Finite Group Databasebeta

← #11785218

Subgroups — #11785218

Order 1152.

765 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×C3⋊Dic3C211yesmaximal, characteristic
2C2×C3×#835C212yesmaximal
3#10591359C211yesmaximal, characteristic
4C2×#63572C211yesmaximal, characteristic
5#10589164C212yesmaximal
6#70221—32nomaximal
7C22×C32×Q8C2211yescharacteristic
8Q8×C3⋊Dic3—22no—
9Q8×C3⋊Dic3C414yescomplemented
10C2×C4⋊(C3⋊Dic3)—21no—
11C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
12C2×C4×C3⋊Dic3—21no—
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×C3×C4⋊Dic3C2212yes—
15C22×C3×C3⋊C8C2212yes—
16C2×#3724—21no—
17C2×#3724—21no—
18C3×#835—24no—
19#63572—22no—
20C2×Q8×Dic3—32no—
21C2×Q8×Dic3—61no—
22C2×C3×#103—32no—
23C2×#835D312yes—
24C2×Dic3⋊C8—32no—
25#4975—32no—
26#4551—32no—
27#4529—32no—
28C2×C32×Q8—21no—
29C2×C32×Q8—21no—
30C2×C32×Q8—21no—
31C2×C32×Q8C2×C412yes—
32C2×C32×Q8D412yes—
33C2×C32×Q8Q812yes—
34C22×C32×C4—21no—
35C22×C32×C4C2311yescharacteristic
36C22×C3⋊Dic3—21no—
37C22×C3⋊Dic3D411yescharacteristic
38C22×C3⋊Dic3D411yescharacteristic
39C22×C3×Dic3—22no—
40C4⋊(C3⋊Dic3)—21no—
41C4⋊(C3⋊Dic3)—24no—
42C4⋊(C3⋊Dic3)C2×C412yes—
43C4×C3⋊Dic3—24no—
44C4×C3⋊Dic3C2×C412yes—
45C4×C3⋊Dic3D412yes—
46C3×C4⋊Dic3—22no—
47C3×C4⋊Dic3—22no—
48C2×C3×C3⋊C8—22no—
49C2×C3×C3⋊C8—22no—
50C2×C3×C3⋊C8—22no—
51#3724—42no—
52#3724—42no—
53#1803—91noSylow
54C22×C3×Q8—21no—
55C22×C3×Q8C2×D312yes—
56C22×C3×C8—32no—
57C2×C3×C4⋊C4—32no—
58Q8×Dic3—38no—
59Q8×Dic3—64no—
60Q8×Dic3—64no—
61Q8×Dic3—64no—
62C2×C4⋊Dic3—32no—
63C2×C4⋊Dic3—61no—
64C2×C4⋊Dic3—62no—
65C2×C4⋊Dic3—62no—
66C2×C4⋊Dic3C2×D312yes—
67C2×Dic3⋊C4—62no—
68C2×Dic3⋊C4—62no—
69C2×C4×Dic3—32no—
70C2×C4×Dic3—61no—
71C2×C4×Dic3—62no—
72C2×C4×Dic3—62no—
73C22×C3⋊C8C2×D312yes—
74C3×#103—64no—
75#835—24no—
76Dic3⋊C8—64no—
77C23×C32C2×D411yescharacteristic
78C32×Q8—22no—
79C32×Q8—22no—
80C32×Q8—22no—
81C32×Q8C4⋊C414yescomplemented
82C2×C32×C4—22no—
83C2×C32×C4—22no—
84C2×C32×C4—22no—
85C2×C32×C4C22×C411yescharacteristic
86C2×C32×C4C2×D411yescharacteristic
87C2×C32×C4C2×D411yescharacteristic
88C2×C32×C4C2×Q811yescharacteristic
89C2×C32×C4#4111yescharacteristic
90C2×C32×C4#4111yescharacteristic
91C2×C3⋊Dic3—22no—
92C2×C3⋊Dic3—21no—
93C2×C3⋊Dic3—21no—
94C2×C3⋊Dic3—41no—
95C2×C3⋊Dic3—41no—
96C2×C3⋊Dic3C22⋊C412yes—
97C2×C3⋊Dic3C22⋊C412yes—
98C2×C3⋊Dic3SD1612yes—
99C2×C3⋊Dic3Q1612yes—
100C2×C3×Dic3—42no—
101C2×C3×Dic3—42no—
102C2×C3×Dic3—42no—
103C3×C3⋊C8—42no—
104C2×C4×Q8—91no—
105C2×C4⋊C8—91no—
106C2×#103—32no—
107#384—91no—
108#340—92no—
109C2×C3×Q8—22no—
110C2×C3×Q8—22no—
111C2×C3×Q8—22no—
112C2×C3×Q8—22no—
113C2×C3×Q8—22no—
114C2×C3×Q8—22no—
115C2×C3×Q8—22no—
116C2×C3×Q8—22no—
117C2×C3×Q8—22no—
118C2×C3×Q8Dic614yes—
119C2×C3×Q8C4×D314yes—
120C2×C3×Q8#6714yes—
121C22×C3×C4—22no—
