Finite Group Databasebeta

← #22619735

Subgroups — #22619735

Order 9344.

376 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 135 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#17989140C211yesmaximal, characteristic
2C2×#14556556C211yesmaximal, characteristic
3#17988897C212yesmaximal, complemented
4#17988893C212yesmaximal, complemented
5#17988881C212yesmaximal, complemented
6#17988871C212yesmaximal, complemented
7#17988627C211yesmaximal, characteristic
8#17988610C211yesmaximal, characteristic
9#17988597C211yesmaximal, characteristic
10#17988595C211yesmaximal, characteristic
11#428×C73C211yesmaximal, characteristic
12C22×Dic146C2211yescharacteristic
13C2×#11924012C2211yescharacteristic
14#14556590C2211yescharacteristic
15#14556590C2211yescharacteristic
16#14556582C2211yescharacteristic
17#14556582C2211yescharacteristic
18#14556568—21no—
19#14556568—21no—
20C4×Dic146—21no—
21C4×Dic146—21no—
22#14556556—21no—
23#14556556—21no—
24#14556556C2212yes—
25#14556556C2212yes—
26#14556550C2211yescharacteristic
27C2×#11924007—21no—
28C2×C4×Dic73—21no—
29C2×C4×Dic73C2211yescharacteristic
30#14556524C2212yes—
31#14556522C2212yes—
32#14556520C2212yes—
33#14556520C2212yes—
34#14556516C2212yes—
35#14556516C2212yes—
36#14556514C2212yes—
37#14556514C2212yes—
38C2×M16×C73C2211yescharacteristic
39#117×C73C2211yescharacteristic
40C2×C4⋊C4×C73C2211yescharacteristic
41#107×C73C2212yes—
42#106×C73C2212yes—
43C2×Dic146—21no—
44C2×Dic146—22no—
45C2×Dic146—21no—
46C2×Dic146—21no—
47C2×Dic146Q814yescomplemented
48C2×Dic146C2312yes—
49C22×Dic73—21no—
50C22×Dic73D411yescharacteristic
51C22×Dic73D411yescharacteristic
52#11924012—22no—
53C2×#10596831C2312yes—
54C4⋊Dic73—21no—
55C4⋊Dic73—21no—
56C4⋊Dic73C2311yescharacteristic
57C4⋊Dic73C2311yescharacteristic
58#11924007—22no—
59#11924007—22no—
60#11924007—21no—
61#11924007—21no—
62#11924007—21no—
63#11924007—21no—
64C22⋊Dic73—21no—
65C4×Dic73—21no—
66C4×Dic73—22no—
67C4×Dic73—22no—
68C4×Dic73D411yescharacteristic
69C4×Dic73D411yescharacteristic
70C4×Dic73C2311yescharacteristic
71C4×Dic73C2311yescharacteristic
72C22×C4×C73—21no—
73C22×C4×C73C2311yescharacteristic
74M16×C73—22no—
75C2×C8×C73C2312yes—
76C4⋊C4×C73—21no—
77C4⋊C4×C73C2311yescharacteristic
78C4⋊C4×C73C2312yes—
79C4⋊C4×C73C2311yescharacteristic
80C22⋊C4×C73—21no—
81C42×C73—21no—
82C23×C73C2×D411yescharacteristic
83C2×C4×C73—21no—
84C2×C4×C73—21no—
85C2×C4×C73—22no—
86C2×C4×C73—42no—
87C2×C4×C73C2×D411yescharacteristic
88C2×C4×C73C2×Q812yes—
89C2×C4×C73#4112yes—
90C2×C4×C73C2411yescharacteristic
91C2×Dic73—24no—
92C2×Dic73—22no—
93C2×Dic73—22no—
94C2×Dic73—21no—
95C2×Dic73—21no—
96C2×Dic73—41no—
97C2×Dic73C2×D411yescharacteristic
98C2×Dic73C2×D411yescharacteristic
99C2×Dic73C2×D411yescharacteristic
100C2×Dic73C2×D411yescharacteristic
101Dic146—24no—
102Dic146—22no—
103Dic146—42no—
104Dic146—42no—
105Dic146C2×Q814yes—
106C8×C73—22no—
107#10596831—22no—
108C22×C73—21no—
109C22×C73—21no—
110C22×C73C22⋊Q812yes—
111C22×C73C22×D411yescharacteristic
112C4×C73—41no—
113C4×C73—41no—
114C4×C73—42no—
