Finite Group Databasebeta

← C29×#25242 #20320142

Subgroups — C29×#25242 #20320142

Order 7424.

870 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#484C211yesmaximal, characteristic, complemented
2C2×C29×#435C211yesmaximal, characteristic
3C29×#2486C211yesmaximal, characteristic
4C29×#2415C211yesmaximal, characteristic
5C29×#2087C211yesmaximal, characteristic, complemented
6C29×#2075C211yesmaximal, characteristic, complemented
7C29×#2068C211yesmaximal, characteristic, complemented
8C29×#2035C211yesmaximal, characteristic, complemented
9C29×#1944C211yesmaximal, characteristic, complemented
10C29×#1935C211yesmaximal, characteristic, complemented
11C29×#1894C211yesmaximal, characteristic, complemented
12C29×#1892C211yesmaximal, characteristic, complemented
13C29×#1854C211yesmaximal, characteristic, complemented
14C29×#1808C211yesmaximal, characteristic, complemented
15C29×#1736C211yesmaximal, characteristic, complemented
16C22×M16×C29C2211yescharacteristic
17C23×C8×C29C2211yescharacteristic
18C2×C29×#123—21no—
19C2×C29×C22⋊Q8C2211yescharacteristic
20C2×C29×C22⋊Q8C2211yescharacteristic
21C2×C4×D4×C29C2211yescharacteristic
22C2×C29×#117C2211yescharacteristic
23C22×C4⋊C4×C29C2211yescharacteristic
24C29×#484—24no—
25C29×#435—24no—
26C2×C29×#107C2211yescharacteristic
27C2×C29×#107C2211yescharacteristic
28C2×C29×#107C2211yescharacteristic
29C2×C29×#106C2211yescharacteristic
30C2×C29×C4⋊C8C2211yescharacteristic
31C2×C29×#103C2211yescharacteristic
32C2×C29×#103C2211yescharacteristic
33C2×C29×#103C2211yescharacteristic
34C2×C29×#103C2211yescharacteristic
35C2×C29×C22⋊C8C2211yescharacteristic
36C2×C29×C22⋊C8C2211yescharacteristic
37C2×C29×#97C2211yescharacteristic
38C29×#398—21no—
39C29×#397—21no—
40C29×#397—21no—
41C29×#394—21no—
42C29×#391C2211yescharacteristic
43C29×#389—21no—
44C29×#389C2211yescharacteristic
45C29×#389C2211yescharacteristic
46C29×#389C2211yescharacteristic
47C29×#388—21no—
48C29×#381—21no—
49C29×#380C2211yescharacteristic
50C29×#380C2211yescharacteristic
51C29×#380C2211yescharacteristic
52C29×#380C2211yescharacteristic
53C29×#340C2211yescharacteristic
54C29×#340C2211yescharacteristic
55C29×#340C2211yescharacteristic
56C29×#340C2211yescharacteristic
57C29×#340C2211yescharacteristic
58C29×#340C2211yescharacteristic
59C29×#340C2211yescharacteristic
60C29×#340C2211yescharacteristic
61C22×Q8×C29C2311yescharacteristic
62C22×D4×C29D411yescharacteristic
63C23×C4×C29—21no—
64C23×C4×C29C2311yescharacteristic
65C23×C4×C29C2311yescharacteristic
66C2×M16×C29—22no—
67C2×M16×C29—22no—
68C2×M16×C29—41no—
69C22×C8×C29—22no—
70C22×C8×C29—22no—
71C22×C8×C29—41no—
72C22×C8×C29C2311yescharacteristic
73C22×C8×C29C2311yescharacteristic
74C22×C8×C29C2311yescharacteristic
75C22×C8×C29C2311yescharacteristic
76C29×#123—44no—
77C29×C22⋊Q8—22no—
78C29×C22⋊Q8—22no—
79C29×C22⋊Q8—22no—
80C29×C22⋊Q8—41no—
81C4×D4×C29—22no—
82C4×D4×C29—22no—
83C29×#117—22no—
84C29×#117—41no—
85C2×C4⋊C4×C29—22no—
86C2×C4⋊C4×C29—22no—
