Finite Group Databasebeta

← #7563396

Subgroups — #7563396

Order 512.

1825 conjugacy classes of subgroups.

The subgroup lattice has 889 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3387C211yesmaximal, characteristic, complemented
2C2×Q8×SD16C211yesmaximal, characteristic
3#59413C211yesmaximal, characteristic
4Q8×C4⋊Q8C211yesmaximal, characteristic, complemented
5#30970C212yesmaximal
6#30949C212yesmaximal, complemented
7#28819C212yesmaximal, complemented
8#28687C211yesmaximal, characteristic, complemented
9#28519C211yesmaximal, characteristic
10#26476C212yesmaximal
11#26389C212yesmaximal, complemented
12#26379C212yesmaximal
13#26054C212yesmaximal, complemented
14#25836C211yesmaximal, characteristic, complemented
15#25834C211yesmaximal, characteristic
16#25477C211yesmaximal, characteristic
17#25471C211yesmaximal, characteristic, complemented
18#24333C211yesmaximal, characteristic, complemented
19#24329C211yesmaximal, characteristic
20#23150C211yesmaximal, characteristic, complemented
21#23013C212yesmaximal
22#21615C211yesmaximal, characteristic, complemented
23C4×#464C211yesmaximal, characteristic
24C2×Q82C2211yescharacteristic
25C2×Q82C2211yescharacteristic
26C2×#557C2211yescharacteristic
27C2×D4×Q8C2211yescharacteristic
28#3387—28no—
29Q8×SD16—28no—
30C2×#501C2212yes—
31C2×#498C2211yescharacteristic
32C2×#498C2211yescharacteristic
33C2×#498C2212yes—
34C2×#479C2212yes—
35C2×#477C2211yescharacteristic
36C2×#477C2211yescharacteristic
37C2×#475C2212yes—
38C2×#475C2212yes—
39C2×#475C2211yescharacteristic
40C2×#476C2211yescharacteristic
41C2×#476C2212yes—
42C2×#476C2211yescharacteristic
43C2×#464C2211yescharacteristic
44C2×#446C2211yescharacteristic
45C2×C8×Q8C2211yescharacteristic
46C2×#441C2212yes—
47C2×C4×Q16C2211yescharacteristic
48C2×C4×SD16C2211yescharacteristic
49C2×C4×SD16C2212yes—
50#2868—21no—
51#2868C2211yescharacteristic
52#2704—22no—
53#2582C2211yescharacteristic
54#2567—21no—
55#2567—21no—
56#2567C2211yescharacteristic
57#2567C2211yescharacteristic
58#2556—22no—
59#2551—22no—
60#2551—22no—
61#2551C2212yes—
62#2551C2212yes—
63#2550C2212yes—
64#2538C2211yescharacteristic
65#2454C2212yes—
66#2451C2212yes—
67#2434—21no—
68#2429—21no—
69#2423—21no—
70#2367C2212yes—
71Q8×C4⋊C4C2212yes—
72Q8×C4⋊C4C2212yes—
73Q8×C22⋊C4—21no—
74C4×C4⋊Q8—21no—
75C4×C4⋊Q8C2211yescharacteristic
76C4×C4⋊Q8C2211yescharacteristic
77C4×#124C2211yescharacteristic
78C42×Q8C2211yescharacteristic
79#2096C2212yes—
80#2093C2212yes—
81#2088C2212yes—
82#2087C2212yes—
83#2084C2212yes—
84#2084C2212yes—
85#2068C2212yes—
86#2067C2212yes—
87#2059C2212yes—
88#2059C2212yes—
89#2058C2212yes—
90#2058C2212yes—
91#2058C2212yes—
92#2057C2212yes—
93#2024C2212yes—
94#2023C2212yes—
95#1990C2211yescharacteristic
96#1990C2211yescharacteristic
97#1988C2211yescharacteristic
