Finite Group Databasebeta

← #13263191

Subgroups — #13263191

Order 1792.

490 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 81 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
1D7×#382C211yesmaximal, characteristic
2#11725898C212yesmaximal
3C7×#1324C211yesmaximal, characteristic, complemented
4#11725438C211yesmaximal, characteristic, complemented
5#11725258C212yesmaximal, complemented
6C2×D7×C4⋊C4C411yescharacteristic
7C2×D7×C4⋊C4C2211yescharacteristic
8C2×C42×D7C411yescharacteristic
9C7×#382C2211yescharacteristic
10#89749C411yescharacteristic
11#89749C2211yescharacteristic
12#89708C411yescharacteristic
13#89498—22no—
14D7×#95—22no—
15#89422—22no—
16C7×#324C2212yes—
17#89323C2212yes—
18#89264—22no—
19#11511—71nomaximal, Sylow
20C22×C4×D7—21no—
21C22×C4×D7—21no—
22C22×C4×D7C2×C411yescharacteristic
23C22×C4×D7D412yes—
24C2×C7×C4⋊C4C2×C411yescharacteristic
25C2×C7×C4⋊C4C2311yescharacteristic
26C2×C42×C7C2×C411yescharacteristic
27C2×C4⋊Dic7C2×C411yescharacteristic
28C2×C4⋊Dic7C2×C411yescharacteristic
29C2×Dic7⋊C4—21no—
30C2×Dic7⋊C4D412yes—
31C2×C4×Dic7—21no—
32C2×C4×Dic7C2×C411yescharacteristic
33C2×#1131—42no—
34D7×C4⋊C4—41no—
35D7×C4⋊C4—41no—
36D7×C4⋊C4—41no—
37D7×C4⋊C4—41no—
38C42×D7—22no—
39C42×D7—22no—
40C7×C22⋊C8—22no—
41C7×#95—22no—
42C7⋊#95—22no—
43C7⋊#95—22no—
44C7⋊#95—22no—
45C22⋊(C7⋊C8)—22no—
46(C2×D7)⋊C8—42no—
47C2×#382—71no—
48#1463—72no—
49#1324—71no—
50#1324—72no—
51#1324D711yescharacteristic, complemented
52C23×D7C22⋊C411yescharacteristic
53C22×C4×C7—21no—
54C22×C4×C7—21no—
55C22×C4×C7C22×C411yescharacteristic
56C22×C4×C7C2×D412yes—
57C22×Dic7—21no—
58C22×Dic7—21no—
59C22×Dic7C22⋊C411yescharacteristic
60C22×Dic7C22⋊C412yes—
61C2×C4×D7—21no—
62C2×C4×D7—21no—
63C2×C4×D7—21no—
64C2×C4×D7—21no—
65C2×C4×D7—22no—
66C2×C4×D7—24no—
67C2×C4×D7—22no—
68C2×C4×D7—22no—
69C2×C4×D7—42no—
70C2×C4×D7—42no—
71C2×C4×D7—44no—
72C2×C4×D7—44no—
73C2×C4×D7—41no—
74C2×C4×D7—41no—
75C2×C7×C8—42no—
76C7×C4⋊C4—41no—
77C7×C4⋊C4—41no—
78C42×C7—21no—
79C42×C7M1612yescomplemented
80C4⋊Dic7—41no—
81C4⋊Dic7—41no—
82Dic7⋊C4—42no—
83Dic7⋊C4—42no—
84C4×Dic7—24no—
85C4×Dic7—21no—
86C4×Dic7M1612yescomplemented
87C2×C7⋊C8—42no—
88#1131—84no—
89C22×C4⋊C4—71no—
90C22×C4⋊C4—71no—
91C22×C42—71no—
92#407—142no—
93#382—71no—
94#382—71no—
95#382—71no—
96#382—142no—
97#382C2×D711yescharacteristic
98C2×#95—142no—
99#324—72no—
100#324—142no—
101#324C2×D712yes—
102C23×C7C2×C22⋊C411yescharacteristic
103C22×D7—21no—
104C22×D7—21no—
105C22×D7—22no—
106C22×D7—22no—
107C22×D7#9911yescharacteristic
108C22×D7#9911yescharacteristic
109C2×C4×C7—21no—
110C2×C4×C7—21no—
111C2×C4×C7—22no—
112C2×C4×C7—22no—
113C2×C4×C7—41no—
114C2×C4×C7—41no—
115C2×C4×C7—42no—
116C2×C4×C7—42no—
117C2×C4×C7—41no—
118C2×C4×C7C2×M1611yescharacteristic
119C2×C4×C7C2×M1611yescharacteristic
120C2×Dic7—21no—
121C2×Dic7—21no—
122C2×Dic7—22no—
123C2×Dic7—22no—
124C2×Dic7—41no—
125C2×Dic7—41no—
126C2×Dic7—42no—
127C2×Dic7—42no—
128C2×Dic7—41no—
129C2×Dic7#10112yes—
130C4×D7—22no—
131C4×D7—22no—
132C4×D7—22no—
133C4×D7—22no—
134C4×D7—48no—
135C4×D7—44no—
136C4×D7—82no—
137C4×D7—82no—
138C4×D7—82no—
139C7×C8—82no—
140C7⋊C8—82no—
141C23×C4—71no—
142C23×C4—72no—
143C23×C4—141no—
