Finite Group Databasebeta

← C73×#60032 #32969436

Subgroups — C73×#60032 #32969436

Order 18688.

2212 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#2736C211yesmaximal, characteristic, complemented
2C73×#2668C213yesmaximal, complemented
3C73×#2578C216yesmaximal, complemented
4C73×#2564C213yesmaximal, complemented
5C73×#2535C213yesmaximal, complemented
6C73×#2517C213yesmaximal, complemented
7C73×#2463C213yesmaximal, complemented
8C73×#2364C216yesmaximal, complemented
9C4×#120×C73C213yesmaximal, complemented
10C24×C4×C73C2211yescharacteristic
11C2×C22⋊Q8×C73C2213yescomplemented
12C2×#121×C73C2216yes—
13C2×#120×C73C2213yes—
14C2×C4×D4×C73C2216yes—
15C2×C4×D4×C73C2213yes—
16C2×C4×D4×C73C2213yescomplemented
17#400×C73C2213yescomplemented
18#399×C73C2213yes—
19#397×C73C2213yes—
20#397×C73C2216yes—
21#397×C73C2213yescomplemented
22#395×C73C2211yescharacteristic, complemented
23#394×C73C2216yes—
24#393×C73C2213yes—
25#392×C73C2213yes—
26#392×C73C2211yescharacteristic, complemented
27#388×C73C2216yes—
28#388×C73C2216yescomplemented
29#387×C73C2216yescomplemented
30#387×C73C2216yescomplemented
31#387×C73C2216yescomplemented
32#386×C73C2216yes—
33#386×C73C2213yes—
34#386×C73C2216yes—
35#386×C73C2216yes—
36#386×C73C2216yescomplemented
37#385×C73C2213yes—
38#385×C73C2216yes—
39#383×C73C2212yescomplemented
40#382×C73C2213yescomplemented
41#380×C73C2216yescomplemented
42#379×C73C2213yes—
43C4×C22⋊C4×C73C2216yes—
44C4×C22⋊C4×C73C2213yes—
45C4×C22⋊C4×C73C2216yescomplemented
46C2×#95×C73C2213yescomplemented
47C25×C73C2311yescharacteristic
48C22×Q8×C73C2311yescharacteristic
49C22×D4×C73C2316yes—
50C22×D4×C73C2313yes—
51C22×D4×C73C2313yes—
52C23×C4×C73—46no—
53C23×C4×C73C2313yes—
54C23×C4×C73C2313yes—
55C23×C4×C73C2316yes—
56C23×C4×C73C2313yes—
57C22⋊Q8×C73—46no—
58#121×C73—224no—
59#120×C73—212no—
60C4×D4×C73—46no—
61C4×D4×C73—46no—
62C4×D4×C73—412no—
63C2×C4⋊C4×C73C2316yes—
64C2×C4⋊C4×C73C2316yes—
65C2×C4⋊C4×C73C2313yes—
66C2×C4⋊C4×C73C2313yes—
67C2×C4⋊C4×C73C2313yes—
68C2×C22⋊C4×C73C2316yes—
69C2×C22⋊C4×C73C2316yes—
70C2×C22⋊C4×C73C2313yes—
71C2×C22⋊C4×C73C2316yes—
72C2×C22⋊C4×C73C2316yes—
73C2×C22⋊C4×C73C2313yes—
74C2×C22⋊C4×C73C2316yes—
75C2×C22⋊C4×C73C2313yes—
76C2×C22⋊C4×C73C2313yes—
77C2×C22⋊C4×C73C2316yes—
78C2×C42×C73C2313yes—
79C2×C42×C73C2316yes—
80C2×C42×C73C2312yes—
81#95×C73C2316yes—
82#95×C73C2316yes—
83#95×C73C2316yes—
84#95×C73C2316yes—
85#95×C73C2316yes—
86#95×C73C2311yescharacteristic
87#95×C73C2313yes—
88#95×C73C2316yes—
89#95×C73C2313yes—
90#95×C73C2313yes—
91C24×C73—26no—
92C24×C73—43no—
93C24×C73—41no—
94C24×C73C2413yes—
95C24×C73C2413yes—
96C2×Q8×C73—43no—
97C2×D4×C73—212no—
98C2×D4×C73—212no—
99C2×D4×C73—212no—
100C2×D4×C73—43no—
