Finite Group Databasebeta

← #13258296

Subgroups — #13258296

Order 1792.

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

normal subgroups only

This group has 374 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
1#11731663C211yesmaximal, characteristic
2C7×#1847C211yesmaximal, characteristic
3#11727329C212yesmaximal
4#11725465C212yesmaximal
5#11725436C211yesmaximal, characteristic
6C2×C7×#107—21no—
7C2×C7×#106—21no—
8C2×C7×#97C2211yescharacteristic
9C7×#384C2211yescharacteristic
10C7×#382C2211yescharacteristic
11#89758—21no—
12#89751—21no—
13#89708C2212yes—
14C2×#6377C2212yes—
15#89432—22no—
16#89428—22no—
17#89324—22no—
18#89324—22no—
19#10584—71nomaximal, Sylow
20C22×Dic14—21no—
21C22×C7×C8—21no—
22C2×C7×C4⋊C4—21no—
23C2×C7×C4⋊C4—22no—
24C2×C7×C4⋊C4D411yescharacteristic
25C2×C7×C4⋊C4D411yescharacteristic
26C2×C42×C7C2311yescharacteristic
27C2×C4⋊Dic7—21no—
28C2×C4⋊Dic7D412yes—
29C2×C4⋊Dic7D412yes—
30C2×Dic7⋊C4—22no—
31C22×C7⋊C8—22no—
32C7×#107—42no—
33C7×#106—42no—
34C7×#97—21no—
35C7×#97Q812yescomplemented
36C7×#95—22no—
37C7⋊#95—22no—
38C7⋊#95—21no—
39C7⋊#95—21no—
40C7⋊#95—22no—
41C7⋊#95—22no—
42#6377—22no—
43#6377Q814yescomplemented
44#2844—71no—
45#1847D711yescharacteristic
46#1836—72no—
47#1295—72no—
48#1295—71no—
49C22×C4×C7—21no—
50C22×C4×C7—21no—
51C22×C4×C7—41no—
52C22×C4×C7C2×D412yes—
53C22×C4×C7C2×D411yescharacteristic
54C22×Dic7—22no—
55C22×Dic7—22no—
56C2×Dic14—81no—
57C2×Dic14—82no—
58C2×C7×C8—22no—
59C2×C7×C8—22no—
60C2×C7×C8—22no—
61C7×C4⋊C4—41no—
62C7×C4⋊C4—41no—
63C7×C4⋊C4—41no—
64C7×C4⋊C4—41no—
65C7×C4⋊C4—44no—
66C42×C7C2×Q811yescharacteristic
67C42×C7C2×Q812yes—
68C42×C7#4111yescharacteristic
69C4⋊Dic7—42no—
70C4⋊Dic7—42no—
71C4⋊Dic7—81no—
72Dic7⋊C4—82no—
73C2×C7⋊C8—24no—
74C2×C7⋊C8—42no—
75C2×C7⋊C8—42no—
76C2×#107—21no—
77C2×#106—21no—
78C2×#97—72no—
79C2×#97C2×D711yescharacteristic
80#400—142no—
81#400—141no—
82#395—142no—
83#395—141no—
84#384C2×D711yescharacteristic
85#382—72no—
86#382C2×D711yescharacteristic
87#340—142no—
88#340—142no—
89C23×C7#12011yescharacteristic
90C2×C4×C7—21no—
91C2×C4×C7—22no—
92C2×C4×C7—22no—
93C2×C4×C7—21no—
94C2×C4×C7—41no—
95C2×C4×C7—41no—
96C2×C4×C7—42no—
97C2×C4×C7—42no—
98C2×C4×C7—81no—
99C2×C4×C7—82no—
100C2×C4×C7C22⋊Q812yes—
101C2×C4×C7C22⋊Q811yescharacteristic
102C2×C4×C7C4⋊Q812yes—
103C2×C4×C7C4⋊Q811yescharacteristic
104C2×Dic7—42no—
105C2×Dic7—42no—
106C2×Dic7—42no—
107C2×Dic7—42no—
108C2×Dic7—42no—
109C2×Dic7—42no—
110Dic14—84no—
111C7×C8—24no—
112C7⋊C8—44no—
113C22×Q8—141no—
114C22×C8—21no—
115C22×C8—142no—
116C2×C4⋊C4—22no—
117C2×C4⋊C4—21no—
118C2×C4⋊C4—72no—
119C2×C4⋊C4—72no—
120C2×C4⋊C4—142no—
