Finite Group Databasebeta

← C29×#16289 #20311189

Subgroups — C29×#16289 #20311189

Order 7424.

2006 conjugacy classes of subgroups.

The subgroup lattice has 1308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#396C211yesmaximal, characteristic, complemented
2C2×C29×#394C211yesmaximal, characteristic, complemented
3C2×C29×#394C211yesmaximal, characteristic, complemented
4C2×C29×#392C211yesmaximal, characteristic
5C2×C29×#390C211yesmaximal, characteristic, complemented
6C2×C29×#387C211yesmaximal, characteristic, complemented
7C29×#1442C211yesmaximal, characteristic, complemented
8C29×#1440C211yesmaximal, characteristic, complemented
9C29×#1439C211yesmaximal, characteristic, complemented
10C29×#1439C211yesmaximal, characteristic, complemented
11C29×#1439C211yesmaximal, characteristic, complemented
12C29×#1438C211yesmaximal, characteristic, complemented
13C29×#1438C211yesmaximal, characteristic, complemented
14C29×#1438C211yesmaximal, characteristic, complemented
15C29×#1437C211yesmaximal, characteristic, complemented
16C23×D4×C29C2211yescharacteristic
17C23×D4×C29C2211yescharacteristic
18C23×D4×C29C2211yescharacteristic
19C22×C4⋊C4×C29C2211yescharacteristic
20C22×C4⋊C4×C29C2211yescharacteristic
21C22×C4⋊C4×C29C2211yescharacteristic
22C22×C4⋊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×C22⋊C4×C29C2211yescharacteristic
37C22×C22⋊C4×C29C2211yescharacteristic
38C22×C42×C29C2211yescharacteristic
39C29×#396—24no—
40C29×#394—24no—
41C29×#394—24no—
42C29×#392—24no—
43C29×#390—24no—
44C29×#387—24no—
45C2×C29×#95C2211yescharacteristic
46C2×C29×#95C2211yescharacteristic
47C2×C29×#95C2211yescharacteristic
48C2×C29×#95C2211yescharacteristic
49C2×C29×#95C2211yescharacteristic
50C2×C29×#95C2211yescharacteristic
51C2×C29×#95C2211yescharacteristic
52C2×C29×#95C2211yescharacteristic
53C2×C29×#95C2211yescharacteristic
54C2×C29×#95C2211yescharacteristic
55C2×C29×#95C2211yescharacteristic
56C2×C29×#95C2211yescharacteristic
57C25×C29C2311yescharacteristic
58C25×C29C2311yescharacteristic
59C25×C29C2311yescharacteristic
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—22no—
68C22×D4×C29—22no—
69C22×D4×C29—22no—
70C22×D4×C29—22no—
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—
79C22×D4×C29—41no—
80C22×D4×C29—41no—
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
91C23×C4×C29C2311yescharacteristic
92C23×C4×C29C2311yescharacteristic
93C2×C4⋊C4×C29—22no—
94C2×C4⋊C4×C29—22no—
95C2×C4⋊C4×C29—22no—
96C2×C4⋊C4×C29—22no—
97C2×C4⋊C4×C29—22no—
98C2×C4⋊C4×C29—22no—
99C2×C4⋊C4×C29—22no—
100C2×C4⋊C4×C29—41no—
101C2×C4⋊C4×C29—41no—
102C2×C4⋊C4×C29—41no—
103C2×C4⋊C4×C29—41no—
104C2×C4⋊C4×C29D414yescomplemented
105C2×C22⋊C4×C29—22no—
106C2×C22⋊C4×C29—22no—
107C2×C22⋊C4×C29—22no—
108C2×C22⋊C4×C29—22no—
109C2×C22⋊C4×C29—22no—
110C2×C22⋊C4×C29—22no—
111C2×C22⋊C4×C29—22no—
112C2×C22⋊C4×C29—22no—
113C2×C22⋊C4×C29—22no—
114C2×C22⋊C4×C29—22no—
115C2×C22⋊C4×C29—22no—
116C2×C22⋊C4×C29—22no—
117C2×C22⋊C4×C29—22no—
118C2×C22⋊C4×C29—22no—
119C2×C22⋊C4×C29—22no—
120C2×C22⋊C4×C29—22no—
121C2×C22⋊C4×C29—22no—
122C2×C22⋊C4×C29—22no—
