Finite Group Databasebeta

← C29×#24463 #20319363

Subgroups — C29×#24463 #20319363

Order 7424.

1336 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#577C211yesmaximal, characteristic
2C2×C29×#471C211yesmaximal, characteristic, complemented
3C29×#3046C211yesmaximal, characteristic, complemented
4C2×C29×#456C211yesmaximal, characteristic, complemented
5C29×#3009C211yesmaximal, characteristic, complemented
6C29×#2898C211yesmaximal, characteristic, complemented
7C29×#2052C211yesmaximal, characteristic, complemented
8C29×#2046C211yesmaximal, characteristic, complemented
9C29×#2013C211yesmaximal, characteristic, complemented
10C29×#2005C211yesmaximal, characteristic, complemented
11C29×#1908C211yesmaximal, characteristic, complemented
12C29×#1883C211yesmaximal, characteristic, complemented
13C29×#1876C211yesmaximal, characteristic, complemented
14C29×#1866C211yesmaximal, characteristic, complemented
15C29×#1792C211yesmaximal, characteristic, complemented
16C2×C29×2−1+4C2211yescharacteristic
17C2×C29×H(5,𝔽2)C2211yescharacteristic
18C29×#577—24no—
19C29×#577—24no—
20C2×C29×#137—21no—
21C2×C29×#137C2211yescharacteristic
22C2×C29×#137C2211yescharacteristic
23C2×C29×#137C2211yescharacteristic, complemented
24C2×C29×AGL(1,ℤ/8)—21no—
25C2×C29×AGL(1,ℤ/8)C2211yescharacteristic
26C2×C29×#135—21no—
27C2×C29×#135C2211yescharacteristic
28C22×SD16×C29—21no—
29C22×SD16×C29C2211yescharacteristic
30C22×SD16×C29C2211yescharacteristic
31C2×C29×#131C2211yescharacteristic
32C2×C29×#131C2211yescharacteristic, complemented
33C29×#536C2211yescharacteristic
34C2×C29×C4⋊Q8C2211yescharacteristic, complemented
35C29×#520C2211yescharacteristic, complemented
36C29×#471—24no—
37C29×#464—21no—
38C29×#463—21no—
39C29×#462—21no—
40C29×#461—21no—
41C29×#456—24no—
42C29×#452—21no—
43C29×#452—21no—
44C29×#450—21no—
45C29×#450—21no—
46C2×C29×#108C2211yescharacteristic, complemented
47C29×#424C2211yescharacteristic, complemented
48C2×C29×#104C2211yescharacteristic
49C2×C29×#104C2211yescharacteristic
50C2×C29×#104C2211yescharacteristic, complemented
51C29×#419—21no—
52C29×#419C2211yescharacteristic, complemented
53C29×#418C2211yescharacteristic
54C29×#417—21no—
55C29×#417C2211yescharacteristic
56C29×#417C2211yescharacteristic
57C29×#416—21no—
58C29×#416C2211yescharacteristic
59C2×C29×#103—21no—
60C2×C29×#103C2211yescharacteristic, complemented
61C2×C29×#103C2211yescharacteristic, complemented
62C2×C29×#101C2211yescharacteristic, complemented
63C2×C29×#101C2211yescharacteristic, complemented
64C2×C29×#100C2211yescharacteristic
65C29×#408C2211yescharacteristic
66C29×#390C2211yescharacteristic
67C29×#343C2211yescharacteristic, complemented
68C29×#341C2211yescharacteristic, complemented
