Finite Group Databasebeta

← C3×#70890 #11798969

Subgroups — C3×#70890 #11798969

Order 1152.

407 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C4×D8C211yesmaximal, characteristic, complemented
2C2×C3×#827C211yesmaximal, characteristic, complemented
3C2×C3×#826C211yesmaximal, characteristic
4C3×#4696C211yesmaximal, characteristic, complemented
5C3×#4492C211yesmaximal, characteristic, complemented
6C3×#4491C211yesmaximal, characteristic, complemented
7C3×C4⋊(C3⋊C16)C211yesmaximal, characteristic, complemented
8C3×#2210—31nomaximal
9#70890C311yesmaximal, characteristic, direct product factor
10C2×C32×D8C2211yescharacteristic
11C32×C4×D4—21no—
12C2×C3×Dic12C2211yescharacteristic
13C2×C3×D24C2211yescharacteristic
14C2×C3×#204—21no—
15C3×#875—21no—
16C32×#107C2211yescharacteristic
17C32×#102—21no—
18C32×C4×C8C2211yescharacteristic
19C3×#827—22no—
20C3×#826—22no—
21C2×C3×C3⋊C16C2211yescharacteristic
22C2×C3×C3⋊C16C2211yescharacteristic
23C2×C3×SD32—31no—
24C2×C3×D16—31no—
25C3×#495—31no—
26C3×C4×D8—21no—
27C3×C4×D8D311yescharacteristic, complemented
28C3×C4×D8C2×C311yescharacteristic, complemented
29C2×#827C2×C311yescharacteristic, complemented
30C2×#826C2×C311yescharacteristic
31#4696C2×C311yescharacteristic, complemented
32C3×C4⋊C16—31no—
33C3×#358—31no—
34C3×#357—31no—
35#4492C2×C311yescharacteristic, complemented
36#4491C2×C311yescharacteristic, complemented
37C4⋊(C3⋊C16)C2×C311yescharacteristic, complemented
38C2×C32×D4—21no—
39C22×C32×C4—41no—
40C2×C3×D12—21no—
41C2×C3×Dic6—21no—
42C32×D8—21no—
43C32×D8D412yes—
44C2×C32×C8D411yescharacteristic
45C2×C32×C8C2311yescharacteristic
46C32×C4⋊C4—21no—
47C32×C22⋊C4—41no—
48C32×C42D411yescharacteristic
49C3×(C2×D3)⋊C4—41no—
50C3×(C2×D3)⋊C4—41no—
51C3×Dic12—21no—
52C3×Dic12—21no—
53C3×D24—21no—
54C3×D24—21no—
55C3×#204—42no—
56C3×C3⋊C16—21no—
57C3×C3⋊C16—21no—
58#2210—31noSylow
59C2×C3×Q16—31no—
60C2×C3×SD16—61no—
61C2×C3×D8—21no—
62C2×C3×D8—31no—
63C2×C3×D8C2×D311yescharacteristic
64C2×C3×D8C22×C311yescharacteristic
65C3×#124—61no—
66C3×C4×D4—22no—
67C3×C4×D4—21no—
68C3×C4×D4—21no—
69C2×Dic12C22×C311yescharacteristic
70C2×D24C22×C311yescharacteristic
71C2×#204—21no—
72#875—21no—
73C3×SD32—62no—
74C3×D16—62no—
75C2×C3×C16—31no—
76C2×C3×C16—31no—
77C3×#107—21no—
78C3×#107C2×D311yescharacteristic
79C3×#107C22×C311yescharacteristic
80C3×#102—22no—
81C3×#102—21no—
82C3×#102—21no—
83C3×C4×C8—21no—
84C3×C4×C8C2×D311yescharacteristic
85C3×C4×C8C22×C311yescharacteristic
86#827—22no—
87#826—22no—
88C2×C3⋊C16C22×C311yescharacteristic
89C2×C3⋊C16C22×C311yescharacteristic
90C23×C32—41no—
91C22×C3×D3—41no—
92C32×D4—22no—
93C32×D4—41no—
94C2×C32×C4—41no—
95C2×C32×C4—82no—
96C2×C32×C4D811yescharacteristic
97C2×C32×C4D811yescharacteristic
98C2×C32×C4C2×D411yescharacteristic
99C2×C3×Dic3—41no—
100C3×D12—41no—
101C3×D12—41no—
102C3×Dic6—41no—
103C3×Dic6—41no—
104C32×C8—21no—
105C32×C8C2×D411yescharacteristic
106C32×C8#4111yescharacteristic
