Finite Group Databasebeta

← C29×#14007 #20308907

Subgroups — C29×#14007 #20308907

Order 7424.

1946 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#390C211yesmaximal, characteristic
2C2×C29×#388C211yesmaximal, characteristic, complemented
3C2×C29×#386C211yesmaximal, characteristic
4C2×C29×#381C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊C4×C29C211yesmaximal, characteristic, complemented
6C29×#1442C211yesmaximal, characteristic, complemented
7C29×#1440C211yesmaximal, characteristic, complemented
8C29×#1439C211yesmaximal, characteristic, complemented
9C29×#1438C211yesmaximal, characteristic
10C29×#1437C211yesmaximal, characteristic, complemented
11C29×#1437C211yesmaximal, characteristic, complemented
12C29×#1437C211yesmaximal, characteristic, complemented
13C29×#1436C211yesmaximal, characteristic, complemented
14C29×#1436C211yesmaximal, characteristic, complemented
15C4×C29×#95C211yesmaximal, characteristic, complemented
16C23×D4×C29C2211yescharacteristic
17C24×C4×C29C2211yescharacteristic
18C22×C4⋊C4×C29C2211yescharacteristic
19C22×C4⋊C4×C29C2211yescharacteristic
20C22×C22⋊C4×C29C2211yescharacteristic
21C22×C22⋊C4×C29C2211yescharacteristic
22C22×C22⋊C4×C29C2211yescharacteristic
23C22×C22⋊C4×C29C2211yescharacteristic
24C22×C22⋊C4×C29C2211yescharacteristic
25C22×C22⋊C4×C29C2211yescharacteristic
26C22×C22⋊C4×C29C2211yescharacteristic
27C22×C22⋊C4×C29C2211yescharacteristic
28C22×C22⋊C4×C29C2211yescharacteristic
29C22×C22⋊C4×C29C2211yescharacteristic
30C22×C22⋊C4×C29C2211yescharacteristic
31C22×C42×C29C2211yescharacteristic
32C22×C42×C29C2211yescharacteristic
33C22×C42×C29C2211yescharacteristic
34C22×C42×C29C2211yescharacteristic
35C29×#390—24no—
36C29×#388—24no—
37C29×#386C418yescomplemented
38C29×#381—24no—
39C4×C22⋊C4×C29—24no—
40C2×C29×#95C2211yescharacteristic
41C2×C29×#95C2211yescharacteristic
42C2×C29×#95C2211yescharacteristic
43C2×C29×#95C2211yescharacteristic
44C2×C29×#95C2211yescharacteristic
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
56C25×C29C2311yescharacteristic
57C25×C29C2311yescharacteristic
58C22×D4×C29—22no—
59C22×D4×C29—22no—
60C22×D4×C29—22no—
61C22×D4×C29—22no—
62C22×D4×C29—41no—
63C22×D4×C29—41no—
64C22×D4×C29C2×C414yes—
65C23×C4×C29—22no—
66C23×C4×C29—22no—
67C23×C4×C29—22no—
68C23×C4×C29—22no—
69C23×C4×C29—41no—
70C23×C4×C29—41no—
71C23×C4×C29C2×C414yes—
72C23×C4×C29C2311yescharacteristic
73C23×C4×C29C2311yescharacteristic
74C23×C4×C29C2311yescharacteristic
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
85C2×C4⋊C4×C29—22no—
86C2×C4⋊C4×C29—22no—
87C2×C4⋊C4×C29—22no—
88C2×C4⋊C4×C29—22no—
89C2×C4⋊C4×C29—41no—
90C2×C4⋊C4×C29—41no—
91C2×C22⋊C4×C29—22no—
92C2×C22⋊C4×C29—22no—
93C2×C22⋊C4×C29—22no—
94C2×C22⋊C4×C29—22no—
95C2×C22⋊C4×C29—22no—
96C2×C22⋊C4×C29—22no—
97C2×C22⋊C4×C29—22no—
