Finite Group Databasebeta

← #34009935

Subgroups — #34009935

Order 18688.

386 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 86 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#22626159C212yesmaximal, complemented
2#22624870C212yesmaximal, complemented
3#22624853C212yesmaximal, complemented
4#22618623C211yesmaximal, characteristic
5C2×#14556666—22no—
6#17989482—22no—
7C22⋊#11924031C2214yes—
8C22×C8×D73C2211yescharacteristic
9#17989094C411yescharacteristic
10#17988656—22no—
11C8×C22⋊D73—22no—
12#17988615C2211yescharacteristic
13#17988554C2211yescharacteristic
14#17988550C411yescharacteristic
15#17988542C411yescharacteristic
16C2×#131×C73C411yescharacteristic
17#14556666—44no—
18C2×#11924031—24no—
19C22×C4×D73C2×C411yescharacteristic
20C2×#11924012C2×C411yescharacteristic
21C22×#10596831C2311yescharacteristic
22C2×C8×D73—42no—
23C2×C8×D73D412yes—
24C2×C8×D73D412yes—
25#14556572—21no—
26#14556567C812yes—
27#14556562C812yes—
28#14556559—21no—
29C4×C22⋊D73—22no—
30#14556550C2×C411yescharacteristic
31#14556520—22no—
32C22⋊#10596831—22no—
33#14556503—22no—
34#14556501—21no—
35C8×Dic73—21no—
36C2×#41×C73C2×C411yescharacteristic
37#131×C73—42no—
38C2×M16×C73—21no—
39C2×M16×C73C2×C411yescharacteristic
40C22×C8×C73—21no—
41C22×C8×C73C2×C411yescharacteristic
42#11924031—44no—
43C23×D73M1611yescharacteristic
44C2×C22⋊D73—22no—
45C22×Dic73M1611yescharacteristic
46C2×C4×D73—41no—
47C2×C4×D73—41no—
48C2×C4×D73C22⋊C412yes—
49C2×C4×D73C2×C812yes—
50#11924012—41no—
51C2×#10596831—21no—
52C2×#10596831—41no—
53C2×#10596831C2×D412yes—
54C8×D73—24no—
55C8×D73—42no—
56C4⋊Dic73C2×C812yes—
57#11924007—22no—
58C22⋊Dic73—21no—
59C22⋊Dic73—22no—
60#11924005—22no—
61C4×Dic73—21no—
62#41×C73—41no—
63#41×C73—41no—
64C2×Q8×C73C2×C811yescharacteristic
65C2×D4×C73—21no—
66C2×D4×C73C2×C811yescharacteristic
67C22×C4×C73—21no—
68C22×C4×C73C22×C411yescharacteristic
69M16×C73—42no—
70M16×C73—41no—
71C2×C8×C73—22no—
72C2×C8×C73—21no—
73C2×C8×C73—42no—
74C2×C8×C73C22⋊C411yescharacteristic
75C2×C8×C73C22⋊C411yescharacteristic
76C23×C73—21no—
77C23×C73C2×M1611yescharacteristic
78C22×D73—41no—
79C22×D73—42no—
80C22×D73C22⋊C812yes—
81Q8×C73—41no—
82D4×C73—41no—
83D4×C73—42no—
84C2×C4×C73—21no—
85C2×C4×C73—21no—
86C2×C4×C73—21no—
87C2×C4×C73—41no—
88C2×C4×C73—41no—
89C2×C4×C73C2×C22⋊C411yescharacteristic
90C2×C4×C73C22×C811yescharacteristic
91C22⋊D73—44no—
92C2×Dic73—22no—
93C2×Dic73—41no—
94C2×Dic73C22⋊C812yes—
95C4×D73—22no—
96C4×D73—22no—
97C4×D73—42no—
98C8×C73—21no—
99C8×C73—41no—
100C8×C73#9912yes—
101#10596831—22no—
102#10596831—41no—
103C22×C73—22no—
104C22×C73—21no—
105C22×C73—42no—
106C22×C73—41no—
107C22×C73C2×C22⋊C811yescharacteristic
108C2×D73—22no—
109C2×D73—22no—
110C2×D73—22no—
111C2×D73—44no—
112C4×C73—21no—
113C4×C73—41no—
114C4×C73C2×#9911yescharacteristic
115C4×C73#41311yescharacteristic
116Dic73—22no—
117Dic73—42no—
118#11469—731nomaximal, Sylow
119C2×C73—41no—
120C2×C73—81no—
