Finite Group Databasebeta

← C29×#18438 #20313338

Subgroups — C29×#18438 #20313338

Order 7424.

908 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3561C211yesmaximal, characteristic
2C29×#3238C211yesmaximal, characteristic, complemented
3C29×#3229C211yesmaximal, characteristic, complemented
4C29×#2640C211yesmaximal, characteristic, complemented
5C29×#1612C214yesmaximal, complemented
6C29×#1608C214yesmaximal, complemented
7C29×#1506C211yesmaximal, characteristic, complemented
8C29×#1500C211yesmaximal, characteristic, complemented
9C29×#1469C211yesmaximal, characteristic, complemented
10C29×#563—21no—
11C29×#562—21no—
12C29×#556—21no—
13C29×#551—22no—
14D4×Q8×C29—21no—
15C29×#548—21no—
16C29×#546—21no—
17C29×#543C2212yes—
18C29×#542—21no—
19C29×#542—22no—
20C29×#538C2212yes—
21C29×#536—21no—
22C29×#533C2211yescharacteristic
23C2×C29×C4⋊Q8C2211yescharacteristic
24C29×#529C2211yescharacteristic
25C2×C29×#124C2211yescharacteristic
26C29×#501—21no—
27C29×#498—21no—
28C29×#489—21no—
29C29×#487—21no—
30C29×#483C2214yes—
31C29×#483C2212yes—
32C29×#480C2212yes—
33C29×#477—21no—
34C29×#476—21no—
35C29×#475—22no—
36C29×#432C2211yescharacteristic
37C29×#431C2211yescharacteristic
38C29×#397C2214yes—
39C29×#393—22no—
40C29×#391—21no—
41C29×#390—21no—
42C29×#376C2211yescharacteristic
43C29×#328C2212yes—
44C29×#328C2214yes—
45C29×#327C2212yes—
46C29×#323C2214yes—
47C2×#41×C29—21no—
48C22×Q8×C29—21no—
49C22×Q8×C29—21no—
50C22×Q8×C29D411yescharacteristic
51C22×D4×C29D411yescharacteristic
52C29×C4⋊Q8—21no—
53C29×C4⋊Q8—22no—
54C29×C4⋊Q8—21no—
55C29×C4⋊Q8—21no—
56C29×C4⋊Q8—21no—
57C29×C4⋊Q8—21no—
58C29×C4⋊Q8D411yescharacteristic
59C29×C4⋊Q8D411yescharacteristic
60C29×#126—22no—
61C29×#126—22no—
62C29×#126—22no—
63C29×#126—21no—
64C29×#125—21no—
65C29×#125D411yescharacteristic
66C29×#124—21no—
67C29×#124—22no—
68C29×#124—22no—
69C29×#124—21no—
70C29×#124—21no—
71C29×#124—21no—
72C29×#124—21no—
73C29×#124D411yescharacteristic
74C29×#123—22no—
75C29×#123—22no—
76C29×#123—22no—
77C29×#123—21no—
78C29×#123—22no—
79C29×C22⋊Q8—22no—
80C29×C22⋊Q8—21no—
81C29×C22⋊Q8—22no—
82C29×C22⋊Q8—22no—
83C29×C22⋊Q8—22no—
84C29×C22⋊Q8—21no—
85C29×C22⋊Q8—22no—
86C29×C22⋊Q8—22no—
87C29×C22⋊Q8—22no—
88C29×C22⋊Q8C2311yescharacteristic
89C29×C22⋊Q8C2312yes—
90C29×#121—21no—
91C29×#121—22no—
92C29×#121—22no—
93C29×#121C2311yescharacteristic
94C29×#120—22no—
95C4×Q8×C29—21no—
96C4×Q8×C29—21no—
97C4×Q8×C29D412yes—
98C4×Q8×C29D411yescharacteristic
99C4×D4×C29—21no—
100C4×D4×C29—22no—
101C4×D4×C29—21no—
102C4×D4×C29—22no—
103C4×D4×C29D411yescharacteristic
104C29×#117—22no—
105C29×#117—21no—
106C29×#117—21no—
107C2×C4⋊C4×C29—21no—
108C2×C4⋊C4×C29C2312yes—
109C2×C22⋊C4×C29—22no—
110C2×C22⋊C4×C29—24no—
111C2×C22⋊C4×C29D412yes—
112C2×C22⋊C4×C29C2312yes—
113C2×C42×C29—21no—
114C2×C42×C29C2311yescharacteristic
115C29×#107—22no—
116C29×#106—24no—
117C29×#106—22no—
118C29×C4⋊C8—21no—
119C29×C4⋊C8—21no—
120C29×#103—24no—
121C29×#103—22no—
122C29×#102—22no—
123C29×C22⋊C8C2312yes—
