Finite Group Databasebeta

← C3×#68394 #11780786

Subgroups — C3×#68394 #11780786

Order 1152.

418 conjugacy classes of subgroups.

The subgroup lattice has 379 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5076C211yesmaximal, characteristic, complemented
2C3×#5072C211yesmaximal, characteristic
3C3×#4846C211yesmaximal, characteristic, complemented
4C3×#4834C211yesmaximal, characteristic, complemented
5C32×#331C211yesmaximal, characteristic, complemented
6C3×#4482C211yesmaximal, characteristic, complemented
7C3×#4480C211yesmaximal, characteristic, complemented
8C3×#1665—31nomaximal
9#68394C311yesmaximal, characteristic, direct product factor
10C32×#127C2211yescharacteristic
11C2×C3×#214—21no—
12C2×C3×#214—21no—
13C2×C3×#213—21no—
14C2×C3×D3×C8—21no—
15C3×C4×D12C2211yescharacteristic
16C3×#869C2211yescharacteristic
17C32×C4⋊C8C2211yescharacteristic
18C32×C4⋊C8C2211yescharacteristic
19C3×#832—21no—
20C3×#821—21no—
21C3×(C2×D3)⋊C8—21no—
22C3×#818—21no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25C3×#492—31no—
26C3×#474—31no—
27C3×#459—31no—
28C3×C8×D4—31no—
29#5076C2×C311yescharacteristic, complemented
30#5072C2×C311yescharacteristic
31#4846C2×C311yescharacteristic, complemented
32#4834C2×C311yescharacteristic, complemented
33C3×#334—31no—
34C3×#332—31no—
35C3×#331—21no—
36C3×#331D311yescharacteristic, complemented
37C3×#331C2×C311yescharacteristic, complemented
38#4482C2×C311yescharacteristic, complemented
39#4480C2×C311yescharacteristic, complemented
40C2×C32×D4—21no—
41C2×C32×D4—21no—
42C2×C32×D4—21no—
43C2×C3×D12D411yescharacteristic
44C2×C3×C4×D3—21no—
45C2×C3×Dic6—21no—
46C2×C32×C8—21no—
47C2×C32×C8—21no—
48C32×C42C2311yescharacteristic
49C3×#214—42no—
50C3×#214—42no—
51C3×#213—42no—
52C3×(C2×D3)⋊C4—21no—
53C3×C4⋊Dic3—21no—
54C3×C4⋊Dic3—21no—
55C3×C4⋊Dic3D411yescharacteristic
56C2×C3×C3⋊C8—21no—
57C2×C3×C3⋊C8D411yescharacteristic
58C2×C3×C3⋊C8D411yescharacteristic
59C3×D3×C8—42no—
60#1665—31noSylow
61C2×C3×SD16—61no—
62C2×C3×SD16—61no—
63C2×C3×D8—61no—
64C22×C3×C8—61no—
65C3×C4⋊Q8—31no—
66C3×#127—21no—
67C3×#127C2×D311yescharacteristic
68C3×#127C22×C311yescharacteristic
69C3×C4×D4—31no—
70C2×#214—21no—
71C2×#214—21no—
72C2×#213—21no—
73C2×D3×C8—21no—
74C4×D12C22×C311yescharacteristic
75#869C22×C311yescharacteristic
76C3×#107—61no—
77C3×C4⋊C8—21no—
78C3×C4⋊C8—21no—
79C3×C4⋊C8—31no—
80C3×C4⋊C8C2×D311yescharacteristic
81C3×C4⋊C8C2×D311yescharacteristic
82C3×C4⋊C8C22×C311yescharacteristic
83C3×C4⋊C8C22×C311yescharacteristic
84C3×#102—61no—
85C3×#102—61no—
86C3×C22⋊C8—61no—
87C3×C4×C8—31no—
88#832—21no—
89#821—21no—
90(C2×D3)⋊C8—21no—
91#818—21no—
92C4⋊(C3⋊C8)C22×C311yescharacteristic
93C4×C3⋊C8C22×C311yescharacteristic
94C23×C32—41no—
95C22×C3×D3—21no—
96C32×D4—41no—
97C32×D4—41no—
98C32×D4—41no—
99C32×D4—41no—
100C32×D4—81no—
101C2×C32×C4C2×D411yescharacteristic
102C2×C32×C4C2×D411yescharacteristic
103C2×C32×C4#4111yescharacteristic
104C2×C3×Dic3—21no—
105C2×C3×Dic3—41no—
106C3×D12—21no—
107C3×D12SD1612yescomplemented
108C3×C4×D3—41no—
109C3×C4×D3—41no—
110C3×Dic6—41no—
111C3×Dic6—41no—
112C32×C8—41no—
113C32×C8—41no—
114C3×C3⋊C8—21no—
115C3×C3⋊C8—41no—
116C3×C3⋊C8D812yescomplemented
