Finite Group Databasebeta

← #11882309

Subgroups — #11882309

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
1C32×#529C211yesmaximal, characteristic, complemented
2#10595948C211yesmaximal, characteristic, complemented
3#10592765C212yesmaximal, complemented
4#10592756C212yesmaximal, complemented
5#10592747C212yesmaximal, complemented
6#10592737C212yesmaximal, complemented
7#10592726C211yesmaximal, characteristic, complemented
8#10592720C211yesmaximal, characteristic, complemented
9#10592714C211yesmaximal, characteristic, complemented
10#10592707C211yesmaximal, characteristic, complemented
11C2×C4⋊(C3⋊(C3⋊C8))C211yesmaximal, characteristic, complemented
12#83148—34nomaximal
13C2×#3828—21no—
14C32×#126—21no—
15C32×#125C2211yescharacteristic
16C32×#124C2211yescharacteristic
17C32×#123—21no—
18C32×C22⋊Q8C2211yescharacteristic
19C32×#121C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic
21C32×C4×D4—21no—
22C32×C4×D4C2211yescharacteristic
23C32×#117—21no—
24C2×C32×C42C2211yescharacteristic
25C2×#3755C2212yes—
26C2×#3753C2212yes—
27#64139—21no—
28#64139C2212yes—
29C22×C3⋊(C3⋊C8)C2212yes—
30#64084—21no—
31#64083C2211yescharacteristic
32C4×C4⋊(C3⋊D3)—21no—
33C4×C4⋊(C3⋊D3)C2212yes—
34#64078C2211yescharacteristic
35#63662C2212yes—
36#63659C2212yes—
37#63636C2212yes—
38#63636C2212yes—
39#63635C2212yes—
40#63634C2212yes—
41C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
42C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
43C4⋊(C3⋊(C3⋊C8))C2212yes—
44C3×#529D314yescomplemented
45#5477—34no—
46#5066—38no—
47#5057—38no—
48#5048—38no—
49#5038—38no—
50#5027—34no—
51#5021—34no—
52#5015—34no—
53#5008—34no—
54C2×C4⋊(C3⋊C8)—34no—
55C2×C32×Q8C2311yescharacteristic
56C2×C32×D4—21no—
57C2×C32×D4C2311yescharacteristic
58C22×C32×C4—21no—
59C22×C32×C4D411yescharacteristic
60C22×C32×C4D411yescharacteristic
61C22×C32×C4C2311yescharacteristic
62C2×#638—22no—
63#3828—44no—
64C2×C4⋊(C3⋊D3)—21no—
65C2×C4⋊(C3⋊D3)—21no—
66C2×C4⋊(C3⋊D3)C2312yes—
67C2×C4×C3⋊D3—22no—
68C2×#634—21no—
69C32×C4⋊C4—21no—
70C32×C4⋊C4—21no—
71C32×C4⋊C4—21no—
72C32×C4⋊C4—21no—
73C32×C4⋊C4C2311yescharacteristic
74C32×C4⋊C4C2311yescharacteristic
75C32×C22⋊C4—21no—
76C32×C22⋊C4—21no—
77C32×C22⋊C4—21no—
78C32×C22⋊C4—21no—
79C32×C22⋊C4—21no—
80C32×C42—21no—
81C32×C42D411yescharacteristic
82C32×C42D411yescharacteristic
83C32×C42C2311yescharacteristic
84C32×C42C2311yescharacteristic
85#3755—42no—
86#3753—42no—
87#3752—22no—
88#3752—22no—
89C4⋊(C3⋊Dic3)—21no—
90C4⋊(C3⋊Dic3)C2312yes—
91C2×C3⋊(C3⋊C8)—42no—
92C2×C3⋊(C3⋊C8)C2312yes—
93C2×C3⋊(C3⋊C8)C2312yes—
94#3247—91noSylow
95C2×#235—64no—
96C3×#126—24no—
97C3×#125C2×D314yes—
98C3×#124C2×D314yes—
99C3×#123—24no—
100C3×C22⋊Q8C2×D314yes—
101C3×#121C2×D314yes—
102C3×C4×Q8C2×D314yes—
103C3×C4×D4—24no—
104C3×C4×D4C2×D314yes—
105C3×#117—24no—
106C2×C3×C42C2×D314yes—
107C2×#215—38no—
108C2×#213—38no—
109#930—38no—
110#930—64no—
111C22×C3⋊C8—38no—
112#875—64no—
113#874—34no—
114C4×D12—38no—
115C4×D12—64no—
116#869—34no—
117#835—38no—
118#832—38no—
119#809—38no—
120#809—38no—
121#808—38no—
122#807—38no—
123C4⋊(C3⋊C8)—34no—
124C4⋊(C3⋊C8)—34no—
125C4⋊(C3⋊C8)—38no—
126C23×C32—21no—
127C23×C32C2×D411yescharacteristic
128C22×C3⋊D3—22no—
