Finite Group Databasebeta

← C29×#14761 #20309661

Subgroups — C29×#14761 #20309661

Order 7424.

2090 conjugacy classes of subgroups.

The subgroup lattice has 1178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C29×#123C211yesmaximal, characteristic
2C2×C29×#394C211yesmaximal, characteristic
3C2×C29×#389C211yesmaximal, characteristic, complemented
4C2×C29×#388C211yesmaximal, characteristic, complemented
5C2×C29×#385C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊C4×C29C211yesmaximal, characteristic, complemented
7C29×#1444C211yesmaximal, characteristic, complemented
8C29×#1442C211yesmaximal, characteristic, complemented
9C29×#1440C211yesmaximal, characteristic, complemented
10C29×#1439C211yesmaximal, characteristic, complemented
11C29×#1439C211yesmaximal, characteristic, complemented
12C29×#1439C211yesmaximal, characteristic, complemented
13C29×#1438C211yesmaximal, characteristic
14C29×#1437C211yesmaximal, characteristic, complemented
15C29×#1436C211yesmaximal, characteristic, complemented
16C23×D4×C29C2211yescharacteristic
17C24×C4×C29C2211yescharacteristic
18C2×C29×#123—24no—
19C2×C29×#123—24no—
20C2×C29×#123—24no—
21C22×C4⋊C4×C29C2211yescharacteristic
22C22×C4⋊C4×C29C2211yescharacteristic
23C22×C4⋊C4×C29C2211yescharacteristic
24C22×C4⋊C4×C29C2211yescharacteristic
25C22×C4⋊C4×C29C2211yescharacteristic
26C22×C4⋊C4×C29C2211yescharacteristic
27C22×C22⋊C4×C29C2211yescharacteristic
28C22×C22⋊C4×C29C2211yescharacteristic
29C22×C22⋊C4×C29C2211yescharacteristic
30C22×C22⋊C4×C29C2211yescharacteristic
31C22×C22⋊C4×C29C2211yescharacteristic
32C22×C22⋊C4×C29C2211yescharacteristic
33C22×C22⋊C4×C29C2211yescharacteristic
34C22×C22⋊C4×C29C2211yescharacteristic
35C22×C22⋊C4×C29C2211yescharacteristic
36C22×C22⋊C4×C29C2211yescharacteristic
37C22×C22⋊C4×C29C2211yescharacteristic
38C22×C42×C29C2211yescharacteristic
39C22×C42×C29C2211yescharacteristic
40C29×#394—24no—
41C29×#389—24no—
42C29×#388—24no—
43C29×#385—24no—
44C4×C22⋊C4×C29—24no—
45C2×C29×#95C2211yescharacteristic
46C2×C29×#95C2211yescharacteristic
47C2×C29×#95C2211yescharacteristic
48C2×C29×#95C2211yescharacteristic
49C2×C29×#95C2211yescharacteristic
50C2×C29×#95C2211yescharacteristic
51C2×C29×#95C2211yescharacteristic
52C2×C29×#95C2211yescharacteristic
53C2×C29×#95C2211yescharacteristic
54C2×C29×#95C2211yescharacteristic
55C2×C29×#95C2211yescharacteristic
56C2×C29×#95C2211yescharacteristic
57C2×C29×#95C2211yescharacteristic
58C2×C29×#95C2211yescharacteristic
59C25×C29C2311yescharacteristic
60C25×C29C2311yescharacteristic
61C22×D4×C29—22no—
62C22×D4×C29—22no—
63C22×D4×C29—22no—
64C22×D4×C29—22no—
65C22×D4×C29—22no—
66C22×D4×C29—41no—
67C22×D4×C29—41no—
68C23×C4×C29—22no—
69C23×C4×C29—22no—
70C23×C4×C29—22no—
71C23×C4×C29—22no—
72C23×C4×C29—41no—
73C23×C4×C29—41no—
74C23×C4×C29D414yes—
75C23×C4×C29C2311yescharacteristic
76C23×C4×C29C2311yescharacteristic
77C23×C4×C29C2311yescharacteristic
