Finite Group Databasebeta

← C29×#14201 #20309101

Subgroups — C29×#14201 #20309101

Order 7424.

2054 conjugacy classes of subgroups.

The subgroup lattice has 1174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#394C211yesmaximal, characteristic
2C2×C29×#390C211yesmaximal, characteristic
3C2×C29×#388C211yesmaximal, characteristic, complemented
4C2×C29×#388C211yesmaximal, characteristic, complemented
5C2×C29×#386C211yesmaximal, characteristic
6C2×C4×C4⋊C4×C29C211yesmaximal, characteristic, complemented
7C2×C4×C22⋊C4×C29C211yesmaximal, characteristic, complemented
8C29×#1441C211yesmaximal, characteristic, complemented
9C29×#1439C211yesmaximal, characteristic, complemented
10C29×#1439C211yesmaximal, characteristic, complemented
11C29×#1437C211yesmaximal, characteristic, complemented
12C29×#1437C211yesmaximal, characteristic, complemented
13C29×#1436C211yesmaximal, characteristic, complemented
14C29×#1436C211yesmaximal, characteristic, complemented
15C29×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C29C2211yescharacteristic
17C24×C4×C29C2211yescharacteristic
18C22×C4⋊C4×C29C2211yescharacteristic
19C22×C4⋊C4×C29C2211yescharacteristic
20C22×C4⋊C4×C29C2211yescharacteristic
21C22×C4⋊C4×C29C2211yescharacteristic
22C22×C22⋊C4×C29C2211yescharacteristic
23C22×C22⋊C4×C29C2211yescharacteristic
24C22×C22⋊C4×C29C2211yescharacteristic
25C22×C22⋊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×C42×C29C2211yescharacteristic
34C22×C42×C29C2211yescharacteristic
35C22×C42×C29C2211yescharacteristic
36C22×C42×C29C2211yescharacteristic
37C29×#394C418yescomplemented
38C29×#390—24no—
39C29×#388—24no—
40C29×#388—24no—
41C29×#386—24no—
42C4×C4⋊C4×C29—24no—
43C4×C22⋊C4×C29—24no—
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
58C25×C29C2311yescharacteristic
59C25×C29C2311yescharacteristic
60C22×D4×C29—22no—
61C22×D4×C29—22no—
62C22×D4×C29—22no—
63C22×D4×C29—22no—
64C22×D4×C29—41no—
65C22×D4×C29—41no—
66C22×D4×C29C2×C414yes—
67C23×C4×C29—22no—
68C23×C4×C29—22no—
69C23×C4×C29—22no—
70C23×C4×C29—22no—
71C23×C4×C29—22no—
72C23×C4×C29—41no—
73C23×C4×C29—41no—
74C23×C4×C29C2311yescharacteristic
75C23×C4×C29C2311yescharacteristic
76C23×C4×C29C2311yescharacteristic
77C23×C4×C29C2311yescharacteristic
78C23×C4×C29C2311yescharacteristic
79C23×C4×C29C2311yescharacteristic
80C23×C4×C29C2311yescharacteristic
81C23×C4×C29C2311yescharacteristic
82C23×C4×C29C2311yescharacteristic
83C23×C4×C29C2311yescharacteristic
84C23×C4×C29C2311yescharacteristic
85C23×C4×C29C2311yescharacteristic
86C23×C4×C29C2311yescharacteristic
87C2×C4⋊C4×C29—22no—
88C2×C4⋊C4×C29—22no—
89C2×C4⋊C4×C29—22no—
90C2×C4⋊C4×C29—22no—
91C2×C4⋊C4×C29—22no—
92C2×C4⋊C4×C29—22no—
93C2×C4⋊C4×C29—22no—
94C2×C4⋊C4×C29—22no—
95C2×C4⋊C4×C29—22no—
96C2×C4⋊C4×C29—22no—
97C2×C4⋊C4×C29—41no—
98C2×C4⋊C4×C29C2×C414yescomplemented
99C2×C22⋊C4×C29—22no—
100C2×C22⋊C4×C29—22no—
101C2×C22⋊C4×C29—22no—
102C2×C22⋊C4×C29—22no—
103C2×C22⋊C4×C29—22no—
104C2×C22⋊C4×C29—22no—
105C2×C22⋊C4×C29—22no—
106C2×C22⋊C4×C29—22no—
107C2×C22⋊C4×C29—22no—
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—41no—
122C2×C22⋊C4×C29—41no—
123C2×C22⋊C4×C29—41no—
124C2×C22⋊C4×C29—41no—
