Finite Group Databasebeta

← #32975326

Subgroups — #32975326

Order 18688.

414 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 87 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#22617924C211yesmaximal, characteristic
2#22611470C212yesmaximal
3#22607757C211yesmaximal, characteristic
4#22607756C212yesmaximal
5C73×#2095C211yesmaximal, characteristic
6C2×#14556524—22no—
7C2×#14556514—22no—
8#17988508—22no—
9#17988507—21no—
10#17988494—21no—
11#17988493C2212yes—
12#17988491—22no—
13#17988342C2212yes—
14C2×#107×C73—21no—
15C2×#103×C73—21no—
16#391×C73C2211yescharacteristic
17#384×C73C2211yescharacteristic
18#336×C73C2211yescharacteristic
19C22×Dic146—21no—
20C22×Dic146D412yes—
21C22×#10596831—22no—
22C2×C4⋊Dic73—21no—
23C2×C4⋊Dic73D412yes—
24C2×#11924007—22no—
25C2×C4×Dic73—21no—
26#14556524—44no—
27#14556514—44no—
28#14556498—21no—
29#14556498—22no—
30#14556498—22no—
31#14556498—22no—
32C22×Q8×C73D411yescharacteristic
33C22×C8×C73—21no—
34C2×C4⋊C4×C73—22no—
35C2×C4⋊C4×C73—21no—
36C2×C4⋊C4×C73D411yescharacteristic
37C2×C42×C73C2311yescharacteristic
38#107×C73—42no—
39#103×C73—42no—
40#95×C73—22no—
41C2×Dic146—22no—
42C2×Dic146—42no—
43C2×Dic146—42no—
44C2×Dic146—82no—
45C2×Dic146—81no—
46C2×Dic146Q1614yes—
47C22×Dic73—22no—
48C22×Dic73—22no—
49C2×#10596831—24no—
50C2×#10596831—42no—
51C2×#10596831—42no—
52C4⋊Dic73—42no—
53C4⋊Dic73—81no—
54#11924007—82no—
55C4×Dic73—81no—
56C2×Q8×C73—21no—
57C2×Q8×C73—41no—
58C2×Q8×C73—41no—
59C2×Q8×C73Q1612yes—
60C22×C4×C73—21no—
61C22×C4×C73—21no—
62C22×C4×C73—41no—
63C22×C4×C73C2×D412yes—
64C22×C4×C73C2×D411yescharacteristic
65C2×C8×C73—22no—
66C2×C8×C73—41no—
67C2×C8×C73—41no—
68C4⋊C4×C73—41no—
69C4⋊C4×C73—41no—
70C4⋊C4×C73—41no—
71C4⋊C4×C73—42no—
72C4⋊C4×C73—42no—
73C42×C73—41no—
74C23×C73#12011yescharacteristic
75Q8×C73—42no—
76Q8×C73—81no—
77C2×C4×C73—21no—
78C2×C4×C73—22no—
79C2×C4×C73—21no—
80C2×C4×C73—22no—
81C2×C4×C73—22no—
82C2×C4×C73—41no—
83C2×C4×C73—41no—
84C2×C4×C73—41no—
85C2×C4×C73—42no—
86C2×C4×C73—82no—
87C2×C4×C73—81no—
88C2×C4×C73C2×Q1612yes—
89C2×C4×C73C2×Q1611yescharacteristic
90C2×C4×C73#13711yescharacteristic
91C2×C4×C73#13712yes—
92C2×Dic73—24no—
93C2×Dic73—42no—
94C2×Dic73—42no—
95C2×Dic73—42no—
96C2×Dic73—42no—
97C2×Dic73—42no—
98Dic146—44no—
99Dic146—82no—
100Dic146—84no—
101C8×C73—42no—
102#10596831—44no—
103C22×C73#45112yes—
104C22×C73#45111yescharacteristic
105C22×C73#45312yes—
106C22×C73#45311yescharacteristic
107C22×C73#45811yescharacteristic
108C4×C73—22no—
109C4×C73—21no—
110C4×C73—22no—
111C4×C73—21no—
112C4×C73—42no—
113C4×C73—81no—
114C4×C73—161no—
115Dic73—44no—
116Dic73—82no—
117#7837—731nomaximal, Sylow
118C2×C73#161412yes—
119C2×C73#161411yescharacteristic
120C2×C73#163311yescharacteristic
121C2×C73#163312yes—
122C2×C73#165511yescharacteristic
