Finite Group Databasebeta

← #34198916

Subgroups — #34198916

Order 20224.

378 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 87 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
1#23768612C211yesmaximal, characteristic
2#23761744C211yesmaximal, characteristic
3#23761426C214yesmaximal
4C4×#101×C79C211yesmaximal, characteristic
5C2×#14579161C411yescharacteristic
6#19098620—21no—
7#19098502C412yes—
8#19098502C2212yes—
9#19098470—21no—
10#19098469—21no—
11#19098469—21no—
12#19098428—21no—
13C4×C4⋊Dic79C411yescharacteristic
14#19098289—21no—
15#19098289C2212yes—
16C2×C4×Q8×C79C2211yescharacteristic
17C2×#101×C79—21no—
18C4×M16×C79—21no—
19#343×C79C2212yes—
20C22×Dic158—21no—
21#14579161—41no—
22#14579161—41no—
23C2×C4⋊Dic79—21no—
24C2×C4⋊Dic79—21no—
25C2×C4⋊Dic79C2×C412yes—
26C2×C4×Dic79—21no—
27C4⋊(C79⋊C8)—41no—
28C22⋊(C79⋊C8)—22no—
29#14579072—41no—
30C79⋊#95—22no—
31C79⋊#95—22no—
32C79⋊#95—22no—
33C79⋊#95—22no—
34C79⋊#95C2×C412yes—
35C22×Q8×C79D411yescharacteristic
36C2×M16×C79—22no—
37C4×Q8×C79—41no—
38C4×Q8×C79—41no—
39C2×C4⋊C4×C79C2×C411yescharacteristic
40C2×C4⋊C4×C79D411yescharacteristic
41C2×C4⋊C4×C79C2311yescharacteristic
42C2×C42×C79C2×C411yescharacteristic
43C2×C42×C79D411yescharacteristic
44C2×C42×C79D411yescharacteristic
45#101×C79—24no—
46#97×C79—41no—
47C4×C8×C79—41no—
48C2×Dic158—44no—
49C2×Dic158—41no—
50C2×Dic158—41no—
51C22×Dic79—22no—
52C22×Dic79—22no—
53C2×C79⋊C8—42no—
54C4⋊Dic79—42no—
55C4⋊Dic79—42no—
56C4⋊Dic79—42no—
57C4×Dic79—42no—
58C2×Q8×C79—22no—
59C2×Q8×C79—22no—
60C2×Q8×C79—41no—
61C22×C4×C79C22⋊C411yescharacteristic
62C22×C4×C79C22⋊C411yescharacteristic
63C22×C4×C79C22⋊C411yescharacteristic
64C22×C4×C79C22⋊C411yescharacteristic
65C22×C4×C79C22×C411yescharacteristic
66C22×C4×C79C2×D411yescharacteristic
67C22×C4×C79C2×D411yescharacteristic
68M16×C79—24no—
69M16×C79—42no—
70C2×C8×C79—42no—
71C4⋊C4×C79—41no—
72C4⋊C4×C79—41no—
73C4⋊C4×C79—41no—
74C42×C79—21no—
75C42×C79—21no—
76C42×C79—21no—
77C42×C79—21no—
78C42×C79—21no—
79C42×C79—21no—
80C23×C79C2×C22⋊C411yescharacteristic
81Q8×C79—44no—
82C2×C4×C79—21no—
83C2×C4×C79—21no—
84C2×C4×C79—21no—
85C2×C4×C79—21no—
86C2×C4×C79—22no—
87C2×C4×C79—21no—
88C2×C4×C79—21no—
89C2×C4×C79—21no—
90C2×C4×C79—21no—
91C2×C4×C79—21no—
92C2×C4×C79—21no—
93C2×C4×C79—41no—
94C2×C4×C79—41no—
95C2×C4×C79—41no—
96C2×C4×C79#9911yescharacteristic
97C2×C4×C79#9911yescharacteristic
98C2×C4×C79#10412yes—
99C2×C4×C79#13712yes—
100C2×Dic79—42no—
101C2×Dic79—42no—
102C2×Dic79—44no—
103C2×Dic79—42no—
104C2×Dic79—42no—
105Dic158—82no—
106Dic158—82no—
107C8×C79—44no—
108C79⋊C8—82no—
109C22×C79—21no—
110C22×C79—21no—
111C22×C79C2×#9911yescharacteristic
112C22×C79#41911yescharacteristic
113C22×C79C2×#10411yescharacteristic
114C4×C79—21no—
115C4×C79—22no—
116C4×C79—22no—
117C4×C79—41no—
118C4×C79—41no—
119C4×C79—41no—
120C4×C79—41no—
121C4×C79#35512yes—
122Dic79—82no—
123Dic79—82no—
124#11794—791nomaximal, Sylow
125C2×C79—21no—
