Finite Group Databasebeta

← C29×#16535 #20311435

Subgroups — C29×#16535 #20311435

Order 7424.

1914 conjugacy classes of subgroups.

The subgroup lattice has 1292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#397C211yesmaximal, characteristic, complemented
2C2×C29×#394C211yesmaximal, characteristic, complemented
3C2×C29×#392C211yesmaximal, characteristic
4C2×C29×#388C211yesmaximal, characteristic, complemented
5C29×#1443C211yesmaximal, characteristic, complemented
6C29×#1442C211yesmaximal, characteristic, complemented
7C29×#1439C211yesmaximal, characteristic, complemented
8C29×#1439C211yesmaximal, characteristic, complemented
9C29×#1438C211yesmaximal, characteristic, complemented
10C29×#1438C211yesmaximal, characteristic, complemented
11C29×#1438C211yesmaximal, characteristic, complemented
12C29×#1438C211yesmaximal, characteristic, complemented
13C29×#1438C211yesmaximal, characteristic, complemented
14C29×#1437C211yesmaximal, characteristic, complemented
15C29×#1437C211yesmaximal, characteristic, complemented
16C23×D4×C29C2211yescharacteristic
17C23×D4×C29C2211yescharacteristic
18C23×D4×C29C2211yescharacteristic
19C22×C4⋊C4×C29C2211yescharacteristic
20C22×C4⋊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×C22⋊C4×C29C2211yescharacteristic
32C22×C22⋊C4×C29C2211yescharacteristic
33C22×C22⋊C4×C29C2211yescharacteristic
34C22×C22⋊C4×C29C2211yescharacteristic
35C22×C22⋊C4×C29C2211yescharacteristic
36C22×C42×C29C2211yescharacteristic
37C29×#397—24no—
38C29×#394—24no—
39C29×#392—24no—
40C29×#388—24no—
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
57C25×C29C2311yescharacteristic
58C22×D4×C29—22no—
59C22×D4×C29—22no—
60C22×D4×C29—22no—
61C22×D4×C29—22no—
62C22×D4×C29—22no—
63C22×D4×C29—22no—
64C22×D4×C29—22no—
65C22×D4×C29—22no—
66C22×D4×C29—22no—
67C22×D4×C29—41no—
68C22×D4×C29—41no—
69C22×D4×C29—41no—
70C22×D4×C29—41no—
71C22×D4×C29—41no—
72C22×D4×C29—41no—
73C22×D4×C29—41no—
74C22×D4×C29—41no—
75C22×D4×C29—41no—
76C22×D4×C29—41no—
77C22×D4×C29—41no—
78C22×D4×C29—41no—
79C23×C4×C29C2311yescharacteristic
80C23×C4×C29C2311yescharacteristic
81C23×C4×C29C2311yescharacteristic
82C23×C4×C29C2311yescharacteristic
83C23×C4×C29C2311yescharacteristic
84C23×C4×C29C2311yescharacteristic
85C23×C4×C29C2311yescharacteristic
86C23×C4×C29C2311yescharacteristic
87C23×C4×C29C2311yescharacteristic
88C23×C4×C29C2311yescharacteristic
89C23×C4×C29C2311yescharacteristic
90C23×C4×C29C2311yescharacteristic
91C2×C4⋊C4×C29—22no—
92C2×C4⋊C4×C29—22no—
93C2×C4⋊C4×C29—22no—
94C2×C4⋊C4×C29—41no—
95C2×C4⋊C4×C29—41no—
96C2×C4⋊C4×C29—41no—
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—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×C29—41no—
128C2×C22⋊C4×C29—41no—
129C2×C22⋊C4×C29—41no—
130C2×C22⋊C4×C29—41no—
131C2×C22⋊C4×C29—41no—
