Finite Group Databasebeta

← C2×#29900 #6433142

Subgroups — C2×#29900 #6433142

Order 512.

2632 conjugacy classes of subgroups.

The subgroup lattice has 807 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2616C211yesmaximal, characteristic
2C2×#2311C211yesmaximal, characteristic
3#29900C2116yesmaximal, direct product factor
4C2×#2076C211yesmaximal, characteristic, complemented
5C2×#2077C211yesmaximal, characteristic, complemented
6C2×#2077C211yesmaximal, characteristic, complemented
7C2×#2077C211yesmaximal, characteristic, complemented
8C2×#2036C211yesmaximal, characteristic, complemented
9C2×#2035C211yesmaximal, characteristic, complemented
10C2×#2035C211yesmaximal, characteristic, complemented
11C2×#2035C211yesmaximal, characteristic, complemented
12C2×#1873C211yesmaximal, characteristic, complemented
13C2×#1872C211yesmaximal, characteristic, complemented
14C2×#1854C211yesmaximal, characteristic, complemented
15C2×#1853C211yesmaximal, characteristic, complemented
16C2×#1780C211yesmaximal, characteristic
17C23×#41C2211yescharacteristic
18C22×C22⋊Q8C2211yescharacteristic
19C22×C22⋊Q8C2211yescharacteristic
20C22×C22⋊Q8C2211yescharacteristic
21C22×#117C2211yescharacteristic
22C23×C4⋊C4C2211yescharacteristic
23C22×#107C2211yescharacteristic
24C22×#106C2211yescharacteristic
25C22×#106C2211yescharacteristic
26C22×#106C2211yescharacteristic
27C22×#103C2211yescharacteristic
28C22×#103C2211yescharacteristic
29C22×#103C2211yescharacteristic
30C22×#103C2211yescharacteristic
31C22×C22⋊C8C2211yescharacteristic
32C22×C22⋊C8C2211yescharacteristic
33C22×C22⋊C8C2211yescharacteristic
34C22×C22⋊C8C2211yescharacteristic
35C22×C22⋊C8C2211yescharacteristic
36C22×C22⋊C8C2211yescharacteristic
37#2616—24no—
38#2616C2218yes—
39C2×#395—21no—
40C2×#394—21no—
41C2×#394—21no—
42C2×#394—21no—
43#2311—24no—
44#2311C2218yes—
45C2×#391—21no—
46C2×#390—21no—
47C2×#386—21no—
48C2×#386—21no—
49C2×#380C2211yescharacteristic
50C2×#380C2211yescharacteristic
51C2×#380C2211yescharacteristic
52C2×#380C2211yescharacteristic
53C2×#380C2211yescharacteristic
54C2×#380C2211yescharacteristic
55C2×#380C2211yescharacteristic
56#2077C2218yescomplemented
57#2077C2218yescomplemented
58#2077C2218yescomplemented
59#2076C2218yescomplemented
60#2036C2218yescomplemented
61#2035C2218yescomplemented
62#2035C2218yescomplemented
63#2035C2218yescomplemented
64#1873C2218yescomplemented
65#1872C2218yescomplemented
66#1854C2218yescomplemented
67#1853C2218yescomplemented
68#1780C2218yes—
69C2×#340C2211yescharacteristic
70C2×#340C2211yescharacteristic
71C2×#340C2211yescharacteristic
72C2×#340C2211yescharacteristic
73C2×#340C2211yescharacteristic
74C2×#340C2211yescharacteristic
75C2×#340C2211yescharacteristic
76C2×#340C2211yescharacteristic
77C22×#41—24no—
78C22×#41—24no—
79C22×#41—42no—
80C22×#41—42no—
81C22×#41—42no—
82C22×#41—42no—
83C22×#41D414yes—
84C22×#41C2314yes—
85C23×Q8D411yescharacteristic
86C23×Q8C2311yescharacteristic
87C23×D4D411yescharacteristic
88C23×D4D411yescharacteristic
89C23×D4D411yescharacteristic
90C24×C4—21no—
91C24×C4C2311yescharacteristic
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C23×C8C2311yescharacteristic
95C23×C8C2311yescharacteristic
96C23×C8C2311yescharacteristic
97C23×C8C2311yescharacteristic
98C2×C22⋊Q8—22no—
99C2×C22⋊Q8—22no—
100C2×C22⋊Q8—22no—
101C2×C22⋊Q8—24no—
