Finite Group Databasebeta

← C2×#11720292 #13139418

Subgroups — C2×#11720292 #13139418

Order 1728.

674 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88736C211yesmaximal, characteristic
2C2×C3×C4×Dic9C211yesmaximal, characteristic, complemented
3C2×C9×#208C211yesmaximal, characteristic, complemented
4#11720292C214yesmaximal, direct product factor
5C2×#63570—31nomaximal
6C2×#63384—31nomaximal
7C22×C3×C4×C9C2211yescharacteristic
8C2×#6233—21no—
9#88736—21no—
10#88736—21no—
11#88736C412yescomplemented
12#88736C2212yes—
13C2×C4⋊(C3⋊D9)C411yescharacteristic, complemented
14C2×C4×C3⋊D9—21no—
15C2×#6226C411yescharacteristic, complemented
16C22×C3×Dic9—21no—
17C3×C4×Dic9—21no—
18C3×C4×Dic9C2212yescomplemented
19C9×#208—21no—
20C9×#208C2212yescomplemented
21C2×C9×C3⋊C8—21no—
22C2×#3828—31no—
23C2×C3×C4×Dic3—31no—
24C2×C3×#208D311yescharacteristic
25C2×#3697—31no—
26C2×#3697—61no—
27#63570—34no—
28C2×C9×M16—31no—
29C2×C4×Dic9D311yescharacteristic, complemented
30#63384—34no—
31C23×C3×C9D411yescharacteristic
32C22×C3⋊D9—21no—
33C2×C3×C4×C9C2×C411yescharacteristic
34C2×C3×C4×C9C2×C411yescharacteristic
35C2×C3×C4×C9D411yescharacteristic
36C2×C3×C4×C9D411yescharacteristic
37C2×C3×C4×C9D411yescharacteristic
38C2×C3×C4×C9C2311yescharacteristic
39#6233—22no—
40#6233—22no—
41C2×C3⋊Dic9—21no—
42C4⋊(C3⋊D9)—21no—
43C4⋊(C3⋊D9)C2×C412yescomplemented
44C4×C3⋊D9—22no—
45C4×C3⋊D9—22no—
46#6226—21no—
47#6226C2×C412yescomplemented
48C2×C3×Dic9—24no—
49C2×C3×Dic9—22no—
50C9×C3⋊C8—22no—
51C2×#825—91no—
52C2×#805—91no—
53C22×C32×C4C2×D311yescharacteristic
54C2×#638—61no—
55#3828—32no—
56#3828—32no—
57#3828—61no—
58#3828—61no—
59C2×C4⋊(C3⋊D3)—31no—
60C2×C4×C3⋊D3—61no—
61C2×#634—31no—
62C22×C3×Dic3—61no—
63C3×C4×Dic3—32no—
64C3×C4×Dic3—61no—
65C3×#208—21no—
66C3×#208C2×D312yes—
67C2×C3×C3⋊C8—21no—
68C22×C4×C9—21no—
69C22×C4×C9C2×D311yescharacteristic
70C2×#611—62no—
71C2×#611—61no—
72C22×Dic9—21no—
73#3697—32no—
74#3697—32no—
75#3697—62no—
76#3697—62no—
77#3697—62no—
78#3697—62no—
79#3697—61no—
80#3697—61no—
81C2×D36—31no—
82C2×D36—61no—
83C2×C4×D9—62no—
84C2×C4×D9—61no—
85C2×Dic18—31no—
86C2×Dic18—61no—
87C9×M16—32no—
88C9×M16—61no—
89C2×C8×C9—61no—
90C4×Dic9—21no—
91C4×Dic9C2×D312yescomplemented
92C22×C3×C9—22no—
93C22×C3×C9C22⋊C411yescharacteristic
94C22×C3×C9C22⋊C411yescharacteristic
95C22×C3×C9C2×D411yescharacteristic
96C2×C3⋊D9—22no—
97C2×C3⋊D9—42no—
98C3×C4×C9C22⋊C411yescharacteristic
99C3×C4×C9C22⋊C411yescharacteristic
100C3×C4×C9C22×C411yescharacteristic
101C3×C4×C9C2×D411yescharacteristic
102C3⋊Dic9—22no—
103C3×Dic9—24no—
104C2×#235—91no—
105C2×#235—91no—
106C2×#235—181no—
107C2×C3×M16—31no—
