Finite Group Databasebeta

← #13061633

Subgroups — #13061633

Order 1344.

428 conjugacy classes of subgroups.

The subgroup lattice has 292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×C7×D4C211yesmaximal, characteristic
2#10621418C212yesmaximal
3#10621409C211yesmaximal, characteristic, complemented
4C2×C4⋊Dic21C211yesmaximal, characteristic, complemented
5#10621407C211yesmaximal, characteristic, complemented
6#10621407C211yesmaximal, characteristic, complemented
7#10621372C212yesmaximal, complemented
8#10621362C212yesmaximal, complemented
9#10621360C212yesmaximal, complemented
10#10621353C211yesmaximal, characteristic, complemented
11C4×Dic42C211yesmaximal, characteristic, complemented
12#90232—31nomaximal, Hall
13C2×C3×C7×D4C2211yescharacteristic
14C22×C3×C4×C7C2211yescharacteristic
15C22×C3×C4×C7C2211yescharacteristic
16C22×Dic21C2212yes—
17C2×Dic42C2211yescharacteristic
18C3×C7×C4⋊C4C2211yescharacteristic
19C3×C7×C22⋊C4C2211yescharacteristic
20C3×C7×C22⋊C4C2211yescharacteristic
21C3×C42×C7C2211yescharacteristic
22#66636C2212yes—
23#66636C2212yes—
24#66636C2212yes—
25C4⋊Dic21C2211yescharacteristic
26C4⋊Dic21C2211yescharacteristic
27C4⋊Dic21C2211yescharacteristic
28C4⋊Dic21C2212yes—
29#66629C2212yes—
30#66629C2212yes—
31#66629C2212yes—
32#66629C2212yes—
33#66629C2212yes—
34C4×Dic21C2212yes—
35C4×Dic21C2212yes—
36C4×C7×D4D311yescharacteristic
37#6498—32no—
38#6489—31no—
39C2×C4⋊Dic7—31no—
40#6487—31no—
41#6487—31no—
42#6452—32no—
43#6442—32no—
44#6440—32no—
45#6433—31no—
46C4×Dic14—31no—
47#5541—71nomaximal, Hall
48C23×C3×C7C2311yescharacteristic
49C23×C3×C7C2311yescharacteristic
50C3×C7×D4—22no—
51C2×C3×C4×C7—22no—
52C2×C3×C4×C7—22no—
53C2×C3×C4×C7C2311yescharacteristic
54C2×C3×C4×C7C2311yescharacteristic
55C2×C3×C4×C7C2311yescharacteristic
56C2×C3×C4×C7C2311yescharacteristic
57C2×C3×C4×C7C2311yescharacteristic
58C2×Dic21—24no—
59C2×Dic21C2312yes—
60C2×Dic21C2312yes—
61C2×Dic21C2312yes—
62C2×Dic21C2312yes—
63Dic42—22no—
64C2×C7×D4C2×D311yescharacteristic
65C22×C4×C7C2×D311yescharacteristic
66C22×C4×C7C2×D311yescharacteristic
67C22×Dic7—32no—
68C2×Dic14—31no—
69C7×C4⋊C4C2×D311yescharacteristic
70C7×C22⋊C4C2×D311yescharacteristic
71C7×C22⋊C4C2×D311yescharacteristic
72C42×C7C2×D311yescharacteristic
73C22⋊Dic7—32no—
74C22⋊Dic7—32no—
75C22⋊Dic7—32no—
76C4⋊Dic7—31no—
77C4⋊Dic7—31no—
78C4⋊Dic7—31no—
79C4⋊Dic7—32no—
80Dic7⋊C4—32no—
81Dic7⋊C4—32no—
82Dic7⋊C4—32no—
83Dic7⋊C4—32no—
84Dic7⋊C4—32no—
85C4×Dic7—32no—
86C4×Dic7—32no—
87C3×C4×D4D711yescharacteristic
88#935—72no—
89#926—71no—
