Finite Group Databasebeta

← C2×#4183⋊D3 #14518341

Subgroups — C2×#4183⋊D3 #14518341

Order 1944.

912 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 912 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3⋊#4175C211yesmaximal, characteristic, complemented
2C2×C3⋊#4174C211yesmaximal, characteristic, complemented
3C2×C3×#4183C211yesmaximal, characteristic, complemented
4#4183⋊D3C214yesmaximal, direct product factor
5C2×C3⋊D32—31nomaximal
6C2×((C3⋊D3)⋊C3)⋊D3—31nomaximal
7C2×#4174⋊C2—31nomaximal
8C2×C3×AΣL(1,𝔽27)C2211yescharacteristic, complemented
9C3⋊#4175C2212yescomplemented
10C3⋊#4174C2212yescomplemented
11C3×#4183C2212yescomplemented
12C2×C3⋊(C3⋊(C3⋊D3))D311yescharacteristic, complemented
13C2×C32×C3⋊D3—31no—
14C2×C32×C3⋊D3—31no—
15C3⋊D32—34no—
16C2×C3⋊#272D311yescharacteristic, complemented
17C2×C3⋊((C3⋊D3)⋊C3)—31no—
18C2×C3×AGL(1,ℤ/9)—61no—
19C2×C3×(C3⋊D3)⋊C3—31no—
20((C3⋊D3)⋊C3)⋊D3—34no—
21C2×#4183D311yescharacteristic, complemented
22C2×#4175—31no—
23C2×#4175—61no—
24C2×#4174—31no—
25C2×#4174—61no—
26#4174⋊C2—34no—
27C3×AΣL(1,𝔽27)C2311yescharacteristic, complemented, Sylow
28C2×#1113—91no—
29C2×D3×C3⋊D3—91no—
30C2×D3×C3⋊D3—91no—
31C2×D3×C3⋊D3—92no—
32C2×D3×C3⋊D3—91no—
33C2×D3×C3⋊D3—93no—
34C2×((C3⋊D3)⋊C3)⋊C2—91no—
35C2×((C3⋊D3)⋊C3)⋊C2—92no—
36C2×C34C2×D311yescharacteristic, complemented
37C3⋊(C3⋊(C3⋊D3))C2×D312yescomplemented
38C32×C3⋊D3—32no—
39C32×C3⋊D3—32no—
40C2×C3×3−1+2—21no—
41C2×C3×H(3,𝔽3)C2×D311yescharacteristic, complemented
42C3⋊#272C2×D312yescomplemented
43C3⋊((C3⋊D3)⋊C3)—32no—
44C3×AGL(1,ℤ/9)—62no—
45C3×(C3⋊D3)⋊C3—32no—
46C2×AΣL(1,𝔽27)—21no—
47C2×AΣL(1,𝔽27)—21no—
48C2×AΣL(1,𝔽27)—41no—
49C2×AΣL(1,𝔽27)C2×D311yescharacteristic, complemented
50#4183C2×D312yescomplemented
51#4175—32no—
52#4175—62no—
53#4174—32no—
54#4174—62no—
55C2×C3⋊(C3⋊D3)—31no—
56C2×C3⋊(C3⋊D3)—31no—
57C2×C3⋊(C3⋊D3)—61no—
58C2×C3⋊(C3⋊D3)—91no—
59C2×C3⋊(C3⋊D3)—92no—
60C2×C3⋊(C3⋊D3)—93no—
61C2×C3⋊(C3⋊D3)—183no—
62C2×C3×C3⋊D3—33no—
63C2×C3×C3⋊D3—31no—
64C2×C3×C3⋊D3—32no—
65C2×C3×C3⋊D3—31no—
66C2×C3×C3⋊D3—31no—
67C2×C3×C3⋊D3—31no—
68C2×C3×C3⋊D3—91no—
69C2×C3×C3⋊D3—91no—
70C2×C32×D3—93no—
71C2×C32×D3—92no—
72C2×C32×D3—91no—
73C2×C32×D3—91no—
74C2×C32×D3—91no—