108C2×C3×C42—91no—
109C2×C4×Dic3—31no—
110C2×#208D911yescharacteristic, complemented
111#825—94no—
112#805—94no—
113C23×C32D1211yescharacteristic
114C22×C3⋊D3—61no—
115C2×C32×C4C4×D311yescharacteristic
116C2×C32×C4C4×D311yescharacteristic
117C2×C32×C4D1211yescharacteristic
118C2×C32×C4#6711yescharacteristic
119C2×C32×C4#6711yescharacteristic
120C2×C32×C4C22×D311yescharacteristic
121#638—62no—
122#638—62no—
123C2×C3⋊Dic3—61no—
124C4⋊(C3⋊D3)—32no—
125C4⋊(C3⋊D3)—61no—
126C4×C3⋊D3—62no—
127C4×C3⋊D3—62no—
128#634—32no—
129#634—61no—
130C2×C3×Dic3—64no—
131C2×C3×Dic3—62no—
132C23×C9—21no—
133C23×C9#6711yescharacteristic
134C22×D9—62no—
135C22×D9—61no—
136C3×C3⋊C8—22no—
137C2×C4×C9—21no—
138C2×C4×C9—21no—
139C2×C4×C9—21no—
140C2×C4×C9—21no—
141C2×C4×C9—21no—
142C2×C4×C9—21no—
143C2×C4×C9C4×D311yescharacteristic
144C2×C4×C9C4×D311yescharacteristic
145C2×C4×C9D1211yescharacteristic
146C2×C4×C9D1211yescharacteristic
147C2×C4×C9#6711yescharacteristic
148C2×C4×C9C22×D311yescharacteristic
149#611—64no—
150#611—64no—
151#611—62no—
152#611—62no—
153C2×Dic9—24no—
154C2×Dic9—22no—
155C2×Dic9—62no—
156C2×Dic9—61no—
157D36—32no—
158D36—62no—
159D36—62no—
160D36—61no—
161C4×D9—64no—
162C4×D9—64no—
163C4×D9—62no—
164C4×D9—62no—
165Dic18—32no—
166Dic18—62no—
167Dic18—62no—
168Dic18—61no—
169C8×C9—62no—
170C2×#104—271noSylow
171C2×C3×C9—21no—
172C2×C3×C9—21no—
173C2×C3×C9#10412yescomplemented
174C2×C3×C9C2×C22⋊C411yescharacteristic
175C3⋊D9—42no—
176C22×C3×C4—21no—
177C22×C3×C4—181no—
178C22×C3×C4C2×D911yescharacteristic
179C22×C3×C4D3211yescharacteristic
180C2×#67—182no—
181C2×#67—181no—
182C2×#67—181no—
183C22×Dic3—61no—
184#235—92no—
185#235—92no—
186#235—92no—
187#235—92no—
188#235—182no—
189#235—182no—
190#235—182no—
191#235—182no—
192#235—181no—
193#235—181no—
194#235—181no—
195#235—181no—
196C2×D12—91no—
197C2×D12—91no—
198C2×D12—181no—
199C2×C4×D3—182no—
200C2×C4×D3—181no—
201C2×C4×D3—181no—
202C2×Dic6—91no—
203C2×Dic6—91no—
204C2×Dic6—181no—
205C3×M16—32no—
206C3×M16—61no—
207C2×C3×C8—61no—
208C3×C42—92no—
209C3×C42—181no—
210C4×Dic3—32no—
211C4×Dic3—61no—
212#208—21no—
213#208C2×D912yescomplemented
214C2×C3⋊C8—21no—
215C22×C32—22no—
216C22×C32(C2×D3)⋊C411yescharacteristic
217C22×C32(C2×D3)⋊C411yescharacteristic
218C22×C32C2×D1211yescharacteristic
219C2×C3⋊D3—62no—
220C2×C3⋊D3—122no—
221C32×C4(C2×D3)⋊C411yescharacteristic
222C32×C4(C2×D3)⋊C411yescharacteristic
223C32×C4C2×C4×D311yescharacteristic
224C32×C4C2×#6711yescharacteristic
225C3⋊Dic3—62no—
226C3×Dic3—64no—
227C22×C9—22no—
228C22×C9—21no—
229C22×C9—21no—
230C22×C9—21no—
231C22×C9—42no—
232C22×C9(C2×D3)⋊C411yescharacteristic
