Finite Group Databasebeta

← C3×#72076 #11796849

Subgroups — C3×#72076 #11796849

Order 1152.

581 conjugacy classes of subgroups.

The subgroup lattice has 409 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#135C211yesmaximal, characteristic
2C3×#5106C211yesmaximal, characteristic, complemented
3C2×C3×#812C211yesmaximal, characteristic, complemented
4C3×#4566C214yesmaximal, complemented
5C3×#2145—31nomaximal
6#72076C311yesmaximal, characteristic, direct product factor
7C2×C32×#41—21no—
8C32×#135—21no—
9C32×#135—21no—
10C32×#135C412yescomplemented
11C32×#135C2212yes—
12C2×C32×Q16C411yescharacteristic, complemented
13C2×C32×SD16—21no—
14C2×C32×D8C411yescharacteristic, complemented
15C22×C32×C8C2211yescharacteristic
16C3×#926—21no—
17C3×#818—21no—
18C3×#817C2212yescomplemented
19C3×#812—21no—
20C3×#812C2212yescomplemented
21C2×C3×C3⋊C16—21no—
22C2×C3×#135—21no—
23C2×C3×#135D311yescharacteristic
24C2×C3×#135C2×C311yescharacteristic
25C2×C3×M32—31no—
26C3×#427—31no—
27#5106C2×C311yescharacteristic, complemented
28C2×#812C2×C311yescharacteristic, complemented
29C3×#360—34no—
30#4566C2×C314yescomplemented
31C32×#41—22no—
32C32×#41—22no—
33C32×#41—41no—
34C32×#41—41no—
35C2×C32×Q8—21no—
36C2×C32×D4—21no—
37C2×C32×D4—41no—
38C22×C32×C4—41no—
39C22×C32×C4D411yescharacteristic
40C32×Q16—21no—
41C32×Q16C2×C412yes—
42C32×SD16—22no—
43C32×SD16—22no—
44C32×D8—21no—
45C32×D8C2×C412yes—
46C2×C32×C8C2×C411yescharacteristic
47C2×C32×C8C2×C411yescharacteristic
48C2×C32×C8D411yescharacteristic
49C2×C32×C8D411yescharacteristic
50C2×C32×C8D411yescharacteristic
51C2×C32×C8C2311yescharacteristic
52C3×#217—41no—
53C3×C4⋊Dic3—22no—
54C3×C4×Dic3—41no—
55C3×C3⋊C16—22no—
56#2145—31noSylow
57C2×C3×#41—22no—
58C2×C3×#41—21no—
59C2×C3×#41—21no—
60C3×#135—22no—
61C3×#135—22no—
62C3×#135—21no—
63C3×#135—21no—
64C3×#135—21no—
65C3×#135—21no—
66C3×#135—22no—
67C3×#135—22no—
68C3×#135Dic312yescomplemented
69C3×#135C3×C412yescomplemented
70C3×#135C2×D312yes—
71C3×#135C22×C312yes—
72C2×C3×Q16—21no—
73C2×C3×Q16Dic311yescharacteristic, complemented
74C2×C3×Q16C3×C411yescharacteristic, complemented
75C2×C3×SD16—22no—
76C2×C3×SD16—21no—
77C2×C3×SD16—21no—
78C2×C3×D8—21no—
79C2×C3×D8Dic311yescharacteristic, complemented
80C2×C3×D8C3×C411yescharacteristic, complemented
81C22×C3×C8—21no—
82C22×C3×C8C2×D311yescharacteristic
83C22×C3×C8C22×C311yescharacteristic
84C3×#117—61no—
85#926—21no—
86C3×M32—32no—
87C3×M32—61no—
88C2×C3×C16—61no—
89C3×#107—61no—
90C3×#106—32no—
91#818—21no—
92#817C22×C312yescomplemented
93#812—21no—
94#812C22×C312yescomplemented
95C2×C3⋊C16—21no—
96C23×C32—41no—
97C23×C32D811yescharacteristic
98C32×Q8—22no—
99C32×Q8—41no—
100C32×D4—22no—
101C32×D4—42no—