125C2×C22⋊C4×C29—41no—
126C2×C22⋊C4×C29—41no—
127C2×C22⋊C4×C29C2×C414yes—
128C2×C22⋊C4×C29C2×C414yes—
129C2×C22⋊C4×C29C2×C414yescomplemented
130C2×C22⋊C4×C29C2×C414yescomplemented
131C2×C22⋊C4×C29D414yes—
132C2×C42×C29—22no—
133C2×C42×C29—22no—
134C2×C42×C29—22no—
135C2×C42×C29—22no—
136C2×C42×C29—22no—
137C2×C42×C29—22no—
138C2×C42×C29—22no—
139C2×C42×C29—41no—
140C2×C42×C29—41no—
141C2×C42×C29—41no—
142C2×C42×C29—41no—
143C2×C42×C29D414yescomplemented
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—41no—
154C29×#95—41no—
155C29×#95—41no—
156C29×#95C2×C414yescomplemented
157C29×#95D414yes—
158C24×C29—21no—
159C24×C29—21no—
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×C29C22×C412yes—
185C24×C29C22×C412yes—
186C24×C29C2×D412yes—
187C24×C29#4112yes—
188C24×C29C2411yescharacteristic
189C2×D4×C29—28no—
190C2×D4×C29—28no—
191C2×D4×C29—44no—
192C2×D4×C29—44no—
193C2×D4×C29—44no—
194C2×D4×C29—44no—
195C2×D4×C29—44no—
196C22×C4×C29—21no—
197C22×C4×C29—21no—
198C22×C4×C29—21no—
199C22×C4×C29—21no—
200C22×C4×C29—21no—
201C22×C4×C29—21no—
202C22×C4×C29—21no—
203C22×C4×C29—21no—
204C22×C4×C29—21no—
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—28no—
213C22×C4×C29—21no—
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—44no—
270C22×C4×C29—44no—
271C22×C4×C29—44no—
272C22×C4×C29—44no—
273C22×C4×C29—44no—
274C22×C4×C29—44no—
275C22×C4×C29C22×C412yes—
276C22×C4×C29C22×C412yes—
277C22×C4×C29C22×C412yes—
278C22×C4×C29C22×C412yes—
279C22×C4×C29C22×C412yes—
280C22×C4×C29C2×D412yes—
281C22×C4×C29C2×D412yes—
282C22×C4×C29C2×D412yes—
283C22×C4×C29C2×D412yes—
284C22×C4×C29C2×D412yes—
285C22×C4×C29C2×D412yes—
286C22×C4×C29C2×D412yes—
287C22×C4×C29C2×D412yes—
288C22×C4×C29#4112yes—
289C22×C4×C29#4112yes—
290C22×C4×C29#4112yes—
291C22×C4×C29#4112yes—
292C22×C4×C29#4112yes—
293C22×C4×C29#4112yes—
294C4⋊C4×C29—28no—
295C4⋊C4×C29—28no—
296C4⋊C4×C29—44no—
297C4⋊C4×C29—44no—
298C22⋊C4×C29—28no—
299C22⋊C4×C29—28no—
300C22⋊C4×C29—28no—
301C22⋊C4×C29—28no—
302C22⋊C4×C29—44no—
303C22⋊C4×C29—44no—
304C22⋊C4×C29—44no—
305C22⋊C4×C29—44no—
306C22⋊C4×C29—44no—
307C22⋊C4×C29—44no—
308C22⋊C4×C29—44no—
309C42×C29—28no—
310C42×C29—44no—
311C42×C29—44no—
312C42×C29—44no—
313#14201C2911yesmaximal, characteristic, direct product factor, Sylow
314C23×C29—22no—
315C23×C29—22no—
316C23×C29—22no—
317C23×C29—22no—
318C23×C29—22no—
319C23×C29—22no—
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—41no—
340C23×C29—41no—
341C23×C29—41no—
342C23×C29—41no—
343C23×C29—41no—
344C23×C29—41no—
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×C29C4×D414yes—
384C23×C29C23×C411yescharacteristic
385C23×C29C22×D411yescharacteristic
386C23×C29C22×D411yescharacteristic
387C23×C29C22×D411yescharacteristic
388C23×C29C2×#4111yescharacteristic
389C23×C29C2×#4111yescharacteristic
390C23×C29C2×#4111yescharacteristic
391C23×C29C2×#4111yescharacteristic
392C23×C29C2×#4111yescharacteristic
393C23×C29C2×#4111yescharacteristic
394C23×C29C2×#4111yescharacteristic
395C23×C29H(5,𝔽2)11yescharacteristic
396C23×C29H(5,𝔽2)11yescharacteristic
397C23×C29H(5,𝔽2)11yescharacteristic
398C23×C292−1+411yescharacteristic
399D4×C29—416no—
400C2×C4×C29—22no—
