Finite Group Databasebeta

← C29×#14303 #20309203

Subgroups — C29×#14303 #20309203

Order 7424.

1774 conjugacy classes of subgroups.

The subgroup lattice has 1142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#394C211yesmaximal, characteristic
2C2×C29×#386C211yesmaximal, characteristic
3C2×C4×C22⋊C4×C29C211yesmaximal, characteristic, complemented
4C29×#1445C211yesmaximal, characteristic, complemented
5C29×#1443C211yesmaximal, characteristic, complemented
6C29×#1440C211yesmaximal, characteristic, complemented
7C29×#1440C211yesmaximal, characteristic, complemented
8C29×#1439C211yesmaximal, characteristic, complemented
9C29×#1439C211yesmaximal, characteristic, complemented
10C29×#1438C211yesmaximal, characteristic
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×C22⋊C4×C29C2211yescharacteristic
21C22×C22⋊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×C42×C29C2211yescharacteristic
32C22×C42×C29C2211yescharacteristic
33C29×#394C418yescomplemented
34C29×#386—24no—
35C4×C22⋊C4×C29—24no—
36C2×C29×#95C2211yescharacteristic
37C2×C29×#95C2211yescharacteristic
38C2×C29×#95C2211yescharacteristic
39C2×C29×#95C2211yescharacteristic
40C2×C29×#95C2211yescharacteristic
41C2×C29×#95C2211yescharacteristic
42C2×C29×#95C2211yescharacteristic
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
54C25×C29C2311yescharacteristic
55C25×C29C2311yescharacteristic
56C22×D4×C29—22no—
57C22×D4×C29—22no—
58C22×D4×C29—41no—
59C22×D4×C29—41no—
60C22×D4×C29—41no—
61C22×D4×C29—41no—
62C22×D4×C29C2×C414yes—
63C23×C4×C29—22no—
64C23×C4×C29—22no—
65C23×C4×C29—41no—
66C23×C4×C29—41no—
67C23×C4×C29—41no—
68C23×C4×C29—41no—
69C23×C4×C29D414yes—
70C23×C4×C29C2311yescharacteristic
71C23×C4×C29C2311yescharacteristic
72C23×C4×C29C2311yescharacteristic
73C23×C4×C29C2311yescharacteristic
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
83C2×C4⋊C4×C29—22no—
84C2×C4⋊C4×C29—41no—
85C2×C4⋊C4×C29—41no—
86C2×C4⋊C4×C29—41no—
87C2×C4⋊C4×C29—41no—
88C2×C4⋊C4×C29C2×C414yescomplemented
89C2×C22⋊C4×C29—22no—
90C2×C22⋊C4×C29—22no—
91C2×C22⋊C4×C29—22no—
92C2×C22⋊C4×C29—22no—
93C2×C22⋊C4×C29—22no—
94C2×C22⋊C4×C29—22no—
95C2×C22⋊C4×C29—22no—
96C2×C22⋊C4×C29—22no—
97C2×C22⋊C4×C29—22no—
98C2×C22⋊C4×C29—22no—
99C2×C22⋊C4×C29—22no—
100C2×C22⋊C4×C29—22no—
101C2×C22⋊C4×C29—22no—
102C2×C22⋊C4×C29—41no—
103C2×C22⋊C4×C29—41no—
104C2×C22⋊C4×C29—41no—
105C2×C22⋊C4×C29—41no—
106C2×C22⋊C4×C29—41no—
107C2×C22⋊C4×C29—41no—
108C2×C22⋊C4×C29—41no—
109C2×C22⋊C4×C29—41no—
110C2×C22⋊C4×C29—41no—
111C2×C22⋊C4×C29—41no—
112C2×C22⋊C4×C29—41no—
113C2×C22⋊C4×C29—41no—
114C2×C22⋊C4×C29—41no—
115C2×C22⋊C4×C29—41no—
116C2×C22⋊C4×C29—41no—
117C2×C22⋊C4×C29—41no—
118C2×C22⋊C4×C29C2×C414yes—
119C2×C22⋊C4×C29C2×C414yes—
120C2×C22⋊C4×C29C2×C414yescomplemented
