Finite Group Databasebeta

← #11876921

Subgroups — #11876921

Order 1152.

794 conjugacy classes of subgroups.

The subgroup lattice has 471 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593974C212yesmaximal, complemented
2#10592415C211yesmaximal, characteristic, complemented
3C3×#4711C211yesmaximal, characteristic, complemented
4C3×#4707C211yesmaximal, characteristic, complemented
5#10590871C211yesmaximal, characteristic, complemented
6#10590864C211yesmaximal, characteristic, complemented
7#10590863C212yesmaximal, complemented
8#10590853C211yesmaximal, characteristic, complemented
9#10590836C211yesmaximal, characteristic
10#10590828C212yesmaximal, complemented
11#10590360C212yesmaximal, complemented
12#79862—31nomaximal
13#78534—31nomaximal
14C2×#3746C2211yescharacteristic
15C4×#634C2212yes—
16C2×C3×D24C2211yescharacteristic
17C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
18C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
19C3×C4×D12C2212yes—
20C3×C42×D3C2211yescharacteristic
21#63908C2212yes—
22#63905—22no—
23C4×#625—22no—
24#63869C2212yes—
25#63860C2212yes—
26#63859—22no—
27#63857C2212yes—
28#63855—22no—
29C2×#3716C2212yes—
30C32×#97C2211yescharacteristic
31#63644C2211yescharacteristic
32#63643C2212yes—
33C3×#821C2212yes—
34C3×#817C2211yescharacteristic
35C3×C8×Dic3C2211yescharacteristic
36C3×C8×Dic3C2211yescharacteristic
37C3×#803C2211yescharacteristic
38#63575C2212yes—
39#63567C2212yes—
40#63563C2212yes—
41#5557—32no—
42#5479—32no—
43C3×#442—31no—
44C3×C4×M16—31no—
45#5159—31no—
46#5155—31no—
47#5137—31no—
48#5135—31no—
49#5134—32no—
50#5018—32no—
51#4867—31no—
52#4858—31no—
53#4780—32no—
54#4768—32no—
55#4716—31no—
56#4716—31no—
57#4716—61no—
58#4711D311yescharacteristic, complemented
59#4710—32no—
60#4707D311yescharacteristic, complemented
61#4697—32no—
62#4696—31no—
63#4683—31no—
64C2×#634C2312yes—
65C2×C3×D12C2312yes—
66C2×C3×C4×D3—22no—
67C2×C3×C4×D3D412yes—
68C2×C3×C4×D3C2311yescharacteristic
69C2×#625—22no—
70C2×C32×C8C2311yescharacteristic
71C2×C32×C8C2311yescharacteristic
72C32×C42C2311yescharacteristic
73C4⋊(C3⋊Dic3)C2312yes—
74#3750—22no—
75C4×C3⋊Dic3—22no—
76#3746—22no—
77C3×(C2×D3)⋊C4—22no—
78C3×C4⋊Dic3C2312yes—
79C3×C4×Dic3D412yes—
80C3×C4×Dic3C2311yescharacteristic
81C2×C3×C3⋊C8C2311yescharacteristic
82C2×C3×C3⋊C8C2311yescharacteristic
83C3×D24—22no—
84C3×ΓL(1,𝔽25)—22no—
85C3×ΓL(1,𝔽25)—22no—
86#3724—22no—
87Dic3⋊Dic3—22no—
88Dic3⋊Dic3—22no—
89(C2×D3)⋊Dic3—22no—
90(C2×D3)⋊Dic3—22no—
91(C2×D3)⋊Dic3—22no—
92(C2×D3)⋊Dic3—22no—
93#3716—24no—
94#3183—91noSylow
95C2×C3×D8—31no—
96C2×C3×M16—31no—