121C2×C4⋊C4—141no—
122C2×C4⋊C4C22⋊D711yescharacteristic
123C2×C4⋊C4C22⋊D711yescharacteristic
124C2×C42C22×D711yescharacteristic
125#107—42no—
126#106—42no—
127#97—21no—
128#97—74no—
129#97—142no—
130#97Dic1412yescomplemented
131#95—22no—
132#95—142no—
133#95—141no—
134#95—141no—
135#95—142no—
136#95—142no—
137C22×C7#39511yescharacteristic
138C22×C7#45311yescharacteristic
139C22×C7#45412yes—
140C22×C7#45512yes—
141C22×C7#45611yescharacteristic
142C4×C7—21no—
143C4×C7—21no—
144C4×C7—22no—
145C4×C7—22no—
146C4×C7—81no—
147C4×C7—81no—
148C4×C7—161no—
149Dic7—82no—
150Dic7—82no—
151C2×Q8—562no—
152C2×Q8—561no—
153C22×C4—21no—
154C22×C4—21no—
155C22×C4—41no—
156C22×C4—142no—
157C22×C4—142no—
158C22×C4D4×D712yes—
159C22×C4C2×C22⋊D711yescharacteristic
160C2×C8—22no—
161C2×C8—22no—
162C2×C8—22no—
163C2×C8—144no—
164C2×C8—282no—
165C2×C8—282no—
166C4⋊C4—41no—
167C4⋊C4—41no—
168C4⋊C4—41no—
169C4⋊C4—41no—
170C4⋊C4—44no—
171C4⋊C4—282no—
172C4⋊C4—282no—
173C4⋊C4—562no—
174C4⋊C4—561no—
175C42C2×Dic1411yescharacteristic
176C42#115711yescharacteristic
177C42Q8×D712yes—
178C2×C7#165711yescharacteristic
179C2×C7#165911yescharacteristic
180C2×C7#166412yes—
181C2×C7#206011yescharacteristic
182C2×C7#206112yes—
183C23#650011yescharacteristic
184Q8—564no—
185C2×C4—21no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—21no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—82no—
194C2×C4—81no—
195C2×C4—282no—
196C2×C4—282no—
197C2×C4—282no—
198C2×C4—282no—
199C2×C4—282no—
200C2×C4—282no—
201C2×C4#645112yes—
202C2×C4#645912yes—
203C2×C4#648711yescharacteristic
204C2×C4#650711yescharacteristic
205C8—24no—
206C8—284no—
207C7#1058411yescharacteristic, complemented, Sylow
208C22#8975111yescharacteristic
209C22#8984911yescharacteristic
210C22#8986711yescharacteristic
211C22#8997312yes—
212C22#8997412yes—
213C4—22no—
214C4—22no—
215C4—21no—
216C4—21no—
217C4—81no—
218C4—81no—
219C4—161no—
220C4—562no—
221C4—562no—
222C2#1172732711yescharacteristic
223C2#1172842112yes—
224C2#1172908211yescharacteristic
225C2#1172908311yescharacteristic
226C2#1172914812yes—
subgroupG/H
centerC23#6500
commutator, cosocleC2×C42×C7C23
FrattiniC2×C42C22×D7
FittingC7×#1847C2
socle, prime radicalC23×C7#120
hypercenter#1847D7
hypocenterC7#10584
LCSG ▷ C2×C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1847

Complements

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

NH ≅ G/Ntype
35. C7×#97Q8semidirect
43. #6377Q8semidirect
130. #97Dic14semidirect
207. C7#10584semidirect

Maximal subgroups

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

subgroupindex
#117316632
C7×#18472
#117273292
#117254652
#117254362
#105847