Finite Group Databasebeta

← C29×#15606 #20310506

Subgroups — C29×#15606 #20310506

Order 7424.

1538 conjugacy classes of subgroups.

The subgroup lattice has 1118 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#397C211yesmaximal, characteristic, complemented
2C2×C29×#388C211yesmaximal, characteristic, complemented
3C29×#1443C211yesmaximal, characteristic, complemented
4C29×#1442C211yesmaximal, characteristic, complemented
5C29×#1440C211yesmaximal, characteristic, complemented
6C29×#1439C211yesmaximal, characteristic, complemented
7C29×#1439C211yesmaximal, characteristic, complemented
8C29×#1438C211yesmaximal, characteristic
9C29×#1438C211yesmaximal, characteristic
10C29×#1438C211yesmaximal, characteristic
11C29×#1437C211yesmaximal, characteristic, complemented
12C29×#1437C211yesmaximal, characteristic, complemented
13C29×#1437C211yesmaximal, characteristic, complemented
14C29×#1436C211yesmaximal, characteristic, complemented
15C29×#1434C211yesmaximal, characteristic, complemented
16C23×D4×C29C2211yescharacteristic
17C22×C4⋊C4×C29C2211yescharacteristic
18C22×C4⋊C4×C29C2211yescharacteristic
19C22×C22⋊C4×C29C2211yescharacteristic
20C22×C22⋊C4×C29C2211yescharacteristic
21C22×C22⋊C4×C29C2211yescharacteristic
22C22×C22⋊C4×C29C2211yescharacteristic
23C22×C22⋊C4×C29C2211yescharacteristic
24C22×C22⋊C4×C29C2211yescharacteristic
25C22×C22⋊C4×C29C2211yescharacteristic
26C22×C22⋊C4×C29C2211yescharacteristic
27C22×C22⋊C4×C29C2211yescharacteristic
28C22×C22⋊C4×C29C2211yescharacteristic
29C22×C22⋊C4×C29C2211yescharacteristic
30C22×C22⋊C4×C29C2211yescharacteristic
31C22×C42×C29C2211yescharacteristic
32C22×C42×C29C2211yescharacteristic
33C29×#397—24no—
34C29×#388—24no—
35C2×C29×#95C2211yescharacteristic
36C2×C29×#95C2211yescharacteristic
37C2×C29×#95C2211yescharacteristic
38C2×C29×#95C2211yescharacteristic
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
53C25×C29C2311yescharacteristic
54C25×C29C2311yescharacteristic
55C22×D4×C29—22no—
56C22×D4×C29—22no—
57C22×D4×C29—22no—
58C22×D4×C29—41no—
59C22×D4×C29—41no—
60C22×D4×C29—41no—
61C22×D4×C29—41no—
62C23×C4×C29C2311yescharacteristic
63C23×C4×C29C2311yescharacteristic
64C23×C4×C29C2311yescharacteristic
65C23×C4×C29C2311yescharacteristic
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
75C2×C4⋊C4×C29—41no—
76C2×C4⋊C4×C29—41no—
77C2×C4⋊C4×C29—41no—
78C2×C4⋊C4×C29—41no—
79C2×C4⋊C4×C29—41no—
80C2×C4⋊C4×C29D414yescomplemented
81C2×C22⋊C4×C29—22no—
82C2×C22⋊C4×C29—22no—
83C2×C22⋊C4×C29—22no—
84C2×C22⋊C4×C29—22no—
85C2×C22⋊C4×C29—22no—
86C2×C22⋊C4×C29—22no—
87C2×C22⋊C4×C29—22no—
88C2×C22⋊C4×C29—22no—
89C2×C22⋊C4×C29—22no—
90C2×C22⋊C4×C29—22no—
91C2×C22⋊C4×C29—22no—
92C2×C22⋊C4×C29—22no—
