Finite Group Databasebeta

← #11859964

Subgroups — #11859964

Order 1152.

1500 conjugacy classes of subgroups.

The subgroup lattice has 405 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×C3⋊Dic3C211yesmaximal, characteristic, complemented
2C2×#64159C211yesmaximal, characteristic
3#10595993C211yesmaximal, characteristic, complemented
4C32×#416C211yesmaximal, characteristic, complemented
5#10592812C211yesmaximal, characteristic, complemented
6C2×C8×C3⋊Dic3C211yesmaximal, characteristic, complemented
7#10592697C211yesmaximal, characteristic, complemented
8#10592489C212yesmaximal, complemented
9#10592487C212yesmaximal, complemented
10#10592457C212yesmaximal, complemented
11#10592455C212yesmaximal, complemented
12#78818—34nomaximal
13C2×C32×#41C2211yescharacteristic
14C2×#3828C2211yescharacteristic
15C22×C32×C8C2211yescharacteristic
16C32×#117C2211yescharacteristic
17#64159C418yescomplemented
18Q8×C3⋊Dic3C2212yes—
19C2×#3756C2211yescharacteristic
20C2×#3755C2211yescharacteristic
21D4×C3⋊Dic3—22no—
22D4×C3⋊Dic3C2212yes—
23C2×#3754C2211yescharacteristic
24C2×#3753C2211yescharacteristic
25#64135—21no—
26#64135C2211yescharacteristic
27C2×C4×C3⋊Dic3—21no—
28C2×C4×C3⋊Dic3C2211yescharacteristic
29C22×C3⋊(C3⋊C8)C2211yescharacteristic
30#64102C2212yes—
31#64096C2212yes—
32#64090—22no—
33#64081—21no—
34C42×C3⋊D3—21no—
35C32×#103C2212yes—
36C32×#102C2212yes—
37#63648C2212yes—
38#63643C2212yes—
39C8×C3⋊Dic3C2212yes—
40C8×C3⋊Dic3C2212yes—
41#63635C2212yes—
42#63634C2212yes—
43Dic3×#41—34no—
44C2×#950—34no—
45#5522—34no—
46C3×#416D314yescomplemented
47#5113—34no—
48C2×C8×Dic3—34no—
49#4998—34no—
50#4790—38no—
51#4788—38no—
52#4758—38no—
53#4756—38no—
54C32×#41—22no—
55C32×#41C2×C414yescomplemented
56C2×C32×Q8C2311yescharacteristic
57C2×C32×D4—21no—
58C2×C32×D4C2311yescharacteristic
59C22×C32×C4—21no—
60C22×C32×C4C2311yescharacteristic
61C2×#638—21no—
62C22×C3⋊Dic3—22no—
63C22×C3⋊Dic3D412yes—
64#3828—22no—
65#3828C2×C414yescomplemented
66C2×C4⋊(C3⋊D3)C2311yescharacteristic
67C2×C4×C3⋊D3—21no—
68C2×C4×C3⋊D3—22no—
69C2×#634C2311yescharacteristic
70C2×C32×C8—22no—
71C2×C32×C8C2312yes—
72C32×C4⋊C4C2312yes—
73C32×C22⋊C4—21no—
74C32×C42—21no—
75#3757—21no—
76#3757—22no—
77#3756C2×C414yescomplemented
78#3755C2×C414yescomplemented
79#3754C2×C414yescomplemented
80#3753C2×C414yescomplemented
81#3752—22no—
82C4⋊(C3⋊Dic3)—22no—
83C4⋊(C3⋊Dic3)C2312yes—
