Finite Group Databasebeta

← C32×#1864 #11768913

Subgroups — C32×#1864 #11768913

Order 1152.

1086 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×C32×C4×D4C211yesmaximal, characteristic
2C2×C32×#106C211yesmaximal, characteristic, complemented
3C2×C32×#102C211yesmaximal, characteristic
4C2×C32×#102C211yesmaximal, characteristic
5C32×#389C211yesmaximal, characteristic, complemented
6C32×#340C211yesmaximal, characteristic, complemented
7C32×#336C211yesmaximal, characteristic, complemented
8C3×#1864C314yesmaximal, direct product factor
9C22×C32×D4C2211yescharacteristic
10C23×C32×C4—21no—
11C22×C32×C8C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C32×C4×D4—22no—
14C32×C4×D4—22no—
15C2×C32×C4⋊C4—21no—
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×C32×C4⋊C4C2211yescharacteristic
18C2×C32×C4⋊C4C2211yescharacteristic
19C2×C32×C22⋊C4—21no—
20C2×C32×C42C2211yescharacteristic
21C32×#106—22no—
22C32×#102—22no—
23C32×#102C414yescomplemented
24C32×#95—21no—
25C2×C3×C4×D4C2×C314yes—
26C2×C3×#106C2×C314yescomplemented
27C2×C3×#102C2×C314yes—
28C2×C3×#102C2×C314yes—
29C3×#389C2×C314yescomplemented
30C3×#340C2×C314yescomplemented
31C3×#336C2×C314yescomplemented
32C24×C32—21no—
33C2×C32×D4—21no—
34C2×C32×D4—21no—
35C2×C32×D4—21no—
36C2×C32×D4C2×C412yes—
37C2×C32×D4D412yes—
38C2×C32×D4Q812yes—
39C22×C32×C4—24no—
40C22×C32×C4—21no—
41C22×C32×C4—21no—
42C22×C32×C4—21no—
43C22×C32×C4—42no—
44C22×C32×C4—42no—
45C22×C32×C4D411yescharacteristic
46C22×C32×C4D411yescharacteristic
47C22×C32×C4C2311yescharacteristic
48C2×C32×C8—21no—
49C2×C32×C8—21no—
50C2×C32×C8—21no—
51C2×C32×C8—21no—
52C2×C32×C8—21no—
53C2×C32×C8C2×C412yescomplemented
54C32×C4⋊C4—21no—
55C32×C4⋊C4—21no—
56C32×C4⋊C4—21no—
57C32×C4⋊C4—21no—
58C32×C4⋊C4—42no—
59C32×C4⋊C4C2×C412yescomplemented
60C32×C4⋊C4D412yes—
61C32×C22⋊C4—24no—
62C32×C42—21no—
63C32×C42—21no—
64#1864C3211yescharacteristic, direct product factor, Sylow
65C22×C3×D4C22×C314yes—
66C23×C3×C4—24no—
67C22×C3×C8C22×C314yes—
68C22×C3×C8C22×C314yes—
69C3×C4×D4—28no—
70C3×C4×D4—28no—
71C2×C3×C4⋊C4—24no—
72C2×C3×C4⋊C4C22×C314yes—
73C2×C3×C4⋊C4C22×C314yes—
74C2×C3×C4⋊C4C22×C314yes—
75C2×C3×C22⋊C4—24no—
76C2×C3×C42C22×C314yes—
77C3×#106—28no—
78C3×#102—28no—
79C3×#102C3×C4116yescomplemented
80C3×#95—24no—
81C23×C32—22no—
82C23×C32—22no—
83C23×C32—22no—
84C23×C32—41no—
85C23×C32—41no—
86C23×C32—41no—
87C23×C32—41no—
88C23×C32C2×D411yescharacteristic
89C32×D4—22no—
90C32×D4—22no—
91C32×D4—22no—
92C32×D4C4⋊C414yescomplemented
93C2×C32×C4—21no—
94C2×C32×C4—21no—
95C2×C32×C4—22no—
96C2×C32×C4—21no—
97C2×C32×C4—22no—
98C2×C32×C4—21no—
99C2×C32×C4—21no—
100C2×C32×C4—48no—
101C2×C32×C4—41no—
102C2×C32×C4—41no—
103C2×C32×C4—41no—
104C2×C32×C4—41no—
105C2×C32×C4—41no—
106C2×C32×C4—41no—
107C2×C32×C4—41no—
108C2×C32×C4SD1612yes—
109C2×C32×C4C22×C411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2×Q811yescharacteristic
113C2×C32×C4#4111yescharacteristic
114C2×C32×C4#4111yescharacteristic
115C32×C8—22no—
116C32×C8—41no—
117C2×C4×D4C2×C3211yescharacteristic
118C2×#106C2×C3211yescharacteristic, complemented
119C2×#102C2×C3211yescharacteristic
120C2×#102C2×C3211yescharacteristic
121#389C2×C3211yescharacteristic, complemented
122#340C2×C3211yescharacteristic, complemented
123#336C2×C3211yescharacteristic, complemented
