Finite Group Databasebeta

← C29×#14220 #20309120

Subgroups — C29×#14220 #20309120

Order 7424.

1786 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#393C211yesmaximal, characteristic
2C2×C29×#391C211yesmaximal, characteristic, complemented
3C2×C29×#391C211yesmaximal, characteristic, complemented
4C2×C29×#385C211yesmaximal, characteristic
5C2×C4×C22⋊C4×C29C211yesmaximal, characteristic
6C29×#1443C211yesmaximal, characteristic, complemented
7C29×#1442C211yesmaximal, characteristic, complemented
8C29×#1439C211yesmaximal, characteristic
9C29×#1437C211yesmaximal, characteristic
10C29×#1437C211yesmaximal, characteristic
11C29×#1436C211yesmaximal, characteristic, complemented
12C29×#1436C211yesmaximal, characteristic, complemented
13C29×#1436C211yesmaximal, characteristic, complemented
14C29×C22⋊#95C211yesmaximal, characteristic
15C4×C29×#95C211yesmaximal, characteristic, complemented
16C23×Q8×C29C2211yescharacteristic
17C24×C4×C29C2211yescharacteristic
18C22×C4⋊C4×C29C2211yescharacteristic
19C22×C4⋊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×C42×C29C2211yescharacteristic
28C22×C42×C29C2211yescharacteristic
29C22×C42×C29C2211yescharacteristic
30C22×C42×C29C2211yescharacteristic
31C29×#393C418yescomplemented
32C29×#391—24no—
33C29×#391—24no—
34C29×#385—24no—
35C4×C22⋊C4×C29—24no—
36C2×C29×#95C2211yescharacteristic
37C2×C29×#95C2211yescharacteristic
38C2×C29×#95C2211yescharacteristic
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
55C2×C29×#95C2211yescharacteristic
56C25×C29C2311yescharacteristic
57C22×Q8×C29—22no—
58C22×Q8×C29—22no—
59C22×Q8×C29—22no—
60C22×Q8×C29—22no—
61C22×Q8×C29—41no—
62C22×Q8×C29—41no—
63C22×Q8×C29C2×C414yescomplemented
64C23×C4×C29—22no—
65C23×C4×C29—22no—
66C23×C4×C29—22no—
67C23×C4×C29—22no—
68C23×C4×C29—22no—
69C23×C4×C29—41no—
70C23×C4×C29—41no—
71C23×C4×C29C2311yescharacteristic
72C23×C4×C29C2311yescharacteristic
73C23×C4×C29C2311yescharacteristic
74C23×C4×C29C2311yescharacteristic
75C23×C4×C29C2311yescharacteristic
76C23×C4×C29C2311yescharacteristic
77C23×C4×C29C2311yescharacteristic
78C23×C4×C29C2311yescharacteristic
79C23×C4×C29C2311yescharacteristic
80C23×C4×C29C2311yescharacteristic
81C23×C4×C29C2311yescharacteristic
82C23×C4×C29C2311yescharacteristic
83C23×C4×C29C2311yescharacteristic
84C23×C4×C29C2311yescharacteristic
85C2×C4⋊C4×C29—22no—
86C2×C4⋊C4×C29—22no—
87C2×C4⋊C4×C29—22no—
88C2×C4⋊C4×C29—22no—
89C2×C4⋊C4×C29—22no—
90C2×C4⋊C4×C29—22no—
91C2×C4⋊C4×C29—22no—
92C2×C4⋊C4×C29—41no—
93C2×C4⋊C4×C29—41no—
94C2×C22⋊C4×C29—22no—
95C2×C22⋊C4×C29—22no—
96C2×C22⋊C4×C29—22no—
97C2×C22⋊C4×C29—22no—
