Finite Group Databasebeta

← C3×#70784 #11774019

Subgroups — C3×#70784 #11774019

Order 1152.

571 conjugacy classes of subgroups.

The subgroup lattice has 375 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#875C211yesmaximal, characteristic
2C32×#431C211yesmaximal, characteristic, complemented
3C3×#4926C211yesmaximal, characteristic, complemented
4C3×#4468C214yesmaximal, complemented
5C3×#1469—31nomaximal
6#70784C311yesmaximal, characteristic, direct product factor
7C22×C3×D12C411yescharacteristic
8C22×C3×Dic6C411yescharacteristic
9C2×C32×C42C2211yescharacteristic
10C2×C3×(C2×D3)⋊C4C412yes—
11C2×C3×(C2×D3)⋊C4C2212yes—
12C3×#875—21no—
13C3×#875—21no—
14C3×#875—21no—
15C3×#875—21no—
16C32×C4⋊C8—21no—
17C32×C22⋊C8C2212yes—
18C32×C4×C8—21no—
19C3×#830C2212yes—
20C3×C4⋊(C3⋊C8)—21no—
21C3×#803—21no—
22C2×C3×#124—31no—
23C2×#875C2×C311yescharacteristic
24C3×#432—31no—
25C3×#431—21no—
26C3×#431D311yescharacteristic, complemented
27C3×#431C2×C311yescharacteristic, complemented
28#4926C2×C311yescharacteristic, complemented
29C3×#323—34no—
30#4468C2×C314yescomplemented
31C23×C3×D3C2×C412yes—
32C22×C32×C4C2×C411yescharacteristic
33C22×C32×C4C2×C411yescharacteristic
34C22×C32×C4C2311yescharacteristic
35C22×C3×Dic3C2×C412yes—
36C2×C3×D12—21no—
37C2×C3×D12—21no—
38C2×C3×D12—42no—
39C2×C3×Dic6—21no—
40C2×C3×Dic6—21no—
41C2×C3×Dic6—42no—
42C2×C32×C8—22no—
43C32×C42D411yescharacteristic
44C32×C42D411yescharacteristic
45C32×C42D411yescharacteristic
46C32×C42D411yescharacteristic
47C3×(C2×D3)⋊C4—22no—
48C3×(C2×D3)⋊C4—22no—
49C3×(C2×D3)⋊C4—22no—
50C3×(C2×D3)⋊C4—22no—
51C2×C3×C3⋊C8—22no—
52#1469—31noSylow
53C22×C3×Q8—31no—
54C22×C3×D4—31no—
55C22×D12C3×C411yescharacteristic
56C22×Dic6C3×C411yescharacteristic
57C3×#124—61no—
58C3×#124—61no—
59C3×#124—61no—
60C3×#124—61no—
61C2×C3×C22⋊C4—32no—
62C2×C3×C22⋊C4—32no—
63C2×C3×C42—21no—
64C2×C3×C42C2×D311yescharacteristic
65C2×C3×C42C22×C311yescharacteristic
66C2×(C2×D3)⋊C4C3×C412yes—
67C2×(C2×D3)⋊C4C22×C312yes—
68#875—21no—
69#875—21no—
70#875—21no—
71#875—21no—
72C3×C4⋊C8—22no—
73C3×C4⋊C8—21no—
74C3×C4⋊C8—21no—
75C3×C4⋊C8—61no—
76C3×C22⋊C8—22no—
77C3×C22⋊C8—32no—
78C3×C22⋊C8C2×D312yes—
79C3×C22⋊C8C22×C312yes—
80C3×#97—61no—
81C3×C4×C8—22no—
82C3×C4×C8—21no—
83C3×C4×C8—21no—
84#830C22×C312yes—
85C4⋊(C3⋊C8)—21no—
86#803—21no—
87C23×C32C22×C411yescharacteristic
88C22×C3×D3—22no—
89C22×C3×D3—24no—
90C22×C3×D3—42no—
91C22×C3×D3—42no—
92C2×C32×C4—22no—
93C2×C32×C4—22no—
94C2×C32×C4—41no—
95C2×C32×C4C22⋊C411yescharacteristic
96C2×C32×C4C22⋊C411yescharacteristic
97C2×C32×C4C22⋊C411yescharacteristic
98C2×C32×C4C22⋊C411yescharacteristic
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4C2×D411yescharacteristic
101C2×C3×Dic3—22no—
102C2×C3×Dic3—42no—
103C3×D12—42no—
104C3×D12—42no—
105C3×Dic6—42no—
106C3×Dic6—42no—
107C32×C8—42no—
108C3×C3⋊C8—42no—
109C2×#124—31no—
110#432—31no—
111#431C3×D311yescharacteristic, complemented
112#323—34no—
113C24×C3—32no—
114C23×D3C2×C3×C412yes—
115C2×C3×Q8—61no—
116C2×C3×Q8—61no—
117C2×C3×Q8—122no—
118C2×C3×D4—61no—
119C2×C3×D4—61no—
