Finite Group Databasebeta

← C29×#27140 #20322040

Subgroups — C29×#27140 #20322040

Order 7424.

642 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×#2513C211yesmaximal, characteristic
2C29×#2370C211yesmaximal, characteristic, complemented
3C29×#2101C211yesmaximal, characteristic, complemented
4C29×#2067C211yesmaximal, characteristic
5C29×#2059C211yesmaximal, characteristic, complemented
6C29×#2025C211yesmaximal, characteristic
7C29×#1949C211yesmaximal, characteristic, complemented
8C29×#1934C211yesmaximal, characteristic
9C29×#1926C211yesmaximal, characteristic
10C29×#1926C211yesmaximal, characteristic
11C29×#1925C211yesmaximal, characteristic
12C29×#1919C211yesmaximal, characteristic, complemented
13C29×#1919C211yesmaximal, characteristic, complemented
14C29×#1916C211yesmaximal, characteristic, complemented
15C4×C29×#107C211yesmaximal, characteristic, complemented
16C2×C29×#125C2211yescharacteristic
17C2×C29×#107C2211yescharacteristic
18C2×C29×#107C2211yescharacteristic
19C2×C29×#106C2211yescharacteristic
20C2×C29×#106C2211yescharacteristic
21C2×C29×C4⋊C8C2211yescharacteristic
22C2×C29×#102C2211yescharacteristic
23C2×C29×#102C2211yescharacteristic
24C2×C29×#102C2211yescharacteristic
25C2×C29×#102C2211yescharacteristic
26C2×C4×C8×C29C2211yescharacteristic
27C29×#397—21no—
28C29×#397—21no—
29C29×#390C2211yescharacteristic
30C29×#390C2211yescharacteristic
31C29×#390C2211yescharacteristic
32C29×#389—21no—
33C29×#389C2211yescharacteristic
34C29×#389C2211yescharacteristic
35C29×#389C2211yescharacteristic
36C29×#388—21no—
37C29×#388—21no—
38C29×#387—21no—
39C29×#387—21no—
40C29×#382C2211yescharacteristic
41C4×C4⋊C4×C29—21no—
42C4×C4⋊C4×C29C2211yescharacteristic
43C4×C4⋊C4×C29C2211yescharacteristic
44C4×C4⋊C4×C29C2211yescharacteristic
45C4×C4⋊C4×C29C2211yescharacteristic
46C4×C4⋊C4×C29C2211yescharacteristic
47C29×#340C2211yescharacteristic
48C29×#340C2211yescharacteristic
49C29×#340C2211yescharacteristic
50C29×#340C2211yescharacteristic
51C29×#340C2211yescharacteristic
52C29×#340C2211yescharacteristic
53C29×#340C2211yescharacteristic
54C29×#340C2211yescharacteristic
55C29×#336C2211yescharacteristic
56C29×#336C2211yescharacteristic
57C29×#336C2211yescharacteristic
58C29×#336C2211yescharacteristic
59C22×D4×C29C2311yescharacteristic
60C22×C8×C29C2311yescharacteristic
61C22×C8×C29C2311yescharacteristic
62C22×C8×C29C2311yescharacteristic
63C22×C8×C29C2311yescharacteristic
64C29×#125—22no—
65C29×#125—22no—
66C2×C4⋊C4×C29—21no—
67C2×C4⋊C4×C29—21no—
68C2×C4⋊C4×C29—21no—
69C2×C4⋊C4×C29—21no—
70C2×C4⋊C4×C29—21no—
71C2×C4⋊C4×C29D411yescharacteristic
72C2×C4⋊C4×C29D411yescharacteristic
73C2×C4⋊C4×C29C2311yescharacteristic
74C2×C4⋊C4×C29C2311yescharacteristic
75C2×C4⋊C4×C29C2311yescharacteristic
76C2×C4⋊C4×C29C2311yescharacteristic
