Finite Group Databasebeta

← #34010181

Subgroups — #34010181

Order 18688.

348 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 70 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#22626305C212yesmaximal, complemented
2#22624865C212yesmaximal, complemented
3#22624864C212yesmaximal, complemented
4#22618623C211yesmaximal, characteristic
5#17989509—22no—
6#17989483C2214yes—
7#17989480—22no—
8C22×C8×D73C411yescharacteristic
9#17989094C411yescharacteristic
10#17988656—22no—
11C8×C22⋊D73—22no—
12#17988615C411yescharacteristic
13#17988554C2211yescharacteristic
14#17988550C2211yescharacteristic
15#17988542C2211yescharacteristic
16C2×#131×C73C411yescharacteristic
17#14556665—24no—
18C22×C4×D73C2×C411yescharacteristic
19C2×#11924012C2311yescharacteristic
20C22×#10596831C2×C411yescharacteristic
21C2×C8×D73—21no—
22C2×C8×D73—21no—
23C2×C8×D73—42no—
24#14556572—21no—
25#14556567—21no—
26#14556562—21no—
27#14556559—21no—
28C4×C22⋊D73—22no—
29#14556550C2×C411yescharacteristic
30#14556520—22no—
31C22⋊#10596831—22no—
32#14556503—22no—
33#14556501D412yes—
34C8×Dic73D412yes—
35C2×#41×C73C2×C411yescharacteristic
36#131×C73—42no—
37C2×M16×C73—21no—
38C2×M16×C73C2×C411yescharacteristic
39C22×C8×C73—21no—
40C22×C8×C73C2×C411yescharacteristic
41#11924031—44no—
42C23×D73M1611yescharacteristic
43C2×C22⋊D73—22no—
44C22×Dic73M1611yescharacteristic
45C2×C4×D73—21no—
46C2×C4×D73—21no—
47C2×C4×D73—41no—
48C2×C4×D73—41no—
49#11924012—41no—
50C2×#10596831—21no—
51C2×#10596831—41no—
52C2×#10596831C2×D412yes—
53C8×D73—42no—
54C8×D73—42no—
55C4⋊Dic73—21no—
56#11924007—22no—
57C22⋊Dic73—22no—
58C22⋊Dic73—21no—
59#11924005—22no—
60C4×Dic73C22⋊C412yes—
61#41×C73—41no—
62#41×C73—41no—
63C2×Q8×C73M1611yescharacteristic
64C2×D4×C73—21no—
65C2×D4×C73M1611yescharacteristic
66C22×C4×C73—21no—
67C22×C4×C73C22×C411yescharacteristic
68M16×C73—42no—
69M16×C73—41no—
70C2×C8×C73—22no—
71C2×C8×C73—21no—
72C2×C8×C73—42no—
73C2×C8×C73C22⋊C411yescharacteristic
74C2×C8×C73C22⋊C411yescharacteristic
75C23×C73—21no—
76C23×C73C2×M1611yescharacteristic
77C22×D73—21no—
78C22×D73—42no—
79C22×D73—41no—
80Q8×C73—41no—
81D4×C73—41no—
82D4×C73—42no—
83C2×C4×C73—21no—
84C2×C4×C73—21no—
85C2×C4×C73—21no—
86C2×C4×C73—41no—
87C2×C4×C73—41no—
88C2×C4×C73C2×C22⋊C411yescharacteristic
89C2×C4×C73C2×M1611yescharacteristic
90C22⋊D73—44no—
91C2×Dic73—22no—
92C2×Dic73—21no—
93C2×Dic73—41no—
94C4×D73—42no—
95C4×D73—41no—
96C4×D73—41no—
97C8×C73—21no—
98C8×C73—41no—
99C8×C73#10012yes—
100#10596831—22no—
101#10596831—41no—
102C22×C73—21no—
103C22×C73—41no—
104C22×C73—42no—
105C22×C73—41no—
106C22×C73#40711yescharacteristic
107C2×D73—22no—
108C2×D73—41no—
109C2×D73—42no—
110C2×D73—41no—
111C2×D73—42no—
112C4×C73—21no—
113C4×C73—41no—
114C4×C73#41011yescharacteristic
115C4×C73C2×#10011yescharacteristic
116Dic73—42no—
117Dic73—41no—
