Finite Group Databasebeta

← #376665

Subgroups — #376665

Order 512.

1672 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#436C211yesmaximal, characteristic
2C2×#1939C211yesmaximal, characteristic, complemented
3C2×#1924C211yesmaximal, characteristic, complemented
4C2×#1851C211yesmaximal, characteristic, complemented
5C2×#1851C211yesmaximal, characteristic, complemented
6C2×#1753C211yesmaximal, characteristic, complemented
7C4×#394C211yesmaximal, characteristic
8#11147C211yesmaximal, characteristic, complemented
9#11042C211yesmaximal, characteristic, complemented
10#10964C211yesmaximal, characteristic
11#10921C211yesmaximal, characteristic, complemented
12#10877C211yesmaximal, characteristic, complemented
13#10876C211yesmaximal, characteristic, complemented
14#10874C211yesmaximal, characteristic, complemented
15#10715C211yesmaximal, characteristic, complemented
16C23×M16C2211yescharacteristic
17C23×M16C2211yescharacteristic
18C22×C4×D4C2211yescharacteristic
19C2×#436—24no—
20C2×#436—24no—
21C2×#436—24no—
22C22×C4⋊C8C2211yescharacteristic
23C22×C4⋊C8C2211yescharacteristic
24C22×C4⋊C8C2211yescharacteristic
25C22×C4⋊C8C2211yescharacteristic
26C22×C22⋊C8C2211yescharacteristic
27C22×C22⋊C8C2211yescharacteristic
28C22×C22⋊C8C2211yescharacteristic
29C22×C22⋊C8C2211yescharacteristic
30C22×C22⋊C8C2211yescharacteristic
31C22×C22⋊C8C2211yescharacteristic
32C22×#97C2211yescharacteristic
33C22×C4×C8C2211yescharacteristic
34C22×C4×C8C2211yescharacteristic
35C2×#394C411yescharacteristic
36C2×C4×C4⋊C4C2211yescharacteristic
37C2×C4×C22⋊C4C2211yescharacteristic
38C2×C4×C22⋊C4C2211yescharacteristic
39C2×C4×C22⋊C4C2211yescharacteristic
40C2×C4×C22⋊C4C2211yescharacteristic
41#1939—24no—
42#1924—24no—
43#1851—24no—
44#1851—24no—
45#1753—24no—
46C2×#336C2211yescharacteristic
47C2×#336C2211yescharacteristic
48C2×#336C2211yescharacteristic
49C2×#336C2211yescharacteristic
50C2×#336C2211yescharacteristic
51C2×#336C2211yescharacteristic
52C2×#336C2211yescharacteristic
53C2×#336C2211yescharacteristic
54C2×#336C2211yescharacteristic
55C2×#336C2211yescharacteristic
56C2×#336C2211yescharacteristic
57C2×#336C2211yescharacteristic
58C2×#336C2211yescharacteristic
59#1442C411yescharacteristic
60#1441C411yescharacteristic
61#1440C411yescharacteristic
62#1440C411yescharacteristic
63#1439C411yescharacteristic
64#1439C411yescharacteristic
65#1438C411yescharacteristic
66C4×#95C2211yescharacteristic
67C23×D4C2×C411yescharacteristic
68C24×C4C2311yescharacteristic
69C24×C4C2311yescharacteristic
70C22×M16—22no—
71C22×M16—22no—
72C22×M16—22no—
73C22×M16—22no—
74C22×M16—22no—
75C22×M16—22no—
76C22×M16—22no—
77C22×M16—22no—
78C22×M16—22no—
79C22×M16—41no—
80C22×M16—41no—
81C22×M16—41no—
82C22×M16—41no—
83C22×M16D414yes—
84C23×C8C2311yescharacteristic
85C23×C8C2311yescharacteristic
86C23×C8C2311yescharacteristic
87C23×C8C2311yescharacteristic
88C23×C8C2311yescharacteristic
89C23×C8C2311yescharacteristic
90C23×C8C2311yescharacteristic
91C23×C8C2311yescharacteristic
92C2×C4×D4—22no—
93C2×C4×D4—22no—
94C2×C4×D4—22no—
95C2×C4×D4—22no—
96C2×C4×D4—22no—
97C2×C4×D4—22no—
