Finite Group Databasebeta

← #22610410

Subgroups — #22610410

Order 9344.

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

normal subgroups only

This group has 324 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
1C2×#14556619C211yesmaximal, characteristic
2#17989353C211yesmaximal, characteristic, complemented
3#17988605C211yesmaximal, characteristic, complemented
4#17988591C211yesmaximal, characteristic, complemented
5C2×#14556507C211yesmaximal, characteristic, complemented
6#17988345C211yesmaximal, characteristic, complemented
7#344×C73C211yesmaximal, characteristic, complemented
8C2×#11924028C2211yescharacteristic
9C22×D292C2211yescharacteristic
10#14556619—22no—
11#14556619—22no—
12C2×#11924017C412yescomplemented
13C2×D584C412yescomplemented
14#14556599—22no—
15#14556597—22no—
16C2×#11924012C2211yescharacteristic
17C2×#11924012C2211yescharacteristic
18M16×D73—22no—
19#14556519—22no—
20#14556511—22no—
21#14556507—22no—
22C2×M16×C73C2211yescharacteristic
23C2×M16×C73C2211yescharacteristic
24#117×C73C2211yescharacteristic
25C23×D73—21no—
26#11924028—21no—
27#11924028—21no—
28#11924028D412yes—
29#11924028D412yes—
30C2×Dic146C2×C411yescharacteristic
31C2×D292—21no—
32C2×D292—21no—
33C2×D292—21no—
34C2×D292—21no—
35C2×D292—21no—
36C2×D292C2×C412yes—
37C2×D292C2×C411yescharacteristic
38C2×C22⋊D73—21no—
39C2×C4×D73—21no—
40#11924017—24no—
41D584—24no—
42#11924012—21no—
43#11924012—21no—
44#11924012—21no—
45#11924012—21no—
46#11924011—24no—
47C2×#10596831—21no—
48C2×#10596831D412yes—
49C8×D73—24no—
50C22×C4×C73C2311yescharacteristic
51M16×C73—21no—
52M16×C73—21no—
53M16×C73—21no—
54M16×C73D412yes—
55C2×C8×C73—21no—
56C2×C8×C73C2×C412yes—
57C4⋊C4×C73—21no—
58C22⋊C4×C73—21no—
59C42×C73—21no—
60C23×C73#4111yescharacteristic
61C22×D73—21no—
62C22×D73—22no—
63C22×D73—41no—
64C22×D73—41no—
65C22×D73—82no—
66C2×C4×C73—41no—
67C2×C4×C73C22×C411yescharacteristic
68C2×C4×C73C2×D411yescharacteristic
69C2×C4×C73C2×D411yescharacteristic
70C2×C4×C73C2×D411yescharacteristic
71C2×C4×C73C2×D411yescharacteristic
72C2×C4×C73#4111yescharacteristic
73C22⋊D73—22no—
74C22⋊D73—22no—
75C2×Dic73—21no—
76D292—22no—
77D292—21no—
78D292—22no—
79D292—41no—
80D292—41no—
81D292C22⋊C412yes—
82C4×D73—22no—
83C4×D73—22no—
84Dic146—21no—
85Dic146C22⋊C412yes—
86C8×C73—22no—
87C8×C73—22no—
88#10596831—22no—
89#10596831—41no—
90C22×C73—41no—
91C22×C73C4×D411yescharacteristic
92C22×C73#12111yescharacteristic
93C22×C73#12311yescharacteristic
94C2×D73—22no—
95C2×D73—42no—
96C2×D73—81no—
97C2×D73—82no—
98C2×D73—82no—
99C2×D73—82no—
100C4×C73—81no—
101C4×C73C2×C22⋊C411yescharacteristic
102C4×C73C4×D411yescharacteristic
103C4×C73#12011yescharacteristic
104C4×C73#12111yescharacteristic
105Dic73—22no—
106C2×C73—21no—
107C2×C73—21no—
108C2×C73—21no—
109C2×C73#38611yescharacteristic
