Finite Group Databasebeta

← C29×#25221 #20320121

Subgroups — C29×#25221 #20320121

Order 7424.

962 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#481C211yesmaximal, characteristic, complemented
2C2×C29×#469C211yesmaximal, characteristic
3C29×#2501C211yesmaximal, characteristic, complemented
4C29×#2363C211yesmaximal, characteristic, complemented
5C29×#2084C211yesmaximal, characteristic, complemented
6C29×#2071C211yesmaximal, characteristic, complemented
7C29×#2065C211yesmaximal, characteristic, complemented
8C29×#2054C211yesmaximal, characteristic, complemented
9C29×#1948C211yesmaximal, characteristic, complemented
10C29×#1926C211yesmaximal, characteristic, complemented
11C29×#1879C211yesmaximal, characteristic, complemented
12C29×#1875C211yesmaximal, characteristic, complemented
13C29×#1851C211yesmaximal, characteristic, complemented
14C29×#1802C211yesmaximal, characteristic, complemented
15C29×#1736C211yesmaximal, characteristic, complemented
16C22×D8×C29C2211yescharacteristic
17C22×M16×C29C2211yescharacteristic
18C2×C29×#123—21no—
19C2×C29×#123—21no—
20C2×C29×#121C2211yescharacteristic
21C2×C29×#121C2211yescharacteristic
22C2×C4×D4×C29C2211yescharacteristic
23C2×C29×#117C2211yescharacteristic
24C22×C4⋊C4×C29C2211yescharacteristic
25C29×#481—24no—
26C29×#469—24no—
27C2×C29×#106C2211yescharacteristic
28C2×C29×#106C2211yescharacteristic
29C2×C29×#106C2211yescharacteristic
30C2×C29×C4⋊C8C2211yescharacteristic
31C2×C29×C4⋊C8C2211yescharacteristic
32C2×C29×#102C2211yescharacteristic
33C2×C29×#102C2211yescharacteristic
34C2×C29×#102C2211yescharacteristic
35C2×C29×#102C2211yescharacteristic
36C2×C29×#102C2211yescharacteristic
37C2×C29×#102C2211yescharacteristic
38C2×C29×C22⋊C8C2211yescharacteristic
39C29×#399—21no—
40C29×#399—21no—
41C29×#390—21no—
42C29×#390C2211yescharacteristic
43C29×#390C2211yescharacteristic
44C29×#390C2211yescharacteristic
45C29×#389C2211yescharacteristic
46C29×#388—21no—
47C29×#386—21no—
48C29×#384C2211yescharacteristic
49C29×#384C2211yescharacteristic
50C4×C4⋊C4×C29C2211yescharacteristic
51C4×C22⋊C4×C29—21no—
52C4×C22⋊C4×C29C2211yescharacteristic
53C29×#340C2211yescharacteristic
54C29×#340C2211yescharacteristic
55C29×#340C2211yescharacteristic
56C29×#340C2211yescharacteristic
57C29×#340C2211yescharacteristic
58C29×#340C2211yescharacteristic
59C29×#336C2211yescharacteristic
60C29×#336C2211yescharacteristic
61C22×D4×C29—21no—
62C22×D4×C29—21no—
63C22×D4×C29C2311yescharacteristic
64C22×D4×C29C2311yescharacteristic
65C23×C4×C29—21no—
66C23×C4×C29—21no—
67C23×C4×C29C2311yescharacteristic
68C2×D8×C29—22no—
69C2×D8×C29—22no—
70C2×D8×C29—41no—
71C2×M16×C29—22no—
72C2×M16×C29—22no—
73C2×M16×C29—41no—
74C22×C8×C29C2311yescharacteristic
75C22×C8×C29C2311yescharacteristic
76C22×C8×C29C2311yescharacteristic
