Finite Group Databasebeta

← #32996739

Subgroups — #32996739

Order 18688.

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

normal subgroups only

This group has 368 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#22607960C214yesmaximal, complemented
4C73×#1822C211yesmaximal, characteristic
5C2×#14556591C411yescharacteristic
6#17988644—21no—
7#17988526—21no—
8#17988523—21no—
9#17988507C2212yes—
10#17988499C412yes—
11#17988485—21no—
12#17988453C411yescharacteristic
13#17988447—21no—
14#17988313C2212yes—
15#17988311—21no—
16C2×#117×C73C2211yescharacteristic
17#407×C73—21no—
18#343×C73—21no—
19#343×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—21no—
32#14556498—22no—
33#14556498—22no—
34#14556498C2×C412yes—
35C23×C4×C73D411yescharacteristic
36C2×M16×C73—22no—
37#117×C73—41no—
38#117×C73—41no—
39C2×C4⋊C4×C73D411yescharacteristic
40C2×C4⋊C4×C73C2311yescharacteristic
41C2×C22⋊C4×C73C2×C411yescharacteristic
42C2×C22⋊C4×C73D411yescharacteristic
43C2×C42×C73C2×C411yescharacteristic
44C2×C42×C73D411yescharacteristic
45C22⋊C8×C73—41no—
46C22⋊C8×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×C73C22⋊C411yescharacteristic
59C22×C4×C73—21no—
60C22×C4×C73—21no—
61C22×C4×C73—22no—
62C22×C4×C73—41no—
63C22×C4×C73C22⋊C411yescharacteristic
64C22×C4×C73C22⋊C411yescharacteristic
65C22×C4×C73C22⋊C411yescharacteristic
66C22×C4×C73C22×C411yescharacteristic
67C22×C4×C73C2×D411yescharacteristic
68C22×C4×C73C2×D411yescharacteristic
69M16×C73—42no—
70M16×C73—42no—
71C2×C8×C73—42no—
72C4⋊C4×C73—41no—
73C4⋊C4×C73—41no—
74C22⋊C4×C73—41no—
75C22⋊C4×C73—41no—
76C42×C73—21no—
77C42×C73—21no—
78C42×C73—21no—
79C42×C73—21no—
80C23×C73—21no—
81C23×C73—21no—
82C23×C73—21no—
83C23×C73—41no—
84C23×C73—41no—
85C23×C73C2×C22⋊C411yescharacteristic
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—42no—
95C2×C4×C73—42no—
96C2×C4×C73—41no—
97C2×C4×C73—41no—
98C2×C4×C73—41no—
99C2×C4×C73—41no—
100C2×C4×C73#9911yescharacteristic
101C2×C4×C73#9911yescharacteristic
102C2×C4×C73#13712yes—
103C2×Dic73—42no—
104C2×Dic73—42no—
105C2×Dic73—42no—
106C2×Dic73—42no—
107C2×Dic73—42no—
108C2×Dic73—42no—
109Dic146—84no—
110C8×C73—82no—
111#10596831—82no—
112C22×C73—21no—
113C22×C73—21no—
114C22×C73—42no—
115C22×C73—41no—
116C22×C73—41no—
117C22×C73—41no—
118C22×C73—81no—
119C22×C73C2×#9911yescharacteristic
120C22×C73#41911yescharacteristic
121C22×C73#42111yescharacteristic
122C4×C73—22no—
123C4×C73—21no—
124C4×C73—21no—
125C4×C73—41no—
126C4×C73—41no—
127C4×C73—41no—
128C4×C73—41no—
129Dic73—82no—
130Dic73—82no—
131#11819—731nomaximal, Sylow
132C2×C73—21no—
133C2×C73—21no—
134C2×C73—81no—
135C2×C73#151111yescharacteristic
136C2×C73#212211yescharacteristic
137C2×C73#213511yescharacteristic
138#2628—731no—
139#1822D7311yescharacteristic
140#1464—731no—
141#1354—734no—
142C73#1181911yescharacteristic, complemented, Sylow
143C2×C4⋊Q8—731no—
144C2×#117C2×D7311yescharacteristic
