Finite Group Databasebeta

← C29×#16517 #20311417

Subgroups — C29×#16517 #20311417

Order 7424.

1234 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#398C211yesmaximal, characteristic
2C2×C29×#398C212yesmaximal
3C2×C29×#389C211yesmaximal, characteristic
4C2×C29×#387C211yesmaximal, characteristic
5C2×C29×#382C211yesmaximal, characteristic
6C29×#1445C211yesmaximal, characteristic
7C29×#1443C212yesmaximal
8C29×#1442C211yesmaximal, characteristic
9C29×#1442C212yesmaximal
10C29×#1441C211yesmaximal, characteristic
11C29×#1441C212yesmaximal
12C22×C4⋊C4×C29C2211yescharacteristic
13C22×C4⋊C4×C29C2211yescharacteristic
14C22×C4⋊C4×C29C2212yes—
15C22×C4⋊C4×C29C2211yescharacteristic
16C22×C4⋊C4×C29C2212yes—
17C22×C4⋊C4×C29C2212yes—
18C22×C4⋊C4×C29C2211yescharacteristic
19C22×C42×C29C2211yescharacteristic
20C29×#398—24no—
21C29×#398—28no—
22C29×#389—24no—
23C29×#387—24no—
24C29×#382—24no—
25C2×C29×#95C2212yes—
26C2×C29×#95C2211yescharacteristic
27C2×C29×#95C2212yes—
28C2×C29×#95C2212yes—
29C2×C29×#95C2212yes—
30C2×C29×#95C2211yescharacteristic
31C2×C29×#95C2211yescharacteristic
32C2×C29×#95C2212yes—
33C2×C29×#95C2212yes—
34C2×C29×#95C2212yes—
35C2×C29×#95C2211yescharacteristic
36C2×C29×#95C2211yescharacteristic
37C2×C29×#95C2212yes—
38C2×C29×#95C2212yes—
39C2×C29×#95C2211yescharacteristic
40C23×C4×C29C2312yes—
41C23×C4×C29C2311yescharacteristic
42C23×C4×C29C2312yes—
43C23×C4×C29C2311yescharacteristic
44C23×C4×C29C2311yescharacteristic
45C23×C4×C29C2311yescharacteristic
46C23×C4×C29C2312yes—
47C23×C4×C29C2311yescharacteristic
48C23×C4×C29C2312yes—
49C23×C4×C29C2311yescharacteristic
50C23×C4×C29C2311yescharacteristic
51C2×C4⋊C4×C29—22no—
52C2×C4⋊C4×C29—22no—
53C2×C4⋊C4×C29—24no—
54C2×C4⋊C4×C29—22no—
55C2×C4⋊C4×C29—24no—
56C2×C4⋊C4×C29—22no—
57C2×C4⋊C4×C29—24no—
58C2×C4⋊C4×C29—22no—
59C2×C4⋊C4×C29—24no—
60C2×C4⋊C4×C29—24no—
61C2×C4⋊C4×C29—24no—
62C2×C4⋊C4×C29—22no—
63C2×C4⋊C4×C29—24no—
64C2×C4⋊C4×C29—22no—
65C2×C4⋊C4×C29—22no—
66C2×C4⋊C4×C29—24no—
67C2×C4⋊C4×C29—22no—
68C2×C4⋊C4×C29—42no—
69C2×C4⋊C4×C29—42no—
70C2×C4⋊C4×C29D414yes—
71C2×C42×C29—22no—
72C2×C42×C29—22no—
73C2×C42×C29D414yes—
74C29×#95—24no—
75C29×#95—22no—
76C29×#95—22no—
77C29×#95—22no—
78C29×#95—22no—
79C29×#95—22no—
80C29×#95—24no—
81C29×#95—24no—
82C29×#95—24no—
83C29×#95—24no—
84C29×#95—24no—
85C29×#95—24no—
86C29×#95—24no—
87C29×#95—42no—
88C29×#95D414yes—
89C24×C29C2411yescharacteristic
90C22×C4×C29—21no—
91C22×C4×C29—21no—
92C22×C4×C29—22no—
93C22×C4×C29—21no—
94C22×C4×C29—22no—
95C22×C4×C29—21no—
96C22×C4×C29—21no—
97C22×C4×C29—21no—
98C22×C4×C29—21no—
99C22×C4×C29—22no—
100C22×C4×C29—22no—
101C22×C4×C29—21no—
102C22×C4×C29—22no—
103C22×C4×C29—21no—
104C22×C4×C29—21no—
105C22×C4×C29—21no—
106C22×C4×C29—22no—
107C22×C4×C29—21no—
108C22×C4×C29—22no—
109C22×C4×C29—22no—
110C22×C4×C29—21no—
111C22×C4×C29—22no—
112C22×C4×C29—22no—
113C22×C4×C29—22no—
114C22×C4×C29—22no—
115C22×C4×C29—22no—
