Finite Group Databasebeta

← C3×#89441 #13055103

Subgroups — C3×#89441 #13055103

Order 1344.

380 conjugacy classes of subgroups.

The subgroup lattice has 300 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
5C2×C3×C4×Dic7C211yesmaximal, characteristic, complemented
6C3×C7×#95C211yesmaximal, characteristic, complemented
7C3×C7⋊#95C211yesmaximal, characteristic, complemented
8#89441C311yesmaximal, 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)⋊C4C414yescomplemented
19C3×Dic7⋊C4—22no—
20C3×C4×Dic7—22no—
21C2×(C2×D7)⋊C4C2×C311yescharacteristic
22C2×(C2×D7)⋊C4C2×C311yescharacteristic
23C2×(C2×D7)⋊C4C2×C311yescharacteristic
24C2×Dic7⋊C4C2×C311yescharacteristic, complemented
25C2×C4×Dic7C2×C311yescharacteristic, complemented
26C7×#95C2×C311yescharacteristic, complemented
27C7⋊#95C2×C311yescharacteristic, complemented
28C3×#388—71nomaximal, Hall
29C23×C3×C7C2311yescharacteristic
30C22×C3×D7—21no—
31C22×C3×D7—21no—
32C22×C3×D7—21no—
33C22×C3×D7—21no—
34C22×C3×D7—21no—
35C22×C3×D7—21no—
36C22×C3×D7C2×C412yes—
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×C4×C7C2×C412yes—
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×Dic7C2×C412yes—
53C2×C3×Dic7D412yes—
54C2×C3×Dic7D412yes—
55C23×D7C22×C311yescharacteristic
56C22×C4×C7C22×C311yescharacteristic
57C22×C4×C7C22×C311yescharacteristic
58C22×C4×C7C22×C311yescharacteristic
59C22×Dic7C22×C311yescharacteristic
60C22×Dic7C22×C311yescharacteristic
61C22×Dic7C22×C311yescharacteristic
62(C2×D7)⋊C4—22no—
63(C2×D7)⋊C4—22no—
64(C2×D7)⋊C4C3×C414yescomplemented
65Dic7⋊C4—22no—
66C4×Dic7—22no—
67C2×C3×C4⋊C4—71no—
68C2×C3×C22⋊C4—71no—
69C2×C3×C22⋊C4—71no—
70C2×C3×C22⋊C4—71no—
71C2×C3×C42—71no—
72C3×#95—71no—
73C3×#95D711yescharacteristic, complemented
74C22×C3×C7C22×C411yescharacteristic
75C22×C3×C7C2×D411yescharacteristic
76C22×C3×C7C2×D411yescharacteristic
77C22×C3×C7#4111yescharacteristic
78C22×C3×C7#4111yescharacteristic
79C22×C3×C7#4111yescharacteristic
80C22×C3×C7#4111yescharacteristic
81C2×C3×D7—22no—
82C2×C3×D7—22no—
83C2×C3×D7—22no—
84C2×C3×D7—41no—
85C2×C3×D7—41no—
86C2×C3×D7—41no—
87C2×C3×D7—41no—
88C3×C4×C7—22no—
89C3×C4×C7—41no—
90C3×C4×C7—41no—
91C3×Dic7—22no—
92C3×Dic7—22no—
93C3×Dic7—22no—
94#388—71noSylow
95C23×C7C23×C311yescharacteristic
96C22×D7—21no—
97C22×D7—21no—
98C22×D7—21no—
99C22×D7—21no—
100C22×D7—21no—
101C22×D7—21no—
102C22×D7C2×C3×C412yes—
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×C4×C7—21no—
111C2×C4×C7C2×C3×C412yes—
112C2×Dic7—21no—
113C2×Dic7—21no—
114C2×Dic7—21no—
115C2×Dic7—21no—
116C2×Dic7—21no—
117C2×Dic7—21no—
118C2×Dic7C2×C3×C412yes—
119C2×Dic7C3×D412yes—
120C2×Dic7C3×D412yes—
121C24×C3—71no—
122C22×C3×C4—71no—
123C22×C3×C4—71no—
124C22×C3×C4—71no—
125C22×C3×C4C2×D711yescharacteristic
126C22×C3×C4C2×D711yescharacteristic
127C22×C3×C4C2×D711yescharacteristic
128C3×C4⋊C4—142no—
129C3×C22⋊C4—74no—
130C3×C22⋊C4—142no—
131C3×C22⋊C4—142no—
132C3×C42—142no—
133C2×C3×C7#11711yescharacteristic
134C2×C3×C7C4×D411yescharacteristic
135C2×C3×C7C4×D411yescharacteristic
136C2×C3×C7#12111yescharacteristic
137C2×C3×C7#12311yescharacteristic
138C2×C3×C7#12411yescharacteristic
139C2×C3×C7#12611yescharacteristic
140C3×D7—42no—
141C2×C4⋊C4—71no—
142C2×C22⋊C4—71no—
143C2×C22⋊C4—71no—
144C2×C22⋊C4—71no—
145C2×C42—71no—
146#95—71no—
147#95C3×D711yescharacteristic, complemented
148C22×C7C22×C3×C411yescharacteristic
149C22×C7C2×C3×D411yescharacteristic
150C22×C7C2×C3×D411yescharacteristic
151C22×C7C3×#4111yescharacteristic
152C22×C7C3×#4111yescharacteristic
153C22×C7C3×#4111yescharacteristic
154C22×C7C3×#4111yescharacteristic
155C2×D7—22no—
156C2×D7—22no—
157C2×D7—22no—
158C2×D7—41no—
159C2×D7—41no—
160C2×D7—41no—
161C2×D7—41no—
