Finite Group Databasebeta

← #32996623

Subgroups — #32996623

Order 18688.

378 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 91 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
1C4×#14556510C211yesmaximal, characteristic
2#22608275C211yesmaximal, characteristic
3#22607961C212yesmaximal
4#22607958C212yesmaximal
5C73×#2581C211yesmaximal, characteristic
6#17988644—21no—
7C2×#14556510—21no—
8C4×#11924012—21no—
9#17988356C2212yes—
10#17988313—21no—
11#17988313C2212yes—
12C2×C4×Q8×C73C411yescharacteristic
13C2×C4×Q8×C73C2211yescharacteristic
14#400×C73C411yescharacteristic
15#400×C73C2211yescharacteristic
16#395×C73C411yescharacteristic
17#395×C73C2211yescharacteristic
18#391×C73—21no—
19#389×C73—21no—
20#387×C73—21no—
21#387×C73—21no—
22#382×C73C411yescharacteristic
23C2×#11924012—22no—
24C4⋊#10596831—41no—
25#14556510—24no—
26C22⋊#10596831—22no—
27#14556502—41no—
28#14556502—41no—
29C4×#10596831—41no—
30C22×Q8×C73C2×C411yescharacteristic
31C22×Q8×C73D411yescharacteristic
32C4×Q8×C73—41no—
33C4×Q8×C73—41no—
34C4×Q8×C73—41no—
35C4×Q8×C73—41no—
36C2×C4⋊C4×C73—21no—
37C2×C4⋊C4×C73—21no—
38C2×C4⋊C4×C73—21no—
39C2×C4⋊C4×C73—21no—
40C2×C4⋊C4×C73C2×C411yescharacteristic
41C2×C4⋊C4×C73C2×C411yescharacteristic
42C2×C4⋊C4×C73D411yescharacteristic
43C2×C4⋊C4×C73C2311yescharacteristic
44C2×C42×C73—21no—
45C2×C42×C73C2×C411yescharacteristic
46C2×C42×C73D411yescharacteristic
47C2×C42×C73D411yescharacteristic
48#95×C73—21no—
49#95×C73—21no—
50#95×C73—21no—
51#95×C73—21no—
52#95×C73—21no—
53#95×C73—21no—
54#95×C73—21no—
55#95×C73C2×C411yescharacteristic
56#95×C73C2×C411yescharacteristic
57#11924012—24no—
58#11924012—42no—
59C2×#10596831—42no—
60C2×#10596831—42no—
61C2×Q8×C73—22no—
62C2×Q8×C73—22no—
63C2×Q8×C73—41no—
64C2×Q8×C73—42no—
65C2×Q8×C73—41no—
66C22×C4×C73—21no—
67C22×C4×C73—21no—
68C22×C4×C73—21no—
69C22×C4×C73—21no—
70C22×C4×C73C22⋊C411yescharacteristic
71C22×C4×C73C22⋊C411yescharacteristic
72C22×C4×C73C22⋊C411yescharacteristic
73C22×C4×C73C22⋊C411yescharacteristic
74C22×C4×C73C22×C411yescharacteristic
75C22×C4×C73C2×D411yescharacteristic
76C22×C4×C73C2×D411yescharacteristic
77C4⋊C4×C73—41no—
78C4⋊C4×C73—41no—
79C4⋊C4×C73—41no—
80C4⋊C4×C73—41no—
81C4⋊C4×C73—42no—
82C4⋊C4×C73—42no—
83C4⋊C4×C73—41no—
84C4⋊C4×C73—41no—
85C4⋊C4×C73—42no—
86C42×C73—21no—
87C42×C73—21no—
88C42×C73—21no—
89C42×C73—21no—
90C42×C73—21no—
91C42×C73—21no—
92C42×C73—42no—
93C23×C73C2×C22⋊C411yescharacteristic
94Q8×C73—44no—
95Q8×C73—42no—
96Q8×C73—42no—
97C2×C4×C73—21no—
98C2×C4×C73—21no—
99C2×C4×C73—21no—
100C2×C4×C73—21no—
101C2×C4×C73—22no—
102C2×C4×C73—21no—
103C2×C4×C73—21no—
104C2×C4×C73—21no—
105C2×C4×C73—21no—
106C2×C4×C73—21no—
107C2×C4×C73—21no—
108C2×C4×C73—41no—
109C2×C4×C73—41no—
110C2×C4×C73—41no—
111C2×C4×C73—41no—
112C2×C4×C73—41no—
113C2×C4×C73—41no—
114C2×C4×C73—41no—
115C2×C4×C73—41no—
116C2×C4×C73—41no—
117C2×C4×C73—41no—
118C2×C4×C73—42no—
119C2×C4×C73—41no—
120C2×C4×C73—41no—
121C2×C4×C73—41no—
122C2×C4×C73#9911yescharacteristic
123C2×C4×C73#9911yescharacteristic
124C2×C4×C73#10412yes—
125C2×C4×C73#13712yes—
126#10596831—44no—
127#10596831—82no—
128C22×C73—21no—
129C22×C73—21no—
130C22×C73C2×#9911yescharacteristic
131C22×C73#41911yescharacteristic
132C22×C73C2×#10411yescharacteristic
133C4×C73—21no—
134C4×C73—21no—
135C4×C73—22no—
136C4×C73—22no—
137C4×C73—41no—
138C4×C73—41no—
139C4×C73—42no—
140C4×C73—41no—
141C4×C73—41no—
142C4×C73—81no—
143C4×C73—81no—
144C4×C73—81no—