132C2×C22⋊C4×C29—41no—
133C2×C22⋊C4×C29—41no—
134C2×C22⋊C4×C29—41no—
135C2×C22⋊C4×C29—41no—
136C2×C22⋊C4×C29—41no—
137C2×C22⋊C4×C29—41no—
138C2×C22⋊C4×C29—41no—
139C2×C22⋊C4×C29—41no—
140C2×C22⋊C4×C29—41no—
141C2×C22⋊C4×C29D414yes—
142C2×C42×C29—22no—
143C2×C42×C29—41no—
144C2×C42×C29—41no—
145C29×#95—22no—
146C29×#95—22no—
147C29×#95—22no—
148C29×#95—22no—
149C29×#95—22no—
150C29×#95—22no—
151C29×#95—41no—
152C29×#95—41no—
153C29×#95—41no—
154C29×#95—41no—
155C29×#95—41no—
156C29×#95—41no—
157C29×#95—41no—
158C29×#95D414yescomplemented
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×C29—21no—
182C24×C29—21no—
183C24×C29—21no—
184C24×C29—21no—
185C24×C29—21no—
186C24×C29—21no—
187C24×C29—21no—
188C24×C29—21no—
189C24×C29—21no—
190C24×C29—21no—
191C24×C29—21no—
192C24×C29—21no—
193C24×C29—21no—
194C24×C29—21no—
195C24×C29—21no—
196C24×C29—21no—
197C24×C29—21no—
198C24×C29—21no—
199C24×C29—21no—
200C24×C29—21no—
201C24×C29C2×D412yes—
202C24×C29#4112yes—
203C24×C29#4112yes—
204C24×C29C2411yescharacteristic
205C2×D4×C29—44no—
206C2×D4×C29—44no—
207C2×D4×C29—44no—
208C2×D4×C29—44no—
209C2×D4×C29—44no—
210C2×D4×C29—44no—
211C2×D4×C29—44no—
212C2×D4×C29—44no—
213C2×D4×C29—44no—
214C2×D4×C29—44no—
215C2×D4×C29—44no—
216C2×D4×C29—44no—
217C2×D4×C29—44no—
218C2×D4×C29—44no—
219C2×D4×C29—44no—
220C2×D4×C29—44no—
221C2×D4×C29—44no—
222C2×D4×C29—44no—
223C2×D4×C29—44no—
224C2×D4×C29—44no—
225C2×D4×C29—44no—
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×C29—21no—
268C22×C4×C29—21no—
269C22×C4×C29—21no—
270C22×C4×C29—21no—
271C22×C4×C29—21no—
272C22×C4×C29—21no—
273C22×C4×C29—21no—
274C22×C4×C29—21no—
275C22×C4×C29—21no—
276C22×C4×C29—21no—
277C22×C4×C29—21no—
278C22×C4×C29—21no—
279C22×C4×C29—21no—
280C22×C4×C29—21no—
281C22×C4×C29—21no—
282C22×C4×C29—21no—
283C22×C4×C29—21no—
284C22×C4×C29—21no—
285C22×C4×C29—21no—
286C22×C4×C29—21no—
287C22×C4×C29—21no—
288C22×C4×C29—21no—
289C22×C4×C29—21no—
290C22×C4×C29—21no—
291C22×C4×C29—21no—
292C22×C4×C29—21no—
293C22×C4×C29—21no—
294C22×C4×C29—21no—
295C22×C4×C29—21no—
296C22×C4×C29—21no—
297C22×C4×C29—21no—
298C22×C4×C29—21no—
299C22×C4×C29—21no—
300C22×C4×C29—21no—
301C22×C4×C29—21no—
302C22×C4×C29C2×D412yes—
303C22×C4×C29C2×D412yes—
304C22×C4×C29C2×D412yes—
305C22×C4×C29C2×D412yes—
306C22×C4×C29C2×D412yes—
307C22×C4×C29#4112yes—
308C22×C4×C29#4112yes—
309C22×C4×C29#4112yes—
310C4⋊C4×C29—44no—
311C4⋊C4×C29—44no—
312C22⋊C4×C29—28no—
313C22⋊C4×C29—44no—
314C22⋊C4×C29—44no—
315C22⋊C4×C29—44no—
316C22⋊C4×C29—44no—
317C22⋊C4×C29—44no—
318C22⋊C4×C29—44no—
319C22⋊C4×C29—44no—
320C22⋊C4×C29—44no—
321C22⋊C4×C29—44no—
322C22⋊C4×C29—44no—
323C22⋊C4×C29—44no—
324C22⋊C4×C29—44no—
325C22⋊C4×C29—44no—
326C22⋊C4×C29—44no—
327C42×C29—44no—
328#16535C2911yesmaximal, characteristic, direct product factor, Sylow
