Finite Group Databasebeta

← C3×#71075 #11798049

Subgroups — C3×#71075 #11798049

Order 1152.

599 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 599 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D24C211yesmaximal, characteristic, complemented
2C32×#466C211yesmaximal, characteristic, complemented
3C2×C3×#826C212yesmaximal, complemented
4C3×#4549C211yesmaximal, characteristic, complemented
5C3×#4491C212yesmaximal, complemented
6C3×#2184—31nomaximal
7#71075C311yesmaximal, characteristic, direct product factor
8C22×C3×D12—21no—
9C2×C32×D8C2211yescharacteristic, complemented
10C22×C32×C8C2211yescharacteristic
11C32×#121—21no—
12C2×C3×D24—21no—
13C2×C3×D24—24no—
14C2×C3×D24C2212yes—
15C32×#107C2211yescharacteristic, complemented
16C32×#102—21no—
17C3×#826—24no—
18C2×C3×C3⋊C16C2212yescomplemented
19C22×C3×D8—31no—
20C22×D24C2×C311yescharacteristic, complemented
21C2×C3×D16—32no—
22C3×#466—21no—
23C3×#466D311yescharacteristic, complemented
24C3×#466C2×C311yescharacteristic, complemented
25C2×#826C2×C312yescomplemented
26C3×#357—32no—
27C3×C22⋊C16—31no—
28#4549C2×C311yescharacteristic, complemented
29#4491C2×C312yescomplemented
30C23×C3×D3—41no—
31C2×C32×D4—21no—
32C2×C32×D4—41no—
33C22×C32×C4D411yescharacteristic
34C2×C3×D12—24no—
35C2×C3×D12—22no—
36C2×C3×D12—42no—
37C2×C3×D12—41no—
38C32×D8—22no—
39C2×C32×C8—22no—
40C2×C32×C8D411yescharacteristic
41C2×C32×C8C2311yescharacteristic
42C32×C4⋊C4—21no—
43C32×C22⋊C4—41no—
44C3×D24—24no—
45C3×D24—22no—
46C3×D24D414yescomplemented
47C3×C3⋊C16—22no—
48#2184—31noSylow
49C22×C3×D4—61no—
50C22×D12—21no—
51C2×C3×D8—21no—
52C2×C3×D8—32no—
53C2×C3×D8—64no—
54C2×C3×D8—61no—
55C2×C3×D8C2×D311yescharacteristic, complemented
56C2×C3×D8C22×C311yescharacteristic, complemented
57C22×C3×C8—21no—
58C22×C3×C8C2×D311yescharacteristic
59C22×C3×C8C22×C311yescharacteristic
60C3×#121—22no—
61C3×#121—21no—
62C3×#121—21no—
63C2×D24—21no—
64C2×D24—24no—
65C2×D24C22×C312yes—
66C3×D16—64no—
67C2×C3×C16—32no—
68C3×#107—21no—
69C3×#107C2×D311yescharacteristic, complemented
70C3×#107C22×C311yescharacteristic, complemented
71C3×#102—22no—
72C3×#102—21no—
73C3×#102—21no—
74#826—24no—
75C2×C3⋊C16C22×C312yescomplemented
76C23×C32—41no—
77C23×C32D811yescharacteristic
78C22×C3×D3—44no—
79C22×C3×D3—42no—
80C22×C3×D3—82no—
81C22×C3×D3—82no—
82C32×D4—41no—
83C32×D4—41no—
84C32×D4—82no—
85C2×C32×C4—21no—
86C2×C32×C4—21no—
87C2×C32×C4—41no—
88C2×C32×C4D811yescharacteristic
89C2×C32×C4C2×D411yescharacteristic
90C3×D12—24no—
91C3×D12—44no—
92C3×D12—42no—
93C32×C8—21no—
94C32×C8C2×D412yes—
95C22×D8—31no—
96C2×D16—32no—
97#466C3×D311yescharacteristic, complemented
98#357—32no—
99C22⋊C16—31no—
100C24×C3—121no—
101C23×D3—41no—
102C2×C3×D4—22no—
103C2×C3×D4—21no—
104C2×C3×D4—21no—
105C2×C3×D4—42no—
106C2×C3×D4—41no—
107C2×C3×D4—41no—
108C2×C3×D4—64no—
109C2×C3×D4—62no—
110C2×C3×D4—122no—
111C2×C3×D4—121no—
112C22×C3×C4—21no—
113C22×C3×C4#6711yescharacteristic
114C22×C3×C4C3×D411yescharacteristic
115C2×D12—24no—
116C2×D12—22no—
117C2×D12—42no—
118C2×D12—41no—
119C3×D8—22no—
120C3×D8—22no—
121C3×D8—34no—
122C3×D8—42no—
123C3×D8—64no—
124C3×D8—62no—
125C2×C3×C8—22no—
126C2×C3×C8—22no—
127C2×C3×C8—21no—
128C2×C3×C8—21no—
129C2×C3×C8—42no—
130C2×C3×C8#6711yescharacteristic
131C2×C3×C8C3×D411yescharacteristic
132C2×C3×C8C22×D311yescharacteristic
133C2×C3×C8C23×C311yescharacteristic
134C3×C4⋊C4—22no—
135C3×C4⋊C4—21no—
136C3×C4⋊C4—21no—
137C3×C22⋊C4—42no—
138C3×C22⋊C4—41no—
139C3×C22⋊C4—41no—
140D24—24no—
141D24—22no—
142D24C3×D414yescomplemented
143C3×C16—62no—
144C3⋊C16—22no—
145C22×C32—21no—
146C22×C32—21no—
147C22×C32—81no—
148C22×C32—81no—
149C22×C32—81no—
150C22×C32D1612yescomplemented
151C22×C32C2×D811yescharacteristic
152C2×C3×D3—44no—
153C2×C3×D3—88no—
154C2×C3×D3—82no—
155C2×C3×D3—82no—
156C32×C4—21no—
157C32×C4—81no—
158C32×C4#12011yescharacteristic
159C32×C4AGL(1,ℤ/8)11yescharacteristic
160C22×D4—61no—
161C2×D8—32no—
162C2×D8—64no—
163C2×D8—61no—
