Finite Group Databasebeta

← #11860952

Subgroups — #11860952

Order 1152.

1022 conjugacy classes of subgroups.

The subgroup lattice has 491 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63807C211yesmaximal, characteristic
2#10593887C212yesmaximal, complemented
3#10592415C211yesmaximal, characteristic, complemented
4C3×#4711C211yesmaximal, characteristic, complemented
5C3×#4708C211yesmaximal, characteristic, complemented
6#10590810C211yesmaximal, characteristic, complemented
7#10590771C211yesmaximal, characteristic, complemented
8#10590744C212yesmaximal, complemented
9D3×#817C211yesmaximal, characteristic, complemented
10#10590670C212yesmaximal, complemented
11C4×#3716C212yesmaximal, complemented
12#79868—31nomaximal
13#78574—31nomaximal
14C2×#3795C2212yes—
15C2×#3746C2211yescharacteristic
16C4×#634C2212yes—
17C2×C3×D24C2211yescharacteristic
18C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
19C2×C3×D3×C8C2211yescharacteristic
20C3×C4×D12C2212yes—
21C3×#872C2211yescharacteristic
22#63902—22no—
23Dic3×D12C2212yes—
24D3×C4⋊Dic3C2212yes—
25#63879—22no—
26#63878—22no—
27D3×Dic3⋊C4—22no—
28#63844C2212yes—
29C2×#3716C2212yes—
30#63807C418yescomplemented
31C32×#97C2211yescharacteristic
32#63644C2211yescharacteristic
33#63643C2212yes—
34C3×#821C2212yes—
35C3×#817C2211yescharacteristic
36C3×#815C2211yescharacteristic
37C3×C8×Dic3C2211yescharacteristic
38C3×C4×C3⋊C8C2211yescharacteristic
39#63573C2212yes—
40#63567C2212yes—
41#63563C2212yes—
42C2×#912—31no—
43C2×#904—31no—
44#5546—32no—
45#5523—32no—
46C3×#442—31no—
47C3×#405—31no—
48#5152—31no—
49#5133—32no—
50C2×#817—31no—
51C4×#214—32no—
52D3×#106—31no—
53#4853—31no—
54#4771—32no—
55#4758—32no—
56#4716—31no—
57#4716—31no—
58#4716—31no—
59#4716—61no—
60#4711—31no—
61#4711D311yescharacteristic, complemented
62#4708D311yescharacteristic, complemented
63C4×#204—32no—
64C4×#204—32no—
65C2×#634C2312yes—
66C2×C3×D12C2312yes—
67C2×C3×C4×D3—22no—
68C2×C3×C4×D3C2311yescharacteristic
69C2×#625—22no—
70C2×D3×Dic3—22no—
71C2×D3×Dic3—22no—
72C2×D3×Dic3—22no—
73#3795—24no—
74#3795C2×C418yescomplemented
75C2×C32×C8C2311yescharacteristic
76C2×C32×C8C2311yescharacteristic
77C32×C42C2311yescharacteristic
78C4⋊(C3⋊Dic3)C2312yes—
79#3750—22no—
80C4×C3⋊Dic3—22no—
81#3746C2×C414yescomplemented
82C3×(C2×D3)⋊C4—22no—
83C3×(C2×D3)⋊C4D412yes—
84C3×C4⋊Dic3C2312yes—
85C3×Dic3⋊C4D412yes—
86C3×C4×Dic3C2311yescharacteristic
87C2×C3×C3⋊C8C2311yescharacteristic
88C2×C3×C3⋊C8C2311yescharacteristic
89C3×D24C2×C414yescomplemented
90C3×ΓL(1,𝔽25)—22no—
91C3×D3×C8C2×C414yescomplemented
92#3724—22no—
93Dic3⋊Dic3—22no—
94(C2×D3)⋊Dic3—22no—
95Dic32—22no—
96#3716C2×C418yescomplemented
97#2952—91noSylow
98C2×#237—32no—
99C2×#235—32no—
100C2×C3×D8—31no—
101C2×C3×M16—31no—
102C22×C3×C8—31no—
103C3×C4×D4—32no—
