Finite Group Databasebeta

← C29×#25218 #20320118

Subgroups — C29×#25218 #20320118

Order 7424.

942 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#482C211yesmaximal, characteristic, complemented
2C2×C29×#469C211yesmaximal, characteristic
3C29×#2500C211yesmaximal, characteristic, complemented
4C29×#2361C211yesmaximal, characteristic, complemented
5C29×#2084C211yesmaximal, characteristic, complemented
6C29×#2073C211yesmaximal, characteristic, complemented
7C29×#2067C211yesmaximal, characteristic, complemented
8C29×#2054C211yesmaximal, characteristic, complemented
9C29×#1949C211yesmaximal, characteristic, complemented
10C29×#1926C211yesmaximal, characteristic, complemented
11C29×#1879C211yesmaximal, characteristic, complemented
12C29×#1874C211yesmaximal, characteristic, complemented
13C29×#1851C211yesmaximal, characteristic, complemented
14C29×#1802C211yesmaximal, characteristic, complemented
15C29×#1736C211yesmaximal, characteristic, complemented
16C22×D8×C29C2211yescharacteristic
17C22×M16×C29C2211yescharacteristic
18C2×C29×#121C2211yescharacteristic
19C2×C29×#121C2211yescharacteristic
20C2×C4×D4×C29—21no—
21C2×C4×D4×C29C2211yescharacteristic
22C2×C29×#117C2211yescharacteristic
23C22×C4⋊C4×C29C2211yescharacteristic
24C29×#482—24no—
25C29×#469—24no—
26C2×C29×#107C2211yescharacteristic
27C2×C29×#106C2211yescharacteristic
28C2×C29×#106C2211yescharacteristic
29C2×C29×C4⋊C8C2211yescharacteristic
30C2×C29×C4⋊C8C2211yescharacteristic
31C2×C29×#102C2211yescharacteristic
32C2×C29×#102C2211yescharacteristic
33C2×C29×#102C2211yescharacteristic
34C2×C29×#102C2211yescharacteristic
35C2×C29×#102C2211yescharacteristic
36C2×C29×#102C2211yescharacteristic
37C2×C29×C22⋊C8C2211yescharacteristic
38C29×#394—21no—
39C29×#394—21no—
40C29×#390C2211yescharacteristic
41C29×#390C2211yescharacteristic
42C29×#390C2211yescharacteristic
43C29×#389C2211yescharacteristic
44C29×#388—21no—
45C29×#388—21no—
46C29×#388—21no—
47C29×#386—21no—
48C29×#385—21no—
49C29×#384C2211yescharacteristic
50C29×#382C2211yescharacteristic
51C4×C4⋊C4×C29C2211yescharacteristic
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×#121—22no—
79C29×#121—22no—
80C29×#121—22no—
81C29×#121D414yes—
82C4×D4×C29—22no—
83C4×D4×C29—41no—
84C4×D4×C29—44no—
85C29×#117—22no—
86C29×#117—22no—
87C2×C4⋊C4×C29—22no—
88C2×C4⋊C4×C29—21no—
89C2×C4⋊C4×C29—21no—
90C2×C4⋊C4×C29—21no—
91C2×C4⋊C4×C29—21no—
92C2×C4⋊C4×C29—41no—
93C2×C4⋊C4×C29C2311yescharacteristic
94C2×C4⋊C4×C29C2311yescharacteristic
95C2×C4⋊C4×C29C2311yescharacteristic
96C2×C4⋊C4×C29C2311yescharacteristic
97C2×C4⋊C4×C29C2311yescharacteristic
98C2×C4⋊C4×C29C2311yescharacteristic
99C2×C22⋊C4×C29—21no—
100C2×C22⋊C4×C29—21no—
101C2×C22⋊C4×C29—21no—
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×C29D411yescharacteristic
110C2×C22⋊C4×C29D411yescharacteristic
111C2×C42×C29—21no—
112C2×C42×C29—21no—
113C2×C42×C29C2311yescharacteristic
114C2×C42×C29C2311yescharacteristic
