Finite Group Databasebeta

← C29×#8504 #20303404

Subgroups — C29×#8504 #20303404

Order 7424.

728 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3529C211yesmaximal, characteristic
2C29×#1963C211yesmaximal, characteristic, complemented
3C29×#1543C211yesmaximal, characteristic, complemented
4C29×#1500C212yesmaximal, complemented
5C29×#1495C212yesmaximal, complemented
6C29×#563—21no—
7C29×#563C411yescharacteristic, complemented
8C29×#562—22no—
9C29×#562C412yescomplemented
10C29×H(3,𝔽4)C411yescharacteristic, complemented
11C29×#560—21no—
12C29×#560—22no—
13C29×#532—21no—
14C29×#532C2211yescharacteristic
15C29×#529—22no—
16C29×#529C2212yes—
17C29×#525—21no—
18C29×#525—22no—
19C29×#431C2212yescomplemented
20C29×#423C2211yescharacteristic, complemented
21C2×C29×#104—21no—
22C2×C29×#104—21no—
23C29×#376C2211yescharacteristic, complemented
24C29×#333—21no—
25C29×#331—21no—
26C29×#328—22no—
27C29×#327—22no—
28C29×Q8⋊C8—22no—
29C29×D4⋊C8—22no—
30C2×#41×C29—21no—
31C2×#41×C29D411yescharacteristic
32C2×#41×C29D411yescharacteristic
33C23×C4×C29—21no—
34C2×M16×C29—21no—
35C29×C4⋊Q8—21no—
36C29×C4⋊Q8D411yescharacteristic
37C29×#127—21no—
38C29×#127D411yescharacteristic
39C29×#126—22no—
40C29×#126—22no—
41C29×#126—22no—
42C29×#125—22no—
43C29×#125C2×C412yes—
44C29×#124—21no—
45C29×#124—22no—
46C29×#124—21no—
47C29×#124C2×C412yes—
48C29×#124C2×C411yescharacteristic
49C29×#124C2×C411yescharacteristic
50C29×#123—22no—
51C29×#123—21no—
52C29×#123—22no—
53C29×#123—21no—
54C29×#123—22no—
55C29×#123—22no—
56C29×#123—22no—
57C29×C22⋊Q8—22no—
58C29×C22⋊Q8—22no—
59C29×C22⋊Q8—22no—
60C29×C22⋊Q8—22no—
61C29×C22⋊Q8D412yes—
62C29×#121—22no—
63C29×#121—22no—
64C29×#121—22no—
65C29×#121—22no—
66C29×#121—22no—
67C29×#121—22no—
68C29×#121—22no—
69C29×#121D412yes—
70C29×#120—21no—
71C29×#120—22no—
72C29×#120—21no—
73C29×#120—22no—
74C4×Q8×C29D412yes—
75C4×D4×C29—22no—
76C4×D4×C29—22no—
77C4×D4×C29—22no—
78C4×D4×C29—22no—
79C4×D4×C29D412yes—
80C29×#117—21no—
81C29×#117—22no—
82C2×C42×C29—21no—
83C2×C42×C29—21no—
84C2×C42×C29C2311yescharacteristic
85C29×C4⋊C8—22no—
86C29×C4⋊C8—22no—
87C29×#104—42no—
88C29×#104—42no—
89C29×C22⋊C8—22no—
90C4×C8×C29—22no—
91C29×#95—22no—
92C24×C29—21no—
93#41×C29—41no—
94#41×C29—41no—
95#41×C29—41no—
96#41×C29—41no—
97#41×C29—81no—
98#41×C29—81no—
99C2×Q8×C29—21no—
100C2×Q8×C29C22⋊C412yes—
101C2×Q8×C29C22⋊C411yescharacteristic
102C2×Q8×C29C22⋊C411yescharacteristic
103C2×D4×C29—22no—
104C2×D4×C29—22no—
105C2×D4×C29—21no—
106C2×D4×C29—22no—
107C2×D4×C29—22no—
108C2×D4×C29—21no—
