Finite Group Databasebeta

← #13263199

Subgroups — #13263199

Order 1792.

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

normal subgroups only

This group has 446 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#11731763C211yesmaximal, characteristic
2#11725880C212yesmaximal
3C7×#1325C211yesmaximal, characteristic, complemented
4#11725441C211yesmaximal, characteristic, complemented
5#11725258C212yesmaximal, complemented
6C2×#6455C411yescharacteristic
7C2×#6455C2211yescharacteristic
8C2×C42×D7C411yescharacteristic
9C7×#384C2211yescharacteristic
10#89759—22no—
11#89749C411yescharacteristic
12#89749C2211yescharacteristic
13C4⋊C4×Dic7—22no—
14#89707C411yescharacteristic
15#89491—22no—
16C7×#324C2212yes—
17#89323C2212yes—
18#89263—22no—
19#11513—71nomaximal, Sylow
20C22×C4×D7—21no—
21C22×C4×D7C2×C411yescharacteristic
22C2×C7×C4⋊C4—22no—
23C2×C7×C4⋊C4C2×C411yescharacteristic
24C2×C7×C4⋊C4C2311yescharacteristic
25C2×C42×C7C2×C411yescharacteristic
26C2×(C2×D7)⋊C4—21no—
27C2×(C2×D7)⋊C4D412yes—
28C2×C4⋊Dic7—22no—
29C2×C4⋊Dic7C2×C411yescharacteristic
30C2×C4⋊Dic7C2×C411yescharacteristic
31C2×C4×Dic7—21no—
32C2×C4×Dic7—21no—
33C2×C4×Dic7C2×C411yescharacteristic
34C2×C4×Dic7D412yes—
35#6455—41no—
36#6455—41no—
37#6455—41no—
38#6455—41no—
39C42×D7—22no—
40C42×D7—22no—
41C7×C22⋊C8—22no—
42C7⋊#95—22no—
43C7⋊#95—22no—
44C22⋊(C7⋊C8)—22no—
45#6389—42no—
46Dic7⋊C8—42no—
47#2285—71no—
48#1464—72no—
49#1325—71no—
50#1325D711yescharacteristic, complemented
51#1324—72no—
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—22no—
62C2×C4×D7—21no—
63C2×C4×D7—21no—
64C2×C4×D7—21no—
65C2×C4×D7—21no—
66C2×C4×D7—24no—
67C2×C4×D7—42no—
68C2×C4×D7—42no—
69C2×C7×C8—42no—
70C7×C4⋊C4—41no—
71C7×C4⋊C4—41no—
72C7×C4⋊C4—44no—
73C42×C7—21no—
74C42×C7M1612yes—
75(C2×D7)⋊C4—42no—
76(C2×D7)⋊C4—42no—
77C4⋊Dic7—41no—
78C4⋊Dic7—44no—
79C4⋊Dic7—41no—
80C4×Dic7—24no—
81C4×Dic7—21no—
82C4×Dic7—22no—
83C4×Dic7—22no—
84C4×Dic7—41no—
85C4×Dic7—41no—
86C4×Dic7M1612yes—
87C2×C7⋊C8—42no—
88C2×#117—71no—
89C2×#117—71no—
90C22×C42—71no—
91#432—142no—
92#384—71no—
93#384C2×D711yescharacteristic
94#382—71no—
95#382—71no—
96#380—142no—
97C4×C4⋊C4—142no—
98#324—72no—
99#324C2×D712yes—
100#323—142no—
101C23×C7C2×C22⋊C411yescharacteristic
102C22×D7—21no—
103C22×D7—21no—
104C22×D7—41no—
105C22×D7—41no—
106C22×D7#10112yes—
107C2×C4×C7—22no—
108C2×C4×C7—22no—
109C2×C4×C7—22no—
110C2×C4×C7—21no—
111C2×C4×C7—21no—
112C2×C4×C7—22no—
113C2×C4×C7—42no—
114C2×C4×C7—42no—
115C2×C4×C7—41no—
116C2×C4×C7C2×M1611yescharacteristic
117C2×C4×C7C2×M1611yescharacteristic
118C2×Dic7—21no—
119C2×Dic7—21no—
120C2×Dic7—22no—
121C2×Dic7—22no—
122C2×Dic7—41no—
123C2×Dic7—41no—
124C2×Dic7—42no—
125C2×Dic7—42no—
126C2×Dic7—41no—
127C2×Dic7#9911yescharacteristic
128C2×Dic7#9911yescharacteristic
129C4×D7—22no—
130C4×D7—22no—
131C4×D7—22no—
132C4×D7—22no—
133C4×D7—48no—
134C7×C8—82no—
135C7⋊C8—82no—
136C23×C4—71no—
137C23×C4—141no—
138#117—281no—
139#117—281no—
140#117—281no—
141#117—281no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—71no—
144C2×C4⋊C4—71no—
145C2×C4⋊C4—142no—
