Finite Group Databasebeta

← C29×#60320 #20355220

Subgroups — C29×#60320 #20355220

Order 7424.

1876 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3483C211yesmaximal, characteristic
2C29×#2990C212yesmaximal, complemented
3C29×#2989C214yesmaximal, complemented
4C29×#2981C214yesmaximal, complemented
5C29×#2980C214yesmaximal, complemented
6C29×#2979C211yesmaximal, characteristic, complemented
7C29×#2970C214yesmaximal, complemented
8C29×#2965C212yesmaximal, complemented
9C29×#2935C214yesmaximal, complemented
10C29×#2932C214yesmaximal, complemented
11C29×#2931C211yesmaximal, characteristic, complemented
12C2×C29×#131C2212yes—
13C2×C29×#131C2214yes—
14Q82×C29C411yescharacteristic
15C29×#555C414yes—
16C29×#555C411yescharacteristic
17C29×#555C414yes—
18C29×#550C412yes—
19C29×#550C414yes—
20C29×#532C2211yescharacteristic
21C29×#532C2214yes—
22C29×#532C2214yes—
23C4×#41×C29C2212yes—
24C4×#41×C29C2214yes—
25C29×#446C2212yes—
26C29×#446C2212yes—
27C29×#446C2214yes—
28C29×#436C2214yes—
29C29×#436C2212yes—
30C29×#436C2214yes—
31C29×#436C2212yes—
32C29×#435C2214yes—
33C29×#435C2218yes—
34C29×#435C2218yes—
35C29×#435C2218yes—
36C29×#435C2218yes—
37C29×#435C2214yes—
38C29×#435C2218yes—
39C8×D4×C29C2214yes—
40C8×D4×C29C2214yes—
41C8×D4×C29C2214yes—
42C29×#432C2218yes—
43C29×#432C2214yes—
44C29×#431C2212yes—
45C29×#431C2214yes—
46C29×#423C2211yescharacteristic
47C29×#423C2214yes—
48C2×C29×C4⋊C8C2214yes—
49C29×#408C2212yes—
50C29×#408C2214yes—
51C29×#408C2214yes—
52C29×#408C2218yes—
53C4×M16×C29C2214yes—
54C2×C29×#97C2214yes—
55C2×C4×C8×C29C2211yescharacteristic
56C2×#41×C29C2×C412yes—
57C2×#41×C29C2×C414yes—
58C2×#41×C29C2312yes—
59C2×#41×C29C2314yes—
60C29×#131—44no—
61C29×#131—48no—
62C2×M16×C29C2314yes—
63C2×M16×C29C2312yes—
64C2×M16×C29C2314yes—
65C2×M16×C29C2314yes—
66C2×M16×C29C2314yes—
67C22×C8×C29C2314yes—
68C22×C8×C29C2311yescharacteristic
69C22×C8×C29C2314yes—
70C22×C8×C29C2318yes—
71C22×C8×C29C2311yescharacteristic
72C29×C4⋊Q8C2×C411yescharacteristic
73C29×C4⋊Q8C2×C414yes—
74C29×C4⋊Q8C2×C414yes—
75C29×#127C2×C411yescharacteristic
76C29×#127C2×C414yes—
77C29×#127C2×C414yes—
78C29×#124C2×C412yes—
79C29×#124C2×C414yes—
80C29×#124C2×C414yes—
81C29×#124C2×C418yes—
82C29×#121C2×C414yes—
83C29×#121C2×C414yes—
84C29×#121C2×C414yes—
85C29×#121C2×C418yes—
86C29×#121C2×C418yes—
87C29×#121C2×C418yes—
88C4×Q8×C29C2×C412yes—
89C4×Q8×C29C2×C414yes—
90C4×Q8×C29C2312yes—
91C4×D4×C29C2×C412yes—
92C4×D4×C29C2×C414yes—
