Finite Group Databasebeta

← C29×#16285 #20311185

Subgroups — C29×#16285 #20311185

Order 7424.

1790 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#397C211yesmaximal, characteristic, complemented
2C2×C29×#396C211yesmaximal, characteristic, complemented
3C2×C29×#394C211yesmaximal, characteristic
4C2×C29×#394C211yesmaximal, characteristic
5C2×C29×#386C211yesmaximal, characteristic
6C2×C29×#385C211yesmaximal, characteristic, complemented
7C29×#1445C211yesmaximal, characteristic, complemented
8C29×#1444C211yesmaximal, characteristic, complemented
9C29×#1441C211yesmaximal, characteristic, complemented
10C29×#1441C211yesmaximal, characteristic, complemented
11C29×#1440C211yesmaximal, characteristic, complemented
12C29×#1440C211yesmaximal, characteristic, complemented
13C29×#1439C211yesmaximal, characteristic, complemented
14C29×#1439C211yesmaximal, characteristic, complemented
15C29×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C29C2211yescharacteristic
17C24×C4×C29C2211yescharacteristic
18C22×C4⋊C4×C29C2211yescharacteristic
19C22×C4⋊C4×C29C2211yescharacteristic
20C22×C4⋊C4×C29C2211yescharacteristic
21C22×C4⋊C4×C29C2211yescharacteristic
22C22×C4⋊C4×C29C2211yescharacteristic
23C22×C4⋊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×C22⋊C4×C29C2211yescharacteristic
32C22×C22⋊C4×C29C2211yescharacteristic
33C22×C22⋊C4×C29C2211yescharacteristic
34C22×C22⋊C4×C29C2211yescharacteristic
35C29×#397—24no—
36C29×#396—24no—
37C29×#394—24no—
38C29×#394—24no—
39C29×#386—24no—
40C29×#385—24no—
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
56C2×C29×#95C2211yescharacteristic
57C25×C29C2311yescharacteristic
58C25×C29C2311yescharacteristic
59C22×D4×C29—22no—
60C22×D4×C29—22no—
61C22×D4×C29—22no—
62C22×D4×C29—22no—
63C22×D4×C29—22no—
64C22×D4×C29—41no—
65C22×D4×C29—41no—
66C23×C4×C29—22no—
67C23×C4×C29—22no—
68C23×C4×C29—22no—
69C23×C4×C29—41no—
70C23×C4×C29—41no—
71C23×C4×C29—41no—
72C23×C4×C29—41no—
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
85C23×C4×C29C2311yescharacteristic
86C2×C4⋊C4×C29—22no—
87C2×C4⋊C4×C29—22no—
88C2×C4⋊C4×C29—22no—
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—41no—
98C2×C4⋊C4×C29—41no—
99C2×C4⋊C4×C29—41no—
100C2×C4⋊C4×C29—41no—
101C2×C4⋊C4×C29—41no—
102C2×C4⋊C4×C29—41no—
103C2×C4⋊C4×C29—41no—
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—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—41no—
123C2×C22⋊C4×C29—41no—
124C2×C22⋊C4×C29—41no—
125C2×C22⋊C4×C29—41no—
126C2×C22⋊C4×C29—41no—
127C2×C22⋊C4×C29—41no—
128C2×C22⋊C4×C29—41no—
129C2×C22⋊C4×C29—41no—
130C2×C22⋊C4×C29—41no—
131C2×C22⋊C4×C29—41no—
132C2×C22⋊C4×C29—41no—
133C2×C22⋊C4×C29—41no—
134C2×C22⋊C4×C29D414yes—
135C2×C22⋊C4×C29D414yes—
136C2×C22⋊C4×C29D414yes—
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—22no—
147C29×#95—22no—
148C29×#95—41no—
149C29×#95—41no—
150C29×#95—41no—
151C29×#95—41no—
152C29×#95—41no—
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×C29—21no—
179C24×C29C2×D412yes—
180C24×C29C2×D412yes—
181C24×C29C2×D412yes—
182C24×C29#4112yes—
183C24×C29C2411yescharacteristic
184C2×D4×C29—28no—
185C2×D4×C29—44no—
