Finite Group Databasebeta

← #11868699

Subgroups — #11868699

Order 1152.

943 conjugacy classes of subgroups.

The subgroup lattice has 469 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3802C211yesmaximal, characteristic
2#10593854C211yesmaximal, characteristic, complemented
3#10592536C211yesmaximal, characteristic, complemented
4C3×#4847C212yesmaximal, complemented
5#10590941C212yesmaximal
6#10590778C212yesmaximal, complemented
7#10590776C212yesmaximal, complemented
8#10590688C212yesmaximal, complemented
9#10590270C212yesmaximal, complemented
10#81166—32nomaximal
11C2×#3802C2211yescharacteristic
12C2×C4×D32—21no—
13C2×#3743C2212yes—
14C42×C3⋊D3C2211yescharacteristic
15C3×C4×D12C2212yes—
16C3×#870C2212yescomplemented
17#63921—21no—
18#63919C2211yescharacteristic, complemented
19#63919C2211yescharacteristic, complemented
20#63902—21no—
21C4×#625—21no—
22#63900C2211yescharacteristic
23#63898C2212yes—
24#63865—21no—
25#63865—21no—
26#63849C2212yes—
27#63838—21no—
28#63838—21no—
29C32×C4⋊C8C2211yescharacteristic, complemented
30#63641C2212yescomplemented
31C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
32C3×#821C2212yes—
33C3×#821C2212yes—
34C3×#818C2212yescomplemented
35C3×#817C2212yescomplemented
36#63576C2212yescomplemented
37#63574C2212yescomplemented
38#63562C2212yes—
39#63562C2212yes—
40#5688—32no—
41C4×D3×D4—32no—
42C3×#478—32no—
43#5066—32no—
44#5009—32no—
45#4890—32no—
46#4881—32no—
47#4870—32no—
48#4861—32no—
49#4847D312yescomplemented
50#4837—32no—
51#4837—61no—
52#4770—32no—
53#4770—32no—
54#4761—32no—
55#4759—32no—
56C22×D32—21no—
57C2×C4×C3⋊D3D411yescharacteristic
58C2×C4×C3⋊D3D411yescharacteristic
59C2×C4×C3⋊D3C2311yescharacteristic
60C2×C3×D12C2312yes—
61C2×C3×C4×D3—22no—
62C2×#627—21no—
63C2×#627—21no—
64C2×#625—21no—
65C2×#624—21no—
66C2×D3×Dic3—22no—
67#3802—22no—
68#3802Q814yescomplemented
69C4×D32—44no—
70C2×C32×C8C2312yes—
71C32×C42C2311yescharacteristic
72C4×C3⋊Dic3D411yescharacteristic
73C4×C3⋊Dic3D411yescharacteristic
74C4×C3⋊Dic3C2311yescharacteristic
75C2×C3⋊(C3⋊C8)C2312yes—
76#3743—24no—
77C3×(C2×D3)⋊C4—22no—
78C3×C4⋊Dic3C2312yes—
79C3×C4⋊Dic3C2312yes—
80C3×C4⋊Dic3C2312yes—
81C3×Dic3⋊C4—22no—
82C3×Dic3⋊C4—22no—
83#3724—21no—
84#3724—21no—
85#3724—21no—
86#3722—22no—
87(C2×D3)⋊Dic3—22no—
88Dic32—22no—
89#3077—91noSylow
90C2×D3×D4—32no—
91C22×C4×D3—62no—
92C3×#125—32no—
93C3×C4×D4—32no—
94D4×Dic3—32no—
95C4×#67—62no—
96C2×ΓL(1,𝔽25)—32no—
97C2×ΓL(1,𝔽25)—32no—
98C2×ΓL(1,𝔽25)—62no—
99#896—62no—
100#896—62no—
101#893—32no—
