Finite Group Databasebeta

← C29×#16294 #20311194

Subgroups — C29×#16294 #20311194

Order 7424.

1746 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#394C211yesmaximal, characteristic
2C2×C29×#394C211yesmaximal, characteristic
3C2×C29×#393C211yesmaximal, characteristic, complemented
4C2×C29×#393C211yesmaximal, characteristic, complemented
5C2×C29×#391C211yesmaximal, characteristic, complemented
6C2×C29×#388C211yesmaximal, characteristic, complemented
7C29×#1444C211yesmaximal, characteristic, complemented
8C29×#1443C211yesmaximal, characteristic, complemented
9C29×#1441C211yesmaximal, characteristic, complemented
10C29×#1440C211yesmaximal, characteristic, complemented
11C29×#1439C211yesmaximal, characteristic, complemented
12C29×#1439C211yesmaximal, characteristic, complemented
13C29×#1439C211yesmaximal, characteristic, complemented
14C29×#1438C211yesmaximal, characteristic
15C29×#1437C211yesmaximal, characteristic, complemented
16C23×Q8×C29C2211yescharacteristic
17C23×D4×C29C2211yescharacteristic
18C22×C4⋊C4×C29C2211yescharacteristic
19C22×C4⋊C4×C29C2211yescharacteristic
20C22×C4⋊C4×C29C2211yescharacteristic
21C22×C4⋊C4×C29C2211yescharacteristic
22C22×C22⋊C4×C29C2211yescharacteristic
23C22×C22⋊C4×C29C2211yescharacteristic
24C22×C22⋊C4×C29C2211yescharacteristic
25C22×C22⋊C4×C29C2211yescharacteristic
26C22×C22⋊C4×C29C2211yescharacteristic
27C22×C22⋊C4×C29C2211yescharacteristic
28C22×C22⋊C4×C29C2211yescharacteristic
29C22×C22⋊C4×C29C2211yescharacteristic
30C22×C22⋊C4×C29C2211yescharacteristic
31C22×C22⋊C4×C29C2211yescharacteristic
32C22×C22⋊C4×C29C2211yescharacteristic
33C22×C22⋊C4×C29C2211yescharacteristic
34C22×C42×C29C2211yescharacteristic
35C29×#394—24no—
36C29×#394—24no—
37C29×#393—24no—
38C29×#393—24no—
39C29×#391—24no—
40C29×#388—24no—
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
56C2×C29×#95C2211yescharacteristic
57C25×C29C2311yescharacteristic
58C25×C29C2311yescharacteristic
59C22×Q8×C29—22no—
60C22×Q8×C29—22no—
61C22×Q8×C29—22no—
62C22×Q8×C29—22no—
63C22×Q8×C29—22no—
64C22×Q8×C29—41no—
65C22×Q8×C29—41no—
66C22×D4×C29—22no—
67C22×D4×C29—22no—
68C22×D4×C29—22no—
69C22×D4×C29—41no—
70C22×D4×C29—41no—
71C22×D4×C29—41no—
72C22×D4×C29—41no—
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
85C23×C4×C29C2311yescharacteristic
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—41no—
92C2×C4⋊C4×C29—41no—
93C2×C4⋊C4×C29—41no—
94C2×C4⋊C4×C29—41no—
95C2×C4⋊C4×C29—41no—
96C2×C4⋊C4×C29—41no—
97C2×C4⋊C4×C29—41no—
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—22no—
105C2×C22⋊C4×C29—22no—
