Finite Group Databasebeta

← C73×#33806 #32943210

Subgroups — C73×#33806 #32943210

Order 18688.

462 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3168C211yesmaximal, characteristic
2C73×#3160C211yesmaximal, characteristic, complemented
3C73×#2255C211yesmaximal, characteristic, complemented
4C73×#2255C211yesmaximal, characteristic, complemented
5C73×#2243C211yesmaximal, characteristic, complemented
6C73×#2243C211yesmaximal, characteristic, complemented
7C73×#2237C212yesmaximal, complemented
8C73×#2234C212yesmaximal
9C73×#2229C212yesmaximal, complemented
10C73×#2228C212yesmaximal, complemented
11C73×#2163C211yesmaximal, characteristic, complemented
12#533×C73—21no—
13#529×C73—21no—
14#500×C73C2211yescharacteristic
15#500×C73C2211yescharacteristic
16#499×C73—21no—
17#499×C73C2212yes—
18#499×C73C2211yescharacteristic
19#498×C73—21no—
20#495×C73C2211yescharacteristic
21#488×C73—21no—
22#467×C73C2211yescharacteristic
23#466×C73C2211yescharacteristic
24#465×C73—21no—
25C4×Q16×C73C2211yescharacteristic
26C4×SD16×C73—21no—
27C4×D8×C73C2211yescharacteristic
28#427×C73—21no—
29#427×C73C2212yes—
30C2×C4×C8×C73C2211yescharacteristic
31#367×C73C2212yes—
32#367×C73C2212yes—
33#366×C73C2212yes—
34#366×C73C2212yes—
35C4⋊C16×C73C2212yes—
36#358×C73C2212yes—
37#358×C73C2212yes—
38#357×C73C2212yes—
39#357×C73C2212yes—
40C22⋊C16×C73C2212yes—
41#346×C73C2211yescharacteristic
42#346×C73C2211yescharacteristic
43C2×Q16×C73C2311yescharacteristic
44C2×SD16×C73—21no—
45C2×D8×C73C2311yescharacteristic
46C22×C8×C73D411yescharacteristic
47C22×C8×C73C2311yescharacteristic
48C4⋊Q8×C73—21no—
49C4⋊Q8×C73—21no—
50#126×C73—41no—
51#125×C73—21no—
52#125×C73—22no—
53#124×C73—21no—
54#123×C73—41no—
55C22⋊Q8×C73—21no—
56C22⋊Q8×C73—41no—
57C22⋊Q8×C73—41no—
58#121×C73—21no—
59C4×Q8×C73—21no—
60C4×Q8×C73—41no—
61C4×Q8×C73—41no—
62C4×D4×C73—21no—
63C4×D4×C73—41no—
64#117×C73—22no—
65#117×C73—41no—
66C2×C42×C73D411yescharacteristic
67C2×C16×C73C2312yes—
68C2×C16×C73C2312yes—
69#107×C73—21no—
70#107×C73—21no—
71#107×C73C2312yes—
72#107×C73C2312yes—
73#107×C73C2311yescharacteristic
74#107×C73C2311yescharacteristic
75#106×C73—22no—
76#106×C73—22no—
77#106×C73—21no—
78#103×C73—21no—
79#103×C73—21no—
80#102×C73—21no—
81#102×C73—21no—
82C4×C8×C73D411yescharacteristic
83C4×C8×C73D411yescharacteristic
84C4×C8×C73C2311yescharacteristic
85C4×C8×C73C2311yescharacteristic
86C2×Q8×C73—21no—
87C2×Q8×C73—41no—
88C2×Q8×C73—41no—
89C2×D4×C73—21no—
90C2×D4×C73—41no—
91C22×C4×C73—41no—
92C22×C4×C73D811yescharacteristic
93C22×C4×C73D811yescharacteristic
94C22×C4×C73C2×D411yescharacteristic
95Q16×C73—22no—
96SD16×C73—42no—
97D8×C73—22no—
98C2×C8×C73—22no—
99C2×C8×C73—22no—
100C2×C8×C73C2×D411yescharacteristic
101C2×C8×C73C2×D411yescharacteristic
102C2×C8×C73C2×D411yescharacteristic
103C2×C8×C73C2411yescharacteristic
104C4⋊C4×C73—21no—
105C4⋊C4×C73—21no—
106C4⋊C4×C73—22no—
107C4⋊C4×C73—22no—
108C4⋊C4×C73—41no—
109C4⋊C4×C73—41no—
110C4⋊C4×C73—41no—
111C4⋊C4×C73—41no—
112C4⋊C4×C73—42no—
113C4⋊C4×C73—42no—
114C4⋊C4×C73—41no—
115C4⋊C4×C73—41no—
116C22⋊C4×C73—42no—
117C22⋊C4×C73—41no—
118C22⋊C4×C73—41no—
119C22⋊C4×C73—41no—
120C22⋊C4×C73—41no—
