Finite Group Databasebeta

← C29×#17597 #20312497

Subgroups — C29×#17597 #20312497

Order 7424.

1060 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3519C211yesmaximal, characteristic
2C29×#2974C211yesmaximal, characteristic, complemented
3C29×#2318C211yesmaximal, characteristic, complemented
4C29×#1521C211yesmaximal, characteristic, complemented
5C29×#1519C211yesmaximal, characteristic, complemented
6C29×#1517C211yesmaximal, characteristic, complemented
7C29×#1516C211yesmaximal, characteristic, complemented
8C29×#1514C211yesmaximal, characteristic, complemented
9C29×#1513C211yesmaximal, characteristic, complemented
10C29×#1512C211yesmaximal, characteristic, complemented
11C29×#1510C211yesmaximal, characteristic, complemented
12C29×#1507C211yesmaximal, characteristic, complemented
13C29×#1504C211yesmaximal, characteristic, complemented
14C29×#1501C211yesmaximal, characteristic, complemented
15C2×C29×#327C211yesmaximal, characteristic, complemented
16C29×#555C411yescharacteristic, complemented
17C29×#554C411yescharacteristic, complemented
18C29×#553—21no—
19C29×#553C411yescharacteristic, complemented
20C29×#553C411yescharacteristic, complemented
21C29×#550C411yescharacteristic, complemented
22C29×#546—21no—
23C29×#546—21no—
24C29×#546C411yescharacteristic, complemented
25C29×#546C411yescharacteristic, complemented
26D42×C29—21no—
27D42×C29C411yescharacteristic, complemented
28C29×#540—21no—
29C29×#538—21no—
30C29×#538—21no—
31C29×#532C2211yescharacteristic
32C29×#529C2211yescharacteristic
33C29×#525C2211yescharacteristic
34C29×#525C2211yescharacteristic
35C2×C29×#121C2211yescharacteristic
36C2×C29×#121C2211yescharacteristic
37C29×#518—21no—
38C2×C4×D4×C29C2211yescharacteristic
39C29×#436—21no—
40C29×#435—21no—
41C29×#435—21no—
42C8×D4×C29—21no—
43C29×#432C2211yescharacteristic, complemented
44C29×#431C2211yescharacteristic, complemented
45C29×#407C2211yescharacteristic, complemented
46C29×#407C2211yescharacteristic, complemented
47C2×C29×C22⋊C8C2211yescharacteristic, complemented
48C2×C29×C22⋊C8C2211yescharacteristic, complemented
49C29×#388—21no—
50C29×#387—21no—
51C29×#386—21no—
52C29×#385—21no—
53C29×#383C2211yescharacteristic, complemented
54C29×#382C2211yescharacteristic, complemented
55C29×#381C2211yescharacteristic, complemented
56C29×#380C2211yescharacteristic, complemented
57C4×C22⋊C4×C29C2211yescharacteristic, complemented
58C2×C29×#95C2211yescharacteristic, complemented
59C29×#328C2211yescharacteristic, complemented
60C29×#328C2211yescharacteristic, complemented
61C29×#328C2211yescharacteristic, complemented
62C29×#328C2211yescharacteristic, complemented
63C29×#327C2211yescharacteristic
64C29×#327C2211yescharacteristic
65C29×#327C2211yescharacteristic
66C29×#327C2211yescharacteristic
67C29×#327C2211yescharacteristic, complemented
68C29×#327C2211yescharacteristic, complemented
69C29×#327C2211yescharacteristic, complemented
70C29×#327C2211yescharacteristic, complemented
71C29×#327C2211yescharacteristic, complemented
72C29×#327C2211yescharacteristic, complemented
73C29×#327C2211yescharacteristic, complemented
74C29×#327C2211yescharacteristic, complemented
75C2×#41×C29—21no—
