Finite Group Databasebeta

← C29×#14730 #20309630

Subgroups — C29×#14730 #20309630

Order 7424.

2578 conjugacy classes of subgroups.

The subgroup lattice has 1346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C29C211yesmaximal, characteristic, complemented
2C2×C29×#394C211yesmaximal, characteristic, complemented
3C2×C29×#392C211yesmaximal, characteristic
4C2×C29×#386C211yesmaximal, characteristic, complemented
5C2×C29×#386C211yesmaximal, characteristic, complemented
6C2×C29×#381C211yesmaximal, characteristic, complemented
7C29×#1442C211yesmaximal, characteristic, complemented
8C29×#1440C211yesmaximal, characteristic, complemented
9C29×#1439C211yesmaximal, characteristic, complemented
10C29×#1439C211yesmaximal, characteristic, complemented
11C29×#1438C211yesmaximal, characteristic, complemented
12C29×#1438C211yesmaximal, characteristic, complemented
13C29×#1437C211yesmaximal, characteristic, complemented
14C29×#1436C211yesmaximal, characteristic, complemented
15C29×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C29C2211yescharacteristic
17C23×D4×C29C2211yescharacteristic
18C23×D4×C29C2211yescharacteristic
19C24×C4×C29C2211yescharacteristic
20C24×C4×C29C2211yescharacteristic
21C2×C4×D4×C29—24no—
22C2×C4×D4×C29—24no—
23C2×C4×D4×C29—24no—
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×C22⋊C4×C29C2211yescharacteristic
38C22×C22⋊C4×C29C2211yescharacteristic
39C22×C42×C29C2211yescharacteristic
40C29×#394—24no—
41C29×#392—24no—
42C29×#386—24no—
43C29×#386—24no—
44C29×#381—24no—
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
61C25×C29C2311yescharacteristic
62C22×D4×C29—22no—
63C22×D4×C29—22no—
64C22×D4×C29—22no—
65C22×D4×C29—22no—
66C22×D4×C29—22no—
67C22×D4×C29—22no—
68C22×D4×C29—22no—
69C22×D4×C29—22no—
70C22×D4×C29—22no—
71C22×D4×C29—22no—
72C22×D4×C29—22no—
73C22×D4×C29—22no—
74C22×D4×C29—22no—
75C22×D4×C29—22no—
76C22×D4×C29—22no—
77C22×D4×C29—22no—
78C22×D4×C29—41no—
79C22×D4×C29—41no—
80C22×D4×C29—41no—
81C22×D4×C29—41no—
82C22×D4×C29D414yes—
83C23×C4×C29—22no—
84C23×C4×C29—22no—
85C23×C4×C29—22no—
86C23×C4×C29—22no—
87C23×C4×C29—22no—
88C23×C4×C29—22no—
89C23×C4×C29—22no—
90C23×C4×C29—22no—
91C23×C4×C29—22no—
92C23×C4×C29—41no—
93C23×C4×C29—41no—
94C23×C4×C29—41no—
95C23×C4×C29—41no—
96C23×C4×C29D414yescomplemented
97C23×C4×C29C2311yescharacteristic
98C23×C4×C29C2311yescharacteristic
99C23×C4×C29C2311yescharacteristic
100C23×C4×C29C2311yescharacteristic
101C23×C4×C29C2311yescharacteristic
102C23×C4×C29C2311yescharacteristic
103C23×C4×C29C2311yescharacteristic
104C23×C4×C29C2311yescharacteristic
105C23×C4×C29C2311yescharacteristic
106C23×C4×C29C2311yescharacteristic
107C23×C4×C29C2311yescharacteristic
108C23×C4×C29C2311yescharacteristic
109C4×D4×C29—232no—
110C2×C4⋊C4×C29—22no—
111C2×C4⋊C4×C29—22no—
112C2×C4⋊C4×C29—22no—
113C2×C4⋊C4×C29—22no—
114C2×C4⋊C4×C29—22no—
115C2×C4⋊C4×C29—41no—
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—22no—
134C2×C22⋊C4×C29—22no—
