Finite Group Databasebeta

← C73×#11819 #32921223

Subgroups — C73×#11819 #32921223

Order 18688.

368 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 98 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
1C73×#2628C211yesmaximal, characteristic
2C73×#1822C211yesmaximal, characteristic
3C73×#1464C211yesmaximal, characteristic
4C73×#1354C214yesmaximal, complemented
5C2×C4⋊Q8×C73C411yescharacteristic
6C2×#117×C73C2211yescharacteristic
7#432×C73—21no—
8#407×C73—21no—
9#400×C73—21no—
10#399×C73—21no—
11#395×C73C2212yes—
12#393×C73C412yes—
13#389×C73—21no—
14#382×C73C411yescharacteristic
15#380×C73—21no—
16#343×C73—21no—
17#343×C73C2212yes—
18#324×C73C2212yes—
19#323×C73—21no—
20C22×Q8×C73C2×C412yes—
21C23×C4×C73D411yescharacteristic
22C2×M16×C73—22no—
23C4⋊Q8×C73—41no—
24C4⋊Q8×C73—41no—
25#117×C73—41no—
26#117×C73—41no—
27C2×C4⋊C4×C73—21no—
28C2×C4⋊C4×C73—21no—
29C2×C4⋊C4×C73—21no—
30C2×C4⋊C4×C73—22no—
31C2×C4⋊C4×C73D411yescharacteristic
32C2×C4⋊C4×C73C2311yescharacteristic
33C2×C22⋊C4×C73—22no—
34C2×C22⋊C4×C73C2×C411yescharacteristic
35C2×C22⋊C4×C73D411yescharacteristic
36C2×C42×C73C2×C411yescharacteristic
37C2×C42×C73D411yescharacteristic
38C4⋊C8×C73—41no—
39C22⋊C8×C73—22no—
40C22⋊C8×C73—41no—
41C22⋊C8×C73—41no—
42#97×C73—41no—
43#95×C73—21no—
44#95×C73—22no—
45#95×C73—22no—
46#95×C73C2×C412yes—
47C24×C73C22⋊C411yescharacteristic
48C2×Q8×C73—42no—
49C2×Q8×C73—82no—
50C22×C4×C73—21no—
51C22×C4×C73—21no—
52C22×C4×C73—22no—
53C22×C4×C73—22no—
54C22×C4×C73—22no—
55C22×C4×C73—41no—
56C22×C4×C73C22⋊C411yescharacteristic
57C22×C4×C73C22⋊C411yescharacteristic
58C22×C4×C73C22⋊C411yescharacteristic
59C22×C4×C73C22×C411yescharacteristic
60C22×C4×C73C2×D411yescharacteristic
61C22×C4×C73C2×D411yescharacteristic
62M16×C73—42no—
63M16×C73—42no—
64C2×C8×C73—42no—
65C2×C8×C73—42no—
66C4⋊C4×C73—41no—
67C4⋊C4×C73—41no—
68C4⋊C4×C73—42no—
69C4⋊C4×C73—42no—
70C4⋊C4×C73—41no—
71C4⋊C4×C73—41no—
72C4⋊C4×C73—82no—
73C22⋊C4×C73—41no—
74C22⋊C4×C73—41no—
75C22⋊C4×C73—82no—
76C42×C73—21no—
77C42×C73—21no—
78C42×C73—21no—
79C42×C73—21no—
80C23×C73—21no—
81C23×C73—21no—
82C23×C73—21no—
83C23×C73—41no—
84C23×C73—41no—
85C23×C73C2×C22⋊C411yescharacteristic
86Q8×C73—84no—
87C2×C4×C73—21no—
88C2×C4×C73—21no—
89C2×C4×C73—21no—
90C2×C4×C73—21no—
91C2×C4×C73—21no—
92C2×C4×C73—21no—
93C2×C4×C73—21no—
94C2×C4×C73—21no—
95C2×C4×C73—42no—
96C2×C4×C73—42no—
97C2×C4×C73—41no—
98C2×C4×C73—41no—
99C2×C4×C73—41no—
100C2×C4×C73—41no—
101C2×C4×C73—42no—
102C2×C4×C73—42no—
103C2×C4×C73—42no—
104C2×C4×C73—42no—
105C2×C4×C73—42no—
106C2×C4×C73—42no—
107C2×C4×C73#9911yescharacteristic
108C2×C4×C73#9911yescharacteristic
109C2×C4×C73#13712yes—
110C8×C73—82no—
111C8×C73—82no—
112C22×C73—21no—
113C22×C73—21no—
114C22×C73—42no—
115C22×C73—41no—
116C22×C73—41no—
117C22×C73—41no—
118C22×C73—81no—
119C22×C73C2×#9911yescharacteristic
120C22×C73#41911yescharacteristic
121C22×C73#42111yescharacteristic
122C4×C73—22no—
123C4×C73—21no—
124C4×C73—21no—
125C4×C73—41no—
126C4×C73—41no—
127C4×C73—41no—
128C4×C73—41no—
129C4×C73—82no—
130C4×C73—82no—
131#11819C7311yesmaximal, characteristic, direct product factor, Sylow
