Finite Group Databasebeta

← #32980647

Subgroups — #32980647

Order 18688.

558 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 119 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#22618972C211yesmaximal, characteristic
2C4×#14556578C211yesmaximal, characteristic
3#22608327C212yesmaximal, complemented
4#22607763C212yesmaximal, complemented
5C73×#1460C211yesmaximal, characteristic
6C2×#14556578C411yescharacteristic
7C2×C4×Dic146C2211yescharacteristic
8#17988665—24no—
9#17988640C2212yes—
10#17988551—22no—
11#17988492C411yescharacteristic
12#17988490C411yescharacteristic
13#17988481—22no—
14#17988452C411yescharacteristic
15C4×C22⋊Dic73—22no—
16C42×Dic73C2211yescharacteristic
17#17988319—24no—
18C2×C4×D4×C73C2211yescharacteristic
19#431×C73C2212yes—
20#323×C73—22no—
21C22×Dic146C2×C411yescharacteristic
22C2×#11924012—24no—
23#14556578—22no—
24#14556578—22no—
25C4×Dic146—22no—
26C4×Dic146—22no—
27C2×C4⋊Dic73C2×C411yescharacteristic
28C2×#11924007—21no—
29C2×C22⋊Dic73—22no—
30C2×C22⋊Dic73—22no—
31C2×C4×Dic73—21no—
32C2×C4×Dic73—21no—
33C2×C4×Dic73—21no—
34C2×C4×Dic73C2×C411yescharacteristic
35C2×C4×Dic73C2×C411yescharacteristic
36C4⋊#10596831D414yes—
37C22⋊#10596831—24no—
38C22⋊#10596831—22no—
39C4×#10596831—22no—
40#14556498—22no—
41#14556498—22no—
42C22×D4×C73C2×C411yescharacteristic
43C23×C4×C73D412yes—
44C4×D4×C73—22no—
45C4×D4×C73—22no—
46C2×C4⋊C4×C73C2×C411yescharacteristic
47C2×C22⋊C4×C73D412yes—
48C2×C42×C73C2311yescharacteristic
49C4⋊C8×C73—22no—
50C22⋊C8×C73—22no—
51C4×C8×C73—22no—
52C2×Dic146—22no—
53C2×Dic146—22no—
54C2×Dic146—21no—
55C2×Dic146M1612yescomplemented
56C22×Dic73—21no—
57C22×Dic73—21no—
58C22×Dic73—21no—
59C22×Dic73—21no—
60#11924012—84no—
61C2×#10596831—24no—
62C4⋊Dic73—22no—
63#11924007—42no—
64C22⋊Dic73—28no—
65C22⋊Dic73—44no—
66C4×Dic73—21no—
67C4×Dic73—22no—
68C4×Dic73—42no—
69C4×Dic73—42no—
70C4×Dic73—41no—
71C4×Dic73—41no—
72C4×Dic73M1612yescomplemented
73C24×C73C22⋊C412yes—
74C2×D4×C73—22no—
75C2×D4×C73—21no—
76C2×D4×C73—21no—
77C2×D4×C73—22no—
78C22×C4×C73—22no—
79C22×C4×C73—22no—
80C22×C4×C73—44no—
81C22×C4×C73C22⋊C412yes—
82C22×C4×C73C22×C411yescharacteristic
83C22×C4×C73C2×D411yescharacteristic
84C22×C4×C73C2×D411yescharacteristic
85C2×C8×C73—42no—
86C4⋊C4×C73—22no—
87C22⋊C4×C73—24no—
88C42×C73C2×D412yes—
89C42×C73#4112yes—
90C23×C73—22no—
91C23×C73—22no—
92C23×C73—22no—
93C23×C73—42no—
94C23×C73—42no—
95C23×C73C2×C22⋊C411yescharacteristic
96D4×C73—42no—
97D4×C73—42no—
98C2×C4×C73—22no—
99C2×C4×C73—22no—
100C2×C4×C73—41no—
101C2×C4×C73—44no—
102C2×C4×C73—42no—
103C2×C4×C73—82no—
104C2×C4×C73C4×D412yes—
105C2×C4×C73#12011yescharacteristic
106C2×C4×C73#12112yes—
107C2×C4×C73#12311yescharacteristic
108C2×C4×C73C2×M1611yescharacteristic
109C2×C4×C73C2×M1611yescharacteristic
110C2×C4×C73#13112yes—
111C2×Dic73—22no—
112C2×Dic73—22no—
113C2×Dic73—22no—
114C2×Dic73—41no—
115C2×Dic73—41no—
116C2×Dic73—41no—
117C2×Dic73—41no—
118C2×Dic73—41no—
119C2×Dic73—41no—
120C2×Dic73—42no—
121C2×Dic73—41no—
122Dic146—24no—
123Dic146—42no—
124C8×C73—82no—
125#10596831—44no—
126C22×C73—21no—
127C22×C73—21no—
128C22×C73—44no—
129C22×C73—42no—
130C22×C73—42no—
131C22×C73—42no—
132C22×C73—82no—
133C22×C73#38611yescharacteristic
134C22×C73#40711yescharacteristic
135C22×C73#40811yescharacteristic
136C4×C73—22no—
137C4×C73—21no—
138C4×C73—42no—
139C4×C73#43512yes—
140C4×C73#43612yes—
141C4×C73#45512yes—
142Dic73—42no—
143Dic73—42no—
144Dic73—42no—
145Dic73—81no—
146#8961—731nomaximal, Sylow
147C2×C73—21no—
148C2×C73—21no—
149C2×C73—82no—
150C2×C73#187011yescharacteristic
151C2×C73#188411yescharacteristic
