Finite Group Databasebeta

← C29×#19027 #20313927

Subgroups — C29×#19027 #20313927

Order 7424.

884 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3561C211yesmaximal, characteristic
2C29×#3238C211yesmaximal, characteristic, complemented
3C29×#3139C211yesmaximal, characteristic, complemented
4C2×C29×#489C211yesmaximal, characteristic, complemented
5C29×#1664C214yesmaximal, complemented
6C29×#1662C214yesmaximal, complemented
7C29×#1531C211yesmaximal, characteristic, complemented
8C29×#1527C211yesmaximal, characteristic, complemented
9C29×#1524C211yesmaximal, characteristic, complemented
10C29×#563C2212yes—
11C29×#562C2212yes—
12C29×#556—21no—
13C29×#551—22no—
14D4×Q8×C29—21no—
15C29×#548—21no—
16C29×#546—21no—
17C29×#543—21no—
18C29×#542—21no—
19C29×#542—22no—
20C29×#538—21no—
21C29×#536—21no—
22C29×#533C2211yescharacteristic
23C2×C29×C4⋊Q8C2211yescharacteristic
24C29×#529C2211yescharacteristic
25C2×C29×#124C2211yescharacteristic
26C29×#501C2212yescomplemented
27C29×#491C2214yescomplemented
28C29×#489—22no—
29C29×#489C2214yes—
30C29×#489C2212yescomplemented
31C29×#487—21no—
32C29×#487—21no—
33C29×#483—21no—
34C29×#480—21no—
35C29×#477—21no—
36C29×#476—21no—
37C29×#432C2211yescharacteristic
38C29×#419—22no—
39C2×C29×#103—21no—
40C2×C29×#102—21no—
41C4×M16×C29C2211yescharacteristic
42C2×C29×#97C2211yescharacteristic
43C29×#330C2214yescomplemented
44C29×#330C2212yescomplemented
45C29×#329C2214yes—
46C29×#329C2212yescomplemented
47C2×#41×C29—21no—
48C22×Q8×C29—21no—
49C22×Q8×C29—21no—
50C22×Q8×C29D411yescharacteristic
51C22×D4×C29D411yescharacteristic
52C2×M16×C29—21no—
53C22×C8×C29—21no—
54C29×C4⋊Q8—21no—
55C29×C4⋊Q8—22no—
56C29×C4⋊Q8—21no—
57C29×C4⋊Q8—21no—
58C29×C4⋊Q8—21no—
59C29×C4⋊Q8D411yescharacteristic
60C29×C4⋊Q8D411yescharacteristic
61C29×C4⋊Q8C2312yes—
62C29×#126—22no—
63C29×#126—22no—
64C29×#126—22no—
65C29×#126—21no—
66C29×#125C2312yes—
67C29×#125C2311yescharacteristic
68C29×#124—21no—
69C29×#124—22no—
70C29×#124—22no—
71C29×#124—21no—
72C29×#124—21no—
73C29×#124D412yes—
74C29×#124C2312yes—
75C29×#124C2311yescharacteristic
76C29×#123—22no—
77C29×#123—22no—
78C29×#123—21no—
79C29×#123—22no—
80C29×#123—22no—
81C29×C22⋊Q8—22no—
82C29×C22⋊Q8—22no—
83C29×C22⋊Q8—21no—
84C29×C22⋊Q8—22no—
85C29×C22⋊Q8—22no—
86C29×C22⋊Q8—22no—
87C29×C22⋊Q8—21no—
88C29×C22⋊Q8—21no—
89C29×C22⋊Q8—22no—
90C29×C22⋊Q8—22no—
91C29×C22⋊Q8D411yescharacteristic
92C29×#121—21no—
93C29×#121—22no—
94C29×#121—22no—
95C29×#121D411yescharacteristic
96C29×#120—22no—
97C4×Q8×C29—21no—
98C4×Q8×C29—21no—
99C4×Q8×C29—21no—
100C4×Q8×C29D411yescharacteristic
101C4×D4×C29—22no—
102C4×D4×C29—21no—
103C4×D4×C29—22no—
104C4×D4×C29—21no—
105C4×D4×C29D411yescharacteristic
106C29×#117—22no—
107C29×#117—21no—
108C29×#117D412yes—
109C2×C4⋊C4×C29—21no—
110C2×C4⋊C4×C29—21no—
111C2×C22⋊C4×C29—22no—
112C2×C22⋊C4×C29—21no—
113C2×C22⋊C4×C29—21no—
114C2×C42×C29C2311yescharacteristic
115C29×#107—22no—
116C29×#106—22no—
117C29×C4⋊C8—21no—
118C29×#103—22no—
119C29×#103—24no—
120C29×#103—24no—
121C29×#103—24no—
122C29×#102—22no—
123C29×#102—24no—
124C29×C22⋊C8—21no—
125C29×#97—21no—
126C29×#97C2312yes—
127C29×#97C2312yes—
128C29×#97C2312yes—
129C4×C8×C29—21no—
130C24×C29—21no—
