Finite Group Databasebeta

← C2×#23584 #6432021

Subgroups — C2×#23584 #6432021

Order 512.

3590 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#541C211yesmaximal, characteristic, complemented
2C22×#440C211yesmaximal, characteristic, complemented
3C22×C4×SD16C211yesmaximal, characteristic, complemented
4C2×#2324C211yesmaximal, characteristic
5#23584C2116yesmaximal, direct product factor
6C2×#2059C211yesmaximal, characteristic, complemented
7C2×#2043C211yesmaximal, characteristic, complemented
8C2×#2036C211yesmaximal, characteristic, complemented
9C2×#2035C211yesmaximal, characteristic, complemented
10C2×#2025C211yesmaximal, characteristic, complemented
11C2×#2013C211yesmaximal, characteristic, complemented
12C2×#2000C211yesmaximal, characteristic
13C2×#2000C211yesmaximal, characteristic
14C2×#1763C211yesmaximal, characteristic, complemented
15C2×C4×#103C211yesmaximal, characteristic, complemented
16C2×#1750C211yesmaximal, characteristic, complemented
17C23×SD16C2211yescharacteristic
18C23×SD16C2211yescharacteristic
19C2×#541—28no—
20C2×#541—28no—
21C2×#541—24no—
22C2×#541C2218yescomplemented
23C22×C4⋊Q8C2211yescharacteristic
24C22×#126—21no—
25C22×#126—21no—
26C22×#125—21no—
27C22×#125—21no—
28C22×#125C2211yescharacteristic
29C22×C22⋊Q8C2211yescharacteristic
30C22×C22⋊Q8C2211yescharacteristic
31C22×#121C2211yescharacteristic
32C22×C4×Q8C2211yescharacteristic
33C22×C4×Q8C2211yescharacteristic
34C22×C4×D4C2211yescharacteristic
35C22×#117C2211yescharacteristic
36C2×#440—28no—
37C2×#440C2218yescomplemented
38C2×C4×SD16—28no—
39C2×C4×SD16C2218yescomplemented
40C22×#107C2211yescharacteristic
41C22×#106C2211yescharacteristic
42C22×#103C2211yescharacteristic
43C22×#103C2211yescharacteristic
44C22×#103C2211yescharacteristic
45C22×#103C2211yescharacteristic
46C22×#103C2211yescharacteristic
47C22×#103C2211yescharacteristic
48C22×#102C2211yescharacteristic
49C22×#102C2211yescharacteristic
50C22×C22⋊C8C2211yescharacteristic
51C22×C22⋊C8C2211yescharacteristic
52C22×#97C2211yescharacteristic
53C22×C4×C8C2211yescharacteristic
54#2324—24no—
55#2324C2218yes—
56C2×#390—21no—
57C2×#390C2211yescharacteristic
58C2×#389C2211yescharacteristic
59C2×#388—21no—
60C2×#386—21no—
61C2×#385—21no—
62C2×#380C2211yescharacteristic
63C2×C4×C4⋊C4C2211yescharacteristic
64#2059C2218yescomplemented
65#2043C2218yescomplemented
66#2036C2218yescomplemented
67#2035C2218yescomplemented
68#2025C2218yescomplemented
69#2013C2218yescomplemented
70#2000C2218yes—
71#2000C2218yes—
72#1763C2218yescomplemented
73C4×#103C2218yescomplemented
74#1750C2218yescomplemented
75C2×#340C2211yescharacteristic
76C2×#340C2211yescharacteristic
77C2×#340C2211yescharacteristic
78C2×#340C2211yescharacteristic
79C2×#336C2211yescharacteristic
80C2×#336C2211yescharacteristic
81C23×Q8C2311yescharacteristic
82C23×Q8C2311yescharacteristic
83C23×D4—21no—
84C23×D4C2311yescharacteristic
