Finite Group Databasebeta

← C2×#15629 #609246

Subgroups — C2×#15629 #609246

Order 512.

4138 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#398C211yesmaximal, characteristic
2C22×#398C211yesmaximal, characteristic
3C22×#398C211yesmaximal, characteristic
4C22×#389C211yesmaximal, characteristic
5C22×#387C211yesmaximal, characteristic
6C22×#384C211yesmaximal, characteristic
7#15629C2116yesmaximal, direct product factor
8C2×#1445C211yesmaximal, characteristic
9C2×#1444C211yesmaximal, characteristic
10C2×#1444C211yesmaximal, characteristic
11C2×#1442C211yesmaximal, characteristic
12C2×#1441C211yesmaximal, characteristic
13C2×#1441C211yesmaximal, characteristic
14C2×#1436C211yesmaximal, characteristic
15C2×#1436C211yesmaximal, characteristic
16C2×#1436C211yesmaximal, characteristic
17C23×C4⋊C4C2211yescharacteristic
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×C4⋊C4C2211yescharacteristic
27C23×C4⋊C4C2211yescharacteristic
28C23×C4⋊C4C2211yescharacteristic
29C23×C4⋊C4C2211yescharacteristic
30C23×C42C2211yescharacteristic
31C23×C42C2211yescharacteristic
32C2×#398—28no—
33C2×#398—28no—
34C2×#398—28no—
35C2×#398C2218yes—
36C2×#398C2218yes—
37C2×#398C2218yes—
38C2×#389—28no—
39C2×#389C2218yes—
40C2×#387—28no—
41C2×#387C2218yes—
42C2×#384—28no—
43C2×#384C2218yes—
44C22×#95C2211yescharacteristic
45C22×#95C2211yescharacteristic
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
62C22×#95C2211yescharacteristic
63C22×#95C2211yescharacteristic
64#1445C2218yes—
65#1444C2218yes—
66#1444C2218yes—
67#1442C2218yes—
68#1441C2218yes—
69#1441C2218yes—
70#1436C2218yes—
71#1436C2218yes—
72#1436C2218yes—
73C24×C4C2311yescharacteristic
74C24×C4C2311yescharacteristic
75C24×C4C2311yescharacteristic
76C24×C4C2311yescharacteristic
77C24×C4C2311yescharacteristic
78C24×C4C2311yescharacteristic
79C24×C4C2311yescharacteristic
80C24×C4C2311yescharacteristic
81C24×C4C2311yescharacteristic
82C24×C4C2311yescharacteristic
83C24×C4C2311yescharacteristic
84C24×C4C2311yescharacteristic
85C24×C4C2311yescharacteristic
86C24×C4C2311yescharacteristic
87C24×C4C2311yescharacteristic
88C22×C4⋊C4—24no—
89C22×C4⋊C4—24no—
90C22×C4⋊C4—24no—
91C22×C4⋊C4—24no—
92C22×C4⋊C4—24no—
93C22×C4⋊C4—24no—
94C22×C4⋊C4—24no—
95C22×C4⋊C4—24no—
96C22×C4⋊C4—24no—
97C22×C4⋊C4—24no—
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—24no—
116C22×C4⋊C4—42no—
117C22×C4⋊C4—42no—
118C22×C4⋊C4—42no—
119C22×C4⋊C4—42no—
120C22×C4⋊C4—42no—
121C22×C4⋊C4—42no—
122C22×C4⋊C4—42no—
123C22×C4⋊C4—42no—
124C22×C4⋊C4—42no—
125C22×C4⋊C4D418yes—
126C22×C4⋊C4Q818yes—
127C22×C4⋊C4C2314yes—
128C22×C4⋊C4C2314yes—
129C22×C4⋊C4C2314yes—
130C22×C4⋊C4C2314yes—
131C22×C4⋊C4C2314yes—
132C22×C4⋊C4C2314yes—
133C22×C4⋊C4C2314yes—
134C22×C4⋊C4C2314yes—
135C22×C4⋊C4C2314yes—
136C22×C4⋊C4C2314yes—
137C22×C4⋊C4C2314yes—
138C22×C4⋊C4C2314yes—
139C22×C4⋊C4C2314yes—
140C22×C42—24no—
141C22×C42—24no—
142C22×C42—24no—
143C22×C42—24no—
144C22×C42—24no—
145C22×C42—42no—
146C22×C42C2314yes—
147C22×C42C2314yes—
148#398—232no—
149#398—232no—
150#398—232no—
151#389—232no—
152#387—232no—
153#384—232no—
154C2×#95—24no—
155C2×#95—24no—
156C2×#95—24no—
157C2×#95—24no—
