Finite Group Databasebeta

← C2×C29×#2008 #20318310

Subgroups — C2×C29×#2008 #20318310

Order 7424.

2118 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#575C211yesmaximal, characteristic, complemented
2C22×C29×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
3C2×C29×#535C211yesmaximal, characteristic, complemented
4C2×C29×#421C211yesmaximal, characteristic, complemented
5C2×C29×#418C211yesmaximal, characteristic, complemented
6C2×C29×#410C211yesmaximal, characteristic, complemented
7C29×#2008C218yesmaximal, direct product factor
8C2×C29×#344C211yesmaximal, characteristic, complemented
9C22×#41×C29C2211yescharacteristic
10C22×#41×C29C2211yescharacteristic
11C23×D4×C29C2211yescharacteristic
12C29×#575—22no—
13C29×#575—22no—
14C29×#575—22no—
15C29×#575C2214yescomplemented
16C2×C29×#137—21no—
17C2×C29×#137—21no—
18C2×C29×AGL(1,ℤ/8)—22no—
19C2×C29×AGL(1,ℤ/8)—22no—
20C2×C29×AGL(1,ℤ/8)—22no—
21C2×C29×AGL(1,ℤ/8)—21no—
22C2×C29×AGL(1,ℤ/8)—21no—
23C2×C29×AGL(1,ℤ/8)—22no—
24C2×C29×AGL(1,ℤ/8)—22no—
25C2×C29×AGL(1,ℤ/8)C2214yescomplemented
26C2×C29×#135—22no—
27C22×SD16×C29—21no—
28C22×D8×C29—21no—
29C22×M16×C29C2211yescharacteristic
30C22×M16×C29C2211yescharacteristic
31C29×#535—22no—
32C29×#535—22no—
33C29×#535—22no—
34C29×#535C2214yescomplemented
35C2×C29×#127—21no—
36C2×C29×#124—21no—
37C2×C29×#121—22no—
38C2×C29×#120—22no—
39C2×C29×#117C2211yescharacteristic
40C2×C29×#117C2211yescharacteristic
41C29×#421—22no—
42C29×#421C2214yescomplemented
43C2×C29×#104—22no—
44C29×#418—22no—
45C29×#418C2214yescomplemented
46C2×C29×#102—22no—
47C29×#410—22no—
48C29×#410C2214yescomplemented
49C2×C29×#99—22no—
50C29×#344C2214yescomplemented
51C25×C29—21no—
52C2×#41×C29—21no—
53C2×#41×C29—21no—
54C2×#41×C29—21no—
55C2×#41×C29—21no—
56C2×#41×C29—21no—
57C2×#41×C29—21no—
58C2×#41×C29—21no—
59C2×#41×C29—21no—
60C2×#41×C29—21no—
61C2×#41×C29—21no—
62C2×#41×C29—21no—
63C2×#41×C29—21no—
64C2×#41×C29—21no—
65C2×#41×C29—21no—
66C2×#41×C29—21no—
67C2×#41×C29—21no—
68C2×#41×C29—21no—
69C2×#41×C29—21no—
70C2×#41×C29—21no—
71C2×#41×C29—21no—
72C2×#41×C29D412yes—
73C2×#41×C29D412yescomplemented
74C2×#41×C29C2312yes—
75C2×#41×C29C2312yes—
76C22×Q8×C29D411yescharacteristic
77C22×Q8×C29D411yescharacteristic, complemented
78C22×D4×C29—21no—
79C22×D4×C29—21no—
80C22×D4×C29—24no—
81C22×D4×C29—21no—
82C22×D4×C29—21no—
83C22×D4×C29—21no—
84C22×D4×C29—21no—
85C22×D4×C29—21no—
86C22×D4×C29—21no—
87C22×D4×C29—21no—
88C22×D4×C29—21no—
89C22×D4×C29—21no—
90C22×D4×C29—21no—
91C22×D4×C29—21no—
92C22×D4×C29D412yes—
93C22×D4×C29D411yescharacteristic
94C22×D4×C29D412yes—
95C22×D4×C29D411yescharacteristic, complemented
96C22×D4×C29C2312yes—
97C23×C4×C29—21no—
98C23×C4×C29—21no—
99C23×C4×C29C2311yescharacteristic
100C29×#137—24no—
101C29×#137—24no—
102C29×#137—24no—
103C29×#137—24no—
104C29×AGL(1,ℤ/8)—28no—
105C29×AGL(1,ℤ/8)—28no—
106C29×AGL(1,ℤ/8)—24no—
107C29×AGL(1,ℤ/8)—24no—