121C2×C22⋊C4×C29C2×C414yescomplemented
122C2×C42×C29—22no—
123C2×C42×C29—22no—
124C2×C42×C29—41no—
125C2×C42×C29—41no—
126C2×C42×C29—41no—
127C2×C42×C29—41no—
128C29×#95—22no—
129C29×#95—22no—
130C29×#95—22no—
131C29×#95—22no—
132C29×#95—22no—
133C29×#95—22no—
134C29×#95—22no—
135C29×#95—41no—
136C29×#95—41no—
137C29×#95—41no—
138C29×#95—41no—
139C29×#95—41no—
140C29×#95—41no—
141C29×#95—41no—
142C29×#95—41no—
143C29×#95—41no—
144C29×#95—41no—
145C29×#95C2×C414yescomplemented
146C24×C29—21no—
147C24×C29—21no—
148C24×C29—21no—
149C24×C29—21no—
150C24×C29—21no—
151C24×C29—21no—
152C24×C29—21no—
153C24×C29—21no—
154C24×C29—21no—
155C24×C29—21no—
156C24×C29—21no—
157C24×C29—21no—
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×C29C22×C412yes—
173C24×C29C22×C412yes—
174C24×C29C2×D412yes—
175C24×C29#4112yes—
176C24×C29C2411yescharacteristic
177C2×D4×C29—28no—
178C2×D4×C29—44no—
179C2×D4×C29—44no—
180C2×D4×C29—44no—
181C2×D4×C29—44no—
182C2×D4×C29—44no—
183C2×D4×C29—44no—
184C22×C4×C29—21no—
185C22×C4×C29—21no—
186C22×C4×C29—21no—
187C22×C4×C29—21no—
188C22×C4×C29—21no—
189C22×C4×C29—21no—
190C22×C4×C29—21no—
191C22×C4×C29—21no—
192C22×C4×C29—21no—
193C22×C4×C29—21no—
194C22×C4×C29—21no—
195C22×C4×C29—21no—
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—21no—
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—28no—
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—44no—
266C22×C4×C29—44no—
267C22×C4×C29—44no—
268C22×C4×C29—44no—
269C22×C4×C29—44no—
270C22×C4×C29—44no—
271C22×C4×C29C22×C412yes—
272C22×C4×C29C22×C412yes—
273C22×C4×C29C22×C412yes—
274C22×C4×C29C22×C412yes—
275C22×C4×C29C22×C412yes—
276C22×C4×C29C2×D412yes—
277C22×C4×C29C2×D412yes—
278C22×C4×C29#4112yes—
279C22×C4×C29#4112yes—
280C22×C4×C29#4112yes—
281C22×C4×C29#4112yes—
282C4⋊C4×C29—44no—
283C4⋊C4×C29—44no—
284C22⋊C4×C29—28no—
285C22⋊C4×C29—28no—
286C22⋊C4×C29—44no—
287C22⋊C4×C29—44no—
288C22⋊C4×C29—44no—
289C22⋊C4×C29—44no—
290C22⋊C4×C29—44no—
291C22⋊C4×C29—44no—
292C22⋊C4×C29—44no—
293C22⋊C4×C29—44no—
294C22⋊C4×C29—44no—
295C42×C29—44no—
296C42×C29—44no—
297#14303C2911yesmaximal, characteristic, direct product factor, Sylow
298C23×C29—22no—
299C23×C29—22no—
300C23×C29—22no—
301C23×C29—22no—
302C23×C29—22no—
303C23×C29—22no—
304C23×C29—22no—
305C23×C29—22no—
306C23×C29—22no—
307C23×C29—22no—
308C23×C29—22no—
309C23×C29—22no—
310C23×C29—22no—
311C23×C29—22no—
312C23×C29—22no—
313C23×C29—22no—
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—41no—
324C23×C29—41no—
325C23×C29—41no—
326C23×C29—41no—
327C23×C29—41no—
328C23×C29—41no—
329C23×C29—41no—
330C23×C29—41no—
331C23×C29—41no—
332C23×C29—41no—
333C23×C29—41no—
334C23×C29—41no—
335C23×C29—41no—
336C23×C29—41no—
337C23×C29—41no—
