Finite Group Databasebeta

← C2×#128050 #72314540

Subgroups — C2×#128050 #72314540

Order 1024.

5697 conjugacy classes of subgroups.

The subgroup lattice has 1218 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#20722C212yesmaximal
2C2×#14345C211yesmaximal, characteristic
3#128050C218yesmaximal, direct product factor
4C2×#7307C214yesmaximal
5C23×C4×D4C2211yescharacteristic
6C22×#383C411yescharacteristic, complemented
7C22×#382C411yescharacteristic, complemented
8C2×#2280—22no—
9#20722—24no—
10#20722—24no—
11#20722C418yescomplemented
12#20722C2218yes—
13C2×#1819—22no—
14C2×#1799—22no—
15C2×#1799C414yescomplemented
16C2×#1781C2214yes—
17C2×C4×#99—22no—
18C2×C4×#99C414yescomplemented
19#14345—24no—
20#14345C414yescomplemented
21#14345C2214yes—
22C2×#1445C412yescomplemented
23C2×#1439—22no—
24C2×#1438C2212yes—
25C2×C22⋊#95—22no—
26#7307C22116yes—
27C24×D4C2311yescharacteristic
28C25×C4D412yes—
29C22×C4×D4—42no—
30C22×C4×D4—42no—
31C22×C4×D4—42no—
32C22×C4×D4—42no—
33C22×C4×D4C2×C412yes—
34C22×C4×D4C2×C412yes—
35C22×C4×D4C2×C412yes—
36C22×C4×D4C2×C414yes—
37C22×C4×D4D411yescharacteristic
38C22×C4×D4D411yescharacteristic
39C22×C4×D4D412yes—
40C22×C4×D4D414yes—
41C22×C4×D4Q811yescharacteristic
42C22×C4×D4Q811yescharacteristic
43C22×C4×D4Q812yes—
44C22×C4×D4C2312yes—
45C22×#117—42no—
46C23×C4⋊C4—21no—
47C23×C4⋊C4C2×C411yescharacteristic
48C23×C22⋊C4—24no—
49C23×C22⋊C4D412yes—
50C23×C42C2×C411yescharacteristic
51C22×#99—24no—
52C22×#99C2×C418yes—
53C2×#383—22no—
54C2×#383—42no—
55C2×#383—42no—
56C2×#383C2×C414yescomplemented
57C2×#382—22no—
58C2×#382—42no—
59C2×#382—42no—
60C2×#382C2×C414yescomplemented
61#2280—28no—
62#2280—28no—
63#2280—44no—
64#2280—44no—
65C2×#381—42no—
66C2×#380—24no—
67C2×#380—42no—
68C2×#379—24no—
69C2×C4×C22⋊C4—24no—
70C2×C4×C22⋊C4—42no—
71C22×#95—21no—
72C22×#95—24no—
73C22×#95—21no—
74C22×#95—21no—
75C22×#95C2×C412yes—
76C22×#95C2×C412yes—
77#1819—28no—
78#1819—28no—
79#1799—28no—
80#1799—28no—
81#1799—28no—
82#1799C2×C4116yescomplemented
83#1781—24no—
84#1781—24no—
85#1781C2×C418yes—
86#1781C2318yes—
87C4×#99—28no—
88C4×#99—28no—
89C4×#99—28no—
90C4×#99C2×C4116yescomplemented
91C2×#342—24no—
92C2×#342—24no—
93#1445—24no—
94#1445C2×C418yescomplemented
95#1439—28no—
96#1439—28no—
97#1438—24no—
98#1438C2×C414yes—
99#1438C2314yes—
100C22⋊#95—28no—
101C22⋊#95—28no—
102C26C2×D412yes—
103C23×D4—41no—
104C23×D4—41no—
105C23×D4—41no—
106C23×D4—41no—
107C23×D4—48no—
108C23×D4C22×C412yes—
109C23×D4C22×C412yes—
110C23×D4C22×C411yescharacteristic
111C23×D4C2×D412yes—
112C23×D4C2×D411yescharacteristic
113C23×D4C2×D411yescharacteristic
114C23×D4C2×Q811yescharacteristic
115C23×D4C2×Q811yescharacteristic
116C23×D4C2411yescharacteristic
117C24×C4—22no—
118C24×C4—22no—
