Finite Group Databasebeta

← C2×#14591 #521080

Subgroups — C2×#14591 #521080

Order 512.

4594 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#396C211yesmaximal, characteristic
2#14591C2116yesmaximal, direct product factor
3C2×#1445C211yesmaximal, characteristic, complemented
4C2×#1445C211yesmaximal, characteristic, complemented
5C2×#1445C211yesmaximal, characteristic, complemented
6C2×#1441C211yesmaximal, characteristic, complemented
7C2×#1439C211yesmaximal, characteristic
8C2×#1437C211yesmaximal, characteristic
9C2×#1437C211yesmaximal, characteristic
10C2×#1436C211yesmaximal, characteristic, complemented
11C2×#1436C211yesmaximal, characteristic, complemented
12C2×#1436C211yesmaximal, characteristic, complemented
13C2×#1434C211yesmaximal, characteristic, complemented
14C2×C22⋊#95C211yesmaximal, characteristic
15C2×C22⋊#95C211yesmaximal, characteristic
16C2×C22⋊#95C211yesmaximal, characteristic
17C25×C4C2211yescharacteristic
18C23×C4⋊C4C2211yescharacteristic
19C23×C4⋊C4C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic
21C23×C4⋊C4C2211yescharacteristic
22C23×C22⋊C4C2211yescharacteristic
23C23×C22⋊C4C2211yescharacteristic
24C23×C22⋊C4C2211yescharacteristic
25C23×C22⋊C4C2211yescharacteristic
26C23×C22⋊C4C2211yescharacteristic
27C23×C22⋊C4C2211yescharacteristic
28C23×C42C2211yescharacteristic
29C23×C42C2211yescharacteristic
30C2×#396C4116yescomplemented
31C2×#396C2218yes—
32C22×#95C2211yescharacteristic
33C22×#95C2211yescharacteristic
34C22×#95C2211yescharacteristic
35C22×#95C2211yescharacteristic
36C22×#95C2211yescharacteristic
37C22×#95C2211yescharacteristic
38C22×#95C2211yescharacteristic
39C22×#95C2211yescharacteristic
40C22×#95C2211yescharacteristic
41C22×#95C2211yescharacteristic
42C22×#95C2211yescharacteristic
43C22×#95C2211yescharacteristic
44C22×#95C2211yescharacteristic
45C22×#95C2211yescharacteristic
46C22×#95C2211yescharacteristic
47C22×#95C2211yescharacteristic
48C22×#95C2211yescharacteristic
49C22×#95C2211yescharacteristic
50C22×#95C2211yescharacteristic
51C22×#95C2211yescharacteristic
52C22×#95C2211yescharacteristic
53C22×#95C2211yescharacteristic
54#1445C2218yescomplemented
55#1445C2218yescomplemented
56#1445C2218yescomplemented
57#1441C2218yescomplemented
58#1439C2218yes—
59#1437C2218yes—
60#1437C2218yes—
61#1436C2218yescomplemented
62#1436C2218yescomplemented
63#1436C2218yescomplemented
64#1434C2218yescomplemented
65C22⋊#95C2218yes—
66C22⋊#95C2218yes—
67C22⋊#95C2218yes—
68C26C2311yescharacteristic
69C24×C4—24no—
70C24×C4—24no—
71C24×C4—24no—
72C24×C4—42no—
73C24×C4—42no—
74C24×C4—42no—
75C24×C4—42no—
76C24×C4C2311yescharacteristic
77C24×C4C2311yescharacteristic
78C24×C4C2311yescharacteristic
79C24×C4C2311yescharacteristic
80C24×C4C2311yescharacteristic
81C24×C4C2311yescharacteristic
