Finite Group Databasebeta

← #11868636

Subgroups — #11868636

Order 1152.

1320 conjugacy classes of subgroups.

The subgroup lattice has 435 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596199C211yesmaximal, characteristic, complemented
2C4×D4×C3⋊D3C211yesmaximal, characteristic
3C32×#474C211yesmaximal, characteristic, complemented
4#10592786C211yesmaximal, characteristic, complemented
5#10592707C211yesmaximal, characteristic, complemented
6#10592590C212yesmaximal, complemented
7#10592580C212yesmaximal, complemented
8#10592541C211yesmaximal, characteristic, complemented
9#10592536C211yesmaximal, characteristic, complemented
10#10592469C212yesmaximal
11#10592462C212yesmaximal, complemented
12#80965—34nomaximal
13C2×D4×C3⋊D3C2211yescharacteristic
14C22×C4×C3⋊D3—21no—
15C32×C4⋊Q8C2211yescharacteristic, complemented
16C32×C4×D4C2211yescharacteristic
17#64155—21no—
18Q8×C3⋊Dic3—21no—
19D4×C3⋊Dic3C2211yescharacteristic
20C4×#638—21no—
21C2×#3743C2212yes—
22#64106—21no—
23#64102C2211yescharacteristic
24#64101C2212yes—
25C4⋊C4×C3⋊D3C2211yescharacteristic
26#64099C2212yescomplemented
27#64096—21no—
28#64090—21no—
29C22⋊C4×C3⋊D3—21no—
30C4×C4⋊(C3⋊D3)C2211yescharacteristic
31C42×C3⋊D3C2211yescharacteristic
32#64078C2211yescharacteristic, complemented
33C32×#107C2212yescomplemented
34C32×C4⋊C8C2211yescharacteristic, complemented
35C32×#102C2212yes—
36#63659C2212yes—
37#63648C2212yes—
38#63644C2212yescomplemented
39#63641C2212yescomplemented
40#63636C2212yes—
41#63635C2212yescomplemented
42#63634C2212yescomplemented
43C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
44#5728—34no—
45C4×D3×D4—34no—
46C3×#474D314yescomplemented
47#5087—34no—
48#5008—34no—
49#4891—38no—
50#4881—38no—
51#4842—34no—
52#4837—34no—
53#4770—38no—
54#4763—38no—
55C23×C3⋊D3—21no—
56C2×C32×Q8—21no—
57C2×C32×D4C2311yescharacteristic
58C22×C32×C4—21no—
59C2×#638—21no—
60C22×C3⋊Dic3—21no—
61D4×C3⋊D3—22no—
62D4×C3⋊D3Q814yescomplemented
63C2×C4⋊(C3⋊D3)C2311yescharacteristic
64C2×C4×C3⋊D3—21no—
65C2×C4×C3⋊D3—21no—
66C2×C4×C3⋊D3—21no—
67C2×C4×C3⋊D3—44no—
68C2×C4×C3⋊D3D411yescharacteristic
69C2×C4×C3⋊D3D411yescharacteristic
70C2×C4×C3⋊D3C2311yescharacteristic
71C2×#634—21no—
72C2×C32×C8C2312yes—
73C32×C4⋊C4—21no—
74C32×C4⋊C4C2312yes—
75C32×C4⋊C4C2311yescharacteristic
76C32×C22⋊C4—21no—
77C32×C42C2311yescharacteristic
78#3757—21no—
79#3752—22no—
80#3752—21no—
81#3752—21no—
82C4⋊(C3⋊Dic3)—21no—
83C4⋊(C3⋊Dic3)—22no—
84C4⋊(C3⋊Dic3)C2312yes—
85C4⋊(C3⋊Dic3)C2311yescharacteristic
86#3750—21no—
87#3750—22no—
88C4×C3⋊Dic3—22no—
