Finite Group Databasebeta

← #32995283

Subgroups — #32995283

Order 18688.

382 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 83 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#22618621C211yesmaximal, characteristic
2#22611550C212yesmaximal, complemented
3#22607883C212yesmaximal, complemented
4#22607867C211yesmaximal, characteristic, complemented
5C73×#1320C211yesmaximal, characteristic, complemented
6C2×#14556599C2211yescharacteristic
7C23×#10596831C411yescharacteristic
8#17989098C411yescharacteristic
9M32×D73—22no—
10#17988655—22no—
11#17988650—22no—
12#17988615C2211yescharacteristic
13#17988555C411yescharacteristic
14#17988545C411yescharacteristic
15#17988369C2212yes—
16#17988368—22no—
17#407×C73C2211yescharacteristic
18#349×C73C2212yes—
19C2×#11924028C2×C411yescharacteristic
20#14556599—41no—
21#14556599—41no—
22C2×#11924011D412yes—
23C22×#10596831—21no—
24C22×#10596831—21no—
25C22×#10596831—41no—
26C22×#10596831—41no—
27C22×#10596831C2×C411yescharacteristic
28C22×#10596831C2×C411yescharacteristic
29C2×C8×D73D412yes—
30#14556574C812yes—
31#14556570—21no—
32#14556565—21no—
33#14556560C812yes—
34C4×C22⋊D73—22no—
35#14556550C2×C411yescharacteristic
36#14556531—22no—
37#14556530—42no—
38C16×D73—42no—
39#14556520—22no—
40#14556503—22no—
41#14556501—21no—
42C8×Dic73—21no—
43C23×C4×C73C2×C411yescharacteristic
44C2×M16×C73C2×C411yescharacteristic
45C2×M16×C73C2311yescharacteristic
46M32×C73—22no—
47C22⋊C8×C73—22no—
48#11924028—41no—
49#11924028—41no—
50C2×Dic146M1611yescharacteristic
51C2×D292M1611yescharacteristic
52C2×C22⋊D73—22no—
53C2×C22⋊D73C2×C812yes—
54C2×C4×D73C22⋊C412yes—
55#11924011—42no—
56C2×#10596831—21no—
57C2×#10596831—21no—
58C2×#10596831—21no—
59C2×#10596831—42no—
60C2×#10596831—41no—
61C2×#10596831—41no—
62C2×#10596831—41no—
63C2×#10596831C22⋊C411yescharacteristic
64C2×#10596831C22⋊C411yescharacteristic
65C8×D73—22no—
66C8×D73—22no—
67C4⋊Dic73—21no—
68#11924007—22no—
69C22⋊Dic73—22no—
70C22⋊Dic73C2×C812yes—
71#11924005—22no—
72C4×Dic73—21no—
73#11924003—42no—
74C24×C73C2×C811yescharacteristic
75C22×C4×C73—21no—
76C22×C4×C73—21no—
77C22×C4×C73—41no—
78C22×C4×C73—41no—
79C22×C4×C73C2×C811yescharacteristic
80C22×C4×C73C22×C411yescharacteristic
81M16×C73—41no—
82M16×C73—41no—
83C2×C8×C73—21no—
84C2×C8×C73C2×D412yes—
85C16×C73—42no—
86C23×C73—21no—
87C23×C73—41no—
88C23×C73—42no—
89C23×C73C22×C811yescharacteristic
90C22×D73C22⋊C812yes—
91C2×C4×C73—21no—
92C2×C4×C73—21no—
93C2×C4×C73—21no—
94C2×C4×C73—42no—
95C2×C4×C73—41no—
96C2×C4×C73—41no—
97C2×C4×C73—41no—
98C2×C4×C73C2×C22⋊C411yescharacteristic
99C2×C4×C73C2×M1611yescharacteristic
100C22⋊D73—42no—
101C22⋊D73—44no—
102C2×Dic73—22no—
103C2×Dic73C22⋊C812yes—
104D292—41no—
105C4×D73—22no—
106C4×D73—22no—
107Dic146—41no—
108C8×C73—22no—
109C8×C73—41no—
110#10596831—21no—
111#10596831—41no—
112#10596831#9911yescharacteristic
113#10596831#9911yescharacteristic
114C22×C73—22no—
115C22×C73—21no—
116C22×C73—41no—
117C22×C73—41no—
118C22×C73—42no—
119C22×C73—42no—
120C22×C73—41no—
121C22×C73C2×C22⋊C811yescharacteristic
122C2×D73—22no—
123C2×D73—42no—
124C4×C73—21no—
125C4×C73—41no—
126C4×C73C2×#9911yescharacteristic
127C4×C73#41311yescharacteristic
128Dic73—22no—
129Dic73—42no—
