Finite Group Databasebeta

← #32995477

Subgroups — #32995477

Order 18688.

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

normal subgroups only

This group has 376 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#22612649C211yesmaximal, characteristic
2#22608273C212yesmaximal
3#22607874C212yesmaximal
4#22607865C211yesmaximal, characteristic
5C73×#1319C211yesmaximal, characteristic
6C2×#14556589C411yescharacteristic
7C2×Q8×Dic73C411yescharacteristic
8C2×#14556556C2211yescharacteristic
9#17988641—22no—
10#17988493C411yescharacteristic
11#17988474—22no—
12#17988469—22no—
13#17988452C2211yescharacteristic
14#17988433C411yescharacteristic
15#17988313C2212yes—
16#17988312—22no—
17#391×C73C2211yescharacteristic
18#324×C73C2212yes—
19C22×Dic146C2×C411yescharacteristic
20#14556589—22no—
21#14556589—22no—
22Q8×Dic73—42no—
23#14556556—42no—
24C2×C4⋊Dic73—21no—
25C2×C4⋊Dic73C2×C411yescharacteristic
26C2×#11924007—22no—
27C2×#11924007D412yes—
28C2×C4×Dic73—21no—
29C2×C4×Dic73C2×C411yescharacteristic
30C2×C4×Dic73C2×C411yescharacteristic
31C2×C4×Dic73D412yes—
32#14556520—42no—
33C22⋊#10596831—22no—
34#14556501—42no—
35#14556498—21no—
36#14556498—21no—
37#14556498—22no—
38#14556498—22no—
39C22×Q8×C73C2×C411yescharacteristic
40C2×C4⋊C4×C73C2311yescharacteristic
41C2×C42×C73C2×C411yescharacteristic
42C22⋊C8×C73—22no—
43#95×C73—22no—
44C2×Dic146—21no—
45C2×Dic146—21no—
46C2×Dic146—41no—
47C2×Dic146—41no—
48C22×Dic73—21no—
49C22×Dic73—21no—
50C22×Dic73C22⋊C412yes—
51C22×Dic73C22⋊C411yescharacteristic
52C22×Dic73C22⋊C411yescharacteristic
53C2×#10596831—42no—
54C4⋊Dic73—42no—
55C4⋊Dic73—41no—
56#11924007—28no—
57#11924007—42no—
58C4×Dic73—21no—
59C4×Dic73—22no—
60C4×Dic73—22no—
61C4×Dic73—22no—
62C4×Dic73—42no—
63C4×Dic73M1612yes—
64C2×Q8×C73—21no—
65C2×Q8×C73—41no—
66C2×Q8×C73—41no—
67C2×Q8×C73M1612yes—
68C22×C4×C73—21no—
69C22×C4×C73—21no—
70C22×C4×C73C22×C411yescharacteristic
71C22×C4×C73C2×D412yes—
72C2×C8×C73—42no—
73C4⋊C4×C73—41no—
74C42×C73—41no—
75C23×C73C2×C22⋊C411yescharacteristic
76Q8×C73—42no—
77Q8×C73—42no—
78C2×C4×C73—21no—
79C2×C4×C73—21no—
80C2×C4×C73—22no—
81C2×C4×C73—22no—
82C2×C4×C73—41no—
83C2×C4×C73—41no—
84C2×C4×C73—42no—
85C2×C4×C73—41no—
86C2×C4×C73—41no—
87C2×C4×C73—41no—
88C2×C4×C73C2×M1611yescharacteristic
89C2×C4×C73C2×M1611yescharacteristic
90C2×Dic73—22no—
91C2×Dic73—22no—
92C2×Dic73—21no—
93C2×Dic73—22no—
94C2×Dic73—22no—
95C2×Dic73—41no—
96C2×Dic73—41no—
97C2×Dic73—41no—
98C2×Dic73—41no—
99C2×Dic73—42no—
100C2×Dic73—41no—
101C2×Dic73#9912yes—
102Dic146—42no—
103Dic146—42no—
104C8×C73—82no—
105#10596831—82no—
106C22×C73—21no—
107C22×C73—21no—
108C22×C73#40711yescharacteristic
109C22×C73C2×#9911yescharacteristic
110C22×C73#41311yescharacteristic
111C4×C73—21no—
112C4×C73—21no—
113C4×C73—42no—
114C4×C73—42no—
115C4×C73—81no—
116Dic73—22no—
117Dic73—42no—
118Dic73—41no—
119Dic73—42no—
120Dic73—81no—
121#11536—731nomaximal, Sylow
122C2×C73—21no—
