Finite Group Databasebeta

← C29×#16270 #20311170

Subgroups — C29×#16270 #20311170

Order 7424.

2030 conjugacy classes of subgroups.

The subgroup lattice has 1302 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#397C211yesmaximal, characteristic, complemented
2C2×C29×#392C211yesmaximal, characteristic
3C2×C29×#386C211yesmaximal, characteristic, complemented
4C2×C29×#386C211yesmaximal, characteristic, complemented
5C29×#1443C211yesmaximal, characteristic, complemented
6C29×#1443C211yesmaximal, characteristic, complemented
7C29×#1440C211yesmaximal, characteristic, complemented
8C29×#1440C211yesmaximal, characteristic, complemented
9C29×#1439C211yesmaximal, characteristic, complemented
10C29×#1439C211yesmaximal, characteristic, complemented
11C29×#1438C211yesmaximal, characteristic, complemented
12C29×#1438C211yesmaximal, characteristic, complemented
13C29×#1438C211yesmaximal, characteristic, complemented
14C29×#1438C211yesmaximal, characteristic, complemented
15C29×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C29C2211yescharacteristic
17C23×D4×C29C2211yescharacteristic
18C23×D4×C29C2211yescharacteristic
19C24×C4×C29C2211yescharacteristic
20C22×C4⋊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×C22⋊C4×C29C2211yescharacteristic
32C22×C22⋊C4×C29C2211yescharacteristic
33C22×C22⋊C4×C29C2211yescharacteristic
34C22×C22⋊C4×C29C2211yescharacteristic
35C29×#397—24no—
36C29×#392—24no—
37C29×#386—24no—
38C29×#386—24no—
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
54C2×C29×#95C2211yescharacteristic
55C25×C29C2311yescharacteristic
56C25×C29C2311yescharacteristic
57C25×C29C2311yescharacteristic
58C22×D4×C29—22no—
59C22×D4×C29—22no—
60C22×D4×C29—22no—
61C22×D4×C29—22no—
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—41no—
69C22×D4×C29—41no—
70C22×D4×C29—41no—
71C22×D4×C29—41no—
72C22×D4×C29—41no—
73C22×D4×C29—41no—
74C22×D4×C29—41no—
75C22×D4×C29—41no—
76C22×D4×C29—41no—
77C22×D4×C29—41no—
78C22×D4×C29D414yes—
79C23×C4×C29—22no—
80C23×C4×C29—22no—
81C23×C4×C29—22no—
82C23×C4×C29—41no—
83C23×C4×C29—41no—
84C23×C4×C29—41no—
85C23×C4×C29—41no—
86C23×C4×C29C2311yescharacteristic
87C23×C4×C29C2311yescharacteristic
88C23×C4×C29C2311yescharacteristic
89C23×C4×C29C2311yescharacteristic
90C23×C4×C29C2311yescharacteristic
91C23×C4×C29C2311yescharacteristic
92C23×C4×C29C2311yescharacteristic
93C23×C4×C29C2311yescharacteristic
94C23×C4×C29C2311yescharacteristic
95C23×C4×C29C2311yescharacteristic
96C23×C4×C29C2311yescharacteristic
97C23×C4×C29C2311yescharacteristic
98C2×C4⋊C4×C29—22no—
99C2×C4⋊C4×C29—41no—
100C2×C4⋊C4×C29—41no—
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—41no—
120C2×C22⋊C4×C29—41no—
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×C29—41no—
130C2×C22⋊C4×C29—41no—
131C2×C22⋊C4×C29—41no—
132C2×C22⋊C4×C29—41no—
133C2×C22⋊C4×C29—41no—
134C2×C22⋊C4×C29—41no—
135C2×C22⋊C4×C29—41no—
136C2×C22⋊C4×C29—41no—
137C2×C22⋊C4×C29—41no—
138C2×C22⋊C4×C29—41no—
139C2×C22⋊C4×C29—41no—
140C2×C22⋊C4×C29—41no—
141C2×C22⋊C4×C29—41no—
142C2×C22⋊C4×C29—41no—
143C29×#95—22no—
144C29×#95—22no—
145C29×#95—22no—
146C29×#95—22no—
147C29×#95—22no—
148C29×#95—22no—
