Finite Group Databasebeta

← #6394008

Subgroups — #6394008

Order 512.

2970 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3509C211yesmaximal, characteristic
2C2×#2970C211yesmaximal, characteristic
3#34191C211yesmaximal, characteristic
4#22527C214yesmaximal, complemented
5#22494C214yesmaximal, complemented
6#22491C214yesmaximal, complemented
7#22486C214yesmaximal, complemented
8#21870C211yesmaximal, characteristic, complemented
9#21866C211yesmaximal, characteristic, complemented
10#21866C211yesmaximal, characteristic, complemented
11#21842C211yesmaximal, characteristic, complemented
12#21842C211yesmaximal, characteristic, complemented
13#21840C211yesmaximal, characteristic, complemented
14#21407C211yesmaximal, characteristic, complemented
15#21407C211yesmaximal, characteristic, complemented
16#21404C211yesmaximal, characteristic, complemented
17#21323C211yesmaximal, characteristic, complemented
18#21321C211yesmaximal, characteristic, complemented
19C2×#1993C211yesmaximal, characteristic, complemented
20#3509—28no—
21#3509C4116yescomplemented
22C2×#557—21no—
23C2×#557C2212yes—
24C2×#556—21no—
25C2×#556C2212yes—
26C2×#552—21no—
27C2×#552—21no—
28C2×#552C2212yes—
29C2×#552C2212yes—
30C2×#541—21no—
31C2×#541—21no—
32C2×#536—21no—
33C2×#533C2211yescharacteristic
34C2×#533C2211yescharacteristic
35C2×#533C2211yescharacteristic
36C2×#533C2211yescharacteristic
37C2×#533C2211yescharacteristic
38C22×C4⋊Q8C2211yescharacteristic
39C2×#519—21no—
40C2×C4×#41C2211yescharacteristic
41#2970—28no—
42C2×#446C2212yes—
43C2×#435C2212yes—
44C2×#435C2212yes—
45C2×C8×D4C2212yes—
46C2×#432C2211yescharacteristic
47C2×#432C2211yescharacteristic
48C2×#432C2211yescharacteristic
49C2×C4×M16C2211yescharacteristic
50C22×#97C2211yescharacteristic
51C22×#97C2211yescharacteristic
52#2355C2212yes—
53#2352C2212yes—
54#2352C2212yes—
55D4×C4⋊C4C2212yes—
56#2346—21no—
57#2343—21no—
58#2343—21no—
59#2339—21no—
60#2320—21no—
61#2318—21no—
62#2318—21no—
63#2285C2211yescharacteristic
64#2283C2211yescharacteristic
65#2283C2211yescharacteristic
66#2283C2211yescharacteristic
67C2×#382C2211yescharacteristic
68C2×#382C2211yescharacteristic
69#2275—21no—
70#1993C2211yescharacteristic
71#1993C2211yescharacteristic
72#1993C2211yescharacteristic
73#1993C2211yescharacteristic
74#1993C2214yes—
75#1993C2211yescharacteristic
76#1993C2211yescharacteristic
77#1993C2211yescharacteristic
78#1993C2211yescharacteristic
79#1993C2211yescharacteristic
80#1993C2211yescharacteristic
81#1993C2211yescharacteristic
82#1993C2211yescharacteristic
83#1992C2214yes—
84#1991C2214yes—
85#1989C2214yes—
86#1989C2214yes—
87#1987C2214yes—
88#1960C2211yescharacteristic
89#1960C2211yescharacteristic
90#1960C2211yescharacteristic
91#1960C2211yescharacteristic
92#1894C2214yes—
93#1892C2214yes—
94#1892C2214yes—
95#1873C2214yes—
96#1872C2214yes—
