Finite Group Databasebeta

← C29×#21594 #20316494

Subgroups — C29×#21594 #20316494

Order 7424.

768 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3091C211yesmaximal, characteristic
2C29×#2930C211yesmaximal, characteristic
3C29×#2873C211yesmaximal, characteristic, complemented
4C29×#1929C211yesmaximal, characteristic, complemented
5C29×#1929C211yesmaximal, characteristic, complemented
6C29×#1922C211yesmaximal, characteristic, complemented
7C29×#1922C211yesmaximal, characteristic, complemented
8C29×#1871C211yesmaximal, characteristic
9C29×#1855C211yesmaximal, characteristic, complemented
10C29×#1826C211yesmaximal, characteristic, complemented
11C29×#1773C211yesmaximal, characteristic, complemented
12C29×#1772C211yesmaximal, characteristic, complemented
13C29×#1765C211yesmaximal, characteristic, complemented
14C29×#1764C211yesmaximal, characteristic, complemented
15C29×#1753C211yesmaximal, characteristic, complemented
16C2×C29×#131C2211yescharacteristic
17C22×M16×C29C2211yescharacteristic
18C22×M16×C29C2211yescharacteristic
19C29×#525C2211yescharacteristic
20C2×C29×#117C2211yescharacteristic
21C29×#485C411yescharacteristic, complemented
22C29×#485C411yescharacteristic, complemented
23C29×#484C411yescharacteristic, complemented
24C29×#483C411yescharacteristic, complemented
25C29×#482C411yescharacteristic, complemented
26C29×#482C411yescharacteristic, complemented
27C29×#481C411yescharacteristic, complemented
28C29×#480C411yescharacteristic, complemented
29C29×#436—21no—
30C29×#436—21no—
31C29×#435—21no—
32C29×#435—21no—
33C2×C29×#108C2211yescharacteristic
34C2×C29×#108C2211yescharacteristic
35C29×#427C2211yescharacteristic
36C29×#427C2211yescharacteristic
37C29×#424C2211yescharacteristic
38C2×C29×#104C2211yescharacteristic
39C2×C29×#104C2211yescharacteristic
40C29×#416C2211yescharacteristic
41C29×#416C2211yescharacteristic
42C29×#408C2211yescharacteristic
43C29×#407C2211yescharacteristic
44C2×C29×C22⋊C8C2211yescharacteristic
45C29×#405—21no—
46C29×#405—21no—
47C29×#405C2211yescharacteristic
48C29×#405C2211yescharacteristic
49C29×#405C2211yescharacteristic
50C29×#405C2211yescharacteristic
51C29×#405C2211yescharacteristic
52C4×M16×C29—21no—
53C4×M16×C29—21no—
54C2×C29×#97C2211yescharacteristic
55C2×C4×C8×C29C2211yescharacteristic
56C4×C22⋊C4×C29C2211yescharacteristic
57C29×#341C2211yescharacteristic
58C29×#341C2211yescharacteristic
59C29×#339C2211yescharacteristic
60C29×#339C2211yescharacteristic
61C29×#339C2211yescharacteristic
62C29×#339C2211yescharacteristic
63C29×#339C2211yescharacteristic
64C29×#339C2211yescharacteristic
65C29×#336C2211yescharacteristic
66C29×#336C2211yescharacteristic
67C2×#41×C29C2311yescharacteristic
68C23×C4×C29C2311yescharacteristic