82C24×C4C2311yescharacteristic
83C24×C4C2311yescharacteristic
84C24×C4C2311yescharacteristic
85C24×C4C2311yescharacteristic
86C24×C4C2311yescharacteristic
87C24×C4C2311yescharacteristic
88C24×C4C2311yescharacteristic
89C24×C4C2311yescharacteristic
90C24×C4C2314yes—
91C22×C4⋊C4—24no—
92C22×C4⋊C4—42no—
93C22×C4⋊C4—42no—
94C22×C4⋊C4—42no—
95C22×C4⋊C4—42no—
96C22×C4⋊C4—42no—
97C22×C4⋊C4—42no—
98C22×C4⋊C4—42no—
99C22×C4⋊C4—42no—
100C22×C4⋊C4C2×C418yescomplemented
101C22×C4⋊C4C2×C418yescomplemented
102C22×C4⋊C4C2×C418yescomplemented
103C22×C4⋊C4C2314yes—
104C22×C4⋊C4C2314yes—
105C22×C4⋊C4C2314yes—
106C22×C4⋊C4C2314yes—
107C22×C22⋊C4—24no—
108C22×C22⋊C4—24no—
109C22×C22⋊C4—24no—
110C22×C22⋊C4—24no—
111C22×C22⋊C4—42no—
112C22×C22⋊C4—42no—
113C22×C22⋊C4—42no—
114C22×C22⋊C4—42no—
115C22×C22⋊C4—42no—
116C22×C22⋊C4—42no—
117C22×C22⋊C4—42no—
118C22×C22⋊C4—42no—
119C22×C22⋊C4—42no—
120C22×C22⋊C4—42no—
121C22×C22⋊C4C2×C418yes—
122C22×C22⋊C4C2×C418yes—
123C22×C22⋊C4C2×C418yes—
124C22×C22⋊C4Q818yes—
125C22×C22⋊C4C2314yes—
126C22×C22⋊C4C2314yes—
127C22×C22⋊C4C2314yes—
128C22×C22⋊C4C2314yes—
129C22×C22⋊C4C2314yes—
130C22×C22⋊C4C2314yes—
131C22×C42—24no—
132C22×C42—42no—
133C22×C42—42no—
134C22×C42—42no—
135C22×C42—42no—
136C22×C42—42no—
137C22×C42C2314yes—
138C22×C42C2314yes—
139#396C2×C4164yescomplemented
140C2×#95—24no—
141C2×#95—24no—
142C2×#95—24no—
143C2×#95—24no—
144C2×#95—24no—
145C2×#95—24no—
146C2×#95—42no—
147C2×#95—42no—
148C2×#95—42no—
149C2×#95—42no—
150C2×#95—42no—
151C2×#95—42no—
152C2×#95—42no—
153C2×#95—42no—
154C2×#95—42no—
155C2×#95—42no—
156C2×#95—42no—
157C2×#95—42no—
158C2×#95—42no—
159C2×#95—42no—
160C2×#95—42no—
161C2×#95C2×C418yescomplemented
162C2×#95C2314yes—
163C2×#95C2314yes—
164C2×#95C2314yes—
165C2×#95C2314yes—
166C2×#95C2314yes—
167C2×#95C2314yes—
168C2×#95C2314yes—
169C2×#95C2314yes—
170C2×#95C2314yes—
171C2×#95C2314yes—
172C2×#95C2314yes—
173C2×#95C2314yes—
174C2×#95C2314yes—
175C2×#95C2314yes—
176C2×#95C2314yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C25—22no—
185C25—22no—
186C25—22no—
187C25—22no—
188C25—22no—
189C25—22no—
190C25—22no—
191C25—22no—
192C25—22no—
193C25—22no—
194C25—22no—
195C25—22no—
196C25C22×C414yes—
197C25C2×Q814yes—
198C25#4114yes—
199C25C2412yes—
200C25C2411yescharacteristic
201C23×C4—22no—
202C23×C4—22no—
203C23×C4—22no—
204C23×C4—22no—
205C23×C4—22no—
206C23×C4—22no—
207C23×C4—22no—
208C23×C4—22no—
209C23×C4—22no—
210C23×C4—22no—
211C23×C4—22no—
212C23×C4—22no—
213C23×C4—22no—
214C23×C4—22no—
215C23×C4—22no—
216C23×C4—22no—
217C23×C4—22no—
218C23×C4—22no—
219C23×C4—22no—
220C23×C4—22no—
221C23×C4—22no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
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—28no—
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—28no—
