Finite Group Databasebeta

← C29×#16512 #20311412

Subgroups — C29×#16512 #20311412

Order 7424.

2122 conjugacy classes of subgroups.

The subgroup lattice has 1318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#394C211yesmaximal, characteristic, complemented
2C2×C29×#394C211yesmaximal, characteristic, complemented
3C2×C29×#392C211yesmaximal, characteristic
4C2×C29×#386C211yesmaximal, characteristic, complemented
5C2×C29×#386C211yesmaximal, characteristic, complemented
6C2×C29×#380C211yesmaximal, characteristic, complemented
7C29×#1443C211yesmaximal, characteristic, complemented
8C29×#1441C211yesmaximal, characteristic, complemented
9C29×#1440C211yesmaximal, characteristic, complemented
10C29×#1440C211yesmaximal, characteristic, complemented
11C29×#1439C211yesmaximal, characteristic, complemented
12C29×#1439C211yesmaximal, characteristic, complemented
13C29×#1439C211yesmaximal, characteristic, complemented
14C29×#1438C211yesmaximal, characteristic, complemented
15C29×#1438C211yesmaximal, characteristic, complemented
16C23×D4×C29C2211yescharacteristic
17C23×D4×C29C2211yescharacteristic
18C23×D4×C29C2211yescharacteristic
19C24×C4×C29C2211yescharacteristic
20C22×C4⋊C4×C29C2211yescharacteristic
21C22×C4⋊C4×C29C2211yescharacteristic
22C22×C4⋊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
35C22×C22⋊C4×C29C2211yescharacteristic
36C22×C22⋊C4×C29C2211yescharacteristic
37C29×#394—24no—
38C29×#394—24no—
39C29×#392—24no—
40C29×#386—24no—
41C29×#386—24no—
42C29×#380—24no—
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
55C2×C29×#95C2211yescharacteristic
56C2×C29×#95C2211yescharacteristic
57C25×C29C2311yescharacteristic
58C25×C29C2311yescharacteristic
59C25×C29C2311yescharacteristic
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—22no—
69C22×D4×C29—22no—
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×C29—41no—
79C22×D4×C29—41no—
80C22×D4×C29D414yes—
81C23×C4×C29—22no—
82C23×C4×C29—22no—
83C23×C4×C29—41no—
84C23×C4×C29—41no—
85C23×C4×C29—41no—
86C23×C4×C29—41no—
87C23×C4×C29D414yescomplemented
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
98C23×C4×C29C2311yescharacteristic
99C23×C4×C29C2311yescharacteristic
100C2×C4⋊C4×C29—22no—
101C2×C4⋊C4×C29—22no—
102C2×C4⋊C4×C29—41no—
103C2×C4⋊C4×C29—41no—
104C2×C4⋊C4×C29—41no—
105C2×C4⋊C4×C29—41no—
106C2×C4⋊C4×C29—41no—
107C2×C4⋊C4×C29—41no—
108C2×C4⋊C4×C29D414yescomplemented
109C2×C22⋊C4×C29—22no—
110C2×C22⋊C4×C29—22no—
111C2×C22⋊C4×C29—22no—
112C2×C22⋊C4×C29—22no—
113C2×C22⋊C4×C29—22no—
114C2×C22⋊C4×C29—22no—
115C2×C22⋊C4×C29—22no—
116C2×C22⋊C4×C29—22no—
117C2×C22⋊C4×C29—22no—
118C2×C22⋊C4×C29—22no—
119C2×C22⋊C4×C29—22no—
120C2×C22⋊C4×C29—22no—
121C2×C22⋊C4×C29—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—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—
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—
151C29×#95—22no—
152C29×#95—22no—
153C29×#95—22no—
154C29×#95—22no—
155C29×#95—22no—
156C29×#95—22no—
