Finite Group Databasebeta

← C29×#23878 #20318778

Subgroups — C29×#23878 #20318778

Order 7424.

1814 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#575C211yesmaximal, characteristic, complemented
2C29×#3488C211yesmaximal, characteristic, complemented
3C2×C29×#455C211yesmaximal, characteristic, complemented
4C2×C29×#453C211yesmaximal, characteristic, complemented
5C29×#3005C211yesmaximal, characteristic, complemented
6C29×#2431C211yesmaximal, characteristic, complemented
7C29×#2007C211yesmaximal, characteristic, complemented
8C29×#2006C211yesmaximal, characteristic, complemented
9C29×#2004C211yesmaximal, characteristic, complemented
10C29×#2002C211yesmaximal, characteristic, complemented
11C29×#1900C211yesmaximal, characteristic, complemented
12C29×#1883C211yesmaximal, characteristic, complemented
13C29×#1882C211yesmaximal, characteristic, complemented
14C29×#1871C211yesmaximal, characteristic, complemented
15C29×#1789C211yesmaximal, characteristic, complemented
16C2×C29×H(5,𝔽2)C2211yescharacteristic
17C22×#41×C29C2211yescharacteristic
18C22×#41×C29C2211yescharacteristic, complemented
19C29×#575—24no—
20C29×#575—24no—
21C2×C29×#137—21no—
22C2×C29×#137C2211yescharacteristic
23C2×C29×#137C2211yescharacteristic, complemented
24C2×C29×#137C2211yescharacteristic, complemented
25C2×C29×AGL(1,ℤ/8)—21no—
26C2×C29×AGL(1,ℤ/8)C2211yescharacteristic
27C2×C29×AGL(1,ℤ/8)C2211yescharacteristic, complemented
28C2×C29×AGL(1,ℤ/8)C2211yescharacteristic, complemented
29C2×C29×#135—21no—
30C2×C29×#135—21no—
31C22×M16×C29C2211yescharacteristic, complemented
32C29×#550—21no—
33C29×#548—21no—
34C29×#546—21no—
35C29×#546—22no—
36D42×C29—22no—
37D42×C29—21no—
38C29×#537—21no—
39C29×#537C2211yescharacteristic
40C29×#535—21no—
41C29×#535C2211yescharacteristic
42C2×C29×#127C2211yescharacteristic, complemented
43C2×C29×#124C2211yescharacteristic, complemented
44C29×#525—21no—
45C29×#525C2211yescharacteristic
46C2×C29×#121—21no—
47C2×C29×#121C2211yescharacteristic
48C29×#520C2211yescharacteristic
49C29×#455—24no—
50C29×#453—24no—
51C29×#452—21no—
52C29×#452—21no—
53C29×#449—21no—
54C29×#449—21no—
55C2×C29×#104C2211yescharacteristic
56C2×C29×#104C2211yescharacteristic
57C2×C29×#104C2211yescharacteristic, complemented
58C2×C29×#104C2211yescharacteristic, complemented
59C2×C29×#104C2211yescharacteristic, complemented
60C2×C29×#104C2211yescharacteristic, complemented
61C29×#419C2211yescharacteristic, complemented
62C29×#418C2211yescharacteristic, complemented
63C2×C29×#100C2211yescharacteristic, complemented
64C2×C29×#100C2211yescharacteristic, complemented
65C29×#407C2211yescharacteristic, complemented
66C29×#392—22no—
67C29×#391C2211yescharacteristic, complemented
68C29×#390C2211yescharacteristic, complemented
69C29×#386—22no—
70C4×C22⋊C4×C29C2211yescharacteristic, complemented
71C29×#343C2211yescharacteristic, complemented
72C29×#343C2211yescharacteristic, complemented
73C29×#339C2211yescharacteristic, complemented
74C29×#339C2211yescharacteristic, complemented
75C29×H(5,𝔽2)—22no—
76C29×H(5,𝔽2)—22no—
77C29×H(5,𝔽2)—41no—
78C29×H(5,𝔽2)—41no—
79C2×#41×C29—21no—
80C2×#41×C29—21no—
81C2×#41×C29—21no—
82C2×#41×C29—21no—
83C2×#41×C29—22no—
84C2×#41×C29—22no—
85C2×#41×C29—22no—
86C2×#41×C29—22no—
87C2×#41×C29—21no—
88C2×#41×C29—21no—
89C2×#41×C29—21no—
90C2×#41×C29—21no—
91C2×#41×C29—41no—
92C2×#41×C29—41no—
93C2×#41×C29—41no—
94C2×#41×C29—41no—
95C2×#41×C29D411yescharacteristic, complemented
96C2×#41×C29D411yescharacteristic, complemented
97C2×#41×C29C2311yescharacteristic
98C2×#41×C29C2311yescharacteristic
