Finite Group Databasebeta

← #11860063

Subgroups — #11860063

Order 1152.

1161 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63796C211yesmaximal, characteristic
2C4×#3802C211yesmaximal, characteristic
3C4×#3797C211yesmaximal, characteristic, complemented
4C3⋊D3×#97C211yesmaximal, characteristic, complemented
5C3×#4710C212yesmaximal, complemented
6#10590940C211yesmaximal, characteristic
7#10590779C212yesmaximal, complemented
8#10590743C212yesmaximal, complemented
9#10590687C211yesmaximal, characteristic, complemented
10#10590672C211yesmaximal, characteristic, complemented
11#10590358C212yesmaximal, complemented
12D3×#440—32nomaximal
13C2×#3802C2211yescharacteristic
14C2×C4×D32—21no—
15C2×#3797C2211yescharacteristic
16C2×C8×C3⋊D3C2211yescharacteristic
17C2×C8×C3⋊D3C2211yescharacteristic
18C42×C3⋊D3C2211yescharacteristic
19C2×C3×#204C2212yes—
20C3×C4×D12C2212yes—
21C3×C4×Dic6C2212yescomplemented
22#63921—21no—
23C4×#627—21no—
24#63902—21no—
25C4×#625—21no—
26#63900C2211yescharacteristic
27#63900C2211yescharacteristic
28#63898C2212yes—
29#63883—21no—
30C4×#624—21no—
31#63843C2212yescomplemented
32#63838—21no—
33C2×#3715C2212yes—
34#63796C418yescomplemented
35C32×#97C2211yescharacteristic, complemented
36#63642C2211yescharacteristic, complemented
37#63642C2211yescharacteristic, complemented
38#63630C2211yescharacteristic, complemented
39C3×#821C2212yes—
40C3×#818C2212yescomplemented
41C3×#816C2212yescomplemented
42#63576C2212yescomplemented
43#63565C2212yescomplemented
44#63562C2212yes—
45C2×D3×SD16—32no—
46C4×D3×Q8—32no—
47C4×D3×D4—32no—
48C3×#440—32no—
49#5164—32no—
50#5026—32no—
51#5018—32no—
52#4889—32no—
53D3×#107—32no—
54#4817—32no—
55D3×#103—32no—
56D3×#102—32no—
57#4757—32no—
58#4710D312yescomplemented
59D3×#97—32no—
60D3×#97—61no—
61C22×D32—21no—
62C2×C4×C3⋊D3D411yescharacteristic
63C2×C4×C3⋊D3D411yescharacteristic
64C2×C4×C3⋊D3C2311yescharacteristic
65C2×C3×D12C2312yes—
66C2×C3×C4×D3—22no—
67C2×C3×Dic6C2312yes—
68C2×#627—21no—
69C2×#625—21no—
70C2×#624—21no—
71C2×#624—21no—
72C2×#624—21no—
73C2×D3×Dic3—22no—
74#3802—22no—
75#3802C2×C414yes—
76C4×D32—44no—
77#3797—22no—
78#3797C2×C414yescomplemented
79C2×C32×C8C2311yescharacteristic
80C2×C32×C8C2311yescharacteristic
81C32×C42C2311yescharacteristic
82C4×C3⋊Dic3D411yescharacteristic
83C4×C3⋊Dic3D411yescharacteristic
84C4×C3⋊Dic3C2311yescharacteristic
85C2×C3⋊(C3⋊C8)C2311yescharacteristic
86C2×C3⋊(C3⋊C8)C2311yescharacteristic
87C8×C3⋊D3—22no—
88C8×C3⋊D3C2×C414yescomplemented
89C3×(C2×D3)⋊C4—22no—
90C3×C4⋊Dic3C2312yes—
91C3×C4⋊Dic3C2312yes—
92C3×Dic3⋊C4—22no—
93C3×C4×Dic3—22no—
94C3×#204C2×C418yescomplemented
95#3724—21no—
96#3724—21no—
97Dic3⋊Dic3—22no—
98(C2×D3)⋊Dic3—22no—
99Dic32—22no—
100#3715C2×C418yescomplemented
101C2×#440—91noSylow
102C2×D3×Q8—32no—
103C2×D3×D4—32no—
104C22×C4×D3—62no—
105C2×C3×SD16—32no—
106C3×C4×Q8—32no—
107C3×C4×D4—32no—
108Q8×Dic3—32no—
109C2×#215—32no—
110D4×Dic3—32no—
111C2×#214—32no—
112C4×#67—62no—