119C24×C4—22no—
120C24×C4—22no—
121C24×C4—24no—
122C24×C4—24no—
123C24×C4—22no—
124C24×C4—22no—
125C24×C4—88no—
126C24×C4C22⋊C412yes—
127C24×C4C22⋊C411yescharacteristic
128C24×C4C22⋊C414yes—
129C24×C4C22⋊C412yes—
130C24×C4C22⋊C412yes—
131C24×C4C22⋊C414yes—
132C24×C4C22⋊C411yescharacteristic
133C24×C4C4⋊C412yes—
134C24×C4C4⋊C412yes—
135C24×C4C4⋊C414yes—
136C24×C4C22×C411yescharacteristic
137C24×C4C2×D414yes—
138C2×C4×D4—42no—
139C2×C4×D4—44no—
140C2×C4×D4—42no—
141C2×C4×D4—42no—
142C2×C4×D4—42no—
143C2×C4×D4—44no—
144C2×C4×D4—44no—
145C2×C4×D4—44no—
146C2×C4×D4—44no—
147C2×C4×D4—44no—
148C2×C4×D4—44no—
149C2×C4×D4—44no—
150C2×C4×D4—42no—
151C2×C4×D4—44no—
152C2×C4×D4—42no—
153C2×C4×D4—42no—
154C2×C4×D4—44no—
155C2×C4×D4—42no—
156C2×C4×D4—44no—
157C2×C4×D4—44no—
158C2×C4×D4—44no—
159C2×C4×D4—44no—
160C2×C4×D4—44no—
161C2×C4×D4—42no—
162C2×C4×D4—42no—
163C2×C4×D4—44no—
164C2×C4×D4—42no—
165C2×C4×D4—42no—
166C2×C4×D4—44no—
167C2×C4×D4—44no—
168C2×C4×D4C4214yes—
169C2×C4×D4C4214yes—
170C2×C4×D4C22⋊C414yes—
171C2×C4×D4C22⋊C414yes—
172C2×C4×D4C22⋊C414yes—
173C2×C4×D4C22⋊C414yes—
174C2×C4×D4C4⋊C414yes—
175C2×C4×D4C4⋊C414yes—
176C2×C4×D4C4⋊C414yes—
177C2×C4×D4C4⋊C414yes—
178C2×C4×D4C4⋊C412yes—
179C2×C4×D4C4⋊C412yes—
180C2×C4×D4C4⋊C412yes—
181C2×C4×D4C4⋊C412yes—
182C2×C4×D4C22×C414yes—
183C2×C4×D4C22×C414yes—
184C2×C4×D4C2×D412yes—
185C2×C4×D4C2×D412yes—
186C2×C4×D4C2×Q812yes—
187C2×C4×D4C2×Q812yes—
188C2×#117—48no—
189C2×#117—48no—
190C2×#117—816no—
191C22×C4⋊C4—24no—
192C22×C4⋊C4—41no—
193C22×C4⋊C4—41no—
194C22×C4⋊C4—41no—
195C22×C4⋊C4—41no—
196C22×C4⋊C4—42no—
197C22×C4⋊C4—42no—
198C22×C4⋊C4—44no—
199C22×C4⋊C4—84no—
200C22×C4⋊C4C4212yes—
201C22×C4⋊C4C4212yes—
202C22×C4⋊C4C22⋊C412yes—
203C22×C4⋊C4C4⋊C411yescharacteristic
204C22×C4⋊C4C4⋊C411yescharacteristic
205C22×C4⋊C4C4⋊C412yes—
206C22×C4⋊C4C22×C412yes—
207C22×C22⋊C4—28no—
208C22×C22⋊C4—28no—
209C22×C22⋊C4—28no—
210C22×C22⋊C4—42no—
211C22×C22⋊C4—42no—
212C22×C22⋊C4—42no—
213C22×C22⋊C4—42no—
214C22×C22⋊C4—416no—
215C22×C22⋊C4—44no—
216C22×C22⋊C4—44no—
217C22×C22⋊C4—88no—
218C22×C22⋊C4—88no—
219C22×C22⋊C4C22⋊C414yes—
220C22×C22⋊C4C22⋊C414yes—
221C22×C22⋊C4C22⋊C412yes—
222C22×C22⋊C4C22⋊C412yes—
223C22×C22⋊C4C4⋊C412yes—
224C22×C22⋊C4C4⋊C412yes—
225C22×C22⋊C4C4⋊C414yes—
226C22×C22⋊C4C2×D414yes—
227C22×C42—22no—
228C22×C42—22no—
229C22×C42—22no—
230C22×C42—22no—
231C22×C42—44no—
232C22×C42C4211yescharacteristic
233C22×C42C4211yescharacteristic
234C22×C42C4212yes—
235C22×C42C22⋊C412yes—
236C22×C42C4⋊C411yescharacteristic
237C22×C42C4⋊C411yescharacteristic
238C22×C42C4⋊C412yes—
239C22×C42C22×C412yes—
240C2×#99—28no—
241C2×#99—28no—
242C2×#99—28no—
243C2×#99—416no—
244C2×#99—416no—
245C2×#99C22×C4116yes—
246#383—48no—
247#383—48no—
