Finite Group Databasebeta

← #6394006

Subgroups — #6394006

Order 512.

3154 conjugacy classes of subgroups.

The subgroup lattice has 887 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3511C211yesmaximal, characteristic
2C2×#2970C211yesmaximal, characteristic, complemented
3#34191C211yesmaximal, characteristic, complemented
4#22526C214yesmaximal, complemented
5#22493C214yesmaximal, complemented
6#22492C214yesmaximal, complemented
7#22488C214yesmaximal, complemented
8#21869C211yesmaximal, characteristic, complemented
9#21865C211yesmaximal, characteristic, complemented
10#21865C211yesmaximal, characteristic, complemented
11#21842C211yesmaximal, characteristic, complemented
12#21842C211yesmaximal, characteristic, complemented
13#21841C211yesmaximal, characteristic, complemented
14#21408C211yesmaximal, characteristic, complemented
15#21408C211yesmaximal, characteristic, complemented
16#21405C211yesmaximal, characteristic, complemented
17#21323C211yesmaximal, characteristic, complemented
18#21321C211yesmaximal, characteristic, complemented
19C2×#1993C211yesmaximal, characteristic, complemented
20#3511—28no—
21#3511C4116yescomplemented
22C2×#556—21no—
23C2×#555C2212yes—
24C2×#554C2212yes—
25C2×#553C2212yes—
26C2×#553C2212yes—
27C2×#548—21no—
28C2×#548—21no—
29C2×#547—21no—
30C2×#542—21no—
31C2×#542—21no—
32C2×#537—21no—
33C2×#533C2211yescharacteristic
34C2×#533C2211yescharacteristic
35C2×#532C2211yescharacteristic
36C2×#532C2211yescharacteristic
37C2×#532C2211yescharacteristic
38C22×C4⋊Q8C2211yescharacteristic
39C2×#520—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#1988C2214yes—
88#1961C2211yescharacteristic
89#1961C2211yescharacteristic
90#1961C2211yescharacteristic
91#1961C2211yescharacteristic
92#1895C2214yes—
93#1893C2214yes—
94#1893C2214yes—
95#1875C2214yes—
96#1874C2214yes—
97#1874C2214yes—
98#1825C2214yes—
99#1825C2214yes—
100#1824C2214yes—
101#1804C2214yes—
102#1804C2214yes—
103#1802C2214yes—
104#1762C2214yes—
105#1762C2214yes—
106C4×#102C2214yes—
107#1736C2214yes—
108#1735C2214yes—
109C2×#340C2214yes—
110C22×#41—21no—
111C22×#41—21no—
112C22×#41—21no—
113C22×#41D411yescharacteristic
114C23×Q8—21no—
115C22×M16C2312yes—
116C23×C8C2312yes—
117C23×C8C2312yes—
118#556—216no—
119#555—28no—
120#555C2×C4116yescomplemented
121#554—28no—
122#554C2×C4116yescomplemented
123#553—28no—
124#553—28no—
125#553C2×C4116yes—
126#553C2×C4116yescomplemented
127#548—216no—
128#548—216no—
129#547—216no—
130#542—216no—
131#542—216no—
132#537—216no—
133#533—24no—
134#533—24no—
135#533C2×C418yescomplemented
136#533C2×C418yescomplemented
137#532—24no—
138#532—24no—
139#532—24no—
140#532C2×C418yescomplemented
141#532C2×C418yescomplemented
142#532C2×C418yescomplemented
143C2×C4⋊Q8—21no—
144C2×C4⋊Q8—21no—
145C2×C4⋊Q8—24no—
146C2×C4⋊Q8C2×C418yescomplemented
147C2×C4⋊Q8C2311yescharacteristic
148C2×C4⋊Q8C2311yescharacteristic
149C2×C4⋊Q8C2312yes—
150C2×C4⋊Q8C2311yescharacteristic
151C2×#127C2311yescharacteristic
152C2×#126—22no—
153C2×#126—22no—
154C2×#125C2312yes—
