Finite Group Databasebeta

← #22621057

Subgroups — #22621057

Order 9344.

404 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 123 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
1#17989132C211yesmaximal, characteristic
2C2×#14556590C211yesmaximal, characteristic, complemented
3#17988984C212yesmaximal, complemented
4#17988932C212yesmaximal, complemented
5#17988906C211yesmaximal, characteristic, complemented
6#17988905C211yesmaximal, characteristic, complemented
7#17988903C211yesmaximal, characteristic, complemented
8#17988876C212yesmaximal, complemented
9#17988875C212yesmaximal, complemented
10#17988637C211yesmaximal, characteristic, complemented
11#481×C73C211yesmaximal, characteristic, complemented
12C2×#11924027—21no—
13C22×Dic146—21no—
14#14556590—21no—
15#14556590—21no—
16#14556590C2212yes—
17#14556590C2212yes—
18#14556590C2211yescharacteristic
19#14556587C2211yescharacteristic
20#14556577—21no—
21#14556565C2211yescharacteristic
22#14556563—21no—
23D4×Dic73C2211yescharacteristic
24#14556553C2211yescharacteristic
25#14556551—21no—
26C2×C4⋊Dic73C2211yescharacteristic
27C2×#11924007—21no—
28C2×C4×Dic73C2211yescharacteristic
29#14556523C2212yes—
30#14556522C2212yes—
31#14556522C2212yes—
32#14556520C2212yes—
33#14556513C2212yes—
34#14556512C2212yes—
35#14556511C2212yes—
36C22⋊#10596831C2211yescharacteristic
37C8×Dic73C2212yes—
38#121×C73C2211yescharacteristic
39C2×C4⋊C4×C73C2211yescharacteristic
40#106×C73C2212yes—
41#102×C73C2212yes—
42C22⋊C8×C73C2211yescharacteristic
43#11924027—44no—
44C2×Dic146—21no—
45C2×Dic146—22no—
46C2×Dic146—22no—
47C2×Dic146—44no—
48C2×D292C2311yescharacteristic
49C2×C22⋊D73—21no—
50C2×C22⋊D73—21no—
51C2×C22⋊D73—21no—
52C22×Dic73—21no—
53C22×Dic73—21no—
54C22×Dic73D411yescharacteristic
55C22×Dic73D411yescharacteristic
56C2×C4×D73—21no—
57C2×#10596831C2312yes—
58C4⋊Dic73—21no—
59C4⋊Dic73C2312yes—
60C4⋊Dic73C2311yescharacteristic
61#11924007—22no—
62#11924007—22no—
63#11924007—21no—
64C22⋊Dic73—21no—
65#11924005—21no—
66#11924005—21no—
67C4×Dic73D411yescharacteristic
68C4×Dic73D411yescharacteristic
69C4×Dic73C2311yescharacteristic
70C4×Dic73C2311yescharacteristic
71C2×D4×C73—21no—
72C2×D4×C73C2311yescharacteristic
73C22×C4×C73—21no—
74C22×C4×C73C2311yescharacteristic
75C2×C8×C73C2312yes—
76C4⋊C4×C73—21no—
77C4⋊C4×C73C2312yes—
78C4⋊C4×C73C2311yescharacteristic
79C22⋊C4×C73—21no—
80C23×C73—21no—
81C23×C73C2×D411yescharacteristic
82C22×D73—21no—
83D4×C73—22no—
84D4×C73—42no—
85C2×C4×C73—22no—
86C2×C4×C73—21no—
87C2×C4×C73—22no—
88C2×C4×C73—42no—
89C2×C4×C73C2×D411yescharacteristic
90C2×C4×C73C2411yescharacteristic
91C22⋊D73—42no—
92C22⋊D73—42no—
93C22⋊D73—42no—
94C2×Dic73—22no—
95C2×Dic73—21no—
96C2×Dic73—22no—
97C2×Dic73—42no—
98C2×Dic73—42no—
99C2×Dic73SD1614yes—
100C2×Dic73C2×D411yescharacteristic
101C2×Dic73C2×D411yescharacteristic
102C2×Dic73C2×D411yescharacteristic
103C2×Dic73C2×D411yescharacteristic
104D292—22no—
105C4×D73—42no—
106Dic146—44no—
107Dic146—42no—
108Dic146—44no—
109C8×C73—22no—
110#10596831—22no—
111C22×C73—21no—
112C22×C73—21no—
113C22×C73—41no—
114C22×C73—41no—
115C22×C73—41no—
116C22×C73C2×SD1612yes—
117C22×C73C22×D411yescharacteristic
118C2×D73—41no—
119C2×D73—41no—
120C2×D73—41no—
121C4×C73—21no—
122C4×C73—41no—
123C4×C73—42no—