90C2×C4⋊Dic3—71no—
91#924—71no—
92#924—71no—
93#889—72no—
94#879—72no—
95#877—72no—
96#870—71no—
97C4×Dic6—71no—
98C22×C3×C7—21no—
99C22×C3×C7—21no—
100C22×C3×C7—21no—
101C22×C3×C7—21no—
102C22×C3×C7—21no—
103C22×C3×C7#4112yes—
104C22×C3×C7C2411yescharacteristic
105C3×C4×C7—21no—
106C3×C4×C7—21no—
107C3×C4×C7—21no—
108C3×C4×C7—21no—
109C3×C4×C7#4112yes—
110Dic21—22no—
111Dic21—22no—
112Dic21—22no—
113Dic21—22no—
114#552—211noSylow
115C23×C7C22×D311yescharacteristic
116C23×C7C22×D311yescharacteristic
117C7×D4—22no—
118C2×C4×C7—22no—
119C2×C4×C7—22no—
120C2×C4×C7C22×D311yescharacteristic
121C2×C4×C7C22×D311yescharacteristic
122C2×C4×C7C22×D311yescharacteristic
123C2×C4×C7C22×D311yescharacteristic
124C2×C4×C7C22×D311yescharacteristic
125C2×Dic7—32no—
126C2×Dic7—32no—
127C2×Dic7—32no—
128C2×Dic7—32no—
129C2×Dic7—64no—
130Dic14—62no—
131C2×C3×D4C2×D711yescharacteristic
132C22×C3×C4C2×D711yescharacteristic
133C22×C3×C4C2×D711yescharacteristic
134C22×Dic3—72no—
135C2×Dic6—71no—
136C3×C4⋊C4C2×D711yescharacteristic
137C3×C22⋊C4C2×D711yescharacteristic
138C3×C22⋊C4C2×D711yescharacteristic
139C3×C42C2×D711yescharacteristic
140#217—72no—
141#217—72no—
142#217—72no—
143C4⋊Dic3—71no—
144C4⋊Dic3—71no—
145C4⋊Dic3—71no—
146C4⋊Dic3—72no—
147Dic3⋊C4—72no—
148Dic3⋊C4—72no—
149Dic3⋊C4—72no—
150Dic3⋊C4—72no—
151Dic3⋊C4—72no—
152C4×Dic3—72no—
153C4×Dic3—72no—
154C2×C3×C7—22no—
155C2×C3×C7—41no—
156C2×C3×C7C2×#4111yescharacteristic
157C2×C3×C7C2×#4111yescharacteristic
158C2×C3×C72−1+411yescharacteristic
159#126—212no—
160#125—212no—
161#125—211no—
162#123—212no—
163C22⋊Q8—211no—
164C22⋊Q8—211no—
165C4×Q8—211no—
166C4×D4D2111yescharacteristic
167#117—211no—
168#117—212no—
169C2×C4⋊C4—211no—
170C22×C7—21no—
171C22×C7—21no—
172C22×C7—21no—
173C22×C7—21no—
174C22×C7—21no—
175C22×C7#23512yes—
176C22×C7C23×D311yescharacteristic
177C4×C7—21no—
178C4×C7—21no—
179C4×C7—21no—
180C4×C7—21no—
181C4×C7#23712yes—
182Dic7—62no—
183Dic7—62no—
184Dic7—62no—
185Dic7—62no—
186C23×C3C22×D711yescharacteristic
187C23×C3C22×D711yescharacteristic
188C3×D4—22no—
189C2×C3×C4—22no—
190C2×C3×C4—22no—
191C2×C3×C4C22×D711yescharacteristic
192C2×C3×C4C22×D711yescharacteristic
193C2×C3×C4C22×D711yescharacteristic
194C2×C3×C4C22×D711yescharacteristic
195C2×C3×C4C22×D711yescharacteristic
196C2×Dic3—72no—
197C2×Dic3—72no—
198C2×Dic3—72no—
199C2×Dic3—72no—
200C2×Dic3—144no—
201Dic6—142no—
202C3×C7#55211yescharacteristic, complemented, Hall
203C2×Q8—211no—
204C2×D4C2×D2111yescharacteristic
205C22×C4—212no—
206C22×C4C2×D2111yescharacteristic
