Finite Group Databasebeta

← C73×#11903 #32921307

Subgroups — C73×#11903 #32921307

Order 18688.

440 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 118 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×#2487C211yesmaximal, characteristic
2C73×#1800C211yesmaximal, characteristic
3C73×#1459C211yesmaximal, characteristic
4C73×#1353C214yesmaximal, complemented
5C2×C4×D4×C73C2211yescharacteristic
6C22×C4⋊C4×C73C411yescharacteristic
7#423×C73—21no—
8C2×#100×C73—21no—
9C2×C22⋊C8×C73—21no—
10#400×C73C2212yes—
11#399×C73C412yes—
12#389×C73—21no—
13#386×C73—21no—
14#385×C73—21no—
15#380×C73—21no—
16#380×C73C411yescharacteristic
17#343×C73C2212yes—
18#324×C73C2212yes—
19#323×C73—21no—
20C22×D4×C73D411yescharacteristic
21C23×C4×C73—21no—
22C23×C4×C73C2×C411yescharacteristic
23C23×C4×C73D411yescharacteristic
24C2×M16×C73—22no—
25C22×C8×C73—41no—
26C4×D4×C73—41no—
27C4×D4×C73—41no—
28C2×C4⋊C4×C73—21no—
29C2×C4⋊C4×C73—21no—
30C2×C4⋊C4×C73—22no—
31C2×C4⋊C4×C73—41no—
32C2×C4⋊C4×C73—41no—
33C2×C4⋊C4×C73C2×C412yes—
34C2×C4⋊C4×C73C2311yescharacteristic
35C2×C22⋊C4×C73—21no—
36C2×C22⋊C4×C73—22no—
37C2×C22⋊C4×C73C2×C411yescharacteristic
38C2×C22⋊C4×C73D411yescharacteristic
39C2×C42×C73D411yescharacteristic
40C4⋊C8×C73—41no—
41C4⋊C8×C73—41no—
42#100×C73—42no—
43C22⋊C8×C73—22no—
44C22⋊C8×C73—41no—
45#95×C73—22no—
46#95×C73—22no—
47#95×C73C2×C412yes—
48C24×C73C22⋊C411yescharacteristic
49C24×C73C22⋊C411yescharacteristic
50C2×D4×C73—41no—
51C2×D4×C73—41no—
52C2×D4×C73SD1612yes—
53C2×D4×C73Q1612yes—
54C22×C4×C73—21no—
55C22×C4×C73—21no—
56C22×C4×C73—21no—
57C22×C4×C73—21no—
58C22×C4×C73—22no—
59C22×C4×C73—22no—
60C22×C4×C73—42no—
61C22×C4×C73—42no—
62C22×C4×C73—42no—
63C22×C4×C73—82no—
64C22×C4×C73C22⋊C411yescharacteristic
65C22×C4×C73C22⋊C411yescharacteristic
66C22×C4×C73C22×C411yescharacteristic
67C22×C4×C73C2×D411yescharacteristic
68C22×C4×C73C2×D411yescharacteristic
69M16×C73—42no—
70M16×C73—42no—
71C2×C8×C73—42no—
72C2×C8×C73—42no—
73C2×C8×C73—82no—
74C4⋊C4×C73—41no—
75C4⋊C4×C73—42no—
76C4⋊C4×C73—42no—
77C4⋊C4×C73—41no—
78C4⋊C4×C73—41no—
79C4⋊C4×C73—82no—
80C22⋊C4×C73—41no—
81C22⋊C4×C73—41no—
82C22⋊C4×C73—42no—
83C22⋊C4×C73—82no—
84C42×C73—21no—
85C42×C73—21no—
86C23×C73—21no—
87C23×C73—21no—
88C23×C73—21no—
89C23×C73—21no—
90C23×C73—41no—
91C23×C73—41no—
92C23×C73—41no—
93C23×C73—41no—
94C23×C73#10312yes—
95C23×C73#10312yes—
96C23×C73C2×C22⋊C411yescharacteristic
97D4×C73—42no—
98D4×C73—42no—
99C2×C4×C73—21no—
100C2×C4×C73—21no—
101C2×C4×C73—22no—
102C2×C4×C73—21no—
103C2×C4×C73—21no—
104C2×C4×C73—21no—
105C2×C4×C73—42no—
106C2×C4×C73—42no—
107C2×C4×C73—42no—
108C2×C4×C73—41no—
109C2×C4×C73—41no—
110C2×C4×C73—41no—
111C2×C4×C73—42no—
112C2×C4×C73—42no—
113C2×C4×C73—42no—
114C2×C4×C73—42no—
115C2×C4×C73—42no—
116C2×C4×C73—42no—
117C2×C4×C73—81no—
118C2×C4×C73—84no—
119C2×C4×C73#9911yescharacteristic
120C2×C4×C73#9911yescharacteristic
121C2×C4×C73C2×SD1611yescharacteristic
122C2×C4×C73C2×Q1611yescharacteristic
123C8×C73—82no—
124C8×C73—82no—
125C22×C73—21no—
126C22×C73—21no—
127C22×C73—22no—
128C22×C73—22no—
129C22×C73—42no—
130C22×C73—42no—
131C22×C73—42no—
132C22×C73—41no—
133C22×C73—41no—
134C22×C73—41no—
135C22×C73—41no—
136C22×C73—81no—
137C22×C73C2×#9911yescharacteristic
138C22×C73C2×#10311yescharacteristic
139C22×C73#42111yescharacteristic
140C4×C73—21no—
141C4×C73—21no—
142C4×C73—21no—
143C4×C73—41no—
144C4×C73—41no—
145C4×C73—41no—
146C4×C73—82no—
147C4×C73—82no—
148C4×C73#35212yes—
