Finite Group Databasebeta

← C29×#16534 #20311434

Subgroups — C29×#16534 #20311434

Order 7424.

1590 conjugacy classes of subgroups.

The subgroup lattice has 1134 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×#388C211yesmaximal, characteristic, complemented
5C29×#1442C211yesmaximal, characteristic, complemented
6C29×#1441C211yesmaximal, characteristic, complemented
7C29×#1441C211yesmaximal, characteristic, complemented
8C29×#1440C211yesmaximal, characteristic, complemented
9C29×#1439C211yesmaximal, characteristic, complemented
10C29×#1439C211yesmaximal, characteristic, complemented
11C29×#1439C211yesmaximal, characteristic, complemented
12C29×#1438C211yesmaximal, characteristic
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
35C29×#397—24no—
36C29×#396—24no—
37C29×#394—24no—
38C29×#388—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
55C25×C29C2311yescharacteristic
56C25×C29C2311yescharacteristic
57C22×D4×C29—22no—
58C22×D4×C29—22no—
59C22×D4×C29—22no—
60C22×D4×C29—41no—
61C22×D4×C29—41no—
62C22×D4×C29—41no—
63C22×D4×C29—41no—
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
75C23×C4×C29C2311yescharacteristic
76C23×C4×C29C2311yescharacteristic
77C2×C4⋊C4×C29—22no—
78C2×C4⋊C4×C29—22no—
79C2×C4⋊C4×C29—22no—
80C2×C4⋊C4×C29—22no—
81C2×C4⋊C4×C29—22no—
82C2×C4⋊C4×C29—22no—
83C2×C4⋊C4×C29—22no—
84C2×C4⋊C4×C29—22no—
85C2×C4⋊C4×C29—22no—
86C2×C4⋊C4×C29—41no—
87C2×C4⋊C4×C29—41no—
88C2×C4⋊C4×C29—41no—
89C2×C4⋊C4×C29—41no—
90C2×C4⋊C4×C29—41no—
91C2×C4⋊C4×C29—41no—
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—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—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×C22⋊C4×C29—41no—
118C2×C22⋊C4×C29—41no—
119C2×C22⋊C4×C29—41no—
120C2×C22⋊C4×C29—41no—
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×C29D414yes—
128C2×C42×C29—22no—
129C2×C42×C29—41no—
130C2×C42×C29—41no—
131C29×#95—22no—
132C29×#95—22no—
133C29×#95—22no—
134C29×#95—22no—
135C29×#95—22no—
136C29×#95—22no—
137C29×#95—22no—
138C29×#95—41no—
139C29×#95—41no—
140C29×#95—41no—
141C29×#95—41no—
142C29×#95—41no—
143C29×#95—41no—
144C29×#95—41no—
145C29×#95—41no—
146C29×#95D414yescomplemented
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—21no—
170C24×C29—21no—
171C24×C29—21no—
172C24×C29—21no—
173C24×C29—21no—
174C24×C29—21no—
175C24×C29C2×D412yes—
176C24×C29#4112yes—
177C24×C29C2411yescharacteristic
178C2×D4×C29—44no—
179C2×D4×C29—44no—
180C2×D4×C29—44no—
181C2×D4×C29—44no—
182C2×D4×C29—44no—
183C2×D4×C29—44no—
184C2×D4×C29—44no—
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×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×C29#4112yes—
273C22×C4×C29#4112yes—
274C22×C4×C29#4112yes—
275C22×C4×C29#4112yes—
276C4⋊C4×C29—44no—
277C4⋊C4×C29—44no—
278C4⋊C4×C29—44no—
279C4⋊C4×C29—44no—
280C4⋊C4×C29—44no—
281C22⋊C4×C29—28no—
282C22⋊C4×C29—44no—
283C22⋊C4×C29—44no—
284C22⋊C4×C29—44no—
285C22⋊C4×C29—44no—
286C22⋊C4×C29—44no—
287C22⋊C4×C29—44no—
288C22⋊C4×C29—44no—
289C22⋊C4×C29—44no—
290C22⋊C4×C29—44no—
291C22⋊C4×C29—44no—
292C22⋊C4×C29—44no—
293C42×C29—44no—
294#16534C2911yesmaximal, characteristic, direct product factor, Sylow
295C23×C29—22no—
