Finite Group Databasebeta

← #11783260

Subgroups — #11783260

Order 1152.

1013 conjugacy classes of subgroups.

The subgroup lattice has 397 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64101C211yesmaximal, characteristic
2C2×#63849C211yesmaximal, characteristic
3C22×#3710C211yesmaximal, characteristic
4C3×#4529C212yesmaximal, complemented
5#10589164C212yesmaximal, complemented
6#68866—32nomaximal
7C22×C4×C3⋊D3C2211yescharacteristic
8C2×C32×C4⋊C4C2211yescharacteristic
9C2×#3752—21no—
10C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
11C2×C4×C3⋊Dic3—21no—
12#64101—22no—
13#64101C414yescomplemented
14C2×C3×C4⋊Dic3C2212yes—
15C22×C3×C3⋊C8C2212yes—
16C2×#3722—21no—
17C2×Dic32—21no—
18#63849—22no—
19#63849C414yescomplemented
20C2×#3710—22no—
21C2×#3710—22no—
22C2×#3710C414yescomplemented
23C22×D3×C8—32no—
24C2×#892—32no—
25C2×#892—32no—
26C2×#892—61no—
27C3×#340—32no—
28#4551—32no—
29#4529—32no—
30#4529D312yescomplemented
31C23×C3⋊D3D411yescharacteristic
32C22×C32×C4—21no—
33C22×C32×C4C2311yescharacteristic
34C22×C3⋊Dic3—21no—
35C22×C3⋊Dic3D411yescharacteristic
36C2×C4×C3⋊D3C2×C412yes—
37C2×C4×C3⋊D3C2×C412yes—
38C2×C4×C3⋊D3C2×C412yes—
39C2×C4×C3⋊D3D412yes—
40C2×C4×C3⋊D3D412yes—
41C2×C4×C3⋊D3Q812yes—
42C22×C3×Dic3—22no—
43C32×C4⋊C4—21no—
44C32×C4⋊C4C2×C412yes—
45#3752—24no—
46C4⋊(C3⋊Dic3)—21no—
47C4⋊(C3⋊Dic3)C2×C412yes—
48C4×C3⋊Dic3—24no—
49C3×C4⋊Dic3—22no—
50C3×C4⋊Dic3C2×C414yes—
51C2×C3×C3⋊C8—22no—
52C2×C3×C3⋊C8—22no—
53C2×C3×C3⋊C8C2×C414yes—
54#3722—24no—
55Dic32—24no—
56#3710—28no—
57#1735—91noSylow
58C22×C4×D3—32no—
59C22×C4×D3—61no—
60C22×C3×C8—32no—
61C2×C3×C4⋊C4—21no—
62C2×C3×C4⋊C4—32no—
63C2×C3×C4⋊C4C2×D312yes—
64C2×(C2×D3)⋊C4—62no—
65C2×(C2×D3)⋊C4—62no—
66C2×(C2×D3)⋊C4—62no—
67C2×C4⋊Dic3—32no—
68C2×C4⋊Dic3—61no—
69C2×C4⋊Dic3C2×D312yes—
70C2×C4×Dic3—62no—
71C2×C4×Dic3—62no—
72C2×C4×Dic3—62no—
73C22×C3⋊C8C2×D312yes—
74C2×D3×C8—38no—
75C2×D3×C8—64no—
76C2×D3×C8—64no—
77#892—38no—
78#892—38no—
79#892—64no—
80#892—64no—
81#892—64no—
82#892—64no—
83C23×C32C2×D411yescharacteristic
84C22×C3⋊D3—22no—
85C22×C3⋊D3—22no—
86C22×C3⋊D3C22⋊C412yes—
87C22×C3⋊D3C22⋊C412yes—
88C22×C3⋊D3C4⋊C412yes—
89C2×C32×C4—22no—
90C2×C32×C4—42no—
91C2×C32×C4C22×C411yescharacteristic
92C2×C32×C4C22×C411yescharacteristic
93C2×C32×C4C22×C411yescharacteristic
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4C2×Q811yescharacteristic
97C2×C3⋊Dic3—22no—
98C2×C3⋊Dic3—42no—
99C2×C3⋊Dic3C22⋊C412yes—
100C2×C3⋊Dic3C22⋊C412yes—
101C2×C3⋊Dic3C4⋊C412yes—
102C4×C3⋊D3C4214yes—
103C4×C3⋊D3C22⋊C414yes—
104C4×C3⋊D3C4⋊C414yes—
105C4×C3⋊D3C4⋊C414yes—
106C2×C3×Dic3—24no—
107C2×C3×Dic3—42no—
108C2×C3×Dic3—42no—
109C3×C3⋊C8—24no—
110C23×C8—91no—
111C2×#117—91no—
112C2×#117—91no—
113#340—32no—
114#340—92no—
115C23×D3—32no—
116C23×D3—61no—
117C22×C3×C4—22no—
118C22×C3×C4—22no—
119C22×C3×C4—21no—
120C22×C3×C4—62no—
