Finite Group Databasebeta

← C29×#16522 #20311422

Subgroups — C29×#16522 #20311422

Order 7424.

1414 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#398C212yesmaximal
2C2×C29×#395C212yesmaximal
3C2×C29×#395C211yesmaximal, characteristic
4C2×C29×#384C211yesmaximal, characteristic
5C29×#1444C212yesmaximal
6C29×#1444C212yesmaximal
7C29×#1442C212yesmaximal
8C29×#1441C211yesmaximal, characteristic
9C29×#1434C212yesmaximal
10C23×Q8×C29C2211yescharacteristic
11C22×C4⋊C4×C29C2211yescharacteristic
12C22×C4⋊C4×C29C2212yes—
13C22×C4⋊C4×C29C2212yes—
14C22×C4⋊C4×C29C2212yes—
15C22×C4⋊C4×C29C2212yes—
16C22×C4⋊C4×C29C2211yescharacteristic
17C22×C4⋊C4×C29C2212yes—
18C22×C4⋊C4×C29C2211yescharacteristic
19C22×C42×C29C2211yescharacteristic
20C29×#398—28no—
21C29×#395—28no—
22C29×#395—24no—
23C29×#384—24no—
24C2×C29×#95C2212yes—
25C2×C29×#95C2212yes—
26C2×C29×#95C2212yes—
27C2×C29×#95C2212yes—
28C2×C29×#95C2212yes—
29C2×C29×#95C2211yescharacteristic
30C2×C29×#95C2212yes—
31C2×C29×#95C2211yescharacteristic
32C2×C29×#95C2212yes—
33C2×C29×#95C2212yes—
34C2×C29×#95C2212yes—
35C22×Q8×C29—24no—
36C22×Q8×C29—22no—
37C22×Q8×C29—41no—
38C22×Q8×C29—42no—
39C22×Q8×C29—41no—
40C23×C4×C29C2312yes—
41C23×C4×C29C2311yescharacteristic
42C23×C4×C29C2312yes—
43C23×C4×C29C2311yescharacteristic
44C23×C4×C29C2312yes—
45C23×C4×C29C2312yes—
46C23×C4×C29C2312yes—
47C23×C4×C29C2312yes—
48C23×C4×C29C2311yescharacteristic
49C2×C4⋊C4×C29—24no—
50C2×C4⋊C4×C29—24no—
51C2×C4⋊C4×C29—22no—
52C2×C4⋊C4×C29—24no—
53C2×C4⋊C4×C29—24no—
54C2×C4⋊C4×C29—24no—
55C2×C4⋊C4×C29—24no—
56C2×C4⋊C4×C29—24no—
57C2×C4⋊C4×C29—24no—
58C2×C4⋊C4×C29—24no—
59C2×C4⋊C4×C29—24no—
60C2×C4⋊C4×C29—41no—
61C2×C4⋊C4×C29—41no—
62C2×C4⋊C4×C29—42no—
63C2×C4⋊C4×C29—42no—
64C2×C4⋊C4×C29—41no—
65C2×C4⋊C4×C29—42no—
66C2×C4⋊C4×C29—42no—
67C2×C4⋊C4×C29—41no—
68C2×C4⋊C4×C29—41no—
69C2×C4⋊C4×C29—42no—
70C2×C4⋊C4×C29—42no—
71C2×C4⋊C4×C29D414yes—
72C2×C42×C29—22no—
73C2×C42×C29—22no—
74C2×C42×C29Q814yescomplemented
75C29×#95—24no—
76C29×#95—24no—
77C29×#95—24no—
78C29×#95—22no—
79C29×#95—24no—
80C29×#95—24no—
81C29×#95—24no—
82C29×#95—41no—
83C29×#95—42no—
84C29×#95D418yes—
85C29×#95Q818yescomplemented
86C24×C29C2411yescharacteristic
87C2×Q8×C29—48no—
88C2×Q8×C29—44no—
89C2×Q8×C29—44no—
90C2×Q8×C29—48no—
91C2×Q8×C29—44no—
92C22×C4×C29—22no—
93C22×C4×C29—22no—
94C22×C4×C29—21no—
95C22×C4×C29—21no—
96C22×C4×C29—22no—
97C22×C4×C29—21no—
98C22×C4×C29—21no—
99C22×C4×C29—22no—
100C22×C4×C29—22no—
101C22×C4×C29—22no—
102C22×C4×C29—22no—
103C22×C4×C29—22no—
104C22×C4×C29—22no—
105C22×C4×C29—22no—
106C22×C4×C29—22no—
107C22×C4×C29—22no—
108C22×C4×C29—22no—
109C22×C4×C29—22no—
110C22×C4×C29—21no—
111C22×C4×C29—22no—
112C22×C4×C29—22no—
113C22×C4×C29—21no—
114C22×C4×C29—21no—
115C22×C4×C29—22no—
116C22×C4×C29—22no—
117C22×C4×C29—22no—
118C22×C4×C29—22no—
119C22×C4×C29—22no—