157C29×#95—22no—
158C29×#95—22no—
159C29×#95—22no—
160C29×#95—22no—
161C29×#95—41no—
162C29×#95—41no—
163C29×#95—41no—
164C29×#95—41no—
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×C29—21no—
200C24×C29—21no—
201C24×C29—21no—
202C24×C29—21no—
203C24×C29—21no—
204C24×C29—21no—
205C24×C29C2×D412yes—
206C24×C29C2×D412yes—
207C24×C29C2×D412yes—
208C24×C29#4112yes—
209C24×C29#4112yes—
210C24×C29C2411yescharacteristic
211C2×D4×C29—28no—
212C2×D4×C29—28no—
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—
226C2×D4×C29—44no—
227C2×D4×C29—44no—
228C2×D4×C29—44no—
229C2×D4×C29—44no—
230C2×D4×C29—44no—
231C2×D4×C29—44no—
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—28no—
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—21no—
305C22×C4×C29—21no—
306C22×C4×C29—21no—
307C22×C4×C29—21no—
308C22×C4×C29—21no—
309C22×C4×C29—44no—
310C22×C4×C29—44no—
311C22×C4×C29—44no—
312C22×C4×C29—44no—
313C22×C4×C29—44no—
314C22×C4×C29—44no—
315C22×C4×C29C2×D412yes—
316C22×C4×C29C2×D412yes—
317C22×C4×C29C2×D412yes—
318C22×C4×C29C2×D412yes—
319C22×C4×C29C2×D412yes—
320C22×C4×C29C2×D412yes—
321C22×C4×C29#4112yes—
322C22×C4×C29#4112yes—
323C4⋊C4×C29—44no—
324C4⋊C4×C29—44no—
325C4⋊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—
332C22⋊C4×C29—44no—
333C22⋊C4×C29—44no—
334C22⋊C4×C29—44no—
335C22⋊C4×C29—44no—
336C22⋊C4×C29—44no—
337C22⋊C4×C29—44no—
338C22⋊C4×C29—44no—
339C22⋊C4×C29—44no—
340#16512C2911yesmaximal, characteristic, direct product factor, Sylow
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—22no—
366C23×C29—22no—
367C23×C29—22no—
368C23×C29—22no—
369C23×C29—22no—
370C23×C29—22no—
371C23×C29—22no—
372C23×C29—22no—
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—41no—
438C23×C29—41no—
439C23×C29—41no—
440C23×C29—41no—
441C23×C29—41no—
442C23×C29—41no—
443C23×C29—41no—
444C23×C29—41no—
445C23×C29#12114yes—
446C23×C29C22×D411yescharacteristic
447C23×C29C22×D411yescharacteristic
448C23×C29C22×D411yescharacteristic
449C23×C29C2×#4111yescharacteristic
450C23×C29C2×#4111yescharacteristic
451C23×C29C2×#4111yescharacteristic
452C23×C29C2×#4111yescharacteristic
453C23×C29H(5,𝔽2)11yescharacteristic
454C23×C29H(5,𝔽2)11yescharacteristic
455C23×C29H(5,𝔽2)11yescharacteristic
456C23×C29H(5,𝔽2)11yescharacteristic
457C23×C29H(5,𝔽2)11yescharacteristic
458C23×C29H(5,𝔽2)11yescharacteristic
459C23×C29H(5,𝔽2)11yescharacteristic
460C23×C292−1+411yescharacteristic
461D4×C29—416no—
462D4×C29—416no—
463D4×C29—416no—
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—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—416no—
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×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#12114yes—
549C2×#394C2×C2911yescharacteristic, complemented
550C2×#394C2×C2911yescharacteristic, complemented
551C2×#392C2×C2911yescharacteristic
552C2×#386C2×C2911yescharacteristic, complemented
553C2×#386C2×C2911yescharacteristic, complemented
