Finite Group Databasebeta

← #23776330

Subgroups — #23776330

Order 10112.

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

normal subgroups only

This group has 326 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
1Q8×Dic158C211yesmaximal, characteristic
2#19099292C211yesmaximal, characteristic
3#19098971C212yesmaximal
4#19098961C211yesmaximal, characteristic
5#19098868C212yesmaximal
6#19098858C211yesmaximal, characteristic
7#19098848C211yesmaximal, characteristic
8#19098846C212yesmaximal
9#19098693C211yesmaximal, characteristic
10#19098670C212yesmaximal
11C4×Q16×C79C211yesmaximal, characteristic
12#14579161—21no—
13#14579161—21no—
14#14579161C2211yescharacteristic
15#14579161C2211yescharacteristic
16#14579160—22no—
17#14579160C2212yes—
18#14579152—22no—
19#14579152C2212yes—
20Q8×Dic79C2212yes—
21Q8×Dic79C2212yes—
22C4×Dic158—21no—
23C4×Dic158—21no—
24C4×Dic158C2211yescharacteristic
25#14579094C2212yes—
26#14579093C2212yes—
27#14579093C2212yes—
28#14579092C2212yes—
29C4⋊(C79⋊C8)C2211yescharacteristic
30Dic79⋊C8C2212yes—
31#14579085C2212yes—
32#14579085C2212yes—
33#14579071C2212yes—
34C2×Q16×C79C2211yescharacteristic
35C4×Q8×C79C2211yescharacteristic
36C4×Q8×C79C2211yescharacteristic
37#107×C79C2211yescharacteristic
38#103×C79C2211yescharacteristic
39#103×C79C2211yescharacteristic
40C4×C8×C79C2211yescharacteristic
41C2×Dic158—22no—
42C2×Dic158—21no—
43C2×Dic158—21no—
44C2×Dic158D411yescharacteristic
45C2×C79⋊C8C2312yes—
46C4⋊Dic79—22no—
47C4⋊Dic79—22no—
48C4⋊Dic79—22no—
49C4⋊Dic79—21no—
50C4⋊Dic79—21no—
51C4⋊Dic79D411yescharacteristic
52C4⋊Dic79C2312yes—
53C4⋊Dic79C2312yes—
54Dic79⋊C4—22no—
55Dic79⋊C4—22no—
56Dic79⋊C4D412yes—
57C4×Dic79—22no—
58C4×Dic79—22no—
59C4×Dic79C2312yes—
60C2×Q8×C79C2311yescharacteristic
61C2×Q8×C79C2311yescharacteristic
62Q16×C79Q814yescomplemented
63C2×C8×C79C2311yescharacteristic
64C2×C8×C79C2311yescharacteristic
65C4⋊C4×C79—21no—
66C4⋊C4×C79—21no—
67C4⋊C4×C79C2311yescharacteristic
68C4⋊C4×C79C2311yescharacteristic
69C42×C79—21no—
70C42×C79—21no—
71C42×C79C2311yescharacteristic
72Q8×C79—21no—
73Q8×C79—21no—
74Q8×C79C2×Q812yes—
75Q8×C79C2×Q812yes—
76C2×C4×C79—21no—
77C2×C4×C79—21no—
78C2×C4×C79—21no—
79C2×C4×C79—21no—
80C2×C4×C79C2×D411yescharacteristic
81C2×C4×C79C2×D411yescharacteristic
82C2×C4×C79C2411yescharacteristic
83C2×Dic79—22no—
84C2×Dic79—22no—
85C2×Dic79C2×D412yes—
86C2×Dic79C2×D412yes—
87Dic158—22no—
88Dic158—42no—
89Dic158—82no—
90Dic158—81no—
91C8×C79—21no—
92C8×C79C2×Q812yes—
93C79⋊C8—22no—
94C22×C79C22×D411yescharacteristic
95C4×C79—22no—
96C4×C79—22no—
97C4×C79—21no—
98C4×C79—41no—
99C4×C79—41no—
100C4×C79#13712yes—
101C4×C79C22×Q811yescharacteristic
