Finite Group Databasebeta

← C3×#70731 #11794983

Subgroups — C3×#70731 #11794983

Order 1152.

459 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#430C211yesmaximal, characteristic, complemented
2C3×#5131C211yesmaximal, characteristic
3C3×#5131C211yesmaximal, characteristic
4C2×C3×#823C211yesmaximal, characteristic
5C3×#4559C211yesmaximal, characteristic, complemented
6C3×#4557C211yesmaximal, characteristic, complemented
7C3×#4556C211yesmaximal, characteristic, complemented
8C3×#2081—31nomaximal
9#70731C311yesmaximal, characteristic, direct product factor
10C22×C3×D12C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×C32×M16C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C3×#926C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C32×#108—22no—
18C3×#823—22no—
19C3×#821—22no—
20C3×#821—22no—
21C3×#430—21no—
22C3×#430D311yescharacteristic, complemented
23C3×#430C2×C311yescharacteristic, complemented
24C3×#418—31no—
25C3×#418—31no—
26C2×C3×#100—31no—
27#5131C2×C311yescharacteristic
28#5131C2×C311yescharacteristic
29C2×#823C2×C311yescharacteristic
30C3×#344—31no—
31C3×#344—31no—
32C3×H(3,ℤ/4)—31no—
33#4559C2×C311yescharacteristic, complemented
34#4557C2×C311yescharacteristic, complemented
35#4556C2×C311yescharacteristic, complemented
36C23×C3×D3—21no—
37C22×C32×C4C2311yescharacteristic
38C2×C3×D12—21no—
39C2×C3×D12—21no—
40C2×C3×D12—21no—
41C2×C3×D12—21no—
42C2×C3×D12—21no—
43C2×C3×D12D412yes—
44C32×M16—21no—
45C32×M16—21no—
46C32×M16—21no—
47C32×M16—21no—
48C32×M16—21no—
49C32×M16—21no—
50C2×C32×C8—21no—
51C2×C32×C8—21no—
52C2×C32×C8D412yes—
53C3×#217—21no—
54C3×#217—21no—
55C3×C4⋊Dic3—21no—
56C3×C4⋊Dic3—21no—
57C3×C4×Dic3—21no—
58C3×C4×Dic3—21no—
59C3×#208—21no—
60C3×#208—21no—
61C2×C3×C3⋊C8—21no—
62#2081—31noSylow
63C22×C3×D4—31no—
64C22×D12C22×C311yescharacteristic
65C2×C3×M16—21no—
66C2×C3×M16—21no—
67C2×C3×M16—21no—
68C2×C3×M16—31no—
69C2×C3×M16C2×D311yescharacteristic
70C2×C3×M16C2×D311yescharacteristic
71C2×C3×M16C2×D311yescharacteristic
72C2×C3×M16C22×C311yescharacteristic
73C2×C3×M16C22×C311yescharacteristic
74C2×C3×M16C22×C311yescharacteristic
75C3×#117—31no—
76C3×#117—31no—
77#926C22×C311yescharacteristic
78#926C22×C311yescharacteristic
79C2×#208C22×C311yescharacteristic
80C3×#108—24no—
81C3×#108—22no—
82C3×#108—22no—
83C3×#102—62no—
84C3×#102—62no—
85C3×#100—62no—
86#823—22no—
87#821—22no—
88#821—22no—
89C23×C32#4111yescharacteristic
90C22×C3×D3—22no—
91C22×C3×D3—41no—
92C22×C3×D3—41no—
93C22×C3×D3—82no—
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4#4111yescharacteristic
97C2×C32×C4#4111yescharacteristic
98C2×C32×C4#4111yescharacteristic
99C2×C32×C4#4111yescharacteristic
100C2×C3×Dic3—41no—
101C2×C3×Dic3—41no—
102C3×D12—22no—
103C3×D12—22no—
104C3×D12—41no—
105C3×D12—41no—
106C32×C8—22no—
107C32×C8—41no—
108C32×C8—41no—
109C3×C3⋊C8—41no—
110#430C3×D311yescharacteristic, complemented
111#418—31no—
112#418—31no—
113C2×#100—31no—
114#344—31no—
115#344—31no—
116H(3,ℤ/4)—31no—
117C24×C3—61no—
118C23×D3—21no—
119C2×C3×D4—32no—
120C2×C3×D4—61no—
121C2×C3×D4—61no—
