Finite Group Databasebeta

← C2×#15696 #609336

Subgroups — C2×#15696 #609336

Order 512.

5938 conjugacy classes of subgroups.

The subgroup lattice has 1166 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#399C211yesmaximal, characteristic, complemented
2C22×#399C211yesmaximal, characteristic, complemented
3C22×#397C211yesmaximal, characteristic, complemented
4C22×#394C211yesmaximal, characteristic
5C22×#390C211yesmaximal, characteristic
6C22×#389C211yesmaximal, characteristic, complemented
7C22×#388C211yesmaximal, characteristic, complemented
8C22×#388C211yesmaximal, characteristic, complemented
9#15696C2116yesmaximal, direct product factor
10C2×#1444C211yesmaximal, characteristic, complemented
11C2×#1439C211yesmaximal, characteristic, complemented
12C2×#1439C211yesmaximal, characteristic, complemented
13C2×#1439C211yesmaximal, characteristic, complemented
14C2×#1438C211yesmaximal, characteristic
15C2×#1436C211yesmaximal, characteristic, complemented
16C2×C4⋊#95C211yesmaximal, characteristic, complemented
17C24×D4C2211yescharacteristic
18C23×C4⋊C4C2211yescharacteristic
19C23×C4⋊C4C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic
21C23×C4⋊C4C2211yescharacteristic
22C23×C4⋊C4C2211yescharacteristic
23C23×C4⋊C4C2211yescharacteristic
24C23×C4⋊C4C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic
26C23×C22⋊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×C22⋊C4C2211yescharacteristic
38C23×C42C2211yescharacteristic
39C23×C42C2211yescharacteristic
40C2×#399—28no—
41C2×#399—28no—
42C2×#399C2218yescomplemented
43C2×#399C2218yescomplemented
44C2×#397—28no—
45C2×#397C2218yescomplemented
46C2×#394—28no—
47C2×#394C2218yes—
48C2×#390—28no—
49C2×#390C2218yes—
50C2×#389—28no—
51C2×#389C2218yescomplemented
52C2×#388—28no—
53C2×#388—28no—
54C2×#388C2218yescomplemented
55C2×#388C2218yescomplemented
56C22×#95C2211yescharacteristic
57C22×#95C2211yescharacteristic
58C22×#95C2211yescharacteristic
59C22×#95C2211yescharacteristic
60C22×#95C2211yescharacteristic
61C22×#95C2211yescharacteristic
62C22×#95C2211yescharacteristic
63C22×#95C2211yescharacteristic
64C22×#95C2211yescharacteristic
65C22×#95C2211yescharacteristic
66C22×#95C2211yescharacteristic
67C22×#95C2211yescharacteristic
68#1444C2218yescomplemented
69#1439C2218yescomplemented
70#1439C2218yescomplemented
71#1439C2218yescomplemented
72#1438C2218yes—
73#1436C2218yescomplemented
74C4⋊#95C2218yescomplemented
75C26C2311yescharacteristic
76C26C2311yescharacteristic
77C23×D4—24no—
78C23×D4—24no—
79C23×D4—24no—
80C23×D4—24no—
81C23×D4—24no—
82C23×D4—42no—
83C23×D4—42no—
84C23×D4C2314yes—
85C24×C4C2311yescharacteristic
86C24×C4C2311yescharacteristic
87C24×C4C2311yescharacteristic
88C24×C4C2311yescharacteristic
89C24×C4C2311yescharacteristic
90C24×C4C2311yescharacteristic
91C24×C4C2311yescharacteristic
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C22×C4⋊C4—24no—
99C22×C4⋊C4—24no—
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—24no—
113C22×C4⋊C4—24no—
114C22×C4⋊C4—24no—
115C22×C4⋊C4—42no—
116C22×C4⋊C4—42no—
117C22×C4⋊C4—42no—
118C22×C4⋊C4—42no—
119C22×C4⋊C4—42no—
120C22×C4⋊C4—42no—
121C22×C4⋊C4D418yes—
122C22×C4⋊C4C2314yes—
