Finite Group Databasebeta

← C29×#25584 #20320484

Subgroups — C29×#25584 #20320484

Order 7424.

1126 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
1C2×C29×#552C211yesmaximal, characteristic
2C2×C29×#491C211yesmaximal, characteristic, complemented
3C2×C29×#462C211yesmaximal, characteristic, complemented
4C29×#2542C211yesmaximal, characteristic
5C29×#2001C212yesmaximal, complemented
6C29×#2001C212yesmaximal, complemented
7C29×#1989C211yesmaximal, characteristic, complemented
8C29×#1955C211yesmaximal, characteristic
9C29×#1873C212yesmaximal, complemented
10C29×#1872C212yesmaximal, complemented
11C29×#1763C211yesmaximal, characteristic, complemented
12C22×Q16×C29C2212yes—
13C29×#552—24no—
14C29×#552—24no—
15C2×C29×C4⋊Q8C2211yescharacteristic
16C2×C29×#126—21no—
17C2×C29×#125—21no—
18C2×C29×#125C2211yescharacteristic
19C2×C29×#123—21no—
20C2×C29×C22⋊Q8C2211yescharacteristic
21C2×C29×C22⋊Q8C2211yescharacteristic
22C2×C29×C22⋊Q8C2212yes—
23C2×C29×C22⋊Q8C2212yes—
24C2×C4×Q8×C29C2211yescharacteristic
25C2×C4×D4×C29C2211yescharacteristic
26C2×C29×#117—21no—
27C2×C29×#117C2211yescharacteristic
28C22×C4⋊C4×C29C2211yescharacteristic
29C29×#491—24no—
30C29×#462—24no—
31C2×C29×C4⋊C8C2211yescharacteristic
32C2×C29×#103C2212yes—
33C2×C29×#103C2212yes—
34C2×C29×#103C2212yes—
35C2×C29×#103C2212yes—
36C2×C29×C22⋊C8C2212yes—
37C2×C29×C22⋊C8C2212yes—
38C2×C29×#97C2211yescharacteristic
39C29×#399—21no—
40C29×#399—21no—
41C29×#390—21no—
42C29×#384—21no—
43C4×C4⋊C4×C29C2211yescharacteristic
44C29×#340C2212yes—
45C29×#340C2212yes—
46C29×#340C2212yes—
47C22×Q8×C29C2312yes—
48C22×Q8×C29C2311yescharacteristic
49C22×D4×C29D411yescharacteristic
50C23×C4×C29—21no—
51C23×C4×C29C2311yescharacteristic
52C23×C4×C29C2311yescharacteristic
53C2×Q16×C29—24no—
54C2×Q16×C29—42no—
55C2×Q16×C29—42no—
56C22×C8×C29C2312yes—
57C22×C8×C29C2312yes—
58C29×C4⋊Q8—22no—
59C29×C4⋊Q8—22no—
60C29×#126—28no—
61C29×#125—28no—
62C29×#125—22no—
63C29×#125D414yes—
64C29×#123—28no—
65C29×C22⋊Q8—22no—
66C29×C22⋊Q8—22no—
67C29×C22⋊Q8—22no—
68C29×C22⋊Q8—22no—
69C29×C22⋊Q8—24no—
70C29×C22⋊Q8—24no—
71C29×C22⋊Q8—42no—
72C29×C22⋊Q8—42no—
73C4×Q8×C29—22no—
74C4×Q8×C29D414yes—
75C4×D4×C29—22no—
76C4×D4×C29—22no—
77C29×#117—28no—
78C29×#117—22no—
79C29×#117—22no—
80C2×C4⋊C4×C29—21no—
81C2×C4⋊C4×C29—21no—
82C2×C4⋊C4×C29—21no—
83C2×C4⋊C4×C29—21no—
84C2×C4⋊C4×C29—21no—
85C2×C4⋊C4×C29—21no—
86C2×C4⋊C4×C29—22no—
87C2×C4⋊C4×C29—22no—
88C2×C4⋊C4×C29—22no—
89C2×C4⋊C4×C29—22no—
90C2×C4⋊C4×C29—21no—
91C2×C4⋊C4×C29—21no—
92C2×C4⋊C4×C29D411yescharacteristic