155C2×#125C2312yes—
156C2×#124—22no—
157C2×#124—22no—
158C2×#124—21no—
159C2×#124—21no—
160C2×#124—21no—
161C2×#123—22no—
162C2×#123—22no—
163C2×C22⋊Q8—22no—
164C2×C22⋊Q8—21no—
165C2×C22⋊Q8—21no—
166C2×C22⋊Q8—21no—
167C2×C22⋊Q8—21no—
168C2×C22⋊Q8—22no—
169C2×C22⋊Q8—22no—
170C2×#121—22no—
171C2×#121—22no—
172C2×#121—22no—
173C2×#121—21no—
174C2×#121—21no—
175C2×#121—21no—
176C2×#121C2312yes—
177C2×#121C2312yes—
178C2×#121C2312yes—
179#520—216no—
180C4×#41C2×C418yes—
181C4×#41D418yes—
182C2×C4×Q8—21no—
183C2×C4×Q8—21no—
184C2×C4×Q8—21no—
185C2×C4×Q8—21no—
186C2×C4×Q8D411yescharacteristic
187C2×C4×Q8C2311yescharacteristic
188C2×C4×D4—22no—
189C2×C4×D4—22no—
190C2×C4×D4—22no—
191C2×C4×D4—21no—
192C2×C4×D4—21no—
193C2×C4×D4—21no—
194C2×C4×D4D411yescharacteristic
195C2×C4×D4D411yescharacteristic
196C2×C4×D4D411yescharacteristic
197C2×C4×D4C2312yes—
198C2×C4×D4C2312yes—
199C2×C4×D4C2312yes—
200C2×C4×D4C2311yescharacteristic
201C2×C4×D4C2311yescharacteristic
202C2×C4×D4C2311yescharacteristic
203C2×#117—22no—
204C2×#117D411yescharacteristic
205C2×#117D411yescharacteristic
206C2×#117D411yescharacteristic
207C2×#117C2312yes—
208C2×#117C2312yes—
209C2×#117C2312yes—
210C22×C4⋊C4—21no—
211C22×C4⋊C4—22no—
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×#102C2314yes—
229C2×#102C2314yes—
230C2×#102C2314yes—
231C2×#102C2314yes—
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—28no—
310C2×#41—28no—
311C2×#41—28no—
312C2×#41—44no—
313C2×#41—48no—
314C2×#41—84no—
315C2×#41—84no—
316C2×#41C22⋊C418yes—
317C22×Q8—28no—
318C22×Q8—21no—
319C22×Q8—21no—
320C22×Q8—21no—
321C22×Q8—22no—
322C22×Q8—84no—
323C22×Q8C2×D411yescharacteristic
324C22×D4—22no—
325C22×D4—22no—
326C22×D4—22no—
327C22×D4—21no—
328C22×D4—21no—
329C22×D4C2×D411yescharacteristic
330C22×D4C2×D411yescharacteristic
331C22×D4C2×D411yescharacteristic
332C22×D4C2412yes—
333C23×C4—22no—
334C23×C4—22no—
335C23×C4—22no—
336C23×C4—22no—
337C23×C4—22no—
338C23×C4—22no—
339C23×C4C2×D411yescharacteristic
340C23×C4C2×D411yescharacteristic
341C23×C4C2×D411yescharacteristic
342C23×C4C2×D411yescharacteristic
343C23×C4C2×D411yescharacteristic
344C23×C4C2×D411yescharacteristic
345C23×C4C2411yescharacteristic
346C23×C4C2411yescharacteristic
347C23×C4C2411yescharacteristic
348C2×M16—24no—
349C2×M16—24no—
350C2×M16—42no—
351C22×C8—24no—
352C22×C8—24no—
353C22×C8—24no—
354C22×C8—24no—
355C22×C8—42no—
356C22×C8—42no—
357C22×C8C2412yes—
358C22×C8C2412yes—
359C22×C8C2412yes—
360C22×C8C2412yes—
361C4⋊Q8—28no—
362C4⋊Q8—28no—
363C4⋊Q8—22no—
364C4⋊Q8—22no—
365C4⋊Q8—24no—
366C4⋊Q8—22no—
367C4⋊Q8C22×C414yes—
368C4⋊Q8C22×C414yes—
369C4⋊Q8C22×C418yes—
370C4⋊Q8C22×C414yes—
371#127—22no—
372#127C22×C414yes—
373#126—216no—
374#126—216no—
375#125—24no—
376#125—24no—
377#125C22×C418yes—
378#125C22×C418yes—
379#124—216no—
380#124—216no—
381#124—28no—
382#124—28no—
383#124—28no—
384#123—216no—
385#123—216no—
386C22⋊Q8—216no—
387C22⋊Q8—28no—
388C22⋊Q8—28no—
389C22⋊Q8—28no—
390C22⋊Q8—28no—
391C22⋊Q8—216no—
392C22⋊Q8—216no—