102C2×C22⋊Q8—24no—
103C2×C22⋊Q8—42no—
104C2×C22⋊Q8—42no—
105C2×C22⋊Q8—42no—
106C2×C22⋊Q8—42no—
107C2×C22⋊Q8C2314yes—
108C2×C22⋊Q8C2314yes—
109C2×C22⋊Q8C2314yes—
110C2×#117—22no—
111C2×#117—42no—
112C2×#117—42no—
113C2×#117C2314yes—
114C22×C4⋊C4—22no—
115C22×C4⋊C4—21no—
116C22×C4⋊C4—21no—
117C22×C4⋊C4—21no—
118C22×C4⋊C4—21no—
119C22×C4⋊C4—42no—
120C22×C4⋊C4—42no—
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2314yes—
129C22×C22⋊C4—21no—
130C22×C22⋊C4—21no—
131C22×C22⋊C4—21no—
132C22×C22⋊C4—21no—
133C22×C22⋊C4—21no—
134C22×C22⋊C4—21no—
135C22×C22⋊C4—21no—
136C22×C22⋊C4—21no—
137C22×C22⋊C4—21no—
138C22×C22⋊C4—21no—
139C22×C22⋊C4—21no—
140C22×C42—21no—
141C2×#107—42no—
142C2×#107C2314yes—
143C2×#106—42no—
144C2×#106—42no—
145C2×#106—42no—
146C2×#106C2314yes—
147C2×#106C2314yes—
148C2×#106C2314yes—
149C2×#103—42no—
150C2×#103—42no—
151C2×#103—42no—
152C2×#103—42no—
153C2×#103C2314yes—
154C2×#103C2314yes—
155C2×#103C2314yes—
156C2×#103C2314yes—
157C2×C22⋊C8—24no—
158C2×C22⋊C8—24no—
159C2×C22⋊C8—42no—
160C2×C22⋊C8—42no—
161C2×C22⋊C8—42no—
162C2×C22⋊C8—42no—
163C2×C22⋊C8C2314yes—
164C2×C22⋊C8C2314yes—
165C2×C22⋊C8C2314yes—
166C2×C22⋊C8C2314yes—
167C2×C22⋊C8C2314yes—
168C2×C22⋊C8C2314yes—
169#395—28no—
170#394—28no—
171#394—28no—
172#394—28no—
173#391—28no—
174#390—28no—
175#386—28no—
176#386—28no—
177#380—22no—
178#380—22no—
179#380—22no—
180#380—22no—
181#380—22no—
182#380—22no—
183#380—22no—
184#380C2314yes—
185#380C2314yes—
186#380C2314yes—
187#380C2314yes—
188#380C2314yes—
189#380C2314yes—
190#380C2314yes—
191C2×#95—21no—
192C2×#95—21no—
193C2×#95—21no—
194C2×#95—21no—
195C2×#95—21no—
196C2×#95—21no—
197C2×#95—21no—
198#340C2314yes—
199#340C2314yes—
200#340C2314yes—
201#340C2314yes—
202#340C2314yes—
203#340C2314yes—
204#340C2314yes—
205#340C2314yes—
206C25C2×D411yescharacteristic
207C25C2×D411yescharacteristic
208C25C2×D411yescharacteristic
209C2×#41—216no—
210C2×#41—28no—
211C2×#41—28no—
212C2×#41—48no—
213C2×#41—48no—
214C2×#41—44no—
215C2×#41—44no—
216C2×#41—44no—
217C2×#41—44no—
218C2×#41—416no—
219C2×#41—416no—
220C2×#41—416no—
221C2×#41—416no—
222C22×Q8—24no—
223C22×Q8—21no—
224C22×Q8—22no—
225C22×Q8—22no—
226C22×Q8—22no—
227C22×Q8—22no—
228C22×Q8—22no—
229C22×Q8—22no—
230C22×Q8—42no—
231C22×Q8—42no—
232C22×Q8C2×D414yes—
233C22×Q8C2412yes—
234C22×D4—24no—
235C22×D4—24no—
236C22×D4—24no—
237C22×D4—42no—
238C22×D4—42no—
239C22×D4—42no—
240C22×D4—42no—
241C22×D4—42no—
242C22×D4—42no—
243C22×D4C2×D414yes—
244C22×D4C2×D414yes—
245C22×D4C2×D414yes—
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—21no—
263C23×C4—21no—
264C23×C4—21no—
265C23×C4—21no—
266C23×C4—21no—
267C23×C4—21no—
268C23×C4—21no—
269C23×C4—21no—
270C23×C4—24no—
271C23×C4—44no—
272C23×C4—82no—
273C23×C4—82no—
274C23×C4C2×D412yes—
275C23×C4C2×D412yes—
276C23×C4C2×D411yescharacteristic
277C23×C4C2×D411yescharacteristic
278C23×C4C2×D412yes—
279C23×C4C2×D411yescharacteristic
280C23×C4#4114yes—
281C23×C4#4114yes—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2411yescharacteristic
286C22×C8—22no—
287C22×C8—22no—
288C22×C8—22no—
289C22×C8—22no—
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×C8C2412yes—
299C22×C8C2412yes—
300C22×C8C2412yes—
301C22×C8C2412yes—
302C22⋊Q8—28no—
303C22⋊Q8—28no—
304C22⋊Q8—44no—
305C22⋊Q8—44no—
306C22⋊Q8—44no—
307C22⋊Q8—44no—
