Finite Group Databasebeta

← C29×#15613 #20310513

Subgroups — C29×#15613 #20310513

Order 7424.

2090 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C29×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×C29×#397C211yesmaximal, characteristic, complemented
3C2×C29×#394C211yesmaximal, characteristic
4C2×C29×#393C211yesmaximal, characteristic, complemented
5C2×C29×#388C211yesmaximal, characteristic, complemented
6C2×C29×#386C211yesmaximal, characteristic
7C29×#1446C211yesmaximal, characteristic, complemented
8C29×#1442C211yesmaximal, characteristic, complemented
9C29×#1441C211yesmaximal, characteristic, complemented
10C29×#1440C211yesmaximal, characteristic, complemented
11C29×#1439C211yesmaximal, characteristic, complemented
12C29×#1438C211yesmaximal, characteristic
13C29×#1437C211yesmaximal, characteristic, complemented
14C29×C4⋊#95C211yesmaximal, characteristic, complemented
15C29×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×Q8×C29C2211yescharacteristic
17C23×D4×C29C2211yescharacteristic
18C24×C4×C29C2211yescharacteristic
19C2×C29×C22⋊Q8—24no—
20C2×C29×C22⋊Q8—24no—
21C2×C29×C22⋊Q8—24no—
22C22×C4⋊C4×C29C2211yescharacteristic
23C22×C4⋊C4×C29C2211yescharacteristic
24C22×C4⋊C4×C29C2211yescharacteristic
25C22×C4⋊C4×C29C2211yescharacteristic
26C22×C22⋊C4×C29C2211yescharacteristic
27C22×C22⋊C4×C29C2211yescharacteristic
28C22×C22⋊C4×C29C2211yescharacteristic
29C22×C22⋊C4×C29C2211yescharacteristic
30C22×C22⋊C4×C29C2211yescharacteristic
31C22×C22⋊C4×C29C2211yescharacteristic
32C22×C22⋊C4×C29C2211yescharacteristic
33C22×C22⋊C4×C29C2211yescharacteristic
34C22×C22⋊C4×C29C2211yescharacteristic
35C22×C22⋊C4×C29C2211yescharacteristic
36C22×C22⋊C4×C29C2211yescharacteristic
37C22×C42×C29C2211yescharacteristic
38C29×#397—24no—
39C29×#394—24no—
40C29×#393—24no—
41C29×#388—24no—
42C29×#386—24no—
43C2×C29×#95C2211yescharacteristic
44C2×C29×#95C2211yescharacteristic
45C2×C29×#95C2211yescharacteristic
46C2×C29×#95C2211yescharacteristic
47C2×C29×#95C2211yescharacteristic
48C2×C29×#95C2211yescharacteristic
49C2×C29×#95C2211yescharacteristic
50C2×C29×#95C2211yescharacteristic
51C2×C29×#95C2211yescharacteristic
52C2×C29×#95C2211yescharacteristic
53C2×C29×#95C2211yescharacteristic
54C2×C29×#95C2211yescharacteristic
55C2×C29×#95C2211yescharacteristic
56C2×C29×#95C2211yescharacteristic
57C2×C29×#95C2211yescharacteristic
58C2×C29×#95C2211yescharacteristic
59C25×C29C2311yescharacteristic
60C25×C29C2311yescharacteristic
61C22×Q8×C29—22no—
62C22×Q8×C29—22no—
63C22×Q8×C29—22no—
64C22×Q8×C29—22no—
65C22×Q8×C29—22no—
66C22×Q8×C29—41no—
67C22×Q8×C29—41no—
68C22×D4×C29—22no—
69C22×D4×C29—22no—
70C22×D4×C29—22no—
71C22×D4×C29—22no—
72C22×D4×C29—22no—
73C22×D4×C29—41no—
74C22×D4×C29—41no—
75C23×C4×C29—22no—
76C23×C4×C29—22no—
77C23×C4×C29—22no—
78C23×C4×C29—22no—
79C23×C4×C29—22no—
80C23×C4×C29—41no—
81C23×C4×C29—41no—
82C23×C4×C29C2311yescharacteristic
