Finite Group Databasebeta

← #354541

Subgroups — #354541

Order 512.

2008 conjugacy classes of subgroups.

The subgroup lattice has 869 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2290C211yesmaximal, characteristic
2C2×#1955C211yesmaximal, characteristic
3C2×#1954C211yesmaximal, characteristic
4C2×#1768C211yesmaximal, characteristic, complemented
5C2×#1749C211yesmaximal, characteristic, complemented
6C2×#1750C211yesmaximal, characteristic, complemented
7C2×#1750C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊C8C211yesmaximal, characteristic, complemented
9C2×#1726C211yesmaximal, characteristic, complemented
10#10922C211yesmaximal, characteristic, complemented
11#10922C211yesmaximal, characteristic, complemented
12#10921C211yesmaximal, characteristic, complemented
13#10921C211yesmaximal, characteristic, complemented
14#10835C211yesmaximal, characteristic, complemented
15#10834C211yesmaximal, characteristic, complemented
16C22×C4×D4C2211yescharacteristic
17C22×#117C2211yescharacteristic
18C23×C42C2211yescharacteristic
19C22×C4⋊C8C2211yescharacteristic
20C22×C4⋊C8C2211yescharacteristic
21C22×C22⋊C8C2211yescharacteristic
22C22×C22⋊C8C2211yescharacteristic
23C22×C22⋊C8C2211yescharacteristic
24C22×C22⋊C8C2211yescharacteristic
25C22×C22⋊C8C2211yescharacteristic
26C22×C22⋊C8C2211yescharacteristic
27C22×C22⋊C8C2211yescharacteristic
28C22×C22⋊C8C2211yescharacteristic
29C22×#97C2211yescharacteristic
30C22×#97C2211yescharacteristic
31C22×#97C2211yescharacteristic
32C22×#97C2211yescharacteristic
33C22×C4×C8C2211yescharacteristic
34C22×C4×C8C2211yescharacteristic
35C22×C4×C8C2211yescharacteristic
36C22×C4×C8C2211yescharacteristic
37#2290—24no—
38#2290—24no—
39C2×#388C412yes—
40C2×#387C412yes—
41C2×#386C412yes—
42C2×#385C412yes—
43C2×C4×C4⋊C4C2211yescharacteristic
44C2×C4×C22⋊C4C2211yescharacteristic
45C2×C4×C22⋊C4C2211yescharacteristic
46C2×#376C2211yescharacteristic
47#1955C418yescomplemented
48#1954C418yescomplemented
49#1768—24no—
50#1750—24no—
51#1750—24no—
52#1749—24no—
53C4×C22⋊C8—24no—
54C2×#336C2211yescharacteristic
55C2×#336C2211yescharacteristic
56C2×#336C2211yescharacteristic
57C2×#336C2211yescharacteristic
58C2×#336C2211yescharacteristic
59C2×#336C2211yescharacteristic
60C2×#336C2211yescharacteristic
61C2×#336C2211yescharacteristic
62C2×#336C2211yescharacteristic
63C2×#336C2211yescharacteristic
64#1726—24no—
65C23×D4C2×C411yescharacteristic
66C24×C4C2×C412yes—
67C24×C4C2311yescharacteristic
68C24×C4C2311yescharacteristic
69C23×C8C2311yescharacteristic
70C23×C8C2311yescharacteristic
71C23×C8C2311yescharacteristic
72C23×C8C2311yescharacteristic
73C23×C8C2311yescharacteristic
74C23×C8C2311yescharacteristic
75C23×C8C2311yescharacteristic
76C23×C8C2311yescharacteristic
77C2×C4×D4—22no—
78C2×C4×D4—22no—
79C2×C4×D4—22no—
80C2×C4×D4—22no—
81C2×C4×D4C2×C414yes—
82C2×C4×D4C2×C414yes—
83C2×#117—22no—
84C2×#117—22no—
85C2×#117—22no—
86C2×#117—22no—
87C2×#117—22no—
88C2×#117—22no—
89C22×C4⋊C4C2×C412yes—
90C22×C4⋊C4C2×C412yes—
91C22×C4⋊C4C2×C411yescharacteristic
92C22×C22⋊C4C2×C412yes—
