Finite Group Databasebeta

← #11895316

Subgroups — #11895316

Order 1152.

1086 conjugacy classes of subgroups.

The subgroup lattice has 369 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596056C211yesmaximal, characteristic, complemented
2#10596050C211yesmaximal, characteristic, complemented
3C32×C8×Q8C211yesmaximal, characteristic, complemented
4#10592549C211yesmaximal, characteristic, complemented
5#10592546C212yesmaximal, complemented
6#10592543C212yesmaximal, complemented
7#10592542C211yesmaximal, characteristic
8#10592396C212yesmaximal, complemented
9#10592393C211yesmaximal, characteristic, complemented
10C4×#3745C212yesmaximal, complemented
11C4×#3744C211yesmaximal, characteristic, complemented
12#79927—34nomaximal
13C32×C4×Q8C2211yescharacteristic
14#64156—21no—
15#64155—21no—
16C2×#3745C2212yes—
17C2×#3744C2211yescharacteristic
18#64105—22no—
19#64103—22no—
20#64102—21no—
21C4⋊C4×C3⋊D3—21no—
22#64084C2212yes—
23#64083C2211yescharacteristic
24C4×C4⋊(C3⋊D3)C2211yescharacteristic
25C4×C4⋊(C3⋊D3)C2212yes—
26C4×C4⋊(C3⋊D3)C2212yes—
27#64079C2212yes—
28#64078C2211yescharacteristic
29C4×#634C2211yescharacteristic
30C32×C4⋊C8C2211yescharacteristic
31C32×C4⋊C8C2212yes—
32C32×C4×C8C2211yescharacteristic
33C32×C4×C8C2212yes—
34#63648C2212yes—
35#63648C2212yes—
36#63648C2211yescharacteristic
37#63648C2212yes—
38#63645C2212yes—
39#63644C2211yescharacteristic
40#63643C2212yes—
41#63643C2211yescharacteristic
42#5585—34no—
43#5579—34no—
44C3×C8×Q8D314yescomplemented
45#4850—34no—
46#4847—38no—
47#4844—38no—
48#4843—34no—
49#4697—38no—
50#4694—34no—
51C4×D24—38no—
52C4×#204—34no—
53C2×C32×Q8D411yescharacteristic
54C2×C4⋊(C3⋊D3)—21no—
55C2×C4⋊(C3⋊D3)—21no—
56C2×C4⋊(C3⋊D3)C2312yes—
57C2×C4⋊(C3⋊D3)C2311yescharacteristic
58C2×C4×C3⋊D3—21no—
59C2×C4×C3⋊D3—22no—
60C2×C4×C3⋊D3—22no—
61C2×#634—21no—
62C2×#634C2311yescharacteristic
63C2×C32×C8C2311yescharacteristic
64C2×C32×C8C2312yes—
65C2×C32×C8C2311yescharacteristic
66C32×C4⋊C4D411yescharacteristic
67C32×C4⋊C4D412yes—
68C32×C42C2311yescharacteristic
69C32×C42C2312yes—
70#3752—22no—
71#3752—21no—
72#3752—22no—
73#3752—22no—
74#3752—22no—
75C4⋊(C3⋊Dic3)—21no—
76C4⋊(C3⋊Dic3)C2311yescharacteristic
77C4⋊(C3⋊Dic3)C2312yes—
78C4⋊(C3⋊Dic3)C2311yescharacteristic
79#3750—21no—
80#3750—22no—
81#3750—22no—
82C4×C3⋊Dic3—21no—
83#3745—24no—
84#3744—22no—
85#3361—91noSylow
86C3×C4×Q8C2×D314yes—
87#947—64no—
88#946—64no—
89C2×D24—38no—
90C2×#204—34no—
91#896—68no—
92#894—68no—
93#893—64no—
94D3×C4⋊C4—64no—
95#875—38no—
96#874—34no—
97C4×D12—34no—
98C4×D12—38no—
99C4×D12—38no—
100#870—38no—
101#869—34no—
102C4×Dic6—34no—
103C3×C4⋊C8C2×D314yes—
104C3×C4⋊C8C2×D318yes—
105C3×C4×C8C2×D314yes—
106C3×C4×C8C2×D318yes—
107#821—34no—
108#821—38no—
109#821—38no—
110#821—38no—
111#818—38no—
112#817—34no—
113#816—34no—
114#816—38no—
115C22×C3⋊D3—21no—
116C22×C3⋊D3—22no—
