Finite Group Databasebeta

← C29×#15126 #20310026

Subgroups — C29×#15126 #20310026

Order 7424.

2506 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C29×#121C211yesmaximal, characteristic
2C2×C29×#394C212yesmaximal, complemented
3C2×C29×#390C211yesmaximal, characteristic, complemented
4C2×C29×#390C211yesmaximal, characteristic, complemented
5C2×C29×#389C211yesmaximal, characteristic, complemented
6C2×C29×#380C211yesmaximal, characteristic, complemented
7C2×C4×C22⋊C4×C29C211yesmaximal, characteristic, complemented
8C29×#1440C212yesmaximal, complemented
9C29×#1439C212yesmaximal, complemented
10C29×#1438C212yesmaximal, complemented
11C29×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×D4×C29C2211yescharacteristic
13C23×D4×C29C2212yes—
14C24×C4×C29C2211yescharacteristic
15C2×C29×#121—24no—
16C2×C29×#121—24no—
17C2×C29×#121—24no—
18C22×C4⋊C4×C29C2211yescharacteristic
19C22×C4⋊C4×C29C2212yes—
20C22×C4⋊C4×C29C2211yescharacteristic
21C22×C4⋊C4×C29C2211yescharacteristic
22C22×C22⋊C4×C29C2211yescharacteristic
23C22×C22⋊C4×C29C2212yes—
24C22×C22⋊C4×C29C2212yes—
25C22×C22⋊C4×C29C2212yes—
26C22×C22⋊C4×C29C2212yes—
27C22×C22⋊C4×C29C2212yes—
28C22×C22⋊C4×C29C2212yes—
29C22×C22⋊C4×C29C2211yescharacteristic
30C22×C42×C29C2211yescharacteristic
31C22×C42×C29C2211yescharacteristic
32C29×#394—28no—
33C29×#390—24no—
34C29×#390—24no—
35C29×#389—24no—
36C29×#380—24no—
37C4×C22⋊C4×C29—24no—
38C2×C29×#95C2212yes—
39C2×C29×#95C2212yes—
40C2×C29×#95C2211yescharacteristic
41C2×C29×#95C2212yes—
42C2×C29×#95C2211yescharacteristic
43C2×C29×#95C2212yes—
44C25×C29C2312yes—
45C25×C29C2311yescharacteristic
46C22×D4×C29—24no—
47C22×D4×C29—24no—
48C22×D4×C29—24no—
49C22×D4×C29—24no—
50C22×D4×C29—24no—
51C22×D4×C29—22no—
52C22×D4×C29—22no—
53C22×D4×C29—22no—
54C22×D4×C29—22no—
55C22×D4×C29—22no—
56C22×D4×C29—22no—
57C22×D4×C29—42no—
58C22×D4×C29—42no—
59C22×D4×C29D414yes—
60C23×C4×C29—22no—
61C23×C4×C29—22no—
62C23×C4×C29—22no—
63C23×C4×C29—22no—
64C23×C4×C29—22no—
65C23×C4×C29—22no—
66C23×C4×C29D414yes—
67C23×C4×C29C2312yes—
68C23×C4×C29C2311yescharacteristic
69C23×C4×C29C2311yescharacteristic
70C23×C4×C29C2312yes—
71C23×C4×C29C2311yescharacteristic
72C23×C4×C29C2312yes—
73C23×C4×C29C2311yescharacteristic
74C23×C4×C29C2311yescharacteristic
75C23×C4×C29C2311yescharacteristic
76C29×#121—232no—
77C2×C4⋊C4×C29—22no—
78C2×C4⋊C4×C29—22no—
79C2×C4⋊C4×C29—22no—
80C2×C4⋊C4×C29—22no—
81C2×C4⋊C4×C29—22no—
82C2×C4⋊C4×C29—24no—
83C2×C4⋊C4×C29—22no—
84C2×C4⋊C4×C29—24no—
85C2×C4⋊C4×C29—22no—
86C2×C4⋊C4×C29—42no—
87C2×C4⋊C4×C29D414yes—
88C2×C4⋊C4×C29D414yescomplemented
89C2×C22⋊C4×C29—24no—
90C2×C22⋊C4×C29—22no—