118#11537—731nomaximal, Sylow
119C2×C73—21no—
120C2×C73—41no—
121C2×C73—81no—
122C2×C73#146611yescharacteristic
123D73—42no—
124#2929—731no—
125#2166—732no—
126#1321—732no—
127#1320—732no—
128C73#1153711yescharacteristic, complemented, Sylow
129C2×#131#6440811yescharacteristic
130C23×C8—731no—
131#525—731no—
132#435—1462no—
133C8×D4—1462no—
134#424—731no—
135#408—731no—
136#407—731no—
137#405—731no—
138#364—1462no—
139#349—734no—
140#347—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—1461no—
151C22×C8—1461no—
152C22×C8C2×#6440811yescharacteristic
153#123—1461no—
154C22⋊Q8—1461no—
155#121—1461no—
156#120—1461no—
157C4×D4—1462no—
158#117—731no—
159M32—1464no—
160C4⋊C8—1462no—
161C22⋊C8—1462no—
162C22⋊C8—1462no—
163#97—732no—
164C4×C8—732no—
165C24—731no—
166#41—41no—
167#41—41no—
168C2×Q8#1192403811yescharacteristic
169C2×D4—21no—
170C2×D4—1462no—
171C2×D4#1192403811yescharacteristic
172C22×C4—21no—
173C22×C4—2921no—
174C22×C4—2921no—
175C22×C4—731no—
176C22×C4—1461no—
177C22×C4—1461no—
178C22×C4C22×#6440811yescharacteristic
179M16—42no—
180M16—41no—
181M16—2921no—
182C2×C8—22no—
183C2×C8—21no—
184C2×C8—42no—
185C2×C8—2922no—
186C2×C8—2922no—
187C2×C8—2921no—
188C2×C8—732no—
189C2×C8—1461no—
190C2×C8C22⋊#6440811yescharacteristic
191C2×C8C22⋊#6440811yescharacteristic
192C4⋊C4—1462no—
193C4⋊C4—1461no—
194C22⋊C4—1462no—
195C22⋊C4—1462no—
196C22⋊C4—1461no—
197C42—732no—
198C16—2924no—
199C23—21no—
200C23—2921no—
201C23—2922no—
202C23—1461no—
203C23D73⋊M1611yescharacteristic
204Q8—41no—
205D4—41no—
206D4—42no—
207D4—2924no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—2922no—
214C2×C4—2921no—
215C2×C4—2921no—
216C2×C4—2921no—
217C2×C4—1462no—
218C2×C4—1461no—
219C2×C4C2×C22⋊#6440811yescharacteristic
220C2×C4C2×#1192403811yescharacteristic
221C8—21no—
222C8—41no—
223C8—2921no—
224C8—1462no—
225C8#1455665112yes—
226C22—21no—
227C22—41no—
228C22—42no—
229C22—41no—
230C22—2921no—
231C22—2922no—
232C22—2922no—
233C22—2921no—
234C22—1462no—
235C22#1798955811yescharacteristic
236C4—21no—
237C4—41no—
238C4—2922no—
239C4—2921no—
240C4#1798956611yescharacteristic
241C4C2×#1455665111yescharacteristic
242C2—21no—
243C2—41no—
244C2—81no—
245C2—2922no—
246C2#2262519011yescharacteristic
subgroupG/H
centerC4#17989566
commutatorC22×C4×C73C22×C4
FrattiniC22×C4C22×#64408
FittingC2×#131×C73C4
socleC2×C73#1466
prime radical#17989094C4
cosocleC2×#11924012C23
hypercenterC2×#131#64408
hypocenterC73#11537
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C4 ◁ C2×C8 ◁ C22×C8 ◁ C2×#131

Complements

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

NH ≅ G/Ntype
1. #22626305C2semidirect
2. #22624865C2semidirect
3. #22624864C2semidirect
128. C73#11537semidirect

Maximal subgroups

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

subgroupindex
#226263052
#226248652
#226248642
#226186232
#1153773