329C23×C29—22no—
330C23×C29—22no—
331C23×C29—22no—
332C23×C29—22no—
333C23×C29—22no—
334C23×C29—22no—
335C23×C29—22no—
336C23×C29—22no—
337C23×C29—22no—
338C23×C29—22no—
339C23×C29—22no—
340C23×C29—22no—
341C23×C29—22no—
342C23×C29—22no—
343C23×C29—22no—
344C23×C29—22no—
345C23×C29—22no—
346C23×C29—22no—
347C23×C29—22no—
348C23×C29—22no—
349C23×C29—22no—
350C23×C29—41no—
351C23×C29—41no—
352C23×C29—41no—
353C23×C29—41no—
354C23×C29—41no—
355C23×C29—41no—
356C23×C29—41no—
357C23×C29—41no—
358C23×C29—41no—
359C23×C29—41no—
360C23×C29—41no—
361C23×C29—41no—
362C23×C29—41no—
363C23×C29—41no—
364C23×C29—41no—
365C23×C29—41no—
366C23×C29—41no—
367C23×C29—41no—
368C23×C29—41no—
369C23×C29—41no—
370C23×C29—41no—
371C23×C29—41no—
372C23×C29—41no—
373C23×C29—41no—
374C23×C29—41no—
375C23×C29—41no—
376C23×C29—41no—
377C23×C29—41no—
378C23×C29—41no—
379C23×C29—41no—
380C23×C29—41no—
381C23×C29—41no—
382C23×C29—41no—
383C23×C29—41no—
384C23×C29—41no—
385C23×C29—41no—
386C23×C29—41no—
387C23×C29—41no—
388C23×C29—41no—
389C23×C29—41no—
390C23×C29—41no—
391C23×C29—41no—
392C23×C29—41no—
393C23×C29—41no—
394C23×C29—41no—
395C23×C29—41no—
396C23×C29—41no—
397C23×C29—41no—
398C23×C29—41no—
399C23×C29—41no—
400C23×C29—41no—
401C23×C29—41no—
402C23×C29—41no—
403C23×C29—41no—
404C23×C29—41no—
405C23×C29—41no—
406C23×C29—41no—
407C23×C29—41no—
408C23×C29—41no—
409C23×C29—41no—
410C23×C29—41no—
411C23×C29—41no—
412C23×C29—41no—
413C23×C29—41no—
414C23×C29—41no—
415C23×C29—41no—
416C23×C29—41no—
417C23×C29—41no—
418C23×C29—41no—
419C23×C29—41no—
420C23×C29—41no—
421C23×C29—41no—
422C23×C29—41no—
423C23×C29—41no—
424C23×C29—41no—
425C23×C29—41no—
426C23×C29—41no—
427C23×C29—41no—
428C23×C29—41no—
429C23×C29—41no—
430C23×C29—41no—
431C23×C29—41no—
432C23×C29—41no—
433C23×C29—41no—
434C23×C29C22×D411yescharacteristic
435C23×C29C22×D411yescharacteristic
436C23×C29C2×#4111yescharacteristic
437C23×C29C2×#4111yescharacteristic
438C23×C29C2×#4111yescharacteristic
439C23×C29C2×#4111yescharacteristic
440C23×C29C2×#4111yescharacteristic
441C23×C29H(5,𝔽2)11yescharacteristic
442C23×C29H(5,𝔽2)11yescharacteristic
443C23×C29H(5,𝔽2)11yescharacteristic
444C23×C29H(5,𝔽2)11yescharacteristic
445C23×C29H(5,𝔽2)11yescharacteristic
446C23×C29H(5,𝔽2)11yescharacteristic
447C23×C29H(5,𝔽2)11yescharacteristic
448C23×C29H(5,𝔽2)11yescharacteristic
449D4×C29—416no—
450D4×C29—416no—
451D4×C29—416no—
452C2×C4×C29—22no—
453C2×C4×C29—22no—
454C2×C4×C29—22no—
455C2×C4×C29—22no—
456C2×C4×C29—22no—
457C2×C4×C29—22no—
458C2×C4×C29—22no—
459C2×C4×C29—22no—
460C2×C4×C29—22no—
461C2×C4×C29—22no—
462C2×C4×C29—22no—
463C2×C4×C29—22no—
464C2×C4×C29—22no—
465C2×C4×C29—22no—
466C2×C4×C29—22no—
467C2×C4×C29—22no—
468C2×C4×C29—22no—
469C2×C4×C29—22no—
470C2×C4×C29—22no—
471C2×C4×C29—22no—
