Finite Group Databasebeta

← C29×#22464 #20317364

Subgroups — C29×#22464 #20317364

Order 7424.

1346 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#577C211yesmaximal, characteristic
2C2×C29×#444C211yesmaximal, characteristic, complemented
3C29×#2951C211yesmaximal, characteristic, complemented
4C29×#2898C211yesmaximal, characteristic, complemented
5C29×#2897C211yesmaximal, characteristic, complemented
6C29×#1977C211yesmaximal, characteristic, complemented
7C29×#1973C211yesmaximal, characteristic, complemented
8C29×#1908C211yesmaximal, characteristic, complemented
9C29×#1907C211yesmaximal, characteristic, complemented
10C29×#1883C211yesmaximal, characteristic, complemented
11C29×#1882C211yesmaximal, characteristic, complemented
12C29×#1816C211yesmaximal, characteristic, complemented
13C29×#1793C211yesmaximal, characteristic, complemented
14C29×#1792C211yesmaximal, characteristic, complemented
15C29×#1765C211yesmaximal, characteristic, complemented
16C2×C29×2−1+4C2211yescharacteristic
17C2×C29×H(5,𝔽2)C2211yescharacteristic
18C29×#577—24no—
19C29×#577C418yescomplemented
20C2×C29×#137—21no—
21C2×C29×#137C2211yescharacteristic
22C2×C29×AGL(1,ℤ/8)—21no—
23C2×C29×AGL(1,ℤ/8)C2211yescharacteristic
24C2×C29×#135—21no—
25C2×C29×#135C2211yescharacteristic
26C22×SD16×C29—21no—
27C22×SD16×C29C2211yescharacteristic
28C2×C29×#131C2211yescharacteristic
29C2×C29×#131C2211yescharacteristic
30C2×C29×#131C2211yescharacteristic, complemented
31C29×#520C2211yescharacteristic
32C29×#520C2211yescharacteristic, complemented
33C29×#444—24no—
34C29×#440—21no—
35C29×#440—21no—
36C4×Q16×C29—21no—
37C4×D8×C29—21no—
38C2×C29×#108C2211yescharacteristic, complemented
39C2×C29×#107C2211yescharacteristic, complemented
40C2×C29×#104C2211yescharacteristic
41C2×C29×#104C2211yescharacteristic
42C2×C29×#104C2211yescharacteristic, complemented
43C29×#419—21no—
44C29×#419C2211yescharacteristic, complemented
45C29×#418—21no—
46C29×#418C2211yescharacteristic
47C29×#417—21no—
48C29×#417—21no—
49C29×#417C2211yescharacteristic
50C29×#417C2211yescharacteristic
51C29×#417C2211yescharacteristic
52C29×#417C2211yescharacteristic, complemented
53C29×#416—21no—
54C29×#416—21no—
55C29×#416C2211yescharacteristic
56C2×C29×#103—21no—
57C2×C29×#103C2211yescharacteristic, complemented
58C2×C29×#102—21no—
59C2×C29×#102C2211yescharacteristic
60C2×C29×#101C2211yescharacteristic, complemented
61C2×C29×#100C2211yescharacteristic
62C29×#405C2211yescharacteristic, complemented
63C2×C29×#97C2211yescharacteristic, complemented
64C29×#391C2211yescharacteristic, complemented
65C29×#390C2211yescharacteristic
66C29×#343C2211yescharacteristic, complemented
67C29×#343C2211yescharacteristic, complemented
68C29×#341C2211yescharacteristic, complemented
69C29×#339C2211yescharacteristic, complemented