149C29×#95—22no—
150C29×#95—41no—
151C29×#95—41no—
152C29×#95—41no—
153C29×#95—41no—
154C29×#95—41no—
155C29×#95—41no—
156C29×#95—41no—
157C29×#95—41no—
158C29×#95D414yescomplemented
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×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×C29C2×D412yes—
200C24×C29C2×D412yes—
201C24×C29#4112yes—
202C24×C29#4112yes—
203C24×C29#4112yes—
204C24×C29C2411yescharacteristic
205C2×D4×C29—28no—
206C2×D4×C29—28no—
207C2×D4×C29—44no—
208C2×D4×C29—44no—
209C2×D4×C29—44no—
210C2×D4×C29—44no—
211C2×D4×C29—44no—
212C2×D4×C29—44no—
213C2×D4×C29—44no—
214C2×D4×C29—44no—
215C2×D4×C29—44no—
216C2×D4×C29—44no—
217C2×D4×C29—44no—
218C2×D4×C29—44no—
219C2×D4×C29—44no—
220C2×D4×C29—44no—
221C2×D4×C29—44no—
222C2×D4×C29—44no—
223C2×D4×C29—44no—
224C2×D4×C29—44no—
225C2×D4×C29—44no—
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×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—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—44no—
305C22×C4×C29—44no—
306C22×C4×C29—44no—
307C22×C4×C29—44no—
308C22×C4×C29—44no—
309C22×C4×C29—44no—
310C22×C4×C29—44no—
311C22×C4×C29C2×D412yes—
312C22×C4×C29C2×D412yes—
313C22×C4×C29C2×D412yes—
314C22×C4×C29C2×D412yes—
315C22×C4×C29#4112yes—
316C22×C4×C29#4112yes—
317C4⋊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×C29—44no—
326C22⋊C4×C29—44no—
327C22⋊C4×C29—44no—
328C22⋊C4×C29—44no—
329C22⋊C4×C29—44no—
330C22⋊C4×C29—44no—
331C22⋊C4×C29—44no—
332#16270C2911yesmaximal, characteristic, direct product factor, Sylow
333C23×C29—22no—
334C23×C29—22no—
335C23×C29—22no—
336C23×C29—22no—
337C23×C29—22no—
338C23×C29—22no—
339C23×C29—22no—
340C23×C29—22no—
341C23×C29—22no—
342C23×C29—22no—
343C23×C29—22no—
344C23×C29—22no—
345C23×C29—22no—
346C23×C29—22no—
347C23×C29—22no—
348C23×C29—22no—
349C23×C29—22no—
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—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×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#12314yes—
438C23×C29C22×D411yescharacteristic
439C23×C29C22×D411yescharacteristic
440C23×C29C2×#4111yescharacteristic
441C23×C29C2×#4111yescharacteristic
442C23×C29C2×#4111yescharacteristic
443C23×C29C2×#4111yescharacteristic
444C23×C29C2×#4111yescharacteristic
445C23×C29H(5,𝔽2)11yescharacteristic
446C23×C29H(5,𝔽2)11yescharacteristic
447C23×C29H(5,𝔽2)11yescharacteristic
448C23×C29H(5,𝔽2)11yescharacteristic
449C23×C29H(5,𝔽2)11yescharacteristic
450C23×C29H(5,𝔽2)11yescharacteristic
451C23×C29H(5,𝔽2)11yescharacteristic
452C23×C29H(5,𝔽2)11yescharacteristic
453D4×C29—416no—
454D4×C29—416no—
455D4×C29—416no—
456C2×C4×C29—22no—
457C2×C4×C29—22no—
458C2×C4×C29—22no—
459C2×C4×C29—22no—
460C2×C4×C29—22no—
461C2×C4×C29—22no—
462C2×C4×C29—22no—
463C2×C4×C29—22no—
464C2×C4×C29—22no—
465C2×C4×C29—22no—
466C2×C4×C29—22no—
467C2×C4×C29—22no—
468C2×C4×C29—22no—
469C2×C4×C29—22no—
470C2×C4×C29—22no—
471C2×C4×C29—22no—
472C2×C4×C29—22no—
473C2×C4×C29—22no—
474C2×C4×C29—416no—
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—41no—
490C2×C4×C29—41no—
491C2×C4×C29—41no—
492C2×C4×C29—41no—
493C2×C4×C29—41no—
494C2×C4×C29—41no—
495C2×C4×C29—41no—
496C2×C4×C29—41no—
497C2×C4×C29—41no—