102C32×D4—42no—
103C32×D4—41no—
104C2×C32×C4—41no—
105C2×C32×C4—42no—
106C2×C32×C4—42no—
107C2×C32×C4C22⋊C411yescharacteristic
108C2×C32×C4C22⋊C411yescharacteristic
109C2×C32×C4D811yescharacteristic
110C2×C32×C4SD1611yescharacteristic
111C2×C32×C4SD1611yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C3×Dic3—42no—
114C32×C8C22⋊C411yescharacteristic
115C32×C8C22⋊C411yescharacteristic
116C32×C8C22×C411yescharacteristic
117C32×C8C2×D411yescharacteristic
118C2×#135C3×D311yescharacteristic
119C2×M32—31no—
120#427—31no—
121#360—34no—
122C3×#41—24no—
123C3×#41—24no—
124C3×#41—22no—
125C3×#41—22no—
126C3×#41—22no—
127C3×#41—22no—
128C3×#41—42no—
129C3×#41—42no—
130C3×#41—41no—
131C3×#41—41no—
132C3×#41—41no—
133C3×#41—41no—
134C2×C3×Q8—22no—
135C2×C3×Q8—21no—
136C2×C3×Q8—21no—
137C2×C3×D4—22no—
138C2×C3×D4—21no—
139C2×C3×D4—21no—
140C2×C3×D4—42no—
141C2×C3×D4—41no—
142C2×C3×D4—41no—
143C22×C3×C4—21no—
144C22×C3×C4—42no—
145C22×C3×C4—41no—
146C22×C3×C4—41no—
147C22×C3×C4#6711yescharacteristic
148C22×C3×C4C3×D411yescharacteristic
149C3×Q16—22no—
150C3×Q16—21no—
151C3×Q16—21no—
152C3×Q16—22no—
153C3×Q16C2×Dic312yes—
154C3×Q16C2×C3×C412yes—
155C3×SD16—24no—
156C3×SD16—24no—
157C3×SD16—22no—
158C3×SD16—22no—
159C3×SD16—22no—
160C3×SD16—22no—
161C3×D8—22no—
162C3×D8—21no—
163C3×D8—21no—
164C3×D8—22no—
165C3×D8C2×Dic312yes—
166C3×D8C2×C3×C412yes—
167C2×C3×C8—21no—
168C2×C3×C8—21no—
169C2×C3×C8—21no—
170C2×C3×C8—21no—
171C2×C3×C8—21no—
172C2×C3×C8—21no—
173C2×C3×C8C2×Dic311yescharacteristic
174C2×C3×C8C2×Dic311yescharacteristic
175C2×C3×C8#6711yescharacteristic
176C2×C3×C8#6711yescharacteristic
177C2×C3×C8#6711yescharacteristic
178C2×C3×C8C2×C3×C411yescharacteristic
179C2×C3×C8C2×C3×C411yescharacteristic
180C2×C3×C8C3×D411yescharacteristic
181C2×C3×C8C3×D411yescharacteristic
182C2×C3×C8C3×D411yescharacteristic
183C2×C3×C8C22×D311yescharacteristic
184C2×C3×C8C23×C311yescharacteristic
185C3×C4⋊C4—62no—
186C3×C22⋊C4—121no—
187C3×C42—121no—
188#217—41no—
189C4⋊Dic3—22no—
190C4×Dic3—41no—
191C3×C16—62no—
192C3⋊C16—22no—
193C22×C32—41no—
194C22×C32—42no—
195C22×C32—82no—
196C22×C32#10211yescharacteristic
197C22×C32#10211yescharacteristic
198C22×C32C2×D811yescharacteristic
199C32×C4—42no—
200C32×C4#10211yescharacteristic
201C32×C4#10211yescharacteristic
202C32×C4C2×C22⋊C411yescharacteristic
203C32×C4C2×SD1611yescharacteristic
204C3×Dic3—82no—
205C2×#41—21no—
206#135—21no—
207#135—21no—
208#135C3×Dic312yescomplemented
209#135C2×C3×D312yes—
210C2×Q16C3×Dic311yescharacteristic, complemented
211C2×SD16—21no—
212C2×D8C3×Dic311yescharacteristic, complemented
213C22×C8C2×C3×D311yescharacteristic
214#117—61no—
215M32—32no—
216M32—61no—
217C2×C16—61no—
218#107—61no—
219#106—32no—
