Finite Group Databasebeta

← C2×C29×#2009 #20318311

Subgroups — C2×C29×#2009 #20318311

Order 7424.

1926 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#575C211yesmaximal, characteristic
2C22×C29×#137C211yesmaximal, characteristic, complemented
3C2×C29×#536C211yesmaximal, characteristic, complemented
4C2×C29×#421C211yesmaximal, characteristic, complemented
5C2×C29×#419C211yesmaximal, characteristic, complemented
6C2×C29×#410C211yesmaximal, characteristic, complemented
7C29×#2009C218yesmaximal, direct product factor
8C2×C29×#344C211yesmaximal, characteristic, complemented
9C22×#41×C29C2211yescharacteristic
10C22×#41×C29C2211yescharacteristic
11C23×Q8×C29C2211yescharacteristic
12C29×#575—22no—
13C29×#575—22no—
14C29×#575—22no—
15C29×#575C2214yes—
16C2×C29×#137—22no—
17C2×C29×#137—22no—
18C2×C29×#137—22no—
19C2×C29×#137—21no—
20C2×C29×#137—21no—
21C2×C29×#137—22no—
22C2×C29×#137—22no—
23C2×C29×#137C2214yescomplemented
24C2×C29×AGL(1,ℤ/8)—21no—
25C2×C29×AGL(1,ℤ/8)—21no—
26C2×C29×#135—22no—
27C22×Q16×C29—21no—
28C22×SD16×C29—21no—
29C22×M16×C29C2211yescharacteristic
30C22×M16×C29C2211yescharacteristic
31C29×#536—22no—
32C29×#536—22no—
33C29×#536—22no—
34C29×#536C2214yescomplemented
35C2×C29×C4⋊Q8—21no—
36C2×C29×#124—21no—
37C2×C29×#123—22no—
38C2×C29×C22⋊Q8—22no—
39C2×C29×#117C2211yescharacteristic
40C2×C29×#117C2211yescharacteristic
41C29×#421—22no—
42C29×#421C2214yescomplemented
43C2×C29×#104—22no—
44C29×#419—22no—
45C29×#419C2214yescomplemented
46C2×C29×#103—22no—
47C29×#410—22no—
48C29×#410C2214yescomplemented
49C2×C29×#99—22no—
50C29×#344C2214yescomplemented
51C2×#41×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×C29D412yes—
72C2×#41×C29D412yes—
73C2×#41×C29C2312yes—
74C2×#41×C29C2312yes—
75C22×Q8×C29—21no—
76C22×Q8×C29—21no—
77C22×Q8×C29—21no—
78C22×Q8×C29—21no—
79C22×Q8×C29—21no—
80C22×Q8×C29—21no—
81C22×Q8×C29—21no—
82C22×Q8×C29—21no—
83C22×Q8×C29—21no—
84C22×Q8×C29—21no—
85C22×Q8×C29—21no—
86C22×Q8×C29D412yes—
87C22×Q8×C29D411yescharacteristic
88C22×Q8×C29D412yes—
89C22×Q8×C29D411yescharacteristic
90C22×Q8×C29C2312yes—
91C22×D4×C29—21no—
92C22×D4×C29—21no—
93C22×D4×C29D411yescharacteristic
94C22×D4×C29D411yescharacteristic
95C23×C4×C29—21no—
96C23×C4×C29—21no—
97C23×C4×C29—21no—
98C23×C4×C29C2311yescharacteristic
99C29×#137—28no—
100C29×#137—28no—
101C29×#137—24no—
102C29×#137—24no—
103C29×#137—28no—
104C29×#137—24no—
105C29×#137—24no—
106C29×#137—28no—
107C29×AGL(1,ℤ/8)—24no—
108C29×AGL(1,ℤ/8)—24no—
109C29×AGL(1,ℤ/8)—24no—
110C29×AGL(1,ℤ/8)—24no—
111C29×#135—28no—
112C29×#135—28no—
113C2×Q16×C29—24no—
114C2×Q16×C29—24no—
115C2×Q16×C29—22no—
116C2×Q16×C29—24no—
117C2×SD16×C29—24no—
118C2×SD16×C29—24no—
119C2×SD16×C29—22no—
120C2×SD16×C29—22no—
121C2×SD16×C29—24no—
122C2×D8×C29—22no—
123C2×M16×C29—21no—
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×C29D412yes—
131C2×M16×C29D412yes—