120C2×C3×D4—122no—
121C22×C3×C4—21no—
122C22×C3×C4—21no—
123C22×C3×C4—21no—
124C22×C3×C4—32no—
125C22×C3×C4C4×D311yescharacteristic
126C22×C3×C4C4×D311yescharacteristic
127C22×C3×C4C2×C3×C411yescharacteristic
128C22×C3×C4C2×C3×C411yescharacteristic
129C22×C3×C4C22×D311yescharacteristic
130C22×C3×C4C23×C311yescharacteristic
131C22×Dic3C2×C3×C412yes—
132C2×D12—21no—
133C2×D12—21no—
134C2×D12—42no—
135C2×Dic6—21no—
136C2×Dic6—21no—
137C2×Dic6—42no—
138C2×C3×C8—24no—
139C2×C3×C8—22no—
140C2×C3×C8—22no—
141C2×C3×C8—62no—
142C3×C22⋊C4—62no—
143C3×C22⋊C4—62no—
144C3×C22⋊C4—62no—
145C3×C22⋊C4—62no—
146C3×C42—21no—
147C3×C42—21no—
148C3×C42—21no—
149C3×C42—21no—
150C3×C42D1211yescharacteristic
151C3×C42D1211yescharacteristic
152C3×C42#6711yescharacteristic
153C3×C42#6711yescharacteristic
154C3×C42C3×D411yescharacteristic
155C3×C42C3×D411yescharacteristic
156C3×C42C3×D411yescharacteristic
157C3×C42C3×D411yescharacteristic
158(C2×D3)⋊C4—22no—
159(C2×D3)⋊C4—22no—
160(C2×D3)⋊C4—22no—
161(C2×D3)⋊C4—22no—
162C2×C3⋊C8—22no—
163C22×C32—21no—
164C22×C32—21no—
165C22×C32C2×C22⋊C411yescharacteristic
166C22×C32#13112yes—
167C2×C3×D3—42no—
168C2×C3×D3—42no—
169C2×C3×D3—42no—
170C2×C3×D3—84no—
171C32×C4—21no—
172C32×C4—21no—
173C32×C4—21no—
174C32×C4—21no—
175C32×C4—21no—
176C32×C4#10012yes—
177C3×Dic3—42no—
178C22×Q8—31no—
179C22×D4—31no—
180#124—61no—
181#124—61no—
182#124—61no—
183#124—61no—
184C2×C22⋊C4—32no—
185C2×C22⋊C4—32no—
186C2×C42C2×C3×D311yescharacteristic
187C4⋊C8—21no—
188C4⋊C8—61no—
189C22⋊C8—32no—
190C22⋊C8C2×C3×D312yes—
191#97—61no—
192C4×C8—21no—
193C23×C3—21no—
194C23×C3—62no—
195C23×C3—64no—
196C23×C3—122no—
197C23×C3—122no—
198C23×C3C2×C4×D311yescharacteristic
199C23×C3C22×C3×C411yescharacteristic
200C22×D3—22no—
201C22×D3—24no—
202C22×D3—42no—
203C22×D3—42no—
204C3×Q8—122no—
205C3×Q8—122no—
206C3×D4—122no—
207C3×D4—122no—
208C2×C3×C4—24no—
209C2×C3×C4—22no—
210C2×C3×C4—22no—
211C2×C3×C4—22no—
212C2×C3×C4—22no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4—42no—
220C2×C3×C4—41no—
221C2×C3×C4—41no—
222C2×C3×C4—42no—
223C2×C3×C4—62no—
224C2×C3×C4—122no—
225C2×C3×C4(C2×D3)⋊C411yescharacteristic
226C2×C3×C4(C2×D3)⋊C411yescharacteristic
227C2×C3×C4(C2×D3)⋊C411yescharacteristic
228C2×C3×C4(C2×D3)⋊C411yescharacteristic
229C2×C3×C4C3×C22⋊C411yescharacteristic
230C2×C3×C4C3×C22⋊C411yescharacteristic
231C2×C3×C4C3×C22⋊C411yescharacteristic
232C2×C3×C4C3×C22⋊C411yescharacteristic
233C2×C3×C4C2×D1211yescharacteristic
234C2×C3×C4C2×#6711yescharacteristic
235C2×C3×C4C2×C3×D411yescharacteristic
236C2×C3×C4C2×C3×D411yescharacteristic
237C2×Dic3—22no—
238C2×Dic3—42no—
239D12—42no—
240D12—42no—
241Dic6—42no—
242Dic6—42no—
243C3×C8—44no—
244C3×C8—42no—
245C3×C8—42no—
246C3×C8—122no—
247C3⋊C8—42no—
248C2×C32—22no—
249C2×C32#40811yescharacteristic
250C2×C32#41011yescharacteristic
251C2×C32C2×#10011yescharacteristic
252C3×D3—82no—
253C24—32no—
254C2×Q8—61no—
255C2×Q8—61no—
256C2×Q8—122no—
257C2×D4—61no—
258C2×D4—61no—
259C2×D4—122no—
260C22×C4—32no—
261C22×C4C3×C4×D311yescharacteristic
262C22×C4C3×C4×D311yescharacteristic