338C23×C29—41no—
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×C29C4×D414yes—
368C23×C29C23×C411yescharacteristic
369C23×C29C22×D411yescharacteristic
370C23×C29C2×#4111yescharacteristic
371C23×C29C2×#4111yescharacteristic
372C23×C29C2×#4111yescharacteristic
373C23×C29C2×#4111yescharacteristic
374C23×C29C2×#4111yescharacteristic
375C23×C29H(5,𝔽2)11yescharacteristic
376C23×C29H(5,𝔽2)11yescharacteristic
377C23×C29H(5,𝔽2)11yescharacteristic
378C23×C29H(5,𝔽2)11yescharacteristic
379C23×C29H(5,𝔽2)11yescharacteristic
380C23×C29H(5,𝔽2)11yescharacteristic
381C23×C29H(5,𝔽2)11yescharacteristic
382C23×C292−1+411yescharacteristic
383D4×C29—416no—
384C2×C4×C29—22no—
385C2×C4×C29—22no—
386C2×C4×C29—22no—
387C2×C4×C29—22no—
388C2×C4×C29—22no—
389C2×C4×C29—22no—
390C2×C4×C29—22no—
391C2×C4×C29—22no—
392C2×C4×C29—22no—
393C2×C4×C29—22no—
394C2×C4×C29—22no—
395C2×C4×C29—22no—
396C2×C4×C29—22no—
397C2×C4×C29—22no—
398C2×C4×C29—22no—
399C2×C4×C29—22no—
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—416no—
415C2×C4×C29—41no—
416C2×C4×C29—41no—
417C2×C4×C29—41no—
418C2×C4×C29—41no—
419C2×C4×C29—41no—
420C2×C4×C29—41no—
421C2×C4×C29—41no—
422C2×C4×C29—41no—
423C2×C4×C29—41no—
424C2×C4×C29—41no—
425C2×C4×C29—41no—
426C2×C4×C29—41no—
427C2×C4×C29—41no—
428C2×C4×C29—41no—
429C2×C4×C29—41no—
430C2×C4×C29—41no—
431C2×C4×C29—41no—
432C2×C4×C29—41no—
433C2×C4×C29—41no—
434C2×C4×C29—41no—
435C2×C4×C29—41no—
436C2×C4×C29—41no—
437C2×C4×C29—41no—
438C2×C4×C29—41no—
439C2×C4×C29—41no—
440C2×C4×C29—41no—
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#12314yes—
476C2×#394C2×C2911yescharacteristic
477C2×#386C2×C2911yescharacteristic
478C2×C4×C22⋊C4C2×C2911yescharacteristic, complemented
479#1445C2×C2911yescharacteristic, complemented
480#1443C2×C2911yescharacteristic, complemented
481#1440C2×C2911yescharacteristic, complemented
482#1440C2×C2911yescharacteristic, complemented
483#1439C2×C2911yescharacteristic, complemented
484#1439C2×C2911yescharacteristic, complemented
485#1438C2×C2911yescharacteristic
486#1437C2×C2911yescharacteristic, complemented
487#1437C2×C2911yescharacteristic, complemented
488#1436C2×C2911yescharacteristic, complemented
489#1436C2×C2911yescharacteristic, complemented
490C22⋊#95C2×C2911yescharacteristic, complemented
491C22×C29—24no—
492C22×C29—24no—
493C22×C29—24no—
494C22×C29—42no—
495C22×C29—42no—
496C22×C29—42no—
497C22×C29—42no—
498C22×C29—42no—
499C22×C29—42no—
500C22×C29—42no—
501C22×C29—42no—
502C22×C29—42no—
503C22×C29—42no—
504C22×C29—42no—
505C22×C29—42no—
506C22×C29—42no—
507C22×C29—42no—
508C22×C29—42no—
509C22×C29—42no—
510C22×C29—42no—
511C22×C29—42no—
512C22×C29—42no—
513C22×C29—81no—
514C22×C29—81no—
515C22×C29—81no—
516C22×C29—81no—
517C22×C29—81no—
518C22×C29—81no—