117#492—31no—
118#474—31no—
119#459—31no—
120C8×D4—31no—
121#334—31no—
122#332—31no—
123#331C3×D311yescharacteristic, complemented
124C2×C3×Q8—61no—
125C2×C3×D4—22no—
126C2×C3×D4—21no—
127C2×C3×D4—21no—
128C2×C3×D4—21no—
129C2×C3×D4—21no—
130C2×C3×D4—21no—
131C2×C3×D4—21no—
132C2×C3×D4—31no—
133C2×C3×D4—41no—
134C2×C3×D4—41no—
135C22×C3×C4—61no—
136C2×D12C3×D411yescharacteristic
137C2×C4×D3—21no—
138C2×Dic6—21no—
139C3×SD16—122no—
140C3×SD16—122no—
141C3×D8—122no—
142C2×C3×C8—21no—
143C2×C3×C8—21no—
144C2×C3×C8—21no—
145C2×C3×C8—21no—
146C2×C3×C8—31no—
147C2×C3×C8—31no—
148C2×C3×C8—41no—
149C2×C3×C8—41no—
150C2×C3×C8—61no—
151C2×C3×C8—122no—
152C3×C4⋊C4—31no—
153C3×C4⋊C4—61no—
154C3×C4⋊C4—61no—
155C3×C22⋊C4—61no—
156C3×C42—21no—
157C3×C42C22×D311yescharacteristic
158C3×C42C23×C311yescharacteristic
159#214—42no—
160#214—42no—
161#213—42no—
162(C2×D3)⋊C4—21no—
163C4⋊Dic3—21no—
164C4⋊Dic3—21no—
165C4⋊Dic3C3×D411yescharacteristic
166C2×C3⋊C8—21no—
167C2×C3⋊C8C3×D411yescharacteristic
168C2×C3⋊C8C3×D411yescharacteristic
169D3×C8—42no—
170C22×C32—81no—
171C22×C32—81no—
172C22×C32—81no—
173C22×C32#12111yescharacteristic
174C2×C3×D3—22no—
175C2×C3×D3—41no—
176C2×C3×D3—41no—
177C32×C4—21no—
178C32×C4C2×D811yescharacteristic
179C32×C4C2×SD1611yescharacteristic
180C32×C4#13511yescharacteristic
181C32×C4AGL(1,ℤ/8)11yescharacteristic
182C3×Dic3—41no—
183C3×Dic3—81no—
184C2×SD16—61no—
185C2×SD16—61no—
186C2×D8—61no—
187C22×C8—61no—
188C4⋊Q8—31no—
189#127C2×C3×D311yescharacteristic
190C4×D4—31no—
191#107—61no—
192C4⋊C8—31no—
193C4⋊C8C2×C3×D311yescharacteristic
194C4⋊C8C2×C3×D311yescharacteristic
195#102—61no—
196#102—61no—
197C22⋊C8—61no—
198C4×C8—31no—
199C23×C3—42no—
200C23×C3—41no—
201C23×C3—41no—
202C23×C3—61no—
203C22×D3—21no—
204C3×Q8—121no—
205C3×Q8—121no—
206C3×D4—32no—
207C3×D4—41no—
208C3×D4—41no—
209C3×D4—41no—
210C3×D4—41no—
211C3×D4—41no—
212C3×D4—41no—
213C3×D4—41no—
214C3×D4—41no—
215C3×D4—61no—
216C3×D4—81no—
217C3×D4—81no—
218C3×D4—81no—
219C3×D4—81no—
220C3×D4—81no—
221C3×D4—81no—
222C3×D4—82no—
223C2×C3×C4—21no—
224C2×C3×C4—21no—
225C2×C3×C4—21no—
226C2×C3×C4—61no—
227C2×C3×C4—121no—
228C2×C3×C4—121no—
229C2×C3×C4—121no—
230C2×C3×C4#23511yescharacteristic
231C2×C3×C4D3×D411yescharacteristic
232C2×C3×C4D3×D411yescharacteristic
233C2×C3×C4C2×C3×D411yescharacteristic
234C2×C3×C4C2×C3×D411yescharacteristic
235C2×C3×C4C3×#4111yescharacteristic
236C2×Dic3—21no—
237C2×Dic3—41no—
238D12—21no—
239D12C3×SD1612yescomplemented
240C4×D3—41no—
241C4×D3—41no—
242Dic6—41no—
243Dic6—41no—
244C3×C8—32no—
245C3×C8—41no—
246C3×C8—41no—
247C3×C8—41no—
248C3×C8—41no—
249C3×C8—61no—
250C3×C8—81no—
251C3×C8—81no—
252C3×C8—121no—
253C3⋊C8—21no—
254C3⋊C8—41no—
255C3⋊C8C3×D812yescomplemented
256C2×C32—161no—
257C2×C32#45911yescharacteristic
258C2×C32#46511yescharacteristic
259C2×C32#47111yescharacteristic
260C3×D3—42no—
261C2×Q8—61no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—31no—
266C22×C4—61no—
267SD16—122no—
268SD16—122no—
269D8—122no—
270C2×C8—21no—
271C2×C8—21no—
272C2×C8—31no—
273C2×C8—31no—
274C2×C8—61no—
275C2×C8—122no—
276C4⋊C4—31no—
277C4⋊C4—61no—
278C4⋊C4—61no—
279C22⋊C4—61no—
