Finite Group Databasebeta

← C2×#10624887⋊C2 #72244086

Subgroups — C2×#10624887⋊C2 #72244086

Order 2916.

585 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10624887⋊C2C212yesmaximal, direct product factor
2C2×#10624887C211yesmaximal, characteristic, complemented
3C2×C3×#4207C311yesmaximal, characteristic
4C2×#92294C311yesmaximal, characteristic, complemented
5C2×#92294C311yesmaximal, characteristic, complemented
6C2×C3⋊(D9⋊C9)C311yesmaximal, characteristic, complemented
7C2×#92265—31nomaximal
8C2×#92264—31nomaximal
9C2×#6894⋊C2—31nomaximal
10C2×#92262—31nomaximal
11#10624887C2211yescharacteristic, complemented, Sylow
12C2×C3×#737C2×C311yescharacteristic
13C3×#4207C2×C312yes—
14C2×#6900—21no—
15C2×#6900D311yescharacteristic, complemented
16C2×#6899—21no—
17C2×#6899—21no—
18C2×#6899—21no—
19C2×#6896—21no—
20C2×#6896—21no—
21C2×#6896—21no—
22C2×#6896—21no—
23C2×#6896D311yescharacteristic, complemented
24C2×#6894—21no—
25C2×#6894—21no—
26C2×#6894—21no—
27C2×#6894—21no—
28C2×#6894—21no—
29C2×#6894—21no—
30C2×#6894—21no—
31C2×#6894D311yescharacteristic, complemented
32C2×C9⋊H(3,𝔽3)—21no—
33C2×C9⋊H(3,𝔽3)D311yescharacteristic
34C2×#6887C2×C311yescharacteristic, complemented
35C2×#6887C2×C311yescharacteristic, complemented
36C2×C3×C9⋊C9C2×C311yescharacteristic, complemented
37#92294C2×C312yescomplemented
38#92294C2×C312yescomplemented
39C3⋊(D9⋊C9)C2×C312yescomplemented
40#92265—32no—
41#92264—32no—
42#6894⋊C2—32no—
43#92262—32no—
44C2×#4207—31no—
45C2×C9×C3⋊D3—31no—
46C2×C3×C3⋊D9C3211yescharacteristic
47C2×D3×3−1+2—91no—
48C2×C3×AGL(1,ℤ/9)—31no—
49C2×C3×AGL(1,ℤ/9)—31no—
50C2×C3×(C3⋊D3)⋊C3—31no—
51C2×C32×D9—31no—
52C2×D9⋊C9—31no—
53C2×D9⋊C9—31no—
54C2×D9⋊C9—31no—
55C2×D9⋊C9—31no—
56C2×D9⋊C9—31no—
57C2×D9⋊C9—31no—
58C2×D9⋊C9—31no—
59C2×(C3⋊D3)⋊C9—31no—
60C2×(C3⋊D3)⋊C9—31no—
61C2×C9×D9—31no—
62C2×C9×D9—31no—
63C3×#737C22×C311yescharacteristic
64#6900—21no—
65#6900C2×D311yescharacteristic, complemented
66#6899—21no—
67#6899—21no—
68#6899—21no—
69#6896—21no—
70#6896—21no—
71#6896—21no—
72#6896—21no—
73#6896C2×D311yescharacteristic, complemented
74#6894—21no—
75#6894—21no—
76#6894—21no—
77#6894—21no—
78#6894—21no—
79#6894—21no—
80#6894—21no—
81#6894C2×D311yescharacteristic, complemented
82C9⋊H(3,𝔽3)—21no—
83C9⋊H(3,𝔽3)C2×D311yescharacteristic
84#6887C22×C311yescharacteristic, complemented
85#6887C22×C311yescharacteristic, complemented
86C3×C9⋊C9C22×C311yescharacteristic, complemented
