Finite Group Databasebeta

← #32983679

Subgroups — #32983679

Order 18688.

448 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 111 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#22619016C211yesmaximal, characteristic
2#22608648C212yesmaximal
3#22608275C211yesmaximal, characteristic
4#22607787C212yesmaximal
5C73×#2567C211yesmaximal, characteristic
6#17988718—24no—
7#17988644—21no—
8#17988644C2212yes—
9#17988644C2212yes—
10#17988640—21no—
11#17988333—24no—
12#17988313—21no—
13#17988313—21no—
14C2×C4⋊Q8×C73C2211yescharacteristic
15C2×C4×Q8×C73C2211yescharacteristic
16#395×C73—21no—
17#395×C73—21no—
18#391×C73C412yes—
19#389×C73—21no—
20#389×C73—21no—
21#384×C73C412yes—
22C4×C4⋊C4×C73C2211yescharacteristic
23C4⋊#10596831—22no—
24C4⋊#10596831—22no—
25C4⋊#10596831—22no—
26C4⋊#10596831D414yes—
27C22⋊#10596831—22no—
28C22⋊#10596831—22no—
29#14556502—22no—
30#14556502—22no—
31#14556502—22no—
32C4×#10596831—22no—
33C22×Q8×C73—21no—
34C22×Q8×C73C2×C411yescharacteristic
35C4⋊Q8×C73—22no—
36C4⋊Q8×C73—22no—
37C4×Q8×C73—22no—
38C4×Q8×C73—22no—
39C2×C4⋊C4×C73—21no—
40C2×C4⋊C4×C73—21no—
41C2×C4⋊C4×C73—22no—
42C2×C4⋊C4×C73—22no—
43C2×C4⋊C4×C73C2×C412yes—
44C2×C4⋊C4×C73C2×C411yescharacteristic
45C2×C4⋊C4×C73D411yescharacteristic
46C2×C4⋊C4×C73D411yescharacteristic
47C2×C42×C73C2×C412yes—
48C2×C42×C73D411yescharacteristic
49C2×C42×C73D411yescharacteristic
50C2×C42×C73C2311yescharacteristic
51#95×C73—22no—
52#95×C73—22no—
53#95×C73—21no—
54C2×#10596831—24no—
55C2×#10596831—42no—
56C2×Q8×C73—22no—
57C2×Q8×C73—22no—
58C2×Q8×C73—41no—
59C2×Q8×C73—42no—
60C2×Q8×C73—82no—
61C22×C4×C73—22no—
62C22×C4×C73—22no—
63C22×C4×C73C22⋊C411yescharacteristic
64C22×C4×C73C22⋊C411yescharacteristic
65C22×C4×C73C22⋊C411yescharacteristic
66C22×C4×C73C22⋊C411yescharacteristic
67C22×C4×C73C22×C411yescharacteristic
68C22×C4×C73C2×D411yescharacteristic
69C22×C4×C73C2×D411yescharacteristic
70C4⋊C4×C73—24no—
71C4⋊C4×C73—22no—
72C4⋊C4×C73—22no—
73C4⋊C4×C73—22no—
74C4⋊C4×C73—24no—
75C4⋊C4×C73—41no—
76C4⋊C4×C73—41no—
77C4⋊C4×C73—82no—
78C4⋊C4×C73—82no—
79C42×C73—21no—
80C42×C73—21no—
81C42×C73—21no—
82C42×C73—21no—
83C42×C73—42no—
84C42×C73C2×D412yes—
85C42×C73#4112yes—
86C23×C73C2×C22⋊C411yescharacteristic
87Q8×C73—44no—
88Q8×C73—84no—
89C2×C4×C73—21no—
90C2×C4×C73—21no—
91C2×C4×C73—21no—
92C2×C4×C73—21no—
93C2×C4×C73—22no—
94C2×C4×C73—24no—
95C2×C4×C73—21no—
96C2×C4×C73—21no—
97C2×C4×C73—21no—
98C2×C4×C73—21no—
99C2×C4×C73—21no—
100C2×C4×C73—41no—
101C2×C4×C73—42no—
102C2×C4×C73—42no—
103C2×C4×C73—41no—
104C2×C4×C73—41no—
105C2×C4×C73—42no—
106C2×C4×C73—42no—
107C2×C4×C73—42no—
108C2×C4×C73#10112yes—
109C2×C4×C73C4×D412yes—
110C2×C4×C73#12011yescharacteristic
111C2×C4×C73#12112yes—
112C2×C4×C73#12311yescharacteristic
113#10596831—44no—
114#10596831—82no—
115C22×C73—21no—
116C22×C73—21no—
117C22×C73#38611yescharacteristic
118C22×C73C2×#10111yescharacteristic
119C22×C73#41311yescharacteristic
120C4×C73—21no—
121C4×C73—22no—
122C4×C73—22no—
123C4×C73—22no—
124C4×C73—44no—
125C4×C73—41no—
126C4×C73—41no—
127C4×C73—41no—
128C4×C73—82no—
129C4×C73#45612yes—
130#9454—731nomaximal, Sylow
131C2×C73—21no—
132C2×C73—21no—
133C2×C73#188611yescharacteristic