308C22⋊Q8—48no—
309C22⋊Q8—48no—
310C22⋊Q8—48no—
311#117—44no—
312#117—44no—
313#117—48no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—44no—
340C2×C4⋊C4—44no—
341C2×C4⋊C4—44no—
342C2×C4⋊C4—48no—
343C2×C4⋊C4—44no—
344C2×C4⋊C4—44no—
345C2×C4⋊C4—44no—
346C2×C4⋊C4C2412yes—
347C2×C4⋊C4C2412yes—
348C2×C4⋊C4C2412yes—
349C2×C4⋊C4C2412yes—
350C2×C4⋊C4C2412yes—
351C2×C4⋊C4C2412yes—
352C2×C4⋊C4C2412yes—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—44no—
365C2×C22⋊C4—44no—
366C2×C22⋊C4—44no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—82no—
369C2×C22⋊C4—82no—
370C2×C22⋊C4—82no—
371C2×C22⋊C4—82no—
372C2×C22⋊C4—82no—
373C2×C22⋊C4—82no—
374C2×C22⋊C4—82no—
375C2×C42—24no—
376C2×C42—44no—
377#107—44no—
378#106—44no—
379#106—44no—
380#106—44no—
381#103—44no—
382#103—44no—
383#103—44no—
384#103—44no—
385C22⋊C8—28no—
386C22⋊C8—28no—
387C22⋊C8—44no—
388C22⋊C8—44no—
389C22⋊C8—44no—
390C22⋊C8—44no—
391#95—24no—
392#95—24no—
393#95—24no—
394#95—24no—
395#95—24no—
396#95—24no—
397#95—24no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24#12314yes—
419C24C22×D412yes—
420C24C22×D412yes—
421C24C22×D412yes—
422C24C22×D411yescharacteristic
423#41—464no—
424#41—416no—
425#41—416no—
426#41—416no—
427#41—416no—
428C2×Q8—28no—
429C2×Q8—22no—
430C2×Q8—22no—
431C2×Q8—22no—
432C2×Q8—22no—
433C2×Q8—22no—
434C2×Q8—22no—
435C2×Q8—44no—
436C2×Q8—44no—
437C2×Q8—416no—
438C2×Q8—42no—
439C2×Q8—42no—
440C2×Q8—42no—
441C2×Q8—44no—
442C2×Q8—44no—
443C2×Q8—44no—
444C2×Q8—44no—
445C2×D4—28no—
446C2×D4—28no—
447C2×D4—28no—
448C2×D4—44no—
449C2×D4—44no—
450C2×D4—44no—
451C2×D4—44no—
452C2×D4—44no—
453C2×D4—44no—
454C2×D4—416no—
455C2×D4—416no—
456C2×D4—416no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—28no—
462C22×C4—28no—
463C22×C4—28no—
464C22×C4—28no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—24no—
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—44no—
502C22×C4—44no—
503C22×C4—44no—
504C22×C4—44no—
505C22×C4—44no—
506C22×C4—44no—
507C22×C4—44no—
508C22×C4—44no—
509C22×C4—48no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
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—42no—
533C22×C4—42no—
534C22×C4—84no—
535C22×C4—84no—
536C22×C4—816no—
537C22×C4#12314yes—
538C22×C4#12318yes—
539C22×C4C22×D412yes—
540C22×C4C22×D412yes—
541C22×C4C22×D412yes—
542C22×C4C22×D411yescharacteristic
543C22×C4C2×#4114yes—
544C22×C4C2×#4114yes—
545C22×C4C2×#4112yes—
546C22×C4C2×#4112yes—
547C22×C4H(5,𝔽2)12yes—
548C22×C4H(5,𝔽2)12yes—
549C22×C4H(5,𝔽2)12yes—
550C22×C4H(5,𝔽2)12yes—
551C22×C4C2511yescharacteristic
552C2×C8—22no—
553C2×C8—22no—
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—22no—
557C2×C8—22no—
558C2×C8—22no—
559C2×C8—22no—
560C2×C8—22no—
561C2×C8—22no—
562C2×C8—22no—
563C2×C8—22no—
564C2×C8—44no—
565C2×C8—44no—
566C2×C8—44no—
567C2×C8—44no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—22no—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—48no—
583C4⋊C4—48no—
584C4⋊C4—48no—
585C4⋊C4—42no—
586C4⋊C4—48no—
587C4⋊C4—42no—
588C4⋊C4—42no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C22⋊C4—48no—
594C22⋊C4—48no—
595C22⋊C4—48no—
596C22⋊C4—48no—
597C22⋊C4—84no—
598C22⋊C4—84no—
599C22⋊C4—84no—
600C22⋊C4—84no—
601C22⋊C4—84no—
602C22⋊C4—84no—
603C22⋊C4—84no—
604C42—48no—
605C23—28no—
606C23—28no—
607C23—28no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—44no—
