Finite Group Databasebeta

← #384302

Subgroups — #384302

Order 512.

1458 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1923C211yesmaximal, characteristic, complemented
2C2×#1870C211yesmaximal, characteristic
3C2×#1851C211yesmaximal, characteristic, complemented
4C2×#1831C211yesmaximal, characteristic, complemented
5C4×#390C211yesmaximal, characteristic
6#11202C211yesmaximal, characteristic, complemented
7#11147C211yesmaximal, characteristic, complemented
8#11042C211yesmaximal, characteristic, complemented
9#11042C211yesmaximal, characteristic, complemented
10#11042C211yesmaximal, characteristic, complemented
11#10964C211yesmaximal, characteristic
12#10921C211yesmaximal, characteristic, complemented
13#10874C211yesmaximal, characteristic, complemented
14#10795C211yesmaximal, characteristic, complemented
15#10715C211yesmaximal, characteristic, complemented
16C23×M16C2211yescharacteristic
17C22×C4×D4C2211yescharacteristic
18C22×C4⋊C8C2211yescharacteristic
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×C4×C8C2211yescharacteristic
29C2×#390C411yescharacteristic
30C2×#390C411yescharacteristic
31C2×C4×C4⋊C4C2211yescharacteristic
32C2×C4×C22⋊C4C2211yescharacteristic
33C2×C4×C22⋊C4C2211yescharacteristic
34C2×C4×C22⋊C4C2211yescharacteristic
35C2×C4×C22⋊C4C2211yescharacteristic
36C2×C43C2211yescharacteristic
37#1923—24no—
38#1870—24no—
39#1851—24no—
40#1831—24no—
41C2×#336C2211yescharacteristic
42C2×#336C2211yescharacteristic
43C2×#336C2211yescharacteristic
44C2×#336C2211yescharacteristic
45C2×#336C2211yescharacteristic
46C2×#336C2211yescharacteristic
47C2×#336C2211yescharacteristic
48C2×#336C2211yescharacteristic
49C2×#336C2211yescharacteristic
50C2×#336C2211yescharacteristic
51C2×#336C2211yescharacteristic
52C2×#336C2211yescharacteristic
53C2×#336C2211yescharacteristic
54C2×#336C2211yescharacteristic
55C2×#336C2211yescharacteristic
56C2×#336C2211yescharacteristic
57#1437C411yescharacteristic
58#1437C411yescharacteristic
59#1437C411yescharacteristic
60#1437C411yescharacteristic
61C4⋊#95C411yescharacteristic
62C4⋊#95C411yescharacteristic
63C23×D4C2×C411yescharacteristic
64C24×C4C2311yescharacteristic
65C24×C4C2311yescharacteristic
66C22×M16—22no—
67C22×M16—22no—
68C22×M16—22no—
69C22×M16—41no—
70C22×M16—41no—
71C22×M16—41no—
72C22×M16—41no—
73C23×C8C2311yescharacteristic
74C23×C8C2311yescharacteristic
75C23×C8C2311yescharacteristic
76C23×C8C2311yescharacteristic
77C23×C8C2311yescharacteristic
78C23×C8C2311yescharacteristic
79C23×C8C2311yescharacteristic
80C23×C8C2311yescharacteristic
81C2×C4×D4—22no—
82C2×C4×D4—22no—
83C2×C4×D4—22no—
84C2×C4×D4—22no—
85C2×C4×D4—41no—
86C2×C4×D4—41no—
87C22×C4⋊C4C2×C411yescharacteristic
88C22×C4⋊C4C2×C411yescharacteristic
89C22×C4⋊C4C2×C411yescharacteristic
90C22×C22⋊C4C2×C411yescharacteristic
91C22×C22⋊C4C2×C411yescharacteristic
92C22×C22⋊C4C2×C411yescharacteristic
93C22×C22⋊C4C2×C411yescharacteristic
94C22×C22⋊C4C2×C411yescharacteristic
95C22×C22⋊C4C2×C411yescharacteristic
96C22×C22⋊C4C2×C411yescharacteristic
97C22×C22⋊C4C2×C411yescharacteristic
98C22×C22⋊C4C2×C411yescharacteristic
99C22×C22⋊C4C2×C411yescharacteristic
100C22×C42C2×C411yescharacteristic
101C22×C42C2×C411yescharacteristic
102C22×C42C2×C411yescharacteristic
103C22×C42C2×C411yescharacteristic
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⋊C8—22no—
114C2×C4⋊C8—41no—
115C2×C4⋊C8—41no—
116C2×C4⋊C8—41no—
117C2×C4⋊C8—41no—
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—41no—
128C2×C22⋊C8—41no—
129C2×C22⋊C8—41no—
130C2×C22⋊C8—41no—
131C2×C22⋊C8—41no—
132C2×C22⋊C8—41no—
133C2×C22⋊C8—41no—
134C2×C22⋊C8—41no—
135C2×C22⋊C8—41no—