135C2×C22⋊C4×C29—22no—
136C2×C22⋊C4×C29—22no—
137C2×C22⋊C4×C29—22no—
138C2×C22⋊C4×C29—22no—
139C2×C22⋊C4×C29—22no—
140C2×C22⋊C4×C29—22no—
141C2×C22⋊C4×C29—22no—
142C2×C22⋊C4×C29—41no—
143C2×C22⋊C4×C29—41no—
144C2×C22⋊C4×C29—41no—
145C2×C22⋊C4×C29—41no—
146C2×C22⋊C4×C29—41no—
147C2×C22⋊C4×C29—41no—
148C2×C22⋊C4×C29—41no—
149C2×C22⋊C4×C29—41no—
150C2×C22⋊C4×C29—41no—
151C2×C22⋊C4×C29—41no—
152C2×C22⋊C4×C29—41no—
153C2×C22⋊C4×C29—41no—
154C2×C22⋊C4×C29D414yescomplemented
155C2×C42×C29—22no—
156C2×C42×C29—22no—
157C2×C42×C29—22no—
158C29×#95—22no—
159C29×#95—22no—
160C29×#95—22no—
161C29×#95—22no—
162C29×#95—22no—
163C29×#95—22no—
164C29×#95—22no—
165C29×#95—22no—
166C29×#95—22no—
167C29×#95—22no—
168C29×#95—41no—
169C29×#95—41no—
170C29×#95—41no—
171C29×#95D414yescomplemented
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×C29—21no—
187C24×C29—21no—
188C24×C29—21no—
189C24×C29—21no—
190C24×C29—21no—
191C24×C29—21no—
192C24×C29—21no—
193C24×C29—21no—
194C24×C29—21no—
195C24×C29—21no—
196C24×C29—21no—
197C24×C29—21no—
198C24×C29—21no—
199C24×C29—21no—
200C24×C29—21no—
201C24×C29—21no—
202C24×C29—21no—
203C24×C29—21no—
204C24×C29—21no—
205C24×C29—21no—
206C24×C29—21no—
207C24×C29—21no—
208C24×C29—21no—
209C24×C29—21no—
210C24×C29C2×D412yes—
211C24×C29C2×D412yes—
212C24×C29C2×D412yes—
213C24×C29C2×D412yes—
214C24×C29#4112yes—
215C24×C29#4112yes—
216C24×C29#4112yes—
217C24×C29C2411yescharacteristic
218C2×D4×C29—28no—
219C2×D4×C29—28no—
220C2×D4×C29—28no—
221C2×D4×C29—28no—
222C2×D4×C29—28no—
223C2×D4×C29—28no—
224C2×D4×C29—28no—
225C2×D4×C29—28no—
226C2×D4×C29—28no—
227C2×D4×C29—44no—
228C2×D4×C29—44no—
229C2×D4×C29—44no—
230C2×D4×C29—44no—
231C2×D4×C29—44no—
232C2×D4×C29—44no—
233C2×D4×C29—44no—
234C2×D4×C29—44no—
235C2×D4×C29—44no—
236C2×D4×C29—44no—
237C2×D4×C29—44no—
238C2×D4×C29—44no—
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—28no—
248C22×C4×C29—28no—
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—21no—
285C22×C4×C29—28no—
286C22×C4×C29—21no—
287C22×C4×C29—21no—
288C22×C4×C29—21no—
289C22×C4×C29—21no—
290C22×C4×C29—21no—
291C22×C4×C29—21no—
292C22×C4×C29—21no—
293C22×C4×C29—21no—
294C22×C4×C29—21no—
295C22×C4×C29—21no—
296C22×C4×C29—21no—
297C22×C4×C29—21no—
298C22×C4×C29—21no—
299C22×C4×C29—21no—
300C22×C4×C29—21no—
301C22×C4×C29—21no—
302C22×C4×C29—21no—
303C22×C4×C29—21no—
304C22×C4×C29—21no—
305C22×C4×C29—21no—
306C22×C4×C29—21no—
307C22×C4×C29—21no—
308C22×C4×C29—21no—
309C22×C4×C29—21no—
310C22×C4×C29—21no—
311C22×C4×C29—21no—
312C22×C4×C29—21no—
313C22×C4×C29—21no—
314C22×C4×C29—44no—
315C22×C4×C29—44no—
316C22×C4×C29—44no—
317C22×C4×C29—44no—
318C22×C4×C29—44no—
319C22×C4×C29—44no—
320C22×C4×C29—44no—
321C22×C4×C29—44no—
322C22×C4×C29—44no—
323C22×C4×C29—44no—
324C22×C4×C29—44no—
325C22×C4×C29C2×D412yes—
326C22×C4×C29C2×D412yes—
327C22×C4×C29C2×D412yes—
328C22×C4×C29C2×D412yes—
329C22×C4×C29C2×D412yes—
330C22×C4×C29C2×D412yes—
331C22×C4×C29C2×D412yes—
332C22×C4×C29C2×D412yes—
