Finite Group Databasebeta

← #13243096

Subgroups — #13243096

Order 1792.

394 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 95 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×#2734C211yesmaximal, characteristic
2#11727438C211yesmaximal, characteristic
3#11727366C212yesmaximal
4#11725448C211yesmaximal, characteristic
5#11725444C212yesmaximal
6C2×C7×C4⋊Q8—21no—
7C7×#398—21no—
8C7×#395—22no—
9C7×#391C2211yescharacteristic
10C7×#389C2212yes—
11C7×#387—22no—
12C2×#6409—21no—
13C2×#6381—21no—
14#89707C2211yescharacteristic
15#89324—22no—
16#89324—22no—
17#89319C2212yes—
18#89319C2211yescharacteristic
19#7829—71nomaximal, Sylow
20C22×C7×Q8—21no—
21C22×C7×Q8D411yescharacteristic
22C7×C4⋊Q8—42no—
23C7×C4⋊Q8—42no—
24C2×C7×C4⋊C4—22no—
25C2×C7×C4⋊C4—22no—
26C2×C7×C4⋊C4—21no—
27C2×C7×C4⋊C4D412yes—
28C2×C7×C4⋊C4D411yescharacteristic
29C2×C7×C4⋊C4D412yes—
30C2×C42×C7—21no—
31C2×C42×C7C2311yescharacteristic
32C2×C4⋊Dic7—21no—
33C2×C4⋊Dic7—22no—
34C22×C7⋊C8—21no—
35C22×C7⋊C8—22no—
36C7×#95—21no—
37C7×#95—22no—
38C7×#95—22no—
39C7×#95—22no—
40#6409—42no—
41#6381—42no—
42#2734D711yescharacteristic
43#2100—72no—
44#2095—71no—
45#1272—71no—
46#1271—72no—
47C2×C7×Q8—21no—
48C2×C7×Q8—42no—
49C2×C7×Q8—41no—
50C2×C7×Q8—41no—
51C2×C7×Q8—81no—
52C2×C7×Q8—81no—
53C2×C7×Q8SD1612yes—
54C22×C4×C7—22no—
55C22×C4×C7—21no—
56C22×C4×C7—21no—
57C22×C4×C7—22no—
58C22×C4×C7C2×D411yescharacteristic
59C22×C4×C7C2×D412yes—
60C22×Dic7—41no—
61C7×C4⋊C4—22no—
62C7×C4⋊C4—42no—
63C7×C4⋊C4—41no—
64C7×C4⋊C4—44no—
65C7×C4⋊C4—42no—
66C7×C4⋊C4—42no—
67C7×C4⋊C4—81no—
68C7×C4⋊C4Q1614yes—
69C42×C7—41no—
70C42×C7—42no—
71C4⋊Dic7—41no—
72C4⋊Dic7—44no—
73C4⋊Dic7—41no—
74C2×C7⋊C8—22no—
75C2×C7⋊C8—41no—
76C2×C7⋊C8—41no—
77C2×C7⋊C8—42no—
78C2×C7⋊C8—42no—
79C2×C7⋊C8—42no—
80C2×C4⋊Q8—21no—
81C2×#107—141no—
82C2×#103—141no—
83#398—21no—
84#395—22no—
85#391C2×D711yescharacteristic
86#389C2×D712yes—
87#387—22no—
88#384—71no—
89#340—142no—
90#340—142no—
91#336—71no—
92#336—72no—
93C23×C7#12011yescharacteristic
94C7×Q8—42no—
95C7×Q8—81no—
96C7×Q8—84no—
97C2×C4×C7—21no—
98C2×C4×C7—22no—
99C2×C4×C7—22no—
100C2×C4×C7—21no—
101C2×C4×C7—22no—
102C2×C4×C7—24no—
103C2×C4×C7—42no—
104C2×C4×C7—41no—
105C2×C4×C7—42no—
106C2×C4×C7—41no—
107C2×C4×C7—42no—
108C2×C4×C7—41no—
109C2×C4×C7—42no—
110C2×C4×C7—42no—
111C2×C4×C7—42no—
112C2×C4×C7C2×SD1611yescharacteristic
113C2×C4×C7C2×Q1612yes—
114C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
115C2×C4×C7#13712yes—
116C2×Dic7—81no—
117C2×Dic7—82no—
118C7⋊C8—42no—
119C7⋊C8—82no—
120C22×Q8—21no—
121C22×Q8C22⋊D711yescharacteristic
122C22×C8—141no—
123C22×C8—142no—
124C4⋊Q8—42no—
125C4⋊Q8—42no—
126C2×C4⋊C4—22no—
