Finite Group Databasebeta

← #32975265

Subgroups — #32975265

Order 18688.

462 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 95 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#22611494C212yesmaximal, complemented
2#22611464C211yesmaximal, characteristic
3#22607754C212yesmaximal, complemented
4#22607752C211yesmaximal, characteristic
5C73×#2683C211yesmaximal, characteristic
6C2×#14556522—21no—
7C2×#14556512—21no—
8#17988457C2211yescharacteristic
9#17988349—22no—
10#17988349—22no—
11#17988342C2211yescharacteristic
12#17988342C2212yes—
13C2×C22⋊Q8×C73—22no—
14#396×C73—22no—
15#395×C73—21no—
16#390×C73C2211yescharacteristic
17#389×C73C2212yes—
18#386×C73—21no—
19C22×#10596831—21no—
20C22×#10596831—22no—
21C2×C4⋊Dic73—21no—
22C2×C4⋊Dic73—22no—
23#14556522—42no—
24#14556512—42no—
25C22×Q8×C73—21no—
26C22×D4×C73D411yescharacteristic
27C23×C4×C73—21no—
28C22⋊Q8×C73—44no—
29C22⋊Q8×C73—44no—
30C2×C4⋊C4×C73—22no—
31C2×C4⋊C4×C73—22no—
32C2×C4⋊C4×C73D412yes—
33C2×C4⋊C4×C73D411yescharacteristic
34C2×C4⋊C4×C73D412yes—
35C2×C22⋊C4×C73—22no—
36C2×C22⋊C4×C73—22no—
37C2×C22⋊C4×C73—21no—
38C2×C42×C73C2311yescharacteristic
39#95×C73—21no—
40#95×C73—22no—
41C22×Dic73—41no—
42C2×#10596831—22no—
43C2×#10596831—41no—
44C2×#10596831—41no—
45C2×#10596831—42no—
46C2×#10596831—42no—
47C2×#10596831—42no—
48C4⋊Dic73—41no—
49C4⋊Dic73—41no—
50C4⋊Dic73—44no—
51C24×C73—21no—
52C2×Q8×C73—44no—
53C2×Q8×C73—81no—
54C2×D4×C73—21no—
55C2×D4×C73—41no—
56C2×D4×C73—41no—
57C2×D4×C73Q1612yes—
58C22×C4×C73—22no—
59C22×C4×C73—22no—
60C22×C4×C73—21no—
61C22×C4×C73—44no—
62C22×C4×C73—81no—
63C22×C4×C73C2×D412yes—
64C22×C4×C73C2×D411yescharacteristic
65C4⋊C4×C73—22no—
66C4⋊C4×C73—42no—
67C4⋊C4×C73—41no—
68C4⋊C4×C73—44no—
69C4⋊C4×C73—42no—
70C4⋊C4×C73—42no—
71C4⋊C4×C73SD1614yes—
72C22⋊C4×C73—44no—
73C22⋊C4×C73—42no—
74C22⋊C4×C73—42no—
75C22⋊C4×C73—81no—
76C42×C73—41no—
77C23×C73—22no—
78C23×C73—42no—
79C23×C73—41no—
80C23×C73—42no—
81C23×C73—41no—
82C23×C73#12011yescharacteristic
83Q8×C73—84no—
84D4×C73—42no—
85D4×C73—81no—
86C2×C4×C73—21no—
87C2×C4×C73—22no—
88C2×C4×C73—22no—
89C2×C4×C73—21no—
90C2×C4×C73—24no—
91C2×C4×C73—42no—
92C2×C4×C73—42no—
93C2×C4×C73—42no—
94C2×C4×C73—42no—
95C2×C4×C73—41no—
96C2×C4×C73—42no—
97C2×C4×C73—42no—
98C2×C4×C73—84no—
99C2×C4×C73C2×SD1612yes—
100C2×C4×C73C2×Q1611yescharacteristic
101C2×C4×C73AGL(1,ℤ/8)12yes—
102C2×C4×C73#13711yescharacteristic
103C2×Dic73—81no—
104C2×Dic73—82no—
105#10596831—42no—
106#10596831—82no—
107C22×C73—42no—
108C22×C73—44no—
109C22×C73—82no—
110C22×C73—81no—
111C22×C73—81no—
112C22×C73#45012yes—
113C22×C73#45111yescharacteristic
114C22×C73#45311yescharacteristic
115C22×C73#45412yes—
116C22×C73#45811yescharacteristic
117C4×C73—21no—
118C4×C73—21no—
119C4×C73—22no—
120C4×C73—22no—
121C4×C73—44no—
122C4×C73—82no—
123C4×C73—81no—
124Dic73—161no—
125#7826—731nomaximal, Sylow
126C2×C73—82no—
127C2×C73#161411yescharacteristic
128C2×C73#161612yes—
129C2×C73#162911yescharacteristic
130C2×C73#163712yes—
131C2×C73#165711yescharacteristic
