Finite Group Databasebeta

← #32983678

Subgroups — #32983678

Order 18688.

448 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 107 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#22615136C211yesmaximal, characteristic
2#22608647C212yesmaximal
3#22608275C211yesmaximal, characteristic
4#22607788C212yesmaximal
5C73×#2983C211yesmaximal, characteristic
6C2×#14556591C2211yescharacteristic
7#17988644C2212yes—
8#17988507—21no—
9#17988507—21no—
10#17988494C412yes—
11#17988485—21no—
12#17988485—21no—
13#17988456C412yes—
14C4×C4⋊Dic73C2211yescharacteristic
15#17988332—24no—
16#17988313—21no—
17#17988313—21no—
18C2×C4×Q8×C73C2211yescharacteristic
19#446×C73—24no—
20#432×C73—21no—
21#432×C73C2212yes—
22#431×C73—21no—
23C22×Dic146—21no—
24#14556591—22no—
25#14556591—22no—
26C2×C4⋊Dic73—21no—
27C2×C4⋊Dic73—21no—
28C2×C4⋊Dic73C2×C412yes—
29C2×#11924007—22no—
30C2×#11924007—22no—
31C2×C4×Dic73C2×C412yes—
32C4⋊#10596831—22no—
33C22⋊#10596831—22no—
34#14556502—22no—
35#14556498—22no—
36#14556498—22no—
37#14556498—21no—
38C22×Q8×C73C2×C411yescharacteristic
39C4×Q8×C73—22no—
40C4×Q8×C73—22no—
41C2×C4⋊C4×C73C2×C411yescharacteristic
42C2×C4⋊C4×C73D411yescharacteristic
43C2×C4⋊C4×C73D411yescharacteristic
44C2×C42×C73D411yescharacteristic
45C2×C42×C73D411yescharacteristic
46C2×C42×C73C2311yescharacteristic
47C4⋊C8×C73—22no—
48C4⋊C8×C73—22no—
49C4⋊C8×C73D414yes—
50C22⋊C8×C73—22no—
51#97×C73—22no—
52#97×C73—22no—
53C4×C8×C73—22no—
54C2×Dic146—42no—
55C2×Dic146—82no—
56C22×Dic73—22no—
57C22×Dic73—22no—
58C2×#10596831—42no—
59C4⋊Dic73—24no—
60C4⋊Dic73—24no—
61C4⋊Dic73—41no—
62C4⋊Dic73—41no—
63#11924007—82no—
64#11924007—82no—
65C4×Dic73—42no—
66C2×Q8×C73—22no—
67C2×Q8×C73—22no—
68C2×Q8×C73—41no—
69C22×C4×C73C22⋊C411yescharacteristic
70C22×C4×C73C22⋊C411yescharacteristic
71C22×C4×C73C22⋊C411yescharacteristic
72C22×C4×C73C22⋊C411yescharacteristic
73C22×C4×C73C22×C411yescharacteristic
74C22×C4×C73C2×D411yescharacteristic
75C22×C4×C73C2×D411yescharacteristic
76C2×C8×C73—24no—
77C4⋊C4×C73—22no—
78C4⋊C4×C73—22no—
79C4⋊C4×C73—22no—
80C42×C73—21no—
81C42×C73—21no—
82C42×C73—21no—
83C42×C73—21no—
84C42×C73C2×D412yes—
85C42×C73#4112yes—
86C23×C73C2×C22⋊C411yescharacteristic
87Q8×C73—44no—
88C2×C4×C73—21no—
89C2×C4×C73—21no—
90C2×C4×C73—21no—
91C2×C4×C73—21no—
92C2×C4×C73—22no—
93C2×C4×C73—21no—
94C2×C4×C73—21no—
95C2×C4×C73—21no—
96C2×C4×C73—21no—
97C2×C4×C73—21no—
98C2×C4×C73—41no—
99C2×C4×C73—41no—
100C2×C4×C73—41no—
101C2×C4×C73#10112yes—
102C2×C4×C73C4×D412yes—
103C2×C4×C73#12011yescharacteristic
104C2×C4×C73#12112yes—
105C2×C4×C73#12311yescharacteristic
106C2×Dic73—24no—
107C2×Dic73—42no—
108C2×Dic73—42no—
109C2×Dic73—42no—
110C2×Dic73—42no—
111C2×Dic73—42no—
112Dic146—84no—
113C8×C73—44no—
114#10596831—82no—
115C22×C73—21no—
116C22×C73—21no—
117C22×C73#38611yescharacteristic
118C22×C73C2×#10111yescharacteristic
119C22×C73#41311yescharacteristic
120C4×C73—21no—
121C4×C73—22no—
122C4×C73—22no—
123C4×C73—22no—
124C4×C73—41no—
125C4×C73—41no—
126C4×C73—41no—
127C4×C73#45612yes—
128Dic73—44no—
129Dic73—82no—
130#9454—731nomaximal, Sylow
131C2×C73—21no—
132C2×C73—21no—
133C2×C73#188611yescharacteristic