333C22×C4×C29#4112yes—
334C22×C4×C29#4112yes—
335C22×C4×C29#4112yes—
336C22×C4×C29#4112yes—
337C4⋊C4×C29—28no—
338C4⋊C4×C29—44no—
339C22⋊C4×C29—28no—
340C22⋊C4×C29—28no—
341C22⋊C4×C29—44no—
342C22⋊C4×C29—44no—
343C22⋊C4×C29—44no—
344C22⋊C4×C29—44no—
345C22⋊C4×C29—44no—
346C22⋊C4×C29—44no—
347C22⋊C4×C29—44no—
348C22⋊C4×C29—44no—
349C22⋊C4×C29—44no—
350C22⋊C4×C29—44no—
351C22⋊C4×C29—44no—
352C42×C29—28no—
353#14730C2911yesmaximal, characteristic, direct product factor, Sylow
354C23×C29—22no—
355C23×C29—22no—
356C23×C29—22no—
357C23×C29—22no—
358C23×C29—22no—
359C23×C29—22no—
360C23×C29—22no—
361C23×C29—22no—
362C23×C29—22no—
363C23×C29—22no—
364C23×C29—22no—
365C23×C29—22no—
366C23×C29—22no—
367C23×C29—22no—
368C23×C29—22no—
369C23×C29—22no—
370C23×C29—22no—
371C23×C29—22no—
372C23×C29—22no—
373C23×C29—22no—
374C23×C29—22no—
375C23×C29—22no—
376C23×C29—22no—
377C23×C29—22no—
378C23×C29—22no—
379C23×C29—22no—
380C23×C29—22no—
381C23×C29—22no—
382C23×C29—22no—
383C23×C29—22no—
384C23×C29—22no—
385C23×C29—22no—
386C23×C29—22no—
387C23×C29—22no—
388C23×C29—22no—
389C23×C29—22no—
390C23×C29—22no—
391C23×C29—22no—
392C23×C29—22no—
393C23×C29—22no—
394C23×C29—22no—
395C23×C29—22no—
396C23×C29—22no—
397C23×C29—41no—
398C23×C29—41no—
399C23×C29—41no—
400C23×C29—41no—
401C23×C29—41no—
402C23×C29—41no—
403C23×C29—41no—
404C23×C29—41no—
405C23×C29—41no—
406C23×C29—41no—
407C23×C29—41no—
408C23×C29—41no—
409C23×C29—41no—
410C23×C29—41no—
411C23×C29—41no—
412C23×C29—41no—
413C23×C29—41no—
414C23×C29—41no—
415C23×C29—41no—
416C23×C29—41no—
417C23×C29—41no—
418C23×C29—41no—
419C23×C29—41no—
420C23×C29—41no—
421C23×C29—41no—
422C23×C29—41no—
423C23×C29—41no—
424C23×C29—41no—
425C23×C29—41no—
426C23×C29—41no—
427C23×C29—41no—
428C23×C29—41no—
429C23×C29—41no—
430C23×C29—41no—
431C23×C29—41no—
432C23×C29—41no—
433C23×C29—41no—
434C23×C29—41no—
435C23×C29—41no—
436C23×C29—41no—
437C23×C29—41no—
438C23×C29—41no—
439C23×C29—41no—
440C23×C29—41no—
441C23×C29—41no—
442C23×C29—41no—
443C23×C29—41no—
444C23×C29—41no—
445C23×C29—41no—
446C23×C29—41no—
447C23×C29—41no—
448C23×C29—41no—
449C23×C29—41no—
450C23×C29—41no—
451C23×C29—41no—
452C23×C29—41no—
453C23×C29—41no—
454C23×C29—41no—
455C23×C29—41no—
456C23×C29—41no—
457C23×C29#12014yes—
458C23×C29#12314yes—
459C23×C29C22×D411yescharacteristic
460C23×C29C22×D411yescharacteristic
461C23×C29C22×D411yescharacteristic
462C23×C29C22×D411yescharacteristic
463C23×C29C2×#4111yescharacteristic
464C23×C29C2×#4111yescharacteristic
465C23×C29C2×#4111yescharacteristic
466C23×C29C2×#4111yescharacteristic
467C23×C29C2×#4111yescharacteristic
468C23×C29C2×#4111yescharacteristic
469C23×C29C2×#4111yescharacteristic
470C23×C29H(5,𝔽2)11yescharacteristic
471C23×C29H(5,𝔽2)11yescharacteristic
472C23×C29H(5,𝔽2)11yescharacteristic
473C23×C29H(5,𝔽2)11yescharacteristic
474D4×C29—232no—
475D4×C29—416no—
476D4×C29—416no—
477C2×C4×C29—22no—
478C2×C4×C29—22no—
479C2×C4×C29—22no—
480C2×C4×C29—22no—
481C2×C4×C29—22no—
