Finite Group Databasebeta

← C73×#3118 #22607271

Subgroups — C73×#3118 #22607271

Order 9344.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#542×C73C211yesmaximal, characteristic, complemented
2#518×C73C211yesmaximal, characteristic, complemented
3#485×C73C211yesmaximal, characteristic, complemented
4#482×C73C211yesmaximal, characteristic, complemented
5#476×C73C211yesmaximal, characteristic, complemented
6#474×C73C211yesmaximal, characteristic, complemented
7#463×C73C211yesmaximal, characteristic, complemented
8#463×C73C211yesmaximal, characteristic, complemented
9#450×C73C211yesmaximal, characteristic, complemented
10#447×C73C211yesmaximal, characteristic
11#442×C73C211yesmaximal, characteristic, complemented
12#440×C73C211yesmaximal, characteristic, complemented
13C4×SD16×C73C211yesmaximal, characteristic, complemented
14C4×D8×C73C211yesmaximal, characteristic, complemented
15#433×C73C211yesmaximal, characteristic, complemented
16C22×D4×C73C2211yescharacteristic
17C2×SD16×C73C2211yescharacteristic
18C2×SD16×C73C2211yescharacteristic
19C2×D8×C73C2211yescharacteristic
20C2×D8×C73C2211yescharacteristic
21C4⋊Q8×C73C2211yescharacteristic, complemented
22#126×C73—21no—
23#124×C73—21no—
24#124×C73C2211yescharacteristic, complemented
25#123×C73—21no—
26C22⋊Q8×C73—21no—
27C22⋊Q8×C73C2211yescharacteristic
28#121×C73C2211yescharacteristic
29C4×Q8×C73C2211yescharacteristic, complemented
30C4×D4×C73—21no—
31C4×D4×C73—21no—
32C4×D4×C73C2211yescharacteristic
33C4×D4×C73C2211yescharacteristic
34C4×D4×C73C2211yescharacteristic
35C4×D4×C73C2211yescharacteristic
36C4×D4×C73C2211yescharacteristic, complemented
37#117×C73C2211yescharacteristic
38#117×C73C2211yescharacteristic
39C2×C22⋊C4×C73—21no—
40C2×C22⋊C4×C73—21no—
41#107×C73C2211yescharacteristic, complemented
42#107×C73C2211yescharacteristic, complemented
43#106×C73C2211yescharacteristic, complemented
44#106×C73C2211yescharacteristic, complemented
45C4⋊C8×C73C2211yescharacteristic, complemented
46C4⋊C8×C73C2211yescharacteristic, complemented
47#103×C73C2211yescharacteristic, complemented
48#103×C73C2211yescharacteristic, complemented
49#102×C73C2211yescharacteristic
50#102×C73C2211yescharacteristic
51#102×C73C2211yescharacteristic
52#102×C73C2211yescharacteristic
53#102×C73C2211yescharacteristic, complemented
54#102×C73C2211yescharacteristic, complemented
55C22⋊C8×C73C2211yescharacteristic
56C22⋊C8×C73C2211yescharacteristic
57#97×C73C2211yescharacteristic, complemented
58C4×C8×C73C2211yescharacteristic, complemented
59C24×C73—21no—
60C2×Q8×C73—21no—
61C2×Q8×C73C2311yescharacteristic
62C2×D4×C73—22no—
63C2×D4×C73—22no—
64C2×D4×C73—21no—
65C2×D4×C73—21no—
66C2×D4×C73C2311yescharacteristic
67C2×D4×C73C2311yescharacteristic
68C2×D4×C73C2311yescharacteristic
69C22×C4×C73—21no—
70C22×C4×C73—21no—
71C22×C4×C73—21no—
72C22×C4×C73—21no—
73C22×C4×C73—21no—
74C22×C4×C73C2311yescharacteristic