108C29×AGL(1,ℤ/8)—28no—
109C29×AGL(1,ℤ/8)—24no—
110C29×AGL(1,ℤ/8)—24no—
111C29×AGL(1,ℤ/8)—28no—
112C29×#135—28no—
113C29×#135—28no—
114C2×Q16×C29—22no—
115C2×SD16×C29—24no—
116C2×SD16×C29—24no—
117C2×SD16×C29—22no—
118C2×SD16×C29—22no—
119C2×SD16×C29—24no—
120C2×D8×C29—24no—
121C2×D8×C29—24no—
122C2×D8×C29—22no—
123C2×D8×C29—24no—
124C2×M16×C29—21no—
125C2×M16×C29—21no—
126C2×M16×C29—21no—
127C2×M16×C29—21no—
128C2×M16×C29—21no—
129C2×M16×C29—21no—
130C2×M16×C29—21no—
131C2×M16×C29D412yescomplemented
132C2×M16×C29D412yescomplemented
133C2×M16×C29D412yescomplemented
134C2×M16×C29C2312yes—
135C2×M16×C29C2312yes—
136C22×C8×C29—21no—
137C22×C8×C29D412yescomplemented
138C29×#127—24no—
139C29×#127—24no—
140C29×#124—24no—
141C29×#124—24no—
142C29×#121—28no—
143C29×#121—28no—
144C29×#120—28no—
145C29×#120—28no—
146C29×#117—21no—
147C29×#117—21no—
148C29×#117—21no—
149C29×#117—21no—
150C29×#117—21no—
151C29×#117D412yes—
152C29×#117C2312yes—
153C29×#117C2312yes—
154C2×C4⋊C4×C29—21no—
155C2×C4⋊C4×C29—21no—
156C2×C22⋊C4×C29—24no—
157C2×C22⋊C4×C29—21no—
158C2×C22⋊C4×C29D412yes—
159C2×C42×C29—21no—
160C2×C42×C29—21no—
161C29×#104—28no—
162C29×#102—28no—
163C29×#99—28no—
164C24×C29—22no—
165C24×C29—21no—
166C24×C29—22no—
167C24×C29—21no—
168C24×C29—22no—
169C24×C29—41no—
170C24×C29—41no—
171C24×C29—41no—
172C24×C29—41no—
173C24×C29—84no—
174C24×C29C2×D411yescharacteristic
175#41×C29—22no—
176#41×C29—22no—
177#41×C29—22no—
178#41×C29—22no—
179#41×C29—22no—
180#41×C29—22no—
181#41×C29—22no—
182#41×C29—22no—
183#41×C29—22no—
184#41×C29—22no—
185#41×C29—22no—
186#41×C29—22no—
187#41×C29—22no—
188#41×C29—22no—
189#41×C29—22no—
190#41×C29—22no—
191#41×C29—41no—
192#41×C29—41no—
193#41×C29—41no—
194#41×C29—41no—
195#41×C29—41no—
196#41×C29—41no—
197#41×C29—41no—
198#41×C29—41no—
199#41×C29—41no—
200#41×C29—41no—
201#41×C29—41no—
202#41×C29—41no—
203#41×C29—41no—
204#41×C29—41no—
205#41×C29—41no—
206#41×C29—41no—
207C2×Q8×C29—21no—
208C2×Q8×C29—21no—
209C2×Q8×C29—21no—
210C2×Q8×C29—21no—
211C2×Q8×C29—21no—
212C2×Q8×C29—21no—
213C2×Q8×C29—21no—
214C2×Q8×C29—21no—
215C2×Q8×C29—21no—
216C2×Q8×C29—21no—
217C2×Q8×C29C2×D412yes—
218C2×Q8×C29C2×D412yescomplemented
219C2×D4×C29—22no—
220C2×D4×C29—22no—
221C2×D4×C29—22no—
222C2×D4×C29—22no—
223C2×D4×C29—216no—
224C2×D4×C29—21no—
225C2×D4×C29—21no—
226C2×D4×C29—22no—
227C2×D4×C29—22no—
228C2×D4×C29—21no—
229C2×D4×C29—21no—
230C2×D4×C29—22no—
231C2×D4×C29—22no—
232C2×D4×C29—21no—
233C2×D4×C29—21no—
234C2×D4×C29—22no—
235C2×D4×C29—22no—
236C2×D4×C29—21no—
237C2×D4×C29—22no—
238C2×D4×C29—22no—
239C2×D4×C29—22no—
240C2×D4×C29—22no—
241C2×D4×C29—21no—
242C2×D4×C29—21no—
243C2×D4×C29—21no—
244C2×D4×C29—22no—
245C2×D4×C29—22no—
246C2×D4×C29—22no—
247C2×D4×C29—22no—
248C2×D4×C29—22no—
249C2×D4×C29—41no—
250C2×D4×C29—41no—
251C2×D4×C29—41no—
252C2×D4×C29—41no—
253C2×D4×C29—41no—
254C2×D4×C29—41no—
255C2×D4×C29—41no—