124C24×C3—24no—
125C2×C3×D4—24no—
126C2×C3×D4—24no—
127C2×C3×D4—24no—
128C2×C3×D4C2×C3×C418yes—
129C2×C3×D4C3×D418yes—
130C2×C3×D4C3×Q818yes—
131C22×C3×C4—216no—
132C22×C3×C4—24no—
133C22×C3×C4—24no—
134C22×C3×C4—24no—
135C22×C3×C4—48no—
136C22×C3×C4—48no—
137C22×C3×C4C3×D414yes—
138C22×C3×C4C3×D414yes—
139C22×C3×C4C23×C314yes—
140C2×C3×C8—24no—
141C2×C3×C8—24no—
142C2×C3×C8—24no—
143C2×C3×C8—24no—
144C2×C3×C8—24no—
145C2×C3×C8C2×C3×C418yescomplemented
146C3×C4⋊C4—24no—
147C3×C4⋊C4—24no—
148C3×C4⋊C4—24no—
149C3×C4⋊C4—24no—
150C3×C4⋊C4—48no—
151C3×C4⋊C4C2×C3×C418yescomplemented
152C3×C4⋊C4C3×D418yes—
153C3×C22⋊C4—216no—
154C3×C42—24no—
155C3×C42—24no—
156C22×C32—24no—
157C22×C32—42no—
158C22×C32—42no—
159C22×C32—42no—
160C22×C32—42no—
161C22×C32—42no—
162C22×C32—42no—
163C22×C32C4×D411yescharacteristic
164C22×C32#12011yescharacteristic
165C22×C32C22⋊Q811yescharacteristic
166C22×C32C2×SD1611yescharacteristic
167C22×C32#13511yescharacteristic
168C22×C32AGL(1,ℤ/8)11yescharacteristic
169C22×C32AGL(1,ℤ/8)11yescharacteristic
170C32×C4—22no—
171C32×C4—42no—
172C32×C4—41no—
173C32×C4—42no—
174C32×C4—81no—
175C32×C4C2×C4⋊C411yescharacteristic
176C32×C4C4×D411yescharacteristic
177C32×C4C22⋊Q811yescharacteristic
178C32×C4#12311yescharacteristic
179C22×D4C22×C3211yescharacteristic
180C23×C4—21no—
181C22×C8C22×C3211yescharacteristic
182C22×C8C22×C3211yescharacteristic
183C4×D4—22no—
184C4×D4—22no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4C22×C3211yescharacteristic
187C2×C4⋊C4C22×C3211yescharacteristic
188C2×C4⋊C4C22×C3211yescharacteristic
189C2×C22⋊C4—21no—
190C2×C42C22×C3211yescharacteristic
191#106—22no—
192#102—22no—
193#102C32×C414yescomplemented
194#95—21no—
195C23×C3—28no—
196C23×C3—28no—
197C23×C3—28no—
198C23×C3—44no—
199C23×C3—44no—
200C23×C3—44no—
201C23×C3—44no—
202C23×C3C2×C3×D414yes—
203C3×D4—28no—
204C3×D4—28no—
205C3×D4—28no—
206C3×D4C3×C4⋊C4116yescomplemented
207C2×C3×C4—24no—
208C2×C3×C4—24no—
209C2×C3×C4—28no—
210C2×C3×C4—24no—
211C2×C3×C4—28no—
212C2×C3×C4—24no—
213C2×C3×C4—24no—
214C2×C3×C4—432no—
215C2×C3×C4—44no—
216C2×C3×C4—44no—
217C2×C3×C4—44no—
218C2×C3×C4—44no—
219C2×C3×C4—44no—
220C2×C3×C4—44no—
221C2×C3×C4—44no—
222C2×C3×C4C3×SD1618yes—
223C2×C3×C4C22×C3×C414yes—
224C2×C3×C4C2×C3×D414yes—
225C2×C3×C4C2×C3×D414yes—
226C2×C3×C4C2×C3×Q814yes—
227C2×C3×C4C3×#4114yes—
228C2×C3×C4C3×#4114yes—
229C3×C8—28no—
230C3×C8—44no—
231C2×C32—44no—
232C2×C32#38511yescharacteristic
233C2×C32C4×SD1611yescharacteristic
234C2×C32#44211yescharacteristic
235C2×C32#44911yescharacteristic
236C2×C32#45011yescharacteristic
237C2×C32#47611yescharacteristic
238C2×C32#47811yescharacteristic
239C24—21no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—21no—
243C2×D4C2×C32×C412yes—
244C2×D4C32×D412yes—
245C2×D4C32×Q812yes—
246C22×C4—24no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—42no—
251C22×C4—42no—
252C22×C4C32×D411yescharacteristic
253C22×C4C32×D411yescharacteristic
254C22×C4C23×C3211yescharacteristic
255C2×C8—21no—
256C2×C8—21no—
257C2×C8—21no—
258C2×C8—21no—
259C2×C8—21no—
260C2×C8C2×C32×C412yescomplemented
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—42no—
266C4⋊C4C2×C32×C412yescomplemented
267C4⋊C4C32×D412yes—
268C22⋊C4—24no—
269C42—21no—
270C42—21no—
271C22×C3—216no—
272C22×C3—48no—
