Finite Group Databasebeta

← C32×#1908 #11768957

Subgroups — C32×#1908 #11768957

Order 1152.

936 conjugacy classes of subgroups.

The subgroup lattice has 351 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#137C211yesmaximal, characteristic
2C2×C32×#131C211yesmaximal, characteristic
3C32×#417C211yesmaximal, characteristic
4C2×C32×#103C211yesmaximal, characteristic, complemented
5C2×C32×#101C211yesmaximal, characteristic, complemented
6C32×#343C211yesmaximal, characteristic, complemented
7C32×#341C211yesmaximal, characteristic, complemented
8C3×#1908C314yesmaximal, direct product factor
9C2×C32×#41C2211yescharacteristic
10C22×C32×Q8C2211yescharacteristic
11C32×#137—22no—
12C32×#137C414yescomplemented
13C2×C32×Q16—21no—
14C2×C32×SD16—21no—
15C32×#131—22no—
16C32×#131—22no—
17C2×C32×M16—21no—
18C2×C32×M16C2211yescharacteristic
19C2×C32×M16C2211yescharacteristic
20C2×C32×M16C2211yescharacteristic
21C22×C32×C8—21no—
22C22×C32×C8C2211yescharacteristic
23C2×C32×C4⋊C4C2211yescharacteristic
24C32×#103—21no—
25C32×#103—21no—
26C32×#103—21no—
27C32×#102—21no—
28C32×#101—22no—
29C2×C3×#137C2×C314yes—
30C2×C3×#131C2×C314yes—
31C3×#417C2×C314yes—
32C2×C3×#103C2×C314yescomplemented
33C2×C3×#101C2×C314yescomplemented
34C3×#343C2×C314yescomplemented
35C3×#341C2×C314yescomplemented
36C32×#41—21no—
37C32×#41—21no—
38C32×#41C2×C412yes—
39C32×#41D412yes—
40C2×C32×Q8—21no—
41C2×C32×Q8—21no—
42C2×C32×Q8—21no—
43C2×C32×Q8—21no—
44C2×C32×Q8—21no—
45C2×C32×Q8C2×C412yes—
46C2×C32×Q8D411yescharacteristic
47C2×C32×D4—21no—
48C2×C32×D4D411yescharacteristic
49C22×C32×C4—21no—
50C22×C32×C4—21no—
51C22×C32×C4—21no—
52C22×C32×C4C2311yescharacteristic
53C32×Q16—24no—
54C32×SD16—24no—
55C32×M16—24no—
56C32×M16—21no—
57C32×M16—21no—
58C32×M16—21no—
59C32×M16—21no—
60C32×M16C2×C412yes—
61C32×M16D412yes—
62C2×C32×C8—24no—
63C2×C32×C8—21no—
64C2×C32×C8—21no—
65C2×C32×C8—21no—
66C2×C32×C8—21no—
67C2×C32×C8—21no—
68C2×C32×C8D411yescharacteristic
69C2×C32×C8D411yescharacteristic
70C32×C4⋊C4—21no—
71C32×C4⋊C4—21no—
72#1908C3211yescharacteristic, direct product factor, Sylow
73C2×C3×#41C22×C314yes—
74C22×C3×Q8C22×C314yes—
75C3×#137—28no—
76C3×#137C3×C4116yescomplemented
77C2×C3×Q16—24no—
78C2×C3×SD16—24no—
79C3×#131—28no—
80C3×#131—28no—
81C2×C3×M16—24no—
82C2×C3×M16C22×C314yes—
83C2×C3×M16C22×C314yes—
84C2×C3×M16C22×C314yes—
85C22×C3×C8—24no—
86C22×C3×C8C22×C314yes—
87C2×C3×C4⋊C4C22×C314yes—
88C3×#103—24no—
89C3×#103—24no—
90C3×#103—24no—
91C3×#102—24no—
92C3×#101—28no—
93C23×C32—21no—
94C23×C32#4111yescharacteristic
95C32×Q8—21no—
96C32×Q8—22no—
97C32×Q8—22no—
98C32×Q8—41no—
99C32×Q8—41no—
100C32×Q8C22⋊C412yes—
101C32×D4—22no—
102C32×D4—22no—
103C32×D4—21no—
104C32×D4C22⋊C412yes—
105C2×C32×C4—21no—
106C2×C32×C4—22no—
107C2×C32×C4—22no—
108C2×C32×C4—22no—
109C2×C32×C4—41no—
110C2×C32×C4—41no—
111C2×C32×C4—41no—
112C2×C32×C4—81no—
