Finite Group Databasebeta

← C29×#14071 #20308971

Subgroups — C29×#14071 #20308971

Order 7424.

2206 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C29×#117C211yesmaximal, characteristic, complemented
2C2×C29×#390C211yesmaximal, characteristic
3C2×C29×#388C211yesmaximal, characteristic, complemented
4C2×C29×#388C211yesmaximal, characteristic, complemented
5C2×C29×#386C211yesmaximal, characteristic
6C29×#1444C211yesmaximal, characteristic, complemented
7C29×#1439C211yesmaximal, characteristic, complemented
8C29×#1439C211yesmaximal, characteristic, complemented
9C29×#1438C211yesmaximal, characteristic
10C29×#1437C211yesmaximal, characteristic, complemented
11C29×#1437C211yesmaximal, characteristic, complemented
12C29×#1436C211yesmaximal, characteristic, complemented
13C29×#1436C211yesmaximal, characteristic, complemented
14C29×C22⋊#95C211yesmaximal, characteristic, complemented
15C4×C29×#95C211yesmaximal, characteristic, complemented
16C23×D4×C29C2211yescharacteristic
17C24×C4×C29C2211yescharacteristic
18C2×C29×#117—24no—
19C2×C29×#117—24no—
20C2×C29×#117—24no—
21C22×C4⋊C4×C29C2211yescharacteristic
22C22×C4⋊C4×C29C2211yescharacteristic
23C22×C4⋊C4×C29C2211yescharacteristic
24C22×C4⋊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×C22⋊C4×C29C2211yescharacteristic
34C22×C22⋊C4×C29C2211yescharacteristic
35C22×C22⋊C4×C29C2211yescharacteristic
36C22×C42×C29C2211yescharacteristic
37C22×C42×C29C2211yescharacteristic
38C22×C42×C29C2211yescharacteristic
39C22×C42×C29C2211yescharacteristic
40C29×#390—24no—
41C29×#388—24no—
42C29×#388—24no—
43C29×#386C418yescomplemented
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—22no—
73C23×C4×C29C2×C414yes—
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
87C29×#117—232no—
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—41no—
97C2×C4⋊C4×C29—41no—
98C2×C4⋊C4×C29—41no—
99C2×C4⋊C4×C29D414yescomplemented
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×C29—41no—
128C2×C22⋊C4×C29—41no—
129C2×C22⋊C4×C29C2×C414yes—
130C2×C22⋊C4×C29C2×C414yes—
131C2×C22⋊C4×C29C2×C414yes—
132C2×C22⋊C4×C29D414yes—
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—22no—
140C2×C42×C29—22no—
141C2×C42×C29—22no—
142C2×C42×C29—41no—
143C2×C42×C29—41no—
144C2×C42×C29D414yescomplemented
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—41no—
155C29×#95—41no—
156C29×#95—41no—
157C29×#95C2×C414yes—
158C29×#95C2×C414yes—
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×C29—21no—
185C24×C29C22×C412yes—
186C24×C29C22×C412yes—
187C24×C29C2×D412yes—
188C24×C29#4112yes—
189C24×C29C2411yescharacteristic
190C2×D4×C29—28no—
191C2×D4×C29—28no—
192C2×D4×C29—44no—
193C2×D4×C29—44no—
194C2×D4×C29—44no—
195C2×D4×C29—44no—
196C2×D4×C29—44no—
197C22×C4×C29—28no—
198C22×C4×C29—28no—
199C22×C4×C29—28no—
200C22×C4×C29—28no—
201C22×C4×C29—28no—
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—21no—
213C22×C4×C29—21no—
214C22×C4×C29—21no—
215C22×C4×C29—21no—
216C22×C4×C29—21no—
217C22×C4×C29—21no—
218C22×C4×C29—28no—
219C22×C4×C29—28no—
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×C29C22×C412yes—
