Finite Group Databasebeta

← C2×#30464 #7500784

Subgroups — C2×#30464 #7500784

Order 512.

3870 conjugacy classes of subgroups.

The subgroup lattice has 915 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#497C211yesmaximal, characteristic, complemented
2C22×#464C211yesmaximal, characteristic, complemented
3C22×#450C211yesmaximal, characteristic
4C22×#450C211yesmaximal, characteristic
5C2×#2435C211yesmaximal, characteristic
6C2×#2429C211yesmaximal, characteristic, complemented
7#30464C2116yesmaximal, direct product factor
8C2×#2055C211yesmaximal, characteristic, complemented
9C2×#2042C211yesmaximal, characteristic, complemented
10C2×#2013C211yesmaximal, characteristic, complemented
11C2×#2015C211yesmaximal, characteristic, complemented
12C2×#2001C211yesmaximal, characteristic, complemented
13C2×#2001C211yesmaximal, characteristic, complemented
14C2×#1936C211yesmaximal, characteristic, complemented
15C2×#1924C211yesmaximal, characteristic, complemented
16C2×#1880C211yesmaximal, characteristic, complemented
17C24×D4C2211yescharacteristic
18C23×Q16C2211yescharacteristic, complemented
19C23×Q16C2211yescharacteristic, complemented
20C23×SD16C2211yescharacteristic
21C23×SD16C2211yescharacteristic
22C23×SD16C2211yescharacteristic
23C23×SD16C2211yescharacteristic
24C22×C4⋊Q8C2211yescharacteristic, complemented
25C22×#124C2211yescharacteristic
26C22×#124C2211yescharacteristic
27C22×C22⋊Q8C2211yescharacteristic
28C22×C22⋊Q8C2211yescharacteristic
29C22×C22⋊Q8C2211yescharacteristic
30C22×C4×Q8C2211yescharacteristic, complemented
31C2×#497—28no—
32C2×#497C2218yescomplemented
33C2×#464—28no—
34C2×#464C2218yescomplemented
35C2×#450—28no—
36C2×#450—28no—
37C2×#450C2218yes—
38C2×#450C2218yes—
39C22×C4⋊C8C2211yescharacteristic, complemented
40C22×#103C2211yescharacteristic, complemented
41C22×#103C2211yescharacteristic, complemented
42C22×#103C2211yescharacteristic, complemented
43C22×#103C2211yescharacteristic, complemented
44C22×#102C2211yescharacteristic
45C22×#102C2211yescharacteristic
46C22×#102C2211yescharacteristic
47C22×#102C2211yescharacteristic
48C22×C22⋊C8C2211yescharacteristic
49C22×C22⋊C8C2211yescharacteristic
50C22×#97C2211yescharacteristic, complemented
51#2435—24no—
52#2435C2218yes—
53#2429—24no—
54#2429C2218yescomplemented
55C2×#398—21no—
56C2×#396—21no—
57C2×#394—21no—
58C2×#394—21no—
59C2×#391C2211yescharacteristic, complemented
60C2×#390C2211yescharacteristic
61C2×#390C2211yescharacteristic
62C2×#389—21no—
63C2×#389C2211yescharacteristic, complemented
64C2×#388—21no—
65C2×#379—21no—
66C2×#379—21no—
67C2×C4×C22⋊C4C2211yescharacteristic
68#2055C2218yescomplemented
69#2042C2218yescomplemented
70#2015C2218yescomplemented
71#2013C2218yescomplemented
72#2001C2218yescomplemented
73#2001C2218yescomplemented
74#1936C2218yescomplemented
75#1924C2218yescomplemented
76#1880C2218yescomplemented
77C2×#340C2211yescharacteristic, complemented
78C2×#340C2211yescharacteristic, complemented
79C2×#336C2211yescharacteristic, complemented