77C22×C8×C29C2311yescharacteristic
78C29×#123—44no—
79C29×#123—44no—
80C29×#121—22no—
81C29×#121—22no—
82C29×#121—22no—
83C29×#121D414yes—
84C4×D4×C29—22no—
85C4×D4×C29—41no—
86C29×#117—22no—
87C29×#117—41no—
88C2×C4⋊C4×C29—22no—
89C2×C4⋊C4×C29—22no—
90C2×C4⋊C4×C29—21no—
91C2×C4⋊C4×C29—21no—
92C2×C4⋊C4×C29—21no—
93C2×C4⋊C4×C29—21no—
94C2×C4⋊C4×C29—21no—
95C2×C4⋊C4×C29—21no—
96C2×C4⋊C4×C29C2311yescharacteristic
97C2×C4⋊C4×C29C2311yescharacteristic
98C2×C4⋊C4×C29C2311yescharacteristic
99C2×C4⋊C4×C29C2311yescharacteristic
100C2×C4⋊C4×C29C2311yescharacteristic
101C2×C4⋊C4×C29C2311yescharacteristic
102C2×C22⋊C4×C29—21no—
103C2×C22⋊C4×C29—21no—
104C2×C22⋊C4×C29—21no—
105C2×C22⋊C4×C29—21no—
106C2×C22⋊C4×C29—21no—
107C2×C22⋊C4×C29—21no—
108C2×C22⋊C4×C29—21no—
109C2×C22⋊C4×C29—21no—
110C2×C22⋊C4×C29—21no—
111C2×C22⋊C4×C29—21no—
112C2×C22⋊C4×C29D411yescharacteristic
113C2×C22⋊C4×C29D411yescharacteristic
114C2×C42×C29—21no—
115C2×C42×C29—21no—
116C2×C42×C29C2311yescharacteristic
117C2×C42×C29C2311yescharacteristic
118C29×#106—22no—
119C29×#106—22no—
120C29×#106—22no—
121C29×C4⋊C8—22no—
122C29×C4⋊C8—41no—
123C29×#102—22no—
124C29×#102—22no—
125C29×#102—22no—
126C29×#102—22no—
127C29×#102—22no—
128C29×#102—41no—
129C29×C22⋊C8—22no—
130C29×#95—21no—
131C29×#95—21no—
132C29×#95D411yescharacteristic
133C29×#95D411yescharacteristic
134C24×C29—21no—
135C24×C29—21no—
136C24×C29C2×D411yescharacteristic
137C2×D4×C29—24no—
138C2×D4×C29—21no—
139C2×D4×C29—21no—
140C2×D4×C29—21no—
141C2×D4×C29—21no—
142C2×D4×C29—21no—
143C2×D4×C29—21no—
144C2×D4×C29—21no—
145C2×D4×C29—21no—
146C2×D4×C29—21no—
147C2×D4×C29—21no—
148C2×D4×C29—21no—
149C2×D4×C29—42no—
150C2×D4×C29—42no—
151C2×D4×C29—42no—
152C2×D4×C29—81no—
153C2×D4×C29—81no—
154C2×D4×C29C2×D412yes—
155C22×C4×C29—21no—
156C22×C4×C29—21no—
157C22×C4×C29—21no—
158C22×C4×C29—21no—
159C22×C4×C29—21no—
160C22×C4×C29—21no—
161C22×C4×C29—21no—
162C22×C4×C29—21no—
163C22×C4×C29—21no—
164C22×C4×C29—21no—
165C22×C4×C29—42no—
166C22×C4×C29—42no—
167C22×C4×C29—42no—
168C22×C4×C29—42no—
169C22×C4×C29—42no—
170C22×C4×C29—81no—
171C22×C4×C29C2×D411yescharacteristic
172C22×C4×C29C2×D411yescharacteristic
173C22×C4×C29C2×D411yescharacteristic
174C22×C4×C29C2×D412yes—
175C22×C4×C29C2×D411yescharacteristic
176C22×C4×C29C2×D411yescharacteristic
177C22×C4×C29#4112yes—
178C22×C4×C29C2411yescharacteristic
179D8×C29—44no—
180M16×C29—44no—
181C2×C8×C29—21no—
182C2×C8×C29—21no—
183C2×C8×C29—21no—
184C2×C8×C29—21no—
185C2×C8×C29—21no—
186C2×C8×C29—21no—
187C2×C8×C29—21no—
188C2×C8×C29—21no—
189C2×C8×C29—21no—
190C2×C8×C29—21no—
191C2×C8×C29—21no—
192C2×C8×C29#4112yes—
193C4⋊C4×C29—21no—
194C4⋊C4×C29—21no—
195C4⋊C4×C29—21no—
196C4⋊C4×C29—21no—
197C4⋊C4×C29—21no—
198C4⋊C4×C29—21no—
199C4⋊C4×C29—21no—
200C4⋊C4×C29—21no—
