Finite Group Databasebeta

← #13247208

Subgroups — #13247208

Order 1792.

526 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 107 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#11731593C211yesmaximal, characteristic
2#11727561C212yesmaximal
3C7×#1295C211yesmaximal, characteristic, complemented
4#11725465C212yesmaximal, complemented
5#11725436C211yesmaximal, characteristic, complemented
6C2×#6455C412yes—
7C2×C42×D7C2211yescharacteristic
8C2×C7×#97C2212yes—
9C7×#382C2211yescharacteristic
10C2×(C2×D7)⋊C8—22no—
11#89748C412yes—
12#89708C2211yescharacteristic
13C2×#6377C2212yes—
14#89439—22no—
15#89421—22no—
16#89345—22no—
17#8722—71nomaximal, Sylow
18C22×C4×D7C2×C411yescharacteristic
19C22×C4×D7D412yes—
20C22×C7×C8—22no—
21C2×C7×C4⋊C4C2×C412yes—
22C2×C42×C7C2311yescharacteristic
23C2×(C2×D7)⋊C4—22no—
24C2×C4⋊Dic7C2×C412yes—
25C2×Dic7⋊C4—22no—
26C2×Dic7⋊C4—22no—
27C2×C4×Dic7—22no—
28C2×C4×Dic7C2×C411yescharacteristic
29C2×C4×Dic7D412yes—
30C22×C7⋊C8—22no—
31#6455—44no—
32C42×D7—22no—
33C42×D7—21no—
34C42×D7—21no—
35C7×#97—22no—
36C7×#97—22no—
37C7×#95—22no—
38C7⋊#95—22no—
39(C2×D7)⋊C8—28no—
40#6377—22no—
41#6377—22no—
42#2285—71no—
43#1749—72no—
44#1295—72no—
45#1295—71no—
46#1295D711yescharacteristic, complemented
47C23×D7C22⋊C411yescharacteristic
48C22×C4×C7—22no—
49C22×C4×C7C22×C411yescharacteristic
50C22×C4×C7C2×D412yes—
51C22×Dic7—22no—
52C22×Dic7C22⋊C411yescharacteristic
53C22×Dic7C22⋊C412yes—
54C2×C4×D7—22no—
55C2×C4×D7—21no—
56C2×C4×D7—21no—
57C2×C4×D7—22no—
58C2×C4×D7—22no—
59C2×C4×D7—22no—
60C2×C4×D7—24no—
61C2×C4×D7—42no—
62C2×C7×C8—24no—
63C2×C7×C8—42no—
64C2×C7×C8—42no—
65C7×C4⋊C4—42no—
66C42×C7#4112yes—
67C42×C7#4111yescharacteristic
68C42×C7#4111yescharacteristic
69(C2×D7)⋊C4—44no—
70C4⋊Dic7—42no—
71Dic7⋊C4—44no—
72Dic7⋊C4—44no—
73C4×Dic7—21no—
74C4×Dic7—21no—
75C4×Dic7—22no—
76C4×Dic7—22no—
77C4×Dic7—44no—
78C2×C7⋊C8—24no—
79C2×C7⋊C8—42no—
80C2×C7⋊C8—42no—
81C2×#117—72no—
82C22×C42—71no—
83C2×C22⋊C8—142no—
84C2×#97—72no—
85C2×#97C2×D712yes—
86#384—72no—
87#382—71no—
88#382C2×D711yescharacteristic
89#380—142no—
90C4×C4⋊C4—142no—
91#336—142no—
92C23×C7C2×C22⋊C411yescharacteristic
93C22×D7—21no—
94C22×D7—21no—
95C22×D7—22no—
96C22×D7—22no—
97C22×D7#10012yes—
98C2×C4×C7—21no—
99C2×C4×C7—21no—
100C2×C4×C7—22no—
101C2×C4×C7—22no—
102C2×C4×C7—42no—
103C2×C4×C7—42no—
104C2×C4×C7—42no—
105C2×C4×C7#11711yescharacteristic
106C2×C4×C7#11711yescharacteristic
107C2×C4×C7#12312yes—
108C2×C4×C7#12312yes—
109C2×Dic7—21no—
110C2×Dic7—22no—
111C2×Dic7—21no—
112C2×Dic7—22no—
113C2×Dic7—42no—
114C2×Dic7—42no—
115C2×Dic7—42no—
116C2×Dic7#10112yes—
117C2×Dic7#10414yes—
118C4×D7—24no—
119C4×D7—24no—
120C4×D7—44no—
121C4×D7—44no—
122C7×C8—44no—
123C7⋊C8—44no—
124C23×C4—71no—
125C23×C4—72no—
126C22×C8—22no—
127C22×C8—142no—
128#117—284no—
129C2×C4⋊C4—72no—
130C2×C4⋊C4—142no—
131C2×C4⋊C4—142no—
132C2×C4⋊C4C4×D712yes—