123#2811—731no—
124#2095—732no—
125#2095D7311yescharacteristic
126#1272—731no—
127#1272—732no—
128C73#783711yescharacteristic, complemented, Sylow
129C2×#107—21no—
130C2×#107—1462no—
131C2×#103—21no—
132C2×#103—1462no—
133#395—1462no—
134#395—1461no—
135#391—732no—
136#391—1462no—
137#391—1461no—
138#391C2×D7311yescharacteristic
139#384C2×D7311yescharacteristic
140#336—732no—
141#336C2×D7311yescharacteristic
142C22×Q8—732no—
143C22×Q8—1461no—
144C22×Q8C22⋊D7311yescharacteristic
145C22×C8—21no—
146C22×C8—1462no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—732no—
150C2×C4⋊C4—1462no—
151C2×C4⋊C4—1461no—
152C2×C4⋊C4C22⋊D7311yescharacteristic
153C2×C42—1461no—
154C2×C42C22×D7311yescharacteristic
155#107—42no—
156#107—2924no—
157#103—42no—
158#103—2924no—
159#95—22no—
160#95—1462no—
161#95—1461no—
162#95—1462no—
163#95—1462no—
164C2×Q8—21no—
165C2×Q8—41no—
166C2×Q8—41no—
167C2×Q8—2922no—
168C2×Q8—2922no—
169C2×Q8—5842no—
170C2×Q8—5841no—
171C2×Q8—734no—
172C2×Q8—1462no—
173C2×Q8#1192401812yes—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—41no—
177C22×C4—1462no—
178C22×C4—1462no—
179C22×C4D4×D7312yes—
180C22×C4C2×C22⋊D7311yescharacteristic
181C2×C8—22no—
182C2×C8—41no—
183C2×C8—41no—
184C2×C8—2922no—
185C2×C8—2922no—
186C2×C8—1464no—
187C4⋊C4—41no—
188C4⋊C4—41no—
189C4⋊C4—42no—
190C4⋊C4—41no—
191C4⋊C4—42no—
192C4⋊C4—2922no—
193C4⋊C4—5842no—
194C4⋊C4—5841no—
195C42—41no—
196C42—5841no—
197C23#1455655911yescharacteristic
198Q8—42no—
199Q8—81no—
200Q8—2924no—
201Q8—5842no—
202Q8—5844no—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—42no—
211C2×C4—41no—
212C2×C4—82no—
213C2×C4—81no—
214C2×C4—2922no—
215C2×C4—2922no—
216C2×C4—2922no—
217C2×C4—2922no—
218C2×C4—2922no—
219C2×C4—1464no—
220C2×C4Q16×D7312yes—
221C2×C4C2×#1192401811yescharacteristic
222C2×C4#1455662111yescharacteristic
223C2×C4#1455662312yes—
224C8—42no—
225C8—2924no—
226C22#1798874112yes—
227C22#1798874211yescharacteristic
228C22#1798875312yes—
229C22#1798875411yescharacteristic
230C22#1798877611yescharacteristic
231C4—22no—
232C4—22no—
233C4—21no—
234C4—21no—
235C4—42no—
236C4—81no—
237C4—161no—
238C4—2924no—
239C4—5842no—
240C2#2260895412yes—
241C2#2260895511yescharacteristic
242C2#2260906911yescharacteristic
243C2#2260907012yes—
244C2#2260921911yescharacteristic
subgroupG/H
centerC23#14556559
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#2095C2
socle, prime radicalC23×C73#120
hypercenter#2095D73
hypocenterC73#7837
LCSG ▷ C2×C42×C73 ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2095

Complements

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

NH ≅ G/Ntype
128. C73#7837semidirect

Maximal subgroups

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

subgroupindex
#226179242
#226114702
#226077572
#226077562
C73×#20952
#783773