519C22×C29—81no—
520C22×C29—81no—
521C22×C29C2×C4×D411yescharacteristic
522C22×C29C4×#4111yescharacteristic
523C22×C29C4×#4111yescharacteristic
524C22×C29#51811yescharacteristic
525C22×C29#51811yescharacteristic
526C22×C29#51811yescharacteristic
527C22×C29#52011yescharacteristic
528C22×C29C2×#12311yescharacteristic
529C22×C29#52511yescharacteristic
530C22×C29#52911yescharacteristic
531C22×C29#52911yescharacteristic
532C22×C29#53411yescharacteristic
533C22×C29#53411yescharacteristic
534C22×C29#53511yescharacteristic
535C22×C29#53711yescharacteristic
536C22×C29#53811yescharacteristic
537C22×C29#53811yescharacteristic
538C22×C29#53811yescharacteristic
539C22×C29#53811yescharacteristic
540C22×C29#53811yescharacteristic
541C22×C29#53811yescharacteristic
542C22×C29#53811yescharacteristic
543C22×C29#53811yescharacteristic
544C22×C29#53811yescharacteristic
545C22×C29#53811yescharacteristic
546C22×C29#53911yescharacteristic
547C22×C29#53911yescharacteristic
548C22×C29#54011yescharacteristic
549C22×C29#54011yescharacteristic
550C22×C29#54011yescharacteristic
551C22×C29#54011yescharacteristic
552C22×C29#54011yescharacteristic
553C22×C29#54211yescharacteristic
554C22×C29#54211yescharacteristic
555C22×C29#54211yescharacteristic
556C4×C29—24no—
557C4×C29—42no—
558C4×C29—42no—
559C4×C29—42no—
560C4×C29—42no—
561C4×C29—42no—
562C4×C29—42no—
563C4×C29—42no—
564C4×C29—42no—
565C4×C29—81no—
566C4×C29—81no—
567C4×C29—81no—
568C4×C29—81no—
569C23×D4C22×C2911yescharacteristic
570C24×C4C22×C2911yescharacteristic
571C22×C4⋊C4C22×C2911yescharacteristic
572C22×C4⋊C4C22×C2911yescharacteristic
573C22×C22⋊C4C22×C2911yescharacteristic
574C22×C22⋊C4C22×C2911yescharacteristic
575C22×C22⋊C4C22×C2911yescharacteristic
576C22×C22⋊C4C22×C2911yescharacteristic
577C22×C22⋊C4C22×C2911yescharacteristic
578C22×C22⋊C4C22×C2911yescharacteristic
579C22×C22⋊C4C22×C2911yescharacteristic
580C22×C22⋊C4C22×C2911yescharacteristic
581C22×C22⋊C4C22×C2911yescharacteristic
582C22×C22⋊C4C22×C2911yescharacteristic
583C22×C22⋊C4C22×C2911yescharacteristic
584C22×C42C22×C2911yescharacteristic
585C22×C42C22×C2911yescharacteristic
586#394C4×C2918yescomplemented
587#386—24no—
588C4×C22⋊C4—24no—
589C2×#95C22×C2911yescharacteristic
590C2×#95C22×C2911yescharacteristic
591C2×#95C22×C2911yescharacteristic
592C2×#95C22×C2911yescharacteristic
593C2×#95C22×C2911yescharacteristic
594C2×#95C22×C2911yescharacteristic
595C2×#95C22×C2911yescharacteristic
596C2×#95C22×C2911yescharacteristic
597C2×#95C22×C2911yescharacteristic
598C2×#95C22×C2911yescharacteristic
599C2×#95C22×C2911yescharacteristic
600C2×#95C22×C2911yescharacteristic
601C2×#95C22×C2911yescharacteristic
602C2×#95C22×C2911yescharacteristic
603C2×#95C22×C2911yescharacteristic
