Finite Group Databasebeta

← #32983671

Subgroups — #32983671

Order 18688.

498 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 103 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#22618960C211yesmaximal, characteristic
2#22615104C211yesmaximal, characteristic
3#22608649C212yesmaximal, complemented
4#22607786C212yesmaximal, complemented
5C73×#1466C211yesmaximal, characteristic
6C2×#14556591C2211yescharacteristic
7#17988659—24no—
8#17988644C2212yes—
9#17988551—21no—
10C2×C22⋊#10596831—21no—
11#17988499—21no—
12#17988499—21no—
13#17988490C412yes—
14#17988452C412yes—
15#17988447—21no—
16#17988447—21no—
17C4×C4⋊Dic73C2211yescharacteristic
18#17988334—24no—
19C2×C4×D4×C73C2211yescharacteristic
20#432×C73C2212yes—
21#323×C73—21no—
22#323×C73—21no—
23C22×Dic146—21no—
24C2×#11924012—22no—
25C22×#10596831—22no—
26#14556591—22no—
27#14556591—22no—
28C2×C4⋊Dic73—21no—
29C2×C4⋊Dic73—21no—
30C2×C4⋊Dic73C2×C412yes—
31C2×C22⋊Dic73—22no—
32C2×C22⋊Dic73—22no—
33C2×C4×Dic73C2×C412yes—
34C4⋊#10596831D414yes—
35C22⋊#10596831—22no—
36C22⋊#10596831—22no—
37C22⋊#10596831—22no—
38#14556502—22no—
39#14556498—22no—
40#14556498—22no—
41#14556498—21no—
42C22×D4×C73C2×C411yescharacteristic
43C23×C4×C73D411yescharacteristic
44C23×C4×C73D411yescharacteristic
45C4×D4×C73—22no—
46C4×D4×C73—22no—
47C2×C4⋊C4×C73C2×C411yescharacteristic
48C2×C22⋊C4×C73D411yescharacteristic
49C2×C22⋊C4×C73D411yescharacteristic
50C2×C42×C73C2311yescharacteristic
51C4⋊C8×C73—22no—
52C22⋊C8×C73—22no—
53#97×C73—22no—
54C2×Dic146—42no—
55C2×Dic146—82no—
56C22×Dic73—22no—
57C22×Dic73—22no—
58#11924012—82no—
59C2×#10596831—24no—
60C2×#10596831—82no—
61C4⋊Dic73—24no—
62C4⋊Dic73—42no—
63C4⋊Dic73—41no—
64C4⋊Dic73—41no—
65C22⋊Dic73—82no—
66C22⋊Dic73—82no—
67C4×Dic73—42no—
68C24×C73C22⋊C411yescharacteristic
69C24×C73C22⋊C411yescharacteristic
70C2×D4×C73—22no—
71C2×D4×C73—22no—
72C2×D4×C73—41no—
73C22×C4×C73—21no—
74C22×C4×C73—21no—
75C22×C4×C73—21no—
76C22×C4×C73—21no—
77C22×C4×C73—42no—
78C22×C4×C73—42no—
79C22×C4×C73C22⋊C411yescharacteristic
80C22×C4×C73C22⋊C411yescharacteristic
81C22×C4×C73C22×C411yescharacteristic
82C22×C4×C73C2×D411yescharacteristic
83C22×C4×C73C2×D411yescharacteristic
84C2×C8×C73—42no—
85C4⋊C4×C73—22no—
86C22⋊C4×C73—22no—
87C22⋊C4×C73—22no—
88C42×C73C2×D412yes—
89C42×C73#4112yes—
90C23×C73—21no—
91C23×C73—21no—
92C23×C73—21no—
93C23×C73—21no—
94C23×C73—21no—
95C23×C73—41no—
96C23×C73—41no—
97C23×C73—41no—
98C23×C73—41no—
99C23×C73#10112yes—
100C23×C73C2×C22⋊C411yescharacteristic
101D4×C73—44no—
102C2×C4×C73—21no—
103C2×C4×C73—21no—
104C2×C4×C73—22no—
105C2×C4×C73—21no—
106C2×C4×C73—21no—
107C2×C4×C73—41no—
108C2×C4×C73—42no—
109C2×C4×C73—42no—
110C2×C4×C73—41no—
111C2×C4×C73—41no—
112C2×C4×C73—81no—
113C2×C4×C73—81no—
114C2×C4×C73C4×D412yes—
115C2×C4×C73#12011yescharacteristic
116C2×C4×C73#12112yes—
117C2×C4×C73#12311yescharacteristic
118C2×Dic73—42no—
119C2×Dic73—42no—
120C2×Dic73—42no—
121C2×Dic73—42no—
122C2×Dic73—42no—
123C2×Dic73—42no—
124Dic146—84no—
125C8×C73—82no—
126#10596831—44no—
127C22×C73—21no—
128C22×C73—21no—
129C22×C73—22no—
130C22×C73—42no—
131C22×C73—42no—
132C22×C73—41no—
133C22×C73—41no—
134C22×C73—41no—
135C22×C73—41no—
136C22×C73—41no—
137C22×C73—81no—
138C22×C73—81no—
139C22×C73#38611yescharacteristic
140C22×C73C2×#10111yescharacteristic
141C22×C73#41311yescharacteristic
142C4×C73—21no—
143C4×C73—22no—
144C4×C73—22no—
145C4×C73—41no—
146C4×C73—41no—
147C4×C73#45512yes—
148Dic73—82no—
149Dic73—82no—
150#9453—731nomaximal, Sylow
151C2×C73—21no—
152C2×C73—21no—
153C2×C73—42no—
