Finite Group Databasebeta

← C29×#14799 #20309699

Subgroups — C29×#14799 #20309699

Order 7424.

1786 conjugacy classes of subgroups.

The subgroup lattice has 1150 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#394C211yesmaximal, characteristic
2C2×C29×#390C211yesmaximal, characteristic
3C2×C29×#388C211yesmaximal, characteristic, complemented
4C2×C29×#388C211yesmaximal, characteristic, complemented
5C2×C29×#388C211yesmaximal, characteristic, complemented
6C2×C4×C4⋊C4×C29C211yesmaximal, characteristic, complemented
7C29×#1441C211yesmaximal, characteristic, complemented
8C29×#1441C211yesmaximal, characteristic, complemented
9C29×#1440C211yesmaximal, characteristic, complemented
10C29×#1439C211yesmaximal, characteristic, complemented
11C29×#1439C211yesmaximal, characteristic, complemented
12C29×#1439C211yesmaximal, characteristic, complemented
13C29×#1438C211yesmaximal, characteristic
14C29×#1437C211yesmaximal, characteristic, complemented
15C29×#1436C211yesmaximal, characteristic, complemented
16C23×D4×C29C2211yescharacteristic
17C22×C4⋊C4×C29C2211yescharacteristic
18C22×C4⋊C4×C29C2211yescharacteristic
19C22×C4⋊C4×C29C2211yescharacteristic
20C22×C4⋊C4×C29C2211yescharacteristic
21C22×C4⋊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×C22⋊C4×C29C2211yescharacteristic
32C22×C22⋊C4×C29C2211yescharacteristic
33C22×C22⋊C4×C29C2211yescharacteristic
34C22×C42×C29C2211yescharacteristic
35C22×C42×C29C2211yescharacteristic
36C22×C42×C29C2211yescharacteristic
37C29×#394—24no—
38C29×#390—24no—
39C29×#388—24no—
40C29×#388—24no—
41C29×#388—24no—
42C4×C4⋊C4×C29—24no—
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×C29C2311yescharacteristic
67C23×C4×C29C2311yescharacteristic
68C23×C4×C29C2311yescharacteristic
69C23×C4×C29C2311yescharacteristic
70C23×C4×C29C2311yescharacteristic
71C23×C4×C29C2311yescharacteristic
72C23×C4×C29C2311yescharacteristic
73C23×C4×C29C2311yescharacteristic
74C23×C4×C29C2311yescharacteristic
75C23×C4×C29C2311yescharacteristic
76C23×C4×C29C2311yescharacteristic
77C23×C4×C29C2311yescharacteristic
78C23×C4×C29C2311yescharacteristic
79C2×C4⋊C4×C29—22no—
80C2×C4⋊C4×C29—22no—
81C2×C4⋊C4×C29—22no—
82C2×C4⋊C4×C29—22no—
83C2×C4⋊C4×C29—22no—
84C2×C4⋊C4×C29—22no—
85C2×C4⋊C4×C29—22no—
86C2×C4⋊C4×C29—22no—
87C2×C4⋊C4×C29—22no—
88C2×C4⋊C4×C29—22no—
89C2×C4⋊C4×C29—22no—
90C2×C4⋊C4×C29—41no—
91C2×C4⋊C4×C29—41no—
92C2×C4⋊C4×C29—41no—
93C2×C4⋊C4×C29D414yes—
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—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—41no—
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×C29D414yes—
130C2×C42×C29—22no—
131C2×C42×C29—22no—
132C2×C42×C29—22no—
133C2×C42×C29—22no—
134C2×C42×C29—22no—
135C2×C42×C29—22no—
136C2×C42×C29—41no—
137C2×C42×C29—41no—
138C2×C42×C29D414yescomplemented
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—22no—
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×C29—21no—
180C24×C29—21no—
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×C29C2×D412yes—
268C22×C4×C29C2×D412yes—
269C22×C4×C29C2×D412yes—
270C22×C4×C29C2×D412yes—
271C22×C4×C29C2×D412yes—