113C2×C32×C4C22×C411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4#4111yescharacteristic
119C32×C8—22no—
120C32×C8—21no—
121C32×C8—22no—
122C32×C8—21no—
123C32×C8—41no—
124C2×#137C2×C3211yescharacteristic
125C2×#131C2×C3211yescharacteristic
126#417C2×C3211yescharacteristic
127C2×#103C2×C3211yescharacteristic, complemented
128C2×#101C2×C3211yescharacteristic, complemented
129#343C2×C3211yescharacteristic, complemented
130#341C2×C3211yescharacteristic, complemented
131C3×#41—24no—
132C3×#41—24no—
133C3×#41C2×C3×C418yes—
134C3×#41C3×D418yes—
135C2×C3×Q8—24no—
136C2×C3×Q8—24no—
137C2×C3×Q8—24no—
138C2×C3×Q8—24no—
139C2×C3×Q8—24no—
140C2×C3×Q8C2×C3×C418yes—
141C2×C3×Q8C3×D414yes—
142C2×C3×D4—24no—
143C2×C3×D4C3×D414yes—
144C22×C3×C4—24no—
145C22×C3×C4—24no—
146C22×C3×C4—24no—
147C22×C3×C4C23×C314yes—
148C3×Q16—216no—
149C3×SD16—216no—
150C3×M16—216no—
151C3×M16—24no—
152C3×M16—24no—
153C3×M16—24no—
154C3×M16—24no—
155C3×M16C2×C3×C418yes—
156C3×M16C3×D418yes—
157C2×C3×C8—216no—
158C2×C3×C8—24no—
159C2×C3×C8—24no—
160C2×C3×C8—24no—
161C2×C3×C8—24no—
162C2×C3×C8—24no—
163C2×C3×C8C3×D414yes—
164C2×C3×C8C3×D414yes—
165C3×C4⋊C4—24no—
166C3×C4⋊C4—24no—
167C22×C32—21no—
168C22×C32—21no—
169C22×C32—22no—
170C22×C32—41no—
171C22×C32—41no—
172C22×C32C4×D411yescharacteristic
173C22×C32#12111yescharacteristic
174C22×C32#12311yescharacteristic
175C32×C4—22no—
176C32×C4—42no—
177C32×C4—81no—
178C32×C4C2×C22⋊C411yescharacteristic
179C32×C4C4×D411yescharacteristic
180C32×C4#12011yescharacteristic
181C32×C4#12111yescharacteristic
182C2×#41C22×C3211yescharacteristic
183C22×Q8C22×C3211yescharacteristic
184#137—22no—
185#137C32×C414yescomplemented
186C2×Q16—21no—
187C2×SD16—21no—
188#131—22no—
189#131—22no—
190C2×M16—21no—
191C2×M16C22×C3211yescharacteristic
192C2×M16C22×C3211yescharacteristic
193C2×M16C22×C3211yescharacteristic
194C22×C8—21no—
195C22×C8C22×C3211yescharacteristic
196C2×C4⋊C4C22×C3211yescharacteristic
197#103—21no—
198#103—21no—
199#103—21no—
200#102—21no—
201#101—22no—
202C23×C3—24no—
203C23×C3C3×#4114yes—
204C3×Q8—24no—
205C3×Q8—28no—
206C3×Q8—28no—
207C3×Q8—44no—
208C3×Q8—44no—
209C3×Q8C3×C22⋊C418yes—
210C3×D4—28no—
211C3×D4—28no—
212C3×D4—24no—
213C3×D4C3×C22⋊C418yes—
214C2×C3×C4—24no—
215C2×C3×C4—28no—
216C2×C3×C4—28no—
217C2×C3×C4—28no—
218C2×C3×C4—44no—
219C2×C3×C4—44no—
220C2×C3×C4—44no—
221C2×C3×C4—84no—
222C2×C3×C4C22×C3×C414yes—
223C2×C3×C4C2×C3×D414yes—
224C2×C3×C4C2×C3×D414yes—
225C2×C3×C4C2×C3×D414yes—
226C2×C3×C4C2×C3×D414yes—
227C2×C3×C4C3×#4114yes—
228C3×C8—28no—
229C3×C8—24no—
230C3×C8—28no—
231C3×C8—24no—
232C3×C8—44no—
233C2×C32—21no—
234C2×C32—21no—
235C2×C32—42no—
236C2×C32#38611yescharacteristic
237C2×C32#47111yescharacteristic
238C2×C32#47311yescharacteristic
239#41—21no—
240#41—21no—
241#41C2×C32×C412yes—
242#41C32×D412yes—
243C2×Q8—21no—
244C2×Q8—21no—
245C2×Q8—21no—
246C2×Q8—21no—
247C2×Q8—21no—
248C2×Q8C2×C32×C412yes—