115C29×#107—22no—
116C29×#106—22no—
117C29×#106—22no—
118C29×C4⋊C8—22no—
119C29×C4⋊C8—41no—
120C29×#102—22no—
121C29×#102—22no—
122C29×#102—22no—
123C29×#102—22no—
124C29×#102—22no—
125C29×#102—41no—
126C29×C22⋊C8—22no—
127C29×#95—21no—
128C29×#95—21no—
129C29×#95—21no—
130C29×#95—21no—
131C29×#95D411yescharacteristic
132C29×#95D411yescharacteristic
133C24×C29—21no—
134C24×C29—21no—
135C24×C29C2×D411yescharacteristic
136C2×D4×C29—24no—
137C2×D4×C29—21no—
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—42no—
149C2×D4×C29—42no—
150C2×D4×C29—42no—
151C2×D4×C29—81no—
152C2×D4×C29—81no—
153C2×D4×C29C2×D412yes—
154C22×C4×C29—21no—
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—42no—
165C22×C4×C29—42no—
166C22×C4×C29—42no—
167C22×C4×C29—42no—
168C22×C4×C29—81no—
169C22×C4×C29—81no—
170C22×C4×C29C2×D411yescharacteristic
171C22×C4×C29C2×D411yescharacteristic
172C22×C4×C29C2×D411yescharacteristic
173C22×C4×C29C2×D411yescharacteristic
174C22×C4×C29C2×D412yes—
175C22×C4×C29C2×D411yescharacteristic
176C22×C4×C29#4112yes—
177C22×C4×C29C2411yescharacteristic
178D8×C29—44no—
179M16×C29—44no—
180C2×C8×C29—21no—
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#4112yes—
192C4⋊C4×C29—21no—
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—42no—
203C4⋊C4×C29—42no—
204C4⋊C4×C29—81no—
205C4⋊C4×C29—81no—
206C4⋊C4×C29C2×D412yes—
207C4⋊C4×C29#4112yes—
208C22⋊C4×C29—24no—
209C22⋊C4×C29—22no—
210C22⋊C4×C29—41no—
211C22⋊C4×C29—42no—
212C22⋊C4×C29—42no—
213C22⋊C4×C29—42no—
214C22⋊C4×C29—42no—
215C22⋊C4×C29—42no—
216C22⋊C4×C29—42no—
217C22⋊C4×C29—81no—
218C22⋊C4×C29—81no—
219C22⋊C4×C29—81no—
220C42×C29—21no—
221C42×C29—21no—
222C42×C29—21no—
223C42×C29—21no—
224C42×C29—42no—
225C42×C29—42no—
226#25218C2911yesmaximal, characteristic, direct product factor, Sylow
227C23×C29—21no—
228C23×C29—21no—
229C23×C29—21no—
230C23×C29—21no—
231C23×C29—21no—
232C23×C29—21no—
233C23×C29—22no—
234C23×C29—41no—
235C23×C29—41no—
236C23×C29—41no—
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#12112yes—
248C23×C29C22×D411yescharacteristic
249D4×C29—22no—
250D4×C29—22no—
251D4×C29—48no—
252D4×C29—41no—
253D4×C29—41no—
254D4×C29—41no—
255D4×C29—41no—
256D4×C29—41no—
257D4×C29—41no—
258D4×C29—84no—
259C2×C4×C29—21no—
260C2×C4×C29—21no—
261C2×C4×C29—21no—
262C2×C4×C29—21no—
263C2×C4×C29—22no—
264C2×C4×C29—22no—
265C2×C4×C29—22no—
266C2×C4×C29—22no—
267C2×C4×C29—22no—
268C2×C4×C29—21no—
269C2×C4×C29—22no—
270C2×C4×C29—21no—
271C2×C4×C29—21no—
272C2×C4×C29—21no—
273C2×C4×C29—21no—
274C2×C4×C29—21no—
275C2×C4×C29—21no—
276C2×C4×C29—21no—
277C2×C4×C29—21no—
278C2×C4×C29—41no—
279C2×C4×C29—41no—
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—84no—
295C2×C4×C29—84no—
296C2×C4×C29#12112yes—
297C2×C4×C29AGL(1,ℤ/8)12yes—
298C2×C4×C29C22×D411yescharacteristic
299C2×C4×C29C2×#4111yescharacteristic
300C2×C4×C29C2×#4111yescharacteristic
301C2×C4×C29C2×#4111yescharacteristic