145#11792—731nomaximal, Sylow
146C2×C73—21no—
147C2×C73—21no—
148C2×C73#150811yescharacteristic
149C2×C73#212011yescharacteristic
150C2×C73#213311yescharacteristic
151#2581D7311yescharacteristic
152C4×#101—731no—
153#1467—731no—
154#1354—732no—
155#1353—732no—
156C73#1179211yescharacteristic, complemented, Sylow
157C2×C4×Q8Dic7311yescharacteristic
158C2×C4×Q8C2×D7311yescharacteristic
159#432—1461no—
160C2×#101—1461no—
161C4×M16—1461no—
162#400Dic7311yescharacteristic
163#400C2×D7311yescharacteristic
164#395Dic7311yescharacteristic
165#395C2×D7311yescharacteristic
166#391—21no—
167#389—21no—
168#387—21no—
169#387—21no—
170#382Dic7311yescharacteristic
171#343—732no—
172#324—732no—
173#324—1461no—
174C22×Q8C2×Dic7311yescharacteristic
175C22×Q8C22⋊D7311yescharacteristic
176C2×M16—1462no—
177C4×Q8—41no—
178C4×Q8—41no—
179C4×Q8—41no—
180C4×Q8—41no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4C2×Dic7311yescharacteristic
186C2×C4⋊C4C2×Dic7311yescharacteristic
187C2×C4⋊C4C22⋊D7311yescharacteristic
188C2×C4⋊C4C22×D7311yescharacteristic
189C2×C42—21no—
190C2×C42C2×Dic7311yescharacteristic
191C2×C42C22⋊D7311yescharacteristic
192C2×C42C22⋊D7311yescharacteristic
193C4⋊C8—2921no—
194#101—1464no—
195C22⋊C8—1462no—
196#97—2921no—
197#97—2921no—
198C4×C8—2921no—
199#95—21no—
200#95—21no—
201#95—21no—
202#95—21no—
203#95—21no—
204#95—21no—
205#95—21no—
206#95C2×Dic7311yescharacteristic
207#95C2×Dic7311yescharacteristic
208C2×Q8—22no—
209C2×Q8—22no—
210C2×Q8—41no—
211C2×Q8—42no—
212C2×Q8—41no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4C22⋊Dic7311yescharacteristic
218C22×C4C22⋊Dic7311yescharacteristic
219C22×C4C22⋊Dic7311yescharacteristic
220C22×C4C22⋊Dic7311yescharacteristic
221C22×C4C22×Dic7311yescharacteristic
222C22×C4C2×C22⋊D7311yescharacteristic
223C22×C4C2×C22⋊D7311yescharacteristic
224M16—2922no—
225M16—1464no—
226C2×C8—2922no—
227C2×C8—2922no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C4⋊C4—41no—
231C4⋊C4—41no—
232C4⋊C4—42no—
233C4⋊C4—42no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—42no—
237C42—21no—
238C42—21no—
239C42—21no—
240C42—21no—
241C42—21no—
242C42—21no—
243C42—42no—
244C23C2×C22⋊Dic7311yescharacteristic
245Q8—44no—
246Q8—42no—
247Q8—42no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—42no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4#1455650611yescharacteristic
274C2×C4#1455650611yescharacteristic
275C2×C4#1455651812yes—
276C2×C4#1455662212yes—
277C8—2924no—
278C8—5842no—
279C22—21no—
280C22—21no—
281C22C2×#1455650611yescharacteristic
282C22#1798859611yescharacteristic
283C22C2×#1455651811yescharacteristic
284C4—22no—
285C4—22no—
286C4—21no—
287C4—21no—
288C4—41no—
289C4—41no—
290C4—42no—
291C4—41no—
292C4—41no—
293C4—81no—
294C4—81no—
295C4—81no—
296C2—21no—
297C2—21no—
298C2#2260845111yescharacteristic
299C2#2261157211yescharacteristic
300C2#2261162011yescharacteristic
subgroupG/H
centerC22C2×#14556506
commutatorC22×C4×C73C22×C4
FrattiniC2×C4⋊C4C22×D73
FittingC73×#2581C2
socleC22×C73C2×#99
prime radicalC23×C73C2×C22⋊C4
cosocleC2×C4⋊C4×C73C23
hypercenter#2581D73
hypocenterC73#11792
LCSG ▷ C22×C4×C73 ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2581

Complements

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

NH ≅ G/Ntype
156. C73#11792semidirect

Maximal subgroups

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

subgroupindex
C4×#145565102
#226082752
#226079612
#226079582
C73×#25812
#1179273