77C2×C4⋊C4×C29C2311yescharacteristic
78C2×C4⋊C4×C29C2311yescharacteristic
79C2×C4⋊C4×C29C2311yescharacteristic
80C2×C22⋊C4×C29—21no—
81C2×C22⋊C4×C29—21no—
82C2×C22⋊C4×C29—21no—
83C2×C22⋊C4×C29—21no—
84C2×C22⋊C4×C29—21no—
85C2×C22⋊C4×C29—21no—
86C2×C42×C29—21no—
87C2×C42×C29—21no—
88C2×C42×C29—21no—
89C2×C42×C29—21no—
90C2×C42×C29C2311yescharacteristic
91C2×C42×C29C2311yescharacteristic
92C2×C42×C29C2311yescharacteristic
93C29×#107—22no—
94C29×#107—22no—
95C29×#106—22no—
96C29×#106—22no—
97C29×C4⋊C8—22no—
98C29×#102—22no—
99C29×#102—22no—
100C29×#102—22no—
101C29×#102—22no—
102C4×C8×C29—22no—
103C29×#95—21no—
104C29×#95—21no—
105C29×#95—21no—
106C29×#95—21no—
107C29×#95—21no—
108C29×#95—21no—
109C29×#95—21no—
110C29×#95—21no—
111C29×#95—21no—
112C29×#95D411yescharacteristic
113C29×#95D411yescharacteristic
114C24×C29—21no—
115C2×D4×C29—21no—
116C2×D4×C29—21no—
117C2×D4×C29—21no—
118C2×D4×C29—21no—
119C2×D4×C29—21no—
120C2×D4×C29—21no—
121C22×C4×C29—21no—
122C22×C4×C29—21no—
123C22×C4×C29—21no—
124C22×C4×C29—21no—
125C22×C4×C29—21no—
126C22×C4×C29—21no—
127C22×C4×C29—21no—
128C22×C4×C29C2×D411yescharacteristic
129C22×C4×C29C2×D411yescharacteristic
130C22×C4×C29C2×D411yescharacteristic
131C22×C4×C29C2×D411yescharacteristic
132C22×C4×C29C2×D411yescharacteristic
133C22×C4×C29C2×D411yescharacteristic
134C22×C4×C29C2411yescharacteristic
135C2×C8×C29—21no—
136C2×C8×C29—21no—
137C2×C8×C29—21no—
138C2×C8×C29—21no—
139C2×C8×C29—21no—
140C2×C8×C29—21no—
141C2×C8×C29—21no—
142C2×C8×C29—21no—
143C2×C8×C29—21no—
144C2×C8×C29—21no—
145C2×C8×C29—21no—
146C2×C8×C29#4112yes—
147C4⋊C4×C29—24no—
148C4⋊C4×C29—24no—
149C4⋊C4×C29—22no—
150C4⋊C4×C29—21no—
151C4⋊C4×C29—21no—
152C4⋊C4×C29—21no—
153C4⋊C4×C29—21no—
154C4⋊C4×C29—21no—
155C4⋊C4×C29—21no—
156C4⋊C4×C29—21no—
157C4⋊C4×C29—21no—
158C4⋊C4×C29—21no—
159C4⋊C4×C29—21no—
160C4⋊C4×C29—21no—
161C4⋊C4×C29—41no—
162C4⋊C4×C29—42no—
163C4⋊C4×C29—81no—
164C4⋊C4×C29—81no—
165C4⋊C4×C29#4112yes—
166C4⋊C4×C29#4112yes—
167C4⋊C4×C29#4112yes—
168C22⋊C4×C29—42no—
169C22⋊C4×C29—42no—
170C22⋊C4×C29—81no—
171C22⋊C4×C29—81no—
172C22⋊C4×C29—81no—
173C22⋊C4×C29—81no—
174C42×C29—21no—
175C42×C29—21no—
176C42×C29—21no—
177C42×C29—21no—
178C42×C29—21no—
179C42×C29—21no—
180C42×C29—42no—
181C42×C29—81no—
182C42×C29—81no—
183C42×C29—81no—
184#27140C2911yesmaximal, characteristic, direct product factor, Sylow
185C23×C29—41no—
186C23×C29—41no—
187C23×C29—41no—
188C23×C29—41no—
189C23×C29—41no—
190C23×C29—41no—
191C23×C29—41no—
192C23×C29C22×D411yescharacteristic
193D4×C29—41no—
194D4×C29—41no—
195D4×C29—41no—
196D4×C29—41no—
197C2×C4×C29—21no—
198C2×C4×C29—21no—
199C2×C4×C29—21no—
200C2×C4×C29—21no—
201C2×C4×C29—22no—
202C2×C4×C29—22no—
203C2×C4×C29—21no—
204C2×C4×C29—21no—
205C2×C4×C29—21no—
206C2×C4×C29—22no—