604C2×#95C22×C2911yescharacteristic
605C2×#95C22×C2911yescharacteristic
606C2×#95C22×C2911yescharacteristic
607C2×C29—44no—
608C2×C29—82no—
609C2×C29C4×#12311yescharacteristic
610C2×C29#232111yescharacteristic
611C2×C29#232511yescharacteristic
612C2×C29#233311yescharacteristic
613C2×C29#233311yescharacteristic
614C2×C29#233511yescharacteristic
615C2×C29#233711yescharacteristic
616C2×C29#262211yescharacteristic
617C2×C29#262411yescharacteristic
618C2×C29#263011yescharacteristic
619C2×C29#263511yescharacteristic
620C2×C29#264811yescharacteristic
621C2×C29#264811yescharacteristic
622C2×C29#264911yescharacteristic
623C2×C29#265311yescharacteristic
624C25C23×C2911yescharacteristic
625C25C23×C2911yescharacteristic
626C22×D4—22no—
627C22×D4—22no—
628C22×D4—41no—
629C22×D4—41no—
630C22×D4—41no—
631C22×D4—41no—
632C22×D4C2×C4×C2914yes—
633C23×C4—22no—
634C23×C4—22no—
635C23×C4—41no—
636C23×C4—41no—
637C23×C4—41no—
638C23×C4—41no—
639C23×C4D4×C2914yes—
640C23×C4C23×C2911yescharacteristic
641C23×C4C23×C2911yescharacteristic
642C23×C4C23×C2911yescharacteristic
643C23×C4C23×C2911yescharacteristic
644C23×C4C23×C2911yescharacteristic
645C23×C4C23×C2911yescharacteristic
646C23×C4C23×C2911yescharacteristic
647C23×C4C23×C2911yescharacteristic
648C23×C4C23×C2911yescharacteristic
649C23×C4C23×C2911yescharacteristic
650C23×C4C23×C2911yescharacteristic
651C23×C4C23×C2911yescharacteristic
652C23×C4C23×C2911yescharacteristic
653C2×C4⋊C4—22no—
654C2×C4⋊C4—41no—
655C2×C4⋊C4—41no—
656C2×C4⋊C4—41no—
657C2×C4⋊C4—41no—
658C2×C4⋊C4C2×C4×C2914yescomplemented
659C2×C22⋊C4—22no—
660C2×C22⋊C4—22no—
661C2×C22⋊C4—22no—
662C2×C22⋊C4—22no—
663C2×C22⋊C4—22no—
664C2×C22⋊C4—22no—
665C2×C22⋊C4—22no—
666C2×C22⋊C4—22no—
667C2×C22⋊C4—22no—
668C2×C22⋊C4—22no—
669C2×C22⋊C4—22no—
670C2×C22⋊C4—22no—
671C2×C22⋊C4—22no—
672C2×C22⋊C4—41no—
673C2×C22⋊C4—41no—
674C2×C22⋊C4—41no—
675C2×C22⋊C4—41no—
676C2×C22⋊C4—41no—
677C2×C22⋊C4—41no—
678C2×C22⋊C4—41no—
679C2×C22⋊C4—41no—
680C2×C22⋊C4—41no—
681C2×C22⋊C4—41no—
682C2×C22⋊C4—41no—
683C2×C22⋊C4—41no—
684C2×C22⋊C4—41no—
685C2×C22⋊C4—41no—
686C2×C22⋊C4—41no—
687C2×C22⋊C4—41no—
688C2×C22⋊C4C2×C4×C2914yes—
689C2×C22⋊C4C2×C4×C2914yes—
690C2×C22⋊C4C2×C4×C2914yescomplemented
691C2×C22⋊C4C2×C4×C2914yescomplemented
692C2×C42—22no—
693C2×C42—22no—
694C2×C42—41no—
695C2×C42—41no—
696C2×C42—41no—
697C2×C42—41no—
698#95—22no—
699#95—22no—
700#95—22no—
701#95—22no—
702#95—22no—
703#95—22no—
704#95—22no—
705#95—41no—
706#95—41no—
707#95—41no—
708#95—41no—
709#95—41no—
710#95—41no—
711#95—41no—
712#95—41no—
713#95—41no—
714#95—41no—
715#95C2×C4×C2914yescomplemented
716C29#1430311yescharacteristic, direct product factor, Sylow
717C24—21no—
718C24—21no—
719C24—21no—
720C24—21no—
721C24—21no—
722C24—21no—
723C24—21no—
