Finite Group Databasebeta

← C29×#22918 #20317818

Subgroups — C29×#22918 #20317818

Order 7424.

942 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#481C211yesmaximal, characteristic
2C29×#2361C211yesmaximal, characteristic
3C29×#2345C211yesmaximal, characteristic, complemented
4C29×#1941C211yesmaximal, characteristic, complemented
5C29×#1934C211yesmaximal, characteristic, complemented
6C29×#1926C211yesmaximal, characteristic, complemented
7C29×#1920C211yesmaximal, characteristic, complemented
8C29×#1919C211yesmaximal, characteristic, complemented
9C29×#1893C211yesmaximal, characteristic
10C29×#1864C211yesmaximal, characteristic, complemented
11C29×#1853C211yesmaximal, characteristic, complemented
12C4×C29×#106C211yesmaximal, characteristic, complemented
13C4×C29×#102C211yesmaximal, characteristic, complemented
14C8×C22⋊C4×C29C211yesmaximal, characteristic, complemented
15C2×C29×#340C211yesmaximal, characteristic, complemented
16C23×C8×C29C2211yescharacteristic
17C2×C29×#121C2211yescharacteristic
18C2×C4×D4×C29—21no—
19C2×C4×D4×C29C2211yescharacteristic
20C22×C4⋊C4×C29C2211yescharacteristic
21C22×C4⋊C4×C29C2211yescharacteristic
22C29×#481C418yescomplemented
23C2×C29×#106C2211yescharacteristic
24C2×C29×#106C2211yescharacteristic
25C2×C29×#106C2211yescharacteristic
26C2×C29×#106C2211yescharacteristic
27C2×C29×#102C2211yescharacteristic
28C2×C29×#102C2211yescharacteristic
29C2×C29×#102C2211yescharacteristic
30C2×C29×#102C2211yescharacteristic
31C2×C29×C22⋊C8C2211yescharacteristic
32C2×C4×C8×C29C2211yescharacteristic
33C2×C4×C8×C29C2211yescharacteristic
34C29×#390C2211yescharacteristic
35C29×#389C2211yescharacteristic
36C29×#389C2211yescharacteristic
37C29×#389C2211yescharacteristic
38C29×#388—21no—
39C29×#387—21no—
40C29×#387—21no—
41C29×#386—21no—
42C29×#385—21no—
43C29×#380—21no—
44C29×#380C2211yescharacteristic
45C4×C4⋊C4×C29C2211yescharacteristic
46C4×C4⋊C4×C29C2211yescharacteristic
47C4×C4⋊C4×C29C2211yescharacteristic
48C4×C22⋊C4×C29—21no—
49C4×C22⋊C4×C29C2211yescharacteristic
50C29×#340C2211yescharacteristic
51C29×#340C2211yescharacteristic
52C29×#340C2211yescharacteristic
53C29×#340C2211yescharacteristic
54C29×#340C2211yescharacteristic
55C29×#340C2211yescharacteristic
56C29×#340C2211yescharacteristic
57C29×#340C2211yescharacteristic
58C29×#336C2211yescharacteristic
59C29×#336C2211yescharacteristic
60C22×D4×C29—21no—
61C22×D4×C29C2311yescharacteristic
62C23×C4×C29—21no—
63C23×C4×C29—21no—
64C23×C4×C29—21no—
65C23×C4×C29C2311yescharacteristic
66C22×C8×C29—22no—
67C22×C8×C29—22no—
68C22×C8×C29—41no—
69C22×C8×C29C2311yescharacteristic
70C22×C8×C29C2311yescharacteristic
71C22×C8×C29C2311yescharacteristic
72C22×C8×C29C2311yescharacteristic
73C29×#121—22no—
74C29×#121C2×C414yes—
75C4×D4×C29—22no—
76C4×D4×C29—41no—
