Finite Group Databasebeta

← C3×#69256 #11796931

Subgroups — C3×#69256 #11796931

Order 1152.

471 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#912C211yesmaximal, characteristic
2C3×D3×M32C211yesmaximal, characteristic, complemented
3C3×D3×#108C211yesmaximal, characteristic, complemented
4C32×#361C211yesmaximal, characteristic, complemented
5C3×#4563C211yesmaximal, characteristic, complemented
6C3×#4517C211yesmaximal, characteristic, complemented
7C3×#4496C211yesmaximal, characteristic, complemented
8C3×#2148—31nomaximal
9#69256C311yesmaximal, characteristic, direct product factor
10C2×C3×#237—21no—
11C2×C32×D8C2211yescharacteristic
12C2×C3×#214—21no—
13C3×#912—21no—
14C3×#912—21no—
15C3×#912C412yes—
16C3×#912C412yes—
17C3×D3×M16—21no—
18C2×C3×Dic12C2211yescharacteristic
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×#912C2×C311yescharacteristic
29C2×C3×M32—31no—
30C2×C3×#108—31no—
31D3×M32C2×C311yescharacteristic, complemented
32D3×#108C2×C311yescharacteristic, complemented
33C3×#362—31no—
34C3×#362—31no—
35C3×#361—21no—
36C3×#361—31no—
37C3×#361D311yescharacteristic, complemented
38C3×#361C2×C311yescharacteristic, complemented
39#4563C2×C311yescharacteristic, complemented
40#4517C2×C311yescharacteristic, complemented
41#4496C2×C311yescharacteristic, complemented
42C2×C32×D4—21no—
43C2×C3×#67—41no—
44C22×C3×Dic3—41no—
45C3×#237—22no—
46C3×#237—22no—
47C3×#237—41no—
48C3×#237—41no—
49C2×C3×C4×D3D411yescharacteristic
50C2×C3×Dic6—21no—
51C32×D8—21no—
52C32×D8C2×C412yes—
53C32×M16—21no—
54C2×C32×C8C2311yescharacteristic
55C3×#214—22no—
56C3×#214—22no—
57C3×#208—21no—
58C2×C3×C3⋊C8D411yescharacteristic
59C3×Dic12—21no—
60C3×Dic12C2×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×#237—21no—
72C3×#135—32no—
73C3×#135—32no—
74C3×#135—61no—
75C3×#135—61no—
76C2×C3×Q16—31no—
77C2×C3×SD16—61no—
78C2×C3×D8—21no—
79C2×C3×D8C2×D311yescharacteristic
80C2×C3×D8C22×C311yescharacteristic
81C2×C3×M16—61no—
82C22×C3×C8—31no—
83C2×#214—21no—
84#912—21no—
85#912—21no—
86#912C3×C412yes—
87#912C3×C412yes—
88D3×M16—21no—
89C2×Dic12C22×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—
107C23×C32—41no—
108C22×C3×D3SD1611yescharacteristic
109C32×D4—22no—
110C32×D4—41no—
111C2×C32×C4C2×D411yescharacteristic
112C3×#67—42no—
113C3×#67—42no—
114C2×C3×Dic3—41no—
115C2×C3×Dic3—42no—
116C2×C3×Dic3—42no—
117C2×C3×Dic3SD1611yescharacteristic
118C3×C4×D3C22⋊C411yescharacteristic
119C3×C4×D3C22⋊C411yescharacteristic
120C3×C4×D3D811yescharacteristic
121C3×C4×D3D811yescharacteristic
122C3×Dic6—22no—
123C3×Dic6—41no—
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#362—31no—
135#361—31no—
136#361C3×D311yescharacteristic, complemented
137C3×#41—62no—
138C3×#41—62no—
139C3×#41—121no—
140C3×#41—121no—
141C2×C3×Q8—61no—
142C2×C3×D4—21no—
143C2×C3×D4—21no—
144C2×C3×D4—41no—
145C2×C3×D4—121no—
146C22×C3×C4—31no—
147C22×C3×C4—121no—
148C2×#67—41no—
149C22×Dic3—41no—
150#237—22no—
151#237—22no—
152#237—41no—
153#237—41no—
154C2×C4×D3C3×D411yescharacteristic
155C2×Dic6—21no—
156C3×Q16—32no—
157C3×Q16—61no—
158C3×SD16—62no—
159C3×SD16—62no—
160C3×D8—21no—
161C3×D8—21no—
162C3×D8—22no—
163C3×D8—41no—
164C3×D8C4×D312yes—
165C3×D8C2×C3×C412yes—
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#214—22no—
181#214—22no—
182#208—21no—
183C2×C3⋊C8C3×D411yescharacteristic
184Dic12—21no—
185Dic12C2×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×C32—42no—
198C22×C32—82no—
199C22×C32C2×SD1611yescharacteristic
200C2×C3×D3—41no—
201C2×C3×D3#10211yescharacteristic
202C2×C3×D3#10211yescharacteristic
203C32×C4C2×C22⋊C411yescharacteristic
204C32×C4C2×D811yescharacteristic
205C3×Dic3—42no—
206C3×Dic3#10211yescharacteristic
207C3×Dic3#10211yescharacteristic
208C2×#41—61no—
209#135—32no—
210#135—32no—
211#135—61no—
212#135—61no—
213C2×Q16—31no—
214C2×SD16—61no—
