Finite Group Databasebeta

← #32988985

Subgroups — #32988985

Order 18688.

500 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 105 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#22615901C211yesmaximal, characteristic
2#22610018C212yesmaximal
3#22608198C211yesmaximal, characteristic
4#22607811C212yesmaximal
5C73×#1280C211yesmaximal, characteristic
6C22×C4⋊Dic73C2211yescharacteristic
7#17988529—22no—
8#17988521—22no—
9#17988460—22no—
10#17988447C2212yes—
11C2×#14556498—22no—
12C2×#14556498C2211yescharacteristic
13#17988350—22no—
14#17988350—22no—
15C2×C22⋊C8×C73C2212yes—
16C2×#95×C73C2211yescharacteristic
17C23×Dic73—21no—
18C23×Dic73—21no—
19C2×C4⋊Dic73—22no—
20C2×C4⋊Dic73—22no—
21C2×C4⋊Dic73—21no—
22C2×C4⋊Dic73D412yes—
23C2×C4⋊Dic73D412yes—
24C2×C4⋊Dic73Q812yes—
25C2×#11924007—22no—
26C2×#11924007—22no—
27C2×C22⋊Dic73—22no—
28#14556498—22no—
29#14556498—22no—
30#14556498—22no—
31#14556498—22no—
32#14556498—44no—
33C23×C4×C73D412yes—
34C23×C4×C73C2311yescharacteristic
35C22×C8×C73—22no—
36C22⋊C8×C73—22no—
37C22⋊C8×C73—22no—
38#95×C73—22no—
39C22×Dic73—22no—
40C22×Dic73—22no—
41C22×Dic73—22no—
42C22×Dic73—22no—
43C22×Dic73—41no—
44C22×Dic73—42no—
45C22×Dic73—41no—
46C22×Dic73—41no—
47C22×Dic73—41no—
48C22×Dic73—42no—
49C22×Dic73—42no—
50C22×Dic73—42no—
51C4⋊Dic73—24no—
52C4⋊Dic73—42no—
53C4⋊Dic73—42no—
54C4⋊Dic73—42no—
55#11924007—82no—
56#11924007—82no—
57C22⋊Dic73—42no—
58C22⋊Dic73—42no—
59C24×C73C2×D411yescharacteristic
60C22×C4×C73—22no—
61C22×C4×C73—22no—
62C22×C4×C73—22no—
63C22×C4×C73—42no—
64C22×C4×C73—42no—
65C22×C4×C73—42no—
66C22×C4×C73C2×D412yes—
67C22×C4×C73C2×Q811yescharacteristic
68C22×C4×C73#4111yescharacteristic
69C22×C4×C73#4112yes—
70C2×C8×C73—42no—
71C2×C8×C73—42no—
72C2×C8×C73—42no—
73C23×C73—21no—
74C23×C73—21no—
75C23×C73—22no—
76C23×C73#12011yescharacteristic
77C23×C73C22⋊Q811yescharacteristic
78C23×C73#12411yescharacteristic
79C23×C73#13512yes—
80C23×C73AGL(1,ℤ/8)12yes—
81C2×C4×C73—22no—
82C2×C4×C73—22no—
83C2×C4×C73—41no—
84C2×C4×C73—41no—
85C2×C4×C73—42no—
86C2×C4×C73—44no—
87C2×C4×C73—42no—
88C2×C4×C73—42no—
89C2×C4×C73—42no—
90C2×C4×C73—82no—
91C2×C4×C73C22⋊Q812yes—
92C2×C4×C73#12412yes—
93C2×Dic73—44no—
94C2×Dic73—42no—
95C2×Dic73—42no—
96C2×Dic73—42no—
97C2×Dic73—42no—
98C2×Dic73—42no—
99C2×Dic73—42no—
100C2×Dic73—42no—
101C2×Dic73—42no—
102C2×Dic73—44no—
103C2×Dic73—82no—
104C2×Dic73—81no—
105C2×Dic73—82no—
106C2×Dic73—81no—
107C2×Dic73—81no—
108C2×Dic73—81no—
109C8×C73—82no—
110C22×C73—22no—
111C22×C73—22no—
112C22×C73—22no—
113C22×C73—22no—
114C22×C73—21no—
115C22×C73—21no—
116C22×C73—21no—
117C22×C73—21no—
118C22×C73#39311yescharacteristic
119C22×C73#44912yes—
120C22×C73#45511yescharacteristic
121C22×C73#45611yescharacteristic
122C22×C73#45812yes—
123C22×C73#47812yes—
124C22×C73#48811yescharacteristic
125C22×C73#49011yescharacteristic
126C4×C73—22no—
127C4×C73—22no—
128C4×C73—82no—
129Dic73—82no—
130Dic73—82no—
131Dic73—82no—
132Dic73—82no—
133#10346—731nomaximal, Sylow
134C2×C73—21no—
135C2×C73—22no—
136C2×C73—21no—
137C2×C73#160912yes—
138C2×C73#161212yes—
139C2×C73#202511yescharacteristic
140C2×C73#202811yescharacteristic