158C2×#95—24no—
159C2×#95—24no—
160C2×#95—24no—
161C2×#95—24no—
162C2×#95—24no—
163C2×#95—24no—
164C2×#95—24no—
165C2×#95—24no—
166C2×#95—24no—
167C2×#95—24no—
168C2×#95—24no—
169C2×#95—42no—
170C2×#95—42no—
171C2×#95D418yes—
172C2×#95D418yes—
173C2×#95Q818yes—
174C2×#95C2314yes—
175C2×#95C2314yes—
176C2×#95C2314yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C25C2411yescharacteristic
195C23×C4—22no—
196C23×C4—22no—
197C23×C4—22no—
198C23×C4—22no—
199C23×C4—22no—
200C23×C4—22no—
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—22no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4C2×D414yes—
282C23×C4C2×D414yes—
283C23×C4C2×D414yes—
284C23×C4C2×D414yes—
285C23×C4C2×D414yes—
286C23×C4C2×D414yes—
287C23×C4C2×D414yes—
288C23×C4C2×D414yes—
289C23×C4C2×D414yes—
290C23×C4C2×Q814yes—
291C23×C4C2×Q814yes—
292C23×C4C2×Q814yes—
293C23×C4C2×Q814yes—
294C23×C4C2×Q814yes—
295C23×C4C2×Q814yes—
296C23×C4#4114yes—
297C23×C4#4114yes—
298C23×C4#4114yes—
299C23×C4#4114yes—
300C23×C4C2412yes—
301C23×C4C2412yes—
302C23×C4C2412yes—
303C23×C4C2412yes—
304C23×C4C2412yes—
305C23×C4C2412yes—
306C23×C4C2412yes—
307C23×C4C2412yes—
308C23×C4C2412yes—
309C23×C4C2412yes—
310C23×C4C2412yes—
311C23×C4C2412yes—
312C23×C4C2412yes—
313C23×C4C2412yes—
314C23×C4C2412yes—
315C2×C4⋊C4—232no—
316C2×C4⋊C4—232no—
317C2×C4⋊C4—28no—
318C2×C4⋊C4—28no—
319C2×C4⋊C4—28no—
320C2×C4⋊C4—28no—
321C2×C4⋊C4—28no—
322C2×C4⋊C4—28no—
323C2×C4⋊C4—28no—
324C2×C4⋊C4—28no—
325C2×C4⋊C4—28no—
326C2×C4⋊C4—28no—
327C2×C4⋊C4—28no—
328C2×C4⋊C4—28no—
329C2×C4⋊C4—28no—
330C2×C4⋊C4—28no—
331C2×C4⋊C4—28no—
332C2×C4⋊C4—28no—
333C2×C4⋊C4—28no—
334C2×C4⋊C4—28no—
335C2×C4⋊C4—28no—
336C2×C4⋊C4—28no—
337C2×C4⋊C4—28no—
338C2×C4⋊C4—28no—
339C2×C4⋊C4—28no—
340C2×C4⋊C4—28no—
341C2×C4⋊C4—28no—
342C2×C4⋊C4—28no—
343C2×C4⋊C4—28no—
344C2×C4⋊C4—28no—
345C2×C4⋊C4—44no—
346C2×C4⋊C4—44no—
347C2×C4⋊C4—44no—
348C2×C4⋊C4—44no—
349C2×C4⋊C4—44no—
350C2×C4⋊C4—44no—
351C2×C4⋊C4—44no—
352C2×C4⋊C4—44no—
353C2×C4⋊C4—44no—
354C2×C4⋊C4—416no—
355C2×C4⋊C4—416no—
356C2×C4⋊C4—416no—
357C2×C4⋊C4—416no—
358C2×C4⋊C4—416no—
359C2×C4⋊C4—416no—
360C2×C4⋊C4—416no—
361C2×C4⋊C4—416no—
362C2×C4⋊C4—416no—
363C2×C4⋊C4—416no—
364C2×C4⋊C4—416no—
365C2×C4⋊C4C2×D4116yes—
366C2×C4⋊C4C2×Q8116yes—
367C2×C42—232no—
368C2×C42—28no—
369C2×C42—28no—
370C2×C42—28no—
371C2×C42—28no—
372C2×C42—28no—
373C2×C42—44no—
374C2×C42—416no—
375#95—28no—
376#95—28no—
377#95—28no—
378#95—28no—
379#95—28no—
380#95—28no—
381#95—28no—
382#95—28no—
383#95—28no—
384#95—28no—
385#95—28no—
386#95—28no—
387#95—28no—
388#95—28no—
389#95—28no—
390#95—44no—
391#95—44no—
392#95C2×D4116yes—
393#95C2×D4116yes—
394#95C2×Q8116yes—
395C24C22×D412yes—
396C24C22×D412yes—
397C24C22×D412yes—
398C24C22×Q812yes—
399C24C22×Q812yes—
400C24C2×#4112yes—
401C24C2×#4112yes—
402C24C2×#4112yes—
403C24C2×#4112yes—
404C24H(5,𝔽2)12yes—
405C24H(5,𝔽2)12yes—
406C242−1+412yes—
407C242−1+412yes—
408C242−1+412yes—
409C242−1+412yes—
410C24C2511yescharacteristic
411C22×C4—28no—
412C22×C4—28no—
413C22×C4—28no—
414C22×C4—28no—
415C22×C4—28no—
416C22×C4—28no—
417C22×C4—28no—
418C22×C4—28no—
419C22×C4—28no—
420C22×C4—28no—