97#1872C2214yes—
98#1825C2214yes—
99#1825C2214yes—
100#1823C2214yes—
101#1805C2214yes—
102#1805C2214yes—
103#1803C2214yes—
104#1763C2214yes—
105#1763C2214yes—
106C4×#103C2214yes—
107#1736C2214yes—
108#1735C2214yes—
109C2×#340C2214yes—
110C22×#41D411yescharacteristic
111C23×Q8—21no—
112C22×M16C2312yes—
113C23×C8C2312yes—
114C23×C8C2312yes—
115#557—216no—
116#557—28no—
117#557C2×C4116yescomplemented
118#556—216no—
119#556—28no—
120#556C2×C4116yescomplemented
121#552—216no—
122#552—216no—
123#552—28no—
124#552—28no—
125#552C2×C4116yes—
126#552C2×C4116yescomplemented
127#541—216no—
128#541—216no—
129#536—216no—
130#533—24no—
131#533—24no—
132#533—24no—
133#533—24no—
134#533—24no—
135#533C2×C418yescomplemented
136#533C2×C418yescomplemented
137#533C2×C418yescomplemented
138#533C2×C418yescomplemented
139#533C2×C418yescomplemented
140C2×C4⋊Q8—22no—
141C2×C4⋊Q8—21no—
142C2×C4⋊Q8—21no—
143C2×C4⋊Q8—24no—
144C2×C4⋊Q8C2×C418yescomplemented
145C2×C4⋊Q8C2311yescharacteristic
146C2×C4⋊Q8C2311yescharacteristic
147C2×C4⋊Q8C2311yescharacteristic
148C2×C4⋊Q8C2312yes—
149C2×C4⋊Q8C2311yescharacteristic
150C2×#126—22no—
151C2×#126—22no—
152C2×#126—22no—
153C2×#126—22no—
154C2×#125—22no—
155C2×#125—22no—
156C2×#125—22no—
157C2×#125—22no—
158C2×#125—21no—
159C2×#125—21no—
160C2×#125—21no—
161C2×#125C2312yes—
162C2×#125C2312yes—
163C2×#124—22no—
164C2×#123—22no—
165C2×#123—22no—
166C2×C22⋊Q8—21no—
167C2×C22⋊Q8—21no—
168C2×C22⋊Q8—21no—
169C2×C22⋊Q8—21no—
170C2×C22⋊Q8—21no—
171C2×C22⋊Q8—21no—
172C2×C22⋊Q8—21no—
173C2×C22⋊Q8C2312yes—
174C2×C22⋊Q8C2312yes—
175C2×C22⋊Q8C2312yes—
176#519—216no—
177C4×#41C2×C418yes—
178C4×#41D418yes—
179C2×C4×Q8—22no—
180C2×C4×Q8—22no—
181C2×C4×Q8—21no—
182C2×C4×Q8—21no—
183C2×C4×Q8—21no—
184C2×C4×Q8—21no—
185C2×C4×Q8—21no—
186C2×C4×Q8—21no—
187C2×C4×Q8—21no—
188C2×C4×Q8D411yescharacteristic
189C2×C4×Q8C2312yes—
190C2×C4×Q8C2312yes—
191C2×C4×Q8C2312yes—
192C2×C4×Q8C2311yescharacteristic
193C2×C4×D4—22no—
194C2×C4×D4D411yescharacteristic
195C2×C4×D4D411yescharacteristic
196C2×C4×D4D411yescharacteristic
197C2×C4×D4C2311yescharacteristic
198C2×C4×D4C2311yescharacteristic
199C2×C4×D4C2311yescharacteristic
200C2×#117—21no—
201C2×#117—21no—
202C2×#117—21no—
203C2×#117—22no—
204C2×#117—22no—
205C2×#117D411yescharacteristic
206C2×#117D411yescharacteristic
207C2×#117D411yescharacteristic
208C2×#117C2312yes—
209C2×#117C2312yes—
210C2×#117C2312yes—
211C22×C4⋊C4—21no—
212C22×C4⋊C4C2312yes—
213C22×C4⋊C4C2312yes—
214C22×C4⋊C4C2312yes—
215C22×C42C2311yescharacteristic
216C22×C42C2311yescharacteristic
217C22×C42C2311yescharacteristic
218#446—28no—
219#435—28no—
220#435—28no—
221C8×D4—28no—
222#432—24no—
223#432—24no—
224#432—24no—
225C2×C4⋊C8C2312yes—
226C2×C4⋊C8C2312yes—
227C2×C4⋊C8C2312yes—
228C2×#103C2314yes—
229C2×#103C2314yes—
230C2×#103C2314yes—
231C2×#103C2314yes—