116C22×C4×C29—22no—
117C22×C4×C29—22no—
118C22×C4×C29—22no—
119C22×C4×C29—21no—
120C22×C4×C29—22no—
121C22×C4×C29—22no—
122C22×C4×C29—22no—
123C22×C4×C29—22no—
124C22×C4×C29—22no—
125C22×C4×C29—21no—
126C22×C4×C29—21no—
127C22×C4×C29—22no—
128C22×C4×C29—22no—
129C22×C4×C29—21no—
130C22×C4×C29—22no—
131C22×C4×C29—22no—
132C22×C4×C29—21no—
133C22×C4×C29—22no—
134C22×C4×C29—22no—
135C22×C4×C29—22no—
136C22×C4×C29—22no—
137C22×C4×C29—22no—
138C22×C4×C29—21no—
139C22×C4×C29—22no—
140C22×C4×C29—22no—
141C22×C4×C29—22no—
142C22×C4×C29—22no—
143C22×C4×C29—22no—
144C22×C4×C29—21no—
145C22×C4×C29—22no—
146C22×C4×C29C2×D412yes—
147C22×C4×C29C2×D412yes—
148C22×C4×C29C2×D414yes—
149C22×C4×C29C2×D412yes—
150C22×C4×C29C2×D412yes—
151C22×C4×C29C2×D412yes—
152C22×C4×C29C2×D412yes—
153C22×C4×C29C2×D412yes—
154C22×C4×C29#4114yes—
155C22×C4×C29#4112yes—
156C22×C4×C29#4112yes—
157C4⋊C4×C29—28no—
158C4⋊C4×C29—28no—
159C4⋊C4×C29—48no—
160C4⋊C4×C29—48no—
161C4⋊C4×C29—44no—
162C4⋊C4×C29—48no—
163C4⋊C4×C29—44no—
164C42×C29—28no—
165#16517C2911yesmaximal, characteristic, direct product factor, Sylow
166C23×C29C22×D411yescharacteristic
167C23×C29C22×D411yescharacteristic
168C23×C29C22×D411yescharacteristic
169C23×C29C2×#4111yescharacteristic
170C23×C29C2×#4111yescharacteristic
171C23×C29C2×#4112yes—
172C23×C29H(5,𝔽2)11yescharacteristic
173C23×C292−1+412yes—
174C23×C292−1+412yes—
175C23×C292−1+412yes—
176C23×C292−1+411yescharacteristic
177C2×C4×C29—22no—
178C2×C4×C29—22no—
179C2×C4×C29—22no—
180C2×C4×C29—22no—
181C2×C4×C29—22no—
182C2×C4×C29—24no—
183C2×C4×C29—22no—
184C2×C4×C29—22no—
185C2×C4×C29—24no—
186C2×C4×C29—22no—
187C2×C4×C29—22no—
188C2×C4×C29—22no—
189C2×C4×C29—22no—
190C2×C4×C29—24no—
191C2×C4×C29—22no—
192C2×C4×C29—22no—
193C2×C4×C29—24no—
194C2×C4×C29—24no—
195C2×C4×C29—22no—
196C2×C4×C29—24no—
197C2×C4×C29—22no—
198C2×C4×C29—24no—
199C2×C4×C29—24no—
200C2×C4×C29—24no—
201C2×C4×C29—41no—
202C2×C4×C29—42no—
203C2×C4×C29—41no—
204C2×C4×C29—41no—
205C2×C4×C29—42no—
206C2×C4×C29—42no—
207C2×C4×C29—42no—
208C2×C4×C29—41no—
209C2×C4×C29—42no—
210C2×C4×C29—42no—
211C2×C4×C29—42no—
212C2×C4×C29—41no—
213C2×C4×C29—42no—
214C2×C4×C29—42no—
215C2×C4×C29—42no—
216C2×C4×C29—41no—
217C2×C4×C29—42no—
218C2×C4×C29—41no—
219C2×C4×C29—42no—
220C2×C4×C29—42no—
221C2×C4×C29—41no—
222C2×C4×C29—41no—
223C2×C4×C29—41no—
224C2×C4×C29—41no—
225C2×C4×C29—42no—
226C2×C4×C29—42no—
227C2×C4×C29—41no—
228C2×C4×C29—42no—
229C2×C4×C29—42no—
230C2×C4×C29—42no—
231C2×C4×C29—42no—
232C2×C4×C29—42no—
233C2×C4×C29—42no—
234C2×C4×C29—42no—
235C2×C4×C29—42no—
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#12114yes—
243C2×C4×C29#12114yes—
244C2×#398C2×C2911yescharacteristic
245C2×#398C2×C2912yes—
246C2×#389C2×C2911yescharacteristic
247C2×#387C2×C2911yescharacteristic
248C2×#382C2×C2911yescharacteristic
249#1445C2×C2911yescharacteristic
250#1443C2×C2912yes—
251#1442C2×C2911yescharacteristic