93C22×C22⋊C4C2×C412yes—
94C22×C22⋊C4C2×C412yes—
95C22×C22⋊C4C2×C411yescharacteristic
96C22×C22⋊C4C2×C411yescharacteristic
97C22×C42—22no—
98C22×C42—22no—
99C22×C42—22no—
100C22×C42—22no—
101C22×C42—22no—
102C22×C42—22no—
103C22×C42C2×C412yes—
104C22×C42C2311yescharacteristic
105C22×C42C2311yescharacteristic
106C22×C42C2311yescharacteristic
107C22×C42C2311yescharacteristic
108C22×C42C2311yescharacteristic
109C2×C4⋊C8—22no—
110C2×C4⋊C8—22no—
111C2×C4⋊C8—22no—
112C2×C4⋊C8—22no—
113C2×C4⋊C8C2×C414yescomplemented
114C2×C4⋊C8C2×C414yescomplemented
115C2×C22⋊C8—22no—
116C2×C22⋊C8—22no—
117C2×C22⋊C8—22no—
118C2×C22⋊C8—22no—
119C2×C22⋊C8—22no—
120C2×C22⋊C8—22no—
121C2×C22⋊C8—22no—
122C2×C22⋊C8—22no—
123C2×C22⋊C8—22no—
124C2×C22⋊C8—22no—
125C2×C22⋊C8—22no—
126C2×C22⋊C8—22no—
127C2×C22⋊C8—22no—
128C2×C22⋊C8—22no—
129C2×C22⋊C8—22no—
130C2×C22⋊C8—22no—
131C2×C22⋊C8C2×C414yes—
132C2×C22⋊C8C2×C414yes—
133C2×C22⋊C8C2×C414yes—
134C2×C22⋊C8C2×C414yes—
135C2×C22⋊C8C2×C414yescomplemented
136C2×C22⋊C8C2×C414yescomplemented
137C2×C22⋊C8C2×C414yescomplemented
138C2×C22⋊C8C2×C414yescomplemented
139C2×#97—22no—
140C2×#97—22no—
141C2×#97—22no—
142C2×#97—22no—
143C2×#97—22no—
144C2×#97—22no—
145C2×#97—22no—
146C2×#97—22no—
147C2×#97—22no—
148C2×#97—22no—
149C2×#97C2×C414yescomplemented
150C2×#97D414yescomplemented
151C2×C4×C8—22no—
152C2×C4×C8—22no—
153C2×C4×C8—22no—
154C2×C4×C8—22no—
155C2×C4×C8—22no—
156C2×C4×C8—22no—
157C2×C4×C8—22no—
158C2×C4×C8—22no—
159C2×C4×C8—22no—
160C2×C4×C8—22no—
161C2×C4×C8C2×C414yescomplemented
162C2×C4×C8D414yescomplemented
163#388—28no—
164#387—28no—
165#386—28no—
166#385—28no—
167C4×C4⋊C4—22no—
168C4×C4⋊C4—22no—
169C4×C22⋊C4—22no—
170C4×C22⋊C4—22no—
171C4×C22⋊C4—22no—
172C4×C22⋊C4—22no—
173#376D414yes—
174#376D414yes—
175C2×#95C2×C412yes—
176C2×#95C2×C412yes—
177C2×#95C2×C412yes—
178C2×#95C2×C412yes—
179C2×#95C2×C412yes—
180#336—22no—
181#336—22no—
182#336—22no—
183#336—22no—
184#336—22no—
185#336—22no—
186#336—22no—
187#336—22no—
188#336—22no—
189#336—22no—
190C25C22×C411yescharacteristic
191C25C22×C411yescharacteristic
192C22×D4—24no—
193C22×D4—22no—
194C22×D4—22no—
195C22×D4—42no—
196C22×D4C4214yes—
197C23×C4—24no—
198C23×C4—24no—
199C23×C4—24no—
200C23×C4—21no—
201C23×C4—21no—
202C23×C4—21no—
203C23×C4—21no—
204C23×C4—21no—
205C23×C4—21no—
206C23×C4—21no—
207C23×C4—21no—
208C23×C4—21no—
209C23×C4—21no—
210C23×C4—21no—
211C23×C4—21no—
212C23×C4—21no—
213C23×C4—21no—
214C23×C4—21no—
215C23×C4—21no—
216C23×C4—21no—
217C23×C4—21no—
218C23×C4—21no—
219C23×C4—21no—
220C23×C4—21no—
221C23×C4—21no—
222C23×C4—21no—
223C23×C4—21no—
224C23×C4—24no—
225C23×C4—24no—
226C23×C4—42no—
227C23×C4—42no—
228C23×C4C22×C412yes—
229C23×C4C22×C411yescharacteristic
230C23×C4C22×C411yescharacteristic
231C23×C4C22×C412yes—
232C23×C4C22×C412yes—
233C23×C4C22×C412yes—
234C23×C4C22×C412yes—
235C23×C4C22×C412yes—
236C23×C4C22×C412yes—
237C23×C4C22×C411yescharacteristic
238C23×C4C22×C411yescharacteristic
239C23×C4C22×C412yes—
240C23×C4C2411yescharacteristic
241C22×C8—21no—
