Finite Group Databasebeta

← C73×#33629 #32943033

Subgroups — C73×#33629 #32943033

Order 18688.

574 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#500×C73C211yesmaximal, characteristic, complemented
2C4×#135×C73C211yesmaximal, characteristic
3C73×#2227C212yesmaximal, complemented
4C73×#2226C212yesmaximal, complemented
5C73×#2225C212yesmaximal, complemented
6C73×#2224C212yesmaximal, complemented
7C73×#2159C212yesmaximal, complemented
8C73×#2150C211yesmaximal, characteristic, complemented
9C73×#2139C212yesmaximal
10C2×#135×C73C2211yescharacteristic
11C2×C4⋊Q8×C73—21no—
12C4×#41×C73—21no—
13C2×M32×C73C2212yes—
14#500×C73—21no—
15#500×C73—21no—
16#500×C73C2212yes—
17#500×C73C2212yes—
18C4×Q16×C73C2211yescharacteristic
19C4×Q16×C73C2211yescharacteristic
20C4×SD16×C73—21no—
21C4×SD16×C73—21no—
22C4×D8×C73C2211yescharacteristic
23C4×D8×C73C2211yescharacteristic
24#427×C73C2211yescharacteristic
25C2×#107×C73—21no—
26C2×#107×C73C2212yes—
27#416×C73—21no—
28C2×C4×C8×C73C2211yescharacteristic
29#367×C73C2214yes—
30#366×C73C2214yes—
31C4⋊C16×C73C2212yes—
32C4⋊C16×C73C2212yes—
33#358×C73C2214yes—
34#357×C73C2214yes—
35C2×#41×C73—21no—
36C22×Q8×C73—41no—
37#135×C73—22no—
38#135×C73Q814yescomplemented
39C2×Q16×C73C2311yescharacteristic
40C2×SD16×C73—21no—
41C2×D8×C73C2311yescharacteristic
42C22×C8×C73D411yescharacteristic
43C22×C8×C73C2311yescharacteristic
44C4⋊Q8×C73—22no—
45C4⋊Q8×C73—22no—
46C4⋊Q8×C73—41no—
47C4⋊Q8×C73—41no—
48C4×Q8×C73—21no—
49C4×Q8×C73—21no—
50C4×D4×C73—21no—
51C4×D4×C73—21no—
52C4×D4×C73—41no—
53C4×D4×C73—41no—
54#117×C73—21no—
55#117×C73—41no—
56C2×C4⋊C4×C73—22no—
57C2×C4⋊C4×C73—41no—
58C2×C42×C73—41no—
59C2×C42×C73D411yescharacteristic
60M32×C73—24no—
61C2×C16×C73C2314yes—
62#107×C73—22no—
63#107×C73—22no—
64#107×C73—22no—
65#107×C73C2314yes—
66#107×C73C2311yescharacteristic
67#107×C73C2311yescharacteristic
68#106×C73—21no—
69#103×C73—21no—
70#103×C73—21no—
71#102×C73—21no—
72#102×C73—21no—
73C4×C8×C73D411yescharacteristic
74C4×C8×C73D411yescharacteristic
75C4×C8×C73C2311yescharacteristic
76C4×C8×C73C2311yescharacteristic
77#41×C73—24no—
78#41×C73—42no—
79C2×Q8×C73—21no—
80C2×Q8×C73—42no—
81C2×Q8×C73—42no—
82C2×Q8×C73—84no—
83C2×D4×C73—21no—
84C2×D4×C73—41no—
85C22×C4×C73—41no—
86C22×C4×C73—42no—
87C22×C4×C73—41no—
88C22×C4×C73—41no—
89C22×C4×C73D811yescharacteristic
90C22×C4×C73D811yescharacteristic
91C22×C4×C73C2×D411yescharacteristic
92Q16×C73—21no—
93Q16×C73C2×Q812yescomplemented
94SD16×C73—24no—
95D8×C73—21no—
96D8×C73C2×Q812yescomplemented
97C2×C8×C73—22no—
98C2×C8×C73C2×D411yescharacteristic
99C2×C8×C73C2×D411yescharacteristic
100C2×C8×C73C2×D411yescharacteristic
101C2×C8×C73C2×Q812yes—
102C2×C8×C73#4112yes—
103C2×C8×C73C2411yescharacteristic
104C4⋊C4×C73—21no—
105C4⋊C4×C73—21no—
106C4⋊C4×C73—24no—
107C4⋊C4×C73—42no—
108C4⋊C4×C73—42no—
109C4⋊C4×C73—42no—
110C4⋊C4×C73—41no—
111C4⋊C4×C73—41no—
112C22⋊C4×C73—41no—
113C22⋊C4×C73—41no—
114C22⋊C4×C73—41no—
115C42×C73—41no—
116C42×C73—41no—
117C42×C73—41no—
118C42×C73D811yescharacteristic
119C42×C73D811yescharacteristic
120C42×C73C2×D411yescharacteristic
121C42×C73C2×D411yescharacteristic
122C16×C73—24no—