104C3×#117—31no—
105D4×Dic3—32no—
106C2×#214—32no—
107C4×#67—62no—
108C2×C4⋊Dic3—32no—
109C2×Dic3⋊C4—62no—
110#912—38no—
111C2×Dic12—31no—
112C2×Dic12—31no—
113C2×Dic12—61no—
114#904—38no—
115C2×D24C2×D311yescharacteristic
116C2×#204—32no—
117C2×ΓL(1,𝔽25)C2×D311yescharacteristic
118C2×D3×C8C2×D311yescharacteristic
119#892—62no—
120D3×C4⋊C4—32no—
121D3×C4⋊C4—62no—
122#887—32no—
123#67⋊C4—62no—
124#67⋊C4—62no—
125#67⋊C4—62no—
126#877—62no—
127C4×D12—32no—
128C4×D12C2×D312yes—
129#872C2×D311yescharacteristic
130C4×Dic6—32no—
131C4×Dic6—32no—
132C4×Dic6—32no—
133C4×Dic6—62no—
134C3×#106—31no—
135C3×#102—32no—
136C3×#97—21no—
137C3×#97—31no—
138C3×#97C2×D311yescharacteristic
139C3×#97C2×D311yescharacteristic
140C3×C4×C8—31no—
141C3×C4×C8—31no—
142#832—32no—
143#821—32no—
144#821C2×D312yes—
145#817—31no—
146#817—31no—
147#817—32no—
148#817—61no—
149#817C2×D311yescharacteristic
150#816—32no—
151#816—32no—
152#816—32no—
153#816—62no—
154#815C2×D311yescharacteristic
155C8×Dic3C2×D311yescharacteristic
156#810—32no—
157#808—32no—
158C4×C3⋊C8C2×D311yescharacteristic
159C22×C3×D3—22no—
160C22×C3×D3C2×D411yescharacteristic
161C2×C32×C4C2×D412yes—
162C2×C32×C4C2411yescharacteristic
163C2×C3⋊Dic3—22no—
164C2×C3⋊Dic3—22no—
165#634—22no—
166#634C22×C414yes—
167C2×C3×Dic3—22no—
168C2×C3×Dic3C2×D412yes—
169C2×C3×Dic3C2×D411yescharacteristic
170C3×D12—22no—
171C3×D12C22×C414yes—
172C3×C4×D3—82no—
173C3×C4×D3C22×C412yes—
174C3×C4×D3#4112yes—
175#625—28no—
176D3×Dic3—28no—
177D3×Dic3—82no—
178D3×Dic3—82no—
179C32×C8—21no—
180C32×C8C22×C412yes—
181C3×C3⋊C8—21no—
182C3×C3⋊C8C22×C412yes—
183C2×#135—91no—
184#520—92no—
185#442—31no—
186#442—91no—
187#441—91no—
188#441—91no—
189C4×SD16—92no—
190C4×SD16—92no—
191C2×#106—91no—
192#417—92no—
193#405—31no—
194C2×C3×D4—32no—
195C22×C3×C4—31no—
196C22×C3×C4—62no—
197C2×#67—62no—
198C2×#67—62no—
199C22×Dic3—62no—
200C22×Dic3—62no—
201C22×Dic3—62no—
202#237—38no—
203#237—64no—
204#235—38no—
205#235—64no—
206C2×D12C22×D312yes—
207C2×C4×D3—22no—
208C2×C4×D3—62no—
209C2×C4×D3—62no—
210C2×C4×D3—62no—
211C2×C4×D3C22×D311yescharacteristic
212C2×Dic6—32no—
213C2×Dic6—32no—
214C2×Dic6—62no—
215C3×D8—34no—
216C3×M16—62no—
217C2×C3×C8—21no—
218C2×C3×C8—21no—
219C2×C3×C8—31no—
220C2×C3×C8—34no—
221C2×C3×C8—31no—
222C2×C3×C8C22×D311yescharacteristic
223C2×C3×C8C22×D311yescharacteristic
224C2×C3×C8C22×D311yescharacteristic
225C2×C3×C8C22×D311yescharacteristic
226C3×C4⋊C4—32no—
227C3×C4⋊C4—32no—
228C3×C22⋊C4—32no—
229C3×C22⋊C4—62no—
230C3×C42—21no—
231C3×C42—31no—
232C3×C42C22×D311yescharacteristic
233C3×C42C22×D311yescharacteristic
234#217—62no—
235#214—38no—
236(C2×D3)⋊C4—22no—
237(C2×D3)⋊C4—62no—
238(C2×D3)⋊C4D1212yes—
239C4⋊Dic3—32no—
240C4⋊Dic3—32no—
241C4⋊Dic3—62no—
242C4⋊Dic3—62no—
243C4⋊Dic3C22×D312yes—
244Dic3⋊C4—62no—
