Finite Group Databasebeta

← #23764009

Subgroups — #23764009

Order 10112.

292 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 105 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×Dic79⋊C8C211yesmaximal, characteristic, complemented
2C2×C22⋊(C79⋊C8)C211yesmaximal, characteristic
3C2×C8×Dic79C211yesmaximal, characteristic, complemented
4C4×C22⋊Dic79C211yesmaximal, characteristic
5#19098317C211yesmaximal, characteristic, complemented
6#19098317C211yesmaximal, characteristic, complemented
7C2×C22⋊C8×C79C211yesmaximal, characteristic
8C22×C79⋊C8C2211yescharacteristic
9C22×C79⋊C8C2211yescharacteristic
10C2×C22⋊Dic79C411yescharacteristic
11C2×C22⋊Dic79C411yescharacteristic
12C2×C4×Dic79C2211yescharacteristic
13C2×C4×Dic79C2211yescharacteristic
14Dic79⋊C8—22no—
15C22⋊(C79⋊C8)—22no—
16C8×Dic79—22no—
17C79⋊#95C411yescharacteristic
18C79⋊#95C411yescharacteristic
19C23×C4×C79C2211yescharacteristic
20C22×C8×C79C2211yescharacteristic
21C22×C8×C79C2211yescharacteristic
22C22⋊C8×C79—22no—
23C22×Dic79C2×C411yescharacteristic
24C22×Dic79C2×C411yescharacteristic
25C22×Dic79C2×C411yescharacteristic
26C22×Dic79C2×C411yescharacteristic
27C2×C79⋊C8—21no—
28C2×C79⋊C8—21no—
29C2×C79⋊C8—21no—
30C2×C79⋊C8—21no—
31C2×C79⋊C8—21no—
32C2×C79⋊C8D412yes—
33C22⋊Dic79—22no—
34C22⋊Dic79C814yescomplemented
35C4×Dic79—21no—
36C4×Dic79—21no—
37C4×Dic79—21no—
38C4×Dic79—21no—
39C24×C79C2×C411yescharacteristic
40C22×C4×C79—21no—
41C22×C4×C79—21no—
42C22×C4×C79—21no—
43C22×C4×C79—21no—
44C22×C4×C79—21no—
45C22×C4×C79—21no—
46C22×C4×C79C2×C411yescharacteristic
47C22×C4×C79C2311yescharacteristic
48C2×C8×C79—21no—
49C2×C8×C79—21no—
50C2×C8×C79—21no—
51C2×C8×C79—21no—
52C2×C8×C79—21no—
53C2×C8×C79D412yes—
54C23×C79—21no—
55C23×C79—21no—
56C23×C79—21no—
57C23×C79—21no—
58C23×C79—21no—
59C23×C79—21no—
60C23×C79C2×C812yes—
61C23×C79C22×C411yescharacteristic
62C2×C4×C79—21no—
63C2×C4×C79—21no—
64C2×C4×C79—21no—
65C2×C4×C79—41no—
66C2×C4×C79—41no—
67C2×C4×C79—41no—
68C2×C4×C79—41no—
69C2×C4×C79C2×D411yescharacteristic
70C2×C4×C79C2×D411yescharacteristic
71C2×C4×C79#4111yescharacteristic
72C2×C4×C79#4111yescharacteristic
73C2×C4×C79#4111yescharacteristic
74C2×C4×C79#4111yescharacteristic
75C2×Dic79—21no—
76C2×Dic79—21no—
77C2×Dic79—21no—
78C2×Dic79—21no—
79C2×Dic79—21no—
80C2×Dic79—21no—
81C2×Dic79—21no—
82C2×Dic79—21no—
83C2×Dic79—21no—
84C2×Dic79C2×C812yes—
85C2×Dic79C2×C812yes—
86C2×Dic79M1612yes—
87C8×C79—22no—
88C8×C79—41no—
89C79⋊C8—22no—
90C79⋊C8—41no—
91C22×C79—22no—
92C22×C79—22no—
93C22×C79—22no—
94C22×C79—41no—
95C22×C79—41no—
96C22×C79—41no—
97C22×C79—41no—
98C22×C79#11711yescharacteristic
99C22×C79C4×D411yescharacteristic
100C22×C79C4×D411yescharacteristic
101C22×C79C22×C811yescharacteristic
102C22×C79C2×M1611yescharacteristic
103C22×C79#13111yescharacteristic
104C22×C79#13111yescharacteristic
105C4×C79—41no—
106C4×C79#12111yescharacteristic
107C4×C79#12311yescharacteristic
108C4×C79#12411yescharacteristic
109C4×C79#12611yescharacteristic
110Dic79—22no—
111Dic79—22no—
112Dic79—22no—
113Dic79—41no—
114C2×C79—42no—
115C2×C79#38811yescharacteristic
116C2×C79#43111yescharacteristic
