Finite Group Databasebeta

← #32989221

Subgroups — #32989221

Order 18688.

414 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 75 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#22615596C211yesmaximal, characteristic
2#22610030C212yesmaximal
3#22607839C211yesmaximal, characteristic
4#22607783C212yesmaximal
5C73×#1820C211yesmaximal, characteristic
6#17988551C2212yes—
7#17988523—21no—
8#17988499—21no—
9#17988491—22no—
10#17988474—22no—
11C4×C22⋊Dic73C2212yes—
12#17988346—22no—
13#17988346—22no—
14C2×#117×C73C2211yescharacteristic
15#381×C73C2211yescharacteristic
16#381×C73C2211yescharacteristic
17#342×C73—21no—
18#342×C73—21no—
19C22×Dic146—21no—
20C2×#11924012—22no—
21C2×C4⋊Dic73—21no—
22C2×#11924007—22no—
23C2×C22⋊Dic73—22no—
24C2×C4×Dic73D412yes—
25C2×C4×Dic73D412yes—
26C22⋊#10596831—22no—
27C22⋊#10596831—22no—
28#14556498—21no—
29#14556498—22no—
30#14556498—21no—
31#14556498—22no—
32C23×C4×C73C2311yescharacteristic
33#117×C73—22no—
34#117×C73—22no—
35C2×C4⋊C4×C73Q812yescomplemented
36C2×C22⋊C4×C73—21no—
37C2×C22⋊C4×C73—21no—
38C2×C22⋊C4×C73D411yescharacteristic
39C2×C22⋊C4×C73D411yescharacteristic
40C2×C42×C73—21no—
41#95×C73—22no—
42#95×C73—22no—
43C2×Dic146—44no—
44C2×Dic146—81no—
45C22×Dic73—22no—
46C22×Dic73—22no—
47#11924012—42no—
48#11924012—42no—
49C2×#10596831—42no—
50C4⋊Dic73—81no—
51#11924007—44no—
52C22⋊Dic73—44no—
53C4×Dic73—42no—
54C4×Dic73—42no—
55C24×C73C2×D411yescharacteristic
56C22×C4×C73—21no—
57C22×C4×C73—21no—
58C22×C4×C73—22no—
59C22×C4×C73—41no—
60C22×C4×C73—41no—
61C22×C4×C73—41no—
62C22×C4×C73C2×D412yes—
63C22×C4×C73C2×Q811yescharacteristic
64C22×C4×C73#4112yes—
65C22×C4×C73#4111yescharacteristic
66C4⋊C4×C73—24no—
67C22⋊C4×C73—41no—
68C22⋊C4×C73—41no—
69C22⋊C4×C73—41no—
70C22⋊C4×C73—41no—
71C22⋊C4×C73—41no—
72C22⋊C4×C73—41no—
73C42×C73—42no—
74C23×C73—21no—
75C23×C73—21no—
76C23×C73—42no—
77C23×C73#12011yescharacteristic
78C23×C73C22⋊Q811yescharacteristic
79C23×C73#12411yescharacteristic
80C2×C4×C73—22no—
81C2×C4×C73—22no—
82C2×C4×C73—41no—
83C2×C4×C73—42no—
84C2×C4×C73—41no—
85C2×C4×C73—42no—
86C2×C4×C73—42no—
87C2×C4×C73—42no—
88C2×C4×C73—41no—
89C2×C4×C73—41no—
90C2×C4×C73—82no—
91C2×C4×C73—81no—
92C2×C4×C73—82no—
93C2×C4×C73C22⋊Q812yes—
94C2×C4×C73#12412yes—
95C2×Dic73—24no—
96C2×Dic73—42no—
97C2×Dic73—42no—
98C2×Dic73—42no—
99C2×Dic73—42no—
100C2×Dic73—42no—
101Dic146—84no—
102#10596831—82no—
103C22×C73—22no—
104C22×C73—21no—
105C22×C73—21no—
106C22×C73—22no—
107C22×C73—22no—
108C22×C73—81no—
109C22×C73—81no—
110C22×C73#39311yescharacteristic
111C22×C73#45811yescharacteristic
112C22×C73#45811yescharacteristic
113C4×C73—22no—
114C4×C73—22no—
115C4×C73—81no—
116C4×C73—81no—
117C4×C73—82no—
118C4×C73—161no—
119Dic73—44no—
120Dic73—82no—
121#10387—731nomaximal, Sylow
122C2×C73—21no—
123C2×C73—21no—
124C2×C73—41no—
125C2×C73—41no—
126C2×C73#203011yescharacteristic
127C2×C73#203112yes—
128#2607—731no—
129#1826—732no—