289C23×C4—28no—
290C23×C4—44no—
291C23×C4—44no—
292C23×C4—44no—
293C23×C4—44no—
294C23×C4—416no—
295C23×C4—416no—
296C23×C4—416no—
297C23×C4—416no—
298C23×C4—416no—
299C23×C4—416no—
300C23×C4—416no—
301C23×C4C22×C414yes—
302C23×C4C22×C414yes—
303C23×C4C22×C414yes—
304C23×C4C22×C414yes—
305C23×C4C22×C414yes—
306C23×C4C22×C414yes—
307C23×C4C2×Q814yes—
308C23×C4C2×Q814yes—
309C23×C4#4114yes—
310C23×C4#4114yes—
311C23×C4#4114yes—
312C23×C4#4114yes—
313C23×C4C2412yes—
314C23×C4C2412yes—
315C23×C4C2412yes—
316C23×C4C2412yes—
317C23×C4C2412yes—
318C23×C4C2412yes—
319C23×C4C2412yes—
320C23×C4C2412yes—
321C23×C4C2412yes—
322C23×C4C2412yes—
323C23×C4C2412yes—
324C23×C4C2412yes—
325C23×C4C2412yes—
326C23×C4C2412yes—
327C2×C4⋊C4—28no—
328C2×C4⋊C4—416no—
329C2×C4⋊C4—416no—
330C2×C4⋊C4—416no—
331C2×C4⋊C4—44no—
332C2×C4⋊C4—44no—
333C2×C4⋊C4—44no—
334C2×C4⋊C4—44no—
335C2×C4⋊C4—44no—
336C2×C4⋊C4—44no—
337C2×C4⋊C4—44no—
338C2×C4⋊C4—44no—
339C2×C4⋊C4—416no—
340C2×C4⋊C4C22×C4116yescomplemented
341C2×C4⋊C4C22×C4116yescomplemented
342C2×C4⋊C4C22×C4116yescomplemented
343C2×C22⋊C4—28no—
344C2×C22⋊C4—28no—
345C2×C22⋊C4—28no—
346C2×C22⋊C4—28no—
347C2×C22⋊C4—416no—
348C2×C22⋊C4—416no—
349C2×C22⋊C4—416no—
350C2×C22⋊C4—416no—
351C2×C22⋊C4—44no—
352C2×C22⋊C4—44no—
353C2×C22⋊C4—44no—
354C2×C22⋊C4—44no—
355C2×C22⋊C4—44no—
356C2×C22⋊C4—44no—
357C2×C22⋊C4—44no—
358C2×C22⋊C4—44no—
359C2×C22⋊C4—44no—
360C2×C22⋊C4—44no—
361C2×C22⋊C4—416no—
362C2×C22⋊C4—416no—
363C2×C22⋊C4C22×C4116yes—
364C2×C22⋊C4C22×C4116yes—
365C2×C22⋊C4C22×C4116yes—
366C2×C22⋊C4C2×Q8116yes—
367C2×C42—28no—
368C2×C42—44no—
369C2×C42—44no—
370C2×C42—44no—
371C2×C42—44no—
372C2×C42—44no—
373C2×C42—416no—
374C2×C42—416no—
375#95—28no—
376#95—28no—
377#95—28no—
378#95—28no—
379#95—28no—
380#95—28no—
381#95—44no—
382#95—44no—
383#95—44no—
384#95—44no—
385#95—44no—
386#95—44no—
387#95—44no—
388#95—44no—
389#95—44no—
390#95—44no—
391#95—44no—
392#95—44no—
393#95—44no—
394#95—44no—
395#95—44no—
396#95C22×C4116yescomplemented
397C24—28no—
398C24—28no—
399C24—28no—
400C24—28no—
401C24—28no—
402C24—28no—
403C24—28no—
404C24—28no—
405C24—28no—
406C24—28no—
407C24—28no—
408C24—28no—
409C24—28no—
410C24—28no—
411C24—28no—
412C24—28no—
413C24—28no—
414C24—28no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—44no—
428C24—44no—
429C24—44no—
430C24—44no—
431C24—44no—
432C24—44no—
433C24—44no—
434C24—44no—
435C24—44no—
436C24—44no—
437C24—44no—
438C24—44no—
439C24—44no—
440C24—44no—
441C24—44no—
442C24—44no—
443C24C4×Q8116yes—
444C24C23×C414yes—
445C24C23×C412yes—
446C24C22×Q814yes—
447C24C22×Q812yes—
448C24C2×#4114yes—
449C24C2×#4112yes—
450C24C2×#4112yes—
451C24C2×#4112yes—
452C24C2×#4112yes—
453C24C2×#4112yes—
454C24H(5,𝔽2)12yes—
455C24H(5,𝔽2)12yes—
456C24H(5,𝔽2)12yes—
457C24H(5,𝔽2)12yes—
458C24H(5,𝔽2)12yes—
