Finite Group Databasebeta

← #11860242

Subgroups — #11860242

Order 1152.

1041 conjugacy classes of subgroups.

The subgroup lattice has 495 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63810C211yesmaximal, characteristic
2#10594360C212yesmaximal, complemented
3#10592559C211yesmaximal, characteristic, complemented
4C3×#4869C211yesmaximal, characteristic, complemented
5C3×#4853C211yesmaximal, characteristic, complemented
6#10590812C211yesmaximal, characteristic, complemented
7#10590771C211yesmaximal, characteristic, complemented
8#10590668C211yesmaximal, characteristic, complemented
9#10590611C212yesmaximal, complemented
10#10590478C212yesmaximal, complemented
11#10590454C212yesmaximal, complemented
12#79864—31nomaximal
13#79828—31nomaximal
14C2×#3796C2212yes—
15C2×C8×C3⋊D3C2211yescharacteristic
16#64101C2212yes—
17C2×C3×Dic12C2211yescharacteristic
18C2×C3×D24C2211yescharacteristic
19C3×#893C2212yes—
20C3×#887C2212yes—
21#63904—22no—
22Dic3×D12C2212yes—
23C4×#624C2211yescharacteristic
24#63880—22no—
25#63878—22no—
26C4×D3×Dic3—22no—
27Dic3×Dic6C2212yes—
28C2×#3715C2212yes—
29C2×#3710C2211yescharacteristic
30#63810C418yescomplemented
31C32×#106C2211yescharacteristic
32#63644C2211yescharacteristic
33#63634C2212yes—
34C3×#815C2211yescharacteristic
35C3×#815C2211yescharacteristic
36C3×#810C2212yes—
37C3×#809C2212yes—
38#63566C2212yes—
39#63563C2212yes—
40#63554C2211yescharacteristic
41#63554C2211yescharacteristic
42C2×#919—31no—
43C2×#912—31no—
44C4×#239—32no—
45C4×#237—32no—
46C3×#442—31no—
47C3×#441—31no—
48#5184—31no—
49#5152—31no—
50#5026—32no—
51#5018—32no—
52#4869D311yescharacteristic, complemented
53#4860—31no—
54#4860—31no—
55#4860—61no—
56#4853D311yescharacteristic, complemented
57#4817—32no—
58#4804—32no—
59#4772—32no—
60#4757—32no—
61#4716—31no—
62#4711—31no—
63D3×#97—31no—
64D3×#97—31no—
65C2×C4×C3⋊D3C2311yescharacteristic
66C2×C3×D12C2312yes—
67C2×C3×C4×D3—22no—
68C2×C3×Dic6C2312yes—
69C2×#626—22no—
70C2×#624D412yes—
71C2×D3×Dic3—22no—
72C2×D3×Dic3—22no—
73#3796—24no—
74#3796C2×C418yescomplemented
75C2×C32×C8C2311yescharacteristic
76C32×C4⋊C4C2312yes—
77#3752—22no—
78C4⋊(C3⋊Dic3)C2312yes—
79C4×C3⋊Dic3—22no—
80C2×C3⋊(C3⋊C8)C2311yescharacteristic
81C8×C3⋊D3C2×C414yescomplemented
82C3×(C2×D3)⋊C4—22no—
83C3×Dic3⋊C4—22no—
84C3×C4×Dic3—22no—
85C3×C4×Dic3C2311yescharacteristic
86C3×C4×Dic3C2311yescharacteristic
87C2×C3×C3⋊C8C2311yescharacteristic
88C2×C3×C3⋊C8C2311yescharacteristic
89C3×Dic12C2×C414yescomplemented
90C3×D24C2×C414yescomplemented
91Dic3⋊Dic3—22no—
92(C2×D3)⋊Dic3—22no—
93Dic32—22no—
94Dic32D412yes—
95#3715C2×C418yescomplemented
96#3710—22no—
97#2943—91noSylow
98C2×#239—32no—
99C2×#237—32no—
100C2×C3×Q16—31no—
101C2×C3×D8—31no—