99C2×#41×C29C2311yescharacteristic
100C22×Q8×C29D411yescharacteristic, complemented
101C22×Q8×C29C2311yescharacteristic
102C22×D4×C29—21no—
103C22×D4×C29—22no—
104C22×D4×C29—22no—
105C22×D4×C29—21no—
106C22×D4×C29—21no—
107C22×D4×C29—21no—
108C22×D4×C29—22no—
109C22×D4×C29D412yes—
110C22×D4×C29D411yescharacteristic, complemented
111C22×D4×C29C2311yescharacteristic
112C22×D4×C29C2311yescharacteristic
113C23×C4×C29—21no—
114C23×C4×C29—21no—
115C23×C4×C29C2311yescharacteristic
116C29×#137—28no—
117C29×#137—22no—
118C29×#137—22no—
119C29×#137—22no—
120C29×#137—22no—
121C29×#137—41no—
122C29×#137D414yescomplemented
123C29×AGL(1,ℤ/8)—28no—
124C29×AGL(1,ℤ/8)—22no—
125C29×AGL(1,ℤ/8)—22no—
126C29×AGL(1,ℤ/8)—22no—
127C29×AGL(1,ℤ/8)—22no—
128C29×AGL(1,ℤ/8)—41no—
129C29×AGL(1,ℤ/8)D414yescomplemented
130C29×#135—28no—
131C29×#135—28no—
132C2×Q16×C29—21no—
133C2×Q16×C29—21no—
134C2×Q16×C29—21no—
135C2×SD16×C29—21no—
136C2×SD16×C29—21no—
137C2×SD16×C29—21no—
138C2×SD16×C29—21no—
139C2×SD16×C29—21no—
140C2×SD16×C29—21no—
141C2×D8×C29—21no—
142C2×D8×C29—21no—
143C2×D8×C29—21no—
144C2×M16×C29—21no—
145C2×M16×C29—22no—
146C2×M16×C29—22no—
147C2×M16×C29C2311yescharacteristic
148C2×M16×C29C2311yescharacteristic
149C2×M16×C29C2311yescharacteristic
150C2×M16×C29C2311yescharacteristic
151C22×C8×C29—21no—
152C29×#127—22no—
153C29×#127—21no—
154C29×#127—22no—
155C29×#127—41no—
156C29×#124—22no—
157C29×#124—21no—
158C29×#124—22no—
159C29×#124—41no—
160C29×#123—22no—
161C29×#123—21no—
162C29×C22⋊Q8—22no—
163C29×C22⋊Q8—21no—
164C29×C22⋊Q8—21no—
165C29×C22⋊Q8D411yescharacteristic, complemented
166C29×C22⋊Q8D411yescharacteristic, complemented
167C29×#121—22no—
168C29×#121—22no—
169C29×#121—22no—
170C29×#121—22no—
171C29×#121—22no—
172C29×#121—21no—
173C29×#121—21no—
174C29×#121—21no—
175C29×#121—21no—
176C29×#121—21no—
177C29×#121—21no—
178C29×#121—22no—
179C29×#121—21no—
180C29×#121—21no—
181C29×#121D411yescharacteristic, complemented
182C29×#121D411yescharacteristic, complemented
183C29×#120—22no—
184C29×#120—22no—
185C29×#120—22no—
186C29×#120—21no—
187C29×#120—22no—
188C4×Q8×C29—21no—
189C4×D4×C29—22no—
190C4×D4×C29—22no—
191C4×D4×C29—21no—
192C4×D4×C29—22no—
193C4×D4×C29—21no—
194C4×D4×C29—21no—
195C29×#117—21no—
196C29×#117C2311yescharacteristic
197C2×C4⋊C4×C29—21no—
198C2×C4⋊C4×C29C2311yescharacteristic
199C2×C22⋊C4×C29—22no—
200C2×C22⋊C4×C29—22no—
201C2×C22⋊C4×C29—21no—
202C2×C22⋊C4×C29—22no—
203C2×C22⋊C4×C29D412yes—
204C2×C42×C29C2311yescharacteristic
205C2×C42×C29C2311yescharacteristic
206C29×#104—22no—
207C29×#104—22no—
208C29×#104—22no—
209C29×#104—22no—
210C29×#104—41no—
211C29×#104—41no—
212C29×#103—21no—
213C29×#103—21no—
214C29×#102—21no—
215C29×#102—21no—
216C29×#100—22no—
217C29×#100—22no—
218C29×C22⋊C8—21no—
219C29×C22⋊C8—21no—
220C29×#95—21no—
221C29×#95—22no—
222C24×C29—22no—
223C24×C29—21no—
224C24×C29—21no—
225C24×C29C2×D412yes—
226C24×C29C2×D411yescharacteristic
227#41×C29—21no—
228#41×C29—21no—
229#41×C29—24no—
230#41×C29—24no—
231#41×C29—22no—
232#41×C29—22no—
233#41×C29—21no—
234#41×C29—21no—
235#41×C29—21no—
236#41×C29—21no—
237#41×C29—21no—
238#41×C29—21no—
239#41×C29—21no—
240#41×C29—21no—
241#41×C29—42no—
242#41×C29—42no—
243#41×C29—41no—
244#41×C29—41no—
245#41×C29—42no—
246#41×C29—42no—
247#41×C29—42no—
248#41×C29—42no—
249#41×C29—42no—
250#41×C29—42no—
251#41×C29—42no—
252#41×C29—42no—
253#41×C29—42no—
254#41×C29—42no—
255#41×C29—42no—
256#41×C29—42no—
257#41×C29C2×D412yes—
258#41×C29C2×D412yes—
259C2×Q8×C29—21no—
260C2×Q8×C29—21no—
261C2×Q8×C29—22no—
262C2×Q8×C29—21no—
263C2×Q8×C29—21no—