93C2×C22⋊C4×C29—22no—
94C2×C22⋊C4×C29—22no—
95C2×C22⋊C4×C29—22no—
96C2×C22⋊C4×C29—22no—
97C2×C22⋊C4×C29—22no—
98C2×C22⋊C4×C29—22no—
99C2×C22⋊C4×C29—22no—
100C2×C22⋊C4×C29—22no—
101C2×C22⋊C4×C29—41no—
102C2×C22⋊C4×C29—41no—
103C2×C22⋊C4×C29—41no—
104C2×C22⋊C4×C29—41no—
105C2×C22⋊C4×C29—41no—
106C2×C22⋊C4×C29—41no—
107C2×C22⋊C4×C29—41no—
108C2×C22⋊C4×C29—41no—
109C2×C22⋊C4×C29—41no—
110C2×C22⋊C4×C29—41no—
111C2×C22⋊C4×C29—41no—
112C2×C22⋊C4×C29—41no—
113C2×C22⋊C4×C29—41no—
114C2×C22⋊C4×C29—41no—
115C2×C22⋊C4×C29—41no—
116C2×C22⋊C4×C29—41no—
117C2×C42×C29—22no—
118C2×C42×C29—22no—
119C2×C42×C29—41no—
120C2×C42×C29—41no—
121C2×C42×C29—41no—
122C2×C42×C29—41no—
123C29×#95—22no—
124C29×#95—22no—
125C29×#95—22no—
126C29×#95—22no—
127C29×#95—22no—
128C29×#95—22no—
129C29×#95—22no—
130C29×#95—22no—
131C29×#95—22no—
132C29×#95—22no—
133C29×#95—22no—
134C29×#95—41no—
135C29×#95—41no—
136C29×#95—41no—
137C29×#95—41no—
138C29×#95—41no—
139C29×#95—41no—
140C29×#95—41no—
141C24×C29—21no—
142C24×C29—21no—
143C24×C29—21no—
144C24×C29—21no—
145C24×C29—21no—
146C24×C29—21no—
147C24×C29—21no—
148C24×C29—21no—
149C24×C29—21no—
150C24×C29—21no—
151C24×C29—21no—
152C24×C29—21no—
153C24×C29—21no—
154C24×C29—21no—
155C24×C29—21no—
156C24×C29—21no—
157C24×C29—21no—
158C24×C29—21no—
159C24×C29—21no—
160C24×C29—21no—
161C24×C29—21no—
162C24×C29—21no—
163C24×C29—21no—
164C24×C29—21no—
165C24×C29—21no—
166C24×C29—21no—
167C24×C29—21no—
168C24×C29—21no—
169C24×C29#4112yes—
170C24×C29#4112yes—
171C24×C29C2411yescharacteristic
172C2×D4×C29—44no—
173C2×D4×C29—44no—
174C2×D4×C29—44no—
175C2×D4×C29—44no—
176C2×D4×C29—44no—
177C2×D4×C29—44no—
178C2×D4×C29—44no—
179C22×C4×C29—21no—
180C22×C4×C29—21no—
181C22×C4×C29—21no—
182C22×C4×C29—21no—
183C22×C4×C29—21no—
184C22×C4×C29—21no—
185C22×C4×C29—21no—
186C22×C4×C29—21no—
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—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×C29C2×D412yes—
262C22×C4×C29C2×D412yes—
263C22×C4×C29C2×D412yes—
264C22×C4×C29#4112yes—
265C22×C4×C29#4112yes—
266C22×C4×C29#4112yes—
267C22×C4×C29#4112yes—
268C22×C4×C29#4112yes—
269C22×C4×C29#4112yes—
270C4⋊C4×C29—44no—
271C4⋊C4×C29—44no—
272C22⋊C4×C29—28no—
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×C29—44no—
281C22⋊C4×C29—44no—
282C22⋊C4×C29—44no—
283C22⋊C4×C29—44no—
284C42×C29—44no—
285C42×C29—44no—
286#15606C2911yesmaximal, characteristic, direct product factor, Sylow
287C23×C29—22no—
288C23×C29—22no—
289C23×C29—22no—
290C23×C29—22no—
291C23×C29—22no—
292C23×C29—22no—
293C23×C29—22no—
294C23×C29—22no—
295C23×C29—22no—
296C23×C29—22no—
297C23×C29—22no—
298C23×C29—22no—
299C23×C29—22no—
300C23×C29—22no—
301C23×C29—41no—
302C23×C29—41no—
