Finite Group Databasebeta

← C8×#638⋊C3 #13143124

Subgroups — C8×#638⋊C3 #13143124

Order 1728.

545 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C8×H(3,𝔽3)C211yesmaximal, characteristic, complemented
2C4×#638⋊C3C211yesmaximal, characteristic
3C2×C8×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
4#63657⋊C3C211yesmaximal, characteristic, complemented
5#63647⋊C3C211yesmaximal, characteristic, complemented
6#63641⋊C3C211yesmaximal, characteristic, complemented
7C8×(C3⋊Dic3)⋊C3C211yesmaximal, characteristic, complemented
8C8×#638C311yesmaximal, characteristic, complemented
9C3×C8×#67—31nomaximal
10C22×C4×H(3,𝔽3)C2211yescharacteristic
11C2×#638⋊C3C411yescharacteristic
12C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
13C2×C8×H(3,𝔽3)—22no—
14C2×C8×H(3,𝔽3)C2211yescharacteristic
15C2×C8×H(3,𝔽3)C2211yescharacteristic
16#3757⋊C3C411yescharacteristic
17#3752⋊C3C411yescharacteristic
18#3750⋊C3C411yescharacteristic
19C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
20C2×(C3⋊(C3⋊C8))⋊C3C2211yescharacteristic
21C2×(C3⋊(C3⋊C8))⋊C3C2211yescharacteristic
22C8×(C3⋊D3)⋊C3—22no—
23C22×C32×C8—21no—
24C22×C32×C8D311yescharacteristic, complemented
25C22×C32×C8C2×C311yescharacteristic, complemented
26C4×#638C2×C311yescharacteristic
27C2×C8×C3⋊D3C2×C311yescharacteristic, complemented
28C3×C4×#67—31no—
29C2×C3×D3×C8—31no—
30#63657C2×C311yescharacteristic, complemented
31#63647C2×C311yescharacteristic, complemented
32#63641C2×C311yescharacteristic, complemented
33C8×C3⋊Dic3C2×C311yescharacteristic, complemented
34C3×#830—31no—
35C3×(C2×D3)⋊C8—31no—
36C3×Dic3⋊C8—31no—
37C3×C8×Dic3—31no—
38C23×H(3,𝔽3)C2×C411yescharacteristic
39C22×(C3⋊D3)⋊C3C2×C411yescharacteristic
40C2×C4×H(3,𝔽3)—21no—
41C2×C4×H(3,𝔽3)—21no—
42C2×C4×H(3,𝔽3)C2×C411yescharacteristic
43C2×C4×H(3,𝔽3)C2311yescharacteristic
44#638⋊C3C814yesdirect product factor
45C2×(C3⋊Dic3)⋊C3C2×C411yescharacteristic
46C2×(C3⋊Dic3)⋊C3C2×C411yescharacteristic
47C2×(C3⋊Dic3)⋊C3C2×C411yescharacteristic
48C4×(C3⋊D3)⋊C3—21no—
49C4×(C3⋊D3)⋊C3—21no—
50C8×H(3,𝔽3)—21no—
51C8×H(3,𝔽3)D412yescomplemented
52(C3⋊(C3⋊C8))⋊C3—21no—
53(C3⋊(C3⋊C8))⋊C3—21no—
54C3×C8×D4—91no—
55C8×#67—31no—
56C8×#67—91no—
57C22×C32×C4—21no—
58C22×C32×C4C2×D311yescharacteristic
59C22×C32×C4C22×C311yescharacteristic
60C2×#638C3×C411yescharacteristic
61C2×C4×C3⋊D3C22×C311yescharacteristic
62C2×C3×#67—31no—