263C22×C4C22×C3×D311yescharacteristic
264C2×C8—22no—
265C2×C8—62no—
266C22⋊C4—62no—
267C22⋊C4—62no—
268C22⋊C4—62no—
269C22⋊C4—62no—
270C42C3×D1211yescharacteristic
271C42C3×D1211yescharacteristic
272C42C3×#6711yescharacteristic
273C42C3×#6711yescharacteristic
274C22×C3—21no—
275C22×C3—21no—
276C22×C3—21no—
277C22×C3—21no—
278C22×C3—22no—
279C22×C3—21no—
280C22×C3—41no—
281C22×C3—41no—
282C22×C3—122no—
283C22×C3—122no—
284C22×C3—122no—
285C22×C3—244no—
286C22×C3#90112yes—
287C22×C3C2×(C2×D3)⋊C411yescharacteristic
288C22×C3C2×C3×C22⋊C411yescharacteristic
289C22×C3C3×#13112yes—
290C2×D3—42no—
291C2×D3—42no—
292C2×D3—42no—
293C2×D3—84no—
294C3×C4—22no—
295C3×C4—22no—
296C3×C4—22no—
297C3×C4—21no—
298C3×C4—21no—
299C3×C4—21no—
300C3×C4—21no—
301C3×C4—21no—
302C3×C4—21no—
303C3×C4—21no—
304C3×C4—21no—
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—22no—
308C3×C4—41no—
309C3×C4—41no—
310C3×C4—122no—
311C3×C4#82312yes—
312C3×C4C3×#10012yes—
313Dic3—42no—
314C32#146911yescharacteristic, complemented, Sylow
315C23—62no—
316C23—64no—
317C23—122no—
318C23—122no—
319C23C2×C3×C4×D311yescharacteristic
320Q8—122no—
321Q8—122no—
322D4—122no—
323D4—122no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—41no—
327C2×C4—62no—
328C2×C4—122no—
329C2×C4C3×(C2×D3)⋊C411yescharacteristic
330C2×C4C3×(C2×D3)⋊C411yescharacteristic
331C2×C4C3×(C2×D3)⋊C411yescharacteristic
332C2×C4C3×(C2×D3)⋊C411yescharacteristic
333C2×C4C2×C3×D1211yescharacteristic
334C2×C4C2×C3×#6711yescharacteristic
335C8—42no—
336C8—122no—
337C2×C3—22no—
338C2×C3—22no—
339C2×C3—21no—
340C2×C3—21no—
341C2×C3—21no—
342C2×C3—42no—
343C2×C3—242no—
344C2×C3#500611yescharacteristic
345C2×C3#511011yescharacteristic
346C2×C3C2×#82311yescharacteristic
347C2×C3C3×#40811yescharacteristic
348C2×C3C3×#41011yescharacteristic
349C2×C3C2×C3×#10011yescharacteristic
350D3—82no—
351C22—21no—
352C22—21no—
353C22—122no—
354C22—122no—
355C22—122no—
356C22—244no—
357C22C3×#90112yes—
358C22C2×C3×(C2×D3)⋊C411yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—122no—
365C4C3×#82312yes—
366C3—21no—
367C3#7078411yescharacteristic, direct product factor
368C3C3×#146911yescharacteristic, complemented
369C2—22no—
370C2—242no—
371C2C3×#500611yescharacteristic
372C2C3×#511011yescharacteristic
373C2C2×C3×#82311yescharacteristic
subgroupG/H
centerC22×C3C2×(C2×D3)⋊C4
commutatorC23×C3C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#431C2
socleC22×C32C2×C22⋊C4
prime radicalC22×C3×D12C4
cosocleC22×C3×C4C23×C3
hypercenterC3×#431D3
hypocenterC3C3×#1469
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ C3×#431

Complements

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

NH ≅ G/Ntype
2. C32×#431C2semidirect
3. C3×#4926C2semidirect
4. C3×#4468C2semidirect
6. #70784C3direct (N × H)
26. C3×#431D3semidirect
27. C3×#431C2×C3semidirect
28. #4926C2×C3semidirect
30. #4468C2×C3semidirect
111. #431C3×D3semidirect
314. C32#1469semidirect
367. C3#70784direct (N × H)
368. C3C3×#1469semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8752
C32×#4312
C3×#49262
C3×#44682
C3×#14693
#707843