78C23×C4×C29C2311yescharacteristic
79C23×C4×C29C2311yescharacteristic
80C23×C4×C29C2311yescharacteristic
81C23×C4×C29C2311yescharacteristic
82C23×C4×C29C2311yescharacteristic
83C23×C4×C29C2311yescharacteristic
84C23×C4×C29C2311yescharacteristic
85C23×C4×C29C2311yescharacteristic
86C23×C4×C29C2311yescharacteristic
87C23×C4×C29C2311yescharacteristic
88C29×#123—232no—
89C2×C4⋊C4×C29—22no—
90C2×C4⋊C4×C29—22no—
91C2×C4⋊C4×C29—22no—
92C2×C4⋊C4×C29—22no—
93C2×C4⋊C4×C29—22no—
94C2×C4⋊C4×C29—22no—
95C2×C4⋊C4×C29—22no—
96C2×C4⋊C4×C29—22no—
97C2×C4⋊C4×C29—22no—
98C2×C4⋊C4×C29—22no—
99C2×C4⋊C4×C29—22no—
100C2×C4⋊C4×C29—22no—
101C2×C4⋊C4×C29—22no—
102C2×C4⋊C4×C29—22no—
103C2×C4⋊C4×C29—41no—
104C2×C4⋊C4×C29—41no—
105C2×C4⋊C4×C29—41no—
106C2×C4⋊C4×C29D414yes—
107C2×C22⋊C4×C29—22no—
108C2×C22⋊C4×C29—22no—
109C2×C22⋊C4×C29—22no—
110C2×C22⋊C4×C29—22no—
111C2×C22⋊C4×C29—22no—
112C2×C22⋊C4×C29—22no—
113C2×C22⋊C4×C29—22no—
114C2×C22⋊C4×C29—22no—
115C2×C22⋊C4×C29—22no—
116C2×C22⋊C4×C29—22no—
117C2×C22⋊C4×C29—22no—
118C2×C22⋊C4×C29—22no—
119C2×C22⋊C4×C29—22no—
120C2×C22⋊C4×C29—22no—
121C2×C22⋊C4×C29—22no—
122C2×C22⋊C4×C29—22no—
123C2×C22⋊C4×C29—22no—
124C2×C22⋊C4×C29—22no—
125C2×C22⋊C4×C29—22no—
126C2×C22⋊C4×C29—22no—
127C2×C22⋊C4×C29—22no—
128C2×C22⋊C4×C29—22no—
129C2×C22⋊C4×C29—22no—
130C2×C22⋊C4×C29—22no—
131C2×C22⋊C4×C29—22no—
132C2×C22⋊C4×C29—22no—
133C2×C22⋊C4×C29—22no—
134C2×C22⋊C4×C29—22no—
135C2×C22⋊C4×C29—22no—
136C2×C22⋊C4×C29—41no—
137C2×C22⋊C4×C29—41no—
138C2×C22⋊C4×C29D414yes—
139C2×C22⋊C4×C29D414yes—
140C2×C42×C29—22no—
141C2×C42×C29—22no—
142C2×C42×C29—22no—
143C2×C42×C29—22no—
144C2×C42×C29—41no—
145C2×C42×C29—41no—
146C29×#95—22no—
147C29×#95—22no—
148C29×#95—22no—
149C29×#95—22no—
150C29×#95—22no—
151C29×#95—22no—
152C29×#95—22no—
153C29×#95—22no—
154C29×#95—22no—
155C29×#95—22no—
156C29×#95—22no—
157C29×#95—22no—
158C29×#95—22no—
159C29×#95—41no—
160C24×C29—21no—
161C24×C29—21no—
162C24×C29—21no—
163C24×C29—21no—
164C24×C29—21no—
165C24×C29—21no—
166C24×C29—21no—
167C24×C29—21no—
168C24×C29—21no—
169C24×C29—21no—
170C24×C29—21no—
171C24×C29—21no—
172C24×C29—21no—
173C24×C29—21no—
174C24×C29—21no—
175C24×C29—21no—
176C24×C29—21no—
177C24×C29—21no—
178C24×C29—21no—
179C24×C29—21no—
180C24×C29—21no—
181C24×C29—21no—
182C24×C29—21no—
183C24×C29—21no—
184C24×C29—21no—
185C24×C29—21no—
186C24×C29C2×D412yes—
187C24×C29C2×D412yes—
188C24×C29C2×D412yes—
189C24×C29#4112yes—
190C24×C29C2411yescharacteristic
191C2×D4×C29—28no—
192C2×D4×C29—44no—
193C2×D4×C29—44no—
194C2×D4×C29—44no—
195C2×D4×C29—44no—
196C2×D4×C29—44no—
197C2×D4×C29—44no—
198C22×C4×C29—21no—
199C22×C4×C29—21no—
200C22×C4×C29—21no—
201C22×C4×C29—21no—
202C22×C4×C29—21no—
203C22×C4×C29—21no—
204C22×C4×C29—21no—
205C22×C4×C29—21no—
206C22×C4×C29—28no—
207C22×C4×C29—21no—
208C22×C4×C29—21no—
209C22×C4×C29—21no—
210C22×C4×C29—21no—
211C22×C4×C29—21no—
212C22×C4×C29—21no—
213C22×C4×C29—21no—
