Finite Group Databasebeta

← #11876987

Subgroups — #11876987

Order 1152.

957 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594518C212yesmaximal, complemented
2#10592564C211yesmaximal, characteristic, complemented
3C3×#4869C211yesmaximal, characteristic, complemented
4C3×#4855C211yesmaximal, characteristic, complemented
5#10590880C211yesmaximal, characteristic, complemented
6#10590846C211yesmaximal, characteristic, complemented
7#10590768C211yesmaximal, characteristic, complemented
8#10590664C211yesmaximal, characteristic, complemented
9#10590589C212yesmaximal, complemented
10#10590548C212yesmaximal, complemented
11#10590508C212yesmaximal, complemented
12#81888—31nomaximal
13#79877—31nomaximal
14C2×#3799—22no—
15C2×#3745C2211yescharacteristic
16C2×#3743C2211yescharacteristic
17#64104C2212yes—
18C2×C3×D24C2211yescharacteristic
19C3×#893C2212yes—
20C3×#888C2212yes—
21#63916C2212yes—
22#63911C2212yes—
23#63910—22no—
24#63907—22no—
25#63904—22no—
26#63894C2212yes—
27C4×#624C2211yescharacteristic
28C2×#3714C2212yes—
29C2×#3712C2211yescharacteristic
30C32×#106C2211yescharacteristic
31#63636C2212yes—
32C3×#817C2211yescharacteristic
33C3×#815C2211yescharacteristic
34C3×C8×Dic3C2211yescharacteristic
35C3×#809C2212yes—
36C3×#808C2212yes—
37#63564C2212yes—
38#63562C2212yes—
39#63554C2211yescharacteristic
40Dic3×C3⋊C8C2211yescharacteristic
41#5725—32no—
42#5548—32no—
43C3×#498—31no—
44C3×#442—31no—
45#5159—31no—
46#5151—31no—
47#5088—32no—
48#5014—32no—
49#4869—32no—
50#4869—31no—
51#4869D311yescharacteristic, complemented
52#4865—31no—
53#4865—31no—
54#4865—31no—
55#4865—32no—
56#4865—61no—
57#4855D311yescharacteristic, complemented
58#4782—32no—
59#4760—32no—
60#4711—31no—
61#4707—31no—
62#4695—31no—
63C4×ΓL(1,𝔽25)—31no—
64C2×C4⋊(C3⋊D3)—22no—
65C2×C4⋊(C3⋊D3)C2312yes—
66C2×C4×C3⋊D3C2311yescharacteristic
67C2×C3×D12C2312yes—
68C2×C3×C4×D3—22no—
69C2×C3×Dic6—22no—
70C2×#626—22no—
71C2×#626—22no—
72C2×#626—22no—
73C2×#624—22no—
74C2×#624D412yes—
75#3799—48no—
76C2×C32×C8C2311yescharacteristic
77C32×C4⋊C4C2312yes—
78#3752—22no—
79C2×C3⋊(C3⋊C8)C2311yescharacteristic
80#3745—22no—
81#3743—22no—
82C3×(C2×D3)⋊C4—22no—
83C3×C4⋊Dic3C2312yes—
84C3×Dic3⋊C4—22no—
85C3×C4×Dic3C2311yescharacteristic
86C3×C4×Dic3C2311yescharacteristic
87C2×C3×C3⋊C8C2311yescharacteristic
88C2×C3×C3⋊C8C2311yescharacteristic
89C3×D24—22no—
90#3722—22no—
91(C2×D3)⋊Dic3—22no—
92Dic32D412yes—
93#3714—24no—
94#3712—22no—
95#3184—91noSylow
96C2×#239—62no—
97C2×#235—62no—
98C2×C3×D8—31no—
99C3×C4⋊Q8—32no—
100C3×C4×D4—32no—
101#947—62no—
102#940—32no—
103#938—32no—
104C2×#213—32no—
105C4×#67—62no—
106C2×D24—32no—
107C2×D24—31no—
108C2×D24—31no—
109C2×D24—61no—
110C2×D24C2×D311yescharacteristic
111C2×ΓL(1,𝔽25)—31no—
112C2×ΓL(1,𝔽25)—31no—