248#382—48no—
249#382—48no—
250#381—48no—
251#381—48no—
252#380—216no—
253#380—48no—
254#380—48no—
255#380—48no—
256#379—28no—
257#379—28no—
258#379—44no—
259#379—44no—
260C4×C22⋊C4—216no—
261C4×C22⋊C4—48no—
262C4×C22⋊C4—48no—
263C4×C22⋊C4—48no—
264C2×#95—24no—
265C2×#95—24no—
266C2×#95—22no—
267C2×#95—22no—
268C2×#95—24no—
269C2×#95—216no—
270C2×#95—42no—
271C2×#95—42no—
272C2×#95—42no—
273C2×#95—42no—
274C2×#95—42no—
275C2×#95—42no—
276C2×#95—44no—
277C2×#95—44no—
278C2×#95—42no—
279C2×#95—42no—
280C2×#95—42no—
281C2×#95—42no—
282C2×#95—88no—
283C2×#95C22×C414yes—
284C2×#95C22×C414yes—
285#342—216no—
286#342—216no—
287C25—28no—
288C25—22no—
289C25—22no—
290C25—22no—
291C25—22no—
292C25—44no—
293C25—44no—
294C25—48no—
295C25—44no—
296C25C2×C22⋊C411yescharacteristic
297C25C2×C22⋊C412yes—
298C25C2×C22⋊C412yes—
299C25C2×C22⋊C412yes—
300C25C2×C4⋊C412yes—
301C25C2×C4⋊C412yes—
302C25C22×D412yes—
303C22×D4—28no—
304C22×D4—28no—
305C22×D4—41no—
306C22×D4—41no—
307C22×D4—42no—
308C22×D4—42no—
309C22×D4—42no—
310C22×D4—42no—
311C22×D4—42no—
312C22×D4—42no—
313C22×D4—41no—
314C22×D4—41no—
315C22×D4—41no—
316C22×D4—41no—
317C22×D4—41no—
318C22×D4—41no—
319C22×D4—41no—
320C22×D4—41no—
321C22×D4—41no—
322C22×D4—41no—
323C22×D4—44no—
324C22×D4—44no—
325C22×D4—44no—
326C22×D4—44no—
327C22×D4—44no—
328C22×D4—44no—
329C22×D4—44no—
330C22×D4—44no—
331C22×D4—44no—
332C22×D4—44no—
333C22×D4—416no—
334C22×D4—416no—
335C22×D4—416no—
336C22×D4—416no—
337C22×D4C2×C4212yes—
338C22×D4C2×C22⋊C412yes—
339C22×D4C2×C22⋊C412yes—
340C22×D4C2×C4⋊C411yescharacteristic
341C22×D4C2×C4⋊C411yescharacteristic
342C22×D4C2×C4⋊C412yes—
343C22×D4C2×C4⋊C412yes—
344C22×D4C23×C412yes—
345C22×D4C22×D411yescharacteristic
346C22×D4C22×Q811yescharacteristic
347C23×C4—21no—
348C23×C4—21no—
349C23×C4—21no—
350C23×C4—21no—
351C23×C4—22no—
352C23×C4—21no—
353C23×C4—21no—
354C23×C4—21no—
355C23×C4—21no—
356C23×C4—22no—
357C23×C4—22no—
358C23×C4—22no—
359C23×C4—22no—
360C23×C4—24no—
361C23×C4—22no—
362C23×C4—24no—
363C23×C4—22no—
364C23×C4—22no—
365C23×C4—24no—
366C23×C4—24no—
367C23×C4—22no—
368C23×C4—22no—
369C23×C4—24no—
370C23×C4—24no—
371C23×C4—24no—
372C23×C4—24no—
373C23×C4—24no—
374C23×C4—24no—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—24no—
378C23×C4—24no—
379C23×C4—24no—
380C23×C4—24no—
381C23×C4—24no—
382C23×C4—24no—
383C23×C4—24no—
384C23×C4—24no—
385C23×C4—24no—
386C23×C4—24no—
387C23×C4—24no—
388C23×C4—24no—
389C23×C4—44no—
390C23×C4—44no—
391C23×C4—416no—
392C23×C4—42no—
393C23×C4—42no—
394C23×C4—48no—
395C23×C4—48no—
396C23×C4—48no—
397C23×C4—48no—
398C23×C4—44no—
399C23×C4—44no—
400C23×C4—48no—
401C23×C4—48no—
402C23×C4—44no—
403C23×C4—44no—
404C23×C4—42no—
405C23×C4—42no—
406C23×C4—42no—
407C23×C4—42no—
