Finite Group Databasebeta

← C2×#17989574 #22626540

Subgroups — C2×#17989574 #22626540

Order 9344.

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

normal subgroups only

This group has 756 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×#11924037C212yesmaximal, complemented
2#17989574C218yesmaximal, direct product factor
3C2×#14556652C212yesmaximal, complemented
4C2×#14556651C212yesmaximal, complemented
5C22×#11924027C211yesmaximal, characteristic
6C2×#11924037—22no—
7C2×#11924037—24no—
8C2×#11924037C2214yes—
9C2×#11924037C2218yescomplemented
10C22×#10596833—22no—
11#14556652C2218yescomplemented
12#14556651C2218yescomplemented
13C2×#11924027—22no—
14C2×#11924027—22no—
15C2×#11924027—24no—
16C2×#11924027C414yes—
17C2×#11924027C2214yes—
18C22×Dic146C2211yescharacteristic
19C22×C22⋊D73C411yescharacteristic
20C22×C22⋊D73C2211yescharacteristic
21C23×Dic73C411yescharacteristic
22C23×Dic73C2211yescharacteristic
23C22×C4×D73C411yescharacteristic
24C22×D4×C73C411yescharacteristic
25#11924037—24no—
26#11924037—28no—
27#11924037C2318yes—
28C2×#10596833—24no—
29C2×#10596833—28no—
30C23×D73C2×C411yescharacteristic
31#11924027—28no—
32#11924027—28no—
33#11924027—28no—
34#11924027—28no—
35C2×Dic146—22no—
36C2×Dic146—22no—
37C2×Dic146C2×C412yes—
38C2×Dic146C2312yes—
39C2×C22⋊D73—22no—
40C2×C22⋊D73—22no—
41C2×C22⋊D73—22no—
42C2×C22⋊D73—22no—
43C2×C22⋊D73C2×C414yes—
44C2×C22⋊D73C2×C412yes—
45C2×C22⋊D73C2312yes—
46C22×Dic73—22no—
47C22×Dic73—21no—
48C22×Dic73—21no—
49C22×Dic73C2×C411yescharacteristic
50C22×Dic73C2×C414yes—
51C22×Dic73C2×C411yescharacteristic
52C22×Dic73C2×C412yes—
53C22×Dic73D412yes—
54C22×Dic73D412yes—
55C22×Dic73D414yes—
56C22×Dic73C2311yescharacteristic
57C22×Dic73C2312yes—
58C2×C4×D73—22no—
59C2×C4×D73—21no—
60C2×C4×D73—21no—
61C2×C4×D73C2×C414yes—
62C24×C73C2×C411yescharacteristic
63C24×C73C2×C411yescharacteristic
64C2×D4×C73—22no—
65C2×D4×C73—22no—
66C2×D4×C73C2×C414yes—
67C22×C4×C73C2×C411yescharacteristic
68C23×C73—21no—
69C23×C73—21no—
70C23×C73—42no—
71C23×C73—42no—
72C23×C73C22⋊C412yes—
73C23×C73C22⋊C412yes—
74C23×C73C22×C411yescharacteristic
75C23×C73C22×C412yes—
76C23×C73C22×C412yes—
77C22×D73—21no—
78C22×D73—21no—
79C22×D73—42no—
80C22×D73C22×C412yes—
81D4×C73—28no—
82C2×C4×C73—21no—
83C2×C4×C73—21no—
84C2×C4×C73C22×C412yes—
85C22⋊D73—28no—
86C22⋊D73—24no—
87C22⋊D73—24no—
88C2×Dic73—21no—
89C2×Dic73—21no—
90C2×Dic73—24no—
91C2×Dic73—24no—
92C2×Dic73C22⋊C412yes—
93C2×Dic73C22⋊C411yescharacteristic
94C2×Dic73C22⋊C411yescharacteristic
95C2×Dic73C22⋊C414yes—
96C2×Dic73C22⋊C414yes—
97C2×Dic73C22×C412yes—
98C2×Dic73C22×C412yes—
99C2×Dic73C22×C411yescharacteristic
100C2×Dic73C2×D412yes—
101C2×Dic73C2×D412yes—
102C2×Dic73C2×D414yes—
103C2×Dic73C2×D414yes—
104C2×Dic73C2411yescharacteristic
105C4×D73—24no—
106C4×D73—24no—
107Dic146—24no—
108Dic146—24no—
109#10596833—28no—
110C22×C73—22no—
111C22×C73—24no—
112C22×C73—22no—
113C22×C73—42no—
114C22×C73—42no—
115C22×C73—42no—
116C22×C73—42no—
117C22×C73—42no—
118C22×C73C2×C22⋊C411yescharacteristic
119C22×C73C2×C22⋊C414yes—
120C22×C73C2×C22⋊C411yescharacteristic
121C22×C73C23×C411yescharacteristic
122C2×D73—22no—
123C2×D73—42no—
124C2×D73—42no—
125C2×D73—42no—
126C4×C73—22no—
127Dic73—22no—
128Dic73C2×C22⋊C412yes—
