Finite Group Databasebeta

← #11876953

Subgroups — #11876953

Order 1152.

795 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594447C212yesmaximal, complemented
2#10592566C211yesmaximal, characteristic, complemented
3C3×#4869C211yesmaximal, characteristic, complemented
4C3×#4858C211yesmaximal, characteristic, complemented
5#10590864C211yesmaximal, characteristic, complemented
6#10590846C211yesmaximal, characteristic
7#10590810C211yesmaximal, characteristic, complemented
8#10590664C211yesmaximal, characteristic, complemented
9#10590590C212yesmaximal, complemented
10#10590533C212yesmaximal, complemented
11#10590506C212yesmaximal, complemented
12#81911—31nomaximal
13#79862—31nomaximal
14C2×#3746C2211yescharacteristic
15C2×#3743C2211yescharacteristic
16#64106C2212yes—
17C2×C3×D24C2211yescharacteristic
18C3×#893C2212yes—
19C3×#890C2212yes—
20#63916C2212yes—
21#63904—22no—
22C4×#624C2211yescharacteristic
23#63861—22no—
24#63860C2212yes—
25#63854—22no—
26#63844C2212yes—
27#63841—22no—
28C2×#3716C2212yes—
29C2×#3712C2211yescharacteristic
30C32×#106C2211yescharacteristic
31#63637C2212yes—
32C3×#817C2211yescharacteristic
33C3×#815C2211yescharacteristic
34C3×C8×Dic3C2211yescharacteristic
35C3×#809C2212yes—
36C3×#807C2212yes—
37#63567C2212yes—
38#63562C2212yes—
39#63554C2211yescharacteristic
40Dic3×C3⋊C8C2211yescharacteristic
41#5691—32no—
42#5557—32no—
43C3×#499—31no—
44C3×#442—31no—
45#5159—31no—
46#5155—31no—
47#5068—32no—
48#5018—32no—
49#4889—32no—
50#4886—32no—
51#4869D311yescharacteristic, complemented
52#4867—31no—
53#4867—31no—
54#4867—61no—
55#4865—31no—
56#4858D311yescharacteristic, complemented
57#4853—31no—
58#4780—32no—
59#4768—32no—
60#4716—31no—
61#4707—31no—
62#4696—31no—
63C4×ΓL(1,𝔽25)—31no—
64C2×C4×C3⋊D3C2311yescharacteristic
65C2×#634C2312yes—
66C2×C3×D12C2312yes—
67C2×C3×C4×D3—22no—
68C2×#626—22no—
69C2×#624D412yes—
70C2×C32×C8C2311yescharacteristic
71C32×C4⋊C4C2312yes—
72#3752—22no—
73C4⋊(C3⋊Dic3)—22no—
74C2×C3⋊(C3⋊C8)C2311yescharacteristic
75#3746—22no—
76#3743—22no—
77C3×(C2×D3)⋊C4—22no—
78C3×C4⋊Dic3—22no—
79C3×C4⋊Dic3C2312yes—
80C3×Dic3⋊C4—22no—
81C3×C4×Dic3C2311yescharacteristic
82C3×C4×Dic3C2311yescharacteristic
83C2×C3×C3⋊C8C2311yescharacteristic
84C2×C3×C3⋊C8C2311yescharacteristic
85C3×D24—22no—
86#3724—22no—
87(C2×D3)⋊Dic3—22no—
88(C2×D3)⋊Dic3—22no—
89(C2×D3)⋊Dic3—22no—
90Dic32—22no—
91Dic32D412yes—
92#3716—24no—
93#3712—22no—
94#3183—91noSylow
95C2×C3×D8—31no—
96C3×#125—32no—
97C3×C4×D4—32no—
98#938—32no—
99#936—32no—
100C2×#214—32no—
101C4×#67—62no—
102#926—62no—
103C2×Dic12—31no—
104C2×Dic12—31no—
105C2×Dic12—61no—
106C2×D24C2×D311yescharacteristic
107C2×#204—32no—
108C2×ΓL(1,𝔽25)—31no—
109C2×ΓL(1,𝔽25)—31no—
110C2×ΓL(1,𝔽25)—31no—
111C2×ΓL(1,𝔽25)—31no—
112C2×ΓL(1,𝔽25)—61no—
113#898—62no—
114#897—32no—
115#897—32no—
116#897—62no—
117#895—32no—
118#894—62no—
119#893—62no—
120#893C2×D312yes—
121#892—62no—
122#890C2×D312yes—
123#887—32no—
124#883—62no—
125#879—62no—
126#875—32no—
127C42×D3—31no—
128C42×D3—31no—
129C4×Dic6—32no—
130C3×#107—32no—
131C3×#106—21no—
132C3×#106—31no—
133C3×#106C2×D311yescharacteristic
134C3×#106C2×D311yescharacteristic
