Finite Group Databasebeta

← C29×#22951 #20317851

Subgroups — C29×#22951 #20317851

Order 7424.

730 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3091C211yesmaximal, characteristic
2C29×#2933C211yesmaximal, characteristic
3C29×#2924C211yesmaximal, characteristic, complemented
4C29×#1946C211yesmaximal, characteristic, complemented
5C29×#1937C211yesmaximal, characteristic, complemented
6C29×#1929C211yesmaximal, characteristic, complemented
7C29×#1922C211yesmaximal, characteristic, complemented
8C29×#1922C211yesmaximal, characteristic, complemented
9C29×#1897C211yesmaximal, characteristic
10C29×#1866C211yesmaximal, characteristic, complemented
11C29×#1855C211yesmaximal, characteristic, complemented
12C29×#1772C211yesmaximal, characteristic, complemented
13C29×#1765C211yesmaximal, characteristic, complemented
14C29×#1750C211yesmaximal, characteristic, complemented
15C29×#1733C211yesmaximal, characteristic, complemented
16C2×C29×#131C2211yescharacteristic
17C22×M16×C29C2211yescharacteristic
18C29×#525C2211yescharacteristic
19C2×C29×#117C2211yescharacteristic
20C2×C29×#117C2211yescharacteristic
21C29×#485C411yescharacteristic, complemented
22C29×#485C411yescharacteristic, complemented
23C29×#484C411yescharacteristic, complemented
24C29×#483C411yescharacteristic, complemented
25C29×#482C411yescharacteristic, complemented
26C29×#482C411yescharacteristic, complemented
27C29×#481C411yescharacteristic, complemented
28C29×#480C411yescharacteristic, complemented
29C29×#436—21no—
30C29×#435—21no—
31C29×#435—21no—
32C8×D4×C29—21no—
33C29×#433—21no—
34C29×#433—21no—
35C29×#432—21no—
36C29×#431—21no—
37C2×C29×#108C2211yescharacteristic
38C2×C29×#108C2211yescharacteristic
39C29×#427C2211yescharacteristic
40C29×#427C2211yescharacteristic
41C29×#424C2211yescharacteristic
42C29×#424C2211yescharacteristic
43C29×#424C2211yescharacteristic
44C2×C29×#104C2211yescharacteristic
45C2×C29×#104C2211yescharacteristic
46C29×#416C2211yescharacteristic
47C29×#416C2211yescharacteristic
48C29×#408C2211yescharacteristic
49C29×#407C2211yescharacteristic
50C2×C29×C22⋊C8C2211yescharacteristic
51C2×C29×C22⋊C8C2211yescharacteristic
52C29×#405C2211yescharacteristic
53C29×#405C2211yescharacteristic
54C29×#405C2211yescharacteristic
55C2×C29×#97C2211yescharacteristic
56C2×C4×C8×C29C2211yescharacteristic
57C29×#341C2211yescharacteristic
58C29×#341C2211yescharacteristic
59C29×#339C2211yescharacteristic
60C29×#339C2211yescharacteristic
61C29×#339C2211yescharacteristic
62C29×#339C2211yescharacteristic
63C29×#339C2211yescharacteristic
64C29×#339C2211yescharacteristic
65C29×#336C2211yescharacteristic
66C29×#336C2211yescharacteristic
67C2×#41×C29C2311yescharacteristic
68C23×C4×C29C2311yescharacteristic
69C29×#131—22no—
70C29×#131—41no—
71C2×M16×C29—21no—
72C2×M16×C29—21no—
73C2×M16×C29—22no—
74C2×M16×C29—41no—
75C2×M16×C29C2311yescharacteristic
76C2×M16×C29C2311yescharacteristic
77C2×M16×C29C2311yescharacteristic
78C2×M16×C29C2311yescharacteristic
79C22×C8×C29—21no—
80C22×C8×C29—21no—
81C22×C8×C29C2311yescharacteristic
82C22×C8×C29C2311yescharacteristic
83C22×C8×C29C2311yescharacteristic
