Finite Group Databasebeta

← D73⋊#352 #22626180

Subgroups — D73⋊#352 #22626180

Order 9344.

278 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 54 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
1D73⋊#100C211yesmaximal, characteristic
2D73⋊#99C211yesmaximal, characteristic
3#17989490C212yesmaximal, complemented
4#17989489C212yesmaximal, complemented
5#123×D73C211yesmaximal, characteristic
6D73⋊M16—21no—
7C2×C22⋊#64408—21no—
8#14556651—21no—
9#14556651C2212yes—
10#14556650—21no—
11#14556649C2212yes—
12C2×D4×D73C2211yescharacteristic
13C22×C4×D73C411yescharacteristic, complemented
14#14556576—21no—
15#14556575C2211yescharacteristic
16#14556574C2211yescharacteristic
17#14556573—21no—
18#14556572C411yescharacteristic, complemented
19C4⋊C4×D73—21no—
20C22⋊C4×D73—21no—
21C22⋊C4×D73C411yescharacteristic, complemented
22#123×C73C411yescharacteristic, complemented
23C22×#64408—41no—
24#11924038—41no—
25#11924037—22no—
26#11924036—41no—
27C22⋊#64408—22no—
28C22⋊#64408—41no—
29C23×D73C2×C411yescharacteristic
30C23×D73D411yescharacteristic
31C2×D292D411yescharacteristic
32C2×C22⋊D73D411yescharacteristic
33C2×C22⋊D73C2311yescharacteristic
34D4×D73—41no—
35D4×D73—41no—
36C22×Dic73C2×C411yescharacteristic, complemented
37C2×C4×D73—21no—
38C2×C4×D73—21no—
39C2×C4×D73—21no—
40C2×C4×D73—41no—
41C2×C4×D73—41no—
42C2×C4×D73D411yescharacteristic
43C4⋊Dic73—21no—
44#11924007—21no—
45#11924007—21no—
46C22⋊Dic73—21no—
47C22⋊Dic73C2×C411yescharacteristic, complemented
48#11924005—21no—
49#11924005—21no—
50#11924005—21no—
51C2×D4×C73C2×C411yescharacteristic
52C22×C4×C73C2×C411yescharacteristic, complemented
53C4⋊C4×C73—21no—
54C22⋊C4×C73—21no—
55C22⋊C4×C73C2×C411yescharacteristic, complemented
56C23×C73C22⋊C411yescharacteristic
57C23×C73C22×C411yescharacteristic
58C22×D73—21no—
59C22×D73—21no—
60C22×D73—21no—
61C22×D73—21no—
62C22×D73—42no—
63C22×D73—42no—
64C22×D73C22⋊C411yescharacteristic
65C22×D73C22⋊C411yescharacteristic
66C22×D73C2×D411yescharacteristic
67C2×#64408—42no—
68C2×#64408—82no—
69D4×C73—41no—
70C2×C4×C73—21no—
71C2×C4×C73—21no—
72C2×C4×C73—41no—
73C2×C4×C73C22⋊C411yescharacteristic
74C22⋊D73—41no—
75C22⋊D73—41no—
76C2×Dic73—21no—
77C2×Dic73—21no—
78C2×Dic73—41no—
79C2×Dic73C2×D411yescharacteristic
80D292—41no—
81C4×D73—21no—
82C4×D73—21no—
83C4×D73—42no—
84C4×D73—42no—
85C4×D73—41no—
86C4×D73—41no—
87#10596833—42no—
88C22×C73—21no—
89C22×C73—21no—
90C22×C73—41no—
91C22×C73—41no—
92C22×C73C2×C22⋊C411yescharacteristic
93C2×D73—22no—
94C2×D73—21no—
95C2×D73—21no—
96C2×D73—42no—
97C2×D73—42no—
98C2×D73—42no—
99C2×D73—41no—
100C2×D73—41no—
101C2×D73—81no—
102C2×D73#9911yescharacteristic
103C2×D73#9911yescharacteristic
104#64408—82no—
105C4×C73—21no—
106C4×C73—41no—
107C4×C73—41no—
108Dic73—21no—
109Dic73—41no—
110Dic73—41no—
111C2×C73—21no—
112C2×C73—41no—
113C2×C73—41no—
114C2×C73C2×#9911yescharacteristic
115D73—21no—
116D73—41no—
117D73—41no—