69C29×#131—22no—
70C29×#131—22no—
71C2×M16×C29—21no—
72C2×M16×C29—22no—
73C2×M16×C29—22no—
74C2×M16×C29—21no—
75C2×M16×C29—22no—
76C2×M16×C29—22no—
77C2×M16×C29D411yescharacteristic
78C2×M16×C29D411yescharacteristic
79C2×M16×C29D411yescharacteristic
80C2×M16×C29D411yescharacteristic
81C2×M16×C29C2311yescharacteristic
82C2×M16×C29C2311yescharacteristic
83C2×M16×C29C2311yescharacteristic
84C2×M16×C29C2311yescharacteristic
85C22×C8×C29—21no—
86C22×C8×C29—21no—
87C22×C8×C29C2311yescharacteristic
88C22×C8×C29C2311yescharacteristic
89C22×C8×C29C2311yescharacteristic
90C22×C8×C29C2311yescharacteristic
91C29×#123—21no—
92C29×C22⋊Q8C2×C411yescharacteristic
93C29×C22⋊Q8C2×C411yescharacteristic
94C29×#121C2×C411yescharacteristic
95C29×#121C2×C411yescharacteristic
96C29×#120—21no—
97C4×D4×C29—21no—
98C4×D4×C29—21no—
99C29×#117—21no—
100C29×#117—21no—
101C29×#117C2×C411yescharacteristic
102C29×#117C2×C411yescharacteristic
103C29×#117C2311yescharacteristic
104C29×#117C2311yescharacteristic
105C29×#117C2311yescharacteristic
106C2×C4⋊C4×C29C2×C411yescharacteristic
107C2×C4⋊C4×C29C2×C411yescharacteristic
108C2×C22⋊C4×C29—21no—
109C2×C22⋊C4×C29—21no—
110C2×C42×C29—21no—
111C2×C42×C29C2311yescharacteristic
112C2×C42×C29C2311yescharacteristic
113C29×#108—22no—
114C29×#108—22no—
115C29×#107C2×C411yescharacteristic
116C29×#107C2×C411yescharacteristic
117C29×#107C2×C411yescharacteristic
118C29×#107C2×C411yescharacteristic
119C29×#106C2×C411yescharacteristic
120C29×#106C2×C411yescharacteristic
121C29×#106C2×C411yescharacteristic
122C29×#106C2×C411yescharacteristic
123C29×C4⋊C8—21no—
124C29×C4⋊C8—21no—
125C29×#104—22no—
126C29×#104—22no—
127C29×#103C2×C411yescharacteristic
128C29×#103C2×C411yescharacteristic
129C29×#103C2×C411yescharacteristic
130C29×#103C2×C411yescharacteristic
131C29×#102C2×C411yescharacteristic
132C29×#102C2×C411yescharacteristic
133C29×#102C2×C411yescharacteristic
134C29×#102C2×C411yescharacteristic
135C29×C22⋊C8—21no—
136C29×C22⋊C8—21no—
137C29×C22⋊C8—21no—
138C29×C22⋊C8—21no—
139C29×C22⋊C8C2×C411yescharacteristic
140C29×C22⋊C8C2×C411yescharacteristic
141C29×C22⋊C8C2×C411yescharacteristic
142C29×C22⋊C8C2×C411yescharacteristic
143C29×#97—21no—
144C29×#97—21no—
145C29×#97—21no—
146C29×#97—21no—
147C29×#97—21no—
148C29×#97—22no—
149C4×C8×C29—21no—
150C4×C8×C29—21no—
151C4×C8×C29—21no—
152C4×C8×C29—21no—
153C4×C8×C29—21no—
154C4×C8×C29—22no—
155C29×#95—21no—
156C24×C29#4111yescharacteristic
157#41×C29—21no—
158#41×C29—21no—
159#41×C29—21no—
160#41×C29—21no—
161C2×Q8×C29C22×C411yescharacteristic
162C2×D4×C29—21no—
163C2×D4×C29—21no—
164C2×D4×C29—21no—
165C2×D4×C29C22×C411yescharacteristic
166C22×C4×C29—21no—
167C22×C4×C29—21no—
168C22×C4×C29—21no—
169C22×C4×C29—21no—
170C22×C4×C29—21no—
