Finite Group Databasebeta

← C3×#68918 #11789928

Subgroups — C3×#68918 #11789928

Order 1152.

505 conjugacy classes of subgroups.

The subgroup lattice has 401 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#825C211yesmaximal, characteristic
2C3×#5129C211yesmaximal, characteristic
3C3×#5119C211yesmaximal, characteristic, complemented
4C3×#5113C211yesmaximal, characteristic
5C2×C3×C8×Dic3C211yesmaximal, characteristic, complemented
6C32×#341C211yesmaximal, characteristic, complemented
7C3×#4555C211yesmaximal, characteristic, complemented
8C3×#1937—31nomaximal
9#68918C311yesmaximal, characteristic, direct product factor
10C2×C3×#235C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C22×C32×C8C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C3×#825—22no—
18C3×#821C412yescomplemented
19C3×(C2×D3)⋊C8—22no—
20C3×#816C412yescomplemented
21C3×Dic3⋊C8—22no—
22C3×C8×Dic3—22no—
23C3×#424—31no—
24C2×C3×#104—31no—
25C3×#416—31no—
26C3×#408—31no—
27C2×C3×C4×C8—31no—
28C2×#825C2×C311yescharacteristic
29#5129C2×C311yescharacteristic
30#5119C2×C311yescharacteristic, complemented
31#5113C2×C311yescharacteristic
32C2×C8×Dic3C2×C311yescharacteristic, complemented
33C3×#341—21no—
34C3×#341D311yescharacteristic, complemented
35C3×#341C2×C311yescharacteristic, complemented
36C3×#339—31no—
37#4555C2×C311yescharacteristic, complemented
38C22×C32×C4C2311yescharacteristic
39C2×C3×#67—21no—
40C22×C3×Dic3—21no—
41C3×#235—21no—
42C3×#235—21no—
43C3×#235—21no—
44C3×#235—21no—
45C2×C3×D12C2×C411yescharacteristic
46C2×C3×C4×D3—21no—
47C2×C3×Dic6C2×C411yescharacteristic
48C32×M16—21no—
49C32×M16—21no—
50C32×M16—21no—
51C32×M16—21no—
52C2×C32×C8—21no—
53C2×C32×C8—21no—
54C2×C32×C8—21no—
55C2×C32×C8—21no—
56C2×C32×C8C2×C412yes—
57C3×#217—21no—
58C3×C4⋊Dic3C2×C412yes—
59C3×C4×Dic3—21no—
60C3×C4×Dic3—21no—
61C3×C4×Dic3D412yes—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8D412yes—
65#1937—31noSylow
66C2×C3×#41—31no—
67C2×#235C22×C311yescharacteristic
68C2×C3×M16—21no—
69C2×C3×M16—21no—
70C2×C3×M16C2×D311yescharacteristic
71C2×C3×M16C2×D311yescharacteristic
72C2×C3×M16C22×C311yescharacteristic
73C2×C3×M16C22×C311yescharacteristic
74C22×C3×C8—21no—
75C22×C3×C8—31no—
76C22×C3×C8C2×D311yescharacteristic
77C22×C3×C8C22×C311yescharacteristic
78C3×#117—31no—
79C2×C3×C42—31no—
80#926C22×C311yescharacteristic
81C2×C4×Dic3C22×C311yescharacteristic
82C22×C3⋊C8C22×C311yescharacteristic
83C3×C4⋊C8—62no—
84C3×#104—62no—
85C3×#103—32no—
86C3×#102—32no—
87C3×C22⋊C8—62no—
88C3×C4×C8—62no—
89#825—22no—
90#821C3×C412yescomplemented
91(C2×D3)⋊C8—22no—
92#816C3×C412yescomplemented
93Dic3⋊C8—22no—
94C8×Dic3—22no—
95C23×C32#4111yescharacteristic
96C22×C3×D3—21no—
97C2×C32×C4C22×C411yescharacteristic
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4#4111yescharacteristic
101C2×C32×C4#4111yescharacteristic
102C2×C32×C4#4111yescharacteristic
103C3×#67—41no—
104C3×#67—41no—
105C2×C3×Dic3—24no—
106C2×C3×Dic3—22no—
107C2×C3×Dic3—22no—
108C2×C3×Dic3—21no—
109C3×D12—21no—
110C3×D12—21no—
111C3×C4×D3—41no—
112C3×C4×D3—41no—
113C3×Dic6—21no—
114C3×Dic6—21no—
115C32×C8—22no—
116C32×C8—41no—
117C32×C8—41no—
118C3×C3⋊C8—22no—
119#424—31no—
120C2×#104—31no—
121#416—31no—
122#408—31no—
123C2×C4×C8—31no—