69C29×#339C2211yescharacteristic, complemented
70C29×#336C2211yescharacteristic, complemented
71C29×2−1+4—22no—
72C29×2−1+4—22no—
73C29×2−1+4—41no—
74C29×2−1+4D414yes—
75C29×H(5,𝔽2)—22no—
76C29×H(5,𝔽2)—22no—
77C29×H(5,𝔽2)—22no—
78C29×H(5,𝔽2)—41no—
79C2×#41×C29—21no—
80C2×#41×C29—21no—
81C2×#41×C29—21no—
82C2×#41×C29—21no—
83C2×#41×C29—41no—
84C2×#41×C29C2311yescharacteristic
85C2×#41×C29C2311yescharacteristic
86C2×#41×C29C2311yescharacteristic
87C22×Q8×C29—21no—
88C22×Q8×C29—21no—
89C22×Q8×C29C2311yescharacteristic
90C22×Q8×C29C2311yescharacteristic
91C22×D4×C29—21no—
92C22×D4×C29—21no—
93C22×D4×C29—41no—
94C22×D4×C29C2311yescharacteristic
95C29×#137—28no—
96C29×#137—22no—
97C29×#137—22no—
98C29×#137—22no—
99C29×#137—22no—
100C29×#137—22no—
101C29×#137—22no—
102C29×AGL(1,ℤ/8)—28no—
103C29×AGL(1,ℤ/8)—22no—
104C29×AGL(1,ℤ/8)D414yes—
105C29×#135—28no—
106C29×#135—22no—
107C29×#135—22no—
108C2×Q16×C29—21no—
109C2×Q16×C29—21no—
110C2×Q16×C29—21no—
111C2×Q16×C29D411yescharacteristic
112C2×SD16×C29—28no—
113C2×SD16×C29—21no—
114C2×SD16×C29—22no—
115C2×SD16×C29—21no—
116C2×SD16×C29—22no—
117C2×SD16×C29—21no—
118C2×SD16×C29—21no—
119C2×SD16×C29—22no—
120C2×SD16×C29—21no—
121C2×SD16×C29—21no—
122C2×SD16×C29—21no—
123C2×SD16×C29—21no—
124C2×SD16×C29—41no—
125C2×SD16×C29D411yescharacteristic
126C2×SD16×C29D411yescharacteristic
127C2×D8×C29—21no—
128C2×D8×C29D411yescharacteristic
129C29×#131—22no—
130C29×#131—22no—
131C29×#131—22no—
132C29×#131—41no—
133C2×M16×C29—21no—
134C2×M16×C29—21no—
135C2×M16×C29C2311yescharacteristic
136C2×M16×C29C2311yescharacteristic
137C2×M16×C29C2311yescharacteristic
138C2×M16×C29C2311yescharacteristic
139C22×C8×C29—21no—
140C22×C8×C29—21no—
141C22×C8×C29C2311yescharacteristic
142C22×C8×C29C2311yescharacteristic
143C29×C4⋊Q8—22no—
144C29×C4⋊Q8—21no—
145C29×C4⋊Q8—41no—
146C29×#124—21no—
147C29×#123—41no—
148C29×C22⋊Q8—21no—
149C29×C22⋊Q8—21no—
150C4×Q8×C29—21no—
151C4×D4×C29—21no—
152C4×D4×C29—41no—
153C29×#117—21no—
154C29×#117C2311yescharacteristic
155C2×C4⋊C4×C29—21no—
156C2×C4⋊C4×C29—41no—
157C2×C4⋊C4×C29C2311yescharacteristic
158C2×C22⋊C4×C29—41no—
159C2×C42×C29C2311yescharacteristic
160C29×#108—22no—
161C29×C4⋊C8—21no—
162C29×C4⋊C8—21no—
163C29×#104—22no—
164C29×#104—22no—
165C29×#104—41no—
166C29×#103—21no—
167C29×#103—21no—
168C29×#103—21no—
169C29×#103—21no—
170C29×#103—21no—
171C29×#103—21no—
172C29×#103—21no—
173C29×#103—21no—
174C29×#103D411yescharacteristic
175C29×#103D411yescharacteristic
176C29×#102—21no—
177C29×#102—21no—
178C29×#102—21no—
179C29×#102—21no—
180C29×#102D411yescharacteristic
181C29×#102D411yescharacteristic
182C29×#101—22no—
183C29×#101—22no—
184C29×#100—22no—
185C29×C22⋊C8—21no—
