Finite Group Databasebeta

← C29×#8503 #20303403

Subgroups — C29×#8503 #20303403

Order 7424.

672 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3554C211yesmaximal, characteristic
2C29×#1554C211yesmaximal, characteristic, complemented
3C29×#1535C211yesmaximal, characteristic, complemented
4C29×#1521C211yesmaximal, characteristic, complemented
5C29×#1515C211yesmaximal, characteristic, complemented
6C29×#1514C211yesmaximal, characteristic, complemented
7C29×#1496C211yesmaximal, characteristic, complemented
8C29×#562—22no—
9C29×#559—21no—
10C29×#559C411yescharacteristic, complemented
11C29×#557C411yescharacteristic, complemented
12C29×#554—21no—
13C29×#550C411yescharacteristic, complemented
14D4×Q8×C29C411yescharacteristic, complemented
15C29×#548—21no—
16C29×#547—21no—
17C29×#542—21no—
18C29×#542—21no—
19C29×#540—21no—
20C29×#539—22no—
21C29×#536—21no—
22C29×#533C2211yescharacteristic
23C29×#532C2211yescharacteristic
24C29×#529C2211yescharacteristic
25C29×#432C2211yescharacteristic
26C29×#432C2211yescharacteristic
27C29×#431C2211yescharacteristic
28C29×#383C2211yescharacteristic
29C29×#333—21no—
30C29×#332—21no—
31C29×#330—21no—
32C29×#329—21no—
33C29×#328—21no—
34C29×#328—21no—
35C29×#328—21no—
36C29×#327—22no—
37C29×#327—21no—
38C29×D4⋊C8—22no—
39C2×#41×C29—21no—
40C2×#41×C29—21no—
41C22×Q8×C29—21no—
42C29×C4⋊Q8—21no—
43C29×C4⋊Q8—21no—
44C29×C4⋊Q8C2×C411yescharacteristic
45C29×C4⋊Q8D411yescharacteristic
46C29×C4⋊Q8D411yescharacteristic
47C29×#127—21no—
48C29×#127C2×C411yescharacteristic
49C29×#126—22no—
50C29×#126—21no—
51C29×#125—22no—
52C29×#125—21no—
53C29×#125—21no—
54C29×#125D411yescharacteristic
55C29×#124—22no—
56C29×#124—22no—
57C29×#124—21no—
58C29×#124—21no—
59C29×#124—21no—
60C29×#124D411yescharacteristic
61C29×#123—22no—
62C29×#123—22no—
63C29×#123—22no—
64C29×#123—22no—
65C29×#123—22no—
66C29×#123—22no—
67C29×#123—21no—
68C29×C22⋊Q8—22no—
69C29×C22⋊Q8—22no—
70C29×C22⋊Q8—22no—
71C29×C22⋊Q8—22no—
72C29×C22⋊Q8—21no—
73C29×C22⋊Q8—22no—
74C29×C22⋊Q8—21no—
75C29×C22⋊Q8D411yescharacteristic
76C29×C22⋊Q8D411yescharacteristic
77C29×C22⋊Q8D411yescharacteristic
78C29×#121—22no—
79C29×#121—22no—
80C29×#121—22no—
81C29×#121—21no—
82C29×#121—21no—
83C29×#121D411yescharacteristic
84C29×#121D412yes—
85C4×Q8×C29—21no—
86C4×Q8×C29—21no—
87C4×Q8×C29—21no—
88C4×Q8×C29C2×C411yescharacteristic
89C4×Q8×C29C2×C411yescharacteristic
90C4×Q8×C29C2×C411yescharacteristic
91C4×D4×C29—22no—
92C4×D4×C29—21no—
93C4×D4×C29—21no—
94C4×D4×C29—21no—
95C4×D4×C29—21no—
96C4×D4×C29—21no—
97C4×D4×C29—21no—
98C4×D4×C29C2×C411yescharacteristic
99C4×D4×C29D412yes—
100C29×#117—21no—
101C29×#117—21no—
102C2×C4⋊C4×C29—22no—
103C2×C42×C29C2311yescharacteristic
104C29×C4⋊C8—21no—
105C29×C4⋊C8—21no—
106C29×C4⋊C8—21no—
107C29×C22⋊C8—21no—
108C29×C22⋊C8—21no—
109C29×C22⋊C8—21no—
110C29×#97—21no—
111C29×#97—21no—
112C4×C8×C29—21no—
113C29×#95—21no—
114C29×#95—21no—
115C29×#95—21no—
116#41×C29—82no—
117#41×C29—82no—
118C2×Q8×C29—22no—
119C2×Q8×C29—21no—
120C2×Q8×C29—21no—
121C2×Q8×C29—82no—
