Finite Group Databasebeta

← C2×#30862 #7502093

Subgroups — C2×#30862 #7502093

Order 512.

2856 conjugacy classes of subgroups.

The subgroup lattice has 819 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#470C211yesmaximal, characteristic, complemented
2C22×#468C211yesmaximal, characteristic
3C22×#464C211yesmaximal, characteristic, complemented
4C22×#462C211yesmaximal, characteristic, complemented
5C2×#2426C211yesmaximal, characteristic
6C2×#2429C211yesmaximal, characteristic, complemented
7#30862C2116yesmaximal, direct product factor
8C2×#2068C211yesmaximal, characteristic, complemented
9C2×#2065C211yesmaximal, characteristic, complemented
10C2×#2013C211yesmaximal, characteristic, complemented
11C2×#2015C211yesmaximal, characteristic, complemented
12C2×#2001C211yesmaximal, characteristic, complemented
13C2×#2000C211yesmaximal, characteristic
14C2×#1865C211yesmaximal, characteristic, complemented
15C2×#1863C211yesmaximal, characteristic, complemented
16C2×#1851C211yesmaximal, characteristic, complemented
17C23×Q16C2211yescharacteristic
18C23×Q16C2211yescharacteristic
19C23×SD16C2211yescharacteristic
20C23×SD16C2211yescharacteristic
21C23×M16C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23C22×#124C2211yescharacteristic
24C22×C22⋊Q8C2211yescharacteristic
25C22×C22⋊Q8C2211yescharacteristic
26C22×C22⋊Q8C2211yescharacteristic
27C22×#121C2211yescharacteristic
28C22×C4×Q8C2211yescharacteristic
29C22×C4×Q8C2211yescharacteristic
30C2×#470—28no—
31C2×#470C2218yescomplemented
32C2×#468—28no—
33C2×#468C2218yes—
34C2×#464—28no—
35C2×#464C2218yescomplemented
36C2×#462—28no—
37C2×#462C2218yescomplemented
38C22×#107C2211yescharacteristic
39C22×#106C2211yescharacteristic
40C22×C4⋊C8C2211yescharacteristic
41C22×C4⋊C8C2211yescharacteristic
42C22×#103C2211yescharacteristic
43C22×#103C2211yescharacteristic
44C22×#103C2211yescharacteristic
45C22×#103C2211yescharacteristic
46C22×#103C2211yescharacteristic
47C22×#103C2211yescharacteristic
48C22×#102C2211yescharacteristic
49C22×#102C2211yescharacteristic
50C22×C22⋊C8C2211yescharacteristic
51#2429—24no—
52#2429C2218yescomplemented
53#2426—24no—
54#2426C2218yes—
55C2×#398—21no—
56C2×#396—21no—
57C2×#396—21no—
58C2×#394—21no—
59C2×#391C2211yescharacteristic
60C2×#390—21no—
61C2×#390C2211yescharacteristic
62C2×#389—21no—
63C2×#389C2211yescharacteristic
64C2×#389C2211yescharacteristic
65C2×#388—21no—
66C2×#388—21no—
67C2×C4×C22⋊C4C2211yescharacteristic
68#2068C2218yescomplemented
69#2065C2218yescomplemented
70#2015C2218yescomplemented
71#2013C2218yescomplemented
72#2001C2218yescomplemented
73#2000C2218yes—
74#1865C2218yescomplemented
75#1863C2218yescomplemented
76#1851C2218yescomplemented
77C2×#340C2211yescharacteristic
78C2×#340C2211yescharacteristic
79C2×#336C2211yescharacteristic
80C2×#336C2211yescharacteristic
