Finite Group Databasebeta

← #32995461

Subgroups — #32995461

Order 18688.

412 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 77 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#22612500C211yesmaximal, characteristic
2#22608273C212yesmaximal
3#22607876C212yesmaximal
4#22607865C211yesmaximal, characteristic
5C73×#1319C211yesmaximal, characteristic
6C2×#14556589C411yescharacteristic
7C2×Q8×Dic73C411yescharacteristic
8C2×#14556556C2211yescharacteristic
9#17988641—22no—
10#17988493C411yescharacteristic
11#17988484—22no—
12#17988456C2211yescharacteristic
13#17988438—22no—
14C42×Dic73C411yescharacteristic
15#17988313C2212yes—
16#17988312—22no—
17#391×C73C2211yescharacteristic
18#324×C73C2212yes—
19C22×Dic146C2×C411yescharacteristic
20#14556589—22no—
21#14556589—22no—
22Q8×Dic73—41no—
23Q8×Dic73—41no—
24#14556556—41no—
25#14556556—41no—
26C2×C4⋊Dic73—21no—
27C2×C4⋊Dic73C2×C411yescharacteristic
28C2×#11924007—22no—
29C2×#11924007—22no—
30C2×#11924007D412yes—
31C2×C4×Dic73—21no—
32C2×C4×Dic73—21no—
33C2×C4×Dic73—21no—
34C2×C4×Dic73C2×C411yescharacteristic
35C2×C4×Dic73C2×C411yescharacteristic
36C2×C4×Dic73D412yes—
37#14556520—42no—
38C22⋊#10596831—22no—
39#14556501—42no—
40#14556498—22no—
41C22×Q8×C73C2×C411yescharacteristic
42C2×C4⋊C4×C73C2311yescharacteristic
43C2×C42×C73C2×C411yescharacteristic
44C22⋊C8×C73—22no—
45#95×C73—22no—
46C2×Dic146—21no—
47C2×Dic146—21no—
48C2×Dic146—41no—
49C2×Dic146—41no—
50C22×Dic73—21no—
51C22×Dic73—21no—
52C22×Dic73C22⋊C412yes—
53C22×Dic73C22⋊C411yescharacteristic
54C22×Dic73C22⋊C411yescharacteristic
55C2×#10596831—42no—
56C4⋊Dic73—42no—
57C4⋊Dic73—41no—
58#11924007—28no—
59#11924007—42no—
60#11924007—44no—
61C4×Dic73—24no—
62C4×Dic73—21no—
63C4×Dic73—22no—
64C4×Dic73—22no—
65C4×Dic73—21no—
66C4×Dic73—21no—
67C4×Dic73—42no—
68C4×Dic73—41no—
69C4×Dic73—41no—
70C4×Dic73M1612yes—
71C2×Q8×C73—21no—
72C2×Q8×C73—41no—
73C2×Q8×C73—41no—
74C2×Q8×C73M1612yes—
75C22×C4×C73—21no—
76C22×C4×C73—21no—
77C22×C4×C73C22×C411yescharacteristic
78C22×C4×C73C2×D412yes—
79C2×C8×C73—42no—
80C4⋊C4×C73—41no—
81C42×C73—41no—
82C23×C73C2×C22⋊C411yescharacteristic
83Q8×C73—42no—
84Q8×C73—42no—
85C2×C4×C73—21no—
86C2×C4×C73—21no—
87C2×C4×C73—22no—
88C2×C4×C73—22no—
89C2×C4×C73—22no—
90C2×C4×C73—41no—
91C2×C4×C73—41no—
92C2×C4×C73—41no—
93C2×C4×C73—41no—
94C2×C4×C73—42no—
95C2×C4×C73C2×M1611yescharacteristic
96C2×C4×C73C2×M1611yescharacteristic
97C2×Dic73—22no—
98C2×Dic73—22no—
99C2×Dic73—22no—
100C2×Dic73—22no—
101C2×Dic73—22no—
102C2×Dic73—21no—
103C2×Dic73—22no—
104C2×Dic73—22no—
105C2×Dic73—41no—
106C2×Dic73—42no—
107C2×Dic73—41no—
108C2×Dic73#9911yescharacteristic
109C2×Dic73#9911yescharacteristic
110Dic146—42no—
111Dic146—42no—
112C8×C73—82no—
113#10596831—82no—
114C22×C73—21no—
115C22×C73—21no—
116C22×C73#40711yescharacteristic
117C22×C73C2×#9911yescharacteristic
118C22×C73#41311yescharacteristic
119C4×C73—21no—
120C4×C73—21no—
121C4×C73—42no—
122C4×C73—42no—
123C4×C73—42no—
