Finite Group Databasebeta

← #385013

Subgroups — #385013

Order 512.

1532 conjugacy classes of subgroups.

The subgroup lattice has 1021 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1955C211yesmaximal, characteristic
2C2×#1923C211yesmaximal, characteristic, complemented
3C2×#1923C211yesmaximal, characteristic, complemented
4C2×#1797C211yesmaximal, characteristic, complemented
5C4×#386C211yesmaximal, characteristic
6#11322C211yesmaximal, characteristic, complemented
7#11147C211yesmaximal, characteristic, complemented
8#11147C211yesmaximal, characteristic, complemented
9#11042C211yesmaximal, characteristic, complemented
10#11042C211yesmaximal, characteristic, complemented
11#10964C211yesmaximal, characteristic
12#10877C211yesmaximal, characteristic, complemented
13#10876C211yesmaximal, characteristic, complemented
14#10798C211yesmaximal, characteristic, complemented
15#10712C211yesmaximal, characteristic, complemented
16C22×C4×D4C2211yescharacteristic
17C23×C42C2211yescharacteristic
18C22×C4⋊C8C2211yescharacteristic
19C22×C4⋊C8C2211yescharacteristic
20C22×C4⋊C8C2211yescharacteristic
21C22×C4⋊C8C2211yescharacteristic
22C22×C22⋊C8C2211yescharacteristic
23C22×C22⋊C8C2211yescharacteristic
24C22×C22⋊C8C2211yescharacteristic
25C22×C22⋊C8C2211yescharacteristic
26C22×C22⋊C8C2211yescharacteristic
27C22×C22⋊C8C2211yescharacteristic
28C22×C22⋊C8C2211yescharacteristic
29C22×C22⋊C8C2211yescharacteristic
30C22×#97C2211yescharacteristic
31C22×C4×C8C2211yescharacteristic
32C2×#386C411yescharacteristic
33C2×#386C411yescharacteristic
34C2×C4×C22⋊C4C2211yescharacteristic
35C2×C4×C22⋊C4C2211yescharacteristic
36C2×C4×C22⋊C4C2211yescharacteristic
37#1955—24no—
38#1923—24no—
39#1923—24no—
40#1797—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
55#1437C411yescharacteristic
56#1437C411yescharacteristic
57#1436C411yescharacteristic
58#1436C411yescharacteristic
59C22⋊#95C411yescharacteristic
60C22⋊#95C411yescharacteristic
61C4×#95C2211yescharacteristic
62C4×#95C2211yescharacteristic
63C23×D4C2×C411yescharacteristic
64C24×C4C2×C411yescharacteristic
65C24×C4C2×C411yescharacteristic
66C24×C4C2311yescharacteristic
67C24×C4C2311yescharacteristic
68C23×C8C2311yescharacteristic
69C23×C8C2311yescharacteristic
70C23×C8C2311yescharacteristic
71C23×C8C2311yescharacteristic
72C23×C8C2311yescharacteristic
73C23×C8C2311yescharacteristic
74C23×C8C2311yescharacteristic
75C23×C8C2311yescharacteristic
76C2×C4×D4—22no—
77C2×C4×D4—22no—
78C2×C4×D4—22no—
79C2×C4×D4—22no—
80C2×C4×D4—41no—
81C2×C4×D4—41no—
82C22×C4⋊C4C2×C411yescharacteristic
83C22×C22⋊C4C2×C411yescharacteristic
84C22×C22⋊C4C2×C411yescharacteristic
85C22×C22⋊C4C2×C411yescharacteristic
86C22×C22⋊C4C2×C411yescharacteristic
87C22×C22⋊C4C2×C411yescharacteristic
88C22×C22⋊C4C2×C411yescharacteristic
89C22×C22⋊C4C2×C411yescharacteristic
90C22×C22⋊C4C2×C411yescharacteristic
91C22×C42—22no—
92C22×C42—22no—
93C22×C42—41no—
94C22×C42—41no—
95C22×C42—41no—
96C22×C42—41no—
97C22×C42C2×C411yescharacteristic
98C22×C42C2×C411yescharacteristic
99C22×C42C2311yescharacteristic
100C22×C42C2311yescharacteristic
101C22×C42C2311yescharacteristic
102C22×C42C2311yescharacteristic
103C22×C42C2311yescharacteristic
104C2×C4⋊C8—22no—
105C2×C4⋊C8—22no—
106C2×C4⋊C8—22no—
107C2×C4⋊C8—22no—
108C2×C4⋊C8—41no—
109C2×C4⋊C8—41no—
110C2×C4⋊C8—41no—
111C2×C4⋊C8—41no—
112C2×C4⋊C8—41no—