135C3×#102—32no—
136C3×#97—31no—
137C3×C4×C8—31no—
138#832—32no—
139#817C2×D311yescharacteristic
140#816—32no—
141#815—31no—
142#815C2×D311yescharacteristic
143C8×Dic3—31no—
144C8×Dic3C2×D311yescharacteristic
145#810—32no—
146#810—32no—
147#810—32no—
148#810—62no—
149#809—32no—
150#809C2×D312yes—
151#807C2×D312yes—
152#803—31no—
153C4×C3⋊C8—31no—
154C22×C3⋊D3C2×D411yescharacteristic
155C22×C3×D3—22no—
156C2×C32×C4—22no—
157C2×C32×C4C2411yescharacteristic
158C2×C3⋊Dic3—22no—
159C2×C3⋊Dic3C2×D411yescharacteristic
160C4×C3⋊D3—21no—
161C4×C3⋊D3—21no—
162#634—22no—
163#634—22no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3C2×D412yes—
166C2×C3×Dic3C2×D412yes—
167C3×D12—22no—
168C3×D12—22no—
169C3×C4×D3—44no—
170#626—44no—
171#624—42no—
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—31no—
184#441—91no—
185#440—92no—
186C4×M16—91no—
187C2×C3×D4—32no—
188C22×C3×C4—62no—
189C2×#67—62no—
190C2×D12—62no—
191C2×D12C22×D312yes—
192C2×C4×D3—22no—
193C2×C4×D3—31no—
194C2×C4×D3—31no—
195C2×C4×D3—32no—
196C2×C4×D3—32no—
197C2×C4×D3—61no—
198C2×Dic6—32no—
199C2×Dic6—32no—
200C2×Dic6—62no—
201C3×D8—62no—
202C2×C3×C8—21no—
203C2×C3×C8—31no—
204C2×C3×C8—31no—
205C2×C3×C8C22×D311yescharacteristic
206C2×C3×C8C22×D311yescharacteristic
207C3×C4⋊C4—22no—
208C3×C4⋊C4—32no—
209C3×C4⋊C4—62no—
210C3×C4⋊C4—62no—
211C3×C4⋊C4C22×D312yes—
212C3×C4⋊C4C22×D312yes—
213C3×C22⋊C4—62no—
214C3×C42—31no—
215C3×C42—31no—
216#217—62no—
217#217—62no—
218#217—62no—
219#214—64no—
220(C2×D3)⋊C4—22no—
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—122no—
227C4⋊Dic3—22no—
228C4⋊Dic3—62no—
229C4⋊Dic3—62no—
230C4⋊Dic3—122no—
231C4⋊Dic3C22×D312yes—
232Dic3⋊C4—22no—
233Dic3⋊C4—62no—
234Dic3⋊C4—62no—
235C4×Dic3—32no—
236C4×Dic3—32no—
237C4×Dic3—62no—
238C4×Dic3—62no—
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—62no—
247Dic12—62no—
248Dic12—122no—
249D24—22no—
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—42no—
267C3×Dic3—22no—
268C3×Dic3—22no—
269C3×Dic3—42no—
270C2×Q16—91no—
271C2×SD16—92no—
272C2×D8—31no—
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—92no—
282C4×D4—32no—
283C4×D4—182no—
284#117—182no—
285C2×C42—91no—
286#107—32no—
287#106—31no—
288#106D3211yescharacteristic
289#103—92no—
290#103—92no—
291#102—32no—
292#102—92no—
293#97—31no—
294#97—91no—
295C4×C8—31no—
296C4×C8—91no—
297C23×C3—62no—
298C22×D3—22no—
299C22×D3—31no—
300C22×D3—31no—
301C22×D3—61no—
302C3×D4—62no—
303C3×D4—62no—
304C2×C3×C4—22no—
305C2×C3×C4—22no—
306C2×C3×C4—21no—
307C2×C3×C4—32no—
308C2×C3×C4—32no—
309C2×C3×C4—42no—
310C2×C3×C4—62no—
311C2×C3×C4—124no—
312C2×C3×C4C23×D311yescharacteristic
313C2×C3×C4C23×D311yescharacteristic
314#67—124no—
315C2×Dic3—22no—
316C2×Dic3—31no—
317C2×Dic3—31no—
318C2×Dic3—61no—
319C2×Dic3—62no—
320C2×Dic3—62no—
321C2×Dic3—122no—
322C2×Dic3D3×D412yes—
323C2×Dic3D3×D412yes—
324D12—22no—
325D12—22no—
326D12—124no—
327C4×D3—44no—
328C4×D3—61no—
329C4×D3—61no—
330C4×D3—61no—
331C4×D3—61no—
332C4×D3—121no—
333C4×D3—121no—
334C4×D3—122no—
335C4×D3—122no—
336Dic6—62no—
337Dic6—62no—
338Dic6—62no—
339Dic6—62no—
340Dic6—122no—
341Dic6—122no—