77C4×D4×C29—44no—
78C2×C4⋊C4×C29—21no—
79C2×C4⋊C4×C29—22no—
80C2×C4⋊C4×C29—22no—
81C2×C4⋊C4×C29—21no—
82C2×C4⋊C4×C29—21no—
83C2×C4⋊C4×C29—21no—
84C2×C4⋊C4×C29—21no—
85C2×C4⋊C4×C29—41no—
86C2×C4⋊C4×C29C2×C414yescomplemented
87C2×C4⋊C4×C29C2311yescharacteristic
88C2×C4⋊C4×C29C2311yescharacteristic
89C2×C4⋊C4×C29C2311yescharacteristic
90C2×C4⋊C4×C29C2311yescharacteristic
91C2×C4⋊C4×C29C2311yescharacteristic
92C2×C4⋊C4×C29C2311yescharacteristic
93C2×C4⋊C4×C29C2311yescharacteristic
94C2×C22⋊C4×C29—21no—
95C2×C22⋊C4×C29—21no—
96C2×C22⋊C4×C29—21no—
97C2×C22⋊C4×C29—21no—
98C2×C22⋊C4×C29—21no—
99C2×C22⋊C4×C29D411yescharacteristic
100C2×C22⋊C4×C29D411yescharacteristic
101C2×C42×C29—21no—
102C2×C42×C29—21no—
103C2×C42×C29—21no—
104C2×C42×C29C2311yescharacteristic
105C2×C42×C29C2311yescharacteristic
106C29×#106—22no—
107C29×#106—41no—
108C29×#106C2×C414yescomplemented
109C29×#106C2×C414yescomplemented
110C29×#102—22no—
111C29×#102—41no—
112C29×#102C2×C414yescomplemented
113C29×#102C2×C414yescomplemented
114C29×C22⋊C8C2×C414yescomplemented
115C4×C8×C29—22no—
116C4×C8×C29—41no—
117C29×#95—21no—
118C29×#95—21no—
119C29×#95—21no—
120C29×#95—21no—
121C29×#95—21no—
122C29×#95—21no—
123C29×#95—21no—
124C29×#95D411yescharacteristic
125C29×#95D411yescharacteristic
126C24×C29—21no—
127C24×C29C2×D411yescharacteristic
128C2×D4×C29—24no—
129C2×D4×C29—21no—
130C2×D4×C29—21no—
131C2×D4×C29—21no—
132C2×D4×C29—21no—
133C2×D4×C29—21no—
134C2×D4×C29—42no—
135C2×D4×C29—42no—
136C2×D4×C29C22×C412yes—
137C22×C4×C29—21no—
138C22×C4×C29—21no—
139C22×C4×C29—21no—
140C22×C4×C29—21no—
141C22×C4×C29—21no—
142C22×C4×C29—21no—
143C22×C4×C29—21no—
144C22×C4×C29—21no—
145C22×C4×C29—24no—
146C22×C4×C29—21no—
147C22×C4×C29—21no—
148C22×C4×C29—21no—
149C22×C4×C29—42no—
150C22×C4×C29—42no—
151C22×C4×C29—42no—
152C22×C4×C29—42no—
153C22×C4×C29—81no—
154C22×C4×C29—81no—
155C22×C4×C29—81no—
156C22×C4×C29—81no—
157C22×C4×C29C22×C412yes—
158C22×C4×C29C2×D411yescharacteristic
159C22×C4×C29C2×D411yescharacteristic
160C22×C4×C29C2×D411yescharacteristic
161C22×C4×C29C2×D411yescharacteristic
162C22×C4×C29C2×D411yescharacteristic
163C22×C4×C29#4112yes—
164C22×C4×C29C2411yescharacteristic
165C2×C8×C29—21no—
166C2×C8×C29—21no—
167C2×C8×C29—21no—
168C2×C8×C29—21no—
169C2×C8×C29—21no—
170C2×C8×C29—21no—
171C2×C8×C29—21no—
172C2×C8×C29—21no—
173C2×C8×C29—21no—
174C2×C8×C29—44no—
175C2×C8×C29C22×C412yes—
176C2×C8×C29C22×C412yes—
177C2×C8×C29#4112yes—
178C4⋊C4×C29—24no—
179C4⋊C4×C29—21no—
180C4⋊C4×C29—21no—
181C4⋊C4×C29—21no—
182C4⋊C4×C29—21no—
183C4⋊C4×C29—21no—
184C4⋊C4×C29—21no—
185C4⋊C4×C29—21no—
186C4⋊C4×C29—21no—
187C4⋊C4×C29—21no—
188C4⋊C4×C29—21no—
189C4⋊C4×C29—42no—
190C4⋊C4×C29—42no—
191C4⋊C4×C29—81no—
192C4⋊C4×C29—81no—
193C4⋊C4×C29C22×C412yes—
194C4⋊C4×C29C22×C412yes—
