Finite Group Databasebeta

← C29×#25334 #20320234

Subgroups — C29×#25334 #20320234

Order 7424.

928 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#489C211yesmaximal, characteristic, complemented
2C2×C29×#463C211yesmaximal, characteristic
3C29×#2542C211yesmaximal, characteristic, complemented
4C29×#2367C211yesmaximal, characteristic, complemented
5C29×#2072C211yesmaximal, characteristic, complemented
6C29×#2071C211yesmaximal, characteristic, complemented
7C29×#2055C211yesmaximal, characteristic, complemented
8C29×#2054C211yesmaximal, characteristic
9C29×#1987C211yesmaximal, characteristic, complemented
10C29×#1940C211yesmaximal, characteristic, complemented
11C29×#1880C211yesmaximal, characteristic, complemented
12C29×#1879C211yesmaximal, characteristic
13C29×#1803C211yesmaximal, characteristic, complemented
14C29×#1802C211yesmaximal, characteristic, complemented
15C29×#1762C211yesmaximal, characteristic, complemented
16C22×SD16×C29C2211yescharacteristic
17C22×D8×C29C2211yescharacteristic
18C2×C29×C4⋊Q8C2211yescharacteristic
19C2×C29×#124C2211yescharacteristic
20C2×C29×C22⋊Q8—21no—
21C2×C29×C22⋊Q8—21no—
22C2×C4×Q8×C29C2211yescharacteristic
23C2×C4×D4×C29C2211yescharacteristic
24C2×C4×D4×C29C2211yescharacteristic
25C29×#489—24no—
26C29×#463—24no—
27C2×C29×C4⋊C8C2211yescharacteristic
28C2×C29×C4⋊C8C2211yescharacteristic
29C2×C29×C4⋊C8C2211yescharacteristic
30C2×C29×#103C2211yescharacteristic
31C2×C29×#103C2211yescharacteristic
32C2×C29×#103C2211yescharacteristic
33C2×C29×#102C2211yescharacteristic
34C2×C29×#102C2211yescharacteristic
35C2×C29×#102C2211yescharacteristic
36C2×C29×#102C2211yescharacteristic
37C2×C29×#102C2211yescharacteristic
38C2×C29×#97C2211yescharacteristic
39C29×#399—21no—
40C29×#399—21no—
41C29×#391C2211yescharacteristic
42C29×#390C2211yescharacteristic
43C29×#390C2211yescharacteristic
44C29×#390C2211yescharacteristic
45C29×#388—21no—
46C29×#388—21no—
47C29×#385—21no—
48C29×#384C2211yescharacteristic
49C29×#384C2211yescharacteristic
50C4×C4⋊C4×C29C2211yescharacteristic
51C4×C4⋊C4×C29C2211yescharacteristic
52C4×C22⋊C4×C29—21no—
53C29×#340C2211yescharacteristic
54C29×#340C2211yescharacteristic
55C29×#340C2211yescharacteristic
56C29×#340C2211yescharacteristic
57C29×#340C2211yescharacteristic
58C29×#340C2211yescharacteristic
59C29×#336C2211yescharacteristic
60C29×#336C2211yescharacteristic
61C22×Q8×C29—21no—
62C22×Q8×C29C2311yescharacteristic
63C22×D4×C29C2311yescharacteristic
64C22×D4×C29C2311yescharacteristic
65C23×C4×C29—21no—
66C23×C4×C29—21no—
67C2×SD16×C29—22no—
68C2×SD16×C29—22no—
69C2×SD16×C29—41no—
70C2×D8×C29—22no—
71C2×D8×C29—22no—
72C2×D8×C29—41no—
73C22×C8×C29C2311yescharacteristic
74C22×C8×C29C2311yescharacteristic
75C22×C8×C29C2311yescharacteristic
76C22×C8×C29C2311yescharacteristic
77C29×C4⋊Q8—22no—
78C29×C4⋊Q8—22no—
79C29×#124—22no—
80C29×#124D414yes—
81C29×C22⋊Q8—44no—
82C29×C22⋊Q8—44no—
83C4×Q8×C29—22no—
84C4×Q8×C29—41no—
85C4×D4×C29—22no—
86C4×D4×C29—22no—
87C4×D4×C29—22no—
88C4×D4×C29—41no—
89C2×C4⋊C4×C29—21no—