84#3750—22no—
85C4×C3⋊Dic3—21no—
86C4×C3⋊Dic3—22no—
87C4×C3⋊Dic3—22no—
88C4×C3⋊Dic3D411yescharacteristic
89C4×C3⋊Dic3D411yescharacteristic
90C4×C3⋊Dic3C2312yes—
91C2×C3⋊(C3⋊C8)C2×C414yescomplemented
92C2×C3⋊(C3⋊C8)C2311yescharacteristic
93C2×C3⋊(C3⋊C8)C2311yescharacteristic
94C4×#135—91noSylow
95C2×C3×#41C2×D314yes—
96C2×#235—34no—
97C22×C3×C8C2×D314yes—
98C3×#117C2×D314yes—
99#950—332no—
100Q8×Dic3—38no—
101C2×#216—34no—
102C2×#215—34no—
103D4×Dic3—38no—
104D4×Dic3—68no—
105C2×#214—34no—
106C2×#213—34no—
107#926—34no—
108#926—64no—
109C2×C4×Dic3—34no—
110C2×C4×Dic3—64no—
111C22×C3⋊C8—34no—
112#893—38no—
113#887—38no—
114#67⋊C4—68no—
115#872—64no—
116C42×D3—64no—
117C3×#103C2×D318yes—
118C3×#102C2×D318yes—
119#821—38no—
120#816—38no—
121C8×Dic3—38no—
122C8×Dic3—38no—
123#808—38no—
124#807—38no—
125C23×C32—21no—
126C23×C32C2×D411yescharacteristic
127C22×C3⋊D3—21no—
128C32×Q8—21no—
129C32×Q8C22×C412yes—
130C32×D4—24no—
131C32×D4—21no—
132C32×D4C22×C412yes—
133C2×C32×C4—21no—
134C2×C32×C4—24no—
135C2×C32×C4—22no—
136C2×C32×C4C22×C412yes—
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4#4112yes—
139C2×C32×C4C2411yescharacteristic
140#638—24no—
141C2×C3⋊Dic3—21no—
142C2×C3⋊Dic3—24no—
143C2×C3⋊Dic3—22no—
144C2×C3⋊Dic3—44no—
145C2×C3⋊Dic3C2×D412yes—
146C2×C3⋊Dic3C2×D412yes—
147C4⋊(C3⋊D3)—21no—
148C4⋊(C3⋊D3)C22×C412yes—
149C4×C3⋊D3—24no—
150C4×C3⋊D3—44no—
151#634—21no—
152#634C22×C412yes—
153C32×C8—22no—
154C3⋊(C3⋊C8)C22×C412yes—
155C3⋊(C3⋊C8)C22×C412yes—
156C2×#135—91no—
157C4×#41—91no—
158C4×#41—91no—
159C4×Q16—92no—
160C4×SD16—92no—
161C4×SD16—92no—
162C4×D8—92no—
163#427—91no—
164#416—91no—
165#416C3⋊D311yescharacteristic, complemented
166C2×C4×C8—91no—
167C3×#41—28no—
168C3×#41C4×D3116yescomplemented
169C2×C3×Q8C22×D314yes—
170C2×C3×D4—24no—
171C2×C3×D4C22×D314yes—
172C22×C3×C4—24no—
173C22×C3×C4C22×D314yes—
174C2×#67—64no—
175C22×Dic3—38no—
176C22×Dic3—68no—
177#235—316no—
178#235—68no—
179C2×D12—34no—
180C2×C4×D3—64no—
181C2×C4×D3—68no—
182C2×Dic6—34no—
183C2×C3×C8—28no—
184C2×C3×C8C22×D318yes—
185C3×C4⋊C4C22×D318yes—
186C3×C22⋊C4—24no—
187C3×C42—24no—
188#217—68no—
189#217—64no—
190#216—316no—
191#215—316no—
192#214—316no—
193#213—316no—
194(C2×D3)⋊C4—68no—
195C4⋊Dic3—38no—
196C4⋊Dic3—68no—
197Dic3⋊C4—68no—
198C4×Dic3—34no—
199C4×Dic3—34no—
200C4×Dic3—38no—
201C4×Dic3—68no—
202C4×Dic3—68no—
203C4×Dic3—64no—
204C2×C3⋊C8—316no—