107C2×SD32—31no—
108C2×D16—31no—
109#495—31no—
110C4×D8C3×D311yescharacteristic, complemented
111C4⋊C16—31no—
112#358—31no—
113#357—31no—
114C2×C3×Q8—61no—
115C2×C3×D4—22no—
116C2×C3×D4—21no—
117C2×C3×D4—21no—
118C2×C3×D4—61no—
119C22×C3×C4—42no—
120C22×C3×C4—41no—
121C22×C3×C4—41no—
122C2×D12—21no—
123C2×Dic6—21no—
124C3×Q16—61no—
125C3×Q16—61no—
126C3×SD16—122no—
127C3×D8—22no—
128C3×D8—21no—
129C3×D8—21no—
130C3×D8—22no—
131C3×D8—61no—
132C3×D8—61no—
133C3×D8D1212yes—
134C3×D8C3×D412yes—
135C2×C3×C8—21no—
136C2×C3×C8—21no—
137C2×C3×C8#6711yescharacteristic
138C2×C3×C8C3×D411yescharacteristic
139C2×C3×C8C22×D311yescharacteristic
140C2×C3×C8C23×C311yescharacteristic
141C3×C4⋊C4—22no—
142C3×C4⋊C4—21no—
143C3×C4⋊C4—21no—
144C3×C22⋊C4—42no—
145C3×C22⋊C4—41no—
146C3×C22⋊C4—41no—
147C3×C22⋊C4—121no—
148C3×C22⋊C4—121no—
149C3×C42—21no—
150C3×C42#6711yescharacteristic
151C3×C42C3×D411yescharacteristic
152(C2×D3)⋊C4—41no—
153(C2×D3)⋊C4—41no—
154Dic12—21no—
155Dic12—21no—
156D24—21no—
157D24—21no—
158#204—42no—
159C3×C16—61no—
160C3×C16—61no—
161C3⋊C16—21no—
162C3⋊C16—21no—
163C22×C32—42no—
164C22×C32—81no—
165C22×C32—81no—
166C22×C32C2×D811yescharacteristic
167C2×C3×D3—81no—
168C2×C3×D3—81no—
169C2×C3×D3—81no—
170C32×C4—21no—
171C32×C4—21no—
172C32×C4—81no—
173C32×C4#12111yescharacteristic
174C32×C4AGL(1,ℤ/8)11yescharacteristic
175C3×Dic3—81no—
176C2×Q16—31no—
177C2×SD16—61no—
178C2×D8—31no—
179C2×D8C2×C3×D311yescharacteristic
180#124—61no—
181C4×D4—21no—
182SD32—62no—
183D16—62no—
184C2×C16—31no—
185C2×C16—31no—
186#107C2×C3×D311yescharacteristic
187#102—21no—
188C4×C8C2×C3×D311yescharacteristic
189C23×C3—42no—
190C23×C3—41no—
191C23×C3—41no—
192C23×C3—121no—
193C22×D3—41no—
194C3×Q8—121no—
195C3×Q8—121no—
196C3×D4—24no—
197C3×D4—22no—
198C3×D4—22no—
199C3×D4—42no—
200C3×D4—41no—
201C3×D4—41no—
202C3×D4—121no—
203C3×D4—121no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—42no—
208C2×C3×C4—41no—
209C2×C3×C4—41no—
210C2×C3×C4—84no—
211C2×C3×C4—82no—
212C2×C3×C4—82no—
213C2×C3×C4—121no—
214C2×C3×C4#21311yescharacteristic
215C2×C3×C4#21311yescharacteristic
216C2×C3×C4C3×D811yescharacteristic
217C2×C3×C4C3×D811yescharacteristic
218C2×C3×C4C2×#6711yescharacteristic
219C2×C3×C4C2×C3×D411yescharacteristic
220C2×Dic3—41no—
221D12—41no—
222D12—41no—
223Dic6—41no—
224Dic6—41no—
225C3×C8—21no—
226C3×C8—21no—
227C3×C8—21no—
228C3×C8—21no—
229C3×C8—41no—
230C3×C8C2×D1211yescharacteristic
231C3×C8#23511yescharacteristic
232C3×C8C2×C3×D411yescharacteristic
233C3×C8C3×#4111yescharacteristic
234C2×C32—82no—
235C2×C32#45911yescharacteristic
236C2×C32#50811yescharacteristic
237C2×C32#50911yescharacteristic
238C3×D3—161no—
239C2×Q8—61no—
240C2×D4—21no—
241C2×D4—61no—
242C22×C4—41no—
243Q16—61no—
244Q16—61no—
245SD16—122no—
246D8—21no—
247D8—61no—
248D8—61no—
249D8C3×D1212yes—
250C2×C8C3×#6711yescharacteristic
251C2×C8C22×C3×D311yescharacteristic
252C4⋊C4—21no—
253C22⋊C4—41no—
254C22⋊C4—121no—
255C22⋊C4—121no—