83C23×C4×C29C2311yescharacteristic
84C23×C4×C29C2311yescharacteristic
85C23×C4×C29C2311yescharacteristic
86C23×C4×C29C2311yescharacteristic
87C23×C4×C29C2311yescharacteristic
88C23×C4×C29C2311yescharacteristic
89C23×C4×C29C2311yescharacteristic
90C23×C4×C29C2311yescharacteristic
91C23×C4×C29C2311yescharacteristic
92C23×C4×C29C2311yescharacteristic
93C23×C4×C29C2311yescharacteristic
94C23×C4×C29C2311yescharacteristic
95C29×C22⋊Q8—232no—
96C2×C4⋊C4×C29—22no—
97C2×C4⋊C4×C29—22no—
98C2×C4⋊C4×C29—22no—
99C2×C4⋊C4×C29—22no—
100C2×C4⋊C4×C29—22no—
101C2×C4⋊C4×C29—22no—
102C2×C4⋊C4×C29—22no—
103C2×C4⋊C4×C29—22no—
104C2×C4⋊C4×C29—22no—
105C2×C4⋊C4×C29—41no—
106C2×C4⋊C4×C29D414yescomplemented
107C2×C4⋊C4×C29D414yescomplemented
108C2×C22⋊C4×C29—22no—
109C2×C22⋊C4×C29—22no—
110C2×C22⋊C4×C29—22no—
111C2×C22⋊C4×C29—22no—
112C2×C22⋊C4×C29—22no—
113C2×C22⋊C4×C29—22no—
114C2×C22⋊C4×C29—22no—
115C2×C22⋊C4×C29—22no—
116C2×C22⋊C4×C29—22no—
117C2×C22⋊C4×C29—22no—
118C2×C22⋊C4×C29—22no—
119C2×C22⋊C4×C29—22no—
120C2×C22⋊C4×C29—22no—
121C2×C22⋊C4×C29—22no—
122C2×C22⋊C4×C29—22no—
123C2×C22⋊C4×C29—22no—
124C2×C22⋊C4×C29—22no—
125C2×C22⋊C4×C29—22no—
126C2×C22⋊C4×C29—22no—
127C2×C22⋊C4×C29—22no—
128C2×C22⋊C4×C29—22no—
129C2×C22⋊C4×C29—22no—
130C2×C22⋊C4×C29—22no—
131C2×C22⋊C4×C29—22no—
132C2×C22⋊C4×C29—22no—
133C2×C22⋊C4×C29—41no—
134C2×C22⋊C4×C29—41no—
135C2×C22⋊C4×C29—41no—
136C2×C22⋊C4×C29—41no—
137C2×C22⋊C4×C29—41no—
138C2×C22⋊C4×C29—41no—
139C2×C22⋊C4×C29D414yes—
140C2×C22⋊C4×C29D414yes—
141C2×C42×C29—22no—
142C2×C42×C29—22no—
143C2×C42×C29—41no—
144C29×#95—22no—
145C29×#95—22no—
146C29×#95—22no—
147C29×#95—22no—
148C29×#95—22no—
149C29×#95—22no—
150C29×#95—22no—
151C29×#95—22no—
152C29×#95—22no—
153C29×#95—22no—
154C29×#95—22no—
155C29×#95—22no—
156C29×#95—41no—
157C29×#95—41no—
158C29×#95—41no—
159C29×#95—41no—
160C24×C29—21no—
161C24×C29—21no—
162C24×C29—21no—
163C24×C29—21no—
164C24×C29—21no—
165C24×C29—21no—
166C24×C29—21no—
167C24×C29—21no—
168C24×C29—21no—
169C24×C29—21no—
170C24×C29—21no—
171C24×C29—21no—
172C24×C29—21no—
173C24×C29—21no—
174C24×C29—21no—
175C24×C29—21no—
176C24×C29—21no—
177C24×C29—21no—
178C24×C29—21no—
179C24×C29—21no—
180C24×C29—21no—
181C24×C29—21no—
182C24×C29—21no—
183C24×C29—21no—
184C24×C29—21no—
185C24×C29—21no—
186C24×C29C2×D412yes—
187C24×C29C2×D412yes—
188C24×C29#4112yes—
189C24×C29#4112yes—
190C24×C29C2411yescharacteristic
191C2×Q8×C29—28no—
192C2×Q8×C29—44no—
193C2×Q8×C29—44no—
194C2×Q8×C29—44no—
195C2×Q8×C29—44no—
196C2×Q8×C29—44no—
197C2×Q8×C29—44no—
198C2×D4×C29—28no—
199C2×D4×C29—44no—
200C2×D4×C29—44no—
201C2×D4×C29—44no—
202C2×D4×C29—44no—
203C2×D4×C29—44no—
204C2×D4×C29—44no—
205C22×C4×C29—21no—
206C22×C4×C29—21no—
207C22×C4×C29—21no—
208C22×C4×C29—21no—
209C22×C4×C29—21no—
210C22×C4×C29—21no—
211C22×C4×C29—21no—
212C22×C4×C29—21no—
213C22×C4×C29—28no—
214C22×C4×C29—21no—
215C22×C4×C29—21no—