106C2×C22⋊C4×C29—22no—
107C2×C22⋊C4×C29—22no—
108C2×C22⋊C4×C29—22no—
109C2×C22⋊C4×C29—22no—
110C2×C22⋊C4×C29—22no—
111C2×C22⋊C4×C29—22no—
112C2×C22⋊C4×C29—22no—
113C2×C22⋊C4×C29—22no—
114C2×C22⋊C4×C29—22no—
115C2×C22⋊C4×C29—22no—
116C2×C22⋊C4×C29—22no—
117C2×C22⋊C4×C29—22no—
118C2×C22⋊C4×C29—22no—
119C2×C22⋊C4×C29—22no—
120C2×C22⋊C4×C29—22no—
121C2×C22⋊C4×C29—41no—
122C2×C22⋊C4×C29—41no—
123C2×C22⋊C4×C29—41no—
124C2×C22⋊C4×C29—41no—
125C2×C22⋊C4×C29—41no—
126C2×C22⋊C4×C29—41no—
127C2×C22⋊C4×C29—41no—
128C2×C22⋊C4×C29—41no—
129C2×C22⋊C4×C29—41no—
130C2×C22⋊C4×C29—41no—
131C2×C22⋊C4×C29—41no—
132C2×C22⋊C4×C29—41no—
133C2×C22⋊C4×C29D414yes—
134C2×C42×C29—22no—
135C2×C42×C29—22no—
136C2×C42×C29—41no—
137C29×#95—22no—
138C29×#95—22no—
139C29×#95—22no—
140C29×#95—22no—
141C29×#95—22no—
142C29×#95—22no—
143C29×#95—22no—
144C29×#95—22no—
145C29×#95—22no—
146C29×#95—22no—
147C29×#95—41no—
148C29×#95—41no—
149C29×#95—41no—
150C29×#95—41no—
151C29×#95D414yes—
152C29×#95D414yescomplemented
153C24×C29—21no—
154C24×C29—21no—
155C24×C29—21no—
156C24×C29—21no—
157C24×C29—21no—
158C24×C29—21no—
159C24×C29—21no—
160C24×C29—21no—
161C24×C29—21no—
162C24×C29—21no—
163C24×C29—21no—
164C24×C29—21no—
165C24×C29—21no—
166C24×C29—21no—
167C24×C29—21no—
168C24×C29—21no—
169C24×C29—21no—
170C24×C29—21no—
171C24×C29—21no—
172C24×C29—21no—
173C24×C29—21no—
174C24×C29—21no—
175C24×C29—21no—
176C24×C29—21no—
177C24×C29—21no—
178C24×C29—21no—
179C24×C29—21no—
180C24×C29—21no—
181C24×C29C2×D412yes—
182C24×C29#4112yes—
183C24×C29C2411yescharacteristic
184C2×Q8×C29—28no—
185C2×Q8×C29—44no—
186C2×Q8×C29—44no—
187C2×Q8×C29—44no—
188C2×Q8×C29—44no—
189C2×Q8×C29—44no—
190C2×Q8×C29—44no—
191C2×D4×C29—44no—
192C2×D4×C29—44no—
193C2×D4×C29—44no—
194C2×D4×C29—44no—
195C2×D4×C29—44no—
196C2×D4×C29—44no—
197C2×D4×C29—44no—
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—21no—
247C22×C4×C29—21no—
248C22×C4×C29—21no—
249C22×C4×C29—21no—
250C22×C4×C29—21no—
251C22×C4×C29—21no—
252C22×C4×C29—21no—
253C22×C4×C29—21no—
254C22×C4×C29—21no—
255C22×C4×C29—21no—
256C22×C4×C29—21no—
257C22×C4×C29—21no—
258C22×C4×C29—21no—
259C22×C4×C29—21no—
260C22×C4×C29—21no—
261C22×C4×C29—21no—
262C22×C4×C29—21no—
263C22×C4×C29—21no—
264C22×C4×C29—21no—
265C22×C4×C29—21no—
266C22×C4×C29—21no—
267C22×C4×C29—21no—
268C22×C4×C29—21no—
269C22×C4×C29—21no—
270C22×C4×C29—21no—
271C22×C4×C29—21no—
272C22×C4×C29—21no—
273C22×C4×C29—21no—
274C22×C4×C29—21no—
275C22×C4×C29—21no—
276C22×C4×C29—21no—
277C22×C4×C29—21no—
278C22×C4×C29C2×D412yes—
279C22×C4×C29C2×D412yes—
280C22×C4×C29C2×D412yes—
