Finite Group Databasebeta

← #11876948

Subgroups — #11876948

Order 1152.

805 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#10595376C212yesmaximal, complemented
2#10592890C211yesmaximal, characteristic, complemented
3C3×#5189C211yesmaximal, characteristic, complemented
4C3×#5184C211yesmaximal, characteristic, complemented
5#10591589C212yesmaximal, complemented
6#10591540C212yesmaximal, complemented
7#10591539C212yesmaximal, complemented
8#10590874C211yesmaximal, characteristic, complemented
9#10590835C211yesmaximal, characteristic
10#10590768C211yesmaximal, characteristic, complemented
11#10590667C211yesmaximal, characteristic, complemented
12#80892—31nomaximal
13#79826—31nomaximal
14C2×C32×Q16C2211yescharacteristic
15#64156C2212yes—
16C2×#3755C2212yes—
17C2×#3745C2211yescharacteristic
18C3×#946C2212yes—
19C3×Q8×Dic3C2212yes—
20C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
21#63909C2212yes—
22#63894C2212yes—
23#63890—22no—
24#63880—22no—
25C4×D3×Dic3C2211yescharacteristic
26#63872C2212yes—
27#63848—22no—
28#63836—22no—
29C2×#3711C2211yescharacteristic
30C8×C3⋊Dic3C2211yescharacteristic
31C3×#835C2212yes—
32C3×#835C2212yes—
33C3×#817C2211yescharacteristic
34C3×#817C2211yescharacteristic
35C3×#815C2211yescharacteristic
36#63576C2212yes—
37#63564C2212yes—
38#63564C2212yes—
39#63554C2211yescharacteristic
40#63553C2211yescharacteristic
41#5624—32no—
42#5580—32no—
43C3×#470—31no—
44C3×#441—31no—
45#5191—31no—
46#5191—31no—
47#5191—61no—
48#5189D311yescharacteristic, complemented
49#5184D311yescharacteristic, complemented
50#5135—31no—
51Dic3×M16—31no—
52#5049—32no—
53#5026—32no—
54#4869—31no—
55#4865—31no—
56#4858—31no—
57#4858—31no—
58#4817—32no—
59#4812—32no—
60#4800—32no—
61#4800—32no—
62#4711—31no—
63#4707—31no—
64C2×C32×Q8C2312yes—
65C2×C4⋊(C3⋊D3)C2312yes—
66C2×C3×C4×D3C2311yescharacteristic
67C2×#626—22no—
68C2×#624—22no—
69C2×D3×Dic3D412yes—
70C32×Q16—22no—
71C2×C32×C8C2311yescharacteristic
72#3755—24no—
73#3752—22no—
74#3752—22no—
75C4×C3⋊Dic3C2311yescharacteristic
76C2×C3⋊(C3⋊C8)C2311yescharacteristic
77#3745—22no—
78C3×(C2×D3)⋊C4—22no—
79C3×C4⋊Dic3—22no—
80C3×C4⋊Dic3C2312yes—
81C3×C4⋊Dic3C2312yes—
82C3×Dic3⋊C4—22no—
83C3×C4×Dic3—22no—
84C3×C4×Dic3C2311yescharacteristic
85C2×C3×C3⋊C8C2311yescharacteristic
86C2×C3×C3⋊C8C2311yescharacteristic
87C3×ΓL(1,𝔽25)—22no—
88Dic3⋊Dic3—22no—
89Dic3⋊Dic3—22no—
90#3722—22no—
91#3722—22no—
92Dic32D412yes—
93#3711—22no—
94#3183—91noSylow
95C2×C3×Q16—21no—
96C2×C3×Q16C2×D311yescharacteristic
97C2×C3×Q16C2×D311yescharacteristic