280C42C22×C3×D311yescharacteristic
281C22×C3—21no—
282C22×C3—62no—
283C22×C3—82no—
284C22×C3—82no—
285C22×C3—82no—
286C22×C3—81no—
287C22×C3—81no—
288C22×C3—81no—
289C22×C3—81no—
290C22×C3—81no—
291C22×C3—81no—
292C22×C3—121no—
293C22×C3—121no—
294C22×C3#88411yescharacteristic
295C22×C3C3×#12111yescharacteristic
296C2×D3—22no—
297C2×D3—41no—
298C2×D3—41no—
299C3×C4—21no—
300C3×C4—21no—
301C3×C4—21no—
302C3×C4—21no—
303C3×C4—21no—
304C3×C4—21no—
305C3×C4—41no—
306C3×C4—121no—
307C3×C4—241no—
308C3×C4D3×D811yescharacteristic
309C3×C4#91211yescharacteristic
310C3×C4D3×SD1611yescharacteristic
311C3×C4#91411yescharacteristic
312C3×C4C2×C3×D811yescharacteristic
313C3×C4C2×C3×SD1611yescharacteristic
314C3×C4C3×#13511yescharacteristic
315C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
316Dic3—41no—
317Dic3—81no—
318C32#166511yescharacteristic, complemented, Sylow
319C23—41no—
320C23—61no—
321Q8—121no—
322Q8—121no—
323D4—32no—
324D4—41no—
325D4—41no—
326D4—41no—
327D4—41no—
328D4—61no—
329D4—81no—
330C2×C4—61no—
331C2×C4—121no—
332C2×C4—121no—
333C2×C4—121no—
334C2×C4C3×#23511yescharacteristic
335C2×C4C3×D3×D411yescharacteristic
336C2×C4C3×D3×D411yescharacteristic
337C8—32no—
338C8—41no—
339C8—41no—
340C8—61no—
341C8—121no—
342C2×C3—21no—
343C2×C3—21no—
344C2×C3—21no—
345C2×C3—122no—
346C2×C3—162no—
347C2×C3—161no—
348C2×C3—161no—
349C2×C3#474811yescharacteristic
350C2×C3#477811yescharacteristic
351C2×C3#478611yescharacteristic
352C2×C3C3×#45911yescharacteristic
353C2×C3C3×#46511yescharacteristic
354C2×C3C3×#47111yescharacteristic
355D3—42no—
356C22—62no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22—121no—
361C22—121no—
362C22C3×#88411yescharacteristic
363C4—21no—
364C4—121no—
365C4—241no—
366C4C3×D3×D811yescharacteristic
367C4C3×#91211yescharacteristic
368C4C3×D3×SD1611yescharacteristic
369C4C3×#91411yescharacteristic
370C3—21no—
371C3#6839411yescharacteristic, direct product factor
372C3C3×#166511yescharacteristic, complemented
373C2—122no—
374C2—161no—
375C2C3×#474811yescharacteristic
376C2C3×#477811yescharacteristic
377C2C3×#478611yescharacteristic
subgroupG/H
centerC22×C3#884
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#331C2
socleC22×C32#121
prime radicalC3×#5072C2
hypercenterC3×#331D3
hypocenterC3C3×#1665
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#331

Complements

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

NH ≅ G/Ntype
1. C3×#5076C2semidirect
3. C3×#4846C2semidirect
4. C3×#4834C2semidirect
5. C32×#331C2semidirect
6. C3×#4482C2semidirect
7. C3×#4480C2semidirect
9. #68394C3direct (N × H)
29. #5076C2×C3semidirect
31. #4846C2×C3semidirect
32. #4834C2×C3semidirect
36. C3×#331D3semidirect
37. C3×#331C2×C3semidirect
38. #4482C2×C3semidirect
39. #4480C2×C3semidirect
107. C3×D12SD16semidirect
116. C3×C3⋊C8D8semidirect
123. #331C3×D3semidirect
239. D12C3×SD16semidirect
255. C3⋊C8C3×D8semidirect
318. C32#1665semidirect
371. C3#68394direct (N × H)
372. C3C3×#1665semidirect

Maximal subgroups

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

subgroupindex
C3×#50762
C3×#50722
C3×#48462
C3×#48342
C32×#3312
C3×#44822
C3×#44802
C3×#16653
#683943