Finite Group Databasebeta

← C2×#15908 #609688

Subgroups — C2×#15908 #609688

Order 512.

6670 conjugacy classes of subgroups.

The subgroup lattice has 1162 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#126C211yesmaximal, characteristic, complemented
2C22×#394C211yesmaximal, characteristic
3C22×#394C211yesmaximal, characteristic
4C22×#386C211yesmaximal, characteristic
5#15908C2116yesmaximal, direct product factor
6C2×#1444C211yesmaximal, characteristic, complemented
7C2×#1442C211yesmaximal, characteristic, complemented
8C2×#1441C211yesmaximal, characteristic, complemented
9C2×#1440C211yesmaximal, characteristic, complemented
10C2×#1439C211yesmaximal, characteristic, complemented
11C2×#1439C211yesmaximal, characteristic, complemented
12C2×#1439C211yesmaximal, characteristic, complemented
13C2×#1437C211yesmaximal, characteristic, complemented
14C2×#1436C211yesmaximal, characteristic, complemented
15C2×C22⋊#95C211yesmaximal, characteristic, complemented
16C2×C22⋊#95C211yesmaximal, characteristic, complemented
17C24×D4C2211yescharacteristic
18C25×C4C2211yescharacteristic
19C22×#126—28no—
20C22×#126—28no—
21C22×#126—28no—
22C22×#126C2218yescomplemented
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×C42C2211yescharacteristic
40C2×#394—28no—
41C2×#394—28no—
42C2×#394C2218yes—
43C2×#394C2218yes—
44C2×#386—28no—
45C2×#386C2218yes—
46C22×#95C2211yescharacteristic
47C22×#95C2211yescharacteristic
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#1442C2218yescomplemented
64#1441C2218yescomplemented
65#1440C2218yescomplemented
66#1439C2218yescomplemented
67#1439C2218yescomplemented
68#1439C2218yescomplemented
69#1437C2218yescomplemented
70#1436C2218yescomplemented
71C22⋊#95C2218yescomplemented
72C22⋊#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×C4—24no—
84C24×C4—24no—
85C24×C4—24no—
86C24×C4—42no—
87C24×C4—42no—
88C24×C4—42no—
89C24×C4—42no—
90C24×C4C2311yescharacteristic
91C24×C4C2311yescharacteristic
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C24×C4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C24×C4C2311yescharacteristic
103C24×C4C2314yes—
104C2×#126—2128no—
105C2×#126—232no—
106C2×#126—232no—
107C2×#126—232no—
108C22×C4⋊C4—24no—
109C22×C4⋊C4—24no—
110C22×C4⋊C4—24no—
111C22×C4⋊C4—24no—
112C22×C4⋊C4—24no—
113C22×C4⋊C4—24no—
114C22×C4⋊C4—24no—
115C22×C4⋊C4—24no—
116C22×C4⋊C4—24no—
117C22×C4⋊C4—24no—
118C22×C4⋊C4—24no—
119C22×C4⋊C4—24no—
120C22×C4⋊C4—24no—
121C22×C4⋊C4—42no—
122C22×C4⋊C4—42no—
123C22×C4⋊C4C2314yes—
124C22×C4⋊C4C2314yes—
125C22×C4⋊C4C2314yes—
126C22×C4⋊C4C2314yes—
127C22×C4⋊C4C2314yes—
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—24no—
148C22×C22⋊C4—24no—
149C22×C22⋊C4—24no—
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⋊C4D418yes—
159C22×C22⋊C4D418yes—
160C22×C22⋊C4D418yes—
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×C42C2314yes—
176#394—232no—
