Finite Group Databasebeta

← #34014345

Subgroups — #34014345

Order 18688.

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

normal subgroups only

This group has 398 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
1C2×#17989498C212yesmaximal, complemented
2#22625068C212yesmaximal, complemented
3#22625066C212yesmaximal, complemented
4#22620391C211yesmaximal, characteristic
5C2×#14556652—22no—
6#17989498—22no—
7#17989498C2214yes—
8C2×#14556621—22no—
9C2×#14556591C2211yescharacteristic
10#17988982—22no—
11#17988966C411yescharacteristic
12#17988966C2211yescharacteristic
13#17988959C411yescharacteristic
14#17988959C2211yescharacteristic
15C4×#11924012C411yescharacteristic
16#532×C73C411yescharacteristic
17C2×#11924037—42no—
18#14556652—24no—
19#14556652—42no—
20C22×Dic146D412yes—
21#14556621—44no—
22#14556621—44no—
23C2×#11924018—22no—
24C2×#11924018—22no—
25C2×#11924016—22no—
26C2×#11924016—22no—
27C2×#11924012—21no—
28#14556591—41no—
29#14556591C2×C411yescharacteristic
30#14556591D412yes—
31#14556591C2311yescharacteristic
32C2×C4⋊Dic73—41no—
33#14556502—21no—
34C4×#10596831C2×C411yescharacteristic
35C4×#10596831C2×C411yescharacteristic
36C2×#41×C73—21no—
37C4⋊Q8×C73C2×C411yescharacteristic
38#127×C73C2×C411yescharacteristic
39#124×C73—21no—
40#121×C73—41no—
41C4×D4×C73—41no—
42C2×C42×C73C2×C411yescharacteristic
43#11924037—44no—
44#11924037—82no—
45C2×#10596833—82no—
46C2×Dic146—22no—
47C2×Dic146—42no—
48C2×Dic146—42no—
49C2×Dic146C22⋊C412yes—
50C2×Dic146C2×D412yes—
51C22×Dic73—22no—
52#11924018—44no—
53#11924018—44no—
54#11924016—44no—
55#11924016—44no—
56#11924012—24no—
57C2×#10596831—21no—
58C2×#10596831—21no—
59C4⋊Dic73—41no—
60C4⋊Dic73—42no—
61C4⋊Dic73—41no—
62#41×C73—42no—
63#41×C73—42no—
64C2×Q8×C73—21no—
65C2×D4×C73—21no—
66C2×D4×C73—41no—
67C2×D4×C73—41no—
68C22×C4×C73—21no—
69C22×C4×C73—41no—
70C22×C4×C73C22⋊C411yescharacteristic
71C4⋊C4×C73—41no—
72C22⋊C4×C73—42no—
73C42×C73—21no—
74C42×C73C22⋊C411yescharacteristic
75C42×C73C22×C411yescharacteristic
76C23×C73—41no—
77C23×C73#9911yescharacteristic
78Q8×C73—42no—
79D4×C73—42no—
80D4×C73—82no—
81D4×C73—82no—
82C2×C4×C73—22no—
83C2×C4×C73—21no—
84C2×C4×C73—21no—
85C2×C4×C73—42no—
86C2×C4×C73—41no—
87C2×C4×C73—81no—
88C2×C4×C73—81no—
89C2×C4×C73#9911yescharacteristic
90C2×C4×C73C2×C22⋊C411yescharacteristic
91C2×Dic73—22no—
92C2×Dic73—22no—
93C2×Dic73—42no—
94C2×Dic73—42no—
95Dic146—42no—
96Dic146—42no—
97Dic146—82no—
98#10596833—84no—
99#10596831—22no—
100#10596831—22no—
101C22×C73—41no—
102C22×C73—82no—
103C22×C73—81no—
104C22×C73#35312yes—
105C22×C73C2×#9911yescharacteristic
106C4×C73—22no—
107C4×C73—21no—
108C4×C73—21no—
109C4×C73—41no—
110C4×C73—81no—
111Dic73—42no—
112Dic73—42no—
