Finite Group Databasebeta

← #32973781

Subgroups — #32973781

Order 18688.

266 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 59 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#22611616C211yesmaximal, characteristic
2#22610764C211yesmaximal, characteristic
3C73×#2132C211yesmaximal, characteristic
4#17988611C411yescharacteristic
5C2×#14556518—21no—
6C2×#14556518—21no—
7#17988571—21no—
8#17988433C411yescharacteristic
9#17988386—21no—
10#17988384C412yescomplemented
11#532×C73C2211yescharacteristic
12#413×C73—21no—
13#356×C73—21no—
14#355×C73C412yescomplemented
15C2×#11924012—21no—
16C2×#11924012—41no—
17C2×C4×Dic73—21no—
18C4⋊#10596831—41no—
19#14556518—42no—
20#14556518—42no—
21#14556510—22no—
22#14556508—41no—
23#14556498—41no—
24C2×#41×C73D411yescharacteristic
25C2×#41×C73D411yescharacteristic
26C2×M16×C73—41no—
27C4⋊Q8×C73D411yescharacteristic
28#127×C73Q811yescharacteristic
29#124×C73C2×C411yescharacteristic
30#124×C73C2×C411yescharacteristic
31#121×C73—41no—
32C4×D4×C73—41no—
33C2×C42×C73C2×C411yescharacteristic
34#101×C73—22no—
35#100×C73—41no—
36C22×Dic73—41no—
37#11924012—42no—
38#11924012—41no—
39#11924012—41no—
40#11924012—81no—
41C2×#10596831—41no—
42C2×#10596831—81no—
43C4×Dic73—22no—
44C4×Dic73—41no—
45#41×C73—41no—
46#41×C73—41no—
47#41×C73—41no—
48#41×C73—41no—
49C2×Q8×C73C22⋊C411yescharacteristic
50C2×Q8×C73C22⋊C411yescharacteristic
51C2×D4×C73—21no—
52C2×D4×C73—21no—
53C2×D4×C73—41no—
54C2×D4×C73C4⋊C411yescharacteristic
55C2×D4×C73C4⋊C411yescharacteristic
56C22×C4×C73—21no—
57C22×C4×C73—21no—
58C22×C4×C73—21no—
59C22×C4×C73C22⋊C411yescharacteristic
60M16×C73—42no—
61M16×C73—81no—
62C2×C8×C73—81no—
63C4⋊C4×C73—41no—
64C22⋊C4×C73—41no—
65C22⋊C4×C73—41no—
66C42×C73—21no—
67C42×C73C4211yescharacteristic
68C42×C73C4⋊C411yescharacteristic
69C23×C73—21no—
70C23×C73—21no—
71C23×C73#9911yescharacteristic
72Q8×C73—41no—
73Q8×C73—41no—
74D4×C73—41no—
75D4×C73—41no—
76D4×C73—81no—
77D4×C73—81no—
78D4×C73—82no—
79C2×C4×C73—21no—
80C2×C4×C73—21no—
81C2×C4×C73—21no—
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—41no—
89C2×C4×C73—81no—
90C2×C4×C73#9511yescharacteristic
91C2×C4×C73#9911yescharacteristic
92C2×Dic73—42no—
93C2×Dic73—82no—
94C8×C73—82no—
95#10596831—82no—
96#10596831—81no—
97C22×C73—21no—
98C22×C73—41no—
99C22×C73—41no—
100C22×C73—41no—
101C22×C73—81no—
102C22×C73—81no—
103C22×C73#34211yescharacteristic
104C4×C73—21no—
105C4×C73—41no—
106C4×C73—41no—
107C4×C73—41no—
108C4×C73—41no—
109C4×C73#35311yescharacteristic
110C4×C73#35411yescharacteristic
111Dic73—82no—
112#7507—731nomaximal, Sylow
113C2×C73—21no—
114C2×C73—41no—
115C2×C73—81no—
116C2×C73—81no—
117C2×C73#139311yescharacteristic
118#2132—731no—
119#2132D7311yescharacteristic
120#1963—731no—
121C73#750711yescharacteristic, complemented, Sylow
122#532C2×D7311yescharacteristic
123#423—731no—
124C2×#104—1461no—
125C2×#104—1461no—
126#413—21no—
127#413—1461no—
128#376—731no—
129#356—21no—
130#356—1461no—
131#355—732no—
132#355Dic7312yescomplemented
133C2×#41D29211yescharacteristic
134C2×#41C22⋊D7311yescharacteristic
135C2×M16—41no—
136C2×M16—2921no—
137C2×M16—1461no—
138C4⋊Q8C22⋊D7311yescharacteristic
139#127Dic14611yescharacteristic
140#124C4×D7311yescharacteristic
141#124C2×Dic7311yescharacteristic
142#121—41no—
143C4×D4—41no—
144C2×C42—1461no—
145C2×C42C4×D7311yescharacteristic
146C4⋊C8—2921no—
147#104—2922no—
148#104—2922no—
149#101—22no—
150#101—1462no—
151#100—41no—
152#100—2921no—
153#95—2921no—
154#41—41no—
155#41—41no—
156#41—41no—
157#41—41no—
158C2×Q8#1192400511yescharacteristic
159C2×Q8C22⋊Dic7311yescharacteristic
160C2×D4—21no—
161C2×D4—21no—
162C2×D4—41no—
163C2×D4#1192400711yescharacteristic
164C2×D4C4⋊Dic7311yescharacteristic
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—2921no—
169C22×C4#1192400511yescharacteristic
170M16—42no—
171M16—81no—
172M16—2922no—
173M16—2921no—
174M16—2921no—
175M16—5841no—
176C2×C8—81no—
177C2×C8—2921no—
178C2×C8—5841no—
179C4⋊C4—41no—
180C22⋊C4—41no—
181C22⋊C4—41no—
182C42—21no—
183C42—2921no—
184C42—1462no—
185C42C4×Dic7311yescharacteristic
186C42#1192400711yescharacteristic
187C23—21no—
188C23—21no—
189C23#1455650511yescharacteristic
190Q8—41no—
191Q8—41no—
192D4—41no—
193D4—41no—
194D4—81no—
195D4—81no—
196D4—82no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—81no—
208C2×C4—2922no—
209C2×C4—5842no—
210C2×C4#1455649811yescharacteristic
211C2×C4#1455650511yescharacteristic
212C8—82no—
213C8—5842no—
214C8—5841no—
215C22—21no—
216C22—41no—
217C22—41no—
218C22—41no—
219C22—81no—
220C22—81no—
221C22#1798835311yescharacteristic
222C4—21no—
223C4—41no—
224C4—41no—
225C4—41no—
226C4—41no—
227C4—5842no—
228C4#1798837911yescharacteristic
229C4#1798838111yescharacteristic
230C2—21no—
231C2—41no—
232C2—81no—
233C2—81no—
234C2#2260805511yescharacteristic
subgroupG/H
centerC4#17988379
commutatorC42×C73C42
Frattini#532C2×D73
FittingC73×#2132C2
socleC2×C73#1393
prime radical, cosocle#532×C73C22
hypercenter#2132D73
hypocenterC73#7507
LCSG ▷ C42×C73 ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ #532 ◁ #2132

Complements

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

NH ≅ G/Ntype
10. #17988384C4semidirect
14. #355×C73C4semidirect
121. C73#7507semidirect
132. #355Dic73semidirect

Maximal subgroups

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

subgroupindex
#226116162
#226107642
C73×#21322
#750773