171C22×C4×C29—21no—
172C22×C4×C29—21no—
173C22×C4×C29—21no—
174C22×C4×C29—21no—
175C22×C4×C29C22×C411yescharacteristic
176C22×C4×C29C22×C411yescharacteristic
177C22×C4×C29C2×D411yescharacteristic
178C22×C4×C29C2×D411yescharacteristic
179C22×C4×C29#4111yescharacteristic
180C22×C4×C29C2411yescharacteristic
181M16×C29—24no—
182M16×C29—21no—
183M16×C29—21no—
184M16×C29—22no—
185M16×C29—22no—
186M16×C29—22no—
187M16×C29—22no—
188M16×C29—21no—
189M16×C29—21no—
190M16×C29—21no—
191M16×C29—21no—
192M16×C29—42no—
193M16×C29#4112yes—
194M16×C29#4112yes—
195C2×C8×C29—24no—
196C2×C8×C29—21no—
197C2×C8×C29—21no—
198C2×C8×C29—21no—
199C2×C8×C29—21no—
200C2×C8×C29—21no—
201C2×C8×C29—21no—
202C2×C8×C29—21no—
203C2×C8×C29—21no—
204C2×C8×C29—21no—
205C2×C8×C29—21no—
206C2×C8×C29—42no—
207C2×C8×C29C22×C411yescharacteristic
208C2×C8×C29C22×C411yescharacteristic
209C2×C8×C29C22×C411yescharacteristic
210C2×C8×C29C22×C411yescharacteristic
211C2×C8×C29C2×D411yescharacteristic
212C2×C8×C29C2×D411yescharacteristic
213C2×C8×C29C2×D411yescharacteristic
214C2×C8×C29C2×D411yescharacteristic
215C2×C8×C29#4112yes—
216C2×C8×C29#4112yes—
217C4⋊C4×C29—21no—
218C4⋊C4×C29—21no—
219C4⋊C4×C29—21no—
220C4⋊C4×C29—21no—
221C4⋊C4×C29C22×C411yescharacteristic
222C4⋊C4×C29C22×C411yescharacteristic
223C4⋊C4×C29C22×C411yescharacteristic
224C4⋊C4×C29C22×C411yescharacteristic
225C4⋊C4×C29C22×C411yescharacteristic
226C4⋊C4×C29C22×C411yescharacteristic
227C22⋊C4×C29—21no—
228C22⋊C4×C29—21no—
229C22⋊C4×C29—21no—
230C22⋊C4×C29—21no—
231C22⋊C4×C29—21no—
232C22⋊C4×C29—21no—
233C22⋊C4×C29—21no—
234C22⋊C4×C29—21no—
235C22⋊C4×C29—21no—
236C22⋊C4×C29—42no—
237C42×C29—21no—
238C42×C29—21no—
239C42×C29—21no—
240C42×C29—21no—
241C42×C29—21no—
242C42×C29—21no—
243C42×C29—21no—
244C42×C29—21no—
245C42×C29—21no—
246#21594C2911yesmaximal, characteristic, direct product factor, Sylow
247C23×C29—21no—
248C23×C29—21no—
249C23×C29—21no—
250C23×C29—41no—
251C23×C29—41no—
252C23×C29C4×D411yescharacteristic
253C23×C29C4×D411yescharacteristic
254C23×C29C2×#4111yescharacteristic
255Q8×C29—21no—
256Q8×C29—21no—
257D4×C29—21no—
258D4×C29—21no—
259D4×C29—41no—
260D4×C29—41no—
261D4×C29—81no—
262D4×C29—81no—
263C2×C4×C29—21no—
264C2×C4×C29—21no—
265C2×C4×C29—21no—
266C2×C4×C29—21no—
267C2×C4×C29—21no—
268C2×C4×C29—21no—
269C2×C4×C29—21no—
270C2×C4×C29—21no—
271C2×C4×C29—21no—
272C2×C4×C29—21no—
273C2×C4×C29—22no—
274C2×C4×C29—21no—
275C2×C4×C29—21no—
276C2×C4×C29—21no—
277C2×C4×C29—21no—
278C2×C4×C29—21no—
279C2×C4×C29—21no—
280C2×C4×C29—21no—
281C2×C4×C29—41no—
282C2×C4×C29—41no—
283C2×C4×C29—41no—
284C2×C4×C29—41no—
285C2×C4×C29—41no—
286C2×C4×C29—41no—
287C2×C4×C29—41no—
288C2×C4×C29—81no—
289C2×C4×C29—81no—
290C2×C4×C29C4×D411yescharacteristic
