Finite Group Databasebeta

← C2×#17578 #6343350

Subgroups — C2×#17578 #6343350

Order 512.

5002 conjugacy classes of subgroups.

The subgroup lattice has 855 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊Q8C211yesmaximal, characteristic
2C22×#407C211yesmaximal, characteristic
3C2×#2280C211yesmaximal, characteristic
4#17578C2116yesmaximal, direct product factor
5C2×#1520C214yesmaximal, complemented
6C2×#1511C214yesmaximal, complemented
7C2×#1508C214yesmaximal, complemented
8C24×Q8C411yescharacteristic, complemented
9C25×C4C2211yescharacteristic
10C23×M16—21no—
11C22×C22⋊Q8—21no—
12C22×C22⋊Q8—21no—
13C22×C22⋊Q8—24no—
14C22×C22⋊Q8—21no—
15C22×C22⋊Q8—21no—
16C22×C22⋊Q8—21no—
17C22×C22⋊Q8—21no—
18C22×C22⋊Q8—24no—
19C22×C22⋊Q8C412yescomplemented
20C22×C22⋊Q8C412yescomplemented
21C22×C22⋊Q8C412yescomplemented
22C22×C22⋊Q8C418yescomplemented
23C22×C22⋊Q8C2212yes—
24C22×C22⋊Q8C2212yes—
25C22×C22⋊Q8C2212yes—
26C22×C22⋊Q8C2218yes—
27C22×#117—21no—
28C23×C4⋊C4—21no—
29C23×C4⋊C4C411yescharacteristic, complemented
30C23×C22⋊C4—21no—
31C2×#407—21no—
32C2×#407—21no—
33C2×#407—24no—
34C2×#407C2212yes—
35C2×#407C2212yes—
36C2×#407C2218yes—
37C22×C22⋊C8—21no—
38C22×C22⋊C8C2212yes—
39#2280—24no—
40#2280C2218yes—
41C2×#381C2212yes—
42C2×#380—21no—
43C2×#380C2212yes—
44C2×#379—21no—
45C2×C4×C22⋊C4—21no—
46C2×C4×C22⋊C4C2212yes—
47#1520C22132yescomplemented
48#1511C22132yescomplemented
49#1508C22132yescomplemented
50C2×#328C22116yescomplemented
51C26D411yescharacteristic
52C23×Q8—21no—
53C23×Q8—21no—
54C23×Q8—21no—
55C23×Q8—24no—
56C23×Q8—48no—
57C23×Q8C2×C412yes—
58C23×Q8C2×C412yes—
59C23×Q8C2×C412yes—
60C23×Q8C2×C418yescomplemented
61C24×C4—21no—
62C24×C4—21no—
63C24×C4—48no—
64C24×C4C2×C411yescharacteristic
65C24×C4C2×C411yescharacteristic
66C24×C4C2×C411yescharacteristic
67C24×C4C2×C414yes—
68C24×C4C2×C411yescharacteristic
69C24×C4D411yescharacteristic
70C24×C4D411yescharacteristic
71C24×C4D411yescharacteristic
72C24×C4D411yescharacteristic
73C24×C4D414yes—
74C24×C4D411yescharacteristic
75C24×C4D411yescharacteristic
76C24×C4D411yescharacteristic
77C24×C4D414yes—
78C24×C4C2311yescharacteristic
79C24×C4C2311yescharacteristic
80C24×C4C2311yescharacteristic
81C24×C4C2314yes—
82C22×M16—22no—
83C22×M16—22no—
84C22×M16—28no—
85C22×M16—48no—
86C23×C8—22no—
87C2×C22⋊Q8—22no—
88C2×C22⋊Q8—22no—
89C2×C22⋊Q8—22no—
90C2×C22⋊Q8—22no—
91C2×C22⋊Q8—22no—
92C2×C22⋊Q8—22no—
93C2×C22⋊Q8—28no—
94C2×C22⋊Q8—28no—
95C2×C22⋊Q8—28no—
96C2×C22⋊Q8—28no—
97C2×C22⋊Q8—28no—
98C2×C22⋊Q8—28no—
99C2×C22⋊Q8—28no—
100C2×C22⋊Q8—28no—
101C2×C22⋊Q8—28no—
102C2×C22⋊Q8—22no—
103C2×C22⋊Q8—22no—
104C2×C22⋊Q8—22no—
105C2×C22⋊Q8—24no—
106C2×C22⋊Q8—24no—
107C2×C22⋊Q8—24no—
108C2×C22⋊Q8—28no—
109C2×C22⋊Q8—28no—
110C2×C22⋊Q8—28no—
111C2×C22⋊Q8—22no—
112C2×C22⋊Q8—22no—
113C2×C22⋊Q8—22no—
114C2×C22⋊Q8—24no—
115C2×C22⋊Q8—24no—
116C2×C22⋊Q8—24no—
117C2×C22⋊Q8—28no—
