Finite Group Databasebeta

← #23776205

Subgroups — #23776205

Order 10112.

326 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 123 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#19099292C211yesmaximal, characteristic
2#19099291C211yesmaximal, characteristic
3#19098932C212yesmaximal
4#19098914C211yesmaximal, characteristic
5#19098871C212yesmaximal
6#19098849C211yesmaximal, characteristic
7#19098774C211yesmaximal, characteristic
8#19098774C212yesmaximal
9#19098671C212yesmaximal
10C4×Dic316C211yesmaximal, characteristic
11#446×C79C211yesmaximal, characteristic
12C2×Dic316C2211yescharacteristic
13C2×Dic316C2212yes—
14#14579161C2211yescharacteristic
15#14579161C2212yes—
16#14579161C2211yescharacteristic
17#14579159—21no—
18#14579153C2212yes—
19#14579152—21no—
20#14579152—22no—
21#14579151—22no—
22Q8×Dic79—21no—
23C4×Dic158C2211yescharacteristic
24C4×Dic158C2211yescharacteristic
25C4×Dic158C2212yes—
26C4×Dic158C2212yes—
27#14579126—21no—
28#14579095C2211yescharacteristic
29#14579093C2212yes—
30#14579086C2212yes—
31#14579086C2212yes—
32#14579086C2211yescharacteristic
33#14579086C2211yescharacteristic
34#14579086C2212yes—
35#14579086C2212yes—
36C4×Q8×C79C2211yescharacteristic
37C4⋊C8×C79C2211yescharacteristic
38C4⋊C8×C79C2212yes—
39#97×C79C2212yes—
40C4×C8×C79C2211yescharacteristic
41C2×Dic158—21no—
42C2×Dic158C2312yes—
43C2×Dic158C2311yescharacteristic
44C2×Dic158C2311yescharacteristic
45Dic316—22no—
46Dic316—24no—
47C4⋊Dic79—22no—
48C4⋊Dic79—21no—
49C4⋊Dic79—21no—
50C4⋊Dic79—22no—
51C4⋊Dic79—21no—
52C4⋊Dic79C2312yes—
53C4⋊Dic79C2311yescharacteristic
54C4⋊Dic79C2311yescharacteristic
55Dic79⋊C4—22no—
56Dic79⋊C4—21no—
57Dic79⋊C4—22no—
58Dic79⋊C4—22no—
59Dic79⋊C4—21no—
60Dic79⋊C4—22no—
61C4×Dic79—22no—
62C4×Dic79—21no—
63C4×Dic79—22no—
64C4×Dic79—21no—
65C2×Q8×C79D411yescharacteristic
66C2×C8×C79C2311yescharacteristic
67C2×C8×C79C2311yescharacteristic
68C2×C8×C79C2312yes—
69C4⋊C4×C79D411yescharacteristic
70C4⋊C4×C79D412yes—
71C42×C79C2311yescharacteristic
72C42×C79C2312yes—
73Q8×C79—22no—
74C2×C4×C79C2×D412yes—
75C2×C4×C79C2×D412yes—
76C2×C4×C79C2×D411yescharacteristic
77C2×C4×C79C2×D411yescharacteristic
78C2×C4×C79C2411yescharacteristic
79C2×Dic79—21no—
80C2×Dic79—21no—
81C2×Dic79—21no—
82C2×Dic79—22no—
83C2×Dic79—22no—
84C2×Dic79—21no—
85Dic158—21no—
86Dic158—21no—
87Dic158—22no—
88Dic158—22no—
89Dic158—21no—
90Dic158—42no—
91Dic158#4112yes—
92C8×C79—21no—
93C8×C79—22no—
94C8×C79—21no—
95C22×C79C22×D411yescharacteristic
96C4×C79—22no—
97C4×C79—22no—
98C4×C79—21no—
99C4×C79#13712yes—
100C4×C79C2×#4111yescharacteristic
101C4×C792−1+411yescharacteristic
102Dic79—22no—
103Dic79—41no—