98C22×C4⋊C4C2×C411yescharacteristic
99C22×C4⋊C4C2×C411yescharacteristic
100C22×C4⋊C4C2×C411yescharacteristic
101C22×C22⋊C4C2×C411yescharacteristic
102C22×C22⋊C4C2×C411yescharacteristic
103C22×C22⋊C4C2×C411yescharacteristic
104C22×C22⋊C4C2×C411yescharacteristic
105C22×C22⋊C4C2×C411yescharacteristic
106C22×C22⋊C4C2×C411yescharacteristic
107C22×C22⋊C4C2×C411yescharacteristic
108C22×C22⋊C4C2×C411yescharacteristic
109C22×C22⋊C4C2×C411yescharacteristic
110C22×C22⋊C4C2×C411yescharacteristic
111C22×C42C2311yescharacteristic
112C22×C42C2311yescharacteristic
113C22×C42C2311yescharacteristic
114C22×C42C2311yescharacteristic
115C22×C42C2311yescharacteristic
116#436—232no—
117C2×C4⋊C8—22no—
118C2×C4⋊C8—22no—
119C2×C4⋊C8—22no—
120C2×C4⋊C8—22no—
121C2×C4⋊C8—22no—
122C2×C4⋊C8—22no—
123C2×C4⋊C8—22no—
124C2×C4⋊C8—22no—
125C2×C4⋊C8—22no—
126C2×C4⋊C8—22no—
127C2×C4⋊C8—41no—
128C2×C4⋊C8D414yes—
129C2×C22⋊C8—22no—
130C2×C22⋊C8—22no—
131C2×C22⋊C8—22no—
132C2×C22⋊C8—22no—
133C2×C22⋊C8—22no—
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—41no—
143C2×C22⋊C8—41no—
144C2×C22⋊C8—41no—
145C2×C22⋊C8—41no—
146C2×C22⋊C8D414yes—
147C2×#97—22no—
148C2×#97—22no—
149C2×#97—41no—
150C2×C4×C8—22no—
151C2×C4×C8—22no—
152C2×C4×C8—22no—
153C2×C4×C8—22no—
154C2×C4×C8—22no—
155C2×C4×C8—41no—
156#394—24no—
157C4×C4⋊C4—22no—
158C4×C4⋊C4—22no—
159C4×C22⋊C4—22no—
160C4×C22⋊C4—22no—
161C4×C22⋊C4—22no—
162C4×C22⋊C4—22no—
163C4×C22⋊C4—22no—
164C4×C22⋊C4—22no—
165C4×C22⋊C4—22no—
166C4×C22⋊C4—22no—
167C2×#95C2×C411yescharacteristic
168C2×#95C2×C411yescharacteristic
169C2×#95C2×C411yescharacteristic
170C2×#95C2×C411yescharacteristic
171C2×#95C2×C411yescharacteristic
172C2×#95C2×C411yescharacteristic
173C2×#95C2×C411yescharacteristic
174C2×#95C2×C411yescharacteristic
175C2×#95C2×C411yescharacteristic
176C2×#95C2×C411yescharacteristic
177C2×#95C2×C411yescharacteristic
178C2×#95C2×C411yescharacteristic
179C2×#95C2×C411yescharacteristic
180C2×#95C2×C411yescharacteristic
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—
190#336—22no—
191#336—22no—
192#336—41no—
193#336D414yescomplemented
194C25C22×C411yescharacteristic
195C25C22×C411yescharacteristic
196C22×D4—22no—
197C22×D4—22no—
198C22×D4—22no—
199C22×D4—22no—
200C22×D4—22no—
201C22×D4—41no—
202C22×D4—41no—
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—21no—
225C23×C4—21no—
226C23×C4—21no—
227C23×C4C22×C411yescharacteristic
228C23×C4C22×C411yescharacteristic
229C23×C4C22×C411yescharacteristic
230C23×C4C22×C411yescharacteristic
231C23×C4C22×C411yescharacteristic
232C23×C4C22×C411yescharacteristic
233C23×C4C22×C411yescharacteristic
234C23×C4C22×C411yescharacteristic
235C23×C4C22×C411yescharacteristic
236C23×C4C22×C411yescharacteristic
237C23×C4C22×C411yescharacteristic
238C23×C4C22×C411yescharacteristic
239C23×C4C2×D412yes—
240C23×C4C2×D412yes—
241C23×C4#4112yes—
242C23×C4#4112yes—
243C23×C4C2411yescharacteristic
244C2×M16—28no—
245C2×M16—28no—
246C2×M16—28no—
247C2×M16—44no—
248C2×M16—44no—
249C2×M16—44no—
250C2×M16—44no—
251C2×M16—44no—
252C2×M16—44no—
253C2×M16—44no—
254C2×M16—44no—
255C2×M16—44no—
256C2×M16—44no—
257C2×M16—44no—