118C2×C22⋊Q8—28no—
119C2×C22⋊Q8—28no—
120C2×C22⋊Q8C2×C414yes—
121C2×C22⋊Q8C2×C414yes—
122C2×C22⋊Q8C2×C414yes—
123C2×C22⋊Q8C2×C418yes—
124C2×C22⋊Q8C2×C418yes—
125C2×C22⋊Q8C2×C418yes—
126C2×C22⋊Q8C2×C4116yescomplemented
127C2×C22⋊Q8C2×C4116yescomplemented
128C2×C22⋊Q8C2×C4116yescomplemented
129C2×C22⋊Q8C2314yes—
130C2×C22⋊Q8C2318yes—
131C2×C22⋊Q8C2318yes—
132C2×C22⋊Q8C2318yes—
133C2×#117—28no—
134C2×#117—48no—
135C22×C4⋊C4—28no—
136C22×C4⋊C4—22no—
137C22×C4⋊C4—22no—
138C22×C4⋊C4—22no—
139C22×C4⋊C4—24no—
140C22×C4⋊C4—21no—
141C22×C4⋊C4—21no—
142C22×C4⋊C4—21no—
143C22×C4⋊C4—22no—
144C22×C4⋊C4—22no—
145C22×C4⋊C4—22no—
146C22×C4⋊C4—28no—
147C22×C4⋊C4—22no—
148C22×C4⋊C4C2×C412yes—
149C22×C4⋊C4C2×C412yes—
150C22×C4⋊C4C2×C412yes—
151C22×C4⋊C4C2×C418yescomplemented
152C22×C22⋊C4—28no—
153C22×C22⋊C4—22no—
154C22×C22⋊C4—22no—
155C22×C22⋊C4—22no—
156C22×C22⋊C4—22no—
157C22×C22⋊C4—22no—
158C22×C22⋊C4—22no—
159C22×C22⋊C4—28no—
160C22×C22⋊C4—22no—
161C22×C22⋊C4—22no—
162C22×C22⋊C4—22no—
163C22×C42—22no—
164#407—28no—
165#407—24no—
166#407—24no—
167#407—28no—
168#407C2318yes—
169#407C2318yes—
170C2×C22⋊C8—22no—
171C2×C22⋊C8—22no—
172C2×C22⋊C8—28no—
173C2×C22⋊C8—22no—
174C2×C22⋊C8—24no—
175C2×C22⋊C8C2314yes—
176C2×C22⋊C8C2318yes—
177#381—24no—
178#381C2318yes—
179#380—28no—
180#380—24no—
181#380C2318yes—
182#379—28no—
183C4×C22⋊C4—28no—
184C4×C22⋊C4—24no—
185C4×C22⋊C4C2318yes—
186C2×#95—22no—
187C2×#95C2314yes—
188#328C23164yescomplemented
189C25—28no—
190C25—44no—
191C25—44no—
192C25C22⋊C411yescharacteristic
193C25C22⋊C411yescharacteristic
194C25C22⋊C411yescharacteristic
195C25C22⋊C414yes—
196C25C22⋊C411yescharacteristic
197C25C2×D411yescharacteristic
198C25C2×D411yescharacteristic
199C25C2×D414yes—
200C25C2×D411yescharacteristic
201C22×Q8—24no—
202C22×Q8—24no—
203C22×Q8—24no—
204C22×Q8—22no—
205C22×Q8—22no—
206C22×Q8—22no—
207C22×Q8—28no—
208C22×Q8—28no—
209C22×Q8—28no—
210C22×Q8—48no—
211C22×Q8—48no—
212C22×Q8—432no—
213C22×Q8—48no—
214C22×Q8—48no—
215C22×Q8—432no—
216C22×Q8—48no—
217C22×Q8—48no—
218C22×Q8C22×C414yes—
219C22×Q8C22×C418yes—
220C22×Q8C22×C418yes—
221C22×Q8C22×C418yes—
222C23×C4—28no—
223C23×C4—28no—
224C23×C4—28no—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—28no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—28no—
233C23×C4—24no—
234C23×C4—44no—
235C23×C4—44no—
236C23×C4—416no—
237C23×C4—44no—
238C23×C4—44no—
239C23×C4—416no—
240C23×C4—44no—
241C23×C4—44no—
242C23×C4—416no—
243C23×C4—44no—
244C23×C4—44no—
245C23×C4—416no—
246C23×C4—44no—
247C23×C4—44no—
248C23×C4—44no—
249C23×C4—48no—
250C23×C4—48no—
251C23×C4C22⋊C411yescharacteristic
252C23×C4C22⋊C414yes—
253C23×C4C22⋊C411yescharacteristic
254C23×C4C22⋊C411yescharacteristic
255C23×C4C22⋊C414yes—
256C23×C4C22⋊C414yes—
257C23×C4C22⋊C411yescharacteristic
258C23×C4C22⋊C411yescharacteristic
259C23×C4C22⋊C411yescharacteristic
260C23×C4C22⋊C411yescharacteristic