98C2×C3×M16—31no—
99C3×C22⋊Q8—32no—
100C3×C4×Q8—32no—
101#947—32no—
102#947—32no—
103#947—62no—
104#946C2×D312yes—
105Q8×Dic3C2×D312yes—
106C2×#215—32no—
107C2×#215—32no—
108C2×#215—62no—
109#930—32no—
110C2×C4×Dic3—31no—
111C2×#208—31no—
112C2×D24—31no—
113C2×D24—31no—
114C2×D24—61no—
115C2×ΓL(1,𝔽25)—31no—
116C2×ΓL(1,𝔽25)C2×D311yescharacteristic
117#898—62no—
118#898—62no—
119#895—32no—
120#894—62no—
121#893—32no—
122#892—62no—
123#890—32no—
124#890—32no—
125#886—62no—
126#67⋊C4—62no—
127C4×D12—32no—
128C4×D12—62no—
129#872—62no—
130C42×D3—31no—
131C3×#106—31no—
132C3×#106—31no—
133C3×#103—32no—
134C3×#103—32no—
135C3×#97—31no—
136#835C2×D312yes—
137#835C2×D312yes—
138#821—32no—
139#821—32no—
140#817C2×D311yescharacteristic
141#817C2×D311yescharacteristic
142#815—31no—
143#815C2×D311yescharacteristic
144C8×Dic3—31no—
145C8×Dic3—31no—
146C8×Dic3—31no—
147C8×Dic3—31no—
148C8×Dic3—61no—
149#809—32no—
150#809—32no—
151#807—32no—
152#807—32no—
153#803—31no—
154C22×C3⋊D3—22no—
155C22×C3×D3C2×D411yescharacteristic
156C32×Q8—22no—
157C32×Q8—22no—
158C2×C32×C4—22no—
159C2×C32×C4C2411yescharacteristic
160C2×C3⋊Dic3C2×D412yes—
161C4⋊(C3⋊D3)—22no—
162C4⋊(C3⋊D3)—22no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3C2×D411yescharacteristic
166C2×C3×Dic3C2×D412yes—
167C3×C4×D3—21no—
168C3×C4×D3—21no—
169#626—44no—
170#624—44no—
171D3×Dic3—42no—
172C32×C8#4112yes—
173C3⋊(C3⋊C8)#4112yes—
174C3×C3⋊C8—21no—
175C3×C3⋊C8—21no—
176#529—92no—
177#499—91no—
178#495—91no—
179#488—92no—
180#470—31no—
181#469—91no—
182#468—92no—
183#442—91no—
184#441—31no—
185#440—92no—
186C4×M16—91no—
187C2×C3×Q8—22no—
188C2×C3×Q8C22×D312yes—
189C2×C3×Q8C22×D312yes—
190C22×C3×C4—31no—
191C2×#67—62no—
192C22×Dic3—32no—
193C2×D12—32no—
194C2×D12—32no—
195C2×D12—62no—
196C2×D12—62no—
197C2×C4×D3—32no—
198C2×C4×D3—62no—
199C2×C4×D3—62no—
200C2×C4×D3C22×D311yescharacteristic
201C3×Q16—22no—
202C3×Q16—22no—
203C3×Q16—42no—
204C3×M16—62no—
205C2×C3×C8—21no—
206C2×C3×C8—31no—
207C2×C3×C8—31no—
208C2×C3×C8C22×D311yescharacteristic
209C2×C3×C8C22×D311yescharacteristic
210C3×C4⋊C4—32no—
211C3×C4⋊C4—32no—
212C3×C4⋊C4—62no—
213C3×C4⋊C4—62no—
214C3×C22⋊C4—62no—
215C3×C42—31no—
216C3×C42—62no—
217#215—64no—
218#215—64no—
219#215—124no—
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—62no—
227(C2×D3)⋊C4—62no—
228(C2×D3)⋊C4—62no—
229(C2×D3)⋊C4—122no—
230(C2×D3)⋊C4—122no—
231C4⋊Dic3—22no—
232C4⋊Dic3—62no—
233C4⋊Dic3—62no—
234C4⋊Dic3C22×D312yes—
235C4⋊Dic3C22×D312yes—
236Dic3⋊C4—22no—
237Dic3⋊C4—62no—
