Finite Group Databasebeta

← C3×#70897 #11777571

Subgroups — C3×#70897 #11777571

Order 1152.

397 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C4×SD16C211yesmaximal, characteristic
2C3×#5024C211yesmaximal, characteristic, complemented
3C3×D4×C3⋊C8C211yesmaximal, characteristic
4C3×#4535C211yesmaximal, characteristic, complemented
5C3×D4⋊(C3⋊C8)C211yesmaximal, characteristic
6C3×#4458C211yesmaximal, characteristic, complemented
7C3×#4454C211yesmaximal, characteristic, complemented
8C3×#1585—31nomaximal
9#70897C311yesmaximal, characteristic, direct product factor
10C2×C32×SD16C411yescharacteristic
11C32×C4×Q8C2211yescharacteristic
12C32×C4×D4C2211yescharacteristic
13C22×C3×C3⋊C8—21no—
14C32×#106C411yescharacteristic
15C32×#103C411yescharacteristic
16C32×#102C411yescharacteristic
17C32×C4×C8C2211yescharacteristic
18C3×#830—21no—
19C3×C4⋊(C3⋊C8)—21no—
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×#803—21no—
23C3×C4×C3⋊C8C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25C3×#446—31no—
26C3×C4×SD16—21no—
27C3×C4×SD16D311yescharacteristic
28C3×C4×SD16C2×C311yescharacteristic
29C3×C8×D4—31no—
30#5024C2×C311yescharacteristic, complemented
31D4×C3⋊C8C2×C311yescharacteristic
32C3×#335—31no—
33C3×Q8⋊C8—31no—
34C3×D4⋊C8—31no—
35C3×#322—31no—
36#4535C2×C311yescharacteristic, complemented
37D4⋊(C3⋊C8)C2×C311yescharacteristic
38#4458C2×C311yescharacteristic, complemented
39#4454C2×C311yescharacteristic, complemented
40C2×C32×Q8C2×C411yescharacteristic
41C2×C32×D4C2×C411yescharacteristic
42C22×C32×C4—21no—
43C32×SD16—22no—
44C2×C32×C8C2×C411yescharacteristic
45C2×C32×C8C2×C411yescharacteristic
46C32×C4⋊C4—21no—
47C32×C4⋊C4C2×C411yescharacteristic
48C32×C4⋊C4C2×C411yescharacteristic
49C32×C22⋊C4—21no—
50C32×C42—21no—
51C32×C42C2311yescharacteristic
52C2×C3×C3⋊C8—21no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8—42no—
56C2×C3×C3⋊C8D411yescharacteristic
57C2×C3×C3⋊C8D411yescharacteristic
58#1585—31noSylow
59C2×C3×SD16—21no—
60C2×C3×SD16Dic311yescharacteristic
61C2×C3×SD16C3×C411yescharacteristic
62C22×C3×C8—61no—
63C3×C4×Q8—21no—
64C3×C4×Q8C2×D311yescharacteristic
65C3×C4×Q8C22×C311yescharacteristic
66C3×C4×D4—21no—
67C3×C4×D4C2×D311yescharacteristic
68C3×C4×D4C22×C311yescharacteristic
69C22×C3⋊C8—21no—
70C3×#106—21no—
71C3×#106Dic311yescharacteristic
72C3×#106C3×C411yescharacteristic
73C3×C4⋊C8—31no—
74C3×C4⋊C8—31no—
75C3×C4⋊C8—61no—
76C3×#103—21no—
77C3×#103Dic311yescharacteristic
78C3×#103C3×C411yescharacteristic
79C3×#102—21no—
80C3×#102Dic311yescharacteristic
81C3×#102C3×C411yescharacteristic
82C3×C22⋊C8—61no—
83C3×#97—61no—
84C3×C4×C8—21no—
85C3×C4×C8—31no—
86C3×C4×C8—31no—
87C3×C4×C8C2×D311yescharacteristic
88C3×C4×C8C22×C311yescharacteristic
89#830—21no—
90C4⋊(C3⋊C8)—21no—
91C4⋊(C3⋊C8)C22×C311yescharacteristic
92C4⋊(C3⋊C8)C22×C311yescharacteristic
93#803—21no—
94C4×C3⋊C8C22×C311yescharacteristic
95C4×C3⋊C8C22×C311yescharacteristic
96C23×C32—21no—
97C32×Q8—21no—
98C32×Q8—21no—
99C32×D4—21no—
100C32×D4M1612yes—
101C2×C32×C4—21no—
102C2×C32×C4—21no—
103C2×C32×C4—21no—
104C2×C32×C4—41no—
105C2×C32×C4—41no—
106C2×C32×C4C22×C411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4#4111yescharacteristic
