Finite Group Databasebeta

← #11786463

Subgroups — #11786463

Order 1152.

837 conjugacy classes of subgroups.

The subgroup lattice has 387 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63900C211yesmaximal, characteristic
2#10592686C211yesmaximal, characteristic
3C2×C3×#808C212yesmaximal, complemented
4C2×#63557C211yesmaximal, characteristic
5#10589164C212yesmaximal, complemented
6#70579—32nomaximal
7C22×C4×C3⋊D3C2211yescharacteristic
8C22×#624—21no—
9C2×C32×C4⋊C4C2211yescharacteristic
10C2×#3752—21no—
11C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
12C2×C3×C4⋊Dic3C2212yes—
13C22×C3×C3⋊C8C2212yes—
14C2×#3724—21no—
15#63900—24no—
16#63658—21no—
17C3×#808—24no—
18#63557C414yescomplemented
19C2×D3×C4⋊C4—32no—
20C2×C3×#106—32no—
21C2×(C2×D3)⋊C8—32no—
22#4987—32no—
23#4987—61no—
24C2×#808D312yescomplemented
25#4551—32no—
26#4529—32no—
27C23×C3⋊D3D411yescharacteristic
28C22×C32×C4—21no—
29C22×C32×C4C2311yescharacteristic
30C22×C3⋊Dic3—21no—
31C22×C3⋊Dic3D411yescharacteristic
32C2×C4×C3⋊D3—22no—
33C2×C4×C3⋊D3—22no—
34C2×C4×C3⋊D3C2×C412yes—
35C2×C4×C3⋊D3Q812yes—
36C22×C3×Dic3—22no—
37C2×#624—24no—
38C2×#624—42no—
39C2×#624—42no—
40C32×C4⋊C4—22no—
41#3752—42no—
42C4⋊(C3⋊Dic3)—22no—
43C3×C4⋊Dic3—22no—
44C3×C4⋊Dic3D414yes—
45C2×C3×C3⋊C8—22no—
46C2×C3×C3⋊C8—22no—
47C2×C3×C3⋊C8C2×C414yescomplemented
48#3724—24no—
49#1853—91noSylow
50C22×C4×D3—32no—
51C22×C4×D3—61no—
52C22×C4×D3—62no—
53C22×C3×C8—32no—
54C2×C3×C4⋊C4—21no—
55C2×C3×C4⋊C4—32no—
56C2×C3×C4⋊C4C2×D312yes—
57C2×(C2×D3)⋊C4—62no—
58C2×(C2×D3)⋊C4—62no—
59C2×C4⋊Dic3—32no—
60C2×C4⋊Dic3—61no—
61C2×C4⋊Dic3C2×D312yes—
62C2×Dic3⋊C4—62no—
63C22×C3⋊C8C2×D312yes—
64D3×C4⋊C4—64no—
65D3×C4⋊C4—64no—
66C3×#106—64no—
67C3⋊#95—62no—
68C3⋊#95—62no—
69(C2×D3)⋊C8—38no—
70#808—24no—
71C23×C32C2×D411yescharacteristic
72C22×C3⋊D3—21no—
73C22×C3⋊D3—21no—
74C22×C3⋊D3—21no—
75C22×C3⋊D3—21no—
76C22×C3⋊D3C4⋊C412yes—
77C22×C3⋊D3SD1612yes—
78C22×C3⋊D3SD1612yes—
79C2×C32×C4—41no—
80C2×C32×C4—41no—
81C2×C32×C4—41no—
82C2×C32×C4C22×C411yescharacteristic
83C2×C32×C4C2×D412yes—
84C2×C32×C4C2×Q811yescharacteristic
85C2×C32×C4#4112yes—
86C2×C3⋊Dic3—21no—
87C2×C3⋊Dic3—21no—
88C2×C3⋊Dic3—41no—
89C2×C3⋊Dic3—41no—
90C2×C3⋊Dic3—41no—
91C2×C3⋊Dic3C4⋊C412yes—
92C4×C3⋊D3—24no—
93C4×C3⋊D3—24no—
94C2×C3×Dic3—24no—
95C2×C3×Dic3—42no—
96C2×C3×Dic3—42no—
97#624—48no—
98C3×C3⋊C8—24no—
99C22×C4⋊C4—91no—
100C2×#106—32no—
101C2×C22⋊C8—91no—
102#380—91no—
103#340—92no—
104C23×D3—32no—
105C23×D3—61no—
106C22×C3×C4—22no—
107C22×C3×C4—22no—
108C22×C3×C4—21no—
109C22×C3×C4—62no—
110C22×C3×C4C22×D312yes—
111C22×Dic3—22no—
112C22×Dic3—32no—
113C22×Dic3—61no—
114C22×Dic3—62no—
115C22×Dic3—62no—
116C2×C4×D3—34no—
117C2×C4×D3—34no—
118C2×C4×D3—62no—
119C2×C4×D3—62no—
120C2×C4×D3—62no—
121C2×C4×D3—62no—
122C2×C4×D3—62no—
123C2×C4×D3—62no—