63C2×C3×C4×D3—31no—
64C2×C32×C8—24no—
65C2×C32×C8—21no—
66C2×C32×C8—21no—
67C2×C32×C8—22no—
68C2×C32×C8—22no—
69C2×C32×C8C2×D311yescharacteristic
70C2×C32×C8C2×D311yescharacteristic
71C2×C32×C8C22×C311yescharacteristic
72C2×C32×C8C22×C311yescharacteristic
73#3757C3×C411yescharacteristic
74#3752C3×C411yescharacteristic
75#3750C3×C411yescharacteristic
76C4×C3⋊Dic3C22×C311yescharacteristic
77C2×C3⋊(C3⋊C8)C22×C311yescharacteristic
78C2×C3⋊(C3⋊C8)C22×C311yescharacteristic
79C8×C3⋊D3—22no—
80C3×#217—31no—
81C3×(C2×D3)⋊C4—31no—
82C3×Dic3⋊C4—31no—
83C3×C4×Dic3—31no—
84C2×C3×C3⋊C8—31no—
85C2×C3×C3⋊C8—31no—
86C3×D3×C8—62no—
87C22×H(3,𝔽3)—21no—
88C22×H(3,𝔽3)—21no—
89C22×H(3,𝔽3)C2×C812yescomplemented
90C22×H(3,𝔽3)C22×C411yescharacteristic
91C2×(C3⋊D3)⋊C3—21no—
92C2×(C3⋊D3)⋊C3—21no—
93C2×(C3⋊D3)⋊C3C2×C812yescomplemented
94C4×H(3,𝔽3)—21no—
95C4×H(3,𝔽3)C2×D411yescharacteristic
96C4×H(3,𝔽3)#4111yescharacteristic
97(C3⋊Dic3)⋊C3—21no—
98(C3⋊Dic3)⋊C3—21no—
99(C3⋊Dic3)⋊C3C2×C812yescomplemented
100C22×C3×C8—31no—
101C22×C3×C8—31no—
102C22×C3×C8—61no—
103C22×C3×C8—91no—
104C22×C3×C8C3×D311yescharacteristic
105C3×C4×D4—91no—
106C4×#67—31no—
107C4×#67—91no—
108C2×D3×C8—31no—
109C2×D3×C8—91no—
110C3×C4⋊C8—91no—
111C3×C22⋊C8—91no—
112C3×C22⋊C8—91no—
113C3×C4×C8—91no—
114#830—31no—
115#830—91no—
116(C2×D3)⋊C8—31no—
117(C2×D3)⋊C8—91no—
118Dic3⋊C8—31no—
119Dic3⋊C8—91no—
120C8×Dic3—31no—
121C8×Dic3—91no—
122C23×C32—21no—
123C23×C32C4×D311yescharacteristic
124C23×C32C2×C3×C411yescharacteristic
125C22×C3⋊D3C2×C3×C411yescharacteristic
126C22×C3×D3—31no—
127C2×C32×C4—22no—
128C2×C32×C4—22no—
129C2×C32×C4—21no—
130C2×C32×C4—21no—
131C2×C32×C4—21no—
132C2×C32×C4—21no—
133C2×C32×C4—21no—
134C2×C32×C4—21no—
135C2×C32×C4C4×D311yescharacteristic
136C2×C32×C4C2×C3×C411yescharacteristic
137C2×C32×C4C22×D311yescharacteristic
138C2×C32×C4C23×C311yescharacteristic
139#638C3×C814yescomplemented
140C2×C3⋊Dic3C2×C3×C411yescharacteristic
141C2×C3⋊Dic3C2×C3×C411yescharacteristic
142C2×C3⋊Dic3C2×C3×C411yescharacteristic
143C4×C3⋊D3—21no—
144C4×C3⋊D3—21no—
145C3×#67—34no—
146C2×C3×Dic3—31no—
147C2×C3×Dic3—31no—
148C2×C3×Dic3—31no—
149C3×C4×D3—61no—
150C3×C4×D3—61no—
151C32×C8—22no—
152C32×C8—21no—
153C32×C8—21no—
154C32×C8—22no—
155C32×C8#6712yescomplemented
156C32×C8C3×D412yescomplemented
157C3⋊(C3⋊C8)—21no—
158C3⋊(C3⋊C8)—21no—
159C3×C3⋊C8—61no—
160C3×C3⋊C8—61no—