498C2×C4×C29—41no—
499C2×C4×C29—41no—
500C2×C4×C29—41no—
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×#397C2×C2911yescharacteristic, complemented
542C2×#392C2×C2911yescharacteristic
543C2×#386C2×C2911yescharacteristic, complemented
544C2×#386C2×C2911yescharacteristic, complemented
545#1443C2×C2911yescharacteristic, complemented
546#1443C2×C2911yescharacteristic, complemented
547#1440C2×C2911yescharacteristic, complemented
548#1440C2×C2911yescharacteristic, complemented
549#1439C2×C2911yescharacteristic, complemented
550#1439C2×C2911yescharacteristic, complemented
551#1438C2×C2911yescharacteristic, complemented
552#1438C2×C2911yescharacteristic, complemented
553#1438C2×C2911yescharacteristic, complemented
554#1438C2×C2911yescharacteristic, complemented
555C22⋊#95C2×C2911yescharacteristic, complemented
556C22×C29—24no—
557C22×C29—24no—
558C22×C29—24no—
559C22×C29—42no—
560C22×C29—42no—
561C22×C29—42no—
562C22×C29—42no—
563C22×C29—42no—
564C22×C29—42no—
565C22×C29—42no—
566C22×C29—42no—
567C22×C29—42no—
568C22×C29—42no—
569C22×C29—42no—
570C22×C29—42no—
571C22×C29—42no—
572C22×C29—42no—
573C22×C29—42no—
574C22×C29—42no—
575C22×C29—42no—
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—81no—
586C22×C29—81no—
587C22×C29—81no—
588C22×C29—81no—
589C22×C29—81no—
590C22×C29—81no—
591C22×C29—81no—
592C22×C29—81no—
593C22×C29—81no—
594C22×C29—81no—
595C22×C29—81no—
596C22×C29—81no—
597C22×C29—81no—
598C22×C29—81no—
599C22×C29—81no—
600C22×C29—81no—
601C22×C29C2×#12311yescharacteristic
602C22×C29#52511yescharacteristic
603C22×C29#52911yescharacteristic
604C22×C29#53411yescharacteristic
605C22×C29#53411yescharacteristic
606C22×C29#53511yescharacteristic
607C22×C29#53511yescharacteristic
608C22×C29#53811yescharacteristic
609C22×C29#53811yescharacteristic
610C22×C29#53811yescharacteristic
611C22×C29#53811yescharacteristic
612C22×C29#53811yescharacteristic
613C22×C29#53811yescharacteristic
614C22×C29#53811yescharacteristic
615C22×C29#53811yescharacteristic
616C22×C29#53811yescharacteristic
617C22×C29#53811yescharacteristic
618C22×C29#54011yescharacteristic
619C22×C29#54011yescharacteristic
620C22×C29D4211yescharacteristic
621C22×C29#54611yescharacteristic
622C22×C29#54611yescharacteristic
623C22×C29#54611yescharacteristic
624C22×C29#54611yescharacteristic
625C22×C29#54611yescharacteristic
626C22×C29#55011yescharacteristic
627C22×C29#55111yescharacteristic
628C22×C29#55111yescharacteristic
629C22×C29#55311yescharacteristic
630C22×C29#55311yescharacteristic
631C22×C29#55311yescharacteristic
632C22×C29#56011yescharacteristic
633C22×C29#56011yescharacteristic
634C22×C29#56011yescharacteristic
635C22×C29#56011yescharacteristic
636C4×C29—42no—
637C4×C29—42no—
638C4×C29—42no—
639C4×C29—42no—
640C4×C29—42no—
641C4×C29—42no—
642C4×C29—81no—
643C4×C29—81no—
644C4×C29—81no—
645C4×C29—81no—
646C4×C29—81no—
647C4×C29—81no—
648C23×D4C22×C2911yescharacteristic
649C23×D4C22×C2911yescharacteristic
650C23×D4C22×C2911yescharacteristic
651C24×C4C22×C2911yescharacteristic
652C22×C4⋊C4C22×C2911yescharacteristic
653C22×C22⋊C4C22×C2911yescharacteristic
654C22×C22⋊C4C22×C2911yescharacteristic
