Finite Group Databasebeta

← #22620424

Subgroups — #22620424

Order 9344.

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

normal subgroups only

This group has 532 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×#14556624C211yesmaximal, characteristic, complemented
2C2×#14556611C211yesmaximal, characteristic
3C22×#11924018C211yesmaximal, characteristic, complemented
4#17989161C211yesmaximal, characteristic, complemented
5#17989158C211yesmaximal, characteristic, complemented
6#17988980C212yesmaximal, complemented
7#17988978C212yesmaximal, complemented
8#17988968C212yesmaximal, complemented
9#17988965C212yesmaximal, complemented
10#17988545C211yesmaximal, characteristic, complemented
11C2×#137×C73C211yesmaximal, characteristic, complemented
12C2×#11924028C2211yescharacteristic
13C22×Dic146C2211yescharacteristic
14#14556624—24no—
15#14556611—24no—
16C2×Dic292C2212yes—
17C2×#11924018—24no—
18C2×#11924018C2211yescharacteristic
19C2×#11924018C2212yes—
20C2×#11924018C2212yes—
21C2×#11924017C2212yes—
22C2×#11924016C2211yescharacteristic
23C2×#11924015C2211yescharacteristic
24C2×#11924013C2211yescharacteristic
25C22×#10596831C2211yescharacteristic
26#14556589C2212yes—
27#14556589C2212yes—
28#14556580C2212yes—
29#14556578C2212yes—
30#14556574—22no—
31#14556572—22no—
32#14556570—22no—
33#14556567—22no—
34#14556550C2211yescharacteristic
35#14556501C2212yes—
36C8×Dic73C2212yes—
37C2×#41×C73C2211yescharacteristic
38C22×Q8×C73C2211yescharacteristic
39#137×C73—24no—
40C2×Q16×C73C2212yes—
41C2×SD16×C73C2212yes—
42C2×M16×C73C2211yescharacteristic
43#11924028—22no—
44#11924028—22no—
45C2×Dic146—22no—
46C2×Dic146—22no—
47C2×Dic146—21no—
48C2×Dic146C2312yes—
49C2×Dic146C2311yescharacteristic
50C2×D292C2311yescharacteristic
51C2×C22⋊D73—21no—
52C22×Dic73—21no—
53C2×C4×D73—21no—
54Dic292—24no—
55#11924018—24no—
56#11924018—24no—
57#11924018—22no—
58#11924017—24no—
59#11924016—22no—
60#11924015—22no—
61#11924013—22no—
62C2×#10596831D414yes—
63C2×#10596831C2311yescharacteristic
64C2×#10596831C2311yescharacteristic
65C4⋊Dic73D412yes—
66#11924007—24no—
67#11924007—24no—
68C22⋊Dic73—24no—
69C22⋊Dic73D412yes—
70#11924005—24no—
71C4×Dic73C2312yes—
72#41×C73—22no—
73#41×C73—22no—
74C2×Q8×C73—21no—
75C2×Q8×C73—22no—
76C2×Q8×C73—22no—
77C2×Q8×C73C2312yes—
78C2×Q8×C73C2311yescharacteristic
79C2×D4×C73—21no—
80C2×D4×C73C2311yescharacteristic
81C22×C4×C73—21no—
82C22×C4×C73—21no—
83C22×C4×C73C2311yescharacteristic
84Q16×C73—24no—
85SD16×C73—24no—
86M16×C73D414yes—
87C2×C8×C73C2312yes—
88C23×C73—21no—
89C23×C73C2×D411yescharacteristic
90C22×D73—21no—
91Q8×C73—22no—
92Q8×C73—21no—
93Q8×C73—22no—
94Q8×C73—21no—
95Q8×C73—42no—
96D4×C73—21no—
97D4×C73—21no—
98D4×C73—42no—
99C2×C4×C73—21no—
100C2×C4×C73—22no—
101C2×C4×C73—42no—
102C2×C4×C73—42no—
103C2×C4×C73C2×D411yescharacteristic
104C2×C4×C73C2×D412yes—
105C2×C4×C73C2×D412yes—
106C2×C4×C73C2411yescharacteristic
107C22⋊D73—42no—
108C2×Dic73—22no—
109C2×Dic73—21no—
110C2×Dic73—42no—
111C2×Dic73C2×D414yes—
112D292—21no—
113D292—21no—
114C4×D73—42no—
115Dic146—21no—
116Dic146—22no—
117Dic146—22no—
118Dic146—21no—
119Dic146—42no—
120C8×C73C2×D414yes—
121#10596831C2×D412yes—
122#10596831C2×D412yes—
123C22×C73—22no—
124C22×C73—41no—
125C22×C73—42no—
126C22×C73#12712yes—
127C22×C73C22×D411yescharacteristic
128C2×D73—41no—
129C2×D73—42no—
130C4×C73—41no—
131C4×C73—42no—
