Finite Group Databasebeta

← C2×#14173 #514656

Subgroups — C2×#14173 #514656

Order 512.

8274 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×C4×D4C211yesmaximal, characteristic
2C22×#394C211yesmaximal, characteristic
3C22×#388C211yesmaximal, characteristic, complemented
4C22×#387C211yesmaximal, characteristic, complemented
5C22×C4×C22⋊C4C211yesmaximal, characteristic, complemented
6#14173C2116yesmaximal, direct product factor
7C2×#1440C211yesmaximal, characteristic, complemented
8C2×#1439C211yesmaximal, characteristic, complemented
9C2×#1438C211yesmaximal, characteristic
10C2×#1437C211yesmaximal, characteristic, complemented
11C2×#1436C211yesmaximal, characteristic, complemented
12C2×#1436C211yesmaximal, characteristic, complemented
13C2×#1436C211yesmaximal, characteristic, complemented
14C2×C22⋊#95C211yesmaximal, characteristic, complemented
15C2×C22⋊#95C211yesmaximal, characteristic, complemented
16C2×C22⋊#95C211yesmaximal, characteristic, complemented
17C24×D4C2211yescharacteristic
18C25×C4C2211yescharacteristic
19C25×C4C2211yescharacteristic
20C22×C4×D4—28no—
21C22×C4×D4—28no—
22C22×C4×D4—28no—
23C22×C4×D4C2218yes—
24C23×C4⋊C4C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27C23×C22⋊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×C42C2211yescharacteristic
38C23×C42C2211yescharacteristic
39C23×C42C2211yescharacteristic
40C2×#394C4116yescomplemented
41C2×#394C2218yes—
42C2×#388—28no—
43C2×#388C2218yescomplemented
44C2×#387—28no—
45C2×#387C2218yescomplemented
46C2×C4×C22⋊C4—28no—
47C2×C4×C22⋊C4C2218yescomplemented
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#1440C2218yescomplemented
65#1439C2218yescomplemented
66#1438C2218yes—
67#1437C2218yescomplemented
68#1436C2218yescomplemented
69#1436C2218yescomplemented
70#1436C2218yescomplemented
71C22⋊#95C2218yescomplemented
72C22⋊#95C2218yescomplemented
73C22⋊#95C2218yescomplemented
74C26C2311yescharacteristic
75C26C2311yescharacteristic
76C23×D4—24no—
77C23×D4—24no—
78C23×D4—24no—
79C23×D4—24no—
80C23×D4—24no—
81C23×D4—24no—
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—24no—
92C24×C4—24no—
93C24×C4—42no—
94C24×C4—42no—
95C24×C4—42no—
96C24×C4—42no—
97C24×C4D418yes—
98C24×C4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C24×C4C2311yescharacteristic
103C24×C4C2311yescharacteristic
104C24×C4C2311yescharacteristic
105C24×C4C2311yescharacteristic
106C24×C4C2311yescharacteristic
107C24×C4C2311yescharacteristic
108C24×C4C2314yes—
109C24×C4C2314yes—
110C24×C4C2311yescharacteristic
111C24×C4C2311yescharacteristic
112C24×C4C2311yescharacteristic
113C2×C4×D4—2128no—
114C2×C4×D4—232no—
115C2×C4×D4—232no—
116C2×C4×D4—232no—
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—42no—
124C22×C4⋊C4C2×C418yescomplemented
125C22×C4⋊C4D418yes—
126C22×C4⋊C4C2314yes—
127C22×C4⋊C4C2314yes—
128C22×C4⋊C4C2314yes—
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—42no—
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⋊C4C2×C418yescomplemented