131#41×C29—82no—
132C2×Q8×C29—22no—
133C2×Q8×C29—21no—
134C2×Q8×C29—21no—
135C2×Q8×C29—21no—
136C2×Q8×C29—22no—
137C2×Q8×C29—42no—
138C2×Q8×C29—44no—
139C2×Q8×C29—41no—
140C2×Q8×C29—82no—
141C2×Q8×C29C2×D411yescharacteristic
142C2×Q8×C29C2×D412yes—
143C2×D4×C29—21no—
144C2×D4×C29—22no—
145C2×D4×C29—22no—
146C2×D4×C29—21no—
147C2×D4×C29—42no—
148C2×D4×C29C2×D411yescharacteristic
149C2×D4×C29C2×D412yes—
150C22×C4×C29—22no—
151C22×C4×C29—22no—
152C22×C4×C29—22no—
153C22×C4×C29—21no—
154C22×C4×C29—21no—
155C22×C4×C29—41no—
156C22×C4×C29C2×D411yescharacteristic
157C22×C4×C29C2×D411yescharacteristic
158C22×C4×C29C2×D411yescharacteristic
159M16×C29—42no—
160C2×C8×C29—22no—
161C2×C8×C29—22no—
162C2×C8×C29—22no—
163C2×C8×C29—42no—
164C4⋊C4×C29—22no—
165C4⋊C4×C29—22no—
166C4⋊C4×C29—22no—
167C4⋊C4×C29—22no—
168C4⋊C4×C29—21no—
169C4⋊C4×C29—21no—
170C4⋊C4×C29—21no—
171C4⋊C4×C29—21no—
172C4⋊C4×C29—21no—
173C4⋊C4×C29—21no—
174C4⋊C4×C29—22no—
175C4⋊C4×C29—22no—
176C4⋊C4×C29—22no—
177C4⋊C4×C29—22no—
178C4⋊C4×C29—41no—
179C4⋊C4×C29—41no—
180C4⋊C4×C29C2×D412yes—
181C4⋊C4×C29C2×D412yes—
182C4⋊C4×C29C2×D411yescharacteristic
183C4⋊C4×C29C2×D411yescharacteristic
184C22⋊C4×C29—22no—
185C22⋊C4×C29—22no—
186C22⋊C4×C29—22no—
187C22⋊C4×C29—22no—
188C22⋊C4×C29—22no—
189C22⋊C4×C29—21no—
190C22⋊C4×C29—22no—
191C22⋊C4×C29—22no—
192C22⋊C4×C29—22no—
193C22⋊C4×C29—21no—
194C22⋊C4×C29—21no—
195C22⋊C4×C29—22no—
196C22⋊C4×C29—22no—
197C22⋊C4×C29—21no—
198C22⋊C4×C29—21no—
199C42×C29—22no—
200C42×C29—22no—
201C42×C29—21no—
202C42×C29C2×D411yescharacteristic
203C42×C29C2×D411yescharacteristic
204C42×C29C2×D411yescharacteristic
205C42×C29C2411yescharacteristic
206#19027C2911yesmaximal, characteristic, direct product factor, Sylow
207C23×C29—22no—
208C23×C29—21no—
209C23×C29—42no—
210C23×C29—81no—
211C23×C29—81no—
212C23×C29#12011yescharacteristic
213Q8×C29—42no—
214Q8×C29—41no—
215Q8×C29—44no—
216Q8×C29—42no—
217Q8×C29—42no—
218Q8×C29—81no—
219Q8×C29—82no—
220Q8×C29—82no—
221D4×C29—42no—
222D4×C29—41no—
223D4×C29—42no—
224D4×C29—42no—
225D4×C29—82no—
226D4×C29—82no—
227C2×C4×C29—22no—
228C2×C4×C29—22no—
229C2×C4×C29—21no—
230C2×C4×C29—22no—
231C2×C4×C29—21no—
232C2×C4×C29—22no—
233C2×C4×C29—22no—
234C2×C4×C29—21no—
235C2×C4×C29—41no—
236C2×C4×C29—42no—
237C2×C4×C29—42no—
238C2×C4×C29—81no—
239C2×C4×C29—82no—
240C2×C4×C29—82no—
241C2×C4×C29—82no—
242C2×C4×C29—82no—
243C2×C4×C29#12011yescharacteristic
244C2×C4×C29#12011yescharacteristic
245C2×C4×C29#12011yescharacteristic
246C2×C4×C29C22×D411yescharacteristic
247C2×C4×C29C22×D411yescharacteristic
248C2×C4×C29C22×D411yescharacteristic
249C8×C29—42no—
250C8×C29—42no—
251C8×C29—42no—
252#3561C2×C2911yescharacteristic
253#3238C2×C2911yescharacteristic, complemented
254#3139C2×C2911yescharacteristic, complemented
255C2×#489C2×C2911yescharacteristic, complemented
256#1664C2×C2914yescomplemented
257#1662C2×C2914yescomplemented
258#1531C2×C2911yescharacteristic, complemented
259#1527C2×C2911yescharacteristic, complemented
260#1524C2×C2911yescharacteristic, complemented
261C22×C29—21no—
262C22×C29—21no—
263C22×C29—41no—
264C22×C29—42no—
265C22×C29—41no—
266C22×C29—42no—
267C22×C29—42no—
268C22×C29—41no—
269C22×C29—162no—