272C22×C4×C29C2×D412yes—
273C22×C4×C29C2×D412yes—
274C22×C4×C29C2×D412yes—
275C22×C4×C29#4112yes—
276C22×C4×C29#4112yes—
277C22×C4×C29#4112yes—
278C22×C4×C29#4112yes—
279C22×C4×C29#4112yes—
280C22×C4×C29#4112yes—
281C22×C4×C29#4112yes—
282C4⋊C4×C29—28no—
283C4⋊C4×C29—28no—
284C4⋊C4×C29—44no—
285C4⋊C4×C29—44no—
286C4⋊C4×C29—44no—
287C22⋊C4×C29—28no—
288C22⋊C4×C29—28no—
289C22⋊C4×C29—28no—
290C22⋊C4×C29—44no—
291C22⋊C4×C29—44no—
292C22⋊C4×C29—44no—
293C22⋊C4×C29—44no—
294C22⋊C4×C29—44no—
295C22⋊C4×C29—44no—
296C22⋊C4×C29—44no—
297C22⋊C4×C29—44no—
298C22⋊C4×C29—44no—
299C42×C29—28no—
300C42×C29—44no—
301C42×C29—44no—
302#14799C2911yesmaximal, characteristic, direct product factor, Sylow
303C23×C29—22no—
304C23×C29—22no—
305C23×C29—22no—
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—41no—
318C23×C29—41no—
319C23×C29—41no—
320C23×C29—41no—
321C23×C29—41no—
322C23×C29—41no—
323C23×C29—41no—
324C23×C29—41no—
325C23×C29—41no—
326C23×C29—41no—
327C23×C29—41no—
328C23×C29—41no—
329C23×C29—41no—
330C23×C29—41no—
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×C29C22×D411yescharacteristic
374C23×C29C22×D411yescharacteristic
375C23×C29C22×D411yescharacteristic
376C23×C29C2×#4111yescharacteristic
377C23×C29C2×#4111yescharacteristic
378C23×C29C2×#4111yescharacteristic
379C23×C29C2×#4111yescharacteristic
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×C292−1+411yescharacteristic
388D4×C29—416no—
389C2×C4×C29—22no—
390C2×C4×C29—22no—
391C2×C4×C29—22no—
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—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#12114yes—
478C2×C4×C29#12114yes—
479C2×C4×C29#12314yes—
480C2×#394C2×C2911yescharacteristic
481C2×#390C2×C2911yescharacteristic
482C2×#388C2×C2911yescharacteristic, complemented
483C2×#388C2×C2911yescharacteristic, complemented
484C2×#388C2×C2911yescharacteristic, complemented
485C2×C4×C4⋊C4C2×C2911yescharacteristic, complemented
486#1441C2×C2911yescharacteristic, complemented
487#1441C2×C2911yescharacteristic, complemented
488#1440C2×C2911yescharacteristic, complemented
489#1439C2×C2911yescharacteristic, complemented
490#1439C2×C2911yescharacteristic, complemented
491#1439C2×C2911yescharacteristic, complemented
492#1438C2×C2911yescharacteristic
493#1437C2×C2911yescharacteristic, complemented
494#1436C2×C2911yescharacteristic, complemented
495C22×C29—42no—
496C22×C29—42no—
497C22×C29—42no—
498C22×C29—42no—
499C22×C29—42no—
500C22×C29—42no—
501C22×C29—42no—
502C22×C29—42no—
503C22×C29—42no—
504C22×C29—42no—
505C22×C29—42no—
506C22×C29—42no—
507C22×C29—42no—
508C22×C29—42no—
509C22×C29—81no—
510C22×C29—81no—
511C22×C29—81no—
512C22×C29—81no—
513C22×C29—81no—
514C22×C29—81no—
515C22×C29—81no—
516C22×C29—81no—
517C22×C29—81no—
518C22×C29—81no—
519C22×C29—81no—
520C22×C29—81no—
521C22×C29—81no—
522C22×C29—81no—
523C22×C29—81no—
524C22×C29—81no—
525C22×C29C2×#12111yescharacteristic
526C22×C29C2×#12111yescharacteristic
527C22×C29C2×#12311yescharacteristic
528C22×C29#52511yescharacteristic
529C22×C29#52511yescharacteristic
530C22×C29#52511yescharacteristic
531C22×C29#52511yescharacteristic
