Finite Group Databasebeta

← C29×#24234 #20319134

Subgroups — C29×#24234 #20319134

Order 7424.

1440 conjugacy classes of subgroups.

The subgroup lattice has 1020 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3500C211yesmaximal, characteristic, complemented
2C29×#3036C211yesmaximal, characteristic, complemented
3C2×C29×#454C211yesmaximal, characteristic, complemented
4C2×C29×#453C211yesmaximal, characteristic, complemented
5C4×C29×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
6C29×#2544C211yesmaximal, characteristic, complemented
7C29×#2038C211yesmaximal, characteristic, complemented
8C29×#2037C211yesmaximal, characteristic, complemented
9C29×#2003C211yesmaximal, characteristic, complemented
10C29×#2002C211yesmaximal, characteristic, complemented
11C29×#1980C211yesmaximal, characteristic, complemented
12C29×#1967C211yesmaximal, characteristic, complemented
13C29×#1806C211yesmaximal, characteristic, complemented
14C29×#1793C211yesmaximal, characteristic, complemented
15C29×#1792C211yesmaximal, characteristic, complemented
16C2×C29×2−1+4C2211yescharacteristic
17C2×C29×H(5,𝔽2)C2211yescharacteristic
18C2×C29×AGL(1,ℤ/8)C2211yescharacteristic
19C2×C29×AGL(1,ℤ/8)C2211yescharacteristic
20C2×C29×AGL(1,ℤ/8)C2211yescharacteristic, complemented
21C29×#548—21no—
22C29×#548—21no—
23C29×#546—21no—
24C29×#546—21no—
25C29×#546—22no—
26C29×#546—22no—
27C29×#536—21no—
28C29×#536C2211yescharacteristic
29C29×#535—21no—
30C29×#535C2211yescharacteristic
31C29×#532—21no—
32C29×#532C2211yescharacteristic
33C2×C29×#127C2211yescharacteristic
34C2×C29×#124—21no—
35C2×C29×#124C2211yescharacteristic
36C2×C29×#124C2211yescharacteristic, complemented
37C4×#41×C29C2211yescharacteristic
38C2×C4×D4×C29C2211yescharacteristic, complemented
39C29×#463—21no—
40C29×#463—21no—
41C29×#461—21no—
42C29×#459—21no—
43C29×#454—24no—
44C29×#453—24no—
45C29×#442—21no—
46C29×#440—21no—
47C4×SD16×C29—21no—
48C4×D8×C29—21no—
49C29×#428C2211yescharacteristic, complemented
50C29×#423C2211yescharacteristic, complemented
51C2×C29×#104C2211yescharacteristic
52C2×C29×#104C2211yescharacteristic
53C2×C29×#104C2211yescharacteristic
54C2×C29×#104C2211yescharacteristic
55C2×C29×#104C2211yescharacteristic, complemented
56C2×C29×#104C2211yescharacteristic, complemented
57C29×#418C2211yescharacteristic, complemented
58C29×#417C2211yescharacteristic
59C29×#417C2211yescharacteristic
60C29×#417C2211yescharacteristic, complemented
61C2×C29×#101C2211yescharacteristic, complemented
62C2×C29×#101C2211yescharacteristic, complemented
63C2×C29×#100C2211yescharacteristic
64C2×C29×#100C2211yescharacteristic
65C4×M16×C29C2211yescharacteristic, complemented
66C29×#394—22no—
67C29×#391C2211yescharacteristic, complemented
68C29×#390C2211yescharacteristic
69C29×#386—22no—
70C4×C4⋊C4×C29C2211yescharacteristic, complemented
71C29×#339C2211yescharacteristic, complemented
72C29×#339C2211yescharacteristic, complemented
73C29×2−1+4—22no—
74C29×2−1+4—22no—
75C29×2−1+4—41no—
76C29×2−1+4—41no—
77C29×H(5,𝔽2)—22no—
78C29×H(5,𝔽2)—22no—
79C29×H(5,𝔽2)—41no—
80C29×H(5,𝔽2)—41no—
81C2×#41×C29—21no—