80C2×#336C2211yescharacteristic, complemented
81C26—21no—
82C23×Q8C2311yescharacteristic
83C23×Q8C2311yescharacteristic
84C23×Q8C2311yescharacteristic
85C23×D4—24no—
86C23×D4—24no—
87C23×D4—21no—
88C23×D4—22no—
89C23×D4—42no—
90C23×D4—42no—
91C23×D4—42no—
92C23×D4—42no—
93C23×D4C2311yescharacteristic
94C23×D4C2311yescharacteristic
95C23×D4C2314yes—
96C24×C4C2311yescharacteristic
97C22×Q16—24no—
98C22×Q16—24no—
99C22×Q16—24no—
100C22×Q16—42no—
101C22×Q16—42no—
102C22×Q16—42no—
103C22×Q16C2314yescomplemented
104C22×Q16C2314yescomplemented
105C22×SD16—24no—
106C22×SD16—24no—
107C22×SD16—24no—
108C22×SD16—24no—
109C22×SD16—24no—
110C22×SD16—42no—
111C22×SD16—42no—
112C22×SD16—42no—
113C22×SD16—42no—
114C22×SD16—42no—
115C22×SD16—42no—
116C22×SD16D418yes—
117C22×SD16C2314yes—
118C22×SD16C2314yes—
119C22×SD16C2314yes—
120C22×SD16C2314yes—
121C23×C8C2311yescharacteristic
122C23×C8C2311yescharacteristic
123C23×C8C2311yescharacteristic
124C23×C8C2311yescharacteristic
125C2×C4⋊Q8—24no—
126C2×C4⋊Q8—22no—
127C2×C4⋊Q8—42no—
128C2×C4⋊Q8C2314yescomplemented
129C2×#124—24no—
130C2×#124—24no—
131C2×#124—22no—
132C2×#124—22no—
133C2×#124—42no—
134C2×#124—42no—
135C2×#124C2314yes—
136C2×#124C2314yes—
137C2×C22⋊Q8—22no—
138C2×C22⋊Q8—22no—
139C2×C22⋊Q8—22no—
140C2×C22⋊Q8—24no—
141C2×C22⋊Q8—24no—
142C2×C22⋊Q8—42no—
143C2×C22⋊Q8—42no—
144C2×C22⋊Q8—42no—
145C2×C22⋊Q8—42no—
146C2×C22⋊Q8C2314yes—
147C2×C22⋊Q8C2314yes—
148C2×C22⋊Q8C2314yes—
149C2×C4×Q8—22no—
150C2×C4×Q8—24no—
151C2×C4×Q8—42no—
152C2×C4×Q8C2314yescomplemented
153C22×C4⋊C4—21no—
154C22×C4⋊C4—21no—
155C22×C4⋊C4—21no—
156C22×C4⋊C4—21no—
157C22×C4⋊C4—21no—
158C22×C4⋊C4—21no—
159C22×C4⋊C4—21no—
160C22×C4⋊C4C2311yescharacteristic
161C22×C4⋊C4C2311yescharacteristic
162C22×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
170C22×C22⋊C4—21no—
171C22×C22⋊C4—21no—
172C22×C22⋊C4—21no—
173C22×C22⋊C4—21no—
174C22×C22⋊C4D411yescharacteristic
175C22×C22⋊C4D411yescharacteristic
176C22×C42—21no—
177C22×C42C2311yescharacteristic
178C22×C42C2311yescharacteristic
179#497—232no—
180#464—232no—
181#450—232no—
182#450—232no—
183C2×C4⋊C8—24no—
184C2×C4⋊C8C2314yescomplemented
185C2×#103—24no—
186C2×#103—42no—
187C2×#103—42no—
188C2×#103—42no—
189C2×#103C2314yescomplemented
190C2×#103C2314yescomplemented
191C2×#103C2314yescomplemented
192C2×#103C2314yescomplemented
193C2×#102—24no—
194C2×#102—24no—
195C2×#102—24no—
196C2×#102D418yes—
197C2×#102C2314yes—
198C2×#102C2314yes—
199C2×#102C2314yes—
200C2×#102C2314yes—
201C2×C22⋊C8—24no—
202C2×C22⋊C8—24no—
203C2×C22⋊C8C2314yes—
204C2×C22⋊C8C2314yes—
205C2×#97—24no—
206C2×#97C2314yescomplemented
207#398—28no—
208#396—28no—
209#394—28no—
210#394—28no—
211#391—22no—
212#391C2314yescomplemented
213#390—22no—
214#390—22no—
215#390C2314yes—
216#390C2314yes—
217#389—22no—
218#389—28no—
219#389C2314yescomplemented
220#388—28no—
221#379—28no—
222#379—28no—
223C4×C22⋊C4D414yes—
224C4×C22⋊C4C2314yes—
225C2×#95—21no—
226C2×#95—21no—
227C2×#95—21no—
228C2×#95D411yescharacteristic