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×C29D411yescharacteristic
96C2×C4⋊C4×C29D411yescharacteristic
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×C42×C29—21no—
113C2×C42×C29—21no—
114C2×C42×C29C2311yescharacteristic
115C2×C42×C29C2311yescharacteristic
116C2×C42×C29C2311yescharacteristic
117C29×C4⋊C8—22no—
118C29×C4⋊C8—41no—
119C29×C4⋊C8—41no—
120C29×#103—22no—
121C29×#103—22no—
122C29×#103—22no—
123C29×#102—22no—
124C29×#102—22no—
125C29×#102—22no—
126C29×#102—22no—
127C29×#102—22no—
128C29×#97—22no—
129C29×#95—21no—
130C29×#95—21no—
131C29×#95—21no—
132C29×#95D411yescharacteristic
133C29×#95D411yescharacteristic
134C24×C29—21no—
135C24×C29—21no—
136C2×Q8×C29—21no—
137C2×Q8×C29—21no—
138C2×Q8×C29—21no—
139C2×Q8×C29—21no—
140C2×Q8×C29—21no—
141C2×Q8×C29—42no—
142C2×Q8×C29—42no—
143C2×Q8×C29—42no—
144C2×Q8×C29C2×D412yes—
145C2×D4×C29—21no—
146C2×D4×C29—21no—
147C2×D4×C29—21no—
148C2×D4×C29—21no—
149C2×D4×C29—21no—
150C2×D4×C29—21no—
151C2×D4×C29—21no—
152C2×D4×C29—21no—
153C2×D4×C29—21no—
154C2×D4×C29—21no—
155C2×D4×C29C2×D412yes—
156C2×D4×C29#4112yes—
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—42no—
164C22×C4×C29—42no—
165C22×C4×C29—42no—
166C22×C4×C29—42no—
167C22×C4×C29—42no—
168C22×C4×C29—81no—
169C22×C4×C29C2×D411yescharacteristic
170C22×C4×C29C2×D411yescharacteristic
171C22×C4×C29C2×D411yescharacteristic
172C22×C4×C29C2×D411yescharacteristic
173C22×C4×C29C2×D411yescharacteristic
174C22×C4×C29C2×D411yescharacteristic
175C22×C4×C29C2411yescharacteristic
176SD16×C29—44no—
177D8×C29—44no—
178C2×C8×C29—21no—
179C2×C8×C29—21no—
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—
190C4⋊C4×C29—22no—
191C4⋊C4×C29—22no—
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—42no—
202C4⋊C4×C29—42no—
203C4⋊C4×C29—42no—
204C4⋊C4×C29—42no—
205C4⋊C4×C29—42no—
206C4⋊C4×C29—42no—
207C4⋊C4×C29#4112yes—
208C22⋊C4×C29—24no—
209C22⋊C4×C29—24no—
210C22⋊C4×C29—42no—
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—
218C42×C29—21no—
219C42×C29—21no—
220C42×C29—21no—
221C42×C29—21no—
222C42×C29—42no—
223C42×C29—81no—
224C42×C29C2×D412yes—
225C42×C29#4112yes—
226#25334C2911yesmaximal, characteristic, direct product factor, Sylow
227C23×C29—22no—
228C23×C29—22no—
229C23×C29—41no—
230C23×C29—41no—
231C23×C29—41no—
232C23×C29—41no—
233C23×C29—41no—
234C23×C29—41no—
235C23×C29—41no—
236C23×C29—41no—
237C23×C29—41no—
238C23×C29—41no—
239C23×C29—41no—
240C23×C29—41no—
241C23×C29C22×D411yescharacteristic
242Q8×C29—22no—
243Q8×C29—22no—
244Q8×C29—41no—
245Q8×C29—41no—
246Q8×C29—84no—
247D4×C29—22no—
248D4×C29—22no—
249D4×C29—22no—
250D4×C29—22no—
251D4×C29—41no—
252D4×C29—41no—
253D4×C29—41no—
254D4×C29—41no—
255C2×C4×C29—21no—
256C2×C4×C29—21no—
257C2×C4×C29—21no—
258C2×C4×C29—21no—
259C2×C4×C29—21no—
260C2×C4×C29—21no—
261C2×C4×C29—21no—
262C2×C4×C29—21no—
263C2×C4×C29—22no—
264C2×C4×C29—21no—
265C2×C4×C29—21no—
266C2×C4×C29—22no—
267C2×C4×C29—21no—
268C2×C4×C29—21no—
269C2×C4×C29—21no—
270C2×C4×C29—21no—
271C2×C4×C29—41no—
272C2×C4×C29—41no—
273C2×C4×C29—41no—
274C2×C4×C29—41no—