87C2×C4⋊C4×C29—21no—
88C2×C4⋊C4×C29—21no—
89C2×C4⋊C4×C29—21no—
90C2×C4⋊C4×C29—21no—
91C2×C4⋊C4×C29—21no—
92C2×C4⋊C4×C29—21no—
93C2×C4⋊C4×C29D411yescharacteristic
94C2×C4⋊C4×C29C2311yescharacteristic
95C2×C4⋊C4×C29C2311yescharacteristic
96C2×C4⋊C4×C29C2311yescharacteristic
97C2×C4⋊C4×C29C2311yescharacteristic
98C2×C4⋊C4×C29C2311yescharacteristic
99C2×C4⋊C4×C29C2311yescharacteristic
100C2×C4⋊C4×C29C2311yescharacteristic
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×C29D411yescharacteristic
109C2×C22⋊C4×C29D411yescharacteristic
110C2×C42×C29—21no—
111C2×C42×C29C2311yescharacteristic
112C29×#107—22no—
113C29×#107—22no—
114C29×#107—41no—
115C29×#106—22no—
116C29×C4⋊C8—22no—
117C29×#103—22no—
118C29×#103—22no—
119C29×#103—22no—
120C29×#103—41no—
121C29×C22⋊C8—22no—
122C29×C22⋊C8D414yes—
123C29×#97—22no—
124C29×#95—21no—
125C29×#95—21no—
126C29×#95—21no—
127C29×#95—21no—
128C29×#95—21no—
129C29×#95—21no—
130C29×#95—21no—
131C29×#95—21no—
132C29×#95—21no—
133C24×C29C2×D411yescharacteristic
134C24×C29C2×D411yescharacteristic
135C2×Q8×C29—21no—
136C2×Q8×C29—21no—
137C2×Q8×C29—21no—
138C2×Q8×C29—21no—
139C2×Q8×C29—21no—
140C2×Q8×C29—21no—
141C2×D4×C29—22no—
142C2×D4×C29—22no—
143C2×D4×C29—41no—
144C22×C4×C29—21no—
145C22×C4×C29—21no—
146C22×C4×C29—21no—
147C22×C4×C29—21no—
148C22×C4×C29—21no—
149C22×C4×C29—21no—
150C22×C4×C29—21no—
151C22×C4×C29—21no—
152C22×C4×C29—21no—
153C22×C4×C29—21no—
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—42no—
163C22×C4×C29—42no—
164C22×C4×C29—42no—
165C22×C4×C29C2×D411yescharacteristic
166C22×C4×C29C2×D411yescharacteristic
167C22×C4×C29C2×D411yescharacteristic
168C22×C4×C29C2×D411yescharacteristic
169C22×C4×C29C2×D412yes—
170C22×C4×C29#4112yes—
171C22×C4×C29C2411yescharacteristic
172M16×C29—44no—
173C2×C8×C29—21no—
174C2×C8×C29—21no—
175C2×C8×C29—21no—
176C2×C8×C29—21no—
177C2×C8×C29—21no—
178C2×C8×C29—21no—
179C2×C8×C29—21no—
180C2×C8×C29—21no—
181C2×C8×C29—21no—
182C2×C8×C29—44no—
183C2×C8×C29C2×D412yes—
184C2×C8×C29C2×D412yes—
185C2×C8×C29#4112yes—
186C4⋊C4×C29—22no—
187C4⋊C4×C29—21no—
188C4⋊C4×C29—21no—
189C4⋊C4×C29—21no—
190C4⋊C4×C29—21no—
191C4⋊C4×C29—21no—
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—42no—
201C4⋊C4×C29—42no—
202C4⋊C4×C29—42no—
203C4⋊C4×C29—42no—
204C4⋊C4×C29—42no—
205C4⋊C4×C29—42no—
206C4⋊C4×C29#4112yes—
207C22⋊C4×C29—22no—
208C22⋊C4×C29—22no—
209C22⋊C4×C29—42no—
210C22⋊C4×C29—42no—
211C22⋊C4×C29—42no—
212C22⋊C4×C29—42no—
213C22⋊C4×C29—42no—
214C22⋊C4×C29—42no—
215C22⋊C4×C29—42no—
216C42×C29—21no—
217C42×C29—21no—
218C42×C29—42no—
219#25242C2911yesmaximal, characteristic, direct product factor, Sylow
220C23×C29—21no—
221C23×C29—21no—
222C23×C29—21no—
223C23×C29—21no—
224C23×C29—21no—
225C23×C29—21no—
226C23×C29—21no—
227C23×C29—21no—
228C23×C29—21no—
229C23×C29—21no—
230C23×C29—21no—
231C23×C29—21no—
232C23×C29#12112yes—
233C23×C29AGL(1,ℤ/8)12yes—
234C23×C29C22×D411yescharacteristic
235Q8×C29—41no—
236Q8×C29—41no—
237Q8×C29—41no—
