Finite Group Databasebeta

← #32997460

Subgroups — #32997460

Order 18688.

358 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 91 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#22620511C211yesmaximal, characteristic
2C4⋊C16×D73C211yesmaximal, characteristic, complemented
3#22608688C211yesmaximal, characteristic, complemented
4#22607986C211yesmaximal, characteristic, complemented
5#22607978C211yesmaximal, characteristic, complemented
6#22607976C211yesmaximal, characteristic, complemented
7C73×#1364C211yesmaximal, characteristic, complemented
8#17989138—21no—
9C2×C16×D73—21no—
10#17988964C2211yescharacteristic
11#17988935—21no—
12#17988824—21no—
13#17988824C412yes—
14#17988669—21no—
15#17988669C412yes—
16#17988609—21no—
17C4×C8×D73C2211yescharacteristic
18C4⋊#11924003C2211yescharacteristic
19#17988405—21no—
20#17988340C2211yescharacteristic
21#17988339—21no—
22#500×C73C2211yescharacteristic
23C4⋊C16×C73C2211yescharacteristic
24#335×C73C2211yescharacteristic
25C2×#11924029—41no—
26C2×D584—21no—
27C2×D584C2×C412yes—
28C2×#11924011—41no—
29C2×C8×D73C2×C411yescharacteristic
30C2×C8×D73D411yescharacteristic
31#14556588—21no—
32#14556580—41no—
33#14556566—22no—
34#14556566—41no—
35#14556553—22no—
36#14556553—41no—
37C42×D73D411yescharacteristic
38C2×#11924003—21no—
39C16×D73—42no—
40C4⋊#10596831—21no—
41#14556520—41no—
42#14556511—22no—
43#14556511—22no—
44C4×#10596831D411yescharacteristic
45C8×Dic73C2×C411yescharacteristic
46C8×Dic73D411yescharacteristic
47C4⋊Q8×C73—21no—
48C2×C16×C73—21no—
49#107×C73—21no—
50#107×C73C2×C412yes—
51C4⋊C8×C73—21no—
52C4×C8×C73C2311yescharacteristic
53#11924029—82no—
54#11924029—82no—
55C2×D292—22no—
56C2×D292—42no—
57C2×D292—41no—
58C2×D292—41no—
59C2×C4×D73—42no—
60C2×C4×D73C22⋊C411yescharacteristic
61C2×C4×D73D811yescharacteristic
62C2×C4×D73SD1611yescharacteristic
63D584—42no—
64D584—41no—
65D584—41no—
66#11924011—82no—
67C2×#10596831—41no—
68C2×#10596831C22⋊C411yescharacteristic
69C2×#10596831C22⋊C411yescharacteristic
70C8×D73—21no—
71C8×D73—21no—
72C8×D73—41no—
73#11924005—42no—
74#11924005—42no—
75C4×Dic73C22⋊C411yescharacteristic
76C4×Dic73D811yescharacteristic
77C4×Dic73SD1611yescharacteristic
78#11924003—41no—
79C2×Q8×C73—41no—
80C2×C8×C73—41no—
81C2×C8×C73C22×C411yescharacteristic
82C2×C8×C73C2×D411yescharacteristic
83C4⋊C4×C73—22no—
84C4⋊C4×C73—41no—
85C42×C73C2×D411yescharacteristic
86C16×C73—41no—
87C22×D73—42no—
88C22×D73#10211yescharacteristic
89Q8×C73—81no—
90Q8×C73—81no—
91C2×C4×C73—42no—
92C2×C4×C73C2×C22⋊C411yescharacteristic
93C2×C4×C73C2×D811yescharacteristic
94C2×C4×C73C2×SD1611yescharacteristic
95C2×Dic73#10211yescharacteristic
96C2×Dic73#10211yescharacteristic
97C2×Dic73#10211yescharacteristic
98D292—42no—
99D292—42no—
100D292—82no—
101D292—84no—
102D292—81no—
103D292—81no—
104C4×D73—21no—
105C4×D73—21no—
106C4×D73—41no—
107C4×D73—84no—
108C4×D73D1612yes—
109C4×D73SD3212yes—
110C8×C73—21no—
111C8×C73—81no—
112C8×C73AGL(1,ℤ/8)11yescharacteristic
113C8×C73#13711yescharacteristic
114#10596831—21no—
115#10596831—21no—
116#10596831—81no—
117C22×C73C2×#10211yescharacteristic
118C2×D73—21no—
119C2×D73—21no—
120C2×D73—82no—
121C2×D73—82no—
122C2×D73—82no—
123C2×D73#35712yes—
124C4×C73—21no—
125C4×C73—82no—
126C4×C73#41311yescharacteristic
127C4×C73#41711yescharacteristic
128C4×C73C2×D1611yescharacteristic
129C4×C73C2×SD3211yescharacteristic
130Dic73—21no—
131Dic73—21no—
132Dic73#35712yes—
133#11981—731nomaximal, Sylow