238Dic3⋊C4—62no—
239C4×Dic3—22no—
240C4×Dic3—31no—
241C4×Dic3—31no—
242C4×Dic3—32no—
243C4×Dic3—32no—
244C4×Dic3—61no—
245C4×Dic3C22×D311yescharacteristic
246#208—62no—
247C2×C3⋊C8—31no—
248C2×C3⋊C8—31no—
249C2×C3⋊C8—61no—
250C2×C3⋊C8C22×D311yescharacteristic
251C2×C3⋊C8C22×D311yescharacteristic
252D24—62no—
253D24—62no—
254D24—122no—
255ΓL(1,𝔽25)—22no—
256ΓL(1,𝔽25)—62no—
257C22×C32C22×D411yescharacteristic
258C2×C3⋊D3—42no—
259C2×C3⋊D3—42no—
260C2×C3⋊D3—42no—
261C2×C3×D3—21no—
262C2×C3×D3—22no—
263C32×C4—42no—
264C32×C4C2×#4111yescharacteristic
265C32×C4C2×#4111yescharacteristic
266C3⋊Dic3—22no—
267C3×Dic3—21no—
268C3×Dic3—22no—
269C3×Dic3—42no—
270C3×Dic3—42no—
271C2×Q16D3211yescharacteristic
272C2×SD16—92no—
273C2×D8—91no—
274C2×M16—31no—
275C2×M16—91no—
276#126—182no—
277#125—92no—
278#124—92no—
279#123—182no—
280C22⋊Q8—32no—
281#121—92no—
282C4×Q8—32no—
283C4×D4—92no—
284C4×D4—182no—
285#117—182no—
286C2×C42—91no—
287#107—92no—
288#106—31no—
289#106—31no—
290#103—32no—
291#103—32no—
292#102—92no—
293#102—92no—
294#97—31no—
295#97—91no—
296C4×C8—91no—
297C4×C8—91no—
298C23×C3—31no—
299C22×D3—62no—
300C22×D3—62no—
301C22×D3—122no—
302C22×D3D3×D411yescharacteristic
303C3×Q8—22no—
304C3×Q8—22no—
305C3×Q8—22no—
306C3×Q8—22no—
307C3×Q8—42no—
308C3×Q8—42no—
309C2×C3×C4—22no—
310C2×C3×C4—22no—
311C2×C3×C4—21no—
312C2×C3×C4—31no—
313C2×C3×C4—32no—
314C2×C3×C4—42no—
315C2×C3×C4—61no—
316C2×C3×C4—61no—
317C2×C3×C4—62no—
318C2×C3×C4—62no—
319C2×C3×C4C23×D311yescharacteristic
320C2×C3×C4C23×D311yescharacteristic
321#67—124no—
322C2×Dic3—22no—
323C2×Dic3—22no—
324C2×Dic3—32no—
325C2×Dic3—32no—
326C2×Dic3—62no—
327C2×Dic3—122no—
328C2×Dic3D3×D412yes—
329C2×Dic3D3×D411yescharacteristic
330D12—62no—
331D12—62no—
332D12—62no—
333D12—62no—
334D12—122no—
335D12—122no—
336D12—124no—
337C4×D3—21no—
338C4×D3—21no—
339C4×D3—124no—
340C4×D3—124no—
341C4×D3—122no—
342C3×C8—22no—
343C3×C8—61no—
344C3×C8—61no—
345C3×C8#23512yes—
346C3×C8#23712yes—
347C3⋊C8—21no—
348C3⋊C8—21no—
349C3⋊C8—32no—
350C3⋊C8—32no—
351C3⋊C8—62no—
352C2×C32#53211yescharacteristic
353C2×C32#57512yes—
354C3⋊D3—82no—
355C3×D3—41no—
356C2×Q8C2×D3212yes—
357C2×D4—92no—
358C2×D4—182no—
359C22×C4—31no—
360C22×C4—92no—
361C22×C4—182no—
362Q16—22no—
363SD16—184no—
364D8—182no—
365M16—62no—
366M16—182no—
367C2×C8—31no—
368C2×C8—31no—
369C2×C8—91no—
370C2×C8C2×D3211yescharacteristic
371C4⋊C4—32no—
372C4⋊C4—32no—
373C4⋊C4—62no—
374C4⋊C4—62no—
375C4⋊C4—182no—
376C4⋊C4—182no—
377C22⋊C4—62no—
378C22⋊C4—182no—
379C22⋊C4—182no—
