Finite Group Databasebeta

← #378993

Subgroups — #378993

Order 512.

1810 conjugacy classes of subgroups.

The subgroup lattice has 1163 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1955C211yesmaximal, characteristic, complemented
2C2×#1955C211yesmaximal, characteristic, complemented
3C2×#1954C211yesmaximal, characteristic, complemented
4C2×#1923C211yesmaximal, characteristic, complemented
5C2×#1923C211yesmaximal, characteristic, complemented
6C2×#1870C211yesmaximal, characteristic, complemented
7C2×#1870C211yesmaximal, characteristic, complemented
8C2×#1753C211yesmaximal, characteristic, complemented
9C4×#392C211yesmaximal, characteristic
10#11322C211yesmaximal, characteristic, complemented
11#11042C211yesmaximal, characteristic, complemented
12#10964C211yesmaximal, characteristic, complemented
13#10922C211yesmaximal, characteristic, complemented
14#10921C211yesmaximal, characteristic, complemented
15#10696C211yesmaximal, characteristic, complemented
16C23×M16C2211yescharacteristic
17C22×C4×D4C2211yescharacteristic
18C22×C4×D4C2211yescharacteristic
19C22×C4×D4C2211yescharacteristic
20C22×C4⋊C8C2211yescharacteristic
21C22×C4⋊C8C2211yescharacteristic
22C22×C4⋊C8C2211yescharacteristic
23C22×C22⋊C8C2211yescharacteristic
24C22×C22⋊C8C2211yescharacteristic
25C22×C22⋊C8C2211yescharacteristic
26C22×C22⋊C8C2211yescharacteristic
27C22×C22⋊C8C2211yescharacteristic
28C22×C22⋊C8C2211yescharacteristic
29C22×C22⋊C8C2211yescharacteristic
30C22×C22⋊C8C2211yescharacteristic
31C22×C22⋊C8C2211yescharacteristic
32C22×C22⋊C8C2211yescharacteristic
33C22×C22⋊C8C2211yescharacteristic
34C22×#97C2211yescharacteristic
35C22×#97C2211yescharacteristic
36C22×C4×C8C2211yescharacteristic
37C22×C4×C8C2211yescharacteristic
38C2×#392C411yescharacteristic
39C2×C4×C22⋊C4C2211yescharacteristic
40C2×C4×C22⋊C4C2211yescharacteristic
41C2×C4×C22⋊C4C2211yescharacteristic
42#1955—24no—
43#1955—24no—
44#1954—24no—
45#1923—24no—
46#1923—24no—
47#1870—24no—
48#1870—24no—
49#1753—24no—
50C2×#336C2211yescharacteristic
51C2×#336C2211yescharacteristic
52C2×#336C2211yescharacteristic
53C2×#336C2211yescharacteristic
54C2×#336C2211yescharacteristic
55C2×#336C2211yescharacteristic
56C2×#336C2211yescharacteristic
57C2×#336C2211yescharacteristic
58C2×#336C2211yescharacteristic
59#1444C411yescharacteristic
60#1439C411yescharacteristic
61#1439C411yescharacteristic
62#1439C411yescharacteristic
63#1438C411yescharacteristic
64#1438C411yescharacteristic
65#1438C411yescharacteristic
66C4×#95C2211yescharacteristic
67C23×D4C2×C411yescharacteristic
68C23×D4C2×C411yescharacteristic
69C23×D4C2×C411yescharacteristic
70C24×C4C2311yescharacteristic
71C24×C4C2311yescharacteristic
72C24×C4C2311yescharacteristic
73C22×M16—22no—
74C22×M16—22no—
75C22×M16—22no—
76C22×M16—22no—
77C22×M16—22no—
78C22×M16—41no—
79C22×M16—41no—