102C4×C792−1+411yescharacteristic
103Dic79—22no—
104Dic79—22no—
105Dic79—42no—
106Dic79—42no—
107C2×C79D4×Q811yescharacteristic
108C2×C79C2×#13711yescharacteristic
109C2×C79#57711yescharacteristic
110#3387—791nomaximal, Sylow
111C79#338711yescharacteristic, complemented, Sylow
112Q82—791no—
113#557—791no—
114#501—792no—
115#498—791no—
116#479—792no—
117#477—791no—
118#475—791no—
119#475—792no—
120#446—791no—
121#441—792no—
122C4×Q16D7911yescharacteristic
123C2×Q16C2×D7911yescharacteristic
124C4⋊Q8—792no—
125C4⋊Q8—791no—
126C4⋊Q8—791no—
127C4⋊Q8—1581no—
128C4⋊Q8—1581no—
129C4⋊Q8—1582no—
130#125—792no—
131#125—1582no—
132C4×Q8—791no—
133C4×Q8—792no—
134C4×Q8—792no—
135C4×Q8—1581no—
136C4×Q8—1581no—
137C4×Q8C2×D7911yescharacteristic
138C4×Q8C2×D7911yescharacteristic
139#107—792no—
140#107C2×D7911yescharacteristic
141#106—792no—
142#106—792no—
143#106—792no—
144C4⋊C8—792no—
145C4⋊C8—791no—
146#103—792no—
147#103—792no—
148#103C2×D7911yescharacteristic
149#103C2×D7911yescharacteristic
150#97—792no—
151C4×C8C2×D7911yescharacteristic
152C2×Q8—791no—
153C2×Q8—1582no—
154C2×Q8—1581no—
155C2×Q8—1581no—
156C2×Q8C22×D7911yescharacteristic
157C2×Q8C22×D7911yescharacteristic
158Q16Dic15814yescomplemented
159C2×C8—792no—
160C2×C8C22×D7911yescharacteristic
161C2×C8C22×D7911yescharacteristic
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—792no—
165C4⋊C4—791no—
166C4⋊C4—792no—
167C4⋊C4—792no—
168C4⋊C4—1582no—
169C4⋊C4—1582no—
170C4⋊C4—1582no—
171C4⋊C4—1582no—
172C4⋊C4—1582no—
173C4⋊C4—1581no—
174C4⋊C4—1581no—
175C4⋊C4C22×D7911yescharacteristic
176C4⋊C4C22×D7911yescharacteristic
177C42—21no—
178C42—21no—
179C42—792no—
180C42—1582no—
181C42—1582no—
182C42C22×D7911yescharacteristic
183Q8—21no—
184Q8—21no—
185Q8—3162no—
186Q8—6321no—
187Q8—6322no—
188Q8—1582no—
189Q8C2×Dic15812yes—
190Q8C2×Dic15812yes—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—792no—
196C2×C4—792no—
197C2×C4—1582no—
198C2×C4—1582no—
199C2×C4D4×D7911yescharacteristic
200C2×C4D4×D7911yescharacteristic
201C2×C4C23×D7911yescharacteristic
202C8—21no—
203C8—1582no—
204C8C2×Dic15812yes—
205C22C2×D4×D7911yescharacteristic
206C4—22no—
207C4—22no—
208C4—21no—
209C4—41no—
210C4—41no—
211C4—3162no—
212C4—3162no—
213C4—1582no—
214C4—1582no—
215C4#1457919312yes—
216C4C22×Dic15811yescharacteristic
217C4#1457920811yescharacteristic
218C2D4×Dic15811yescharacteristic
219C2C2×#1457919311yescharacteristic
220C2#1909937011yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
FittingC4×Q16×C79C2
socle, prime radicalC22×C79C22×D4
hypercenterC4×Q16D79
hypocenterC79#3387
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
62. Q16×C79Q8semidirect
111. C79#3387semidirect
158. Q16Dic158semidirect