201C4⋊C4×C29—21no—
202C4⋊C4×C29—21no—
203C4⋊C4×C29—42no—
204C4⋊C4×C29—42no—
205C4⋊C4×C29—42no—
206C4⋊C4×C29—42no—
207C4⋊C4×C29—42no—
208C4⋊C4×C29—81no—
209C4⋊C4×C29C2×D412yes—
210C4⋊C4×C29#4112yes—
211C22⋊C4×C29—24no—
212C22⋊C4×C29—22no—
213C22⋊C4×C29—22no—
214C22⋊C4×C29—42no—
215C22⋊C4×C29—42no—
216C22⋊C4×C29—42no—
217C22⋊C4×C29—42no—
218C22⋊C4×C29—42no—
219C22⋊C4×C29—42no—
220C22⋊C4×C29—42no—
221C22⋊C4×C29—42no—
222C22⋊C4×C29—81no—
223C42×C29—21no—
224C42×C29—21no—
225C42×C29—21no—
226C42×C29—21no—
227C42×C29—42no—
228C42×C29—81no—
229#25221C2911yesmaximal, characteristic, direct product factor, Sylow
230C23×C29—21no—
231C23×C29—21no—
232C23×C29—21no—
233C23×C29—21no—
234C23×C29—21no—
235C23×C29—21no—
236C23×C29—22no—
237C23×C29—41no—
238C23×C29—41no—
239C23×C29—41no—
240C23×C29—41no—
241C23×C29—41no—
242C23×C29—41no—
243C23×C29—41no—
244C23×C29—41no—
245C23×C29—41no—
246C23×C29—41no—
247C23×C29—41no—
248C23×C29—41no—
249C23×C29—41no—
250C23×C29#12112yes—
251C23×C29C22×D411yescharacteristic
252D4×C29—22no—
253D4×C29—22no—
254D4×C29—41no—
255D4×C29—41no—
256D4×C29—41no—
257D4×C29—41no—
258D4×C29—41no—
259D4×C29—41no—
260D4×C29—84no—
261D4×C29—84no—
262C2×C4×C29—21no—
263C2×C4×C29—21no—
264C2×C4×C29—21no—
265C2×C4×C29—21no—
266C2×C4×C29—21no—
267C2×C4×C29—21no—
268C2×C4×C29—22no—
269C2×C4×C29—22no—
270C2×C4×C29—22no—
271C2×C4×C29—22no—
272C2×C4×C29—22no—
273C2×C4×C29—21no—
274C2×C4×C29—22no—
275C2×C4×C29—21no—
276C2×C4×C29—21no—
277C2×C4×C29—21no—
278C2×C4×C29—21no—
279C2×C4×C29—21no—
280C2×C4×C29—41no—
281C2×C4×C29—41no—
282C2×C4×C29—41no—
283C2×C4×C29—41no—
284C2×C4×C29—41no—
285C2×C4×C29—41no—
286C2×C4×C29—41no—
287C2×C4×C29—41no—
288C2×C4×C29—41no—
289C2×C4×C29—41no—
290C2×C4×C29—41no—
291C2×C4×C29—41no—
292C2×C4×C29—41no—
293C2×C4×C29—41no—
294C2×C4×C29—41no—
295C2×C4×C29—41no—
296C2×C4×C29—84no—
297C2×C4×C29—84no—
298C2×C4×C29#12112yes—
299C2×C4×C29AGL(1,ℤ/8)12yes—
300C2×C4×C29AGL(1,ℤ/8)12yes—
301C2×C4×C29C22×D411yescharacteristic
302C2×C4×C29C2×#4111yescharacteristic
303C2×C4×C29C2×#4111yescharacteristic
304C2×C4×C29C2×#4111yescharacteristic
305C2×C4×C29H(5,𝔽2)11yescharacteristic
306C2×C4×C292−1+411yescharacteristic
307C8×C29—22no—
308C8×C29—41no—
309C8×C29—41no—
310C8×C29—41no—
311C2×#481C2×C2911yescharacteristic, complemented
312C2×#469C2×C2911yescharacteristic
313#2501C2×C2911yescharacteristic, complemented
314#2363C2×C2911yescharacteristic, complemented
315#2084C2×C2911yescharacteristic, complemented
316#2071C2×C2911yescharacteristic, complemented
317#2065C2×C2911yescharacteristic, complemented
318#2054C2×C2911yescharacteristic, complemented
319#1948C2×C2911yescharacteristic, complemented
320#1926C2×C2911yescharacteristic, complemented
321#1879C2×C2911yescharacteristic, complemented