233C22×C9(C2×D3)⋊C411yescharacteristic
234C22×C9C2×#6711yescharacteristic
235C2×D9—64no—
236C2×D9—62no—
237C2×D9—124no—
238C2×D9—122no—
239C4×C9—21no—
240C4×C9—21no—
241C4×C9—21no—
242C4×C9—21no—
243C4×C9(C2×D3)⋊C411yescharacteristic
244C4×C9(C2×D3)⋊C411yescharacteristic
245C4×C9C2×C4×D311yescharacteristic
246C4×C9C2×D1211yescharacteristic
247Dic9—24no—
248Dic9—64no—
249Dic9—62no—
250C2×#41—271no—
251C2×M16—31no—
252C2×C42—91no—
253#104—274no—
254C3×C9C2×#10411yescharacteristic, complemented, Sylow
255C23×C3—21no—
256C23×C3D3611yescharacteristic
257C23×C3#62611yescharacteristic
258C22×D3—182no—
259C22×D3—181no—
260C22×D3—181no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—184no—
268C2×C3×C4—182no—
269C2×C3×C4C4×D911yescharacteristic
270C2×C3×C4C4×D911yescharacteristic
271C2×C3×C4D3611yescharacteristic
272C2×C3×C4#61111yescharacteristic
273C2×C3×C4#61111yescharacteristic
274C2×C3×C4C22×D911yescharacteristic
275C2×C3×C4#62411yescharacteristic
276C2×C3×C4#62411yescharacteristic
277C2×C3×C4#62611yescharacteristic
278C2×C3×C4#62611yescharacteristic
279C2×C3×C4#62611yescharacteristic
280C2×C3×C4C2×D3211yescharacteristic
281#67—184no—
282#67—184no—
283#67—182no—
284#67—182no—
285#67—182no—
286#67—182no—
287C2×Dic3—64no—
288C2×Dic3—62no—
289C2×Dic3—182no—
290C2×Dic3—181no—
291C2×Dic3—181no—
292D12—92no—
293D12—92no—
294D12—182no—
295D12—182no—
296D12—181no—
297D12—181no—
298C4×D3—184no—
299C4×D3—184no—
300C4×D3—182no—
301C4×D3—182no—
302C4×D3—182no—
303C4×D3—182no—
304Dic6—92no—
305Dic6—92no—
306Dic6—182no—
307Dic6—182no—
308Dic6—181no—
309Dic6—181no—
310C3×C8—62no—
311C3⋊C8—22no—
312C2×C32—21no—
313C2×C32—21no—
314C2×C32#82512yes—
315C2×C32C2×(C2×D3)⋊C411yescharacteristic
316C3⋊D3—122no—
317C2×C9—21no—
318C2×C9—21no—
319C2×C9—22no—
320C2×C9—21no—
321C2×C9—41no—
322C2×C9—41no—
323C2×C9#80512yescomplemented
324C2×C9C2×(C2×D3)⋊C411yescharacteristic
325D9—124no—
326D9—122no—
327#41—272no—
328#41—272no—
329#41—541no—
330#41—541no—
331C2×Q8—271no—
332C2×D4—271no—
333C2×D4—541no—
334C22×C4—181no—
335C22×C4—541no—
336C22×C4D3×D911yescharacteristic
337M16—32no—
338M16—61no—
339C2×C8—61no—
340C42—92no—
341C42—181no—
342C22×C3—22no—
343C22×C3—22no—
344C22×C3—21no—
345C22×C3—21no—
346C22×C3—21no—
347C22×C3—42no—
348C22×C3(C2×D9)⋊C411yescharacteristic
349C22×C3(C2×D9)⋊C411yescharacteristic
350C22×C3C2×D3611yescharacteristic
351C22×C3#372211yescharacteristic
352C22×C3#372211yescharacteristic
353C22×C3C2×#62611yescharacteristic
354C2×D3—184no—
355C2×D3—182no—
356C2×D3—182no—
357C2×D3—364no—
358C2×D3—362no—
359C2×D3—362no—
360C3×C4—21no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—184no—
