Finite Group Databasebeta

← C3×#69266 #11796937

Subgroups — C3×#69266 #11796937

Order 1152.

467 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#919C211yesmaximal, characteristic
2C3×D3×M32C211yesmaximal, characteristic, complemented
3C3×D3×#108C211yesmaximal, characteristic, complemented
4C32×#362C211yesmaximal, characteristic, complemented
5C3×#4565C211yesmaximal, characteristic, complemented
6C3×#4516C211yesmaximal, characteristic, complemented
7C3×#4495C211yesmaximal, characteristic, complemented
8C3×#2148—31nomaximal
9#69266C311yesmaximal, characteristic, direct product factor
10C2×C3×#239—21no—
11C2×C32×Q16C2211yescharacteristic
12C2×C3×#215—21no—
13C3×#919—21no—
14C3×#919—21no—
15C3×#919C412yes—
16C3×#919C412yes—
17C3×D3×M16—21no—
18C2×C3×D24C2211yescharacteristic
19C2×C3×D3×C8C2211yescharacteristic
20C32×M32C2211yescharacteristic
21C32×#108C2211yescharacteristic
22C3×#822—21no—
23C3×#819C2211yescharacteristic
24C3×#812C2211yescharacteristic
25C3×#798—21no—
26C3×D3×C16—21no—
27C2×C3×#135—31no—
28C2×#919C2×C311yescharacteristic
29C2×C3×M32—31no—
30C2×C3×#108—31no—
31D3×M32C2×C311yescharacteristic, complemented
32D3×#108C2×C311yescharacteristic, complemented
33C3×#362—21no—
34C3×#362—31no—
35C3×#362D311yescharacteristic, complemented
36C3×#362C2×C311yescharacteristic, complemented
37C3×#361—31no—
38C3×#361—31no—
39#4565C2×C311yescharacteristic, complemented
40#4516C2×C311yescharacteristic, complemented
41#4495C2×C311yescharacteristic, complemented
42C2×C32×Q8—21no—
43C3×#239—22no—
44C3×#239—22no—
45C3×#239—41no—
46C3×#239—41no—
47C2×C3×D12—21no—
48C2×C3×D12—41no—
49C2×C3×C4×D3—41no—
50C2×C3×C4×D3D411yescharacteristic
51C32×Q16—21no—
52C32×Q16C2×C412yes—
53C32×M16—21no—
54C2×C32×C8C2311yescharacteristic
55C3×#215—22no—
56C3×#215—22no—
57C3×#208—21no—
58C2×C3×C3⋊C8D411yescharacteristic
59C3×D24—21no—
60C3×D24C2×C412yes—
61C3×ΓL(1,𝔽25)—41no—
62C3×D3×C8—41no—
63C3×D3×C8C2×C411yescharacteristic
64C3×D3×C8C2×C411yescharacteristic
65C3×D3×C8D411yescharacteristic
66C3×D3×C8D411yescharacteristic
67C32×C16—21no—
68C3×C3⋊C16—21no—
69#2148—31noSylow
70C2×C3×#41—61no—
71C2×#239—21no—
72C3×#135—32no—
73C3×#135—32no—
74C3×#135—61no—
75C3×#135—61no—
76C2×C3×Q16—21no—
77C2×C3×Q16C2×D311yescharacteristic
78C2×C3×Q16C22×C311yescharacteristic
79C2×C3×SD16—61no—
80C2×C3×D8—31no—
81C2×C3×M16—61no—
82C22×C3×C8—31no—
83C2×#215—21no—
84#919—21no—
85#919—21no—
86#919C3×C412yes—
87#919C3×C412yes—
88D3×M16—21no—
89C2×D24C22×C311yescharacteristic
90C2×D3×C8C22×C311yescharacteristic
91C3×M32—21no—
92C3×M32—31no—
93C3×M32—61no—
94C3×M32C2×D311yescharacteristic
95C3×M32C22×C311yescharacteristic
96C2×C3×C16—61no—
97C3×#108—21no—
98C3×#108—31no—
99C3×#108—61no—
100C3×#108C2×D311yescharacteristic
101C3×#108C22×C311yescharacteristic
102#822—21no—
103#819C22×C311yescharacteristic
104#812C22×C311yescharacteristic
105#798—21no—
106D3×C16—21no—
107C22×C3×D3—41no—
108C22×C3×D3SD1611yescharacteristic
109C32×Q8—22no—
110C32×Q8—41no—
111C2×C32×C4—41no—
112C2×C32×C4C2×D411yescharacteristic
113C2×C3×Dic3SD1611yescharacteristic
114C3×D12—22no—
115C3×D12—42no—
116C3×D12—42no—
117C3×D12—41no—
118C3×C4×D3—42no—
119C3×C4×D3—42no—
120C3×C4×D3C22⋊C411yescharacteristic
121C3×C4×D3C22⋊C411yescharacteristic