123C23×C73—41no—
124C23×C73C2×D811yescharacteristic
125Q8×C73—22no—
126Q8×C73—41no—
127Q8×C73—84no—
128Q8×C73—84no—
129D4×C73—22no—
130D4×C73—44no—
131D4×C73—41no—
132C2×C4×C73—22no—
133C2×C4×C73—22no—
134C2×C4×C73—41no—
135C2×C4×C73—44no—
136C2×C4×C73—41no—
137C2×C4×C73—41no—
138C2×C4×C73—44no—
139C2×C4×C73—84no—
140C2×C4×C73—82no—
141C2×C4×C73—82no—
142C2×C4×C73C22⋊Q812yes—
143C2×C4×C73C2×D811yescharacteristic
144C2×C4×C73C2×D811yescharacteristic
145C2×C4×C73C2×D811yescharacteristic
146C2×C4×C73C2×D811yescharacteristic
147C2×C4×C73C2×D811yescharacteristic
148C2×C4×C73#13712yes—
149C2×C4×C73C22×D411yescharacteristic
150C8×C73—21no—
151C8×C73—21no—
152C8×C73C22⋊Q812yes—
153C8×C73C22×Q811yescharacteristic
154C8×C73C2×#4111yescharacteristic
155C22×C73—21no—
156C22×C73—21no—
157C22×C73—42no—
158C22×C73—81no—
159C22×C73—81no—
160C22×C73#47412yes—
161C22×C73C22×D811yescharacteristic
162C4×C73—21no—
163C4×C73—21no—
164C4×C73—42no—
165C4×C73—81no—
166C4×C73—84no—
167C4×C73—81no—
168C4×C73#47412yes—
169C4×C73#50912yes—
170C4×C73#51012yes—
171C4×C73C2×C22⋊Q811yescharacteristic
172C4×C73C2×#13711yescharacteristic
173#33629C7311yesmaximal, characteristic, direct product factor, Sylow
174C2×C73—22no—
175C2×C73—82no—
176C2×C73C2×#47411yescharacteristic
177C2×C73C2×#50911yescharacteristic
178C2×C73C2×#51011yescharacteristic
179C2×#500C2×C7311yescharacteristic, complemented
180C4×#135C2×C7311yescharacteristic
181#2227C2×C7312yescomplemented
182#2226C2×C7312yescomplemented
183#2225C2×C7312yescomplemented
184#2224C2×C7312yescomplemented
185#2159C2×C7312yescomplemented
186#2150C2×C7311yescharacteristic, complemented
187#2139C2×C7312yes—
188C73#3362911yescharacteristic, direct product factor, Sylow
189C2×#135C22×C7311yescharacteristic
190C2×C4⋊Q8—21no—
191C4×#41—21no—
192C2×M32C22×C7312yes—
193#500—21no—
194#500—21no—
195#500C22×C7312yes—
196#500C22×C7312yes—
197C4×Q16C22×C7311yescharacteristic
198C4×Q16C22×C7311yescharacteristic
199C4×SD16—21no—
200C4×SD16—21no—
201C4×D8C22×C7311yescharacteristic
202C4×D8C22×C7311yescharacteristic
203#427C22×C7311yescharacteristic
204C2×#107—21no—
205C2×#107C22×C7312yes—
206#416—21no—
207C2×C4×C8C22×C7311yescharacteristic
208#367C22×C7314yes—
209#366C22×C7314yes—
210C4⋊C16C22×C7312yes—
211C4⋊C16C22×C7312yes—
212#358C22×C7314yes—
213#357C22×C7314yes—
214C2×#41—21no—
215C22×Q8—41no—
216#135—22no—
217#135Q8×C7314yescomplemented
218C2×Q16C23×C7311yescharacteristic
219C2×SD16—21no—
220C2×D8C23×C7311yescharacteristic
221C22×C8D4×C7311yescharacteristic
222C22×C8C23×C7311yescharacteristic
223C4⋊Q8—22no—
224C4⋊Q8—22no—
225C4⋊Q8—41no—
226C4⋊Q8—41no—
227C4×Q8—21no—
228C4×Q8—21no—
229C4×D4—21no—
230C4×D4—21no—
231C4×D4—41no—
232C4×D4—41no—
233#117—21no—
234#117—41no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4—41no—
237C2×C42—41no—
238C2×C42D4×C7311yescharacteristic
239M32—24no—
240C2×C16C23×C7314yes—
241#107—22no—
242#107—22no—
243#107—22no—
244#107C23×C7314yes—
245#107C23×C7311yescharacteristic
246#107C23×C7311yescharacteristic
247#106—21no—
248#103—21no—
249#103—21no—
250#102—21no—
251#102—21no—
252C4×C8D4×C7311yescharacteristic
253C4×C8D4×C7311yescharacteristic