91C2×C22⋊C4×C29—22no—
92C2×C22⋊C4×C29—22no—
93C2×C22⋊C4×C29—24no—
94C2×C22⋊C4×C29—24no—
95C2×C22⋊C4×C29—22no—
96C2×C22⋊C4×C29—22no—
97C2×C22⋊C4×C29—24no—
98C2×C22⋊C4×C29—24no—
99C2×C22⋊C4×C29—24no—
100C2×C22⋊C4×C29—24no—
101C2×C22⋊C4×C29—24no—
102C2×C22⋊C4×C29—24no—
103C2×C22⋊C4×C29—24no—
104C2×C22⋊C4×C29—24no—
105C2×C22⋊C4×C29—24no—
106C2×C22⋊C4×C29—24no—
107C2×C22⋊C4×C29—42no—
108C2×C22⋊C4×C29—42no—
109C2×C22⋊C4×C29—42no—
110C2×C22⋊C4×C29—42no—
111C2×C22⋊C4×C29—42no—
112C2×C22⋊C4×C29D414yescomplemented
113C2×C42×C29—22no—
114C2×C42×C29—22no—
115C2×C42×C29—22no—
116C2×C42×C29—22no—
117C2×C42×C29—22no—
118C2×C42×C29—22no—
119C29×#95—22no—
120C29×#95—22no—
121C29×#95—24no—
122C29×#95—24no—
123C29×#95—24no—
124C29×#95—42no—
125C24×C29—21no—
126C24×C29—21no—
127C24×C29—21no—
128C24×C29—21no—
129C24×C29—21no—
130C24×C29—21no—
131C24×C29—21no—
132C24×C29—21no—
133C24×C29—21no—
134C24×C29—21no—
135C24×C29—21no—
136C24×C29—21no—
137C24×C29—22no—
138C24×C29—22no—
139C24×C29—22no—
140C24×C29—22no—
141C24×C29—22no—
142C24×C29—22no—
143C24×C29—22no—
144C24×C29—22no—
145C24×C29—22no—
146C24×C29—22no—
147C24×C29—22no—
148C24×C29—22no—
149C24×C29—22no—
150C24×C29—22no—
151C24×C29C2×D414yes—
152C24×C29C2×D412yes—
153C24×C29C2×D412yes—
154C24×C29#4112yes—
155C24×C29C2411yescharacteristic
156C2×D4×C29—216no—
157C2×D4×C29—28no—
158C2×D4×C29—28no—
159C2×D4×C29—28no—
160C2×D4×C29—48no—
161C2×D4×C29—48no—
162C2×D4×C29—48no—
163C2×D4×C29—48no—
164C2×D4×C29—48no—
165C2×D4×C29—48no—
166C2×D4×C29—44no—
167C2×D4×C29—44no—
168C2×D4×C29—44no—
169C2×D4×C29—44no—
170C22×C4×C29—21no—
171C22×C4×C29—21no—
172C22×C4×C29—21no—
173C22×C4×C29—21no—
174C22×C4×C29—21no—
175C22×C4×C29—21no—
176C22×C4×C29—21no—
177C22×C4×C29—21no—
178C22×C4×C29—21no—
179C22×C4×C29—21no—
180C22×C4×C29—22no—
181C22×C4×C29—21no—
182C22×C4×C29—21no—
183C22×C4×C29—22no—
184C22×C4×C29—22no—
185C22×C4×C29—22no—
186C22×C4×C29—22no—
187C22×C4×C29—21no—
188C22×C4×C29—21no—
189C22×C4×C29—21no—
190C22×C4×C29—21no—
191C22×C4×C29—21no—
192C22×C4×C29—21no—
193C22×C4×C29—21no—
194C22×C4×C29—22no—
195C22×C4×C29—22no—
196C22×C4×C29—21no—
197C22×C4×C29—21no—
198C22×C4×C29—21no—
199C22×C4×C29—22no—
200C22×C4×C29—21no—
201C22×C4×C29—21no—
202C22×C4×C29—22no—
203C22×C4×C29—21no—
204C22×C4×C29—21no—
205C22×C4×C29—22no—
206C22×C4×C29—21no—
207C22×C4×C29—22no—
208C22×C4×C29—22no—
209C22×C4×C29—21no—
210C22×C4×C29—21no—
211C22×C4×C29—21no—
212C22×C4×C29—28no—
213C22×C4×C29—28no—
214C22×C4×C29—28no—
215C22×C4×C29—22no—
216C22×C4×C29—22no—
217C22×C4×C29—22no—
218C22×C4×C29—22no—
219C22×C4×C29—22no—
220C22×C4×C29—22no—
221C22×C4×C29—22no—
222C22×C4×C29—44no—