121C22⋊C4×C73—41no—
122C42×C73—42no—
123C42×C73—41no—
124C42×C73D811yescharacteristic
125C42×C73D811yescharacteristic
126C42×C73C2×D411yescharacteristic
127C42×C73C2×D411yescharacteristic
128C16×C73—22no—
129C16×C73—22no—
130C23×C73—41no—
131C23×C73C2×D811yescharacteristic
132Q8×C73—41no—
133Q8×C73—41no—
134Q8×C73—82no—
135Q8×C73—82no—
136D4×C73—41no—
137D4×C73—41no—
138D4×C73—82no—
139C2×C4×C73—21no—
140C2×C4×C73—21no—
141C2×C4×C73—41no—
142C2×C4×C73—41no—
143C2×C4×C73—41no—
144C2×C4×C73—41no—
145C2×C4×C73—42no—
146C2×C4×C73—42no—
147C2×C4×C73—41no—
148C2×C4×C73—82no—
149C2×C4×C73C2×D811yescharacteristic
150C2×C4×C73C2×D811yescharacteristic
151C2×C4×C73C2×D811yescharacteristic
152C2×C4×C73C2×D811yescharacteristic
153C2×C4×C73C2×D811yescharacteristic
154C2×C4×C73C22×D411yescharacteristic
155C8×C73—21no—
156C8×C73—21no—
157C8×C73#13712yes—
158C8×C732−1+412yes—
159C22×C73—21no—
160C22×C73—21no—
161C22×C73—21no—
162C22×C73—81no—
163C22×C73—81no—
164C22×C73—81no—
165C22×C73C22×D811yescharacteristic
166C4×C73—21no—
167C4×C73—21no—
168C4×C73—21no—
169C4×C73—21no—
170C4×C73—21no—
171C4×C73—81no—
172C4×C73—81no—
173C4×C73—82no—
174C4×C73—82no—
175C4×C73—81no—
176C4×C73#53611yescharacteristic
177C4×C73C2×#13711yescharacteristic
178#33806C7311yesmaximal, characteristic, direct product factor, Sylow
179C2×C73—41no—
180C2×C73—161no—
181C2×C73#322611yescharacteristic
182C2×C73#341411yescharacteristic
183C2×C73#341411yescharacteristic
184#3168C2×C7311yescharacteristic
185#3160C2×C7311yescharacteristic, complemented
186#2255C2×C7311yescharacteristic, complemented
187#2255C2×C7311yescharacteristic, complemented
188#2243C2×C7311yescharacteristic, complemented
189#2243C2×C7311yescharacteristic, complemented
190#2237C2×C7312yescomplemented
191#2234C2×C7312yes—
192#2229C2×C7312yescomplemented
193#2228C2×C7312yescomplemented
194#2163C2×C7311yescharacteristic, complemented
195C73#3380611yescharacteristic, direct product factor, Sylow
196#533—21no—
197#529—21no—
198#500C22×C7311yescharacteristic
199#500C22×C7311yescharacteristic
200#499—21no—
201#499C22×C7312yes—
202#499C22×C7311yescharacteristic
203#498—21no—
204#495C22×C7311yescharacteristic
205#488—21no—
206#467C22×C7311yescharacteristic
207#466C22×C7311yescharacteristic
208#465—21no—
209C4×Q16C22×C7311yescharacteristic
210C4×SD16—21no—
211C4×D8C22×C7311yescharacteristic
212#427—21no—
213#427C22×C7312yes—
214C2×C4×C8C22×C7311yescharacteristic
215#367C22×C7312yes—
216#367C22×C7312yes—
217#366C22×C7312yes—
218#366C22×C7312yes—
219C4⋊C16C22×C7312yes—
220#358C22×C7312yes—
221#358C22×C7312yes—
222#357C22×C7312yes—
223#357C22×C7312yes—
224C22⋊C16C22×C7312yes—
225#346C22×C7311yescharacteristic
226#346C22×C7311yescharacteristic
227C2×Q16C23×C7311yescharacteristic
228C2×SD16—21no—
229C2×D8C23×C7311yescharacteristic
230C22×C8D4×C7311yescharacteristic
231C22×C8C23×C7311yescharacteristic
232C4⋊Q8—21no—
233C4⋊Q8—21no—
234#126—41no—
235#125—21no—
236#125—22no—
237#124—21no—
238#123—41no—
239C22⋊Q8—21no—
240C22⋊Q8—41no—
241C22⋊Q8—41no—
242#121—21no—
243C4×Q8—21no—
244C4×Q8—41no—
245C4×Q8—41no—
246C4×D4—21no—
247C4×D4—41no—
248#117—22no—
249#117—41no—
