Finite Group Databasebeta

← #22611878

Subgroups — #22611878

Order 9344.

226 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 47 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#17989384C211yesmaximal, characteristic, complemented
2#17989025C211yesmaximal, characteristic, complemented
3#17989022C211yesmaximal, characteristic, complemented
4#17988841C211yesmaximal, characteristic, complemented
5#17988396C211yesmaximal, characteristic, complemented
6#17988368C211yesmaximal, characteristic, complemented
7#360×C73C211yesmaximal, characteristic, complemented
8#41×D73—21no—
9#14556623—21no—
10#14556620—21no—
11#14556618—21no—
12#14556615—21no—
13#14556613C2211yescharacteristic
14#14556611—21no—
15C2×D584C2211yescharacteristic, complemented
16C2×#11924011C2211yescharacteristic
17#14556566—21no—
18#14556536—21no—
19#14556534—21no—
20D1168—21no—
21#14556532—21no—
22#14556531C2211yescharacteristic, complemented
23#14556511—21no—
24#135×C73C2211yescharacteristic
25M32×C73C2211yescharacteristic, complemented
26#106×C73C2211yescharacteristic, complemented
27#11924029—21no—
28#11924028—21no—
29#11924028—41no—
30#11924027—21no—
31#11924027—41no—
32Q8×D73—21no—
33C2×D292—21no—
34C2×D292—41no—
35D4×D73—21no—
36D4×D73—41no—
37C2×C4×D73—41no—
38C2×C4×D73D411yescharacteristic
39Dic292D411yescharacteristic, complemented
40#11924018—21no—
41#11924017—21no—
42#11924016—21no—
43#11924015—21no—
44D584—21no—
45D584—21no—
46D584D411yescharacteristic, complemented
47#11924013—21no—
48#11924011—21no—
49#11924011—21no—
50C2×#10596831D411yescharacteristic
51#11924005—41no—
52#11924003—21no—
53#41×C73—21no—
54Q16×C73D411yescharacteristic, complemented
55SD16×C73—21no—
56D8×C73D411yescharacteristic, complemented
57C2×C8×C73C2311yescharacteristic
58C4⋊C4×C73—21no—
59C16×C73—21no—
60C22×D73—41no—
61C22×D73—41no—
62C22×D73D811yescharacteristic
63Q8×C73—21no—
64D4×C73—21no—
65D4×C73—41no—
66C2×C4×C73—41no—
67C2×C4×C73—41no—
68C2×C4×C73C2×D411yescharacteristic
69C22⋊D73—41no—
70C22⋊D73—41no—
71C22⋊D73—41no—
72C2×Dic73—41no—
73C2×Dic73D811yescharacteristic
74D292—21no—
75D292—41no—
76D292—41no—
77D292—41no—
78D292—82no—
79C4×D73—21no—
80C4×D73—21no—
81C4×D73—41no—
82C4×D73—41no—
83C4×D73—41no—
84Dic146—21no—
85Dic146—41no—
86C8×C73C2×D411yescharacteristic
87C8×C73C2×D411yescharacteristic
88#10596831—21no—
89C22×C73—41no—
90C22×C73C2×D811yescharacteristic
91C2×D73—21no—
92C2×D73—41no—
93C2×D73—41no—
94C2×D73—82no—
95C2×D73—81no—
96C2×D73—81no—
97C2×D73—81no—
98C4×C73—41no—
99C4×C73—81no—
100C4×C73#12011yescharacteristic
101C4×C73AGL(1,ℤ/8)11yescharacteristic
102Dic73—21no—
103Dic73—41no—
104C2×C73—21no—
105C2×C73—81no—
106C2×C73#44711yescharacteristic
107D73—41no—
108D73—81no—
109D73—161no—
110#2190—731nomaximal, Sylow
111C73#219011yescharacteristic, complemented, Sylow
112#575—731no—
113#509—731no—
114#509—731no—
115#469—731no—
116#360—731no—
117#360D7311yescharacteristic, complemented
118#349—731no—
119C2×#41—1461no—
120#137—1461no—
121#137—1461no—
122AGL(1,ℤ/8)—1461no—
123AGL(1,ℤ/8)—1461no—
124#135—731no—
125#135—1461no—
126#135C2×D7311yescharacteristic
127C2×D8—731no—
128C2×M16—731no—
129#121—1461no—
130SD32—1461no—
131SD32—1461no—
132D16—1461no—
133D16—1461no—
134M32—731no—
135M32C2×D7311yescharacteristic, complemented
136#106C2×D7311yescharacteristic, complemented
137#102—1461no—
138#41—21no—
139#41—2921no—
140#41—2921no—
141#41—1461no—
142#41—1461no—
143#41—1461no—
144C2×Q8—1461no—
145C2×D4—2921no—
146C2×D4—2921no—
147C2×D4—1461no—
148C2×D4—1461no—
149C22×C4—2921no—
150C22×C4—731no—
151Q16—731no—
152Q16—1461no—
153Q16D29211yescharacteristic, complemented
154SD16—21no—
155SD16—1461no—
156SD16—1461no—
157SD16—1461no—
158D8—731no—
159D8—1461no—
160D8—1461no—
161D8—1461no—
162D8D29211yescharacteristic, complemented
163M16—1461no—
164M16—1461no—
165C2×C8—731no—
166C2×C8C22×D7311yescharacteristic
167C4⋊C4—21no—
168C22⋊C4—2921no—
169C16—21no—
170C16—1461no—
171C23—2921no—
172C23—2921no—
173C23—731no—
174Q8—21no—
175Q8—2921no—
176Q8—1461no—
177D4—21no—
178D4—41no—
179D4—2921no—
180D4—2921no—
181D4—2921no—
182D4—2921no—
183D4—2921no—
184D4—2921no—
185D4—5842no—
186D4—1461no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—2921no—
190C2×C4—2921no—
191C2×C4—2921no—
192C2×C4—2921no—
193C2×C4—731no—
194C2×C4—1461no—
195C2×C4—1461no—
196C2×C4D4×D7311yescharacteristic
197C8—1461no—
198C8D4×D7311yescharacteristic
199C8C2×D29211yescharacteristic
200C22—41no—
201C22—2921no—
202C22—2921no—
203C22—5841no—
204C22—5841no—
205C22—5842no—
206C22—5841no—
207C22—1461no—
208C22D8×D7311yescharacteristic
209C4—41no—
210C4—81no—
211C4—2921no—
212C4—1461no—
213C4#1455656111yescharacteristic
214C4#1455661811yescharacteristic
215C2—21no—
216C2—81no—
217C2—2921no—
218C2—5841no—
219C2—11681no—
220C2#1798872211yescharacteristic
subgroupG/H
centerC2#17988722
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
Fitting#360×C73C2
socleC2×C73#447
hypercenter#360D73
hypocenterC73#2190
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #360

Complements

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

NH ≅ G/Ntype
1. #17989384C2semidirect
2. #17989025C2semidirect
3. #17989022C2semidirect
4. #17988841C2semidirect
5. #17988396C2semidirect
6. #17988368C2semidirect
7. #360×C73C2semidirect
15. C2×D584C22semidirect
22. #14556531C22semidirect
25. M32×C73C22semidirect
26. #106×C73C22semidirect
39. Dic292D4semidirect
46. D584D4semidirect
54. Q16×C73D4semidirect
56. D8×C73D4semidirect
111. C73#2190semidirect
117. #360D73semidirect
135. M32C2×D73semidirect
136. #106C2×D73semidirect
153. Q16D292semidirect
162. D8D292semidirect