186C29×C22⋊C8—21no—
187C24×C29—21no—
188C24×C29—41no—
189#41×C29—21no—
190#41×C29—21no—
191#41×C29—21no—
192#41×C29—21no—
193#41×C29—24no—
194#41×C29—24no—
195#41×C29—24no—
196#41×C29—21no—
197#41×C29—21no—
198#41×C29—21no—
199#41×C29—21no—
200#41×C29—44no—
201#41×C29—42no—
202#41×C29—42no—
203#41×C29—42no—
204#41×C29—44no—
205#41×C29—42no—
206#41×C29—42no—
207#41×C29C2×D412yes—
208#41×C29C2×D412yes—
209#41×C29C2×D412yes—
210#41×C29#4112yes—
211C2×Q8×C29—21no—
212C2×Q8×C29—24no—
213C2×Q8×C29—24no—
214C2×Q8×C29—21no—
215C2×Q8×C29—21no—
216C2×Q8×C29—21no—
217C2×Q8×C29—21no—
218C2×Q8×C29—21no—
219C2×Q8×C29—21no—
220C2×Q8×C29—21no—
221C2×Q8×C29—21no—
222C2×Q8×C29—21no—
223C2×Q8×C29—21no—
224C2×Q8×C29—41no—
225C2×Q8×C29—42no—
226C2×Q8×C29—42no—
227C2×Q8×C29C2×D412yes—
228C2×Q8×C29C2×D411yescharacteristic
229C2×Q8×C29C2×D411yescharacteristic
230C2×Q8×C29C2×D411yescharacteristic
231C2×D4×C29—21no—
232C2×D4×C29—21no—
233C2×D4×C29—24no—
234C2×D4×C29—21no—
235C2×D4×C29—21no—
236C2×D4×C29—21no—
237C2×D4×C29—21no—
238C2×D4×C29—21no—
239C2×D4×C29—21no—
240C2×D4×C29—42no—
241C2×D4×C29—41no—
242C2×D4×C29—41no—
243C2×D4×C29—42no—
244C2×D4×C29—44no—
245C2×D4×C29—44no—
246C2×D4×C29—41no—
247C2×D4×C29—42no—
248C2×D4×C29C2×D411yescharacteristic
249C2×D4×C29C2×D412yes—
250C2×D4×C29C2×D411yescharacteristic
251C2×D4×C29C2×D411yescharacteristic
252C22×C4×C29—21no—
253C22×C4×C29—21no—
254C22×C4×C29—21no—
255C22×C4×C29—21no—
256C22×C4×C29—21no—
257C22×C4×C29—21no—
258C22×C4×C29—21no—
259C22×C4×C29—41no—
260C22×C4×C29—41no—
261C22×C4×C29—41no—
262C22×C4×C29—41no—
263C22×C4×C29C2411yescharacteristic
264Q16×C29—24no—
265Q16×C29—22no—
266Q16×C29—42no—
267Q16×C29—42no—
268SD16×C29—24no—
269SD16×C29—24no—
270SD16×C29—24no—
271SD16×C29—22no—
272SD16×C29—24no—
273SD16×C29—22no—
274SD16×C29—42no—
275SD16×C29—42no—
276SD16×C29—42no—
277SD16×C29—42no—
278D8×C29—24no—
279D8×C29—22no—
280M16×C29—24no—
281M16×C29—21no—
282M16×C29—21no—
283M16×C29—21no—
284M16×C29—21no—
285M16×C29—21no—
286M16×C29—21no—
287M16×C29—21no—
288M16×C29—42no—
289M16×C29C2×D412yes—
290C2×C8×C29—24no—
291C2×C8×C29—21no—
292C2×C8×C29—21no—
293C2×C8×C29—21no—
294C2×C8×C29—21no—
295C2×C8×C29—21no—
296C2×C8×C29—21no—
297C2×C8×C29—21no—
298C2×C8×C29—21no—
299C2×C8×C29—42no—
300C2×C8×C29C2×D411yescharacteristic
301C2×C8×C29C2×D411yescharacteristic
302C2×C8×C29C2×D411yescharacteristic
303C2×C8×C29C2×D411yescharacteristic
304C4⋊C4×C29—21no—
305C4⋊C4×C29—21no—
306C4⋊C4×C29—41no—
307C4⋊C4×C29—41no—
308C4⋊C4×C29—41no—
309C4⋊C4×C29—44no—
310C4⋊C4×C29C2×D411yescharacteristic
311C4⋊C4×C29C2×D411yescharacteristic
312C22⋊C4×C29—21no—
313C22⋊C4×C29—41no—
314C22⋊C4×C29—41no—
315C22⋊C4×C29—41no—
316C22⋊C4×C29—82no—
317C42×C29—21no—
