Finite Group Databasebeta

← #11898417

Subgroups — #11898417

Order 1152.

1116 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#556C211yesmaximal, characteristic, complemented
2#10596056C211yesmaximal, characteristic, complemented
3#10592789C211yesmaximal, characteristic, complemented
4#10592784C211yesmaximal, characteristic, complemented
5#10592758C212yesmaximal, complemented
6#10592756C212yesmaximal, complemented
7#10592727C212yesmaximal, complemented
8C4×#3755C212yesmaximal, complemented
9Q8×C3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
10C4×#3754C211yesmaximal, characteristic, complemented
11#10592714C211yesmaximal, characteristic
12#83679—34nomaximal
13C32×C4⋊Q8C2211yescharacteristic
14C32×#126—22no—
15C32×#124C2212yes—
16C32×C22⋊Q8—21no—
17C32×C4×Q8C2212yes—
18C32×C4×Q8C2211yescharacteristic
19C32×C4×D4C2211yescharacteristic
20C32×#117—21no—
21#64156—21no—
22C2×#3756C2212yes—
23C2×#3755C2212yes—
24C2×#3755C2212yes—
25C2×#3754C2211yescharacteristic
26C2×#3753C2212yes—
27#64103—22no—
28#64102—21no—
29#64084C2212yes—
30#64083C2211yescharacteristic
31C4×C4⋊(C3⋊D3)C2212yes—
32C4×#634C2211yescharacteristic
33#63662C2212yes—
34#63659C2211yescharacteristic
35#63637C2211yescharacteristic
36#63636C2212yes—
37#63635C2211yescharacteristic
38C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
39C4⋊(C3⋊(C3⋊C8))C2212yes—
40C4×C3⋊(C3⋊C8)C2211yescharacteristic
41C4×C3⋊(C3⋊C8)C2212yes—
42C3×#556D314yescomplemented
43#5585—34no—
44#5090—34no—
45#5085—34no—
46#5059—38no—
47#5057—38no—
48#5028—38no—
49C4×#215—38no—
50Q8×C3⋊C8—34no—
51C4×#214—34no—
52#5015—34no—
53C2×C32×Q8D411yescharacteristic
54C2×C32×Q8C2312yes—
55C2×C32×D4C2311yescharacteristic
56C22×C32×C4—21no—
57C2×C4⋊(C3⋊D3)—21no—
58C2×C4⋊(C3⋊D3)—21no—
59C2×C4⋊(C3⋊D3)C2312yes—
60C2×C4×C3⋊D3—22no—
61C2×#634C2311yescharacteristic
62C32×C4⋊C4—21no—
63C32×C4⋊C4—22no—
64C32×C4⋊C4—21no—
65C32×C4⋊C4D411yescharacteristic
66C32×C4⋊C4D412yes—
67C32×C4⋊C4C2311yescharacteristic
68C32×C22⋊C4—22no—
69C32×C22⋊C4—21no—
70C32×C22⋊C4—22no—
71C32×C42—22no—
72C32×C42C2311yescharacteristic
73C32×C42C2312yes—
74#3756—42no—
75#3755—24no—
76#3755—42no—
77#3754—22no—
78#3753—42no—
79#3752—22no—
80#3752—22no—
81#3752—22no—
82C4⋊(C3⋊Dic3)C2311yescharacteristic
83#3750—21no—
84C4×C3⋊Dic3—21no—
85C2×C3⋊(C3⋊C8)C2312yes—
86C2×C3⋊(C3⋊C8)C2311yescharacteristic
87C2×C3⋊(C3⋊C8)C2311yescharacteristic
88#3394—91noSylow
89C3×C4⋊Q8C2×D314yes—
90C3×#126—28no—
91C3×#124C2×D318yes—
92C3×C22⋊Q8—24no—
93C3×C4×Q8C2×D318yes—
94C3×C4×Q8C2×D314yes—
95C3×C4×D4C2×D314yes—
96C3×#117—24no—
97#947—64no—
98C2×#216—38no—
99C2×#215—38no—
100C2×#215—38no—
101C2×#214—34no—
102C2×#213—38no—
103#894—68no—
104#893—64no—
105#875—38no—
106#874—34no—
107C4×D12—38no—
108C4×Dic6—34no—
109#835—38no—
110#832—34no—
111#810—34no—
112#809—38no—
113#808—34no—
114C4⋊(C3⋊C8)—34no—
115C4⋊(C3⋊C8)—38no—
116C4×C3⋊C8—34no—