281C22×C4×C29C2×D412yes—
282C22×C4×C29C2×D412yes—
283C22×C4×C29C2×D412yes—
284C22×C4×C29C2×D412yes—
285C22×C4×C29C2×D412yes—
286C22×C4×C29#4112yes—
287C22×C4×C29#4112yes—
288C22×C4×C29#4112yes—
289C4⋊C4×C29—44no—
290C4⋊C4×C29—44no—
291C4⋊C4×C29—44no—
292C4⋊C4×C29—44no—
293C22⋊C4×C29—28no—
294C22⋊C4×C29—44no—
295C22⋊C4×C29—44no—
296C22⋊C4×C29—44no—
297C22⋊C4×C29—44no—
298C22⋊C4×C29—44no—
299C22⋊C4×C29—44no—
300C22⋊C4×C29—44no—
301C22⋊C4×C29—44no—
302C22⋊C4×C29—44no—
303C22⋊C4×C29—44no—
304C22⋊C4×C29—44no—
305C42×C29—44no—
306#16294C2911yesmaximal, characteristic, direct product factor, Sylow
307C23×C29—22no—
308C23×C29—22no—
309C23×C29—22no—
310C23×C29—22no—
311C23×C29—22no—
312C23×C29—22no—
313C23×C29—22no—
314C23×C29—22no—
315C23×C29—22no—
316C23×C29—22no—
317C23×C29—22no—
318C23×C29—22no—
319C23×C29—22no—
320C23×C29—22no—
321C23×C29—41no—
322C23×C29—41no—
323C23×C29—41no—
324C23×C29—41no—
325C23×C29—41no—
326C23×C29—41no—
327C23×C29—41no—
328C23×C29—41no—
329C23×C29—41no—
330C23×C29—41no—
331C23×C29—41no—
332C23×C29—41no—
333C23×C29—41no—
334C23×C29—41no—
335C23×C29—41no—
336C23×C29—41no—
337C23×C29—41no—
338C23×C29—41no—
339C23×C29—41no—
340C23×C29—41no—
341C23×C29—41no—
342C23×C29—41no—
343C23×C29—41no—
344C23×C29—41no—
345C23×C29—41no—
346C23×C29—41no—
347C23×C29—41no—
348C23×C29—41no—
349C23×C29—41no—
350C23×C29—41no—
351C23×C29—41no—
352C23×C29—41no—
353C23×C29—41no—
354C23×C29—41no—
355C23×C29—41no—
356C23×C29—41no—
357C23×C29—41no—
358C23×C29—41no—
359C23×C29—41no—
360C23×C29—41no—
361C23×C29—41no—
362C23×C29—41no—
363C23×C29—41no—
364C23×C29—41no—
365C23×C29—41no—
366C23×C29—41no—
367C23×C29—41no—
368C23×C29—41no—
369C23×C29—41no—
370C23×C29—41no—
371C23×C29—41no—
372C23×C29—41no—
373C23×C29—41no—
374C23×C29—41no—
375C23×C29—41no—
376C23×C29—41no—
377C23×C29C22×D411yescharacteristic
378C23×C29C22×D411yescharacteristic
379C23×C29C22×D411yescharacteristic
380C23×C29C2×#4111yescharacteristic
381C23×C29C2×#4111yescharacteristic
382C23×C29C2×#4111yescharacteristic
383C23×C29C2×#4111yescharacteristic
384C23×C29H(5,𝔽2)11yescharacteristic
385C23×C29H(5,𝔽2)11yescharacteristic
386C23×C29H(5,𝔽2)11yescharacteristic
387C23×C29H(5,𝔽2)11yescharacteristic
388C23×C29H(5,𝔽2)11yescharacteristic
389C23×C292−1+411yescharacteristic
390C23×C292−1+411yescharacteristic
391C23×C292−1+411yescharacteristic
392Q8×C29—416no—
393D4×C29—416no—
394C2×C4×C29—22no—
395C2×C4×C29—22no—
396C2×C4×C29—22no—
397C2×C4×C29—22no—
398C2×C4×C29—22no—
399C2×C4×C29—22no—
400C2×C4×C29—22no—
401C2×C4×C29—22no—
402C2×C4×C29—22no—
403C2×C4×C29—22no—