81C23×Q8C2311yescharacteristic
82C23×Q8C2311yescharacteristic
83C23×Q8C2311yescharacteristic
84C23×D4—21no—
85C23×D4C2311yescharacteristic
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×SD16—24no—
96C22×SD16—24no—
97C22×SD16—42no—
98C22×SD16—42no—
99C22×SD16—42no—
100C22×SD16—42no—
101C22×SD16C2314yes—
102C22×SD16C2314yes—
103C22×M16—24no—
104C22×M16—24no—
105C22×M16—42no—
106C22×M16C2314yes—
107C23×C8C2311yescharacteristic
108C23×C8C2311yescharacteristic
109C23×C8C2311yescharacteristic
110C23×C8C2311yescharacteristic
111C2×C4⋊Q8—24no—
112C2×C4⋊Q8—22no—
113C2×C4⋊Q8—42no—
114C2×C4⋊Q8C2314yes—
115C2×#124—24no—
116C2×#124—22no—
117C2×#124—42no—
118C2×#124C2314yes—
119C2×C22⋊Q8—22no—
120C2×C22⋊Q8—22no—
121C2×C22⋊Q8—22no—
122C2×C22⋊Q8—24no—
123C2×C22⋊Q8—24no—
124C2×C22⋊Q8—24no—
125C2×C22⋊Q8—42no—
126C2×C22⋊Q8—42no—
127C2×C22⋊Q8—42no—
128C2×C22⋊Q8C2314yes—
129C2×C22⋊Q8C2314yes—
130C2×C22⋊Q8C2314yes—
131C2×#121—22no—
132C2×#121—24no—
133C2×#121—42no—
134C2×#121C2314yes—
135C2×C4×Q8—22no—
136C2×C4×Q8—22no—
137C2×C4×Q8—24no—
138C2×C4×Q8—24no—
139C2×C4×Q8—42no—
140C2×C4×Q8—42no—
141C2×C4×Q8C2314yes—
142C2×C4×Q8C2314yes—
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⋊C4C2311yescharacteristic
153C22×C4⋊C4C2311yescharacteristic
154C22×C4⋊C4C2311yescharacteristic
155C22×C4⋊C4C2311yescharacteristic
156C22×C22⋊C4—21no—
157C22×C22⋊C4—21no—
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⋊C4D411yescharacteristic
165C22×C22⋊C4D411yescharacteristic
166C22×C42—21no—
167C22×C42—21no—
168C22×C42C2311yescharacteristic
169C22×C42C2311yescharacteristic
170#470—232no—
171#468—232no—
172#464—232no—
173#462—232no—
174C2×#107—24no—
175C2×#107C2314yes—
176C2×#106—24no—
177C2×#106C2314yes—
178C2×C4⋊C8—24no—
179C2×C4⋊C8—24no—
180C2×C4⋊C8C2314yes—
181C2×C4⋊C8C2314yes—
182C2×#103—24no—
183C2×#103—24no—
184C2×#103—42no—
185C2×#103—42no—
186C2×#103D418yes—
187C2×#103D418yescomplemented
188C2×#103C2314yes—
189C2×#103C2314yes—
190C2×#103C2314yes—
191C2×#103C2314yes—
192C2×#103C2314yes—
193C2×#103C2314yes—
194C2×#102—24no—
195C2×#102—24no—
196C2×#102C2314yes—
197C2×#102C2314yes—
198C2×C22⋊C8—42no—
199C2×C22⋊C8C2314yes—
200#398—28no—
201#396—28no—
202#396—28no—
203#394—28no—
204#391—22no—
205#391C2314yes—
206#390—28no—
207#390—22no—
208#390C2314yes—
209#389—22no—
210#389—22no—
211#389—28no—
212#389C2314yes—
213#389C2314yes—
214#388—28no—
215#388—28no—
216C4×C22⋊C4D414yes—
217C4×C22⋊C4C2314yes—
218C2×#95—21no—
219C2×#95—21no—
220C2×#95—21no—
221C2×#95—21no—
222C2×#95D411yescharacteristic
223C2×#95D411yescharacteristic
224#340C2314yes—
225#340C2314yes—
226#336C2314yes—
227#336C2314yes—
228C25—21no—
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×Q8C2×D414yes—
250C22×Q8C2×D414yes—
251C22×Q8C2412yes—
252C22×Q8C2412yes—
253C22×Q8C2412yes—
254C22×D4—24no—
255C22×D4—22no—