102C3×C4×Q8—32no—
103C3×C4×D4—32no—
104Q8×Dic3—32no—
105C2×#215—32no—
106D4×Dic3—32no—
107C2×#214—32no—
108C4×#67—62no—
109C2×C4×Dic3—62no—
110#919—38no—
111#912—38no—
112C2×Dic12C2×D311yescharacteristic
113C2×D24C2×D311yescharacteristic
114C2×D3×C8—31no—
115C2×D3×C8—31no—
116C2×D3×C8—31no—
117C2×D3×C8—31no—
118C2×D3×C8—61no—
119#893—62no—
120#893C2×D312yes—
121#892—32no—
122#892—32no—
123#892—62no—
124#892—62no—
125#887C2×D312yes—
126#67⋊C4—62no—
127#877—62no—
128C4×D12—32no—
129C4×D12—62no—
130C42×D3—31no—
131C42×D3—31no—
132C42×D3—62no—
133C4×Dic6—32no—
134C3×#106—21no—
135C3×#106C2×D311yescharacteristic
136C3×#106C2×D311yescharacteristic
137C3×#103—32no—
138C3×#102—32no—
139C3×#97—31no—
140C3×#97—31no—
141#835—32no—
142#832—32no—
143#821—32no—
144#817—31no—
145#817—31no—
146#817—61no—
147#816—32no—
148#815—31no—
149#815—31no—
150#815C2×D311yescharacteristic
151#815C2×D311yescharacteristic
152#810C2×D312yes—
153#809C2×D312yes—
154#807—32no—
155#807—32no—
156#807—62no—
157#803—31no—
158#803—31no—
159C22×C3⋊D3C2×D411yescharacteristic
160C22×C3×D3—22no—
161C2×C32×C4—22no—
162C2×C32×C4C2411yescharacteristic
163C2×C3⋊Dic3—22no—
164C2×C3⋊Dic3C2×D411yescharacteristic
165C4×C3⋊D3C22×C412yes—
166C4×C3⋊D3#4112yes—
167C2×C3×Dic3—22no—
168C2×C3×Dic3C2×D412yes—
169C2×C3×Dic3C2×D412yes—
170C3×D12—22no—
171C3×D12C22×C414yes—
172C3×C4×D3—44no—
173C3×Dic6—22no—
174C3×Dic6C22×C414yes—
175#626—28no—
176#624—42no—
177D3×Dic3—28no—
178D3×Dic3—44no—
179C32×C8C22×C412yes—
180C3⋊(C3⋊C8)C22×C412yes—
181C3×C3⋊C8—21no—
182C3×C3⋊C8—21no—
183C2×#135—91no—
184C4×#41—92no—
185#442—31no—
186#442—91no—
187#441—31no—
188#441—91no—
189#440—92no—
190#440—92no—
191#427—91no—
192#416—92no—
193C2×#97—91no—
194C2×C3×Q8—32no—
195C2×C3×D4—32no—
196C22×C3×C4—62no—
197C2×#67—62no—
198C22×Dic3—62no—
199C22×Dic3—62no—
200#239—38no—
201#239—64no—
202#237—38no—
203#237—64no—
204C2×D12—62no—
205C2×D12C22×D312yes—
206C2×C4×D3—22no—
207C2×C4×D3—31no—
208C2×C4×D3—31no—
209C2×C4×D3—32no—
210C2×C4×D3—32no—
211C2×C4×D3—61no—
212C2×C4×D3—62no—
213C2×C4×D3—62no—
214C2×Dic6C22×D312yes—
215C3×Q16—34no—
216C3×D8—34no—
217C2×C3×C8—21no—
218C2×C3×C8—31no—
219C2×C3×C8—31no—
220C2×C3×C8C22×D311yescharacteristic
221C2×C3×C8C22×D311yescharacteristic
222C3×C4⋊C4—22no—
223C3×C4⋊C4—62no—
224C3×C4⋊C4C22×D312yes—
225C3×C4⋊C4C22×D312yes—
226C3×C22⋊C4—62no—
227C3×C42—31no—
228C3×C42—31no—
229C3×C42—62no—
230#217—62no—
231#215—38no—
232#214—38no—
233(C2×D3)⋊C4—22no—
234(C2×D3)⋊C4—62no—
235(C2×D3)⋊C4—62no—
236(C2×D3)⋊C4—62no—
237(C2×D3)⋊C4—122no—
238C4⋊Dic3—32no—
239C4⋊Dic3—32no—
240C4⋊Dic3—62no—
241C4⋊Dic3—62no—
242Dic3⋊C4—22no—
243Dic3⋊C4—62no—
244C4×Dic3—22no—
245C4×Dic3—32no—
246C4×Dic3—32no—
247C4×Dic3—62no—