421C22×C4—28no—
422C22×C4—28no—
423C22×C4—28no—
424C22×C4—28no—
425C22×C4—28no—
426C22×C4—28no—
427C22×C4—28no—
428C22×C4—28no—
429C22×C4—28no—
430C22×C4—28no—
431C22×C4—28no—
432C22×C4—28no—
433C22×C4—28no—
434C22×C4—28no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—28no—
452C22×C4—28no—
453C22×C4—28no—
454C22×C4—28no—
455C22×C4—28no—
456C22×C4—28no—
457C22×C4—28no—
458C22×C4—28no—
459C22×C4—28no—
460C22×C4—28no—
461C22×C4—28no—
462C22×C4—28no—
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—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
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—44no—
543C22×C4—44no—
544C22×C4—44no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4—44no—
548C22×C4—44no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—44no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4—44no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4—44no—
561C22×C4—44no—
562C22×C4—44no—
563C22×C4—44no—
564C22×C4—44no—
565C22×C4—44no—
566C22×C4—44no—
567C22×C4—44no—
568C22×C4—44no—
569C22×C4—44no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—44no—
574C22×C4—44no—
575C22×C4—44no—
576C22×C4—44no—
577C22×C4—44no—
578C22×C4—44no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4#121116yes—
599C22×C4C22⋊Q8116yes—
600C22×C4#125116yes—
601C22×C4C4⋊Q8116yes—
602C22×C4C22×D414yes—
603C22×C4C22×D414yes—
604C22×C4C22×D414yes—
605C22×C4C22×D414yes—
606C22×C4C22×D414yes—
607C22×C4C22×D414yes—
608C22×C4C22×D414yes—
609C22×C4C22×D414yes—
610C22×C4C22×D414yes—
611C22×C4C22×Q814yes—
612C22×C4C22×Q814yes—
613C22×C4C22×Q814yes—
614C22×C4C22×Q814yes—
615C22×C4C22×Q814yes—
616C22×C4C22×Q814yes—
617C22×C4C2×#4114yes—
618C22×C4C2×#4114yes—
619C22×C4C2×#4114yes—
620C22×C4C2×#4114yes—
621C4⋊C4—232no—
622C4⋊C4—232no—
623C4⋊C4—416no—
624C4⋊C4—416no—
625C4⋊C4—416no—
626C4⋊C4—416no—
627C4⋊C4—416no—
628C4⋊C4—416no—
629C4⋊C4—416no—
630C4⋊C4—416no—
631C4⋊C4—416no—
632C4⋊C4—416no—
633C4⋊C4—416no—
634C42—232no—
635C42—416no—
636C23C2×#12114yes—
637C23C2×C22⋊Q814yes—
638C23#52514yes—
639C23C2×#12514yes—
640C23C2×C4⋊Q814yes—
641C23#53214yes—
642C23#53614yes—
643C23#53614yes—
644C23#53614yes—
645C23#53914yes—
646C23#53914yes—
647C23#54014yes—
648C23#54114yes—
649C23#54414yes—
650C23#54414yes—
651C23D4214yes—
652C23D4214yes—
653C23#54614yes—
654C23#54714yes—
655C23#54714yes—
656C23#54714yes—
657C23D4×Q814yes—
658C23D4×Q814yes—
659C23D4×Q814yes—
660C23#55014yes—
661C23#55214yes—
662C23#55214yes—
663C23#55214yes—
664C23#55414yes—
665C23#55414yes—
666C23#55714yes—
667C23#55714yes—
668C23#55714yes—
669C23#56314yes—
670C23#56314yes—
671C23C23×D411yescharacteristic
672C23C23×D411yescharacteristic
673C23C23×D411yescharacteristic
674C23C23×Q811yescharacteristic
675C23C23×Q811yescharacteristic
676C23C22×#4111yescharacteristic
677C23C22×#4111yescharacteristic
678C23C22×#4111yescharacteristic
679C23C22×#4111yescharacteristic
680C23C2×H(5,𝔽2)11yescharacteristic
681C23C2×H(5,𝔽2)11yescharacteristic
682C23C2×2−1+411yescharacteristic
683C23C2×2−1+411yescharacteristic
684C23C2×2−1+411yescharacteristic
685C23C2×2−1+411yescharacteristic