84C22×C8×C29C2311yescharacteristic
85C29×#123—21no—
86C29×C22⋊Q8C2×C411yescharacteristic
87C29×C22⋊Q8C2×C411yescharacteristic
88C29×#121C2×C411yescharacteristic
89C29×#121C2×C411yescharacteristic
90C29×#120—21no—
91C4×D4×C29—21no—
92C4×D4×C29—21no—
93C29×#117—21no—
94C29×#117—21no—
95C29×#117—22no—
96C29×#117—41no—
97C29×#117C2×C411yescharacteristic
98C29×#117C2×C411yescharacteristic
99C29×#117C2311yescharacteristic
100C29×#117C2311yescharacteristic
101C29×#117C2311yescharacteristic
102C2×C4⋊C4×C29—21no—
103C2×C4⋊C4×C29C2×C411yescharacteristic
104C2×C4⋊C4×C29C2×C411yescharacteristic
105C2×C22⋊C4×C29—21no—
106C2×C22⋊C4×C29—21no—
107C2×C42×C29—21no—
108C2×C42×C29C2311yescharacteristic
109C2×C42×C29C2311yescharacteristic
110C29×#108—22no—
111C29×#108—41no—
112C29×#107C2×C411yescharacteristic
113C29×#107C2×C411yescharacteristic
114C29×#107C2×C411yescharacteristic
115C29×#107C2×C411yescharacteristic
116C29×#106C2×C411yescharacteristic
117C29×#106C2×C411yescharacteristic
118C29×#106C2×C411yescharacteristic
119C29×#106C2×C411yescharacteristic
120C29×C4⋊C8—21no—
121C29×C4⋊C8—21no—
122C29×C4⋊C8—21no—
123C29×C4⋊C8—21no—
124C29×C4⋊C8—21no—
125C29×C4⋊C8—21no—
126C29×#104—22no—
127C29×#104—41no—
128C29×#103C2×C411yescharacteristic
129C29×#103C2×C411yescharacteristic
130C29×#103C2×C411yescharacteristic
131C29×#103C2×C411yescharacteristic
132C29×#102C2×C411yescharacteristic
133C29×#102C2×C411yescharacteristic
134C29×#102C2×C411yescharacteristic
135C29×#102C2×C411yescharacteristic
136C29×C22⋊C8—21no—
137C29×C22⋊C8—21no—
138C29×C22⋊C8—21no—
139C29×C22⋊C8—21no—
140C29×C22⋊C8C2×C411yescharacteristic
141C29×C22⋊C8C2×C411yescharacteristic
142C29×C22⋊C8C2×C411yescharacteristic
143C29×C22⋊C8C2×C411yescharacteristic
144C29×C22⋊C8D411yescharacteristic
145C29×C22⋊C8D411yescharacteristic
146C29×C22⋊C8D411yescharacteristic
147C29×C22⋊C8D411yescharacteristic
148C29×#97—21no—
149C29×#97—21no—
150C29×#97—21no—
151C29×#97—41no—
152C4×C8×C29—21no—
153C4×C8×C29—21no—
154C4×C8×C29—21no—
155C4×C8×C29—22no—
156C24×C29#4111yescharacteristic
157#41×C29—21no—
158#41×C29—21no—
159#41×C29—21no—
160#41×C29—21no—
161C2×Q8×C29C22×C411yescharacteristic
162C2×D4×C29—21no—
163C2×D4×C29—21no—
164C2×D4×C29—21no—
165C2×D4×C29C22×C411yescharacteristic
166C22×C4×C29—21no—
167C22×C4×C29—21no—
168C22×C4×C29—21no—
169C22×C4×C29—21no—
170C22×C4×C29—21no—
171C22×C4×C29—21no—
172C22×C4×C29—21no—
173C22×C4×C29—21no—
174C22×C4×C29—21no—
175C22×C4×C29C22×C411yescharacteristic
176C22×C4×C29C22×C411yescharacteristic
177C22×C4×C29C2×D411yescharacteristic
178C22×C4×C29C2×D411yescharacteristic
179C22×C4×C29#4111yescharacteristic
180C22×C4×C29C2411yescharacteristic
181M16×C29—21no—
182M16×C29—21no—
183M16×C29—21no—
184M16×C29—21no—
185M16×C29—21no—
186M16×C29—21no—
187M16×C29—21no—
188M16×C29—42no—
189M16×C29—42no—
190M16×C29#4112yes—
191C2×C8×C29—21no—
192C2×C8×C29—21no—
193C2×C8×C29—21no—
194C2×C8×C29—21no—
195C2×C8×C29—21no—
196C2×C8×C29—21no—
197C2×C8×C29—21no—
198C2×C8×C29—21no—
199C2×C8×C29—21no—
200C2×C8×C29—21no—
201C2×C8×C29—21no—
202C2×C8×C29—21no—
203C2×C8×C29—42no—
204C2×C8×C29—42no—
205C2×C8×C29C22×C411yescharacteristic