724C24—21no—
725C24—21no—
726C24—21no—
727C24—21no—
728C24—21no—
729C24—21no—
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24C22×C4×C2912yes—
744C24C22×C4×C2912yes—
745C24C2×D4×C2912yes—
746C24#41×C2912yes—
747C24C24×C2911yescharacteristic
748C2×D4—28no—
749C2×D4—44no—
750C2×D4—44no—
751C2×D4—44no—
752C2×D4—44no—
753C2×D4—44no—
754C2×D4—44no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
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—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—44no—
837C22×C4—44no—
838C22×C4—44no—
839C22×C4—44no—
840C22×C4—44no—
841C22×C4—44no—
842C22×C4C22×C4×C2912yes—
843C22×C4C22×C4×C2912yes—
844C22×C4C22×C4×C2912yes—
845C22×C4C22×C4×C2912yes—
846C22×C4C22×C4×C2912yes—
847C22×C4C2×D4×C2912yes—
848C22×C4C2×D4×C2912yes—
849C22×C4#41×C2912yes—
850C22×C4#41×C2912yes—
851C22×C4#41×C2912yes—
852C22×C4#41×C2912yes—
853C4⋊C4—44no—
854C4⋊C4—44no—
855C22⋊C4—28no—
856C22⋊C4—28no—
857C22⋊C4—44no—
858C22⋊C4—44no—
859C22⋊C4—44no—
860C22⋊C4—44no—
861C22⋊C4—44no—
862C22⋊C4—44no—
863C22⋊C4—44no—
864C22⋊C4—44no—
865C22⋊C4—44no—
866C42—44no—
867C42—44no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23C4×D4×C2914yes—
938C23C23×C4×C2911yescharacteristic
939C23C22×D4×C2911yescharacteristic
940C23C2×#41×C2911yescharacteristic
941C23C2×#41×C2911yescharacteristic
942C23C2×#41×C2911yescharacteristic
943C23C2×#41×C2911yescharacteristic
944C23C2×#41×C2911yescharacteristic
945C23C29×H(5,𝔽2)11yescharacteristic
946C23C29×H(5,𝔽2)11yescharacteristic
947C23C29×H(5,𝔽2)11yescharacteristic
948C23C29×H(5,𝔽2)11yescharacteristic
949C23C29×H(5,𝔽2)11yescharacteristic
950C23C29×H(5,𝔽2)11yescharacteristic
951C23C29×H(5,𝔽2)11yescharacteristic
952C23C29×2−1+411yescharacteristic
953D4—416no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—416no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
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×C4C29×#12314yes—
1046C22—24no—
1047C22—24no—
1048C22—24no—
1049C22—42no—
1050C22—42no—
1051C22—42no—
1052C22—42no—
1053C22—42no—
1054C22—42no—
1055C22—42no—
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—42no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—81no—
1069C22—81no—
1070C22—81no—
1071C22—81no—
1072C22—81no—
1073C22—81no—
1074C22—81no—
1075C22—81no—
1076C22C2×C4×D4×C2911yescharacteristic
1077C22C4×#41×C2911yescharacteristic
1078C22C4×#41×C2911yescharacteristic
1079C22C29×#51811yescharacteristic
1080C22C29×#51811yescharacteristic
1081C22C29×#51811yescharacteristic
1082C22C29×#52011yescharacteristic
1083C22C2×C29×#12311yescharacteristic
1084C22C29×#52511yescharacteristic
1085C22C29×#52911yescharacteristic
1086C22C29×#52911yescharacteristic
1087C22C29×#53411yescharacteristic
1088C22C29×#53411yescharacteristic
