Finite Group Databasebeta

← C29×#14823 #20309723

Subgroups — C29×#14823 #20309723

Order 7424.

2154 conjugacy classes of subgroups.

The subgroup lattice has 1172 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C29C211yesmaximal, characteristic
2C2×C29×#397C211yesmaximal, characteristic, complemented
3C2×C29×#394C211yesmaximal, characteristic
4C2×C29×#381C211yesmaximal, characteristic, complemented
5C29×#1442C211yesmaximal, characteristic, complemented
6C29×#1441C211yesmaximal, characteristic, complemented
7C29×#1440C211yesmaximal, characteristic, complemented
8C29×#1440C211yesmaximal, characteristic, complemented
9C29×#1439C211yesmaximal, characteristic, complemented
10C29×#1438C211yesmaximal, characteristic
11C29×#1436C211yesmaximal, characteristic, complemented
12C29×#1436C211yesmaximal, characteristic, complemented
13C29×C22⋊#95C211yesmaximal, characteristic, complemented
14C29×C22⋊#95C211yesmaximal, characteristic, complemented
15C29×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C29C2211yescharacteristic
17C24×C4×C29C2211yescharacteristic
18C24×C4×C29C2211yescharacteristic
19C2×C4×D4×C29—24no—
20C2×C4×D4×C29—24no—
21C2×C4×D4×C29—24no—
22C22×C4⋊C4×C29C2211yescharacteristic
23C22×C4⋊C4×C29C2211yescharacteristic
24C22×C4⋊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
35C22×C42×C29C2211yescharacteristic
36C29×#397—24no—
37C29×#394—24no—
38C29×#381—24no—
39C2×C29×#95C2211yescharacteristic
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
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—22no—
65C22×D4×C29D414yes—
66C23×C4×C29—22no—
67C23×C4×C29—22no—
68C23×C4×C29—22no—
69C23×C4×C29—22no—
70C23×C4×C29—22no—
71C23×C4×C29—22no—
72C23×C4×C29—22no—
73C23×C4×C29—22no—
74C23×C4×C29—22no—
75C23×C4×C29—41no—
76C23×C4×C29—41no—
77C23×C4×C29—41no—
78C23×C4×C29—41no—
79C23×C4×C29D414yes—
80C23×C4×C29C2311yescharacteristic
81C23×C4×C29C2311yescharacteristic
82C23×C4×C29C2311yescharacteristic
83C23×C4×C29C2311yescharacteristic
84C23×C4×C29C2311yescharacteristic
85C23×C4×C29C2311yescharacteristic
86C23×C4×C29C2311yescharacteristic
87C23×C4×C29C2311yescharacteristic
88C23×C4×C29C2311yescharacteristic
89C23×C4×C29C2311yescharacteristic
90C23×C4×C29C2311yescharacteristic
91C23×C4×C29C2311yescharacteristic
92C23×C4×C29C2311yescharacteristic
93C4×D4×C29—232no—
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—41no—
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—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—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×C29D414yes—
133C2×C42×C29—22no—
134C2×C42×C29—22no—
135C2×C42×C29—22no—
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—22no—
147C29×#95—22no—
148C29×#95—22no—
149C29×#95—41no—
150C29×#95—41no—
151C29×#95—41no—
152C29×#95—41no—
153C29×#95—41no—
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×C29C2×D412yes—
179C24×C29C2×D412yes—
180C24×C29C2×D412yes—
181C24×C29C2×D412yes—
182C24×C29#4112yes—
183C24×C29#4112yes—
184C24×C29C2411yescharacteristic
185C2×D4×C29—28no—
186C2×D4×C29—28no—
187C2×D4×C29—28no—
188C2×D4×C29—28no—
189C2×D4×C29—28no—
190C2×D4×C29—28no—
191C2×D4×C29—28no—
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—28no—
