Finite Group Databasebeta

← C29×#8989 #20303889

Subgroups — C29×#8989 #20303889

Order 7424.

540 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3101C211yesmaximal, characteristic
2D4×M16×C29C211yesmaximal, characteristic
3C29×#1986C211yesmaximal, characteristic, complemented
4C4×C29×#102C211yesmaximal, characteristic
5C29×#1493C211yesmaximal, characteristic, complemented
6C29×#1303C211yesmaximal, characteristic, complemented
7C29×#1278C211yesmaximal, characteristic, complemented
8C22×M16×C29—21no—
9C29×#533C2211yescharacteristic
10C2×C4×D4×C29C2211yescharacteristic
11C29×#483—21no—
12C29×#476C411yescharacteristic, complemented
13C29×#476C411yescharacteristic, complemented
14C29×#461C411yescharacteristic, complemented
15C29×#461C411yescharacteristic, complemented
16C29×#450—21no—
17C4×SD16×C29—21no—
18C4×SD16×C29—21no—
19C29×#436—21no—
20C29×#435—22no—
21C8×D4×C29—21no—
22C29×#431C2211yescharacteristic
23C29×#423C2211yescharacteristic
24C2×C29×#102—21no—
25C29×#407—21no—
26C4×M16×C29C2211yescharacteristic
27C2×C4×C8×C29C2211yescharacteristic
28C4×C4⋊C4×C29C2211yescharacteristic
29C29×#340—21no—
30C29×#339—21no—
31C29×#339—21no—
32C29×Q8⋊C8—22no—
33C22×D4×C29D411yescharacteristic
34C23×C4×C29—21no—
35C2×SD16×C29—21no—
36C2×SD16×C29—21no—
37C2×M16×C29—22no—
38C2×M16×C29—21no—
39C2×M16×C29—42no—
40C2×M16×C29—42no—
41C2×M16×C29D411yescharacteristic
42C2×M16×C29D411yescharacteristic
43C22×C8×C29—22no—
44C22×C8×C29—21no—
45C29×C4⋊Q8C2×C411yescharacteristic
46C29×C4⋊Q8C2×C411yescharacteristic
47C29×#125—21no—
48C29×C22⋊Q8—21no—
49C29×C22⋊Q8—21no—
50C4×Q8×C29—21no—
51C4×Q8×C29—21no—
52C4×D4×C29—21no—
53C4×D4×C29—21no—
54C4×D4×C29C2×C411yescharacteristic
55C4×D4×C29C2×C411yescharacteristic
56C4×D4×C29D411yescharacteristic
57C4×D4×C29D411yescharacteristic
58C29×#117—21no—
59C2×C4⋊C4×C29—21no—
60C2×C4⋊C4×C29D411yescharacteristic
61C2×C22⋊C4×C29—21no—
62C2×C42×C29—21no—
63C2×C42×C29C2311yescharacteristic
64C29×#106—21no—
65C29×#106—21no—
66C29×C4⋊C8—21no—
67C29×C4⋊C8C2×C411yescharacteristic
68C29×C4⋊C8C2×C411yescharacteristic
69C29×C4⋊C8D412yes—
70C29×#103—21no—
71C29×#103—21no—
72C29×#102—24no—
73C29×#102—21no—
74C29×#102—21no—
75C29×C22⋊C8—22no—
76C29×C22⋊C8—22no—
77C29×C22⋊C8—21no—
78C29×#97—21no—
79C4×C8×C29—21no—
80C4×C8×C29—21no—
81C4×C8×C29—21no—
82C4×C8×C29—21no—
83C29×#95—21no—
84C24×C29—21no—
85C2×Q8×C29—21no—
86C2×Q8×C29—21no—
87C2×D4×C29—22no—
88C2×D4×C29—21no—
89C2×D4×C29—41no—
90C2×D4×C29C22⋊C411yescharacteristic
91C2×D4×C29C22⋊C411yescharacteristic
92C22×C4×C29—21no—
93C22×C4×C29—21no—
94C22×C4×C29—21no—
95C22×C4×C29—21no—
96C22×C4×C29—21no—
97C22×C4×C29—41no—
98C22×C4×C29—41no—
99C22×C4×C29—41no—
100C22×C4×C29—41no—
101C22×C4×C29—41no—
102C22×C4×C29C2×D411yescharacteristic
103C22×C4×C29C2×D411yescharacteristic
104C22×C4×C29#4111yescharacteristic