245Dic3⋊C4—62no—
246Dic3⋊C4—62no—
247Dic3⋊C4—62no—
248Dic3⋊C4—62no—
249Dic3⋊C4—122no—
250Dic3⋊C4D1212yes—
251C4×Dic3—62no—
252C4×Dic3—62no—
253C4×Dic3—62no—
254C4×Dic3—62no—
255C4×Dic3—122no—
256C4×Dic3C22×D311yescharacteristic
257C2×C3⋊C8C22×D311yescharacteristic
258C2×C3⋊C8C22×D311yescharacteristic
259Dic12—34no—
260Dic12—34no—
261Dic12—64no—
262D24C4×D314yescomplemented
263#204—38no—
264ΓL(1,𝔽25)—22no—
265D3×C8C4×D314yescomplemented
266C22×C32C22×D411yescharacteristic
267C2×C3×D3—22no—
268C2×C3×D3—24no—
269C2×C3×D3—42no—
270C2×C3×D3—42no—
271C2×C3×D3C4×D412yes—
272C32×C4—22no—
273C32×C4C23×C411yescharacteristic
274C32×C4C2×#4111yescharacteristic
275C3⋊Dic3—24no—
276C3⋊Dic3—42no—
277C3×Dic3—22no—
278C3×Dic3—42no—
279C3×Dic3C4×D412yes—
280C2×#41—92no—
281#135—98no—
282C2×Q16—91no—
283C2×SD16—92no—
284C2×D8—31no—
285C2×M16—31no—
286C22×C8—31no—
287C4×Q8—92no—
288C4×Q8—92no—
289C4×D4—32no—
290C4×D4—92no—
291C4×D4—182no—
292C4×D4—182no—
293#117—31no—
294#117—182no—
295C2×C4⋊C4—92no—
296C2×C4⋊C4—182no—
297#106—31no—
298#106—92no—
299#106—91no—
300#103—92no—
301#103—92no—
302#102—32no—
303#102—92no—
304#97—31no—
305#97D3211yescharacteristic
306C4×C8—31no—
307C4×C8—31no—
308C23×C3—31no—
309C23×C3—62no—
310C22×D3—22no—
311C22×D3C2×D1211yescharacteristic
312C3×D4—34no—
313C3×D4—62no—
314C2×C3×C4—21no—
315C2×C3×C4—22no—
316C2×C3×C4—31no—
317C2×C3×C4—32no—
318C2×C3×C4—32no—
319C2×C3×C4—32no—
320C2×C3×C4—62no—
321C2×C3×C4—242no—
322C2×C3×C4C2×D1212yes—
323C2×C3×C4D3×D412yes—
324C2×C3×C4C23×D311yescharacteristic
325C2×C3×C4C23×D311yescharacteristic
326#67—68no—
327#67—68no—
328C2×Dic3—22no—
329C2×Dic3—62no—
330C2×Dic3—62no—
331C2×Dic3—68no—
332C2×Dic3—62no—
333C2×Dic3—62no—
334C2×Dic3—122no—
335C2×Dic3—122no—
336C2×Dic3—242no—
337C2×Dic3—242no—
338C2×Dic3C2×D1212yes—
339C2×Dic3C2×D1211yescharacteristic
340D12—22no—
341D12C2×C4×D314yes—
342C4×D3—68no—
343C4×D3—82no—
344C4×D3—242no—
345C4×D3—242no—
346C4×D3C2×C4×D312yes—
347C4×D3#23512yes—
348Dic6—34no—
349Dic6—34no—
350Dic6—64no—
351Dic6—62no—
352Dic6—62no—
353Dic6—122no—
354C3×C8—21no—
355C3×C8—21no—
356C3×C8—22no—
357C3×C8—32no—
358C3×C8—41no—
359C3×C8—61no—
360C3×C8C2×C4×D312yes—
361C3×C8C2×C4×D312yes—
362C3⋊C8—21no—
363C3⋊C8C2×C4×D312yes—
364C2×C32C2×C4×D411yescharacteristic
365C2×C32#57712yes—
366C3×D3—22no—
367C3×D3—44no—
368#41—98no—
369#41—184no—
370C2×Q8—92no—
371C2×D4—32no—
372C2×D4—182no—
373C22×C4—31no—
374C22×C4—62no—
375C22×C4—182no—
376C22×C4—182no—
377C22×C4—182no—
378Q16—94no—
379SD16—98no—
380D8—34no—
381M16—62no—
382C2×C8—31no—
383C2×C8—34no—
384C2×C8—31no—
385C2×C8C2×D3211yescharacteristic
386C2×C8C2×D3211yescharacteristic
387C4⋊C4—32no—
388C4⋊C4—32no—
389C4⋊C4—92no—
390C4⋊C4—182no—
391C4⋊C4—182no—
392C4⋊C4—182no—
393C22⋊C4—32no—
394C22⋊C4—62no—
395C22⋊C4—182no—
396C42—31no—