459C24H(5,𝔽2)12yes—
460C24H(5,𝔽2)12yes—
461C242−1+412yes—
462C24C2511yescharacteristic
463C22×C4—28no—
464C22×C4—28no—
465C22×C4—28no—
466C22×C4—28no—
467C22×C4—28no—
468C22×C4—28no—
469C22×C4—28no—
470C22×C4—28no—
471C22×C4—28no—
472C22×C4—28no—
473C22×C4—28no—
474C22×C4—28no—
475C22×C4—28no—
476C22×C4—28no—
477C22×C4—28no—
478C22×C4—28no—
479C22×C4—28no—
480C22×C4—28no—
481C22×C4—28no—
482C22×C4—28no—
483C22×C4—28no—
484C22×C4—28no—
485C22×C4—28no—
486C22×C4—28no—
487C22×C4—28no—
488C22×C4—28no—
489C22×C4—28no—
490C22×C4—28no—
491C22×C4—28no—
492C22×C4—28no—
493C22×C4—28no—
494C22×C4—28no—
495C22×C4—28no—
496C22×C4—28no—
497C22×C4—28no—
498C22×C4—28no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—416no—
586C22×C4—416no—
587C22×C4—416no—
588C22×C4—416no—
589C22×C4—416no—
590C22×C4—416no—
591C22×C4—4128no—
592C22×C4—416no—
593C22×C4—44no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4—44no—
600C22×C4—44no—
601C22×C4—44no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—44no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4—44no—
608C22×C4—44no—
609C22×C4—44no—
610C22×C4—44no—
611C22×C4—44no—
612C22×C4—44no—
613C22×C4—44no—
614C22×C4—44no—
615C22×C4—44no—
616C22×C4—44no—
617C22×C4—44no—
618C22×C4—44no—
619C22×C4—44no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4—44no—
623C22×C4—44no—
624C22×C4—44no—
625C22×C4—44no—
626C22×C4—44no—
627C22×C4—44no—
628C22×C4—44no—
629C22×C4—44no—
630C22×C4—44no—
631C22×C4—44no—
632C22×C4—44no—
633C22×C4—44no—
634C22×C4—44no—
635C22×C4—44no—
636C22×C4—44no—
637C22×C4—44no—
638C22×C4—44no—
639C22×C4—44no—
640C22×C4—44no—
641C22×C4—44no—
642C22×C4—44no—
643C22×C4—44no—
644C22×C4—44no—
645C22×C4—44no—
646C22×C4—44no—
647C22×C4—44no—
648C22×C4—44no—
649C22×C4—44no—
650C22×C4—44no—
651C22×C4—44no—
652C22×C4—44no—
653C22×C4—44no—
654C22×C4—44no—
655C22×C4C23×C414yes—
656C22×C4C23×C414yes—
657C22×C4C23×C414yes—
658C22×C4C23×C414yes—
659C22×C4C23×C414yes—
660C22×C4C23×C414yes—
661C22×C4C22×Q814yes—
662C22×C4C22×Q814yes—
663C22×C4C2×#4114yes—
664C22×C4C2×#4114yes—
665C22×C4C2×#4114yes—
666C22×C4C2×#4114yes—
667C4⋊C4—416no—
668C4⋊C4—416no—
669C4⋊C4—416no—
670C4⋊C4—416no—
671C22⋊C4—416no—
672C22⋊C4—416no—
673C22⋊C4—416no—
674C22⋊C4—416no—
675C22⋊C4—416no—
676C22⋊C4—416no—
677C42—416no—
678C42—416no—
679C23—232no—
680C23—232no—
681C23—232no—
682C23—24no—
683C23—24no—
684C23—24no—
685C23—24no—
686C23—24no—
687C23—24no—
688C23—24no—
689C23—24no—
690C23—24no—
691C23—24no—
692C23—24no—
693C23—24no—
694C23—24no—
695C23—24no—
696C23—24no—
697C23—24no—
698C23—24no—
699C23—24no—
700C23—416no—
701C23—416no—
702C23—416no—
703C23—416no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—416no—
717C23—416no—
718C23—416no—
719C23—416no—
720C23—416no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—416no—
