Finite Group Databasebeta

← #13248261

Subgroups — #13248261

Order 1792.

476 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 155 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
1C7×#2369C211yesmaximal, characteristic
2#11729539C211yesmaximal, characteristic
3C2×#89341C211yesmaximal, characteristic
4#11727221C212yesmaximal
5#11725425C212yesmaximal
6C2×C7×C4⋊Q8C2211yescharacteristic
7C7×#391—22no—
8C7×#389—22no—
9C4×C7×C4⋊C4—22no—
10C4×C7×C4⋊C4C2212yes—
11C2×#6409—22no—
12C2×#6382—22no—
13#89707C2211yescharacteristic
14C2×C4⋊(C7⋊C8)C2212yes—
15C2×C4×C7⋊C8C2211yescharacteristic
16#89341C414yescomplemented
17#89324—22no—
18#8928—71nomaximal, Sylow
19C22×C7×Q8D412yes—
20C7×C4⋊Q8—22no—
21C7×C4⋊Q8C2×C412yes—
22C7×C4⋊Q8Q812yes—
23C2×C7×C4⋊C4—22no—
24C2×C7×C4⋊C4—22no—
25C2×C7×C4⋊C4D412yes—
26C2×C7×C4⋊C4D412yes—
27C2×C42×C7—22no—
28C2×C42×C7—22no—
29C2×C42×C7C2311yescharacteristic
30C2×C4⋊Dic7—22no—
31C2×C4⋊Dic7—21no—
32C22×C7⋊C8—21no—
33C22×C7⋊C8—22no—
34C7×#95—24no—
35C7×#95—22no—
36#6409—44no—
37#6382—44no—
38C4⋊(C7⋊C8)—22no—
39C4⋊(C7⋊C8)C2×C414yes—
40C4×C7⋊C8—22no—
41#2369D711yescharacteristic
42#1956—71no—
43#1948—72no—
44C2×#333—71no—
45#1279—72no—
46C2×C7×Q8—22no—
47C2×C7×Q8—42no—
48C2×C7×Q8—42no—
49C2×C7×Q8C4⋊C414yes—
50C22×C4×C7—22no—
51C22×C4×C7—22no—
52C22×C4×C7—22no—
53C22×C4×C7C2×D411yescharacteristic
54C22×C4×C7C2×D412yes—
55C22×Dic7—41no—
56C7×C4⋊C4—24no—
57C7×C4⋊C4—24no—
58C7×C4⋊C4—22no—
59C7×C4⋊C4—22no—
60C7×C4⋊C4—22no—
61C7×C4⋊C4—82no—
62C7×C4⋊C4SD1614yes—
63C42×C7—42no—
64C42×C7—42no—
65C42×C7—82no—
66C42×C7C22×C411yescharacteristic
67C42×C7C2×Q811yescharacteristic
68C42×C7#4112yes—
69C4⋊Dic7—42no—
70C4⋊Dic7—42no—
71C4⋊Dic7—42no—
72C2×C7⋊C8—22no—
73C2×C7⋊C8—24no—
74C2×C7⋊C8—41no—
75C2×C7⋊C8—41no—
76C2×C7⋊C8—42no—
77C2×C7⋊C8—42no—
78C2×C4⋊Q8C2×D711yescharacteristic
79C2×#106—142no—
80C2×C4⋊C8—72no—
81C2×#103—142no—
82C2×C4×C8—71no—
83#391—22no—
84#389—22no—
85#384—71no—
86C4×C4⋊C4—22no—
87C4×C4⋊C4C2×D712yes—
88#340—142no—
89#333—74no—
90C23×C7#12011yescharacteristic
91C7×Q8—44no—
92C7×Q8—82no—
93C2×C4×C7—21no—
94C2×C4×C7—21no—
95C2×C4×C7—24no—
96C2×C4×C7—24no—
97C2×C4×C7—42no—
98C2×C4×C7—42no—
99C2×C4×C7—42no—
100C2×C4×C7—42no—
101C2×C4×C7—42no—
102C2×C4×C7—42no—
103C2×C4×C7—42no—
104C2×C4×C7C2×C4⋊C411yescharacteristic
105C2×C4×C7C4×D412yes—
106C2×C4×C7C22⋊Q812yes—
107C2×C4×C7#12311yescharacteristic
108C2×C4×C7C2×SD1612yes—
109C2×C4×C7#13512yes—
110C2×C4×C7#13712yes—
111C2×C4×C7#13712yes—
112C2×Dic7—82no—
113C2×Dic7—81no—
114C7⋊C8—42no—
115C7⋊C8—44no—
116C22×Q8C22⋊D712yes—
117C22×C8—142no—
118C22×C8—141no—
119C4⋊Q8—22no—
120C4⋊Q8Dic1412yes—
121C4⋊Q8C4×D712yes—
122C2×C4⋊C4—22no—
123C2×C4⋊C4—22no—
124C2×C4⋊C4—142no—
125C2×C4⋊C4—141no—