130#1820D7311yescharacteristic
131#1306—731no—
132#1284—732no—
133C73#1038711yescharacteristic, complemented, Sylow
134C2×#117C2×D7311yescharacteristic
135#407—732no—
136#399—1461no—
137#393—1461no—
138#391—1462no—
139#387—1462no—
140#381C2×D7311yescharacteristic
141#381C2×D7311yescharacteristic
142C4×C22⋊C4—732no—
143#342—21no—
144#342—21no—
145#339—1462no—
146#339—1462no—
147C22×Q8—1461no—
148C23×C4C22×D7311yescharacteristic
149C2×M16—1462no—
150#117—22no—
151#117—22no—
152C2×C4⋊C4—1462no—
153C2×C4⋊C4—1461no—
154C2×C4⋊C4Dic14612yescomplemented
155C2×C22⋊C4—21no—
156C2×C22⋊C4—21no—
157C2×C22⋊C4—1462no—
158C2×C22⋊C4C22⋊D7311yescharacteristic
159C2×C22⋊C4C22⋊D7311yescharacteristic
160C2×C42—21no—
161C2×C42—732no—
162C2×C42—732no—
163C22⋊C8—1462no—
164C22⋊C8—1462no—
165#95—22no—
166#95—22no—
167#95—1461no—
168#95—1462no—
169#95—1461no—
170#95—1462no—
171C24C2×C22⋊D7311yescharacteristic
172C2×Q8—2924no—
173C2×Q8—5841no—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—22no—
177C22×C4—41no—
178C22×C4—41no—
179C22×C4—41no—
180C22×C4—1462no—
181C22×C4—1462no—
182C22×C4D4×D7312yes—
183C22×C4C2×Dic14611yescharacteristic
184C22×C4#1192402712yes—
185C22×C4#1192402811yescharacteristic
186M16—2922no—
187M16—2922no—
188C2×C8—2922no—
189C4⋊C4—24no—
190C4⋊C4—2924no—
191C4⋊C4—5841no—
192C22⋊C4—41no—
193C22⋊C4—41no—
194C22⋊C4—41no—
195C22⋊C4—41no—
196C22⋊C4—41no—
197C22⋊C4—41no—
198C22⋊C4—2924no—
199C42—42no—
200C42—2922no—
201C42—2922no—
202C23—21no—
203C23—21no—
204C23—42no—
205C23#1455655911yescharacteristic
206C23#1455657011yescharacteristic
207C23#1455657811yescharacteristic
208Q8—5844no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—41no—
212C2×C4—42no—
213C2×C4—41no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4—82no—
220C2×C4—81no—
221C2×C4—82no—
222C2×C4—2922no—
223C2×C4—2922no—
224C2×C4—2922no—
225C2×C4—2922no—
226C2×C4—2922no—
227C2×C4—1464no—
228C2×C4#1455656812yes—
229C2×C4#1455657712yes—
230C8—5842no—
231C22—22no—
232C22—21no—
233C22—21no—
234C22—22no—
235C22—22no—
236C22—81no—
237C22—81no—
238C22#1798849911yescharacteristic
239C22#1798877611yescharacteristic
240C22#1798877611yescharacteristic
241C4—22no—
242C4—22no—
243C4—81no—
244C4—81no—
245C4—82no—
246C4—161no—
247C4—2924no—
248C4—5842no—
249C2—21no—
250C2—21no—
251C2—41no—
252C2—41no—
253C2#2261109811yescharacteristic
254C2#2261110512yes—
subgroupG/H
centerC22#17988499
commutator, cosocleC23×C4×C73C23
FrattiniC23×C4C22×D73
FittingC73×#1820C2
socleC22×C73#393
prime radicalC24×C73C2×D4
hypercenter#1820D73
hypocenterC73#10387
LCSG ▷ C23×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1820

Complements

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

NH ≅ G/Ntype
35. C2×C4⋊C4×C73Q8semidirect
133. C73#10387semidirect
154. C2×C4⋊C4Dic146semidirect

Maximal subgroups

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

subgroupindex
#226155962
#226100302
#226078392
#226077832
C73×#18202
#1038773