232C2×C22⋊C8C2312yes—
233C2×C22⋊C8C2312yes—
234C2×C22⋊C8C2312yes—
235C4×M16—24no—
236C2×#97—24no—
237C2×#97—24no—
238C2×#97C2311yescharacteristic
239C2×#97C2311yescharacteristic
240C2×#97C2311yescharacteristic
241C2×#97C2312yes—
242C2×#97C2312yes—
243C2×#97C2311yescharacteristic
244C2×C4×C8C2312yes—
245#391—22no—
246#389—22no—
247#388—22no—
248#388—22no—
249#387—22no—
250#387—22no—
251#387—22no—
252#387—22no—
253#386—22no—
254#386—22no—
255#385—22no—
256#385—22no—
257#384C2312yes—
258#383—21no—
259#383—21no—
260#383—21no—
261#382—21no—
262#382—21no—
263#382—21no—
264#382—21no—
265#382C2312yes—
266#382C2312yes—
267#382C2311yescharacteristic
268#382C2311yescharacteristic
269#382C2311yescharacteristic
270#382C2311yescharacteristic
271#381—21no—
272#381—21no—
273#381—21no—
274#380—21no—
275#380—21no—
276#380C2312yes—
277#380C2312yes—
278#380C2312yes—
279C4×C4⋊C4—22no—
280C4×C4⋊C4—21no—
281C4×C4⋊C4—21no—
282C4×C4⋊C4C2312yes—
283C4×C4⋊C4C2312yes—
284C4×C4⋊C4C2312yes—
285C4×C22⋊C4—21no—
286C4×C22⋊C4—21no—
287C4×C22⋊C4—21no—
288C4×C22⋊C4—22no—
289C4×C22⋊C4—22no—
290#376—21no—
291#376—21no—
292#376—21no—
293C2×#95—21no—
294C2×#95—21no—
295C2×#95—21no—
296C2×#95—21no—
297#340C2314yes—
298#340C2314yes—
299#340C2314yes—
300#340C2314yes—
301#340C2314yes—
302#340C2314yes—
303#340C2314yes—
304#340C2314yes—
305#340C2314yes—
306#340C2314yes—
307#340C2314yes—
308#340C2314yes—
309C2×#41—44no—
310C2×#41C22⋊C418yes—
311C22×Q8—28no—
312C22×Q8—21no—
313C22×Q8—21no—
314C22×Q8—21no—
315C22×Q8—22no—
316C22×Q8—48no—
317C22×Q8C2×D411yescharacteristic
318C22×Q8C2412yes—
319C22×D4C2×D411yescharacteristic
320C22×D4C2×D411yescharacteristic
321C22×D4C2×D411yescharacteristic
322C23×C4—22no—
323C23×C4—22no—
324C23×C4—22no—
325C23×C4C2×D411yescharacteristic
326C23×C4C2×D411yescharacteristic
327C23×C4C2×D411yescharacteristic
328C23×C4C2×D411yescharacteristic
329C23×C4C2×D411yescharacteristic
330C23×C4C2×D411yescharacteristic
331C23×C4C2411yescharacteristic
332C23×C4C2411yescharacteristic
333C23×C4C2411yescharacteristic
334C2×M16—24no—
335C2×M16—24no—
336C2×M16—42no—
337C22×C8—24no—
338C22×C8—24no—
339C22×C8—24no—
340C22×C8—24no—
341C22×C8—42no—
342C22×C8—42no—
343C22×C8C2412yes—
344C22×C8C2412yes—
345C22×C8C2412yes—
346C22×C8C2412yes—
347C4⋊Q8—216no—
348C4⋊Q8—28no—
349C4⋊Q8—28no—
350C4⋊Q8—22no—
351C4⋊Q8—22no—
352C4⋊Q8—24no—
353C4⋊Q8—22no—
354C4⋊Q8—22no—
355C4⋊Q8C22×C414yes—
356C4⋊Q8C22×C414yes—
357C4⋊Q8C22×C414yes—
358C4⋊Q8C22×C418yes—
359C4⋊Q8C22×C414yes—
360#126—216no—
361#126—216no—
362#126—216no—
363#126—216no—
364#125—216no—
365#125—216no—
366#125—216no—
367#125—216no—
368#125—28no—
369#125—28no—
370#125—28no—
371#125—24no—
372#125—24no—
373#125C22×C418yes—
374#125C22×C418yes—
375#124—216no—
376#123—216no—
377#123—216no—
378C22⋊Q8—28no—
379C22⋊Q8—28no—
380C22⋊Q8—28no—
381C22⋊Q8—28no—
