Finite Group Databasebeta

← #22610396

Subgroups — #22610396

Order 9344.

338 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 85 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×M16×D73C211yesmaximal, characteristic
2C2×#14556567C211yesmaximal, characteristic
3C2×#14556510C211yesmaximal, characteristic, complemented
4#17988550C211yesmaximal, characteristic
5#17988355C211yesmaximal, characteristic, complemented
6#17988355C211yesmaximal, characteristic, complemented
7C2×#101×C73C211yesmaximal, characteristic, complemented
8C22×C4×D73C2211yescharacteristic
9C2×#11924012C2211yescharacteristic
10C2×#11924012C2211yescharacteristic
11C2×#11924011—21no—
12M16×D73—22no—
13M16×D73—22no—
14C2×C8×D73—21no—
15#14556567—21no—
16#14556567—21no—
17#14556567—21no—
18#14556567—21no—
19C2×C4⋊Dic73C2211yescharacteristic
20C2×#11924007C412yes—
21C2×#11924005C412yes—
22#14556510—22no—
23#14556503—21no—
24#14556503—21no—
25C22×Q8×C73C2211yescharacteristic
26C2×M16×C73C2211yescharacteristic
27C2×M16×C73C2211yescharacteristic
28#101×C73—22no—
29C23×D73C2×C411yescharacteristic
30C22×Dic73C2×C411yescharacteristic
31C22×Dic73C2×C412yes—
32C2×C4×D73—21no—
33C2×C4×D73—21no—
34C2×C4×D73—21no—
35C2×C4×D73—21no—
36C2×C4×D73D411yescharacteristic
37C2×C4×D73D411yescharacteristic
38C2×C4×D73D411yescharacteristic
39C2×C4×D73D411yescharacteristic
40#11924012—21no—
41#11924012—21no—
42#11924012—21no—
43#11924012D412yes—
44#11924011—24no—
45C2×#10596831—21no—
46C2×#10596831—21no—
47C8×D73—24no—
48C4⋊Dic73—21no—
49C4⋊Dic73—21no—
50#11924007—22no—
51#11924007—22no—
52#11924005—22no—
53#11924005—22no—
54C2×Q8×C73—21no—
55C2×Q8×C73—21no—
56C2×Q8×C73—21no—
57C2×Q8×C73—21no—
58C2×Q8×C73—21no—
59C2×Q8×C73—21no—
60C22×C4×C73C2×C412yes—
61C22×C4×C73C2311yescharacteristic
62M16×C73—21no—
63M16×C73—21no—
64M16×C73—21no—
65M16×C73D412yes—
66C2×C8×C73—21no—
67C2×C8×C73—21no—
68C23×C73C22×C411yescharacteristic
69C22×D73—21no—
70C22×D73—21no—
71C22×D73—22no—
72C22×D73—41no—
73C22×D73C22⋊C411yescharacteristic
74C22×D73C22⋊C411yescharacteristic
75Q8×C73—41no—
76Q8×C73—41no—
77Q8×C73—41no—
78Q8×C73—41no—
79C2×C4×C73—22no—
80C2×C4×C73—22no—
81C2×C4×C73—22no—
82C2×C4×C73C2×D411yescharacteristic
83C2×C4×C73C2×D411yescharacteristic
84C2×C4×C73C2×D411yescharacteristic
85C2×C4×C73C2×D411yescharacteristic
86C2×C4×C73#4111yescharacteristic
87C2×C4×C73#4111yescharacteristic
88C2×Dic73—21no—
89C2×Dic73—21no—
90C2×Dic73—22no—
91C2×Dic73—42no—
92C2×Dic73C22⋊C411yescharacteristic
93C2×Dic73C22⋊C411yescharacteristic
94C4×D73—21no—
95C4×D73—21no—
96C4×D73—21no—
97C4×D73—21no—
98C4×D73—21no—
99C4×D73—21no—
100C4×D73—21no—
101C4×D73—21no—
102C8×C73—22no—
103C8×C73—41no—
104#10596831—22no—
105#10596831—41no—
106C22×C73—21no—
107C22×C73—21no—
108C22×C73C2×C22⋊C411yescharacteristic
109C22×C73C4×D411yescharacteristic
110C22×C73C4×D411yescharacteristic
111C2×D73—21no—
112C2×D73—21no—
113C2×D73—21no—
114C2×D73—21no—
115C2×D73—21no—
116C2×D73—42no—
117C2×D73—42no—
118C2×D73#10112yescomplemented
119C4×C73—42no—
120C4×C73#12011yescharacteristic
121C4×C73#12111yescharacteristic
122C4×C73#12111yescharacteristic
123C4×C73#12311yescharacteristic
124Dic73—21no—
125Dic73—21no—
126Dic73—42no—