93C4×D4×C29C2×C414yes—
94C4×D4×C29C2×C418yes—
95C4×D4×C29C2314yes—
96C4×D4×C29C2312yes—
97C4×D4×C29C2314yes—
98C4×D4×C29C2318yes—
99C29×#117C2×C412yes—
100C29×#117C2×C414yes—
101C29×#117C2×C414yes—
102C29×#117C2×C418yes—
103C2×C42×C29C2311yescharacteristic
104C2×C42×C29C2314yes—
105C2×C42×C29C2314yes—
106C29×C4⋊C8C2312yes—
107C29×C4⋊C8C2314yes—
108C29×C4⋊C8C2314yes—
109C29×C4⋊C8C2312yes—
110C29×C4⋊C8C2314yes—
111C29×C4⋊C8C2318yes—
112C29×C22⋊C8C2314yes—
113C29×C22⋊C8C2314yes—
114C29×C22⋊C8C2314yes—
115C29×C22⋊C8C2318yes—
116C29×C22⋊C8C2318yes—
117C29×C22⋊C8C2318yes—
118C29×#97C2318yes—
119C29×#97C2314yes—
120C29×#97C2314yes—
121C4×C8×C29C2314yes—
122C4×C8×C29C2312yes—
123C4×C8×C29C2312yes—
124#41×C29—42no—
125#41×C29—44no—
126#41×C29—42no—
127#41×C29—44no—
128#41×C29—44no—
129#41×C29—48no—
130C2×Q8×C29C22×C412yes—
131C2×Q8×C29C22×C412yes—
132C2×Q8×C29C22×C414yes—
133C2×D4×C29C22×C412yes—
134C2×D4×C29C22×C414yes—
135C2×D4×C29C22×C414yes—
136C2×D4×C29C22×C418yes—
137C2×D4×C29C22×C414yes—
138C2×D4×C29C22×C414yes—
139C2×D4×C29C22×C418yes—
140C2×D4×C29C22×C412yes—
141C22×C4×C29C22×C412yes—
142C22×C4×C29C22×C414yes—
143C22×C4×C29C22×C414yes—
144C22×C4×C29C22×C418yes—
145C22×C4×C29C2411yescharacteristic
146C22×C4×C29C2414yes—
147C22×C4×C29C2414yes—
148M16×C29—28no—
149M16×C29—44no—
150M16×C29—42no—
151M16×C29—44no—
152M16×C29—44no—
153C2×C8×C29—28no—
154C2×C8×C29—22no—
155C2×C8×C29—44no—
156C2×C8×C29—41no—
157C2×C8×C29—48no—
158C2×C8×C29C2414yes—
159C2×C8×C29C2414yes—
160C2×C8×C29C2414yes—
161C2×C8×C29C2411yescharacteristic
162C2×C8×C29C2412yes—
163C2×C8×C29C2411yescharacteristic
164C4⋊C4×C29C22×C414yes—
165C4⋊C4×C29C22×C412yes—
166C4⋊C4×C29C22×C414yes—
167C4⋊C4×C29C22×C418yes—
168C4⋊C4×C29C22×C412yes—
169C4⋊C4×C29C22×C414yes—
170C22⋊C4×C29C22×C414yes—
171C22⋊C4×C29C22×C418yes—
172C22⋊C4×C29C22×C414yes—
173C22⋊C4×C29C22×C418yes—
174C22⋊C4×C29C22×C414yes—
175C22⋊C4×C29C22×C418yes—
176C42×C29C22×C411yescharacteristic
177C42×C29C22×C414yes—
178C42×C29C22×C414yes—
179C42×C29C22×C414yes—
180C42×C29C22×C414yes—
181C42×C29C22×C411yescharacteristic
182C42×C29C2412yes—
183C42×C29C2414yes—
184#60320C2911yesmaximal, characteristic, direct product factor, Sylow
185C23×C29C23×C411yescharacteristic
186C23×C29C23×C414yes—
187C23×C29C23×C414yes—
188Q8×C29—24no—
189Q8×C29—42no—
190Q8×C29—44no—
191D4×C29—24no—
192D4×C29—28no—
193D4×C29—44no—
194D4×C29—42no—
195D4×C29—44no—
196D4×C29—48no—
197D4×C29—44no—
198D4×C29—48no—
199C2×C4×C29—24no—