397C42—182no—
398C42—182no—
399C42C2×D3211yescharacteristic
400C22×C3—21no—
401C22×C3—32no—
402C22×C3—62no—
403C22×C3—64no—
404C22×C3—122no—
405C22×C3—122no—
406C22×C3C22×D1211yescharacteristic
407C22×C3C2×D3×D411yescharacteristic
408C2×D3—22no—
409C2×D3—24no—
410C2×D3—42no—
411C2×D3—42no—
412C2×D3C4×D1212yes—
413C3×C4—22no—
414C3×C4—22no—
415C3×C4—21no—
416C3×C4—21no—
417C3×C4—32no—
418C3×C4—42no—
419C3×C4—62no—
420C3×C4—122no—
421C3×C4C22×C4×D311yescharacteristic
422C3×C4C22×C4×D311yescharacteristic
423C3×C4C2×#23511yescharacteristic
424C3×C4D3×#4111yescharacteristic
425Dic3—22no—
426Dic3—42no—
427Dic3—64no—
428Dic3—64no—
429Dic3—124no—
430Dic3—122no—
431Dic3—122no—
432Dic3—242no—
433Dic3C4×D1212yes—
434C32#295211yescharacteristic, complemented, Sylow
435C23—31no—
436C23—62no—
437Q8—94no—
438Q8—182no—
439D4—34no—
440D4—62no—
441D4—188no—
442C2×C4—31no—
443C2×C4—32no—
444C2×C4—32no—
445C2×C4—32no—
446C2×C4—62no—
447C2×C4—188no—
448C2×C4—182no—
449C2×C4—182no—
450C2×C4—242no—
451C2×C4—722no—
452C2×C4—722no—
453C2×C4D3×D1212yes—
454C2×C4C22×D3211yescharacteristic
455C8—21no—
456C8—32no—
457C8—61no—
458C8C4×D3212yes—
459C2×C3—22no—
460C2×C3—21no—
461C2×C3—62no—
462C2×C3—124no—
463C2×C3C2×C4×D1211yescharacteristic
464C2×C3C4×D3×D411yescharacteristic
465C2×C3#575112yes—
466C2×C3#577512yes—
467D3—22no—
468D3—44no—
469C22—32no—
470C22—62no—
471C22—64no—
472C22—122no—
473C22—122no—
474C22C2×D3×D1211yescharacteristic
475C4—22no—
476C4—32no—
477C4—62no—
478C4—122no—
479C4—184no—
480C4—362no—
481C4C2×C4×D3211yescharacteristic
482C4D3×#23511yescharacteristic
483C3—21no—
484C3#7857411yescharacteristic, complemented
485C3#7986811yescharacteristic, complemented
486C2—62no—
487C2—124no—
488C2C4×D3×D1211yescharacteristic
489C2#1059471312yes—
subgroupG/H
centerC22C2×D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#97C22
socleC22×C32C22×D4
prime radicalC2×#63807C2
cosocleC2×C32×C4C24
hypercenter#97D32
hypocenterC32#2952
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
2. #10593887C2semidirect
3. #10592415C2semidirect
4. C3×#4711C2semidirect
5. C3×#4708C2semidirect
6. #10590810C2semidirect
7. #10590771C2semidirect
8. #10590744C2semidirect
9. D3×#817C2semidirect
10. #10590670C2semidirect
11. C4×#3716C2semidirect
30. #63807C4semidirect
61. #4711D3semidirect
62. #4708D3semidirect
74. #3795C2×C4semidirect
81. #3746C2×C4semidirect
89. C3×D24C2×C4semidirect
91. C3×D3×C8C2×C4semidirect
96. #3716C2×C4semidirect
262. D24C4×D3semidirect
265. D3×C8C4×D3semidirect
434. C32#2952semidirect
484. C3#78574semidirect
485. C3#79868semidirect

Maximal subgroups

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

subgroupindex
C2×#638072
#105938872
#105924152
C3×#47112
C3×#47082
#105908102
#105907712
#105907442
D3×#8172
#105906702
C4×#37162
#798683
#785743