Finite Group Databasebeta

← C29×#14751 #20309651

Subgroups — C29×#14751 #20309651

Order 7424.

2302 conjugacy classes of subgroups.

The subgroup lattice has 1334 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×#390C211yesmaximal, characteristic, complemented
5C2×C29×#388C211yesmaximal, characteristic, complemented
6C2×C29×#386C211yesmaximal, characteristic, complemented
7C2×C29×#386C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊C4×C29C211yesmaximal, characteristic, complemented
9C29×#1441C211yesmaximal, characteristic, complemented
10C29×#1440C211yesmaximal, characteristic, complemented
11C29×#1439C211yesmaximal, characteristic, complemented
12C29×#1439C211yesmaximal, characteristic, complemented
13C29×#1438C211yesmaximal, characteristic, complemented
14C29×#1437C211yesmaximal, characteristic, complemented
15C29×#1436C211yesmaximal, 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
37C22×C42×C29C2211yescharacteristic
38C22×C42×C29C2211yescharacteristic
39C29×#394—24no—
40C29×#394—24no—
41C29×#392—24no—
42C29×#390—24no—
43C29×#388—24no—
44C29×#386—24no—
45C29×#386—24no—
46C4×C22⋊C4×C29—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—22no—
76C22×D4×C29—22no—
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—22no—
88C23×C4×C29—41no—
89C23×C4×C29—41no—
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
102C2×C4⋊C4×C29—22no—
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—41no—
109C2×C4⋊C4×C29—41no—
110C2×C4⋊C4×C29—41no—
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—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×C29D414yes—
151C2×C22⋊C4×C29D414yescomplemented
152C2×C22⋊C4×C29D414yescomplemented
153C2×C42×C29—22no—
154C2×C42×C29—22no—
155C2×C42×C29—22no—
156C2×C42×C29—22no—
157C2×C42×C29—41no—
158C2×C42×C29—41no—
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—22no—
169C29×#95—41no—
170C29×#95D414yescomplemented
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×C29—21no—
206C24×C29—21no—
207C24×C29—21no—
208C24×C29—21no—
209C24×C29—21no—
210C24×C29—21no—
211C24×C29C2×D412yes—
212C24×C29C2×D412yes—
213C24×C29C2×D412yes—
214C24×C29#4112yes—
215C24×C29#4112yes—
216C24×C29C2411yescharacteristic
217C2×D4×C29—28no—
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—
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—28no—
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—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×C29C2×D412yes—
322C22×C4×C29C2×D412yes—
323C22×C4×C29C2×D412yes—
324C22×C4×C29#4112yes—
325C22×C4×C29#4112yes—
326C22×C4×C29#4112yes—
327C22×C4×C29#4112yes—
328C22×C4×C29#4112yes—
329C4⋊C4×C29—44no—
330C4⋊C4×C29—44no—
331C4⋊C4×C29—44no—
332C22⋊C4×C29—28no—
333C22⋊C4×C29—28no—
334C22⋊C4×C29—28no—
335C22⋊C4×C29—44no—
336C22⋊C4×C29—44no—
337C22⋊C4×C29—44no—
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—
346C42×C29—44no—
347C42×C29—44no—
348#14751C2911yesmaximal, characteristic, direct product factor, Sylow
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—22no—
374C23×C29—22no—
375C23×C29—22no—
376C23×C29—22no—
377C23×C29—22no—
378C23×C29—22no—
379C23×C29—22no—
380C23×C29—22no—
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—41no—
446C23×C29—41no—
447C23×C29—41no—
448C23×C29—41no—
449C23×C29—41no—
450C23×C29—41no—
451C23×C29—41no—
452C23×C29—41no—
453C23×C29#12114yes—
454C23×C29C22×D411yescharacteristic
455C23×C29C22×D411yescharacteristic
456C23×C29C22×D411yescharacteristic
457C23×C29C22×D411yescharacteristic
458C23×C29C2×#4111yescharacteristic
459C23×C29C2×#4111yescharacteristic
460C23×C29C2×#4111yescharacteristic
461C23×C29C2×#4111yescharacteristic
462C23×C29C2×#4111yescharacteristic
