Finite Group Databasebeta

← #32986580

Subgroups — #32986580

Order 18688.

632 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 632 conjugacy classes of subgroups — too many to draw. Only its 121 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
1C2×#17988918C212yesmaximal
2#22616045C211yesmaximal, characteristic
3C2×#17988325C212yesmaximal
4#22608198C211yesmaximal, characteristic
5C73×#1280C211yesmaximal, characteristic
6C2×#14556570C2212yes—
7C22×C4⋊Dic73C2211yescharacteristic
8#17988918—24no—
9#17988918—24no—
10C2×#14556523—22no—
11C2×#14556516—22no—
12#17988519—22no—
13#17988508—22no—
14#17988447—22no—
15C2×#14556498—22no—
16C2×#14556498C2211yescharacteristic
17#17988325—24no—
18C2×C22⋊C8×C73C2212yes—
19C2×#95×C73C2211yescharacteristic
20C22×Dic146D412yes—
21C23×Dic73—21no—
22C23×Dic73—21no—
23#14556570—22no—
24#14556570—22no—
25#14556570—22no—
26#14556570—22no—
27C2×C4⋊Dic73—22no—
28C2×C4⋊Dic73—22no—
29C2×C4⋊Dic73—22no—
30C2×C4⋊Dic73—22no—
31C2×C4⋊Dic73—21no—
32C2×C4⋊Dic73D412yes—
33C2×C4⋊Dic73D412yes—
34C2×#11924007—22no—
35C2×C22⋊Dic73—22no—
36#14556523—28no—
37#14556516—28no—
38#14556498—24no—
39#14556498—22no—
40#14556498—44no—
41C23×C4×C73D412yes—
42C23×C4×C73C2311yescharacteristic
43C22×C8×C73—22no—
44C22⋊C8×C73—22no—
45C22⋊C8×C73D414yes—
46#95×C73—22no—
47C2×Dic146—22no—
48C2×Dic146—22no—
49C2×Dic146—44no—
50C22×Dic73—22no—
51C22×Dic73—22no—
52C22×Dic73—22no—
53C22×Dic73—22no—
54C22×Dic73—41no—
55C22×Dic73—42no—
56C22×Dic73—41no—
57C22×Dic73—41no—
58C22×Dic73—41no—
59C22×Dic73—42no—
60C22×Dic73—42no—
61C22×Dic73—42no—
62C4⋊Dic73—24no—
63C4⋊Dic73—22no—
64C4⋊Dic73—22no—
65C4⋊Dic73—42no—
66C4⋊Dic73—82no—
67C4⋊Dic73—82no—
68#11924007—42no—
69#11924007—42no—
70C22⋊Dic73—42no—
71C22⋊Dic73—42no—
72C24×C73C2×D411yescharacteristic
73C22×C4×C73—22no—
74C22×C4×C73—22no—
75C22×C4×C73—42no—
76C22×C4×C73—42no—
77C22×C4×C73—42no—
78C22×C4×C73SD1614yes—
79C22×C4×C73C2×D412yes—
80C22×C4×C73C2×D411yescharacteristic
81C22×C4×C73C2×D412yes—
82C22×C4×C73#4111yescharacteristic
83C2×C8×C73—24no—
84C2×C8×C73—44no—
85C23×C73—21no—
86C23×C73—21no—
87C23×C73—22no—
88C23×C73#12011yescharacteristic
89C23×C73#12111yescharacteristic
90C23×C73#12711yescharacteristic
91C23×C73C2×SD1612yes—
92C23×C73#13712yes—
93C2×C4×C73—24no—
94C2×C4×C73—24no—
95C2×C4×C73—41no—
96C2×C4×C73—42no—
97C2×C4×C73—41no—
98C2×C4×C73—42no—
99C2×C4×C73—42no—
100C2×C4×C73—44no—
101C2×C4×C73—82no—
102C2×C4×C73#12012yes—
103C2×C4×C73#12112yes—
104C2×Dic73—44no—
105C2×Dic73—42no—
106C2×Dic73—42no—
107C2×Dic73—42no—
108C2×Dic73—42no—
109C2×Dic73—42no—
110C2×Dic73—42no—
111C2×Dic73—44no—
112C2×Dic73—44no—
113C2×Dic73—82no—
114C2×Dic73—81no—
115C2×Dic73—82no—
116C2×Dic73—81no—
117C2×Dic73—81no—
118C2×Dic73—81no—
119Dic146—44no—
120Dic146—82no—
121C8×C73—44no—
122C22×C73—22no—
123C22×C73—22no—
124C22×C73—22no—
125C22×C73—22no—
126C22×C73—21no—
127C22×C73—21no—
128C22×C73—21no—
129C22×C73—21no—
130C22×C73#39211yescharacteristic
131C22×C73#44812yes—
132C22×C73#45511yescharacteristic
133C22×C73#45611yescharacteristic
134C22×C73#45812yes—
135C22×C73#46112yes—
136C22×C73#49211yescharacteristic
137C22×C73#49711yescharacteristic
138C4×C73—22no—
139C4×C73—22no—
140C4×C73—44no—
141Dic73—82no—
142Dic73—82no—
143Dic73—82no—
144Dic73—82no—
145#9973—731nomaximal, Sylow
146C2×C73—21no—
147C2×C73—22no—
148C2×C73—21no—
149C2×C73#160812yes—
150C2×C73#161112yes—
151C2×C73#200711yescharacteristic
152C2×C73#201311yescharacteristic