261C23×C4C22⋊C414yes—
262C23×C4C22⋊C411yescharacteristic
263C23×C4C22⋊C411yescharacteristic
264C23×C4C22⋊C414yes—
265C23×C4C22⋊C414yes—
266C23×C4C22⋊C414yes—
267C23×C4C22⋊C414yes—
268C23×C4C22⋊C414yes—
269C23×C4C22⋊C414yes—
270C23×C4C22⋊C414yes—
271C23×C4C22⋊C411yescharacteristic
272C23×C4C22⋊C411yescharacteristic
273C23×C4C22⋊C411yescharacteristic
274C23×C4C22×C411yescharacteristic
275C23×C4C22×C411yescharacteristic
276C23×C4C22×C411yescharacteristic
277C23×C4C22×C414yes—
278C23×C4C22×C412yes—
279C23×C4C22×C412yes—
280C23×C4C22×C412yes—
281C23×C4C22×C411yescharacteristic
282C23×C4C22×C411yescharacteristic
283C23×C4C22×C411yescharacteristic
284C23×C4C22×C414yes—
285C23×C4C22×C414yes—
286C23×C4C22×C414yes—
287C23×C4C2×D411yescharacteristic
288C23×C4C2×D414yes—
289C23×C4C2×D411yescharacteristic
290C23×C4C2×D411yescharacteristic
291C23×C4C2×D411yescharacteristic
292C23×C4C2×D414yes—
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D412yes—
296C23×C4C2×D414yes—
297C23×C4C2×D414yes—
298C23×C4C2×D412yes—
299C23×C4C2×D412yes—
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2×D414yes—
303C23×C4C2×D414yes—
304C23×C4C2×D412yes—
305C23×C4C2×D411yescharacteristic
306C23×C4C2×D412yes—
307C23×C4C2×D414yes—
308C23×C4C2×D412yes—
309C23×C4C2411yescharacteristic
310C23×C4C2412yes—
311C23×C4C2412yes—
312C23×C4C2412yes—
313C2×M16—28no—
314C2×M16—28no—
315C2×M16—48no—
316C2×M16—48no—
317C2×M16—432no—
318C22×C8—28no—
319C22×C8—24no—
320C22×C8—48no—
321C22⋊Q8—28no—
322C22⋊Q8—28no—
323C22⋊Q8—28no—
324C22⋊Q8—28no—
325C22⋊Q8—28no—
326C22⋊Q8—28no—
327C22⋊Q8—28no—
328C22⋊Q8—28no—
329C22⋊Q8—28no—
330C22⋊Q8—216no—
331C22⋊Q8—216no—
332C22⋊Q8—216no—
333C22⋊Q8—216no—
334C22⋊Q8—216no—
335C22⋊Q8—216no—
336C22⋊Q8—28no—
337C22⋊Q8—28no—
338C22⋊Q8—24no—
339C22⋊Q8—28no—
340C22⋊Q8—28no—
341C22⋊Q8—28no—
342C22⋊Q8—24no—
343C22⋊Q8—28no—
344C22⋊Q8C22×C418yes—
345C22⋊Q8C22×C4116yes—
346C22⋊Q8C22×C4116yes—
347C22⋊Q8C22×C4116yes—
348C22⋊Q8C2418yes—
349#117—432no—
350C2×C4⋊C4—28no—
351C2×C4⋊C4—28no—
352C2×C4⋊C4—28no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—216no—
357C2×C4⋊C4—216no—
358C2×C4⋊C4—216no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—28no—
366C2×C4⋊C4—28no—
367C2×C4⋊C4—28no—
368C2×C4⋊C4—28no—
369C2×C4⋊C4—28no—
370C2×C4⋊C4—28no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—28no—
373C2×C4⋊C4—48no—
374C2×C4⋊C4C22×C414yes—
375C2×C4⋊C4C22×C418yes—
376C2×C4⋊C4C22×C418yes—
377C2×C4⋊C4C22×C418yes—
378C2×C22⋊C4—28no—
379C2×C22⋊C4—28no—
380C2×C22⋊C4—28no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—216no—
385C2×C22⋊C4—216no—
386C2×C22⋊C4—216no—
387C2×C22⋊C4—28no—
388C2×C22⋊C4—28no—
389C2×C22⋊C4—28no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—28no—
392C2×C22⋊C4—28no—
393C2×C22⋊C4—28no—
394C2×C22⋊C4—48no—
395C2×C22⋊C4—48no—
396C2×C22⋊C4—48no—
397C2×C42—28no—
398C2×C42—48no—
399C22⋊C8—28no—