249C2×Q8C32×D411yescharacteristic
250C2×D4—21no—
251C2×D4C32×D411yescharacteristic
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4C23×C3211yescharacteristic
256Q16—24no—
257SD16—24no—
258M16—24no—
259M16—21no—
260M16—21no—
261M16—21no—
262M16—21no—
263M16C2×C32×C412yes—
264M16C32×D412yes—
265C2×C8—24no—
266C2×C8—21no—
267C2×C8—21no—
268C2×C8—21no—
269C2×C8—21no—
270C2×C8—21no—
271C2×C8C32×D411yescharacteristic
272C2×C8C32×D411yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—21no—
275C22×C3—24no—
276C22×C3—24no—
277C22×C3—28no—
278C22×C3—44no—
279C22×C3—44no—
280C22×C3C3×C4×D414yes—
281C22×C3C3×#12114yes—
282C22×C3C3×#12314yes—
283C3×C4—28no—
284C3×C4—48no—
285C3×C4—84no—
286C3×C4C2×C3×C22⋊C414yes—
287C3×C4C3×C4×D414yes—
288C3×C4C3×#12014yes—
289C3×C4C3×#12114yes—
290C32#190811yescharacteristic, direct product factor, Sylow
291C23—21no—
292C23C32×#4111yescharacteristic
293Q8—21no—
294Q8—22no—
295Q8—22no—
296Q8—41no—
297Q8—41no—
298Q8C32×C22⋊C412yes—
299D4—22no—
300D4—22no—
301D4—21no—
302D4C32×C22⋊C412yes—
303C2×C4—21no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—81no—
311C2×C4C22×C32×C411yescharacteristic
312C2×C4C2×C32×D411yescharacteristic
313C2×C4C2×C32×D411yescharacteristic
314C2×C4C2×C32×D411yescharacteristic
315C2×C4C2×C32×D411yescharacteristic
316C2×C4C32×#4111yescharacteristic
317C8—22no—
318C8—21no—
319C8—22no—
320C8—21no—
321C8—41no—
322C2×C3—24no—
323C2×C3—24no—
324C2×C3—48no—
325C2×C3C3×#38614yes—
326C2×C3C3×#47114yes—
327C2×C3C3×#47314yes—
328C22—21no—
329C22—21no—
330C22—22no—
331C22—41no—
332C22—41no—
333C22C32×C4×D411yescharacteristic
334C22C32×#12111yescharacteristic
335C22C32×#12311yescharacteristic
336C4—22no—
337C4—42no—
338C4—81no—
339C4C2×C32×C22⋊C411yescharacteristic
340C4C32×C4×D411yescharacteristic
341C4C32×#12011yescharacteristic
342C4C32×#12111yescharacteristic
343C3C3×#190814yesdirect product factor
344C2—21no—
345C2—21no—
346C2—42no—
347C2C32×#38611yescharacteristic
348C2C32×#47111yescharacteristic
349C2C32×#47311yescharacteristic
subgroupG/H
center, socleC22×C32#121
commutatorC2×C4C22×C32×C4
Frattini, cosocleC22×C4C23×C32
prime radicalC2×C32×#41C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C32 ◁ C22×C32×C4 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C32×#103C2semidirect
5. C2×C32×#101C2semidirect
6. C32×#343C2semidirect
7. C32×#341C2semidirect
8. C3×#1908C3direct (N × H)
12. C32×#137C4semidirect
32. C2×C3×#103C2×C3semidirect
33. C2×C3×#101C2×C3semidirect
34. C3×#343C2×C3semidirect
35. C3×#341C2×C3semidirect
72. #1908C32direct (N × H)
76. C3×#137C3×C4semidirect
127. C2×#103C2×C32semidirect
128. C2×#101C2×C32semidirect
129. #343C2×C32semidirect
130. #341C2×C32semidirect
185. #137C32×C4semidirect
290. C32#1908direct (N × H)
343. C3C3×#1908direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×#1372
C2×C32×#1312
C32×#4172
C2×C32×#1032
C2×C32×#1012
C32×#3432
C32×#3412
C3×#19083