Finite Group Databasebeta

← #23769347

Subgroups — #23769347

Order 10112.

416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14579160C211yesmaximal, characteristic
2C2×#14579151C211yesmaximal, characteristic
3#19098505C212yesmaximal
4#19098504C212yesmaximal
5#19098503C211yesmaximal, characteristic
6#19098502C211yesmaximal, characteristic
7#19098501C211yesmaximal, characteristic
8#19098467C212yesmaximal
9#19098467C212yesmaximal
10#19098408C211yesmaximal, characteristic
11#400×C79C211yesmaximal, characteristic
12C22×Dic158C2212yes—
13#14579160—24no—
14#14579151—24no—
15C2×C4⋊Dic79C2211yescharacteristic
16C2×C4⋊Dic79C2211yescharacteristic
17C2×Dic79⋊C4C2211yescharacteristic
18C2×Dic79⋊C4C2211yescharacteristic
19C2×Dic79⋊C4C2211yescharacteristic
20C2×Dic79⋊C4C2211yescharacteristic
21C2×Dic79⋊C4C2212yes—
22C2×C4×Dic79C2212yes—
23C2×C4×Dic79C2211yescharacteristic
24C79⋊#95C2211yescharacteristic
25C79⋊#95C2212yes—
26C79⋊#95C2212yes—
27C79⋊#95C2212yes—
28C79⋊#95C2212yes—
29C79⋊#95C2212yes—
30C79⋊#95C2212yes—
31C79⋊#95C2212yes—
32C2×C4⋊C4×C79C2211yescharacteristic
33C2×C4⋊C4×C79C2211yescharacteristic
34#95×C79C2211yescharacteristic
35#95×C79C2212yes—
36#95×C79C2212yes—
37C2×Dic158—24no—
38C2×Dic158—28no—
39C22×Dic79C2312yes—
40C22×Dic79C2312yes—
41C22×Dic79C2311yescharacteristic
42C22×Dic79C2311yescharacteristic
43C22×Dic79C2311yescharacteristic
44C22×Dic79C2311yescharacteristic
45C4⋊Dic79—22no—
46C4⋊Dic79—22no—
47Dic79⋊C4—22no—
48Dic79⋊C4—22no—
49Dic79⋊C4—22no—
50Dic79⋊C4—24no—
51Dic79⋊C4—22no—
52C4×Dic79—24no—
53C4×Dic79D414yes—
54C22×C4×C79C2312yes—
55C22×C4×C79C2312yes—
56C22×C4×C79C2311yescharacteristic
57C22×C4×C79C2311yescharacteristic
58C22×C4×C79C2311yescharacteristic
59C4⋊C4×C79—22no—
60C4⋊C4×C79—22no—
61C23×C79C2411yescharacteristic
62C2×C4×C79—22no—
63C2×C4×C79—21no—
64C2×C4×C79—21no—
65C2×C4×C79—22no—
66C2×C4×C79—22no—
67C2×C4×C79—24no—
68C2×C4×C79—21no—
69C2×C4×C79—22no—
70C2×C4×C79—22no—
71C2×C4×C79—22no—
72C2×C4×C79—21no—
73C2×C4×C79C2×D412yes—
74C2×Dic79—21no—
75C2×Dic79—21no—
76C2×Dic79—21no—
77C2×Dic79—21no—
78C2×Dic79—22no—
79C2×Dic79—22no—
80C2×Dic79—24no—
81C2×Dic79—22no—
82C2×Dic79—21no—
83C2×Dic79—22no—
84C2×Dic79—21no—
85C2×Dic79—22no—
86C2×Dic79C2×D412yes—
87C2×Dic79C2×D412yes—
88C2×Dic79#4114yes—
89Dic158—48no—
90C22×C79C22×D411yescharacteristic
91C22×C79C2×#4112yes—
92C22×C792−1+411yescharacteristic
93C22×C792−1+412yes—
94C22×C792−1+411yescharacteristic
95C4×C79—22no—
96C4×C79—42no—
97C4×C79—41no—
98C4×C79—41no—
99C4×C79—42no—
100Dic79—22no—