117C4×C3⋊C8—38no—
118C23×C32—21no—
119C22×C3⋊D3—22no—
120C32×Q8—22no—
121C32×Q8—22no—
122C32×Q8—22no—
123C32×D4—21no—
124C32×D4—21no—
125C2×C32×C4—21no—
126C2×C32×C4—22no—
127C2×C32×C4—42no—
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×D412yes—
130C2×C32×C4C2×D412yes—
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4C2411yescharacteristic
133C2×C3⋊Dic3—21no—
134C2×C3⋊Dic3—21no—
135C4⋊(C3⋊D3)—22no—
136C4⋊(C3⋊D3)—22no—
137C4⋊(C3⋊D3)—42no—
138C4⋊(C3⋊D3)—81no—
139C4×C3⋊D3—82no—
140#634—21no—
141#634—21no—
142C3⋊(C3⋊C8)—22no—
143C3⋊(C3⋊C8)—21no—
144C3⋊(C3⋊C8)#4112yes—
145#559—91no—
146#556C3⋊D311yescharacteristic, complemented
147#495—92no—
148#492—91no—
149#464—92no—
150#463—92no—
151#462—91no—
152#459—91no—
153C8×Q8—91no—
154C4×SD16—92no—
155C4×SD16—91no—
156C2×C3×Q8#6714yes—
157C2×C3×Q8C22×D318yes—
158C2×C3×D4C22×D314yes—
159C22×C3×C4—24no—
160C2×D12—38no—
161C2×D12—64no—
162C2×D12—64no—
163C2×C4×D3—68no—
164C2×Dic6—34no—
165C3×C4⋊C4—24no—
166C3×C4⋊C4—28no—
167C3×C4⋊C4—24no—
168C3×C4⋊C4#6714yes—
169C3×C4⋊C4#6718yes—
170C3×C4⋊C4C22×D314yes—
171C3×C22⋊C4—28no—
172C3×C22⋊C4—24no—
173C3×C22⋊C4—28no—
174C3×C42—28no—
175C3×C42C22×D314yes—
176C3×C42C22×D318yes—
177#216—128no—
178#215—616no—
179#215—128no—
180#214—68no—
181#213—128no—
182(C2×D3)⋊C4—68no—
183(C2×D3)⋊C4—68no—
184(C2×D3)⋊C4—68no—
185C4⋊Dic3—34no—
186Dic3⋊C4—64no—
187C4×Dic3—64no—
188C2×C3⋊C8—34no—
189C2×C3⋊C8—38no—
190C2×C3⋊C8—34no—
191C22×C32—41no—
192C22×C32—41no—
193C22×C32—41no—
194C22×C32C22×D411yescharacteristic
195C2×C3⋊D3—42no—
196C2×C3⋊D3—42no—
197C2×C3⋊D3—42no—
198C32×C4—22no—
199C32×C4—22no—
200C32×C4—21no—
201C32×C4—42no—
202C32×C4—41no—
203C32×C4#13512yes—
204C32×C4C2×#4111yescharacteristic
205C32×C4H(5,𝔽2)11yescharacteristic
206C3⋊Dic3—41no—
207C3⋊Dic3—41no—
208C2×Q16—92no—
209C2×SD16—92no—
210C2×SD16—91no—
211C2×SD16—92no—
212C2×D8—92no—
213C4⋊Q8C2×C3⋊D311yescharacteristic
214#127—91no—
215#126—22no—
216#124—92no—
217#124—181no—
218#124C2×C3⋊D312yes—
219#123—182no—
220C22⋊Q8—21no—
221C4×Q8—91no—
222C4×Q8C2×C3⋊D312yes—
223C4×Q8C2×C3⋊D311yescharacteristic
224C4×D4—92no—
225C4×D4—181no—
226C4×D4C2×C3⋊D311yescharacteristic
227#117—21no—
228#106—91no—
229C4⋊C8—91no—
230C4⋊C8—92no—
231#103—92no—
232#103—91no—
233#102—91no—
234#102—92no—
235C4×C8—91no—
236C4×C8—92no—
237C23×C3—24no—
238C22×D3—68no—
239C3×Q8—28no—
240C3×Q8—28no—
241C3×Q8—28no—
242C3×D4—24no—
243C3×D4—24no—
244C2×C3×C4—24no—
245C2×C3×C4—28no—
246C2×C3×C4—48no—
247C2×C3×C4C2×#6714yes—
248C2×C3×C4C2×#6718yes—
249C2×C3×C4C2×#6718yes—
250C2×C3×C4C2×#6714yes—
251C2×C3×C4C23×D314yes—
252C2×Dic3—64no—
253C2×Dic3—64no—
254D12—68no—
255D12—68no—
256D12—128no—
257D12—244no—
258C4×D3—248no—
259Dic6—64no—
260Dic6—64no—
261C3⋊C8—38no—
262C3⋊C8—68no—
263C3⋊C8—64no—
264C2×C32—81no—
265C2×C32#55011yescharacteristic
266C2×C32C2×#13511yescharacteristic
267C2×C32#57711yescharacteristic