141C2×C73#203011yescharacteristic
142#2646—731no—
143#1823—732no—
144#1445—731no—
145#1294—732no—
146#1280D7311yescharacteristic
147C73#1034611yescharacteristic, complemented, Sylow
148C22×C4⋊C4—731no—
149C2×C22⋊C8C2×D7312yes—
150#400—1462no—
151#398—1462no—
152#385—1462no—
153#380—732no—
154C2×#95—731no—
155C2×#95—1462no—
156C2×#95C2×D7311yescharacteristic
157#340—1462no—
158#340—1462no—
159C23×C4—1461no—
160C23×C4—1461no—
161C23×C4D29212yes—
162C23×C4C22×D7311yescharacteristic
163C22×C8—22no—
164C2×C4⋊C4—732no—
165C2×C4⋊C4—732no—
166C2×C4⋊C4—732no—
167C2×C4⋊C4—1461no—
168C2×C4⋊C4—1462no—
169C2×C4⋊C4—1462no—
170C2×C4⋊C4—1462no—
171C2×C4⋊C4—1462no—
172C2×C22⋊C4—1462no—
173C22⋊C8—22no—
174C22⋊C8—22no—
175#95—22no—
176#95—2924no—
177#95—1462no—
178#95—1462no—
179#95—1462no—
180#95—1462no—
181C24C2×D29211yescharacteristic
182C22×C4—22no—
183C22×C4—22no—
184C22×C4—22no—
185C22×C4—42no—
186C22×C4—42no—
187C22×C4—42no—
188C22×C4—2921no—
189C22×C4—2922no—
190C22×C4—2921no—
191C22×C4—2921no—
192C22×C4—2921no—
193C22×C4—2922no—
194C22×C4—2922no—
195C22×C4—2922no—
196C22×C4—1462no—
197C22×C4—1462no—
198C22×C4—1462no—
199C22×C4—1462no—
200C22×C4D4×D7312yes—
201C22×C4Q8×D7311yescharacteristic
202C22×C4#1192402711yescharacteristic
203C22×C4#1192402812yes—
204C2×C8—42no—
205C2×C8—42no—
206C2×C8—42no—
207C4⋊C4—2922no—
208C4⋊C4—2922no—
209C4⋊C4—2922no—
210C4⋊C4—5842no—
211C4⋊C4—5842no—
212C4⋊C4—1464no—
213C22⋊C4—2922no—
214C22⋊C4—2922no—
215C23—21no—
216C23—21no—
217C23—22no—
218C23#1455656111yescharacteristic
219C23#1455657111yescharacteristic
220C23#1455657911yescharacteristic
221C23#1455661312yes—
222C23#1455661912yes—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—44no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4—82no—
233C2×C4—2924no—
234C2×C4—2922no—
235C2×C4—2924no—
236C2×C4—2922no—
237C2×C4—2922no—
238C2×C4—2922no—
239C2×C4—2922no—
240C2×C4—2922no—
241C2×C4—2922no—
242C2×C4—2922no—
243C2×C4—5842no—
244C2×C4—5841no—
245C2×C4—5841no—
246C2×C4—5841no—
247C2×C4—5841no—
248C2×C4—5842no—
249C2×C4#1455656912yes—
250C2×C4#1455657712yes—
251C8—82no—
252C22—22no—
253C22—22no—
254C22—22no—
255C22—22no—
256C22—21no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22#1798850011yescharacteristic
261C22#1798873412yes—
262C22#1798876711yescharacteristic
263C22#1798877211yescharacteristic
264C22#1798877812yes—
265C22#1798888812yes—
266C22#1798894211yescharacteristic
267C22#1798895211yescharacteristic
268C4—22no—
269C4—22no—
270C4—82no—
271C4—5842no—
272C4—5842no—
273C4—5842no—
274C4—5842no—
275C2—21no—
276C2—22no—
277C2—21no—
278C2#2260893012yes—
279C2#2260894712yes—
280C2#2261107811yescharacteristic
281C2#2261109311yescharacteristic
282C2#2261109911yescharacteristic
subgroupG/H
centerC23#14556561
commutator, cosocleC23×C4×C73C23
FrattiniC23×C4C22×D73
FittingC73×#1280C2
socleC23×C73#120
prime radicalC24×C73C2×D4
hypercenter#1280D73
hypocenterC73#10346
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
147. C73#10346semidirect

Maximal subgroups

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

subgroupindex
#226159012
#226100182
#226081982
#226078112
C73×#12802
#1034673