382C22⋊Q8—28no—
383C22⋊Q8—28no—
384C22⋊Q8—28no—
385C22⋊Q8—24no—
386C22⋊Q8—24no—
387C22⋊Q8—24no—
388C22⋊Q8C22×C418yes—
389C22⋊Q8C22×C418yes—
390C22⋊Q8C22×C418yes—
391C4×Q8—216no—
392C4×Q8—216no—
393C4×Q8—28no—
394C4×Q8—28no—
395C4×Q8—28no—
396C4×Q8—28no—
397C4×Q8—28no—
398C4×Q8—28no—
399C4×Q8—28no—
400C4×Q8—24no—
401C4×Q8—24no—
402C4×Q8—24no—
403C4×Q8C22⋊C418yes—
404C4×Q8C22×C418yes—
405C4×Q8C22×C418yes—
406C4×Q8C22×C418yes—
407C4×Q8C22×C414yes—
408C4×Q8C2×D414yes—
409C4×D4—48no—
410C4×D4C22⋊C418yes—
411C4×D4C22⋊C418yes—
412C4×D4C22⋊C418yes—
413C4×D4C22×C414yes—
414C4×D4C22×C414yes—
415C4×D4C22×C414yes—
416C4×D4C2×D414yes—
417C4×D4C2×D414yes—
418C4×D4C2×D414yes—
419#117—28no—
420#117—28no—
421#117—28no—
422#117—24no—
423#117—24no—
424#117—216no—
425#117—216no—
426#117—44no—
427#117C22⋊C418yes—
428#117C22⋊C418yes—
429#117C22⋊C418yes—
430#117C22×C418yes—
431#117C22×C418yes—
432C2×C4⋊C4—28no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—24no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—44no—
456C2×C4⋊C4—44no—
457C2×C4⋊C4C22×C418yes—
458C2×C4⋊C4C2×D411yescharacteristic
459C2×C4⋊C4C2×D411yescharacteristic
460C2×C4⋊C4C2×D411yescharacteristic
461C2×C4⋊C4C2×D411yescharacteristic
462C2×C4⋊C4C2×D411yescharacteristic
463C2×C4⋊C4C2×D411yescharacteristic
464C2×C4⋊C4C2412yes—
465C2×C4⋊C4C2412yes—
466C2×C4⋊C4C2412yes—
467C2×C4⋊C4C2412yes—
468C2×C4⋊C4C2412yes—
469C2×C4⋊C4C2412yes—
470C2×C4⋊C4C2412yes—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4C2×D411yescharacteristic
481C2×C22⋊C4C2×D411yescharacteristic
482C2×C22⋊C4C2×D411yescharacteristic
483C2×C22⋊C4C2×D411yescharacteristic
484C2×C22⋊C4C2×D411yescharacteristic
485C2×C22⋊C4C2×D411yescharacteristic
486C2×C42—22no—
487C2×C42—22no—
488C2×C42—22no—
489C2×C42—22no—
490C2×C42—22no—
491C2×C42—22no—
492C2×C42—22no—
493C2×C42—22no—
494C2×C42—22no—
495C2×C42C22×C414yes—
496C2×C42C22×C414yes—
497C2×C42C22×C414yes—
498C2×C42C2×D411yescharacteristic
499C2×C42C2×D411yescharacteristic
500C2×C42C2×D411yescharacteristic
501C2×C42C2×D411yescharacteristic
502C2×C42C2×D411yescharacteristic
503C2×C42C2×D411yescharacteristic
504C2×C42C2×D414yes—
505C2×C42C2×D414yes—
506C2×C42C2×D414yes—
507C2×C42C2411yescharacteristic
508C2×C42C2411yescharacteristic
509C2×C42C2411yescharacteristic
510C2×C42C2411yescharacteristic
511C4⋊C8—24no—
512C4⋊C8—24no—
513C4⋊C8—24no—
514#103—28no—
515#103—44no—
516#103—44no—
517#103—44no—
518C22⋊C8—24no—
519C22⋊C8—24no—
520C22⋊C8—24no—
521#97—22no—
522#97—22no—
523#97—22no—
524#97—24no—
525#97—24no—
526#97—22no—
527C4×C8—24no—
528#95—21no—
529#95—21no—
530#95—21no—
531#95—21no—
532#95—21no—
533#95—21no—
534#95—22no—
535#95—22no—
536#95—22no—
537#95—22no—
538#95—21no—
539#95—22no—
540#95—21no—
541#95—22no—
542#95—22no—
543#95—22no—
544#95—22no—
545#95—22no—
546C24C22×D411yescharacteristic
547C24C22×D411yescharacteristic