98#1984C2211yescharacteristic
99#1984C2211yescharacteristic
100#1983C2211yescharacteristic
101#1959C2212yes—
102#1949C2211yescharacteristic
103#1948C2212yes—
104#1948C2212yes—
105#1947C2211yescharacteristic
106#1943C2212yes—
107#1942C2212yes—
108#1940C2212yes—
109#1936C2212yes—
110#1933C2212yes—
111#1927C2211yescharacteristic
112#1925C2211yescharacteristic
113#1920C2212yes—
114#1917C2212yes—
115#1916C2212yes—
116#1880C2212yes—
117#1880C2211yescharacteristic
118#1878C2212yes—
119#1878C2211yescharacteristic
120#1865C2212yes—
121#1865C2212yes—
122#1865C2212yes—
123#1864C2212yes—
124#1864C2212yes—
125#1863C2212yes—
126#1863C2212yes—
127#1847C2212yes—
128#1805C2211yescharacteristic
129#1803C2211yescharacteristic
130#1776C2212yes—
131#1771C2212yes—
132#1767C2211yescharacteristic
133C4×C4⋊C8C2211yescharacteristic
134#1763C2212yes—
135C4×#103C2211yescharacteristic
136C4×#102C2211yescharacteristic
137C23×Q8—21no—
138C22×Q16C2311yescharacteristic
139C22×SD16C2311yescharacteristic
140Q82—24no—
141Q82—24no—
142Q82—42no—
143Q82—42no—
144#557—24no—
145#557—42no—
146D4×Q8—24no—
147D4×Q8—42no—
148C2×C4⋊Q8—21no—
149C2×C4⋊Q8—21no—
150C2×C4⋊Q8—21no—
151C2×C4⋊Q8—22no—
152C2×C4⋊Q8—22no—
153C2×C4⋊Q8—22no—
154C2×C4⋊Q8—22no—
155C2×C4⋊Q8—21no—
156C2×C4⋊Q8—21no—
157C2×C4⋊Q8D411yescharacteristic
158C2×C4⋊Q8C2311yescharacteristic
159C2×C4⋊Q8C2311yescharacteristic
160C2×C4⋊Q8C2312yes—
161C2×C4⋊Q8C2312yes—
162C2×C4⋊Q8C2312yes—
163C2×C4⋊Q8C2311yescharacteristic
164C2×#125—22no—
165C2×#125C2312yes—
166C2×#124C2311yescharacteristic
167C2×C22⋊Q8—21no—
168C2×C22⋊Q8—21no—
169C2×C22⋊Q8—22no—
170C2×C4×Q8—21no—
171C2×C4×Q8—21no—
172C2×C4×Q8—21no—
173C2×C4×Q8—21no—
174C2×C4×Q8C2311yescharacteristic
175C2×C4×Q8C2311yescharacteristic
176C2×C4×Q8C2312yes—
177C2×C4×Q8C2312yes—
178C2×C4×Q8C2312yes—
179C2×C4×Q8C2311yescharacteristic
180C2×C4×Q8C2311yescharacteristic
181C2×C4×Q8C2311yescharacteristic
182C2×C4×Q8C2311yescharacteristic
183C2×C4×D4C2311yescharacteristic
184C2×C4×D4C2312yes—
185#501—28no—
186#498—24no—
187#498—24no—
188#498—28no—
189#479—28no—
190#477—24no—
191#477—42no—
192#476—28no—
193#476—24no—
194#476—42no—
195#475—28no—
196#475—28no—
197#475D418yes—
198#464Q818yescomplemented
199#446—24no—
200C8×Q8—24no—
201#441—28no—
202C4×Q16—24no—
203C4×SD16—24no—
204C4×SD16—28no—
205C2×#107C2312yes—
206C2×#107C2311yescharacteristic
207C2×#107C2312yes—
208C2×#107C2312yes—
209C2×#106C2312yes—
210C2×#106C2312yes—
211C2×#106C2312yes—
212C2×#106C2311yescharacteristic
213C2×#106C2312yes—
214C2×#106C2312yes—
215C2×#106C2312yes—
216C2×#106C2312yes—
217C2×C4⋊C8C2312yes—
218C2×C4⋊C8C2312yes—
219C2×C4⋊C8C2311yescharacteristic
220C2×C4⋊C8C2311yescharacteristic
221C2×C4⋊C8C2311yescharacteristic
222C2×C4⋊C8C2311yescharacteristic
223C2×#103C2311yescharacteristic
224C2×#103C2311yescharacteristic