554C2×#380C2×C2911yescharacteristic, complemented
555#1443C2×C2911yescharacteristic, complemented
556#1441C2×C2911yescharacteristic, complemented
557#1440C2×C2911yescharacteristic, complemented
558#1440C2×C2911yescharacteristic, complemented
559#1439C2×C2911yescharacteristic, complemented
560#1439C2×C2911yescharacteristic, complemented
561#1439C2×C2911yescharacteristic, complemented
562#1438C2×C2911yescharacteristic, complemented
563#1438C2×C2911yescharacteristic, complemented
564C22×C29—24no—
565C22×C29—24no—
566C22×C29—24no—
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—42no—
586C22×C29—42no—
587C22×C29—42no—
588C22×C29—42no—
589C22×C29—42no—
590C22×C29—42no—
591C22×C29—42no—
592C22×C29—42no—
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×C29—81no—
602C22×C29—81no—
603C22×C29—81no—
604C22×C29—81no—
605C22×C29—81no—
606C22×C29—81no—
607C22×C29—81no—
608C22×C29—81no—
609C22×C29C2×#12111yescharacteristic
610C22×C29C2×#12111yescharacteristic
611C22×C29#52511yescharacteristic
612C22×C29#53411yescharacteristic
613C22×C29#53411yescharacteristic
614C22×C29#53411yescharacteristic
615C22×C29#53411yescharacteristic
616C22×C29#53411yescharacteristic
617C22×C29#53511yescharacteristic
618C22×C29#53511yescharacteristic
619C22×C29#53711yescharacteristic
620C22×C29#53811yescharacteristic
621C22×C29#53811yescharacteristic
622C22×C29#53811yescharacteristic
623C22×C29#53811yescharacteristic
624C22×C29#53811yescharacteristic
625C22×C29#53911yescharacteristic
626C22×C29#54011yescharacteristic
627C22×C29#54211yescharacteristic
628C22×C29D4211yescharacteristic
629C22×C29#54611yescharacteristic
630C22×C29#54611yescharacteristic
631C22×C29#54611yescharacteristic
632C22×C29#54711yescharacteristic
633C22×C29#54811yescharacteristic
634C22×C29#55011yescharacteristic
635C22×C29#55111yescharacteristic
636C22×C29#55111yescharacteristic
637C22×C29#55311yescharacteristic
638C22×C29#55311yescharacteristic
639C22×C29#55511yescharacteristic
640C22×C29#56011yescharacteristic
641C22×C29#56011yescharacteristic
642C22×C29#56211yescharacteristic
643C22×C29#56211yescharacteristic
644C4×C29—24no—
645C4×C29—42no—
646C4×C29—42no—
647C4×C29—42no—
648C4×C29—42no—
649C4×C29—42no—
650C4×C29—81no—
651C4×C29—81no—
652C4×C29—81no—
653C4×C29—81no—
654C4×C29—81no—
655C4×C29—81no—
656C23×D4C22×C2911yescharacteristic
657C23×D4C22×C2911yescharacteristic
658C23×D4C22×C2911yescharacteristic
659C24×C4C22×C2911yescharacteristic
660C22×C4⋊C4C22×C2911yescharacteristic
661C22×C4⋊C4C22×C2911yescharacteristic
662C22×C4⋊C4C22×C2911yescharacteristic
663C22×C22⋊C4C22×C2911yescharacteristic
664C22×C22⋊C4C22×C2911yescharacteristic
665C22×C22⋊C4C22×C2911yescharacteristic
666C22×C22⋊C4C22×C2911yescharacteristic
667C22×C22⋊C4C22×C2911yescharacteristic
668C22×C22⋊C4C22×C2911yescharacteristic
669C22×C22⋊C4C22×C2911yescharacteristic
670C22×C22⋊C4C22×C2911yescharacteristic
671C22×C22⋊C4C22×C2911yescharacteristic
672C22×C22⋊C4C22×C2911yescharacteristic