134C2×C73#190111yescharacteristic
135C2×C73#191011yescharacteristic
136#2983—731no—
137#2567D7311yescharacteristic
138#1556—732no—
139#1467—731no—
140#1285—732no—
141C73#945411yescharacteristic, complemented, Sylow
142C2×C4⋊Q8C2×D7311yescharacteristic
143C2×C4×Q8C2×D7311yescharacteristic
144#446—1464no—
145#432—732no—
146#432—732no—
147#432—1461no—
148#431—1461no—
149#395—21no—
150#395—21no—
151#391Dic7312yes—
152#389—21no—
153#389—21no—
154#384Dic7312yes—
155C4×C4⋊C4C2×D7311yescharacteristic
156#332—1464no—
157#324—1461no—
158#324—1461no—
159C22×Q8—21no—
160C22×Q8C2×Dic7311yescharacteristic
161C4⋊Q8—22no—
162C4⋊Q8—22no—
163C4×Q8—22no—
164C4×Q8—22no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4C2×Dic7312yes—
170C2×C4⋊C4C2×Dic7311yescharacteristic
171C2×C4⋊C4C22⋊D7311yescharacteristic
172C2×C4⋊C4C22⋊D7311yescharacteristic
173C2×C42C2×Dic7312yes—
174C2×C42C22⋊D7311yescharacteristic
175C2×C42C22⋊D7311yescharacteristic
176C2×C42C22×D7311yescharacteristic
177C4⋊C8—734no—
178C4⋊C8—1462no—
179C4⋊C8—1462no—
180C4⋊C8—1462no—
181C22⋊C8—1462no—
182C22⋊C8—1462no—
183#97—1462no—
184#97—1462no—
185#97—1462no—
186C4×C8—1462no—
187#95—22no—
188#95—22no—
189#95—21no—
190C2×Q8—22no—
191C2×Q8—22no—
192C2×Q8—41no—
193C2×Q8—42no—
194C2×Q8—82no—
195C22×C4—22no—
196C22×C4—22no—
197C22×C4C22⋊Dic7311yescharacteristic
198C22×C4C22⋊Dic7311yescharacteristic
199C22×C4C22⋊Dic7311yescharacteristic
200C22×C4C22⋊Dic7311yescharacteristic
201C22×C4C22×Dic7311yescharacteristic
202C22×C4C2×C22⋊D7311yescharacteristic
203C22×C4C2×C22⋊D7311yescharacteristic
204C2×C8—2922no—
205C2×C8—1464no—
206C4⋊C4—24no—
207C4⋊C4—22no—
208C4⋊C4—22no—
209C4⋊C4—22no—
210C4⋊C4—24no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—82no—
214C4⋊C4—82no—
215C42—21no—
216C42—21no—
217C42—21no—
218C42—21no—
219C42—42no—
220C42D4×D7312yes—
221C42#1192402712yes—
222C23C2×C22⋊Dic7311yescharacteristic
223Q8—44no—
224Q8—84no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—24no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—41no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4#1455651012yes—
245C2×C4D4×Dic7312yes—
246C2×C4#1455655911yescharacteristic
247C2×C4#1455656312yes—
248C2×C4#1455657211yescharacteristic
249C8—2924no—
250C8—5842no—
251C22—21no—
252C22—21no—
253C22#1798846711yescharacteristic
254C22C2×#1455651011yescharacteristic
255C22#1798857111yescharacteristic
256C4—22no—
257C4—21no—
258C4—22no—
259C4—22no—
260C4—44no—
261C4—41no—
262C4—41no—
263C4—41no—
264C4—82no—
265C4#1798876912yes—
266C2—21no—
267C2—21no—
268C2#2261032511yescharacteristic
269C2#2261040011yescharacteristic
270C2#2261045911yescharacteristic
subgroupG/H
centerC22#17988467
commutatorC22×C4×C73C22×C4
FrattiniC2×C42C22×D73
FittingC73×#2567C2
socleC22×C73#386
prime radicalC23×C73C2×C22⋊C4
cosocleC2×C42×C73C23
hypercenter#2567D73
hypocenterC73#9454
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2567

Complements

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

NH ≅ G/Ntype
141. C73#9454semidirect

Maximal subgroups

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

subgroupindex
#226190162
#226086482
#226082752
#226077872
C73×#25672
#945473