Finite Group Databasebeta

← #11876956

Subgroups — #11876956

Order 1152.

805 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594464C212yesmaximal, complemented
2#10592564C211yesmaximal, characteristic
3C3×#4858C211yesmaximal, characteristic, complemented
4C3×#4853C211yesmaximal, characteristic, complemented
5#10590865C211yesmaximal, characteristic, complemented
6#10590858C211yesmaximal, characteristic, complemented
7#10590768C211yesmaximal, characteristic, complemented
8#10590664C211yesmaximal, characteristic, complemented
9#10590537C212yesmaximal, complemented
10#10590522C212yesmaximal, complemented
11#10590457C212yesmaximal, complemented
12#81911—31nomaximal
13#79826—31nomaximal
14C2×#3745C2211yescharacteristic
15C2×#3743C2211yescharacteristic
16#64104C2212yes—
17C2×C3×Dic12C2211yescharacteristic
18C3×#890C2212yes—
19C3×#887C2212yes—
20#63897—22no—
21#63894—22no—
22#63894C2212yes—
23C4×#624C2211yescharacteristic
24#63871C2212yes—
25#63864C2212yes—
26#63848—22no—
27#63836—22no—
28C2×#3717C2212yes—
29C2×#3712C2211yescharacteristic
30C32×#106C2211yescharacteristic
31#63636C2212yes—
32C3×#817C2211yescharacteristic
33C3×#815C2211yescharacteristic
34C3×C8×Dic3C2211yescharacteristic
35C3×#810C2212yes—
36C3×#807C2212yes—
37#63565C2212yes—
38#63564C2212yes—
39#63554C2211yescharacteristic
40Dic3×C3⋊C8C2211yescharacteristic
41#5691—32no—
42#5580—32no—
43C3×#499—31no—
44C3×#441—31no—
45#5191—31no—
46#5189—31no—
47#5068—32no—
48#5026—32no—
49#4889—32no—
50#4886—32no—
51#4869—31no—
52#4867—31no—
53#4865—31no—
54#4865—31no—
55#4865—61no—
56#4858D311yescharacteristic, complemented
57#4853D311yescharacteristic, complemented
58#4812—32no—
59#4800—32no—
60#4711—31no—
61#4707—31no—
62#4696—31no—
63C4×ΓL(1,𝔽25)—31no—
64C2×C4⋊(C3⋊D3)—22no—
65C2×C4⋊(C3⋊D3)C2312yes—
66C2×C4×C3⋊D3C2311yescharacteristic
67C2×C3×Dic6C2312yes—
68C2×#624—22no—
69C2×#624D412yes—
70C2×C32×C8C2311yescharacteristic
71C32×C4⋊C4C2312yes—
72#3752—22no—
73C2×C3⋊(C3⋊C8)C2311yescharacteristic
74#3745—22no—
75#3743—22no—
76C3×C4⋊Dic3—22no—
77C3×C4⋊Dic3C2312yes—
78C3×Dic3⋊C4—22no—
79C3×Dic3⋊C4—22no—
80C3×C4×Dic3—22no—
81C3×C4×Dic3C2311yescharacteristic
82C3×C4×Dic3C2311yescharacteristic
83C2×C3×C3⋊C8C2311yescharacteristic
84C2×C3×C3⋊C8C2311yescharacteristic
85C3×Dic12—22no—
86Dic3⋊Dic3—22no—
87#3722—22no—
88#3722—22no—
89#3722—22no—
90#3722—22no—
91Dic32D412yes—
92#3717—24no—
93#3712—22no—
94#3183—91noSylow
95C2×C3×Q16—31no—
96C3×#125—32no—
97C3×C4×Q8—32no—
98#947—32no—
99#946—32no—
100C2×#215—32no—
101C2×Dic12C2×D311yescharacteristic