655C22×C22⋊C4C22×C2911yescharacteristic
656C22×C22⋊C4C22×C2911yescharacteristic
657C22×C22⋊C4C22×C2911yescharacteristic
658C22×C22⋊C4C22×C2911yescharacteristic
659C22×C22⋊C4C22×C2911yescharacteristic
660C22×C22⋊C4C22×C2911yescharacteristic
661C22×C22⋊C4C22×C2911yescharacteristic
662C22×C22⋊C4C22×C2911yescharacteristic
663C22×C22⋊C4C22×C2911yescharacteristic
664C22×C22⋊C4C22×C2911yescharacteristic
665C22×C22⋊C4C22×C2911yescharacteristic
666C22×C22⋊C4C22×C2911yescharacteristic
667#397—24no—
668#392—24no—
669#386—24no—
670#386—24no—
671C2×#95C22×C2911yescharacteristic
672C2×#95C22×C2911yescharacteristic
673C2×#95C22×C2911yescharacteristic
674C2×#95C22×C2911yescharacteristic
675C2×#95C22×C2911yescharacteristic
676C2×#95C22×C2911yescharacteristic
677C2×#95C22×C2911yescharacteristic
678C2×#95C22×C2911yescharacteristic
679C2×#95C22×C2911yescharacteristic
680C2×#95C22×C2911yescharacteristic
681C2×#95C22×C2911yescharacteristic
682C2×#95C22×C2911yescharacteristic
683C2×#95C22×C2911yescharacteristic
684C2×#95C22×C2911yescharacteristic
685C2×#95C22×C2911yescharacteristic
686C2×#95C22×C2911yescharacteristic
687C2×C29—44no—
688C2×C29—82no—
689C2×C29—82no—
690C2×C29#241811yescharacteristic
691C2×C29#244411yescharacteristic
692C2×C29#246711yescharacteristic
693C2×C29#262211yescharacteristic
694C2×C29#263111yescharacteristic
695C2×C29#264811yescharacteristic
696C2×C29#267311yescharacteristic
697C2×C29#267811yescharacteristic
698C2×C29#268811yescharacteristic
699C2×C29#269711yescharacteristic
700C2×C29#270311yescharacteristic
701C2×C29#271411yescharacteristic
702C2×C29#274911yescharacteristic
703C2×C29#277811yescharacteristic
704C2×C29#282511yescharacteristic
705C25C23×C2911yescharacteristic
706C25C23×C2911yescharacteristic
707C25C23×C2911yescharacteristic
708C22×D4—22no—
709C22×D4—22no—
710C22×D4—22no—
711C22×D4—22no—
712C22×D4—22no—
713C22×D4—22no—
714C22×D4—22no—
715C22×D4—22no—
716C22×D4—22no—
717C22×D4—22no—
718C22×D4—41no—
719C22×D4—41no—
720C22×D4—41no—
721C22×D4—41no—
722C22×D4—41no—
723C22×D4—41no—
724C22×D4—41no—
725C22×D4—41no—
726C22×D4—41no—
727C22×D4—41no—
728C22×D4D4×C2914yes—
729C23×C4—22no—
730C23×C4—22no—
731C23×C4—22no—
732C23×C4—41no—
733C23×C4—41no—
734C23×C4—41no—
735C23×C4—41no—
736C23×C4C23×C2911yescharacteristic
737C23×C4C23×C2911yescharacteristic
738C23×C4C23×C2911yescharacteristic
739C23×C4C23×C2911yescharacteristic
740C23×C4C23×C2911yescharacteristic
741C23×C4C23×C2911yescharacteristic
742C23×C4C23×C2911yescharacteristic
743C23×C4C23×C2911yescharacteristic
744C23×C4C23×C2911yescharacteristic
745C23×C4C23×C2911yescharacteristic
746C23×C4C23×C2911yescharacteristic
747C23×C4C23×C2911yescharacteristic
748C2×C4⋊C4—22no—
749C2×C4⋊C4—41no—
750C2×C4⋊C4—41no—
751C2×C22⋊C4—22no—
752C2×C22⋊C4—22no—
753C2×C22⋊C4—22no—
754C2×C22⋊C4—22no—
755C2×C22⋊C4—22no—
756C2×C22⋊C4—22no—
757C2×C22⋊C4—22no—
758C2×C22⋊C4—22no—
759C2×C22⋊C4—22no—
760C2×C22⋊C4—22no—
761C2×C22⋊C4—22no—
762C2×C22⋊C4—22no—
763C2×C22⋊C4—22no—
764C2×C22⋊C4—22no—
765C2×C22⋊C4—22no—
766C2×C22⋊C4—22no—
767C2×C22⋊C4—22no—
768C2×C22⋊C4—22no—
769C2×C22⋊C4—41no—
770C2×C22⋊C4—41no—
771C2×C22⋊C4—41no—
772C2×C22⋊C4—41no—
773C2×C22⋊C4—41no—