152C2×C73#188511yescharacteristic
153#2975—731no—
154C4×#124—731no—
155#1479—732no—
156#1460D7311yescharacteristic
157#1276—732no—
158C73#896111yescharacteristic, complemented, Sylow
159C2×#124—731no—
160C2×C4×Q8—731no—
161C2×C4×D4C2×D7311yescharacteristic
162#436—1464no—
163#431—732no—
164#431C2×D7312yes—
165#407—1462no—
166#391—731no—
167#390—731no—
168#388—1462no—
169#382—731no—
170C4×C22⋊C4—1462no—
171C43—731no—
172Q8⋊C8—1464no—
173#323—22no—
174C22×Q8—731no—
175C22×D4C4×D7311yescharacteristic
176C23×C4D29212yes—
177C2×M16—1464no—
178#124—1462no—
179#124—1462no—
180C4×Q8—1462no—
181C4×Q8—1462no—
182C4×D4—22no—
183C4×D4—22no—
184C2×C4⋊C4—731no—
185C2×C4⋊C4—1461no—
186C2×C4⋊C4C4×D7311yescharacteristic
187C2×C22⋊C4—1462no—
188C2×C22⋊C4—1462no—
189C2×C22⋊C4C22⋊D7312yes—
190C2×C42—731no—
191C2×C42—731no—
192C2×C42—1461no—
193C2×C42—1461no—
194C2×C42—1461no—
195C2×C42C22×D7311yescharacteristic
196C4⋊C8—22no—
197C4⋊C8—734no—
198C22⋊C8—22no—
199C22⋊C8—1464no—
200C22⋊C8—1462no—
201C4×C8—22no—
202C4×C8—1462no—
203#95—1462no—
204#95—1462no—
205C24#1192400512yes—
206C2×Q8—732no—
207C2×Q8—1462no—
208C2×Q8—1462no—
209C2×Q8—1461no—
210C2×D4—22no—
211C2×D4—21no—
212C2×D4—21no—
213C2×D4—22no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—44no—
217C22×C4—1461no—
218C22×C4—1461no—
219C22×C4—1461no—
220C22×C4—1461no—
221C22×C4#1192400512yes—
222C22×C4C2×C4×D7311yescharacteristic
223C22×C4C2×C22⋊D7311yescharacteristic
224C22×C4C2×D29211yescharacteristic
225M16—5844no—
226C2×C8—42no—
227C2×C8—1464no—
228C4⋊C4—22no—
229C4⋊C4—2922no—
230C4⋊C4—1462no—
231C22⋊C4—24no—
232C22⋊C4—2924no—
233C22⋊C4—1468no—
234C42—2922no—
235C42—2922no—
236C42—2921no—
237C42—2921no—
238C42—732no—
239C42—1462no—
240C42—1461no—
241C42D4×D7312yes—
242C42#1192402712yes—
243C23—22no—
244C23—22no—
245C23—22no—
246C23—42no—
247C23—42no—
248C23C2×#1192400511yescharacteristic
249Q8—2922no—
250Q8—1464no—
251D4—42no—
252D4—42no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—41no—
256C2×C4—44no—
257C2×C4—42no—
258C2×C4—82no—
259C2×C4—2921no—
260C2×C4—2921no—
261C2×C4—2921no—
262C2×C4—2921no—
263C2×C4—2921no—
264C2×C4—2921no—
265C2×C4—2922no—
266C2×C4—2921no—
267C2×C4—1462no—
268C2×C4—1462no—
269C2×C4—1462no—
270C2×C4#1455655112yes—
271C2×C4#1455656111yescharacteristic
272C2×C4#1455656312yes—
273C2×C4#1455657511yescharacteristic
274C2×C4M16×D7311yescharacteristic
275C2×C4M16×D7311yescharacteristic
276C2×C4#1455659712yes—
277C8—82no—
278C8—2924no—
279C22—21no—
280C22—21no—
281C22—44no—
282C22—42no—
283C22—42no—
284C22—42no—
285C22—82no—
286C22#1798846411yescharacteristic
287C22#1798855011yescharacteristic
288C22#1798855311yescharacteristic
289C4—22no—
290C4—21no—
291C4—42no—
292C4—2922no—
293C4—2922no—
294C4—2922no—
295C4—5841no—
296C4#1798866112yes—
297C4#1798866212yes—
298C4#1798876712yes—
299C2—21no—
300C2—21no—
301C2—82no—
302C2#2261022611yescharacteristic
303C2#2261031211yescharacteristic
304C2#2261031711yescharacteristic
subgroupG/H
centerC2×C4#14556561
commutatorC22×C4×C73C22×C4
FrattiniC2×C42C22×D73
FittingC73×#1460C2
socleC22×C73#386
prime radicalC22×D4×C73C2×C4
cosocleC2×C42×C73C23
hypercenter#1460D73
hypocenterC73#8961
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1460

Complements

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

NH ≅ G/Ntype
3. #22608327C2semidirect
4. #22607763C2semidirect
55. C2×Dic146M16semidirect
72. C4×Dic73M16semidirect
158. C73#8961semidirect

Maximal subgroups

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

subgroupindex
#226189722
C4×#145565782
#226083272
#226077632
C73×#14602
#896173