98C2×C22⋊C4×C29—22no—
99C2×C22⋊C4×C29—22no—
100C2×C22⋊C4×C29—22no—
101C2×C22⋊C4×C29—22no—
102C2×C22⋊C4×C29—22no—
103C2×C22⋊C4×C29—22no—
104C2×C22⋊C4×C29—41no—
105C2×C22⋊C4×C29—41no—
106C2×C22⋊C4×C29—41no—
107C2×C22⋊C4×C29—41no—
108C2×C22⋊C4×C29C2×C414yes—
109C2×C22⋊C4×C29C2×C414yes—
110C2×C22⋊C4×C29C2×C414yes—
111C2×C22⋊C4×C29Q814yescomplemented
112C2×C42×C29—22no—
113C2×C42×C29—22no—
114C2×C42×C29—22no—
115C2×C42×C29—22no—
116C2×C42×C29—22no—
117C2×C42×C29—22no—
118C2×C42×C29—22no—
119C2×C42×C29—41no—
120C2×C42×C29—41no—
121C2×C42×C29—41no—
122C2×C42×C29—41no—
123C2×C42×C29—41no—
124C29×#95—22no—
125C29×#95—22no—
126C29×#95—22no—
127C29×#95—22no—
128C29×#95—22no—
129C29×#95—22no—
130C29×#95—22no—
131C29×#95—22no—
132C29×#95—22no—
133C29×#95—22no—
134C29×#95—22no—
135C29×#95—22no—
136C29×#95—41no—
137C29×#95—41no—
138C29×#95—41no—
139C29×#95C2×C414yescomplemented
140C29×#95C2×C414yescomplemented
141C29×#95C2×C414yescomplemented
142C29×#95D414yes—
143C29×#95D414yes—
144C24×C29—21no—
145C24×C29—21no—
146C24×C29—21no—
147C24×C29—21no—
148C24×C29—21no—
149C24×C29—21no—
150C24×C29—21no—
151C24×C29—21no—
152C24×C29—21no—
153C24×C29—21no—
154C24×C29—21no—
155C24×C29—21no—
156C24×C29C22×C412yes—
157C24×C29C2×Q812yes—
158C24×C29#4112yes—
159C24×C29C2411yescharacteristic
160C2×Q8×C29—28no—
161C2×Q8×C29—28no—
162C2×Q8×C29—44no—
163C2×Q8×C29—44no—
164C2×Q8×C29—44no—
165C2×Q8×C29—44no—
166C2×Q8×C29—44no—
167C22×C4×C29—21no—
168C22×C4×C29—21no—
169C22×C4×C29—21no—
170C22×C4×C29—21no—
171C22×C4×C29—21no—
172C22×C4×C29—21no—
173C22×C4×C29—21no—
174C22×C4×C29—21no—
175C22×C4×C29—21no—
176C22×C4×C29—21no—
177C22×C4×C29—21no—
178C22×C4×C29—21no—
179C22×C4×C29—21no—
180C22×C4×C29—21no—
181C22×C4×C29—21no—
182C22×C4×C29—21no—
183C22×C4×C29—28no—
184C22×C4×C29—21no—
185C22×C4×C29—21no—
186C22×C4×C29—21no—
187C22×C4×C29—21no—
188C22×C4×C29—21no—
189C22×C4×C29—21no—
190C22×C4×C29—21no—
191C22×C4×C29—21no—
192C22×C4×C29—21no—
193C22×C4×C29—21no—
194C22×C4×C29—21no—
195C22×C4×C29—21no—
196C22×C4×C29—21no—
197C22×C4×C29—21no—
198C22×C4×C29—21no—
199C22×C4×C29—21no—
200C22×C4×C29—21no—
201C22×C4×C29—21no—
202C22×C4×C29—21no—
203C22×C4×C29—21no—
204C22×C4×C29—21no—
205C22×C4×C29—21no—
206C22×C4×C29—21no—
207C22×C4×C29—21no—
208C22×C4×C29—21no—
209C22×C4×C29—21no—
210C22×C4×C29—21no—
211C22×C4×C29—21no—
212C22×C4×C29—21no—
213C22×C4×C29—21no—
214C22×C4×C29—21no—
215C22×C4×C29—21no—
216C22×C4×C29—21no—
217C22×C4×C29—21no—
218C22×C4×C29—21no—
219C22×C4×C29—21no—
220C22×C4×C29—21no—
221C22×C4×C29—21no—
222C22×C4×C29—21no—
223C22×C4×C29—21no—
224C22×C4×C29—21no—