177#394—232no—
178#386—232no—
179C2×#95—24no—
180C2×#95—24no—
181C2×#95—24no—
182C2×#95—24no—
183C2×#95—24no—
184C2×#95—24no—
185C2×#95—24no—
186C2×#95—24no—
187C2×#95—42no—
188C2×#95—42no—
189C2×#95—42no—
190C2×#95—42no—
191C2×#95—42no—
192C2×#95—42no—
193C2×#95—42no—
194C2×#95—42no—
195C2×#95C2314yes—
196C2×#95C2314yes—
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—
237C25C2×D414yes—
238C25C2×D414yes—
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—28no—
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×C4—22no—
337C23×C4—22no—
338C23×C4—22no—
339C23×C4—28no—
340C23×C4—28no—
341C23×C4—44no—
342C23×C4—44no—
343C23×C4—44no—
344C23×C4—44no—
345C23×C4—416no—
346C23×C4—416no—
347C23×C4—416no—
348C23×C4—416no—
349C23×C4—416no—
350C23×C4—416no—
351C23×C4—416no—
352C23×C4C2×D414yes—
353C23×C4C2×D414yes—
354C23×C4C2×D414yes—
355C23×C4C2×D414yes—
356C23×C4C2×D414yes—
357C23×C4C2×D414yes—
358C23×C4#4114yes—
359C23×C4#4114yes—
360C23×C4#4114yes—
361C23×C4#4114yes—
362C23×C4#4114yes—
363C23×C4C2412yes—
364C23×C4C2412yes—
365C23×C4C2412yes—
366C23×C4C2412yes—
367C23×C4C2412yes—
368C23×C4C2412yes—
369C23×C4C2412yes—
370C23×C4C2412yes—
371C23×C4C2412yes—
372C23×C4C2412yes—
373C23×C4C2412yes—
374C23×C4C2412yes—
375C23×C4C2412yes—
376#126—2256no—
377C2×C4⋊C4—232no—
378C2×C4⋊C4—232no—
379C2×C4⋊C4—232no—
380C2×C4⋊C4—28no—
381C2×C4⋊C4—28no—
382C2×C4⋊C4—28no—
383C2×C4⋊C4—28no—
384C2×C4⋊C4—28no—
385C2×C4⋊C4—28no—
386C2×C4⋊C4—28no—
387C2×C4⋊C4—28no—
388C2×C4⋊C4—28no—
389C2×C4⋊C4—28no—
390C2×C4⋊C4—28no—
391C2×C4⋊C4—28no—
392C2×C4⋊C4—28no—
393C2×C4⋊C4—44no—
394C2×C4⋊C4—44no—
395C2×C4⋊C4—416no—
396C2×C4⋊C4—416no—
397C2×C22⋊C4—232no—
398C2×C22⋊C4—232no—
399C2×C22⋊C4—232no—
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—28no—
414C2×C22⋊C4—28no—
415C2×C22⋊C4—28no—
416C2×C22⋊C4—28no—
417C2×C22⋊C4—28no—
418C2×C22⋊C4—28no—
419C2×C22⋊C4—28no—
420C2×C22⋊C4—28no—
421C2×C22⋊C4—28no—
422C2×C22⋊C4—44no—
423C2×C22⋊C4—44no—
424C2×C22⋊C4—44no—
425C2×C22⋊C4—44no—
426C2×C22⋊C4—44no—
427C2×C22⋊C4—44no—
428C2×C22⋊C4—44no—
429C2×C22⋊C4—44no—
430C2×C22⋊C4—416no—
431C2×C22⋊C4—416no—
432C2×C22⋊C4—416no—
433C2×C22⋊C4—416no—
434C2×C22⋊C4—416no—
435C2×C22⋊C4—416no—
436C2×C22⋊C4—416no—
437C2×C22⋊C4—416no—
438C2×C22⋊C4C2×D4116yes—
439C2×C22⋊C4C2×D4116yes—
440C2×C22⋊C4C2×D4116yes—
441C2×C42—232no—
442C2×C42—28no—
443C2×C42—28no—
444C2×C42—28no—
445#95—28no—
446#95—28no—
447#95—28no—
448#95—28no—
449#95—28no—
450#95—28no—
451#95—28no—
452#95—28no—
453#95—44no—
454#95—44no—
455#95—44no—
456#95—44no—
457#95—44no—
458#95—44no—
459#95—44no—
460#95—44no—
461C24—28no—
462C24—28no—
463C24—28no—
464C24—28no—
465C24—28no—
466C24—28no—
467C24—28no—
468C24—28no—
469C24—28no—
470C24—28no—
471C24—28no—
472C24—28no—
473C24—28no—
474C24—28no—
475C24—28no—
476C24—28no—
477C24—28no—
478C24—28no—
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—28no—