256C2×D4×C29—41no—
257C2×D4×C29—41no—
258C2×D4×C29—41no—
259C2×D4×C29—41no—
260C2×D4×C29—41no—
261C2×D4×C29—41no—
262C2×D4×C29—41no—
263C2×D4×C29—41no—
264C2×D4×C29—41no—
265C2×D4×C29—41no—
266C2×D4×C29—41no—
267C2×D4×C29—41no—
268C2×D4×C29—41no—
269C2×D4×C29—88no—
270C2×D4×C29C2×D414yes—
271C2×D4×C29C2×D412yes—
272C2×D4×C29C2×D412yescomplemented
273C22×C4×C29—22no—
274C22×C4×C29—21no—
275C22×C4×C29—21no—
276C22×C4×C29—22no—
277C22×C4×C29—22no—
278C22×C4×C29—22no—
279C22×C4×C29—22no—
280C22×C4×C29—41no—
281C22×C4×C29—41no—
282C22×C4×C29—41no—
283C22×C4×C29—41no—
284C22×C4×C29—41no—
285C22×C4×C29—41no—
286C22×C4×C29—41no—
287C22×C4×C29—41no—
288C22×C4×C29—41no—
289C22×C4×C29C2×D411yescharacteristic
290C22×C4×C29C2×D411yescharacteristic
291C22×C4×C29C2×D411yescharacteristic
292C22×C4×C29C2×D411yescharacteristic
293C22×C4×C29C2×D411yescharacteristic
294C22×C4×C29C2×D411yescharacteristic
295C22×C4×C29C2×D411yescharacteristic
296C22×C4×C29C2×D411yescharacteristic
297C22×C4×C29C2×D411yescharacteristic
298C22×C4×C29C2×D411yescharacteristic
299C22×C4×C29C2×D411yescharacteristic
300C22×C4×C29#4111yescharacteristic
301C22×C4×C29#4111yescharacteristic
302C22×C4×C29C2411yescharacteristic
303Q16×C29—28no—
304SD16×C29—216no—
305SD16×C29—28no—
306SD16×C29—28no—
307D8×C29—216no—
308D8×C29—28no—
309M16×C29—22no—
310M16×C29—22no—
311M16×C29—22no—
312M16×C29—22no—
313M16×C29—22no—
314M16×C29—22no—
315M16×C29—22no—
316M16×C29C2×D414yescomplemented
317C2×C8×C29—22no—
318C2×C8×C29—22no—
319C2×C8×C29—22no—
320C2×C8×C29—22no—
321C2×C8×C29—22no—
322C2×C8×C29C2×D414yescomplemented
323C4⋊C4×C29—22no—
324C4⋊C4×C29—22no—
325C4⋊C4×C29—22no—
326C4⋊C4×C29—41no—
327C22⋊C4×C29—216no—
328C22⋊C4×C29—22no—
329C22⋊C4×C29—22no—
330C22⋊C4×C29—41no—
331C22⋊C4×C29C2×D414yes—
332C42×C29—22no—
333C42×C29—22no—
334C42×C29—22no—
335C42×C29—41no—
336C2×#2008C2911yesmaximal, characteristic, direct product factor, Sylow
337C23×C29—24no—
338C23×C29—22no—
339C23×C29—22no—
340C23×C29—42no—
341C23×C29—44no—
342C23×C29—48no—
343C23×C29—42no—
344C23×C29—42no—
345C23×C29—41no—
346C23×C29—41no—
347C23×C29—42no—
348C23×C29—42no—
349C23×C29—42no—
350C23×C29—41no—
351C23×C29—41no—
352C23×C29—42no—
353C23×C29—82no—
354C23×C29—84no—
355C23×C29—84no—
356C23×C29—84no—
357C23×C29—84no—
358C23×C29—84no—
359C23×C29—84no—
360C23×C29#12011yescharacteristic
361C23×C29#12011yescharacteristic
362C23×C29#12111yescharacteristic
363C23×C29#12111yescharacteristic
364C23×C29#12711yescharacteristic
365C23×C29#12711yescharacteristic
366C23×C29C22×D411yescharacteristic
367Q8×C29—22no—
368Q8×C29—22no—
369Q8×C29—22no—
370Q8×C29—22no—
371Q8×C29—41no—
372Q8×C29—41no—
373Q8×C29—41no—
374Q8×C29—41no—
375D4×C29—22no—
376D4×C29—24no—
377D4×C29—22no—
378D4×C29—22no—
379D4×C29—24no—
380D4×C29—22no—
381D4×C29—42no—
382D4×C29—42no—
383D4×C29—42no—
384D4×C29—42no—
385D4×C29—42no—
386D4×C29—42no—
387D4×C29—42no—