122C2×Q8×C29C22⋊C411yescharacteristic
123C2×Q8×C29C22⋊C411yescharacteristic
124C2×Q8×C29C22⋊C411yescharacteristic
125C2×D4×C29—22no—
126C2×D4×C29—22no—
127C2×D4×C29—21no—
128C2×D4×C29—22no—
129C2×D4×C29—21no—
130C2×D4×C29—21no—
131C2×D4×C29C22⋊C411yescharacteristic
132C2×D4×C29C22⋊C412yes—
133C22×C4×C29—22no—
134C22×C4×C29—22no—
135C22×C4×C29—22no—
136C22×C4×C29—21no—
137C22×C4×C29—22no—
138C22×C4×C29—41no—
139C22×C4×C29C2×D411yescharacteristic
140C22×C4×C29C2×D411yescharacteristic
141C22×C4×C29C2×D411yescharacteristic
142C2×C8×C29—41no—
143C2×C8×C29—41no—
144C2×C8×C29—41no—
145C4⋊C4×C29—22no—
146C4⋊C4×C29—22no—
147C4⋊C4×C29—22no—
148C4⋊C4×C29—22no—
149C4⋊C4×C29—21no—
150C4⋊C4×C29—21no—
151C4⋊C4×C29—21no—
152C4⋊C4×C29—21no—
153C4⋊C4×C29—21no—
154C4⋊C4×C29—21no—
155C4⋊C4×C29—21no—
156C4⋊C4×C29—21no—
157C4⋊C4×C29—21no—
158C4⋊C4×C29—21no—
159C4⋊C4×C29—21no—
160C4⋊C4×C29—21no—
161C4⋊C4×C29C22⋊C411yescharacteristic
162C4⋊C4×C29C22⋊C411yescharacteristic
163C4⋊C4×C29C22⋊C411yescharacteristic
164C4⋊C4×C29C22⋊C412yes—
165C4⋊C4×C29C22⋊C411yescharacteristic
166C22⋊C4×C29—22no—
167C22⋊C4×C29—22no—
168C22⋊C4×C29—22no—
169C22⋊C4×C29—22no—
170C22⋊C4×C29—22no—
171C22⋊C4×C29—21no—
172C22⋊C4×C29—21no—
173C22⋊C4×C29—21no—
174C22⋊C4×C29—21no—
175C22⋊C4×C29—21no—
176C22⋊C4×C29—21no—
177C22⋊C4×C29—21no—
178C22⋊C4×C29—22no—
179C22⋊C4×C29—22no—
180C42×C29—22no—
181C42×C29—21no—
182C42×C29—21no—
183C42×C29—21no—
184C42×C29C22×C411yescharacteristic
185C42×C29C2×D411yescharacteristic
186C42×C29C2×D411yescharacteristic
187C42×C29C2×D411yescharacteristic
188#8503C2911yesmaximal, characteristic, direct product factor, Sylow
189C23×C29—22no—
190C23×C29—21no—
191C23×C29#12011yescharacteristic
192Q8×C29—41no—
193Q8×C29—41no—
194Q8×C29—41no—
195Q8×C29—42no—
196Q8×C29—81no—
197Q8×C29—82no—
198D4×C29—42no—
199D4×C29—41no—
200D4×C29—42no—
201D4×C29—42no—
202D4×C29—81no—
203D4×C29—82no—
204D4×C29—82no—
205D4×C29—82no—
206C2×C4×C29—21no—
207C2×C4×C29—21no—
208C2×C4×C29—21no—
209C2×C4×C29—21no—
210C2×C4×C29—21no—
211C2×C4×C29—22no—
212C2×C4×C29—21no—
213C2×C4×C29—21no—
214C2×C4×C29—41no—
215C2×C4×C29—41no—
216C2×C4×C29—41no—
217C2×C4×C29—42no—
218C2×C4×C29—82no—
219C2×C4×C29—82no—
220C2×C4×C29—82no—
221C2×C4×C29—82no—
222C2×C4×C29—81no—
223C2×C4×C29—81no—
224C2×C4×C29—81no—
225C2×C4×C29C2×C22⋊C411yescharacteristic
226C2×C4×C29C2×C22⋊C411yescharacteristic
227C2×C4×C29C2×C22⋊C411yescharacteristic
228C2×C4×C29#12011yescharacteristic
229C2×C4×C29#12011yescharacteristic
230C2×C4×C29#12011yescharacteristic
231C8×C29—81no—
232C8×C29—81no—
233C8×C29—81no—
234#3554C2×C2911yescharacteristic
235#1554C2×C2911yescharacteristic, complemented
236#1535C2×C2911yescharacteristic, complemented
237#1521C2×C2911yescharacteristic, complemented
238#1515C2×C2911yescharacteristic, complemented
239#1514C2×C2911yescharacteristic, complemented
240#1496C2×C2911yescharacteristic, complemented
241C22×C29—21no—
242C22×C29—21no—
243C22×C29—21no—
244C22×C29—42no—
245C22×C29—41no—
246C22×C29—41no—
247C22×C29—42no—