70C29×2−1+4—22no—
71C29×2−1+4—22no—
72C29×2−1+4—41no—
73C29×2−1+4C2×C414yescomplemented
74C29×H(5,𝔽2)—22no—
75C29×H(5,𝔽2)—22no—
76C29×H(5,𝔽2)—41no—
77C29×H(5,𝔽2)C2×C414yescomplemented
78C2×#41×C29—21no—
79C2×#41×C29—21no—
80C2×#41×C29—21no—
81C2×#41×C29—21no—
82C2×#41×C29—41no—
83C2×#41×C29C2311yescharacteristic
84C2×#41×C29C2311yescharacteristic
85C2×#41×C29C2311yescharacteristic
86C22×Q8×C29—21no—
87C22×Q8×C29—21no—
88C22×Q8×C29C2311yescharacteristic
89C22×D4×C29—21no—
90C22×D4×C29—21no—
91C22×D4×C29—41no—
92C22×D4×C29C2311yescharacteristic
93C29×#137—22no—
94C29×#137—28no—
95C29×#137C2×C414yescomplemented
96C29×AGL(1,ℤ/8)—22no—
97C29×AGL(1,ℤ/8)—28no—
98C29×AGL(1,ℤ/8)C2×C414yescomplemented
99C29×#135—28no—
100C29×#135C2×C414yes—
101C29×#135D414yes—
102C2×Q16×C29—21no—
103C2×Q16×C29D411yescharacteristic
104C2×SD16×C29—21no—
105C2×SD16×C29—21no—
106C2×SD16×C29—28no—
107C2×SD16×C29—21no—
108C2×SD16×C29—21no—
109C2×SD16×C29—22no—
110C2×SD16×C29C2×C414yescomplemented
111C2×SD16×C29D411yescharacteristic
112C2×SD16×C29D411yescharacteristic
113C2×D8×C29—21no—
114C2×D8×C29D411yescharacteristic
115C29×#131—22no—
116C29×#131—22no—
117C29×#131—22no—
118C29×#131—41no—
119C29×#131—41no—
120C29×#131C2×C414yescomplemented
121C2×M16×C29—21no—
122C2×M16×C29—21no—
123C2×M16×C29—21no—
124C2×M16×C29C2311yescharacteristic
125C2×M16×C29C2311yescharacteristic
126C2×M16×C29C2311yescharacteristic
127C2×M16×C29C2311yescharacteristic
128C22×C8×C29—21no—
129C22×C8×C29—21no—
130C22×C8×C29—21no—
131C22×C8×C29C2311yescharacteristic
132C22×C8×C29C2311yescharacteristic
133C4×Q8×C29—21no—
134C4×Q8×C29—21no—
135C4×D4×C29—21no—
136C4×D4×C29—21no—
137C4×D4×C29—41no—
138C4×D4×C29—41no—
139C29×#117—21no—
140C29×#117—21no—
141C29×#117C2311yescharacteristic
142C2×C4⋊C4×C29—21no—
143C2×C4⋊C4×C29—21no—
144C2×C4⋊C4×C29C2311yescharacteristic
145C2×C4⋊C4×C29C2311yescharacteristic
146C2×C22⋊C4×C29—41no—
147C2×C42×C29C2311yescharacteristic
148C29×#108—22no—
149C29×#107—21no—
150C29×#107—21no—
151C29×#104—22no—
152C29×#104—22no—
153C29×#104—22no—
154C29×#103—21no—
155C29×#103—21no—
156C29×#103—21no—
157C29×#103—21no—
158C29×#103—21no—
159C29×#103—21no—
160C29×#103—21no—
161C29×#103—21no—
162C29×#103D411yescharacteristic
163C29×#103D411yescharacteristic
164C29×#102—21no—
165C29×#102—21no—
166C29×#102—21no—
167C29×#102—21no—
168C29×#102—21no—
169C29×#102—21no—
170C29×#102—21no—
171C29×#102—21no—
172C29×#102D411yescharacteristic
173C29×#102D411yescharacteristic
174C29×#101—41no—
175C29×#100—41no—
176C29×#97—21no—
177C29×#97—22no—
178C4×C8×C29—21no—
179C29×#95—41no—
180C24×C29—21no—
181C24×C29—41no—
182#41×C29—21no—
183#41×C29—21no—
184#41×C29—21no—
185#41×C29—21no—
186#41×C29—21no—
187#41×C29—21no—
188#41×C29—24no—
189#41×C29—24no—
