Finite Group Databasebeta

← #11895615

Subgroups — #11895615

Order 1152.

1044 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596056C211yesmaximal, characteristic
2#10596041C211yesmaximal, characteristic, complemented
3C32×C4×Q16C211yesmaximal, characteristic, complemented
4#10592884C212yesmaximal, complemented
5#10592726C211yesmaximal, characteristic
6#10592719C211yesmaximal, characteristic, complemented
7#10592590C212yesmaximal, complemented
8#10592499C212yesmaximal, complemented
9#10592487C212yesmaximal, complemented
10#10592393C211yesmaximal, characteristic
11C8×#634C211yesmaximal, characteristic, complemented
12#79701—34nomaximal
13C2×C32×Q16C2211yescharacteristic
14C32×C4×Q8C2211yescharacteristic
15C32×C4×Q8C2211yescharacteristic
16#64156C2212yes—
17Q8×C3⋊Dic3C2212yes—
18C2×#3755C2212yes—
19#64103—22no—
20#64102C2212yes—
21#64099—22no—
22#64099C2212yes—
23#64084—21no—
24#64083C2211yescharacteristic
25C4×C4⋊(C3⋊D3)—21no—
26#64078—21no—
27#64078C2211yescharacteristic
28C4×#634—21no—
29C4×#634C2211yescharacteristic
30C32×#107C2211yescharacteristic
31C32×#103C2211yescharacteristic
32C32×#103C2211yescharacteristic
33C32×C4×C8C2211yescharacteristic
34#63662C2212yes—
35#63648C2212yes—
36#63648C2212yes—
37#63641C2212yes—
38C8×C3⋊Dic3C2212yes—
39#63636C2212yes—
40#63635C2212yes—
41C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
42#5585—34no—
43#5570—34no—
44C3×C4×Q16D314yescomplemented
45#5185—38no—
46#5027—34no—
47#5020—34no—
48#4891—38no—
49#4800—38no—
50#4788—38no—
51#4694—34no—
52C8×Dic6—34no—
53C2×C32×Q8C2311yescharacteristic
54C2×C32×Q8C2311yescharacteristic
55C2×C4⋊(C3⋊D3)—21no—
56C2×C4⋊(C3⋊D3)—21no—
57C2×C4⋊(C3⋊D3)C2312yes—
58C2×C4×C3⋊D3—22no—
59C2×#634—21no—
60C2×#634D411yescharacteristic
61C32×Q16—22no—
62C2×C32×C8C2311yescharacteristic
63C2×C32×C8C2311yescharacteristic
64C32×C4⋊C4—21no—
65C32×C4⋊C4—21no—
66C32×C4⋊C4C2311yescharacteristic
67C32×C4⋊C4C2311yescharacteristic
68C32×C42—21no—
69C32×C42—21no—
70C32×C42C2311yescharacteristic
71#3755—24no—
72#3752—22no—
73#3752—22no—
74#3752—22no—
75C4⋊(C3⋊Dic3)—21no—
76C4⋊(C3⋊Dic3)—22no—
77C4⋊(C3⋊Dic3)—22no—
78C4⋊(C3⋊Dic3)D411yescharacteristic
79C4⋊(C3⋊Dic3)C2312yes—
80#3750—22no—
81#3750D412yes—
82C4×C3⋊Dic3—22no—
83C4×C3⋊Dic3C2312yes—
84C2×C3⋊(C3⋊C8)C2312yes—
85#3365—91noSylow
86C2×C3×Q16C2×D314yes—
87C3×C4×Q8C2×D314yes—
88C3×C4×Q8C2×D314yes—
89#947—38no—
90Q8×Dic3—38no—
91C2×#215—38no—
92#894—68no—
93#893—38no—
94#890—38no—
95#890—68no—
96#875—64no—
97#874—34no—
98C4×D12—64no—
99#869—34no—
100#869—64no—
101C4×Dic6—34no—
102C4×Dic6—64no—
103C3×#107C2×D314yes—
104C3×#103C2×D314yes—
105C3×#103C2×D314yes—
106C3×C4×C8C2×D314yes—
107#835—38no—
108#821—38no—