93C2×C4⋊C4×C29C2311yescharacteristic
94C2×C4⋊C4×C29C2311yescharacteristic
95C2×C4⋊C4×C29C2311yescharacteristic
96C2×C4⋊C4×C29C2312yes—
97C2×C22⋊C4×C29—21no—
98C2×C22⋊C4×C29—21no—
99C2×C22⋊C4×C29—21no—
100C2×C22⋊C4×C29—22no—
101C2×C22⋊C4×C29—22no—
102C2×C22⋊C4×C29D411yescharacteristic
103C2×C22⋊C4×C29D411yescharacteristic
104C2×C42×C29—21no—
105C2×C42×C29—21no—
106C2×C42×C29—21no—
107C2×C42×C29C2311yescharacteristic
108C29×C4⋊C8—22no—
109C29×#103—24no—
110C29×#103—24no—
111C29×#103—24no—
112C29×#103—24no—
113C29×C22⋊C8—42no—
114C29×C22⋊C8—42no—
115C29×#97—22no—
116C29×#95—21no—
117C24×C29C2×D411yescharacteristic
118C24×C29C2×D411yescharacteristic
119C2×Q8×C29—21no—
120C2×Q8×C29—22no—
121C2×Q8×C29—22no—
122C2×Q8×C29—22no—
123C2×Q8×C29—22no—
124C2×Q8×C29—22no—
125C2×Q8×C29—22no—
126C2×Q8×C29—22no—
127C2×Q8×C29—22no—
128C2×Q8×C29C2×D412yes—
129C2×D4×C29—22no—
130C2×D4×C29—22no—
131C2×D4×C29—41no—
132C22×C4×C29—24no—
133C22×C4×C29—21no—
134C22×C4×C29—21no—
135C22×C4×C29—21no—
136C22×C4×C29—22no—
137C22×C4×C29—21no—
138C22×C4×C29—21no—
139C22×C4×C29—21no—
140C22×C4×C29—21no—
141C22×C4×C29—21no—
142C22×C4×C29—22no—
143C22×C4×C29—22no—
144C22×C4×C29—22no—
145C22×C4×C29—22no—
146C22×C4×C29—22no—
147C22×C4×C29—42no—
148C22×C4×C29—42no—
149C22×C4×C29C2×D411yescharacteristic
150C22×C4×C29C2×D411yescharacteristic
151C22×C4×C29C2×D411yescharacteristic
152C22×C4×C29C2×D411yescharacteristic
153C22×C4×C29C2411yescharacteristic
154Q16×C29—48no—
155C2×C8×C29—22no—
156C2×C8×C29—22no—
157C2×C8×C29—22no—
158C2×C8×C29—22no—
159C2×C8×C29—22no—
160C2×C8×C29—22no—
161C4⋊C4×C29—24no—
162C4⋊C4×C29—24no—
163C4⋊C4×C29—24no—
164C4⋊C4×C29—24no—
165C4⋊C4×C29—24no—
166C4⋊C4×C29—24no—
167C4⋊C4×C29—22no—
168C4⋊C4×C29—21no—
169C4⋊C4×C29—21no—
170C4⋊C4×C29—21no—
171C4⋊C4×C29—22no—
172C4⋊C4×C29—44no—
173C4⋊C4×C29—44no—
174C4⋊C4×C29—42no—
175C4⋊C4×C29—42no—
176C4⋊C4×C29C2×D412yes—
177C4⋊C4×C29C2×D412yes—
178C4⋊C4×C29C2×D412yes—
179C4⋊C4×C29#4114yes—
180C22⋊C4×C29—24no—
181C22⋊C4×C29—24no—
182C22⋊C4×C29—24no—
183C22⋊C4×C29—22no—
184C22⋊C4×C29—22no—
185C22⋊C4×C29—44no—
186C22⋊C4×C29—44no—
187C42×C29—24no—
188C42×C29—24no—
189C42×C29—42no—
190C42×C29C2×D412yes—
191C42×C29C2×D412yes—
192#25584C2911yesmaximal, characteristic, direct product factor, Sylow
193C23×C29—21no—
194C23×C29—22no—
195C23×C29—21no—
196C23×C29—22no—
197C23×C29—21no—
198C23×C29—22no—
199C23×C29—21no—
200C23×C29—21no—
201C23×C29—22no—
202C23×C29#13712yes—
203C23×C29C22×D411yescharacteristic
204Q8×C29—22no—
205Q8×C29—22no—
206Q8×C29—42no—
