Finite Group Databasebeta

← #23776334

Subgroups — #23776334

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#19099291C211yesmaximal, characteristic
3#19098972C212yesmaximal
4#19098961C211yesmaximal, characteristic
5#19098871C212yesmaximal
6#19098859C211yesmaximal, characteristic
7#19098849C211yesmaximal, characteristic
8#19098849C212yesmaximal
9#19098671C212yesmaximal
10C4×Dic316C211yesmaximal, characteristic
11#446×C79C211yesmaximal, characteristic
12C2×Dic316C2211yescharacteristic
13#14579161C2211yescharacteristic
14#14579161C2211yescharacteristic
15#14579161C2212yes—
16#14579160—21no—
17#14579160—22no—
18#14579159—21no—
19#14579153C2212yes—
20#14579151—22no—
21Q8×Dic79—21no—
22C4×Dic158C2211yescharacteristic
23C4×Dic158C2211yescharacteristic
24C4×Dic158C2212yes—
25C4×Dic158C2212yes—
26#14579126—21no—
27#14579095C2211yescharacteristic
28#14579095C2212yes—
29#14579093C2212yes—
30#14579093C2212yes—
31#14579093C2212yes—
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×Dic158—22no—
43C2×Dic158—21no—
44C2×Dic158C2311yescharacteristic
45C2×Dic158C2311yescharacteristic
46Dic316Q814yescomplemented
47C4⋊Dic79—22no—
48C4⋊Dic79—21no—
49C4⋊Dic79—21no—
50C4⋊Dic79C2312yes—
51C4⋊Dic79C2311yescharacteristic
52C4⋊Dic79C2312yes—
53C4⋊Dic79C2311yescharacteristic
54Dic79⋊C4—22no—
55Dic79⋊C4—21no—
56Dic79⋊C4—22no—
57Dic79⋊C4—22no—
58Dic79⋊C4—21no—
59Dic79⋊C4—22no—
60C4×Dic79—22no—
61C4×Dic79—21no—
62C4×Dic79—22no—
63C4×Dic79—21no—
64C2×Q8×C79D411yescharacteristic
65C2×C8×C79C2311yescharacteristic
66C2×C8×C79C2312yes—
67C2×C8×C79C2311yescharacteristic
68C4⋊C4×C79D411yescharacteristic
69C4⋊C4×C79D412yes—
70C42×C79C2311yescharacteristic
71C42×C79C2312yes—
72Q8×C79—22no—
73C2×C4×C79C2×D412yes—
74C2×C4×C79C2×D412yes—
75C2×C4×C79C2×D411yescharacteristic
76C2×C4×C79C2×D411yescharacteristic
77C2×C4×C79C2411yescharacteristic
78C2×Dic79—21no—
79C2×Dic79—21no—
80C2×Dic79—21no—
81C2×Dic79—22no—
82C2×Dic79—22no—
83C2×Dic79—21no—
84Dic158—21no—
85Dic158—21no—
86Dic158—42no—
87Dic158—82no—
88Dic158—81no—
89Dic158C2×Q812yes—
90Dic158C2×Q812yes—
91C8×C79—21no—
92C8×C79—22no—
93C8×C79C2×Q812yes—
94C22×C79C22×D411yescharacteristic
95C4×C79—22no—
96C4×C79—22no—
97C4×C79—21no—
98C4×C79#13712yes—
99C4×C79C22×Q811yescharacteristic
100C4×C792−1+411yescharacteristic
101Dic79—22no—
102Dic79—22no—
103Dic79—42no—
104Dic79—41no—
105Dic79—42no—
106Dic79—41no—
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—792no—
119#475—791no—
120#446D7911yescharacteristic
121#441—792no—
122C4×Q16—791no—
123C2×Q16—791no—
124C4⋊Q8—791no—
125C4⋊Q8—792no—
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—791no—
135C4×Q8—792no—
136C4×Q8—1581no—
137C4×Q8—1581no—
138C4×Q8C2×D7911yescharacteristic
139#107—791no—
140#107—792no—
141#106—792no—
142#106—792no—
143#106—792no—
144C4⋊C8C2×D7911yescharacteristic
145C4⋊C8C2×D7912yes—
146#103—791no—
147#103—791no—
148#103—792no—
149#103—792no—
150#97C2×D7912yes—
151C4×C8C2×D7911yescharacteristic
152C2×Q8—791no—
153C2×Q8—791no—
154C2×Q8—1581no—
155C2×Q8—1582no—
156C2×Q8—1581no—
157C2×Q8D31611yescharacteristic
158Q16—794no—
159C2×C8C22×D7911yescharacteristic
160C2×C8C22×D7912yes—
161C2×C8C22×D7911yescharacteristic
162C4⋊C4—792no—
163C4⋊C4—791no—
164C4⋊C4—792no—
165C4⋊C4—791no—
166C4⋊C4—1581no—
167C4⋊C4—1582no—
168C4⋊C4—1582no—
169C4⋊C4—1581no—
170C4⋊C4—1582no—
171C4⋊C4—1582no—
172C4⋊C4—1582no—
173C4⋊C4—1581no—
174C4⋊C4—1581no—
175C4⋊C4D31611yescharacteristic
176C4⋊C4D31612yes—
177C42—1582no—
178C42—1581no—
179C42—1582no—
180C42—1581no—
181C42C22×D7911yescharacteristic
182C42C22×D7912yes—
183Q8—22no—
184Q8—3162no—
185Q8—792no—
186Q8—792no—
187Q8—6322no—
188Q8—6321no—
189Q8—1581no—
190Q8—1581no—
191C2×C4—1581no—
192C2×C4—1582no—
193C2×C4—1582no—
194C2×C4—1581no—
195C2×C4—1581no—
196C2×C4—1581no—
197C2×C4C2×D31612yes—
198C2×C4C2×D31612yes—
199C2×C4C2×D31611yescharacteristic
200C2×C4C2×D31611yescharacteristic
201C2×C4C23×D7911yescharacteristic
202C8—21no—
203C8—22no—
204C8Q8×D7912yes—
205C22C22×D31611yescharacteristic
206C4—22no—
207C4—22no—
208C4—21no—
209C4—3162no—
210C4—3162no—
211C4—3161no—
212C4—3161no—
213C4—1582no—
214C4—1582no—
215C4#1457919412yes—
216C4C2×Q8×D7911yescharacteristic
217C4#1457920811yescharacteristic
218C2Q8×D31611yescharacteristic
219C2C2×#1457919411yescharacteristic
220C2#1909937511yescharacteristic
subgroupG/H
centerC22C22×D316
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#446×C79C2
socle, prime radicalC22×C79C22×D4
hypercenter#446D79
hypocenterC79#3387
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
46. Dic316Q8semidirect
111. C79#3387semidirect