190#41×C29—24no—
191#41×C29—24no—
192#41×C29—44no—
193#41×C29—42no—
194#41×C29—42no—
195#41×C29—42no—
196#41×C29—42no—
197#41×C29—44no—
198#41×C29C22×C412yes—
199#41×C29C22×C412yes—
200#41×C29C22×C412yes—
201#41×C29C2×D412yes—
202#41×C29C2×D412yes—
203#41×C29#4112yes—
204C2×Q8×C29—21no—
205C2×Q8×C29—24no—
206C2×Q8×C29—24no—
207C2×Q8×C29—21no—
208C2×Q8×C29—21no—
209C2×Q8×C29—21no—
210C2×Q8×C29—21no—
211C2×Q8×C29—41no—
212C2×Q8×C29—42no—
213C2×Q8×C29—42no—
214C2×Q8×C29C22×C412yes—
215C2×Q8×C29C2×D411yescharacteristic
216C2×Q8×C29C2×D411yescharacteristic
217C2×Q8×C29C2×D411yescharacteristic
218C2×D4×C29—21no—
219C2×D4×C29—21no—
220C2×D4×C29—21no—
221C2×D4×C29—24no—
222C2×D4×C29—24no—
223C2×D4×C29—21no—
224C2×D4×C29—21no—
225C2×D4×C29—21no—
226C2×D4×C29—21no—
227C2×D4×C29—21no—
228C2×D4×C29—42no—
229C2×D4×C29—42no—
230C2×D4×C29—41no—
231C2×D4×C29—41no—
232C2×D4×C29—44no—
233C2×D4×C29—44no—
234C2×D4×C29—41no—
235C2×D4×C29C22×C412yes—
236C2×D4×C29C2×D411yescharacteristic
237C2×D4×C29C2×D411yescharacteristic
238C2×D4×C29C2×D411yescharacteristic
239C22×C4×C29—21no—
240C22×C4×C29—21no—
241C22×C4×C29—21no—
242C22×C4×C29—21no—
243C22×C4×C29—21no—
244C22×C4×C29—21no—
245C22×C4×C29—21no—
246C22×C4×C29—41no—
247C22×C4×C29—41no—
248C22×C4×C29—41no—
249C22×C4×C29—41no—
250C22×C4×C29—41no—
251C22×C4×C29C2411yescharacteristic
252Q16×C29—24no—
253Q16×C29C22⋊C414yescomplemented
254SD16×C29—24no—
255SD16×C29—24no—
256SD16×C29—24no—
257SD16×C29—24no—
258SD16×C29C22⋊C414yescomplemented
259SD16×C29C22⋊C414yescomplemented
260D8×C29—24no—
261D8×C29C22⋊C414yescomplemented
262M16×C29—21no—
263M16×C29—24no—
264M16×C29—21no—
265M16×C29—21no—
266M16×C29—21no—
267M16×C29—21no—
268M16×C29—21no—
269M16×C29—21no—
270M16×C29—42no—
271M16×C29—42no—
272M16×C29C22×C412yes—
273C2×C8×C29—21no—
274C2×C8×C29—21no—
275C2×C8×C29—21no—
276C2×C8×C29—24no—
277C2×C8×C29—21no—
278C2×C8×C29—21no—
279C2×C8×C29—21no—
280C2×C8×C29—42no—
281C2×C8×C29—42no—
282C2×C8×C29C22×C412yes—
283C2×C8×C29C2×D411yescharacteristic
284C2×C8×C29C2×D411yescharacteristic
285C2×C8×C29C2×D411yescharacteristic
286C2×C8×C29C2×D411yescharacteristic
287C2×C8×C29C2×D412yes—
288C4⋊C4×C29—21no—
289C4⋊C4×C29—21no—
290C4⋊C4×C29—21no—
291C4⋊C4×C29—21no—
292C4⋊C4×C29—41no—
293C4⋊C4×C29—41no—
294C4⋊C4×C29C2×D411yescharacteristic
295C4⋊C4×C29C2×D411yescharacteristic
296C22⋊C4×C29—21no—
297C22⋊C4×C29—41no—
298C22⋊C4×C29—41no—
299C22⋊C4×C29—82no—
300C42×C29—21no—
301C42×C29—21no—
302C42×C29—21no—
303C42×C29—41no—
304C42×C29—41no—
305#22464C2911yesmaximal, characteristic, direct product factor, Sylow
306C23×C29—21no—
307C23×C29—21no—
308C23×C29—21no—
309C23×C29—22no—
310C23×C29—44no—
311C23×C29—41no—
312C23×C29—41no—
313C23×C29—81no—
314C23×C29—81no—
315C23×C29—161no—
316C23×C29—161no—