207Q8×C29—42no—
208Q8×C29—42no—
209Q8×C29—42no—
210Q8×C29—42no—
211D4×C29—44no—
212C2×C4×C29—21no—
213C2×C4×C29—21no—
214C2×C4×C29—22no—
215C2×C4×C29—21no—
216C2×C4×C29—22no—
217C2×C4×C29—22no—
218C2×C4×C29—22no—
219C2×C4×C29—21no—
220C2×C4×C29—22no—
221C2×C4×C29—24no—
222C2×C4×C29—22no—
223C2×C4×C29—22no—
224C2×C4×C29—48no—
225C2×C4×C29—42no—
226C2×C4×C29—41no—
227C2×C4×C29—41no—
228C2×C4×C29—42no—
229C2×C4×C29—41no—
230C2×C4×C29—41no—
231C2×C4×C29—42no—
232C2×C4×C29—42no—
233C2×C4×C29—41no—
234C2×C4×C29—41no—
235C2×C4×C29—41no—
236C2×C4×C29—41no—
237C2×C4×C29—42no—
238C2×C4×C29—42no—
239C2×C4×C29—42no—
240C2×C4×C29—42no—
241C2×C4×C29—42no—
242C2×C4×C29#12012yes—
243C2×C4×C29#12012yes—
244C2×C4×C29C22×D411yescharacteristic
245C2×C4×C29C22×D411yescharacteristic
246C2×C4×C29C2×#4112yes—
247C2×C4×C29H(5,𝔽2)12yes—
248C8×C29—42no—
249C8×C29—42no—
250C2×#552C2×C2911yescharacteristic
251C2×#491C2×C2911yescharacteristic, complemented
252C2×#462C2×C2911yescharacteristic, complemented
253#2542C2×C2911yescharacteristic
254#2001C2×C2912yescomplemented
255#2001C2×C2912yescomplemented
256#1989C2×C2911yescharacteristic, complemented
257#1955C2×C2911yescharacteristic
258#1873C2×C2912yescomplemented
259#1872C2×C2912yescomplemented
260#1763C2×C2911yescharacteristic, complemented
261C22×C29—22no—
262C22×C29—24no—
263C22×C29—41no—
264C22×C29—41no—
265C22×C29—42no—
266C22×C29—41no—
267C22×C29—41no—
268C22×C29—41no—
269C22×C29—42no—
270C22×C29—42no—
271C22×C29C2×#12011yescharacteristic
272C22×C29#54612yes—
273C22×C29C2×#13711yescharacteristic
274C22×C29#57511yescharacteristic
275C22×C29#57812yes—
276C4×C29—22no—
277C4×C29—22no—
278C4×C29—41no—
279C4×C29—41no—
280C4×C29—42no—
281C4×C29—42no—
282C4×C29—42no—
283C4×C29—42no—
284C4×C29—44no—
285C4×C29—82no—
286C4×C29#53211yescharacteristic
287C4×C29#53511yescharacteristic
288C4×C29#55012yes—
289C22×Q16C22×C2912yes—
290#552—24no—
291#552—24no—
292C2×C4⋊Q8C22×C2911yescharacteristic
293C2×#126—21no—
294C2×#125—21no—
295C2×#125C22×C2911yescharacteristic
296C2×#123—21no—
297C2×C22⋊Q8C22×C2911yescharacteristic
298C2×C22⋊Q8C22×C2911yescharacteristic
299C2×C22⋊Q8C22×C2912yes—
300C2×C22⋊Q8C22×C2912yes—
301C2×C4×Q8C22×C2911yescharacteristic
302C2×C4×D4C22×C2911yescharacteristic
303C2×#117—21no—
304C2×#117C22×C2911yescharacteristic
305C22×C4⋊C4C22×C2911yescharacteristic
306#491—24no—
307#462—24no—
308C2×C4⋊C8C22×C2911yescharacteristic
309C2×#103C22×C2912yes—
310C2×#103C22×C2912yes—
311C2×#103C22×C2912yes—
312C2×#103C22×C2912yes—
313C2×C22⋊C8C22×C2912yes—