200C2×C4×C29—28no—
201C2×C4×C29—24no—
202C2×C4×C29—21no—
203C2×C4×C29—24no—
204C2×C4×C29—24no—
205C2×C4×C29—21no—
206C2×C4×C29—24no—
207C2×C4×C29—44no—
208C2×C4×C29—48no—
209C2×C4×C29C23×C412yes—
210C2×C4×C29C23×C414yes—
211C2×C4×C29C23×C414yes—
212C2×C4×C29C23×C411yescharacteristic
213C2×C4×C29C23×C414yes—
214C2×C4×C29C23×C414yes—
215C2×C4×C29C23×C412yes—
216C2×C4×C29C2511yescharacteristic
217C8×C29—24no—
218C8×C29—21no—
219C8×C29—24no—
220C8×C29—24no—
221C8×C29—22no—
222C8×C29H(5,𝔽2)12yes—
223#3483C2×C2911yescharacteristic
224#2990C2×C2912yescomplemented
225#2989C2×C2914yescomplemented
226#2981C2×C2914yescomplemented
227#2980C2×C2914yescomplemented
228#2979C2×C2911yescharacteristic, complemented
229#2970C2×C2914yescomplemented
230#2965C2×C2912yescomplemented
231#2935C2×C2914yescomplemented
232#2932C2×C2914yescomplemented
233#2931C2×C2911yescharacteristic, complemented
234C22×C29—21no—
235C22×C29—24no—
236C22×C29—24no—
237C22×C29—22no—
238C22×C29—24no—
239C22×C29—24no—
240C22×C29—28no—
241C22×C29C24×C411yescharacteristic
242C4×C29—24no—
243C4×C29—21no—
244C4×C29—24no—
245C4×C29—22no—
246C4×C29—24no—
247C4×C29—24no—
248C4×C29#56814yes—
249C4×C29C2×H(5,𝔽2)11yescharacteristic
250C4×C29#58511yescharacteristic
251C2×#131C22×C2912yes—
252C2×#131C22×C2914yes—
253Q82C4×C2911yescharacteristic
254#555C4×C2914yes—
255#555C4×C2911yescharacteristic
256#555C4×C2914yes—
257#550C4×C2912yes—
258#550C4×C2914yes—
259#532C22×C2911yescharacteristic
260#532C22×C2914yes—
261#532C22×C2914yes—
262C4×#41C22×C2912yes—
263C4×#41C22×C2914yes—
264#446C22×C2912yes—
265#446C22×C2912yes—
266#446C22×C2914yes—
267#436C22×C2914yes—
268#436C22×C2912yes—
269#436C22×C2914yes—
270#436C22×C2912yes—
271#435C22×C2914yes—
272#435C22×C2918yes—
273#435C22×C2918yes—
274#435C22×C2918yes—
275#435C22×C2918yes—
276#435C22×C2914yes—
277#435C22×C2918yes—
278C8×D4C22×C2914yes—
279C8×D4C22×C2914yes—
280C8×D4C22×C2914yes—
281#432C22×C2918yes—
282#432C22×C2914yes—
283#431C22×C2912yes—
284#431C22×C2914yes—
285#423C22×C2911yescharacteristic
286#423C22×C2914yes—
287C2×C4⋊C8C22×C2914yes—
288#408C22×C2912yes—
289#408C22×C2914yes—
290#408C22×C2914yes—
291#408C22×C2918yes—
292C4×M16C22×C2914yes—
293C2×#97C22×C2914yes—
294C2×C4×C8C22×C2911yescharacteristic
295C2×C29—41no—
296C2×C29—44no—
297C2×C29—44no—
298C2×C29C4×H(5,𝔽2)11yescharacteristic
299C2×C29C2×#56812yes—
300C2×#41C2×C4×C2912yes—
301C2×#41C2×C4×C2914yes—
302C2×#41C23×C2912yes—
303C2×#41C23×C2914yes—
