Finite Group Databasebeta

← C3×#68399 #11781701

Subgroups — C3×#68399 #11781701

Order 1152.

438 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
1C3×#5073C211yesmaximal, characteristic, complemented
2C3×#5072C211yesmaximal, characteristic, complemented
3C3×#4843C211yesmaximal, characteristic, complemented
4C3×#4838C211yesmaximal, characteristic, complemented
5C32×#331C211yesmaximal, characteristic, complemented
6C3×#4485C211yesmaximal, characteristic, complemented
7C3×#4480C211yesmaximal, characteristic, complemented
8C3×#1687—31nomaximal
9#68399C311yesmaximal, characteristic, direct product factor
10C32×#127C2211yescharacteristic
11C2×C3×#213—21no—
12C2×C3×#213—21no—
13C2×C3×#213—21no—
14C2×C3×D24—21no—
15C2×C3×ΓL(1,𝔽25)—21no—
16C3×#874C2211yescharacteristic
17C3×C4×D12C2211yescharacteristic
18C32×C4⋊C8C2211yescharacteristic
19C32×C4⋊C8C2211yescharacteristic
20C3×#832—21no—
21C3×#821—21no—
22C3×(C2×D3)⋊C8—21no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25C3×#493—31no—
26C3×#459—31no—
27C3×#459—31no—
28C3×#436—31no—
29#5073C2×C311yescharacteristic, complemented
30#5072C2×C311yescharacteristic, complemented
31#4843C2×C311yescharacteristic, complemented
32#4838C2×C311yescharacteristic, complemented
33C3×#334—31no—
34C3×#331—21no—
35C3×#331—31no—
36C3×#331D311yescharacteristic, complemented
37C3×#331C2×C311yescharacteristic, complemented
38#4485C2×C311yescharacteristic, complemented
39#4480C2×C311yescharacteristic, complemented
40C2×C32×D4—21no—
41C2×C32×D4—21no—
42C2×C32×D4—21no—
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C2×C3×D12D411yescharacteristic
47C2×C3×C4×D3—21no—
48C2×C32×C8—21no—
49C2×C32×C8—21no—
50C32×C42C2311yescharacteristic
51C3×#213—42no—
52C3×#213—42no—
53C3×#213—42no—
54C3×(C2×D3)⋊C4—21no—
55C3×C4⋊Dic3D411yescharacteristic
56C2×C3×C3⋊C8—21no—
57C2×C3×C3⋊C8D411yescharacteristic
58C2×C3×C3⋊C8D411yescharacteristic
59C3×D24—42no—
60C3×ΓL(1,𝔽25)—42no—
61#1687—31noSylow
62C2×C3×D8—61no—
63C2×C3×D8—61no—
64C2×C3×D8—61no—
65C2×C3×D8—61no—
66C2×C3×M16—61no—
67C3×#127—21no—
68C3×#127—31no—
69C3×#127C2×D311yescharacteristic
70C3×#127C22×C311yescharacteristic
71C3×C4×D4—31no—
72C2×#213—21no—
73C2×#213—21no—
74C2×#213—21no—
75C2×D24—21no—
76C2×ΓL(1,𝔽25)—21no—
77#874C22×C311yescharacteristic
78C4×D12C22×C311yescharacteristic
79C3×C4⋊C8—21no—
80C3×C4⋊C8—21no—
81C3×C4⋊C8—31no—
82C3×C4⋊C8C2×D311yescharacteristic
83C3×C4⋊C8C2×D311yescharacteristic
84C3×C4⋊C8C22×C311yescharacteristic
85C3×C4⋊C8C22×C311yescharacteristic
86C3×#102—61no—
87C3×#102—61no—
88C3×C22⋊C8—61no—
89C3×C4×C8—31no—
90#832—21no—
91#821—21no—
92(C2×D3)⋊C8—21no—
93C4⋊(C3⋊C8)C22×C311yescharacteristic
94C4×C3⋊C8C22×C311yescharacteristic
95C23×C32—41no—
96C22×C3×D3—21no—
97C22×C3×D3—41no—
98C32×D4—41no—
99C32×D4—41no—
100C32×D4—41no—
101C32×D4—41no—
102C32×D4—81no—
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4#4111yescharacteristic
106C2×C3×Dic3—21no—
107C3×D12—21no—
108C3×D12—21no—
109C3×D12—41no—
110C3×D12—41no—
111C3×D12—41no—
112C3×D12—41no—
113C3×D12—81no—
114C3×C4×D3—41no—
115C3×C4×D3—41no—
116C32×C8—41no—
117C32×C8—41no—
118C3×C3⋊C8—21no—
119C3×C3⋊C8—41no—
120C3×C3⋊C8D812yescomplemented
121#493—31no—
122#459—31no—
123#459—31no—
124#436—31no—
125#334—31no—
126#331—31no—