186C2×D4×C29—44no—
187C2×D4×C29—44no—
188C2×D4×C29—44no—
189C2×D4×C29—44no—
190C2×D4×C29—44no—
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—21no—
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—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—21no—
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—44no—
274C22×C4×C29—44no—
275C22×C4×C29—44no—
276C22×C4×C29—44no—
277C22×C4×C29—44no—
278C22×C4×C29—44no—
279C22×C4×C29—44no—
280C22×C4×C29C2×D412yes—
281C22×C4×C29C2×D412yes—
282C22×C4×C29C2×D412yes—
283C22×C4×C29C2×D412yes—
284C22×C4×C29C2×D412yes—
285C22×C4×C29C2×D412yes—
286C22×C4×C29#4112yes—
287C22×C4×C29#4112yes—
288C22×C4×C29#4112yes—
289C4⋊C4×C29—44no—
290C4⋊C4×C29—44no—
291C4⋊C4×C29—44no—
292C4⋊C4×C29—44no—
293C4⋊C4×C29—44no—
294C4⋊C4×C29—44no—
295C22⋊C4×C29—28no—
296C22⋊C4×C29—44no—
297C22⋊C4×C29—44no—
298C22⋊C4×C29—44no—
299C22⋊C4×C29—44no—
300C22⋊C4×C29—44no—
301C22⋊C4×C29—44no—
302C22⋊C4×C29—44no—
303C22⋊C4×C29—44no—
304C22⋊C4×C29—44no—
305C22⋊C4×C29—44no—
306#16285C2911yesmaximal, characteristic, direct product factor, Sylow
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—22no—
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×C29—41no—
376C23×C29#12114yes—
377C23×C29C22×D411yescharacteristic
378C23×C29C22×D411yescharacteristic
379C23×C29C22×D411yescharacteristic
380C23×C29C2×#4111yescharacteristic
381C23×C29C2×#4111yescharacteristic
382C23×C29C2×#4111yescharacteristic
383C23×C29C2×#4111yescharacteristic
384C23×C29H(5,𝔽2)11yescharacteristic
385C23×C29H(5,𝔽2)11yescharacteristic
386C23×C29H(5,𝔽2)11yescharacteristic
387C23×C29H(5,𝔽2)11yescharacteristic
388C23×C29H(5,𝔽2)11yescharacteristic
389C23×C292−1+411yescharacteristic
390C23×C292−1+411yescharacteristic
391C23×C292−1+411yescharacteristic
392D4×C29—416no—
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—416no—
421C2×C4×C29—41no—
422C2×C4×C29—41no—
423C2×C4×C29—41no—
424C2×C4×C29—41no—
425C2×C4×C29—41no—
426C2×C4×C29—41no—
427C2×C4×C29—41no—
428C2×C4×C29—41no—
429C2×C4×C29—41no—
430C2×C4×C29—41no—
431C2×C4×C29—41no—
432C2×C4×C29—41no—
433C2×C4×C29—41no—
434C2×C4×C29—41no—
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—41no—
482C2×C4×C29—41no—
483C2×C4×C29—41no—
484C2×C4×C29—41no—
485C2×#397C2×C2911yescharacteristic, complemented
486C2×#396C2×C2911yescharacteristic, complemented
487C2×#394C2×C2911yescharacteristic
488C2×#394C2×C2911yescharacteristic
489C2×#386C2×C2911yescharacteristic
490C2×#385C2×C2911yescharacteristic, complemented
491#1445C2×C2911yescharacteristic, complemented
492#1444C2×C2911yescharacteristic, complemented
493#1441C2×C2911yescharacteristic, complemented
494#1441C2×C2911yescharacteristic, complemented
495#1440C2×C2911yescharacteristic, complemented
496#1440C2×C2911yescharacteristic, complemented
497#1439C2×C2911yescharacteristic, complemented
498#1439C2×C2911yescharacteristic, complemented
499C22⋊#95C2×C2911yescharacteristic, complemented
500C22×C29—24no—
501C22×C29—24no—
502C22×C29—24no—
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—42no—
522C22×C29—81no—
523C22×C29—81no—
524C22×C29—81no—
525C22×C29—81no—
526C22×C29—81no—