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×C8—21no—
282C22×C8—21no—
283C22×C8—21no—
284C22×C8—21no—
285C22×C8—21no—
286C22×C8—21no—
287C22×C8—21no—
288C22×C8—21no—
289C22×C8—21no—
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×C8C2×D412yes—
305C22×C8C2×D412yes—
306C22×C8C2×D412yes—
307C22×C8C2×D412yes—
308C22×C8C2×D412yes—
309C22×C8C2×D412yes—
310C22×C8C2×D412yes—
311C22×C8C2×D412yes—
312C22×C8#4112yes—
313C22×C8#4112yes—
314C4×D4—28no—
315C4×D4—28no—
316C4×D4—28no—
317C4×D4—28no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—41no—
326C2×C4⋊C4M1614yescomplemented
327C2×C22⋊C4—22no—
328C2×C22⋊C4—22no—
329C2×C22⋊C4—22no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—22no—
340C2×C22⋊C4—22no—
341C2×C22⋊C4—22no—
342C2×C22⋊C4—22no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—41no—
350C2×C22⋊C4—41no—
351C2×C22⋊C4—41no—
352C2×C22⋊C4—41no—
353C2×C22⋊C4—41no—
354C2×C22⋊C4—41no—
355C2×C22⋊C4—41no—
356C2×C22⋊C4—41no—
357C2×C42—21no—
358C2×C42—21no—
359C2×C42—21no—
360C2×C42—21no—
361C2×C42—21no—
362C2×C42—21no—
363C2×C42—21no—
364C2×C42—21no—
365C2×C42—21no—
366C2×C42—21no—
367C2×C42—21no—
368C2×C42—21no—
369C2×C42—21no—
370C2×C42—21no—
371C2×C42—21no—
372C2×C42—21no—
373C2×C42—21no—
374C2×C42—21no—
375C2×C42—21no—
376C2×C42—21no—
377C2×C42—21no—
378C2×C42—21no—
379C2×C42—21no—
380C2×C42—21no—
381C2×C42—21no—
382C2×C42—21no—
383C2×C42C2×D412yes—
384C2×C42C2×D412yes—
385C2×C42#4112yes—
386C2×C42#4112yes—
387C4⋊C8—28no—
388C4⋊C8—44no—
389C4⋊C8—44no—
390C4⋊C8—44no—
391C22⋊C8—28no—
392C22⋊C8—28no—
393C22⋊C8—28no—
394C22⋊C8—44no—
395C22⋊C8—44no—
396C22⋊C8—44no—
397#97—44no—
398C4×C8—28no—
399C4×C8—44no—
400#95—22no—
401#95—22no—
402#95—22no—
403#95—22no—
404#95—22no—
405#95—22no—
406#95—22no—
407#95—22no—
408#95—22no—
409#95—22no—
410#95—22no—
411#95—22no—
412#95—22no—
413#95—41no—
414C24—21no—
415C24—21no—
416C24—21no—
417C24—21no—
418C24—21no—
419C24—21no—
420C24—21no—
421C24—21no—
422C24—21no—
423C24—21no—
424C24—21no—
425C24—21no—
426C24—21no—
427C24—21no—
428C24—21no—
429C24—21no—
430C24—21no—
431C24—21no—
432C24—21no—
433C24—21no—
434C24—21no—
435C24—21no—
436C24—21no—
437C24—21no—
438C24—21no—
439C24—21no—
440C24—21no—
441C24—21no—
442C24C4×D412yes—
443C24C4×D412yes—
444C24C23×C411yescharacteristic
445C2×D4—28no—
446C2×D4—44no—
447C2×D4—44no—
448C2×D4—44no—
449C2×D4—44no—
450C2×D4—44no—
451C2×D4—44no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—21no—
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—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4—41no—
574C22×C4—41no—
575C22×C4—41no—
576C22×C4—41no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4C4×D412yes—
581C22×C4C4×D412yes—
582C22×C4C4×D412yes—
583C22×C4C4×D412yes—
584C22×C4C4×D412yes—
585C22×C4C4×D412yes—
586C22×C4C2×M1612yes—
587C22×C4C2×M1612yes—
588C22×C4C2×M1612yes—
589C22×C4#13112yes—
590C22×C4#13112yes—
591C22×C4#13112yes—
592C22×C4C22×D411yescharacteristic
593C22×C4C22×D411yescharacteristic
594C22×C4C22×D411yescharacteristic
595C22×C4C22×D411yescharacteristic
596C22×C4C2×#4111yescharacteristic
597C22×C4C2×#4111yescharacteristic