207C22×C4C2×D2111yescharacteristic
208C4⋊C4—212no—
209C4⋊C4—212no—
210C4⋊C4—212no—
211C4⋊C4—212no—
212C4⋊C4—212no—
213C4⋊C4—211no—
214C4⋊C4—211no—
215C4⋊C4—212no—
216C4⋊C4—211no—
217C4⋊C4C2×D2111yescharacteristic
218C22⋊C4—212no—
219C22⋊C4—212no—
220C22⋊C4—212no—
221C22⋊C4C2×D2111yescharacteristic
222C22⋊C4C2×D2111yescharacteristic
223C42—212no—
224C42—212no—
225C42C2×D2111yescharacteristic
226C2×C7—22no—
227C2×C7—41no—
228C2×C7C2×#23511yescharacteristic
229C2×C7C2×#23711yescharacteristic
230C2×C7#101011yescharacteristic
231C22×C3—21no—
232C22×C3—21no—
233C22×C3—21no—
234C22×C3—21no—
235C22×C3—21no—
236C22×C3#115712yes—
237C22×C3C23×D711yescharacteristic
238C3×C4—21no—
239C3×C4—21no—
240C3×C4—21no—
241C3×C4—21no—
242C3×C4#115912yes—
243Dic3—142no—
244Dic3—142no—
245Dic3—142no—
246Dic3—142no—
247C23C22×D2111yescharacteristic
248C23C22×D2111yescharacteristic
249Q8—422no—
250D4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—212no—
254C2×C4—212no—
255C2×C4—212no—
256C2×C4—212no—
257C2×C4—424no—
258C2×C4C22×D2111yescharacteristic
259C2×C4C22×D2111yescharacteristic
260C2×C4C22×D2111yescharacteristic
261C2×C4C22×D2111yescharacteristic
262C2×C4C22×D2111yescharacteristic
263C7#554111yescharacteristic, complemented, Sylow
264C2×C3—22no—
265C2×C3—41no—
266C2×C3C2×#115711yescharacteristic
267C2×C3C2×#115911yescharacteristic
268C2×C3#655411yescharacteristic
269C22—21no—
270C22—21no—
271C22—21no—
272C22—21no—
273C22—21no—
274C22#6672812yes—
275C22C23×D2111yescharacteristic
276C4—21no—
277C4—21no—
278C4—21no—
279C4—21no—
280C4—422no—
281C4—422no—
282C4—422no—
283C4—422no—
284C4#6673012yes—
285C3#9023211yescharacteristic, complemented, Sylow
286C2—22no—
287C2—41no—
288C2C2×#6672811yescharacteristic
289C2C2×#6673011yescharacteristic
290C2#1062166311yescharacteristic
subgroupG/H
center, FrattiniC22C23×D21
commutator, socle, cosocleC22×C3×C7C24
FittingC3×C4×C7×D4C2
prime radicalC2×C3×C7×D4C22
hypercenterC4×D4D21
hypocenterC3×C7#552
LCSG ▷ C22×C3×C7 ▷ C3×C7
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
3. #10621409C2semidirect
4. C2×C4⋊Dic21C2semidirect
5. #10621407C2semidirect
6. #10621407C2semidirect
7. #10621372C2semidirect
8. #10621362C2semidirect
9. #10621360C2semidirect
10. #10621353C2semidirect
11. C4×Dic42C2semidirect
202. C3×C7#552semidirect
263. C7#5541semidirect
285. C3#90232semidirect

Maximal subgroups

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

subgroupindex
C3×C4×C7×D42
#106214182
#106214092
C2×C4⋊Dic212
#106214072
#106213722
#106213622
#106213602
#106213532
C4×Dic422
#902323
#55417