242C22×C8—21no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—21no—
246C22×C8—21no—
247C22×C8—21no—
248C22×C8—21no—
249C22×C8—21no—
250C22×C8—21no—
251C22×C8—21no—
252C22×C8—21no—
253C22×C8—21no—
254C22×C8—21no—
255C22×C8—21no—
256C22×C8—21no—
257C22×C8—21no—
258C22×C8—21no—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—21no—
264C22×C8—21no—
265C22×C8—21no—
266C22×C8—21no—
267C22×C8—21no—
268C22×C8—21no—
269C22×C8—21no—
270C22×C8—21no—
271C22×C8—21no—
272C22×C8—21no—
273C22×C8—21no—
274C22×C8—21no—
275C22×C8—21no—
276C22×C8—21no—
277C22×C8—21no—
278C22×C8—21no—
279C22×C8—21no—
280C22×C8—21no—
281C22×C8C22×C412yes—
282C22×C8C22×C412yes—
283C22×C8C22×C412yes—
284C22×C8C22×C412yes—
285C22×C8C22×C412yes—
286C22×C8C22×C412yes—
287C22×C8C22×C412yes—
288C22×C8C22×C412yes—
289C22×C8C2×D412yes—
290C22×C8C2×D412yes—
291C22×C8C2×D412yes—
292C22×C8C2×D412yes—
293C22×C8#4112yes—
294C22×C8#4112yes—
295C22×C8#4112yes—
296C22×C8#4112yes—
297C4×D4—28no—
298C4×D4—28no—
299C4×D4—28no—
300C4×D4—28no—
301#117—44no—
302#117—44no—
303#117—44no—
304#117—44no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4C4214yes—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—22no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—42no—
326C2×C22⋊C4—42no—
327C2×C22⋊C4C4214yes—
328C2×C22⋊C4C4214yes—
329C2×C42—21no—
330C2×C42—21no—
331C2×C42—21no—
332C2×C42—21no—
333C2×C42—24no—
334C2×C42—24no—
335C2×C42—24no—
336C2×C42—21no—
337C2×C42—21no—
338C2×C42—21no—
339C2×C42—21no—
340C2×C42—21no—
341C2×C42—21no—
342C2×C42—21no—
343C2×C42—21no—
344C2×C42—21no—
345C2×C42—21no—
346C2×C42—21no—
347C2×C42—21no—
348C2×C42—44no—
349C2×C42—44no—
350C2×C42—44no—
351C2×C42—44no—
352C2×C42C22×C412yes—
353C2×C42C22×C412yes—
354C2×C42C2×D412yes—
355C2×C42C2×D412yes—
356C2×C42C2×D412yes—
357C2×C42C2×D412yes—
358C2×C42C2×D412yes—
359C2×C42C2×D412yes—
360C2×C42C2×D412yes—
361C2×C42C2×D412yes—
362C2×C42#4112yes—
363C2×C42#4112yes—
364C2×C42#4112yes—
365C2×C42#4112yes—
366C4⋊C8—28no—
367C4⋊C8—28no—
368C22⋊C8—28no—
369C22⋊C8—28no—
370C22⋊C8—28no—
371C22⋊C8—28no—
372C22⋊C8—28no—
373C22⋊C8—28no—
374C22⋊C8—28no—
375C22⋊C8—28no—
376#97—28no—
377#97—28no—
378#97—28no—
379#97—44no—
380C4×C8—28no—
381C4×C8—28no—
382C4×C8—28no—
383C4×C8—44no—
384#95—24no—
385#95—24no—
386#95—24no—
387#95C22⋊C418yes—
388#95C22⋊C418yes—
389C24—21no—
390C24—21no—
391C24—21no—
392C24—21no—
393C24—21no—
394C24—21no—
395C24—22no—
396C24—22no—
397C24—22no—
398C24—21no—
399C24—21no—
400C24—21no—
401C24—21no—
402C24—21no—
403C24—21no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24C2×C4212yes—
409C24C2×C4212yes—
410C24#13114yes—
411C24C23×C411yescharacteristic
412C2×D4—28no—
413C2×D4—28no—
414C2×D4—44no—
415C2×D4—48no—
416C2×D4—48no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—216no—
426C22×C4—22no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
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—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—48no—
482C22×C4—48no—
483C22×C4—48no—
484C22×C4—48no—
