Finite Group Databasebeta

← C29×#15131 #20310031

Subgroups — C29×#15131 #20310031

Order 7424.

1814 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#396C212yesmaximal
2C2×C29×#389C211yesmaximal, characteristic, complemented
3C2×C29×#389C211yesmaximal, characteristic, complemented
4C2×C29×#384C211yesmaximal, characteristic, complemented
5C2×C29×#380C211yesmaximal, characteristic
6C2×C29×#380C211yesmaximal, characteristic
7C2×C4×C22⋊C4×C29C211yesmaximal, characteristic
8C29×#1441C212yesmaximal, complemented
9C29×#1441C212yesmaximal, complemented
10C29×#1439C212yesmaximal
11C29×C4⋊#95C211yesmaximal, characteristic, complemented
12C24×C4×C29C2211yescharacteristic
13C22×C4⋊C4×C29C2211yescharacteristic
14C22×C4⋊C4×C29C2211yescharacteristic
15C22×C4⋊C4×C29C2212yes—
16C22×C4⋊C4×C29C2212yes—
17C22×C4⋊C4×C29C2212yes—
18C22×C4⋊C4×C29C2212yes—
19C22×C4⋊C4×C29C2211yescharacteristic
20C22×C4⋊C4×C29C2211yescharacteristic
21C22×C22⋊C4×C29C2212yes—
22C22×C22⋊C4×C29C2212yes—
23C22×C22⋊C4×C29C2211yescharacteristic
24C22×C22⋊C4×C29C2211yescharacteristic
25C22×C42×C29C2211yescharacteristic
26C22×C42×C29C2211yescharacteristic
27C29×#396—28no—
28C29×#389—24no—
29C29×#389—24no—
30C29×#384—24no—
31C29×#380—24no—
32C29×#380—24no—
33C4×C22⋊C4×C29—24no—
34C2×C29×#95C2212yes—
35C2×C29×#95C2212yes—
36C2×C29×#95C2212yes—
37C2×C29×#95C2211yescharacteristic
38C2×C29×#95C2211yescharacteristic
39C2×C29×#95C2212yes—
40C2×C29×#95C2212yes—
41C2×C29×#95C2212yes—
42C25×C29C2311yescharacteristic
43C23×C4×C29—22no—
44C23×C4×C29—22no—
45C23×C4×C29—22no—
46C23×C4×C29—22no—
47C23×C4×C29—22no—
48C23×C4×C29—22no—
49C23×C4×C29Q814yes—
50C23×C4×C29C2312yes—
51C23×C4×C29C2312yes—
52C23×C4×C29C2311yescharacteristic
53C23×C4×C29C2312yes—
54C23×C4×C29C2312yes—
55C23×C4×C29C2311yescharacteristic
56C23×C4×C29C2311yescharacteristic
57C23×C4×C29C2311yescharacteristic
58C23×C4×C29C2311yescharacteristic
59C23×C4×C29C2311yescharacteristic
60C2×C4⋊C4×C29—22no—
61C2×C4⋊C4×C29—22no—
62C2×C4⋊C4×C29—22no—
63C2×C4⋊C4×C29—22no—
64C2×C4⋊C4×C29—22no—
65C2×C4⋊C4×C29—22no—
66C2×C4⋊C4×C29—24no—
67C2×C4⋊C4×C29—24no—
68C2×C4⋊C4×C29—22no—
69C2×C4⋊C4×C29—24no—
70C2×C4⋊C4×C29—24no—
71C2×C4⋊C4×C29—22no—
72C2×C4⋊C4×C29—24no—
73C2×C4⋊C4×C29—24no—
74C2×C4⋊C4×C29—24no—
75C2×C4⋊C4×C29—24no—
76C2×C4⋊C4×C29—24no—
77C2×C4⋊C4×C29—22no—
78C2×C4⋊C4×C29—22no—
79C2×C4⋊C4×C29—42no—
80C2×C4⋊C4×C29—42no—
81C2×C4⋊C4×C29—42no—
82C2×C4⋊C4×C29D414yes—
83C2×C4⋊C4×C29D414yes—
84C2×C22⋊C4×C29—22no—
85C2×C22⋊C4×C29—22no—
86C2×C22⋊C4×C29—22no—
87C2×C22⋊C4×C29—22no—
88C2×C22⋊C4×C29—24no—
89C2×C22⋊C4×C29—24no—
90C2×C22⋊C4×C29—24no—
91C2×C22⋊C4×C29—24no—
92C2×C22⋊C4×C29—42no—
93C2×C22⋊C4×C29—42no—
94C2×C22⋊C4×C29D414yes—
95C2×C22⋊C4×C29Q814yes—
96C2×C42×C29—22no—
97C2×C42×C29—22no—
98C2×C42×C29—22no—
99C2×C42×C29—22no—
100C2×C42×C29—22no—
101C2×C42×C29D414yes—
102C29×#95—22no—
103C29×#95—22no—
104C29×#95—24no—
105C29×#95—24no—
106C29×#95—24no—