98C2×C22⋊C4×C29—22no—
99C2×C22⋊C4×C29—22no—
100C2×C22⋊C4×C29—22no—
101C2×C22⋊C4×C29—22no—
102C2×C22⋊C4×C29—22no—
103C2×C22⋊C4×C29—22no—
104C2×C22⋊C4×C29—22no—
105C2×C22⋊C4×C29—22no—
106C2×C22⋊C4×C29—22no—
107C2×C22⋊C4×C29—22no—
108C2×C22⋊C4×C29—22no—
109C2×C22⋊C4×C29—22no—
110C2×C22⋊C4×C29—41no—
111C2×C22⋊C4×C29—41no—
112C2×C22⋊C4×C29—41no—
113C2×C22⋊C4×C29—41no—
114C2×C22⋊C4×C29—41no—
115C2×C22⋊C4×C29—41no—
116C2×C22⋊C4×C29—41no—
117C2×C22⋊C4×C29—41no—
118C2×C22⋊C4×C29—41no—
119C2×C22⋊C4×C29—41no—
120C2×C22⋊C4×C29C2×C414yes—
121C2×C22⋊C4×C29C2×C414yes—
122C2×C22⋊C4×C29C2×C414yes—
123C2×C22⋊C4×C29D414yes—
124C2×C42×C29—22no—
125C2×C42×C29—22no—
126C2×C42×C29—22no—
127C2×C42×C29—22no—
128C2×C42×C29—22no—
129C2×C42×C29—22no—
130C2×C42×C29—22no—
131C2×C42×C29—41no—
132C2×C42×C29—41no—
133C2×C42×C29—41no—
134C2×C42×C29—41no—
135C2×C42×C29—41no—
136C29×#95—22no—
137C29×#95—22no—
138C29×#95—22no—
139C29×#95—22no—
140C29×#95—22no—
141C29×#95—22no—
142C29×#95—22no—
143C29×#95—22no—
144C29×#95—22no—
145C29×#95—22no—
146C29×#95—41no—
147C29×#95—41no—
148C29×#95—41no—
149C29×#95C2×C414yes—
150C29×#95C2×C414yes—
151C29×#95D414yescomplemented
152C24×C29—21no—
153C24×C29—21no—
154C24×C29—21no—
155C24×C29—21no—
156C24×C29—21no—
157C24×C29—21no—
158C24×C29—21no—
159C24×C29—21no—
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×C29C22×C412yes—
179C24×C29C22×C412yes—
180C24×C29C2×D412yes—
181C24×C29#4112yes—
182C24×C29C2411yescharacteristic
183C2×D4×C29—28no—
184C2×D4×C29—28no—
185C2×D4×C29—44no—
186C2×D4×C29—44no—
187C2×D4×C29—44no—
188C2×D4×C29—44no—
189C2×D4×C29—44no—
190C22×C4×C29—21no—
191C22×C4×C29—21no—
192C22×C4×C29—21no—
193C22×C4×C29—21no—
194C22×C4×C29—21no—
195C22×C4×C29—21no—
196C22×C4×C29—21no—
197C22×C4×C29—21no—
198C22×C4×C29—21no—
199C22×C4×C29—21no—
200C22×C4×C29—21no—
201C22×C4×C29—21no—
202C22×C4×C29—28no—
203C22×C4×C29—21no—
204C22×C4×C29—21no—
205C22×C4×C29—21no—
206C22×C4×C29—21no—
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—28no—
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—21no—
262C22×C4×C29—21no—
263C22×C4×C29—21no—
264C22×C4×C29—21no—
265C22×C4×C29—21no—
266C22×C4×C29—44no—
267C22×C4×C29—44no—
268C22×C4×C29—44no—
269C22×C4×C29—44no—
270C22×C4×C29—44no—
271C22×C4×C29C22×C412yes—
272C22×C4×C29C22×C412yes—
273C22×C4×C29C22×C412yes—
274C22×C4×C29C22×C412yes—
275C22×C4×C29C22×C412yes—
276C22×C4×C29C2×D412yes—
277C22×C4×C29C2×D412yes—
278C22×C4×C29C2×D412yes—
279C22×C4×C29C2×D412yes—
280C22×C4×C29C2×D412yes—
281C22×C4×C29#4112yes—
282C22×C4×C29#4112yes—
283C22×C4×C29#4112yes—
284C22×C4×C29#4112yes—
285C22×C4×C29#4112yes—
286C22×C4×C29#4112yes—
287C22×C4×C29#4112yes—
288C4⋊C4×C29—44no—
289C4⋊C4×C29—44no—
290C22⋊C4×C29—28no—
291C22⋊C4×C29—28no—
292C22⋊C4×C29—28no—
293C22⋊C4×C29—44no—
294C22⋊C4×C29—44no—
295C22⋊C4×C29—44no—