76C2×#41×C29C2×C411yescharacteristic
77C2×#41×C29C2×C411yescharacteristic, complemented
78C22×D4×C29—21no—
79C22×D4×C29—21no—
80C22×D4×C29—21no—
81C22×D4×C29C2×C411yescharacteristic
82C22×D4×C29C2×C411yescharacteristic, complemented
83C22×D4×C29D411yescharacteristic
84C23×C4×C29—21no—
85C23×C4×C29C2311yescharacteristic
86C23×C4×C29C2311yescharacteristic
87C2×M16×C29—21no—
88C2×M16×C29—21no—
89C22×C8×C29—21no—
90C22×C8×C29—21no—
91C29×C4⋊Q8C2×C411yescharacteristic, complemented
92C29×#127—21no—
93C29×#127C2×C411yescharacteristic, complemented
94C29×#126—21no—
95C29×#126—21no—
96C29×#126—21no—
97C29×#125—21no—
98C29×#125C2×C411yescharacteristic, complemented
99C29×#124—21no—
100C29×#124—21no—
101C29×#124—21no—
102C29×#124C2×C411yescharacteristic, complemented
103C29×#123—21no—
104C29×#123—21no—
105C29×#123—21no—
106C29×#123—21no—
107C29×#123—21no—
108C29×#123—21no—
109C29×#123—21no—
110C29×C22⋊Q8—21no—
111C29×C22⋊Q8—21no—
112C29×C22⋊Q8C2×C411yescharacteristic
113C29×C22⋊Q8C2×C411yescharacteristic, complemented
114C29×C22⋊Q8C2311yescharacteristic
115C29×#121—21no—
116C29×#121—21no—
117C29×#121—21no—
118C29×#121—21no—
119C29×#121—21no—
120C29×#121—21no—
121C29×#121—21no—
122C29×#121—21no—
123C29×#121—21no—
124C29×#121—21no—
125C29×#121—21no—
126C29×#121—21no—
127C29×#121—21no—
128C29×#121C2×C411yescharacteristic
129C29×#121C2×C411yescharacteristic
130C29×#121C2×C411yescharacteristic
131C29×#121C2×C411yescharacteristic, complemented
132C29×#121C2×C411yescharacteristic, complemented
133C29×#121C2×C411yescharacteristic, complemented
134C29×#121C2311yescharacteristic
135C29×#121C2311yescharacteristic
136C29×#121C2311yescharacteristic
137C29×#120—21no—
138C29×#120—21no—
139C29×#120—21no—
140C29×#120—21no—
141C29×#120—21no—
142C29×#120—21no—
143C4×Q8×C29C2×C411yescharacteristic, complemented
144C4×D4×C29—21no—
145C4×D4×C29—21no—
146C4×D4×C29—21no—
147C4×D4×C29—21no—
148C4×D4×C29—21no—
149C4×D4×C29—21no—
150C4×D4×C29—21no—
151C4×D4×C29—21no—
152C4×D4×C29—21no—
153C4×D4×C29—21no—
154C4×D4×C29C2×C411yescharacteristic
155C4×D4×C29C2×C411yescharacteristic
156C4×D4×C29C2×C411yescharacteristic
157C4×D4×C29C2×C411yescharacteristic
158C4×D4×C29C2×C411yescharacteristic, complemented
159C4×D4×C29C2×C411yescharacteristic, complemented
160C4×D4×C29C2×C411yescharacteristic, complemented
161C4×D4×C29D411yescharacteristic
162C4×D4×C29D411yescharacteristic
163C4×D4×C29D411yescharacteristic
164C4×D4×C29D411yescharacteristic
165C29×#117—21no—
166C29×#117—21no—
167C29×#117C2×C411yescharacteristic
168C29×#117C2×C411yescharacteristic, complemented
169C2×C4⋊C4×C29—21no—
170C2×C4⋊C4×C29—21no—
171C2×C4⋊C4×C29C2×C411yescharacteristic
172C2×C4⋊C4×C29C2×C411yescharacteristic, complemented
173C2×C4⋊C4×C29D411yescharacteristic
174C2×C22⋊C4×C29—21no—
175C2×C22⋊C4×C29—21no—
176C2×C22⋊C4×C29—21no—
177C2×C22⋊C4×C29—21no—
178C2×C22⋊C4×C29—21no—
179C2×C22⋊C4×C29—21no—
180C2×C22⋊C4×C29—21no—
181C2×C22⋊C4×C29D411yescharacteristic
182C2×C22⋊C4×C29D411yescharacteristic
183C2×C42×C29—21no—
184C2×C42×C29C2311yescharacteristic
185C29×C4⋊C8—21no—
186C29×C4⋊C8—21no—
187C29×C22⋊C8—21no—
188C29×C22⋊C8—21no—
189C29×C22⋊C8—21no—
190C29×C22⋊C8—21no—
191C29×C22⋊C8C2311yescharacteristic