123C2×C22⋊C4×C29—22no—
124C2×C22⋊C4×C29—22no—
125C2×C22⋊C4×C29—22no—
126C2×C22⋊C4×C29—22no—
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×C29—41no—
142C2×C22⋊C4×C29—41no—
143C2×C22⋊C4×C29—41no—
144C2×C22⋊C4×C29—41no—
145C2×C22⋊C4×C29—41no—
146C2×C22⋊C4×C29—41no—
147C2×C22⋊C4×C29—41no—
148C2×C22⋊C4×C29—41no—
149C2×C22⋊C4×C29D414yescomplemented
150C2×C42×C29—22no—
151C2×C42×C29—22no—
152C2×C42×C29—41no—
153C29×#95—22no—
154C29×#95—22no—
155C29×#95—22no—
156C29×#95—22no—
157C29×#95—22no—
158C29×#95—22no—
159C29×#95—41no—
160C29×#95—41no—
161C29×#95—41no—
162C29×#95—41no—
163C29×#95—41no—
164C29×#95D414yes—
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×C29—21no—
202C24×C29—21no—
203C24×C29—21no—
204C24×C29—21no—
205C24×C29—21no—
206C24×C29—21no—
207C24×C29C2×D412yes—
208C24×C29#4112yes—
209C24×C29#4112yes—
210C24×C29C2411yescharacteristic
211C2×D4×C29—28no—
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—
226C2×D4×C29—44no—
227C2×D4×C29—44no—
228C2×D4×C29—44no—
229C2×D4×C29—44no—
230C2×D4×C29—44no—
231C2×D4×C29—44no—
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×C29—21no—
303C22×C4×C29—21no—
304C22×C4×C29—21no—
305C22×C4×C29—21no—
306C22×C4×C29C2×D412yes—
307C22×C4×C29C2×D412yes—
308C22×C4×C29C2×D412yes—
309C22×C4×C29C2×D412yes—
310C22×C4×C29C2×D412yes—
311C22×C4×C29C2×D412yes—
312C22×C4×C29C2×D412yes—
313C22×C4×C29C2×D412yes—
314C22×C4×C29#4112yes—
315C22×C4×C29#4112yes—
316C4⋊C4×C29—28no—
317C4⋊C4×C29—44no—
318C4⋊C4×C29—44no—
319C4⋊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—
327C22⋊C4×C29—44no—
328C22⋊C4×C29—44no—
329C22⋊C4×C29—44no—
330C22⋊C4×C29—44no—
331C22⋊C4×C29—44no—
332C22⋊C4×C29—44no—
333C22⋊C4×C29—44no—
334C22⋊C4×C29—44no—
335C42×C29—44no—
336#16289C2911yesmaximal, characteristic, direct product factor, Sylow
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—22no—
351C23×C29—22no—
352C23×C29—22no—
353C23×C29—22no—
354C23×C29—22no—
355C23×C29—22no—
356C23×C29—22no—
357C23×C29—22no—
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×C29—41no—
435C23×C29—41no—
436C23×C29—41no—
437C23×C29—41no—
438C23×C29—41no—
439C23×C29—41no—
440C23×C29—41no—
441C23×C29—41no—
442C23×C29C22×D411yescharacteristic
443C23×C29C22×D411yescharacteristic
444C23×C29C22×D411yescharacteristic
445C23×C29C2×#4111yescharacteristic
446C23×C29C2×#4111yescharacteristic
447C23×C29C2×#4111yescharacteristic
448C23×C29C2×#4111yescharacteristic
449C23×C29H(5,𝔽2)11yescharacteristic
450C23×C29H(5,𝔽2)11yescharacteristic
451C23×C29H(5,𝔽2)11yescharacteristic
452C23×C29H(5,𝔽2)11yescharacteristic
453C23×C29H(5,𝔽2)11yescharacteristic
454C23×C29H(5,𝔽2)11yescharacteristic
455C23×C29H(5,𝔽2)11yescharacteristic
456C23×C292−1+411yescharacteristic
457D4×C29—416no—
458D4×C29—416no—
459D4×C29—416no—
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—22no—
477C2×C4×C29—22no—
478C2×C4×C29—22no—
479C2×C4×C29—22no—
480C2×C4×C29—22no—
481C2×C4×C29—22no—
482C2×C4×C29—22no—
483C2×C4×C29—22no—
484C2×C4×C29—22no—
485C2×C4×C29—22no—
486C2×C4×C29—22no—
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×C4×C29—41no—