118D73#35212yescomplemented
119C2×#352—731nomaximal, Sylow
120C73C2×#35211yescharacteristic, complemented, Sylow
121C2×#123—731no—
122C2×#100—731no—
123C2×#99—731no—
124#352—732no—
125#352—732no—
126C22×D4—731no—
127C23×C4—731no—
128C2×M16—1461no—
129#123—731no—
130#123—731no—
131#123—731no—
132#123—1461no—
133#123—1461no—
134#123#6440811yescharacteristic, complemented
135C2×C4⋊C4—1461no—
136C2×C22⋊C4—731no—
137C2×C22⋊C4—1461no—
138C2×C22⋊C4—1461no—
139#100—732no—
140#100—1461no—
141#99—732no—
142#99—1461no—
143C24—731no—
144C24—731no—
145C2×D4—2921no—
146C2×D4—2921no—
147C2×D4—731no—
148C2×D4—731no—
149C2×D4—731no—
150C2×D4C2×#6440811yescharacteristic
151C22×C4—2921no—
152C22×C4—2921no—
153C22×C4—2921no—
154C22×C4—731no—
155C22×C4—731no—
156C22×C4—1461no—
157C22×C4—1461no—
158C22×C4—1461no—
159C22×C4C2×#6440811yescharacteristic, complemented
160M16—2921no—
161M16—1462no—
162C2×C8—2921no—
163C4⋊C4—21no—
164C4⋊C4—1461no—
165C4⋊C4—1461no—
166C4⋊C4—1461no—
167C22⋊C4—21no—
168C22⋊C4—2921no—
169C22⋊C4—731no—
170C22⋊C4—1461no—
171C22⋊C4—1461no—
172C22⋊C4—1461no—
173C22⋊C4—1462no—
174C22⋊C4—1461no—
175C22⋊C4C2×#6440811yescharacteristic, complemented
176C23—2922no—
177C23—2922no—
178C23—731no—
179C23—731no—
180C23—731no—
181C23—1461no—
182C23—1461no—
183C23—1461no—
184C23—1461no—
185C23C22⋊#6440811yescharacteristic
186C23C22×#6440811yescharacteristic
187D4—41no—
188D4—2921no—
189D4—2921no—
190D4—2921no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—41no—
194C2×C4—2921no—
195C2×C4—2921no—
196C2×C4—2922no—
197C2×C4—2922no—
198C2×C4—2921no—
199C2×C4—2922no—
200C2×C4—5842no—
201C2×C4—731no—
202C2×C4—1461no—
203C2×C4—1461no—
204C2×C4—1461no—
205C2×C4—1461no—
206C2×C4C22⋊#6440811yescharacteristic
207C8—2922no—
208C22—21no—
209C22—21no—
210C22—41no—
211C22—41no—
212C22—2921no—
213C22—2921no—
214C22—2922no—
215C22—2922no—
216C22—2922no—
217C22—5841no—
218C22—731no—
219C22—731no—
220C22—1462no—
221C22—1461no—
222C22—1461no—
223C22C2×C22⋊#6440811yescharacteristic
224C4—21no—
225C4—41no—
226C4—41no—
227C4—2921no—
228C4—2921no—
229C4—5842no—
230C4—1461no—
231C2—21no—
232C2—41no—
233C2—41no—
234C2—2921no—
235C2—2921no—
236C2—732no—
237C2—1461no—
238C2D73⋊#9911yescharacteristic
subgroupG/H
centerC2D73⋊#99
commutatorC23×C73C22×C4
FrattiniC23C22×#64408
Fitting#123×C73C4
socleC2×C73C2×#99
hypercenter#123#64408
hypocenterC73C2×#352
LCSG ▷ C23×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #123

Complements

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

NH ≅ G/Ntype
3. #17989490C2semidirect
4. #17989489C2semidirect
13. C22×C4×D73C4semidirect
18. #14556572C4semidirect
21. C22⋊C4×D73C4semidirect
22. #123×C73C4semidirect
36. C22×Dic73C2×C4semidirect
47. C22⋊Dic73C2×C4semidirect
52. C22×C4×C73C2×C4semidirect
55. C22⋊C4×C73C2×C4semidirect
118. D73#352semidirect
120. C73C2×#352semidirect
134. #123#64408semidirect
159. C22×C4C2×#64408semidirect
175. C22⋊C4C2×#64408semidirect