124C29×C22⋊C8C2312yes—
125C29×#97—21no—
126C4×C8×C29—21no—
127C29×#95—21no—
128C29×#95—24no—
129C29×#95C2312yes—
130C24×C29C2×D412yes—
131#41×C29—82no—
132C2×Q8×C29—22no—
133C2×Q8×C29—21no—
134C2×Q8×C29—21no—
135C2×Q8×C29—21no—
136C2×Q8×C29—42no—
137C2×Q8×C29—41no—
138C2×Q8×C29—41no—
139C2×Q8×C29—82no—
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—21no—
148C2×D4×C29—42no—
149C2×D4×C29C2×D411yescharacteristic
150C22×C4×C29—22no—
151C22×C4×C29—22no—
152C22×C4×C29—22no—
153C22×C4×C29—21no—
154C22×C4×C29—22no—
155C22×C4×C29—22no—
156C22×C4×C29C2×D411yescharacteristic
157C22×C4×C29C2×D411yescharacteristic
158C22×C4×C29C2×D412yes—
159C22×C4×C29C2411yescharacteristic
160C2×C8×C29—22no—
161C2×C8×C29—22no—
162C4⋊C4×C29—22no—
163C4⋊C4×C29—22no—
164C4⋊C4×C29—22no—
165C4⋊C4×C29—22no—
166C4⋊C4×C29—21no—
167C4⋊C4×C29—21no—
168C4⋊C4×C29—21no—
169C4⋊C4×C29—21no—
170C4⋊C4×C29—21no—
171C4⋊C4×C29—21no—
172C4⋊C4×C29—22no—
173C4⋊C4×C29—21no—
174C4⋊C4×C29—22no—
175C4⋊C4×C29—22no—
176C4⋊C4×C29—22no—
177C4⋊C4×C29—41no—
178C4⋊C4×C29—41no—
179C4⋊C4×C29C2×D411yescharacteristic
180C4⋊C4×C29C2×D411yescharacteristic
181C4⋊C4×C29C2×D412yes—
182C22⋊C4×C29—22no—
183C22⋊C4×C29—22no—
184C22⋊C4×C29—22no—
185C22⋊C4×C29—22no—
186C22⋊C4×C29—22no—
187C22⋊C4×C29—21no—
188C22⋊C4×C29—22no—
189C22⋊C4×C29—22no—
190C22⋊C4×C29—22no—
191C22⋊C4×C29—21no—
192C22⋊C4×C29—21no—
193C22⋊C4×C29—21no—
194C22⋊C4×C29—22no—
195C22⋊C4×C29—22no—
196C22⋊C4×C29—21no—
197C22⋊C4×C29—84no—
198C42×C29—22no—
199C42×C29—22no—
200C42×C29—21no—
201C42×C29—42no—
202C42×C29C2×D411yescharacteristic
203C42×C29C2×D411yescharacteristic
204C42×C29C2×D411yescharacteristic
205C42×C29C2×D411yescharacteristic
206#18438C2911yesmaximal, characteristic, direct product factor, Sylow
207C23×C29—22no—
208C23×C29—21no—
209C23×C29—24no—
210C23×C29—42no—
211C23×C29—42no—
212C23×C29C22×D411yescharacteristic
213Q8×C29—41no—
214Q8×C29—42no—
215Q8×C29—42no—
216Q8×C29—42no—
217Q8×C29—81no—
218Q8×C29—82no—
219Q8×C29—82no—
220Q8×C29—82no—
221D4×C29—41no—
222D4×C29—42no—
223D4×C29—42no—
224D4×C29—81no—
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—42no—
239C2×C4×C29—42no—
240C2×C4×C29—42no—
241C2×C4×C29—42no—
242C2×C4×C29—44no—
243C2×C4×C29—82no—
244C2×C4×C29—82no—
245C2×C4×C29—82no—
246C2×C4×C29#12011yescharacteristic
247C2×C4×C29#12011yescharacteristic
248C2×C4×C29#12011yescharacteristic
249C2×C4×C29#12011yescharacteristic
250C2×C4×C29C22×D411yescharacteristic
251C2×C4×C29C22×D411yescharacteristic
252C8×C29—42no—
253C8×C29—42no—
254#3561C2×C2911yescharacteristic
255#3238C2×C2911yescharacteristic, complemented
256#3229C2×C2911yescharacteristic, complemented
257#2640C2×C2911yescharacteristic, complemented
258#1612C2×C2914yescomplemented
259#1608C2×C2914yescomplemented
260#1506C2×C2911yescharacteristic, complemented
261#1500C2×C2911yescharacteristic, complemented
262#1469C2×C2911yescharacteristic, complemented
263C22×C29—21no—
264C22×C29—21no—
265C22×C29—41no—
266C22×C29—42no—
267C22×C29—41no—
