Finite Group Databasebeta

← C3×#84099 #11858007

Subgroups — C3×#84099 #11858007

Order 1152.

2005 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×H(5,𝔽2)C211yesmaximal, characteristic
2C3×#5827C211yesmaximal, characteristic, complemented
3C2×C3×#948C211yesmaximal, characteristic, complemented
4C3×#5233C213yesmaximal, complemented
5C3×#5232C213yesmaximal, complemented
6C3×#5215C213yesmaximal, complemented
7C2×C3×#832C213yesmaximal, complemented
8C3×#2897—31nomaximal
9#84099C311yesmaximal, characteristic, direct product factor
10C32×H(5,𝔽2)—24no—
11C32×H(5,𝔽2)C418yescomplemented
12C2×C32×#41—21no—
13C2×C32×#41C2213yes—
14C2×C32×#41C2211yescharacteristic
15C22×C32×D4—23no—
16C22×C32×D4C2213yes—
17C3×#948—24no—
18C3×Q8×Dic3—21no—
19C3×D4×Dic3—23no—
20C3×#926C2213yescomplemented
21C2×C3×C4⋊Dic3C2213yescomplemented
22C2×C3×#208C2213yescomplemented
23C22×C3×C3⋊C8C2213yescomplemented
24C3×#835C2213yescomplemented
25C3×#835C2211yescharacteristic, complemented
26C3×#832C2213yescomplemented
27C3×#832C2216yescomplemented
28C3×#832C2213yescomplemented
29C2×C3×H(5,𝔽2)—21no—
30C2×C3×H(5,𝔽2)D311yescharacteristic
31C2×C3×H(5,𝔽2)C2×C311yescharacteristic
32C2×C3×#131—31no—
33C3×#520—31no—
34#5827C2×C311yescharacteristic, complemented
35C2×#948C2×C311yescharacteristic, complemented
36C3×#418—33no—
37C3×#417—33no—
38C3×#416—33no—
39C2×C3×#102—33no—
40#5233C2×C313yescomplemented
41#5232C2×C313yescomplemented
42#5215C2×C313yescomplemented
43C2×#832C2×C313yescomplemented
44C24×C32—23no—
45C32×#41—28no—
46C32×#41—26no—
47C32×#41C2×C414yes—
48C32×#41C2×C4112yescomplemented
49C32×#41D414yes—
50C2×C32×Q8D411yescharacteristic
51C2×C32×Q8C2311yescharacteristic
52C2×C32×D4—23no—
53C2×C32×D4—224no—
54C2×C32×D4—23no—
55C2×C32×D4—26no—
56C2×C32×D4C2×C4112yescomplemented
57C2×C32×D4D413yes—
58C2×C32×D4C2313yes—
59C22×C32×C4—23no—
60C22×C32×C4C2313yes—
61C22×C3×Dic3—23no—
62C3×#217—23no—
63C3×C4⋊Dic3—23no—
64C3×C4⋊Dic3C2313yes—
65C3×C4⋊Dic3C2311yescharacteristic
66C3×C4×Dic3—23no—
67C3×#208—26no—
68C2×C3×C3⋊C8—26no—
69C2×C3×C3⋊C8C2311yescharacteristic
70C2×C3×C3⋊C8C2313yes—
71#2897—31noSylow
72C3×H(5,𝔽2)—28no—
73C3×H(5,𝔽2)—24no—
74C3×H(5,𝔽2)—24no—
75C3×H(5,𝔽2)—28no—
76C3×H(5,𝔽2)Dic318yescomplemented
77C3×H(5,𝔽2)C3×C418yescomplemented
78C2×C3×#41—22no—
79C2×C3×#41—21no—
80C2×C3×#41—21no—
81C2×C3×#41—23no—
82C2×C3×#41—21no—
83C2×C3×#41C2×D313yes—
84C2×C3×#41C2×D311yescharacteristic
85C2×C3×#41C22×C313yes—
86C2×C3×#41C22×C311yescharacteristic
87C22×C3×D4—26no—
88C22×C3×D4—23no—
89C22×C3×D4—23no—
90C22×C3×D4—23no—
91C22×C3×D4C2×D313yes—
92C22×C3×D4C22×C313yes—
93C3×#131—64no—
94C2×C3×M16—33no—
95C22×C3×C8—33no—
96C3×C4×Q8—61no—
97C3×C4×D4—63no—
98C3×#117—33no—
99C2×C3×C4⋊C4—33no—
100#948—24no—
101Q8×Dic3—21no—
102D4×Dic3—23no—
103#926C22×C313yescomplemented
104C2×C4⋊Dic3C22×C313yescomplemented
105C2×#208C22×C313yescomplemented
106C22×C3⋊C8C22×C313yescomplemented
107C3×#103—31no—
108C3×#103—33no—
109C3×#102—33no—