109C2×D4×C29—21no—
110C2×D4×C29—22no—
111C2×D4×C29C22⋊C412yes—
112C2×D4×C29C22⋊C411yescharacteristic
113C2×D4×C29C22⋊C411yescharacteristic
114C22×C4×C29—22no—
115C22×C4×C29—22no—
116C22×C4×C29—21no—
117C22×C4×C29—21no—
118C22×C4×C29—21no—
119C22×C4×C29—22no—
120C22×C4×C29—41no—
121C22×C4×C29—81no—
122C22×C4×C29—81no—
123C22×C4×C29C2×D411yescharacteristic
124C22×C4×C29C2×D412yes—
125M16×C29—41no—
126M16×C29—41no—
127C2×C8×C29—42no—
128C2×C8×C29—41no—
129C4⋊C4×C29—22no—
130C4⋊C4×C29—22no—
131C4⋊C4×C29—22no—
132C4⋊C4×C29—22no—
133C4⋊C4×C29—22no—
134C4⋊C4×C29—22no—
135C4⋊C4×C29—22no—
136C4⋊C4×C29—22no—
137C4⋊C4×C29C22⋊C412yes—
138C4⋊C4×C29C22⋊C412yes—
139C22⋊C4×C29—21no—
140C22⋊C4×C29—21no—
141C22⋊C4×C29—22no—
142C22⋊C4×C29—22no—
143C22⋊C4×C29—22no—
144C22⋊C4×C29—22no—
145C22⋊C4×C29—22no—
146C22⋊C4×C29—22no—
147C22⋊C4×C29—22no—
148C22⋊C4×C29—22no—
149C22⋊C4×C29—22no—
150C22⋊C4×C29—22no—
151C22⋊C4×C29—22no—
152C42×C29—21no—
153C42×C29—21no—
154C42×C29—22no—
155C42×C29—22no—
156C42×C29—41no—
157C42×C29C22×C411yescharacteristic
158C42×C29C2×D411yescharacteristic
159C42×C29C2×D412yes—
160#8504C2911yesmaximal, characteristic, direct product factor, Sylow
161C23×C29—21no—
162C23×C29—22no—
163C23×C29—21no—
164C23×C29—81no—
165C23×C29—82no—
166C23×C29#12011yescharacteristic
167Q8×C29—42no—
168Q8×C29—41no—
169Q8×C29—41no—
170Q8×C29—81no—
171D4×C29—42no—
172D4×C29—41no—
173D4×C29—41no—
174D4×C29—82no—
175D4×C29—82no—
176D4×C29—81no—
177D4×C29—81no—
178D4×C29—82no—
179D4×C29—82no—
180D4×C29—82no—
181D4×C29—81no—
182C2×C4×C29—21no—
183C2×C4×C29—21no—
184C2×C4×C29—22no—
185C2×C4×C29—22no—
186C2×C4×C29—21no—
187C2×C4×C29—21no—
188C2×C4×C29—22no—
189C2×C4×C29—42no—
190C2×C4×C29—41no—
191C2×C4×C29—42no—
192C2×C4×C29—41no—
193C2×C4×C29—41no—
194C2×C4×C29—42no—
195C2×C4×C29—41no—
196C2×C4×C29—42no—
197C2×C4×C29—82no—
198C2×C4×C29—82no—
199C2×C4×C29—81no—
200C2×C4×C29—82no—
201C2×C4×C29C2×C22⋊C412yes—
202C2×C4×C29C2×C22⋊C411yescharacteristic
203C2×C4×C29#12012yes—
204C2×C4×C29#12011yescharacteristic
205C8×C29—82no—
206C8×C29—81no—
207#3529C2×C2911yescharacteristic
208#1963C2×C2911yescharacteristic, complemented
209#1543C2×C2911yescharacteristic, complemented
210#1500C2×C2912yescomplemented
211#1495C2×C2912yescomplemented
212C22×C29—21no—
213C22×C29—22no—
214C22×C29—41no—
215C22×C29—42no—
216C22×C29—41no—
217C22×C29—42no—
218C22×C29—42no—
219C22×C29—42no—
220C22×C29—42no—
221C22×C29—84no—
222C22×C29#37911yescharacteristic
223C4×C29—21no—
224C4×C29—22no—
225C4×C29—22no—
226C4×C29—41no—
227C4×C29—42no—
228C4×C29—41no—