146C2×C4⋊C4C4×D711yescharacteristic
147C2×C4⋊C4C22×D711yescharacteristic
148C2×C22⋊C4—72no—
149C2×C22⋊C4—141no—
150C2×C42—71no—
151C2×C42—72no—
152C2×C42—142no—
153C2×C42—141no—
154C2×C42—142no—
155C2×C42—141no—
156C2×C42C4×D711yescharacteristic
157C4⋊C8—282no—
158C22⋊C8—22no—
159C22⋊C8—142no—
160#97—282no—
161#95—142no—
162#95—142no—
163C22×C7—21no—
164C22×C7—21no—
165C22×C7#40711yescharacteristic
166C22×C7C2×#9911yescharacteristic
167C22×C7C2×#10111yescharacteristic
168C2×D7—22no—
169C2×D7—42no—
170C2×D7—41no—
171C2×D7—41no—
172C2×D7—42no—
173C4×C7—24no—
174C4×C7—21no—
175C4×C7—21no—
176C4×C7—42no—
177C4×C7—81no—
178Dic7—21no—
179Dic7—21no—
180Dic7—42no—
181Dic7—42no—
182Dic7—81no—
183C24—71no—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—71no—
187C22×C4—72no—
188C22×C4—141no—
189C22×C4—141no—
190C22×C4—142no—
191C22×C4—144no—
192C22×C4—141no—
193C22×C4—141no—
194C22×C4—141no—
195C22×C4—141no—
196C22×C4—282no—
197C22×C4—282no—
198C22×C4C2×C4×D711yescharacteristic
199C22×C4D4×D712yes—
200C2×C8—42no—
201C2×C8—282no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—44no—
205C4⋊C4—281no—
206C4⋊C4—281no—
207C4⋊C4—284no—
208C22⋊C4—282no—
209C22⋊C4—282no—
210C42—21no—
211C42—72no—
212C42—142no—
213C42—142no—
214C42—144no—
215C42—141no—
216C42—281no—
217C42—281no—
218C42#113112yes—
219C2×C7—21no—
220C2×C7—21no—
221C2×C7#146311yescharacteristic
222C2×C7#212611yescharacteristic
223C2×C7#213211yescharacteristic
224D7—42no—
225C23—72no—
226C23—141no—
227C23—141no—
228C23—281no—
229C23—281no—
230C23D7×C22⋊C411yescharacteristic
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—41no—
240C2×C4—71no—
241C2×C4—71no—
242C2×C4—142no—
243C2×C4—142no—
244C2×C4—142no—
245C2×C4—142no—
246C2×C4—141no—
247C2×C4—141no—
248C2×C4—142no—
249C2×C4—142no—
250C2×C4—288no—
251C2×C4—281no—
252C2×C4—281no—
253C2×C4—282no—
254C2×C4—282no—
255C2×C4—281no—
256C2×C4C2×#113111yescharacteristic
257C2×C4D7×M1611yescharacteristic
258C8—82no—
259C8—562no—
260C7#1151311yescharacteristic, complemented, Sylow
261C22—21no—
262C22—21no—
263C22—142no—
264C22—282no—
265C22—282no—
266C22—281no—
267C22—281no—
268C22#8949811yescharacteristic
269C22D7×#9911yescharacteristic
270C22D7×#10111yescharacteristic
271C4—24no—
272C4—21no—
273C4—21no—
274C4—42no—
275C4—81no—
276C4—141no—
277C4—141no—
278C4—282no—
279C4—282no—
280C4—561no—
281C2—21no—
282C2—21no—
283C2—282no—
284C2#1172589811yescharacteristic
285C2#1172690511yescharacteristic
286C2#1172692611yescharacteristic
subgroupG/H
centerC22D7×#99
commutatorC22×C4×C7C22×C4
FrattiniC2×C4⋊C4C22×D7
FittingC7×#1325C2
socleC22×C7C2×#99
prime radicalC23×D7C22⋊C4
cosocleC2×C7×C4⋊C4C23
hypercenter#1325D7
hypocenterC7#11513
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1325

Complements

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

NH ≅ G/Ntype
3. C7×#1325C2semidirect
4. #11725441C2semidirect
5. #11725258C2semidirect
50. #1325D7semidirect
260. C7#11513semidirect

Maximal subgroups

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

subgroupindex
#117317632
#117258802
C7×#13252
#117254412
#117252582
#115137