Finite Group Databasebeta

← C29×#14563 #20309463

Subgroups — C29×#14563 #20309463

Order 7424.

1750 conjugacy classes of subgroups.

The subgroup lattice has 1148 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×#389C211yesmaximal, characteristic, complemented
4C2×C29×#388C211yesmaximal, characteristic, complemented
5C2×C29×#388C211yesmaximal, characteristic, complemented
6C29×#1439C211yesmaximal, characteristic, complemented
7C29×#1439C211yesmaximal, characteristic, complemented
8C29×#1439C211yesmaximal, characteristic, complemented
9C29×#1439C211yesmaximal, characteristic, complemented
10C29×#1438C211yesmaximal, characteristic
11C29×#1437C211yesmaximal, characteristic, complemented
12C29×#1437C211yesmaximal, characteristic, complemented
13C29×#1436C211yesmaximal, characteristic, complemented
14C29×#1436C211yesmaximal, 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×#394C418yescomplemented
38C29×#390—24no—
39C29×#389—24no—
40C29×#388—24no—
41C29×#388—24no—
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
56C25×C29C2311yescharacteristic
57C25×C29C2311yescharacteristic
58C22×D4×C29—22no—
59C22×D4×C29—22no—
60C22×D4×C29—41no—
61C22×D4×C29—41no—
62C22×D4×C29—41no—
63C22×D4×C29—41no—
64C22×D4×C29C2×C414yes—
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
77C23×C4×C29C2311yescharacteristic
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—41no—
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×C29C2×C414yes—
92C2×C4⋊C4×C29D414yes—
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—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×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×C29C2×C414yes—
126C2×C22⋊C4×C29C2×C414yes—
127C2×C22⋊C4×C29C2×C414yes—
128C2×C22⋊C4×C29C2×C414yes—
129C2×C42×C29—22no—
130C2×C42×C29—22no—
131C2×C42×C29—22no—
132C2×C42×C29—22no—
133C2×C42×C29—41no—
134C2×C42×C29—41no—
135C2×C42×C29—41no—
136C2×C42×C29—41no—
137C2×C42×C29—41no—
138C29×#95—22no—
139C29×#95—22no—
140C29×#95—22no—
141C29×#95—22no—
142C29×#95—22no—
143C29×#95—22no—
144C29×#95—22no—
145C29×#95—41no—
146C29×#95—41no—
147C29×#95—41no—
148C29×#95—41no—
149C29×#95—41no—
150C29×#95C2×C414yes—
151C29×#95D414yescomplemented
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×C29—21no—
176C24×C29—21no—
177C24×C29—21no—
178C24×C29—21no—
179C24×C29—21no—
180C24×C29C22×C412yes—
181C24×C29C22×C412yes—
182C24×C29C2411yescharacteristic
183C2×D4×C29—28no—
184C2×D4×C29—44no—
185C2×D4×C29—44no—
186C2×D4×C29—44no—
187C2×D4×C29—44no—
188C2×D4×C29—44no—
189C2×D4×C29—44no—
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×C29C22×C412yes—
267C22×C4×C29C22×C412yes—
268C22×C4×C29C22×C412yes—
269C22×C4×C29C22×C412yes—
270C22×C4×C29C22×C412yes—
271C22×C4×C29C2×D412yes—
272C22×C4×C29C2×D412yes—
273C22×C4×C29C2×D412yes—
274C22×C4×C29C2×D412yes—
275C22×C4×C29C2×D412yes—
276C22×C4×C29C2×D412yes—
277C22×C4×C29#4112yes—
278C22×C4×C29#4112yes—
279C22×C4×C29#4112yes—
280C22×C4×C29#4112yes—
281C4⋊C4×C29—28no—
282C4⋊C4×C29—44no—
283C4⋊C4×C29—44no—
284C4⋊C4×C29—44no—
285C4⋊C4×C29—44no—
286C22⋊C4×C29—28no—
287C22⋊C4×C29—28no—
288C22⋊C4×C29—44no—
289C22⋊C4×C29—44no—
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—
298C42×C29—44no—
299C42×C29—44no—
300C42×C29—44no—
301#14563C2911yesmaximal, characteristic, direct product factor, Sylow
302C23×C29—22no—
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—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×C29—41no—
366C23×C29—41no—
367C23×C29—41no—
368C23×C29—41no—
369C23×C29—41no—
370C23×C29—41no—
371C23×C29—41no—
372C23×C29C23×C411yescharacteristic
373C23×C29C22×D411yescharacteristic
