Finite Group Databasebeta

← #13264388

Subgroups — #13264388

Order 1792.

482 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 87 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#11739921C211yesmaximal, characteristic
2C7×#1467C211yesmaximal, characteristic, complemented
3C4×#6410C211yesmaximal, characteristic, complemented
4#11725262C214yesmaximal, complemented
5C2×C4×C7×Q8C2211yescharacteristic
6C2×#6510—21no—
7C2×#6437C411yescharacteristic
8C7×#432—21no—
9C2×#6410—21no—
10#89763C412yes—
11#89763C2212yes—
12#89760—21no—
13#89711—21no—
14#89711—21no—
15C4×C4⋊Dic7C411yescharacteristic
16C4×#1136—21no—
17C7×#324—21no—
18C7×#324C2212yes—
19#89325C2212yes—
20#11781—71nomaximal, Sylow
21C22×C7×Q8D411yescharacteristic
22C22×D28—21no—
23C22×D28—21no—
24C22×D28C2×C412yes—
25C4×C7×Q8—41no—
26C4×C7×Q8—41no—
27C2×C7×C4⋊C4C2×C411yescharacteristic
28C2×C7×C4⋊C4D411yescharacteristic
29C2×C7×C4⋊C4C2311yescharacteristic
30C2×C42×C7C2×C411yescharacteristic
31C2×C42×C7D411yescharacteristic
32C2×C42×C7D411yescharacteristic
33#6510—44no—
34C2×(C2×D7)⋊C4—22no—
35C2×(C2×D7)⋊C4—22no—
36C2×(C2×D7)⋊C4—22no—
37C2×(C2×D7)⋊C4—22no—
38C2×C4⋊Dic7—21no—
39C2×C4×Dic7—21no—
40C2×#1136—22no—
41#6437—41no—
42#6437—41no—
43C7×C4⋊C8—41no—
44C7×C22⋊C8—22no—
45C7×#97—41no—
46#6410—24no—
47C7⋊#95C2×C412yes—
48#6377—41no—
49C4×C7⋊C8—41no—
50#2548—71no—
51C4×#101—71no—
52#1467D711yescharacteristic, complemented
53#1345—74no—
54C23×D7—22no—
55C2×C7×Q8—22no—
56C2×C7×Q8—22no—
57C2×C7×Q8—41no—
58C22×C4×C7C22⋊C411yescharacteristic
59C22×C4×C7C22⋊C411yescharacteristic
60C22×C4×C7C22⋊C411yescharacteristic
61C22×C4×C7C22⋊C411yescharacteristic
62C22×C4×C7C22×C411yescharacteristic
63C22×C4×C7C2×D411yescharacteristic
64C22×C4×C7C2×D411yescharacteristic
65C22×Dic7—22no—
66C2×D28—42no—
67C2×D28—42no—
68C2×D28—42no—
69C2×D28—42no—
70C2×D28—42no—
71C2×D28—41no—
72C2×D28—41no—
73C2×D28—42no—
74C2×D28—82no—
75C2×C7×C8—42no—
76C7×C4⋊C4—41no—
77C7×C4⋊C4—41no—
78C7×C4⋊C4—41no—
79C42×C7—21no—
80C42×C7—21no—
81C42×C7—21no—
82C42×C7—21no—
83C42×C7—21no—
84C42×C7—21no—
85(C2×D7)⋊C4—44no—
86(C2×D7)⋊C4—44no—
87(C2×D7)⋊C4—82no—
88(C2×D7)⋊C4—82no—
89C4⋊Dic7—42no—
90C4×Dic7—42no—
91#1136—24no—
92#1136—42no—
93C2×C7⋊C8—42no—
94C2×#127—71no—
95C2×#124—141no—
96C2×C4×Q8C2×D711yescharacteristic
97#432—21no—
98C2×#101—141no—
99C4×M16—141no—
100#394—72no—
101#394—72no—
102#390—141no—
103#390—141no—
104#390—141no—
105C4×C4⋊C4—71no—
106#343—72no—
107#324—21no—
108#324C2×D712yes—
109C23×C7C2×C22⋊C411yescharacteristic
110C22×D7—42no—
111C22×D7—42no—
112C22×D7—42no—
113C22×D7—42no—
114C22×D7—42no—
115C22×D7—42no—
116C22×D7—42no—
117C7×Q8—44no—
118C2×C4×C7—21no—
119C2×C4×C7—21no—
120C2×C4×C7—21no—
121C2×C4×C7—21no—
122C2×C4×C7—22no—
123C2×C4×C7—21no—
124C2×C4×C7—21no—
125C2×C4×C7—21no—
126C2×C4×C7—21no—
127C2×C4×C7—21no—
128C2×C4×C7—21no—
129C2×C4×C7—41no—
130C2×C4×C7—41no—
131C2×C4×C7—41no—
132C2×C4×C7#9911yescharacteristic
133C2×C4×C7#9911yescharacteristic
134C2×C4×C7#10412yes—
135C2×C4×C7AGL(1,ℤ/8)12yes—
136C2×Dic7—42no—
137C2×Dic7—42no—
138C2×Dic7—42no—
139D28—82no—
140D28—84no—
141D28—84no—
142D28—82no—
143C7×C8—82no—
144C7⋊C8—44no—
145C22×Q8D2811yescharacteristic
146C22×D4—72no—
147C22×D4—141no—
148C22×D4—141no—
149C2×M16—142no—
150#127—281no—
151#127—281no—
152#124—284no—
153C4×Q8—41no—