122C2×C3×D4—61no—
123C2×C3×D4—61no—
124C2×C3×D4—61no—
125C22×C3×C4—21no—
126C22×C3×C4C22×D311yescharacteristic
127C22×C3×C4C23×C311yescharacteristic
128C2×D12—21no—
129C2×D12—21no—
130C2×D12—21no—
131C2×D12—21no—
132C2×D12—21no—
133C2×D12C3×D412yes—
134C3×M16—22no—
135C3×M16—22no—
136C3×M16—21no—
137C3×M16—21no—
138C3×M16—21no—
139C3×M16—21no—
140C3×M16—22no—
141C3×M16—22no—
142C3×M16—21no—
143C3×M16—21no—
144C3×M16—21no—
145C3×M16—21no—
146C3×M16—21no—
147C3×M16—21no—
148C3×M16—21no—
149C3×M16—21no—
150C3×M16—41no—
151C3×M16—41no—
152C3×M16—61no—
153C3×M16—61no—
154C2×C3×C8—21no—
155C2×C3×C8—21no—
156C2×C3×C8—21no—
157C2×C3×C8—21no—
158C2×C3×C8—22no—
159C2×C3×C8—41no—
160C2×C3×C8—41no—
161C2×C3×C8—61no—
162C2×C3×C8#6712yes—
163C2×C3×C8C3×D412yes—
164C3×C4⋊C4—61no—
165C3×C4⋊C4—61no—
166C3×C22⋊C4—61no—
167C3×C22⋊C4—61no—
168C3×C42—61no—
169C3×C42—61no—
170#217—21no—
171#217—21no—
172C4⋊Dic3—21no—
173C4⋊Dic3—21no—
174C4×Dic3—21no—
175C4×Dic3—21no—
176#208—21no—
177#208—21no—
178C2×C3⋊C8—21no—
179C22×C32—41no—
180C22×C32#12311yescharacteristic
181C22×C32#12411yescharacteristic
182C22×C32#12611yescharacteristic
183C2×C3×D3—42no—
184C2×C3×D3—82no—
185C2×C3×D3—82no—
186C2×C3×D3—82no—
187C32×C4#12111yescharacteristic
188C32×C4#12311yescharacteristic
189C32×C4#12311yescharacteristic
190C32×C4#12611yescharacteristic
191C3×Dic3—81no—
192C3×Dic3—81no—
193C22×D4—31no—
194C2×M16—31no—
195C2×M16C2×C3×D311yescharacteristic
196C2×M16C2×C3×D311yescharacteristic
197C2×M16C2×C3×D311yescharacteristic
198#117—31no—
199#117—31no—
200#108—22no—
201#102—62no—
202#102—62no—
203#100—62no—
204C23×C3—21no—
205C23×C3—62no—
206C23×C3—121no—
207C23×C3—121no—
208C23×C3—242no—
209C23×C3#23911yescharacteristic
210C23×C3C3×#4111yescharacteristic
211C22×D3—22no—
212C22×D3—41no—
213C22×D3—41no—
214C22×D3—82no—
215C3×D4—62no—
216C3×D4—62no—
217C3×D4—121no—
218C3×D4—121no—
219C2×C3×C4—21no—
220C2×C3×C4—21no—
221C2×C3×C4—21no—
222C2×C3×C4—21no—
223C2×C3×C4—21no—
224C2×C3×C4—21no—
225C2×C3×C4—121no—
226C2×C3×C4—121no—
227C2×C3×C4#23511yescharacteristic
228C2×C3×C4#23511yescharacteristic
229C2×C3×C4D3×D411yescharacteristic
230C2×C3×C4#23711yescharacteristic
231C2×C3×C4#23911yescharacteristic
232C2×C3×C4C2×#6711yescharacteristic
233C2×C3×C4C2×C3×D411yescharacteristic
234C2×C3×C4C2×C3×D411yescharacteristic
235C2×C3×C4C3×#4111yescharacteristic
236C2×C3×C4C3×#4111yescharacteristic
237C2×C3×C4C3×#4111yescharacteristic
238C2×C3×C4C3×#4111yescharacteristic
239C2×Dic3—41no—
240C2×Dic3—41no—
241D12—22no—
242D12—22no—
243D12—41no—
244D12—41no—
245C3×C8—24no—
246C3×C8—22no—
247C3×C8—22no—
248C3×C8—42no—
249C3×C8—42no—
250C3×C8—41no—
251C3×C8—41no—
252C3×C8—41no—
253C3×C8—41no—
254C3×C8—121no—
255C3⋊C8—41no—
256C2×C32—21no—
257C2×C32—21no—
258C2×C32—21no—
259C2×C32#39711yescharacteristic
260C3×D3—82no—
261C24—61no—
262C2×D4—32no—
263C2×D4—61no—
264C2×D4—61no—
265C2×D4—61no—
266C2×D4—61no—
267C2×D4—61no—
268C22×C4C22×C3×D311yescharacteristic
269M16—21no—
270M16—21no—
271M16—21no—
272M16—21no—
273M16—21no—
274M16—21no—
275M16—61no—
276M16—61no—