216C22×C4×C29—21no—
217C22×C4×C29—21no—
218C22×C4×C29—21no—
219C22×C4×C29—21no—
220C22×C4×C29—21no—
221C22×C4×C29—21no—
222C22×C4×C29—21no—
223C22×C4×C29—21no—
224C22×C4×C29—21no—
225C22×C4×C29—21no—
226C22×C4×C29—21no—
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—21no—
237C22×C4×C29—21no—
238C22×C4×C29—21no—
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—21no—
247C22×C4×C29—21no—
248C22×C4×C29—21no—
249C22×C4×C29—21no—
250C22×C4×C29—21no—
251C22×C4×C29—21no—
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—21no—
260C22×C4×C29—21no—
261C22×C4×C29—21no—
262C22×C4×C29—21no—
263C22×C4×C29—21no—
264C22×C4×C29—21no—
265C22×C4×C29—21no—
266C22×C4×C29—21no—
267C22×C4×C29—21no—
268C22×C4×C29—21no—
269C22×C4×C29—21no—
270C22×C4×C29—21no—
271C22×C4×C29—21no—
272C22×C4×C29—21no—
273C22×C4×C29—21no—
274C22×C4×C29—21no—
275C22×C4×C29—21no—
276C22×C4×C29—21no—
277C22×C4×C29—21no—
278C22×C4×C29—21no—
279C22×C4×C29—21no—
280C22×C4×C29—21no—
281C22×C4×C29—21no—
282C22×C4×C29—21no—
283C22×C4×C29—21no—
284C22×C4×C29—44no—
285C22×C4×C29—44no—
286C22×C4×C29—44no—
287C22×C4×C29—44no—
288C22×C4×C29—44no—
289C22×C4×C29—44no—
290C22×C4×C29C2×D412yes—
291C22×C4×C29C2×D412yes—
292C22×C4×C29C2×D412yes—
293C22×C4×C29C2×D412yes—
294C22×C4×C29C2×D412yes—
295C22×C4×C29C2×D412yes—
296C22×C4×C29C2×D412yes—
297C22×C4×C29C2×D412yes—
298C22×C4×C29C2×D412yes—
299C22×C4×C29C2×D412yes—
300C22×C4×C29#4112yes—
301C22×C4×C29#4112yes—
302C22×C4×C29#4112yes—
303C4⋊C4×C29—28no—
304C4⋊C4×C29—28no—
305C4⋊C4×C29—28no—
306C4⋊C4×C29—44no—
307C22⋊C4×C29—28no—
308C22⋊C4×C29—28no—
309C22⋊C4×C29—28no—
310C22⋊C4×C29—44no—
311C22⋊C4×C29—44no—
312C22⋊C4×C29—44no—
313C22⋊C4×C29—44no—
314C22⋊C4×C29—44no—
315C22⋊C4×C29—44no—
316C22⋊C4×C29—44no—
317C22⋊C4×C29—44no—
318C42×C29—44no—
319#15613C2911yesmaximal, characteristic, direct product factor, Sylow
320C23×C29—22no—
321C23×C29—22no—
322C23×C29—22no—
323C23×C29—22no—
324C23×C29—22no—
325C23×C29—22no—
326C23×C29—22no—
327C23×C29—22no—
328C23×C29—22no—
329C23×C29—22no—
330C23×C29—22no—
331C23×C29—22no—
332C23×C29—22no—
333C23×C29—22no—
334C23×C29—22no—
335C23×C29—22no—
336C23×C29—22no—
337C23×C29—22no—
338C23×C29—22no—
339C23×C29—22no—
340C23×C29—22no—
341C23×C29—22no—
342C23×C29—22no—
343C23×C29—22no—
344C23×C29—22no—
345C23×C29—41no—
346C23×C29—41no—
347C23×C29—41no—
348C23×C29—41no—
349C23×C29—41no—
350C23×C29—41no—
351C23×C29—41no—
352C23×C29—41no—
353C23×C29—41no—
354C23×C29—41no—
355C23×C29—41no—
356C23×C29—41no—
357C23×C29—41no—
358C23×C29—41no—
359C23×C29—41no—
360C23×C29—41no—
361C23×C29—41no—
362C23×C29—41no—
363C23×C29—41no—
364C23×C29—41no—
365C23×C29—41no—
366C23×C29—41no—
367C23×C29—41no—
368C23×C29—41no—
369C23×C29—41no—
370C23×C29—41no—
371C23×C29—41no—
372C23×C29—41no—
373C23×C29—41no—
374C23×C29—41no—
375C23×C29—41no—
376C23×C29—41no—
377C23×C29—41no—
378C23×C29—41no—
379C23×C29—41no—
380C23×C29—41no—
