Finite Group Databasebeta

← #14518828

Subgroups — #14518828

Order 1944.

719 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 719 conjugacy classes of subgroups — too many to draw. Only its 75 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
1C3×C3⋊#1084C211yesmaximal, characteristic
2C3⋊(C3⋊((C3⋊Dic3)⋊C3))C211yesmaximal, characteristic
3C3×C3⋊((C3⋊Dic3)⋊C3)C211yesmaximal, characteristic
4C3⋊#6296—31nomaximal
5#10620153—31nomaximal
6#10619900—33nomaximal
7#10619881—31nomaximal
8C2×C32×H(3,𝔽3)C2211yescharacteristic
9C3⋊(C3⋊(C3⋊Dic3))D311yescharacteristic
10C3×C3⋊(C3⋊Dic3)—31no—
11C3×C3⋊(C3⋊Dic3)D311yescharacteristic
12C32×C3⋊Dic3—31no—
13C32×C3⋊Dic3—31no—
14C32×C3⋊Dic3—31no—
15C32×C3⋊Dic3—61no—
16C3⋊#1084D311yescharacteristic
17C3×#1084—33no—
18C3×#1084—63no—
19C3⋊((C3⋊Dic3)⋊C3)—31no—
20C3⋊((C3⋊Dic3)⋊C3)—33no—
21C3⋊((C3⋊Dic3)⋊C3)—63no—
22C3⋊((C3⋊Dic3)⋊C3)—61no—
23C3⋊((C3⋊Dic3)⋊C3)D313yes—
24C3×(C3⋊Dic3)⋊C3—31no—
25C3×(C3⋊Dic3)⋊C3—61no—
26C32×H(3,𝔽3)Q811yescharacteristic, complemented, Sylow
27#6296—91no—
28#6296—93no—
29#6293—91no—
30#6293—93no—
31#6293—91no—
32#6293—93no—
33#6293—91no—
34#6196—93no—
35C2×C34—21no—
36C2×C34C2×D311yescharacteristic
37C2×C34C2×D311yescharacteristic
38C2×C3×H(3,𝔽3)—21no—
39C2×C3×H(3,𝔽3)—21no—
40C2×C3×H(3,𝔽3)—23no—
41C2×C3×H(3,𝔽3)—23no—
42C2×C3×H(3,𝔽3)—43no—
43C2×C3×H(3,𝔽3)—41no—
44C2×C3×H(3,𝔽3)C2×D311yescharacteristic
45C2×C3×H(3,𝔽3)C2×D313yes—
46C3⋊(C3⋊Dic3)—31no—
47C3⋊(C3⋊Dic3)—31no—
48C3⋊(C3⋊Dic3)—33no—
49C3⋊(C3⋊Dic3)—61no—
50C3⋊(C3⋊Dic3)—63no—
51C3⋊(C3⋊Dic3)—93no—
52C3⋊(C3⋊Dic3)—183no—
53C3⋊(C3⋊Dic3)C3⋊D311yescharacteristic
54C3×C3⋊Dic3—33no—
55C3×C3⋊Dic3—33no—
56C3×C3⋊Dic3—33no—
57C3×C3⋊Dic3—31no—
58C3×C3⋊Dic3—31no—
59C3×C3⋊Dic3—31no—
60C3×C3⋊Dic3—31no—
61C3×C3⋊Dic3—61no—
62C3×C3⋊Dic3—61no—
63C3×C3⋊Dic3—63no—
64C3×C3⋊Dic3—93no—
65C3×C3⋊Dic3—93no—
66C3×C3⋊Dic3—91no—
67C3×C3⋊Dic3—91no—
68C3×C3⋊Dic3—181no—
69C3×C3⋊Dic3—183no—
70C32×Dic3—93no—
71C32×Dic3—91no—
72C32×Dic3—93no—
73C32×Dic3—91no—
74C32×Dic3—91no—
75C32×Dic3—183no—
76C32×Dic3—181no—
77#1084—33no—
78#1084—63no—
79(C3⋊Dic3)⋊C3—33no—
80(C3⋊Dic3)⋊C3—63no—
81(C3⋊Dic3)⋊C3—93no—
82(C3⋊Dic3)⋊C3—183no—
83C34—21no—
84C34Dic611yescharacteristic, complemented
85C34Dic611yescharacteristic, complemented
86C3×H(3,𝔽3)—21no—
87C3×H(3,𝔽3)—21no—
88C3×H(3,𝔽3)—23no—
89C3×H(3,𝔽3)—23no—
90C3×H(3,𝔽3)—43no—
91C3×H(3,𝔽3)—41no—
92C3×H(3,𝔽3)Dic611yescharacteristic, complemented
93C3×H(3,𝔽3)Dic613yescomplemented
94#634—271no—
95#634—271no—
