Finite Group Databasebeta

← C2×#33883 #7623689

Subgroups — C2×#33883 #7623689

Order 512.

1558 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3338C211yesmaximal, characteristic, complemented
2C2×#3285C211yesmaximal, characteristic
3#33883C2116yesmaximal, direct product factor
4C2×#2243C211yesmaximal, characteristic, complemented
5C2×#2233C211yesmaximal, characteristic, complemented
6C2×#2235C211yesmaximal, characteristic, complemented
7C2×#2225C211yesmaximal, characteristic, complemented
8C2×#2219C211yesmaximal, characteristic, complemented
9C2×#2217C211yesmaximal, characteristic, complemented
10C2×#2211C211yesmaximal, characteristic, complemented
11C2×#2189C211yesmaximal, characteristic, complemented
12C2×#2188C211yesmaximal, characteristic, complemented
13C2×#2176C211yesmaximal, characteristic, complemented
14C2×#2168C211yesmaximal, characteristic, complemented
15C2×#2139C211yesmaximal, characteristic, complemented
16C22×#358C211yesmaximal, characteristic, complemented
17C22×#135C2211yescharacteristic
18C23×Q16C2211yescharacteristic
19C2×#554—21no—
20C2×#548—21no—
21C22×Q32C2211yescharacteristic
22C22×Q32C2211yescharacteristic
23C22×SD32C2211yescharacteristic
24C22×M32C2211yescharacteristic
25C23×C16C2211yescharacteristic
26#3338—24no—
27#3338C2218yescomplemented
28#3285—24no—
29#3285C2218yes—
30C2×#500C2211yescharacteristic
31C2×#495C2211yescharacteristic
32C2×#484—21no—
33C2×#484—21no—
34C2×#477—21no—
35C2×#467C2211yescharacteristic
36C2×#467C2211yescharacteristic
37C2×#467C2211yescharacteristic
38C2×#466C2211yescharacteristic
39C2×#464—21no—
40C2×#452—21no—
41C2×#448—21no—
42C2×C4×Q16C2211yescharacteristic
43C2×C4×Q16C2211yescharacteristic
44C2×C8×D4C2211yescharacteristic
45C22×#107C2211yescharacteristic
46C22×#107C2211yescharacteristic
47#2243C2218yescomplemented
48#2235C2218yescomplemented
49#2233C2218yescomplemented
50#2225C2218yescomplemented
51#2219C2218yescomplemented
52#2217C2218yescomplemented
53#2211C2218yescomplemented
54#2189C2218yescomplemented
55#2188C2218yescomplemented
56#2176C2218yescomplemented
57#2168C2218yescomplemented
58C2×#367C2211yescharacteristic
59C2×#367C2211yescharacteristic
60C2×#367C2211yescharacteristic
61C2×C4⋊C16C2211yescharacteristic
62#2139C2218yescomplemented
63C2×#358C2211yescharacteristic
64C2×#358C2211yescharacteristic
65C2×#358C2211yescharacteristic
66C2×#358C2211yescharacteristic
67C2×#358C2211yescharacteristic
68C2×#358C2211yescharacteristic
69C2×#358C2211yescharacteristic
70C2×#358C2218yescomplemented
71C2×#357C2211yescharacteristic
72C2×#357C2211yescharacteristic
73C2×#357C2211yescharacteristic
74C2×C22⋊C16C2211yescharacteristic
75C2×C22⋊C16C2211yescharacteristic
76C2×#346C2211yescharacteristic
77C22×#41—21no—
78C23×Q8—21no—
79C2×#135—24no—
80C2×#135—22no—
81C2×#135—42no—
82C2×#135C2314yes—
83C22×Q16—24no—
84C22×Q16—21no—
85C22×Q16—22no—
86C22×Q16—42no—
87C22×Q16C2311yescharacteristic
88C22×Q16C2311yescharacteristic
89C22×Q16C2314yes—
90C22×Q16C2311yescharacteristic
91C22×SD16—21no—