153C2×C73#202211yescharacteristic
154C2×#483—732no—
155#2659—731no—
156C2×#328—732no—
157#1445—731no—
158#1280D7311yescharacteristic
159C73#997311yescharacteristic, complemented, Sylow
160C2×C22⋊Q8—732no—
161C22×C4⋊C4—731no—
162#483—1464no—
163#483—1464no—
164C2×#106—1462no—
165C2×#103—1462no—
166C2×C22⋊C8C2×D7312yes—
167#398—1462no—
168#395—1462no—
169#380—1462no—
170C2×#95—731no—
171C2×#95—1462no—
172C2×#95C2×D7311yescharacteristic
173#328—1464no—
174C22×Q8—732no—
175C23×C4—1461no—
176C23×C4—1461no—
177C23×C4D29212yes—
178C23×C4C22×D7311yescharacteristic
179C22×C8—22no—
180C22⋊Q8—1462no—
181C22⋊Q8—1462no—
182C22⋊Q8—1462no—
183C22⋊Q8—1462no—
184C2×C4⋊C4—732no—
185C2×C4⋊C4—732no—
186C2×C4⋊C4—1462no—
187C2×C4⋊C4—1461no—
188C2×C4⋊C4—1462no—
189C2×C4⋊C4—1462no—
190C2×C4⋊C4—1462no—
191C2×C4⋊C4—1462no—
192C2×C22⋊C4—1462no—
193#106—1468no—
194#103—1468no—
195C22⋊C8—22no—
196C22⋊C8D29214yes—
197#95—22no—
198#95—2924no—
199#95—1464no—
200#95—1462no—
201C24C2×D29211yescharacteristic
202C2×Q8—2924no—
203C2×Q8—1462no—
204C2×Q8—1462no—
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—42no—
208C22×C4—42no—
209C22×C4—42no—
210C22×C4—2921no—
211C22×C4—2922no—
212C22×C4—2921no—
213C22×C4—2921no—
214C22×C4—2921no—
215C22×C4—2922no—
216C22×C4—2922no—
217C22×C4—2922no—
218C22×C4—1462no—
219C22×C4—1462no—
220C22×C4—1462no—
221C22×C4—1462no—
222C22×C4#1192401714yes—
223C22×C4D4×D7312yes—
224C22×C4D4×D7311yescharacteristic
225C22×C4C2×D29212yes—
226C22×C4#1192402911yescharacteristic
227C2×C8—24no—
228C2×C8—44no—
229C4⋊C4—2922no—
230C4⋊C4—2922no—
231C4⋊C4—2922no—
232C4⋊C4—5842no—
233C4⋊C4—5842no—
234C4⋊C4—1464no—
235C4⋊C4—1462no—
236C4⋊C4—1462no—
237C22⋊C4—2922no—
238C22⋊C4—2922no—
239C23—21no—
240C23—21no—
241C23—22no—
242C23#1455656111yescharacteristic
243C23#1455656611yescharacteristic
244C23#1455658811yescharacteristic
245C23C2×#1192401712yes—
246C23#1455662412yes—
247Q8—2924no—
248Q8—5842no—
249C2×C4—24no—
250C2×C4—24no—
251C2×C4—41no—
252C2×C4—42no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—44no—
257C2×C4—82no—
258C2×C4—2922no—
259C2×C4—2924no—
260C2×C4—2922no—
261C2×C4—2922no—
262C2×C4—2922no—
263C2×C4—2922no—
264C2×C4—2922no—
265C2×C4—2924no—
266C2×C4—2924no—
267C2×C4—5842no—
268C2×C4—5841no—
269C2×C4—5841no—
270C2×C4—5841no—
271C2×C4—5841no—
272C2×C4—5842no—
273C2×C4#1455656112yes—
274C2×C4#1455656612yes—
275C8—44no—
276C22—22no—
277C22—22no—
278C22—21no—
279C22—21no—
280C22—22no—
281C22—22no—
282C22—21no—
283C22—21no—
284C22#1798849711yescharacteristic
285C22#1798872812yes—
286C22#1798876711yescharacteristic
287C22#1798877211yescharacteristic
288C22#1798877812yes—
289C22#1798879312yes—
290C22#1798896011yescharacteristic
291C22#1798898111yescharacteristic
292C4—22no—
293C4—22no—
294C4—44no—
295C4—5842no—
296C4—5842no—
297C4—5842no—
298C4—5842no—
299C2—21no—
300C2—21no—
301C2—22no—
302C2#2260892412yes—
303C2#2260894112yes—
304C2#2261098011yescharacteristic
305C2#2261101611yescharacteristic
306C2#2261106311yescharacteristic
subgroupG/H
centerC23#14556561
commutator, cosocleC23×C4×C73C23
FrattiniC23×C4C22×D73
FittingC73×#1280C2
socleC23×C73#120
prime radicalC24×C73C2×D4
hypercenter#1280D73
hypocenterC73#9973
LCSG ▷ C23×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
159. C73#9973semidirect

Maximal subgroups

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

subgroupindex
C2×#179889182
#226160452
C2×#179883252
#226081982
C73×#12802
#997373