Finite Group Databasebeta

← C3×#71076 #11798111

Subgroups — C3×#71076 #11798111

Order 1152.

527 conjugacy classes of subgroups.

The subgroup lattice has 407 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#904C211yesmaximal, characteristic, complemented
2C32×#466C211yesmaximal, characteristic, complemented
3C2×C3×#827C211yesmaximal, characteristic, complemented
4C2×C3×#826C211yesmaximal, characteristic, complemented
5C3×#4549C211yesmaximal, characteristic, complemented
6C3×#4492C211yesmaximal, characteristic, complemented
7C3×#4491C211yesmaximal, characteristic, complemented
8C3×#2186—31nomaximal
9#71076C311yesmaximal, characteristic, direct product factor
10C2×C3×#235—21no—
11C2×C32×D8C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C32×#121—21no—
14C2×C3×Dic12C2211yescharacteristic
15C3×#904—22no—
16C3×#904—22no—
17C2×C3×D24C2211yescharacteristic
18C2×C3×#204—21no—
19C32×#107C2211yescharacteristic
20C32×#102—21no—
21C3×#827—22no—
22C3×#826—22no—
23C2×C3×C3⋊C16C2211yescharacteristic
24C2×C3×C3⋊C16C2211yescharacteristic
25C2×C3×#135—31no—
26C2×#904C2×C311yescharacteristic, complemented
27C2×C3×SD32—31no—
28C2×C3×D16—31no—
29C3×#466—21no—
30C3×#466D311yescharacteristic, complemented
31C3×#466C2×C311yescharacteristic, complemented
32C2×#827C2×C311yescharacteristic, complemented
33C2×#826C2×C311yescharacteristic, complemented
34C3×#358—31no—
35C3×#357—31no—
36C3×C22⋊C16—31no—
37#4549C2×C311yescharacteristic, complemented
38#4492C2×C311yescharacteristic, complemented
39#4491C2×C311yescharacteristic, complemented
40C2×C32×D4—21no—
41C2×C32×D4—41no—
42C22×C32×C4D411yescharacteristic
43C2×C3×#67—41no—
44C3×#235—24no—
45C3×#235—42no—
46C2×C3×D12—21no—
47C2×C3×C4×D3—41no—
48C2×C3×Dic6—21no—
49C32×D8—21no—
50C32×D8—21no—
51C2×C32×C8—21no—
52C2×C32×C8—21no—
53C2×C32×C8D411yescharacteristic
54C2×C32×C8C2311yescharacteristic
55C32×C4⋊C4—21no—
56C32×C22⋊C4—41no—
57C3×Dic12—21no—
58C3×Dic12D412yescomplemented
59C3×D24—21no—
60C3×D24D412yescomplemented
61C3×#204—24no—
62C3×C3⋊C16—21no—
63C3×C3⋊C16—21no—
64#2186—31noSylow
65C2×C3×#41—61no—
66C2×#235—21no—
67C3×#135—62no—
68C3×#135—62no—
69C2×C3×Q16—31no—
70C2×C3×SD16—61no—
71C2×C3×D8—21no—
72C2×C3×D8—31no—
73C2×C3×D8C2×D311yescharacteristic
74C2×C3×D8C22×C311yescharacteristic
75C22×C3×C8—21no—
76C22×C3×C8C2×D311yescharacteristic
77C22×C3×C8C22×C311yescharacteristic
78C3×#121—22no—
79C3×#121—21no—
80C3×#121—21no—
81C2×Dic12C22×C311yescharacteristic
82#904—22no—
83#904—22no—
84C2×D24C22×C311yescharacteristic
85C2×#204—21no—
86C3×SD32—62no—
87C3×D16—62no—
88C2×C3×C16—31no—
89C2×C3×C16—31no—
90C3×#107—21no—
91C3×#107C2×D311yescharacteristic
92C3×#107C22×C311yescharacteristic
93C3×#102—22no—
94C3×#102—21no—
95C3×#102—21no—
96#827—22no—
97#826—22no—
98C2×C3⋊C16C22×C311yescharacteristic
99C2×C3⋊C16C22×C311yescharacteristic
100C23×C32—41no—
101C23×C32D811yescharacteristic
102C22×C3×D3—41no—
103C32×D4—41no—
104C32×D4—41no—
105C32×D4—82no—
106C2×C32×C4—21no—
107C2×C32×C4—21no—
108C2×C32×C4—41no—
109C2×C32×C4D811yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C3×#67—44no—
112C2×C3×Dic3—41no—
113C3×D12—22no—
114C3×D12—41no—
115C3×C4×D3—44no—
116C3×Dic6—22no—
117C3×Dic6—41no—
118C32×C8—21no—
119C32×C8C2×D411yescharacteristic
120C32×C8C2×D411yescharacteristic
