Finite Group Databasebeta

← C29×#16256 #20311156

Subgroups — C29×#16256 #20311156

Order 7424.

2318 conjugacy classes of subgroups.

The subgroup lattice has 1336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C29×#123C211yesmaximal, characteristic, complemented
2C2×C29×#396C211yesmaximal, characteristic, complemented
3C2×C29×#394C211yesmaximal, characteristic, complemented
4C2×C29×#392C211yesmaximal, characteristic
5C2×C29×#386C211yesmaximal, characteristic, complemented
6C2×C29×#380C211yesmaximal, characteristic, complemented
7C29×#1442C211yesmaximal, characteristic, complemented
8C29×#1441C211yesmaximal, characteristic, complemented
9C29×#1439C211yesmaximal, characteristic, complemented
10C29×#1439C211yesmaximal, characteristic, complemented
11C29×#1439C211yesmaximal, characteristic, complemented
12C29×#1439C211yesmaximal, characteristic, complemented
13C29×#1438C211yesmaximal, characteristic, complemented
14C29×#1438C211yesmaximal, characteristic, complemented
15C29×#1438C211yesmaximal, characteristic, complemented
16C23×D4×C29C2211yescharacteristic
17C23×D4×C29C2211yescharacteristic
18C23×D4×C29C2211yescharacteristic
19C24×C4×C29C2211yescharacteristic
20C2×C29×#123—24no—
21C2×C29×#123—24no—
22C2×C29×#123—24no—
23C22×C4⋊C4×C29C2211yescharacteristic
24C22×C4⋊C4×C29C2211yescharacteristic
25C22×C4⋊C4×C29C2211yescharacteristic
26C22×C4⋊C4×C29C2211yescharacteristic
27C22×C4⋊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×C22⋊C4×C29C2211yescharacteristic
40C22×C22⋊C4×C29C2211yescharacteristic
41C22×C22⋊C4×C29C2211yescharacteristic
42C29×#396—24no—
43C29×#394—24no—
44C29×#392—24no—
45C29×#386—24no—
46C29×#380—24no—
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—41no—
76C22×D4×C29—41no—
77C22×D4×C29—41no—
78C22×D4×C29—41no—
79C22×D4×C29—41no—
80C22×D4×C29—41no—
81C22×D4×C29—41no—
82C22×D4×C29—41no—
83C23×C4×C29—22no—
84C23×C4×C29—22no—
85C23×C4×C29—22no—
86C23×C4×C29—22no—
87C23×C4×C29—41no—
88C23×C4×C29—41no—
89C23×C4×C29D414yescomplemented
90C23×C4×C29C2311yescharacteristic
91C23×C4×C29C2311yescharacteristic
92C23×C4×C29C2311yescharacteristic
93C23×C4×C29C2311yescharacteristic
94C23×C4×C29C2311yescharacteristic
95C23×C4×C29C2311yescharacteristic
96C23×C4×C29C2311yescharacteristic
97C23×C4×C29C2311yescharacteristic
98C23×C4×C29C2311yescharacteristic
99C23×C4×C29C2311yescharacteristic
100C23×C4×C29C2311yescharacteristic
101C23×C4×C29C2311yescharacteristic
102C29×#123—232no—
103C2×C4⋊C4×C29—22no—
104C2×C4⋊C4×C29—22no—
105C2×C4⋊C4×C29—22no—
106C2×C4⋊C4×C29—22no—
107C2×C4⋊C4×C29—22no—
108C2×C4⋊C4×C29—22no—
109C2×C4⋊C4×C29—22no—
110C2×C4⋊C4×C29—22no—
111C2×C4⋊C4×C29—22no—
112C2×C4⋊C4×C29—22no—
113C2×C4⋊C4×C29—41no—
114C2×C4⋊C4×C29—41no—
115C2×C4⋊C4×C29—41no—
116C2×C4⋊C4×C29—41no—
117C2×C4⋊C4×C29D414yescomplemented
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—41no—
141C2×C22⋊C4×C29—41no—
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×C29—41no—
155C2×C22⋊C4×C29—41no—
156C2×C22⋊C4×C29—41no—
157C2×C22⋊C4×C29—41no—
158C2×C22⋊C4×C29D414yes—