774C2×C22⋊C4—41no—
775C2×C22⋊C4—41no—
776C2×C22⋊C4—41no—
777C2×C22⋊C4—41no—
778C2×C22⋊C4—41no—
779C2×C22⋊C4—41no—
780C2×C22⋊C4—41no—
781C2×C22⋊C4—41no—
782C2×C22⋊C4—41no—
783C2×C22⋊C4—41no—
784C2×C22⋊C4—41no—
785C2×C22⋊C4—41no—
786C2×C22⋊C4—41no—
787C2×C22⋊C4—41no—
788C2×C22⋊C4—41no—
789C2×C22⋊C4—41no—
790C2×C22⋊C4—41no—
791C2×C22⋊C4—41no—
792C2×C22⋊C4—41no—
793#95—22no—
794#95—22no—
795#95—22no—
796#95—22no—
797#95—22no—
798#95—22no—
799#95—22no—
800#95—41no—
801#95—41no—
802#95—41no—
803#95—41no—
804#95—41no—
805#95—41no—
806#95—41no—
807#95—41no—
808#95D4×C2914yescomplemented
809C29#1627011yescharacteristic, direct product factor, Sylow
810C24—21no—
811C24—21no—
812C24—21no—
813C24—21no—
814C24—21no—
815C24—21no—
816C24—21no—
817C24—21no—
818C24—21no—
819C24—21no—
820C24—21no—
821C24—21no—
822C24—21no—
823C24—21no—
824C24—21no—
825C24—21no—
826C24—21no—
827C24—21no—
828C24—21no—
829C24—21no—
830C24—21no—
831C24—21no—
832C24—21no—
833C24—21no—
834C24—21no—
835C24—21no—
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24C2×D4×C2912yes—
851C24C2×D4×C2912yes—
852C24#41×C2912yes—
853C24#41×C2912yes—
854C24#41×C2912yes—
855C24C24×C2911yescharacteristic
856C2×D4—28no—
857C2×D4—28no—
858C2×D4—44no—
859C2×D4—44no—
860C2×D4—44no—
861C2×D4—44no—
862C2×D4—44no—
863C2×D4—44no—
864C2×D4—44no—
865C2×D4—44no—
866C2×D4—44no—
867C2×D4—44no—
868C2×D4—44no—
869C2×D4—44no—
870C2×D4—44no—
871C2×D4—44no—
872C2×D4—44no—
873C2×D4—44no—
874C2×D4—44no—
875C2×D4—44no—
876C2×D4—44no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
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—21no—
955C22×C4—44no—
956C22×C4—44no—
957C22×C4—44no—
958C22×C4—44no—
959C22×C4—44no—
960C22×C4—44no—
961C22×C4—44no—
962C22×C4C2×D4×C2912yes—
963C22×C4C2×D4×C2912yes—
964C22×C4C2×D4×C2912yes—
965C22×C4C2×D4×C2912yes—
966C22×C4#41×C2912yes—
967C22×C4#41×C2912yes—
968C4⋊C4—44no—
969C22⋊C4—44no—
970C22⋊C4—44no—
971C22⋊C4—44no—
972C22⋊C4—44no—
973C22⋊C4—44no—
974C22⋊C4—44no—
975C22⋊C4—44no—
976C22⋊C4—44no—
977C22⋊C4—44no—
978C22⋊C4—44no—
979C22⋊C4—44no—
980C22⋊C4—44no—
981C22⋊C4—44no—
982C22⋊C4—44no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
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—
1087C23C29×#12314yes—
1088C23C22×D4×C2911yescharacteristic
1089C23C22×D4×C2911yescharacteristic
1090C23C2×#41×C2911yescharacteristic
1091C23C2×#41×C2911yescharacteristic
1092C23C2×#41×C2911yescharacteristic
1093C23C2×#41×C2911yescharacteristic
1094C23C2×#41×C2911yescharacteristic
1095C23C29×H(5,𝔽2)11yescharacteristic
1096C23C29×H(5,𝔽2)11yescharacteristic
1097C23C29×H(5,𝔽2)11yescharacteristic
1098C23C29×H(5,𝔽2)11yescharacteristic
1099C23C29×H(5,𝔽2)11yescharacteristic
1100C23C29×H(5,𝔽2)11yescharacteristic
1101C23C29×H(5,𝔽2)11yescharacteristic
1102C23C29×H(5,𝔽2)11yescharacteristic
1103D4—416no—
1104D4—416no—
1105D4—416no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—416no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
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—
1191C22—24no—
1192C22—24no—
1193C22—24no—
1194C22—42no—
1195C22—42no—
1196C22—42no—
1197C22—42no—
1198C22—42no—
1199C22—42no—
1200C22—42no—