223C22×C4×C29—44no—
224C22×C4×C29—44no—
225C22×C4×C29—44no—
226C22×C4×C29C2×D414yes—
227C22×C4×C29C2×D412yes—
228C22×C4×C29C2×D412yes—
229C22×C4×C29C2×D412yes—
230C22×C4×C29C2×D414yes—
231C22×C4×C29C2×D412yes—
232C22×C4×C29C2×D412yes—
233C22×C4×C29C2×D412yes—
234C22×C4×C29C2×D412yes—
235C22×C4×C29#4112yes—
236C22×C4×C29#4112yes—
237C22×C4×C29#4112yes—
238C22×C4×C29#4112yes—
239C22×C4×C29#4112yes—
240C4⋊C4×C29—28no—
241C4⋊C4×C29—28no—
242C4⋊C4×C29—48no—
243C4⋊C4×C29—44no—
244C22⋊C4×C29—28no—
245C22⋊C4×C29—216no—
246C22⋊C4×C29—28no—
247C22⋊C4×C29—48no—
248C22⋊C4×C29—48no—
249C22⋊C4×C29—48no—
250C22⋊C4×C29—48no—
251C22⋊C4×C29—48no—
252C42×C29—44no—
253C42×C29—44no—
254#15126C2911yesmaximal, characteristic, direct product factor, Sylow
255C23×C29—22no—
256C23×C29—22no—
257C23×C29—22no—
258C23×C29—22no—
259C23×C29—22no—
260C23×C29—22no—
261C23×C29—22no—
262C23×C29—22no—
263C23×C29—22no—
264C23×C29—22no—
265C23×C29—22no—
266C23×C29—22no—
267C23×C29—22no—
268C23×C29—22no—
269C23×C29—22no—
270C23×C29—22no—
271C23×C29—22no—
272C23×C29—22no—
273C23×C29—24no—
274C23×C29—24no—
275C23×C29—24no—
276C23×C29—24no—
277C23×C29—24no—
278C23×C29—24no—
279C23×C29—24no—
280C23×C29—41no—
281C23×C29—41no—
282C23×C29—41no—
283C23×C29—41no—
284C23×C29—41no—
285C23×C29—41no—
286C23×C29—41no—
287C23×C29—41no—
288C23×C29—41no—
289C23×C29—41no—
290C23×C29—41no—
291C23×C29—41no—
292C23×C29—41no—
293C23×C29—41no—
294C23×C29—41no—
295C23×C29—41no—
296C23×C29—42no—
297C23×C29—42no—
298C23×C29—42no—
299C23×C29—42no—
300C23×C29—42no—
301C23×C29—42no—
302C23×C29—42no—
303C23×C29—42no—
304C23×C29—42no—
305C23×C29—42no—
306C23×C29—42no—
307C23×C29—42no—
308C23×C29—42no—
309C23×C29—42no—
310C23×C29—42no—
311C23×C29—42no—
312C23×C29—42no—
313C23×C29—42no—
314C23×C29—42no—
315C23×C29—42no—
316C23×C29—42no—
317C23×C29—42no—
318C23×C29—42no—
319C23×C29—42no—
320C23×C29—42no—
321C23×C29—42no—
322C23×C29—42no—
323C23×C29—42no—
324C23×C29#12114yes—
325C23×C29C22×D411yescharacteristic
326C23×C29C22×D411yescharacteristic
327C23×C29C22×D411yescharacteristic
328C23×C29C22×D411yescharacteristic
329C23×C29C22×D411yescharacteristic
330C23×C29C2×#4111yescharacteristic
331C23×C29C2×#4111yescharacteristic
332C23×C29C2×#4111yescharacteristic
333C23×C29C2×#4111yescharacteristic
334C23×C29C2×#4111yescharacteristic
335C23×C29C2×#4111yescharacteristic
336C23×C29H(5,𝔽2)11yescharacteristic
337C23×C29H(5,𝔽2)11yescharacteristic
338C23×C29H(5,𝔽2)11yescharacteristic
339C23×C292−1+411yescharacteristic
340D4×C29—432no—
341D4×C29—416no—
342C2×C4×C29—22no—
343C2×C4×C29—24no—
344C2×C4×C29—22no—
345C2×C4×C29—22no—
346C2×C4×C29—24no—
347C2×C4×C29—22no—
