Finite Group Databasebeta

← C3×#69026 #11785919

Subgroups — C3×#69026 #11785919

Order 1152.

589 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5521C211yesmaximal, characteristic
2C2×C3×#823C211yesmaximal, characteristic
3C2×C3×#823C211yesmaximal, characteristic
4C32×#344C211yesmaximal, characteristic, complemented
5C3×#4559C211yesmaximal, characteristic, complemented
6C3×#4556C211yesmaximal, characteristic, complemented
7C3×#4533C211yesmaximal, characteristic, complemented
8C3×#1829—31nomaximal
9#69026C311yesmaximal, characteristic, direct product factor
10C22×C3×D12C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C32×#117C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#893—22no—
18C3×D3×C22⋊C4C414yes—
19C3×C4×D12—22no—
20C3×#823—22no—
21C3×#823—22no—
22C3×#518—31no—
23#5521C2×C311yescharacteristic
24C2×C3×#100—31no—
25C2×C3×#100—31no—
26C2×#823C2×C311yescharacteristic
27C2×#823C2×C311yescharacteristic
28C3×#344—21no—
29C3×#344—31no—
30C3×#344—31no—
31C3×#344—31no—
32C3×#344D311yescharacteristic, complemented
33C3×#344C2×C311yescharacteristic, complemented
34#4559C2×C311yescharacteristic, complemented
35#4556C2×C311yescharacteristic, complemented
36#4533C2×C311yescharacteristic, complemented
37C23×C3×D3C2×C412yes—
38C22×C32×C4C2311yescharacteristic
39C2×C3×D12—21no—
40C2×C3×D12—21no—
41C2×C3×D12—21no—
42C2×C3×D12—21no—
43C2×C3×D12D412yes—
44C2×C3×D12D412yes—
45C2×C3×C4×D3—24no—
46C32×M16—21no—
47C32×M16—21no—
48C32×M16—21no—
49C32×M16—21no—
50C2×C32×C8—21no—
51C2×C32×C8—21no—
52C32×C4⋊C4—21no—
53C32×C22⋊C4C2×C412yes—
54C32×C42—21no—
55C3×#217C2×C412yes—
56C3×(C2×D3)⋊C4—24no—
57C3×C4⋊Dic3—21no—
58C3×C4×Dic3—21no—
59C3×#208—21no—
60C3×#208—21no—
61C3×#208—21no—
62C3×#208—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65#1829—31noSylow
66C22×C3×D4—31no—
67C22×D12C22×C311yescharacteristic
68C2×C3×M16—21no—
69C2×C3×M16—21no—
70C2×C3×M16—31no—
71C2×C3×M16—31no—
72C2×C3×M16C2×D311yescharacteristic
73C2×C3×M16C2×D311yescharacteristic
74C2×C3×M16C22×C311yescharacteristic
75C2×C3×M16C22×C311yescharacteristic
76C3×C4×D4—62no—
77C3×C4×D4—62no—
78C3×#117—21no—
79C3×#117—31no—
80C3×#117C2×D311yescharacteristic
81C3×#117C22×C311yescharacteristic
82C2×C3×C22⋊C4—34no—
83#926C22×C311yescharacteristic
84C2×#208C22×C311yescharacteristic
85C2×#208C22×C311yescharacteristic
86#893—22no—
87D3×C22⋊C4C3×C414yes—
88C4×D12—22no—
89C3×#100—62no—
90C3×#100—62no—
91#823—22no—
92#823—22no—
93C23×C32C22×C411yescharacteristic
94C22×C3×D3—22no—
95C22×C3×D3—22no—
96C22×C3×D3—82no—
97C22×C3×D3C22⋊C414yes—
98C2×C32×C4—22no—
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4#4111yescharacteristic
102C2×C32×C4#4111yescharacteristic
103C2×C32×C4#4111yescharacteristic
104C2×C32×C4#4111yescharacteristic
105C2×C3×Dic3—22no—
106C3×D12—22no—
107C3×D12—22no—
108C3×D12—22no—
109C3×D12—22no—
110C3×C4×D3—84no—
111C32×C8—41no—
112C32×C8—41no—
113C3×C3⋊C8—41no—
114C3×C3⋊C8—41no—
115#518—31no—
116C2×#100—31no—
117C2×#100—31no—
118#344—31no—
119#344—31no—
120#344—31no—
121#344C3×D311yescharacteristic, complemented
122C24×C3—32no—
123C23×D3C2×C3×C412yes—
124C2×C3×D4—32no—
125C2×C3×D4—32no—
126C2×C3×D4—61no—
127C2×C3×D4—61no—