472C2×C4×C29—22no—
473C2×C4×C29—22no—
474C2×C4×C29—22no—
475C2×C4×C29—22no—
476C2×C4×C29—41no—
477C2×C4×C29—41no—
478C2×C4×C29—41no—
479C2×C4×C29—41no—
480C2×C4×C29—41no—
481C2×C4×C29—41no—
482C2×C4×C29—41no—
483C2×C4×C29—41no—
484C2×C4×C29—41no—
485C2×C4×C29—41no—
486C2×C4×C29—41no—
487C2×C4×C29—41no—
488C2×C4×C29—41no—
489C2×C4×C29—41no—
490C2×C4×C29—41no—
491C2×C4×C29—41no—
492C2×C4×C29—41no—
493C2×C4×C29—41no—
494C2×C4×C29—41no—
495C2×C4×C29—41no—
496C2×C4×C29—41no—
497C2×C4×C29—41no—
498C2×C4×C29—41no—
499C2×C4×C29—41no—
500C2×C4×C29—41no—
501C2×C4×C29—41no—
502C2×C4×C29—41no—
503C2×C4×C29—41no—
504C2×C4×C29—41no—
505C2×C4×C29—41no—
506C2×C4×C29—41no—
507C2×C4×C29—41no—
508C2×C4×C29—41no—
509C2×C4×C29—41no—
510C2×C4×C29—41no—
511C2×C4×C29—41no—
512C2×C4×C29—41no—
513C2×C4×C29—41no—
514C2×C4×C29—41no—
515C2×C4×C29—41no—
516C2×C4×C29—41no—
517C2×C4×C29—41no—
518C2×C4×C29—41no—
519C2×C4×C29—41no—
520C2×C4×C29—41no—
521C2×C4×C29—41no—
522C2×C4×C29—41no—
523C2×C4×C29—41no—
524C2×C4×C29—41no—
525C2×C4×C29—41no—
526C2×C4×C29—41no—
527C2×C4×C29—41no—
528C2×C4×C29—41no—
529C2×C4×C29—41no—
530C2×C4×C29—41no—
531C2×C4×C29—41no—
532C2×C4×C29—41no—
533C2×C4×C29—41no—
534C2×C4×C29—41no—
535C2×C4×C29—41no—
536C2×#397C2×C2911yescharacteristic, complemented
537C2×#394C2×C2911yescharacteristic, complemented
538C2×#392C2×C2911yescharacteristic
539C2×#388C2×C2911yescharacteristic, complemented
540#1443C2×C2911yescharacteristic, complemented
541#1442C2×C2911yescharacteristic, complemented
542#1439C2×C2911yescharacteristic, complemented
543#1439C2×C2911yescharacteristic, complemented
544#1438C2×C2911yescharacteristic, complemented
545#1438C2×C2911yescharacteristic, complemented
546#1438C2×C2911yescharacteristic, complemented
547#1438C2×C2911yescharacteristic, complemented
548#1438C2×C2911yescharacteristic, complemented
549#1437C2×C2911yescharacteristic, complemented
550#1437C2×C2911yescharacteristic, complemented
551C22×C29—42no—
552C22×C29—42no—
553C22×C29—42no—
554C22×C29—42no—
555C22×C29—42no—
556C22×C29—42no—
557C22×C29—42no—
558C22×C29—42no—
559C22×C29—42no—
560C22×C29—42no—
561C22×C29—42no—
562C22×C29—42no—
563C22×C29—42no—
564C22×C29—42no—
565C22×C29—42no—
566C22×C29—42no—
567C22×C29—42no—
568C22×C29—42no—
569C22×C29—42no—
570C22×C29—42no—
571C22×C29—42no—
572C22×C29—81no—
573C22×C29—81no—
574C22×C29—81no—
575C22×C29—81no—
576C22×C29—81no—
577C22×C29—81no—
578C22×C29—81no—
579C22×C29—81no—
580C22×C29—81no—
581C22×C29—81no—
582C22×C29—81no—
583C22×C29—81no—
584C22×C29—81no—
585C22×C29—81no—
586C22×C29—81no—
587C22×C29—81no—
588C22×C29—81no—
589C22×C29—81no—
590C22×C29—81no—
591C22×C29—81no—
592C22×C29—81no—
593C22×C29—81no—
594C22×C29—81no—
595C22×C29—81no—
596C22×C29#52511yescharacteristic
597C22×C29#52911yescharacteristic
598C22×C29#53211yescharacteristic
