Finite Group Databasebeta

← #11868660

Subgroups — #11868660

Order 1152.

991 conjugacy classes of subgroups; only the 176 normal subgroups are shown.

normal subgroups only

This group has 991 conjugacy classes of subgroups — too many to draw. Only its 176 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596199C211yesmaximal, characteristic, complemented
2C4×#3802C211yesmaximal, characteristic
3C3×#5087C212yesmaximal, complemented
4#10590594C212yesmaximal
5#10590582C212yesmaximal, complemented
6#10590473C214yesmaximal, complemented
7#10590340C211yesmaximal, characteristic, complemented
8#10590268C212yesmaximal, complemented
9#80965—32nomaximal
10C2×#3802C2211yescharacteristic
11C2×C4×D32—21no—
12C32×C4⋊Q8C2211yescharacteristic, complemented
13#64155—21no—
14Q8×C3⋊Dic3—21no—
15#64106—21no—
16#64101C2212yes—
17#64099C2212yescomplemented
18#64096—21no—
19C42×C3⋊D3C2211yescharacteristic
20#64078C2211yescharacteristic, complemented
21C3×C4×D12C2212yes—
22#63921—21no—
23#63902—21no—
24C4×#625—21no—
25#63900C2211yescharacteristic
26#63898C2212yes—
27C2×#3712C2212yes—
28C3×#809C2214yes—
29C3×#807C2214yescomplemented
30C3×C4⋊(C3⋊C8)C2212yescomplemented
31#63573C2214yescomplemented
32#63572C2212yescomplemented
33#63563C2214yes—
34#5728—32no—
35#5728—61no—
36C4×D3×D4—32no—
37C3×#474—32no—
38#5087D312yescomplemented
39#5008—32no—
40#4891—34no—
41#4881—34no—
42#4842—32no—
43#4837—32no—
44#4770—34no—
45#4763—34no—
46C22×D32—21no—
47C2×C32×Q8—21no—
48C2×C4×C3⋊D3D411yescharacteristic
49C2×C4×C3⋊D3D411yescharacteristic
50C2×C4×C3⋊D3C2311yescharacteristic
51C2×#634—21no—
52C2×C3×D12C2312yes—
53C2×C3×C4×D3—22no—
54C2×#625—21no—
55C2×#624—21no—
56C2×D3×Dic3—22no—
57#3802—22no—
58#3802Q814yescomplemented
59C4×D32—44no—
60C32×C4⋊C4—21no—
61C32×C4⋊C4C2312yes—
62C32×C42C2311yescharacteristic
63#3752—22no—
64C4⋊(C3⋊Dic3)—21no—
65C4⋊(C3⋊Dic3)—22no—
66C4⋊(C3⋊Dic3)C2312yes—
67#3750—22no—
68C4×C3⋊Dic3—22no—
69C4×C3⋊Dic3D411yescharacteristic
70C4×C3⋊Dic3D411yescharacteristic
71C4×C3⋊Dic3C2311yescharacteristic
72C3×(C2×D3)⋊C4—22no—
73C3×C4⋊Dic3C2312yes—
74C2×C3×C3⋊C8C2314yes—
75#3724—21no—
76(C2×D3)⋊Dic3—22no—
77#3712—24no—
78#3077—91noSylow
79C2×D3×D4—32no—
80C22×C4×D3—62no—
81C3×C4⋊Q8—21no—
82C3×C4⋊Q8C2×D312yescomplemented
83C3×C4×D4—32no—
84#946—62no—
85#946—62no—
86Q8×Dic3—62no—
87Q8×Dic3—62no—
88D4×Dic3—32no—
89C4×#67—62no—
90C2×ΓL(1,𝔽25)—34no—
91#897—62no—
92#897—62no—
93#893—32no—
94#892—34no—
95#892—62no—
96D3×C4⋊C4—32no—
97#890—34no—
98#890—62no—
99#887—62no—
100#887—62no—
101#67⋊C4—62no—
102D3×C22⋊C4—62no—
103C4×D12C2×D312yes—
104C42×D3—32no—
105C42×D3—61no—
106#869—32no—
107#869—61no—
108C3×#107—34no—
109C3×C4⋊C8—32no—
110C3×#102—34no—
111#832—34no—
112#821—34no—
113#817—34no—
114Dic3⋊C8—34no—
115#809C2×D314yes—
116#808—34no—
117#807C2×D314yescomplemented
118C4⋊(C3⋊C8)C2×D312yescomplemented
119C22×C3⋊D3C2×D411yescharacteristic
120C22×C3×D3—22no—
121C2×D32—24no—
122C2×D32—42no—
123C2×D32—42no—
124C32×Q8—42no—
125C2×C32×C4—22no—
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2411yescharacteristic
129C2×C3⋊Dic3—22no—
130C2×C3⋊Dic3C2×D411yescharacteristic