75SD16×C73—22no—
76SD16×C73—22no—
77D8×C73—22no—
78D8×C73—22no—
79C2×C8×C73C2311yescharacteristic
80C2×C8×C73C2311yescharacteristic
81C2×C8×C73C2311yescharacteristic
82C2×C8×C73C2311yescharacteristic
83C4⋊C4×C73—21no—
84C4⋊C4×C73—21no—
85C4⋊C4×C73—21no—
86C4⋊C4×C73D411yescharacteristic
87C4⋊C4×C73D411yescharacteristic
88C4⋊C4×C73C2311yescharacteristic
89C4⋊C4×C73C2311yescharacteristic
90C4⋊C4×C73C2311yescharacteristic
91C4⋊C4×C73C2311yescharacteristic
92C22⋊C4×C73—21no—
93C22⋊C4×C73—21no—
94C22⋊C4×C73—21no—
95C22⋊C4×C73—21no—
96C22⋊C4×C73—21no—
97C22⋊C4×C73—21no—
98C22⋊C4×C73—21no—
99C22⋊C4×C73—21no—
100C22⋊C4×C73—21no—
101C22⋊C4×C73—21no—
102C22⋊C4×C73D411yescharacteristic
103C22⋊C4×C73D411yescharacteristic
104C42×C73—21no—
105C42×C73—21no—
106C42×C73C2311yescharacteristic
107C42×C73C2311yescharacteristic
108C23×C73—24no—
109C23×C73—21no—
110C23×C73—21no—
111C23×C73—21no—
112C23×C73—81no—
113C23×C73—81no—
114C23×C73C2×D411yescharacteristic
115Q8×C73—21no—
116Q8×C73—21no—
117Q8×C73—81no—
118D4×C73—24no—
119D4×C73—21no—
120D4×C73—21no—
121D4×C73—21no—
122D4×C73—21no—
123D4×C73—81no—
124D4×C73#4112yes—
125D4×C73#4112yes—
126C2×C4×C73—21no—
127C2×C4×C73—21no—
128C2×C4×C73—21no—
129C2×C4×C73—21no—
130C2×C4×C73—21no—
131C2×C4×C73—21no—
132C2×C4×C73—21no—
133C2×C4×C73—81no—
134C2×C4×C73—81no—
135C2×C4×C73—81no—
136C2×C4×C73—81no—
137C2×C4×C73—81no—
138C2×C4×C73C2×D411yescharacteristic
139C2×C4×C73C2×D411yescharacteristic
140C2×C4×C73C2×D411yescharacteristic
141C2×C4×C73C2×D411yescharacteristic
142C2×C4×C73C2×D411yescharacteristic
143C2×C4×C73C2411yescharacteristic
144C8×C73—21no—
145C8×C73—21no—
146C8×C73—21no—
147C8×C73—21no—
148C22×C73—21no—
149C22×C73—22no—
150C22×C73—22no—
151C22×C73—21no—
152C22×C73—21no—
153C22×C73—41no—
154C22×C73—41no—
155C22×C73—41no—
156C22×C73—41no—
157C22×C73—41no—
158C22×C73—41no—
159C22×C73—41no—
160C22×C73—84no—
161C22×C73C22×D411yescharacteristic
162C4×C73—21no—
163C4×C73—21no—
164C4×C73—21no—
165C4×C73—21no—
166C4×C73—21no—
167C4×C73—41no—
168C4×C73—41no—
169C4×C73—41no—
170C4×C73—41no—
171C4×C73—41no—
172C4×C73C2×#4111yescharacteristic
173C4×C73C2×#4111yescharacteristic
174C2×C73—41no—
175C2×C73—42no—
176C2×C73—42no—
177C2×C73—81no—
178C2×C73#52511yescharacteristic
179C2×C73#57611yescharacteristic
180C2×C73#57711yescharacteristic
181#3118C7311yesmaximal, characteristic, direct product factor, Sylow
182C73#311811yescharacteristic, direct product factor, Sylow
183#542C2×C7311yescharacteristic, complemented
184#518C2×C7311yescharacteristic, complemented
185#485C2×C7311yescharacteristic, complemented
186#482C2×C7311yescharacteristic, complemented
187#476C2×C7311yescharacteristic, complemented
188#474C2×C7311yescharacteristic, complemented
189#463C2×C7311yescharacteristic, complemented
190#463C2×C7311yescharacteristic, complemented
191#450C2×C7311yescharacteristic, complemented
192#447C2×C7311yescharacteristic