380C22⋊C4—182no—
381C22⋊C4—182no—
382C42—31no—
383C42—62no—
384C42—92no—
385C42—91no—
386C22×C3—21no—
387C22×C3—62no—
388C22×C3—61no—
389C22×C3C2×D3×D411yescharacteristic
390C22×C3C2×D3×D411yescharacteristic
391C2×D3—22no—
392C2×D3—21no—
393C2×D3—122no—
394C2×D3—122no—
395C2×D3—122no—
396C2×D3—122no—
397C2×D3—122no—
398C2×D3—122no—
399C2×D3—242no—
400C2×D3—242no—
401C2×D3—242no—
402C3×C4—21no—
403C3×C4—21no—
404C3×C4—42no—
405C3×C4—42no—
406C3×C4—62no—
407C3×C4—61no—
408C3×C4—82no—
409C3×C4—122no—
410C3×C4—122no—
411C3×C4C2×#23511yescharacteristic
412C3×C4C2×#23711yescharacteristic
413C3×C4D3×#4111yescharacteristic
414C3×C4D3×#4111yescharacteristic
415Dic3—22no—
416Dic3—21no—
417Dic3—42no—
418Dic3—42no—
419Dic3—62no—
420Dic3—62no—
421Dic3—122no—
422C32#318311yescharacteristic, complemented, Sylow
423C23—31no—
424C23—182no—
425Q8—22no—
426Q8—22no—
427D4—182no—
428D4—182no—
429D4—364no—
430C2×C4—22no—
431C2×C4—32no—
432C2×C4—31no—
433C2×C4—61no—
434C2×C4—61no—
435C2×C4—62no—
436C2×C4—62no—
437C2×C4—92no—
438C2×C4—364no—
439C2×C4—362no—
440C2×C4C22×D3211yescharacteristic
441C8—61no—
442C8—61no—
443C8—92no—
444C8#380412yes—
445C2×C3—21no—
446C2×C3—22no—
447C2×C3—121no—
448C2×C3#554811yescharacteristic
449C2×C3#559611yescharacteristic
450C2×C3#577712yes—
451C2×C3#577712yes—
452D3—41no—
453D3—242no—
454D3—242no—
455D3—482no—
456C22—61no—
457C22—62no—
458C22—362no—
459C22—362no—
460C22—362no—
461C22D32×D411yescharacteristic
462C4—42no—
463C4—61no—
464C4—62no—
465C4—122no—
466C4—122no—
467C4—182no—
468C4#6431211yescharacteristic
469C4C2×#380411yescharacteristic
470C3—21no—
471C3#7982611yescharacteristic, complemented
472C3#8089211yescharacteristic, complemented
473C2—121no—
474C2—722no—
475C2#1059476212yes—
476C2#1059513111yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
prime radical#10590835C2
hypercenterC2×Q16D32
hypocenterC32#3183
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
1. #10595376C2semidirect
2. #10592890C2semidirect
3. C3×#5189C2semidirect
4. C3×#5184C2semidirect
5. #10591589C2semidirect
6. #10591540C2semidirect
7. #10591539C2semidirect
8. #10590874C2semidirect
10. #10590768C2semidirect
11. #10590667C2semidirect
48. #5189D3semidirect
49. #5184D3semidirect
422. C32#3183semidirect
471. C3#79826semidirect
472. C3#80892semidirect

Maximal subgroups

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

subgroupindex
#105953762
#105928902
C3×#51892
C3×#51842
#105915892
#105915402
#105915392
#105908742
#105908352
#105907682
#105906672
#808923
#798263