92C22×SD16—21no—
93C22×D8C2311yescharacteristic
94C23×C8C2311yescharacteristic
95C23×C8C2311yescharacteristic
96#554—28no—
97#554—44no—
98#548—28no—
99#548—44no—
100C2×C4⋊Q8—21no—
101C2×#125—41no—
102C2×#124—21no—
103C2×#124—41no—
104C2×C22⋊Q8—21no—
105C2×C22⋊Q8—21no—
106C2×C22⋊Q8—21no—
107C2×C22⋊Q8—41no—
108C2×C22⋊Q8—41no—
109C2×C22⋊Q8—41no—
110C2×#121—21no—
111C2×#121—41no—
112C2×C4×Q8—21no—
113C2×C4×Q8—21no—
114C2×C4×D4—41no—
115C2×C4×D4—41no—
116C2×C4×D4D411yescharacteristic
117C22×C4⋊C4—21no—
118C22×C4⋊C4—21no—
119C2×Q32—24no—
120C2×Q32—42no—
121C2×Q32C2314yes—
122C2×Q32C2314yes—
123C2×SD32—42no—
124C2×SD32C2314yes—
125C2×M32—42no—
126C2×M32C2314yes—
127C22×C16—42no—
128C22×C16C2311yescharacteristic
129C22×C16C2311yescharacteristic
130C22×C16C2311yescharacteristic
131C22×C16C2311yescharacteristic
132C22×C16C2314yes—
133#500—22no—
134#500C2314yes—
135#495—22no—
136#495C2314yes—
137#484—28no—
138#484—28no—
139#477—28no—
140#467—22no—
141#467—22no—
142#467—22no—
143#467C2314yes—
144#467C2314yes—
145#467C2314yes—
146#466—22no—
147#466C2314yes—
148#464—28no—
149#452—28no—
150#448—28no—
151C4×Q16—22no—
152C4×Q16—22no—
153C4×Q16C2314yes—
154C4×Q16C2314yes—
155C8×D4D414yes—
156C8×D4C2314yes—
157C2×#107—21no—
158C2×#107—21no—
159C2×#107—22no—
160C2×#107—22no—
161C2×#107—21no—
162C2×#107C2314yes—
163C2×#107C2314yes—
164C2×#107C2311yescharacteristic
165C2×#107C2311yescharacteristic
166C2×#107C2311yescharacteristic
167C2×#107C2311yescharacteristic
168C2×C4⋊C8D411yescharacteristic
169C2×#103—21no—
170C2×#103—21no—
171C2×#103—21no—
172C2×#103—21no—
173C2×#103—21no—
174C2×#102—21no—
175C2×C22⋊C8D411yescharacteristic
176C2×C22⋊C8D411yescharacteristic
177C2×C4×C8C2311yescharacteristic
178#367C2314yes—
179#367C2314yes—
180#367C2314yes—
181C4⋊C16C2314yes—
182#358C2314yes—
183#358C2314yes—
184#358C2314yes—
185#358C2314yes—
186#358C2314yes—
187#358C2314yes—
188#358C2314yes—
189#357C2314yes—
190#357C2314yes—
191#357C2314yes—
192C22⋊C16C2314yes—
193C22⋊C16C2314yes—
194#346C2314yes—
195C2×#41—24no—
196C2×#41—44no—
197C2×#41—42no—
198C2×#41—82no—
199C22×Q8—21no—
200C22×Q8—21no—
201C22×Q8—21no—
202C22×Q8—24no—
203C22×Q8—44no—
204C22×Q8—41no—
205C22×Q8—42no—
206C22×Q8—41no—
207C22×Q8—82no—
208C22×D4—21no—
209C22×D4—41no—
210C22×D4—41no—
211C22×D4D811yescharacteristic
212C23×C4—41no—
213C23×C4—41no—
214C23×C4—41no—
215C23×C4—41no—
216C23×C4C2×D411yescharacteristic
217C23×C4C2×D411yescharacteristic
218#135—28no—
219#135—44no—
220#135—48no—
221C2×Q16—28no—
222C2×Q16—21no—
223C2×Q16—24no—
224C2×Q16—21no—
225C2×Q16—21no—
226C2×Q16—22no—
227C2×Q16—22no—
228C2×Q16—22no—
229C2×Q16—22no—
230C2×Q16—22no—
231C2×Q16—44no—
232C2×Q16—48no—
233C2×Q16—44no—
234C2×Q16#4114yes—
235C2×Q16C2412yes—
236C2×Q16C2412yes—
237C2×Q16C2412yes—
238C2×SD16—24no—
239C2×SD16—24no—
240C2×SD16—44no—
241C2×SD16—82no—
242C2×D8—21no—
243C2×D8—22no—
244C2×D8—22no—
245C2×D8C2412yes—
246C22×C8—22no—
247C22×C8—22no—
248C22×C8—22no—
249C22×C8—22no—
250C22×C8C2×D411yescharacteristic
251C22×C8C2×D411yescharacteristic