303C23×C29—41no—
304C23×C29—41no—
305C23×C29—41no—
306C23×C29—41no—
307C23×C29—41no—
308C23×C29—41no—
309C23×C29—41no—
310C23×C29—41no—
311C23×C29—41no—
312C23×C29—41no—
313C23×C29—41no—
314C23×C29—41no—
315C23×C29—41no—
316C23×C29—41no—
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×C29C22×D411yescharacteristic
358C23×C29C2×#4111yescharacteristic
359C23×C29C2×#4111yescharacteristic
360C23×C29C2×#4111yescharacteristic
361C23×C29C2×#4111yescharacteristic
362C23×C29C2×#4111yescharacteristic
363C23×C29C2×#4111yescharacteristic
364C23×C29C2×#4111yescharacteristic
365C23×C29C2×#4111yescharacteristic
366C23×C29H(5,𝔽2)11yescharacteristic
367C23×C29H(5,𝔽2)11yescharacteristic
368C23×C29H(5,𝔽2)11yescharacteristic
369C23×C29H(5,𝔽2)11yescharacteristic
370C23×C29H(5,𝔽2)11yescharacteristic
371C23×C29H(5,𝔽2)11yescharacteristic
372D4×C29—416no—
373C2×C4×C29—22no—
374C2×C4×C29—22no—
375C2×C4×C29—22no—
376C2×C4×C29—22no—
377C2×C4×C29—22no—
378C2×C4×C29—22no—
379C2×C4×C29—22no—
380C2×C4×C29—22no—
381C2×C4×C29—22no—
382C2×C4×C29—22no—
383C2×C4×C29—22no—
384C2×C4×C29—22no—
385C2×C4×C29—22no—
386C2×C4×C29—22no—
387C2×C4×C29—22no—
388C2×C4×C29—22no—
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—41no—
401C2×C4×C29—41no—
402C2×C4×C29—41no—
403C2×C4×C29—41no—
404C2×C4×C29—41no—
405C2×C4×C29—41no—
406C2×C4×C29—41no—
407C2×C4×C29—41no—
408C2×C4×C29—41no—
409C2×C4×C29—41no—
410C2×C4×C29—41no—
411C2×C4×C29—41no—
412C2×C4×C29—41no—
413C2×C4×C29—41no—
414C2×C4×C29—41no—
415C2×C4×C29—41no—
416C2×C4×C29—41no—
417C2×C4×C29—41no—
418C2×C4×C29—41no—
419C2×C4×C29—41no—
420C2×C4×C29—41no—
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×#397C2×C2911yescharacteristic, complemented
465C2×#388C2×C2911yescharacteristic, complemented
466#1443C2×C2911yescharacteristic, complemented
467#1442C2×C2911yescharacteristic, complemented
468#1440C2×C2911yescharacteristic, complemented
469#1439C2×C2911yescharacteristic, complemented
470#1439C2×C2911yescharacteristic, complemented
471#1438C2×C2911yescharacteristic
472#1438C2×C2911yescharacteristic
473#1438C2×C2911yescharacteristic
474#1437C2×C2911yescharacteristic, complemented
475#1437C2×C2911yescharacteristic, complemented
476#1437C2×C2911yescharacteristic, complemented
477#1436C2×C2911yescharacteristic, complemented
478#1434C2×C2911yescharacteristic, complemented
479C22×C29—42no—
480C22×C29—42no—
481C22×C29—42no—
482C22×C29—42no—
483C22×C29—42no—
484C22×C29—42no—
485C22×C29—42no—
486C22×C29—42no—
487C22×C29—42no—
488C22×C29—42no—
489C22×C29—42no—
490C22×C29—42no—
491C22×C29—42no—
492C22×C29—42no—
493C22×C29—81no—
494C22×C29—81no—
495C22×C29—81no—
496C22×C29—81no—
497C22×C29—81no—
498C22×C29—81no—
499C22×C29—81no—
