Finite Group Databasebeta

← #32995078

Subgroups — #32995078

Order 18688.

526 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 93 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#22612516C211yesmaximal, characteristic
2#22608242C212yesmaximal
3#22607861C211yesmaximal, characteristic
4#22607860C212yesmaximal
5C73×#1317C211yesmaximal, characteristic
6C23×Dic146C411yescharacteristic
7C2×#14556547C411yescharacteristic
8C2×#14556547C2211yescharacteristic
9#17988637—22no—
10#17988491—22no—
11#17988491—22no—
12#17988450C411yescharacteristic
13#17988448C411yescharacteristic
14#17988448C2211yescharacteristic
15#17988312—22no—
16#17988311C2212yes—
17#381×C73C2211yescharacteristic
18#323×C73C2212yes—
19C22×Dic146—21no—
20C22×Dic146—21no—
21C22×Dic146—22no—
22C22×Dic146—42no—
23C22×Dic146—42no—
24C22×Dic146C814yescomplemented
25C23×Dic73C2×C411yescharacteristic
26C23×Dic73C2×C411yescharacteristic
27#14556547—42no—
28#14556547—42no—
29C2×#11924007—21no—
30C2×#11924007D412yes—
31C2×C22⋊Dic73C2×C411yescharacteristic
32C2×C22⋊Dic73C2×C411yescharacteristic
33C2×C4×Dic73—21no—
34C2×C4×Dic73D412yes—
35#14556520—42no—
36C22⋊#10596831—22no—
37C8×Dic73—42no—
38#14556498—22no—
39#14556498—22no—
40#14556498—22no—
41C23×C4×C73C2×C411yescharacteristic
42C2×C22⋊C4×C73C2×C411yescharacteristic
43C2×C22⋊C4×C73C2311yescharacteristic
44C22⋊C8×C73—22no—
45#95×C73—22no—
46C2×Dic146—24no—
47C2×Dic146—24no—
48C2×Dic146—42no—
49C2×Dic146—42no—
50C2×Dic146—48no—
51C2×Dic146—42no—
52C2×Dic146—42no—
53C2×Dic146—48no—
54C22×Dic73—22no—
55C22×Dic73—22no—
56C22×Dic73—21no—
57C22×Dic73—21no—
58C22×Dic73—21no—
59C22×Dic73—41no—
60C22×Dic73—41no—
61C22×Dic73C22⋊C411yescharacteristic
62C22×Dic73C22⋊C412yes—
63C22×Dic73C22⋊C411yescharacteristic
64C22×Dic73C2×C812yes—
65C22×Dic73C2×C812yes—
66C22×Dic73M1612yes—
67C2×#10596831—42no—
68#11924007—42no—
69#11924007—42no—
70C22⋊Dic73—41no—
71C22⋊Dic73—41no—
72C4×Dic73—22no—
73C4×Dic73—22no—
74C4×Dic73—42no—
75C24×C73C22×C411yescharacteristic
76C22×C4×C73—21no—
77C22×C4×C73—21no—
78C22×C4×C73—21no—
79C22×C4×C73—41no—
80C22×C4×C73—41no—
81C22×C4×C73C2×C812yes—
82C22×C4×C73C2×D412yes—
83C2×C8×C73—42no—
84C22⋊C4×C73—41no—
85C22⋊C4×C73—41no—
86C23×C73—21no—
87C23×C73—21no—
88C23×C73—42no—
89C23×C73C2×C22⋊C411yescharacteristic
90C23×C73C22×C811yescharacteristic
91C23×C73C2×M1611yescharacteristic
92C2×C4×C73—22no—
93C2×C4×C73—22no—
94C2×C4×C73—42no—
95C2×C4×C73—41no—
96C2×C4×C73—41no—
97C2×C4×C73—42no—
98C2×C4×C73—42no—
99C2×C4×C73—42no—
100C2×C4×C73—41no—
101C2×Dic73—21no—
102C2×Dic73—21no—
103C2×Dic73—24no—
104C2×Dic73—24no—
105C2×Dic73—22no—
106C2×Dic73—22no—
107C2×Dic73—42no—
108C2×Dic73—41no—
109C2×Dic73—41no—
110C2×Dic73—42no—
111C2×Dic73—42no—
112C2×Dic73—42no—
113C2×Dic73—41no—
114C2×Dic73C22⋊C812yes—
115C2×Dic73C22⋊C812yes—
116C2×Dic73#9912yes—
117C2×Dic73#10012yes—
118Dic146—48no—
119Dic146—48no—
120C8×C73—82no—
121#10596831—82no—
122C22×C73—22no—
123C22×C73—21no—
124C22×C73—21no—
125C22×C73—41no—
126C22×C73—41no—
127C22×C73—42no—
128C22×C73—42no—
129C22×C73C2×C22⋊C811yescharacteristic
130C22×C73C2×#9911yescharacteristic
131C22×C73C2×#10011yescharacteristic
132C4×C73—42no—
133C4×C73—42no—
134C4×C73—81no—
135Dic73—22no—
136Dic73—42no—
137Dic73—42no—
138Dic73—81no—
139Dic73#32314yes—
140#11428—731nomaximal, Sylow