302C2×C4×C29H(5,𝔽2)11yescharacteristic
303C2×C4×C292−1+411yescharacteristic
304C8×C29—22no—
305C8×C29—41no—
306C8×C29—41no—
307C8×C29—41no—
308C2×#482C2×C2911yescharacteristic, complemented
309C2×#469C2×C2911yescharacteristic
310#2500C2×C2911yescharacteristic, complemented
311#2361C2×C2911yescharacteristic, complemented
312#2084C2×C2911yescharacteristic, complemented
313#2073C2×C2911yescharacteristic, complemented
314#2067C2×C2911yescharacteristic, complemented
315#2054C2×C2911yescharacteristic, complemented
316#1949C2×C2911yescharacteristic, complemented
317#1926C2×C2911yescharacteristic, complemented
318#1879C2×C2911yescharacteristic, complemented
319#1874C2×C2911yescharacteristic, complemented
320#1851C2×C2911yescharacteristic, complemented
321#1802C2×C2911yescharacteristic, complemented
322#1736C2×C2911yescharacteristic, complemented
323C22×C29—22no—
324C22×C29—22no—
325C22×C29—22no—
326C22×C29—41no—
327C22×C29—41no—
328C22×C29—41no—
329C22×C29—41no—
330C22×C29—42no—
331C22×C29—42no—
332C22×C29—42no—
333C22×C29—81no—
334C22×C29—81no—
335C22×C29—81no—
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×C29C2×#12111yescharacteristic
345C22×C29#54611yescharacteristic
346C22×C29#54711yescharacteristic
347C22×C29C2×AGL(1,ℤ/8)11yescharacteristic
348C22×C29#57511yescharacteristic
349C22×C29#57611yescharacteristic
350C22×C29#57711yescharacteristic
351C4×C29—22no—
352C4×C29—22no—
353C4×C29—41no—
354C4×C29—41no—
355C4×C29—42no—
356C4×C29—42no—
357C4×C29—41no—
358C4×C29—81no—
359C4×C29—81no—
360C4×C29—81no—
361C4×C29—81no—
362C4×C29#52911yescharacteristic
363C4×C29#53911yescharacteristic
364C4×C29#54611yescharacteristic
365C4×C29#54711yescharacteristic
366C22×D8C22×C2911yescharacteristic
367C22×M16C22×C2911yescharacteristic
368C2×#121C22×C2911yescharacteristic
369C2×#121C22×C2911yescharacteristic
370C2×C4×D4—21no—
371C2×C4×D4C22×C2911yescharacteristic
372C2×#117C22×C2911yescharacteristic
373C22×C4⋊C4C22×C2911yescharacteristic
374#482—24no—
375#469—24no—
376C2×#107C22×C2911yescharacteristic
377C2×#106C22×C2911yescharacteristic
378C2×#106C22×C2911yescharacteristic
379C2×C4⋊C8C22×C2911yescharacteristic
380C2×C4⋊C8C22×C2911yescharacteristic
381C2×#102C22×C2911yescharacteristic
382C2×#102C22×C2911yescharacteristic
383C2×#102C22×C2911yescharacteristic
384C2×#102C22×C2911yescharacteristic
385C2×#102C22×C2911yescharacteristic
386C2×#102C22×C2911yescharacteristic
387C2×C22⋊C8C22×C2911yescharacteristic
388#394—21no—
389#394—21no—
390#390C22×C2911yescharacteristic
391#390C22×C2911yescharacteristic
392#390C22×C2911yescharacteristic
393#389C22×C2911yescharacteristic
394#388—21no—
395#388—21no—
396#388—21no—
397#386—21no—
398#385—21no—
399#384C22×C2911yescharacteristic
400#382C22×C2911yescharacteristic
401C4×C4⋊C4C22×C2911yescharacteristic
402C4×C22⋊C4C22×C2911yescharacteristic
403#340C22×C2911yescharacteristic
404#340C22×C2911yescharacteristic