537C2×C4×C29—41no—
538C2×C4×C29—41no—
539C2×C4×C29—41no—
540C2×C4×C29—41no—
541C2×C4×C29—41no—
542C2×C4×C29—41no—
543C2×C4×C29#12114yes—
544C2×#396C2×C2911yescharacteristic, complemented
545C2×#394C2×C2911yescharacteristic, complemented
546C2×#394C2×C2911yescharacteristic, complemented
547C2×#392C2×C2911yescharacteristic
548C2×#390C2×C2911yescharacteristic, complemented
549C2×#387C2×C2911yescharacteristic, complemented
550#1442C2×C2911yescharacteristic, complemented
551#1440C2×C2911yescharacteristic, complemented
552#1439C2×C2911yescharacteristic, complemented
553#1439C2×C2911yescharacteristic, complemented
554#1439C2×C2911yescharacteristic, complemented
555#1438C2×C2911yescharacteristic, complemented
556#1438C2×C2911yescharacteristic, complemented
557#1438C2×C2911yescharacteristic, complemented
558#1437C2×C2911yescharacteristic, complemented
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—42no—
573C22×C29—42no—
574C22×C29—42no—
575C22×C29—42no—
576C22×C29—42no—
577C22×C29—42no—
578C22×C29—42no—
579C22×C29—42no—
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—81no—
597C22×C29—81no—
598C22×C29—81no—
599C22×C29—81no—
600C22×C29—81no—
601C22×C29—81no—
602C22×C29—81no—
603C22×C29—81no—
604C22×C29C2×#12111yescharacteristic
605C22×C29#52511yescharacteristic
606C22×C29#52911yescharacteristic
607C22×C29#53411yescharacteristic
608C22×C29#53511yescharacteristic
609C22×C29#53511yescharacteristic
610C22×C29#53511yescharacteristic
611C22×C29#53511yescharacteristic
612C22×C29#53711yescharacteristic
613C22×C29#53811yescharacteristic
614C22×C29#53811yescharacteristic
615C22×C29#53811yescharacteristic
616C22×C29#53811yescharacteristic
617C22×C29#53811yescharacteristic
618C22×C29#53911yescharacteristic
619C22×C29#54011yescharacteristic
620C22×C29#54011yescharacteristic
621C22×C29#54011yescharacteristic
622C22×C29#54211yescharacteristic
623C22×C29D4211yescharacteristic
624C22×C29D4211yescharacteristic
625C22×C29#54611yescharacteristic
626C22×C29#54611yescharacteristic
627C22×C29#54611yescharacteristic
628C22×C29#54611yescharacteristic
629C22×C29#54611yescharacteristic
630C22×C29#54811yescharacteristic
631C22×C29#54811yescharacteristic
632C22×C29#55011yescharacteristic
633C22×C29#55111yescharacteristic
634C22×C29#55311yescharacteristic
635C22×C29#56011yescharacteristic
636C22×C29#56011yescharacteristic
637C22×C29#56211yescharacteristic
638C22×C29#56211yescharacteristic
639C4×C29—24no—
640C4×C29—42no—
641C4×C29—42no—
642C4×C29—42no—
643C4×C29—42no—
644C4×C29—42no—
645C4×C29—42no—
646C4×C29—42no—
647C4×C29—81no—
648C4×C29—81no—
649C4×C29—81no—
650C4×C29—81no—
651C23×D4C22×C2911yescharacteristic
652C23×D4C22×C2911yescharacteristic
653C23×D4C22×C2911yescharacteristic
654C22×C4⋊C4C22×C2911yescharacteristic
655C22×C4⋊C4C22×C2911yescharacteristic
656C22×C4⋊C4C22×C2911yescharacteristic
657C22×C4⋊C4C22×C2911yescharacteristic
658C22×C22⋊C4C22×C2911yescharacteristic
659C22×C22⋊C4C22×C2911yescharacteristic
660C22×C22⋊C4C22×C2911yescharacteristic
661C22×C22⋊C4C22×C2911yescharacteristic
662C22×C22⋊C4C22×C2911yescharacteristic