96#627—273no—
97#627—273no—
98#627—271no—
99#627—279no—
100#627—271no—
101#627—273no—
102#627—271no—
103C2×C33—23no—
104C2×C33—21no—
105C2×C33—21no—
106C2×C33—21no—
107C2×C33—23no—
108C2×C33—21no—
109C2×C33—21no—
110C2×C33—33no—
111C2×C33—33no—
112C2×C33—41no—
113C2×C33—43no—
114C2×C33—41no—
115C2×C33—63no—
116C2×C33—63no—
117C2×C33—63no—
118C2×C33—123no—
119C2×C33D3211yescharacteristic
120C2×C33D3213yes—
121C2×C33D3211yescharacteristic
122C2×C33D3211yescharacteristic
123C2×C33C2×C3⋊D311yescharacteristic
124C2×H(3,𝔽3)—23no—
125C2×H(3,𝔽3)—23no—
126C2×H(3,𝔽3)—23no—
127C2×H(3,𝔽3)—43no—
128C2×H(3,𝔽3)—43no—
129C2×H(3,𝔽3)—46no—
130C2×H(3,𝔽3)—43no—
131C2×H(3,𝔽3)D3213yes—
132C32×C4—271no—
133C32×C4—271no—
134C3⋊Dic3—31no—
135C3⋊Dic3—31no—
136C3⋊Dic3—31no—
137C3⋊Dic3—31no—
138C3⋊Dic3—61no—
139C3⋊Dic3—61no—
140C3⋊Dic3—93no—
141C3⋊Dic3—91no—
142C3⋊Dic3—93no—
143C3⋊Dic3—91no—
144C3⋊Dic3—93no—
145C3⋊Dic3—181no—
146C3⋊Dic3—183no—
147C3⋊Dic3—183no—
148C3⋊Dic3—271no—
149C3⋊Dic3—279no—
150C3⋊Dic3—541no—
151C3⋊Dic3—541no—
152C3⋊Dic3—549no—
153C3⋊Dic3—542no—
154C3×Dic3—99no—
155C3×Dic3—93no—
156C3×Dic3—99no—
157C3×Dic3—93no—
158C3×Dic3—93no—
159C3×Dic3—91no—
160C3×Dic3—93no—
161C3×Dic3—93no—
162C3×Dic3—91no—
163C3×Dic3—91no—
164C3×Dic3—183no—
165C3×Dic3—181no—
166C3×Dic3—183no—
167C3×Dic3—189no—
168C3×Dic3—271no—
169C3×Dic3—271no—
170C3×Dic3—273no—
171C3×Dic3—271no—
172C3×Dic3—541no—
173C3×Dic3—541no—
174C3×Dic3—543no—
175C33—21no—
176C33—23no—
177C33—21no—
178C33—21no—
179C33—23no—
180C33—21no—
181C33—21no—
182C33—33no—
183C33—33no—
184C33—41no—
185C33—43no—
186C33—41no—
187C33—63no—
188C33—63no—
189C33—63no—
190C33—123no—
191C33#62711yescharacteristic
192C33#62713yescomplemented
193C33#62711yescharacteristic, complemented
194C33#62711yescharacteristic, complemented
195C33#63411yescharacteristic, complemented
196H(3,𝔽3)—23no—
197H(3,𝔽3)—23no—
198H(3,𝔽3)—23no—
199H(3,𝔽3)—43no—
200H(3,𝔽3)—43no—
201H(3,𝔽3)—46no—
202H(3,𝔽3)—43no—
203H(3,𝔽3)#62713yescomplemented
204Dic6—813no—
205Dic6—811no—
206Dic6—811no—
207Dic6—811no—
208Dic6—813no—
209C2×C32—23no—
210C2×C32—21no—
211C2×C32—21no—
212C2×C32—21no—
213C2×C32—23no—
214C2×C32—23no—
215C2×C32—31no—
216C2×C32—39no—
217C2×C32—33no—
218C2×C32—31no—
219C2×C32—43no—
220C2×C32—41no—
221C2×C32—61no—
222C2×C32—69no—
223C2×C32—61no—
224C2×C32—63no—
225C2×C32—62no—
226C2×C32—61no—
227C2×C32—61no—
228C2×C32—63no—
229C2×C32—69no—
230C2×C32—61no—
231C2×C32—121no—
232C2×C32—123no—
233C2×C32—129no—