75#1113—94no—
76D3×C3⋊D3—94no—
77D3×C3⋊D3—94no—
78D3×C3⋊D3—98no—
79D3×C3⋊D3—94no—
80D3×C3⋊D3—912no—
81C2×#272—31no—
82C2×#272—61no—
83C2×#272—92no—
84C2×AGL(1,ℤ/9)—61no—
85C2×AGL(1,ℤ/9)—62no—
86C2×(C3⋊D3)⋊C3—32no—
87C2×(C3⋊D3)⋊C3—31no—
88C2×(C3⋊D3)⋊C3—92no—
89C2×(C3⋊D3)⋊C3—91no—
90C2×C3×D9—61no—
91((C3⋊D3)⋊C3)⋊C2—94no—
92((C3⋊D3)⋊C3)⋊C2—98no—
93C34C22×D311yescharacteristic, complemented
94C3×3−1+2—21no—
95C3×H(3,𝔽3)C22×D311yescharacteristic, complemented
96AΣL(1,𝔽27)—21no—
97AΣL(1,𝔽27)—21no—
98AΣL(1,𝔽27)—41no—
99AΣL(1,𝔽27)C22×D311yescharacteristic, complemented
100C22×C3⋊D3—271no—
101C22×C3⋊D3—271no—
102C2×D32—272no—
103C2×D32—271no—
104C2×D32—271no—
105C2×D32—273no—
106C2×D32—273no—
107C2×D32—276no—
108C2×D32—271no—
109C2×D32—271no—
110C2×C33—21no—
111C2×C33—33no—
112C2×C33—32no—
113C2×C33—31no—
114C2×C33—31no—
115C2×C33—63no—
116C2×C33D3211yescharacteristic
117C2×C33D3211yescharacteristic, complemented
118C3⋊(C3⋊D3)—32no—
119C3⋊(C3⋊D3)—32no—
120C3⋊(C3⋊D3)—62no—
121C3⋊(C3⋊D3)—92no—
122C3⋊(C3⋊D3)—94no—
123C3⋊(C3⋊D3)—96no—
124C3⋊(C3⋊D3)—186no—
125C3×C3⋊D3—36no—
126C3×C3⋊D3—32no—
127C3×C3⋊D3—34no—
128C3×C3⋊D3—32no—
129C3×C3⋊D3—32no—
130C3×C3⋊D3—32no—
131C3×C3⋊D3—92no—
132C3×C3⋊D3—92no—
133C32×D3—96no—
134C32×D3—94no—
135C32×D3—92no—
136C32×D3—92no—
137C32×D3—92no—
138C2×3−1+2—21no—
139C2×3−1+2—41no—
140C2×3−1+2—62no—
141C2×H(3,𝔽3)—21no—
142C2×H(3,𝔽3)—32no—
143C2×H(3,𝔽3)D3211yescharacteristic, complemented
144C2×C3×C9—61no—
145#272—32no—
146#272—62no—
147#272—94no—
148AGL(1,ℤ/9)—62no—
149AGL(1,ℤ/9)—64no—
150(C3⋊D3)⋊C3—34no—
151(C3⋊D3)⋊C3—32no—
152(C3⋊D3)⋊C3—94no—
153(C3⋊D3)⋊C3—92no—
154C3×D9—62no—
155C22×C32—271no—
156C22×C32—271no—
157C2×C3⋊D3—31no—
158C2×C3⋊D3—31no—
159C2×C3⋊D3—31no—
160C2×C3⋊D3—91no—
161C2×C3⋊D3—91no—
162C2×C3⋊D3—92no—
163C2×C3⋊D3—91no—
164C2×C3⋊D3—271no—
165C2×C3⋊D3—271no—
166C2×C3⋊D3—273no—
167C2×C3⋊D3—274no—
168C2×C3⋊D3—274no—
169C2×C3⋊D3—273no—
170C2×C3⋊D3—276no—
171C2×C3⋊D3—541no—
172C2×C3⋊D3—541no—
173C2×C3⋊D3—543no—
174C2×C3⋊D3—546no—
175C2×C3⋊D3—543no—
176C2×C3×D3—93no—
177C2×C3×D3—93no—
178C2×C3×D3—96no—
179C2×C3×D3—96no—
180C2×C3×D3—93no—
181C2×C3×D3—93no—
182C2×C3×D3—91no—
183C2×C3×D3—92no—
184C2×C3×D3—92no—
185C2×C3×D3—91no—