322#1875C2×C2911yescharacteristic, complemented
323#1851C2×C2911yescharacteristic, complemented
324#1802C2×C2911yescharacteristic, complemented
325#1736C2×C2911yescharacteristic, complemented
326C22×C29—22no—
327C22×C29—22no—
328C22×C29—22no—
329C22×C29—41no—
330C22×C29—41no—
331C22×C29—41no—
332C22×C29—41no—
333C22×C29—42no—
334C22×C29—42no—
335C22×C29—42no—
336C22×C29—81no—
337C22×C29—81no—
338C22×C29—81no—
339C22×C29—81no—
340C22×C29—81no—
341C22×C29—81no—
342C22×C29—81no—
343C22×C29—81no—
344C22×C29—81no—
345C22×C29—81no—
346C22×C29—81no—
347C22×C29C2×#12111yescharacteristic
348C22×C29#54611yescharacteristic
349C22×C29#54711yescharacteristic
350C22×C29C2×AGL(1,ℤ/8)11yescharacteristic
351C22×C29C2×AGL(1,ℤ/8)11yescharacteristic
352C22×C29#57711yescharacteristic
353C22×C29#57711yescharacteristic
354C4×C29—22no—
355C4×C29—22no—
356C4×C29—22no—
357C4×C29—41no—
358C4×C29—41no—
359C4×C29—42no—
360C4×C29—42no—
361C4×C29—81no—
362C4×C29—81no—
363C4×C29—81no—
364C4×C29—81no—
365C4×C29#52911yescharacteristic
366C4×C29#53911yescharacteristic
367C4×C29#54611yescharacteristic
368C4×C29#54711yescharacteristic
369C22×D8C22×C2911yescharacteristic
370C22×M16C22×C2911yescharacteristic
371C2×#123—21no—
372C2×#123—21no—
373C2×#121C22×C2911yescharacteristic
374C2×#121C22×C2911yescharacteristic
375C2×C4×D4C22×C2911yescharacteristic
376C2×#117C22×C2911yescharacteristic
377C22×C4⋊C4C22×C2911yescharacteristic
378#481—24no—
379#469—24no—
380C2×#106C22×C2911yescharacteristic
381C2×#106C22×C2911yescharacteristic
382C2×#106C22×C2911yescharacteristic
383C2×C4⋊C8C22×C2911yescharacteristic
384C2×C4⋊C8C22×C2911yescharacteristic
385C2×#102C22×C2911yescharacteristic
386C2×#102C22×C2911yescharacteristic
387C2×#102C22×C2911yescharacteristic
388C2×#102C22×C2911yescharacteristic
389C2×#102C22×C2911yescharacteristic
390C2×#102C22×C2911yescharacteristic
391C2×C22⋊C8C22×C2911yescharacteristic
392#399—21no—
393#399—21no—
394#390—21no—
395#390C22×C2911yescharacteristic
396#390C22×C2911yescharacteristic
397#390C22×C2911yescharacteristic
398#389C22×C2911yescharacteristic
399#388—21no—
400#386—21no—
401#384C22×C2911yescharacteristic
402#384C22×C2911yescharacteristic
403C4×C4⋊C4C22×C2911yescharacteristic
404C4×C22⋊C4—21no—
405C4×C22⋊C4C22×C2911yescharacteristic
406#340C22×C2911yescharacteristic
407#340C22×C2911yescharacteristic
408#340C22×C2911yescharacteristic
409#340C22×C2911yescharacteristic
410#340C22×C2911yescharacteristic
411#340C22×C2911yescharacteristic
412#336C22×C2911yescharacteristic
413#336C22×C2911yescharacteristic
414C2×C29—42no—
415C2×C29—82no—
416C2×C29—161no—
417C2×C29#242511yescharacteristic
418C2×C29#303811yescharacteristic
419C2×C29#304211yescharacteristic
420C2×C29#330611yescharacteristic
421C2×C29#333211yescharacteristic
422C2×C29#334511yescharacteristic