393#121—216no—
394#121—216no—
395#121—216no—
396#121—28no—
397#121—28no—
398#121—28no—
399#121—24no—
400#121—24no—
401#121—24no—
402#121C22×C418yes—
403#121C22×C418yes—
404#121C22×C418yes—
405C4×Q8—28no—
406C4×Q8—28no—
407C4×Q8—28no—
408C4×Q8—28no—
409C4×Q8C22⋊C418yes—
410C4×Q8C22×C414yes—
411C4×Q8C2×D414yes—
412C4×D4—216no—
413C4×D4—216no—
414C4×D4—28no—
415C4×D4—28no—
416C4×D4—28no—
417C4×D4—24no—
418C4×D4—24no—
419C4×D4—24no—
420C4×D4—48no—
421C4×D4C22⋊C418yes—
422C4×D4C22⋊C418yes—
423C4×D4C22⋊C418yes—
424C4×D4C22×C418yes—
425C4×D4C22×C418yes—
426C4×D4C22×C418yes—
427C4×D4C22×C414yes—
428C4×D4C22×C414yes—
429C4×D4C22×C414yes—
430C4×D4C2×D414yes—
431C4×D4C2×D414yes—
432C4×D4C2×D414yes—
433#117—24no—
434#117—24no—
435#117—216no—
436#117—44no—
437#117C22⋊C418yes—
438#117C22⋊C418yes—
439#117C22⋊C418yes—
440#117C22×C418yes—
441#117C22×C418yes—
442C2×C4⋊C4—28no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—24no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—216no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—44no—
459C2×C4⋊C4—44no—
460C2×C4⋊C4C22×C418yes—
461C2×C4⋊C4C2×D411yescharacteristic
462C2×C4⋊C4C2×D411yescharacteristic
463C2×C4⋊C4C2×D411yescharacteristic
464C2×C4⋊C4C2×D411yescharacteristic
465C2×C4⋊C4C2×D411yescharacteristic
466C2×C4⋊C4C2×D411yescharacteristic
467C2×C4⋊C4C2412yes—
468C2×C4⋊C4C2412yes—
469C2×C4⋊C4C2412yes—
470C2×C4⋊C4C2412yes—
471C2×C4⋊C4C2412yes—
472C2×C4⋊C4C2412yes—
473C2×C4⋊C4C2412yes—
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⋊C4—22no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4C2×D411yescharacteristic
487C2×C22⋊C4C2×D411yescharacteristic
488C2×C22⋊C4C2×D411yescharacteristic
489C2×C22⋊C4C2×D411yescharacteristic
490C2×C22⋊C4C2×D411yescharacteristic
491C2×C22⋊C4C2×D411yescharacteristic
492C2×C42—22no—
493C2×C42—22no—
494C2×C42—22no—
495C2×C42—22no—
496C2×C42—22no—
497C2×C42—22no—
498C2×C42C22×C414yes—
499C2×C42C22×C414yes—
500C2×C42C22×C414yes—
501C2×C42C2×D411yescharacteristic
502C2×C42C2×D411yescharacteristic
503C2×C42C2×D411yescharacteristic
504C2×C42C2×D411yescharacteristic
505C2×C42C2×D411yescharacteristic
506C2×C42C2×D411yescharacteristic
507C2×C42C2×D414yes—
508C2×C42C2×D414yes—
509C2×C42C2×D414yes—
510C2×C42C2411yescharacteristic
511C2×C42C2411yescharacteristic
512C2×C42C2411yescharacteristic
513C2×C42C2411yescharacteristic
514C4⋊C8—24no—
515C4⋊C8—24no—
516C4⋊C8—24no—
517#102—28no—
518#102—44no—
519#102—44no—
520#102—44no—
521C22⋊C8—24no—
522C22⋊C8—24no—
523C22⋊C8—24no—
524#97—22no—
525#97—22no—
526#97—22no—
527#97—24no—
528#97—24no—
529#97—22no—
530C4×C8—24no—
531#95—21no—
532#95—21no—
533#95—21no—
534#95—21no—
535#95—21no—
536#95—21no—
537#95—22no—
538#95—22no—
539#95—22no—
540#95—22no—
541#95—21no—
542#95—22no—
543#95—21no—
544#95—22no—
545#95—22no—
546#95—22no—
547#95—22no—
548#95—22no—
549C24—22no—
550C24C22×D411yescharacteristic
551C24C22×D411yescharacteristic
552C24C22×D411yescharacteristic
553#41—416no—
554#41—432no—
555#41—816no—
556#41—816no—
557C2×Q8—24no—
558C2×Q8—24no—