122C22×C3×C4—22no—
123C22×C3×C4—21no—
124C22×C3×C4—62no—
125C22×C3×C4C22×D312yes—
126C22×Dic3—22no—
127C22×Dic3—32no—
128C22×Dic3—32no—
129C22×Dic3—61no—
130C22×Dic3—61no—
131C22×Dic3—62no—
132C22×Dic3—62no—
133C2×C3×C8—62no—
134C2×C3×C8—62no—
135C2×C3×C8—62no—
136C3×C4⋊C4—62no—
137C3×C4⋊C4—62no—
138C4⋊Dic3—22no—
139C4⋊Dic3—22no—
140C4⋊Dic3—34no—
141C4⋊Dic3—62no—
142C4⋊Dic3—68no—
143C4⋊Dic3—68no—
144C4⋊Dic3—62no—
145C4⋊Dic3—62no—
146Dic3⋊C4—124no—
147Dic3⋊C4—124no—
148C4×Dic3—34no—
149C4×Dic3—34no—
150C4×Dic3—62no—
151C4×Dic3—62no—
152C4×Dic3—68no—
153C4×Dic3—68no—
154C2×C3⋊C8—22no—
155C2×C3⋊C8—22no—
156C2×C3⋊C8—22no—
157C22×C32C2×C22⋊C411yescharacteristic
158C22×C32#12111yescharacteristic
159C22×C32C22⋊Q811yescharacteristic
160C22×C32C2×SD1611yescharacteristic
161C22×C32C2×Q1611yescharacteristic
162C22×C32AGL(1,ℤ/8)11yescharacteristic
163C22×C32#13711yescharacteristic
164C32×C4—24no—
165C32×C4C2×C4⋊C411yescharacteristic
166C32×C4#11711yescharacteristic
167C32×C4#12111yescharacteristic
168C32×C4C22⋊Q811yescharacteristic
169C3⋊Dic3—22no—
170C3⋊Dic3—42no—
171C3⋊Dic3#10314yescomplemented
172C3×Dic3—82no—
173C22×Q8D3211yescharacteristic
174C22×C8—32no—
175C4×Q8—94no—
176C4×Q8—182no—
177C2×C4⋊C4—32no—
178C2×C4⋊C4—91no—
179C2×C4⋊C4—181no—
180C2×C4⋊C4—181no—
181C2×C4⋊C4—181no—
182C2×C42—91no—
183C2×C42—181no—
184C4⋊C8—182no—
185#103—64no—
186C23×C3—21no—
187C23×C3D3×D412yes—
188C3×Q8—24no—
189C3×Q8—24no—
190C3×Q8—24no—
191C3×Q8—24no—
192C3×Q8—24no—
193C3×Q8—24no—
194C3×Q8—24no—
195C3×Q8Dic3⋊C418yescomplemented
196C2×C3×C4—24no—
197C2×C3×C4—24no—
198C2×C3×C4—24no—
199C2×C3×C4—24no—
200C2×C3×C4—24no—
201C2×C3×C4—24no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—21no—
208C2×C3×C4—122no—
209C2×C3×C4—122no—
210C2×C3×C4—122no—
211C2×C3×C4C2×Dic612yes—
212C2×C3×C4C2×C4×D312yes—
213C2×C3×C4D3×D412yes—
214C2×C3×C4#23712yes—
215C2×C3×C4#23712yes—
216C2×C3×C4C2×#6712yes—
217C2×Dic3—34no—
218C2×Dic3—34no—
219C2×Dic3—34no—
220C2×Dic3—34no—
221C2×Dic3—42no—
222C2×Dic3—42no—
223C2×Dic3—42no—
224C2×Dic3—62no—
225C2×Dic3—62no—
226C2×Dic3—62no—
227C2×Dic3—62no—
228C2×Dic3—62no—
229C2×Dic3—62no—
230C2×Dic3—64no—
231C2×Dic3—64no—
232C2×Dic3—121no—
233C2×Dic3—121no—
234C2×Dic3—122no—
235C2×Dic3—122no—
236C2×Dic3—122no—
237C2×Dic3—122no—
238C3×C8—122no—
239C3⋊C8—42no—
240C2×C32#38011yescharacteristic
241C2×C32C2×#10311yescharacteristic
242C2×C32#41711yescharacteristic
243C2×C32#46011yescharacteristic
244C2×C32#46211yescharacteristic
245C2×C32#47511yescharacteristic
246C2×C32#47711yescharacteristic
247C2×Q8—21no—
248C2×Q8—21no—
249C2×Q8—21no—
250C2×Q8#62412yes—
251C2×Q8#62512yes—
252C2×Q8#62712yes—
253C22×C4—21no—
254C22×C4—62no—
255C22×C4—91no—
256C22×C4—91no—
257C22×C4—181no—
258C22×C4C2×D3211yescharacteristic
259C2×C8—62no—
260C2×C8—62no—