120C22×C4×C29—21no—
121C22×C4×C29—22no—
122C22×C4×C29—22no—
123C22×C4×C29—22no—
124C22×C4×C29—22no—
125C22×C4×C29—22no—
126C22×C4×C29—22no—
127C22×C4×C29—22no—
128C22×C4×C29—22no—
129C22×C4×C29—22no—
130C22×C4×C29—22no—
131C22×C4×C29—22no—
132C22×C4×C29—22no—
133C22×C4×C29—22no—
134C22×C4×C29—22no—
135C22×C4×C29—22no—
136C22×C4×C29—22no—
137C22×C4×C29—22no—
138C22×C4×C29—22no—
139C22×C4×C29C2×D412yes—
140C22×C4×C29C2×D414yes—
141C22×C4×C29C2×D412yes—
142C22×C4×C29C2×D414yes—
143C22×C4×C29C2×D412yes—
144C22×C4×C29C2×D414yes—
145C22×C4×C29C2×Q814yes—
146C22×C4×C29C2×Q814yes—
147C22×C4×C29C2×Q812yes—
148C22×C4×C29C2×Q814yes—
149C22×C4×C29C2×Q814yes—
150C22×C4×C29#4112yes—
151C4⋊C4×C29—44no—
152C4⋊C4×C29—48no—
153C4⋊C4×C29—48no—
154C4⋊C4×C29—44no—
155C4⋊C4×C29—48no—
156C4⋊C4×C29—48no—
157C4⋊C4×C29—44no—
158C4⋊C4×C29—48no—
159C42×C29—28no—
160#16522C2911yesmaximal, characteristic, direct product factor, Sylow
161C23×C29C22×D411yescharacteristic
162C23×C29C22×D412yes—
163C23×C29C22×Q811yescharacteristic
164C23×C29C22×Q812yes—
165C23×C29C2×#4111yescharacteristic
166C23×C29H(5,𝔽2)11yescharacteristic
167C23×C29H(5,𝔽2)11yescharacteristic
168C23×C29H(5,𝔽2)12yes—
169C23×C292−1+411yescharacteristic
170C23×C292−1+411yescharacteristic
171C23×C292−1+412yes—
172Q8×C29—416no—
173C2×C4×C29—24no—
174C2×C4×C29—22no—
175C2×C4×C29—22no—
176C2×C4×C29—22no—
177C2×C4×C29—22no—
178C2×C4×C29—22no—
179C2×C4×C29—22no—
180C2×C4×C29—24no—
181C2×C4×C29—24no—
182C2×C4×C29—24no—
183C2×C4×C29—24no—
184C2×C4×C29—24no—
185C2×C4×C29—22no—
186C2×C4×C29—22no—
187C2×C4×C29—24no—
188C2×C4×C29—24no—
189C2×C4×C29—24no—
190C2×C4×C29—24no—
191C2×C4×C29—24no—
192C2×C4×C29—24no—
193C2×C4×C29—24no—
194C2×C4×C29—24no—
195C2×C4×C29—24no—
196C2×C4×C29—24no—
197C2×C4×C29—24no—
198C2×C4×C29—24no—
199C2×C4×C29—24no—
200C2×C4×C29—24no—
201C2×C4×C29—42no—
202C2×C4×C29—42no—
203C2×C4×C29—42no—
204C2×C4×C29—42no—
205C2×C4×C29—42no—
206C2×C4×C29—42no—
207C2×C4×C29—42no—
208C2×C4×C29—42no—
209C2×C4×C29—42no—
210C2×C4×C29—42no—
211C2×C4×C29—41no—
212C2×C4×C29—42no—
213C2×C4×C29—42no—
214C2×C4×C29—41no—
215C2×C4×C29—42no—
216C2×C4×C29—42no—
217C2×C4×C29—41no—
218C2×C4×C29—41no—
219C2×C4×C29—42no—
220C2×C4×C29—42no—
221C2×C4×C29—42no—
222C2×C4×C29—42no—
223C2×C4×C29—42no—
224C2×C4×C29—42no—
225C2×C4×C29—42no—
226C2×C4×C29—42no—
227C2×C4×C29—42no—
228C2×C4×C29—42no—
229C2×C4×C29—42no—
230C2×C4×C29C22⋊Q814yes—
231C2×C4×C29C4⋊Q818yes—
232C2×#398C2×C2912yes—
233C2×#395C2×C2911yescharacteristic
234C2×#395C2×C2912yes—
235C2×#384C2×C2911yescharacteristic
236#1444C2×C2912yes—
237#1444C2×C2912yes—
238#1442C2×C2912yes—
239#1441C2×C2911yescharacteristic
240#1434C2×C2912yes—
241C22×C29C2×C22⋊Q811yescharacteristic
242C22×C29C2×C4⋊Q812yes—
243C22×C29#53411yescharacteristic
244C22×C29#53512yes—
245C22×C29#53611yescharacteristic
246C22×C29#53612yes—