270C22×C29#45412yes—
271C22×C29C2×#12011yescharacteristic
272C4×C29—21no—
273C4×C29—21no—
274C4×C29—21no—
275C4×C29—21no—
276C4×C29—21no—
277C4×C29—41no—
278C4×C29—42no—
279C4×C29—42no—
280C4×C29—41no—
281C4×C29—41no—
282C4×C29—42no—
283C4×C29—82no—
284C4×C29#45512yes—
285#563C22×C2912yes—
286#562C22×C2912yes—
287#556—21no—
288#551—22no—
289D4×Q8—21no—
290#548—21no—
291#546—21no—
292#543—21no—
293#542—21no—
294#542—22no—
295#538—21no—
296#536—21no—
297#533C22×C2911yescharacteristic
298C2×C4⋊Q8C22×C2911yescharacteristic
299#529C22×C2911yescharacteristic
300C2×#124C22×C2911yescharacteristic
301#501C22×C2912yescomplemented
302#491C22×C2914yescomplemented
303#489—22no—
304#489C22×C2914yes—
305#489C22×C2912yescomplemented
306#487—21no—
307#487—21no—
308#483—21no—
309#480—21no—
310#477—21no—
311#476—21no—
312#432C22×C2911yescharacteristic
313#419—22no—
314C2×#103—21no—
315C2×#102—21no—
316C4×M16C22×C2911yescharacteristic
317C2×#97C22×C2911yescharacteristic
318#330C22×C2914yescomplemented
319#330C22×C2912yescomplemented
320#329C22×C2914yes—
321#329C22×C2912yescomplemented
322C2×C29—22no—
323C2×C29—81no—
324C2×C29—82no—
325C2×C29C2×#45511yescharacteristic
326C2×C29C2×#45411yescharacteristic
327C2×C29#302211yescharacteristic
328C2×#41—21no—
329C22×Q8—21no—
330C22×Q8—21no—
331C22×Q8D4×C2911yescharacteristic
332C22×D4D4×C2911yescharacteristic
333C2×M16—21no—
334C22×C8—21no—
335C4⋊Q8—21no—
336C4⋊Q8—22no—
337C4⋊Q8—21no—
338C4⋊Q8—21no—
339C4⋊Q8—21no—
340C4⋊Q8D4×C2911yescharacteristic
341C4⋊Q8D4×C2911yescharacteristic
342C4⋊Q8C23×C2912yes—
343#126—22no—
344#126—22no—
345#126—22no—
346#126—21no—
347#125C23×C2911yescharacteristic
348#125C23×C2912yes—
349#124—21no—
350#124—22no—
351#124—22no—
352#124—21no—
353#124—21no—
354#124D4×C2912yes—
355#124C23×C2912yes—
356#124C23×C2911yescharacteristic
357#123—22no—
358#123—22no—
359#123—21no—
360#123—22no—
361#123—22no—
362C22⋊Q8—22no—
363C22⋊Q8—22no—
364C22⋊Q8—21no—
365C22⋊Q8—22no—
366C22⋊Q8—22no—
367C22⋊Q8—22no—
368C22⋊Q8—21no—
369C22⋊Q8—21no—
370C22⋊Q8—22no—
371C22⋊Q8—22no—
372C22⋊Q8D4×C2911yescharacteristic
373#121—21no—
374#121—22no—
375#121—22no—
376#121D4×C2911yescharacteristic
377#120—22no—
378C4×Q8—21no—
379C4×Q8—21no—
380C4×Q8—21no—
381C4×Q8D4×C2911yescharacteristic
382C4×D4—22no—
383C4×D4—21no—
384C4×D4—22no—
385C4×D4—21no—
386C4×D4D4×C2911yescharacteristic
387#117—22no—
388#117—21no—
389#117D4×C2912yes—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C42C23×C2911yescharacteristic
396#107—22no—
397#106—22no—
398C4⋊C8—21no—
399#103—24no—
400#103—22no—
401#103—24no—
402#103—24no—
403#102—24no—
404#102—22no—
405C22⋊C8—21no—
406#97—21no—
407#97C23×C2912yes—
408#97C23×C2912yes—
409#97C23×C2912yes—
410C4×C8—21no—
411C29#1902711yescharacteristic, direct product factor, Sylow
412C24—21no—
413#41—82no—
414C2×Q8—22no—
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8—22no—
419C2×Q8—42no—
420C2×Q8—44no—
421C2×Q8—41no—
422C2×Q8—82no—
423C2×Q8C2×D4×C2911yescharacteristic
424C2×Q8C2×D4×C2912yes—
425C2×D4—21no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—21no—
429C2×D4—42no—
430C2×D4C2×D4×C2911yescharacteristic
431C2×D4C2×D4×C2912yes—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—41no—