273C22×C3—48no—
274C22×C3—48no—
275C22×C3—48no—
276C22×C3—48no—
277C22×C3—48no—
278C22×C3C3×C4×D414yes—
279C22×C3C3×#12014yes—
280C22×C3C3×C22⋊Q814yes—
281C22×C3C2×C3×SD1614yes—
282C22×C3C3×#13514yes—
283C22×C3C3×AGL(1,ℤ/8)14yes—
284C22×C3C3×AGL(1,ℤ/8)14yes—
285C3×C4—28no—
286C3×C4—48no—
287C3×C4—44no—
288C3×C4—48no—
289C3×C4—84no—
290C3×C4C2×C3×C4⋊C414yes—
291C3×C4C3×C4×D414yes—
292C3×C4C3×C22⋊Q814yes—
293C3×C4C3×#12314yes—
294C32#186411yescharacteristic, direct product factor, Sylow
295C23—22no—
296C23—22no—
297C23—22no—
298C23—41no—
299C23—41no—
300C23—41no—
301C23—41no—
302C23C2×C32×D411yescharacteristic
303D4—22no—
304D4—22no—
305D4—22no—
306D4C32×C4⋊C414yescomplemented
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—22no—
310C2×C4—21no—
311C2×C4—22no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—48no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4C32×SD1612yes—
323C2×C4C22×C32×C411yescharacteristic
324C2×C4C2×C32×D411yescharacteristic
325C2×C4C2×C32×D411yescharacteristic
326C2×C4C2×C32×Q811yescharacteristic
327C2×C4C32×#4111yescharacteristic
328C2×C4C32×#4111yescharacteristic
329C8—22no—
330C8—41no—
331C2×C3—416no—
332C2×C3C3×#38514yes—
333C2×C3C3×C4×SD1614yes—
334C2×C3C3×#44214yes—
335C2×C3C3×#44914yes—
336C2×C3C3×#45014yes—
337C2×C3C3×#47614yes—
338C2×C3C3×#47814yes—
339C22—24no—
340C22—42no—
341C22—42no—
342C22—42no—
343C22—42no—
344C22—42no—
345C22—42no—
346C22C32×C4×D411yescharacteristic
347C22C32×#12011yescharacteristic
348C22C32×C22⋊Q811yescharacteristic
349C22C2×C32×SD1611yescharacteristic
350C22C32×#13511yescharacteristic
351C22C32×AGL(1,ℤ/8)11yescharacteristic
352C22C32×AGL(1,ℤ/8)11yescharacteristic
353C4—22no—
354C4—42no—
355C4—41no—
356C4—42no—
357C4—81no—
358C4C2×C32×C4⋊C411yescharacteristic
359C4C32×C4×D411yescharacteristic
360C4C32×C22⋊Q811yescharacteristic
361C4C32×#12311yescharacteristic
362C3C3×#186414yesdirect product factor
363C2—44no—
364C2C32×#38511yescharacteristic
365C2C32×C4×SD1611yescharacteristic
366C2C32×#44211yescharacteristic
367C2C32×#44911yescharacteristic
368C2C32×#45011yescharacteristic
369C2C32×#47611yescharacteristic
370C2C32×#47811yescharacteristic
subgroupG/H
center, socleC23×C32C2×D4
commutatorC2×C4C22×C32×C4
Frattini, cosocleC22×C4C23×C32
prime radicalC22×C32×D4C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C32 ◁ C2×C32×C42 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C32×#106C2semidirect
5. C32×#389C2semidirect
6. C32×#340C2semidirect
7. C32×#336C2semidirect
8. C3×#1864C3direct (N × H)
23. C32×#102C4semidirect
26. C2×C3×#106C2×C3semidirect
29. C3×#389C2×C3semidirect
30. C3×#340C2×C3semidirect
31. C3×#336C2×C3semidirect
53. C2×C32×C8C2×C4semidirect
59. C32×C4⋊C4C2×C4semidirect
64. #1864C32direct (N × H)
79. C3×#102C3×C4semidirect
92. C32×D4C4⋊C4semidirect
118. C2×#106C2×C32semidirect
121. #389C2×C32semidirect
122. #340C2×C32semidirect
123. #336C2×C32semidirect
145. C2×C3×C8C2×C3×C4semidirect
151. C3×C4⋊C4C2×C3×C4semidirect
193. #102C32×C4semidirect
206. C3×D4C3×C4⋊C4semidirect
260. C2×C8C2×C32×C4semidirect
266. C4⋊C4C2×C32×C4semidirect
294. C32#1864direct (N × H)
306. D4C32×C4⋊C4semidirect
362. C3C3×#1864direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×C4×D42
C2×C32×#1062
C2×C32×#1022
C32×#3892
C32×#3402
C32×#3362
C3×#18643