261C2×C8—62no—
262C4⋊C4—62no—
263C4⋊C4—62no—
264C4⋊C4—92no—
265C4⋊C4—184no—
266C4⋊C4—181no—
267C4⋊C4—362no—
268C4⋊C4—362no—
269C42—92no—
270C42—92no—
271C42—184no—
272C22×C3—21no—
273C22×C3—21no—
274C22×C3—21no—
275C22×C3—21no—
276C22×C3—21no—
277C22×C3—21no—
278C22×C3—21no—
279C22×C3#87812yes—
280C22×C3D3×C22⋊C412yes—
281C22×C3D3×SD1612yes—
282C22×C3#91412yes—
283C22×C3D3×Q1612yes—
284C22×C3#91812yes—
285C22×C3#93912yes—
286C3×C4—28no—
287C3×C4—28no—
288C3×C4—21no—
289C3×C4—21no—
290C3×C4—21no—
291C3×C4—21no—
292C3×C4—242no—
293C3×C4#87712yes—
294C3×C4#87812yes—
295C3×C4C2×Dic3⋊C412yes—
296C3×C4#93912yes—
297Dic3—38no—
298Dic3—64no—
299Dic3—64no—
300Dic3—82no—
301Dic3—122no—
302Dic3—124no—
303Dic3—124no—
304C32#180311yescharacteristic, complemented, Sylow
305C23#381111yescharacteristic
306Q8—22no—
307Q8—22no—
308Q8—22no—
309Q8#372414yescomplemented
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—92no—
314C2×C4—92no—
315C2×C4—92no—
316C2×C4—92no—
317C2×C4—122no—
318C2×C4—122no—
319C2×C4—122no—
320C2×C4—181no—
321C2×C4—181no—
322C2×C4—182no—
323C2×C4—361no—
324C2×C4—361no—
325C2×C4#380511yescharacteristic
326C2×C4#380511yescharacteristic
327C2×C4C2×#62411yescharacteristic
328C2×C4C2×#62511yescharacteristic
329C2×C4C2×#62711yescharacteristic
330C2×C4#381111yescharacteristic
331C8—122no—
332C2×C3—21no—
333C2×C3—21no—
334C2×C3—21no—
335C2×C3—21no—
336C2×C3—21no—
337C2×C3—21no—
338C2×C3—21no—
339C2×C3#479112yes—
340C2×C3#479312yes—
341C2×C3D3×#10312yes—
342C2×C3#480312yes—
343C2×C3#494212yes—
344C2×C3#516312yes—
345C2×C3#518212yes—
346C22#6394011yescharacteristic
347C22#6394111yescharacteristic
348C22#6394411yescharacteristic
349C22#6394511yescharacteristic
350C22#6397411yescharacteristic
351C22#6398011yescharacteristic
352C22#6398211yescharacteristic
353C4—24no—
354C4—94no—
355C4—182no—
356C4—242no—
357C4—362no—
358C4#6395711yescharacteristic
359C4C2×#372411yescharacteristic
360C4#6398011yescharacteristic
361C4#6398211yescharacteristic
362C3—21no—
363C3#7022112yescomplemented
364C2#1059155211yescharacteristic
365C2#1059155411yescharacteristic
366C2#1059162211yescharacteristic
367C2#1059163011yescharacteristic
368C2#1059163111yescharacteristic
369C2#1059163311yescharacteristic
370C2#1059172011yescharacteristic
subgroupG/H
centerC23#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×Q8C22
socle, prime radicalC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC22×Q8D32
hypocenterC32#1803
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
9. Q8×C3⋊Dic3C4semidirect
81. C32×Q8C4⋊C4semidirect
171. C3⋊Dic3#103semidirect
195. C3×Q8Dic3⋊C4semidirect
304. C32#1803semidirect
309. Q8#3724semidirect
363. C3#70221semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C3⋊Dic32
C2×C3×#8352
#105913592
C2×#635722
#105891642
#702213