247C22×C29#53911yescharacteristic
248C22×C29#53911yescharacteristic
249C22×C29#54411yescharacteristic
250C22×C29#54412yes—
251C22×C29#54411yescharacteristic
252C22×C29#54412yes—
253C22×C29#54412yes—
254C22×C29D4212yes—
255C22×C29D4211yescharacteristic
256C22×C29#54712yes—
257C22×C29D4×Q812yes—
258C22×C29D4×Q812yes—
259C22×C29#55412yes—
260C22×C29Q8211yescharacteristic
261C22×C29#56011yescharacteristic
262C22×C29#56312yes—
263C22×C29#56311yescharacteristic
264C4×C29—24no—
265C4×C29—28no—
266C4×C29—42no—
267C4×C29—42no—
268C4×C29—44no—
269C4×C29—44no—
270C4×C29—44no—
271C4×C29—44no—
272C4×C29—82no—
273C23×Q8C22×C2911yescharacteristic
274C22×C4⋊C4C22×C2912yes—
275C22×C4⋊C4C22×C2912yes—
276C22×C4⋊C4C22×C2912yes—
277C22×C4⋊C4C22×C2911yescharacteristic
278C22×C4⋊C4C22×C2912yes—
279C22×C4⋊C4C22×C2912yes—
280C22×C4⋊C4C22×C2911yescharacteristic
281C22×C4⋊C4C22×C2911yescharacteristic
282C22×C42C22×C2911yescharacteristic
283#398—28no—
284#395—24no—
285#395—28no—
286#384—24no—
287C2×#95C22×C2912yes—
288C2×#95C22×C2912yes—
289C2×#95C22×C2912yes—
290C2×#95C22×C2911yescharacteristic
291C2×#95C22×C2912yes—
292C2×#95C22×C2912yes—
293C2×#95C22×C2912yes—
294C2×#95C22×C2911yescharacteristic
295C2×#95C22×C2912yes—
296C2×#95C22×C2912yes—
297C2×#95C22×C2912yes—
298C2×C29#244012yes—
299C2×C29#255111yescharacteristic
300C2×C29#262711yescharacteristic
301C2×C29#266012yes—
302C2×C29#266911yescharacteristic
303C2×C29#267712yes—
304C2×C29#268011yescharacteristic
305C2×C29#272012yes—
306C2×C29#273411yescharacteristic
307C2×C29#279211yescharacteristic
308C2×C29#284311yescharacteristic
309C22×Q8—22no—
310C22×Q8—24no—
311C22×Q8—41no—
312C22×Q8—42no—
313C22×Q8—41no—
314C23×C4C23×C2912yes—
315C23×C4C23×C2911yescharacteristic
316C23×C4C23×C2911yescharacteristic
317C23×C4C23×C2912yes—
318C23×C4C23×C2912yes—
319C23×C4C23×C2912yes—
320C23×C4C23×C2912yes—
321C23×C4C23×C2912yes—
322C23×C4C23×C2911yescharacteristic
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—41no—
335C2×C4⋊C4—41no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—41no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4—41no—
342C2×C4⋊C4—41no—
343C2×C4⋊C4—42no—
344C2×C4⋊C4—42no—
345C2×C4⋊C4D4×C2914yes—
346C2×C42—22no—
347C2×C42—22no—
348C2×C42Q8×C2914yescomplemented
349#95—22no—
350#95—24no—
351#95—24no—
352#95—24no—
353#95—24no—
354#95—24no—
355#95—24no—
356#95—41no—
357#95—42no—
358#95D4×C2918yes—
359#95Q8×C2918yescomplemented
360C29#1652211yescharacteristic, direct product factor, Sylow
361C24C24×C2911yescharacteristic
362C2×Q8—48no—
363C2×Q8—44no—
364C2×Q8—44no—
365C2×Q8—48no—
366C2×Q8—44no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—22no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—22no—
375C22×C4—22no—
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—21no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—21no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