388D4×C29—42no—
389D4×C29—42no—
390D4×C29—42no—
391D4×C29—42no—
392D4×C29—42no—
393D4×C29—42no—
394D4×C29—42no—
395D4×C29—41no—
396D4×C29—41no—
397D4×C29—41no—
398D4×C29—41no—
399D4×C29—816no—
400C2×C4×C29—24no—
401C2×C4×C29—22no—
402C2×C4×C29—22no—
403C2×C4×C29—44no—
404C2×C4×C29—41no—
405C2×C4×C29—41no—
406C2×C4×C29—41no—
407C2×C4×C29—41no—
408C2×C4×C29—42no—
409C2×C4×C29—42no—
410C2×C4×C29—42no—
411C2×C4×C29—42no—
412C2×C4×C29—42no—
413C2×C4×C29—42no—
414C2×C4×C29—42no—
415C2×C4×C29—42no—
416C2×C4×C29—42no—
417C2×C4×C29—82no—
418C2×C4×C29#12011yescharacteristic
419C2×C4×C29#12011yescharacteristic
420C2×C4×C29#12011yescharacteristic
421C2×C4×C29#12011yescharacteristic
422C2×C4×C29#12011yescharacteristic
423C2×C4×C29#12011yescharacteristic
424C2×C4×C29#12011yescharacteristic
425C2×C4×C29#12011yescharacteristic
426C2×C4×C29#12011yescharacteristic
427C2×C4×C29#12011yescharacteristic
428C2×C4×C29#12111yescharacteristic
429C2×C4×C29#12111yescharacteristic
430C2×C4×C29#12111yescharacteristic
431C2×C4×C29#12111yescharacteristic
432C2×C4×C29#12111yescharacteristic
433C2×C4×C29#12111yescharacteristic
434C2×C4×C29#12111yescharacteristic
435C2×C4×C29#12111yescharacteristic
436C2×C4×C29#12111yescharacteristic
437C2×C4×C29#12111yescharacteristic
438C2×C4×C29#12711yescharacteristic
439C2×C4×C29#12711yescharacteristic
440C2×C4×C29C22×D411yescharacteristic
441C2×C4×C29C22×D411yescharacteristic
442C2×C4×C29C22×D411yescharacteristic
443C2×C4×C29C22×D411yescharacteristic
444C2×C4×C29C22×D411yescharacteristic
445C2×C4×C29C2×#4111yescharacteristic
446C8×C29—24no—
447C8×C29—24no—
448C2×#575C2×C2911yescharacteristic, complemented
449C22×AGL(1,ℤ/8)C2×C2911yescharacteristic, complemented
450C2×#535C2×C2911yescharacteristic, complemented
451C2×#421C2×C2911yescharacteristic, complemented
452C2×#418C2×C2911yescharacteristic, complemented
453C2×#410C2×C2911yescharacteristic, complemented
454#2008C2×C2918yesdirect product factor
455C2×#344C2×C2911yescharacteristic, complemented
456C22×C29—22no—
457C22×C29—22no—
458C22×C29—22no—
459C22×C29—41no—
460C22×C29—41no—
461C22×C29—41no—
462C22×C29—41no—
463C22×C29—44no—
464C22×C29—48no—
465C22×C29—42no—
466C22×C29—42no—
467C22×C29—44no—
468C22×C29—82no—
469C22×C29—82no—
470C22×C29—84no—
471C22×C29—82no—
472C22×C29—84no—
473C22×C29—84no—
474C22×C29—84no—
475C22×C29—84no—
476C22×C29—82no—
477C22×C29—84no—
478C22×C29—82no—
479C22×C29#39211yescharacteristic
480C22×C29#39211yescharacteristic
481C22×C29#39211yescharacteristic
482C22×C29#39211yescharacteristic
483C22×C29C2×#12011yescharacteristic
484C22×C29C2×#12111yescharacteristic
485C22×C29C2×#12711yescharacteristic
486C4×C29—44no—
487C4×C29—42no—
488C4×C29—42no—
489C4×C29—82no—
490C4×C29#39211yescharacteristic
491C4×C29#39211yescharacteristic
492C4×C29#39211yescharacteristic
493C4×C29#39211yescharacteristic
494C4×C29C2×#12011yescharacteristic
495C4×C29C2×#12011yescharacteristic