207C2×C4×C29—21no—
208C2×C4×C29—21no—
209C2×C4×C29—21no—
210C2×C4×C29—21no—
211C2×C4×C29—21no—
212C2×C4×C29—21no—
213C2×C4×C29—21no—
214C2×C4×C29—21no—
215C2×C4×C29—21no—
216C2×C4×C29—21no—
217C2×C4×C29—41no—
218C2×C4×C29—41no—
219C2×C4×C29—41no—
220C2×C4×C29—41no—
221C2×C4×C29—41no—
222C2×C4×C29—41no—
223C2×C4×C29—41no—
224C2×C4×C29—41no—
225C2×C4×C29—41no—
226C2×C4×C29—41no—
227C2×C4×C29—41no—
228C2×C4×C29—41no—
229C2×C4×C29—41no—
230C2×C4×C29—41no—
231C2×C4×C29—41no—
232C2×C4×C29—41no—
233C2×C4×C29—41no—
234C2×C4×C29—41no—
235C2×C4×C29#13512yes—
236C2×C4×C29C2×#4111yescharacteristic
237C2×C4×C29C2×#4111yescharacteristic
238C2×C4×C29C2×#4111yescharacteristic
239C2×C4×C29C2×#4111yescharacteristic
240C2×C4×C292−1+411yescharacteristic
241C2×C4×C292−1+411yescharacteristic
242C8×C29—22no—
243C8×C29—41no—
244C8×C29—41no—
245C8×C29—41no—
246#2513C2×C2911yescharacteristic
247#2370C2×C2911yescharacteristic, complemented
248#2101C2×C2911yescharacteristic, complemented
249#2067C2×C2911yescharacteristic
250#2059C2×C2911yescharacteristic, complemented
251#2025C2×C2911yescharacteristic
252#1949C2×C2911yescharacteristic, complemented
253#1934C2×C2911yescharacteristic
254#1926C2×C2911yescharacteristic
255#1926C2×C2911yescharacteristic
256#1925C2×C2911yescharacteristic
257#1919C2×C2911yescharacteristic, complemented
258#1919C2×C2911yescharacteristic, complemented
259#1916C2×C2911yescharacteristic, complemented
260C4×#107C2×C2911yescharacteristic, complemented
261C22×C29—81no—
262C22×C29—81no—
263C22×C29—81no—
264C22×C29—81no—
265C22×C29—81no—
266C22×C29—81no—
267C22×C29—81no—
268C22×C29#52511yescharacteristic
269C22×C29#54711yescharacteristic
270C22×C29#54811yescharacteristic
271C22×C29C2×#13511yescharacteristic
272C22×C29#57511yescharacteristic
273C22×C29#57611yescharacteristic
274C22×C29#57711yescharacteristic
275C4×C29—22no—
276C4×C29—41no—
277C4×C29—41no—
278C4×C29—41no—
279C4×C29—41no—
280C4×C29—42no—
281C4×C29—42no—
282C4×C29—41no—
283C4×C29—42no—
284C4×C29—81no—
285C4×C29—81no—
286C4×C29—81no—
287C4×C29—81no—
288C4×C29#52911yescharacteristic
289C4×C29#54111yescharacteristic
290C4×C29#55611yescharacteristic
291C4×C29#55611yescharacteristic
292C2×#125C22×C2911yescharacteristic
293C2×#107C22×C2911yescharacteristic
294C2×#107C22×C2911yescharacteristic
295C2×#106C22×C2911yescharacteristic
296C2×#106C22×C2911yescharacteristic
297C2×C4⋊C8C22×C2911yescharacteristic
298C2×#102C22×C2911yescharacteristic
299C2×#102C22×C2911yescharacteristic
300C2×#102C22×C2911yescharacteristic
301C2×#102C22×C2911yescharacteristic
302C2×C4×C8C22×C2911yescharacteristic
303#397—21no—
304#397—21no—
305#390C22×C2911yescharacteristic
306#390C22×C2911yescharacteristic
307#390C22×C2911yescharacteristic
308#389—21no—
309#389C22×C2911yescharacteristic
