Finite Group Databasebeta

← #11873556

Subgroups — #11873556

Order 1152.

1017 conjugacy classes of subgroups; only the 164 normal subgroups are shown.

normal subgroups only

This group has 1017 conjugacy classes of subgroups — too many to draw. Only its 164 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
1C3⋊D3×C4⋊Q8C211yesmaximal, characteristic, complemented
2#10594009C211yesmaximal, characteristic
3C3×#5089C212yesmaximal, complemented
4#10590601C212yesmaximal, complemented
5#10590593C212yesmaximal
6#10590541C214yesmaximal, complemented
7#10590322C211yesmaximal, characteristic, complemented
8#10590276C212yesmaximal, complemented
9D3×#489—32nomaximal
10C2×Q8×C3⋊D3—21no—
11C2×#3802C2211yescharacteristic
12C2×#3797C2211yescharacteristic
13C32×C4⋊Q8C2211yescharacteristic, complemented
14#64153—21no—
15C4⋊C4×C3⋊D3—21no—
16C4⋊C4×C3⋊D3C2212yes—
17#64097—21no—
18#64097C2212yescomplemented
19C42×C3⋊D3C2211yescharacteristic
20#64078C2211yescharacteristic, complemented
21C3×#875C2212yes—
22#63921—21no—
23#63921—21no—
24#63915—21no—
25#63915—21no—
26#63863C2212yes—
27C2×#3710C2212yes—
28C3×#810C2214yescomplemented
29C3×#809C2214yes—
30C3×#803C2212yescomplemented
31#63566C2214yescomplemented
32#63563C2214yes—
33#63555C2212yescomplemented
34D3×C4⋊Q8—32no—
35D3×C4⋊Q8—61no—
36D3×#124—32no—
37C3×#489—32no—
38#5089D312yescomplemented
39#5055—32no—
40D3×#103—34no—
41#4794—34no—
42D3×#102—34no—
43#4765—34no—
44#4714—32no—
45D3×#97—32no—
46C22×D32—21no—
47C2×C32×Q8—21no—
48Q8×C3⋊D3—44no—
49C2×C4×C3⋊D3—22no—
50C2×C4×C3⋊D3D411yescharacteristic
51C2×C4×C3⋊D3D411yescharacteristic
52C2×C4×C3⋊D3C2311yescharacteristic
53C2×#634—21no—
54C2×#634—22no—
55C2×C3×D12C2312yes—
56C2×C3×Dic6C2312yes—
57C2×#627—21no—
58C2×#625—21no—
59C2×#624—21no—
60#3802—24no—
61#3797—24no—
62C32×C4⋊C4—21no—
63C32×C4⋊C4C2312yes—
64C32×C42C2311yescharacteristic
65C4⋊(C3⋊Dic3)—21no—
66C4⋊(C3⋊Dic3)C2312yes—
67#3750—22no—
68#3750—22no—
69C4×C3⋊Dic3D411yescharacteristic
70C4×C3⋊Dic3D411yescharacteristic
71C4×C3⋊Dic3C2311yescharacteristic
72C3×(C2×D3)⋊C4—22no—
73C3×(C2×D3)⋊C4—22no—
74C2×C3×C3⋊C8C2314yes—
75(C2×D3)⋊Dic3—22no—
76(C2×D3)⋊Dic3—22no—
77#3710—24no—
78C2×#489—91noSylow
79C2×D3×Q8—32no—
80C2×D3×Q8—62no—
81C2×D3×Q8—62no—
82C2×D3×D4—32no—
83C3×C4⋊Q8—21no—
84C3×C4⋊Q8C2×D312yescomplemented
85C3×#124—32no—
86#947—32no—
87#944—62no—
88#944—62no—
89#936—32no—
90C2×D3×C8—34no—
91D3×C4⋊C4—34no—
92D3×C4⋊C4—62no—
93D3×C4⋊C4—62no—
94D3×C4⋊C4—62no—
95#888—34no—
96#888—62no—
97#888—62no—
98#888—62no—
99#885—62no—
100#885—62no—
101D3×C22⋊C4—62no—
102D3×C22⋊C4—62no—
103#875C2×D312yes—
104C42×D3—32no—
105C42×D3—61no—
106#869—32no—
107#869—61no—
108C3×#103—34no—
109C3×#102—34no—
110C3×#97—32no—
111#835—34no—
112#832—34no—
113#821—34no—
114#816—34no—
115#815—34no—
116#810C2×D314yescomplemented
117#809C2×D314yes—
118#803C2×D312yescomplemented
119C22×C3⋊D3C2×D411yescharacteristic
120C22×C3×D3—22no—
121C2×D32—42no—