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—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4C2×D4×C2914yes—
415C22×C4C2×D4×C2912yes—
416C22×C4C2×D4×C2914yes—
417C22×C4C2×D4×C2912yes—
418C22×C4C2×D4×C2912yes—
419C22×C4C2×D4×C2914yes—
420C22×C4C2×Q8×C2914yes—
421C22×C4C2×Q8×C2914yes—
422C22×C4C2×Q8×C2912yes—
423C22×C4C2×Q8×C2914yes—
424C22×C4C2×Q8×C2914yes—
425C22×C4#41×C2912yes—
426C4⋊C4—44no—
427C4⋊C4—48no—
428C4⋊C4—48no—
429C4⋊C4—44no—
430C4⋊C4—48no—
431C4⋊C4—48no—
432C4⋊C4—44no—
433C4⋊C4—48no—
434C42—28no—
435C23C22×D4×C2911yescharacteristic
436C23C22×D4×C2912yes—
437C23C22×Q8×C2911yescharacteristic
438C23C22×Q8×C2912yes—
439C23C2×#41×C2911yescharacteristic
440C23C29×H(5,𝔽2)11yescharacteristic
441C23C29×H(5,𝔽2)11yescharacteristic
442C23C29×H(5,𝔽2)12yes—
443C23C29×2−1+411yescharacteristic
444C23C29×2−1+411yescharacteristic
445C23C29×2−1+412yes—
446Q8—416no—
447C2×C4—24no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—24no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—24no—
456C2×C4—24no—
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—24no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—41no—
487C2×C4—42no—
488C2×C4—41no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—41no—
492C2×C4—42no—
493C2×C4—41no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4C29×C22⋊Q814yes—
505C2×C4C29×C4⋊Q818yes—
506C22C2×C29×C22⋊Q811yescharacteristic
507C22C2×C29×C4⋊Q812yes—
508C22C29×#53411yescharacteristic
509C22C29×#53512yes—
510C22C29×#53611yescharacteristic
511C22C29×#53612yes—
512C22C29×#53911yescharacteristic
513C22C29×#53911yescharacteristic
514C22C29×#54412yes—
515C22C29×#54412yes—
516C22C29×#54412yes—
517C22C29×#54411yescharacteristic
518C22C29×#54411yescharacteristic
519C22D42×C2912yes—
520C22D42×C2911yescharacteristic
521C22C29×#54712yes—
522C22D4×Q8×C2912yes—
523C22D4×Q8×C2912yes—
524C22C29×#55412yes—
525C22Q82×C2911yescharacteristic
526C22C29×#56011yescharacteristic
527C22C29×#56312yes—
528C22C29×#56311yescharacteristic
529C4—28no—
530C4—24no—
531C4—44no—
532C4—44no—
533C4—44no—
534C4—42no—
535C4—44no—
536C4—42no—
537C4—82no—
538C2C29×#244012yes—
539C2C29×#255111yescharacteristic
540C2C29×#262711yescharacteristic
541C2C29×#266012yes—
542C2C29×#266911yescharacteristic
543C2C29×#267712yes—
544C2C29×#268011yescharacteristic
545C2C29×#272012yes—
546C2C29×#273411yescharacteristic
547C2C29×#279211yescharacteristic
548C2C29×#284311yescharacteristic
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
74. C2×C42×C29Q8semidirect
85. C29×#95Q8semidirect
160. #16522C29direct (N × H)
348. C2×C42Q8×C29semidirect
359. #95Q8×C29semidirect
360. C29#16522direct (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×#3952
C2×C29×#3842
C29×#14442
C29×#14422
C29×#14412
C29×#14342
#1652229