128C2×C3×D4—61no—
129C2×C3×D4—61no—
130C22×C3×C4—21no—
131C22×C3×C4—64no—
132C22×C3×C4C22×D311yescharacteristic
133C22×C3×C4C23×C311yescharacteristic
134C2×D12—21no—
135C2×D12—21no—
136C2×D12—21no—
137C2×D12—21no—
138C2×D12C3×D412yes—
139C2×D12C3×D412yes—
140C2×C4×D3—24no—
141C3×M16—22no—
142C3×M16—21no—
143C3×M16—21no—
144C3×M16—21no—
145C3×M16—21no—
146C3×M16—21no—
147C3×M16—21no—
148C3×M16—21no—
149C3×M16—21no—
150C3×M16—41no—
151C3×M16—41no—
152C3×M16—41no—
153C3×M16—61no—
154C3×M16—61no—
155C3×M16—61no—
156C3×M16—61no—
157C2×C3×C8—22no—
158C2×C3×C8—21no—
159C2×C3×C8—21no—
160C2×C3×C8—21no—
161C2×C3×C8—21no—
162C2×C3×C8—41no—
163C2×C3×C8—61no—
164C2×C3×C8—61no—
165C3×C4⋊C4—21no—
166C3×C4⋊C4—21no—
167C3×C4⋊C4—41no—
168C3×C4⋊C4—61no—
169C3×C22⋊C4—22no—
170C3×C22⋊C4—32no—
171C3×C22⋊C4—64no—
172C3×C22⋊C4C4×D312yes—
173C3×C22⋊C4C2×C3×C412yes—
174C3×C42—21no—
175C3×C42—21no—
176C3×C42—41no—
177C3×C42—61no—
178#217C2×C3×C412yes—
179(C2×D3)⋊C4—24no—
180C4⋊Dic3—21no—
181C4×Dic3—21no—
182#208—21no—
183#208—21no—
184#208—21no—
185#208—21no—
186C2×C3⋊C8—21no—
187C2×C3⋊C8—21no—
188C22×C32—41no—
189C22×C32C2×C22⋊C411yescharacteristic
190C22×C32#11711yescharacteristic
191C22×C32#11711yescharacteristic
192C2×C3×D3—24no—
193C2×C3×D3—44no—
194C2×C3×D3—82no—
195C2×C3×D3—82no—
196C32×C4—42no—
197C32×C4#12311yescharacteristic
198C32×C4#12311yescharacteristic
199C32×C4#12311yescharacteristic
200C32×C4#12311yescharacteristic
201C3×Dic3—42no—
202C22×D4—31no—
203C2×M16—31no—
204C2×M16—31no—
205C2×M16C2×C3×D311yescharacteristic
206C2×M16C2×C3×D311yescharacteristic
207C4×D4—62no—
208C4×D4—62no—
209#117—31no—
210#117C2×C3×D311yescharacteristic
211C2×C22⋊C4—34no—
212#100—62no—
213#100—62no—
214C23×C3—21no—
215C23×C3—34no—
216C23×C3—62no—
217C23×C3—62no—
218C23×C3—242no—
219C23×C3C2×C4×D311yescharacteristic
220C23×C3C22×C3×C411yescharacteristic
221C22×D3—22no—
222C22×D3—22no—
223C22×D3—82no—
224C22×D3C3×C22⋊C414yes—
225C3×D4—62no—
226C3×D4—62no—
227C3×D4—62no—
228C3×D4—62no—
229C2×C3×C4—22no—
230C2×C3×C4—22no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—42no—
238C2×C3×C4—62no—
239C2×C3×C4—244no—
240C2×C3×C4#23511yescharacteristic
241C2×C3×C4#23511yescharacteristic
242C2×C3×C4D3×D411yescharacteristic
243C2×C3×C4D3×D411yescharacteristic
244C2×C3×C4#23711yescharacteristic
245C2×C3×C4#23911yescharacteristic
246C2×C3×C4C2×C3×D411yescharacteristic
247C2×C3×C4C2×C3×D411yescharacteristic
248C2×C3×C4C3×#4111yescharacteristic
249C2×C3×C4C3×#4111yescharacteristic
250C2×C3×C4C3×#4111yescharacteristic
251C2×C3×C4C3×#4111yescharacteristic
252C2×Dic3—22no—
253D12—22no—
254D12—22no—
255D12—22no—
256D12—22no—
257C4×D3—84no—
258C3×C8—42no—
259C3×C8—42no—
260C3×C8—41no—
261C3×C8—41no—
262C3×C8—41no—
263C3×C8—41no—
264C3×C8—121no—
265C3×C8—121no—
266C3⋊C8—41no—
267C3⋊C8—41no—
268C2×C32—21no—
269C2×C32—21no—
270C2×C32—21no—
271C2×C32#38111yescharacteristic
272C3×D3—44no—
273C24—32no—
274C2×D4—32no—
275C2×D4—32no—
276C2×D4—61no—
277C2×D4—61no—
278C2×D4—61no—
279C2×D4—61no—
280C22×C4—64no—
281C22×C4C22×C3×D311yescharacteristic
282M16—21no—
283M16—21no—
284M16—21no—
285M16—21no—
286M16—61no—
287M16—61no—
288M16—61no—
289M16—61no—
