Finite Group Databasebeta

← #13263436

Subgroups — #13263436

Order 1792.

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

normal subgroups only

This group has 462 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
3#11729378C211yesmaximal, characteristic, complemented
4#11725260C214yesmaximal, complemented
5C2×C4×C7×Q8C2211yescharacteristic
6C2×#6510C412yes—
7C2×#6437C411yescharacteristic
8C7×#432—21no—
9#89763—21no—
10#89763—21no—
11#89760C2212yes—
12#89711—21no—
13#89711—21no—
14C4×C4⋊Dic7C411yescharacteristic
15#89697—21no—
16C7×#324—21no—
17C7×#324C2212yes—
18#89323—21no—
19#89323C2212yes—
20#11567—71nomaximal, Sylow
21C22×C7×Q8C2×C411yescharacteristic
22C22×D28—21no—
23C22×D28—21no—
24C22×D28C2×C412yes—
25C4×C7×Q8—41no—
26C4×C7×Q8—41no—
27C2×C7×C4⋊C4D411yescharacteristic
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×Dic7C2×C412yes—
40#6437—41no—
41#6437—41no—
42C7×C4⋊C8—41no—
43C7×C22⋊C8—22no—
44C7×#97—41no—
45C7⋊#95—21no—
46C22⋊(C7⋊C8)—22no—
47C4⋊(C7⋊C8)—41no—
48C4×C7⋊C8—41no—
49#2548—71no—
50#1467D711yescharacteristic, complemented
51#1461—71no—
52#1318—74no—
53C23×D7—22no—
54C2×C7×Q8—22no—
55C2×C7×Q8—22no—
56C2×C7×Q8—41no—
57C22×C4×C7C22⋊C411yescharacteristic
58C22×C4×C7C22⋊C411yescharacteristic
59C22×C4×C7C22⋊C411yescharacteristic
60C22×C4×C7C22⋊C411yescharacteristic
61C22×C4×C7C22×C411yescharacteristic
62C22×C4×C7C2×D411yescharacteristic
63C22×C4×C7C2×D411yescharacteristic
64C22×Dic7—22no—
65C2×D28—24no—
66C2×D28—42no—
67C2×D28—42no—
68C2×D28—42no—
69C2×D28—42no—
70C2×D28—42no—
71C2×D28—41no—
72C2×D28—41no—
73C2×D28—82no—
74C2×C7×C8—42no—
75C7×C4⋊C4—41no—
76C7×C4⋊C4—41no—
77C7×C4⋊C4—41no—
78C42×C7—21no—
79C42×C7—21no—
80C42×C7—21no—
81C42×C7—21no—
82C42×C7—21no—
83C42×C7—21no—
84(C2×D7)⋊C4—44no—
85(C2×D7)⋊C4—44no—
86(C2×D7)⋊C4—82no—
87(C2×D7)⋊C4—82no—
88C4⋊Dic7—42no—
89C4×Dic7—42no—
90C2×C7⋊C8—42no—
91C2×#127—71no—
92C2×#124—72no—
93C2×C4×Q8C2×D711yescharacteristic
94#432—21no—
95#431—141no—
96#394—141no—
97#394—141no—
98#390—72no—
99#390—141no—
100#390—141no—
101C4×C4⋊C4—71no—
102#324—21no—
103#324—72no—
104#324—141no—
105#324C2×D712yes—
106C23×C7C2×C22⋊C411yescharacteristic
107C22×D7—42no—
108C22×D7—42no—
109C22×D7—42no—
110C22×D7—42no—
111C22×D7—42no—
112C22×D7—42no—
113C22×D7—42no—
114C7×Q8—44no—
115C2×C4×C7—21no—
116C2×C4×C7—21no—
117C2×C4×C7—21no—
118C2×C4×C7—21no—
119C2×C4×C7—22no—
120C2×C4×C7—21no—
121C2×C4×C7—21no—
122C2×C4×C7—21no—
123C2×C4×C7—21no—
124C2×C4×C7—21no—
125C2×C4×C7—21no—
126C2×C4×C7—41no—
127C2×C4×C7—41no—
128C2×C4×C7—41no—
129C2×C4×C7#9911yescharacteristic
130C2×C4×C7#9911yescharacteristic
131C2×C4×C7#10012yes—
132C2×C4×C7#13112yes—
133C2×Dic7—42no—
134C2×Dic7—42no—
135C2×Dic7—42no—
136D28—84no—
137D28—82no—
138D28—84no—
139D28—82no—
140C7×C8—82no—
141C7⋊C8—82no—
142C22×Q8C4×D711yescharacteristic
143C22×D4—72no—
144C22×D4—141no—
145C22×D4—141no—
146#127—281no—
147#127—281no—
148#124—284no—
149C4×Q8—41no—
150C4×Q8—41no—
151C2×C4⋊C4—141no—