598C22×C4C2×#4111yescharacteristic
599C22×C4C2×#4111yescharacteristic
600C22×C4C2×#4111yescharacteristic
601C22×C4C2×#4111yescharacteristic
602C22×C4H(5,𝔽2)11yescharacteristic
603C22×C4H(5,𝔽2)11yescharacteristic
604C22×C42−1+411yescharacteristic
605C22×C42−1+411yescharacteristic
606M16—416no—
607M16—416no—
608C2×C8—22no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—22no—
612C2×C8—22no—
613C2×C8—22no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8—22no—
621C2×C8—22no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8—22no—
629C2×C8—22no—
630C2×C8—22no—
631C2×C8—22no—
632C2×C8—41no—
633C2×C8—41no—
634C2×C8—41no—
635C2×C8—41no—
636C2×C8—41no—
637C2×C8—41no—
638C2×C8—41no—
639C2×C8—41no—
640C2×C8—41no—
641C2×C8—41no—
642C2×C8—41no—
643C2×C8—41no—
644C2×C8—41no—
645C2×C8—41no—
646C2×C8—41no—
647C2×C8—41no—
648C2×C8—41no—
649C2×C8—41no—
650C2×C8—41no—
651C2×C8—41no—
652C2×C8—41no—
653C2×C8—41no—
654C2×C8—41no—
655C2×C8—41no—
656C2×C8—41no—
657C2×C8—41no—
658C2×C8—41no—
659C2×C8—41no—
660C2×C8—41no—
661C2×C8—41no—
662C2×C8#12014yes—
663C2×C8#12114yes—
664C4⋊C4—28no—
665C4⋊C4—28no—
666C4⋊C4—44no—
667C22⋊C4—28no—
668C22⋊C4—28no—
669C22⋊C4—44no—
670C22⋊C4—44no—
671C22⋊C4—44no—
672C22⋊C4—44no—
673C22⋊C4—44no—
674C22⋊C4—44no—
675C22⋊C4—44no—
676C22⋊C4—44no—
677C42—22no—
678C42—22no—
679C42—22no—
680C42—22no—
681C42—22no—
682C42—22no—
683C42—22no—
684C42—22no—
685C42—41no—
686C42—41no—
687C42—41no—
688C42—41no—
689C42—41no—
690C42—41no—
691C42—41no—
692C42—41no—
693C42—41no—
694C42—41no—
695C42—41no—
696C42—41no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23C2×C4×D411yescharacteristic
768C23C2×C4×D411yescharacteristic
769C23C2×C4×D411yescharacteristic
770C23C2×C4×D411yescharacteristic
771C23C4×#4111yescharacteristic
772C23#52011yescharacteristic
773C23#52011yescharacteristic
774C23C22×M1611yescharacteristic
775C23C2×#13111yescharacteristic
776C23C2×#13111yescharacteristic
777C23C2×#13111yescharacteristic
778C23#56811yescharacteristic
779C23#56811yescharacteristic
780C23#56811yescharacteristic
781C23#56811yescharacteristic
782D4—416no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
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—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4#43514yes—
882C2×C4#43614yescomplemented
883C2×C4C2×#12011yescharacteristic
884C2×C4C2×#12111yescharacteristic
885C2×C4#52511yescharacteristic
886C2×C4#52511yescharacteristic
887C2×C4#52511yescharacteristic
888C2×C4#52511yescharacteristic
889C2×C4#52911yescharacteristic
890C2×C4#53211yescharacteristic
891C2×C4#53411yescharacteristic
892C2×C4#53611yescharacteristic
893C2×C4#53911yescharacteristic
894C2×C4#53911yescharacteristic
895C2×C4D4211yescharacteristic
896C2×C4D4211yescharacteristic
897C2×C4#54611yescharacteristic
898C2×C4#54611yescharacteristic
899C2×C4#54711yescharacteristic
900C2×C4#54711yescharacteristic
901C2×C4#54711yescharacteristic
902C2×C4#54811yescharacteristic
903C2×C4#54811yescharacteristic
904C2×C4#54811yescharacteristic
905C2×C4#55111yescharacteristic
906C2×C4#55211yescharacteristic
907C2×C4#55311yescharacteristic