404C2×C4×C29—22no—
405C2×C4×C29—22no—
406C2×C4×C29—22no—
407C2×C4×C29—22no—
408C2×C4×C29—22no—
409C2×C4×C29—22no—
410C2×C4×C29—22no—
411C2×C4×C29—22no—
412C2×C4×C29—22no—
413C2×C4×C29—22no—
414C2×C4×C29—22no—
415C2×C4×C29—22no—
416C2×C4×C29—22no—
417C2×C4×C29—22no—
418C2×C4×C29—22no—
419C2×C4×C29—22no—
420C2×C4×C29—22no—
421C2×C4×C29—22no—
422C2×C4×C29—22no—
423C2×C4×C29—22no—
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×C29—41no—
433C2×C4×C29—41no—
434C2×C4×C29—41no—
435C2×C4×C29—41no—
436C2×C4×C29—41no—
437C2×C4×C29—41no—
438C2×C4×C29—41no—
439C2×C4×C29—41no—
440C2×C4×C29—41no—
441C2×C4×C29—41no—
442C2×C4×C29—41no—
443C2×C4×C29—41no—
444C2×C4×C29—41no—
445C2×C4×C29—41no—
446C2×C4×C29—41no—
447C2×C4×C29—41no—
448C2×C4×C29—41no—
449C2×C4×C29—41no—
450C2×C4×C29—41no—
451C2×C4×C29—41no—
452C2×C4×C29—41no—
453C2×C4×C29—41no—
454C2×C4×C29—41no—
455C2×C4×C29—41no—
456C2×C4×C29—41no—
457C2×C4×C29—41no—
458C2×C4×C29—41no—
459C2×C4×C29—41no—
460C2×C4×C29—41no—
461C2×C4×C29—41no—
462C2×C4×C29—41no—
463C2×C4×C29—41no—
464C2×C4×C29—41no—
465C2×C4×C29—41no—
466C2×C4×C29—41no—
467C2×C4×C29—41no—
468C2×C4×C29—41no—
469C2×C4×C29—41no—
470C2×C4×C29—41no—
471C2×C4×C29—41no—
472C2×C4×C29—41no—
473C2×C4×C29—41no—
474C2×C4×C29—41no—
475C2×C4×C29—41no—
476C2×C4×C29—41no—
477C2×C4×C29—41no—
478C2×C4×C29—41no—
479C2×C4×C29—41no—
480C2×C4×C29—41no—
481C2×C4×C29—41no—
482C2×C4×C29—41no—
483C2×C4×C29—41no—
484C2×C4×C29#12114yes—
485C2×#394C2×C2911yescharacteristic
486C2×#394C2×C2911yescharacteristic
487C2×#393C2×C2911yescharacteristic, complemented
488C2×#393C2×C2911yescharacteristic, complemented
489C2×#391C2×C2911yescharacteristic, complemented
490C2×#388C2×C2911yescharacteristic, complemented
491#1444C2×C2911yescharacteristic, complemented
492#1443C2×C2911yescharacteristic, complemented
493#1441C2×C2911yescharacteristic, complemented
494#1440C2×C2911yescharacteristic, complemented
495#1439C2×C2911yescharacteristic, complemented
496#1439C2×C2911yescharacteristic, complemented
497#1439C2×C2911yescharacteristic, complemented
498#1438C2×C2911yescharacteristic
499#1437C2×C2911yescharacteristic, complemented
500C22×C29—42no—
501C22×C29—42no—
502C22×C29—42no—
503C22×C29—42no—
504C22×C29—42no—
505C22×C29—42no—
506C22×C29—42no—
507C22×C29—42no—
508C22×C29—42no—
509C22×C29—42no—
510C22×C29—42no—
511C22×C29—42no—
512C22×C29—42no—
513C22×C29—42no—
514C22×C29—81no—
515C22×C29—81no—
516C22×C29—81no—
517C22×C29—81no—
518C22×C29—81no—
519C22×C29—81no—
520C22×C29—81no—
521C22×C29—81no—
522C22×C29—81no—
523C22×C29—81no—
524C22×C29—81no—