264C2×Q8×C29—21no—
265C2×Q8×C29—21no—
266C2×Q8×C29—41no—
267C2×Q8×C29C2×D411yescharacteristic
268C2×Q8×C29C2×D411yescharacteristic
269C2×Q8×C29C2×D411yescharacteristic
270C2×Q8×C29C2×D412yescomplemented
271C2×D4×C29—21no—
272C2×D4×C29—22no—
273C2×D4×C29—22no—
274C2×D4×C29—22no—
275C2×D4×C29—22no—
276C2×D4×C29—21no—
277C2×D4×C29—21no—
278C2×D4×C29—21no—
279C2×D4×C29—21no—
280C2×D4×C29—21no—
281C2×D4×C29—22no—
282C2×D4×C29—22no—
283C2×D4×C29—22no—
284C2×D4×C29—21no—
285C2×D4×C29—22no—
286C2×D4×C29—21no—
287C2×D4×C29—21no—
288C2×D4×C29—21no—
289C2×D4×C29—21no—
290C2×D4×C29—21no—
291C2×D4×C29—21no—
292C2×D4×C29—21no—
293C2×D4×C29—21no—
294C2×D4×C29—21no—
295C2×D4×C29—21no—
296C2×D4×C29—21no—
297C2×D4×C29—21no—
298C2×D4×C29—41no—
299C2×D4×C29—42no—
300C2×D4×C29—42no—
301C2×D4×C29—42no—
302C2×D4×C29—44no—
303C2×D4×C29—42no—
304C2×D4×C29—42no—
305C2×D4×C29—44no—
306C2×D4×C29—44no—
307C2×D4×C29—42no—
308C2×D4×C29—42no—
309C2×D4×C29—41no—
310C2×D4×C29—41no—
311C2×D4×C29—42no—
312C2×D4×C29—44no—
313C2×D4×C29—82no—
314C2×D4×C29—82no—
315C2×D4×C29—84no—
316C2×D4×C29C2×D411yescharacteristic
317C2×D4×C29C2×D411yescharacteristic
318C2×D4×C29C2×D411yescharacteristic
319C2×D4×C29C2×D412yescomplemented
320C22×C4×C29—21no—
321C22×C4×C29—21no—
322C22×C4×C29—21no—
323C22×C4×C29—21no—
324C22×C4×C29—21no—
325C22×C4×C29—22no—
326C22×C4×C29—21no—
327C22×C4×C29—21no—
328C22×C4×C29—21no—
329C22×C4×C29—22no—
330C22×C4×C29—21no—
331C22×C4×C29—21no—
332C22×C4×C29—21no—
333C22×C4×C29—21no—
334C22×C4×C29—21no—
335C22×C4×C29—42no—
336C22×C4×C29—42no—
337C22×C4×C29—42no—
338C22×C4×C29—42no—
339C22×C4×C29—41no—
340C22×C4×C29—41no—
341C22×C4×C29C2×D411yescharacteristic
342C22×C4×C29C2×D411yescharacteristic
343C22×C4×C29C2×D411yescharacteristic
344C22×C4×C29C2×D411yescharacteristic
345C22×C4×C29C2×D411yescharacteristic
346C22×C4×C29C2×D412yes—
347C22×C4×C29C2411yescharacteristic
348Q16×C29—24no—
349Q16×C29—24no—
350Q16×C29—42no—
351SD16×C29—24no—
352SD16×C29—24no—
353SD16×C29—24no—
354SD16×C29—24no—
355SD16×C29—42no—
356SD16×C29—42no—
357D8×C29—24no—
358D8×C29—24no—
359D8×C29—42no—
360M16×C29—24no—
361M16×C29—21no—
362M16×C29—21no—
363M16×C29—21no—
364M16×C29—21no—
365M16×C29—21no—
366M16×C29—21no—
367M16×C29C2×D412yescomplemented
368M16×C29C2×D412yescomplemented
369C2×C8×C29—24no—
370C2×C8×C29—21no—
371C2×C8×C29—21no—
372C2×C8×C29—21no—
373C2×C8×C29—21no—
374C4⋊C4×C29—22no—
375C4⋊C4×C29—22no—
376C4⋊C4×C29—21no—
377C4⋊C4×C29—21no—
378C4⋊C4×C29—21no—
379C4⋊C4×C29—21no—
380C4⋊C4×C29C2×D411yescharacteristic
381C4⋊C4×C29C2×D411yescharacteristic
382C22⋊C4×C29—22no—
383C22⋊C4×C29—22no—
384C22⋊C4×C29—22no—
385C22⋊C4×C29—22no—
386C22⋊C4×C29—22no—
387C22⋊C4×C29—21no—
388C22⋊C4×C29—21no—
389C22⋊C4×C29—21no—
390C22⋊C4×C29—21no—
391C22⋊C4×C29—22no—
392C22⋊C4×C29—22no—
393C22⋊C4×C29—21no—
394C22⋊C4×C29—44no—
395C22⋊C4×C29—42no—
396C22⋊C4×C29—82no—
397C42×C29—22no—
398C42×C29—21no—
399C42×C29—21no—
400C42×C29—21no—
401C42×C29—21no—
402C42×C29—21no—
403#23878C2911yesmaximal, characteristic, direct product factor, Sylow
404C23×C29—21no—
405C23×C29—21no—
406C23×C29—21no—
407C23×C29—22no—
408C23×C29—21no—
409C23×C29—21no—
410C23×C29—22no—
411C23×C29—22no—
412C23×C29—22no—
413C23×C29—41no—
414C23×C29—41no—
415C23×C29—42no—
416C23×C29—42no—
417C23×C29—42no—
418C23×C29—42no—
419C23×C29—44no—
420C23×C29—42no—
421C23×C29—42no—
422C23×C29—41no—
423C23×C29—41no—
424C23×C29—81no—
425C23×C29—82no—
426C23×C29—82no—
427C23×C29#12011yescharacteristic
428C23×C29#12011yescharacteristic
429C23×C29C22×D411yescharacteristic
430Q8×C29—21no—
431Q8×C29—21no—