485C22×C4—48no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—41no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—41no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—48no—
519C22×C4C2×C4212yes—
520C22×C4C2×C4212yes—
521C22×C4C2×C4212yes—
522C22×C4C2×C4212yes—
523C22×C4C2×C22⋊C414yes—
524C22×C4C2×C22⋊C412yes—
525C22×C4C2×C22⋊C412yes—
526C22×C4C2×C22⋊C414yes—
527C22×C4#11712yes—
528C22×C4#11712yes—
529C22×C4C4×D414yes—
530C22×C4C4×D414yes—
531C22×C4#13114yes—
532C22×C4C23×C411yescharacteristic
533C22×C4C23×C411yescharacteristic
534C22×C4C22×D411yescharacteristic
535C22×C4C22×D411yescharacteristic
536C22×C4C22×D411yescharacteristic
537C22×C4C22×D411yescharacteristic
538C22×C4C2×#4111yescharacteristic
539C22×C4C2×#4111yescharacteristic
540C22×C4C2×#4111yescharacteristic
541C22×C4C2×#4111yescharacteristic
542C22×C4C2×#4111yescharacteristic
543C22×C4C2×#4111yescharacteristic
544C22×C4C2×#4111yescharacteristic
545C22×C4C2×#4111yescharacteristic
546C2×C8—22no—
547C2×C8—22no—
548C2×C8—22no—
549C2×C8—22no—
550C2×C8—22no—
551C2×C8—22no—
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—22no—
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—22no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—22no—
580C2×C8—22no—
581C2×C8—22no—
582C2×C8—41no—
583C2×C8—41no—
584C2×C8—41no—
585C2×C8—41no—
586C2×C8—41no—
587C2×C8—41no—
588C2×C8—41no—
589C2×C8—41no—
590C2×C8—41no—
591C2×C8—41no—
592C2×C8—41no—
593C2×C8—41no—
594C2×C8—41no—
595C2×C8—41no—
596C2×C8—41no—
597C2×C8—41no—
598C2×C8C4×D414yes—
599C2×C8C4×D414yes—
600C2×C8C4×D414yes—
601C2×C8C4×D414yes—
602C4⋊C4—28no—
603C4⋊C4—48no—
604C4⋊C4—48no—
605C22⋊C4—28no—
606C22⋊C4—28no—
607C22⋊C4—48no—
608C22⋊C4—48no—
609C22⋊C4—48no—
610C42—22no—
611C42—22no—
612C42—22no—
613C42—22no—
614C42—41no—
615C42—41no—
616C42—41no—
617C42—41no—
618C42—41no—
619C42—41no—
620C42—41no—
621C42—41no—
622C42—48no—
623C42C4×D414yes—
624C42C4×D414yes—
625C42C4×D414yes—
626C42C4×D414yes—
627C42#12114yes—
628C42#12114yes—
629C42#12414yes—
630C42#12714yes—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23#40514yes—
677C23C22×C4211yescharacteristic
678C23C22×C22⋊C411yescharacteristic
679C23C2×#11711yescharacteristic
680C23C2×C4×D411yescharacteristic
681C23C2×C4×D411yescharacteristic
682C23C4×#4111yescharacteristic
683C23C4×#4111yescharacteristic
684C23C2×#13112yes—
685C23C2×#13112yes—
686C23#56812yes—
687C23#56812yes—
688D4—416no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—432no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—41no—
724C2×C4—42no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4C4×C22⋊C414yes—
756C2×C4C4×C22⋊C414yes—
757C2×C4#39018yes—
758C2×C4C2×C4×D411yescharacteristic
759C2×C4C2×C4×D411yescharacteristic
760C2×C4C2×C4×D411yescharacteristic
761C2×C4C2×C4×D411yescharacteristic
762C2×C4C2×C4×D411yescharacteristic
763C2×C4C2×C4×D411yescharacteristic
764C2×C4C2×C4×D411yescharacteristic
765C2×C4C2×C4×D411yescharacteristic
766C2×C4C4×#4111yescharacteristic
767C2×C4C4×#4111yescharacteristic
768C2×C4C4×#4111yescharacteristic
769C2×C4C4×#4111yescharacteristic
770C2×C4C2×#12111yescharacteristic
