Finite Group Databasebeta

← C29×#8956 #20303856

Subgroups — C29×#8956 #20303856

Order 7424.

540 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#2989C211yesmaximal, characteristic, complemented
2C4×C29×AGL(1,ℤ/8)C211yesmaximal, characteristic
3C29×#1954C211yesmaximal, characteristic, complemented
4C29×#1478C211yesmaximal, characteristic, complemented
5C29×#1476C211yesmaximal, characteristic, complemented
6C29×#1283C211yesmaximal, characteristic, complemented
7C29×#1278C211yesmaximal, characteristic, complemented
8C2×C29×AGL(1,ℤ/8)C411yescharacteristic
9C4×#41×C29C2211yescharacteristic
10C2×C4×D4×C29C2211yescharacteristic
11C29×#446—21no—
12C29×#442—21no—
13C29×#440—21no—
14C4×SD16×C29—21no—
15C4×D8×C29—21no—
16C29×#436—21no—
17C29×#435—22no—
18C29×#432—21no—
19C29×#431C2211yescharacteristic
20C29×#431C2211yescharacteristic
21C29×#428C411yescharacteristic
22C29×#423—21no—
23C2×C29×C4⋊C8C2211yescharacteristic
24C29×#418C411yescharacteristic
25C29×#417C411yescharacteristic
26C2×C29×C22⋊C8—22no—
27C4×M16×C29C2211yescharacteristic
28C2×C4×C8×C29C2211yescharacteristic
29C29×Q8⋊C8—21no—
30C29×D4⋊C8—21no—
31C29×D4⋊C8—21no—
32C29×D4⋊C8—21no—
33C2×#41×C29C2×C411yescharacteristic
34C22×D4×C29C2×C411yescharacteristic
35C23×C4×C29—21no—
36C29×AGL(1,ℤ/8)—22no—
37C29×AGL(1,ℤ/8)—22no—
38C2×SD16×C29—21no—
39C2×D8×C29—21no—
40C2×M16×C29—22no—
41C2×M16×C29C2×C411yescharacteristic
42C2×M16×C29C2×C411yescharacteristic
43C22×C8×C29—21no—
44C22×C8×C29D412yes—
45C4×Q8×C29D411yescharacteristic
46C4×Q8×C29D411yescharacteristic
47C4×D4×C29—21no—
48C4×D4×C29—21no—
49C4×D4×C29—21no—
50C4×D4×C29—21no—
51C4×D4×C29—21no—
52C4×D4×C29—21no—
53C4×D4×C29D411yescharacteristic
54C4×D4×C29D411yescharacteristic
55C29×#117—21no—
56C29×#117C2×C411yescharacteristic
57C2×C4⋊C4×C29C2×C411yescharacteristic
58C2×C22⋊C4×C29—21no—
59C2×C42×C29—21no—
60C2×C42×C29C2311yescharacteristic
61C29×#107—21no—
62C29×#106—21no—
63C29×C4⋊C8—22no—
64C29×C4⋊C8—21no—
65C29×C4⋊C8—21no—
66C29×C4⋊C8—21no—
67C29×C4⋊C8D411yescharacteristic
68C29×C4⋊C8D411yescharacteristic
69C29×#103—21no—
70C29×#102—21no—
71C29×#102—21no—
72C29×#102—21no—
73C29×C22⋊C8—22no—
74C29×C22⋊C8—21no—
75C29×C22⋊C8—21no—
76C29×C22⋊C8—44no—
77C29×#97—22no—
78C29×#97—21no—
79C4×C8×C29—21no—
80C4×C8×C29—21no—
81C4×C8×C29—21no—
82C4×C8×C29—21no—
83C4×C8×C29—21no—
84C24×C29—21no—
85#41×C29—21no—
86#41×C29—21no—
87#41×C29—21no—
88#41×C29—21no—
89C2×Q8×C29C22⋊C411yescharacteristic
90C2×D4×C29—21no—
91C2×D4×C29—21no—
92C2×D4×C29—21no—
93C2×D4×C29—21no—
94C2×D4×C29—21no—
95C2×D4×C29—21no—
96C2×D4×C29C22⋊C411yescharacteristic
97C2×D4×C29M1612yescomplemented
98C22×C4×C29—21no—
99C22×C4×C29—21no—
100C22×C4×C29—21no—
101C22×C4×C29—21no—
102C22×C4×C29—42no—
103C22×C4×C29—42no—
104C22×C4×C29—41no—
105C22×C4×C29—41no—