201C22×C4×C29—28no—
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—28no—
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—21no—
274C22×C4×C29—21no—
275C22×C4×C29—44no—
276C22×C4×C29—44no—
277C22×C4×C29—44no—
278C22×C4×C29—44no—
279C22×C4×C29—44no—
280C22×C4×C29—44no—
281C22×C4×C29—44no—
282C22×C4×C29—44no—
283C22×C4×C29—44no—
284C22×C4×C29—44no—
285C22×C4×C29—44no—
286C22×C4×C29C2×D412yes—
287C22×C4×C29C2×D412yes—
288C22×C4×C29C2×D412yes—
289C22×C4×C29C2×D412yes—
290C22×C4×C29C2×D412yes—
291C22×C4×C29#4112yes—
292C22×C4×C29#4112yes—
293C22×C4×C29#4112yes—
294C22×C4×C29#4112yes—
295C22×C4×C29#4112yes—
296C22×C4×C29#4112yes—
297C4⋊C4×C29—28no—
298C4⋊C4×C29—44no—
299C4⋊C4×C29—44no—
300C22⋊C4×C29—28no—
301C22⋊C4×C29—28no—
302C22⋊C4×C29—44no—
303C22⋊C4×C29—44no—
304C22⋊C4×C29—44no—
305C22⋊C4×C29—44no—
306C22⋊C4×C29—44no—
307C22⋊C4×C29—44no—
308C22⋊C4×C29—44no—
309C22⋊C4×C29—44no—
310C42×C29—28no—
311#14823C2911yesmaximal, characteristic, direct product factor, Sylow
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—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—22no—
342C23×C29—22no—
343C23×C29—22no—
344C23×C29—22no—
345C23×C29—22no—
346C23×C29—22no—
347C23×C29—22no—
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#12014yes—
381C23×C29#12314yes—
382C23×C29C22×D411yescharacteristic
383C23×C29C22×D411yescharacteristic
384C23×C29C22×D411yescharacteristic
385C23×C29C2×#4111yescharacteristic
386C23×C29C2×#4111yescharacteristic
387C23×C29C2×#4111yescharacteristic
388C23×C29C2×#4111yescharacteristic
389C23×C29C2×#4111yescharacteristic
390C23×C29C2×#4111yescharacteristic
391C23×C29C2×#4111yescharacteristic
392C23×C29C2×#4111yescharacteristic
393C23×C29H(5,𝔽2)11yescharacteristic
394C23×C29H(5,𝔽2)11yescharacteristic
395C23×C29H(5,𝔽2)11yescharacteristic
396C23×C292−1+411yescharacteristic
397D4×C29—232no—
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—416no—
426C2×C4×C29—416no—
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×C4×C29—41no—
486C2×C4×C29—41no—
487C2×C4×C29—41no—
488C2×C4×C29—41no—
489C2×C4×C29#12314yes—
490C2×C4×C29#12314yes—
491C22×C4×D4C2×C2911yescharacteristic
492C2×#397C2×C2911yescharacteristic, complemented
493C2×#394C2×C2911yescharacteristic
494C2×#381C2×C2911yescharacteristic, complemented
495#1442C2×C2911yescharacteristic, complemented
496#1441C2×C2911yescharacteristic, complemented
497#1440C2×C2911yescharacteristic, complemented
498#1440C2×C2911yescharacteristic, complemented
499#1439C2×C2911yescharacteristic, complemented
500#1438C2×C2911yescharacteristic
501#1436C2×C2911yescharacteristic, complemented
502#1436C2×C2911yescharacteristic, complemented
503C22⋊#95C2×C2911yescharacteristic, complemented
504C22⋊#95C2×C2911yescharacteristic, complemented
505C22⋊#95C2×C2911yescharacteristic, complemented
506C22×C29—24no—
507C22×C29—24no—
508C22×C29—24no—
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—42no—
532C22×C29—42no—
533C22×C29—42no—
534C22×C29—42no—
535C22×C29—42no—
536C22×C29C2×#12011yescharacteristic
537C22×C29C2×#12311yescharacteristic
538C22×C29C2×#12311yescharacteristic
539C22×C29C2×#12311yescharacteristic