401C2×C4×C29—22no—
402C2×C4×C29—22no—
403C2×C4×C29—22no—
404C2×C4×C29—22no—
405C2×C4×C29—22no—
406C2×C4×C29—22no—
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—22no—
441C2×C4×C29—22no—
442C2×C4×C29—22no—
443C2×C4×C29—22no—
444C2×C4×C29—22no—
445C2×C4×C29—416no—
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×C29C4×D414yes—
489C2×C4×C29C4×D414yes—
490C2×C4×C29#12114yes—
491C2×C4×C29#12114yes—
492C2×#394C2×C2911yescharacteristic
493C2×#390C2×C2911yescharacteristic
494C2×#388C2×C2911yescharacteristic, complemented
495C2×#388C2×C2911yescharacteristic, complemented
496C2×#386C2×C2911yescharacteristic
497C2×C4×C4⋊C4C2×C2911yescharacteristic, complemented
498C2×C4×C22⋊C4C2×C2911yescharacteristic, complemented
499#1441C2×C2911yescharacteristic, complemented
500#1439C2×C2911yescharacteristic, complemented
501#1439C2×C2911yescharacteristic, complemented
502#1437C2×C2911yescharacteristic, complemented
503#1437C2×C2911yescharacteristic, complemented
504#1436C2×C2911yescharacteristic, complemented
505#1436C2×C2911yescharacteristic, complemented
506C22⋊#95C2×C2911yescharacteristic, complemented
507C22×C29—24no—
508C22×C29—24no—
509C22×C29—24no—
510C22×C29—42no—
511C22×C29—42no—
512C22×C29—42no—
513C22×C29—42no—
514C22×C29—42no—
515C22×C29—42no—
516C22×C29—42no—
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—81no—
530C22×C29—81no—
531C22×C29—81no—
532C22×C29—81no—
533C22×C29—81no—
534C22×C29—81no—
535C22×C29—81no—
536C22×C29—81no—
537C22×C29C2×C4×D411yescharacteristic
538C22×C29C2×C4×D411yescharacteristic
539C22×C29C2×C4×D411yescharacteristic
540C22×C29C4×#4111yescharacteristic
541C22×C29C4×#4111yescharacteristic
542C22×C29#51811yescharacteristic
543C22×C29#52011yescharacteristic
544C22×C29C2×#12111yescharacteristic
545C22×C29C2×#12111yescharacteristic
546C22×C29#52511yescharacteristic
547C22×C29#52511yescharacteristic
548C22×C29#52911yescharacteristic
549C22×C29#52911yescharacteristic
550C22×C29#53211yescharacteristic
551C22×C29#53211yescharacteristic
552C22×C29#53511yescharacteristic
553C22×C29#53711yescharacteristic
554C22×C29#54011yescharacteristic
555C22×C29#54211yescharacteristic
556C22×C29D4211yescharacteristic
557C22×C29#54611yescharacteristic
558C22×C29#54611yescharacteristic
559C22×C29#54611yescharacteristic
560C22×C29#54611yescharacteristic
561C22×C29#54711yescharacteristic
562C22×C29#54811yescharacteristic
563C22×C29#55111yescharacteristic
564C22×C29#55111yescharacteristic
565C22×C29#55111yescharacteristic
566C22×C29#55211yescharacteristic
567C22×C29#55311yescharacteristic
568C22×C29#55311yescharacteristic
569C22×C29#55611yescharacteristic
570C22×C29#55911yescharacteristic
571C22×C29#55911yescharacteristic
572C4×C29—24no—
573C4×C29—24no—
574C4×C29—24no—
575C4×C29—24no—
576C4×C29—42no—
577C4×C29—42no—
578C4×C29—42no—
579C4×C29—42no—
580C4×C29—42no—
581C4×C29—42no—
582C4×C29—42no—
583C4×C29—81no—
584C4×C29—81no—
585C23×D4C22×C2911yescharacteristic
586C24×C4C22×C2911yescharacteristic
587C22×C4⋊C4C22×C2911yescharacteristic
588C22×C4⋊C4C22×C2911yescharacteristic
589C22×C4⋊C4C22×C2911yescharacteristic
590C22×C4⋊C4C22×C2911yescharacteristic
591C22×C22⋊C4C22×C2911yescharacteristic