268C22×C29—42no—
269C22×C29—42no—
270C22×C29—41no—
271C22×C29—84no—
272C22×C29C2×#12011yescharacteristic
273C22×C29#57712yes—
274C4×C29—21no—
275C4×C29—21no—
276C4×C29—21no—
277C4×C29—21no—
278C4×C29—21no—
279C4×C29—41no—
280C4×C29—41no—
281C4×C29—42no—
282C4×C29—42no—
283C4×C29—41no—
284C4×C29—42no—
285C4×C29—82no—
286C4×C29—82no—
287C4×C29#45512yes—
288#563—21no—
289#562—21no—
290#556—21no—
291#551—22no—
292D4×Q8—21no—
293#548—21no—
294#546—21no—
295#543C22×C2912yes—
296#542—21no—
297#542—22no—
298#538C22×C2912yes—
299#536—21no—
300#533C22×C2911yescharacteristic
301C2×C4⋊Q8C22×C2911yescharacteristic
302#529C22×C2911yescharacteristic
303C2×#124C22×C2911yescharacteristic
304#501—21no—
305#498—21no—
306#489—21no—
307#487—21no—
308#483C22×C2912yes—
309#483C22×C2914yes—
310#480C22×C2912yes—
311#477—21no—
312#476—21no—
313#475—22no—
314#432C22×C2911yescharacteristic
315#431C22×C2911yescharacteristic
316#397C22×C2914yes—
317#393—22no—
318#391—21no—
319#390—21no—
320#376C22×C2911yescharacteristic
321#328C22×C2912yes—
322#328C22×C2914yes—
323#327C22×C2912yes—
324#323C22×C2914yes—
325C2×C29—22no—
326C2×C29—81no—
327C2×C29—82no—
328C2×C29#301011yescharacteristic
329C2×C29C2×#45511yescharacteristic
330C2×C29#302811yescharacteristic
331C2×#41—21no—
332C22×Q8—21no—
333C22×Q8—21no—
334C22×Q8D4×C2911yescharacteristic
335C22×D4D4×C2911yescharacteristic
336C4⋊Q8—21no—
337C4⋊Q8—22no—
338C4⋊Q8—21no—
339C4⋊Q8—21no—
340C4⋊Q8—21no—
341C4⋊Q8—21no—
342C4⋊Q8D4×C2911yescharacteristic
343C4⋊Q8D4×C2911yescharacteristic
344#126—22no—
345#126—22no—
346#126—22no—
347#126—21no—
348#125—21no—
349#125D4×C2911yescharacteristic
350#124—21no—
351#124—22no—
352#124—22no—
353#124—21no—
354#124—21no—
355#124—21no—
356#124—21no—
357#124D4×C2911yescharacteristic
358#123—22no—
359#123—22no—
360#123—22no—
361#123—21no—
362#123—22no—
363C22⋊Q8—22no—
364C22⋊Q8—21no—
365C22⋊Q8—22no—
366C22⋊Q8—22no—
367C22⋊Q8—22no—
368C22⋊Q8—21no—
369C22⋊Q8—22no—
370C22⋊Q8—22no—
371C22⋊Q8—22no—
372C22⋊Q8C23×C2911yescharacteristic
373C22⋊Q8C23×C2912yes—
374#121—21no—
375#121—22no—
376#121—22no—
377#121C23×C2911yescharacteristic
378#120—22no—
379C4×Q8—21no—
380C4×Q8—21no—
381C4×Q8D4×C2911yescharacteristic
382C4×Q8D4×C2912yes—
383C4×D4—21no—
384C4×D4—22no—
385C4×D4—21no—
386C4×D4—22no—
387C4×D4D4×C2911yescharacteristic
388#117—22no—
389#117—21no—
390#117—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4C23×C2912yes—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4D4×C2912yes—
396C2×C22⋊C4C23×C2912yes—
397C2×C42—21no—
398C2×C42C23×C2911yescharacteristic
399#107—22no—
400#106—24no—
401#106—22no—
402C4⋊C8—21no—
403C4⋊C8—21no—
404#103—24no—
405#103—22no—
406#102—22no—
407C22⋊C8C23×C2912yes—
408C22⋊C8C23×C2912yes—
409#97—21no—
410C4×C8—21no—
411#95—21no—
412#95—24no—
413#95C23×C2912yes—
414C29#1843811yescharacteristic, direct product factor, Sylow
415C24C2×D4×C2912yes—
416#41—82no—
417C2×Q8—22no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—42no—
422C2×Q8—41no—
423C2×Q8—41no—