492C24—28no—
493C24—28no—
494C24—28no—
495C24—28no—
496C24—28no—
497C24—28no—
498C24—22no—
499C24—22no—
500C24—22no—
501C24—22no—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24—22no—
511C24—22no—
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—
555C24—44no—
556C24#120116yes—
557C24C22×D414yes—
558C24C22×D414yes—
559C24C22×D414yes—
560C24C22×D412yes—
561C24C22×D412yes—
562C24C22×D412yes—
563C24C2×#4114yes—
564C24C2×#4112yes—
565C24C2×#4112yes—
566C24C2×#4112yes—
567C24C2×#4112yes—
568C24C2×#4112yes—
569C24C2×#4112yes—
570C24H(5,𝔽2)12yes—
571C24H(5,𝔽2)12yes—
572C24H(5,𝔽2)12yes—
573C24H(5,𝔽2)12yes—
574C242−1+412yes—
575C242−1+412yes—
576C24C2511yescharacteristic
577C2×D4—232no—
578C2×D4—416no—
579C2×D4—416no—
580C2×D4—416no—
581C2×D4—416no—
582C2×D4—4128no—
583C2×D4—416no—
584C2×D4—416no—
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—28no—
594C22×C4—28no—
595C22×C4—28no—
596C22×C4—28no—
597C22×C4—28no—
598C22×C4—28no—
599C22×C4—28no—
600C22×C4—28no—
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—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
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—22no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—416no—
699C22×C4—416no—
700C22×C4—416no—
701C22×C4—416no—
702C22×C4—416no—
703C22×C4—416no—
704C22×C4—4128no—
705C22×C4—416no—
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—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×C4C22×D414yes—
765C22×C4C22×D414yes—
766C22×C4C22×D414yes—
767C22×C4C22×D414yes—
768C22×C4C22×D414yes—
769C22×C4C22×D414yes—
770C22×C4C2×#4114yes—
771C22×C4C2×#4114yes—
772C22×C4C2×#4114yes—
773C22×C4C2×#4114yes—
774C22×C4C2×#4114yes—
775C4⋊C4—232no—
776C4⋊C4—232no—
777C4⋊C4—232no—
778C4⋊C4—416no—
779C4⋊C4—416no—
780C22⋊C4—232no—
781C22⋊C4—232no—
782C22⋊C4—232no—
783C22⋊C4—416no—
784C22⋊C4—416no—
785C22⋊C4—416no—
786C22⋊C4—416no—
787C22⋊C4—416no—
788C22⋊C4—416no—
789C22⋊C4—416no—
790C22⋊C4—416no—
791C42—232no—
792C23—232no—
793C23—24no—
794C23—24no—
795C23—24no—
796C23—24no—
797C23—24no—
798C23—24no—
799C23—232no—
800C23—232no—
801C23—24no—
802C23—24no—
803C23—24no—
804C23—24no—
805C23—24no—
806C23—24no—
807C23—24no—
808C23—24no—
809C23—24no—
810C23—24no—
811C23—24no—
812C23—24no—
813C23—24no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—24no—
818C23—24no—
819C23—24no—
820C23—42no—
821C23—42no—
822C23—42no—
823C23—42no—
824C23—42no—
825C23—42no—
826C23—416no—
827C23—42no—
828C23—42no—
829C23—416no—
830C23—416no—
831C23—416no—
832C23—42no—
833C23—42no—
834C23—42no—
835C23—42no—
836C23—42no—
837C23—42no—
838C23—416no—
839C23—416no—
840C23—416no—
841C23—416no—
842C23—42no—
843C23—42no—
844C23—416no—
845C23—416no—
846C23—416no—
847C23—416no—
848C23—416no—
849C23—42no—
850C23—42no—
851C23—42no—
852C23—42no—
853C23—42no—
854C23—42no—
855C23—42no—
856C23—42no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—42no—