117C2×C79#43311yescharacteristic
118C2×C79C8×D411yescharacteristic
119C2×C79C8×D411yescharacteristic
120C2×C79#43511yescharacteristic
121C2×C79#43611yescharacteristic
122#1923—791nomaximal, Sylow
123C79#192311yescharacteristic, complemented, Sylow
124C2×C4⋊C8—791no—
125C2×C22⋊C8—791no—
126C2×C22⋊C8D7911yescharacteristic
127C2×C4×C8—791no—
128C4×C22⋊C4—791no—
129#336—791no—
130#336—791no—
131C23×C4C2×D7911yescharacteristic
132C22×C8—791no—
133C22×C8—791no—
134C22×C8C2×D7911yescharacteristic
135C22×C8C2×D7911yescharacteristic
136C2×C22⋊C4—791no—
137C2×C22⋊C4—791no—
138C2×C42—791no—
139C2×C42—791no—
140C4⋊C8—1582no—
141C22⋊C8—22no—
142C22⋊C8—1582no—
143C4×C8—1582no—
144#95—791no—
145#95—791no—
146C24C4×D7911yescharacteristic
147C22×C4—21no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—21no—
151C22×C4—21no—
152C22×C4—21no—
153C22×C4—791no—
154C22×C4—791no—
155C22×C4—791no—
156C22×C4—791no—
157C22×C4C4×D7911yescharacteristic
158C22×C4C22×D7911yescharacteristic
159C2×C8—21no—
160C2×C8—21no—
161C2×C8—21no—
162C2×C8—21no—
163C2×C8—21no—
164C2×C8—792no—
165C2×C8—1581no—
166C2×C8—1581no—
167C2×C8—1581no—
168C2×C8—1581no—
169C2×C8—1581no—
170C2×C8C22⋊D7912yes—
171C22⋊C4—794no—
172C22⋊C4—1582no—
173C42—1581no—
174C42—1581no—
175C42—1581no—
176C42—1581no—
177C23—21no—
178C23—21no—
179C23—21no—
180C23—21no—
181C23—21no—
182C23—21no—
183C23C8×D7912yes—
184C23C2×C4×D7911yescharacteristic
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—792no—
193C2×C4—792no—
194C2×C4—792no—
195C2×C4—1581no—
196C2×C4—1581no—
197C2×C4—1581no—
198C2×C4—1581no—
199C2×C4—1581no—
200C2×C4—1581no—
201C2×C4—1581no—
202C2×C4—1581no—
203C2×C4—1581no—
204C2×C4D4×D7911yescharacteristic
205C2×C4C2×C22⋊D7911yescharacteristic
206C2×C4#1192962311yescharacteristic
207C2×C4#1192962311yescharacteristic
208C2×C4#1192962311yescharacteristic
209C2×C4#1192962411yescharacteristic
210C8—22no—
211C8—41no—
212C8—3161no—
213C8—1582no—
214C22—22no—
215C22—22no—
216C22—22no—
217C22—41no—
218C22—41no—
219C22—41no—
220C22—41no—
221C22#1457911711yescharacteristic
222C22(C22⋊D79)⋊C411yescharacteristic
223C22C4×C22⋊D7911yescharacteristic
224C22C2×C8×D7911yescharacteristic
225C22M16×D7911yescharacteristic
226C22#1457916711yescharacteristic
227C22#1457916911yescharacteristic
228C4—41no—
229C4—3161no—
230C4—1582no—
231C4—1582no—
232C4—1582no—
233C4#1457913311yescharacteristic
234C4#1457914311yescharacteristic
235C4#1457914811yescharacteristic
236C4#1457915411yescharacteristic
237C2—42no—
238C2#1909845711yescharacteristic
239C2#1909861311yescharacteristic
240C2#1909862111yescharacteristic
241C2(C22⋊D79)⋊C811yescharacteristic
242C2C8×C22⋊D7911yescharacteristic
243C2#1909863711yescharacteristic
244C2#1909863911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C22×D79
commutatorC22×C79C22×C8
FittingC2×C22⋊C8×C79C2
socleC23×C79C22×C4
prime radicalC24×C79C2×C4
cosocleC22×C4×C79C23
hypercenterC2×C22⋊C8D79
hypocenterC79#1923
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×Dic79⋊C8C2semidirect
3. C2×C8×Dic79C2semidirect
5. #19098317C2semidirect
6. #19098317C2semidirect
34. C22⋊Dic79C8semidirect
123. C79#1923semidirect