275C2×C4×C29—41no—
276C2×C4×C29—41no—
277C2×C4×C29—41no—
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—84no—
288C2×C4×C29—84no—
289C2×C4×C29#12112yes—
290C2×C4×C29#12112yes—
291C2×C4×C29AGL(1,ℤ/8)12yes—
292C2×C4×C29AGL(1,ℤ/8)12yes—
293C2×C4×C29C22×D411yescharacteristic
294C2×C4×C29C2×#4111yescharacteristic
295C2×C4×C29C2×#4111yescharacteristic
296C2×C4×C29C2×#4111yescharacteristic
297C2×C4×C29H(5,𝔽2)11yescharacteristic
298C2×C4×C292−1+411yescharacteristic
299C8×C29—41no—
300C8×C29—41no—
301C8×C29—41no—
302C8×C29—41no—
303C2×#489C2×C2911yescharacteristic, complemented
304C2×#463C2×C2911yescharacteristic
305#2542C2×C2911yescharacteristic, complemented
306#2367C2×C2911yescharacteristic, complemented
307#2072C2×C2911yescharacteristic, complemented
308#2071C2×C2911yescharacteristic, complemented
309#2055C2×C2911yescharacteristic, complemented
310#2054C2×C2911yescharacteristic
311#1987C2×C2911yescharacteristic, complemented
312#1940C2×C2911yescharacteristic, complemented
313#1880C2×C2911yescharacteristic, complemented
314#1879C2×C2911yescharacteristic
315#1803C2×C2911yescharacteristic, complemented
316#1802C2×C2911yescharacteristic, complemented
317#1762C2×C2911yescharacteristic, complemented
318C22×C29—42no—
319C22×C29—42no—
320C22×C29—42no—
321C22×C29—42no—
322C22×C29—42no—
323C22×C29—42no—
324C22×C29—81no—
325C22×C29—81no—
326C22×C29—81no—
327C22×C29—81no—
328C22×C29—81no—
329C22×C29—81no—
330C22×C29—81no—
331C22×C29—81no—
332C22×C29C2×#12111yescharacteristic
333C22×C29#54611yescharacteristic
334C22×C29#54811yescharacteristic
335C22×C29C2×AGL(1,ℤ/8)11yescharacteristic
336C22×C29C2×AGL(1,ℤ/8)11yescharacteristic
337C22×C29#57711yescharacteristic
338C22×C29#57811yescharacteristic
339C4×C29—22no—
340C4×C29—22no—
341C4×C29—22no—
342C4×C29—22no—
343C4×C29—42no—
344C4×C29—41no—
345C4×C29—42no—
346C4×C29—41no—
347C4×C29—81no—
348C4×C29—81no—
349C4×C29—81no—
350C4×C29—81no—
351C4×C29#52911yescharacteristic
352C4×C29#54211yescharacteristic
353C4×C29#54611yescharacteristic
354C4×C29#54711yescharacteristic
355C22×SD16C22×C2911yescharacteristic
356C22×D8C22×C2911yescharacteristic
357C2×C4⋊Q8C22×C2911yescharacteristic
358C2×#124C22×C2911yescharacteristic
359C2×C22⋊Q8—21no—
360C2×C22⋊Q8—21no—
361C2×C4×Q8C22×C2911yescharacteristic
362C2×C4×D4C22×C2911yescharacteristic
363C2×C4×D4C22×C2911yescharacteristic
364#489—24no—
365#463—24no—
366C2×C4⋊C8C22×C2911yescharacteristic
367C2×C4⋊C8C22×C2911yescharacteristic
368C2×C4⋊C8C22×C2911yescharacteristic
369C2×#103C22×C2911yescharacteristic
370C2×#103C22×C2911yescharacteristic
371C2×#103C22×C2911yescharacteristic
372C2×#102C22×C2911yescharacteristic
373C2×#102C22×C2911yescharacteristic
374C2×#102C22×C2911yescharacteristic
375C2×#102C22×C2911yescharacteristic
376C2×#102C22×C2911yescharacteristic
377C2×#97C22×C2911yescharacteristic
378#399—21no—
379#399—21no—
380#391C22×C2911yescharacteristic
381#390C22×C2911yescharacteristic
382#390C22×C2911yescharacteristic
383#390C22×C2911yescharacteristic
384#388—21no—
385#388—21no—
386#385—21no—
387#384C22×C2911yescharacteristic