127C2×C73—21no—
128C2×C73—21no—
129C2×C73#38611yescharacteristic
130C2×C73C2×#10111yescharacteristic
131C2×C73#41311yescharacteristic
132D73—22no—
133D73—41no—
134#1901—731nomaximal, Sylow
135C73#190111yescharacteristic, complemented, Sylow
136C22×M16—731no—
137C2×C22⋊Q8—731no—
138C2×#101—731no—
139C2×#101D7311yescharacteristic, complemented
140#407—731no—
141#343—731no—
142#343—731no—
143C22×Q8C2×D7311yescharacteristic
144C23×C4—731no—
145C2×M16—731no—
146C2×M16—731no—
147C2×M16—1461no—
148C2×M16—1462no—
149C2×M16—1462no—
150C2×M16C2×D7311yescharacteristic
151C2×M16C2×D7311yescharacteristic
152C22×C8—1461no—
153C22⋊Q8—1461no—
154C22⋊Q8—1461no—
155C22⋊Q8—1461no—
156C22⋊Q8—1461no—
157C2×C4⋊C4—732no—
158C2×C4⋊C4—731no—
159C2×C22⋊C4—732no—
160#101—22no—
161#101—1462no—
162C22⋊C8—1461no—
163C22⋊C8—1461no—
164C24—731no—
165C2×Q8—21no—
166C2×Q8—21no—
167C2×Q8—21no—
168C2×Q8—21no—
169C2×Q8—21no—
170C2×Q8—21no—
171C22×C4—732no—
172C22×C4—731no—
173C22×C4—731no—
174C22×C4—731no—
175C22×C4—731no—
176C22×C4—731no—
177C22×C4—1461no—
178C22×C4—1461no—
179C22×C4—1461no—
180C22×C4—1461no—
181C22×C4C4×D7312yes—
182C22×C4C22×D7311yescharacteristic
183M16—21no—
184M16—21no—
185M16—21no—
186M16—732no—
187M16—1464no—
188M16—1461no—
189M16—1461no—
190M16—1461no—
191M16C22⋊D7312yes—
192C2×C8—21no—
193C2×C8—21no—
194C2×C8—1464no—
195C2×C8—1461no—
196C2×C8—1461no—
197C4⋊C4—1462no—
198C4⋊C4—1462no—
199C4⋊C4—1461no—
200C4⋊C4—1461no—
201C22⋊C4—1462no—
202C22⋊C4—1462no—
203C23—2921no—
204C23—731no—
205C23—731no—
206C23—1462no—
207C23—1461no—
208C23—1461no—
209C23C2×C4×D7311yescharacteristic
210Q8—41no—
211Q8—41no—
212Q8—41no—
213Q8—41no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—2922no—
218C2×C4—731no—
219C2×C4—731no—
220C2×C4—1462no—
221C2×C4—1461no—
222C2×C4—1461no—
223C2×C4—1461no—
224C2×C4—1461no—
225C2×C4—1461no—
226C2×C4—1461no—
227C2×C4—1461no—
228C2×C4—1461no—
229C2×C4—1461no—
230C2×C4—1461no—
231C2×C4D4×D7311yescharacteristic
232C2×C4D4×D7311yescharacteristic
233C2×C4D4×D7311yescharacteristic
234C2×C4C2×C22⋊D7311yescharacteristic
235C2×C4#1192402711yescharacteristic
236C2×C4#1192402811yescharacteristic
237C8—22no—
238C8—41no—
239C8—2921no—
240C8—1462no—
241C22—21no—
242C22—21no—
243C22—2922no—
244C22—2922no—
245C22—732no—
246C22—1461no—
247C22—1461no—
248C22—1461no—
249C22—1461no—
250C22—1461no—
251C22C22⋊C4×D7311yescharacteristic
252C22#1455655111yescharacteristic
253C22C4×C22⋊D7311yescharacteristic
254C4—42no—
255C4—2922no—
256C4—1461no—
257C4—1461no—
258C4#1455655911yescharacteristic
259C4#1455656211yescharacteristic
260C4#1455656411yescharacteristic
261C4#1455657311yescharacteristic
262C2—21no—
263C2—21no—
264C2—2921no—
265C2—1462no—
266C2#1798846311yescharacteristic
267C2#101×D7311yescharacteristic
268C2#1798857011yescharacteristic
subgroupG/H
centerC22C22⋊C4×D73
commutatorC23×C73C22×C4
FrattiniC22×C4C22×D73
FittingC2×#101×C73C2
socleC22×C73C2×C22⋊C4
hypercenterC2×#101D73
hypocenterC73#1901
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
3. C2×#14556510C2semidirect
5. #17988355C2semidirect
6. #17988355C2semidirect
7. C2×#101×C73C2semidirect
118. C2×D73#101semidirect
135. C73#1901semidirect
139. C2×#101D73semidirect