206C2×C8×C29C22×C411yescharacteristic
207C2×C8×C29C22×C411yescharacteristic
208C2×C8×C29C22×C411yescharacteristic
209C2×C8×C29C2×D411yescharacteristic
210C2×C8×C29C2×D411yescharacteristic
211C2×C8×C29C2×D411yescharacteristic
212C2×C8×C29C2×D411yescharacteristic
213C4⋊C4×C29—21no—
214C4⋊C4×C29—21no—
215C4⋊C4×C29—21no—
216C4⋊C4×C29—21no—
217C4⋊C4×C29—42no—
218C4⋊C4×C29C22×C411yescharacteristic
219C4⋊C4×C29C22×C411yescharacteristic
220C4⋊C4×C29C22×C411yescharacteristic
221C4⋊C4×C29C22×C411yescharacteristic
222C4⋊C4×C29C22×C411yescharacteristic
223C4⋊C4×C29C22×C411yescharacteristic
224C22⋊C4×C29—21no—
225C22⋊C4×C29—21no—
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—42no—
234C42×C29—21no—
235C42×C29—21no—
236C42×C29—21no—
237C42×C29—21no—
238C42×C29—21no—
239C42×C29—21no—
240C42×C29—21no—
241C42×C29—21no—
242C42×C29#4112yes—
243#22951C2911yesmaximal, characteristic, direct product factor, Sylow
244C23×C29—21no—
245C23×C29—21no—
246C23×C29—21no—
247C23×C29—41no—
248C23×C29—41no—
249C23×C29C4×D411yescharacteristic
250C23×C29C4×D411yescharacteristic
251C23×C29C2×#4111yescharacteristic
252Q8×C29—21no—
253Q8×C29—21no—
254D4×C29—21no—
255D4×C29—21no—
256D4×C29—42no—
257D4×C29—41no—
258D4×C29—41no—
259D4×C29—81no—
260C2×C4×C29—21no—
261C2×C4×C29—21no—
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—21no—
269C2×C4×C29—21no—
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—22no—
278C2×C4×C29—41no—
279C2×C4×C29—41no—
280C2×C4×C29—42no—
281C2×C4×C29—41no—
282C2×C4×C29—41no—
283C2×C4×C29—41no—
284C2×C4×C29—41no—
285C2×C4×C29—41no—
286C2×C4×C29—81no—
287C2×C4×C29C4×D411yescharacteristic
288C2×C4×C29C4×D411yescharacteristic
289C2×C4×C29C23×C411yescharacteristic
290C2×C4×C29C22×D411yescharacteristic
291C2×C4×C29C2×#4111yescharacteristic
292C2×C4×C29C2×#4111yescharacteristic
293C2×C4×C29H(5,𝔽2)11yescharacteristic
294C2×C4×C292−1+411yescharacteristic
295C8×C29—21no—
296C8×C29—21no—
297C8×C29—21no—
298C8×C29—21no—
299C8×C29—21no—
300C8×C29—21no—
301C8×C29—22no—
302C8×C29—21no—
303C8×C29—21no—
304C8×C29—41no—
305C8×C29—41no—
306C8×C29—41no—
307#3091C2×C2911yescharacteristic
308#2933C2×C2911yescharacteristic
309#2924C2×C2911yescharacteristic, complemented
310#1946C2×C2911yescharacteristic, complemented
311#1937C2×C2911yescharacteristic, complemented
312#1929C2×C2911yescharacteristic, complemented
313#1922C2×C2911yescharacteristic, complemented
314#1922C2×C2911yescharacteristic, complemented
315#1897C2×C2911yescharacteristic
316#1866C2×C2911yescharacteristic, complemented
317#1855C2×C2911yescharacteristic, complemented
318#1772C2×C2911yescharacteristic, complemented
319#1765C2×C2911yescharacteristic, complemented
320#1750C2×C2911yescharacteristic, complemented
321#1733C2×C2911yescharacteristic, complemented
322C22×C29—21no—
323C22×C29—21no—
324C22×C29—21no—
325C22×C29—21no—
326C22×C29—21no—
327C22×C29—21no—
328C22×C29—21no—
329C22×C29—21no—
330C22×C29—41no—
331C22×C29—41no—
332C22×C29—41no—
333C22×C29—81no—
334C22×C29—81no—
335C22×C29C2×C4×D411yescharacteristic
336C22×C29#55111yescharacteristic
337C22×C29#55211yescharacteristic
338C4×C29—21no—
339C4×C29—21no—