113D3×SD16—316no—
114C2×#204C2×D312yes—
115C2×D3×C8—32no—
116C2×D3×C8—32no—
117C2×D3×C8—61no—
118C2×D3×C8—61no—
119#893—32no—
120D3×C4⋊C4—32no—
121D3×C4⋊C4—32no—
122D3×C4⋊C4—62no—
123#887—32no—
124#887—62no—
125#67⋊C4—62no—
126D3×C22⋊C4—62no—
127C4×D12C2×D312yes—
128C42×D3—32no—
129C42×D3—61no—
130C42×D3—62no—
131C4×Dic6—62no—
132C4×Dic6C2×D312yescomplemented
133C3×#107—32no—
134C3×#103—32no—
135C3×#102—32no—
136C3×#97—21no—
137C3×#97C2×D312yescomplemented
138#835—32no—
139#832—32no—
140#821C2×D312yes—
141#818C2×D312yescomplemented
142#816C2×D312yescomplemented
143#815—32no—
144#815—32no—
145#815—61no—
146#815—61no—
147#810—32no—
148#809—32no—
149#807—32no—
150#807—32no—
151#803—32no—
152#803—61no—
153C22×C3⋊D3C2×D411yescharacteristic
154C22×C3×D3—22no—
155C2×D32—24no—
156C2×D32—42no—
157C2×D32—42no—
158C2×C32×C4C2×D411yescharacteristic
159C2×C32×C4C2×D411yescharacteristic
160C2×C32×C4C2411yescharacteristic
161C2×C3⋊Dic3C2×D411yescharacteristic
162C2×C3⋊Dic3C2×D411yescharacteristic
163C2×C3⋊Dic3C2×D411yescharacteristic
164C4×C3⋊D3—22no—
165C4×C3⋊D3—22no—
166C4×C3⋊D3C22×C412yes—
167C4×C3⋊D3#4112yes—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
171C3×D12—22no—
172C3×D12C22×C414yes—
173C3×C4×D3—44no—
174C3×Dic6—22no—
175C3×Dic6C22×C414yescomplemented
176#627—24no—
177#625—24no—
178#624—24no—
179#624—42no—
180#624—42no—
181D3×Dic3—44no—
182C32×C8—21no—
183C32×C8C22×C412yescomplemented
184C3⋊(C3⋊C8)—21no—
185C3⋊(C3⋊C8)C22×C412yescomplemented
186C22×SD16—91no—
187C2×C4×Q8—91no—
188C2×C4×D4—91no—
189#440—32no—
190#440—92no—
191#440—92no—
192#440—92no—
193C2×#107—91no—
194C2×#103—91no—
195C2×#102—91no—
196C2×#97—91no—
197C23×D3—62no—
198C2×C3×Q8—32no—
199C2×C3×D4—32no—
200C22×C3×C4—62no—
201C2×#67—62no—
202C22×Dic3—62no—
203D3×Q8—38no—
204D3×Q8—64no—
205D3×D4—38no—
206D3×D4—64no—
207C2×D12C22×D312yes—
208C2×C4×D3—22no—
209C2×C4×D3—32no—
210C2×C4×D3—32no—
211C2×C4×D3—32no—
212C2×C4×D3—61no—
213C2×C4×D3—61no—
214C2×C4×D3—61no—
215C2×C4×D3—62no—
216C2×C4×D3—62no—
217C2×C4×D3—62no—
218C2×C4×D3—62no—
219C2×C4×D3—128no—
220C2×Dic6—62no—
221C2×Dic6C22×D312yes—
222C3×SD16—38no—
223C2×C3×C8—21no—
224C2×C3×C8—21no—
225C2×C3×C8C22×D312yes—
226C2×C3×C8C22×D312yes—
227C3×C4⋊C4—32no—
228C3×C4⋊C4—32no—
229C3×C4⋊C4—62no—
230C3×C22⋊C4—62no—
231C3×C42—21no—
232C3×C42—62no—
233C3×C42C22×D312yes—
234#217—62no—
235#215—38no—
236#214—38no—
237(C2×D3)⋊C4—22no—
238(C2×D3)⋊C4—62no—
239C4⋊Dic3—62no—
240C4⋊Dic3C22×D312yes—
241C4⋊Dic3C22×D312yes—
242Dic3⋊C4—22no—
243Dic3⋊C4—62no—
244Dic3⋊C4—62no—
245Dic3⋊C4—62no—
246C4×Dic3—22no—
247C4×Dic3—32no—
248C4×Dic3—32no—
249C4×Dic3—32no—
250C4×Dic3—61no—
251C4×Dic3—61no—
252C4×Dic3—61no—
253C4×Dic3—62no—
254C4×Dic3—62no—
255C2×C3⋊C8—32no—
256C2×C3⋊C8—32no—
257C2×C3⋊C8—61no—
258C2×C3⋊C8—61no—
259#204C4×D318yescomplemented
260D3×C8—38no—
261D3×C8—64no—
262D3×C8—64no—
263D3×C8—64no—
264C22×C32C22×D411yescharacteristic
265C2×C3⋊D3C4×D412yes—
266C2×C3⋊D3AGL(1,ℤ/8)12yes—