317C23×C29H(5,𝔽2)11yescharacteristic
318Q8×C29—21no—
319Q8×C29—21no—
320Q8×C29—21no—
321Q8×C29—22no—
322Q8×C29—22no—
323Q8×C29—44no—
324Q8×C29—41no—
325Q8×C29—41no—
326Q8×C29C2×C22⋊C412yes—
327Q8×C29C2×C22⋊C412yes—
328Q8×C29C4×D412yes—
329D4×C29—22no—
330D4×C29—22no—
331D4×C29—22no—
332D4×C29—22no—
333D4×C29—22no—
334D4×C29—22no—
335D4×C29—22no—
336D4×C29—22no—
337D4×C29—21no—
338D4×C29—21no—
339D4×C29—21no—
340D4×C29—44no—
341D4×C29—44no—
342D4×C29—44no—
343D4×C29—41no—
344D4×C29—41no—
345D4×C29C2×C22⋊C412yes—
346D4×C29C2×C22⋊C412yes—
347D4×C29C4×D412yes—
348C2×C4×C29—21no—
349C2×C4×C29—21no—
350C2×C4×C29—21no—
351C2×C4×C29—22no—
352C2×C4×C29—22no—
353C2×C4×C29—22no—
354C2×C4×C29—22no—
355C2×C4×C29—22no—
356C2×C4×C29—22no—
357C2×C4×C29—22no—
358C2×C4×C29—21no—
359C2×C4×C29—21no—
360C2×C4×C29—44no—
361C2×C4×C29—44no—
362C2×C4×C29—44no—
363C2×C4×C29—41no—
364C2×C4×C29—41no—
365C2×C4×C29—41no—
366C2×C4×C29—41no—
367C2×C4×C29—41no—
368C2×C4×C29—41no—
369C2×C4×C29—41no—
370C2×C4×C29—81no—
371C2×C4×C29—81no—
372C2×C4×C29—161no—
373C2×C4×C29—161no—
374C2×C4×C29C23×C411yescharacteristic
375C2×C4×C29C22×D411yescharacteristic
376C2×C4×C29C22×D411yescharacteristic
377C2×C4×C29C22×D411yescharacteristic
378C2×C4×C29C2×#4111yescharacteristic
379C2×C4×C29H(5,𝔽2)11yescharacteristic
380C8×C29—22no—
381C8×C29—21no—
382C8×C29—21no—
383C8×C29—41no—
384C8×C29—41no—
385C8×C29—41no—
386C8×C29C2×C22⋊C412yes—
387C8×C29C2×C22⋊C412yes—
388C2×#577C2×C2911yescharacteristic
389C2×#444C2×C2911yescharacteristic, complemented
390#2951C2×C2911yescharacteristic, complemented
391#2898C2×C2911yescharacteristic, complemented
392#2897C2×C2911yescharacteristic, complemented
393#1977C2×C2911yescharacteristic, complemented
394#1973C2×C2911yescharacteristic, complemented
395#1908C2×C2911yescharacteristic, complemented
396#1907C2×C2911yescharacteristic, complemented
397#1883C2×C2911yescharacteristic, complemented
398#1882C2×C2911yescharacteristic, complemented
399#1816C2×C2911yescharacteristic, complemented
400#1793C2×C2911yescharacteristic, complemented
401#1792C2×C2911yescharacteristic, complemented
402#1765C2×C2911yescharacteristic, complemented
403C22×C29—21no—
404C22×C29—21no—
405C22×C29—22no—
406C22×C29—22no—
407C22×C29—22no—
408C22×C29—41no—
409C22×C29—41no—
410C22×C29—41no—
411C22×C29—41no—
412C22×C29—41no—
413C22×C29—41no—
414C22×C29—42no—
415C22×C29—82no—
416C22×C29—81no—
417C22×C29—81no—
418C22×C29—161no—
419C22×C29—164no—
420C22×C29#51811yescharacteristic
421C22×C29D4211yescharacteristic
422C22×C29#54611yescharacteristic
423C4×C29—22no—
424C4×C29—22no—
425C4×C29—22no—
426C4×C29—42no—
427C4×C29—41no—
428C4×C29—41no—
429C4×C29—81no—
430C4×C29—81no—
431C4×C29—81no—
432C4×C29C22×C22⋊C411yescharacteristic
433C4×C29C2×C4×D411yescharacteristic
