Finite Group Databasebeta

← C2×#30858 #7502091

Subgroups — C2×#30858 #7502091

Order 512.

2910 conjugacy classes of subgroups.

The subgroup lattice has 821 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×#461C211yesmaximal, characteristic, complemented
5C2×#2427C211yesmaximal, characteristic
6C2×#2429C211yesmaximal, characteristic, complemented
7#30858C2116yesmaximal, direct product factor
8C2×#2068C211yesmaximal, characteristic, complemented
9C2×#2066C211yesmaximal, characteristic, complemented
10C2×#2016C211yesmaximal, characteristic, complemented
11C2×#2015C211yesmaximal, characteristic, complemented
12C2×#2001C211yesmaximal, characteristic, complemented
13C2×#2000C211yesmaximal, characteristic
14C2×#1863C211yesmaximal, characteristic, complemented
15C2×#1864C211yesmaximal, 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×D4C2211yescharacteristic
30C2×#470—28no—
31C2×#470C2218yescomplemented
32C2×#468—28no—
33C2×#468C2218yes—
34C2×#464—28no—
35C2×#464C2218yescomplemented
36C2×#461—28no—
37C2×#461C2218yescomplemented
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#2427—24no—
54#2427C2218yes—
55C2×#398—21no—
56C2×#397—21no—
57C2×#396—21no—
58C2×#394—21no—
59C2×#391C2211yescharacteristic
60C2×#391C2211yescharacteristic
61C2×#389—21no—
62C2×#389C2211yescharacteristic
63C2×#389C2211yescharacteristic
64C2×#388—21no—
65C2×#386—21no—
66C2×#380—21no—
67C2×C4×C22⋊C4C2211yescharacteristic
68#2068C2218yescomplemented
69#2066C2218yescomplemented
70#2016C2218yescomplemented
71#2015C2218yescomplemented
72#2001C2218yescomplemented
73#2000C2218yes—
74#1864C2218yescomplemented
75#1863C2218yescomplemented
76#1851C2218yescomplemented
77C2×#340C2211yescharacteristic
78C2×#340C2211yescharacteristic
79C2×#336C2211yescharacteristic
80C2×#336C2211yescharacteristic
81C23×Q8C2311yescharacteristic
82C23×Q8C2311yescharacteristic
83C23×Q8C2311yescharacteristic
84C23×D4—21no—
85C23×D4C2311yescharacteristic
86C24×C4—21no—
87C24×C4C2311yescharacteristic
88C22×Q16—24no—
89C22×Q16—24no—
90C22×Q16—42no—
91C22×Q16—42no—
92C22×Q16—42no—
93C22×Q16—42no—
94C22×Q16C2314yes—
95C22×Q16C2314yes—
96C22×SD16—24no—
97C22×SD16—24no—
98C22×SD16—24no—
99C22×SD16—24no—
100C22×SD16—42no—
101C22×SD16—42no—
102C22×SD16C2314yes—
103C22×SD16C2314yes—
104C22×M16—24no—
105C22×M16—24no—
106C22×M16—42no—
107C22×M16C2314yes—
108C23×C8C2311yescharacteristic
109C23×C8C2311yescharacteristic
110C23×C8C2311yescharacteristic
111C23×C8C2311yescharacteristic
112C2×C4⋊Q8—24no—
113C2×C4⋊Q8—22no—
114C2×C4⋊Q8—42no—
115C2×C4⋊Q8C2314yes—
116C2×#124—24no—
117C2×#124—22no—
118C2×#124—42no—
119C2×#124C2314yes—
120C2×C22⋊Q8—22no—
121C2×C22⋊Q8—22no—
122C2×C22⋊Q8—22no—
123C2×C22⋊Q8—24no—
124C2×C22⋊Q8—24no—
125C2×C22⋊Q8—24no—
126C2×C22⋊Q8—42no—
127C2×C22⋊Q8—42no—
128C2×C22⋊Q8—42no—
129C2×C22⋊Q8C2314yes—
130C2×C22⋊Q8C2314yes—
131C2×C22⋊Q8C2314yes—
132C2×#121—22no—
133C2×#121—24no—
134C2×#121—42no—
135C2×#121C2314yes—
136C2×C4×Q8—22no—
137C2×C4×Q8—24no—
138C2×C4×Q8—42no—
139C2×C4×Q8C2314yes—
140C2×C4×D4—24no—
141C2×C4×D4—22no—
142C2×C4×D4—42no—
143C2×C4×D4C2314yes—
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⋊C4D411yescharacteristic