540C22×C29#52511yescharacteristic
541C22×C29#52511yescharacteristic
542C22×C29#52511yescharacteristic
543C22×C29#52511yescharacteristic
544C22×C29#52911yescharacteristic
545C22×C29#52911yescharacteristic
546C22×C29#52911yescharacteristic
547C22×C29#52911yescharacteristic
548C22×C29#53211yescharacteristic
549C22×C29#53411yescharacteristic
550C22×C29#53711yescharacteristic
551C22×C29#53811yescharacteristic
552C22×C29#53911yescharacteristic
553C22×C29#54011yescharacteristic
554C22×C29#54211yescharacteristic
555C22×C29#54611yescharacteristic
556C22×C29#54611yescharacteristic
557C22×C29#54611yescharacteristic
558C22×C29#54611yescharacteristic
559C22×C29#54611yescharacteristic
560C22×C29#54611yescharacteristic
561C22×C29#54711yescharacteristic
562C22×C29#54711yescharacteristic
563C22×C29#55111yescharacteristic
564C22×C29#55211yescharacteristic
565C22×C29#55311yescharacteristic
566C22×C29#55311yescharacteristic
567C22×C29#55311yescharacteristic
568C22×C29#55511yescharacteristic
569C22×C29#55611yescharacteristic
570C22×C29#55911yescharacteristic
571C4×C29—24no—
572C4×C29—24no—
573C4×C29—42no—
574C4×C29—42no—
575C4×C29—42no—
576C4×C29—42no—
577C4×C29—42no—
578C4×C29—81no—
579C4×C29—81no—
580C4×C29—81no—
581C4×C29—81no—
582C4×C29—81no—
583C4×C29—81no—
584C23×D4C22×C2911yescharacteristic
585C24×C4C22×C2911yescharacteristic
586C24×C4C22×C2911yescharacteristic
587C2×C4×D4—24no—
588C2×C4×D4—24no—
589C2×C4×D4—24no—
590C22×C4⋊C4C22×C2911yescharacteristic
591C22×C4⋊C4C22×C2911yescharacteristic
592C22×C4⋊C4C22×C2911yescharacteristic
593C22×C22⋊C4C22×C2911yescharacteristic
594C22×C22⋊C4C22×C2911yescharacteristic
595C22×C22⋊C4C22×C2911yescharacteristic
596C22×C22⋊C4C22×C2911yescharacteristic
597C22×C22⋊C4C22×C2911yescharacteristic
598C22×C22⋊C4C22×C2911yescharacteristic
599C22×C22⋊C4C22×C2911yescharacteristic
600C22×C22⋊C4C22×C2911yescharacteristic
601C22×C22⋊C4C22×C2911yescharacteristic
602C22×C22⋊C4C22×C2911yescharacteristic
603C22×C42C22×C2911yescharacteristic
604#397—24no—
605#394—24no—
606#381—24no—
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×#95C22×C2911yescharacteristic
620C2×#95C22×C2911yescharacteristic
621C2×#95C22×C2911yescharacteristic
622C2×#95C22×C2911yescharacteristic
623C2×#95C22×C2911yescharacteristic
624C2×#95C22×C2911yescharacteristic
625C2×C29—44no—
626C2×C29—44no—
627C2×C29#239511yescharacteristic
628C2×C29#240511yescharacteristic
629C2×C29#241911yescharacteristic
630C2×C29#242011yescharacteristic
631C2×C29#243011yescharacteristic
632C2×C29#244411yescharacteristic
633C2×C29#244711yescharacteristic
634C2×C29#245711yescharacteristic
635C2×C29#245911yescharacteristic
636C2×C29#246611yescharacteristic
637C2×C29#246811yescharacteristic
638C2×C29#248511yescharacteristic
639C2×C29#260211yescharacteristic
640C2×C29#263011yescharacteristic
641C2×C29#284911yescharacteristic
642C25C23×C2911yescharacteristic
643C25C23×C2911yescharacteristic
644C22×D4—22no—
645C22×D4—22no—
646C22×D4—22no—
647C22×D4—22no—
648C22×D4—22no—
649C22×D4—22no—
650C22×D4D4×C2914yes—
651C23×C4—22no—
652C23×C4—22no—
653C23×C4—22no—
654C23×C4—22no—
655C23×C4—22no—
656C23×C4—22no—
657C23×C4—22no—
658C23×C4—22no—
659C23×C4—22no—
660C23×C4—41no—