267C2×C3⋊D3#13712yes—
268C2×C3×D3—24no—
269C2×C3×D3—42no—
270C2×C3×D3—42no—
271D32—48no—
272C32×C4—21no—
273C32×C4—21no—
274C32×C4C23×C411yescharacteristic
275C32×C4C2×#4111yescharacteristic
276C3⋊Dic3—21no—
277C3⋊Dic3—21no—
278C3⋊Dic3C4×D412yes—
279C3×Dic3—24no—
280C3×Dic3—42no—
281C3×Dic3—42no—
282C22×Q8—91no—
283C22×D4—91no—
284C23×C4—181no—
285C2×SD16—32no—
286C2×SD16—98no—
287C2×SD16—92no—
288C22×C8—91no—
289C22×C8—91no—
290C4×Q8—32no—
291C4×Q8—92no—
292C4×Q8—181no—
293C4×Q8—181no—
294C4×D4—32no—
295C4×D4—92no—
296C4×D4—181no—
297C4×D4—181no—
298C2×C4⋊C4—91no—
299C2×C4⋊C4—91no—
300C2×C4⋊C4—181no—
301C2×C22⋊C4—181no—
302C2×C42—91no—
303C2×C42—181no—
304#107—32no—
305#107—92no—
306#103—32no—
307#103—92no—
308#102—32no—
309#102—92no—
310#97—91no—
311#97—91no—
312#97—91no—
313#97D3211yescharacteristic, complemented
314C23×C3—62no—
315C22×D3—22no—
316C22×D3—32no—
317C22×D3—61no—
318C22×D3—68no—
319C22×D3—124no—
320C22×D3—124no—
321C3×Q8—34no—
322C3×Q8—62no—
323C3×D4—34no—
324C3×D4—62no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—62no—
329C2×C3×C4—62no—
330C2×C3×C4—62no—
331C2×C3×C4—124no—
332C2×C3×C4D3×D412yes—
333C2×C3×C4D3×D412yes—
334C2×C3×C4C23×D312yes—
335#67—68no—
336C2×Dic3—22no—
337C2×Dic3—22no—
338C2×Dic3—22no—
339C2×Dic3—32no—
340C2×Dic3—32no—
341C2×Dic3—32no—
342C2×Dic3—61no—
343C2×Dic3—61no—
344C2×Dic3—61no—
345C2×Dic3—124no—
346D12—22no—
347D12C2×C4×D314yes—
348C4×D3—34no—
349C4×D3—34no—
350C4×D3—44no—
351C4×D3—62no—
352C4×D3—62no—
353C4×D3—68no—
354C4×D3—64no—
355C4×D3—64no—
356C4×D3—122no—
357C4×D3—122no—
358C4×D3—124no—
359C4×D3—124no—
360C4×D3—124no—
361Dic6—22no—
362Dic6—68no—
363Dic6C2×C4×D314yescomplemented
364C3×C8—22no—
365C3×C8—22no—
366C3×C8—22no—
367C3×C8C2×C4×D314yescomplemented
368C3⋊C8—34no—
369C3⋊C8—62no—
370C3⋊C8—62no—
371C3⋊C8—62no—
372C2×C32C2×C4×D411yescharacteristic
373C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
374C2×C32C2×#13711yescharacteristic
375C3⋊D3#44014yescomplemented
376C3×D3—44no—
377C24—181no—
378C2×Q8—32no—
379C2×Q8—94no—
380C2×Q8—181no—
381C2×Q8—182no—
382C2×D4—32no—
383C2×D4—94no—
384C2×D4—182no—
385C2×D4—181no—
386C22×C4—62no—
387C22×C4—91no—
388C22×C4—91no—
389C22×C4—91no—
390C22×C4—181no—
391C22×C4—181no—
392C22×C4—181no—
393C22×C4—182no—
394C22×C4—364no—
395SD16—38no—
396SD16—98no—
397C2×C8—91no—
398C2×C8—94no—
399C2×C8—91no—
400C2×C8—182no—
401C2×C8C2×D3211yescharacteristic
402C2×C8C2×D3211yescharacteristic
403C4⋊C4—32no—
404C4⋊C4—32no—
405C4⋊C4—62no—
406C4⋊C4—181no—
407C4⋊C4—181no—
408C4⋊C4—182no—
409C22⋊C4—62no—
410C22⋊C4—182no—
411C42—62no—
412C42—91no—
413C42—91no—
414C42—91no—
415C42—182no—
416C42C2×D3211yescharacteristic
417C22×C3—21no—
418C22×C3—64no—
419C22×C3—122no—
420C22×C3—122no—
421C22×C3C2×D3×D412yes—
422C2×D3—24no—
423C2×D3—34no—
424C2×D3—34no—
425C2×D3—34no—
426C2×D3—42no—
427C2×D3—42no—
428C2×D3—62no—
429C2×D3—62no—
430C2×D3—62no—
431C2×D3—1216no—
432C3×C4—22no—
433C3×C4—22no—
434C3×C4—21no—
435C3×C4—21no—