381C23×C29—41no—
382C23×C29—41no—
383C23×C29—41no—
384C23×C29—41no—
385C23×C29—41no—
386C23×C29—41no—
387C23×C29—41no—
388C23×C29—41no—
389C23×C29#12414yes—
390C23×C29C22×D411yescharacteristic
391C23×C29C22×D411yescharacteristic
392C23×C29C22×D411yescharacteristic
393C23×C29C22×D411yescharacteristic
394C23×C29C2×#4111yescharacteristic
395C23×C29C2×#4111yescharacteristic
396C23×C29C2×#4111yescharacteristic
397C23×C29C2×#4111yescharacteristic
398C23×C29C2×#4111yescharacteristic
399C23×C29H(5,𝔽2)11yescharacteristic
400C23×C29H(5,𝔽2)11yescharacteristic
401C23×C29H(5,𝔽2)11yescharacteristic
402C23×C292−1+411yescharacteristic
403C23×C292−1+411yescharacteristic
404C23×C292−1+411yescharacteristic
405Q8×C29—416no—
406D4×C29—416no—
407C2×C4×C29—22no—
408C2×C4×C29—22no—
409C2×C4×C29—22no—
410C2×C4×C29—22no—
411C2×C4×C29—22no—
412C2×C4×C29—22no—
413C2×C4×C29—22no—
414C2×C4×C29—22no—
415C2×C4×C29—22no—
416C2×C4×C29—22no—
417C2×C4×C29—22no—
418C2×C4×C29—22no—
419C2×C4×C29—22no—
420C2×C4×C29—22no—
421C2×C4×C29—22no—
422C2×C4×C29—22no—
423C2×C4×C29—22no—
424C2×C4×C29—22no—
425C2×C4×C29—22no—
426C2×C4×C29—22no—
427C2×C4×C29—22no—
428C2×C4×C29—22no—
429C2×C4×C29—22no—
430C2×C4×C29—22no—
431C2×C4×C29—22no—
432C2×C4×C29—22no—
433C2×C4×C29—22no—
434C2×C4×C29—22no—
435C2×C4×C29—22no—
436C2×C4×C29—22no—
437C2×C4×C29—22no—
438C2×C4×C29—22no—
439C2×C4×C29—22no—
440C2×C4×C29—416no—
441C2×C4×C29—41no—
442C2×C4×C29—41no—
443C2×C4×C29—41no—
444C2×C4×C29—41no—
445C2×C4×C29—41no—
446C2×C4×C29—41no—
447C2×C4×C29—41no—
448C2×C4×C29—41no—
449C2×C4×C29—41no—
450C2×C4×C29—41no—
451C2×C4×C29—41no—
452C2×C4×C29—41no—
453C2×C4×C29—41no—
454C2×C4×C29—41no—
455C2×C4×C29—41no—
456C2×C4×C29—41no—
457C2×C4×C29—41no—
458C2×C4×C29—41no—
459C2×C4×C29—41no—
460C2×C4×C29—41no—
461C2×C4×C29—41no—
462C2×C4×C29—41no—
463C2×C4×C29—41no—
464C2×C4×C29—41no—
465C2×C4×C29—41no—
466C2×C4×C29—41no—
467C2×C4×C29—41no—
468C2×C4×C29—41no—
469C2×C4×C29—41no—
470C2×C4×C29—41no—
471C2×C4×C29—41no—
472C2×C4×C29—41no—
473C2×C4×C29—41no—
474C2×C4×C29—41no—
475C2×C4×C29—41no—
476C2×C4×C29—41no—
477C2×C4×C29—41no—
478C2×C4×C29—41no—
479C2×C4×C29—41no—
480C2×C4×C29—41no—
481C2×C4×C29—41no—
482C2×C4×C29—41no—
483C2×C4×C29—41no—
484C2×C4×C29—41no—
485C2×C4×C29—41no—
486C2×C4×C29—41no—
487C2×C4×C29—41no—
488C2×C4×C29—41no—
489C2×C4×C29—41no—
490C2×C4×C29—41no—
491C2×C4×C29—41no—
492C2×C4×C29—41no—
493C2×C4×C29—41no—
494C2×C4×C29—41no—
495C2×C4×C29—41no—
496C2×C4×C29—41no—
497C2×C4×C29#12014yes—
498C2×C4×C29#12114yes—
499C22×C22⋊Q8C2×C2911yescharacteristic, complemented
500C2×#397C2×C2911yescharacteristic, complemented
501C2×#394C2×C2911yescharacteristic
502C2×#393C2×C2911yescharacteristic, complemented
503C2×#388C2×C2911yescharacteristic, complemented
504C2×#386C2×C2911yescharacteristic
505#1446C2×C2911yescharacteristic, complemented
506#1442C2×C2911yescharacteristic, complemented
