Finite Group Databasebeta

← C2×#63632⋊C3 #13142413

Subgroups — C2×#63632⋊C3 #13142413

Order 1728.

703 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3828⋊C3C211yesmaximal, characteristic
2C2×C42×H(3,𝔽3)C211yesmaximal, characteristic, complemented
3C2×#3748⋊C3C211yesmaximal, characteristic, complemented
4#63632⋊C3C214yesmaximal, direct product factor
5C2×#63632C311yesmaximal, characteristic, complemented
6C2×C3×#805—31nomaximal
7C22×C4×H(3,𝔽3)—21no—
8C22×C4×H(3,𝔽3)C2211yescharacteristic
9C2×#638⋊C3—21no—
10#3828⋊C3—21no—
11#3828⋊C3—21no—
12#3828⋊C3C412yescomplemented
13#3828⋊C3C2212yes—
14C2×C4⋊((C3⋊D3)⋊C3)C411yescharacteristic, complemented
15C2×C4×(C3⋊D3)⋊C3—21no—
16C2×#634⋊C3C411yescharacteristic, complemented
17C42×H(3,𝔽3)—21no—
18C42×H(3,𝔽3)C2212yescomplemented
19#3748⋊C3—21no—
20#3748⋊C3C2212yescomplemented
21C2×(C3⋊(C3⋊C8))⋊C3—21no—
22C2×#3828C2×C311yescharacteristic
23C2×C3×#235—31no—
24C2×C32×C42—21no—
25C2×C32×C42D311yescharacteristic, complemented
26C2×C32×C42C2×C311yescharacteristic, complemented
27C2×#3748C2×C311yescharacteristic, complemented
28C2×C3×#208—31no—
29#63632C2×C314yescomplemented
30C3×#805—34no—
31C23×H(3,𝔽3)D411yescharacteristic
32C22×(C3⋊D3)⋊C3—21no—
33C2×C4×H(3,𝔽3)—24no—
34C2×C4×H(3,𝔽3)—22no—
35C2×C4×H(3,𝔽3)C2×C411yescharacteristic
36C2×C4×H(3,𝔽3)C2×C411yescharacteristic
37C2×C4×H(3,𝔽3)D411yescharacteristic
38C2×C4×H(3,𝔽3)D411yescharacteristic
39C2×C4×H(3,𝔽3)D411yescharacteristic
40C2×C4×H(3,𝔽3)C2311yescharacteristic
41#638⋊C3—22no—
42#638⋊C3—22no—
43C2×(C3⋊Dic3)⋊C3—21no—
44C4⋊((C3⋊D3)⋊C3)—21no—
45C4⋊((C3⋊D3)⋊C3)C2×C412yescomplemented
46C4×(C3⋊D3)⋊C3—22no—
47C4×(C3⋊D3)⋊C3—22no—
48#634⋊C3—21no—
49#634⋊C3C2×C412yescomplemented
50(C3⋊(C3⋊C8))⋊C3—22no—
51C2×C3×#104—91no—
52C2×#805—31no—
53C2×#805—91no—
54C22×C32×C4—22no—
55C22×C32×C4—21no—
56C22×C32×C4—21no—
57C22×C32×C4—21no—
58C22×C32×C4C2×D311yescharacteristic
59C22×C32×C4C22×C311yescharacteristic
60C2×#638—21no—
61#3828—21no—
62#3828—21no—
63#3828C3×C412yescomplemented
64#3828C22×C312yes—
65C2×C4⋊(C3⋊D3)C3×C411yescharacteristic, complemented
66C2×C4×C3⋊D3—21no—
67C2×#634C3×C411yescharacteristic, complemented
68C2×C3×#67—61no—
69C3×#235—32no—
70C3×#235—32no—
71C3×#235—61no—
72C3×#235—61no—
73C2×C3×D12—31no—
74C2×C3×C4×D3—61no—
75C2×C3×Dic6—31no—
76C32×C42—22no—
77C32×C42—22no—
78C32×C42—21no—
79C32×C42—21no—
80C32×C42C2×D312yescomplemented
