Finite Group Databasebeta

← C3×#89447 #13055106

Subgroups — C3×#89447 #13055106

Order 1344.

340 conjugacy classes of subgroups.

The subgroup lattice has 296 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×(C2×D7)⋊C4C211yesmaximal, characteristic
2C2×C3×(C2×D7)⋊C4C211yesmaximal, characteristic
3C2×C3×(C2×D7)⋊C4C211yesmaximal, characteristic
4C2×C3×Dic7⋊C4C211yesmaximal, characteristic, complemented
5C3×C7×#95C211yesmaximal, characteristic, complemented
6C3×C7⋊#95C211yesmaximal, characteristic, complemented
7C3×C7⋊#95C211yesmaximal, characteristic, complemented
8#89447C311yesmaximal, characteristic, direct product factor, Hall
9C23×C3×D7C2211yescharacteristic
10C22×C3×C4×C7C2211yescharacteristic
11C22×C3×C4×C7C2211yescharacteristic
12C22×C3×C4×C7C2211yescharacteristic
13C22×C3×Dic7C2211yescharacteristic
14C22×C3×Dic7C2211yescharacteristic
15C22×C3×Dic7C2211yescharacteristic
16C3×(C2×D7)⋊C4—22no—
17C3×(C2×D7)⋊C4—22no—
18C3×(C2×D7)⋊C4—22no—
19C3×Dic7⋊C4—22no—
20C2×(C2×D7)⋊C4C2×C311yescharacteristic
21C2×(C2×D7)⋊C4C2×C311yescharacteristic
22C2×(C2×D7)⋊C4C2×C311yescharacteristic
23C2×Dic7⋊C4C2×C311yescharacteristic, complemented
24C7×#95C2×C311yescharacteristic, complemented
25C7⋊#95C2×C311yescharacteristic, complemented
26C7⋊#95C2×C311yescharacteristic, complemented
27C3×#397—71nomaximal, Hall
28C23×C3×C7C2311yescharacteristic
29C22×C3×D7—21no—
30C22×C3×D7—21no—
31C22×C3×D7—21no—
32C22×C3×D7—21no—
33C22×C3×D7—21no—
34C22×C3×D7—21no—
35C22×C3×D7D412yes—
36C2×C3×C4×C7—21no—
37C2×C3×C4×C7—21no—
38C2×C3×C4×C7—21no—
39C2×C3×C4×C7—21no—
40C2×C3×C4×C7—21no—
41C2×C3×C4×C7—21no—
42C2×C3×C4×C7—21no—
43C2×C3×C4×C7—21no—
44C2×C3×C4×C7—21no—
45C2×C3×Dic7—21no—
46C2×C3×Dic7—21no—
47C2×C3×Dic7—21no—
48C2×C3×Dic7—21no—
49C2×C3×Dic7—21no—
50C2×C3×Dic7—21no—
51C2×C3×Dic7—21no—
52C2×C3×Dic7—21no—
53C2×C3×Dic7D412yes—
54C23×D7C22×C311yescharacteristic
55C22×C4×C7C22×C311yescharacteristic
56C22×C4×C7C22×C311yescharacteristic
57C22×C4×C7C22×C311yescharacteristic
58C22×Dic7C22×C311yescharacteristic
59C22×Dic7C22×C311yescharacteristic
60C22×Dic7C22×C311yescharacteristic
61(C2×D7)⋊C4—22no—
62(C2×D7)⋊C4—22no—
63(C2×D7)⋊C4—22no—
64Dic7⋊C4—22no—
65C2×C3×C4⋊C4—71no—
66C2×C3×C22⋊C4—71no—
67C2×C3×C22⋊C4—71no—
68C2×C3×C22⋊C4—71no—
69C3×#95—71no—
70C3×#95—71no—
71C3×#95D711yescharacteristic, complemented
72C22×C3×C7C2×D411yescharacteristic
73C22×C3×C7C2×D411yescharacteristic
74C22×C3×C7#4111yescharacteristic
75C22×C3×C7#4111yescharacteristic
76C22×C3×C7#4111yescharacteristic
77C22×C3×C7#4111yescharacteristic
78C22×C3×C7#4111yescharacteristic
79C2×C3×D7—22no—
80C2×C3×D7—22no—
81C2×C3×D7—22no—
82C2×C3×D7—41no—
83C2×C3×D7—41no—
84C2×C3×D7—41no—