432Q8×C29—22no—
433Q8×C29—21no—
434Q8×C29—21no—
435Q8×C29—22no—
436Q8×C29—21no—
437Q8×C29—42no—
438Q8×C29—41no—
439Q8×C29—41no—
440Q8×C29#12012yes—
441D4×C29—22no—
442D4×C29—22no—
443D4×C29—21no—
444D4×C29—22no—
445D4×C29—21no—
446D4×C29—21no—
447D4×C29—21no—
448D4×C29—22no—
449D4×C29—21no—
450D4×C29—42no—
451D4×C29—42no—
452D4×C29—44no—
453D4×C29—42no—
454D4×C29—44no—
455D4×C29—44no—
456D4×C29—42no—
457D4×C29—44no—
458D4×C29—44no—
459D4×C29—41no—
460D4×C29—41no—
461D4×C29—41no—
462D4×C29—41no—
463D4×C29—41no—
464D4×C29—41no—
465D4×C29—41no—
466D4×C29—41no—
467D4×C29—41no—
468D4×C29—41no—
469D4×C29—81no—
470D4×C29—82no—
471D4×C29—82no—
472D4×C29—82no—
473D4×C29—82no—
474D4×C29—88no—
475D4×C29#12012yes—
476C2×C4×C29—21no—
477C2×C4×C29—21no—
478C2×C4×C29—21no—
479C2×C4×C29—21no—
480C2×C4×C29—21no—
481C2×C4×C29—21no—
482C2×C4×C29—21no—
483C2×C4×C29—21no—
484C2×C4×C29—21no—
485C2×C4×C29—21no—
486C2×C4×C29—21no—
487C2×C4×C29—22no—
488C2×C4×C29—22no—
489C2×C4×C29—22no—
490C2×C4×C29—21no—
491C2×C4×C29—22no—
492C2×C4×C29—21no—
493C2×C4×C29—21no—
494C2×C4×C29—21no—
495C2×C4×C29—22no—
496C2×C4×C29—42no—
497C2×C4×C29—42no—
498C2×C4×C29—42no—
499C2×C4×C29—44no—
500C2×C4×C29—44no—
501C2×C4×C29—44no—
502C2×C4×C29—41no—
503C2×C4×C29—41no—
504C2×C4×C29—41no—
505C2×C4×C29—41no—
506C2×C4×C29—41no—
507C2×C4×C29—41no—
508C2×C4×C29—41no—
509C2×C4×C29—41no—
510C2×C4×C29—42no—
511C2×C4×C29—41no—
512C2×C4×C29—41no—
513C2×C4×C29—41no—
514C2×C4×C29—82no—
515C2×C4×C29#12011yescharacteristic
516C2×C4×C29#12011yescharacteristic
517C2×C4×C29C22×D411yescharacteristic
518C2×C4×C29C22×D411yescharacteristic
519C2×C4×C29C22×D411yescharacteristic
520C2×C4×C29C22×D411yescharacteristic
521C2×C4×C29H(5,𝔽2)11yescharacteristic
522C2×C4×C29H(5,𝔽2)11yescharacteristic
523C8×C29—22no—
524C8×C29—22no—
525C8×C29—41no—
526C8×C29—41no—
527C2×#575C2×C2911yescharacteristic, complemented
528#3488C2×C2911yescharacteristic, complemented
529C2×#455C2×C2911yescharacteristic, complemented
530C2×#453C2×C2911yescharacteristic, complemented
531#3005C2×C2911yescharacteristic, complemented
532#2431C2×C2911yescharacteristic, complemented
533#2007C2×C2911yescharacteristic, complemented
534#2006C2×C2911yescharacteristic, complemented
535#2004C2×C2911yescharacteristic, complemented
536#2002C2×C2911yescharacteristic, complemented
537#1900C2×C2911yescharacteristic, complemented
538#1883C2×C2911yescharacteristic, complemented
539#1882C2×C2911yescharacteristic, complemented
540#1871C2×C2911yescharacteristic, complemented
541#1789C2×C2911yescharacteristic, complemented
542C22×C29—21no—
543C22×C29—21no—
544C22×C29—21no—
545C22×C29—21no—
546C22×C29—22no—
547C22×C29—21no—
548C22×C29—21no—
549C22×C29—21no—
550C22×C29—21no—
551C22×C29—44no—
552C22×C29—41no—
553C22×C29—41no—
554C22×C29—41no—
555C22×C29—42no—
556C22×C29—41no—
557C22×C29—42no—
558C22×C29—41no—
559C22×C29—42no—
560C22×C29—41no—
561C22×C29—42no—
562C22×C29—41no—
563C22×C29—41no—
564C22×C29—81no—
565C22×C29—81no—
566C22×C29—82no—
567C22×C29—82no—
568C22×C29—82no—
569C22×C29—84no—
570C22×C29—81no—
571C22×C29—81no—
572C22×C29—164no—
573C22×C29C2×#12011yescharacteristic
574C22×C29D4211yescharacteristic
575C22×C29D4211yescharacteristic
576C4×C29—21no—
577C4×C29—21no—
578C4×C29—22no—
579C4×C29—42no—
580C4×C29—41no—
581C4×C29—41no—
582C4×C29—42no—
583C4×C29—41no—
584C4×C29—42no—
585C4×C29—41no—
586C4×C29—81no—
587C4×C29C2×#12011yescharacteristic
588C4×C29#53411yescharacteristic
589C4×C29D4211yescharacteristic
590C4×C29D4211yescharacteristic
591C2×H(5,𝔽2)C22×C2911yescharacteristic