482C2×C4×C29—22no—
483C2×C4×C29—22no—
484C2×C4×C29—22no—
485C2×C4×C29—22no—
486C2×C4×C29—22no—
487C2×C4×C29—22no—
488C2×C4×C29—22no—
489C2×C4×C29—22no—
490C2×C4×C29—22no—
491C2×C4×C29—22no—
492C2×C4×C29—22no—
493C2×C4×C29—22no—
494C2×C4×C29—22no—
495C2×C4×C29—22no—
496C2×C4×C29—22no—
497C2×C4×C29—22no—
498C2×C4×C29—22no—
499C2×C4×C29—22no—
500C2×C4×C29—22no—
501C2×C4×C29—22no—
502C2×C4×C29—22no—
503C2×C4×C29—22no—
504C2×C4×C29—22no—
505C2×C4×C29—22no—
506C2×C4×C29—22no—
507C2×C4×C29—416no—
508C2×C4×C29—416no—
509C2×C4×C29—41no—
510C2×C4×C29—41no—
511C2×C4×C29—41no—
512C2×C4×C29—41no—
513C2×C4×C29—41no—
514C2×C4×C29—41no—
515C2×C4×C29—41no—
516C2×C4×C29—41no—
517C2×C4×C29—41no—
518C2×C4×C29—41no—
519C2×C4×C29—41no—
520C2×C4×C29—41no—
521C2×C4×C29—41no—
522C2×C4×C29—41no—
523C2×C4×C29—41no—
524C2×C4×C29—41no—
525C2×C4×C29—41no—
526C2×C4×C29—41no—
527C2×C4×C29—41no—
528C2×C4×C29—41no—
529C2×C4×C29—41no—
530C2×C4×C29—41no—
531C2×C4×C29—41no—
532C2×C4×C29—41no—
533C2×C4×C29—41no—
534C2×C4×C29—41no—
535C2×C4×C29—41no—
536C2×C4×C29—41no—
537C2×C4×C29—41no—
538C2×C4×C29—41no—
539C2×C4×C29—41no—
540C2×C4×C29—41no—
541C2×C4×C29—41no—
542C2×C4×C29—41no—
543C2×C4×C29—41no—
544C2×C4×C29—41no—
545C2×C4×C29—41no—
546C2×C4×C29—41no—
547C2×C4×C29—41no—
548C2×C4×C29—41no—
549C2×C4×C29—41no—
550C2×C4×C29—41no—
551C2×C4×C29—41no—
552C2×C4×C29—41no—
553C2×C4×C29—41no—
554C2×C4×C29—41no—
555C2×C4×C29—41no—
556C2×C4×C29—41no—
557C2×C4×C29—41no—
558C2×C4×C29—41no—
559C2×C4×C29—41no—
560C2×C4×C29—41no—
561C2×C4×C29#12114yes—
562C2×C4×C29#12314yes—
563C22×C4×D4C2×C2911yescharacteristic, complemented
564C2×#394C2×C2911yescharacteristic, complemented
565C2×#392C2×C2911yescharacteristic
566C2×#386C2×C2911yescharacteristic, complemented
567C2×#386C2×C2911yescharacteristic, complemented
568C2×#381C2×C2911yescharacteristic, complemented
569#1442C2×C2911yescharacteristic, complemented
570#1440C2×C2911yescharacteristic, complemented
571#1439C2×C2911yescharacteristic, complemented
572#1439C2×C2911yescharacteristic, complemented
573#1438C2×C2911yescharacteristic, complemented
574#1438C2×C2911yescharacteristic, complemented
575#1437C2×C2911yescharacteristic, complemented
576#1436C2×C2911yescharacteristic, complemented
577C22⋊#95C2×C2911yescharacteristic, complemented
578C22×C29—24no—
579C22×C29—24no—
580C22×C29—24no—
581C22×C29—24no—
582C22×C29—24no—
583C22×C29—24no—
584C22×C29—42no—
585C22×C29—42no—
586C22×C29—42no—
587C22×C29—42no—
588C22×C29—42no—
589C22×C29—42no—
590C22×C29—42no—
591C22×C29—42no—
592C22×C29—42no—
593C22×C29—42no—
594C22×C29—42no—
595C22×C29—42no—
596C22×C29—42no—
597C22×C29—42no—
598C22×C29—42no—
599C22×C29—42no—
600C22×C29—42no—
601C22×C29—42no—
602C22×C29—42no—
603C22×C29—42no—
604C22×C29—42no—
605C22×C29—42no—
606C22×C29—42no—
607C22×C29—42no—
608C22×C29—42no—
609C22×C29—42no—
610C22×C29—42no—
611C22×C29—42no—
612C22×C29—42no—
613C22×C29—42no—
614C22×C29—42no—
615C22×C29—81no—
616C22×C29—81no—
617C22×C29—81no—