109#821—38no—
110Dic3⋊C8—38no—
111C8×Dic3—38no—
112#809—38no—
113#808—38no—
114C4⋊(C3⋊C8)—34no—
115C22×C3⋊D3—22no—
116C32×Q8—21no—
117C32×Q8—21no—
118C32×Q8—21no—
119C32×Q8#4112yes—
120C2×C32×C4—21no—
121C2×C32×C4—21no—
122C2×C32×C4—21no—
123C2×C32×C4—21no—
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2411yescharacteristic
127C2×C3⋊Dic3—22no—
128C2×C3⋊Dic3C2×D412yes—
129C2×C3⋊Dic3C2×D412yes—
130C4⋊(C3⋊D3)—22no—
131C4⋊(C3⋊D3)—22no—
132C4⋊(C3⋊D3)—42no—
133C4⋊(C3⋊D3)—81no—
134C4×C3⋊D3—82no—
135#634—22no—
136#634—42no—
137C32×C8—21no—
138C32×C8—21no—
139C3⋊(C3⋊C8)—22no—
140#559—91no—
141#557—91no—
142#488—92no—
143#486—91no—
144#478—92no—
145#475—91no—
146#464—92no—
147#460—91no—
148C8×Q8—91no—
149C4×Q16C3⋊D311yescharacteristic, complemented
150C4×SD16—92no—
151C2×C3×Q8C22×D314yes—
152C2×C3×Q8C22×D314yes—
153C2×D12—38no—
154C2×D12—64no—
155C2×D12—64no—
156C2×C4×D3—68no—
157C2×Dic6—34no—
158C2×Dic6—64no—
159C3×Q16—28no—
160C2×C3×C8C22×D314yes—
161C2×C3×C8C22×D314yes—
162C3×C4⋊C4—24no—
163C3×C4⋊C4—24no—
164C3×C4⋊C4C22×D314yes—
165C3×C4⋊C4C22×D314yes—
166C3×C42—24no—
167C3×C42—24no—
168C3×C42C22×D314yes—
169#215—616no—
170(C2×D3)⋊C4—68no—
171(C2×D3)⋊C4—68no—
172(C2×D3)⋊C4—68no—
173C4⋊Dic3—34no—
174C4⋊Dic3—38no—
175C4⋊Dic3—68no—
176C4⋊Dic3—68no—
177C4⋊Dic3—64no—
178Dic3⋊C4—38no—
179Dic3⋊C4—68no—
180C4×Dic3—38no—
181C4×Dic3—68no—
182C2×C3⋊C8—38no—
183C22×C32C22×D411yescharacteristic
184C2×C3⋊D3—42no—
185C2×C3⋊D3—42no—
186C2×C3⋊D3—42no—
187C32×C4—22no—
188C32×C4—21no—
189C32×C4—41no—
190C32×C4—41no—
191C32×C4—41no—
192C32×C4#13512yes—
193C32×C4C2×#4111yescharacteristic
194C32×C42−1+411yescharacteristic
195C3⋊Dic3—22no—
196C3⋊Dic3—22no—
197C3⋊Dic3—42no—
198C2×Q16C2×C3⋊D311yescharacteristic
199C2×SD16—92no—
200C4⋊Q8—91no—
201C4⋊Q8—181no—
202#127—91no—
203#125—92no—
204#125—182no—
205#124—92no—
206#124—181no—
207#123—182no—
208C4×Q8—91no—
209C4×Q8—92no—
210C4×Q8—181no—
211C4×Q8C2×C3⋊D311yescharacteristic
212C4×Q8C2×C3⋊D311yescharacteristic
213C4×D4—92no—
214C4×D4—181no—
215#107C2×C3⋊D311yescharacteristic
216#106—92no—
217C4⋊C8—92no—
218C4⋊C8—91no—
219#103—92no—
220#103C2×C3⋊D311yescharacteristic
221#103C2×C3⋊D311yescharacteristic
222#102—92no—
223#102—92no—
224#102—92no—
225C4×C8—92no—
226C4×C8C2×C3⋊D311yescharacteristic
227C22×D3—68no—
228C3×Q8—24no—
229C3×Q8—24no—
230C3×Q8—24no—
231C3×Q8#23518yes—
232C2×C3×C4—24no—
233C2×C3×C4—24no—
234C2×C3×C4—24no—
235C2×C3×C4—24no—
236C2×C3×C4D3×D414yes—
237C2×C3×C4D3×D414yes—
238C2×C3×C4C23×D314yes—
239C2×Dic3—38no—
240C2×Dic3—38no—
241C2×Dic3—68no—
242D12—68no—
243D12—68no—
244D12—128no—
245D12—244no—
246C4×D3—248no—
247Dic6—68no—
248Dic6—128no—
249C3×C8—24no—
250C3×C8—24no—
251C3⋊C8—68no—
