Finite Group Databasebeta

← C29×#24623 #20319523

Subgroups — C29×#24623 #20319523

Order 7424.

718 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3094C211yesmaximal, characteristic
2C2×C29×#481C211yesmaximal, characteristic
3C29×#2924C211yesmaximal, characteristic, complemented
4C2×C29×#428C211yesmaximal, characteristic, complemented
5C29×#2090C212yesmaximal, complemented
6C29×#2063C212yesmaximal, complemented
7C29×#1951C212yesmaximal, complemented
8C29×#1931C212yesmaximal, complemented
9C29×#1900C211yesmaximal, characteristic
10C29×#1855C211yesmaximal, characteristic, complemented
11C29×#1821C211yesmaximal, characteristic, complemented
12C22×M16×C29C2211yescharacteristic
13C2×C29×#121C2211yescharacteristic
14C2×C29×#117C2211yescharacteristic
15C22×C4⋊C4×C29C2211yescharacteristic
16C29×#482—21no—
17C29×#482—21no—
18C29×#481—21no—
19C29×#481—21no—
20C29×#481—22no—
21C29×#481—21no—
22C29×#480—21no—
23C29×#433—22no—
24C29×#432—21no—
25C29×#431—21no—
26C2×C29×#108C2212yes—
27C29×#428—21no—
28C29×#428—21no—
29C29×#428C2212yes—
30C29×#428C2211yescharacteristic
31C29×#428C2212yes—
32C29×#428C2211yescharacteristic
33C2×C29×#107—21no—
34C2×C29×#106—21no—
35C2×C29×#106C2212yes—
36C29×#424C2212yes—
37C29×#418C2211yescharacteristic
38C29×#418C2211yescharacteristic
39C2×C29×#102C2212yes—
40C2×C29×#100C2212yes—
41C29×#407C2211yescharacteristic
42C29×#407C2211yescharacteristic
43C2×C29×C22⋊C8C2211yescharacteristic
44C29×#405C2212yes—
45C29×#343C2212yes—
46C29×#343C2212yes—
47C29×#343C2212yes—
48C29×#341C2212yes—
49C22×D4×C29—21no—
50C22×D4×C29C2311yescharacteristic
51C23×C4×C29—21no—
52C23×C4×C29C2311yescharacteristic
53C2×M16×C29—21no—
54C2×M16×C29—24no—
55C2×M16×C29C2311yescharacteristic
56C2×M16×C29C2311yescharacteristic
57C2×M16×C29C2312yes—
58C2×M16×C29C2312yes—
59C22×C8×C29—21no—
60C22×C8×C29C2312yes—
61C29×#121—21no—
62C29×#121—21no—
63C29×#121—21no—
64C29×#121—21no—
65C29×#117—21no—
66C29×#117—21no—
67C29×#117D411yescharacteristic
68C29×#117D411yescharacteristic
69C29×#117C2311yescharacteristic
70C29×#117C2311yescharacteristic
71C2×C4⋊C4×C29—21no—
72C2×C4⋊C4×C29—21no—
73C2×C4⋊C4×C29—21no—
74C2×C4⋊C4×C29—21no—
75C2×C4⋊C4×C29—21no—
76C2×C4⋊C4×C29D411yescharacteristic
77C2×C4⋊C4×C29D411yescharacteristic
78C2×C4⋊C4×C29C2311yescharacteristic
79C2×C4⋊C4×C29C2312yes—
80C2×C22⋊C4×C29—21no—
81C2×C22⋊C4×C29—21no—
82C2×C42×C29—21no—
83C29×#108—24no—
84C29×#107—22no—
85C29×#107—22no—
86C29×#107—21no—
87C29×#107—21no—
88C29×#106—22no—
89C29×#106—22no—
90C29×#106—22no—
91C29×#106—22no—
92C29×#106—21no—
93C29×#106—21no—
94C29×C4⋊C8—22no—
95C29×C4⋊C8—22no—
96C29×#102—22no—
97C29×#102—22no—
98C29×#102—21no—
99C29×#102—21no—
100C29×#102—21no—
101C29×#102—21no—
102C29×#100—24no—
103C29×C22⋊C8—21no—
104C29×C22⋊C8—21no—
105C29×C22⋊C8—21no—
106C29×C22⋊C8—21no—
107C29×C22⋊C8D411yescharacteristic
108C29×C22⋊C8D411yescharacteristic
109C29×C22⋊C8D412yes—
110C29×#97—22no—
111C4×C8×C29—22no—
112C24×C29—21no—
