Finite Group Databasebeta

← C2×#17989602 #22626590

Subgroups — C2×#17989602 #22626590

Order 9344.

460 conjugacy classes of subgroups; only the 202 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 202 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
1C22×#11924038C211yesmaximal, characteristic
2C2×D73⋊M16C211yesmaximal, characteristic
3#17989602C218yesmaximal, direct product factor
4C2×#14556662C212yesmaximal, complemented
5C2×#14556661C212yesmaximal, complemented
6C2×M16×D73C211yesmaximal, characteristic
7C2×#11924038—21no—
8C2×#11924038—22no—
9C2×#11924038C2211yescharacteristic
10C2×#11924038C2211yescharacteristic
11C2×#11924038C2212yes—
12C2×#11924038C2214yes—
13D73⋊M16—22no—
14D73⋊M16C2214yes—
15C2×#11924037—21no—
16C2×#11924036—21no—
17C22×#10596833—21no—
18#14556662C2218yescomplemented
19#14556661C2218yescomplemented
20C22×C4×D73C2211yescharacteristic
21C2×#11924012C411yescharacteristic
22C2×#11924011C412yes—
23M16×D73C414yes—
24M16×D73C2214yes—
25C2×C8×D73C2212yes—
26C2×M16×C73C411yescharacteristic
27#11924038—21no—
28#11924038—21no—
29#11924038—24no—
30#11924038—22no—
31#11924038C2312yes—
32#11924038C2312yes—
33#11924038C2314yes—
34#11924037—24no—
35#11924036—24no—
36C2×#10596833—22no—
37C2×#10596833—24no—
38C2×#10596833—21no—
39C2×#10596833—21no—
40C23×D73Q811yescharacteristic
41C22×Dic73D411yescharacteristic
42C2×C4×D73C2×C412yes—
43C2×C4×D73C2×C411yescharacteristic
44C2×C4×D73D411yescharacteristic
45C2×C4×D73D412yes—
46C2×C4×D73Q811yescharacteristic
47C2×C4×D73Q812yes—
48C2×C4×D73C2312yes—
49C2×C4×D73C2311yescharacteristic
50#11924012C2×C414yes—
51#11924011C2×C418yes—
52C2×#10596831C2×C412yes—
53C8×D73C2×C414yes—
54C8×D73C2314yes—
55C22×C4×C73C2×C411yescharacteristic
56M16×C73C2×C414yes—
57C2×C8×C73C2×C412yes—
58C23×C73C4⋊C411yescharacteristic
59C22×D73—42no—
60C22×D73C4⋊C411yescharacteristic
61C22×D73C4⋊C412yes—
62C22×D73C2×Q811yescharacteristic
63C22×D73C2×Q812yes—
64C2×C4×C73C4⋊C412yes—
65C2×C4×C73C4⋊C411yescharacteristic
66C2×C4×C73C22×C411yescharacteristic
67C2×C4×C73C22×C412yes—
68C2×Dic73C4⋊C412yes—
69C2×Dic73C4⋊C411yescharacteristic
70C2×Dic73C2×D411yescharacteristic
71C2×Dic73C2×D412yes—
72C4×D73C4⋊C412yes—
73C4×D73C4⋊C412yes—
74C4×D73C4⋊C412yes—
75C4×D73C22×C411yescharacteristic
76C4×D73C22×C412yes—
77C4×D73C2×D412yes—
78C4×D73C2×D411yescharacteristic
79C4×D73C2×Q812yes—
80C4×D73C2×Q811yescharacteristic
81C4×D73C2411yescharacteristic
82#10596833—24no—
83#10596833—22no—
84#10596833—22no—
85C8×C73C22×C414yes—
86#10596831C22×C414yes—
87C22×C73—22no—
88C22×C73C2×C4⋊C412yes—
89C22×C73C2×C4⋊C411yescharacteristic
90C2×D73—22no—
91C2×D73—22no—
92C2×D73—42no—
93C2×D73—42no—
94C2×D73C2×C4⋊C411yescharacteristic
95C2×D73C2×C4⋊C412yes—
96C2×D73C22×Q811yescharacteristic
97C4×C73C2×C4⋊C412yes—