80C23×C8C2311yescharacteristic
81C23×C8C2311yescharacteristic
82C23×C8C2311yescharacteristic
83C23×C8C2311yescharacteristic
84C23×C8C2311yescharacteristic
85C23×C8C2311yescharacteristic
86C23×C8C2311yescharacteristic
87C23×C8C2311yescharacteristic
88C2×C4×D4—22no—
89C2×C4×D4—22no—
90C2×C4×D4—22no—
91C2×C4×D4—22no—
92C2×C4×D4—22no—
93C2×C4×D4—22no—
94C2×C4×D4—22no—
95C2×C4×D4—22no—
96C2×C4×D4—22no—
97C2×C4×D4—22no—
98C2×C4×D4—41no—
99C2×C4×D4—41no—
100C2×C4×D4—41no—
101C2×C4×D4—41no—
102C2×C4×D4—41no—
103C2×C4×D4—41no—
104C2×C4×D4—41no—
105C2×C4×D4—41no—
106C22×C4⋊C4C2×C411yescharacteristic
107C22×C4⋊C4C2×C411yescharacteristic
108C22×C4⋊C4C2×C411yescharacteristic
109C22×C22⋊C4C2×C411yescharacteristic
110C22×C22⋊C4C2×C411yescharacteristic
111C22×C22⋊C4C2×C411yescharacteristic
112C22×C22⋊C4C2×C411yescharacteristic
113C22×C22⋊C4C2×C411yescharacteristic
114C22×C22⋊C4C2×C411yescharacteristic
115C22×C22⋊C4C2×C411yescharacteristic
116C22×C22⋊C4C2×C411yescharacteristic
117C22×C22⋊C4C2×C411yescharacteristic
118C22×C22⋊C4C2×C411yescharacteristic
119C22×C22⋊C4C2×C411yescharacteristic
120C22×C22⋊C4C2×C411yescharacteristic
121C22×C42C2311yescharacteristic
122C22×C42C2311yescharacteristic
123C22×C42C2311yescharacteristic
124C22×C42C2311yescharacteristic
125C2×C4⋊C8—22no—
126C2×C4⋊C8—22no—
127C2×C4⋊C8—22no—
128C2×C4⋊C8—22no—
129C2×C4⋊C8—22no—
130C2×C4⋊C8—41no—
131C2×C4⋊C8—41no—
132C2×C4⋊C8—41no—
133C2×C4⋊C8—41no—
134C2×C22⋊C8—22no—
135C2×C22⋊C8—22no—
136C2×C22⋊C8—22no—
137C2×C22⋊C8—22no—
138C2×C22⋊C8—22no—
139C2×C22⋊C8—22no—
140C2×C22⋊C8—22no—
141C2×C22⋊C8—22no—
142C2×C22⋊C8—22no—
143C2×C22⋊C8—22no—
144C2×C22⋊C8—22no—
145C2×C22⋊C8—22no—
146C2×C22⋊C8—22no—
147C2×C22⋊C8—22no—
148C2×C22⋊C8—22no—
149C2×C22⋊C8—22no—
150C2×C22⋊C8—22no—
151C2×C22⋊C8—22no—
152C2×C22⋊C8—22no—
153C2×C22⋊C8—22no—
154C2×C22⋊C8—22no—
155C2×C22⋊C8—22no—
156C2×C22⋊C8—22no—
157C2×C22⋊C8—22no—
158C2×C22⋊C8—22no—
159C2×C22⋊C8—22no—
160C2×C22⋊C8—41no—
161C2×C22⋊C8—41no—
162C2×C22⋊C8—41no—
163C2×C22⋊C8—41no—
164C2×C22⋊C8—41no—
165C2×C22⋊C8—41no—
166C2×C22⋊C8D414yescomplemented
167C2×#97—22no—
168C2×#97—22no—
169C2×#97—41no—
170C2×#97—41no—
171C2×#97—41no—
172C2×#97D414yescomplemented
173C2×C4×C8—22no—
174C2×C4×C8—22no—
175C2×C4×C8—22no—
176C2×C4×C8—22no—
177C2×C4×C8—22no—
178C2×C4×C8—41no—
179#392—24no—
180C4×C22⋊C4—22no—
181C4×C22⋊C4—22no—
182C4×C22⋊C4—22no—
183C4×C22⋊C4—22no—
184C4×C22⋊C4—22no—
185C4×C22⋊C4—22no—
186C2×#95C2×C411yescharacteristic
187C2×#95C2×C411yescharacteristic
188C2×#95C2×C411yescharacteristic
189C2×#95C2×C411yescharacteristic
190C2×#95C2×C411yescharacteristic
191C2×#95C2×C411yescharacteristic
192C2×#95C2×C411yescharacteristic
193C2×#95C2×C411yescharacteristic
194C2×#95C2×C411yescharacteristic
195C2×#95C2×C411yescharacteristic
196#336—22no—
197#336—22no—
198#336—22no—
199#336—22no—