214C22×C4×C29—21no—
215C22×C4×C29—21no—
216C22×C4×C29—21no—
217C22×C4×C29—21no—
218C22×C4×C29—21no—
219C22×C4×C29—21no—
220C22×C4×C29—21no—
221C22×C4×C29—21no—
222C22×C4×C29—21no—
223C22×C4×C29—21no—
224C22×C4×C29—21no—
225C22×C4×C29—21no—
226C22×C4×C29—21no—
227C22×C4×C29—21no—
228C22×C4×C29—21no—
229C22×C4×C29—21no—
230C22×C4×C29—21no—
231C22×C4×C29—21no—
232C22×C4×C29—21no—
233C22×C4×C29—21no—
234C22×C4×C29—21no—
235C22×C4×C29—21no—
236C22×C4×C29—21no—
237C22×C4×C29—21no—
238C22×C4×C29—21no—
239C22×C4×C29—21no—
240C22×C4×C29—21no—
241C22×C4×C29—21no—
242C22×C4×C29—21no—
243C22×C4×C29—21no—
244C22×C4×C29—21no—
245C22×C4×C29—21no—
246C22×C4×C29—21no—
247C22×C4×C29—21no—
248C22×C4×C29—21no—
249C22×C4×C29—21no—
250C22×C4×C29—21no—
251C22×C4×C29—21no—
252C22×C4×C29—21no—
253C22×C4×C29—21no—
254C22×C4×C29—21no—
255C22×C4×C29—21no—
256C22×C4×C29—21no—
257C22×C4×C29—21no—
258C22×C4×C29—21no—
259C22×C4×C29—21no—
260C22×C4×C29—21no—
261C22×C4×C29—28no—
262C22×C4×C29—21no—
263C22×C4×C29—21no—
264C22×C4×C29—21no—
265C22×C4×C29—21no—
266C22×C4×C29—21no—
267C22×C4×C29—21no—
268C22×C4×C29—21no—
269C22×C4×C29—21no—
270C22×C4×C29—21no—
271C22×C4×C29—21no—
272C22×C4×C29—21no—
273C22×C4×C29—21no—
274C22×C4×C29—21no—
275C22×C4×C29—21no—
276C22×C4×C29—44no—
277C22×C4×C29—44no—
278C22×C4×C29—44no—
279C22×C4×C29—44no—
280C22×C4×C29—44no—
281C22×C4×C29C2×D412yes—
282C22×C4×C29C2×D412yes—
283C22×C4×C29C2×D412yes—
284C22×C4×C29C2×D412yes—
285C22×C4×C29C2×D412yes—
286C22×C4×C29C2×D412yes—
287C22×C4×C29C2×D412yes—
288C22×C4×C29C2×D412yes—
289C22×C4×C29C2×D412yes—
290C22×C4×C29#4112yes—
291C22×C4×C29#4112yes—
292C22×C4×C29#4112yes—
293C22×C4×C29#4112yes—
294C22×C4×C29#4112yes—
295C22×C4×C29#4112yes—
296C4⋊C4×C29—28no—
297C4⋊C4×C29—28no—
298C4⋊C4×C29—28no—
299C4⋊C4×C29—44no—
300C4⋊C4×C29—44no—
301C4⋊C4×C29—44no—
302C22⋊C4×C29—28no—
303C22⋊C4×C29—28no—
304C22⋊C4×C29—28no—
305C22⋊C4×C29—28no—
306C22⋊C4×C29—28no—
307C22⋊C4×C29—28no—
308C22⋊C4×C29—28no—
309C22⋊C4×C29—44no—
310C22⋊C4×C29—44no—
311C22⋊C4×C29—44no—
312C22⋊C4×C29—44no—
313C42×C29—44no—
314C42×C29—44no—
315#14761C2911yesmaximal, characteristic, direct product factor, Sylow
316C23×C29—22no—
317C23×C29—22no—
318C23×C29—22no—
319C23×C29—22no—
320C23×C29—22no—
321C23×C29—22no—
322C23×C29—22no—
323C23×C29—22no—
324C23×C29—22no—
325C23×C29—22no—
326C23×C29—22no—
327C23×C29—22no—
328C23×C29—22no—
329C23×C29—22no—
330C23×C29—22no—
331C23×C29—22no—
332C23×C29—22no—
333C23×C29—22no—
334C23×C29—22no—
335C23×C29—22no—
336C23×C29—22no—
337C23×C29—22no—
338C23×C29—22no—
339C23×C29—22no—
340C23×C29—22no—
341C23×C29—41no—
342C23×C29—41no—
343C23×C29—41no—
344C23×C29—41no—
345C23×C29—41no—
346C23×C29—41no—
347C23×C29—41no—
348C23×C29—41no—
349C23×C29—41no—
350C23×C29—41no—
351C23×C29—41no—
352C23×C29—41no—
353C23×C29—41no—
354C23×C29—41no—
355C23×C29—41no—
356C23×C29—41no—
357C23×C29—41no—
358C23×C29—41no—
359C23×C29—41no—