559C2×Q8—24no—
560C2×Q8—28no—
561C2×Q8—42no—
562C2×Q8—44no—
563C2×Q8—44no—
564C2×Q8—44no—
565C2×Q8—84no—
566C2×Q8—816no—
567C2×Q8C2×C22⋊C414yes—
568C2×D4—24no—
569C2×D4—24no—
570C2×D4—28no—
571C2×D4—28no—
572C2×D4—28no—
573C2×D4—24no—
574C2×D4—24no—
575C2×D4—22no—
576C2×D4—24no—
577C2×D4—24no—
578C2×D4—42no—
579C2×D4—44no—
580C2×D4—44no—
581C2×D4—48no—
582C2×D4—84no—
583C2×D4—84no—
584C2×D4C2×C22⋊C414yes—
585C2×D4C2×C22⋊C414yes—
586C2×D4C2×C22⋊C414yes—
587C2×D4C23×C414yes—
588C22×C4—24no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—28no—
599C22×C4—28no—
600C22×C4—28no—
601C22×C4—28no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—48no—
612C22×C4—44no—
613C22×C4—44no—
614C22×C4—84no—
615C22×C4—84no—
616C22×C4—84no—
617C22×C4—82no—
618C22×C4—82no—
619C22×C4—82no—
620C22×C4—82no—
621C22×C4C2×C22⋊C414yes—
622C22×C4C2×C22⋊C414yes—
623C22×C4C2×C22⋊C414yes—
624C22×C4C2×C22⋊C414yes—
625C22×C4C2×C22⋊C414yes—
626C22×C4C2×C22⋊C414yes—
627C22×C4C23×C412yes—
628C22×C4C23×C412yes—
629C22×C4C23×C412yes—
630C22×C4C22×D411yescharacteristic
631C22×C4C22×D411yescharacteristic
632C22×C4C22×D411yescharacteristic
633C22×C4C22×D411yescharacteristic
634C22×C4C22×D411yescharacteristic
635C22×C4C22×D411yescharacteristic
636C22×C4C22×D411yescharacteristic
637C22×C4C22×D411yescharacteristic
638C22×C4C22×D411yescharacteristic
639C22×C4C22×D411yescharacteristic
640C22×C4C22×D411yescharacteristic
641C22×C4C22×D412yes—
642C22×C4C22×D412yes—
643C22×C4C22×D412yes—
644C22×C4C2511yescharacteristic
645M16—48no—
646C2×C8—22no—
647C2×C8—22no—
648C2×C8—22no—
649C2×C8—22no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—22no—
654C2×C8—22no—
655C2×C8—22no—
656C2×C8—22no—
657C2×C8—48no—
658C2×C8—48no—
659C2×C82−1+414yes—
660C4⋊C4—28no—
661C4⋊C4—24no—
662C4⋊C4—24no—
663C4⋊C4—28no—
664C4⋊C4—28no—
665C4⋊C4—28no—
666C4⋊C4—24no—
667C4⋊C4—28no—
668C4⋊C4—28no—
669C4⋊C4—22no—
670C4⋊C4—22no—
671C4⋊C4—22no—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—24no—
675C4⋊C4—24no—
676C4⋊C4—44no—
677C4⋊C4—82no—
678C4⋊C4—82no—
679C4⋊C4—82no—
680C4⋊C4C2×C22⋊C414yes—
681C4⋊C4C2×C22⋊C414yes—
682C4⋊C4C2×C22⋊C414yes—
683C4⋊C4C2×C22⋊C414yes—
684C4⋊C4C2×C22⋊C414yes—
685C4⋊C4C2×C22⋊C414yes—
686C4⋊C4C23×C414yes—
687C4⋊C4C23×C414yes—
688C4⋊C4C23×C414yes—
689C22⋊C4—28no—
690C22⋊C4—28no—
691C22⋊C4—28no—
692C22⋊C4—28no—
693C22⋊C4—28no—
694C22⋊C4—28no—
695C22⋊C4—28no—
696C22⋊C4—28no—
697C22⋊C4—44no—
698C22⋊C4—44no—
699C22⋊C4—82no—
700C22⋊C4—82no—
701C22⋊C4C2×C22⋊C414yes—
702C22⋊C4C2×C22⋊C414yes—
703C22⋊C4C2×C22⋊C414yes—
704C22⋊C4C2×C22⋊C414yes—
705C22⋊C4C2×C22⋊C414yes—
706C22⋊C4C2×C22⋊C414yes—
707C42—28no—
708C42—28no—
709C42—44no—
710C42—82no—
711C42—82no—
712C42—82no—
713C42C2×C22⋊C414yes—
714C42C2×C22⋊C414yes—
715C42C2×C22⋊C414yes—
716C42C2×C22⋊C414yes—
717C42C2×C22⋊C414yes—
718C42C2×C22⋊C414yes—
719C42C23×C412yes—
720C42C23×C412yes—
721C42C23×C412yes—
722C42C23×C412yes—
723C42C22×D412yes—
724C42C22×D412yes—
725C42C22×D412yes—
726C42C22×D412yes—
727C23—22no—
728C23—21no—
729C23—21no—
730C23—22no—