89C4×C3⋊Dic3D411yescharacteristic
90C4×C3⋊Dic3D411yescharacteristic
91C4×C3⋊Dic3C2311yescharacteristic
92C2×C3⋊(C3⋊C8)C2312yes—
93#3743—24no—
94#3077—91noSylow
95C2×D3×D4—34no—
96C22×C4×D3—64no—
97C3×C4⋊Q8C2×D314yescomplemented
98C3×C4×D4C2×D314yes—
99#946—64no—
100Q8×Dic3—64no—
101D4×Dic3—34no—
102C4×#67—64no—
103C2×ΓL(1,𝔽25)—38no—
104#897—64no—
105#893—34no—
106#892—38no—
107D3×C4⋊C4—34no—
108#890—38no—
109#887—64no—
110#67⋊C4—64no—
111D3×C22⋊C4—64no—
112C4×D12—34no—
113C42×D3—34no—
114#869—34no—
115C3×#107C2×D318yescomplemented
116C3×C4⋊C8C2×D314yescomplemented
117C3×#102C2×D318yes—
118#832—38no—
119#821—38no—
120#817—38no—
121Dic3⋊C8—38no—
122#809—38no—
123#808—38no—
124#807—38no—
125C4⋊(C3⋊C8)—34no—
126C23×C32—21no—
127C22×C3⋊D3—21no—
128C22×C3⋊D3—24no—
129C22×C3⋊D3—42no—
130C22×C3⋊D3—42no—
131C22×C3⋊D3C2×D411yescharacteristic
132C32×Q8—42no—
133C32×D4—21no—
134C32×D4C2×Q812yes—
135C2×C32×C4—22no—
136C2×C32×C4—21no—
137C2×C32×C4—42no—
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2411yescharacteristic
141#638—24no—
142C2×C3⋊Dic3—22no—
143C2×C3⋊Dic3—21no—
144C2×C3⋊Dic3—42no—
145C2×C3⋊Dic3C2×D411yescharacteristic
146C2×C3⋊Dic3C2×D411yescharacteristic
147C2×C3⋊Dic3C2×D411yescharacteristic
148C4⋊(C3⋊D3)—21no—
149C4⋊(C3⋊D3)C2×Q812yes—
150C4×C3⋊D3—22no—
151C4×C3⋊D3—41no—
152C4×C3⋊D3—42no—
153C4×C3⋊D3—42no—
154C4×C3⋊D3—42no—
155C4×C3⋊D3C2×Q812yes—
156C4×C3⋊D3#4112yes—
157#634—42no—
158C32×C8—22no—
159C3⋊(C3⋊C8)—22no—
160#533—91no—
161C2×C4×D4—91no—
162#478—92no—
163#478—92no—
164#476—91no—
165#476—91no—
166#474—91no—
167#474C3⋊D311yescharacteristic, complemented
168#428—92no—
169#423—91no—
170#418—92no—
171C23×D3—64no—
172C2×C3×Q8—24no—
173C2×C3×D4C22×D314yes—
174C22×C3×C4—24no—
175C2×#67—64no—
176C22×Dic3—64no—
177D3×D4—316no—
178D3×D4—68no—
179C2×D12—34no—
180C2×C4×D3—34no—
181C2×C4×D3—34no—
182C2×C4×D3—34no—
183C2×C4×D3—64no—
184C2×C4×D3—64no—
185C2×C4×D3—64no—
186C2×C4×D3—1216no—
187C2×Dic6—64no—
188C2×C3×C8C22×D318yes—
189C3×C4⋊C4—24no—
190C3×C4⋊C4C22×D318yes—
191C3×C4⋊C4C22×D314yes—
192C3×C22⋊C4—24no—
193C3×C42C22×D314yes—
194#217—64no—
195(C2×D3)⋊C4—64no—
196(C2×D3)⋊C4—68no—
197(C2×D3)⋊C4—64no—
198C4⋊Dic3—34no—
199C4⋊Dic3—38no—
200C4⋊Dic3—68no—
201C4⋊Dic3—64no—
202Dic3⋊C4—64no—
203Dic3⋊C4—68no—
204C4×Dic3—34no—
205C4×Dic3—34no—
206C4×Dic3—34no—
207C4×Dic3—68no—
208C2×C3⋊C8—38no—
209ΓL(1,𝔽25)—616no—
210C22×C32—22no—
211C22×C32—41no—
212C22×C32—41no—
213C22×C32C22×D411yescharacteristic
214C2×C3⋊D3—21no—
215C2×C3⋊D3—21no—
216C2×C3⋊D3—22no—
217C2×C3⋊D3—48no—
218C2×C3⋊D3—41no—
219C2×C3⋊D3—41no—