113#13590—731nomaximal, Sylow
114C2×C73—21no—
115C2×C73—22no—
116C2×C73—161no—
117C2×C73C2×#35311yescharacteristic
118#3152—731no—
119C2×#356—732no—
120#1411—732no—
121#1410—732no—
122C73#1359011yescharacteristic, complemented, Sylow
123C2×#137—1462no—
124#532#6440811yescharacteristic
125C2×C4⋊Q8—731no—
126#497—1462no—
127#494—731no—
128#494—731no—
129#492—731no—
130#492—731no—
131C2×#101—1462no—
132C4×M16—731no—
133#356—734no—
134#356—1462no—
135C2×#41—21no—
136C22×Q8—732no—
137#137—2924no—
138#137—2924no—
139C2×Q16—1462no—
140C2×Q16—1462no—
141C2×SD16—1462no—
142C2×SD16—1462no—
143C2×M16—2922no—
144C2×M16—1461no—
145C4⋊Q8—2921no—
146C4⋊Q8—732no—
147C4⋊Q8—731no—
148C4⋊Q8—731no—
149C4⋊Q8C2×#6440811yescharacteristic
150#127C2×#6440811yescharacteristic
151#124—21no—
152#121—41no—
153C4×D4—41no—
154C2×C4⋊C4—2921no—
155C2×C42C2×#6440811yescharacteristic
156#101—2922no—
157#101—1464no—
158#97—1461no—
159C4×C8—731no—
160C4×C8—731no—
161#41—42no—
162#41—42no—
163C2×Q8—21no—
164C2×Q8—2922no—
165C2×Q8—2922no—
166C2×Q8—732no—
167C2×Q8—732no—
168C2×Q8—1462no—
169C2×D4—21no—
170C2×D4—41no—
171C2×D4—41no—
172C22×C4—21no—
173C22×C4—41no—
174C22×C4—1462no—
175C22×C4C22⋊#6440811yescharacteristic
176Q16—2924no—
177Q16—2924no—
178SD16—2924no—
179SD16—2924no—
180M16—2924no—
181M16—5842no—
182M16—1464no—
183C2×C8—5842no—
184C2×C8—1461no—
185C2×C8—1461no—
186C4⋊C4—41no—
187C4⋊C4—2921no—
188C4⋊C4—2921no—
189C4⋊C4—2922no—
190C22⋊C4—42no—
191C42—21no—
192C42C22⋊#6440811yescharacteristic
193C42C22×#6440811yescharacteristic
194C23—41no—
195C23#1455664911yescharacteristic
196Q8—42no—
197Q8—2922no—
198Q8—2922no—
199Q8—5842no—
200D4—42no—
201D4—82no—
202D4—82no—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—42no—
207C2×C4—41no—
208C2×C4—81no—
209C2×C4—81no—
210C2×C4—2922no—
211C2×C4—2922no—
212C2×C4—1462no—
213C2×C4—1462no—
214C2×C4#1455664911yescharacteristic
215C2×C4C2×C22⋊#6440811yescharacteristic
216C8—5844no—
217C8—1462no—
218C8—1462no—
219C22—41no—
220C22—82no—
221C22—81no—
222C22#1798949112yes—
223C22C2×#1455664911yescharacteristic
224C4—22no—
225C4—21no—
226C4—21no—
227C4—41no—
228C4—81no—
229C4—2922no—
230C4—2922no—
231C2—21no—
232C2—22no—
233C2—161no—
234C2C2×#1798949111yescharacteristic
subgroupG/H
centerC2C2×#17989491
commutatorC42×C73C22×C4
FrattiniC42C22×#64408
Fitting, prime radical#532×C73C4
socleC2×C73C2×#353
cosocle#14556591C23
hypercenter#532#64408
hypocenterC73#13590
LCSG ▷ C42×C73 ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. C2×#17989498C2semidirect
2. #22625068C2semidirect
3. #22625066C2semidirect
122. C73#13590semidirect

Maximal subgroups

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

subgroupindex
C2×#179894982
#226250682
#226250662
#226203912
#1359073