159C2×C22⋊C4×C29D414yescomplemented
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×#95—41no—
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×C29—21no—
211C24×C29—21no—
212C24×C29C2×D412yes—
213C24×C29C2×D412yes—
214C24×C29C2×D412yes—
215C24×C29#4112yes—
216C24×C29#4112yes—
217C24×C29C2411yescharacteristic
218C2×D4×C29—28no—
219C2×D4×C29—28no—
220C2×D4×C29—44no—
221C2×D4×C29—44no—
222C2×D4×C29—44no—
223C2×D4×C29—44no—
224C2×D4×C29—44no—
225C2×D4×C29—44no—
226C2×D4×C29—44no—
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—28no—
244C22×C4×C29—21no—
245C22×C4×C29—21no—
246C22×C4×C29—21no—
247C22×C4×C29—21no—
248C22×C4×C29—21no—
249C22×C4×C29—21no—
250C22×C4×C29—21no—
251C22×C4×C29—21no—
252C22×C4×C29—21no—
253C22×C4×C29—21no—
254C22×C4×C29—21no—
255C22×C4×C29—21no—
256C22×C4×C29—21no—
257C22×C4×C29—21no—
258C22×C4×C29—21no—
259C22×C4×C29—21no—
260C22×C4×C29—21no—
261C22×C4×C29—21no—
262C22×C4×C29—21no—
263C22×C4×C29—21no—
264C22×C4×C29—21no—
265C22×C4×C29—21no—
266C22×C4×C29—21no—
267C22×C4×C29—21no—
268C22×C4×C29—21no—
269C22×C4×C29—21no—
270C22×C4×C29—21no—
271C22×C4×C29—21no—
272C22×C4×C29—21no—
273C22×C4×C29—21no—
274C22×C4×C29—21no—
275C22×C4×C29—21no—
276C22×C4×C29—21no—
277C22×C4×C29—21no—
278C22×C4×C29—21no—
279C22×C4×C29—21no—
280C22×C4×C29—21no—
281C22×C4×C29—21no—
282C22×C4×C29—21no—
283C22×C4×C29—21no—
284C22×C4×C29—21no—
285C22×C4×C29—21no—
286C22×C4×C29—28no—
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—21no—
315C22×C4×C29—44no—
316C22×C4×C29—44no—
317C22×C4×C29—44no—
318C22×C4×C29—44no—
319C22×C4×C29—44no—
320C22×C4×C29C2×D412yes—
321C22×C4×C29C2×D412yes—
322C22×C4×C29C2×D412yes—
323C22×C4×C29C2×D412yes—
324C22×C4×C29C2×D412yes—
325C22×C4×C29C2×D412yes—
326C22×C4×C29C2×D412yes—
327C22×C4×C29C2×D412yes—
328C22×C4×C29C2×D412yes—
329C22×C4×C29#4112yes—
330C4⋊C4×C29—28no—
331C4⋊C4×C29—28no—
332C4⋊C4×C29—44no—
333C4⋊C4×C29—44no—
334C4⋊C4×C29—44no—
335C22⋊C4×C29—28no—
336C22⋊C4×C29—28no—
337C22⋊C4×C29—28no—
338C22⋊C4×C29—44no—
339C22⋊C4×C29—44no—
340C22⋊C4×C29—44no—
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—
349#16256C2911yesmaximal, characteristic, direct product factor, Sylow
350C23×C29—22no—
351C23×C29—22no—
352C23×C29—22no—
353C23×C29—22no—
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—41no—
383C23×C29—41no—
384C23×C29—41no—
385C23×C29—41no—
386C23×C29—41no—
387C23×C29—41no—
388C23×C29—41no—
389C23×C29—41no—
390C23×C29—41no—
391C23×C29—41no—
392C23×C29—41no—
393C23×C29—41no—
394C23×C29—41no—
395C23×C29—41no—
396C23×C29—41no—
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#12114yes—
455C23×C29C22×D411yescharacteristic
456C23×C29C22×D411yescharacteristic
457C23×C29C22×D411yescharacteristic
458C23×C29C22×D411yescharacteristic
459C23×C29C2×#4111yescharacteristic
460C23×C29C2×#4111yescharacteristic
461C23×C29C2×#4111yescharacteristic
462C23×C29H(5,𝔽2)11yescharacteristic
463C23×C29H(5,𝔽2)11yescharacteristic
464C23×C29H(5,𝔽2)11yescharacteristic
465C23×C29H(5,𝔽2)11yescharacteristic
466C23×C29H(5,𝔽2)11yescharacteristic