277C22×C4×C29C22×C412yes—
278C22×C4×C29C22×C412yes—
279C22×C4×C29C22×C412yes—
280C22×C4×C29C22×C412yes—
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×C29C2×D412yes—
289C22×C4×C29#4112yes—
290C22×C4×C29#4112yes—
291C22×C4×C29#4112yes—
292C22×C4×C29#4112yes—
293C22×C4×C29#4112yes—
294C22×C4×C29#4112yes—
295C4⋊C4×C29—28no—
296C4⋊C4×C29—28no—
297C4⋊C4×C29—44no—
298C4⋊C4×C29—44no—
299C22⋊C4×C29—28no—
300C22⋊C4×C29—28no—
301C22⋊C4×C29—28no—
302C22⋊C4×C29—28no—
303C22⋊C4×C29—44no—
304C22⋊C4×C29—44no—
305C22⋊C4×C29—44no—
306C22⋊C4×C29—44no—
307C22⋊C4×C29—44no—
308C22⋊C4×C29—44no—
309C22⋊C4×C29—44no—
310C42×C29—28no—
311C42×C29—28no—
312C42×C29—44no—
313C42×C29—44no—
314#14071C2911yesmaximal, characteristic, direct product factor, Sylow
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—22no—
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×C29—41no—
384C23×C29C4×D414yes—
385C23×C29C23×C411yescharacteristic
386C23×C29C22×D411yescharacteristic
387C23×C29C22×D411yescharacteristic
388C23×C29C22×D411yescharacteristic
389C23×C29C2×#4111yescharacteristic
390C23×C29C2×#4111yescharacteristic
391C23×C29C2×#4111yescharacteristic
392C23×C29C2×#4111yescharacteristic
393C23×C29C2×#4111yescharacteristic
394C23×C29C2×#4111yescharacteristic
395C23×C29C2×#4111yescharacteristic
396C23×C29H(5,𝔽2)11yescharacteristic
397C23×C29H(5,𝔽2)11yescharacteristic
398C23×C29H(5,𝔽2)11yescharacteristic
399C23×C292−1+411yescharacteristic
400D4×C29—416no—
401C2×C4×C29—232no—
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—22no—
446C2×C4×C29—22no—
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#11714yescomplemented
490C2×C4×C29C4×D414yes—
491C2×C4×C29C4×D414yes—
492C2×C4×C29#12014yes—
493C22×#117C2×C2911yescharacteristic, complemented
494C2×#390C2×C2911yescharacteristic
495C2×#388C2×C2911yescharacteristic, complemented
496C2×#388C2×C2911yescharacteristic, complemented
497C2×#386C2×C2911yescharacteristic
498#1444C2×C2911yescharacteristic, complemented
499#1439C2×C2911yescharacteristic, complemented
500#1439C2×C2911yescharacteristic, complemented
501#1438C2×C2911yescharacteristic
502#1437C2×C2911yescharacteristic, complemented
503#1437C2×C2911yescharacteristic, complemented
504#1436C2×C2911yescharacteristic, complemented
505#1436C2×C2911yescharacteristic, complemented
506C22⋊#95C2×C2911yescharacteristic, complemented
507C4×#95C2×C2911yescharacteristic, complemented
508C22×C29—24no—
509C22×C29—24no—
510C22×C29—24no—
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—42no—
530C22×C29—81no—
531C22×C29—81no—
532C22×C29—81no—
533C22×C29—81no—
534C22×C29—81no—
535C22×C29—81no—
536C22×C29—81no—
537C22×C29—81no—
538C22×C29C2×#11711yescharacteristic
539C22×C29C2×C4×D411yescharacteristic
540C22×C29C2×C4×D411yescharacteristic
541C22×C29C2×C4×D411yescharacteristic
542C22×C29C4×#4111yescharacteristic
543C22×C29#51811yescharacteristic
544C22×C29#52011yescharacteristic
545C22×C29C2×#12011yescharacteristic
546C22×C29#52511yescharacteristic
547C22×C29#52511yescharacteristic
548C22×C29#52511yescharacteristic