225C22×C4×C29—21no—
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—44no—
247C22×C4×C29—44no—
248C22×C4×C29—44no—
249C22×C4×C29—44no—
250C22×C4×C29—44no—
251C22×C4×C29—44no—
252C22×C4×C29C22×C412yes—
253C22×C4×C29C22×C412yes—
254C22×C4×C29C22×C412yes—
255C22×C4×C29C22×C412yes—
256C22×C4×C29C22×C412yes—
257C22×C4×C29C22×C412yes—
258C22×C4×C29C2×D412yes—
259C22×C4×C29C2×D412yes—
260C22×C4×C29C2×D412yes—
261C22×C4×C29C2×D412yes—
262C22×C4×C29C2×D412yes—
263C22×C4×C29C2×D412yes—
264C22×C4×C29C2×Q812yes—
265C22×C4×C29C2×Q812yes—
266C22×C4×C29#4112yes—
267C22×C4×C29#4112yes—
268C22×C4×C29#4112yes—
269C22×C4×C29#4112yes—
270C22×C4×C29#4112yes—
271C22×C4×C29#4112yes—
272C4⋊C4×C29—44no—
273C4⋊C4×C29—44no—
274C4⋊C4×C29—44no—
275C22⋊C4×C29—28no—
276C22⋊C4×C29—28no—
277C22⋊C4×C29—28no—
278C22⋊C4×C29—44no—
279C22⋊C4×C29—44no—
280C22⋊C4×C29—44no—
281C42×C29—44no—
282C42×C29—44no—
283C42×C29—44no—
284C42×C29—44no—
285#14220C2911yesmaximal, characteristic, direct product factor, Sylow
286C23×C29—22no—
287C23×C29—22no—
288C23×C29—22no—
289C23×C29—22no—
290C23×C29—22no—
291C23×C29—22no—
292C23×C29—22no—
293C23×C29—22no—
294C23×C29—22no—
295C23×C29—22no—
296C23×C29—22no—
297C23×C29—22no—
298C23×C29—22no—
299C23×C29—22no—
300C23×C29—22no—
301C23×C29—22no—
302C23×C29—22no—
303C23×C29—22no—
304C23×C29—41no—
305C23×C29—41no—
306C23×C29—41no—
307C23×C29—41no—
308C23×C29—41no—
309C23×C29—41no—
310C23×C29—41no—
311C23×C29—41no—
312C23×C29—41no—
313C23×C29—41no—
314C23×C29—41no—
315C23×C29—41no—
316C23×C29—41no—
317C23×C29—41no—
318C23×C29—41no—
319C23×C29—41no—
320C23×C29C4×Q814yes—
321C23×C29C23×C411yescharacteristic
322C23×C29C22×D411yescharacteristic
323C23×C29C22×D411yescharacteristic
324C23×C29C22×Q811yescharacteristic
325C23×C29C2×#4111yescharacteristic
326C23×C29C2×#4111yescharacteristic
327C23×C29C2×#4111yescharacteristic
328C23×C29C2×#4111yescharacteristic
329C23×C29C2×#4111yescharacteristic
330C23×C29C2×#4111yescharacteristic
331C23×C29C2×#4111yescharacteristic
332C23×C29H(5,𝔽2)11yescharacteristic
333C23×C29H(5,𝔽2)11yescharacteristic
334C23×C29H(5,𝔽2)11yescharacteristic
335C23×C292−1+411yescharacteristic
336Q8×C29—416no—
337C2×C4×C29—22no—
338C2×C4×C29—22no—
339C2×C4×C29—22no—
340C2×C4×C29—22no—
341C2×C4×C29—22no—
342C2×C4×C29—22no—
343C2×C4×C29—22no—
344C2×C4×C29—22no—
345C2×C4×C29—22no—
346C2×C4×C29—22no—
347C2×C4×C29—22no—
348C2×C4×C29—22no—
349C2×C4×C29—22no—
350C2×C4×C29—22no—
351C2×C4×C29—22no—
352C2×C4×C29—22no—
353C2×C4×C29—22no—
354C2×C4×C29—22no—
355C2×C4×C29—22no—
356C2×C4×C29—22no—
357C2×C4×C29—22no—
358C2×C4×C29—22no—
