Finite Group Databasebeta

← #11860780

Subgroups — #11860780

Order 1152.

1041 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63796C211yesmaximal, characteristic
2#10594606C211yesmaximal, characteristic
3#10594347C211yesmaximal, characteristic, complemented
4#10592559C211yesmaximal, characteristic, complemented
5C3×#4852C212yesmaximal, complemented
6Dic3×#204C212yesmaximal, complemented
7#10590700C211yesmaximal, characteristic, complemented
8#10590602C211yesmaximal, characteristic, complemented
9#10590594C211yesmaximal, characteristic
10#10590478C212yesmaximal, complemented
11#10590454C212yesmaximal, complemented
12#79649—32nomaximal
13C2×#3802C2211yescharacteristic
14C2×#3797C2211yescharacteristic
15C2×C8×C3⋊D3C2211yescharacteristic
16#64101C2211yescharacteristic
17#64101C2211yescharacteristic
18C2×C3×#204C2212yes—
19C3×#893C2212yes—
20C3×#887C2212yescomplemented
21D3×(C2×D3)⋊C4—22no—
22C4×#627—21no—
23#63902—21no—
24C4×#625—21no—
25Dic3×D12C2212yes—
26#63874C2211yescharacteristic
27Dic3×Dic6C2212yescomplemented
28#63838—21no—
29#63836—22no—
30C2×#3715C2212yes—
31C2×#3712C2211yescharacteristic
32#63796C418yescomplemented
33C32×#106C2211yescharacteristic, complemented
34#63644C2211yescharacteristic, complemented
35#63634C2211yescharacteristic, complemented
36#63634C2211yescharacteristic, complemented
37C3×C8×Dic3C2212yescomplemented
38C3×#810C2212yescomplemented
39C3×#809C2212yes—
40#63566C2212yescomplemented
41#63563C2212yes—
42#63554C2212yescomplemented
43C2×D3×SD16—32no—
44#5572—32no—
45#5545—32no—
46C3×C4×SD16—32no—
47Dic3×SD16—32no—
48#5026—32no—
49#5018—32no—
50#4860—32no—
51#4860—61no—
52#4852D312yescomplemented
53#4817—32no—
54#4802—32no—
55#4770—32no—
56#4757—32no—
57C4×#204—32no—
58#4689—32no—
59C22×D32—21no—
60C2×C4×C3⋊D3C2311yescharacteristic
61C2×C3×D12C2312yes—
62C2×C3×C4×D3—22no—
63C2×C3×Dic6C2312yes—
64C2×#627—21no—
65C2×#625—21no—
66C2×#624—21no—
67C2×D3×Dic3—22no—
68#3802—22no—
69#3802C2×C414yes—
70#3797—22no—
71#3797C2×C414yescomplemented
72C2×C32×C8C2311yescharacteristic
73C32×C4⋊C4C2311yescharacteristic
74C32×C4⋊C4C2311yescharacteristic
75#3752—21no—
76#3752—21no—
77C4⋊(C3⋊Dic3)C2311yescharacteristic
78C4⋊(C3⋊Dic3)C2311yescharacteristic
79C4×C3⋊Dic3—21no—
80C4×C3⋊Dic3—21no—
81C2×C3⋊(C3⋊C8)C2311yescharacteristic
82C8×C3⋊D3C2×C414yescomplemented
83C3×(C2×D3)⋊C4—22no—
84C3×Dic3⋊C4—22no—
85C3×C4×Dic3—22no—
86C3×C4×Dic3C2312yes—
87C2×C3×C3⋊C8C2312yes—
88C3×#204C2×C418yescomplemented
89#3724D411yescharacteristic
90#3724D411yescharacteristic
91Dic3⋊Dic3—22no—
92#3722D412yes—
93(C2×D3)⋊Dic3—22no—
94Dic32—22no—
95#3715C2×C418yescomplemented
96#3712—22no—
97#2949—91noSylow
98C2×D3×Q8—32no—
99C2×D3×D4—32no—
100C2×C3×SD16—32no—
