Finite Group Databasebeta

← #10949657

Subgroups — #10949657

Order 768.

738 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4911C211yesmaximal, characteristic, complemented
2C22×#798C211yesmaximal, characteristic, complemented
3#80714C211yesmaximal, characteristic, complemented
4D3×#466C211yesmaximal, characteristic, complemented
5C3×#2215C211yesmaximal, characteristic, complemented
6#71470C211yesmaximal, characteristic, complemented
7#71414C211yesmaximal, characteristic, complemented
8#71072C211yesmaximal, characteristic, complemented
9#71071C211yesmaximal, characteristic, complemented
10#69329C211yesmaximal, characteristic, complemented
11#69326C211yesmaximal, characteristic, complemented
12#69198C211yesmaximal, characteristic, complemented
13#69197C211yesmaximal, characteristic, complemented
14#69190C211yesmaximal, characteristic, complemented
15#69189C211yesmaximal, characteristic, complemented
16#33605—31nomaximal, Sylow
17C2×#912C2211yescharacteristic
18C2×D3×D8C2211yescharacteristic
19C22×D3×C8C2211yescharacteristic
20#5606—21no—
21D3×#121—21no—
22C2×C3×D16C2211yescharacteristic, complemented
23C22×C3×C16C2211yescharacteristic, complemented
24C3×#466C2211yescharacteristic
25C3×#466C2211yescharacteristic, complemented
26#5157C2211yescharacteristic
27#5157C2211yescharacteristic, complemented
28C2×#827C2211yescharacteristic, complemented
29C2×#826C2211yescharacteristic, complemented
30#5116C2211yescharacteristic, complemented
31#5115C2211yescharacteristic
32C22×C3⋊C16C2211yescharacteristic, complemented
33#5041—21no—
34#5038—21no—
35#4911—24no—
36C2×#800C2211yescharacteristic, complemented
37C2×#798—24no—
38C2×#798C2211yescharacteristic
39C2×#798C2211yescharacteristic
40C2×#798C2211yescharacteristic, complemented
41C2×#798C2211yescharacteristic, complemented
42#4887C2211yescharacteristic, complemented
43#4883C2211yescharacteristic
44#4880C2211yescharacteristic
45D3×#107C2211yescharacteristic
46#4778—21no—
47#4775—21no—
48#4772—21no—
49D3×#102—21no—
50C3×#366C2211yescharacteristic, complemented
51C3×#357C2211yescharacteristic, complemented
52C3×#357C2211yescharacteristic, complemented
53#4562C2211yescharacteristic, complemented
54#4562C2211yescharacteristic, complemented
55#4509C2211yescharacteristic, complemented
56#4505C2211yescharacteristic, complemented
57#4503C2211yescharacteristic, complemented
58#4492C2211yescharacteristic, complemented
59#4491C2211yescharacteristic, complemented
60#4490C2211yescharacteristic, complemented
61#4489C2211yescharacteristic, complemented
62C2×#509—31no—
63C22×M32—31no—
64#3050—31no—
65C2×#466—31no—
66#2220—31no—
67#2220—31no—
68#2218—31no—
69#2218—31no—
70#2217—31no—
71#2217—31no—
72#2215—31no—
73#2215D311yescharacteristic, complemented
74#2159—31no—
75#2140—31no—
76#2139—31no—
77C2×#237—21no—
78C2×D3×D4—21no—
79C2×D3×D4—41no—
80C22×C4×D3D411yescharacteristic
81C2×C3×D8C2311yescharacteristic
82C2×C3×D8C2311yescharacteristic
83C22×C3×C8C2311yescharacteristic
84C3×#121—21no—
85C3×#121—21no—
86#939—41no—
87#938—21no—
88#938—21no—
89#937—41no—
90D4×Dic3—41no—
91C2×#214—21no—