467C23×C29H(5,𝔽2)11yescharacteristic
468C23×C292−1+411yescharacteristic
469C23×C292−1+411yescharacteristic
470D4×C29—416no—
471D4×C29—416no—
472D4×C29—416no—
473C2×C4×C29—22no—
474C2×C4×C29—22no—
475C2×C4×C29—22no—
476C2×C4×C29—22no—
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—416no—
501C2×C4×C29—41no—
502C2×C4×C29—41no—
503C2×C4×C29—41no—
504C2×C4×C29—41no—
505C2×C4×C29—41no—
506C2×C4×C29—41no—
507C2×C4×C29—41no—
508C2×C4×C29—41no—
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#12014yes—
558C22×#123C2×C2911yescharacteristic, complemented
559C2×#396C2×C2911yescharacteristic, complemented
560C2×#394C2×C2911yescharacteristic, complemented
561C2×#392C2×C2911yescharacteristic
562C2×#386C2×C2911yescharacteristic, complemented
563C2×#380C2×C2911yescharacteristic, complemented
564#1442C2×C2911yescharacteristic, complemented
565#1441C2×C2911yescharacteristic, complemented
566#1439C2×C2911yescharacteristic, complemented
567#1439C2×C2911yescharacteristic, complemented
568#1439C2×C2911yescharacteristic, complemented
569#1439C2×C2911yescharacteristic, complemented
570#1438C2×C2911yescharacteristic, complemented
571#1438C2×C2911yescharacteristic, complemented
572#1438C2×C2911yescharacteristic, complemented
573C22×C29—24no—
574C22×C29—24no—
575C22×C29—24no—
576C22×C29—42no—
577C22×C29—42no—
578C22×C29—42no—
579C22×C29—42no—
580C22×C29—42no—
581C22×C29—42no—
582C22×C29—42no—
583C22×C29—42no—
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—81no—
603C22×C29—81no—
604C22×C29—81no—
605C22×C29—81no—
606C22×C29—81no—
607C22×C29—81no—
608C22×C29—81no—
609C22×C29—81no—
610C22×C29—81no—
611C22×C29—81no—
612C22×C29—81no—
613C22×C29—81no—
614C22×C29—81no—
615C22×C29—81no—
616C22×C29—81no—
617C22×C29—81no—
618C22×C29C2×#12011yescharacteristic
619C22×C29C2×#12111yescharacteristic
620C22×C29#52511yescharacteristic
621C22×C29#53411yescharacteristic
622C22×C29#53411yescharacteristic
623C22×C29#53511yescharacteristic
624C22×C29#53511yescharacteristic
625C22×C29#53511yescharacteristic
626C22×C29#53611yescharacteristic
627C22×C29#53711yescharacteristic
628C22×C29#53711yescharacteristic
629C22×C29#53711yescharacteristic
630C22×C29#53711yescharacteristic
631C22×C29#53811yescharacteristic
632C22×C29#53911yescharacteristic
633C22×C29#53911yescharacteristic
634C22×C29#53911yescharacteristic
635C22×C29#54011yescharacteristic
636C22×C29#54211yescharacteristic
637C22×C29D4211yescharacteristic
638C22×C29D4211yescharacteristic
639C22×C29#54611yescharacteristic
640C22×C29#54611yescharacteristic
641C22×C29#54611yescharacteristic
642C22×C29#54611yescharacteristic
643C22×C29#54611yescharacteristic
644C22×C29#54711yescharacteristic
645C22×C29#54811yescharacteristic
646C22×C29#55011yescharacteristic
647C22×C29#55111yescharacteristic
648C22×C29#55111yescharacteristic
649C22×C29#56011yescharacteristic
650C22×C29#56011yescharacteristic
651C22×C29#56211yescharacteristic
652C22×C29#56211yescharacteristic
653C4×C29—24no—
654C4×C29—42no—
655C4×C29—42no—
656C4×C29—42no—
657C4×C29—42no—
658C4×C29—42no—
659C4×C29—42no—
660C4×C29—42no—