374C23×C29C22×D411yescharacteristic
375C23×C29C2×#4111yescharacteristic
376C23×C29C2×#4111yescharacteristic
377C23×C29C2×#4111yescharacteristic
378C23×C29C2×#4111yescharacteristic
379C23×C29H(5,𝔽2)11yescharacteristic
380C23×C29H(5,𝔽2)11yescharacteristic
381C23×C29H(5,𝔽2)11yescharacteristic
382C23×C29H(5,𝔽2)11yescharacteristic
383C23×C29H(5,𝔽2)11yescharacteristic
384C23×C29H(5,𝔽2)11yescharacteristic
385C23×C292−1+411yescharacteristic
386C23×C292−1+411yescharacteristic
387D4×C29—416no—
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—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—22no—
426C2×C4×C29—22no—
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×C29C4×D414yes—
478C2×C4×C29C4×D414yes—
479C2×#394C2×C2911yescharacteristic
480C2×#390C2×C2911yescharacteristic
481C2×#389C2×C2911yescharacteristic, complemented
482C2×#388C2×C2911yescharacteristic, complemented
483C2×#388C2×C2911yescharacteristic, complemented
484#1439C2×C2911yescharacteristic, complemented
485#1439C2×C2911yescharacteristic, complemented
486#1439C2×C2911yescharacteristic, complemented
487#1439C2×C2911yescharacteristic, complemented
488#1438C2×C2911yescharacteristic
489#1437C2×C2911yescharacteristic, complemented
490#1437C2×C2911yescharacteristic, complemented
491#1436C2×C2911yescharacteristic, complemented
492#1436C2×C2911yescharacteristic, complemented
493#1436C2×C2911yescharacteristic, complemented
494C22×C29—42no—
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—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—81no—
518C22×C29—81no—
519C22×C29—81no—
520C22×C29—81no—
521C22×C29—81no—
522C22×C29—81no—
523C22×C29—81no—
524C22×C29C2×C4×D411yescharacteristic
525C22×C29C2×C4×D411yescharacteristic
526C22×C29C4×#4111yescharacteristic
527C22×C29#51811yescharacteristic
528C22×C29#51811yescharacteristic
529C22×C29#52011yescharacteristic
530C22×C29#52011yescharacteristic
531C22×C29#53411yescharacteristic
532C22×C29#53511yescharacteristic
533C22×C29#53511yescharacteristic
534C22×C29#53711yescharacteristic
535C22×C29#53811yescharacteristic
536C22×C29#53811yescharacteristic
537C22×C29#53811yescharacteristic
538C22×C29#53911yescharacteristic
539C22×C29#54011yescharacteristic
540C22×C29#54011yescharacteristic
541C22×C29#54211yescharacteristic
542C22×C29#54211yescharacteristic
543C22×C29D4211yescharacteristic
544C22×C29#54611yescharacteristic
545C22×C29#54611yescharacteristic
546C22×C29#54711yescharacteristic
547C22×C29#54811yescharacteristic
548C22×C29#54811yescharacteristic
549C22×C29#55011yescharacteristic
550C22×C29#55311yescharacteristic
551C22×C29#55311yescharacteristic
552C22×C29#55511yescharacteristic
553C22×C29#55611yescharacteristic
554C22×C29#55911yescharacteristic
555C22×C29#56011yescharacteristic
556C22×C29#56211yescharacteristic
557C22×C29#56211yescharacteristic
558C22×C29#56311yescharacteristic
559C4×C29—24no—
560C4×C29—24no—
561C4×C29—42no—
562C4×C29—42no—
563C4×C29—42no—
564C4×C29—42no—
565C4×C29—42no—
566C4×C29—42no—
567C4×C29—42no—
568C4×C29—42no—
569C4×C29—42no—
570C4×C29—81no—
571C4×C29—81no—
572C23×D4C22×C2911yescharacteristic
573C22×C4⋊C4C22×C2911yescharacteristic
574C22×C4⋊C4C22×C2911yescharacteristic
575C22×C4⋊C4C22×C2911yescharacteristic
576C22×C4⋊C4C22×C2911yescharacteristic
577C22×C4⋊C4C22×C2911yescharacteristic
578C22×C22⋊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×C42C22×C2911yescharacteristic
591C22×C42C22×C2911yescharacteristic
592C22×C42C22×C2911yescharacteristic
593#394C4×C2918yescomplemented
594#390—24no—
595#389—24no—
596#388—24no—
597#388—24no—
598C2×#95C22×C2911yescharacteristic
599C2×#95C22×C2911yescharacteristic