629C23—44no—
630C23—44no—
631C23—44no—
632C23—44no—
633C23—44no—
634C23—44no—
635C23—44no—
636C23—44no—
637C23—44no—
638C23—44no—
639C23—44no—
640C23—44no—
641C23—44no—
642C23—44no—
643C23—44no—
644C23—44no—
645C23—44no—
646C23C2×#12314yes—
647C23C2×#12312yes—
648C23#53412yes—
649C23#53412yes—
650C23#57712yes—
651C23#57712yes—
652C23#57712yes—
653C23#57812yes—
654C23C23×D411yescharacteristic
655Q8—416no—
656Q8—42no—
657Q8—42no—
658Q8—42no—
659Q8—42no—
660Q8—84no—
661D4—416no—
662D4—416no—
663D4—416no—
664C2×C4—28no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—216no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—44no—
679C2×C4—44no—
680C2×C4—48no—
681C2×C4—48no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—816no—
715C2×C4—84no—
716C2×C4—84no—
717C2×C4—84no—
718C2×C4—84no—
719C2×C4—84no—
720C2×C4—84no—
721C2×C4—84no—
722C2×C4—84no—
723C2×C4C2×#12314yes—
724C2×C4C2×#12312yes—
725C2×C4#53412yes—
726C2×C4#53412yes—
727C2×C4#53814yes—
728C2×C4#53814yes—
729C2×C4#53814yes—
730C2×C4#53814yes—
731C2×C4C22×#4111yescharacteristic
732C2×C4C22×#4111yescharacteristic
733C2×C4C2×H(5,𝔽2)11yescharacteristic
734C2×C4C2×H(5,𝔽2)11yescharacteristic
735C2×C4C2×H(5,𝔽2)11yescharacteristic
736C2×C4C2×H(5,𝔽2)11yescharacteristic
737C8—42no—
738C8—42no—
739C8—42no—
740C8—42no—
741C22—24no—
742C22—24no—
743C22—24no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—416no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—88no—
764C22—88no—
765C22#262214yes—
766C22#309714yes—
767C22#309914yes—
768C22#320014yes—
769C22#320114yes—
770C22#320114yes—
771C22#320414yes—
772C22C22×#12311yescharacteristic
773C22C2×#53411yescharacteristic
774C22C2×#53411yescharacteristic
775C22C2×#57711yescharacteristic
776C22C2×#57711yescharacteristic
777C22C2×#57711yescharacteristic
778C22C2×#57811yescharacteristic
779C4—24no—
780C4—42no—
781C4—42no—
782C4—82no—
783C4—82no—
784C4—82no—
785C4—82no—
786C4—82no—
787C4—82no—
788C4—82no—
789C4—82no—
790C4#262214yes—
791C4C2×#53811yescharacteristic
792C4C2×#53811yescharacteristic
793C4C2×#53811yescharacteristic
794C4C2×#53811yescharacteristic
795C2—44no—
796C2—82no—
797C2—82no—
798C2#2990018yesdirect product factor
799C2C2×#262211yescharacteristic
800C2C2×#309711yescharacteristic
801C2C2×#309911yescharacteristic
802C2C2×#320011yescharacteristic
803C2C2×#320111yescharacteristic
804C2C2×#320111yescharacteristic
805C2C2×#320411yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C23×#41 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #29900C2direct (N × H)
4. C2×#2076C2semidirect
5. C2×#2077C2semidirect
6. C2×#2077C2semidirect
7. C2×#2077C2semidirect
8. C2×#2036C2semidirect
9. C2×#2035C2semidirect
10. C2×#2035C2semidirect
11. C2×#2035C2semidirect
12. C2×#1873C2semidirect
13. C2×#1872C2semidirect
14. C2×#1854C2semidirect
15. C2×#1853C2semidirect
56. #2077C22semidirect
57. #2077C22semidirect
58. #2077C22semidirect
59. #2076C22semidirect
60. #2036C22semidirect
61. #2035C22semidirect
62. #2035C22semidirect
63. #2035C22semidirect
64. #1873C22semidirect
65. #1872C22semidirect
66. #1854C22semidirect
67. #1853C22semidirect
798. C2#29900direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#26162
C2×#23112
#299002
C2×#20762
C2×#20772
C2×#20362
C2×#20352
C2×#18732
C2×#18722
C2×#18542
C2×#18532
C2×#17802