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—61no—
280C2×C8C3×#6712yes—
281C4⋊C4—61no—
282C4⋊C4—61no—
283C22⋊C4—61no—
284C22⋊C4—61no—
285C42—61no—
286C42—61no—
287C22×C3—21no—
288C22×C3—21no—
289C22×C3—21no—
290C22×C3—41no—
291C22×C3—41no—
292C22×C3—81no—
293C22×C3—122no—
294C22×C3—242no—
295C22×C3—242no—
296C22×C3—242no—
297C22×C3#89411yescharacteristic
298C22×C3#89811yescharacteristic
299C22×C3#94711yescharacteristic
300C22×C3C3×#12311yescharacteristic
301C22×C3C3×#12411yescharacteristic
302C22×C3C3×#12611yescharacteristic
303C2×D3—42no—
304C2×D3—82no—
305C2×D3—82no—
306C2×D3—82no—
307C3×C4—21no—
308C3×C4—21no—
309C3×C4—21no—
310C3×C4—21no—
311C3×C4—241no—
312C3×C4—241no—
313C3×C4#89411yescharacteristic
314C3×C4#89811yescharacteristic
315C3×C4#92911yescharacteristic
316C3×C4#93811yescharacteristic
317C3×C4C3×#12111yescharacteristic
318C3×C4C3×#12311yescharacteristic
319C3×C4C3×#12311yescharacteristic
320C3×C4C3×#12611yescharacteristic
321Dic3—81no—
322Dic3—81no—
323C32#208111yescharacteristic, complemented, Sylow
324C23—62no—
325C23—121no—
326C23—121no—
327C23—242no—
328C23C3×#23911yescharacteristic
329D4—62no—
330D4—62no—
331D4—121no—
332D4—121no—
333C2×C4—121no—
334C2×C4—121no—
335C2×C4C3×#23511yescharacteristic
336C2×C4C3×#23511yescharacteristic
337C2×C4C3×D3×D411yescharacteristic
338C2×C4C3×#23711yescharacteristic
339C2×C4C3×#23911yescharacteristic
340C2×C4C2×C3×#6711yescharacteristic
341C8—22no—
342C8—41no—
343C8—41no—
344C8—121no—
345C2×C3—21no—
346C2×C3—21no—
347C2×C3—21no—
348C2×C3—21no—
349C2×C3—21no—
350C2×C3—21no—
351C2×C3—21no—
352C2×C3—41no—
353C2×C3—41no—
354C2×C3—41no—
355C2×C3—242no—
356C2×C3#499211yescharacteristic
357C2×C3C3×#39711yescharacteristic
358D3—82no—
359C22—41no—
360C22—122no—
361C22—242no—
362C22—242no—
363C22—242no—
364C22C3×#89411yescharacteristic
365C22C3×#89811yescharacteristic
366C22C3×#94711yescharacteristic
367C4—241no—
368C4—241no—
369C4C3×#89411yescharacteristic
370C4C3×#89811yescharacteristic
371C4C3×#92911yescharacteristic
372C4C3×#93811yescharacteristic
373C3—21no—
374C3#7073111yescharacteristic, direct product factor
375C3C3×#208111yescharacteristic, complemented
376C2—21no—
377C2—21no—
378C2—21no—
379C2—242no—
380C2C3×#499211yescharacteristic
subgroupG/H
centerC2×C3#4992
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#430C2
socleC2×C32#397
prime radicalC22×C3×D12C22
hypercenterC3×#430D3
hypocenterC3C3×#2081
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C3×#430

Complements

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

NH ≅ G/Ntype
1. C32×#430C2semidirect
5. C3×#4559C2semidirect
6. C3×#4557C2semidirect
7. C3×#4556C2semidirect
9. #70731C3direct (N × H)
22. C3×#430D3semidirect
23. C3×#430C2×C3semidirect
33. #4559C2×C3semidirect
34. #4557C2×C3semidirect
35. #4556C2×C3semidirect
110. #430C3×D3semidirect
323. C32#2081semidirect
374. C3#70731direct (N × H)
375. C3C3×#2081semidirect

Maximal subgroups

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

subgroupindex
C32×#4302
C3×#51312
C2×C3×#8232
C3×#45592
C3×#45572
C3×#45562
C3×#20813
#707313