252C2×C32#54811yescharacteristic
253C2×C32C2×#13511yescharacteristic
254C2×C32#57711yescharacteristic
255C3⋊D3—82no—
256C2×Q8—91no—
257C2×Q8—181no—
258C2×Q8C22×C3⋊D311yescharacteristic
259C2×Q8C22×C3⋊D311yescharacteristic
260C2×D4—92no—
261C2×D4—181no—
262C2×D4—181no—
263C22×C4—182no—
264Q16—22no—
265SD16—184no—
266C2×C8—92no—
267C2×C8C22×C3⋊D311yescharacteristic
268C2×C8C22×C3⋊D311yescharacteristic
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—91no—
272C4⋊C4—92no—
273C4⋊C4—92no—
274C4⋊C4—182no—
275C4⋊C4—182no—
276C4⋊C4—182no—
277C4⋊C4—181no—
278C4⋊C4C22×C3⋊D311yescharacteristic
279C4⋊C4C22×C3⋊D311yescharacteristic
280C22⋊C4—182no—
281C22⋊C4—182no—
282C22⋊C4—182no—
283C42—21no—
284C42—21no—
285C42—92no—
286C42—182no—
287C42C22×C3⋊D311yescharacteristic
288C22×C3C2×D3×D414yes—
289C2×D3—128no—
290C2×D3—128no—
291C2×D3—128no—
292C3×C4—24no—
293C3×C4—28no—
294C3×C4—44no—
295C3×C4—44no—
296C3×C4—44no—
297C3×C4#91918yes—
298C3×C4C2×#23514yes—
299C3×C4#101014yes—
300Dic3—68no—
301Dic3—68no—
302Dic3—128no—
303C32#336511yescharacteristic, complemented, Sylow
304C23—182no—
305Q8—21no—
306Q8—21no—
307Q8—21no—
308Q8—182no—
309Q8—362no—
310Q8#382812yes—
311D4—182no—
312D4—182no—
313D4—362no—
314D4—721no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—92no—
320C2×C4—92no—
321C2×C4—182no—
322C2×C4—722no—
323C2×C4D4×C3⋊D311yescharacteristic
324C2×C4D4×C3⋊D311yescharacteristic
325C2×C4C23×C3⋊D311yescharacteristic
326C8—21no—
327C8—21no—
328C8—182no—
329C2×C3#555214yes—
330C2×C3C2×#91914yes—
331C2×C3#577014yes—
332D3—248no—
333C22—362no—
334C22—362no—
335C22—362no—
336C22C2×D4×C3⋊D311yescharacteristic
337C4—21no—
338C4—22no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—182no—
343C4—182no—
344C4—362no—
345C4#6412812yes—
346C4C2×#382811yescharacteristic
347C4#6436711yescharacteristic
348C3#7970114yescomplemented
349C2—722no—
350C2#1059602311yescharacteristic
351C2C2×#6412811yescharacteristic
352C2#1059624111yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×C4×Q16C2
socleC22×C32C22×D4
prime radical#64083C22
hypercenterC4×Q16C3⋊D3
hypocenterC32#3365
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
2. #10596041C2semidirect
3. C32×C4×Q16C2semidirect
4. #10592884C2semidirect
6. #10592719C2semidirect
7. #10592590C2semidirect
8. #10592499C2semidirect
9. #10592487C2semidirect
11. C8×#634C2semidirect
44. C3×C4×Q16D3semidirect
149. C4×Q16C3⋊D3semidirect
303. C32#3365semidirect
348. C3#79701semidirect

Maximal subgroups

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

subgroupindex
#105960562
#105960412
C32×C4×Q162
#105928842
#105927262
#105927192
#105925902
#105924992
#105924872
#105923932
C8×#6342
#797013