110C3×#102—36no—
111C3×#102—33no—
112#835C22×C313yescomplemented
113#835C22×C311yescharacteristic, complemented
114#832C22×C313yescomplemented
115#832C22×C316yescomplemented
116#832C22×C313yescomplemented
117C23×C32—23no—
118C23×C32—212no—
119C23×C32—83no—
120C23×C32—83no—
121C23×C32C2×D413yes—
122C32×Q8—21no—
123C32×Q8C22⋊C414yes—
124C32×Q8C22×C412yes—
125C32×D4—212no—
126C32×D4—212no—
127C32×D4—23no—
128C32×D4C22⋊C4112yes—
129C32×D4C22×C416yes—
130C2×C32×C4—21no—
131C2×C32×C4—212no—
132C2×C32×C4C22×C416yes—
133C2×C32×C4C2×D413yes—
134C2×C32×C4C2×D416yes—
135C2×C32×C4C2411yescharacteristic
136C2×C3×Dic3—21no—
137C2×C3×Dic3—23no—
138C2×C3×Dic3—83no—
139C3×C3⋊C8—21no—
140C3×C3⋊C8—23no—
141C2×H(5,𝔽2)C3×D311yescharacteristic
142C2×#131—31no—
143#520—31no—
144#418—33no—
145#417—33no—
146#416—33no—
147C2×#102—33no—
148C24×C3—26no—
149C24×C3—23no—
150C24×C3—23no—
151C3×#41—216no—
152C3×#41—212no—
153C3×#41—28no—
154C3×#41—28no—
155C3×#41—26no—
156C3×#41—26no—
157C3×#41—24no—
158C3×#41—212no—
159C3×#41—24no—
160C3×#41C2×Dic314yes—
161C3×#41C2×Dic3112yescomplemented
162C3×#41#6714yes—
163C3×#41C2×C3×C414yes—
164C3×#41C2×C3×C4112yescomplemented
165C3×#41C3×D414yes—
166C2×C3×Q8—21no—
167C2×C3×Q8—21no—
168C2×C3×Q8#6711yescharacteristic
169C2×C3×Q8C3×D411yescharacteristic
170C2×C3×Q8C22×D311yescharacteristic
171C2×C3×Q8C23×C311yescharacteristic
172C2×C3×D4—26no—
173C2×C3×D4—26no—
174C2×C3×D4—248no—
175C2×C3×D4—212no—
176C2×C3×D4—23no—
177C2×C3×D4—23no—
178C2×C3×D4—224no—
179C2×C3×D4—224no—
180C2×C3×D4—23no—
181C2×C3×D4—26no—
182C2×C3×D4—23no—
183C2×C3×D4—26no—
184C2×C3×D4—212no—
185C2×C3×D4—23no—
186C2×C3×D4—23no—
187C2×C3×D4C2×Dic3112yescomplemented
188C2×C3×D4#6713yes—
189C2×C3×D4C2×C3×C4112yescomplemented
190C2×C3×D4C3×D413yes—
191C2×C3×D4C22×D313yes—
192C2×C3×D4C23×C313yes—
193C22×C3×C4—26no—
194C22×C3×C4—23no—
195C22×C3×C4—23no—
196C22×C3×C4—23no—
197C22×C3×C4—63no—
198C22×C3×C4C22×D313yes—
199C22×C3×C4C23×C313yes—
200C22×Dic3—23no—
201C3×M16—66no—
202C2×C3×C8—31no—
203C2×C3×C8—33no—
204C2×C3×C8—66no—
205C3×C4⋊C4—33no—
206C3×C4⋊C4—31no—
207C3×C4⋊C4—63no—
208C3×C22⋊C4—63no—
209C3×C42—63no—
210#217—23no—
211C4⋊Dic3—23no—
212C4⋊Dic3C23×C313yes—
213C4⋊Dic3C23×C311yescharacteristic
214C4×Dic3—23no—
215#208—26no—
216C2×C3⋊C8—26no—
217C2×C3⋊C8C23×C311yescharacteristic
218C2×C3⋊C8C23×C313yes—
219C22×C32—26no—
220C22×C32—23no—
221C22×C32—23no—
222C22×C32—43no—
223C22×C32—43no—
224C22×C32—812no—
225C22×C32C2×C22⋊C416yes—
226C22×C32C22×D411yescharacteristic
227C32×C4—22no—
228C32×C4C2×C22⋊C416yes—
229C32×C4C23×C411yescharacteristic
230C32×C4C22×D411yescharacteristic
231C3×Dic3—43no—
232C3×Dic3—41no—
233H(5,𝔽2)—24no—
234H(5,𝔽2)C3×Dic318yescomplemented
235C2×#41—21no—
236C2×#41C2×C3×D313yes—
237C2×#41C2×C3×D311yescharacteristic
238C22×D4—23no—
239C22×D4C2×C3×D313yes—
240#131—64no—
241C2×M16—33no—
242C22×C8—33no—
243C4×Q8—61no—
244C4×D4—63no—
245#117—33no—
246C2×C4⋊C4—33no—
247#103—31no—