132C2×M16×C29D412yes—
133C2×M16×C29C2312yes—
134C2×M16×C29C2312yes—
135C22×C8×C29—21no—
136C22×C8×C29D412yes—
137C29×C4⋊Q8—24no—
138C29×C4⋊Q8—24no—
139C29×#124—24no—
140C29×#124—24no—
141C29×#123—28no—
142C29×#123—28no—
143C29×C22⋊Q8—28no—
144C29×C22⋊Q8—28no—
145C29×#117—21no—
146C29×#117—21no—
147C29×#117—21no—
148C29×#117—21no—
149C29×#117—21no—
150C29×#117D412yes—
151C29×#117C2312yes—
152C29×#117C2312yes—
153C2×C4⋊C4×C29—24no—
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×#103—28no—
163C29×#99—28no—
164C24×C29—21no—
165C24×C29—21no—
166C24×C29C2×D411yescharacteristic
167#41×C29—22no—
168#41×C29—22no—
169#41×C29—22no—
170#41×C29—22no—
171#41×C29—22no—
172#41×C29—22no—
173#41×C29—22no—
174#41×C29—22no—
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—41no—
184#41×C29—41no—
185#41×C29—41no—
186#41×C29—41no—
187#41×C29—41no—
188#41×C29—41no—
189#41×C29—41no—
190#41×C29—41no—
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—
199C2×Q8×C29—22no—
200C2×Q8×C29—22no—
201C2×Q8×C29—21no—
202C2×Q8×C29—21no—
203C2×Q8×C29—22no—
204C2×Q8×C29—22no—
205C2×Q8×C29—22no—
206C2×Q8×C29—21no—
207C2×Q8×C29—21no—
208C2×Q8×C29—21no—
209C2×Q8×C29—21no—
210C2×Q8×C29—22no—
211C2×Q8×C29—22no—
212C2×Q8×C29—21no—
213C2×Q8×C29—21no—
214C2×Q8×C29—22no—
215C2×Q8×C29—22no—
216C2×Q8×C29—22no—
217C2×Q8×C29—22no—
218C2×Q8×C29—21no—
219C2×Q8×C29—21no—
220C2×Q8×C29—22no—
221C2×Q8×C29—22no—
222C2×Q8×C29—22no—
223C2×Q8×C29—22no—
224C2×Q8×C29—41no—
225C2×Q8×C29—41no—
226C2×Q8×C29—41no—
227C2×Q8×C29—41no—
228C2×Q8×C29—41no—
229C2×Q8×C29—41no—
230C2×Q8×C29—41no—
231C2×Q8×C29—41no—
232C2×Q8×C29—41no—
233C2×Q8×C29—41no—
234C2×Q8×C29—41no—
235C2×Q8×C29—41no—
236C2×Q8×C29C2×D414yes—
237C2×Q8×C29C2×D412yes—
238C2×Q8×C29C2×D412yes—
239C2×D4×C29—22no—
240C2×D4×C29—22no—
241C2×D4×C29—22no—
242C2×D4×C29—22no—
243C2×D4×C29—21no—
244C2×D4×C29—21no—
245C2×D4×C29—21no—
246C2×D4×C29—21no—
247C2×D4×C29—21no—
248C2×D4×C29—21no—
249C2×D4×C29—21no—
250C2×D4×C29—21no—
251C2×D4×C29—21no—
252C2×D4×C29—21no—
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×C29C2×D412yes—
262C2×D4×C29C2×D412yes—
263C22×C4×C29—22no—
264C22×C4×C29—22no—
265C22×C4×C29—21no—
266C22×C4×C29—22no—
267C22×C4×C29—21no—
268C22×C4×C29—22no—
269C22×C4×C29—22no—
270C22×C4×C29—22no—
271C22×C4×C29—22no—
272C22×C4×C29—22no—
273C22×C4×C29—41no—
274C22×C4×C29—41no—
275C22×C4×C29—41no—
276C22×C4×C29—41no—
277C22×C4×C29—41no—
278C22×C4×C29—41no—
279C22×C4×C29—41no—
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×C29C2×D411yescharacteristic
287C22×C4×C29C2×D411yescharacteristic
288C22×C4×C29C2×D411yescharacteristic
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×C29#4111yescharacteristic
298C22×C4×C29#4111yescharacteristic
299C22×C4×C29C2411yescharacteristic
300Q16×C29—216no—
301Q16×C29—28no—
302SD16×C29—216no—
303SD16×C29—28no—
304SD16×C29—28no—
305D8×C29—28no—
306M16×C29—22no—
307M16×C29—22no—