438C22×C4C2×D4×C2911yescharacteristic
439C22×C4C2×D4×C2911yescharacteristic
440C22×C4C2×D4×C2911yescharacteristic
441M16—42no—
442C2×C8—22no—
443C2×C8—22no—
444C2×C8—22no—
445C2×C8—42no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4—22no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4C2×D4×C2912yes—
463C4⋊C4C2×D4×C2912yes—
464C4⋊C4C2×D4×C2911yescharacteristic
465C4⋊C4C2×D4×C2911yescharacteristic
466C22⋊C4—22no—
467C22⋊C4—22no—
468C22⋊C4—22no—
469C22⋊C4—22no—
470C22⋊C4—22no—
471C22⋊C4—21no—
472C22⋊C4—22no—
473C22⋊C4—22no—
474C22⋊C4—22no—
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—22no—
478C22⋊C4—22no—
479C22⋊C4—21no—
480C22⋊C4—21no—
481C42—22no—
482C42—22no—
483C42—21no—
484C42C2×D4×C2911yescharacteristic
485C42C2×D4×C2911yescharacteristic
486C42C2×D4×C2911yescharacteristic
487C42C24×C2911yescharacteristic
488C23—22no—
489C23—21no—
490C23—42no—
491C23—81no—
492C23—81no—
493C23C29×#12011yescharacteristic
494Q8—42no—
495Q8—41no—
496Q8—44no—
497Q8—42no—
498Q8—42no—
499Q8—81no—
500Q8—82no—
501Q8—82no—
502D4—42no—
503D4—41no—
504D4—42no—
505D4—42no—
506D4—82no—
507D4—82no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—21no—
511C2×C4—22no—
512C2×C4—21no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—21no—
516C2×C4—41no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—81no—
520C2×C4—82no—
521C2×C4—82no—
522C2×C4—82no—
523C2×C4—82no—
524C2×C4C29×#12011yescharacteristic
525C2×C4C29×#12011yescharacteristic
526C2×C4C29×#12011yescharacteristic
527C2×C4C22×D4×C2911yescharacteristic
528C2×C4C22×D4×C2911yescharacteristic
529C2×C4C22×D4×C2911yescharacteristic
530C8—42no—
531C8—42no—
532C8—42no—
533C22—21no—
534C22—21no—
535C22—41no—
536C22—42no—
537C22—41no—
538C22—42no—
539C22—42no—
540C22—41no—
541C22—162no—
542C22C29×#45412yes—
543C22C2×C29×#12011yescharacteristic
544C4—21no—
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—41no—
550C4—42no—
551C4—42no—
552C4—41no—
553C4—41no—
554C4—42no—
555C4—82no—
556C4C29×#45512yes—
557C2—22no—
558C2—82no—
559C2—81no—
560C2C2×C29×#45511yescharacteristic
561C2C2×C29×#45411yescharacteristic
562C2C29×#302211yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3561C2
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×#3238C2semidirect
3. C29×#3139C2semidirect
4. C2×C29×#489C2semidirect
5. C29×#1664C2semidirect
6. C29×#1662C2semidirect
7. C29×#1531C2semidirect
8. C29×#1527C2semidirect
9. C29×#1524C2semidirect
26. C29×#501C22semidirect
27. C29×#491C22semidirect
30. C29×#489C22semidirect
43. C29×#330C22semidirect
44. C29×#330C22semidirect
46. C29×#329C22semidirect
206. #19027C29direct (N × H)
253. #3238C2×C29semidirect
254. #3139C2×C29semidirect
255. C2×#489C2×C29semidirect
256. #1664C2×C29semidirect
257. #1662C2×C29semidirect
258. #1531C2×C29semidirect
259. #1527C2×C29semidirect
260. #1524C2×C29semidirect
301. #501C22×C29semidirect
302. #491C22×C29semidirect
305. #489C22×C29semidirect
318. #330C22×C29semidirect
319. #330C22×C29semidirect
321. #329C22×C29semidirect
411. C29#19027direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35612
C29×#32382
C29×#31392
C2×C29×#4892
C29×#16642
C29×#16622
C29×#15312
C29×#15272
C29×#15242
#1902729