229C4×C29—42no—
230C4×C29—42no—
231C4×C29—82no—
232C4×C29#45311yescharacteristic
233C4×C29#45511yescharacteristic
234#563—21no—
235#563C4×C2911yescharacteristic, complemented
236#562—22no—
237#562C4×C2912yescomplemented
238H(3,𝔽4)C4×C2911yescharacteristic, complemented
239#560—21no—
240#560—22no—
241#532—21no—
242#532C22×C2911yescharacteristic
243#529—22no—
244#529C22×C2912yes—
245#525—21no—
246#525—22no—
247#431C22×C2912yescomplemented
248#423C22×C2911yescharacteristic, complemented
249C2×#104—21no—
250C2×#104—21no—
251#376C22×C2911yescharacteristic, complemented
252#333—21no—
253#331—21no—
254#328—22no—
255#327—22no—
256Q8⋊C8—22no—
257D4⋊C8—22no—
258C2×C29—41no—
259C2×C29—81no—
260C2×C29—81no—
261C2×C29—82no—
262C2×C29#179211yescharacteristic
263C2×C29#179412yes—
264C2×#41—21no—
265C2×#41D4×C2911yescharacteristic
266C2×#41D4×C2911yescharacteristic
267C23×C4—21no—
268C2×M16—21no—
269C4⋊Q8—21no—
270C4⋊Q8D4×C2911yescharacteristic
271#127—21no—
272#127D4×C2911yescharacteristic
273#126—22no—
274#126—22no—
275#126—22no—
276#125—22no—
277#125C2×C4×C2912yes—
278#124—21no—
279#124—22no—
280#124—21no—
281#124C2×C4×C2912yes—
282#124C2×C4×C2911yescharacteristic
283#124C2×C4×C2911yescharacteristic
284#123—22no—
285#123—21no—
286#123—22no—
287#123—21no—
288#123—22no—
289#123—22no—
290#123—22no—
291C22⋊Q8—22no—
292C22⋊Q8—22no—
293C22⋊Q8—22no—
294C22⋊Q8—22no—
295C22⋊Q8D4×C2912yes—
296#121—22no—
297#121—22no—
298#121—22no—
299#121—22no—
300#121—22no—
301#121—22no—
302#121—22no—
303#121D4×C2912yes—
304#120—21no—
305#120—22no—
306#120—21no—
307#120—22no—
308C4×Q8D4×C2912yes—
309C4×D4—22no—
310C4×D4—22no—
311C4×D4—22no—
312C4×D4—22no—
313C4×D4D4×C2912yes—
314#117—21no—
315#117—22no—
316C2×C42—21no—
317C2×C42—21no—
318C2×C42C23×C2911yescharacteristic
319C4⋊C8—22no—
320C4⋊C8—22no—
321#104—42no—
322#104—42no—
323C22⋊C8—22no—
324C4×C8—22no—
325#95—22no—
326C29#850411yescharacteristic, direct product factor, Sylow
327C24—21no—
328#41—41no—
329#41—41no—
330#41—41no—
331#41—41no—
332#41—81no—
333#41—81no—
334C2×Q8—21no—
335C2×Q8C22⋊C4×C2912yes—
336C2×Q8C22⋊C4×C2911yescharacteristic
337C2×Q8C22⋊C4×C2911yescharacteristic
338C2×D4—22no—
339C2×D4—22no—
340C2×D4—21no—
341C2×D4—22no—
342C2×D4—22no—
343C2×D4—21no—
344C2×D4—21no—
345C2×D4—22no—
346C2×D4C22⋊C4×C2912yes—
347C2×D4C22⋊C4×C2911yescharacteristic
348C2×D4C22⋊C4×C2911yescharacteristic
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—22no—
355C22×C4—41no—
356C22×C4—81no—
357C22×C4—81no—
358C22×C4C2×D4×C2911yescharacteristic
359C22×C4C2×D4×C2912yes—