348C2×C4×C29—22no—
349C2×C4×C29—22no—
350C2×C4×C29—22no—
351C2×C4×C29—22no—
352C2×C4×C29—22no—
353C2×C4×C29—24no—
354C2×C4×C29—22no—
355C2×C4×C29—24no—
356C2×C4×C29—22no—
357C2×C4×C29—22no—
358C2×C4×C29—24no—
359C2×C4×C29—24no—
360C2×C4×C29—22no—
361C2×C4×C29—22no—
362C2×C4×C29—22no—
363C2×C4×C29—41no—
364C2×C4×C29—41no—
365C2×C4×C29—41no—
366C2×C4×C29—41no—
367C2×C4×C29—41no—
368C2×C4×C29—41no—
369C2×C4×C29—42no—
370C2×C4×C29—41no—
371C2×C4×C29—41no—
372C2×C4×C29—42no—
373C2×C4×C29—41no—
374C2×C4×C29—41no—
375C2×C4×C29—42no—
376C2×C4×C29—41no—
377C2×C4×C29—41no—
378C2×C4×C29—42no—
379C2×C4×C29—42no—
380C2×C4×C29—42no—
381C2×C4×C29—41no—
382C2×C4×C29—41no—
383C2×C4×C29—42no—
384C2×C4×C29—41no—
385C2×C4×C29—41no—
386C2×C4×C29—41no—
387C2×C4×C29—41no—
388C2×C4×C29—42no—
389C2×C4×C29—41no—
390C2×C4×C29—41no—
391C2×C4×C29—416no—
392C2×C4×C29—42no—
393C2×C4×C29—42no—
394C2×C4×C29—42no—
395C2×C4×C29—42no—
396C2×C4×C29—42no—
397C2×C4×C29—42no—
398C2×C4×C29—42no—
399C2×C4×C29#12014yes—
400C2×C4×C29#12114yes—
401C2×C4×C29#12114yes—
402C2×C4×C29#12114yes—
403C2×C4×C29#12314yes—
404C2×C4×C29#12314yes—
405C2×C4×C29#12414yes—
406C22×#121C2×C2911yescharacteristic
407C2×#394C2×C2912yescomplemented
408C2×#390C2×C2911yescharacteristic, complemented
409C2×#390C2×C2911yescharacteristic, complemented
410C2×#389C2×C2911yescharacteristic, complemented
411C2×#380C2×C2911yescharacteristic, complemented
412C2×C4×C22⋊C4C2×C2911yescharacteristic, complemented
413#1440C2×C2912yescomplemented
414#1439C2×C2912yescomplemented
415#1438C2×C2912yescomplemented
416C4⋊#95C2×C2911yescharacteristic, complemented
417C22×C29—24no—
418C22×C29—24no—
419C22×C29—24no—
420C22×C29—42no—
421C22×C29—42no—
422C22×C29—42no—
423C22×C29—42no—
424C22×C29—42no—
425C22×C29—42no—
426C22×C29—42no—
427C22×C29—42no—
428C22×C29—42no—
429C22×C29—42no—
430C22×C29—42no—
431C22×C29—42no—
432C22×C29—44no—
433C22×C29—44no—
434C22×C29—44no—
435C22×C29—44no—
436C22×C29—44no—
437C22×C29—44no—
438C22×C29—44no—
439C22×C29—82no—
440C22×C29—82no—
441C22×C29—82no—
442C22×C29—82no—
443C22×C29—82no—
444C22×C29—82no—
445C22×C29—82no—
446C22×C29—82no—
447C22×C29C2×#12011yescharacteristic
448C22×C29C2×#12111yescharacteristic
449C22×C29C2×#12111yescharacteristic
450C22×C29C2×#12111yescharacteristic
451C22×C29C2×#12111yescharacteristic
452C22×C29C2×#12311yescharacteristic
453C22×C29C2×#12311yescharacteristic
454C22×C29#52511yescharacteristic
455C22×C29C2×#12411yescharacteristic
456C22×C29#52911yescharacteristic
457C22×C29#52911yescharacteristic
458C22×C29#53211yescharacteristic
459C22×C29#53211yescharacteristic
460C22×C29#53511yescharacteristic