359C2×C4×C29—22no—
360C2×C4×C29—22no—
361C2×C4×C29—22no—
362C2×C4×C29—22no—
363C2×C4×C29—22no—
364C2×C4×C29—22no—
365C2×C4×C29—22no—
366C2×C4×C29—22no—
367C2×C4×C29—22no—
368C2×C4×C29—22no—
369C2×C4×C29—22no—
370C2×C4×C29—22no—
371C2×C4×C29—22no—
372C2×C4×C29—22no—
373C2×C4×C29—22no—
374C2×C4×C29—22no—
375C2×C4×C29—22no—
376C2×C4×C29—22no—
377C2×C4×C29—22no—
378C2×C4×C29—22no—
379C2×C4×C29—22no—
380C2×C4×C29—22no—
381C2×C4×C29—22no—
382C2×C4×C29—22no—
383C2×C4×C29—22no—
384C2×C4×C29—22no—
385C2×C4×C29—416no—
386C2×C4×C29—41no—
387C2×C4×C29—41no—
388C2×C4×C29—41no—
389C2×C4×C29—41no—
390C2×C4×C29—41no—
391C2×C4×C29—41no—
392C2×C4×C29—41no—
393C2×C4×C29—41no—
394C2×C4×C29—41no—
395C2×C4×C29—41no—
396C2×C4×C29—41no—
397C2×C4×C29—41no—
398C2×C4×C29—41no—
399C2×C4×C29—41no—
400C2×C4×C29—41no—
401C2×C4×C29—41no—
402C2×C4×C29—41no—
403C2×C4×C29—41no—
404C2×C4×C29—41no—
405C2×C4×C29—41no—
406C2×C4×C29—41no—
407C2×C4×C29—41no—
408C2×C4×C29—41no—
409C2×C4×C29—41no—
410C2×C4×C29—41no—
411C2×C4×C29—41no—
412C2×C4×C29—41no—
413C2×C4×C29—41no—
414C2×C4×C29—41no—
415C2×C4×C29—41no—
416C2×C4×C29—41no—
417C2×C4×C29—41no—
418C2×C4×C29—41no—
419C2×C4×C29—41no—
420C2×C4×C29—41no—
421C2×C4×C29—41no—
422C2×C4×C29—41no—
423C2×C4×C29—41no—
424C2×C4×C29—41no—
425C2×C4×C29—41no—
426C2×C4×C29—41no—
427C2×C4×C29—41no—
428C2×C4×C29—41no—
429C2×C4×C29—41no—
430C2×C4×C29—41no—
431C2×C4×C29—41no—
432C2×C4×C29C4×D414yes—
433C2×C4×C29C4×D414yes—
434C2×C4×C29C22⋊Q814yes—
435C2×C4×C29#12414yes—
436C2×#393C2×C2911yescharacteristic
437C2×#391C2×C2911yescharacteristic, complemented
438C2×#391C2×C2911yescharacteristic, complemented
439C2×#385C2×C2911yescharacteristic
440C2×C4×C22⋊C4C2×C2911yescharacteristic
441#1443C2×C2911yescharacteristic, complemented
442#1442C2×C2911yescharacteristic, complemented
443#1439C2×C2911yescharacteristic
444#1437C2×C2911yescharacteristic
445#1437C2×C2911yescharacteristic
446#1436C2×C2911yescharacteristic, complemented
447#1436C2×C2911yescharacteristic, complemented
448#1436C2×C2911yescharacteristic, complemented
449C22⋊#95C2×C2911yescharacteristic
450C4×#95C2×C2911yescharacteristic, complemented
451C22×C29—24no—
452C22×C29—24no—
453C22×C29—24no—
454C22×C29—42no—
455C22×C29—42no—
456C22×C29—42no—
457C22×C29—42no—
458C22×C29—42no—
459C22×C29—42no—
460C22×C29—42no—
461C22×C29—42no—
462C22×C29—42no—
463C22×C29—42no—
464C22×C29—42no—
465C22×C29—42no—
466C22×C29C2×C4×D411yescharacteristic
467C22×C29C2×C4×D411yescharacteristic
468C22×C29C2×C4×Q811yescharacteristic
469C22×C29C4×#4111yescharacteristic
470C22×C29C4×#4111yescharacteristic