726C23—416no—
727C23—416no—
728C23C2×C4×Q818yes—
729C23C2×C4×Q814yes—
730C23C4×#4114yes—
731C23C4×#4114yes—
732C23#51814yes—
733C23#51814yes—
734C23#51814yes—
735C23#52014yes—
736C23#53814yes—
737C23#53814yes—
738C23#53814yes—
739C23#53814yes—
740C23#53814yes—
741C23#53914yes—
742C23#54014yes—
743C23#54014yes—
744C23#54014yes—
745C23#54014yes—
746C23#54314yes—
747C23#54414yes—
748C23#55114yes—
749C23#55114yes—
750C23#55114yes—
751C23#55114yes—
752C23#55114yes—
753C23#55214yes—
754C23#55314yes—
755C23#55414yes—
756C23#55414yes—
757C23#55414yes—
758C23#55414yes—
759C23#55614yes—
760C23#56014yes—
761C23#56014yes—
762C23#56214yes—
763C23#56214yes—
764C23C24×C411yescharacteristic
765C23C23×Q811yescharacteristic
766C23C22×#4111yescharacteristic
767C23C22×#4111yescharacteristic
768C23C22×#4111yescharacteristic
769C23C22×#4111yescharacteristic
770C23C22×#4111yescharacteristic
771C23C2×H(5,𝔽2)11yescharacteristic
772C23C2×H(5,𝔽2)11yescharacteristic
773C23C2×H(5,𝔽2)11yescharacteristic
774C23C2×H(5,𝔽2)11yescharacteristic
775C23C2×H(5,𝔽2)11yescharacteristic
776C23C2×H(5,𝔽2)11yescharacteristic
777C23C2×H(5,𝔽2)11yescharacteristic
778C23C2×2−1+411yescharacteristic
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—24no—
784C2×C4—24no—
785C2×C4—24no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—24no—
791C2×C4—24no—
792C2×C4—24no—
793C2×C4—24no—
794C2×C4—24no—
795C2×C4—24no—
796C2×C4—24no—
797C2×C4—24no—
798C2×C4—24no—
799C2×C4—24no—
800C2×C4—24no—
801C2×C4—24no—
802C2×C4—24no—
803C2×C4—24no—
804C2×C4—24no—
805C2×C4—24no—
806C2×C4—24no—
807C2×C4—24no—
808C2×C4—24no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—24no—
813C2×C4—24no—
814C2×C4—24no—
815C2×C4—464no—
816C2×C4—416no—
817C2×C4—416no—
818C2×C4—416no—
819C2×C4—416no—
820C2×C4—416no—
821C2×C4—416no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—416no—
857C2×C4—416no—
858C2×C4—416no—
859C2×C4—416no—
860C2×C4—416no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—42no—
875C2×C4—416no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—42no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—42no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—88no—
891C2×C4—88no—
892C22—28no—
893C22—28no—
894C22—28no—
895C22—44no—
896C22—44no—
897C22—44no—
898C22—44no—
899C22—44no—
900C22—44no—
901C22—44no—
902C22—44no—
903C22—44no—
904C22—44no—
905C22—44no—
906C22—44no—
907C22—464no—
908C22#232918yes—
909C22#233318yes—
910C22#233318yes—
911C22#236818yes—
912C22#236818yes—
913C22#237318yes—
914C22#237718yes—
915C22#273518yes—
916C22#274018yes—
917C22#274318yes—
918C22#274818yes—
919C22#274918yes—
920C22#276818yes—
921C22#278018yes—
922C22#278818yes—
923C22C22×C4×Q811yescharacteristic
924C22C2×C4×#4111yescharacteristic
925C22C2×C4×#4111yescharacteristic