195C4⋊C4×C29C22×C412yes—
196C4⋊C4×C29#4112yes—
197C22⋊C4×C29—22no—
198C22⋊C4×C29—24no—
199C22⋊C4×C29—42no—
200C22⋊C4×C29—42no—
201C22⋊C4×C29—42no—
202C22⋊C4×C29—81no—
203C22⋊C4×C29SD1614yes—
204C42×C29—21no—
205C42×C29—21no—
206C42×C29—21no—
207C42×C29—21no—
208C42×C29—42no—
209C42×C29—81no—
210C42×C29—81no—
211#22918C2911yesmaximal, characteristic, direct product factor, Sylow
212C23×C29—21no—
213C23×C29—21no—
214C23×C29—21no—
215C23×C29—21no—
216C23×C29—22no—
217C23×C29—41no—
218C23×C29—41no—
219C23×C29—41no—
220C23×C29—41no—
221C23×C29—41no—
222C23×C29—41no—
223C23×C29C4×D412yes—
224C23×C29C2×SD1612yes—
225C23×C29#13512yes—
226C23×C29C22×D411yescharacteristic
227D4×C29—22no—
228D4×C29—22no—
229D4×C29—48no—
230D4×C29—41no—
231D4×C29—41no—
232C2×C4×C29—21no—
233C2×C4×C29—21no—
234C2×C4×C29—21no—
235C2×C4×C29—21no—
236C2×C4×C29—21no—
237C2×C4×C29—21no—
238C2×C4×C29—22no—
239C2×C4×C29—22no—
240C2×C4×C29—22no—
241C2×C4×C29—22no—
242C2×C4×C29—22no—
243C2×C4×C29—22no—
244C2×C4×C29—22no—
245C2×C4×C29—21no—
246C2×C4×C29—22no—
247C2×C4×C29—21no—
248C2×C4×C29—21no—
249C2×C4×C29—21no—
250C2×C4×C29—21no—
251C2×C4×C29—21no—
252C2×C4×C29—41no—
253C2×C4×C29—41no—
254C2×C4×C29—41no—
255C2×C4×C29—41no—
256C2×C4×C29—41no—
257C2×C4×C29—41no—
258C2×C4×C29—41no—
259C2×C4×C29—41no—
260C2×C4×C29—41no—
261C2×C4×C29—41no—
262C2×C4×C29—41no—
263C2×C4×C29—41no—
264C2×C4×C29—41no—
265C2×C4×C29—41no—
266C2×C4×C29—41no—
267C2×C4×C29—41no—
268C2×C4×C29—41no—
269C2×C4×C29—84no—
270C2×C4×C29—84no—
271C2×C4×C29—84no—
272C2×C4×C29C4×D412yes—
273C2×C4×C29C2×SD1612yes—
274C2×C4×C29C2×SD1612yes—
275C2×C4×C29C23×C411yescharacteristic
276C2×C4×C29C2×#4111yescharacteristic
277C2×C4×C29C2×#4111yescharacteristic
278C2×C4×C29C2×#4111yescharacteristic
279C2×C4×C29H(5,𝔽2)11yescharacteristic
280C2×C4×C292−1+411yescharacteristic
281C8×C29—22no—
282C8×C29—22no—
283C8×C29—22no—
284C8×C29—41no—
285C2×#481C2×C2911yescharacteristic
286#2361C2×C2911yescharacteristic
287#2345C2×C2911yescharacteristic, complemented
288#1941C2×C2911yescharacteristic, complemented
289#1934C2×C2911yescharacteristic, complemented
290#1926C2×C2911yescharacteristic, complemented
291#1920C2×C2911yescharacteristic, complemented
292#1919C2×C2911yescharacteristic, complemented
293#1893C2×C2911yescharacteristic
294#1864C2×C2911yescharacteristic, complemented
295#1853C2×C2911yescharacteristic, complemented
296C4×#106C2×C2911yescharacteristic, complemented
297C4×#102C2×C2911yescharacteristic, complemented
298C8×C22⋊C4C2×C2911yescharacteristic, complemented
299C2×#340C2×C2911yescharacteristic, complemented
300C22×C29—22no—
301C22×C29—22no—
302C22×C29—22no—
303C22×C29—22no—
304C22×C29—22no—
305C22×C29—22no—
306C22×C29—42no—
307C22×C29—42no—
308C22×C29—42no—
309C22×C29—81no—
310C22×C29—81no—