592C22×#41C22×C2911yescharacteristic
593C22×#41C22×C2911yescharacteristic, complemented
594#575—24no—
595#575—24no—
596C2×#137—21no—
597C2×#137C22×C2911yescharacteristic
598C2×#137C22×C2911yescharacteristic, complemented
599C2×#137C22×C2911yescharacteristic, complemented
600C2×AGL(1,ℤ/8)—21no—
601C2×AGL(1,ℤ/8)C22×C2911yescharacteristic
602C2×AGL(1,ℤ/8)C22×C2911yescharacteristic, complemented
603C2×AGL(1,ℤ/8)C22×C2911yescharacteristic, complemented
604C2×#135—21no—
605C2×#135—21no—
606C22×M16C22×C2911yescharacteristic, complemented
607#550—21no—
608#548—21no—
609#546—21no—
610#546—22no—
611D42—22no—
612D42—21no—
613#537—21no—
614#537C22×C2911yescharacteristic
615#535—21no—
616#535C22×C2911yescharacteristic
617C2×#127C22×C2911yescharacteristic, complemented
618C2×#124C22×C2911yescharacteristic, complemented
619#525—21no—
620#525C22×C2911yescharacteristic
621C2×#121—21no—
622C2×#121C22×C2911yescharacteristic
623#520C22×C2911yescharacteristic
624#455—24no—
625#453—24no—
626#452—21no—
627#452—21no—
628#449—21no—
629#449—21no—
630C2×#104C22×C2911yescharacteristic
631C2×#104C22×C2911yescharacteristic
632C2×#104C22×C2911yescharacteristic, complemented
633C2×#104C22×C2911yescharacteristic, complemented
634C2×#104C22×C2911yescharacteristic, complemented
635C2×#104C22×C2911yescharacteristic, complemented
636#419C22×C2911yescharacteristic, complemented
637#418C22×C2911yescharacteristic, complemented
638C2×#100C22×C2911yescharacteristic, complemented
639C2×#100C22×C2911yescharacteristic, complemented
640#407C22×C2911yescharacteristic, complemented
641#392—22no—
642#391C22×C2911yescharacteristic, complemented
643#390C22×C2911yescharacteristic, complemented
644#386—22no—
645C4×C22⋊C4C22×C2911yescharacteristic, complemented
646#343C22×C2911yescharacteristic, complemented
647#343C22×C2911yescharacteristic, complemented
648#339C22×C2911yescharacteristic, complemented
649#339C22×C2911yescharacteristic, complemented
650C2×C29—21no—
651C2×C29—21no—
652C2×C29—41no—
653C2×C29—41no—
654C2×C29—42no—
655C2×C29—82no—
656C2×C29—81no—
657C2×C29—82no—
658C2×C29—81no—
659C2×C29#240311yescharacteristic
660C2×C29#301811yescharacteristic
661C2×C29#301911yescharacteristic
662H(5,𝔽2)—22no—
663H(5,𝔽2)—22no—
664H(5,𝔽2)—41no—
665H(5,𝔽2)—41no—
666C2×#41—21no—
667C2×#41—21no—
668C2×#41—21no—
669C2×#41—21no—
670C2×#41—22no—
671C2×#41—22no—
672C2×#41—22no—
673C2×#41—22no—
674C2×#41—21no—
675C2×#41—21no—
676C2×#41—21no—
677C2×#41—21no—
678C2×#41—41no—
679C2×#41—41no—
680C2×#41—41no—
681C2×#41—41no—
682C2×#41D4×C2911yescharacteristic, complemented
683C2×#41D4×C2911yescharacteristic, complemented
684C2×#41C23×C2911yescharacteristic
685C2×#41C23×C2911yescharacteristic
686C2×#41C23×C2911yescharacteristic
687C22×Q8D4×C2911yescharacteristic, complemented
688C22×Q8C23×C2911yescharacteristic
689C22×D4—21no—
690C22×D4—22no—
691C22×D4—22no—
692C22×D4—21no—
693C22×D4—21no—
694C22×D4—21no—
695C22×D4—22no—
696C22×D4D4×C2912yes—
697C22×D4D4×C2911yescharacteristic, complemented
698C22×D4C23×C2911yescharacteristic
699C22×D4C23×C2911yescharacteristic
700C23×C4—21no—
701C23×C4—21no—
702C23×C4C23×C2911yescharacteristic
703#137—28no—
704#137—22no—
705#137—22no—
706#137—22no—
707#137—22no—
708#137—41no—
709#137D4×C2914yescomplemented
710AGL(1,ℤ/8)—28no—
711AGL(1,ℤ/8)—22no—
712AGL(1,ℤ/8)—22no—
713AGL(1,ℤ/8)—22no—
714AGL(1,ℤ/8)—22no—
715AGL(1,ℤ/8)—41no—
716AGL(1,ℤ/8)D4×C2914yescomplemented
717#135—28no—
718#135—28no—
719C2×Q16—21no—
720C2×Q16—21no—
721C2×Q16—21no—
722C2×SD16—21no—
723C2×SD16—21no—
724C2×SD16—21no—
725C2×SD16—21no—
726C2×SD16—21no—
727C2×SD16—21no—
