Finite Group Databasebeta

← C3×#89723 #13055382

Subgroups — C3×#89723 #13055382

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×C7×C22⋊C4C211yesmaximal, characteristic
2C2×C3×C22⋊Dic7C211yesmaximal, characteristic
3C2×C3×C22⋊Dic7C211yesmaximal, characteristic
4C2×C3×C4⋊Dic7C211yesmaximal, characteristic, complemented
5C2×C3×C4×Dic7C211yesmaximal, characteristic, complemented
6C3×C7⋊#95C211yesmaximal, characteristic, complemented
7C3×C7⋊#95C211yesmaximal, characteristic, complemented
8#89723C311yesmaximal, characteristic, direct product factor, Hall
9C24×C3×C7C2211yescharacteristic
10C22×C3×C4×C7C2211yescharacteristic
11C22×C3×C4×C7C2211yescharacteristic
12C22×C3×Dic7C2211yescharacteristic
13C22×C3×Dic7C2211yescharacteristic
14C22×C3×Dic7C2211yescharacteristic
15C22×C3×Dic7C2211yescharacteristic
16C3×C7×C22⋊C4C414yescomplemented
17C3×C22⋊Dic7—22no—
18C3×C22⋊Dic7—22no—
19C3×C4⋊Dic7—22no—
20C3×C4×Dic7—22no—
21C2×C7×C22⋊C4C2×C311yescharacteristic
22C2×C22⋊Dic7C2×C311yescharacteristic
23C2×C22⋊Dic7C2×C311yescharacteristic
24C2×C4⋊Dic7C2×C311yescharacteristic, complemented
25C2×C4×Dic7C2×C311yescharacteristic, complemented
26C7⋊#95C2×C311yescharacteristic, complemented
27C7⋊#95C2×C311yescharacteristic, complemented
28C3×#388—71nomaximal, Hall
29C23×C3×C7—21no—
30C23×C3×C7—21no—
31C23×C3×C7—21no—
32C23×C3×C7—21no—
33C23×C3×C7—21no—
34C23×C3×C7—21no—
35C23×C3×C7C2×C412yes—
36C23×C3×C7C2311yescharacteristic
37C2×C3×C4×C7—21no—
38C2×C3×C4×C7—21no—
39C2×C3×C4×C7—21no—
40C2×C3×C4×C7—21no—
41C2×C3×C4×C7C2×C412yes—
42C2×C3×C4×C7C2×C412yes—
43C2×C3×Dic7—21no—
44C2×C3×Dic7—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—
54C2×C3×Dic7D412yes—
55C24×C7C22×C311yescharacteristic
56C22×C4×C7C22×C311yescharacteristic
57C22×C4×C7C22×C311yescharacteristic
58C22×Dic7C22×C311yescharacteristic
59C22×Dic7C22×C311yescharacteristic
60C22×Dic7C22×C311yescharacteristic
61C22×Dic7C22×C311yescharacteristic
62C7×C22⋊C4C3×C414yescomplemented
63C22⋊Dic7—22no—
64C22⋊Dic7—22no—
65C4⋊Dic7—22no—
66C4×Dic7—22no—
67C2×C3×C4⋊C4—71no—
68C2×C3×C22⋊C4—71no—
69C2×C3×C22⋊C4—71no—
70C2×C3×C22⋊C4D711yescharacteristic
71C2×C3×C42—71no—
72C3×#95—71no—
73C3×#95—71no—
74C22×C3×C7—22no—
75C22×C3×C7—22no—
76C22×C3×C7—22no—
77C22×C3×C7—41no—
78C22×C3×C7—41no—
79C22×C3×C7—41no—
80C22×C3×C7—41no—
81C22×C3×C7C22×C411yescharacteristic
82C22×C3×C7C2×D411yescharacteristic
83C22×C3×C7C2×D411yescharacteristic
84C22×C3×C7#4111yescharacteristic
85C22×C3×C7#4111yescharacteristic
86C22×C3×C7#4111yescharacteristic
87C22×C3×C7#4111yescharacteristic
88C3×C4×C7—22no—
89C3×C4×C7—22no—
90C3×Dic7—22no—
91C3×Dic7—22no—
92C3×Dic7—41no—