82C2×#41×C29—21no—
83C2×#41×C29—21no—
84C2×#41×C29—21no—
85C2×#41×C29—22no—
86C2×#41×C29C2311yescharacteristic
87C2×#41×C29C2311yescharacteristic
88C2×#41×C29C2311yescharacteristic
89C22×Q8×C29—21no—
90C22×Q8×C29—21no—
91C22×Q8×C29C2311yescharacteristic
92C22×D4×C29—22no—
93C22×D4×C29—21no—
94C22×D4×C29—21no—
95C22×D4×C29—22no—
96C22×D4×C29C2311yescharacteristic
97C22×D4×C29C2311yescharacteristic
98C23×C4×C29—21no—
99C29×AGL(1,ℤ/8)—22no—
100C29×AGL(1,ℤ/8)—22no—
101C29×AGL(1,ℤ/8)—22no—
102C29×AGL(1,ℤ/8)—41no—
103C29×AGL(1,ℤ/8)—41no—
104C29×AGL(1,ℤ/8)D414yescomplemented
105C2×SD16×C29—21no—
106C2×SD16×C29—21no—
107C2×SD16×C29—21no—
108C2×D8×C29—21no—
109C2×D8×C29—21no—
110C2×D8×C29—21no—
111C2×M16×C29C2311yescharacteristic
112C2×M16×C29C2311yescharacteristic
113C2×M16×C29C2311yescharacteristic
114C2×M16×C29C2311yescharacteristic
115C29×C4⋊Q8—21no—
116C29×C4⋊Q8D411yescharacteristic, complemented
117C29×#127—21no—
118C29×#127—22no—
119C29×#127—41no—
120C29×#127D411yescharacteristic, complemented
121C29×#124—22no—
122C29×#124—22no—
123C29×#124—21no—
124C29×#124—21no—
125C29×#124—22no—
126C29×#124—21no—
127C29×#124—21no—
128C29×#124—21no—
129C29×#124—21no—
130C29×#124—41no—
131C29×#124D411yescharacteristic, complemented
132C29×#124D411yescharacteristic, complemented
133C29×#123—22no—
134C29×#123—22no—
135C29×#123—22no—
136C29×C22⋊Q8—22no—
137C29×C22⋊Q8—22no—
138C29×C22⋊Q8—21no—
139C29×C22⋊Q8—21no—
140C29×#121—22no—
141C29×#121—22no—
142C29×#121—22no—
143C29×#121—22no—
144C29×#121—21no—
145C29×#121—21no—
146C29×#121—21no—
147C29×#121—21no—
148C29×#120—22no—
149C29×#120—22no—
150C29×#120—22no—
151C4×Q8×C29D411yescharacteristic, complemented
152C4×Q8×C29D411yescharacteristic, complemented
153C4×D4×C29—22no—
154C4×D4×C29—22no—
155C4×D4×C29—21no—
156C4×D4×C29—21no—
157C4×D4×C29—21no—
158C4×D4×C29—21no—
159C4×D4×C29—21no—
160C4×D4×C29—21no—
161C4×D4×C29—21no—
162C4×D4×C29—21no—
163C4×D4×C29D411yescharacteristic, complemented
164C4×D4×C29D411yescharacteristic, complemented
165C29×#117—21no—
166C29×#117C2311yescharacteristic
167C2×C4⋊C4×C29—21no—
168C2×C4⋊C4×C29C2311yescharacteristic
169C2×C22⋊C4×C29—22no—
170C2×C22⋊C4×C29—22no—
171C2×C22⋊C4×C29—21no—
172C2×C22⋊C4×C29—22no—
173C2×C22⋊C4×C29—22no—
174C2×C22⋊C4×C29D412yes—
175C2×C22⋊C4×C29D412yes—
176C2×C42×C29—21no—
177C2×C42×C29C2311yescharacteristic
178C2×C42×C29C2311yescharacteristic
179C2×C42×C29C2311yescharacteristic
180C29×#107—21no—
181C29×#106—21no—
182C29×C4⋊C8—21no—
183C29×C4⋊C8—21no—
184C29×#104—22no—
185C29×#104—22no—
186C29×#104—22no—
187C29×#104—22no—
188C29×#104—41no—
189C29×#104—41no—
190C29×#103—21no—
191C29×#103—21no—
192C29×#103—21no—
193C29×#102—21no—
194C29×#102—21no—
195C29×#102—21no—
196C29×#102—21no—
197C29×#102—21no—
198C29×#101—22no—
199C29×#101—41no—
200C29×#100—22no—
201C29×#100—41no—
202C29×#97—21no—
203C4×C8×C29—21no—
204C29×#95—21no—
205C29×#95—22no—
206C24×C29—22no—
207C24×C29—21no—
208C24×C29C2×D412yes—
209#41×C29—21no—
210#41×C29—21no—
211#41×C29—21no—
212#41×C29—21no—
213#41×C29—21no—
214#41×C29—21no—
215#41×C29—21no—
216#41×C29—21no—
217#41×C29—21no—
218#41×C29—21no—