193#442C2×C7311yescharacteristic, complemented
194#440C2×C7311yescharacteristic, complemented
195C4×SD16C2×C7311yescharacteristic, complemented
196C4×D8C2×C7311yescharacteristic, complemented
197#433C2×C7311yescharacteristic, complemented
198C22×D4C22×C7311yescharacteristic
199C2×SD16C22×C7311yescharacteristic
200C2×SD16C22×C7311yescharacteristic
201C2×D8C22×C7311yescharacteristic
202C2×D8C22×C7311yescharacteristic
203C4⋊Q8C22×C7311yescharacteristic, complemented
204#126—21no—
205#124—21no—
206#124C22×C7311yescharacteristic, complemented
207#123—21no—
208C22⋊Q8—21no—
209C22⋊Q8C22×C7311yescharacteristic
210#121C22×C7311yescharacteristic
211C4×Q8C22×C7311yescharacteristic, complemented
212C4×D4—21no—
213C4×D4—21no—
214C4×D4C22×C7311yescharacteristic
215C4×D4C22×C7311yescharacteristic
216C4×D4C22×C7311yescharacteristic
217C4×D4C22×C7311yescharacteristic
218C4×D4C22×C7311yescharacteristic, complemented
219#117C22×C7311yescharacteristic
220#117C22×C7311yescharacteristic
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223#107C22×C7311yescharacteristic, complemented
224#107C22×C7311yescharacteristic, complemented
225#106C22×C7311yescharacteristic, complemented
226#106C22×C7311yescharacteristic, complemented
227C4⋊C8C22×C7311yescharacteristic, complemented
228C4⋊C8C22×C7311yescharacteristic, complemented
229#103C22×C7311yescharacteristic, complemented
230#103C22×C7311yescharacteristic, complemented
231#102C22×C7311yescharacteristic
232#102C22×C7311yescharacteristic
233#102C22×C7311yescharacteristic
234#102C22×C7311yescharacteristic
235#102C22×C7311yescharacteristic, complemented
236#102C22×C7311yescharacteristic, complemented
237C22⋊C8C22×C7311yescharacteristic
238C22⋊C8C22×C7311yescharacteristic
239#97C22×C7311yescharacteristic, complemented
240C4×C8C22×C7311yescharacteristic, complemented
241C24—21no—
242C2×Q8—21no—
243C2×Q8C23×C7311yescharacteristic
244C2×D4—22no—
245C2×D4—22no—
246C2×D4—21no—
247C2×D4—21no—
248C2×D4C23×C7311yescharacteristic
249C2×D4C23×C7311yescharacteristic
250C2×D4C23×C7311yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4C23×C7311yescharacteristic
257SD16—22no—
258SD16—22no—
259D8—22no—
260D8—22no—
261C2×C8C23×C7311yescharacteristic
262C2×C8C23×C7311yescharacteristic
263C2×C8C23×C7311yescharacteristic
264C2×C8C23×C7311yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4D4×C7311yescharacteristic
269C4⋊C4D4×C7311yescharacteristic
270C4⋊C4C23×C7311yescharacteristic
271C4⋊C4C23×C7311yescharacteristic
272C4⋊C4C23×C7311yescharacteristic
273C4⋊C4C23×C7311yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4D4×C7311yescharacteristic
285C22⋊C4D4×C7311yescharacteristic
286C42—21no—
287C42—21no—
288C42C23×C7311yescharacteristic
289C42C23×C7311yescharacteristic
290C23—24no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—81no—
295C23—81no—
296C23C2×D4×C7311yescharacteristic
297Q8—21no—
298Q8—21no—
299Q8—81no—