549C22×C29#52911yescharacteristic
550C22×C29#52911yescharacteristic
551C22×C29#53211yescharacteristic
552C22×C29#53211yescharacteristic
553C22×C29#53511yescharacteristic
554C22×C29#53711yescharacteristic
555C22×C29#54011yescharacteristic
556C22×C29#54211yescharacteristic
557C22×C29#54611yescharacteristic
558C22×C29#54611yescharacteristic
559C22×C29#54611yescharacteristic
560C22×C29#54611yescharacteristic
561C22×C29#54711yescharacteristic
562C22×C29#54711yescharacteristic
563C22×C29#55011yescharacteristic
564C22×C29#55011yescharacteristic
565C22×C29#55111yescharacteristic
566C22×C29#55111yescharacteristic
567C22×C29#55111yescharacteristic
568C22×C29#55211yescharacteristic
569C22×C29#55311yescharacteristic
570C22×C29#55511yescharacteristic
571C22×C29#55511yescharacteristic
572C22×C29#55611yescharacteristic
573C4×C29—24no—
574C4×C29—24no—
575C4×C29—24no—
576C4×C29—24no—
577C4×C29—42no—
578C4×C29—42no—
579C4×C29—42no—
580C4×C29—42no—
581C4×C29—42no—
582C4×C29—42no—
583C4×C29—42no—
584C4×C29—81no—
585C4×C29—81no—
586C23×D4C22×C2911yescharacteristic
587C24×C4C22×C2911yescharacteristic
588C2×#117—24no—
589C2×#117—24no—
590C2×#117—24no—
591C22×C4⋊C4C22×C2911yescharacteristic
592C22×C4⋊C4C22×C2911yescharacteristic
593C22×C4⋊C4C22×C2911yescharacteristic
594C22×C4⋊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×C22⋊C4C22×C2911yescharacteristic
603C22×C22⋊C4C22×C2911yescharacteristic
604C22×C22⋊C4C22×C2911yescharacteristic
605C22×C22⋊C4C22×C2911yescharacteristic
606C22×C42C22×C2911yescharacteristic
607C22×C42C22×C2911yescharacteristic
608C22×C42C22×C2911yescharacteristic
609C22×C42C22×C2911yescharacteristic
610#390—24no—
611#388—24no—
612#388—24no—
613#386C4×C2918yescomplemented
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×#95C22×C2911yescharacteristic
628C2×C29—44no—
629C2×C29—82no—
630C2×C29#229311yescharacteristic
631C2×C29C4×#12011yescharacteristic
632C2×C29#232411yescharacteristic
633C2×C29#234211yescharacteristic
634C2×C29#235411yescharacteristic
635C2×C29#235911yescharacteristic
636C2×C29#236311yescharacteristic
637C2×C29#243011yescharacteristic
638C2×C29#243111yescharacteristic
639C2×C29#247111yescharacteristic
640C2×C29#247411yescharacteristic
641C2×C29#247611yescharacteristic
642C2×C29#247911yescharacteristic
643C2×C29#260111yescharacteristic
644C2×C29#261011yescharacteristic
645C25C23×C2911yescharacteristic
646C25C23×C2911yescharacteristic
647C22×D4—22no—
648C22×D4—22no—
649C22×D4—22no—
650C22×D4—22no—
651C22×D4—41no—
652C22×D4—41no—
653C22×D4C2×C4×C2914yes—
654C23×C4—22no—
655C23×C4—22no—
656C23×C4—22no—
657C23×C4—22no—
658C23×C4—22no—
659C23×C4—22no—
660C23×C4C2×C4×C2914yes—
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
673C23×C4C23×C2911yescharacteristic
674#117—232no—
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⋊C4—41no—
685C2×C4⋊C4—41no—
686C2×C4⋊C4D4×C2914yescomplemented
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—22no—
708C2×C22⋊C4—41no—
709C2×C22⋊C4—41no—
710C2×C22⋊C4—41no—
711C2×C22⋊C4—41no—
712C2×C22⋊C4—41no—
713C2×C22⋊C4—41no—
714C2×C22⋊C4—41no—
715C2×C22⋊C4—41no—
