Finite Group Databasebeta

← Q16×#624 #11859937

Subgroups — Q16×#624 #11859937

Order 1152.

1105 conjugacy classes of subgroups.

The subgroup lattice has 357 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q16×C3⋊D3C211yesmaximal, characteristic
2Q8×#624C212yesmaximal
3C3×Dic3×Q16C212yesmaximal, complemented
4#10591552C212yesmaximal
5#10591537C214yesmaximal, complemented
6#10590807C212yesmaximal, complemented
7#10590687C211yesmaximal, characteristic
8C8×#624C211yesmaximal, characteristic
9C4×D3×Q16—32nomaximal
10C2×Q8×C3⋊D3C2212yes—
11C2×C32×Q16C2211yescharacteristic
12C2×#3756C2212yes—
13Q16×C3⋊D3C418yescomplemented
14C2×#3746C2211yescharacteristic
15C2×C8×C3⋊D3C2211yescharacteristic
16C3×Q8×Dic3C2214yes—
17#63900—22no—
18#63900C2212yes—
19C4×#624—22no—
20C4×#624C2211yescharacteristic
21#63844—24no—
22#63844C2214yes—
23C2×#3710C2211yescharacteristic
24C3×#835C2214yes—
25C3×#818C2212yes—
26C3×C8×Dic3C2212yes—
27#63576C2212yes—
28#63567C2214yes—
29Dic3×C3⋊C8C2212yes—
30C2×D3×Q16—32no—
31C2×D3×Q16—61no—
32C4×D3×Q8—34no—
33C3×C4×Q16—32no—
34Dic3×Q16D312yescomplemented
35C4×#216—34no—
36D3×#107—32no—
37#4873—32no—
38D3×#103—34no—
39#4790—34no—
40C4×Dic12—32no—
41C4×D3×C8—32no—
42C2×C32×Q8C2312yes—
43Q8×C3⋊D3—24no—
44Q8×C3⋊D3C2×C418yes—
45C2×C4×C3⋊D3—22no—
46C2×C4×C3⋊D3C2311yescharacteristic
47C2×#634—22no—
48C2×#634C2312yes—
49C2×#624—22no—
50C2×#624D411yescharacteristic
51C2×#624D411yescharacteristic
52C32×Q16C2×C414yescomplemented
53C2×C32×C8C2311yescharacteristic
54#3756C2×C418yescomplemented
55C2×C3⋊(C3⋊C8)C2311yescharacteristic
56#3746C2×C414yescomplemented
57C8×C3⋊D3C2×C414yes—
58C3×C4⋊Dic3—24no—
59C3×C4⋊Dic3C2314yes—
60C3×C4×Dic3—24no—
61C3×C4×Dic3C2312yes—
62C2×C3×C3⋊C8C2312yes—
63#3724—22no—
64#3724—24no—
65Dic32—24no—
66Dic32D412yes—
67#3710—22no—
68C2×C4×Q16—91noSylow
69C2×D3×Q8—34no—
70C2×D3×Q8—62no—
71C2×C3×Q16—21no—
72C2×C3×Q16C2×D312yes—
73C3×C4×Q8—34no—
74Q8×Dic3C2×D314yes—
75C2×#216—34no—
76C2×#216—62no—
77D3×Q16—316no—
78D3×Q16—68no—
79C2×Dic12—32no—
80C2×Dic12—61no—
81C2×D3×C8—32no—
82C2×D3×C8—32no—
83C2×D3×C8—61no—
84D3×C4⋊C4—34no—
85D3×C4⋊C4—64no—
86#887—34no—
87#887—64no—
88C42×D3—32no—
89C42×D3—64no—
90C4×Dic6—34no—
91C4×Dic6—64no—
92C3×#107—32no—
93C3×#103—34no—
94C3×C4×C8—32no—
95#835C2×D314yes—
96#818C2×D312yes—
97#816—34no—
98C8×Dic3—32no—
99C8×Dic3C2×D312yes—
100#810—34no—
101#807—34no—
102C4×C3⋊C8—32no—
103C22×C3⋊D3C2×D411yescharacteristic
104C32×Q8—22no—
105C32×Q8C22×C414yes—
106C2×C32×C4—22no—
107C2×C32×C4C2411yescharacteristic
108C2×C3⋊Dic3—22no—
109C2×C3⋊Dic3C2×D411yescharacteristic
110C4×C3⋊D3—28no—
111C4×C3⋊D3C22×C412yes—