136C2×C22⋊C8—41no—
137C2×C22⋊C8—41no—
138C2×C22⋊C8—41no—
139C2×C4×C8—22no—
140C2×C4×C8—41no—
141C2×C4×C8—41no—
142#390—24no—
143#390—24no—
144C4×C4⋊C4—41no—
145C4×C4⋊C4—41no—
146C4×C22⋊C4—22no—
147C4×C22⋊C4—22no—
148C4×C22⋊C4—22no—
149C4×C22⋊C4—22no—
150C4×C22⋊C4—41no—
151C4×C22⋊C4—41no—
152C4×C22⋊C4—41no—
153C4×C22⋊C4—41no—
154C2×#95C2×C411yescharacteristic
155C2×#95C2×C411yescharacteristic
156C2×#95C2×C411yescharacteristic
157C2×#95C2×C411yescharacteristic
158C2×#95C2×C411yescharacteristic
159C2×#95C2×C411yescharacteristic
160C2×#95C2×C411yescharacteristic
161C2×#95C2×C411yescharacteristic
162C2×#95C2×C411yescharacteristic
163C2×#95C2×C411yescharacteristic
164C43—22no—
165C43—22no—
166#336—22no—
167#336—22no—
168#336—22no—
169#336—22no—
170#336—22no—
171#336—22no—
172#336—22no—
173#336—22no—
174#336—41no—
175#336—41no—
176#336—41no—
177#336—41no—
178#336—41no—
179#336—41no—
180#336D414yes—
181#336D414yescomplemented
182C25C22×C411yescharacteristic
183C25C22×C411yescharacteristic
184C22×D4—22no—
185C22×D4—22no—
186C22×D4—22no—
187C22×D4—22no—
188C22×D4—22no—
189C22×D4—41no—
190C22×D4—41no—
191C23×C4—21no—
192C23×C4—21no—
193C23×C4—21no—
194C23×C4—21no—
195C23×C4—21no—
196C23×C4—21no—
197C23×C4—21no—
198C23×C4—21no—
199C23×C4—21no—
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×C4C22×C411yescharacteristic
218C23×C4C22×C411yescharacteristic
219C23×C4C22×C411yescharacteristic
220C23×C4C22×C411yescharacteristic
221C23×C4C22×C411yescharacteristic
222C23×C4C22×C411yescharacteristic
223C23×C4C22×C411yescharacteristic
224C23×C4C22×C411yescharacteristic
225C23×C4C22×C411yescharacteristic
226C23×C4C22×C411yescharacteristic
227C23×C4C22×C411yescharacteristic
228C23×C4C22×C411yescharacteristic
229C23×C4#4112yes—
230C23×C4#4112yes—
231C23×C4C2411yescharacteristic
232C2×M16—44no—
233C2×M16—44no—
234C2×M16—44no—
235C2×M16—44no—
236C2×M16—44no—
237C2×M16—44no—
238C2×M16—44no—
239C22×C8—21no—
240C22×C8—21no—
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×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×C8C2×D412yes—
292C22×C8C2×D412yes—
293C22×C8C2×D412yes—
294C22×C8C2×D412yes—
295C4×D4—44no—
296C4×D4—44no—
297C4×D4—44no—
298C4×D4—44no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—41no—
304C2×C4⋊C4—41no—
305C2×C4⋊C4—41no—
306C2×C4⋊C4—41no—
307C2×C4⋊C4M1614yescomplemented
308C2×C22⋊C4—22no—
309C2×C22⋊C4—22no—
310C2×C22⋊C4—22no—
311C2×C22⋊C4—22no—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—22no—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—22no—
329C2×C22⋊C4—41no—
330C2×C22⋊C4—41no—
331C2×C22⋊C4—41no—
332C2×C22⋊C4—41no—
333C2×C22⋊C4—41no—
334C2×C22⋊C4—41no—
335C2×C22⋊C4—41no—
336C2×C22⋊C4—41no—
337C2×C22⋊C4M1614yescomplemented
338C2×C42—22no—
339C2×C42—22no—
340C2×C42—22no—
341C2×C42—21no—
342C2×C42—21no—
343C2×C42—21no—
344C2×C42—21no—
345C2×C42—21no—
346C2×C42—21no—
347C2×C42—21no—
348C2×C42—21no—
349C2×C42—22no—
350C2×C42—22no—
351C2×C42—22no—
352C2×C42—22no—
353C2×C42—22no—
354C2×C42—22no—
355C2×C42—22no—
356C2×C42—21no—
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—41no—
375C2×C42—41no—
376C2×C42C2×D412yes—
377C2×C42C2×D412yes—
378C2×C42#4112yes—
379C2×C42#4112yes—
380C4⋊C8—44no—
381C4⋊C8—44no—
382C4⋊C8—44no—
383C22⋊C8—44no—
384C22⋊C8—44no—
385C22⋊C8—44no—
386C22⋊C8—44no—
387C22⋊C8—44no—
388C22⋊C8—44no—
389C22⋊C8—44no—
390C4×C8—44no—
391#95—22no—
392#95—22no—
393#95—22no—
394#95—22no—
395#95—41no—
396#95—41no—
397#95—41no—
398#95—41no—
399#95—41no—
400#95—41no—
401C24—21no—
402C24—21no—
403C24—21no—
404C24—21no—
405C24—21no—
406C24—21no—
407C24—21no—
408C24—21no—
409C24—21no—