164C22×C22⋊C4D411yescharacteristic
165C22×C42—21no—
166C22×C42C2311yescharacteristic
167C22×C42C2311yescharacteristic
168#470—232no—
169#468—232no—
170#464—232no—
171#461—232no—
172C2×#107—24no—
173C2×#107C2314yes—
174C2×#106—24no—
175C2×#106C2314yes—
176C2×C4⋊C8—24no—
177C2×C4⋊C8—24no—
178C2×C4⋊C8C2314yes—
179C2×C4⋊C8C2314yes—
180C2×#103—24no—
181C2×#103—24no—
182C2×#103—24no—
183C2×#103—24no—
184C2×#103—42no—
185C2×#103D418yescomplemented
186C2×#103C2314yes—
187C2×#103C2314yes—
188C2×#103C2314yes—
189C2×#103C2314yes—
190C2×#103C2314yes—
191C2×#103C2314yes—
192C2×#102—42no—
193C2×#102D418yes—
194C2×#102C2314yes—
195C2×#102C2314yes—
196C2×C22⋊C8—42no—
197C2×C22⋊C8C2314yes—
198#398—28no—
199#397—28no—
200#396—28no—
201#394—28no—
202#391—22no—
203#391—22no—
204#391C2314yes—
205#391C2314yes—
206#389—22no—
207#389—22no—
208#389—28no—
209#389C2314yes—
210#389C2314yes—
211#388—28no—
212#386—28no—
213#380—28no—
214C4×C22⋊C4D414yes—
215C4×C22⋊C4C2314yes—
216C2×#95—21no—
217C2×#95—21no—
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×Q8—22no—
250C22×Q8C2×D414yes—
251C22×Q8C2412yes—
252C22×Q8C2412yes—
253C22×Q8C2412yes—
254C22×D4—24no—
255C22×D4—22no—
256C22×D4—21no—
257C22×D4—22no—
258C22×D4—22no—
259C22×D4—22no—
260C22×D4—22no—
261C22×D4—44no—
262C22×D4—44no—
263C22×D4—82no—
264C22×D4C2×D414yes—
265C22×D4C2412yes—
266C23×C4—21no—
267C23×C4—21no—
268C23×C4—21no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—21no—
276C23×C4—21no—
277C23×C4—21no—
278C23×C4—21no—
279C23×C4—24no—
280C23×C4—44no—
281C23×C4—44no—
282C23×C4—82no—
283C23×C4C2×D412yes—
284C23×C4C2×D411yescharacteristic
285C23×C4C2×D411yescharacteristic
286C23×C4C2×D411yescharacteristic
287C23×C4C2×D411yescharacteristic
288C23×C4C2×D411yescharacteristic
289C23×C4C2412yes—
290C23×C4C2411yescharacteristic
291C2×Q16—28no—
292C2×Q16—28no—
293C2×Q16—44no—
294C2×Q16—44no—
295C2×Q16—44no—
296C2×Q16—44no—
297C2×Q16—416no—
298C2×Q16—416no—
299C2×SD16—28no—
300C2×SD16—28no—
301C2×SD16—28no—
302C2×SD16—28no—
303C2×SD16—44no—
304C2×SD16—44no—
305C2×SD16—416no—
306C2×SD16—416no—
307C2×M16—28no—
308C2×M16—28no—
309C2×M16—44no—
310C2×M16—416no—
311C22×C8—22no—
312C22×C8—22no—
313C22×C8—22no—
314C22×C8—22no—
315C22×C8—22no—
316C22×C8—22no—
317C22×C8—22no—
318C22×C8—22no—
319C22×C8—22no—
320C22×C8—22no—
321C22×C8C2×D414yes—
322C22×C8C2×D414yes—
323C22×C8C2412yes—
324C22×C8C2412yes—
325C22×C8C2412yes—
326C22×C8C2412yes—
327C4⋊Q8—28no—
328C4⋊Q8—44no—
329C4⋊Q8—48no—
330#124—28no—
331#124—44no—
332#124—48no—
333C22⋊Q8—28no—
334C22⋊Q8—28no—
335C22⋊Q8—28no—
336C22⋊Q8—44no—
337C22⋊Q8—44no—
338C22⋊Q8—44no—
339C22⋊Q8—48no—
340C22⋊Q8—48no—
341C22⋊Q8—48no—
342#121—28no—
343#121—44no—
344#121—48no—
345C4×Q8—28no—
346C4×Q8—44no—
347C4×Q8—48no—
348C4×D4—28no—
349C4×D4—44no—
350C4×D4—48no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
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—24no—
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—82no—
377C2×C4⋊C4C2×D414yes—
378C2×C4⋊C4C2×D414yes—
379C2×C4⋊C4C2412yes—
380C2×C4⋊C4C2412yes—
381C2×C4⋊C4C2412yes—
382C2×C4⋊C4C2412yes—
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—24no—