238Q8×C29—41no—
239D4×C29—44no—
240C2×C4×C29—21no—
241C2×C4×C29—21no—
242C2×C4×C29—22no—
243C2×C4×C29—22no—
244C2×C4×C29—22no—
245C2×C4×C29—22no—
246C2×C4×C29—21no—
247C2×C4×C29—21no—
248C2×C4×C29—21no—
249C2×C4×C29—22no—
250C2×C4×C29—21no—
251C2×C4×C29—21no—
252C2×C4×C29—21no—
253C2×C4×C29—21no—
254C2×C4×C29—21no—
255C2×C4×C29—21no—
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—41no—
270C2×C4×C29—41no—
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—84no—
284C2×C4×C29#12112yes—
285C2×C4×C29C22×D411yescharacteristic
286C2×C4×C29C2×#4111yescharacteristic
287C2×C4×C29C2×#4111yescharacteristic
288C2×C4×C29C2×#4111yescharacteristic
289C2×C4×C29H(5,𝔽2)11yescharacteristic
290C2×C4×C292−1+411yescharacteristic
291C8×C29—22no—
292C8×C29—22no—
293C8×C29—22no—
294C8×C29—41no—
295C2×#484C2×C2911yescharacteristic, complemented
296C2×#435C2×C2911yescharacteristic
297#2486C2×C2911yescharacteristic
298#2415C2×C2911yescharacteristic
299#2087C2×C2911yescharacteristic, complemented
300#2075C2×C2911yescharacteristic, complemented
301#2068C2×C2911yescharacteristic, complemented
302#2035C2×C2911yescharacteristic, complemented
303#1944C2×C2911yescharacteristic, complemented
304#1935C2×C2911yescharacteristic, complemented
305#1894C2×C2911yescharacteristic, complemented
306#1892C2×C2911yescharacteristic, complemented
307#1854C2×C2911yescharacteristic, complemented
308#1808C2×C2911yescharacteristic, complemented
309#1736C2×C2911yescharacteristic, complemented
310C22×C29—22no—
311C22×C29—22no—
312C22×C29—22no—
313C22×C29—22no—
314C22×C29—22no—
315C22×C29—22no—
316C22×C29—41no—
317C22×C29—41no—
318C22×C29—41no—
319C22×C29—41no—
320C22×C29—41no—
321C22×C29—41no—
322C22×C29—41no—
323C22×C29—41no—
324C22×C29C2×#12111yescharacteristic
325C22×C29#54611yescharacteristic
326C22×C29#54711yescharacteristic
327C22×C29C2×AGL(1,ℤ/8)11yescharacteristic
328C22×C29#57511yescharacteristic
329C22×C29#57811yescharacteristic
330C22×C29#57811yescharacteristic
331C4×C29—22no—
332C4×C29—41no—
333C4×C29—41no—
334C4×C29—41no—
335C4×C29—42no—
336C4×C29—81no—
337C4×C29—81no—
338C4×C29—81no—
339C4×C29—81no—
340C4×C29—81no—
341C4×C29—81no—
342C4×C29—81no—
343C4×C29#52911yescharacteristic
344C4×C29#53911yescharacteristic
345C4×C29#54611yescharacteristic
346C4×C29#54711yescharacteristic
347C22×M16C22×C2911yescharacteristic
348C23×C8C22×C2911yescharacteristic
349C2×#123—21no—
350C2×C22⋊Q8C22×C2911yescharacteristic
351C2×C22⋊Q8C22×C2911yescharacteristic
352C2×C4×D4C22×C2911yescharacteristic
353C2×#117C22×C2911yescharacteristic
354C22×C4⋊C4C22×C2911yescharacteristic
355#484—24no—
356#435—24no—
357C2×#107C22×C2911yescharacteristic
358C2×#107C22×C2911yescharacteristic
359C2×#107C22×C2911yescharacteristic
360C2×#106C22×C2911yescharacteristic
361C2×C4⋊C8C22×C2911yescharacteristic
362C2×#103C22×C2911yescharacteristic
363C2×#103C22×C2911yescharacteristic
364C2×#103C22×C2911yescharacteristic
365C2×#103C22×C2911yescharacteristic
366C2×C22⋊C8C22×C2911yescharacteristic
