Finite Group Databasebeta

← #22610480

Subgroups — #22610480

Order 9344.

308 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 79 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#17989353C211yesmaximal, characteristic
2#17989161C211yesmaximal, characteristic
3#17988569C211yesmaximal, characteristic
4C2×#14556510C211yesmaximal, characteristic, complemented
5#17988359C211yesmaximal, characteristic, complemented
6#17988358C211yesmaximal, characteristic, complemented
7C2×#101×C73C211yesmaximal, characteristic, complemented
8C2×#11924028C2211yescharacteristic
9#14556599—22no—
10#14556597—22no—
11C2×#11924012C2211yescharacteristic
12C2×#11924012C2211yescharacteristic
13M16×D73—22no—
14#14556589—21no—
15#14556580—21no—
16#14556574C414yes—
17#14556567—22no—
18#14556550C2211yescharacteristic
19#14556510—22no—
20#14556509—21no—
21#14556507—21no—
22C22×Q8×C73C2211yescharacteristic
23C2×M16×C73C2211yescharacteristic
24C2×M16×C73C2211yescharacteristic
25#101×C73—22no—
26#11924028—21no—
27#11924028—21no—
28#11924028—21no—
29#11924028—21no—
30C2×Dic146D411yescharacteristic
31C2×D292D411yescharacteristic
32C2×C22⋊D73C2×C412yes—
33C2×C4×D73D412yes—
34#11924012—21no—
35#11924012—21no—
36#11924012—21no—
37#11924012D412yes—
38#11924011—24no—
39C2×#10596831—21no—
40C2×#10596831—21no—
41C8×D73—24no—
42C4⋊Dic73—21no—
43#11924007—24no—
44C22⋊Dic73C2×C412yes—
45#11924005—24no—
46C4×Dic73—21no—
47C2×Q8×C73—21no—
48C2×Q8×C73—21no—
49C2×Q8×C73—21no—
50C2×Q8×C73—21no—
51C2×Q8×C73—21no—
52C2×Q8×C73—21no—
53C22×C4×C73C2×C412yes—
54C22×C4×C73C2311yescharacteristic
55M16×C73—21no—
56M16×C73—21no—
57M16×C73—21no—
58M16×C73D412yes—
59C2×C8×C73—21no—
60C2×C8×C73—21no—
61C23×C73C22×C411yescharacteristic
62C22×D73C22⋊C412yes—
63Q8×C73—41no—
64Q8×C73—41no—
65Q8×C73—41no—
66Q8×C73—41no—
67C2×C4×C73—22no—
68C2×C4×C73—22no—
69C2×C4×C73—22no—
70C2×C4×C73C2×D411yescharacteristic
71C2×C4×C73C2×D411yescharacteristic
72C2×C4×C73C2×D411yescharacteristic
73C2×C4×C73C2×D411yescharacteristic
74C2×C4×C73#4111yescharacteristic
75C2×C4×C73#4111yescharacteristic
76C22⋊D73—22no—
77C22⋊D73—22no—
78C2×Dic73—22no—
79C2×Dic73C22⋊C412yes—
80D292—21no—
81D292—21no—
82C4×D73—22no—
83C4×D73—22no—
84Dic146—21no—
85Dic146—21no—
86C8×C73—22no—
87C8×C73—41no—
88#10596831—22no—
89#10596831—41no—
90C22×C73—41no—
91C22×C73C2×C22⋊C411yescharacteristic
92C22×C73C4×D411yescharacteristic
93C22×C73C4×D411yescharacteristic
94C2×D73—22no—
95C2×D73—42no—
96C4×C73—42no—
97C4×C73#12011yescharacteristic
98C4×C73#12111yescharacteristic
99C4×C73#12111yescharacteristic
100C4×C73#12311yescharacteristic
101Dic73—22no—
102Dic73—42no—
103C2×C73—21no—
104C2×C73—21no—
105C2×C73—21no—
106C2×C73#38611yescharacteristic
107D73—42no—
108#1915—731nomaximal, Sylow
109C73#191511yescharacteristic, complemented, Sylow
110#568—731no—
111#536—731no—
112#413—731no—
113C2×#101—731no—
114C2×#101D7311yescharacteristic, complemented
115#344—731no—
116#344—731no—
117C2×#41—731no—
118C22×Q8C2×D7311yescharacteristic
119#131—1462no—
120#131—1462no—
121C2×M16—731no—
122C2×M16—731no—
123C2×M16—1462no—
124C2×M16C2×D7311yescharacteristic
125C2×M16C2×D7311yescharacteristic
126C4⋊Q8—1461no—
127#124—1461no—
128#123—734no—
129C22⋊Q8—1462no—
130#117—731no—
131#101—22no—
132#101—1461no—
133#101—1462no—
134#100—1461no—
135#41—1461no—
136#41—1461no—
137#41—1461no—
138#41—1461no—
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—21no—
142C2×Q8—21no—
143C2×Q8—21no—
144C2×Q8—21no—
145C2×Q8—731no—
146C2×D4—732no—
147C2×D4—731no—
148C22×C4—732no—
149C22×C4C4×D7312yes—
150C22×C4C22×D7311yescharacteristic
151M16—21no—
152M16—21no—
153M16—21no—
154M16—732no—
155M16—1464no—
156M16—1461no—
157M16—1461no—
158M16—1461no—
159M16C22⋊D7312yes—
160C2×C8—21no—
161C2×C8—21no—
162C2×C8—1464no—
163C2×C8—1461no—
164C2×C8—1461no—
165C4⋊C4—1464no—
166C4⋊C4—1461no—
167C22⋊C4—732no—
168C22⋊C4—1464no—
169C42—1461no—
170C23—732no—
171C23C2×C4×D7311yescharacteristic
172Q8—41no—
173Q8—41no—
174Q8—41no—
175Q8—41no—
176Q8—1461no—
177Q8—1461no—
178D4—1462no—
179D4—1462no—
180D4—1461no—
181D4—1461no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—732no—
186C2×C4—1462no—
187C2×C4—1462no—
188C2×C4—1462no—
189C2×C4D4×D7311yescharacteristic
190C2×C4D4×D7311yescharacteristic
191C2×C4D4×D7311yescharacteristic
192C2×C4C2×C22⋊D7311yescharacteristic
193C2×C4#1192402711yescharacteristic
194C2×C4#1192402811yescharacteristic
195C8—22no—
196C8—41no—
197C8—2921no—
198C8—1462no—
199C22—41no—
200C22—2922no—
201C22—1462no—
202C22C22⋊C4×D7311yescharacteristic
203C22#1455655111yescharacteristic
204C22C4×C22⋊D7311yescharacteristic
205C4—42no—
206C4—2922no—
207C4—1462no—
208C4#1455655911yescharacteristic
209C4#1455656211yescharacteristic
210C4#1455656411yescharacteristic
211C4#1455657311yescharacteristic
212C2—21no—
213C2—21no—
214C2—21no—
215C2—2922no—
216C2#1798846311yescharacteristic
subgroupG/H
centerC2#17988463
commutatorC23×C73C22×C4
FrattiniC22×C4C22×D73
FittingC2×#101×C73C2
socleC2×C73#386
hypercenterC2×#101D73
hypocenterC73#1915
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
4. C2×#14556510C2semidirect
5. #17988359C2semidirect
6. #17988358C2semidirect
7. C2×#101×C73C2semidirect
109. C73#1915semidirect
114. C2×#101D73semidirect