87C2×#737—31no—
88C2×#737—61no—
89C2×#737—61no—
90C2×#737—61no—
91C2×#737—61no—
92C2×C3×3−1+2—21no—
93C2×C3×3−1+2—21no—
94C2×C3×3−1+2—21no—
95C2×C3×3−1+2—21no—
96C2×C3×3−1+2—21no—
97C2×C3×3−1+2—21no—
98C2×C3×3−1+2—21no—
99C2×C3×3−1+2C3×D311yescharacteristic
100C2×C3×3−1+2C3×D311yescharacteristic
101C2×C3×3−1+2C3⋊D311yescharacteristic
102C2×C3×H(3,𝔽3)C3×D311yescharacteristic
103C2×C32×C9—21no—
104C2×C32×C9—21no—
105C2×C32×C9C3×D311yescharacteristic
106C2×C32×C9C3×D311yescharacteristic
107C2×C32×C9C2×C3211yescharacteristic
108#4207—32no—
109C9×C3⋊D3—32no—
110C3×C3⋊D9C2×C3212yes—
111D3×3−1+2—92no—
112C3×AGL(1,ℤ/9)—32no—
113C3×AGL(1,ℤ/9)—32no—
114C3×(C3⋊D3)⋊C3—32no—
115C32×D9—32no—
116C2×C9⋊C9—21no—
117C2×C9⋊C9—21no—
118C2×C9⋊C9—21no—
119C2×C9⋊C9—21no—
120C2×C9⋊C9—21no—
121C2×C9⋊C9—21no—
122C2×C9⋊C9—21no—
123C2×C9⋊C9—21no—
124C2×C9⋊C9—21no—
125C2×C9⋊C9—21no—
126C2×C9⋊C9—21no—
127C2×C9⋊C9—21no—
128C2×C9⋊C9—21no—
129C2×C9⋊C9—21no—
130C2×C9⋊C9—21no—
131C2×C9⋊C9—21no—
132C2×C9⋊C9—21no—
133C2×C9⋊C9—21no—
134C2×C9⋊C9—21no—
135C2×C9⋊C9—21no—
136C2×C9⋊C9—21no—
137C2×C9⋊C9—21no—
138C2×C9⋊C9—21no—
139C2×C9⋊C9—21no—
140C2×C9⋊C9—21no—
141C2×C9⋊C9—21no—
142C2×C9⋊C9—21no—
143C2×C9⋊C9—21no—
144C2×C9⋊C9—21no—
145C2×C9⋊C9—21no—
146C2×C9⋊C9—21no—
147C2×C9⋊C9—21no—
148C2×C9⋊C9—21no—
149C2×C9⋊C9—21no—
150C2×C9⋊C9C3×D311yescharacteristic
151C2×C9⋊C9C3×D311yescharacteristic
152C2×C9⋊C9C3×D311yescharacteristic
153C2×C9⋊C9C3×D311yescharacteristic
154C2×C9⋊C9C3×D311yescharacteristic
155C2×C9⋊C9C3×D311yescharacteristic
156C2×C9⋊C9C3×D311yescharacteristic
157C2×C32⋊C9—21no—
158C2×C32⋊C9—21no—
159C2×C32⋊C9—21no—
160C2×C32⋊C9—21no—
161C2×C32⋊C9—21no—
162C2×C32⋊C9—21no—
163C2×C32⋊C9—21no—
164C2×C32⋊C9—21no—
165C2×C32⋊C9—21no—
166C2×C32⋊C9—21no—
167C2×C32⋊C9—21no—
168C2×C32⋊C9C3×D311yescharacteristic
169C2×C32⋊C9C3×D311yescharacteristic
170C2×C92—21no—
171C2×C92—21no—
172C2×C92C3×D311yescharacteristic
173C2×C92C3×D311yescharacteristic
174D9⋊C9—32no—
175D9⋊C9—32no—
176D9⋊C9—32no—
177D9⋊C9—32no—
178D9⋊C9—32no—
179D9⋊C9—32no—
180D9⋊C9—32no—
181(C3⋊D3)⋊C9—32no—
182(C3⋊D3)⋊C9—32no—
183C9×D9—32no—
184C9×D9—32no—
185C2×C3×C3⋊D3—31no—
186C2×C32×D3—91no—
187C22×3−1+2—271no—
188C2×C3⋊D93−1+211yescharacteristic, complemented
189C2×AGL(1,ℤ/9)—91no—
190C2×AGL(1,ℤ/9)—91no—
191C2×(C3⋊D3)⋊C3—91no—
192C2×D3×C9—91no—
193C2×D3×C9—91no—
194C2×D3×C9—91no—
195C2×D3×C9—271no—
196C2×C3×D9—31no—
197C2×C3×D9—31no—
198C2×C3×D9—31no—