105SD16×C29—42no—
106SD16×C29—42no—
107M16×C29—21no—
108M16×C29—21no—
109M16×C29—21no—
110M16×C29—44no—
111M16×C29—41no—
112M16×C29—41no—
113M16×C29SD1612yescomplemented
114C2×C8×C29—21no—
115C2×C8×C29—22no—
116C2×C8×C29—21no—
117C2×C8×C29—21no—
118C2×C8×C29—22no—
119C2×C8×C29—21no—
120C2×C8×C29—44no—
121C2×C8×C29—41no—
122C2×C8×C29—41no—
123C4⋊C4×C29—21no—
124C4⋊C4×C29—22no—
125C4⋊C4×C29—21no—
126C4⋊C4×C29—21no—
127C4⋊C4×C29—21no—
128C4⋊C4×C29—21no—
129C4⋊C4×C29—41no—
130C4⋊C4×C29—41no—
131C4⋊C4×C29—41no—
132C4⋊C4×C29C22⋊C411yescharacteristic
133C4⋊C4×C29C22⋊C411yescharacteristic
134C22⋊C4×C29—21no—
135C22⋊C4×C29—21no—
136C22⋊C4×C29—21no—
137C22⋊C4×C29—21no—
138C22⋊C4×C29—41no—
139C42×C29—41no—
140C42×C29—41no—
141C42×C29—41no—
142C42×C29C22×C411yescharacteristic
143C42×C29C2×D411yescharacteristic
144C42×C29C2×D411yescharacteristic
145C42×C29#4111yescharacteristic
146#8989C2911yesmaximal, characteristic, direct product factor, Sylow
147C23×C29—21no—
148C23×C29—21no—
149C23×C29—42no—
150C23×C29—41no—
151C23×C29—41no—
152C23×C29—81no—
153C23×C29#12111yescharacteristic
154Q8×C29—42no—
155Q8×C29—41no—
156Q8×C29—41no—
157D4×C29—21no—
158D4×C29—21no—
159D4×C29—21no—
160D4×C29—42no—
161D4×C29#10412yes—
162C2×C4×C29—21no—
163C2×C4×C29—21no—
164C2×C4×C29—21no—
165C2×C4×C29—21no—
166C2×C4×C29—41no—
167C2×C4×C29—41no—
168C2×C4×C29—41no—
169C2×C4×C29—41no—
170C2×C4×C29—41no—
171C2×C4×C29—41no—
172C2×C4×C29—41no—
173C2×C4×C29—41no—
174C2×C4×C29—41no—
175C2×C4×C29—41no—
176C2×C4×C29—41no—
177C2×C4×C29—42no—
178C2×C4×C29—41no—
179C2×C4×C29—41no—
180C2×C4×C29—81no—
181C2×C4×C29—81no—
182C2×C4×C29C2×C22⋊C411yescharacteristic
183C2×C4×C29C4×D411yescharacteristic
184C2×C4×C29C4×D411yescharacteristic
185C2×C4×C29#12011yescharacteristic
186C2×C4×C29#12111yescharacteristic
187C2×C4×C29#12311yescharacteristic
188C2×C4×C29C2×SD1611yescharacteristic
189C2×C4×C29#13511yescharacteristic
190C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
191C2×C4×C29#13711yescharacteristic
192C8×C29—22no—
193C8×C29—42no—
194C8×C29—41no—
195C8×C29—41no—
196C8×C29—42no—
197C8×C29—41no—
198#3101C2×C2911yescharacteristic
199D4×M16C2×C2911yescharacteristic
200#1986C2×C2911yescharacteristic, complemented
201C4×#102C2×C2911yescharacteristic
202#1493C2×C2911yescharacteristic, complemented
203#1303C2×C2911yescharacteristic, complemented
204#1278C2×C2911yescharacteristic, complemented
205C22×C29—21no—
206C22×C29—21no—
207C22×C29—22no—
208C22×C29—41no—
209C22×C29—41no—
210C22×C29—41no—
211C22×C29—41no—
212C22×C29—41no—
213C22×C29—82no—
214C22×C29—82no—
215C22×C29#38611yescharacteristic
216C22×C29#46111yescharacteristic
217C22×C29#46311yescharacteristic
218C4×C29—21no—
219C4×C29—21no—
220C4×C29—21no—
221C4×C29—41no—
222C4×C29—41no—
223C4×C29—82no—
224C4×C29—81no—
225C4×C29—81no—
