Finite Group Databasebeta

← C29×#24669 #20319569

Subgroups — C29×#24669 #20319569

Order 7424.

856 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#464C211yesmaximal, characteristic, complemented
2C2×C29×#433C211yesmaximal, characteristic, complemented
3C29×#2620C211yesmaximal, characteristic
4C29×#2323C211yesmaximal, characteristic, complemented
5C29×#2035C211yesmaximal, characteristic, complemented
6C29×#2034C211yesmaximal, characteristic
7C29×#2001C211yesmaximal, characteristic, complemented
8C29×#2000C211yesmaximal, characteristic
9C29×#1983C211yesmaximal, characteristic, complemented
10C29×#1971C211yesmaximal, characteristic, complemented
11C29×#1968C211yesmaximal, characteristic, complemented
12C29×#1948C211yesmaximal, characteristic, complemented
13C29×#1936C211yesmaximal, characteristic, complemented
14C29×#1933C211yesmaximal, characteristic, complemented
15C29×#1803C211yesmaximal, characteristic, complemented
16C22×Q16×C29C2211yescharacteristic
17C22×SD16×C29C2211yescharacteristic
18C2×C29×#124C2211yescharacteristic
19C2×C29×C22⋊Q8C2211yescharacteristic
20C2×C29×C22⋊Q8C2211yescharacteristic
21C2×C29×#121C2211yescharacteristic
22C2×C4×Q8×C29C2211yescharacteristic
23C2×C29×#117C2211yescharacteristic
24C29×#464—24no—
25C29×#433—24no—
26C2×C29×#106C2211yescharacteristic
27C2×C29×#106C2211yescharacteristic
28C2×C29×C4⋊C8C2211yescharacteristic
29C2×C29×C4⋊C8C2211yescharacteristic
30C2×C29×#103C2211yescharacteristic
31C2×C29×#103C2211yescharacteristic
32C2×C29×#103C2211yescharacteristic
33C2×C29×#103C2211yescharacteristic
34C2×C29×#103C2211yescharacteristic
35C2×C29×#102C2211yescharacteristic
36C2×C29×#102C2211yescharacteristic
37C2×C29×#102C2211yescharacteristic
38C2×C29×C22⋊C8C2211yescharacteristic
39C2×C29×C22⋊C8C2211yescharacteristic
40C2×C29×#97C2211yescharacteristic
41C2×C4×C8×C29C2211yescharacteristic
42C29×#396—21no—
43C29×#396—21no—
44C29×#394—21no—
45C29×#394—21no—
46C29×#391C2211yescharacteristic
47C29×#391C2211yescharacteristic
48C29×#390C2211yescharacteristic
49C29×#389—21no—
50C29×#389C2211yescharacteristic
51C29×#388—21no—
52C29×#388—21no—
53C29×#387—21no—
54C29×#384C2211yescharacteristic
55C29×#380C2211yescharacteristic
56C4×C4⋊C4×C29C2211yescharacteristic
57C29×#340C2211yescharacteristic
58C29×#340C2211yescharacteristic
59C29×#340C2211yescharacteristic
60C29×#340C2211yescharacteristic
61C22×Q8×C29C2311yescharacteristic
62C22×Q8×C29C2311yescharacteristic
63C22×D4×C29—21no—
64C22×D4×C29C2311yescharacteristic
65C23×C4×C29C2311yescharacteristic
66C2×Q16×C29—22no—
67C2×Q16×C29—22no—
68C2×Q16×C29—41no—
69C2×SD16×C29—22no—
70C2×SD16×C29—22no—
71C2×SD16×C29—41no—
72C22×C8×C29C2311yescharacteristic
73C22×C8×C29C2311yescharacteristic
74C22×C8×C29C2311yescharacteristic
75C22×C8×C29C2311yescharacteristic
76C29×#124—22no—
77C29×#124—22no—
78C29×C22⋊Q8—22no—
79C29×C22⋊Q8—22no—
80C29×C22⋊Q8—41no—
81C29×C22⋊Q8—41no—
82C29×#121—41no—
83C29×#121—41no—
84C4×Q8×C29—22no—
85C4×Q8×C29—22no—
86C29×#117—22no—
87C29×#117—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—21no—