131C2×C3⋊Dic3C2×D411yescharacteristic
132C2×C3⋊Dic3C2×D411yescharacteristic
133C4×C3⋊D3—22no—
134C4×C3⋊D3—41no—
135C4×C3⋊D3C2×Q812yes—
136C4×C3⋊D3#4112yes—
137#634—42no—
138C2×C3×Dic3—22no—
139C3×D12—22no—
140C3×D12C2×Q814yes—
141C3×C4×D3—44no—
142#625—24no—
143#624—42no—
144D3×Dic3—44no—
145C3×C3⋊C8—24no—
146#533—91no—
147C2×C4×D4—91no—
148#478—94no—
149#476—92no—
150#474—32no—
151#428—92no—
152#423—91no—
153#418—92no—
154C23×D3—62no—
155C2×C3×Q8—22no—
156C2×C3×Q8—22no—
157C2×C3×D4—32no—
158C22×C3×C4—62no—
159C2×#67—62no—
160C22×Dic3—62no—
161D3×D4—38no—
162D3×D4—64no—
163C2×D12C22×D312yes—
164C2×C4×D3—22no—
165C2×C4×D3—32no—
166C2×C4×D3—32no—
167C2×C4×D3—32no—
168C2×C4×D3—61no—
169C2×C4×D3—61no—
170C2×C4×D3—61no—
171C2×C4×D3—62no—
172C2×C4×D3—62no—
173C2×C4×D3—128no—
174C2×Dic6—62no—
175C2×Dic6—62no—
176C2×C3×C8—34no—
177C3×C4⋊C4—22no—
178C3×C4⋊C4—22no—
179C3×C4⋊C4—22no—
180C3×C4⋊C4—32no—
181C3×C4⋊C4C22×D314yes—
182C3×C22⋊C4—62no—
183C3×C42—21no—
184C3×C42C22×D312yes—
185#217—62no—
186(C2×D3)⋊C4—22no—
187(C2×D3)⋊C4—62no—
188(C2×D3)⋊C4—64no—
189(C2×D3)⋊C4—64no—
190C4⋊Dic3—34no—
191C4⋊Dic3—62no—
192C4⋊Dic3—64no—
193C4⋊Dic3—62no—
194C4⋊Dic3—64no—
195C4⋊Dic3—62no—
196C4⋊Dic3C22×D312yes—
197Dic3⋊C4—62no—
198Dic3⋊C4—64no—
199Dic3⋊C4—64no—
200C4×Dic3—32no—
201C4×Dic3—32no—
202C4×Dic3—32no—
203C4×Dic3—61no—
204C4×Dic3—61no—
205C4×Dic3—61no—
206C4×Dic3—64no—
207C4×Dic3—64no—
208C2×C3⋊C8C22×D314yes—
209ΓL(1,𝔽25)—68no—
210C22×C32C22×D411yescharacteristic
211C2×C3⋊D3—21no—
212C2×C3⋊D3—21no—
213C2×C3⋊D3C22⋊Q812yes—
214C2×C3×D3—24no—
215C2×C3×D3—42no—
216C2×C3×D3—42no—
217D32—48no—
218C32×C4—21no—
219C32×C4—42no—
220C32×C4AGL(1,ℤ/8)12yes—
221C32×C4C22×Q811yescharacteristic
222C32×C4C2×#4111yescharacteristic
223C3⋊Dic3—21no—
224C3⋊Dic3—21no—
225C3⋊Dic3—42no—
226C3⋊Dic3C22⋊Q812yes—
227C3×Dic3—42no—
228C22×D4—91no—
229C23×C4—181no—
230C2×M16—92no—
231C4⋊Q8—91no—
232C4⋊Q8D3211yescharacteristic, complemented
233#125—92no—
234C22⋊Q8—181no—
235C22⋊Q8—181no—
236C4×Q8—181no—
237C4×Q8—181no—
238C4×D4—32no—
239C4×D4—92no—
240C4×D4—181no—
241C4×D4—181no—
242#117—92no—
243C2×C4⋊C4—91no—
244C2×C22⋊C4—181no—
245C2×C42—91no—
246#107—34no—
247#106—94no—
248C4⋊C8—32no—
249C4⋊C8—92no—
250#102—34no—
251#102—94no—
252C23×C3—62no—
253C22×D3—22no—
254C22×D3—32no—
255C22×D3—61no—
256C22×D3—68no—
257C22×D3—124no—
258C22×D3—124no—
259C3×Q8—44no—
260C3×Q8—44no—
261C3×D4—34no—
262C3×D4—62no—
263C2×C3×C4—24no—
264C2×C3×C4—24no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—62no—
269C2×C3×C4—124no—
270C2×C3×C4D3×D412yes—
271C2×C3×C4D3×D412yes—
272C2×C3×C4C23×D312yes—
273#67—68no—
274C2×Dic3—22no—
275C2×Dic3—32no—
276C2×Dic3—32no—
277C2×Dic3—32no—
278C2×Dic3—61no—
279C2×Dic3—61no—
280C2×Dic3—61no—
281C2×Dic3—64no—
282C2×Dic3—64no—
283C2×Dic3—124no—
284D12—22no—
285D12D3×Q814yes—
286C4×D3—34no—
287C4×D3—34no—
288C4×D3—44no—
289C4×D3—62no—
290C4×D3—62no—
291C4×D3—64no—
292C4×D3—122no—
293C4×D3—124no—
294C4×D3—122no—
295C4×D3—124no—
296C4×D3—122no—
297Dic6—124no—
298Dic6—124no—
299C3×C8—64no—
300C3⋊C8—24no—
301C2×C32C2×C22⋊Q811yescharacteristic
302C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
