Finite Group Databasebeta

← #11882312

Subgroups — #11882312

Order 1152.

1194 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595950C211yesmaximal, characteristic, complemented
2#10595948C211yesmaximal, characteristic, complemented
3C2×C32×C4⋊C8C211yesmaximal, characteristic, complemented
4#10592814C212yesmaximal, complemented
5#10592813C212yesmaximal, complemented
6#10592549C211yesmaximal, characteristic, complemented
7#10592547C211yesmaximal, characteristic, complemented
8#10592546C212yesmaximal, complemented
9#10592543C212yesmaximal, complemented
10#10592542C211yesmaximal, characteristic, complemented
11#10592541C211yesmaximal, characteristic, complemented
12#79028—34nomaximal
13C2×#3828—21no—
14C22×C32×C8C2212yes—
15C2×C32×C42C2211yescharacteristic
16#64139—21no—
17#64139C2212yes—
18#64139C2211yescharacteristic
19#64138—21no—
20C4×#638—21no—
21#64133C2211yescharacteristic
22C2×#3745C2212yes—
23C2×#3744C2212yes—
24#64085—21no—
25#64084—21no—
26#64084C2211yescharacteristic
27#64083C2211yescharacteristic
28C4×C4⋊(C3⋊D3)—21no—
29C4×C4⋊(C3⋊D3)C2211yescharacteristic
30C4×C4⋊(C3⋊D3)C2212yes—
31#64081—21no—
32#64079C2211yescharacteristic
33#64078C2211yescharacteristic
34C4×#634C2211yescharacteristic
35C32×C4⋊C8C2211yescharacteristic
36C32×C4⋊C8C2211yescharacteristic
37C32×C4⋊C8C2212yes—
38#63648C2212yes—
39#63648C2212yes—
40#63648C2212yes—
41#63645C2212yes—
42#63644C2212yes—
43#63643C2212yes—
44#5479—34no—
45#5477—34no—
46C2×C3×C4⋊C8D314yescomplemented
47#5115—38no—
48#5114—38no—
49#4850—34no—
50#4848—34no—
51#4847—38no—
52#4844—38no—
53#4843—34no—
54#4842—34no—
55C22×C32×C4D411yescharacteristic
56C22×C32×C4D411yescharacteristic
57C22×C32×C4C2311yescharacteristic
58C2×#638—22no—
59C2×#638—21no—
60#3828—44no—
61C2×C4⋊(C3⋊D3)—21no—
62C2×C4⋊(C3⋊D3)—21no—
63C2×C4⋊(C3⋊D3)C2312yes—
64C2×C4⋊(C3⋊D3)C2311yescharacteristic
65C2×C4×C3⋊D3—21no—
66C2×C4×C3⋊D3—22no—
67C2×#634—21no—
68C2×#634C2311yescharacteristic
69C2×C32×C8—42no—
70C2×C32×C8C2312yes—
71C2×C32×C8C2312yes—
72C32×C42D411yescharacteristic
73C32×C42D411yescharacteristic
74C32×C42C2311yescharacteristic
75C32×C42C2311yescharacteristic
76#3757—21no—
77#3752—21no—
78#3752—21no—
79#3752—22no—
80#3752—22no—
81#3752—21no—
82#3752—21no—
83C4⋊(C3⋊Dic3)—21no—
84C4⋊(C3⋊Dic3)C2311yescharacteristic
85C4⋊(C3⋊Dic3)C2312yes—
86C4⋊(C3⋊Dic3)C2311yescharacteristic
87#3750—21no—
88#3750—21no—
89#3750—21no—
90#3750—21no—
91C4×C3⋊Dic3—21no—
92#3745—42no—
93#3744—42no—
94#3247—91noSylow
95C2×#235—64no—
96C22×C3×C8C2×D318yes—
97C2×C3×C42C2×D314yes—
98#930—38no—
99#930—34no—
100#930—64no—
101#929—64no—
102C4×#67—64no—
103#924—34no—
104C2×D24—38no—
105C2×#204—38no—
106#876—64no—
107#875—34no—
108#875—64no—
109#874—34no—
110C4×D12—38no—
111C4×D12—34no—
112C4×D12—64no—
113#872—64no—
114#870—34no—
115#869—34no—
116C4×Dic6—34no—
117C3×C4⋊C8C2×D314yes—
118C3×C4⋊C8C2×D314yes—
119C3×C4⋊C8C2×D318yes—
120#821—38no—
121#821—38no—
122#821—38no—
123#818—38no—
124#817—38no—
125#816—38no—
126C23×C32C2×D411yescharacteristic
127C22×C3⋊D3—21no—
128C22×C3⋊D3—22no—
129C2×C32×C4—22no—
130C2×C32×C4—22no—
131C2×C32×C4—21no—
132C2×C32×C4—21no—
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2411yescharacteristic