101C3×C4×Q8—32no—
102C3×C4×D4—32no—
103Q8×Dic3—32no—
104C2×#215—32no—
105D4×Dic3—32no—
106C2×#214—32no—
107C4×#67—62no—
108C2×(C2×D3)⋊C4—62no—
109D3×SD16—316no—
110C2×#204C2×D312yes—
111C2×ΓL(1,𝔽25)—32no—
112C2×D3×C8—32no—
113C2×D3×C8—61no—
114#893C2×D312yes—
115#892—32no—
116#892—32no—
117#892—61no—
118#892—61no—
119#892—62no—
120#887—62no—
121#887C2×D312yescomplemented
122#67⋊C4—62no—
123D3×C22⋊C4—62no—
124C4×D12—32no—
125#872—32no—
126#872—62no—
127C4×Dic6—32no—
128C4×Dic6—62no—
129C3×#106—21no—
130C3×#106C2×D312yescomplemented
131C3×#103—32no—
132C3×#102—32no—
133C3×C4×C8—32no—
134#835—32no—
135#832—32no—
136#821—32no—
137#817—32no—
138#817—61no—
139#816—32no—
140#815—32no—
141C8×Dic3C2×D312yescomplemented
142#810C2×D312yescomplemented
143#809C2×D312yes—
144#807—32no—
145#807—32no—
146#807—61no—
147#807—61no—
148#803—32no—
149C22×C3⋊D3C2×D411yescharacteristic
150C22×C3×D3—22no—
151C2×D32—24no—
152C2×D32—81no—
153C2×D32—81no—
154C2×C32×C4—21no—
155C2×C32×C4—21no—
156C2×C32×C4C2411yescharacteristic
157C2×C3⋊Dic3—21no—
158C2×C3⋊Dic3—21no—
159C2×C3⋊Dic3C2×D411yescharacteristic
160C4×C3⋊D3C22×C412yes—
161C4×C3⋊D3#4112yes—
162C2×C3×Dic3—22no—
163C2×C3×Dic3C2×D412yes—
164C2×C3×Dic3C2×D412yes—
165C3×D12—22no—
166C3×D12C22×C414yes—
167C3×C4×D3—82no—
168C3×Dic6—22no—
169C3×Dic6C22×C414yes—
170#627—24no—
171#625—24no—
172#624—24no—
173D3×Dic3—82no—
174C32×C8C22×C412yes—
175C3⋊(C3⋊C8)C22×C412yes—
176C3×C3⋊C8—22no—
177C22×SD16—91no—
178#519—91no—
179#518—91no—
180#440—92no—
181#440—92no—
182C4×SD16—32no—
183C4×SD16—92no—
184#427—91no—
185#419—91no—
186#418—91no—
187#405—91no—
188C23×D3—62no—
189C2×C3×Q8—32no—
190C2×C3×D4—32no—
191C22×C3×C4—62no—
192C2×#67—62no—
193C22×Dic3—62no—
194D3×Q8—38no—
195D3×Q8—64no—
196D3×D4—38no—
197D3×D4—64no—
198C2×D12C22×D312yes—
199C2×C4×D3—22no—
200C2×C4×D3—32no—
201C2×C4×D3—61no—
202C2×C4×D3—62no—
203C2×C4×D3—62no—
204C2×Dic6—62no—
205C2×Dic6C22×D312yes—
206C3×SD16—38no—
207C2×C3×C8—21no—
208C2×C3×C8—32no—
209C2×C3×C8C22×D312yes—
210C3×C4⋊C4—21no—
211C3×C4⋊C4—21no—
212C3×C4⋊C4—62no—
213C3×C4⋊C4C22×D312yes—
214C3×C4⋊C4C22×D312yes—
215C3×C22⋊C4—62no—
216C3×C42—32no—
217C3×C42—62no—
218#217—62no—
219#215—38no—
220#214—38no—
221(C2×D3)⋊C4—22no—
222(C2×D3)⋊C4—32no—
223(C2×D3)⋊C4—32no—
224(C2×D3)⋊C4—62no—
225(C2×D3)⋊C4—62no—
226(C2×D3)⋊C4—62no—
227(C2×D3)⋊C4—121no—
228(C2×D3)⋊C4—121no—
229C4⋊Dic3—32no—
230C4⋊Dic3—32no—
231C4⋊Dic3—61no—
232C4⋊Dic3—61no—
233C4⋊Dic3—62no—
234Dic3⋊C4—22no—
235Dic3⋊C4—32no—
236Dic3⋊C4—32no—
237Dic3⋊C4—62no—
238C4×Dic3—22no—
239C4×Dic3—62no—
240C4×Dic3—62no—
241C4×Dic3—62no—
242C4×Dic3—62no—
243C4×Dic3—121no—
244C4×Dic3—121no—
245C4×Dic3C22×D312yes—
246C2×C3⋊C8—32no—
247C2×C3⋊C8—61no—
248C2×C3⋊C8C22×D312yes—