771C2×C4C2×#12111yescharacteristic
772C2×C4#52511yescharacteristic
773C2×C4#52511yescharacteristic
774C2×C4C2×#12411yescharacteristic
775C2×C4#52911yescharacteristic
776C2×C4#52911yescharacteristic
777C2×C4#52911yescharacteristic
778C2×C4#52911yescharacteristic
779C2×C4C2×#12711yescharacteristic
780C2×C4#53211yescharacteristic
781C2×C4#53211yescharacteristic
782C2×C4#53211yescharacteristic
783C2×C4#53211yescharacteristic
784C2×C4#53211yescharacteristic
785C2×C4#53211yescharacteristic
786C8—24no—
787C8—24no—
788C8—24no—
789C8—24no—
790C8—42no—
791C8—42no—
792C8—42no—
793C8—42no—
794C22—24no—
795C22—24no—
796C22—24no—
797C22—42no—
798C22—42no—
799C22—44no—
800C22—44no—
801C22—44no—
802C22—42no—
803C22—42no—
804C22—44no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—42no—
812C22—82no—
813C22—82no—
814C22—82no—
815C22—82no—
816C22C2×C4×C22⋊C411yescharacteristic
817C22C42×D411yescharacteristic
818C22C42×D411yescharacteristic
819C22C2×#39011yescharacteristic
820C22#229311yescharacteristic
821C22#229311yescharacteristic
822C22#229711yescharacteristic
823C22C2×#40511yescharacteristic
824C22#287311yescharacteristic
825C22C4×#13111yescharacteristic
826C22#287511yescharacteristic
827C22#288012yes—
828C22#288012yes—
829C22#292412yes—
830C22#292512yes—
831C22#292912yes—
832C22#293012yes—
833C22#293312yes—
834C22#293312yes—
835C22#296612yes—
836C22#296712yes—
837C22#296812yes—
838C22#296912yes—
839C4—24no—
840C4—24no—
841C4—28no—
842C4—44no—
843C4—42no—
844C4—42no—
845C4—44no—
846C4—82no—
847C4C4×#12111yescharacteristic
848C4C4×#12111yescharacteristic
849C4C4×#12111yescharacteristic
850C4C4×#12111yescharacteristic
851C4C4×#12411yescharacteristic
852C4C4×#12411yescharacteristic
853C4C4×#12711yescharacteristic
854C4C4×#12711yescharacteristic
855C2—44no—
856C2—82no—
857C2C4×#39011yescharacteristic
858C2#2037811yescharacteristic
859C2#2037911yescharacteristic
860C2#2048411yescharacteristic
861C2#2048711yescharacteristic
862C2#2049011yescharacteristic
863C2#2049311yescharacteristic
864C2#2119112yes—
865C2#2127212yes—
866C2#2127312yes—
867C2#2138112yes—
subgroupG/H
center, Frattini, cosocleC23×C4C24
commutatorC23C22×C42
socleC24C23×C4
prime radicalC23×D4C2×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C2×#1768C2semidirect
5. C2×#1749C2semidirect
6. C2×#1750C2semidirect
7. C2×#1750C2semidirect
8. C2×C4×C22⋊C8C2semidirect
9. C2×#1726C2semidirect
10. #10922C2semidirect
11. #10922C2semidirect
12. #10921C2semidirect
13. #10921C2semidirect
14. #10835C2semidirect
15. #10834C2semidirect
47. #1955C4semidirect
48. #1954C4semidirect
113. C2×C4⋊C8C2×C4semidirect
114. C2×C4⋊C8C2×C4semidirect
135. C2×C22⋊C8C2×C4semidirect
136. C2×C22⋊C8C2×C4semidirect
137. C2×C22⋊C8C2×C4semidirect
138. C2×C22⋊C8C2×C4semidirect
149. C2×#97C2×C4semidirect
150. C2×#97D4semidirect
161. C2×C4×C8C2×C4semidirect
162. C2×C4×C8D4semidirect

Maximal subgroups

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

subgroupindex
C2×#22902
C2×#19552
C2×#19542
C2×#17682
C2×#17492
C2×#17502
C2×C4×C22⋊C82
C2×#17262
#109222
#109212
#108352
#108342