410C24—21no—
411C24—21no—
412C24—21no—
413C24—21no—
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#11712yes—
430C24C2×M1612yes—
431C24C23×C411yescharacteristic
432C2×D4—28no—
433C2×D4—44no—
434C2×D4—44no—
435C2×D4—44no—
436C2×D4—44no—
437C2×D4—44no—
438C2×D4—44no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
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—22no—
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—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—41no—
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#11712yes—
566C22×C4C4×D412yes—
567C22×C4C4×D412yes—
568C22×C4C4×D412yes—
569C22×C4C4×D412yes—
570C22×C4C2×M1612yes—
571C22×C4C2×M1612yes—
572C22×C4C2×M1612yes—
573C22×C4C2×M1612yes—
574C22×C4C2×M1612yes—
575C22×C4#13112yes—
576C22×C4#13112yes—
577C22×C4#13112yes—
578C22×C4#13112yes—
579C22×C4C22×D411yescharacteristic
580C22×C4C22×D411yescharacteristic
581C22×C4C2×#4111yescharacteristic
582C22×C4C2×#4111yescharacteristic
583C22×C4C2×#4111yescharacteristic
584C22×C4C2×#4111yescharacteristic
585C22×C4H(5,𝔽2)11yescharacteristic
586C22×C4H(5,𝔽2)11yescharacteristic
587C22×C4H(5,𝔽2)11yescharacteristic
588C22×C4H(5,𝔽2)11yescharacteristic
589C22×C4H(5,𝔽2)11yescharacteristic
590C22×C4H(5,𝔽2)11yescharacteristic
591C22×C42−1+411yescharacteristic
592C22×C42−1+411yescharacteristic
593M16—416no—
594C2×C8—22no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—41no—
607C2×C8—41no—
608C2×C8—41no—
609C2×C8—41no—
610C2×C8—41no—
611C2×C8—41no—
612C2×C8—41no—
613C2×C8—41no—
614C2×C8—41no—
615C2×C8—41no—
616C2×C8—41no—
617C2×C8—41no—
618C2×C8—41no—
619C2×C8—41no—
620C2×C8—41no—
621C2×C8—41no—
622C2×C8—41no—
623C2×C8—41no—
624C2×C8—41no—
625C2×C8—41no—
626C2×C8—41no—
627C2×C8—41no—
628C2×C8—41no—
629C2×C8—41no—
630C2×C8—41no—
631C2×C8—41no—
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—
650C4⋊C4—44no—
651C4⋊C4—44no—
652C4⋊C4—44no—
653C22⋊C4—28no—
654C22⋊C4—44no—
655C22⋊C4—44no—
656C22⋊C4—44no—
657C22⋊C4—44no—
658C22⋊C4—44no—
659C22⋊C4—44no—
660C22⋊C4—44no—
661C22⋊C4—44no—
662C22⋊C4—44no—
663C42—28no—
664C42—22no—
665C42—22no—
666C42—22no—
667C42—22no—
668C42—22no—
669C42—22no—
670C42—22no—
671C42—22no—
672C42—44no—
673C42—44no—
674C42—41no—
675C42—41no—
676C42—41no—
677C42—41no—
678C42—41no—
679C42—41no—
680C42—41no—
681C42—41no—
682C42—41no—
683C42—41no—
684C42—41no—
685C42—41no—
686C42—44no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
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—
757C23C2×#11711yescharacteristic
758C23C2×C4×D411yescharacteristic
759C23C2×C4×D411yescharacteristic
760C23#51811yescharacteristic
761C23#51811yescharacteristic
762C23#52011yescharacteristic
763C23#52011yescharacteristic
764C23C22×M1611yescharacteristic
765C23C22×M1611yescharacteristic
766C23C2×#13111yescharacteristic
767C23C2×#13111yescharacteristic
768C23C2×#13111yescharacteristic
769C23C2×#13111yescharacteristic
770C23#56811yescharacteristic
771C23#56811yescharacteristic
772D4—416no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
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—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
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—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
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—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
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—81no—
864C2×C4—81no—
865C2×C4—81no—
866C2×C4—81no—
867C2×C4—81no—
868C2×C4—81no—
869C2×C4—81no—
870C2×C4—81no—
871C2×C4#43514yes—
872C2×C4#43614yes—
873C2×C4#53511yescharacteristic
874C2×C4#53511yescharacteristic