548C24C22×D411yescharacteristic
549#41—416no—
550C2×Q8—24no—
551C2×Q8—24no—
552C2×Q8—24no—
553C2×Q8—28no—
554C2×Q8—22no—
555C2×Q8—24no—
556C2×Q8—24no—
557C2×Q8—42no—
558C2×Q8—44no—
559C2×Q8—432no—
560C2×Q8—44no—
561C2×Q8—44no—
562C2×Q8—48no—
563C2×Q8C2×C22⋊C414yes—
564C2×Q8C23×C414yes—
565C2×D4—24no—
566C2×D4—24no—
567C2×D4—42no—
568C2×D4C2×C22⋊C414yes—
569C2×D4C2×C22⋊C414yes—
570C2×D4C2×C22⋊C414yes—
571C22×C4—24no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—28no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—48no—
593C22×C4—44no—
594C22×C4—44no—
595C22×C4—82no—
596C22×C4—82no—
597C22×C4—82no—
598C22×C4—82no—
599C22×C4C2×C22⋊C414yes—
600C22×C4C2×C22⋊C414yes—
601C22×C4C2×C22⋊C414yes—
602C22×C4C2×C22⋊C414yes—
603C22×C4C2×C22⋊C414yes—
604C22×C4C2×C22⋊C414yes—
605C22×C4C23×C412yes—
606C22×C4C23×C412yes—
607C22×C4C23×C412yes—
608C22×C4C22×D411yescharacteristic
609C22×C4C22×D411yescharacteristic
610C22×C4C22×D411yescharacteristic
611C22×C4C22×D411yescharacteristic
612C22×C4C22×D411yescharacteristic
613C22×C4C22×D411yescharacteristic
614C22×C4C22×D411yescharacteristic
615C22×C4C22×D411yescharacteristic
616C22×C4C22×D411yescharacteristic
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D411yescharacteristic
619C22×C4C22×D412yes—
620C22×C4C22×D412yes—
621C22×C4C22×D412yes—
622C22×C4C2511yescharacteristic
623M16—48no—
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—22no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—48no—
636C2×C8—48no—
637C2×C82−1+414yes—
638C4⋊C4—24no—
639C4⋊C4—24no—
640C4⋊C4—28no—
641C4⋊C4—28no—
642C4⋊C4—24no—
643C4⋊C4—24no—
644C4⋊C4—24no—
645C4⋊C4—28no—
646C4⋊C4—28no—
647C4⋊C4—28no—
648C4⋊C4—28no—
649C4⋊C4—28no—
650C4⋊C4—28no—
651C4⋊C4—28no—
652C4⋊C4—28no—
653C4⋊C4—28no—
654C4⋊C4—28no—
655C4⋊C4—22no—
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—24no—
659C4⋊C4—24no—
660C4⋊C4—24no—
661C4⋊C4—24no—
662C4⋊C4—44no—
663C4⋊C4—82no—
664C4⋊C4—82no—
665C4⋊C4—82no—
666C4⋊C4C2×C22⋊C414yes—
667C4⋊C4C2×C22⋊C414yes—
668C4⋊C4C2×C22⋊C414yes—
669C4⋊C4C2×C22⋊C414yes—
670C4⋊C4C2×C22⋊C414yes—
671C4⋊C4C2×C22⋊C414yes—
672C4⋊C4C23×C414yes—
673C4⋊C4C23×C414yes—
674C4⋊C4C23×C414yes—
675C22⋊C4—28no—
676C22⋊C4—28no—
677C22⋊C4—28no—
678C22⋊C4—28no—
679C22⋊C4—28no—
680C22⋊C4—44no—
681C22⋊C4—44no—
682C22⋊C4—82no—
683C22⋊C4—82no—
684C22⋊C4C2×C22⋊C414yes—
685C22⋊C4C2×C22⋊C414yes—
686C22⋊C4C2×C22⋊C414yes—
687C22⋊C4C2×C22⋊C414yes—
688C22⋊C4C2×C22⋊C414yes—
689C22⋊C4C2×C22⋊C414yes—
690C42—28no—
691C42—28no—
692C42—28no—
693C42—28no—
694C42—28no—
695C42—44no—
696C42—82no—
697C42—82no—
698C42—82no—
699C42C2×C22⋊C414yes—
700C42C2×C22⋊C414yes—
701C42C2×C22⋊C414yes—
702C42C2×C22⋊C414yes—
703C42C2×C22⋊C414yes—
704C42C2×C22⋊C414yes—
705C42C23×C412yes—
706C42C23×C412yes—
707C42C23×C412yes—
708C42C23×C412yes—
709C42C22×D412yes—
710C42C22×D412yes—