162C4×C7—22no—
163C4×C7—41no—
164C4×C7—41no—
165Dic7—22no—
166Dic7—22no—
167Dic7—22no—
168C23×C3—72no—
169C23×C3—141no—
170C23×C3—141no—
171C23×C3—141no—
172C23×C3—141no—
173C23×C3—141no—
174C23×C3—141no—
175C23×C3C22×D711yescharacteristic
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—21no—
183C2×C3×C4—21no—
184C2×C3×C4—72no—
185C2×C3×C4—72no—
186C2×C3×C4—72no—
187C2×C3×C4—141no—
188C2×C3×C4—141no—
189C2×C3×C4—141no—
190C2×C3×C4—141no—
191C2×C3×C4—141no—
192C2×C3×C4—141no—
193C2×C3×C4C4×D712yes—
194C3×C7#38811yescharacteristic, complemented, Hall
195C24—71no—
196C22×C4—71no—
197C22×C4—71no—
198C22×C4—71no—
199C22×C4C2×C3×D711yescharacteristic
200C22×C4C2×C3×D711yescharacteristic
201C22×C4C2×C3×D711yescharacteristic
202C4⋊C4—142no—
203C22⋊C4—74no—
204C22⋊C4—142no—
205C22⋊C4—142no—
206C42—142no—
207C2×C7C3×#11711yescharacteristic
208C2×C7C3×C4×D411yescharacteristic
209C2×C7C3×C4×D411yescharacteristic
210C2×C7C3×#12111yescharacteristic
211C2×C7C3×#12311yescharacteristic
212C2×C7C3×#12411yescharacteristic
213C2×C7C3×#12611yescharacteristic
214D7—42no—
215C22×C3—142no—
216C22×C3—142no—
217C22×C3—142no—
218C22×C3—281no—
219C22×C3—281no—
220C22×C3—281no—
221C22×C3—281no—
222C22×C3C2×C4×D711yescharacteristic
223C22×C3#115711yescharacteristic
224C22×C3#115711yescharacteristic
225C22×C3D4×D711yescharacteristic
226C22×C3D4×D711yescharacteristic
227C22×C3#115911yescharacteristic
228C22×C3#116111yescharacteristic
229C3×C4—22no—
230C3×C4—41no—
231C3×C4—41no—
232C3×C4—142no—
233C3×C4—142no—
234C3×C4—142no—
235C23—72no—
236C23—141no—
237C23—141no—
238C23—141no—
239C23—141no—
240C23—141no—
241C23—141no—
242C23C22×C3×D711yescharacteristic
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—72no—
252C2×C4—72no—
253C2×C4—72no—
254C2×C4—141no—
255C2×C4—141no—
256C2×C4—141no—
257C2×C4—141no—
258C2×C4—141no—
259C2×C4—141no—
260C2×C4C3×C4×D712yes—
261C7C3×#38811yescharacteristic, complemented, Sylow
262C2×C3—282no—
263C2×C3#643511yescharacteristic
264C2×C3(C22⋊D7)⋊C411yescharacteristic
265C2×C3#644711yescharacteristic
266C2×C3#644811yescharacteristic
267C2×C3#645611yescharacteristic
268C2×C3#645711yescharacteristic
269C2×C3#646111yescharacteristic
270C22—142no—
271C22—142no—
272C22—142no—
273C22—281no—
274C22—281no—
275C22—281no—
276C22—281no—
277C22C2×C3×C4×D711yescharacteristic
278C22C3×#115711yescharacteristic
279C22C3×#115711yescharacteristic
280C22C3×D4×D711yescharacteristic
281C22C3×D4×D711yescharacteristic
282C22C3×#115911yescharacteristic
283C22C3×#116111yescharacteristic
284C4—22no—
285C4—41no—
286C4—41no—
287C4—142no—
288C4—142no—
289C4—142no—
290C3#8944111yescharacteristic, direct product factor, Sylow
291C2—282no—
292C2C3×#643511yescharacteristic
293C2C3×(C22⋊D7)⋊C411yescharacteristic
294C2C3×#644711yescharacteristic
295C2C3×#644811yescharacteristic
296C2C3×#645611yescharacteristic
297C2C3×#645711yescharacteristic
298C2C3×#646111yescharacteristic
subgroupG/H
centerC23×C3C22×D7
commutatorC22×C7C22×C3×C4
FrattiniC23C22×C3×D7
FittingC3×C7×#95C2
socleC23×C3×C7C23
prime radicalC23×C3×D7C22
cosocleC23×C7C23×C3
hypercenterC3×#95D7
hypocenterC7C3×#388
LCSG ▷ C22×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. C2×C3×C4×Dic7C2semidirect
6. C3×C7×#95C2semidirect
7. C3×C7⋊#95C2semidirect
8. #89441C3direct (N × H)
18. C3×(C2×D7)⋊C4C4semidirect
24. C2×Dic7⋊C4C2×C3semidirect
25. C2×C4×Dic7C2×C3semidirect
26. C7×#95C2×C3semidirect
27. C7⋊#95C2×C3semidirect
64. (C2×D7)⋊C4C3×C4semidirect
73. C3×#95D7semidirect
147. #95C3×D7semidirect
194. C3×C7#388semidirect
261. C7C3×#388semidirect
290. C3#89441direct (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
C2×C3×C4×Dic72
C3×C7×#952
C3×C7⋊#952
#894413
C3×#3887