Finite Group Databasebeta

← #32995255

Subgroups — #32995255

Order 18688.

460 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 89 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#22612478C211yesmaximal, characteristic
2#22608253C212yesmaximal, complemented
3#22607874C212yesmaximal, complemented
4#22607863C211yesmaximal, characteristic
5C73×#1318C211yesmaximal, characteristic
6C2×#14556578C411yescharacteristic
7C2×#14556556C2211yescharacteristic
8C2×D4×Dic73C411yescharacteristic
9#17988637—22no—
10#17988493C411yescharacteristic
11#17988475—22no—
12#17988452C2211yescharacteristic
13C22⋊C4×Dic73—22no—
14C42×Dic73C411yescharacteristic
15#17988313C2212yes—
16#17988312—22no—
17#390×C73C2211yescharacteristic
18#324×C73C2212yes—
19C22×Dic146C2×C411yescharacteristic
20C23×Dic73—21no—
21#14556578—22no—
22#14556578C814yescomplemented
23#14556556—41no—
24#14556556—41no—
25D4×Dic73—41no—
26D4×Dic73—41no—
27C2×C4⋊Dic73C2×C411yescharacteristic
28C2×#11924007D412yes—
29C2×C22⋊Dic73—22no—
30C2×C22⋊Dic73—21no—
31C2×C4×Dic73—21no—
32C2×C4×Dic73—21no—
33C2×C4×Dic73C2×C411yescharacteristic
34C2×C4×Dic73C2×C411yescharacteristic
35C2×C4×Dic73D412yes—
36#14556520—42no—
37C22⋊#10596831—22no—
38C8×Dic73—42no—
39#14556498—22no—
40#14556498—22no—
41C22×D4×C73C2×C411yescharacteristic
42C2×C4⋊C4×C73C2311yescharacteristic
43C2×C22⋊C4×C73—22no—
44C2×C42×C73C2×C411yescharacteristic
45C22⋊C8×C73—22no—
46C2×Dic146—41no—
47C2×Dic146—41no—
48C2×Dic146C2×C812yes—
49C2×Dic146M1612yes—
50C22×Dic73—21no—
51C22×Dic73—21no—
52C22×Dic73—44no—
53C22×Dic73—41no—
54C22×Dic73—41no—
55C22×Dic73C22⋊C412yes—
56C22×Dic73C22⋊C411yescharacteristic
57C22×Dic73C22⋊C411yescharacteristic
58C2×#10596831—42no—
59C4⋊Dic73—41no—
60#11924007—42no—
61C22⋊Dic73—28no—
62C22⋊Dic73—42no—
63C4×Dic73—21no—
64C4×Dic73—22no—
65C4×Dic73—22no—
66C4×Dic73—21no—
67C4×Dic73—21no—
68C4×Dic73—42no—
69C4×Dic73—42no—
70C4×Dic73C2×C812yes—
71C24×C73—21no—
72C2×D4×C73—21no—
73C2×D4×C73—41no—
74C2×D4×C73—41no—
75C2×D4×C73C2×C812yes—
76C22×C4×C73—21no—
77C22×C4×C73C22×C411yescharacteristic
78C22×C4×C73C2×D412yes—
79C2×C8×C73—42no—
80C4⋊C4×C73—41no—
81C22⋊C4×C73—44no—
82C42×C73—41no—
83C23×C73—22no—
84C23×C73—42no—
85C23×C73—42no—
86C23×C73—41no—
87C23×C73—41no—
88C23×C73C2×C22⋊C411yescharacteristic
89D4×C73—42no—
90D4×C73—42no—
91C2×C4×C73—21no—
92C2×C4×C73—21no—
93C2×C4×C73—22no—
94C2×C4×C73—22no—
95C2×C4×C73—41no—
96C2×C4×C73—41no—
97C2×C4×C73—42no—
98C2×C4×C73C22×C811yescharacteristic
99C2×C4×C73C2×M1611yescharacteristic
100C2×Dic73—22no—
101C2×Dic73—22no—
102C2×Dic73—22no—
103C2×Dic73—22no—
104C2×Dic73—21no—
105C2×Dic73—41no—
106C2×Dic73—41no—
107C2×Dic73—41no—
108C2×Dic73—42no—
109C2×Dic73—41no—
110C2×Dic73—82no—
111C2×Dic73—82no—
112C2×Dic73C22⋊C814yes—
113C2×Dic73#9911yescharacteristic
114C2×Dic73#9911yescharacteristic
115Dic146—42no—
116Dic146—42no—
117C8×C73—82no—
118#10596831—82no—
119C22×C73—21no—
120C22×C73—21no—
121C22×C73—44no—
122C22×C73—42no—
123C22×C73—82no—
124C22×C73—81no—
125C22×C73—81no—
126C22×C73C2×C22⋊C811yescharacteristic
127C22×C73C2×#9911yescharacteristic
128C22×C73#41311yescharacteristic
129C4×C73—21no—
130C4×C73—21no—
131C4×C73—42no—
132C4×C73—42no—
133Dic73—21no—
134Dic73—24no—
135Dic73—42no—
136Dic73—41no—
137Dic73—81no—
138Dic73#35512yes—
139#11476—731nomaximal, Sylow