112C4×C3⋊D3#4112yes—
113#634—22no—
114#634—28no—
115#634C22×C414yes—
116C2×C3×Dic3—24no—
117C2×C3×Dic3C2×D412yes—
118C2×C3×Dic3C2×D412yes—
119#624—22no—
120#624—44no—
121#624Q1614yesdirect product factor
122C32×C8C22×C412yes—
123C3⋊(C3⋊C8)C22×C412yes—
124C3×C3⋊C8—22no—
125C22×Q16—91no—
126C2×C4×Q8—92no—
127C4×Q16—32no—
128C4×Q16—92no—
129C4×Q16—94no—
130C2×#107—91no—
131C2×#103—92no—
132C2×C4×C8—91no—
133C2×C3×Q8—22no—
134C2×C3×Q8C22×D314yes—
135D3×Q8—316no—
136D3×Q8—68no—
137D3×Q8—68no—
138D3×Q8—124no—
139C2×C4×D3—32no—
140C2×C4×D3—32no—
141C2×C4×D3—32no—
142C2×C4×D3—61no—
143C2×C4×D3—64no—
144C2×C4×D3—64no—
145C2×C4×D3—122no—
146C2×Dic6—34no—
147C2×Dic6—62no—
148C2×Dic6—64no—
149C2×Dic6—122no—
150C3×Q16—24no—
151C3×Q16C4×D318yescomplemented
152C2×C3×C8—21no—
153C2×C3×C8—32no—
154C2×C3×C8C22×D312yes—
155C3×C4⋊C4—34no—
156C3×C4⋊C4—64no—
157C3×C42—32no—
158C3×C42—64no—
159#216—316no—
160#216—68no—
161C4⋊Dic3—24no—
162C4⋊Dic3C22×D314yes—
163Dic3⋊C4—64no—
164Dic3⋊C4—64no—
165Dic3⋊C4—64no—
166C4×Dic3—24no—
167C4×Dic3—32no—
168C4×Dic3—32no—
169C4×Dic3—64no—
170C4×Dic3—64no—
171C4×Dic3C22×D312yes—
172C2×C3⋊C8—32no—
173C2×C3⋊C8—61no—
174C2×C3⋊C8C22×D312yes—
175Dic12—38no—
176Dic12—64no—
177D3×C8—38no—
178D3×C8—64no—
179D3×C8—64no—
180C22×C32C22×D411yescharacteristic
181C2×C3⋊D3C4×D412yes—
182C2×C3⋊D3C2×Q1612yes—
183C2×C3⋊D3#13512yes—
184C32×C4—24no—
185C32×C4C23×C411yescharacteristic
186C32×C4C2×#4111yescharacteristic
187C3⋊Dic3—24no—
188C3⋊Dic3C4×D412yes—
189C3×Dic3—22no—
190C3×Dic3—44no—
191C3×Dic3C2×Q1614yescomplemented
192C22×Q8—92no—
193C2×Q16—92no—
194C2×Q16—98no—
195C2×Q16—91no—
196C2×Q16D3211yescharacteristic
197C22×C8—91no—
198C22×C8—91no—
199C4×Q8—34no—
200C4×Q8—94no—
201C4×Q8—184no—
202C2×C4⋊C4—92no—
203C2×C4⋊C4—182no—
204C2×C42—91no—
205C2×C42—182no—
206#107—32no—
207#107—92no—
208#103—34no—
209#103—94no—
210C4×C8—32no—
211C4×C8—92no—
212C22×D3—32no—
213C22×D3—61no—
214C3×Q8—24no—
215C3×Q8—24no—
216C3×Q8—42no—
217C3×Q8C2×C4×D318yes—
218C2×C3×C4—24no—
219C2×C3×C4—21no—
220C2×C3×C4—32no—
221C2×C3×C4—32no—
222C2×C3×C4—42no—
223C2×C3×C4—64no—
224C2×C3×C4C23×D312yes—
225C2×Dic3—24no—
226C2×Dic3—32no—
227C2×Dic3—61no—
228C2×Dic3—64no—
229C2×Dic3—122no—
230C2×Dic3D3×D412yes—
231C2×Dic3D3×D412yes—
232C4×D3—34no—
233C4×D3—34no—
234C4×D3—38no—
235C4×D3—62no—
236C4×D3—62no—
237C4×D3—64no—
238C4×D3—616no—
239C4×D3—128no—
240C4×D3—128no—
241Dic6—38no—
242Dic6—64no—
243Dic6—616no—
244Dic6—64no—
245Dic6—128no—
246Dic6—122no—
247C3×C8—22no—
248C3×C8—62no—
249C3×C8C2×C4×D314yes—
250C3⋊C8—22no—
251C3⋊C8—34no—
252C3⋊C8—62no—
253C2×C32C2×C4×D411yescharacteristic