311C22×C29—81no—
312C22×C29—81no—
313C22×C29C4×SD1614yes—
314C22×C29C2×C4×D411yescharacteristic
315C22×C29#54611yescharacteristic
316C22×C29#54711yescharacteristic
317C22×C29C22×SD1611yescharacteristic
318C22×C29C2×#13511yescharacteristic
319C22×C29#57611yescharacteristic
320C22×C29#57711yescharacteristic
321C4×C29—22no—
322C4×C29—22no—
323C4×C29—22no—
324C4×C29—41no—
325C4×C29—42no—
326C4×C29—42no—
327C4×C29—42no—
328C4×C29—42no—
329C4×C29—41no—
330C4×C29—81no—
331C4×C29—81no—
332C4×C29—81no—
333C4×C29C4×#4111yescharacteristic
334C4×C29#52011yescharacteristic
335C4×C29#55111yescharacteristic
336C4×C29#55211yescharacteristic
337C23×C8C22×C2911yescharacteristic
338C2×#121C22×C2911yescharacteristic
339C2×C4×D4—21no—
340C2×C4×D4C22×C2911yescharacteristic
341C22×C4⋊C4C22×C2911yescharacteristic
342C22×C4⋊C4C22×C2911yescharacteristic
343#481C4×C2918yescomplemented
344C2×#106C22×C2911yescharacteristic
345C2×#106C22×C2911yescharacteristic
346C2×#106C22×C2911yescharacteristic
347C2×#106C22×C2911yescharacteristic
348C2×#102C22×C2911yescharacteristic
349C2×#102C22×C2911yescharacteristic
350C2×#102C22×C2911yescharacteristic
351C2×#102C22×C2911yescharacteristic
352C2×C22⋊C8C22×C2911yescharacteristic
353C2×C4×C8C22×C2911yescharacteristic
354C2×C4×C8C22×C2911yescharacteristic
355#390C22×C2911yescharacteristic
356#389C22×C2911yescharacteristic
357#389C22×C2911yescharacteristic
358#389C22×C2911yescharacteristic
359#388—21no—
360#387—21no—
361#387—21no—
362#386—21no—
363#385—21no—
364#380—21no—
365#380C22×C2911yescharacteristic
366C4×C4⋊C4C22×C2911yescharacteristic
367C4×C4⋊C4C22×C2911yescharacteristic
368C4×C4⋊C4C22×C2911yescharacteristic
369C4×C22⋊C4—21no—
370C4×C22⋊C4C22×C2911yescharacteristic
371#340C22×C2911yescharacteristic
372#340C22×C2911yescharacteristic
373#340C22×C2911yescharacteristic
374#340C22×C2911yescharacteristic
375#340C22×C2911yescharacteristic
376#340C22×C2911yescharacteristic
377#340C22×C2911yescharacteristic
378#340C22×C2911yescharacteristic
379#336C22×C2911yescharacteristic
380#336C22×C2911yescharacteristic
381C2×C29—24no—
382C2×C29—82no—
383C2×C29#235911yescharacteristic
384C2×C29C2×C4×SD1611yescharacteristic
385C2×C29#294611yescharacteristic
386C2×C29#329511yescharacteristic
387C2×C29#330111yescharacteristic
388C2×C29#333511yescharacteristic
389C2×C29#333911yescharacteristic
390C22×D4—21no—
391C22×D4C23×C2911yescharacteristic
392C23×C4—21no—
393C23×C4—21no—
394C23×C4—21no—
395C23×C4C23×C2911yescharacteristic
396C22×C8—22no—
397C22×C8—22no—
398C22×C8—41no—
399C22×C8C23×C2911yescharacteristic
400C22×C8C23×C2911yescharacteristic
401C22×C8C23×C2911yescharacteristic
402C22×C8C23×C2911yescharacteristic
403#121—22no—
404#121C2×C4×C2914yes—
405C4×D4—22no—
406C4×D4—41no—
407C4×D4—44no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—41no—