1089C22C29×#53511yescharacteristic
1090C22C29×#53711yescharacteristic
1091C22C29×#53811yescharacteristic
1092C22C29×#53811yescharacteristic
1093C22C29×#53811yescharacteristic
1094C22C29×#53811yescharacteristic
1095C22C29×#53811yescharacteristic
1096C22C29×#53811yescharacteristic
1097C22C29×#53811yescharacteristic
1098C22C29×#53811yescharacteristic
1099C22C29×#53811yescharacteristic
1100C22C29×#53811yescharacteristic
1101C22C29×#53911yescharacteristic
1102C22C29×#53911yescharacteristic
1103C22C29×#54011yescharacteristic
1104C22C29×#54011yescharacteristic
1105C22C29×#54011yescharacteristic
1106C22C29×#54011yescharacteristic
1107C22C29×#54011yescharacteristic
1108C22C29×#54211yescharacteristic
1109C22C29×#54211yescharacteristic
1110C22C29×#54211yescharacteristic
1111C4—24no—
1112C4—42no—
1113C4—42no—
1114C4—42no—
1115C4—42no—
1116C4—42no—
1117C4—42no—
1118C4—42no—
1119C4—42no—
1120C4—81no—
1121C4—81no—
1122C4—81no—
1123C4—81no—
1124C2—44no—
1125C2—82no—
1126C2C4×C29×#12311yescharacteristic
1127C2C29×#232111yescharacteristic
1128C2C29×#232511yescharacteristic
1129C2C29×#233311yescharacteristic
1130C2C29×#233311yescharacteristic
1131C2C29×#233511yescharacteristic
1132C2C29×#233711yescharacteristic
1133C2C29×#262211yescharacteristic
1134C2C29×#262411yescharacteristic
1135C2C29×#263011yescharacteristic
1136C2C29×#263511yescharacteristic
1137C2C29×#264811yescharacteristic
1138C2C29×#264811yescharacteristic
1139C2C29×#264911yescharacteristic
1140C2C29×#265311yescharacteristic
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×C4×C22⋊C4×C29C2semidirect
4. C29×#1445C2semidirect
5. C29×#1443C2semidirect
6. C29×#1440C2semidirect
7. C29×#1440C2semidirect
8. C29×#1439C2semidirect
9. C29×#1439C2semidirect
11. C29×#1437C2semidirect
12. C29×#1437C2semidirect
13. C29×#1436C2semidirect
14. C29×#1436C2semidirect
15. C29×C22⋊#95C2semidirect
33. C29×#394C4semidirect
88. C2×C4⋊C4×C29C2×C4semidirect
120. C2×C22⋊C4×C29C2×C4semidirect
121. C2×C22⋊C4×C29C2×C4semidirect
145. C29×#95C2×C4semidirect
297. #14303C29direct (N × H)
478. C2×C4×C22⋊C4C2×C29semidirect
479. #1445C2×C29semidirect
480. #1443C2×C29semidirect
481. #1440C2×C29semidirect
482. #1440C2×C29semidirect
483. #1439C2×C29semidirect
484. #1439C2×C29semidirect
486. #1437C2×C29semidirect
487. #1437C2×C29semidirect
488. #1436C2×C29semidirect
489. #1436C2×C29semidirect
490. C22⋊#95C2×C29semidirect
586. #394C4×C29semidirect
658. C2×C4⋊C4C2×C4×C29semidirect
690. C2×C22⋊C4C2×C4×C29semidirect
691. C2×C22⋊C4C2×C4×C29semidirect
715. #95C2×C4×C29semidirect
716. C29#14303direct (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×#3862
C2×C4×C22⋊C4×C292
C29×#14452
C29×#14432
C29×#14402
C29×#14392
C29×#14382
C29×#14372
C29×#14362
C29×C22⋊#952
#1430329