496C4×C29C2×#12111yescharacteristic
497C4×C29C2×#12111yescharacteristic
498C22×#41C22×C2911yescharacteristic
499C22×#41C22×C2911yescharacteristic
500C23×D4C22×C2911yescharacteristic
501#575—22no—
502#575—22no—
503#575—22no—
504#575C22×C2914yescomplemented
505C2×#137—21no—
506C2×#137—21no—
507C2×AGL(1,ℤ/8)—22no—
508C2×AGL(1,ℤ/8)—22no—
509C2×AGL(1,ℤ/8)—22no—
510C2×AGL(1,ℤ/8)—21no—
511C2×AGL(1,ℤ/8)—21no—
512C2×AGL(1,ℤ/8)—22no—
513C2×AGL(1,ℤ/8)—22no—
514C2×AGL(1,ℤ/8)C22×C2914yescomplemented
515C2×#135—22no—
516C22×SD16—21no—
517C22×D8—21no—
518C22×M16C22×C2911yescharacteristic
519C22×M16C22×C2911yescharacteristic
520#535—22no—
521#535—22no—
522#535—22no—
523#535C22×C2914yescomplemented
524C2×#127—21no—
525C2×#124—21no—
526C2×#121—22no—
527C2×#120—22no—
528C2×#117C22×C2911yescharacteristic
529C2×#117C22×C2911yescharacteristic
530#421—22no—
531#421C22×C2914yescomplemented
532C2×#104—22no—
533#418—22no—
534#418C22×C2914yescomplemented
535C2×#102—22no—
536#410—22no—
537#410C22×C2914yescomplemented
538C2×#99—22no—
539#344C22×C2914yescomplemented
540C2×C29—21no—
541C2×C29—21no—
542C2×C29—21no—
543C2×C29—21no—
544C2×C29—21no—
545C2×C29—21no—
546C2×C29—82no—
547C2×C29—84no—
548C2×C29—82no—
549C2×C29#200812yesdirect product factor
550C2×C29C2×#39211yescharacteristic
551C25—21no—
552C2×#41—21no—
553C2×#41—21no—
554C2×#41—21no—
555C2×#41—21no—
556C2×#41—21no—
557C2×#41—21no—
558C2×#41—21no—
559C2×#41—21no—
560C2×#41—21no—
561C2×#41—21no—
562C2×#41—21no—
563C2×#41—21no—
564C2×#41—21no—
565C2×#41—21no—
566C2×#41—21no—
567C2×#41—21no—
568C2×#41—21no—
569C2×#41—21no—
570C2×#41—21no—
571C2×#41—21no—
572C2×#41D4×C2912yes—
573C2×#41D4×C2912yescomplemented
574C2×#41C23×C2912yes—
575C2×#41C23×C2912yes—
576C22×Q8D4×C2911yescharacteristic
577C22×Q8D4×C2911yescharacteristic, complemented
578C22×D4—21no—
579C22×D4—21no—
580C22×D4—24no—
581C22×D4—21no—
582C22×D4—21no—
583C22×D4—21no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—21no—
587C22×D4—21no—
588C22×D4—21no—
589C22×D4—21no—
590C22×D4—21no—
591C22×D4—21no—
592C22×D4D4×C2912yes—
593C22×D4D4×C2911yescharacteristic
594C22×D4D4×C2912yes—
595C22×D4D4×C2911yescharacteristic, complemented
596C22×D4C23×C2912yes—
597C23×C4—21no—
598C23×C4—21no—
599C23×C4C23×C2911yescharacteristic
600#137—24no—
601#137—24no—
602#137—24no—
603#137—24no—
604AGL(1,ℤ/8)—28no—
605AGL(1,ℤ/8)—28no—
606AGL(1,ℤ/8)—24no—
607AGL(1,ℤ/8)—24no—
608AGL(1,ℤ/8)—28no—
609AGL(1,ℤ/8)—24no—
610AGL(1,ℤ/8)—24no—
611AGL(1,ℤ/8)—28no—
612#135—28no—
613#135—28no—
614C2×Q16—22no—
615C2×SD16—24no—
616C2×SD16—24no—
617C2×SD16—22no—
618C2×SD16—22no—
619C2×SD16—24no—
620C2×D8—24no—
621C2×D8—24no—
622C2×D8—22no—
623C2×D8—24no—
624C2×M16—21no—
625C2×M16—21no—
626C2×M16—21no—
627C2×M16—21no—
628C2×M16—21no—
629C2×M16—21no—
630C2×M16—21no—
631C2×M16D4×C2912yescomplemented
632C2×M16D4×C2912yescomplemented
633C2×M16D4×C2912yescomplemented