318C42×C29—21no—
319C42×C29—21no—
320C42×C29—41no—
321#24463C2911yesmaximal, characteristic, direct product factor, Sylow
322C23×C29—21no—
323C23×C29—21no—
324C23×C29—21no—
325C23×C29—22no—
326C23×C29—44no—
327C23×C29—41no—
328C23×C29—41no—
329C23×C29—81no—
330C23×C29—81no—
331C23×C29—161no—
332C23×C29—161no—
333C23×C29H(5,𝔽2)11yescharacteristic
334Q8×C29—21no—
335Q8×C29—21no—
336Q8×C29—22no—
337Q8×C29—21no—
338Q8×C29—22no—
339Q8×C29—21no—
340Q8×C29—44no—
341Q8×C29—41no—
342Q8×C29—41no—
343Q8×C29—41no—
344Q8×C29—41no—
345Q8×C29—41no—
346Q8×C29—41no—
347Q8×C29#12012yes—
348Q8×C29#12112yes—
349D4×C29—22no—
350D4×C29—22no—
351D4×C29—22no—
352D4×C29—22no—
353D4×C29—22no—
354D4×C29—21no—
355D4×C29—21no—
356D4×C29—22no—
357D4×C29—21no—
358D4×C29—21no—
359D4×C29—44no—
360D4×C29—44no—
361D4×C29—44no—
362D4×C29—41no—
363D4×C29—41no—
364D4×C29—41no—
365D4×C29—41no—
366D4×C29#12012yes—
367D4×C29#12112yes—
368C2×C4×C29—21no—
369C2×C4×C29—21no—
370C2×C4×C29—22no—
371C2×C4×C29—22no—
372C2×C4×C29—22no—
373C2×C4×C29—22no—
374C2×C4×C29—22no—
375C2×C4×C29—22no—
376C2×C4×C29—21no—
377C2×C4×C29—21no—
378C2×C4×C29—21no—
379C2×C4×C29—44no—
380C2×C4×C29—44no—
381C2×C4×C29—44no—
382C2×C4×C29—41no—
383C2×C4×C29—41no—
384C2×C4×C29—41no—
385C2×C4×C29—41no—
386C2×C4×C29—41no—
387C2×C4×C29—41no—
388C2×C4×C29—41no—
389C2×C4×C29—41no—
390C2×C4×C29—41no—
391C2×C4×C29—41no—
392C2×C4×C29—81no—
393C2×C4×C29—161no—
394C2×C4×C29C22×D411yescharacteristic
395C2×C4×C29C22×D411yescharacteristic
396C2×C4×C29C22×D411yescharacteristic
397C2×C4×C29C22×D411yescharacteristic
398C2×C4×C29C2×#4111yescharacteristic
399C2×C4×C29H(5,𝔽2)11yescharacteristic
400C8×C29—21no—
401C8×C29—22no—
402C8×C29—21no—
403C8×C29—21no—
404C8×C29—21no—
405C8×C29—41no—
406C8×C29—41no—
407C8×C29—41no—
408C2×#577C2×C2911yescharacteristic
409C2×#471C2×C2911yescharacteristic, complemented
410#3046C2×C2911yescharacteristic, complemented
411C2×#456C2×C2911yescharacteristic, complemented
412#3009C2×C2911yescharacteristic, complemented
413#2898C2×C2911yescharacteristic, complemented
414#2052C2×C2911yescharacteristic, complemented
415#2046C2×C2911yescharacteristic, complemented
416#2013C2×C2911yescharacteristic, complemented
417#2005C2×C2911yescharacteristic, complemented
418#1908C2×C2911yescharacteristic, complemented
419#1883C2×C2911yescharacteristic, complemented
420#1876C2×C2911yescharacteristic, complemented
421#1866C2×C2911yescharacteristic, complemented
422#1792C2×C2911yescharacteristic, complemented
423C22×C29—21no—
424C22×C29—21no—
425C22×C29—22no—
426C22×C29—22no—
427C22×C29—41no—
428C22×C29—41no—
429C22×C29—41no—
430C22×C29—41no—
431C22×C29—41no—
432C22×C29—42no—
433C22×C29—41no—
434C22×C29—41no—
435C22×C29—82no—