463C23×C29C2×#4111yescharacteristic
464C23×C29C2×#4111yescharacteristic
465C23×C29H(5,𝔽2)11yescharacteristic
466C23×C29H(5,𝔽2)11yescharacteristic
467C23×C29H(5,𝔽2)11yescharacteristic
468C23×C29H(5,𝔽2)11yescharacteristic
469D4×C29—416no—
470D4×C29—416no—
471D4×C29—416no—
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—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—22no—
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#12114yes—
556C2×C4×C29#12314yes—
557C2×#394C2×C2911yescharacteristic, complemented
558C2×#394C2×C2911yescharacteristic, complemented
559C2×#392C2×C2911yescharacteristic
560C2×#390C2×C2911yescharacteristic, complemented
561C2×#388C2×C2911yescharacteristic, complemented
562C2×#386C2×C2911yescharacteristic, complemented
563C2×#386C2×C2911yescharacteristic, complemented
564C2×C4×C22⋊C4C2×C2911yescharacteristic, complemented
565#1441C2×C2911yescharacteristic, complemented
566#1440C2×C2911yescharacteristic, complemented
567#1439C2×C2911yescharacteristic, complemented
568#1439C2×C2911yescharacteristic, complemented
569#1438C2×C2911yescharacteristic, complemented
570#1437C2×C2911yescharacteristic, complemented
571#1436C2×C2911yescharacteristic, complemented
572C22×C29—24no—
573C22×C29—24no—
574C22×C29—24no—
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—42no—
594C22×C29—42no—
595C22×C29—42no—
596C22×C29—42no—
597C22×C29—42no—
598C22×C29—42no—
599C22×C29—42no—
600C22×C29—42no—
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×C29—81no—
610C22×C29—81no—
611C22×C29—81no—
612C22×C29—81no—
613C22×C29—81no—
614C22×C29—81no—
615C22×C29—81no—
616C22×C29—81no—
617C22×C29C2×#12111yescharacteristic
618C22×C29C2×#12111yescharacteristic
619C22×C29C2×#12311yescharacteristic
620C22×C29#52511yescharacteristic
621C22×C29#52511yescharacteristic
622C22×C29#52511yescharacteristic
623C22×C29#52511yescharacteristic
624C22×C29#52911yescharacteristic
625C22×C29#52911yescharacteristic
626C22×C29#52911yescharacteristic
627C22×C29#53211yescharacteristic
628C22×C29#53211yescharacteristic
629C22×C29#53211yescharacteristic
630C22×C29#53811yescharacteristic
631C22×C29#53811yescharacteristic
632C22×C29#53811yescharacteristic
633C22×C29#53811yescharacteristic
634C22×C29#54011yescharacteristic
635C22×C29#54011yescharacteristic
636C22×C29D4211yescharacteristic
637C22×C29D4211yescharacteristic
638C22×C29D4211yescharacteristic
639C22×C29D4211yescharacteristic
640C22×C29#54611yescharacteristic
641C22×C29#54611yescharacteristic
642C22×C29#54611yescharacteristic
643C22×C29#54611yescharacteristic
644C22×C29#54611yescharacteristic
645C22×C29#54611yescharacteristic
646C22×C29#54611yescharacteristic
647C22×C29#55011yescharacteristic
648C22×C29#55111yescharacteristic
649C22×C29#55311yescharacteristic
650C22×C29#55511yescharacteristic
651C22×C29#55911yescharacteristic
652C4×C29—24no—
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—42no—
662C4×C29—81no—
663C4×C29—81no—
664C23×D4C22×C2911yescharacteristic
665C23×D4C22×C2911yescharacteristic
666C23×D4C22×C2911yescharacteristic
667C24×C4C22×C2911yescharacteristic
668C22×C4⋊C4C22×C2911yescharacteristic
669C22×C4⋊C4C22×C2911yescharacteristic
670C22×C4⋊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
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×C42C22×C2911yescharacteristic
686C22×C42C22×C2911yescharacteristic
687#394—24no—
688#394—24no—
689#392—24no—
690#390—24no—
691#388—24no—
692#386—24no—
693#386—24no—
694C4×C22⋊C4—24no—
695C2×#95C22×C2911yescharacteristic
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×C29—44no—
708C2×C29—82no—
709C2×C29—82no—
710C2×C29#239211yescharacteristic
711C2×C29#241811yescharacteristic