1201C22—42no—
1202C22—42no—
1203C22—42no—
1204C22—42no—
1205C22—42no—
1206C22—42no—
1207C22—42no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22C2×C29×#12311yescharacteristic
1237C22C29×#52511yescharacteristic
1238C22C29×#52911yescharacteristic
1239C22C29×#53411yescharacteristic
1240C22C29×#53411yescharacteristic
1241C22C29×#53511yescharacteristic
1242C22C29×#53511yescharacteristic
1243C22C29×#53811yescharacteristic
1244C22C29×#53811yescharacteristic
1245C22C29×#53811yescharacteristic
1246C22C29×#53811yescharacteristic
1247C22C29×#53811yescharacteristic
1248C22C29×#53811yescharacteristic
1249C22C29×#53811yescharacteristic
1250C22C29×#53811yescharacteristic
1251C22C29×#53811yescharacteristic
1252C22C29×#53811yescharacteristic
1253C22C29×#54011yescharacteristic
1254C22C29×#54011yescharacteristic
1255C22D42×C2911yescharacteristic
1256C22C29×#54611yescharacteristic
1257C22C29×#54611yescharacteristic
1258C22C29×#54611yescharacteristic
1259C22C29×#54611yescharacteristic
1260C22C29×#54611yescharacteristic
1261C22C29×#55011yescharacteristic
1262C22C29×#55111yescharacteristic
1263C22C29×#55111yescharacteristic
1264C22C29×#55311yescharacteristic
1265C22C29×#55311yescharacteristic
1266C22C29×#55311yescharacteristic
1267C22C29×#56011yescharacteristic
1268C22C29×#56011yescharacteristic
1269C22C29×#56011yescharacteristic
1270C22C29×#56011yescharacteristic
1271C4—42no—
1272C4—42no—
1273C4—42no—
1274C4—42no—
1275C4—42no—
1276C4—42no—
1277C4—81no—
1278C4—81no—
1279C4—81no—
1280C4—81no—
1281C4—81no—
1282C4—81no—
1283C2—44no—
1284C2—82no—
1285C2—82no—
1286C2C29×#241811yescharacteristic
1287C2C29×#244411yescharacteristic
1288C2C29×#246711yescharacteristic
1289C2C29×#262211yescharacteristic
1290C2C29×#263111yescharacteristic
1291C2C29×#264811yescharacteristic
1292C2C29×#267311yescharacteristic
1293C2C29×#267811yescharacteristic
1294C2C29×#268811yescharacteristic
1295C2C29×#269711yescharacteristic
1296C2C29×#270311yescharacteristic
1297C2C29×#271411yescharacteristic
1298C2C29×#274911yescharacteristic
1299C2C29×#277811yescharacteristic
1300C2C29×#282511yescharacteristic
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. C2×C29×#397C2semidirect
3. C2×C29×#386C2semidirect
4. C2×C29×#386C2semidirect
5. C29×#1443C2semidirect
6. C29×#1443C2semidirect
7. C29×#1440C2semidirect
8. C29×#1440C2semidirect
9. C29×#1439C2semidirect
10. C29×#1439C2semidirect
11. C29×#1438C2semidirect
12. C29×#1438C2semidirect
13. C29×#1438C2semidirect
14. C29×#1438C2semidirect
15. C29×C22⋊#95C2semidirect
158. C29×#95D4semidirect
332. #16270C29direct (N × H)
541. C2×#397C2×C29semidirect
543. C2×#386C2×C29semidirect
544. C2×#386C2×C29semidirect
545. #1443C2×C29semidirect
546. #1443C2×C29semidirect
547. #1440C2×C29semidirect
548. #1440C2×C29semidirect
549. #1439C2×C29semidirect
550. #1439C2×C29semidirect
551. #1438C2×C29semidirect
552. #1438C2×C29semidirect
553. #1438C2×C29semidirect
554. #1438C2×C29semidirect
555. C22⋊#95C2×C29semidirect
808. #95D4×C29semidirect
809. C29#16270direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#3972
C2×C29×#3922
C2×C29×#3862
C29×#14432
C29×#14402
C29×#14392
C29×#14382
C29×C22⋊#952
#1627029