926C22C2×#51811yescharacteristic
927C22C2×#51811yescharacteristic
928C22C2×#51811yescharacteristic
929C22C2×#52011yescharacteristic
930C22C2×#53811yescharacteristic
931C22C2×#53811yescharacteristic
932C22C2×#53811yescharacteristic
933C22C2×#53811yescharacteristic
934C22C2×#53811yescharacteristic
935C22C2×#53911yescharacteristic
936C22C2×#54011yescharacteristic
937C22C2×#54011yescharacteristic
938C22C2×#54011yescharacteristic
939C22C2×#54011yescharacteristic
940C22C2×#54311yescharacteristic
941C22C2×#54411yescharacteristic
942C22C2×#55111yescharacteristic
943C22C2×#55111yescharacteristic
944C22C2×#55111yescharacteristic
945C22C2×#55111yescharacteristic
946C22C2×#55111yescharacteristic
947C22C2×#55211yescharacteristic
948C22C2×#55311yescharacteristic
949C22C2×#55411yescharacteristic
950C22C2×#55411yescharacteristic
951C22C2×#55411yescharacteristic
952C22C2×#55411yescharacteristic
953C22C2×#55611yescharacteristic
954C22C2×#56011yescharacteristic
955C22C2×#56011yescharacteristic
956C22C2×#56211yescharacteristic
957C22C2×#56211yescharacteristic
958C4—44no—
959C4—44no—
960C4—44no—
961C4—44no—
962C4—44no—
963C4—44no—
964C4—44no—
965C4—44no—
966C4—44no—
967C4—44no—
968C4—44no—
969C4—44no—
970C4—82no—
971C4—82no—
972C2—48no—
973C2#14591116yesdirect product factor
974C2C2×#232911yescharacteristic
975C2C2×#233311yescharacteristic
976C2C2×#233311yescharacteristic
977C2C2×#236811yescharacteristic
978C2C2×#236811yescharacteristic
979C2C2×#237311yescharacteristic
980C2C2×#237711yescharacteristic
981C2C2×#273511yescharacteristic
982C2C2×#274011yescharacteristic
983C2C2×#274311yescharacteristic
984C2C2×#274811yescharacteristic
985C2C2×#274911yescharacteristic
986C2C2×#276811yescharacteristic
987C2C2×#278011yescharacteristic
988C2C2×#278811yescharacteristic
subgroupG/H
center, socleC25C24
commutatorC23C24×C4
Frattini, cosocleC24C25
prime radicalC26C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #14591C2direct (N × H)
3. C2×#1445C2semidirect
4. C2×#1445C2semidirect
5. C2×#1445C2semidirect
6. C2×#1441C2semidirect
10. C2×#1436C2semidirect
11. C2×#1436C2semidirect
12. C2×#1436C2semidirect
13. C2×#1434C2semidirect
30. C2×#396C4semidirect
54. #1445C22semidirect
55. #1445C22semidirect
56. #1445C22semidirect
57. #1441C22semidirect
61. #1436C22semidirect
62. #1436C22semidirect
63. #1436C22semidirect
64. #1434C22semidirect
100. C22×C4⋊C4C2×C4semidirect
101. C22×C4⋊C4C2×C4semidirect
102. C22×C4⋊C4C2×C4semidirect
139. #396C2×C4semidirect
161. C2×#95C2×C4semidirect
340. C2×C4⋊C4C22×C4semidirect
341. C2×C4⋊C4C22×C4semidirect
342. C2×C4⋊C4C22×C4semidirect
396. #95C22×C4semidirect
973. C2#14591direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#3962
#145912
C2×#14452
C2×#14412
C2×#14392
C2×#14372
C2×#14362
C2×#14342
C2×C22⋊#952