Finite Group Databasebeta

← C73×#33799 #32943203

Subgroups — C73×#33799 #32943203

Order 18688.

466 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×#3168C211yesmaximal, characteristic
2C73×#3160C211yesmaximal, characteristic, complemented
3C73×#2253C212yesmaximal, complemented
4C73×#2242C212yesmaximal, complemented
5C73×#2237C212yesmaximal, complemented
6C73×#2234C212yesmaximal
7C73×#2227C211yesmaximal, characteristic, complemented
8C73×#2226C211yesmaximal, characteristic, complemented
9C73×#2225C211yesmaximal, characteristic, complemented
10C73×#2224C211yesmaximal, characteristic, complemented
11C73×#2162C211yesmaximal, 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×C73C2211yescharacteristic
36C4⋊C16×C73C2211yescharacteristic
37#358×C73C2212yes—
38#358×C73C2212yes—
39#357×C73C2212yes—
40#357×C73C2212yes—
41C22⋊C16×C73C2212yes—
42C4×C16×C73C2212yes—
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—21no—
96Q16×C73—21no—
97SD16×C73—42no—
98D8×C73—21no—
99D8×C73—21no—
100C2×C8×C73—22no—
101C2×C8×C73—21no—
102C2×C8×C73—21no—
103C2×C8×C73C2×D411yescharacteristic
104C2×C8×C73C2×D411yescharacteristic
105C2×C8×C73C2×D411yescharacteristic
106C2×C8×C73C2411yescharacteristic
107C4⋊C4×C73—21no—
108C4⋊C4×C73—21no—
109C4⋊C4×C73—22no—
110C4⋊C4×C73—22no—
111C4⋊C4×C73—41no—
112C4⋊C4×C73—41no—
113C4⋊C4×C73—41no—
114C4⋊C4×C73—41no—
115C4⋊C4×C73—42no—
116C4⋊C4×C73—42no—
117C4⋊C4×C73—41no—
118C4⋊C4×C73—41no—
119C22⋊C4×C73—42no—
120C22⋊C4×C73—41no—
121C22⋊C4×C73—41no—
122C22⋊C4×C73—41no—
123C22⋊C4×C73—41no—
124C22⋊C4×C73—41no—
125C42×C73—42no—
126C42×C73—41no—
127C42×C73D811yescharacteristic
128C42×C73D811yescharacteristic
129C42×C73C2×D411yescharacteristic
130C42×C73C2×D411yescharacteristic
131C16×C73—22no—
132C16×C73—22no—
133C23×C73—41no—
134C23×C73C2×D811yescharacteristic
135Q8×C73—41no—
136Q8×C73—41no—
137Q8×C73—82no—
138Q8×C73—82no—
139D4×C73—41no—
140D4×C73—41no—
141D4×C73—82no—
142C2×C4×C73—21no—
143C2×C4×C73—21no—
144C2×C4×C73—22no—
145C2×C4×C73—41no—
146C2×C4×C73—41no—
147C2×C4×C73—41no—
148C2×C4×C73—42no—
149C2×C4×C73—42no—
150C2×C4×C73—41no—
151C2×C4×C73—82no—
152C2×C4×C73C2×D811yescharacteristic
153C2×C4×C73C2×D811yescharacteristic
154C2×C4×C73C2×D811yescharacteristic
155C2×C4×C73C2×D811yescharacteristic
156C2×C4×C73C2×D811yescharacteristic
157C2×C4×C73C22×D411yescharacteristic
158C8×C73—21no—
159C8×C73—21no—
160C8×C73#13712yes—
161C8×C732−1+411yescharacteristic
162C8×C732−1+411yescharacteristic
163C22×C73—21no—
164C22×C73—21no—
165C22×C73—21no—
166C22×C73—81no—
167C22×C73—81no—
168C22×C73—81no—
169C22×C73C22×D811yescharacteristic
170C4×C73—21no—
171C4×C73—21no—
172C4×C73—21no—
173C4×C73—21no—
174C4×C73—81no—
175C4×C73—82no—
176C4×C73—81no—
177C4×C73—82no—
178C4×C73—81no—
179C4×C73#50812yes—
180C4×C73#53611yescharacteristic
181C4×C73C2×#13711yescharacteristic
182#33799C7311yesmaximal, characteristic, direct product factor, Sylow
183C2×C73—41no—
184C2×C73—161no—
185C2×C73#322611yescharacteristic
186C2×C73C2×#50811yescharacteristic
187C2×C73#341411yescharacteristic
188#3168C2×C7311yescharacteristic
189#3160C2×C7311yescharacteristic, complemented
190#2253C2×C7312yescomplemented
191#2242C2×C7312yescomplemented
192#2237C2×C7312yescomplemented
193#2234C2×C7312yes—
194#2227C2×C7311yescharacteristic, complemented
195#2226C2×C7311yescharacteristic, complemented
196#2225C2×C7311yescharacteristic, complemented
197#2224C2×C7311yescharacteristic, complemented
198#2162C2×C7311yescharacteristic, complemented
199C73#3379911yescharacteristic, direct product factor, Sylow
200#533—21no—
201#529—21no—
202#500C22×C7311yescharacteristic
203#500C22×C7311yescharacteristic
204#499—21no—
205#499C22×C7312yes—
206#499C22×C7311yescharacteristic
207#498—21no—
208#495C22×C7311yescharacteristic
209#488—21no—
210#467C22×C7311yescharacteristic
211#466C22×C7311yescharacteristic
212#465—21no—
213C4×Q16C22×C7311yescharacteristic
214C4×SD16—21no—