291C2×C4×C29C4×D411yescharacteristic
292C2×C4×C29C23×C411yescharacteristic
293C2×C4×C29C22×D411yescharacteristic
294C2×C4×C29C2×#4111yescharacteristic
295C2×C4×C29C2×#4111yescharacteristic
296C2×C4×C29C2×#4111yescharacteristic
297C2×C4×C29C2×#4111yescharacteristic
298C8×C29—21no—
299C8×C29—21no—
300C8×C29—21no—
301C8×C29—21no—
302C8×C29—21no—
303C8×C29—21no—
304C8×C29—22no—
305C8×C29—22no—
306C8×C29—41no—
307C8×C29—41no—
308C8×C29#12312yes—
309C8×C29#12312yes—
310#3091C2×C2911yescharacteristic
311#2930C2×C2911yescharacteristic
312#2873C2×C2911yescharacteristic, complemented
313#1929C2×C2911yescharacteristic, complemented
314#1929C2×C2911yescharacteristic, complemented
315#1922C2×C2911yescharacteristic, complemented
316#1922C2×C2911yescharacteristic, complemented
317#1871C2×C2911yescharacteristic
318#1855C2×C2911yescharacteristic, complemented
319#1826C2×C2911yescharacteristic, complemented
320#1773C2×C2911yescharacteristic, complemented
321#1772C2×C2911yescharacteristic, complemented
322#1765C2×C2911yescharacteristic, complemented
323#1764C2×C2911yescharacteristic, complemented
324#1753C2×C2911yescharacteristic, complemented
325C22×C29—21no—
326C22×C29—21no—
327C22×C29—21no—
328C22×C29—21no—
329C22×C29—21no—
330C22×C29—21no—
331C22×C29—21no—
332C22×C29—21no—
333C22×C29—41no—
334C22×C29—41no—
335C22×C29—41no—
336C22×C29—81no—
337C22×C29—81no—
338C22×C29C2×C4×D411yescharacteristic
339C22×C29#52911yescharacteristic
340C22×C29#52911yescharacteristic
341C4×C29—21no—
342C4×C29—21no—
343C4×C29—42no—
344C4×C29—41no—
345C4×C29—41no—
346C4×C29—41no—
347C4×C29—41no—
348C4×C29—41no—
349C4×C29—41no—
350C4×C29—41no—
351C4×C29—81no—
352C4×C29C4×#4111yescharacteristic
353C4×C29C4×#4111yescharacteristic
354C4×C29C2×#12311yescharacteristic
355C4×C29#52511yescharacteristic
356C2×#131C22×C2911yescharacteristic
357C22×M16C22×C2911yescharacteristic
358C22×M16C22×C2911yescharacteristic
359#525C22×C2911yescharacteristic
360C2×#117C22×C2911yescharacteristic
361#485C4×C2911yescharacteristic, complemented
362#485C4×C2911yescharacteristic, complemented
363#484C4×C2911yescharacteristic, complemented
364#483C4×C2911yescharacteristic, complemented
365#482C4×C2911yescharacteristic, complemented
366#482C4×C2911yescharacteristic, complemented
367#481C4×C2911yescharacteristic, complemented
368#480C4×C2911yescharacteristic, complemented
369#436—21no—
370#436—21no—
371#435—21no—
372#435—21no—
373C2×#108C22×C2911yescharacteristic
374C2×#108C22×C2911yescharacteristic
375#427C22×C2911yescharacteristic
376#427C22×C2911yescharacteristic
377#424C22×C2911yescharacteristic
378C2×#104C22×C2911yescharacteristic
379C2×#104C22×C2911yescharacteristic
380#416C22×C2911yescharacteristic
381#416C22×C2911yescharacteristic