129Dic73C2×C22⋊C412yes—
130Dic73C2×C22⋊C412yes—
131Dic73C22×D412yes—
132C2×C73—21no—
133C2×C73—21no—
134C2×C73—24no—
135C2×C73—42no—
136C2×C73#41312yescomplemented
137C2×C73C22×C22⋊C411yescharacteristic
138D73—42no—
139C2×#413—731nomaximal, Sylow
140C73C2×#41311yescharacteristic, complemented, Sylow
141C22×#41—731no—
142C22×M16—732no—
143#413—738no—
144C2×#101—732no—
145C2×#100—732no—
146C2×#41—734no—
147C2×#41—734no—
148C2×#41—1462no—
149C2×#41—1464no—
150C2×#41—1462no—
151C22×Q8—731no—
152C22×D4—731no—
153C22×D4—731no—
154C22×D4#6440811yescharacteristic
155C23×C4—731no—
156C23×C4—731no—
157C23×C4—731no—
158C2×M16—734no—
159C2×M16—738no—
160C2×M16—1464no—
161C2×M16—1462no—
162C22×C8—1462no—
163#101—738no—
164#100—738no—
165C24—731no—
166C24C2×#6440811yescharacteristic
167C24C2×#6440811yescharacteristic
168#41—1468no—
169#41—1468no—
170#41—1468no—
171#41—1468no—
172C2×Q8—732no—
173C2×Q8—732no—
174C2×Q8—1462no—
175C2×Q8—1462no—
176C2×D4—22no—
177C2×D4—22no—
178C2×D4—732no—
179C2×D4—734no—
180C2×D4—732no—
181C2×D4—1462no—
182C2×D4—1462no—
183C2×D4—1462no—
184C2×D4—1462no—
185C2×D4C2×#6440814yes—
186C22×C4—732no—
187C22×C4—734no—
188C22×C4—732no—
189C22×C4—731no—
190C22×C4—732no—
191C22×C4—731no—
192C22×C4—732no—
193C22×C4—731no—
194C22×C4—734no—
195C22×C4—734no—
196C22×C4—1462no—
197C22×C4—1461no—
198C22×C4—1461no—
199C22×C4—1462no—
200C22×C4—1461no—
201C22×C4—1461no—
202C22×C4C2×#6440811yescharacteristic
203M16—738no—
204M16—1464no—
205M16—1468no—
206C2×C8—1468no—
207C2×C8—1464no—
208C23—21no—
209C23—21no—
210C23—42no—
211C23—42no—
212C23—2922no—
213C23—732no—
214C23—1461no—
215C23—1461no—
216C23C22⋊#6440812yes—
217C23C22⋊#6440812yes—
218C23C22×#6440811yescharacteristic
219C23C22×#6440812yes—
220C23C22×#6440812yes—
221Q8—1464no—
222Q8—1464no—
223D4—28no—
224D4—1464no—
225D4—1464no—
226D4—1468no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—731no—
230C2×C4—732no—
231C2×C4—731no—
232C2×C4—734no—
233C2×C4—732no—
234C2×C4—734no—
235C2×C4—732no—
236C2×C4—734no—
237C2×C4—734no—
238C2×C4—732no—
239C2×C4—731no—
240C2×C4—731no—
241C2×C4—732no—
242C2×C4—1464no—
243C2×C4—1464no—
244C2×C4—1464no—
245C2×C4—1464no—
246C2×C4—1461no—
247C2×C4—1461no—
248C2×C4C22×#6440812yes—
249C8—1468no—
250C22—22no—
251C22—24no—
252C22—22no—
253C22—42no—
254C22—42no—
255C22—42no—
256C22—42no—
257C22—42no—
258C22—2922no—
259C22—2922no—
260C22—2922no—
261C22—1462no—
262C22C2×C22⋊#6440811yescharacteristic
263C22C2×C22⋊#6440814yes—
264C22C2×C22⋊#6440811yescharacteristic
265C22C23×#6440811yescharacteristic
266C4—22no—
267C4—732no—
268C4—732no—
269C4—732no—
270C4—732no—
271C4—1462no—
272C2—21no—
273C2—21no—
274C2—24no—
275C2—42no—
276C2—2922no—
277C2#1798957412yesdirect product factor
278C2C22×C22⋊#6440811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC22×C73C23×C4
FrattiniC22C23×#64408
FittingC22×D4×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC22×D4#64408
hypocenterC73C2×#413
LCSG ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×#11924037C2semidirect
2. #17989574C2direct (N × H)
3. C2×#14556652C2semidirect
4. C2×#14556651C2semidirect
9. C2×#11924037C22semidirect
11. #14556652C22semidirect
12. #14556651C22semidirect
136. C2×C73#413semidirect
140. C73C2×#413semidirect
277. C2#17989574direct (N × H)