85C24×C4—21no—
86C24×C4C2311yescharacteristic
87C22×SD16—24no—
88C22×SD16—24no—
89C22×SD16—24no—
90C22×SD16—24no—
91C22×SD16—24no—
92C22×SD16—24no—
93C22×SD16C2314yes—
94C22×SD16C2314yes—
95C23×C8C2311yescharacteristic
96C23×C8C2311yescharacteristic
97C23×C8C2311yescharacteristic
98C23×C8C2311yescharacteristic
99#541—264no—
100#541—232no—
101#541—232no—
102C2×C4⋊Q8—24no—
103C2×C4⋊Q8—24no—
104C2×C4⋊Q8—22no—
105C2×C4⋊Q8C2314yes—
106C2×#126—216no—
107C2×#126—216no—
108C2×#126—28no—
109C2×#126—28no—
110C2×#125—216no—
111C2×#125—216no—
112C2×#125—28no—
113C2×#125—28no—
114C2×#125—24no—
115C2×#125—24no—
116C2×#125—22no—
117C2×#125C2314yes—
118C2×C22⋊Q8—24no—
119C2×C22⋊Q8—24no—
120C2×C22⋊Q8—22no—
121C2×C22⋊Q8—22no—
122C2×C22⋊Q8—24no—
123C2×C22⋊Q8—24no—
124C2×C22⋊Q8C2314yes—
125C2×C22⋊Q8C2314yes—
126C2×#121—24no—
127C2×#121—22no—
128C2×#121—24no—
129C2×#121C2314yes—
130C2×C4×Q8—24no—
131C2×C4×Q8—24no—
132C2×C4×Q8—22no—
133C2×C4×Q8—22no—
134C2×C4×Q8D418yescomplemented
135C2×C4×Q8D418yescomplemented
136C2×C4×Q8C2314yes—
137C2×C4×Q8C2314yes—
138C2×C4×D4—22no—
139C2×C4×D4—24no—
140C2×C4×D4—24no—
141C2×C4×D4C2314yes—
142C2×#117—24no—
143C2×#117—24no—
144C2×#117D414yes—
145C2×#117C2314yes—
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⋊C4—21no—
153C22×C4⋊C4—21no—
154C22×C4⋊C4—21no—
155C22×C4⋊C4D411yescharacteristic
156C22×C4⋊C4D411yescharacteristic
157C22×C4⋊C4C2311yescharacteristic
158C22×C4⋊C4C2311yescharacteristic
159C22×C4⋊C4C2311yescharacteristic
160C22×C4⋊C4C2311yescharacteristic
161C22×C4⋊C4C2311yescharacteristic
162C22×C22⋊C4—21no—
163C22×C22⋊C4—21no—
164C22×C22⋊C4—21no—
165C22×C22⋊C4—21no—
166C22×C22⋊C4—21no—
167C22×C22⋊C4—21no—
168C22×C22⋊C4—21no—
169C22×C22⋊C4D411yescharacteristic
170C22×C22⋊C4D411yescharacteristic
171C22×C42—21no—
172C22×C42—21no—
173C22×C42—21no—
174C22×C42C2311yescharacteristic
175C22×C42C2311yescharacteristic
176#440—232no—
177C4×SD16—232no—
178C2×#107—24no—
179C2×#107C2314yes—
180C2×#106—24no—
181C2×#106C2314yes—
182C2×#103—24no—
183C2×#103—24no—
184C2×#103—24no—
185C2×#103—24no—
186C2×#103—24no—
187C2×#103—24no—
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—24no—
199C2×C22⋊C8—24no—
200C2×C22⋊C8C2314yes—
201C2×C22⋊C8C2314yes—
202C2×#97—24no—
203C2×#97C2314yes—
204C2×C4×C8—24no—
205C2×C4×C8C2314yes—
206#390—28no—
207#390—22no—
208#390C2314yes—
209#389—22no—
210#389C2314yes—
211#388—28no—
212#386—28no—
213#385—28no—
214#380—22no—
215#380C2314yes—
216C4×C4⋊C4—22no—
217C4×C4⋊C4C2314yes—
218C2×#95—21no—
219C2×#95—21no—
220C2×#95—21no—
221#340C2314yes—
222#340C2314yes—
223#340C2314yes—
224#340C2314yes—
225#336C2314yes—
226#336C2314yes—
227C25—21no—
228C25C2×D411yescharacteristic
229C22×Q8—22no—
230C22×Q8—22no—
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×Q8C2×D414yes—
242C22×Q8C2×D414yes—
243C22×Q8C2412yes—
244C22×Q8C2412yes—
245C22×D4—28no—
246C22×D4—24no—