360C23×C29—41no—
361C23×C29—41no—
362C23×C29—41no—
363C23×C29—41no—
364C23×C29—41no—
365C23×C29—41no—
366C23×C29—41no—
367C23×C29—41no—
368C23×C29—41no—
369C23×C29—41no—
370C23×C29—41no—
371C23×C29—41no—
372C23×C29—41no—
373C23×C29—41no—
374C23×C29—41no—
375C23×C29—41no—
376C23×C29—41no—
377C23×C29—41no—
378C23×C29—41no—
379C23×C29—41no—
380C23×C29—41no—
381C23×C29—41no—
382C23×C29—41no—
383C23×C29—41no—
384C23×C29—41no—
385C23×C29#12114yes—
386C23×C29C22×D411yescharacteristic
387C23×C29C22×D411yescharacteristic
388C23×C29C22×D411yescharacteristic
389C23×C29C22×D411yescharacteristic
390C23×C29C2×#4111yescharacteristic
391C23×C29C2×#4111yescharacteristic
392C23×C29C2×#4111yescharacteristic
393C23×C29C2×#4111yescharacteristic
394C23×C29C2×#4111yescharacteristic
395C23×C29C2×#4111yescharacteristic
396C23×C29C2×#4111yescharacteristic
397C23×C29H(5,𝔽2)11yescharacteristic
398C23×C29H(5,𝔽2)11yescharacteristic
399C23×C292−1+411yescharacteristic
400C23×C292−1+411yescharacteristic
401D4×C29—416no—
402C2×C4×C29—22no—
403C2×C4×C29—22no—
404C2×C4×C29—22no—
405C2×C4×C29—22no—
406C2×C4×C29—22no—
407C2×C4×C29—22no—
408C2×C4×C29—22no—
409C2×C4×C29—22no—
410C2×C4×C29—22no—
411C2×C4×C29—22no—
412C2×C4×C29—22no—
413C2×C4×C29—22no—
414C2×C4×C29—22no—
415C2×C4×C29—22no—
416C2×C4×C29—22no—
417C2×C4×C29—22no—
418C2×C4×C29—22no—
419C2×C4×C29—22no—
420C2×C4×C29—22no—
421C2×C4×C29—22no—
422C2×C4×C29—22no—
423C2×C4×C29—22no—
424C2×C4×C29—22no—
425C2×C4×C29—22no—
426C2×C4×C29—22no—
427C2×C4×C29—22no—
428C2×C4×C29—22no—
429C2×C4×C29—22no—
430C2×C4×C29—22no—
431C2×C4×C29—22no—
432C2×C4×C29—22no—
433C2×C4×C29—22no—
434C2×C4×C29—22no—
435C2×C4×C29—22no—
436C2×C4×C29—22no—
437C2×C4×C29—22no—
438C2×C4×C29—22no—
439C2×C4×C29—22no—
440C2×C4×C29—22no—
441C2×C4×C29—416no—
442C2×C4×C29—41no—
443C2×C4×C29—41no—
444C2×C4×C29—41no—
445C2×C4×C29—41no—
446C2×C4×C29—41no—
447C2×C4×C29—41no—
448C2×C4×C29—41no—
449C2×C4×C29—41no—
450C2×C4×C29—41no—
451C2×C4×C29—41no—
452C2×C4×C29—41no—
453C2×C4×C29—41no—
454C2×C4×C29—41no—
455C2×C4×C29—41no—
456C2×C4×C29—41no—
457C2×C4×C29—41no—
458C2×C4×C29—41no—
459C2×C4×C29—41no—
460C2×C4×C29—41no—
461C2×C4×C29—41no—
462C2×C4×C29—41no—
463C2×C4×C29—41no—
464C2×C4×C29—41no—
465C2×C4×C29—41no—
466C2×C4×C29—41no—
467C2×C4×C29—41no—
468C2×C4×C29—41no—
469C2×C4×C29—41no—
470C2×C4×C29—41no—
471C2×C4×C29—41no—
472C2×C4×C29—41no—
473C2×C4×C29—41no—
474C2×C4×C29—41no—
475C2×C4×C29—41no—
476C2×C4×C29—41no—
477C2×C4×C29—41no—
478C2×C4×C29—41no—
479C2×C4×C29—41no—
480C2×C4×C29—41no—
481C2×C4×C29—41no—
482C2×C4×C29—41no—
483C2×C4×C29—41no—
484C2×C4×C29—41no—
485C2×C4×C29—41no—
486C2×C4×C29—41no—
487C2×C4×C29—41no—
488C2×C4×C29—41no—
489C2×C4×C29—41no—
490C2×C4×C29—41no—
491C2×C4×C29—41no—
492C2×C4×C29#12014yes—
493C2×C4×C29#12314yescomplemented
494C22×#123C2×C2911yescharacteristic
495C2×#394C2×C2911yescharacteristic
496C2×#389C2×C2911yescharacteristic, complemented