134C2×C73#154711yescharacteristic
135C2×C73C2×#35711yescharacteristic
136C2×C73#214811yescharacteristic
137D73—22no—
138D73—162no—
139#3169—731no—
140C2×C4⋊C16—731no—
141#1567—731no—
142#1364—731no—
143#1364D7311yescharacteristic, complemented
144#1361—731no—
145#1361—731no—
146C73#1198111yescharacteristic, complemented, Sylow
147#532—1461no—
148C22×C16—1461no—
149#500C2×D7311yescharacteristic
150#493—731no—
151#486—1461no—
152#466—732no—
153#466—1461no—
154C4×D8—732no—
155C4×D8—1461no—
156#423—1461no—
157C2×C4×C8—731no—
158C4⋊C16—731no—
159C4⋊C16—1461no—
160C4⋊C16C2×D7311yescharacteristic
161#335—731no—
162#335—1461no—
163#335C2×D7311yescharacteristic
164C2×#41—2921no—
165C2×D8—732no—
166C2×D8—1461no—
167C2×M16—2921no—
168C22×C8—731no—
169C22×C8—731no—
170C4⋊Q8—21no—
171#127—1461no—
172#124—2921no—
173#121—2921no—
174#121—1462no—
175C4×D4—2921no—
176C4×D4—1462no—
177C2×C42—731no—
178C2×C16—21no—
179C2×C16—2922no—
180C2×C16—1461no—
181#107—21no—
182#107C4×D7312yes—
183C4⋊C8—21no—
184C4⋊C8—2921no—
185C4⋊C8—1461no—
186#102—1462no—
187#102—1462no—
188C4×C8—731no—
189C4×C8—731no—
190C4×C8—731no—
191C4×C8C22×D7311yescharacteristic
192#41—5842no—
193#41—5842no—
194C2×Q8—41no—
195C2×D4—2922no—
196C2×D4—2921no—
197C2×D4—2921no—
198C2×D4—1462no—
199C22×C4—2922no—
200C22×C4—731no—
201C22×C4—731no—
202C22×C4—731no—
203D8—2922no—
204D8—2921no—
205D8—2921no—
206M16—5842no—
207C2×C8—41no—
208C2×C8—2921no—
209C2×C8—2921no—
210C2×C8—731no—
211C2×C8—731no—
212C2×C8—1461no—
213C2×C8—1461no—
214C2×C8C2×C4×D7311yescharacteristic
215C2×C8D4×D7311yescharacteristic
216C4⋊C4—22no—
217C4⋊C4—41no—
218C22⋊C4—2922no—
219C22⋊C4—2922no—
220C42—731no—
221C42—731no—
222C42—731no—
223C42D4×D7311yescharacteristic
224C16—41no—
225C16—2921no—
226C23—2922no—
227C23—731no—
228Q8—81no—
229Q8—81no—
230D4—2922no—
231D4—2922no—
232D4—5842no—
233D4—5844no—
234D4—5841no—
235D4—5841no—
236C2×C4—42no—
237C2×C4—2921no—
238C2×C4—5844no—
239C2×C4—731no—
240C2×C4—732no—
241C2×C4—732no—
242C2×C4—731no—
243C2×C4—731no—
244C2×C4—1461no—
245C2×C4—1461no—
246C2×C4C22⋊C4×D7311yescharacteristic
247C2×C4D8×D7311yescharacteristic
248C2×C4SD16×D7311yescharacteristic
249C8—21no—
250C8—81no—
251C8—5841no—
252C8—1461no—
253C8—1461no—
254C8#1455661811yescharacteristic
255C8#1455662311yescharacteristic
256C22—5842no—
257C22—5842no—
258C22—5842no—
259C22—732no—
260C22—1461no—
261C22—1461no—
262C22#102×D7311yescharacteristic
263C4—21no—
264C4—82no—
265C4—732no—
266C4—1461no—
267C4—1461no—
268C4#1798857011yescharacteristic
269C4#1798858711yescharacteristic
270C4D16×D7311yescharacteristic
271C4SD32×D7311yescharacteristic
272C2—11682no—
273C2—1462no—
274C2#2260860711yescharacteristic
275C2#357×D7311yescharacteristic
276C2#2261167911yescharacteristic
subgroupG/H
centerC22#102×D73
commutatorC2×C8×C73C22×C4
FrattiniC4×C8C22×D73
FittingC73×#1364C2
socleC22×C73C2×#102
prime radical#22620511C2
cosocleC4×C8×C73C23
hypercenter#1364D73
hypocenterC73#11981
LCSG ▷ C2×C8×C73 ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1364

Complements

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

NH ≅ G/Ntype
2. C4⋊C16×D73C2semidirect
3. #22608688C2semidirect
4. #22607986C2semidirect
5. #22607978C2semidirect
6. #22607976C2semidirect
7. C73×#1364C2semidirect
143. #1364D73semidirect
146. C73#11981semidirect

Maximal subgroups

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

subgroupindex
#226205112
C4⋊C16×D732
#226086882
#226079862
#226079782
#226079762
C73×#13642
#1198173