728C2×D8—21no—
729C2×D8—21no—
730C2×D8—21no—
731C2×M16—21no—
732C2×M16—22no—
733C2×M16—22no—
734C2×M16C23×C2911yescharacteristic
735C2×M16C23×C2911yescharacteristic
736C2×M16C23×C2911yescharacteristic
737C2×M16C23×C2911yescharacteristic
738C22×C8—21no—
739#127—22no—
740#127—21no—
741#127—22no—
742#127—41no—
743#124—22no—
744#124—21no—
745#124—22no—
746#124—41no—
747#123—22no—
748#123—21no—
749C22⋊Q8—22no—
750C22⋊Q8—21no—
751C22⋊Q8—21no—
752C22⋊Q8D4×C2911yescharacteristic, complemented
753C22⋊Q8D4×C2911yescharacteristic, complemented
754#121—22no—
755#121—22no—
756#121—22no—
757#121—22no—
758#121—22no—
759#121—21no—
760#121—21no—
761#121—21no—
762#121—21no—
763#121—21no—
764#121—21no—
765#121—22no—
766#121—21no—
767#121—21no—
768#121D4×C2911yescharacteristic, complemented
769#121D4×C2911yescharacteristic, complemented
770#120—22no—
771#120—22no—
772#120—22no—
773#120—21no—
774#120—22no—
775C4×Q8—21no—
776C4×D4—22no—
777C4×D4—22no—
778C4×D4—21no—
779C4×D4—22no—
780C4×D4—21no—
781C4×D4—21no—
782#117—21no—
783#117C23×C2911yescharacteristic
784C2×C4⋊C4—21no—
785C2×C4⋊C4C23×C2911yescharacteristic
786C2×C22⋊C4—22no—
787C2×C22⋊C4—22no—
788C2×C22⋊C4—21no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4D4×C2912yes—
791C2×C42C23×C2911yescharacteristic
792C2×C42C23×C2911yescharacteristic
793#104—22no—
794#104—22no—
795#104—22no—
796#104—22no—
797#104—41no—
798#104—41no—
799#103—21no—
800#103—21no—
801#102—21no—
802#102—21no—
803#100—22no—
804#100—22no—
805C22⋊C8—21no—
806C22⋊C8—21no—
807#95—21no—
808#95—22no—
809C29#2387811yescharacteristic, direct product factor, Sylow
810C24—22no—
811C24—21no—
812C24—21no—
813C24C2×D4×C2912yes—
814C24C2×D4×C2911yescharacteristic
815#41—21no—
816#41—21no—
817#41—24no—
818#41—24no—
819#41—22no—
820#41—22no—
821#41—21no—
822#41—21no—
823#41—21no—
824#41—21no—
825#41—21no—
826#41—21no—
827#41—21no—
828#41—21no—
829#41—42no—
830#41—42no—
831#41—41no—
832#41—41no—
833#41—42no—
834#41—42no—
835#41—42no—
836#41—42no—
837#41—42no—
838#41—42no—
839#41—42no—
840#41—42no—
841#41—42no—
842#41—42no—
843#41—42no—
844#41—42no—
845#41C2×D4×C2912yes—
846#41C2×D4×C2912yes—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—22no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—41no—
855C2×Q8C2×D4×C2911yescharacteristic
856C2×Q8C2×D4×C2911yescharacteristic
857C2×Q8C2×D4×C2911yescharacteristic
858C2×Q8C2×D4×C2912yescomplemented
859C2×D4—21no—
860C2×D4—22no—
861C2×D4—22no—
862C2×D4—22no—
863C2×D4—22no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—22no—
870C2×D4—22no—
871C2×D4—22no—
872C2×D4—21no—
873C2×D4—22no—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—41no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—44no—
891C2×D4—42no—
892C2×D4—42no—
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—42no—
896C2×D4—42no—
897C2×D4—41no—
898C2×D4—41no—
899C2×D4—42no—
900C2×D4—44no—
901C2×D4—82no—
902C2×D4—82no—
903C2×D4—84no—
904C2×D4C2×D4×C2911yescharacteristic
905C2×D4C2×D4×C2911yescharacteristic
906C2×D4C2×D4×C2911yescharacteristic
907C2×D4C2×D4×C2912yescomplemented
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—22no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—22no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—42no—
924C22×C4—42no—
925C22×C4—42no—
926C22×C4—42no—
927C22×C4—41no—
928C22×C4—41no—
929C22×C4C2×D4×C2911yescharacteristic
930C22×C4C2×D4×C2911yescharacteristic
931C22×C4C2×D4×C2911yescharacteristic
932C22×C4C2×D4×C2911yescharacteristic
933C22×C4C2×D4×C2911yescharacteristic
934C22×C4C2×D4×C2912yes—
935C22×C4C24×C2911yescharacteristic