673C22×C22⋊C4C22×C2911yescharacteristic
674C22×C22⋊C4C22×C2911yescharacteristic
675C22×C22⋊C4C22×C2911yescharacteristic
676C22×C22⋊C4C22×C2911yescharacteristic
677#394—24no—
678#394—24no—
679#392—24no—
680#386—24no—
681#386—24no—
682#380—24no—
683C2×#95C22×C2911yescharacteristic
684C2×#95C22×C2911yescharacteristic
685C2×#95C22×C2911yescharacteristic
686C2×#95C22×C2911yescharacteristic
687C2×#95C22×C2911yescharacteristic
688C2×#95C22×C2911yescharacteristic
689C2×#95C22×C2911yescharacteristic
690C2×#95C22×C2911yescharacteristic
691C2×#95C22×C2911yescharacteristic
692C2×#95C22×C2911yescharacteristic
693C2×#95C22×C2911yescharacteristic
694C2×#95C22×C2911yescharacteristic
695C2×#95C22×C2911yescharacteristic
696C2×#95C22×C2911yescharacteristic
697C2×C29—44no—
698C2×C29—82no—
699C2×C29—82no—
700C2×C29#241411yescharacteristic
701C2×C29#241611yescharacteristic
702C2×C29#253411yescharacteristic
703C2×C29#261711yescharacteristic
704C2×C29#261711yescharacteristic
705C2×C29#263011yescharacteristic
706C2×C29#266811yescharacteristic
707C2×C29#267311yescharacteristic
708C2×C29#268611yescharacteristic
709C2×C29#269611yescharacteristic
710C2×C29#270811yescharacteristic
711C2×C29#273011yescharacteristic
712C2×C29#275611yescharacteristic
713C2×C29#277811yescharacteristic
714C2×C29#281311yescharacteristic
715C25C23×C2911yescharacteristic
716C25C23×C2911yescharacteristic
717C25C23×C2911yescharacteristic
718C22×D4—22no—
719C22×D4—22no—
720C22×D4—22no—
721C22×D4—22no—
722C22×D4—22no—
723C22×D4—22no—
724C22×D4—22no—
725C22×D4—22no—
726C22×D4—22no—
727C22×D4—22no—
728C22×D4—41no—
729C22×D4—41no—
730C22×D4—41no—
731C22×D4—41no—
732C22×D4—41no—
733C22×D4—41no—
734C22×D4—41no—
735C22×D4—41no—
736C22×D4—41no—
737C22×D4—41no—
738C22×D4D4×C2914yes—
739C23×C4—22no—
740C23×C4—22no—
741C23×C4—41no—
742C23×C4—41no—
743C23×C4—41no—
744C23×C4—41no—
745C23×C4D4×C2914yescomplemented
746C23×C4C23×C2911yescharacteristic
747C23×C4C23×C2911yescharacteristic
748C23×C4C23×C2911yescharacteristic
749C23×C4C23×C2911yescharacteristic
750C23×C4C23×C2911yescharacteristic
751C23×C4C23×C2911yescharacteristic
752C23×C4C23×C2911yescharacteristic
753C23×C4C23×C2911yescharacteristic
754C23×C4C23×C2911yescharacteristic
755C23×C4C23×C2911yescharacteristic
756C23×C4C23×C2911yescharacteristic
757C23×C4C23×C2911yescharacteristic
758C2×C4⋊C4—22no—
759C2×C4⋊C4—22no—
760C2×C4⋊C4—41no—
761C2×C4⋊C4—41no—
762C2×C4⋊C4—41no—
763C2×C4⋊C4—41no—
764C2×C4⋊C4—41no—
765C2×C4⋊C4—41no—
766C2×C4⋊C4D4×C2914yescomplemented
767C2×C22⋊C4—22no—
768C2×C22⋊C4—22no—
769C2×C22⋊C4—22no—
770C2×C22⋊C4—22no—
771C2×C22⋊C4—22no—
772C2×C22⋊C4—22no—
773C2×C22⋊C4—22no—
774C2×C22⋊C4—22no—
775C2×C22⋊C4—22no—
776C2×C22⋊C4—22no—
777C2×C22⋊C4—22no—
778C2×C22⋊C4—22no—
779C2×C22⋊C4—22no—
780C2×C22⋊C4—22no—
781C2×C22⋊C4—22no—
782C2×C22⋊C4—22no—
783C2×C22⋊C4—22no—
784C2×C22⋊C4—22no—
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—41no—
792C2×C22⋊C4—41no—
793C2×C22⋊C4—41no—