663C22×C22⋊C4C22×C2911yescharacteristic
664C22×C22⋊C4C22×C2911yescharacteristic
665C22×C22⋊C4C22×C2911yescharacteristic
666C22×C22⋊C4C22×C2911yescharacteristic
667C22×C22⋊C4C22×C2911yescharacteristic
668C22×C22⋊C4C22×C2911yescharacteristic
669C22×C22⋊C4C22×C2911yescharacteristic
670C22×C22⋊C4C22×C2911yescharacteristic
671C22×C22⋊C4C22×C2911yescharacteristic
672C22×C22⋊C4C22×C2911yescharacteristic
673C22×C42C22×C2911yescharacteristic
674#396—24no—
675#394—24no—
676#394—24no—
677#392—24no—
678#390—24no—
679#387—24no—
680C2×#95C22×C2911yescharacteristic
681C2×#95C22×C2911yescharacteristic
682C2×#95C22×C2911yescharacteristic
683C2×#95C22×C2911yescharacteristic
684C2×#95C22×C2911yescharacteristic
685C2×#95C22×C2911yescharacteristic
686C2×#95C22×C2911yescharacteristic
687C2×#95C22×C2911yescharacteristic
688C2×#95C22×C2911yescharacteristic
689C2×#95C22×C2911yescharacteristic
690C2×#95C22×C2911yescharacteristic
691C2×#95C22×C2911yescharacteristic
692C2×C29—82no—
693C2×C29—82no—
694C2×C29—82no—
695C2×C29#242411yescharacteristic
696C2×C29#242611yescharacteristic
697C2×C29#245711yescharacteristic
698C2×C29#261911yescharacteristic
699C2×C29#263011yescharacteristic
700C2×C29#264811yescharacteristic
701C2×C29#267311yescharacteristic
702C2×C29#267611yescharacteristic
703C2×C29#267611yescharacteristic
704C2×C29#267811yescharacteristic
705C2×C29#268511yescharacteristic
706C2×C29#269611yescharacteristic
707C2×C29#271111yescharacteristic
708C2×C29#271411yescharacteristic
709C2×C29#282911yescharacteristic
710C25C23×C2911yescharacteristic
711C25C23×C2911yescharacteristic
712C25C23×C2911yescharacteristic
713C22×D4—22no—
714C22×D4—22no—
715C22×D4—22no—
716C22×D4—22no—
717C22×D4—22no—
718C22×D4—22no—
719C22×D4—22no—
720C22×D4—22no—
721C22×D4—22no—
722C22×D4—22no—
723C22×D4—22no—
724C22×D4—41no—
725C22×D4—41no—
726C22×D4—41no—
727C22×D4—41no—
728C22×D4—41no—
729C22×D4—41no—
730C22×D4—41no—
731C22×D4—41no—
732C22×D4—41no—
733C22×D4—41no—
734C23×C4C23×C2911yescharacteristic
735C23×C4C23×C2911yescharacteristic
736C23×C4C23×C2911yescharacteristic
737C23×C4C23×C2911yescharacteristic
738C23×C4C23×C2911yescharacteristic
739C23×C4C23×C2911yescharacteristic
740C23×C4C23×C2911yescharacteristic
741C23×C4C23×C2911yescharacteristic
742C23×C4C23×C2911yescharacteristic
743C23×C4C23×C2911yescharacteristic
744C23×C4C23×C2911yescharacteristic
745C23×C4C23×C2911yescharacteristic
746C2×C4⋊C4—22no—
747C2×C4⋊C4—22no—
748C2×C4⋊C4—22no—
749C2×C4⋊C4—22no—
750C2×C4⋊C4—22no—
751C2×C4⋊C4—22no—
752C2×C4⋊C4—22no—
753C2×C4⋊C4—41no—
754C2×C4⋊C4—41no—
755C2×C4⋊C4—41no—
756C2×C4⋊C4—41no—
757C2×C4⋊C4D4×C2914yescomplemented
758C2×C22⋊C4—22no—
759C2×C22⋊C4—22no—
760C2×C22⋊C4—22no—
761C2×C22⋊C4—22no—
762C2×C22⋊C4—22no—
763C2×C22⋊C4—22no—
764C2×C22⋊C4—22no—
765C2×C22⋊C4—22no—
766C2×C22⋊C4—22no—
767C2×C22⋊C4—22no—
768C2×C22⋊C4—22no—
769C2×C22⋊C4—22no—
770C2×C22⋊C4—22no—
771C2×C22⋊C4—22no—
772C2×C22⋊C4—22no—
773C2×C22⋊C4—22no—
774C2×C22⋊C4—22no—
775C2×C22⋊C4—22no—
776C2×C22⋊C4—22no—
777C2×C22⋊C4—22no—
778C2×C22⋊C4—22no—
779C2×C22⋊C4—22no—
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⋊C4—41no—