92C2×#213—21no—
93#930—21no—
94#924—21no—
95C22×C3⋊C8D411yescharacteristic
96#912—22no—
97#912—22no—
98D3×D8—22no—
99D3×D8—22no—
100C2×Dic12C2311yescharacteristic
101C2×D24C2311yescharacteristic
102C2×D3×C8—22no—
103C2×D3×C8—22no—
104C2×D3×C8D411yescharacteristic
105C2×D3×C8D411yescharacteristic
106C2×D3×C8C2311yescharacteristic
107C2×D3×C8C2311yescharacteristic
108#897—21no—
109#895—21no—
110#892—21no—
111D3×C4⋊C4—21no—
112#884—41no—
113#883—41no—
114#67⋊C4—41no—
115D3×C22⋊C4—41no—
116C3×D16—22no—
117C2×C3×C16—22no—
118C2×C3×C16C2311yescharacteristic
119C2×C3×C16C2311yescharacteristic
120C3×#107C2311yescharacteristic
121C3×#107C2311yescharacteristic
122C3×#102—21no—
123C3×#102—21no—
124#832—21no—
125#832—21no—
126#827—22no—
127#826—22no—
128#821—21no—
129#818C2311yescharacteristic
130#818C2311yescharacteristic
131#816—21no—
132C2×C3⋊C16—22no—
133C2×C3⋊C16C2311yescharacteristic
134C2×C3⋊C16C2311yescharacteristic
135#810—21no—
136#809—21no—
137#808—21no—
138#807—21no—
139#800—22no—
140#798—22no—
141#798—22no—
142#798—22no—
143#798D414yescomplemented
144C2×#135—31no—
145C22×D8—31no—
146C23×C8—31no—
147#525—61no—
148C2×#121—61no—
149#509—64no—
150C2×SD32—31no—
151C2×SD32—31no—
152C2×D16—31no—
153C2×D16C2×D311yescharacteristic, complemented
154C2×M32—31no—
155C2×M32—31no—
156C2×M32—31no—
157C2×M32—31no—
158C2×M32—64no—
159C22×C16—31no—
160C22×C16C2×D311yescharacteristic, complemented
161#467—31no—
162#467—31no—
163#466—31no—
164#466—31no—
165#466—31no—
166#466—31no—
167#466—61no—
168#466—61no—
169#466C2×D311yescharacteristic
170#466C2×D311yescharacteristic, complemented
171#465—61no—
172#465—61no—
173#427—31no—
174C2×#107—31no—
175#416—61no—
176C2×#102—61no—
177#367—31no—
178#367—31no—
179#366—31no—
180#366C2×D311yescharacteristic, complemented
181#358—31no—
182#358—31no—
183#357—31no—
184#357—31no—
185#357—31no—
186#357—31no—
187#357C2×D311yescharacteristic, complemented
188#357C2×D311yescharacteristic, complemented
189C23×D3—41no—
190C23×D3D811yescharacteristic
191C2×C3×D4—21no—
192C2×C3×D4—21no—
193C2×C3×D4—41no—
194C2×C3×D4—41no—
195C22×C3×C4C2×D411yescharacteristic
196C2×#67—41no—
197C2×#67—41no—
198C2×#67—41no—
199C2×#67—41no—
200C2×#67—41no—
201C22×Dic3—41no—
202C22×Dic3D811yescharacteristic
203#237—42no—
204#237—42no—
205D3×D4—42no—
206D3×D4—42no—
207D3×D4—84no—
208C2×D12—21no—
209C2×D12—41no—
210C2×C4×D3—22no—
211C2×C4×D3—22no—
212C2×C4×D3—41no—
213C2×C4×D3D811yescharacteristic
214C2×C4×D3D811yescharacteristic
215C2×C4×D3C2×D411yescharacteristic
216C2×C4×D3C2×D411yescharacteristic
217C2×Dic6—21no—
218C3×D8—21no—
219C3×D8—21no—
220C3×D8—21no—
221C3×D8—21no—
222C2×C3×C8—21no—
223C2×C3×C8—21no—
224C2×C3×C8C2×D411yescharacteristic
225C2×C3×C8C2411yescharacteristic
226C3×C4⋊C4—21no—
227C3×C4⋊C4—21no—
228C3×C22⋊C4—41no—
229C3×C22⋊C4—41no—
230#217—41no—
231#217—41no—
232#217—41no—
233#214—42no—
234#213—42no—
235(C2×D3)⋊C4—41no—
236(C2×D3)⋊C4—41no—
237(C2×D3)⋊C4—41no—
238(C2×D3)⋊C4—41no—
239C4⋊Dic3—21no—
240C4⋊Dic3—21no—
241C4⋊Dic3—41no—
242Dic3⋊C4—41no—
243Dic3⋊C4—41no—
244C4×Dic3—41no—
245C2×C3⋊C8—22no—
246C2×C3⋊C8C2×D411yescharacteristic