716C2×C22⋊C4C2×C4×C2914yes—
717C2×C22⋊C4C2×C4×C2914yes—
718C2×C22⋊C4C2×C4×C2914yes—
719C2×C22⋊C4D4×C2914yes—
720C2×C42—22no—
721C2×C42—22no—
722C2×C42—22no—
723C2×C42—22no—
724C2×C42—22no—
725C2×C42—22no—
726C2×C42—22no—
727C2×C42—22no—
728C2×C42—22no—
729C2×C42—41no—
730C2×C42—41no—
731C2×C42D4×C2914yescomplemented
732#95—22no—
733#95—22no—
734#95—22no—
735#95—22no—
736#95—22no—
737#95—22no—
738#95—22no—
739#95—22no—
740#95—22no—
741#95—41no—
742#95—41no—
743#95—41no—
744#95C2×C4×C2914yes—
745#95C2×C4×C2914yes—
746C29#1407111yescharacteristic, direct product factor, Sylow
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—
771C24—21no—
772C24—21no—
773C24C22×C4×C2912yes—
774C24C22×C4×C2912yes—
775C24C2×D4×C2912yes—
776C24#41×C2912yes—
777C24C24×C2911yescharacteristic
778C2×D4—28no—
779C2×D4—28no—
780C2×D4—44no—
781C2×D4—44no—
782C2×D4—44no—
783C2×D4—44no—
784C2×D4—44no—
785C22×C4—28no—
786C22×C4—28no—
787C22×C4—28no—
788C22×C4—28no—
789C22×C4—28no—
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—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—28no—
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×C4C22×C4×C2912yes—
865C22×C4C22×C4×C2912yes—
866C22×C4C22×C4×C2912yes—
867C22×C4C22×C4×C2912yes—
868C22×C4C22×C4×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×C4C2×D4×C2912yes—
876C22×C4C2×D4×C2912yes—
877C22×C4#41×C2912yes—
878C22×C4#41×C2912yes—
879C22×C4#41×C2912yes—
880C22×C4#41×C2912yes—
881C22×C4#41×C2912yes—
882C22×C4#41×C2912yes—
883C4⋊C4—28no—
884C4⋊C4—28no—
885C4⋊C4—44no—
886C4⋊C4—44no—
887C22⋊C4—28no—
888C22⋊C4—28no—
889C22⋊C4—28no—
890C22⋊C4—28no—
891C22⋊C4—44no—
892C22⋊C4—44no—
893C22⋊C4—44no—
894C22⋊C4—44no—
895C22⋊C4—44no—
896C22⋊C4—44no—
897C22⋊C4—44no—
898C42—28no—
899C42—28no—
900C42—44no—
901C42—44no—
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—22no—
926C23—22no—
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—
969C23—41no—
970C23—41no—
971C23C4×D4×C2914yes—
972C23C23×C4×C2911yescharacteristic
973C23C22×D4×C2911yescharacteristic
974C23C22×D4×C2911yescharacteristic
975C23C22×D4×C2911yescharacteristic
976C23C2×#41×C2911yescharacteristic
977C23C2×#41×C2911yescharacteristic
978C23C2×#41×C2911yescharacteristic
979C23C2×#41×C2911yescharacteristic
980C23C2×#41×C2911yescharacteristic
981C23C2×#41×C2911yescharacteristic
982C23C2×#41×C2911yescharacteristic
983C23C29×H(5,𝔽2)11yescharacteristic
984C23C29×H(5,𝔽2)11yescharacteristic
985C23C29×H(5,𝔽2)11yescharacteristic
986C23C29×2−1+411yescharacteristic
987D4—416no—
988C2×C4—232no—
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—22no—
1032C2×C4—22no—
1033C2×C4—22no—
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×C4C29×#11714yescomplemented
1077C2×C4C4×D4×C2914yes—
1078C2×C4C4×D4×C2914yes—
1079C2×C4C29×#12014yes—
1080C22—24no—
1081C22—24no—
1082C22—24no—
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—42no—
1101C22—42no—
1102C22—81no—
1103C22—81no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22C2×C29×#11711yescharacteristic
1111C22C2×C4×D4×C2911yescharacteristic
1112C22C2×C4×D4×C2911yescharacteristic