123C2×C73—21no—
124C2×C73#146511yescharacteristic
125C2×C73#212911yescharacteristic
126C2×C73#213311yescharacteristic
127#2327—731no—
128#1467—732no—
129#1324—732no—
130#1319—731no—
131#1319D7311yescharacteristic
132C73#1153611yescharacteristic, complemented, Sylow
133C2×C4⋊Q8—731no—
134C2×C4×Q8—731no—
135C2×C4×Q8—731no—
136#432—1462no—
137#391—731no—
138#391C2×D7311yescharacteristic
139#387—1462no—
140#387—1462no—
141#382—731no—
142#376—731no—
143#324—732no—
144#324—1462no—
145#324C2×D7312yes—
146C22×Q8—731no—
147C22×Q8C4×D7311yescharacteristic
148C4⋊Q8—1462no—
149C4⋊Q8—1462no—
150C4×Q8—2922no—
151C4×Q8—2922no—
152C2×C4⋊C4—732no—
153C2×C4⋊C4—731no—
154C2×C4⋊C4—1461no—
155C2×C4⋊C4—1462no—
156C2×C4⋊C4C22×D7311yescharacteristic
157C2×C42—731no—
158C2×C42—731no—
159C2×C42—732no—
160C2×C42—1461no—
161C2×C42C4×D7311yescharacteristic
162C4⋊C8—2922no—
163C22⋊C8—22no—
164C22⋊C8—1462no—
165#97—2922no—
166#95—22no—
167#95—1461no—
168#95—1461no—
169#95—1462no—
170#95—1462no—
171C2×Q8—21no—
172C2×Q8—41no—
173C2×Q8—41no—
174C2×Q8—2921no—
175C2×Q8—2921no—
176C2×Q8—1461no—
177C2×Q8—1461no—
178C2×Q8#1192401112yes—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—731no—
182C22×C4—731no—
183C22×C4—732no—
184C22×C4—1461no—
185C22×C4—1461no—
186C22×C4C2×C4×D7311yescharacteristic
187C22×C4D4×D7312yes—
188C2×C8—42no—
189C2×C8—2922no—
190C4⋊C4—41no—
191C4⋊C4—2921no—
192C4⋊C4—2922no—
193C4⋊C4—2922no—
194C4⋊C4—1468no—
195C42—41no—
196C42—2922no—
197C42—732no—
198C42—1462no—
199C42—1462no—
200C42—1462no—
201C42—1461no—
202C23C22⋊C4×D7311yescharacteristic
203Q8—42no—
204Q8—42no—
205Q8—2922no—
206Q8—2922no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—42no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—2921no—
218C2×C4—2921no—
219C2×C4—2921no—
220C2×C4—2922no—
221C2×C4—2921no—
222C2×C4—2921no—
223C2×C4—732no—
224C2×C4—1462no—
225C2×C4—1462no—
226C2×C4—1461no—
227C2×C4—1462no—
228C2×C4—1462no—
229C2×C4M16×D7311yescharacteristic
230C2×C4C2×#1192401111yescharacteristic
231C8—82no—
232C8—5842no—
233C22—21no—
234C22—21no—
235C22#1798854911yescharacteristic
236C22#99×D7311yescharacteristic
237C22#1798856811yescharacteristic
238C4—21no—
239C4—21no—
240C4—42no—
241C4—42no—
242C4—81no—
243C4—2922no—
244C4—2922no—
245C4—2921no—
246C4—5841no—
247C4—1462no—
248C2—21no—
249C2—21no—
250C2#2260826611yescharacteristic
251C2#2261160411yescharacteristic
252C2#2261161911yescharacteristic
subgroupG/H
centerC22#99×D73
commutatorC22×C4×C73C22×C4
FrattiniC2×C4⋊C4C22×D73
FittingC73×#1319C2
socleC22×C73C2×#99
prime radicalC23×C73C2×C22⋊C4
cosocleC2×C4⋊C4×C73C23
hypercenter#1319D73
hypocenterC73#11536
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1319

Complements

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

NH ≅ G/Ntype
132. C73#11536semidirect

Maximal subgroups

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

subgroupindex
#226126492
#226082732
#226078742
#226078652
C73×#13192
#1153673