Finite Group Databasebeta

← C73×#10795 #32920199

Subgroups — C73×#10795 #32920199

Order 18688.

1062 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×C73C211yesmaximal, characteristic
2C2×#336×C73C212yesmaximal
3C2×#336×C73C212yesmaximal
4C2×#336×C73C212yesmaximal
5C23×C8×C73C2214yes—
6C22×C42×C73C412yes—
7C22×C42×C73C412yes—
8C22×C42×C73C2211yescharacteristic
9C22×C42×C73C2211yescharacteristic
10C22×C42×C73C2211yescharacteristic
11C43×C73—24no—
12#336×C73—24no—
13#336×C73—24no—
14#336×C73C418yescomplemented
15C23×C4×C73C2×C411yescharacteristic
16C23×C4×C73C2×C411yescharacteristic
17C23×C4×C73C2×C412yes—
18C23×C4×C73C2×C412yes—
19C23×C4×C73C2311yescharacteristic
20C22×C8×C73—24no—
21C22×C8×C73—24no—
22C22×C8×C73—24no—
23C22×C8×C73—24no—
24C22×C8×C73—24no—
25C22×C8×C73—24no—
26C22×C8×C73C2×C418yes—
27C2×C42×C73—24no—
28C2×C42×C73—24no—
29C2×C42×C73—24no—
30C2×C42×C73—24no—
31C2×C42×C73—24no—
32C2×C42×C73—22no—
33C2×C42×C73—22no—
34C2×C42×C73—22no—
35C2×C42×C73—22no—
36C2×C42×C73—22no—
37C2×C42×C73—22no—
38C2×C42×C73C818yescomplemented
39C2×C42×C73C2×C414yes—
40C2×C42×C73D414yes—
41C2×C42×C73D412yes—
42C2×C42×C73Q812yes—
43C24×C73C22×C411yescharacteristic
44C22×C4×C73—21no—
45C22×C4×C73—21no—
46C22×C4×C73—22no—
47C22×C4×C73—21no—
48C22×C4×C73—21no—
49C22×C4×C73—22no—
50C22×C4×C73—22no—
51C22×C4×C73—22no—
52C22×C4×C73—22no—
53C22×C4×C73—22no—
54C22×C4×C73—22no—
55C22×C4×C73—22no—
56C22×C4×C73—22no—
57C22×C4×C73—22no—
58C22×C4×C73C4212yes—
59C22×C4×C73C4212yes—
60C22×C4×C73C22⋊C414yes—
61C22×C4×C73C4⋊C414yes—
62C22×C4×C73C2×C814yes—
63C22×C4×C73C2×C814yes—
64C22×C4×C73C2×C814yes—
65C22×C4×C73M1614yes—
66C22×C4×C73M1614yes—
67C22×C4×C73M1614yes—
68C22×C4×C73C22×C412yes—
69C22×C4×C73C2×D411yescharacteristic
70C22×C4×C73C2×D412yes—
71C22×C4×C73C2×Q811yescharacteristic
72C22×C4×C73#4112yes—
73C22×C4×C73#4112yes—
74C22×C4×C73#4112yes—
75C22×C4×C73#4112yes—
76C2×C8×C73—28no—
77C2×C8×C73—28no—
78C2×C8×C73—28no—
79C2×C8×C73—44no—
80C2×C8×C73—44no—
81C2×C8×C73—44no—
82C2×C8×C73—44no—
83C42×C73—216no—
84C42×C73—216no—
85C42×C73—28no—
86C42×C73—24no—
87C42×C73—24no—
88C42×C73—28no—
89C23×C73C2×C4211yescharacteristic
90C23×C73C2×C22⋊C411yescharacteristic
91C23×C73C2×C4⋊C411yescharacteristic
92C23×C73#11711yescharacteristic
93C23×C73#11711yescharacteristic
94C23×C73#11711yescharacteristic
95C23×C73#11711yescharacteristic
96C23×C73C22×C812yes—
97C23×C73C2×M1612yes—
98C23×C73C2×M1612yes—
99C23×C73C2×M1612yes—
100C2×C4×C73—22no—
101C2×C4×C73—22no—
102C2×C4×C73—24no—
103C2×C4×C73—24no—
104C2×C4×C73—22no—
105C2×C4×C73—22no—
106C2×C4×C73—24no—
107C2×C4×C73—24no—
108C2×C4×C73—24no—
109C2×C4×C73—24no—
110C2×C4×C73—24no—
111C2×C4×C73—24no—
112C2×C4×C73—24no—
113C2×C4×C73—24no—
114C2×C4×C73—24no—
115C2×C4×C73—24no—
116C2×C4×C73—24no—
117C2×C4×C73—24no—
118C2×C4×C73—24no—
119C2×C4×C73—24no—
120C2×C4×C73C4×C814yes—
121C2×C4×C73#9714yes—
122C2×C4×C73C22⋊C818yes—