634C2×M16C23×C2912yes—
635C2×M16C23×C2912yes—
636C22×C8—21no—
637C22×C8D4×C2912yescomplemented
638#127—24no—
639#127—24no—
640#124—24no—
641#124—24no—
642#121—28no—
643#121—28no—
644#120—28no—
645#120—28no—
646#117—21no—
647#117—21no—
648#117—21no—
649#117—21no—
650#117—21no—
651#117D4×C2912yes—
652#117C23×C2912yes—
653#117C23×C2912yes—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C22⋊C4—24no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4D4×C2912yes—
659C2×C42—21no—
660C2×C42—21no—
661#104—28no—
662#102—28no—
663#99—28no—
664C29C2×#200811yescharacteristic, direct product factor, Sylow
665C24—22no—
666C24—21no—
667C24—22no—
668C24—21no—
669C24—22no—
670C24—41no—
671C24—41no—
672C24—41no—
673C24—41no—
674C24—84no—
675C24C2×D4×C2911yescharacteristic
676#41—22no—
677#41—22no—
678#41—22no—
679#41—22no—
680#41—22no—
681#41—22no—
682#41—22no—
683#41—22no—
684#41—22no—
685#41—22no—
686#41—22no—
687#41—22no—
688#41—22no—
689#41—22no—
690#41—22no—
691#41—22no—
692#41—41no—
693#41—41no—
694#41—41no—
695#41—41no—
696#41—41no—
697#41—41no—
698#41—41no—
699#41—41no—
700#41—41no—
701#41—41no—
702#41—41no—
703#41—41no—
704#41—41no—
705#41—41no—
706#41—41no—
707#41—41no—
708C2×Q8—21no—
709C2×Q8—21no—
710C2×Q8—21no—
711C2×Q8—21no—
712C2×Q8—21no—
713C2×Q8—21no—
714C2×Q8—21no—
715C2×Q8—21no—
716C2×Q8—21no—
717C2×Q8—21no—
718C2×Q8C2×D4×C2912yes—
719C2×Q8C2×D4×C2912yescomplemented
720C2×D4—22no—
721C2×D4—22no—
722C2×D4—22no—
723C2×D4—22no—
724C2×D4—216no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—22no—
728C2×D4—22no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—22no—
732C2×D4—22no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—21no—
738C2×D4—22no—
739C2×D4—22no—
740C2×D4—22no—
741C2×D4—22no—
742C2×D4—21no—
743C2×D4—21no—
744C2×D4—21no—
745C2×D4—22no—
746C2×D4—22no—
747C2×D4—22no—
748C2×D4—22no—
749C2×D4—22no—
750C2×D4—41no—
751C2×D4—41no—
752C2×D4—41no—
753C2×D4—41no—
754C2×D4—41no—
755C2×D4—41no—
756C2×D4—41no—
757C2×D4—41no—
758C2×D4—41no—
759C2×D4—41no—
760C2×D4—41no—
761C2×D4—41no—
762C2×D4—41no—
763C2×D4—41no—
764C2×D4—41no—
765C2×D4—41no—
766C2×D4—41no—
767C2×D4—41no—
768C2×D4—41no—
769C2×D4—41no—
770C2×D4—88no—
771C2×D4C2×D4×C2914yes—
772C2×D4C2×D4×C2912yes—
773C2×D4C2×D4×C2912yescomplemented
774C22×C4—22no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—41no—
782C22×C4—41no—
783C22×C4—41no—
784C22×C4—41no—
785C22×C4—41no—
786C22×C4—41no—
787C22×C4—41no—
788C22×C4—41no—
789C22×C4—41no—
790C22×C4C2×D4×C2911yescharacteristic
791C22×C4C2×D4×C2911yescharacteristic
792C22×C4C2×D4×C2911yescharacteristic
793C22×C4C2×D4×C2911yescharacteristic
794C22×C4C2×D4×C2911yescharacteristic
795C22×C4C2×D4×C2911yescharacteristic
796C22×C4C2×D4×C2911yescharacteristic
797C22×C4C2×D4×C2911yescharacteristic
798C22×C4C2×D4×C2911yescharacteristic
799C22×C4C2×D4×C2911yescharacteristic
800C22×C4C2×D4×C2911yescharacteristic