599C22×C29#53411yescharacteristic
600C22×C29#53511yescharacteristic
601C22×C29#53511yescharacteristic
602C22×C29#53511yescharacteristic
603C22×C29#53811yescharacteristic
604C22×C29#53811yescharacteristic
605C22×C29#53811yescharacteristic
606C22×C29#53811yescharacteristic
607C22×C29#53811yescharacteristic
608C22×C29#53811yescharacteristic
609C22×C29#53811yescharacteristic
610C22×C29#53811yescharacteristic
611C22×C29#54011yescharacteristic
612C22×C29#54011yescharacteristic
613C22×C29#54011yescharacteristic
614C22×C29#54011yescharacteristic
615C22×C29D4211yescharacteristic
616C22×C29#54611yescharacteristic
617C22×C29#54611yescharacteristic
618C22×C29#54611yescharacteristic
619C22×C29#54611yescharacteristic
620C22×C29#54611yescharacteristic
621C22×C29#55011yescharacteristic
622C22×C29#55111yescharacteristic
623C22×C29#55111yescharacteristic
624C22×C29#55311yescharacteristic
625C22×C29#55311yescharacteristic
626C22×C29#55311yescharacteristic
627C22×C29#56011yescharacteristic
628C22×C29#56011yescharacteristic
629C22×C29#56011yescharacteristic
630C22×C29H(3,𝔽4)11yescharacteristic
631C4×C29—42no—
632C4×C29—42no—
633C4×C29—42no—
634C4×C29—42no—
635C4×C29—42no—
636C4×C29—42no—
637C4×C29—42no—
638C4×C29—42no—
639C4×C29—81no—
640C4×C29—81no—
641C4×C29—81no—
642C4×C29—81no—
643C23×D4C22×C2911yescharacteristic
644C23×D4C22×C2911yescharacteristic
645C23×D4C22×C2911yescharacteristic
646C22×C4⋊C4C22×C2911yescharacteristic
647C22×C4⋊C4C22×C2911yescharacteristic
648C22×C22⋊C4C22×C2911yescharacteristic
649C22×C22⋊C4C22×C2911yescharacteristic
650C22×C22⋊C4C22×C2911yescharacteristic
651C22×C22⋊C4C22×C2911yescharacteristic
652C22×C22⋊C4C22×C2911yescharacteristic
653C22×C22⋊C4C22×C2911yescharacteristic
654C22×C22⋊C4C22×C2911yescharacteristic
655C22×C22⋊C4C22×C2911yescharacteristic
656C22×C22⋊C4C22×C2911yescharacteristic
657C22×C22⋊C4C22×C2911yescharacteristic
658C22×C22⋊C4C22×C2911yescharacteristic
659C22×C22⋊C4C22×C2911yescharacteristic
660C22×C22⋊C4C22×C2911yescharacteristic
661C22×C22⋊C4C22×C2911yescharacteristic
662C22×C22⋊C4C22×C2911yescharacteristic
663C22×C42C22×C2911yescharacteristic
664#397—24no—
665#394—24no—
666#392—24no—
667#388—24no—
668C2×#95C22×C2911yescharacteristic
669C2×#95C22×C2911yescharacteristic
670C2×#95C22×C2911yescharacteristic
671C2×#95C22×C2911yescharacteristic
672C2×#95C22×C2911yescharacteristic
673C2×#95C22×C2911yescharacteristic
674C2×#95C22×C2911yescharacteristic
675C2×#95C22×C2911yescharacteristic
676C2×#95C22×C2911yescharacteristic
677C2×#95C22×C2911yescharacteristic
678C2×#95C22×C2911yescharacteristic
679C2×#95C22×C2911yescharacteristic
680C2×#95C22×C2911yescharacteristic
681C2×#95C22×C2911yescharacteristic
682C2×C29—82no—
683C2×C29—82no—
684C2×C29—82no—
685C2×C29#246411yescharacteristic
686C2×C29#247111yescharacteristic