113C2×C4⋊C8—41no—
114C2×C4⋊C8—41no—
115C2×C4⋊C8D414yescomplemented
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—41no—
126C2×C22⋊C8—41no—
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×C22⋊C8D414yes—
140C2×#97—22no—
141C2×#97—22no—
142C2×#97—41no—
143C2×C4×C8—22no—
144C2×C4×C8—22no—
145C2×C4×C8—41no—
146#386—24no—
147#386—24no—
148C4×C22⋊C4—22no—
149C4×C22⋊C4—22no—
150C4×C22⋊C4—22no—
151C4×C22⋊C4—22no—
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
164C2×#95C2×C411yescharacteristic
165C2×#95C2×C411yescharacteristic
166C2×#95C2×C411yescharacteristic
167C2×#95C2×C411yescharacteristic
168#336—22no—
169#336—22no—
170#336—22no—
171#336—22no—
172#336—22no—
173#336—22no—
174#336—22no—
175#336—22no—
176#336—22no—
177#336—41no—
178#336—41no—
179#336—41no—
180#336—41no—
181#336—41no—
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—22no—
192C23×C4—22no—
193C23×C4—22no—
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—22no—
207C23×C4—22no—
208C23×C4—22no—
209C23×C4—22no—
210C23×C4—22no—
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—41no—
226C23×C4—41no—
227C23×C4—41no—
228C23×C4—41no—
229C23×C4—41no—
230C23×C4—41no—
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×C4C22×C411yescharacteristic
240C23×C4C22×C411yescharacteristic
241C23×C4C22×C411yescharacteristic
242C23×C4C22×C411yescharacteristic
243C23×C4C2×D412yes—
244C23×C4#4112yes—
245C23×C4C2411yescharacteristic
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×C8—21no—
292C22×C8—21no—
293C22×C8—21no—
294C22×C8—21no—
295C22×C8—21no—
296C22×C8—21no—
297C22×C8—21no—
298C22×C8C2×D412yes—
299C22×C8C2×D412yes—
300C22×C8C2×D412yes—
301C22×C8C2×D412yes—
302C4×D4—44no—
303C4×D4—44no—
304C4×D4—44no—
305C4×D4—44no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—41no—
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—41no—
326C2×C22⋊C4—41no—
327C2×C22⋊C4—41no—
328C2×C22⋊C4—41no—
329C2×C22⋊C4—41no—
330C2×C22⋊C4—41no—
331C2×C22⋊C4M1614yes—
332C2×C22⋊C4M1614yes—
333C2×C42—21no—
334C2×C42—21no—
335C2×C42—21no—
336C2×C42—21no—
337C2×C42—21no—
338C2×C42—21no—
339C2×C42—21no—
340C2×C42—21no—
341C2×C42—22no—
342C2×C42—22no—
343C2×C42—21no—
344C2×C42—21no—
345C2×C42—21no—
346C2×C42—21no—
347C2×C42—21no—
348C2×C42—21no—
349C2×C42—21no—
350C2×C42—21no—
351C2×C42—21no—
352C2×C42—21no—
353C2×C42—21no—
354C2×C42—21no—
355C2×C42—21no—
356C2×C42—21no—
357C2×C42—21no—
358C2×C42—21no—
359C2×C42—21no—
360C2×C42—21no—
361C2×C42—44no—
362C2×C42—44no—
363C2×C42—44no—
364C2×C42—44no—
365C2×C42—41no—
366C2×C42—41no—
367C2×C42—41no—
368C2×C42—41no—
369C2×C42C2×D412yes—
370C2×C42#4112yes—
371C2×C42#4112yes—
372C2×C42#4112yes—
373C4⋊C8—44no—
374C4⋊C8—44no—
375C4⋊C8—44no—
376C4⋊C8—44no—
377C22⋊C8—44no—
378C22⋊C8—44no—
379C22⋊C8—44no—
380C22⋊C8—44no—
381C22⋊C8—44no—
382C22⋊C8—44no—
383C22⋊C8—44no—
384C22⋊C8—44no—
385#97—44no—
386C4×C8—44no—
387#95—22no—
388#95—22no—
389#95—22no—
390#95—22no—
391#95—22no—
392#95—22no—
393#95—22no—
394#95—22no—
395#95—22no—
396#95—22no—
397#95—22no—
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—
427C24C4×D412yes—
428C24C2×M1612yes—
429C24C2×M1612yes—
430C24#13112yes—
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—28no—
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—21no—
496C22×C4—21no—
497C22×C4—21no—