436C22×C29—81no—
437C22×C29—81no—
438C22×C29—161no—
439C22×C29—164no—
440C22×C29#53411yescharacteristic
441C22×C29D4211yescharacteristic
442C22×C29#54611yescharacteristic
443C4×C29—22no—
444C4×C29—22no—
445C4×C29—42no—
446C4×C29—41no—
447C4×C29—42no—
448C4×C29—41no—
449C4×C29—41no—
450C4×C29—81no—
451C4×C29—81no—
452C4×C29C2×#12011yescharacteristic
453C4×C29C2×#12111yescharacteristic
454C4×C29D4211yescharacteristic
455C4×C29#54611yescharacteristic
456C2×2−1+4C22×C2911yescharacteristic
457C2×H(5,𝔽2)C22×C2911yescharacteristic
458#577—24no—
459#577—24no—
460C2×#137—21no—
461C2×#137C22×C2911yescharacteristic
462C2×#137C22×C2911yescharacteristic
463C2×#137C22×C2911yescharacteristic, complemented
464C2×AGL(1,ℤ/8)—21no—
465C2×AGL(1,ℤ/8)C22×C2911yescharacteristic
466C2×#135—21no—
467C2×#135C22×C2911yescharacteristic
468C22×SD16—21no—
469C22×SD16C22×C2911yescharacteristic
470C22×SD16C22×C2911yescharacteristic
471C2×#131C22×C2911yescharacteristic
472C2×#131C22×C2911yescharacteristic, complemented
473#536C22×C2911yescharacteristic
474C2×C4⋊Q8C22×C2911yescharacteristic, complemented
475#520C22×C2911yescharacteristic, complemented
476#471—24no—
477#464—21no—
478#463—21no—
479#462—21no—
480#461—21no—
481#456—24no—
482#452—21no—
483#452—21no—
484#450—21no—
485#450—21no—
486C2×#108C22×C2911yescharacteristic, complemented
487#424C22×C2911yescharacteristic, complemented
488C2×#104C22×C2911yescharacteristic
489C2×#104C22×C2911yescharacteristic
490C2×#104C22×C2911yescharacteristic, complemented
491#419—21no—
492#419C22×C2911yescharacteristic, complemented
493#418C22×C2911yescharacteristic
494#417—21no—
495#417C22×C2911yescharacteristic
496#417C22×C2911yescharacteristic
497#416—21no—
498#416C22×C2911yescharacteristic
499C2×#103—21no—
500C2×#103C22×C2911yescharacteristic, complemented
501C2×#103C22×C2911yescharacteristic, complemented
502C2×#101C22×C2911yescharacteristic, complemented
503C2×#101C22×C2911yescharacteristic, complemented
504C2×#100C22×C2911yescharacteristic
505#408C22×C2911yescharacteristic
506#390C22×C2911yescharacteristic
507#343C22×C2911yescharacteristic, complemented
508#341C22×C2911yescharacteristic, complemented
509#339C22×C2911yescharacteristic, complemented
510#336C22×C2911yescharacteristic, complemented
511C2×C29—21no—
512C2×C29—21no—
513C2×C29—42no—
514C2×C29—42no—
515C2×C29—81no—
516C2×C29—82no—
517C2×C29#241011yescharacteristic
518C2×C29#328911yescharacteristic
519C2×C29#329111yescharacteristic
5202−1+4—22no—
5212−1+4—22no—
5222−1+4—41no—
5232−1+4D4×C2914yes—
524H(5,𝔽2)—22no—
525H(5,𝔽2)—22no—
526H(5,𝔽2)—22no—
527H(5,𝔽2)—41no—
528C2×#41—21no—
529C2×#41—21no—
530C2×#41—21no—
531C2×#41—21no—
532C2×#41—41no—
533C2×#41C23×C2911yescharacteristic