139#638—44no—
140#638—42no—
141C2×C3⋊Dic3—21no—
142C2×C3⋊Dic3—21no—
143C2×C3⋊Dic3—21no—
144C2×C3⋊Dic3—22no—
145C4⋊(C3⋊D3)—22no—
146C4⋊(C3⋊D3)—21no—
147C4⋊(C3⋊D3)—22no—
148C4⋊(C3⋊D3)—21no—
149C4⋊(C3⋊D3)—42no—
150C4⋊(C3⋊D3)—42no—
151C4×C3⋊D3—44no—
152C4×C3⋊D3—42no—
153#634—21no—
154#634—21no—
155#634—42no—
156C32×C8—22no—
157C32×C8—22no—
158#532—91no—
159#529—91no—
160#478—92no—
161#477—91no—
162#476—91no—
163#466—92no—
164#465—92no—
165#463—92no—
166#460—91no—
167#459—91no—
168C2×C4⋊C8C3⋊D311yescharacteristic, complemented
169C22×C3×C4D1214yes—
170C22×C3×C4D1214yes—
171C22×C3×C4C22×D314yes—
172C2×#67—64no—
173C2×#67—68no—
174#235—1216no—
175C2×D12—38no—
176C2×D12—34no—
177C2×D12—64no—
178C2×D12—64no—
179C2×C4×D3—64no—
180C2×C4×D3—68no—
181C2×Dic6—34no—
182C2×Dic6—64no—
183C2×C3×C8—48no—
184C2×C3×C8C22×D318yes—
185C2×C3×C8C22×D318yes—
186C3×C42D1214yes—
187C3×C42D1214yes—
188C3×C42C22×D314yes—
189C3×C42C22×D314yes—
190#217—64no—
191(C2×D3)⋊C4—64no—
192(C2×D3)⋊C4—64no—
193(C2×D3)⋊C4—68no—
194(C2×D3)⋊C4—64no—
195(C2×D3)⋊C4—68no—
196(C2×D3)⋊C4—64no—
197C4⋊Dic3—38no—
198C4⋊Dic3—34no—
199C4⋊Dic3—34no—
200C4⋊Dic3—64no—
201Dic3⋊C4—64no—
202Dic3⋊C4—64no—
203Dic3⋊C4—64no—
204Dic3⋊C4—64no—
205C4×Dic3—64no—
206D24—128no—
207#204—128no—
208C22×C32—21no—
209C22×C32—21no—
210C22×C32AGL(1,ℤ/8)12yes—
211C22×C32C22×D411yescharacteristic
212C2×C3⋊D3—42no—
213C2×C3⋊D3—41no—
214C2×C3⋊D3—41no—
215C2×C3⋊D3—42no—
216C2×C3⋊D3—42no—
217C2×C3⋊D3—41no—
218C32×C4—21no—
219C32×C4—21no—
220C32×C4—21no—
221C32×C4—21no—
222C32×C4#13512yes—
223C32×C4H(5,𝔽2)11yescharacteristic
224C32×C42−1+411yescharacteristic
225C3⋊Dic3—41no—
226C3⋊Dic3—41no—
227C3⋊Dic3—42no—
228C3⋊Dic3—41no—
229C2×#41—181no—
230C2×SD16—92no—
231C2×D8—92no—
232C22×C8C2×C3⋊D312yes—
233C4⋊Q8—91no—
234#127—91no—
235#126—181no—
236#125—91no—
237#124—91no—
238#124—181no—
239#123—181no—
240C22⋊Q8—91no—
241#121—91no—
242#121—92no—
243#121—181no—
244C4×Q8—91no—
245C4×D4—91no—
246C4×D4—92no—
247C4×D4—181no—
248C4×D4—181no—
249#117—181no—
250C2×C42C2×C3⋊D311yescharacteristic
251#107—92no—
252#106—92no—
253C4⋊C8C2×C3⋊D311yescharacteristic
254C4⋊C8C2×C3⋊D311yescharacteristic
255C4⋊C8C2×C3⋊D312yes—
256#103—92no—
257#102—92no—
258#102—92no—
259#102—92no—
260C23×C3C2×D1214yes—
261C22×D3—64no—
262C22×D3—68no—
263C2×C3×C4—28no—
264C2×C3×C4—28no—
265C2×C3×C4—24no—
266C2×C3×C4—24no—
267C2×C3×C4C2×D1214yes—
268C2×C3×C4C2×D1214yes—
269C2×C3×C4C2×D1214yes—
270C2×C3×C4C2×D1214yes—
271C2×C3×C4C2×D1214yes—
272C2×C3×C4C23×D314yes—
273#67—1216no—
274#67—128no—
275C2×Dic3—64no—
276C2×Dic3—64no—
277C2×Dic3—64no—
278C2×Dic3—68no—
279D12—68no—
280D12—64no—
281D12—68no—
282D12—64no—
283D12—128no—
284D12—128no—
285C4×D3—1216no—
286C4×D3—128no—
287Dic6—64no—
288Dic6—64no—
289Dic6—128no—
290C3×C8—28no—
291C3×C8—28no—
292C2×C32—22no—
293C2×C32#53711yescharacteristic
294C2×C32C2×#13511yescharacteristic
295C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
296C3⋊D3—81no—
297C3⋊D3—82no—
298#41—364no—
299C2×Q8—91no—
300C2×Q8—181no—
301C2×D4—91no—
302C2×D4—92no—
303C2×D4—181no—
304C2×D4—182no—
305C2×D4—181no—
306C2×D4—181no—
307C22×C4—181no—
308C22×C4—182no—
309C22×C4C4⋊(C3⋊D3)11yescharacteristic