525C22×C29—81no—
526C22×C29—81no—
527C22×C29—81no—
528C22×C29—81no—
529C22×C29—81no—
530C22×C29C2×#12111yescharacteristic
531C22×C29#52511yescharacteristic
532C22×C29#52911yescharacteristic
533C22×C29#53511yescharacteristic
534C22×C29#53511yescharacteristic
535C22×C29#53611yescharacteristic
536C22×C29#53611yescharacteristic
537C22×C29#53711yescharacteristic
538C22×C29#53711yescharacteristic
539C22×C29#53811yescharacteristic
540C22×C29#53811yescharacteristic
541C22×C29#53811yescharacteristic
542C22×C29#53911yescharacteristic
543C22×C29#54211yescharacteristic
544C22×C29#54211yescharacteristic
545C22×C29#54211yescharacteristic
546C22×C29#54211yescharacteristic
547C22×C29#54211yescharacteristic
548C22×C29#54211yescharacteristic
549C22×C29D4211yescharacteristic
550C22×C29D4211yescharacteristic
551C22×C29#54611yescharacteristic
552C22×C29#54611yescharacteristic
553C22×C29#54611yescharacteristic
554C22×C29#54611yescharacteristic
555C22×C29#54611yescharacteristic
556C22×C29#54711yescharacteristic
557C22×C29#54811yescharacteristic
558C22×C29#54811yescharacteristic
559C22×C29#55211yescharacteristic
560C22×C29#55911yescharacteristic
561C22×C29H(3,𝔽4)11yescharacteristic
562C22×C29#56211yescharacteristic
563C22×C29#56211yescharacteristic
564C22×C29#56311yescharacteristic
565C4×C29—24no—
566C4×C29—42no—
567C4×C29—42no—
568C4×C29—42no—
569C4×C29—42no—
570C4×C29—42no—
571C4×C29—42no—
572C4×C29—42no—
573C4×C29—42no—
574C4×C29—81no—
575C4×C29—81no—
576C4×C29—81no—
577C4×C29—81no—
578C23×Q8C22×C2911yescharacteristic
579C23×D4C22×C2911yescharacteristic
580C22×C4⋊C4C22×C2911yescharacteristic
581C22×C4⋊C4C22×C2911yescharacteristic
582C22×C4⋊C4C22×C2911yescharacteristic
583C22×C4⋊C4C22×C2911yescharacteristic
584C22×C22⋊C4C22×C2911yescharacteristic
585C22×C22⋊C4C22×C2911yescharacteristic
586C22×C22⋊C4C22×C2911yescharacteristic
587C22×C22⋊C4C22×C2911yescharacteristic
588C22×C22⋊C4C22×C2911yescharacteristic
589C22×C22⋊C4C22×C2911yescharacteristic
590C22×C22⋊C4C22×C2911yescharacteristic
591C22×C22⋊C4C22×C2911yescharacteristic
592C22×C22⋊C4C22×C2911yescharacteristic
593C22×C22⋊C4C22×C2911yescharacteristic
594C22×C22⋊C4C22×C2911yescharacteristic
595C22×C22⋊C4C22×C2911yescharacteristic
596C22×C42C22×C2911yescharacteristic
597#394—24no—
598#394—24no—
599#393—24no—
600#393—24no—
601#391—24no—
602#388—24no—
603C2×#95C22×C2911yescharacteristic
604C2×#95C22×C2911yescharacteristic
605C2×#95C22×C2911yescharacteristic
606C2×#95C22×C2911yescharacteristic
607C2×#95C22×C2911yescharacteristic
608C2×#95C22×C2911yescharacteristic
609C2×#95C22×C2911yescharacteristic