618C22×C29—81no—
619C22×C29—81no—
620C22×C29—81no—
621C22×C29—81no—
622C22×C29—81no—
623C22×C29C2×#12011yescharacteristic
624C22×C29C2×#12111yescharacteristic
625C22×C29C2×#12311yescharacteristic
626C22×C29C2×#12311yescharacteristic
627C22×C29#52511yescharacteristic
628C22×C29#52511yescharacteristic
629C22×C29#52511yescharacteristic
630C22×C29#52511yescharacteristic
631C22×C29#52511yescharacteristic
632C22×C29#52511yescharacteristic
633C22×C29#52911yescharacteristic
634C22×C29#52911yescharacteristic
635C22×C29#53211yescharacteristic
636C22×C29#53411yescharacteristic
637C22×C29#53511yescharacteristic
638C22×C29#53811yescharacteristic
639C22×C29#53811yescharacteristic
640C22×C29#54011yescharacteristic
641C22×C29#54011yescharacteristic
642C22×C29D4211yescharacteristic
643C22×C29D4211yescharacteristic
644C22×C29#54611yescharacteristic
645C22×C29#54611yescharacteristic
646C22×C29#54611yescharacteristic
647C22×C29#54611yescharacteristic
648C22×C29#54611yescharacteristic
649C22×C29#54611yescharacteristic
650C22×C29#54611yescharacteristic
651C22×C29#55011yescharacteristic
652C22×C29#55111yescharacteristic
653C22×C29#55311yescharacteristic
654C22×C29#55311yescharacteristic
655C22×C29#55311yescharacteristic
656C22×C29#55511yescharacteristic
657C22×C29#55911yescharacteristic
658C4×C29—24no—
659C4×C29—24no—
660C4×C29—42no—
661C4×C29—42no—
662C4×C29—42no—
663C4×C29—42no—
664C4×C29—42no—
665C4×C29—42no—
666C4×C29—81no—
667C4×C29—81no—
668C4×C29—81no—
669C4×C29—81no—
670C23×D4C22×C2911yescharacteristic
671C23×D4C22×C2911yescharacteristic
672C23×D4C22×C2911yescharacteristic
673C24×C4C22×C2911yescharacteristic
674C24×C4C22×C2911yescharacteristic
675C2×C4×D4—24no—
676C2×C4×D4—24no—
677C2×C4×D4—24no—
678C22×C4⋊C4C22×C2911yescharacteristic
679C22×C4⋊C4C22×C2911yescharacteristic
680C22×C22⋊C4C22×C2911yescharacteristic
681C22×C22⋊C4C22×C2911yescharacteristic
682C22×C22⋊C4C22×C2911yescharacteristic
683C22×C22⋊C4C22×C2911yescharacteristic
684C22×C22⋊C4C22×C2911yescharacteristic
685C22×C22⋊C4C22×C2911yescharacteristic
686C22×C22⋊C4C22×C2911yescharacteristic
687C22×C22⋊C4C22×C2911yescharacteristic
688C22×C22⋊C4C22×C2911yescharacteristic
689C22×C22⋊C4C22×C2911yescharacteristic
690C22×C22⋊C4C22×C2911yescharacteristic
691C22×C22⋊C4C22×C2911yescharacteristic
692C22×C22⋊C4C22×C2911yescharacteristic
693C22×C42C22×C2911yescharacteristic
694#394—24no—
695#392—24no—
696#386—24no—
697#386—24no—
698#381—24no—
699C2×#95C22×C2911yescharacteristic
700C2×#95C22×C2911yescharacteristic
701C2×#95C22×C2911yescharacteristic
702C2×#95C22×C2911yescharacteristic
703C2×#95C22×C2911yescharacteristic
704C2×#95C22×C2911yescharacteristic
705C2×#95C22×C2911yescharacteristic
706C2×#95C22×C2911yescharacteristic
707C2×#95C22×C2911yescharacteristic
708C2×#95C22×C2911yescharacteristic
709C2×#95C22×C2911yescharacteristic
710C2×#95C22×C2911yescharacteristic
711C2×#95C22×C2911yescharacteristic
712C2×#95C22×C2911yescharacteristic
713C2×C29—44no—
714C2×C29—44no—
715C2×C29—82no—