787C2×C22⋊C4—41no—
788C2×C22⋊C4—41no—
789C2×C22⋊C4—41no—
790C2×C22⋊C4—41no—
791C2×C22⋊C4—41no—
792C2×C22⋊C4—41no—
793C2×C22⋊C4—41no—
794C2×C22⋊C4—41no—
795C2×C22⋊C4—41no—
796C2×C22⋊C4—41no—
797C2×C22⋊C4—41no—
798C2×C22⋊C4—41no—
799C2×C22⋊C4—41no—
800C2×C22⋊C4—41no—
801C2×C22⋊C4—41no—
802C2×C22⋊C4D4×C2914yescomplemented
803C2×C42—22no—
804C2×C42—22no—
805C2×C42—41no—
806#95—22no—
807#95—22no—
808#95—22no—
809#95—22no—
810#95—22no—
811#95—22no—
812#95—41no—
813#95—41no—
814#95—41no—
815#95—41no—
816#95—41no—
817#95D4×C2914yes—
818C29#1628911yescharacteristic, direct product factor, Sylow
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—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24C2×D4×C2912yes—
862C24#41×C2912yes—
863C24#41×C2912yes—
864C24C24×C2911yescharacteristic
865C2×D4—28no—
866C2×D4—44no—
867C2×D4—44no—
868C2×D4—44no—
869C2×D4—44no—
870C2×D4—44no—
871C2×D4—44no—
872C2×D4—44no—
873C2×D4—44no—
874C2×D4—44no—
875C2×D4—44no—
876C2×D4—44no—
877C2×D4—44no—
878C2×D4—44no—
879C2×D4—44no—
880C2×D4—44no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—44no—
884C2×D4—44no—
885C2×D4—44no—
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×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4C2×D4×C2912yes—
961C22×C4C2×D4×C2912yes—
962C22×C4C2×D4×C2912yes—
963C22×C4C2×D4×C2912yes—
964C22×C4C2×D4×C2912yes—
965C22×C4C2×D4×C2912yes—
966C22×C4C2×D4×C2912yes—
967C22×C4C2×D4×C2912yes—
968C22×C4#41×C2912yes—
969C22×C4#41×C2912yes—
970C4⋊C4—28no—
971C4⋊C4—44no—
972C4⋊C4—44no—
973C4⋊C4—44no—
974C22⋊C4—44no—
975C22⋊C4—44no—
976C22⋊C4—44no—
977C22⋊C4—44no—
978C22⋊C4—44no—
979C22⋊C4—44no—
980C22⋊C4—44no—
981C22⋊C4—44no—
982C22⋊C4—44no—
983C22⋊C4—44no—
984C22⋊C4—44no—
985C22⋊C4—44no—
986C22⋊C4—44no—
987C22⋊C4—44no—
988C22⋊C4—44no—
989C42—44no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
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—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23C22×D4×C2911yescharacteristic
1096C23C22×D4×C2911yescharacteristic
1097C23C22×D4×C2911yescharacteristic
1098C23C2×#41×C2911yescharacteristic
1099C23C2×#41×C2911yescharacteristic
1100C23C2×#41×C2911yescharacteristic
1101C23C2×#41×C2911yescharacteristic
1102C23C29×H(5,𝔽2)11yescharacteristic
1103C23C29×H(5,𝔽2)11yescharacteristic
1104C23C29×H(5,𝔽2)11yescharacteristic
1105C23C29×H(5,𝔽2)11yescharacteristic
1106C23C29×H(5,𝔽2)11yescharacteristic
1107C23C29×H(5,𝔽2)11yescharacteristic
1108C23C29×H(5,𝔽2)11yescharacteristic
1109C23C29×2−1+411yescharacteristic
1110D4—416no—
1111D4—416no—
1112D4—416no—
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—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
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—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4C29×#12114yes—
1197C22—42no—
1198C22—42no—
1199C22—42no—
1200C22—42no—
1201C22—42no—
1202C22—42no—
1203C22—42no—
1204C22—42no—
1205C22—42no—
1206C22—42no—
1207C22—42no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—81no—
1219C22—81no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22C2×C29×#12111yescharacteristic