461C22×C29#53711yescharacteristic
462C22×C29#54011yescharacteristic
463C22×C29#54011yescharacteristic
464C22×C29#54211yescharacteristic
465C22×C29#54211yescharacteristic
466C22×C29D4211yescharacteristic
467C22×C29D4211yescharacteristic
468C22×C29D4211yescharacteristic
469C22×C29#54611yescharacteristic
470C22×C29#54611yescharacteristic
471C22×C29#54611yescharacteristic
472C22×C29#54611yescharacteristic
473C22×C29#54711yescharacteristic
474C22×C29#54711yescharacteristic
475C22×C29#54811yescharacteristic
476C22×C29#54811yescharacteristic
477C22×C29#55011yescharacteristic
478C22×C29#55011yescharacteristic
479C22×C29#55311yescharacteristic
480C22×C29#55311yescharacteristic
481C22×C29#55511yescharacteristic
482C4×C29—42no—
483C4×C29—42no—
484C4×C29—42no—
485C4×C29—44no—
486C4×C29—42no—
487C4×C29—42no—
488C4×C29—44no—
489C4×C29—82no—
490C4×C29#39418yescomplemented
491C23×D4C22×C2911yescharacteristic
492C23×D4C22×C2912yes—
493C24×C4C22×C2911yescharacteristic
494C2×#121—24no—
495C2×#121—24no—
496C2×#121—24no—
497C22×C4⋊C4C22×C2911yescharacteristic
498C22×C4⋊C4C22×C2912yes—
499C22×C4⋊C4C22×C2911yescharacteristic
500C22×C4⋊C4C22×C2911yescharacteristic
501C22×C22⋊C4C22×C2912yes—
502C22×C22⋊C4C22×C2911yescharacteristic
503C22×C22⋊C4C22×C2912yes—
504C22×C22⋊C4C22×C2912yes—
505C22×C22⋊C4C22×C2912yes—
506C22×C22⋊C4C22×C2912yes—
507C22×C22⋊C4C22×C2912yes—
508C22×C22⋊C4C22×C2911yescharacteristic
509C22×C42C22×C2911yescharacteristic
510C22×C42C22×C2911yescharacteristic
511#394—28no—
512#390—24no—
513#390—24no—
514#389—24no—
515#380—24no—
516C4×C22⋊C4—24no—
517C2×#95C22×C2912yes—
518C2×#95C22×C2912yes—
519C2×#95C22×C2911yescharacteristic
520C2×#95C22×C2912yes—
521C2×#95C22×C2911yescharacteristic
522C2×#95C22×C2912yes—
523C2×C29—44no—
524C2×C29—84no—
525C2×C29C2×#39411yescharacteristic
526C2×C29#240711yescharacteristic
527C2×C29#240811yescharacteristic
528C2×C29#241411yescharacteristic
529C2×C29#241611yescharacteristic
530C2×C29#242011yescharacteristic
531C2×C29#242211yescharacteristic
532C2×C29#242611yescharacteristic
533C2×C29#242711yescharacteristic
534C2×C29#242811yescharacteristic
535C2×C29#242811yescharacteristic
536C2×C29#249011yescharacteristic
537C2×C29#249111yescharacteristic
538C2×C29#262411yescharacteristic
539C2×C29#285411yescharacteristic
540C25C23×C2912yes—
541C25C23×C2911yescharacteristic
542C22×D4—24no—
543C22×D4—24no—
544C22×D4—24no—
545C22×D4—24no—
546C22×D4—24no—
547C22×D4—22no—
548C22×D4—22no—
549C22×D4—22no—
550C22×D4—22no—
551C22×D4—22no—
552C22×D4—22no—
553C22×D4—42no—
554C22×D4—42no—
555C22×D4D4×C2914yes—
556C23×C4—22no—
557C23×C4—22no—
558C23×C4—22no—
559C23×C4—22no—