592C22×C22⋊C4C22×C2911yescharacteristic
593C22×C22⋊C4C22×C2911yescharacteristic
594C22×C22⋊C4C22×C2911yescharacteristic
595C22×C22⋊C4C22×C2911yescharacteristic
596C22×C22⋊C4C22×C2911yescharacteristic
597C22×C22⋊C4C22×C2911yescharacteristic
598C22×C22⋊C4C22×C2911yescharacteristic
599C22×C22⋊C4C22×C2911yescharacteristic
600C22×C22⋊C4C22×C2911yescharacteristic
601C22×C22⋊C4C22×C2911yescharacteristic
602C22×C42C22×C2911yescharacteristic
603C22×C42C22×C2911yescharacteristic
604C22×C42C22×C2911yescharacteristic
605C22×C42C22×C2911yescharacteristic
606#394C4×C2918yescomplemented
607#390—24no—
608#388—24no—
609#388—24no—
610#386—24no—
611C4×C4⋊C4—24no—
612C4×C22⋊C4—24no—
613C2×#95C22×C2911yescharacteristic
614C2×#95C22×C2911yescharacteristic
615C2×#95C22×C2911yescharacteristic
616C2×#95C22×C2911yescharacteristic
617C2×#95C22×C2911yescharacteristic
618C2×#95C22×C2911yescharacteristic
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×C29—44no—
628C2×C29—82no—
629C2×C29C4×#12111yescharacteristic
630C2×C29C4×#12111yescharacteristic
631C2×C29#232411yescharacteristic
632C2×C29#235811yescharacteristic
633C2×C29#235911yescharacteristic
634C2×C29#236711yescharacteristic
635C2×C29#237411yescharacteristic
636C2×C29#241111yescharacteristic
637C2×C29#241611yescharacteristic
638C2×C29#245811yescharacteristic
639C2×C29#246411yescharacteristic
640C2×C29#251611yescharacteristic
641C2×C29#252111yescharacteristic
642C2×C29#254411yescharacteristic
643C2×C29#260111yescharacteristic
644C25C23×C2911yescharacteristic
645C25C23×C2911yescharacteristic
646C22×D4—22no—
647C22×D4—22no—
648C22×D4—22no—
649C22×D4—22no—
650C22×D4—41no—
651C22×D4—41no—
652C22×D4C2×C4×C2914yes—
653C23×C4—22no—
654C23×C4—22no—
655C23×C4—22no—
656C23×C4—22no—
657C23×C4—22no—
658C23×C4—41no—
659C23×C4—41no—
660C23×C4C23×C2911yescharacteristic
661C23×C4C23×C2911yescharacteristic
662C23×C4C23×C2911yescharacteristic
663C23×C4C23×C2911yescharacteristic
664C23×C4C23×C2911yescharacteristic
665C23×C4C23×C2911yescharacteristic
666C23×C4C23×C2911yescharacteristic
667C23×C4C23×C2911yescharacteristic
668C23×C4C23×C2911yescharacteristic
669C23×C4C23×C2911yescharacteristic
670C23×C4C23×C2911yescharacteristic
671C23×C4C23×C2911yescharacteristic
672C23×C4C23×C2911yescharacteristic
673C2×C4⋊C4—22no—
674C2×C4⋊C4—22no—
675C2×C4⋊C4—22no—
676C2×C4⋊C4—22no—
677C2×C4⋊C4—22no—
678C2×C4⋊C4—22no—
679C2×C4⋊C4—22no—
680C2×C4⋊C4—22no—
681C2×C4⋊C4—22no—
682C2×C4⋊C4—22no—
683C2×C4⋊C4—41no—
684C2×C4⋊C4C2×C4×C2914yescomplemented
685C2×C22⋊C4—22no—
686C2×C22⋊C4—22no—
687C2×C22⋊C4—22no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
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—41no—
708C2×C22⋊C4—41no—
709C2×C22⋊C4—41no—
710C2×C22⋊C4—41no—
711C2×C22⋊C4—41no—
712C2×C22⋊C4—41no—
713C2×C22⋊C4C2×C4×C2914yes—
714C2×C22⋊C4C2×C4×C2914yes—
715C2×C22⋊C4C2×C4×C2914yescomplemented
716C2×C22⋊C4C2×C4×C2914yescomplemented
717C2×C22⋊C4D4×C2914yes—
718C2×C42—22no—
719C2×C42—22no—
720C2×C42—22no—
721C2×C42—22no—
722C2×C42—22no—
723C2×C42—22no—
724C2×C42—22no—
725C2×C42—41no—
726C2×C42—41no—
727C2×C42—41no—
728C2×C42—41no—
729C2×C42D4×C2914yescomplemented
730#95—22no—
731#95—22no—