256C22×D4—22no—
257C22×D4—21no—
258C22×D4—22no—
259C22×D4—22no—
260C22×D4—22no—
261C22×D4—22no—
262C22×D4—44no—
263C22×D4—44no—
264C22×D4—82no—
265C22×D4C2412yes—
266C23×C4—21no—
267C23×C4—21no—
268C23×C4—21no—
269C23×C4—21no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—21no—
277C23×C4—21no—
278C23×C4—21no—
279C23×C4C2×D412yes—
280C23×C4C2×D411yescharacteristic
281C23×C4C2×D411yescharacteristic
282C23×C4C2×D411yescharacteristic
283C23×C4C2×D411yescharacteristic
284C23×C4C2×D411yescharacteristic
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×SD16—28no—
296C2×SD16—28no—
297C2×SD16—44no—
298C2×SD16—44no—
299C2×SD16—44no—
300C2×SD16—44no—
301C2×SD16—416no—
302C2×SD16—416no—
303C2×M16—28no—
304C2×M16—28no—
305C2×M16—44no—
306C2×M16—416no—
307C22×C8—22no—
308C22×C8—22no—
309C22×C8—22no—
310C22×C8—22no—
311C22×C8—22no—
312C22×C8—22no—
313C22×C8—22no—
314C22×C8—22no—
315C22×C8—22no—
316C22×C8—22no—
317C22×C8C2×D414yes—
318C22×C8C2×D414yes—
319C22×C8C2412yes—
320C22×C8C2412yes—
321C22×C8C2412yes—
322C22×C8C2412yes—
323C4⋊Q8—28no—
324C4⋊Q8—44no—
325C4⋊Q8—48no—
326#124—28no—
327#124—44no—
328#124—48no—
329C22⋊Q8—28no—
330C22⋊Q8—28no—
331C22⋊Q8—28no—
332C22⋊Q8—44no—
333C22⋊Q8—44no—
334C22⋊Q8—44no—
335C22⋊Q8—48no—
336C22⋊Q8—48no—
337C22⋊Q8—48no—
338#121—28no—
339#121—44no—
340#121—48no—
341C4×Q8—28no—
342C4×Q8—28no—
343C4×Q8—44no—
344C4×Q8—44no—
345C4×Q8—48no—
346C4×Q8—48no—
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—24no—
356C2×C4⋊C4—24no—
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—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—24no—
366C2×C4⋊C4—44no—
367C2×C4⋊C4—44no—
368C2×C4⋊C4—44no—
369C2×C4⋊C4—44no—
370C2×C4⋊C4—44no—
371C2×C4⋊C4—44no—
372C2×C4⋊C4—44no—
373C2×C4⋊C4—44no—
374C2×C4⋊C4—82no—
375C2×C4⋊C4C2×D414yes—
376C2×C4⋊C4C2×D414yes—
377C2×C4⋊C4C2412yes—
378C2×C4⋊C4C2412yes—
379C2×C4⋊C4C2412yes—
380C2×C4⋊C4C2412yes—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—42no—
391C2×C22⋊C4—44no—
392C2×C22⋊C4—44no—
393C2×C22⋊C4—44no—
394C2×C22⋊C4—44no—
395C2×C22⋊C4—44no—
396C2×C22⋊C4—44no—
397C2×C22⋊C4—44no—
398C2×C22⋊C4—82no—
399C2×C22⋊C4C2×D414yes—
400C2×C22⋊C4C2×D414yes—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—24no—
406C2×C42—24no—
407C2×C42—44no—
408C2×C42—44no—
409C2×C42C2×D412yes—
410C2×C42C2×D412yes—
411C2×C42C2412yes—
412C2×C42C2412yes—
413#107—28no—
414#106—28no—
415C4⋊C8—28no—
416C4⋊C8—28no—
417#103—28no—
418#103—28no—
419#103—44no—
420#103—44no—
421#103C2×D4116yes—
422#103C2×D4116yescomplemented
423#102—28no—
424#102—28no—
425C22⋊C8—44no—
426#95—24no—
427#95—24no—
428#95—24no—
429#95—24no—
430#95C2×D414yes—
431#95C2×D414yes—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—42no—
441C24—42no—
442C24—42no—
443C24—42no—
444C24—42no—
445C24—42no—
446C24—42no—
447C24C22×D412yes—
448C24C22×D411yescharacteristic