367C2×C22⋊C8C22×C2911yescharacteristic
368C2×#97C22×C2911yescharacteristic
369#398—21no—
370#397—21no—
371#397—21no—
372#394—21no—
373#391C22×C2911yescharacteristic
374#389—21no—
375#389C22×C2911yescharacteristic
376#389C22×C2911yescharacteristic
377#389C22×C2911yescharacteristic
378#388—21no—
379#381—21no—
380#380C22×C2911yescharacteristic
381#380C22×C2911yescharacteristic
382#380C22×C2911yescharacteristic
383#380C22×C2911yescharacteristic
384#340C22×C2911yescharacteristic
385#340C22×C2911yescharacteristic
386#340C22×C2911yescharacteristic
387#340C22×C2911yescharacteristic
388#340C22×C2911yescharacteristic
389#340C22×C2911yescharacteristic
390#340C22×C2911yescharacteristic
391#340C22×C2911yescharacteristic
392C2×C29—42no—
393C2×C29—42no—
394C2×C29#242511yescharacteristic
395C2×C29#305511yescharacteristic
396C2×C29#305911yescharacteristic
397C2×C29#330811yescharacteristic
398C2×C29#331511yescharacteristic
399C2×C29#334311yescharacteristic
400C2×C29#334911yescharacteristic
401C22×Q8C23×C2911yescharacteristic
402C22×D4D4×C2911yescharacteristic
403C23×C4—21no—
404C23×C4C23×C2911yescharacteristic
405C23×C4C23×C2911yescharacteristic
406C2×M16—22no—
407C2×M16—22no—
408C2×M16—41no—
409C22×C8—22no—
410C22×C8—22no—
411C22×C8—41no—
412C22×C8C23×C2911yescharacteristic
413C22×C8C23×C2911yescharacteristic
414C22×C8C23×C2911yescharacteristic
415C22×C8C23×C2911yescharacteristic
416#123—44no—
417C22⋊Q8—22no—
418C22⋊Q8—22no—
419C22⋊Q8—22no—
420C22⋊Q8—41no—
421C4×D4—22no—
422C4×D4—22no—
423#117—22no—
424#117—41no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4D4×C2911yescharacteristic
434C2×C4⋊C4C23×C2911yescharacteristic
435C2×C4⋊C4C23×C2911yescharacteristic
436C2×C4⋊C4C23×C2911yescharacteristic
437C2×C4⋊C4C23×C2911yescharacteristic
438C2×C4⋊C4C23×C2911yescharacteristic
439C2×C4⋊C4C23×C2911yescharacteristic
440C2×C4⋊C4C23×C2911yescharacteristic
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4D4×C2911yescharacteristic
449C2×C22⋊C4D4×C2911yescharacteristic
450C2×C42—21no—
451C2×C42C23×C2911yescharacteristic
452#107—22no—
453#107—22no—
454#107—41no—
455#106—22no—
456C4⋊C8—22no—
457#103—22no—
458#103—22no—
459#103—22no—
460#103—41no—
461C22⋊C8—22no—
462C22⋊C8D4×C2914yes—
463#97—22no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473C29#2524211yescharacteristic, direct product factor, Sylow
474C24C2×D4×C2911yescharacteristic
475C24C2×D4×C2911yescharacteristic
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—41no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—42no—
506C22×C4C2×D4×C2911yescharacteristic
507C22×C4C2×D4×C2911yescharacteristic
508C22×C4C2×D4×C2911yescharacteristic
509C22×C4C2×D4×C2911yescharacteristic
510C22×C4C2×D4×C2912yes—
511C22×C4#41×C2912yes—
512C22×C4C24×C2911yescharacteristic
513M16—44no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—44no—
524C2×C8C2×D4×C2912yes—
525C2×C8C2×D4×C2912yes—
526C2×C8#41×C2912yes—
527C4⋊C4—22no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—42no—