388#384C22×C2911yescharacteristic
389C4×C4⋊C4C22×C2911yescharacteristic
390C4×C4⋊C4C22×C2911yescharacteristic
391C4×C22⋊C4—21no—
392#340C22×C2911yescharacteristic
393#340C22×C2911yescharacteristic
394#340C22×C2911yescharacteristic
395#340C22×C2911yescharacteristic
396#340C22×C2911yescharacteristic
397#340C22×C2911yescharacteristic
398#336C22×C2911yescharacteristic
399#336C22×C2911yescharacteristic
400C2×C29—82no—
401C2×C29—82no—
402C2×C29#242711yescharacteristic
403C2×C29#303811yescharacteristic
404C2×C29#304611yescharacteristic
405C2×C29#330611yescharacteristic
406C2×C29#330811yescharacteristic
407C2×C29#336711yescharacteristic
408C2×C29#337311yescharacteristic
409C22×Q8—21no—
410C22×Q8C23×C2911yescharacteristic
411C22×D4C23×C2911yescharacteristic
412C22×D4C23×C2911yescharacteristic
413C23×C4—21no—
414C23×C4—21no—
415C2×SD16—22no—
416C2×SD16—22no—
417C2×SD16—41no—
418C2×D8—22no—
419C2×D8—22no—
420C2×D8—41no—
421C22×C8C23×C2911yescharacteristic
422C22×C8C23×C2911yescharacteristic
423C22×C8C23×C2911yescharacteristic
424C22×C8C23×C2911yescharacteristic
425C4⋊Q8—22no—
426C4⋊Q8—22no—
427#124—22no—
428#124D4×C2914yes—
429C22⋊Q8—44no—
430C22⋊Q8—44no—
431C4×Q8—22no—
432C4×Q8—41no—
433C4×D4—22no—
434C4×D4—22no—
435C4×D4—22no—
436C4×D4—41no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4D4×C2911yescharacteristic
444C2×C4⋊C4D4×C2911yescharacteristic
445C2×C4⋊C4C23×C2911yescharacteristic
446C2×C4⋊C4C23×C2911yescharacteristic
447C2×C4⋊C4C23×C2911yescharacteristic
448C2×C4⋊C4C23×C2911yescharacteristic
449C2×C4⋊C4C23×C2911yescharacteristic
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C42—21no—
461C2×C42—21no—
462C2×C42C23×C2911yescharacteristic
463C2×C42C23×C2911yescharacteristic
464C2×C42C23×C2911yescharacteristic
465C4⋊C8—22no—
466C4⋊C8—41no—
467C4⋊C8—41no—
468#103—22no—
469#103—22no—
470#103—22no—
471#102—22no—
472#102—22no—
473#102—22no—
474#102—22no—
475#102—22no—
476#97—22no—
477#95—21no—
478#95—21no—
479#95—21no—
480#95D4×C2911yescharacteristic
481#95D4×C2911yescharacteristic
482C29#2533411yescharacteristic, direct product factor, Sylow
483C24—21no—
484C24—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—42no—
491C2×Q8—42no—
492C2×Q8—42no—
493C2×Q8C2×D4×C2912yes—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4C2×D4×C2912yes—
505C2×D4#41×C2912yes—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—81no—
518C22×C4C2×D4×C2911yescharacteristic
519C22×C4C2×D4×C2911yescharacteristic
520C22×C4C2×D4×C2911yescharacteristic
521C22×C4C2×D4×C2911yescharacteristic
522C22×C4C2×D4×C2911yescharacteristic
523C22×C4C2×D4×C2911yescharacteristic
524C22×C4C24×C2911yescharacteristic
525SD16—44no—
526D8—44no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—42no—
551C4⋊C4—42no—
552C4⋊C4—42no—
553C4⋊C4—42no—
554C4⋊C4—42no—
555C4⋊C4—42no—
556C4⋊C4#41×C2912yes—
557C22⋊C4—24no—
558C22⋊C4—24no—
559C22⋊C4—42no—
560C22⋊C4—42no—
561C22⋊C4—42no—
562C22⋊C4—42no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C22⋊C4—42no—
566C22⋊C4—81no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42—21no—