200#336—22no—
201#336—22no—
202#336—22no—
203#336D414yescomplemented
204#336D414yescomplemented
205C25C22×C411yescharacteristic
206C25C22×C411yescharacteristic
207C25C22×C411yescharacteristic
208C22×D4—22no—
209C22×D4—22no—
210C22×D4—22no—
211C22×D4—22no—
212C22×D4—22no—
213C22×D4—22no—
214C22×D4—22no—
215C22×D4—22no—
216C22×D4—22no—
217C22×D4—22no—
218C22×D4—22no—
219C22×D4—41no—
220C22×D4—41no—
221C22×D4—41no—
222C22×D4—41no—
223C22×D4—41no—
224C22×D4—41no—
225C22×D4—41no—
226C22×D4—41no—
227C22×D4—41no—
228C22×D4—41no—
229C23×C4—21no—
230C23×C4—21no—
231C23×C4—21no—
232C23×C4—21no—
233C23×C4—21no—
234C23×C4—21no—
235C23×C4—21no—
236C23×C4—21no—
237C23×C4—21no—
238C23×C4—21no—
239C23×C4—21no—
240C23×C4—21no—
241C23×C4—21no—
242C23×C4—21no—
243C23×C4—21no—
244C23×C4—21no—
245C23×C4—21no—
246C23×C4—21no—
247C23×C4—21no—
248C23×C4—21no—
249C23×C4—21no—
250C23×C4—21no—
251C23×C4—21no—
252C23×C4—21no—
253C23×C4—21no—
254C23×C4—21no—
255C23×C4—21no—
256C23×C4—21no—
257C23×C4—21no—
258C23×C4—21no—
259C23×C4—21no—
260C23×C4—21no—
261C23×C4—21no—
262C23×C4—21no—
263C23×C4—21no—
264C23×C4—21no—
265C23×C4—21no—
266C23×C4—21no—
267C23×C4—21no—
268C23×C4—21no—
269C23×C4C22×C411yescharacteristic
270C23×C4C22×C411yescharacteristic
271C23×C4C22×C411yescharacteristic
272C23×C4C22×C411yescharacteristic
273C23×C4C22×C411yescharacteristic
274C23×C4C22×C411yescharacteristic
275C23×C4C22×C411yescharacteristic
276C23×C4C22×C411yescharacteristic
277C23×C4C22×C411yescharacteristic
278C23×C4C22×C411yescharacteristic
279C23×C4C22×C411yescharacteristic
280C23×C4C2×D412yes—
281C23×C4#4112yes—
282C23×C4C2411yescharacteristic
283C2×M16—28no—
284C2×M16—44no—
285C2×M16—44no—
286C2×M16—44no—
287C2×M16—44no—
288C2×M16—44no—
289C2×M16—44no—
290C22×C8—21no—
291C22×C8—21no—
292C22×C8—21no—
293C22×C8—21no—
294C22×C8—21no—
295C22×C8—21no—
296C22×C8—21no—
297C22×C8—21no—
298C22×C8—21no—
299C22×C8—21no—
300C22×C8—21no—
301C22×C8—21no—
302C22×C8—21no—
303C22×C8—21no—
304C22×C8—21no—
305C22×C8—21no—
306C22×C8—21no—
307C22×C8—21no—
308C22×C8—21no—
309C22×C8—21no—
310C22×C8—21no—
311C22×C8—21no—
312C22×C8—21no—
313C22×C8—21no—
314C22×C8—21no—
315C22×C8—21no—
316C22×C8—21no—
317C22×C8—21no—
318C22×C8—21no—
319C22×C8—21no—
320C22×C8—21no—
321C22×C8—21no—
322C22×C8—21no—
323C22×C8—21no—
324C22×C8—21no—
325C22×C8—21no—
326C22×C8—21no—
327C22×C8—21no—
328C22×C8—21no—
329C22×C8—21no—
330C22×C8—21no—
331C22×C8—21no—
332C22×C8—21no—
333C22×C8—21no—
334C22×C8—21no—
335C22×C8—21no—
336C22×C8C2×D412yes—
337C22×C8C2×D412yes—
338C22×C8C2×D412yes—
339C22×C8C2×D412yes—
340C22×C8C2×D412yes—
341C22×C8C2×D412yes—
342C22×C8C2×D412yes—
343C22×C8C2×D412yes—
344C22×C8#4112yes—
345C22×C8#4112yes—
346C4×D4—44no—
347C4×D4—44no—
348C4×D4—44no—
349C4×D4—44no—
350C4×D4—44no—
351C4×D4—44no—
352C4×D4—44no—
353C4×D4—44no—
354C4×D4—44no—