434C4×C29D4211yescharacteristic
435C4×C29#54611yescharacteristic
436C2×2−1+4C22×C2911yescharacteristic
437C2×H(5,𝔽2)C22×C2911yescharacteristic
438#577—24no—
439#577C4×C2918yescomplemented
440C2×#137—21no—
441C2×#137C22×C2911yescharacteristic
442C2×AGL(1,ℤ/8)—21no—
443C2×AGL(1,ℤ/8)C22×C2911yescharacteristic
444C2×#135—21no—
445C2×#135C22×C2911yescharacteristic
446C22×SD16—21no—
447C22×SD16C22×C2911yescharacteristic
448C2×#131C22×C2911yescharacteristic
449C2×#131C22×C2911yescharacteristic
450C2×#131C22×C2911yescharacteristic, complemented
451#520C22×C2911yescharacteristic
452#520C22×C2911yescharacteristic, complemented
453#444—24no—
454#440—21no—
455#440—21no—
456C4×Q16—21no—
457C4×D8—21no—
458C2×#108C22×C2911yescharacteristic, complemented
459C2×#107C22×C2911yescharacteristic, complemented
460C2×#104C22×C2911yescharacteristic
461C2×#104C22×C2911yescharacteristic
462C2×#104C22×C2911yescharacteristic, complemented
463#419—21no—
464#419C22×C2911yescharacteristic, complemented
465#418—21no—
466#418C22×C2911yescharacteristic
467#417—21no—
468#417—21no—
469#417C22×C2911yescharacteristic
470#417C22×C2911yescharacteristic
471#417C22×C2911yescharacteristic
472#417C22×C2911yescharacteristic, complemented
473#416—21no—
474#416—21no—
475#416C22×C2911yescharacteristic
476C2×#103—21no—
477C2×#103C22×C2911yescharacteristic, complemented
478C2×#102—21no—
479C2×#102C22×C2911yescharacteristic
480C2×#101C22×C2911yescharacteristic, complemented
481C2×#100C22×C2911yescharacteristic
482#405C22×C2911yescharacteristic, complemented
483C2×#97C22×C2911yescharacteristic, complemented
484#391C22×C2911yescharacteristic, complemented
485#390C22×C2911yescharacteristic
486#343C22×C2911yescharacteristic, complemented
487#343C22×C2911yescharacteristic, complemented
488#341C22×C2911yescharacteristic, complemented
489#339C22×C2911yescharacteristic, complemented
490C2×C29—21no—
491C2×C29—21no—
492C2×C29—42no—
493C2×C29—42no—
494C2×C29—42no—
495C2×C29—82no—
496C2×C29D4×C22⋊C411yescharacteristic
497C2×C29#328811yescharacteristic
498C2×C29#328911yescharacteristic
4992−1+4—22no—
5002−1+4—22no—
5012−1+4—41no—
5022−1+4C2×C4×C2914yescomplemented
503H(5,𝔽2)—22no—
504H(5,𝔽2)—22no—
505H(5,𝔽2)—41no—
506H(5,𝔽2)C2×C4×C2914yescomplemented
507C2×#41—21no—
508C2×#41—21no—
509C2×#41—21no—
510C2×#41—21no—
511C2×#41—41no—
512C2×#41C23×C2911yescharacteristic
513C2×#41C23×C2911yescharacteristic
514C2×#41C23×C2911yescharacteristic
515C22×Q8—21no—
516C22×Q8—21no—
517C22×Q8C23×C2911yescharacteristic
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—41no—
521C22×D4C23×C2911yescharacteristic
522#137—22no—
523#137—28no—
524#137C2×C4×C2914yescomplemented
525AGL(1,ℤ/8)—22no—
526AGL(1,ℤ/8)—28no—
527AGL(1,ℤ/8)C2×C4×C2914yescomplemented
528#135—28no—
529#135C2×C4×C2914yes—
530#135D4×C2914yes—