115C4×C73C22⋊Q812yes—
116C4×C73C22×Q811yescharacteristic
117C4×C73C2×#4111yescharacteristic
118Dic73—24no—
119Dic73—21no—
120Dic73—21no—
121Dic73—21no—
122Dic73—41no—
123Dic73—41no—
124Dic73#13712yes—
125C2×C73—22no—
126C2×C73C2×C22⋊Q811yescharacteristic
127C2×C73C2×#13711yescharacteristic
128C2×C73#57511yescharacteristic
129#3078—731nomaximal, Sylow
130C73#307811yescharacteristic, complemented, Sylow
131#533—731no—
132C2×C4×Q8—731no—
133#479—732no—
134#479—732no—
135#477—732no—
136#475—732no—
137#428—731no—
138#428D7311yescharacteristic
139#423—731no—
140#419—731no—
141#419—731no—
142C22×Q8—731no—
143C2×M16—731no—
144C2×M16C2×D7311yescharacteristic
145C4⋊Q8—731no—
146C4⋊Q8—731no—
147#125—731no—
148#125—731no—
149C22⋊Q8—1461no—
150C22⋊Q8—1461no—
151C4×Q8—732no—
152C4×Q8—732no—
153C4×Q8—1461no—
154C4×Q8—1461no—
155C4×Q8—1461no—
156C4×Q8—1461no—
157#117—731no—
158#117C2×D7311yescharacteristic
159C2×C4⋊C4—1461no—
160C2×C4⋊C4C2×D7311yescharacteristic
161C2×C42—731no—
162C2×C42—1461no—
163#107—732no—
164#107C2×D7312yes—
165#106—732no—
166#106C2×D7312yes—
167C4⋊C8—732no—
168C4⋊C8—732no—
169#103—732no—
170#103—732no—
171#103—732no—
172#103—732no—
173C2×Q8—734no—
174C2×Q8—732no—
175C2×Q8—1461no—
176C2×Q8—1461no—
177C2×Q8—1461no—
178C2×Q8—1462no—
179C22×C4—21no—
180C22×C4—731no—
181C22×C4—731no—
182C22×C4—1461no—
183C22×C4C22×D7311yescharacteristic
184M16—22no—
185M16—1462no—
186C2×C8—732no—
187C2×C8C22×D7312yes—
188C4⋊C4—21no—
189C4⋊C4—731no—
190C4⋊C4—731no—
191C4⋊C4—1462no—
192C4⋊C4—1462no—
193C4⋊C4—1461no—
194C4⋊C4—1461no—
195C4⋊C4—1461no—
196C4⋊C4—1461no—
197C4⋊C4—1461no—
198C4⋊C4—1461no—
199C4⋊C4C22×D7311yescharacteristic
200C4⋊C4C22×D7311yescharacteristic
201C4⋊C4C22×D7312yes—
202C22⋊C4—21no—
203C22⋊C4—1461no—
204C42—21no—
205C42—731no—
206C42—731no—
207C42—731no—
208C42—731no—
209C42—1462no—
210C42—1462no—
211C42—1461no—
212C23D4×D7311yescharacteristic
213Q8—2922no—
214Q8—2922no—
215Q8—734no—
216Q8—1464no—
217Q8—1462no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—42no—
222C2×C4—2921no—
223C2×C4—731no—
224C2×C4—731no—
225C2×C4—731no—
226C2×C4—731no—
227C2×C4—1461no—
228C2×C4—1461no—
229C2×C4—1462no—
230C2×C4—1464no—
231C2×C4—1462no—
232C2×C4D4×D7311yescharacteristic
233C2×C4Q8×D7312yes—
234C2×C4#1192402812yes—
235C2×C4C23×D7311yescharacteristic
236C8—22no—
237C8—1462no—
238C22—21no—
239C22—21no—
240C22#1455656912yes—
241C22C2×D4×D7311yescharacteristic
242C4—41no—
243C4—42no—
244C4—41no—
245C4—2921no—
246C4—2921no—
247C4—732no—
248C4—1461no—
249C4—1461no—
250C4—1461no—
251C4—1464no—
252C4#1455656912yes—
253C4C2×Q8×D7311yescharacteristic
254C4C2×#1192402811yescharacteristic
255C2—22no—
256C2C2×#1455656911yescharacteristic
257C2#137×D7311yescharacteristic
258C2#1798938311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#428×C73C2
socleC22×C73C22×D4
hypercenter#428D73
hypocenterC73#3078
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
3. #17988897C2semidirect
4. #17988893C2semidirect
5. #17988881C2semidirect
6. #17988871C2semidirect
47. C2×Dic146Q8semidirect
130. C73#3078semidirect