801C22×C4#41×C2911yescharacteristic
802C22×C4#41×C2911yescharacteristic
803C22×C4C24×C2911yescharacteristic
804Q16—28no—
805SD16—216no—
806SD16—28no—
807SD16—28no—
808D8—216no—
809D8—28no—
810M16—22no—
811M16—22no—
812M16—22no—
813M16—22no—
814M16—22no—
815M16—22no—
816M16—22no—
817M16C2×D4×C2914yescomplemented
818C2×C8—22no—
819C2×C8—22no—
820C2×C8—22no—
821C2×C8—22no—
822C2×C8—22no—
823C2×C8C2×D4×C2914yescomplemented
824C4⋊C4—22no—
825C4⋊C4—22no—
826C4⋊C4—22no—
827C4⋊C4—41no—
828C22⋊C4—216no—
829C22⋊C4—22no—
830C22⋊C4—22no—
831C22⋊C4—41no—
832C22⋊C4C2×D4×C2914yes—
833C42—22no—
834C42—22no—
835C42—22no—
836C42—41no—
837C23—24no—
838C23—22no—
839C23—22no—
840C23—42no—
841C23—44no—
842C23—48no—
843C23—42no—
844C23—42no—
845C23—41no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23—42no—
850C23—42no—
851C23—42no—
852C23—42no—
853C23—82no—
854C23—84no—
855C23—84no—
856C23—84no—
857C23—84no—
858C23—84no—
859C23—84no—
860C23C29×#12011yescharacteristic
861C23C29×#12011yescharacteristic
862C23C29×#12111yescharacteristic
863C23C29×#12111yescharacteristic
864C23C29×#12711yescharacteristic
865C23C29×#12711yescharacteristic
866C23C22×D4×C2911yescharacteristic
867Q8—22no—
868Q8—22no—
869Q8—22no—
870Q8—22no—
871Q8—41no—
872Q8—41no—
873Q8—41no—
874Q8—41no—
875D4—22no—
876D4—24no—
877D4—22no—
878D4—22no—
879D4—24no—
880D4—22no—
881D4—42no—
882D4—42no—
883D4—42no—
884D4—42no—
885D4—42no—
886D4—42no—
887D4—42no—
888D4—42no—
889D4—42no—
890D4—42no—
891D4—42no—
892D4—42no—
893D4—42no—
894D4—42no—
895D4—41no—
896D4—41no—
897D4—41no—
898D4—41no—
899D4—816no—
900C2×C4—24no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—44no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—42no—
909C2×C4—42no—
910C2×C4—42no—
911C2×C4—42no—
912C2×C4—42no—
913C2×C4—42no—
914C2×C4—42no—
915C2×C4—42no—
916C2×C4—42no—
917C2×C4—82no—
918C2×C4C29×#12011yescharacteristic
919C2×C4C29×#12011yescharacteristic
920C2×C4C29×#12011yescharacteristic
921C2×C4C29×#12011yescharacteristic
922C2×C4C29×#12011yescharacteristic
923C2×C4C29×#12011yescharacteristic
924C2×C4C29×#12011yescharacteristic
925C2×C4C29×#12011yescharacteristic
926C2×C4C29×#12011yescharacteristic
927C2×C4C29×#12011yescharacteristic
928C2×C4C29×#12111yescharacteristic
929C2×C4C29×#12111yescharacteristic
930C2×C4C29×#12111yescharacteristic
931C2×C4C29×#12111yescharacteristic
932C2×C4C29×#12111yescharacteristic
933C2×C4C29×#12111yescharacteristic
934C2×C4C29×#12111yescharacteristic
935C2×C4C29×#12111yescharacteristic
936C2×C4C29×#12111yescharacteristic
937C2×C4C29×#12111yescharacteristic
938C2×C4C29×#12711yescharacteristic
939C2×C4C29×#12711yescharacteristic
940C2×C4C22×D4×C2911yescharacteristic
941C2×C4C22×D4×C2911yescharacteristic
942C2×C4C22×D4×C2911yescharacteristic
943C2×C4C22×D4×C2911yescharacteristic
944C2×C4C22×D4×C2911yescharacteristic
945C2×C4C2×#41×C2911yescharacteristic
946C8—24no—
947C8—24no—