102#892—32no—
103#892—32no—
104D3×C4⋊C4—32no—
105#888—32no—
106#888—32no—
107#887—62no—
108#887—62no—
109#67⋊C4—62no—
110D3×C22⋊C4—62no—
111C4×D12C2×D312yes—
112C42×D3—32no—
113C42×D3—61no—
114#870C2×D312yescomplemented
115C3×#107—32no—
116C3×#106—32no—
117C3×C4⋊C8—21no—
118C3×C4⋊C8C2×D312yescomplemented
119C3×#102—32no—
120C3×#102—32no—
121#832—32no—
122#832—32no—
123#821C2×D312yes—
124#821C2×D312yes—
125#818C2×D312yescomplemented
126#817C2×D312yescomplemented
127Dic3⋊C8—32no—
128Dic3⋊C8—32no—
129Dic3⋊C8—62no—
130#809—32no—
131#809—32no—
132#808—32no—
133#808—32no—
134#807—32no—
135#807—32no—
136C4⋊(C3⋊C8)—32no—
137C4⋊(C3⋊C8)—61no—
138C22×C3⋊D3C2×D411yescharacteristic
139C22×C3×D3—22no—
140C2×D32—24no—
141C2×D32—42no—
142C2×D32—42no—
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2411yescharacteristic
146C2×C3⋊Dic3C2×D411yescharacteristic
147C2×C3⋊Dic3C2×D411yescharacteristic
148C2×C3⋊Dic3C2×D411yescharacteristic
149C4×C3⋊D3—22no—
150C4×C3⋊D3—41no—
151C4×C3⋊D3C2×Q812yes—
152C4×C3⋊D3#4112yes—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3—22no—
156C3×D12—22no—
157C3×D12C2×Q814yes—
158C3×C4×D3—44no—
159#627—42no—
160#627—42no—
161#625—24no—
162#624—42no—
163D3×Dic3—44no—
164C32×C8—22no—
165C3⋊(C3⋊C8)—22no—
166#533—91no—
167C2×C4×D4—91no—
168#478—32no—
169#478—92no—
170#476—92no—
171#474—92no—
172#428—92no—
173#423—91no—
174#418—92no—
175C23×D3—62no—
176C2×C3×D4—32no—
177C22×C3×C4—62no—
178C2×#67—62no—
179C22×Dic3—62no—
180D3×D4—38no—
181D3×D4—64no—
182C2×D12C22×D312yes—
183C2×C4×D3—22no—
184C2×C4×D3—32no—
185C2×C4×D3—32no—
186C2×C4×D3—32no—
187C2×C4×D3—61no—
188C2×C4×D3—61no—
189C2×C4×D3—61no—
190C2×C4×D3—62no—
191C2×C4×D3—62no—
192C2×C4×D3—128no—
193C2×Dic6—62no—
194C2×Dic6—62no—
195C2×C3×C8—22no—
196C2×C3×C8C22×D312yes—
197C2×C3×C8C22×D312yes—
198C3×C4⋊C4—32no—
199C3×C4⋊C4—32no—
200C3×C4⋊C4—32no—
201C3×C4⋊C4—62no—
202C3×C4⋊C4—62no—
203C3×C22⋊C4—62no—
204C3×C42—21no—
205C3×C42C22×D312yes—
206#217—62no—
207(C2×D3)⋊C4—22no—
208(C2×D3)⋊C4—62no—
209(C2×D3)⋊C4—62no—
210(C2×D3)⋊C4—62no—
211C4⋊Dic3C22×D312yes—
212C4⋊Dic3C22×D312yes—
213C4⋊Dic3C22×D312yes—
214Dic3⋊C4—22no—
215Dic3⋊C4—22no—
216Dic3⋊C4—62no—
217Dic3⋊C4—62no—
218Dic3⋊C4—62no—
219C4×Dic3—32no—
220C4×Dic3—32no—
221C4×Dic3—32no—
222C4×Dic3—61no—
223C4×Dic3—61no—
224C4×Dic3—61no—
225C4×Dic3—62no—
226C4×Dic3—62no—
227C2×C3⋊C8—32no—
228C2×C3⋊C8—32no—
229C2×C3⋊C8—62no—
230ΓL(1,𝔽25)—64no—
231ΓL(1,𝔽25)—64no—
232ΓL(1,𝔽25)—124no—
233C22×C32C22×D411yescharacteristic
234C2×C3⋊D3—21no—
235C2×C3⋊D3—21no—