248C4×Dic3—62no—
249C4×Dic3—62no—
250C4×Dic3—62no—
251C4×Dic3—122no—
252C4×Dic3C22×D311yescharacteristic
253C4×Dic3C22×D311yescharacteristic
254C2×C3⋊C8—31no—
255C2×C3⋊C8—31no—
256C2×C3⋊C8—61no—
257C2×C3⋊C8C22×D311yescharacteristic
258C2×C3⋊C8C22×D311yescharacteristic
259Dic12C4×D314yescomplemented
260D24C4×D314yescomplemented
261D3×C8—34no—
262D3×C8—34no—
263D3×C8—64no—
264D3×C8—62no—
265D3×C8—62no—
266C22×C32C22×D411yescharacteristic
267C2×C3⋊D3—22no—
268C2×C3⋊D3C4×D412yes—
269C2×C3×D3—24no—
270C2×C3×D3—42no—
271C2×C3×D3—42no—
272C32×C4—42no—
273C32×C4C23×C411yescharacteristic
274C32×C4C2×#4111yescharacteristic
275C3⋊Dic3—42no—
276C3⋊Dic3C4×D412yes—
277C3×Dic3—24no—
278C3×Dic3—22no—
279C3×Dic3—22no—
280C2×#41—92no—
281#135—98no—
282C2×Q16—31no—
283C2×SD16—92no—
284C2×D8—31no—
285C22×C8—91no—
286C22×C8—91no—
287C4×Q8—32no—
288C4×Q8—92no—
289C4×D4—32no—
290C4×D4—92no—
291C4×D4—182no—
292C4×D4—182no—
293#117—92no—
294#117—182no—
295C2×C42—91no—
296C2×C42—182no—
297#107—92no—
298#106—91no—
299#106D3211yescharacteristic
300#103—32no—
301#103—92no—
302#102—32no—
303#102—92no—
304#97—31no—
305#97—31no—
306#97—91no—
307#97—91no—
308C23×C3—62no—
309C22×D3—22no—
310C22×D3—31no—
311C22×D3—31no—
312C22×D3—61no—
313C3×Q8—34no—
314C3×Q8—62no—
315C3×D4—34no—
316C3×D4—62no—
317C2×C3×C4—22no—
318C2×C3×C4—22no—
319C2×C3×C4—21no—
320C2×C3×C4—32no—
321C2×C3×C4—32no—
322C2×C3×C4—42no—
323C2×C3×C4—62no—
324C2×C3×C4—124no—
325C2×C3×C4C23×D311yescharacteristic
326C2×C3×C4C23×D311yescharacteristic
327#67—68no—
328C2×Dic3—22no—
329C2×Dic3—31no—
330C2×Dic3—31no—
331C2×Dic3—61no—
332C2×Dic3—68no—
333C2×Dic3—62no—
334C2×Dic3—62no—
335C2×Dic3—122no—
336C2×Dic3—124no—
337C2×Dic3D3×D412yes—
338C2×Dic3D3×D412yes—
339D12—22no—
340D12—68no—
341D12C2×C4×D314yes—
342C4×D3—32no—
343C4×D3—32no—
344C4×D3—32no—
345C4×D3—32no—
346C4×D3—44no—
347C4×D3—62no—
348C4×D3—62no—
349C4×D3—68no—
350C4×D3—122no—
351C4×D3—122no—
352C4×D3—124no—
353Dic6—22no—
354Dic6C2×C4×D314yes—
355C3×C8—22no—
356C3×C8—61no—
357C3×C8—61no—
358C3×C8C2×C4×D312yes—
359C3×C8C2×C4×D312yes—
360C3⋊C8—21no—
361C3⋊C8—21no—
362C3⋊C8—32no—
363C3⋊C8—32no—
364C3⋊C8—62no—
365C2×C32C2×C4×D411yescharacteristic
366C2×C32#57512yes—
367C3⋊D3—22no—
368C3×D3—44no—
369#41—98no—
370#41—184no—
371C2×Q8—32no—
372C2×D4—32no—
373C2×D4—182no—
374C22×C4—62no—
375C22×C4—92no—
376C22×C4—91no—
377C22×C4—182no—
378C22×C4—182no—
379Q16—34no—
380SD16—98no—
381D8—34no—
382C2×C8—31no—
383C2×C8—31no—
384C2×C8—91no—
385C2×C8—94no—
386C2×C8—182no—
387C2×C8C2×D3211yescharacteristic
388C4⋊C4—62no—
389C4⋊C4—92no—
390C4⋊C4—182no—
391C4⋊C4C2×D3212yes—
392C22⋊C4—62no—
393C22⋊C4—182no—
394C22⋊C4—182no—
395C42—31no—
396C42—31no—
397C42—62no—
398C42—92no—
399C42—182no—