161C8×D4—91noSylow
162C2×H(3,𝔽3)—22no—
163C2×H(3,𝔽3)C4×D411yescharacteristic
164C2×H(3,𝔽3)C22×C811yescharacteristic
165C2×H(3,𝔽3)#13111yescharacteristic
166(C3⋊D3)⋊C3—22no—
167C2×C3×D4—91no—
168C22×C3×C4—31no—
169C22×C3×C4—31no—
170C22×C3×C4—61no—
171C22×C3×C4—91no—
172C22×C3×C4C2×C3×D311yescharacteristic
173C2×#67—31no—
174C2×#67—91no—
175C2×C4×D3—31no—
176C2×C4×D3—91no—
177C2×C3×C8—22no—
178C2×C3×C8—31no—
179C2×C3×C8—31no—
180C2×C3×C8—31no—
181C2×C3×C8—31no—
182C2×C3×C8—62no—
183C2×C3×C8—62no—
184C2×C3×C8—64no—
185C2×C3×C8—61no—
186C2×C3×C8—61no—
187C2×C3×C8—91no—
188C2×C3×C8—91no—
189C2×C3×C8—182no—
190C2×C3×C8C2×C3×D311yescharacteristic
191C2×C3×C8C2×C3×D311yescharacteristic
192C3×C4⋊C4—91no—
193C3×C22⋊C4—91no—
194C3×C22⋊C4—91no—
195C3×C42—91no—
196#217—31no—
197#217—91no—
198(C2×D3)⋊C4—31no—
199(C2×D3)⋊C4—91no—
200Dic3⋊C4—31no—
201Dic3⋊C4—91no—
202C4×Dic3—31no—
203C4×Dic3—91no—
204C2×C3⋊C8—31no—
205C2×C3⋊C8—31no—
206C2×C3⋊C8—91no—
207C2×C3⋊C8—91no—
208D3×C8—62no—
209D3×C8—182no—
210C22×C32—22no—
211C22×C32—22no—
212C22×C32—21no—
213C22×C32—21no—
214C22×C32—21no—
215C22×C32—21no—
216C22×C32—22no—
217C22×C32—21no—
218C22×C32D3×C812yescomplemented
219C22×C32C2×C3×C812yescomplemented
220C22×C32C2×C4×D311yescharacteristic
221C22×C32C22×C3×C411yescharacteristic
222C2×C3⋊D3—21no—
223C2×C3⋊D3—21no—
224C2×C3⋊D3C2×C3×C812yescomplemented
225C2×C3×D3—32no—
226C2×C3×D3—61no—
227C2×C3×D3—61no—
228C32×C4—22no—
229C32×C4—21no—
230C32×C4—21no—
231C32×C4—21no—
232C32×C4—21no—
233C32×C4#23511yescharacteristic
234C32×C4C2×#6711yescharacteristic
235C32×C4C2×C3×D411yescharacteristic
236C32×C4C3×#4111yescharacteristic
237C3⋊Dic3—21no—
238C3⋊Dic3—21no—
239C3⋊Dic3C2×C3×C812yescomplemented
240C3×Dic3—32no—
241C3×Dic3—61no—
242C3×Dic3—61no—
243C22×C8—91no—
244C22×C8(C3⋊D3)⋊C311yescharacteristic, complemented
245C4×D4—91no—
246C4⋊C8—91no—
247C22⋊C8—91no—
248C22⋊C8—91no—
249C4×C8—91no—
250H(3,𝔽3)C8×D411yescharacteristic, complemented, Sylow
251C23×C3—31no—
252C23×C3—31no—
253C23×C3—61no—
254C23×C3—91no—
255C23×C3C3×C4×D311yescharacteristic
256C22×D3—31no—
257C22×D3—91no—
258C3×D4—94no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—31no—
262C2×C3×C4—31no—
263C2×C3×C4—31no—
264C2×C3×C4—31no—
265C2×C3×C4—61no—
266C2×C3×C4—61no—
267C2×C3×C4—61no—
268C2×C3×C4—61no—
269C2×C3×C4—62no—
270C2×C3×C4—62no—
271C2×C3×C4—61no—
272C2×C3×C4—61no—