127#331C3×D311yescharacteristic, complemented
128C2×C3×D4—22no—
129C2×C3×D4—21no—
130C2×C3×D4—21no—
131C2×C3×D4—21no—
132C2×C3×D4—21no—
133C2×C3×D4—21no—
134C2×C3×D4—21no—
135C2×C3×D4—31no—
136C2×C3×D4—41no—
137C2×C3×D4—41no—
138C2×C3×D4—61no—
139C2×C3×D4—61no—
140C2×C3×D4—61no—
141C22×C3×C4—61no—
142C2×D12—21no—
143C2×D12—21no—
144C2×D12—21no—
145C2×D12C3×D411yescharacteristic
146C2×C4×D3—21no—
147C3×D8—122no—
148C3×D8—122no—
149C3×D8—122no—
150C3×D8—122no—
151C3×M16—122no—
152C2×C3×C8—21no—
153C2×C3×C8—21no—
154C2×C3×C8—21no—
155C2×C3×C8—21no—
156C2×C3×C8—31no—
157C2×C3×C8—31no—
158C2×C3×C8—41no—
159C2×C3×C8—41no—
160C2×C3×C8—61no—
161C3×C4⋊C4—31no—
162C3×C22⋊C4—61no—
163C3×C42—21no—
164C3×C42C22×D311yescharacteristic
165C3×C42C23×C311yescharacteristic
166#213—42no—
167#213—42no—
168#213—42no—
169(C2×D3)⋊C4—21no—
170C4⋊Dic3C3×D411yescharacteristic
171C2×C3⋊C8—21no—
172C2×C3⋊C8C3×D411yescharacteristic
173C2×C3⋊C8C3×D411yescharacteristic
174D24—42no—
175ΓL(1,𝔽25)—42no—
176C22×C32—81no—
177C22×C32—81no—
178C22×C32—81no—
179C22×C32#12111yescharacteristic
180C2×C3×D3—41no—
181C2×C3×D3—41no—
182C2×C3×D3—41no—
183C2×C3×D3—81no—
184C2×C3×D3—81no—
185C2×C3×D3—81no—
186C32×C4—21no—
187C32×C4C2×D811yescharacteristic
188C32×C4AGL(1,ℤ/8)11yescharacteristic
189C32×C4AGL(1,ℤ/8)11yescharacteristic
190C32×C4AGL(1,ℤ/8)11yescharacteristic
191C3×Dic3—41no—
192C2×D8—61no—
193C2×D8—61no—
194C2×D8—61no—
195C2×D8—61no—
196C2×M16—61no—
197#127—31no—
198#127C2×C3×D311yescharacteristic
199C4×D4—31no—
200C4⋊C8—31no—
201C4⋊C8C2×C3×D311yescharacteristic
202C4⋊C8C2×C3×D311yescharacteristic
203#102—61no—
204#102—61no—
205C22⋊C8—61no—
206C4×C8—31no—
207C23×C3—42no—
208C23×C3—41no—
209C23×C3—41no—
210C23×C3—61no—
211C23×C3—121no—
212C22×D3—21no—
213C22×D3—41no—
214C3×D4—41no—
215C3×D4—41no—
216C3×D4—41no—
217C3×D4—41no—
218C3×D4—41no—
219C3×D4—41no—
220C3×D4—41no—
221C3×D4—41no—
222C3×D4—61no—
223C3×D4—61no—
224C3×D4—81no—
225C3×D4—81no—
226C3×D4—81no—
227C3×D4—81no—
228C3×D4—81no—
229C3×D4—81no—
230C3×D4—82no—
231C3×D4—121no—
232C3×D4—121no—
233C3×D4—121no—
234C3×D4—121no—
235C3×D4—241no—
236C2×C3×C4—21no—
237C2×C3×C4—21no—
238C2×C3×C4—21no—
239C2×C3×C4—61no—
240C2×C3×C4—121no—
241C2×C3×C4—121no—
242C2×C3×C4#23511yescharacteristic
243C2×C3×C4D3×D411yescharacteristic
244C2×C3×C4D3×D411yescharacteristic
245C2×C3×C4C2×C3×D411yescharacteristic
246C2×C3×C4C2×C3×D411yescharacteristic
247C2×C3×C4C3×#4111yescharacteristic
248C2×Dic3—21no—
249D12—21no—
250D12—21no—
251D12—41no—
252D12—41no—
253D12—41no—
254D12—41no—
255D12—81no—
256C4×D3—41no—
257C4×D3—41no—
258C3×C8—32no—
259C3×C8—41no—
260C3×C8—41no—
261C3×C8—41no—
262C3×C8—41no—
263C3×C8—61no—
264C3×C8—81no—
265C3×C8—81no—
266C3×C8—121no—
267C3⋊C8—21no—
268C3⋊C8—41no—
269C3⋊C8C3×D812yescomplemented
270C2×C32—161no—
271C2×C32#45911yescharacteristic
272C2×C32#46911yescharacteristic
273C2×C32#47211yescharacteristic
274C3×D3—81no—
275C3×D3—161no—
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—21no—
279C2×D4—31no—
280C2×D4—61no—
281C2×D4—61no—
282C2×D4—61no—
283C22×C4—61no—
284D8—122no—
285D8—122no—
286D8—122no—
287D8—122no—
288M16—122no—
289C2×C8—21no—
290C2×C8—21no—
291C2×C8—31no—
292C2×C8—31no—
293C2×C8—61no—
294C4⋊C4—31no—
295C22⋊C4—61no—
296C42C22×C3×D311yescharacteristic
297C22×C3—21no—
298C22×C3—82no—