408C23×C4—88no—
409C23×C4—84no—
410C23×C4—84no—
411C23×C4—88no—
412C23×C4—88no—
413C23×C4—84no—
414C23×C4—84no—
415C23×C4—88no—
416C23×C4—88no—
417C23×C4—88no—
418C23×C4—88no—
419C23×C4—816no—
420C23×C4—816no—
421C23×C4#9512yes—
422C23×C4#9511yescharacteristic
423C23×C4#9511yescharacteristic
424C23×C4#9514yes—
425C23×C4#9512yes—
426C23×C4#9512yes—
427C23×C4#9514yes—
428C23×C4#9514yes—
429C23×C4#9514yes—
430C23×C4#9514yes—
431C23×C4#9512yes—
432C23×C4#9511yescharacteristic
433C23×C4#9511yescharacteristic
434C23×C4#9912yes—
435C23×C4#9912yes—
436C23×C4#9912yes—
437C23×C4#9912yes—
438C23×C4C2×C4211yescharacteristic
439C23×C4C2×C4211yescharacteristic
440C23×C4C2×C22⋊C412yes—
441C23×C4C2×C22⋊C414yes—
442C23×C4C2×C22⋊C411yescharacteristic
443C23×C4C2×C22⋊C414yes—
444C23×C4C2×C22⋊C414yes—
445C23×C4C2×C22⋊C412yes—
446C23×C4C2×C4⋊C411yescharacteristic
447C23×C4C2×C4⋊C411yescharacteristic
448C23×C4C2×C4⋊C414yes—
449C23×C4C2×C4⋊C414yes—
450C23×C4C23×C411yescharacteristic
451C4×D4—44no—
452C4×D4—44no—
453C4×D4—44no—
454C4×D4—44no—
455C4×D4—44no—
456C4×D4—44no—
457C4×D4—44no—
458C4×D4—44no—
459C4×D4—44no—
460C4×D4—44no—
461C4×D4—44no—
462C4×D4—44no—
463C4×D4—44no—
464C4×D4—44no—
465C4×D4—44no—
466C4×D4—44no—
467C4×D4—44no—
468C4×D4—44no—
469C4×D4—44no—
470C4×D4—44no—
471C4×D4—44no—
472C4×D4—44no—
473C4×D4—44no—
474C4×D4—44no—
475C4×D4—44no—
476C4×D4—44no—
477C4×D4—44no—
478C4×D4—44no—
479C4×D4—44no—
480C4×D4—44no—
481C4×D4—44no—
482C4×D4—44no—
483#117—832no—
484#117—832no—
485C2×C4⋊C4—42no—
486C2×C4⋊C4—42no—
487C2×C4⋊C4—42no—
488C2×C4⋊C4—42no—
489C2×C4⋊C4—42no—
490C2×C4⋊C4—42no—
491C2×C4⋊C4—42no—
492C2×C4⋊C4—42no—
493C2×C4⋊C4—41no—
494C2×C4⋊C4—41no—
495C2×C4⋊C4—41no—
496C2×C4⋊C4—41no—
497C2×C4⋊C4—42no—
498C2×C4⋊C4—42no—
499C2×C4⋊C4—48no—
500C2×C4⋊C4—416no—
501C2×C4⋊C4—88no—
502C2×C4⋊C4—88no—
503C2×C4⋊C4—88no—
504C2×C4⋊C4—816no—
505C2×C4⋊C4#9512yes—
506C2×C4⋊C4#9514yes—
507C2×C4⋊C4#9512yes—
508C2×C4⋊C4C2×C4214yes—
509C2×C4⋊C4C2×C4⋊C412yes—
510C2×C4⋊C4C2×C4⋊C412yes—
511C2×C22⋊C4—216no—
512C2×C22⋊C4—44no—
513C2×C22⋊C4—44no—
514C2×C22⋊C4—44no—
515C2×C22⋊C4—42no—
516C2×C22⋊C4—42no—
517C2×C22⋊C4—44no—
518C2×C22⋊C4—42no—
519C2×C22⋊C4—42no—
520C2×C22⋊C4—44no—
521C2×C22⋊C4—44no—
522C2×C22⋊C4—42no—
523C2×C22⋊C4—42no—
524C2×C22⋊C4—42no—
525C2×C22⋊C4—42no—
526C2×C22⋊C4—44no—
527C2×C22⋊C4—44no—
528C2×C22⋊C4—416no—
529C2×C22⋊C4—416no—
530C2×C22⋊C4—416no—
531C2×C22⋊C4—416no—
532C2×C22⋊C4—48no—
533C2×C22⋊C4—48no—
534C2×C22⋊C4—48no—
535C2×C22⋊C4—48no—
536C2×C22⋊C4—48no—
537C2×C22⋊C4—88no—
538C2×C22⋊C4—88no—
539C2×C22⋊C4—88no—
540C2×C22⋊C4—88no—
541C2×C22⋊C4—88no—
542C2×C22⋊C4—88no—
543C2×C22⋊C4—864no—
544C2×C22⋊C4—816no—
545C2×C22⋊C4#9514yes—
546C2×C22⋊C4#9514yes—
547C2×C22⋊C4#9514yes—