382#408C22×C2911yescharacteristic
383#407C22×C2911yescharacteristic
384C2×C22⋊C8C22×C2911yescharacteristic
385#405—21no—
386#405—21no—
387#405C22×C2911yescharacteristic
388#405C22×C2911yescharacteristic
389#405C22×C2911yescharacteristic
390#405C22×C2911yescharacteristic
391#405C22×C2911yescharacteristic
392C4×M16—21no—
393C4×M16—21no—
394C2×#97C22×C2911yescharacteristic
395C2×C4×C8C22×C2911yescharacteristic
396C4×C22⋊C4C22×C2911yescharacteristic
397#341C22×C2911yescharacteristic
398#341C22×C2911yescharacteristic
399#339C22×C2911yescharacteristic
400#339C22×C2911yescharacteristic
401#339C22×C2911yescharacteristic
402#339C22×C2911yescharacteristic
403#339C22×C2911yescharacteristic
404#339C22×C2911yescharacteristic
405#336C22×C2911yescharacteristic
406#336C22×C2911yescharacteristic
407C2×C29—21no—
408C2×C29—21no—
409C2×C29—41no—
410C2×C29—41no—
411C2×C29—81no—
412C2×C29C4×#12311yescharacteristic
413C2×C29#295611yescharacteristic
414C2×C29#295711yescharacteristic
415C2×#41C23×C2911yescharacteristic
416C23×C4C23×C2911yescharacteristic
417#131—22no—
418#131—22no—
419C2×M16—21no—
420C2×M16—22no—
421C2×M16—22no—
422C2×M16—21no—
423C2×M16—22no—
424C2×M16—22no—
425C2×M16D4×C2911yescharacteristic
426C2×M16D4×C2911yescharacteristic
427C2×M16D4×C2911yescharacteristic
428C2×M16D4×C2911yescharacteristic
429C2×M16C23×C2911yescharacteristic
430C2×M16C23×C2911yescharacteristic
431C2×M16C23×C2911yescharacteristic
432C2×M16C23×C2911yescharacteristic
433C22×C8—21no—
434C22×C8—21no—
435C22×C8C23×C2911yescharacteristic
436C22×C8C23×C2911yescharacteristic
437C22×C8C23×C2911yescharacteristic
438C22×C8C23×C2911yescharacteristic
439#123—21no—
440C22⋊Q8C2×C4×C2911yescharacteristic
441C22⋊Q8C2×C4×C2911yescharacteristic
442#121C2×C4×C2911yescharacteristic
443#121C2×C4×C2911yescharacteristic
444#120—21no—
445C4×D4—21no—
446C4×D4—21no—
447#117—21no—
448#117—21no—
449#117C2×C4×C2911yescharacteristic
450#117C2×C4×C2911yescharacteristic
451#117C23×C2911yescharacteristic
452#117C23×C2911yescharacteristic
453#117C23×C2911yescharacteristic
454C2×C4⋊C4C2×C4×C2911yescharacteristic
455C2×C4⋊C4C2×C4×C2911yescharacteristic
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C42—21no—
459C2×C42C23×C2911yescharacteristic
460C2×C42C23×C2911yescharacteristic
461#108—22no—
462#108—22no—
463#107C2×C4×C2911yescharacteristic
464#107C2×C4×C2911yescharacteristic
465#107C2×C4×C2911yescharacteristic
466#107C2×C4×C2911yescharacteristic
467#106C2×C4×C2911yescharacteristic
468#106C2×C4×C2911yescharacteristic
469#106C2×C4×C2911yescharacteristic
470#106C2×C4×C2911yescharacteristic
471C4⋊C8—21no—
472C4⋊C8—21no—
473#104—22no—
474#104—22no—
475#103C2×C4×C2911yescharacteristic
476#103C2×C4×C2911yescharacteristic