542C4⋊C4—42no—
543C4⋊C4—42no—
544C4⋊C4—42no—
545C4⋊C4—42no—
546C4⋊C4—42no—
547C4⋊C4#41×C2912yes—
548C22⋊C4—22no—
549C22⋊C4—22no—
550C22⋊C4—42no—
551C22⋊C4—42no—
552C22⋊C4—42no—
553C22⋊C4—42no—
554C22⋊C4—42no—
555C22⋊C4—42no—
556C22⋊C4—42no—
557C42—21no—
558C42—21no—
559C42—42no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23C29×#12112yes—
573C23C29×AGL(1,ℤ/8)12yes—
574C23C22×D4×C2911yescharacteristic
575Q8—41no—
576Q8—41no—
577Q8—41no—
578Q8—41no—
579D4—44no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—22no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—84no—
624C2×C4C29×#12112yes—
625C2×C4C22×D4×C2911yescharacteristic
626C2×C4C2×#41×C2911yescharacteristic
627C2×C4C2×#41×C2911yescharacteristic
628C2×C4C2×#41×C2911yescharacteristic
629C2×C4C29×H(5,𝔽2)11yescharacteristic
630C2×C4C29×2−1+411yescharacteristic
631C8—22no—
632C8—22no—
633C8—22no—
634C8—41no—
635C22—22no—
636C22—22no—
637C22—22no—
638C22—22no—
639C22—22no—
640C22—22no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22C2×C29×#12111yescharacteristic
650C22C29×#54611yescharacteristic
651C22C29×#54711yescharacteristic
652C22C2×C29×AGL(1,ℤ/8)11yescharacteristic
653C22C29×#57511yescharacteristic
654C22C29×#57811yescharacteristic
655C22C29×#57811yescharacteristic
656C4—22no—
657C4—41no—
658C4—41no—
659C4—41no—
660C4—42no—
661C4—81no—
662C4—81no—
663C4—81no—
664C4—81no—
665C4—81no—
666C4—81no—
667C4—81no—
668C4C29×#52911yescharacteristic
669C4C29×#53911yescharacteristic
670C4C29×#54611yescharacteristic
671C4C29×#54711yescharacteristic
672C2—42no—
673C2—42no—
674C2C29×#242511yescharacteristic
675C2C29×#305511yescharacteristic
676C2C29×#305911yescharacteristic
677C2C29×#330811yescharacteristic
678C2C29×#331511yescharacteristic
679C2C29×#334311yescharacteristic
680C2C29×#334911yescharacteristic
subgroupG/H
center, socleC23×C29C22×D4
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC22×D4×C29D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C29 ◁ C2×C4×D4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C29×#484C2semidirect
5. C29×#2087C2semidirect
6. C29×#2075C2semidirect
7. C29×#2068C2semidirect
8. C29×#2035C2semidirect
9. C29×#1944C2semidirect
10. C29×#1935C2semidirect
11. C29×#1894C2semidirect
12. C29×#1892C2semidirect
13. C29×#1854C2semidirect
14. C29×#1808C2semidirect
15. C29×#1736C2semidirect
219. #25242C29direct (N × H)
295. C2×#484C2×C29semidirect
299. #2087C2×C29semidirect
300. #2075C2×C29semidirect
301. #2068C2×C29semidirect
302. #2035C2×C29semidirect
303. #1944C2×C29semidirect
304. #1935C2×C29semidirect
305. #1894C2×C29semidirect
306. #1892C2×C29semidirect
307. #1854C2×C29semidirect
308. #1808C2×C29semidirect
309. #1736C2×C29semidirect
473. C29#25242direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#4842
C2×C29×#4352
C29×#24862
C29×#24152
C29×#20872
C29×#20752
C29×#20682
C29×#20352
C29×#19442
C29×#19352
C29×#18942
C29×#18922
C29×#18542
C29×#18082
C29×#17362
#2524229