219#41×C29—42no—
220#41×C29—42no—
221#41×C29—44no—
222#41×C29—44no—
223#41×C29—42no—
224#41×C29—42no—
225#41×C29—42no—
226#41×C29—42no—
227#41×C29—42no—
228#41×C29—42no—
229#41×C29C2×D412yes—
230#41×C29#4112yes—
231C2×Q8×C29—22no—
232C2×Q8×C29—21no—
233C2×Q8×C29—21no—
234C2×Q8×C29—21no—
235C2×Q8×C29—21no—
236C2×Q8×C29—21no—
237C2×Q8×C29—21no—
238C2×Q8×C29—42no—
239C2×Q8×C29—42no—
240C2×Q8×C29—42no—
241C2×Q8×C29—42no—
242C2×Q8×C29C2×D411yescharacteristic
243C2×Q8×C29C2×D411yescharacteristic
244C2×Q8×C29C2×D411yescharacteristic
245C2×D4×C29—21no—
246C2×D4×C29—22no—
247C2×D4×C29—22no—
248C2×D4×C29—22no—
249C2×D4×C29—21no—
250C2×D4×C29—21no—
251C2×D4×C29—22no—
252C2×D4×C29—22no—
253C2×D4×C29—21no—
254C2×D4×C29—21no—
255C2×D4×C29—21no—
256C2×D4×C29—21no—
257C2×D4×C29—21no—
258C2×D4×C29—21no—
259C2×D4×C29—21no—
260C2×D4×C29—21no—
261C2×D4×C29—21no—
262C2×D4×C29—21no—
263C2×D4×C29—21no—
264C2×D4×C29—21no—
265C2×D4×C29—21no—
266C2×D4×C29—42no—
267C2×D4×C29—42no—
268C2×D4×C29—44no—
269C2×D4×C29—44no—
270C2×D4×C29—44no—
271C2×D4×C29—42no—
272C2×D4×C29—42no—
273C2×D4×C29—44no—
274C2×D4×C29—82no—
275C2×D4×C29C2×D411yescharacteristic
276C2×D4×C29C2×D412yes—
277C2×D4×C29C2×D411yescharacteristic
278C2×D4×C29C2×D411yescharacteristic
279C22×C4×C29—21no—
280C22×C4×C29—22no—
281C22×C4×C29—22no—
282C22×C4×C29—22no—
283C22×C4×C29—21no—
284C22×C4×C29—21no—
285C22×C4×C29—21no—
286C22×C4×C29—21no—
287C22×C4×C29—21no—
288C22×C4×C29—21no—
289C22×C4×C29—21no—
290C22×C4×C29—41no—
291C22×C4×C29—41no—
292C22×C4×C29—82no—
293C22×C4×C29C2×D412yes—
294C22×C4×C29C2×D411yescharacteristic
295C22×C4×C29C2×D411yescharacteristic
296C22×C4×C29C2411yescharacteristic
297SD16×C29—24no—
298SD16×C29—42no—
299SD16×C29—42no—
300D8×C29—24no—
301D8×C29—42no—
302D8×C29—42no—
303M16×C29—21no—
304M16×C29—21no—
305M16×C29—21no—
306M16×C29—21no—
307M16×C29—21no—
308M16×C29—21no—
309M16×C29—21no—
310M16×C29C2×D412yes—
311C2×C8×C29—21no—
312C2×C8×C29—21no—
313C2×C8×C29—21no—
314C2×C8×C29—21no—
315C4⋊C4×C29—22no—
316C4⋊C4×C29—22no—
317C4⋊C4×C29—21no—
318C4⋊C4×C29—21no—
319C4⋊C4×C29—21no—
320C4⋊C4×C29—21no—
321C4⋊C4×C29—21no—
322C4⋊C4×C29—21no—
323C4⋊C4×C29—42no—
324C4⋊C4×C29C2×D411yescharacteristic
325C4⋊C4×C29C2×D411yescharacteristic
326C22⋊C4×C29—22no—
327C22⋊C4×C29—22no—
328C22⋊C4×C29—22no—
329C22⋊C4×C29—22no—
330C22⋊C4×C29—21no—
331C22⋊C4×C29—21no—
332C22⋊C4×C29—21no—
333C22⋊C4×C29—22no—
334C22⋊C4×C29—22no—
335C22⋊C4×C29—22no—
336C22⋊C4×C29—22no—
337C22⋊C4×C29—21no—
338C22⋊C4×C29—21no—
339C22⋊C4×C29—21no—
340C22⋊C4×C29—21no—
341C22⋊C4×C29—44no—
342C22⋊C4×C29—41no—
343C22⋊C4×C29—41no—
344C22⋊C4×C29—82no—
345C42×C29—21no—
346C42×C29—21no—
347C42×C29—21no—
348C42×C29—21no—
349C42×C29—21no—
350C42×C29—21no—
351C42×C29—21no—
352C42×C29C2×D411yescharacteristic
353C42×C29C2×D411yescharacteristic
354C42×C29C2×D411yescharacteristic
355C42×C29C2×D411yescharacteristic
356#24234C2911yesmaximal, characteristic, direct product factor, Sylow
357C23×C29—21no—
358C23×C29—22no—
359C23×C29—21no—
360C23×C29—21no—
361C23×C29—22no—
362C23×C29—22no—
363C23×C29—22no—
364C23×C29—42no—
365C23×C29—42no—