340C4×C29—42no—
341C4×C29—41no—
342C4×C29—41no—
343C4×C29—41no—
344C4×C29—41no—
345C4×C29—41no—
346C4×C29—41no—
347C4×C29—41no—
348C4×C29—81no—
349C4×C29C4×#4111yescharacteristic
350C4×C29#52011yescharacteristic
351C4×C29#54611yescharacteristic
352C4×C29#54711yescharacteristic
353C2×#131C22×C2911yescharacteristic
354C22×M16C22×C2911yescharacteristic
355#525C22×C2911yescharacteristic
356C2×#117C22×C2911yescharacteristic
357C2×#117C22×C2911yescharacteristic
358#485C4×C2911yescharacteristic, complemented
359#485C4×C2911yescharacteristic, complemented
360#484C4×C2911yescharacteristic, complemented
361#483C4×C2911yescharacteristic, complemented
362#482C4×C2911yescharacteristic, complemented
363#482C4×C2911yescharacteristic, complemented
364#481C4×C2911yescharacteristic, complemented
365#480C4×C2911yescharacteristic, complemented
366#436—21no—
367#435—21no—
368#435—21no—
369C8×D4—21no—
370#433—21no—
371#433—21no—
372#432—21no—
373#431—21no—
374C2×#108C22×C2911yescharacteristic
375C2×#108C22×C2911yescharacteristic
376#427C22×C2911yescharacteristic
377#427C22×C2911yescharacteristic
378#424C22×C2911yescharacteristic
379#424C22×C2911yescharacteristic
380#424C22×C2911yescharacteristic
381C2×#104C22×C2911yescharacteristic
382C2×#104C22×C2911yescharacteristic
383#416C22×C2911yescharacteristic
384#416C22×C2911yescharacteristic
385#408C22×C2911yescharacteristic
386#407C22×C2911yescharacteristic
387C2×C22⋊C8C22×C2911yescharacteristic
388C2×C22⋊C8C22×C2911yescharacteristic
389#405C22×C2911yescharacteristic
390#405C22×C2911yescharacteristic
391#405C22×C2911yescharacteristic
392C2×#97C22×C2911yescharacteristic
393C2×C4×C8C22×C2911yescharacteristic
394#341C22×C2911yescharacteristic
395#341C22×C2911yescharacteristic
396#339C22×C2911yescharacteristic
397#339C22×C2911yescharacteristic
398#339C22×C2911yescharacteristic
399#339C22×C2911yescharacteristic
400#339C22×C2911yescharacteristic
401#339C22×C2911yescharacteristic
402#336C22×C2911yescharacteristic
403#336C22×C2911yescharacteristic
404C2×C29—21no—
405C2×C29—21no—
406C2×C29—41no—
407C2×C29—41no—
408C2×C29—81no—
409C2×C29#235911yescharacteristic
410C2×C29#295511yescharacteristic
411C2×C29#295711yescharacteristic
412C2×#41C23×C2911yescharacteristic
413C23×C4C23×C2911yescharacteristic
414#131—22no—
415#131—41no—
416C2×M16—21no—
417C2×M16—21no—
418C2×M16—22no—
419C2×M16—41no—
420C2×M16C23×C2911yescharacteristic
421C2×M16C23×C2911yescharacteristic
422C2×M16C23×C2911yescharacteristic
423C2×M16C23×C2911yescharacteristic
424C22×C8—21no—
425C22×C8—21no—
426C22×C8C23×C2911yescharacteristic
427C22×C8C23×C2911yescharacteristic
428C22×C8C23×C2911yescharacteristic
429C22×C8C23×C2911yescharacteristic
430#123—21no—
431C22⋊Q8C2×C4×C2911yescharacteristic
432C22⋊Q8C2×C4×C2911yescharacteristic
433#121C2×C4×C2911yescharacteristic
434#121C2×C4×C2911yescharacteristic
435#120—21no—
436C4×D4—21no—
437C4×D4—21no—
438#117—21no—
439#117—21no—
440#117—22no—
441#117—41no—
442#117C2×C4×C2911yescharacteristic
443#117C2×C4×C2911yescharacteristic
444#117C23×C2911yescharacteristic
445#117C23×C2911yescharacteristic
446#117C23×C2911yescharacteristic