500C22×C29—81no—
501C22×C29—81no—
502C22×C29—81no—
503C22×C29—81no—
504C22×C29—81no—
505C22×C29—81no—
506C22×C29—81no—
507C22×C29—81no—
508C22×C29—81no—
509C22×C29#52511yescharacteristic
510C22×C29#52911yescharacteristic
511C22×C29#52911yescharacteristic
512C22×C29#52911yescharacteristic
513C22×C29#52911yescharacteristic
514C22×C29#53211yescharacteristic
515C22×C29#53411yescharacteristic
516C22×C29#53811yescharacteristic
517C22×C29#53811yescharacteristic
518C22×C29#53811yescharacteristic
519C22×C29#53811yescharacteristic
520C22×C29#53811yescharacteristic
521C22×C29#53811yescharacteristic
522C22×C29#54011yescharacteristic
523C22×C29#54011yescharacteristic
524C22×C29#54611yescharacteristic
525C22×C29#54611yescharacteristic
526C22×C29#55011yescharacteristic
527C22×C29#55011yescharacteristic
528C22×C29#55111yescharacteristic
529C22×C29#55111yescharacteristic
530C22×C29#55111yescharacteristic
531C22×C29#55111yescharacteristic
532C22×C29#55111yescharacteristic
533C22×C29#55111yescharacteristic
534C22×C29#55311yescharacteristic
535C22×C29#55311yescharacteristic
536C22×C29#55311yescharacteristic
537C22×C29#55311yescharacteristic
538C22×C29#55311yescharacteristic
539C22×C29#55311yescharacteristic
540C22×C29#55511yescharacteristic
541C22×C29#55911yescharacteristic
542C22×C29#56011yescharacteristic
543C22×C29H(3,𝔽4)11yescharacteristic
544C4×C29—42no—
545C4×C29—42no—
546C4×C29—42no—
547C4×C29—42no—
548C4×C29—42no—
549C4×C29—42no—
550C4×C29—42no—
551C4×C29—42no—
552C4×C29—42no—
553C4×C29—81no—
554C4×C29—81no—
555C4×C29—81no—
556C4×C29—81no—
557C23×D4C22×C2911yescharacteristic
558C22×C4⋊C4C22×C2911yescharacteristic
559C22×C4⋊C4C22×C2911yescharacteristic
560C22×C22⋊C4C22×C2911yescharacteristic
561C22×C22⋊C4C22×C2911yescharacteristic
562C22×C22⋊C4C22×C2911yescharacteristic
563C22×C22⋊C4C22×C2911yescharacteristic
564C22×C22⋊C4C22×C2911yescharacteristic
565C22×C22⋊C4C22×C2911yescharacteristic
566C22×C22⋊C4C22×C2911yescharacteristic
567C22×C22⋊C4C22×C2911yescharacteristic
568C22×C22⋊C4C22×C2911yescharacteristic
569C22×C22⋊C4C22×C2911yescharacteristic
570C22×C22⋊C4C22×C2911yescharacteristic
571C22×C22⋊C4C22×C2911yescharacteristic
572C22×C42C22×C2911yescharacteristic
573C22×C42C22×C2911yescharacteristic
574#397—24no—
575#388—24no—
576C2×#95C22×C2911yescharacteristic
577C2×#95C22×C2911yescharacteristic
578C2×#95C22×C2911yescharacteristic
579C2×#95C22×C2911yescharacteristic
580C2×#95C22×C2911yescharacteristic
581C2×#95C22×C2911yescharacteristic
582C2×#95C22×C2911yescharacteristic
583C2×#95C22×C2911yescharacteristic
584C2×#95C22×C2911yescharacteristic
585C2×#95C22×C2911yescharacteristic
586C2×#95C22×C2911yescharacteristic
587C2×#95C22×C2911yescharacteristic
