Finite Group Databasebeta

← C3⋊(#1790⋊C3) #11920179

Subgroups — C3⋊(#1790⋊C3) #11920179

Order 1152.

336 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 25 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×#997C211yesmaximal, characteristic
2#72142C311yesmaximal, characteristic, complemented
3#1790⋊C3—31nomaximal
4C3×#997C411yescharacteristic, complemented
5C2×Dic3×A4—41nomaximal
6C2×C3×H(5,𝔽2)C2×C311yescharacteristic
7C2×#997—21no—
8C2×#997D311yescharacteristic
9#5220—31no—
10C2×#834—31no—
11C22×C3×A4—41no—
12C22×C3×A4—81no—
13C2×C3×SL(2,𝔽3)—81no—
14Dic3×A4—42no—
15#1790—31noSylow
16C3×H(5,𝔽2)—31no—
17C3×H(5,𝔽2)—61no—
18C3×H(5,𝔽2)—61no—
19C3×H(5,𝔽2)C3×C411yescharacteristic, complemented
20C2×C3×#41—61no—
21C22×C3×D4—31no—
22C22×C3×D4—61no—
23C23×Dic3A411yescharacteristic, complemented
24#997—21no—
25#997Dic311yescharacteristic, complemented
26C2×C4×A4—121no—
27C2×#217—31no—
28C2×#217—61no—
29#834—61no—
30#834—61no—
31C3⋊#95—61no—
32C2×C3×A4—41no—
33C2×C3×A4—41no—
34C2×C3×A4—41no—
35C2×C3×A4—81no—
36C2×C3×A4—81no—
37C2×C3×A4—81no—
38C2×C3×Dic3—161no—
39C3×SL(2,𝔽3)—81no—
40C2×H(5,𝔽2)C3×D311yescharacteristic
41C2×#99—91no—
42#386—91no—
43C24×C3—21no—
44C24×C3—31no—
45C24×C3C2×A411yescharacteristic
46C22×A4—41no—
47C22×A4—81no—
48C22×A4—82no—
49C22×A4—81no—
50C3×#41—61no—
51C3×#41—62no—
52C3×#41—61no—
53C3×#41—61no—
54C3×#41—62no—
55C3×#41—61no—
56C2×C3×Q8—21no—
57C2×C3×D4—31no—
58C2×C3×D4—31no—
59C2×C3×D4—31no—
60C2×C3×D4—31no—
61C2×C3×D4—61no—
62C2×C3×D4—62no—
63C2×C3×D4—62no—
64C2×C3×D4—62no—
65C2×C3×D4—61no—
66C2×C3×D4—61no—
67C2×C3×D4—62no—
68C2×C3×D4—61no—
69C2×C3×D4—61no—
70C22×C3×C4—31no—
71C22×C3×C4—61no—
72C22×Dic3—42no—
73C22×Dic3—61no—
74C22×Dic3—61no—
75C2×SL(2,𝔽3)—81no—
76C2×SL(2,𝔽3)—82no—
77C4×A4—122no—
78#217—62no—
79#217—122no—
80C22×C32—161no—
81C3×A4—41no—
82C3×A4—81no—
83C3×Dic3—162no—
84H(5,𝔽2)—31no—
85H(5,𝔽2)—61no—
86H(5,𝔽2)—61no—
87H(5,𝔽2)C3×Dic311yescharacteristic, complemented
88C2×#41—61no—
89C22×D4—31no—
90C22×D4—61no—
91C23×C4—31no—
92C2×C22⋊C4—91no—
93C2×C22⋊C4—181no—
94#99—181no—
95#99—181no—
96#95—181no—
97C23×C3—21no—
98C23×C3—31no—
99C23×C3—31no—
100C23×C3—31no—
101C23×C3—31no—
102C23×C3—41no—
103C23×C3—41no—
104C23×C3—61no—
105C23×C3—61no—
106C23×C3—61no—
107C23×C3—81no—
108C23×C3—81no—
109C23×C3—121no—
110C23×C3—121no—
111C23×C3C4×A411yescharacteristic
112C2×A4—41no—
113C2×A4—41no—
114C2×A4—41no—
115C2×A4—81no—
116C2×A4—81no—
117C2×A4—81no—
118C2×A4—82no—
119C2×A4—81no—
120C2×A4—81no—
121C2×A4—82no—
122C2×A4—82no—
123C2×A4—81no—
124C3×Q8—21no—
125C3×Q8—61no—
126C3×D4—62no—
127C3×D4—62no—
128C3×D4—62no—
129C3×D4—62no—
130C3×D4—61no—
131C3×D4—61no—
132C3×D4—62no—
133C2×C3×C4—31no—
134C2×C3×C4—31no—
135C2×C3×C4—61no—
136C2×C3×C4—62no—
137C2×C3×C4—61no—
138C2×C3×C4—61no—
139C2×C3×C4—61no—
140C2×C3×C4—481no—
141C2×Dic3—41no—
142C2×Dic3—62no—
143C2×Dic3—121no—
144C2×Dic3—121no—