154C2×C73—81no—
155C2×C73#188511yescharacteristic
156C2×C73#190111yescharacteristic
157C2×C73#191011yescharacteristic
158#2973—731no—
159#2563—731no—
160#1556—732no—
161#1466D7311yescharacteristic
162#1285—732no—
163C73#945311yescharacteristic, complemented, Sylow
164C2×C4⋊Q8—731no—
165C2×C4×D4C2×D7311yescharacteristic
166#435—1464no—
167#432—732no—
168#432C2×D7312yes—
169#407—1461no—
170C2×C22⋊C8—1461no—
171#393—1461no—
172#393—1461no—
173#390—732no—
174#382—732no—
175#380—1461no—
176#380—1461no—
177C4×C4⋊C4—731no—
178#332—1464no—
179#323—21no—
180#323—21no—
181C22×Q8—1461no—
182C22×D4C4×D7311yescharacteristic
183C23×C4D29211yescharacteristic
184C23×C4D29211yescharacteristic
185C2×M16—1462no—
186C22×C8—1462no—
187C4⋊Q8—1462no—
188C4⋊Q8—1462no—
189C4×D4—22no—
190C4×D4—22no—
191C2×C4⋊C4—732no—
192C2×C4⋊C4—1461no—
193C2×C4⋊C4—1461no—
194C2×C4⋊C4C4×D7311yescharacteristic
195C2×C22⋊C4—1462no—
196C2×C22⋊C4—1462no—
197C2×C22⋊C4C22⋊D7311yescharacteristic
198C2×C22⋊C4C22⋊D7311yescharacteristic
199C2×C42—732no—
200C2×C42C22×D7311yescharacteristic
201C4⋊C8—22no—
202C4⋊C8—734no—
203C22⋊C8—22no—
204C22⋊C8—1462no—
205C22⋊C8—1462no—
206C22⋊C8—1462no—
207#97—22no—
208#97—1462no—
209#95—1462no—
210#95—1462no—
211#95—1461no—
212C24#1192400511yescharacteristic
213C24#1192400511yescharacteristic
214C2×Q8—2922no—
215C2×Q8—5842no—
216C2×D4—22no—
217C2×D4—22no—
218C2×D4—41no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4—1462no—
226C22×C4—1462no—
227C22×C4#1192400511yescharacteristic
228C22×C4#1192400511yescharacteristic
229C22×C4C2×C4×D7311yescharacteristic
230C22×C4C2×C22⋊D7311yescharacteristic
231C22×C4C2×D29211yescharacteristic
232M16—5842no—
233C2×C8—42no—
234C2×C8—5842no—
235C2×C8—1464no—
236C4⋊C4—22no—
237C4⋊C4—2922no—
238C4⋊C4—2921no—
239C4⋊C4—2921no—
240C4⋊C4—1464no—
241C22⋊C4—22no—
242C22⋊C4—22no—
243C22⋊C4—5842no—
244C22⋊C4—5842no—
245C42—2922no—
246C42D4×D7312yes—
247C42#1192402712yes—
248C23—21no—
249C23—21no—
250C23—21no—
251C23—21no—
252C23—21no—
253C23—41no—
254C23—41no—
255C23—41no—
256C23—41no—
257C23#1455650912yes—
258C23C2×#1192400511yescharacteristic
259Q8—5844no—
260D4—44no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—81no—
272C2×C4—81no—
273C2×C4—2922no—
274C2×C4—2922no—
275C2×C4—2922no—
276C2×C4—2922no—
277C2×C4—2922no—
278C2×C4—2922no—
279C2×C4#1455655112yes—
280C2×C4#1455656111yescharacteristic
281C2×C4#1455656312yes—
282C2×C4#1455657511yescharacteristic
283C8—82no—
284C8—2924no—
285C22—21no—
286C22—21no—
287C22—22no—
288C22—42no—
289C22—42no—
290C22—41no—
291C22—41no—
292C22—41no—
293C22—41no—
294C22—41no—
295C22—81no—
296C22—81no—
297C22#1798846411yescharacteristic
298C22C2×#1455650911yescharacteristic
299C22#1798856911yescharacteristic
300C4—22no—
301C4—21no—
302C4—22no—
303C4—41no—
304C4—41no—
305C4—5842no—
306C4—5842no—
307C4#1798876712yes—
308C2—21no—
309C2—21no—
310C2—42no—
311C2—81no—
312C2#2261031711yescharacteristic
313C2#2261039711yescharacteristic
314C2#2261045611yescharacteristic
subgroupG/H
centerC22#17988464
commutatorC22×C4×C73C22×C4
FrattiniC2×C42C22×D73
FittingC73×#1466C2
socleC22×C73#386
prime radicalC22×D4×C73C2×C4
cosocleC2×C42×C73C23
hypercenter#1466D73
hypocenterC73#9453
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1466

Complements

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

NH ≅ G/Ntype
3. #22608649C2semidirect
4. #22607786C2semidirect
163. C73#9453semidirect

Maximal subgroups

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

subgroupindex
#226189602
#226151042
#226086492
#226077862
C73×#14662
#945373