534C2×#41C23×C2911yescharacteristic
535C2×#41C23×C2911yescharacteristic
536C22×Q8—21no—
537C22×Q8—21no—
538C22×Q8C23×C2911yescharacteristic
539C22×Q8C23×C2911yescharacteristic
540C22×D4—21no—
541C22×D4—21no—
542C22×D4—41no—
543C22×D4C23×C2911yescharacteristic
544#137—28no—
545#137—22no—
546#137—22no—
547#137—22no—
548#137—22no—
549#137—22no—
550#137—22no—
551AGL(1,ℤ/8)—28no—
552AGL(1,ℤ/8)—22no—
553AGL(1,ℤ/8)D4×C2914yes—
554#135—28no—
555#135—22no—
556#135—22no—
557C2×Q16—21no—
558C2×Q16—21no—
559C2×Q16—21no—
560C2×Q16D4×C2911yescharacteristic
561C2×SD16—28no—
562C2×SD16—21no—
563C2×SD16—22no—
564C2×SD16—21no—
565C2×SD16—22no—
566C2×SD16—22no—
567C2×SD16—21no—
568C2×SD16—21no—
569C2×SD16—21no—
570C2×SD16—21no—
571C2×SD16—21no—
572C2×SD16—21no—
573C2×SD16—41no—
574C2×SD16D4×C2911yescharacteristic
575C2×SD16D4×C2911yescharacteristic
576C2×D8—21no—
577C2×D8D4×C2911yescharacteristic
578#131—22no—
579#131—22no—
580#131—22no—
581#131—41no—
582C2×M16—21no—
583C2×M16—21no—
584C2×M16C23×C2911yescharacteristic
585C2×M16C23×C2911yescharacteristic
586C2×M16C23×C2911yescharacteristic
587C2×M16C23×C2911yescharacteristic
588C22×C8—21no—
589C22×C8—21no—
590C22×C8C23×C2911yescharacteristic
591C22×C8C23×C2911yescharacteristic
592C4⋊Q8—22no—
593C4⋊Q8—21no—
594C4⋊Q8—41no—
595#124—21no—
596#123—41no—
597C22⋊Q8—21no—
598C22⋊Q8—21no—
599C4×Q8—21no—
600C4×D4—21no—
601C4×D4—41no—
602#117—21no—
603#117C23×C2911yescharacteristic
604C2×C4⋊C4—21no—
605C2×C4⋊C4—41no—
606C2×C4⋊C4C23×C2911yescharacteristic
607C2×C22⋊C4—41no—
608C2×C42C23×C2911yescharacteristic
609#108—22no—
610C4⋊C8—21no—
611C4⋊C8—21no—
612#104—22no—
613#104—22no—
614#104—41no—
615#103—21no—
616#103—21no—
617#103—21no—
618#103—21no—
619#103—21no—
620#103—21no—
621#103—21no—
622#103—21no—
623#103D4×C2911yescharacteristic
624#103D4×C2911yescharacteristic
625#102—21no—
626#102—21no—
627#102—21no—
628#102—21no—
629#102D4×C2911yescharacteristic
630#102D4×C2911yescharacteristic
631#101—22no—
632#101—22no—
633#100—22no—
634C22⋊C8—21no—
635C22⋊C8—21no—
636C29#2446311yescharacteristic, direct product factor, Sylow
637C24—21no—
638C24—41no—
639#41—21no—
640#41—21no—
641#41—21no—
642#41—21no—
643#41—24no—
644#41—24no—
645#41—24no—
646#41—21no—
647#41—21no—
648#41—21no—
649#41—21no—
650#41—44no—
651#41—42no—
652#41—42no—
653#41—42no—
654#41—44no—
655#41—42no—
656#41—42no—
657#41C2×D4×C2912yes—
658#41C2×D4×C2912yes—
659#41C2×D4×C2912yes—
660#41#41×C2912yes—
661C2×Q8—21no—
662C2×Q8—24no—
663C2×Q8—24no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8—21no—
672C2×Q8—21no—
673C2×Q8—21no—
674C2×Q8—41no—
675C2×Q8—42no—
676C2×Q8—42no—
677C2×Q8C2×D4×C2912yes—
678C2×Q8C2×D4×C2911yescharacteristic