124#341C3×D311yescharacteristic, complemented
125#339—31no—
126C3×#41—61no—
127C3×#41—61no—
128C3×#41—61no—
129C3×#41—61no—
130C2×C3×Q8—31no—
131C2×C3×D4—31no—
132C2×C3×D4—61no—
133C22×C3×C4—21no—
134C22×C3×C4—61no—
135C22×C3×C4—61no—
136C22×C3×C4C22×D311yescharacteristic
137C22×C3×C4C23×C311yescharacteristic
138C2×#67—21no—
139C22×Dic3—21no—
140#235—21no—
141#235—21no—
142#235—21no—
143#235—21no—
144C2×D12C2×C3×C411yescharacteristic
145C2×C4×D3—21no—
146C2×Dic6C2×C3×C411yescharacteristic
147C3×M16—22no—
148C3×M16—22no—
149C3×M16—21no—
150C3×M16—21no—
151C3×M16—21no—
152C3×M16—21no—
153C3×M16—21no—
154C3×M16—21no—
155C3×M16—21no—
156C3×M16—21no—
157C3×M16—41no—
158C3×M16—41no—
159C2×C3×C8—21no—
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—21no—
167C2×C3×C8—22no—
168C2×C3×C8—32no—
169C2×C3×C8—41no—
170C2×C3×C8—41no—
171C2×C3×C8—41no—
172C2×C3×C8—41no—
173C2×C3×C8—61no—
174C2×C3×C8—61no—
175C2×C3×C8C4×D312yes—
176C2×C3×C8C2×C3×C412yes—
177C3×C4⋊C4—32no—
178C3×C22⋊C4—61no—
179C3×C42—32no—
180C3×C42—61no—
181C3×C42—61no—
182#217—21no—
183C4⋊Dic3C2×C3×C412yes—
184C4×Dic3—21no—
185C4×Dic3—21no—
186C4×Dic3C3×D412yes—
187C2×C3⋊C8—21no—
188C2×C3⋊C8—21no—
189C2×C3⋊C8C3×D412yes—
190C22×C32—22no—
191C22×C32C4×D411yescharacteristic
192C22×C32#12311yescharacteristic
193C22×C32#12611yescharacteristic
194C2×C3×D3—41no—
195C2×C3×D3—42no—
196C32×C4#11711yescharacteristic
197C32×C4C4×D411yescharacteristic
198C32×C4#12111yescharacteristic
199C32×C4#12411yescharacteristic
200C3×Dic3—24no—
201C3×Dic3—41no—
202C3×Dic3—42no—
203C2×#41—31no—
204C2×M16C2×C3×D311yescharacteristic
205C2×M16C2×C3×D311yescharacteristic
206C22×C8—31no—
207C22×C8C2×C3×D311yescharacteristic
208#117—31no—
209C2×C42—31no—
210C4⋊C8—62no—
211#104—62no—
212#103—32no—
213#102—32no—
214C22⋊C8—62no—
215C4×C8—62no—
216C23×C3—21no—
217C23×C3—61no—
218C23×C3#23911yescharacteristic
219C23×C3C3×#4111yescharacteristic
220C22×D3—21no—
221C3×Q8—61no—
222C3×Q8—61no—
223C3×D4—61no—
224C3×D4—61no—
225C3×D4—121no—
226C3×D4—121no—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—64no—
234C2×C3×C4—62no—
235C2×C3×C4—62no—
236C2×C3×C4—61no—
237C2×C3×C4—121no—
238C2×C3×C4—121no—
239C2×C3×C4C2×C4×D311yescharacteristic
240C2×C3×C4#23511yescharacteristic
241C2×C3×C4#23511yescharacteristic
242C2×C3×C4D3×D411yescharacteristic
243C2×C3×C4D3×D411yescharacteristic
244C2×C3×C4#23711yescharacteristic
245C2×C3×C4C22×C3×C411yescharacteristic
246C2×C3×C4C2×C3×D411yescharacteristic
247C2×C3×C4C2×C3×D411yescharacteristic
248C2×C3×C4C3×#4111yescharacteristic
249C2×C3×C4C3×#4111yescharacteristic
250C2×C3×C4C3×#4111yescharacteristic
251#67—41no—
252#67—41no—
253C2×Dic3—24no—
254C2×Dic3—22no—
255C2×Dic3—22no—
256C2×Dic3—21no—
257D12—21no—
258D12—21no—
259C4×D3—41no—
260C4×D3—41no—
261Dic6—21no—
262Dic6—21no—
263C3×C8—22no—
264C3×C8—22no—
265C3×C8—42no—
266C3×C8—42no—
267C3×C8—42no—
268C3×C8—41no—
269C3×C8—41no—
270C3×C8—41no—
271C3×C8—41no—
272C3×C8—62no—
273C3⋊C8—22no—
274C2×C32—21no—
275C2×C32—21no—
276C2×C32#38811yescharacteristic
277C2×C32#44312yes—
278C3×D3—81no—
279#41—61no—
280#41—61no—
281#41—61no—
282#41—61no—
283C2×Q8—31no—
284C2×D4—31no—
285C2×D4—61no—
286C22×C4—61no—
287C22×C4—61no—
288C22×C4C22×C3×D311yescharacteristic
289M16—21no—
290M16—21no—
291M16—21no—
292M16—21no—