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—22no—
135C4×C3⋊D3—44no—
136C4×C3⋊D3#4114yes—
137#634—44no—
138#634—42no—
139C2×C3×Dic3—22no—
140C3×D12—24no—
141C3×Dic6—24no—
142#627—42no—
143#625—42no—
144#624—42no—
145C3×C3⋊C8—24no—
146C2×C4⋊Q8—91no—
147C2×#124—91no—
148#489—32no—
149#489—92no—
150#489—94no—
151C2×#103—92no—
152C2×#102—92no—
153C2×#97—91no—
154C23×D3—62no—
155C2×C3×Q8—22no—
156C2×C3×Q8—22no—
157C2×C3×Q8—32no—
158C2×C3×D4—32no—
159C2×#67—62no—
160D3×Q8—68no—
161D3×Q8—128no—
162D3×Q8—128no—
163D3×D4—68no—
164C2×D12C22×D312yes—
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—64no—
173C2×C4×D3—64no—
174C2×Dic6—62no—
175C2×Dic6—64no—
176C2×Dic6—62no—
177C2×Dic6—64no—
178C2×Dic6—62no—
179C2×Dic6C22×D312yes—
180C2×C3×C8—34no—
181C3×C4⋊C4—22no—
182C3×C4⋊C4—22no—
183C3×C4⋊C4—22no—
184C3×C4⋊C4C22×D314yes—
185C3×C22⋊C4—62no—
186C3×C22⋊C4—62no—
187C3×C42—21no—
188C3×C42C22×D312yes—
189#217—62no—
190#217—62no—
191(C2×D3)⋊C4—22no—
192(C2×D3)⋊C4—22no—
193(C2×D3)⋊C4—62no—
194(C2×D3)⋊C4—62no—
195C4⋊Dic3—34no—
196C4⋊Dic3—62no—
197C4⋊Dic3—62no—
198C4⋊Dic3—62no—
199Dic3⋊C4—64no—
200Dic3⋊C4—64no—
201Dic3⋊C4—64no—
202Dic3⋊C4—64no—
203C4×Dic3—32no—
204C4×Dic3—32no—
205C4×Dic3—32no—
206C4×Dic3—61no—
207C4×Dic3—61no—
208C4×Dic3—61no—
209C2×C3⋊C8C22×D314yes—
210D3×C8—68no—
211C22×C32C22×D411yescharacteristic
212C2×C3⋊D3#12412yes—
213C2×C3⋊D3AGL(1,ℤ/8)12yes—
214C2×C3⋊D3#13712yes—
215C2×C3×D3—42no—
216C2×C3×D3—42no—
217C2×C3×D3—42no—
218D32—84no—
219C32×C4—21no—
220C32×C4—21no—
221C32×C4—42no—
222C32×C4C2×#4112yes—
223C3⋊Dic3—21no—
224C3⋊Dic3—21no—
225C3⋊Dic3—42no—
226C3⋊Dic3#12412yes—
227C3×Dic3—42no—
228C22×Q8—91no—
229C22×Q8—181no—
230C22×D4—91no—
231C22×C8—92no—
232C4⋊Q8—92no—
233C4⋊Q8—91no—
234C4⋊Q8—181no—
235C4⋊Q8—181no—
236C4⋊Q8D3211yescharacteristic, complemented
237#124—32no—
238#124—92no—
239#124—181no—
240#124—181no—
241C2×C4⋊C4—92no—
242C2×C4⋊C4—181no—
243C2×C22⋊C4—181no—
244C2×C22⋊C4—181no—
245C2×C42—91no—
246#103—34no—
247#103—94no—
248#102—34no—
249#102—94no—
250#97—32no—
251#97—92no—
252C23×C3—62no—
253C22×D3—22no—
254C22×D3—32no—
255C22×D3—61no—
256C22×D3—124no—
257C22×D3—124no—
258C22×D3—124no—
259C3×Q8—44no—
260C3×Q8—44no—
261C3×Q8—64no—
262C3×D4—64no—
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×C4D3×D412yes—
270C2×C3×C4D3×D412yes—
271C2×C3×C4C23×D312yes—
272#67—124no—
273C2×Dic3—22no—
274C2×Dic3—32no—
275C2×Dic3—32no—
276C2×Dic3—32no—
277C2×Dic3—61no—
278C2×Dic3—61no—
279C2×Dic3—61no—
280C2×Dic3—64no—
281C2×Dic3—64no—
282D12—24no—
283C4×D3—38no—
284C4×D3—64no—
285C4×D3—64no—
286C4×D3—64no—
287C4×D3—64no—
288C4×D3—64no—
289C4×D3—124no—
290C4×D3—128no—
291C4×D3—128no—
292Dic6—24no—
293Dic6—124no—
294Dic6—128no—
295Dic6—128no—
296Dic6—124no—
297Dic6—124no—
298C3×C8—64no—
299C3⋊C8—24no—
300C2×C32C2×#12411yescharacteristic
301C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
302C2×C32C2×#13711yescharacteristic
303C3⋊D3#48914yescomplemented
304C3×D3—82no—