254C4×C8C23×C7311yescharacteristic
255C4×C8C23×C7311yescharacteristic
256#41—24no—
257#41—42no—
258C2×Q8—21no—
259C2×Q8—42no—
260C2×Q8—42no—
261C2×Q8—84no—
262C2×D4—21no—
263C2×D4—41no—
264C22×C4—41no—
265C22×C4—42no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4D8×C7311yescharacteristic
269C22×C4D8×C7311yescharacteristic
270C22×C4C2×D4×C7311yescharacteristic
271Q16—21no—
272Q16C2×Q8×C7312yescomplemented
273SD16—24no—
274D8—21no—
275D8C2×Q8×C7312yescomplemented
276C2×C8—22no—
277C2×C8C2×D4×C7311yescharacteristic
278C2×C8C2×D4×C7311yescharacteristic
279C2×C8C2×D4×C7311yescharacteristic
280C2×C8C2×Q8×C7312yes—
281C2×C8#41×C7312yes—
282C2×C8C24×C7311yescharacteristic
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—24no—
286C4⋊C4—42no—
287C4⋊C4—42no—
288C4⋊C4—42no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C22⋊C4—41no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C42—41no—
295C42—41no—
296C42—41no—
297C42D8×C7311yescharacteristic
298C42D8×C7311yescharacteristic
299C42C2×D4×C7311yescharacteristic
300C42C2×D4×C7311yescharacteristic
301C16—24no—
302C23—41no—
303C23C2×D8×C7311yescharacteristic
304Q8—22no—
305Q8—41no—
306Q8—84no—
307Q8—84no—
308D4—22no—
309D4—44no—
310D4—41no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—41no—
314C2×C4—44no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—44no—
318C2×C4—84no—
319C2×C4—82no—
320C2×C4—82no—
321C2×C4C22⋊Q8×C7312yes—
322C2×C4C2×D8×C7311yescharacteristic
323C2×C4C2×D8×C7311yescharacteristic
324C2×C4C2×D8×C7311yescharacteristic
325C2×C4C2×D8×C7311yescharacteristic
326C2×C4C2×D8×C7311yescharacteristic
327C2×C4#137×C7312yes—
328C2×C4C22×D4×C7311yescharacteristic
329C8—21no—
330C8—21no—
331C8C22⋊Q8×C7312yes—
332C8C22×Q8×C7311yescharacteristic
333C8C2×#41×C7311yescharacteristic
334C22—21no—
335C22—21no—
336C22—42no—
337C22—81no—
338C22—81no—
339C22#474×C7312yes—
340C22C22×D8×C7311yescharacteristic
341C4—21no—
342C4—21no—
343C4—42no—
344C4—84no—
345C4—81no—
346C4—81no—
347C4#474×C7312yes—
348C4#509×C7312yes—
349C4#510×C7312yes—
350C4C2×C22⋊Q8×C7311yescharacteristic
351C4C2×#137×C7311yescharacteristic
352C2—22no—
353C2—82no—
354C2C2×#474×C7311yescharacteristic
355C2C2×#509×C7311yescharacteristic
356C2C2×#510×C7311yescharacteristic
subgroupG/H
center, socleC22×C73C22×D8
commutator, Frattini, cosocleC2×C8C24×C73
prime radicalC2×#135×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
1. C2×#500×C73C2semidirect
3. C73×#2227C2semidirect
4. C73×#2226C2semidirect
5. C73×#2225C2semidirect
6. C73×#2224C2semidirect
7. C73×#2159C2semidirect
8. C73×#2150C2semidirect
38. #135×C73Q8semidirect
93. Q16×C73C2×Q8semidirect
96. D8×C73C2×Q8semidirect
173. #33629C73direct (N × H)
179. C2×#500C2×C73semidirect
181. #2227C2×C73semidirect
182. #2226C2×C73semidirect
183. #2225C2×C73semidirect
184. #2224C2×C73semidirect
185. #2159C2×C73semidirect
186. #2150C2×C73semidirect
188. C73#33629direct (N × H)
217. #135Q8×C73semidirect
272. Q16C2×Q8×C73semidirect
275. D8C2×Q8×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#500×C732
C4×#135×C732
C73×#22272
C73×#22262
C73×#22252
C73×#22242
C73×#21592
C73×#21502
C73×#21392
#3362973