588C2×#95C22×C2911yescharacteristic
589C2×#95C22×C2911yescharacteristic
590C2×#95C22×C2911yescharacteristic
591C2×#95C22×C2911yescharacteristic
592C2×#95C22×C2911yescharacteristic
593C2×#95C22×C2911yescharacteristic
594C2×C29—82no—
595C2×C29—82no—
596C2×C29#246711yescharacteristic
597C2×C29#247111yescharacteristic
598C2×C29#251811yescharacteristic
599C2×C29#252611yescharacteristic
600C2×C29#255411yescharacteristic
601C2×C29#255411yescharacteristic
602C2×C29#257811yescharacteristic
603C2×C29#259511yescharacteristic
604C2×C29#260211yescharacteristic
605C2×C29#268811yescharacteristic
606C2×C29#273311yescharacteristic
607C2×C29#273611yescharacteristic
608C2×C29#275311yescharacteristic
609C2×C29#277811yescharacteristic
610C2×C29#279711yescharacteristic
611C25C23×C2911yescharacteristic
612C25C23×C2911yescharacteristic
613C22×D4—22no—
614C22×D4—22no—
615C22×D4—22no—
616C22×D4—41no—
617C22×D4—41no—
618C22×D4—41no—
619C22×D4—41no—
620C23×C4C23×C2911yescharacteristic
621C23×C4C23×C2911yescharacteristic
622C23×C4C23×C2911yescharacteristic
623C23×C4C23×C2911yescharacteristic
624C23×C4C23×C2911yescharacteristic
625C23×C4C23×C2911yescharacteristic
626C23×C4C23×C2911yescharacteristic
627C23×C4C23×C2911yescharacteristic
628C23×C4C23×C2911yescharacteristic
629C23×C4C23×C2911yescharacteristic
630C23×C4C23×C2911yescharacteristic
631C23×C4C23×C2911yescharacteristic
632C23×C4C23×C2911yescharacteristic
633C2×C4⋊C4—41no—
634C2×C4⋊C4—41no—
635C2×C4⋊C4—41no—
636C2×C4⋊C4—41no—
637C2×C4⋊C4—41no—
638C2×C4⋊C4D4×C2914yescomplemented
639C2×C22⋊C4—22no—
640C2×C22⋊C4—22no—
641C2×C22⋊C4—22no—
642C2×C22⋊C4—22no—
643C2×C22⋊C4—22no—
644C2×C22⋊C4—22no—
645C2×C22⋊C4—22no—
646C2×C22⋊C4—22no—
647C2×C22⋊C4—22no—
648C2×C22⋊C4—22no—
649C2×C22⋊C4—22no—
650C2×C22⋊C4—22no—
651C2×C22⋊C4—22no—
652C2×C22⋊C4—22no—
653C2×C22⋊C4—22no—
654C2×C22⋊C4—22no—
655C2×C22⋊C4—22no—
656C2×C22⋊C4—22no—
657C2×C22⋊C4—22no—
658C2×C22⋊C4—22no—
659C2×C22⋊C4—41no—
660C2×C22⋊C4—41no—
661C2×C22⋊C4—41no—
662C2×C22⋊C4—41no—
663C2×C22⋊C4—41no—
664C2×C22⋊C4—41no—
665C2×C22⋊C4—41no—
666C2×C22⋊C4—41no—
667C2×C22⋊C4—41no—
668C2×C22⋊C4—41no—
669C2×C22⋊C4—41no—
670C2×C22⋊C4—41no—
671C2×C22⋊C4—41no—
672C2×C22⋊C4—41no—
673C2×C22⋊C4—41no—
674C2×C22⋊C4—41no—
675C2×C42—22no—
676C2×C42—22no—
677C2×C42—41no—
678C2×C42—41no—
679C2×C42—41no—
680C2×C42—41no—
681#95—22no—
682#95—22no—
683#95—22no—
684#95—22no—
685#95—22no—
686#95—22no—
687#95—22no—
688#95—22no—
689#95—22no—
690#95—22no—
691#95—22no—
692#95—41no—
693#95—41no—
694#95—41no—
695#95—41no—
696#95—41no—
697#95—41no—
698#95—41no—
699C29#1560611yescharacteristic, direct product factor, Sylow
700C24—21no—
701C24—21no—
702C24—21no—
703C24—21no—
704C24—21no—
705C24—21no—