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—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—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—44no—
525C22×C4—44no—
526C22×C4—44no—
527C22×C4—44no—
528C22×C4—44no—
529C22×C4—44no—
530C22×C4—44no—
531C22×C4—44no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—44no—
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—44no—
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×C4—41no—
581C22×C4#11712yes—
582C22×C4#11712yes—
583C22×C4C4×D412yes—
584C22×C4C4×D412yes—
585C22×C4C4×D412yes—
586C22×C4C2×M1612yes—
587C22×C4C2×M1612yes—
588C22×C4C2×M1612yes—
589C22×C4C2×M1612yes—
590C22×C4#13112yes—
591C22×C4#13112yes—
592C22×C4#13112yes—
593C22×C4C22×D411yescharacteristic
594C22×C4C22×D411yescharacteristic
595C22×C4C2×#4111yescharacteristic
596C22×C4C2×#4111yescharacteristic
597C22×C4C2×#4111yescharacteristic
598C22×C4C2×#4111yescharacteristic
599C22×C4H(5,𝔽2)11yescharacteristic
600C22×C4H(5,𝔽2)11yescharacteristic
601C22×C4H(5,𝔽2)11yescharacteristic
602C22×C4H(5,𝔽2)11yescharacteristic
603C22×C4H(5,𝔽2)11yescharacteristic
604C22×C4H(5,𝔽2)11yescharacteristic
605C22×C42−1+411yescharacteristic
606C22×C42−1+411yescharacteristic
607C2×C8—22no—
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—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—
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—41no—
663C4⋊C4—44no—
664C22⋊C4—28no—
665C22⋊C4—28no—
666C22⋊C4—44no—
667C22⋊C4—44no—
668C22⋊C4—44no—
669C22⋊C4—44no—
670C22⋊C4—44no—
671C22⋊C4—44no—
672C42—22no—
673C42—22no—
674C42—22no—
675C42—22no—
676C42—22no—
677C42—22no—
678C42—22no—
679C42—22no—
680C42—44no—
681C42—44no—
682C42—41no—
683C42—41no—
684C42—41no—
685C42—41no—
686C42—41no—
687C42—41no—
688C42—41no—
689C42—41no—
690C42—41no—
691C42—41no—
692C42—41no—
693C42—41no—
694C23—22no—
695C23—22no—
696C23—22no—
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—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
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#43514yes—
764C23C2×#11711yescharacteristic
765C23C2×C4×D411yescharacteristic
766C23C2×C4×D411yescharacteristic
767C23#51811yescharacteristic
768C23#51811yescharacteristic
769C23#52011yescharacteristic
770C23#52011yescharacteristic
771C23C22×M1611yescharacteristic
772C23C22×M1611yescharacteristic
773C23C2×#13111yescharacteristic
774C23C2×#13111yescharacteristic
775C23C2×#13111yescharacteristic
776C23C2×#13111yescharacteristic
777C23#56811yescharacteristic
778C23#56811yescharacteristic
779D4—416no—
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—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—416no—
814C2×C4—416no—
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—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—42no—
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—81no—
874C2×C4—81no—
875C2×C4—81no—
876C2×C4—81no—
877C2×C4—81no—
878C2×C4—81no—
879C2×C4—81no—
880C2×C4—81no—
881C2×C4#43514yes—
882C2×C4#53411yescharacteristic
883C2×C4#53411yescharacteristic
884C2×C4#53511yescharacteristic
885C2×C4#53711yescharacteristic
886C2×C4#53811yescharacteristic
887C2×C4#53811yescharacteristic
888C2×C4#53811yescharacteristic
889C2×C4#53911yescharacteristic
890C2×C4#54011yescharacteristic
891C2×C4#54011yescharacteristic
892C2×C4#54211yescharacteristic
893C2×C4#54211yescharacteristic
894C2×C4D4211yescharacteristic
