Finite Group Databasebeta

← C2×#33876 #7623696

Subgroups — C2×#33876 #7623696

Order 512.

1600 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3339C211yesmaximal, characteristic, complemented
2C2×#3287C211yesmaximal, characteristic, complemented
3#33876C2116yesmaximal, direct product factor
4C2×#2244C211yesmaximal, characteristic, complemented
5C2×#2234C211yesmaximal, characteristic, complemented
6C2×#2232C211yesmaximal, characteristic, complemented
7C2×#2229C211yesmaximal, characteristic, complemented
8C2×#2218C211yesmaximal, characteristic, complemented
9C2×#2215C211yesmaximal, characteristic, complemented
10C2×#2206C211yesmaximal, characteristic, complemented
11C2×#2186C211yesmaximal, characteristic, complemented
12C2×#2186C211yesmaximal, characteristic, complemented
13C2×#2175C211yesmaximal, characteristic, complemented
14C2×#2168C211yesmaximal, characteristic, complemented
15C2×#2139C211yesmaximal, characteristic, complemented
16C2×#2138C211yesmaximal, characteristic, complemented
17C22×#135C2211yescharacteristic
18C22×#135C2211yescharacteristic
19C2×#553—21no—
20C2×#550—21no—
21C22×SD32C2211yescharacteristic
22C22×D16C2211yescharacteristic
23C22×D16C2211yescharacteristic
24C22×M32C2211yescharacteristic
25C23×C16C2211yescharacteristic
26#3339—24no—
27#3339C2218yescomplemented
28#3287—24no—
29#3287C2218yescomplemented
30C2×#499C2211yescharacteristic
31C2×#493C2211yescharacteristic
32C2×#481—21no—
33C2×#482—21no—
34C2×#478—21no—
35C2×#466C2211yescharacteristic
36C2×#466C2211yescharacteristic
37C2×#466C2211yescharacteristic
38C2×#466C2211yescharacteristic
39C2×#460—21no—
40C2×#449—21no—
41C2×#449—21no—
42C2×C4×Q16C2211yescharacteristic
43C2×C4×D8C2211yescharacteristic
44C2×C8×D4C2211yescharacteristic
45C2×#427C2211yescharacteristic
46C22×#107C2211yescharacteristic
47#2244C2218yescomplemented
48#2234C2218yescomplemented
49#2232C2218yescomplemented
50#2229C2218yescomplemented
51#2218C2218yescomplemented
52#2215C2218yescomplemented
53#2206C2218yescomplemented
54#2186C2218yescomplemented
55#2186C2218yescomplemented
56#2175C2218yescomplemented
57#2168C2218yescomplemented
58C2×#367C2211yescharacteristic
59C2×#366C2211yescharacteristic
60C2×#366C2211yescharacteristic
61C2×C4⋊C16C2211yescharacteristic
62#2139C2218yescomplemented
63#2138C2218yescomplemented
64C2×#358C2211yescharacteristic
65C2×#358C2211yescharacteristic
66C2×#358C2211yescharacteristic
67C2×#357C2211yescharacteristic
68C2×#357C2211yescharacteristic
69C2×#357C2211yescharacteristic
70C2×#357C2211yescharacteristic
71C2×#357C2211yescharacteristic
72C2×#357C2211yescharacteristic
73C2×#357C2211yescharacteristic
74C2×C22⋊C16C2211yescharacteristic
75C2×C22⋊C16C2211yescharacteristic
76C2×#346C2211yescharacteristic
77C22×#41—21no—
78C22×#41—21no—
79C2×#135—24no—
80C2×#135—24no—
81C2×#135—22no—
82C2×#135—22no—
83C2×#135—42no—
84C2×#135—42no—
85C2×#135C2314yes—
86C2×#135C2314yes—
87C22×Q16C2311yescharacteristic
88C22×SD16—21no—
89C22×SD16—21no—
90C22×D8—21no—
91C22×D8C2311yescharacteristic
92C22×D8C2311yescharacteristic
93C22×D8C2311yescharacteristic
94C23×C8C2311yescharacteristic
95C23×C8C2311yescharacteristic
96#553—28no—
97#553—44no—
98#550—28no—
99#550—44no—