109C32×C8—21no—
110C32×C8—21no—
111C3×C3⋊C8—22no—
112C3×C3⋊C8—21no—
113C3×C3⋊C8—21no—
114C3×C3⋊C8—41no—
115C3×C3⋊C8—41no—
116#446—31no—
117C4×SD16C3×D311yescharacteristic
118C8×D4—31no—
119#335—31no—
120Q8⋊C8—31no—
121D4⋊C8—31no—
122#322—31no—
123C2×C3×Q8—21no—
124C2×C3×Q8C2×Dic311yescharacteristic
125C2×C3×Q8C2×C3×C411yescharacteristic
126C2×C3×D4—21no—
127C2×C3×D4C2×Dic311yescharacteristic
128C2×C3×D4C2×C3×C411yescharacteristic
129C22×C3×C4—21no—
130C22×C3×C4—21no—
131C22×C3×C4—41no—
132C3×SD16—24no—
133C3×SD16—22no—
134C3×SD16—22no—
135C2×C3×C8—21no—
136C2×C3×C8—21no—
137C2×C3×C8—31no—
138C2×C3×C8—31no—
139C2×C3×C8—61no—
140C2×C3×C8—61no—
141C2×C3×C8—61no—
142C2×C3×C8—122no—
143C2×C3×C8C2×Dic311yescharacteristic
144C2×C3×C8C2×Dic311yescharacteristic
145C2×C3×C8C2×C3×C411yescharacteristic
146C2×C3×C8C2×C3×C411yescharacteristic
147C3×C4⋊C4—21no—
148C3×C4⋊C4—21no—
149C3×C4⋊C4—21no—
150C3×C4⋊C4—21no—
151C3×C4⋊C4—41no—
152C3×C4⋊C4C2×Dic311yescharacteristic
153C3×C4⋊C4C2×Dic311yescharacteristic
154C3×C4⋊C4C2×C3×C411yescharacteristic
155C3×C4⋊C4C2×C3×C411yescharacteristic
156C3×C22⋊C4—21no—
157C3×C22⋊C4—21no—
158C3×C22⋊C4—41no—
159C3×C42—21no—
160C3×C42—21no—
161C3×C42—21no—
162C3×C42—41no—
163C3×C42C22×D311yescharacteristic
164C3×C42C23×C311yescharacteristic
165C2×C3⋊C8—21no—
166C2×C3⋊C8—21no—
167C2×C3⋊C8—21no—
168C2×C3⋊C8—42no—
169C2×C3⋊C8C3×D411yescharacteristic
170C2×C3⋊C8C3×D411yescharacteristic
171C22×C32—22no—
172C22×C32—41no—
173C22×C32—41no—
174C22×C32C4×D411yescharacteristic
175C32×C4—21no—
176C32×C4—41no—
177C32×C4—41no—
178C32×C4—41no—
179C32×C4C2×M1611yescharacteristic
180C32×C4#13111yescharacteristic
181C32×C4AGL(1,ℤ/8)11yescharacteristic
182C32×C4#13711yescharacteristic
183C2×SD16C3×Dic311yescharacteristic
184C22×C8—61no—
185C4×Q8C2×C3×D311yescharacteristic
186C4×D4C2×C3×D311yescharacteristic
187#106C3×Dic311yescharacteristic
188C4⋊C8—31no—
189C4⋊C8—31no—
190C4⋊C8—61no—
191#103C3×Dic311yescharacteristic
192#102C3×Dic311yescharacteristic
193C22⋊C8—61no—
194#97—61no—
195C4×C8—31no—
196C4×C8—31no—
197C4×C8C2×C3×D311yescharacteristic
198C23×C3—21no—
199C23×C3—21no—
200C23×C3—41no—
201C3×Q8—22no—
202C3×Q8—21no—
203C3×Q8—21no—
204C3×Q8—21no—
205C3×Q8—21no—
206C3×Q8—41no—
207C3×D4—21no—
208C3×D4—21no—
209C3×D4—22no—
210C3×D4—41no—
211C3×D4#20812yes—
212C3×D4C3×M1612yes—
213C2×C3×C4—21no—
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—21no—
221C2×C3×C4—21no—
222C2×C3×C4—41no—
223C2×C3×C4—41no—
224C2×C3×C4—41no—
225C2×C3×C4—41no—
226C2×C3×C4—41no—
227C2×C3×C4—41no—
228C2×C3×C4—41no—
229C2×C3×C4—81no—
230C2×C3×C4—81no—
231C2×C3×C4D3×D411yescharacteristic
232C2×C3×C4#23711yescharacteristic
233C2×C3×C4C22×Dic311yescharacteristic
234C2×C3×C4C22×C3×C411yescharacteristic
235C2×C3×C4C2×C3×D411yescharacteristic
236C2×C3×C4C3×#4111yescharacteristic
237C3×C8—22no—
238C3×C8—21no—
239C3×C8—21no—
240C3×C8—21no—
241C3×C8—21no—
242C3×C8—41no—
243C3×C8—62no—
244C3×C8—61no—
245C3×C8—61no—
246C3×C8—121no—
247C3×C8—121no—
248C3⋊C8—22no—
249C3⋊C8—21no—
250C3⋊C8—21no—
251C3⋊C8—41no—
252C3⋊C8—41no—
253C2×C32—42no—
254C2×C32#43511yescharacteristic
255C2×C32#44011yescharacteristic
256C2×C32#44311yescharacteristic
