Finite Group Databasebeta

← #22619225

Subgroups — #22619225

Order 9344.

700 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 700 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14556638C211yesmaximal, characteristic
2C22×#11924018C211yesmaximal, characteristic, complemented
3#17989161C211yesmaximal, characteristic, complemented
4#17988746C214yesmaximal, complemented
5#17988741C214yesmaximal, complemented
6#17988597C211yesmaximal, characteristic, complemented
7#17988583C211yesmaximal, characteristic, complemented
8#17988555C211yesmaximal, characteristic, complemented
9C2×#137×C73C211yesmaximal, characteristic, complemented
10#14556638—24no—
11#14556638—24no—
12C2×#11924028—21no—
13C2×#11924028C2211yescharacteristic
14C2×#11924027—22no—
15C2×#11924027C2212yes—
16C22×Dic146—21no—
17C22×Dic146C2211yescharacteristic
18C2×Q8×D73C2212yes—
19C2×#11924018—24no—
20C2×#11924018C2214yes—
21C22×#10596831C2211yescharacteristic
22#14556589—21no—
23#14556580—21no—
24#14556574—22no—
25#14556567C2214yes—
26#14556550C2211yescharacteristic
27#14556516C2214yes—
28#14556515C2212yes—
29#14556512C2212yes—
30#14556503C2214yes—
31C2×#41×C73C2211yescharacteristic
32C22×Q8×C73C2211yescharacteristic
33#137×C73—24no—
34C2×Q16×C73C2212yes—
35C2×SD16×C73C2212yes—
36C2×M16×C73C2211yescharacteristic
37#11924028—28no—
38#11924028—22no—
39#11924028—22no—
40#11924027—216no—
41#11924027—24no—
42#11924027—24no—
43C2×Dic146—28no—
44C2×Dic146—21no—
45C2×Dic146—22no—
46C2×Dic146—22no—
47C2×Dic146D411yescharacteristic
48C2×Dic146D414yes—
49C2×Dic146C2312yes—
50Q8×D73—24no—
51Q8×D73—24no—
52C2×D292D411yescharacteristic
53C2×C22⋊D73—22no—
54C2×C22⋊D73D412yes—
55C22×Dic73—21no—
56C22×Dic73—22no—
57C2×C4×D73—22no—
58C2×C4×D73C2312yes—
59#11924018—28no—
60C2×#10596831—22no—
61C2×#10596831C2312yes—
62C4⋊Dic73C2312yes—
63#11924007—24no—
64C22⋊Dic73—21no—
65#11924005—24no—
66C4×Dic73—21no—
67#41×C73—22no—
68#41×C73D414yes—
69C2×Q8×C73—21no—
70C2×Q8×C73—22no—
71C2×Q8×C73—22no—
72C2×Q8×C73C2312yes—
73C2×Q8×C73C2311yescharacteristic
74C2×D4×C73—21no—
75C2×D4×C73C2311yescharacteristic
76C22×C4×C73—21no—
77C22×C4×C73—21no—
78C22×C4×C73C2311yescharacteristic
79Q16×C73—24no—
80SD16×C73—24no—
81M16×C73—22no—
82C2×C8×C73C2312yes—
83C23×C73—21no—
84C23×C73C2×D411yescharacteristic
85C22×D73C2×D412yes—
86Q8×C73—21no—
87Q8×C73—22no—
88Q8×C73—22no—
89Q8×C73—42no—
90Q8×C73C2×D412yes—
91D4×C73—24no—
92D4×C73—21no—
93D4×C73C2×D412yes—
94C2×C4×C73—21no—
95C2×C4×C73—24no—
96C2×C4×C73—22no—
97C2×C4×C73—42no—
98C2×C4×C73C2×D411yescharacteristic
99C2×C4×C73C2×D412yes—
100C2×C4×C73C2×D412yes—
101C2×C4×C73C2411yescharacteristic
102C22⋊D73—28no—
103C22⋊D73—24no—
104C2×Dic73—28no—
105C2×Dic73—24no—
106C2×Dic73—22no—
107C2×Dic73—22no—
108C2×Dic73C2×D412yes—
109D292—22no—
110C4×D73—28no—
111C4×D73—22no—
112C4×D73—22no—
113Dic146—28no—
114Dic146—22no—
115Dic146—24no—
116Dic146—22no—
117Dic146C2×D414yes—
118C8×C73—22no—
119#10596831—22no—
120C22×C73—22no—
121C22×C73—22no—
122C22×C73—42no—
123C22×C73#12012yes—
124C22×C73C22×D411yescharacteristic
125C2×D73—22no—
126C2×D73—24no—
127C4×C73—22no—
128C4×C73—42no—
129C4×C73#12012yes—
130C4×C73C22×D411yescharacteristic
131C4×C73C22×D411yescharacteristic