199C2×C3×D9—91no—
200#737—31no—
201#737—61no—
202#737—61no—
203#737—61no—
204#737—61no—
205C3×3−1+2—21no—
206C3×3−1+2—21no—
207C3×3−1+2—21no—
208C3×3−1+2—21no—
209C3×3−1+2—21no—
210C3×3−1+2—21no—
211C3×3−1+2—21no—
212C3×3−1+2C2×C3×D311yescharacteristic
213C3×3−1+2C2×C3×D311yescharacteristic
214C3×3−1+2C2×C3⋊D311yescharacteristic
215C3×H(3,𝔽3)C2×C3×D311yescharacteristic
216C32×C9—21no—
217C32×C9—21no—
218C32×C9C2×C3×D311yescharacteristic
219C32×C9C2×C3×D311yescharacteristic
220C32×C9C22×C3211yescharacteristic
221C9⋊C9—21no—
222C9⋊C9—21no—
223C9⋊C9—21no—
224C9⋊C9—21no—
225C9⋊C9—21no—
226C9⋊C9—21no—
227C9⋊C9—21no—
228C9⋊C9—21no—
229C9⋊C9—21no—
230C9⋊C9—21no—
231C9⋊C9—21no—
232C9⋊C9—21no—
233C9⋊C9—21no—
234C9⋊C9—21no—
235C9⋊C9—21no—
236C9⋊C9—21no—
237C9⋊C9—21no—
238C9⋊C9—21no—
239C9⋊C9—21no—
240C9⋊C9—21no—
241C9⋊C9—21no—
242C9⋊C9—21no—
243C9⋊C9—21no—
244C9⋊C9—21no—
245C9⋊C9—21no—
246C9⋊C9—21no—
247C9⋊C9—21no—
248C9⋊C9—21no—
249C9⋊C9—21no—
250C9⋊C9—21no—
251C9⋊C9—21no—
252C9⋊C9—21no—
253C9⋊C9—21no—
254C9⋊C9—21no—
255C9⋊C9C2×C3×D311yescharacteristic
256C9⋊C9C2×C3×D311yescharacteristic
257C9⋊C9C2×C3×D311yescharacteristic
258C9⋊C9C2×C3×D311yescharacteristic
259C9⋊C9C2×C3×D311yescharacteristic
260C9⋊C9C2×C3×D311yescharacteristic
261C9⋊C9C2×C3×D311yescharacteristic
262C32⋊C9—21no—
263C32⋊C9—21no—
264C32⋊C9—21no—
265C32⋊C9—21no—
266C32⋊C9—21no—
267C32⋊C9—21no—
268C32⋊C9—21no—
269C32⋊C9—21no—
270C32⋊C9—21no—
271C32⋊C9—21no—
272C32⋊C9—21no—
273C32⋊C9C2×C3×D311yescharacteristic
274C32⋊C9C2×C3×D311yescharacteristic
275C92—21no—
276C92—21no—
277C92C2×C3×D311yescharacteristic
278C92C2×C3×D311yescharacteristic
279C2×C33—21no—
280C2×C33C32×D311yescharacteristic
281C2×C33C3×C3⋊D311yescharacteristic
282C3×C3⋊D3—32no—
283C32×D3—92no—
284C2×3−1+2—31no—
285C2×3−1+2—31no—
286C2×3−1+2—62no—
287C2×3−1+2—62no—
288C2×3−1+2—61no—
289C2×3−1+2—61no—
290C2×3−1+2—62no—
291C2×3−1+2—61no—
292C2×3−1+2—61no—
293C2×3−1+2—61no—
294C2×3−1+2—181no—
295C2×3−1+2—181no—
296C2×3−1+2—181no—
297C2×3−1+2—181no—
298C2×3−1+2—181no—
299C2×3−1+2—272no—
300C2×H(3,𝔽3)—31no—
301C2×H(3,𝔽3)—61no—
302C2×C3×C9—21no—
303C2×C3×C9—21no—
304C2×C3×C9—21no—
305C2×C3×C9—21no—
306C2×C3×C9—21no—
307C2×C3×C9—21no—
308C2×C3×C9—21no—
309C2×C3×C9—21no—
310C2×C3×C9—21no—
311C2×C3×C9—21no—
312C2×C3×C9—21no—
313C2×C3×C9—21no—
314C2×C3×C9—21no—
315C2×C3×C9—21no—
316C2×C3×C9—21no—
317C2×C3×C9—21no—
318C2×C3×C9—21no—
319C2×C3×C9—21no—
320C2×C3×C9—21no—
321C2×C3×C9—31no—
