Finite Group Databasebeta

← #32999189

Subgroups — #32999189

Order 18688.

344 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 67 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#22620706C211yesmaximal, characteristic
2#22612128C212yesmaximal, complemented
3#22607942C212yesmaximal, complemented
4#22607855C211yesmaximal, characteristic
5C73×#2075C211yesmaximal, characteristic
6C2×#14556570—21no—
7#17988923—22no—
8#17988828—21no—
9#17988828C2212yes—
10#17988745—22no—
11#17988414—22no—
12#17988390—22no—
13C22⋊#11924003C2212yes—
14C2×#107×C73C2211yescharacteristic
15C2×C22⋊C8×C73C2211yescharacteristic
16#380×C73—21no—
17#340×C73—21no—
18#340×C73C2211yescharacteristic
19C22×Dic146—21no—
20C2×Dic292—21no—
21C2×Dic292D412yes—
22#14556570—22no—
23#14556570—22no—
24#14556570—41no—
25#14556570—41no—
26C2×C4⋊Dic73—21no—
27C2×#11924007—41no—
28C2×C22⋊Dic73—41no—
29C2×#11924003—22no—
30#14556525—21no—
31#14556525D412yes—
32#14556516—22no—
33#14556516—22no—
34C23×C4×C73D411yescharacteristic
35C22×C8×C73D411yescharacteristic
36C22×C8×C73C2311yescharacteristic
37C2×C4⋊C4×C73—21no—
38C2×C4⋊C4×C73—21no—
39C2×C22⋊C4×C73—41no—
40#107×C73—22no—
41C22⋊C8×C73—22no—
42#95×C73—41no—
43C2×Dic146—22no—
44C2×Dic146—41no—
45C2×Dic146—81no—
46C2×Dic146—81no—
47C22×Dic73—41no—
48C22×Dic73—41no—
49Dic292—42no—
50Dic292—81no—
51C4⋊Dic73—22no—
52C4⋊Dic73—41no—
53#11924007—42no—
54#11924007—42no—
55C22⋊Dic73—42no—
56C22⋊Dic73—42no—
57#11924003—42no—
58C24×C73D811yescharacteristic
59C22×C4×C73—21no—
60C22×C4×C73—21no—
61C22×C4×C73—41no—
62C22×C4×C73—41no—
63C22×C4×C73—41no—
64C22×C4×C73—41no—
65C22×C4×C73D811yescharacteristic
66C22×C4×C73C2×D411yescharacteristic
67C2×C8×C73—21no—
68C2×C8×C73—41no—
69C2×C8×C73—41no—
70C2×C8×C73C2×D412yes—
71C4⋊C4×C73—41no—
72C4⋊C4×C73—41no—
73C4⋊C4×C73—41no—
74C4⋊C4×C73—41no—
75C22⋊C4×C73—82no—
76C23×C73—21no—
77C23×C73—21no—
78C23×C73—41no—
79C23×C73—41no—
80C23×C73SD3212yes—
81C23×C73C2×D811yescharacteristic
82C2×C4×C73—21no—
83C2×C4×C73—21no—
84C2×C4×C73—21no—
85C2×C4×C73—41no—
86C2×C4×C73—41no—
87C2×C4×C73—41no—
88C2×C4×C73—81no—
89C2×C4×C73—81no—
90C2×C4×C73—81no—
91C2×C4×C73—81no—
92C2×C4×C73—81no—
93C2×C4×C73—81no—
94C2×C4×C73—81no—
95C2×C4×C73#12011yescharacteristic
96C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
97C2×Dic73—42no—
98C2×Dic73—42no—
99C2×Dic73—82no—
100C2×Dic73—82no—
101Dic146—42no—
102Dic146—42no—
103Dic146—82no—
104C8×C73—22no—
105C8×C73—41no—
106C22×C73—21no—
107C22×C73—21no—
108C22×C73—22no—
109C22×C73—42no—
110C22×C73—41no—
111C22×C73—41no—
112C22×C73—81no—
113C22×C73#44711yescharacteristic
114C22×C73C2×SD3211yescharacteristic
115C22×C73#51011yescharacteristic
116C4×C73—21no—
117C4×C73—41no—
118C4×C73—161no—
119C4×C73—161no—
120C4×C73#45511yescharacteristic
121C4×C73#45811yescharacteristic
122Dic73—82no—
123Dic73—82no—
124#12279—731nomaximal, Sylow
125C2×C73—21no—
126C2×C73—21no—
127C2×C73—42no—
128C2×C73#160711yescharacteristic
129C2×C73#218511yescharacteristic
130C2×C73#219111yescharacteristic
131#3189—731no—
132#2235—732no—