129C32×Q8—21no—
130C32×Q8—21no—
131C32×D4—21no—
132C32×D4—21no—
133C32×D4—42no—
134C2×C32×C4—22no—
135C2×C32×C4—22no—
136C2×C32×C4—21no—
137C2×C32×C4—21no—
138C2×C32×C4—21no—
139C2×C32×C4—21no—
140C2×C32×C4—21no—
141C2×C32×C4—42no—
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2411yescharacteristic
148#638—44no—
149C2×C3⋊Dic3—22no—
150C4⋊(C3⋊D3)—22no—
151C4⋊(C3⋊D3)—22no—
152C4⋊(C3⋊D3)—42no—
153C4⋊(C3⋊D3)—42no—
154C4×C3⋊D3—44no—
155#634—42no—
156C3⋊(C3⋊C8)—22no—
157C3⋊(C3⋊C8)—22no—
158#532—91no—
159#529C3⋊D311yescharacteristic, complemented
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⋊C8—91no—
169C2×C3×Q8C22×D314yes—
170C2×C3×D4—24no—
171C2×C3×D4C22×D314yes—
172C22×C3×C4—24no—
173C22×C3×C4#6714yes—
174C22×C3×C4#6714yes—
175C22×C3×C4C22×D314yes—
176C2×#67—68no—
177#235—1216no—
178C2×D12—38no—
179C2×D12—64no—
180C2×D12—64no—
181C2×C4×D3—68no—
182C2×Dic6—64no—
183C3×C4⋊C4—24no—
184C3×C4⋊C4—24no—
185C3×C4⋊C4—24no—
186C3×C4⋊C4—24no—
187C3×C4⋊C4C22×D314yes—
188C3×C4⋊C4C22×D314yes—
189C3×C22⋊C4—24no—
190C3×C22⋊C4—24no—
191C3×C22⋊C4—24no—
192C3×C22⋊C4—24no—
193C3×C22⋊C4—24no—
194C3×C42—24no—
195C3×C42#6714yes—
196C3×C42#6714yes—
197C3×C42C22×D314yes—
198C3×C42C22×D314yes—
199#215—128no—
200#213—128no—
201(C2×D3)⋊C4—68no—
202(C2×D3)⋊C4—68no—
203C4⋊Dic3—38no—
204C4⋊Dic3—64no—
205C2×C3⋊C8—38no—
206C2×C3⋊C8—38no—
207C2×C3⋊C8—128no—
208C22×C32—21no—
209C22×C32—21no—
210C22×C32—41no—
211C22×C32—41no—
212C22×C32—41no—
213C22×C32AGL(1,ℤ/8)12yes—
214C22×C32C22×D411yescharacteristic
215C2×C3⋊D3—42no—
216C2×C3⋊D3—42no—
217C2×C3⋊D3—42no—
218C32×C4—21no—
219C32×C4—21no—
220C32×C4—21no—
221C32×C4—21no—
222C32×C4—41no—
223C32×C4—41no—
224C32×C4—41no—
225C32×C4#13512yes—
226C32×C4H(5,𝔽2)11yescharacteristic
227C32×C42−1+411yescharacteristic
228C3⋊Dic3—42no—
229C2×#41—181no—
230C2×SD16—92no—
231C2×D8—92no—
232C22×C8—92no—
233C4⋊Q8—91no—
234#127—91no—
235#126—21no—
236#125C2×C3⋊D311yescharacteristic
237#124—181no—
238#124C2×C3⋊D311yescharacteristic
239#123—21no—
240C22⋊Q8C2×C3⋊D311yescharacteristic
241#121—92no—
242#121—181no—
243#121C2×C3⋊D311yescharacteristic
244C4×Q8C2×C3⋊D311yescharacteristic
245C4×D4—21no—
246C4×D4—92no—
247C4×D4—181no—
248C4×D4C2×C3⋊D311yescharacteristic
249#117—21no—
250C2×C42C2×C3⋊D311yescharacteristic
251#107—92no—
252#106—92no—
253C4⋊C8—91no—
254C4⋊C8—91no—
255C4⋊C8—92no—
256#103—92no—
257#102—92no—
258#102—92no—
259#102—92no—
260C23×C3—24no—
261C23×C3C2×#6714yes—
262C22×D3—68no—
263C3×Q8—24no—
264C3×Q8—24no—
265C3×D4—24no—
266C3×D4—24no—
267C3×D4—48no—
268C2×C3×C4—28no—
269C2×C3×C4—28no—
270C2×C3×C4—24no—
271C2×C3×C4—24no—
272C2×C3×C4—24no—
273C2×C3×C4—24no—
274C2×C3×C4—24no—
275C2×C3×C4—48no—
276C2×C3×C4C2×#6714yes—
277C2×C3×C4C2×#6714yes—
278C2×C3×C4C2×#6714yes—
279C2×C3×C4C2×#6714yes—
280C2×C3×C4C2×#6714yes—
281C2×C3×C4C23×D314yes—
282#67—1216no—
283C2×Dic3—68no—
284D12—68no—
285D12—68no—
286D12—128no—
287D12—128no—
288C4×D3—1216no—
289Dic6—128no—
290C3⋊C8—68no—
291C3⋊C8—68no—
292C2×C32—22no—
293C2×C32—81no—
294C2×C32#53711yescharacteristic
295C2×C32C2×#13511yescharacteristic
296C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
297C3⋊D3—82no—
298#41—364no—
299C2×Q8—181no—
300C2×Q8C22×C3⋊D311yescharacteristic