220C2×C3⋊D3C22⋊Q812yes—
221C32×C4—21no—
222C32×C4—41no—
223C32×C4—42no—
224C32×C4AGL(1,ℤ/8)12yes—
225C32×C4C22×Q811yescharacteristic
226C32×C4C2×#4111yescharacteristic
227C3⋊Dic3—21no—
228C3⋊Dic3—21no—
229C3⋊Dic3—41no—
230C3⋊Dic3—42no—
231C3⋊Dic3C22⋊Q812yes—
232C22×D4—91no—
233C23×C4—181no—
234C2×M16—92no—
235C4⋊Q8—91no—
236C4⋊Q8C2×C3⋊D311yescharacteristic, complemented
237#125—92no—
238C22⋊Q8—181no—
239C22⋊Q8—181no—
240C4×Q8—181no—
241C4×Q8—181no—
242C4×D4—91no—
243C4×D4—91no—
244C4×D4—91no—
245C4×D4—181no—
246C4×D4—181no—
247C4×D4C2×C3⋊D311yescharacteristic
248#117—92no—
249C2×C4⋊C4—91no—
250C2×C22⋊C4—181no—
251C2×C42—91no—
252#107—92no—
253#107C2×C3⋊D312yescomplemented
254#106—92no—
255#106—92no—
256C4⋊C8—92no—
257C4⋊C8—91no—
258C4⋊C8C2×C3⋊D311yescharacteristic, complemented
259#102—92no—
260#102—92no—
261#102—92no—
262#102C2×C3⋊D312yes—
263C23×C3—24no—
264C22×D3—34no—
265C22×D3—616no—
266C22×D3—64no—
267C22×D3—128no—
268C22×D3—128no—
269C3×Q8—48no—
270C3×D4—24no—
271C3×D4D3×Q818yes—
272C2×C3×C4—28no—
273C2×C3×C4—24no—
274C2×C3×C4—48no—
275C2×C3×C4D3×D414yes—
276C2×C3×C4D3×D414yes—
277C2×C3×C4C23×D314yes—
278#67—616no—
279C2×Dic3—34no—
280C2×Dic3—34no—
281C2×Dic3—34no—
282C2×Dic3—68no—
283C2×Dic3—64no—
284C2×Dic3—128no—
285D12—38no—
286D12—64no—
287C4×D3—38no—
288C4×D3—38no—
289C4×D3—68no—
290C4×D3—124no—
291C4×D3—128no—
292C4×D3—128no—
293C4×D3—128no—
294Dic6—128no—
295C3×C8—28no—
296C3⋊C8—68no—
297C2×C32—42no—
298C2×C32C2×C22⋊Q811yescharacteristic
299C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
300C2×C32#57511yescharacteristic
301C3⋊D3—22no—
302C3⋊D3—42no—
303C24—181no—
304C2×Q8—21no—
305C2×Q8—181no—
306C2×D4—94no—
307C2×D4—91no—
308C2×D4—182no—
309C2×D4—181no—
310C2×D4C22×C3⋊D311yescharacteristic
311C22×C4—21no—
312C22×C4—91no—
313C22×C4—91no—
314C22×C4—91no—
315C22×C4—181no—
316C22×C4—181no—
317C22×C4—181no—
318C22×C4—181no—
319C22×C4—364no—
320M16—184no—
321C2×C8—92no—
322C2×C8C22×C3⋊D312yes—
323C4⋊C4—21no—
324C4⋊C4—92no—
325C4⋊C4—91no—
326C4⋊C4—181no—
327C4⋊C4—182no—
328C4⋊C4—182no—
329C4⋊C4—181no—
330C4⋊C4C22×C3⋊D312yes—
331C4⋊C4C22×C3⋊D311yescharacteristic
332C22⋊C4—21no—
333C22⋊C4—181no—
334C22⋊C4—182no—
335C22⋊C4—181no—
336C22⋊C4—181no—
337C42—91no—
338C42—91no—
339C42—91no—
340C42—182no—
341C42C22×C3⋊D311yescharacteristic
342C22×C3—28no—
343C22×C3—44no—
344C22×C3—44no—
345C22×C3C2×D3×D414yes—
346C2×D3—38no—
347C2×D3—64no—
348C2×D3—64no—
349C2×D3—68no—
350C2×D3—1232no—
351C2×D3—124no—
352C2×D3—124no—
353C3×C4—24no—
354C3×C4—44no—
355C3×C4—48no—
356C3×C4#91118yes—