113C2×ΓL(1,𝔽25)—31no—
114C2×ΓL(1,𝔽25)—31no—
115C2×ΓL(1,𝔽25)—61no—
116#895—32no—
117#895—32no—
118#895—32no—
119#895—62no—
120#895—62no—
121#893—32no—
122#893—62no—
123#893C2×D312yes—
124#888C2×D312yes—
125#885—62no—
126#884—62no—
127#874—32no—
128C4×D12—32no—
129C42×D3—31no—
130C42×D3—31no—
131C3×#106—21no—
132C3×#106—31no—
133C3×#106—32no—
134C3×#106C2×D311yescharacteristic
135C3×#106C2×D311yescharacteristic
136C3×#102—32no—
137C3×#97—31no—
138C3×C4×C8—31no—
139#832—32no—
140#821—32no—
141#817C2×D311yescharacteristic
142#815—31no—
143#815C2×D311yescharacteristic
144C8×Dic3—31no—
145C8×Dic3C2×D311yescharacteristic
146#809—32no—
147#809—32no—
148#809—32no—
149#809—32no—
150#809—62no—
151#809C2×D312yes—
152#808C2×D312yes—
153#803—31no—
154C4×C3⋊C8—31no—
155C22×C3⋊D3—22no—
156C22×C3⋊D3C2×D411yescharacteristic
157C22×C3×D3—22no—
158C2×C32×C4—22no—
159C2×C32×C4C2411yescharacteristic
160C2×C3⋊Dic3C2×D411yescharacteristic
161C4⋊(C3⋊D3)—22no—
162C4⋊(C3⋊D3)—22no—
163C4⋊(C3⋊D3)—44no—
164C4×C3⋊D3—21no—
165C4×C3⋊D3—21no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3C2×D412yes—
168C2×C3×Dic3C2×D412yes—
169C3×D12—22no—
170C3×D12—22no—
171C3×C4×D3—44no—
172C3×Dic6—44no—
173#626—44no—
174#626—44no—
175#626—44no—
176#624—24no—
177#624—44no—
178C32×C8#4112yescomplemented
179C3⋊(C3⋊C8)—21no—
180C3×C3⋊C8—21no—
181C3×C3⋊C8#4112yescomplemented
182#532—92no—
183#498—31no—
184#493—91no—
185#486—92no—
186#469—92no—
187#469—91no—
188#469—91no—
189#442—31no—
190#442—91no—
191#442—92no—
192C4×M16—91no—
193C2×C3×Q8—62no—
194C2×C3×D4—32no—
195C22×C3×C4—62no—
196C2×#67—62no—
197C2×#67—62no—
198C2×#67—62no—
199#239—128no—
200#235—128no—
201C2×D12—32no—
202C2×D12—32no—
203C2×D12—62no—
204C2×D12—62no—
205C2×D12—62no—
206C2×D12—62no—
207C2×D12—62no—
208C2×D12—62no—
209C2×D12—122no—
210C2×D12C22×D312yes—
211C2×C4×D3—22no—
212C2×C4×D3—31no—
213C2×C4×D3—31no—
214C2×C4×D3—32no—
215C2×C4×D3—32no—
216C2×C4×D3—61no—
217C2×C4×D3—62no—
218C2×C4×D3—62no—
219C2×Dic6—22no—
220C3×D8—62no—
221C2×C3×C8—21no—
222C2×C3×C8—31no—
223C2×C3×C8—31no—
224C2×C3×C8C22×D311yescharacteristic
225C2×C3×C8C22×D311yescharacteristic
226C3×C4⋊C4—22no—
227C3×C4⋊C4—32no—
228C3×C4⋊C4—62no—
229C3×C4⋊C4C22×D312yes—
230C3×C4⋊C4C22×D312yes—
231C3×C22⋊C4—62no—
232C3×C42—31no—
233C3×C42—31no—
234#217—62no—
235#213—64no—
236(C2×D3)⋊C4—22no—
237(C2×D3)⋊C4—62no—
238(C2×D3)⋊C4—62no—
239(C2×D3)⋊C4—62no—
240(C2×D3)⋊C4—62no—
241(C2×D3)⋊C4—62no—
242(C2×D3)⋊C4—122no—
243C4⋊Dic3C22×D312yes—
244Dic3⋊C4—22no—
245C4×Dic3—32no—
246C4×Dic3—32no—
247C4×Dic3C22×D311yescharacteristic
248C4×Dic3C22×D311yescharacteristic
249C2×C3⋊C8—31no—
250C2×C3⋊C8—31no—
251C2×C3⋊C8—61no—
252C2×C3⋊C8C22×D311yescharacteristic
253C2×C3⋊C8C22×D311yescharacteristic
254D24—22no—
255D24—64no—