679C2×Q8C2×D4×C2911yescharacteristic
680C2×Q8C2×D4×C2911yescharacteristic
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—24no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—42no—
691C2×D4—41no—
692C2×D4—41no—
693C2×D4—42no—
694C2×D4—44no—
695C2×D4—44no—
696C2×D4—41no—
697C2×D4—42no—
698C2×D4C2×D4×C2912yes—
699C2×D4C2×D4×C2911yescharacteristic
700C2×D4C2×D4×C2911yescharacteristic
701C2×D4C2×D4×C2911yescharacteristic
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—41no—
710C22×C4—41no—
711C22×C4—41no—
712C22×C4—41no—
713C22×C4C24×C2911yescharacteristic
714Q16—24no—
715Q16—22no—
716Q16—42no—
717Q16—42no—
718SD16—24no—
719SD16—24no—
720SD16—24no—
721SD16—22no—
722SD16—24no—
723SD16—22no—
724SD16—42no—
725SD16—42no—
726SD16—42no—
727SD16—42no—
728D8—24no—
729D8—22no—
730M16—24no—
731M16—21no—
732M16—21no—
733M16—21no—
734M16—21no—
735M16—21no—
736M16—21no—
737M16—21no—
738M16—42no—
739M16C2×D4×C2912yes—
740C2×C8—24no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—42no—
750C2×C8C2×D4×C2911yescharacteristic
751C2×C8C2×D4×C2911yescharacteristic
752C2×C8C2×D4×C2911yescharacteristic
753C2×C8C2×D4×C2911yescharacteristic
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—41no—
757C4⋊C4—41no—
758C4⋊C4—41no—
759C4⋊C4—44no—
760C4⋊C4C2×D4×C2911yescharacteristic
761C4⋊C4C2×D4×C2911yescharacteristic
762C22⋊C4—21no—
763C22⋊C4—41no—
764C22⋊C4—41no—
765C22⋊C4—41no—
766C22⋊C4—82no—
767C42—21no—
768C42—21no—
769C42—21no—
770C42—41no—
771C23—21no—
772C23—21no—
773C23—21no—
774C23—22no—
775C23—44no—
776C23—41no—
777C23—41no—
778C23—81no—
779C23—81no—
780C23—161no—
781C23—161no—
782C23C29×H(5,𝔽2)11yescharacteristic
783Q8—21no—
784Q8—21no—
785Q8—22no—
786Q8—21no—
787Q8—22no—
788Q8—21no—
789Q8—44no—
790Q8—41no—
791Q8—41no—
792Q8—41no—
793Q8—41no—
794Q8—41no—
795Q8—41no—
796Q8C29×#12012yes—
797Q8C29×#12112yes—
798D4—22no—
799D4—22no—
800D4—22no—
801D4—22no—
802D4—22no—
803D4—21no—
804D4—21no—
805D4—22no—
806D4—21no—
807D4—21no—
808D4—44no—
809D4—44no—
810D4—44no—
811D4—41no—
812D4—41no—
813D4—41no—
814D4—41no—
815D4C29×#12012yes—
816D4C29×#12112yes—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—44no—
829C2×C4—44no—
830C2×C4—44no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—81no—
842C2×C4—161no—
843C2×C4C22×D4×C2911yescharacteristic
844C2×C4C22×D4×C2911yescharacteristic
845C2×C4C22×D4×C2911yescharacteristic
846C2×C4C22×D4×C2911yescharacteristic
847C2×C4C2×#41×C2911yescharacteristic
848C2×C4C29×H(5,𝔽2)11yescharacteristic
849C8—21no—
850C8—22no—
851C8—21no—
852C8—21no—
853C8—21no—
854C8—41no—
855C8—41no—
856C8—41no—
857C22—21no—
858C22—21no—
859C22—22no—
860C22—22no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—42no—
869C22—82no—
870C22—81no—