229C2×#95D411yescharacteristic
230#340C2314yescomplemented
231#340C2314yescomplemented
232#336C2314yescomplemented
233#336C2314yescomplemented
234C25—21no—
235C25—21no—
236C25—24no—
237C25—44no—
238C25—44no—
239C25—44no—
240C25—44no—
241C25—44no—
242C25—82no—
243C25—82no—
244C25C2×D411yescharacteristic
245C22×Q8—21no—
246C22×Q8—21no—
247C22×Q8—21no—
248C22×Q8—22no—
249C22×Q8—22no—
250C22×Q8—22no—
251C22×Q8—22no—
252C22×Q8—22no—
253C22×Q8—22no—
254C22×Q8—22no—
255C22×Q8—22no—
256C22×Q8—22no—
257C22×Q8—22no—
258C22×Q8—22no—
259C22×Q8—22no—
260C22×Q8—22no—
261C22×Q8—22no—
262C22×Q8—22no—
263C22×Q8—22no—
264C22×Q8—22no—
265C22×Q8C2×D414yes—
266C22×Q8C2412yes—
267C22×Q8C2412yes—
268C22×Q8C2412yes—
269C22×D4—28no—
270C22×D4—28no—
271C22×D4—22no—
272C22×D4—22no—
273C22×D4—21no—
274C22×D4—21no—
275C22×D4—24no—
276C22×D4—22no—
277C22×D4—22no—
278C22×D4—22no—
279C22×D4—22no—
280C22×D4—22no—
281C22×D4—22no—
282C22×D4—22no—
283C22×D4—22no—
284C22×D4—44no—
285C22×D4—44no—
286C22×D4—44no—
287C22×D4—44no—
288C22×D4—48no—
289C22×D4—48no—
290C22×D4—44no—
291C22×D4—44no—
292C22×D4—44no—
293C22×D4—48no—
294C22×D4—416no—
295C22×D4—416no—
296C22×D4—416no—
297C22×D4—416no—
298C22×D4C2×D414yes—
299C22×D4C2×D414yes—
300C22×D4C2412yes—
301C22×D4C2412yes—
302C23×C4—21no—
303C23×C4—21no—
304C23×C4—22no—
305C23×C4—22no—
306C23×C4—22no—
307C23×C4—22no—
308C23×C4—22no—
309C23×C4—22no—
310C23×C4—21no—
311C23×C4—21no—
312C23×C4—21no—
313C23×C4—21no—
314C23×C4C2×D412yes—
315C23×C4C2×D411yescharacteristic
316C23×C4C2×D411yescharacteristic
317C23×C4C2×D411yescharacteristic
318C23×C4C2×D411yescharacteristic
319C23×C4C2×D411yescharacteristic
320C23×C4C2412yes—
321C23×C4C2411yescharacteristic
322C2×Q16—28no—
323C2×Q16—28no—
324C2×Q16—28no—
325C2×Q16—44no—
326C2×Q16—44no—
327C2×Q16—44no—
328C2×Q16—416no—
329C2×Q16—416no—
330C2×SD16—28no—
331C2×SD16—28no—
332C2×SD16—28no—
333C2×SD16—28no—
334C2×SD16—28no—
335C2×SD16—416no—
336C2×SD16—44no—
337C2×SD16—44no—
338C2×SD16—44no—
339C2×SD16—44no—
340C2×SD16—44no—
341C2×SD16—44no—
342C2×SD16—416no—
343C2×SD16—416no—
344C2×SD16—416no—
345C2×SD16C2×D4116yes—
346C22×C8—22no—
347C22×C8—22no—
348C22×C8—22no—
349C22×C8—22no—
350C22×C8—22no—
351C22×C8—22no—
352C22×C8—22no—
353C22×C8—22no—
354C22×C8—22no—
355C22×C8—22no—
356C22×C8C2×D414yes—
357C22×C8C2×D414yes—
358C22×C8C2412yes—
359C22×C8C2412yes—
360C22×C8C2412yes—
361C22×C8C2412yes—
362C4⋊Q8—28no—
363C4⋊Q8—44no—
364C4⋊Q8—48no—
365#124—28no—
366#124—28no—
367#124—44no—
368#124—44no—
369#124—48no—
370#124—48no—
371C22⋊Q8—28no—
372C22⋊Q8—28no—
373C22⋊Q8—44no—
374C22⋊Q8—44no—
375C22⋊Q8—44no—
376C22⋊Q8—44no—
377C22⋊Q8—48no—
378C22⋊Q8—48no—
379C22⋊Q8—48no—
380C4×Q8—28no—
381C4×Q8—44no—
382C4×Q8—48no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—24no—
391C2×C4⋊C4—24no—
392C2×C4⋊C4—24no—
393C2×C4⋊C4—24no—
394C2×C4⋊C4—24no—
395C2×C4⋊C4—24no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—44no—
399C2×C4⋊C4—44no—
400C2×C4⋊C4—44no—
401C2×C4⋊C4—44no—
402C2×C4⋊C4—44no—