661C23×C4—41no—
662C23×C4—41no—
663C23×C4—41no—
664C23×C4D4×C2914yes—
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
676C23×C4C23×C2911yescharacteristic
677C23×C4C23×C2911yescharacteristic
678C4×D4—232no—
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—41no—
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—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—41no—
710C2×C22⋊C4—41no—
711C2×C22⋊C4—41no—
712C2×C22⋊C4—41no—
713C2×C22⋊C4—41no—
714C2×C22⋊C4—41no—
715C2×C22⋊C4—41no—
716C2×C22⋊C4—41no—
717C2×C22⋊C4D4×C2914yes—
718C2×C42—22no—
719C2×C42—22no—
720C2×C42—22no—
721#95—22no—
722#95—22no—
723#95—22no—
724#95—22no—
725#95—22no—
726#95—22no—
727#95—22no—
728#95—22no—
729#95—22no—
730#95—22no—
731#95—22no—
732#95—22no—
733#95—22no—
734#95—41no—
735#95—41no—
736#95—41no—
737#95—41no—
738#95—41no—
739C29#1482311yescharacteristic, direct product factor, Sylow
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—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24C2×D4×C2912yes—
765C24C2×D4×C2912yes—
766C24C2×D4×C2912yes—
767C24C2×D4×C2912yes—
768C24#41×C2912yes—
769C24#41×C2912yes—
770C24C24×C2911yescharacteristic
771C2×D4—28no—
772C2×D4—28no—
773C2×D4—28no—
774C2×D4—28no—
775C2×D4—28no—
776C2×D4—28no—
777C2×D4—28no—
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—28no—
787C22×C4—28no—
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—28no—
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—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—44no—
862C22×C4—44no—
863C22×C4—44no—
864C22×C4—44no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C4—44no—
868C22×C4—44no—
869C22×C4—44no—
870C22×C4—44no—
871C22×C4—44no—
872C22×C4C2×D4×C2912yes—
873C22×C4C2×D4×C2912yes—
874C22×C4C2×D4×C2912yes—
875C22×C4C2×D4×C2912yes—
876C22×C4C2×D4×C2912yes—
877C22×C4#41×C2912yes—
878C22×C4#41×C2912yes—
879C22×C4#41×C2912yes—
880C22×C4#41×C2912yes—
881C22×C4#41×C2912yes—
882C22×C4#41×C2912yes—
883C4⋊C4—28no—
884C4⋊C4—44no—
885C4⋊C4—44no—
886C22⋊C4—28no—
887C22⋊C4—28no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4—44no—
891C22⋊C4—44no—
892C22⋊C4—44no—
893C22⋊C4—44no—
894C22⋊C4—44no—
895C22⋊C4—44no—
896C42—28no—
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—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—22no—
930C23—22no—
931C23—22no—
932C23—22no—
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—
965C23C29×#12014yes—
966C23C29×#12314yes—
967C23C22×D4×C2911yescharacteristic
968C23C22×D4×C2911yescharacteristic
969C23C22×D4×C2911yescharacteristic
970C23C2×#41×C2911yescharacteristic
971C23C2×#41×C2911yescharacteristic
972C23C2×#41×C2911yescharacteristic
973C23C2×#41×C2911yescharacteristic
974C23C2×#41×C2911yescharacteristic
975C23C2×#41×C2911yescharacteristic
976C23C2×#41×C2911yescharacteristic
977C23C2×#41×C2911yescharacteristic
978C23C29×H(5,𝔽2)11yescharacteristic
979C23C29×H(5,𝔽2)11yescharacteristic
980C23C29×H(5,𝔽2)11yescharacteristic
981C23C29×2−1+411yescharacteristic
982D4—232no—
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—416no—
1011C2×C4—416no—
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—
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×C4C29×#12314yes—