247C22×D4—22no—
248C22×D4—22no—
249C22×D4—21no—
250C22×D4—22no—
251C22×D4—22no—
252C22×D4—22no—
253C22×D4—82no—
254C22×D4—82no—
255C22×D4#4114yes—
256C22×D4C2412yes—
257C23×C4—21no—
258C23×C4—21no—
259C23×C4—21no—
260C23×C4—21no—
261C23×C4—21no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—21no—
269C23×C4—21no—
270C23×C4—24no—
271C23×C4—44no—
272C23×C4—82no—
273C23×C4—82no—
274C23×C4C2×D412yes—
275C23×C4C2×D411yescharacteristic
276C23×C4C2×D411yescharacteristic
277C23×C4C2×D411yescharacteristic
278C23×C4C2×D411yescharacteristic
279C23×C4C2×D411yescharacteristic
280C23×C4C2412yes—
281C23×C4C2411yescharacteristic
282C2×SD16—232no—
283C2×SD16—232no—
284C2×SD16—28no—
285C2×SD16—28no—
286C2×SD16—28no—
287C2×SD16—28no—
288C2×SD16—28no—
289C2×SD16—28no—
290C22×C8—22no—
291C22×C8—22no—
292C22×C8—22no—
293C22×C8—22no—
294C22×C8—22no—
295C22×C8—22no—
296C22×C8—22no—
297C22×C8—22no—
298C22×C8—22no—
299C22×C8—22no—
300C22×C8#4114yes—
301C22×C8#4114yes—
302C22×C8C2412yes—
303C22×C8C2412yes—
304C22×C8C2412yes—
305C22×C8C2412yes—
306C4⋊Q8—216no—
307C4⋊Q8—28no—
308C4⋊Q8—28no—
309#126—264no—
310#126—264no—
311#125—264no—
312#125—264no—
313#125—216no—
314#125—28no—
315#125—28no—
316C22⋊Q8—216no—
317C22⋊Q8—216no—
318C22⋊Q8—28no—
319C22⋊Q8—28no—
320C22⋊Q8—28no—
321C22⋊Q8—28no—
322#121—216no—
323#121—28no—
324#121—28no—
325C4×Q8—216no—
326C4×Q8—216no—
327C4×Q8—28no—
328C4×Q8—28no—
329C4×Q8C2×D4116yescomplemented
330C4×Q8C2×D4116yescomplemented
331C4×D4—28no—
332C4×D4—28no—
333C4×D4—48no—
334#117—216no—
335#117—28no—
336#117—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—24no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—24no—
368C2×C4⋊C4—82no—
369C2×C4⋊C4C2×D414yes—
370C2×C4⋊C4C2×D414yes—
371C2×C4⋊C4C2×D414yes—
372C2×C4⋊C4C2×D414yes—
373C2×C4⋊C4#4114yes—
374C2×C4⋊C4C2412yes—
375C2×C4⋊C4C2412yes—
376C2×C4⋊C4C2412yes—
377C2×C4⋊C4C2412yes—
378C2×C4⋊C4C2412yes—
379C2×C22⋊C4—28no—
380C2×C22⋊C4—28no—
381C2×C22⋊C4—28no—
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—24no—
391C2×C22⋊C4—44no—
392C2×C22⋊C4—82no—
393C2×C22⋊C4—82no—
394C2×C22⋊C4—82no—
395C2×C22⋊C4C2×D414yes—
396C2×C22⋊C4C2×D414yes—
397C2×C42—28no—
398C2×C42—28no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—24no—
402C2×C42—24no—
403C2×C42—24no—
404C2×C42—82no—
405C2×C42C2×D412yes—
406C2×C42C2×D412yes—
407C2×C42C2×D414yes—
408C2×C42C2×D414yes—
409C2×C42C2412yes—
410C2×C42C2412yes—
411#107—28no—
412#106—28no—
413#103—28no—
414#103—28no—
415#103—28no—
416#103—28no—
417#103—28no—
418#103—28no—
419#102—28no—
420#102—28no—
421C22⋊C8—28no—
422C22⋊C8—28no—
423#97—28no—
424C4×C8—28no—
425#95—24no—
426#95—24no—
427#95—24no—
428C24—22no—
429C24—24no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—42no—
438C24—42no—
439C24—42no—
440C24—42no—
441C24—42no—
442C24—42no—
443C24C22×D412yes—
444C24C22×D411yescharacteristic
445C2×Q8—24no—
446C2×Q8—24no—
