Finite Group Databasebeta

← #23768604

Subgroups — #23768604

Order 10112.

500 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 171 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×#14579159C211yesmaximal, characteristic
2C2×#14579126C211yesmaximal, characteristic
3#19098484C211yesmaximal, characteristic
4#19098483C211yesmaximal, characteristic
5#19098482C211yesmaximal, characteristic
6#19098467C212yesmaximal
7#19098460C212yesmaximal
8#19098458C212yesmaximal
9#19098432C212yesmaximal
10#19098414C211yesmaximal, characteristic
11#395×C79C211yesmaximal, characteristic
12C22×Dic158C2211yescharacteristic
13C22×Dic158C2211yescharacteristic
14#14579159—24no—
15#14579126—24no—
16C2×C4⋊Dic79C2212yes—
17C2×Dic79⋊C4C2211yescharacteristic
18C2×Dic79⋊C4C2212yes—
19C2×Dic79⋊C4C2212yes—
20C2×Dic79⋊C4C2211yescharacteristic
21C2×Dic79⋊C4C2212yes—
22C2×Dic79⋊C4C2212yes—
23C2×Dic79⋊C4C2212yes—
24C2×C4×Dic79C2212yes—
25C2×C4×Dic79C2211yescharacteristic
26C2×C4×Dic79C2211yescharacteristic
27C2×C4×Dic79C2211yescharacteristic
28C79⋊#95C2211yescharacteristic
29C79⋊#95C2212yes—
30C79⋊#95C2212yes—
31C79⋊#95C2212yes—
32C22×Q8×C79C2211yescharacteristic
33C2×C4⋊C4×C79C2211yescharacteristic
34C2×C4⋊C4×C79C2212yes—
35#95×C79C2211yescharacteristic
36#95×C79C2212yes—
37C2×Dic158—22no—
38C2×Dic158—22no—
39C2×Dic158—22no—
40C2×Dic158—42no—
41C2×Dic158Q814yescomplemented
42C22×Dic79C2312yes—
43C22×Dic79C2311yescharacteristic
44C22×Dic79C2311yescharacteristic
45C22×Dic79C2312yes—
46C22×Dic79C2311yescharacteristic
47C22×Dic79C2311yescharacteristic
48C4⋊Dic79—42no—
49Dic79⋊C4—22no—
50Dic79⋊C4—24no—
51Dic79⋊C4—24no—
52Dic79⋊C4—22no—
53Dic79⋊C4—42no—
54Dic79⋊C4—42no—
55Dic79⋊C4Q818yescomplemented
56C4×Dic79—22no—
57C4×Dic79—22no—
58C4×Dic79—24no—
59C4×Dic79D414yes—
60C2×Q8×C79—22no—
61C2×Q8×C79—42no—
62C22×C4×C79C2312yes—
63C22×C4×C79C2311yescharacteristic
64C22×C4×C79C2311yescharacteristic
65C22×C4×C79C2311yescharacteristic
66C22×C4×C79C2312yes—
67C4⋊C4×C79—22no—
68C4⋊C4×C79—42no—
69C23×C79C2411yescharacteristic
70Q8×C79—44no—
71C2×C4×C79—21no—
72C2×C4×C79—22no—
73C2×C4×C79—21no—
74C2×C4×C79—22no—
75C2×C4×C79—22no—
76C2×C4×C79—21no—
77C2×C4×C79—22no—
78C2×C4×C79—22no—
79C2×C4×C79—22no—
80C2×C4×C79—22no—
81C2×C4×C79C2×D412yes—
82C2×C4×C79C2×Q814yes—
83C2×C4×C79C2×Q812yes—
84C2×Dic79—21no—
85C2×Dic79—22no—
86C2×Dic79—21no—
87C2×Dic79—22no—
88C2×Dic79—21no—
89C2×Dic79—22no—
90C2×Dic79—22no—
91C2×Dic79—22no—
92C2×Dic79—22no—
93C2×Dic79C2×D412yes—
94C2×Dic79C2×D412yes—
95C2×Dic79C2×Q814yes—
96C2×Dic79C2×Q812yes—
97C2×Dic79C2×Q812yes—
98C2×Dic79C2×Q814yes—
99C2×Dic79#4112yes—
100Dic158—28no—
101Dic158—44no—
102C22×C79C22×D411yescharacteristic
103C22×C79C22×Q811yescharacteristic
104C22×C79C22×Q812yes—
105C22×C79C2×#4111yescharacteristic
106C22×C79H(5,𝔽2)12yes—
107C4×C79—22no—
108C4×C79—22no—