249#204C4×D318yescomplemented
250ΓL(1,𝔽25)—64no—
251D3×C8—38no—
252D3×C8—64no—
253C22×C32C22×D411yescharacteristic
254C2×C3⋊D3—21no—
255C2×C3⋊D3—21no—
256C2×C3⋊D3C4×D412yes—
257C2×C3×D3—24no—
258C2×C3×D3—42no—
259C2×C3×D3—42no—
260D32—84no—
261C32×C4—41no—
262C32×C4—41no—
263C32×C4C23×C411yescharacteristic
264C32×C4C2×#4111yescharacteristic
265C3⋊Dic3—41no—
266C3⋊Dic3—41no—
267C3⋊Dic3C4×D412yes—
268C3×Dic3—24no—
269C3×Dic3—22no—
270C3×Dic3—22no—
271C22×Q8—91no—
272C22×D4—91no—
273C2×SD16—32no—
274C2×SD16—98no—
275C2×SD16—92no—
276C2×M16—91no—
277C22×C8—91no—
278C4×Q8—32no—
279C4×Q8—92no—
280C4×Q8—181no—
281C4×Q8—181no—
282C4×D4—32no—
283C4×D4—92no—
284C4×D4—181no—
285C4×D4—181no—
286#117—91no—
287#117—91no—
288#117—91no—
289#117—182no—
290C2×C22⋊C4—182no—
291#107—91no—
292#107—91no—
293#106—91no—
294#106D3211yescharacteristic, complemented
295#103—32no—
296#103—92no—
297#102—32no—
298#102—92no—
299#97—92no—
300C4×C8—32no—
301C23×C3—62no—
302C22×D3—22no—
303C22×D3—32no—
304C22×D3—61no—
305C22×D3—68no—
306C22×D3—242no—
307C22×D3—242no—
308C3×Q8—34no—
309C3×Q8—62no—
310C3×D4—34no—
311C3×D4—62no—
312C2×C3×C4—22no—
313C2×C3×C4—22no—
314C2×C3×C4—21no—
315C2×C3×C4—32no—
316C2×C3×C4—32no—
317C2×C3×C4—41no—
318C2×C3×C4—41no—
319C2×C3×C4—62no—
320C2×C3×C4—242no—
321C2×C3×C4C23×D312yes—
322#67—68no—
323C2×Dic3—22no—
324C2×Dic3—32no—
325C2×Dic3—61no—
326C2×Dic3—62no—
327C2×Dic3—62no—
328C2×Dic3—121no—
329C2×Dic3—121no—
330C2×Dic3—242no—
331C2×Dic3D3×D412yes—
332C2×Dic3D3×D412yes—
333D12—22no—
334D12C2×C4×D314yes—
335C4×D3—34no—
336C4×D3—34no—
337C4×D3—62no—
338C4×D3—62no—
339C4×D3—68no—
340C4×D3—82no—
341C4×D3—242no—
342Dic6—22no—
343Dic6—68no—
344Dic6C2×C4×D314yes—
345C3×C8—22no—
346C3×C8—62no—
347C3×C8C2×C4×D314yes—
348C3⋊C8—22no—
349C3⋊C8—34no—
350C3⋊C8—62no—
351C2×C32C2×C4×D411yescharacteristic
352C2×C32#57711yescharacteristic
353C2×C32#57711yescharacteristic
354C3⋊D3—22no—
355C3×D3—44no—
356C24—181no—
357C2×Q8—32no—
358C2×Q8—94no—
359C2×Q8—181no—
360C2×Q8—182no—
361C2×D4—32no—
362C2×D4—94no—
363C2×D4—182no—
364C2×D4—181no—
365C22×C4—62no—
366C22×C4—91no—
367C22×C4—182no—
368C22×C4—181no—
369SD16—38no—
370SD16—98no—
371M16—182no—
372C2×C8—32no—
373C2×C8—91no—
374C2×C8—94no—
375C2×C8C2×D3211yescharacteristic
376C4⋊C4—62no—
377C4⋊C4—91no—
378C4⋊C4—91no—
379C4⋊C4—91no—
380C4⋊C4—91no—
381C4⋊C4—182no—
382C4⋊C4C2×D3211yescharacteristic
383C4⋊C4C2×D3211yescharacteristic
384C22⋊C4—62no—
385C22⋊C4—92no—
386C22⋊C4—181no—
387C22⋊C4—181no—
388C22⋊C4—182no—
389C42—32no—
390C42—62no—
391C42—181no—
392C42—181no—
393C42—182no—
394C22×C3—21no—
395C22×C3—64no—
396C22×C3—122no—
397C22×C3—122no—
398C22×C3C2×D3×D412yes—
399C2×D3—24no—
400C2×D3—34no—
401C2×D3—42no—
402C2×D3—42no—