548C2×C22⋊C4#9514yes—
549C2×C22⋊C4C2×C22⋊C414yes—
550C2×C22⋊C4C2×C22⋊C414yes—
551C2×C22⋊C4C2×C4⋊C414yes—
552C2×C22⋊C4C2×C4⋊C414yes—
553C2×C42—24no—
554C2×C42—22no—
555C2×C42—22no—
556C2×C42—24no—
557C2×C42—22no—
558C2×C42—22no—
559C2×C42—24no—
560C2×C42—22no—
561C2×C42—22no—
562C2×C42—24no—
563C2×C42—22no—
564C2×C42—22no—
565C2×C42—24no—
566C2×C42—24no—
567C2×C42—24no—
568C2×C42—24no—
569C2×C42—416no—
570C2×C42—816no—
571C2×C42#9512yes—
572C2×C42#9512yes—
573C2×C42#9512yes—
574C2×C42#9512yes—
575C2×C42C2×C4212yes—
576C2×C42C2×C4212yes—
577C2×C42C2×C4⋊C412yes—
578C2×C42C2×C4⋊C412yes—
579#99—416no—
580#99—416no—
581#99—416no—
582#99—416no—
583#95—44no—
584#95—44no—
585#95—44no—
586#95—48no—
587#95—44no—
588#95—416no—
589#95—416no—
590#95—48no—
591#95—48no—
592#95—816no—
593C24—24no—
594C24—22no—
595C24—22no—
596C24—24no—
597C24—22no—
598C24—22no—
599C24—24no—
600C24—24no—
601C24—24no—
602C24—22no—
603C24—24no—
604C24—24no—
605C24—24no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—24no—
616C24—42no—
617C24—42no—
618C24—42no—
619C24—42no—
620C24—48no—
621C24—48no—
622C24—48no—
623C24—48no—
624C24—42no—
625C24—42no—
626C24—44no—
627C24—44no—
628C24—44no—
629C24—44no—
630C24—44no—
631C24—44no—
632C24—44no—
633C24—44no—
634C24—42no—
635C24—44no—
636C24—44no—
637C24—42no—
638C24—432no—
639C24—432no—
640C24—48no—
641C24—44no—
642C24—44no—
643C24—84no—
644C24—84no—
645C24—84no—
646C24—84no—
647C24—84no—
648C24—82no—
649C24—82no—
650C24—816no—
651C24—816no—
652C24C2×#9511yescharacteristic
653C24C2×#9511yescharacteristic
654C24C2×#9512yes—
655C24C2×#9512yes—
656C24C2×#9911yescharacteristic
657C24C2×#9911yescharacteristic
658C24C2×#9911yescharacteristic
659C24C2×#9911yescharacteristic
660C24#41018yes—
661C24C22×C22⋊C411yescharacteristic
662C24C22×C22⋊C412yes—
663C24C22×C4⋊C412yes—
664C2×D4—24no—
665C2×D4—24no—
666C2×D4—24no—
667C2×D4—24no—
668C2×D4—24no—
669C2×D4—24no—
670C2×D4—24no—
671C2×D4—24no—
672C2×D4—42no—
673C2×D4—42no—
674C2×D4—42no—
675C2×D4—41no—
676C2×D4—41no—
677C2×D4—42no—
678C2×D4—42no—
679C2×D4—42no—
680C2×D4—41no—
681C2×D4—41no—
682C2×D4—42no—
683C2×D4—42no—
684C2×D4—42no—
685C2×D4—42no—
686C2×D4—42no—
687C2×D4—42no—
688C2×D4—42no—
689C2×D4—42no—
690C2×D4—48no—
691C2×D4—48no—
692C2×D4—416no—
693C2×D4—416no—
694C2×D4—48no—
695C2×D4—48no—
696C2×D4—416no—
697C2×D4—416no—
698C2×D4—416no—
699C2×D4—416no—
700C2×D4—48no—
701C2×D4—48no—
702C2×D4—48no—
703C2×D4—48no—
704C2×D4—48no—
705C2×D4—48no—
706C2×D4—48no—
707C2×D4—48no—
708C22×C4—28no—
709C22×C4—22no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—22no—
715C22×C4—24no—
716C22×C4—22no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—22no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—24no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—22no—