248#103—33no—
249#102—33no—
250#102—36no—
251#102—33no—
252C23×C3—26no—
253C23×C3—224no—
254C23×C3—23no—
255C23×C3—23no—
256C23×C3—212no—
257C23×C3—212no—
258C23×C3—23no—
259C23×C3—83no—
260C23×C3—83no—
261C23×C3—83no—
262C23×C3—83no—
263C23×C3—86no—
264C23×C3—86no—
265C23×C3C2×#6713yes—
266C23×C3C2×C3×D413yes—
267C3×Q8—22no—
268C3×Q8—21no—
269C3×Q8—21no—
270C3×Q8—24no—
271C3×Q8—22no—
272C3×Q8#21714yes—
273C3×Q8C3×C22⋊C414yes—
274C3×Q8C22×Dic312yes—
275C3×Q8C22×C3×C412yes—
276C3×D4—224no—
277C3×D4—224no—
278C3×D4—26no—
279C3×D4—212no—
280C3×D4—212no—
281C3×D4—212no—
282C3×D4—212no—
283C3×D4—23no—
284C3×D4—23no—
285C3×D4—212no—
286C3×D4—26no—
287C3×D4#217112yes—
288C3×D4C3×C22⋊C4112yes—
289C3×D4C22×Dic316yes—
290C3×D4C22×C3×C416yes—
291C2×C3×C4—22no—
292C2×C3×C4—224no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—212no—
296C2×C3×C4—212no—
297C2×C3×C4—21no—
298C2×C3×C4—26no—
299C2×C3×C4—23no—
300C2×C3×C4—26no—
301C2×C3×C4—61no—
302C2×C3×C4—63no—
303C2×C3×C4—243no—
304C2×C3×C4C22×Dic316yes—
305C2×C3×C4C2×#6713yes—
306C2×C3×C4C2×#6716yes—
307C2×C3×C4C22×C3×C416yes—
308C2×C3×C4C2×C3×D413yes—
309C2×C3×C4C2×C3×D416yes—
310C2×C3×C4C23×D311yescharacteristic
311C2×C3×C4C24×C311yescharacteristic
312C2×Dic3—21no—
313C2×Dic3—23no—
314C2×Dic3—83no—
315C3×C8—61no—
316C3×C8—63no—
317C3⋊C8—21no—
318C3⋊C8—23no—
319C2×C32—26no—
320C2×C32—46no—
321C2×C32C22×C22⋊C411yescharacteristic
322C2×C32#57611yescharacteristic
323C2×C32#57711yescharacteristic
324C24—23no—
325#41—28no—
326#41—26no—
327#41C2×C3×Dic314yes—
328#41C2×C3×Dic3112yescomplemented
329#41C3×#6714yes—
330C2×Q8C3×#6711yescharacteristic
331C2×Q8C22×C3×D311yescharacteristic
332C2×D4—23no—
333C2×D4—224no—
334C2×D4—23no—
335C2×D4—26no—
336C2×D4C2×C3×Dic3112yescomplemented
337C2×D4C3×#6713yes—
338C2×D4C22×C3×D313yes—
339C22×C4—23no—
340C22×C4—63no—
341C22×C4C22×C3×D313yes—
342M16—66no—
343C2×C8—31no—
344C2×C8—33no—
345C2×C8—66no—
346C4⋊C4—33no—
347C4⋊C4—31no—
348C4⋊C4—63no—
349C22⋊C4—63no—
350C42—63no—
351C22×C3—23no—
352C22×C3—23no—
353C22×C3—23no—
354C22×C3—23no—
355C22×C3—212no—
356C22×C3—26no—
357C22×C3—26no—
358C22×C3—26no—
359C22×C3—21no—
360C22×C3—43no—
361C22×C3—43no—
362C22×C3—46no—
363C22×C3—46no—
364C22×C3—43no—
365C22×C3—43no—
366C22×C3—43no—
367C22×C3—43no—
368C22×C3—812no—
369C22×C3—812no—
370C22×C3—824no—
371C22×C3C2×#21716yes—
372C22×C3C2×C3×C22⋊C416yes—
373C22×C3C22×#6711yescharacteristic
374C22×C3C22×C3×D411yescharacteristic
375C3×C4—24no—
376C3×C4—22no—
377C3×C4—22no—
378C3×C4—26no—
379C3×C4—21no—
380C3×C4—21no—
381C3×C4—123no—
382C3×C4—121no—
383C3×C4C2×#21716yes—
384C3×C4C2×C3×C22⋊C416yes—
385C3×C4C23×Dic311yescharacteristic
386C3×C4C22×#6711yescharacteristic
387C3×C4C23×C3×C411yescharacteristic
388C3×C4C22×C3×D411yescharacteristic
389Dic3—43no—
390Dic3—41no—
391C32#289711yescharacteristic, complemented, Sylow
392C23—23no—
393C23—212no—
394C23—83no—
395C23—83no—
396C23C2×C3×#6713yes—
397Q8—21no—
398Q8C3×#21714yes—