497C2×#388C2×C2911yescharacteristic, complemented
498C2×#385C2×C2911yescharacteristic, complemented
499C2×C4×C22⋊C4C2×C2911yescharacteristic, complemented
500#1444C2×C2911yescharacteristic, complemented
501#1442C2×C2911yescharacteristic, complemented
502#1440C2×C2911yescharacteristic, complemented
503#1439C2×C2911yescharacteristic, complemented
504#1439C2×C2911yescharacteristic, complemented
505#1439C2×C2911yescharacteristic, complemented
506#1438C2×C2911yescharacteristic
507#1437C2×C2911yescharacteristic, complemented
508#1436C2×C2911yescharacteristic, complemented
509C22×C29—24no—
510C22×C29—24no—
511C22×C29—24no—
512C22×C29—42no—
513C22×C29—42no—
514C22×C29—42no—
515C22×C29—42no—
516C22×C29—42no—
517C22×C29—42no—
518C22×C29—42no—
519C22×C29—42no—
520C22×C29—42no—
521C22×C29—42no—
522C22×C29—42no—
523C22×C29—42no—
524C22×C29—42no—
525C22×C29—42no—
526C22×C29—42no—
527C22×C29—42no—
528C22×C29—42no—
529C22×C29—42no—
530C22×C29—42no—
531C22×C29—81no—
532C22×C29—81no—
533C22×C29—81no—
534C22×C29—81no—
535C22×C29—81no—
536C22×C29—81no—
537C22×C29—81no—
538C22×C29—81no—
539C22×C29C2×#12011yescharacteristic
540C22×C29C2×#12111yescharacteristic
541C22×C29C2×#12311yescharacteristic
542C22×C29#52511yescharacteristic
543C22×C29#52511yescharacteristic
544C22×C29#52511yescharacteristic
545C22×C29#52511yescharacteristic
546C22×C29#52911yescharacteristic
547C22×C29#52911yescharacteristic
548C22×C29#53211yescharacteristic
549C22×C29#53211yescharacteristic
550C22×C29#53211yescharacteristic
551C22×C29#53211yescharacteristic
552C22×C29#53411yescharacteristic
553C22×C29#53611yescharacteristic
554C22×C29#53911yescharacteristic
555C22×C29#53911yescharacteristic
556C22×C29#54211yescharacteristic
557C22×C29#54211yescharacteristic
558C22×C29D4211yescharacteristic
559C22×C29D4211yescharacteristic
560C22×C29#54611yescharacteristic
561C22×C29#54611yescharacteristic
562C22×C29#54711yescharacteristic
563C22×C29#54711yescharacteristic
564C22×C29#54711yescharacteristic
565C22×C29#54711yescharacteristic
566C22×C29#54811yescharacteristic
567C22×C29#54811yescharacteristic
568C22×C29#55111yescharacteristic
569C22×C29#55211yescharacteristic
570C22×C29#55211yescharacteristic
571C22×C29#55311yescharacteristic
572C22×C29#55311yescharacteristic
573C22×C29#55911yescharacteristic
574C4×C29—24no—
575C4×C29—24no—
576C4×C29—42no—
577C4×C29—42no—
578C4×C29—42no—
579C4×C29—42no—
580C4×C29—42no—
581C4×C29—42no—
582C4×C29—42no—
583C4×C29—42no—
584C4×C29—42no—
585C4×C29—81no—
586C4×C29—81no—
587C23×D4C22×C2911yescharacteristic
588C24×C4C22×C2911yescharacteristic
589C2×#123—24no—
590C2×#123—24no—
591C2×#123—24no—
592C22×C4⋊C4C22×C2911yescharacteristic
593C22×C4⋊C4C22×C2911yescharacteristic
594C22×C4⋊C4C22×C2911yescharacteristic
595C22×C4⋊C4C22×C2911yescharacteristic
596C22×C4⋊C4C22×C2911yescharacteristic
597C22×C4⋊C4C22×C2911yescharacteristic
598C22×C22⋊C4C22×C2911yescharacteristic