308M16×C29—22no—
309M16×C29—22no—
310M16×C29—22no—
311M16×C29—22no—
312M16×C29—22no—
313M16×C29C2×D414yes—
314C2×C8×C29—22no—
315C2×C8×C29—22no—
316C2×C8×C29—22no—
317C2×C8×C29—22no—
318C2×C8×C29—22no—
319C2×C8×C29C2×D414yes—
320C4⋊C4×C29—216no—
321C4⋊C4×C29—22no—
322C4⋊C4×C29—22no—
323C4⋊C4×C29—22no—
324C4⋊C4×C29—41no—
325C22⋊C4×C29—216no—
326C22⋊C4×C29—22no—
327C22⋊C4×C29—22no—
328C22⋊C4×C29—41no—
329C22⋊C4×C29C2×D414yes—
330C42×C29—22no—
331C42×C29—22no—
332C42×C29—22no—
333C42×C29—41no—
334C2×#2009C2911yesmaximal, characteristic, direct product factor, Sylow
335C23×C29—22no—
336C23×C29—22no—
337C23×C29—42no—
338C23×C29—44no—
339C23×C29—41no—
340C23×C29—41no—
341C23×C29—41no—
342C23×C29—41no—
343C23×C29—82no—
344C23×C29#12011yescharacteristic
345C23×C29#12011yescharacteristic
346C23×C29#12111yescharacteristic
347C23×C29#12111yescharacteristic
348C23×C29#12711yescharacteristic
349C23×C29#12711yescharacteristic
350C23×C29C22×D411yescharacteristic
351Q8×C29—24no—
352Q8×C29—22no—
353Q8×C29—22no—
354Q8×C29—22no—
355Q8×C29—24no—
356Q8×C29—22no—
357Q8×C29—42no—
358Q8×C29—42no—
359Q8×C29—42no—
360Q8×C29—42no—
361Q8×C29—42no—
362Q8×C29—42no—
363Q8×C29—41no—
364Q8×C29—41no—
365Q8×C29—41no—
366Q8×C29—41no—
367D4×C29—22no—
368D4×C29—22no—
369D4×C29—22no—
370D4×C29—22no—
371D4×C29—42no—
372D4×C29—42no—
373D4×C29—42no—
374D4×C29—42no—
375D4×C29—42no—
376D4×C29—42no—
377D4×C29—42no—
378D4×C29—42no—
379D4×C29—41no—
380D4×C29—41no—
381D4×C29—41no—
382D4×C29—41no—
383C2×C4×C29—24no—
384C2×C4×C29—24no—
385C2×C4×C29—22no—
386C2×C4×C29—22no—
387C2×C4×C29—44no—
388C2×C4×C29—42no—
389C2×C4×C29—42no—
390C2×C4×C29—41no—
391C2×C4×C29—41no—
392C2×C4×C29—42no—
393C2×C4×C29—42no—
394C2×C4×C29—42no—
395C2×C4×C29—41no—
396C2×C4×C29—41no—
397C2×C4×C29—42no—
398C2×C4×C29—42no—
399C2×C4×C29—42no—
400C2×C4×C29—42no—
401C2×C4×C29—42no—
402C2×C4×C29—42no—
403C2×C4×C29—42no—
404C2×C4×C29—42no—
405C2×C4×C29—42no—
406C2×C4×C29—42no—
407C2×C4×C29—82no—
408C2×C4×C29#12011yescharacteristic
409C2×C4×C29#12011yescharacteristic
410C2×C4×C29#12011yescharacteristic
411C2×C4×C29#12011yescharacteristic
412C2×C4×C29#12011yescharacteristic
413C2×C4×C29#12011yescharacteristic
414C2×C4×C29#12011yescharacteristic
415C2×C4×C29#12011yescharacteristic
416C2×C4×C29#12011yescharacteristic
417C2×C4×C29#12011yescharacteristic
418C2×C4×C29#12111yescharacteristic
419C2×C4×C29#12111yescharacteristic
420C2×C4×C29#12111yescharacteristic
421C2×C4×C29#12111yescharacteristic
422C2×C4×C29#12111yescharacteristic
423C2×C4×C29#12111yescharacteristic
424C2×C4×C29#12111yescharacteristic
425C2×C4×C29#12111yescharacteristic
426C2×C4×C29#12111yescharacteristic
427C2×C4×C29#12111yescharacteristic
428C2×C4×C29#12711yescharacteristic
429C2×C4×C29#12711yescharacteristic
430C2×C4×C29C22×D411yescharacteristic
431C2×C4×C29C22×D411yescharacteristic
432C2×C4×C29C22×D411yescharacteristic