256C42C3×#6711yescharacteristic
257C16—61no—
258C16—61no—
259C22×C3—21no—
260C22×C3—44no—
261C22×C3—42no—
262C22×C3—42no—
263C22×C3—82no—
264C22×C3—82no—
265C22×C3—81no—
266C22×C3—81no—
267C22×C3—81no—
268C22×C3—81no—
269C22×C3—241no—
270C22×C3—241no—
271C22×C3—241no—
272C22×C3C2×#21311yescharacteristic
273C22×C3C2×C3×D811yescharacteristic
274C2×D3—81no—
275C2×D3—81no—
276C2×D3—81no—
277C3×C4—22no—
278C3×C4—21no—
279C3×C4—21no—
280C3×C4—21no—
281C3×C4—21no—
282C3×C4—21no—
283C3×C4—21no—
284C3×C4—41no—
285C3×C4—82no—
286C3×C4—81no—
287C3×C4—81no—
288C3×C4—241no—
289C3×C4#93011yescharacteristic
290C3×C4#94911yescharacteristic
291C3×C4C3×#12111yescharacteristic
292C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
293Dic3—81no—
294C32#221011yescharacteristic, complemented, Sylow
295C23—41no—
296C23—121no—
297Q8—121no—
298Q8—121no—
299D4—22no—
300D4—41no—
301D4—121no—
302D4—121no—
303C2×C4—41no—
304C2×C4—82no—
305C2×C4—121no—
306C2×C4C3×#21311yescharacteristic
307C2×C4C3×#21311yescharacteristic
308C2×C4C2×C3×#6711yescharacteristic
309C8—21no—
310C8C2×C3×D1211yescharacteristic
311C8C3×#23511yescharacteristic
312C2×C3—21no—
313C2×C3—21no—
314C2×C3—21no—
315C2×C3—84no—
316C2×C3—82no—
317C2×C3—82no—
318C2×C3—481no—
319C2×C3#501511yescharacteristic
320C2×C3#514711yescharacteristic
321C2×C3#519411yescharacteristic
322C2×C3C3×#45911yescharacteristic
323C2×C3C3×#50811yescharacteristic
324C2×C3C3×#50911yescharacteristic
325D3—161no—
326C22—42no—
327C22—81no—
328C22—81no—
329C22—241no—
330C22—241no—
331C22—241no—
332C22C2×C3×#21311yescharacteristic
333C4—21no—
334C4—21no—
335C4—81no—
336C4—241no—
337C4C3×#93011yescharacteristic
338C4C3×#94911yescharacteristic
339C3—21no—
340C3#7089011yescharacteristic, direct product factor
341C3C3×#221011yescharacteristic, complemented
342C2—82no—
343C2—481no—
344C2C3×#501511yescharacteristic
345C2C3×#514711yescharacteristic
346C2C3×#519411yescharacteristic
subgroupG/H
centerC22×C3C2×#213
commutator, cosocleC2×C3×C8C23×C3
FrattiniC2×C8C22×C3×D3
FittingC32×C4×D8C2
socleC22×C32C2×D8
prime radicalC2×C3×#826C2
hypercenterC3×C4×D8D3
hypocenterC3C3×#2210
LCSG ▷ C2×C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×C4×C8 ◁ C3×C4×D8

Complements

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

NH ≅ G/Ntype
1. C32×C4×D8C2semidirect
2. C2×C3×#827C2semidirect
4. C3×#4696C2semidirect
5. C3×#4492C2semidirect
6. C3×#4491C2semidirect
7. C3×C4⋊(C3⋊C16)C2semidirect
9. #70890C3direct (N × H)
27. C3×C4×D8D3semidirect
28. C3×C4×D8C2×C3semidirect
29. C2×#827C2×C3semidirect
31. #4696C2×C3semidirect
35. #4492C2×C3semidirect
36. #4491C2×C3semidirect
37. C4⋊(C3⋊C16)C2×C3semidirect
110. C4×D8C3×D3semidirect
294. C32#2210semidirect
340. C3#70890direct (N × H)
341. C3C3×#2210semidirect

Maximal subgroups

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

subgroupindex
C32×C4×D82
C2×C3×#8272
C2×C3×#8262
C3×#46962
C3×#44922
C3×#44912
C3×C4⋊(C3⋊C16)2
C3×#22103
#708903