Finite Group Databasebeta

← #13257030

Subgroups — #13257030

Order 1792.

414 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 77 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×#2607C211yesmaximal, characteristic
2#11727288C211yesmaximal, characteristic
3#11727196C212yesmaximal
4#11725435C211yesmaximal, characteristic
5#11725422C212yesmaximal
6C2×#6489C2211yescharacteristic
7C7×#399—21no—
8C7×#393—21no—
9C7×#391—22no—
10C7×#387—22no—
11C7×#381C2211yescharacteristic
12C4×C7×C22⋊C4C2212yes—
13#89983C2211yescharacteristic
14#89979C2212yes—
15#89322—21no—
16#89322—21no—
17#89318—22no—
18#89318—22no—
19#10387—71nomaximal, Sylow
20C22×C7×Q8—21no—
21C23×C4×C7C2311yescharacteristic
22C2×C7×C4⋊C4—22no—
23C2×C7×C4⋊C4—21no—
24C2×C7×C22⋊C4—22no—
25C2×C7×C22⋊C4D411yescharacteristic
26C2×C7×C22⋊C4D411yescharacteristic
27C2×C42×C7D412yes—
28C2×C42×C7D412yes—
29C2×C22⋊Dic7—21no—
30C2×C22⋊Dic7—21no—
31#6489—22no—
32#6489—22no—
33C2×C4⋊Dic7Q812yescomplemented
34C2×C4×Dic7—21no—
35C2×#1136—22no—
36C7×#95—21no—
37C7×#95—22no—
38C7×#95—21no—
39C7×#95—22no—
40C7×#95—22no—
41C7⋊#95—22no—
42C22⋊(C7⋊C8)—22no—
43C22⋊(C7⋊C8)—22no—
44#2607D711yescharacteristic
45#1826—72no—
46#1820—71no—
47#1306—71no—
48#1284—72no—
49C24×C7C2×D411yescharacteristic
50C2×C7×Q8—44no—
51C2×C7×Q8—81no—
52C22×C4×C7—22no—
53C22×C4×C7—21no—
54C22×C4×C7—22no—
55C22×C4×C7—21no—
56C22×C4×C7—41no—
57C22×C4×C7—41no—
58C22×C4×C7C2×D412yes—
59C22×C4×C7C2×Q811yescharacteristic
60C22×C4×C7#4112yes—
61C22×C4×C7#4111yescharacteristic
62C22×Dic7—22no—
63C22×Dic7—41no—
64C7×C4⋊C4—44no—
65C7×C4⋊C4—81no—
66C7×C22⋊C4—44no—
67C7×C22⋊C4—41no—
68C7×C22⋊C4—41no—
69C42×C7—42no—
70C42×C7—42no—
71C22⋊Dic7—41no—
72C22⋊Dic7—41no—
73C22⋊Dic7—41no—
74C22⋊Dic7—41no—
75C4⋊Dic7—24no—
76C4×Dic7—42no—
77#1136—42no—
78#1136—42no—
79C2×C7⋊C8—42no—
80C2×#117—71no—
81#407—72no—
82#399—21no—
83#393—21no—
84#391—22no—
85#387—22no—
86#381—71no—
87#381C2×D711yescharacteristic
88C4×C22⋊C4C2×D712yes—
89#342—141no—
90#342—141no—
91#339—142no—
92#339—142no—
93C23×C7—21no—
94C23×C7—21no—
95C23×C7—42no—
96C23×C7#12011yescharacteristic
97C23×C7C22⋊Q811yescharacteristic
98C23×C7#12411yescharacteristic
99C7×Q8—84no—
100C2×C4×C7—22no—
101C2×C4×C7—22no—
102C2×C4×C7—24no—
103C2×C4×C7—41no—
104C2×C4×C7—41no—
105C2×C4×C7—42no—
106C2×C4×C7—42no—
107C2×C4×C7—42no—
108C2×C4×C7—42no—
109C2×C4×C7—42no—
110C2×C4×C7—42no—
111C2×C4×C7—42no—
112C2×C4×C7—42no—
113C2×C4×C7—41no—
114C2×C4×C7—41no—
115C2×C4×C7C22⋊Q812yes—
116C2×C4×C7#12412yes—
117C2×Dic7—42no—
118C2×Dic7—82no—
119C2×Dic7—81no—
120C2×Dic7—82no—
121C7⋊C8—82no—
122C22×Q8—21no—
123C23×C4C22×D711yescharacteristic
124C2×M16—142no—
125#117—142no—
126#117—142no—
127C2×C4⋊C4—22no—