531C2×Q16—21no—
532C2×Q16D4×C2911yescharacteristic
533C2×SD16—21no—
534C2×SD16—21no—
535C2×SD16—28no—
536C2×SD16—21no—
537C2×SD16—21no—
538C2×SD16—22no—
539C2×SD16C2×C4×C2914yescomplemented
540C2×SD16D4×C2911yescharacteristic
541C2×SD16D4×C2911yescharacteristic
542C2×D8—21no—
543C2×D8D4×C2911yescharacteristic
544#131—22no—
545#131—22no—
546#131—22no—
547#131—41no—
548#131—41no—
549#131C2×C4×C2914yescomplemented
550C2×M16—21no—
551C2×M16—21no—
552C2×M16—21no—
553C2×M16C23×C2911yescharacteristic
554C2×M16C23×C2911yescharacteristic
555C2×M16C23×C2911yescharacteristic
556C2×M16C23×C2911yescharacteristic
557C22×C8—21no—
558C22×C8—21no—
559C22×C8—21no—
560C22×C8C23×C2911yescharacteristic
561C22×C8C23×C2911yescharacteristic
562C4×Q8—21no—
563C4×Q8—21no—
564C4×D4—21no—
565C4×D4—21no—
566C4×D4—41no—
567C4×D4—41no—
568#117—21no—
569#117—21no—
570#117C23×C2911yescharacteristic
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4C23×C2911yescharacteristic
574C2×C4⋊C4C23×C2911yescharacteristic
575C2×C22⋊C4—41no—
576C2×C42C23×C2911yescharacteristic
577#108—22no—
578#107—21no—
579#107—21no—
580#104—22no—
581#104—22no—
582#104—22no—
583#103—21no—
584#103—21no—
585#103—21no—
586#103—21no—
587#103—21no—
588#103—21no—
589#103—21no—
590#103—21no—
591#103D4×C2911yescharacteristic
592#103D4×C2911yescharacteristic
593#102—21no—
594#102—21no—
595#102—21no—
596#102—21no—
597#102—21no—
598#102—21no—
599#102—21no—
600#102—21no—
601#102D4×C2911yescharacteristic
602#102D4×C2911yescharacteristic
603#101—41no—
604#100—41no—
605#97—22no—
606#97—21no—
607C4×C8—21no—
608#95—41no—
609C29#2246411yescharacteristic, direct product factor, Sylow
610C24—21no—
611C24—41no—
612#41—21no—
613#41—21no—
614#41—21no—
615#41—21no—
616#41—21no—
617#41—21no—
618#41—24no—
619#41—24no—
620#41—24no—
621#41—24no—
622#41—44no—
623#41—42no—
624#41—42no—
625#41—42no—
626#41—42no—
627#41—44no—
628#41C22×C4×C2912yes—
629#41C22×C4×C2912yes—
630#41C22×C4×C2912yes—
631#41C2×D4×C2912yes—
632#41C2×D4×C2912yes—
633#41#41×C2912yes—
634C2×Q8—21no—
635C2×Q8—24no—
636C2×Q8—24no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—41no—
642C2×Q8—42no—
643C2×Q8—42no—
644C2×Q8C22×C4×C2912yes—
645C2×Q8C2×D4×C2911yescharacteristic
646C2×Q8C2×D4×C2911yescharacteristic
647C2×Q8C2×D4×C2911yescharacteristic
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—24no—
652C2×D4—24no—
653C2×D4—21no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—42no—
659C2×D4—42no—
660C2×D4—41no—
661C2×D4—41no—
662C2×D4—44no—
663C2×D4—44no—
664C2×D4—41no—
665C2×D4C22×C4×C2912yes—
666C2×D4C2×D4×C2911yescharacteristic
667C2×D4C2×D4×C2911yescharacteristic
668C2×D4C2×D4×C2911yescharacteristic
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—41no—
677C22×C4—41no—
678C22×C4—41no—
679C22×C4—41no—