101C2×D4×C73—43no—
102C2×D4×C73—46no—
103C2×D4×C73—43no—
104C2×D4×C73#41112yes—
105C22×C4×C73—212no—
106C22×C4×C73—26no—
107C22×C4×C73—212no—
108C22×C4×C73—26no—
109C22×C4×C73—43no—
110C22×C4×C73—46no—
111C22×C4×C73—46no—
112C22×C4×C73—46no—
113C22×C4×C73—46no—
114C22×C4×C73—416no—
115C22×C4×C73C2416yes—
116C22×C4×C73C2416yes—
117C22×C4×C73C2413yes—
118C22×C4×C73C2411yescharacteristic
119C22×C4×C73C2413yes—
120C22×C4×C73C2413yes—
121C22×C4×C73C2413yes—
122C4⋊C4×C73—212no—
123C4⋊C4×C73—212no—
124C4⋊C4×C73—43no—
125C4⋊C4×C73—43no—
126C4⋊C4×C73—43no—
127C22⋊C4×C73—26no—
128C22⋊C4×C73—212no—
129C22⋊C4×C73—212no—
130C22⋊C4×C73—212no—
131C22⋊C4×C73—212no—
132C22⋊C4×C73—43no—
133C22⋊C4×C73—43no—
134C22⋊C4×C73—43no—
135C22⋊C4×C73—46no—
136C22⋊C4×C73—46no—
137C42×C73—26no—
138C42×C73—42no—
139C42×C73—46no—
140C23×C73—26no—
141C23×C73—26no—
142C23×C73—26no—
143C23×C73—23no—
144C23×C73—26no—
145C23×C73—23no—
146C23×C73—23no—
147C23×C73—23no—
148C23×C73—412no—
149C23×C73—412no—
150C23×C73—44no—
151C23×C73C2×#4116yes—
152C23×C73C2×#4116yes—
153C23×C73C2511yescharacteristic
154Q8×C73—82no—
155D4×C73—412no—
156D4×C73—412no—
157D4×C73—424no—
158C2×C4×C73—23no—
159C2×C4×C73—26no—
160C2×C4×C73—23no—
161C2×C4×C73—26no—
162C2×C4×C73—26no—
163C2×C4×C73—26no—
164C2×C4×C73—26no—
165C2×C4×C73—23no—
166C2×C4×C73—26no—
167C2×C4×C73—26no—
168C2×C4×C73—26no—
169C2×C4×C73—23no—
170C2×C4×C73—23no—
171C2×C4×C73—26no—
172C2×C4×C73—412no—
173C2×C4×C73—412no—
174C2×C4×C73—812no—
175C2×C4×C73—86no—
176C2×C4×C73C2×#4116yes—
177C2×C4×C73H(5,𝔽2)16yes—
178C22×C73—212no—
179C22×C73—212no—
180C22×C73—26no—
181C22×C73—26no—
182C22×C73—416no—
183C22×C73—43no—
184C22×C73—43no—
185C22×C73—46no—
186C22×C73—46no—
187C22×C73—43no—
188C22×C73—43no—
189C22×C73C22×#4113yes—
190C22×C73C2×H(5,𝔽2)13yes—
191C22×C73#58511yescharacteristic
192C4×C73—26no—
193C4×C73—26no—
194C4×C73—46no—
195C4×C73—43no—
196C4×C73—46no—
197C4×C73—41no—
198C4×C73—43no—
199#60032C7311yesmaximal, characteristic, direct product factor, Sylow
200C2×C73—46no—
201C2×C73—46no—
202C2×C73#348113yes—
203C2×C73#350513yes—
204C2×C73#353211yescharacteristic
205#2736C2×C7311yescharacteristic, complemented
206#2668C2×C7313yescomplemented
207#2578C2×C7316yescomplemented
208#2564C2×C7313yescomplemented
209#2535C2×C7313yescomplemented
210#2517C2×C7313yescomplemented
211#2463C2×C7313yescomplemented
212#2364C2×C7316yescomplemented
213C4×#120C2×C7313yescomplemented
214C73#6003211yescharacteristic, direct product factor, Sylow
215C24×C4C22×C7311yescharacteristic
216C2×C22⋊Q8C22×C7313yescomplemented
217C2×#121C22×C7316yes—
218C2×#120C22×C7313yes—
219C2×C4×D4C22×C7313yes—
220C2×C4×D4C22×C7316yes—
221C2×C4×D4C22×C7313yescomplemented