106C22×C4×C29C22×C411yescharacteristic
107C22×C4×C29C2×D411yescharacteristic
108C22×C4×C29#4111yescharacteristic
109SD16×C29—24no—
110D8×C29—24no—
111M16×C29—21no—
112M16×C29—21no—
113M16×C29—21no—
114M16×C29—82no—
115M16×C29M1612yescomplemented
116C2×C8×C29—21no—
117C2×C8×C29—22no—
118C2×C8×C29—21no—
119C2×C8×C29—22no—
120C2×C8×C29—21no—
121C2×C8×C29—21no—
122C2×C8×C29—41no—
123C2×C8×C29—41no—
124C2×C8×C29—42no—
125C2×C8×C29—41no—
126C4⋊C4×C29—21no—
127C4⋊C4×C29—21no—
128C4⋊C4×C29—21no—
129C4⋊C4×C29—21no—
130C4⋊C4×C29C22⋊C411yescharacteristic
131C4⋊C4×C29C22⋊C411yescharacteristic
132C22⋊C4×C29—21no—
133C22⋊C4×C29—21no—
134C22⋊C4×C29—21no—
135C22⋊C4×C29—41no—
136C22⋊C4×C29—41no—
137C42×C29—21no—
138C42×C29—21no—
139C42×C29—21no—
140C42×C29C2×D411yescharacteristic
141C42×C29C2×D411yescharacteristic
142C42×C29C2×D411yescharacteristic
143C42×C29#4111yescharacteristic
144#8956C2911yesmaximal, characteristic, direct product factor, Sylow
145C23×C29—21no—
146C23×C29—22no—
147C23×C29—42no—
148C23×C29—42no—
149C23×C29—41no—
150C23×C29—41no—
151C23×C29C4×D411yescharacteristic
152Q8×C29—21no—
153Q8×C29—21no—
154D4×C29—21no—
155D4×C29—22no—
156D4×C29—21no—
157D4×C29—22no—
158D4×C29—41no—
159D4×C29—41no—
160D4×C29—41no—
161D4×C29—41no—
162C2×C4×C29—21no—
163C2×C4×C29—21no—
164C2×C4×C29—21no—
165C2×C4×C29—21no—
166C2×C4×C29—21no—
167C2×C4×C29—41no—
168C2×C4×C29—41no—
169C2×C4×C29—41no—
170C2×C4×C29—41no—
171C2×C4×C29—41no—
172C2×C4×C29—42no—
173C2×C4×C29—41no—
174C2×C4×C29—81no—
175C2×C4×C29—82no—
176C2×C4×C29—81no—
177C2×C4×C29—81no—
178C2×C4×C29C2×C22⋊C411yescharacteristic
179C2×C4×C29C4×D411yescharacteristic
180C2×C4×C29#12011yescharacteristic
181C2×C4×C29#12111yescharacteristic
182C2×C4×C29#12111yescharacteristic
183C2×C4×C29#12311yescharacteristic
184C2×C4×C29C2×M1611yescharacteristic
185C2×C4×C29C2×M1611yescharacteristic
186C2×C4×C29#13111yescharacteristic
187C2×C4×C29#13111yescharacteristic
188C8×C29—22no—
189C8×C29—42no—
190C8×C29—41no—
191C8×C29—42no—
192C8×C29—41no—
193C8×C29—41no—
194C8×C29—81no—
195#2989C2×C2911yescharacteristic, complemented
196C4×AGL(1,ℤ/8)C2×C2911yescharacteristic
197#1954C2×C2911yescharacteristic, complemented
198#1478C2×C2911yescharacteristic, complemented
199#1476C2×C2911yescharacteristic, complemented
200#1283C2×C2911yescharacteristic, complemented
201#1278C2×C2911yescharacteristic, complemented
202C22×C29—21no—
203C22×C29—21no—
204C22×C29—44no—
205C22×C29—41no—
206C22×C29—42no—
207C22×C29—41no—
208C22×C29—41no—
209C22×C29—82no—
210C22×C29—81no—
211C22×C29—81no—
212C22×C29#38611yescharacteristic
213C22×C29#43511yescharacteristic
214C22×C29#43611yescharacteristic
215C4×C29—21no—
216C4×C29—21no—
217C4×C29—21no—
218C4×C29—41no—
219C4×C29—41no—
220C4×C29—41no—
221C4×C29—81no—
222C4×C29#40711yescharacteristic