296C23×C29—22no—
297C23×C29—22no—
298C23×C29—22no—
299C23×C29—22no—
300C23×C29—22no—
301C23×C29—22no—
302C23×C29—22no—
303C23×C29—22no—
304C23×C29—22no—
305C23×C29—22no—
306C23×C29—22no—
307C23×C29—22no—
308C23×C29—22no—
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×C29—41no—
358C23×C29—41no—
359C23×C29—41no—
360C23×C29—41no—
361C23×C29—41no—
362C23×C29—41no—
363C23×C29—41no—
364C23×C29—41no—
365C23×C29C22×D411yescharacteristic
366C23×C29C22×D411yescharacteristic
367C23×C29C2×#4111yescharacteristic
368C23×C29C2×#4111yescharacteristic
369C23×C29C2×#4111yescharacteristic
370C23×C29C2×#4111yescharacteristic
371C23×C29C2×#4111yescharacteristic
372C23×C29H(5,𝔽2)11yescharacteristic
373C23×C29H(5,𝔽2)11yescharacteristic
374C23×C29H(5,𝔽2)11yescharacteristic
375C23×C29H(5,𝔽2)11yescharacteristic
376C23×C29H(5,𝔽2)11yescharacteristic
377C23×C29H(5,𝔽2)11yescharacteristic
378C23×C292−1+411yescharacteristic
379C23×C292−1+411yescharacteristic
380D4×C29—416no—
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—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—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×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×#397C2×C2911yescharacteristic, complemented
473C2×#396C2×C2911yescharacteristic, complemented
474C2×#394C2×C2911yescharacteristic
475C2×#388C2×C2911yescharacteristic, complemented
476#1442C2×C2911yescharacteristic, complemented
477#1441C2×C2911yescharacteristic, complemented
478#1441C2×C2911yescharacteristic, complemented
479#1440C2×C2911yescharacteristic, complemented
480#1439C2×C2911yescharacteristic, complemented
481#1439C2×C2911yescharacteristic, complemented
482#1439C2×C2911yescharacteristic, complemented
483#1438C2×C2911yescharacteristic
484#1438C2×C2911yescharacteristic
485#1437C2×C2911yescharacteristic, complemented
486#1436C2×C2911yescharacteristic, complemented
487C22×C29—42no—
488C22×C29—42no—
489C22×C29—42no—
490C22×C29—42no—
491C22×C29—42no—
492C22×C29—42no—
493C22×C29—42no—
494C22×C29—42no—
495C22×C29—42no—
496C22×C29—42no—
497C22×C29—42no—
498C22×C29—42no—
499C22×C29—42no—
500C22×C29—42no—
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—81no—
510C22×C29—81no—
511C22×C29—81no—
512C22×C29—81no—
513C22×C29—81no—
514C22×C29—81no—
515C22×C29—81no—
516C22×C29—81no—
517C22×C29#52511yescharacteristic
518C22×C29#52911yescharacteristic
519C22×C29#53211yescharacteristic
520C22×C29#53411yescharacteristic
521C22×C29#53511yescharacteristic
522C22×C29#53711yescharacteristic
523C22×C29#53711yescharacteristic
524C22×C29#53811yescharacteristic
525C22×C29#53811yescharacteristic
526C22×C29#53811yescharacteristic
527C22×C29#53811yescharacteristic
528C22×C29#53811yescharacteristic
529C22×C29#53911yescharacteristic
530C22×C29#54011yescharacteristic
531C22×C29#54011yescharacteristic
532C22×C29#54011yescharacteristic
533C22×C29#54211yescharacteristic
534C22×C29#54211yescharacteristic
535C22×C29#54211yescharacteristic
536C22×C29D4211yescharacteristic
537C22×C29#54611yescharacteristic
538C22×C29#54611yescharacteristic
539C22×C29#54611yescharacteristic
540C22×C29#54611yescharacteristic
541C22×C29#54711yescharacteristic
542C22×C29#54811yescharacteristic
