Finite Group Databasebeta

← #32995261

Subgroups — #32995261

Order 18688.

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

normal subgroups only

This group has 480 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#22612470C211yesmaximal, characteristic
2#22608248C212yesmaximal
3#22607875C211yesmaximal, characteristic, complemented
4#22607864C212yesmaximal, complemented
5C73×#1324C211yesmaximal, characteristic, complemented
6C2×#14556579C411yescharacteristic
7C2×#14556556C411yescharacteristic
8C2×#14556553C2211yescharacteristic
9C22⋊C8×D73—22no—
10#17988492C2211yescharacteristic
11#17988488C411yescharacteristic
12#17988476—22no—
13#17988434—22no—
14C42×Dic73C411yescharacteristic
15#17988313C2212yes—
16#17988310—22no—
17#382×C73C2211yescharacteristic
18#324×C73C2212yes—
19C22×Dic146C2×C411yescharacteristic
20C22×D292C2×C411yescharacteristic
21C22×C4×D73D412yes—
22C2×C8×D73—42no—
23#14556579—22no—
24#14556579C814yescomplemented
25#14556556—41no—
26#14556556—41no—
27#14556553—41no—
28#14556553—41no—
29C2×#11924007—21no—
30C2×#11924005—22no—
31C2×#11924005—22no—
32C2×#11924005D412yes—
33C2×C4×Dic73—21no—
34C2×C4×Dic73—21no—
35C2×C4×Dic73—21no—
36C2×C4×Dic73C2×C411yescharacteristic
37C2×C4×Dic73C2×C411yescharacteristic
38C22⋊#10596831—22no—
39#14556503—42no—
40#14556498—22no—
41C2×C4⋊C4×C73C2×C411yescharacteristic
42C2×C4⋊C4×C73C2311yescharacteristic
43C2×C42×C73C2×C411yescharacteristic
44C22⋊C8×C73—22no—
45#95×C73—22no—
46C23×D73C22⋊C412yes—
47C2×Dic146—21no—
48C2×Dic146—41no—
49C2×Dic146—41no—
50C2×Dic146C2×C812yescomplemented
51C2×D292—41no—
52C2×D292—41no—
53C2×D292C2×C812yes—
54C2×D292M1612yes—
55C22×Dic73—21no—
56C22×Dic73—21no—
57C22×Dic73C22⋊C411yescharacteristic
58C22×Dic73C22⋊C411yescharacteristic
59C2×C4×D73—22no—
60C2×C4×D73—22no—
61C2×C4×D73—44no—
62C2×#10596831—42no—
63C8×D73—84no—
64#11924007—42no—
65#11924005—28no—
66#11924005—42no—
67#11924005—44no—
68C4×Dic73—21no—
69C4×Dic73—21no—
70C4×Dic73—42no—
71C4×Dic73—42no—
72C4×Dic73—41no—
73C4×Dic73—41no—
74C4×Dic73—41no—
75C22×C4×C73—21no—
76C22×C4×C73—21no—
77C22×C4×C73C22×C411yescharacteristic
78C22×C4×C73C2×D412yes—
79C2×C8×C73—42no—
80C4⋊C4×C73—41no—
81C4⋊C4×C73—41no—
82C42×C73—21no—
83C42×C73C2×C812yescomplemented
84C23×C73C2×C22⋊C411yescharacteristic
85C22×D73—22no—
86C22×D73—22no—
87C22×D73—42no—
88C22×D73—42no—
89C22×D73C22⋊C814yes—
90C2×C4×C73—21no—
91C2×C4×C73—21no—
92C2×C4×C73—22no—
93C2×C4×C73—22no—
94C2×C4×C73—41no—
95C2×C4×C73—41no—
96C2×C4×C73—42no—
97C2×C4×C73—42no—
98C2×C4×C73—41no—
99C2×C4×C73C22×C811yescharacteristic
100C2×C4×C73C2×M1611yescharacteristic
101C2×Dic73—22no—
102C2×Dic73—22no—
103C2×Dic73—22no—
104C2×Dic73—21no—
105C2×Dic73—41no—
106C2×Dic73—41no—
107C2×Dic73—41no—
108C2×Dic73—41no—
109C2×Dic73—41no—
110C2×Dic73#9911yescharacteristic
111C2×Dic73#9911yescharacteristic
112D292—42no—
113D292—42no—
114C4×D73—44no—
115C4×D73—82no—
116Dic146—42no—
117Dic146—42no—
118C8×C73—82no—
119#10596831—82no—
120C22×C73—21no—
121C22×C73—21no—
122C22×C73C2×C22⋊C811yescharacteristic
123C22×C73C2×#9911yescharacteristic
124C22×C73#41311yescharacteristic
125C2×D73—24no—
126C2×D73—42no—
127C2×D73—42no—
128C2×D73—44no—
129C2×D73—82no—
130C4×C73—21no—
131C4×C73—21no—
132C4×C73—42no—
133C4×C73—42no—
134C4×C73—81no—
135Dic73—21no—
136Dic73—42no—
137Dic73—41no—
138Dic73—42no—
139Dic73#35412yes—
140#11477—731nomaximal, Sylow
141C2×C73—21no—
142C2×C73—21no—
143C2×C73#145911yescharacteristic