226C4×C29C2×#10411yescharacteristic
227C4×C29#42111yescharacteristic
228C4×C29C4×SD1611yescharacteristic
229C4×C29#44011yescharacteristic
230C4×C29#45011yescharacteristic
231C4×C29#45211yescharacteristic
232C22×M16—21no—
233#533C22×C2911yescharacteristic
234C2×C4×D4C22×C2911yescharacteristic
235#483—21no—
236#476C4×C2911yescharacteristic, complemented
237#476C4×C2911yescharacteristic, complemented
238#461C4×C2911yescharacteristic, complemented
239#461C4×C2911yescharacteristic, complemented
240#450—21no—
241C4×SD16—21no—
242C4×SD16—21no—
243#436—21no—
244#435—22no—
245C8×D4—21no—
246#431C22×C2911yescharacteristic
247#423C22×C2911yescharacteristic
248C2×#102—21no—
249#407—21no—
250C4×M16C22×C2911yescharacteristic
251C2×C4×C8C22×C2911yescharacteristic
252C4×C4⋊C4C22×C2911yescharacteristic
253#340—21no—
254#339—21no—
255#339—21no—
256Q8⋊C8—22no—
257C2×C29—21no—
258C2×C29—21no—
259C2×C29—42no—
260C2×C29—81no—
261C2×C29#187111yescharacteristic
262C2×C29#187711yescharacteristic
263C2×C29#188111yescharacteristic
264C22×D4D4×C2911yescharacteristic
265C23×C4—21no—
266C2×SD16—21no—
267C2×SD16—21no—
268C2×M16—22no—
269C2×M16—21no—
270C2×M16—42no—
271C2×M16—42no—
272C2×M16D4×C2911yescharacteristic
273C2×M16D4×C2911yescharacteristic
274C22×C8—22no—
275C22×C8—21no—
276C4⋊Q8C2×C4×C2911yescharacteristic
277C4⋊Q8C2×C4×C2911yescharacteristic
278#125—21no—
279C22⋊Q8—21no—
280C22⋊Q8—21no—
281C4×Q8—21no—
282C4×Q8—21no—
283C4×D4—21no—
284C4×D4—21no—
285C4×D4C2×C4×C2911yescharacteristic
286C4×D4C2×C4×C2911yescharacteristic
287C4×D4D4×C2911yescharacteristic
288C4×D4D4×C2911yescharacteristic
289#117—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4D4×C2911yescharacteristic
292C2×C22⋊C4—21no—
293C2×C42—21no—
294C2×C42C23×C2911yescharacteristic
295#106—21no—
296#106—21no—
297C4⋊C8—21no—
298C4⋊C8C2×C4×C2911yescharacteristic
299C4⋊C8C2×C4×C2911yescharacteristic
300C4⋊C8D4×C2912yes—
301#103—21no—
302#103—21no—
303#102—24no—
304#102—21no—
305#102—21no—
306C22⋊C8—22no—
307C22⋊C8—22no—
308C22⋊C8—21no—
309#97—21no—
310C4×C8—21no—
311C4×C8—21no—
312C4×C8—21no—
313C4×C8—21no—
314#95—21no—
315C29#898911yescharacteristic, direct product factor, Sylow
316C24—21no—
317C2×Q8—21no—
318C2×Q8—21no—
319C2×D4—22no—
320C2×D4—21no—
321C2×D4—41no—
322C2×D4C22⋊C4×C2911yescharacteristic
323C2×D4C22⋊C4×C2911yescharacteristic
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4C2×D4×C2911yescharacteristic
335C22×C4C2×D4×C2911yescharacteristic
336C22×C4#41×C2911yescharacteristic
337SD16—42no—
338SD16—42no—
339M16—21no—
340M16—21no—
341M16—21no—
342M16—44no—
343M16—41no—
344M16—41no—
345M16SD16×C2912yescomplemented
346C2×C8—21no—
347C2×C8—22no—
348C2×C8—21no—
349C2×C8—21no—
350C2×C8—21no—
351C2×C8—22no—
352C2×C8—44no—
353C2×C8—41no—
354C2×C8—41no—
355C4⋊C4—21no—