101Dic79—42no—
102Dic79—41no—
103Dic79—41no—
104Dic79—42no—
105Dic79#12414yes—
106C2×C79C2×#12411yescharacteristic
107C2×C79#53611yescharacteristic
108C2×C79#53611yescharacteristic
109C2×C79#54112yes—
110C2×C79#54112yes—
111#2642—791nomaximal, Sylow
112C79#264211yescharacteristic, complemented, Sylow
113C2×C4⋊Q8—791no—
114C2×#125—791no—
115#400—791no—
116#400—791no—
117#400—791no—
118#400—792no—
119#400—792no—
120#400D7911yescharacteristic
121#391—792no—
122#391—792no—
123#376—791no—
124C22×Q8—792no—
125C4⋊Q8—1584no—
126#125—1584no—
127C2×C4⋊C4—791no—
128C2×C4⋊C4—791no—
129C2×C4⋊C4—791no—
130C2×C4⋊C4—791no—
131C2×C4⋊C4—791no—
132C2×C4⋊C4—792no—
133C2×C4⋊C4—791no—
134C2×C4⋊C4C2×D7911yescharacteristic
135C2×C4⋊C4C2×D7911yescharacteristic
136C2×C42—791no—
137C2×C42—792no—
138#95—792no—
139#95—791no—
140#95—792no—
141#95—792no—
142#95—792no—
143#95—792no—
144#95—792no—
145#95—792no—
146#95C2×D7911yescharacteristic
147#95C2×D7912yes—
148#95C2×D7912yes—
149C2×Q8—1584no—
150C2×Q8—1588no—
151C22×C4—791no—
152C22×C4—791no—
153C22×C4—792no—
154C22×C4—791no—
155C22×C4—791no—
156C22×C4—792no—
157C22×C4C22×D7912yes—
158C22×C4C22×D7911yescharacteristic
159C22×C4C22×D7911yescharacteristic
160C22×C4C22×D7912yes—
161C22×C4C22×D7911yescharacteristic
162C4⋊C4—22no—
163C4⋊C4—22no—
164C4⋊C4—1582no—
165C4⋊C4—1582no—
166C4⋊C4—1582no—
167C4⋊C4—1584no—
168C4⋊C4—1582no—
169C4⋊C4—1582no—
170C4⋊C4—1582no—
171C42—794no—
172C42—1584no—
173C23C23×D7911yescharacteristic
174Q8—3168no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—24no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—794no—
187C2×C4—792no—
188C2×C4—792no—
189C2×C4—1582no—
190C2×C4—1584no—
191C2×C4—1581no—
192C2×C4—1582no—
193C2×C4—1582no—
194C2×C4—1581no—
195C2×C4—1582no—
196C2×C4—1581no—
197C2×C4—1581no—
198C2×C4—1582no—
199C2×C4—1581no—
200C2×C4—1581no—
201C2×C4D4×D7912yes—
202C22C2×D4×D7911yescharacteristic
203C22#41×D7912yes—
204C22#1457920811yescharacteristic
205C22#1457920812yes—
206C22#1457920911yescharacteristic
207C4—22no—
208C4—41no—
209C4—42no—
210C4—42no—
211C4—41no—
212C4—3161no—
213C4—3162no—
214C4—3162no—
215C4—3161no—
216C4—794no—
217C4—1582no—
218C2#124×D7911yescharacteristic
219C2#1909913511yescharacteristic
220C2#1909913611yescharacteristic
221C2#1909917012yes—
222C2#1909917212yes—
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, prime radical, cosocleC23×C79C24
Fitting#400×C79C2
hypercenter#400D79
hypocenterC79#2642
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
112. C79#2642semidirect