268C3⋊D3—82no—
269C2×Q8—91no—
270C2×Q8#63811yescharacteristic
271C2×Q8C22×C3⋊D312yes—
272C2×D4—92no—
273C2×D4—181no—
274C2×D4—181no—
275C2×D4C22×C3⋊D311yescharacteristic
276C22×C4—21no—
277C22×C4—182no—
278Q16—362no—
279SD16—182no—
280SD16—184no—
281SD16—362no—
282D8—362no—
283C2×C8—91no—
284C2×C8—92no—
285C2×C8—91no—
286C4⋊C4—21no—
287C4⋊C4—22no—
288C4⋊C4—21no—
289C4⋊C4—91no—
290C4⋊C4—181no—
291C4⋊C4#63811yescharacteristic
292C4⋊C4#63812yes—
293C4⋊C4C22×C3⋊D311yescharacteristic
294C22⋊C4—22no—
295C22⋊C4—21no—
296C22⋊C4—22no—
297C22⋊C4—182no—
298C22⋊C4—182no—
299C22⋊C4—182no—
300C42—22no—
301C42—181no—
302C42C22×C3⋊D312yes—
303C42C22×C3⋊D311yescharacteristic
304C22×C3—44no—
305C22×C3—44no—
306C22×C3—44no—
307C22×C3C22×#6714yes—
308C2×D3—128no—
309C2×D3—128no—
310C2×D3—128no—
311C3×C4—28no—
312C3×C4—28no—
313C3×C4—24no—
314C3×C4—44no—
315C3×C4—48no—
316C3×C4#95018yes—
317C3×C4D3×#4114yes—
318C3×C4#100914yes—
319Dic3—124no—
320Dic3—124no—
321C32#339411yescharacteristic, complemented, Sylow
322C23—21no—
323C23—182no—
324Q8—22no—
325Q8—22no—
326Q8—22no—
327Q8—181no—
328Q8—181no—
329D4—21no—
330D4—21no—
331D4—182no—
332D4—182no—
333D4—362no—
334D4—721no—
335C2×C4—21no—
336C2×C4—22no—
337C2×C4—42no—
338C2×C4—181no—
339C2×C4—181no—
340C2×C4—722no—
341C2×C4C2×#63812yes—
342C2×C4C2×#63812yes—
343C2×C4C2×#63811yescharacteristic
344C2×C4C2×#63811yescharacteristic
345C2×C4C23×C3⋊D311yescharacteristic
346C8—92no—
347C8—182no—
348C8—181no—
349C2×C3—84no—
350C2×C3C2×#95014yes—
351C2×C3#583414yes—
352C2×C3#583714yes—
353D3—248no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—362no—
358C22—362no—
359C22—362no—
360C22C22×#63811yescharacteristic
361C4—22no—
362C4—22no—
363C4—21no—
364C4—41no—
365C4—42no—
366C4—361no—
367C4—361no—
368C4#6415912yes—
369C4#41×C3⋊D311yescharacteristic
370C4#6436611yescharacteristic
371C3#8367914yescomplemented
372C2—81no—
373C2—722no—
374C2C2×#6415911yescharacteristic
375C2#1059630511yescharacteristic
376C2#1059630811yescharacteristic
subgroupG/H
centerC22C22×#638
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#556C2
socleC22×C32C22×D4
prime radical#10592714C2
hypercenter#556C3⋊D3
hypocenterC32#3394
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #556

Complements

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

NH ≅ G/Ntype
1. C32×#556C2semidirect
2. #10596056C2semidirect
3. #10592789C2semidirect
4. #10592784C2semidirect
5. #10592758C2semidirect
6. #10592756C2semidirect
7. #10592727C2semidirect
8. C4×#3755C2semidirect
9. Q8×C3⋊(C3⋊C8)C2semidirect
10. C4×#3754C2semidirect
42. C3×#556D3semidirect
146. #556C3⋊D3semidirect
321. C32#3394semidirect
371. C3#83679semidirect

Maximal subgroups

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

subgroupindex
C32×#5562
#105960562
#105927892
#105927842
#105927582
#105927562
#105927272
C4×#37552
Q8×C3⋊(C3⋊C8)2
C4×#37542
#105927142
#836793