423C2×C29#335411yescharacteristic
424C22×D4—21no—
425C22×D4—21no—
426C22×D4C23×C2911yescharacteristic
427C22×D4C23×C2911yescharacteristic
428C23×C4—21no—
429C23×C4—21no—
430C23×C4C23×C2911yescharacteristic
431C2×D8—22no—
432C2×D8—22no—
433C2×D8—41no—
434C2×M16—22no—
435C2×M16—22no—
436C2×M16—41no—
437C22×C8C23×C2911yescharacteristic
438C22×C8C23×C2911yescharacteristic
439C22×C8C23×C2911yescharacteristic
440C22×C8C23×C2911yescharacteristic
441#123—44no—
442#123—44no—
443#121—22no—
444#121—22no—
445#121—22no—
446#121D4×C2914yes—
447C4×D4—22no—
448C4×D4—41no—
449#117—22no—
450#117—41no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4C23×C2911yescharacteristic
460C2×C4⋊C4C23×C2911yescharacteristic
461C2×C4⋊C4C23×C2911yescharacteristic
462C2×C4⋊C4C23×C2911yescharacteristic
463C2×C4⋊C4C23×C2911yescharacteristic
464C2×C4⋊C4C23×C2911yescharacteristic
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4D4×C2911yescharacteristic
476C2×C22⋊C4D4×C2911yescharacteristic
477C2×C42—21no—
478C2×C42—21no—
479C2×C42C23×C2911yescharacteristic
480C2×C42C23×C2911yescharacteristic
481#106—22no—
482#106—22no—
483#106—22no—
484C4⋊C8—22no—
485C4⋊C8—41no—
486#102—22no—
487#102—22no—
488#102—22no—
489#102—22no—
490#102—22no—
491#102—41no—
492C22⋊C8—22no—
493#95—21no—
494#95—21no—
495#95D4×C2911yescharacteristic
496#95D4×C2911yescharacteristic
497C29#2522111yescharacteristic, direct product factor, Sylow
498C24—21no—
499C24—21no—
500C24C2×D4×C2911yescharacteristic
501C2×D4—24no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—42no—
514C2×D4—42no—
515C2×D4—42no—
516C2×D4—81no—
517C2×D4—81no—
518C2×D4C2×D4×C2912yes—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—81no—
535C22×C4C2×D4×C2911yescharacteristic
536C22×C4C2×D4×C2911yescharacteristic
537C22×C4C2×D4×C2911yescharacteristic
538C22×C4C2×D4×C2912yes—
539C22×C4C2×D4×C2911yescharacteristic
540C22×C4C2×D4×C2911yescharacteristic
541C22×C4#41×C2912yes—
542C22×C4C24×C2911yescharacteristic
543D8—44no—
544M16—44no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8#41×C2912yes—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—42no—
568C4⋊C4—42no—
569C4⋊C4—42no—
570C4⋊C4—42no—
571C4⋊C4—42no—
572C4⋊C4—81no—
573C4⋊C4C2×D4×C2912yes—
574C4⋊C4#41×C2912yes—
575C22⋊C4—24no—
576C22⋊C4—22no—
577C22⋊C4—22no—
578C22⋊C4—42no—
579C22⋊C4—42no—
580C22⋊C4—42no—
581C22⋊C4—42no—
582C22⋊C4—42no—
583C22⋊C4—42no—
584C22⋊C4—42no—
585C22⋊C4—42no—
586C22⋊C4—81no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—42no—
592C42—81no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—22no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23C29×#12112yes—
614C23C22×D4×C2911yescharacteristic
615D4—22no—
616D4—22no—
617D4—41no—
618D4—41no—
619D4—41no—
620D4—41no—
621D4—41no—
622D4—41no—
623D4—84no—