716C2×C29#239211yescharacteristic
717C2×C29#240411yescharacteristic
718C2×C29#241011yescharacteristic
719C2×C29#241411yescharacteristic
720C2×C29#241811yescharacteristic
721C2×C29#242011yescharacteristic
722C2×C29#244411yescharacteristic
723C2×C29#244511yescharacteristic
724C2×C29#245611yescharacteristic
725C2×C29#245711yescharacteristic
726C2×C29#245911yescharacteristic
727C2×C29#246411yescharacteristic
728C2×C29#260011yescharacteristic
729C2×C29#263511yescharacteristic
730C2×C29#284911yescharacteristic
731C25C23×C2911yescharacteristic
732C25C23×C2911yescharacteristic
733C25C23×C2911yescharacteristic
734C22×D4—22no—
735C22×D4—22no—
736C22×D4—22no—
737C22×D4—22no—
738C22×D4—22no—
739C22×D4—22no—
740C22×D4—22no—
741C22×D4—22no—
742C22×D4—22no—
743C22×D4—22no—
744C22×D4—22no—
745C22×D4—22no—
746C22×D4—22no—
747C22×D4—22no—
748C22×D4—22no—
749C22×D4—22no—
750C22×D4—41no—
751C22×D4—41no—
752C22×D4—41no—
753C22×D4—41no—
754C22×D4D4×C2914yes—
755C23×C4—22no—
756C23×C4—22no—
757C23×C4—22no—
758C23×C4—22no—
759C23×C4—22no—
760C23×C4—22no—
761C23×C4—22no—
762C23×C4—22no—
763C23×C4—22no—
764C23×C4—41no—
765C23×C4—41no—
766C23×C4—41no—
767C23×C4—41no—
768C23×C4D4×C2914yescomplemented
769C23×C4C23×C2911yescharacteristic
770C23×C4C23×C2911yescharacteristic
771C23×C4C23×C2911yescharacteristic
772C23×C4C23×C2911yescharacteristic
773C23×C4C23×C2911yescharacteristic
774C23×C4C23×C2911yescharacteristic
775C23×C4C23×C2911yescharacteristic
776C23×C4C23×C2911yescharacteristic
777C23×C4C23×C2911yescharacteristic
778C23×C4C23×C2911yescharacteristic
779C23×C4C23×C2911yescharacteristic
780C23×C4C23×C2911yescharacteristic
781C4×D4—232no—
782C2×C4⋊C4—22no—
783C2×C4⋊C4—22no—
784C2×C4⋊C4—22no—
785C2×C4⋊C4—22no—
786C2×C4⋊C4—22no—
787C2×C4⋊C4—41no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4—22no—
791C2×C22⋊C4—22no—
792C2×C22⋊C4—22no—
793C2×C22⋊C4—22no—
794C2×C22⋊C4—22no—
795C2×C22⋊C4—22no—
796C2×C22⋊C4—22no—
797C2×C22⋊C4—22no—
798C2×C22⋊C4—22no—
799C2×C22⋊C4—22no—
800C2×C22⋊C4—22no—
801C2×C22⋊C4—22no—
802C2×C22⋊C4—22no—
803C2×C22⋊C4—22no—
804C2×C22⋊C4—22no—
805C2×C22⋊C4—22no—
806C2×C22⋊C4—22no—
807C2×C22⋊C4—22no—
808C2×C22⋊C4—22no—
809C2×C22⋊C4—22no—
810C2×C22⋊C4—22no—
811C2×C22⋊C4—22no—
812C2×C22⋊C4—22no—
813C2×C22⋊C4—22no—
814C2×C22⋊C4—41no—
815C2×C22⋊C4—41no—
816C2×C22⋊C4—41no—
817C2×C22⋊C4—41no—
818C2×C22⋊C4—41no—
819C2×C22⋊C4—41no—
820C2×C22⋊C4—41no—
821C2×C22⋊C4—41no—
822C2×C22⋊C4—41no—
823C2×C22⋊C4—41no—
824C2×C22⋊C4—41no—
825C2×C22⋊C4—41no—
826C2×C22⋊C4D4×C2914yescomplemented
827C2×C42—22no—
828C2×C42—22no—
829C2×C42—22no—
830#95—22no—
831#95—22no—
832#95—22no—
833#95—22no—
834#95—22no—
835#95—22no—
836#95—22no—
837#95—22no—
838#95—22no—
839#95—22no—
840#95—41no—
841#95—41no—
842#95—41no—
843#95D4×C2914yescomplemented
844C29#1473011yescharacteristic, direct product factor, Sylow
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24—21no—
876C24—21no—
877C24—21no—
878C24—21no—
879C24—21no—
880C24—21no—