687C2×C29#255911yescharacteristic
688C2×C29#263111yescharacteristic
689C2×C29#264811yescharacteristic
690C2×C29#266111yescharacteristic
691C2×C29#267011yescharacteristic
692C2×C29#267311yescharacteristic
693C2×C29#268511yescharacteristic
694C2×C29#269711yescharacteristic
695C2×C29#270311yescharacteristic
696C2×C29#271411yescharacteristic
697C2×C29#275311yescharacteristic
698C2×C29#277811yescharacteristic
699C2×C29#282811yescharacteristic
700C25C23×C2911yescharacteristic
701C25C23×C2911yescharacteristic
702C25C23×C2911yescharacteristic
703C22×D4—22no—
704C22×D4—22no—
705C22×D4—22no—
706C22×D4—22no—
707C22×D4—22no—
708C22×D4—22no—
709C22×D4—22no—
710C22×D4—22no—
711C22×D4—22no—
712C22×D4—41no—
713C22×D4—41no—
714C22×D4—41no—
715C22×D4—41no—
716C22×D4—41no—
717C22×D4—41no—
718C22×D4—41no—
719C22×D4—41no—
720C22×D4—41no—
721C22×D4—41no—
722C22×D4—41no—
723C22×D4—41no—
724C23×C4C23×C2911yescharacteristic
725C23×C4C23×C2911yescharacteristic
726C23×C4C23×C2911yescharacteristic
727C23×C4C23×C2911yescharacteristic
728C23×C4C23×C2911yescharacteristic
729C23×C4C23×C2911yescharacteristic
730C23×C4C23×C2911yescharacteristic
731C23×C4C23×C2911yescharacteristic
732C23×C4C23×C2911yescharacteristic
733C23×C4C23×C2911yescharacteristic
734C23×C4C23×C2911yescharacteristic
735C23×C4C23×C2911yescharacteristic
736C2×C4⋊C4—22no—
737C2×C4⋊C4—22no—
738C2×C4⋊C4—22no—
739C2×C4⋊C4—41no—
740C2×C4⋊C4—41no—
741C2×C4⋊C4—41no—
742C2×C22⋊C4—22no—
743C2×C22⋊C4—22no—
744C2×C22⋊C4—22no—
745C2×C22⋊C4—22no—
746C2×C22⋊C4—22no—
747C2×C22⋊C4—22no—
748C2×C22⋊C4—22no—
749C2×C22⋊C4—22no—
750C2×C22⋊C4—22no—
751C2×C22⋊C4—22no—
752C2×C22⋊C4—22no—
753C2×C22⋊C4—22no—
754C2×C22⋊C4—22no—
755C2×C22⋊C4—22no—
756C2×C22⋊C4—22no—
757C2×C22⋊C4—22no—
758C2×C22⋊C4—22no—
759C2×C22⋊C4—22no—
760C2×C22⋊C4—22no—
761C2×C22⋊C4—22no—
762C2×C22⋊C4—41no—
763C2×C22⋊C4—41no—
764C2×C22⋊C4—41no—
765C2×C22⋊C4—41no—
766C2×C22⋊C4—41no—
767C2×C22⋊C4—41no—
768C2×C22⋊C4—41no—
769C2×C22⋊C4—41no—
770C2×C22⋊C4—41no—
771C2×C22⋊C4—41no—
772C2×C22⋊C4—41no—
773C2×C22⋊C4—41no—
774C2×C22⋊C4—41no—
775C2×C22⋊C4—41no—
776C2×C22⋊C4—41no—
777C2×C22⋊C4—41no—
778C2×C22⋊C4—41no—
779C2×C22⋊C4—41no—
780C2×C22⋊C4—41no—
781C2×C22⋊C4—41no—
782C2×C22⋊C4—41no—
783C2×C22⋊C4—41no—
784C2×C22⋊C4—41no—
785C2×C22⋊C4—41no—
786C2×C22⋊C4D4×C2914yes—
787C2×C42—22no—
788C2×C42—41no—
789C2×C42—41no—
790#95—22no—
791#95—22no—
792#95—22no—
793#95—22no—
794#95—22no—
795#95—22no—
796#95—41no—
797#95—41no—
798#95—41no—
799#95—41no—
800#95—41no—
801#95—41no—
802#95—41no—
803#95D4×C2914yescomplemented
804C29#1653511yescharacteristic, direct product factor, Sylow
805C24—21no—
806C24—21no—
807C24—21no—
808C24—21no—
809C24—21no—
810C24—21no—
811C24—21no—
812C24—21no—
813C24—21no—
814C24—21no—
815C24—21no—
816C24—21no—
817C24—21no—
818C24—21no—