624D4—84no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—21no—
637C2×C4—22no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—84no—
660C2×C4—84no—
661C2×C4C29×#12112yes—
662C2×C4C29×AGL(1,ℤ/8)12yes—
663C2×C4C29×AGL(1,ℤ/8)12yes—
664C2×C4C22×D4×C2911yescharacteristic
665C2×C4C2×#41×C2911yescharacteristic
666C2×C4C2×#41×C2911yescharacteristic
667C2×C4C2×#41×C2911yescharacteristic
668C2×C4C29×H(5,𝔽2)11yescharacteristic
669C2×C4C29×2−1+411yescharacteristic
670C8—22no—
671C8—41no—
672C8—41no—
673C8—41no—
674C22—22no—
675C22—22no—
676C22—22no—
677C22—41no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—42no—
682C22—42no—
683C22—42no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22—81no—
692C22—81no—
693C22—81no—
694C22—81no—
695C22C2×C29×#12111yescharacteristic
696C22C29×#54611yescharacteristic
697C22C29×#54711yescharacteristic
698C22C2×C29×AGL(1,ℤ/8)11yescharacteristic
699C22C2×C29×AGL(1,ℤ/8)11yescharacteristic
700C22C29×#57711yescharacteristic
701C22C29×#57711yescharacteristic
702C4—22no—
703C4—22no—
704C4—22no—
705C4—42no—
706C4—42no—
707C4—41no—
708C4—41no—
709C4—81no—
710C4—81no—
711C4—81no—
712C4—81no—
713C4C29×#52911yescharacteristic
714C4C29×#53911yescharacteristic
715C4C29×#54611yescharacteristic
716C4C29×#54711yescharacteristic
717C2—42no—
718C2—82no—
719C2—161no—
720C2C29×#242511yescharacteristic
721C2C29×#303811yescharacteristic
722C2C29×#304211yescharacteristic
723C2C29×#330611yescharacteristic
724C2C29×#333211yescharacteristic
725C2C29×#334511yescharacteristic
726C2C29×#335411yescharacteristic
subgroupG/H
center, socleC23×C29C22×D4
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC2×C29×#469C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C29 ◁ C4×C22⋊C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C29×#481C2semidirect
3. C29×#2501C2semidirect
4. C29×#2363C2semidirect
5. C29×#2084C2semidirect
6. C29×#2071C2semidirect
7. C29×#2065C2semidirect
8. C29×#2054C2semidirect
9. C29×#1948C2semidirect
10. C29×#1926C2semidirect
11. C29×#1879C2semidirect
12. C29×#1875C2semidirect
13. C29×#1851C2semidirect
14. C29×#1802C2semidirect
15. C29×#1736C2semidirect
229. #25221C29direct (N × H)
311. C2×#481C2×C29semidirect
313. #2501C2×C29semidirect
314. #2363C2×C29semidirect
315. #2084C2×C29semidirect
316. #2071C2×C29semidirect
317. #2065C2×C29semidirect
318. #2054C2×C29semidirect
319. #1948C2×C29semidirect
320. #1926C2×C29semidirect
321. #1879C2×C29semidirect
322. #1875C2×C29semidirect
323. #1851C2×C29semidirect
324. #1802C2×C29semidirect
325. #1736C2×C29semidirect
497. C29#25221direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#4812
C2×C29×#4692
C29×#25012
C29×#23632
C29×#20842
C29×#20712
C29×#20652
C29×#20542
C29×#19482
C29×#19262
C29×#18792
C29×#18752
C29×#18512
C29×#18022
C29×#17362
#2522129