192C29×C22⋊C8C2311yescharacteristic
193C29×C22⋊C8C2311yescharacteristic
194C29×C22⋊C8C2311yescharacteristic
195C29×#97—21no—
196C4×C8×C29—21no—
197C29×#95—21no—
198C29×#95—21no—
199C29×#95—21no—
200C29×#95—21no—
201C29×#95—21no—
202C29×#95C2311yescharacteristic
203C29×#95C2311yescharacteristic
204C29×#95C2311yescharacteristic
205C29×#95C2311yescharacteristic
206C24×C29—21no—
207C24×C29—21no—
208C24×C29C2×D411yescharacteristic
209C24×C29C2×D411yescharacteristic
210#41×C29—81no—
211#41×C29—81no—
212#41×C29—81no—
213#41×C29—81no—
214C2×Q8×C29—21no—
215C2×Q8×C29C22×C411yescharacteristic
216C2×D4×C29—21no—
217C2×D4×C29—21no—
218C2×D4×C29—21no—
219C2×D4×C29—21no—
220C2×D4×C29—21no—
221C2×D4×C29—21no—
222C2×D4×C29—21no—
223C2×D4×C29—21no—
224C2×D4×C29—21no—
225C2×D4×C29—21no—
226C2×D4×C29—21no—
227C2×D4×C29—21no—
228C2×D4×C29—21no—
229C2×D4×C29—21no—
230C2×D4×C29—21no—
231C2×D4×C29—42no—
232C2×D4×C29—44no—
233C2×D4×C29—81no—
234C2×D4×C29—81no—
235C2×D4×C29—81no—
236C2×D4×C29—81no—
237C2×D4×C29—81no—
238C2×D4×C29—81no—
239C2×D4×C29C22⋊C411yescharacteristic
240C2×D4×C29C22⋊C411yescharacteristic
241C2×D4×C29C22⋊C411yescharacteristic
242C2×D4×C29C22⋊C411yescharacteristic
243C2×D4×C29C22×C411yescharacteristic
244C2×D4×C29C22×C411yescharacteristic
245C2×D4×C29C22×C411yescharacteristic
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—42no—
258C22×C4×C29—81no—
259C22×C4×C29—81no—
260C22×C4×C29—81no—
261C22×C4×C29—81no—
262C22×C4×C29C22×C411yescharacteristic
263C22×C4×C29C22×C411yescharacteristic
264C22×C4×C29C22×C411yescharacteristic
265C22×C4×C29C22×C411yescharacteristic
266C22×C4×C29C2×D411yescharacteristic
267C22×C4×C29C2×D411yescharacteristic
268C22×C4×C29C2×D411yescharacteristic
269C22×C4×C29C2×D411yescharacteristic
270C22×C4×C29C2×D411yescharacteristic
271C22×C4×C29C2×D411yescharacteristic
272C22×C4×C29C2×D411yescharacteristic
273C22×C4×C29C2×D411yescharacteristic
274C22×C4×C29C2411yescharacteristic
275M16×C29—81no—
276M16×C29—81no—
277C2×C8×C29—21no—
278C2×C8×C29—21no—
279C2×C8×C29—21no—
280C2×C8×C29—21no—
281C2×C8×C29—81no—
282C2×C8×C29—81no—
283C4⋊C4×C29—21no—
284C4⋊C4×C29—21no—
285C4⋊C4×C29—21no—
286C4⋊C4×C29—21no—
287C4⋊C4×C29—21no—
288C4⋊C4×C29—21no—
289C4⋊C4×C29—21no—
290C4⋊C4×C29—21no—
291C4⋊C4×C29—21no—
292C4⋊C4×C29—81no—
293C4⋊C4×C29—81no—
294C4⋊C4×C29C22⋊C411yescharacteristic
295C4⋊C4×C29C22⋊C411yescharacteristic
296C4⋊C4×C29C22⋊C411yescharacteristic
297C4⋊C4×C29C22⋊C411yescharacteristic
298C4⋊C4×C29C22×C411yescharacteristic
299C4⋊C4×C29C22×C411yescharacteristic
300C4⋊C4×C29C22×C411yescharacteristic
301C4⋊C4×C29C22×C411yescharacteristic
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—21no—
310C22⋊C4×C29—21no—
311C22⋊C4×C29—21no—
312C22⋊C4×C29—21no—
313C22⋊C4×C29—21no—
314C22⋊C4×C29—21no—
315C22⋊C4×C29—21no—
316C22⋊C4×C29—21no—
317C22⋊C4×C29—21no—
318C22⋊C4×C29—21no—
319C22⋊C4×C29—21no—
320C22⋊C4×C29—21no—
321C22⋊C4×C29—42no—
322C22⋊C4×C29—81no—
323C22⋊C4×C29—81no—
324C22⋊C4×C29C22⋊C411yescharacteristic
325C22⋊C4×C29C22⋊C411yescharacteristic
326C22⋊C4×C29C22⋊C411yescharacteristic
327C22⋊C4×C29C22⋊C411yescharacteristic
328C22⋊C4×C29C22⋊C411yescharacteristic
329C22⋊C4×C29C22⋊C411yescharacteristic