610C2×#95C22×C2911yescharacteristic
611C2×#95C22×C2911yescharacteristic
612C2×#95C22×C2911yescharacteristic
613C2×#95C22×C2911yescharacteristic
614C2×#95C22×C2911yescharacteristic
615C2×#95C22×C2911yescharacteristic
616C2×#95C22×C2911yescharacteristic
617C2×#95C22×C2911yescharacteristic
618C2×#95C22×C2911yescharacteristic
619C2×C29—82no—
620C2×C29—82no—
621C2×C29#242411yescharacteristic
622C2×C29#242711yescharacteristic
623C2×C29#245811yescharacteristic
624C2×C29#262011yescharacteristic
625C2×C29#263211yescharacteristic
626C2×C29#265311yescharacteristic
627C2×C29#267011yescharacteristic
628C2×C29#267411yescharacteristic
629C2×C29#267611yescharacteristic
630C2×C29#268111yescharacteristic
631C2×C29#268711yescharacteristic
632C2×C29#270211yescharacteristic
633C2×C29#271011yescharacteristic
634C2×C29#271211yescharacteristic
635C2×C29#283211yescharacteristic
636C25C23×C2911yescharacteristic
637C25C23×C2911yescharacteristic
638C22×Q8—22no—
639C22×Q8—22no—
640C22×Q8—22no—
641C22×Q8—22no—
642C22×Q8—22no—
643C22×Q8—41no—
644C22×Q8—41no—
645C22×D4—22no—
646C22×D4—22no—
647C22×D4—22no—
648C22×D4—41no—
649C22×D4—41no—
650C22×D4—41no—
651C22×D4—41no—
652C23×C4C23×C2911yescharacteristic
653C23×C4C23×C2911yescharacteristic
654C23×C4C23×C2911yescharacteristic
655C23×C4C23×C2911yescharacteristic
656C23×C4C23×C2911yescharacteristic
657C23×C4C23×C2911yescharacteristic
658C23×C4C23×C2911yescharacteristic
659C23×C4C23×C2911yescharacteristic
660C23×C4C23×C2911yescharacteristic
661C23×C4C23×C2911yescharacteristic
662C23×C4C23×C2911yescharacteristic
663C23×C4C23×C2911yescharacteristic
664C23×C4C23×C2911yescharacteristic
665C2×C4⋊C4—22no—
666C2×C4⋊C4—22no—
667C2×C4⋊C4—22no—
668C2×C4⋊C4—22no—
669C2×C4⋊C4—22no—
670C2×C4⋊C4—41no—
671C2×C4⋊C4—41no—
672C2×C4⋊C4—41no—
673C2×C4⋊C4—41no—
674C2×C4⋊C4—41no—
675C2×C4⋊C4—41no—
676C2×C4⋊C4—41no—
677C2×C22⋊C4—22no—
678C2×C22⋊C4—22no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—22no—
681C2×C22⋊C4—22no—
682C2×C22⋊C4—22no—
683C2×C22⋊C4—22no—
684C2×C22⋊C4—22no—
685C2×C22⋊C4—22no—
686C2×C22⋊C4—22no—
687C2×C22⋊C4—22no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—41no—
701C2×C22⋊C4—41no—
702C2×C22⋊C4—41no—
703C2×C22⋊C4—41no—
704C2×C22⋊C4—41no—
705C2×C22⋊C4—41no—
706C2×C22⋊C4—41no—
707C2×C22⋊C4—41no—
708C2×C22⋊C4—41no—
709C2×C22⋊C4—41no—
710C2×C22⋊C4—41no—
711C2×C22⋊C4—41no—
712C2×C22⋊C4D4×C2914yes—
713C2×C42—22no—
714C2×C42—22no—
715C2×C42—41no—
716#95—22no—
717#95—22no—
718#95—22no—
719#95—22no—
720#95—22no—
721#95—22no—
722#95—22no—
723#95—22no—
724#95—22no—
725#95—22no—
726#95—41no—