433C2×C4×C29C22×D411yescharacteristic
434C2×C4×C29C22×D411yescharacteristic
435C2×C4×C29C2×#4111yescharacteristic
436C8×C29—24no—
437C8×C29—24no—
438C2×#575C2×C2911yescharacteristic
439C22×#137C2×C2911yescharacteristic, complemented
440C2×#536C2×C2911yescharacteristic, complemented
441C2×#421C2×C2911yescharacteristic, complemented
442C2×#419C2×C2911yescharacteristic, complemented
443C2×#410C2×C2911yescharacteristic, complemented
444#2009C2×C2918yesdirect product factor
445C2×#344C2×C2911yescharacteristic, complemented
446C22×C29—22no—
447C22×C29—22no—
448C22×C29—22no—
449C22×C29—41no—
450C22×C29—41no—
451C22×C29—41no—
452C22×C29—41no—
453C22×C29—44no—
454C22×C29—42no—
455C22×C29—42no—
456C22×C29—82no—
457C22×C29—82no—
458C22×C29—82no—
459C22×C29—82no—
460C22×C29—82no—
461C22×C29#39211yescharacteristic
462C22×C29#39211yescharacteristic
463C22×C29#39211yescharacteristic
464C22×C29#39211yescharacteristic
465C22×C29C2×#12011yescharacteristic
466C22×C29C2×#12111yescharacteristic
467C22×C29C2×#12711yescharacteristic
468C4×C29—44no—
469C4×C29—42no—
470C4×C29—42no—
471C4×C29—44no—
472C4×C29—82no—
473C4×C29#39211yescharacteristic
474C4×C29#39211yescharacteristic
475C4×C29#39211yescharacteristic
476C4×C29#39211yescharacteristic
477C4×C29C2×#12011yescharacteristic
478C4×C29C2×#12011yescharacteristic
479C4×C29C2×#12111yescharacteristic
480C4×C29C2×#12111yescharacteristic
481C22×#41C22×C2911yescharacteristic
482C22×#41C22×C2911yescharacteristic
483C23×Q8C22×C2911yescharacteristic
484#575—22no—
485#575—22no—
486#575—22no—
487#575C22×C2914yes—
488C2×#137—22no—
489C2×#137—22no—
490C2×#137—22no—
491C2×#137—21no—
492C2×#137—21no—
493C2×#137—22no—
494C2×#137—22no—
495C2×#137C22×C2914yescomplemented
496C2×AGL(1,ℤ/8)—21no—
497C2×AGL(1,ℤ/8)—21no—
498C2×#135—22no—
499C22×Q16—21no—
500C22×SD16—21no—
501C22×M16C22×C2911yescharacteristic
502C22×M16C22×C2911yescharacteristic
503#536—22no—
504#536—22no—
505#536—22no—
506#536C22×C2914yescomplemented
507C2×C4⋊Q8—21no—
508C2×#124—21no—
509C2×#123—22no—
510C2×C22⋊Q8—22no—
511C2×#117C22×C2911yescharacteristic
512C2×#117C22×C2911yescharacteristic
513#421—22no—
514#421C22×C2914yescomplemented
515C2×#104—22no—
516#419—22no—
517#419C22×C2914yescomplemented
518C2×#103—22no—
519#410—22no—
520#410C22×C2914yescomplemented
521C2×#99—22no—
522#344C22×C2914yescomplemented
523C2×C29—21no—
524C2×C29—21no—
525C2×C29—21no—
526C2×C29—21no—
527C2×C29—21no—
528C2×C29—21no—
529C2×C29—82no—
530C2×C29—82no—
531C2×C29#200912yesdirect product factor
532C2×C29C2×#39211yescharacteristic
533C2×#41—21no—
534C2×#41—21no—
535C2×#41—21no—
536C2×#41—21no—
537C2×#41—21no—
538C2×#41—21no—
539C2×#41—21no—
540C2×#41—21no—
541C2×#41—21no—
542C2×#41—21no—
543C2×#41—21no—
544C2×#41—21no—
545C2×#41—21no—
546C2×#41—21no—
547C2×#41—21no—
548C2×#41—21no—
549C2×#41—21no—
550C2×#41—21no—
551C2×#41—21no—
552C2×#41—21no—
553C2×#41D4×C2912yes—