305C24—181no—
306C2×Q8—21no—
307C2×Q8—32no—
308C2×Q8—182no—
309C2×Q8—181no—
310C2×Q8—184no—
311C2×Q8—181no—
312C2×Q8—364no—
313C2×D4—32no—
314C2×D4—184no—
315C2×D4—181no—
316C22×C4—91no—
317C22×C4—91no—
318C22×C4—91no—
319C22×C4—182no—
320C22×C4—181no—
321C2×C8—34no—
322C2×C8—184no—
323C4⋊C4—21no—
324C4⋊C4—92no—
325C4⋊C4—182no—
326C4⋊C4—182no—
327C4⋊C4—181no—
328C4⋊C4C2×D3212yes—
329C22⋊C4—62no—
330C22⋊C4—62no—
331C22⋊C4—182no—
332C22⋊C4—182no—
333C42—91no—
334C42—91no—
335C42—91no—
336C42C2×D3211yescharacteristic
337C22×C3—21no—
338C22×C3—122no—
339C22×C3—122no—
340C22×C3—122no—
341C22×C3C2×D3×D412yes—
342C2×D3—34no—
343C2×D3—34no—
344C2×D3—34no—
345C2×D3—42no—
346C2×D3—42no—
347C2×D3—42no—
348C2×D3—62no—
349C2×D3—62no—
350C2×D3—62no—
351C2×D3—248no—
352C3×C4—22no—
353C3×C4—22no—
354C3×C4—22no—
355C3×C4—22no—
356C3×C4—22no—
357C3×C4—44no—
358C3×C4—44no—
359C3×C4—122no—
360C3×C4D3×#4114yes—
361Dic3—34no—
362Dic3—42no—
363Dic3—62no—
364Dic3—62no—
365Dic3—62no—
366Dic3—62no—
367Dic3—62no—
368Dic3—124no—
369Dic3—124no—
370C32C2×#48911yescharacteristic, complemented, Sylow
371C23—62no—
372C23—91no—
373C23—362no—
374C23—362no—
375C23—362no—
376Q8—42no—
377Q8—64no—
378Q8—362no—
379Q8—364no—
380Q8—362no—
381D4—64no—
382D4—362no—
383C2×C4—22no—
384C2×C4—62no—
385C2×C4—91no—
386C2×C4—94no—
387C2×C4—91no—
388C2×C4—91no—
389C2×C4—182no—
390C2×C4—182no—
391C2×C4—182no—
392C2×C4—364no—
393C2×C4—362no—
394C2×C4#381111yescharacteristic
395C2×C4#381111yescharacteristic
396C2×C4C22×D3211yescharacteristic
397C8—64no—
398C2×C3—21no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3—242no—
402C2×C3D3×#12412yes—
403C2×C3D3×AGL(1,ℤ/8)12yes—
404C2×C3D3×#13712yes—
405D3—38no—
406D3—64no—
407D3—82no—
408C22—92no—
409C22—92no—
410C22—92no—
411C22—122no—
412C22—122no—
413C22—122no—
414C22—724no—
415C22C2×#381111yescharacteristic
416C4—21no—
417C4—21no—
418C4—42no—
419C4—92no—
420C4—122no—
421C4—181no—
422C4—181no—
423C4—362no—
424C4#6431912yes—
425C3—21no—
426C3D3×#48912yescomplemented
427C2—94no—
428C2—242no—
429C2#1059510011yescharacteristic
430C2#1059532211yescharacteristic
431C2#1059543211yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×#3802C22
hypercenterC4⋊Q8D32
hypocenterC32C2×#489
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. C3⋊D3×C4⋊Q8C2semidirect
3. C3×#5089C2semidirect
4. #10590601C2semidirect
6. #10590541C2semidirect
7. #10590322C2semidirect
8. #10590276C2semidirect
13. C32×C4⋊Q8C22semidirect
18. #64097C22semidirect
20. #64078C22semidirect
28. C3×#810C22semidirect
30. C3×#803C22semidirect
31. #63566C22semidirect
33. #63555C22semidirect
38. #5089D3semidirect
84. C3×C4⋊Q8C2×D3semidirect
116. #810C2×D3semidirect
118. #803C2×D3semidirect
236. C4⋊Q8D32semidirect
303. C3⋊D3#489semidirect
370. C32C2×#489semidirect
426. C3D3×#489semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×C4⋊Q82
#105940092
C3×#50892
#105906012
#105905932
#105905412
#105903222
#105902762
D3×#4893