123C22×C4⋊C4C2314yes—
124C22×C4⋊C4C2314yes—
125C22×C4⋊C4C2314yes—
126C22×C4⋊C4C2314yes—
127C22×C4⋊C4C2314yes—
128C22×C4⋊C4C2314yes—
129C22×C4⋊C4C2314yes—
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—24no—
151C22×C22⋊C4—24no—
152C22×C22⋊C4—24no—
153C22×C22⋊C4—24no—
154C22×C22⋊C4—24no—
155C22×C22⋊C4—24no—
156C22×C22⋊C4—24no—
157C22×C22⋊C4—42no—
158C22×C22⋊C4—42no—
159C22×C22⋊C4—42no—
160C22×C22⋊C4—42no—
161C22×C22⋊C4—42no—
162C22×C22⋊C4—42no—
163C22×C22⋊C4—42no—
164C22×C22⋊C4—42no—
165C22×C22⋊C4D418yes—
166C22×C22⋊C4C2314yes—
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×C22⋊C4C2314yes—
178C22×C42—24no—
179C22×C42—24no—
180C22×C42—24no—
181C22×C42—24no—
182C22×C42—24no—
183C22×C42—42no—
184C22×C42C2314yes—
185C22×C42C2314yes—
186#399—232no—
187#399—232no—
188#397—232no—
189#394—232no—
190#390—232no—
191#389—232no—
192#388—232no—
193#388—232no—
194C2×#95—24no—
195C2×#95—24no—
196C2×#95—24no—
197C2×#95—24no—
198C2×#95—24no—
199C2×#95—24no—
200C2×#95—24no—
201C2×#95—24no—
202C2×#95—24no—
203C2×#95—42no—
204C2×#95D418yescomplemented
205C2×#95D418yescomplemented
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2314yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
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—
241C25—22no—
242C25—22no—
243C25—22no—
244C25—22no—
245C25—22no—
246C25C2×D414yes—
247C25#4114yes—
248C25C2412yes—
249C25C2412yes—
250C25C2411yescharacteristic
251C22×D4—232no—
252C22×D4—28no—
253C22×D4—28no—
254C22×D4—28no—
255C22×D4—28no—
256C22×D4—28no—
257C22×D4—44no—
258C22×D4—44no—
259C22×D4—416no—
260C22×D4—416no—
261C22×D4—416no—
262C22×D4—416no—
263C22×D4—416no—
264C22×D4—416no—
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×C4—22no—
337C23×C4—22no—
338C23×C4—22no—
339C23×C4—22no—
340C23×C4—22no—
341C23×C4C2×D414yes—
342C23×C4C2×D414yes—
343C23×C4C2×D414yes—
344C23×C4C2×D414yes—
345C23×C4C2×D414yes—
346C23×C4C2×D414yes—
347C23×C4C2×D414yes—
348C23×C4C2×D414yes—
349C23×C4C2×D414yes—
350C23×C4C2×D414yes—
351C23×C4C2×D414yes—
352C23×C4#4114yes—
353C23×C4#4114yes—
354C23×C4#4114yes—
355C23×C4#4114yes—
356C23×C4C2412yes—
357C23×C4C2412yes—
358C23×C4C2412yes—
359C23×C4C2412yes—
360C23×C4C2412yes—
361C23×C4C2412yes—
362C23×C4C2412yes—
363C23×C4C2412yes—
364C23×C4C2412yes—
365C23×C4C2412yes—
366C23×C4C2412yes—
367C23×C4C2412yes—
368C23×C4C2412yes—
369C2×C4⋊C4—232no—
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—28no—
379C2×C4⋊C4—28no—
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—44no—
388C2×C4⋊C4—44no—
389C2×C4⋊C4—44no—
390C2×C4⋊C4—44no—
391C2×C4⋊C4—44no—
392C2×C4⋊C4—44no—
393C2×C4⋊C4—416no—
394C2×C4⋊C4—416no—
395C2×C4⋊C4—416no—
396C2×C4⋊C4—416no—
397C2×C4⋊C4—416no—
398C2×C4⋊C4—416no—
399C2×C4⋊C4—416no—
400C2×C4⋊C4C2×D4116yes—
401C2×C22⋊C4—232no—
402C2×C22⋊C4—28no—
403C2×C22⋊C4—232no—
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—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—44no—
431C2×C22⋊C4—44no—
432C2×C22⋊C4—44no—
433C2×C22⋊C4—44no—
434C2×C22⋊C4—44no—
435C2×C22⋊C4—44no—
436C2×C22⋊C4—44no—
437C2×C22⋊C4—44no—
438C2×C22⋊C4—416no—
439C2×C22⋊C4—416no—
440C2×C22⋊C4—416no—
441C2×C22⋊C4—416no—
442C2×C22⋊C4—416no—
443C2×C22⋊C4—416no—