144C23×C4—141no—
145C2×M16—282no—
146C2×C4⋊C4—71no—
147C2×C4⋊C4—72no—
148C2×C4⋊C4—71no—
149C2×C4⋊C4—141no—
150C2×C4⋊C4—281no—
151C2×C4⋊C4—281no—
152C2×C4⋊C4—281no—
153C2×C4⋊C4—281no—
154C2×C4⋊C4C4×D711yescharacteristic
155C2×C4⋊C4C22×D711yescharacteristic
156C2×C42—71no—
157C2×C42—142no—
158C2×C42—141no—
159C2×C42—142no—
160C2×C42C4×D711yescharacteristic
161C22⋊C8—22no—
162C22⋊C8—142no—
163C22⋊C8—282no—
164#95—22no—
165#95—142no—
166#95—142no—
167#95—142no—
168C22×C7—21no—
169C22×C7—21no—
170C22×C7#40711yescharacteristic
171C22×C7C2×#9911yescharacteristic
172C22×C7C2×#10111yescharacteristic
173C2×D7—24no—
174C2×D7—24no—
175C2×D7—21no—
176C2×D7—21no—
177C2×D7—21no—
178C2×D7—21no—
179C2×D7#35412yes—
180C2×D7#35512yes—
181C4×C7—21no—
182C4×C7—21no—
183C4×C7—42no—
184C4×C7—42no—
185C4×C7—81no—
186Dic7—22no—
187Dic7—42no—
188Dic7—42no—
189Dic7—81no—
190C24—71no—
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—71no—
194C22×C4—72no—
195C22×C4—142no—
196C22×C4—141no—
197C22×C4—141no—
198C22×C4—142no—
199C22×C4—144no—
200C22×C4—142no—
201C22×C4—141no—
202C22×C4—141no—
203C22×C4—141no—
204C22×C4—141no—
205C22×C4—282no—
206C22×C4—282no—
207C22×C4—284no—
208C22×C4—281no—
209C22×C4—281no—
210C22×C4—284no—
211C22×C4C2×C4×D711yescharacteristic
212C22×C4D4×D712yes—
213M16—564no—
214C2×C8—42no—
215C2×C8—282no—
216C4⋊C4—41no—
217C4⋊C4—41no—
218C4⋊C4—282no—
219C4⋊C4—281no—
220C4⋊C4—281no—
221C4⋊C4—282no—
222C42—21no—
223C42—72no—
224C42—144no—
225C42—141no—
226C42#113112yescomplemented
227C2×C7—21no—
228C2×C7—21no—
229C2×C7#146311yescharacteristic
230C2×C7C2×#35411yescharacteristic
231C2×C7C2×#35511yescharacteristic
232D7—22no—
233D7—22no—
234C23—71no—
235C23—71no—
236C23—142no—
237C23—142no—
238C23—141no—
239C23—141no—
240C23D7×C22⋊C411yescharacteristic
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—41no—
250C2×C4—72no—
251C2×C4—142no—
252C2×C4—142no—
253C2×C4—142no—
254C2×C4—142no—
255C2×C4—141no—
256C2×C4—141no—
257C2×C4—142no—
258C2×C4—142no—
259C2×C4—284no—
260C2×C4—288no—
261C2×C4—281no—
262C2×C4—281no—
263C2×C4—282no—
264C2×C4—282no—
265C2×C4—281no—
266C2×C4—562no—
267C2×C4—562no—
268C2×C4—562no—
269C2×C4C2×#113111yescharacteristic
270C2×C4D7×M1611yescharacteristic
271C8—82no—
272C8—562no—
273C7#1151111yescharacteristic, complemented, Sylow
274C22—21no—
275C22—21no—
276C22—72no—
277C22—72no—
278C22—144no—
279C22—144no—
280C22—141no—
281C22—141no—
282C22—141no—
283C22—141no—
284C22#8949811yescharacteristic
285C22D7×#9911yescharacteristic
286C22D7×#10111yescharacteristic
287C4—21no—
288C4—21no—
289C4—42no—
290C4—42no—
291C4—81no—
292C4—142no—
293C4—282no—
294C4—282no—
295C4—561no—
296C2—21no—
297C2—21no—
298C2—142no—
299C2—142no—
300C2#1172589811yescharacteristic
301C2D7×#35411yescharacteristic
302C2D7×#35511yescharacteristic
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#11511
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. #11725258C2semidirect
51. #1324D7semidirect
79. C42×C7M16semidirect
86. C4×Dic7M16semidirect
226. C42#1131semidirect
273. C7#11511semidirect

Maximal subgroups

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

subgroupindex
D7×#3822
#117258982
C7×#13242
#117254382
#117252582
#115117