247C2×C3⋊C8C2×D411yescharacteristic
248Dic12—21no—
249Dic12—21no—
250D24—21no—
251D24—21no—
252D3×C8—22no—
253D3×C8—21no—
254D3×C8—21no—
255D3×C8—22no—
256D3×C8C2×D412yes—
257D3×C8#4112yes—
258C3×C16—21no—
259C3×C16C2×D412yescomplemented
260C3⋊C16—21no—
261C3⋊C16C2×D412yescomplemented
262C2×#41—61no—
263C22×D4—61no—
264C22×D4—121no—
265C23×C4—31no—
266#135—62no—
267#135—62no—
268C2×Q16—31no—
269C2×SD16—61no—
270C2×D8—31no—
271C2×D8—62no—
272C2×D8—62no—
273C2×D8—61no—
274C2×D8C22×D311yescharacteristic
275C2×D8C22×D311yescharacteristic
276C22×C8—31no—
277C22×C8—31no—
278C22×C8—31no—
279C22×C8—31no—
280C22×C8—31no—
281C22×C8—62no—
282C22×C8—62no—
283C22×C8C22×D311yescharacteristic
284#123—121no—
285C22⋊Q8—61no—
286C22⋊Q8—61no—
287#121—21no—
288#121—21no—
289#121—61no—
290#121—61no—
291#121—61no—
292#121—61no—
293#121—121no—
294#121—121no—
295#120—121no—
296C4×D4—121no—
297C4×D4—121no—
298#117—61no—
299C2×C4⋊C4—61no—
300C2×C22⋊C4—121no—
301SD32—62no—
302SD32—62no—
303D16—22no—
304D16—62no—
305M32—34no—
306M32—62no—
307M32—62no—
308M32—62no—
309C2×C16—22no—
310C2×C16—31no—
311C2×C16—31no—
312C2×C16—62no—
313C2×C16C22×D311yescharacteristic
314C2×C16C22×D311yescharacteristic
315#107—31no—
316#107—31no—
317#107—61no—
318#107C22×D311yescharacteristic
319#107C22×D311yescharacteristic
320#106—61no—
321#103—61no—
322#103—61no—
323#102—21no—
324#102—21no—
325#102—61no—
326#102—61no—
327#102—61no—
328#102—61no—
329C23×C3—41no—
330C23×C3—41no—
331C23×C3C2×D811yescharacteristic
332C22×D3—22no—
333C22×D3—22no—
334C22×D3—41no—
335C22×D3—41no—
336C22×D3—82no—
337C22×D3—82no—
338C22×D3—82no—
339C22×D3C2×D811yescharacteristic
340C22×D3C2×D811yescharacteristic
341C3×D4—41no—
342C3×D4—41no—
343C3×D4—41no—
344C3×D4—41no—
345C3×D4—82no—
346C3×D4—82no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—41no—
350C2×C3×C4—41no—
351C2×C3×C4C2×D811yescharacteristic
352C2×C3×C4C22×D411yescharacteristic
353#67—82no—
354#67—82no—
355#67—82no—
356#67—82no—
357#67—82no—
358C2×Dic3—22no—
359C2×Dic3—41no—
360C2×Dic3—41no—
361C2×Dic3—41no—
362C2×Dic3—82no—
363C2×Dic3C2×D811yescharacteristic
364C2×Dic3C2×D811yescharacteristic
365D12—41no—
366D12—41no—
367D12—82no—
368C4×D3—22no—
369C4×D3—21no—
370C4×D3—21no—
371C4×D3—22no—
372C4×D3—82no—
373C4×D3#12112yes—
374C4×D3#13512yes—
375Dic6—41no—
376Dic6—41no—
377C3×C8—21no—
378C3×C8C22×D411yescharacteristic
379C3×C8C2×#4111yescharacteristic
380C3⋊C8—21no—
381C3⋊C8#12112yes—
382C24—31no—
383C24—121no—
384#41—122no—
385#41—122no—
386C2×Q8—61no—
387C2×D4—21no—
388C2×D4—21no—
389C2×D4—41no—
390C2×D4—41no—
391C2×D4—61no—
392C2×D4—122no—
393C2×D4—122no—
394C2×D4—121no—
395C2×D4—121no—
396C2×D4—121no—
397C2×D4—121no—
398C2×D4—121no—
399C2×D4—121no—
400C2×D4—244no—
401C22×C4—31no—
402C22×C4—31no—
403C22×C4—31no—
404C22×C4—31no—
405C22×C4—31no—
406C22×C4—62no—
407C22×C4—62no—
408C22×C4—121no—
409C22×C4—121no—
410C22×C4D3×D411yescharacteristic
411Q16—61no—
412Q16—61no—
413SD16—122no—
414D8—21no—
415D8—21no—
416D8—21no—
417D8—21no—
418D8—61no—
419D8—61no—
420D8—122no—
421C2×C8—21no—
422C2×C8—21no—
423C2×C8—31no—