123C2×C4×C73C4⋊C818yes—
124C2×C4×C73#11714yes—
125C2×C4×C73C4×D414yes—
126C2×C4×C73C4×D412yes—
127C2×C4×C73C4×Q812yes—
128C2×C4×C73#12112yes—
129C2×C4×C73C22⋊Q812yes—
130C2×C4×C73#12314yes—
131C2×C4×C73#12412yes—
132C2×C4×C73#12512yes—
133C2×C4×C73#12614yes—
134C8×C73—48no—
135C22×C73#37611yescharacteristic
136C22×C73C4×C22⋊C411yescharacteristic
137C22×C73C4×C4⋊C411yescharacteristic
138C22×C73#38011yescharacteristic
139C22×C73#38111yescharacteristic
140C22×C73#38211yescharacteristic
141C22×C73#38311yescharacteristic
142C22×C73C2×C4×C811yescharacteristic
143C22×C73C2×#9711yescharacteristic
144C22×C73C4×M1611yescharacteristic
145C22×C73C4×M1611yescharacteristic
146C22×C73C2×C22⋊C812yes—
147C22×C73#40712yes—
148C22×C73C2×C4⋊C812yes—
149C22×C73#42312yes—
150C22×C73#43112yes—
151C22×C73#43112yes—
152C22×C73#43112yes—
153C22×C73#43112yes—
154C22×C73#43212yes—
155C22×C73#43212yes—
156C22×C73#43212yes—
157C22×C73#43212yes—
158C4×C73—28no—
159C4×C73—28no—
160C4×C73—24no—
161C4×C73—24no—
162C4×C73#38714yes—
163C4×C73#38814yes—
164#10795C7311yesmaximal, characteristic, direct product factor, Sylow
165C2×C73#143411yescharacteristic
166C2×C73#174411yescharacteristic
167C2×C73#174511yescharacteristic
168C2×C73C4×C22⋊C811yescharacteristic
169C2×C73#174911yescharacteristic
170C2×C73C4×C4⋊C811yescharacteristic
171C2×C73#176711yescharacteristic
172C2×C73#179712yes—
173C2×C73#181712yes—
174C2×C73#183112yes—
175C2×C73#183912yes—
176C2×C43C2×C7311yescharacteristic
177C2×#336C2×C7312yes—
178C2×#336C2×C7312yes—
179C2×#336C2×C7312yes—
180C73#1079511yescharacteristic, direct product factor, Sylow
181C23×C8C22×C7314yes—
182C22×C42C4×C7312yes—
183C22×C42C4×C7312yes—
184C22×C42C22×C7311yescharacteristic
185C22×C42C22×C7311yescharacteristic
186C22×C42C22×C7311yescharacteristic
187C43—24no—
188#336—24no—
189#336—24no—
190#336C4×C7318yescomplemented
191C23×C4C2×C4×C7311yescharacteristic
192C23×C4C2×C4×C7311yescharacteristic
193C23×C4C2×C4×C7312yes—
194C23×C4C2×C4×C7312yes—
195C23×C4C23×C7311yescharacteristic
196C22×C8—24no—
197C22×C8—24no—
198C22×C8—24no—
199C22×C8—24no—
200C22×C8—24no—
201C22×C8—24no—
202C22×C8C2×C4×C7318yes—
203C2×C42—24no—
204C2×C42—24no—
205C2×C42—24no—
206C2×C42—24no—
207C2×C42—24no—
208C2×C42—22no—
209C2×C42—22no—
210C2×C42—22no—
211C2×C42—22no—
212C2×C42—22no—
213C2×C42—22no—
214C2×C42C8×C7318yescomplemented
215C2×C42C2×C4×C7314yes—
216C2×C42D4×C7314yes—
217C2×C42D4×C7312yes—
218C2×C42Q8×C7312yes—
219C24C22×C4×C7311yescharacteristic
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—22no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4C42×C7312yes—
235C22×C4C42×C7312yes—
236C22×C4C22⋊C4×C7314yes—
237C22×C4C4⋊C4×C7314yes—
238C22×C4C2×C8×C7314yes—
239C22×C4C2×C8×C7314yes—
240C22×C4C2×C8×C7314yes—
241C22×C4M16×C7314yes—
242C22×C4M16×C7314yes—
243C22×C4M16×C7314yes—
244C22×C4C22×C4×C7312yes—
245C22×C4C2×D4×C7311yescharacteristic