113C24×C29#4111yescharacteristic
114C2×D4×C29—21no—
115C2×D4×C29—21no—
116C2×D4×C29—22no—
117C2×D4×C29—22no—
118C2×D4×C29—41no—
119C2×D4×C29—41no—
120C2×D4×C29—82no—
121C22×C4×C29—22no—
122C22×C4×C29—22no—
123C22×C4×C29—21no—
124C22×C4×C29—21no—
125C22×C4×C29—21no—
126C22×C4×C29—22no—
127C22×C4×C29—41no—
128C22×C4×C29—41no—
129C22×C4×C29—82no—
130C22×C4×C29C2×D411yescharacteristic
131C22×C4×C29C2×D411yescharacteristic
132C22×C4×C29C2×D411yescharacteristic
133C22×C4×C29C2×D411yescharacteristic
134C22×C4×C29#4111yescharacteristic
135C22×C4×C29C2411yescharacteristic
136M16×C29—24no—
137M16×C29—22no—
138M16×C29—22no—
139M16×C29—22no—
140M16×C29—22no—
141M16×C29—22no—
142M16×C29#4114yes—
143C2×C8×C29—24no—
144C2×C8×C29—22no—
145C2×C8×C29—22no—
146C2×C8×C29—22no—
147C2×C8×C29—22no—
148C2×C8×C29—21no—
149C2×C8×C29—21no—
150C2×C8×C29C2×D412yes—
151C2×C8×C29C2×D412yes—
152C4⋊C4×C29—21no—
153C4⋊C4×C29—21no—
154C4⋊C4×C29—22no—
155C4⋊C4×C29—22no—
156C4⋊C4×C29—21no—
157C4⋊C4×C29—21no—
158C4⋊C4×C29—41no—
159C4⋊C4×C29—41no—
160C4⋊C4×C29C2×D411yescharacteristic
161C4⋊C4×C29C2×D411yescharacteristic
162C4⋊C4×C29C2×D411yescharacteristic
163C4⋊C4×C29C2×D411yescharacteristic
164C22⋊C4×C29—21no—
165C22⋊C4×C29—21no—
166C22⋊C4×C29—21no—
167C22⋊C4×C29—21no—
168C22⋊C4×C29—41no—
169C22⋊C4×C29—41no—
170C42×C29—21no—
171C42×C29—21no—
172C42×C29—21no—
173C42×C29—21no—
174#24623C2911yesmaximal, characteristic, direct product factor, Sylow
175C23×C29—22no—
176C23×C29—22no—
177C23×C29—41no—
178C23×C29—41no—
179C23×C29—42no—
180C23×C29—81no—
181C23×C29—81no—
182C23×C29#12111yescharacteristic
183C23×C29#12111yescharacteristic
184C23×C29C2×#4111yescharacteristic
185D4×C29—41no—
186D4×C29—41no—
187D4×C29—42no—
188D4×C29—82no—
189D4×C29—82no—
190C2×C4×C29—22no—
191C2×C4×C29—21no—
192C2×C4×C29—21no—
193C2×C4×C29—21no—
194C2×C4×C29—21no—
195C2×C4×C29—22no—
196C2×C4×C29—22no—
197C2×C4×C29—21no—
198C2×C4×C29—21no—
199C2×C4×C29—21no—
200C2×C4×C29—21no—
201C2×C4×C29—42no—
202C2×C4×C29—41no—
203C2×C4×C29—42no—
204C2×C4×C29—81no—
205C2×C4×C29—82no—
206C2×C4×C29—82no—
207C2×C4×C29—82no—
208C2×C4×C29—81no—
209C2×C4×C29#12111yescharacteristic
210C2×C4×C29#12111yescharacteristic
211C2×C4×C29C22×D411yescharacteristic
212C2×C4×C29C22×D411yescharacteristic
213C2×C4×C29C2×#4112yes—
214C2×C4×C292−1+412yes—
215C8×C29—24no—
216C8×C29—22no—
217C8×C29—22no—
218C8×C29—41no—
219C8×C29—41no—
220C8×C29—42no—
221#3094C2×C2911yescharacteristic
222C2×#481C2×C2911yescharacteristic
223#2924C2×C2911yescharacteristic, complemented
224C2×#428C2×C2911yescharacteristic, complemented
225#2090C2×C2912yescomplemented
226#2063C2×C2912yescomplemented
227#1951C2×C2912yescomplemented
228#1931C2×C2912yescomplemented
229#1900C2×C2911yescharacteristic
230#1855C2×C2911yescharacteristic, complemented
231#1821C2×C2911yescharacteristic, complemented
232C22×C29—21no—
233C22×C29—21no—
234C22×C29—21no—
235C22×C29—21no—
236C22×C29—21no—
237C22×C29—21no—
238C22×C29—21no—
239C22×C29—44no—