155C22×C22⋊C4C2×C418yescomplemented
156C22×C22⋊C4C2×C418yescomplemented
157C22×C22⋊C4C2×C418yescomplemented
158C22×C22⋊C4D418yes—
159C22×C22⋊C4C2314yes—
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×C42—24no—
170C22×C42—24no—
171C22×C42—24no—
172C22×C42—24no—
173C22×C42—24no—
174C22×C42—24no—
175C22×C42—24no—
176C22×C42—42no—
177C22×C42—42no—
178C22×C42C2314yes—
179C22×C42C2314yes—
180C22×C42C2314yes—
181#394C2×C4164yescomplemented
182#388—232no—
183#387—232no—
184C4×C22⋊C4—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—24no—
194C2×#95—24no—
195C2×#95—24no—
196C2×#95—24no—
197C2×#95—42no—
198C2×#95—42no—
199C2×#95—42no—
200C2×#95C2×C418yescomplemented
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—
245C25#4114yes—
246C25#4114yes—
247C25C2412yes—
248C25C2412yes—
249C25C2411yescharacteristic
250C22×D4—232no—
251C22×D4—232no—
252C22×D4—232no—
253C22×D4—232no—
254C22×D4—232no—
255C22×D4—232no—
256C22×D4—28no—
257C22×D4—28no—
258C22×D4—28no—
259C22×D4—28no—
260C22×D4—232no—
261C22×D4—28no—
262C22×D4—28no—
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—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—232no—
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—28no—
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—232no—
327C23×C4—232no—
328C23×C4—28no—
329C23×C4—28no—
330C23×C4—28no—
331C23×C4—28no—
332C23×C4—28no—
333C23×C4—28no—
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—28no—
349C23×C4—28no—
350C23×C4—416no—
351C23×C4—44no—
352C23×C4—44no—
353C23×C4—44no—
354C23×C4—44no—
355C23×C4—416no—
356C23×C4—416no—
357C23×C4—416no—
358C23×C4—416no—
359C23×C4—416no—
360C23×C4—416no—
361C23×C4—416no—
362C23×C4—416no—
363C23×C4—416no—
364C23×C4—416no—
365C23×C4C22×C414yes—
366C23×C4C22×C414yes—
367C23×C4C22×C414yes—
368C23×C4C22×C414yes—
369C23×C4C22×C414yes—
370C23×C4C2×D414yes—
371C23×C4C2×D414yes—
372C23×C4C2×D4116yes—
373C23×C4C2×D414yes—
374C23×C4C2×D414yes—
375C23×C4C2×D414yes—
376C23×C4C2×D414yes—
377C23×C4C2×D414yes—
378C23×C4#4114yes—
379C23×C4#4114yes—
380C23×C4#4114yes—
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—
396C4×D4—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—44no—
406C2×C4⋊C4—416no—
407C2×C4⋊C4C22×C4116yescomplemented
408C2×C4⋊C4C2×D4116yes—
409C2×C22⋊C4—232no—
410C2×C22⋊C4—232no—
411C2×C22⋊C4—232no—
412C2×C22⋊C4—232no—
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—232no—
420C2×C22⋊C4—28no—
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—416no—
432C2×C22⋊C4—416no—
433C2×C22⋊C4—44no—
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—416no—
442C2×C22⋊C4—416no—
443C2×C22⋊C4—416no—
444C2×C22⋊C4C22×C4116yescomplemented
445C2×C22⋊C4C22×C4116yescomplemented
446C2×C22⋊C4C22×C4116yescomplemented
447C2×C22⋊C4C22×C4116yescomplemented
448C2×C22⋊C4C2×D4116yes—
449C2×C42—232no—
450C2×C42—28no—
451C2×C42—28no—
452C2×C42—28no—
453C2×C42—28no—
454C2×C42—28no—
455C2×C42—28no—
456C2×C42—28no—
457C2×C42—44no—
458C2×C42—44no—
459C2×C42—416no—