399Q8C22×C3×Dic312yes—
400D4—212no—
401D4—212no—
402D4—23no—
403D4C3×#217112yes—
404D4C22×C3×Dic316yes—
405C2×C4—21no—
406C2×C4—212no—
407C2×C4—61no—
408C2×C4—63no—
409C2×C4—243no—
410C2×C4C22×C3×Dic316yes—
411C2×C4C2×C3×#6713yes—
412C2×C4C2×C3×#6716yes—
413C2×C4C23×C3×D311yescharacteristic
414C8—61no—
415C8—63no—
416C2×C3—26no—
417C2×C3—26no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—46no—
422C2×C3—412no—
423C2×C3—46no—
424C2×C3—46no—
425C2×C3#583511yescharacteristic
426C2×C3#583611yescharacteristic
427C2×C3C22×#21711yescharacteristic
428C2×C3C22×C3×C22⋊C411yescharacteristic
429C2×C3C3×#57611yescharacteristic
430C2×C3C3×#57711yescharacteristic
431C22—23no—
432C22—23no—
433C22—26no—
434C22—43no—
435C22—43no—
436C22—812no—
437C22C2×C3×#21716yes—
438C22C22×C3×#6711yescharacteristic
439C4—22no—
440C4—123no—
441C4—121no—
442C4C2×C3×#21716yes—
443C4C23×C3×Dic311yescharacteristic
444C4C22×C3×#6711yescharacteristic
445C3—21no—
446C3#8409911yescharacteristic, direct product factor
447C3C3×#289711yescharacteristic, complemented
448C2—26no—
449C2—46no—
450C2C3×#583511yescharacteristic
451C2C3×#583611yescharacteristic
452C2C22×C3×#21711yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutatorC3×C4C23×C3×C4
FrattiniC2×C4C23×C3×D3
Fitting, prime radicalC2×C32×H(5,𝔽2)C2
socleC22×C32C22×D4
cosocleC2×C3×C4C24×C3
hypercenterC2×C3×H(5,𝔽2)D3
hypocenterC3C3×#2897
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C2×C3×#41 ◁ C2×C3×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
2. C3×#5827C2semidirect
3. C2×C3×#948C2semidirect
4. C3×#5233C2semidirect
5. C3×#5232C2semidirect
6. C3×#5215C2semidirect
7. C2×C3×#832C2semidirect
9. #84099C3direct (N × H)
11. C32×H(5,𝔽2)C4semidirect
20. C3×#926C22semidirect
21. C2×C3×C4⋊Dic3C22semidirect
22. C2×C3×#208C22semidirect
23. C22×C3×C3⋊C8C22semidirect
24. C3×#835C22semidirect
25. C3×#835C22semidirect
26. C3×#832C22semidirect
27. C3×#832C22semidirect
28. C3×#832C22semidirect
34. #5827C2×C3semidirect
35. C2×#948C2×C3semidirect
40. #5233C2×C3semidirect
41. #5232C2×C3semidirect
42. #5215C2×C3semidirect
43. C2×#832C2×C3semidirect
48. C32×#41C2×C4semidirect
56. C2×C32×D4C2×C4semidirect
76. C3×H(5,𝔽2)Dic3semidirect
77. C3×H(5,𝔽2)C3×C4semidirect
103. #926C22×C3semidirect
104. C2×C4⋊Dic3C22×C3semidirect
105. C2×#208C22×C3semidirect
106. C22×C3⋊C8C22×C3semidirect
112. #835C22×C3semidirect
113. #835C22×C3semidirect
114. #832C22×C3semidirect
115. #832C22×C3semidirect
116. #832C22×C3semidirect
161. C3×#41C2×Dic3semidirect
164. C3×#41C2×C3×C4semidirect
187. C2×C3×D4C2×Dic3semidirect
189. C2×C3×D4C2×C3×C4semidirect
234. H(5,𝔽2)C3×Dic3semidirect
328. #41C2×C3×Dic3semidirect
336. C2×D4C2×C3×Dic3semidirect
391. C32#2897semidirect
446. C3#84099direct (N × H)
447. C3C3×#2897semidirect

Maximal subgroups

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

subgroupindex
C2×C32×H(5,𝔽2)2
C3×#58272
C2×C3×#9482
C3×#52332
C3×#52322
C3×#52152
C2×C3×#8322
C3×#28973
#840993