236C2×C3⋊D3C22⋊Q812yes—
237C2×C3×D3—24no—
238C2×C3×D3—42no—
239C2×C3×D3—42no—
240D32—48no—
241C32×C4—21no—
242C32×C4—21no—
243C32×C4C22×Q811yescharacteristic
244C32×C4C2×#4111yescharacteristic
245C3⋊Dic3—21no—
246C3⋊Dic3C22⋊Q812yes—
247C3⋊Dic3AGL(1,ℤ/8)12yes—
248C3×Dic3—42no—
249C3×Dic3—42no—
250C3×Dic3—42no—
251C22×D4—91no—
252C23×C4—181no—
253C2×M16—92no—
254C4⋊Q8—91no—
255C4⋊Q8—91no—
256#125—32no—
257C22⋊Q8—181no—
258C22⋊Q8—181no—
259C4×Q8—181no—
260C4×Q8—181no—
261C4×D4—32no—
262C4×D4—92no—
263C4×D4—181no—
264C4×D4—181no—
265#117—92no—
266C2×C4⋊C4—91no—
267C2×C22⋊C4—181no—
268C2×C42—91no—
269#107—32no—
270#107—92no—
271#106—32no—
272#106—92no—
273C4⋊C8—92no—
274C4⋊C8—91no—
275C4⋊C8D3211yescharacteristic, complemented
276#102—32no—
277#102—32no—
278#102—92no—
279#102—92no—
280C23×C3—62no—
281C22×D3—22no—
282C22×D3—32no—
283C22×D3—61no—
284C22×D3—68no—
285C22×D3—124no—
286C22×D3—124no—
287C3×D4—34no—
288C3×D4—62no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—62no—
293C2×C3×C4—62no—
294C2×C3×C4—62no—
295C2×C3×C4—124no—
296C2×C3×C4D3×D412yes—
297C2×C3×C4D3×D412yes—
298C2×C3×C4C23×D312yes—
299#67—68no—
300C2×Dic3—22no—
301C2×Dic3—22no—
302C2×Dic3—22no—
303C2×Dic3—32no—
304C2×Dic3—32no—
305C2×Dic3—32no—
306C2×Dic3—61no—
307C2×Dic3—61no—
308C2×Dic3—61no—
309C2×Dic3—124no—
310D12—22no—
311D12D3×Q814yes—
312C4×D3—34no—
313C4×D3—34no—
314C4×D3—44no—
315C4×D3—62no—
316C4×D3—62no—
317C4×D3—64no—
318C4×D3—122no—
319C4×D3—124no—
320C4×D3—124no—
321C4×D3—122no—
322C4×D3—122no—
323Dic6—124no—
324Dic6—124no—
325C3×C8—22no—
326C3×C8—22no—
327C3×C8—42no—
328C3⋊C8—62no—
329C3⋊C8—62no—
330C3⋊C8—122no—
331C2×C32C2×C22⋊Q811yescharacteristic
332C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
333C2×C32#57511yescharacteristic
334C3⋊D3—22no—
335C3×D3—44no—
336C24—181no—
337C2×Q8—181no—
338C2×Q8—181no—
339C2×D4—32no—
340C2×D4—94no—
341C2×D4—182no—
342C2×D4—181no—
343C22×C4—62no—
344C22×C4—91no—
345C22×C4—91no—
346C22×C4—91no—
347C22×C4—181no—
348C22×C4—182no—
349C22×C4—364no—
350M16—184no—
351C2×C8—92no—
352C2×C8C2×D3212yes—
353C4⋊C4—32no—
354C4⋊C4—32no—
355C4⋊C4—32no—
356C4⋊C4—62no—
357C4⋊C4—62no—
358C4⋊C4—181no—
359C4⋊C4—181no—
360C4⋊C4—181no—
361C22⋊C4—62no—
362C22⋊C4—182no—
363C22⋊C4—182no—
364C42—91no—
365C42—91no—
366C42—91no—
367C42—182no—
368C42C2×D3211yescharacteristic
369C22×C3—21no—
370C22×C3—64no—
371C22×C3—122no—
372C22×C3—122no—
373C22×C3C2×D3×D412yes—
374C2×D3—24no—
375C2×D3—34no—
376C2×D3—42no—
377C2×D3—42no—
378C2×D3—62no—
379C2×D3—62no—