447C2×C4⋊C4—21no—
448C2×C4⋊C4C2×C4×C2911yescharacteristic
449C2×C4⋊C4C2×C4×C2911yescharacteristic
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C42—21no—
453C2×C42C23×C2911yescharacteristic
454C2×C42C23×C2911yescharacteristic
455#108—22no—
456#108—41no—
457#107C2×C4×C2911yescharacteristic
458#107C2×C4×C2911yescharacteristic
459#107C2×C4×C2911yescharacteristic
460#107C2×C4×C2911yescharacteristic
461#106C2×C4×C2911yescharacteristic
462#106C2×C4×C2911yescharacteristic
463#106C2×C4×C2911yescharacteristic
464#106C2×C4×C2911yescharacteristic
465C4⋊C8—21no—
466C4⋊C8—21no—
467C4⋊C8—21no—
468C4⋊C8—21no—
469C4⋊C8—21no—
470C4⋊C8—21no—
471#104—22no—
472#104—41no—
473#103C2×C4×C2911yescharacteristic
474#103C2×C4×C2911yescharacteristic
475#103C2×C4×C2911yescharacteristic
476#103C2×C4×C2911yescharacteristic
477#102C2×C4×C2911yescharacteristic
478#102C2×C4×C2911yescharacteristic
479#102C2×C4×C2911yescharacteristic
480#102C2×C4×C2911yescharacteristic
481C22⋊C8—21no—
482C22⋊C8—21no—
483C22⋊C8—21no—
484C22⋊C8—21no—
485C22⋊C8C2×C4×C2911yescharacteristic
486C22⋊C8C2×C4×C2911yescharacteristic
487C22⋊C8C2×C4×C2911yescharacteristic
488C22⋊C8C2×C4×C2911yescharacteristic
489C22⋊C8D4×C2911yescharacteristic
490C22⋊C8D4×C2911yescharacteristic
491C22⋊C8D4×C2911yescharacteristic
492C22⋊C8D4×C2911yescharacteristic
493#97—21no—
494#97—21no—
495#97—21no—
496#97—41no—
497C4×C8—21no—
498C4×C8—21no—
499C4×C8—21no—
500C4×C8—22no—
501C29#2295111yescharacteristic, direct product factor, Sylow
502C24#41×C2911yescharacteristic
503#41—21no—
504#41—21no—
505#41—21no—
506#41—21no—
507C2×Q8C22×C4×C2911yescharacteristic
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4C22×C4×C2911yescharacteristic
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4C22×C4×C2911yescharacteristic
522C22×C4C22×C4×C2911yescharacteristic
523C22×C4C2×D4×C2911yescharacteristic
524C22×C4C2×D4×C2911yescharacteristic
525C22×C4#41×C2911yescharacteristic
526C22×C4C24×C2911yescharacteristic
527M16—21no—
528M16—21no—
529M16—21no—
530M16—21no—
531M16—21no—
532M16—21no—
533M16—21no—
534M16—42no—
535M16—42no—
536M16#41×C2912yes—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
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—42no—
550C2×C8—42no—
551C2×C8C22×C4×C2911yescharacteristic
552C2×C8C22×C4×C2911yescharacteristic
553C2×C8C22×C4×C2911yescharacteristic
554C2×C8C22×C4×C2911yescharacteristic
555C2×C8C2×D4×C2911yescharacteristic
556C2×C8C2×D4×C2911yescharacteristic
557C2×C8C2×D4×C2911yescharacteristic
558C2×C8C2×D4×C2911yescharacteristic
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—42no—
564C4⋊C4C22×C4×C2911yescharacteristic
565C4⋊C4C22×C4×C2911yescharacteristic
566C4⋊C4C22×C4×C2911yescharacteristic
567C4⋊C4C22×C4×C2911yescharacteristic
568C4⋊C4C22×C4×C2911yescharacteristic
569C4⋊C4C22×C4×C2911yescharacteristic
570C22⋊C4—21no—
571C22⋊C4—21no—
572C22⋊C4—21no—
573C22⋊C4—21no—
574C22⋊C4—21no—
575C22⋊C4—21no—
576C22⋊C4—21no—
577C22⋊C4—21no—
578C22⋊C4—21no—
579C22⋊C4—42no—
580C42—21no—
581C42—21no—
582C42—21no—
583C42—21no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42#41×C2912yes—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—41no—