109C4×C79—24no—
110C4×C79—41no—
111C4×C79—42no—
112Dic79—22no—
113Dic79—24no—
114Dic79—42no—
115Dic79—41no—
116Dic79C22⋊Q814yes—
117Dic79C4⋊Q814yes—
118C2×C79C2×C22⋊Q811yescharacteristic
119C2×C79C2×C4⋊Q811yescharacteristic
120C2×C79#53511yescharacteristic
121C2×C79#55412yes—
122C2×C79Q8212yes—
123#2567—791nomaximal, Sylow
124C79#256711yescharacteristic, complemented, Sylow
125C2×C4⋊Q8—791no—
126C2×C4×Q8—791no—
127#395—791no—
128#395—791no—
129#395—791no—
130#395D7911yescharacteristic
131#391—792no—
132#389—792no—
133#389—792no—
134#384—792no—
135C4×C4⋊C4—791no—
136C22×Q8—791no—
137C22×Q8—791no—
138C22×Q8C2×D7911yescharacteristic
139C4⋊Q8—1584no—
140C4×Q8—1584no—
141C2×C4⋊C4—792no—
142C2×C4⋊C4—792no—
143C2×C4⋊C4—792no—
144C2×C4⋊C4—792no—
145C2×C4⋊C4—791no—
146C2×C4⋊C4—791no—
147C2×C4⋊C4—792no—
148C2×C4⋊C4—792no—
149C2×C4⋊C4C2×D7911yescharacteristic
150C2×C4⋊C4C2×D7912yes—
151C2×C42—791no—
152C2×C42—791no—
153C2×C42—791no—
154C2×C42—792no—
155#95—791no—
156#95—792no—
157#95—792no—
158#95—792no—
159#95C2×D7911yescharacteristic
160#95C2×D7912yes—
161C2×Q8—22no—
162C2×Q8—42no—
163C2×Q8—3162no—
164C2×Q8—794no—
165C2×Q8—1582no—
166C2×Q8—1582no—
167C2×Q8—1582no—
168C22×C4—791no—
169C22×C4—791no—
170C22×C4—791no—
171C22×C4—792no—
172C22×C4—792no—
173C22×C4—791no—
174C22×C4C22×D7912yes—
175C22×C4C22×D7911yescharacteristic
176C22×C4C22×D7911yescharacteristic
177C22×C4C22×D7911yescharacteristic
178C22×C4C22×D7912yes—
179C4⋊C4—22no—
180C4⋊C4—42no—
181C4⋊C4—3162no—
182C4⋊C4—3162no—
183C4⋊C4—3162no—
184C4⋊C4—798no—
185C4⋊C4—1582no—
186C4⋊C4—1584no—
187C4⋊C4—1584no—
188C4⋊C4—1582no—
189C42—794no—
190C42—1584no—
191C42—1582no—
192C42—1582no—
193C23C23×D7911yescharacteristic
194Q8—44no—
195Q8—3164no—
196Q8—1588no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—794no—
208C2×C4—792no—
209C2×C4—792no—
210C2×C4—792no—
211C2×C4—792no—
212C2×C4—794no—
213C2×C4—792no—
214C2×C4—1582no—
215C2×C4—1582no—
216C2×C4—1582no—
217C2×C4—1581no—
218C2×C4—1582no—
219C2×C4—1582no—
220C2×C4—1581no—
221C2×C4—1582no—
222C2×C4—1581no—
223C2×C4D4×D7912yes—
224C2×C4Q8×D7914yes—
225C2×C4Q8×D7912yes—
226C22C2×D4×D7911yescharacteristic
227C22C2×Q8×D7912yes—
228C22C2×Q8×D7911yescharacteristic
229C22#41×D7911yescharacteristic
230C22#1457920612yes—
231C4—24no—
232C4—22no—
233C4—22no—
234C4—42no—
235C4—41no—
236C4—3162no—
237C4—3161no—
238C4—794no—
239C4—794no—
240C4—1584no—
241C4—1582no—
242C2C22⋊Q8×D7911yescharacteristic
243C2C4⋊Q8×D7911yescharacteristic
244C2#1909912811yescharacteristic
245C2#1909926712yes—
246C2#1909929312yes—
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, prime radical, cosocleC23×C79C24
Fitting#395×C79C2
hypercenter#395D79
hypocenterC79#2567
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
41. C2×Dic158Q8semidirect
55. Dic79⋊C4Q8semidirect
124. C79#2567semidirect