100C2×#127—21no—
101C2×#127—41no—
102C2×#126—41no—
103C2×#125—21no—
104C2×#123—41no—
105C2×#121—21no—
106C2×#121—21no—
107C2×#121—21no—
108C2×#121—21no—
109C2×#121—41no—
110C2×#121—41no—
111C2×#121—41no—
112C2×C4×Q8—21no—
113C2×C4×D4—21no—
114C2×C4×D4—41no—
115C2×C4×D4—41no—
116C2×C4×D4D411yescharacteristic
117C2×#117—21no—
118C22×C4⋊C4—21no—
119C2×SD32—24no—
120C2×SD32C2314yes—
121C2×D16—42no—
122C2×D16—42no—
123C2×D16C2314yes—
124C2×D16C2314yes—
125C2×M32—42no—
126C2×M32C2314yes—
127C22×C16—42no—
128C22×C16C2311yescharacteristic
129C22×C16C2311yescharacteristic
130C22×C16C2311yescharacteristic
131C22×C16C2311yescharacteristic
132C22×C16C2314yes—
133#499—22no—
134#499C2314yes—
135#493—22no—
136#493C2314yes—
137#482—28no—
138#481—28no—
139#478—28no—
140#466—22no—
141#466—22no—
142#466—22no—
143#466—22no—
144#466C2314yes—
145#466C2314yes—
146#466C2314yes—
147#466C2314yes—
148#460—28no—
149#449—28no—
150#449—28no—
151C4×Q16—22no—
152C4×Q16C2314yes—
153C4×D8—22no—
154C4×D8C2314yes—
155C8×D4D414yes—
156C8×D4C2314yes—
157#427—22no—
158#427C2314yes—
159C2×#107—21no—
160C2×#107—22no—
161C2×#107C2314yes—
162C2×#107C2311yescharacteristic
163C2×#107C2311yescharacteristic
164C2×#107C2311yescharacteristic
165C2×#107C2311yescharacteristic
166C2×#106—21no—
167C2×#106—21no—
168C2×C4⋊C8D411yescharacteristic
169C2×#103—21no—
170C2×#102—21no—
171C2×#102—21no—
172C2×#102—21no—
173C2×#102—21no—
174C2×#102—21no—
175C2×C22⋊C8D411yescharacteristic
176C2×C22⋊C8D411yescharacteristic
177C2×C4×C8C2311yescharacteristic
178#367C2314yes—
179#366C2314yes—
180#366C2314yes—
181C4⋊C16C2314yes—
182#358C2314yes—
183#358C2314yes—
184#358C2314yes—
185#357C2314yes—
186#357C2314yes—
187#357C2314yes—
188#357C2314yes—
189#357C2314yes—
190#357C2314yes—
191#357C2314yes—
192C22⋊C16C2314yes—
193C22⋊C16C2314yes—
194#346C2314yes—
195C2×#41—24no—
196C2×#41—24no—
197C2×#41—44no—
198C2×#41—44no—
199C2×#41—42no—
200C2×#41—42no—
201C2×#41—82no—
202C2×#41—82no—
203C22×Q8—21no—
204C22×D4—21no—
205C22×D4—21no—
206C22×D4—21no—
207C22×D4—41no—
208C22×D4—41no—
209C22×D4—41no—
210C22×D4—41no—
211C22×D4—41no—
212C22×D4—41no—
213C22×D4—41no—
214C22×D4—41no—
215C22×D4D811yescharacteristic
216C23×C4—41no—
217C23×C4—41no—
218C23×C4—41no—
219C23×C4—41no—
220C23×C4C2×D411yescharacteristic
221C23×C4C2×D411yescharacteristic
222#135—28no—
223#135—28no—
224#135—44no—
225#135—44no—
226#135—48no—
227#135—48no—
228C2×Q16—21no—
229C2×Q16—22no—
230C2×Q16#4114yes—
231C2×Q16C2412yes—
232C2×SD16—24no—
233C2×SD16—24no—
234C2×SD16—44no—
235C2×SD16—44no—
236C2×D8—21no—
237C2×D8—21no—
238C2×D8—21no—
239C2×D8—24no—
240C2×D8—22no—
241C2×D8—22no—
242C2×D8—22no—
243C2×D8—22no—
244C2×D8—22no—
245C2×D8—22no—
246C2×D8—82no—
247C2×D8C2412yes—
248C2×D8C2412yes—
249C2×D8C2412yes—
250C22×C8—22no—
251C22×C8—22no—
252C22×C8—22no—
253C22×C8—22no—
254C22×C8C2×D411yescharacteristic
255C22×C8C2×D411yescharacteristic
256C22×C8C2×D412yes—
257C22×C8C2×D412yes—
258C22×C8C2×D411yescharacteristic
259C22×C8C2412yes—
260C22×C8C2412yes—
261C22×C8C2411yescharacteristic
262#127—24no—
263#127—48no—
264#127—42no—
265#126—48no—
266#125—24no—
267#125—42no—
268#123—48no—
269#121—24no—
270#121—24no—
271#121—24no—
272#121—24no—
273#121—48no—