93C2×C4⋊C4×C29—21no—
94C2×C4⋊C4×C29D411yescharacteristic
95C2×C4⋊C4×C29D411yescharacteristic
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×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×#106—41no—
116C29×#106—41no—
117C29×C4⋊C8—22no—
118C29×C4⋊C8D414yescomplemented
119C29×#103—22no—
120C29×#103—22no—
121C29×#103—41no—
122C29×#103—41no—
123C29×#103—41no—
124C29×#102—22no—
125C29×#102—22no—
126C29×#102—41no—
127C29×C22⋊C8—22no—
128C29×C22⋊C8—22no—
129C29×#97—22no—
130C4×C8×C29—22no—
131C29×#95—21no—
132C29×#95—21no—
133C29×#95—21no—
134C29×#95—21no—
135C29×#95—21no—
136C29×#95—21no—
137C29×#95—21no—
138C24×C29—21no—
139C24×C29C2×D411yescharacteristic
140C2×Q8×C29—21no—
141C2×Q8×C29—21no—
142C2×Q8×C29—21no—
143C2×Q8×C29—21no—
144C2×Q8×C29—21no—
145C2×Q8×C29—21no—
146C2×Q8×C29—21no—
147C2×Q8×C29—21no—
148C2×Q8×C29—21no—
149C2×Q8×C29—21no—
150C2×Q8×C29—21no—
151C2×Q8×C29#4112yes—
152C2×D4×C29—21no—
153C2×D4×C29—21no—
154C2×D4×C29—21no—
155C2×D4×C29—21no—
156C2×D4×C29—21no—
157C2×D4×C29—21no—
158C2×D4×C29—42no—
159C2×D4×C29—81no—
160C2×D4×C29—81no—
161C22×C4×C29—21no—
162C22×C4×C29—21no—
163C22×C4×C29—21no—
164C22×C4×C29—21no—
165C22×C4×C29—21no—
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×C29C2×D411yescharacteristic
175C22×C4×C29C2×D411yescharacteristic
176C22×C4×C29C2×D411yescharacteristic
177C22×C4×C29C2×D411yescharacteristic
178C22×C4×C29C2×D411yescharacteristic
179C22×C4×C29C2411yescharacteristic
180Q16×C29—44no—
181SD16×C29—44no—
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—21no—
192C2×C8×C29C2×D412yes—
193C2×C8×C29C2×D412yes—
194C4⋊C4×C29—24no—
195C4⋊C4×C29—22no—
196C4⋊C4×C29—22no—
197C4⋊C4×C29—21no—
198C4⋊C4×C29—21no—
199C4⋊C4×C29—21no—
200C4⋊C4×C29—21no—
201C4⋊C4×C29—21no—
202C4⋊C4×C29—21no—
203C4⋊C4×C29—21no—
204C4⋊C4×C29—21no—
205C4⋊C4×C29—21no—
206C4⋊C4×C29—42no—
207C4⋊C4×C29—42no—
208C4⋊C4×C29—81no—
209C4⋊C4×C29—81no—
210C4⋊C4×C29—81no—
211C4⋊C4×C29#4112yes—
212C22⋊C4×C29—24no—
213C22⋊C4×C29—22no—
214C22⋊C4×C29—22no—
215C22⋊C4×C29—42no—
216C22⋊C4×C29—42no—
217C22⋊C4×C29—42no—
218C22⋊C4×C29—42no—
219C22⋊C4×C29—81no—
220C22⋊C4×C29—81no—
221C22⋊C4×C29—81no—
222C42×C29—21no—
223C42×C29—21no—
224C42×C29—42no—
225C42×C29—81no—
226C42×C29C2×D412yes—
227C42×C29#4112yes—
228#24669C2911yesmaximal, characteristic, direct product factor, Sylow
229C23×C29—21no—
230C23×C29—21no—
231C23×C29—21no—
232C23×C29—21no—
233C23×C29—21no—
234C23×C29—21no—
235C23×C29—21no—
236C23×C29—41no—
237C23×C29—41no—
238C23×C29—41no—
239C23×C29—41no—
240C23×C29—41no—
241C23×C29—41no—
242C23×C29—41no—
243C23×C29C22×D411yescharacteristic
244Q8×C29—22no—
245Q8×C29—22no—
246Q8×C29—41no—
247Q8×C29—41no—
248Q8×C29—41no—
249Q8×C29—41no—
250Q8×C29—41no—
251Q8×C29—41no—
252D4×C29—41no—
253D4×C29—41no—
254D4×C29—41no—
255D4×C29—41no—
256D4×C29—84no—
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—21no—
264C2×C4×C29—22no—
265C2×C4×C29—22no—
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—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—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—41no—