527C22×C29—81no—
528C22×C29—81no—
529C22×C29—81no—
530C22×C29C2×#12111yescharacteristic
531C22×C29#52511yescharacteristic
532C22×C29#52911yescharacteristic
533C22×C29#53411yescharacteristic
534C22×C29#53411yescharacteristic
535C22×C29#53611yescharacteristic
536C22×C29#53611yescharacteristic
537C22×C29#53711yescharacteristic
538C22×C29#53711yescharacteristic
539C22×C29#53811yescharacteristic
540C22×C29#53811yescharacteristic
541C22×C29#53911yescharacteristic
542C22×C29#53911yescharacteristic
543C22×C29#53911yescharacteristic
544C22×C29#53911yescharacteristic
545C22×C29#54011yescharacteristic
546C22×C29#54211yescharacteristic
547C22×C29#54211yescharacteristic
548C22×C29#54211yescharacteristic
549C22×C29D4211yescharacteristic
550C22×C29D4211yescharacteristic
551C22×C29#54611yescharacteristic
552C22×C29#54611yescharacteristic
553C22×C29#54611yescharacteristic
554C22×C29#54611yescharacteristic
555C22×C29#54611yescharacteristic
556C22×C29#54711yescharacteristic
557C22×C29#54711yescharacteristic
558C22×C29#54711yescharacteristic
559C22×C29#55311yescharacteristic
560C22×C29#55611yescharacteristic
561C22×C29#56011yescharacteristic
562C22×C29#56211yescharacteristic
563C22×C29#56211yescharacteristic
564C22×C29#56311yescharacteristic
565C4×C29—42no—
566C4×C29—42no—
567C4×C29—42no—
568C4×C29—42no—
569C4×C29—42no—
570C4×C29—42no—
571C4×C29—42no—
572C4×C29—42no—
573C4×C29—42no—
574C4×C29—81no—
575C4×C29—81no—
576C4×C29—81no—
577C4×C29—81no—
578C23×D4C22×C2911yescharacteristic
579C24×C4C22×C2911yescharacteristic
580C22×C4⋊C4C22×C2911yescharacteristic
581C22×C4⋊C4C22×C2911yescharacteristic
582C22×C4⋊C4C22×C2911yescharacteristic
583C22×C4⋊C4C22×C2911yescharacteristic
584C22×C4⋊C4C22×C2911yescharacteristic
585C22×C4⋊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×C22⋊C4C22×C2911yescharacteristic
593C22×C22⋊C4C22×C2911yescharacteristic
594C22×C22⋊C4C22×C2911yescharacteristic
595C22×C22⋊C4C22×C2911yescharacteristic
596C22×C22⋊C4C22×C2911yescharacteristic
597#397—24no—
598#396—24no—
599#394—24no—
600#394—24no—
601#386—24no—
602#385—24no—
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×#95C22×C2911yescharacteristic
618C2×#95C22×C2911yescharacteristic
619C2×C29—44no—
620C2×C29—82no—
621C2×C29#242411yescharacteristic
622C2×C29#242511yescharacteristic
623C2×C29#246611yescharacteristic
624C2×C29#261811yescharacteristic
625C2×C29#263811yescharacteristic
626C2×C29#264911yescharacteristic
627C2×C29#266811yescharacteristic
628C2×C29#267111yescharacteristic
629C2×C29#267211yescharacteristic
630C2×C29#268011yescharacteristic
631C2×C29#269111yescharacteristic
632C2×C29#270011yescharacteristic
633C2×C29#270111yescharacteristic
634C2×C29#271511yescharacteristic
635C2×C29#282711yescharacteristic
636C25C23×C2911yescharacteristic
637C25C23×C2911yescharacteristic
638C22×D4—22no—
639C22×D4—22no—
640C22×D4—22no—
641C22×D4—22no—
642C22×D4—22no—
643C22×D4—41no—
644C22×D4—41no—
645C23×C4—22no—
646C23×C4—22no—
647C23×C4—22no—
648C23×C4—41no—
649C23×C4—41no—
650C23×C4—41no—
651C23×C4—41no—
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
663C23×C4C23×C2911yescharacteristic