731C23—22no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—22no—
737C23—22no—
738C23—24no—
739C23—44no—
740C23—42no—
741C23—42no—
742C23—44no—
743C23C22×C22⋊C412yes—
744C23C22×C22⋊C412yes—
745C23C22×C22⋊C412yes—
746C23#57514yes—
747C23C23×D411yescharacteristic
748Q8—44no—
749Q8—48no—
750Q8—48no—
751Q8—48no—
752Q8—88no—
753D4—28no—
754D4—28no—
755D4—28no—
756D4—44no—
757D4—48no—
758D4—48no—
759D4—416no—
760D4—44no—
761D4—88no—
762D4—88no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—28no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—24no—
784C2×C4—24no—
785C2×C4—24no—
786C2×C4—24no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—416no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—88no—
809C2×C4—88no—
810C2×C4—88no—
811C2×C4—164no—
812C2×C4—164no—
813C2×C4C22×C22⋊C412yes—
814C2×C4C22×C22⋊C412yes—
815C2×C4C22×C22⋊C412yes—
816C2×C4C22×C22⋊C412yes—
817C2×C4C22×C22⋊C412yes—
818C2×C4C22×C22⋊C412yes—
819C2×C4C22×C22⋊C412yes—
820C2×C4C22×C22⋊C412yes—
821C2×C4C22×C22⋊C412yes—
822C2×C4C22×C22⋊C412yes—
823C2×C4C22×C22⋊C412yes—
824C2×C4C24×C411yescharacteristic
825C2×C4C23×D411yescharacteristic
826C2×C4C2×2−1+412yes—
827C2×C4#58512yes—
828C8—24no—
829C8—42no—
830C8—42no—
831C8—42no—
832C22—24no—
833C22—24no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—22no—
841C22—22no—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—42no—
846C22—44no—
847C22—44no—
848C22—44no—
849C22—84no—
850C22—84no—
851C22#289614yes—
852C22C23×C22⋊C411yescharacteristic
853C22#349911yescharacteristic
854C22#350011yescharacteristic
855C22C2×#57512yes—
856C22#358512yes—
857C4—22no—
858C4—22no—
859C4—22no—
860C4—22no—
861C4—22no—
862C4—22no—
863C4—22no—
864C4—22no—
865C4—22no—
866C4—22no—
867C4—22no—
868C4—44no—
869C4—44no—
870C4—44no—
871C4—82no—
872C4—82no—
873C4—82no—
874C4—82no—
875C4C4×2−1+412yes—
876C4#348912yes—
877C2—24no—
878C2—42no—
879C2—42no—
880C2—84no—
881C2#3425911yescharacteristic
882C2C2×#289611yescharacteristic
883C2#6008711yescharacteristic
884C2#6250612yes—
885C2#6258412yes—
subgroupG/H
center, socleC23C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#3511C2
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
2. C2×#2970C2semidirect
3. #34191C2semidirect
4. #22526C2semidirect
5. #22493C2semidirect
6. #22492C2semidirect
7. #22488C2semidirect
8. #21869C2semidirect
9. #21865C2semidirect
10. #21865C2semidirect
11. #21842C2semidirect
12. #21842C2semidirect
13. #21841C2semidirect
14. #21408C2semidirect
15. #21408C2semidirect
16. #21405C2semidirect
17. #21323C2semidirect
18. #21321C2semidirect
19. C2×#1993C2semidirect
21. #3511C4semidirect
120. #555C2×C4semidirect
122. #554C2×C4semidirect
126. #553C2×C4semidirect
135. #533C2×C4semidirect
136. #533C2×C4semidirect
140. #532C2×C4semidirect
141. #532C2×C4semidirect
142. #532C2×C4semidirect
146. 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×#35112
C2×#29702
#341912
#225262
#224932
#224922
#224882
#218692
#218652
#218422
#218412
#214082
#214052
#213232
#213212
C2×#19932