295C2×C4×C29#12112yes—
296C2×C4×C29#12112yes—
297C2×C4×C29C22×D411yescharacteristic
298C2×C4×C29C2×#4111yescharacteristic
299C2×C4×C29C2×#4111yescharacteristic
300C2×C4×C29C2×#4111yescharacteristic
301C2×C4×C29H(5,𝔽2)11yescharacteristic
302C2×C4×C29H(5,𝔽2)11yescharacteristic
303C8×C29—22no—
304C8×C29—22no—
305C8×C29—41no—
306C8×C29—41no—
307C2×#464C2×C2911yescharacteristic, complemented
308C2×#433C2×C2911yescharacteristic, complemented
309#2620C2×C2911yescharacteristic
310#2323C2×C2911yescharacteristic, complemented
311#2035C2×C2911yescharacteristic, complemented
312#2034C2×C2911yescharacteristic
313#2001C2×C2911yescharacteristic, complemented
314#2000C2×C2911yescharacteristic
315#1983C2×C2911yescharacteristic, complemented
316#1971C2×C2911yescharacteristic, complemented
317#1968C2×C2911yescharacteristic, complemented
318#1948C2×C2911yescharacteristic, complemented
319#1936C2×C2911yescharacteristic, complemented
320#1933C2×C2911yescharacteristic, complemented
321#1803C2×C2911yescharacteristic, complemented
322C22×C29—41no—
323C22×C29—41no—
324C22×C29—41no—
325C22×C29—41no—
326C22×C29—41no—
327C22×C29—41no—
328C22×C29—41no—
329C22×C29—81no—
330C22×C29—81no—
331C22×C29—81no—
332C22×C29—81no—
333C22×C29—81no—
334C22×C29—81no—
335C22×C29—81no—
336C22×C29C2×#12111yescharacteristic
337C22×C29#52511yescharacteristic
338C22×C29#53511yescharacteristic
339C22×C29#57711yescharacteristic
340C22×C29#57711yescharacteristic
341C22×C29#57711yescharacteristic
342C22×C29#57811yescharacteristic
343C4×C29—22no—
344C4×C29—22no—
345C4×C29—42no—
346C4×C29—41no—
347C4×C29—42no—
348C4×C29—41no—
349C4×C29—41no—
350C4×C29—81no—
351C4×C29—81no—
352C4×C29—81no—
353C4×C29—81no—
354C4×C29—81no—
355C4×C29#54611yescharacteristic
356C4×C29#55011yescharacteristic
357C4×C29#55311yescharacteristic
358C4×C29#55511yescharacteristic
359C22×Q16C22×C2911yescharacteristic
360C22×SD16C22×C2911yescharacteristic
361C2×#124C22×C2911yescharacteristic
362C2×C22⋊Q8C22×C2911yescharacteristic
363C2×C22⋊Q8C22×C2911yescharacteristic
364C2×#121C22×C2911yescharacteristic
365C2×C4×Q8C22×C2911yescharacteristic
366C2×#117C22×C2911yescharacteristic
367#464—24no—
368#433—24no—
369C2×#106C22×C2911yescharacteristic
370C2×#106C22×C2911yescharacteristic
371C2×C4⋊C8C22×C2911yescharacteristic
372C2×C4⋊C8C22×C2911yescharacteristic
373C2×#103C22×C2911yescharacteristic
374C2×#103C22×C2911yescharacteristic
375C2×#103C22×C2911yescharacteristic
376C2×#103C22×C2911yescharacteristic
377C2×#103C22×C2911yescharacteristic
378C2×#102C22×C2911yescharacteristic
379C2×#102C22×C2911yescharacteristic
380C2×#102C22×C2911yescharacteristic
381C2×C22⋊C8C22×C2911yescharacteristic
382C2×C22⋊C8C22×C2911yescharacteristic
383C2×#97C22×C2911yescharacteristic
384C2×C4×C8C22×C2911yescharacteristic
385#396—21no—
386#396—21no—
387#394—21no—
388#394—21no—
389#391C22×C2911yescharacteristic
390#391C22×C2911yescharacteristic
391#390C22×C2911yescharacteristic
392#389—21no—
393#389C22×C2911yescharacteristic
394#388—21no—
395#388—21no—
396#387—21no—