164C2×D8C2×C3×D311yescharacteristic, complemented
165C22×C8C2×C3×D311yescharacteristic
166#121—21no—
167D16—64no—
168C2×C16—32no—
169#107C2×C3×D311yescharacteristic, complemented
170#102—21no—
171C23×C3—21no—
172C23×C3—42no—
173C23×C3—41no—
174C23×C3—41no—
175C23×C3—124no—
176C23×C3—122no—
177C23×C3—242no—
178C23×C3—242no—
179C23×C3#21311yescharacteristic
180C23×C3C3×D811yescharacteristic
181C22×D3—44no—
182C22×D3—42no—
183C22×D3—82no—
184C22×D3—82no—
185C3×D4—42no—
186C3×D4—42no—
187C3×D4—41no—
188C3×D4—41no—
189C3×D4—41no—
190C3×D4—41no—
191C3×D4—64no—
192C3×D4—84no—
193C3×D4—82no—
194C3×D4—82no—
195C3×D4—124no—
196C3×D4—122no—
197C2×C3×C4—21no—
198C2×C3×C4—21no—
199C2×C3×C4—21no—
200C2×C3×C4—21no—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4—41no—
204C2×C3×C4—41no—
205C2×C3×C4—42no—
206C2×C3×C4—41no—
207C2×C3×C4—41no—
208C2×C3×C4#21311yescharacteristic
209C2×C3×C4C3×D811yescharacteristic
210C2×C3×C4C2×#6711yescharacteristic
211C2×C3×C4C2×C3×D411yescharacteristic
212D12—24no—
213D12—44no—
214D12—42no—
215C3×C8—21no—
216C3×C8—21no—
217C3×C8—22no—
218C3×C8—41no—
219C3×C8D3×D412yes—
220C3×C8C2×C3×D412yes—
221C2×C32—22no—
222C2×C32—161no—
223C2×C32#44711yescharacteristic
224C2×C32C2×D1611yescharacteristic
225C2×C32#50911yescharacteristic
226C3×D3—84no—
227C24—121no—
228C2×D4—21no—
229C2×D4—41no—
230C2×D4—64no—
231C2×D4—62no—
232C2×D4—122no—
233C2×D4—121no—
234C22×C4C3×#6711yescharacteristic
235D8—22no—
236D8—34no—
237D8—64no—
238D8—62no—
239C2×C8—22no—
240C2×C8C3×#6711yescharacteristic
241C2×C8C22×C3×D311yescharacteristic
242C4⋊C4—21no—
243C22⋊C4—41no—
244C16—62no—
245C22×C3—21no—
246C22×C3—21no—
247C22×C3—21no—
248C22×C3—21no—
249C22×C3—21no—
250C22×C3—22no—
251C22×C3—41no—
252C22×C3—41no—
253C22×C3—82no—
254C22×C3—82no—
255C22×C3—82no—
256C22×C3—81no—
257C22×C3—81no—
258C22×C3—81no—
259C22×C3—81no—
260C22×C3—81no—
261C22×C3—81no—
262C22×C3—124no—
263C22×C3—248no—
264C22×C3—242no—
265C22×C3—242no—
266C22×C3#82612yescomplemented
267C22×C3C3×D1612yescomplemented
268C22×C3C2×#21311yescharacteristic
269C22×C3C2×C3×D811yescharacteristic
270C2×D3—44no—
271C2×D3—88no—
272C2×D3—82no—
273C2×D3—82no—
274C3×C4—21no—
275C3×C4—21no—
276C3×C4—21no—
277C3×C4—21no—
278C3×C4—41no—
279C3×C4—82no—
280C3×C4—81no—
281C3×C4—81no—
282C3×C4#93711yescharacteristic
283C3×C4#94911yescharacteristic
284C3×C4C3×#12011yescharacteristic
285C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
286C32#218411yescharacteristic, complemented, Sylow
287C23—41no—
288C23—124no—
289C23—122no—
290C23—242no—
291C23—242no—
292C23C3×#21311yescharacteristic
293D4—41no—
294D4—41no—
295D4—64no—
296D4—82no—
297D4—124no—
298D4—122no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—41no—
302C2×C4C3×#21311yescharacteristic
303C2×C4C2×C3×#6711yescharacteristic
304C8—21no—
305C8C3×D3×D412yes—
306C2×C3—22no—
307C2×C3—22no—
308C2×C3—21no—
309C2×C3—21no—
310C2×C3—21no—
311C2×C3—42no—
312C2×C3—162no—
313C2×C3—161no—
314C2×C3—161no—
315C2×C3—244no—
316C2×C3#503611yescharacteristic
317C2×C3C2×#82611yescharacteristic
318C2×C3#519311yescharacteristic
319C2×C3C3×#44711yescharacteristic
320C2×C3C2×C3×D1611yescharacteristic
321C2×C3C3×#50911yescharacteristic
322D3—84no—
323C22—21no—
324C22—21no—
325C22—81no—
326C22—81no—
327C22—81no—
328C22—124no—
329C22—248no—
330C22—242no—
331C22—242no—
332C22C3×#82612yescomplemented
333C22C2×C3×#21311yescharacteristic
334C4—21no—
335C4—81no—
336C4C3×#93711yescharacteristic
337C4C3×#94911yescharacteristic
338C3—21no—
339C3#7107511yescharacteristic, direct product factor
340C3C3×#218411yescharacteristic, complemented
341C2—22no—
342C2—161no—
343C2—244no—
344C2C3×#503611yescharacteristic
345C2C2×C3×#82611yescharacteristic
346C2C3×#519311yescharacteristic
subgroupG/H
centerC22×C3C2×#213
commutator, cosocleC2×C3×C8C23×C3
FrattiniC2×C8C22×C3×D3
FittingC32×#466C2
socleC22×C32C2×D8
hypercenterC3×#466D3
hypocenterC3C3×#2184
LCSG ▷ C2×C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C22×C3×C8 ◁ C3×#466