85C2×C3×D7—41no—
86C3×C4×C7—41no—
87C3×C4×C7—41no—
88C3×C4×C7—41no—
89C3×Dic7—22no—
90C3×Dic7—41no—
91C3×Dic7—41no—
92#397—71noSylow
93C23×C7C23×C311yescharacteristic
94C22×D7—21no—
95C22×D7—21no—
96C22×D7—21no—
97C22×D7—21no—
98C22×D7—21no—
99C22×D7—21no—
100C22×D7C3×D412yes—
101C2×C4×C7—21no—
102C2×C4×C7—21no—
103C2×C4×C7—21no—
104C2×C4×C7—21no—
105C2×C4×C7—21no—
106C2×C4×C7—21no—
107C2×C4×C7—21no—
108C2×C4×C7—21no—
109C2×C4×C7—21no—
110C2×Dic7—21no—
111C2×Dic7—21no—
112C2×Dic7—21no—
113C2×Dic7—21no—
114C2×Dic7—21no—
115C2×Dic7—21no—
116C2×Dic7—21no—
117C2×Dic7—21no—
118C2×Dic7C3×D412yes—
119C24×C3—71no—
120C22×C3×C4—71no—
121C22×C3×C4—71no—
122C22×C3×C4—71no—
123C22×C3×C4C2×D711yescharacteristic
124C22×C3×C4C2×D711yescharacteristic
125C22×C3×C4C2×D711yescharacteristic
126C3×C4⋊C4—142no—
127C3×C22⋊C4—142no—
128C3×C22⋊C4—142no—
129C3×C22⋊C4—142no—
130C2×C3×C7#12111yescharacteristic
131C2×C3×C7#12311yescharacteristic
132C2×C3×C7#12311yescharacteristic
133C2×C3×C7#12311yescharacteristic
134C2×C3×C7#12411yescharacteristic
135C2×C3×C7#12611yescharacteristic
136C2×C3×C7#12611yescharacteristic
137C3×D7—42no—
138C2×C4⋊C4—71no—
139C2×C22⋊C4—71no—
140C2×C22⋊C4—71no—
141C2×C22⋊C4—71no—
142#95—71no—
143#95—71no—
144#95C3×D711yescharacteristic, complemented
145C22×C7C2×C3×D411yescharacteristic
146C22×C7C2×C3×D411yescharacteristic
147C22×C7C3×#4111yescharacteristic
148C22×C7C3×#4111yescharacteristic
149C22×C7C3×#4111yescharacteristic
150C22×C7C3×#4111yescharacteristic
151C22×C7C3×#4111yescharacteristic
152C2×D7—22no—
153C2×D7—22no—
154C2×D7—22no—
155C2×D7—41no—
156C2×D7—41no—
157C2×D7—41no—
158C2×D7—41no—
159C4×C7—41no—
160C4×C7—41no—
161C4×C7—41no—
162Dic7—22no—
163Dic7—41no—
164Dic7—41no—
165C23×C3—72no—
166C23×C3—141no—
167C23×C3—141no—
168C23×C3—141no—
169C23×C3—141no—
170C23×C3—141no—
171C23×C3—141no—
172C23×C3C22×D711yescharacteristic
173C2×C3×C4—21no—
174C2×C3×C4—21no—
175C2×C3×C4—21no—
176C2×C3×C4—21no—
177C2×C3×C4—21no—
178C2×C3×C4—21no—
179C2×C3×C4—21no—
180C2×C3×C4—21no—
181C2×C3×C4—21no—
182C2×C3×C4—72no—
183C2×C3×C4—141no—
184C2×C3×C4—141no—
185C2×C3×C4—141no—
186C2×C3×C4—141no—
187C2×C3×C4—141no—
188C2×C3×C4—141no—
189C2×C3×C4—141no—
190C2×C3×C4—141no—
191C3×C7#39711yescharacteristic, complemented, Hall
192C24—71no—
193C22×C4—71no—
194C22×C4—71no—
195C22×C4—71no—
196C22×C4C2×C3×D711yescharacteristic
197C22×C4C2×C3×D711yescharacteristic
198C22×C4C2×C3×D711yescharacteristic
199C4⋊C4—142no—
200C22⋊C4—142no—
201C22⋊C4—142no—
202C22⋊C4—142no—
203C2×C7C3×#12111yescharacteristic
204C2×C7C3×#12311yescharacteristic
205C2×C7C3×#12311yescharacteristic
206C2×C7C3×#12311yescharacteristic
207C2×C7C3×#12411yescharacteristic