296C22⋊C4×C29—44no—
297C22⋊C4×C29—44no—
298C22⋊C4×C29—44no—
299C22⋊C4×C29—44no—
300C22⋊C4×C29—44no—
301C42×C29—44no—
302C42×C29—44no—
303C42×C29—44no—
304C42×C29—44no—
305#14007C2911yesmaximal, characteristic, direct product factor, Sylow
306C23×C29—22no—
307C23×C29—22no—
308C23×C29—22no—
309C23×C29—22no—
310C23×C29—22no—
311C23×C29—22no—
312C23×C29—22no—
313C23×C29—22no—
314C23×C29—22no—
315C23×C29—22no—
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—41no—
332C23×C29—41no—
333C23×C29—41no—
334C23×C29—41no—
335C23×C29—41no—
336C23×C29—41no—
337C23×C29—41no—
338C23×C29—41no—
339C23×C29—41no—
340C23×C29—41no—
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×C29C4×D414yes—
376C23×C29C23×C411yescharacteristic
377C23×C29C22×D411yescharacteristic
378C23×C29C22×D411yescharacteristic
379C23×C29C2×#4111yescharacteristic
380C23×C29C2×#4111yescharacteristic
381C23×C29C2×#4111yescharacteristic
382C23×C29C2×#4111yescharacteristic
383C23×C29C2×#4111yescharacteristic
384C23×C29C2×#4111yescharacteristic
385C23×C29C2×#4111yescharacteristic
386C23×C29C2×#4111yescharacteristic
387C23×C29H(5,𝔽2)11yescharacteristic
388C23×C29H(5,𝔽2)11yescharacteristic
389C23×C29H(5,𝔽2)11yescharacteristic
390C23×C29H(5,𝔽2)11yescharacteristic
391D4×C29—416no—
392C2×C4×C29—22no—
393C2×C4×C29—22no—
394C2×C4×C29—22no—
395C2×C4×C29—22no—
396C2×C4×C29—22no—
397C2×C4×C29—22no—
398C2×C4×C29—22no—
399C2×C4×C29—22no—
400C2×C4×C29—22no—
401C2×C4×C29—22no—
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—416no—
435C2×C4×C29—41no—
436C2×C4×C29—41no—
437C2×C4×C29—41no—
438C2×C4×C29—41no—
439C2×C4×C29—41no—
440C2×C4×C29—41no—
441C2×C4×C29—41no—
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#11714yes—
482C2×C4×C29C4×D414yes—
483C2×C4×C29#12314yes—
484C2×#390C2×C2911yescharacteristic
485C2×#388C2×C2911yescharacteristic, complemented
486C2×#386C2×C2911yescharacteristic
487C2×#381C2×C2911yescharacteristic, complemented
488C2×C4×C22⋊C4C2×C2911yescharacteristic, complemented
489#1442C2×C2911yescharacteristic, complemented
490#1440C2×C2911yescharacteristic, complemented
491#1439C2×C2911yescharacteristic, complemented
492#1438C2×C2911yescharacteristic
493#1437C2×C2911yescharacteristic, complemented
494#1437C2×C2911yescharacteristic, complemented
495#1437C2×C2911yescharacteristic, complemented
496#1436C2×C2911yescharacteristic, complemented
497#1436C2×C2911yescharacteristic, complemented
498C4×#95C2×C2911yescharacteristic, complemented
499C22×C29—24no—
500C22×C29—24no—
501C22×C29—24no—
502C22×C29—42no—
503C22×C29—42no—
504C22×C29—42no—
505C22×C29—42no—
506C22×C29—42no—
507C22×C29—42no—
508C22×C29—42no—
509C22×C29—42no—
510C22×C29—42no—
511C22×C29—42no—
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—81no—
522C22×C29—81no—
523C22×C29—81no—
524C22×C29—81no—