447C2×Q8—22no—
448C2×Q8—22no—
449C2×Q8—28no—
450C2×Q8—28no—
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—44no—
462C2×Q8—44no—
463C2×Q8—42no—
464C2×Q8—42no—
465C2×Q8—44no—
466C2×Q8—44no—
467C2×Q8—42no—
468C2×Q8—42no—
469C2×Q8C22×D414yes—
470C2×Q8C22×D414yes—
471C2×D4—216no—
472C2×D4—28no—
473C2×D4—28no—
474C2×D4—24no—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—22no—
479C2×D4—22no—
480C2×D4—42no—
481C2×D4—42no—
482C2×D4—44no—
483C2×D4—44no—
484C2×D4—84no—
485C2×D4—84no—
486C2×D4—816no—
487C2×D4C2×#4114yes—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—24no—
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—24no—
512C22×C4—24no—
513C22×C4—24no—
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—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—48no—
543C22×C4—84no—
544C22×C4—84no—
545C22×C4—816no—
546C22×C4#12014yes—
547C22×C4#12014yes—
548C22×C4C22×D412yes—
549C22×C4C22×D412yes—
550C22×C4C22×D412yes—
551C22×C4C22×D412yes—
552C22×C4C22×D412yes—
553C22×C4C22×D411yescharacteristic
554C22×C4C22×D412yes—
555C22×C4C22×D412yes—
556C22×C4C2×#4112yes—
557C22×C4C2×#4112yes—
558C22×C4C2×#4112yes—
559C22×C4C2×#4112yes—
560C22×C4C2511yescharacteristic
561SD16—232no—
562SD16—232no—
563C2×C8—28no—
564C2×C8—28no—
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—22no—
572C2×C8—22no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—44no—
576C2×C8—44no—
577C2×C8C2×#4114yes—
578C2×C8C2×#4114yes—
579C4⋊C4—216no—
580C4⋊C4—216no—
581C4⋊C4—216no—
582C4⋊C4—216no—
583C4⋊C4—216no—
584C4⋊C4—216no—
585C4⋊C4—216no—
586C4⋊C4—216no—
587C4⋊C4—28no—
588C4⋊C4—28no—
589C4⋊C4—24no—
590C4⋊C4—24no—
591C4⋊C4—24no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4—84no—
602C4⋊C4C22×D414yes—
603C4⋊C4C22×D414yes—
604C4⋊C4C2×#4114yes—
605C22⋊C4—216no—
606C22⋊C4—216no—
607C22⋊C4—216no—
608C22⋊C4—28no—
609C22⋊C4—28no—
610C22⋊C4—48no—
611C22⋊C4—84no—
612C22⋊C4—84no—
613C22⋊C4—84no—
614C42—216no—
615C42—216no—
616C42—24no—
617C42—22no—
618C42—22no—
619C42—84no—
620C42#12018yes—
621C42C22×D414yes—
622C42C22×D414yes—
623C23—22no—
624C23—24no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—44no—
632C23—48no—
633C23—44no—
634C23—48no—
635C23—44no—
636C23—48no—
637C23—44no—
638C23—42no—
639C23—44no—
640C23—42no—
641C23—44no—
642C23—44no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—84no—
648C23—84no—
649C23—84no—
650C23—84no—
651C23C2×#12012yes—
652C23#52512yes—
653C23#53212yes—
654C23#57712yes—
655C23#57712yes—
656C23#57712yes—
657C23#57812yes—
658C23C23×D411yescharacteristic
659Q8—24no—
660Q8—24no—
661Q8—24no—
662Q8—24no—
663Q8—48no—
664Q8—48no—
665Q8—42no—
666Q8—42no—
667Q8—42no—
668Q8—42no—
669D4—24no—
670D4—24no—
671D4—48no—
672D4—42no—
673D4—42no—
674D4—816no—
675C2×C4—28no—
676C2×C4—28no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—24no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—48no—