102C2×D24—31no—
103C2×D24—31no—
104C2×D24—61no—
105C2×#204—32no—
106C2×ΓL(1,𝔽25)—31no—
107C2×ΓL(1,𝔽25)—31no—
108C2×ΓL(1,𝔽25)—31no—
109C2×ΓL(1,𝔽25)—31no—
110C2×ΓL(1,𝔽25)—61no—
111#898—62no—
112#898—62no—
113#897—32no—
114#895—32no—
115#895—32no—
116#895—62no—
117#894—62no—
118#894—62no—
119#893—32no—
120#893—62no—
121#892—62no—
122#890C2×D312yes—
123#887C2×D312yes—
124#875—32no—
125C4×D12—32no—
126C4×D12—62no—
127#872—62no—
128C42×D3—31no—
129C42×D3—31no—
130C3×#107—32no—
131C3×#106—21no—
132C3×#106—31no—
133C3×#106C2×D311yescharacteristic
134C3×#106C2×D311yescharacteristic
135C3×#103—32no—
136C3×#97—31no—
137C3×C4×C8—31no—
138#835—32no—
139#821—32no—
140#817C2×D311yescharacteristic
141#815—31no—
142#815C2×D311yescharacteristic
143C8×Dic3—31no—
144C8×Dic3C2×D311yescharacteristic
145#810—32no—
146#810C2×D312yes—
147#809—32no—
148#809—32no—
149#809—32no—
150#809—62no—
151#807C2×D312yes—
152#803—31no—
153C4×C3⋊C8—31no—
154C22×C3⋊D3—22no—
155C22×C3⋊D3C2×D411yescharacteristic
156C2×C32×C4—22no—
157C2×C32×C4C2411yescharacteristic
158C2×C3⋊Dic3C2×D411yescharacteristic
159C4⋊(C3⋊D3)—22no—
160C4⋊(C3⋊D3)—22no—
161C4⋊(C3⋊D3)—44no—
162C4×C3⋊D3—21no—
163C4×C3⋊D3—21no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3C2×D412yes—
167C2×C3×Dic3C2×D412yes—
168C3×Dic6—22no—
169C3×Dic6—22no—
170#624—42no—
171#624—44no—
172C32×C8#4112yes—
173C3⋊(C3⋊C8)—21no—
174C3×C3⋊C8—21no—
175C3×C3⋊C8#4112yes—
176#529—92no—
177#499—31no—
178#495—91no—
179#488—92no—
180#470—91no—
181#469—91no—
182#468—92no—
183#442—91no—
184#441—31no—
185#440—92no—
186C4×M16—91no—
187C2×C3×Q8—32no—
188C2×D12—32no—
189C2×D12—32no—
190C2×D12—62no—
191C2×D12—62no—
192C2×D12—62no—
193C2×D12—122no—
194C2×C4×D3—31no—
195C2×C4×D3—31no—
196C2×C4×D3—32no—
197C2×C4×D3—32no—
198C2×C4×D3—61no—
199C2×C4×D3—62no—
200C2×C4×D3—62no—
201C2×Dic6C22×D312yes—
202C3×Q16—62no—
203C2×C3×C8—21no—
204C2×C3×C8—31no—
205C2×C3×C8—31no—
206C2×C3×C8C22×D311yescharacteristic
207C2×C3×C8C22×D311yescharacteristic
208C3×C4⋊C4—22no—
209C3×C4⋊C4—32no—
210C3×C4⋊C4—62no—
211C3×C4⋊C4—62no—
212C3×C4⋊C4—62no—
213C3×C4⋊C4C22×D312yes—
214C3×C4⋊C4C22×D312yes—
215C3×C42—31no—
216C3×C42—31no—
217C3×C42—62no—
218#215—64no—
219(C2×D3)⋊C4—62no—
220(C2×D3)⋊C4—62no—
221(C2×D3)⋊C4—62no—
222(C2×D3)⋊C4—62no—
223(C2×D3)⋊C4—62no—
224(C2×D3)⋊C4—62no—
225(C2×D3)⋊C4—62no—
226(C2×D3)⋊C4—62no—
227(C2×D3)⋊C4—62no—
228(C2×D3)⋊C4—62no—
229(C2×D3)⋊C4—122no—
230C4⋊Dic3—22no—
231C4⋊Dic3—62no—
232C4⋊Dic3C22×D312yes—
233Dic3⋊C4—22no—
234Dic3⋊C4—22no—
235Dic3⋊C4—62no—
236C4×Dic3—22no—
237C4×Dic3—32no—