449C2×Q8—24no—
450C2×Q8—24no—
451C2×Q8—22no—
452C2×Q8—22no—
453C2×Q8—28no—
454C2×Q8—28no—
455C2×Q8—28no—
456C2×Q8—28no—
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—22no—
471C2×Q8—44no—
472C2×Q8—44no—
473C2×Q8—42no—
474C2×Q8—42no—
475C2×Q8—42no—
476C2×Q8—42no—
477C2×Q8—42no—
478C2×Q8—42no—
479C2×Q8—42no—
480C2×Q8—44no—
481C2×Q8—44no—
482C2×Q8—44no—
483C2×Q8—44no—
484C2×Q8—44no—
485C2×Q8—44no—
486C2×Q8C22×D414yes—
487C2×Q8C22×D414yes—
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—22no—
494C2×D4—48no—
495C2×D4—48no—
496C2×D4—44no—
497C2×D4—44no—
498C2×D4—42no—
499C2×D4—44no—
500C2×D4—42no—
501C2×D4—42no—
502C2×D4—44no—
503C2×D4—84no—
504C2×D4—816no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—22no—
515C22×C4—24no—
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—24no—
528C22×C4—24no—
529C22×C4—24no—
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—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—44no—
548C22×C4—44no—
549C22×C4—44no—
550C22×C4—44no—
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#13714yes—
561C22×C4C22×D412yes—
562C22×C4C22×D412yes—
563C22×C4C22×D412yes—
564C22×C4C22×D412yes—
565C22×C4C22×D412yes—
566C22×C4C22×D411yescharacteristic
567C22×C4C22×D412yes—
568C22×C4C22×D412yes—
569C22×C4H(5,𝔽2)12yes—
570C22×C4H(5,𝔽2)12yes—
571C22×C4H(5,𝔽2)12yes—
572C22×C42−1+412yes—
573C22×C4C2511yescharacteristic
574Q16—416no—
575Q16—416no—
576SD16—416no—
577SD16—416no—
578M16—416no—
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—22no—
591C2×C8—44no—
592C2×C8—44no—
593C2×C8C22×D414yes—
594C2×C8C22×D414yes—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—48no—
604C4⋊C4—48no—
605C4⋊C4—48no—
606C4⋊C4—48no—
607C4⋊C4—48no—
608C4⋊C4—48no—
609C4⋊C4—48no—
610C4⋊C4—48no—
611C4⋊C4—42no—
612C4⋊C4—42no—
613C4⋊C4—84no—
614C4⋊C4C22×D414yes—
615C4⋊C4C22×D414yes—
616C22⋊C4—28no—
617C22⋊C4—44no—
618C22⋊C4—48no—
619C22⋊C4—48no—
620C22⋊C4—48no—
621C22⋊C4—48no—
622C22⋊C4—48no—
623C22⋊C4—48no—
624C22⋊C4—48no—
625C22⋊C4—84no—
626C42—24no—
627C42—24no—
628C42—22no—
629C42—22no—
630C42—22no—
631C42—22no—
632C42—48no—
633C42—48no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—44no—
642C23—44no—
643C23—44no—
644C23—44no—
645C23—44no—
646C23—44no—
647C23—44no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—84no—
656C23—84no—
657C23—84no—
658C23—84no—
659C23—84no—
660C23—84no—
661C23—84no—
662C23#53712yes—
663C23D4212yes—
664C23D4212yes—
665C23C2×#13712yes—
666C23#57512yes—
667C23#57712yes—
668C23#57812yes—
669C23C23×D411yescharacteristic
670Q8—24no—
671Q8—24no—
672Q8—24no—
673Q8—24no—
674Q8—48no—
675Q8—48no—
676Q8—42no—
677Q8—42no—
678Q8—42no—
679Q8—42no—
680Q8—42no—
681Q8—42no—
682Q8—42no—
683Q8—42no—
684Q8—84no—
685D4—42no—
686D4—42no—
687D4—42no—
688D4—42no—
689D4—816no—
690D4—84no—
691C2×C4—22no—