225C2×#103C2312yes—
226C2×#103C2311yescharacteristic
227C2×#103C2312yes—
228C2×#103C2311yescharacteristic
229C2×#103C2312yes—
230C2×#103C2312yes—
231C2×#103C2311yescharacteristic
232C2×#102C2311yescharacteristic
233C2×#102C2312yes—
234C2×#102C2311yescharacteristic
235C2×#102C2312yes—
236C2×#102C2311yescharacteristic
237C2×#97C2312yes—
238C2×#97C2312yes—
239C2×C4×C8C2312yes—
240C2×C4×C8C2311yescharacteristic
241C2×C4×C8C2311yescharacteristic
242#399—22no—
243#398—22no—
244#398—22no—
245#398—22no—
246#396—22no—
247#396—22no—
248#395—22no—
249#395—22no—
250#395—22no—
251#395—22no—
252#395—22no—
253#395—22no—
254#395—22no—
255#395—22no—
256#391—21no—
257#391—21no—
258#391—21no—
259#391—21no—
260#391—22no—
261#391—22no—
262#391D411yescharacteristic
263#391D411yescharacteristic
264#391C2312yes—
265#391C2311yescharacteristic
266#390C2312yes—
267#390C2311yescharacteristic
268#389—22no—
269#389—22no—
270#389—21no—
271#389—21no—
272#389—22no—
273#389—22no—
274#389—22no—
275#389—22no—
276#389—22no—
277#389D412yes—
278#389D412yes—
279#389C2312yes—
280#389C2312yes—
281#389C2312yes—
282#389C2312yes—
283#389C2312yes—
284#389C2312yes—
285#389C2312yes—
286#388—22no—
287#388—21no—
288#388—21no—
289#388—22no—
290#387—22no—
291#385—22no—
292#385—22no—
293#384—21no—
294#384—21no—
295#384—22no—
296#384—22no—
297#384—21no—
298#384—21no—
299#384D411yescharacteristic
300#384C2311yescharacteristic
301#384C2312yes—
302#384C2312yes—
303#382C2311yescharacteristic
304#380—21no—
305#380—22no—
306C4×C4⋊C4—22no—
307C4×C4⋊C4—22no—
308C4×C4⋊C4—21no—
309C4×C4⋊C4—21no—
310C4×C4⋊C4—21no—
311C4×C4⋊C4—21no—
312C4×C4⋊C4C2312yes—
313C4×C4⋊C4C2311yescharacteristic
314C4×C4⋊C4C2311yescharacteristic
315C4×C4⋊C4C2311yescharacteristic
316C4×C4⋊C4C2312yes—
317C4×C4⋊C4C2312yes—
318C4×C22⋊C4—21no—
319C4×C22⋊C4—21no—
320C4×C22⋊C4—22no—
321C43—21no—
322C43C2311yescharacteristic
323#340C2312yes—
324#340C2312yes—
325#340C2311yescharacteristic
326#340C2311yescharacteristic
327#340C2312yes—
328#340C2312yes—
329#340C2312yes—
330#340C2311yescharacteristic
331#340C2311yescharacteristic
332#340C2312yes—
333#340C2312yes—
334#340C2312yes—
335#336C2312yes—
336#336C2312yes—
337#336C2312yes—
338#336C2312yes—
339#336C2311yescharacteristic
340#336C2311yescharacteristic
341#336C2312yes—
342C22×Q8—21no—
343C22×Q8—22no—
344C22×Q8—22no—
345C22×Q8—22no—
346C22×Q8—21no—
347C22×Q8—21no—
348C22×Q8—44no—
349C22×Q8—44no—
350C22×Q8—82no—
351C22×Q8C2×D411yescharacteristic
352C22×Q8C2×D411yescharacteristic
353C22×Q8C2411yescharacteristic
354C22×Q8C2411yescharacteristic
355C22×D4C2411yescharacteristic
356C23×C4—21no—
357C23×C4—22no—
358C2×Q16—22no—
359C2×Q16—22no—
360C2×Q16C2×Q814yescomplemented
361C2×SD16—22no—
362C2×SD16—22no—
363C2×SD16C2×Q814yes—
364C22×C8C2412yes—
365C22×C8C2411yescharacteristic