532C22×C29#52911yescharacteristic
533C22×C29#52911yescharacteristic
534C22×C29#52911yescharacteristic
535C22×C29#52911yescharacteristic
536C22×C29#53211yescharacteristic
537C22×C29#53211yescharacteristic
538C22×C29#53511yescharacteristic
539C22×C29#53711yescharacteristic
540C22×C29#53811yescharacteristic
541C22×C29#53811yescharacteristic
542C22×C29#54211yescharacteristic
543C22×C29#54211yescharacteristic
544C22×C29D4211yescharacteristic
545C22×C29#54611yescharacteristic
546C22×C29#54611yescharacteristic
547C22×C29#54611yescharacteristic
548C22×C29#54711yescharacteristic
549C22×C29#54811yescharacteristic
550C22×C29#55011yescharacteristic
551C22×C29#55111yescharacteristic
552C22×C29#55211yescharacteristic
553C22×C29#55311yescharacteristic
554C22×C29#55311yescharacteristic
555C22×C29#55311yescharacteristic
556C22×C29#55511yescharacteristic
557C22×C29#55611yescharacteristic
558C22×C29#55911yescharacteristic
559C22×C29#55911yescharacteristic
560C4×C29—24no—
561C4×C29—24no—
562C4×C29—24no—
563C4×C29—42no—
564C4×C29—42no—
565C4×C29—42no—
566C4×C29—42no—
567C4×C29—42no—
568C4×C29—42no—
569C4×C29—81no—
570C4×C29—81no—
571C4×C29—81no—
572C4×C29—81no—
573C23×D4C22×C2911yescharacteristic
574C22×C4⋊C4C22×C2911yescharacteristic
575C22×C4⋊C4C22×C2911yescharacteristic
576C22×C4⋊C4C22×C2911yescharacteristic
577C22×C4⋊C4C22×C2911yescharacteristic
578C22×C4⋊C4C22×C2911yescharacteristic
579C22×C22⋊C4C22×C2911yescharacteristic
580C22×C22⋊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×C42C22×C2911yescharacteristic
592C22×C42C22×C2911yescharacteristic
593C22×C42C22×C2911yescharacteristic
594#394—24no—
595#390—24no—
596#388—24no—
597#388—24no—
598#388—24no—
599C4×C4⋊C4—24no—
600C2×#95C22×C2911yescharacteristic
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×C29—82no—
615C2×C29—82no—
616C2×C29#239211yescharacteristic
617C2×C29#241411yescharacteristic
618C2×C29#241611yescharacteristic
619C2×C29#241811yescharacteristic
620C2×C29#244811yescharacteristic
621C2×C29#245611yescharacteristic
622C2×C29#245811yescharacteristic
623C2×C29#246811yescharacteristic
624C2×C29#247411yescharacteristic
625C2×C29#254411yescharacteristic
626C2×C29#259311yescharacteristic
627C2×C29#259511yescharacteristic
628C2×C29#260111yescharacteristic
629C2×C29#266211yescharacteristic
630C2×C29#285411yescharacteristic
631C25C23×C2911yescharacteristic
632C25C23×C2911yescharacteristic
633C22×D4—22no—
634C22×D4—22no—
635C22×D4—22no—
636C22×D4—22no—
637C22×D4—22no—
638C22×D4—41no—
639C22×D4—41no—
640C23×C4C23×C2911yescharacteristic
641C23×C4C23×C2911yescharacteristic
642C23×C4C23×C2911yescharacteristic
643C23×C4C23×C2911yescharacteristic
644C23×C4C23×C2911yescharacteristic
645C23×C4C23×C2911yescharacteristic
646C23×C4C23×C2911yescharacteristic
647C23×C4C23×C2911yescharacteristic
648C23×C4C23×C2911yescharacteristic
649C23×C4C23×C2911yescharacteristic
650C23×C4C23×C2911yescharacteristic
651C23×C4C23×C2911yescharacteristic
652C23×C4C23×C2911yescharacteristic
653C2×C4⋊C4—22no—
654C2×C4⋊C4—22no—
655C2×C4⋊C4—22no—
656C2×C4⋊C4—22no—
657C2×C4⋊C4—22no—
658C2×C4⋊C4—22no—
659C2×C4⋊C4—22no—
660C2×C4⋊C4—22no—
661C2×C4⋊C4—22no—