948C22—22no—
949C22—22no—
950C22—22no—
951C22—41no—
952C22—41no—
953C22—41no—
954C22—41no—
955C22—44no—
956C22—48no—
957C22—42no—
958C22—42no—
959C22—44no—
960C22—82no—
961C22—84no—
962C22—82no—
963C22—84no—
964C22—84no—
965C22—84no—
966C22—84no—
967C22—82no—
968C22—84no—
969C22—82no—
970C22—82no—
971C22C29×#39211yescharacteristic
972C22C29×#39211yescharacteristic
973C22C29×#39211yescharacteristic
974C22C29×#39211yescharacteristic
975C22C2×C29×#12011yescharacteristic
976C22C2×C29×#12111yescharacteristic
977C22C2×C29×#12711yescharacteristic
978C4—44no—
979C4—42no—
980C4—42no—
981C4—82no—
982C4C29×#39211yescharacteristic
983C4C29×#39211yescharacteristic
984C4C29×#39211yescharacteristic
985C4C29×#39211yescharacteristic
986C4C2×C29×#12011yescharacteristic
987C4C2×C29×#12011yescharacteristic
988C4C2×C29×#12111yescharacteristic
989C4C2×C29×#12111yescharacteristic
990C2—21no—
991C2—21no—
992C2—21no—
993C2—21no—
994C2—21no—
995C2—21no—
996C2—84no—
997C2—82no—
998C2—82no—
999C2C29×#200812yesdirect product factor
1000C2C2×C29×#39211yescharacteristic
subgroupG/H
center, socleC22×C29#392
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. C22×C29×AGL(1,ℤ/8)C2semidirect
3. C2×C29×#535C2semidirect
4. C2×C29×#421C2semidirect
5. C2×C29×#418C2semidirect
6. C2×C29×#410C2semidirect
7. C29×#2008C2direct (N × H)
8. C2×C29×#344C2semidirect
15. C29×#575C22semidirect
25. C2×C29×AGL(1,ℤ/8)C22semidirect
34. C29×#535C22semidirect
42. C29×#421C22semidirect
45. C29×#418C22semidirect
48. C29×#410C22semidirect
50. C29×#344C22semidirect
73. C2×#41×C29D4semidirect
77. C22×Q8×C29D4semidirect
95. C22×D4×C29D4semidirect
131. C2×M16×C29D4semidirect
132. C2×M16×C29D4semidirect
133. C2×M16×C29D4semidirect
137. C22×C8×C29D4semidirect
218. C2×Q8×C29C2×D4semidirect
272. C2×D4×C29C2×D4semidirect
316. M16×C29C2×D4semidirect
322. C2×C8×C29C2×D4semidirect
336. C2×#2008C29direct (N × H)
448. C2×#575C2×C29semidirect
449. C22×AGL(1,ℤ/8)C2×C29semidirect
450. C2×#535C2×C29semidirect
451. C2×#421C2×C29semidirect
452. C2×#418C2×C29semidirect
453. C2×#410C2×C29semidirect
454. #2008C2×C29direct (N × H)
455. C2×#344C2×C29semidirect
504. #575C22×C29semidirect
514. C2×AGL(1,ℤ/8)C22×C29semidirect
523. #535C22×C29semidirect
531. #421C22×C29semidirect
534. #418C22×C29semidirect
537. #410C22×C29semidirect
539. #344C22×C29semidirect
549. C2×C29#2008direct (N × H)
573. C2×#41D4×C29semidirect
577. C22×Q8D4×C29semidirect
595. C22×D4D4×C29semidirect
631. C2×M16D4×C29semidirect
632. C2×M16D4×C29semidirect
633. C2×M16D4×C29semidirect
637. C22×C8D4×C29semidirect
664. C29C2×#2008direct (N × H)
719. C2×Q8C2×D4×C29semidirect
773. C2×D4C2×D4×C29semidirect
817. M16C2×D4×C29semidirect
823. C2×C8C2×D4×C29semidirect
999. C2C29×#2008direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#5752
C22×C29×AGL(1,ℤ/8)2
C2×C29×#5352
C2×C29×#4212
C2×C29×#4182
C2×C29×#4102
C29×#20082
C2×C29×#3442
C2×#200829