444C2×C22⋊C4—416no—
445C2×C22⋊C4—416no—
446C2×C22⋊C4—416no—
447C2×C22⋊C4—416no—
448C2×C22⋊C4C2×D4116yes—
449C2×C42—28no—
450C2×C42—28no—
451C2×C42—28no—
452C2×C42—28no—
453C2×C42—28no—
454C2×C42—44no—
455C2×C42—416no—
456C2×C42—416no—
457#95—28no—
458#95—28no—
459#95—28no—
460#95—28no—
461#95—28no—
462#95—28no—
463#95—28no—
464#95—28no—
465#95—28no—
466#95—44no—
467#95C2×D4116yescomplemented
468#95C2×D4116yescomplemented
469C24—28no—
470C24—28no—
471C24—28no—
472C24—28no—
473C24—28no—
474C24—28no—
475C24—28no—
476C24—28no—
477C24—28no—
478C24—28no—
479C24—28no—
480C24—28no—
481C24—28no—
482C24—28no—
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—22no—
500C24—22no—
501C24—22no—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24—22no—
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—
555C24—44no—
556C24—44no—
557C24—44no—
558C24—44no—
559C24—44no—
560C24—44no—
561C24—44no—
562C24—44no—
563C24—44no—
564C24—44no—
565C24—44no—
566C24—44no—
567C24C22×D414yes—
568C24C22×D412yes—
569C24C22×D412yes—
570C24C22×D412yes—
571C24C22×D412yes—
572C24C2×#4114yes—
573C24C2×#4112yes—
574C24C2×#4112yes—
575C24C2×#4112yes—
576C24C2×#4112yes—
577C24C2×#4112yes—
578C24H(5,𝔽2)12yes—
579C24H(5,𝔽2)12yes—
580C24H(5,𝔽2)12yes—
581C242−1+412yes—
582C242−1+412yes—
583C242−1+412yes—
584C24C2511yescharacteristic
585C2×D4—232no—
586C2×D4—416no—
587C2×D4—416no—
588C2×D4—416no—
589C2×D4—416no—
590C2×D4—4128no—
591C2×D4—416no—
592C2×D4—416no—
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—22no—
612C22×C4—22no—
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—22no—
622C22×C4—22no—
623C22×C4—28no—
624C22×C4—28no—
625C22×C4—28no—
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—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—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—22no—
704C22×C4—22no—
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—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#121116yes—
758C22×C4#123116yes—
759C22×C4#127116yes—
760C22×C4C22×D414yes—
761C22×C4C22×D414yes—
762C22×C4C22×D414yes—
763C22×C4C22×D414yes—
764C22×C4C22×D414yes—
765C22×C4C22×D414yes—
766C22×C4C22×D414yes—
767C22×C4C22×D414yes—
768C22×C4C22×D414yes—
769C22×C4C22×D414yes—
770C22×C4C22×D414yes—
771C22×C4C2×#4114yes—
772C22×C4C2×#4114yes—
773C22×C4C2×#4114yes—
774C22×C4C2×#4114yes—
775C4⋊C4—232no—
776C4⋊C4—416no—
777C4⋊C4—416no—
778C4⋊C4—416no—
779C4⋊C4—416no—
780C4⋊C4—416no—
781C4⋊C4—416no—
782C4⋊C4—416no—
783C22⋊C4—232no—
784C22⋊C4—232no—
785C22⋊C4—416no—
786C22⋊C4—416no—
787C22⋊C4—416no—
788C22⋊C4—416no—
789C22⋊C4—416no—
790C22⋊C4—416no—
791C22⋊C4—416no—
792C22⋊C4—416no—
793C22⋊C4—416no—
794C22⋊C4—416no—
795C42—416no—
796C42—416no—
797C23—24no—
798C23—24no—
799C23—24no—
800C23—24no—
801C23—24no—
802C23—24no—
803C23—24no—
804C23—24no—
805C23—24no—
806C23—24no—
807C23—24no—
808C23—24no—
809C23—24no—
810C23—24no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23—42no—
815C23—416no—
816C23—416no—
817C23—42no—
818C23—42no—
819C23—416no—
820C23—42no—
821C23—42no—
822C23—416no—
823C23—416no—
824C23—416no—
825C23—42no—
826C23—42no—
827C23—42no—
828C23—42no—
829C23—42no—
830C23—42no—