680C22×C4—41no—
681C22×C4C24×C2911yescharacteristic
682Q16—24no—
683Q16C22⋊C4×C2914yescomplemented
684SD16—24no—
685SD16—24no—
686SD16—24no—
687SD16—24no—
688SD16C22⋊C4×C2914yescomplemented
689SD16C22⋊C4×C2914yescomplemented
690D8—24no—
691D8C22⋊C4×C2914yescomplemented
692M16—21no—
693M16—24no—
694M16—21no—
695M16—21no—
696M16—21no—
697M16—21no—
698M16—21no—
699M16—21no—
700M16—42no—
701M16—42no—
702M16C22×C4×C2912yes—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—24no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—42no—
711C2×C8—42no—
712C2×C8C22×C4×C2912yes—
713C2×C8C2×D4×C2911yescharacteristic
714C2×C8C2×D4×C2911yescharacteristic
715C2×C8C2×D4×C2911yescharacteristic
716C2×C8C2×D4×C2911yescharacteristic
717C2×C8C2×D4×C2912yes—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—41no—
723C4⋊C4—41no—
724C4⋊C4C2×D4×C2911yescharacteristic
725C4⋊C4C2×D4×C2911yescharacteristic
726C22⋊C4—21no—
727C22⋊C4—41no—
728C22⋊C4—41no—
729C22⋊C4—82no—
730C42—21no—
731C42—21no—
732C42—21no—
733C42—41no—
734C42—41no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—22no—
739C23—44no—
740C23—41no—
741C23—41no—
742C23—81no—
743C23—81no—
744C23—161no—
745C23—161no—
746C23C29×H(5,𝔽2)11yescharacteristic
747Q8—21no—
748Q8—21no—
749Q8—21no—
750Q8—22no—
751Q8—22no—
752Q8—44no—
753Q8—41no—
754Q8—41no—
755Q8C2×C22⋊C4×C2912yes—
756Q8C2×C22⋊C4×C2912yes—
757Q8C4×D4×C2912yes—
758D4—22no—
759D4—22no—
760D4—22no—
761D4—22no—
762D4—22no—
763D4—22no—
764D4—22no—
765D4—22no—
766D4—21no—
767D4—21no—
768D4—21no—
769D4—44no—
770D4—44no—
771D4—44no—
772D4—41no—
773D4—41no—
774D4C2×C22⋊C4×C2912yes—
775D4C2×C22⋊C4×C2912yes—
776D4C4×D4×C2912yes—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—81no—
800C2×C4—81no—
801C2×C4—161no—
802C2×C4—161no—
803C2×C4C23×C4×C2911yescharacteristic
804C2×C4C22×D4×C2911yescharacteristic
805C2×C4C22×D4×C2911yescharacteristic
806C2×C4C22×D4×C2911yescharacteristic
807C2×C4C2×#41×C2911yescharacteristic
808C2×C4C29×H(5,𝔽2)11yescharacteristic
809C8—22no—
810C8—21no—
811C8—21no—
812C8—41no—
813C8—41no—
814C8—41no—
815C8C2×C22⋊C4×C2912yes—
816C8C2×C22⋊C4×C2912yes—
817C22—21no—
818C22—21no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—42no—
829C22—82no—
830C22—81no—
831C22—81no—
832C22—161no—
833C22—164no—
834C22C29×#51811yescharacteristic
835C22D42×C2911yescharacteristic
836C22C29×#54611yescharacteristic
837C4—22no—
838C4—22no—
839C4—22no—
840C4—41no—
841C4—41no—
842C4—42no—
843C4—81no—
844C4—81no—
845C4—81no—
846C4C22×C22⋊C4×C2911yescharacteristic
847C4C2×C4×D4×C2911yescharacteristic
848C4D42×C2911yescharacteristic
849C4C29×#54611yescharacteristic
850C2—21no—
851C2—21no—
852C2—42no—
853C2—42no—
854C2—42no—
855C2—82no—
856C2D4×C22⋊C4×C2911yescharacteristic
857C2C29×#328811yescharacteristic