405#340C22×C2911yescharacteristic
406#340C22×C2911yescharacteristic
407#340C22×C2911yescharacteristic
408#340C22×C2911yescharacteristic
409#336C22×C2911yescharacteristic
410#336C22×C2911yescharacteristic
411C2×C29—42no—
412C2×C29—82no—
413C2×C29—161no—
414C2×C29#242511yescharacteristic
415C2×C29#303611yescharacteristic
416C2×C29#304511yescharacteristic
417C2×C29#331811yescharacteristic
418C2×C29#332611yescharacteristic
419C2×C29#334711yescharacteristic
420C2×C29#335411yescharacteristic
421C22×D4—21no—
422C22×D4—21no—
423C22×D4C23×C2911yescharacteristic
424C22×D4C23×C2911yescharacteristic
425C23×C4—21no—
426C23×C4—21no—
427C23×C4C23×C2911yescharacteristic
428C2×D8—22no—
429C2×D8—22no—
430C2×D8—41no—
431C2×M16—22no—
432C2×M16—22no—
433C2×M16—41no—
434C22×C8C23×C2911yescharacteristic
435C22×C8C23×C2911yescharacteristic
436C22×C8C23×C2911yescharacteristic
437C22×C8C23×C2911yescharacteristic
438#121—22no—
439#121—22no—
440#121—22no—
441#121D4×C2914yes—
442C4×D4—22no—
443C4×D4—41no—
444C4×D4—44no—
445#117—22no—
446#117—22no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—41no—
453C2×C4⋊C4C23×C2911yescharacteristic
454C2×C4⋊C4C23×C2911yescharacteristic
455C2×C4⋊C4C23×C2911yescharacteristic
456C2×C4⋊C4C23×C2911yescharacteristic
457C2×C4⋊C4C23×C2911yescharacteristic
458C2×C4⋊C4C23×C2911yescharacteristic
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4D4×C2911yescharacteristic
470C2×C22⋊C4D4×C2911yescharacteristic
471C2×C42—21no—
472C2×C42—21no—
473C2×C42C23×C2911yescharacteristic
474C2×C42C23×C2911yescharacteristic
475#107—22no—
476#106—22no—
477#106—22no—
478C4⋊C8—22no—
479C4⋊C8—41no—
480#102—22no—
481#102—22no—
482#102—22no—
483#102—22no—
484#102—22no—
485#102—41no—
486C22⋊C8—22no—
487#95—21no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95D4×C2911yescharacteristic
492#95D4×C2911yescharacteristic
493C29#2521811yescharacteristic, direct product factor, Sylow
494C24—21no—
495C24—21no—
496C24C2×D4×C2911yescharacteristic
497C2×D4—24no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—42no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—81no—
513C2×D4—81no—
514C2×D4C2×D4×C2912yes—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—81no—
530C22×C4—81no—
531C22×C4C2×D4×C2911yescharacteristic
532C22×C4C2×D4×C2911yescharacteristic
533C22×C4C2×D4×C2911yescharacteristic
534C22×C4C2×D4×C2911yescharacteristic
535C22×C4C2×D4×C2912yes—
536C22×C4C2×D4×C2911yescharacteristic
537C22×C4#41×C2912yes—
538C22×C4C24×C2911yescharacteristic
539D8—44no—
540M16—44no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8#41×C2912yes—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—42no—
564C4⋊C4—42no—
565C4⋊C4—81no—
566C4⋊C4—81no—
567C4⋊C4C2×D4×C2912yes—
568C4⋊C4#41×C2912yes—
569C22⋊C4—24no—
570C22⋊C4—22no—
571C22⋊C4—41no—
572C22⋊C4—42no—
573C22⋊C4—42no—
574C22⋊C4—42no—
575C22⋊C4—42no—
576C22⋊C4—42no—
577C22⋊C4—42no—
578C22⋊C4—81no—
579C22⋊C4—81no—
580C22⋊C4—81no—
