Finite Group Databasebeta

← #13059481

Subgroups — #13059481

Order 1344.

540 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1157C211yesmaximal, characteristic
2C2×D7×Dic6C211yesmaximal, characteristic, complemented
3#10621407C211yesmaximal, characteristic, complemented
4C7×#924C211yesmaximal, characteristic, complemented
5#10621110C212yesmaximal, complemented
6#10621096C212yesmaximal, complemented
7#10620969C212yesmaximal, complemented
8#10620922C211yesmaximal, characteristic, complemented
9#10620921C211yesmaximal, characteristic, complemented
10#10620920C211yesmaximal, characteristic, complemented
11#10620889C212yesmaximal, complemented
12#90319—31nomaximal, Hall
13C22×C3×C4×C7C2211yescharacteristic
14C2×Dic42C2211yescharacteristic
15C2×C7×Dic6C2211yescharacteristic
16C2×C3×C22⋊D7C2211yescharacteristic
17C2×C3×C22⋊D7C2211yescharacteristic
18C3×#1157—24no—
19C2×C3×D28C2211yescharacteristic
20C2×C3×C4×D7C2211yescharacteristic
21C2×C3×C4×D7C2211yescharacteristic
22C2×C3×Dic14C2211yescharacteristic
23C2×#4248C2212yes—
24C2×Dic3×D7C2212yes—
25D7×Dic6—24no—
26#66636C2212yes—
27C4⋊Dic21C2211yescharacteristic
28#66629C2212yes—
29C7×#217C2212yes—
30C7×C4⋊Dic3C2211yescharacteristic
31C7×Dic3⋊C4C2212yes—
32Dic3⋊Dic7C2212yes—
33#66577C2212yes—
34(C2×D7)⋊Dic3C2212yes—
35(C2×D7)⋊Dic3C2212yes—
36(C2×D7)⋊Dic3C2212yes—
37Dic3×Dic7C2212yes—
38C2×Q8×D7—31no—
39C2×#1157D311yescharacteristic
40C7×C22⋊Q8—31no—
41#6509—31no—
42#6487—31no—
43#6460—31no—
44#6457—32no—
45#6455—31no—
46#6451—32no—
47#6448—32no—
48#6446—32no—
49#5825—71nomaximal, Hall
50C23×C3×C7C2311yescharacteristic
51C22×C3×D7C2311yescharacteristic
52C22×C3×D7C2311yescharacteristic
53C2×C3×C4×C7—22no—
54C2×C3×C4×C7C2311yescharacteristic
55C2×C3×C4×C7C2311yescharacteristic
56C2×Dic21C2312yes—
57C2×Dic21C2312yes—
58Dic42—22no—
59C2×C7×Dic3C2312yes—
60C2×C7×Dic3C2312yes—
61C7×Dic6—22no—
62C3×C22⋊D7—22no—
63C3×C22⋊D7—22no—
64C2×C3×Dic7C2311yescharacteristic
65C2×C3×Dic7C2311yescharacteristic
66C3×D28—22no—
67C3×C4×D7—22no—
68C3×C4×D7D414yes—
69C3×Dic14—22no—
70#4248—24no—
71Dic3×D7—24no—
72C2×C7×Q8—31no—
73C22×C4×C7C2×D311yescharacteristic
74C2×C22⋊D7C2×D311yescharacteristic
75C2×C22⋊D7C2×D311yescharacteristic
76Q8×D7—64no—
77#1157—24no—
78C2×D28C2×D311yescharacteristic
79C2×C4×D7—32no—
80C2×C4×D7C2×D311yescharacteristic
81C2×C4×D7C2×D311yescharacteristic
82C2×Dic14—31no—
83C2×Dic14—32no—
84C2×Dic14C2×D311yescharacteristic
85C7×C4⋊C4—32no—
86C7×C4⋊C4—31no—
87C7×C22⋊C4—32no—
88C22⋊Dic7—32no—
89(C2×D7)⋊C4—32no—
90(C2×D7)⋊C4—32no—
91(C2×D7)⋊C4—32no—
92C4⋊Dic7—31no—
93C4⋊Dic7—32no—
94Dic7⋊C4—32no—
95Dic7⋊C4—32no—
96C4×Dic7—32no—
97C2×C3×#41—71no—