366C23×C29—44no—
367C23×C29—42no—
368C23×C29—42no—
369C23×C29—41no—
370C23×C29—41no—
371C23×C29—82no—
372C23×C29—82no—
373C23×C29C22×D411yescharacteristic
374Q8×C29—21no—
375Q8×C29—21no—
376Q8×C29—21no—
377Q8×C29—21no—
378Q8×C29—21no—
379Q8×C29—44no—
380Q8×C29—41no—
381Q8×C29—41no—
382Q8×C29—41no—
383Q8×C29—41no—
384Q8×C29#12112yes—
385D4×C29—22no—
386D4×C29—22no—
387D4×C29—22no—
388D4×C29—21no—
389D4×C29—22no—
390D4×C29—21no—
391D4×C29—21no—
392D4×C29—21no—
393D4×C29—21no—
394D4×C29—44no—
395D4×C29—44no—
396D4×C29—44no—
397D4×C29—41no—
398D4×C29—41no—
399D4×C29—41no—
400D4×C29—41no—
401D4×C29—41no—
402D4×C29—41no—
403D4×C29—41no—
404D4×C29—41no—
405D4×C29—41no—
406D4×C29—41no—
407D4×C29—81no—
408D4×C29—81no—
409D4×C29—82no—
410D4×C29—82no—
411D4×C29—88no—
412D4×C29#12112yes—
413C2×C4×C29—21no—
414C2×C4×C29—22no—
415C2×C4×C29—22no—
416C2×C4×C29—22no—
417C2×C4×C29—21no—
418C2×C4×C29—21no—
419C2×C4×C29—21no—
420C2×C4×C29—22no—
421C2×C4×C29—21no—
422C2×C4×C29—22no—
423C2×C4×C29—22no—
424C2×C4×C29—41no—
425C2×C4×C29—41no—
426C2×C4×C29—44no—
427C2×C4×C29—44no—
428C2×C4×C29—41no—
429C2×C4×C29—44no—
430C2×C4×C29—41no—
431C2×C4×C29—41no—
432C2×C4×C29—41no—
433C2×C4×C29—41no—
434C2×C4×C29—41no—
435C2×C4×C29—41no—
436C2×C4×C29—42no—
437C2×C4×C29—41no—
438C2×C4×C29—41no—
439C2×C4×C29—41no—
440C2×C4×C29—81no—
441C2×C4×C29—81no—
442C2×C4×C29—82no—
443C2×C4×C29—82no—
444C2×C4×C29#12011yescharacteristic
445C2×C4×C29#12011yescharacteristic
446C2×C4×C29#12011yescharacteristic
447C2×C4×C29#12011yescharacteristic
448C2×C4×C29C22×D411yescharacteristic
449C2×C4×C29C22×D411yescharacteristic
450C2×C4×C29C22×D411yescharacteristic
451C2×C4×C29C2×#4111yescharacteristic
452C2×C4×C29H(5,𝔽2)11yescharacteristic
453C2×C4×C29H(5,𝔽2)11yescharacteristic
454C8×C29—22no—
455C8×C29—41no—
456C8×C29—41no—
457C8×C29—41no—
458#3500C2×C2911yescharacteristic, complemented
459#3036C2×C2911yescharacteristic, complemented
460C2×#454C2×C2911yescharacteristic, complemented
461C2×#453C2×C2911yescharacteristic, complemented
462C4×AGL(1,ℤ/8)C2×C2911yescharacteristic, complemented
463#2544C2×C2911yescharacteristic, complemented
464#2038C2×C2911yescharacteristic, complemented
465#2037C2×C2911yescharacteristic, complemented
466#2003C2×C2911yescharacteristic, complemented
467#2002C2×C2911yescharacteristic, complemented
468#1980C2×C2911yescharacteristic, complemented
469#1967C2×C2911yescharacteristic, complemented
470#1806C2×C2911yescharacteristic, complemented
471#1793C2×C2911yescharacteristic, complemented
472#1792C2×C2911yescharacteristic, complemented
473C22×C29—21no—
474C22×C29—21no—
475C22×C29—22no—
476C22×C29—44no—
477C22×C29—41no—
478C22×C29—41no—
479C22×C29—41no—
480C22×C29—41no—
481C22×C29—42no—
482C22×C29—42no—
483C22×C29—41no—
484C22×C29—42no—
485C22×C29—41no—
486C22×C29—41no—
487C22×C29—42no—
488C22×C29—41no—
489C22×C29—82no—
490C22×C29—82no—
491C22×C29—82no—
492C22×C29—81no—
493C22×C29—81no—
494C22×C29—164no—
495C22×C29C2×#12011yescharacteristic
496C22×C29D4211yescharacteristic
497C22×C29#54611yescharacteristic
498C4×C29—22no—
499C4×C29—21no—
500C4×C29—21no—
501C4×C29—21no—