471C22×C29#51811yescharacteristic
472C22×C29#52011yescharacteristic
473C22×C29C2×C22⋊Q811yescharacteristic
474C22×C29#52511yescharacteristic
475C22×C29C2×#12411yescharacteristic
476C22×C29#52911yescharacteristic
477C22×C29#52911yescharacteristic
478C22×C29#52911yescharacteristic
479C22×C29#53211yescharacteristic
480C22×C29#53311yescharacteristic
481C22×C29#53811yescharacteristic
482C22×C29#53811yescharacteristic
483C22×C29#54211yescharacteristic
484C22×C29#54211yescharacteristic
485C22×C29D4211yescharacteristic
486C22×C29#54611yescharacteristic
487C22×C29#54611yescharacteristic
488C22×C29#54611yescharacteristic
489C22×C29#54611yescharacteristic
490C22×C29#54811yescharacteristic
491C22×C29D4×Q811yescharacteristic
492C22×C29#55111yescharacteristic
493C22×C29#55111yescharacteristic
494C22×C29#55111yescharacteristic
495C22×C29#55211yescharacteristic
496C22×C29#55411yescharacteristic
497C22×C29#55411yescharacteristic
498C22×C29#55411yescharacteristic
499C22×C29#55611yescharacteristic
500C22×C29#55911yescharacteristic
501C4×C29—24no—
502C4×C29—24no—
503C4×C29—24no—
504C4×C29—24no—
505C4×C29—42no—
506C4×C29—42no—
507C4×C29—42no—
508C4×C29—42no—
509C4×C29—42no—
510C4×C29—42no—
511C4×C29—42no—
512C4×C29—42no—
513C4×C29—81no—
514C4×C29—81no—
515C23×Q8C22×C2911yescharacteristic
516C24×C4C22×C2911yescharacteristic
517C22×C4⋊C4C22×C2911yescharacteristic
518C22×C4⋊C4C22×C2911yescharacteristic
519C22×C4⋊C4C22×C2911yescharacteristic
520C22×C22⋊C4C22×C2911yescharacteristic
521C22×C22⋊C4C22×C2911yescharacteristic
522C22×C22⋊C4C22×C2911yescharacteristic
523C22×C22⋊C4C22×C2911yescharacteristic
524C22×C22⋊C4C22×C2911yescharacteristic
525C22×C22⋊C4C22×C2911yescharacteristic
526C22×C42C22×C2911yescharacteristic
527C22×C42C22×C2911yescharacteristic
528C22×C42C22×C2911yescharacteristic
529C22×C42C22×C2911yescharacteristic
530#393C4×C2918yescomplemented
531#391—24no—
532#391—24no—
533#385—24no—
534C4×C22⋊C4—24no—
535C2×#95C22×C2911yescharacteristic
536C2×#95C22×C2911yescharacteristic
537C2×#95C22×C2911yescharacteristic
538C2×#95C22×C2911yescharacteristic
539C2×#95C22×C2911yescharacteristic
540C2×#95C22×C2911yescharacteristic
541C2×#95C22×C2911yescharacteristic
542C2×#95C22×C2911yescharacteristic
543C2×#95C22×C2911yescharacteristic
544C2×#95C22×C2911yescharacteristic
545C2×#95C22×C2911yescharacteristic
546C2×#95C22×C2911yescharacteristic
547C2×#95C22×C2911yescharacteristic
548C2×#95C22×C2911yescharacteristic
549C2×#95C22×C2911yescharacteristic
550C2×#95C22×C2911yescharacteristic
551C2×#95C22×C2911yescharacteristic
552C2×#95C22×C2911yescharacteristic
553C2×#95C22×C2911yescharacteristic