871C22—81no—
872C22—161no—
873C22—164no—
874C22C29×#53411yescharacteristic
875C22D42×C2911yescharacteristic
876C22C29×#54611yescharacteristic
877C4—22no—
878C4—22no—
879C4—42no—
880C4—41no—
881C4—41no—
882C4—41no—
883C4—42no—
884C4—81no—
885C4—81no—
886C4C2×C29×#12011yescharacteristic
887C4C2×C29×#12111yescharacteristic
888C4D42×C2911yescharacteristic
889C4C29×#54611yescharacteristic
890C2—21no—
891C2—21no—
892C2—42no—
893C2—42no—
894C2—81no—
895C2—82no—
896C2C29×#241011yescharacteristic
897C2C29×#328911yescharacteristic
898C2C29×#329111yescharacteristic
subgroupG/H
center, socleC22×C29D42
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC2×C29×#577C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C22×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C29×#471C2semidirect
3. C29×#3046C2semidirect
4. C2×C29×#456C2semidirect
5. C29×#3009C2semidirect
6. C29×#2898C2semidirect
7. C29×#2052C2semidirect
8. C29×#2046C2semidirect
9. C29×#2013C2semidirect
10. C29×#2005C2semidirect
11. C29×#1908C2semidirect
12. C29×#1883C2semidirect
13. C29×#1876C2semidirect
14. C29×#1866C2semidirect
15. C29×#1792C2semidirect
23. C2×C29×#137C22semidirect
32. C2×C29×#131C22semidirect
34. C2×C29×C4⋊Q8C22semidirect
35. C29×#520C22semidirect
46. C2×C29×#108C22semidirect
47. C29×#424C22semidirect
50. C2×C29×#104C22semidirect
52. C29×#419C22semidirect
60. C2×C29×#103C22semidirect
61. C2×C29×#103C22semidirect
62. C2×C29×#101C22semidirect
63. C2×C29×#101C22semidirect
67. C29×#343C22semidirect
68. C29×#341C22semidirect
69. C29×#339C22semidirect
70. C29×#336C22semidirect
321. #24463C29direct (N × H)
409. C2×#471C2×C29semidirect
410. #3046C2×C29semidirect
411. C2×#456C2×C29semidirect
412. #3009C2×C29semidirect
413. #2898C2×C29semidirect
414. #2052C2×C29semidirect
415. #2046C2×C29semidirect
416. #2013C2×C29semidirect
417. #2005C2×C29semidirect
418. #1908C2×C29semidirect
419. #1883C2×C29semidirect
420. #1876C2×C29semidirect
421. #1866C2×C29semidirect
422. #1792C2×C29semidirect
463. C2×#137C22×C29semidirect
472. C2×#131C22×C29semidirect
474. C2×C4⋊Q8C22×C29semidirect
475. #520C22×C29semidirect
486. C2×#108C22×C29semidirect
487. #424C22×C29semidirect
490. C2×#104C22×C29semidirect
492. #419C22×C29semidirect
500. C2×#103C22×C29semidirect
501. C2×#103C22×C29semidirect
502. C2×#101C22×C29semidirect
503. C2×#101C22×C29semidirect
507. #343C22×C29semidirect
508. #341C22×C29semidirect
509. #339C22×C29semidirect
510. #336C22×C29semidirect
636. C29#24463direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#5772
C2×C29×#4712
C29×#30462
C2×C29×#4562
C29×#30092
C29×#28982
C29×#20522
C29×#20462
C29×#20132
C29×#20052
C29×#19082
C29×#18832
C29×#18762
C29×#18662
C29×#17922
#2446329