107C29×#95—24no—
108C29×#95—24no—
109C29×#95—42no—
110C24×C29—21no—
111C24×C29—21no—
112C24×C29—21no—
113C24×C29—21no—
114C24×C29—21no—
115C24×C29—21no—
116C24×C29—21no—
117C24×C29—21no—
118C24×C29—21no—
119C24×C29—21no—
120C24×C29—21no—
121C24×C29—21no—
122C24×C29C2×D412yes—
123C24×C29C2×Q812yes—
124C24×C29C2×Q812yes—
125C24×C29C2411yescharacteristic
126C22×C4×C29—21no—
127C22×C4×C29—21no—
128C22×C4×C29—21no—
129C22×C4×C29—21no—
130C22×C4×C29—21no—
131C22×C4×C29—21no—
132C22×C4×C29—21no—
133C22×C4×C29—21no—
134C22×C4×C29—21no—
135C22×C4×C29—21no—
136C22×C4×C29—21no—
137C22×C4×C29—21no—
138C22×C4×C29—22no—
139C22×C4×C29—22no—
140C22×C4×C29—22no—
141C22×C4×C29—22no—
142C22×C4×C29—21no—
143C22×C4×C29—21no—
144C22×C4×C29—21no—
145C22×C4×C29—21no—
146C22×C4×C29—21no—
147C22×C4×C29—21no—
148C22×C4×C29—21no—
149C22×C4×C29—22no—
150C22×C4×C29—22no—
151C22×C4×C29—22no—
152C22×C4×C29—22no—
153C22×C4×C29—21no—
154C22×C4×C29—21no—
155C22×C4×C29—21no—
156C22×C4×C29—22no—
157C22×C4×C29—22no—
158C22×C4×C29—21no—
159C22×C4×C29—22no—
160C22×C4×C29—21no—
161C22×C4×C29—21no—
162C22×C4×C29—22no—
163C22×C4×C29—21no—
164C22×C4×C29—28no—
165C22×C4×C29—28no—
166C22×C4×C29—28no—
167C22×C4×C29—22no—
168C22×C4×C29—22no—
169C22×C4×C29—22no—
170C22×C4×C29—22no—
171C22×C4×C29—22no—
172C22×C4×C29—22no—
173C22×C4×C29—22no—
174C22×C4×C29—22no—
175C22×C4×C29—22no—
176C22×C4×C29—22no—
177C22×C4×C29—22no—
178C22×C4×C29—22no—
179C22×C4×C29—22no—
180C22×C4×C29—22no—
181C22×C4×C29—44no—
182C22×C4×C29—44no—
183C22×C4×C29—44no—
184C22×C4×C29—44no—
185C22×C4×C29C2×D414yes—
186C22×C4×C29C2×D414yes—
187C22×C4×C29C2×D412yes—
188C22×C4×C29C2×D412yes—
189C22×C4×C29C2×D412yes—
190C22×C4×C29C2×D412yes—
191C22×C4×C29C2×D412yes—
192C22×C4×C29C2×D412yes—
193C22×C4×C29C2×D412yes—
194C22×C4×C29C2×Q812yes—
195C22×C4×C29C2×Q812yes—
196C22×C4×C29C2×Q812yes—
197C22×C4×C29C2×Q812yes—
198C22×C4×C29#4112yes—
199C22×C4×C29#4112yes—
200C22×C4×C29#4112yes—
201C22×C4×C29#4112yes—
202C22×C4×C29#4112yes—
203C4⋊C4×C29—28no—
204C4⋊C4×C29—28no—
205C4⋊C4×C29—48no—
206C4⋊C4×C29—48no—
207C4⋊C4×C29—48no—
208C4⋊C4×C29—48no—
209C4⋊C4×C29—44no—
210C4⋊C4×C29—44no—
211C22⋊C4×C29—28no—
212C22⋊C4×C29—28no—
213C22⋊C4×C29—48no—
214C22⋊C4×C29—48no—
215C42×C29—28no—
216C42×C29—44no—
217#15131C2911yesmaximal, characteristic, direct product factor, Sylow
218C23×C29—22no—
219C23×C29—22no—
220C23×C29—22no—
221C23×C29—22no—
222C23×C29—22no—
223C23×C29—22no—
224C23×C29—22no—
225C23×C29—22no—
226C23×C29—22no—
227C23×C29—22no—
228C23×C29—22no—
229C23×C29—22no—
230C23×C29—22no—
231C23×C29—22no—
232C23×C29—22no—
233C23×C29—22no—
234C23×C29—22no—
235C23×C29—22no—
236C23×C29—41no—
237C23×C29—41no—
238C23×C29—41no—
239C23×C29—41no—
240C23×C29—41no—
241C23×C29—41no—
242C23×C29—41no—
243C23×C29—41no—
244C23×C29—41no—
245C23×C29—41no—
246C23×C29—41no—
247C23×C29—41no—
248C23×C29—41no—
249C23×C29—41no—
250C23×C29—41no—
251C23×C29—41no—