543C22×C29#55111yescharacteristic
544C22×C29#55211yescharacteristic
545C22×C29#55311yescharacteristic
546C22×C29#55311yescharacteristic
547C22×C29#55611yescharacteristic
548C22×C29#56011yescharacteristic
549C22×C29#56211yescharacteristic
550C22×C29#56211yescharacteristic
551C22×C29#56311yescharacteristic
552C4×C29—42no—
553C4×C29—42no—
554C4×C29—42no—
555C4×C29—42no—
556C4×C29—42no—
557C4×C29—42no—
558C4×C29—42no—
559C4×C29—42no—
560C4×C29—42no—
561C4×C29—81no—
562C4×C29—81no—
563C4×C29—81no—
564C4×C29—81no—
565C23×D4C22×C2911yescharacteristic
566C22×C4⋊C4C22×C2911yescharacteristic
567C22×C4⋊C4C22×C2911yescharacteristic
568C22×C4⋊C4C22×C2911yescharacteristic
569C22×C4⋊C4C22×C2911yescharacteristic
570C22×C4⋊C4C22×C2911yescharacteristic
571C22×C22⋊C4C22×C2911yescharacteristic
572C22×C22⋊C4C22×C2911yescharacteristic
573C22×C22⋊C4C22×C2911yescharacteristic
574C22×C22⋊C4C22×C2911yescharacteristic
575C22×C22⋊C4C22×C2911yescharacteristic
576C22×C22⋊C4C22×C2911yescharacteristic
577C22×C22⋊C4C22×C2911yescharacteristic
578C22×C22⋊C4C22×C2911yescharacteristic
579C22×C22⋊C4C22×C2911yescharacteristic
580C22×C22⋊C4C22×C2911yescharacteristic
581C22×C22⋊C4C22×C2911yescharacteristic
582C22×C22⋊C4C22×C2911yescharacteristic
583C22×C42C22×C2911yescharacteristic
584#397—24no—
585#396—24no—
586#394—24no—
587#388—24no—
588C2×#95C22×C2911yescharacteristic
589C2×#95C22×C2911yescharacteristic
590C2×#95C22×C2911yescharacteristic
591C2×#95C22×C2911yescharacteristic
592C2×#95C22×C2911yescharacteristic
593C2×#95C22×C2911yescharacteristic
594C2×#95C22×C2911yescharacteristic
595C2×#95C22×C2911yescharacteristic
596C2×#95C22×C2911yescharacteristic
597C2×#95C22×C2911yescharacteristic
598C2×#95C22×C2911yescharacteristic
599C2×#95C22×C2911yescharacteristic
600C2×#95C22×C2911yescharacteristic
601C2×#95C22×C2911yescharacteristic
602C2×#95C22×C2911yescharacteristic
603C2×#95C22×C2911yescharacteristic
604C2×C29—82no—
605C2×C29—82no—
606C2×C29#246411yescharacteristic
607C2×C29#247011yescharacteristic
608C2×C29#256011yescharacteristic
609C2×C29#263011yescharacteristic
610C2×C29#264811yescharacteristic
611C2×C29#266211yescharacteristic
612C2×C29#267111yescharacteristic
613C2×C29#267611yescharacteristic
614C2×C29#269711yescharacteristic
615C2×C29#270211yescharacteristic
616C2×C29#270311yescharacteristic
617C2×C29#271511yescharacteristic
618C2×C29#276111yescharacteristic
619C2×C29#280011yescharacteristic
620C2×C29#283711yescharacteristic
621C25C23×C2911yescharacteristic
622C25C23×C2911yescharacteristic
623C22×D4—22no—
624C22×D4—22no—
625C22×D4—22no—
626C22×D4—41no—
627C22×D4—41no—
628C22×D4—41no—
629C22×D4—41no—
630C23×C4C23×C2911yescharacteristic
631C23×C4C23×C2911yescharacteristic
632C23×C4C23×C2911yescharacteristic
633C23×C4C23×C2911yescharacteristic
634C23×C4C23×C2911yescharacteristic
635C23×C4C23×C2911yescharacteristic
636C23×C4C23×C2911yescharacteristic
637C23×C4C23×C2911yescharacteristic
638C23×C4C23×C2911yescharacteristic
639C23×C4C23×C2911yescharacteristic
640C23×C4C23×C2911yescharacteristic
641C23×C4C23×C2911yescharacteristic
642C23×C4C23×C2911yescharacteristic
643C2×C4⋊C4—22no—
644C2×C4⋊C4—22no—
645C2×C4⋊C4—22no—