525C22×C29—81no—
526C22×C29—81no—
527C22×C29—81no—
528C22×C29—81no—
529C22×C29C2×#11711yescharacteristic
530C22×C29C2×C4×D411yescharacteristic
531C22×C29C2×C4×D411yescharacteristic
532C22×C29C4×#4111yescharacteristic
533C22×C29C4×#4111yescharacteristic
534C22×C29#51811yescharacteristic
535C22×C29#51811yescharacteristic
536C22×C29C2×#12311yescharacteristic
537C22×C29#52511yescharacteristic
538C22×C29#52911yescharacteristic
539C22×C29#52911yescharacteristic
540C22×C29#52911yescharacteristic
541C22×C29#52911yescharacteristic
542C22×C29#53211yescharacteristic
543C22×C29#53211yescharacteristic
544C22×C29#53811yescharacteristic
545C22×C29#53811yescharacteristic
546C22×C29#54011yescharacteristic
547C22×C29#54011yescharacteristic
548C22×C29D4211yescharacteristic
549C22×C29#54611yescharacteristic
550C22×C29#54611yescharacteristic
551C22×C29#54611yescharacteristic
552C22×C29#54611yescharacteristic
553C22×C29#54611yescharacteristic
554C22×C29#55011yescharacteristic
555C22×C29#55111yescharacteristic
556C22×C29#55111yescharacteristic
557C22×C29#55111yescharacteristic
558C22×C29#55311yescharacteristic
559C22×C29#55311yescharacteristic
560C22×C29#55311yescharacteristic
561C22×C29#55511yescharacteristic
562C22×C29#55911yescharacteristic
563C22×C29#55911yescharacteristic
564C4×C29—24no—
565C4×C29—24no—
566C4×C29—24no—
567C4×C29—42no—
568C4×C29—42no—
569C4×C29—42no—
570C4×C29—42no—
571C4×C29—42no—
572C4×C29—42no—
573C4×C29—42no—
574C4×C29—42no—
575C4×C29—81no—
576C4×C29—81no—
577C23×D4C22×C2911yescharacteristic
578C24×C4C22×C2911yescharacteristic
579C22×C4⋊C4C22×C2911yescharacteristic
580C22×C4⋊C4C22×C2911yescharacteristic
581C22×C22⋊C4C22×C2911yescharacteristic
582C22×C22⋊C4C22×C2911yescharacteristic
583C22×C22⋊C4C22×C2911yescharacteristic
584C22×C22⋊C4C22×C2911yescharacteristic
585C22×C22⋊C4C22×C2911yescharacteristic
586C22×C22⋊C4C22×C2911yescharacteristic
587C22×C22⋊C4C22×C2911yescharacteristic
588C22×C22⋊C4C22×C2911yescharacteristic
589C22×C22⋊C4C22×C2911yescharacteristic
590C22×C22⋊C4C22×C2911yescharacteristic
591C22×C22⋊C4C22×C2911yescharacteristic
592C22×C42C22×C2911yescharacteristic
593C22×C42C22×C2911yescharacteristic
594C22×C42C22×C2911yescharacteristic
595C22×C42C22×C2911yescharacteristic
596#390—24no—
597#388—24no—
598#386C4×C2918yescomplemented
599#381—24no—
600C4×C22⋊C4—24no—
601C2×#95C22×C2911yescharacteristic
602C2×#95C22×C2911yescharacteristic
603C2×#95C22×C2911yescharacteristic
604C2×#95C22×C2911yescharacteristic
605C2×#95C22×C2911yescharacteristic
606C2×#95C22×C2911yescharacteristic
607C2×#95C22×C2911yescharacteristic
608C2×#95C22×C2911yescharacteristic
609C2×#95C22×C2911yescharacteristic
610C2×#95C22×C2911yescharacteristic
611C2×#95C22×C2911yescharacteristic
612C2×#95C22×C2911yescharacteristic
613C2×#95C22×C2911yescharacteristic