248C22×C29—42no—
249C22×C29—41no—
250C22×C29#37911yescharacteristic
251C4×C29—21no—
252C4×C29—21no—
253C4×C29—21no—
254C4×C29—21no—
255C4×C29—21no—
256C4×C29—21no—
257C4×C29—41no—
258C4×C29—41no—
259C4×C29—41no—
260C4×C29—41no—
261C4×C29—41no—
262C4×C29—42no—
263C4×C29—41no—
264C4×C29—41no—
265C4×C29—161no—
266#562—22no—
267#559—21no—
268#559C4×C2911yescharacteristic, complemented
269#557C4×C2911yescharacteristic, complemented
270#554—21no—
271#550C4×C2911yescharacteristic, complemented
272D4×Q8C4×C2911yescharacteristic, complemented
273#548—21no—
274#547—21no—
275#542—21no—
276#542—21no—
277#540—21no—
278#539—22no—
279#536—21no—
280#533C22×C2911yescharacteristic
281#532C22×C2911yescharacteristic
282#529C22×C2911yescharacteristic
283#432C22×C2911yescharacteristic
284#432C22×C2911yescharacteristic
285#431C22×C2911yescharacteristic
286#383C22×C2911yescharacteristic
287#333—21no—
288#332—21no—
289#330—21no—
290#329—21no—
291#328—21no—
292#328—21no—
293#328—21no—
294#327—22no—
295#327—21no—
296D4⋊C8—22no—
297C2×C29—41no—
298C2×C29—82no—
299C2×C29—81no—
300C2×C29#179411yescharacteristic
301C2×C29#179511yescharacteristic
302C2×C29#179611yescharacteristic
303C2×#41—21no—
304C2×#41—21no—
305C22×Q8—21no—
306C4⋊Q8—21no—
307C4⋊Q8—21no—
308C4⋊Q8C2×C4×C2911yescharacteristic
309C4⋊Q8D4×C2911yescharacteristic
310C4⋊Q8D4×C2911yescharacteristic
311#127—21no—
312#127C2×C4×C2911yescharacteristic
313#126—22no—
314#126—21no—
315#125—22no—
316#125—21no—
317#125—21no—
318#125D4×C2911yescharacteristic
319#124—22no—
320#124—22no—
321#124—21no—
322#124—21no—
323#124—21no—
324#124D4×C2911yescharacteristic
325#123—22no—
326#123—22no—
327#123—22no—
328#123—22no—
329#123—22no—
330#123—22no—
331#123—21no—
332C22⋊Q8—22no—
333C22⋊Q8—22no—
334C22⋊Q8—22no—
335C22⋊Q8—22no—
336C22⋊Q8—21no—
337C22⋊Q8—22no—
338C22⋊Q8—21no—
339C22⋊Q8D4×C2911yescharacteristic
340C22⋊Q8D4×C2911yescharacteristic
341C22⋊Q8D4×C2911yescharacteristic
342#121—22no—
343#121—22no—
344#121—22no—
345#121—21no—
346#121—21no—
347#121D4×C2911yescharacteristic
348#121D4×C2912yes—
349C4×Q8—21no—
350C4×Q8—21no—
351C4×Q8—21no—
352C4×Q8C2×C4×C2911yescharacteristic
353C4×Q8C2×C4×C2911yescharacteristic
354C4×Q8C2×C4×C2911yescharacteristic
355C4×D4—22no—
356C4×D4—21no—
357C4×D4—21no—
358C4×D4—21no—
359C4×D4—21no—
360C4×D4—21no—
361C4×D4—21no—
362C4×D4C2×C4×C2911yescharacteristic
363C4×D4D4×C2912yes—
364#117—21no—
365#117—21no—
366C2×C4⋊C4—22no—
367C2×C42C23×C2911yescharacteristic
368C4⋊C8—21no—
369C4⋊C8—21no—
370C4⋊C8—21no—
371C22⋊C8—21no—
372C22⋊C8—21no—
373C22⋊C8—21no—
374#97—21no—
375#97—21no—
376C4×C8—21no—
377#95—21no—
378#95—21no—
379#95—21no—
380C29#850311yescharacteristic, direct product factor, Sylow
381#41—82no—
382#41—82no—
383C2×Q8—22no—
384C2×Q8—21no—
385C2×Q8—21no—
386C2×Q8—82no—
387C2×Q8C22⋊C4×C2911yescharacteristic
388C2×Q8C22⋊C4×C2911yescharacteristic
389C2×Q8C22⋊C4×C2911yescharacteristic
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—21no—
393C2×D4—22no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4C22⋊C4×C2911yescharacteristic