117C32×Q8—22no—
118C2×C32×C4C2×D412yes—
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D412yes—
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2411yescharacteristic
123C2×C3⋊Dic3—21no—
124C2×C3⋊Dic3—21no—
125C2×C3⋊Dic3—21no—
126C2×C3⋊Dic3—22no—
127C4⋊(C3⋊D3)—22no—
128C4⋊(C3⋊D3)—21no—
129C4⋊(C3⋊D3)—22no—
130C4⋊(C3⋊D3)—42no—
131C4⋊(C3⋊D3)—81no—
132C4⋊(C3⋊D3)#4112yes—
133C4×C3⋊D3—42no—
134C4×C3⋊D3—82no—
135C4×C3⋊D3—82no—
136#634—21no—
137#634—21no—
138#634—81no—
139C32×C8—21no—
140C32×C8—22no—
141C32×C8—21no—
142#559—91no—
143#554—91no—
144#488—92no—
145#486—91no—
146#478—92no—
147#477—91no—
148#463—92no—
149#459—91no—
150C8×Q8C3⋊D311yescharacteristic, complemented
151C4×SD16—91no—
152C4×D8—92no—
153C2×C3×Q8D1214yes—
154C2×D12—34no—
155C2×D12—38no—
156C2×D12—64no—
157C2×D12—64no—
158C2×C4×D3—64no—
159C2×C4×D3—68no—
160C2×C4×D3—68no—
161C2×Dic6—34no—
162C2×Dic6—64no—
163C2×C3×C8C22×D318yes—
164C2×C3×C8C22×D314yes—
165C2×C3×C8C22×D314yes—
166C3×C4⋊C4D1214yes—
167C3×C4⋊C4D1218yes—
168C3×C42C22×D314yes—
169C3×C42C22×D318yes—
170(C2×D3)⋊C4—68no—
171(C2×D3)⋊C4—64no—
172(C2×D3)⋊C4—68no—
173(C2×D3)⋊C4—68no—
174(C2×D3)⋊C4—68no—
175C4⋊Dic3—34no—
176C4⋊Dic3—38no—
177C4⋊Dic3—34no—
178C4⋊Dic3—64no—
179Dic3⋊C4—64no—
180Dic3⋊C4—68no—
181Dic3⋊C4—68no—
182C4×Dic3—64no—
183D24—616no—
184#204—68no—
185C22×C32C22×D411yescharacteristic
186C2×C3⋊D3—22no—
187C2×C3⋊D3—41no—
188C2×C3⋊D3—41no—
189C2×C3⋊D3—42no—
190C2×C3⋊D3—42no—
191C2×C3⋊D3—42no—
192C32×C4—22no—
193C32×C4—21no—
194C32×C4—22no—
195C32×C4#13512yes—
196C32×C4C2×#4111yescharacteristic
197C32×C42−1+411yescharacteristic
198C3⋊Dic3—41no—
199C3⋊Dic3—41no—
200C3⋊Dic3—42no—
201C3⋊Dic3—41no—
202C2×SD16—91no—
203C2×D8—92no—
204C4⋊Q8—91no—
205#127—91no—
206#125—92no—
207#124—92no—
208#124—181no—
209#123—182no—
210C22⋊Q8—181no—
211C22⋊Q8—182no—
212C4×Q8—91no—
213C4×Q8C2×C3⋊D311yescharacteristic
214C4×D4—92no—
215C4×D4—91no—
216C4×D4—92no—
217C4×D4—181no—
218C2×C4⋊C4—181no—
219#107—92no—
220#106—91no—
221C4⋊C8C2×C3⋊D311yescharacteristic
222C4⋊C8C2×C3⋊D312yes—
223#103—91no—
224#103—92no—
225#102—91no—
226#102—92no—
227#102—92no—
228#102—92no—
229C4×C8C2×C3⋊D312yes—
230C4×C8C2×C3⋊D311yescharacteristic
231C22×D3—64no—
232C22×D3—68no—
233C3×Q8—28no—
234C2×C3×C4C2×D1218yes—
235C2×C3×C4C2×D1214yes—
236C2×C3×C4C2×D1218yes—
237C2×C3×C4C2×D1214yes—
238C2×C3×C4C23×D314yes—
239C2×Dic3—64no—
240C2×Dic3—64no—
241C2×Dic3—64no—
242C2×Dic3—68no—
243D12—38no—
244D12—64no—
245D12—68no—
246D12—68no—
247D12—128no—
248D12—244no—
249C4×D3—128no—
250C4×D3—248no—
251C4×D3—248no—
252Dic6—64no—
253Dic6—64no—
254Dic6—244no—
255C3×C8—24no—
256C3×C8—24no—
257C3×C8—28no—
258C2×C32#54811yescharacteristic
259C2×C32C2×#13511yescharacteristic
260C2×C32#57611yescharacteristic
261C3⋊D3—42no—
262C3⋊D3—82no—
263C2×Q8—91no—
264C2×Q8—181no—
265C2×Q8C4⋊(C3⋊D3)11yescharacteristic
266C2×D4—91no—