400C22⋊C8—28no—
401C22⋊C8—28no—
402C22⋊C8—24no—
403C22⋊C8C2418yes—
404#95—28no—
405#95—24no—
406#95C2418yes—
407C24—24no—
408C24—24no—
409C24—24no—
410C24—24no—
411C24—24no—
412C24—216no—
413C24—24no—
414C24—24no—
415C24—24no—
416C24—24no—
417C24—216no—
418C24—24no—
419C24—24no—
420C24—24no—
421C24—42no—
422C24—48no—
423C24—42no—
424C24—42no—
425C24—42no—
426C24—48no—
427C24—42no—
428C24—48no—
429C24—42no—
430C24—42no—
431C24—42no—
432C24—48no—
433C24—464no—
434C24C2×C22⋊C414yes—
435C24C2×C22⋊C411yescharacteristic
436C24C2×C22⋊C411yescharacteristic
437C24C2×C22⋊C412yes—
438C24C2×C22⋊C414yes—
439C24C2×C22⋊C412yes—
440C24C2×C22⋊C414yes—
441C24C2×C22⋊C411yescharacteristic
442C24C2×C22⋊C411yescharacteristic
443C24C2×C22⋊C411yescharacteristic
444C24C2×C22⋊C411yescharacteristic
445C24C2×C22⋊C414yes—
446C24C2×C22⋊C412yes—
447C24#13718yes—
448C24C22×D412yes—
449C24C22×D412yes—
450C24C22×D411yescharacteristic
451C24C22×D412yes—
452C2×Q8—24no—
453C2×Q8—28no—
454C2×Q8—28no—
455C2×Q8—28no—
456C2×Q8—416no—
457C2×Q8—416no—
458C2×Q8—416no—
459C2×Q8—48no—
460C2×Q8—416no—
461C2×Q8—416no—
462C2×Q8—432no—
463C2×Q8—432no—
464C2×Q8—48no—
465C2×Q8—416no—
466C2×Q8—48no—
467C2×Q8—48no—
468C2×Q8—432no—
469C2×Q8C23×C418yes—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—24no—
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—216no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—216no—
479C22×C4—24no—
480C22×C4—216no—
481C22×C4—24no—
482C22×C4—24no—
483C22×C4—216no—
484C22×C4—24no—
485C22×C4—216no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—24no—
489C22×C4—24no—
490C22×C4—216no—
491C22×C4—28no—
492C22×C4—28no—
493C22×C4—28no—
494C22×C4—28no—
495C22×C4—28no—
496C22×C4—28no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—28no—
500C22×C4—48no—
501C22×C4—48no—
502C22×C4—48no—
503C22×C4—48no—
504C22×C4—48no—
505C22×C4—48no—
506C22×C4—44no—
507C22×C4—44no—
508C22×C4—48no—
509C22×C4—48no—
510C22×C4—48no—
511C22×C4—44no—
512C22×C4—44no—
513C22×C4—48no—
514C22×C4—44no—
515C22×C4—48no—
516C22×C4—44no—
517C22×C4—48no—
518C22×C4—44no—
519C22×C4—44no—
520C22×C4—48no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—48no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—44no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—48no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—48no—
535C22×C4—44no—
536C22×C4—42no—
537C22×C4—44no—
538C22×C4—42no—
539C22×C4—44no—
540C22×C4—48no—
541C22×C4—48no—
542C22×C4—432no—
543C22×C4—48no—
544C22×C4—48no—
545C22×C4—432no—
546C22×C4—48no—
547C22×C4—48no—
548C22×C4—48no—
549C22×C4—48no—
550C22×C4—48no—
551C22×C4#9918yes—
552C22×C4C2×C22⋊C412yes—
553C22×C4C2×C22⋊C414yes—
554C22×C4C2×C22⋊C412yes—
555C22×C4C2×C22⋊C412yes—
556C22×C4C2×C22⋊C414yes—
557C22×C4C2×C22⋊C412yes—
558C22×C4C2×C22⋊C414yes—
559C22×C4C2×C22⋊C412yes—
560C22×C4C2×C22⋊C414yes—
561C22×C4C2×C22⋊C414yes—