365C3×C4(C2×D9)⋊C411yescharacteristic
366C3×C4(C2×D9)⋊C411yescharacteristic
367C3×C4C2×C4×D911yescharacteristic
368C3×C4C2×#61111yescharacteristic
369C3×C4#372211yescharacteristic
370C3×C4#372211yescharacteristic
371C3×C4C2×#62411yescharacteristic
372C3×C4C2×#62611yescharacteristic
373Dic3—64no—
374Dic3—184no—
375Dic3—182no—
376Dic3—182no—
377C32C2×#82511yescharacteristic
378C9—21no—
379C9C2×#80511yescharacteristic, complemented
380C23—541no—
381C23#619211yescharacteristic
382Q8—272no—
383Q8—541no—
384D4—272no—
385D4—542no—
386D4—542no—
387D4—541no—
388C2×C4—184no—
389C2×C4—182no—
390C2×C4—541no—
391C2×C4—542no—
392C2×C4—542no—
393C2×C4(C3⋊D9)⋊C411yescharacteristic
394C2×C4(C3⋊D9)⋊C411yescharacteristic
395C2×C4#619211yescharacteristic
396C2×C4#619511yescharacteristic
397C2×C4#619511yescharacteristic
398C2×C4C2×D3×D911yescharacteristic
399C8—62no—
400C2×C3—21no—
401C2×C3—21no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3—21no—
405C2×C3—22no—
406C2×C3—41no—
407C2×C3—41no—
408C2×C3#6338412yescomplemented
409C2×C3C2×(C2×D9)⋊C411yescharacteristic
410C2×C3#6357012yes—
411C2×C3C2×#372211yescharacteristic
412D3—364no—
413D3—362no—
414D3—362no—
415C22—22no—
416C22—542no—
417C22—1082no—
418C22#8844511yescharacteristic
419C22#8844511yescharacteristic
420C22C2×#619211yescharacteristic
421C4—184no—
422C4—542no—
423C4#8844511yescharacteristic
424C4#8844511yescharacteristic
425C4C2×(C3⋊D9)⋊C411yescharacteristic
426C4C2×#619511yescharacteristic
427C3—21no—
428C3C2×#6338411yescharacteristic, complemented
429C3C2×#6357011yescharacteristic
430C2—21no—
431C2—21no—
432C2—1082no—
433C2#1172029212yesdirect product factor
434C2C2×#8844511yescharacteristic
subgroupG/H
centerC2×C4#6195
commutatorC3×C4×C9C22×C4
FrattiniC2×C3×C4C2×D32
FittingC22×C3×C4×C9C22
socleC22×C32(C2×D3)⋊C4
prime radicalC2×#88736C2
cosocleC2×C3×C4×C9C23
hypercenterC22×C4D3×D9
hypocenterC3×C9C2×#104
LCSG ▷ C3×C4×C9 ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4×Dic9C2semidirect
3. C2×C9×#208C2semidirect
4. #11720292C2direct (N × H)
11. #88736C4semidirect
13. C2×C4⋊(C3⋊D9)C4semidirect
15. C2×#6226C4semidirect
18. C3×C4×Dic9C22semidirect
20. C9×#208C22semidirect
29. C2×C4×Dic9D3semidirect
43. C4⋊(C3⋊D9)C2×C4semidirect
47. #6226C2×C4semidirect
91. C4×Dic9C2×D3semidirect
110. C2×#208D9semidirect
173. C2×C3×C9#104semidirect
213. #208C2×D9semidirect
254. C3×C9C2×#104semidirect
323. C2×C9#805semidirect
379. C9C2×#805semidirect
408. C2×C3#63384semidirect
428. C3C2×#63384semidirect
433. C2#11720292direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#887362
C2×C3×C4×Dic92
C2×C9×#2082
#117202922
C2×#635703
C2×#633843