664C23×C4C23×C2911yescharacteristic
665C2×C4⋊C4—22no—
666C2×C4⋊C4—22no—
667C2×C4⋊C4—22no—
668C2×C4⋊C4—22no—
669C2×C4⋊C4—22no—
670C2×C4⋊C4—22no—
671C2×C4⋊C4—22no—
672C2×C4⋊C4—22no—
673C2×C4⋊C4—22no—
674C2×C4⋊C4—22no—
675C2×C4⋊C4—22no—
676C2×C4⋊C4—41no—
677C2×C4⋊C4—41no—
678C2×C4⋊C4—41no—
679C2×C4⋊C4—41no—
680C2×C4⋊C4—41no—
681C2×C4⋊C4—41no—
682C2×C4⋊C4—41no—
683C2×C22⋊C4—22no—
684C2×C22⋊C4—22no—
685C2×C22⋊C4—22no—
686C2×C22⋊C4—22no—
687C2×C22⋊C4—22no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—22no—
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—41no—
702C2×C22⋊C4—41no—
703C2×C22⋊C4—41no—
704C2×C22⋊C4—41no—
705C2×C22⋊C4—41no—
706C2×C22⋊C4—41no—
707C2×C22⋊C4—41no—
708C2×C22⋊C4—41no—
709C2×C22⋊C4—41no—
710C2×C22⋊C4—41no—
711C2×C22⋊C4—41no—
712C2×C22⋊C4—41no—
713C2×C22⋊C4D4×C2914yes—
714C2×C22⋊C4D4×C2914yes—
715C2×C22⋊C4D4×C2914yes—
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—22no—
725#95—22no—
726#95—22no—
727#95—41no—
728#95—41no—
729#95—41no—
730#95—41no—
731#95—41no—
732C29#1628511yescharacteristic, direct product factor, Sylow
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—
757C24—21no—
758C24—21no—
759C24C2×D4×C2912yes—
760C24C2×D4×C2912yes—
761C24C2×D4×C2912yes—
762C24#41×C2912yes—
763C24C24×C2911yescharacteristic
764C2×D4—28no—
765C2×D4—44no—
766C2×D4—44no—
767C2×D4—44no—
768C2×D4—44no—
769C2×D4—44no—
770C2×D4—44no—
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—21no—
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—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—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—44no—
854C22×C4—44no—
855C22×C4—44no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—44no—
860C22×C4C2×D4×C2912yes—
861C22×C4C2×D4×C2912yes—
862C22×C4C2×D4×C2912yes—
863C22×C4C2×D4×C2912yes—
864C22×C4C2×D4×C2912yes—
865C22×C4C2×D4×C2912yes—
866C22×C4#41×C2912yes—
867C22×C4#41×C2912yes—
868C22×C4#41×C2912yes—
869C4⋊C4—44no—
870C4⋊C4—44no—
871C4⋊C4—44no—
872C4⋊C4—44no—
873C4⋊C4—44no—
874C4⋊C4—44no—
875C22⋊C4—28no—
876C22⋊C4—44no—
877C22⋊C4—44no—
878C22⋊C4—44no—
879C22⋊C4—44no—
880C22⋊C4—44no—
881C22⋊C4—44no—
882C22⋊C4—44no—
883C22⋊C4—44no—
884C22⋊C4—44no—
885C22⋊C4—44no—
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—22no—
910C23—22no—
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—
953C23—41no—
954C23—41no—
955C23C29×#12114yes—
956C23C22×D4×C2911yescharacteristic
957C23C22×D4×C2911yescharacteristic
958C23C22×D4×C2911yescharacteristic
959C23C2×#41×C2911yescharacteristic
960C23C2×#41×C2911yescharacteristic
961C23C2×#41×C2911yescharacteristic
962C23C2×#41×C2911yescharacteristic
963C23C29×H(5,𝔽2)11yescharacteristic
964C23C29×H(5,𝔽2)11yescharacteristic
965C23C29×H(5,𝔽2)11yescharacteristic
966C23C29×H(5,𝔽2)11yescharacteristic
967C23C29×H(5,𝔽2)11yescharacteristic
968C23C29×2−1+411yescharacteristic
969C23C29×2−1+411yescharacteristic
970C23C29×2−1+411yescharacteristic
971D4—416no—
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—416no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
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×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C22—24no—