133#2075D7311yescharacteristic
134#1348—732no—
135#1314—731no—
136C73#1227911yescharacteristic, complemented, Sylow
137C2×C22⋊Q8—1461no—
138#484—1462no—
139#467—732no—
140#467—1461no—
141#451—1462no—
142C2×#107C2×D7311yescharacteristic
143C2×C22⋊C8C2×D7311yescharacteristic
144#380—21no—
145#367—1462no—
146#358—1462no—
147C22⋊C16—732no—
148#340—21no—
149#340C2×D7311yescharacteristic
150C22×Q8—1461no—
151C23×C4C22⋊D7311yescharacteristic
152C2×Q16—732no—
153C2×Q16—1461no—
154C22×C8C22⋊D7311yescharacteristic
155C22×C8C22×D7311yescharacteristic
156C22⋊Q8—2921no—
157C22⋊Q8—2921no—
158C22⋊Q8—1462no—
159C22⋊Q8—1462no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—2921no—
163C2×C4⋊C4—1461no—
164C2×C22⋊C4—41no—
165C2×C22⋊C4—2921no—
166C2×C16—1462no—
167#107—22no—
168#107—732no—
169#107—1461no—
170#103—1462no—
171#103—1462no—
172C22⋊C8—22no—
173#95—41no—
174C24#1192401311yescharacteristic
175C2×Q8—2921no—
176C2×Q8—5841no—
177C2×Q8—5841no—
178C2×Q8—1462no—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—41no—
182C22×C4—41no—
183C22×C4—41no—
184C22×C4—41no—
185C22×C4—2921no—
186C22×C4—2921no—
187C22×C4#1192401311yescharacteristic
188C22×C4C2×C22⋊D7311yescharacteristic
189Q16—2922no—
190Q16—5841no—
191C2×C8—21no—
192C2×C8—41no—
193C2×C8—41no—
194C2×C8D4×D7312yes—
195C4⋊C4—41no—
196C4⋊C4—41no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—2922no—
200C4⋊C4—2921no—
201C4⋊C4—2922no—
202C4⋊C4—1462no—
203C22⋊C4—82no—
204C22⋊C4—2922no—
205C22⋊C4—2922no—
206C16—2922no—
207C23—21no—
208C23—21no—
209C23—41no—
210C23—41no—
211C23#1455653512yes—
212C23C2×#1192401311yescharacteristic
213Q8—2922no—
214Q8—2922no—
215Q8—5842no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—81no—
223C2×C4—81no—
224C2×C4—81no—
225C2×C4—81no—
226C2×C4—81no—
227C2×C4—81no—
228C2×C4—81no—
229C2×C4—2922no—
230C2×C4—2922no—
231C2×C4—5842no—
232C2×C4—5842no—
233C2×C4#1455655911yescharacteristic
234C2×C4#1455661611yescharacteristic
235C8—22no—
236C8—41no—
237C22—21no—
238C22—21no—
239C22—22no—
240C22—42no—
241C22—41no—
242C22—41no—
243C22—81no—
244C22#1798872011yescharacteristic
245C22C2×#1455653511yescharacteristic
246C22#1798902711yescharacteristic
247C4—21no—
248C4—41no—
249C4—161no—
250C4—161no—
251C4—5842no—
252C4—5842no—
253C4#1798876411yescharacteristic
254C4#1798877611yescharacteristic
255C2—21no—
256C2—21no—
257C2—42no—
258C2#2260891611yescharacteristic
259C2#2261184711yescharacteristic
260C2#2261188111yescharacteristic
subgroupG/H
centerC22#17988720
commutator, cosocleC22×C8×C73C23
FrattiniC22×C8C22×D73
FittingC73×#2075C2
socleC22×C73#447
prime radicalC24×C73D8
hypercenter#2075D73
hypocenterC73#12279
LCSG ▷ C22×C8×C73 ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C8 ◁ #2075

Complements

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

NH ≅ G/Ntype
2. #22612128C2semidirect
3. #22607942C2semidirect
136. C73#12279semidirect

Maximal subgroups

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

subgroupindex
#226207062
#226121282
#226079422
#226078552
C73×#20752
#1227973