Finite Group Databasebeta

← #13264971

Subgroups — #13264971

Order 1792.

318 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 69 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#11739158C211yesmaximal, characteristic
2D7×#347C212yesmaximal, complemented
3C7×#1355C211yesmaximal, characteristic, complemented
4#11725589C211yesmaximal, characteristic, complemented
5#11725327C212yesmaximal, complemented
6#90407C411yescharacteristic
7#90379C411yescharacteristic
8C7×#490C2211yescharacteristic
9#89843C411yescharacteristic
10#89841C411yescharacteristic
11D7×M32—22no—
12#89544—22no—
13#89537—22no—
14D7×#97C2211yescharacteristic
15#89475C2211yescharacteristic
16C7×#347C2212yes—
17#89307—22no—
18#89261C2212yes—
19#11911—71nomaximal, Sylow
20C2×#1159—21no—
21C7×#127C2×C411yescharacteristic
22C7×#125C2×C411yescharacteristic
23#6501—41no—
24#6499—21no—
25D4×Dic7—41no—
26C2×C8×D7D412yes—
27#6459—41no—
28#6455—21no—
29#6451—21no—
30#6450—41no—
31C42×D7C2×C411yescharacteristic
32#6433C2×C411yescharacteristic
33#6432C2×C411yescharacteristic
34C7×M32—22no—
35C7×#102—22no—
36C7×#97C2311yescharacteristic
37#6406—22no—
38#6390—22no—
39#6389D412yes—
40#6386—22no—
41#6384—22no—
42#6377C2×C411yescharacteristic
43#6372—24no—
44D7×C16—24no—
45#3135—71no—
46C2×#347—72no—
47#1356—72no—
48#1355—71no—
49#1355D711yescharacteristic, complemented
50C2×C7×D4—21no—
51C2×C7×D4—41no—
52C2×C22⋊D7—41no—
53C22×Dic7—41no—
54#1159—42no—
55#1159—42no—
56C2×C4×D7—21no—
57C2×C4×D7C22⋊C411yescharacteristic
58C2×Dic14—21no—
59C2×Dic14—41no—
60C2×C7×C8C2×D412yes—
61C7×C4⋊C4—21no—
62C7×C4⋊C4—41no—
63C42×C7C22×C411yescharacteristic
64C22⋊Dic7—42no—
65(C2×D7)⋊C4—41no—
66C4⋊Dic7—21no—
67C4⋊Dic7—41no—
68Dic7⋊C4—41no—
69Dic7⋊C4—41no—
70C4×Dic7—21no—
71C4×Dic7—41no—
72C4×Dic7C22⋊C411yescharacteristic
73C2×C7⋊C8C22⋊C412yes—
74C8×D7—22no—
75C8×D7—22no—
76C7×C16—24no—
77C7⋊C16—24no—
78#533—71no—
79#532—71no—
80C2×M32—142no—
81#491—71no—
82#491—71no—
83#490—71no—
84#490C2×D711yescharacteristic
85#489—142no—
86#416—142no—
87C2×#97—71no—
88#347—72no—
89#347—142no—
90#347C2×D712yes—
91C23×C7—41no—
92C22×D7#10011yescharacteristic
93C7×D4—42no—
94C7×D4—82no—
95C2×C4×C7—21no—
96C2×C4×C7—41no—
97C2×C4×C7C2×C22⋊C411yescharacteristic
98C22⋊D7—82no—
99C2×Dic7—21no—
100C2×Dic7—41no—
101C2×Dic7—41no—
102C2×Dic7—81no—
103C2×Dic7—81no—
104C2×Dic7#10011yescharacteristic
105C4×D7—81no—
106C4×D7#10412yes—
107C4×D7#10412yes—
108Dic14—42no—
109Dic14—82no—
110C7×C8—22no—
111C7⋊C8—22no—
112C2×#41—141no—
113C22×C8—72no—
114C4⋊Q8—71no—
115C4⋊Q8—141no—
116#127C4×D711yescharacteristic
117#125—71no—
118#125C4×D711yescharacteristic
119#124—141no—
120C22⋊Q8—281no—
121#121—281no—
122C4×Q8—281no—
123C4×D4—281no—
124#117—141no—
125C2×C42—71no—
126M32—22no—
127M32—144no—
128M32—142no—
129C2×C16—144no—
130#103—142no—
131#103—142no—
132#102—22no—
133#102—142no—
134#97—72no—
135#97—71no—
136#97C22×D711yescharacteristic
137C22×C7—82no—
138C22×C7—81no—
139C22×C7C2×#10011yescharacteristic
140C2×D7—41no—
141C2×D7#32912yes—
142C4×C7—41no—
143C4×C7—81no—
144C4×C7C2×#10412yes—
145Dic7—41no—
146Dic7—81no—
147Dic7—81no—
148Dic7#32911yescharacteristic
149Dic7#32911yescharacteristic
150#41—282no—
151#41—282no—
152C2×Q8—141no—
153C2×Q8—281no—
154C2×D4—21no—
155C2×D4—41no—
156C2×D4—281no—
157C22×C4—71no—
158C22×C4—141no—
159C22×C4—281no—
160C2×C8—72no—
161C2×C8—142no—
162C2×C8—142no—
163C2×C8D4×D712yes—
164C4⋊C4—21no—
165C4⋊C4—41no—
166C4⋊C4—141no—
167C4⋊C4—281no—
168C4⋊C4—281no—
169C4⋊C4—281no—
170C22⋊C4—281no—
171C22⋊C4—282no—
172C42—71no—
173C42—141no—
174C42—281no—
175C42C2×C4×D711yescharacteristic
176C16—24no—
177C16—144no—
178C2×C7—21no—
179C2×C7—161no—
180C2×C7C2×#32911yescharacteristic
181D7—22no—
182C23—41no—
183C23—71no—
184Q8—282no—
185Q8—562no—
186D4—42no—
187D4—82no—
188D4—562no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—71no—
192C2×C4—72no—
193C2×C4—72no—
194C2×C4—141no—
195C2×C4—281no—
196C2×C4—281no—
197C2×C4—561no—
198C2×C4—561no—
199C2×C4—561no—
200C2×C4D7×C22⋊C411yescharacteristic
201C8—22no—
202C8—142no—
203C7#1191111yescharacteristic, complemented, Sylow
204C22—72no—
205C22—82no—
206C22—81no—
207C22—281no—
208C22D7×#10011yescharacteristic
209C4—41no—
210C4—71no—
211C4—71no—
212C4—81no—
213C4—281no—
214C4—561no—
215C4—561no—
216C4D7×#10412yes—
217C2—21no—
218C2—142no—
219C2—161no—
220C2D7×#32911yescharacteristic
subgroupG/H
centerC2D7×#329
commutatorC42×C7C22×C4
Frattini#97C22×D7
FittingC7×#1355C2
socleC2×C7C2×#329
prime radical#90407C4
cosocleC7×#97C23
hypercenter#1355D7
hypocenterC7#11911
LCSG ▷ C42×C7 ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #1355

Complements

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

NH ≅ G/Ntype
2. D7×#347C2semidirect
3. C7×#1355C2semidirect
4. #11725589C2semidirect
5. #11725327C2semidirect
49. #1355D7semidirect
203. C7#11911semidirect

Maximal subgroups

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

subgroupindex
#117391582
D7×#3472
C7×#13552
#117255892
#117253272
#119117