599C22×C22⋊C4C22×C2911yescharacteristic
600C22×C22⋊C4C22×C2911yescharacteristic
601C22×C22⋊C4C22×C2911yescharacteristic
602C22×C22⋊C4C22×C2911yescharacteristic
603C22×C22⋊C4C22×C2911yescharacteristic
604C22×C22⋊C4C22×C2911yescharacteristic
605C22×C22⋊C4C22×C2911yescharacteristic
606C22×C22⋊C4C22×C2911yescharacteristic
607C22×C22⋊C4C22×C2911yescharacteristic
608C22×C22⋊C4C22×C2911yescharacteristic
609C22×C42C22×C2911yescharacteristic
610C22×C42C22×C2911yescharacteristic
611#394—24no—
612#389—24no—
613#388—24no—
614#385—24no—
615C4×C22⋊C4—24no—
616C2×#95C22×C2911yescharacteristic
617C2×#95C22×C2911yescharacteristic
618C2×#95C22×C2911yescharacteristic
619C2×#95C22×C2911yescharacteristic
620C2×#95C22×C2911yescharacteristic
621C2×#95C22×C2911yescharacteristic
622C2×#95C22×C2911yescharacteristic
623C2×#95C22×C2911yescharacteristic
624C2×#95C22×C2911yescharacteristic
625C2×#95C22×C2911yescharacteristic
626C2×#95C22×C2911yescharacteristic
627C2×#95C22×C2911yescharacteristic
628C2×#95C22×C2911yescharacteristic
629C2×#95C22×C2911yescharacteristic
630C2×C29—44no—
631C2×C29—82no—
632C2×C29#238811yescharacteristic
633C2×C29#241011yescharacteristic
634C2×C29#241311yescharacteristic
635C2×C29#242211yescharacteristic
636C2×C29#243211yescharacteristic
637C2×C29#244311yescharacteristic
638C2×C29#245511yescharacteristic
639C2×C29#245811yescharacteristic
640C2×C29#246111yescharacteristic
641C2×C29#247011yescharacteristic
642C2×C29#255311yescharacteristic
643C2×C29#255811yescharacteristic
644C2×C29#260211yescharacteristic
645C2×C29#266311yescharacteristic
646C2×C29#285411yescharacteristic
647C25C23×C2911yescharacteristic
648C25C23×C2911yescharacteristic
649C22×D4—22no—
650C22×D4—22no—
651C22×D4—22no—
652C22×D4—22no—
653C22×D4—22no—
654C22×D4—41no—
655C22×D4—41no—
656C23×C4—22no—
657C23×C4—22no—
658C23×C4—22no—
659C23×C4—22no—
660C23×C4—41no—
661C23×C4—41no—
662C23×C4D4×C2914yes—
663C23×C4C23×C2911yescharacteristic
664C23×C4C23×C2911yescharacteristic
665C23×C4C23×C2911yescharacteristic
666C23×C4C23×C2911yescharacteristic
667C23×C4C23×C2911yescharacteristic
668C23×C4C23×C2911yescharacteristic
669C23×C4C23×C2911yescharacteristic
670C23×C4C23×C2911yescharacteristic
671C23×C4C23×C2911yescharacteristic
672C23×C4C23×C2911yescharacteristic
673C23×C4C23×C2911yescharacteristic
674C23×C4C23×C2911yescharacteristic
675C23×C4C23×C2911yescharacteristic
676#123—232no—
677C2×C4⋊C4—22no—
678C2×C4⋊C4—22no—
679C2×C4⋊C4—22no—
680C2×C4⋊C4—22no—
681C2×C4⋊C4—22no—
682C2×C4⋊C4—22no—
683C2×C4⋊C4—22no—
684C2×C4⋊C4—22no—
685C2×C4⋊C4—22no—
686C2×C4⋊C4—22no—
687C2×C4⋊C4—22no—
688C2×C4⋊C4—22no—
689C2×C4⋊C4—22no—
690C2×C4⋊C4—22no—
691C2×C4⋊C4—41no—
692C2×C4⋊C4—41no—
693C2×C4⋊C4—41no—
694C2×C4⋊C4D4×C2914yes—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—22no—
709C2×C22⋊C4—22no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4—22no—
715C2×C22⋊C4—22no—
716C2×C22⋊C4—22no—