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×C29—82no—
613C2×C29—82no—
614C2×C29#232111yescharacteristic
615C2×C29#232411yescharacteristic
616C2×C29#233511yescharacteristic
617C2×C29#236111yescharacteristic
618C2×C29#236311yescharacteristic
619C2×C29#236711yescharacteristic
620C2×C29#237611yescharacteristic
621C2×C29#267311yescharacteristic
622C2×C29#267611yescharacteristic
623C2×C29#271011yescharacteristic
624C2×C29#271111yescharacteristic
625C2×C29#272711yescharacteristic
626C2×C29#273111yescharacteristic
627C2×C29#280011yescharacteristic
628C2×C29#280311yescharacteristic
629C25C23×C2911yescharacteristic
630C25C23×C2911yescharacteristic
631C22×D4—22no—
632C22×D4—22no—
633C22×D4—41no—
634C22×D4—41no—
635C22×D4—41no—
636C22×D4—41no—
637C22×D4C2×C4×C2914yes—
638C23×C4C23×C2911yescharacteristic
639C23×C4C23×C2911yescharacteristic
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
651C2×C4⋊C4—22no—
652C2×C4⋊C4—22no—
653C2×C4⋊C4—22no—
654C2×C4⋊C4—22no—
655C2×C4⋊C4—22no—
656C2×C4⋊C4—22no—
657C2×C4⋊C4—22no—
658C2×C4⋊C4—41no—
659C2×C4⋊C4—41no—
660C2×C4⋊C4—41no—
661C2×C4⋊C4—41no—
662C2×C4⋊C4—41no—
663C2×C4⋊C4—41no—
664C2×C4⋊C4C2×C4×C2914yes—
665C2×C4⋊C4D4×C2914yes—
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—22no—
678C2×C22⋊C4—22no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—22no—
681C2×C22⋊C4—22no—
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⋊C4—41no—
694C2×C22⋊C4—41no—
695C2×C22⋊C4—41no—
696C2×C22⋊C4—41no—
697C2×C22⋊C4—41no—
698C2×C22⋊C4C2×C4×C2914yes—
699C2×C22⋊C4C2×C4×C2914yes—
700C2×C22⋊C4C2×C4×C2914yes—
701C2×C22⋊C4C2×C4×C2914yes—
702C2×C42—22no—
703C2×C42—22no—
704C2×C42—22no—
705C2×C42—22no—
706C2×C42—41no—
707C2×C42—41no—
708C2×C42—41no—
709C2×C42—41no—
710C2×C42—41no—
711#95—22no—
712#95—22no—
713#95—22no—
714#95—22no—
715#95—22no—
716#95—22no—
717#95—22no—
718#95—41no—
719#95—41no—
720#95—41no—
721#95—41no—
722#95—41no—
723#95C2×C4×C2914yes—
724#95D4×C2914yescomplemented
725C29#1456311yescharacteristic, direct product factor, Sylow
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—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24C22×C4×C2912yes—
755C24C22×C4×C2912yes—
756C24C24×C2911yescharacteristic
757C2×D4—28no—
758C2×D4—44no—
759C2×D4—44no—
760C2×D4—44no—
761C2×D4—44no—
762C2×D4—44no—
763C2×D4—44no—
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×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4C22×C4×C2912yes—
841C22×C4C22×C4×C2912yes—
842C22×C4C22×C4×C2912yes—
843C22×C4C22×C4×C2912yes—
844C22×C4C22×C4×C2912yes—
845C22×C4C2×D4×C2912yes—
846C22×C4C2×D4×C2912yes—
847C22×C4C2×D4×C2912yes—
848C22×C4C2×D4×C2912yes—
849C22×C4C2×D4×C2912yes—
850C22×C4C2×D4×C2912yes—
851C22×C4#41×C2912yes—
852C22×C4#41×C2912yes—
853C22×C4#41×C2912yes—
854C22×C4#41×C2912yes—
855C4⋊C4—28no—
856C4⋊C4—44no—
857C4⋊C4—44no—
858C4⋊C4—44no—
859C4⋊C4—44no—
860C22⋊C4—28no—
861C22⋊C4—28no—
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—
872C42—44no—
873C42—44no—
874C42—44no—
875C23—22no—
876C23—22no—
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—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—
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—
945C23C23×C4×C2911yescharacteristic
946C23C22×D4×C2911yescharacteristic
947C23C22×D4×C2911yescharacteristic
948C23C2×#41×C2911yescharacteristic
949C23C2×#41×C2911yescharacteristic
950C23C2×#41×C2911yescharacteristic
951C23C2×#41×C2911yescharacteristic
952C23C29×H(5,𝔽2)11yescharacteristic
953C23C29×H(5,𝔽2)11yescharacteristic
954C23C29×H(5,𝔽2)11yescharacteristic
955C23C29×H(5,𝔽2)11yescharacteristic
956C23C29×H(5,𝔽2)11yescharacteristic