256D24—62no—
257D24—62no—
258D24—122no—
259ΓL(1,𝔽25)—62no—
260ΓL(1,𝔽25)—62no—
261ΓL(1,𝔽25)—62no—
262ΓL(1,𝔽25)—62no—
263ΓL(1,𝔽25)—122no—
264C22×C32C22×D411yescharacteristic
265C2×C3⋊D3—21no—
266C2×C3⋊D3—22no—
267C2×C3⋊D3—42no—
268C2×C3⋊D3—42no—
269C2×C3⋊D3—42no—
270C2×C3×D3—42no—
271C2×C3×D3—42no—
272C2×C3×D3—42no—
273C32×C4—42no—
274C32×C4C2×#4111yescharacteristic
275C32×C4C2×#4111yescharacteristic
276C3⋊Dic3—21no—
277C3×Dic3—22no—
278C3×Dic3—42no—
279C3×Dic3AGL(1,ℤ/8)14yes—
280C2×#41—182no—
281C2×D8—31no—
282C2×D8—92no—
283C2×D8—91no—
284C2×M16—91no—
285C2×M16—91no—
286C4⋊Q8—32no—
287#127—92no—
288#124—182no—
289#121—92no—
290#121—92no—
291#121—182no—
292C4×D4—32no—
293C4×D4—92no—
294C4×D4—182no—
295C2×C42—91no—
296#106—31no—
297#106—32no—
298#106D3211yescharacteristic
299#102—32no—
300#102—92no—
301#102—92no—
302#102—92no—
303#97—31no—
304#97—91no—
305C4×C8—31no—
306C4×C8—91no—
307C23×C3—62no—
308C22×D3—22no—
309C22×D3—31no—
310C22×D3—31no—
311C22×D3—61no—
312C22×D3—62no—
313C22×D3—62no—
314C22×D3—122no—
315C3×Q8—124no—
316C3×D4—62no—
317C3×D4—62no—
318C2×C3×C4—22no—
319C2×C3×C4—22no—
320C2×C3×C4—21no—
321C2×C3×C4—32no—
322C2×C3×C4—32no—
323C2×C3×C4—42no—
324C2×C3×C4—62no—
325C2×C3×C4—124no—
326C2×C3×C4C23×D311yescharacteristic
327C2×C3×C4C23×D311yescharacteristic
328#67—124no—
329#67—124no—
330#67—124no—
331C2×Dic3—22no—
332C2×Dic3—31no—
333C2×Dic3—31no—
334C2×Dic3—61no—
335C2×Dic3D3×D412yes—
336C2×Dic3D3×D412yes—
337D12—22no—
338D12—22no—
339D12—62no—
340D12—62no—
341D12—62no—
342D12—62no—
343D12—122no—
344D12—122no—
345D12—124no—
346D12—124no—
347D12—124no—
348D12—124no—
349D12—124no—
350D12—244no—
351C4×D3—44no—
352C4×D3—64no—
353C4×D3—61no—
354C4×D3—61no—
355C4×D3—61no—
356C4×D3—61no—
357C4×D3—64no—
358C4×D3—121no—
359C4×D3—121no—
360C4×D3—124no—
361C4×D3—124no—
362Dic6—44no—
363C3×C8—22no—
364C3×C8—32no—
365C3×C8—61no—
366C3×C8#23512yescomplemented
367C3×C8#23912yescomplemented
368C3⋊C8—21no—
369C3⋊C8—61no—
370C3⋊C8—61no—
371C3⋊C8—121no—
372C3⋊C8#23912yescomplemented
373C2×C32#53211yescharacteristic
374C2×C32C2×AGL(1,ℤ/8)12yes—
375C3⋊D3—41no—
376C3⋊D3—82no—
377C3×D3—82no—
378#41—368no—
379C2×Q8—62no—
380C2×D4—32no—
381C2×D4—92no—
382C2×D4—182no—
383C2×D4—182no—
384C2×D4—182no—
385C2×D4—182no—
386C22×C4—62no—
387C22×C4—92no—
388C22×C4—91no—
389C22×C4—182no—
390D8—62no—
391D8—184no—
392D8—182no—
393M16—182no—
394M16—182no—
395C2×C8—31no—
396C2×C8—31no—
397C2×C8—91no—
398C2×C8C2×D3211yescharacteristic
399C4⋊C4—32no—
400C4⋊C4—62no—
401C4⋊C4C2×D3212yes—
402C22⋊C4—62no—
403C22⋊C4—182no—
404C22⋊C4—182no—
405C22⋊C4—182no—
406C42—31no—
407C42—31no—
408C42—92no—
409C22×C3—21no—
410C22×C3—122no—
411C22×C3—122no—
412C22×C3—122no—
413C22×C3C2×D3×D411yescharacteristic
414C22×C3C2×D3×D411yescharacteristic