554C2×#41D4×C2912yes—
555C2×#41C23×C2912yes—
556C2×#41C23×C2912yes—
557C22×Q8—21no—
558C22×Q8—21no—
559C22×Q8—21no—
560C22×Q8—21no—
561C22×Q8—21no—
562C22×Q8—21no—
563C22×Q8—21no—
564C22×Q8—21no—
565C22×Q8—21no—
566C22×Q8—21no—
567C22×Q8—21no—
568C22×Q8D4×C2912yes—
569C22×Q8D4×C2911yescharacteristic
570C22×Q8D4×C2912yes—
571C22×Q8D4×C2911yescharacteristic
572C22×Q8C23×C2912yes—
573C22×D4—21no—
574C22×D4—21no—
575C22×D4D4×C2911yescharacteristic
576C22×D4D4×C2911yescharacteristic
577C23×C4—21no—
578C23×C4—21no—
579C23×C4—21no—
580C23×C4C23×C2911yescharacteristic
581#137—28no—
582#137—28no—
583#137—24no—
584#137—24no—
585#137—28no—
586#137—24no—
587#137—24no—
588#137—28no—
589AGL(1,ℤ/8)—24no—
590AGL(1,ℤ/8)—24no—
591AGL(1,ℤ/8)—24no—
592AGL(1,ℤ/8)—24no—
593#135—28no—
594#135—28no—
595C2×Q16—24no—
596C2×Q16—24no—
597C2×Q16—22no—
598C2×Q16—24no—
599C2×SD16—24no—
600C2×SD16—24no—
601C2×SD16—22no—
602C2×SD16—22no—
603C2×SD16—24no—
604C2×D8—22no—
605C2×M16—21no—
606C2×M16—21no—
607C2×M16—21no—
608C2×M16—21no—
609C2×M16—21no—
610C2×M16—21no—
611C2×M16—21no—
612C2×M16D4×C2912yes—
613C2×M16D4×C2912yes—
614C2×M16D4×C2912yes—
615C2×M16C23×C2912yes—
616C2×M16C23×C2912yes—
617C22×C8—21no—
618C22×C8D4×C2912yes—
619C4⋊Q8—24no—
620C4⋊Q8—24no—
621#124—24no—
622#124—24no—
623#123—28no—
624#123—28no—
625C22⋊Q8—28no—
626C22⋊Q8—28no—
627#117—21no—
628#117—21no—
629#117—21no—
630#117—21no—
631#117—21no—
632#117D4×C2912yes—
633#117C23×C2912yes—
634#117C23×C2912yes—
635C2×C4⋊C4—24no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C22⋊C4—24no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4D4×C2912yes—
641C2×C42—21no—
642C2×C42—21no—
643#104—28no—
644#103—28no—
645#99—28no—
646C29C2×#200911yescharacteristic, direct product factor, Sylow
647C24—21no—
648C24—21no—
649C24C2×D4×C2911yescharacteristic
650#41—22no—
651#41—22no—
652#41—22no—
653#41—22no—
654#41—22no—
655#41—22no—
656#41—22no—
657#41—22no—
658#41—22no—
659#41—22no—
660#41—22no—
661#41—22no—
662#41—22no—
663#41—22no—
664#41—22no—
665#41—22no—
666#41—41no—
667#41—41no—
668#41—41no—
669#41—41no—
670#41—41no—
671#41—41no—
672#41—41no—
673#41—41no—
674#41—41no—
675#41—41no—
676#41—41no—
677#41—41no—
678#41—41no—
679#41—41no—
680#41—41no—
681#41—41no—
682C2×Q8—22no—
683C2×Q8—22no—
684C2×Q8—21no—
685C2×Q8—21no—
686C2×Q8—22no—
687C2×Q8—22no—
688C2×Q8—22no—
689C2×Q8—21no—
690C2×Q8—21no—
691C2×Q8—21no—
692C2×Q8—21no—
693C2×Q8—22no—
694C2×Q8—22no—
695C2×Q8—21no—
696C2×Q8—21no—
697C2×Q8—22no—
698C2×Q8—22no—
699C2×Q8—22no—
700C2×Q8—22no—
701C2×Q8—21no—
702C2×Q8—21no—
703C2×Q8—22no—
704C2×Q8—22no—
705C2×Q8—22no—
706C2×Q8—22no—
707C2×Q8—41no—
708C2×Q8—41no—
709C2×Q8—41no—
710C2×Q8—41no—
711C2×Q8—41no—
712C2×Q8—41no—
713C2×Q8—41no—
714C2×Q8—41no—
715C2×Q8—41no—
716C2×Q8—41no—
717C2×Q8—41no—
718C2×Q8—41no—
719C2×Q8C2×D4×C2914yes—
720C2×Q8C2×D4×C2912yes—
721C2×Q8C2×D4×C2912yes—
722C2×D4—22no—
723C2×D4—22no—