273C2×C3×C4—91no—
274C2×C3×C4—91no—
275C2×C3×C4—91no—
276C2×C3×C4—181no—
277C2×C3×C4—181no—
278C2×C3×C4C3×C4×D311yescharacteristic
279C2×C3×C4C22×C3×D311yescharacteristic
280#67—34no—
281#67—94no—
282C2×Dic3—31no—
283C2×Dic3—31no—
284C2×Dic3—31no—
285C2×Dic3—91no—
286C2×Dic3—91no—
287C2×Dic3—91no—
288C4×D3—61no—
289C4×D3—61no—
290C4×D3—181no—
291C4×D3—181no—
292C3×C8—21no—
293C3×C8—32no—
294C3×C8—32no—
295C3×C8—61no—
296C3×C8—61no—
297C3×C8—62no—
298C3×C8—62no—
299C3×C8—181no—
300C3×C8—181no—
301C3×C8C3×#6712yes—
302C3⋊C8—61no—
303C3⋊C8—61no—
304C3⋊C8—181no—
305C3⋊C8—181no—
306C2×C32—24no—
307C2×C32—22no—
308C2×C32—22no—
309C2×C32—21no—
310C2×C32—21no—
311C2×C32—21no—
312C2×C32C2×D3×C811yescharacteristic
313C2×C32#90111yescharacteristic
314C2×C32C4×#6711yescharacteristic
315C2×C32C3×C4×D411yescharacteristic
316C2×C32C22×C3×C811yescharacteristic
317C2×C32C3×#13111yescharacteristic
318C3⋊D3—22no—
319C3×D3—62no—
320C2×D4—91no—
321C22×C4—91no—
322C22×C4C2×(C3⋊D3)⋊C311yescharacteristic
323C2×C8—22no—
324C2×C8—91no—
325C2×C8—91no—
326C2×C8—182no—
327C2×C8C2×(C3⋊D3)⋊C311yescharacteristic
328C2×C8C2×(C3⋊D3)⋊C311yescharacteristic
329C4⋊C4—91no—
330C22⋊C4—91no—
331C22⋊C4—91no—
332C42—91no—
333C22×C3—21no—
334C22×C3—21no—
335C22×C3—31no—
336C22×C3—31no—
337C22×C3—32no—
338C22×C3—32no—
339C22×C3—61no—
340C22×C3—61no—
341C22×C3—61no—
342C22×C3—61no—
343C22×C3—62no—
344C22×C3—62no—
345C22×C3—61no—
346C22×C3—62no—
347C22×C3—92no—
348C22×C3—181no—
349C22×C3—181no—
350C22×C3C3×D3×C812yes—
351C22×C3C2×C3×C4×D311yescharacteristic
352C2×D3—32no—
353C2×D3—61no—
354C2×D3—61no—
355C2×D3—92no—
356C2×D3—181no—
357C2×D3—181no—
358C3×C4—21no—
359C3×C4—31no—
360C3×C4—31no—
361C3×C4—31no—
362C3×C4—31no—
363C3×C4—61no—
364C3×C4—61no—
365C3×C4—62no—
366C3×C4—61no—
367C3×C4—61no—
368C3×C4—92no—
369C3×C4—181no—
370C3×C4—181no—
371C3×C4C3×#23511yescharacteristic
372C3×C4C2×C3×#6711yescharacteristic
373Dic3—32no—
374Dic3—61no—
375Dic3—61no—
376Dic3—92no—
377Dic3—181no—
378Dic3—181no—
379C32—21no—
380C32C8×#6711yescharacteristic, complemented
381C32C3×C8×D411yescharacteristic, complemented
382C23—91no—
383C23C4×(C3⋊D3)⋊C311yescharacteristic
384D4—94no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—91no—
388C2×C4—91no—
389C2×C4—91no—
390C2×C4—181no—
391C2×C4—181no—
392C2×C4C4×(C3⋊D3)⋊C311yescharacteristic
393C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