661C4×C29—81no—
662C4×C29—81no—
663C4×C29—81no—
664C4×C29—81no—
665C23×D4C22×C2911yescharacteristic
666C23×D4C22×C2911yescharacteristic
667C23×D4C22×C2911yescharacteristic
668C24×C4C22×C2911yescharacteristic
669C2×#123—24no—
670C2×#123—24no—
671C2×#123—24no—
672C22×C4⋊C4C22×C2911yescharacteristic
673C22×C4⋊C4C22×C2911yescharacteristic
674C22×C4⋊C4C22×C2911yescharacteristic
675C22×C4⋊C4C22×C2911yescharacteristic
676C22×C4⋊C4C22×C2911yescharacteristic
677C22×C22⋊C4C22×C2911yescharacteristic
678C22×C22⋊C4C22×C2911yescharacteristic
679C22×C22⋊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
691#396—24no—
692#394—24no—
693#392—24no—
694#386—24no—
695#380—24no—
696C2×#95C22×C2911yescharacteristic
697C2×#95C22×C2911yescharacteristic
698C2×#95C22×C2911yescharacteristic
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×C29—44no—
709C2×C29—82no—
710C2×C29—82no—
711C2×C29#240711yescharacteristic
712C2×C29#241011yescharacteristic
713C2×C29#241111yescharacteristic
714C2×C29#261511yescharacteristic
715C2×C29#261811yescharacteristic
716C2×C29#263011yescharacteristic
717C2×C29#267211yescharacteristic
718C2×C29#267311yescharacteristic
719C2×C29#267811yescharacteristic
720C2×C29#268111yescharacteristic
721C2×C29#269311yescharacteristic
722C2×C29#269611yescharacteristic
723C2×C29#270511yescharacteristic
724C2×C29#270611yescharacteristic
725C2×C29#281311yescharacteristic
726C25C23×C2911yescharacteristic
727C25C23×C2911yescharacteristic
728C25C23×C2911yescharacteristic
729C22×D4—22no—
730C22×D4—22no—
731C22×D4—22no—
732C22×D4—22no—
733C22×D4—22no—
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—41no—
743C22×D4—41no—
744C22×D4—41no—
745C22×D4—41no—
746C22×D4—41no—
747C22×D4—41no—
748C22×D4—41no—
749C22×D4—41no—
750C23×C4—22no—
751C23×C4—22no—
752C23×C4—22no—
753C23×C4—22no—
754C23×C4—41no—
755C23×C4—41no—
756C23×C4D4×C2914yescomplemented
757C23×C4C23×C2911yescharacteristic
758C23×C4C23×C2911yescharacteristic
759C23×C4C23×C2911yescharacteristic
760C23×C4C23×C2911yescharacteristic
761C23×C4C23×C2911yescharacteristic
762C23×C4C23×C2911yescharacteristic
763C23×C4C23×C2911yescharacteristic
764C23×C4C23×C2911yescharacteristic
765C23×C4C23×C2911yescharacteristic
766C23×C4C23×C2911yescharacteristic
767C23×C4C23×C2911yescharacteristic
768C23×C4C23×C2911yescharacteristic
769#123—232no—
770C2×C4⋊C4—22no—
771C2×C4⋊C4—22no—
772C2×C4⋊C4—22no—
773C2×C4⋊C4—22no—
774C2×C4⋊C4—22no—
775C2×C4⋊C4—22no—
776C2×C4⋊C4—22no—
777C2×C4⋊C4—22no—
778C2×C4⋊C4—22no—
779C2×C4⋊C4—22no—
780C2×C4⋊C4—41no—
781C2×C4⋊C4—41no—
782C2×C4⋊C4—41no—
783C2×C4⋊C4—41no—
784C2×C4⋊C4D4×C2914yescomplemented
785C2×C22⋊C4—22no—
786C2×C22⋊C4—22no—
787C2×C22⋊C4—22no—
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—41no—
808C2×C22⋊C4—41no—
809C2×C22⋊C4—41no—
810C2×C22⋊C4—41no—
811C2×C22⋊C4—41no—
812C2×C22⋊C4—41no—
813C2×C22⋊C4—41no—
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⋊C4D4×C2914yes—
826C2×C22⋊C4D4×C2914yescomplemented
827#95—22no—
828#95—22no—
829#95—22no—
830#95—22no—
831#95—22no—
832#95—22no—
833#95—22no—
