator, Frattini, cosocleC24C25
prime radicalC24×D4C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C23×#126C2semidirect
2. C22×#397C2semidirect
3. C22×#396C2semidirect
5. #15913C2direct (N × H)
6. C2×#1444C2semidirect
7. C2×#1440C2semidirect
8. C2×#1439C2semidirect
9. C2×#1439C2semidirect
10. C2×#1439C2semidirect
13. C2×#1437C2semidirect
14. C2×#1436C2semidirect
15. C2×#1436C2semidirect
16. C2×C4⋊#95C2semidirect
21. C22×#126C22semidirect
43. C2×#397C22semidirect
45. C2×#396C22semidirect
62. #1444C22semidirect
63. #1440C22semidirect
64. #1439C22semidirect
65. #1439C22semidirect
66. #1439C22semidirect
69. #1437C22semidirect
70. #1436C22semidirect
71. #1436C22semidirect
72. C4⋊#95C22semidirect
116. C22×C4⋊C4D4semidirect
117. C22×C4⋊C4D4semidirect
385. C2×C4⋊C4C2×D4semidirect
386. C2×C4⋊C4C2×D4semidirect
749. C22×C4#126semidirect
1037. C2×C4C2×#126semidirect
1135. C2#15913direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#1262
C22×#3972
C22×#3962
C22×#3902
#159132
C2×#14442
C2×#14402
C2×#14392
C2×#14382
C2×#14372
C2×#14362
C2×C4⋊#952