205C2×C3⋊C8—34no—
206C2×C3⋊C8—34no—
207C22×C32—22no—
208C22×C32—22no—
209C22×C32—42no—
210C22×C32C4×D412yes—
211C22×C32C22×D411yescharacteristic
212C2×C3⋊D3—22no—
213C2×C3⋊D3—42no—
214C32×C4—22no—
215C32×C4—42no—
216C32×C4C4×D412yes—
217C32×C4C23×C411yescharacteristic
218C32×C4C2×#4111yescharacteristic
219C3⋊Dic3—22no—
220C3⋊Dic3—22no—
221C3⋊Dic3—42no—
222C3⋊Dic3#13514yescomplemented
223C2×#41—91no—
224C2×#41C2×C3⋊D311yescharacteristic
225#135—98no—
226C2×Q16—91no—
227C2×SD16—91no—
228C2×SD16—91no—
229C2×D8—91no—
230C22×C8—91no—
231C22×C8C2×C3⋊D311yescharacteristic
232C4×Q8—92no—
233C4×Q8—92no—
234C4×D4—92no—
235C4×D4—92no—
236C4×D4—182no—
237C4×D4—182no—
238#117—91no—
239#117—181no—
240#117—181no—
241#117C2×C3⋊D311yescharacteristic
242C2×C42—91no—
243C2×C42—181no—
244C2×C42—181no—
245#107—92no—
246#106—92no—
247#103—92no—
248#103C2×C3⋊D312yes—
249#102—92no—
250#102C2×C3⋊D312yes—
251C4×C8—92no—
252C4×C8—92no—
253C23×C3—24no—
254C23×C3D3×D414yes—
255C22×D3—64no—
256C3×Q8—24no—
257C3×Q8C2×C4×D318yes—
258C3×D4—216no—
259C3×D4—24no—
260C3×D4C2×C4×D318yes—
261C2×C3×C4—24no—
262C2×C3×C4—216no—
263C2×C3×C4—28no—
264C2×C3×C4C2×C4×D318yes—
265C2×C3×C4D3×D414yes—
266C2×C3×C4#23718yes—
267C2×C3×C4C23×D314yes—
268#67—616no—
269C2×Dic3—38no—
270C2×Dic3—38no—
271C2×Dic3—616no—
272C2×Dic3—64no—
273C2×Dic3—68no—
274C2×Dic3—1216no—
275D12—38no—
276D12—64no—
277C4×D3—616no—
278C4×D3—1216no—
279Dic6—38no—
280Dic6—64no—
281C3×C8—28no—
282C3⋊C8—38no—
283C3⋊C8—38no—
284C2×C32—22no—
285C2×C32—42no—
286C2×C32C2×C4×D411yescharacteristic
287C2×C32C2×#13512yes—
288C3⋊D3—42no—
289#41—22no—
290#41—94no—
291#41—182no—
292#41C4×C3⋊D314yescomplemented
293C2×Q8—91no—
294C2×Q8C22×C3⋊D311yescharacteristic
295C2×D4—21no—
296C2×D4—91no—
297C2×D4—181no—
298C2×D4C22×C3⋊D311yescharacteristic
299C22×C4—21no—
300C22×C4—92no—
301C22×C4—182no—
302C22×C4—182no—
303C22×C4—181no—
304C22×C4C22×C3⋊D311yescharacteristic
305Q16—94no—
306SD16—94no—
307SD16—94no—
308D8—94no—
309C2×C8—22no—
310C2×C8—91no—
311C2×C8—91no—
312C2×C8—94no—
313C2×C8C22×C3⋊D312yes—
314C4⋊C4—92no—
315C4⋊C4—182no—
316C4⋊C4—182no—
317C4⋊C4C22×C3⋊D312yes—
318C22⋊C4—21no—
319C22⋊C4—182no—
320C22⋊C4—182no—
321C22⋊C4—181no—
322C42—21no—
323C42—92no—
324C42—91no—
325C42—91no—
326C42—182no—
327C42—182no—
328C42—181no—
329C22×C3—28no—
330C22×C3—28no—
331C22×C3—48no—
332C22×C3#67⋊C418yes—
333C22×C3C2×D3×D414yes—
334C2×D3—68no—