554C2×#95C22×C2911yescharacteristic
555C2×C29—44no—
556C2×C29C4×C22⋊Q811yescharacteristic
557C2×C29C4×#12411yescharacteristic
558C2×C29#233711yescharacteristic
559C2×C29#235811yescharacteristic
560C2×C29#236011yescharacteristic
561C2×C29#236711yescharacteristic
562C2×C29#236811yescharacteristic
563C2×C29#245011yescharacteristic
564C2×C29#245211yescharacteristic
565C2×C29#247211yescharacteristic
566C2×C29#247711yescharacteristic
567C2×C29#249211yescharacteristic
568C2×C29#252711yescharacteristic
569C2×C29#255711yescharacteristic
570C2×C29#258911yescharacteristic
571C25C23×C2911yescharacteristic
572C22×Q8—22no—
573C22×Q8—22no—
574C22×Q8—22no—
575C22×Q8—22no—
576C22×Q8—41no—
577C22×Q8—41no—
578C22×Q8C2×C4×C2914yescomplemented
579C23×C4—22no—
580C23×C4—22no—
581C23×C4—22no—
582C23×C4—22no—
583C23×C4—22no—
584C23×C4—41no—
585C23×C4—41no—
586C23×C4C23×C2911yescharacteristic
587C23×C4C23×C2911yescharacteristic
588C23×C4C23×C2911yescharacteristic
589C23×C4C23×C2911yescharacteristic
590C23×C4C23×C2911yescharacteristic
591C23×C4C23×C2911yescharacteristic
592C23×C4C23×C2911yescharacteristic
593C23×C4C23×C2911yescharacteristic
594C23×C4C23×C2911yescharacteristic
595C23×C4C23×C2911yescharacteristic
596C23×C4C23×C2911yescharacteristic
597C23×C4C23×C2911yescharacteristic
598C23×C4C23×C2911yescharacteristic
599C23×C4C23×C2911yescharacteristic
600C2×C4⋊C4—22no—
601C2×C4⋊C4—22no—
602C2×C4⋊C4—22no—
603C2×C4⋊C4—22no—
604C2×C4⋊C4—22no—
605C2×C4⋊C4—22no—
606C2×C4⋊C4—22no—
607C2×C4⋊C4—41no—
608C2×C4⋊C4—41no—
609C2×C22⋊C4—22no—
610C2×C22⋊C4—22no—
611C2×C22⋊C4—22no—
612C2×C22⋊C4—22no—
613C2×C22⋊C4—22no—
614C2×C22⋊C4—22no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—22no—
618C2×C22⋊C4—22no—
619C2×C22⋊C4—41no—
620C2×C22⋊C4—41no—
621C2×C22⋊C4—41no—
622C2×C22⋊C4—41no—
623C2×C22⋊C4C2×C4×C2914yes—
624C2×C22⋊C4C2×C4×C2914yes—
625C2×C22⋊C4C2×C4×C2914yes—
626C2×C22⋊C4Q8×C2914yescomplemented
627C2×C42—22no—
628C2×C42—22no—
629C2×C42—22no—
630C2×C42—22no—
631C2×C42—22no—
632C2×C42—22no—
633C2×C42—22no—
634C2×C42—41no—
635C2×C42—41no—
636C2×C42—41no—
637C2×C42—41no—
638C2×C42—41no—
639#95—22no—
640#95—22no—
641#95—22no—
642#95—22no—
643#95—22no—
644#95—22no—
645#95—22no—
646#95—22no—
647#95—22no—
648#95—22no—
649#95—22no—
650#95—22no—
651#95—41no—
652#95—41no—
653#95—41no—
654#95C2×C4×C2914yescomplemented
655#95C2×C4×C2914yescomplemented
656#95C2×C4×C2914yescomplemented
657#95D4×C2914yes—
658#95D4×C2914yes—
659C29#1422011yescharacteristic, direct product factor, Sylow
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24C22×C4×C2912yes—