126C2×C4⋊C4C22⋊D712yes—
127C2×C4⋊C4C22⋊D712yes—
128C2×C42—22no—
129C2×C42—22no—
130C2×C42C22×D711yescharacteristic
131#106—284no—
132C4⋊C8—74no—
133C4⋊C8—142no—
134#103—284no—
135C4×C8—142no—
136#95—24no—
137#95—22no—
138C22×C7#38511yescharacteristic
139C22×C7#44812yes—
140C22×C7#45212yes—
141C22×C7#45311yescharacteristic
142C22×C7#45511yescharacteristic
143C4×C7—21no—
144C4×C7—21no—
145C4×C7—44no—
146C4×C7—44no—
147C4×C7—82no—
148C4×C7C4×SD1612yes—
149C4×C7#44112yes—
150C4×C7#47512yes—
151C4×C7#47912yes—
152Dic7—161no—
153C2×Q8—22no—
154C2×Q8—42no—
155C2×Q8—42no—
156C2×Q8Dic7⋊C414yes—
157C22×C4—22no—
158C22×C4—22no—
159C22×C4—22no—
160C22×C4—281no—
161C22×C4C2×C22⋊D711yescharacteristic
162C22×C4C2×C22⋊D712yes—
163C2×C8—142no—
164C2×C8—144no—
165C2×C8—281no—
166C2×C8—281no—
167C2×C8—282no—
168C2×C8—282no—
169C4⋊C4—24no—
170C4⋊C4—24no—
171C4⋊C4—22no—
172C4⋊C4—22no—
173C4⋊C4—22no—
174C4⋊C4—82no—
175C4⋊C4—282no—
176C4⋊C4—282no—
177C4⋊C4—282no—
178C4⋊C4#114314yes—
179C42—42no—
180C42—42no—
181C42—82no—
182C42C2×Dic1411yescharacteristic
183C42C2×C4×D711yescharacteristic
184C42#115712yes—
185C2×C7#162311yescharacteristic
186C2×C7#163411yescharacteristic
187C2×C7#164312yes—
188C2×C7#185611yescharacteristic
189C2×C7#186512yes—
190C23#651611yescharacteristic
191Q8—44no—
192Q8—82no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—24no—
196C2×C4—24no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—42no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—562no—
205C2×C4—561no—
206C2×C4C2×Dic7⋊C411yescharacteristic
207C2×C4#648712yes—
208C2×C4C4×C22⋊D712yes—
209C2×C4#649211yescharacteristic
210C2×C4C2×#114312yes—
211C2×C4#650512yes—
212C2×C4#651312yes—
213C2×C4#651412yes—
214C8—282no—
215C8—284no—
216C7#892811yescharacteristic, complemented, Sylow
217C22#8998211yescharacteristic
218C22#8999912yes—
219C22#9001112yes—
220C22#9001311yescharacteristic
221C22#9001411yescharacteristic
222C4—21no—
223C4—21no—
224C4—44no—
225C4—44no—
226C4—82no—
227C4—1121no—
228C4#8979212yes—
229C4#8979412yes—
230C4C4×#114312yes—
231C4#8980212yes—
232C2#1172938312yes—
233C2#1172940111yescharacteristic
234C2#1172967912yes—
235C2#1172968211yescharacteristic
236C2#1172969311yescharacteristic
subgroupG/H
centerC23#6516
commutatorC42×C7C22×C4
FrattiniC2×C42C22×D7
FittingC7×#2369C2
socle, prime radicalC23×C7#120
cosocleC2×C42×C7C23
hypercenter#2369D7
hypocenterC7#8928
LCSG ▷ C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2369

Complements

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

NH ≅ G/Ntype
16. #89341C4semidirect
216. C7#8928semidirect

Maximal subgroups

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

subgroupindex
C7×#23692
#117295392
C2×#893412
#117272212
#117254252
#89287