215C2×D8C2×C3×D311yescharacteristic
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—41no—
227C23×C3—41no—
228C23×C3—81no—
229C22×D3C3×SD1611yescharacteristic
230C3×Q8—62no—
231C3×Q8—121no—
232C3×D4—22no—
233C3×D4—22no—
234C3×D4—42no—
235C3×D4—41no—
236C3×D4—41no—
237C3×D4—81no—
238C3×D4—122no—
239C3×D4—122no—
240C2×C3×C4—21no—
241C2×C3×C4—31no—
242C2×C3×C4—31no—
243C2×C3×C4—31no—
244C2×C3×C4—31no—
245C2×C3×C4—31no—
246C2×C3×C4—122no—
247C2×C3×C4—122no—
248C2×C3×C4—121no—
249C2×C3×C4D3×D411yescharacteristic
250C2×C3×C4C2×C3×D411yescharacteristic
251#67—42no—
252#67—42no—
253C2×Dic3—41no—
254C2×Dic3—42no—
255C2×Dic3—42no—
256C2×Dic3C3×SD1611yescharacteristic
257C4×D3C3×C22⋊C411yescharacteristic
258C4×D3C3×C22⋊C411yescharacteristic
259C4×D3C3×D811yescharacteristic
260C4×D3C3×D811yescharacteristic
261Dic6—22no—
262Dic6—41no—
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×C32—82no—
280C2×C32C2×#10211yescharacteristic
281C3×D3—21no—
282C3×D3—21no—
283#41—62no—
284#41—62no—
285#41—121no—
286#41—121no—
287C2×Q8—61no—
288C2×D4—21no—
289C2×D4—121no—
290C22×C4—31no—
291C22×C4—121no—
292Q16—32no—
293Q16—61no—
294SD16—62no—
295SD16—62no—
296D8—21no—
297D8C3×C4×D312yes—
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—42no—
314C22×C3—42no—
315C22×C3—82no—
316C22×C3—82no—
317C22×C3—82no—
318C22×C3—121no—
319C22×C3—162no—
320C22×C3D3×SD1611yescharacteristic
321C22×C3C2×C3×SD1611yescharacteristic
322C2×D3—41no—
323C2×D3C3×#10211yescharacteristic
324C2×D3C3×#10211yescharacteristic
325C3×C4—21no—
326C3×C4—21no—
327C3×C4—31no—
328C3×C4—31no—
329C3×C4—122no—
330C3×C4D3×C22⋊C411yescharacteristic
331C3×C4D3×D811yescharacteristic
332C3×C4C2×C3×C22⋊C411yescharacteristic
333C3×C4C2×C3×D811yescharacteristic
334Dic3—42no—
335Dic3C3×#10211yescharacteristic
336Dic3C3×#10211yescharacteristic
337C32#214811yescharacteristic, complemented, Sylow
338C23—31no—
339C23—41no—
340Q8—62no—
341Q8—121no—
342D4—22no—
343D4—41no—
344D4—122no—
345D4—122no—
346C2×C4—31no—
347C2×C4—31no—
348C2×C4—31no—
349C2×C4—31no—
350C2×C4—31no—
351C2×C4—122no—
352C2×C4—122no—
353C2×C4—121no—
354C2×C4C3×D3×D411yescharacteristic
355C8—31no—
356C8—31no—
357C8—41no—
358C8—121no—
359C8C2×C3×C4×D311yescharacteristic
360C8C3×D3×D411yescharacteristic
361C2×C3—21no—
362C2×C3—21no—
363C2×C3—21no—
364C2×C3—41no—
365C2×C3—61no—
366C2×C3—61no—
367C2×C3—82no—
368C2×C3—82no—
369C2×C3—162no—
370C2×C3D3×#10211yescharacteristic
371C2×C3C2×C3×#10211yescharacteristic
372D3—21no—
373D3—21no—
374C22—31no—
375C22—31no—
376C22—42no—
377C22—82no—
378C22—121no—
379C22C3×D3×SD1611yescharacteristic
380C4—31no—
381C4—31no—
382C4—122no—
383C4C3×D3×C22⋊C411yescharacteristic
384C4C3×D3×D811yescharacteristic
385C3—21no—
386C3#6925611yescharacteristic, direct product factor
387C3C3×#214811yescharacteristic, complemented
388C2—21no—
389C2—61no—
390C2—61no—
391C2—82no—
392C2C3×D3×#10211yescharacteristic
subgroupG/H
centerC2×C3D3×#102
commutatorC3×C8C22×C3×C4
FrattiniC2×C8C22×C3×D3
FittingC32×#361C2
socleC2×C32C2×#102
prime radicalC2×C3×#912C2
cosocleC2×C3×C8C23×C3
hypercenterC3×#361D3
hypocenterC3C3×#2148
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C2×C3×C8 ◁ C3×#361

Complements

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

NH ≅ G/Ntype
2. C3×D3×M32C2semidirect
3. C3×D3×#108C2semidirect
4. C32×#361C2semidirect
5. C3×#4563C2semidirect
6. C3×#4517C2semidirect
7. C3×#4496C2semidirect
9. #69256C3direct (N × H)
31. D3×M32C2×C3semidirect
32. D3×#108C2×C3semidirect
37. C3×#361D3semidirect
38. C3×#361C2×C3semidirect
39. #4563C2×C3semidirect
40. #4517C2×C3semidirect
41. #4496C2×C3semidirect
136. #361C3×D3semidirect
337. C32#2148semidirect
386. C3#69256direct (N × H)
387. C3C3×#2148semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9122
C3×D3×M322
C3×D3×#1082
C32×#3612
C3×#45632
C3×#45172
C3×#44962
C3×#21483
#692563