149#11903C7311yesmaximal, characteristic, direct product factor, Sylow
150C2×C73—21no—
151C2×C73—21no—
152C2×C73—42no—
153C2×C73—42no—
154C2×C73#152011yescharacteristic
155C2×C73C2×#35211yescharacteristic
156C2×C73#213411yescharacteristic
157#2487C2×C7311yescharacteristic
158#1800C2×C7311yescharacteristic
159#1459C2×C7311yescharacteristic
160#1353C2×C7314yescomplemented
161C73#1190311yescharacteristic, direct product factor, Sylow
162C2×C4×D4C22×C7311yescharacteristic
163C22×C4⋊C4C4×C7311yescharacteristic
164#423—21no—
165C2×#100—21no—
166C2×C22⋊C8—21no—
167#400C22×C7312yes—
168#399C4×C7312yes—
169#389—21no—
170#386—21no—
171#385—21no—
172#380—21no—
173#380C4×C7311yescharacteristic
174#343C22×C7312yes—
175#324C22×C7312yes—
176#323—21no—
177C22×D4D4×C7311yescharacteristic
178C23×C4—21no—
179C23×C4C2×C4×C7311yescharacteristic
180C23×C4D4×C7311yescharacteristic
181C2×M16—22no—
182C22×C8—41no—
183C4×D4—41no—
184C4×D4—41no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—41no—
189C2×C4⋊C4—41no—
190C2×C4⋊C4C2×C4×C7312yes—
191C2×C4⋊C4C23×C7311yescharacteristic
192C2×C22⋊C4—21no—
193C2×C22⋊C4—22no—
194C2×C22⋊C4C2×C4×C7311yescharacteristic
195C2×C22⋊C4D4×C7311yescharacteristic
196C2×C42D4×C7311yescharacteristic
197C4⋊C8—41no—
198C4⋊C8—41no—
199#100—42no—
200C22⋊C8—22no—
201C22⋊C8—41no—
202#95—22no—
203#95—22no—
204#95C2×C4×C7312yes—
205C24C22⋊C4×C7311yescharacteristic
206C24C22⋊C4×C7311yescharacteristic
207C2×D4—41no—
208C2×D4—41no—
209C2×D4SD16×C7312yes—
210C2×D4Q16×C7312yes—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—42no—
218C22×C4—42no—
219C22×C4—42no—
220C22×C4—82no—
221C22×C4C22⋊C4×C7311yescharacteristic
222C22×C4C22⋊C4×C7311yescharacteristic
223C22×C4C22×C4×C7311yescharacteristic
224C22×C4C2×D4×C7311yescharacteristic
225C22×C4C2×D4×C7311yescharacteristic
226M16—42no—
227M16—42no—
228C2×C8—42no—
229C2×C8—42no—
230C2×C8—82no—
231C4⋊C4—41no—
232C4⋊C4—42no—
233C4⋊C4—42no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—82no—
237C22⋊C4—41no—
238C22⋊C4—41no—
239C22⋊C4—42no—
240C22⋊C4—82no—
241C42—21no—
242C42—21no—
243C23—21no—
244C23—21no—
245C23—21no—
246C23—21no—
247C23—41no—
248C23—41no—
249C23—41no—
250C23—41no—
251C23#103×C7312yes—
252C23#103×C7312yes—
253C23C2×C22⋊C4×C7311yescharacteristic
254D4—42no—
255D4—42no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—81no—
275C2×C4—84no—
276C2×C4#99×C7311yescharacteristic
277C2×C4#99×C7311yescharacteristic
278C2×C4C2×SD16×C7311yescharacteristic
279C2×C4C2×Q16×C7311yescharacteristic
280C8—82no—
281C8—82no—
282C22—21no—
283C22—21no—
284C22—22no—
285C22—22no—
286C22—42no—
287C22—42no—
288C22—42no—
289C22—41no—
290C22—41no—
291C22—41no—
292C22—41no—
293C22—81no—
294C22C2×#99×C7311yescharacteristic
295C22C2×#103×C7311yescharacteristic
296C22#421×C7311yescharacteristic
297C4—21no—
298C4—21no—
299C4—21no—
300C4—41no—
301C4—41no—
302C4—41no—
303C4—82no—
304C4—82no—
305C4#352×C7312yes—
306C2—21no—
307C2—21no—
308C2—42no—
309C2—42no—
310C2C73×#152011yescharacteristic
311C2C2×#352×C7311yescharacteristic
312C2C73×#213411yescharacteristic
subgroupG/H
center, socleC22×C73C2×#99
commutatorC22×C4C22×C4×C73
Frattini, cosocleC2×C4⋊C4C23×C73
prime radicalC22×D4×C73D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C73 ◁ C22×C4×C73 ◁ C2×C4×D4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
4. C73×#1353C2semidirect
149. #11903C73direct (N × H)
160. #1353C2×C73semidirect
161. C73#11903direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#24872
C73×#18002
C73×#14592
C73×#13532
#1190373