Finite Group Databasebeta

← #22625946

Subgroups — #22625946

Order 9344.

360 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 78 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×D73⋊M16C211yesmaximal, characteristic
2C2×#14556654C212yesmaximal, complemented
3#17989529C211yesmaximal, characteristic
4#17989460C212yesmaximal, complemented
5C22⋊Q8×D73C211yesmaximal, characteristic
6C2×#11924038—21no—
7D73⋊M16—24no—
8C2×#11924037—21no—
9C2×#11924036C2212yes—
10C2×C4⋊#64408C2212yes—
11C2×C22⋊#64408—21no—
12#14556654—24no—
13(C2×#64408)⋊C4—21no—
14C2×Q8×D73C2211yescharacteristic
15C22×C4×D73C2211yescharacteristic
16#14556571C411yescharacteristic, complemented
17#14556570C411yescharacteristic, complemented
18#14556569—21no—
19#14556568—21no—
20#14556567C411yescharacteristic, complemented
21C4⋊C4×D73—21no—
22C4⋊C4×D73C2211yescharacteristic
23C22⋊C4×D73—21no—
24C22⋊Q8×C73C411yescharacteristic, complemented
25C22×#64408—22no—
26#11924038—24no—
27#11924037—24no—
28#11924036—22no—
29#11924036D414yes—
30C2×#10596833—22no—
31C4⋊#64408—22no—
32C4⋊#64408—22no—
33C22⋊#64408—42no—
34C23×D73D411yescharacteristic
35C2×Dic146—21no—
36C2×Dic146C2×C411yescharacteristic
37Q8×D73—22no—
38Q8×D73—22no—
39C22×Dic73D411yescharacteristic
40C2×C4×D73—22no—
41C2×C4×D73—22no—
42C2×C4×D73—21no—
43C2×C4×D73—21no—
44C2×C4×D73C2×C411yescharacteristic
45C2×C4×D73D411yescharacteristic
46C2×C4×D73D411yescharacteristic
47C2×C4×D73C2311yescharacteristic
48C4⋊Dic73—21no—
49C4⋊Dic73C2×C411yescharacteristic
50#11924007—21no—
51#11924007—21no—
52#11924007—21no—
53C22⋊Dic73—21no—
54#11924005—21no—
55#11924005—21no—
56C2×Q8×C73C2×C411yescharacteristic
57C22×C4×C73C2×C411yescharacteristic
58C4⋊C4×C73—21no—
59C4⋊C4×C73C2×C411yescharacteristic
60C22⋊C4×C73—21no—
61C23×C73C22⋊C411yescharacteristic
62C22×D73—22no—
63C22×D73—21no—
64C22×D73—21no—
65C22×D73—22no—
66C22×D73C22⋊C411yescharacteristic
67C22×D73C2×D411yescharacteristic
68C2×#64408—42no—
69C2×#64408—42no—
70C2×#64408—42no—
71Q8×C73—22no—
72C2×C4×C73—22no—
73C2×C4×C73—21no—
74C2×C4×C73—21no—
75C2×C4×C73C22⋊C411yescharacteristic
76C2×C4×C73C22×C411yescharacteristic
77C2×Dic73—21no—
78C2×Dic73—21no—
79C2×Dic73—21no—
80C2×Dic73—21no—
81C2×Dic73C22⋊C411yescharacteristic
82C2×Dic73C2×D411yescharacteristic
83C4×D73—22no—
84C4×D73—22no—
85C4×D73—21no—
86C4×D73—21no—
87C4×D73—42no—
88C4×D73—41no—
89C4×D73—41no—
90C4×D73C2×D412yes—
91C4×D73#4112yes—
92Dic146—22no—
93Dic146—41no—
94Dic146—41no—
95#10596833—24no—
96C22×C73—21no—
97C22×C73—21no—
98C22×C73—21no—
99C22×C73C2×C22⋊C411yescharacteristic
100C2×D73—21no—
101C2×D73—21no—
102C2×D73—21no—
103C2×D73—42no—
104C2×D73—42no—
105C2×D73#12112yes—
106C2×D73AGL(1,ℤ/8)11yescharacteristic
107C2×D73#13712yes—
108C2×D73#13711yescharacteristic
109#64408—82no—
110C4×C73—21no—
111C4×C73—41no—
112C4×C73—41no—
113C4×C73C4×D412yes—
114Dic73—21no—
115Dic73—41no—
116Dic73—41no—
117Dic73#12011yescharacteristic