366C22×C8C2411yescharacteristic
367C22×C8C2412yes—
368C22×C8C2411yescharacteristic
369C22×C8C2411yescharacteristic
370C4⋊Q8—24no—
371C4⋊Q8—24no—
372C4⋊Q8—24no—
373C4⋊Q8—24no—
374C4⋊Q8—22no—
375C4⋊Q8—22no—
376C4⋊Q8—22no—
377C4⋊Q8—22no—
378C4⋊Q8—22no—
379C4⋊Q8—42no—
380C4⋊Q8—42no—
381C4⋊Q8—42no—
382C4⋊Q8—44no—
383C4⋊Q8—44no—
384C4⋊Q8—48no—
385C4⋊Q8—48no—
386C4⋊Q8—44no—
387C4⋊Q8—82no—
388C4⋊Q8—84no—
389C4⋊Q8—82no—
390C4⋊Q8—84no—
391C4⋊Q8C2×D414yes—
392#125—24no—
393#125—42no—
394#125—48no—
395#124—22no—
396#124C2×Q814yes—
397C22⋊Q8—48no—
398C22⋊Q8—44no—
399C22⋊Q8—82no—
400C4×Q8—22no—
401C4×Q8—22no—
402C4×Q8—22no—
403C4×Q8—22no—
404C4×Q8—22no—
405C4×Q8—22no—
406C4×Q8—22no—
407C4×Q8—22no—
408C4×Q8—24no—
409C4×Q8—24no—
410C4×Q8—24no—
411C4×Q8—22no—
412C4×Q8—22no—
413C4×Q8—42no—
414C4×Q8—42no—
415C4×Q8—42no—
416C4×Q8—44no—
417C4×Q8—44no—
418C4×Q8—44no—
419C4×Q8—82no—
420C4×Q8C2×D414yes—
421C4×Q8C2×Q814yescomplemented
422C4×D4—24no—
423C4×D4—22no—
424C4×D4—22no—
425C4×D4—42no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—22no—
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—21no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4C2×D411yescharacteristic
455C2×C4⋊C4C2×D411yescharacteristic
456C2×C4⋊C4C2×D412yes—
457C2×C4⋊C4C2×D412yes—
458C2×C4⋊C4C2×D412yes—
459C2×C4⋊C4C2×D412yes—
460C2×C4⋊C4C2×D412yes—
461C2×C4⋊C4C2×D412yes—
462C2×C4⋊C4C2411yescharacteristic
463C2×C4⋊C4C2411yescharacteristic
464C2×C4⋊C4C2412yes—
465C2×C4⋊C4C2412yes—
466C2×C4⋊C4C2412yes—
467C2×C4⋊C4C2412yes—
468C2×C4⋊C4C2411yescharacteristic
469C2×C4⋊C4C2411yescharacteristic
470C2×C4⋊C4C2411yescharacteristic
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—22no—
479C2×C42—21no—
480C2×C42—21no—
481C2×C42—21no—
482C2×C42—22no—
483C2×C42—21no—
484C2×C42—22no—
485C2×C42—22no—
486C2×C42—21no—
487C2×C42—21no—
488C2×C42—21no—
489C2×C42—22no—
490C2×C42C2×D411yescharacteristic
491C2×C42C2×D411yescharacteristic
492C2×C42C2×D411yescharacteristic
493C2×C42C2×D411yescharacteristic
494C2×C42C2412yes—
495C2×C42C2412yes—
496C2×C42C2411yescharacteristic
497C2×C42C2411yescharacteristic
498C2×C42C2411yescharacteristic
499#107—24no—
500#107—22no—
501#107—24no—
502#107—42no—
503#106—24no—
504#106—24no—
505#106—22no—
506#106—24no—
507#106—24no—
508#106—24no—
509#106—42no—
510#106C2×D418yes—
511C4⋊C8—24no—
512C4⋊C8—24no—
513C4⋊C8—22no—
514C4⋊C8—22no—
515C4⋊C8C2×D414yes—
516C4⋊C8C2×Q814yescomplemented
517#103—22no—
518#103—22no—
519#103—24no—
520#103—24no—
521#103—22no—
522#103—22no—
523#103—42no—
524#103C2×D418yes—
525#103C2×Q814yescomplemented
526#102—24no—
527#102—22no—
528#102—22no—
529#102—42no—
530#102C2×Q814yes—
531#97—24no—
532#97—24no—
533C4×C8—24no—
534C4×C8—22no—
535C4×C8—22no—
536#95—21no—
537#95—21no—
538#95—22no—
539#95—21no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95—21no—