502C4×C29—21no—
503C4×C29—42no—
504C4×C29—42no—
505C4×C29—41no—
506C4×C29—41no—
507C4×C29—41no—
508C4×C29—41no—
509C4×C29—81no—
510C4×C29—81no—
511C4×C29C2×#12111yescharacteristic
512C4×C29#53511yescharacteristic
513C4×C29D4211yescharacteristic
514C4×C29#54611yescharacteristic
515C2×2−1+4C22×C2911yescharacteristic
516C2×H(5,𝔽2)C22×C2911yescharacteristic
517C2×AGL(1,ℤ/8)C22×C2911yescharacteristic
518C2×AGL(1,ℤ/8)C22×C2911yescharacteristic
519C2×AGL(1,ℤ/8)C22×C2911yescharacteristic, complemented
520#548—21no—
521#548—21no—
522#546—21no—
523#546—21no—
524#546—22no—
525#546—22no—
526#536—21no—
527#536C22×C2911yescharacteristic
528#535—21no—
529#535C22×C2911yescharacteristic
530#532—21no—
531#532C22×C2911yescharacteristic
532C2×#127C22×C2911yescharacteristic
533C2×#124—21no—
534C2×#124C22×C2911yescharacteristic
535C2×#124C22×C2911yescharacteristic, complemented
536C4×#41C22×C2911yescharacteristic
537C2×C4×D4C22×C2911yescharacteristic, complemented
538#463—21no—
539#463—21no—
540#461—21no—
541#459—21no—
542#454—24no—
543#453—24no—
544#442—21no—
545#440—21no—
546C4×SD16—21no—
547C4×D8—21no—
548#428C22×C2911yescharacteristic, complemented
549#423C22×C2911yescharacteristic, complemented
550C2×#104C22×C2911yescharacteristic
551C2×#104C22×C2911yescharacteristic
552C2×#104C22×C2911yescharacteristic
553C2×#104C22×C2911yescharacteristic
554C2×#104C22×C2911yescharacteristic, complemented
555C2×#104C22×C2911yescharacteristic, complemented
556#418C22×C2911yescharacteristic, complemented
557#417C22×C2911yescharacteristic
558#417C22×C2911yescharacteristic
559#417C22×C2911yescharacteristic, complemented
560C2×#101C22×C2911yescharacteristic, complemented
561C2×#101C22×C2911yescharacteristic, complemented
562C2×#100C22×C2911yescharacteristic
563C2×#100C22×C2911yescharacteristic
564C4×M16C22×C2911yescharacteristic, complemented
565#394—22no—
566#391C22×C2911yescharacteristic, complemented
567#390C22×C2911yescharacteristic
568#386—22no—
569C4×C4⋊C4C22×C2911yescharacteristic, complemented
570#339C22×C2911yescharacteristic, complemented
571#339C22×C2911yescharacteristic, complemented
572C2×C29—21no—
573C2×C29—21no—
574C2×C29—42no—
575C2×C29—81no—
576C2×C29—82no—
577C2×C29—82no—
578C2×C29—81no—
579C2×C29#240811yescharacteristic
580C2×C29#301811yescharacteristic
581C2×C29#302111yescharacteristic
5822−1+4—22no—
5832−1+4—22no—
5842−1+4—41no—
5852−1+4—41no—
586H(5,𝔽2)—22no—
587H(5,𝔽2)—22no—
588H(5,𝔽2)—41no—
589H(5,𝔽2)—41no—
590C2×#41—21no—
591C2×#41—21no—
592C2×#41—21no—
593C2×#41—21no—
594C2×#41—22no—
595C2×#41C23×C2911yescharacteristic
596C2×#41C23×C2911yescharacteristic
597C2×#41C23×C2911yescharacteristic
598C22×Q8—21no—
599C22×Q8—21no—
600C22×Q8C23×C2911yescharacteristic
601C22×D4—22no—
602C22×D4—21no—
603C22×D4—21no—
604C22×D4—22no—
605C22×D4C23×C2911yescharacteristic
606C22×D4C23×C2911yescharacteristic
607C23×C4—21no—
608AGL(1,ℤ/8)—22no—
609AGL(1,ℤ/8)—22no—
610AGL(1,ℤ/8)—22no—
611AGL(1,ℤ/8)—41no—
612AGL(1,ℤ/8)—41no—
613AGL(1,ℤ/8)D4×C2914yescomplemented
614C2×SD16—21no—
615C2×SD16—21no—
616C2×SD16—21no—
617C2×D8—21no—
618C2×D8—21no—
619C2×D8—21no—