424C2×Q8—82no—
425C2×Q8—82no—
426C2×Q8C2×D4×C2911yescharacteristic
427C2×Q8C2×D4×C2912yes—
428C2×D4—21no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—42no—
434C2×D4C2×D4×C2911yescharacteristic
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4C2×D4×C2911yescharacteristic
442C22×C4C2×D4×C2911yescharacteristic
443C22×C4C2×D4×C2912yes—
444C22×C4C24×C2911yescharacteristic
445C2×C8—22no—
446C2×C8—22no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—22no—
458C4⋊C4—21no—
459C4⋊C4—22no—
460C4⋊C4—22no—
461C4⋊C4—22no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4C2×D4×C2911yescharacteristic
465C4⋊C4C2×D4×C2912yes—
466C4⋊C4C2×D4×C2911yescharacteristic
467C22⋊C4—22no—
468C22⋊C4—22no—
469C22⋊C4—22no—
470C22⋊C4—22no—
471C22⋊C4—22no—
472C22⋊C4—21no—
473C22⋊C4—22no—
474C22⋊C4—22no—
475C22⋊C4—22no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—22no—
480C22⋊C4—22no—
481C22⋊C4—21no—
482C22⋊C4—84no—
483C42—22no—
484C42—22no—
485C42—21no—
486C42—42no—
487C42C2×D4×C2911yescharacteristic
488C42C2×D4×C2911yescharacteristic
489C42C2×D4×C2911yescharacteristic
490C42C2×D4×C2911yescharacteristic
491C23—22no—
492C23—21no—
493C23—24no—
494C23—42no—
495C23—42no—
496C23C22×D4×C2911yescharacteristic
497Q8—41no—
498Q8—42no—
499Q8—42no—
500Q8—42no—
501Q8—81no—
502Q8—82no—
503Q8—82no—
504Q8—82no—
505D4—41no—
506D4—42no—
507D4—42no—
508D4—81no—
509D4—82no—
510D4—82no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—21no—
514C2×C4—22no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—44no—
527C2×C4—82no—
528C2×C4—82no—
529C2×C4—82no—
530C2×C4C29×#12011yescharacteristic
531C2×C4C29×#12011yescharacteristic
532C2×C4C29×#12011yescharacteristic
533C2×C4C29×#12011yescharacteristic
534C2×C4C22×D4×C2911yescharacteristic
535C2×C4C22×D4×C2911yescharacteristic
536C8—42no—
537C8—42no—
538C22—21no—
539C22—21no—
540C22—41no—
541C22—42no—
542C22—41no—
543C22—42no—
544C22—42no—
545C22—41no—
546C22—84no—
547C22C2×C29×#12011yescharacteristic
548C22C29×#57712yes—
549C4—21no—
550C4—21no—
551C4—21no—
552C4—21no—
553C4—21no—
554C4—41no—
555C4—41no—
556C4—42no—
557C4—42no—
558C4—41no—
559C4—42no—
560C4—82no—
561C4—82no—
562C4C29×#45512yes—
563C2—22no—
564C2—82no—
565C2—81no—
566C2C29×#301011yescharacteristic
567C2C2×C29×#45511yescharacteristic
568C2C29×#302811yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC29×#3561C2
LCSG ▷ C22×C4 ▷ 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×#3229C2semidirect
4. C29×#2640C2semidirect
5. C29×#1612C2semidirect
6. C29×#1608C2semidirect
7. C29×#1506C2semidirect
8. C29×#1500C2semidirect
9. C29×#1469C2semidirect
206. #18438C29direct (N × H)
255. #3238C2×C29semidirect
256. #3229C2×C29semidirect
257. #2640C2×C29semidirect
258. #1612C2×C29semidirect
259. #1608C2×C29semidirect
260. #1506C2×C29semidirect
261. #1500C2×C29semidirect
262. #1469C2×C29semidirect
414. C29#18438direct (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×#32292
C29×#26402
C29×#16122
C29×#16082
C29×#15062
C29×#15002
C29×#14692
#1843829