571C42—42no—
572C42—81no—
573C42C2×D4×C2912yes—
574C42#41×C2912yes—
575C23—22no—
576C23—22no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23C22×D4×C2911yescharacteristic
590Q8—22no—
591Q8—22no—
592Q8—41no—
593Q8—41no—
594Q8—84no—
595D4—22no—
596D4—22no—
597D4—22no—
598D4—22no—
599D4—41no—
600D4—41no—
601D4—41no—
602D4—41no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—22no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—22no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—84no—
636C2×C4—84no—
637C2×C4C29×#12112yes—
638C2×C4C29×#12112yes—
639C2×C4C29×AGL(1,ℤ/8)12yes—
640C2×C4C29×AGL(1,ℤ/8)12yes—
641C2×C4C22×D4×C2911yescharacteristic
642C2×C4C2×#41×C2911yescharacteristic
643C2×C4C2×#41×C2911yescharacteristic
644C2×C4C2×#41×C2911yescharacteristic
645C2×C4C29×H(5,𝔽2)11yescharacteristic
646C2×C4C29×2−1+411yescharacteristic
647C8—41no—
648C8—41no—
649C8—41no—
650C8—41no—
651C22—42no—
652C22—42no—
653C22—42no—
654C22—42no—
655C22—42no—
656C22—42no—
657C22—81no—
658C22—81no—
659C22—81no—
660C22—81no—
661C22—81no—
662C22—81no—
663C22—81no—
664C22—81no—
665C22C2×C29×#12111yescharacteristic
666C22C29×#54611yescharacteristic
667C22C29×#54811yescharacteristic
668C22C2×C29×AGL(1,ℤ/8)11yescharacteristic
669C22C2×C29×AGL(1,ℤ/8)11yescharacteristic
670C22C29×#57711yescharacteristic
671C22C29×#57811yescharacteristic
672C4—22no—
673C4—22no—
674C4—22no—
675C4—22no—
676C4—42no—
677C4—41no—
678C4—42no—
679C4—41no—
680C4—81no—
681C4—81no—
682C4—81no—
683C4—81no—
684C4C29×#52911yescharacteristic
685C4C29×#54211yescharacteristic
686C4C29×#54611yescharacteristic
687C4C29×#54711yescharacteristic
688C2—82no—
689C2—82no—
690C2C29×#242711yescharacteristic
691C2C29×#303811yescharacteristic
692C2C29×#304611yescharacteristic
693C2C29×#330611yescharacteristic
694C2C29×#330811yescharacteristic
695C2C29×#336711yescharacteristic
696C2C29×#337311yescharacteristic
subgroupG/H
center, socleC23×C29C22×D4
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC22×D8×C29C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C29 ◁ C4×C4⋊C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C29×#489C2semidirect
3. C29×#2542C2semidirect
4. C29×#2367C2semidirect
5. C29×#2072C2semidirect
6. C29×#2071C2semidirect
7. C29×#2055C2semidirect
9. C29×#1987C2semidirect
10. C29×#1940C2semidirect
11. C29×#1880C2semidirect
13. C29×#1803C2semidirect
14. C29×#1802C2semidirect
15. C29×#1762C2semidirect
226. #25334C29direct (N × H)
303. C2×#489C2×C29semidirect
305. #2542C2×C29semidirect
306. #2367C2×C29semidirect
307. #2072C2×C29semidirect
308. #2071C2×C29semidirect
309. #2055C2×C29semidirect
311. #1987C2×C29semidirect
312. #1940C2×C29semidirect
313. #1880C2×C29semidirect
315. #1803C2×C29semidirect
316. #1802C2×C29semidirect
317. #1762C2×C29semidirect
482. C29#25334direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#4892
C2×C29×#4632
C29×#25422
C29×#23672
C29×#20722
C29×#20712
C29×#20552
C29×#20542
C29×#19872
C29×#19402
C29×#18802
C29×#18792
C29×#18032
C29×#18022
C29×#17622
#2533429