252C23×C29C4⋊Q814yes—
253C23×C29C22×D411yescharacteristic
254C23×C29C22×D411yescharacteristic
255C23×C29C22×D411yescharacteristic
256C23×C29C22×D411yescharacteristic
257C23×C29C22×Q811yescharacteristic
258C23×C29C22×Q811yescharacteristic
259C23×C29C2×#4111yescharacteristic
260C23×C29C2×#4111yescharacteristic
261C23×C29C2×#4111yescharacteristic
262C23×C29C2×#4111yescharacteristic
263C23×C29C2×#4111yescharacteristic
264C23×C29H(5,𝔽2)11yescharacteristic
265C23×C29H(5,𝔽2)11yescharacteristic
266C23×C292−1+411yescharacteristic
267C23×C292−1+411yescharacteristic
268C2×C4×C29—22no—
269C2×C4×C29—22no—
270C2×C4×C29—22no—
271C2×C4×C29—22no—
272C2×C4×C29—22no—
273C2×C4×C29—22no—
274C2×C4×C29—22no—
275C2×C4×C29—22no—
276C2×C4×C29—22no—
277C2×C4×C29—22no—
278C2×C4×C29—22no—
279C2×C4×C29—22no—
280C2×C4×C29—22no—
281C2×C4×C29—24no—
282C2×C4×C29—24no—
283C2×C4×C29—22no—
284C2×C4×C29—22no—
285C2×C4×C29—22no—
286C2×C4×C29—22no—
287C2×C4×C29—24no—
288C2×C4×C29—24no—
289C2×C4×C29—22no—
290C2×C4×C29—24no—
291C2×C4×C29—24no—
292C2×C4×C29—22no—
293C2×C4×C29—22no—
294C2×C4×C29—22no—
295C2×C4×C29—41no—
296C2×C4×C29—41no—
297C2×C4×C29—42no—
298C2×C4×C29—41no—
299C2×C4×C29—41no—
300C2×C4×C29—41no—
301C2×C4×C29—41no—
302C2×C4×C29—42no—
303C2×C4×C29—41no—
304C2×C4×C29—42no—
305C2×C4×C29—41no—
306C2×C4×C29—42no—
307C2×C4×C29—42no—
308C2×C4×C29—41no—
309C2×C4×C29—42no—
310C2×C4×C29—42no—
311C2×C4×C29—41no—
312C2×C4×C29—41no—
313C2×C4×C29—42no—
314C2×C4×C29—41no—
315C2×C4×C29—416no—
316C2×C4×C29—42no—
317C2×C4×C29—42no—
318C2×C4×C29—42no—
319C2×C4×C29—42no—
320C2×C4×C29—42no—
321C2×C4×C29—42no—
322C2×C4×C29—42no—
323C2×C4×C29—42no—
324C2×C4×C29—42no—
325C2×C4×C29—42no—
326C2×C4×C29—42no—
327C2×C4×C29—42no—
328C2×C4×C29—42no—
329C2×C4×C29—42no—
330C2×C4×C29#12114yes—
331C2×C4×C29#12114yes—
332C2×C4×C29#12114yes—
333C2×C4×C29#12114yes—
334C2×C4×C29C22⋊Q814yes—
335C2×C4×C29C22⋊Q814yes—
336C2×C4×C29C22⋊Q814yes—
337C2×C4×C29C22⋊Q814yes—
338C2×C4×C29#12614yes—
339C2×#396C2×C2912yes—
340C2×#389C2×C2911yescharacteristic, complemented
341C2×#389C2×C2911yescharacteristic, complemented
342C2×#384C2×C2911yescharacteristic, complemented
343C2×#380C2×C2911yescharacteristic
344C2×#380C2×C2911yescharacteristic
345C2×C4×C22⋊C4C2×C2911yescharacteristic
346#1441C2×C2912yescomplemented
347#1441C2×C2912yescomplemented
348#1439C2×C2912yes—
349C4⋊#95C2×C2911yescharacteristic, complemented
350C22×C29—24no—
351C22×C29—24no—
352C22×C29—24no—
353C22×C29—42no—
354C22×C29—42no—
355C22×C29—42no—
356C22×C29—42no—
357C22×C29—42no—
358C22×C29—42no—
359C22×C29—42no—
360C22×C29—42no—
361C22×C29—42no—
362C22×C29—42no—
363C22×C29—42no—
364C22×C29—42no—
365C22×C29C2×#12111yescharacteristic
366C22×C29C2×#12111yescharacteristic
367C22×C29C2×#12111yescharacteristic
368C22×C29C2×#12111yescharacteristic
369C22×C29C2×C22⋊Q811yescharacteristic
370C22×C29C2×C22⋊Q811yescharacteristic
371C22×C29C2×C22⋊Q811yescharacteristic
