Finite Group Databasebeta

← C73×#32830 #32942234

Subgroups — C73×#32830 #32942234

Order 18688.

612 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#2647C211yesmaximal, characteristic, complemented
2C73×#2640C211yesmaximal, characteristic
3C73×#2096C211yesmaximal, characteristic, complemented
4C73×#2094C211yesmaximal, characteristic
5C73×#2074C211yesmaximal, characteristic, complemented
6C73×#2073C211yesmaximal, characteristic
7C73×#2066C212yesmaximal, complemented
8C73×#2065C212yesmaximal
9C73×#2058C212yesmaximal, complemented
10C73×#2042C212yesmaximal
11C73×#1832C211yesmaximal, characteristic, complemented
12C2×C4⋊Q8×C73C2211yescharacteristic
13C2×#124×C73C2211yescharacteristic
14C2×#106×C73C2212yes—
15C2×#106×C73C2212yes—
16C2×C4⋊C8×C73C2212yes—
17C2×#103×C73C2212yes—
18C2×#103×C73C2212yes—
19C2×#102×C73C2212yes—
20C2×#102×C73C2212yes—
21#400×C73—22no—
22#398×C73—22no—
23#397×C73—22no—
24#393×C73—22no—
25#391×C73C2211yescharacteristic
26#391×C73C2211yescharacteristic
27#390×C73C2211yescharacteristic
28#390×C73C2211yescharacteristic
29#389×C73C2212yes—
30#389×C73C2212yes—
31#384×C73C2211yescharacteristic
32#382×C73C2211yescharacteristic
33#376×C73C2211yescharacteristic
34#340×C73C2212yes—
35#340×C73C2212yes—
36#336×C73C2212yes—
37#336×C73C2211yescharacteristic
38#336×C73C2211yescharacteristic
39C22×Q8×C73—21no—
40C22×Q8×C73C2311yescharacteristic
41C22×D4×C73C2311yescharacteristic
42C22×C8×C73C2312yes—
43C22×C8×C73C2312yes—
44C4⋊Q8×C73—42no—
45#124×C73—42no—
46C2×C4⋊C4×C73—21no—
47C2×C4⋊C4×C73—22no—
48C2×C4⋊C4×C73—22no—
49C2×C4⋊C4×C73—22no—
50C2×C4⋊C4×C73C2312yes—
51C2×C4⋊C4×C73C2312yes—
52C2×C4⋊C4×C73C2311yescharacteristic
53C2×C4⋊C4×C73C2311yescharacteristic
54C2×C22⋊C4×C73—21no—
55C2×C22⋊C4×C73—21no—
56C2×C22⋊C4×C73—22no—
57C2×C22⋊C4×C73—22no—
58C2×C42×C73C2311yescharacteristic
59C2×C42×C73C2311yescharacteristic
60C2×C42×C73C2311yescharacteristic
61#106×C73—42no—
62#106×C73—42no—
63C4⋊C8×C73—42no—
64#103×C73—42no—
65#103×C73—42no—
66#102×C73—42no—
67#102×C73—42no—
68#95×C73—22no—
69#95×C73—22no—
70#95×C73—22no—
71#95×C73—22no—
72#95×C73—22no—
73#95×C73D412yes—
74#95×C73D412yes—
75C24×C73—21no—
76C2×Q8×C73—21no—
77C2×Q8×C73—22no—
78C2×Q8×C73—22no—
79C2×Q8×C73—21no—
80C2×Q8×C73—42no—
81C2×Q8×C73—82no—
82C2×D4×C73—21no—
83C2×D4×C73—22no—
84C2×D4×C73—22no—
85C2×D4×C73—21no—
86C22×C4×C73—21no—
87C22×C4×C73—22no—
88C22×C4×C73—21no—
89C22×C4×C73—21no—
90C22×C4×C73—22no—
91C22×C4×C73C2×D412yes—
92C22×C4×C73C2×D412yes—
93C22×C4×C73C2×D411yescharacteristic
94C22×C4×C73C2×D411yescharacteristic
95C22×C4×C73C2411yescharacteristic
96C2×C8×C73—22no—
97C2×C8×C73—22no—
98C2×C8×C73—22no—
99C2×C8×C73—22no—
100C2×C8×C73—22no—
101C2×C8×C73—22no—
102C4⋊C4×C73—22no—
103C4⋊C4×C73—22no—
104C4⋊C4×C73—22no—
105C4⋊C4×C73—22no—
106C4⋊C4×C73—22no—
107C4⋊C4×C73—22no—
108C4⋊C4×C73—42no—
109C4⋊C4×C73—82no—
110C4⋊C4×C73—82no—
111C4⋊C4×C73—82no—
112C22⋊C4×C73—42no—
113C22⋊C4×C73—42no—