834#95—22no—
835#95—41no—
836#95—41no—
837#95—41no—
838#95—41no—
839C29#1625611yescharacteristic, direct product factor, Sylow
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
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—
880C24C2×D4×C2912yes—
881C24C2×D4×C2912yes—
882C24C2×D4×C2912yes—
883C24#41×C2912yes—
884C24#41×C2912yes—
885C24C24×C2911yescharacteristic
886C2×D4—28no—
887C2×D4—28no—
888C2×D4—44no—
889C2×D4—44no—
890C2×D4—44no—
891C2×D4—44no—
892C2×D4—44no—
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—44no—
896C2×D4—44no—
897C2×D4—44no—
898C2×D4—44no—
899C2×D4—44no—
900C2×D4—44no—
901C2×D4—44no—
902C2×D4—44no—
903C2×D4—44no—
904C2×D4—44no—
905C2×D4—44no—
906C2×D4—44no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—28no—
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—21no—
921C22×C4—21no—
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—28no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
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—44no—
984C22×C4—44no—
985C22×C4—44no—
986C22×C4—44no—
987C22×C4—44no—
988C22×C4C2×D4×C2912yes—
989C22×C4C2×D4×C2912yes—
990C22×C4C2×D4×C2912yes—
991C22×C4C2×D4×C2912yes—
992C22×C4C2×D4×C2912yes—
993C22×C4C2×D4×C2912yes—
994C22×C4C2×D4×C2912yes—
995C22×C4C2×D4×C2912yes—
996C22×C4C2×D4×C2912yes—
997C22×C4#41×C2912yes—
998C4⋊C4—28no—
999C4⋊C4—28no—
1000C4⋊C4—44no—
1001C4⋊C4—44no—
1002C4⋊C4—44no—
1003C22⋊C4—28no—
1004C22⋊C4—28no—
1005C22⋊C4—28no—
1006C22⋊C4—44no—
1007C22⋊C4—44no—
1008C22⋊C4—44no—
1009C22⋊C4—44no—
1010C22⋊C4—44no—
1011C22⋊C4—44no—
1012C22⋊C4—44no—
1013C22⋊C4—44no—
1014C22⋊C4—44no—
1015C22⋊C4—44no—
1016C22⋊C4—44no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
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—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
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—
1121C23C29×#12114yes—
1122C23C22×D4×C2911yescharacteristic
1123C23C22×D4×C2911yescharacteristic
1124C23C22×D4×C2911yescharacteristic
1125C23C22×D4×C2911yescharacteristic
1126C23C2×#41×C2911yescharacteristic
1127C23C2×#41×C2911yescharacteristic
1128C23C2×#41×C2911yescharacteristic
1129C23C29×H(5,𝔽2)11yescharacteristic
1130C23C29×H(5,𝔽2)11yescharacteristic
1131C23C29×H(5,𝔽2)11yescharacteristic
1132C23C29×H(5,𝔽2)11yescharacteristic
1133C23C29×H(5,𝔽2)11yescharacteristic
1134C23C29×H(5,𝔽2)11yescharacteristic
1135C23C29×2−1+411yescharacteristic
1136C23C29×2−1+411yescharacteristic
1137D4—416no—
1138D4—416no—
1139D4—416no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
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—416no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
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×C4C29×#12014yes—
1225C22—24no—
1226C22—24no—
1227C22—24no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
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—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22C2×C29×#12011yescharacteristic
1271C22C2×C29×#12111yescharacteristic
1272C22C29×#52511yescharacteristic