252#1442C2×C2912yes—
253#1441C2×C2911yescharacteristic
254#1441C2×C2912yes—
255C22×C29C2×#12111yescharacteristic
256C22×C29C2×#12111yescharacteristic
257C22×C29#52511yescharacteristic
258C22×C29#53611yescharacteristic
259C22×C29#53611yescharacteristic
260C22×C29#53611yescharacteristic
261C22×C29#53612yes—
262C22×C29#53612yes—
263C22×C29#53711yescharacteristic
264C22×C29#54112yes—
265C22×C29#54112yes—
266C22×C29#54112yes—
267C22×C29#54212yes—
268C22×C29D4211yescharacteristic
269C22×C29#54712yes—
270C22×C29#54711yescharacteristic
271C22×C29#54811yescharacteristic
272C22×C29#54812yes—
273C22×C29#55212yes—
274C22×C29#55212yes—
275C22×C29#55311yescharacteristic
276C22×C29#56312yes—
277C22×C29#56412yes—
278C4×C29—24no—
279C4×C29—24no—
280C4×C29—42no—
281C4×C29—42no—
282C4×C29—42no—
283C4×C29—44no—
284C4×C29—44no—
285C4×C29—81no—
286C4×C29—81no—
287C4×C29—82no—
288C4×C29—82no—
289C22×C4⋊C4C22×C2911yescharacteristic
290C22×C4⋊C4C22×C2912yes—
291C22×C4⋊C4C22×C2911yescharacteristic
292C22×C4⋊C4C22×C2911yescharacteristic
293C22×C4⋊C4C22×C2912yes—
294C22×C4⋊C4C22×C2912yes—
295C22×C4⋊C4C22×C2911yescharacteristic
296C22×C42C22×C2911yescharacteristic
297#398—28no—
298#398—24no—
299#389—24no—
300#387—24no—
301#382—24no—
302C2×#95C22×C2912yes—
303C2×#95C22×C2912yes—
304C2×#95C22×C2912yes—
305C2×#95C22×C2912yes—
306C2×#95C22×C2912yes—
307C2×#95C22×C2911yescharacteristic
308C2×#95C22×C2912yes—
309C2×#95C22×C2911yescharacteristic
310C2×#95C22×C2911yescharacteristic
311C2×#95C22×C2912yes—
312C2×#95C22×C2912yes—
313C2×#95C22×C2911yescharacteristic
314C2×#95C22×C2911yescharacteristic
315C2×#95C22×C2912yes—
316C2×#95C22×C2911yescharacteristic
317C2×C29#241311yescharacteristic
318C2×C29#241611yescharacteristic
319C2×C29#253611yescharacteristic
320C2×C29#262111yescharacteristic
321C2×C29#262111yescharacteristic
322C2×C29#263711yescharacteristic
323C2×C29#267412yes—
324C2×C29#271912yes—
325C2×C29#271912yes—
326C2×C29#276612yes—
327C2×C29#282211yescharacteristic
328C23×C4C23×C2912yes—
329C23×C4C23×C2911yescharacteristic
330C23×C4C23×C2912yes—
331C23×C4C23×C2911yescharacteristic
332C23×C4C23×C2911yescharacteristic
333C23×C4C23×C2912yes—
334C23×C4C23×C2911yescharacteristic
335C23×C4C23×C2911yescharacteristic
336C23×C4C23×C2912yes—
337C23×C4C23×C2911yescharacteristic
338C23×C4C23×C2911yescharacteristic
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—42no—
357C2×C4⋊C4—42no—
358C2×C4⋊C4D4×C2914yes—
359C2×C42—22no—
360C2×C42—22no—
361C2×C42D4×C2914yes—
362#95—24no—
363#95—22no—
364#95—22no—
365#95—22no—
366#95—22no—
367#95—22no—
368#95—24no—
369#95—24no—
370#95—24no—
371#95—24no—
372#95—24no—
373#95—24no—
374#95—24no—
375#95—42no—
376#95D4×C2914yes—
377C29#1651711yescharacteristic, direct product factor, Sylow
378C24C24×C2911yescharacteristic
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—22no—
382C22×C4—21no—
383C22×C4—22no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—22no—