126C2×C79—21no—
127C2×C79#150811yescharacteristic
128C2×C79#212311yescharacteristic
129C2×C79C2×#35511yescharacteristic
130#2568—791no—
131C4×#101D7911yescharacteristic
132#1467—791no—
133#1353—794no—
134C79#1179411yescharacteristic, complemented, Sylow
135C2×C4⋊Q8—791no—
136C2×C4×Q8C2×D7911yescharacteristic
137#432—1581no—
138C2×#101—21no—
139C4×M16—21no—
140#400—792no—
141#400—792no—
142#391—1581no—
143#391—1581no—
144#391—1581no—
145#382—1581no—
146C4×C4⋊C4—791no—
147#343C2×D7912yes—
148#324—792no—
149#324—1581no—
150C22×Q8—1581no—
151C22×Q8C22⋊D7911yescharacteristic
152C2×M16—22no—
153C4⋊Q8—3161no—
154C4⋊Q8—3161no—
155C4×Q8—41no—
156C4×Q8—41no—
157C2×C4⋊C4—792no—
158C2×C4⋊C4—1581no—
159C2×C4⋊C4—1581no—
160C2×C4⋊C4C4×D7911yescharacteristic
161C2×C4⋊C4D31611yescharacteristic
162C2×C4⋊C4C22×D7911yescharacteristic
163C2×C42—1581no—
164C2×C42C4×D7911yescharacteristic
165C2×C42D31611yescharacteristic
166C2×C42C22⋊D7911yescharacteristic
167C4⋊C8—3161no—
168#101—24no—
169C22⋊C8—1582no—
170#97—41no—
171#97—3161no—
172C4×C8—41no—
173#95—792no—
174#95—1582no—
175#95—1582no—
176#95—1582no—
177#95—1582no—
178C2×Q8—22no—
179C2×Q8—22no—
180C2×Q8—41no—
181C2×Q8—3164no—
182C2×Q8—3161no—
183C2×Q8—3161no—
184C22×C4—1582no—
185C22×C4—1582no—
186C22×C4(C2×D79)⋊C411yescharacteristic
187C22×C4(C2×D79)⋊C411yescharacteristic
188C22×C4(C2×D79)⋊C411yescharacteristic
189C22×C4(C2×D79)⋊C411yescharacteristic
190C22×C4C2×C4×D7911yescharacteristic
191C22×C4C2×C22⋊D7911yescharacteristic
192C22×C4C2×D31611yescharacteristic
193M16—24no—
194M16—42no—
195C2×C8—42no—
196C2×C8—3162no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C4⋊C4—3162no—
201C4⋊C4—3162no—
202C4⋊C4—3162no—
203C42—21no—
204C42—21no—
205C42—21no—
206C42—21no—
207C42—21no—
208C42—21no—
209C42—3162no—
210C23C2×(C2×D79)⋊C411yescharacteristic
211Q8—44no—
212Q8—6322no—
213Q8—6322no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—3162no—
229C2×C4—3164no—
230C2×C4—3162no—
231C2×C4—3162no—
232C2×C4—3162no—
233C2×C4#1457907511yescharacteristic
234C2×C4#1457907511yescharacteristic
235C2×C4#1457908912yes—
236C2×C4#1457919112yes—
237C8—44no—
238C8—6322no—
239C22—21no—
240C22—21no—
241C22C2×#1457907511yescharacteristic
242C22#1909857111yescharacteristic
243C22C2×#1457908911yescharacteristic
244C4—21no—
245C4—22no—
246C4—22no—
247C4—41no—
248C4—41no—
249C4—41no—
250C4—41no—
251C4—6322no—
252C4—6322no—
253C4#1909835912yes—
254C2—21no—
255C2—21no—
256C2#2376191911yescharacteristic
257C2#2376505511yescharacteristic
258C2C2×#1909835911yescharacteristic
subgroupG/H
centerC22C2×#14579075
commutatorC22×C4×C79C22×C4
FrattiniC2×C4⋊C4C22×D79
FittingC4×#101×C79C2
socleC22×C79C2×#99
prime radicalC23×C79C2×C22⋊C4
cosocleC2×C4⋊C4×C79C23
hypercenterC4×#101D79
hypocenterC79#11794
LCSG ▷ C22×C4×C79 ▷ C23×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
134. C79#11794semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237686122
#237617442
#237614262
C4×#101×C792
#1179479