132C2×C73—21no—
133C2×C73—21no—
134C2×C73—81no—
135C2×C73#151111yescharacteristic
136C2×C73#212211yescharacteristic
137C2×C73#213511yescharacteristic
138#2628C2×C7311yescharacteristic
139#1822C2×C7311yescharacteristic
140#1464C2×C7311yescharacteristic
141#1354C2×C7314yescomplemented
142C73#1181911yescharacteristic, direct product factor, Sylow
143C2×C4⋊Q8C4×C7311yescharacteristic
144C2×#117C22×C7311yescharacteristic
145#432—21no—
146#407—21no—
147#400—21no—
148#399—21no—
149#395C22×C7312yes—
150#393C4×C7312yes—
151#389—21no—
152#382C4×C7311yescharacteristic
153#380—21no—
154#343—21no—
155#343C22×C7312yes—
156#324C22×C7312yes—
157#323—21no—
158C22×Q8C2×C4×C7312yes—
159C23×C4D4×C7311yescharacteristic
160C2×M16—22no—
161C4⋊Q8—41no—
162C4⋊Q8—41no—
163#117—41no—
164#117—41no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4D4×C7311yescharacteristic
170C2×C4⋊C4C23×C7311yescharacteristic
171C2×C22⋊C4—22no—
172C2×C22⋊C4C2×C4×C7311yescharacteristic
173C2×C22⋊C4D4×C7311yescharacteristic
174C2×C42C2×C4×C7311yescharacteristic
175C2×C42D4×C7311yescharacteristic
176C4⋊C8—41no—
177C22⋊C8—22no—
178C22⋊C8—41no—
179C22⋊C8—41no—
180#97—41no—
181#95—21no—
182#95—22no—
183#95—22no—
184#95C2×C4×C7312yes—
185C24C22⋊C4×C7311yescharacteristic
186C2×Q8—42no—
187C2×Q8—82no—
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—22no—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—41no—
194C22×C4C22⋊C4×C7311yescharacteristic
195C22×C4C22⋊C4×C7311yescharacteristic
196C22×C4C22⋊C4×C7311yescharacteristic
197C22×C4C22×C4×C7311yescharacteristic
198C22×C4C2×D4×C7311yescharacteristic
199C22×C4C2×D4×C7311yescharacteristic
200M16—42no—
201M16—42no—
202C2×C8—42no—
203C2×C8—42no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—42no—
207C4⋊C4—42no—
208C4⋊C4—41no—
209C4⋊C4—41no—
210C4⋊C4—82no—
211C22⋊C4—41no—
212C22⋊C4—41no—
213C22⋊C4—82no—
214C42—21no—
215C42—21no—
216C42—21no—
217C42—21no—
218C23—21no—
219C23—21no—
220C23—21no—
221C23—41no—
222C23—41no—
223C23C2×C22⋊C4×C7311yescharacteristic
224Q8—84no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4#99×C7311yescharacteristic
246C2×C4#99×C7311yescharacteristic
247C2×C4#137×C7312yes—
248C8—82no—
249C8—82no—
250C22—21no—
251C22—21no—
252C22—42no—
253C22—41no—
254C22—41no—
255C22—41no—
256C22—81no—
257C22C2×#99×C7311yescharacteristic
258C22#419×C7311yescharacteristic
259C22#421×C7311yescharacteristic
260C4—22no—
261C4—21no—
262C4—21no—
263C4—41no—
264C4—41no—
265C4—41no—
266C4—41no—
267C4—82no—
268C4—82no—
269C2—21no—
270C2—21no—
271C2—81no—
272C2C73×#151111yescharacteristic
273C2C73×#212211yescharacteristic
274C2C73×#213511yescharacteristic
subgroupG/H
center, socleC22×C73C2×#99
commutatorC22×C4C22×C4×C73
Frattini, cosocleC2×C4⋊C4C23×C73
prime radicalC24×C73C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C73 ◁ C22×C4×C73 ◁ C2×#117×C73 ◁ G

Complements

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

NH ≅ G/Ntype
4. C73×#1354C2semidirect
131. #11819C73direct (N × H)
141. #1354C2×C73semidirect
142. C73#11819direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#26282
C73×#18222
C73×#14642
C73×#13542
#1181973