477#103C2×C4×C2911yescharacteristic
478#103C2×C4×C2911yescharacteristic
479#102C2×C4×C2911yescharacteristic
480#102C2×C4×C2911yescharacteristic
481#102C2×C4×C2911yescharacteristic
482#102C2×C4×C2911yescharacteristic
483C22⋊C8—21no—
484C22⋊C8—21no—
485C22⋊C8—21no—
486C22⋊C8—21no—
487C22⋊C8C2×C4×C2911yescharacteristic
488C22⋊C8C2×C4×C2911yescharacteristic
489C22⋊C8C2×C4×C2911yescharacteristic
490C22⋊C8C2×C4×C2911yescharacteristic
491#97—21no—
492#97—21no—
493#97—21no—
494#97—21no—
495#97—21no—
496#97—22no—
497C4×C8—21no—
498C4×C8—21no—
499C4×C8—21no—
500C4×C8—21no—
501C4×C8—21no—
502C4×C8—22no—
503#95—21no—
504C29#2159411yescharacteristic, direct product factor, Sylow
505C24#41×C2911yescharacteristic
506#41—21no—
507#41—21no—
508#41—21no—
509#41—21no—
510C2×Q8C22×C4×C2911yescharacteristic
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4C22×C4×C2911yescharacteristic
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4C22×C4×C2911yescharacteristic
525C22×C4C22×C4×C2911yescharacteristic
526C22×C4C2×D4×C2911yescharacteristic
527C22×C4C2×D4×C2911yescharacteristic
528C22×C4#41×C2911yescharacteristic
529C22×C4C24×C2911yescharacteristic
530M16—24no—
531M16—21no—
532M16—21no—
533M16—22no—
534M16—22no—
535M16—22no—
536M16—22no—
537M16—21no—
538M16—21no—
539M16—21no—
540M16—21no—
541M16—42no—
542M16#41×C2912yes—
543M16#41×C2912yes—
544C2×C8—24no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—42no—
556C2×C8C22×C4×C2911yescharacteristic
557C2×C8C22×C4×C2911yescharacteristic
558C2×C8C22×C4×C2911yescharacteristic
559C2×C8C22×C4×C2911yescharacteristic
560C2×C8C2×D4×C2911yescharacteristic
561C2×C8C2×D4×C2911yescharacteristic
562C2×C8C2×D4×C2911yescharacteristic
563C2×C8C2×D4×C2911yescharacteristic
564C2×C8#41×C2912yes—
565C2×C8#41×C2912yes—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4C22×C4×C2911yescharacteristic
571C4⋊C4C22×C4×C2911yescharacteristic
572C4⋊C4C22×C4×C2911yescharacteristic
573C4⋊C4C22×C4×C2911yescharacteristic
574C4⋊C4C22×C4×C2911yescharacteristic
575C4⋊C4C22×C4×C2911yescharacteristic
576C22⋊C4—21no—
577C22⋊C4—21no—
578C22⋊C4—21no—
579C22⋊C4—21no—
580C22⋊C4—21no—
581C22⋊C4—21no—
582C22⋊C4—21no—
583C22⋊C4—21no—
584C22⋊C4—21no—
585C22⋊C4—42no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—21no—
592C42—21no—
593C42—21no—
594C42—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—41no—
599C23—41no—
600C23C4×D4×C2911yescharacteristic
601C23C4×D4×C2911yescharacteristic
602C23C2×#41×C2911yescharacteristic
603Q8—21no—
604Q8—21no—
605D4—21no—
606D4—21no—
607D4—41no—
608D4—41no—
609D4—81no—
610D4—81no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—22no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—81no—
637C2×C4—81no—
638C2×C4C4×D4×C2911yescharacteristic