121C22×C3×C4C22×D312yes—
122C22×Dic3—22no—
123C22×Dic3—32no—
124C22×Dic3—61no—
125C22×Dic3—62no—
126C22×Dic3—62no—
127C2×C4×D3—34no—
128C2×C4×D3—34no—
129C2×C4×D3—34no—
130C2×C4×D3—34no—
131C2×C4×D3—34no—
132C2×C4×D3—34no—
133C2×C4×D3—62no—
134C2×C4×D3—62no—
135C2×C4×D3—62no—
136C2×C4×D3—62no—
137C2×C4×D3—62no—
138C2×C4×D3—62no—
139C2×C3×C8—34no—
140C2×C3×C8—62no—
141C2×C3×C8—62no—
142C3×C4⋊C4—22no—
143C3×C4⋊C4—22no—
144C3×C4⋊C4—22no—
145C3×C4⋊C4—34no—
146C3×C4⋊C4—62no—
147C3×C4⋊C4C4×D314yes—
148(C2×D3)⋊C4—68no—
149(C2×D3)⋊C4—68no—
150(C2×D3)⋊C4—68no—
151C4⋊Dic3—22no—
152C4⋊Dic3—34no—
153C4⋊Dic3—62no—
154C4⋊Dic3—62no—
155C4⋊Dic3—62no—
156C4⋊Dic3C4×D314yes—
157C4×Dic3—68no—
158C4×Dic3—68no—
159C4×Dic3—68no—
160C2×C3⋊C8—22no—
161C2×C3⋊C8—22no—
162C2×C3⋊C8C4×D314yes—
163D3×C8—616no—
164C22×C32C2×C22⋊C411yescharacteristic
165C22×C32C2×C22⋊C411yescharacteristic
166C22×C32C2×C4⋊C411yescharacteristic
167C22×C32#13512yes—
168C22×C32#13512yes—
169C2×C3⋊D3—22no—
170C2×C3⋊D3—24no—
171C2×C3⋊D3—22no—
172C2×C3⋊D3—24no—
173C2×C3⋊D3#9514yes—
174C32×C4—42no—
175C32×C4C2×C4211yescharacteristic
176C32×C4C2×C22⋊C411yescharacteristic
177C32×C4C2×C4⋊C411yescharacteristic
178C32×C4C2×C4⋊C411yescharacteristic
179C3⋊Dic3—42no—
180C3⋊Dic3#9514yes—
181C3×Dic3—44no—
182C23×C4—91no—
183C22×C8—32no—
184C22×C8—94no—
185C22×C8—182no—
186C22×C8—182no—
187#117—94no—
188#117—94no—
189#117—182no—
190#117—182no—
191C2×C4⋊C4—32no—
192C2×C4⋊C4—91no—
193C2×C4⋊C4D3211yescharacteristic
194C2×C22⋊C4—181no—
195C2×C22⋊C4—181no—
196C2×C42—181no—
197C2×C42—181no—
198C23×C3—21no—
199C23×C3D3×D412yes—
200C22×D3—34no—
201C22×D3—34no—
202C22×D3—34no—
203C22×D3—62no—
204C22×D3—62no—
205C22×D3—62no—
206C22×D3—62no—
207C22×D3—62no—
208C22×D3—62no—
209C22×D3—62no—
210C22×D3—122no—
211C22×D3—122no—
212C2×C3×C4—24no—
213C2×C3×C4—24no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4—21no—
220C2×C3×C4—44no—
221C2×C3×C4—42no—
222C2×C3×C4—42no—
223C2×C3×C4—64no—
224C2×C3×C4—122no—
225C2×C3×C4—122no—
226C2×C3×C4C2×C4×D312yes—
227C2×C3×C4C2×C4×D312yes—
228C2×C3×C4C2×C4×D312yes—
229C2×C3×C4D3×D412yes—
230C2×C3×C4D3×D412yes—
231C2×C3×C4D3×Q812yes—
232C2×Dic3—24no—
233C2×Dic3—34no—
234C2×Dic3—34no—
235C2×Dic3—34no—
236C2×Dic3—42no—
237C2×Dic3—42no—
238C2×Dic3—62no—
239C2×Dic3—62no—
240C2×Dic3—62no—
241C2×Dic3—64no—
242C2×Dic3—64no—
243C2×Dic3—124no—
244C2×Dic3—122no—
245C2×Dic3—122no—
246C4×D3—38no—
247C4×D3—38no—
248C4×D3—38no—
249C4×D3—38no—
250C4×D3—64no—
251C4×D3—64no—
252C4×D3—64no—
253C4×D3—64no—
254C3×C8—64no—
255C3⋊C8—24no—
256C2×C32C2×#9511yescharacteristic
257C2×C32#41611yescharacteristic
258C2×C32#41612yes—
259C2×C32#41611yescharacteristic
260C2×C32#42712yes—
261C3⋊D3—24no—
262C24—91no—
263C22×C4—21no—
264C22×C4—62no—
265C22×C4—91no—
266C22×C4—92no—
267C22×C4—92no—
268C22×C4—92no—
269C22×C4—92no—
270C22×C4—92no—
271C22×C4—92no—
272C22×C4—181no—