861C23—416no—
862C23—416no—
863C23—42no—
864C23—42no—
865C23—42no—
866C23—42no—
867C23—42no—
868C23—42no—
869C23—42no—
870C23—42no—
871C23—42no—
872C23—42no—
873C23—42no—
874C23—42no—
875C23—42no—
876C23—42no—
877C23—416no—
878C23—416no—
879C23—42no—
880C23—42no—
881C23—416no—
882C23—416no—
883C23—88no—
884C23—88no—
885C23—88no—
886C23—88no—
887C23—88no—
888C23—88no—
889C23—88no—
890C23—88no—
891C23C2×#12018yes—
892C23C2×#12014yes—
893C23#52514yes—
894C23#52914yes—
895C23#52914yes—
896C23#53214yes—
897C23#53214yes—
898C23#53514yes—
899C23#53714yes—
900C23#53714yes—
901C23#53814yes—
902C23#53814yes—
903C23#53914yes—
904C23#53914yes—
905C23#54214yes—
906C23#54214yes—
907C23#54614yes—
908C23#54614yes—
909C23#54614yes—
910C23#54614yes—
911C23#54614yes—
912C23#54614yes—
913C23#54614yes—
914C23#54614yes—
915C23#54714yes—
916C23#54714yes—
917C23#54714yes—
918C23#54714yes—
919C23#55114yes—
920C23#55214yes—
921C23#55314yes—
922C23#55314yes—
923C23#55314yes—
924C23#55614yes—
925C23#56014yes—
926C23#56314yes—
927C23C23×D411yescharacteristic
928C23C23×D411yescharacteristic
929C23C23×D411yescharacteristic
930C23C22×#4111yescharacteristic
931C23C22×#4111yescharacteristic
932C23C22×#4111yescharacteristic
933C23C22×#4111yescharacteristic
934C23C22×#4111yescharacteristic
935C23C22×#4111yescharacteristic
936C23C2×H(5,𝔽2)11yescharacteristic
937C23C2×H(5,𝔽2)11yescharacteristic
938C23C2×H(5,𝔽2)11yescharacteristic
939C23C2×H(5,𝔽2)11yescharacteristic
940C23C2×2−1+411yescharacteristic
941C23C2×2−1+411yescharacteristic
942D4—464no—
943C2×C4—24no—
944C2×C4—24no—
945C2×C4—24no—
946C2×C4—24no—
947C2×C4—24no—
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—24no—
970C2×C4—24no—
971C2×C4—24no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—24no—
975C2×C4—24no—
976C2×C4—464no—
977C2×C4—416no—
978C2×C4—416no—
979C2×C4—416no—
980C2×C4—42no—
981C2×C4—42no—
982C2×C4—42no—
983C2×C4—42no—
984C2×C4—42no—
985C2×C4—42no—
986C2×C4—42no—
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—416no—
1003C2×C4—416no—
1004C2×C4—416no—
1005C2×C4—416no—
1006C2×C4—416no—
1007C2×C4—42no—
1008C2×C4—416no—
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—416no—
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—88no—
1047C2×C4—88no—
1048C22—28no—
1049C22—28no—
1050C22—28no—
1051C22—44no—
1052C22—44no—
1053C22—44no—
1054C22—464no—
1055C22—44no—
1056C22—44no—
1057C22—44no—
1058C22—44no—
1059C22—44no—
1060C22—44no—
1061C22—44no—
1062C22—44no—
1063C22—44no—
1064C22—44no—
1065C22—44no—
1066C22—44no—
1067C22—44no—
1068C22—44no—
1069C22—44no—
1070C22—44no—
1071C22—82no—
1072C22—832no—
1073C22—82no—
1074C22—82no—
1075C22—82no—
1076C22—82no—
1077C22—82no—
1078C22—82no—
1079C22—82no—
1080C22#240418yes—
1081C22#243018yes—
1082C22#243018yes—
1083C22#246618yes—
1084C22#246818yes—
1085C22#252118yes—
1086C22#255318yes—
1087C22#255918yes—
1088C22#255918yes—