732#95—22no—
733#95—22no—
734#95—22no—
735#95—22no—
736#95—22no—
737#95—22no—
738#95—22no—
739#95—41no—
740#95—41no—
741#95—41no—
742#95C2×C4×C2914yescomplemented
743#95D4×C2914yes—
744C29#1420111yescharacteristic, direct product factor, Sylow
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
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—
771C24C22×C4×C2912yes—
772C24C22×C4×C2912yes—
773C24C2×D4×C2912yes—
774C24#41×C2912yes—
775C24C24×C2911yescharacteristic
776C2×D4—28no—
777C2×D4—28no—
778C2×D4—44no—
779C2×D4—44no—
780C2×D4—44no—
781C2×D4—44no—
782C2×D4—44no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—28no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
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—44no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—44no—
862C22×C4C22×C4×C2912yes—
863C22×C4C22×C4×C2912yes—
864C22×C4C22×C4×C2912yes—
865C22×C4C22×C4×C2912yes—
866C22×C4C22×C4×C2912yes—
867C22×C4C2×D4×C2912yes—
868C22×C4C2×D4×C2912yes—
869C22×C4C2×D4×C2912yes—
870C22×C4C2×D4×C2912yes—
871C22×C4C2×D4×C2912yes—
872C22×C4C2×D4×C2912yes—
873C22×C4C2×D4×C2912yes—
874C22×C4C2×D4×C2912yes—
875C22×C4#41×C2912yes—
876C22×C4#41×C2912yes—
877C22×C4#41×C2912yes—
878C22×C4#41×C2912yes—
879C22×C4#41×C2912yes—
880C22×C4#41×C2912yes—
881C4⋊C4—28no—
882C4⋊C4—28no—
883C4⋊C4—44no—
884C4⋊C4—44no—
885C22⋊C4—28no—
886C22⋊C4—28no—
887C22⋊C4—28no—
888C22⋊C4—28no—
889C22⋊C4—44no—
890C22⋊C4—44no—
891C22⋊C4—44no—
892C22⋊C4—44no—
893C22⋊C4—44no—
894C22⋊C4—44no—
895C22⋊C4—44no—
896C42—28no—
897C42—44no—
898C42—44no—
899C42—44no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
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—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
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—
969C23C4×D4×C2914yes—
970C23C23×C4×C2911yescharacteristic
971C23C22×D4×C2911yescharacteristic
972C23C22×D4×C2911yescharacteristic
973C23C22×D4×C2911yescharacteristic
974C23C2×#41×C2911yescharacteristic
975C23C2×#41×C2911yescharacteristic
976C23C2×#41×C2911yescharacteristic
977C23C2×#41×C2911yescharacteristic
978C23C2×#41×C2911yescharacteristic
979C23C2×#41×C2911yescharacteristic
980C23C2×#41×C2911yescharacteristic
981C23C29×H(5,𝔽2)11yescharacteristic
982C23C29×H(5,𝔽2)11yescharacteristic
983C23C29×H(5,𝔽2)11yescharacteristic
984C23C29×2−1+411yescharacteristic
985D4—416no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
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—416no—
1032C2×C4—41no—
1033C2×C4—41no—
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×C4C4×D4×C2914yes—
1075C2×C4C4×D4×C2914yes—
1076C2×C4C29×#12114yes—
1077C2×C4C29×#12114yes—
1078C22—24no—
1079C22—24no—
1080C22—24no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—81no—
1101C22—81no—
1102C22—81no—
1103C22—81no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22C2×C4×D4×C2911yescharacteristic
1109C22C2×C4×D4×C2911yescharacteristic
1110C22C2×C4×D4×C2911yescharacteristic
1111C22C4×#41×C2911yescharacteristic
1112C22C4×#41×C2911yescharacteristic
1113C22C29×#51811yescharacteristic
1114C22C29×#52011yescharacteristic
1115C22C2×C29×#12111yescharacteristic