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—28no—
470#95—28no—
471#95—28no—
472#95—28no—
473#95—44no—
474#95—44no—
475#95—44no—
476#95C22×C4116yescomplemented
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—
569C24C4×D4116yes—
570C24C4×D4116yes—
571C24C23×C414yes—
572C24C23×C414yes—
573C24C23×C412yes—
574C24C22×D414yes—
575C24C22×D414yes—
576C24C22×D412yes—
577C24C22×D412yes—
578C24C22×D412yes—
579C24C2×#4114yes—
580C24C2×#4114yes—
581C24C2×#4112yes—
582C24C2×#4112yes—
583C24C2×#4112yes—
584C24C2×#4112yes—
585C24C2×#4112yes—
586C24C2×#4112yes—
587C24C2×#4112yes—
588C24H(5,𝔽2)12yes—
589C24H(5,𝔽2)12yes—
590C24H(5,𝔽2)12yes—
591C242−1+412yes—
592C24C2511yescharacteristic
593C2×D4—232no—
594C2×D4—232no—
595C2×D4—232no—
596C2×D4—232no—
597C2×D4—2256no—
598C2×D4—232no—
599C2×D4—232no—
600C2×D4—232no—
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—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—232no—
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—28no—
644C22×C4—28no—
645C22×C4—28no—
646C22×C4—28no—
647C22×C4—28no—
648C22×C4—28no—
649C22×C4—28no—
650C22×C4—28no—
651C22×C4—28no—
652C22×C4—28no—
653C22×C4—28no—
654C22×C4—28no—
655C22×C4—28no—
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—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—22no—
704C22×C4—232no—
705C22×C4—232no—
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—22no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—416no—
721C22×C4—4128no—
722C22×C4—416no—
723C22×C4—416no—
724C22×C4—416no—
725C22×C4—416no—
726C22×C4—416no—
727C22×C4—416no—
728C22×C4—416no—
729C22×C4—416no—
730C22×C4—4128no—
731C22×C4—416no—
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—416no—
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×C4C4×D4116yes—
780C22×C4#120116yes—
781C22×C4#123116yes—
782C22×C4C23×C414yes—
783C22×C4C23×C414yes—
784C22×C4C23×C414yes—
785C22×C4C23×C414yes—
786C22×C4C23×C414yes—
787C22×C4C22×D414yes—
788C22×C4C22×D414yes—
789C22×C4C22×D414yes—
790C22×C4C22×D414yes—
791C22×C4C22×D414yes—
792C22×C4C22×D414yes—
793C22×C4C22×D414yes—
794C22×C4C2×#4114yes—
795C22×C4C2×#4114yes—
796C22×C4C2×#4114yes—
797C22×C4C2×#4114yes—
798C22×C4C2×#4114yes—
799C4⋊C4—232no—
800C4⋊C4—232no—
801C4⋊C4—416no—
802C22⋊C4—232no—
803C22⋊C4—232no—
804C22⋊C4—232no—
805C22⋊C4—232no—
806C22⋊C4—232no—
807C22⋊C4—416no—
808C22⋊C4—416no—
809C22⋊C4—416no—
810C22⋊C4—416no—
811C22⋊C4—416no—
812C42—232no—
813C42—416no—
814C42—416no—
815C23—232no—
816C23—232no—
817C23—232no—
818C23—24no—
819C23—24no—
820C23—24no—
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—232no—
855C23—232no—
856C23—232no—
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—416no—
870C23—42no—
871C23—42no—
872C23—42no—
873C23—42no—
874C23—42no—
875C23—42no—
876C23—42no—
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—42no—
890C23—42no—
891C23—42no—
892C23—42no—
893C23—42no—
894C23—42no—
895C23—42no—
896C23—42no—
897C23—42no—
898C23—42no—
899C23—42no—