145C2×Dic3—121no—
146C2×Dic3—121no—
147SL(2,𝔽3)—81no—
148SL(2,𝔽3)—82no—
149C2×C32—161no—
150C2×C32—161no—
151C2×C32—161no—
152C24—21no—
153C24—31no—
154C24D3×A411yescharacteristic
155#41—61no—
156#41—62no—
157#41—61no—
158#41—61no—
159#41—62no—
160#41—61no—
161C2×Q8—21no—
162C2×D4—31no—
163C2×D4—31no—
164C2×D4—31no—
165C2×D4—31no—
166C2×D4—61no—
167C2×D4—62no—
168C2×D4—62no—
169C2×D4—62no—
170C2×D4—61no—
171C2×D4—61no—
172C2×D4—62no—
173C2×D4—61no—
174C2×D4—61no—
175C22×C4—31no—
176C22×C4—61no—
177C22×C4—122no—
178C22×C4—181no—
179C22×C4—181no—
180C22⋊C4—182no—
181C22⋊C4—362no—
182C22×C3—31no—
183C22×C3—31no—
184C22×C3—41no—
185C22×C3—61no—
186C22×C3—61no—
187C22×C3—61no—
188C22×C3—61no—
189C22×C3—81no—
190C22×C3—121no—
191C22×C3—121no—
192C22×C3—121no—
193C22×C3—121no—
194C22×C3—121no—
195C22×C3—161no—
196C22×C3—241no—
197C22×C3—241no—
198C22×C3—321no—
199C22×C3#120⋊C311yescharacteristic
200A4—41no—
201A4—81no—
202A4—81no—
203A4—82no—
204C3×C4—61no—
205C3×C4—61no—
206C3×C4—482no—
207Dic3—42no—
208Dic3—241no—
209C32—161noSylow
210C23—21no—
211C23—31no—
212C23—31no—
213C23—31no—
214C23—31no—
215C23—41no—
216C23—41no—
217C23—61no—
218C23—61no—
219C23—61no—
220C23—81no—
221C23—81no—
222C23—121no—
223C23—121no—
224C23Dic3×A411yescharacteristic
225Q8—21no—
226Q8—61no—
227D4—62no—
228D4—62no—
229D4—62no—
230D4—62no—
231D4—61no—
232D4—61no—
233D4—62no—
234C2×C4—31no—
235C2×C4—31no—
236C2×C4—61no—
237C2×C4—62no—
238C2×C4—61no—
239C2×C4—61no—
240C2×C4—61no—
241C2×C4—121no—
242C2×C4—182no—
243C2×C4—361no—
244C2×C4—361no—
245C2×C4—361no—
246C2×C4—361no—
247C2×C3—61no—
248C2×C3—61no—
249C2×C3—121no—
250C2×C3—121no—
251C2×C3—161no—
252C2×C3—161no—
253C2×C3—161no—
254C2×C3—321no—
255C2×C3—321no—
256C2×C3—321no—
257C2×C3#379⋊C311yescharacteristic
258C2×C3B(4,𝔽2)⋊C311yescharacteristic
259C2×C3#458⋊C311yescharacteristic
260C22—31no—
261C22—31no—
262C22—41no—
263C22—61no—
264C22—61no—
265C22—61no—
266C22—61no—
267C22—81no—
268C22—121no—
269C22—121no—
270C22—121no—
271C22—121no—
272C22—121no—
273C22—241no—
274C22—241no—
275C22C3⋊(#120⋊C3)11yescharacteristic
276C4—61no—
277C4—61no—
278C4—122no—
279C4—721no—
280C3—161no—
281C3—321no—
282C3#1790⋊C311yescharacteristic, complemented
283C2—61no—
284C2—61no—
285C2—121no—
286C2—121no—
287C2C3⋊(#458⋊C3)11yescharacteristic
288C2C3⋊(B(4,𝔽2)⋊C3)11yescharacteristic
289C2C3⋊(#379⋊C3)11yescharacteristic
subgroupG/H
center, hypercenterC22C3⋊(#120⋊C3)
commutator, hypocenterC3×H(5,𝔽2)C3×C4
FrattiniC24D3×A4
Fitting, cosocleC2×C3×H(5,𝔽2)C2×C3
socleC22×C3#120⋊C3
prime radicalC2×C3×#997C2
LCSG ▷ C3×H(5,𝔽2)
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
2. #72142C3semidirect
4. C3×#997C4semidirect
19. C3×H(5,𝔽2)C3×C4semidirect
23. C23×Dic3A4semidirect
25. #997Dic3semidirect
87. H(5,𝔽2)C3×Dic3semidirect
282. C3#1790⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9972
#721423
#1790⋊C33
C2×Dic3×A44