133C2×C22⋊C4—142no—
134C2×C42—71no—
135C2×C42—72no—
136C2×C42—142no—
137C2×C42—141no—
138C2×C42—141no—
139C2×C42—142no—
140C2×C42C22×D711yescharacteristic
141C22⋊C8—148no—
142#97—22no—
143#97—22no—
144#97—142no—
145#97—142no—
146#95—22no—
147#95—142no—
148C22×C7#38111yescharacteristic
149C22×C7C2×#10011yescharacteristic
150C22×C7C2×#10111yescharacteristic
151C22×C7C2×#10412yes—
152C22×C7#42112yes—
153C2×D7—22no—
154C2×D7—24no—
155C2×D7—41no—
156C2×D7—42no—
157C2×D7—41no—
158C4×C7—21no—
159C4×C7—21no—
160C4×C7—22no—
161C4×C7—22no—
162C4×C7—82no—
163Dic7—22no—
164Dic7—24no—
165Dic7—82no—
166C24—71no—
167C22×C4—22no—
168C22×C4—71no—
169C22×C4—72no—
170C22×C4—142no—
171C22×C4—144no—
172C22×C4—142no—
173C22×C4—141no—
174C22×C4—141no—
175C22×C4—142no—
176C22×C4—142no—
177C22×C4—142no—
178C22×C4—282no—
179C22×C4C2×C4×D711yescharacteristic
180C22×C4D4×D712yes—
181C2×C8—24no—
182C2×C8—42no—
183C2×C8—42no—
184C2×C8—144no—
185C2×C8—282no—
186C2×C8—282no—
187C4⋊C4—42no—
188C4⋊C4—282no—
189C4⋊C4—284no—
190C4⋊C4—284no—
191C22⋊C4—284no—
192C42—141no—
193C42—142no—
194C42—141no—
195C42—142no—
196C42—284no—
197C42#115712yes—
198C42#115911yescharacteristic
199C42#116111yescharacteristic
200C2×C7#152611yescharacteristic
201C2×C7#153012yes—
202C2×C7#153711yescharacteristic
203C2×C7#182111yescharacteristic
204C2×C7#182612yes—
205D7—42no—
206C23—72no—
207C23—141no—
208C23—141no—
209C23—142no—
210C23—142no—
211C23D7×C22⋊C411yescharacteristic
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—72no—
220C2×C4—74no—
221C2×C4—144no—
222C2×C4—144no—
223C2×C4—141no—
224C2×C4—142no—
225C2×C4—141no—
226C2×C4—142no—
227C2×C4—284no—
228C2×C4—284no—
229C2×C4—282no—
230C2×C4—282no—
231C2×C4—282no—
232C2×C4#643511yescharacteristic
233C2×C4#644612yes—
234C2×C4#645511yescharacteristic
235C2×C4#645712yes—
236C8—44no—
237C8—284no—
238C7#872211yescharacteristic, complemented, Sylow
239C22—144no—
240C22—142no—
241C22—281no—
242C22—281no—
243C22—282no—
244C22#8943611yescharacteristic
245C22D7×#10011yescharacteristic
246C22D7×#10111yescharacteristic
247C22D7×#10412yes—
248C22#8959312yes—
249C4—21no—
250C4—21no—
251C4—22no—
252C4—22no—
253C4—82no—
254C4—142no—
255C4—144no—
256C4—562no—
257C2—282no—
258C2#1172609912yes—
259C2#1172611611yescharacteristic
260C2#1172612311yescharacteristic
261C2#1172650812yes—
262C2#1172674411yescharacteristic
subgroupG/H
centerC23D7×C22⋊C4
commutatorC22×C4×C7C22×C4
FrattiniC2×C42C22×D7
FittingC7×#1295C2
socleC23×C7C2×C22⋊C4
prime radicalC23×D7C22⋊C4
cosocleC2×C42×C7C23
hypercenter#1295D7
hypocenterC7#8722
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
3. C7×#1295C2semidirect
4. #11725465C2semidirect
5. #11725436C2semidirect
46. #1295D7semidirect
238. C7#8722semidirect

Maximal subgroups

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

subgroupindex
#117315932
#117275612
C7×#12952
#117254652
#117254362
#87227