646C2×C4⋊C4—22no—
647C2×C4⋊C4—22no—
648C2×C4⋊C4—22no—
649C2×C4⋊C4—22no—
650C2×C4⋊C4—22no—
651C2×C4⋊C4—22no—
652C2×C4⋊C4—41no—
653C2×C4⋊C4—41no—
654C2×C4⋊C4—41no—
655C2×C4⋊C4—41no—
656C2×C4⋊C4—41no—
657C2×C4⋊C4—41no—
658C2×C22⋊C4—22no—
659C2×C22⋊C4—22no—
660C2×C22⋊C4—22no—
661C2×C22⋊C4—22no—
662C2×C22⋊C4—22no—
663C2×C22⋊C4—22no—
664C2×C22⋊C4—22no—
665C2×C22⋊C4—22no—
666C2×C22⋊C4—22no—
667C2×C22⋊C4—22no—
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—41no—
678C2×C22⋊C4—41no—
679C2×C22⋊C4—41no—
680C2×C22⋊C4—41no—
681C2×C22⋊C4—41no—
682C2×C22⋊C4—41no—
683C2×C22⋊C4—41no—
684C2×C22⋊C4—41no—
685C2×C22⋊C4—41no—
686C2×C22⋊C4—41no—
687C2×C22⋊C4—41no—
688C2×C22⋊C4—41no—
689C2×C22⋊C4—41no—
690C2×C22⋊C4—41no—
691C2×C22⋊C4—41no—
692C2×C22⋊C4—41no—
693C2×C22⋊C4D4×C2914yes—
694C2×C42—22no—
695C2×C42—41no—
696C2×C42—41no—
697#95—22no—
698#95—22no—
699#95—22no—
700#95—22no—
701#95—22no—
702#95—22no—
703#95—22no—
704#95—41no—
705#95—41no—
706#95—41no—
707#95—41no—
708#95—41no—
709#95—41no—
710#95—41no—
711#95—41no—
712#95D4×C2914yescomplemented
713C29#1653411yescharacteristic, direct product factor, Sylow
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—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—
742C24C2×D4×C2912yes—
743C24#41×C2912yes—
744C24C24×C2911yescharacteristic
745C2×D4—44no—
746C2×D4—44no—
747C2×D4—44no—
748C2×D4—44no—
749C2×D4—44no—
750C2×D4—44no—
751C2×D4—44no—
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×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×C4C2×D4×C2912yes—
835C22×C4C2×D4×C2912yes—
836C22×C4C2×D4×C2912yes—
837C22×C4C2×D4×C2912yes—
838C22×C4C2×D4×C2912yes—
839C22×C4#41×C2912yes—
840C22×C4#41×C2912yes—
841C22×C4#41×C2912yes—
842C22×C4#41×C2912yes—
843C4⋊C4—44no—
844C4⋊C4—44no—
845C4⋊C4—44no—
846C4⋊C4—44no—
847C4⋊C4—44no—
848C22⋊C4—28no—
849C22⋊C4—44no—
850C22⋊C4—44no—
851C22⋊C4—44no—
852C22⋊C4—44no—
853C22⋊C4—44no—
854C22⋊C4—44no—
855C22⋊C4—44no—
856C22⋊C4—44no—
857C22⋊C4—44no—
858C22⋊C4—44no—
859C22⋊C4—44no—
860C42—44no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—22no—
867C23—22no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
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—
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—
931C23C22×D4×C2911yescharacteristic
932C23C22×D4×C2911yescharacteristic
933C23C2×#41×C2911yescharacteristic
934C23C2×#41×C2911yescharacteristic
935C23C2×#41×C2911yescharacteristic
936C23C2×#41×C2911yescharacteristic
937C23C2×#41×C2911yescharacteristic
938C23C29×H(5,𝔽2)11yescharacteristic
939C23C29×H(5,𝔽2)11yescharacteristic
940C23C29×H(5,𝔽2)11yescharacteristic
941C23C29×H(5,𝔽2)11yescharacteristic
942C23C29×H(5,𝔽2)11yescharacteristic
943C23C29×H(5,𝔽2)11yescharacteristic
944C23C29×2−1+411yescharacteristic
945C23C29×2−1+411yescharacteristic
946D4—416no—
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—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
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—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—
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—
1038C22—42no—
1039C22—42no—
1040C22—42no—
1041C22—42no—
1042C22—42no—
1043C22—42no—
1044C22—42no—