581C42—21no—
582C42—21no—
583C42—21no—
584C42—21no—
585C42—42no—
586C42—42no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—22no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23C29×#12112yes—
608C23C22×D4×C2911yescharacteristic
609D4—22no—
610D4—22no—
611D4—48no—
612D4—41no—
613D4—41no—
614D4—41no—
615D4—41no—
616D4—41no—
617D4—41no—
618D4—84no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—21no—
629C2×C4—22no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
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—84no—
655C2×C4—84no—
656C2×C4C29×#12112yes—
657C2×C4C29×AGL(1,ℤ/8)12yes—
658C2×C4C22×D4×C2911yescharacteristic
659C2×C4C2×#41×C2911yescharacteristic
660C2×C4C2×#41×C2911yescharacteristic
661C2×C4C2×#41×C2911yescharacteristic
662C2×C4C29×H(5,𝔽2)11yescharacteristic
663C2×C4C29×2−1+411yescharacteristic
664C8—22no—
665C8—41no—
666C8—41no—
667C8—41no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—42no—
676C22—42no—
677C22—42no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22—81no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22C2×C29×#12111yescharacteristic
690C22C29×#54611yescharacteristic
691C22C29×#54711yescharacteristic
692C22C2×C29×AGL(1,ℤ/8)11yescharacteristic
693C22C29×#57511yescharacteristic
694C22C29×#57611yescharacteristic
695C22C29×#57711yescharacteristic
696C4—22no—
697C4—22no—
698C4—42no—
699C4—42no—
700C4—41no—
701C4—41no—
702C4—41no—
703C4—81no—
704C4—81no—
705C4—81no—
706C4—81no—
707C4C29×#52911yescharacteristic
708C4C29×#53911yescharacteristic
709C4C29×#54611yescharacteristic
710C4C29×#54711yescharacteristic
711C2—42no—
712C2—82no—
713C2—161no—
714C2C29×#242511yescharacteristic
715C2C29×#303611yescharacteristic
716C2C29×#304511yescharacteristic
717C2C29×#331811yescharacteristic
718C2C29×#332611yescharacteristic
719C2C29×#334711yescharacteristic
720C2C29×#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×#482C2semidirect
3. C29×#2500C2semidirect
4. C29×#2361C2semidirect
5. C29×#2084C2semidirect
6. C29×#2073C2semidirect
7. C29×#2067C2semidirect
8. C29×#2054C2semidirect
9. C29×#1949C2semidirect
10. C29×#1926C2semidirect
11. C29×#1879C2semidirect
12. C29×#1874C2semidirect
13. C29×#1851C2semidirect
14. C29×#1802C2semidirect
15. C29×#1736C2semidirect
226. #25218C29direct (N × H)
308. C2×#482C2×C29semidirect
310. #2500C2×C29semidirect
311. #2361C2×C29semidirect
312. #2084C2×C29semidirect
313. #2073C2×C29semidirect
314. #2067C2×C29semidirect
315. #2054C2×C29semidirect
316. #1949C2×C29semidirect
317. #1926C2×C29semidirect
318. #1879C2×C29semidirect
319. #1874C2×C29semidirect
320. #1851C2×C29semidirect
321. #1802C2×C29semidirect
322. #1736C2×C29semidirect
493. C29#25218direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#4822
C2×C29×#4692
C29×#25002
C29×#23612
C29×#20842
C29×#20732
C29×#20672
C29×#20542
C29×#19492
C29×#19262
C29×#18792
C29×#18742
C29×#18512
C29×#18022
C29×#17362
#2521829