222#400C22×C7313yescomplemented
223#399C22×C7313yes—
224#397C22×C7316yes—
225#397C22×C7313yes—
226#397C22×C7313yescomplemented
227#395C22×C7311yescharacteristic, complemented
228#394C22×C7316yes—
229#393C22×C7313yes—
230#392C22×C7313yes—
231#392C22×C7311yescharacteristic, complemented
232#388C22×C7316yes—
233#388C22×C7316yescomplemented
234#387C22×C7316yescomplemented
235#387C22×C7316yescomplemented
236#387C22×C7316yescomplemented
237#386C22×C7316yes—
238#386C22×C7316yes—
239#386C22×C7316yes—
240#386C22×C7313yes—
241#386C22×C7316yescomplemented
242#385C22×C7316yes—
243#385C22×C7313yes—
244#383C22×C7312yescomplemented
245#382C22×C7313yescomplemented
246#380C22×C7316yescomplemented
247#379C22×C7313yes—
248C4×C22⋊C4C22×C7313yes—
249C4×C22⋊C4C22×C7316yes—
250C4×C22⋊C4C22×C7316yescomplemented
251C2×#95C22×C7313yescomplemented
252C25C23×C7311yescharacteristic
253C22×Q8C23×C7311yescharacteristic
254C22×D4C23×C7316yes—
255C22×D4C23×C7313yes—
256C22×D4C23×C7313yes—
257C23×C4—46no—
258C23×C4C23×C7313yes—
259C23×C4C23×C7313yes—
260C23×C4C23×C7313yes—
261C23×C4C23×C7316yes—
262C22⋊Q8—46no—
263#121—224no—
264#120—212no—
265C4×D4—46no—
266C4×D4—46no—
267C4×D4—412no—
268C2×C4⋊C4C23×C7316yes—
269C2×C4⋊C4C23×C7316yes—
270C2×C4⋊C4C23×C7313yes—
271C2×C4⋊C4C23×C7313yes—
272C2×C4⋊C4C23×C7313yes—
273C2×C22⋊C4C23×C7316yes—
274C2×C22⋊C4C23×C7316yes—
275C2×C22⋊C4C23×C7313yes—
276C2×C22⋊C4C23×C7316yes—
277C2×C22⋊C4C23×C7316yes—
278C2×C22⋊C4C23×C7316yes—
279C2×C22⋊C4C23×C7313yes—
280C2×C22⋊C4C23×C7313yes—
281C2×C22⋊C4C23×C7316yes—
282C2×C22⋊C4C23×C7313yes—
283C2×C42C23×C7313yes—
284C2×C42C23×C7316yes—
285C2×C42C23×C7312yes—
286#95C23×C7316yes—
287#95C23×C7313yes—
288#95C23×C7313yes—
289#95C23×C7316yes—
290#95C23×C7316yes—
291#95C23×C7316yes—
292#95C23×C7316yes—
293#95C23×C7311yescharacteristic
294#95C23×C7313yes—
295#95C23×C7316yes—
296C24—26no—
297C24—43no—
298C24—41no—
299C24C24×C7313yes—
300C24C24×C7313yes—
301C2×Q8—43no—
302C2×D4—212no—
303C2×D4—212no—
304C2×D4—212no—
305C2×D4—43no—
306C2×D4—43no—
307C2×D4—46no—
308C2×D4—43no—
309C2×D4#41×C73112yes—
310C22×C4—212no—
311C22×C4—26no—
312C22×C4—212no—
313C22×C4—26no—
314C22×C4—43no—
315C22×C4—46no—
316C22×C4—46no—
317C22×C4—46no—
318C22×C4—46no—
319C22×C4—416no—
320C22×C4C24×C7316yes—
321C22×C4C24×C7316yes—
322C22×C4C24×C7313yes—
323C22×C4C24×C7311yescharacteristic
324C22×C4C24×C7313yes—
325C22×C4C24×C7313yes—
326C22×C4C24×C7313yes—
327C4⋊C4—212no—
328C4⋊C4—212no—
329C4⋊C4—43no—
330C4⋊C4—43no—
331C4⋊C4—43no—
332C22⋊C4—26no—
333C22⋊C4—212no—
334C22⋊C4—212no—
335C22⋊C4—212no—
336C22⋊C4—212no—
337C22⋊C4—43no—
338C22⋊C4—43no—
339C22⋊C4—43no—
340C22⋊C4—46no—
341C22⋊C4—46no—
342C42—26no—
343C42—42no—
344C42—46no—
345C23—26no—