1045C22—42no—
1046C22—42no—
1047C22—42no—
1048C22—42no—
1049C22—42no—
1050C22—42no—
1051C22—42no—
1052C22—81no—
1053C22—81no—
1054C22—81no—
1055C22—81no—
1056C22—81no—
1057C22—81no—
1058C22—81no—
1059C22—81no—
1060C22—81no—
1061C22—81no—
1062C22—81no—
1063C22—81no—
1064C22—81no—
1065C22—81no—
1066C22—81no—
1067C22—81no—
1068C22C29×#52511yescharacteristic
1069C22C29×#52911yescharacteristic
1070C22C29×#53211yescharacteristic
1071C22C29×#53411yescharacteristic
1072C22C29×#53511yescharacteristic
1073C22C29×#53711yescharacteristic
1074C22C29×#53711yescharacteristic
1075C22C29×#53811yescharacteristic
1076C22C29×#53811yescharacteristic
1077C22C29×#53811yescharacteristic
1078C22C29×#53811yescharacteristic
1079C22C29×#53811yescharacteristic
1080C22C29×#53911yescharacteristic
1081C22C29×#54011yescharacteristic
1082C22C29×#54011yescharacteristic
1083C22C29×#54011yescharacteristic
1084C22C29×#54211yescharacteristic
1085C22C29×#54211yescharacteristic
1086C22C29×#54211yescharacteristic
1087C22D42×C2911yescharacteristic
1088C22C29×#54611yescharacteristic
1089C22C29×#54611yescharacteristic
1090C22C29×#54611yescharacteristic
1091C22C29×#54611yescharacteristic
1092C22C29×#54711yescharacteristic
1093C22C29×#54811yescharacteristic
1094C22C29×#55111yescharacteristic
1095C22C29×#55211yescharacteristic
1096C22C29×#55311yescharacteristic
1097C22C29×#55311yescharacteristic
1098C22C29×#55611yescharacteristic
1099C22C29×#56011yescharacteristic
1100C22C29×#56211yescharacteristic
1101C22C29×#56211yescharacteristic
1102C22C29×#56311yescharacteristic
1103C4—42no—
1104C4—42no—
1105C4—42no—
1106C4—42no—
1107C4—42no—
1108C4—42no—
1109C4—42no—
1110C4—42no—
1111C4—42no—
1112C4—81no—
1113C4—81no—
1114C4—81no—
1115C4—81no—
1116C2—82no—
1117C2—82no—
1118C2C29×#246411yescharacteristic
1119C2C29×#247011yescharacteristic
1120C2C29×#256011yescharacteristic
1121C2C29×#263011yescharacteristic
1122C2C29×#264811yescharacteristic
1123C2C29×#266211yescharacteristic
1124C2C29×#267111yescharacteristic
1125C2C29×#267611yescharacteristic
1126C2C29×#269711yescharacteristic
1127C2C29×#270211yescharacteristic
1128C2C29×#270311yescharacteristic
1129C2C29×#271511yescharacteristic
1130C2C29×#276111yescharacteristic
1131C2C29×#280011yescharacteristic
1132C2C29×#283711yescharacteristic
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
4. C2×C29×#388C2semidirect
5. C29×#1442C2semidirect
6. C29×#1441C2semidirect
7. C29×#1441C2semidirect
8. C29×#1440C2semidirect
9. C29×#1439C2semidirect
10. C29×#1439C2semidirect
11. C29×#1439C2semidirect
14. C29×#1437C2semidirect
15. C29×#1436C2semidirect
146. C29×#95D4semidirect
294. #16534C29direct (N × H)
472. C2×#397C2×C29semidirect
473. C2×#396C2×C29semidirect
475. C2×#388C2×C29semidirect
476. #1442C2×C29semidirect
477. #1441C2×C29semidirect
478. #1441C2×C29semidirect
479. #1440C2×C29semidirect
480. #1439C2×C29semidirect
481. #1439C2×C29semidirect
482. #1439C2×C29semidirect
485. #1437C2×C29semidirect
486. #1436C2×C29semidirect
712. #95D4×C29semidirect
713. C29#16534direct (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×#3882
C29×#14422
C29×#14412
C29×#14402
C29×#14392
C29×#14382
C29×#14372
C29×#14362
#1653429