310#389C22×C2911yescharacteristic
311#389C22×C2911yescharacteristic
312#388—21no—
313#388—21no—
314#387—21no—
315#387—21no—
316#382C22×C2911yescharacteristic
317C4×C4⋊C4—21no—
318C4×C4⋊C4C22×C2911yescharacteristic
319C4×C4⋊C4C22×C2911yescharacteristic
320C4×C4⋊C4C22×C2911yescharacteristic
321C4×C4⋊C4C22×C2911yescharacteristic
322C4×C4⋊C4C22×C2911yescharacteristic
323#340C22×C2911yescharacteristic
324#340C22×C2911yescharacteristic
325#340C22×C2911yescharacteristic
326#340C22×C2911yescharacteristic
327#340C22×C2911yescharacteristic
328#340C22×C2911yescharacteristic
329#340C22×C2911yescharacteristic
330#340C22×C2911yescharacteristic
331#336C22×C2911yescharacteristic
332#336C22×C2911yescharacteristic
333#336C22×C2911yescharacteristic
334#336C22×C2911yescharacteristic
335C2×C29—161no—
336C2×C29#246911yescharacteristic
337C2×C29#310211yescharacteristic
338C2×C29#311911yescharacteristic
339C2×C29#333911yescharacteristic
340C2×C29#334811yescharacteristic
341C2×C29#336511yescharacteristic
342C2×C29#337011yescharacteristic
343C22×D4C23×C2911yescharacteristic
344C22×C8C23×C2911yescharacteristic
345C22×C8C23×C2911yescharacteristic
346C22×C8C23×C2911yescharacteristic
347C22×C8C23×C2911yescharacteristic
348#125—22no—
349#125—22no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4D4×C2911yescharacteristic
356C2×C4⋊C4D4×C2911yescharacteristic
357C2×C4⋊C4C23×C2911yescharacteristic
358C2×C4⋊C4C23×C2911yescharacteristic
359C2×C4⋊C4C23×C2911yescharacteristic
360C2×C4⋊C4C23×C2911yescharacteristic
361C2×C4⋊C4C23×C2911yescharacteristic
362C2×C4⋊C4C23×C2911yescharacteristic
363C2×C4⋊C4C23×C2911yescharacteristic
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C42—21no—
371C2×C42—21no—
372C2×C42—21no—
373C2×C42—21no—
374C2×C42C23×C2911yescharacteristic
375C2×C42C23×C2911yescharacteristic
376C2×C42C23×C2911yescharacteristic
377#107—22no—
378#107—22no—
379#106—22no—
380#106—22no—
381C4⋊C8—22no—
382#102—22no—
383#102—22no—
384#102—22no—
385#102—22no—
386C4×C8—22no—
387#95—21no—
388#95—21no—
389#95—21no—
390#95—21no—
391#95—21no—
392#95—21no—
393#95—21no—
394#95—21no—
395#95—21no—
396#95D4×C2911yescharacteristic
397#95D4×C2911yescharacteristic
398C29#2714011yescharacteristic, direct product factor, Sylow
399C24—21no—
400C2×D4—21no—
401C2×D4—21no—
402C2×D4—21no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4C2×D4×C2911yescharacteristic
414C22×C4C2×D4×C2911yescharacteristic
415C22×C4C2×D4×C2911yescharacteristic
416C22×C4C2×D4×C2911yescharacteristic
417C22×C4C2×D4×C2911yescharacteristic
418C22×C4C2×D4×C2911yescharacteristic
419C22×C4C24×C2911yescharacteristic
420C2×C8—21no—
421C2×C8—21no—
422C2×C8—21no—
423C2×C8—21no—
424C2×C8—21no—
425C2×C8—21no—
426C2×C8—21no—
427C2×C8—21no—
428C2×C8—21no—
429C2×C8—21no—
430C2×C8—21no—
431C2×C8#41×C2912yes—