274#121—42no—
275#121—42no—
276#121—42no—
277#121—42no—
278#121—48no—
279#121—48no—
280C4×Q8—24no—
281C4×Q8—42no—
282C4×D4—24no—
283C4×D4—48no—
284C4×D4—48no—
285C4×D4—42no—
286C4×D4D814yes—
287C4×D4C2×D414yes—
288#117—24no—
289#117—42no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—41no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—41no—
298C2×C4⋊C4—41no—
299C2×C4⋊C4—41no—
300C2×C4⋊C4D811yescharacteristic
301C2×C22⋊C4—41no—
302C2×C22⋊C4—41no—
303C2×C22⋊C4—41no—
304C2×C22⋊C4—41no—
305C2×C22⋊C4—41no—
306C2×C22⋊C4—41no—
307C2×C22⋊C4D811yescharacteristic
308C2×C22⋊C4D811yescharacteristic
309C2×C42—41no—
310C2×C42—41no—
311C2×C42C2×D411yescharacteristic
312SD32—28no—
313D16—44no—
314D16—44no—
315M32—44no—
316C2×C16—22no—
317C2×C16—22no—
318C2×C16—22no—
319C2×C16—22no—
320C2×C16—44no—
321C2×C16C2412yes—
322C2×C16C2412yes—
323C2×C16C2412yes—
324C2×C16C2412yes—
325#107—21no—
326#107—21no—
327#107—24no—
328#107—21no—
329#107—21no—
330#107C2412yes—
331#107C2412yes—
332#107C2412yes—
333#107C2412yes—
334#106—24no—
335#106—24no—
336C4⋊C8C2×D414yes—
337#103—24no—
338#102—24no—
339#102—24no—
340#102—24no—
341#102—24no—
342#102—24no—
343C22⋊C8C2×D414yes—
344C22⋊C8C2×D414yes—
345C4×C8C2×D412yes—
346C4×C8C2412yes—
347C24—41no—
348C24—41no—
349C24—41no—
350C24C2×D811yescharacteristic
351C24C2×D811yescharacteristic
352#41—48no—
353#41—48no—
354#41—84no—
355#41—84no—
356#41—88no—
357#41—88no—
358C2×Q8—24no—
359C2×Q8—22no—
360C2×Q8—41no—
361C2×Q8—42no—
362C2×D4—22no—
363C2×D4—22no—
364C2×D4—22no—
365C2×D4—42no—
366C2×D4—44no—
367C2×D4—44no—
368C2×D4—44no—
369C2×D4—44no—
370C2×D4—44no—
371C2×D4—44no—
372C2×D4—42no—
373C2×D4—42no—
374C2×D4—42no—
375C2×D4—41no—
376C2×D4—44no—
377C2×D4—41no—
378C2×D4—41no—
379C2×D4—44no—
380C2×D4—42no—
381C2×D4—42no—
382C2×D4—42no—
383C2×D4—84no—
384C2×D4—84no—
385C2×D4—84no—
386C2×D4—84no—
387C2×D4—162no—
388C2×D4—162no—
389C2×D4—162no—
390C2×D4—162no—
391C2×D4C2×D814yes—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—41no—
397C22×C4—41no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4—44no—
402C22×C4—44no—
403C22×C4—44no—
404C22×C4—44no—
405C22×C4—84no—
406C22×C4—84no—
407C22×C4—162no—
408C22×C4—162no—
409C22×C4C2×D812yes—
410C22×C4C2×D812yes—
411C22×C4C2×D811yescharacteristic
412C22×C4C2×D811yescharacteristic
413C22×C4C2×D811yescharacteristic
414C22×C4C2×D811yescharacteristic
415C22×C4C22×D412yes—
416C22×C4C22×D412yes—
417C22×C4C22×D411yescharacteristic
418Q16—24no—
419Q16—22no—
420Q16C2×#4114yes—
421SD16—48no—
422SD16—48no—
423D8—22no—
424D8—22no—
425D8—22no—
426D8—22no—
427D8—22no—
428D8—22no—
429D8—42no—
430D8—42no—
431D8—42no—
432D8—84no—
433C2×C8—22no—
434C2×C8—22no—
435C2×C8—22no—
436C2×C8—24no—
437C2×C8—24no—
438C2×C8—22no—
439C2×C8—22no—
440C2×C8—22no—
441C2×C8—22no—
442C2×C8C22×D412yes—
443C2×C8C22×D412yes—
444C2×C8C22×D412yes—
445C2×C8C22×D411yescharacteristic
446C2×C8C2×#4112yes—
447C2×C8H(5,𝔽2)12yes—
448C2×C8C2511yescharacteristic
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—22no—
452C4⋊C4—22no—
453C4⋊C4—41no—
454C4⋊C4—41no—
455C4⋊C4—44no—
456C4⋊C4—41no—
457C4⋊C4—41no—
458C4⋊C4—44no—
459C4⋊C4—44no—
460C4⋊C4—44no—
461C4⋊C4C2×D814yes—
462C22⋊C4—44no—
463C22⋊C4—44no—