732C22×C4—22no—
733C22×C4—24no—
734C22×C4—24no—
735C22×C4—24no—
736C22×C4—24no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—24no—
740C22×C4—24no—
741C22×C4—24no—
742C22×C4—24no—
743C22×C4—24no—
744C22×C4—24no—
745C22×C4—24no—
746C22×C4—24no—
747C22×C4—24no—
748C22×C4—24no—
749C22×C4—24no—
750C22×C4—24no—
751C22×C4—24no—
752C22×C4—24no—
753C22×C4—24no—
754C22×C4—24no—
755C22×C4—44no—
756C22×C4—42no—
757C22×C4—42no—
758C22×C4—44no—
759C22×C4—44no—
760C22×C4—44no—
761C22×C4—44no—
762C22×C4—42no—
763C22×C4—42no—
764C22×C4—42no—
765C22×C4—42no—
766C22×C4—48no—
767C22×C4—48no—
768C22×C4—416no—
769C22×C4—416no—
770C22×C4—416no—
771C22×C4—48no—
772C22×C4—48no—
773C22×C4—416no—
774C22×C4—42no—
775C22×C4—44no—
776C22×C4—44no—
777C22×C4—42no—
778C22×C4—44no—
779C22×C4—44no—
780C22×C4—44no—
781C22×C4—44no—
782C22×C4—48no—
783C22×C4—42no—
784C22×C4—42no—
785C22×C4—42no—
786C22×C4—44no—
787C22×C4—42no—
788C22×C4—42no—
789C22×C4—42no—
790C22×C4—48no—
791C22×C4—48no—
792C22×C4—44no—
793C22×C4—44no—
794C22×C4—416no—
795C22×C4—44no—
796C22×C4—48no—
797C22×C4—48no—
798C22×C4—48no—
799C22×C4—44no—
800C22×C4—44no—
801C22×C4—48no—
802C22×C4—44no—
803C22×C4—44no—
804C22×C4—44no—
805C22×C4—84no—
806C22×C4—84no—
807C22×C4—88no—
808C22×C4—88no—
809C22×C4—84no—
810C22×C4—84no—
811C22×C4—88no—
812C22×C4—88no—
813C22×C4—84no—
814C22×C4—84no—
815C22×C4—84no—
816C22×C4—84no—
817C22×C4—84no—
818C22×C4—84no—
819C22×C4—84no—
820C22×C4—84no—
821C22×C4—88no—
822C22×C4—88no—
823C22×C4—88no—
824C22×C4—88no—
825C22×C4—88no—
826C22×C4—88no—
827C22×C4—88no—
828C22×C4—88no—
829C22×C4—88no—
830C22×C4—88no—
831C22×C4—88no—
832C22×C4—88no—
833C22×C4—84no—
834C22×C4—84no—
835C22×C4—84no—
836C22×C4—816no—
837C22×C4—816no—
838C22×C4—816no—
839C22×C4—84no—
840C22×C4—816no—
841C22×C4—816no—
842C22×C4—84no—
843C22×C4—84no—
844C22×C4—84no—
845C22×C4—84no—
846C22×C4—84no—
847C22×C4—84no—
848C22×C4—84no—
849C22×C4—84no—
850C22×C4—84no—
851C22×C4—816no—
852C22×C4—816no—
853C22×C4—84no—
854C22×C4—84no—
855C22×C4#34214yes—
856C22×C4#34212yes—
857C22×C4#34212yes—
858C22×C4#34214yes—
859C22×C4#34212yes—
860C22×C4#34212yes—
861C22×C4C2×#9511yescharacteristic
862C22×C4C2×#9511yescharacteristic
863C22×C4C2×#9512yes—
864C22×C4C2×#9512yes—
865C22×C4C2×#9514yes—
866C22×C4C2×#9514yes—
867C22×C4C2×#9512yes—
868C22×C4C2×#9512yes—
869C22×C4C2×#9914yes—
870C22×C4C2×#9914yes—
871C22×C4C22×C4211yescharacteristic
872C22×C4C22×C4⋊C411yescharacteristic
873C4⋊C4—42no—
874C4⋊C4—42no—
875C4⋊C4—44no—
876C4⋊C4—44no—
877C4⋊C4—42no—
878C4⋊C4—42no—
879C4⋊C4—816no—
880C4⋊C4—832no—
881C22⋊C4—44no—
882C22⋊C4—44no—
883C22⋊C4—44no—
884C22⋊C4—44no—
885C22⋊C4—44no—
886C22⋊C4—44no—
887C22⋊C4—44no—
888C22⋊C4—44no—