727#95—41no—
728#95—41no—
729#95—41no—
730#95D4×C2914yes—
731#95D4×C2914yescomplemented
732C29#1629411yescharacteristic, direct product factor, Sylow
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24C2×D4×C2912yes—
762C24#41×C2912yes—
763C24C24×C2911yescharacteristic
764C2×Q8—28no—
765C2×Q8—44no—
766C2×Q8—44no—
767C2×Q8—44no—
768C2×Q8—44no—
769C2×Q8—44no—
770C2×Q8—44no—
771C2×D4—44no—
772C2×D4—44no—
773C2×D4—44no—
774C2×D4—44no—
775C2×D4—44no—
776C2×D4—44no—
777C2×D4—44no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4C2×D4×C2912yes—
859C22×C4C2×D4×C2912yes—
860C22×C4C2×D4×C2912yes—
861C22×C4C2×D4×C2912yes—
862C22×C4C2×D4×C2912yes—
863C22×C4C2×D4×C2912yes—
864C22×C4C2×D4×C2912yes—
865C22×C4C2×D4×C2912yes—
866C22×C4#41×C2912yes—
867C22×C4#41×C2912yes—
868C22×C4#41×C2912yes—
869C4⋊C4—44no—
870C4⋊C4—44no—
871C4⋊C4—44no—
872C4⋊C4—44no—
873C22⋊C4—28no—
874C22⋊C4—44no—
875C22⋊C4—44no—
876C22⋊C4—44no—
877C22⋊C4—44no—
878C22⋊C4—44no—
879C22⋊C4—44no—
880C22⋊C4—44no—
881C22⋊C4—44no—
882C22⋊C4—44no—
883C22⋊C4—44no—
884C22⋊C4—44no—
885C42—44no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23C22×D4×C2911yescharacteristic
957C23C22×D4×C2911yescharacteristic
958C23C22×D4×C2911yescharacteristic
959C23C2×#41×C2911yescharacteristic
960C23C2×#41×C2911yescharacteristic
961C23C2×#41×C2911yescharacteristic
962C23C2×#41×C2911yescharacteristic
963C23C29×H(5,𝔽2)11yescharacteristic
964C23C29×H(5,𝔽2)11yescharacteristic
965C23C29×H(5,𝔽2)11yescharacteristic
966C23C29×H(5,𝔽2)11yescharacteristic
967C23C29×H(5,𝔽2)11yescharacteristic
968C23C29×2−1+411yescharacteristic
969C23C29×2−1+411yescharacteristic
970C23C29×2−1+411yescharacteristic
971Q8—416no—
972D4—416no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4C29×#12114yes—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—42no—
1077C22—42no—
1078C22—81no—
1079C22—81no—
1080C22—81no—
1081C22—81no—
1082C22—81no—
1083C22—81no—
1084C22—81no—
1085C22—81no—
1086C22—81no—
1087C22—81no—
1088C22—81no—
1089C22—81no—
1090C22—81no—
1091C22—81no—
1092C22—81no—
1093C22—81no—
1094C22C2×C29×#12111yescharacteristic
1095C22C29×#52511yescharacteristic
1096C22C29×#52911yescharacteristic
1097C22C29×#53511yescharacteristic
1098C22C29×#53511yescharacteristic
1099C22C29×#53611yescharacteristic
1100C22C29×#53611yescharacteristic
1101C22C29×#53711yescharacteristic
1102C22C29×#53711yescharacteristic
1103C22C29×#53811yescharacteristic
1104C22C29×#53811yescharacteristic
1105C22C29×#53811yescharacteristic
1106C22C29×#53911yescharacteristic
1107C22C29×#54211yescharacteristic
1108C22C29×#54211yescharacteristic