98C4×C73C2×C4⋊C411yescharacteristic
99C4×C73C23×C411yescharacteristic
100Dic73C2×C4⋊C411yescharacteristic
101Dic73C2×C4⋊C412yes—
102Dic73C22×D411yescharacteristic
103C2×C73—22no—
104C2×C73#43012yescomplemented
105C2×C73C22×C4⋊C411yescharacteristic
106D73—22no—
107D73—21no—
108D73—21no—
109C2×#430—731nomaximal, Sylow
110C73C2×#43011yescharacteristic, complemented, Sylow
111C22×M16—731no—
112C22×M16—731no—
113C22×M16—731no—
114#430—738no—
115C2×#108—732no—
116C2×#108—732no—
117C23×C4—731no—
118C2×M16—731no—
119C2×M16—734no—
120C2×M16—734no—
121C2×M16—732no—
122C2×M16—734no—
123C2×M16—731no—
124C2×M16—731no—
125C2×M16—732no—
126C2×M16—734no—
127C2×M16—1461no—
128C2×M16—1462no—
129C2×M16—1461no—
130C2×M16—1462no—
131C2×M16#6440811yescharacteristic
132C22×C8—732no—
133C22×C8—1461no—
134C22×C8—1461no—
135#108—738no—
136#108—738no—
137C24—731no—
138C22×C4—731no—
139C22×C4—731no—
140C22×C4—732no—
141C22×C4—732no—
142C22×C4—731no—
143C22×C4—732no—
144C22×C4—731no—
145C22×C4—731no—
146C22×C4—732no—
147C22×C4C2×#6440811yescharacteristic
148M16—734no—
149M16—738no—
150M16—732no—
151M16—732no—
152M16—734no—
153M16—1464no—
154M16—1464no—
155M16—1461no—
156M16—1461no—
157M16—1462no—
158M16C2×#6440814yes—
159C2×C8—732no—
160C2×C8—734no—
161C2×C8—734no—
162C2×C8—1464no—
163C2×C8—1462no—
164C2×C8—1461no—
165C2×C8—1461no—
166C2×C8—1464no—
167C2×C8C2×#6440812yes—
168C23—2922no—
169C23—732no—
170C23—732no—
171C23—731no—
172C23—731no—
173C23C4⋊#6440811yescharacteristic
174C2×C4—732no—
175C2×C4—732no—
176C2×C4—731no—
177C2×C4—731no—
178C2×C4—731no—
179C2×C4—731no—
180C2×C4—732no—
181C2×C4—732no—
182C2×C4—731no—
183C2×C4—732no—
184C2×C4—732no—
185C2×C4—732no—
186C2×C4—731no—
187C2×C4—732no—
188C2×C4C4⋊#6440812yes—
189C2×C4C4⋊#6440811yescharacteristic
190C2×C4C22×#6440812yes—
191C2×C4C22×#6440811yescharacteristic
192C8—734no—
193C8—1464no—
194C8—1462no—
195C8—1462no—
196C8C22×#6440814yes—
197C22—22no—
198C22—2922no—
199C22—2922no—
200C22—731no—
201C22—732no—
202C22—731no—
203C22—1462no—
204C22—1462no—
205C22C2×C4⋊#6440812yes—
206C22C2×C4⋊#6440811yescharacteristic
207C4—731no—
208C4—732no—
209C4—731no—
210C4C2×C4⋊#6440812yes—
211C4C2×C4⋊#6440811yescharacteristic
212C4C23×#6440811yescharacteristic
213C2—22no—
214C2—1461no—
215C2—1462no—
216C2—1461no—
217C2#1798960212yesdirect product factor
218C2C22×C4⋊#6440811yescharacteristic
subgroupG/H
centerC22C2×C4⋊#64408
commutatorC4×C73C23×C4
FrattiniC4C23×#64408
FittingC2×M16×C73C4
socleC22×C73C2×C4⋊C4
hypercenterC2×M16#64408
hypocenterC73C2×#430
LCSG ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
3. #17989602C2direct (N × H)
4. C2×#14556662C2semidirect
5. C2×#14556661C2semidirect
18. #14556662C22semidirect
19. #14556661C22semidirect
104. C2×C73#430semidirect
110. C73C2×#430semidirect
217. C2#17989602direct (N × H)