639C2×C4C4×D4×C2911yescharacteristic
640C2×C4C23×C4×C2911yescharacteristic
641C2×C4C22×D4×C2911yescharacteristic
642C2×C4C2×#41×C2911yescharacteristic
643C2×C4C2×#41×C2911yescharacteristic
644C2×C4C2×#41×C2911yescharacteristic
645C2×C4C2×#41×C2911yescharacteristic
646C8—21no—
647C8—21no—
648C8—21no—
649C8—21no—
650C8—21no—
651C8—21no—
652C8—22no—
653C8—22no—
654C8—41no—
655C8—41no—
656C8C29×#12312yes—
657C8C29×#12312yes—
658C22—21no—
659C22—21no—
660C22—21no—
661C22—21no—
662C22—21no—
663C22—21no—
664C22—21no—
665C22—21no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—81no—
670C22—81no—
671C22C2×C4×D4×C2911yescharacteristic
672C22C29×#52911yescharacteristic
673C22C29×#52911yescharacteristic
674C4—21no—
675C4—21no—
676C4—42no—
677C4—41no—
678C4—41no—
679C4—41no—
680C4—41no—
681C4—41no—
682C4—41no—
683C4—41no—
684C4—81no—
685C4C4×#41×C2911yescharacteristic
686C4C4×#41×C2911yescharacteristic
687C4C2×C29×#12311yescharacteristic
688C4C29×#52511yescharacteristic
689C2—21no—
690C2—21no—
691C2—41no—
692C2—41no—
693C2—81no—
694C2C4×C29×#12311yescharacteristic
695C2C29×#295611yescharacteristic
696C2C29×#295711yescharacteristic
subgroupG/H
centerC2×C4×C29C22×D4
commutatorC2×C4C23×C4×C29
Frattini, cosocleC22×C4C24×C29
socleC22×C29C2×C4×D4
prime radicalC29×#525C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C29 ◁ C22×M16×C29 ◁ G

Complements

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

NH ≅ G/Ntype
3. C29×#2873C2semidirect
4. C29×#1929C2semidirect
5. C29×#1929C2semidirect
6. C29×#1922C2semidirect
7. C29×#1922C2semidirect
9. C29×#1855C2semidirect
10. C29×#1826C2semidirect
11. C29×#1773C2semidirect
12. C29×#1772C2semidirect
13. C29×#1765C2semidirect
14. C29×#1764C2semidirect
15. C29×#1753C2semidirect
21. C29×#485C4semidirect
22. C29×#485C4semidirect
23. C29×#484C4semidirect
24. C29×#483C4semidirect
25. C29×#482C4semidirect
26. C29×#482C4semidirect
27. C29×#481C4semidirect
28. C29×#480C4semidirect
246. #21594C29direct (N × H)
312. #2873C2×C29semidirect
313. #1929C2×C29semidirect
314. #1929C2×C29semidirect
315. #1922C2×C29semidirect
316. #1922C2×C29semidirect
318. #1855C2×C29semidirect
319. #1826C2×C29semidirect
320. #1773C2×C29semidirect
321. #1772C2×C29semidirect
322. #1765C2×C29semidirect
323. #1764C2×C29semidirect
324. #1753C2×C29semidirect
361. #485C4×C29semidirect
362. #485C4×C29semidirect
363. #484C4×C29semidirect
364. #483C4×C29semidirect
365. #482C4×C29semidirect
366. #482C4×C29semidirect
367. #481C4×C29semidirect
368. #480C4×C29semidirect
504. C29#21594direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#30912
C29×#29302
C29×#28732
C29×#19292
C29×#19222
C29×#18712
C29×#18552
C29×#18262
C29×#17732
C29×#17722
C29×#17652
C29×#17642
C29×#17532
#2159429