301C2×D4—21no—
302C2×D4—92no—
303C2×D4—182no—
304C2×D4—181no—
305C2×D4—181no—
306C2×D4C22×C3⋊D311yescharacteristic
307C22×C4—21no—
308C22×C4—182no—
309C22×C4#63811yescharacteristic
310C22×C4#63811yescharacteristic
311C22×C4C22×C3⋊D311yescharacteristic
312SD16—362no—
313D8—362no—
314C2×C8—92no—
315C2×C8—92no—
316C2×C8—362no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—92no—
322C4⋊C4—181no—
323C4⋊C4C22×C3⋊D311yescharacteristic
324C4⋊C4C22×C3⋊D311yescharacteristic
325C22⋊C4—21no—
326C22⋊C4—21no—
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—21no—
330C22⋊C4—182no—
331C22⋊C4—182no—
332C42—21no—
333C42#63811yescharacteristic
334C42#63811yescharacteristic
335C42C22×C3⋊D311yescharacteristic
336C42C22×C3⋊D311yescharacteristic
337C22×C3—24no—
338C22×C3—24no—
339C22×C3—44no—
340C22×C3—44no—
341C22×C3—44no—
342C22×C3#94918yes—
343C22×C3C22×#6714yes—
344C2×D3—128no—
345C2×D3—128no—
346C2×D3—128no—
347C3×C4—24no—
348C3×C4—24no—
349C3×C4—24no—
350C3×C4—24no—
351C3×C4—44no—
352C3×C4—44no—
353C3×C4—44no—
354C3×C4#95018yes—
355C3×C4#100914yes—
356C3×C4#101014yes—
357Dic3—128no—
358C32#324711yescharacteristic, complemented, Sylow
359C23—21no—
360C23—182no—
361C23C2×#63811yescharacteristic
362Q8—21no—
363Q8—21no—
364Q8—362no—
365D4—21no—
366D4—21no—
367D4—42no—
368D4—182no—
369D4—182no—
370D4—362no—
371D4—364no—
372D4—362no—
373C2×C4—22no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—22no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—42no—
381C2×C4—182no—
382C2×C4—364no—
383C2×C4C2×#63811yescharacteristic
384C2×C4C2×#63811yescharacteristic
385C2×C4C2×#63811yescharacteristic
386C2×C4C2×#63811yescharacteristic
387C2×C4C2×#63811yescharacteristic
388C2×C4C23×C3⋊D311yescharacteristic
389C8—182no—
390C8—182no—
391C2×C3—28no—
392C2×C3—84no—
393C2×C3C2×#94914yes—
394C2×C3C2×#95014yes—
395C2×C3#583314yes—
396D3—248no—
397C22—21no—
398C22—21no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—362no—
403C22—362no—
404C22—362no—
405C22#6415812yes—
406C22C22×#63811yescharacteristic
407C4—21no—
408C4—21no—
409C4—21no—
410C4—21no—
411C4—41no—
412C4—41no—
413C4—41no—
414C4—362no—
415C4#6415912yes—
416C4#6436611yescharacteristic
417C4#6436711yescharacteristic
418C3#8314814yescomplemented
419C2—22no—
420C2—81no—
421C2—722no—
422C2C2×#6415811yescharacteristic
423C2C2×#6415911yescharacteristic
424C2#1059630411yescharacteristic
subgroupG/H
centerC22C22×#638
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#529C2
socleC22×C32C22×D4
hypercenter#529C3⋊D3
hypocenterC32#3247
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. C32×#529C2semidirect
2. #10595948C2semidirect
3. #10592765C2semidirect
4. #10592756C2semidirect
5. #10592747C2semidirect
6. #10592737C2semidirect
7. #10592726C2semidirect
8. #10592720C2semidirect
9. #10592714C2semidirect
10. #10592707C2semidirect
11. C2×C4⋊(C3⋊(C3⋊C8))C2semidirect
44. C3×#529D3semidirect
159. #529C3⋊D3semidirect
358. C32#3247semidirect
418. C3#83148semidirect

Maximal subgroups

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

subgroupindex
C32×#5292
#105959482
#105927652
#105927562
#105927472
#105927372
#105927262
#105927202
#105927142
#105927072
C2×C4⋊(C3⋊(C3⋊C8))2
#831483