1109C22C29×#54211yescharacteristic
1110C22C29×#54211yescharacteristic
1111C22C29×#54211yescharacteristic
1112C22C29×#54211yescharacteristic
1113C22D42×C2911yescharacteristic
1114C22D42×C2911yescharacteristic
1115C22C29×#54611yescharacteristic
1116C22C29×#54611yescharacteristic
1117C22C29×#54611yescharacteristic
1118C22C29×#54611yescharacteristic
1119C22C29×#54611yescharacteristic
1120C22C29×#54711yescharacteristic
1121C22C29×#54811yescharacteristic
1122C22C29×#54811yescharacteristic
1123C22C29×#55211yescharacteristic
1124C22C29×#55911yescharacteristic
1125C22C29×H(3,𝔽4)11yescharacteristic
1126C22C29×#56211yescharacteristic
1127C22C29×#56211yescharacteristic
1128C22C29×#56311yescharacteristic
1129C4—24no—
1130C4—42no—
1131C4—42no—
1132C4—42no—
1133C4—42no—
1134C4—42no—
1135C4—42no—
1136C4—42no—
1137C4—42no—
1138C4—81no—
1139C4—81no—
1140C4—81no—
1141C4—81no—
1142C2—82no—
1143C2—82no—
1144C2C29×#242411yescharacteristic
1145C2C29×#242711yescharacteristic
1146C2C29×#245811yescharacteristic
1147C2C29×#262011yescharacteristic
1148C2C29×#263211yescharacteristic
1149C2C29×#265311yescharacteristic
1150C2C29×#267011yescharacteristic
1151C2C29×#267411yescharacteristic
1152C2C29×#267611yescharacteristic
1153C2C29×#268111yescharacteristic
1154C2C29×#268711yescharacteristic
1155C2C29×#270211yescharacteristic
1156C2C29×#271011yescharacteristic
1157C2C29×#271211yescharacteristic
1158C2C29×#283211yescharacteristic
subgroupG/H
center, socleC24×C29C24
commutator, Frattini, cosocleC24C24×C29
prime radicalC23×D4×C29C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C29 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C29×#393C2semidirect
4. C2×C29×#393C2semidirect
5. C2×C29×#391C2semidirect
6. C2×C29×#388C2semidirect
7. C29×#1444C2semidirect
8. C29×#1443C2semidirect
9. C29×#1441C2semidirect
10. C29×#1440C2semidirect
11. C29×#1439C2semidirect
12. C29×#1439C2semidirect
13. C29×#1439C2semidirect
15. C29×#1437C2semidirect
152. C29×#95D4semidirect
306. #16294C29direct (N × H)
487. C2×#393C2×C29semidirect
488. C2×#393C2×C29semidirect
489. C2×#391C2×C29semidirect
490. C2×#388C2×C29semidirect
491. #1444C2×C29semidirect
492. #1443C2×C29semidirect
493. #1441C2×C29semidirect
494. #1440C2×C29semidirect
495. #1439C2×C29semidirect
496. #1439C2×C29semidirect
497. #1439C2×C29semidirect
499. #1437C2×C29semidirect
731. #95D4×C29semidirect
732. C29#16294direct (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×#3932
C2×C29×#3912
C2×C29×#3882
C29×#14442
C29×#14432
C29×#14412
C29×#14402
C29×#14392
C29×#14382
C29×#14372
#1629429