98C22×Dic6—71no—
99#944—72no—
100#936—72no—
101#935—72no—
102#935—72no—
103#926—71no—
104#924—71no—
105#924—71no—
106#924—71no—
107#924D711yescharacteristic, complemented
108C22×C3×C7—21no—
109C22×C3×C7—21no—
110C22×C3×C7—21no—
111C22×C3×C7C2411yescharacteristic
112C2×C3×D7—21no—
113C2×C3×D7—21no—
114C2×C3×D7—21no—
115C2×C3×D7—21no—
116C2×C3×D7—21no—
117C2×C3×D7C2×D412yes—
118C3×C4×C7—21no—
119C3×C4×C7C2×D412yes—
120Dic21—22no—
121Dic21—22no—
122C3×Dic7—21no—
123C3×Dic7C2×D412yes—
124C7×Dic3—22no—
125C7×Dic3—22no—
126#536—211noSylow
127C23×C7C22×D311yescharacteristic
128C22×D7C22×D311yescharacteristic
129C22×D7C22×D311yescharacteristic
130C7×Q8—62no—
131C2×C4×C7—22no—
132C2×C4×C7—32no—
133C2×C4×C7—32no—
134C2×C4×C7C22×D311yescharacteristic
135C2×C4×C7C22×D311yescharacteristic
136C22⋊D7—22no—
137C22⋊D7—22no—
138C2×Dic7—32no—
139C2×Dic7—32no—
140C2×Dic7C22×D311yescharacteristic
141C2×Dic7C22×D311yescharacteristic
142D28—22no—
143C4×D7—22no—
144C4×D7—64no—
145C4×D7#6714yes—
146Dic14—22no—
147Dic14—62no—
148Dic14—64no—
149C3×#41—144no—
150C2×C3×Q8—71no—
151C2×C3×D4—71no—
152C2×C3×D4—71no—
153C2×C3×D4—71no—
154C22×C3×C4—71no—
155C22×C3×C4—71no—
156C22×C3×C4C2×D711yescharacteristic
157C22×Dic3—72no—
158C2×Dic6—71no—
159C2×Dic6—72no—
160C2×Dic6—144no—
161C2×Dic6C2×D711yescharacteristic
162#217—72no—
163#217—72no—
164#217—72no—
165#217—72no—
166#217C2×D712yes—
167C4⋊Dic3—71no—
168C4⋊Dic3C2×D711yescharacteristic
169Dic3⋊C4—72no—
170Dic3⋊C4—72no—
171Dic3⋊C4—72no—
172Dic3⋊C4C2×D712yes—
173C4×Dic3—72no—
174C2×C3×C7—41no—
175C2×C3×C7C22×D411yescharacteristic
176C2×C3×C72−1+411yescharacteristic
177C2×C3×C72−1+411yescharacteristic
178C3×D7—22no—
179C3×D7—41no—
180C2×#41—71no—
181C22×Q8—211no—
182C4⋊Q8—212no—
183#124—212no—
184#123—212no—
185#123—212no—
186C22⋊Q8—31no—
187C22⋊Q8—211no—
188C22⋊Q8—211no—
189C22⋊Q8—211no—
190#117—211no—
191C22×C7—21no—
192C22×C7—21no—
193C22×C7—21no—
194C22×C7C23×D311yescharacteristic
195C2×D7—21no—
196C2×D7—21no—
197C2×D7—21no—
198C2×D7—21no—
199C2×D7—21no—
200C2×D7C2×#6712yes—
201C4×C7—21no—
202C4×C7—62no—
203C4×C7—62no—
204C4×C7C2×#6712yes—
205Dic7—21no—
206Dic7—62no—
207Dic7—62no—
208Dic7C2×#6712yes—
209C23×C3—71no—
210C23×C3—71no—
211C23×C3C22×D711yescharacteristic
212C3×Q8—142no—
213C3×D4—142no—
214C3×D4—142no—
215C3×D4—142no—
216C2×C3×C4—22no—
217C2×C3×C4—71no—
218C2×C3×C4—74no—
219C2×C3×C4—71no—
220C2×C3×C4—142no—
221C2×C3×C4C22×D711yescharacteristic
222C2×C3×C4C22×D711yescharacteristic
223C2×Dic3—72no—
224C2×Dic3—72no—
225C2×Dic3—144no—
226C2×Dic3C22×D712yes—
227C2×Dic3C22×D712yes—
228Dic6—22no—
229Dic6—144no—
230Dic6—142no—
231C3×C7#53611yescharacteristic, complemented, Hall