372C22×C29C2×C22⋊Q811yescharacteristic
373C22×C29C2×#12611yescharacteristic
374C22×C29C2×C4⋊Q811yescharacteristic
375C22×C29#53211yescharacteristic
376C22×C29#53311yescharacteristic
377C22×C29#53311yescharacteristic
378C22×C29#53711yescharacteristic
379C22×C29#53711yescharacteristic
380C22×C29#54011yescharacteristic
381C22×C29#54111yescharacteristic
382C22×C29#54411yescharacteristic
383C22×C29#54411yescharacteristic
384C22×C29D4211yescharacteristic
385C22×C29D4211yescharacteristic
386C22×C29#54611yescharacteristic
387C22×C29#54711yescharacteristic
388C22×C29#54711yescharacteristic
389C22×C29#54711yescharacteristic
390C22×C29#54811yescharacteristic
391C22×C29D4×Q811yescharacteristic
392C22×C29D4×Q811yescharacteristic
393C22×C29#55011yescharacteristic
394C22×C29#55211yescharacteristic
395C22×C29#55311yescharacteristic
396C22×C29#55411yescharacteristic
397C22×C29#55411yescharacteristic
398C22×C29#55511yescharacteristic
399C22×C29#55611yescharacteristic
400C4×C29—24no—
401C4×C29—24no—
402C4×C29—42no—
403C4×C29—44no—
404C4×C29—42no—
405C4×C29—44no—
406C4×C29—42no—
407C4×C29—82no—
408C4×C29—82no—
409C4×C29#39618yescomplemented
410C24×C4C22×C2911yescharacteristic
411C22×C4⋊C4C22×C2912yes—
412C22×C4⋊C4C22×C2911yescharacteristic
413C22×C4⋊C4C22×C2911yescharacteristic
414C22×C4⋊C4C22×C2912yes—
415C22×C4⋊C4C22×C2912yes—
416C22×C4⋊C4C22×C2912yes—
417C22×C4⋊C4C22×C2911yescharacteristic
418C22×C4⋊C4C22×C2911yescharacteristic
419C22×C22⋊C4C22×C2912yes—
420C22×C22⋊C4C22×C2912yes—
421C22×C22⋊C4C22×C2911yescharacteristic
422C22×C22⋊C4C22×C2911yescharacteristic
423C22×C42C22×C2911yescharacteristic
424C22×C42C22×C2911yescharacteristic
425#396—28no—
426#389—24no—
427#389—24no—
428#384—24no—
429#380—24no—
430#380—24no—
431C4×C22⋊C4—24no—
432C2×#95C22×C2912yes—
433C2×#95C22×C2912yes—
434C2×#95C22×C2912yes—
435C2×#95C22×C2911yescharacteristic
436C2×#95C22×C2911yescharacteristic
437C2×#95C22×C2912yes—
438C2×#95C22×C2912yes—
439C2×#95C22×C2912yes—
440C2×C29—44no—
441C2×C29C2×#39611yescharacteristic
442C2×C29#241611yescharacteristic
443C2×C29#241711yescharacteristic
444C2×C29#242811yescharacteristic
445C2×C29#242911yescharacteristic
446C2×C29#243911yescharacteristic
447C2×C29#244011yescharacteristic
448C2×C29#244011yescharacteristic
449C2×C29#244111yescharacteristic
450C2×C29#249611yescharacteristic
451C2×C29#249711yescharacteristic
452C2×C29#253711yescharacteristic
453C2×C29#253811yescharacteristic
454C2×C29#262911yescharacteristic
455C2×C29#285711yescharacteristic
456C25C23×C2911yescharacteristic
457C23×C4—22no—
458C23×C4—22no—
459C23×C4—22no—
460C23×C4—22no—
461C23×C4—22no—
462C23×C4—22no—
463C23×C4Q8×C2914yes—
464C23×C4C23×C2912yes—
465C23×C4C23×C2912yes—
466C23×C4C23×C2912yes—
467C23×C4C23×C2912yes—
468C23×C4C23×C2911yescharacteristic
469C23×C4C23×C2911yescharacteristic
470C23×C4C23×C2911yescharacteristic
471C23×C4C23×C2911yescharacteristic