900C23—42no—
901C23—42no—
902C23—416no—
903C23—416no—
904C23—416no—
905C23—416no—
906C23—416no—
907C23—416no—
908C23—416no—
909C23—416no—
910C23—416no—
911C23—416no—
912C23—416no—
913C23C2×C4×D418yes—
914C23C2×C4×D418yes—
915C23C2×C4×D414yes—
916C23C2×C4×D414yes—
917C23C2×C4×D414yes—
918C23C4×#4114yes—
919C23C4×#4114yes—
920C23#51814yes—
921C23#52014yes—
922C23C2×#12014yes—
923C23C2×#12314yes—
924C23#52514yes—
925C23#52514yes—
926C23#52514yes—
927C23#52514yes—
928C23#52914yes—
929C23#52914yes—
930C23#53414yes—
931C23#53714yes—
932C23#53814yes—
933C23#53914yes—
934C23#54614yes—
935C23#54614yes—
936C23#54614yes—
937C23#54614yes—
938C23#54614yes—
939C23#54714yes—
940C23#54814yes—
941C23#55014yes—
942C23#55114yes—
943C23#55214yes—
944C23#55314yes—
945C23#55314yes—
946C23#55314yes—
947C23#55514yes—
948C23#55614yes—
949C23#55914yes—
950C23C24×C411yescharacteristic
951C23C23×D411yescharacteristic
952C23C23×D411yescharacteristic
953C23C23×D411yescharacteristic
954C23C22×#4111yescharacteristic
955C23C22×#4111yescharacteristic
956C23C22×#4111yescharacteristic
957C23C22×#4111yescharacteristic
958C23C22×#4111yescharacteristic
959C23C22×#4111yescharacteristic
960C23C22×#4111yescharacteristic
961C23C2×H(5,𝔽2)11yescharacteristic
962C23C2×H(5,𝔽2)11yescharacteristic
963C23C2×H(5,𝔽2)11yescharacteristic
964C23C2×2−1+411yescharacteristic
965D4—2128no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—232no—
969C2×C4—232no—
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—232no—
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—24no—
1002C2×C4—24no—
1003C2×C4—24no—
1004C2×C4—24no—
1005C2×C4—24no—
1006C2×C4—24no—
1007C2×C4—24no—
1008C2×C4—24no—
1009C2×C4—24no—
1010C2×C4—24no—
1011C2×C4—464no—
1012C2×C4—464no—
1013C2×C4—416no—
1014C2×C4—416no—
1015C2×C4—416no—
1016C2×C4—416no—
1017C2×C4—416no—
1018C2×C4—416no—
1019C2×C4—416no—
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—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—416no—
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—42no—
1067C2×C4—88no—
1068C2×C4—88no—
1069C2×C4C2×C4×D418yes—
1070C2×C4C2×#12018yes—
1071C2×C4C2×#12318yes—
1072C22—28no—
1073C22—28no—
1074C22—28no—
1075C22—28no—
1076C22—28no—
1077C22—28no—
1078C22—44no—
1079C22—44no—
1080C22—44no—
1081C22—44no—
1082C22—44no—
1083C22—44no—
1084C22—44no—
1085C22—44no—
1086C22—44no—
1087C22—464no—
1088C22—464no—
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—
1104C22C4×#12018yes—
1105C22C4×#12318yes—
1106C22#232518yes—
1107C22#235918yes—
1108C22#236318yes—
1109C22#236418yes—
1110C22#236718yes—
1111C22#240518yes—
1112C22#240718yes—
1113C22#245918yes—
1114C22#246018yes—
1115C22#246618yes—
1116C22#246718yes—
1117C22#248518yes—
1118C22#260018yes—
1119C22C22×C4×D411yescharacteristic
1120C22C22×C4×D411yescharacteristic
1121C22C22×C4×D411yescharacteristic
1122C22C2×C4×#4111yescharacteristic
1123C22C2×C4×#4111yescharacteristic
1124C22C2×#51811yescharacteristic
1125C22C2×#52011yescharacteristic