267C2×D4—92no—
268C2×D4—181no—
269C2×D4—181no—
270C22×C4—181no—
271C22×C4—182no—
272C22×C4—182no—
273SD16—182no—
274D8—184no—
275C2×C8C22×C3⋊D311yescharacteristic
276C2×C8C22×C3⋊D311yescharacteristic
277C2×C8C22×C3⋊D312yes—
278C4⋊C4—91no—
279C4⋊C4—92no—
280C4⋊C4—91no—
281C4⋊C4—182no—
282C4⋊C4—181no—
283C4⋊C4—181no—
284C4⋊C4—182no—
285C4⋊C4C4⋊(C3⋊D3)11yescharacteristic
286C4⋊C4C4⋊(C3⋊D3)12yes—
287C22⋊C4—181no—
288C22⋊C4—182no—
289C22⋊C4—182no—
290C22⋊C4—182no—
291C22⋊C4—182no—
292C42—181no—
293C42C22×C3⋊D312yes—
294C42C22×C3⋊D311yescharacteristic
295C22×C3C22×D1214yes—
296C2×D3—68no—
297C2×D3—124no—
298C2×D3—124no—
299C2×D3—128no—
300C2×D3—128no—
301C2×D3—128no—
302C3×C4—28no—
303C3×C4—24no—
304C3×C4—28no—
305C3×C4#90418yes—
306C3×C4#100714yes—
307C3×C4D3×#4114yes—
308Dic3—124no—
309Dic3—128no—
310Dic3—124no—
311Dic3—124no—
312C32#336111yescharacteristic, complemented, Sylow
313C23—181no—
314C23—182no—
315Q8—22no—
316Q8—181no—
317Q8—181no—
318Q8—721no—
319D4—92no—
320D4—181no—
321D4—182no—
322D4—182no—
323D4—362no—
324D4—721no—
325C2×C4—181no—
326C2×C4—181no—
327C2×C4—181no—
328C2×C4—182no—
329C2×C4—362no—
330C2×C4—722no—
331C2×C4—722no—
332C2×C4C2×C4⋊(C3⋊D3)12yes—
333C2×C4C2×C4⋊(C3⋊D3)12yes—
334C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
335C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
336C2×C4C23×C3⋊D311yescharacteristic
337C8—21no—
338C8—22no—
339C8—21no—
340C2×C3#557614yes—
341C2×C3C2×#90414yes—
342C2×C3#575214yes—
343D3—128no—
344D3—248no—
345C22—182no—
346C22—361no—
347C22—361no—
348C22—362no—
349C22—362no—
350C22—362no—
351C22C22×C4⋊(C3⋊D3)11yescharacteristic
352C4—22no—
353C4—22no—
354C4—21no—
355C4—361no—
356C4—361no—
357C4—362no—
358C4—361no—
359C4#6411312yes—
360C4#6436411yescharacteristic
361C4#41×C3⋊D311yescharacteristic
362C3#7992714yescomplemented
363C2—362no—
364C2—722no—
365C2#1059604711yescharacteristic
366C2C2×#6411311yescharacteristic
367C2#1059622311yescharacteristic
subgroupG/H
centerC22C22×C4⋊(C3⋊D3)
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×C8×Q8C2
socleC22×C32C22×D4
prime radical#10592542C2
hypercenterC8×Q8C3⋊D3
hypocenterC32#3361
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8 ◁ C8×Q8

Complements

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

NH ≅ G/Ntype
1. #10596056C2semidirect
2. #10596050C2semidirect
3. C32×C8×Q8C2semidirect
4. #10592549C2semidirect
5. #10592546C2semidirect
6. #10592543C2semidirect
8. #10592396C2semidirect
9. #10592393C2semidirect
10. C4×#3745C2semidirect
11. C4×#3744C2semidirect
44. C3×C8×Q8D3semidirect
150. C8×Q8C3⋊D3semidirect
312. C32#3361semidirect
362. C3#79927semidirect

Maximal subgroups

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

subgroupindex
#105960562
#105960502
C32×C8×Q82
#105925492
#105925462
#105925432
#105925422
#105923962
#105923932
C4×#37452
C4×#37442
#799273