357C3×C4C2×D3×Q814yes—
358C3×C4D3×#4114yes—
359Dic3—38no—
360Dic3—64no—
361Dic3—64no—
362Dic3—124no—
363Dic3—128no—
364C32#307711yescharacteristic, complemented, Sylow
365C23—21no—
366C23—91no—
367C23—184no—
368C23—181no—
369C23—362no—
370C23—362no—
371Q8—42no—
372Q8—362no—
373D4—21no—
374D4—92no—
375D4—184no—
376D4—181no—
377D4Q8×C3⋊D312yes—
378C2×C4—22no—
379C2×C4—21no—
380C2×C4—42no—
381C2×C4—91no—
382C2×C4—92no—
383C2×C4—92no—
384C2×C4—91no—
385C2×C4—91no—
386C2×C4—182no—
387C2×C4—182no—
388C2×C4—181no—
389C2×C4—361no—
390C2×C4—362no—
391C2×C4—362no—
392C2×C4—362no—
393C2×C4—362no—
394C2×C4D4×C3⋊D311yescharacteristic
395C2×C4D4×C3⋊D311yescharacteristic
396C2×C4C23×C3⋊D311yescharacteristic
397C8—22no—
398C8—182no—
399C2×C3—48no—
400C2×C3D3×C22⋊Q814yes—
401C2×C3C2×#91114yes—
402C2×C3#577714yes—
403D3—68no—
404D3—128no—
405C22—22no—
406C22—41no—
407C22—41no—
408C22—92no—
409C22—181no—
410C22—181no—
411C22—182no—
412C22—368no—
413C22—361no—
414C22—361no—
415C22C2×D4×C3⋊D311yescharacteristic
416C4—21no—
417C4—41no—
418C4—42no—
419C4—92no—
420C4—181no—
421C4—181no—
422C4—361no—
423C4—362no—
424C4#6412012yes—
425C4C2×Q8×C3⋊D311yescharacteristic
426C4#41×C3⋊D311yescharacteristic
427C3#8096514yescomplemented
428C2—42no—
429C2—182no—
430C2—362no—
431C2C3⋊D3×C22⋊Q811yescharacteristic
432C2C2×#6412011yescharacteristic
433C2#1059624811yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#474C2
socleC22×C32C22×D4
prime radicalC2×D4×C3⋊D3C22
hypercenter#474C3⋊D3
hypocenterC32#3077
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #10596199C2semidirect
3. C32×#474C2semidirect
4. #10592786C2semidirect
5. #10592707C2semidirect
6. #10592590C2semidirect
7. #10592580C2semidirect
8. #10592541C2semidirect
9. #10592536C2semidirect
11. #10592462C2semidirect
15. C32×C4⋊Q8C22semidirect
26. #64099C22semidirect
32. #64078C22semidirect
33. C32×#107C22semidirect
34. C32×C4⋊C8C22semidirect
38. #63644C22semidirect
39. #63641C22semidirect
41. #63635C22semidirect
42. #63634C22semidirect
43. C4⋊(C3⋊(C3⋊C8))C22semidirect
46. C3×#474D3semidirect
62. D4×C3⋊D3Q8semidirect
97. C3×C4⋊Q8C2×D3semidirect
115. C3×#107C2×D3semidirect
116. C3×C4⋊C8C2×D3semidirect
167. #474C3⋊D3semidirect
236. C4⋊Q8C2×C3⋊D3semidirect
253. #107C2×C3⋊D3semidirect
258. C4⋊C8C2×C3⋊D3semidirect
364. C32#3077semidirect
427. C3#80965semidirect

Maximal subgroups

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

subgroupindex
#105961992
C4×D4×C3⋊D32
C32×#4742
#105927862
#105927072
#105925902
#105925802
#105925412
#105925362
#105924692
#105924622
#809653