97C2×C3×M16—31no—
98C3×C4×D4—32no—
99C2×C3×C42—31no—
100#938—32no—
101#936—32no—
102C2×#214—32no—
103#930—32no—
104#929—62no—
105C4×#67—62no—
106C4×#67—62no—
107#926—62no—
108#924—32no—
109C2×Dic12—31no—
110C2×Dic12—31no—
111C2×Dic12—61no—
112C2×D24C2×D311yescharacteristic
113C2×#204—32no—
114C2×ΓL(1,𝔽25)C2×D311yescharacteristic
115C2×ΓL(1,𝔽25)C2×D311yescharacteristic
116#897—32no—
117#890—32no—
118#883—62no—
119#879—62no—
120#876—62no—
121#875—32no—
122C4×D12C2×D312yes—
123#872—62no—
124C42×D3C2×D311yescharacteristic
125#870—32no—
126C4×Dic6—32no—
127C4×Dic6—32no—
128C4×Dic6—62no—
129C3×#106—31no—
130C3×#102—32no—
131C3×#97—21no—
132C3×#97—31no—
133C3×#97C2×D311yescharacteristic
134C3×#97C2×D311yescharacteristic
135C3×C4×C8—31no—
136C3×C4×C8—31no—
137#832—32no—
138#821—32no—
139#821C2×D312yes—
140#818—32no—
141#817—31no—
142#817—31no—
143#817—61no—
144#817C2×D311yescharacteristic
145#816—32no—
146#816—32no—
147#816—32no—
148#816—62no—
149C8×Dic3C2×D311yescharacteristic
150C8×Dic3C2×D311yescharacteristic
151#810—32no—
152#807—32no—
153#803C2×D311yescharacteristic
154C22×C3×D3—22no—
155C22×C3×D3C2×D411yescharacteristic
156C2×C32×C4C2×D412yes—
157C2×C32×C4C2411yescharacteristic
158C2×C3⋊Dic3—22no—
159C2×C3⋊Dic3—22no—
160#634—22no—
161#634—22no—
162C2×C3×Dic3—22no—
163C2×C3×Dic3C2×D411yescharacteristic
164C2×C3×Dic3C2×D412yes—
165C3×D12—22no—
166C3×D12—22no—
167C3×C4×D3—21no—
168C3×C4×D3—21no—
169C3×C4×D3—42no—
170C3×C4×D3—44no—
171#625—44no—
172C32×C8—21no—
173C32×C8#4112yes—
174C3×C3⋊C8—21no—
175C3×C3⋊C8#4112yes—
176#529—92no—
177#499—91no—
178#495—91no—
179#488—92no—
180#470—91no—
181#469—91no—
182#468—92no—
183#442—31no—
184#441—91no—
185#440—92no—
186C4×M16—31no—
187C2×C3×D4—32no—
188C22×C3×C4—31no—
189C22×C3×C4—32no—
190C22×C3×C4—62no—
191C2×#67—62no—
192C2×#67—62no—
193C2×D12C22×D312yes—
194C2×C4×D3—22no—
195C2×C4×D3D1212yes—
196C2×C4×D3C22×D311yescharacteristic
197C2×Dic6—32no—
198C2×Dic6—32no—
199C2×Dic6—62no—
200C3×D8—62no—
201C3×M16—62no—
202C3×M16—62no—
203C2×C3×C8—21no—
204C2×C3×C8—21no—
205C2×C3×C8—31no—
206C2×C3×C8—31no—
207C2×C3×C8C22×D311yescharacteristic
208C2×C3×C8C22×D311yescharacteristic
209C2×C3×C8C22×D311yescharacteristic
210C2×C3×C8C22×D311yescharacteristic
211C3×C4⋊C4—32no—
212C3×C22⋊C4—62no—
213C3×C42—21no—
214C3×C42—32no—
215C3×C42—31no—
216C3×C42C22×D311yescharacteristic
217C3×C42C22×D311yescharacteristic
218#217—62no—
219#217—62no—
220#217—62no—
221#217—62no—
222#214—64no—
223(C2×D3)⋊C4—22no—
224(C2×D3)⋊C4—62no—
225(C2×D3)⋊C4—62no—
226(C2×D3)⋊C4—62no—
227(C2×D3)⋊C4—62no—
228C4⋊Dic3—32no—
229C4⋊Dic3—32no—