1113C22C2×C4×D4×C2911yescharacteristic
1114C22C4×#41×C2911yescharacteristic
1115C22C29×#51811yescharacteristic
1116C22C29×#52011yescharacteristic
1117C22C2×C29×#12011yescharacteristic
1118C22C29×#52511yescharacteristic
1119C22C29×#52511yescharacteristic
1120C22C29×#52511yescharacteristic
1121C22C29×#52911yescharacteristic
1122C22C29×#52911yescharacteristic
1123C22C29×#53211yescharacteristic
1124C22C29×#53211yescharacteristic
1125C22C29×#53511yescharacteristic
1126C22C29×#53711yescharacteristic
1127C22C29×#54011yescharacteristic
1128C22C29×#54211yescharacteristic
1129C22C29×#54611yescharacteristic
1130C22C29×#54611yescharacteristic
1131C22C29×#54611yescharacteristic
1132C22C29×#54611yescharacteristic
1133C22C29×#54711yescharacteristic
1134C22C29×#54711yescharacteristic
1135C22C29×#55011yescharacteristic
1136C22C29×#55011yescharacteristic
1137C22C29×#55111yescharacteristic
1138C22C29×#55111yescharacteristic
1139C22C29×#55111yescharacteristic
1140C22C29×#55211yescharacteristic
1141C22C29×#55311yescharacteristic
1142C22C29×#55511yescharacteristic
1143C22C29×#55511yescharacteristic
1144C22C29×#55611yescharacteristic
1145C4—24no—
1146C4—24no—
1147C4—24no—
1148C4—24no—
1149C4—42no—
1150C4—42no—
1151C4—42no—
1152C4—42no—
1153C4—42no—
1154C4—42no—
1155C4—42no—
1156C4—81no—
1157C4—81no—
1158C2—44no—
1159C2—82no—
1160C2C29×#229311yescharacteristic
1161C2C4×C29×#12011yescharacteristic
1162C2C29×#232411yescharacteristic
1163C2C29×#234211yescharacteristic
1164C2C29×#235411yescharacteristic
1165C2C29×#235911yescharacteristic
1166C2C29×#236311yescharacteristic
1167C2C29×#243011yescharacteristic
1168C2C29×#243111yescharacteristic
1169C2C29×#247111yescharacteristic
1170C2C29×#247411yescharacteristic
1171C2C29×#247611yescharacteristic
1172C2C29×#247911yescharacteristic
1173C2C29×#260111yescharacteristic
1174C2C29×#261011yescharacteristic
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
1. C22×C29×#117C2semidirect
3. C2×C29×#388C2semidirect
4. C2×C29×#388C2semidirect
6. C29×#1444C2semidirect
7. C29×#1439C2semidirect
8. C29×#1439C2semidirect
10. C29×#1437C2semidirect
11. C29×#1437C2semidirect
12. C29×#1436C2semidirect
13. C29×#1436C2semidirect
14. C29×C22⋊#95C2semidirect
15. C4×C29×#95C2semidirect
43. C29×#386C4semidirect
99. C2×C4⋊C4×C29D4semidirect
144. C2×C42×C29D4semidirect
314. #14071C29direct (N × H)
489. C2×C4×C29#117semidirect
493. C22×#117C2×C29semidirect
495. C2×#388C2×C29semidirect
496. C2×#388C2×C29semidirect
498. #1444C2×C29semidirect
499. #1439C2×C29semidirect
500. #1439C2×C29semidirect
502. #1437C2×C29semidirect
503. #1437C2×C29semidirect
504. #1436C2×C29semidirect
505. #1436C2×C29semidirect
506. C22⋊#95C2×C29semidirect
507. C4×#95C2×C29semidirect
613. #386C4×C29semidirect
686. C2×C4⋊C4D4×C29semidirect
731. C2×C42D4×C29semidirect
746. C29#14071direct (N × H)
1076. C2×C4C29×#117semidirect

Maximal subgroups

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

subgroupindex
C22×C29×#1172
C2×C29×#3902
C2×C29×#3882
C2×C29×#3862
C29×#14442
C29×#14392
C29×#14382
C29×#14372
C29×#14362
C29×C22⋊#952
C4×C29×#952
#1407129