93C3×Dic7—41no—
94#388—71noSylow
95C23×C7—21no—
96C23×C7—21no—
97C23×C7—21no—
98C23×C7—21no—
99C23×C7—21no—
100C23×C7—21no—
101C23×C7C2×C3×C412yes—
102C23×C7C23×C311yescharacteristic
103C2×C4×C7—21no—
104C2×C4×C7—21no—
105C2×C4×C7—21no—
106C2×C4×C7—21no—
107C2×C4×C7C2×C3×C412yes—
108C2×C4×C7C2×C3×C412yes—
109C2×Dic7—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×Dic7—21no—
119C2×Dic7C3×D412yes—
120C2×Dic7C3×D412yes—
121C24×C3C2×D711yescharacteristic
122C22×C3×C4—71no—
123C22×C3×C4—71no—
124C22×C3×C4—71no—
125C22×C3×C4—71no—
126C22×C3×C4C2×D711yescharacteristic
127C22×C3×C4C2×D711yescharacteristic
128C3×C4⋊C4—142no—
129C3×C22⋊C4—142no—
130C3×C22⋊C4—142no—
131C3×C22⋊C4Dic714yescomplemented
132C3×C42—142no—
133C2×C3×C7—42no—
134C2×C3×C7#11711yescharacteristic
135C2×C3×C7C4×D411yescharacteristic
136C2×C3×C7C4×D411yescharacteristic
137C2×C3×C7#12111yescharacteristic
138C2×C3×C7#12311yescharacteristic
139C2×C3×C7#12411yescharacteristic
140C2×C3×C7#12611yescharacteristic
141C2×C4⋊C4—71no—
142C2×C22⋊C4—71no—
143C2×C22⋊C4—71no—
144C2×C22⋊C4C3×D711yescharacteristic
145C2×C42—71no—
146#95—71no—
147#95—71no—
148C22×C7—22no—
149C22×C7—22no—
150C22×C7—22no—
151C22×C7—41no—
152C22×C7—41no—
153C22×C7—41no—
154C22×C7—41no—
155C22×C7C22×C3×C411yescharacteristic
156C22×C7C2×C3×D411yescharacteristic
157C22×C7C2×C3×D411yescharacteristic
158C22×C7C3×#4111yescharacteristic
159C22×C7C3×#4111yescharacteristic
160C22×C7C3×#4111yescharacteristic
161C22×C7C3×#4111yescharacteristic
162C4×C7—22no—
163C4×C7—22no—
164Dic7—22no—
165Dic7—22no—
166Dic7—41no—
167Dic7—41no—
168C23×C3—21no—
169C23×C3—21no—
170C23×C3—21no—
171C23×C3—21no—
172C23×C3—21no—
173C23×C3—21no—
174C23×C3C2×Dic712yes—
175C23×C3C22×D711yescharacteristic
176C2×C3×C4—21no—
177C2×C3×C4—21no—
178C2×C3×C4—21no—
179C2×C3×C4—21no—
180C2×C3×C4—72no—
181C2×C3×C4—72no—
182C2×C3×C4—141no—
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—
191C2×C3×C4—141no—
192C2×C3×C4C2×Dic712yes—
193C2×C3×C4C2×Dic712yes—
194C3×C7#38811yescharacteristic, complemented, Hall
195C24C2×C3×D711yescharacteristic
196C22×C4—71no—
197C22×C4—71no—
198C22×C4—71no—
199C22×C4—71no—
200C22×C4C2×C3×D711yescharacteristic
201C22×C4C2×C3×D711yescharacteristic
202C4⋊C4—142no—
203C22⋊C4—142no—
204C22⋊C4—142no—
205C22⋊C4C3×Dic714yescomplemented
206C42—142no—
207C2×C7—42no—
208C2×C7C3×#11711yescharacteristic
209C2×C7C3×C4×D411yescharacteristic
210C2×C7C3×C4×D411yescharacteristic
211C2×C7C3×#12111yescharacteristic
212C2×C7C3×#12311yescharacteristic
213C2×C7C3×#12411yescharacteristic
214C2×C7C3×#12611yescharacteristic
215C22×C3—22no—
216C22×C3—22no—
217C22×C3—22no—
218C22×C3—41no—