342C3×C8—22no—
343C3×C8—32no—
344C3×C8—61no—
345C3×C8#23512yes—
346C3×C8#23912yes—
347C3⋊C8—21no—
348C3⋊C8—61no—
349C3⋊C8—61no—
350C3⋊C8—121no—
351C3⋊C8#23912yes—
352C2×C32#53211yescharacteristic
353C2×C32#57512yes—
354C3⋊D3—41no—
355C3×D3—82no—
356C2×Q8—92no—
357C2×D4—32no—
358C2×D4—182no—
359C22×C4—62no—
360C22×C4—92no—
361C22×C4—91no—
362Q16—182no—
363SD16—184no—
364D8—62no—
365M16—182no—
366M16—182no—
367C2×C8—31no—
368C2×C8—31no—
369C2×C8—91no—
370C2×C8C2×D3211yescharacteristic
371C4⋊C4—32no—
372C4⋊C4—62no—
373C4⋊C4—62no—
374C4⋊C4—182no—
375C4⋊C4—182no—
376C4⋊C4C2×D3212yes—
377C22⋊C4—62no—
378C22⋊C4—182no—
379C22⋊C4—182no—
380C22⋊C4—182no—
381C22⋊C4—182no—
382C42—31no—
383C42—31no—
384C42—92no—
385C42—182no—
386C22×C3—21no—
387C22×C3—122no—
388C22×C3—122no—
389C22×C3—122no—
390C22×C3C2×D3×D411yescharacteristic
391C22×C3C2×D3×D411yescharacteristic
392C2×D3—42no—
393C2×D3—42no—
394C2×D3—42no—
395C2×D3—61no—
396C2×D3—62no—
397C2×D3—62no—
398C2×D3—61no—
399C2×D3—121no—
400C2×D3—122no—
401C3×C4—21no—
402C3×C4—21no—
403C3×C4—42no—
404C3×C4—42no—
405C3×C4—62no—
406C3×C4—62no—
407C3×C4—82no—
408C3×C4—122no—
409C3×C4C2×#23511yescharacteristic
410C3×C4C2×#23911yescharacteristic
411C3×C4C2×#23911yescharacteristic
412C3×C4D3×#4111yescharacteristic
413Dic3—22no—
414Dic3—22no—
415Dic3—42no—
416Dic3—61no—
417Dic3—61no—
418Dic3—121no—
419Dic3—122no—
420Dic3—122no—
421Dic3—242no—
422C32#318311yescharacteristic, complemented, Sylow
423C23—62no—
424C23—91no—
425Q8—182no—
426Q8—182no—
427D4—62no—
428D4—62no—
429D4—364no—
430C2×C4—22no—
431C2×C4—32no—
432C2×C4—32no—
433C2×C4—62no—
434C2×C4—91no—
435C2×C4—124no—
436C2×C4—181no—
437C2×C4—181no—
438C2×C4—182no—
439C2×C4—362no—
440C2×C4C22×D3211yescharacteristic
441C8—32no—
442C8—61no—
443C8—181no—
444C8#379912yes—
445C2×C3—22no—
446C2×C3—21no—
447C2×C3—242no—
448C2×C3#554811yescharacteristic
449C2×C3#572511yescharacteristic
450C2×C3#576812yes—
451C2×C3#577312yes—
452D3—82no—
453D3—121no—
454D3—121no—
455D3—241no—
456C22—122no—
457C22—122no—
458C22—122no—
459C22—182no—
460C22—181no—
461C22D32×D411yescharacteristic
462C4—42no—
463C4—62no—
464C4—62no—
465C4—122no—
466C4—181no—
467C4—362no—
468C4C2×#379911yescharacteristic
469C4D3×#23911yescharacteristic
470C3—21no—
471C3#7986211yescharacteristic, complemented
472C3#8191111yescharacteristic, complemented
473C2—242no—
474C2—361no—
475C2#1059451811yescharacteristic
476C2#1059474512yes—
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radical#10590846C2
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. #10594447C2semidirect
2. #10592566C2semidirect
3. C3×#4869C2semidirect
4. C3×#4858C2semidirect
5. #10590864C2semidirect
7. #10590810C2semidirect
8. #10590664C2semidirect
9. #10590590C2semidirect
10. #10590533C2semidirect
11. #10590506C2semidirect
51. #4869D3semidirect
56. #4858D3semidirect
422. C32#3183semidirect
471. C3#79862semidirect
472. C3#81911semidirect

Maximal subgroups

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

subgroupindex
#105944472
#105925662
C3×#48692
C3×#48582
#105908642
#105908462
#105908102
#105906642
#105905902
#105905332
#105905062
#819113
#798623