Finite Group Databasebeta

← #34014359

Subgroups — #34014359

Order 18688.

326 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 60 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#22626204C212yesmaximal
2#22625071C212yesmaximal, complemented
3#22625070C212yesmaximal, complemented
4#22620279C211yesmaximal, characteristic
5#17989566—22no—
6#17989494—22no—
7#17989492C2214yes—
8#17989137C2211yescharacteristic
9#17988957C411yescharacteristic, complemented
10#17988957C411yescharacteristic, complemented
11#17988953C2211yescharacteristic
12#17988953C2211yescharacteristic
13#17988949—22no—
14#17988581—22no—
15C2×#14556502C411yescharacteristic, complemented
16#533×C73C411yescharacteristic, complemented
17#14556670—42no—
18#14556650—24no—
19#14556649—42no—
20C2×#11924028D412yes—
21C22×#10596831—21no—
22#14556591C2×C411yescharacteristic
23#14556588C2311yescharacteristic
24#14556579D412yes—
25#14556565—41no—
26C4×D292—41no—
27#14556514—22no—
28#14556514—22no—
29#14556511—22no—
30#14556511—22no—
31#14556502—21no—
32#14556502C2×C411yescharacteristic
33#14556502C2×C411yescharacteristic
34C4⋊Q8×C73—21no—
35#125×C73C2×C411yescharacteristic
36#125×C73C2×C411yescharacteristic
37C22⋊Q8×C73—41no—
38C4×Q8×C73—41no—
39#117×C73—21no—
40C2×C42×C73C2×C411yescharacteristic
41C4⋊#64408—82no—
42C22⋊#64408—44no—
43C4×#64408—82no—
44#11924028—42no—
45#11924028—42no—
46C2×Dic146C22⋊C412yes—
47C2×D292—41no—
48C2×D292C2×D412yes—
49C2×C22⋊D73—22no—
50C2×C4×D73—22no—
51C2×#10596831—21no—
52C2×#10596831—21no—
53C2×#10596831—41no—
54C2×#10596831—41no—
55C4⋊Dic73—41no—
56#11924005—42no—
57C2×Q8×C73—41no—
58C22×C4×C73—21no—
59C22×C4×C73C22⋊C411yescharacteristic
60C4⋊C4×C73—21no—
61C4⋊C4×C73—21no—
62C4⋊C4×C73—41no—
63C4⋊C4×C73—41no—
64C4⋊C4×C73—41no—
65C22⋊C4×C73—41no—
66C42×C73—21no—
67C42×C73—41no—
68C42×C73C22⋊C411yescharacteristic
69C42×C73C22×C411yescharacteristic
70C23×C73#9911yescharacteristic
71C22×D73—22no—
72C2×#64408—84no—
73Q8×C73—82no—
74C2×C4×C73—21no—
75C2×C4×C73—21no—
76C2×C4×C73—21no—
77C2×C4×C73—21no—
78C2×C4×C73—41no—
79C2×C4×C73—41no—
80C2×C4×C73—81no—
81C2×C4×C73#9911yescharacteristic
82C2×C4×C73C2×C22⋊C411yescharacteristic
83C22⋊D73—82no—
84C2×Dic73—22no—
85D292—42no—
86D292—82no—
87C4×D73—42no—
88C4×D73—42no—
89Dic146—42no—
90#10596831—41no—
91#10596831—41no—
92C22×C73—21no—
93C22×C73—41no—
94C22×C73C2×#9911yescharacteristic
95C2×D73—42no—
96C2×D73—82no—
97#64408—164no—
98C4×C73—21no—
99C4×C73—41no—
100C4×C73—41no—
101C4×C73—81no—
102C4×C73—81no—
103C4×C73#35411yescharacteristic
104C4×C73#35411yescharacteristic
105Dic73—42no—
106#13594—731nomaximal, Sylow
107C2×C73—21no—
108C2×C73—41no—
109C2×C73C2×#35411yescharacteristic
110D73—82no—
111#3135—731no—
112#2126—732no—
113#1412—732no—
114#1412—732no—
115C73#1359411yescharacteristic, complemented, Sylow
116#533#6440811yescharacteristic, complemented
117#532—731no—
118#491—731no—
119#491—731no—
120#490—731no—
121#490—731no—
122#489—1462no—
123#416—1462no—
124#410—1462no—
125C2×#97—731no—
126#354—1462no—
127#353—734no—
128C2×#41—732no—
129C22×C8—1461no—
130C4⋊Q8—21no—
131C4⋊Q8—731no—
132#127—731no—
133#125C2×#6440811yescharacteristic
134#125C2×#6440811yescharacteristic
135#124—732no—
136C22⋊Q8—41no—
137#121—2921no—
138C4×Q8—41no—
139C4×D4—2921no—
140#117—21no—
141#117—2922no—
142C2×C42C2×#6440811yescharacteristic
143#103—1462no—
144#103—1462no—
145#102—1462no—
146#102—1462no—
147#99—2922no—
148#99—1464no—
149#97—731no—
150#97—731no—
151#97—1461no—
152#41—2922no—
153#41—2922no—
154C2×Q8—41no—
155C2×Q8—732no—
156C2×D4—2921no—
157C2×D4—732no—
158C2×D4—1462no—
159C22×C4—21no—
160C22×C4—1462no—
161C22×C4C22⋊#6440811yescharacteristic
162C2×C8—2921no—
163C2×C8—2921no—
164C2×C8—1461no—
165C2×C8—1461no—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—41no—
169C4⋊C4—41no—
170C4⋊C4—41no—
171C4⋊C4—2921no—
172C4⋊C4—5842no—
173C22⋊C4—41no—
174C22⋊C4—2922no—
175C22⋊C4—2924no—
176C42—21no—
177C42—41no—
178C42—5842no—
179C42C22⋊#6440811yescharacteristic
180C42C22×#6440811yescharacteristic
181C23—1462no—
182C23#1455664911yescharacteristic
183Q8—82no—
184Q8—2922no—
185D4—2922no—
186D4—5842no—
187D4—5842no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—81no—
195C2×C4—2922no—
196C2×C4—2922no—
197C2×C4—5844no—
198C2×C4—1462no—
199C2×C4#1455664911yescharacteristic
200C2×C4C2×C22⋊#6440811yescharacteristic
201C8—2921no—
202C8—2921no—
203C22—21no—
204C22—41no—
205C22—2922no—
206C22—5842no—
207C22C2×#1455664911yescharacteristic
208C4—21no—
209C4—41no—
210C4—41no—
211C4—81no—
212C4—81no—
213C4—2922no—
214C4—11684no—
215C4#1798949311yescharacteristic
216C4#1798949311yescharacteristic
217C2—21no—
218C2—41no—
219C2—5842no—
220C2C2×#1798949311yescharacteristic
subgroupG/H
centerC4#17989493
commutatorC42×C73C22×C4
FrattiniC42C22×#64408
Fitting#533×C73C4
socleC2×C73C2×#354
prime radical#17989137C22
cosocle#14556588C23
hypercenter#533#64408
hypocenterC73#13594
LCSG ▷ C42×C73 ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #22625071C2semidirect
3. #22625070C2semidirect
9. #17988957C4semidirect
10. #17988957C4semidirect
15. C2×#14556502C4semidirect
16. #533×C73C4semidirect
115. C73#13594semidirect
116. #533#64408semidirect

Maximal subgroups

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

subgroupindex
#226262042
#226250712
#226250702
#226202792
#1359473