304#131—44no—
305#131—48no—
306C2×M16C23×C2914yes—
307C2×M16C23×C2912yes—
308C2×M16C23×C2914yes—
309C2×M16C23×C2914yes—
310C2×M16C23×C2914yes—
311C22×C8C23×C2911yescharacteristic
312C22×C8C23×C2914yes—
313C22×C8C23×C2918yes—
314C22×C8C23×C2911yescharacteristic
315C22×C8C23×C2914yes—
316C4⋊Q8C2×C4×C2911yescharacteristic
317C4⋊Q8C2×C4×C2914yes—
318C4⋊Q8C2×C4×C2914yes—
319#127C2×C4×C2911yescharacteristic
320#127C2×C4×C2914yes—
321#127C2×C4×C2914yes—
322#124C2×C4×C2912yes—
323#124C2×C4×C2914yes—
324#124C2×C4×C2914yes—
325#124C2×C4×C2918yes—
326#121C2×C4×C2914yes—
327#121C2×C4×C2914yes—
328#121C2×C4×C2914yes—
329#121C2×C4×C2918yes—
330#121C2×C4×C2918yes—
331#121C2×C4×C2918yes—
332C4×Q8C2×C4×C2912yes—
333C4×Q8C2×C4×C2914yes—
334C4×Q8C23×C2912yes—
335C4×D4C2×C4×C2912yes—
336C4×D4C2×C4×C2914yes—
337C4×D4C2×C4×C2914yes—
338C4×D4C2×C4×C2918yes—
339C4×D4C23×C2912yes—
340C4×D4C23×C2914yes—
341C4×D4C23×C2914yes—
342C4×D4C23×C2918yes—
343#117C2×C4×C2912yes—
344#117C2×C4×C2914yes—
345#117C2×C4×C2914yes—
346#117C2×C4×C2918yes—
347C2×C42C23×C2911yescharacteristic
348C2×C42C23×C2914yes—
349C2×C42C23×C2914yes—
350C4⋊C8C23×C2912yes—
351C4⋊C8C23×C2914yes—
352C4⋊C8C23×C2918yes—
353C4⋊C8C23×C2914yes—
354C4⋊C8C23×C2912yes—
355C4⋊C8C23×C2914yes—
356C22⋊C8C23×C2914yes—
357C22⋊C8C23×C2914yes—
358C22⋊C8C23×C2914yes—
359C22⋊C8C23×C2918yes—
360C22⋊C8C23×C2918yes—
361C22⋊C8C23×C2918yes—
362#97C23×C2914yes—
363#97C23×C2918yes—
364#97C23×C2914yes—
365C4×C8C23×C2912yes—
366C4×C8C23×C2912yes—
367C4×C8C23×C2914yes—
368C29#6032011yescharacteristic, direct product factor, Sylow
369#41—42no—
370#41—44no—
371#41—42no—
372#41—44no—
373#41—44no—
374#41—48no—
375C2×Q8C22×C4×C2912yes—
376C2×Q8C22×C4×C2912yes—
377C2×Q8C22×C4×C2914yes—
378C2×D4C22×C4×C2912yes—
379C2×D4C22×C4×C2914yes—
380C2×D4C22×C4×C2914yes—
381C2×D4C22×C4×C2918yes—
382C2×D4C22×C4×C2914yes—
383C2×D4C22×C4×C2914yes—
384C2×D4C22×C4×C2918yes—
385C2×D4C22×C4×C2912yes—
386C22×C4C22×C4×C2912yes—
387C22×C4C22×C4×C2914yes—
388C22×C4C22×C4×C2918yes—
389C22×C4C22×C4×C2914yes—
390C22×C4C24×C2911yescharacteristic
391C22×C4C24×C2914yes—
392C22×C4C24×C2914yes—
393M16—28no—
394M16—42no—
395M16—44no—
396M16—44no—
397M16—44no—
398C2×C8—28no—
399C2×C8—22no—
400C2×C8—48no—
401C2×C8—44no—
402C2×C8—41no—
403C2×C8C24×C2912yes—
404C2×C8C24×C2911yescharacteristic
405C2×C8C24×C2914yes—
406C2×C8C24×C2914yes—
407C2×C8C24×C2914yes—
408C2×C8C24×C2911yescharacteristic
409C4⋊C4C22×C4×C2914yes—
410C4⋊C4C22×C4×C2912yes—