141C2×C73—21no—
142C2×C73—21no—
143C2×C73—41no—
144C2×C73—41no—
145C2×C73C2×#32311yescharacteristic
146C2×C73#212312yes—
147#2310—731no—
148#1458—732no—
149#1317—731no—
150#1317—732no—
151#1317D7311yescharacteristic
152C73#1142811yescharacteristic, complemented, Sylow
153C23×Q8—731no—
154C2×#117—731no—
155C2×#117—731no—
156#431—1462no—
157#391—1462no—
158#391—1462no—
159#381—731no—
160#381—731no—
161#381—731no—
162#381C2×D7311yescharacteristic
163#324—1462no—
164#323—732no—
165#323C2×D7312yes—
166C22×Q8—2922no—
167C22×Q8—2922no—
168C22×Q8—734no—
169C22×Q8—1461no—
170C22×Q8—1461no—
171C22×Q8—1462no—
172C23×C4—731no—
173C23×C4—731no—
174C23×C4C4×D7311yescharacteristic
175#117—2922no—
176#117—2922no—
177C2×C4⋊C4—732no—
178C2×C4⋊C4—1461no—
179C2×C22⋊C4—731no—
180C2×C22⋊C4—731no—
181C2×C22⋊C4C4×D7311yescharacteristic
182C2×C22⋊C4C22×D7311yescharacteristic
183C2×C42—732no—
184C2×C42—1461no—
185C4⋊C8—2922no—
186C22⋊C8—22no—
187C22⋊C8—1462no—
188C4×C8—2922no—
189#95—22no—
190#95—1462no—
191#95—1462no—
192#95—1462no—
193C24C2×C4×D7311yescharacteristic
194C2×Q8—2922no—
195C2×Q8—2922no—
196C2×Q8—2928no—
197C2×Q8—2928no—
198C2×Q8—2922no—
199C2×Q8—2922no—
200C2×Q8—1464no—
201C2×Q8—1464no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—41no—
206C22×C4—41no—
207C22×C4—2921no—
208C22×C4—2921no—
209C22×C4—732no—
210C22×C4—732no—
211C22×C4—731no—
212C22×C4—731no—
213C22×C4—732no—
214C22×C4—732no—
215C22×C4—1461no—
216C22×C4—1461no—
217C22×C4—1461no—
218C22×C4—1462no—
219C22×C4—1462no—
220C22×C4C8×D7312yes—
221C22×C4D4×D7312yes—
222C2×C8—42no—
223C2×C8—2922no—
224C4⋊C4—2922no—
225C4⋊C4—2922no—
226C22⋊C4—41no—
227C22⋊C4—41no—
228C22⋊C4—2921no—
229C22⋊C4—2921no—
230C42—2922no—
231C42—1462no—
232C42—1462no—
233C23—21no—
234C23—21no—
235C23—42no—
236C23C22⋊C4×D7311yescharacteristic
237C23C2×C8×D7311yescharacteristic
238C23M16×D7311yescharacteristic
239Q8—2928no—
240Q8—2928no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—42no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—41no—
250C2×C4—2922no—
251C2×C4—2921no—
252C2×C4—2921no—
253C2×C4—2922no—
254C2×C4—2922no—
255C2×C4—2922no—
256C2×C4—2921no—
257C2×C4—732no—
258C2×C4—732no—
259C2×C4—732no—
260C2×C4—732no—
261C2×C4—1462no—
262C2×C4—1462no—
263C2×C4—1464no—
264C2×C4—1464no—
265C2×C4—1461no—
266C2×C4—1461no—
267C8—82no—
268C8—5842no—
269C22—22no—
270C22—21no—
271C22—21no—
272C22—41no—
273C22—41no—
274C22—42no—
275C22—42no—
276C22C22⋊C8×D7311yescharacteristic
277C22#99×D7311yescharacteristic
278C22#100×D7311yescharacteristic
279C4—42no—
280C4—42no—
281C4—81no—
282C4—2922no—
283C4—2922no—
284C4—5841no—
285C4—734no—
286C4—1462no—
287C2—21no—
288C2—21no—
289C2—41no—
290C2—41no—
291C2#323×D7311yescharacteristic
292C2#2261158312yes—
subgroupG/H
centerC22#99×D73
commutatorC23×C73C22×C8
FrattiniC2×C22⋊C4C22×D73
FittingC73×#1317C2
socleC22×C73C2×#99
prime radicalC24×C73C22×C4
cosocleC2×C22⋊C4×C73C23
hypercenter#1317D73
hypocenterC73#11428
LCSG ▷ C23×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1317

Complements

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

NH ≅ G/Ntype
24. C22×Dic146C8semidirect
152. C73#11428semidirect

Maximal subgroups

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

subgroupindex
#226125162
#226082422
#226078612
#226078602
C73×#13172
#1142873