397#384C22×C2911yescharacteristic
398#380C22×C2911yescharacteristic
399C4×C4⋊C4C22×C2911yescharacteristic
400#340C22×C2911yescharacteristic
401#340C22×C2911yescharacteristic
402#340C22×C2911yescharacteristic
403#340C22×C2911yescharacteristic
404C2×C29—81no—
405C2×C29—161no—
406C2×C29#241411yescharacteristic
407C2×C29#306011yescharacteristic
408C2×C29#306311yescharacteristic
409C2×C29#312111yescharacteristic
410C2×C29#312511yescharacteristic
411C2×C29#322211yescharacteristic
412C2×C29#322511yescharacteristic
413C22×Q8C23×C2911yescharacteristic
414C22×Q8C23×C2911yescharacteristic
415C22×D4—21no—
416C22×D4C23×C2911yescharacteristic
417C23×C4C23×C2911yescharacteristic
418C2×Q16—22no—
419C2×Q16—22no—
420C2×Q16—41no—
421C2×SD16—22no—
422C2×SD16—22no—
423C2×SD16—41no—
424C22×C8C23×C2911yescharacteristic
425C22×C8C23×C2911yescharacteristic
426C22×C8C23×C2911yescharacteristic
427C22×C8C23×C2911yescharacteristic
428#124—22no—
429#124—22no—
430C22⋊Q8—22no—
431C22⋊Q8—22no—
432C22⋊Q8—41no—
433C22⋊Q8—41no—
434#121—41no—
435#121—41no—
436C4×Q8—22no—
437C4×Q8—22no—
438#117—22no—
439#117—22no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4D4×C2911yescharacteristic
447C2×C4⋊C4D4×C2911yescharacteristic
448C2×C4⋊C4C23×C2911yescharacteristic
449C2×C4⋊C4C23×C2911yescharacteristic
450C2×C4⋊C4C23×C2911yescharacteristic
451C2×C4⋊C4C23×C2911yescharacteristic
452C2×C4⋊C4C23×C2911yescharacteristic
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×C22⋊C4—21no—
461C2×C22⋊C4D4×C2911yescharacteristic
462C2×C22⋊C4D4×C2911yescharacteristic
463C2×C42—21no—
464C2×C42—21no—
465C2×C42C23×C2911yescharacteristic
466C2×C42C23×C2911yescharacteristic
467#106—41no—
468#106—41no—
469C4⋊C8—22no—
470C4⋊C8D4×C2914yescomplemented
471#103—22no—
472#103—22no—
473#103—41no—
474#103—41no—
475#103—41no—
476#102—22no—
477#102—22no—
478#102—41no—
479C22⋊C8—22no—
480C22⋊C8—22no—
481#97—22no—
482C4×C8—22no—
483#95—21no—
484#95—21no—
485#95—21no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—21no—
490C29#2466911yescharacteristic, direct product factor, Sylow
491C24—21no—
492C24C2×D4×C2911yescharacteristic
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8#41×C2912yes—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—42no—
512C2×D4—81no—
513C2×D4—81no—
514C22×C4—21no—
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—21no—
526C22×C4—21no—
527C22×C4C2×D4×C2911yescharacteristic
528C22×C4C2×D4×C2911yescharacteristic
529C22×C4C2×D4×C2911yescharacteristic
530C22×C4C2×D4×C2911yescharacteristic
531C22×C4C2×D4×C2911yescharacteristic
532C22×C4C24×C2911yescharacteristic
533Q16—44no—
534SD16—44no—
535C2×C8—21no—
536C2×C8—21no—
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×C8C2×D4×C2912yes—
546C2×C8C2×D4×C2912yes—
547C4⋊C4—24no—
548C4⋊C4—22no—
549C4⋊C4—22no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—42no—
560C4⋊C4—42no—
561C4⋊C4—81no—
562C4⋊C4—81no—
563C4⋊C4—81no—
564C4⋊C4#41×C2912yes—
565C22⋊C4—24no—
566C22⋊C4—22no—
567C22⋊C4—22no—
568C22⋊C4—42no—
569C22⋊C4—42no—
570C22⋊C4—42no—
571C22⋊C4—42no—
