Finite Group Databasebeta

← D73⋊#1412 #34014357

Subgroups — D73⋊#1412 #34014357

Order 18688.

390 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 58 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⋊#353C212yesmaximal
2#22625072C212yesmaximal, complemented
3#22625071C211yesmaximal, characteristic, complemented
4#22625070C211yesmaximal, characteristic, complemented
5#490×D73C211yesmaximal, characteristic
6D73⋊#99—22no—
7#17989492C2212yes—
8#17989492C2212yes—
9#17989491—22no—
10#127×D73C2211yescharacteristic
11#125×D73C411yescharacteristic, complemented
12#17988953C2211yescharacteristic
13#17988952C2211yescharacteristic
14#17988951C411yescharacteristic, complemented
15#17988950—22no—
16#102×D73—22no—
17#97×D73C411yescharacteristic, complemented
18#490×C73C411yescharacteristic, complemented
19C2×C22⋊#64408—42no—
20#14556650—22no—
21#14556650—22no—
22#14556649—42no—
23C2×D4×D73—41no—
24C2×D4×D73D412yes—
25C2×C8×D73—21no—
26#14556588C2311yescharacteristic
27#14556587—41no—
28#14556587D412yes—
29#14556583C2×C411yescharacteristic, complemented
30#14556582—21no—
31#14556581—41no—
32C4⋊C4×D73—21no—
33C4⋊C4×D73—41no—
34C42×D73C2×C411yescharacteristic
35#14556513—22no—
36#14556512—22no—
37#14556511—22no—
38#14556502C2×C411yescharacteristic, complemented
39#14556501—21no—
40#127×C73C2×C411yescharacteristic
41#125×C73C2×C411yescharacteristic, complemented
42#102×C73—22no—
43#97×C73C2×C411yescharacteristic, complemented
44C22×#64408—82no—
45C22⋊#64408—42no—
46C22⋊#64408—42no—
47C22⋊#64408—82no—
48C23×D73—22no—
49C2×D292—41no—
50C2×D292C2×D412yes—
51C2×C22⋊D73—22no—
52C2×C22⋊D73—42no—
53D4×D73—42no—
54D4×D73—42no—
55D4×D73—84no—
56C2×C4×D73—21no—
57C2×C4×D73—41no—
58C2×C4×D73C22⋊C411yescharacteristic
59C2×#10596831—21no—
60C8×D73—41no—
61C8×D73—41no—
62C4⋊Dic73—21no—
63C4⋊Dic73—41no—
64#11924007—41no—
65#11924007—41no—
66#11924007—41no—
67C4×Dic73—21no—
68C4×Dic73C22⋊C411yescharacteristic
69C2×D4×C73—41no—
70C2×D4×C73C22⋊C412yes—
71C2×C8×C73—21no—
72C4⋊C4×C73—21no—
73C4⋊C4×C73—41no—
74C42×C73C22×C411yescharacteristic
75C23×C73—22no—
76C22×D73—22no—
77C22×D73—42no—
78C22×D73—42no—
79C22×D73—84no—
80C22×D73#9911yescharacteristic
81C2×#64408—82no—
82C2×#64408—82no—
83C2×#64408—164no—
84D4×C73—42no—
85D4×C73—82no—
86C2×C4×C73—21no—
87C2×C4×C73—41no—
88C2×C4×C73C2×C22⋊C411yescharacteristic
89C22⋊D73—82no—
90C22⋊D73—84no—
91C2×Dic73—21no—
92C2×Dic73—41no—
93C2×Dic73#9911yescharacteristic
94D292—42no—
95D292—82no—
96C4×D73—21no—
97C4×D73—21no—
98C4×D73—42no—
99C4×D73—82no—
100C8×C73—41no—
101#10596831—41no—
102C22×C73—42no—
103C22×C73—82no—
104C22×C73C2×#9911yescharacteristic
105C2×D73—22no—
106C2×D73—42no—
107C2×D73—84no—
108C2×D73—82no—
109C2×D73—162no—
110C2×D73#35411yescharacteristic
111C2×D73#35411yescharacteristic
112#64408—162no—
113#64408—162no—
114C4×C73—21no—
115C4×C73—41no—
116C4×C73—81no—
117Dic73—21no—
118Dic73—41no—
119Dic73—81no—
120C2×#1412—731nomaximal, Sylow
121C2×C73—21no—
122C2×C73—82no—
123C2×C73C2×#35411yescharacteristic
124D73—21no—
125D73—82no—
126D73#141212yescomplemented
127C2×#490—731no—
128C2×#353—732no—
