Finite Group Databasebeta

← C2×#25398 #6444351

Subgroups — C2×#25398 #6444351

Order 512.

2946 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#470C211yesmaximal, characteristic, complemented
2C22×#467C211yesmaximal, characteristic, complemented
3C22×#462C211yesmaximal, characteristic, complemented
4C22×#435C211yesmaximal, characteristic
5C2×#2542C211yesmaximal, characteristic
6C2×#2536C211yesmaximal, characteristic
7#25398C2116yesmaximal, direct product factor
8C2×#2036C211yesmaximal, characteristic, complemented
9C2×#2035C211yesmaximal, characteristic, complemented
10C2×#2001C211yesmaximal, characteristic, complemented
11C2×#2001C211yesmaximal, characteristic, complemented
12C2×#1960C211yesmaximal, characteristic, complemented
13C2×#1949C211yesmaximal, characteristic, complemented
14C2×#1894C211yesmaximal, characteristic, complemented
15C2×#1892C211yesmaximal, characteristic, complemented
16C2×#1763C211yesmaximal, characteristic, complemented
17C23×Q16C2211yescharacteristic
18C23×Q16C2211yescharacteristic
19C23×M16C2211yescharacteristic
20C24×C8C2211yescharacteristic
21C22×C4⋊Q8C2211yescharacteristic
22C22×C22⋊Q8C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C22×C22⋊Q8C2211yescharacteristic
25C22×C22⋊Q8C2211yescharacteristic
26C22×C22⋊Q8C2211yescharacteristic
27C22×C22⋊Q8C2211yescharacteristic
28C22×C4×Q8C2211yescharacteristic
29C22×C4×D4C2211yescharacteristic
30C2×#470—28no—
31C2×#470C2218yescomplemented
32C2×#467—28no—
33C2×#467C2218yescomplemented
34C2×#462—28no—
35C2×#462C2218yescomplemented
36C2×#435—28no—
37C2×#435C2218yes—
38C22×#107C2211yescharacteristic
39C22×#106C2211yescharacteristic
40C22×C4⋊C8C2211yescharacteristic
41C22×#103C2211yescharacteristic
42C22×#103C2211yescharacteristic
43C22×#103C2211yescharacteristic
44C22×#103C2211yescharacteristic
45C22×#103C2211yescharacteristic
46C22×#103C2211yescharacteristic
47C22×#103C2211yescharacteristic
48C22×#103C2211yescharacteristic
49C22×C22⋊C8C2211yescharacteristic
50C22×C22⋊C8C2211yescharacteristic
51C22×#97C2211yescharacteristic
52#2542—24no—
53#2542C2218yes—
54#2536—24no—
55#2536C2218yes—
56C2×#399—21no—
57C2×#399—21no—
58C2×#398—21no—
59C2×#394—21no—
60C2×#390—21no—
61C2×#388—21no—
62C2×#388—21no—
63C2×#384—21no—
64C2×#382C2211yescharacteristic
65C2×#380C2211yescharacteristic
66C2×#380C2211yescharacteristic
67C2×C4×C4⋊C4C2211yescharacteristic
68#2036C2218yescomplemented
69#2035C2218yescomplemented
70#2001C2218yescomplemented
71#2001C2218yescomplemented
72#1960C2218yescomplemented
73#1949C2218yescomplemented
74#1894C2218yescomplemented
75#1892C2218yescomplemented
76#1763C2218yescomplemented
77C2×#340C2211yescharacteristic
78C2×#340C2211yescharacteristic
79C2×#340C2211yescharacteristic
80C2×#340C2211yescharacteristic
81C23×Q8C2311yescharacteristic
82C23×Q8C2311yescharacteristic
83C23×Q8C2311yescharacteristic
84C23×D4D411yescharacteristic
85C24×C4C2311yescharacteristic