134C2×C73#190111yescharacteristic
135C2×C73#191011yescharacteristic
136#2983D7311yescharacteristic
137#2567—731no—
138#1556—732no—
139#1467—731no—
140#1285—732no—
141C73#945411yescharacteristic, complemented, Sylow
142C2×C4⋊Q8—731no—
143C2×C4×Q8C2×D7311yescharacteristic
144#446—24no—
145#432—21no—
146#432—732no—
147#432C2×D7312yes—
148#431—21no—
149#395—1461no—
150#395—1461no—
151#391—732no—
152#389—1461no—
153#389—1461no—
154#384—732no—
155C4×C4⋊C4—731no—
156#332—1464no—
157#324—1461no—
158#324—1461no—
159C22×Q8—1461no—
160C22×Q8C4×D7311yescharacteristic
161C4⋊Q8—1462no—
162C4⋊Q8—1462no—
163C4×Q8—22no—
164C4×Q8—22no—
165C2×C4⋊C4—732no—
166C2×C4⋊C4—1461no—
167C2×C4⋊C4—1462no—
168C2×C4⋊C4—1462no—
169C2×C4⋊C4—1461no—
170C2×C4⋊C4C4×D7311yescharacteristic
171C2×C4⋊C4D29211yescharacteristic
172C2×C4⋊C4D29211yescharacteristic
173C2×C42—732no—
174C2×C42C22⋊D7311yescharacteristic
175C2×C42C22⋊D7311yescharacteristic
176C2×C42C22×D7311yescharacteristic
177C4⋊C8—22no—
178C4⋊C8—22no—
179C4⋊C8—1462no—
180C4⋊C8C22⋊D7314yes—
181C22⋊C8—22no—
182C22⋊C8—1462no—
183#97—22no—
184#97—22no—
185#97—1462no—
186C4×C8—22no—
187#95—1462no—
188#95—1462no—
189#95—1461no—
190C2×Q8—22no—
191C2×Q8—22no—
192C2×Q8—41no—
193C2×Q8—2922no—
194C2×Q8—5842no—
195C22×C4—1462no—
196C22×C4—1462no—
197C22×C4#1192400511yescharacteristic
198C22×C4#1192400511yescharacteristic
199C22×C4#1192400511yescharacteristic
200C22×C4#1192400511yescharacteristic
201C22×C4C2×C4×D7311yescharacteristic
202C22×C4C2×C22⋊D7311yescharacteristic
203C22×C4C2×D29211yescharacteristic
204C2×C8—24no—
205C2×C8—2922no—
206C4⋊C4—22no—
207C4⋊C4—22no—
208C4⋊C4—22no—
209C4⋊C4—2921no—
210C4⋊C4—2921no—
211C4⋊C4—5842no—
212C4⋊C4—5842no—
213C4⋊C4—1464no—
214C4⋊C4—1464no—
215C42—21no—
216C42—21no—
217C42—21no—
218C42—21no—
219C42—2922no—
220C42C2×C22⋊D7312yes—
221C42#1192402812yes—
222C23C2×#1192400511yescharacteristic
223Q8—44no—
224Q8—5844no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—2922no—
239C2×C4—2922no—
240C2×C4—2922no—
241C2×C4—2922no—
242C2×C4—2922no—
243C2×C4—1464no—
244C2×C4#1455650912yes—
245C2×C4C4×C22⋊D7312yes—
246C2×C4#1455656011yescharacteristic
247C2×C4#1455656512yes—
248C2×C4#1455657411yescharacteristic
249C8—44no—
250C8—5842no—
251C22—21no—
252C22—21no—
253C22#1798846611yescharacteristic
254C22C2×#1455650911yescharacteristic
255C22#1798856911yescharacteristic
256C4—22no—
257C4—21no—
258C4—22no—
259C4—22no—
260C4—41no—
261C4—41no—
262C4—41no—
263C4—2924no—
264C4—5842no—
265C4#1798877012yes—
266C2—21no—
267C2—21no—
268C2#2261032411yescharacteristic
269C2#2261039911yescharacteristic
270C2#2261045811yescharacteristic
subgroupG/H
centerC22#17988466
commutatorC22×C4×C73C22×C4
FrattiniC2×C42C22×D73
FittingC73×#2983C2
socleC22×C73#386
prime radicalC23×C73C2×C22⋊C4
cosocleC2×C42×C73C23
hypercenter#2983D73
hypocenterC73#9454
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2983

Complements

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

NH ≅ G/Ntype
141. C73#9454semidirect

Maximal subgroups

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

subgroupindex
#226151362
#226086472
#226082752
#226077882
C73×#29832
#945473