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—232no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—232no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—232no—
713C2×C4—232no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—416no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—416no—
745C2×C4—416no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—416no—
750C2×C4—416no—
751C2×C4—416no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—416no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—88no—
799C2×C4—88no—
800C2×C4—88no—
801C2×C4—88no—
802C2×C4C2×#12118yes—
803C2×C4C2×C22⋊Q818yes—
804C2×C4C2×#12518yes—
805C2×C4C2×C4⋊Q818yes—
806C22#241318yes—
807C22#242818yes—
808C22#244018yes—
809C22#244918yes—
810C22#247318yes—
811C22#250618yes—
812C22#254618yes—
813C22#255218yes—
814C22#256518yes—
815C22#267718yes—
816C22#268018yes—
817C22#271318yes—
818C22#272118yes—
819C22#279118yes—
820C22#279118yes—
821C22C22×#12111yescharacteristic
822C22C22×C22⋊Q811yescharacteristic
823C22C2×#52511yescharacteristic
824C22C22×#12511yescharacteristic
825C22C22×C4⋊Q811yescharacteristic
826C22C2×#53211yescharacteristic
827C22C2×#53611yescharacteristic
828C22C2×#53611yescharacteristic
829C22C2×#53611yescharacteristic
830C22C2×#53911yescharacteristic
831C22C2×#53911yescharacteristic
832C22C2×#54011yescharacteristic
833C22C2×#54111yescharacteristic
834C22C2×#54411yescharacteristic
835C22C2×#54411yescharacteristic
836C22C2×D4211yescharacteristic
837C22C2×D4211yescharacteristic
838C22C2×#54611yescharacteristic
839C22C2×#54711yescharacteristic
840C22C2×#54711yescharacteristic
841C22C2×#54711yescharacteristic
842C22C2×D4×Q811yescharacteristic
843C22C2×D4×Q811yescharacteristic
844C22C2×D4×Q811yescharacteristic
845C22C2×#55011yescharacteristic
846C22C2×#55211yescharacteristic
847C22C2×#55211yescharacteristic
848C22C2×#55211yescharacteristic
849C22C2×#55411yescharacteristic
850C22C2×#55411yescharacteristic
851C22C2×#55711yescharacteristic
852C22C2×#55711yescharacteristic
853C22C2×#55711yescharacteristic
854C22C2×#56311yescharacteristic
855C22C2×#56311yescharacteristic
856C4—28no—
857C4—28no—
858C4—28no—
859C4—28no—
860C4—44no—
861C4—44no—
862C4—44no—
863C4—44no—
864C4—44no—
865C4—44no—
866C4—44no—
867C4—82no—
868C4—82no—
869C4—82no—
870C4—82no—
871C2#15629116yesdirect product factor
872C2C2×#244911yescharacteristic
873C2C2×#247311yescharacteristic
874C2C2×#244011yescharacteristic
875C2C2×#242811yescharacteristic
876C2C2×#241311yescharacteristic
877C2C2×#250611yescharacteristic
878C2C2×#256511yescharacteristic
879C2C2×#254611yescharacteristic
880C2C2×#255211yescharacteristic
881C2C2×#267711yescharacteristic
882C2C2×#268011yescharacteristic
883C2C2×#271311yescharacteristic
884C2C2×#272111yescharacteristic
885C2C2×#279111yescharacteristic
886C2C2×#279111yescharacteristic
subgroupG/H
center, socle, prime radicalC25C24
commutator, Frattini, cosocleC24C25
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
7. #15629C2direct (N × H)
871. C2#15629direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#3982
C22×#3892
C22×#3872
C22×#3842
#156292
C2×#14452
C2×#14442
C2×#14422
C2×#14412
C2×#14362