560C23×C4—22no—
561C23×C4—22no—
562C23×C4D4×C2914yes—
563C23×C4C23×C2912yes—
564C23×C4C23×C2912yes—
565C23×C4C23×C2911yescharacteristic
566C23×C4C23×C2911yescharacteristic
567C23×C4C23×C2911yescharacteristic
568C23×C4C23×C2912yes—
569C23×C4C23×C2911yescharacteristic
570C23×C4C23×C2911yescharacteristic
571C23×C4C23×C2911yescharacteristic
572#121—232no—
573C2×C4⋊C4—22no—
574C2×C4⋊C4—22no—
575C2×C4⋊C4—22no—
576C2×C4⋊C4—22no—
577C2×C4⋊C4—22no—
578C2×C4⋊C4—24no—
579C2×C4⋊C4—22no—
580C2×C4⋊C4—24no—
581C2×C4⋊C4—22no—
582C2×C4⋊C4—42no—
583C2×C4⋊C4D4×C2914yes—
584C2×C4⋊C4D4×C2914yescomplemented
585C2×C22⋊C4—24no—
586C2×C22⋊C4—22no—
587C2×C22⋊C4—22no—
588C2×C22⋊C4—22no—
589C2×C22⋊C4—24no—
590C2×C22⋊C4—24no—
591C2×C22⋊C4—22no—
592C2×C22⋊C4—22no—
593C2×C22⋊C4—24no—
594C2×C22⋊C4—24no—
595C2×C22⋊C4—24no—
596C2×C22⋊C4—24no—
597C2×C22⋊C4—24no—
598C2×C22⋊C4—24no—
599C2×C22⋊C4—24no—
600C2×C22⋊C4—24no—
601C2×C22⋊C4—24no—
602C2×C22⋊C4—24no—
603C2×C22⋊C4—42no—
604C2×C22⋊C4—42no—
605C2×C22⋊C4—42no—
606C2×C22⋊C4—42no—
607C2×C22⋊C4—42no—
608C2×C22⋊C4D4×C2914yescomplemented
609C2×C42—22no—
610C2×C42—22no—
611C2×C42—22no—
612C2×C42—22no—
613C2×C42—22no—
614C2×C42—22no—
615#95—22no—
616#95—22no—
617#95—24no—
618#95—24no—
619#95—24no—
620#95—42no—
621C29#1512611yescharacteristic, direct product factor, Sylow
622C24—21no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—22no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24C2×D4×C2914yes—
649C24C2×D4×C2912yes—
650C24C2×D4×C2912yes—
651C24#41×C2912yes—
652C24C24×C2911yescharacteristic
653C2×D4—216no—
654C2×D4—28no—
655C2×D4—28no—
656C2×D4—28no—
657C2×D4—48no—
658C2×D4—48no—
659C2×D4—48no—
660C2×D4—48no—
661C2×D4—48no—
662C2×D4—48no—
663C2×D4—44no—
664C2×D4—44no—
665C2×D4—44no—
666C2×D4—44no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—22no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—22no—
697C22×C4—21no—
698C22×C4—22no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—22no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—22no—
705C22×C4—21no—
706C22×C4—22no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—28no—
710C22×C4—28no—
711C22×C4—28no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—44no—
720C22×C4—44no—
721C22×C4—44no—
722C22×C4—44no—
723C22×C4C2×D4×C2912yes—
724C22×C4C2×D4×C2912yes—
725C22×C4C2×D4×C2914yes—
726C22×C4C2×D4×C2914yes—
727C22×C4C2×D4×C2912yes—
728C22×C4C2×D4×C2912yes—
729C22×C4C2×D4×C2912yes—
730C22×C4C2×D4×C2912yes—
731C22×C4C2×D4×C2912yes—
732C22×C4#41×C2912yes—
733C22×C4#41×C2912yes—
734C22×C4#41×C2912yes—
735C22×C4#41×C2912yes—
736C22×C4#41×C2912yes—
737C4⋊C4—28no—
738C4⋊C4—28no—