124C2×C4×D3—68no—
125C2×C4×D3—122no—
126C2×C4×D3—122no—
127C2×C4×D3—124no—
128C2×C4×D3—124no—
129C2×C3×C8—34no—
130C2×C3×C8—62no—
131C2×C3×C8—62no—
132C3×C4⋊C4—22no—
133C3×C4⋊C4—22no—
134C3×C4⋊C4—34no—
135C3×C4⋊C4—42no—
136C3×C4⋊C4—62no—
137(C2×D3)⋊C4—124no—
138(C2×D3)⋊C4—124no—
139C4⋊Dic3—22no—
140C4⋊Dic3—62no—
141C4⋊Dic3—62no—
142C4⋊Dic3—122no—
143C4⋊Dic3#6714yes—
144Dic3⋊C4—68no—
145C2×C3⋊C8—22no—
146C2×C3⋊C8—22no—
147C2×C3⋊C8C4×D314yescomplemented
148C22×C32C2×C4⋊C411yescharacteristic
149C22×C32#12011yescharacteristic
150C22×C32#12311yescharacteristic
151C22×C32C2×SD1611yescharacteristic
152C22×C32C2×SD1611yescharacteristic
153C22×C32AGL(1,ℤ/8)11yescharacteristic
154C22×C32#13711yescharacteristic
155C2×C3⋊D3—22no—
156C2×C3⋊D3—22no—
157C2×C3⋊D3—22no—
158C2×C3⋊D3—22no—
159C2×C3⋊D3—22no—
160C2×C3⋊D3—22no—
161C2×C3⋊D3#10614yescomplemented
162C32×C4—81no—
163C32×C4C4×D412yes—
164C32×C4C22⋊Q812yes—
165C3⋊Dic3—22no—
166C3⋊Dic3—81no—
167C3×Dic3—44no—
168C23×C4—91no—
169C23×C4—181no—
170C22×C8—32no—
171C2×C4⋊C4—32no—
172C2×C4⋊C4—91no—
173C2×C4⋊C4—184no—
174C2×C4⋊C4—181no—
175C2×C4⋊C4D3211yescharacteristic
176C2×C22⋊C4—181no—
177#106—64no—
178C22⋊C8—94no—
179#95—181no—
180C23×C3—21no—
181C23×C3D3×D412yes—
182C22×D3—34no—
183C22×D3—34no—
184C22×D3—34no—
185C22×D3—62no—
186C22×D3—62no—
187C22×D3—62no—
188C22×D3—62no—
189C22×D3—62no—
190C22×D3—62no—
191C22×D3—62no—
192C22×D3—121no—
193C22×D3—121no—
194C22×D3—121no—
195C22×D3—121no—
196C2×C3×C4—21no—
197C2×C3×C4—22no—
198C2×C3×C4—21no—
199C2×C3×C4—22no—
200C2×C3×C4—42no—
201C2×C3×C4—42no—
202C2×C3×C4—42no—
203C2×C3×C4—42no—
204C2×C3×C4—42no—
205C2×C3×C4—42no—
206C2×C3×C4—64no—
207C2×C3×C4—122no—
208C2×C3×C4—122no—
209C2×C3×C4C2×C4×D312yes—
210C2×C3×C4#23512yes—
211C2×C3×C4D3×D412yes—
212C2×C3×C4D3×Q812yes—
213C2×C3×C4#23912yes—
214C2×C3×C4C2×#6712yes—
215C2×Dic3—24no—
216C2×Dic3—34no—
217C2×Dic3—42no—
218C2×Dic3—42no—
219C2×Dic3—62no—
220C2×Dic3—62no—
221C2×Dic3—62no—
222C2×Dic3—121no—
223C2×Dic3—121no—
224C2×Dic3—122no—
225C2×Dic3—122no—
226C2×Dic3—122no—
227C2×Dic3—122no—
228C2×Dic3—122no—
229C2×Dic3—122no—
230C4×D3—64no—
231C4×D3—64no—
232C4×D3—64no—
233C4×D3—64no—
234C4×D3—124no—
235C4×D3—124no—
236C4×D3—1216no—
237C3×C8—64no—
238C3⋊C8—24no—
239C2×C32#38511yescharacteristic
240C2×C32C2×#10611yescharacteristic
241C2×C32#42811yescharacteristic
242C2×C32#44811yescharacteristic
243C2×C32#45011yescharacteristic
244C2×C32#48111yescharacteristic
245C2×C32#48311yescharacteristic
246C3⋊D3—24no—
247C24—91no—
248C22×C4—21no—
249C22×C4—62no—
250C22×C4—91no—
251C22×C4—92no—
252C22×C4—92no—
253C22×C4—184no—
254C22×C4—182no—
255C22×C4—182no—
256C22×C4—181no—
257C22×C4—362no—
258C22×C4—362no—
259C22×C4C2×D3211yescharacteristic
260C2×C8—34no—
261C2×C8—62no—
262C2×C8—62no—
263C4⋊C4—22no—
264C4⋊C4—34no—