86C24×C4C2311yescharacteristic
87C22×Q16—24no—
88C22×Q16—24no—
89C22×Q16—24no—
90C22×Q16—24no—
91C22×Q16—42no—
92C22×Q16—42no—
93C22×Q16C2314yes—
94C22×Q16C2314yes—
95C22×M16—24no—
96C22×M16—24no—
97C22×M16—42no—
98C22×M16C2314yes—
99C23×C8—24no—
100C23×C8—24no—
101C23×C8—42no—
102C23×C8C2311yescharacteristic
103C23×C8C2314yes—
104C23×C8C2311yescharacteristic
105C23×C8C2311yescharacteristic
106C23×C8C2311yescharacteristic
107C2×C4⋊Q8—22no—
108C2×C4⋊Q8—24no—
109C2×C4⋊Q8—24no—
110C2×C4⋊Q8C2314yes—
111C2×C22⋊Q8—22no—
112C2×C22⋊Q8—22no—
113C2×C22⋊Q8—22no—
114C2×C22⋊Q8—22no—
115C2×C22⋊Q8—22no—
116C2×C22⋊Q8—22no—
117C2×C22⋊Q8—24no—
118C2×C22⋊Q8—24no—
119C2×C22⋊Q8—24no—
120C2×C22⋊Q8—24no—
121C2×C22⋊Q8—24no—
122C2×C22⋊Q8—24no—
123C2×C22⋊Q8—42no—
124C2×C22⋊Q8—42no—
125C2×C22⋊Q8—42no—
126C2×C22⋊Q8—42no—
127C2×C22⋊Q8—42no—
128C2×C22⋊Q8—42no—
129C2×C22⋊Q8C2314yes—
130C2×C22⋊Q8C2314yes—
131C2×C22⋊Q8C2314yes—
132C2×C22⋊Q8C2314yes—
133C2×C22⋊Q8C2314yes—
134C2×C22⋊Q8C2314yes—
135C2×C4×Q8—22no—
136C2×C4×Q8—24no—
137C2×C4×Q8—24no—
138C2×C4×Q8C2314yes—
139C2×C4×D4—24no—
140C2×C4×D4—24no—
141C2×C4×D4D414yes—
142C2×C4×D4C2314yes—
143C22×C4⋊C4—21no—
144C22×C4⋊C4—21no—
145C22×C4⋊C4—21no—
146C22×C4⋊C4—21no—
147C22×C4⋊C4—21no—
148C22×C4⋊C4—21no—
149C22×C4⋊C4—21no—
150C22×C4⋊C4—21no—
151C22×C4⋊C4—21no—
152C22×C4⋊C4D411yescharacteristic
153C22×C4⋊C4C2311yescharacteristic
154C22×C4⋊C4C2311yescharacteristic
155C22×C4⋊C4C2311yescharacteristic
156C22×C4⋊C4C2311yescharacteristic
157C22×C4⋊C4C2311yescharacteristic
158C22×C22⋊C4—21no—
159C22×C22⋊C4—21no—
160C22×C22⋊C4—21no—
161C22×C22⋊C4—21no—
162C22×C22⋊C4—21no—
163C22×C22⋊C4—21no—
164C22×C22⋊C4—21no—
165C22×C22⋊C4—21no—
166C22×C22⋊C4D411yescharacteristic
167C22×C22⋊C4D411yescharacteristic
168C22×C42—21no—
169C22×C42—21no—
170C22×C42C2311yescharacteristic
171#470—232no—
172#467—232no—
173#462—232no—
174#435—232no—
175C2×#107—24no—
176C2×#107C2314yes—
177C2×#106—24no—
178C2×#106C2314yes—
179C2×C4⋊C8D418yes—
180C2×C4⋊C8C2314yes—
181C2×#103—24no—
182C2×#103—24no—
183C2×#103—24no—
184C2×#103—24no—
185C2×#103—24no—
186C2×#103—42no—
187C2×#103—42no—
188C2×#103D418yescomplemented
189C2×#103C2314yes—
190C2×#103C2314yes—
191C2×#103C2314yes—
192C2×#103C2314yes—
193C2×#103C2314yes—
194C2×#103C2314yes—
195C2×#103C2314yes—
196C2×#103C2314yes—
197C2×C22⋊C8—24no—
198C2×C22⋊C8—24no—
199C2×C22⋊C8C2314yes—
200C2×C22⋊C8C2314yes—
201C2×#97—24no—
202C2×#97C2314yes—
203#399—28no—
204#399—28no—
205#398—28no—
206#394—28no—
207#390—28no—
208#388—28no—
209#388—28no—
210#384—28no—
211#382—22no—
212#382C2314yes—
213#380—22no—
214#380—22no—
215#380C2314yes—
216#380C2314yes—
217C4×C4⋊C4—22no—
218C4×C4⋊C4C2314yes—
219C2×#95—21no—
220C2×#95—21no—
221C2×#95—21no—
222C2×#95—21no—
223C2×#95—21no—
224#340C2314yes—
225#340C2314yes—
226#340C2314yes—
227#340C2314yes—
228C25C2×D411yescharacteristic
229C25C2×D411yescharacteristic
230C22×Q8—21no—
231C22×Q8—21no—
