Finite Group Databasebeta

← #23776076

Subgroups — #23776076

Order 10112.

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

normal subgroups only

This group has 336 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
1Q8×Dic158C211yesmaximal, characteristic
2#19099291C211yesmaximal, characteristic
3#19098914C211yesmaximal, characteristic
4#19098912C212yesmaximal
5#19098858C211yesmaximal, characteristic
6#19098857C212yesmaximal
7#19098773C211yesmaximal, characteristic
8#19098771C212yesmaximal
9C8×Dic158C211yesmaximal, characteristic
10#19098655C212yesmaximal
11C4×Q16×C79C211yesmaximal, characteristic
12C2×#11929614C2212yes—
13#14579161—21no—
14#14579161C2211yescharacteristic
15#14579161C2211yescharacteristic
16#14579160—22no—
17#14579160C2212yes—
18#14579159C2212yes—
19#14579153—21no—
20#14579151—22no—
21Q8×Dic79C2212yes—
22C4×Dic158—21no—
23C4×Dic158—21no—
24C4×Dic158C2211yescharacteristic
25#14579126C2212yes—
26#14579094C2212yes—
27C4⋊(C79⋊C8)C2211yescharacteristic
28Dic79⋊C8C2212yes—
29#14579086C2212yes—
30#14579086C2212yes—
31#14579085C2212yes—
32#14579084C2212yes—
33C8×Dic79C2212yes—
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×Dic158D411yescharacteristic
44C2×Dic158C2312yes—
45#11929614—24no—
46C2×C79⋊C8C2312yes—
47C4⋊Dic79—22no—
48C4⋊Dic79—21no—
49C4⋊Dic79—21no—
50C4⋊Dic79—21no—
51C4⋊Dic79D411yescharacteristic
52C4⋊Dic79C2312yes—
53Dic79⋊C4—22no—
54Dic79⋊C4—22no—
55Dic79⋊C4—22no—
56Dic79⋊C4—22no—
57Dic79⋊C4D412yes—
58C4×Dic79—22no—
59C4×Dic79—22no—
60C4×Dic79C2312yes—
61C2×Q8×C79C2311yescharacteristic
62C2×Q8×C79C2311yescharacteristic
63Q16×C79—22no—
64C2×C8×C79C2311yescharacteristic
65C2×C8×C79C2311yescharacteristic
66C4⋊C4×C79—21no—
67C4⋊C4×C79—21no—
68C4⋊C4×C79C2311yescharacteristic
69C4⋊C4×C79C2311yescharacteristic
70C42×C79—21no—
71C42×C79—21no—
72C42×C79C2311yescharacteristic
73Q8×C79—21no—
74Q8×C79—21no—
75Q8×C79—21no—
76Q8×C79#4112yes—
77C2×C4×C79—21no—
78C2×C4×C79—21no—
79C2×C4×C79—21no—
80C2×C4×C79—21no—
81C2×C4×C79C2×D411yescharacteristic
82C2×C4×C79C2×D411yescharacteristic
83C2×C4×C79C2411yescharacteristic
84C2×Dic79—22no—
85C2×Dic79—22no—
86C2×Dic79C2×D412yes—
87C2×Dic79C2×D412yes—
88Dic158—22no—
89Dic158—22no—
90Dic158—82no—
91Dic158—81no—
92Dic158Q1614yescomplemented
93C8×C79—21no—
94C8×C79—21no—
95C79⋊C8—22no—
96C22×C79C22×D411yescharacteristic
97C4×C79—22no—
98C4×C79—21no—
99C4×C79—41no—
100C4×C79—41no—
101C4×C79—41no—
102C4×C79C2×Q1612yes—
103C4×C79C2×#4111yescharacteristic
104C4×C792−1+411yescharacteristic
105Dic79—22no—
106Dic79—42no—
107Dic79—42no—
108Dic79C2×Q1614yes—
109C2×C79#54811yescharacteristic
110C2×C79C22×Q1611yescharacteristic
111C2×C79#57711yescharacteristic
112#3363—791nomaximal, Sylow
113C79#336311yescharacteristic, complemented, Sylow
114Q82—791no—
115#557—791no—
116#487—792no—
117#487—791no—
118#477—791no—
119#477—792no—
120#462—792no—
121#462—791no—
122C8×Q8—791no—
123C4×Q16—792no—
124C4×Q16D7911yescharacteristic
125C2×Q16—792no—
126C2×Q16C2×D7911yescharacteristic
127C4⋊Q8—792no—
128C4⋊Q8—792no—
129C4⋊Q8—791no—
130C4⋊Q8—791no—
131C4⋊Q8—1581no—
132C4⋊Q8—1582no—
133#125—1581no—
134#125—1582no—
135C4×Q8—791no—
136C4×Q8—792no—
137C4×Q8—792no—
138C4×Q8—1581no—
139C4×Q8—1581no—
140C4×Q8C2×D7911yescharacteristic
141C4×Q8C2×D7911yescharacteristic
142#107—792no—
143#107C2×D7911yescharacteristic
144C4⋊C8—792no—
145C4⋊C8—791no—
146#103—792no—
147#103—792no—
148#103—792no—
149#103—792no—
150#103C2×D7911yescharacteristic
151#103C2×D7911yescharacteristic
152C4×C8—792no—
153C4×C8C2×D7911yescharacteristic
154C2×Q8—791no—
155C2×Q8—792no—
156C2×Q8—1582no—
157C2×Q8—1581no—
158C2×Q8C22×D7911yescharacteristic
159C2×Q8C22×D7911yescharacteristic
160Q16—22no—
161Q16—1584no—
162C2×C8—792no—
163C2×C8C22×D7911yescharacteristic
164C2×C8C22×D7911yescharacteristic
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—792no—
168C4⋊C4—791no—
169C4⋊C4—792no—
170C4⋊C4—1582no—
171C4⋊C4—1582no—
172C4⋊C4—1582no—
173C4⋊C4—1582no—
174C4⋊C4—1582no—
175C4⋊C4—1581no—
176C4⋊C4—1581no—
177C4⋊C4—1581no—
178C4⋊C4C22×D7911yescharacteristic
179C4⋊C4C22×D7911yescharacteristic
180C42—21no—
181C42—21no—
182C42—792no—
183C42—1582no—
184C42—1582no—
185C42C22×D7911yescharacteristic
186Q8—21no—
187Q8—21no—
188Q8—21no—
189Q8—794no—
190Q8—6321no—
191Q8—6322no—
192Q8—1582no—
193Q8—1582no—
194Q8#1192962412yes—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—792no—
200C2×C4—792no—
201C2×C4—1582no—
202C2×C4—1582no—
203C2×C4D4×D7911yescharacteristic
204C2×C4D4×D7911yescharacteristic
205C2×C4C23×D7911yescharacteristic
206C8—21no—
207C8—21no—
208C8—1582no—
209C22C2×D4×D7911yescharacteristic
210C4—22no—
211C4—21no—
212C4—41no—
213C4—41no—
214C4—41no—
215C4—3162no—
216C4—3162no—
217C4—794no—
218C4—1582no—
219C4Q16×D7912yes—
220C4C2×#1192962411yescharacteristic
221C4#1457920811yescharacteristic
222C2#1909922211yescharacteristic
223C2C2×Q16×D7911yescharacteristic
224C2#1909937011yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
FittingC4×Q16×C79C2
socle, prime radicalC22×C79C22×D4
hypercenterC4×Q16D79
hypocenterC79#3363
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
92. Dic158Q16semidirect
113. C79#3363semidirect