121C2×C73#145911yescharacteristic
122C2×C73#211712yes—
123D73—42no—
124#2929—731no—
125#2112—732no—
126#1323—732no—
127#1315—732no—
128C73#1146911yescharacteristic, complemented, Sylow
129C2×#131#6440811yescharacteristic
130C23×C8—731no—
131#525—731no—
132C2×M32—1462no—
133#435—1462no—
134C8×D4—1462no—
135#424—731no—
136#408—731no—
137#407—731no—
138#405—731no—
139C22⋊C16—734no—
140C22⋊C16—1462no—
141C2×#41C2×#6440811yescharacteristic
142C23×C4—731no—
143#131—42no—
144C2×M16—21no—
145C2×M16—731no—
146C2×M16C2×#6440811yescharacteristic
147C22×C8—21no—
148C22×C8—2922no—
149C22×C8—731no—
150C22×C8—732no—
151C22×C8—732no—
152C22×C8C2×#6440811yescharacteristic
153#123—1461no—
154C22⋊Q8—732no—
155#121—732no—
156#120—1461no—
157C4×D4—1462no—
158#117—731no—
159M32—2924no—
160C2×C16—1464no—
161C4⋊C8—1462no—
162C22⋊C8—1462no—
163C22⋊C8—1462no—
164#97—1461no—
165C4×C8—1461no—
166C24—731no—
167#41—41no—
168#41—41no—
169C2×Q8#1192403611yescharacteristic
170C2×D4—21no—
171C2×D4—1462no—
172C2×D4#1192403611yescharacteristic
173C22×C4—21no—
174C22×C4—2921no—
175C22×C4—2921no—
176C22×C4—731no—
177C22×C4—732no—
178C22×C4—732no—
179C22×C4C22×#6440811yescharacteristic
180M16—42no—
181M16—41no—
182M16—2921no—
183C2×C8—22no—
184C2×C8—21no—
185C2×C8—42no—
186C2×C8—2922no—
187C2×C8—2921no—
188C2×C8—732no—
189C2×C8—1461no—
190C2×C8—1464no—
191C2×C8C22⋊#6440811yescharacteristic
192C2×C8C22⋊#6440811yescharacteristic
193C4⋊C4—732no—
194C4⋊C4—1462no—
195C22⋊C4—1462no—
196C22⋊C4—1462no—
197C22⋊C4—1461no—
198C42—1461no—
199C16—2924no—
200C23—21no—
201C23—2921no—
202C23—2922no—
203C23—732no—
204C23D73⋊M1611yescharacteristic
205Q8—41no—
206D4—41no—
207D4—42no—
208D4—2924no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—2922no—
215C2×C4—2921no—
216C2×C4—732no—
217C2×C4—1462no—
218C2×C4—1462no—
219C2×C4—1462no—
220C2×C4C2×C22⋊#6440811yescharacteristic
221C2×C4C2×#1192403611yescharacteristic
222C8—21no—
223C8—41no—
224C8—2921no—
225C8—1462no—
226C8#1455664912yes—
227C22—22no—
228C22—21no—
229C22—42no—
230C22—41no—
231C22—2924no—
232C22—1462no—
233C22—1462no—
234C22—1462no—
235C22#1798955511yescharacteristic
236C4—21no—
237C4—41no—
238C4—2922no—
239C4—1462no—
240C4C2×#1455664911yescharacteristic
241C4#1798957311yescharacteristic
242C2—41no—
243C2—81no—
244C2—2922no—
245C2#2262516611yescharacteristic
246C2#2262617412yes—
subgroupG/H
centerC2×C4C2×C22⋊#64408
commutatorC2×C4×C73C22×C8
FrattiniC22×C4C22×#64408
FittingC2×#131×C73C4
socleC22×C73C2×C22⋊C8
prime radical#17989094C4
cosocleC22×#10596831C23
hypercenterC2×#131#64408
hypocenterC73#11469
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×#131

Complements

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

NH ≅ G/Ntype
1. #22626159C2semidirect
2. #22624870C2semidirect
3. #22624853C2semidirect
128. C73#11469semidirect

Maximal subgroups

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

subgroupindex
#226261592
#226248702
#226248532
#226186232
#1146973