330C22⋊C4×C29C22⋊C411yescharacteristic
331C22⋊C4×C29C22⋊C411yescharacteristic
332C42×C29—21no—
333C42×C29—21no—
334C42×C29—21no—
335C42×C29—81no—
336C42×C29C22×C411yescharacteristic
337C42×C29C22×C411yescharacteristic
338C42×C29C2×D411yescharacteristic
339C42×C29C2×D411yescharacteristic
340#17597C2911yesmaximal, characteristic, direct product factor, Sylow
341C23×C29—21no—
342C23×C29—21no—
343C23×C29—22no—
344C23×C29—21no—
345C23×C29—21no—
346C23×C29—21no—
347C23×C29—21no—
348C23×C29—21no—
349C23×C29—41no—
350C23×C29—41no—
351C23×C29—41no—
352C23×C29—42no—
353C23×C29—42no—
354C23×C29—81no—
355C23×C29—81no—
356C23×C29—81no—
357C23×C29—81no—
358C23×C29C2×C22⋊C411yescharacteristic
359C23×C29C2×C22⋊C411yescharacteristic
360C23×C29C2×C22⋊C411yescharacteristic
361C23×C29C2×C22⋊C411yescharacteristic
362C23×C29C22×D411yescharacteristic
363Q8×C29—41no—
364Q8×C29—81no—
365D4×C29—22no—
366D4×C29—22no—
367D4×C29—41no—
368D4×C29—41no—
369D4×C29—41no—
370D4×C29—41no—
371D4×C29—41no—
372D4×C29—42no—
373D4×C29—42no—
374D4×C29—41no—
375D4×C29—41no—
376D4×C29—41no—
377D4×C29—41no—
378D4×C29—41no—
379D4×C29—41no—
380D4×C29—42no—
381D4×C29—81no—
382D4×C29—81no—
383D4×C29—81no—
384D4×C29—81no—
385D4×C29—81no—
386D4×C29—81no—
387D4×C29—81no—
388D4×C29—81no—
389D4×C29—81no—
390C2×C4×C29—21no—
391C2×C4×C29—21no—
392C2×C4×C29—21no—
393C2×C4×C29—21no—
394C2×C4×C29—21no—
395C2×C4×C29—21no—
396C2×C4×C29—21no—
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—42no—
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—81no—
423C2×C4×C29—81no—
424C2×C4×C29—81no—
425C2×C4×C29—81no—
426C2×C4×C29—81no—
427C2×C4×C29—81no—
428C2×C4×C29—84no—
429C2×C4×C29C2×C22⋊C411yescharacteristic
430C2×C4×C29C2×C22⋊C411yescharacteristic
431C2×C4×C29C2×C22⋊C411yescharacteristic
432C2×C4×C29C2×C22⋊C411yescharacteristic
433C2×C4×C29C2×C22⋊C411yescharacteristic
434C2×C4×C29C2×C22⋊C411yescharacteristic
435C2×C4×C29C2×C22⋊C411yescharacteristic
436C2×C4×C29C2×C22⋊C411yescharacteristic
437C2×C4×C29C23×C411yescharacteristic
438C2×C4×C29C22×D411yescharacteristic
439C8×C29—41no—
440C8×C29—41no—
441C8×C29—41no—
442C8×C29—41no—
443#3519C2×C2911yescharacteristic
444#2974C2×C2911yescharacteristic, complemented
445#2318C2×C2911yescharacteristic, complemented
446#1521C2×C2911yescharacteristic, complemented
447#1519C2×C2911yescharacteristic, complemented
448#1517C2×C2911yescharacteristic, complemented
449#1516C2×C2911yescharacteristic, complemented
450#1514C2×C2911yescharacteristic, complemented
451#1513C2×C2911yescharacteristic, complemented
452#1512C2×C2911yescharacteristic, complemented
453#1510C2×C2911yescharacteristic, complemented
454#1507C2×C2911yescharacteristic, complemented
455#1504C2×C2911yescharacteristic, complemented
456#1501C2×C2911yescharacteristic, complemented
457C2×#327C2×C2911yescharacteristic, complemented
458C22×C29—21no—
459C22×C29—21no—
460C22×C29—21no—
461C22×C29—21no—
462C22×C29—21no—
463C22×C29—21no—
464C22×C29—21no—
465C22×C29—21no—
466C22×C29—21no—
467C22×C29—21no—
468C22×C29—21no—
469C22×C29—21no—
470C22×C29—21no—
471C22×C29—42no—
472C22×C29—42no—
473C22×C29—41no—
474C22×C29—41no—
475C22×C29—41no—
476C22×C29—41no—