355C4×D4—44no—
356C4×D4—44no—
357C4×D4—44no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—41no—
364C2×C4⋊C4—41no—
365C2×C4⋊C4—41no—
366C2×C4⋊C4—41no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—41no—
391C2×C22⋊C4—41no—
392C2×C22⋊C4—41no—
393C2×C22⋊C4—41no—
394C2×C22⋊C4—41no—
395C2×C22⋊C4—41no—
396C2×C22⋊C4—41no—
397C2×C22⋊C4—41no—
398C2×C22⋊C4—41no—
399C2×C22⋊C4—41no—
400C2×C22⋊C4—41no—
401C2×C22⋊C4—41no—
402C2×C22⋊C4M1614yescomplemented
403C2×C42—21no—
404C2×C42—21no—
405C2×C42—21no—
406C2×C42—21no—
407C2×C42—21no—
408C2×C42—21no—
409C2×C42—21no—
410C2×C42—21no—
411C2×C42—21no—
412C2×C42—21no—
413C2×C42—21no—
414C2×C42—21no—
415C2×C42—21no—
416C2×C42—21no—
417C2×C42—21no—
418C2×C42—21no—
419C2×C42—21no—
420C2×C42—21no—
421C2×C42C2×D412yes—
422C2×C42C2×D412yes—
423C2×C42C2×D412yes—
424C2×C42#4112yes—
425C2×C42#4112yes—
426C2×C42#4112yes—
427C4⋊C8—44no—
428C4⋊C8—44no—
429C4⋊C8—44no—
430C22⋊C8—28no—
431C22⋊C8—44no—
432C22⋊C8—44no—
433C22⋊C8—44no—
434C22⋊C8—44no—
435C22⋊C8—44no—
436C22⋊C8—44no—
437C22⋊C8—44no—
438C22⋊C8—44no—
439C22⋊C8—44no—
440C22⋊C8—44no—
441#97—44no—
442#97—44no—
443C4×C8—44no—
444C4×C8—44no—
445#95—22no—
446#95—22no—
447#95—22no—
448#95—22no—
449#95—22no—
450#95—22no—
451#95—22no—
452#95—22no—
453#95—41no—
454#95—41no—
455C24—21no—
456C24—21no—
457C24—21no—
458C24—21no—
459C24—21no—
460C24—21no—
461C24—21no—
462C24—21no—
463C24—21no—
464C24—21no—
465C24—21no—
466C24—21no—
467C24—21no—
468C24—21no—
469C24—21no—
470C24—21no—
471C24—21no—
472C24—21no—
473C24—21no—
474C24—21no—
475C24—21no—
476C24—21no—
477C24—21no—
478C24—21no—
479C24—21no—
480C24—21no—
481C24—21no—
482C24—21no—
483C24—21no—
484C24—21no—
485C24—21no—
486C24—21no—
487C24—21no—
488C24—21no—
489C24—21no—
490C24—21no—
491C24—21no—
492C24—21no—
493C24—21no—
494C24—21no—
495C24—21no—
496C24—21no—
497C24C4×D412yes—
498C24C2×M1612yes—
499C24#13112yes—
500C24C23×C411yescharacteristic
501C2×D4—28no—
502C2×D4—44no—
503C2×D4—44no—
504C2×D4—44no—
505C2×D4—44no—
506C2×D4—44no—
507C2×D4—44no—
508C2×D4—44no—
509C2×D4—44no—
510C2×D4—44no—
511C2×D4—44no—
512C2×D4—44no—
513C2×D4—44no—
514C2×D4—44no—
515C2×D4—44no—
516C2×D4—44no—
517C2×D4—44no—
518C2×D4—44no—
519C2×D4—44no—
520C2×D4—44no—
521C2×D4—44no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—41no—
604C22×C4—41no—
605C22×C4—41no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—41no—
619C22×C4—41no—
620C22×C4—41no—
621C22×C4—41no—
622C22×C4—41no—
623C22×C4—41no—
624C22×C4—41no—
625C22×C4—41no—
626C22×C4—41no—
627C22×C4—41no—
628C22×C4—41no—
629C22×C4—41no—
630C22×C4—41no—
631C22×C4—41no—
632C22×C4—41no—
633C22×C4—41no—
634C22×C4—41no—
635C22×C4—41no—
636C22×C4—41no—
637C22×C4—41no—
638C22×C4—41no—
639C22×C4—41no—
640C22×C4—41no—
641C22×C4—41no—
642C22×C4—41no—
643C22×C4—41no—
644C22×C4—41no—
645C22×C4—41no—
646C22×C4—41no—