881C24—21no—
882C24—21no—
883C24C2×D4×C2912yes—
884C24C2×D4×C2912yes—
885C24C2×D4×C2912yes—
886C24C2×D4×C2912yes—
887C24#41×C2912yes—
888C24#41×C2912yes—
889C24#41×C2912yes—
890C24C24×C2911yescharacteristic
891C2×D4—28no—
892C2×D4—28no—
893C2×D4—28no—
894C2×D4—28no—
895C2×D4—28no—
896C2×D4—28no—
897C2×D4—28no—
898C2×D4—28no—
899C2×D4—28no—
900C2×D4—44no—
901C2×D4—44no—
902C2×D4—44no—
903C2×D4—44no—
904C2×D4—44no—
905C2×D4—44no—
906C2×D4—44no—
907C2×D4—44no—
908C2×D4—44no—
909C2×D4—44no—
910C2×D4—44no—
911C2×D4—44no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—28no—
921C22×C4—28no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—28no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—21no—
980C22×C4—21no—
981C22×C4—21no—
982C22×C4—21no—
983C22×C4—21no—
984C22×C4—21no—
985C22×C4—21no—
986C22×C4—21no—
987C22×C4—44no—
988C22×C4—44no—
989C22×C4—44no—
990C22×C4—44no—
991C22×C4—44no—
992C22×C4—44no—
993C22×C4—44no—
994C22×C4—44no—
995C22×C4—44no—
996C22×C4—44no—
997C22×C4—44no—
998C22×C4C2×D4×C2912yes—
999C22×C4C2×D4×C2912yes—
1000C22×C4C2×D4×C2912yes—
1001C22×C4C2×D4×C2912yes—
1002C22×C4C2×D4×C2912yes—
1003C22×C4C2×D4×C2912yes—
1004C22×C4C2×D4×C2912yes—
1005C22×C4C2×D4×C2912yes—
1006C22×C4#41×C2912yes—
1007C22×C4#41×C2912yes—
1008C22×C4#41×C2912yes—
1009C22×C4#41×C2912yes—
1010C4⋊C4—28no—
1011C4⋊C4—44no—
1012C22⋊C4—28no—
1013C22⋊C4—28no—
1014C22⋊C4—44no—
1015C22⋊C4—44no—
1016C22⋊C4—44no—
1017C22⋊C4—44no—
1018C22⋊C4—44no—
1019C22⋊C4—44no—
1020C22⋊C4—44no—
1021C22⋊C4—44no—
1022C22⋊C4—44no—
1023C22⋊C4—44no—
1024C22⋊C4—44no—
1025C42—28no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—22no—
1067C23—22no—
1068C23—22no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23C29×#12014yes—
1130C23C29×#12314yes—
1131C23C22×D4×C2911yescharacteristic
1132C23C22×D4×C2911yescharacteristic
1133C23C22×D4×C2911yescharacteristic
1134C23C22×D4×C2911yescharacteristic
1135C23C2×#41×C2911yescharacteristic
1136C23C2×#41×C2911yescharacteristic
1137C23C2×#41×C2911yescharacteristic
1138C23C2×#41×C2911yescharacteristic
1139C23C2×#41×C2911yescharacteristic
1140C23C2×#41×C2911yescharacteristic
1141C23C2×#41×C2911yescharacteristic
1142C23C29×H(5,𝔽2)11yescharacteristic
1143C23C29×H(5,𝔽2)11yescharacteristic
1144C23C29×H(5,𝔽2)11yescharacteristic
1145C23C29×H(5,𝔽2)11yescharacteristic
1146D4—232no—
1147D4—416no—
1148D4—416no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—416no—
1180C2×C4—416no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4C29×#12114yes—
1234C2×C4C29×#12314yes—
1235C22—24no—
1236C22—24no—
1237C22—24no—
1238C22—24no—
1239C22—24no—
1240C22—24no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22C2×C29×#12011yescharacteristic
1281C22C2×C29×#12111yescharacteristic
1282C22C2×C29×#12311yescharacteristic
1283C22C2×C29×#12311yescharacteristic
1284C22C29×#52511yescharacteristic
1285C22C29×#52511yescharacteristic
1286C22C29×#52511yescharacteristic
1287C22C29×#52511yescharacteristic
1288C22C29×#52511yescharacteristic