265C4⋊C4—62no—
266C4⋊C4—184no—
267C4⋊C4—182no—
268C22⋊C4—362no—
269C22×C3—21no—
270C22×C3—21no—
271C22×C3—21no—
272C22×C3—21no—
273C22×C3—21no—
274C22×C3—21no—
275C22×C3—21no—
276C22×C3D3×C4⋊C412yes—
277C22×C3#89412yes—
278C22×C3D3×SD1612yes—
279C22×C3D3×SD1612yes—
280C22×C3#91412yes—
281C22×C3#91512yes—
282C22×C3#93712yes—
283C2×D3—38no—
284C2×D3—64no—
285C2×D3—64no—
286C2×D3—64no—
287C2×D3—64no—
288C2×D3—64no—
289C2×D3—64no—
290C2×D3—64no—
291C2×D3—122no—
292C2×D3—122no—
293C2×D3—122no—
294C2×D3—122no—
295C2×D3—122no—
296C2×D3—122no—
297C3×C4—22no—
298C3×C4—22no—
299C3×C4—82no—
300C3×C4—82no—
301C3×C4—124no—
302C3×C4#89312yes—
303C3×C4#89612yes—
304C3×C4C4×#6712yes—
305C3×C4#94612yes—
306Dic3—44no—
307Dic3—64no—
308Dic3—122no—
309Dic3—242no—
310Dic3—242no—
311C32#185311yescharacteristic, complemented, Sylow
312C23—92no—
313C23—92no—
314C23—92no—
315C23—181no—
316C23—181no—
317C23—181no—
318C23—181no—
319C23#381111yescharacteristic
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—64no—
324C2×C4—92no—
325C2×C4—122no—
326C2×C4—122no—
327C2×C4—181no—
328C2×C4—181no—
329C2×C4—184no—
330C2×C4—184no—
331C2×C4—368no—
332C2×C4—361no—
333C2×C4—361no—
334C2×C4—361no—
335C2×C4#379711yescharacteristic
336C2×C4#379912yes—
337C2×C4C4×D3211yescharacteristic
338C2×C4D3×#6712yes—
339C8—64no—
340C2×C3—21no—
341C2×C3—21no—
342C2×C3—21no—
343C2×C3—21no—
344C2×C3—21no—
345C2×C3—21no—
346C2×C3—21no—
347C2×C3D3×#10612yes—
348C2×C3#486112yes—
349C2×C3#486212yes—
350C2×C3#486312yes—
351C2×C3#498912yes—
352C2×C3#516912yes—
353C2×C3#517012yes—
354D3—68no—
355D3—124no—
356C22—94no—
357C22—182no—
358C22—182no—
359C22—182no—
360C22—182no—
361C22—182no—
362C22—182no—
363C22#6388311yescharacteristic
364C22#6389711yescharacteristic
365C22#6393011yescharacteristic
366C22#6393111yescharacteristic
367C22#6394011yescharacteristic
368C22#6394111yescharacteristic
369C22#6398311yescharacteristic
370C4—81no—
371C4—124no—
372C4—182no—
373C4—721no—
374C4#6388812yes—
375C4#6390412yes—
376C3—21no—
377C3#7057912yescomplemented
378C2—184no—
379C2#1059044311yescharacteristic
380C2#1059044511yescharacteristic
381C2#1059057511yescharacteristic
382C2#1059058411yescharacteristic
383C2#1059137411yescharacteristic
384C2#1059151811yescharacteristic
385C2#1059165211yescharacteristic
subgroupG/H
centerC23#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1853
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C3×#808C2semidirect
5. #10589164C2semidirect
18. #63557C4semidirect
24. C2×#808D3semidirect
47. C2×C3×C3⋊C8C2×C4semidirect
147. C2×C3⋊C8C4×D3semidirect
161. C2×C3⋊D3#106semidirect
311. C32#1853semidirect
377. C3#70579semidirect

Maximal subgroups

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

subgroupindex
C2×#639002
#105926862
C2×C3×#8082
C2×#635572
#105891642
#705793