416C2×C4⋊C4C2×C4×C2914yescomplemented
417C2×C4⋊C4C23×C2911yescharacteristic
418C2×C4⋊C4C23×C2911yescharacteristic
419C2×C4⋊C4C23×C2911yescharacteristic
420C2×C4⋊C4C23×C2911yescharacteristic
421C2×C4⋊C4C23×C2911yescharacteristic
422C2×C4⋊C4C23×C2911yescharacteristic
423C2×C4⋊C4C23×C2911yescharacteristic
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4D4×C2911yescharacteristic
430C2×C22⋊C4D4×C2911yescharacteristic
431C2×C42—21no—
432C2×C42—21no—
433C2×C42—21no—
434C2×C42C23×C2911yescharacteristic
435C2×C42C23×C2911yescharacteristic
436#106—22no—
437#106—41no—
438#106C2×C4×C2914yescomplemented
439#106C2×C4×C2914yescomplemented
440#102—22no—
441#102—41no—
442#102C2×C4×C2914yescomplemented
443#102C2×C4×C2914yescomplemented
444C22⋊C8C2×C4×C2914yescomplemented
445C4×C8—22no—
446C4×C8—41no—
447#95—21no—
448#95—21no—
449#95—21no—
450#95—21no—
451#95—21no—
452#95—21no—
453#95—21no—
454#95D4×C2911yescharacteristic
455#95D4×C2911yescharacteristic
456C29#2291811yescharacteristic, direct product factor, Sylow
457C24—21no—
458C24C2×D4×C2911yescharacteristic
459C2×D4—24no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—42no—
466C2×D4—42no—
467C2×D4C22×C4×C2912yes—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—24no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—81no—
485C22×C4—81no—
486C22×C4—81no—
487C22×C4—81no—
488C22×C4C22×C4×C2912yes—
489C22×C4C2×D4×C2911yescharacteristic
490C22×C4C2×D4×C2911yescharacteristic
491C22×C4C2×D4×C2911yescharacteristic
492C22×C4C2×D4×C2911yescharacteristic
493C22×C4C2×D4×C2911yescharacteristic
494C22×C4#41×C2912yes—
495C22×C4C24×C2911yescharacteristic
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—44no—
506C2×C8C22×C4×C2912yes—
507C2×C8C22×C4×C2912yes—
508C2×C8#41×C2912yes—
509C4⋊C4—24no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—42no—
521C4⋊C4—42no—
522C4⋊C4—81no—
523C4⋊C4—81no—
524C4⋊C4C22×C4×C2912yes—
525C4⋊C4C22×C4×C2912yes—
526C4⋊C4C22×C4×C2912yes—
527C4⋊C4#41×C2912yes—
528C22⋊C4—22no—
529C22⋊C4—24no—
530C22⋊C4—42no—
531C22⋊C4—42no—
532C22⋊C4—42no—
533C22⋊C4—81no—
534C22⋊C4SD16×C2914yes—
535C42—21no—
536C42—21no—
537C42—21no—
538C42—21no—
539C42—42no—
540C42—81no—
541C42—81no—
542C23—21no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—22no—
547C23—41no—
548C23—41no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23—41no—
553C23C4×D4×C2912yes—
554C23C2×SD16×C2912yes—
555C23C29×#13512yes—
556C23C22×D4×C2911yescharacteristic
557D4—22no—
558D4—22no—
559D4—48no—
560D4—41no—
561D4—41no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—21no—
576C2×C4—22no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—84no—
600C2×C4—84no—
601C2×C4—84no—
602C2×C4C4×D4×C2912yes—
603C2×C4C2×SD16×C2912yes—
604C2×C4C2×SD16×C2912yes—