1289C22C29×#52511yescharacteristic
1290C22C29×#52911yescharacteristic
1291C22C29×#52911yescharacteristic
1292C22C29×#53211yescharacteristic
1293C22C29×#53411yescharacteristic
1294C22C29×#53511yescharacteristic
1295C22C29×#53811yescharacteristic
1296C22C29×#53811yescharacteristic
1297C22C29×#54011yescharacteristic
1298C22C29×#54011yescharacteristic
1299C22D42×C2911yescharacteristic
1300C22D42×C2911yescharacteristic
1301C22C29×#54611yescharacteristic
1302C22C29×#54611yescharacteristic
1303C22C29×#54611yescharacteristic
1304C22C29×#54611yescharacteristic
1305C22C29×#54611yescharacteristic
1306C22C29×#54611yescharacteristic
1307C22C29×#54611yescharacteristic
1308C22C29×#55011yescharacteristic
1309C22C29×#55111yescharacteristic
1310C22C29×#55311yescharacteristic
1311C22C29×#55311yescharacteristic
1312C22C29×#55311yescharacteristic
1313C22C29×#55511yescharacteristic
1314C22C29×#55911yescharacteristic
1315C4—24no—
1316C4—24no—
1317C4—42no—
1318C4—42no—
1319C4—42no—
1320C4—42no—
1321C4—42no—
1322C4—42no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C2—44no—
1328C2—44no—
1329C2—82no—
1330C2C29×#239211yescharacteristic
1331C2C29×#240411yescharacteristic
1332C2C29×#241011yescharacteristic
1333C2C29×#241411yescharacteristic
1334C2C29×#241811yescharacteristic
1335C2C29×#242011yescharacteristic
1336C2C29×#244411yescharacteristic
1337C2C29×#244511yescharacteristic
1338C2C29×#245611yescharacteristic
1339C2C29×#245711yescharacteristic
1340C2C29×#245911yescharacteristic
1341C2C29×#246411yescharacteristic
1342C2C29×#260011yescharacteristic
1343C2C29×#263511yescharacteristic
1344C2C29×#284911yescharacteristic
subgroupG/H
center, socleC24×C29C24
commutator, Frattini, cosocleC24C24×C29
prime radicalC2×C29×#392C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C4×D4×C29C2semidirect
2. C2×C29×#394C2semidirect
4. C2×C29×#386C2semidirect
5. C2×C29×#386C2semidirect
6. C2×C29×#381C2semidirect
7. C29×#1442C2semidirect
8. C29×#1440C2semidirect
9. C29×#1439C2semidirect
10. C29×#1439C2semidirect
11. C29×#1438C2semidirect
12. C29×#1438C2semidirect
13. C29×#1437C2semidirect
14. C29×#1436C2semidirect
15. C29×C22⋊#95C2semidirect
96. C23×C4×C29D4semidirect
154. C2×C22⋊C4×C29D4semidirect
171. C29×#95D4semidirect
353. #14730C29direct (N × H)
563. C22×C4×D4C2×C29semidirect
564. C2×#394C2×C29semidirect
566. C2×#386C2×C29semidirect
567. C2×#386C2×C29semidirect
568. C2×#381C2×C29semidirect
569. #1442C2×C29semidirect
570. #1440C2×C29semidirect
571. #1439C2×C29semidirect
572. #1439C2×C29semidirect
573. #1438C2×C29semidirect
574. #1438C2×C29semidirect
575. #1437C2×C29semidirect
576. #1436C2×C29semidirect
577. C22⋊#95C2×C29semidirect
768. C23×C4D4×C29semidirect
826. C2×C22⋊C4D4×C29semidirect
843. #95D4×C29semidirect
844. C29#14730direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×D4×C292
C2×C29×#3942
C2×C29×#3922
C2×C29×#3862
C2×C29×#3812
C29×#14422
C29×#14402
C29×#14392
C29×#14382
C29×#14372
C29×#14362
C29×C22⋊#952
#1473029