81C32×C42C22×C312yescomplemented
82#3748—21no—
83#3748C22×C312yescomplemented
84C2×C3⋊(C3⋊C8)—21no—
85C3×#208—32no—
86C3×#208—61no—
87C2×C3×C3⋊C8—61no—
88C22×H(3,𝔽3)—22no—
89C22×H(3,𝔽3)C22⋊C411yescharacteristic
90C22×H(3,𝔽3)C22⋊C411yescharacteristic
91C22×H(3,𝔽3)C2×D411yescharacteristic
92C2×(C3⋊D3)⋊C3—22no—
93C2×(C3⋊D3)⋊C3—42no—
94C4×H(3,𝔽3)—24no—
95C4×H(3,𝔽3)C22⋊C411yescharacteristic
96C4×H(3,𝔽3)C22⋊C411yescharacteristic
97C4×H(3,𝔽3)C22×C411yescharacteristic
98C4×H(3,𝔽3)C2×D411yescharacteristic
99(C3⋊Dic3)⋊C3—22no—
100C2×C3×#41—91no—
101C2×#235—31no—
102C2×#235—91no—
103C2×C3×M16—91no—
104C2×C3×C42—31no—
105C2×C3×C42—31no—
106C2×C3×C42—61no—
107C2×C3×C42C3×D311yescharacteristic
108C2×#208—31no—
109C2×#208—91no—
110C3×#104—94no—
111#805—34no—
112#805—94no—
113C23×C32—21no—
114C23×C32#6711yescharacteristic
115C23×C32C3×D411yescharacteristic
116C22×C3⋊D3—21no—
117C22×C3×D3—61no—
118C2×C32×C4—24no—
119C2×C32×C4—28no—
120C2×C32×C4—24no—
121C2×C32×C4—24no—
122C2×C32×C4—22no—
123C2×C32×C4—22no—
124C2×C32×C4—21no—
125C2×C32×C4—21no—
126C2×C32×C4—21no—
127C2×C32×C4—21no—
128C2×C32×C4—21no—
129C2×C32×C4—21no—
130C2×C32×C4C4×D311yescharacteristic
131C2×C32×C4C4×D311yescharacteristic
132C2×C32×C4D1211yescharacteristic
133C2×C32×C4D1211yescharacteristic
134C2×C32×C4#6711yescharacteristic
135C2×C32×C4C2×C3×C411yescharacteristic
136C2×C32×C4C2×C3×C411yescharacteristic
137C2×C32×C4C3×D411yescharacteristic
138C2×C32×C4C3×D411yescharacteristic
139C2×C32×C4C3×D411yescharacteristic
140C2×C32×C4C22×D311yescharacteristic
141C2×C32×C4C23×C311yescharacteristic
142#638—22no—
143#638—22no—
144C2×C3⋊Dic3—21no—
145C4⋊(C3⋊D3)—21no—
146C4⋊(C3⋊D3)C2×C3×C412yescomplemented
147C4×C3⋊D3—22no—
148C4×C3⋊D3—22no—
149#634—21no—
150#634C2×C3×C412yescomplemented
151C3×#67—62no—
152C3×#67—62no—
153C2×C3×Dic3—61no—
154C3×D12—32no—
155C3×D12—61no—
156C3×C4×D3—62no—
157C3×C4×D3—62no—
158C3×Dic6—32no—
159C3×Dic6—61no—
160C3⋊(C3⋊C8)—22no—
161C3×C3⋊C8—62no—
162C2×#104—91noSylow
163C2×H(3,𝔽3)—21no—
164C2×H(3,𝔽3)—21no—
165C2×H(3,𝔽3)#10412yescomplemented
166C2×H(3,𝔽3)C2×C22⋊C411yescharacteristic
167(C3⋊D3)⋊C3—42no—
168C3×#41—92no—
169C3×#41—92no—
170C3×#41—181no—
171C3×#41—181no—
172C2×C3×Q8—91no—
173C2×C3×D4—91no—
174C2×C3×D4—181no—
175C22×C3×C4—21no—
176C22×C3×C4—31no—
177C22×C3×C4—31no—
178C22×C3×C4—61no—
179C22×C3×C4—61no—
180C22×C3×C4—62no—
