Finite Group Databasebeta

← #23771470

Subgroups — #23771470

Order 10112.

380 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 125 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
1C2×#14579152C211yesmaximal, characteristic
2C2×#14579151C211yesmaximal, characteristic
3#19098505C212yesmaximal
4#19098503C211yesmaximal, characteristic
5#19098502C211yesmaximal, characteristic
6#19098497C212yesmaximal
7#19098496C212yesmaximal
8#19098494C211yesmaximal, characteristic
9#19098494C212yesmaximal
10#19098427C211yesmaximal, characteristic
11#398×C79C211yesmaximal, characteristic
12#14579152—24no—
13#14579151—24no—
14C2×C4⋊Dic79C2212yes—
15C2×C4⋊Dic79C2211yescharacteristic
16C2×C4⋊Dic79C2211yescharacteristic
17C2×Dic79⋊C4C2211yescharacteristic
18C2×Dic79⋊C4C2212yes—
19C2×Dic79⋊C4C2211yescharacteristic
20C2×Dic79⋊C4C2211yescharacteristic
21C2×Dic79⋊C4C2211yescharacteristic
22C2×Dic79⋊C4C2212yes—
23C2×Dic79⋊C4C2212yes—
24C2×C4×Dic79C2211yescharacteristic
25C79⋊#95C2211yescharacteristic
26C79⋊#95C2212yes—
27C79⋊#95C2212yes—
28C79⋊#95C2212yes—
29C79⋊#95C2212yes—
30C79⋊#95C2212yes—
31C79⋊#95C2212yes—
32C2×C4⋊C4×C79C2211yescharacteristic
33C2×C4⋊C4×C79C2211yescharacteristic
34C2×C4⋊C4×C79C2212yes—
35#95×C79C2211yescharacteristic
36#95×C79C2212yes—
37C22×Dic79C2312yes—
38C22×Dic79C2311yescharacteristic
39C22×Dic79C2312yes—
40C22×Dic79C2311yescharacteristic
41C22×Dic79C2311yescharacteristic
42C22×Dic79C2311yescharacteristic
43C4⋊Dic79—22no—
44C4⋊Dic79—24no—
45C4⋊Dic79—22no—
46Dic79⋊C4—22no—
47Dic79⋊C4—22no—
48Dic79⋊C4—22no—
49Dic79⋊C4—24no—
50Dic79⋊C4—22no—
51Dic79⋊C4—42no—
52Dic79⋊C4—42no—
53C4×Dic79D414yes—
54C22×C4×C79C2312yes—
55C22×C4×C79C2311yescharacteristic
56C22×C4×C79C2312yes—
57C22×C4×C79C2311yescharacteristic
58C22×C4×C79C2311yescharacteristic
59C4⋊C4×C79—22no—
60C4⋊C4×C79—22no—
61C4⋊C4×C79—42no—
62C23×C79C2411yescharacteristic
63C2×C4×C79—22no—
64C2×C4×C79—21no—
65C2×C4×C79—21no—
66C2×C4×C79—22no—
67C2×C4×C79—22no—
68C2×C4×C79—22no—
69C2×C4×C79—21no—
70C2×C4×C79—22no—
71C2×C4×C79—22no—
72C2×C4×C79—21no—
73C2×C4×C79—22no—
74C2×C4×C79—22no—
75C2×C4×C79C2×D412yes—
76C2×Dic79—21no—
77C2×Dic79—21no—
78C2×Dic79—22no—
79C2×Dic79—21no—
80C2×Dic79—21no—
81C2×Dic79—22no—
82C2×Dic79—21no—
83C2×Dic79—22no—
84C2×Dic79—22no—
85C2×Dic79—21no—
86C2×Dic79—22no—
87C2×Dic79—24no—
88C2×Dic79—22no—
89C2×Dic79C2×D412yes—
90C2×Dic79C2×D412yes—
91C22×C79C22×D411yescharacteristic
92C22×C79H(5,𝔽2)11yescharacteristic
93C22×C792−1+412yes—
94C22×C792−1+411yescharacteristic
95C22×C792−1+412yes—
96C4×C79—22no—
97C4×C79—41no—