360M16—41no—
361M16—41no—
362C2×C8—42no—
363C2×C8—41no—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—22no—
371C4⋊C4—22no—
372C4⋊C4C22⋊C4×C2912yes—
373C4⋊C4C22⋊C4×C2912yes—
374C22⋊C4—21no—
375C22⋊C4—21no—
376C22⋊C4—22no—
377C22⋊C4—22no—
378C22⋊C4—22no—
379C22⋊C4—22no—
380C22⋊C4—22no—
381C22⋊C4—22no—
382C22⋊C4—22no—
383C22⋊C4—22no—
384C22⋊C4—22no—
385C22⋊C4—22no—
386C22⋊C4—22no—
387C42—21no—
388C42—21no—
389C42—22no—
390C42—22no—
391C42—41no—
392C42C22×C4×C2911yescharacteristic
393C42C2×D4×C2912yes—
394C42C2×D4×C2911yescharacteristic
395C23—21no—
396C23—22no—
397C23—21no—
398C23—81no—
399C23—82no—
400C23C29×#12011yescharacteristic
401Q8—41no—
402Q8—41no—
403Q8—42no—
404Q8—81no—
405D4—41no—
406D4—41no—
407D4—42no—
408D4—82no—
409D4—81no—
410D4—81no—
411D4—82no—
412D4—82no—
413D4—81no—
414D4—82no—
415D4—82no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—22no—
423C2×C4—42no—
424C2×C4—41no—
425C2×C4—42no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—42no—
429C2×C4—41no—
430C2×C4—42no—
431C2×C4—82no—
432C2×C4—81no—
433C2×C4—82no—
434C2×C4—82no—
435C2×C4C2×C22⋊C4×C2912yes—
436C2×C4C2×C22⋊C4×C2911yescharacteristic
437C2×C4C29×#12012yes—
438C2×C4C29×#12011yescharacteristic
439C8—82no—
440C8—81no—
441C22—21no—
442C22—22no—
443C22—41no—
444C22—42no—
445C22—41no—
446C22—42no—
447C22—42no—
448C22—42no—
449C22—42no—
450C22—84no—
451C22C29×#37911yescharacteristic
452C4—21no—
453C4—22no—
454C4—22no—
455C4—41no—
456C4—42no—
457C4—41no—
458C4—42no—
459C4—42no—
460C4—82no—
461C4C29×#45311yescharacteristic
462C4C29×#45511yescharacteristic
463C2—41no—
464C2—81no—
465C2—82no—
466C2—81no—
467C2C29×#179211yescharacteristic
468C2C29×#179412yes—
subgroupG/H
centerC2×C4×C29#120
commutatorC42C22×C4×C29
Frattini, cosocleC2×C42C23×C29
socleC22×C29#379
prime radicalC29×#3529C2
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
2. C29×#1963C2semidirect
3. C29×#1543C2semidirect
4. C29×#1500C2semidirect
5. C29×#1495C2semidirect
7. C29×#563C4semidirect
9. C29×#562C4semidirect
10. C29×H(3,𝔽4)C4semidirect
19. C29×#431C22semidirect
20. C29×#423C22semidirect
23. C29×#376C22semidirect
160. #8504C29direct (N × H)
208. #1963C2×C29semidirect
209. #1543C2×C29semidirect
210. #1500C2×C29semidirect
211. #1495C2×C29semidirect
235. #563C4×C29semidirect
237. #562C4×C29semidirect
238. H(3,𝔽4)C4×C29semidirect
247. #431C22×C29semidirect
248. #423C22×C29semidirect
251. #376C22×C29semidirect
326. C29#8504direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35292
C29×#19632
C29×#15432
C29×#15002
C29×#14952
#850429