220C23×C3—21no—
221C23×C3—42no—
222C23×C3—41no—
223C23×C3—41no—
224C23×C3#21311yescharacteristic
225C23×C3C3×D811yescharacteristic
226C3×Q8—24no—
227C3×Q8—22no—
228C3×Q8—22no—
229C3×Q8—42no—
230C3×Q8—41no—
231C3×Q8—41no—
232C3×D4—24no—
233C3×D4—22no—
234C3×D4—22no—
235C3×D4—42no—
236C3×D4—44no—
237C3×D4—44no—
238C3×D4—42no—
239C3×D4—42no—
240C3×D4—42no—
241C3×D4—42no—
242C3×D4—41no—
243C3×D4—41no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—44no—
251C2×C3×C4—44no—
252C2×C3×C4—42no—
253C2×C3×C4—41no—
254C2×C3×C4—41no—
255C2×C3×C4—42no—
256C2×C3×C4—42no—
257C2×C3×C4—42no—
258C2×C3×C4—42no—
259C2×C3×C4—122no—
260C2×C3×C4#21311yescharacteristic
261C2×C3×C4#21411yescharacteristic
262C2×C3×C4#21411yescharacteristic
263C2×C3×C4#21711yescharacteristic
264C2×C3×C4#21711yescharacteristic
265C2×C3×C4C3×C22⋊C411yescharacteristic
266C2×C3×C4C3×C22⋊C411yescharacteristic
267C2×C3×C4C3×D811yescharacteristic
268C2×C3×C4C3×SD1611yescharacteristic
269C2×C3×C4C3×SD1611yescharacteristic
270C2×C3×C4C2×#6711yescharacteristic
271C2×C3×C4C2×C3×D411yescharacteristic
272C2×Dic3—42no—
273C3×C8—21no—
274C3×C8—21no—
275C3×C8—21no—
276C3×C8—21no—
277C3×C8#21711yescharacteristic
278C3×C8#21711yescharacteristic
279C3×C8C3×C22⋊C411yescharacteristic
280C3×C8C3×C22⋊C411yescharacteristic
281C3×C8C22×Dic311yescharacteristic
282C3×C8C2×#6711yescharacteristic
283C3×C8C22×C3×C411yescharacteristic
284C3×C8C2×C3×D411yescharacteristic
285C2×C32—21no—
286C2×C32—21no—
287C2×C32—21no—
288C2×C32—82no—
289C2×C32C2×#10211yescharacteristic
290#41—22no—
291#41—22no—
292#41—41no—
293#41—41no—
294C2×Q8—21no—
295C2×D4—21no—
296C2×D4—41no—
297C22×C4—41no—
298C22×C4C3×#6711yescharacteristic
299Q16—21no—
300Q16C2×C3×Dic312yes—
301SD16—22no—
302SD16—22no—
303D8—21no—
304D8C2×C3×Dic312yes—
305C2×C8C2×C3×Dic311yescharacteristic
306C2×C8C2×C3×Dic311yescharacteristic
307C2×C8C3×#6711yescharacteristic
308C2×C8C3×#6711yescharacteristic
309C2×C8C3×#6711yescharacteristic
310C2×C8C22×C3×D311yescharacteristic
311C4⋊C4—62no—
312C22⋊C4—121no—
313C42—121no—
314C16—62no—
315C22×C3—21no—
316C22×C3—21no—
317C22×C3—21no—
318C22×C3—41no—
319C22×C3—41no—
320C22×C3—42no—
321C22×C3—44no—
322C22×C3—42no—
323C22×C3—42no—
324C22×C3—84no—
325C22×C3—82no—
326C22×C3—82no—
327C22×C3#83211yescharacteristic
328C22×C3#83211yescharacteristic
329C22×C3C3×#10211yescharacteristic
330C22×C3C3×#10211yescharacteristic
331C22×C3C2×#21311yescharacteristic
332C22×C3C2×C3×D811yescharacteristic
333C3×C4—21no—
334C3×C4—21no—
335C3×C4—21no—
336C3×C4—21no—
337C3×C4—44no—
338C3×C4—42no—
339C3×C4—42no—
340C3×C4—242no—
341C3×C4#83211yescharacteristic
342C3×C4#83211yescharacteristic
343C3×C4C3×#10211yescharacteristic
344C3×C4C3×#10211yescharacteristic