436C3×C4—41no—
437C3×C4—41no—
438C3×C4—64no—
439C3×C4—122no—
440C3×C4—122no—
441C3×C4C22×C4×D312yes—
442C3×C4D3×#4112yes—
443Dic3—24no—
444Dic3—34no—
445Dic3—42no—
446Dic3—42no—
447Dic3—62no—
448Dic3—62no—
449Dic3—62no—
450Dic3—121no—
451Dic3—121no—
452C32C2×#44011yescharacteristic, complemented, Sylow
453C23—62no—
454C23—91no—
455C23—184no—
456C23—362no—
457C23—362no—
458Q8—34no—
459Q8—62no—
460Q8—184no—
461D4—34no—
462D4—62no—
463D4—184no—
464C2×C4—62no—
465C2×C4—62no—
466C2×C4—62no—
467C2×C4—91no—
468C2×C4—92no—
469C2×C4—92no—
470C2×C4—91no—
471C2×C4—91no—
472C2×C4—124no—
473C2×C4—182no—
474C2×C4—182no—
475C2×C4—184no—
476C2×C4—362no—
477C2×C4—362no—
478C2×C4—364no—
479C2×C4#380211yescharacteristic
480C2×C4#380211yescharacteristic
481C2×C4C22×D3211yescharacteristic
482C8—21no—
483C8—92no—
484C8—181no—
485C8C4×D3212yescomplemented
486C2×C3—21no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—124no—
490C2×C3C4×D3×D412yes—
491C2×C3D3×AGL(1,ℤ/8)12yes—
492C2×C3D3×#13712yes—
493D3—38no—
494D3—44no—
495D3—64no—
496C22—64no—
497C22—92no—
498C22—92no—
499C22—92no—
500C22—122no—
501C22—122no—
502C22—368no—
503C22C2×#380211yescharacteristic
504C4—21no—
505C4—21no—
506C4—64no—
507C4—92no—
508C4—122no—
509C4—122no—
510C4—181no—
511C4—181no—
512C4C2×C4×D3211yescharacteristic
513C4#6430611yescharacteristic
514C3—21no—
515C3D3×#44012yescomplemented
516C2—94no—
517C2—124no—
518C2C4×#380211yescharacteristic
519C2#1059471611yescharacteristic
520C2#1059471711yescharacteristic
subgroupG/H
centerC22C2×#3802
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#97C22
socleC22×C32C22×D4
prime radicalC2×#3802C22
cosocleC2×C32×C4C24
hypercenter#97D32
hypocenterC32C2×#440
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
3. C4×#3797C2semidirect
4. C3⋊D3×#97C2semidirect
5. C3×#4710C2semidirect
7. #10590779C2semidirect
8. #10590743C2semidirect
9. #10590687C2semidirect
10. #10590672C2semidirect
11. #10590358C2semidirect
21. C3×C4×Dic6C22semidirect
31. #63843C22semidirect
34. #63796C4semidirect
35. C32×#97C22semidirect
36. #63642C22semidirect
37. #63642C22semidirect
38. #63630C22semidirect
40. C3×#818C22semidirect
41. C3×#816C22semidirect
42. #63576C22semidirect
43. #63565C22semidirect
58. #4710D3semidirect
78. #3797C2×C4semidirect
88. C8×C3⋊D3C2×C4semidirect
94. C3×#204C2×C4semidirect
100. #3715C2×C4semidirect
132. C4×Dic6C2×D3semidirect
137. C3×#97C2×D3semidirect
141. #818C2×D3semidirect
142. #816C2×D3semidirect
175. C3×Dic6C22×C4semidirect
183. C32×C8C22×C4semidirect
185. C3⋊(C3⋊C8)C22×C4semidirect
259. #204C4×D3semidirect
313. #97D32semidirect
363. Dic6C2×C4×D3semidirect
367. C3×C8C2×C4×D3semidirect
375. C3⋊D3#440semidirect
452. C32C2×#440semidirect
485. C8C4×D32semidirect
515. C3D3×#440semidirect

Maximal subgroups

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

subgroupindex
C2×#637962
C4×#38022
C4×#37972
C3⋊D3×#972
C3×#47102
#105909402
#105907792
#105907432
#105906872
#105906722
#105903582
D3×#4403