124C4×C732−1+412yes—
125Dic73—21no—
126Dic73—41no—
127Dic73—42no—
128Dic73C2×SD1612yes—
129Dic73C2×SD1612yes—
130Dic73AGL(1,ℤ/8)12yes—
131C2×C73—22no—
132C2×C73—81no—
133C2×C73#53611yescharacteristic
134C2×C73C22×SD1611yescharacteristic
135C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
136D73—81no—
137#3227—731nomaximal, Sylow
138C73#322711yescharacteristic, complemented, Sylow
139#532—731no—
140C2×C4⋊Q8—731no—
141#498—732no—
142#486—732no—
143#481—731no—
144#481—731no—
145#481—731no—
146#481D7311yescharacteristic, complemented
147#476—732no—
148#476—732no—
149#431—731no—
150C2×#41—1461no—
151C22×Q8—1461no—
152C4⋊Q8—732no—
153C4⋊Q8—732no—
154C4⋊Q8—731no—
155C4⋊Q8—1461no—
156C4⋊Q8—1461no—
157#127—731no—
158#124—1461no—
159#121—731no—
160#121—1461no—
161#121C2×D7311yescharacteristic
162C4×D4—731no—
163C4×D4—731no—
164C4×D4—1461no—
165C2×C4⋊C4—731no—
166C2×C4⋊C4—1461no—
167C2×C4⋊C4C2×D7311yescharacteristic
168C2×C42—731no—
169#106—732no—
170#106—732no—
171#106—732no—
172#106C2×D7312yes—
173C4⋊C8—732no—
174#102—732no—
175#102—732no—
176#102—732no—
177#102C2×D7312yes—
178C22⋊C8—731no—
179C22⋊C8C2×D7311yescharacteristic
180C4×C8—732no—
181#41—2924no—
182C2×Q8—2924no—
183C2×Q8—1461no—
184C2×Q8—1462no—
185C2×Q8—1462no—
186C2×D4—21no—
187C2×D4—731no—
188C2×D4—1461no—
189C2×D4—1461no—
190C2×D4—1461no—
191C2×D4C22×D7311yescharacteristic
192C22×C4—21no—
193C22×C4—731no—
194C22×C4—731no—
195C22×C4—1461no—
196C22×C4—1461no—
197C22×C4—1461no—
198C22×C4C22×D7311yescharacteristic
199C2×C8—732no—
200C2×C8C22×D7312yes—
201C4⋊C4—21no—
202C4⋊C4—732no—
203C4⋊C4—731no—
204C4⋊C4—1462no—
205C4⋊C4—1462no—
206C4⋊C4—1461no—
207C4⋊C4—1461no—
208C4⋊C4C22×D7312yes—
209C4⋊C4C22×D7311yescharacteristic
210C22⋊C4—21no—
211C22⋊C4—1461no—
212C22⋊C4—1461no—
213C22⋊C4—1461no—
214C42—731no—
215C42—731no—
216C42—731no—
217C42—731no—
218C23—21no—
219C23—1461no—
220C23D4×D7311yescharacteristic
221Q8—2924no—
222Q8—2922no—
223Q8—2924no—
224D4—22no—
225D4—42no—
226D4—2922no—
227D4—2922no—
228D4—2922no—
229D4—1462no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—42no—
234C2×C4—2922no—
235C2×C4—2922no—
236C2×C4—2922no—
237C2×C4—734no—
238C2×C4—731no—
239C2×C4—731no—
240C2×C4—731no—
241C2×C4—731no—
242C2×C4—1461no—
243C2×C4—1462no—
244C2×C4—1462no—
245C2×C4D4×D7311yescharacteristic
246C2×C4C23×D7311yescharacteristic
247C8—22no—
248C8—1462no—
249C22—21no—
250C22—21no—
251C22—41no—
252C22—41no—
253C22—41no—
254C22—2921no—
255C22—2921no—
256C22—2921no—
257C22SD16×D7312yes—
258C22C2×D4×D7311yescharacteristic
259C4—21no—
260C4—41no—
261C4—42no—
262C4—2921no—
263C4—2922no—
264C4—732no—
265C4—732no—
266C4—732no—
267C4—1461no—
268C4#1455663812yes—
269C2—22no—
270C2—81no—
271C2—5841no—
272C2#1798915911yescharacteristic
273C2C2×SD16×D7311yescharacteristic
274C2AGL(1,ℤ/8)×D7311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#481×C73C2
socleC22×C73C22×D4
hypercenter#481D73
hypocenterC73#3227
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. C2×#14556590C2semidirect
3. #17988984C2semidirect
4. #17988932C2semidirect
5. #17988906C2semidirect
6. #17988905C2semidirect
7. #17988903C2semidirect
8. #17988876C2semidirect
9. #17988875C2semidirect
10. #17988637C2semidirect
11. #481×C73C2semidirect
138. C73#3227semidirect
146. #481D73semidirect