234C2×C32—121no—
235C2×C32—122no—
236C2×C32—121no—
237C2×C32((C3⋊D3)⋊C3)⋊C213yes—
238C2×C32D3×C3⋊D311yescharacteristic
239C2×C32D3×C3⋊D311yescharacteristic
240C2×C32#111311yescharacteristic
241C2×C32#111313yes—
242C3×C4—273no—
243C3×C4—273no—
244C3×C4—271no—
245C3×C4—271no—
246C3×C4—811no—
247Dic3—91no—
248Dic3—93no—
249Dic3—93no—
250Dic3—91no—
251Dic3—91no—
252Dic3—181no—
253Dic3—183no—
254Dic3—271no—
255Dic3—273no—
256Dic3—271no—
257Dic3—271no—
258Dic3—541no—
259Dic3—543no—
260Dic3—541no—
261Dic3—813no—
262Dic3—1623no—
263C32—23no—
264C32—21no—
265C32—21no—
266C32—21no—
267C32—23no—
268C32—23no—
269C32—31no—
270C32—39no—
271C32—33no—
272C32—31no—
273C32—43no—
274C32—41no—
275C32—61no—
276C32—61no—
277C32—69no—
278C32—63no—
279C32—62no—
280C32—61no—
281C32—61no—
282C32—63no—
283C32—69no—
284C32—61no—
285C32—121no—
286C32—123no—
287C32—121no—
288C32—129no—
289C32—122no—
290C32—121no—
291C32#619613yescomplemented
292C32#629311yescharacteristic
293C32#629311yescharacteristic, complemented
294C32#629611yescharacteristic
295C32#629613yescomplemented
296Q8—2431noSylow
297C2×C3—23no—
298C2×C3—21no—
299C2×C3—31no—
300C2×C3—33no—
301C2×C3—61no—
302C2×C3—63no—
303C2×C3—61no—
304C2×C3—63no—
305C2×C3—121no—
306C2×C3—123no—
307C2×C3((C3⋊D3)⋊C3)⋊D313yes—
308C2×C3#6643211yescharacteristic
309C2×C3C3⋊#111311yescharacteristic
310C4—271no—
311C4—271no—
312C4—811no—
313C3—23no—
314C3—21no—
315C3—31no—
316C3—33no—
317C3—63no—
318C3—61no—
319C3—61no—
320C3—63no—
321C3—121no—
322C3—123no—
323C3#1061988113yescomplemented
324C3#1061990011yescharacteristic, complemented
325C3C3⋊#629611yescharacteristic
326C2#1175809011yescharacteristic
subgroupG/H
center, hypercenterC2#11758090
commutator, Fitting, prime radical, cosocleC2×C32×H(3,𝔽3)C22
FrattiniC2×C3C3⋊#1113
socleC2×C33D32
hypocenterC32×H(3,𝔽3)Q8
LCSG ▷ C2×C32×H(3,𝔽3) ▷ C32×H(3,𝔽3)
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
26. C32×H(3,𝔽3)Q8semidirect
84. C34Dic6semidirect
85. C34Dic6semidirect
92. C3×H(3,𝔽3)Dic6semidirect
93. C3×H(3,𝔽3)Dic6semidirect
192. C33#627semidirect
193. C33#627semidirect
194. C33#627semidirect
195. C33#634semidirect
203. H(3,𝔽3)#627semidirect
291. C32#6196semidirect
293. C32#6293semidirect
295. C32#6296semidirect
323. C3#10619881semidirect
324. C3#10619900semidirect

Maximal subgroups

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

subgroupindex
C3×C3⋊#10842
C3⋊(C3⋊((C3⋊Dic3)⋊C3))2
C3×C3⋊((C3⋊Dic3)⋊C3)2
C3⋊#62963
#106201533
#106199003
#106198813