464C22⋊C4—44no—
465C22⋊C4—44no—
466C22⋊C4—44no—
467C22⋊C4—44no—
468C22⋊C4C2×D814yes—
469C22⋊C4C2×D814yes—
470C42—44no—
471C42—44no—
472C42C2×D812yes—
473C42C22×D412yes—
474C16—22no—
475C16—22no—
476C16—22no—
477C16—22no—
478C23—22no—
479C23—22no—
480C23—22no—
481C23—22no—
482C23—22no—
483C23—22no—
484C23—42no—
485C23—42no—
486C23—42no—
487C23—82no—
488C23—82no—
489C23—82no—
490C23—82no—
491C23—82no—
492C23—82no—
493C23—82no—
494C23—82no—
495C23—82no—
496C23C22×D812yes—
497C23C22×D812yes—
498C23C22×D811yescharacteristic
499Q8—24no—
500Q8—44no—
501Q8—42no—
502D4—44no—
503D4—42no—
504D4—42no—
505D4—42no—
506D4—42no—
507D4—42no—
508D4—42no—
509D4—88no—
510D4—88no—
511D4—88no—
512D4—88no—
513D4—82no—
514D4—82no—
515D4—82no—
516D4—164no—
517D4—164no—
518D4—164no—
519D4—164no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—44no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—88no—
537C2×C4—88no—
538C2×C4—82no—
539C2×C4—82no—
540C2×C4—82no—
541C2×C4—82no—
542C2×C4—164no—
543C2×C4—164no—
544C2×C4#54612yes—
545C2×C4C22×D812yes—
546C2×C4C22×D812yes—
547C2×C4C22×D812yes—
548C2×C4C22×D812yes—
549C2×C4C22×D811yescharacteristic
550C2×C4#57712yes—
551C2×C4C23×D411yescharacteristic
552C8—22no—
553C8—22no—
554C8—22no—
555C8#54612yes—
556C8C22×#4111yescharacteristic
557C8C2×H(5,𝔽2)11yescharacteristic
558C22—22no—
559C22—22no—
560C22—22no—
561C22—22no—
562C22—22no—
563C22—22no—
564C22—44no—
565C22—44no—
566C22—82no—
567C22—82no—
568C22—82no—
569C22—82no—
570C22—82no—
571C22—82no—
572C22—82no—
573C22—82no—
574C22—82no—
575C22—164no—
576C22—164no—
577C22—164no—
578C22#329412yes—
579C22#341412yes—
580C22#341512yes—
581C22C23×D811yescharacteristic
582C4—22no—
583C4—22no—
584C4—22no—
585C4—22no—
586C4—44no—
587C4—82no—
588C4—82no—
589C4—82no—
590C4—82no—
591C4#329412yes—
592C4C2×#54611yescharacteristic
593C4C2×#57711yescharacteristic
594C2—42no—
595C2—42no—
596C2—162no—
597C2—162no—
598C2—162no—
599C2#3387614yesdirect product factor
600C2C2×#329411yescharacteristic
601C2C2×#341411yescharacteristic
602C2C2×#341511yescharacteristic
subgroupG/H
center, socleC23C22×D8
commutator, Frattini, cosocleC2×C8C25
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×C8×D4 ◁ G
LECSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3339C2semidirect
2. C2×#3287C2semidirect
3. #33876C2direct (N × H)
4. C2×#2244C2semidirect
5. C2×#2234C2semidirect
6. C2×#2232C2semidirect
7. C2×#2229C2semidirect
8. C2×#2218C2semidirect
9. C2×#2215C2semidirect
10. C2×#2206C2semidirect
11. C2×#2186C2semidirect
12. C2×#2186C2semidirect
13. C2×#2175C2semidirect
14. C2×#2168C2semidirect
15. C2×#2139C2semidirect
16. C2×#2138C2semidirect
27. #3339C22semidirect
29. #3287C22semidirect
47. #2244C22semidirect
48. #2234C22semidirect
49. #2232C22semidirect
50. #2229C22semidirect
51. #2218C22semidirect
52. #2215C22semidirect
53. #2206C22semidirect
54. #2186C22semidirect
55. #2186C22semidirect
56. #2175C22semidirect
57. #2168C22semidirect
62. #2139C22semidirect
63. #2138C22semidirect
599. C2#33876direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#33392
C2×#32872
#338762
C2×#22442
C2×#22342
C2×#22322
C2×#22292
C2×#22182
C2×#22152
C2×#22062
C2×#21862
C2×#21752
C2×#21682
C2×#21392
C2×#21382