Finite Group Databasebeta

← #32996709

Subgroups — #32996709

Order 18688.

382 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 79 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#22615752C211yesmaximal, characteristic
2#22608265C211yesmaximal, characteristic
3#22607951C214yesmaximal
4C73×#1820C211yesmaximal, characteristic
5C2×#14556591C411yescharacteristic, complemented
6#17988644—21no—
7#17988526—21no—
8#17988523—21no—
9#17988507C412yescomplemented
10#17988499C2212yes—
11#17988485—21no—
12#17988453C411yescharacteristic, complemented
13#17988447—21no—
14#17988313—21no—
15#17988311C2212yes—
16C2×#117×C73C2211yescharacteristic
17#381×C73—21no—
18#342×C73—21no—
19#342×C73C2212yes—
20C22×Dic146C2×C412yes—
21#14556591—41no—
22#14556591—41no—
23C2×C4⋊Dic73—21no—
24C2×C4⋊Dic73—21no—
25C2×C4⋊Dic73—21no—
26C2×#11924007—22no—
27C2×C22⋊Dic73—22no—
28C4⋊#10596831—41no—
29C22⋊#10596831—22no—
30#14556502—41no—
31#14556498—22no—
32#14556498—21no—
33#14556498—22no—
34#14556498C2×C412yes—
35C23×C4×C73D411yescharacteristic
36#117×C73—41no—
37#117×C73—41no—
38C2×C4⋊C4×C73C2×C411yescharacteristic
39C2×C4⋊C4×C73D411yescharacteristic
40C2×C22⋊C4×C73—22no—
41C2×C22⋊C4×C73D411yescharacteristic
42C2×C22⋊C4×C73C2311yescharacteristic
43C2×C42×C73C2×C411yescharacteristic
44C2×C42×C73D411yescharacteristic
45#95×C73—41no—
46#95×C73—41no—
47C2×Dic146—42no—
48C2×Dic146—82no—
49C22×Dic73—22no—
50C22×Dic73—22no—
51C2×#10596831—42no—
52C4⋊Dic73—42no—
53C4⋊Dic73—42no—
54C4⋊Dic73—41no—
55C4⋊Dic73—41no—
56#11924007—82no—
57C22⋊Dic73—82no—
58C24×C73C2×D411yescharacteristic
59C22×C4×C73—22no—
60C22×C4×C73—21no—
61C22×C4×C73—21no—
62C22×C4×C73—41no—
63C22×C4×C73—42no—
64C22×C4×C73C22⋊C411yescharacteristic
65C22×C4×C73C22⋊C411yescharacteristic
66C22×C4×C73C22⋊C411yescharacteristic
67C22×C4×C73C22⋊C411yescharacteristic
68C22×C4×C73C22×C411yescharacteristic
69C22×C4×C73C2×D411yescharacteristic
70C4⋊C4×C73—41no—
71C4⋊C4×C73—41no—
72C22⋊C4×C73—41no—
73C22⋊C4×C73—41no—
74C22⋊C4×C73—42no—
75C22⋊C4×C73—42no—
76C42×C73—21no—
77C42×C73—21no—
78C42×C73—21no—
79C42×C73—21no—
80C23×C73—21no—
81C23×C73—21no—
82C23×C73—41no—
83C23×C73—41no—
84C23×C73C2×C22⋊C411yescharacteristic
85C23×C73#13712yes—
86C2×C4×C73—21no—
87C2×C4×C73—21no—
88C2×C4×C73—21no—
89C2×C4×C73—21no—
90C2×C4×C73—21no—
91C2×C4×C73—21no—
92C2×C4×C73—21no—
93C2×C4×C73—21no—
94C2×C4×C73—21no—
95C2×C4×C73—42no—
96C2×C4×C73—42no—
97C2×C4×C73—41no—
98C2×C4×C73—41no—
99C2×C4×C73—41no—
100C2×C4×C73—41no—
101C2×C4×C73—82no—
102C2×C4×C73—82no—
103C2×C4×C73—82no—
104C2×C4×C73#9911yescharacteristic
105C2×C4×C73#9911yescharacteristic
106C2×Dic73—42no—
107C2×Dic73—42no—
108C2×Dic73—42no—
109C2×Dic73—42no—
110C2×Dic73—42no—
111C2×Dic73—42no—
112Dic146—84no—
113#10596831—82no—
114C22×C73—21no—
115C22×C73—21no—
116C22×C73—22no—
117C22×C73—42no—
118C22×C73—41no—
119C22×C73—41no—
120C22×C73—81no—
121C22×C73C2×#9911yescharacteristic
122C22×C73#41911yescharacteristic
123C22×C73#42111yescharacteristic
124C4×C73—21no—
125C4×C73—21no—
126C4×C73—41no—
127C4×C73—41no—
128C4×C73—41no—
129C4×C73—41no—
130C4×C73—41no—
131C4×C73—162no—
132Dic73—82no—
133Dic73—82no—
134#11812—731nomaximal, Sylow
135C2×C73—21no—
136C2×C73—21no—
137C2×C73—42no—
138C2×C73#151111yescharacteristic