706C24—21no—
707C24—21no—
708C24—21no—
709C24—21no—
710C24—21no—
711C24—21no—
712C24—21no—
713C24—21no—
714C24—21no—
715C24—21no—
716C24—21no—
717C24—21no—
718C24—21no—
719C24—21no—
720C24—21no—
721C24—21no—
722C24—21no—
723C24—21no—
724C24—21no—
725C24—21no—
726C24—21no—
727C24—21no—
728C24#41×C2912yes—
729C24#41×C2912yes—
730C24C24×C2911yescharacteristic
731C2×D4—44no—
732C2×D4—44no—
733C2×D4—44no—
734C2×D4—44no—
735C2×D4—44no—
736C2×D4—44no—
737C2×D4—44no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
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×C4C2×D4×C2912yes—
821C22×C4C2×D4×C2912yes—
822C22×C4C2×D4×C2912yes—
823C22×C4#41×C2912yes—
824C22×C4#41×C2912yes—
825C22×C4#41×C2912yes—
826C22×C4#41×C2912yes—
827C22×C4#41×C2912yes—
828C22×C4#41×C2912yes—
829C4⋊C4—44no—
830C4⋊C4—44no—
831C22⋊C4—28no—
832C22⋊C4—44no—
833C22⋊C4—44no—
834C22⋊C4—44no—
835C22⋊C4—44no—
836C22⋊C4—44no—
837C22⋊C4—44no—
838C22⋊C4—44no—
839C22⋊C4—44no—
840C22⋊C4—44no—
841C22⋊C4—44no—
842C22⋊C4—44no—
843C42—44no—
844C42—44no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—41no—
871C23—41no—
872C23—41no—
873C23—41no—
874C23—41no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—41no—
879C23—41no—
880C23—41no—
881C23—41no—
882C23—41no—
883C23—41no—
884C23—41no—
885C23—41no—
886C23—41no—
887C23—41no—
888C23—41no—
889C23—41no—
890C23—41no—
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—
915C23C22×D4×C2911yescharacteristic
916C23C2×#41×C2911yescharacteristic
917C23C2×#41×C2911yescharacteristic
918C23C2×#41×C2911yescharacteristic
919C23C2×#41×C2911yescharacteristic
920C23C2×#41×C2911yescharacteristic
921C23C2×#41×C2911yescharacteristic
922C23C2×#41×C2911yescharacteristic
923C23C2×#41×C2911yescharacteristic
924C23C29×H(5,𝔽2)11yescharacteristic
925C23C29×H(5,𝔽2)11yescharacteristic
926C23C29×H(5,𝔽2)11yescharacteristic
927C23C29×H(5,𝔽2)11yescharacteristic
928C23C29×H(5,𝔽2)11yescharacteristic
929C23C29×H(5,𝔽2)11yescharacteristic
930D4—416no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
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—
1022C22—42no—
1023C22—42no—
1024C22—42no—
1025C22—42no—
1026C22—42no—
1027C22—42no—
1028C22—42no—
1029C22—42no—
1030C22—42no—
1031C22—42no—
1032C22—42no—
1033C22—42no—
1034C22—42no—
1035C22—42no—
1036C22—81no—
1037C22—81no—
1038C22—81no—
1039C22—81no—
1040C22—81no—
1041C22—81no—
1042C22—81no—
1043C22—81no—
1044C22—81no—
1045C22—81no—
1046C22—81no—
1047C22—81no—
1048C22—81no—
1049C22—81no—
1050C22—81no—
1051C22—81no—
1052C22C29×#52511yescharacteristic
1053C22C29×#52911yescharacteristic
1054C22C29×#52911yescharacteristic
1055C22C29×#52911yescharacteristic
1056C22C29×#52911yescharacteristic