122C3×C4×D3D811yescharacteristic
123C3×C4×D3D811yescharacteristic
124C32×C8—41no—
125C32×C8C22×C411yescharacteristic
126C32×C8C2×D411yescharacteristic
127C3×C3⋊C8—41no—
128C3×C3⋊C8C22⋊C411yescharacteristic
129C3×C3⋊C8C22⋊C411yescharacteristic
130C2×#135—31no—
131C2×M32—31no—
132C2×#108—31no—
133#362—31no—
134#362C3×D311yescharacteristic, complemented
135#361—31no—
136#361—31no—
137C3×#41—62no—
138C3×#41—62no—
139C3×#41—121no—
140C3×#41—121no—
141C2×C3×Q8—21no—
142C2×C3×Q8—21no—
143C2×C3×Q8—41no—
144C2×C3×D4—61no—
145C2×C3×D4—121no—
146C22×C3×C4—31no—
147C22×C3×C4—121no—
148#239—22no—
149#239—22no—
150#239—41no—
151#239—41no—
152C2×D12—21no—
153C2×D12—41no—
154C2×C4×D3—41no—
155C2×C4×D3C3×D411yescharacteristic
156C3×Q16—21no—
157C3×Q16—21no—
158C3×Q16—22no—
159C3×Q16—41no—
160C3×Q16C4×D312yes—
161C3×Q16C2×C3×C412yes—
162C3×SD16—62no—
163C3×SD16—62no—
164C3×D8—32no—
165C3×D8—61no—
166C3×M16—21no—
167C3×M16—21no—
168C3×M16—41no—
169C3×M16—61no—
170C3×M16—121no—
171C2×C3×C8—21no—
172C2×C3×C8—31no—
173C2×C3×C8—31no—
174C2×C3×C8—31no—
175C2×C3×C8—31no—
176C2×C3×C8—31no—
177C2×C3×C8—121no—
178C2×C3×C8C22×D311yescharacteristic
179C2×C3×C8C23×C311yescharacteristic
180#215—22no—
181#215—22no—
182#208—21no—
183C2×C3⋊C8C3×D411yescharacteristic
184D24—21no—
185D24C2×C3×C412yes—
186ΓL(1,𝔽25)—41no—
187D3×C8—41no—
188D3×C8C2×C3×C411yescharacteristic
189D3×C8C2×C3×C411yescharacteristic
190D3×C8C3×D411yescharacteristic
191D3×C8C3×D411yescharacteristic
192C3×C16—21no—
193C3×C16—21no—
194C3×C16—41no—
195C3×C16—61no—
196C3⋊C16—21no—
197C22×C32C2×SD1611yescharacteristic
198C2×C3×D3—41no—
199C2×C3×D3—42no—
200C2×C3×D3—82no—
201C2×C3×D3#10211yescharacteristic
202C2×C3×D3#10211yescharacteristic
203C32×C4—42no—
204C32×C4C2×C22⋊C411yescharacteristic
205C32×C4C2×D811yescharacteristic
206C3×Dic3#10211yescharacteristic
207C3×Dic3#10211yescharacteristic
208C2×#41—61no—
209#135—32no—
210#135—32no—
211#135—61no—
212#135—61no—
213C2×Q16C2×C3×D311yescharacteristic
214C2×SD16—61no—
215C2×D8—31no—
216C2×M16—61no—
217C22×C8—31no—
218M32—31no—
219M32—61no—
220M32C2×C3×D311yescharacteristic
221C2×C16—61no—
222#108—31no—
223#108—61no—
224#108C2×C3×D311yescharacteristic
225C23×C3—31no—
226C23×C3—121no—
227C22×D3—41no—
228C22×D3C3×SD1611yescharacteristic
229C3×Q8—22no—
230C3×Q8—22no—
231C3×Q8—42no—
232C3×Q8—41no—
233C3×Q8—41no—
234C3×Q8—81no—
235C3×D4—62no—
236C3×D4—122no—
237C3×D4—122no—
238C3×D4—121no—
239C2×C3×C4—21no—
240C2×C3×C4—31no—
241C2×C3×C4—31no—
242C2×C3×C4—31no—
243C2×C3×C4—31no—
244C2×C3×C4—31no—
245C2×C3×C4—41no—
246C2×C3×C4—41no—
247C2×C3×C4—81no—
248C2×C3×C4—122no—
249C2×C3×C4—122no—
250C2×C3×C4D3×D411yescharacteristic
251C2×C3×C4C2×C3×D411yescharacteristic
252C2×Dic3C3×SD1611yescharacteristic
253D12—22no—
254D12—42no—
255D12—42no—
256D12—41no—
257C4×D3—42no—
258C4×D3—42no—
259C4×D3C3×C22⋊C411yescharacteristic
260C4×D3C3×C22⋊C411yescharacteristic
261C4×D3C3×D811yescharacteristic
262C4×D3C3×D811yescharacteristic
263C3×C8—21no—
264C3×C8—21no—
265C3×C8—31no—
266C3×C8—31no—
267C3×C8—41no—
268C3×C8—41no—
269C3×C8—81no—
270C3×C8—121no—
271C3×C8C2×C4×D311yescharacteristic
272C3×C8D3×D411yescharacteristic
273C3×C8C22×C3×C411yescharacteristic
274C3×C8C2×C3×D411yescharacteristic