238C4×Dic3—32no—
239C4×Dic3C22×D311yescharacteristic
240C4×Dic3C22×D311yescharacteristic
241C2×C3⋊C8—31no—
242C2×C3⋊C8—31no—
243C2×C3⋊C8—61no—
244C2×C3⋊C8C22×D311yescharacteristic
245C2×C3⋊C8C22×D311yescharacteristic
246Dic12—22no—
247D24—62no—
248D24—62no—
249D24—122no—
250#204—64no—
251ΓL(1,𝔽25)—62no—
252ΓL(1,𝔽25)—62no—
253ΓL(1,𝔽25)—62no—
254ΓL(1,𝔽25)—62no—
255ΓL(1,𝔽25)—122no—
256C22×C32C22×D411yescharacteristic
257C2×C3⋊D3—21no—
258C2×C3⋊D3—22no—
259C2×C3⋊D3—42no—
260C2×C3⋊D3—42no—
261C2×C3⋊D3—42no—
262C32×C4—42no—
263C32×C4C2×#4111yescharacteristic
264C32×C4C2×#4111yescharacteristic
265C3⋊Dic3—21no—
266C3×Dic3—22no—
267C3×Dic3—22no—
268C3×Dic3—42no—
269C3×Dic3—42no—
270C2×Q16—31no—
271C2×SD16—92no—
272C2×D8—91no—
273C2×M16—91no—
274C2×M16—91no—
275#126—182no—
276#125—32no—
277#124—92no—
278#123—182no—
279C22⋊Q8—92no—
280#121—92no—
281C4×Q8—32no—
282C4×D4—92no—
283C4×D4—182no—
284#117—182no—
285C2×C42—91no—
286#107—32no—
287#106—31no—
288#106D3211yescharacteristic
289#103—32no—
290#103—92no—
291#102—92no—
292#102—92no—
293#97—31no—
294#97—91no—
295C4×C8—31no—
296C4×C8—91no—
297C22×D3—31no—
298C22×D3—31no—
299C22×D3—61no—
300C22×D3—62no—
301C22×D3—62no—
302C22×D3—122no—
303C3×Q8—62no—
304C3×Q8—62no—
305C2×C3×C4—22no—
306C2×C3×C4—22no—
307C2×C3×C4—21no—
308C2×C3×C4—32no—
309C2×C3×C4—32no—
310C2×C3×C4—42no—
311C2×C3×C4—62no—
312C2×C3×C4—62no—
313C2×C3×C4C23×D311yescharacteristic
314C2×C3×C4C23×D311yescharacteristic
315C2×Dic3—22no—
316C2×Dic3—22no—
317C2×Dic3—31no—
318C2×Dic3—31no—
319C2×Dic3—61no—
320C2×Dic3D3×D412yes—
321C2×Dic3D3×D412yes—
322D12—62no—
323D12—62no—
324D12—62no—
325D12—62no—
326D12—122no—
327D12—122no—
328D12—124no—
329D12—124no—
330D12—244no—
331C4×D3—61no—
332C4×D3—61no—
333C4×D3—61no—
334C4×D3—61no—
335C4×D3—121no—
336C4×D3—121no—
337C4×D3—122no—
338C4×D3—122no—
339C4×D3—124no—
340C4×D3—124no—
341Dic6—22no—
342Dic6—22no—
343C3×C8—22no—
344C3×C8—32no—
345C3×C8—61no—
346C3×C8#23512yes—
347C3×C8#23912yes—
348C3⋊C8—21no—
349C3⋊C8—61no—
350C3⋊C8—61no—
351C3⋊C8—121no—
352C3⋊C8#23912yes—
353C2×C32#53211yescharacteristic
354C2×C32#57512yes—
355C3⋊D3—41no—
356C3⋊D3—82no—
357C2×Q8—32no—
358C2×D4—92no—
359C2×D4—182no—
360C22×C4—92no—
361C22×C4—91no—
362C22×C4—182no—
363Q16—62no—
364SD16—184no—
365D8—182no—
366M16—182no—
367M16—182no—
368C2×C8—31no—
369C2×C8—31no—
370C2×C8—91no—
371C2×C8C2×D3211yescharacteristic
372C4⋊C4—32no—
373C4⋊C4—62no—
374C4⋊C4—62no—
375C4⋊C4—62no—
376C4⋊C4—182no—
377C4⋊C4C2×D3212yes—
378C22⋊C4—182no—
379C22⋊C4—182no—
380C22⋊C4—182no—
381C22⋊C4—182no—
382C22⋊C4—182no—