130#11483—731nomaximal, Sylow
131C2×C73—21no—
132C2×C73—42no—
133C2×C73—41no—
134C2×C73#145911yescharacteristic
135D73—42no—
136#2929—731no—
137#2115—732no—
138#1328—732no—
139#1320—731no—
140#1320D7311yescharacteristic, complemented
141C73#1148311yescharacteristic, complemented, Sylow
142C2×#131—731no—
143C23×C8—731no—
144#525—731no—
145C2×M32—1462no—
146#435—1462no—
147C8×D4—1462no—
148#424—731no—
149#408—731no—
150#407C2×D7311yescharacteristic
151#405—731no—
152#349—732no—
153#349—1462no—
154#349C2×D7312yes—
155C2×#41—731no—
156C23×C4C4×D7311yescharacteristic
157#131—2921no—
158#131—2921no—
159C2×M16—732no—
160C2×M16C4×D7311yescharacteristic
161C2×M16C22×D7311yescharacteristic
162C22×C8—2921no—
163C22×C8—2921no—
164C22×C8—731no—
165C22×C8—731no—
166C22×C8—732no—
167C22×C8—1461no—
168C22×C8—1461no—
169#123—732no—
170C22⋊Q8—1461no—
171#121—1461no—
172#120—732no—
173C4×D4—1462no—
174#117—731no—
175M32—22no—
176M32—2922no—
177M32—1462no—
178C2×C16—2922no—
179C4⋊C8—1462no—
180C22⋊C8—22no—
181C22⋊C8—1462no—
182#97—1461no—
183C4×C8—1461no—
184C24C8×D7311yescharacteristic
185#41—2921no—
186#41—2921no—
187C2×Q8—731no—
188C2×D4—732no—
189C2×D4—731no—
190C2×D4—1462no—
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—41no—
194C22×C4—41no—
195C22×C4—732no—
196C22×C4C8×D7311yescharacteristic
197C22×C4C2×C4×D7311yescharacteristic
198M16—41no—
199M16—41no—
200M16—2922no—
201C2×C8—21no—
202C2×C8—2921no—
203C2×C8—2921no—
204C2×C8—2922no—
205C2×C8—2921no—
206C2×C8—731no—
207C2×C8—731no—
208C2×C8—1462no—
209C2×C8—1462no—
210C2×C8—1461no—
211C2×C8—1461no—
212C2×C8—1461no—
213C2×C8D4×D7312yes—
214C4⋊C4—1462no—
215C4⋊C4—1461no—
216C22⋊C4—732no—
217C22⋊C4—1462no—
218C22⋊C4—1462no—
219C42—1461no—
220C16—42no—
221C16—2922no—
222C23—21no—
223C23—41no—
224C23—42no—
225C23—732no—
226C23C2×C8×D7311yescharacteristic
227Q8—2921no—
228D4—2921no—
229D4—2924no—
230D4—2922no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—42no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—732no—
239C2×C4—1462no—
240C2×C4—1462no—
241C2×C4—1462no—
242C2×C4C22⋊C4×D7311yescharacteristic
243C2×C4M16×D7311yescharacteristic
244C8—22no—
245C8—41no—
246C8—2921no—
247C8—731no—
248C8—731no—
249C8—1461no—
250C22—22no—
251C22—21no—
252C22—41no—
253C22—41no—
254C22—42no—
255C22—42no—
256C22—41no—
257C22—2922no—
258C22—1462no—
259C22C22⋊C8×D7311yescharacteristic
260C4—21no—
261C4—41no—
262C4—2922no—
263C4—1462no—
264C4#99×D7311yescharacteristic
265C4#1798856811yescharacteristic
266C2—21no—
267C2—42no—
268C2—41no—
269C2—2922no—
270C2#2260824611yescharacteristic
subgroupG/H
centerC4#99×D73
commutatorC23×C73C22×C8
FrattiniC2×M16C22×D73
FittingC73×#1320C2
socleC2×C73#1459
prime radical#17989098C4
cosocleC2×M16×C73C23
hypercenter#1320D73
hypocenterC73#11483
LCSG ▷ C23×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1320

Complements

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

NH ≅ G/Ntype
2. #22611550C2semidirect
3. #22607883C2semidirect
4. #22607867C2semidirect
5. C73×#1320C2semidirect
140. #1320D73semidirect
141. C73#11483semidirect

Maximal subgroups

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

subgroupindex
#226186212
#226115502
#226078832
#226078672
C73×#13202
#1148373