739C4⋊C4—48no—
740C4⋊C4—44no—
741C22⋊C4—216no—
742C22⋊C4—28no—
743C22⋊C4—28no—
744C22⋊C4—48no—
745C22⋊C4—48no—
746C22⋊C4—48no—
747C22⋊C4—48no—
748C22⋊C4—48no—
749C42—44no—
750C42—44no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—24no—
770C23—24no—
771C23—24no—
772C23—24no—
773C23—24no—
774C23—24no—
775C23—24no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—42no—
793C23—42no—
794C23—42no—
795C23—42no—
796C23—42no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—42no—
801C23—42no—
802C23—42no—
803C23—42no—
804C23—42no—
805C23—42no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23—42no—
815C23—42no—
816C23—42no—
817C23—42no—
818C23—42no—
819C23—42no—
820C23C29×#12114yes—
821C23C22×D4×C2911yescharacteristic
822C23C22×D4×C2911yescharacteristic
823C23C22×D4×C2911yescharacteristic
824C23C22×D4×C2911yescharacteristic
825C23C22×D4×C2911yescharacteristic
826C23C2×#41×C2911yescharacteristic
827C23C2×#41×C2911yescharacteristic
828C23C2×#41×C2911yescharacteristic
829C23C2×#41×C2911yescharacteristic
830C23C2×#41×C2911yescharacteristic
831C23C2×#41×C2911yescharacteristic
832C23C29×H(5,𝔽2)11yescharacteristic
833C23C29×H(5,𝔽2)11yescharacteristic
834C23C29×H(5,𝔽2)11yescharacteristic
835C23C29×2−1+411yescharacteristic
836D4—432no—
837D4—416no—
838C2×C4—22no—
839C2×C4—24no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—24no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—24no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—24no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—24no—
855C2×C4—24no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—42no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—42no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—416no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4C29×#12014yes—
896C2×C4C29×#12114yes—
897C2×C4C29×#12114yes—
898C2×C4C29×#12114yes—
899C2×C4C29×#12314yes—
900C2×C4C29×#12314yes—
901C2×C4C29×#12414yes—
902C22—24no—
903C22—24no—
904C22—24no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—44no—
918C22—44no—
919C22—44no—
920C22—44no—
921C22—44no—
922C22—44no—
923C22—44no—
924C22—82no—
925C22—82no—
926C22—82no—
927C22—82no—
928C22—82no—
929C22—82no—
930C22—82no—
931C22—82no—
932C22C2×C29×#12011yescharacteristic
933C22C2×C29×#12111yescharacteristic
934C22C2×C29×#12111yescharacteristic
935C22C2×C29×#12111yescharacteristic
936C22C2×C29×#12111yescharacteristic
937C22C2×C29×#12311yescharacteristic
938C22C2×C29×#12311yescharacteristic
939C22C29×#52511yescharacteristic
940C22C2×C29×#12411yescharacteristic
941C22C29×#52911yescharacteristic
942C22C29×#52911yescharacteristic
943C22C29×#53211yescharacteristic