432C4⋊C4—24no—
433C4⋊C4—24no—
434C4⋊C4—22no—
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—41no—
447C4⋊C4—42no—
448C4⋊C4—81no—
449C4⋊C4—81no—
450C4⋊C4#41×C2912yes—
451C4⋊C4#41×C2912yes—
452C4⋊C4#41×C2912yes—
453C22⋊C4—42no—
454C22⋊C4—42no—
455C22⋊C4—81no—
456C22⋊C4—81no—
457C22⋊C4—81no—
458C22⋊C4—81no—
459C42—21no—
460C42—21no—
461C42—21no—
462C42—21no—
463C42—21no—
464C42—21no—
465C42—42no—
466C42—81no—
467C42—81no—
468C42—81no—
469C23—41no—
470C23—41no—
471C23—41no—
472C23—41no—
473C23—41no—
474C23—41no—
475C23—41no—
476C23C22×D4×C2911yescharacteristic
477D4—41no—
478D4—41no—
479D4—41no—
480D4—41no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—22no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4C29×#13512yes—
520C2×C4C2×#41×C2911yescharacteristic
521C2×C4C2×#41×C2911yescharacteristic
522C2×C4C2×#41×C2911yescharacteristic
523C2×C4C2×#41×C2911yescharacteristic
524C2×C4C29×2−1+411yescharacteristic
525C2×C4C29×2−1+411yescharacteristic
526C8—22no—
527C8—41no—
528C8—41no—
529C8—41no—
530C22—81no—
531C22—81no—
532C22—81no—
533C22—81no—
534C22—81no—
535C22—81no—
536C22—81no—
537C22C29×#52511yescharacteristic
538C22C29×#54711yescharacteristic
539C22C29×#54811yescharacteristic
540C22C2×C29×#13511yescharacteristic
541C22C29×#57511yescharacteristic
542C22C29×#57611yescharacteristic
543C22C29×#57711yescharacteristic
544C4—22no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—42no—
550C4—42no—
551C4—41no—
552C4—42no—
553C4—81no—
554C4—81no—
555C4—81no—
556C4—81no—
557C4C29×#52911yescharacteristic
558C4C29×#54111yescharacteristic
559C4C29×#55611yescharacteristic
560C4C29×#55611yescharacteristic
561C2—161no—
562C2C29×#246911yescharacteristic
563C2C29×#310211yescharacteristic
564C2C29×#311911yescharacteristic
565C2C29×#333911yescharacteristic
566C2C29×#334811yescharacteristic
567C2C29×#336511yescharacteristic
568C2C29×#337011yescharacteristic
subgroupG/H
center, socleC23×C29C22×D4
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC22×D4×C29C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C29 ◁ C4×C4⋊C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#2370C2semidirect
3. C29×#2101C2semidirect
5. C29×#2059C2semidirect
7. C29×#1949C2semidirect
12. C29×#1919C2semidirect
13. C29×#1919C2semidirect
14. C29×#1916C2semidirect
15. C4×C29×#107C2semidirect
184. #27140C29direct (N × H)
247. #2370C2×C29semidirect
248. #2101C2×C29semidirect
250. #2059C2×C29semidirect
252. #1949C2×C29semidirect
257. #1919C2×C29semidirect
258. #1919C2×C29semidirect
259. #1916C2×C29semidirect
260. C4×#107C2×C29semidirect
398. C29#27140direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#25132
C29×#23702
C29×#21012
C29×#20672
C29×#20592
C29×#20252
C29×#19492
C29×#19342
C29×#19262
C29×#19252
C29×#19192
C29×#19162
C4×C29×#1072
#2714029