647C22×C4—41no—
648C22×C4—41no—
649C22×C4—41no—
650C22×C4—41no—
651C22×C4—41no—
652C22×C4—41no—
653C22×C4—41no—
654C22×C4—41no—
655C22×C4—41no—
656C22×C4—41no—
657C22×C4—41no—
658C22×C4—41no—
659C22×C4—41no—
660C22×C4—41no—
661C22×C4—41no—
662C22×C4—41no—
663C22×C4—41no—
664C22×C4—41no—
665C22×C4—41no—
666C22×C4—41no—
667C22×C4—41no—
668C22×C4—41no—
669C22×C4—41no—
670C22×C4—41no—
671C22×C4—41no—
672C22×C4C4×D412yes—
673C22×C4C4×D412yes—
674C22×C4C4×D412yes—
675C22×C4C4×D412yes—
676C22×C4C4×D412yes—
677C22×C4C4×D412yes—
678C22×C4C4×D412yes—
679C22×C4C2×M1612yes—
680C22×C4C2×M1612yes—
681C22×C4#13112yes—
682C22×C4#13112yes—
683C22×C4C22×D411yescharacteristic
684C22×C4C22×D411yescharacteristic
685C22×C4C22×D411yescharacteristic
686C22×C4C22×D411yescharacteristic
687C22×C4C2×#4111yescharacteristic
688C22×C4C2×#4111yescharacteristic
689C22×C4C2×#4111yescharacteristic
690C22×C4C2×#4111yescharacteristic
691C22×C4C2×#4111yescharacteristic
692C22×C4C2×#4111yescharacteristic
693C22×C4H(5,𝔽2)11yescharacteristic
694C22×C4H(5,𝔽2)11yescharacteristic
695C22×C4H(5,𝔽2)11yescharacteristic
696C22×C4H(5,𝔽2)11yescharacteristic
697M16—416no—
698C2×C8—22no—
699C2×C8—22no—
700C2×C8—22no—
701C2×C8—22no—
702C2×C8—22no—
703C2×C8—22no—
704C2×C8—22no—
705C2×C8—22no—
706C2×C8—22no—
707C2×C8—22no—
708C2×C8—22no—
709C2×C8—22no—
710C2×C8—22no—
711C2×C8—22no—
712C2×C8—22no—
713C2×C8—22no—
714C2×C8—22no—
715C2×C8—22no—
716C2×C8—22no—
717C2×C8—22no—
718C2×C8—22no—
719C2×C8—22no—
720C2×C8—22no—
721C2×C8—22no—
722C2×C8—41no—
723C2×C8—41no—
724C2×C8—41no—
725C2×C8—41no—
726C2×C8—41no—
727C2×C8—41no—
728C2×C8—41no—
729C2×C8—41no—
730C2×C8—41no—
731C2×C8—41no—
732C2×C8—41no—
733C2×C8—41no—
734C2×C8—41no—
735C2×C8—41no—
736C2×C8—41no—
737C2×C8—41no—
738C2×C8—41no—
739C2×C8—41no—
740C2×C8—41no—
741C2×C8—41no—
742C2×C8—41no—
743C2×C8—41no—
744C2×C8—41no—
745C2×C8—41no—
746C2×C8—41no—
747C2×C8—41no—
748C2×C8—41no—
749C2×C8—41no—
750C2×C8—41no—
751C2×C8—41no—
752C2×C8#12114yes—
753C2×C8#12714yes—
754C4⋊C4—44no—
755C4⋊C4—44no—
756C4⋊C4—44no—
757C22⋊C4—28no—
758C22⋊C4—28no—
759C22⋊C4—44no—
760C22⋊C4—44no—
761C22⋊C4—44no—
762C22⋊C4—44no—
763C22⋊C4—44no—
764C22⋊C4—44no—
765C22⋊C4—44no—
766C22⋊C4—44no—
767C22⋊C4—44no—
768C22⋊C4—44no—
769C42—22no—
770C42—22no—
771C42—22no—
772C42—22no—
773C42—22no—
774C42—22no—
775C42—22no—
776C42—22no—
777C42—22no—
778C42—22no—
779C42—22no—
780C42—22no—
781C42—41no—
782C42—41no—
783C42—41no—
784C42—41no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23—41no—
843C23—41no—
844C23—41no—
845C23—41no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23—41no—
850C23—41no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—41no—
871C23—41no—
872C23—41no—
873C23—41no—
874C23—41no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—41no—
879C23—41no—
880C23—41no—
881C23—41no—