154C4×Q8—41no—
155C2×C4⋊C4—141no—
156C2×C4⋊C4C4×D711yescharacteristic
157C2×C4⋊C4C22⋊D711yescharacteristic
158C2×C4⋊C4C22×D711yescharacteristic
159C2×C22⋊C4—142no—
160C2×C22⋊C4—142no—
161C2×C22⋊C4—142no—
162C2×C22⋊C4—142no—
163C2×C42—141no—
164C2×C42C4×D711yescharacteristic
165C2×C42D2811yescharacteristic
166C2×C42C22⋊D711yescharacteristic
167C4⋊C8—41no—
168#101—144no—
169C22⋊C8—22no—
170#97—41no—
171#97—281no—
172C4×C8—281no—
173#95—72no—
174C22×C7—21no—
175C22×C7—21no—
176C22×C7C2×#9911yescharacteristic
177C22×C7#41811yescharacteristic
178C22×C7C2×#10411yescharacteristic
179C2×D7—82no—
180C2×D7—82no—
181C2×D7—82no—
182C2×D7—82no—
183C2×D7—82no—
184C2×D7—82no—
185C2×D7—82no—
186C4×C7—21no—
187C4×C7—22no—
188C4×C7—22no—
189C4×C7—41no—
190C4×C7—41no—
191C4×C7—41no—
192C4×C7—41no—
193C4×C7#35512yes—
194Dic7—82no—
195C24—142no—
196C2×Q8—22no—
197C2×Q8—22no—
198C2×Q8—41no—
199C2×D4—282no—
200C2×D4—282no—
201C2×D4—282no—
202C2×D4—282no—
203C2×D4—282no—
204C2×D4—281no—
205C2×D4—281no—
206C2×D4—282no—
207C2×D4—562no—
208C22×C4—142no—
209C22×C4(C2×D7)⋊C411yescharacteristic
210C22×C4(C2×D7)⋊C411yescharacteristic
211C22×C4(C2×D7)⋊C411yescharacteristic
212C22×C4(C2×D7)⋊C411yescharacteristic
213C22×C4C2×C4×D711yescharacteristic
214C22×C4C2×D2811yescharacteristic
215C22×C4C2×C22⋊D711yescharacteristic
216M16—144no—
217M16—282no—
218C2×C8—42no—
219C2×C8—282no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—282no—
224C22⋊C4—284no—
225C22⋊C4—284no—
226C22⋊C4—562no—
227C22⋊C4—562no—
228C42—21no—
229C42—21no—
230C42—21no—
231C42—21no—
232C42—21no—
233C42—21no—
234C42—282no—
235C2×C7—21no—
236C2×C7—21no—
237C2×C7#150711yescharacteristic
238C2×C7#212211yescharacteristic
239C2×C7C2×#35511yescharacteristic
240D7—162no—
241C23—282no—
242C23—282no—
243C23—282no—
244C23—282no—
245C23—282no—
246C23—282no—
247C23—282no—
248C23C2×(C2×D7)⋊C411yescharacteristic
249Q8—44no—
250D4—562no—
251D4—564no—
252D4—564no—
253D4—562no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—282no—
269C2×C4—282no—
270C2×C4—282no—
271C2×C4#638011yescharacteristic
272C2×C4#638011yescharacteristic
273C2×C4#639912yes—
274C2×C4#647112yes—
275C8—82no—
276C8—284no—
277C7#1178111yescharacteristic, complemented, Sylow
278C22—21no—
279C22—21no—
280C22—562no—
281C22—562no—
282C22—562no—
283C22—562no—
284C22—562no—
285C22—562no—
286C22—562no—
287C22C2×#638011yescharacteristic
288C22#8990311yescharacteristic
289C22C2×#639911yescharacteristic
290C4—21no—
291C4—22no—
292C4—22no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—562no—
298C4#8927212yes—
299C2—21no—
300C2—21no—
301C2—1122no—
302C2#1172773111yescharacteristic
303C2#1172781111yescharacteristic
304C2C2×#8927211yescharacteristic
subgroupG/H
centerC22C2×#6380
commutatorC22×C4×C7C22×C4
FrattiniC2×C4⋊C4C22×D7
FittingC7×#1467C2
socleC22×C7C2×#99
prime radicalC2×#6437C4
cosocleC2×C7×C4⋊C4C23
hypercenter#1467D7
hypocenterC7#11781
LCSG ▷ C22×C4×C7 ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1467

Complements

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

NH ≅ G/Ntype
2. C7×#1467C2semidirect
3. C4×#6410C2semidirect
4. #11725262C2semidirect
52. #1467D7semidirect
277. C7#11781semidirect

Maximal subgroups

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

subgroupindex
#117399212
C7×#14672
C4×#64102
#117252622
#117817