717C2×C22⋊C4—22no—
718C2×C22⋊C4—22no—
719C2×C22⋊C4—22no—
720C2×C22⋊C4—22no—
721C2×C22⋊C4—22no—
722C2×C22⋊C4—22no—
723C2×C22⋊C4—22no—
724C2×C22⋊C4—41no—
725C2×C22⋊C4—41no—
726C2×C22⋊C4D4×C2914yes—
727C2×C22⋊C4D4×C2914yes—
728C2×C42—22no—
729C2×C42—22no—
730C2×C42—22no—
731C2×C42—22no—
732C2×C42—41no—
733C2×C42—41no—
734#95—22no—
735#95—22no—
736#95—22no—
737#95—22no—
738#95—22no—
739#95—22no—
740#95—22no—
741#95—22no—
742#95—22no—
743#95—22no—
744#95—22no—
745#95—22no—
746#95—22no—
747#95—41no—
748C29#1476111yescharacteristic, direct product factor, Sylow
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24C2×D4×C2912yes—
776C24C2×D4×C2912yes—
777C24C2×D4×C2912yes—
778C24#41×C2912yes—
779C24C24×C2911yescharacteristic
780C2×D4—28no—
781C2×D4—44no—
782C2×D4—44no—
783C2×D4—44no—
784C2×D4—44no—
785C2×D4—44no—
786C2×D4—44no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—28no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—28no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C4—44no—
868C22×C4—44no—
869C22×C4—44no—
870C22×C4C2×D4×C2912yes—
871C22×C4C2×D4×C2912yes—
872C22×C4C2×D4×C2912yes—
873C22×C4C2×D4×C2912yes—
874C22×C4C2×D4×C2912yes—
875C22×C4C2×D4×C2912yes—
876C22×C4C2×D4×C2912yes—
877C22×C4C2×D4×C2912yes—
878C22×C4C2×D4×C2912yes—
879C22×C4#41×C2912yes—
880C22×C4#41×C2912yes—
881C22×C4#41×C2912yes—
882C22×C4#41×C2912yes—
883C22×C4#41×C2912yes—
884C22×C4#41×C2912yes—
885C4⋊C4—28no—
886C4⋊C4—28no—
887C4⋊C4—28no—
888C4⋊C4—44no—
889C4⋊C4—44no—
890C4⋊C4—44no—
891C22⋊C4—28no—
892C22⋊C4—28no—
893C22⋊C4—28no—
894C22⋊C4—28no—
895C22⋊C4—28no—
896C22⋊C4—28no—
897C22⋊C4—28no—
898C22⋊C4—44no—
899C22⋊C4—44no—
900C22⋊C4—44no—
901C22⋊C4—44no—
902C42—44no—
903C42—44no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23C29×#12114yes—
974C23C22×D4×C2911yescharacteristic
975C23C22×D4×C2911yescharacteristic
976C23C22×D4×C2911yescharacteristic
977C23C22×D4×C2911yescharacteristic
978C23C2×#41×C2911yescharacteristic
979C23C2×#41×C2911yescharacteristic
980C23C2×#41×C2911yescharacteristic
981C23C2×#41×C2911yescharacteristic
982C23C2×#41×C2911yescharacteristic
983C23C2×#41×C2911yescharacteristic
984C23C2×#41×C2911yescharacteristic
985C23C29×H(5,𝔽2)11yescharacteristic
986C23C29×H(5,𝔽2)11yescharacteristic
987C23C29×2−1+411yescharacteristic
988C23C29×2−1+411yescharacteristic
989D4—416no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—416no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4C29×#12014yes—
1081C2×C4C29×#12314yescomplemented
1082C22—24no—
1083C22—24no—
1084C22—24no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22—81no—
1111C22—81no—
1112C22C2×C29×#12011yescharacteristic
1113C22C2×C29×#12111yescharacteristic
1114C22C2×C29×#12311yescharacteristic
1115C22C29×#52511yescharacteristic
1116C22C29×#52511yescharacteristic
1117C22C29×#52511yescharacteristic
1118C22C29×#52511yescharacteristic
1119C22C29×#52911yescharacteristic