403C2×C4⋊C4—44no—
404C2×C4⋊C4—44no—
405C2×C4⋊C4C2×D414yes—
406C2×C4⋊C4C2412yes—
407C2×C4⋊C4C2412yes—
408C2×C4⋊C4C2412yes—
409C2×C22⋊C4—24no—
410C2×C22⋊C4—24no—
411C2×C22⋊C4—24no—
412C2×C22⋊C4—24no—
413C2×C22⋊C4—24no—
414C2×C22⋊C4—24no—
415C2×C22⋊C4—24no—
416C2×C22⋊C4—24no—
417C2×C22⋊C4—24no—
418C2×C22⋊C4—24no—
419C2×C22⋊C4—24no—
420C2×C22⋊C4—24no—
421C2×C22⋊C4—42no—
422C2×C22⋊C4—44no—
423C2×C22⋊C4—44no—
424C2×C22⋊C4—44no—
425C2×C22⋊C4—44no—
426C2×C22⋊C4—44no—
427C2×C22⋊C4—44no—
428C2×C22⋊C4—44no—
429C2×C22⋊C4—82no—
430C2×C22⋊C4—82no—
431C2×C22⋊C4—82no—
432C2×C22⋊C4—82no—
433C2×C22⋊C4C2×D414yes—
434C2×C22⋊C4C2×D414yes—
435C2×C42—22no—
436C2×C42—22no—
437C2×C42—22no—
438C2×C42—22no—
439C2×C42—24no—
440C2×C42—44no—
441C2×C42C2×D412yes—
442C2×C42C2×D412yes—
443C2×C42C2412yes—
444C2×C42C2412yes—
445C4⋊C8—28no—
446#103—28no—
447#103—44no—
448#103—44no—
449#103—44no—
450#102—28no—
451#102—28no—
452#102—28no—
453#102C2×D4116yes—
454C22⋊C8—28no—
455C22⋊C8—28no—
456#97—28no—
457#95—24no—
458#95—24no—
459#95—24no—
460#95C2×D414yes—
461#95C2×D414yes—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—24no—
469C24—24no—
470C24—22no—
471C24—22no—
472C24—48no—
473C24—48no—
474C24—48no—
475C24—48no—
476C24—432no—
477C24—42no—
478C24—42no—
479C24—42no—
480C24—42no—
481C24—42no—
482C24—42no—
483C24—42no—
484C24—42no—
485C24—42no—
486C24—42no—
487C24—42no—
488C24—42no—
489C24—48no—
490C24—84no—
491C24—84no—
492C24—816no—
493C24—816no—
494C24—816no—
495C24—816no—
496C24—816no—
497C24—816no—
498C24#13714yes—
499C24C22×D412yes—
500C24C22×D411yescharacteristic
501C2×Q8—24no—
502C2×Q8—22no—
503C2×Q8—28no—
504C2×Q8—28no—
505C2×Q8—22no—
506C2×Q8—22no—
507C2×Q8—22no—
508C2×Q8—22no—
509C2×Q8—22no—
510C2×Q8—22no—
511C2×Q8—22no—
512C2×Q8—22no—
513C2×Q8—22no—
514C2×Q8—22no—
515C2×Q8—22no—
516C2×Q8—22no—
517C2×Q8—22no—
518C2×Q8—22no—
519C2×Q8—22no—
520C2×Q8—22no—
521C2×Q8—44no—
522C2×Q8—42no—
523C2×Q8—42no—
524C2×Q8—42no—
525C2×Q8—42no—
526C2×Q8—42no—
527C2×Q8—42no—
528C2×Q8—42no—
529C2×Q8—42no—
530C2×Q8—44no—
531C2×Q8—44no—
532C2×Q8—44no—
533C2×Q8—44no—
534C2×Q8—44no—
535C2×Q8—44no—
536C2×Q8—44no—
537C2×Q8—44no—
538C2×Q8—44no—
539C2×Q8C22×D414yes—
540C2×D4—28no—
541C2×D4—28no—
542C2×D4—28no—
543C2×D4—28no—
544C2×D4—24no—
545C2×D4—24no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—48no—
557C2×D4—48no—
558C2×D4—48no—
559C2×D4—416no—
560C2×D4—416no—
561C2×D4—416no—
562C2×D4—432no—
563C2×D4—464no—
564C2×D4—416no—
565C2×D4—44no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—44no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—44no—
572C2×D4—44no—
573C2×D4C22×D414yes—
574C2×D4C22×D414yes—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—24no—
581C22×C4—24no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—24no—
595C22×C4—24no—
596C22×C4—24no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—44no—
612C22×C4—44no—
613C22×C4—44no—
614C22×C4—44no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4—42no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4C22×D412yes—