662C2×C4⋊C4—22no—
663C2×C4⋊C4—22no—
664C2×C4⋊C4—41no—
665C2×C4⋊C4—41no—
666C2×C4⋊C4—41no—
667C2×C4⋊C4D4×C2914yes—
668C2×C22⋊C4—22no—
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—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—41no—
696C2×C22⋊C4—41no—
697C2×C22⋊C4—41no—
698C2×C22⋊C4—41no—
699C2×C22⋊C4—41no—
700C2×C22⋊C4—41no—
701C2×C22⋊C4—41no—
702C2×C22⋊C4—41no—
703C2×C22⋊C4D4×C2914yes—
704C2×C42—22no—
705C2×C42—22no—
706C2×C42—22no—
707C2×C42—22no—
708C2×C42—22no—
709C2×C42—22no—
710C2×C42—41no—
711C2×C42—41no—
712C2×C42D4×C2914yescomplemented
713#95—22no—
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—
727C29#1479911yescharacteristic, direct product factor, Sylow
728C24—21no—
729C24—21no—
730C24—21no—
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—
756C24C2×D4×C2912yes—
757C24#41×C2912yes—
758C24C24×C2911yescharacteristic
759C2×D4—28no—
760C2×D4—44no—
761C2×D4—44no—
762C2×D4—44no—
763C2×D4—44no—
764C2×D4—44no—
765C2×D4—44no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
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—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×C4C2×D4×C2912yes—
843C22×C4C2×D4×C2912yes—
844C22×C4C2×D4×C2912yes—
845C22×C4C2×D4×C2912yes—
846C22×C4C2×D4×C2912yes—
847C22×C4C2×D4×C2912yes—
848C22×C4C2×D4×C2912yes—
849C22×C4C2×D4×C2912yes—
850C22×C4#41×C2912yes—
851C22×C4#41×C2912yes—
852C22×C4#41×C2912yes—
853C22×C4#41×C2912yes—
854C22×C4#41×C2912yes—
855C22×C4#41×C2912yes—
856C22×C4#41×C2912yes—
857C4⋊C4—28no—
858C4⋊C4—28no—
859C4⋊C4—44no—
860C4⋊C4—44no—
861C4⋊C4—44no—
862C22⋊C4—28no—
863C22⋊C4—28no—
864C22⋊C4—28no—
865C22⋊C4—44no—
866C22⋊C4—44no—
867C22⋊C4—44no—
868C22⋊C4—44no—
869C22⋊C4—44no—
870C22⋊C4—44no—
871C22⋊C4—44no—
872C22⋊C4—44no—
873C22⋊C4—44no—
874C42—28no—
875C42—44no—
876C42—44no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—41no—
892C23—41no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
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—
947C23C22×D4×C2911yescharacteristic
948C23C22×D4×C2911yescharacteristic
949C23C22×D4×C2911yescharacteristic
950C23C2×#41×C2911yescharacteristic
951C23C2×#41×C2911yescharacteristic
952C23C2×#41×C2911yescharacteristic
953C23C2×#41×C2911yescharacteristic
954C23C2×#41×C2911yescharacteristic
955C23C2×#41×C2911yescharacteristic
956C23C2×#41×C2911yescharacteristic
957C23C2×#41×C2911yescharacteristic
958C23C29×H(5,𝔽2)11yescharacteristic
959C23C29×H(5,𝔽2)11yescharacteristic
960C23C29×H(5,𝔽2)11yescharacteristic
961C23C29×2−1+411yescharacteristic
962D4—416no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
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—41no—
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×C4C29×#12114yes—
1052C2×C4C29×#12114yes—
1053C2×C4C29×#12314yes—
1054C22—42no—
1055C22—42no—
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—42no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—81no—
1069C22—81no—
1070C22—81no—
1071C22—81no—
1072C22—81no—
1073C22—81no—
1074C22—81no—
1075C22—81no—
1076C22—81no—
1077C22—81no—
1078C22—81no—
1079C22—81no—
1080C22—81no—
1081C22—81no—
1082C22—81no—