819C24—21no—
820C24—21no—
821C24—21no—
822C24—21no—
823C24—21no—
824C24—21no—
825C24—21no—
826C24—21no—
827C24—21no—
828C24—21no—
829C24—21no—
830C24—21no—
831C24—21no—
832C24—21no—
833C24—21no—
834C24—21no—
835C24—21no—
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24C2×D4×C2912yes—
848C24#41×C2912yes—
849C24#41×C2912yes—
850C24C24×C2911yescharacteristic
851C2×D4—44no—
852C2×D4—44no—
853C2×D4—44no—
854C2×D4—44no—
855C2×D4—44no—
856C2×D4—44no—
857C2×D4—44no—
858C2×D4—44no—
859C2×D4—44no—
860C2×D4—44no—
861C2×D4—44no—
862C2×D4—44no—
863C2×D4—44no—
864C2×D4—44no—
865C2×D4—44no—
866C2×D4—44no—
867C2×D4—44no—
868C2×D4—44no—
869C2×D4—44no—
870C2×D4—44no—
871C2×D4—44no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4C2×D4×C2912yes—
949C22×C4C2×D4×C2912yes—
950C22×C4C2×D4×C2912yes—
951C22×C4C2×D4×C2912yes—
952C22×C4C2×D4×C2912yes—
953C22×C4#41×C2912yes—
954C22×C4#41×C2912yes—
955C22×C4#41×C2912yes—
956C4⋊C4—44no—
957C4⋊C4—44no—
958C22⋊C4—28no—
959C22⋊C4—44no—
960C22⋊C4—44no—
961C22⋊C4—44no—
962C22⋊C4—44no—
963C22⋊C4—44no—
964C22⋊C4—44no—
965C22⋊C4—44no—
966C22⋊C4—44no—
967C22⋊C4—44no—
968C22⋊C4—44no—
969C22⋊C4—44no—
970C22⋊C4—44no—
971C22⋊C4—44no—
972C22⋊C4—44no—
973C42—44no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23C22×D4×C2911yescharacteristic
1080C23C22×D4×C2911yescharacteristic
1081C23C2×#41×C2911yescharacteristic
1082C23C2×#41×C2911yescharacteristic
1083C23C2×#41×C2911yescharacteristic
1084C23C2×#41×C2911yescharacteristic
1085C23C2×#41×C2911yescharacteristic
1086C23C29×H(5,𝔽2)11yescharacteristic
1087C23C29×H(5,𝔽2)11yescharacteristic
1088C23C29×H(5,𝔽2)11yescharacteristic
1089C23C29×H(5,𝔽2)11yescharacteristic
1090C23C29×H(5,𝔽2)11yescharacteristic
1091C23C29×H(5,𝔽2)11yescharacteristic
1092C23C29×H(5,𝔽2)11yescharacteristic
1093C23C29×H(5,𝔽2)11yescharacteristic
1094D4—416no—
1095D4—416no—
1096D4—416no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C22—42no—
1182C22—42no—
1183C22—42no—
1184C22—42no—
1185C22—42no—
1186C22—42no—
1187C22—42no—
1188C22—42no—
1189C22—42no—
1190C22—42no—
1191C22—42no—
1192C22—42no—
1193C22—42no—
1194C22—42no—
1195C22—42no—
1196C22—42no—
1197C22—42no—
1198C22—42no—
1199C22—42no—
1200C22—42no—
1201C22—42no—
1202C22—81no—
1203C22—81no—
1204C22—81no—
1205C22—81no—
1206C22—81no—
1207C22—81no—
1208C22—81no—
1209C22—81no—
1210C22—81no—
1211C22—81no—
1212C22—81no—
1213C22—81no—
1214C22—81no—
1215C22—81no—
1216C22—81no—
1217C22—81no—
1218C22—81no—
1219C22—81no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22C29×#52511yescharacteristic
1227C22C29×#52911yescharacteristic
1228C22C29×#53211yescharacteristic
1229C22C29×#53411yescharacteristic
1230C22C29×#53511yescharacteristic
1231C22C29×#53511yescharacteristic
1232C22C29×#53511yescharacteristic
1233C22C29×#53811yescharacteristic