831C23—42no—
832C23—416no—
833C23—42no—
834C23—42no—
835C23—42no—
836C23—42no—
837C23—42no—
838C23—42no—
839C23—42no—
840C23—42no—
841C23—42no—
842C23—416no—
843C23—42no—
844C23—42no—
845C23—42no—
846C23—42no—
847C23—42no—
848C23—42no—
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—42no—
862C23—42no—
863C23—42no—
864C23—42no—
865C23—42no—
866C23—42no—
867C23—42no—
868C23—42no—
869C23—416no—
870C23—416no—
871C23—42no—
872C23—42no—
873C23—416no—
874C23—416no—
875C23—42no—
876C23—42no—
877C23—42no—
878C23—42no—
879C23—416no—
880C23—416no—
881C23—88no—
882C23—88no—
883C23—88no—
884C23—88no—
885C23—88no—
886C23—88no—
887C23—88no—
888C23—88no—
889C23—88no—
890C23—88no—
891C23—88no—
892C23—88no—
893C23—88no—
894C23—88no—
895C23—88no—
896C23—88no—
897C23C2×#12114yes—
898C23C2×#12314yes—
899C23#52514yes—
900C23#52514yes—
901C23#52914yes—
902C23C2×#12714yes—
903C23#53514yes—
904C23#53614yes—
905C23#53614yes—
906C23#53714yes—
907C23#53814yes—
908C23#53914yes—
909C23#53914yes—
910C23#54214yes—
911C23#54214yes—
912C23D4214yes—
913C23D4214yes—
914C23#54614yes—
915C23#54614yes—
916C23#54614yes—
917C23#54714yes—
918C23#54714yes—
919C23#54714yes—
920C23#54714yes—
921C23#54714yes—
922C23#54814yes—
923C23#54814yes—
924C23#55014yes—
925C23#55014yes—
926C23#55114yes—
927C23#55214yes—
928C23#55614yes—
929C23#55914yes—
930C23#56214yes—
931C23#56314yes—
932C23C23×D411yescharacteristic
933C23C23×D411yescharacteristic
934C23C23×D411yescharacteristic
935C23C23×D411yescharacteristic
936C23C22×#4111yescharacteristic
937C23C22×#4111yescharacteristic
938C23C22×#4111yescharacteristic
939C23C22×#4111yescharacteristic
940C23C22×#4111yescharacteristic
941C23C2×H(5,𝔽2)11yescharacteristic
942C23C2×H(5,𝔽2)11yescharacteristic
943C23C2×H(5,𝔽2)11yescharacteristic
944C23C2×2−1+411yescharacteristic
945C23C2×2−1+411yescharacteristic
946C23C2×2−1+411yescharacteristic
947D4—464no—
948C2×C4—24no—
949C2×C4—24no—
950C2×C4—24no—
951C2×C4—232no—
952C2×C4—24no—
953C2×C4—232no—
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—232no—
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—42no—
988C2×C4—42no—
989C2×C4—416no—
990C2×C4—42no—
991C2×C4—42no—
992C2×C4—416no—
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—42no—
1002C2×C4—42no—
1003C2×C4—42no—
1004C2×C4—42no—
1005C2×C4—42no—
1006C2×C4—42no—
1007C2×C4—42no—
1008C2×C4—42no—
1009C2×C4—416no—
1010C2×C4—416no—
1011C2×C4—42no—
1012C2×C4—42no—
1013C2×C4—42no—
1014C2×C4—42no—
1015C2×C4—416no—
1016C2×C4—416no—
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—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—88no—
1046C2×C4—88no—
1047C2×C4—88no—
1048C2×C4—88no—
1049C2×C4C2×#12118yes—
1050C2×C4C2×#12318yes—
1051C2×C4C2×#12718yes—
1052C22—44no—
1053C22—44no—
1054C22—44no—
1055C22—44no—
1056C22—44no—
1057C22—44no—
1058C22—44no—
1059C22—44no—
1060C22—44no—
1061C22—44no—
1062C22—44no—
1063C22—44no—
1064C22—44no—
1065C22—44no—
1066C22—82no—
1067C22—832no—
1068C22—832no—
1069C22—82no—
1070C22—82no—
1071C22—82no—
1072C22—82no—
1073C22—82no—
1074C22—82no—
1075C22—82no—
1076C22—82no—
1077C22—82no—
1078C22—82no—
1079C22—82no—
1080C22—82no—
1081C22—82no—
1082C22—82no—
1083C22—82no—