944C22C29×#53211yescharacteristic
945C22C29×#53511yescharacteristic
946C22C29×#53711yescharacteristic
947C22C29×#54011yescharacteristic
948C22C29×#54011yescharacteristic
949C22C29×#54211yescharacteristic
950C22C29×#54211yescharacteristic
951C22D42×C2911yescharacteristic
952C22D42×C2911yescharacteristic
953C22D42×C2911yescharacteristic
954C22C29×#54611yescharacteristic
955C22C29×#54611yescharacteristic
956C22C29×#54611yescharacteristic
957C22C29×#54611yescharacteristic
958C22C29×#54711yescharacteristic
959C22C29×#54711yescharacteristic
960C22C29×#54811yescharacteristic
961C22C29×#54811yescharacteristic
962C22C29×#55011yescharacteristic
963C22C29×#55011yescharacteristic
964C22C29×#55311yescharacteristic
965C22C29×#55311yescharacteristic
966C22C29×#55511yescharacteristic
967C4—42no—
968C4—42no—
969C4—44no—
970C4—42no—
971C4—42no—
972C4—44no—
973C4—42no—
974C4—82no—
975C4C29×#39418yescomplemented
976C2—44no—
977C2—84no—
978C2C2×C29×#39411yescharacteristic
979C2C29×#240711yescharacteristic
980C2C29×#240811yescharacteristic
981C2C29×#241411yescharacteristic
982C2C29×#241611yescharacteristic
983C2C29×#242011yescharacteristic
984C2C29×#242211yescharacteristic
985C2C29×#242611yescharacteristic
986C2C29×#242711yescharacteristic
987C2C29×#242811yescharacteristic
988C2C29×#242811yescharacteristic
989C2C29×#249011yescharacteristic
990C2C29×#249111yescharacteristic
991C2C29×#262411yescharacteristic
992C2C29×#285411yescharacteristic
subgroupG/H
center, socleC24×C29C24
commutator, Frattini, cosocleC24C24×C29
prime radicalC22×C29×#121C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C29×#394C2semidirect
3. C2×C29×#390C2semidirect
4. C2×C29×#390C2semidirect
5. C2×C29×#389C2semidirect
6. C2×C29×#380C2semidirect
7. C2×C4×C22⋊C4×C29C2semidirect
8. C29×#1440C2semidirect
9. C29×#1439C2semidirect
10. C29×#1438C2semidirect
11. C29×C4⋊#95C2semidirect
88. C2×C4⋊C4×C29D4semidirect
112. C2×C22⋊C4×C29D4semidirect
254. #15126C29direct (N × H)
407. C2×#394C2×C29semidirect
408. C2×#390C2×C29semidirect
409. C2×#390C2×C29semidirect
410. C2×#389C2×C29semidirect
411. C2×#380C2×C29semidirect
412. C2×C4×C22⋊C4C2×C29semidirect
413. #1440C2×C29semidirect
414. #1439C2×C29semidirect
415. #1438C2×C29semidirect
416. C4⋊#95C2×C29semidirect
490. C4×C29#394semidirect
584. C2×C4⋊C4D4×C29semidirect
608. C2×C22⋊C4D4×C29semidirect
621. C29#15126direct (N × H)
975. C4C29×#394semidirect

Maximal subgroups

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

subgroupindex
C22×C29×#1212
C2×C29×#3942
C2×C29×#3902
C2×C29×#3892
C2×C29×#3802
C2×C4×C22⋊C4×C292
C29×#14402
C29×#14392
C29×#14382
C29×C4⋊#952
#1512629