882C23—41no—
883C23—41no—
884C23—41no—
885C23—41no—
886C23—41no—
887C23—41no—
888C23—41no—
889C23—41no—
890C23C2×C4×D411yescharacteristic
891C23C2×C4×D411yescharacteristic
892C23C2×C4×D411yescharacteristic
893C23C2×C4×D411yescharacteristic
894C23C4×#4111yescharacteristic
895C23#51811yescharacteristic
896C23#51811yescharacteristic
897C23C22×M1611yescharacteristic
898C23C2×#13111yescharacteristic
899C23C2×#13111yescharacteristic
900C23C2×#13111yescharacteristic
901C23#56811yescharacteristic
902C23#56811yescharacteristic
903C23#56811yescharacteristic
904C23#56811yescharacteristic
905D4—416no—
906D4—416no—
907D4—416no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—42no—
971C2×C4—42no—
972C2×C4—42no—
973C2×C4—42no—
974C2×C4—42no—
975C2×C4—42no—
976C2×C4—42no—
977C2×C4—42no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—81no—
993C2×C4—81no—
994C2×C4—81no—
995C2×C4—81no—
996C2×C4—81no—
997C2×C4—81no—
998C2×C4—81no—
999C2×C4—81no—
1000C2×C4—81no—
1001C2×C4—81no—
1002C2×C4—81no—
1003C2×C4—81no—
1004C2×C4—81no—
1005C2×C4—81no—
1006C2×C4—81no—
1007C2×C4—81no—
1008C2×C4#43514yes—
1009C2×C4C2×#12111yescharacteristic
1010C2×C4#52511yescharacteristic
1011C2×C4#52911yescharacteristic
1012C2×C4C2×#12711yescharacteristic
1013C2×C4#53211yescharacteristic
1014C2×C4#53211yescharacteristic
1015C2×C4#53211yescharacteristic
1016C2×C4#53211yescharacteristic
1017C2×C4#53411yescharacteristic
1018C2×C4#53511yescharacteristic
1019C2×C4#53811yescharacteristic
1020C2×C4#53811yescharacteristic
1021C2×C4D4211yescharacteristic
1022C2×C4D4211yescharacteristic
1023C2×C4#54611yescharacteristic
1024C2×C4#54611yescharacteristic
1025C2×C4#54611yescharacteristic
1026C2×C4#54611yescharacteristic
1027C2×C4#54611yescharacteristic
1028C2×C4#54611yescharacteristic
1029C2×C4#55011yescharacteristic
1030C2×C4#55011yescharacteristic
1031C2×C4#55111yescharacteristic
1032C2×C4#55111yescharacteristic
1033C2×C4#55311yescharacteristic
1034C2×C4#55311yescharacteristic
1035C2×C4#55511yescharacteristic
1036C2×C4#55511yescharacteristic
1037C8—24no—
1038C8—24no—
1039C8—42no—
1040C8—42no—
1041C8—42no—
1042C8—42no—
1043C8—81no—
1044C8—81no—
1045C22—42no—
1046C22—42no—
1047C22—42no—
1048C22—42no—
1049C22—42no—
1050C22—42no—
1051C22—42no—
1052C22—42no—
1053C22—42no—
1054C22—42no—
1055C22—42no—
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—42no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—81no—
1067C22—81no—
1068C22—81no—
1069C22—81no—
1070C22—81no—
1071C22—81no—
1072C22—81no—
1073C22—81no—
1074C22—81no—
1075C22—81no—
1076C22—81no—
1077C22—81no—
1078C22—81no—
1079C22—81no—
1080C22—81no—
1081C22—81no—
1082C22—81no—
1083C22—81no—
1084C22—81no—
1085C22—81no—
1086C22—81no—
1087C22—81no—
1088C22—81no—
1089C22—81no—
1090C22C4×#12111yescharacteristic
1091C22C4×#12711yescharacteristic