140C2×C73—21no—
141C2×C73—21no—
142C2×C73—82no—
143C2×C73#145911yescharacteristic
144C2×C73#212611yescharacteristic
145C2×C73C2×#35511yescharacteristic
146C4×#124—731no—
147#1461—732no—
148#1324—732no—
149#1318—731no—
150#1318D7311yescharacteristic
151C73#1147611yescharacteristic, complemented, Sylow
152C2×#124—731no—
153C2×C4×Q8—731no—
154C2×C4×D4—731no—
155#431—1462no—
156#391—731no—
157#390C2×D7311yescharacteristic
158#388—1462no—
159#382—731no—
160C4×C22⋊C4—1462no—
161C43—731no—
162#324—732no—
163#324—1462no—
164#324C2×D7312yes—
165C22×Q8—731no—
166C22×D4C4×D7311yescharacteristic
167C23×C4—1461no—
168#124—734no—
169#124—1462no—
170C4×Q8—2921no—
171C4×Q8—2921no—
172C4×D4—2921no—
173C4×D4—2921no—
174C2×C4⋊C4—732no—
175C2×C4⋊C4—731no—
176C2×C4⋊C4C22×D7311yescharacteristic
177C2×C22⋊C4—22no—
178C2×C22⋊C4—1461no—
179C2×C22⋊C4—1462no—
180C2×C42—731no—
181C2×C42—731no—
182C2×C42—732no—
183C2×C42—1461no—
184C2×C42—1461no—
185C2×C42C4×D7311yescharacteristic
186C4⋊C8—2922no—
187C22⋊C8—22no—
188C22⋊C8—1462no—
189C4×C8—2922no—
190#95—1462no—
191#95—1462no—
192C24—21no—
193C2×Q8—2921no—
194C2×Q8—2921no—
195C2×Q8—732no—
196C2×Q8—732no—
197C2×D4—21no—
198C2×D4—41no—
199C2×D4—41no—
200C2×D4C8×D7312yes—
201C22×C4—21no—
202C22×C4—2921no—
203C22×C4—2921no—
204C22×C4—2924no—
205C22×C4—731no—
206C22×C4—732no—
207C22×C4—731no—
208C22×C4—1461no—
209C22×C4—1461no—
210C22×C4C2×C4×D7311yescharacteristic
211C22×C4D4×D7312yes—
212C2×C8—42no—
213C2×C8—2922no—
214C4⋊C4—41no—
215C4⋊C4—2921no—
216C4⋊C4—2922no—
217C22⋊C4—44no—
218C22⋊C4—2922no—
219C22⋊C4—1468no—
220C42—41no—
221C42—2922no—
222C42—2922no—
223C42—732no—
224C42—1462no—
225C42—1462no—
226C42—1461no—
227C42—1461no—
228C42—1461no—
229C23—22no—
230C23—42no—
231C23—42no—
232C23—41no—
233C23—41no—
234C23C22⋊C4×D7311yescharacteristic
235Q8—2922no—
236Q8—2922no—
237D4—42no—
238D4—42no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—2921no—
247C2×C4—2921no—
248C2×C4—2921no—
249C2×C4—2922no—
250C2×C4—2921no—
251C2×C4—5842no—
252C2×C4—5842no—
253C2×C4—731no—
254C2×C4—734no—
255C2×C4—731no—
256C2×C4—1462no—
257C2×C4—1461no—
258C2×C4—1462no—
259C2×C4—1462no—
260C2×C4—1462no—
261C2×C4C2×C8×D7311yescharacteristic
262C2×C4M16×D7311yescharacteristic
263C8—82no—
264C8—5842no—
265C22—21no—
266C22—21no—
267C22—44no—
268C22—42no—
269C22—82no—
270C22—81no—
271C22—81no—
272C22C22⋊C8×D7311yescharacteristic
273C22#99×D7311yescharacteristic
274C22#1798856811yescharacteristic
275C4—21no—
276C4—21no—
277C4—42no—
278C4—42no—
279C4—2922no—
280C4—2921no—
281C4—5841no—
282C4—732no—
283C4—1464no—
284C4—1461no—
285C2—21no—
286C2—21no—
287C2—82no—
288C2#2260824611yescharacteristic
289C2#2261159311yescharacteristic
290C2#355×D7311yescharacteristic
subgroupG/H
centerC22#99×D73
commutatorC2×C4×C73C22×C8
FrattiniC2×C4⋊C4C22×D73
FittingC73×#1318C2
socleC22×C73C2×#99
prime radicalC22×D4×C73C2×C4
cosocleC2×C4⋊C4×C73C23
hypercenter#1318D73
hypocenterC73#11476
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1318

Complements

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

NH ≅ G/Ntype
2. #22608253C2semidirect
3. #22607874C2semidirect
22. #14556578C8semidirect
151. C73#11476semidirect

Maximal subgroups

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

subgroupindex
#226124782
#226082532
#226078742
#226078632
C73×#13182
#1147673