1234C22C29×#53811yescharacteristic
1235C22C29×#53811yescharacteristic
1236C22C29×#53811yescharacteristic
1237C22C29×#53811yescharacteristic
1238C22C29×#53811yescharacteristic
1239C22C29×#53811yescharacteristic
1240C22C29×#53811yescharacteristic
1241C22C29×#54011yescharacteristic
1242C22C29×#54011yescharacteristic
1243C22C29×#54011yescharacteristic
1244C22C29×#54011yescharacteristic
1245C22D42×C2911yescharacteristic
1246C22C29×#54611yescharacteristic
1247C22C29×#54611yescharacteristic
1248C22C29×#54611yescharacteristic
1249C22C29×#54611yescharacteristic
1250C22C29×#54611yescharacteristic
1251C22C29×#55011yescharacteristic
1252C22C29×#55111yescharacteristic
1253C22C29×#55111yescharacteristic
1254C22C29×#55311yescharacteristic
1255C22C29×#55311yescharacteristic
1256C22C29×#55311yescharacteristic
1257C22C29×#56011yescharacteristic
1258C22C29×#56011yescharacteristic
1259C22C29×#56011yescharacteristic
1260C22C29×H(3,𝔽4)11yescharacteristic
1261C4—42no—
1262C4—42no—
1263C4—42no—
1264C4—42no—
1265C4—42no—
1266C4—42no—
1267C4—42no—
1268C4—42no—
1269C4—81no—
1270C4—81no—
1271C4—81no—
1272C4—81no—
1273C2—82no—
1274C2—82no—
1275C2—82no—
1276C2C29×#246411yescharacteristic
1277C2C29×#247111yescharacteristic
1278C2C29×#255911yescharacteristic
1279C2C29×#263111yescharacteristic
1280C2C29×#264811yescharacteristic
1281C2C29×#266111yescharacteristic
1282C2C29×#267011yescharacteristic
1283C2C29×#267311yescharacteristic
1284C2C29×#268511yescharacteristic
1285C2C29×#269711yescharacteristic
1286C2C29×#270311yescharacteristic
1287C2C29×#271411yescharacteristic
1288C2C29×#275311yescharacteristic
1289C2C29×#277811yescharacteristic
1290C2C29×#282811yescharacteristic
subgroupG/H
center, socleC24×C29C24
commutator, Frattini, cosocleC24C24×C29
prime radicalC2×C29×#392C2
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×#394C2semidirect
4. C2×C29×#388C2semidirect
5. C29×#1443C2semidirect
6. C29×#1442C2semidirect
7. C29×#1439C2semidirect
8. C29×#1439C2semidirect
9. C29×#1438C2semidirect
10. C29×#1438C2semidirect
11. C29×#1438C2semidirect
12. C29×#1438C2semidirect
13. C29×#1438C2semidirect
14. C29×#1437C2semidirect
15. C29×#1437C2semidirect
158. C29×#95D4semidirect
328. #16535C29direct (N × H)
536. C2×#397C2×C29semidirect
537. C2×#394C2×C29semidirect
539. C2×#388C2×C29semidirect
540. #1443C2×C29semidirect
541. #1442C2×C29semidirect
542. #1439C2×C29semidirect
543. #1439C2×C29semidirect
544. #1438C2×C29semidirect
545. #1438C2×C29semidirect
546. #1438C2×C29semidirect
547. #1438C2×C29semidirect
548. #1438C2×C29semidirect
549. #1437C2×C29semidirect
550. #1437C2×C29semidirect
803. #95D4×C29semidirect
804. C29#16535direct (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×#3942
C2×C29×#3922
C2×C29×#3882
C29×#14432
C29×#14422
C29×#14392
C29×#14382
C29×#14372
#1653529