144C2×C73C2×#35411yescharacteristic
145C2×C73#213211yescharacteristic
146D73—44no—
147C4×#124—731no—
148#1459—732no—
149#1324—731no—
150#1324D7311yescharacteristic, complemented
151#1319—732no—
152C73#1147711yescharacteristic, complemented, Sylow
153C2×#124—731no—
154C2×C4×Q8—731no—
155C2×C4×D4—731no—
156C2×C22⋊C8—1462no—
157#391—731no—
158#390—731no—
159#388—1462no—
160#382C2×D7311yescharacteristic
161C4×C22⋊C4—1462no—
162C43—731no—
163#324—732no—
164#324C2×D7312yes—
165#323—1462no—
166C22×Q8—731no—
167C22×D4—731no—
168C23×C4—732no—
169C22×C8—2922no—
170#124—734no—
171#124—1462no—
172C4×Q8—2921no—
173C4×Q8—2921no—
174C4×D4—2921no—
175C4×D4—2921no—
176C2×C4⋊C4—1461no—
177C2×C4⋊C4C4×D7311yescharacteristic
178C2×C4⋊C4C22×D7311yescharacteristic
179C2×C22⋊C4—732no—
180C2×C22⋊C4—1462no—
181C2×C22⋊C4—1462no—
182C2×C42—731no—
183C2×C42—731no—
184C2×C42—1461no—
185C2×C42—1461no—
186C2×C42—1461no—
187C2×C42C4×D7311yescharacteristic
188C22⋊C8—22no—
189C22⋊C8—2922no—
190C22⋊C8—1462no—
191#95—22no—
192#95—1462no—
193C24—732no—
194C2×Q8—2921no—
195C2×Q8—2921no—
196C2×Q8—732no—
197C2×Q8—1461no—
198C2×D4—2921no—
199C2×D4—2921no—
200C2×D4—732no—
201C2×D4—732no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—2924no—
205C22×C4—731no—
206C22×C4—731no—
207C22×C4—1462no—
208C22×C4—1462no—
209C22×C4—1461no—
210C22×C4—1461no—
211C22×C4C2×C4×D7311yescharacteristic
212C22×C4D4×D7312yes—
213C2×C8—42no—
214C2×C8—2922no—
215C2×C8—5844no—
216C4⋊C4—41no—
217C4⋊C4—41no—
218C4⋊C4—2922no—
219C22⋊C4—2922no—
220C22⋊C4—2924no—
221C22⋊C4—1468no—
222C42—21no—
223C42—2921no—
224C42—2921no—
225C42—2921no—
226C42—2922no—
227C42—2922no—
228C42—1461no—
229C42—1461no—
230C42C8×D7312yescomplemented
231C23—2922no—
232C23—2922no—
233C23—734no—
234C23—1462no—
235C23—1462no—
236C23C22⋊C4×D7311yescharacteristic
237Q8—2922no—
238Q8—2922no—
239D4—2922no—
240D4—2922no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—41no—
250C2×C4—2924no—
251C2×C4—2921no—
252C2×C4—2921no—
253C2×C4—2921no—
254C2×C4—2921no—
255C2×C4—2921no—
256C2×C4—5842no—
257C2×C4—731no—
258C2×C4—731no—
259C2×C4—1462no—
260C2×C4—1462no—
261C2×C4—1461no—
262C2×C4—1462no—
263C2×C4C2×C8×D7311yescharacteristic
264C2×C4M16×D7311yescharacteristic
265C8—82no—
266C8—5842no—
267C22—21no—
268C22—21no—
269C22—2924no—
270C22—2922no—
271C22—2922no—
272C22—5842no—
273C22—1464no—
274C22C22⋊C8×D7311yescharacteristic
275C22#99×D7311yescharacteristic
276C22#1798857011yescharacteristic
277C4—21no—
278C4—21no—
279C4—42no—
280C4—42no—
281C4—81no—
282C4—2922no—
283C4—2922no—
284C4—2921no—
285C4—732no—
286C4—1461no—
287C2—21no—
288C2—21no—
289C2—2924no—
290C2#2260824811yescharacteristic
291C2#354×D7311yescharacteristic
292C2#2261161311yescharacteristic
subgroupG/H
centerC22#99×D73
commutatorC2×C4×C73C22×C8
FrattiniC2×C4⋊C4C22×D73
FittingC73×#1324C2
socleC22×C73C2×#99
prime radicalC22×D292C2×C4
cosocleC2×C4⋊C4×C73C23
hypercenter#1324D73
hypocenterC73#11477
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1324

Complements

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

NH ≅ G/Ntype
3. #22607875C2semidirect
4. #22607864C2semidirect
5. C73×#1324C2semidirect
24. #14556579C8semidirect
50. C2×Dic146C2×C8semidirect
83. C42×C73C2×C8semidirect
150. #1324D73semidirect
152. C73#11477semidirect
230. C42C8×D73semidirect

Maximal subgroups

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

subgroupindex
#226124702
#226082482
#226078752
#226078642
C73×#13242
#1147773