794C2×C22⋊C4—41no—
795C2×C22⋊C4—41no—
796C2×C22⋊C4—41no—
797C2×C22⋊C4—41no—
798C2×C22⋊C4—41no—
799C2×C22⋊C4—41no—
800C2×C22⋊C4—41no—
801C2×C22⋊C4—41no—
802C2×C22⋊C4—41no—
803C2×C22⋊C4—41no—
804C2×C22⋊C4—41no—
805C2×C22⋊C4—41no—
806C2×C22⋊C4—41no—
807C2×C22⋊C4—41no—
808C2×C22⋊C4—41no—
809#95—22no—
810#95—22no—
811#95—22no—
812#95—22no—
813#95—22no—
814#95—22no—
815#95—22no—
816#95—22no—
817#95—22no—
818#95—22no—
819#95—41no—
820#95—41no—
821#95—41no—
822#95—41no—
823C29#1651211yescharacteristic, direct product factor, Sylow
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—
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—
864C24C2×D4×C2912yes—
865C24C2×D4×C2912yes—
866C24C2×D4×C2912yes—
867C24#41×C2912yes—
868C24#41×C2912yes—
869C24C24×C2911yescharacteristic
870C2×D4—28no—
871C2×D4—28no—
872C2×D4—44no—
873C2×D4—44no—
874C2×D4—44no—
875C2×D4—44no—
876C2×D4—44no—
877C2×D4—44no—
878C2×D4—44no—
879C2×D4—44no—
880C2×D4—44no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—44no—
884C2×D4—44no—
885C2×D4—44no—
886C2×D4—44no—
887C2×D4—44no—
888C2×D4—44no—
889C2×D4—44no—
890C2×D4—44no—
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—28no—
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—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—44no—
969C22×C4—44no—
970C22×C4—44no—
971C22×C4—44no—
972C22×C4—44no—
973C22×C4—44no—
974C22×C4C2×D4×C2912yes—
975C22×C4C2×D4×C2912yes—
976C22×C4C2×D4×C2912yes—
977C22×C4C2×D4×C2912yes—
978C22×C4C2×D4×C2912yes—
979C22×C4C2×D4×C2912yes—
980C22×C4#41×C2912yes—
981C22×C4#41×C2912yes—
982C4⋊C4—44no—
983C4⋊C4—44no—
984C4⋊C4—44no—
985C22⋊C4—44no—
986C22⋊C4—44no—
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⋊C4—44no—
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—22no—
1016C23—22no—
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—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—
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—
1103C23C29×#12114yes—
1104C23C22×D4×C2911yescharacteristic
1105C23C22×D4×C2911yescharacteristic
1106C23C22×D4×C2911yescharacteristic
1107C23C2×#41×C2911yescharacteristic
1108C23C2×#41×C2911yescharacteristic
1109C23C2×#41×C2911yescharacteristic
1110C23C2×#41×C2911yescharacteristic
1111C23C29×H(5,𝔽2)11yescharacteristic
1112C23C29×H(5,𝔽2)11yescharacteristic
1113C23C29×H(5,𝔽2)11yescharacteristic
1114C23C29×H(5,𝔽2)11yescharacteristic
1115C23C29×H(5,𝔽2)11yescharacteristic
1116C23C29×H(5,𝔽2)11yescharacteristic
1117C23C29×H(5,𝔽2)11yescharacteristic
1118C23C29×2−1+411yescharacteristic
1119D4—416no—
1120D4—416no—
1121D4—416no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—416no—
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—
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×C4C29×#12114yes—
1207C22—24no—
1208C22—24no—
1209C22—24no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22C2×C29×#12111yescharacteristic
1253C22C2×C29×#12111yescharacteristic
1254C22C29×#52511yescharacteristic