620C2×M16C23×C2911yescharacteristic
621C2×M16C23×C2911yescharacteristic
622C2×M16C23×C2911yescharacteristic
623C2×M16C23×C2911yescharacteristic
624C4⋊Q8—21no—
625C4⋊Q8D4×C2911yescharacteristic, complemented
626#127—21no—
627#127—22no—
628#127—41no—
629#127D4×C2911yescharacteristic, complemented
630#124—22no—
631#124—22no—
632#124—21no—
633#124—21no—
634#124—22no—
635#124—21no—
636#124—21no—
637#124—21no—
638#124—21no—
639#124—41no—
640#124D4×C2911yescharacteristic, complemented
641#124D4×C2911yescharacteristic, complemented
642#123—22no—
643#123—22no—
644#123—22no—
645C22⋊Q8—22no—
646C22⋊Q8—22no—
647C22⋊Q8—21no—
648C22⋊Q8—21no—
649#121—22no—
650#121—22no—
651#121—22no—
652#121—22no—
653#121—21no—
654#121—21no—
655#121—21no—
656#121—21no—
657#120—22no—
658#120—22no—
659#120—22no—
660C4×Q8D4×C2911yescharacteristic, complemented
661C4×Q8D4×C2911yescharacteristic, complemented
662C4×D4—22no—
663C4×D4—22no—
664C4×D4—21no—
665C4×D4—21no—
666C4×D4—21no—
667C4×D4—21no—
668C4×D4—21no—
669C4×D4—21no—
670C4×D4—21no—
671C4×D4—21no—
672C4×D4D4×C2911yescharacteristic, complemented
673C4×D4D4×C2911yescharacteristic, complemented
674#117—21no—
675#117C23×C2911yescharacteristic
676C2×C4⋊C4—21no—
677C2×C4⋊C4C23×C2911yescharacteristic
678C2×C22⋊C4—22no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—22no—
682C2×C22⋊C4—22no—
683C2×C22⋊C4D4×C2912yes—
684C2×C22⋊C4D4×C2912yes—
685C2×C42—21no—
686C2×C42C23×C2911yescharacteristic
687C2×C42C23×C2911yescharacteristic
688C2×C42C23×C2911yescharacteristic
689#107—21no—
690#106—21no—
691C4⋊C8—21no—
692C4⋊C8—21no—
693#104—22no—
694#104—22no—
695#104—22no—
696#104—22no—
697#104—41no—
698#104—41no—
699#103—21no—
700#103—21no—
701#103—21no—
702#102—21no—
703#102—21no—
704#102—21no—
705#102—21no—
706#102—21no—
707#101—22no—
708#101—41no—
709#100—22no—
710#100—41no—
711#97—21no—
712C4×C8—21no—
713#95—21no—
714#95—22no—
715C29#2423411yescharacteristic, direct product factor, Sylow
716C24—22no—
717C24—21no—
718C24C2×D4×C2912yes—
719#41—21no—
720#41—21no—
721#41—21no—
722#41—21no—
723#41—21no—
724#41—21no—
725#41—21no—
726#41—21no—
727#41—21no—
728#41—21no—
729#41—42no—
730#41—42no—
731#41—44no—
732#41—44no—
733#41—42no—
734#41—42no—
735#41—42no—
736#41—42no—
737#41—42no—
738#41—42no—
739#41C2×D4×C2912yes—
740#41#41×C2912yes—
741C2×Q8—22no—
742C2×Q8—21no—
743C2×Q8—21no—
744C2×Q8—21no—
745C2×Q8—21no—
746C2×Q8—21no—
747C2×Q8—21no—
748C2×Q8—42no—
749C2×Q8—42no—
750C2×Q8—42no—
751C2×Q8—42no—
752C2×Q8C2×D4×C2911yescharacteristic
753C2×Q8C2×D4×C2911yescharacteristic
754C2×Q8C2×D4×C2911yescharacteristic
755C2×D4—21no—
756C2×D4—22no—
757C2×D4—22no—
758C2×D4—22no—
759C2×D4—21no—
760C2×D4—21no—
761C2×D4—22no—
762C2×D4—22no—
763C2×D4—21no—
764C2×D4—21no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—42no—
777C2×D4—42no—
778C2×D4—44no—
779C2×D4—44no—
780C2×D4—44no—
781C2×D4—42no—
782C2×D4—42no—
783C2×D4—44no—
784C2×D4—82no—
785C2×D4C2×D4×C2911yescharacteristic
786C2×D4C2×D4×C2911yescharacteristic
787C2×D4C2×D4×C2912yes—
788C2×D4C2×D4×C2911yescharacteristic
789C22×C4—21no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—41no—