335C2×D3—128no—
336C3×C4—28no—
337C3×C4—48no—
338C3×C4#67⋊C418yes—
339C3×C4C22×C4×D314yes—
340C3×C4C2×#23714yes—
341Dic3—316no—
342Dic3—68no—
343Dic3—68no—
344Dic3—128no—
345C32C4×#13511yescharacteristic, complemented, Sylow
346C23—21no—
347C23—181no—
348C23D4×C3⋊D311yescharacteristic
349Q8—21no—
350Q8—92no—
351Q8—181no—
352Q8C2×C4×C3⋊D312yes—
353D4—24no—
354D4—21no—
355D4—92no—
356D4—184no—
357D4—181no—
358D4C2×C4×C3⋊D312yes—
359C2×C4—21no—
360C2×C4—24no—
361C2×C4—22no—
362C2×C4—92no—
363C2×C4—92no—
364C2×C4—184no—
365C2×C4—181no—
366C2×C4—184no—
367C2×C4—182no—
368C2×C4—364no—
369C2×C4—364no—
370C2×C4C2×C4×C3⋊D312yes—
371C2×C4D4×C3⋊D311yescharacteristic
372C2×C4#383012yes—
373C2×C4C23×C3⋊D311yescharacteristic
374C8—22no—
375C8—92no—
376C8—92no—
377C2×C3—28no—
378C2×C3—48no—
379C2×C3C2×#67⋊C414yes—
380C2×C3D3×#13518yes—
381D3—128no—
382C22—22no—
383C22—22no—
384C22—42no—
385C22—182no—
386C22—362no—
387C22#6409012yes—
388C22C2×D4×C3⋊D311yescharacteristic
389C4—22no—
390C4—42no—
391C4—94no—
392C4—182no—
393C4—182no—
394C4—362no—
395C4#6409012yes—
396C4C22×C4×C3⋊D311yescharacteristic
397C4C2×#383011yescharacteristic
398C3#7881814yescomplemented
399C2—22no—
400C2—42no—
401C2—362no—
402C2C2×#6409011yescharacteristic
403C2C3⋊D3×#13512yes—
subgroupG/H
centerC2×C4D4×C3⋊D3
commutatorC32×C4C23×C4
FrattiniC2×C4C23×C3⋊D3
FittingC32×#416C2
socleC22×C32C22×D4
prime radicalC2×#64159C2
cosocleC2×C32×C4C24
hypercenter#416C3⋊D3
hypocenterC32C4×#135
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. #41×C3⋊Dic3C2semidirect
3. #10595993C2semidirect
4. C32×#416C2semidirect
5. #10592812C2semidirect
6. C2×C8×C3⋊Dic3C2semidirect
7. #10592697C2semidirect
8. #10592489C2semidirect
9. #10592487C2semidirect
10. #10592457C2semidirect
11. #10592455C2semidirect
17. #64159C4semidirect
46. C3×#416D3semidirect
55. C32×#41C2×C4semidirect
65. #3828C2×C4semidirect
77. #3756C2×C4semidirect
78. #3755C2×C4semidirect
79. #3754C2×C4semidirect
80. #3753C2×C4semidirect
91. C2×C3⋊(C3⋊C8)C2×C4semidirect
165. #416C3⋊D3semidirect
168. C3×#41C4×D3semidirect
222. C3⋊Dic3#135semidirect
292. #41C4×C3⋊D3semidirect
345. C32C4×#135semidirect
398. C3#78818semidirect

Maximal subgroups

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

subgroupindex
#41×C3⋊Dic32
C2×#641592
#105959932
C32×#4162
#105928122
C2×C8×C3⋊Dic32
#105926972
#105924892
#105924872
#105924572
#105924552
#788183