124Dic73—24no—
125Dic73—21no—
126Dic73—41no—
127Dic73—42no—
128Dic73—81no—
129Dic73#35612yes—
130#11532—731nomaximal, Sylow
131C2×C73—21no—
132C2×C73—21no—
133C2×C73#146511yescharacteristic
134C2×C73#212611yescharacteristic
135C2×C73C2×#35611yescharacteristic
136C4×C4⋊Q8—731no—
137#1467—732no—
138#1325—732no—
139#1319—731no—
140#1319D7311yescharacteristic
141C73#1153211yescharacteristic, complemented, Sylow
142C2×C4⋊Q8—731no—
143C2×C4×Q8—731no—
144C2×C4×Q8—731no—
145#432—1462no—
146#391—731no—
147#391C2×D7311yescharacteristic
148#389—1462no—
149#384—731no—
150C4×C4⋊C4—1462no—
151C43—731no—
152#324—732no—
153#324—1462no—
154#324C2×D7312yes—
155C22×Q8—731no—
156C22×Q8C4×D7311yescharacteristic
157C4⋊Q8—1462no—
158C4⋊Q8—1462no—
159C4×Q8—2921no—
160C4×Q8—2921no—
161C4×Q8—2921no—
162C4×Q8—2921no—
163C2×C4⋊C4—732no—
164C2×C4⋊C4—731no—
165C2×C4⋊C4—1461no—
166C2×C4⋊C4—1462no—
167C2×C4⋊C4—1462no—
168C2×C4⋊C4C22×D7311yescharacteristic
169C2×C42—731no—
170C2×C42—731no—
171C2×C42—732no—
172C2×C42—1461no—
173C2×C42—1461no—
174C2×C42—1461no—
175C2×C42C4×D7311yescharacteristic
176C4⋊C8—2922no—
177C22⋊C8—22no—
178C22⋊C8—1462no—
179#97—2922no—
180#95—22no—
181#95—1462no—
182C2×Q8—21no—
183C2×Q8—41no—
184C2×Q8—41no—
185C2×Q8—2921no—
186C2×Q8—2921no—
187C2×Q8—1461no—
188C2×Q8—1461no—
189C2×Q8#1192401112yes—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—731no—
193C22×C4—731no—
194C22×C4—732no—
195C22×C4—1461no—
196C22×C4—1461no—
197C22×C4C2×C4×D7311yescharacteristic
198C22×C4D4×D7312yes—
199C2×C8—42no—
200C2×C8—2922no—
201C4⋊C4—41no—
202C4⋊C4—2921no—
203C4⋊C4—2922no—
204C4⋊C4—2924no—
205C4⋊C4—2922no—
206C4⋊C4—1468no—
207C42—41no—
208C42—2921no—
209C42—2921no—
210C42—2922no—
211C42—732no—
212C42—1462no—
213C42—1462no—
214C42—1461no—
215C42—1461no—
216C42—1464no—
217C42—1461no—
218C23C22⋊C4×D7311yescharacteristic
219Q8—42no—
220Q8—42no—
221Q8—2922no—
222Q8—2922no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—42no—
233C2×C4—2921no—
234C2×C4—2922no—
235C2×C4—2921no—
236C2×C4—731no—
237C2×C4—731no—
238C2×C4—1462no—
239C2×C4—1461no—
240C2×C4—1462no—
241C2×C4—1462no—
242C2×C4—1462no—
243C2×C4—1462no—
244C2×C4—1462no—
245C2×C4—1462no—
246C2×C4M16×D7311yescharacteristic
247C2×C4C2×#1192401111yescharacteristic
248C8—82no—
249C8—5842no—
250C22—21no—
251C22—21no—
252C22#1798854911yescharacteristic
253C22#99×D7311yescharacteristic
254C22#1798856811yescharacteristic
255C4—21no—
256C4—21no—
257C4—42no—
258C4—42no—
259C4—42no—
260C4—2922no—
261C4—2921no—
262C4—5841no—
263C4—732no—
264C4—1464no—
265C4—1461no—
266C2—21no—
267C2—21no—
268C2#2260826611yescharacteristic
269C2#2261159511yescharacteristic
270C2#356×D7311yescharacteristic
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#11532
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
141. C73#11532semidirect

Maximal subgroups

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

subgroupindex
#226125002
#226082732
#226078762
#226078652
C73×#13192
#1153273