1089C22#268518yes—
1090C22#269118yes—
1091C22#269118yes—
1092C22#269518yes—
1093C22#271518yes—
1094C22#271818yes—
1095C22C22×#12011yescharacteristic
1096C22C2×#52511yescharacteristic
1097C22C2×#52911yescharacteristic
1098C22C2×#52911yescharacteristic
1099C22C2×#53211yescharacteristic
1100C22C2×#53211yescharacteristic
1101C22C2×#53511yescharacteristic
1102C22C2×#53711yescharacteristic
1103C22C2×#53711yescharacteristic
1104C22C2×#53811yescharacteristic
1105C22C2×#53811yescharacteristic
1106C22C2×#53911yescharacteristic
1107C22C2×#53911yescharacteristic
1108C22C2×#54211yescharacteristic
1109C22C2×#54211yescharacteristic
1110C22C2×#54611yescharacteristic
1111C22C2×#54611yescharacteristic
1112C22C2×#54611yescharacteristic
1113C22C2×#54611yescharacteristic
1114C22C2×#54611yescharacteristic
1115C22C2×#54611yescharacteristic
1116C22C2×#54611yescharacteristic
1117C22C2×#54611yescharacteristic
1118C22C2×#54711yescharacteristic
1119C22C2×#54711yescharacteristic
1120C22C2×#54711yescharacteristic
1121C22C2×#54711yescharacteristic
1122C22C2×#55111yescharacteristic
1123C22C2×#55211yescharacteristic
1124C22C2×#55311yescharacteristic
1125C22C2×#55311yescharacteristic
1126C22C2×#55311yescharacteristic
1127C22C2×#55611yescharacteristic
1128C22C2×#56011yescharacteristic
1129C22C2×#56311yescharacteristic
1130C4—44no—
1131C4—44no—
1132C4—44no—
1133C4—44no—
1134C4—44no—
1135C4—44no—
1136C4—44no—
1137C4—44no—
1138C4—44no—
1139C4—44no—
1140C4—44no—
1141C4—82no—
1142C4—82no—
1143C2—48no—
1144C2—84no—
1145C2#15908116yesdirect product factor
1146C2C2×#246611yescharacteristic
1147C2C2×#246811yescharacteristic
1148C2C2×#240411yescharacteristic
1149C2C2×#243011yescharacteristic
1150C2C2×#243011yescharacteristic
1151C2C2×#252111yescharacteristic
1152C2C2×#255311yescharacteristic
1153C2C2×#255911yescharacteristic
1154C2C2×#255911yescharacteristic
1155C2C2×#268511yescharacteristic
1156C2C2×#269111yescharacteristic
1157C2C2×#269111yescharacteristic
1158C2C2×#269511yescharacteristic
1159C2C2×#271511yescharacteristic
1160C2C2×#271811yescharacteristic
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
5. #15908C2direct (N × H)
6. C2×#1444C2semidirect
7. C2×#1442C2semidirect
8. C2×#1441C2semidirect
9. C2×#1440C2semidirect
10. C2×#1439C2semidirect
11. C2×#1439C2semidirect
12. C2×#1439C2semidirect
13. C2×#1437C2semidirect
14. C2×#1436C2semidirect
15. C2×C22⋊#95C2semidirect
16. C2×C22⋊#95C2semidirect
22. C22×#126C22semidirect
62. #1444C22semidirect
63. #1442C22semidirect
64. #1441C22semidirect
65. #1440C22semidirect
66. #1439C22semidirect
67. #1439C22semidirect
68. #1439C22semidirect
69. #1437C22semidirect
70. #1436C22semidirect
71. C22⋊#95C22semidirect
72. C22⋊#95C22semidirect
1145. C2#15908direct (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×#3942
C22×#3862
#159082
C2×#14442
C2×#14422
C2×#14412
C2×#14402
C2×#14392
C2×#14372
C2×#14362
C2×C22⋊#952