299C22×C3—82no—
300C22×C3—82no—
301C22×C3—81no—
302C22×C3—81no—
303C22×C3—81no—
304C22×C3—81no—
305C22×C3—81no—
306C22×C3—81no—
307C22×C3—121no—
308C22×C3—121no—
309C22×C3—121no—
310C22×C3—241no—
311C22×C3—241no—
312C22×C3—241no—
313C22×C3#88411yescharacteristic
314C22×C3C3×#12111yescharacteristic
315C2×D3—41no—
316C2×D3—41no—
317C2×D3—41no—
318C2×D3—81no—
319C2×D3—81no—
320C2×D3—81no—
321C3×C4—21no—
322C3×C4—21no—
323C3×C4—21no—
324C3×C4—21no—
325C3×C4—21no—
326C3×C4—21no—
327C3×C4—41no—
328C3×C4—121no—
329C3×C4D3×D811yescharacteristic
330C3×C4#91111yescharacteristic
331C3×C4#91411yescharacteristic
332C3×C4#91411yescharacteristic
333C3×C4C2×C3×D811yescharacteristic
334C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
335C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
336C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
337Dic3—41no—
338C32#168711yescharacteristic, complemented, Sylow
339C23—41no—
340C23—61no—
341C23—121no—
342D4—41no—
343D4—41no—
344D4—41no—
345D4—41no—
346D4—61no—
347D4—61no—
348D4—81no—
349D4—121no—
350D4—121no—
351D4—121no—
352D4—121no—
353D4—241no—
354C2×C4—61no—
355C2×C4—121no—
356C2×C4—121no—
357C2×C4C3×#23511yescharacteristic
358C2×C4C3×D3×D411yescharacteristic
359C2×C4C3×D3×D411yescharacteristic
360C8—32no—
361C8—41no—
362C8—41no—
363C8—61no—
364C8—121no—
365C2×C3—21no—
366C2×C3—21no—
367C2×C3—21no—
368C2×C3—162no—
369C2×C3—161no—
370C2×C3—161no—
371C2×C3—241no—
372C2×C3—481no—
373C2×C3#474911yescharacteristic
374C2×C3#478211yescharacteristic
375C2×C3#478611yescharacteristic
376C2×C3C3×#45911yescharacteristic
377C2×C3C3×#46911yescharacteristic
378C2×C3C3×#47211yescharacteristic
379D3—81no—
380D3—161no—
381C22—81no—
382C22—81no—
383C22—81no—
384C22—121no—
385C22—121no—
386C22—121no—
387C22—241no—
388C22—241no—
389C22—241no—
390C22C3×#88411yescharacteristic
391C4—21no—
392C4—121no—
393C4C3×D3×D811yescharacteristic
394C4C3×#91111yescharacteristic
395C4C3×#91411yescharacteristic
396C4C3×#91411yescharacteristic
397C3—21no—
398C3#6839911yescharacteristic, direct product factor
399C3C3×#168711yescharacteristic, complemented
400C2—161no—
401C2—241no—
402C2—481no—
403C2C3×#474911yescharacteristic
404C2C3×#478211yescharacteristic
405C2C3×#478611yescharacteristic
subgroupG/H
centerC22×C3#884
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#331C2
socleC22×C32#121
hypercenterC3×#331D3
hypocenterC3C3×#1687
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#331

Complements

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

NH ≅ G/Ntype
1. C3×#5073C2semidirect
2. C3×#5072C2semidirect
3. C3×#4843C2semidirect
4. C3×#4838C2semidirect
5. C32×#331C2semidirect
6. C3×#4485C2semidirect
7. C3×#4480C2semidirect
9. #68399C3direct (N × H)
29. #5073C2×C3semidirect
30. #5072C2×C3semidirect
31. #4843C2×C3semidirect
32. #4838C2×C3semidirect
36. C3×#331D3semidirect
37. C3×#331C2×C3semidirect
38. #4485C2×C3semidirect
39. #4480C2×C3semidirect
120. C3×C3⋊C8D8semidirect
127. #331C3×D3semidirect
269. C3⋊C8C3×D8semidirect
338. C32#1687semidirect
398. C3#68399direct (N × H)
399. C3C3×#1687semidirect

Maximal subgroups

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

subgroupindex
C3×#50732
C3×#50722
C3×#48432
C3×#48382
C32×#3312
C3×#44852
C3×#44802
C3×#16873
#683993