232C22×Q8—21no—
233C22×Q8—22no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—22no—
239C22×Q8—22no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8—22no—
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8—22no—
249C22×Q8—22no—
250C22×Q8C2×D414yes—
251C22×Q8C2412yes—
252C22×Q8C2412yes—
253C22×Q8C2412yes—
254C22×D4—24no—
255C22×D4—24no—
256C22×D4—42no—
257C22×D4C2×D414yes—
258C23×C4—21no—
259C23×C4—21no—
260C23×C4—21no—
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—21no—
274C23×C4—21no—
275C23×C4—21no—
276C23×C4—21no—
277C23×C4—21no—
278C23×C4C2×D412yes—
279C23×C4C2×D412yes—
280C23×C4C2×D411yescharacteristic
281C23×C4C2×D411yescharacteristic
282C23×C4C2×D411yescharacteristic
283C23×C4C2×D411yescharacteristic
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2411yescharacteristic
287C2×Q16—28no—
288C2×Q16—28no—
289C2×Q16—28no—
290C2×Q16—28no—
291C2×Q16—44no—
292C2×Q16—44no—
293C2×Q16—416no—
294C2×Q16—416no—
295C2×M16—28no—
296C2×M16—28no—
297C2×M16—44no—
298C2×M16—416no—
299C22×C8—22no—
300C22×C8—22no—
301C22×C8—22no—
302C22×C8—22no—
303C22×C8—22no—
304C22×C8—22no—
305C22×C8—22no—
306C22×C8—22no—
307C22×C8—22no—
308C22×C8—28no—
309C22×C8—28no—
310C22×C8—44no—
311C22×C8—416no—
312C22×C8C2×D414yes—
313C22×C8C2×D414yes—
314C22×C8C2×D414yes—
315C22×C8C2412yes—
316C22×C8C2412yes—
317C22×C8C2412yes—
318C22×C8C2412yes—
319C4⋊Q8—28no—
320C4⋊Q8—28no—
321C4⋊Q8—48no—
322C22⋊Q8—28no—
323C22⋊Q8—28no—
324C22⋊Q8—28no—
325C22⋊Q8—28no—
326C22⋊Q8—28no—
327C22⋊Q8—28no—
328C22⋊Q8—44no—
329C22⋊Q8—44no—
330C22⋊Q8—44no—
331C22⋊Q8—44no—
332C22⋊Q8—44no—
333C22⋊Q8—44no—
334C22⋊Q8—48no—
335C22⋊Q8—48no—
336C22⋊Q8—48no—
337C22⋊Q8—48no—
338C22⋊Q8—48no—
339C22⋊Q8—48no—
340C4×Q8—28no—
341C4×Q8—28no—
342C4×Q8—48no—
343C4×D4—216no—
344C4×D4—28no—
345C4×D4—28no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—24no—
363C2×C4⋊C4—24no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—24no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—44no—
370C2×C4⋊C4—44no—
371C2×C4⋊C4—44no—
372C2×C4⋊C4—44no—
373C2×C4⋊C4—44no—
374C2×C4⋊C4—44no—
375C2×C4⋊C4—44no—
376C2×C4⋊C4—44no—
377C2×C4⋊C4—44no—
378C2×C4⋊C4C2×D414yes—
379C2×C4⋊C4C2×D414yes—
380C2×C4⋊C4#4114yes—
381C2×C4⋊C4C2412yes—
382C2×C4⋊C4C2412yes—
383C2×C4⋊C4C2412yes—
384C2×C4⋊C4C2412yes—
385C2×C4⋊C4C2412yes—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—44no—
397C2×C22⋊C4—44no—
398C2×C22⋊C4—44no—
399C2×C22⋊C4—44no—
400C2×C22⋊C4—44no—
401C2×C22⋊C4—44no—
402C2×C22⋊C4—44no—
403C2×C22⋊C4—44no—
404C2×C22⋊C4C2×D414yes—
405C2×C22⋊C4C2×D414yes—
406C2×C42—24no—
407C2×C42—24no—
408C2×C42—44no—
409C2×C42—44no—
410C2×C42C2×D412yes—
411C2×C42C2×D414yes—
412C2×C42#4114yes—
413C2×C42C2412yes—
414#107—28no—
415#106—28no—
416C4⋊C8C2×D4116yes—
417#103—28no—
418#103—28no—
419#103—28no—
420#103—28no—
421#103—28no—
422#103—44no—
423#103—44no—
424#103C2×D4116yescomplemented
425C22⋊C8—28no—
426C22⋊C8—28no—
427#97—28no—