936Q16—24no—
937Q16—24no—
938Q16—42no—
939SD16—24no—
940SD16—24no—
941SD16—24no—
942SD16—24no—
943SD16—42no—
944SD16—42no—
945D8—24no—
946D8—24no—
947D8—42no—
948M16—24no—
949M16—21no—
950M16—21no—
951M16—21no—
952M16—21no—
953M16—21no—
954M16—21no—
955M16C2×D4×C2912yescomplemented
956M16C2×D4×C2912yescomplemented
957C2×C8—24no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C4⋊C4—22no—
963C4⋊C4—22no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4C2×D4×C2911yescharacteristic
969C4⋊C4C2×D4×C2911yescharacteristic
970C22⋊C4—22no—
971C22⋊C4—22no—
972C22⋊C4—22no—
973C22⋊C4—22no—
974C22⋊C4—22no—
975C22⋊C4—21no—
976C22⋊C4—21no—
977C22⋊C4—21no—
978C22⋊C4—21no—
979C22⋊C4—22no—
980C22⋊C4—22no—
981C22⋊C4—21no—
982C22⋊C4—44no—
983C22⋊C4—42no—
984C22⋊C4—82no—
985C42—22no—
986C42—21no—
987C42—21no—
988C42—21no—
989C42—21no—
990C42—21no—
991C23—21no—
992C23—21no—
993C23—21no—
994C23—22no—
995C23—21no—
996C23—21no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—41no—
1001C23—41no—
1002C23—42no—
1003C23—42no—
1004C23—42no—
1005C23—42no—
1006C23—44no—
1007C23—42no—
1008C23—42no—
1009C23—41no—
1010C23—41no—
1011C23—81no—
1012C23—82no—
1013C23—82no—
1014C23C29×#12011yescharacteristic
1015C23C29×#12011yescharacteristic
1016C23C22×D4×C2911yescharacteristic
1017Q8—21no—
1018Q8—21no—
1019Q8—22no—
1020Q8—21no—
1021Q8—21no—
1022Q8—22no—
1023Q8—21no—
1024Q8—42no—
1025Q8—41no—
1026Q8—41no—
1027Q8C29×#12012yes—
1028D4—22no—
1029D4—22no—
1030D4—21no—
1031D4—22no—
1032D4—21no—
1033D4—21no—
1034D4—21no—
1035D4—22no—
1036D4—21no—
1037D4—42no—
1038D4—42no—
1039D4—44no—
1040D4—42no—
1041D4—44no—
1042D4—44no—
1043D4—42no—
1044D4—44no—
1045D4—44no—
1046D4—41no—
1047D4—41no—
1048D4—41no—
1049D4—41no—
1050D4—41no—
1051D4—41no—
1052D4—41no—
1053D4—41no—
1054D4—41no—
1055D4—41no—
1056D4—82no—
1057D4—81no—
1058D4—82no—
1059D4—82no—
1060D4—82no—
1061D4—88no—
1062D4C29×#12012yes—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—21no—
1078C2×C4—22no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—22no—
1083C2×C4—42no—
1084C2×C4—42no—
1085C2×C4—42no—
1086C2×C4—44no—
1087C2×C4—44no—
1088C2×C4—44no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—42no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—82no—
1102C2×C4C29×#12011yescharacteristic
1103C2×C4C29×#12011yescharacteristic
1104C2×C4C22×D4×C2911yescharacteristic
1105C2×C4C22×D4×C2911yescharacteristic
1106C2×C4C22×D4×C2911yescharacteristic
1107C2×C4C22×D4×C2911yescharacteristic
1108C2×C4C29×H(5,𝔽2)11yescharacteristic
1109C2×C4C29×H(5,𝔽2)11yescharacteristic
1110C8—22no—
1111C8—22no—
1112C8—41no—
1113C8—41no—
1114C22—21no—
1115C22—21no—
1116C22—21no—
1117C22—21no—
1118C22—21no—
1119C22—21no—
1120C22—21no—
1121C22—21no—
1122C22—22no—
1123C22—44no—
1124C22—41no—
1125C22—41no—
1126C22—41no—
1127C22—42no—
1128C22—41no—
1129C22—42no—
1130C22—41no—
1131C22—41no—
1132C22—41no—
1133C22—42no—
1134C22—41no—
1135C22—42no—
1136C22—81no—
1137C22—81no—
1138C22—82no—
1139C22—82no—
1140C22—82no—
1141C22—84no—
1142C22—81no—
1143C22—81no—
1144C22—164no—
1145C22C2×C29×#12011yescharacteristic
1146C22D42×C2911yescharacteristic
1147C22D42×C2911yescharacteristic
1148C4—21no—
1149C4—21no—
1150C4—22no—
1151C4—42no—
1152C4—41no—
1153C4—42no—
1154C4—41no—
1155C4—41no—
1156C4—41no—
1157C4—42no—
1158C4—81no—
1159C4C2×C29×#12011yescharacteristic
1160C4C29×#53411yescharacteristic
1161C4D42×C2911yescharacteristic
1162C4D42×C2911yescharacteristic
1163C2—21no—
1164C2—21no—
1165C2—41no—
1166C2—41no—
1167C2—42no—
1168C2—82no—
1169C2—81no—
1170C2—82no—
1171C2—81no—
