Finite Group Databasebeta

← #34000380

Subgroups — #34000380

Order 18688.

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

normal subgroups only

This group has 248 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#22626163C211yesmaximal, characteristic
2#22625687C211yesmaximal, characteristic
3#22611550C211yesmaximal, characteristic
4C2×#14556665C411yescharacteristic, complemented
5C22×#11924031C411yescharacteristic, complemented
6#17989573C411yescharacteristic
7#17989566C411yescharacteristic
8#17989550—21no—
9#17989482—21no—
10#17989482—21no—
11#17989469—21no—
12C2×#14556599C2211yescharacteristic
13M32×D73—21no—
14#17988369C411yescharacteristic, complemented
15#17988368—21no—
16#349×C73C411yescharacteristic, complemented
17D73⋊M16—21no—
18#14556670—21no—
19#14556665—41no—
20C2×#11924031—21no—
21C2×#11924031—21no—
22C2×#11924031—41no—
23#14556652C812yes—
24#14556651—21no—
25#14556650C812yes—
26#14556649—21no—
27#14556645—41no—
28C8×#64408—41no—
29C2×#11924028C2×C411yescharacteristic
30#14556599—41no—
31#14556599—41no—
32C2×#11924011D411yescharacteristic
33C2×#11924011Q811yescharacteristic
34C22×#10596831C2×C411yescharacteristic
35C2×C8×D73D411yescharacteristic
36C2×C8×D73D411yescharacteristic
37#14556531—21no—
38#14556530—41no—
39C16×D73—41no—
40C2×M16×C73C2×C411yescharacteristic
41M32×C73—21no—
42#11924038—41no—
43#11924037—22no—
44#11924036—41no—
45C4⋊#64408—41no—
46C22⋊#64408—22no—
47C4×#64408—41no—
48#11924031—41no—
49#11924031—41no—
50#11924028—41no—
51#11924028—41no—
52C2×Dic146C2×C811yescharacteristic
53C2×D292C2×C811yescharacteristic
54C2×C22⋊D73M1611yescharacteristic
55C2×C22⋊D73M1611yescharacteristic
56C2×C4×D73C22⋊C411yescharacteristic
57C2×C4×D73C4⋊C411yescharacteristic
58#11924011—41no—
59#11924011—41no—
60C2×#10596831—21no—
61C2×#10596831—21no—
62C2×#10596831C22⋊C411yescharacteristic
63C2×#10596831C4⋊C411yescharacteristic
64C8×D73—21no—
65C8×D73—21no—
66C8×D73—21no—
67C8×D73—21no—
68#11924003—41no—
69C22×C4×C73C4211yescharacteristic
70M16×C73—41no—
71C2×C8×C73C22⋊C411yescharacteristic
72C2×C8×C73C4⋊C411yescharacteristic
73C16×C73—41no—
74C23×C73#9711yescharacteristic
75C22×D73C22⋊C811yescharacteristic
76C22×D73C4⋊C811yescharacteristic
77C2×#64408—42no—
78C2×C4×C73—21no—
79C2×C4×C73—21no—
80C2×C4×C73#9511yescharacteristic
81C2×C4×C73C4×C811yescharacteristic
82C22⋊D73—41no—
83C22⋊D73—41no—
84C2×Dic73C22⋊C811yescharacteristic
85C2×Dic73C4⋊C811yescharacteristic
86D292—41no—
87C4×D73—21no—
88C4×D73—21no—
89C4×D73—21no—
90C4×D73—21no—
91Dic146—41no—
92#10596833—42no—
93C8×C73—21no—
94C8×C73—21no—
95#10596831—21no—
96#10596831#9911yescharacteristic
97#10596831#9911yescharacteristic
98C22×C73—21no—
99C22×C73—41no—
100C22×C73#33611yescharacteristic
101C2×D73—21no—
102C2×D73—21no—
103C2×D73—41no—
104C2×D73—41no—
105#64408—82no—
106C4×C73—21no—
107C4×C73#34211yescharacteristic
108C4×C73#34411yescharacteristic
109Dic73—21no—