889C22⋊C4—416no—
890C22⋊C4—416no—
891C22⋊C4—816no—
892C22⋊C4—816no—
893C22⋊C4—88no—
894C22⋊C4—88no—
895C22⋊C4—832no—
896C22⋊C4—832no—
897C22⋊C4—816no—
898C22⋊C4—816no—
899C42—24no—
900C42—24no—
901C42—24no—
902C42—24no—
903C42—24no—
904C42—24no—
905C42—24no—
906C42—24no—
907C42—832no—
908C23—216no—
909C23—216no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—21no—
921C23—21no—
922C23—21no—
923C23—21no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—28no—
933C23—22no—
934C23—22no—
935C23—28no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—44no—
943C23—44no—
944C23—44no—
945C23—44no—
946C23—44no—
947C23—44no—
948C23—44no—
949C23—44no—
950C23—42no—
951C23—42no—
952C23—42no—
953C23—42no—
954C23—42no—
955C23—42no—
956C23—42no—
957C23—42no—
958C23—416no—
959C23—48no—
960C23—48no—
961C23—48no—
962C23—48no—
963C23—416no—
964C23—416no—
965C23—416no—
966C23—44no—
967C23—44no—
968C23—44no—
969C23—44no—
970C23—44no—
971C23—44no—
972C23—44no—
973C23—44no—
974C23—44no—
975C23—44no—
976C23—42no—
977C23—42no—
978C23—42no—
979C23—42no—
980C23—44no—
981C23—44no—
982C23—82no—
983C23—82no—
984C23—82no—
985C23—82no—
986C23—82no—
987C23—82no—
988C23—88no—
989C23—82no—
990C23—82no—
991C23—82no—
992C23—82no—
993C23—82no—
994C23—82no—
995C23—816no—
996C23—832no—
997C23—816no—
998C23—88no—
999C23—84no—
1000C23—84no—
1001C23—84no—
1002C23—84no—
1003C23—816no—
1004C23—832no—
1005C23—88no—
1006C23—88no—
1007C23—816no—
1008C23C2×#34211yescharacteristic
1009C23C2×#34211yescharacteristic
1010C23C2×#34211yescharacteristic
1011C23C2×#34211yescharacteristic
1012C23#174014yes—
1013C23#174014yes—
1014C23#212714yes—
1015C23#212812yes—
1016C23#212912yes—
1017C23C22×#9511yescharacteristic
1018C23C22×#9911yescharacteristic
1019C23C22×#9911yescharacteristic
1020C23C2×#41014yes—
1021D4—44no—
1022D4—48no—
1023D4—44no—
1024D4—48no—
1025D4—48no—
1026D4—48no—
1027D4—48no—
1028D4—44no—
1029D4—48no—
1030D4—44no—
1031C2×C4—28no—
1032C2×C4—24no—
1033C2×C4—24no—
1034C2×C4—28no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—42no—
1048C2×C4—44no—
1049C2×C4—42no—
1050C2×C4—42no—
1051C2×C4—42no—
1052C2×C4—44no—
1053C2×C4—48no—
1054C2×C4—48no—
1055C2×C4—48no—
1056C2×C4—48no—
1057C2×C4—48no—
1058C2×C4—48no—
1059C2×C4—48no—
1060C2×C4—48no—
1061C2×C4—44no—
1062C2×C4—44no—
1063C2×C4—42no—
1064C2×C4—42no—
1065C2×C4—42no—
1066C2×C4—42no—
1067C2×C4—42no—
1068C2×C4—42no—
1069C2×C4—42no—
1070C2×C4—42no—
1071C2×C4—42no—
1072C2×C4—42no—
1073C2×C4—48no—
1074C2×C4—44no—
1075C2×C4—44no—
1076C2×C4—44no—
1077C2×C4—42no—
1078C2×C4—42no—
1079C2×C4—48no—
1080C2×C4—42no—
1081C2×C4—42no—
1082C2×C4—42no—
1083C2×C4—42no—
1084C2×C4—42no—
1085C2×C4—42no—
1086C2×C4—44no—
1087C2×C4—44no—
1088C2×C4—42no—
1089C2×C4—42no—
1090C2×C4—84no—