388C22×C4—21no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—21no—
392C22×C4—22no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4C2×D4×C2912yes—
436C22×C4C2×D4×C2912yes—
437C22×C4C2×D4×C2914yes—
438C22×C4C2×D4×C2912yes—
439C22×C4C2×D4×C2912yes—
440C22×C4C2×D4×C2912yes—
441C22×C4C2×D4×C2912yes—
442C22×C4C2×D4×C2912yes—
443C22×C4#41×C2914yes—
444C22×C4#41×C2912yes—
445C22×C4#41×C2912yes—
446C4⋊C4—28no—
447C4⋊C4—28no—
448C4⋊C4—48no—
449C4⋊C4—48no—
450C4⋊C4—44no—
451C4⋊C4—48no—
452C4⋊C4—44no—
453C42—28no—
454C23C22×D4×C2911yescharacteristic
455C23C22×D4×C2911yescharacteristic
456C23C22×D4×C2911yescharacteristic
457C23C2×#41×C2911yescharacteristic
458C23C2×#41×C2911yescharacteristic
459C23C2×#41×C2912yes—
460C23C29×H(5,𝔽2)11yescharacteristic
461C23C29×2−1+412yes—
462C23C29×2−1+412yes—
463C23C29×2−1+412yes—
464C23C29×2−1+411yescharacteristic
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—24no—
472C2×C4—22no—
473C2×C4—24no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—24no—
485C2×C4—22no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—41no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—41no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—41no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—42no—
516C2×C4—41no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4C29×#12114yes—
531C2×C4C29×#12114yes—
532C22C2×C29×#12111yescharacteristic
533C22C2×C29×#12111yescharacteristic
534C22C29×#52511yescharacteristic
535C22C29×#53612yes—
536C22C29×#53612yes—
537C22C29×#53611yescharacteristic
538C22C29×#53611yescharacteristic
539C22C29×#53611yescharacteristic
540C22C29×#53711yescharacteristic
541C22C29×#54112yes—
542C22C29×#54112yes—
543C22C29×#54112yes—
544C22C29×#54212yes—
545C22D42×C2911yescharacteristic
546C22C29×#54711yescharacteristic
547C22C29×#54712yes—
548C22C29×#54811yescharacteristic
549C22C29×#54812yes—
550C22C29×#55212yes—
551C22C29×#55212yes—
552C22C29×#55311yescharacteristic
553C22C29×#56312yes—
554C22C29×#56412yes—
555C4—24no—
556C4—24no—
557C4—42no—
558C4—44no—
559C4—44no—
560C4—42no—
561C4—42no—
562C4—82no—
563C4—82no—
564C4—81no—
565C4—81no—
566C2C29×#241311yescharacteristic
567C2C29×#241611yescharacteristic
568C2C29×#253611yescharacteristic
569C2C29×#262111yescharacteristic
570C2C29×#262111yescharacteristic
571C2C29×#263711yescharacteristic
572C2C29×#267412yes—
573C2C29×#271912yes—
574C2C29×#271912yes—
575C2C29×#276612yes—
576C2C29×#282211yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C29C24
commutator, Frattini, cosocleC24C24×C29
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C29 ◁ G

Complements

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

NH ≅ G/Ntype
165. #16517C29direct (N × H)
377. C29#16517direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#3982
C2×C29×#3892
C2×C29×#3872
C2×C29×#3822
C29×#14452
C29×#14432
C29×#14422
C29×#14412
#1651729