507#1441C2×C2911yescharacteristic, complemented
508#1440C2×C2911yescharacteristic, complemented
509#1439C2×C2911yescharacteristic, complemented
510#1438C2×C2911yescharacteristic
511#1437C2×C2911yescharacteristic, complemented
512C4⋊#95C2×C2911yescharacteristic, complemented
513C22⋊#95C2×C2911yescharacteristic, complemented
514C22×C29—24no—
515C22×C29—24no—
516C22×C29—24no—
517C22×C29—42no—
518C22×C29—42no—
519C22×C29—42no—
520C22×C29—42no—
521C22×C29—42no—
522C22×C29—42no—
523C22×C29—42no—
524C22×C29—42no—
525C22×C29—42no—
526C22×C29—42no—
527C22×C29—42no—
528C22×C29—42no—
529C22×C29—42no—
530C22×C29—42no—
531C22×C29—42no—
532C22×C29—42no—
533C22×C29—42no—
534C22×C29—42no—
535C22×C29—42no—
536C22×C29—81no—
537C22×C29—81no—
538C22×C29—81no—
539C22×C29—81no—
540C22×C29—81no—
541C22×C29—81no—
542C22×C29—81no—
543C22×C29—81no—
544C22×C29C2×#12011yescharacteristic
545C22×C29C2×#12111yescharacteristic
546C22×C29#52511yescharacteristic
547C22×C29C2×#12411yescharacteristic
548C22×C29#52911yescharacteristic
549C22×C29#53211yescharacteristic
550C22×C29#53511yescharacteristic
551C22×C29#53611yescharacteristic
552C22×C29#53611yescharacteristic
553C22×C29#53711yescharacteristic
554C22×C29#53811yescharacteristic
555C22×C29#53911yescharacteristic
556C22×C29#53911yescharacteristic
557C22×C29#54211yescharacteristic
558C22×C29#54211yescharacteristic
559C22×C29D4211yescharacteristic
560C22×C29D4211yescharacteristic
561C22×C29#54611yescharacteristic
562C22×C29#54611yescharacteristic
563C22×C29#54611yescharacteristic
564C22×C29#54611yescharacteristic
565C22×C29#54611yescharacteristic
566C22×C29#54711yescharacteristic
567C22×C29#54711yescharacteristic
568C22×C29#54711yescharacteristic
569C22×C29#54811yescharacteristic
570C22×C29#54811yescharacteristic
571C22×C29#54811yescharacteristic
572C22×C29#54811yescharacteristic
573C22×C29#55111yescharacteristic
574C22×C29#55111yescharacteristic
575C22×C29#55211yescharacteristic
576C22×C29#55611yescharacteristic
577C22×C29#56211yescharacteristic
578C22×C29#56311yescharacteristic
579C4×C29—24no—
580C4×C29—24no—
581C4×C29—42no—
582C4×C29—42no—
583C4×C29—42no—
584C4×C29—42no—
585C4×C29—42no—
586C4×C29—42no—
587C4×C29—42no—
588C4×C29—81no—
589C4×C29—81no—
590C4×C29—81no—
591C4×C29—81no—
592C23×Q8C22×C2911yescharacteristic
593C23×D4C22×C2911yescharacteristic
594C24×C4C22×C2911yescharacteristic
595C2×C22⋊Q8—24no—
596C2×C22⋊Q8—24no—
597C2×C22⋊Q8—24no—
598C22×C4⋊C4C22×C2911yescharacteristic
599C22×C4⋊C4C22×C2911yescharacteristic
600C22×C4⋊C4C22×C2911yescharacteristic
601C22×C4⋊C4C22×C2911yescharacteristic
602C22×C22⋊C4C22×C2911yescharacteristic
603C22×C22⋊C4C22×C2911yescharacteristic
604C22×C22⋊C4C22×C2911yescharacteristic
605C22×C22⋊C4C22×C2911yescharacteristic
606C22×C22⋊C4C22×C2911yescharacteristic
607C22×C22⋊C4C22×C2911yescharacteristic
608C22×C22⋊C4C22×C2911yescharacteristic
609C22×C22⋊C4C22×C2911yescharacteristic