132#2683D7311yescharacteristic
133#2100—732no—
134#2094—731no—
135#1271—732no—
136#1270—731no—
137C73#782611yescharacteristic, complemented, Sylow
138C2×C22⋊Q8—22no—
139C2×#106—1461no—
140C2×#102—1461no—
141#396—22no—
142#395—21no—
143#390C2×D7311yescharacteristic
144#389C2×D7312yes—
145#386—21no—
146#384—731no—
147#340—1462no—
148#340—1462no—
149#336—731no—
150#336—732no—
151C22×Q8—21no—
152C22×D4C22⋊D7311yescharacteristic
153C23×C4—21no—
154C22×C8—1462no—
155C22×C8—1461no—
156C22⋊Q8—44no—
157C22⋊Q8—44no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4—1462no—
161C2×C4⋊C4—1461no—
162C2×C4⋊C4C22⋊D7312yes—
163C2×C4⋊C4C22⋊D7312yes—
164C2×C4⋊C4C22⋊D7311yescharacteristic
165C2×C22⋊C4—22no—
166C2×C22⋊C4—22no—
167C2×C22⋊C4—21no—
168C2×C42C22×D7311yescharacteristic
169#106—2922no—
170#102—2922no—
171#95—21no—
172#95—22no—
173C24—21no—
174C2×Q8—44no—
175C2×Q8—81no—
176C2×D4—21no—
177C2×D4—41no—
178C2×D4—41no—
179C2×D4#1192401812yes—
180C22×C4—22no—
181C22×C4—22no—
182C22×C4—21no—
183C22×C4—44no—
184C22×C4—81no—
185C22×C4—2921no—
186C22×C4C2×C22⋊D7312yes—
187C22×C4C2×C22⋊D7311yescharacteristic
188C2×C8—2921no—
189C2×C8—2921no—
190C2×C8—2922no—
191C2×C8—2922no—
192C2×C8—2922no—
193C2×C8—1462no—
194C4⋊C4—22no—
195C4⋊C4—41no—
196C4⋊C4—42no—
197C4⋊C4—44no—
198C4⋊C4—42no—
199C4⋊C4—42no—
200C4⋊C4—2921no—
201C4⋊C4—2921no—
202C4⋊C4—2924no—
203C4⋊C4#1192401614yes—
204C22⋊C4—44no—
205C22⋊C4—42no—
206C22⋊C4—42no—
207C22⋊C4—81no—
208C42—41no—
209C23—22no—
210C23—42no—
211C23—41no—
212C23—42no—
213C23—41no—
214C23#1455656011yescharacteristic
215Q8—84no—
216D4—42no—
217D4—81no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—24no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—42no—
227C2×C4—41no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—84no—
231C2×C4—5841no—
232C2×C4—5842no—
233C2×C4C2×#1192401612yes—
234C2×C4C2×#1192401811yescharacteristic
235C2×C4#1455661712yes—
236C2×C4#1455662211yescharacteristic
237C8—2922no—
238C8—5842no—
239C22—42no—
240C22—44no—
241C22—82no—
242C22—81no—
243C22—81no—
244C22#1798873812yes—
245C22#1798874311yescharacteristic
246C22#1798875511yescharacteristic
247C22#1798876012yes—
248C22#1798877711yescharacteristic
249C4—21no—
250C4—21no—
251C4—22no—
252C4—22no—
253C4—44no—
254C4—82no—
255C4—81no—
256C4—11681no—
257C2—82no—
258C2#2260895611yescharacteristic
259C2#2260896812yes—
260C2#2260904711yescharacteristic
261C2#2260909612yes—
262C2#2260922911yescharacteristic
subgroupG/H
centerC23#14556560
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#2683C2
socleC23×C73#120
prime radicalC22×D4×C73D4
hypercenter#2683D73
hypocenterC73#7826
LCSG ▷ C2×C42×C73 ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2683

Complements

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

NH ≅ G/Ntype
1. #22611494C2semidirect
3. #22607754C2semidirect
137. C73#7826semidirect

Maximal subgroups

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

subgroupindex
#226114942
#226114642
#226077542
#226077522
C73×#26832
#782673