614C2×#95C22×C2911yescharacteristic
615C2×#95C22×C2911yescharacteristic
616C2×#95C22×C2911yescharacteristic
617C2×C29—44no—
618C2×C29—82no—
619C2×C29#229311yescharacteristic
620C2×C29C4×#12311yescharacteristic
621C2×C29#233311yescharacteristic
622C2×C29#234211yescharacteristic
623C2×C29#235711yescharacteristic
624C2×C29#235811yescharacteristic
625C2×C29#236311yescharacteristic
626C2×C29#244411yescharacteristic
627C2×C29#244511yescharacteristic
628C2×C29#245911yescharacteristic
629C2×C29#246411yescharacteristic
630C2×C29#251611yescharacteristic
631C2×C29#252611yescharacteristic
632C2×C29#255411yescharacteristic
633C2×C29#255711yescharacteristic
634C25C23×C2911yescharacteristic
635C25C23×C2911yescharacteristic
636C22×D4—22no—
637C22×D4—22no—
638C22×D4—22no—
639C22×D4—22no—
640C22×D4—41no—
641C22×D4—41no—
642C22×D4C2×C4×C2914yes—
643C23×C4—22no—
644C23×C4—22no—
645C23×C4—22no—
646C23×C4—22no—
647C23×C4—41no—
648C23×C4—41no—
649C23×C4C2×C4×C2914yes—
650C23×C4C23×C2911yescharacteristic
651C23×C4C23×C2911yescharacteristic
652C23×C4C23×C2911yescharacteristic
653C23×C4C23×C2911yescharacteristic
654C23×C4C23×C2911yescharacteristic
655C23×C4C23×C2911yescharacteristic
656C23×C4C23×C2911yescharacteristic
657C23×C4C23×C2911yescharacteristic
658C23×C4C23×C2911yescharacteristic
659C23×C4C23×C2911yescharacteristic
660C23×C4C23×C2911yescharacteristic
661C23×C4C23×C2911yescharacteristic
662C23×C4C23×C2911yescharacteristic
663C2×C4⋊C4—22no—
664C2×C4⋊C4—22no—
665C2×C4⋊C4—22no—
666C2×C4⋊C4—22no—
667C2×C4⋊C4—41no—
668C2×C4⋊C4—41no—
669C2×C22⋊C4—22no—
670C2×C22⋊C4—22no—
671C2×C22⋊C4—22no—
672C2×C22⋊C4—22no—
673C2×C22⋊C4—22no—
674C2×C22⋊C4—22no—
675C2×C22⋊C4—22no—
676C2×C22⋊C4—22no—
677C2×C22⋊C4—22no—
678C2×C22⋊C4—22no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—22no—
681C2×C22⋊C4—22no—
682C2×C22⋊C4—22no—
683C2×C22⋊C4—22no—
684C2×C22⋊C4—22no—
685C2×C22⋊C4—22no—
686C2×C22⋊C4—22no—
687C2×C22⋊C4—22no—
688C2×C22⋊C4—41no—
689C2×C22⋊C4—41no—
690C2×C22⋊C4—41no—
691C2×C22⋊C4—41no—
692C2×C22⋊C4—41no—
693C2×C22⋊C4—41no—
694C2×C22⋊C4—41no—
695C2×C22⋊C4—41no—
696C2×C22⋊C4—41no—
697C2×C22⋊C4—41no—
698C2×C22⋊C4C2×C4×C2914yes—
699C2×C22⋊C4C2×C4×C2914yes—
700C2×C22⋊C4C2×C4×C2914yes—
701C2×C22⋊C4D4×C2914yes—
702C2×C42—22no—
703C2×C42—22no—
704C2×C42—22no—
705C2×C42—22no—
706C2×C42—22no—
707C2×C42—22no—
708C2×C42—22no—
709C2×C42—41no—
710C2×C42—41no—
711C2×C42—41no—
712C2×C42—41no—
713C2×C42—41no—
714#95—22no—
715#95—22no—
716#95—22no—
717#95—22no—
718#95—22no—
719#95—22no—
720#95—22no—
721#95—22no—
722#95—22no—
723#95—22no—
724#95—41no—
725#95—41no—
726#95—41no—
727#95C2×C4×C2914yes—
728#95C2×C4×C2914yes—
729#95D4×C2914yescomplemented
730C29#1400711yescharacteristic, direct product factor, Sylow
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24C22×C4×C2912yes—
758C24C22×C4×C2912yes—