250C2×C42D4×C7311yescharacteristic
251C2×C16C23×C7312yes—
252C2×C16C23×C7312yes—
253#107—21no—
254#107—21no—
255#107C23×C7312yes—
256#107C23×C7312yes—
257#107C23×C7311yescharacteristic
258#107C23×C7311yescharacteristic
259#106—22no—
260#106—22no—
261#106—21no—
262#103—21no—
263#103—21no—
264#102—21no—
265#102—21no—
266C4×C8D4×C7311yescharacteristic
267C4×C8D4×C7311yescharacteristic
268C4×C8C23×C7311yescharacteristic
269C4×C8C23×C7311yescharacteristic
270C2×Q8—21no—
271C2×Q8—41no—
272C2×Q8—41no—
273C2×D4—21no—
274C2×D4—41no—
275C22×C4—41no—
276C22×C4D8×C7311yescharacteristic
277C22×C4D8×C7311yescharacteristic
278C22×C4C2×D4×C7311yescharacteristic
279Q16—22no—
280SD16—42no—
281D8—22no—
282C2×C8—22no—
283C2×C8—22no—
284C2×C8C2×D4×C7311yescharacteristic
285C2×C8C2×D4×C7311yescharacteristic
286C2×C8C2×D4×C7311yescharacteristic
287C2×C8C24×C7311yescharacteristic
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4—22no—
291C4⋊C4—22no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—42no—
297C4⋊C4—42no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C22⋊C4—42no—
301C22⋊C4—41no—
302C22⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C42—42no—
307C42—41no—
308C42D8×C7311yescharacteristic
309C42D8×C7311yescharacteristic
310C42C2×D4×C7311yescharacteristic
311C42C2×D4×C7311yescharacteristic
312C16—22no—
313C16—22no—
314C23—41no—
315C23C2×D8×C7311yescharacteristic
316Q8—41no—
317Q8—41no—
318Q8—82no—
319Q8—82no—
320D4—41no—
321D4—41no—
322D4—82no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—41no—
332C2×C4—82no—
333C2×C4C2×D8×C7311yescharacteristic
334C2×C4C2×D8×C7311yescharacteristic
335C2×C4C2×D8×C7311yescharacteristic
336C2×C4C2×D8×C7311yescharacteristic
337C2×C4C2×D8×C7311yescharacteristic
338C2×C4C22×D4×C7311yescharacteristic
339C8—21no—
340C8—21no—
341C8#137×C7312yes—
342C82−1+4×C7312yes—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—81no—
347C22—81no—
348C22—81no—
349C22C22×D8×C7311yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—81no—
356C4—81no—
357C4—81no—
358C4—82no—
359C4—82no—
360C4#536×C7311yescharacteristic
361C4C2×#137×C7311yescharacteristic
362C2—41no—
363C2—161no—
364C2C73×#322611yescharacteristic
365C2C73×#341411yescharacteristic
366C2C73×#341411yescharacteristic
subgroupG/H
center, socleC22×C73C22×D8
commutator, Frattini, cosocleC2×C8C24×C73
prime radical#466×C73C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C73 ◁ C2×C42×C73 ◁ C2×C4×C8×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C73×#3160C2semidirect
3. C73×#2255C2semidirect
4. C73×#2255C2semidirect
5. C73×#2243C2semidirect
6. C73×#2243C2semidirect
7. C73×#2237C2semidirect
9. C73×#2229C2semidirect
10. C73×#2228C2semidirect
11. C73×#2163C2semidirect
178. #33806C73direct (N × H)
185. #3160C2×C73semidirect
186. #2255C2×C73semidirect
187. #2255C2×C73semidirect
188. #2243C2×C73semidirect
189. #2243C2×C73semidirect
190. #2237C2×C73semidirect
192. #2229C2×C73semidirect
193. #2228C2×C73semidirect
194. #2163C2×C73semidirect
195. C73#33806direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#31682
C73×#31602
C73×#22552
C73×#22432
C73×#22372
C73×#22342
C73×#22292
C73×#22282
C73×#21632
#3380673