104Dic79—42no—
105Dic79—42no—
106Dic79—41no—
107Dic79—41no—
108C2×C79#54811yescharacteristic
109C2×C79C2×#13711yescharacteristic
110C2×C79#57811yescharacteristic
111#3374—791nomaximal, Sylow
112C79#337411yescharacteristic, complemented, Sylow
113#557—791no—
114#557—791no—
115#491—792no—
116#487—791no—
117#479—792no—
118#475—791no—
119#462—792no—
120#462—791no—
121#446D7911yescharacteristic
122#441—792no—
123C4×Q16—791no—
124C2×Q16—791no—
125C2×Q16—792no—
126C4⋊Q8—791no—
127C4⋊Q8—791no—
128C4⋊Q8—792no—
129C4⋊Q8—1581no—
130#125—792no—
131#125—1582no—
132#125—1581no—
133#125—1582no—
134C4×Q8—791no—
135C4×Q8—791no—
136C4×Q8—792no—
137C4×Q8—792no—
138C4×Q8—1581no—
139C4×Q8—1581no—
140C4×Q8C2×D7911yescharacteristic
141#107—791no—
142#106—792no—
143C4⋊C8C2×D7911yescharacteristic
144C4⋊C8C2×D7912yes—
145#103—791no—
146#103—791no—
147#103—792no—
148#103—792no—
149#103—792no—
150#103—792no—
151#97C2×D7912yes—
152C4×C8C2×D7911yescharacteristic
153C2×Q8—791no—
154C2×Q8—791no—
155C2×Q8—792no—
156C2×Q8—1581no—
157C2×Q8D31611yescharacteristic
158Q16—1582no—
159Q16—1584no—
160C2×C8C22×D7911yescharacteristic
161C2×C8C22×D7911yescharacteristic
162C2×C8C22×D7912yes—
163C4⋊C4—792no—
164C4⋊C4—791no—
165C4⋊C4—791no—
166C4⋊C4—1582no—
167C4⋊C4—1581no—
168C4⋊C4—1581no—
169C4⋊C4—1582no—
170C4⋊C4—1582no—
171C4⋊C4—1582no—
172C4⋊C4—1582no—
173C4⋊C4—1581no—
174C4⋊C4—1581no—
175C4⋊C4—1582no—
176C4⋊C4—1581no—
177C4⋊C4D31611yescharacteristic
178C4⋊C4D31612yes—
179C42—1582no—
180C42—1581no—
181C42—1582no—
182C42—1581no—
183C42C22×D7911yescharacteristic
184C42C22×D7912yes—
185Q8—22no—
186Q8—3162no—
187Q8—792no—
188Q8—1581no—
189Q8—1582no—
190Q8—1581no—
191Q8—1582no—
192Q8—1581no—
193C2×C4—1581no—
194C2×C4—1581no—
195C2×C4—1582no—
196C2×C4—1582no—
197C2×C4—1581no—
198C2×C4—1581no—
199C2×C4C2×D31612yes—
200C2×C4C2×D31612yes—
201C2×C4C2×D31611yescharacteristic
202C2×C4C2×D31611yescharacteristic
203C2×C4C23×D7911yescharacteristic
204C8—21no—
205C8—22no—
206C8—21no—
207C22C22×D31611yescharacteristic
208C4—22no—
209C4—22no—
210C4—21no—
211C4—3162no—
212C4—3161no—
213C4—3162no—
214C4—3161no—
215C4—3161no—
216C4—1582no—
217C4#1457919412yes—
218C4#41×D7911yescharacteristic
219C4#1457920911yescharacteristic
220C2#1909922511yescharacteristic
221C2C2×#1457919411yescharacteristic
222C2#1909938011yescharacteristic
subgroupG/H
centerC22C22×D316
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#446×C79C2
socle, prime radicalC22×C79C22×D4
hypercenter#446D79
hypocenterC79#3374
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #446

Complements

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

NH ≅ G/Ntype
112. C79#3374semidirect