411C4⋊C4C22×C4×C2914yes—
412C4⋊C4C22×C4×C2918yes—
413C4⋊C4C22×C4×C2912yes—
414C4⋊C4C22×C4×C2914yes—
415C22⋊C4C22×C4×C2914yes—
416C22⋊C4C22×C4×C2918yes—
417C22⋊C4C22×C4×C2914yes—
418C22⋊C4C22×C4×C2918yes—
419C22⋊C4C22×C4×C2914yes—
420C22⋊C4C22×C4×C2918yes—
421C42C22×C4×C2911yescharacteristic
422C42C22×C4×C2914yes—
423C42C22×C4×C2914yes—
424C42C22×C4×C2914yes—
425C42C22×C4×C2914yes—
426C42C22×C4×C2911yescharacteristic
427C42C24×C2912yes—
428C42C24×C2914yes—
429C23C23×C4×C2911yescharacteristic
430C23C23×C4×C2914yes—
431C23C23×C4×C2914yes—
432Q8—24no—
433Q8—42no—
434Q8—44no—
435D4—24no—
436D4—28no—
437D4—44no—
438D4—48no—
439D4—44no—
440D4—42no—
441D4—44no—
442D4—48no—
443C2×C4—24no—
444C2×C4—28no—
445C2×C4—24no—
446C2×C4—21no—
447C2×C4—24no—
448C2×C4—24no—
449C2×C4—21no—
450C2×C4—24no—
451C2×C4—48no—
452C2×C4—44no—
453C2×C4C23×C4×C2912yes—
454C2×C4C23×C4×C2914yes—
455C2×C4C23×C4×C2914yes—
456C2×C4C23×C4×C2911yescharacteristic
457C2×C4C23×C4×C2914yes—
458C2×C4C23×C4×C2914yes—
459C2×C4C23×C4×C2912yes—
460C2×C4C25×C2911yescharacteristic
461C8—24no—
462C8—21no—
463C8—24no—
464C8—24no—
465C8—22no—
466C8C29×H(5,𝔽2)12yes—
467C22—22no—
468C22—24no—
469C22—24no—
470C22—28no—
471C22—21no—
472C22—24no—
473C22—24no—
474C22C24×C4×C2911yescharacteristic
475C4—22no—
476C4—24no—
477C4—24no—
478C4—24no—
479C4—21no—
480C4—24no—
481C4C29×#56814yes—
482C4C2×C29×H(5,𝔽2)11yescharacteristic
483C4C29×#58511yescharacteristic
484C2—41no—
485C2—44no—
486C2—44no—
487C2C4×C29×H(5,𝔽2)11yescharacteristic
488C2C2×C29×#56812yes—
subgroupG/H
centerC2×C4×C29C25
commutatorC22C24×C4×C29
Frattini, cosocleC2×C4C25×C29
socleC22×C29C24×C4
prime radicalC29×#3483C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#2990C2semidirect
3. C29×#2989C2semidirect
4. C29×#2981C2semidirect
5. C29×#2980C2semidirect
6. C29×#2979C2semidirect
7. C29×#2970C2semidirect
8. C29×#2965C2semidirect
9. C29×#2935C2semidirect
10. C29×#2932C2semidirect
11. C29×#2931C2semidirect
184. #60320C29direct (N × H)
224. #2990C2×C29semidirect
225. #2989C2×C29semidirect
226. #2981C2×C29semidirect
227. #2980C2×C29semidirect
228. #2979C2×C29semidirect
229. #2970C2×C29semidirect
230. #2965C2×C29semidirect
231. #2935C2×C29semidirect
232. #2932C2×C29semidirect
233. #2931C2×C29semidirect
368. C29#60320direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#34832
C29×#29902
C29×#29892
C29×#29812
C29×#29802
C29×#29792
C29×#29702
C29×#29652
C29×#29352
C29×#29322
C29×#29312
#6032029