303C2×C32#57511yescharacteristic
304C3⋊D3—22no—
305C3×D3—44no—
306C24—181no—
307C2×Q8—21no—
308C2×Q8—181no—
309C2×D4—32no—
310C2×D4—94no—
311C2×D4—182no—
312C2×D4—181no—
313C22×C4—62no—
314C22×C4—91no—
315C22×C4—91no—
316C22×C4—91no—
317C22×C4—181no—
318C22×C4—182no—
319C22×C4—364no—
320M16—184no—
321C2×C8—34no—
322C4⋊C4—21no—
323C4⋊C4—32no—
324C4⋊C4—92no—
325C4⋊C4—182no—
326C4⋊C4—182no—
327C4⋊C4—181no—
328C4⋊C4—181no—
329C4⋊C4C2×D3212yes—
330C22⋊C4—62no—
331C22⋊C4—182no—
332C22⋊C4—182no—
333C42—91no—
334C42—91no—
335C42—91no—
336C42—182no—
337C42C2×D3211yescharacteristic
338C22×C3—21no—
339C22×C3—64no—
340C22×C3—122no—
341C22×C3—122no—
342C22×C3C2×D3×D412yes—
343C2×D3—24no—
344C2×D3—34no—
345C2×D3—42no—
346C2×D3—42no—
347C2×D3—62no—
348C2×D3—62no—
349C2×D3—62no—
350C2×D3—121no—
351C2×D3—121no—
352C2×D3—1216no—
353C3×C4—22no—
354C3×C4—22no—
355C3×C4—21no—
356C3×C4—21no—
357C3×C4—22no—
358C3×C4—44no—
359C3×C4—44no—
360C3×C4—122no—
361C3×C4#91114yes—
362C3×C4C2×D3×Q812yes—
363C3×C4D3×#4112yes—
364Dic3—34no—
365Dic3—42no—
366Dic3—62no—
367Dic3—62no—
368Dic3—62no—
369Dic3—121no—
370Dic3—121no—
371Dic3—124no—
372Dic3—124no—
373C32#307711yescharacteristic, complemented, Sylow
374C23—62no—
375C23—91no—
376C23—184no—
377C23—362no—
378C23—362no—
379Q8—42no—
380Q8—362no—
381D4—34no—
382D4—62no—
383D4—184no—
384C2×C4—22no—
385C2×C4—62no—
386C2×C4—91no—
387C2×C4—92no—
388C2×C4—92no—
389C2×C4—91no—
390C2×C4—91no—
391C2×C4—124no—
392C2×C4—182no—
393C2×C4—182no—
394C2×C4—361no—
395C2×C4—362no—
396C2×C4—364no—
397C2×C4#381111yescharacteristic
398C2×C4#381111yescharacteristic
399C2×C4C22×D3211yescharacteristic
400C8—64no—
401C2×C3—21no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3—124no—
405C2×C3D3×C22⋊Q812yes—
406C2×C3C2×#91112yes—
407C2×C3#577712yes—
408D3—44no—
409D3—64no—
410D3—122no—
411C22—64no—
412C22—92no—
413C22—122no—
414C22—122no—
415C22—181no—
416C22—181no—
417C22—368no—
418C22C2×#381111yescharacteristic
419C4—21no—
420C4—42no—
421C4—92no—
422C4—122no—
423C4—181no—
424C4—181no—
425C4—362no—
426C4#6392712yes—
427C4D32×Q811yescharacteristic
428C4#6431911yescharacteristic
429C3—21no—
430C3#8096512yescomplemented
431C2—124no—
432C2—182no—
433C2C2×#6392711yescharacteristic
434C2#1059532311yescharacteristic
435C2#1059542911yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×#3802C22
hypercenterC4⋊Q8D32
hypocenterC32#3077
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10596199C2semidirect
3. C3×#5087C2semidirect
5. #10590582C2semidirect
6. #10590473C2semidirect
7. #10590340C2semidirect
8. #10590268C2semidirect
12. C32×C4⋊Q8C22semidirect
17. #64099C22semidirect
20. #64078C22semidirect
29. C3×#807C22semidirect
30. C3×C4⋊(C3⋊C8)C22semidirect
31. #63573C22semidirect
32. #63572C22semidirect
38. #5087D3semidirect
58. #3802Q8semidirect
82. C3×C4⋊Q8C2×D3semidirect
117. #807C2×D3semidirect
118. C4⋊(C3⋊C8)C2×D3semidirect
232. C4⋊Q8D32semidirect
373. C32#3077semidirect
430. C3#80965semidirect

Maximal subgroups

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

subgroupindex
#105961992
C4×#38022
C3×#50872
#105905942
#105905822
#105904732
#105903402
#105902682
#809653