275C3⋊C8—41no—
276C3⋊C8C3×C22⋊C411yescharacteristic
277C3⋊C8C3×C22⋊C411yescharacteristic
278C2×C32—21no—
279C2×C32C2×#10211yescharacteristic
280C3×D3—21no—
281C3×D3—21no—
282C3×D3—82no—
283#41—62no—
284#41—62no—
285#41—121no—
286#41—121no—
287C2×Q8—21no—
288C2×D4—61no—
289C2×D4—121no—
290C22×C4—31no—
291C22×C4—121no—
292Q16—21no—
293Q16C3×C4×D312yes—
294SD16—62no—
295SD16—62no—
296D8—32no—
297D8—61no—
298M16—21no—
299M16—61no—
300M16—121no—
301C2×C8—31no—
302C2×C8—31no—
303C2×C8—31no—
304C2×C8—31no—
305C2×C8—31no—
306C2×C8—121no—
307C2×C8C22×C3×D311yescharacteristic
308C16—21no—
309C16—61no—
310C22×C3—21no—
311C22×C3—31no—
312C22×C3—31no—
313C22×C3—121no—
314C22×C3—122no—
315C22×C3—242no—
316C22×C3D3×SD1611yescharacteristic
317C22×C3C2×C3×SD1611yescharacteristic
318C2×D3—41no—
319C2×D3—42no—
320C2×D3—82no—
321C2×D3C3×#10211yescharacteristic
322C2×D3C3×#10211yescharacteristic
323C3×C4—21no—
324C3×C4—21no—
325C3×C4—31no—
326C3×C4—31no—
327C3×C4—42no—
328C3×C4—42no—
329C3×C4—82no—
330C3×C4D3×C22⋊C411yescharacteristic
331C3×C4D3×D811yescharacteristic
332C3×C4C2×C3×C22⋊C411yescharacteristic
333C3×C4C2×C3×D811yescharacteristic
334Dic3C3×#10211yescharacteristic
335Dic3C3×#10211yescharacteristic
336C32#214811yescharacteristic, complemented, Sylow
337C23—31no—
338C23—121no—
339Q8—22no—
340Q8—41no—
341D4—62no—
342D4—122no—
343D4—122no—
344D4—121no—
345C2×C4—31no—
346C2×C4—31no—
347C2×C4—31no—
348C2×C4—31no—
349C2×C4—31no—
350C2×C4—41no—
351C2×C4—122no—
352C2×C4—122no—
353C2×C4C3×D3×D411yescharacteristic
354C8—31no—
355C8—31no—
356C8—41no—
357C8—121no—
358C8C2×C3×C4×D311yescharacteristic
359C8C3×D3×D411yescharacteristic
360C2×C3—21no—
361C2×C3—21no—
362C2×C3—21no—
363C2×C3—41no—
364C2×C3—61no—
365C2×C3—61no—
366C2×C3—242no—
367C2×C3D3×#10211yescharacteristic
368C2×C3C2×C3×#10211yescharacteristic
369D3—21no—
370D3—21no—
371D3—82no—
372C22—31no—
373C22—31no—
374C22—121no—
375C22—122no—
376C22—242no—
377C22C3×D3×SD1611yescharacteristic
378C4—31no—
379C4—31no—
380C4—42no—
381C4C3×D3×C22⋊C411yescharacteristic
382C4C3×D3×D811yescharacteristic
383C3—21no—
384C3#6926611yescharacteristic, direct product factor
385C3C3×#214811yescharacteristic, complemented
386C2—21no—
387C2—61no—
388C2—61no—
389C2—242no—
390C2C3×D3×#10211yescharacteristic
subgroupG/H
centerC2×C3D3×#102
commutatorC3×C8C22×C3×C4
FrattiniC2×C8C22×C3×D3
FittingC32×#362C2
socleC2×C32C2×#102
prime radicalC2×C3×#919C2
cosocleC2×C3×C8C23×C3
hypercenterC3×#362D3
hypocenterC3C3×#2148
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C2×C3×C8 ◁ C3×#362

Complements

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

NH ≅ G/Ntype
2. C3×D3×M32C2semidirect
3. C3×D3×#108C2semidirect
4. C32×#362C2semidirect
5. C3×#4565C2semidirect
6. C3×#4516C2semidirect
7. C3×#4495C2semidirect
9. #69266C3direct (N × H)
31. D3×M32C2×C3semidirect
32. D3×#108C2×C3semidirect
35. C3×#362D3semidirect
36. C3×#362C2×C3semidirect
39. #4565C2×C3semidirect
40. #4516C2×C3semidirect
41. #4495C2×C3semidirect
134. #362C3×D3semidirect
336. C32#2148semidirect
384. C3#69266direct (N × H)
385. C3C3×#2148semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9192
C3×D3×M322
C3×D3×#1082
C32×#3622
C3×#45652
C3×#45162
C3×#44952
C3×#21483
#692663