290C2×C8—21no—
291C2×C8—21no—
292C2×C8—61no—
293C2×C8—61no—
294C4⋊C4—21no—
295C4⋊C4—61no—
296C22⋊C4—32no—
297C22⋊C4—64no—
298C22⋊C4C3×C4×D312yes—
299C42—21no—
300C42—61no—
301C22×C3—21no—
302C22×C3—21no—
303C22×C3—21no—
304C22×C3—41no—
305C22×C3—41no—
306C22×C3—64no—
307C22×C3—81no—
308C22×C3—124no—
309C22×C3—242no—
310C22×C3—242no—
311C22×C3#87211yescharacteristic
312C22×C3D3×C22⋊C411yescharacteristic
313C22×C3#89211yescharacteristic
314C22×C3C2×C3×C22⋊C411yescharacteristic
315C22×C3C3×#11711yescharacteristic
316C22×C3C3×#11711yescharacteristic
317C2×D3—24no—
318C2×D3—44no—
319C2×D3—82no—
320C2×D3—82no—
321C3×C4—21no—
322C3×C4—21no—
323C3×C4—21no—
324C3×C4—21no—
325C3×C4—42no—
326C3×C4—42no—
327C3×C4—82no—
328C3×C4—122no—
329C3×C4#88311yescharacteristic
330C3×C4#88311yescharacteristic
331C3×C4#89411yescharacteristic
332C3×C4#89411yescharacteristic
333C3×C4C3×#12311yescharacteristic
334C3×C4C3×#12311yescharacteristic
335C3×C4C3×#12311yescharacteristic
336C3×C4C3×#12311yescharacteristic
337Dic3—42no—
338C32#182911yescharacteristic, complemented, Sylow
339C23—34no—
340C23—62no—
341C23—62no—
342C23—242no—
343C23C2×C3×C4×D311yescharacteristic
344D4—62no—
345D4—62no—
346D4—62no—
347D4—62no—
348C2×C4—22no—
349C2×C4—62no—
350C2×C4—244no—
351C2×C4C3×#23511yescharacteristic
352C2×C4C3×#23511yescharacteristic
353C2×C4C3×D3×D411yescharacteristic
354C2×C4C3×D3×D411yescharacteristic
355C2×C4C3×#23711yescharacteristic
356C2×C4C3×#23911yescharacteristic
357C8—41no—
358C8—41no—
359C8—121no—
360C8—121no—
361C2×C3—21no—
362C2×C3—21no—
363C2×C3—21no—
364C2×C3—21no—
365C2×C3—21no—
366C2×C3—21no—
367C2×C3—21no—
368C2×C3—41no—
369C2×C3—41no—
370C2×C3—41no—
371C2×C3—124no—
372C2×C3#466411yescharacteristic
373C2×C3C3×#38111yescharacteristic
374D3—44no—
375C22—41no—
376C22—64no—
377C22—124no—
378C22—242no—
379C22—242no—
380C22C3×#87211yescharacteristic
381C22C3×D3×C22⋊C411yescharacteristic
382C22C3×#89211yescharacteristic
383C4—42no—
384C4—122no—
385C4C3×#88311yescharacteristic
386C4C3×#88311yescharacteristic
387C4C3×#89411yescharacteristic
388C4C3×#89411yescharacteristic
389C3—21no—
390C3#6902611yescharacteristic, direct product factor
391C3C3×#182911yescharacteristic, complemented
392C2—21no—
393C2—21no—
394C2—21no—
395C2—124no—
396C2C3×#466411yescharacteristic
subgroupG/H
centerC2×C3#4664
commutatorC23×C3C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#344C2
socleC2×C32#381
prime radicalC22×C3×D12C22
cosocleC22×C3×C4C23×C3
hypercenterC3×#344D3
hypocenterC3C3×#1829
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C3×#344

Complements

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

NH ≅ G/Ntype
4. C32×#344C2semidirect
5. C3×#4559C2semidirect
6. C3×#4556C2semidirect
7. C3×#4533C2semidirect
9. #69026C3direct (N × H)
32. C3×#344D3semidirect
33. C3×#344C2×C3semidirect
34. #4559C2×C3semidirect
35. #4556C2×C3semidirect
36. #4533C2×C3semidirect
121. #344C3×D3semidirect
338. C32#1829semidirect
390. C3#69026direct (N × H)
391. C3C3×#1829semidirect

Maximal subgroups

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

subgroupindex
C3×#55212
C2×C3×#8232
C32×#3442
C3×#45592
C3×#45562
C3×#45332
C3×#18293
#690263