208C2×C7C3×#12611yescharacteristic
209C2×C7C3×#12611yescharacteristic
210D7—42no—
211C22×C3—142no—
212C22×C3—142no—
213C22×C3—142no—
214C22×C3—281no—
215C22×C3—281no—
216C22×C3—281no—
217C22×C3—281no—
218C22×C3#115711yescharacteristic
219C22×C3#115711yescharacteristic
220C22×C3#115711yescharacteristic
221C22×C3D4×D711yescharacteristic
222C22×C3D4×D711yescharacteristic
223C22×C3#115911yescharacteristic
224C22×C3#116111yescharacteristic
225C3×C4—41no—
226C3×C4—41no—
227C3×C4—41no—
228C3×C4—142no—
229C3×C4—281no—
230C3×C4—281no—
231C23—72no—
232C23—141no—
233C23—141no—
234C23—141no—
235C23—141no—
236C23—141no—
237C23—141no—
238C23C22×C3×D711yescharacteristic
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—72no—
249C2×C4—141no—
250C2×C4—141no—
251C2×C4—141no—
252C2×C4—141no—
253C2×C4—141no—
254C2×C4—141no—
255C2×C4—141no—
256C2×C4—141no—
257C7C3×#39711yescharacteristic, complemented, Sylow
258C2×C3—282no—
259C2×C3#643911yescharacteristic
260C2×C3#644611yescharacteristic
261C2×C3#644711yescharacteristic
262C2×C3#644811yescharacteristic
263C2×C3#645711yescharacteristic
264C2×C3#645711yescharacteristic
265C2×C3#646111yescharacteristic
266C22—142no—
267C22—142no—
268C22—142no—
269C22—281no—
270C22—281no—
271C22—281no—
272C22—281no—
273C22C3×#115711yescharacteristic
274C22C3×#115711yescharacteristic
275C22C3×#115711yescharacteristic
276C22C3×D4×D711yescharacteristic
277C22C3×D4×D711yescharacteristic
278C22C3×#115911yescharacteristic
279C22C3×#116111yescharacteristic
280C4—41no—
281C4—41no—
282C4—41no—
283C4—142no—
284C4—281no—
285C4—281no—
286C3#8944711yescharacteristic, direct product factor, Sylow
287C2—282no—
288C2C3×#643911yescharacteristic
289C2C3×#644611yescharacteristic
290C2C3×#644711yescharacteristic
291C2C3×#644811yescharacteristic
292C2C3×#645711yescharacteristic
293C2C3×#645711yescharacteristic
294C2C3×#646111yescharacteristic
subgroupG/H
centerC23×C3C22×D7
commutator, cosocleC23×C7C23×C3
FrattiniC23C22×C3×D7
FittingC3×C7×#95C2
socleC23×C3×C7C23
prime radicalC23×C3×D7C22
hypercenterC3×#95D7
hypocenterC7C3×#397
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23×C3 ◁ C3×#95

Complements

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

NH ≅ G/Ntype
4. C2×C3×Dic7⋊C4C2semidirect
5. C3×C7×#95C2semidirect
6. C3×C7⋊#95C2semidirect
7. C3×C7⋊#95C2semidirect
8. #89447C3direct (N × H)
23. C2×Dic7⋊C4C2×C3semidirect
24. C7×#95C2×C3semidirect
25. C7⋊#95C2×C3semidirect
26. C7⋊#95C2×C3semidirect
71. C3×#95D7semidirect
144. #95C3×D7semidirect
191. C3×C7#397semidirect
257. C7C3×#397semidirect
286. C3#89447direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×(C2×D7)⋊C42
C2×C3×Dic7⋊C42
C3×C7×#952
C3×C7⋊#952
#894473
C3×#3977