310C22×C4C4⋊(C3⋊D3)11yescharacteristic
311C22×C4C22×C3⋊D311yescharacteristic
312SD16—362no—
313D8—362no—
314C2×C8—42no—
315C2×C8C22×C3⋊D312yes—
316C2×C8C22×C3⋊D312yes—
317C4⋊C4—91no—
318C4⋊C4—91no—
319C4⋊C4—92no—
320C4⋊C4—181no—
321C4⋊C4—181no—
322C4⋊C4—181no—
323C4⋊C4—181no—
324C4⋊C4—181no—
325C22⋊C4—181no—
326C22⋊C4—181no—
327C22⋊C4—181no—
328C22⋊C4—182no—
329C22⋊C4—181no—
330C22⋊C4—182no—
331C22⋊C4—181no—
332C42—181no—
333C42C4⋊(C3⋊D3)11yescharacteristic
334C42C4⋊(C3⋊D3)11yescharacteristic
335C42C22×C3⋊D311yescharacteristic
336C42C22×C3⋊D311yescharacteristic
337C22×C3—24no—
338C22×C3—24no—
339C22×C3#90818yes—
340C22×C3C22×D1214yes—
341C2×D3—124no—
342C2×D3—128no—
343C2×D3—128no—
344C2×D3—124no—
345C2×D3—128no—
346C2×D3—124no—
347C3×C4—24no—
348C3×C4—24no—
349C3×C4—24no—
350C3×C4—24no—
351C3×C4#90418yes—
352C3×C4#100414yes—
353C3×C4#100714yes—
354Dic3—124no—
355Dic3—128no—
356Dic3—124no—
357Dic3—124no—
358C32#324711yescharacteristic, complemented, Sylow
359C23—181no—
360C23—182no—
361C23C2×C4⋊(C3⋊D3)11yescharacteristic
362Q8—181no—
363Q8—181no—
364Q8—362no—
365D4—181no—
366D4—182no—
367D4—181no—
368D4—182no—
369D4—362no—
370D4—364no—
371D4—362no—
372D4—362no—
373C2×C4—22no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—22no—
377C2×C4—181no—
378C2×C4—181no—
379C2×C4—181no—
380C2×C4—182no—
381C2×C4—364no—
382C2×C4—362no—
383C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
384C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
385C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
386C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
387C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
388C2×C4C23×C3⋊D311yescharacteristic
389C8—22no—
390C8—22no—
391C2×C3—28no—
392C2×C3#551014yes—
393C2×C3C2×#90414yes—
394C2×C3C2×#90814yes—
395D3—244no—
396D3—248no—
397C22—21no—
398C22—21no—
399C22—361no—
400C22—362no—
401C22—362no—
402C22—361no—
403C22—361no—
404C22—362no—
405C22#6411712yes—
406C22C22×C4⋊(C3⋊D3)11yescharacteristic
407C4—21no—
408C4—21no—
409C4—21no—
410C4—21no—
411C4—361no—
412C4—362no—
413C4—361no—
414C4—361no—
415C4#6411312yes—
416C4#6436111yescharacteristic
417C4#6436411yescharacteristic
418C3#7902814yescomplemented
419C2—22no—
420C2—721no—
421C2—722no—
422C2#1059598111yescharacteristic
423C2C2×#6411311yescharacteristic
424C2C2×#6411711yescharacteristic
subgroupG/H
centerC22C22×C4⋊(C3⋊D3)
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×C4⋊C8C2
socleC22×C32C22×D4
hypercenterC2×C4⋊C8C3⋊D3
hypocenterC32#3247
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
1. #10595950C2semidirect
2. #10595948C2semidirect
3. C2×C32×C4⋊C8C2semidirect
4. #10592814C2semidirect
5. #10592813C2semidirect
6. #10592549C2semidirect
7. #10592547C2semidirect
8. #10592546C2semidirect
9. #10592543C2semidirect
10. #10592542C2semidirect
11. #10592541C2semidirect
46. C2×C3×C4⋊C8D3semidirect
168. C2×C4⋊C8C3⋊D3semidirect
358. C32#3247semidirect
418. C3#79028semidirect

Maximal subgroups

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

subgroupindex
#105959502
#105959482
C2×C32×C4⋊C82
#105928142
#105928132
#105925492
#105925472
#105925462
#105925432
#105925422
#105925412
#790283