1075C2×C4C29×#12314yes—
1076C22—24no—
1077C22—24no—
1078C22—24no—
1079C22—24no—
1080C22—24no—
1081C22—24no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
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—42no—
1105C22—42no—
1106C22C2×C29×#12011yescharacteristic
1107C22C2×C29×#12311yescharacteristic
1108C22C2×C29×#12311yescharacteristic
1109C22C2×C29×#12311yescharacteristic
1110C22C29×#52511yescharacteristic
1111C22C29×#52511yescharacteristic
1112C22C29×#52511yescharacteristic
1113C22C29×#52511yescharacteristic
1114C22C29×#52911yescharacteristic
1115C22C29×#52911yescharacteristic
1116C22C29×#52911yescharacteristic
1117C22C29×#52911yescharacteristic
1118C22C29×#53211yescharacteristic
1119C22C29×#53411yescharacteristic
1120C22C29×#53711yescharacteristic
1121C22C29×#53811yescharacteristic
1122C22C29×#53911yescharacteristic
1123C22C29×#54011yescharacteristic
1124C22C29×#54211yescharacteristic
1125C22C29×#54611yescharacteristic
1126C22C29×#54611yescharacteristic
1127C22C29×#54611yescharacteristic
1128C22C29×#54611yescharacteristic
1129C22C29×#54611yescharacteristic
1130C22C29×#54611yescharacteristic
1131C22C29×#54711yescharacteristic
1132C22C29×#54711yescharacteristic
1133C22C29×#55111yescharacteristic
1134C22C29×#55211yescharacteristic
1135C22C29×#55311yescharacteristic
1136C22C29×#55311yescharacteristic
1137C22C29×#55311yescharacteristic
1138C22C29×#55511yescharacteristic
1139C22C29×#55611yescharacteristic
1140C22C29×#55911yescharacteristic
1141C4—24no—
1142C4—24no—
1143C4—42no—
1144C4—42no—
1145C4—42no—
1146C4—42no—
1147C4—42no—
1148C4—81no—
1149C4—81no—
1150C4—81no—
1151C4—81no—
1152C4—81no—
1153C4—81no—
1154C2—44no—
1155C2—44no—
1156C2C29×#239511yescharacteristic
1157C2C29×#240511yescharacteristic
1158C2C29×#241911yescharacteristic
1159C2C29×#242011yescharacteristic
1160C2C29×#243011yescharacteristic
1161C2C29×#244411yescharacteristic
1162C2C29×#244711yescharacteristic
1163C2C29×#245711yescharacteristic
1164C2C29×#245911yescharacteristic
1165C2C29×#246611yescharacteristic
1166C2C29×#246811yescharacteristic
1167C2C29×#248511yescharacteristic
1168C2C29×#260211yescharacteristic
1169C2C29×#263011yescharacteristic
1170C2C29×#284911yescharacteristic
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
2. C2×C29×#397C2semidirect
4. C2×C29×#381C2semidirect
5. C29×#1442C2semidirect
6. C29×#1441C2semidirect
7. C29×#1440C2semidirect
8. C29×#1440C2semidirect
9. C29×#1439C2semidirect
11. C29×#1436C2semidirect
12. C29×#1436C2semidirect
13. C29×C22⋊#95C2semidirect
14. C29×C22⋊#95C2semidirect
15. C29×C22⋊#95C2semidirect
311. #14823C29direct (N × H)
492. C2×#397C2×C29semidirect
494. C2×#381C2×C29semidirect
495. #1442C2×C29semidirect
496. #1441C2×C29semidirect
497. #1440C2×C29semidirect
498. #1440C2×C29semidirect
499. #1439C2×C29semidirect
501. #1436C2×C29semidirect
502. #1436C2×C29semidirect
503. C22⋊#95C2×C29semidirect
504. C22⋊#95C2×C29semidirect
505. C22⋊#95C2×C29semidirect
739. C29#14823direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×D4×C292
C2×C29×#3972
C2×C29×#3942
C2×C29×#3812
C29×#14422
C29×#14412
C29×#14402
C29×#14392
C29×#14382
C29×#14362
C29×C22⋊#952
#1482329