127C2×C4⋊C4—22no—
128C2×C4⋊C4—21no—
129C2×C4⋊C4—142no—
130C2×C4⋊C4—141no—
131C2×C4⋊C4C22⋊D712yes—
132C2×C4⋊C4C22⋊D712yes—
133C2×C4⋊C4C22⋊D711yescharacteristic
134C2×C42—21no—
135C2×C42C22×D711yescharacteristic
136#107—282no—
137#103—282no—
138#95—21no—
139#95—22no—
140#95—22no—
141#95—22no—
142C22×C7#45011yescharacteristic
143C22×C7#45112yes—
144C22×C7#45311yescharacteristic
145C22×C7#45412yes—
146C22×C7#45811yescharacteristic
147C4×C7—21no—
148C4×C7—21no—
149C4×C7—22no—
150C4×C7—22no—
151C4×C7—42no—
152C4×C7—44no—
153C4×C7—82no—
154C4×C7—81no—
155Dic7—161no—
156C2×Q8—21no—
157C2×Q8—42no—
158C2×Q8—41no—
159C2×Q8—41no—
160C2×Q8—81no—
161C2×Q8—81no—
162C2×Q8#114212yes—
163C22×C4—22no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—22no—
167C22×C4—281no—
168C22×C4C2×C22⋊D711yescharacteristic
169C22×C4C2×C22⋊D712yes—
170C2×C8—142no—
171C2×C8—281no—
172C2×C8—281no—
173C2×C8—282no—
174C2×C8—282no—
175C2×C8—282no—
176C4⋊C4—22no—
177C4⋊C4—41no—
178C4⋊C4—42no—
179C4⋊C4—44no—
180C4⋊C4—42no—
181C4⋊C4—42no—
182C4⋊C4—81no—
183C4⋊C4—281no—
184C4⋊C4—281no—
185C4⋊C4—284no—
186C4⋊C4#114414yes—
187C42—41no—
188C42—42no—
189C2×C7#161311yescharacteristic
190C2×C7#161712yes—
191C2×C7#163311yescharacteristic
192C2×C7#163712yes—
193C2×C7#165711yescharacteristic
194C23#651611yescharacteristic
195Q8—42no—
196Q8—81no—
197Q8—84no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—24no—
204C2×C4—42no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—41no—
210C2×C4—42no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—561no—
214C2×C4—562no—
215C2×C4#649511yescharacteristic
216C2×C4C2×#114211yescharacteristic
217C2×C4#650512yes—
218C2×C4C2×#114412yes—
219C8—282no—
220C8—562no—
221C7#782911yescharacteristic, complemented, Sylow
222C22#8999011yescharacteristic
223C22#9000012yes—
224C22#9001311yescharacteristic
225C22#9001511yescharacteristic
226C22#9001712yes—
227C4—21no—
228C4—21no—
229C4—22no—
230C4—22no—
231C4—44no—
232C4—42no—
233C4—81no—
234C4—82no—
235C4—1121no—
236C2#1172959811yescharacteristic
237C2#1172965312yes—
238C2#1172966912yes—
239C2#1172969411yescharacteristic
240C2#1172970911yescharacteristic
subgroupG/H
centerC23#6516
commutator, cosocleC2×C42×C7C23
FrattiniC2×C42C22×D7
FittingC7×#2734C2
socle, prime radicalC23×C7#120
hypercenter#2734D7
hypocenterC7#7829
LCSG ▷ C2×C42×C7 ▷ C23×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2734

Complements

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

NH ≅ G/Ntype
221. C7#7829semidirect

Maximal subgroups

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

subgroupindex
C7×#27342
#117274382
#117273662
#117254482
#117254442
#78297