801C22×C4—41no—
802C22×C4—82no—
803C22×C4C2×D4×C2912yes—
804C22×C4C2×D4×C2911yescharacteristic
805C22×C4C2×D4×C2911yescharacteristic
806C22×C4C24×C2911yescharacteristic
807SD16—24no—
808SD16—42no—
809SD16—42no—
810D8—24no—
811D8—42no—
812D8—42no—
813M16—21no—
814M16—21no—
815M16—21no—
816M16—21no—
817M16—21no—
818M16—21no—
819M16—21no—
820M16C2×D4×C2912yes—
821C2×C8—21no—
822C2×C8—21no—
823C2×C8—21no—
824C2×C8—21no—
825C4⋊C4—22no—
826C4⋊C4—22no—
827C4⋊C4—21no—
828C4⋊C4—21no—
829C4⋊C4—21no—
830C4⋊C4—21no—
831C4⋊C4—21no—
832C4⋊C4—21no—
833C4⋊C4—42no—
834C4⋊C4C2×D4×C2911yescharacteristic
835C4⋊C4C2×D4×C2911yescharacteristic
836C22⋊C4—22no—
837C22⋊C4—22no—
838C22⋊C4—22no—
839C22⋊C4—22no—
840C22⋊C4—21no—
841C22⋊C4—21no—
842C22⋊C4—21no—
843C22⋊C4—22no—
844C22⋊C4—22no—
845C22⋊C4—22no—
846C22⋊C4—22no—
847C22⋊C4—21no—
848C22⋊C4—21no—
849C22⋊C4—21no—
850C22⋊C4—21no—
851C22⋊C4—44no—
852C22⋊C4—41no—
853C22⋊C4—41no—
854C22⋊C4—82no—
855C42—21no—
856C42—21no—
857C42—21no—
858C42—21no—
859C42—21no—
860C42—21no—
861C42—21no—
862C42C2×D4×C2911yescharacteristic
863C42C2×D4×C2911yescharacteristic
864C42C2×D4×C2911yescharacteristic
865C42C2×D4×C2911yescharacteristic
866C23—21no—
867C23—22no—
868C23—21no—
869C23—21no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—42no—
874C23—42no—
875C23—44no—
876C23—42no—
877C23—42no—
878C23—41no—
879C23—41no—
880C23—82no—
881C23—82no—
882C23C22×D4×C2911yescharacteristic
883Q8—21no—
884Q8—21no—
885Q8—21no—
886Q8—21no—
887Q8—21no—
888Q8—44no—
889Q8—41no—
890Q8—41no—
891Q8—41no—
892Q8—41no—
893Q8C29×#12112yes—
894D4—22no—
895D4—22no—
896D4—22no—
897D4—21no—
898D4—22no—
899D4—21no—
900D4—21no—
901D4—21no—
902D4—21no—
903D4—44no—
904D4—44no—
905D4—44no—
906D4—41no—
907D4—41no—
908D4—41no—
909D4—41no—
910D4—41no—
911D4—41no—
912D4—41no—
913D4—41no—
914D4—41no—
915D4—41no—
916D4—81no—
917D4—81no—
918D4—82no—
919D4—82no—
920D4—88no—
921D4C29×#12112yes—
922C2×C4—21no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—22no—
930C2×C4—21no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—44no—
936C2×C4—44no—
937C2×C4—41no—
938C2×C4—44no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—42no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—81no—
950C2×C4—81no—
951C2×C4—82no—
952C2×C4—82no—
953C2×C4C29×#12011yescharacteristic
954C2×C4C29×#12011yescharacteristic
955C2×C4C29×#12011yescharacteristic
956C2×C4C29×#12011yescharacteristic
957C2×C4C22×D4×C2911yescharacteristic
958C2×C4C22×D4×C2911yescharacteristic
959C2×C4C22×D4×C2911yescharacteristic
960C2×C4C2×#41×C2911yescharacteristic
961C2×C4C29×H(5,𝔽2)11yescharacteristic
962C2×C4C29×H(5,𝔽2)11yescharacteristic
963C8—22no—
964C8—41no—
965C8—41no—
966C8—41no—
967C22—21no—
968C22—21no—
969C22—22no—
970C22—44no—
971C22—41no—
972C22—41no—
973C22—41no—
974C22—42no—
975C22—41no—
976C22—41no—
977C22—42no—
978C22—41no—
979C22—41no—
980C22—41no—
981C22—42no—
982C22—42no—
983C22—82no—
984C22—82no—
985C22—82no—
986C22—81no—
987C22—81no—
988C22—164no—
989C22C2×C29×#12011yescharacteristic
990C22D42×C2911yescharacteristic
991C22C29×#54611yescharacteristic