428#95—24no—
429#95—24no—
430#95—24no—
431#95—24no—
432#95—24no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24#13714yes—
447C24C22×D412yes—
448C24C22×D412yes—
449C24C22×D411yescharacteristic
450C2×Q8—24no—
451C2×Q8—22no—
452C2×Q8—28no—
453C2×Q8—28no—
454C2×Q8—22no—
455C2×Q8—22no—
456C2×Q8—22no—
457C2×Q8—22no—
458C2×Q8—22no—
459C2×Q8—22no—
460C2×Q8—22no—
461C2×Q8—22no—
462C2×Q8—22no—
463C2×Q8—22no—
464C2×Q8—22no—
465C2×Q8—22no—
466C2×Q8—22no—
467C2×Q8—22no—
468C2×Q8—22no—
469C2×Q8—22no—
470C2×Q8—42no—
471C2×Q8—42no—
472C2×Q8—42no—
473C2×Q8—44no—
474C2×Q8—42no—
475C2×Q8—42no—
476C2×Q8—42no—
477C2×Q8—42no—
478C2×Q8—42no—
479C2×Q8—44no—
480C2×Q8—44no—
481C2×Q8—44no—
482C2×Q8—44no—
483C2×Q8—44no—
484C2×Q8—44no—
485C2×Q8—44no—
486C2×Q8—44no—
487C2×Q8—44no—
488C2×Q8C22×D414yes—
489C2×D4—28no—
490C2×D4—28no—
491C2×D4—44no—
492C2×D4—416no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—24no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—24no—
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—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—44no—
539C22×C4—44no—
540C22×C4—44no—
541C22×C4—44no—
542C22×C4—44no—
543C22×C4—44no—
544C22×C4—44no—
545C22×C4—44no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4#12114yes—
562C22×C4#12114yes—
563C22×C4C22×D412yes—
564C22×C4C22×D412yes—
565C22×C4C22×D412yes—
566C22×C4C22×D412yes—
567C22×C4C22×D411yescharacteristic
568C22×C4C22×D412yes—
569C22×C4C22×D412yes—
570C22×C4C2×#4112yes—
571C22×C4C2×#4112yes—
572C22×C4H(5,𝔽2)12yes—
573C22×C4H(5,𝔽2)12yes—
574C22×C4C2511yescharacteristic
575Q16—416no—
576Q16—416no—
577M16—416no—
578C2×C8—28no—
579C2×C8—28no—
580C2×C8—28no—
581C2×C8—22no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—416no—
591C2×C8—44no—
592C2×C8C22×D414yes—
593C2×C8C22×D414yes—
594C2×C8C22×D414yes—
595C4⋊C4—28no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—48no—
607C4⋊C4—48no—
608C4⋊C4—48no—
609C4⋊C4—48no—
610C4⋊C4—48no—
611C4⋊C4—48no—
612C4⋊C4—42no—
613C4⋊C4—48no—
614C4⋊C4—48no—
615C4⋊C4—48no—
616C4⋊C4—42no—
617C4⋊C4—42no—
618C4⋊C4C22×D414yes—
619C4⋊C4C2×#4114yes—
620C22⋊C4—28no—
621C22⋊C4—28no—
622C22⋊C4—48no—
623C22⋊C4—48no—
624C22⋊C4—48no—
625C22⋊C4—48no—
626C22⋊C4—48no—
627C22⋊C4—48no—
628C22⋊C4—48no—
629C22⋊C4—48no—
630C42—48no—
631C42—48no—
632C42#12118yes—
633C42C22×D414yes—
634C42C2×#4114yes—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—28no—
639C23—28no—
640C23—28no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—44no—
652C23—44no—
653C23—44no—
654C23—44no—
655C23—44no—
656C23—44no—
657C23—44no—
658C23—44no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23C2×#12112yes—
663C23D4212yes—
664C23#54612yes—
665C23C2×#13714yes—
666C23C2×#13712yes—
667C23#57512yes—
668C23#57812yes—
669C23#57812yes—
670C23C23×D411yescharacteristic
671Q8—24no—
672Q8—24no—
673Q8—48no—
674Q8—42no—
675Q8—42no—
676Q8—42no—
677Q8—42no—
678Q8—42no—
679Q8—42no—
680Q8—42no—