128C2×C4⋊C4—21no—
129C2×C4⋊C4—72no—
130C2×C22⋊C4—22no—
131C2×C22⋊C4—141no—
132C2×C22⋊C4—141no—
133C2×C22⋊C4C22⋊D711yescharacteristic
134C2×C22⋊C4C22⋊D711yescharacteristic
135C2×C42—141no—
136C2×C42C22⋊D712yes—
137C2×C42C22⋊D712yes—
138C22⋊C8—142no—
139C22⋊C8—142no—
140#95—21no—
141#95—22no—
142#95—21no—
143#95—22no—
144#95—22no—
145#95—142no—
146C22×C7—22no—
147C22×C7—21no—
148C22×C7—21no—
149C22×C7—22no—
150C22×C7—22no—
151C22×C7—81no—
152C22×C7—81no—
153C22×C7#39311yescharacteristic
154C22×C7#45811yescharacteristic
155C22×C7#45811yescharacteristic
156C4×C7—22no—
157C4×C7—22no—
158C4×C7—44no—
159C4×C7—82no—
160C4×C7—81no—
161C4×C7—81no—
162Dic7—82no—
163Dic7—161no—
164C24C2×C22⋊D711yescharacteristic
165C2×Q8—44no—
166C2×Q8—81no—
167C22×C4—22no—
168C22×C4—21no—
169C22×C4—22no—
170C22×C4—21no—
171C22×C4—41no—
172C22×C4—41no—
173C22×C4—142no—
174C22×C4—281no—
175C22×C4Q8×D711yescharacteristic
176C22×C4#116112yes—
177C22×C4#116111yescharacteristic
178C22×C4C2×C22⋊D712yes—
179M16—282no—
180M16—282no—
181C2×C8—282no—
182C4⋊C4—44no—
183C4⋊C4—81no—
184C4⋊C4—144no—
185C22⋊C4—44no—
186C22⋊C4—41no—
187C22⋊C4—41no—
188C22⋊C4—281no—
189C22⋊C4—281no—
190C22⋊C4—281no—
191C22⋊C4—281no—
192C42—42no—
193C42—42no—
194C42—282no—
195C2×C7—21no—
196C2×C7—21no—
197C2×C7—41no—
198C2×C7—41no—
199C2×C7#203011yescharacteristic
200C2×C7#203112yes—
201C23—21no—
202C23—21no—
203C23—42no—
204C23#650911yescharacteristic
205C23#651011yescharacteristic
206C23#651611yescharacteristic
207Q8—84no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—24no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—282no—
224C2×C4—562no—
225C2×C4—561no—
226C2×C4—562no—
227C2×C4#650912yes—
228C2×C4#651012yes—
229C8—562no—
230C7#1038711yescharacteristic, complemented, Sylow
231C22—22no—
232C22—22no—
233C22—22no—
234C22—21no—
235C22—21no—
236C22—81no—
237C22—81no—
238C22#9000311yescharacteristic
239C22#9001511yescharacteristic
240C22#9001511yescharacteristic
241C4—22no—
242C4—22no—
243C4—44no—
244C4—81no—
245C4—82no—
246C4—81no—
247C4—562no—
248C4—1121no—
249C2—21no—
250C2—21no—
251C2—41no—
252C2—41no—
253C2#1172959612yes—
254C2#1172964811yescharacteristic
subgroupG/H
centerC22#90003
commutator, cosocleC23×C4×C7C23
FrattiniC23×C4C22×D7
FittingC7×#2607C2
socleC22×C7#393
prime radicalC24×C7C2×D4
hypercenter#2607D7
hypocenterC7#10387
LCSG ▷ C23×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2607

Complements

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

NH ≅ G/Ntype
33. C2×C4⋊Dic7Q8semidirect
230. C7#10387semidirect

Maximal subgroups

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

subgroupindex
C7×#26072
#117272882
#117271962
#117254352
#117254222
#103877