628C22×C4C22×D412yes—
629C22×C4C22×D412yes—
630C22×C4C22×D412yes—
631C22×C4C22×D412yes—
632C22×C4C22×D412yes—
633C22×C4C22×D411yescharacteristic
634C22×C4C22×D412yes—
635C22×C4H(5,𝔽2)12yes—
636C22×C4H(5,𝔽2)12yes—
637C22×C4H(5,𝔽2)12yes—
638C22×C4H(5,𝔽2)12yes—
639C22×C4C2511yescharacteristic
640Q16—416no—
641Q16—416no—
642SD16—416no—
643SD16—416no—
644SD16—416no—
645SD16—416no—
646C2×C8—28no—
647C2×C8—28no—
648C2×C8—22no—
649C2×C8—22no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—22no—
654C2×C8—22no—
655C2×C8—22no—
656C2×C8—22no—
657C2×C8—22no—
658C2×C8—44no—
659C2×C8—44no—
660C2×C8C22×D414yes—
661C2×C8C22×D414yes—
662C4⋊C4—24no—
663C4⋊C4—22no—
664C4⋊C4—22no—
665C4⋊C4—22no—
666C4⋊C4—22no—
667C4⋊C4—22no—
668C4⋊C4—48no—
669C4⋊C4—48no—
670C4⋊C4—48no—
671C4⋊C4—48no—
672C4⋊C4—48no—
673C4⋊C4—48no—
674C4⋊C4—48no—
675C4⋊C4—42no—
676C4⋊C4—42no—
677C4⋊C4C22×D414yes—
678C22⋊C4—28no—
679C22⋊C4—44no—
680C22⋊C4—48no—
681C22⋊C4—48no—
682C22⋊C4—48no—
683C22⋊C4—48no—
684C22⋊C4—48no—
685C22⋊C4—48no—
686C22⋊C4—48no—
687C22⋊C4—84no—
688C22⋊C4—84no—
689C22⋊C4—84no—
690C22⋊C4—84no—
691C42—24no—
692C42—24no—
693C42—22no—
694C42—22no—
695C42—22no—
696C42—22no—
697C42—48no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—28no—
702C23—28no—
703C23—28no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—24no—
708C23—24no—
709C23—44no—
710C23—44no—
711C23—44no—
712C23—44no—
713C23—432no—
714C23—48no—
715C23—48no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—48no—
721C23—48no—
722C23—48no—
723C23—48no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—816no—
733C23—816no—
734C23—816no—
735C23—816no—
736C23—816no—
737C23—8128no—
738C23—816no—
739C23—84no—
740C23—84no—
741C23—84no—
742C23—84no—
743C23—84no—
744C23—84no—
745C23—84no—
746C23—84no—
747C23#53512yes—
748C23D4212yes—
749C23D4212yes—
750C23C2×#13714yes—
751C23C2×#13712yes—
752C23#57512yes—
753C23#57712yes—
754C23#57712yes—
755C23C23×D411yescharacteristic
756Q8—24no—
757Q8—24no—
758Q8—48no—
759Q8—42no—
760Q8—42no—
761Q8—42no—
762Q8—42no—
763Q8—42no—
764Q8—42no—
765Q8—42no—
766Q8—42no—
767Q8—42no—
768Q8—42no—
769Q8—84no—
770Q8—84no—
771D4—24no—
772D4—24no—
773D4—24no—
774D4—24no—
775D4—432no—
776D4—48no—
777D4—48no—
778D4—42no—
779D4—42no—
780D4—42no—
781D4—42no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—44no—
800C2×C4—48no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—48no—
807C2×C4—44no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—48no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—84no—
828C2×C4—84no—
829C2×C4—84no—
830C2×C4—84no—
831C2×C4#53414yes—
832C2×C4#53512yes—
833C2×C4#53514yes—
834C2×C4D4212yes—
835C2×C4D4212yes—
836C2×C4D4214yes—
837C2×C4#56014yes—
838C2×C4C23×D411yescharacteristic
839C2×C4C23×D411yescharacteristic
840C2×C4C2×H(5,𝔽2)11yescharacteristic
841C2×C4C2×H(5,𝔽2)11yescharacteristic
842C2×C4C2×H(5,𝔽2)11yescharacteristic
843C2×C4C2×H(5,𝔽2)11yescharacteristic
844C8—24no—
845C8—24no—
846C8—42no—