240C22×C29—81no—
241C22×C29—81no—
242C22×C29—81no—
243C22×C29—162no—
244C22×C29#47112yes—
245C22×C29C2×#12111yescharacteristic
246C22×C29#55212yes—
247C4×C29—21no—
248C4×C29—21no—
249C4×C29—41no—
250C4×C29—41no—
251C4×C29—41no—
252C4×C29—41no—
253C4×C29—81no—
254C4×C29—82no—
255C4×C29#52511yescharacteristic
256C4×C29#53611yescharacteristic
257C4×C29#54712yes—
258C22×M16C22×C2911yescharacteristic
259C2×#121C22×C2911yescharacteristic
260C2×#117C22×C2911yescharacteristic
261C22×C4⋊C4C22×C2911yescharacteristic
262#482—21no—
263#482—21no—
264#481—21no—
265#481—21no—
266#481—21no—
267#481—22no—
268#480—21no—
269#433—22no—
270#432—21no—
271#431—21no—
272C2×#108C22×C2912yes—
273#428—21no—
274#428—21no—
275#428C22×C2912yes—
276#428C22×C2911yescharacteristic
277#428C22×C2911yescharacteristic
278#428C22×C2912yes—
279C2×#107—21no—
280C2×#106—21no—
281C2×#106C22×C2912yes—
282#424C22×C2912yes—
283#418C22×C2911yescharacteristic
284#418C22×C2911yescharacteristic
285C2×#102C22×C2912yes—
286C2×#100C22×C2912yes—
287#407C22×C2911yescharacteristic
288#407C22×C2911yescharacteristic
289C2×C22⋊C8C22×C2911yescharacteristic
290#405C22×C2912yes—
291#343C22×C2912yes—
292#343C22×C2912yes—
293#343C22×C2912yes—
294#341C22×C2912yes—
295C2×C29—22no—
296C2×C29—22no—
297C2×C29—41no—
298C2×C29—161no—
299C2×C29#241311yescharacteristic
300C2×C29C2×#47111yescharacteristic
301C2×C29#306811yescharacteristic
302C22×D4—21no—
303C22×D4C23×C2911yescharacteristic
304C23×C4—21no—
305C23×C4C23×C2911yescharacteristic
306C2×M16—21no—
307C2×M16—24no—
308C2×M16C23×C2911yescharacteristic
309C2×M16C23×C2912yes—
310C2×M16C23×C2911yescharacteristic
311C2×M16C23×C2912yes—
312C22×C8—21no—
313C22×C8C23×C2912yes—
314#121—21no—
315#121—21no—
316#121—21no—
317#121—21no—
318#117—21no—
319#117—21no—
320#117D4×C2911yescharacteristic
321#117D4×C2911yescharacteristic
322#117C23×C2911yescharacteristic
323#117C23×C2911yescharacteristic
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4D4×C2911yescharacteristic
330C2×C4⋊C4D4×C2911yescharacteristic
331C2×C4⋊C4C23×C2912yes—
332C2×C4⋊C4C23×C2911yescharacteristic
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C42—21no—
336#108—24no—
337#107—22no—
338#107—22no—
339#107—21no—
340#107—21no—
341#106—22no—
342#106—22no—
343#106—22no—
344#106—22no—
345#106—21no—
346#106—21no—
347C4⋊C8—22no—
348C4⋊C8—22no—
349#102—22no—
350#102—22no—
351#102—21no—
352#102—21no—
353#102—21no—
354#102—21no—
355#100—24no—
356C22⋊C8—21no—
357C22⋊C8—21no—
358C22⋊C8—21no—
359C22⋊C8—21no—
360C22⋊C8D4×C2911yescharacteristic
361C22⋊C8D4×C2911yescharacteristic
362C22⋊C8D4×C2912yes—
363#97—22no—
364C4×C8—22no—
365C29#2462311yescharacteristic, direct product factor, Sylow
366C24—21no—
367C24#41×C2911yescharacteristic
368C2×D4—21no—
369C2×D4—21no—
370C2×D4—22no—
371C2×D4—22no—
372C2×D4—41no—
373C2×D4—41no—
374C2×D4—82no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—22no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—82no—