724C2×D4—22no—
725C2×D4—22no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—41no—
737C2×D4—41no—
738C2×D4—41no—
739C2×D4—41no—
740C2×D4—41no—
741C2×D4—41no—
742C2×D4—41no—
743C2×D4—41no—
744C2×D4C2×D4×C2912yes—
745C2×D4C2×D4×C2912yes—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—21no—
749C22×C4—22no—
750C22×C4—21no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—41no—
757C22×C4—41no—
758C22×C4—41no—
759C22×C4—41no—
760C22×C4—41no—
761C22×C4—41no—
762C22×C4—41no—
763C22×C4—41no—
764C22×C4—41no—
765C22×C4—41no—
766C22×C4—41no—
767C22×C4—41no—
768C22×C4—41no—
769C22×C4C2×D4×C2911yescharacteristic
770C22×C4C2×D4×C2911yescharacteristic
771C22×C4C2×D4×C2911yescharacteristic
772C22×C4C2×D4×C2911yescharacteristic
773C22×C4C2×D4×C2911yescharacteristic
774C22×C4C2×D4×C2911yescharacteristic
775C22×C4C2×D4×C2911yescharacteristic
776C22×C4C2×D4×C2911yescharacteristic
777C22×C4C2×D4×C2911yescharacteristic
778C22×C4C2×D4×C2911yescharacteristic
779C22×C4C2×D4×C2911yescharacteristic
780C22×C4#41×C2911yescharacteristic
781C22×C4#41×C2911yescharacteristic
782C22×C4C24×C2911yescharacteristic
783Q16—216no—
784Q16—28no—
785SD16—216no—
786SD16—28no—
787SD16—28no—
788D8—28no—
789M16—22no—
790M16—22no—
791M16—22no—
792M16—22no—
793M16—22no—
794M16—22no—
795M16—22no—
796M16C2×D4×C2914yes—
797C2×C8—22no—
798C2×C8—22no—
799C2×C8—22no—
800C2×C8—22no—
801C2×C8—22no—
802C2×C8C2×D4×C2914yes—
803C4⋊C4—216no—
804C4⋊C4—22no—
805C4⋊C4—22no—
806C4⋊C4—22no—
807C4⋊C4—41no—
808C22⋊C4—216no—
809C22⋊C4—22no—
810C22⋊C4—22no—
811C22⋊C4—41no—
812C22⋊C4C2×D4×C2914yes—
813C42—22no—
814C42—22no—
815C42—22no—
816C42—41no—
817C23—22no—
818C23—22no—
819C23—42no—
820C23—44no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—82no—
826C23C29×#12011yescharacteristic
827C23C29×#12011yescharacteristic
828C23C29×#12111yescharacteristic
829C23C29×#12111yescharacteristic
830C23C29×#12711yescharacteristic
831C23C29×#12711yescharacteristic
832C23C22×D4×C2911yescharacteristic
833Q8—24no—
834Q8—22no—
835Q8—22no—
836Q8—22no—
837Q8—24no—
838Q8—22no—
839Q8—42no—
840Q8—42no—
841Q8—42no—
842Q8—42no—
843Q8—42no—
844Q8—42no—
845Q8—41no—
846Q8—41no—
847Q8—41no—
848Q8—41no—
849D4—22no—
850D4—22no—
851D4—22no—
852D4—22no—
853D4—42no—
854D4—42no—
855D4—42no—
856D4—42no—
857D4—42no—
858D4—42no—
859D4—42no—
860D4—42no—
861D4—41no—
862D4—41no—
863D4—41no—
864D4—41no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—44no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—42no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—42no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—82no—
890C2×C4C29×#12011yescharacteristic
891C2×C4C29×#12011yescharacteristic
892C2×C4C29×#12011yescharacteristic
893C2×C4C29×#12011yescharacteristic
894C2×C4C29×#12011yescharacteristic
895C2×C4C29×#12011yescharacteristic
896C2×C4C29×#12011yescharacteristic
897C2×C4C29×#12011yescharacteristic