1255C22C29×#53411yescharacteristic
1256C22C29×#53411yescharacteristic
1257C22C29×#53411yescharacteristic
1258C22C29×#53411yescharacteristic
1259C22C29×#53411yescharacteristic
1260C22C29×#53511yescharacteristic
1261C22C29×#53511yescharacteristic
1262C22C29×#53711yescharacteristic
1263C22C29×#53811yescharacteristic
1264C22C29×#53811yescharacteristic
1265C22C29×#53811yescharacteristic
1266C22C29×#53811yescharacteristic
1267C22C29×#53811yescharacteristic
1268C22C29×#53911yescharacteristic
1269C22C29×#54011yescharacteristic
1270C22C29×#54211yescharacteristic
1271C22D42×C2911yescharacteristic
1272C22C29×#54611yescharacteristic
1273C22C29×#54611yescharacteristic
1274C22C29×#54611yescharacteristic
1275C22C29×#54711yescharacteristic
1276C22C29×#54811yescharacteristic
1277C22C29×#55011yescharacteristic
1278C22C29×#55111yescharacteristic
1279C22C29×#55111yescharacteristic
1280C22C29×#55311yescharacteristic
1281C22C29×#55311yescharacteristic
1282C22C29×#55511yescharacteristic
1283C22C29×#56011yescharacteristic
1284C22C29×#56011yescharacteristic
1285C22C29×#56211yescharacteristic
1286C22C29×#56211yescharacteristic
1287C4—24no—
1288C4—42no—
1289C4—42no—
1290C4—42no—
1291C4—42no—
1292C4—42no—
1293C4—81no—
1294C4—81no—
1295C4—81no—
1296C4—81no—
1297C4—81no—
1298C4—81no—
1299C2—44no—
1300C2—82no—
1301C2—82no—
1302C2C29×#241411yescharacteristic
1303C2C29×#241611yescharacteristic
1304C2C29×#253411yescharacteristic
1305C2C29×#261711yescharacteristic
1306C2C29×#261711yescharacteristic
1307C2C29×#263011yescharacteristic
1308C2C29×#266811yescharacteristic
1309C2C29×#267311yescharacteristic
1310C2C29×#268611yescharacteristic
1311C2C29×#269611yescharacteristic
1312C2C29×#270811yescharacteristic
1313C2C29×#273011yescharacteristic
1314C2C29×#275611yescharacteristic
1315C2C29×#277811yescharacteristic
1316C2C29×#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. C2×C29×#394C2semidirect
2. C2×C29×#394C2semidirect
4. C2×C29×#386C2semidirect
5. C2×C29×#386C2semidirect
6. C2×C29×#380C2semidirect
7. C29×#1443C2semidirect
8. C29×#1441C2semidirect
9. C29×#1440C2semidirect
10. C29×#1440C2semidirect
11. C29×#1439C2semidirect
12. C29×#1439C2semidirect
13. C29×#1439C2semidirect
14. C29×#1438C2semidirect
15. C29×#1438C2semidirect
87. C23×C4×C29D4semidirect
108. C2×C4⋊C4×C29D4semidirect
340. #16512C29direct (N × H)
549. C2×#394C2×C29semidirect
550. C2×#394C2×C29semidirect
552. C2×#386C2×C29semidirect
553. C2×#386C2×C29semidirect
554. C2×#380C2×C29semidirect
555. #1443C2×C29semidirect
556. #1441C2×C29semidirect
557. #1440C2×C29semidirect
558. #1440C2×C29semidirect
559. #1439C2×C29semidirect
560. #1439C2×C29semidirect
561. #1439C2×C29semidirect
562. #1438C2×C29semidirect
563. #1438C2×C29semidirect
745. C23×C4D4×C29semidirect
766. C2×C4⋊C4D4×C29semidirect
823. C29#16512direct (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×#3922
C2×C29×#3862
C2×C29×#3802
C29×#14432
C29×#14412
C29×#14402
C29×#14392
C29×#14382
#1651229