246C22×C4C2×D4×C7312yes—
247C22×C4C2×Q8×C7311yescharacteristic
248C22×C4#41×C7312yes—
249C22×C4#41×C7312yes—
250C22×C4#41×C7312yes—
251C22×C4#41×C7312yes—
252C2×C8—28no—
253C2×C8—28no—
254C2×C8—28no—
255C2×C8—44no—
256C2×C8—44no—
257C2×C8—44no—
258C2×C8—44no—
259C42—216no—
260C42—216no—
261C42—28no—
262C42—24no—
263C42—24no—
264C42—28no—
265C23C2×C42×C7311yescharacteristic
266C23C2×C22⋊C4×C7311yescharacteristic
267C23C2×C4⋊C4×C7311yescharacteristic
268C23#117×C7311yescharacteristic
269C23#117×C7311yescharacteristic
270C23#117×C7311yescharacteristic
271C23#117×C7311yescharacteristic
272C23C22×C8×C7312yes—
273C23C2×M16×C7312yes—
274C23C2×M16×C7312yes—
275C23C2×M16×C7312yes—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—24no—
279C2×C4—24no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—24no—
283C2×C4—24no—
284C2×C4—24no—
285C2×C4—24no—
286C2×C4—24no—
287C2×C4—24no—
288C2×C4—24no—
289C2×C4—24no—
290C2×C4—24no—
291C2×C4—24no—
292C2×C4—24no—
293C2×C4—24no—
294C2×C4—24no—
295C2×C4—24no—
296C2×C4C4×C8×C7314yes—
297C2×C4#97×C7314yes—
298C2×C4C22⋊C8×C7318yes—
299C2×C4C4⋊C8×C7318yes—
300C2×C4#117×C7314yes—
301C2×C4C4×D4×C7314yes—
302C2×C4C4×D4×C7312yes—
303C2×C4C4×Q8×C7312yes—
304C2×C4#121×C7312yes—
305C2×C4C22⋊Q8×C7312yes—
306C2×C4#123×C7314yes—
307C2×C4#124×C7312yes—
308C2×C4#125×C7312yes—
309C2×C4#126×C7314yes—
310C8—48no—
311C22#376×C7311yescharacteristic
312C22C4×C22⋊C4×C7311yescharacteristic
313C22C4×C4⋊C4×C7311yescharacteristic
314C22#380×C7311yescharacteristic
315C22#381×C7311yescharacteristic
316C22#382×C7311yescharacteristic
317C22#383×C7311yescharacteristic
318C22C2×C4×C8×C7311yescharacteristic
319C22C2×#97×C7311yescharacteristic
320C22C4×M16×C7311yescharacteristic
321C22C4×M16×C7311yescharacteristic
322C22C2×C22⋊C8×C7312yes—
323C22#407×C7312yes—
324C22C2×C4⋊C8×C7312yes—
325C22#423×C7312yes—
326C22#431×C7312yes—
327C22#431×C7312yes—
328C22#431×C7312yes—
329C22#431×C7312yes—
330C22#432×C7312yes—
331C22#432×C7312yes—
332C22#432×C7312yes—
333C22#432×C7312yes—
334C4—24no—
335C4—24no—
336C4—28no—
337C4—28no—
338C4#387×C7314yes—
339C4#388×C7314yes—
340C2C73×#143411yescharacteristic
341C2C73×#174411yescharacteristic
342C2C73×#174511yescharacteristic
343C2C4×C22⋊C8×C7311yescharacteristic
344C2C73×#174911yescharacteristic
345C2C4×C4⋊C8×C7311yescharacteristic
346C2C73×#176711yescharacteristic
347C2C73×#179712yes—
348C2C73×#181712yes—
349C2C73×#183112yes—
350C2C73×#183912yes—
subgroupG/H
centerC23×C4×C73C23
commutatorC22C2×C4×C8×C73
Frattini, cosocleC23×C4C23×C73
socle, prime radicalC24×C73C22×C4
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
14. #336×C73C4semidirect
38. C2×C42×C73C8semidirect
164. #10795C73direct (N × H)
180. C73#10795direct (N × H)
190. #336C4×C73semidirect
214. C2×C42C8×C73semidirect

Maximal subgroups

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

subgroupindex
C2×C43×C732
C2×#336×C732
#1079573