759C24C2×D4×C2912yes—
760C24#41×C2912yes—
761C24C24×C2911yescharacteristic
762C2×D4—28no—
763C2×D4—28no—
764C2×D4—44no—
765C2×D4—44no—
766C2×D4—44no—
767C2×D4—44no—
768C2×D4—44no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—28no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
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—21no—
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—28no—
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—44no—
846C22×C4—44no—
847C22×C4—44no—
848C22×C4—44no—
849C22×C4—44no—
850C22×C4C22×C4×C2912yes—
851C22×C4C22×C4×C2912yes—
852C22×C4C22×C4×C2912yes—
853C22×C4C22×C4×C2912yes—
854C22×C4C22×C4×C2912yes—
855C22×C4C2×D4×C2912yes—
856C22×C4C2×D4×C2912yes—
857C22×C4C2×D4×C2912yes—
858C22×C4C2×D4×C2912yes—
859C22×C4C2×D4×C2912yes—
860C22×C4#41×C2912yes—
861C22×C4#41×C2912yes—
862C22×C4#41×C2912yes—
863C22×C4#41×C2912yes—
864C22×C4#41×C2912yes—
865C22×C4#41×C2912yes—
866C22×C4#41×C2912yes—
867C4⋊C4—44no—
868C4⋊C4—44no—
869C22⋊C4—28no—
870C22⋊C4—28no—
871C22⋊C4—28no—
872C22⋊C4—44no—
873C22⋊C4—44no—
874C22⋊C4—44no—
875C22⋊C4—44no—
876C22⋊C4—44no—
877C22⋊C4—44no—
878C22⋊C4—44no—
879C22⋊C4—44no—
880C42—44no—
881C42—44no—
882C42—44no—
883C42—44no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
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—
953C23C4×D4×C2914yes—
954C23C23×C4×C2911yescharacteristic
955C23C22×D4×C2911yescharacteristic
956C23C22×D4×C2911yescharacteristic
957C23C2×#41×C2911yescharacteristic
958C23C2×#41×C2911yescharacteristic
959C23C2×#41×C2911yescharacteristic
960C23C2×#41×C2911yescharacteristic
961C23C2×#41×C2911yescharacteristic
962C23C2×#41×C2911yescharacteristic
963C23C2×#41×C2911yescharacteristic
964C23C2×#41×C2911yescharacteristic
965C23C29×H(5,𝔽2)11yescharacteristic
966C23C29×H(5,𝔽2)11yescharacteristic
967C23C29×H(5,𝔽2)11yescharacteristic
968C23C29×H(5,𝔽2)11yescharacteristic
969D4—416no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
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—416no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
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×C4C29×#11714yes—
1060C2×C4C4×D4×C2914yes—
1061C2×C4C29×#12314yes—
1062C22—24no—
1063C22—24no—
1064C22—24no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—42no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—81no—
1085C22—81no—
1086C22—81no—
1087C22—81no—
1088C22—81no—
1089C22—81no—
1090C22—81no—
1091C22—81no—
1092C22C2×C29×#11711yescharacteristic
1093C22C2×C4×D4×C2911yescharacteristic
1094C22C2×C4×D4×C2911yescharacteristic
1095C22C4×#41×C2911yescharacteristic
1096C22C4×#41×C2911yescharacteristic
1097C22C29×#51811yescharacteristic
1098C22C29×#51811yescharacteristic
1099C22C2×C29×#12311yescharacteristic
1100C22C29×#52511yescharacteristic