346C23—26no—
347C23—26no—
348C23—23no—
349C23—26no—
350C23—23no—
351C23—23no—
352C23—23no—
353C23—412no—
354C23—412no—
355C23—44no—
356C23C2×#41×C7316yes—
357C23C2×#41×C7316yes—
358C23C25×C7311yescharacteristic
359Q8—82no—
360D4—412no—
361D4—412no—
362D4—424no—
363C2×C4—23no—
364C2×C4—26no—
365C2×C4—23no—
366C2×C4—26no—
367C2×C4—26no—
368C2×C4—26no—
369C2×C4—26no—
370C2×C4—23no—
371C2×C4—26no—
372C2×C4—26no—
373C2×C4—26no—
374C2×C4—23no—
375C2×C4—23no—
376C2×C4—26no—
377C2×C4—412no—
378C2×C4—412no—
379C2×C4—812no—
380C2×C4—86no—
381C2×C4C2×#41×C7316yes—
382C2×C4H(5,𝔽2)×C7316yes—
383C22—212no—
384C22—212no—
385C22—26no—
386C22—26no—
387C22—416no—
388C22—43no—
389C22—43no—
390C22—46no—
391C22—46no—
392C22—43no—
393C22—43no—
394C22C22×#41×C7313yes—
395C22C2×H(5,𝔽2)×C7313yes—
396C22#585×C7311yescharacteristic
397C4—26no—
398C4—26no—
399C4—46no—
400C4—43no—
401C4—46no—
402C4—41no—
403C4—43no—
404C2—46no—
405C2—46no—
406C2C73×#348113yes—
407C2C73×#350513yes—
408C2C73×#353211yescharacteristic
subgroupG/H
center, socleC23×C73C25
commutator, Frattini, cosocleC23C25×C73
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C73×#2736C2semidirect
2. C73×#2668C2semidirect
3. C73×#2578C2semidirect
4. C73×#2564C2semidirect
5. C73×#2535C2semidirect
6. C73×#2517C2semidirect
7. C73×#2463C2semidirect
8. C73×#2364C2semidirect
9. C4×#120×C73C2semidirect
11. C2×C22⋊Q8×C73C22semidirect
16. C2×C4×D4×C73C22semidirect
17. #400×C73C22semidirect
21. #397×C73C22semidirect
22. #395×C73C22semidirect
26. #392×C73C22semidirect
28. #388×C73C22semidirect
29. #387×C73C22semidirect
30. #387×C73C22semidirect
31. #387×C73C22semidirect
36. #386×C73C22semidirect
39. #383×C73C22semidirect
40. #382×C73C22semidirect
41. #380×C73C22semidirect
45. C4×C22⋊C4×C73C22semidirect
46. C2×#95×C73C22semidirect
199. #60032C73direct (N × H)
205. #2736C2×C73semidirect
206. #2668C2×C73semidirect
207. #2578C2×C73semidirect
208. #2564C2×C73semidirect
209. #2535C2×C73semidirect
210. #2517C2×C73semidirect
211. #2463C2×C73semidirect
212. #2364C2×C73semidirect
213. C4×#120C2×C73semidirect
214. C73#60032direct (N × H)
216. C2×C22⋊Q8C22×C73semidirect
221. C2×C4×D4C22×C73semidirect
222. #400C22×C73semidirect
226. #397C22×C73semidirect
227. #395C22×C73semidirect
231. #392C22×C73semidirect
233. #388C22×C73semidirect
234. #387C22×C73semidirect
235. #387C22×C73semidirect
236. #387C22×C73semidirect
241. #386C22×C73semidirect
244. #383C22×C73semidirect
245. #382C22×C73semidirect
246. #380C22×C73semidirect
250. C4×C22⋊C4C22×C73semidirect
251. C2×#95C22×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#27362
C73×#26682
C73×#25782
C73×#25642
C73×#25352
C73×#25172
C73×#24632
C73×#23642
C4×#120×C732
#6003273