219C22×C3—41no—
220C22×C3—41no—
221C22×C3—41no—
222C22×C3#115711yescharacteristic
223C22×C3#115711yescharacteristic
224C22×C3D4×D711yescharacteristic
225C22×C3D4×D711yescharacteristic
226C22×C3#115911yescharacteristic
227C22×C3#115911yescharacteristic
228C22×C3C22×Dic711yescharacteristic
229C3×C4—22no—
230C3×C4—22no—
231C3×C4—142no—
232C3×C4—142no—
233C3×C4—281no—
234C3×C4—281no—
235C23—21no—
236C23—21no—
237C23—21no—
238C23—21no—
239C23—21no—
240C23—21no—
241C23C2×C3×Dic712yes—
242C23C22×C3×D711yescharacteristic
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—72no—
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—
257C2×C4—141no—
258C2×C4—141no—
259C2×C4C2×C3×Dic712yes—
260C2×C4C2×C3×Dic712yes—
261C7C3×#38811yescharacteristic, complemented, Sylow
262C2×C3—42no—
263C2×C3#644211yescharacteristic
264C2×C3#644611yescharacteristic
265C2×C3#644711yescharacteristic
266C2×C3#644811yescharacteristic
267C2×C3#648911yescharacteristic
268C2×C3D4×Dic711yescharacteristic
269C2×C3D4×Dic711yescharacteristic
270C22—22no—
271C22—22no—
272C22—22no—
273C22—41no—
274C22—41no—
275C22—41no—
276C22—41no—
277C22C3×#115711yescharacteristic
278C22C3×#115711yescharacteristic
279C22C3×D4×D711yescharacteristic
280C22C3×D4×D711yescharacteristic
281C22C3×#115911yescharacteristic
282C22C3×#115911yescharacteristic
283C22C22×C3×Dic711yescharacteristic
284C4—22no—
285C4—22no—
286C4—142no—
287C4—142no—
288C4—281no—
289C4—281no—
290C3#8972311yescharacteristic, direct product factor, Sylow
291C2—42no—
292C2C3×#644211yescharacteristic
293C2C3×#644611yescharacteristic
294C2C3×#644711yescharacteristic
295C2C3×#644811yescharacteristic
296C2C3×#648911yescharacteristic
297C2C3×D4×Dic711yescharacteristic
298C2C3×D4×Dic711yescharacteristic
subgroupG/H
centerC23×C3C22×D7
commutatorC22×C7C22×C3×C4
FrattiniC23C22×C3×D7
FittingC2×C3×C7×C22⋊C4C2
socleC23×C3×C7C23
prime radicalC24×C3×C7C22
cosocleC23×C7C23×C3
hypercenterC2×C3×C22⋊C4D7
hypocenterC7C3×#388
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C23×C3 ◁ C2×C3×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×C3×C4⋊Dic7C2semidirect
5. C2×C3×C4×Dic7C2semidirect
6. C3×C7⋊#95C2semidirect
7. C3×C7⋊#95C2semidirect
8. #89723C3direct (N × H)
16. C3×C7×C22⋊C4C4semidirect
24. C2×C4⋊Dic7C2×C3semidirect
25. C2×C4×Dic7C2×C3semidirect
26. C7⋊#95C2×C3semidirect
27. C7⋊#95C2×C3semidirect
62. C7×C22⋊C4C3×C4semidirect
131. C3×C22⋊C4Dic7semidirect
194. C3×C7#388semidirect
205. C22⋊C4C3×Dic7semidirect
261. C7C3×#388semidirect
290. C3#89723direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C7×C22⋊C42
C2×C3×C22⋊Dic72
C2×C3×C4⋊Dic72
C2×C3×C4×Dic72
C3×C7⋊#952
#897233
C3×#3887