384C22×C4C2×D4×C2911yescharacteristic
385C22×C4C2×D4×C2911yescharacteristic
386C22×C4C2×D4×C2911yescharacteristic
387C22×C4C2×D4×C2911yescharacteristic
388C22×C4#41×C2911yescharacteristic
389C22×C4C24×C2911yescharacteristic
390M16—24no—
391M16—22no—
392M16—22no—
393M16—22no—
394M16—22no—
395M16—22no—
396M16#41×C2914yes—
397C2×C8—24no—
398C2×C8—22no—
399C2×C8—22no—
400C2×C8—22no—
401C2×C8—22no—
402C2×C8—21no—
403C2×C8—21no—
404C2×C8C2×D4×C2912yes—
405C2×C8C2×D4×C2912yes—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—22no—
409C4⋊C4—21no—
410C4⋊C4—22no—
411C4⋊C4—21no—
412C4⋊C4—41no—
413C4⋊C4—41no—
414C4⋊C4C2×D4×C2911yescharacteristic
415C4⋊C4C2×D4×C2911yescharacteristic
416C4⋊C4C2×D4×C2911yescharacteristic
417C4⋊C4C2×D4×C2911yescharacteristic
418C22⋊C4—21no—
419C22⋊C4—21no—
420C22⋊C4—21no—
421C22⋊C4—21no—
422C22⋊C4—41no—
423C22⋊C4—41no—
424C42—21no—
425C42—21no—
426C42—21no—
427C42—21no—
428C23—22no—
429C23—22no—
430C23—41no—
431C23—41no—
432C23—42no—
433C23—81no—
434C23—81no—
435C23C29×#12111yescharacteristic
436C23C29×#12111yescharacteristic
437C23C2×#41×C2911yescharacteristic
438D4—41no—
439D4—41no—
440D4—42no—
441D4—82no—
442D4—82no—
443C2×C4—22no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—42no—
455C2×C4—41no—
456C2×C4—42no—
457C2×C4—81no—
458C2×C4—82no—
459C2×C4—82no—
460C2×C4—82no—
461C2×C4—81no—
462C2×C4C29×#12111yescharacteristic
463C2×C4C29×#12111yescharacteristic
464C2×C4C22×D4×C2911yescharacteristic
465C2×C4C22×D4×C2911yescharacteristic
466C2×C4C2×#41×C2912yes—
467C2×C4C29×2−1+412yes—
468C8—24no—
469C8—22no—
470C8—22no—
471C8—41no—
472C8—41no—
473C8—42no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—21no—
480C22—21no—
481C22—44no—
482C22—81no—
483C22—81no—
484C22—81no—
485C22—162no—
486C22C29×#47112yes—
487C22C2×C29×#12111yescharacteristic
488C22C29×#55212yes—
489C4—21no—
490C4—21no—
491C4—41no—
492C4—41no—
493C4—41no—
494C4—41no—
495C4—81no—
496C4—82no—
497C4C29×#52511yescharacteristic
498C4C29×#53611yescharacteristic
499C4C29×#54712yes—
500C2—22no—
501C2—22no—
502C2—41no—
503C2—161no—
504C2C29×#241311yescharacteristic
505C2C2×C29×#47111yescharacteristic
506C2C29×#306811yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC2×C29×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C23×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
3. C29×#2924C2semidirect
4. C2×C29×#428C2semidirect
5. C29×#2090C2semidirect
6. C29×#2063C2semidirect
7. C29×#1951C2semidirect
8. C29×#1931C2semidirect
10. C29×#1855C2semidirect
11. C29×#1821C2semidirect
174. #24623C29direct (N × H)
223. #2924C2×C29semidirect
224. C2×#428C2×C29semidirect
225. #2090C2×C29semidirect
226. #2063C2×C29semidirect
227. #1951C2×C29semidirect
228. #1931C2×C29semidirect
230. #1855C2×C29semidirect
231. #1821C2×C29semidirect
365. C29#24623direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#30942
C2×C29×#4812
C29×#29242
C2×C29×#4282
C29×#20902
C29×#20632
C29×#19512
C29×#19312
C29×#19002
C29×#18552
C29×#18212
#2462329