1091C2×C4—84no—
1092C2×C4—84no—
1093C2×C4—84no—
1094C2×C4—84no—
1095C2×C4—84no—
1096C2×C4—84no—
1097C2×C4—84no—
1098C2×C4—84no—
1099C2×C4—82no—
1100C2×C4—84no—
1101C2×C4—82no—
1102C2×C4—816no—
1103C2×C4—88no—
1104C2×C4—88no—
1105C2×C4—88no—
1106C2×C4—88no—
1107C2×C4—84no—
1108C2×C4—84no—
1109C2×C4—84no—
1110C2×C4—84no—
1111C2×C4—816no—
1112C2×C4—816no—
1113C2×C4—84no—
1114C2×C4—84no—
1115C2×C4—168no—
1116C2×C4—168no—
1117C2×C4—168no—
1118C2×C4—168no—
1119C2×C4—1632no—
1120C2×C4C2×#34214yes—
1121C2×C4C2×#34214yes—
1122C22—24no—
1123C22—24no—
1124C22—24no—
1125C22—28no—
1126C22—28no—
1127C22—24no—
1128C22—24no—
1129C22—28no—
1130C22—28no—
1131C22—24no—
1132C22—21no—
1133C22—21no—
1134C22—21no—
1135C22—21no—
1136C22—21no—
1137C22—21no—
1138C22—21no—
1139C22—21no—
1140C22—21no—
1141C22—21no—
1142C22—21no—
1143C22—21no—
1144C22—24no—
1145C22—24no—
1146C22—44no—
1147C22—44no—
1148C22—44no—
1149C22—44no—
1150C22—416no—
1151C22—42no—
1152C22—42no—
1153C22—42no—
1154C22—42no—
1155C22—42no—
1156C22—42no—
1157C22—42no—
1158C22—42no—
1159C22—42no—
1160C22—42no—
1161C22—82no—
1162C22—82no—
1163C22—88no—
1164C22—84no—
1165C22—84no—
1166C22—88no—
1167C22—88no—
1168C22—88no—
1169C22—88no—
1170C22—88no—
1171C22—88no—
1172C22—84no—
1173C22—84no—
1174C22—82no—
1175C22—82no—
1176C22—88no—
1177C22—88no—
1178C22#810012yes—
1179C22#810012yes—
1180C22#1258212yes—
1181C22#1258212yes—
1182C22#1258312yes—
1183C22#1258312yes—
1184C22C22×#34211yescharacteristic
1185C22C2×#174012yes—
1186C22C2×#212712yes—
1187C22C2×#212811yescharacteristic
1188C22C2×#212911yescharacteristic
1189C4—24no—
1190C4—24no—
1191C4—41no—
1192C4—41no—
1193C4—41no—
1194C4—41no—
1195C4—44no—
1196C4—44no—
1197C4—42no—
1198C4—42no—
1199C4—164no—
1200C4—164no—
1201C4—1616no—
1202C2—21no—
1203C2—22no—
1204C2—22no—
1205C2—22no—
1206C2—22no—
1207C2—21no—
1208C2—22no—
1209C2—44no—
1210C2—44no—
1211C2—82no—
1212C2—82no—
1213C2#12805014yesdirect product factor
1214C2C2×#810011yescharacteristic
1215C2C2×#1258211yescharacteristic
1216C2C2×#1258311yescharacteristic
subgroupG/H
center, socleC23C2×#342
commutatorC22×C4C22×C42
Frattini, cosocleC23×D4C24
prime radicalC24×D4C23
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C24×C4 ◁ C23×C4×D4 ◁ G
LECSG ▷ C23×D4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #128050C2direct (N × H)
6. C22×#383C4semidirect
7. C22×#382C4semidirect
11. #20722C4semidirect
15. C2×#1799C4semidirect
18. C2×C4×#99C4semidirect
20. #14345C4semidirect
22. C2×#1445C4semidirect
56. C2×#383C2×C4semidirect
60. C2×#382C2×C4semidirect
82. #1799C2×C4semidirect
90. C4×#99C2×C4semidirect
94. #1445C2×C4semidirect
1213. C2#128050direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#207222
C2×#143452
#1280502
C2×#73072