681Q8—42no—
682Q8—42no—
683Q8—42no—
684Q8—84no—
685Q8—84no—
686D4—416no—
687C2×C4—28no—
688C2×C4—28no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—42no—
703C2×C4—44no—
704C2×C4—44no—
705C2×C4—48no—
706C2×C4—42no—
707C2×C4—48no—
708C2×C4—48no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—48no—
716C2×C4—48no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—84no—
739C2×C4—84no—
740C2×C4—84no—
741C2×C4—84no—
742C2×C4—84no—
743C2×C4C2×#12114yes—
744C2×C4C2×#12114yes—
745C2×C4C2×#12112yes—
746C2×C4#53214yes—
747C2×C4#54014yes—
748C2×C4D4212yes—
749C2×C4D4214yes—
750C2×C4#54612yes—
751C2×C4#55014yes—
752C2×C4C23×D411yescharacteristic
753C2×C4C23×D411yescharacteristic
754C2×C4C22×#4111yescharacteristic
755C2×C4C22×#4111yescharacteristic
756C2×C4C2×H(5,𝔽2)11yescharacteristic
757C2×C4C2×H(5,𝔽2)11yescharacteristic
758C8—24no—
759C8—24no—
760C8—24no—
761C8—42no—
762C22—24no—
763C22—24no—
764C22—24no—
765C22—42no—
766C22—416no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—88no—
778C22#242814yes—
779C22#305614yes—
780C22#305914yes—
781C22#326914yes—
782C22#327014yes—
783C22#331214yes—
784C22#331514yes—
785C22C22×#12111yescharacteristic
786C22C2×D4211yescharacteristic
787C22C2×#54611yescharacteristic
788C22C22×#13711yescharacteristic
789C22C2×#57511yescharacteristic
790C22C2×#57811yescharacteristic
791C22C2×#57811yescharacteristic
792C4—24no—
793C4—24no—
794C4—44no—
795C4—42no—
796C4—42no—
797C4—44no—
798C4—44no—
799C4—82no—
800C4—82no—
801C4—82no—
802C4—82no—
803C4—82no—
804C4#242814yes—
805C4C2×#53211yescharacteristic
806C4C2×#54011yescharacteristic
807C4C2×D4211yescharacteristic
808C4C2×#55011yescharacteristic
809C2—44no—
810C2—82no—
811C2#2539818yesdirect product factor
812C2C2×#242811yescharacteristic
813C2C2×#305611yescharacteristic
814C2C2×#305911yescharacteristic
815C2C2×#326911yescharacteristic
816C2C2×#327011yescharacteristic
817C2C2×#331211yescharacteristic
818C2C2×#331511yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×C4×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#470C2semidirect
2. C22×#467C2semidirect
3. C22×#462C2semidirect
7. #25398C2direct (N × H)
8. C2×#2036C2semidirect
9. C2×#2035C2semidirect
10. C2×#2001C2semidirect
11. C2×#2001C2semidirect
12. C2×#1960C2semidirect
13. C2×#1949C2semidirect
14. C2×#1894C2semidirect
15. C2×#1892C2semidirect
16. C2×#1763C2semidirect
31. C2×#470C22semidirect
33. C2×#467C22semidirect
35. C2×#462C22semidirect
68. #2036C22semidirect
69. #2035C22semidirect
70. #2001C22semidirect
71. #2001C22semidirect
72. #1960C22semidirect
73. #1949C22semidirect
74. #1894C22semidirect
75. #1892C22semidirect
76. #1763C22semidirect
188. C2×#103D4semidirect
424. #103C2×D4semidirect
811. C2#25398direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4702
C22×#4672
C22×#4622
C22×#4352
C2×#25422
C2×#25362
#253982
C2×#20362
C2×#20352
C2×#20012
C2×#19602
C2×#19492
C2×#18942
C2×#18922
C2×#17632