610C22×C22⋊C4C22×C2911yescharacteristic
611C22×C22⋊C4C22×C2911yescharacteristic
612C22×C22⋊C4C22×C2911yescharacteristic
613C22×C42C22×C2911yescharacteristic
614#397—24no—
615#394—24no—
616#393—24no—
617#388—24no—
618#386—24no—
619C2×#95C22×C2911yescharacteristic
620C2×#95C22×C2911yescharacteristic
621C2×#95C22×C2911yescharacteristic
622C2×#95C22×C2911yescharacteristic
623C2×#95C22×C2911yescharacteristic
624C2×#95C22×C2911yescharacteristic
625C2×#95C22×C2911yescharacteristic
626C2×#95C22×C2911yescharacteristic
627C2×#95C22×C2911yescharacteristic
628C2×#95C22×C2911yescharacteristic
629C2×#95C22×C2911yescharacteristic
630C2×#95C22×C2911yescharacteristic
631C2×#95C22×C2911yescharacteristic
632C2×#95C22×C2911yescharacteristic
633C2×#95C22×C2911yescharacteristic
634C2×#95C22×C2911yescharacteristic
635C2×C29—44no—
636C2×C29—82no—
637C2×C29#240811yescharacteristic
638C2×C29#241511yescharacteristic
639C2×C29#242711yescharacteristic
640C2×C29#243011yescharacteristic
641C2×C29#243611yescharacteristic
642C2×C29#246111yescharacteristic
643C2×C29#247211yescharacteristic
644C2×C29#248811yescharacteristic
645C2×C29#256011yescharacteristic
646C2×C29#268011yescharacteristic
647C2×C29#268111yescharacteristic
648C2×C29#269611yescharacteristic
649C2×C29#270011yescharacteristic
650C2×C29#270211yescharacteristic
651C2×C29#272311yescharacteristic
652C25C23×C2911yescharacteristic
653C25C23×C2911yescharacteristic
654C22×Q8—22no—
655C22×Q8—22no—
656C22×Q8—22no—
657C22×Q8—22no—
658C22×Q8—22no—
659C22×Q8—41no—
660C22×Q8—41no—
661C22×D4—22no—
662C22×D4—22no—
663C22×D4—22no—
664C22×D4—22no—
665C22×D4—22no—
666C22×D4—41no—
667C22×D4—41no—
668C23×C4—22no—
669C23×C4—22no—
670C23×C4—22no—
671C23×C4—22no—
672C23×C4—22no—
673C23×C4—41no—
674C23×C4—41no—
675C23×C4C23×C2911yescharacteristic
676C23×C4C23×C2911yescharacteristic
677C23×C4C23×C2911yescharacteristic
678C23×C4C23×C2911yescharacteristic
679C23×C4C23×C2911yescharacteristic
680C23×C4C23×C2911yescharacteristic
681C23×C4C23×C2911yescharacteristic
682C23×C4C23×C2911yescharacteristic
683C23×C4C23×C2911yescharacteristic
684C23×C4C23×C2911yescharacteristic
685C23×C4C23×C2911yescharacteristic
686C23×C4C23×C2911yescharacteristic
687C23×C4C23×C2911yescharacteristic
688C22⋊Q8—232no—
689C2×C4⋊C4—22no—
690C2×C4⋊C4—22no—
691C2×C4⋊C4—22no—
692C2×C4⋊C4—22no—
693C2×C4⋊C4—22no—
694C2×C4⋊C4—22no—
695C2×C4⋊C4—22no—
696C2×C4⋊C4—22no—
697C2×C4⋊C4—22no—
698C2×C4⋊C4—41no—
699C2×C4⋊C4D4×C2914yescomplemented
700C2×C4⋊C4D4×C2914yescomplemented
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—22no—
709C2×C22⋊C4—22no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4—22no—
715C2×C22⋊C4—22no—
716C2×C22⋊C4—22no—
717C2×C22⋊C4—22no—
718C2×C22⋊C4—22no—
719C2×C22⋊C4—22no—
720C2×C22⋊C4—22no—
721C2×C22⋊C4—22no—
722C2×C22⋊C4—22no—
723C2×C22⋊C4—22no—
724C2×C22⋊C4—22no—
725C2×C22⋊C4—22no—
726C2×C22⋊C4—41no—
727C2×C22⋊C4—41no—
728C2×C22⋊C4—41no—