605C2×C4C23×C4×C2911yescharacteristic
606C2×C4C2×#41×C2911yescharacteristic
607C2×C4C2×#41×C2911yescharacteristic
608C2×C4C2×#41×C2911yescharacteristic
609C2×C4C29×H(5,𝔽2)11yescharacteristic
610C2×C4C29×2−1+411yescharacteristic
611C8—22no—
612C8—22no—
613C8—22no—
614C8—41no—
615C22—22no—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—22no—
621C22—42no—
622C22—42no—
623C22—42no—
624C22—81no—
625C22—81no—
626C22—81no—
627C22—81no—
628C22C4×SD16×C2914yes—
629C22C2×C4×D4×C2911yescharacteristic
630C22C29×#54611yescharacteristic
631C22C29×#54711yescharacteristic
632C22C22×SD16×C2911yescharacteristic
633C22C2×C29×#13511yescharacteristic
634C22C29×#57611yescharacteristic
635C22C29×#57711yescharacteristic
636C4—22no—
637C4—22no—
638C4—22no—
639C4—42no—
640C4—42no—
641C4—42no—
642C4—42no—
643C4—41no—
644C4—41no—
645C4—81no—
646C4—81no—
647C4—81no—
648C4C4×#41×C2911yescharacteristic
649C4C29×#52011yescharacteristic
650C4C29×#55111yescharacteristic
651C4C29×#55211yescharacteristic
652C2—24no—
653C2—82no—
654C2C29×#235911yescharacteristic
655C2C2×C4×SD16×C2911yescharacteristic
656C2C29×#294611yescharacteristic
657C2C29×#329511yescharacteristic
658C2C29×#330111yescharacteristic
659C2C29×#333511yescharacteristic
660C2C29×#333911yescharacteristic
subgroupG/H
center, socleC23×C29C22×D4
commutatorC2×C4C23×C4×C29
Frattini, cosocleC22×C4C24×C29
prime radicalC2×C29×#121C22
LCSG ▷ C2×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
3. C29×#2345C2semidirect
4. C29×#1941C2semidirect
5. C29×#1934C2semidirect
6. C29×#1926C2semidirect
7. C29×#1920C2semidirect
8. C29×#1919C2semidirect
10. C29×#1864C2semidirect
11. C29×#1853C2semidirect
12. C4×C29×#106C2semidirect
13. C4×C29×#102C2semidirect
14. C8×C22⋊C4×C29C2semidirect
15. C2×C29×#340C2semidirect
22. C29×#481C4semidirect
86. C2×C4⋊C4×C29C2×C4semidirect
108. C29×#106C2×C4semidirect
109. C29×#106C2×C4semidirect
112. C29×#102C2×C4semidirect
113. C29×#102C2×C4semidirect
114. C29×C22⋊C8C2×C4semidirect
211. #22918C29direct (N × H)
287. #2345C2×C29semidirect
288. #1941C2×C29semidirect
289. #1934C2×C29semidirect
290. #1926C2×C29semidirect
291. #1920C2×C29semidirect
292. #1919C2×C29semidirect
294. #1864C2×C29semidirect
295. #1853C2×C29semidirect
296. C4×#106C2×C29semidirect
297. C4×#102C2×C29semidirect
298. C8×C22⋊C4C2×C29semidirect
299. C2×#340C2×C29semidirect
343. #481C4×C29semidirect
416. C2×C4⋊C4C2×C4×C29semidirect
438. #106C2×C4×C29semidirect
439. #106C2×C4×C29semidirect
442. #102C2×C4×C29semidirect
443. #102C2×C4×C29semidirect
444. C22⋊C8C2×C4×C29semidirect
456. C29#22918direct (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
C29×#23612
C29×#23452
C29×#19412
C29×#19342
C29×#19262
C29×#19202
C29×#19192
C29×#18932
C29×#18642
C29×#18532
C4×C29×#1062
C4×C29×#1022
C8×C22⋊C4×C292
C2×C29×#3402
#2291829