Complements

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

NH ≅ G/Ntype
1. C22×C3×D24C2semidirect
2. C32×#466C2semidirect
3. C2×C3×#826C2semidirect
4. C3×#4549C2semidirect
5. C3×#4491C2semidirect
7. #71075C3direct (N × H)
9. C2×C32×D8C22semidirect
15. C32×#107C22semidirect
18. C2×C3×C3⋊C16C22semidirect
20. C22×D24C2×C3semidirect
23. C3×#466D3semidirect
24. C3×#466C2×C3semidirect
25. C2×#826C2×C3semidirect
28. #4549C2×C3semidirect
29. #4491C2×C3semidirect
46. C3×D24D4semidirect
55. C2×C3×D8C2×D3semidirect
56. C2×C3×D8C22×C3semidirect
69. C3×#107C2×D3semidirect
70. C3×#107C22×C3semidirect
75. C2×C3⋊C16C22×C3semidirect
97. #466C3×D3semidirect
142. D24C3×D4semidirect
150. C22×C32D16semidirect
164. C2×D8C2×C3×D3semidirect
169. #107C2×C3×D3semidirect
266. C22×C3#826semidirect
267. C22×C3C3×D16semidirect
286. C32#2184semidirect
332. C22C3×#826semidirect
339. C3#71075direct (N × H)
340. C3C3×#2184semidirect

Maximal subgroups

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

subgroupindex
C22×C3×D242
C32×#4662
C2×C3×#8262
C3×#45492
C3×#44912
C3×#21843
#710753