391C2×C22⋊C4—42no—
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—44no—
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—44no—
407C2×C42C2×D412yes—
408C2×C42C2×D412yes—
409C2×C42C2412yes—
410C2×C42C2412yes—
411#107—28no—
412#106—28no—
413C4⋊C8—28no—
414C4⋊C8—28no—
415#103—28no—
416#103—28no—
417#103—28no—
418#103—28no—
419#103—44no—
420#103C2×D4116yescomplemented
421#102—44no—
422#102C2×D4116yes—
423C22⋊C8—44no—
424#95—24no—
425#95—24no—
426#95—24no—
427#95—24no—
428#95—24no—
429#95—24no—
430#95C2×D414yes—
431#95C2×D414yes—
432C24—22no—
433C24—22no—
434C24—24no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—42no—
442C24—42no—
443C24—42no—
444C24—42no—
445C24—42no—
446C24—42no—
447C24C22×D412yes—
448C24C22×D411yescharacteristic
449C2×Q8—24no—
450C2×Q8—22no—
451C2×Q8—28no—
452C2×Q8—28no—
453C2×Q8—22no—
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—44no—
470C2×Q8—42no—
471C2×Q8—42no—
472C2×Q8—42no—
473C2×Q8—42no—
474C2×Q8—42no—
475C2×Q8—42no—
476C2×Q8—42no—
477C2×Q8—42no—
478C2×Q8—44no—
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×Q8C22×D414yes—
488C2×D4—28no—
489C2×D4—28no—
490C2×D4—24no—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—22no—
494C2×D4—22no—
495C2×D4—22no—
496C2×D4—48no—
497C2×D4—48no—
498C2×D4—42no—
499C2×D4—44no—
500C2×D4—42no—
501C2×D4—44no—
502C2×D4—84no—
503C2×D4—816no—
504C2×D4C22×D414yes—
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—22no—
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—24no—
526C22×C4—24no—
527C22×C4—24no—
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—48no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4—44no—
548C22×C4—44no—
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—48no—
562C22×C4—84no—
563C22×C4—816no—
564C22×C4#13714yes—
565C22×C4C22×D412yes—
566C22×C4C22×D412yes—
567C22×C4C22×D412yes—
568C22×C4C22×D412yes—
569C22×C4C22×D412yes—
570C22×C4C22×D411yescharacteristic
571C22×C4C22×D412yes—
572C22×C4C22×D412yes—
573C22×C4H(5,𝔽2)12yes—
574C22×C4H(5,𝔽2)12yes—
575C22×C4H(5,𝔽2)12yes—
576C22×C42−1+412yes—
577C22×C4C2511yescharacteristic
578Q16—416no—
579Q16—416no—
580SD16—416no—
581SD16—416no—
582M16—416no—
583C2×C8—28no—
584C2×C8—28no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—22no—
594C2×C8—22no—
595C2×C8—44no—
596C2×C8—44no—
597C2×C8C22×D414yes—
598C2×C8C22×D414yes—
599C4⋊C4—24no—
600C4⋊C4—24no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—48no—
608C4⋊C4—48no—
609C4⋊C4—48no—
610C4⋊C4—48no—
611C4⋊C4—48no—
612C4⋊C4—48no—
613C4⋊C4—48no—
614C4⋊C4—42no—
615C4⋊C4—42no—
616C4⋊C4—84no—
617C4⋊C4C22×D414yes—
618C4⋊C4C22×D414yes—
619C22⋊C4—28no—
620C22⋊C4—44no—
621C22⋊C4—48no—
622C22⋊C4—48no—
623C22⋊C4—48no—
624C22⋊C4—48no—
625C22⋊C4—48no—
626C22⋊C4—48no—
627C22⋊C4—48no—
628C42—24no—
629C42—24no—
630C42—22no—
631C42—22no—
632C42—22no—
633C42—22no—
634C42—48no—
635C23—22no—
636C23—22no—
637C23—24no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—44no—
644C23—48no—
645C23—42no—
646C23—42no—
647C23—44no—
648C23—44no—
649C23—44no—
650C23—44no—
651C23—48no—
652C23—44no—
653C23—48no—
654C23—44no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—84no—