673C24C2×Q8×C2912yes—
674C24#41×C2912yes—
675C24C24×C2911yescharacteristic
676C2×Q8—28no—
677C2×Q8—28no—
678C2×Q8—44no—
679C2×Q8—44no—
680C2×Q8—44no—
681C2×Q8—44no—
682C2×Q8—44no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—28no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—44no—
763C22×C4—44no—
764C22×C4—44no—
765C22×C4—44no—
766C22×C4—44no—
767C22×C4—44no—
768C22×C4C22×C4×C2912yes—
769C22×C4C22×C4×C2912yes—
770C22×C4C22×C4×C2912yes—
771C22×C4C22×C4×C2912yes—
772C22×C4C22×C4×C2912yes—
773C22×C4C22×C4×C2912yes—
774C22×C4C2×D4×C2912yes—
775C22×C4C2×D4×C2912yes—
776C22×C4C2×D4×C2912yes—
777C22×C4C2×D4×C2912yes—
778C22×C4C2×D4×C2912yes—
779C22×C4C2×D4×C2912yes—
780C22×C4C2×Q8×C2912yes—
781C22×C4C2×Q8×C2912yes—
782C22×C4#41×C2912yes—
783C22×C4#41×C2912yes—
784C22×C4#41×C2912yes—
785C22×C4#41×C2912yes—
786C22×C4#41×C2912yes—
787C22×C4#41×C2912yes—
788C4⋊C4—44no—
789C4⋊C4—44no—
790C4⋊C4—44no—
791C22⋊C4—28no—
792C22⋊C4—28no—
793C22⋊C4—28no—
794C22⋊C4—44no—
795C22⋊C4—44no—
796C22⋊C4—44no—
797C42—44no—
798C42—44no—
799C42—44no—
800C42—44no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23C4×Q8×C2914yes—
836C23C23×C4×C2911yescharacteristic
837C23C22×D4×C2911yescharacteristic
838C23C22×D4×C2911yescharacteristic
839C23C22×Q8×C2911yescharacteristic
840C23C2×#41×C2911yescharacteristic
841C23C2×#41×C2911yescharacteristic
842C23C2×#41×C2911yescharacteristic
843C23C2×#41×C2911yescharacteristic
844C23C2×#41×C2911yescharacteristic
845C23C2×#41×C2911yescharacteristic
846C23C2×#41×C2911yescharacteristic
847C23C29×H(5,𝔽2)11yescharacteristic
848C23C29×H(5,𝔽2)11yescharacteristic
849C23C29×H(5,𝔽2)11yescharacteristic
850C23C29×2−1+411yescharacteristic
851Q8—416no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—416no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4C4×D4×C2914yes—
948C2×C4C4×D4×C2914yes—
949C2×C4C29×C22⋊Q814yes—
950C2×C4C29×#12414yes—
951C22—24no—
952C22—24no—
953C22—24no—
954C22—42no—
955C22—42no—
956C22—42no—
957C22—42no—
958C22—42no—
959C22—42no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22C2×C4×D4×C2911yescharacteristic
967C22C2×C4×D4×C2911yescharacteristic
968C22C2×C4×Q8×C2911yescharacteristic
969C22C4×#41×C2911yescharacteristic
970C22C4×#41×C2911yescharacteristic
971C22C29×#51811yescharacteristic
972C22C29×#52011yescharacteristic
973C22C2×C29×C22⋊Q811yescharacteristic
974C22C29×#52511yescharacteristic
975C22C2×C29×#12411yescharacteristic
976C22C29×#52911yescharacteristic
977C22C29×#52911yescharacteristic
978C22C29×#52911yescharacteristic
979C22C29×#53211yescharacteristic
980C22C29×#53311yescharacteristic