692C2×C4—28no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—44no—
711C2×C4—48no—
712C2×C4—48no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—44no—
718C2×C4—48no—
719C2×C4—44no—
720C2×C4—48no—
721C2×C4—44no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—48no—
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—42no—
739C2×C4—42no—
740C2×C4—84no—
741C2×C4—84no—
742C2×C4—84no—
743C2×C4#53712yes—
744C2×C4#53714yes—
745C2×C4#53714yes—
746C2×C4D4212yes—
747C2×C4D4212yes—
748C2×C4D4214yes—
749C2×C4#56014yes—
750C2×C4C2×#13714yes—
751C2×C4C23×D411yescharacteristic
752C2×C4C23×D411yescharacteristic
753C2×C4C2×H(5,𝔽2)11yescharacteristic
754C2×C4C2×H(5,𝔽2)11yescharacteristic
755C2×C4C2×H(5,𝔽2)11yescharacteristic
756C2×C4C2×2−1+411yescharacteristic
757C8—24no—
758C8—24no—
759C8—42no—
760C8—42no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—88no—
769C22—82no—
770C22—82no—
771C22—82no—
772C22—82no—
773C22—82no—
774C22—82no—
775C22—82no—
776C22—168no—
777C22#267514yes—
778C22#325214yes—
779C22#325814yes—
780C22#326914yes—
781C22#327014yes—
782C22#327514yes—
783C22#327814yes—
784C22C2×#53711yescharacteristic
785C22C2×D4211yescharacteristic
786C22C2×D4211yescharacteristic
787C22C22×#13711yescharacteristic
788C22C2×#57511yescharacteristic
789C22C2×#57711yescharacteristic
790C22C2×#57811yescharacteristic
791C4—24no—
792C4—42no—
793C4—44no—
794C4—42no—
795C4—44no—
796C4—42no—
797C4—42no—
798C4—44no—
799C4—44no—
800C4—82no—
801C4—82no—
802C4—82no—
803C4#267514yes—
804C4C2×#53711yescharacteristic
805C4C2×#53711yescharacteristic
806C4C2×D4211yescharacteristic
807C4C2×#56011yescharacteristic
808C2—82no—
809C2—162no—
810C2#3086218yesdirect product factor
811C2C2×#267511yescharacteristic
812C2C2×#325211yescharacteristic
813C2C2×#325811yescharacteristic
814C2C2×#326911yescharacteristic
815C2C2×#327011yescharacteristic
816C2C2×#327511yescharacteristic
817C2C2×#327811yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#470C2semidirect
3. C22×#464C2semidirect
4. C22×#462C2semidirect
6. C2×#2429C2semidirect
7. #30862C2direct (N × H)
8. C2×#2068C2semidirect
9. C2×#2065C2semidirect
10. C2×#2013C2semidirect
11. C2×#2015C2semidirect
12. C2×#2001C2semidirect
14. C2×#1865C2semidirect
15. C2×#1863C2semidirect
16. C2×#1851C2semidirect
31. C2×#470C22semidirect
35. C2×#464C22semidirect
37. C2×#462C22semidirect
52. #2429C22semidirect
68. #2068C22semidirect
69. #2065C22semidirect
70. #2015C22semidirect
71. #2013C22semidirect
72. #2001C22semidirect
74. #1865C22semidirect
75. #1863C22semidirect
76. #1851C22semidirect
187. C2×#103D4semidirect
422. #103C2×D4semidirect
810. C2#30862direct (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×#4682
C22×#4642
C22×#4622
C2×#24262
C2×#24292
#308622
C2×#20682
C2×#20652
C2×#20132
C2×#20152
C2×#20012
C2×#20002
C2×#18652
C2×#18632
C2×#18512