1101C22C29×#52911yescharacteristic
1102C22C29×#52911yescharacteristic
1103C22C29×#52911yescharacteristic
1104C22C29×#52911yescharacteristic
1105C22C29×#53211yescharacteristic
1106C22C29×#53211yescharacteristic
1107C22C29×#53811yescharacteristic
1108C22C29×#53811yescharacteristic
1109C22C29×#54011yescharacteristic
1110C22C29×#54011yescharacteristic
1111C22D42×C2911yescharacteristic
1112C22C29×#54611yescharacteristic
1113C22C29×#54611yescharacteristic
1114C22C29×#54611yescharacteristic
1115C22C29×#54611yescharacteristic
1116C22C29×#54611yescharacteristic
1117C22C29×#55011yescharacteristic
1118C22C29×#55111yescharacteristic
1119C22C29×#55111yescharacteristic
1120C22C29×#55111yescharacteristic
1121C22C29×#55311yescharacteristic
1122C22C29×#55311yescharacteristic
1123C22C29×#55311yescharacteristic
1124C22C29×#55511yescharacteristic
1125C22C29×#55911yescharacteristic
1126C22C29×#55911yescharacteristic
1127C4—24no—
1128C4—24no—
1129C4—24no—
1130C4—42no—
1131C4—42no—
1132C4—42no—
1133C4—42no—
1134C4—42no—
1135C4—42no—
1136C4—42no—
1137C4—42no—
1138C4—81no—
1139C4—81no—
1140C2—44no—
1141C2—82no—
1142C2C29×#229311yescharacteristic
1143C2C4×C29×#12311yescharacteristic
1144C2C29×#233311yescharacteristic
1145C2C29×#234211yescharacteristic
1146C2C29×#235711yescharacteristic
1147C2C29×#235811yescharacteristic
1148C2C29×#236311yescharacteristic
1149C2C29×#244411yescharacteristic
1150C2C29×#244511yescharacteristic
1151C2C29×#245911yescharacteristic
1152C2C29×#246411yescharacteristic
1153C2C29×#251611yescharacteristic
1154C2C29×#252611yescharacteristic
1155C2C29×#255411yescharacteristic
1156C2C29×#255711yescharacteristic
subgroupG/H
center, socleC24×C29C24
commutatorC23C23×C4×C29
Frattini, cosocleC24C24×C29
prime radicalC23×D4×C29C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C29×#388C2semidirect
4. C2×C29×#381C2semidirect
5. C2×C4×C22⋊C4×C29C2semidirect
6. C29×#1442C2semidirect
7. C29×#1440C2semidirect
8. C29×#1439C2semidirect
10. C29×#1437C2semidirect
11. C29×#1437C2semidirect
12. C29×#1437C2semidirect
13. C29×#1436C2semidirect
14. C29×#1436C2semidirect
15. C4×C29×#95C2semidirect
37. C29×#386C4semidirect
151. C29×#95D4semidirect
305. #14007C29direct (N × H)
485. C2×#388C2×C29semidirect
487. C2×#381C2×C29semidirect
488. C2×C4×C22⋊C4C2×C29semidirect
489. #1442C2×C29semidirect
490. #1440C2×C29semidirect
491. #1439C2×C29semidirect
493. #1437C2×C29semidirect
494. #1437C2×C29semidirect
495. #1437C2×C29semidirect
496. #1436C2×C29semidirect
497. #1436C2×C29semidirect
498. C4×#95C2×C29semidirect
598. #386C4×C29semidirect
729. #95D4×C29semidirect
730. C29#14007direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#3902
C2×C29×#3882
C2×C29×#3862
C2×C29×#3812
C2×C4×C22⋊C4×C292
C29×#14422
C29×#14402
C29×#14392
C29×#14382
C29×#14372
C29×#14362
C4×C29×#952
#1400729