712C2×C29#242411yescharacteristic
713C2×C29#242411yescharacteristic
714C2×C29#242411yescharacteristic
715C2×C29#242811yescharacteristic
716C2×C29#244511yescharacteristic
717C2×C29#245911yescharacteristic
718C2×C29#246411yescharacteristic
719C2×C29#246711yescharacteristic
720C2×C29#247611yescharacteristic
721C2×C29#255511yescharacteristic
722C2×C29#255711yescharacteristic
723C2×C29#264811yescharacteristic
724C2×C29#285411yescharacteristic
725C25C23×C2911yescharacteristic
726C25C23×C2911yescharacteristic
727C25C23×C2911yescharacteristic
728C22×D4—22no—
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—22no—
743C22×D4—41no—
744C22×D4—41no—
745C22×D4—41no—
746C22×D4—41no—
747C22×D4—41no—
748C22×D4—41no—
749C23×C4—22no—
750C23×C4—22no—
751C23×C4—22no—
752C23×C4—22no—
753C23×C4—22no—
754C23×C4—41no—
755C23×C4—41no—
756C23×C4C23×C2911yescharacteristic
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
768C2×C4⋊C4—22no—
769C2×C4⋊C4—22no—
770C2×C4⋊C4—22no—
771C2×C4⋊C4—22no—
772C2×C4⋊C4—22no—
773C2×C4⋊C4—22no—
774C2×C4⋊C4—41no—
775C2×C4⋊C4—41no—
776C2×C4⋊C4—41no—
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—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—41no—
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⋊C4D4×C2914yes—
817C2×C22⋊C4D4×C2914yescomplemented
818C2×C22⋊C4D4×C2914yescomplemented
819C2×C42—22no—
820C2×C42—22no—
821C2×C42—22no—
822C2×C42—22no—
823C2×C42—41no—
824C2×C42—41no—
825#95—22no—
826#95—22no—
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#95D4×C2914yescomplemented
837C29#1475111yescharacteristic, direct product factor, Sylow
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—
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—
878C24C2×D4×C2912yes—
879C24C2×D4×C2912yes—
880C24C2×D4×C2912yes—
881C24#41×C2912yes—
882C24#41×C2912yes—
883C24C24×C2911yescharacteristic
884C2×D4—28no—
885C2×D4—28no—
886C2×D4—28no—
887C2×D4—44no—
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—
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—28no—
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—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—44no—
977C22×C4—44no—
978C22×C4—44no—
979C22×C4—44no—
980C22×C4—44no—
981C22×C4—44no—
982C22×C4C2×D4×C2912yes—
983C22×C4C2×D4×C2912yes—
984C22×C4C2×D4×C2912yes—
985C22×C4C2×D4×C2912yes—
986C22×C4C2×D4×C2912yes—
987C22×C4C2×D4×C2912yes—
988C22×C4C2×D4×C2912yes—
989C22×C4C2×D4×C2912yes—
990C22×C4C2×D4×C2912yes—
991C22×C4#41×C2912yes—
992C22×C4#41×C2912yes—
993C22×C4#41×C2912yes—
994C22×C4#41×C2912yes—
995C22×C4#41×C2912yes—
996C4⋊C4—44no—
997C4⋊C4—44no—
998C4⋊C4—44no—
999C22⋊C4—28no—
1000C22⋊C4—28no—
1001C22⋊C4—28no—
1002C22⋊C4—44no—
1003C22⋊C4—44no—
1004C22⋊C4—44no—
1005C22⋊C4—44no—
1006C22⋊C4—44no—
1007C22⋊C4—44no—
1008C22⋊C4—44no—
1009C22⋊C4—44no—
1010C22⋊C4—44no—
1011C22⋊C4—44no—
1012C22⋊C4—44no—
1013C42—44no—
1014C42—44no—
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—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—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—
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—
1119C23C29×#12114yes—
1120C23C22×D4×C2911yescharacteristic
1121C23C22×D4×C2911yescharacteristic
1122C23C22×D4×C2911yescharacteristic
1123C23C22×D4×C2911yescharacteristic
1124C23C2×#41×C2911yescharacteristic
1125C23C2×#41×C2911yescharacteristic
1126C23C2×#41×C2911yescharacteristic
1127C23C2×#41×C2911yescharacteristic
1128C23C2×#41×C2911yescharacteristic
1129C23C2×#41×C2911yescharacteristic
1130C23C2×#41×C2911yescharacteristic
1131C23C29×H(5,𝔽2)11yescharacteristic
1132C23C29×H(5,𝔽2)11yescharacteristic
1133C23C29×H(5,𝔽2)11yescharacteristic
