Finite Group Databasebeta

← #23763413

Subgroups — #23763413

Order 10112.

292 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 109 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×Q8×Dic79C211yesmaximal, characteristic
2C2×Dic79⋊C8C211yesmaximal, characteristic
3C2×#14579085C211yesmaximal, characteristic
4#19098428C211yesmaximal, characteristic
5#19098326C211yesmaximal, characteristic
6#19098325C211yesmaximal, characteristic
7C2×#103×C79C211yesmaximal, characteristic
8C22×C79⋊C8C2211yescharacteristic
9Q8×Dic79—22no—
10Q8×Dic79C414yescomplemented
11C2×C4⋊Dic79—21no—
12C2×C4⋊Dic79C2211yescharacteristic
13C2×C4⋊Dic79C2211yescharacteristic
14C2×C4×Dic79—21no—
15C2×C4×Dic79C2211yescharacteristic
16Dic79⋊C8—22no—
17#14579085—22no—
18C79⋊#95—21no—
19C79⋊#95—21no—
20C22×Q8×C79C2211yescharacteristic
21C22×C8×C79C2211yescharacteristic
22C2×C4⋊C4×C79C2211yescharacteristic
23#103×C79—22no—
24C22×Dic79—21no—
25C22×Dic79—21no—
26C22×Dic79D411yescharacteristic
27C22×Dic79D411yescharacteristic
28C2×C79⋊C8—21no—
29C2×C79⋊C8—21no—
30C2×C79⋊C8—21no—
31C4⋊Dic79—24no—
32C4⋊Dic79—21no—
33C4⋊Dic79—21no—
34C4⋊Dic79—21no—
35C4⋊Dic79C2×C412yes—
36C4×Dic79—24no—
37C4×Dic79C2×C412yes—
38C4×Dic79D412yes—
39C2×Q8×C79—21no—
40C2×Q8×C79—21no—
41C2×Q8×C79—21no—
42C2×Q8×C79C2×C412yes—
43C2×Q8×C79D412yes—
44C2×Q8×C79Q812yes—
45C22×C4×C79—21no—
46C22×C4×C79—21no—
47C22×C4×C79C2311yescharacteristic
48C2×C8×C79—21no—
49C2×C8×C79—21no—
50C2×C8×C79—21no—
51C4⋊C4×C79—21no—
52C4⋊C4×C79—21no—
53C23×C79C2×D411yescharacteristic
54Q8×C79—22no—
55Q8×C79—22no—
56Q8×C79—22no—
57Q8×C79C4⋊C414yes—
58C2×C4×C79—22no—
59C2×C4×C79—22no—
60C2×C4×C79—22no—
61C2×C4×C79—41no—
62C2×C4×C79—41no—
63C2×C4×C79—41no—
64C2×C4×C79C22×C411yescharacteristic
65C2×C4×C79C2×D411yescharacteristic
66C2×C4×C79C2×D411yescharacteristic
67C2×C4×C79C2×Q811yescharacteristic
68C2×C4×C79#4111yescharacteristic
69C2×C4×C79#4111yescharacteristic
70C2×Dic79—21no—
71C2×Dic79—21no—
72C2×Dic79—21no—
73C2×Dic79—21no—
74C2×Dic79—22no—
75C2×Dic79—41no—
76C2×Dic79—41no—
77C2×Dic79—41no—
78C2×Dic79—41no—
79C2×Dic79—41no—
80C2×Dic79C22⋊C412yes—
81C2×Dic79C22⋊C412yes—
82C8×C79—41no—
83C79⋊C8—41no—
84C22×C79C2×C22⋊C411yescharacteristic
85C22×C79#12111yescharacteristic
86C22×C79C22⋊Q811yescharacteristic
87C22×C79#13511yescharacteristic
88C22×C79#13511yescharacteristic
89C22×C79#13711yescharacteristic
90C22×C79#13711yescharacteristic
91C4×C79—24no—
92C4×C79—81no—
93C4×C79C2×C4⋊C411yescharacteristic
94C4×C79#11711yescharacteristic
95C4×C79#12111yescharacteristic
96C4×C79C22⋊Q811yescharacteristic
97Dic79—22no—
98Dic79—22no—
99Dic79—42no—
100Dic79—81no—
101C2×C79#38011yescharacteristic
102C2×C79#41611yescharacteristic
103C2×C79#41911yescharacteristic
104C2×C79#46411yescharacteristic