1172C2C29×#240311yescharacteristic
1173C2C29×#301811yescharacteristic
1174C2C29×#301911yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC22×C4C24×C29
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C23×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C29×#575C2semidirect
2. C29×#3488C2semidirect
3. C2×C29×#455C2semidirect
4. C2×C29×#453C2semidirect
5. C29×#3005C2semidirect
6. C29×#2431C2semidirect
7. C29×#2007C2semidirect
8. C29×#2006C2semidirect
9. C29×#2004C2semidirect
10. C29×#2002C2semidirect
11. C29×#1900C2semidirect
12. C29×#1883C2semidirect
13. C29×#1882C2semidirect
14. C29×#1871C2semidirect
15. C29×#1789C2semidirect
18. C22×#41×C29C22semidirect
23. C2×C29×#137C22semidirect
24. C2×C29×#137C22semidirect
27. C2×C29×AGL(1,ℤ/8)C22semidirect
28. C2×C29×AGL(1,ℤ/8)C22semidirect
31. C22×M16×C29C22semidirect
42. C2×C29×#127C22semidirect
43. C2×C29×#124C22semidirect
57. C2×C29×#104C22semidirect
58. C2×C29×#104C22semidirect
59. C2×C29×#104C22semidirect
60. C2×C29×#104C22semidirect
61. C29×#419C22semidirect
62. C29×#418C22semidirect
63. C2×C29×#100C22semidirect
64. C2×C29×#100C22semidirect
65. C29×#407C22semidirect
67. C29×#391C22semidirect
68. C29×#390C22semidirect
70. C4×C22⋊C4×C29C22semidirect
71. C29×#343C22semidirect
72. C29×#343C22semidirect
73. C29×#339C22semidirect
74. C29×#339C22semidirect
95. C2×#41×C29D4semidirect
96. C2×#41×C29D4semidirect
100. C22×Q8×C29D4semidirect
110. C22×D4×C29D4semidirect
122. C29×#137D4semidirect
129. C29×AGL(1,ℤ/8)D4semidirect
165. C29×C22⋊Q8D4semidirect
166. C29×C22⋊Q8D4semidirect
181. C29×#121D4semidirect
182. C29×#121D4semidirect
270. C2×Q8×C29C2×D4semidirect
319. C2×D4×C29C2×D4semidirect
367. M16×C29C2×D4semidirect
368. M16×C29C2×D4semidirect
403. #23878C29direct (N × H)
527. C2×#575C2×C29semidirect
528. #3488C2×C29semidirect
529. C2×#455C2×C29semidirect
530. C2×#453C2×C29semidirect
531. #3005C2×C29semidirect
532. #2431C2×C29semidirect
533. #2007C2×C29semidirect
534. #2006C2×C29semidirect
535. #2004C2×C29semidirect
536. #2002C2×C29semidirect
537. #1900C2×C29semidirect
538. #1883C2×C29semidirect
539. #1882C2×C29semidirect
540. #1871C2×C29semidirect
541. #1789C2×C29semidirect
593. C22×#41C22×C29semidirect
598. C2×#137C22×C29semidirect
599. C2×#137C22×C29semidirect
602. C2×AGL(1,ℤ/8)C22×C29semidirect
603. C2×AGL(1,ℤ/8)C22×C29semidirect
606. C22×M16C22×C29semidirect
617. C2×#127C22×C29semidirect
618. C2×#124C22×C29semidirect
632. C2×#104C22×C29semidirect
633. C2×#104C22×C29semidirect
634. C2×#104C22×C29semidirect
635. C2×#104C22×C29semidirect
636. #419C22×C29semidirect
637. #418C22×C29semidirect
638. C2×#100C22×C29semidirect
639. C2×#100C22×C29semidirect
640. #407C22×C29semidirect
642. #391C22×C29semidirect
643. #390C22×C29semidirect
645. C4×C22⋊C4C22×C29semidirect
646. #343C22×C29semidirect
647. #343C22×C29semidirect
648. #339C22×C29semidirect
649. #339C22×C29semidirect
682. C2×#41D4×C29semidirect
683. C2×#41D4×C29semidirect
687. C22×Q8D4×C29semidirect
697. C22×D4D4×C29semidirect
709. #137D4×C29semidirect
716. AGL(1,ℤ/8)D4×C29semidirect
752. C22⋊Q8D4×C29semidirect
753. C22⋊Q8D4×C29semidirect
768. #121D4×C29semidirect
769. #121D4×C29semidirect
809. C29#23878direct (N × H)
858. C2×Q8C2×D4×C29semidirect
907. C2×D4C2×D4×C29semidirect
955. M16C2×D4×C29semidirect
956. M16C2×D4×C29semidirect

Maximal subgroups

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

subgroupindex
C2×C29×#5752
C29×#34882
C2×C29×#4552
C2×C29×#4532
C29×#30052
C29×#24312
C29×#20072
C29×#20062
C29×#20042
C29×#20022
C29×#19002
C29×#18832
C29×#18822
C29×#18712
C29×#17892
#2387829