345C3×C4C2×#21411yescharacteristic
346C3×C4C2×#21711yescharacteristic
347C3×C4C2×C3×C22⋊C411yescharacteristic
348C3×C4C2×C3×SD1611yescharacteristic
349Dic3—82no—
350C32#214511yescharacteristic, complemented, Sylow
351C23—41no—
352C23C3×#21311yescharacteristic
353Q8—22no—
354Q8—41no—
355D4—22no—
356D4—42no—
357D4—42no—
358D4—41no—
359C2×C4—41no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—122no—
363C2×C4C3×#21311yescharacteristic
364C2×C4C3×#21411yescharacteristic
365C2×C4C3×#21411yescharacteristic
366C2×C4C3×#21711yescharacteristic
367C2×C4C3×#21711yescharacteristic
368C2×C4C2×C3×#6711yescharacteristic
369C8C3×#21711yescharacteristic
370C8C3×#21711yescharacteristic
371C8C22×C3×Dic311yescharacteristic
372C8C2×C3×#6711yescharacteristic
373C2×C3—22no—
374C2×C3—21no—
375C2×C3—21no—
376C2×C3—21no—
377C2×C3—21no—
378C2×C3—21no—
379C2×C3—21no—
380C2×C3—21no—
381C2×C3—41no—
382C2×C3—41no—
383C2×C3—84no—
384C2×C3—82no—
385C2×C3—82no—
386C2×C3C2×#83211yescharacteristic
387C2×C3C2×C3×#10211yescharacteristic
388C22—41no—
389C22—42no—
390C22—82no—
391C22C3×#83211yescharacteristic
392C22C3×#83211yescharacteristic
393C22C2×C3×#21311yescharacteristic
394C4—42no—
395C4—242no—
396C4C3×#83211yescharacteristic
397C4C3×#83211yescharacteristic
398C4C2×C3×#21411yescharacteristic
399C4C2×C3×#21711yescharacteristic
400C3—21no—
401C3#7207611yescharacteristic, direct product factor
402C3C3×#214511yescharacteristic, complemented
403C2—21no—
404C2—21no—
405C2—21no—
406C2—82no—
407C2C2×C3×#83211yescharacteristic
subgroupG/H
centerC3×C4#832
commutatorC3×C8C22×C3×C4
FrattiniC2×C8C22×C3×D3
Fitting, prime radicalC2×C32×#135C2
socleC2×C32C2×#102
cosocleC2×C3×C8C23×C3
hypercenterC2×C3×#135D3
hypocenterC3C3×#2145
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C3×C4 ◁ C22×C3×C4 ◁ C22×C3×C8 ◁ C2×C3×#135

Complements

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

NH ≅ G/Ntype
2. C3×#5106C2semidirect
3. C2×C3×#812C2semidirect
4. C3×#4566C2semidirect
6. #72076C3direct (N × H)
10. C32×#135C4semidirect
12. C2×C32×Q16C4semidirect
14. C2×C32×D8C4semidirect
18. C3×#817C22semidirect
20. C3×#812C22semidirect
27. #5106C2×C3semidirect
28. C2×#812C2×C3semidirect
30. #4566C2×C3semidirect
68. C3×#135Dic3semidirect
69. C3×#135C3×C4semidirect
73. C2×C3×Q16Dic3semidirect
74. C2×C3×Q16C3×C4semidirect
79. C2×C3×D8Dic3semidirect
80. C2×C3×D8C3×C4semidirect
92. #817C22×C3semidirect
94. #812C22×C3semidirect
208. #135C3×Dic3semidirect
210. C2×Q16C3×Dic3semidirect
212. C2×D8C3×Dic3semidirect
350. C32#2145semidirect
401. C3#72076direct (N × H)
402. C3C3×#2145semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1352
C3×#51062
C2×C3×#8122
C3×#45662
C3×#21453
#720763