114C22⋊C4×C73—82no—
115C22⋊C4×C73—82no—
116C42×C73—21no—
117C42×C73—22no—
118C42×C73—22no—
119C42×C73—21no—
120C23×C73—41no—
121C23×C73—41no—
122C23×C73—41no—
123C23×C73—42no—
124C23×C73—42no—
125C23×C73C22×D411yescharacteristic
126Q8×C73—42no—
127Q8×C73—42no—
128Q8×C73—84no—
129D4×C73—42no—
130D4×C73—42no—
131C2×C4×C73—21no—
132C2×C4×C73—21no—
133C2×C4×C73—22no—
134C2×C4×C73—22no—
135C2×C4×C73—22no—
136C2×C4×C73—22no—
137C2×C4×C73—22no—
138C2×C4×C73—22no—
139C2×C4×C73—22no—
140C2×C4×C73—22no—
141C2×C4×C73—41no—
142C2×C4×C73—41no—
143C2×C4×C73—41no—
144C2×C4×C73—42no—
145C2×C4×C73—41no—
146C2×C4×C73—42no—
147C2×C4×C73—41no—
148C2×C4×C73—42no—
149C2×C4×C73—42no—
150C2×C4×C73—42no—
151C2×C4×C73—42no—
152C2×C4×C73—42no—
153C2×C4×C73—42no—
154C2×C4×C73H(5,𝔽2)11yescharacteristic
155C2×C4×C73H(5,𝔽2)12yes—
156C2×C4×C732−1+412yes—
157C2×C4×C732−1+411yescharacteristic
158C8×C73—42no—
159C8×C73—42no—
160C22×C73—81no—
161C22×C73—81no—
162C22×C73—81no—
163C22×C73—82no—
164C22×C73—82no—
165C22×C73#53511yescharacteristic
166C22×C73#53611yescharacteristic
167C22×C73#53711yescharacteristic
168C22×C73#57712yes—
169C22×C73#57712yes—
170C4×C73—41no—
171C4×C73—41no—
172C4×C73—42no—
173C4×C73—42no—
174C4×C73—81no—
175C4×C73—82no—
176C4×C73—81no—
177C4×C73—81no—
178C4×C73—82no—
179C4×C73#56212yes—
180C4×C73#56312yes—
181#32830C7311yesmaximal, characteristic, direct product factor, Sylow
182C2×C73—161no—
183C2×C73#282011yescharacteristic
184C2×C73#322111yescharacteristic
185C2×C73#322211yescharacteristic
186C2×C73#324412yes—
187C2×C73#326312yes—
188#2647C2×C7311yescharacteristic, complemented
189#2640C2×C7311yescharacteristic
190#2096C2×C7311yescharacteristic, complemented
191#2094C2×C7311yescharacteristic
192#2074C2×C7311yescharacteristic, complemented
193#2073C2×C7311yescharacteristic
194#2066C2×C7312yescomplemented
195#2065C2×C7312yes—
196#2058C2×C7312yescomplemented
197#2042C2×C7312yes—
198#1832C2×C7311yescharacteristic, complemented
199C73#3283011yescharacteristic, direct product factor, Sylow
200C2×C4⋊Q8C22×C7311yescharacteristic
201C2×#124C22×C7311yescharacteristic
202C2×#106C22×C7312yes—
203C2×#106C22×C7312yes—
204C2×C4⋊C8C22×C7312yes—
205C2×#103C22×C7312yes—
206C2×#103C22×C7312yes—
207C2×#102C22×C7312yes—
208C2×#102C22×C7312yes—
209#400—22no—
210#398—22no—
211#397—22no—
212#393—22no—
213#391C22×C7311yescharacteristic
214#391C22×C7311yescharacteristic
215#390C22×C7311yescharacteristic
216#390C22×C7311yescharacteristic
217#389C22×C7312yes—
218#389C22×C7312yes—
219#384C22×C7311yescharacteristic
220#382C22×C7311yescharacteristic
221#376C22×C7311yescharacteristic
222#340C22×C7312yes—
223#340C22×C7312yes—
224#336C22×C7312yes—
225#336C22×C7311yescharacteristic
226#336C22×C7311yescharacteristic
227C22×Q8—21no—
228C22×Q8C23×C7311yescharacteristic
229C22×D4C23×C7311yescharacteristic
230C22×C8C23×C7312yes—
231C22×C8C23×C7312yes—
232C4⋊Q8—42no—
233#124—42no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4—22no—