132Dic73—22no—
133Dic73—24no—
134Dic73—42no—
135C2×C73—22no—
136C2×C73—42no—
137C2×C73C2×#12011yescharacteristic
138C2×C73#57812yes—
139D73—42no—
140#3011—731nomaximal, Sylow
141C73#301111yescharacteristic, complemented, Sylow
142C2×2−1+4—731no—
143C2×#137D7311yescharacteristic, complemented
144C22×Q16—731no—
145#536—731no—
146#452—734no—
147#451—734no—
148#419—731no—
149#416—731no—
150#408—731no—
1512−1+4—1464no—
1522−1+4—1464no—
153C2×#41—731no—
154C2×#41—732no—
155C2×#41—1461no—
156C2×#41—1462no—
157C2×#41C2×D7311yescharacteristic
158C22×Q8—732no—
159C22×Q8—731no—
160C22×Q8—1461no—
161C22×Q8C2×D7311yescharacteristic
162#137—24no—
163C2×Q16—734no—
164C2×Q16—1464no—
165C2×Q16C2×D7312yes—
166C2×SD16C2×D7312yes—
167C2×M16C2×D7311yescharacteristic
168C22×C8—731no—
169C4⋊Q8—1461no—
170#124—1461no—
171#123—1462no—
172C22⋊Q8—734no—
173#117—731no—
174#103—732no—
175#103—734no—
176#102—732no—
177C22⋊C8—734no—
178#41—22no—
179#41—1468no—
180#41—1464no—
181#41—14616no—
182#41—1464no—
183#41—1462no—
184#41—1462no—
185#41C22⋊D7314yes—
186C2×Q8—21no—
187C2×Q8—22no—
188C2×Q8—22no—
189C2×Q8—731no—
190C2×Q8—734no—
191C2×Q8—732no—
192C2×Q8—1462no—
193C2×Q8—1468no—
194C2×Q8—1464no—
195C2×Q8—1464no—
196C2×Q8—1461no—
197C2×Q8—1462no—
198C2×Q8C22×D7312yes—
199C2×Q8C22×D7311yescharacteristic
200C2×D4—21no—
201C2×D4—732no—
202C2×D4—731no—
203C2×D4—1462no—
204C2×D4C22×D7311yescharacteristic
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—732no—
208C22×C4—1462no—
209C22×C4—1462no—
210C22×C4—1461no—
211C22×C4C22×D7311yescharacteristic
212Q16—24no—
213Q16—1468no—
214SD16—24no—
215M16—22no—
216C2×C8—732no—
217C2×C8—1462no—
218C2×C8C22×D7312yes—
219C4⋊C4—732no—
220C4⋊C4—1464no—
221C22⋊C4—1464no—
222C22⋊C4—1461no—
223C42—1461no—
224C23—21no—
225C23—732no—
226C23D4×D7311yescharacteristic
227Q8—21no—
228Q8—22no—
229Q8—22no—
230Q8—42no—
231Q8—734no—
232Q8—1468no—
233Q8—1462no—
234Q8—1464no—
235Q8—1462no—
236Q8C2×C22⋊D7312yes—
237D4—24no—
238D4—21no—
239D4—1468no—
240D4—1464no—
241D4—1462no—
242D4C2×C22⋊D7312yes—
243C2×C4—21no—
244C2×C4—24no—
245C2×C4—22no—
246C2×C4—42no—
247C2×C4—732no—
248C2×C4—1468no—
249C2×C4—1462no—
250C2×C4—1468no—
251C2×C4—1464no—
252C2×C4—1462no—
253C2×C4—1462no—
254C2×C4—1462no—
255C2×C4D4×D7311yescharacteristic
256C2×C4D4×D7312yes—
257C2×C4C2×C22⋊D7312yes—
258C2×C4C23×D7311yescharacteristic
259C8—22no—
260C8—1462no—
261C22—22no—
262C22—22no—
263C22—42no—
264C22—1464no—
265C22—1462no—
266C22#1455655912yes—
267C22C2×D4×D7311yescharacteristic
268C4—22no—
269C4—42no—
270C4—2922no—
271C4—1462no—
272C4—1464no—
273C4#1455655912yes—
274C4C2×D4×D7311yescharacteristic
275C4C22×C22⋊D7311yescharacteristic
276C2—22no—
277C2—42no—
278C2—2922no—
279C2C2×#1455655911yescharacteristic
280C2#1798940312yes—
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingC2×#137×C73C2
socleC22×C73C22×D4
hypercenterC2×#137D73
hypocenterC73#3011
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
2. C22×#11924018C2semidirect
3. #17989161C2semidirect
4. #17988746C2semidirect
5. #17988741C2semidirect
6. #17988597C2semidirect
7. #17988583C2semidirect
8. #17988555C2semidirect
9. C2×#137×C73C2semidirect
141. C73#3011semidirect
143. C2×#137D73semidirect