380C2×D3—62no—
381C2×D3—121no—
382C2×D3—121no—
383C2×D3—1216no—
384C3×C4—22no—
385C3×C4—22no—
386C3×C4—22no—
387C3×C4—21no—
388C3×C4—21no—
389C3×C4—41no—
390C3×C4—122no—
391C3×C4—122no—
392C3×C4—122no—
393C3×C4C2×D3×Q812yes—
394C3×C4D3×#4112yes—
395Dic3—34no—
396Dic3—34no—
397Dic3—42no—
398Dic3—42no—
399Dic3—42no—
400Dic3—62no—
401Dic3—62no—
402Dic3—62no—
403Dic3—121no—
404C32#307711yescharacteristic, complemented, Sylow
405C23—62no—
406C23—91no—
407C23—184no—
408C23—362no—
409C23—362no—
410Q8—362no—
411Q8—362no—
412D4—34no—
413D4—62no—
414D4—184no—
415C2×C4—62no—
416C2×C4—62no—
417C2×C4—62no—
418C2×C4—91no—
419C2×C4—91no—
420C2×C4—92no—
421C2×C4—92no—
422C2×C4—91no—
423C2×C4—124no—
424C2×C4—182no—
425C2×C4—361no—
426C2×C4—364no—
427C2×C4—362no—
428C2×C4#380211yescharacteristic
429C2×C4#380211yescharacteristic
430C2×C4C22×D3211yescharacteristic
431C8—22no—
432C8—182no—
433C2×C3—21no—
434C2×C3—21no—
435C2×C3—21no—
436C2×C3—124no—
437C2×C3D3×C22⋊Q812yes—
438C2×C3#576812yes—
439C2×C3D3×AGL(1,ℤ/8)12yes—
440D3—44no—
441D3—64no—
442D3—122no—
443C22—64no—
444C22—92no—
445C22—122no—
446C22—122no—
447C22—181no—
448C22—181no—
449C22—368no—
450C22C2×#380211yescharacteristic
451C4—21no—
452C4—21no—
453C4—92no—
454C4—92no—
455C4—122no—
456C4—122no—
457C4—122no—
458C4—181no—
459C4#6431211yescharacteristic
460C4D32×Q811yescharacteristic
461C3—21no—
462C3#8116612yescomplemented
463C2—124no—
464C2—182no—
465C2#1059463111yescharacteristic
466C2#1059468511yescharacteristic
467C2#1059471611yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radicalC2×#3802C22
hypercenterC4⋊C8D32
hypocenterC32#3077
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10593854C2semidirect
3. #10592536C2semidirect
4. C3×#4847C2semidirect
6. #10590778C2semidirect
7. #10590776C2semidirect
8. #10590688C2semidirect
9. #10590270C2semidirect
16. C3×#870C22semidirect
18. #63919C22semidirect
19. #63919C22semidirect
29. C32×C4⋊C8C22semidirect
30. #63641C22semidirect
31. C4⋊(C3⋊(C3⋊C8))C22semidirect
34. C3×#818C22semidirect
35. C3×#817C22semidirect
36. #63576C22semidirect
37. #63574C22semidirect
49. #4847D3semidirect
68. #3802Q8semidirect
114. #870C2×D3semidirect
118. C3×C4⋊C8C2×D3semidirect
125. #818C2×D3semidirect
126. #817C2×D3semidirect
275. C4⋊C8D32semidirect
404. C32#3077semidirect
462. C3#81166semidirect

Maximal subgroups

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

subgroupindex
C4×#38022
#105938542
#105925362
C3×#48472
#105909412
#105907782
#105907762
#105906882
#105902702
#811663