593C23—41no—
594C23C4×D4×C2911yescharacteristic
595C23C4×D4×C2911yescharacteristic
596C23C2×#41×C2911yescharacteristic
597Q8—21no—
598Q8—21no—
599D4—21no—
600D4—21no—
601D4—42no—
602D4—41no—
603D4—41no—
604D4—81no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—42no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—81no—
632C2×C4C4×D4×C2911yescharacteristic
633C2×C4C4×D4×C2911yescharacteristic
634C2×C4C23×C4×C2911yescharacteristic
635C2×C4C22×D4×C2911yescharacteristic
636C2×C4C2×#41×C2911yescharacteristic
637C2×C4C2×#41×C2911yescharacteristic
638C2×C4C29×H(5,𝔽2)11yescharacteristic
639C2×C4C29×2−1+411yescharacteristic
640C8—21no—
641C8—21no—
642C8—21no—
643C8—21no—
644C8—21no—
645C8—21no—
646C8—22no—
647C8—21no—
648C8—21no—
649C8—41no—
650C8—41no—
651C8—41no—
652C22—21no—
653C22—21no—
654C22—21no—
655C22—21no—
656C22—21no—
657C22—21no—
658C22—21no—
659C22—21no—
660C22—41no—
661C22—41no—
662C22—41no—
663C22—81no—
664C22—81no—
665C22C2×C4×D4×C2911yescharacteristic
666C22C29×#55111yescharacteristic
667C22C29×#55211yescharacteristic
668C4—21no—
669C4—21no—
670C4—42no—
671C4—41no—
672C4—41no—
673C4—41no—
674C4—41no—
675C4—41no—
676C4—41no—
677C4—41no—
678C4—81no—
679C4C4×#41×C2911yescharacteristic
680C4C29×#52011yescharacteristic
681C4C29×#54611yescharacteristic
682C4C29×#54711yescharacteristic
683C2—21no—
684C2—21no—
685C2—41no—
686C2—41no—
687C2—81no—
688C2C29×#235911yescharacteristic
689C2C29×#295511yescharacteristic
690C2C29×#295711yescharacteristic
subgroupG/H
centerC2×C4×C29C22×D4
commutatorC2×C4C23×C4×C29
Frattini, cosocleC22×C4C24×C29
socleC22×C29C2×C4×D4
prime radicalC29×#525C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C29 ◁ C2×C29×C22⋊C8 ◁ G

Complements

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

NH ≅ G/Ntype
3. C29×#2924C2semidirect
4. C29×#1946C2semidirect
5. C29×#1937C2semidirect
6. C29×#1929C2semidirect
7. C29×#1922C2semidirect
8. C29×#1922C2semidirect
10. C29×#1866C2semidirect
11. C29×#1855C2semidirect
12. C29×#1772C2semidirect
13. C29×#1765C2semidirect
14. C29×#1750C2semidirect
15. C29×#1733C2semidirect
21. C29×#485C4semidirect
22. C29×#485C4semidirect
23. C29×#484C4semidirect
24. C29×#483C4semidirect
25. C29×#482C4semidirect
26. C29×#482C4semidirect
27. C29×#481C4semidirect
28. C29×#480C4semidirect
243. #22951C29direct (N × H)
309. #2924C2×C29semidirect
310. #1946C2×C29semidirect
311. #1937C2×C29semidirect
312. #1929C2×C29semidirect
313. #1922C2×C29semidirect
314. #1922C2×C29semidirect
316. #1866C2×C29semidirect
317. #1855C2×C29semidirect
318. #1772C2×C29semidirect
319. #1765C2×C29semidirect
320. #1750C2×C29semidirect
321. #1733C2×C29semidirect
358. #485C4×C29semidirect
359. #485C4×C29semidirect
360. #484C4×C29semidirect
361. #483C4×C29semidirect
362. #482C4×C29semidirect
363. #482C4×C29semidirect
364. #481C4×C29semidirect
365. #480C4×C29semidirect
501. C29#22951direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#30912
C29×#29332
C29×#29242
C29×#19462
C29×#19372
C29×#19292
C29×#19222
C29×#18972
C29×#18662
C29×#18552
C29×#17722
C29×#17652
C29×#17502
C29×#17332
#2295129