1065C22—24no—
1066C22—24no—
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—42no—
1085C22—42no—
1086C22—81no—
1087C22—81no—
1088C22—81no—
1089C22—81no—
1090C22—81no—
1091C22—81no—
1092C22—81no—
1093C22—81no—
1094C22C2×C29×#12111yescharacteristic
1095C22C29×#52511yescharacteristic
1096C22C29×#52911yescharacteristic
1097C22C29×#53411yescharacteristic
1098C22C29×#53411yescharacteristic
1099C22C29×#53611yescharacteristic
1100C22C29×#53611yescharacteristic
1101C22C29×#53711yescharacteristic
1102C22C29×#53711yescharacteristic
1103C22C29×#53811yescharacteristic
1104C22C29×#53811yescharacteristic
1105C22C29×#53911yescharacteristic
1106C22C29×#53911yescharacteristic
1107C22C29×#53911yescharacteristic
1108C22C29×#53911yescharacteristic
1109C22C29×#54011yescharacteristic
1110C22C29×#54211yescharacteristic
1111C22C29×#54211yescharacteristic
1112C22C29×#54211yescharacteristic
1113C22D42×C2911yescharacteristic
1114C22D42×C2911yescharacteristic
1115C22C29×#54611yescharacteristic
1116C22C29×#54611yescharacteristic
1117C22C29×#54611yescharacteristic
1118C22C29×#54611yescharacteristic
1119C22C29×#54611yescharacteristic
1120C22C29×#54711yescharacteristic
1121C22C29×#54711yescharacteristic
1122C22C29×#54711yescharacteristic
1123C22C29×#55311yescharacteristic
1124C22C29×#55611yescharacteristic
1125C22C29×#56011yescharacteristic
1126C22C29×#56211yescharacteristic
1127C22C29×#56211yescharacteristic
1128C22C29×#56311yescharacteristic
1129C4—42no—
1130C4—42no—
1131C4—42no—
1132C4—42no—
1133C4—42no—
1134C4—42no—
1135C4—42no—
1136C4—42no—
1137C4—42no—
1138C4—81no—
1139C4—81no—
1140C4—81no—
1141C4—81no—
1142C2—44no—
1143C2—82no—
1144C2C29×#242411yescharacteristic
1145C2C29×#242511yescharacteristic
1146C2C29×#246611yescharacteristic
1147C2C29×#261811yescharacteristic
1148C2C29×#263811yescharacteristic
1149C2C29×#264911yescharacteristic
1150C2C29×#266811yescharacteristic
1151C2C29×#267111yescharacteristic
1152C2C29×#267211yescharacteristic
1153C2C29×#268011yescharacteristic
1154C2C29×#269111yescharacteristic
1155C2C29×#270011yescharacteristic
1156C2C29×#270111yescharacteristic
1157C2C29×#271511yescharacteristic
1158C2C29×#282711yescharacteristic
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
1. C2×C29×#397C2semidirect
2. C2×C29×#396C2semidirect
6. C2×C29×#385C2semidirect
7. C29×#1445C2semidirect
8. C29×#1444C2semidirect
9. C29×#1441C2semidirect
10. C29×#1441C2semidirect
11. C29×#1440C2semidirect
12. C29×#1440C2semidirect
13. C29×#1439C2semidirect
14. C29×#1439C2semidirect
15. C29×C22⋊#95C2semidirect
306. #16285C29direct (N × H)
485. C2×#397C2×C29semidirect
486. C2×#396C2×C29semidirect
490. C2×#385C2×C29semidirect
491. #1445C2×C29semidirect
492. #1444C2×C29semidirect
493. #1441C2×C29semidirect
494. #1441C2×C29semidirect
495. #1440C2×C29semidirect
496. #1440C2×C29semidirect
497. #1439C2×C29semidirect
498. #1439C2×C29semidirect
499. C22⋊#95C2×C29semidirect
732. C29#16285direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#3972
C2×C29×#3962
C2×C29×#3942
C2×C29×#3862
C2×C29×#3852
C29×#14452
C29×#14442
C29×#14412
C29×#14402
C29×#14392
C29×C22⋊#952
#1628529