230C4⋊Dic3—62no—
231C4⋊Dic3—62no—
232C4⋊Dic3—62no—
233C4⋊Dic3C22×D312yes—
234Dic3⋊C4—62no—
235Dic3⋊C4—62no—
236Dic3⋊C4—62no—
237Dic3⋊C4—62no—
238Dic3⋊C4—62no—
239Dic3⋊C4—62no—
240Dic3⋊C4—122no—
241C4×Dic3—62no—
242C4×Dic3—62no—
243C4×Dic3—122no—
244C4×Dic3D1212yes—
245C4×Dic3C22×D311yescharacteristic
246C2×C3⋊C8C22×D311yescharacteristic
247C2×C3⋊C8C22×D311yescharacteristic
248Dic12—64no—
249Dic12—62no—
250Dic12—62no—
251D24—22no—
252#204—64no—
253ΓL(1,𝔽25)—22no—
254ΓL(1,𝔽25)—22no—
255C22×C32C22×D411yescharacteristic
256C2×C3×D3—21no—
257C2×C3×D3—22no—
258C2×C3×D3—42no—
259C2×C3×D3—42no—
260C2×C3×D3—42no—
261C32×C4—22no—
262C32×C4C2×#4111yescharacteristic
263C32×C4C2×#4111yescharacteristic
264C3⋊Dic3—42no—
265C3⋊Dic3—42no—
266C3×Dic3—21no—
267C3×Dic3—22no—
268C3×Dic3—42no—
269C2×Q16—91no—
270C2×SD16—92no—
271C2×D8—31no—
272C2×M16—31no—
273C2×M16—31no—
274#126—182no—
275#125—92no—
276#124—92no—
277#123—182no—
278C22⋊Q8—92no—
279#121—92no—
280C4×Q8—92no—
281C4×D4—32no—
282C4×D4—182no—
283#117—182no—
284C2×C42—31no—
285#107—92no—
286#106—31no—
287#106—91no—
288#103—92no—
289#103—92no—
290#102—32no—
291#102—92no—
292#97—31no—
293#97D3211yescharacteristic
294C4×C8—31no—
295C4×C8—31no—
296C23×C3—31no—
297C23×C3—62no—
298C22×D3—22no—
299C22×D3C2×D1211yescharacteristic
300C3×D4—62no—
301C3×D4—62no—
302C2×C3×C4—21no—
303C2×C3×C4—22no—
304C2×C3×C4—32no—
305C2×C3×C4—31no—
306C2×C3×C4—61no—
307C2×C3×C4—61no—
308C2×C3×C4—62no—
309C2×C3×C4—122no—
310C2×C3×C4—124no—
311C2×C3×C4C2×D1212yes—
312C2×C3×C4D3×D412yes—
313C2×C3×C4C23×D311yescharacteristic
314C2×C3×C4C23×D311yescharacteristic
315#67—124no—
316#67—124no—
317C2×Dic3—22no—
318C2×Dic3—62no—
319C2×Dic3—62no—
320C2×Dic3—62no—
321C2×Dic3—62no—
322C2×Dic3—122no—
323C2×Dic3—122no—
324C2×Dic3C2×D1211yescharacteristic
325C2×Dic3C2×D1212yes—
326D12—22no—
327D12—22no—
328C4×D3—21no—
329C4×D3—21no—
330C4×D3—42no—
331C4×D3—44no—
332Dic6—64no—
333Dic6—62no—
334Dic6—62no—
335Dic6—62no—
336Dic6—62no—
337Dic6—122no—
338C3×C8—21no—
339C3×C8—21no—
340C3×C8—22no—
341C3×C8—32no—
342C3×C8—41no—
343C3×C8—61no—
344C3×C8#23512yes—
345C3×C8#23512yes—
346C3⋊C8—21no—
347C3⋊C8#23512yes—
348C2×C32#53211yescharacteristic
349C2×C32#57512yes—
350C3×D3—41no—
351C3×D3—82no—
352C2×Q8—92no—
353C2×D4—32no—
354C2×D4—182no—
355C22×C4—31no—
356C22×C4—32no—
357C22×C4—62no—
358Q16—182no—
359SD16—184no—
360D8—62no—
361M16—62no—
362M16—62no—
363C2×C8—31no—
364C2×C8—31no—
365C2×C8C2×D3211yescharacteristic
366C2×C8C2×D3211yescharacteristic
367C4⋊C4—32no—
368C4⋊C4—92no—
369C4⋊C4—182no—
370C4⋊C4—182no—
371C4⋊C4—182no—
372C4⋊C4—182no—