118Dic73#12311yescharacteristic
119C2×C73—41no—
120C2×C73#38611yescharacteristic
121C2×C73#41711yescharacteristic
122C2×C73#41911yescharacteristic
123D73—41no—
124D73#46812yes—
125D73#47012yes—
126#1894—731nomaximal, Sylow
127C73#189411yescharacteristic, complemented, Sylow
128C22×M16—731no—
129C2×C22⋊Q8—731no—
130C2×#103—732no—
131#380—731no—
132#340—732no—
133C22×Q8—731no—
134C23×C4—731no—
135C2×M16—1464no—
136C2×M16—1461no—
137C2×M16—1461no—
138C22×C8—732no—
139C22⋊Q8—731no—
140C22⋊Q8—731no—
141C22⋊Q8—731no—
142C22⋊Q8—1461no—
143C22⋊Q8—1461no—
144C22⋊Q8#6440811yescharacteristic, complemented
145C2×C4⋊C4—731no—
146C2×C4⋊C4—732no—
147C2×C4⋊C4—1461no—
148C2×C22⋊C4—1461no—
149C2×C22⋊C4—1461no—
150#103—1464no—
151#95—1461no—
152C24—731no—
153C2×Q8—731no—
154C2×Q8—1461no—
155C2×Q8—1462no—
156C2×Q8—1462no—
157C2×Q8C2×#6440811yescharacteristic
158C22×C4—731no—
159C22×C4—731no—
160C22×C4—731no—
161C22×C4—731no—
162C22×C4—731no—
163C22×C4—1461no—
164C22×C4—1461no—
165C22×C4—1462no—
166C22×C4—1462no—
167C22×C4—1462no—
168C22×C4C2×#6440811yescharacteristic
169M16—1464no—
170M16—1464no—
171C2×C8—734no—
172C2×C8—1462no—
173C2×C8—1462no—
174C4⋊C4—21no—
175C4⋊C4—731no—
176C4⋊C4—1461no—
177C4⋊C4—1461no—
178C4⋊C4—1461no—
179C4⋊C4—1462no—
180C4⋊C4—1462no—
181C4⋊C4—1461no—
182C4⋊C4C2×#6440811yescharacteristic
183C22⋊C4—21no—
184C22⋊C4—2922no—
185C22⋊C4—1461no—
186C22⋊C4—1461no—
187C22⋊C4—1461no—
188C23—731no—
189C23—731no—
190C23—1461no—
191C23—1462no—
192C23—1461no—
193C23—1462no—
194C23C22⋊#6440811yescharacteristic
195Q8—22no—
196Q8—2921no—
197Q8—2921no—
198Q8—1462no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—2922no—
203C2×C4—2921no—
204C2×C4—2921no—
205C2×C4—2922no—
206C2×C4—2922no—
207C2×C4—2922no—
208C2×C4—731no—
209C2×C4—732no—
210C2×C4—732no—
211C2×C4—731no—
212C2×C4—1461no—
213C2×C4—1461no—
214C2×C4—1462no—
215C2×C4—1461no—
216C2×C4—1461no—
217C2×C4—1461no—
218C2×C4—1461no—
219C2×C4—1462no—
220C2×C4C22⋊#6440811yescharacteristic
221C2×C4C22×#6440811yescharacteristic
222C8—1464no—
223C22—21no—
224C22—21no—
225C22—21no—
226C22—2922no—
227C22—2922no—
228C22—732no—
229C22—731no—
230C22—731no—
231C22—732no—
232C22—1461no—
233C22—1461no—
234C22—1461no—
235C22C2×C22⋊#6440811yescharacteristic
236C4—21no—
237C4—41no—
238C4—41no—
239C4—2921no—
240C4—2921no—
241C4—5842no—
242C4—731no—
243C4—731no—
244C4—1461no—
245C4D4×#6440812yes—
246C2—41no—
247C2—2921no—
248C2—732no—
249C2—732no—
250C2#1798953511yescharacteristic
251C2#1798957811yescharacteristic
252C2#1798958011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC22⋊Q8×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC22⋊Q8#64408
hypocenterC73#1894
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#14556654C2semidirect
4. #17989460C2semidirect
16. #14556571C4semidirect
17. #14556570C4semidirect
20. #14556567C4semidirect
24. C22⋊Q8×C73C4semidirect
127. C73#1894semidirect
144. C22⋊Q8#64408semidirect