181C22×C3×C4—61no—
182C22×C3×C4—181no—
183C22×C3×C4C2×C3×D311yescharacteristic
184C2×#67—61no—
185C2×#67—181no—
186#235—32no—
187#235—32no—
188#235—61no—
189#235—61no—
190#235—92no—
191#235—92no—
192#235—181no—
193#235—181no—
194C2×D12—31no—
195C2×D12—91no—
196C2×C4×D3—61no—
197C2×C4×D3—181no—
198C2×Dic6—31no—
199C2×Dic6—91no—
200C3×M16—92no—
201C3×M16—181no—
202C2×C3×C8—181no—
203C3×C42—21no—
204C3×C42—32no—
205C3×C42—32no—
206C3×C42—61no—
207C3×C42—61no—
208C3×C42—62no—
209C3×C42—62no—
210C3×C42C2×C3×D312yes—
211#208—32no—
212#208—61no—
213#208—92no—
214#208—181no—
215C2×C3⋊C8—61no—
216C2×C3⋊C8—181no—
217C22×C32—24no—
218C22×C32—22no—
219C22×C32—22no—
220C22×C32—21no—
221C22×C32—21no—
222C22×C32—21no—
223C22×C32(C2×D3)⋊C411yescharacteristic
224C22×C32(C2×D3)⋊C411yescharacteristic
225C22×C32C3×C22⋊C411yescharacteristic
226C22×C32C3×C22⋊C411yescharacteristic
227C22×C32C2×#6711yescharacteristic
228C22×C32C2×C3×D411yescharacteristic
229C2×C3⋊D3—22no—
230C2×C3⋊D3—42no—
231C2×C3×D3—62no—
232C2×C3×D3—122no—
233C32×C4—28no—
234C32×C4—24no—
235C32×C4—24no—
236C32×C4—21no—
237C32×C4—21no—
238C32×C4—21no—
239C32×C4—21no—
240C32×C4(C2×D3)⋊C411yescharacteristic
241C32×C4(C2×D3)⋊C411yescharacteristic
242C32×C4C3×C22⋊C411yescharacteristic
243C32×C4C3×C22⋊C411yescharacteristic
244C32×C4C2×C4×D311yescharacteristic
245C32×C4C2×D1211yescharacteristic
246C32×C4C22×C3×C411yescharacteristic
247C32×C4C2×C3×D411yescharacteristic
248C3⋊Dic3—22no—
249C3×Dic3—62no—
250C2×#41—91no—
251C2×M16—91no—
252C2×C42(C3⋊D3)⋊C311yescharacteristic, complemented
253#104—94no—
254H(3,𝔽3)C2×#10411yescharacteristic, complemented, Sylow
255C23×C3—31no—
256C23×C3—31no—
257C23×C3—61no—
258C23×C3—181no—
259C23×C3C3×#6711yescharacteristic
260C22×D3—61no—
261C22×D3—181no—
262C3×Q8—92no—
263C3×Q8—181no—
264C3×D4—92no—
265C3×D4—181no—
266C3×D4—182no—
267C3×D4—182no—
268C2×C3×C4—24no—
269C2×C3×C4—22no—
270C2×C3×C4—31no—
271C2×C3×C4—31no—
272C2×C3×C4—31no—
273C2×C3×C4—31no—
274C2×C3×C4—31no—
275C2×C3×C4—31no—
276C2×C3×C4—31no—
277C2×C3×C4—31no—
278C2×C3×C4—31no—
279C2×C3×C4—31no—
280C2×C3×C4—31no—
281C2×C3×C4—31no—
282C2×C3×C4—62no—
283C2×C3×C4—62no—
284C2×C3×C4—64no—
285C2×C3×C4—64no—
286C2×C3×C4—64no—
287C2×C3×C4—68no—
288C2×C3×C4—61no—
289C2×C3×C4—61no—
290C2×C3×C4—61no—
291C2×C3×C4—61no—
292C2×C3×C4—61no—
293C2×C3×C4—61no—
294C2×C3×C4—182no—
295C2×C3×C4—182no—
296C2×C3×C4—181no—