257C2×Q8C2×C3×Dic311yescharacteristic
258C2×D4C2×C3×Dic311yescharacteristic
259C22×C4—21no—
260SD16—22no—
261C2×C8—31no—
262C2×C8—31no—
263C2×C8—61no—
264C2×C8—61no—
265C2×C8—61no—
266C2×C8—122no—
267C2×C8C2×C3×Dic311yescharacteristic
268C2×C8C2×C3×Dic311yescharacteristic
269C4⋊C4—21no—
270C4⋊C4C2×C3×Dic311yescharacteristic
271C4⋊C4C2×C3×Dic311yescharacteristic
272C22⋊C4—21no—
273C42—21no—
274C42C22×C3×D311yescharacteristic
275C22×C3—22no—
276C22×C3—22no—
277C22×C3—21no—
278C22×C3—42no—
279C22×C3—41no—
280C22×C3—41no—
281C22×C3—41no—
282C22×C3—41no—
283C22×C3—81no—
284C22×C3—81no—
285C22×C3D4×Dic311yescharacteristic
286C22×C3C3×C4×D411yescharacteristic
287C3×C4—21no—
288C3×C4—21no—
289C3×C4—21no—
290C3×C4—21no—
291C3×C4—21no—
292C3×C4—21no—
293C3×C4—41no—
294C3×C4—42no—
295C3×C4—41no—
296C3×C4—41no—
297C3×C4—41no—
298C3×C4—41no—
299C3×C4—41no—
300C3×C4—41no—
301C3×C4—81no—
302C3×C4—81no—
303C3×C4#91411yescharacteristic
304C3×C4#91511yescharacteristic
305C3×C4C2×#20811yescharacteristic
306C3×C4#94811yescharacteristic
307C3×C4C2×C3×M1611yescharacteristic
308C3×C4C3×#13111yescharacteristic
309C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
310C3×C4C3×#13711yescharacteristic
311C32#158511yescharacteristic, complemented, Sylow
312C23—21no—
313Q8—21no—
314Q8—21no—
315D4—21no—
316D4C3×#20812yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4C3×D3×D411yescharacteristic
323C2×C4C3×#23711yescharacteristic
324C2×C4C22×C3×Dic311yescharacteristic
325C8—21no—
326C8—21no—
327C8—62no—
328C8—61no—
329C8—61no—
330C8—121no—
331C8—121no—
332C2×C3—21no—
333C2×C3—21no—
334C2×C3—21no—
335C2×C3—42no—
336C2×C3—42no—
337C2×C3—82no—
338C2×C3#501111yescharacteristic
339C2×C3#516411yescharacteristic
340C2×C3#519611yescharacteristic
341C2×C3C3×#43511yescharacteristic
342C2×C3C3×#44011yescharacteristic
343C2×C3C3×#44311yescharacteristic
344C22—22no—
345C22—41no—
346C22—41no—
347C22C3×D4×Dic311yescharacteristic
348C4—21no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4C3×#91411yescharacteristic
353C4C3×#91511yescharacteristic
354C4C2×C3×#20811yescharacteristic
355C4C3×#94811yescharacteristic
356C3—21no—
357C3#7089711yescharacteristic, direct product factor
358C3C3×#158511yescharacteristic, complemented
359C2—42no—
360C2C3×#501111yescharacteristic
361C2C3×#516411yescharacteristic
362C2C3×#519611yescharacteristic
subgroupG/H
centerC2×C3×C4D3×D4
commutatorC2×C3×C4C22×C3×C4
FrattiniC42C22×C3×D3
FittingC32×C4×SD16C2
socleC22×C32C4×D4
prime radicalC2×C32×D4C2×C4
cosocleC3×C42C23×C3
hypercenterC3×C4×SD16D3
hypocenterC3C3×#1585
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C3×C42 ◁ C3×C4×SD16

Complements

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

NH ≅ G/Ntype
2. C3×#5024C2semidirect
4. C3×#4535C2semidirect
6. C3×#4458C2semidirect
7. C3×#4454C2semidirect
9. #70897C3direct (N × H)
30. #5024C2×C3semidirect
36. #4535C2×C3semidirect
38. #4458C2×C3semidirect
39. #4454C2×C3semidirect
311. C32#1585semidirect
357. C3#70897direct (N × H)
358. C3C3×#1585semidirect

Maximal subgroups

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

subgroupindex
C32×C4×SD162
C3×#50242
C3×D4×C3⋊C82
C3×#45352
C3×D4⋊(C3⋊C8)2
C3×#44582
C3×#44542
C3×#15853
#708973