1092C22#232111yescharacteristic
1093C22#235811yescharacteristic
1094C22#235811yescharacteristic
1095C22#236311yescharacteristic
1096C22#236311yescharacteristic
1097C22C2×#43511yescharacteristic
1098C22#292911yescharacteristic
1099C22#292911yescharacteristic
1100C22#293011yescharacteristic
1101C22#293011yescharacteristic
1102C22#293211yescharacteristic
1103C22#293311yescharacteristic
1104C22#293311yescharacteristic
1105C22#293311yescharacteristic
1106C22#293311yescharacteristic
1107C22D4×M1611yescharacteristic
1108C22D4×M1611yescharacteristic
1109C22D4×M1611yescharacteristic
1110C22#293511yescharacteristic
1111C22#293511yescharacteristic
1112C22#293511yescharacteristic
1113C22#296511yescharacteristic
1114C22#296711yescharacteristic
1115C22#296811yescharacteristic
1116C22#296911yescharacteristic
1117C22#297411yescharacteristic
1118C22#297511yescharacteristic
1119C22#297611yescharacteristic
1120C22#297611yescharacteristic
1121C22#297811yescharacteristic
1122C22#297811yescharacteristic
1123C22#297911yescharacteristic
1124C22#298111yescharacteristic
1125C4—24no—
1126C4—42no—
1127C4—42no—
1128C4—42no—
1129C4—42no—
1130C4—42no—
1131C4—42no—
1132C4—42no—
1133C4—42no—
1134C4—81no—
1135C4—81no—
1136C4#253911yescharacteristic
1137C4#254111yescharacteristic
1138C4#254311yescharacteristic
1139C4#255411yescharacteristic
1140C4#255411yescharacteristic
1141C4#255511yescharacteristic
1142C4#255511yescharacteristic
1143C4#261011yescharacteristic
1144C2—82no—
1145C2—82no—
1146C2—82no—
1147C2#1422811yescharacteristic
1148C2#2149011yescharacteristic
1149C2#2149511yescharacteristic
1150C2#2168211yescharacteristic
1151C2#2168511yescharacteristic
1152C2#2203811yescharacteristic
1153C2#2203911yescharacteristic
1154C2#2284311yescharacteristic
1155C2#2284611yescharacteristic
1156C2#2284911yescharacteristic
1157C2#2285211yescharacteristic
1158C2#2308511yescharacteristic
1159C2#2308711yescharacteristic
1160C2#2309111yescharacteristic
1161C2#2309211yescharacteristic
subgroupG/H
center, Frattini, cosocleC23×C4C24
commutator, socleC24C23×C4
prime radicalC2×#392C4
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C23×C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#1955C2semidirect
2. C2×#1955C2semidirect
3. C2×#1954C2semidirect
4. C2×#1923C2semidirect
5. C2×#1923C2semidirect
6. C2×#1870C2semidirect
7. C2×#1870C2semidirect
8. C2×#1753C2semidirect
10. #11322C2semidirect
11. #11042C2semidirect
12. #10964C2semidirect
13. #10922C2semidirect
14. #10921C2semidirect
15. #10696C2semidirect
166. C2×C22⋊C8D4semidirect
172. C2×#97D4semidirect
203. #336D4semidirect
204. #336D4semidirect
402. C2×C22⋊C4M16semidirect

Maximal subgroups

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

subgroupindex
C2×#19552
C2×#19542
C2×#19232
C2×#18702
C2×#17532
C4×#3922
#113222
#110422
#109642
#109222
#109212
#106962