152C2×C4⋊C4D2811yescharacteristic
153C2×C4⋊C4C22⋊D711yescharacteristic
154C2×C4⋊C4C22×D711yescharacteristic
155C2×C22⋊C4—142no—
156C2×C22⋊C4—142no—
157C2×C22⋊C4—142no—
158C2×C22⋊C4—142no—
159C2×C42—72no—
160C2×C42C4×D711yescharacteristic
161C2×C42D2811yescharacteristic
162C2×C42C22⋊D711yescharacteristic
163C4⋊C8—41no—
164C4⋊C8—281no—
165C22⋊C8—22no—
166C22⋊C8—142no—
167#97—41no—
168C4×C8—281no—
169#95—141no—
170C22×C7—21no—
171C22×C7—21no—
172C22×C7#40811yescharacteristic
173C22×C7C2×#9911yescharacteristic
174C22×C7C2×#10011yescharacteristic
175C2×D7—82no—
176C2×D7—82no—
177C2×D7—82no—
178C2×D7—82no—
179C2×D7—82no—
180C2×D7—82no—
181C2×D7—82no—
182C4×C7—21no—
183C4×C7—22no—
184C4×C7—22no—
185C4×C7—41no—
186C4×C7—41no—
187C4×C7—41no—
188C4×C7—41no—
189C4×C7#35512yes—
190Dic7—82no—
191C24—142no—
192C2×Q8—22no—
193C2×Q8—22no—
194C2×Q8—41no—
195C2×D4—144no—
196C2×D4—282no—
197C2×D4—282no—
198C2×D4—282no—
199C2×D4—282no—
200C2×D4—282no—
201C2×D4—281no—
202C2×D4—281no—
203C2×D4—562no—
204C22×C4—142no—
205C22×C4(C2×D7)⋊C411yescharacteristic
206C22×C4(C2×D7)⋊C411yescharacteristic
207C22×C4(C2×D7)⋊C411yescharacteristic
208C22×C4(C2×D7)⋊C411yescharacteristic
209C22×C4C2×C4×D711yescharacteristic
210C22×C4C2×D2811yescharacteristic
211C22×C4C2×C22⋊D711yescharacteristic
212C2×C8—42no—
213C2×C8—282no—
214C4⋊C4—41no—
215C4⋊C4—41no—
216C4⋊C4—41no—
217C4⋊C4—282no—
218C22⋊C4—284no—
219C22⋊C4—284no—
220C22⋊C4—562no—
221C22⋊C4—562no—
222C42—21no—
223C42—21no—
224C42—21no—
225C42—21no—
226C42—21no—
227C42—21no—
228C42—282no—
229C2×C7—21no—
230C2×C7—21no—
231C2×C7#147111yescharacteristic
232C2×C7#212811yescharacteristic
233C2×C7C2×#35511yescharacteristic
234D7—162no—
235C23—282no—
236C23—282no—
237C23—282no—
238C23—282no—
239C23—282no—
240C23—282no—
241C23—282no—
242C23C2×(C2×D7)⋊C411yescharacteristic
243Q8—44no—
244D4—564no—
245D4—562no—
246D4—564no—
247D4—562no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—282no—
263C2×C4—282no—
264C2×C4—282no—
265C2×C4#638011yescharacteristic
266C2×C4#638011yescharacteristic
267C2×C4#639712yes—
268C2×C4#647012yes—
269C8—82no—
270C8—562no—
271C7#1156711yescharacteristic, complemented, Sylow
272C22—21no—
273C22—21no—
274C22—562no—
275C22—562no—
276C22—562no—
277C22—562no—
278C22—562no—
279C22—562no—
280C22—562no—
281C22C2×#638011yescharacteristic
282C22#8990111yescharacteristic
283C22C2×#639711yescharacteristic
284C4—21no—
285C4—22no—
286C4—22no—
287C4—41no—
288C4—41no—
289C4—41no—
290C4—41no—
291C4—562no—
292C4#8927212yes—
293C2—21no—
294C2—21no—
295C2—1122no—
296C2#1172772411yescharacteristic
297C2#1172781511yescharacteristic
298C2C2×#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#11567
LCSG ▷ C22×C4×C7 ▷ C22×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. #11729378C2semidirect
4. #11725260C2semidirect
50. #1467D7semidirect
271. C7#11567semidirect

Maximal subgroups

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

subgroupindex
#117399212
C7×#14672
#117293782
#117252602
#115677