Finite Group Databasebeta

← #13263201

Subgroups — #13263201

Order 1792.

434 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11731670C211yesmaximal, characteristic
2#11725898C212yesmaximal
3C7×#1324C211yesmaximal, characteristic, complemented
4#11725438C211yesmaximal, characteristic, complemented
5#11725259C212yesmaximal, complemented
6C2×#6455C411yescharacteristic
7C2×D7×C4⋊C4C2211yescharacteristic
8C2×#6435C411yescharacteristic
9C7×#382C2211yescharacteristic
10#89749C411yescharacteristic
11#89748C2211yescharacteristic
12#89707C411yescharacteristic
13#89498—22no—
14#89440—22no—
15#89419—22no—
16C7×#324C2212yes—
17#89323C2212yes—
18#89264—22no—
19#11514—71nomaximal, Sylow
20C22×C4×D7C2×C411yescharacteristic
21C22×C4×D7D412yes—
22C2×C7×C4⋊C4C2×C411yescharacteristic
23C2×C7×C4⋊C4C2311yescharacteristic
24C2×C42×C7C2×C411yescharacteristic
25C2×(C2×D7)⋊C4—21no—
26C2×(C2×D7)⋊C4—21no—
27C2×C4⋊Dic7—22no—
28C2×C4⋊Dic7C2×C411yescharacteristic
29C2×C4⋊Dic7C2×C411yescharacteristic
30C2×Dic7⋊C4—21no—
31C2×Dic7⋊C4—22no—
32C2×Dic7⋊C4D412yes—
33C2×C4×Dic7—21no—
34C2×C4×Dic7C2×C411yescharacteristic
35C2×#1131—42no—
36#6455—42no—
37D7×C4⋊C4—42no—
38#6435—22no—
39#6435—22no—
40C7×C22⋊C8—22no—
41C7×#95—22no—
42C7⋊#95—22no—
43C22⋊(C7⋊C8)—22no—
44(C2×D7)⋊C8—42no—
45#2317—71no—
46#1463—72no—
47#1325—72no—
48#1324—71no—
49#1324D711yescharacteristic, complemented
50C23×D7C22⋊C411yescharacteristic
51C22×C4×C7—21no—
52C22×C4×C7—21no—
53C22×C4×C7C22×C411yescharacteristic
54C22×C4×C7C2×D412yes—
55C22×Dic7—21no—
56C22×Dic7—21no—
57C22×Dic7C22⋊C411yescharacteristic
58C22×Dic7C22⋊C412yes—
59C2×C4×D7—22no—
60C2×C4×D7—21no—
61C2×C4×D7—21no—
62C2×C4×D7—22no—
63C2×C4×D7—22no—
64C2×C4×D7—22no—
65C2×C4×D7—82no—
66C2×C7×C8—42no—
67C7×C4⋊C4—41no—
68C7×C4⋊C4—41no—
69C42×C7—21no—
70C42×C7M1612yescomplemented
71(C2×D7)⋊C4—24no—
72(C2×D7)⋊C4—42no—
73C4⋊Dic7—41no—
74C4⋊Dic7—41no—
75C4⋊Dic7—82no—
76Dic7⋊C4—24no—
77Dic7⋊C4—42no—
78Dic7⋊C4—82no—
79C4×Dic7—21no—
80C4×Dic7—42no—
81C4×Dic7M1612yescomplemented
82C2×C7⋊C8—42no—
83#1131—84no—
84C2×#117—71no—
85C2×#117—71no—
86C22×C4⋊C4—71no—
87#407—142no—
88#389—142no—
89#385—142no—
90#384—71no—
91#384—71no—
92#382—71no—
93#382C2×D711yescharacteristic
94#324—72no—
95#324—142no—
96#324C2×D712yes—
97C23×C7C2×C22⋊C411yescharacteristic
98C22×D7—21no—
99C22×D7—21no—
100C22×D7—41no—
101C22×D7—41no—
102C22×D7#9912yes—
103C2×C4×C7—21no—
104C2×C4×C7—21no—
105C2×C4×C7—22no—
106C2×C4×C7—22no—
107C2×C4×C7—41no—
108C2×C4×C7—41no—
109C2×C4×C7—42no—
110C2×C4×C7—42no—
111C2×C4×C7—41no—
112C2×C4×C7C2×M1611yescharacteristic
113C2×C4×C7C2×M1611yescharacteristic
114C2×Dic7—21no—
115C2×Dic7—21no—
116C2×Dic7—22no—
117C2×Dic7—22no—
118C2×Dic7—41no—
119C2×Dic7—41no—
120C2×Dic7—42no—
121C2×Dic7—42no—
122C2×Dic7—41no—
123C2×Dic7#10112yes—
124C4×D7—24no—
125C4×D7—24no—
126C4×D7—44no—
127C4×D7—82no—
128C7×C8—82no—
129C7⋊C8—82no—
130C23×C4—71no—
131C23×C4—72no—
132C2×M16—282no—
133#117—142no—
134#117—142no—
135#117—282no—
136C2×C4⋊C4—71no—
137C2×C4⋊C4—72no—
138C2×C4⋊C4—71no—
139C2×C4⋊C4—141no—