544#95—22no—
545#95—22no—
546#95—22no—
547#95—22no—
548#95—22no—
549#95—22no—
550#95—22no—
551#95—22no—
552#95—22no—
553#95C2×D412yes—
554#95C2×D412yes—
555#95C2×D412yes—
556#95C2×D412yes—
557C24—21no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—24no—
561C2×Q8—22no—
562C2×Q8—22no—
563C2×Q8—22no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—44no—
573C2×Q8—44no—
574C2×Q8—44no—
575C2×Q8—42no—
576C2×Q8—42no—
577C2×Q8—42no—
578C2×Q8—44no—
579C2×Q8—42no—
580C2×Q8—82no—
581C2×Q8—81no—
582C2×Q8—81no—
583C2×Q8—81no—
584C2×Q8—81no—
585C2×Q8—82no—
586C2×Q8—82no—
587C2×Q8—82no—
588C2×Q8—82no—
589C2×Q8—816no—
590C2×Q8#13714yes—
591C2×Q8C22×D412yes—
592C2×Q8C22×Q812yes—
593C2×Q8C22×Q812yes—
594C2×Q82−1+412yes—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4C22×Q812yes—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—44no—
613C22×C4—42no—
614C22×C4—44no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—82no—
618C22×C4C22×D411yescharacteristic
619C22×C4C22×D412yes—
620C22×C4C22×D412yes—
621C22×C4C22×D412yes—
622C22×C4C22×D411yescharacteristic
623C22×C4C22×D411yescharacteristic
624C22×C4C22×D411yescharacteristic
625C22×C4C22×D412yes—
626C22×C4C22×D411yescharacteristic
627C22×C4C22×D411yescharacteristic
628C22×C4C2511yescharacteristic
629Q16—28no—
630SD16—28no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—22no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8C22×D414yes—
647C2×C8C22×Q812yes—
648C2×C8C22×Q812yes—
649C4⋊C4—24no—
650C4⋊C4—24no—
651C4⋊C4—24no—
652C4⋊C4—22no—
653C4⋊C4—24no—
654C4⋊C4—22no—
655C4⋊C4—24no—
656C4⋊C4—24no—
657C4⋊C4—24no—
658C4⋊C4—24no—
659C4⋊C4—24no—
660C4⋊C4—22no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—22no—
665C4⋊C4—21no—
666C4⋊C4—22no—
667C4⋊C4—21no—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—22no—
673C4⋊C4—22no—
674C4⋊C4—42no—
675C4⋊C4—44no—
676C4⋊C4—44no—
677C4⋊C4—44no—
678C4⋊C4—44no—
679C4⋊C4—44no—
680C4⋊C4—44no—
681C4⋊C4—44no—
682C4⋊C4—44no—
683C4⋊C4—44no—
684C4⋊C4—42no—
685C4⋊C4—42no—
686C4⋊C4—42no—
687C4⋊C4—42no—
688C4⋊C4—44no—
689C4⋊C4—81no—
690C4⋊C4—82no—
691C4⋊C4—82no—
692C4⋊C4—82no—
693C4⋊C4—82no—
694C4⋊C4—82no—
695C4⋊C4—82no—
696C4⋊C4—82no—
697C4⋊C4—82no—
698C4⋊C4—82no—
699C4⋊C4C22×D412yes—
700C4⋊C4C22×D414yes—
701C4⋊C4C22×Q812yes—
702C4⋊C42−1+412yes—
703C22⋊C4—24no—
704C22⋊C4—24no—
705C22⋊C4—44no—
706C22⋊C4—42no—
707C22⋊C4—42no—
708C22⋊C4—81no—
709C22⋊C4—82no—
710C22⋊C4—82no—
711C42—24no—
712C42—24no—
713C42—24no—
714C42—22no—
715C42—22no—
716C42—22no—
717C42—22no—
718C42—22no—
719C42—22no—
720C42—22no—
721C42—21no—
722C42—21no—
723C42—41no—
724C42—44no—
725C42—44no—
726C42—44no—
727C42—42no—
728C42—42no—
729C42—42no—
730C42—42no—
731C42—82no—
732C42C22×D412yes—
733C42C22×Q812yes—
734C42H(5,𝔽2)12yes—
735C422−1+412yes—