314C2×C22⋊C8C22×C2912yes—
315C2×#97C22×C2911yescharacteristic
316#399—21no—
317#399—21no—
318#390—21no—
319#384—21no—
320C4×C4⋊C4C22×C2911yescharacteristic
321#340C22×C2912yes—
322#340C22×C2912yes—
323#340C22×C2912yes—
324C2×C29—42no—
325C2×C29—81no—
326C2×C29#243111yescharacteristic
327C2×C29#300711yescharacteristic
328C2×C29#301111yescharacteristic
329C2×C29#331212yes—
330C2×C29#331512yes—
331C22×Q8C23×C2912yes—
332C22×Q8C23×C2911yescharacteristic
333C22×D4D4×C2911yescharacteristic
334C23×C4—21no—
335C23×C4C23×C2911yescharacteristic
336C23×C4C23×C2911yescharacteristic
337C2×Q16—24no—
338C2×Q16—42no—
339C2×Q16—42no—
340C22×C8C23×C2912yes—
341C22×C8C23×C2912yes—
342C4⋊Q8—22no—
343C4⋊Q8—22no—
344#126—28no—
345#125—28no—
346#125—22no—
347#125D4×C2914yes—
348#123—28no—
349C22⋊Q8—22no—
350C22⋊Q8—22no—
351C22⋊Q8—22no—
352C22⋊Q8—22no—
353C22⋊Q8—24no—
354C22⋊Q8—24no—
355C22⋊Q8—42no—
356C22⋊Q8—42no—
357C4×Q8—22no—
358C4×Q8D4×C2914yes—
359C4×D4—22no—
360C4×D4—22no—
361#117—28no—
362#117—22no—
363#117—22no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4D4×C2911yescharacteristic
377C2×C4⋊C4C23×C2911yescharacteristic
378C2×C4⋊C4C23×C2911yescharacteristic
379C2×C4⋊C4C23×C2911yescharacteristic
380C2×C4⋊C4C23×C2912yes—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4D4×C2911yescharacteristic
387C2×C22⋊C4D4×C2911yescharacteristic
388C2×C42—21no—
389C2×C42—21no—
390C2×C42—21no—
391C2×C42C23×C2911yescharacteristic
392C4⋊C8—22no—
393#103—24no—
394#103—24no—
395#103—24no—
396#103—24no—
397C22⋊C8—42no—
398C22⋊C8—42no—
399#97—22no—
400#95—21no—
401C29#2558411yescharacteristic, direct product factor, Sylow
402C24C2×D4×C2911yescharacteristic
403C24C2×D4×C2911yescharacteristic
404C2×Q8—21no—
405C2×Q8—22no—
406C2×Q8—22no—
407C2×Q8—22no—
408C2×Q8—22no—
409C2×Q8—22no—
410C2×Q8—22no—
411C2×Q8—22no—
412C2×Q8—22no—
413C2×Q8C2×D4×C2912yes—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—41no—
417C22×C4—24no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4C2×D4×C2911yescharacteristic
435C22×C4C2×D4×C2911yescharacteristic
436C22×C4C2×D4×C2911yescharacteristic
437C22×C4C2×D4×C2911yescharacteristic
438C22×C4C24×C2911yescharacteristic
439Q16—48no—
440C2×C8—22no—
441C2×C8—22no—
442C2×C8—22no—
443C2×C8—22no—
444C2×C8—22no—
445C2×C8—22no—
446C4⋊C4—24no—
447C4⋊C4—24no—
448C4⋊C4—24no—
449C4⋊C4—24no—
450C4⋊C4—24no—
451C4⋊C4—24no—
452C4⋊C4—22no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—22no—
457C4⋊C4—44no—
458C4⋊C4—44no—
459C4⋊C4—42no—
460C4⋊C4—42no—
461C4⋊C4C2×D4×C2912yes—