300D4—24no—
301D4—21no—
302D4—21no—
303D4—21no—
304D4—21no—
305D4—81no—
306D4#41×C7312yes—
307D4#41×C7312yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4C2×D4×C7311yescharacteristic
321C2×C4C2×D4×C7311yescharacteristic
322C2×C4C2×D4×C7311yescharacteristic
323C2×C4C2×D4×C7311yescharacteristic
324C2×C4C2×D4×C7311yescharacteristic
325C2×C4C24×C7311yescharacteristic
326C8—21no—
327C8—21no—
328C8—21no—
329C8—21no—
330C22—21no—
331C22—22no—
332C22—22no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—84no—
343C22C22×D4×C7311yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4C2×#41×C7311yescharacteristic
355C4C2×#41×C7311yescharacteristic
356C2—41no—
357C2—42no—
358C2—42no—
359C2—81no—
360C2#525×C7311yescharacteristic
361C2#576×C7311yescharacteristic
362C2#577×C7311yescharacteristic
subgroupG/H
center, socleC22×C73C22×D4
commutator, Frattini, cosocleC2×C4C24×C73
prime radical#447×C73C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C73 ◁ #117×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. #542×C73C2semidirect
2. #518×C73C2semidirect
3. #485×C73C2semidirect
4. #482×C73C2semidirect
5. #476×C73C2semidirect
6. #474×C73C2semidirect
7. #463×C73C2semidirect
8. #463×C73C2semidirect
9. #450×C73C2semidirect
11. #442×C73C2semidirect
12. #440×C73C2semidirect
13. C4×SD16×C73C2semidirect
14. C4×D8×C73C2semidirect
15. #433×C73C2semidirect
21. C4⋊Q8×C73C22semidirect
24. #124×C73C22semidirect
29. C4×Q8×C73C22semidirect
36. C4×D4×C73C22semidirect
41. #107×C73C22semidirect
42. #107×C73C22semidirect
43. #106×C73C22semidirect
44. #106×C73C22semidirect
45. C4⋊C8×C73C22semidirect
46. C4⋊C8×C73C22semidirect
47. #103×C73C22semidirect
48. #103×C73C22semidirect
53. #102×C73C22semidirect
54. #102×C73C22semidirect
57. #97×C73C22semidirect
58. C4×C8×C73C22semidirect
181. #3118C73direct (N × H)
182. C73#3118direct (N × H)
183. #542C2×C73semidirect
184. #518C2×C73semidirect
185. #485C2×C73semidirect
186. #482C2×C73semidirect
187. #476C2×C73semidirect
188. #474C2×C73semidirect
189. #463C2×C73semidirect
190. #463C2×C73semidirect
191. #450C2×C73semidirect
193. #442C2×C73semidirect
194. #440C2×C73semidirect
195. C4×SD16C2×C73semidirect
196. C4×D8C2×C73semidirect
197. #433C2×C73semidirect
203. C4⋊Q8C22×C73semidirect
206. #124C22×C73semidirect
211. C4×Q8C22×C73semidirect
218. C4×D4C22×C73semidirect
223. #107C22×C73semidirect
224. #107C22×C73semidirect
225. #106C22×C73semidirect
226. #106C22×C73semidirect
227. C4⋊C8C22×C73semidirect
228. C4⋊C8C22×C73semidirect
229. #103C22×C73semidirect
230. #103C22×C73semidirect
235. #102C22×C73semidirect
236. #102C22×C73semidirect
239. #97C22×C73semidirect
240. C4×C8C22×C73semidirect

Maximal subgroups

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

subgroupindex
#542×C732
#518×C732
#485×C732
#482×C732
#476×C732
#474×C732
#463×C732
#450×C732
#447×C732
#442×C732
#440×C732
C4×SD16×C732
C4×D8×C732
#433×C732
#311873