273C22×C4C2×D3211yescharacteristic
274C2×C8—34no—
275C2×C8—62no—
276C2×C8—62no—
277C2×C8—188no—
278C4⋊C4—21no—
279C4⋊C4—34no—
280C4⋊C4—62no—
281C4⋊C4—92no—
282C4⋊C4—181no—
283C4⋊C4#62412yes—
284C22⋊C4—184no—
285C22⋊C4—184no—
286C42—184no—
287C42—184no—
288C22×C3—21no—
289C22×C3—21no—
290C22×C3—22no—
291C22×C3—22no—
292C22×C3—21no—
293C22×C3D3×C22⋊C412yes—
294C22×C3D3×C22⋊C412yes—
295C22×C3D3×C4⋊C412yes—
296C22×C3#91212yes—
297C22×C3#91612yes—
298C22×C3#91612yes—
299C22×C3#91912yes—
300C2×D3—38no—
301C2×D3—64no—
302C2×D3—64no—
303C2×D3—64no—
304C2×D3—64no—
305C2×D3—64no—
306C2×D3—64no—
307C2×D3—64no—
308C2×D3—122no—
309C2×D3—124no—
310C2×D3—124no—
311C2×D3—122no—
312C3×C4—21no—
313C3×C4—21no—
314C3×C4—21no—
315C3×C4—21no—
316C3×C4—44no—
317C3×C4—44no—
318C3×C4—124no—
319C3×C4C42×D312yes—
320C3×C4D3×C22⋊C412yes—
321C3×C4D3×C4⋊C412yes—
322C3×C4D3×C4⋊C412yes—
323Dic3—38no—
324Dic3—44no—
325Dic3—64no—
326Dic3—124no—
327Dic3—124no—
328C32#173511yescharacteristic, complemented, Sylow
329C23—92no—
330C23—92no—
331C23—92no—
332C23—182no—
333C23—182no—
334C23#381111yescharacteristic
335C2×C4—22no—
336C2×C4—42no—
337C2×C4—64no—
338C2×C4—92no—
339C2×C4—92no—
340C2×C4—92no—
341C2×C4—94no—
342C2×C4—94no—
343C2×C4—94no—
344C2×C4—94no—
345C2×C4—122no—
346C2×C4—122no—
347C2×C4—182no—
348C2×C4—362no—
349C2×C4#379711yescharacteristic
350C2×C4C4×D3211yescharacteristic
351C2×C4C4×D3211yescharacteristic
352C2×C4#380211yescharacteristic
353C2×C4C2×#62411yescharacteristic
354C2×C4#381111yescharacteristic
355C8—64no—
356C2×C3—21no—
357C2×C3—22no—
358C2×C3—21no—
359C2×C3—22no—
360C2×C3—21no—
361C2×C3D3×#9512yes—
362C2×C3#477212yes—
363C2×C3#477212yes—
364C2×C3#480412yes—
365C2×C3#480412yes—
366C2×C3#486012yes—
367C2×C3#488012yes—
368D3—68no—
369D3—124no—
370C22—94no—
371C22—182no—
372C22—184no—
373C22—184no—
374C22—182no—
375C22#6388311yescharacteristic
376C22#6392111yescharacteristic
377C22#6393612yes—
378C22#6395012yes—
379C22#6397411yescharacteristic
380C4—42no—
381C4—94no—
382C4—124no—
383C4—362no—
384C4C4×#62411yescharacteristic
385C4#6388311yescharacteristic
386C4#6390011yescharacteristic
387C4#6392111yescharacteristic
388C3—21no—
389C3#6886612yescomplemented
390C2—184no—
391C2#1059057412yes—
392C2#1059061112yes—
393C2#1059137011yescharacteristic
394C2#1059142411yescharacteristic
395C2#1059156011yescharacteristic
subgroupG/H
centerC23#3811
commutatorC32×C4C2×C42
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1735
LCSG ▷ 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
4. C3×#4529C2semidirect
5. #10589164C2semidirect
13. #64101C4semidirect
19. #63849C4semidirect
22. C2×#3710C4semidirect
30. #4529D3semidirect
328. C32#1735semidirect
389. C3#68866semidirect

Maximal subgroups

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

subgroupindex
C2×#641012
C2×#638492
C22×#37102
C3×#45292
#105891642
#688663