129#1412—731no—
130#1412—731no—
131#1412—732no—
132C73C2×#141211yescharacteristic, complemented, Sylow
133C2×#127—731no—
134C2×#125—731no—
135#490—731no—
136#490—731no—
137#490—731no—
138#490—1462no—
139#490#6440811yescharacteristic, complemented
140C2×#102—1462no—
141C2×#99—1462no—
142C2×#97—731no—
143#353—732no—
144#353—732no—
145#353—1462no—
146C22×D4—2921no—
147C22×D4—732no—
148C22×C8—1461no—
149#127—2921no—
150#127—732no—
151#127—731no—
152#127C2×#6440811yescharacteristic
153#125—2921no—
154#125—731no—
155#125—1461no—
156#125C2×#6440811yescharacteristic, complemented
157C2×C4⋊C4—2921no—
158C2×C4⋊C4—1461no—
159C2×C22⋊C4—2922no—
160C2×C42—731no—
161#102—22no—
162#102—1462no—
163#102—1462no—
164#102—1462no—
165#99—2922no—
166#99—1462no—
167#99—1462no—
168#97—731no—
169#97—1461no—
170#97C2×#6440811yescharacteristic, complemented
171C24—1462no—
172C2×D4—41no—
173C2×D4—2921no—
174C2×D4—2922no—
175C2×D4—2922no—
176C2×D4—2922no—
177C2×D4—5844no—
178C2×D4—732no—
179C2×D4—1462no—
180C2×D4C22⋊#6440812yes—
181C22×C4—2921no—
182C22×C4—5842no—
183C22×C4—731no—
184C22×C4—1461no—
185C2×C8—21no—
186C2×C8—2921no—
187C2×C8—2921no—
188C2×C8—1461no—
189C4⋊C4—21no—
190C4⋊C4—41no—
191C4⋊C4—2921no—
192C4⋊C4—2921no—
193C4⋊C4—2921no—
194C4⋊C4—2921no—
195C4⋊C4—1461no—
196C22⋊C4—2922no—
197C22⋊C4—2922no—
198C22⋊C4—5842no—
199C42—731no—
200C42—1461no—
201C42C22×#6440811yescharacteristic
202C23—22no—
203C23—2922no—
204C23—2922no—
205C23—5844no—
206C23—731no—
207C23—1462no—
208D4—42no—
209D4—82no—
210D4—2922no—
211D4—5842no—
212D4—5844no—
213D4—5842no—
214C2×C4—21no—
215C2×C4—41no—
216C2×C4—2922no—
217C2×C4—2921no—
218C2×C4—5842no—
219C2×C4—5842no—
220C2×C4—5842no—
221C2×C4—731no—
222C2×C4—11684no—
223C2×C4—1461no—
224C2×C4—1461no—
225C2×C4—1461no—
226C2×C4C2×C22⋊#6440811yescharacteristic
227C8—41no—
228C8—2921no—
229C22—42no—
230C22—82no—
231C22—2922no—
232C22—5842no—
233C22—5844no—
234C22—731no—
235C22—731no—
236C22—11682no—
237C22—1462no—
238C22D73⋊#9911yescharacteristic
239C4—21no—
240C4—41no—
241C4—81no—
242C4—2921no—
243C4—5841no—
244C4—11682no—
245C4—11682no—
246C4—1461no—
247C2—21no—
248C2—82no—
249C2—5842no—
250C2—732no—
251C2—1461no—
252C2D73⋊#35411yescharacteristic
subgroupG/H
centerC2D73⋊#354
commutatorC42×C73C22×C4
FrattiniC42C22×#64408
Fitting#490×C73C4
socleC2×C73C2×#354
prime radical#127×D73C22
cosocle#14556588C23
hypercenter#490#64408
hypocenterC73C2×#1412
LCSG ▷ C42×C73 ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #127 ◁ #490

Complements

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

NH ≅ G/Ntype
2. #22625072C2semidirect
3. #22625071C2semidirect
4. #22625070C2semidirect
11. #125×D73C4semidirect
14. #17988951C4semidirect
17. #97×D73C4semidirect
18. #490×C73C4semidirect
29. #14556583C2×C4semidirect
38. #14556502C2×C4semidirect
41. #125×C73C2×C4semidirect
43. #97×C73C2×C4semidirect
126. D73#1412semidirect
132. C73C2×#1412semidirect
139. #490#64408semidirect
156. #125C2×#64408semidirect
170. #97C2×#64408semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
D73⋊#3532
#226250722
#226250712
#226250702
#490×D732
C2×#141273