98C4×C79—41no—
99C4×C79—42no—
100C4×C79—42no—
101Dic79—22no—
102Dic79—22no—
103Dic79—42no—
104Dic79—41no—
105Dic79—41no—
106Dic79—42no—
107C2×C79#53611yescharacteristic
108C2×C79#53611yescharacteristic
109C2×C79#53711yescharacteristic
110C2×C79#56312yes—
111C2×C79#56412yes—
112#2822—791nomaximal, Sylow
113C79#282211yescharacteristic, complemented, Sylow
114C2×#125—791no—
115C2×#125—791no—
116#400—791no—
117#400—791no—
118#400—792no—
119#398—791no—
120#398—792no—
121#398—792no—
122#398—792no—
123#398D7911yescharacteristic
124#382—791no—
125#125—1584no—
126#125—1584no—
127C2×C4⋊C4—792no—
128C2×C4⋊C4—792no—
129C2×C4⋊C4—791no—
130C2×C4⋊C4—791no—
131C2×C4⋊C4—792no—
132C2×C4⋊C4—791no—
133C2×C4⋊C4—791no—
134C2×C4⋊C4—792no—
135C2×C4⋊C4—791no—
136C2×C4⋊C4—791no—
137C2×C4⋊C4C2×D7911yescharacteristic
138C2×C4⋊C4C2×D7911yescharacteristic
139C2×C4⋊C4C2×D7912yes—
140C2×C42—791no—
141#95—792no—
142#95—791no—
143#95—792no—
144#95—792no—
145#95—792no—
146#95—792no—
147#95—792no—
148#95C2×D7911yescharacteristic
149#95C2×D7912yes—
150C22×C4—791no—
151C22×C4—791no—
152C22×C4—792no—
153C22×C4—791no—
154C22×C4—792no—
155C22×C4—791no—
156C22×C4C22×D7912yes—
157C22×C4C22×D7911yescharacteristic
158C22×C4C22×D7911yescharacteristic
159C22×C4C22×D7912yes—
160C22×C4C22×D7911yescharacteristic
161C4⋊C4—22no—
162C4⋊C4—22no—
163C4⋊C4—42no—
164C4⋊C4—3162no—
165C4⋊C4—3162no—
166C4⋊C4—1582no—
167C4⋊C4—1582no—
168C4⋊C4—1582no—
169C4⋊C4—1584no—
170C4⋊C4—1582no—
171C4⋊C4—1584no—
172C4⋊C4—1582no—
173C4⋊C4—1582no—
174C42—794no—
175C23C23×D7911yescharacteristic
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—22no—
187C2×C4—21no—
188C2×C4—792no—
189C2×C4—792no—
190C2×C4—1581no—
191C2×C4—1582no—
192C2×C4—1581no—
193C2×C4—1582no—
194C2×C4—1582no—
195C2×C4—1584no—
196C2×C4—1582no—
197C2×C4—1582no—
198C2×C4—1581no—
199C2×C4—1581no—
200C2×C4—1581no—
201C2×C4—1581no—
202C2×C4—1582no—
203C2×C4D4×D7912yes—
204C22C2×D4×D7911yescharacteristic
205C22#1457920611yescharacteristic
206C22#1457920811yescharacteristic
207C22#1457920812yes—
208C22#1457920912yes—
209C4—22no—
210C4—41no—
211C4—42no—
212C4—42no—
213C4—41no—
214C4—3162no—
215C4—3161no—
216C4—3162no—
217C4—3161no—
218C4—1582no—
219C4—1582no—
220C2#1909913511yescharacteristic
221C2#1909913811yescharacteristic
222C2#1909914211yescharacteristic
223C2#1909931412yes—
224C2C79⋊#56412yes—
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, prime radical, cosocleC23×C79C24
Fitting#398×C79C2
hypercenter#398D79
hypocenterC79#2822
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
113. C79#2822semidirect