858C2C29×#328911yescharacteristic
subgroupG/H
center, socleC22×C29D42
commutatorC2×C4C23×C4×C29
Frattini, cosocleC22×C4C24×C29
prime radicalC2×C29×#577C2
LCSG ▷ C2×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×#444C2semidirect
3. C29×#2951C2semidirect
4. C29×#2898C2semidirect
5. C29×#2897C2semidirect
6. C29×#1977C2semidirect
7. C29×#1973C2semidirect
8. C29×#1908C2semidirect
9. C29×#1907C2semidirect
10. C29×#1883C2semidirect
11. C29×#1882C2semidirect
12. C29×#1816C2semidirect
13. C29×#1793C2semidirect
14. C29×#1792C2semidirect
15. C29×#1765C2semidirect
19. C29×#577C4semidirect
30. C2×C29×#131C22semidirect
32. C29×#520C22semidirect
38. C2×C29×#108C22semidirect
39. C2×C29×#107C22semidirect
42. C2×C29×#104C22semidirect
44. C29×#419C22semidirect
52. C29×#417C22semidirect
57. C2×C29×#103C22semidirect
60. C2×C29×#101C22semidirect
62. C29×#405C22semidirect
63. C2×C29×#97C22semidirect
64. C29×#391C22semidirect
66. C29×#343C22semidirect
67. C29×#343C22semidirect
68. C29×#341C22semidirect
69. C29×#339C22semidirect
73. C29×2−1+4C2×C4semidirect
77. C29×H(5,𝔽2)C2×C4semidirect
95. C29×#137C2×C4semidirect
98. C29×AGL(1,ℤ/8)C2×C4semidirect
110. C2×SD16×C29C2×C4semidirect
120. C29×#131C2×C4semidirect
253. Q16×C29C22⋊C4semidirect
258. SD16×C29C22⋊C4semidirect
259. SD16×C29C22⋊C4semidirect
261. D8×C29C22⋊C4semidirect
305. #22464C29direct (N × H)
389. C2×#444C2×C29semidirect
390. #2951C2×C29semidirect
391. #2898C2×C29semidirect
392. #2897C2×C29semidirect
393. #1977C2×C29semidirect
394. #1973C2×C29semidirect
395. #1908C2×C29semidirect
396. #1907C2×C29semidirect
397. #1883C2×C29semidirect
398. #1882C2×C29semidirect
399. #1816C2×C29semidirect
400. #1793C2×C29semidirect
401. #1792C2×C29semidirect
402. #1765C2×C29semidirect
439. #577C4×C29semidirect
450. C2×#131C22×C29semidirect
452. #520C22×C29semidirect
458. C2×#108C22×C29semidirect
459. C2×#107C22×C29semidirect
462. C2×#104C22×C29semidirect
464. #419C22×C29semidirect
472. #417C22×C29semidirect
477. C2×#103C22×C29semidirect
480. C2×#101C22×C29semidirect
482. #405C22×C29semidirect
483. C2×#97C22×C29semidirect
484. #391C22×C29semidirect
486. #343C22×C29semidirect
487. #343C22×C29semidirect
488. #341C22×C29semidirect
489. #339C22×C29semidirect
502. 2−1+4C2×C4×C29semidirect
506. H(5,𝔽2)C2×C4×C29semidirect
524. #137C2×C4×C29semidirect
527. AGL(1,ℤ/8)C2×C4×C29semidirect
539. C2×SD16C2×C4×C29semidirect
549. #131C2×C4×C29semidirect
609. C29#22464direct (N × H)
683. Q16C22⋊C4×C29semidirect
688. SD16C22⋊C4×C29semidirect
689. SD16C22⋊C4×C29semidirect
691. D8C22⋊C4×C29semidirect

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×#4442
C29×#29512
C29×#28982
C29×#28972
C29×#19772
C29×#19732
C29×#19082
C29×#19072
C29×#18832
C29×#18822
C29×#18162
C29×#17932
C29×#17922
C29×#17652
#2246429