415C2×D3—42no—
416C2×D3—42no—
417C2×D3—42no—
418C2×D3—61no—
419C2×D3—62no—
420C2×D3—62no—
421C2×D3—61no—
422C2×D3—121no—
423C2×D3—122no—
424C2×D3—122no—
425C2×D3—122no—
426C2×D3—122no—
427C2×D3—122no—
428C2×D3—122no—
429C2×D3—122no—
430C2×D3—242no—
431C2×D3—242no—
432C2×D3—242no—
433C3×C4—21no—
434C3×C4—21no—
435C3×C4—34no—
436C3×C4—42no—
437C3×C4—42no—
438C3×C4—62no—
439C3×C4—82no—
440C3×C4—122no—
441C3×C4C2×#23511yescharacteristic
442C3×C4C2×#23911yescharacteristic
443C3×C4C2×#23911yescharacteristic
444C3×C4D3×#4111yescharacteristic
445Dic3—22no—
446Dic3—42no—
447Dic3—61no—
448Dic3—61no—
449Dic3—121no—
450Dic3#91414yes—
451C32#318411yescharacteristic, complemented, Sylow
452C23—62no—
453C23—91no—
454C23—182no—
455Q8—124no—
456D4—62no—
457D4—62no—
458D4—182no—
459D4—182no—
460D4—364no—
461D4—364no—
462D4—364no—
463D4—364no—
464C2×C4—22no—
465C2×C4—32no—
466C2×C4—32no—
467C2×C4—62no—
468C2×C4—91no—
469C2×C4—124no—
470C2×C4—184no—
471C2×C4—181no—
472C2×C4—181no—
473C2×C4—364no—
474C2×C4C22×D3211yescharacteristic
475C8—32no—
476C8—61no—
477C8—181no—
478C8#379912yescomplemented
479C2×C3—22no—
480C2×C3—21no—
481C2×C3—242no—
482C2×C3#554811yescharacteristic
483C2×C3#572511yescharacteristic
484C2×C3C2×#91412yes—
485C2×C3D3×AGL(1,ℤ/8)12yes—
486D3—82no—
487D3—121no—
488D3—121no—
489D3—241no—
490D3—242no—
491D3—242no—
492D3—482no—
493C22—122no—
494C22—122no—
495C22—122no—
496C22—182no—
497C22—181no—
498C22—362no—
499C22—362no—
500C22—362no—
501C22D32×D411yescharacteristic
502C4—34no—
503C4—42no—
504C4—62no—
505C4—122no—
506C4—181no—
507C4C2×#379911yescharacteristic
508C4D3×#23911yescharacteristic
509C3—21no—
510C3#7987711yescharacteristic, complemented
511C3#8188811yescharacteristic, complemented
512C2—242no—
513C2—361no—
514C2—722no—
515C2#1059451811yescharacteristic
516C2D3×#91412yes—
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
hypercenter#106D32
hypocenterC32#3184
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. #10594518C2semidirect
2. #10592564C2semidirect
3. C3×#4869C2semidirect
4. C3×#4855C2semidirect
5. #10590880C2semidirect
6. #10590846C2semidirect
7. #10590768C2semidirect
8. #10590664C2semidirect
9. #10590589C2semidirect
10. #10590548C2semidirect
11. #10590508C2semidirect
51. #4869D3semidirect
57. #4855D3semidirect
178. C32×C8#41semidirect
181. C3×C3⋊C8#41semidirect
366. C3×C8#235semidirect
367. C3×C8#239semidirect
372. C3⋊C8#239semidirect
451. C32#3184semidirect
478. C8#3799semidirect
510. C3#79877semidirect
511. C3#81888semidirect

Maximal subgroups

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

subgroupindex
#105945182
#105925642
C3×#48692
C3×#48552
#105908802
#105908462
#105907682
#105906642
#105905892
#105905482
#105905082
#818883
#798773