105C2×C79#46411yescharacteristic
106C2×C79#47911yescharacteristic
107C2×C79#47911yescharacteristic
108#1805—791nomaximal, Sylow
109C79#180511yescharacteristic, complemented, Sylow
110C2×C4×Q8—791no—
111C2×C4⋊C8—791no—
112C2×#103—791no—
113C2×#103D7911yescharacteristic
114#382—791no—
115#340—791no—
116#340—791no—
117C22×Q8C2×D7911yescharacteristic
118C22×C8—791no—
119C22×C8C2×D7911yescharacteristic
120C4×Q8—794no—
121C4×Q8—1582no—
122C2×C4⋊C4—791no—
123C2×C4⋊C4—791no—
124C2×C4⋊C4—1581no—
125C2×C4⋊C4C2×D7911yescharacteristic
126C2×C42—791no—
127C2×C42—1581no—
128C4⋊C8—1582no—
129#103—22no—
130#103—1582no—
131#95—1581no—
132#95—1581no—
133C2×Q8—21no—
134C2×Q8—21no—
135C2×Q8—21no—
136C2×Q8Dic15812yes—
137C2×Q8C4×D7912yes—
138C2×Q8C22⋊D7912yes—
139C22×C4—21no—
140C22×C4—21no—
141C22×C4—791no—
142C22×C4—791no—
143C22×C4—1581no—
144C22×C4—1581no—
145C22×C4C22×D7911yescharacteristic
146C2×C8—21no—
147C2×C8—21no—
148C2×C8—21no—
149C2×C8—1581no—
150C2×C8—1581no—
151C2×C8—1581no—
152C4⋊C4—21no—
153C4⋊C4—21no—
154C4⋊C4—792no—
155C4⋊C4—1584no—
156C4⋊C4—1581no—
157C4⋊C4—1581no—
158C4⋊C4—1581no—
159C42—792no—
160C42—792no—
161C42—1584no—
162C23D4×D7911yescharacteristic
163Q8—22no—
164Q8—22no—
165Q8—22no—
166Q8Dic79⋊C414yes—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—3161no—
174C2×C4—3161no—
175C2×C4—3161no—
176C2×C4—3161no—
177C2×C4—3161no—
178C2×C4—792no—
179C2×C4—792no—
180C2×C4—1582no—
181C2×C4—1581no—
182C2×C4—1581no—
183C2×C4—1581no—
184C2×C4—1581no—
185C2×C4C2×C4×D7911yescharacteristic
186C2×C4D4×D7911yescharacteristic
187C2×C4C2×C22⋊D7911yescharacteristic
188C2×C4C2×Dic15811yescharacteristic
189C2×C4#1192962311yescharacteristic
190C2×C4#1192962311yescharacteristic
191C8—41no—
192C8—3161no—
193C22C22⋊C4×D7911yescharacteristic
194C22#1457913311yescharacteristic
195C22#1457913811yescharacteristic
196C22#1457918211yescharacteristic
197C22#1457918411yescharacteristic
198C22#1457919011yescharacteristic
199C22#1457919311yescharacteristic
200C4—24no—
201C4—81no—
202C4—3162no—
203C4—6321no—
204C4—1582no—
205C4—1582no—
206C4C2×Dic79⋊C411yescharacteristic
207C4#1457911711yescharacteristic
208C4#1457913311yescharacteristic
209C4#1457913811yescharacteristic
210C2#1909842111yescharacteristic
211C2#1909855811yescharacteristic
212C2#1909857011yescharacteristic
213C2#1909878311yescharacteristic
214C2#1909878711yescharacteristic
215C2#1909886811yescharacteristic
216C2#1909887211yescharacteristic
subgroupG/H
centerC23D4×D79
commutatorC2×C4×C79C22×C4
FrattiniC22×C4C22×D79
FittingC2×#103×C79C2
socle, prime radicalC23×C79C2×D4
cosocleC22×C4×C79C23
hypercenterC2×#103D79
hypocenterC79#1805
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
10. Q8×Dic79C4semidirect
109. C79#1805semidirect