660C23—84no—
661C23—84no—
662C23—84no—
663C23#53712yes—
664C23D4212yes—
665C23D4212yes—
666C23C2×#13712yes—
667C23#57512yes—
668C23#57712yes—
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—24no—
687D4—24no—
688D4—48no—
689D4—42no—
690D4—42no—
691D4—816no—
692C2×C4—22no—
693C2×C4—28no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
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—42no—
713C2×C4—42no—
714C2×C4—48no—
715C2×C4—44no—
716C2×C4—48no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—48no—
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—42no—
739C2×C4—42no—
740C2×C4—816no—
741C2×C4—84no—
742C2×C4—84no—
743C2×C4—84no—
744C2×C4—84no—
745C2×C4#53712yes—
746C2×C4#53714yes—
747C2×C4#53714yes—
748C2×C4D4212yes—
749C2×C4D4212yes—
750C2×C4D4214yes—
751C2×C4#56014yes—
752C2×C4C2×#13714yes—
753C2×C4C23×D411yescharacteristic
754C2×C4C23×D411yescharacteristic
755C2×C4C2×H(5,𝔽2)11yescharacteristic
756C2×C4C2×H(5,𝔽2)11yescharacteristic
757C2×C4C2×H(5,𝔽2)11yescharacteristic
758C2×C4C2×2−1+411yescharacteristic
759C8—24no—
760C8—24no—
761C8—42no—
762C8—42no—
763C22—42no—
764C22—42no—
765C22—44no—
766C22—42no—
767C22—44no—
768C22—42no—
769C22—42no—
770C22—44no—
771C22—42no—
772C22—42no—
773C22—82no—
774C22—82no—
775C22—88no—
776C22—816no—
777C22—82no—
778C22—82no—
779C22#267514yes—
780C22#325214yes—
781C22#325814yes—
782C22#326614yes—
783C22#326714yes—
784C22#327614yes—
785C22#327714yes—
786C22C2×#53711yescharacteristic
787C22C2×D4211yescharacteristic
788C22C2×D4211yescharacteristic
789C22C22×#13711yescharacteristic
790C22C2×#57511yescharacteristic
791C22C2×#57711yescharacteristic
792C22C2×#57811yescharacteristic
793C4—24no—
794C4—44no—
795C4—42no—
796C4—44no—
797C4—42no—
798C4—42no—
799C4—42no—
800C4—44no—
801C4—82no—
802C4—82no—
803C4—82no—
804C4—82no—
805C4#267514yes—
806C4C2×#53711yescharacteristic
807C4C2×#53711yescharacteristic
808C4C2×D4211yescharacteristic
809C4C2×#56011yescharacteristic
810C2—82no—
811C2—84no—
812C2#3085818yesdirect product factor
813C2C2×#267511yescharacteristic
814C2C2×#325211yescharacteristic
815C2C2×#325811yescharacteristic
816C2C2×#326611yescharacteristic
817C2C2×#326711yescharacteristic
818C2C2×#327611yescharacteristic
819C2C2×#327711yescharacteristic
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×#461C2semidirect
6. C2×#2429C2semidirect
7. #30858C2direct (N × H)
8. C2×#2068C2semidirect
9. C2×#2066C2semidirect
10. C2×#2016C2semidirect
11. C2×#2015C2semidirect
12. C2×#2001C2semidirect
14. C2×#1863C2semidirect
15. C2×#1864C2semidirect
16. C2×#1851C2semidirect
31. C2×#470C22semidirect
35. C2×#464C22semidirect
37. C2×#461C22semidirect
52. #2429C22semidirect
68. #2068C22semidirect
69. #2066C22semidirect
70. #2016C22semidirect
71. #2015C22semidirect
72. #2001C22semidirect
74. #1864C22semidirect
75. #1863C22semidirect
76. #1851C22semidirect
185. C2×#103D4semidirect
420. #103C2×D4semidirect
812. C2#30858direct (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×#4612
C2×#24272
C2×#24292
#308582
C2×#20682
C2×#20662
C2×#20162
C2×#20152
C2×#20012
C2×#20002
C2×#18632
C2×#18642
C2×#18512