898C2×C4C29×#12011yescharacteristic
899C2×C4C29×#12011yescharacteristic
900C2×C4C29×#12111yescharacteristic
901C2×C4C29×#12111yescharacteristic
902C2×C4C29×#12111yescharacteristic
903C2×C4C29×#12111yescharacteristic
904C2×C4C29×#12111yescharacteristic
905C2×C4C29×#12111yescharacteristic
906C2×C4C29×#12111yescharacteristic
907C2×C4C29×#12111yescharacteristic
908C2×C4C29×#12111yescharacteristic
909C2×C4C29×#12111yescharacteristic
910C2×C4C29×#12711yescharacteristic
911C2×C4C29×#12711yescharacteristic
912C2×C4C22×D4×C2911yescharacteristic
913C2×C4C22×D4×C2911yescharacteristic
914C2×C4C22×D4×C2911yescharacteristic
915C2×C4C22×D4×C2911yescharacteristic
916C2×C4C22×D4×C2911yescharacteristic
917C2×C4C2×#41×C2911yescharacteristic
918C8—24no—
919C8—24no—
920C22—22no—
921C22—22no—
922C22—22no—
923C22—41no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—44no—
928C22—42no—
929C22—42no—
930C22—82no—
931C22—82no—
932C22—82no—
933C22—82no—
934C22—82no—
935C22C29×#39211yescharacteristic
936C22C29×#39211yescharacteristic
937C22C29×#39211yescharacteristic
938C22C29×#39211yescharacteristic
939C22C2×C29×#12011yescharacteristic
940C22C2×C29×#12111yescharacteristic
941C22C2×C29×#12711yescharacteristic
942C4—44no—
943C4—42no—
944C4—42no—
945C4—44no—
946C4—82no—
947C4C29×#39211yescharacteristic
948C4C29×#39211yescharacteristic
949C4C29×#39211yescharacteristic
950C4C29×#39211yescharacteristic
951C4C2×C29×#12011yescharacteristic
952C4C2×C29×#12011yescharacteristic
953C4C2×C29×#12111yescharacteristic
954C4C2×C29×#12111yescharacteristic
955C2—21no—
956C2—21no—
957C2—21no—
958C2—21no—
959C2—21no—
960C2—21no—
961C2—82no—
962C2—82no—
963C2C29×#200912yesdirect product factor
964C2C2×C29×#39211yescharacteristic
subgroupG/H
center, socleC22×C29#392
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC2×C29×#575C2
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
2. C22×C29×#137C2semidirect
3. C2×C29×#536C2semidirect
4. C2×C29×#421C2semidirect
5. C2×C29×#419C2semidirect
6. C2×C29×#410C2semidirect
7. C29×#2009C2direct (N × H)
8. C2×C29×#344C2semidirect
23. C2×C29×#137C22semidirect
34. C29×#536C22semidirect
42. C29×#421C22semidirect
45. C29×#419C22semidirect
48. C29×#410C22semidirect
50. C29×#344C22semidirect
334. C2×#2009C29direct (N × H)
439. C22×#137C2×C29semidirect
440. C2×#536C2×C29semidirect
441. C2×#421C2×C29semidirect
442. C2×#419C2×C29semidirect
443. C2×#410C2×C29semidirect
444. #2009C2×C29direct (N × H)
445. C2×#344C2×C29semidirect
495. C2×#137C22×C29semidirect
506. #536C22×C29semidirect
514. #421C22×C29semidirect
517. #419C22×C29semidirect
520. #410C22×C29semidirect
522. #344C22×C29semidirect
531. C2×C29#2009direct (N × H)
646. C29C2×#2009direct (N × H)
963. C2C29×#2009direct (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×#1372
C2×C29×#5362
C2×C29×#4212
C2×C29×#4192
C2×C29×#4102
C29×#20092
C2×C29×#3442
C2×#200929