472C23×C4C23×C2911yescharacteristic
473C23×C4C23×C2911yescharacteristic
474C2×C4⋊C4—22no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—24no—
481C2×C4⋊C4—24no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—24no—
484C2×C4⋊C4—24no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—24no—
487C2×C4⋊C4—24no—
488C2×C4⋊C4—24no—
489C2×C4⋊C4—24no—
490C2×C4⋊C4—24no—
491C2×C4⋊C4—22no—
492C2×C4⋊C4—22no—
493C2×C4⋊C4—42no—
494C2×C4⋊C4—42no—
495C2×C4⋊C4—42no—
496C2×C4⋊C4D4×C2914yes—
497C2×C4⋊C4D4×C2914yes—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—42no—
507C2×C22⋊C4—42no—
508C2×C22⋊C4D4×C2914yes—
509C2×C22⋊C4Q8×C2914yes—
510C2×C42—22no—
511C2×C42—22no—
512C2×C42—22no—
513C2×C42—22no—
514C2×C42—22no—
515C2×C42D4×C2914yes—
516#95—22no—
517#95—22no—
518#95—24no—
519#95—24no—
520#95—24no—
521#95—24no—
522#95—24no—
523#95—42no—
524C29#1513111yescharacteristic, direct product factor, Sylow
525C24—21no—
526C24—21no—
527C24—21no—
528C24—21no—
529C24—21no—
530C24—21no—
531C24—21no—
532C24—21no—
533C24—21no—
534C24—21no—
535C24—21no—
536C24—21no—
537C24C2×D4×C2912yes—
538C24C2×Q8×C2912yes—
539C24C2×Q8×C2912yes—
540C24C24×C2911yescharacteristic
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—28no—
580C22×C4—28no—
581C22×C4—28no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4—44no—
600C22×C4C2×D4×C2914yes—
601C22×C4C2×D4×C2912yes—
602C22×C4C2×D4×C2914yes—
603C22×C4C2×D4×C2912yes—
604C22×C4C2×D4×C2912yes—
605C22×C4C2×D4×C2912yes—
606C22×C4C2×D4×C2912yes—
607C22×C4C2×D4×C2912yes—
608C22×C4C2×D4×C2912yes—
609C22×C4C2×Q8×C2912yes—
610C22×C4C2×Q8×C2912yes—
611C22×C4C2×Q8×C2912yes—
612C22×C4C2×Q8×C2912yes—
613C22×C4#41×C2912yes—
614C22×C4#41×C2912yes—
615C22×C4#41×C2912yes—
616C22×C4#41×C2912yes—
617C22×C4#41×C2912yes—
618C4⋊C4—28no—
619C4⋊C4—28no—
620C4⋊C4—48no—
621C4⋊C4—48no—
622C4⋊C4—48no—
623C4⋊C4—48no—
624C4⋊C4—44no—
625C4⋊C4—44no—
626C22⋊C4—28no—
627C22⋊C4—28no—
628C22⋊C4—48no—
629C22⋊C4—48no—
630C42—28no—
631C42—44no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23C29×C4⋊Q814yes—
667C23C22×D4×C2911yescharacteristic
668C23C22×D4×C2911yescharacteristic
669C23C22×D4×C2911yescharacteristic
670C23C22×D4×C2911yescharacteristic
671C23C22×Q8×C2911yescharacteristic
672C23C22×Q8×C2911yescharacteristic
673C23C2×#41×C2911yescharacteristic
674C23C2×#41×C2911yescharacteristic
675C23C2×#41×C2911yescharacteristic
676C23C2×#41×C2911yescharacteristic
677C23C2×#41×C2911yescharacteristic
678C23C29×H(5,𝔽2)11yescharacteristic
679C23C29×H(5,𝔽2)11yescharacteristic
680C23C29×2−1+411yescharacteristic
681C23C29×2−1+411yescharacteristic
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—42no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—41no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—42no—
728C2×C4—41no—
729C2×C4—416no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4C29×#12114yes—
745C2×C4C29×#12114yes—
746C2×C4C29×#12114yes—
747C2×C4C29×#12114yes—