981C22C29×#53811yescharacteristic
982C22C29×#53811yescharacteristic
983C22C29×#54211yescharacteristic
984C22C29×#54211yescharacteristic
985C22D42×C2911yescharacteristic
986C22C29×#54611yescharacteristic
987C22C29×#54611yescharacteristic
988C22C29×#54611yescharacteristic
989C22C29×#54611yescharacteristic
990C22C29×#54811yescharacteristic
991C22D4×Q8×C2911yescharacteristic
992C22C29×#55111yescharacteristic
993C22C29×#55111yescharacteristic
994C22C29×#55111yescharacteristic
995C22C29×#55211yescharacteristic
996C22C29×#55411yescharacteristic
997C22C29×#55411yescharacteristic
998C22C29×#55411yescharacteristic
999C22C29×#55611yescharacteristic
1000C22C29×#55911yescharacteristic
1001C4—24no—
1002C4—24no—
1003C4—24no—
1004C4—24no—
1005C4—42no—
1006C4—42no—
1007C4—42no—
1008C4—42no—
1009C4—42no—
1010C4—42no—
1011C4—42no—
1012C4—42no—
1013C4—81no—
1014C4—81no—
1015C2—44no—
1016C2C4×C29×C22⋊Q811yescharacteristic
1017C2C4×C29×#12411yescharacteristic
1018C2C29×#233711yescharacteristic
1019C2C29×#235811yescharacteristic
1020C2C29×#236011yescharacteristic
1021C2C29×#236711yescharacteristic
1022C2C29×#236811yescharacteristic
1023C2C29×#245011yescharacteristic
1024C2C29×#245211yescharacteristic
1025C2C29×#247211yescharacteristic
1026C2C29×#247711yescharacteristic
1027C2C29×#249211yescharacteristic
1028C2C29×#252711yescharacteristic
1029C2C29×#255711yescharacteristic
1030C2C29×#258911yescharacteristic
subgroupG/H
center, socleC24×C29C24
commutatorC23C23×C4×C29
Frattini, cosocleC24C24×C29
prime radicalC25×C29C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C29×#391C2semidirect
3. C2×C29×#391C2semidirect
6. C29×#1443C2semidirect
7. C29×#1442C2semidirect
11. C29×#1436C2semidirect
12. C29×#1436C2semidirect
13. C29×#1436C2semidirect
15. C4×C29×#95C2semidirect
31. C29×#393C4semidirect
63. C22×Q8×C29C2×C4semidirect
111. C2×C22⋊C4×C29Q8semidirect
139. C29×#95C2×C4semidirect
140. C29×#95C2×C4semidirect
141. C29×#95C2×C4semidirect
285. #14220C29direct (N × H)
437. C2×#391C2×C29semidirect
438. C2×#391C2×C29semidirect
441. #1443C2×C29semidirect
442. #1442C2×C29semidirect
446. #1436C2×C29semidirect
447. #1436C2×C29semidirect
448. #1436C2×C29semidirect
450. C4×#95C2×C29semidirect
530. #393C4×C29semidirect
578. C22×Q8C2×C4×C29semidirect
626. C2×C22⋊C4Q8×C29semidirect
654. #95C2×C4×C29semidirect
655. #95C2×C4×C29semidirect
656. #95C2×C4×C29semidirect
659. C29#14220direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#3932
C2×C29×#3912
C2×C29×#3852
C2×C4×C22⋊C4×C292
C29×#14432
C29×#14422
C29×#14392
C29×#14372
C29×#14362
C29×C22⋊#952
C4×C29×#952
#1422029