729C2×C22⋊C4—41no—
730C2×C22⋊C4—41no—
731C2×C22⋊C4—41no—
732C2×C22⋊C4D4×C2914yes—
733C2×C22⋊C4D4×C2914yes—
734C2×C42—22no—
735C2×C42—22no—
736C2×C42—41no—
737#95—22no—
738#95—22no—
739#95—22no—
740#95—22no—
741#95—22no—
742#95—22no—
743#95—22no—
744#95—22no—
745#95—22no—
746#95—22no—
747#95—22no—
748#95—22no—
749#95—41no—
750#95—41no—
751#95—41no—
752#95—41no—
753C29#1561311yescharacteristic, direct product factor, Sylow
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24—21no—
778C24—21no—
779C24—21no—
780C24C2×D4×C2912yes—
781C24C2×D4×C2912yes—
782C24#41×C2912yes—
783C24#41×C2912yes—
784C24C24×C2911yescharacteristic
785C2×Q8—28no—
786C2×Q8—44no—
787C2×Q8—44no—
788C2×Q8—44no—
789C2×Q8—44no—
790C2×Q8—44no—
791C2×Q8—44no—
792C2×D4—28no—
793C2×D4—44no—
794C2×D4—44no—
795C2×D4—44no—
796C2×D4—44no—
797C2×D4—44no—
798C2×D4—44no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—28no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—44no—
879C22×C4—44no—
880C22×C4—44no—
881C22×C4—44no—
882C22×C4—44no—
883C22×C4—44no—
884C22×C4C2×D4×C2912yes—
885C22×C4C2×D4×C2912yes—
886C22×C4C2×D4×C2912yes—
887C22×C4C2×D4×C2912yes—
888C22×C4C2×D4×C2912yes—
889C22×C4C2×D4×C2912yes—
890C22×C4C2×D4×C2912yes—
891C22×C4C2×D4×C2912yes—
892C22×C4C2×D4×C2912yes—
893C22×C4C2×D4×C2912yes—
894C22×C4#41×C2912yes—
895C22×C4#41×C2912yes—
896C22×C4#41×C2912yes—
897C4⋊C4—28no—
898C4⋊C4—28no—
899C4⋊C4—28no—
900C4⋊C4—44no—
901C22⋊C4—28no—
902C22⋊C4—28no—
903C22⋊C4—28no—
904C22⋊C4—44no—
905C22⋊C4—44no—
906C22⋊C4—44no—
907C22⋊C4—44no—
908C22⋊C4—44no—
909C22⋊C4—44no—
910C22⋊C4—44no—
911C22⋊C4—44no—
912C42—44no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23C29×#12414yes—
983C23C22×D4×C2911yescharacteristic
984C23C22×D4×C2911yescharacteristic
985C23C22×D4×C2911yescharacteristic
986C23C22×D4×C2911yescharacteristic
987C23C2×#41×C2911yescharacteristic
988C23C2×#41×C2911yescharacteristic
989C23C2×#41×C2911yescharacteristic
990C23C2×#41×C2911yescharacteristic
991C23C2×#41×C2911yescharacteristic
992C23C29×H(5,𝔽2)11yescharacteristic
993C23C29×H(5,𝔽2)11yescharacteristic
994C23C29×H(5,𝔽2)11yescharacteristic
995C23C29×2−1+411yescharacteristic
996C23C29×2−1+411yescharacteristic
997C23C29×2−1+411yescharacteristic
998Q8—416no—
999D4—416no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—416no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4C29×#12014yes—
1091C2×C4C29×#12114yes—
1092C22—24no—
1093C22—24no—
1094C22—24no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—81no—
1115C22—81no—
1116C22—81no—
1117C22—81no—
1118C22—81no—
1119C22—81no—
1120C22—81no—
1121C22—81no—
1122C22C2×C29×#12011yescharacteristic
1123C22C2×C29×#12111yescharacteristic
1124C22C29×#52511yescharacteristic
1125C22C2×C29×#12411yescharacteristic
1126C22C29×#52911yescharacteristic
1127C22C29×#53211yescharacteristic
1128C22C29×#53511yescharacteristic
1129C22C29×#53611yescharacteristic