110Dic73—21no—
111#7208—731nomaximal, Sylow
112C2×C73—21no—
113C2×C73—41no—
114C2×C73#128211yescharacteristic
115D73—41no—
116D73—41no—
117#2115—731no—
118#2113—731no—
119#1757—731no—
120C73#720811yescharacteristic, complemented, Sylow
121C2×#131—731no—
122C2×M32—731no—
123C2×M32—1461no—
124C22×C16—731no—
125#413—731no—
126#410—731no—
127#405—1461no—
128#349—731no—
129#349—1461no—
130#349#6440811yescharacteristic, complemented
131C22⋊C16—1461no—
132C22⋊C16—1461no—
133#344—1461no—
134C2×#41—731no—
135#131—2921no—
136#131—2921no—
137C2×M16—731no—
138C2×M16—731no—
139C2×M16—1461no—
140C2×M16C2×#6440811yescharacteristic
141C22×C8—731no—
142C22×C8—731no—
143C22×C8—731no—
144#117—1461no—
145M32—21no—
146M32—2921no—
147M32—2921no—
148M32—1461no—
149C2×C16—2921no—
150C2×C16—2921no—
151C2×C16—1461no—
152C2×C16—1461no—
153#101—732no—
154#100—1461no—
155#99—732no—
156#99—1461no—
157#97—2921no—
158C4×C8—2921no—
159#41—2921no—
160#41—2921no—
161C2×Q8—731no—
162C2×D4—731no—
163C2×D4—731no—
164C2×D4—731no—
165C22×C4—731no—
166C22×C4—731no—
167C22×C4C4×#6440811yescharacteristic
168M16—41no—
169M16—2921no—
170M16—2921no—
171M16—2921no—
172M16—1462no—
173C2×C8—2921no—
174C2×C8—731no—
175C2×C8—731no—
176C2×C8—1461no—
177C2×C8—1461no—
178C2×C8—1461no—
179C2×C8—1461no—
180C2×C8—1461no—
181C2×C8—1461no—
182C2×C8C22⋊#6440811yescharacteristic
183C2×C8C4⋊#6440811yescharacteristic
184C4⋊C4—2921no—
185C22⋊C4—1462no—
186C42—2921no—
187C16—41no—
188C16—2921no—
189C16—2921no—
190C16—2921no—
191C23—731no—
192C23—731no—
193C23#1455664511yescharacteristic
194Q8—2921no—
195D4—2921no—
196D4—2921no—
197D4—2921no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—2922no—
201C2×C4—731no—
202C2×C4—731no—
203C2×C4—1461no—
204C2×C4—1461no—
205C2×C4—1461no—
206C2×C4—1461no—
207C2×C4(C2×#64408)⋊C411yescharacteristic
208C2×C4C8×#6440811yescharacteristic
209C8—21no—
210C8—21no—
211C8—2922no—
212C8—731no—
213C8—731no—
214C8—1461no—
215C22—21no—
216C22—41no—
217C22—2921no—
218C22—2921no—
219C22—1461no—
220C22—1461no—
221C22#1798945211yescharacteristic
222C4—21no—
223C4—5842no—
224C4—1461no—
225C4—1461no—
226C4#1798946411yescharacteristic
227C4#1798947011yescharacteristic
228C2—21no—
229C2—41no—
230C2—2921no—
231C2—2921no—
232C2#2262477211yescharacteristic
subgroupG/H
centerC4#17989464
commutatorC2×C4×C73C4×C8
FrattiniC2×M16C2×#64408
Fitting#349×C73C4
socleC2×C73#1282
prime radicalC2×#11924028C2×C4
cosocleC2×#14556599C22
hypercenter#349#64408
hypocenterC73#7208
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #349

Complements

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

NH ≅ G/Ntype
4. C2×#14556665C4semidirect
5. C22×#11924031C4semidirect
14. #17988369C4semidirect
16. #349×C73C4semidirect
120. C73#7208semidirect
130. #349#64408semidirect

Maximal subgroups

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

subgroupindex
#226261632
#226256872
#226115502
#720873