908C2×C4#55311yescharacteristic
909C2×C4#55611yescharacteristic
910C2×C4#55911yescharacteristic
911C8—24no—
912C8—24no—
913C8—42no—
914C8—42no—
915C8—42no—
916C8—42no—
917C8—81no—
918C8—81no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22—81no—
938C22—81no—
939C22—81no—
940C22—81no—
941C22—81no—
942C22—81no—
943C22—81no—
944C22—81no—
945C22—81no—
946C22—81no—
947C22—81no—
948C22—81no—
949C22C4×#12011yescharacteristic
950C22C4×#12111yescharacteristic
951C22#232211yescharacteristic
952C22#235911yescharacteristic
953C22#236111yescharacteristic
954C22#236111yescharacteristic
955C22#236711yescharacteristic
956C22C2×#43511yescharacteristic
957C22C2×#43611yescharacteristic
958C22#293011yescharacteristic
959C22#293011yescharacteristic
960C22#293011yescharacteristic
961C22#293111yescharacteristic
962C22#293311yescharacteristic
963C22#293311yescharacteristic
964C22#293311yescharacteristic
965C22#293311yescharacteristic
966C22#293311yescharacteristic
967C22D4×M1611yescharacteristic
968C22D4×M1611yescharacteristic
969C22#293511yescharacteristic
970C22#293511yescharacteristic
971C22#293511yescharacteristic
972C22#296611yescharacteristic
973C22#296711yescharacteristic
974C22#296911yescharacteristic
975C22#297111yescharacteristic
976C22#298911yescharacteristic
977C22#299111yescharacteristic
978C22#299311yescharacteristic
979C22#299311yescharacteristic
980C22#299311yescharacteristic
981C22#299411yescharacteristic
982C22#299511yescharacteristic
983C22#299511yescharacteristic
984C4—24no—
985C4—24no—
986C4—42no—
987C4—42no—
988C4—42no—
989C4—42no—
990C4—42no—
991C4—42no—
992C4—81no—
993C4—81no—
994C4—81no—
995C4—81no—
996C4#241011yescharacteristic
997C4#241511yescharacteristic
998C4#243211yescharacteristic
999C4#245511yescharacteristic
1000C4#246011yescharacteristic
1001C4#246311yescharacteristic
1002C4#246611yescharacteristic
1003C4#260211yescharacteristic
1004C2—82no—
1005C2—82no—
1006C2#1418511yescharacteristic
1007C2#2143911yescharacteristic
1008C2#2144511yescharacteristic
1009C2#2148811yescharacteristic
1010C2#2149611yescharacteristic
1011C2#2207311yescharacteristic
1012C2#2207411yescharacteristic
1013C2#2291411yescharacteristic
1014C2#2291511yescharacteristic
1015C2#2298911yescharacteristic
1016C2#2299011yescharacteristic
1017C2#2299411yescharacteristic
1018C2#2299411yescharacteristic
1019C2#2320511yescharacteristic
1020C2#2321211yescharacteristic
subgroupG/H
center, Frattini, cosocleC23×C4C24
commutator, socleC24C23×C4
prime radicalC23×D4C2×C4
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
2. C2×#1939C2semidirect
3. C2×#1924C2semidirect
4. C2×#1851C2semidirect
5. C2×#1851C2semidirect
6. C2×#1753C2semidirect
8. #11147C2semidirect
9. #11042C2semidirect
11. #10921C2semidirect
12. #10877C2semidirect
13. #10876C2semidirect
14. #10874C2semidirect
15. #10715C2semidirect
193. #336D4semidirect
326. C2×C4⋊C4M16semidirect
882. C2×C4#436semidirect

Maximal subgroups

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

subgroupindex
C22×#4362
C2×#19392
C2×#19242
C2×#18512
C2×#17532
C4×#3942
#111472
#110422
#109642
#109212
#108772
#108762
#108742
#107152