383C42—31no—
384C42—31no—
385C42—62no—
386C42—92no—
387C22×C3—21no—
388C22×C3C2×D3×D411yescharacteristic
389C22×C3C2×D3×D411yescharacteristic
390C2×D3—61no—
391C2×D3—62no—
392C2×D3—62no—
393C2×D3—61no—
394C2×D3—121no—
395C2×D3—122no—
396C2×D3—122no—
397C2×D3—122no—
398C2×D3—122no—
399C2×D3—122no—
400C2×D3—122no—
401C2×D3—122no—
402C2×D3—242no—
403C2×D3—242no—
404C2×D3—242no—
405C3×C4—21no—
406C3×C4—21no—
407C3×C4—42no—
408C3×C4—42no—
409C3×C4—62no—
410C3×C4—62no—
411C3×C4—82no—
412C3×C4—122no—
413C3×C4—122no—
414C3×C4C2×#23511yescharacteristic
415C3×C4C2×#23911yescharacteristic
416C3×C4C2×#23911yescharacteristic
417C3×C4D3×#4111yescharacteristic
418Dic3—22no—
419Dic3—22no—
420Dic3—42no—
421Dic3—42no—
422Dic3—61no—
423Dic3—61no—
424Dic3—121no—
425C32#318311yescharacteristic, complemented, Sylow
426C23—91no—
427C23—182no—
428Q8—62no—
429Q8—62no—
430D4—182no—
431D4—182no—
432D4—364no—
433C2×C4—22no—
434C2×C4—32no—
435C2×C4—32no—
436C2×C4—62no—
437C2×C4—62no—
438C2×C4—91no—
439C2×C4—181no—
440C2×C4—181no—
441C2×C4—362no—
442C2×C4—364no—
443C2×C4C22×D3211yescharacteristic
444C8—32no—
445C8—61no—
446C8—181no—
447C8#379912yes—
448C2×C3—22no—
449C2×C3—21no—
450C2×C3#554811yescharacteristic
451C2×C3#572511yescharacteristic
452C2×C3#576812yes—
453C2×C3#577712yes—
454D3—121no—
455D3—121no—
456D3—241no—
457D3—242no—
458D3—242no—
459D3—482no—
460C22—182no—
461C22—181no—
462C22—362no—
463C22—362no—
464C22—362no—
465C22D32×D411yescharacteristic
466C4—42no—
467C4—62no—
468C4—62no—
469C4—122no—
470C4—122no—
471C4—181no—
472C4C2×#379911yescharacteristic
473C4D3×#23911yescharacteristic
474C3—21no—
475C3#7982611yescharacteristic, complemented
476C3#8191111yescharacteristic, complemented
477C2—361no—
478C2—722no—
479C2#1059451811yescharacteristic
480C2#1059474612yes—
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radical#10592564C2
hypercenter#106D32
hypocenterC32#3183
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
1. #10594464C2semidirect
3. C3×#4858C2semidirect
4. C3×#4853C2semidirect
5. #10590865C2semidirect
6. #10590858C2semidirect
7. #10590768C2semidirect
8. #10590664C2semidirect
9. #10590537C2semidirect
10. #10590522C2semidirect
11. #10590457C2semidirect
56. #4858D3semidirect
57. #4853D3semidirect
425. C32#3183semidirect
475. C3#79826semidirect
476. C3#81911semidirect

Maximal subgroups

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

subgroupindex
#105944642
#105925642
C3×#48582
C3×#48532
#105908652
#105908582
#105907682
#105906642
#105905372
#105905222
#105904572
#819113
#798263