293C2×C8—21no—
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—21no—
297C2×C8—32no—
298C2×C8—61no—
299C2×C8—61no—
300C2×C8C3×C4×D312yes—
301C4⋊C4—32no—
302C22⋊C4—61no—
303C42—32no—
304C42—61no—
305C42—61no—
306C22×C3—22no—
307C22×C3—22no—
308C22×C3—21no—
309C22×C3—21no—
310C22×C3—21no—
311C22×C3—42no—
312C22×C3—122no—
313C22×C3—121no—
314C22×C3#89311yescharacteristic
315C22×C3#89411yescharacteristic
316C22×C3#89811yescharacteristic
317C22×C3C3×C4×D411yescharacteristic
318C22×C3C3×#12311yescharacteristic
319C22×C3C3×#12611yescharacteristic
320C2×D3—41no—
321C2×D3—42no—
322C3×C4—21no—
323C3×C4—21no—
324C3×C4—21no—
325C3×C4—21no—
326C3×C4—64no—
327C3×C4—122no—
328C3×C4—121no—
329C3×C4#87211yescharacteristic
330C3×C4#67⋊C411yescharacteristic
331C3×C4#88411yescharacteristic
332C3×C4#88511yescharacteristic
333C3×C4C3×#11711yescharacteristic
334C3×C4C3×C4×D411yescharacteristic
335C3×C4C3×#12111yescharacteristic
336C3×C4C3×#12411yescharacteristic
337Dic3—24no—
338Dic3—41no—
339Dic3—42no—
340C32#193711yescharacteristic, complemented, Sylow
341C23—61no—
342C23C3×#23911yescharacteristic
343Q8—61no—
344Q8—61no—
345D4—61no—
346D4—61no—
347D4—121no—
348D4—121no—
349C2×C4—64no—
350C2×C4—62no—
351C2×C4—62no—
352C2×C4—61no—
353C2×C4—121no—
354C2×C4—121no—
355C2×C4C2×C3×C4×D311yescharacteristic
356C2×C4C3×#23511yescharacteristic
357C2×C4C3×#23511yescharacteristic
358C2×C4C3×D3×D411yescharacteristic
359C2×C4C3×D3×D411yescharacteristic
360C2×C4C3×#23711yescharacteristic
361C8—22no—
362C8—41no—
363C8—41no—
364C8—62no—
365C2×C3—21no—
366C2×C3—21no—
367C2×C3—21no—
368C2×C3—21no—
369C2×C3—21no—
370C2×C3—22no—
371C2×C3—41no—
372C2×C3—41no—
373C2×C3—241no—
374C2×C3#466911yescharacteristic
375C2×C3#489512yes—
376C2×C3C3×#38811yescharacteristic
377C2×C3C3×#44312yes—
378D3—81no—
379C22—22no—
380C22—121no—
381C22—122no—
382C22C3×#89311yescharacteristic
383C22C3×#89411yescharacteristic
384C22C3×#89811yescharacteristic
385C4—64no—
386C4—121no—
387C4—122no—
388C4C3×#87211yescharacteristic
389C4C3×#67⋊C411yescharacteristic
390C4C3×#88411yescharacteristic
391C4C3×#88511yescharacteristic
392C3—21no—
393C3#6891811yescharacteristic, direct product factor
394C3C3×#193711yescharacteristic, complemented
395C2—21no—
396C2—21no—
397C2—241no—
398C2C3×#466911yescharacteristic
399C2C3×#489512yes—
subgroupG/H
centerC2×C3×C4D3×D4
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#341C2
socleC22×C32C4×D4
prime radicalC2×C3×#235C22
cosocleC22×C3×C4C23×C3
hypercenterC3×#341D3
hypocenterC3C3×#1937
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4 ◁ C3×#341

Complements

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

NH ≅ G/Ntype
3. C3×#5119C2semidirect
5. C2×C3×C8×Dic3C2semidirect
6. C32×#341C2semidirect
7. C3×#4555C2semidirect
9. #68918C3direct (N × H)
18. C3×#821C4semidirect
20. C3×#816C4semidirect
30. #5119C2×C3semidirect
32. C2×C8×Dic3C2×C3semidirect
34. C3×#341D3semidirect
35. C3×#341C2×C3semidirect
37. #4555C2×C3semidirect
90. #821C3×C4semidirect
92. #816C3×C4semidirect
124. #341C3×D3semidirect
340. C32#1937semidirect
393. C3#68918direct (N × H)
394. C3C3×#1937semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8252
C3×#51292
C3×#51192
C3×#51132
C2×C3×C8×Dic32
C32×#3412
C3×#45552
C3×#19373
#689183