562C22×C4C2×C22⋊C414yes—
563C22×C4C2×C22⋊C412yes—
564C22×C4C2×C22⋊C412yes—
565C22×C4C2×C22⋊C412yes—
566C22×C4C2×C22⋊C414yes—
567C22×C4C2×C22⋊C411yescharacteristic
568C22×C4C2×C22⋊C411yescharacteristic
569C22×C4C2×C22⋊C411yescharacteristic
570C22×C4C2×C22⋊C411yescharacteristic
571C22×C4C2×C22⋊C412yes—
572C22×C4C2×C22⋊C414yes—
573C22×C4C2×C22⋊C412yes—
574C22×C4C2×C22⋊C414yes—
575C22×C4C2×C22⋊C412yes—
576C22×C4C2×C22⋊C412yes—
577C22×C4C2×C22⋊C412yes—
578C22×C4C2×C22⋊C414yes—
579C22×C4C2×C22⋊C412yes—
580C22×C4C2×C22⋊C412yes—
581C22×C4C2×C22⋊C414yes—
582C22×C4C2×C22⋊C414yes—
583C22×C4C2×C22⋊C411yescharacteristic
584C22×C4C2×C22⋊C411yescharacteristic
585C22×C4C23×C412yes—
586C22×C4C23×C412yes—
587C22×C4C23×C412yes—
588C22×C4C23×C411yescharacteristic
589C22×C4C23×C412yes—
590C22×C4C23×C412yes—
591C22×C4C23×C411yescharacteristic
592C22×C4C23×C412yes—
593C22×C4C22×D412yes—
594C22×C4C22×D412yes—
595C22×C4C22×D412yes—
596C22×C4C22×D412yes—
597C22×C4C22×D412yes—
598C22×C4C22×D411yescharacteristic
599C22×C4C22×D412yes—
600C22×C4C22×D411yescharacteristic
601C22×C4C22×D412yes—
602C22×C4C22×D412yes—
603C22×C4C22×D412yes—
604C22×C4C22×D411yescharacteristic
605C22×C4C2511yescharacteristic
606M16—416no—
607M16—416no—
608C2×C8—28no—
609C2×C8—48no—
610C2×C8—416no—
611C4⋊C4—28no—
612C4⋊C4—216no—
613C4⋊C4—216no—
614C4⋊C4—216no—
615C4⋊C4—24no—
616C4⋊C4—28no—
617C4⋊C4—28no—
618C4⋊C4—28no—
619C4⋊C4—28no—
620C4⋊C4—416no—
621C4⋊C4C23×C418yes—
622C22⋊C4—216no—
623C22⋊C4—216no—
624C22⋊C4—28no—
625C22⋊C4—216no—
626C22⋊C4—28no—
627C22⋊C4—416no—
628C22⋊C4—416no—
629C22⋊C4—416no—
630C42—416no—
631C23—232no—
632C23—28no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—28no—
638C23—22no—
639C23—22no—
640C23—28no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—24no—
646C23—28no—
647C23—24no—
648C23—22no—
649C23—22no—
650C23—24no—
651C23—28no—
652C23—24no—
653C23—28no—
654C23—28no—
655C23—22no—
656C23—22no—
657C23—24no—
658C23—24no—
659C23—28no—
660C23—22no—
661C23—22no—
662C23—24no—
663C23—24no—
664C23—42no—
665C23—44no—
666C23—42no—
667C23—44no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—44no—
673C23—44no—
674C23—416no—
675C23—42no—
676C23—42no—
677C23—416no—
678C23—416no—
679C23—416no—
680C23—416no—
681C23—464no—
682C23—464no—
683C23—416no—
684C23C2×#9914yes—
685C23#41914yes—
686C23#41914yes—
687C23#41918yes—
688C23#42114yes—
689C23C22×C22⋊C412yes—
690C23C22×C22⋊C412yes—
691C23C22×C22⋊C412yes—
692C23C22×C22⋊C411yescharacteristic
693C23C22×C22⋊C412yes—
694C23C22×C22⋊C412yes—
695C23C22×C22⋊C412yes—
696C23C22×C22⋊C411yescharacteristic
697C23C2×#13714yes—
698C23C2×#13718yes—
699C23C23×D411yescharacteristic
700Q8—48no—
701Q8—48no—
702Q8—416no—
703Q8—416no—
704Q8—416no—
705C2×C4—22no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—28no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—28no—
724C2×C4—28no—
725C2×C4—28no—