1126C22C22×#12011yescharacteristic
1127C22C22×#12311yescharacteristic
1128C22C2×#52511yescharacteristic
1129C22C2×#52511yescharacteristic
1130C22C2×#52511yescharacteristic
1131C22C2×#52511yescharacteristic
1132C22C2×#52911yescharacteristic
1133C22C2×#52911yescharacteristic
1134C22C2×#53411yescharacteristic
1135C22C2×#53711yescharacteristic
1136C22C2×#53811yescharacteristic
1137C22C2×#53911yescharacteristic
1138C22C2×#54611yescharacteristic
1139C22C2×#54611yescharacteristic
1140C22C2×#54611yescharacteristic
1141C22C2×#54611yescharacteristic
1142C22C2×#54611yescharacteristic
1143C22C2×#54711yescharacteristic
1144C22C2×#54811yescharacteristic
1145C22C2×#55011yescharacteristic
1146C22C2×#55111yescharacteristic
1147C22C2×#55211yescharacteristic
1148C22C2×#55311yescharacteristic
1149C22C2×#55311yescharacteristic
1150C22C2×#55311yescharacteristic
1151C22C2×#55511yescharacteristic
1152C22C2×#55611yescharacteristic
1153C22C2×#55911yescharacteristic
1154C4—28no—
1155C4—28no—
1156C4—28no—
1157C4—44no—
1158C4—44no—
1159C4—44no—
1160C4—44no—
1161C4—44no—
1162C4—44no—
1163C4—44no—
1164C4—44no—
1165C4—82no—
1166C4—82no—
1167C2—48no—
1168C2—48no—
1169C2#14173116yesdirect product factor
1170C2C2×C4×#12011yescharacteristic
1171C2C2×C4×#12311yescharacteristic
1172C2C2×#232511yescharacteristic
1173C2C2×#235911yescharacteristic
1174C2C2×#236311yescharacteristic
1175C2C2×#236411yescharacteristic
1176C2C2×#236711yescharacteristic
1177C2C2×#240511yescharacteristic
1178C2C2×#245911yescharacteristic
1179C2C2×#246011yescharacteristic
1180C2C2×#246611yescharacteristic
1181C2C2×#246711yescharacteristic
1182C2C2×#240711yescharacteristic
1183C2C2×#248511yescharacteristic
1184C2C2×#260011yescharacteristic
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
3. C22×#388C2semidirect
4. C22×#387C2semidirect
5. C22×C4×C22⋊C4C2semidirect
6. #14173C2direct (N × H)
7. C2×#1440C2semidirect
8. C2×#1439C2semidirect
10. C2×#1437C2semidirect
11. C2×#1436C2semidirect
12. C2×#1436C2semidirect
13. C2×#1436C2semidirect
14. C2×C22⋊#95C2semidirect
15. C2×C22⋊#95C2semidirect
16. C2×C22⋊#95C2semidirect
40. C2×#394C4semidirect
43. C2×#388C22semidirect
45. C2×#387C22semidirect
47. C2×C4×C22⋊C4C22semidirect
64. #1440C22semidirect
65. #1439C22semidirect
67. #1437C22semidirect
68. #1436C22semidirect
69. #1436C22semidirect
70. #1436C22semidirect
71. C22⋊#95C22semidirect
72. C22⋊#95C22semidirect
73. C22⋊#95C22semidirect
124. C22×C4⋊C4C2×C4semidirect
154. C22×C22⋊C4C2×C4semidirect
155. C22×C22⋊C4C2×C4semidirect
156. C22×C22⋊C4C2×C4semidirect
157. C22×C22⋊C4C2×C4semidirect
181. #394C2×C4semidirect
200. C2×#95C2×C4semidirect
407. C2×C4⋊C4C22×C4semidirect
444. C2×C22⋊C4C22×C4semidirect
445. C2×C22⋊C4C22×C4semidirect
446. C2×C22⋊C4C22×C4semidirect
447. C2×C22⋊C4C22×C4semidirect
476. #95C22×C4semidirect
1169. C2#14173direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C4×D42
C22×#3942
C22×#3882
C22×#3872
C22×C4×C22⋊C42
#141732
C2×#14402
C2×#14392
C2×#14382
C2×#14372
C2×#14362
C2×C22⋊#952