1243C22C29×#52511yescharacteristic
1244C22C29×#52911yescharacteristic
1245C22C29×#53411yescharacteristic
1246C22C29×#53511yescharacteristic
1247C22C29×#53511yescharacteristic
1248C22C29×#53511yescharacteristic
1249C22C29×#53511yescharacteristic
1250C22C29×#53711yescharacteristic
1251C22C29×#53811yescharacteristic
1252C22C29×#53811yescharacteristic
1253C22C29×#53811yescharacteristic
1254C22C29×#53811yescharacteristic
1255C22C29×#53811yescharacteristic
1256C22C29×#53911yescharacteristic
1257C22C29×#54011yescharacteristic
1258C22C29×#54011yescharacteristic
1259C22C29×#54011yescharacteristic
1260C22C29×#54211yescharacteristic
1261C22D42×C2911yescharacteristic
1262C22D42×C2911yescharacteristic
1263C22C29×#54611yescharacteristic
1264C22C29×#54611yescharacteristic
1265C22C29×#54611yescharacteristic
1266C22C29×#54611yescharacteristic
1267C22C29×#54611yescharacteristic
1268C22C29×#54811yescharacteristic
1269C22C29×#54811yescharacteristic
1270C22C29×#55011yescharacteristic
1271C22C29×#55111yescharacteristic
1272C22C29×#55311yescharacteristic
1273C22C29×#56011yescharacteristic
1274C22C29×#56011yescharacteristic
1275C22C29×#56211yescharacteristic
1276C22C29×#56211yescharacteristic
1277C4—24no—
1278C4—42no—
1279C4—42no—
1280C4—42no—
1281C4—42no—
1282C4—42no—
1283C4—42no—
1284C4—42no—
1285C4—81no—
1286C4—81no—
1287C4—81no—
1288C4—81no—
1289C2—82no—
1290C2—82no—
1291C2—82no—
1292C2C29×#242411yescharacteristic
1293C2C29×#242611yescharacteristic
1294C2C29×#245711yescharacteristic
1295C2C29×#261911yescharacteristic
1296C2C29×#263011yescharacteristic
1297C2C29×#264811yescharacteristic
1298C2C29×#267311yescharacteristic
1299C2C29×#267611yescharacteristic
1300C2C29×#267611yescharacteristic
1301C2C29×#267811yescharacteristic
1302C2C29×#268511yescharacteristic
1303C2C29×#269611yescharacteristic
1304C2C29×#271111yescharacteristic
1305C2C29×#271411yescharacteristic
1306C2C29×#282911yescharacteristic
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×#396C2semidirect
2. C2×C29×#394C2semidirect
3. C2×C29×#394C2semidirect
5. C2×C29×#390C2semidirect
6. C2×C29×#387C2semidirect
7. C29×#1442C2semidirect
8. C29×#1440C2semidirect
9. C29×#1439C2semidirect
10. C29×#1439C2semidirect
11. C29×#1439C2semidirect
12. C29×#1438C2semidirect
13. C29×#1438C2semidirect
14. C29×#1438C2semidirect
15. C29×#1437C2semidirect
104. C2×C4⋊C4×C29D4semidirect
149. C2×C22⋊C4×C29D4semidirect
336. #16289C29direct (N × H)
544. C2×#396C2×C29semidirect
545. C2×#394C2×C29semidirect
546. C2×#394C2×C29semidirect
548. C2×#390C2×C29semidirect
549. C2×#387C2×C29semidirect
550. #1442C2×C29semidirect
551. #1440C2×C29semidirect
552. #1439C2×C29semidirect
553. #1439C2×C29semidirect
554. #1439C2×C29semidirect
555. #1438C2×C29semidirect
556. #1438C2×C29semidirect
557. #1438C2×C29semidirect
558. #1437C2×C29semidirect
757. C2×C4⋊C4D4×C29semidirect
802. C2×C22⋊C4D4×C29semidirect
818. C29#16289direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#3962
C2×C29×#3942
C2×C29×#3922
C2×C29×#3902
C2×C29×#3872
C29×#14422
C29×#14402
C29×#14392
C29×#14382
C29×#14372
#1628929