232#41—144no—
233C2×Q8—31no—
234C2×Q8—71no—
235C2×Q8—212no—
236C2×Q8—211no—
237C2×Q8—424no—
238C2×D4—71no—
239C2×D4—71no—
240C2×D4—71no—
241C22×C4—71no—
242C22×C4—71no—
243C22×C4—212no—
244C22×C4D3×D711yescharacteristic
245C4⋊C4—31no—
246C4⋊C4—32no—
247C4⋊C4—212no—
248C4⋊C4—212no—
249C4⋊C4—212no—
250C4⋊C4—211no—
251C22⋊C4—32no—
252C22⋊C4—212no—
253C22⋊C4—212no—
254C22⋊C4—212no—
255C22⋊C4—212no—
256C42—212no—
257C2×C7—41no—
258C2×C7#101011yescharacteristic
259C2×C7#101011yescharacteristic
260C2×C7C22×#6711yescharacteristic
261D7—22no—
262D7—41no—
263C22×C3—21no—
264C22×C3—21no—
265C22×C3—21no—
266C22×C3—72no—
267C22×C3—141no—
268C22×C3—141no—
269C22×C3—141no—
270C22×C3—141no—
271C22×C3—141no—
272C22×C3C23×D711yescharacteristic
273C3×C4—21no—
274C3×C4—72no—
275C3×C4—141no—
276C3×C4D4×D712yes—
277Dic3—22no—
278Dic3—22no—
279Dic3—142no—
280Dic3—142no—
281C23—71no—
282C23—71no—
283C23C2×D3×D711yescharacteristic
284Q8—62no—
285Q8—142no—
286Q8—424no—
287Q8—422no—
288D4—142no—
289D4—142no—
290D4—142no—
291C2×C4—22no—
292C2×C4—32no—
293C2×C4—32no—
294C2×C4—71no—
295C2×C4—74no—
296C2×C4—71no—
297C2×C4—142no—
298C2×C4—212no—
299C2×C4—212no—
300C2×C4—424no—
301C2×C4C2×D3×D711yescharacteristic
302C2×C4C2×D3×D711yescharacteristic
303C7#582511yescharacteristic, complemented, Sylow
304C2×C3—41no—
305C2×C3—142no—
306C2×C3—281no—
307C2×C3C2×D4×D711yescharacteristic
308C2×C3#655111yescharacteristic
309C2×C3#655411yescharacteristic
310C22—21no—
311C22—21no—
312C22—21no—
313C22—72no—
314C22—141no—
315C22—141no—
316C22—141no—
317C22—141no—
318C22—141no—
319C22C22×D3×D711yescharacteristic
320C4—21no—
321C4—62no—
322C4—62no—
323C4—72no—
324C4—141no—
325C4—422no—
326C4—422no—
327C4D7×#6712yes—
328C3#9031911yescharacteristic, complemented, Sylow
329C2—41no—
330C2—142no—
331C2—281no—
332C2#1062154711yescharacteristic
333C2#1062154811yescharacteristic
334C2C2×D7×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D7
commutator, socle, cosocleC22×C3×C7C24
FittingC22×C3×C4×C7C22
prime radicalC2×C3×#1157C2
hypercenterC22×C4D3×D7
hypocenterC3×C7#536
LCSG ▷ C22×C3×C7 ▷ C3×C7
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×D7×Dic6C2semidirect
3. #10621407C2semidirect
4. C7×#924C2semidirect
5. #10621110C2semidirect
6. #10621096C2semidirect
7. #10620969C2semidirect
8. #10620922C2semidirect
9. #10620921C2semidirect
10. #10620920C2semidirect
11. #10620889C2semidirect
107. #924D7semidirect
231. C3×C7#536semidirect
303. C7#5825semidirect
328. C3#90319semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#11572
C2×D7×Dic62
#106214072
C7×#9242
#106211102
#106210962
#106209692
#106209222
#106209212
#106209202
#106208892
#903193
#58257