748C2×C4C29×C22⋊Q814yes—
749C2×C4C29×C22⋊Q814yes—
750C2×C4C29×C22⋊Q814yes—
751C2×C4C29×C22⋊Q814yes—
752C2×C4C29×#12614yes—
753C22—24no—
754C22—24no—
755C22—24no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22C2×C29×#12111yescharacteristic
769C22C2×C29×#12111yescharacteristic
770C22C2×C29×#12111yescharacteristic
771C22C2×C29×#12111yescharacteristic
772C22C2×C29×C22⋊Q811yescharacteristic
773C22C2×C29×C22⋊Q811yescharacteristic
774C22C2×C29×C22⋊Q811yescharacteristic
775C22C2×C29×C22⋊Q811yescharacteristic
776C22C2×C29×#12611yescharacteristic
777C22C2×C29×C4⋊Q811yescharacteristic
778C22C29×#53211yescharacteristic
779C22C29×#53311yescharacteristic
780C22C29×#53311yescharacteristic
781C22C29×#53711yescharacteristic
782C22C29×#53711yescharacteristic
783C22C29×#54011yescharacteristic
784C22C29×#54111yescharacteristic
785C22C29×#54411yescharacteristic
786C22C29×#54411yescharacteristic
787C22D42×C2911yescharacteristic
788C22D42×C2911yescharacteristic
789C22C29×#54611yescharacteristic
790C22C29×#54711yescharacteristic
791C22C29×#54711yescharacteristic
792C22C29×#54711yescharacteristic
793C22C29×#54811yescharacteristic
794C22D4×Q8×C2911yescharacteristic
795C22D4×Q8×C2911yescharacteristic
796C22C29×#55011yescharacteristic
797C22C29×#55211yescharacteristic
798C22C29×#55311yescharacteristic
799C22C29×#55411yescharacteristic
800C22C29×#55411yescharacteristic
801C22C29×#55511yescharacteristic
802C22C29×#55611yescharacteristic
803C4—24no—
804C4—24no—
805C4—44no—
806C4—42no—
807C4—44no—
808C4—42no—
809C4—42no—
810C4—82no—
811C4—82no—
812C4C29×#39618yescomplemented
813C2—44no—
814C2C2×C29×#39611yescharacteristic
815C2C29×#241611yescharacteristic
816C2C29×#241711yescharacteristic
817C2C29×#242811yescharacteristic
818C2C29×#242911yescharacteristic
819C2C29×#243911yescharacteristic
820C2C29×#244011yescharacteristic
821C2C29×#244011yescharacteristic
822C2C29×#244111yescharacteristic
823C2C29×#249611yescharacteristic
824C2C29×#249711yescharacteristic
825C2C29×#253711yescharacteristic
826C2C29×#253811yescharacteristic
827C2C29×#262911yescharacteristic
828C2C29×#285711yescharacteristic
subgroupG/H
center, socleC24×C29C24
commutator, Frattini, cosocleC24C24×C29
prime radicalC25×C29C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C29×#389C2semidirect
3. C2×C29×#389C2semidirect
4. C2×C29×#384C2semidirect
8. C29×#1441C2semidirect
9. C29×#1441C2semidirect
11. C29×C4⋊#95C2semidirect
217. #15131C29direct (N × H)
340. C2×#389C2×C29semidirect
341. C2×#389C2×C29semidirect
342. C2×#384C2×C29semidirect
346. #1441C2×C29semidirect
347. #1441C2×C29semidirect
349. C4⋊#95C2×C29semidirect
409. C4×C29#396semidirect
524. C29#15131direct (N × H)
812. C4C29×#396semidirect

Maximal subgroups

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

subgroupindex
C2×C29×#3962
C2×C29×#3892
C2×C29×#3842
C2×C29×#3802
C2×C4×C22⋊C4×C292
C29×#14412
C29×#14392
C29×C4⋊#952
#1513129