121C2×#135—31no—
122C2×SD32—31no—
123C2×D16—31no—
124#466C3×D311yescharacteristic, complemented
125#358—31no—
126#357—31no—
127C22⋊C16—31no—
128C3×#41—64no—
129C3×#41—122no—
130C2×C3×Q8—61no—
131C2×C3×D4—22no—
132C2×C3×D4—21no—
133C2×C3×D4—21no—
134C2×C3×D4—42no—
135C2×C3×D4—41no—
136C2×C3×D4—41no—
137C2×C3×D4—61no—
138C2×C3×D4—121no—
139C22×C3×C4—21no—
140C22×C3×C4—121no—
141C22×C3×C4#6711yescharacteristic
142C22×C3×C4C3×D411yescharacteristic
143C2×#67—41no—
144#235—24no—
145#235—42no—
146C2×D12—21no—
147C2×C4×D3—41no—
148C2×Dic6—21no—
149C3×Q16—32no—
150C3×Q16—61no—
151C3×SD16—64no—
152C3×D8—21no—
153C3×D8—21no—
154C3×D8—21no—
155C3×D8—21no—
156C3×D8—32no—
157C3×D8—41no—
158C3×D8—41no—
159C3×D8—61no—
160C2×C3×C8—21no—
161C2×C3×C8—21no—
162C2×C3×C8—21no—
163C2×C3×C8—21no—
164C2×C3×C8—21no—
165C2×C3×C8—21no—
166C2×C3×C8—41no—
167C2×C3×C8—41no—
168C2×C3×C8#6711yescharacteristic
169C2×C3×C8C3×D411yescharacteristic
170C2×C3×C8C22×D311yescharacteristic
171C2×C3×C8C23×C311yescharacteristic
172C3×C4⋊C4—22no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4—21no—
175C3×C22⋊C4—42no—
176C3×C22⋊C4—41no—
177C3×C22⋊C4—41no—
178Dic12—21no—
179Dic12C3×D412yescomplemented
180D24—21no—
181D24C3×D412yescomplemented
182#204—24no—
183C3×C16—61no—
184C3×C16—61no—
185C3⋊C16—21no—
186C3⋊C16—21no—
187C22×C32—21no—
188C22×C32—21no—
189C22×C32—21no—
190C22×C32—81no—
191C22×C32—81no—
192C22×C32—81no—
193C22×C32C2×D811yescharacteristic
194C2×C3×D3—42no—
195C2×C3×D3—81no—
196C2×C3×D3—81no—
197C32×C4—21no—
198C32×C4—81no—
199C32×C4#12011yescharacteristic
200C32×C4AGL(1,ℤ/8)11yescharacteristic
201C3×Dic3—42no—
202C2×#41—61no—
203#135—62no—
204#135—62no—
205C2×Q16—31no—
206C2×SD16—61no—
207C2×D8—31no—
208C2×D8C2×C3×D311yescharacteristic
209C22×C8C2×C3×D311yescharacteristic
210#121—21no—
211SD32—62no—
212D16—62no—
213C2×C16—31no—
214C2×C16—31no—
215#107C2×C3×D311yescharacteristic
216#102—21no—
217C23×C3—21no—
218C23×C3—42no—
219C23×C3—41no—
220C23×C3—41no—
221C23×C3—121no—
222C23×C3#21311yescharacteristic
223C23×C3C3×D811yescharacteristic
224C22×D3—41no—
225C3×Q8—62no—
226C3×Q8—121no—
227C3×D4—42no—
228C3×D4—42no—
229C3×D4—41no—
230C3×D4—41no—
231C3×D4—41no—
232C3×D4—41no—
233C3×D4—62no—
234C3×D4—84no—
235C3×D4—82no—
236C3×D4—82no—
237C3×D4—124no—
238C3×D4—121no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—41no—
246C2×C3×C4—41no—
247C2×C3×C4—42no—
248C2×C3×C4—41no—
249C2×C3×C4—41no—
250C2×C3×C4—124no—
251C2×C3×C4—121no—
252C2×C3×C4#21311yescharacteristic
253C2×C3×C4C3×D811yescharacteristic
254C2×C3×C4C2×#6711yescharacteristic
255C2×C3×C4C2×C3×D411yescharacteristic
256#67—44no—
257C2×Dic3—41no—
258D12—22no—
259D12—41no—
260C4×D3—44no—
261Dic6—22no—
262Dic6—41no—
263C3×C8—21no—
264C3×C8—21no—
265C3×C8—21no—
266C3×C8—21no—
267C3×C8—41no—
268C3×C8D3×D411yescharacteristic
269C3×C8D3×D411yescharacteristic
270C3×C8C2×C3×D411yescharacteristic
271C3×C8C2×C3×D411yescharacteristic
272C2×C32—41no—
273C2×C32—161no—
274C2×C32#44711yescharacteristic
275C2×C32#50811yescharacteristic
276C2×C32#50911yescharacteristic
277C3×D3—82no—
278#41—64no—
279#41—122no—
280C2×Q8—61no—
281C2×D4—21no—
282C2×D4—41no—
283C2×D4—61no—
284C2×D4—121no—
285C22×C4—121no—
286C22×C4C3×#6711yescharacteristic
287Q16—32no—
288Q16—61no—
289SD16—64no—
290D8—21no—
291D8—21no—