424C2×C8—32no—
425C2×C8—32no—
426C2×C8—31no—
427C2×C8—62no—
428C2×C8—62no—
429C2×C8—62no—
430C2×C8—61no—
431C2×C8—61no—
432C2×C8D3×D411yescharacteristic
433C2×C8C23×D311yescharacteristic
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—61no—
437C4⋊C4—61no—
438C4⋊C4—121no—
439C4⋊C4—121no—
440C4⋊C4—121no—
441C22⋊C4—41no—
442C22⋊C4—41no—
443C22⋊C4—121no—
444C22⋊C4—121no—
445C22⋊C4—121no—
446C22⋊C4—121no—
447C22⋊C4—121no—
448C22⋊C4—121no—
449C22⋊C4—121no—
450C42—121no—
451C16—21no—
452C16—32no—
453C16—61no—
454C16D3×D412yescomplemented
455C22×C3—21no—
456C22×C3—21no—
457C22×C3—81no—
458C22×C3—81no—
459C22×C3—81no—
460C22×C3—81no—
461C22×C3—81no—
462C22×C3—81no—
463C22×C3#50912yescomplemented
464C22×C3C22×D811yescharacteristic
465C2×D3—21no—
466C2×D3—21no—
467C2×D3—21no—
468C2×D3—21no—
469C2×D3—21no—
470C2×D3—44no—
471C2×D3—81no—
472C2×D3—81no—
473C2×D3—81no—
474C2×D3—164no—
475C2×D3#46612yes—
476C3×C4—21no—
477C3×C4—81no—
478C3×C4—81no—
479C3×C4C2×#12111yescharacteristic
480C3×C4C2×#13511yescharacteristic
481Dic3—21no—
482Dic3—81no—
483Dic3—81no—
484Dic3—81no—
485Dic3#46612yes—
486C23—31no—
487C23—31no—
488C23—41no—
489C23—41no—
490C23—62no—
491C23—62no—
492C23—121no—
493C23—121no—
494C23—242no—
495C23—242no—
496C23—242no—
497C23D3×D811yescharacteristic
498Q8—121no—
499Q8—121no—
500D4—41no—
501D4—41no—
502D4—41no—
503D4—41no—
504D4—82no—
505D4—82no—
506D4—121no—
507D4—121no—
508D4—242no—
509D4—242no—
510D4—242no—
511D4—242no—
512D4—242no—
513D4—242no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—31no—
517C2×C4—32no—
518C2×C4—32no—
519C2×C4—31no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—62no—
523C2×C4—62no—
524C2×C4—62no—
525C2×C4—61no—
526C2×C4—61no—
527C2×C4—121no—
528C2×C4—121no—
529C2×C4—121no—
530C2×C4—242no—
531C2×C4—242no—
532C2×C4D3×D811yescharacteristic
533C2×C4C2×D3×D411yescharacteristic
534C8—21no—
535C8—32no—
536C8—61no—
537C8C2×D3×D411yescharacteristic
538C8D3×#4111yescharacteristic
539C2×C3—22no—
540C2×C3—161no—
541C2×C3—161no—
542C2×C3C2×#46611yescharacteristic
543C2×C3C2×#50911yescharacteristic
544C2×C3#341411yescharacteristic
545D3—22no—
546D3—41no—
547D3—161no—
548C22—21no—
549C22—21no—
550C22—32no—
551C22—61no—
552C22—61no—
553C22—61no—
554C22—61no—
555C22—61no—
556C22—81no—
557C22—81no—
558C22—81no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22—124no—
563C22—241no—
564C22—241no—
565C22—241no—
566C22—484no—
567C22#491112yescomplemented
568C22C2×D3×D811yescharacteristic
569C4—21no—
570C4—32no—
571C4—61no—
572C4—81no—
573C4—81no—
574C4—241no—
575C4—241no—
576C4—241no—
577C4D3×#12111yescharacteristic
578C4D3×#13511yescharacteristic
579C3#3360511yescharacteristic, complemented, Sylow
580C2—22no—
581C2—62no—
582C2—121no—
583C2—161no—
584C2—161no—
585C2—481no—
586C2D3×#46611yescharacteristic
587C2C2×#491111yescharacteristic
588C2#8203011yescharacteristic
subgroupG/H
centerC22C2×D3×D8
commutator, cosocleC2×C3×C8C24
FrattiniC2×C8C23×D3
FittingC3×#2215C2
socleC22×C3C22×D8
hypercenter#2215D3
hypocenterC3#33605
LCSG ▷ C2×C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2215