254C2×C32C22×Q1611yescharacteristic
255C2×C32C2×#13511yescharacteristic
256C3⋊D3C4×Q1614yescomplemented
257C2×Q8—98no—
258C2×Q8—92no—
259C2×Q8—182no—
260C2×Q8—184no—
261C2×Q8C2×D3212yes—
262C22×C4—91no—
263C22×C4—91no—
264C22×C4—91no—
265C22×C4—182no—
266C22×C4—182no—
267Q16—98no—
268Q16—94no—
269Q16#62414yesdirect product factor
270C2×C8—32no—
271C2×C8—91no—
272C2×C8—94no—
273C2×C8—182no—
274C2×C8C2×D3211yescharacteristic
275C4⋊C4—34no—
276C4⋊C4—64no—
277C4⋊C4—184no—
278C4⋊C4—182no—
279C42—32no—
280C42—64no—
281C42—92no—
282C42—184no—
283C22×C3—21no—
284C22×C3C2×D3×D412yes—
285C2×D3—34no—
286C2×D3—34no—
287C2×D3—34no—
288C2×D3—62no—
289C2×D3—62no—
290C2×D3—62no—
291C3×C4—28no—
292C3×C4—21no—
293C3×C4—21no—
294C3×C4—34no—
295C3×C4—44no—
296C3×C4—62no—
297C3×C4—124no—
298C3×C4C22×C4×D312yes—
299C3×C4D3×#4112yes—
300Dic3—22no—
301Dic3—34no—
302Dic3—44no—
303Dic3—62no—
304Dic3—68no—
305Dic3—124no—
306Dic3D3×Q1614yescomplemented
307C32C2×C4×Q1611yescharacteristic, complemented, Sylow
308C23—91no—
309Q8—22no—
310Q8—94no—
311Q8—188no—
312Q8—182no—
313Q8C2×#62414yes—
314C2×C4—22no—
315C2×C4—32no—
316C2×C4—32no—
317C2×C4—64no—
318C2×C4—94no—
319C2×C4—91no—
320C2×C4—92no—
321C2×C4—92no—
322C2×C4—188no—
323C2×C4—182no—
324C2×C4—182no—
325C2×C4—364no—
326C2×C4C22×D3211yescharacteristic
327C8—62no—
328C8—92no—
329C8C2×#62412yes—
330C2×C3—21no—
331C2×C3—21no—
332C2×C3—21no—
333C2×C3C4×D3×D412yes—
334C2×C3C2×D3×Q1612yes—
335C2×C3D3×#13512yes—
336D3—38no—
337D3—64no—
338C22—92no—
339C22—92no—
340C22—92no—
341C22D32×D411yescharacteristic
342C4—24no—
343C4—34no—
344C4—62no—
345C4—92no—
346C4—124no—
347C4—184no—
348C4#6431211yescharacteristic
349C4C22×#62411yescharacteristic
350C3—21no—
351C3C4×D3×Q1612yescomplemented
352C2—94no—
353C2D32×Q1611yescharacteristic
354C2#1059476411yescharacteristic
355C2D4×#62411yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
cosocleC2×C32×C4C24
hypercenterC2×Q16D32
hypocenterC32C2×C4×Q16
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
3. C3×Dic3×Q16C2semidirect
5. #10591537C2semidirect
6. #10590807C2semidirect
13. Q16×C3⋊D3C4semidirect
34. Dic3×Q16D3semidirect
52. C32×Q16C2×C4semidirect
54. #3756C2×C4semidirect
56. #3746C2×C4semidirect
121. #624Q16direct (N × H)
151. C3×Q16C4×D3semidirect
191. C3×Dic3C2×Q16semidirect
256. C3⋊D3C4×Q16semidirect
269. Q16#624direct (N × H)
306. Dic3D3×Q16semidirect
307. C32C2×C4×Q16semidirect
351. C3C4×D3×Q16semidirect

Maximal subgroups

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

subgroupindex
C2×Q16×C3⋊D32
Q8×#6242
C3×Dic3×Q162
#105915522
#105915372
#105908072
#105906872
C8×#6242
C4×D3×Q163