237C2×C4⋊C4—22no—
238C2×C4⋊C4C23×C7311yescharacteristic
239C2×C4⋊C4C23×C7311yescharacteristic
240C2×C4⋊C4C23×C7312yes—
241C2×C4⋊C4C23×C7312yes—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—22no—
245C2×C22⋊C4—22no—
246C2×C42C23×C7311yescharacteristic
247C2×C42C23×C7311yescharacteristic
248C2×C42C23×C7311yescharacteristic
249#106—42no—
250#106—42no—
251C4⋊C8—42no—
252#103—42no—
253#103—42no—
254#102—42no—
255#102—42no—
256#95—22no—
257#95—22no—
258#95—22no—
259#95—22no—
260#95—22no—
261#95D4×C7312yes—
262#95D4×C7312yes—
263C24—21no—
264C2×Q8—21no—
265C2×Q8—22no—
266C2×Q8—22no—
267C2×Q8—21no—
268C2×Q8—42no—
269C2×Q8—82no—
270C2×D4—21no—
271C2×D4—22no—
272C2×D4—22no—
273C2×D4—21no—
274C22×C4—21no—
275C22×C4—22no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—22no—
279C22×C4C2×D4×C7312yes—
280C22×C4C2×D4×C7312yes—
281C22×C4C2×D4×C7311yescharacteristic
282C22×C4C2×D4×C7311yescharacteristic
283C22×C4C24×C7311yescharacteristic
284C2×C8—22no—
285C2×C8—22no—
286C2×C8—22no—
287C2×C8—22no—
288C2×C8—22no—
289C2×C8—22no—
290C4⋊C4—22no—
291C4⋊C4—22no—
292C4⋊C4—22no—
293C4⋊C4—22no—
294C4⋊C4—22no—
295C4⋊C4—22no—
296C4⋊C4—42no—
297C4⋊C4—82no—
298C4⋊C4—82no—
299C4⋊C4—82no—
300C22⋊C4—42no—
301C22⋊C4—42no—
302C22⋊C4—82no—
303C22⋊C4—82no—
304C42—21no—
305C42—22no—
306C42—22no—
307C42—21no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—42no—
312C23—42no—
313C23C22×D4×C7311yescharacteristic
314Q8—42no—
315Q8—42no—
316Q8—84no—
317D4—42no—
318D4—42no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4H(5,𝔽2)×C7311yescharacteristic
343C2×C4H(5,𝔽2)×C7312yes—
344C2×C42−1+4×C7312yes—
345C2×C42−1+4×C7311yescharacteristic
346C8—42no—
347C8—42no—
348C22—81no—
349C22—81no—
350C22—82no—
351C22—82no—
352C22—81no—
353C22#535×C7311yescharacteristic
354C22#536×C7311yescharacteristic
355C22#537×C7311yescharacteristic
356C22#577×C7312yes—
357C22#577×C7312yes—
358C4—41no—
359C4—41no—
360C4—42no—
361C4—42no—
362C4—82no—
363C4—81no—
364C4—81no—
365C4—82no—
366C4—81no—
367C4#562×C7312yes—
368C4#563×C7312yes—
369C2—161no—
370C2C73×#282011yescharacteristic
371C2C73×#322111yescharacteristic
372C2C73×#322211yescharacteristic
373C2C73×#324412yes—
374C2C73×#326312yes—
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC22×D4×C73C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ #376×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C73×#2647C2semidirect
3. C73×#2096C2semidirect
5. C73×#2074C2semidirect
7. C73×#2066C2semidirect
9. C73×#2058C2semidirect
11. C73×#1832C2semidirect
181. #32830C73direct (N × H)
188. #2647C2×C73semidirect
190. #2096C2×C73semidirect
192. #2074C2×C73semidirect
194. #2066C2×C73semidirect
196. #2058C2×C73semidirect
198. #1832C2×C73semidirect
199. C73#32830direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#26472
C73×#26402
C73×#20962
C73×#20942
C73×#20742
C73×#20732
C73×#20662
C73×#20652
C73×#20582
C73×#20422
C73×#18322
#3283073