1120C22C29×#52911yescharacteristic
1121C22C29×#53211yescharacteristic
1122C22C29×#53211yescharacteristic
1123C22C29×#53211yescharacteristic
1124C22C29×#53211yescharacteristic
1125C22C29×#53411yescharacteristic
1126C22C29×#53611yescharacteristic
1127C22C29×#53911yescharacteristic
1128C22C29×#53911yescharacteristic
1129C22C29×#54211yescharacteristic
1130C22C29×#54211yescharacteristic
1131C22D42×C2911yescharacteristic
1132C22D42×C2911yescharacteristic
1133C22C29×#54611yescharacteristic
1134C22C29×#54611yescharacteristic
1135C22C29×#54711yescharacteristic
1136C22C29×#54711yescharacteristic
1137C22C29×#54711yescharacteristic
1138C22C29×#54711yescharacteristic
1139C22C29×#54811yescharacteristic
1140C22C29×#54811yescharacteristic
1141C22C29×#55111yescharacteristic
1142C22C29×#55211yescharacteristic
1143C22C29×#55211yescharacteristic
1144C22C29×#55311yescharacteristic
1145C22C29×#55311yescharacteristic
1146C22C29×#55911yescharacteristic
1147C4—24no—
1148C4—24no—
1149C4—42no—
1150C4—42no—
1151C4—42no—
1152C4—42no—
1153C4—42no—
1154C4—42no—
1155C4—42no—
1156C4—42no—
1157C4—42no—
1158C4—81no—
1159C4—81no—
1160C2—44no—
1161C2—82no—
1162C2C29×#238811yescharacteristic
1163C2C29×#241011yescharacteristic
1164C2C29×#241311yescharacteristic
1165C2C29×#242211yescharacteristic
1166C2C29×#243211yescharacteristic
1167C2C29×#244311yescharacteristic
1168C2C29×#245511yescharacteristic
1169C2C29×#245811yescharacteristic
1170C2C29×#246111yescharacteristic
1171C2C29×#247011yescharacteristic
1172C2C29×#255311yescharacteristic
1173C2C29×#255811yescharacteristic
1174C2C29×#260211yescharacteristic
1175C2C29×#266311yescharacteristic
1176C2C29×#285411yescharacteristic
subgroupG/H
center, socleC24×C29C24
commutator, Frattini, cosocleC24C24×C29
prime radicalC23×D4×C29C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C29 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C29×#389C2semidirect
4. C2×C29×#388C2semidirect
5. C2×C29×#385C2semidirect
6. C2×C4×C22⋊C4×C29C2semidirect
7. C29×#1444C2semidirect
8. C29×#1442C2semidirect
9. C29×#1440C2semidirect
10. C29×#1439C2semidirect
11. C29×#1439C2semidirect
12. C29×#1439C2semidirect
14. C29×#1437C2semidirect
15. C29×#1436C2semidirect
315. #14761C29direct (N × H)
493. C2×C4×C29#123semidirect
496. C2×#389C2×C29semidirect
497. C2×#388C2×C29semidirect
498. C2×#385C2×C29semidirect
499. C2×C4×C22⋊C4C2×C29semidirect
500. #1444C2×C29semidirect
501. #1442C2×C29semidirect
502. #1440C2×C29semidirect
503. #1439C2×C29semidirect
504. #1439C2×C29semidirect
505. #1439C2×C29semidirect
507. #1437C2×C29semidirect
508. #1436C2×C29semidirect
748. C29#14761direct (N × H)
1081. C2×C4C29×#123semidirect

Maximal subgroups

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

subgroupindex
C22×C29×#1232
C2×C29×#3942
C2×C29×#3892
C2×C29×#3882
C2×C29×#3852
C2×C4×C22⋊C4×C292
C29×#14442
C29×#14422
C29×#14402
C29×#14392
C29×#14382
C29×#14372
C29×#14362
#1476129