292D8—32no—
293D8—61no—
294C2×C8—21no—
295C2×C8—21no—
296C2×C8C3×#6711yescharacteristic
297C2×C8C22×C3×D311yescharacteristic
298C4⋊C4—21no—
299C22⋊C4—41no—
300C16—61no—
301C16—61no—
302C22×C3—22no—
303C22×C3—21no—
304C22×C3—21no—
305C22×C3—21no—
306C22×C3—21no—
307C22×C3—21no—
308C22×C3—21no—
309C22×C3—21no—
310C22×C3—41no—
311C22×C3—41no—
312C22×C3—82no—
313C22×C3—82no—
314C22×C3—82no—
315C22×C3—81no—
316C22×C3—81no—
317C22×C3—81no—
318C22×C3—81no—
319C22×C3—81no—
320C22×C3—81no—
321C22×C3—122no—
322C22×C3—241no—
323C22×C3—241no—
324C22×C3C2×#21311yescharacteristic
325C22×C3C2×C3×D811yescharacteristic
326C2×D3—42no—
327C2×D3—81no—
328C2×D3—81no—
329C3×C4—21no—
330C3×C4—21no—
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—41no—
334C3×C4—82no—
335C3×C4—81no—
336C3×C4—81no—
337C3×C4—122no—
338C3×C4#93711yescharacteristic
339C3×C4#94911yescharacteristic
340C3×C4C3×#12011yescharacteristic
341C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
342Dic3—42no—
343C32#218611yescharacteristic, complemented, Sylow
344C23—41no—
345C23—121no—
346C23C3×#21311yescharacteristic
347Q8—62no—
348Q8—121no—
349D4—41no—
350D4—41no—
351D4—62no—
352D4—82no—
353D4—124no—
354D4—121no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—41no—
358C2×C4—124no—
359C2×C4—121no—
360C2×C4C3×#21311yescharacteristic
361C2×C4C2×C3×#6711yescharacteristic
362C8—21no—
363C8C3×D3×D411yescharacteristic
364C8C3×D3×D411yescharacteristic
365C2×C3—21no—
366C2×C3—21no—
367C2×C3—21no—
368C2×C3—42no—
369C2×C3—41no—
370C2×C3—41no—
371C2×C3—162no—
372C2×C3—161no—
373C2×C3—161no—
374C2×C3—242no—
375C2×C3#503611yescharacteristic
376C2×C3#514711yescharacteristic
377C2×C3#519411yescharacteristic
378C2×C3C3×#44711yescharacteristic
379C2×C3C3×#50811yescharacteristic
380C2×C3C3×#50911yescharacteristic
381D3—82no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—81no—
386C22—81no—
387C22—81no—
388C22—122no—
389C22—241no—
390C22—241no—
391C22C2×C3×#21311yescharacteristic
392C4—21no—
393C4—81no—
394C4—122no—
395C4C3×#93711yescharacteristic
396C4C3×#94911yescharacteristic
397C3—21no—
398C3#7107611yescharacteristic, direct product factor
399C3C3×#218611yescharacteristic, complemented
400C2—41no—
401C2—161no—
402C2—242no—
403C2C3×#503611yescharacteristic
404C2C3×#514711yescharacteristic
405C2C3×#519411yescharacteristic
subgroupG/H
centerC22×C3C2×#213
commutator, cosocleC2×C3×C8C23×C3
FrattiniC2×C8C22×C3×D3
FittingC32×#466C2
socleC22×C32C2×D8
hypercenterC3×#466D3
hypocenterC3C3×#2186
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. C2×C3×#904C2semidirect
2. C32×#466C2semidirect
3. C2×C3×#827C2semidirect
4. C2×C3×#826C2semidirect
5. C3×#4549C2semidirect
6. C3×#4492C2semidirect
7. C3×#4491C2semidirect
9. #71076C3direct (N × H)
26. C2×#904C2×C3semidirect
30. C3×#466D3semidirect
31. C3×#466C2×C3semidirect
32. C2×#827C2×C3semidirect
33. C2×#826C2×C3semidirect
37. #4549C2×C3semidirect
38. #4492C2×C3semidirect
39. #4491C2×C3semidirect
58. C3×Dic12D4semidirect
60. C3×D24D4semidirect
124. #466C3×D3semidirect
179. Dic12C3×D4semidirect
181. D24C3×D4semidirect
343. C32#2186semidirect
398. C3#71076direct (N × H)
399. C3C3×#2186semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9042
C32×#4662
C2×C3×#8272
C2×C3×#8262
C3×#45492
C3×#44922
C3×#44912
C3×#21863
#710763