297C2×C3×C4C3×C4×D311yescharacteristic
298C2×C3×C4C3×C4×D311yescharacteristic
299C2×C3×C4C3×D1211yescharacteristic
300C2×C3×C4C3×D1211yescharacteristic
301C2×C3×C4C3×#6711yescharacteristic
302C2×C3×C4C22×C3×D311yescharacteristic
303#67—62no—
304#67—62no—
305#67—182no—
306#67—182no—
307C2×Dic3—61no—
308C2×Dic3—181no—
309D12—32no—
310D12—61no—
311D12—92no—
312D12—181no—
313C4×D3—62no—
314C4×D3—62no—
315C4×D3—182no—
316C4×D3—182no—
317Dic6—32no—
318Dic6—61no—
319Dic6—92no—
320Dic6—181no—
321C3×C8—182no—
322C3⋊C8—62no—
323C3⋊C8—182no—
324C2×C32—22no—
325C2×C32—22no—
326C2×C32—21no—
327C2×C32—21no—
328C2×C32—21no—
329C2×C32—21no—
330C2×C32—21no—
331C2×C32—22no—
332C2×C32#80512yescomplemented
333C2×C32C3×#10412yescomplemented
334C2×C32C2×(C2×D3)⋊C411yescharacteristic
335C2×C32C2×C3×C22⋊C411yescharacteristic
336C3⋊D3—42no—
337C3×D3—122no—
338#41—92no—
339#41—92no—
340#41—181no—
341#41—181no—
342C2×Q8—91no—
343C2×D4—91no—
344C2×D4—181no—
345C22×C4—21no—
346C22×C4—181no—
347C22×C4C2×(C3⋊D3)⋊C311yescharacteristic
348M16—92no—
349M16—181no—
350C2×C8—181no—
351C42—21no—
352C42C2×(C3⋊D3)⋊C312yescomplemented
353C22×C3—22no—
354C22×C3—31no—
355C22×C3—31no—
356C22×C3—31no—
357C22×C3—31no—
358C22×C3—31no—
359C22×C3—31no—
360C22×C3—62no—
361C22×C3—62no—
362C22×C3—64no—
363C22×C3—61no—
364C22×C3—61no—
365C22×C3—61no—
366C22×C3—182no—
367C22×C3—362no—
368C22×C3C3×(C2×D3)⋊C411yescharacteristic
369C22×C3C3×(C2×D3)⋊C411yescharacteristic
370C22×C3C2×C3×#6711yescharacteristic
371C2×D3—62no—
372C2×D3—122no—
373C2×D3—182no—
374C2×D3—362no—
375C3×C4—24no—
376C3×C4—31no—
377C3×C4—31no—
378C3×C4—31no—
379C3×C4—31no—
380C3×C4—31no—
381C3×C4—31no—
382C3×C4—31no—
383C3×C4—31no—
384C3×C4—64no—
385C3×C4—64no—
386C3×C4—68no—
387C3×C4—61no—
388C3×C4—61no—
389C3×C4—61no—
390C3×C4—61no—
391C3×C4—182no—
392C3×C4C3×(C2×D3)⋊C411yescharacteristic
393C3×C4C3×(C2×D3)⋊C411yescharacteristic
394C3×C4C2×C3×C4×D311yescharacteristic
395C3×C4C2×C3×D1211yescharacteristic
396Dic3—62no—
397Dic3—182no—
398C32—21no—
399C32C2×#80511yescharacteristic, complemented
400C32C2×C3×#10411yescharacteristic, complemented
401C23—181no—
402C23#638⋊C311yescharacteristic
403Q8—92no—
404Q8—181no—
405D4—92no—
406D4—182no—
407D4—182no—
408D4—181no—
409C2×C4—24no—
410C2×C4—22no—
411C2×C4—181no—
412C2×C4—182no—
413C2×C4—182no—
414C2×C4C4×(C3⋊D3)⋊C311yescharacteristic
