Finite Group Databasebeta

← #13264991

Subgroups — #13264991

Order 1792.

274 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 61 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#11739184C211yesmaximal, characteristic
2#11726842C212yesmaximal
3C7×#1356C211yesmaximal, characteristic, complemented
4#11725591C211yesmaximal, characteristic, complemented
5#11725327C212yesmaximal, complemented
6D7×C4⋊Q8C411yescharacteristic
7#90379C411yescharacteristic
8C7×#491C2211yescharacteristic
9#89854C411yescharacteristic
10#89841C411yescharacteristic
11#89574—22no—
12#89564—22no—
13#89479C2211yescharacteristic
14#89475C2211yescharacteristic
15C7×#347C2212yes—
16#89309—22no—
17#89306—22no—
18#89261C2212yes—
19#11916—71nomaximal, Sylow
20C2×Q8×D7—21no—
21C7×C4⋊Q8C2×C411yescharacteristic
22C7×#125C2×C411yescharacteristic
23#6507—21no—
24C2×#1131D412yes—
25#6459—41no—
26#6455—21no—
27D7×C4⋊C4—41no—
28#6451—21no—
29#6451—41no—
30#6450—41no—
31C42×D7C2×C411yescharacteristic
32#6433C2×C411yescharacteristic
33#6432C2×C411yescharacteristic
34C7×M32—22no—
35C7×#103—22no—
36C7×#97C2311yescharacteristic
37#6409—22no—
38#6390—22no—
39C8×Dic7D412yes—
40#6386—22no—
41#6384—22no—
42#6377C2×C411yescharacteristic
43#3139—71no—
44#2165—72no—
45#1356—71no—
46#1356—72no—
47#1356D711yescharacteristic, complemented
48C2×C7×Q8—21no—
49Q8×D7—44no—
50C2×C4×D7—21no—
51C2×C4×D7—41no—
52C2×C4×D7C22⋊C411yescharacteristic
53C2×Dic14—21no—
54C2×Dic14—41no—
55C2×Dic14—41no—
56C2×C7×C8C2×D412yes—
57C7×C4⋊C4—21no—
58C7×C4⋊C4—41no—
59C7×C4⋊C4—41no—
60C42×C7C22×C411yescharacteristic
61(C2×D7)⋊C4—41no—
62C4⋊Dic7—21no—
63C4⋊Dic7—41no—
64Dic7⋊C4—41no—
65Dic7⋊C4—42no—
66Dic7⋊C4—41no—
67C4×Dic7—21no—
68C4×Dic7—41no—
69C4×Dic7C22⋊C411yescharacteristic
70C2×C7⋊C8C22⋊C412yes—
71#1131—42no—
72C7×C16—42no—
73C7⋊C16—42no—
74#533—71no—
75C2×C4⋊Q8—71no—
76#491—71no—
77#491—71no—
78#491—71no—
79#491C2×D711yescharacteristic
80#487—142no—
81#419—142no—
82C4×M16—71no—
83#364—142no—
84#349—142no—
85#347—72no—
86#347C2×D712yes—
87C22×D7#10011yescharacteristic
88C7×Q8—42no—
89C2×C4×C7—21no—
90C2×C4×C7—41no—
91C2×C4×C7—41no—
92C2×C4×C7C2×C22⋊C411yescharacteristic
93C2×Dic7—21no—
94C2×Dic7—41no—
95C2×Dic7—41no—
96C2×Dic7#10011yescharacteristic
97C4×D7—22no—
98C4×D7—42no—
99C4×D7—82no—
100Dic14—42no—
101Dic14—82no—
102Dic14—82no—
103C7×C8—22no—
104C7⋊C8—22no—
105C22×Q8—141no—
106C2×M16—72no—
107C4⋊Q8—71no—
108C4⋊Q8—141no—
109C4⋊Q8—141no—
110C4⋊Q8—281no—
111C4⋊Q8C4×D711yescharacteristic
112#125—71no—
113#125C4×D711yescharacteristic
114C22⋊Q8—281no—
115C4×Q8—281no—
116#117—141no—
117C2×C4⋊C4—281no—
118C2×C42—71no—
119M32—22no—
120M32—142no—
121#103—22no—
122#103—142no—
123#103—142no—
124#103—142no—
125#97—71no—
126#97C22×D711yescharacteristic
127C4×C8—72no—
128C22×C7C2×#10011yescharacteristic
129C2×D7—21no—
130C2×D7—41no—
131C4×C7—41no—
132C4×C7—81no—
133C4×C7—81no—
134C4×C7#42112yes—
135Dic7—22no—
136Dic7—21no—
137Dic7—81no—
138Dic7—81no—
139C2×Q8—21no—
140C2×Q8—141no—
141C2×Q8—281no—
142C2×Q8—281no—
143C2×Q8—284no—
144C22×C4—71no—
145C22×C4—141no—
146C22×C4—281no—
147M16—282no—
148C2×C8—72no—
149C2×C8D4×D712yes—
150C4⋊C4—21no—
151C4⋊C4—41no—
152C4⋊C4—41no—
153C4⋊C4—141no—
154C4⋊C4—281no—
155C4⋊C4—281no—
156C4⋊C4—282no—
157C4⋊C4—281no—
158C22⋊C4—281no—
159C42—71no—
160C42—141no—
161C42—281no—
162C42C2×C4×D711yescharacteristic
163C16—42no—
164C16—282no—
165C2×C7—21no—
166C2×C7#153311yescharacteristic
167D7—41no—
168C23—71no—
169Q8—42no—
170Q8—282no—
171Q8—562no—
172Q8—562no—
173C2×C4—21no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—71no—
177C2×C4—141no—
178C2×C4—142no—
179C2×C4—282no—
180C2×C4—281no—
181C2×C4—281no—
182C2×C4—562no—
183C2×C4D7×C22⋊C411yescharacteristic
184C8—22no—
185C8—142no—
186C7#1191611yescharacteristic, complemented, Sylow
187C22—141no—
188C22—281no—
189C22D7×#10011yescharacteristic
190C4—41no—
191C4—81no—
192C4—81no—
193C4—142no—
194C4—141no—
195C4—561no—
196C4—561no—
197C4#8959312yes—
198C2—21no—
199C2—281no—
200C2#1172610111yescharacteristic
subgroupG/H
centerC2#11726101
commutatorC42×C7C22×C4
Frattini#97C22×D7
FittingC7×#1356C2
socleC2×C7#1533
prime radicalC22×D7#100
cosocleC7×#97C23
hypercenter#1356D7
hypocenterC7#11916
LCSG ▷ C42×C7 ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #1356

Complements

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

NH ≅ G/Ntype
3. C7×#1356C2semidirect
4. #11725591C2semidirect
5. #11725327C2semidirect
47. #1356D7semidirect
186. C7#11916semidirect

Maximal subgroups

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

subgroupindex
#117391842
#117268422
C7×#13562
#117255912
#117253272
#119167