572C22⋊C4—81no—
573C22⋊C4—81no—
574C22⋊C4—81no—
575C42—21no—
576C42—21no—
577C42—42no—
578C42—81no—
579C42C2×D4×C2912yes—
580C42#41×C2912yes—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23C22×D4×C2911yescharacteristic
596Q8—22no—
597Q8—22no—
598Q8—41no—
599Q8—41no—
600Q8—41no—
601Q8—41no—
602Q8—41no—
603Q8—41no—
604D4—41no—
605D4—41no—
606D4—41no—
607D4—41no—
608D4—84no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
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—41no—
636C2×C4—41no—
637C2×C4—41no—
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×C4C29×#12112yes—
648C2×C4C29×#12112yes—
649C2×C4C22×D4×C2911yescharacteristic
650C2×C4C2×#41×C2911yescharacteristic
651C2×C4C2×#41×C2911yescharacteristic
652C2×C4C2×#41×C2911yescharacteristic
653C2×C4C29×H(5,𝔽2)11yescharacteristic
654C2×C4C29×H(5,𝔽2)11yescharacteristic
655C8—22no—
656C8—22no—
657C8—41no—
658C8—41no—
659C22—41no—
660C22—41no—
661C22—41no—
662C22—41no—
663C22—41no—
664C22—41no—
665C22—41no—
666C22—81no—
667C22—81no—
668C22—81no—
669C22—81no—
670C22—81no—
671C22—81no—
672C22—81no—
673C22C2×C29×#12111yescharacteristic
674C22C29×#52511yescharacteristic
675C22C29×#53511yescharacteristic
676C22C29×#57711yescharacteristic
677C22C29×#57711yescharacteristic
678C22C29×#57711yescharacteristic
679C22C29×#57811yescharacteristic
680C4—22no—
681C4—22no—
682C4—41no—
683C4—42no—
684C4—41no—
685C4—41no—
686C4—42no—
687C4—81no—
688C4—81no—
689C4—81no—
690C4—81no—
691C4—81no—
692C4C29×#54611yescharacteristic
693C4C29×#55011yescharacteristic
694C4C29×#55311yescharacteristic
695C4C29×#55511yescharacteristic
696C2—81no—
697C2—161no—
698C2C29×#241411yescharacteristic
699C2C29×#306011yescharacteristic
700C2C29×#306311yescharacteristic
701C2C29×#312111yescharacteristic
702C2C29×#312511yescharacteristic
703C2C29×#322211yescharacteristic
704C2C29×#322511yescharacteristic
subgroupG/H
center, socleC23×C29C22×D4
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC2×C29×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C29 ◁ C2×C29×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C29×#464C2semidirect
2. C2×C29×#433C2semidirect
4. C29×#2323C2semidirect
5. C29×#2035C2semidirect
7. C29×#2001C2semidirect
9. C29×#1983C2semidirect
10. C29×#1971C2semidirect
11. C29×#1968C2semidirect
12. C29×#1948C2semidirect
13. C29×#1936C2semidirect
14. C29×#1933C2semidirect
15. C29×#1803C2semidirect
118. C29×C4⋊C8D4semidirect
228. #24669C29direct (N × H)
307. C2×#464C2×C29semidirect
308. C2×#433C2×C29semidirect
310. #2323C2×C29semidirect
311. #2035C2×C29semidirect
313. #2001C2×C29semidirect
315. #1983C2×C29semidirect
316. #1971C2×C29semidirect
317. #1968C2×C29semidirect
318. #1948C2×C29semidirect
319. #1936C2×C29semidirect
320. #1933C2×C29semidirect
321. #1803C2×C29semidirect
470. C4⋊C8D4×C29semidirect
490. C29#24669direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#4642
C2×C29×#4332
C29×#26202
C29×#23232
C29×#20352
C29×#20342
C29×#20012
C29×#20002
C29×#19832
C29×#19712
C29×#19682
C29×#19482
C29×#19362
C29×#19332
C29×#18032
#2466929