110D73—42no—
111D73—82no—
112#1903—731nomaximal, Sylow
113C73#190311yescharacteristic, complemented, Sylow
114C2×AGL(1,ℤ/8)—731no—
115#568—731no—
116#421—731no—
117#418—731no—
118C2×#100—731no—
119#344D7311yescharacteristic, complemented
120#338—731no—
121C2×#41—731no—
122C22×D4—731no—
123AGL(1,ℤ/8)—1462no—
124AGL(1,ℤ/8)—1462no—
125C2×SD16—732no—
126C2×D8—732no—
127#131—1462no—
128#131—1462no—
129C2×M16—731no—
130C2×M16—731no—
131C2×M16—1462no—
132C2×M16C2×D7311yescharacteristic
133C2×M16C2×D7311yescharacteristic
134#117C2×D7311yescharacteristic
135#104—1462no—
136#102—1462no—
137#100—1462no—
138C24—1461no—
139#41—732no—
140#41—732no—
141#41—1461no—
142#41—1461no—
143C2×Q8—731no—
144C2×D4—731no—
145C2×D4—732no—
146C2×D4—1461no—
147C2×D4—1461no—
148C2×D4—1461no—
149C2×D4—1461no—
150C2×D4—1461no—
151C2×D4—1461no—
152C22×C4—1461no—
153C22×C4C22×D7311yescharacteristic
154SD16—1464no—
155D8—1464no—
156M16—21no—
157M16—21no—
158M16—21no—
159M16—1464no—
160M16—1461no—
161M16—1461no—
162M16—1461no—
163M16—1461no—
164M16D29212yes—
165C2×C8—21no—
166C2×C8—732no—
167C2×C8—1464no—
168C2×C8—1461no—
169C2×C8C4×D7312yes—
170C4⋊C4—21no—
171C22⋊C4—21no—
172C42—21no—
173C23—2921no—
174C23—2921no—
175C23—5842no—
176C23—1462no—
177C23—1461no—
178C23#1192402811yescharacteristic
179Q8—732no—
180Q8—1461no—
181D4—2921no—
182D4—2921no—
183D4—732no—
184D4—1462no—
185D4—1462no—
186D4—1462no—
187D4—1462no—
188D4—1461no—
189C2×C4—41no—
190C2×C4—1461no—
191C2×C4—1462no—
192C2×C4—1462no—
193C2×C4C2×C4×D7311yescharacteristic
194C2×C4D4×D7311yescharacteristic
195C2×C4D4×D7311yescharacteristic
196C2×C4D4×D7311yescharacteristic
197C2×C4C2×D29211yescharacteristic
198C2×C4#1192402911yescharacteristic
199C8—22no—
200C8—22no—
201C8—2921no—
202C8—1462no—
203C22—41no—
204C22—2922no—
205C22—5841no—
206C22—5842no—
207C22—5842no—
208C22—5842no—
209C22—1462no—
210C22C4×D29211yescharacteristic
211C22#1455656411yescharacteristic
212C22#1455657611yescharacteristic
213C4—81no—
214C4—1462no—
215C4C22⋊C4×D7311yescharacteristic
216C4#1455655311yescharacteristic
217C4#1455656111yescharacteristic
218C4#1455656611yescharacteristic
219C2—21no—
220C2—21no—
221C2—21no—
222C2—2922no—
223C2—5842no—
224C2#1798846511yescharacteristic
subgroupG/H
centerC2#17988465
commutatorC2×C4×C73C22×C4
FrattiniC22×C4C22×D73
Fitting#344×C73C2
socleC2×C73#386
hypercenter#344D73
hypocenterC73#1903
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C22×C4 ◁ #344

Complements

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

NH ≅ G/Ntype
2. #17989353C2semidirect
3. #17988605C2semidirect
4. #17988591C2semidirect
5. C2×#14556507C2semidirect
6. #17988345C2semidirect
7. #344×C73C2semidirect
12. C2×#11924017C4semidirect
13. C2×D584C4semidirect
113. C73#1903semidirect
119. #344D73semidirect