356C4⋊C4—22no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—41no—
362C4⋊C4—41no—
363C4⋊C4—41no—
364C4⋊C4C22⋊C4×C2911yescharacteristic
365C4⋊C4C22⋊C4×C2911yescharacteristic
366C22⋊C4—21no—
367C22⋊C4—21no—
368C22⋊C4—21no—
369C22⋊C4—21no—
370C22⋊C4—41no—
371C42—41no—
372C42—41no—
373C42—41no—
374C42C22×C4×C2911yescharacteristic
375C42C2×D4×C2911yescharacteristic
376C42C2×D4×C2911yescharacteristic
377C42#41×C2911yescharacteristic
378C23—21no—
379C23—21no—
380C23—42no—
381C23—41no—
382C23—41no—
383C23—81no—
384C23C29×#12111yescharacteristic
385Q8—42no—
386Q8—41no—
387Q8—41no—
388D4—21no—
389D4—21no—
390D4—21no—
391D4—42no—
392D4C29×#10412yes—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—42no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—81no—
412C2×C4—81no—
413C2×C4C2×C22⋊C4×C2911yescharacteristic
414C2×C4C4×D4×C2911yescharacteristic
415C2×C4C4×D4×C2911yescharacteristic
416C2×C4C29×#12011yescharacteristic
417C2×C4C29×#12111yescharacteristic
418C2×C4C29×#12311yescharacteristic
419C2×C4C2×SD16×C2911yescharacteristic
420C2×C4C29×#13511yescharacteristic
421C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
422C2×C4C29×#13711yescharacteristic
423C8—22no—
424C8—42no—
425C8—42no—
426C8—41no—
427C8—41no—
428C8—41no—
429C22—21no—
430C22—21no—
431C22—22no—
432C22—41no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22—41no—
437C22—82no—
438C22—82no—
439C22C29×#38611yescharacteristic
440C22C29×#46111yescharacteristic
441C22C29×#46311yescharacteristic
442C4—21no—
443C4—21no—
444C4—21no—
445C4—41no—
446C4—41no—
447C4—82no—
448C4—81no—
449C4—81no—
450C4C2×C29×#10411yescharacteristic
451C4C29×#42111yescharacteristic
452C4C4×SD16×C2911yescharacteristic
453C4C29×#44011yescharacteristic
454C4C29×#45011yescharacteristic
455C4C29×#45211yescharacteristic
456C2—21no—
457C2—21no—
458C2—42no—
459C2—81no—
460C2C29×#187111yescharacteristic
461C2C29×#187711yescharacteristic
462C2C29×#188111yescharacteristic
subgroupG/H
centerC2×C4×C29#120
commutatorC42C22×C4×C29
Frattini, cosocleC2×C42C23×C29
socleC22×C29#386
prime radicalC22×D4×C29D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
3. C29×#1986C2semidirect
5. C29×#1493C2semidirect
6. C29×#1303C2semidirect
7. C29×#1278C2semidirect
12. C29×#476C4semidirect
13. C29×#476C4semidirect
14. C29×#461C4semidirect
15. C29×#461C4semidirect
113. M16×C29SD16semidirect
146. #8989C29direct (N × H)
200. #1986C2×C29semidirect
202. #1493C2×C29semidirect
203. #1303C2×C29semidirect
204. #1278C2×C29semidirect
236. #476C4×C29semidirect
237. #476C4×C29semidirect
238. #461C4×C29semidirect
239. #461C4×C29semidirect
315. C29#8989direct (N × H)
345. M16SD16×C29semidirect

Maximal subgroups

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

subgroupindex
C29×#31012
D4×M16×C292
C29×#19862
C4×C29×#1022
C29×#14932
C29×#13032
C29×#12782
#898929