140C2×C4⋊C4—142no—
141C2×C4⋊C4—142no—
142C2×C4⋊C4—282no—
143C2×C4⋊C4C4×D711yescharacteristic
144C2×C4⋊C4C22×D711yescharacteristic
145C2×C22⋊C4—141no—
146C2×C22⋊C4—141no—
147C2×C42—71no—
148C2×C42—141no—
149C2×C42C4×D711yescharacteristic
150C22⋊C8—22no—
151C22⋊C8—142no—
152C22⋊C8—282no—
153#95—22no—
154#95—142no—
155C22×C7—21no—
156C22×C7—21no—
157C22×C7#40711yescharacteristic
158C22×C7C2×#9911yescharacteristic
159C22×C7C2×#10111yescharacteristic
160C2×D7—22no—
161C2×D7—22no—
162C2×D7—22no—
163C2×D7—42no—
164C2×D7—42no—
165C4×C7—21no—
166C4×C7—21no—
167C4×C7—42no—
168C4×C7—42no—
169C4×C7—81no—
170Dic7—22no—
171Dic7—42no—
172Dic7—42no—
173Dic7—81no—
174C24—71no—
175C22×C4—21no—
176C22×C4—21no—
177C22×C4—71no—
178C22×C4—72no—
179C22×C4—142no—
180C22×C4—142no—
181C22×C4—142no—
182C22×C4—142no—
183C22×C4—141no—
184C22×C4—141no—
185C22×C4—141no—
186C22×C4—141no—
187C22×C4—562no—
188C22×C4C2×C4×D711yescharacteristic
189C22×C4D4×D712yes—
190M16—564no—
191C2×C8—42no—
192C2×C8—282no—
193C4⋊C4—41no—
194C4⋊C4—41no—
195C4⋊C4—144no—
196C4⋊C4—282no—
197C4⋊C4—281no—
198C4⋊C4—281no—
199C4⋊C4—562no—
200C4⋊C4—562no—
201C22⋊C4—144no—
202C22⋊C4—282no—
203C42—21no—
204C42—72no—
205C42—141no—
206C42—282no—
207C42#113112yescomplemented
208C2×C7—21no—
209C2×C7—21no—
210C2×C7#146311yescharacteristic
211C2×C7#212711yescharacteristic
212C2×C7#213311yescharacteristic
213D7—42no—
214C23—72no—
215C23—141no—
216C23—141no—
217C23—281no—
218C23—281no—
219C23D7×C22⋊C411yescharacteristic
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—41no—
229C2×C4—72no—
230C2×C4—144no—
231C2×C4—144no—
232C2×C4—141no—
233C2×C4—141no—
234C2×C4—142no—
235C2×C4—142no—
236C2×C4—284no—
237C2×C4—281no—
238C2×C4—281no—
239C2×C4—282no—
240C2×C4—282no—
241C2×C4—281no—
242C2×C4—562no—
243C2×C4C2×#113111yescharacteristic
244C2×C4D7×M1611yescharacteristic
245C8—82no—
246C8—562no—
247C7#1151411yescharacteristic, complemented, Sylow
248C22—21no—
249C22—21no—
250C22—142no—
251C22—142no—
252C22—142no—
253C22—282no—
254C22—282no—
255C22#8949811yescharacteristic
256C22D7×#9911yescharacteristic
257C22D7×#10111yescharacteristic
258C4—21no—
259C4—21no—
260C4—42no—
261C4—42no—
262C4—81no—
263C4—142no—
264C4—282no—
265C4—282no—
266C4—561no—
267C2—21no—
268C2—21no—
269C2—282no—
270C2#1172589811yescharacteristic
271C2#1172691111yescharacteristic
272C2#1172691811yescharacteristic
subgroupG/H
centerC22D7×#99
commutatorC22×C4×C7C22×C4
FrattiniC2×C4⋊C4C22×D7
FittingC7×#1324C2
socleC22×C7C2×#99
prime radicalC23×D7C22⋊C4
cosocleC2×C7×C4⋊C4C23
hypercenter#1324D7
hypocenterC7#11514
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1324

Complements

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

NH ≅ G/Ntype
3. C7×#1324C2semidirect
4. #11725438C2semidirect
5. #11725259C2semidirect
49. #1324D7semidirect
70. C42×C7M16semidirect
81. C4×Dic7M16semidirect
207. C42#1131semidirect
247. C7#11514semidirect

Maximal subgroups

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

subgroupindex
#117316702
#117258982
C7×#13242
#117254382
#117252592
#115147