957C23C29×H(5,𝔽2)11yescharacteristic
958C23C29×2−1+411yescharacteristic
959C23C29×2−1+411yescharacteristic
960D4—416no—
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—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—22no—
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×C4C4×D4×C2914yes—
1051C2×C4C4×D4×C2914yes—
1052C22—42no—
1053C22—42no—
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—81no—
1067C22—81no—
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—
1082C22C2×C4×D4×C2911yescharacteristic
1083C22C2×C4×D4×C2911yescharacteristic
1084C22C4×#41×C2911yescharacteristic
1085C22C29×#51811yescharacteristic
1086C22C29×#51811yescharacteristic
1087C22C29×#52011yescharacteristic
1088C22C29×#52011yescharacteristic
1089C22C29×#53411yescharacteristic
1090C22C29×#53511yescharacteristic
1091C22C29×#53511yescharacteristic
1092C22C29×#53711yescharacteristic
1093C22C29×#53811yescharacteristic
1094C22C29×#53811yescharacteristic
1095C22C29×#53811yescharacteristic
1096C22C29×#53911yescharacteristic
1097C22C29×#54011yescharacteristic
1098C22C29×#54011yescharacteristic
1099C22C29×#54211yescharacteristic
1100C22C29×#54211yescharacteristic
1101C22D42×C2911yescharacteristic
1102C22C29×#54611yescharacteristic
1103C22C29×#54611yescharacteristic
1104C22C29×#54711yescharacteristic
1105C22C29×#54811yescharacteristic
1106C22C29×#54811yescharacteristic
1107C22C29×#55011yescharacteristic
1108C22C29×#55311yescharacteristic
1109C22C29×#55311yescharacteristic
1110C22C29×#55511yescharacteristic
1111C22C29×#55611yescharacteristic
1112C22C29×#55911yescharacteristic
1113C22C29×#56011yescharacteristic
1114C22C29×#56211yescharacteristic
1115C22C29×#56211yescharacteristic
1116C22C29×#56311yescharacteristic
1117C4—24no—
1118C4—24no—
1119C4—42no—
1120C4—42no—
1121C4—42no—
1122C4—42no—
1123C4—42no—
1124C4—42no—
1125C4—42no—
1126C4—42no—
1127C4—42no—
1128C4—81no—
1129C4—81no—
1130C2—82no—
1131C2—82no—
1132C2C29×#232111yescharacteristic
1133C2C29×#232411yescharacteristic
1134C2C29×#233511yescharacteristic
1135C2C29×#236111yescharacteristic
1136C2C29×#236311yescharacteristic
1137C2C29×#236711yescharacteristic
1138C2C29×#237611yescharacteristic
1139C2C29×#267311yescharacteristic
1140C2C29×#267611yescharacteristic
1141C2C29×#271011yescharacteristic
1142C2C29×#271111yescharacteristic
1143C2C29×#272711yescharacteristic
1144C2C29×#273111yescharacteristic
1145C2C29×#280011yescharacteristic
1146C2C29×#280311yescharacteristic
subgroupG/H
center, socleC24×C29C24
commutatorC23C23×C4×C29
Frattini, cosocleC24C24×C29
prime radicalC23×D4×C29C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C29 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C29×#389C2semidirect
4. C2×C29×#388C2semidirect
5. C2×C29×#388C2semidirect
6. C29×#1439C2semidirect
7. C29×#1439C2semidirect
8. C29×#1439C2semidirect
9. C29×#1439C2semidirect
11. C29×#1437C2semidirect
12. C29×#1437C2semidirect
13. C29×#1436C2semidirect
14. C29×#1436C2semidirect
15. C29×#1436C2semidirect
37. C29×#394C4semidirect
151. C29×#95D4semidirect
301. #14563C29direct (N × H)
481. C2×#389C2×C29semidirect
482. C2×#388C2×C29semidirect
483. C2×#388C2×C29semidirect
484. #1439C2×C29semidirect
485. #1439C2×C29semidirect
486. #1439C2×C29semidirect
487. #1439C2×C29semidirect
489. #1437C2×C29semidirect
490. #1437C2×C29semidirect
491. #1436C2×C29semidirect
492. #1436C2×C29semidirect
493. #1436C2×C29semidirect
593. #394C4×C29semidirect
724. #95D4×C29semidirect
725. C29#14563direct (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×#3892
C2×C29×#3882
C29×#14392
C29×#14382
C29×#14372
C29×#14362
#1456329