1116C22C2×C29×#12111yescharacteristic
1117C22C29×#52511yescharacteristic
1118C22C29×#52511yescharacteristic
1119C22C29×#52911yescharacteristic
1120C22C29×#52911yescharacteristic
1121C22C29×#53211yescharacteristic
1122C22C29×#53211yescharacteristic
1123C22C29×#53511yescharacteristic
1124C22C29×#53711yescharacteristic
1125C22C29×#54011yescharacteristic
1126C22C29×#54211yescharacteristic
1127C22D42×C2911yescharacteristic
1128C22C29×#54611yescharacteristic
1129C22C29×#54611yescharacteristic
1130C22C29×#54611yescharacteristic
1131C22C29×#54611yescharacteristic
1132C22C29×#54711yescharacteristic
1133C22C29×#54811yescharacteristic
1134C22C29×#55111yescharacteristic
1135C22C29×#55111yescharacteristic
1136C22C29×#55111yescharacteristic
1137C22C29×#55211yescharacteristic
1138C22C29×#55311yescharacteristic
1139C22C29×#55311yescharacteristic
1140C22C29×#55611yescharacteristic
1141C22C29×#55911yescharacteristic
1142C22C29×#55911yescharacteristic
1143C4—24no—
1144C4—24no—
1145C4—24no—
1146C4—24no—
1147C4—42no—
1148C4—42no—
1149C4—42no—
1150C4—42no—
1151C4—42no—
1152C4—42no—
1153C4—42no—
1154C4—81no—
1155C4—81no—
1156C2—44no—
1157C2—82no—
1158C2C4×C29×#12111yescharacteristic
1159C2C4×C29×#12111yescharacteristic
1160C2C29×#232411yescharacteristic
1161C2C29×#235811yescharacteristic
1162C2C29×#235911yescharacteristic
1163C2C29×#236711yescharacteristic
1164C2C29×#237411yescharacteristic
1165C2C29×#241111yescharacteristic
1166C2C29×#241611yescharacteristic
1167C2C29×#245811yescharacteristic
1168C2C29×#246411yescharacteristic
1169C2C29×#251611yescharacteristic
1170C2C29×#252111yescharacteristic
1171C2C29×#254411yescharacteristic
1172C2C29×#260111yescharacteristic
subgroupG/H
center, socleC24×C29C24
commutatorC23C23×C4×C29
Frattini, cosocleC24C24×C29
prime radicalC23×D4×C29C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C29 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C29×#388C2semidirect
4. C2×C29×#388C2semidirect
6. C2×C4×C4⋊C4×C29C2semidirect
7. C2×C4×C22⋊C4×C29C2semidirect
8. C29×#1441C2semidirect
9. C29×#1439C2semidirect
10. C29×#1439C2semidirect
11. C29×#1437C2semidirect
12. C29×#1437C2semidirect
13. C29×#1436C2semidirect
14. C29×#1436C2semidirect
15. C29×C22⋊#95C2semidirect
37. C29×#394C4semidirect
98. C2×C4⋊C4×C29C2×C4semidirect
129. C2×C22⋊C4×C29C2×C4semidirect
130. C2×C22⋊C4×C29C2×C4semidirect
143. C2×C42×C29D4semidirect
156. C29×#95C2×C4semidirect
313. #14201C29direct (N × H)
494. C2×#388C2×C29semidirect
495. C2×#388C2×C29semidirect
497. C2×C4×C4⋊C4C2×C29semidirect
498. C2×C4×C22⋊C4C2×C29semidirect
499. #1441C2×C29semidirect
500. #1439C2×C29semidirect
501. #1439C2×C29semidirect
502. #1437C2×C29semidirect
503. #1437C2×C29semidirect
504. #1436C2×C29semidirect
505. #1436C2×C29semidirect
506. C22⋊#95C2×C29semidirect
606. #394C4×C29semidirect
684. C2×C4⋊C4C2×C4×C29semidirect
715. C2×C22⋊C4C2×C4×C29semidirect
716. C2×C22⋊C4C2×C4×C29semidirect
729. C2×C42D4×C29semidirect
742. #95C2×C4×C29semidirect
744. C29#14201direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#3942
C2×C29×#3902
C2×C29×#3882
C2×C29×#3862
C2×C4×C4⋊C4×C292
C2×C4×C22⋊C4×C292
C29×#14412
C29×#14392
C29×#14372
C29×#14362
C29×C22⋊#952
#1420129