736C23—22no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23C23×D411yescharacteristic
744Q8—22no—
745Q8—22no—
746Q8—28no—
747Q8—22no—
748Q8—22no—
749Q8—22no—
750Q8—41no—
751Q8—44no—
752Q8—48no—
753Q8—41no—
754Q8—88no—
755Q8—162no—
756Q8—162no—
757Q8—164no—
758Q8—164no—
759Q8D4×Q814yes—
760D4—22no—
761D4—22no—
762D4—41no—
763D4—41no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—24no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—21no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—21no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—41no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—41no—
812C2×C4—42no—
813C2×C4—41no—
814C2×C4—42no—
815C2×C4—41no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—41no—
819C2×C4—88no—
820C2×C4—84no—
821C2×C4D4212yes—
822C2×C4D4212yes—
823C2×C4D4×Q812yes—
824C2×C4D4×Q812yes—
825C2×C4C2×#13714yes—
826C2×C4C2×#13712yes—
827C2×C4#57712yes—
828C2×C4#57712yes—
829C2×C4C23×D411yescharacteristic
830C2×C4C23×Q811yescharacteristic
831C2×C4C2×H(5,𝔽2)11yescharacteristic
832C2×C4C2×2−1+411yescharacteristic
833C2×C4C2×2−1+411yescharacteristic
834C2×C4C2×2−1+411yescharacteristic
835C8—22no—
836C8—22no—
837C8—24no—
838C8—41no—
839C8—41no—
840C8—42no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22C2×D4211yescharacteristic
849C22C2×D4×Q811yescharacteristic
850C22#348611yescharacteristic
851C22C22×#13711yescharacteristic
852C22C2×#57711yescharacteristic
853C22C2×#57711yescharacteristic
854C22#358511yescharacteristic
855C4—24no—
856C4—22no—
857C4—22no—
858C4—22no—
859C4—22no—
860C4—24no—
861C4—42no—
862C4—44no—
863C4—41no—
864C4—42no—
865C4—42no—
866C4—42no—
867C4—42no—
868C4—42no—
869C4—42no—
870C4—81no—
871C4—82no—
872C4—81no—
873C4—82no—
874C4—82no—
875C4#326614yes—
876C4C2×D4×Q811yescharacteristic
877C4#349911yescharacteristic
878C4#350311yescharacteristic
879C4#355211yescharacteristic
880C2—82no—
881C2#5912711yescharacteristic
882C2C2×#326611yescharacteristic
883C2#6109511yescharacteristic
884C2Q8×#13711yescharacteristic
885C2#6137411yescharacteristic
886C2#6183811yescharacteristic
887C2#6186011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C4⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3387C2semidirect
4. Q8×C4⋊Q8C2semidirect
6. #30949C2semidirect
7. #28819C2semidirect
8. #28687C2semidirect
11. #26389C2semidirect
13. #26054C2semidirect
14. #25836C2semidirect
17. #25471C2semidirect
18. #24333C2semidirect
20. #23150C2semidirect
22. #21615C2semidirect
198. #464Q8semidirect
360. C2×Q16C2×Q8semidirect
421. C4×Q8C2×Q8semidirect
516. C4⋊C8C2×Q8semidirect
525. #103C2×Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#33872
C2×Q8×SD162
#594132
Q8×C4⋊Q82
#309702
#309492
#288192
#286872
#285192
#264762
#263892
#263792
#260542
#258362
#258342
#254772
#254712
#243332
#243292
#231502
#230132
#216152
C4×#4642