322C2×C3×C9—62no—
323C2×C3×C9—61no—
324C2×C3×C9—61no—
325C2×C3×C9—91no—
326C2×C3×C9—181no—
327C2×C3×C9C2×3−1+211yescharacteristic, complemented
328C2×C3×C9C32×D311yescharacteristic
329C2×C3×C9C32×D311yescharacteristic
330C2×C3×C9C32×D311yescharacteristic
331C2×C3×C9C3×C3⋊D311yescharacteristic
332C2×C3×C9C3×C3⋊D311yescharacteristic
333C2×C3×C9C3×C3⋊D311yescharacteristic
334C3⋊D9C2×3−1+212yescomplemented
335AGL(1,ℤ/9)—92no—
336AGL(1,ℤ/9)—92no—
337(C3⋊D3)⋊C3—92no—
338D3×C9—92no—
339D3×C9—92no—
340D3×C9—92no—
341D3×C9—272no—
342C3×D9—32no—
343C3×D9—32no—
344C3×D9—32no—
345C3×D9—92no—
346C22×C32—271no—
347C2×C3⋊D3—31no—
348C2×C3×D3—91no—
349C2×C3×D3—271no—
350C2×C3×D3—271no—
351C22×C9—271no—
352C22×C9—271no—
353C22×C9—271no—
354C2×D9—31no—
355C2×D9—31no—
356C2×D9—31no—
357C33—21no—
358C33C2×C32×D311yescharacteristic
359C33C2×C3×C3⋊D311yescharacteristic
3603−1+2—31no—
3613−1+2—31no—
3623−1+2—62no—
3633−1+2—62no—
3643−1+2—61no—
3653−1+2—61no—
3663−1+2—62no—
3673−1+2—61no—
3683−1+2—61no—
3693−1+2—61no—
3703−1+2—181no—
3713−1+2—181no—
3723−1+2—181no—
3733−1+2—181no—
3743−1+2—181no—
375H(3,𝔽3)—31no—
376H(3,𝔽3)—61no—
377C3×C9—21no—
378C3×C9—21no—
379C3×C9—21no—
380C3×C9—21no—
381C3×C9—21no—
382C3×C9—21no—
383C3×C9—21no—
384C3×C9—21no—
385C3×C9—21no—
386C3×C9—21no—
387C3×C9—21no—
388C3×C9—21no—
389C3×C9—21no—
390C3×C9—21no—
391C3×C9—21no—
392C3×C9—21no—
393C3×C9—21no—
394C3×C9—21no—
395C3×C9—21no—
396C3×C9—31no—
397C3×C9—62no—
398C3×C9—61no—
399C3×C9—61no—
400C3×C9—91no—
401C3×C9—181no—
402C3×C9C22×3−1+211yescharacteristic, complemented
403C3×C9C2×C32×D311yescharacteristic
404C3×C9C2×C32×D311yescharacteristic
405C3×C9C2×C32×D311yescharacteristic
406C3×C9C2×C3×C3⋊D311yescharacteristic
407C3×C9C2×C3×C3⋊D311yescharacteristic
408C3×C9C2×C3×C3⋊D311yescharacteristic
409C2×C32—21no—
410C2×C32—31no—
411C2×C32—31no—
412C2×C32—31no—
413C2×C32—61no—
414C2×C32—61no—
415C2×C32—61no—
416C2×C32—61no—
417C2×C32—61no—
418C2×C32—61no—
419C2×C32—272no—
420C2×C32D3×3−1+211yescharacteristic
421C2×C32C32×C3⋊D311yescharacteristic
422C3⋊D3—32no—
423C3×D3—92no—
424C3×D3—272no—
425C3×D3—272no—
426C2×C9—21no—
427C2×C9—21no—
428C2×C9—21no—
429C2×C9—61no—
430C2×C9—61no—
431C2×C9—61no—
432C2×C9—61no—
433C2×C9—61no—
434C2×C9—61no—
435C2×C9—61no—
436C2×C9—61no—
437C2×C9—61no—
438C2×C9—61no—
439C2×C9—61no—
440C2×C9—61no—
441C2×C9—61no—
442C2×C9—61no—
443C2×C9—61no—
444C2×C9—61no—
445C2×C9—61no—
446C2×C9—61no—
447C2×C9—272no—