875C2×C4#53511yescharacteristic
876C2×C4#53711yescharacteristic
877C2×C4#53811yescharacteristic
878C2×C4#53811yescharacteristic
879C2×C4#53911yescharacteristic
880C2×C4#53911yescharacteristic
881C2×C4#54011yescharacteristic
882C2×C4#54011yescharacteristic
883C2×C4#54011yescharacteristic
884C2×C4#54211yescharacteristic
885C2×C4D4211yescharacteristic
886C2×C4#54611yescharacteristic
887C2×C4#54611yescharacteristic
888C2×C4#54611yescharacteristic
889C2×C4#54711yescharacteristic
890C2×C4#54811yescharacteristic
891C2×C4#54811yescharacteristic
892C2×C4#55111yescharacteristic
893C2×C4#55111yescharacteristic
894C2×C4#55211yescharacteristic
895C2×C4#55311yescharacteristic
896C2×C4#55311yescharacteristic
897C2×C4H(3,𝔽4)11yescharacteristic
898C2×C4#56211yescharacteristic
899C2×C4#56211yescharacteristic
900C2×C4#56311yescharacteristic
901C8—42no—
902C8—42no—
903C8—42no—
904C8—42no—
905C8—81no—
906C8—81no—
907C8—81no—
908C8—81no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22—81no—
938C22—81no—
939C22#231811yescharacteristic
940C22#232411yescharacteristic
941C22#232811yescharacteristic
942C22#234211yescharacteristic
943C22#235211yescharacteristic
944C22#236111yescharacteristic
945C22#237911yescharacteristic
946C22#292011yescharacteristic
947C22#292211yescharacteristic
948C22#292411yescharacteristic
949C22#292511yescharacteristic
950C22C2×#43511yescharacteristic
951C22C2×#43611yescharacteristic
952C22#292911yescharacteristic
953C22#293111yescharacteristic
954C22#293311yescharacteristic
955C22D4×M1611yescharacteristic
956C22D4×M1611yescharacteristic
957C22#293511yescharacteristic
958C22#297311yescharacteristic
959C22#297411yescharacteristic
960C22#297411yescharacteristic
961C22#297411yescharacteristic
962C22#297911yescharacteristic
963C22#297911yescharacteristic
964C22#298011yescharacteristic
965C22#298111yescharacteristic
966C22#298911yescharacteristic
967C22#299011yescharacteristic
968C22#299111yescharacteristic
969C22#299111yescharacteristic
970C22#299211yescharacteristic
971C22#299211yescharacteristic
972C22#299311yescharacteristic
973C22#299411yescharacteristic
974C4—24no—
975C4—24no—
976C4—42no—
977C4—42no—
978C4—42no—
979C4—42no—
980C4—42no—
981C4—42no—
982C4—42no—
983C4—42no—
984C4—81no—
985C4—81no—
986C4#267011yescharacteristic
987C4#267611yescharacteristic
988C4#270611yescharacteristic
989C4#270711yescharacteristic
990C4#271111yescharacteristic
991C4#272311yescharacteristic
992C4#275311yescharacteristic
993C4#276111yescharacteristic
994C2—82no—
995C2—82no—
996C2#1437711yescharacteristic
997C2#2199811yescharacteristic
998C2#2200511yescharacteristic
999C2#2213711yescharacteristic
1000C2#2214111yescharacteristic
1001C2#2226211yescharacteristic
1002C2#2226611yescharacteristic
1003C2#2255511yescharacteristic
1004C2#2255611yescharacteristic
1005C2#2274911yescharacteristic
1006C2#2275611yescharacteristic
1007C2#2298711yescharacteristic
1008C2#2299011yescharacteristic
1009C2#2334711yescharacteristic
1010C2#2334911yescharacteristic
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
1. C2×#1923C2semidirect
3. C2×#1851C2semidirect
4. C2×#1831C2semidirect
6. #11202C2semidirect
7. #11147C2semidirect
8. #11042C2semidirect
9. #11042C2semidirect
10. #11042C2semidirect
12. #10921C2semidirect
13. #10874C2semidirect
14. #10795C2semidirect
15. #10715C2semidirect
181. #336D4semidirect
307. C2×C4⋊C4M16semidirect
337. C2×C22⋊C4M16semidirect

Maximal subgroups

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

subgroupindex
C2×#19232
C2×#18702
C2×#18512
C2×#18312
C4×#3902
#112022
#111472
#110422
#109642
#109212
#108742
#107952
#107152