394C8—21no—
395C8—181no—
396C8—181no—
397C8#638⋊C312yesdirect product factor
398C2×C3—22no—
399C2×C3—31no—
400C2×C3—31no—
401C2×C3—31no—
402C2×C3—31no—
403C2×C3—31no—
404C2×C3—31no—
405C2×C3—62no—
406C2×C3—62no—
407C2×C3—64no—
408C2×C3—61no—
409C2×C3—61no—
410C2×C3—61no—
411C2×C3—182no—
412C2×C3C2×C3×D3×C811yescharacteristic
413C2×C3C3×#90111yescharacteristic
414C2×C3C3×C4×#6711yescharacteristic
415D3—62no—
416D3—182no—
417C22—21no—
418C22—21no—
419C22—92no—
420C22—181no—
421C22—181no—
422C22C8×(C3⋊D3)⋊C312yescomplemented
423C22C2×C4×(C3⋊D3)⋊C311yescharacteristic
424C4—21no—
425C4—92no—
426C4—181no—
427C4—181no—
428C4#3828⋊C311yescharacteristic
429C4C2×#638⋊C311yescharacteristic
430C3—31no—
431C3—31no—
432C3—61no—
433C3C3×C8×#6711yescharacteristic
434C2—22no—
435C2—182no—
436C2C2×C8×(C3⋊D3)⋊C311yescharacteristic
437C2#64110⋊C311yescharacteristic
438C2C4×#638⋊C311yescharacteristic
subgroupG/H
centerC2×C8C2×(C3⋊D3)⋊C3
commutatorC2×C32C22×C3×C8
FrattiniC2×C3×C4C22×C3×D3
FittingC22×C8×H(3,𝔽3)C2
socleC22×C3C2×C3×C4×D3
prime radicalC2×#638⋊C3C4
cosocleC2×C32×C4C23×C3
hypercenterC22×C8(C3⋊D3)⋊C3
hypocenterC32C3×C8×D4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C8 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C22×C8×H(3,𝔽3)C2semidirect
3. C2×C8×(C3⋊D3)⋊C3C2semidirect
4. #63657⋊C3C2semidirect
5. #63647⋊C3C2semidirect
6. #63641⋊C3C2semidirect
7. C8×(C3⋊Dic3)⋊C3C2semidirect
8. C8×#638C3semidirect
24. C22×C32×C8D3semidirect
25. C22×C32×C8C2×C3semidirect
27. C2×C8×C3⋊D3C2×C3semidirect
30. #63657C2×C3semidirect
31. #63647C2×C3semidirect
32. #63641C2×C3semidirect
33. C8×C3⋊Dic3C2×C3semidirect
44. #638⋊C3C8direct (N × H)
51. C8×H(3,𝔽3)D4semidirect
89. C22×H(3,𝔽3)C2×C8semidirect
93. C2×(C3⋊D3)⋊C3C2×C8semidirect
99. (C3⋊Dic3)⋊C3C2×C8semidirect
139. #638C3×C8semidirect
155. C32×C8#67semidirect
156. C32×C8C3×D4semidirect
218. C22×C32D3×C8semidirect
219. C22×C32C2×C3×C8semidirect
224. C2×C3⋊D3C2×C3×C8semidirect
239. C3⋊Dic3C2×C3×C8semidirect
244. C22×C8(C3⋊D3)⋊C3semidirect
250. H(3,𝔽3)C8×D4semidirect
380. C32C8×#67semidirect
381. C32C3×C8×D4semidirect
397. C8#638⋊C3direct (N × H)
422. C22C8×(C3⋊D3)⋊C3semidirect

Maximal subgroups

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

subgroupindex
C22×C8×H(3,𝔽3)2
C4×#638⋊C32
C2×C8×(C3⋊D3)⋊C32
#63657⋊C32
#63647⋊C32
#63641⋊C32
C8×(C3⋊Dic3)⋊C32
C8×#6383
C3×C8×#673