895C2×C4#54611yescharacteristic
896C2×C4#54611yescharacteristic
897C2×C4#54711yescharacteristic
898C2×C4#54711yescharacteristic
899C2×C4#54811yescharacteristic
900C2×C4#55011yescharacteristic
901C2×C4#55111yescharacteristic
902C2×C4#55111yescharacteristic
903C2×C4#55311yescharacteristic
904C2×C4#55511yescharacteristic
905C2×C4#55611yescharacteristic
906C2×C4#56011yescharacteristic
907C2×C4#56211yescharacteristic
908C2×C4#56211yescharacteristic
909C2×C4#56311yescharacteristic
910C8—42no—
911C8—42no—
912C8—42no—
913C8—42no—
914C8—81no—
915C8—81no—
916C8—81no—
917C8—81no—
918C22—24no—
919C22—24no—
920C22—24no—
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—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—81no—
941C22—81no—
942C22—81no—
943C22—81no—
944C22—81no—
945C22—81no—
946C22—81no—
947C22—81no—
948C22#231911yescharacteristic
949C22#232111yescharacteristic
950C22#232511yescharacteristic
951C22#234211yescharacteristic
952C22#235411yescharacteristic
953C22#236111yescharacteristic
954C22#237611yescharacteristic
955C22#292011yescharacteristic
956C22#292211yescharacteristic
957C22#292411yescharacteristic
958C22#292511yescharacteristic
959C22C2×#43511yescharacteristic
960C22C2×#43511yescharacteristic
961C22#292911yescharacteristic
962C22#293111yescharacteristic
963C22#293311yescharacteristic
964C22D4×M1611yescharacteristic
965C22D4×M1611yescharacteristic
966C22#293511yescharacteristic
967C22#297411yescharacteristic
968C22#297411yescharacteristic
969C22#297411yescharacteristic
970C22#297511yescharacteristic
971C22#297611yescharacteristic
972C22#297711yescharacteristic
973C22#297711yescharacteristic
974C22#297811yescharacteristic
975C22#298911yescharacteristic
976C22#299011yescharacteristic
977C22#299011yescharacteristic
978C22#299011yescharacteristic
979C22#299211yescharacteristic
980C22#299311yescharacteristic
981C22#299311yescharacteristic
982C22#299411yescharacteristic
983C4—24no—
984C4—42no—
985C4—42no—
986C4—42no—
987C4—42no—
988C4—42no—
989C4—42no—
990C4—42no—
991C4—42no—
992C4—42no—
993C4—81no—
994C4—81no—
995C4#267111yescharacteristic
996C4#267311yescharacteristic
997C4#268611yescharacteristic
998C4#271511yescharacteristic
999C4#272311yescharacteristic
1000C4#273011yescharacteristic
1001C4#275611yescharacteristic
1002C4#278611yescharacteristic
1003C2—44no—
1004C2—82no—
1005C2#1439711yescharacteristic
1006C2#2201011yescharacteristic
1007C2#2201711yescharacteristic
1008C2#2203011yescharacteristic
1009C2#2203811yescharacteristic
1010C2#2217211yescharacteristic
1011C2#2217411yescharacteristic
1012C2#2255311yescharacteristic
1013C2#2256011yescharacteristic
1014C2#2279711yescharacteristic
1015C2#2280011yescharacteristic
1016C2#2298611yescharacteristic
1017C2#2298711yescharacteristic
1018C2#2331611yescharacteristic
1019C2#2331811yescharacteristic
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×#1923C2semidirect
3. C2×#1923C2semidirect
4. C2×#1797C2semidirect
6. #11322C2semidirect
7. #11147C2semidirect
8. #11147C2semidirect
9. #11042C2semidirect
10. #11042C2semidirect
12. #10877C2semidirect
13. #10876C2semidirect
14. #10798C2semidirect
15. #10712C2semidirect
115. C2×C4⋊C8D4semidirect

Maximal subgroups

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

subgroupindex
C2×#19552
C2×#19232
C2×#17972
C4×#3862
#113222
#111472
#110422
#109642
#108772
#108762
#107982
#107122