132C4×C73#12712yes—
133C4×C73C22×D411yescharacteristic
134C4×C73C22×D411yescharacteristic
135Dic73—24no—
136Dic73—42no—
137Dic73—41no—
138C2×C73—22no—
139C2×C73—81no—
140C2×C73C2×#12711yescharacteristic
141C2×C73#57812yes—
142D73—81no—
143#3156—731nomaximal, Sylow
144C73#315611yescharacteristic, complemented, Sylow
145C2×#137—731no—
146C2×#137D7311yescharacteristic, complemented
147C2×#135—731no—
148C22×Q16—731no—
149#536—731no—
150#536—731no—
151#497—732no—
152#497—732no—
153#495—732no—
154#494—732no—
155#405—731no—
156C2×#41—731no—
157C2×#41C2×D7311yescharacteristic
158C22×Q8—731no—
159C22×Q8C2×D7311yescharacteristic
160#137—24no—
161#137—1464no—
162#135—1464no—
163C2×Q16—732no—
164C2×Q16—732no—
165C2×Q16—731no—
166C2×Q16—732no—
167C2×Q16—1464no—
168C2×Q16C2×D7312yes—
169C2×SD16—731no—
170C2×SD16—731no—
171C2×SD16—732no—
172C2×SD16C2×D7312yes—
173C2×D8—731no—
174C2×M16C2×D7311yescharacteristic
175C22×C8—731no—
176C4⋊Q8—732no—
177C4⋊Q8—732no—
178#124—732no—
179#124—732no—
180#123—1462no—
181#123—1462no—
182C22⋊Q8—1462no—
183C22⋊Q8—1462no—
184#117—731no—
185#97—732no—
186C4×C8—732no—
187#41—22no—
188#41—22no—
189#41—1462no—
190#41—1462no—
191C2×Q8—21no—
192C2×Q8—22no—
193C2×Q8—22no—
194C2×Q8—732no—
195C2×Q8—731no—
196C2×Q8—1462no—
197C2×Q8—1462no—
198C2×Q8—1461no—
199C2×Q8C22×D7312yes—
200C2×Q8C22×D7311yescharacteristic
201C2×D4—21no—
202C2×D4—731no—
203C2×D4—1461no—
204C2×D4C22×D7311yescharacteristic
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—1461no—
208C22×C4—1461no—
209C22×C4C22×D7311yescharacteristic
210Q16—24no—
211Q16—1464no—
212Q16—1464no—
213Q16—1462no—
214Q16—1464no—
215SD16—24no—
216SD16—1462no—
217SD16—1462no—
218SD16—1464no—
219D8—1462no—
220M16C22⋊D7314yes—
221C2×C8—734no—
222C2×C8—731no—
223C2×C8—731no—
224C2×C8C22×D7312yes—
225C4⋊C4—732no—
226C4⋊C4—1464no—
227C4⋊C4—1464no—
228C22⋊C4—732no—
229C22⋊C4—1464no—
230C22⋊C4—1464no—
231C42—732no—
232C23—21no—
233C23—1461no—
234C23D4×D7311yescharacteristic
235Q8—21no—
236Q8—22no—
237Q8—22no—
238Q8—21no—
239Q8—42no—
240Q8—2922no—
241Q8—1461no—
242Q8—1462no—
243Q8—1462no—
244Q8—1461no—
245D4—21no—
246D4—21no—
247D4—42no—
248D4—2922no—
249D4—1461no—
250D4—1461no—
251C2×C4—22no—
252C2×C4—21no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—2922no—
256C2×C4—2922no—
257C2×C4—734no—
258C2×C4—1462no—
259C2×C4—1461no—
260C2×C4D4×D7311yescharacteristic
261C2×C4D4×D7312yes—
262C2×C4C2×C22⋊D7312yes—
263C2×C4C23×D7311yescharacteristic
264C8—732no—
265C8—732no—
266C8C2×C22⋊D7314yes—
267C22—22no—
268C22—41no—
269C22—42no—
270C22—2921no—
271C22—2922no—
272C22#1455658712yes—
273C22C2×D4×D7311yescharacteristic
274C4—41no—
275C4—42no—
276C4—2921no—
277C4—2922no—
278C4—1464no—
279C4#1455658712yes—
280C4C2×D4×D7311yescharacteristic
281C4C22×C22⋊D7311yescharacteristic
282C2—22no—
283C2—81no—
284C2—5841no—
285C2C2×#1455658711yescharacteristic
286C2#1798940312yes—
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingC2×#137×C73C2
socleC22×C73C22×D4
hypercenterC2×#137D73
hypocenterC73#3156
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
1. C2×#14556624C2semidirect
3. C22×#11924018C2semidirect
4. #17989161C2semidirect
5. #17989158C2semidirect
6. #17988980C2semidirect
7. #17988978C2semidirect
8. #17988968C2semidirect
9. #17988965C2semidirect
10. #17988545C2semidirect
11. C2×#137×C73C2semidirect
144. C73#3156semidirect
146. C2×#137D73semidirect