1134C23C29×H(5,𝔽2)11yescharacteristic
1135D4—416no—
1136D4—416no—
1137D4—416no—
1138C2×C4—22no—
1139C2×C4—22no—
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—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—416no—
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×C4C29×#12114yes—
1222C2×C4C29×#12314yes—
1223C22—24no—
1224C22—24no—
1225C22—24no—
1226C22—42no—
1227C22—42no—
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—81no—
1253C22—81no—
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—
1268C22C2×C29×#12111yescharacteristic
1269C22C2×C29×#12111yescharacteristic
1270C22C2×C29×#12311yescharacteristic
1271C22C29×#52511yescharacteristic
1272C22C29×#52511yescharacteristic
1273C22C29×#52511yescharacteristic
1274C22C29×#52511yescharacteristic
1275C22C29×#52911yescharacteristic
1276C22C29×#52911yescharacteristic
1277C22C29×#52911yescharacteristic
1278C22C29×#53211yescharacteristic
1279C22C29×#53211yescharacteristic
1280C22C29×#53211yescharacteristic
1281C22C29×#53811yescharacteristic
1282C22C29×#53811yescharacteristic
1283C22C29×#53811yescharacteristic
1284C22C29×#53811yescharacteristic
1285C22C29×#54011yescharacteristic
1286C22C29×#54011yescharacteristic
1287C22D42×C2911yescharacteristic
1288C22D42×C2911yescharacteristic
1289C22D42×C2911yescharacteristic
1290C22D42×C2911yescharacteristic
1291C22C29×#54611yescharacteristic
1292C22C29×#54611yescharacteristic
1293C22C29×#54611yescharacteristic
1294C22C29×#54611yescharacteristic
1295C22C29×#54611yescharacteristic
1296C22C29×#54611yescharacteristic
1297C22C29×#54611yescharacteristic
1298C22C29×#55011yescharacteristic
1299C22C29×#55111yescharacteristic
1300C22C29×#55311yescharacteristic
1301C22C29×#55511yescharacteristic
1302C22C29×#55911yescharacteristic
1303C4—24no—
1304C4—24no—
1305C4—42no—
1306C4—42no—
1307C4—42no—
1308C4—42no—
1309C4—42no—
1310C4—42no—
1311C4—42no—
1312C4—42no—
1313C4—81no—
1314C4—81no—
1315C2—44no—
1316C2—82no—
1317C2—82no—
1318C2C29×#239211yescharacteristic
1319C2C29×#241811yescharacteristic
1320C2C29×#242411yescharacteristic
1321C2C29×#242411yescharacteristic
1322C2C29×#242411yescharacteristic
1323C2C29×#242811yescharacteristic
1324C2C29×#244511yescharacteristic
1325C2C29×#245911yescharacteristic
1326C2C29×#246411yescharacteristic
1327C2C29×#246711yescharacteristic
1328C2C29×#247611yescharacteristic
1329C2C29×#255511yescharacteristic
1330C2C29×#255711yescharacteristic
1331C2C29×#264811yescharacteristic
1332C2C29×#285411yescharacteristic
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×#390C2semidirect
5. C2×C29×#388C2semidirect
6. C2×C29×#386C2semidirect
7. C2×C29×#386C2semidirect
8. C2×C4×C22⋊C4×C29C2semidirect
9. C29×#1441C2semidirect
10. C29×#1440C2semidirect
11. C29×#1439C2semidirect
12. C29×#1439C2semidirect
13. C29×#1438C2semidirect
14. C29×#1437C2semidirect
15. C29×#1436C2semidirect
151. C2×C22⋊C4×C29D4semidirect
152. C2×C22⋊C4×C29D4semidirect
170. C29×#95D4semidirect
348. #14751C29direct (N × H)
557. C2×#394C2×C29semidirect
558. C2×#394C2×C29semidirect
560. C2×#390C2×C29semidirect
561. C2×#388C2×C29semidirect
562. C2×#386C2×C29semidirect
563. C2×#386C2×C29semidirect
564. C2×C4×C22⋊C4C2×C29semidirect
565. #1441C2×C29semidirect
566. #1440C2×C29semidirect
567. #1439C2×C29semidirect
568. #1439C2×C29semidirect
569. #1438C2×C29semidirect
570. #1437C2×C29semidirect
571. #1436C2×C29semidirect
817. C2×C22⋊C4D4×C29semidirect
818. C2×C22⋊C4D4×C29semidirect
836. #95D4×C29semidirect
837. C29#14751direct (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×#3902
C2×C29×#3882
C2×C29×#3862
C2×C4×C22⋊C4×C292
C29×#14412
C29×#14402
C29×#14392
C29×#14382
C29×#14372
C29×#14362
#1475129