847C8—42no—
848C22—24no—
849C22—24no—
850C22—24no—
851C22—416no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—44no—
857C22—44no—
858C22—44no—
859C22—44no—
860C22—44no—
861C22—44no—
862C22—864no—
863C22—816no—
864C22—816no—
865C22—82no—
866C22—82no—
867C22—82no—
868C22—82no—
869C22—82no—
870C22—82no—
871C22—82no—
872C22—82no—
873C22#266914yes—
874C22#321514yes—
875C22#322214yes—
876C22#326614yes—
877C22#326614yes—
878C22#326714yes—
879C22#327514yes—
880C22C2×#53511yescharacteristic
881C22C2×D4211yescharacteristic
882C22C2×D4211yescharacteristic
883C22C22×#13711yescharacteristic
884C22C2×#57511yescharacteristic
885C22C2×#57711yescharacteristic
886C22C2×#57711yescharacteristic
887C4—42no—
888C4—42no—
889C4—42no—
890C4—44no—
891C4—42no—
892C4—42no—
893C4—44no—
894C4—82no—
895C4—82no—
896C4—82no—
897C4—82no—
898C4#266914yes—
899C4C2×#53411yescharacteristic
900C4C2×#53511yescharacteristic
901C4C2×D4211yescharacteristic
902C4C2×#56011yescharacteristic
903C2—44no—
904C2—84no—
905C2—84no—
906C2#3046418yesdirect product factor
907C2C2×#266911yescharacteristic
908C2C2×#321511yescharacteristic
909C2C2×#322211yescharacteristic
910C2C2×#326611yescharacteristic
911C2C2×#326611yescharacteristic
912C2C2×#326711yescharacteristic
913C2C2×#327511yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24×D4C22
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×#497C2semidirect
2. C22×#464C2semidirect
6. C2×#2429C2semidirect
7. #30464C2direct (N × H)
8. C2×#2055C2semidirect
9. C2×#2042C2semidirect
10. C2×#2013C2semidirect
11. C2×#2015C2semidirect
12. C2×#2001C2semidirect
13. C2×#2001C2semidirect
14. C2×#1936C2semidirect
15. C2×#1924C2semidirect
16. C2×#1880C2semidirect
18. C23×Q16C22semidirect
19. C23×Q16C22semidirect
24. C22×C4⋊Q8C22semidirect
30. C22×C4×Q8C22semidirect
32. C2×#497C22semidirect
34. C2×#464C22semidirect
39. C22×C4⋊C8C22semidirect
40. C22×#103C22semidirect
41. C22×#103C22semidirect
42. C22×#103C22semidirect
43. C22×#103C22semidirect
50. C22×#97C22semidirect
54. #2429C22semidirect
59. C2×#391C22semidirect
63. C2×#389C22semidirect
68. #2055C22semidirect
69. #2042C22semidirect
70. #2015C22semidirect
71. #2013C22semidirect
72. #2001C22semidirect
73. #2001C22semidirect
74. #1936C22semidirect
75. #1924C22semidirect
76. #1880C22semidirect
77. C2×#340C22semidirect
78. C2×#340C22semidirect
79. C2×#336C22semidirect
80. C2×#336C22semidirect
103. C22×Q16C23semidirect
104. C22×Q16C23semidirect
128. C2×C4⋊Q8C23semidirect
152. C2×C4×Q8C23semidirect
184. C2×C4⋊C8C23semidirect
189. C2×#103C23semidirect
190. C2×#103C23semidirect
191. C2×#103C23semidirect
192. C2×#103C23semidirect
206. C2×#97C23semidirect
212. #391C23semidirect
219. #389C23semidirect
230. #340C23semidirect
231. #340C23semidirect
232. #336C23semidirect
233. #336C23semidirect
906. C2#30464direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4972
C22×#4642
C22×#4502
C2×#24352
C2×#24292
#304642
C2×#20552
C2×#20422
C2×#20132
C2×#20152
C2×#20012
C2×#19362
C2×#19242
C2×#18802