1083C22—81no—
1084C22C2×C29×#12111yescharacteristic
1085C22C2×C29×#12111yescharacteristic
1086C22C2×C29×#12311yescharacteristic
1087C22C29×#52511yescharacteristic
1088C22C29×#52511yescharacteristic
1089C22C29×#52511yescharacteristic
1090C22C29×#52511yescharacteristic
1091C22C29×#52911yescharacteristic
1092C22C29×#52911yescharacteristic
1093C22C29×#52911yescharacteristic
1094C22C29×#52911yescharacteristic
1095C22C29×#53211yescharacteristic
1096C22C29×#53211yescharacteristic
1097C22C29×#53511yescharacteristic
1098C22C29×#53711yescharacteristic
1099C22C29×#53811yescharacteristic
1100C22C29×#53811yescharacteristic
1101C22C29×#54211yescharacteristic
1102C22C29×#54211yescharacteristic
1103C22D42×C2911yescharacteristic
1104C22C29×#54611yescharacteristic
1105C22C29×#54611yescharacteristic
1106C22C29×#54611yescharacteristic
1107C22C29×#54711yescharacteristic
1108C22C29×#54811yescharacteristic
1109C22C29×#55011yescharacteristic
1110C22C29×#55111yescharacteristic
1111C22C29×#55211yescharacteristic
1112C22C29×#55311yescharacteristic
1113C22C29×#55311yescharacteristic
1114C22C29×#55311yescharacteristic
1115C22C29×#55511yescharacteristic
1116C22C29×#55611yescharacteristic
1117C22C29×#55911yescharacteristic
1118C22C29×#55911yescharacteristic
1119C4—24no—
1120C4—24no—
1121C4—24no—
1122C4—42no—
1123C4—42no—
1124C4—42no—
1125C4—42no—
1126C4—42no—
1127C4—42no—
1128C4—81no—
1129C4—81no—
1130C4—81no—
1131C4—81no—
1132C2—82no—
1133C2—82no—
1134C2C29×#239211yescharacteristic
1135C2C29×#241411yescharacteristic
1136C2C29×#241611yescharacteristic
1137C2C29×#241811yescharacteristic
1138C2C29×#244811yescharacteristic
1139C2C29×#245611yescharacteristic
1140C2C29×#245811yescharacteristic
1141C2C29×#246811yescharacteristic
1142C2C29×#247411yescharacteristic
1143C2C29×#254411yescharacteristic
1144C2C29×#259311yescharacteristic
1145C2C29×#259511yescharacteristic
1146C2C29×#260111yescharacteristic
1147C2C29×#266211yescharacteristic
1148C2C29×#285411yescharacteristic
subgroupG/H
center, socleC24×C29C24
commutator, Frattini, cosocleC24C24×C29
prime radicalC23×D4×C29C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C29 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C29×#388C2semidirect
4. C2×C29×#388C2semidirect
5. C2×C29×#388C2semidirect
6. C2×C4×C4⋊C4×C29C2semidirect
7. C29×#1441C2semidirect
8. C29×#1441C2semidirect
9. C29×#1440C2semidirect
10. C29×#1439C2semidirect
11. C29×#1439C2semidirect
12. C29×#1439C2semidirect
14. C29×#1437C2semidirect
15. C29×#1436C2semidirect
138. C2×C42×C29D4semidirect
302. #14799C29direct (N × H)
482. C2×#388C2×C29semidirect
483. C2×#388C2×C29semidirect
484. C2×#388C2×C29semidirect
485. C2×C4×C4⋊C4C2×C29semidirect
486. #1441C2×C29semidirect
487. #1441C2×C29semidirect
488. #1440C2×C29semidirect
489. #1439C2×C29semidirect
490. #1439C2×C29semidirect
491. #1439C2×C29semidirect
493. #1437C2×C29semidirect
494. #1436C2×C29semidirect
712. C2×C42D4×C29semidirect
727. C29#14799direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#3942
C2×C29×#3902
C2×C29×#3882
C2×C4×C4⋊C4×C292
C29×#14412
C29×#14402
C29×#14392
C29×#14382
C29×#14372
C29×#14362
#1479929