252C22×C8C2×D412yes—
253C22×C8C2×D412yes—
254C22×C8C2×D411yescharacteristic
255C22×C8C2412yes—
256C22×C8C2412yes—
257C22×C8C2411yescharacteristic
258C4⋊Q8—24no—
259C4⋊Q8—42no—
260#125—48no—
261#124—24no—
262#124—48no—
263#124—42no—
264C22⋊Q8—24no—
265C22⋊Q8—24no—
266C22⋊Q8—24no—
267C22⋊Q8—42no—
268C22⋊Q8—42no—
269C22⋊Q8—42no—
270C22⋊Q8—48no—
271C22⋊Q8—48no—
272C22⋊Q8—48no—
273#121—24no—
274#121—48no—
275#121—42no—
276C4×Q8—24no—
277C4×Q8—24no—
278C4×Q8—42no—
279C4×Q8—42no—
280C4×D4—48no—
281C4×D4—48no—
282C4×D4D814yes—
283C4×D4C2×D414yes—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—41no—
291C2×C4⋊C4—41no—
292C2×C4⋊C4—42no—
293C2×C4⋊C4—42no—
294C2×C4⋊C4—41no—
295C2×C4⋊C4—41no—
296C2×C4⋊C4—41no—
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
312Q32—28no—
313Q32—44no—
314SD32—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—21no—
328#107—24no—
329#107—24no—
330#107—24no—
331#107—21no—
332#107C2412yes—
333#107C2412yes—
334#107C2412yes—
335#107C2412yes—
336C4⋊C8C2×D414yes—
337#103—24no—
338#103—24no—
339#103—24no—
340#103—24no—
341#103—24no—
342#102—24no—
343C22⋊C8C2×D414yes—
344C22⋊C8C2×D414yes—
345C4×C8C2×D412yes—
346C4×C8C2412yes—
347C24—41no—
348C24C2×D811yescharacteristic
349C24C2×D811yescharacteristic
350#41—48no—
351#41—84no—
352#41—88no—
353C2×Q8—24no—
354C2×Q8—22no—
355C2×Q8—22no—
356C2×Q8—22no—
357C2×Q8—48no—
358C2×Q8—41no—
359C2×Q8—41no—
360C2×Q8—44no—
361C2×Q8—41no—
362C2×Q8—44no—
363C2×Q8—42no—
364C2×Q8—42no—
365C2×Q8—42no—
366C2×Q8—42no—
367C2×Q8—42no—
368C2×Q8—84no—
369C2×Q8—84no—
370C2×Q8—88no—
371C2×Q8—162no—
372C2×D4—24no—
373C2×D4—22no—
374C2×D4—44no—
375C2×D4—44no—
376C2×D4—42no—
377C2×D4—41no—
378C2×D4—42no—
379C2×D4—84no—
380C2×D4—84no—
381C2×D4C2×D814yes—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—41no—
387C22×C4—44no—
388C22×C4—41no—
389C22×C4—41no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4—41no—
393C22×C4—41no—
394C22×C4—44no—
395C22×C4—44no—
396C22×C4—44no—
397C22×C4—84no—
398C22×C4—84no—
399C22×C4—162no—
400C22×C4—162no—
401C22×C4C2×D812yes—
402C22×C4C2×D812yes—
403C22×C4C2×D811yescharacteristic
404C22×C4C2×D811yescharacteristic
405C22×C4C2×D811yescharacteristic
406C22×C4C2×D811yescharacteristic
407C22×C4C22×D412yes—
408C22×C4C22×D412yes—
409C22×C4C22×D411yescharacteristic
410Q16—24no—
411Q16—22no—
412Q16—22no—
413Q16—22no—
414Q16—22no—
415Q16—22no—
416Q16—48no—
417Q16—42no—
418Q16—42no—
419Q16C2×#4114yes—
420SD16—48no—
421SD16—84no—
422D8—22no—
423D8—22no—
424D8—42no—
425C2×C8—22no—
426C2×C8—22no—
427C2×C8—22no—
428C2×C8—24no—
429C2×C8—24no—
430C2×C8—22no—
431C2×C8—22no—
432C2×C8—22no—
433C2×C8—22no—
434C2×C8C22×D412yes—
435C2×C8C22×D412yes—
436C2×C8C22×D412yes—
437C2×C8C22×D411yescharacteristic
438C2×C8C2×#4112yes—
439C2×C8H(5,𝔽2)12yes—
440C2×C8C2511yescharacteristic
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—22no—
444C4⋊C4—22no—
445C4⋊C4—41no—
446C4⋊C4—44no—
447C4⋊C4—44no—
448C4⋊C4—41no—
449C4⋊C4—41no—
450C4⋊C4—41no—
451C4⋊C4—44no—
452C4⋊C4—44no—
453C4⋊C4—44no—