415C2×C4C4×(C3⋊D3)⋊C311yescharacteristic
416C2×C4C4⋊((C3⋊D3)⋊C3)11yescharacteristic
417C2×C4C4⋊((C3⋊D3)⋊C3)11yescharacteristic
418C2×C4#638⋊C311yescharacteristic
419C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
420C8—182no—
421C2×C3—21no—
422C2×C3—21no—
423C2×C3—31no—
424C2×C3—31no—
425C2×C3—32no—
426C2×C3—32no—
427C2×C3—61no—
428C2×C3—61no—
429C2×C3—61no—
430C2×C3—61no—
431C2×C3—62no—
432C2×C3—62no—
433C2×C3—61no—
434C2×C3—62no—
435C2×C3—362no—
436C2×C3C3×#80512yes—
437C2×C3C2×C3×(C2×D3)⋊C411yescharacteristic
438D3—122no—
439D3—362no—
440C22—22no—
441C22—182no—
442C22—362no—
443C22#3752⋊C311yescharacteristic
444C22#3752⋊C311yescharacteristic
445C22C2×#638⋊C311yescharacteristic
446C4—24no—
447C4—182no—
448C4#3752⋊C311yescharacteristic
449C4#3752⋊C311yescharacteristic
450C4C2×C4×(C3⋊D3)⋊C311yescharacteristic
451C4C2×C4⋊((C3⋊D3)⋊C3)11yescharacteristic
452C3—31no—
453C3—31no—
454C3—61no—
455C3C2×C3×#80511yescharacteristic
456C2—21no—
457C2—21no—
458C2—362no—
459C2#63632⋊C312yesdirect product factor
460C2C2×#3752⋊C311yescharacteristic
subgroupG/H
centerC2×C4C4⋊((C3⋊D3)⋊C3)
commutatorC32×C4C22×C3×C4
FrattiniC2×C3×C4C22×C3×D3
FittingC2×C42×H(3,𝔽3)C2
socleC22×C3C3×(C2×D3)⋊C4
prime radicalC2×#3828⋊C3C2
cosocleC2×C32×C4C23×C3
hypercenterC2×C42(C3⋊D3)⋊C3
hypocenterC32C2×C3×#104
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×C42×H(3,𝔽3)C2semidirect
3. C2×#3748⋊C3C2semidirect
4. #63632⋊C3C2direct (N × H)
5. C2×#63632C3semidirect
12. #3828⋊C3C4semidirect
14. C2×C4⋊((C3⋊D3)⋊C3)C4semidirect
16. C2×#634⋊C3C4semidirect
18. C42×H(3,𝔽3)C22semidirect
20. #3748⋊C3C22semidirect
25. C2×C32×C42D3semidirect
26. C2×C32×C42C2×C3semidirect
27. C2×#3748C2×C3semidirect
29. #63632C2×C3semidirect
45. C4⋊((C3⋊D3)⋊C3)C2×C4semidirect
49. #634⋊C3C2×C4semidirect
63. #3828C3×C4semidirect
65. C2×C4⋊(C3⋊D3)C3×C4semidirect
67. C2×#634C3×C4semidirect
80. C32×C42C2×D3semidirect
81. C32×C42C22×C3semidirect
83. #3748C22×C3semidirect
146. C4⋊(C3⋊D3)C2×C3×C4semidirect
150. #634C2×C3×C4semidirect
165. C2×H(3,𝔽3)#104semidirect
252. C2×C42(C3⋊D3)⋊C3semidirect
254. H(3,𝔽3)C2×#104semidirect
332. C2×C32#805semidirect
333. C2×C32C3×#104semidirect
352. C42C2×(C3⋊D3)⋊C3semidirect
399. C32C2×#805semidirect
400. C32C2×C3×#104semidirect
459. C2#63632⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#3828⋊C32
C2×C42×H(3,𝔽3)2
C2×#3748⋊C32
#63632⋊C32
C2×#636323
C2×C3×#8053