403C2×D3—62no—
404C2×D3—62no—
405C2×D3—62no—
406C2×D3—121no—
407C2×D3—121no—
408C2×D3—248no—
409C3×C4—21no—
410C3×C4—21no—
411C3×C4—42no—
412C3×C4—42no—
413C3×C4—62no—
414C3×C4—62no—
415C3×C4—64no—
416C3×C4—81no—
417C3×C4—81no—
418C3×C4C22×C4×D312yes—
419C3×C4D3×#4112yes—
420Dic3—22no—
421Dic3—22no—
422Dic3—24no—
423Dic3—34no—
424Dic3—62no—
425Dic3—122no—
426Dic3—122no—
427Dic3—241no—
428Dic3—241no—
429C32#294911yescharacteristic, complemented, Sylow
430C23—62no—
431C23—91no—
432C23—184no—
433C23—721no—
434C23—721no—
435Q8—34no—
436Q8—62no—
437Q8—184no—
438D4—34no—
439D4—62no—
440D4—184no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—32no—
444C2×C4—32no—
445C2×C4—62no—
446C2×C4—91no—
447C2×C4—92no—
448C2×C4—92no—
449C2×C4—184no—
450C2×C4—181no—
451C2×C4—181no—
452C2×C4—242no—
453C2×C4—722no—
454C2×C4C22×D3211yescharacteristic
455C8—62no—
456C8—92no—
457C8C4×D3212yes—
458C2×C3—21no—
459C2×C3—21no—
460C2×C3—21no—
461C2×C3—124no—
462C2×C3C4×D3×D412yes—
463C2×C3#576212yes—
464C2×C3#577012yes—
465D3—44no—
466D3—64no—
467D3—122no—
468C22—64no—
469C22—92no—
470C22—122no—
471C22—122no—
472C22—181no—
473C22—181no—
474C22—724no—
475C22D32×D411yescharacteristic
476C4—41no—
477C4—41no—
478C4—64no—
479C4—62no—
480C4—62no—
481C4—92no—
482C4—361no—
483C4—361no—
484C4C2×C4×D3211yescharacteristic
485C4#6431911yescharacteristic
486C3—21no—
487C3#7964912yescomplemented
488C2—124no—
489C2—182no—
490C2#1059460511yescharacteristic
491C2#1059474811yescharacteristic
492C2#1059475711yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radicalC2×#3802C22
cosocleC2×C32×C4C24
hypercenter#106D32
hypocenterC32#2949
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
3. #10594347C2semidirect
4. #10592559C2semidirect
5. C3×#4852C2semidirect
6. Dic3×#204C2semidirect
7. #10590700C2semidirect
8. #10590602C2semidirect
10. #10590478C2semidirect
11. #10590454C2semidirect
20. C3×#887C22semidirect
27. Dic3×Dic6C22semidirect
32. #63796C4semidirect
33. C32×#106C22semidirect
34. #63644C22semidirect
35. #63634C22semidirect
36. #63634C22semidirect
37. C3×C8×Dic3C22semidirect
38. C3×#810C22semidirect
40. #63566C22semidirect
42. #63554C22semidirect
52. #4852D3semidirect
71. #3797C2×C4semidirect
82. C8×C3⋊D3C2×C4semidirect
88. C3×#204C2×C4semidirect
95. #3715C2×C4semidirect
121. #887C2×D3semidirect
130. C3×#106C2×D3semidirect
141. C8×Dic3C2×D3semidirect
142. #810C2×D3semidirect
249. #204C4×D3semidirect
294. #106D32semidirect
429. C32#2949semidirect
487. C3#79649semidirect

Maximal subgroups

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

subgroupindex
C2×#637962
#105946062
#105943472
#105925592
C3×#48522
Dic3×#2042
#105907002
#105906022
#105905942
#105904782
#105904542
#796493