696C2×C4—44no—
697C2×C4—48no—
698C2×C4—48no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—44no—
704C2×C4—48no—
705C2×C4—44no—
706C2×C4—48no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—48no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—816no—
725C2×C4—84no—
726C2×C4—84no—
727C2×C4C2×#12014yes—
728C2×C4C2×#12014yes—
729C2×C4C2×#12012yes—
730C2×C4#52512yes—
731C2×C4#52514yes—
732C2×C4#52514yes—
733C2×C4#53212yes—
734C2×C4#53214yes—
735C2×C4#53214yes—
736C2×C4C23×D411yescharacteristic
737C2×C4C23×D411yescharacteristic
738C2×C4C22×#4111yescharacteristic
739C2×C4C22×#4111yescharacteristic
740C2×C4C22×#4111yescharacteristic
741C2×C4C22×#4111yescharacteristic
742C8—24no—
743C8—24no—
744C8—42no—
745C8—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—44no—
750C22—42no—
751C22—44no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—44no—
756C22—82no—
757C22—82no—
758C22—88no—
759C22—816no—
760C22—82no—
761C22—82no—
762C22#238814yes—
763C22#301014yes—
764C22#301314yes—
765C22#312014yes—
766C22#312314yes—
767C22#317414yes—
768C22#317814yes—
769C22C22×#12011yescharacteristic
770C22C2×#52511yescharacteristic
771C22C2×#53211yescharacteristic
772C22C2×#57711yescharacteristic
773C22C2×#57711yescharacteristic
774C22C2×#57711yescharacteristic
775C22C2×#57811yescharacteristic
776C4—24no—
777C4—24no—
778C4—44no—
779C4—42no—
780C4—44no—
781C4—42no—
782C4—44no—
783C4—42no—
784C4—44no—
785C4—44no—
786C4—82no—
787C4—82no—
788C4#238814yes—
789C4C2×#52511yescharacteristic
790C4C2×#52511yescharacteristic
791C4C2×#53211yescharacteristic
792C4C2×#53211yescharacteristic
793C2—82no—
794C2—84no—
795C2#2358418yesdirect product factor
796C2C2×#238811yescharacteristic
797C2C2×#301011yescharacteristic
798C2C2×#301311yescharacteristic
799C2C2×#312011yescharacteristic
800C2C2×#312311yescharacteristic
801C2C2×#317411yescharacteristic
802C2C2×#317811yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#541C2semidirect
2. C22×#440C2semidirect
3. C22×C4×SD16C2semidirect
5. #23584C2direct (N × H)
6. C2×#2059C2semidirect
7. C2×#2043C2semidirect
8. C2×#2036C2semidirect
9. C2×#2035C2semidirect
10. C2×#2025C2semidirect
11. C2×#2013C2semidirect
14. C2×#1763C2semidirect
15. C2×C4×#103C2semidirect
16. C2×#1750C2semidirect
22. C2×#541C22semidirect
37. C2×#440C22semidirect
39. C2×C4×SD16C22semidirect
64. #2059C22semidirect
65. #2043C22semidirect
66. #2036C22semidirect
67. #2035C22semidirect
68. #2025C22semidirect
69. #2013C22semidirect
72. #1763C22semidirect
73. C4×#103C22semidirect
74. #1750C22semidirect
134. C2×C4×Q8D4semidirect
135. C2×C4×Q8D4semidirect
329. C4×Q8C2×D4semidirect
330. C4×Q8C2×D4semidirect
795. C2#23584direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#5412
C22×#4402
C22×C4×SD162
C2×#23242
#235842
C2×#20592
C2×#20432
C2×#20362
C2×#20352
C2×#20252
C2×#20132
C2×#20002
C2×#17632
C2×C4×#1032
C2×#17502