215C4×D8C22×C7311yescharacteristic
216#427—21no—
217#427C22×C7312yes—
218C2×C4×C8C22×C7311yescharacteristic
219#367C22×C7312yes—
220#367C22×C7312yes—
221#366C22×C7312yes—
222#366C22×C7312yes—
223C4⋊C16C22×C7311yescharacteristic
224C4⋊C16C22×C7311yescharacteristic
225#358C22×C7312yes—
226#358C22×C7312yes—
227#357C22×C7312yes—
228#357C22×C7312yes—
229C22⋊C16C22×C7312yes—
230C4×C16C22×C7312yes—
231C2×Q16C23×C7311yescharacteristic
232C2×SD16—21no—
233C2×D8C23×C7311yescharacteristic
234C22×C8D4×C7311yescharacteristic
235C22×C8C23×C7311yescharacteristic
236C4⋊Q8—21no—
237C4⋊Q8—21no—
238#126—41no—
239#125—21no—
240#125—22no—
241#124—21no—
242#123—41no—
243C22⋊Q8—21no—
244C22⋊Q8—41no—
245C22⋊Q8—41no—
246#121—21no—
247C4×Q8—21no—
248C4×Q8—41no—
249C4×Q8—41no—
250C4×D4—21no—
251C4×D4—41no—
252#117—22no—
253#117—41no—
254C2×C42D4×C7311yescharacteristic
255C2×C16C23×C7312yes—
256C2×C16C23×C7312yes—
257#107—21no—
258#107—21no—
259#107C23×C7312yes—
260#107C23×C7312yes—
261#107C23×C7311yescharacteristic
262#107C23×C7311yescharacteristic
263#106—22no—
264#106—22no—
265#106—21no—
266#103—21no—
267#103—21no—
268#102—21no—
269#102—21no—
270C4×C8D4×C7311yescharacteristic
271C4×C8D4×C7311yescharacteristic
272C4×C8C23×C7311yescharacteristic
273C4×C8C23×C7311yescharacteristic
274C2×Q8—21no—
275C2×Q8—41no—
276C2×Q8—41no—
277C2×D4—21no—
278C2×D4—41no—
279C22×C4—41no—
280C22×C4D8×C7311yescharacteristic
281C22×C4D8×C7311yescharacteristic
282C22×C4C2×D4×C7311yescharacteristic
283Q16—21no—
284Q16—21no—
285SD16—42no—
286D8—21no—
287D8—21no—
288C2×C8—22no—
289C2×C8—21no—
290C2×C8—21no—
291C2×C8C2×D4×C7311yescharacteristic
292C2×C8C2×D4×C7311yescharacteristic
293C2×C8C2×D4×C7311yescharacteristic
294C2×C8C24×C7311yescharacteristic
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—22no—
298C4⋊C4—22no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—42no—
304C4⋊C4—42no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C22⋊C4—42no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—41no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C42—42no—
314C42—41no—
315C42D8×C7311yescharacteristic
316C42D8×C7311yescharacteristic
317C42C2×D4×C7311yescharacteristic
318C42C2×D4×C7311yescharacteristic
319C16—22no—
320C16—22no—
321C23—41no—
322C23C2×D8×C7311yescharacteristic
323Q8—41no—
324Q8—41no—
325Q8—82no—
326Q8—82no—
327D4—41no—
328D4—41no—
329D4—82no—
330C2×C4—22no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—41no—
339C2×C4—82no—
340C2×C4C2×D8×C7311yescharacteristic
341C2×C4C2×D8×C7311yescharacteristic
342C2×C4C2×D8×C7311yescharacteristic
343C2×C4C2×D8×C7311yescharacteristic
344C2×C4C2×D8×C7311yescharacteristic
345C2×C4C22×D4×C7311yescharacteristic
346C8—21no—
347C8—21no—
348C8#137×C7312yes—
349C82−1+4×C7311yescharacteristic
350C82−1+4×C7311yescharacteristic
351C22—21no—
352C22—21no—
353C22—21no—
354C22—81no—
355C22—81no—
356C22—81no—
357C22C22×D8×C7311yescharacteristic
358C4—21no—
359C4—21no—
360C4—21no—
361C4—21no—
362C4—81no—
363C4—81no—
364C4—82no—
365C4—81no—
366C4—82no—
367C4#508×C7312yes—
368C4#536×C7311yescharacteristic
369C4C2×#137×C7311yescharacteristic
370C2—41no—
371C2—161no—
372C2C73×#322611yescharacteristic
373C2C2×#508×C7311yescharacteristic
374C2C73×#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×#2253C2semidirect
4. C73×#2242C2semidirect
5. C73×#2237C2semidirect
7. C73×#2227C2semidirect
8. C73×#2226C2semidirect
9. C73×#2225C2semidirect
10. C73×#2224C2semidirect
11. C73×#2162C2semidirect
182. #33799C73direct (N × H)
189. #3160C2×C73semidirect
190. #2253C2×C73semidirect
191. #2242C2×C73semidirect
192. #2237C2×C73semidirect
194. #2227C2×C73semidirect
195. #2226C2×C73semidirect
196. #2225C2×C73semidirect
197. #2224C2×C73semidirect
198. #2162C2×C73semidirect
199. C73#33799direct (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×#22532
C73×#22422
C73×#22372
C73×#22342
C73×#22272
C73×#22262
C73×#22252
C73×#22242
C73×#21622
#3379973