1130C22C29×#53611yescharacteristic
1131C22C29×#53711yescharacteristic
1132C22C29×#53811yescharacteristic
1133C22C29×#53911yescharacteristic
1134C22C29×#53911yescharacteristic
1135C22C29×#54211yescharacteristic
1136C22C29×#54211yescharacteristic
1137C22D42×C2911yescharacteristic
1138C22D42×C2911yescharacteristic
1139C22C29×#54611yescharacteristic
1140C22C29×#54611yescharacteristic
1141C22C29×#54611yescharacteristic
1142C22C29×#54611yescharacteristic
1143C22C29×#54611yescharacteristic
1144C22C29×#54711yescharacteristic
1145C22C29×#54711yescharacteristic
1146C22C29×#54711yescharacteristic
1147C22C29×#54811yescharacteristic
1148C22C29×#54811yescharacteristic
1149C22C29×#54811yescharacteristic
1150C22C29×#54811yescharacteristic
1151C22C29×#55111yescharacteristic
1152C22C29×#55111yescharacteristic
1153C22C29×#55211yescharacteristic
1154C22C29×#55611yescharacteristic
1155C22C29×#56211yescharacteristic
1156C22C29×#56311yescharacteristic
1157C4—24no—
1158C4—24no—
1159C4—42no—
1160C4—42no—
1161C4—42no—
1162C4—42no—
1163C4—42no—
1164C4—42no—
1165C4—42no—
1166C4—81no—
1167C4—81no—
1168C4—81no—
1169C4—81no—
1170C2—44no—
1171C2—82no—
1172C2C29×#240811yescharacteristic
1173C2C29×#241511yescharacteristic
1174C2C29×#242711yescharacteristic
1175C2C29×#243011yescharacteristic
1176C2C29×#243611yescharacteristic
1177C2C29×#246111yescharacteristic
1178C2C29×#247211yescharacteristic
1179C2C29×#248811yescharacteristic
1180C2C29×#256011yescharacteristic
1181C2C29×#268011yescharacteristic
1182C2C29×#268111yescharacteristic
1183C2C29×#269611yescharacteristic
1184C2C29×#270011yescharacteristic
1185C2C29×#270211yescharacteristic
1186C2C29×#272311yescharacteristic
subgroupG/H
center, socleC24×C29C24
commutator, Frattini, cosocleC24C24×C29
prime radicalC23×D4×C29C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C29×C22⋊Q8C2semidirect
2. C2×C29×#397C2semidirect
4. C2×C29×#393C2semidirect
5. C2×C29×#388C2semidirect
7. C29×#1446C2semidirect
8. C29×#1442C2semidirect
9. C29×#1441C2semidirect
10. C29×#1440C2semidirect
11. C29×#1439C2semidirect
13. C29×#1437C2semidirect
14. C29×C4⋊#95C2semidirect
15. C29×C22⋊#95C2semidirect
106. C2×C4⋊C4×C29D4semidirect
107. C2×C4⋊C4×C29D4semidirect
319. #15613C29direct (N × H)
499. C22×C22⋊Q8C2×C29semidirect
500. C2×#397C2×C29semidirect
502. C2×#393C2×C29semidirect
503. C2×#388C2×C29semidirect
505. #1446C2×C29semidirect
506. #1442C2×C29semidirect
507. #1441C2×C29semidirect
508. #1440C2×C29semidirect
509. #1439C2×C29semidirect
511. #1437C2×C29semidirect
512. C4⋊#95C2×C29semidirect
513. C22⋊#95C2×C29semidirect
699. C2×C4⋊C4D4×C29semidirect
700. C2×C4⋊C4D4×C29semidirect
753. C29#15613direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C29×C22⋊Q82
C2×C29×#3972
C2×C29×#3942
C2×C29×#3932
C2×C29×#3882
C2×C29×#3862
C29×#14462
C29×#14422
C29×#14412
C29×#14402
C29×#14392
C29×#14382
C29×#14372
C29×C4⋊#952
C29×C22⋊#952
#1561329