223C4×C29#40811yescharacteristic
224C4×C29#43511yescharacteristic
225C4×C29#43611yescharacteristic
226C4×C29#45311yescharacteristic
227C4×C29#45411yescharacteristic
228C2×AGL(1,ℤ/8)C4×C2911yescharacteristic
229C4×#41C22×C2911yescharacteristic
230C2×C4×D4C22×C2911yescharacteristic
231#446—21no—
232#442—21no—
233#440—21no—
234C4×SD16—21no—
235C4×D8—21no—
236#436—21no—
237#435—22no—
238#432—21no—
239#431C22×C2911yescharacteristic
240#431C22×C2911yescharacteristic
241#428C4×C2911yescharacteristic
242#423—21no—
243C2×C4⋊C8C22×C2911yescharacteristic
244#418C4×C2911yescharacteristic
245#417C4×C2911yescharacteristic
246C2×C22⋊C8—22no—
247C4×M16C22×C2911yescharacteristic
248C2×C4×C8C22×C2911yescharacteristic
249Q8⋊C8—21no—
250D4⋊C8—21no—
251D4⋊C8—21no—
252D4⋊C8—21no—
253C2×C29—21no—
254C2×C29—21no—
255C2×C29—81no—
256C2×C29—82no—
257C2×C29#187011yescharacteristic
258C2×C29#188111yescharacteristic
259C2×C29#188311yescharacteristic
260C2×#41C2×C4×C2911yescharacteristic
261C22×D4C2×C4×C2911yescharacteristic
262C23×C4—21no—
263AGL(1,ℤ/8)—22no—
264AGL(1,ℤ/8)—22no—
265C2×SD16—21no—
266C2×D8—21no—
267C2×M16—22no—
268C2×M16C2×C4×C2911yescharacteristic
269C2×M16C2×C4×C2911yescharacteristic
270C22×C8—21no—
271C22×C8D4×C2912yes—
272C4×Q8D4×C2911yescharacteristic
273C4×Q8D4×C2911yescharacteristic
274C4×D4—21no—
275C4×D4—21no—
276C4×D4—21no—
277C4×D4—21no—
278C4×D4—21no—
279C4×D4—21no—
280C4×D4D4×C2911yescharacteristic
281C4×D4D4×C2911yescharacteristic
282#117—21no—
283#117C2×C4×C2911yescharacteristic
284C2×C4⋊C4C2×C4×C2911yescharacteristic
285C2×C22⋊C4—21no—
286C2×C42—21no—
287C2×C42C23×C2911yescharacteristic
288#107—21no—
289#106—21no—
290C4⋊C8—22no—
291C4⋊C8—21no—
292C4⋊C8—21no—
293C4⋊C8—21no—
294C4⋊C8D4×C2911yescharacteristic
295C4⋊C8D4×C2911yescharacteristic
296#103—21no—
297#102—21no—
298#102—21no—
299#102—21no—
300C22⋊C8—22no—
301C22⋊C8—21no—
302C22⋊C8—21no—
303C22⋊C8—44no—
304#97—22no—
305#97—21no—
306C4×C8—21no—
307C4×C8—21no—
308C4×C8—21no—
309C4×C8—21no—
310C4×C8—21no—
311C29#895611yescharacteristic, direct product factor, Sylow
312C24—21no—
313#41—21no—
314#41—21no—
315#41—21no—
316#41—21no—
317C2×Q8C22⋊C4×C2911yescharacteristic
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—21no—
322C2×D4—21no—
323C2×D4—21no—
324C2×D4C22⋊C4×C2911yescharacteristic
325C2×D4M16×C2912yescomplemented
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—42no—
331C22×C4—42no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4C22×C4×C2911yescharacteristic
335C22×C4C2×D4×C2911yescharacteristic
336C22×C4#41×C2911yescharacteristic
337SD16—24no—
338D8—24no—
339M16—21no—
340M16—21no—
341M16—21no—
342M16—82no—
343M16M16×C2912yescomplemented
344C2×C8—21no—
345C2×C8—22no—
346C2×C8—21no—
347C2×C8—21no—
348C2×C8—21no—
349C2×C8—22no—
350C2×C8—41no—