397C2×D4C22⋊C4×C2912yes—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—41no—
404C22×C4C2×D4×C2911yescharacteristic
405C22×C4C2×D4×C2911yescharacteristic
406C22×C4C2×D4×C2911yescharacteristic
407C2×C8—41no—
408C2×C8—41no—
409C2×C8—41no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—22no—
413C4⋊C4—22no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4C22⋊C4×C2911yescharacteristic
427C4⋊C4C22⋊C4×C2911yescharacteristic
428C4⋊C4C22⋊C4×C2911yescharacteristic
429C4⋊C4C22⋊C4×C2912yes—
430C4⋊C4C22⋊C4×C2911yescharacteristic
431C22⋊C4—22no—
432C22⋊C4—22no—
433C22⋊C4—22no—
434C22⋊C4—22no—
435C22⋊C4—22no—
436C22⋊C4—21no—
437C22⋊C4—21no—
438C22⋊C4—21no—
439C22⋊C4—21no—
440C22⋊C4—21no—
441C22⋊C4—21no—
442C22⋊C4—21no—
443C22⋊C4—22no—
444C22⋊C4—22no—
445C42—22no—
446C42—21no—
447C42—21no—
448C42—21no—
449C42C22×C4×C2911yescharacteristic
450C42C2×D4×C2911yescharacteristic
451C42C2×D4×C2911yescharacteristic
452C42C2×D4×C2911yescharacteristic
453C23—22no—
454C23—21no—
455C23C29×#12011yescharacteristic
456Q8—41no—
457Q8—41no—
458Q8—41no—
459Q8—42no—
460Q8—81no—
461Q8—82no—
462D4—42no—
463D4—41no—
464D4—42no—
465D4—42no—
466D4—82no—
467D4—81no—
468D4—82no—
469D4—82no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—22no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—82no—
483C2×C4—82no—
484C2×C4—82no—
485C2×C4—82no—
486C2×C4—81no—
487C2×C4—81no—
488C2×C4—81no—
489C2×C4C2×C22⋊C4×C2911yescharacteristic
490C2×C4C2×C22⋊C4×C2911yescharacteristic
491C2×C4C2×C22⋊C4×C2911yescharacteristic
492C2×C4C29×#12011yescharacteristic
493C2×C4C29×#12011yescharacteristic
494C2×C4C29×#12011yescharacteristic
495C8—81no—
496C8—81no—
497C8—81no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—42no—
502C22—41no—
503C22—41no—
504C22—42no—
505C22—42no—
506C22—41no—
507C22C29×#37911yescharacteristic
508C4—21no—
509C4—21no—
510C4—21no—
511C4—21no—
512C4—21no—
513C4—21no—
514C4—41no—
515C4—41no—
516C4—41no—
517C4—41no—
518C4—41no—
519C4—42no—
520C4—41no—
521C4—41no—
522C4—161no—
523C2—41no—
524C2—82no—
525C2—81no—
526C2C29×#179411yescharacteristic
527C2C29×#179511yescharacteristic
528C2C29×#179611yescharacteristic
subgroupG/H
center, socleC22×C29#379
commutatorC42C22×C4×C29
Frattini, cosocleC2×C42C23×C29
prime radicalC29×#3554C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#1554C2semidirect
3. C29×#1535C2semidirect
4. C29×#1521C2semidirect
5. C29×#1515C2semidirect
6. C29×#1514C2semidirect
7. C29×#1496C2semidirect
10. C29×#559C4semidirect
11. C29×#557C4semidirect
13. C29×#550C4semidirect
14. D4×Q8×C29C4semidirect
188. #8503C29direct (N × H)
235. #1554C2×C29semidirect
236. #1535C2×C29semidirect
237. #1521C2×C29semidirect
238. #1515C2×C29semidirect
239. #1514C2×C29semidirect
240. #1496C2×C29semidirect
268. #559C4×C29semidirect
269. #557C4×C29semidirect
271. #550C4×C29semidirect
272. D4×Q8C4×C29semidirect
380. C29#8503direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35542
C29×#15542
C29×#15352
C29×#15212
C29×#15152
C29×#15142
C29×#14962
#850329