1057C22C29×#53211yescharacteristic
1058C22C29×#53411yescharacteristic
1059C22C29×#53811yescharacteristic
1060C22C29×#53811yescharacteristic
1061C22C29×#53811yescharacteristic
1062C22C29×#53811yescharacteristic
1063C22C29×#53811yescharacteristic
1064C22C29×#53811yescharacteristic
1065C22C29×#54011yescharacteristic
1066C22C29×#54011yescharacteristic
1067C22C29×#54611yescharacteristic
1068C22C29×#54611yescharacteristic
1069C22C29×#55011yescharacteristic
1070C22C29×#55011yescharacteristic
1071C22C29×#55111yescharacteristic
1072C22C29×#55111yescharacteristic
1073C22C29×#55111yescharacteristic
1074C22C29×#55111yescharacteristic
1075C22C29×#55111yescharacteristic
1076C22C29×#55111yescharacteristic
1077C22C29×#55311yescharacteristic
1078C22C29×#55311yescharacteristic
1079C22C29×#55311yescharacteristic
1080C22C29×#55311yescharacteristic
1081C22C29×#55311yescharacteristic
1082C22C29×#55311yescharacteristic
1083C22C29×#55511yescharacteristic
1084C22C29×#55911yescharacteristic
1085C22C29×#56011yescharacteristic
1086C22C29×H(3,𝔽4)11yescharacteristic
1087C4—42no—
1088C4—42no—
1089C4—42no—
1090C4—42no—
1091C4—42no—
1092C4—42no—
1093C4—42no—
1094C4—42no—
1095C4—42no—
1096C4—81no—
1097C4—81no—
1098C4—81no—
1099C4—81no—
1100C2—82no—
1101C2—82no—
1102C2C29×#246711yescharacteristic
1103C2C29×#247111yescharacteristic
1104C2C29×#251811yescharacteristic
1105C2C29×#252611yescharacteristic
1106C2C29×#255411yescharacteristic
1107C2C29×#255411yescharacteristic
1108C2C29×#257811yescharacteristic
1109C2C29×#259511yescharacteristic
1110C2C29×#260211yescharacteristic
1111C2C29×#268811yescharacteristic
1112C2C29×#273311yescharacteristic
1113C2C29×#273611yescharacteristic
1114C2C29×#275311yescharacteristic
1115C2C29×#277811yescharacteristic
1116C2C29×#279711yescharacteristic
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×#388C2semidirect
3. C29×#1443C2semidirect
4. C29×#1442C2semidirect
5. C29×#1440C2semidirect
6. C29×#1439C2semidirect
7. C29×#1439C2semidirect
11. C29×#1437C2semidirect
12. C29×#1437C2semidirect
13. C29×#1437C2semidirect
14. C29×#1436C2semidirect
15. C29×#1434C2semidirect
80. C2×C4⋊C4×C29D4semidirect
286. #15606C29direct (N × H)
464. C2×#397C2×C29semidirect
465. C2×#388C2×C29semidirect
466. #1443C2×C29semidirect
467. #1442C2×C29semidirect
468. #1440C2×C29semidirect
469. #1439C2×C29semidirect
470. #1439C2×C29semidirect
474. #1437C2×C29semidirect
475. #1437C2×C29semidirect
476. #1437C2×C29semidirect
477. #1436C2×C29semidirect
478. #1434C2×C29semidirect
638. C2×C4⋊C4D4×C29semidirect
699. C29#15606direct (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×#3882
C29×#14432
C29×#14422
C29×#14402
C29×#14392
C29×#14382
C29×#14372
C29×#14362
C29×#14342
#1560629