1273C22C29×#53411yescharacteristic
1274C22C29×#53411yescharacteristic
1275C22C29×#53511yescharacteristic
1276C22C29×#53511yescharacteristic
1277C22C29×#53511yescharacteristic
1278C22C29×#53611yescharacteristic
1279C22C29×#53711yescharacteristic
1280C22C29×#53711yescharacteristic
1281C22C29×#53711yescharacteristic
1282C22C29×#53711yescharacteristic
1283C22C29×#53811yescharacteristic
1284C22C29×#53911yescharacteristic
1285C22C29×#53911yescharacteristic
1286C22C29×#53911yescharacteristic
1287C22C29×#54011yescharacteristic
1288C22C29×#54211yescharacteristic
1289C22D42×C2911yescharacteristic
1290C22D42×C2911yescharacteristic
1291C22C29×#54611yescharacteristic
1292C22C29×#54611yescharacteristic
1293C22C29×#54611yescharacteristic
1294C22C29×#54611yescharacteristic
1295C22C29×#54611yescharacteristic
1296C22C29×#54711yescharacteristic
1297C22C29×#54811yescharacteristic
1298C22C29×#55011yescharacteristic
1299C22C29×#55111yescharacteristic
1300C22C29×#55111yescharacteristic
1301C22C29×#56011yescharacteristic
1302C22C29×#56011yescharacteristic
1303C22C29×#56211yescharacteristic
1304C22C29×#56211yescharacteristic
1305C4—24no—
1306C4—42no—
1307C4—42no—
1308C4—42no—
1309C4—42no—
1310C4—42no—
1311C4—42no—
1312C4—42no—
1313C4—81no—
1314C4—81no—
1315C4—81no—
1316C4—81no—
1317C2—44no—
1318C2—82no—
1319C2—82no—
1320C2C29×#240711yescharacteristic
1321C2C29×#241011yescharacteristic
1322C2C29×#241111yescharacteristic
1323C2C29×#261511yescharacteristic
1324C2C29×#261811yescharacteristic
1325C2C29×#263011yescharacteristic
1326C2C29×#267211yescharacteristic
1327C2C29×#267311yescharacteristic
1328C2C29×#267811yescharacteristic
1329C2C29×#268111yescharacteristic
1330C2C29×#269311yescharacteristic
1331C2C29×#269611yescharacteristic
1332C2C29×#270511yescharacteristic
1333C2C29×#270611yescharacteristic
1334C2C29×#281311yescharacteristic
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×C29×#123C2semidirect
2. C2×C29×#396C2semidirect
3. C2×C29×#394C2semidirect
5. C2×C29×#386C2semidirect
6. C2×C29×#380C2semidirect
7. C29×#1442C2semidirect
8. C29×#1441C2semidirect
9. C29×#1439C2semidirect
10. C29×#1439C2semidirect
11. C29×#1439C2semidirect
12. C29×#1439C2semidirect
13. C29×#1438C2semidirect
14. C29×#1438C2semidirect
15. C29×#1438C2semidirect
89. C23×C4×C29D4semidirect
117. C2×C4⋊C4×C29D4semidirect
159. C2×C22⋊C4×C29D4semidirect
349. #16256C29direct (N × H)
558. C22×#123C2×C29semidirect
559. C2×#396C2×C29semidirect
560. C2×#394C2×C29semidirect
562. C2×#386C2×C29semidirect
563. C2×#380C2×C29semidirect
564. #1442C2×C29semidirect
565. #1441C2×C29semidirect
566. #1439C2×C29semidirect
567. #1439C2×C29semidirect
568. #1439C2×C29semidirect
569. #1439C2×C29semidirect
570. #1438C2×C29semidirect
571. #1438C2×C29semidirect
572. #1438C2×C29semidirect
756. C23×C4D4×C29semidirect
784. C2×C4⋊C4D4×C29semidirect
826. C2×C22⋊C4D4×C29semidirect
839. C29#16256direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C29×#1232
C2×C29×#3962
C2×C29×#3942
C2×C29×#3922
C2×C29×#3862
C2×C29×#3802
C29×#14422
C29×#14412
C29×#14392
C29×#14382
#1625629