186C2×C3×D3—91no—
187C2×C3×D3—91no—
188C2×C3×D3—271no—
189C2×C3×D3—271no—
190C2×C3×D3—271no—
191C2×C3×D3—271no—
192C2×C3×D3—541no—
193C2×C3×D3—541no—
194D32—278no—
195D32—274no—
196D32—274no—
197D32—2712no—
198D32—2712no—
199D32—2724no—
200D32—274no—
201D32—274no—
202C2×D9—61no—
203C33—21no—
204C33—33no—
205C33—32no—
206C33—31no—
207C33—31no—
208C33—63no—
209C33C2×D3211yescharacteristic
210C33C2×D3211yescharacteristic, complemented
2113−1+2—21no—
2123−1+2—41no—
2133−1+2—62no—
214H(3,𝔽3)—21no—
215H(3,𝔽3)—32no—
216H(3,𝔽3)C2×D3211yescharacteristic, complemented
217C3×C9—61no—
218C22×D3—811no—
219C22×D3—811no—
220C22×D3—812no—
221C22×D3—811no—
222C22×D3—813no—
223C22×D3—811no—
224C2×C32—31no—
225C2×C32—31no—
226C2×C32—33no—
227C2×C32—36no—
228C2×C32—33no—
229C2×C32—31no—
230C2×C32—61no—
231C2×C32—63no—
232C2×C32—66no—
233C2×C32—63no—
234C2×C32—61no—
235C2×C32—61no—
236C2×C32—91no—
237C2×C32—181no—
238C2×C32—272no—
239C2×C32—272no—
240C2×C32((C3⋊D3)⋊C3)⋊C211yescharacteristic
241C2×C32((C3⋊D3)⋊C3)⋊C212yes—
242C2×C32#111311yescharacteristic
243C3⋊D3—32no—
244C3⋊D3—32no—
245C3⋊D3—32no—
246C3⋊D3—92no—
247C3⋊D3—92no—
248C3⋊D3—94no—
249C3⋊D3—92no—
250C3⋊D3—272no—
251C3⋊D3—272no—
252C3⋊D3—276no—
253C3⋊D3—276no—
254C3⋊D3—2712no—
255C3⋊D3—542no—
256C3⋊D3—542no—
257C3⋊D3—546no—
258C3⋊D3—5412no—
259C3⋊D3—546no—
260C3×D3—96no—
261C3×D3—96no—
262C3×D3—912no—
263C3×D3—912no—
264C3×D3—96no—
265C3×D3—96no—
266C3×D3—92no—
267C3×D3—94no—
268C3×D3—94no—
269C3×D3—92no—
270C3×D3—92no—
271C3×D3—92no—
272C3×D3—272no—
273C3×D3—272no—
274C3×D3—272no—
275C3×D3—272no—
276C3×D3—542no—
277C3×D3—542no—
278C2×C9—61no—
279C2×C9—121no—
280D9—62no—
281C22×C3—273no—
282C22×C3—272no—
283C22×C3—271no—
284C22×C3—271no—
285C22×C3—271no—
286C22×C3—811no—
287C2×D3—92no—
288C2×D3—91no—
289C2×D3—93no—
290C2×D3—91no—
291C2×D3—91no—
292C2×D3—271no—
293C2×D3—271no—
294C2×D3—271no—
295C2×D3—271no—
296C2×D3—541no—
297C2×D3—541no—
298C2×D3—812no—
299C2×D3—811no—
300C2×D3—813no—
301C2×D3—814no—
302C2×D3—814no—
303C2×D3—818no—
304C2×D3—814no—
305C2×D3—8112no—
306C2×D3—814no—
307C2×D3—1623no—
308C32—33no—
309C32—31no—
310C32—31no—
311C32—36no—
312C32—33no—
313C32—31no—
314C32—61no—
315C32—63no—