373C22⋊C4—62no—
374C22⋊C4—182no—
375C22⋊C4—182no—
376C22⋊C4—182no—
377C22⋊C4—182no—
378C42—31no—
379C42—32no—
380C42—182no—
381C42C2×D3211yescharacteristic
382C22×C3—21no—
383C22×C3—62no—
384C22×C3—61no—
385C22×C3—122no—
386C22×C3—122no—
387C22×C3—122no—
388C22×C3C22×D1211yescharacteristic
389C22×C3C2×D3×D411yescharacteristic
390C2×D3—21no—
391C2×D3—22no—
392C2×D3—42no—
393C2×D3—42no—
394C2×D3—42no—
395C3×C4—22no—
396C3×C4—22no—
397C3×C4—21no—
398C3×C4—21no—
399C3×C4—42no—
400C3×C4—62no—
401C3×C4—61no—
402C3×C4—122no—
403C3×C4C2×#23511yescharacteristic
404C3×C4C2×#23511yescharacteristic
405C3×C4C2×#23511yescharacteristic
406C3×C4D3×#4111yescharacteristic
407Dic3—21no—
408Dic3—22no—
409Dic3—42no—
410Dic3—124no—
411Dic3—122no—
412Dic3—122no—
413Dic3—122no—
414Dic3—122no—
415Dic3—242no—
416C32#318311yescharacteristic, complemented, Sylow
417C23—31no—
418C23—62no—
419Q8—182no—
420Q8—182no—
421D4—62no—
422D4—62no—
423D4—364no—
424C2×C4—32no—
425C2×C4—31no—
426C2×C4—61no—
427C2×C4—61no—
428C2×C4—62no—
429C2×C4—122no—
430C2×C4—124no—
431C2×C4—182no—
432C2×C4—182no—
433C2×C4D3×D1212yes—
434C2×C4C22×D3211yescharacteristic
435C8—21no—
436C8—32no—
437C8—61no—
438C8#379812yes—
439C2×C3—22no—
440C2×C3—21no—
441C2×C3—121no—
442C2×C3—242no—
443C2×C3#547711yescharacteristic
444C2×C3#554811yescharacteristic
445C2×C3#574812yes—
446C2×C3#577312yes—
447D3—41no—
448D3—82no—
449C22—62no—
450C22—61no—
451C22—122no—
452C22—122no—
453C22—122no—
454C22C2×D3×D1211yescharacteristic
455C4—22no—
456C4—62no—
457C4—61no—
458C4—122no—
459C4—362no—
460C4—362no—
461C4C2×#379811yescharacteristic
462C4D3×#23511yescharacteristic
463C3—21no—
464C3#7853411yescharacteristic, complemented
465C3#7986211yescharacteristic, complemented
466C2—121no—
467C2—242no—
468C2#1059396811yescharacteristic
469C2#1059471212yes—
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#97C22
socleC22×C32C22×D4
prime radical#10590836C2
hypercenter#97D32
hypocenterC32#3183
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
1. #10593974C2semidirect
2. #10592415C2semidirect
3. C3×#4711C2semidirect
4. C3×#4707C2semidirect
5. #10590871C2semidirect
6. #10590864C2semidirect
7. #10590863C2semidirect
8. #10590853C2semidirect
10. #10590828C2semidirect
11. #10590360C2semidirect
58. #4711D3semidirect
60. #4707D3semidirect
416. C32#3183semidirect
464. C3#78534semidirect
465. C3#79862semidirect

Maximal subgroups

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

subgroupindex
#105939742
#105924152
C3×#47112
C3×#47072
#105908712
#105908642
#105908632
#105908532
#105908362
#105908282
#105903602
#798623
#785343