448C2×C9—272no—
449C2×C9—272no—
450C2×C9D3×3−1+211yescharacteristic
451C2×C9D3×3−1+211yescharacteristic
452C2×C9D3×3−1+211yescharacteristic
453D9—32no—
454D9—32no—
455D9—32no—
456C22×C3—271no—
457C22×C3—811no—
458C2×D3—91no—
459C2×D3—271no—
460C32—21no—
461C32—31no—
462C32—31no—
463C32—31no—
464C32—61no—
465C32—61no—
466C32—61no—
467C32—61no—
468C32—61no—
469C32—61no—
470C32C2×D3×3−1+211yescharacteristic
471C32C2×C32×C3⋊D311yescharacteristic
472C9—21no—
473C9—21no—
474C9—21no—
475C9—61no—
476C9—61no—
477C9—61no—
478C9—61no—
479C9—61no—
480C9—61no—
481C9—61no—
482C9—61no—
483C9—61no—
484C9—61no—
485C9—61no—
486C9—61no—
487C9—61no—
488C9—61no—
489C9—61no—
490C9—61no—
491C9—61no—
492C9—61no—
493C9C2×D3×3−1+211yescharacteristic
494C9C2×D3×3−1+211yescharacteristic
495C9C2×D3×3−1+211yescharacteristic
496C2×C3—21no—
497C2×C3—31no—
498C2×C3—61no—
499C2×C3—181no—
500C2×C3—181no—
501C2×C3—272no—
502C2×C3—812no—
503C2×C3C3⋊D3×3−1+211yescharacteristic
504C2×C3#4207⋊C311yescharacteristic
505D3—92no—
506D3—272no—
507C22—271noSylow
508C3—21no—
509C3—31no—
510C3—61no—
511C3—181no—
512C3—181no—
513C3C2×C3⋊D3×3−1+211yescharacteristic
514C3C2×#4207⋊C311yescharacteristic
515C2—272no—
516C2#10624887⋊C211yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3#4207⋊C3
commutator, cosocleC32×C9C22×C32
FrattiniC32C2×C32×C3⋊D3
FittingC2×#10624887C2
socleC2×C32C32×C3⋊D3
prime radicalC2×C3×#4207C3
hypocenterC3×C9C22×3−1+2
LCSG ▷ C32×C9 ▷ C3×C9
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
1. #10624887⋊C2C2direct (N × H)
2. C2×#10624887C2semidirect
4. C2×#92294C3semidirect
5. C2×#92294C3semidirect
6. C2×C3⋊(D9⋊C9)C3semidirect
11. #10624887C22semidirect
15. C2×#6900D3semidirect
23. C2×#6896D3semidirect
31. C2×#6894D3semidirect
34. C2×#6887C2×C3semidirect
35. C2×#6887C2×C3semidirect
36. C2×C3×C9⋊C9C2×C3semidirect
37. #92294C2×C3semidirect
38. #92294C2×C3semidirect
39. C3⋊(D9⋊C9)C2×C3semidirect
65. #6900C2×D3semidirect
73. #6896C2×D3semidirect
81. #6894C2×D3semidirect
84. #6887C22×C3semidirect
85. #6887C22×C3semidirect
86. C3×C9⋊C9C22×C3semidirect
188. C2×C3⋊D93−1+2semidirect
327. C2×C3×C9C2×3−1+2semidirect
334. C3⋊D9C2×3−1+2semidirect
402. C3×C9C22×3−1+2semidirect
516. C2#10624887⋊C2direct (N × H)

Maximal subgroups

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

subgroupindex
#10624887⋊C22
C2×#106248872
C2×C3×#42073
C2×#922943
C2×C3⋊(D9⋊C9)3
C2×#922653
C2×#922643
C2×#6894⋊C23
C2×#922623