711C42C22×D412yes—
712C42C22×D412yes—
713C23—22no—
714C23—21no—
715C23—21no—
716C23—22no—
717C23—22no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—22no—
723C23—22no—
724C23C22×C22⋊C412yes—
725C23C22×C22⋊C412yes—
726C23C22×C22⋊C412yes—
727C23#57514yes—
728C23C23×D411yescharacteristic
729Q8—28no—
730Q8—44no—
731Q8—48no—
732Q8—48no—
733Q8—48no—
734Q8—416no—
735Q8—44no—
736D4—28no—
737D4—28no—
738D4—44no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—28no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—44no—
767C2×C4—44no—
768C2×C4—44no—
769C2×C4—44no—
770C2×C4—416no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—44no—
774C2×C4—44no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—164no—
788C2×C4—164no—
789C2×C4C22×C22⋊C412yes—
790C2×C4C22×C22⋊C412yes—
791C2×C4C22×C22⋊C412yes—
792C2×C4C22×C22⋊C412yes—
793C2×C4C22×C22⋊C412yes—
794C2×C4C22×C22⋊C412yes—
795C2×C4C22×C22⋊C412yes—
796C2×C4C22×C22⋊C412yes—
797C2×C4C22×C22⋊C412yes—
798C2×C4C22×C22⋊C412yes—
799C2×C4C22×C22⋊C412yes—
800C2×C4C24×C411yescharacteristic
801C2×C4C23×D411yescharacteristic
802C2×C4C2×2−1+412yes—
803C2×C4#58512yes—
804C8—24no—
805C8—42no—
806C8—42no—
807C8—42no—
808C22—24no—
809C22—24no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22#289614yes—
823C22C23×C22⋊C411yescharacteristic
824C22#349911yescharacteristic
825C22#350011yescharacteristic
826C22C2×#57512yes—
827C22#358612yes—
828C4—22no—
829C4—22no—
830C4—22no—
831C4—22no—
832C4—22no—
833C4—22no—
834C4—22no—
835C4—22no—
836C4—22no—
837C4—22no—
838C4—22no—
839C4—44no—
840C4—44no—
841C4—44no—
842C4—44no—
843C4—82no—
844C4—82no—
845C4—82no—
846C4—82no—
847C4C4×2−1+412yes—
848C4#348912yes—
849C2—24no—
850C2—42no—
851C2—42no—
852C2#3425911yescharacteristic
853C2C2×#289611yescharacteristic
854C2#6008811yescharacteristic
855C2#6250512yes—
856C2#6258512yes—
subgroupG/H
center, socleC23C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC22×#41D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×#41 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #22527C2semidirect
5. #22494C2semidirect
6. #22491C2semidirect
7. #22486C2semidirect
8. #21870C2semidirect
9. #21866C2semidirect
10. #21866C2semidirect
11. #21842C2semidirect
12. #21842C2semidirect
13. #21840C2semidirect
14. #21407C2semidirect
15. #21407C2semidirect
16. #21404C2semidirect
17. #21323C2semidirect
18. #21321C2semidirect
19. C2×#1993C2semidirect
21. #3509C4semidirect
117. #557C2×C4semidirect
120. #556C2×C4semidirect
126. #552C2×C4semidirect
135. #533C2×C4semidirect
136. #533C2×C4semidirect
137. #533C2×C4semidirect
138. #533C2×C4semidirect
139. #533C2×C4semidirect
144. C2×C4⋊Q8C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#35092
C2×#29702
#341912
#225272
#224942
#224912
#224862
#218702
#218662
#218422
#218402
#214072
#214042
#213232
#213212
C2×#19932