316C32—66no—
317C32—63no—
318C32—61no—
319C32—61no—
320C32—91no—
321C32—181no—
322C32C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
323C32C2×((C3⋊D3)⋊C3)⋊C212yes—
324C32C2×#111311yescharacteristic
325C9—61no—
326C9—121no—
327C23—2431noSylow
328C2×C3—21no—
329C2×C3—33no—
330C2×C3—32no—
331C2×C3—31no—
332C2×C3—63no—
333C2×C3—91no—
334C2×C3—181no—
335C2×C3—276no—
336C2×C3—274no—
337C2×C3—272no—
338C2×C3—272no—
339C2×C3—272no—
340C2×C3—812no—
341C2×C3#4174⋊C211yescharacteristic, complemented
342C2×C3#6643211yescharacteristic
343D3—94no—
344D3—92no—
345D3—96no—
346D3—92no—
347D3—92no—
348D3—272no—
349D3—272no—
350D3—272no—
351D3—272no—
352D3—542no—
353D3—542no—
354D3—814no—
355D3—812no—
356D3—816no—
357D3—1626no—
358C22—271no—
359C22—271no—
360C22—811no—
361C22—2434no—
362C3—21no—
363C3—33no—
364C3—32no—
365C3—31no—
366C3—63no—
367C3—91no—
368C3—181no—
369C3C2×#4174⋊C211yescharacteristic, complemented
370C3C2×#6643211yescharacteristic
371C2—272no—
372C2—272no—
373C2—812no—
374C2#4183⋊D311yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2#4183⋊D3
commutator, cosocle, hypocenterC3×AΣL(1,𝔽27)C23
FrattiniC32C2×#1113
FittingC2×C3×AΣL(1,𝔽27)C22
socleC2×C32((C3⋊D3)⋊C3)⋊C2
LCSG ▷ C3×AΣL(1,𝔽27)
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C3⋊#4175C2semidirect
2. C2×C3⋊#4174C2semidirect
3. C2×C3×#4183C2semidirect
4. #4183⋊D3C2direct (N × H)
8. C2×C3×AΣL(1,𝔽27)C22semidirect
9. C3⋊#4175C22semidirect
10. C3⋊#4174C22semidirect
11. C3×#4183C22semidirect
12. C2×C3⋊(C3⋊(C3⋊D3))D3semidirect
16. C2×C3⋊#272D3semidirect
21. C2×#4183D3semidirect
27. C3×AΣL(1,𝔽27)C23semidirect
36. C2×C34C2×D3semidirect
37. C3⋊(C3⋊(C3⋊D3))C2×D3semidirect
41. C2×C3×H(3,𝔽3)C2×D3semidirect
42. C3⋊#272C2×D3semidirect
49. C2×AΣL(1,𝔽27)C2×D3semidirect
50. #4183C2×D3semidirect
93. C34C22×D3semidirect
95. C3×H(3,𝔽3)C22×D3semidirect
99. AΣL(1,𝔽27)C22×D3semidirect
117. C2×C33D32semidirect
143. C2×H(3,𝔽3)D32semidirect
210. C33C2×D32semidirect
216. H(3,𝔽3)C2×D32semidirect
341. C2×C3#4174⋊C2semidirect
369. C3C2×#4174⋊C2semidirect
374. C2#4183⋊D3direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3⋊#41752
C2×C3⋊#41742
C2×C3×#41832
#4183⋊D32
C2×C3⋊D323
C2×((C3⋊D3)⋊C3)⋊D33
C2×#4174⋊C23