400C42—182no—
401C22×C3—21no—
402C22×C3—64no—
403C22×C3—122no—
404C22×C3—122no—
405C22×C3C2×D3×D411yescharacteristic
406C22×C3C2×D3×D411yescharacteristic
407C2×D3—24no—
408C2×D3—32no—
409C2×D3—32no—
410C2×D3—42no—
411C2×D3—42no—
412C2×D3—62no—
413C2×D3—62no—
414C2×D3—62no—
415C2×D3—122no—
416C3×C4—21no—
417C3×C4—21no—
418C3×C4—42no—
419C3×C4—42no—
420C3×C4—62no—
421C3×C4—62no—
422C3×C4—64no—
423C3×C4—82no—
424C3×C4C22×C4×D311yescharacteristic
425C3×C4C22×C4×D311yescharacteristic
426C3×C4D3×#4111yescharacteristic
427C3×C4D3×#4111yescharacteristic
428Dic3—22no—
429Dic3—22no—
430Dic3—24no—
431Dic3—32no—
432Dic3—32no—
433Dic3—62no—
434Dic3—122no—
435Dic3—122no—
436Dic3—242no—
437C32#294311yescharacteristic, complemented, Sylow
438C23—62no—
439C23—91no—
440Q8—34no—
441Q8—62no—
442D4—34no—
443D4—62no—
444D4—188no—
445C2×C4—22no—
446C2×C4—32no—
447C2×C4—32no—
448C2×C4—62no—
449C2×C4—91no—
450C2×C4—92no—
451C2×C4—92no—
452C2×C4—124no—
453C2×C4—188no—
454C2×C4—182no—
455C2×C4—362no—
456C2×C4—364no—
457C2×C4C22×D3211yescharacteristic
458C8—61no—
459C8—61no—
460C8—92no—
461C8C4×D3212yes—
462C2×C3—21no—
463C2×C3—22no—
464C2×C3—124no—
465C2×C3C4×D3×D411yescharacteristic
466C2×C3C4×D3×D411yescharacteristic
467C2×C3#577312yes—
468C2×C3#577712yes—
469D3—44no—
470D3—62no—
471D3—62no—
472D3—122no—
473C22—64no—
474C22—92no—
475C22—122no—
476C22—122no—
477C22—182no—
478C22D32×D411yescharacteristic
479C4—42no—
480C4—64no—
481C4—62no—
482C4—62no—
483C4—92no—
484C4—362no—
485C4C2×C4×D3211yescharacteristic
486C4#6431911yescharacteristic
487C3—21no—
488C3#7982811yescharacteristic, complemented
489C3#7986411yescharacteristic, complemented
490C2—124no—
491C2—182no—
492C2#1059460511yescharacteristic
493C2#1059474412yes—
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radicalC2×#63810C2
cosocleC2×C32×C4C24
hypercenter#106D32
hypocenterC32#2943
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
2. #10594360C2semidirect
3. #10592559C2semidirect
4. C3×#4869C2semidirect
5. C3×#4853C2semidirect
6. #10590812C2semidirect
7. #10590771C2semidirect
8. #10590668C2semidirect
9. #10590611C2semidirect
10. #10590478C2semidirect
11. #10590454C2semidirect
30. #63810C4semidirect
52. #4869D3semidirect
56. #4853D3semidirect
74. #3796C2×C4semidirect
81. C8×C3⋊D3C2×C4semidirect
89. C3×Dic12C2×C4semidirect
90. C3×D24C2×C4semidirect
95. #3715C2×C4semidirect
259. Dic12C4×D3semidirect
260. D24C4×D3semidirect
437. C32#2943semidirect
488. C3#79828semidirect
489. C3#79864semidirect

Maximal subgroups

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

subgroupindex
C2×#638102
#105943602
#105925592
C3×#48692
C3×#48532
#105908122
#105907712
#105906682
#105906112
#105904782
#105904542
#798643
#798283