351C2×C8—41no—
352C2×C8—42no—
353C2×C8—41no—
354C4⋊C4—21no—
355C4⋊C4—21no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4C22⋊C4×C2911yescharacteristic
359C4⋊C4C22⋊C4×C2911yescharacteristic
360C22⋊C4—21no—
361C22⋊C4—21no—
362C22⋊C4—21no—
363C22⋊C4—41no—
364C22⋊C4—41no—
365C42—21no—
366C42—21no—
367C42—21no—
368C42C2×D4×C2911yescharacteristic
369C42C2×D4×C2911yescharacteristic
370C42C2×D4×C2911yescharacteristic
371C42#41×C2911yescharacteristic
372C23—22no—
373C23—21no—
374C23—42no—
375C23—42no—
376C23—41no—
377C23—41no—
378C23C4×D4×C2911yescharacteristic
379Q8—21no—
380Q8—21no—
381D4—22no—
382D4—21no—
383D4—22no—
384D4—21no—
385D4—41no—
386D4—41no—
387D4—41no—
388D4—41no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—42no—
400C2×C4—41no—
401C2×C4—81no—
402C2×C4—82no—
403C2×C4—81no—
404C2×C4—81no—
405C2×C4C2×C22⋊C4×C2911yescharacteristic
406C2×C4C4×D4×C2911yescharacteristic
407C2×C4C29×#12011yescharacteristic
408C2×C4C29×#12111yescharacteristic
409C2×C4C29×#12111yescharacteristic
410C2×C4C29×#12311yescharacteristic
411C2×C4C2×M16×C2911yescharacteristic
412C2×C4C2×M16×C2911yescharacteristic
413C2×C4C29×#13111yescharacteristic
414C2×C4C29×#13111yescharacteristic
415C8—22no—
416C8—42no—
417C8—42no—
418C8—41no—
419C8—41no—
420C8—41no—
421C8—81no—
422C22—21no—
423C22—21no—
424C22—44no—
425C22—41no—
426C22—42no—
427C22—41no—
428C22—41no—
429C22—82no—
430C22—81no—
431C22—81no—
432C22C29×#38611yescharacteristic
433C22C29×#43511yescharacteristic
434C22C29×#43611yescharacteristic
435C4—21no—
436C4—21no—
437C4—21no—
438C4—41no—
439C4—41no—
440C4—41no—
441C4—81no—
442C4C29×#40711yescharacteristic
443C4C29×#40811yescharacteristic
444C4C29×#43511yescharacteristic
445C4C29×#43611yescharacteristic
446C4C29×#45311yescharacteristic
447C4C29×#45411yescharacteristic
448C2—21no—
449C2—21no—
450C2—82no—
451C2—81no—
452C2C29×#187011yescharacteristic
453C2C29×#188111yescharacteristic
454C2C29×#188311yescharacteristic
subgroupG/H
centerC2×C4×C29#120
commutatorC22×C4C22×C4×C29
Frattini, cosocleC2×C42C23×C29
socleC22×C29#386
prime radicalC2×C29×AGL(1,ℤ/8)C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#2989C2semidirect
3. C29×#1954C2semidirect
4. C29×#1478C2semidirect
5. C29×#1476C2semidirect
6. C29×#1283C2semidirect
7. C29×#1278C2semidirect
97. C2×D4×C29M16semidirect
115. M16×C29M16semidirect
144. #8956C29direct (N × H)
195. #2989C2×C29semidirect
197. #1954C2×C29semidirect
198. #1478C2×C29semidirect
199. #1476C2×C29semidirect
200. #1283C2×C29semidirect
201. #1278C2×C29semidirect
311. C29#8956direct (N × H)
325. C2×D4M16×C29semidirect
343. M16M16×C29semidirect

Maximal subgroups

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

subgroupindex
C29×#29892
C4×C29×AGL(1,ℤ/8)2
C29×#19542
C29×#14782
C29×#14762
C29×#12832
C29×#12782
#895629