1084C22#241518yes—
1085C22#241818yes—
1086C22#242518yes—
1087C22#244818yes—
1088C22#245518yes—
1089C22#247918yes—
1090C22#250118yes—
1091C22#254018yes—
1092C22#254118yes—
1093C22#267218yes—
1094C22#267418yes—
1095C22#269418yes—
1096C22#271018yes—
1097C22#272318yes—
1098C22#272718yes—
1099C22C22×#12111yescharacteristic
1100C22C22×#12311yescharacteristic
1101C22C2×#52511yescharacteristic
1102C22C2×#52511yescharacteristic
1103C22C2×#52911yescharacteristic
1104C22C22×#12711yescharacteristic
1105C22C2×#53511yescharacteristic
1106C22C2×#53611yescharacteristic
1107C22C2×#53611yescharacteristic
1108C22C2×#53711yescharacteristic
1109C22C2×#53811yescharacteristic
1110C22C2×#53911yescharacteristic
1111C22C2×#53911yescharacteristic
1112C22C2×#54211yescharacteristic
1113C22C2×#54211yescharacteristic
1114C22C2×D4211yescharacteristic
1115C22C2×D4211yescharacteristic
1116C22C2×#54611yescharacteristic
1117C22C2×#54611yescharacteristic
1118C22C2×#54611yescharacteristic
1119C22C2×#54711yescharacteristic
1120C22C2×#54711yescharacteristic
1121C22C2×#54711yescharacteristic
1122C22C2×#54711yescharacteristic
1123C22C2×#54711yescharacteristic
1124C22C2×#54811yescharacteristic
1125C22C2×#54811yescharacteristic
1126C22C2×#55011yescharacteristic
1127C22C2×#55011yescharacteristic
1128C22C2×#55111yescharacteristic
1129C22C2×#55211yescharacteristic
1130C22C2×#55611yescharacteristic
1131C22C2×#55911yescharacteristic
1132C22C2×#56211yescharacteristic
1133C22C2×#56311yescharacteristic
1134C4—28no—
1135C4—28no—
1136C4—28no—
1137C4—44no—
1138C4—44no—
1139C4—44no—
1140C4—44no—
1141C4—44no—
1142C4—44no—
1143C4—82no—
1144C4—82no—
1145C4—82no—
1146C4—82no—
1147C2—84no—
1148C2—84no—
1149C2#15696116yesdirect product factor
1150C2C2×#241811yescharacteristic
1151C2C2×#245511yescharacteristic
1152C2C2×#242511yescharacteristic
1153C2C2×#244811yescharacteristic
1154C2C2×#241511yescharacteristic
1155C2C2×#247911yescharacteristic
1156C2C2×#250111yescharacteristic
1157C2C2×#254011yescharacteristic
1158C2C2×#254111yescharacteristic
1159C2C2×#267211yescharacteristic
1160C2C2×#267411yescharacteristic
1161C2C2×#269411yescharacteristic
1162C2C2×#271011yescharacteristic
1163C2C2×#272311yescharacteristic
1164C2C2×#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. C22×#399C2semidirect
2. C22×#399C2semidirect
3. C22×#397C2semidirect
6. C22×#389C2semidirect
7. C22×#388C2semidirect
8. C22×#388C2semidirect
9. #15696C2direct (N × H)
10. C2×#1444C2semidirect
11. C2×#1439C2semidirect
12. C2×#1439C2semidirect
13. C2×#1439C2semidirect
15. C2×#1436C2semidirect
16. C2×C4⋊#95C2semidirect
42. C2×#399C22semidirect
43. C2×#399C22semidirect
45. C2×#397C22semidirect
51. C2×#389C22semidirect
54. C2×#388C22semidirect
55. C2×#388C22semidirect
68. #1444C22semidirect
69. #1439C22semidirect
70. #1439C22semidirect
71. #1439C22semidirect
73. #1436C22semidirect
74. C4⋊#95C22semidirect
204. C2×#95D4semidirect
205. C2×#95D4semidirect
467. #95C2×D4semidirect
468. #95C2×D4semidirect
1149. C2#15696direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#3992
C22×#3972
C22×#3942
C22×#3902
C22×#3892
C22×#3882
#156962
C2×#14442
C2×#14392
C2×#14382
C2×#14362
C2×C4⋊#952