139C2×C73#212211yescharacteristic
140C2×C73#212911yescharacteristic
141#2628—731no—
142#1820D7311yescharacteristic
143#1464—731no—
144#1351—734no—
145C73#1181211yescharacteristic, complemented, Sylow
146C2×C4⋊Q8—731no—
147C2×#117C2×D7311yescharacteristic
148#432—1461no—
149#400—1461no—
150#399—1461no—
151#395—732no—
152#393—732no—
153#389—1461no—
154#382—731no—
155#381—21no—
156#380—1461no—
157#342—21no—
158#342C2×D7312yes—
159#324—1461no—
160#323—732no—
161C22×Q8—732no—
162C23×C4C22⋊D7311yescharacteristic
163C4⋊Q8—2921no—
164C4⋊Q8—2921no—
165#117—41no—
166#117—41no—
167C2×C4⋊C4—1461no—
168C2×C4⋊C4—1461no—
169C2×C4⋊C4—1461no—
170C2×C4⋊C4—1462no—
171C2×C4⋊C4C4×D7311yescharacteristic
172C2×C4⋊C4D29211yescharacteristic
173C2×C22⋊C4—22no—
174C2×C22⋊C4—1462no—
175C2×C22⋊C4C22⋊D7311yescharacteristic
176C2×C22⋊C4C22×D7311yescharacteristic
177C2×C42C4×D7311yescharacteristic
178C2×C42D29211yescharacteristic
179C4⋊C8—2921no—
180C22⋊C8—1462no—
181#97—2921no—
182#95—41no—
183#95—41no—
184#95—732no—
185#95—1462no—
186#95—1461no—
187#95—1462no—
188C24C2×C22⋊D7311yescharacteristic
189C2×Q8—2922no—
190C2×Q8—5842no—
191C22×C4—22no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—41no—
195C22×C4—42no—
196C22×C4—1462no—
197C22×C4—1462no—
198C22×C4#1192400511yescharacteristic
199C22×C4#1192400511yescharacteristic
200C22×C4#1192400511yescharacteristic
201C22×C4#1192400511yescharacteristic
202C22×C4C2×C4×D7311yescharacteristic
203C22×C4C2×D29211yescharacteristic
204C2×C8—2922no—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C4⋊C4—2922no—
208C4⋊C4—2922no—
209C4⋊C4—2921no—
210C4⋊C4—2921no—
211C4⋊C4—5842no—
212C22⋊C4—41no—
213C22⋊C4—41no—
214C22⋊C4—42no—
215C22⋊C4—42no—
216C22⋊C4—5842no—
217C42—21no—
218C42—21no—
219C42—21no—
220C42—21no—
221C23—21no—
222C23—21no—
223C23—41no—
224C23—41no—
225C23C2×#1192400511yescharacteristic
226C23#1455662112yes—
227Q8—5844no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—82no—
244C2×C4—82no—
245C2×C4—82no—
246C2×C4—2922no—
247C2×C4—2922no—
248C2×C4—2922no—
249C2×C4—2922no—
250C2×C4—2922no—
251C2×C4—2922no—
252C2×C4#1455650511yescharacteristic
253C2×C4#1455650511yescharacteristic
254C8—5842no—
255C22—21no—
256C22—21no—
257C22—22no—
258C22—42no—
259C22—41no—
260C22—41no—
261C22—81no—
262C22C2×#1455650511yescharacteristic
263C22#1798859511yescharacteristic
264C22#1798860511yescharacteristic
265C4—21no—
266C4—21no—
267C4—41no—
268C4—41no—
269C4—41no—
270C4—41no—
271C4—41no—
272C4—162no—
273C4—5842no—
274C4—5842no—
275C2—21no—
276C2—21no—
277C2—42no—
278C2#2260846311yescharacteristic
279C2#2261158011yescharacteristic
280C2#2261160511yescharacteristic
subgroupG/H
centerC22C2×#14556505
commutatorC22×C4×C73C22×C4
FrattiniC2×C22⋊C4C22×D73
FittingC73×#1820C2
socleC22×C73C2×#99
prime radicalC24×C73C2×D4
cosocleC2×C22⋊C4×C73C23
hypercenter#1820D73
hypocenterC73#11812
LCSG ▷ C22×C4×C73 ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1820

Complements

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

NH ≅ G/Ntype
5. C2×#14556591C4semidirect
9. #17988507C4semidirect
12. #17988453C4semidirect
145. C73#11812semidirect

Maximal subgroups

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

subgroupindex
#226157522
#226082652
#226079512
C73×#18202
#1181273