992C4—21no—
993C4—21no—
994C4—21no—
995C4—21no—
996C4—22no—
997C4—42no—
998C4—41no—
999C4—41no—
1000C4—42no—
1001C4—41no—
1002C4—41no—
1003C4—81no—
1004C4—81no—
1005C4C2×C29×#12111yescharacteristic
1006C4C29×#53511yescharacteristic
1007C4D42×C2911yescharacteristic
1008C4C29×#54611yescharacteristic
1009C2—21no—
1010C2—21no—
1011C2—42no—
1012C2—82no—
1013C2—82no—
1014C2—81no—
1015C2—81no—
1016C2C29×#240811yescharacteristic
1017C2C29×#301811yescharacteristic
1018C2C29×#302111yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC22×C4C24×C29
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#3500C2semidirect
2. C29×#3036C2semidirect
3. C2×C29×#454C2semidirect
4. C2×C29×#453C2semidirect
5. C4×C29×AGL(1,ℤ/8)C2semidirect
6. C29×#2544C2semidirect
7. C29×#2038C2semidirect
8. C29×#2037C2semidirect
9. C29×#2003C2semidirect
10. C29×#2002C2semidirect
11. C29×#1980C2semidirect
12. C29×#1967C2semidirect
13. C29×#1806C2semidirect
14. C29×#1793C2semidirect
15. C29×#1792C2semidirect
20. C2×C29×AGL(1,ℤ/8)C22semidirect
36. C2×C29×#124C22semidirect
38. C2×C4×D4×C29C22semidirect
49. C29×#428C22semidirect
50. C29×#423C22semidirect
55. C2×C29×#104C22semidirect
56. C2×C29×#104C22semidirect
57. C29×#418C22semidirect
60. C29×#417C22semidirect
61. C2×C29×#101C22semidirect
62. C2×C29×#101C22semidirect
65. C4×M16×C29C22semidirect
67. C29×#391C22semidirect
70. C4×C4⋊C4×C29C22semidirect
71. C29×#339C22semidirect
72. C29×#339C22semidirect
104. C29×AGL(1,ℤ/8)D4semidirect
116. C29×C4⋊Q8D4semidirect
120. C29×#127D4semidirect
131. C29×#124D4semidirect
132. C29×#124D4semidirect
151. C4×Q8×C29D4semidirect
152. C4×Q8×C29D4semidirect
163. C4×D4×C29D4semidirect
164. C4×D4×C29D4semidirect
356. #24234C29direct (N × H)
458. #3500C2×C29semidirect
459. #3036C2×C29semidirect
460. C2×#454C2×C29semidirect
461. C2×#453C2×C29semidirect
462. C4×AGL(1,ℤ/8)C2×C29semidirect
463. #2544C2×C29semidirect
464. #2038C2×C29semidirect
465. #2037C2×C29semidirect
466. #2003C2×C29semidirect
467. #2002C2×C29semidirect
468. #1980C2×C29semidirect
469. #1967C2×C29semidirect
470. #1806C2×C29semidirect
471. #1793C2×C29semidirect
472. #1792C2×C29semidirect
519. C2×AGL(1,ℤ/8)C22×C29semidirect
535. C2×#124C22×C29semidirect
537. C2×C4×D4C22×C29semidirect
548. #428C22×C29semidirect
549. #423C22×C29semidirect
554. C2×#104C22×C29semidirect
555. C2×#104C22×C29semidirect
556. #418C22×C29semidirect
559. #417C22×C29semidirect
560. C2×#101C22×C29semidirect
561. C2×#101C22×C29semidirect
564. C4×M16C22×C29semidirect
566. #391C22×C29semidirect
569. C4×C4⋊C4C22×C29semidirect
570. #339C22×C29semidirect
571. #339C22×C29semidirect
613. AGL(1,ℤ/8)D4×C29semidirect
625. C4⋊Q8D4×C29semidirect
629. #127D4×C29semidirect
640. #124D4×C29semidirect
641. #124D4×C29semidirect
660. C4×Q8D4×C29semidirect
661. C4×Q8D4×C29semidirect
672. C4×D4D4×C29semidirect
673. C4×D4D4×C29semidirect
715. C29#24234direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35002
C29×#30362
C2×C29×#4542
C2×C29×#4532
C4×C29×AGL(1,ℤ/8)2
C29×#25442
C29×#20382
C29×#20372
C29×#20032
C29×#20022
C29×#19802
C29×#19672
C29×#18062
C29×#17932
C29×#17922
#2423429