462C4⋊C4C2×D4×C2912yes—
463C4⋊C4C2×D4×C2912yes—
464C4⋊C4#41×C2914yes—
465C22⋊C4—24no—
466C22⋊C4—24no—
467C22⋊C4—24no—
468C22⋊C4—22no—
469C22⋊C4—22no—
470C22⋊C4—44no—
471C22⋊C4—44no—
472C42—24no—
473C42—24no—
474C42—42no—
475C42C2×D4×C2912yes—
476C42C2×D4×C2912yes—
477C23—21no—
478C23—22no—
479C23—21no—
480C23—22no—
481C23—21no—
482C23—22no—
483C23—21no—
484C23—21no—
485C23—22no—
486C23C29×#13712yes—
487C23C22×D4×C2911yescharacteristic
488Q8—22no—
489Q8—22no—
490Q8—42no—
491Q8—42no—
492Q8—42no—
493Q8—42no—
494Q8—42no—
495D4—44no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—22no—
499C2×C4—21no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—22no—
505C2×C4—24no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—48no—
509C2×C4—42no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4C29×#12012yes—
527C2×C4C29×#12012yes—
528C2×C4C22×D4×C2911yescharacteristic
529C2×C4C22×D4×C2911yescharacteristic
530C2×C4C2×#41×C2912yes—
531C2×C4C29×H(5,𝔽2)12yes—
532C8—42no—
533C8—42no—
534C22—22no—
535C22—24no—
536C22—41no—
537C22—41no—
538C22—42no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22—42no—
543C22—42no—
544C22C2×C29×#12011yescharacteristic
545C22C29×#54612yes—
546C22C2×C29×#13711yescharacteristic
547C22C29×#57511yescharacteristic
548C22C29×#57812yes—
549C4—22no—
550C4—22no—
551C4—41no—
552C4—41no—
553C4—42no—
554C4—42no—
555C4—42no—
556C4—42no—
557C4—44no—
558C4—82no—
559C4C29×#53211yescharacteristic
560C4C29×#53511yescharacteristic
561C4C29×#55012yes—
562C2—42no—
563C2—81no—
564C2C29×#243111yescharacteristic
565C2C29×#300711yescharacteristic
566C2C29×#301111yescharacteristic
567C2C29×#331212yes—
568C2C29×#331512yes—
subgroupG/H
center, socleC23×C29C22×D4
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC22×D4×C29D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C29 ◁ C2×C4×D4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C29×#491C2semidirect
3. C2×C29×#462C2semidirect
5. C29×#2001C2semidirect
6. C29×#2001C2semidirect
7. C29×#1989C2semidirect
9. C29×#1873C2semidirect
10. C29×#1872C2semidirect
11. C29×#1763C2semidirect
192. #25584C29direct (N × H)
251. C2×#491C2×C29semidirect
252. C2×#462C2×C29semidirect
254. #2001C2×C29semidirect
255. #2001C2×C29semidirect
256. #1989C2×C29semidirect
258. #1873C2×C29semidirect
259. #1872C2×C29semidirect
260. #1763C2×C29semidirect
401. C29#25584direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#5522
C2×C29×#4912
C2×C29×#4622
C29×#25422
C29×#20012
C29×#19892
C29×#19552
C29×#18732
C29×#18722
C29×#17632
#2558429