145#432—1461no—
146#407—21no—
147#400—1461no—
148#399—1461no—
149#395—732no—
150#393—732no—
151#389—1461no—
152#382—731no—
153#380—1461no—
154#343—21no—
155#343C2×D7312yes—
156#324—732no—
157#323—1461no—
158C22×Q8—732no—
159C23×C4C22⋊D7311yescharacteristic
160C2×M16—22no—
161C4⋊Q8—2921no—
162C4⋊Q8—2921no—
163#117—41no—
164#117—41no—
165C2×C4⋊C4—1461no—
166C2×C4⋊C4—1461no—
167C2×C4⋊C4—1461no—
168C2×C4⋊C4—1462no—
169C2×C4⋊C4C22⋊D7311yescharacteristic
170C2×C4⋊C4C22×D7311yescharacteristic
171C2×C22⋊C4—1462no—
172C2×C22⋊C4C4×D7311yescharacteristic
173C2×C22⋊C4D29211yescharacteristic
174C2×C42C4×D7311yescharacteristic
175C2×C42D29211yescharacteristic
176C4⋊C8—2921no—
177C22⋊C8—41no—
178C22⋊C8—41no—
179C22⋊C8—1462no—
180#97—2921no—
181#95—732no—
182#95—1461no—
183#95—1462no—
184#95—1462no—
185C24#1192400511yescharacteristic
186C2×Q8—2922no—
187C2×Q8—5842no—
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—22no—
191C22×C4—41no—
192C22×C4—1462no—
193C22×C4—1462no—
194C22×C4#1192400511yescharacteristic
195C22×C4#1192400511yescharacteristic
196C22×C4#1192400511yescharacteristic
197C22×C4C2×C4×D7311yescharacteristic
198C22×C4C2×C22⋊D7311yescharacteristic
199C22×C4C2×D29211yescharacteristic
200M16—42no—
201M16—42no—
202C2×C8—42no—
203C2×C8—2922no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—2922no—
207C4⋊C4—2922no—
208C4⋊C4—2921no—
209C4⋊C4—2921no—
210C4⋊C4—5842no—
211C22⋊C4—41no—
212C22⋊C4—41no—
213C22⋊C4—5842no—
214C42—21no—
215C42—21no—
216C42—21no—
217C42—21no—
218C23—21no—
219C23—21no—
220C23—21no—
221C23—41no—
222C23—41no—
223C23C2×#1192400511yescharacteristic
224Q8—5844no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—2922no—
240C2×C4—2922no—
241C2×C4—2922no—
242C2×C4—2922no—
243C2×C4—2922no—
244C2×C4—2922no—
245C2×C4#1455650511yescharacteristic
246C2×C4#1455650511yescharacteristic
247C2×C4#1455662112yes—
248C8—82no—
249C8—5842no—
250C22—21no—
251C22—21no—
252C22—42no—
253C22—41no—
254C22—41no—
255C22—41no—
256C22—81no—
257C22C2×#1455650511yescharacteristic
258C22#1798859511yescharacteristic
259C22#1798860511yescharacteristic
260C4—22no—
261C4—21no—
262C4—21no—
263C4—41no—
264C4—41no—
265C4—41no—
266C4—41no—
267C4—5842no—
268C4—5842no—
269C2—21no—
270C2—21no—
271C2—81no—
272C2#2260846311yescharacteristic
273C2#2261158211yescharacteristic
274C2#2261162511yescharacteristic
subgroupG/H
centerC22C2×#14556505
commutatorC22×C4×C73C22×C4
FrattiniC2×C4⋊C4C22×D73
FittingC73×#1822C2
socleC22×C73C2×#99
prime radicalC24×C73C22⋊C4
cosocleC2×C4⋊C4×C73C23
hypercenter#1822D73
hypocenterC73#11819
LCSG ▷ C22×C4×C73 ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1822

Complements

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

NH ≅ G/Ntype
3. #22607960C2semidirect
142. C73#11819semidirect

Maximal subgroups

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

subgroupindex
#226157522
#226082652
#226079602
C73×#18222
#1181973