726C2×C4—24no—
727C2×C4—28no—
728C2×C4—28no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—28no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—28no—
735C2×C4—28no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—42no—
741C2×C4—44no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—44no—
747C2×C4—41no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—41no—
754C2×C4—42no—
755C2×C4—41no—
756C2×C4—42no—
757C2×C4—41no—
758C2×C4—416no—
759C2×C4—416no—
760C2×C4—416no—
761C2×C4—416no—
762C2×C4—416no—
763C2×C4—48no—
764C2×C4—416no—
765C2×C4—48no—
766C2×C4—48no—
767C2×C4—48no—
768C2×C4—48no—
769C2×C4—816no—
770C2×C4C2×#99116yes—
771C2×C4C2×#9914yes—
772C2×C4C2×#9914yes—
773C2×C4C22×C22⋊C411yescharacteristic
774C2×C4C22×C22⋊C412yes—
775C2×C4C22×C22⋊C412yes—
776C2×C4C22×C22⋊C412yes—
777C2×C4C22×C22⋊C411yescharacteristic
778C2×C4C22×C22⋊C412yes—
779C2×C4C22×C22⋊C412yes—
780C2×C4C22×C22⋊C412yes—
781C2×C4C24×C411yescharacteristic
782C2×C4C23×D411yescharacteristic
783C8—48no—
784C22—232no—
785C22—22no—
786C22—22no—
787C22—21no—
788C22—22no—
789C22—21no—
790C22—28no—
791C22—28no—
792C22—28no—
793C22—28no—
794C22—28no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—21no—
800C22—21no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—22no—
808C22—48no—
809C22—48no—
810C22—48no—
811C22—48no—
812C22—48no—
813C22—416no—
814C22—48no—
815C22—416no—
816C22—416no—
817C22—44no—
818C22—44no—
819C22C22×#9914yes—
820C22C22×#9912yes—
821C22C2×#41914yes—
822C22C2×#41912yes—
823C22C2×#41914yes—
824C22C2×#41912yes—
825C22C2×#42114yes—
826C22C2×#42112yes—
827C22C23×C22⋊C411yescharacteristic
828C22C22×#13712yes—
829C4—21no—
830C4—21no—
831C4—22no—
832C4—22no—
833C4—22no—
834C4—21no—
835C4—22no—
836C4—21no—
837C4—48no—
838C4—48no—
839C4—88no—
840C4C22×#9914yes—
841C4C22×#9914yes—
842C2—22no—
843C2—24no—
844C2—24no—
845C2—24no—
846C2—22no—
847C2—24no—
848C2—42no—
849C2—42no—
850C2#1757814yesdirect product factor
851C2C23×#9911yescharacteristic
852C2C22×#41911yescharacteristic
853C2C22×#42111yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC26D4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C25×C4 ◁ G
LECSG ▷ C22×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #17578C2direct (N × H)
5. C2×#1520C2semidirect
6. C2×#1511C2semidirect
7. C2×#1508C2semidirect
8. C24×Q8C4semidirect
19. C22×C22⋊Q8C4semidirect
20. C22×C22⋊Q8C4semidirect
21. C22×C22⋊Q8C4semidirect
22. C22×C22⋊Q8C4semidirect
29. C23×C4⋊C4C4semidirect
47. #1520C22semidirect
48. #1511C22semidirect
49. #1508C22semidirect
50. C2×#328C22semidirect
60. C23×Q8C2×C4semidirect
126. C2×C22⋊Q8C2×C4semidirect
127. C2×C22⋊Q8C2×C4semidirect
128. C2×C22⋊Q8C2×C4semidirect
151. C22×C4⋊C4C2×C4semidirect
188. #328C23semidirect
850. C2#17578direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C22⋊Q82
C22×#4072
C2×#22802
#175782
C2×#15202
C2×#15112
C2×#15082