454C4⋊C4—44no—
455C4⋊C4—44no—
456C4⋊C4—44no—
457C4⋊C4C2×D814yes—
458C22⋊C4—44no—
459C22⋊C4—44no—
460C22⋊C4—44no—
461C22⋊C4—44no—
462C22⋊C4—44no—
463C22⋊C4—44no—
464C22⋊C4C2×D814yes—
465C22⋊C4C2×D814yes—
466C42—44no—
467C42—44no—
468C42C2×D812yes—
469C42C22×D412yes—
470C16—22no—
471C16—22no—
472C16—22no—
473C16—22no—
474C23—22no—
475C23—22no—
476C23—22no—
477C23—22no—
478C23—22no—
479C23—42no—
480C23—82no—
481C23—82no—
482C23—82no—
483C23#51014yes—
484C23C22×D812yes—
485C23C22×D812yes—
486C23C22×D811yescharacteristic
487Q8—24no—
488Q8—44no—
489Q8—42no—
490Q8—42no—
491Q8—42no—
492Q8—42no—
493Q8—42no—
494Q8—88no—
495Q8—82no—
496Q8—82no—
497Q8—164no—
498D4—28no—
499D4—42no—
500D4—42no—
501D4—88no—
502D4—88no—
503D4—82no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—44no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—88no—
523C2×C4—88no—
524C2×C4—82no—
525C2×C4—82no—
526C2×C4—82no—
527C2×C4—82no—
528C2×C4—82no—
529C2×C4—82no—
530C2×C4—164no—
531C2×C4—164no—
532C2×C4#54612yes—
533C2×C4C22×D812yes—
534C2×C4C22×D812yes—
535C2×C4C22×D812yes—
536C2×C4C22×D812yes—
537C2×C4C22×D811yescharacteristic
538C2×C4#57712yes—
539C2×C4C23×D411yescharacteristic
540C8—22no—
541C8—22no—
542C8—22no—
543C8#54612yes—
544C8C22×#4111yescharacteristic
545C8C2×H(5,𝔽2)11yescharacteristic
546C22—28no—
547C22—22no—
548C22—22no—
549C22—22no—
550C22—22no—
551C22—22no—
552C22—44no—
553C22—82no—
554C22—82no—
555C22—82no—
556C22—164no—
557C22#329412yes—
558C22C2×#51014yes—
559C22C2×#51012yes—
560C22#341612yes—
561C22C23×D811yescharacteristic
562C4—22no—
563C4—22no—
564C4—22no—
565C4—22no—
566C4—44no—
567C4—82no—
568C4—82no—
569C4—82no—
570C4—82no—
571C4—82no—
572C4—82no—
573C4#329412yes—
574C4C2×#54611yescharacteristic
575C4C2×#57711yescharacteristic
576C2—24no—
577C2—42no—
578C2—162no—
579C2#3388314yesdirect product factor
580C2C2×#329411yescharacteristic
581C2C22×#51011yescharacteristic
582C2C2×#341611yescharacteristic
subgroupG/H
center, socleC23C22×D8
commutator, Frattini, cosocleC2×C8C25
prime radicalC2×#3285C2
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×#3338C2semidirect
3. #33883C2direct (N × H)
4. C2×#2243C2semidirect
5. C2×#2233C2semidirect
6. C2×#2235C2semidirect
7. C2×#2225C2semidirect
8. C2×#2219C2semidirect
9. C2×#2217C2semidirect
10. C2×#2211C2semidirect
11. C2×#2189C2semidirect
12. C2×#2188C2semidirect
13. C2×#2176C2semidirect
14. C2×#2168C2semidirect
15. C2×#2139C2semidirect
16. C22×#358C2semidirect
27. #3338C22semidirect
47. #2243C22semidirect
48. #2235C22semidirect
49. #2233C22semidirect
50. #2225C22semidirect
51. #2219C22semidirect
52. #2217C22semidirect
53. #2211C22semidirect
54. #2189C22semidirect
55. #2188C22semidirect
56. #2176C22semidirect
57. #2168C22semidirect
62. #2139C22semidirect
70. C2×#358C22semidirect
579. C2#33883direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#33382
C2×#32852
#338832
C2×#22432
C2×#22332
C2×#22352
C2×#22252
C2×#22192
C2×#22172
C2×#22112
C2×#21892
C2×#21882
C2×#21762
C2×#21682
C2×#21392
C22×#3582