Complements

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

NH ≅ G/Ntype
1. C2×#4911C2semidirect
2. C22×#798C2semidirect
3. #80714C2semidirect
4. D3×#466C2semidirect
5. C3×#2215C2semidirect
6. #71470C2semidirect
7. #71414C2semidirect
8. #71072C2semidirect
9. #71071C2semidirect
10. #69329C2semidirect
11. #69326C2semidirect
12. #69198C2semidirect
13. #69197C2semidirect
14. #69190C2semidirect
15. #69189C2semidirect
22. C2×C3×D16C22semidirect
23. C22×C3×C16C22semidirect
25. C3×#466C22semidirect
27. #5157C22semidirect
28. C2×#827C22semidirect
29. C2×#826C22semidirect
30. #5116C22semidirect
32. C22×C3⋊C16C22semidirect
36. C2×#800C22semidirect
40. C2×#798C22semidirect
41. C2×#798C22semidirect
42. #4887C22semidirect
50. C3×#366C22semidirect
51. C3×#357C22semidirect
52. C3×#357C22semidirect
53. #4562C22semidirect
54. #4562C22semidirect
55. #4509C22semidirect
56. #4505C22semidirect
57. #4503C22semidirect
58. #4492C22semidirect
59. #4491C22semidirect
60. #4490C22semidirect
61. #4489C22semidirect
73. #2215D3semidirect
143. #798D4semidirect
153. C2×D16C2×D3semidirect
160. C22×C16C2×D3semidirect
170. #466C2×D3semidirect
180. #366C2×D3semidirect
187. #357C2×D3semidirect
188. #357C2×D3semidirect
259. C3×C16C2×D4semidirect
261. C3⋊C16C2×D4semidirect
454. C16D3×D4semidirect
463. C22×C3#509semidirect
567. C22#4911semidirect
579. C3#33605semidirect

Maximal subgroups

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

subgroupindex
C2×#49112
C22×#7982
#807142
D3×#4662
C3×#22152
#714702
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