477C22×C29—41no—
478C22×C29—41no—
479C22×C29—41no—
480C22×C29—41no—
481C22×C29—41no—
482C22×C29—81no—
483C22×C29—81no—
484C22×C29—162no—
485C22×C29—162no—
486C22×C29#42112yes—
487C22×C29C22×C22⋊C411yescharacteristic
488C22×C29#57611yescharacteristic
489C22×C29#57711yescharacteristic
490C4×C29—21no—
491C4×C29—21no—
492C4×C29—21no—
493C4×C29—21no—
494C4×C29—21no—
495C4×C29—21no—
496C4×C29—21no—
497C4×C29—21no—
498C4×C29—21no—
499C4×C29—21no—
500C4×C29—41no—
501C4×C29—41no—
502C4×C29—41no—
503C4×C29—41no—
504C4×C29—41no—
505C4×C29—81no—
506C4×C29—81no—
507C4×C29—81no—
508C4×C29—81no—
509#555C4×C2911yescharacteristic, complemented
510#554C4×C2911yescharacteristic, complemented
511#553—21no—
512#553C4×C2911yescharacteristic, complemented
513#553C4×C2911yescharacteristic, complemented
514#550C4×C2911yescharacteristic, complemented
515#546—21no—
516#546—21no—
517#546C4×C2911yescharacteristic, complemented
518#546C4×C2911yescharacteristic, complemented
519D42—21no—
520D42C4×C2911yescharacteristic, complemented
521#540—21no—
522#538—21no—
523#538—21no—
524#532C22×C2911yescharacteristic
525#529C22×C2911yescharacteristic
526#525C22×C2911yescharacteristic
527#525C22×C2911yescharacteristic
528C2×#121C22×C2911yescharacteristic
529C2×#121C22×C2911yescharacteristic
530#518—21no—
531C2×C4×D4C22×C2911yescharacteristic
532#436—21no—
533#435—21no—
534#435—21no—
535C8×D4—21no—
536#432C22×C2911yescharacteristic, complemented
537#431C22×C2911yescharacteristic, complemented
538#407C22×C2911yescharacteristic, complemented
539#407C22×C2911yescharacteristic, complemented
540C2×C22⋊C8C22×C2911yescharacteristic, complemented
541C2×C22⋊C8C22×C2911yescharacteristic, complemented
542#388—21no—
543#387—21no—
544#386—21no—
545#385—21no—
546#383C22×C2911yescharacteristic, complemented
547#382C22×C2911yescharacteristic, complemented
548#381C22×C2911yescharacteristic, complemented
549#380C22×C2911yescharacteristic, complemented
550C4×C22⋊C4C22×C2911yescharacteristic, complemented
551C2×#95C22×C2911yescharacteristic, complemented
552#328C22×C2911yescharacteristic, complemented
553#328C22×C2911yescharacteristic, complemented
554#328C22×C2911yescharacteristic, complemented
555#328C22×C2911yescharacteristic, complemented
556#327C22×C2911yescharacteristic
557#327C22×C2911yescharacteristic
558#327C22×C2911yescharacteristic
559#327C22×C2911yescharacteristic
560#327C22×C2911yescharacteristic, complemented
561#327C22×C2911yescharacteristic, complemented
562#327C22×C2911yescharacteristic, complemented
563#327C22×C2911yescharacteristic, complemented
564#327C22×C2911yescharacteristic, complemented
565#327C22×C2911yescharacteristic, complemented
566#327C22×C2911yescharacteristic, complemented
567#327C22×C2911yescharacteristic, complemented
568C2×C29—21no—
569C2×C29—21no—
570C2×C29—22no—
571C2×C29—41no—
572C2×C29—41no—
573C2×C29—41no—
574C2×C29—81no—
575C2×C29—81no—
576C2×C29—81no—
577C2×C29#288311yescharacteristic
578C2×C29#289711yescharacteristic
579C2×C29C2×#42111yescharacteristic
580C2×#41—21no—
581C2×#41C2×C4×C2911yescharacteristic
582C2×#41C2×C4×C2911yescharacteristic, complemented
583C22×D4—21no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4C2×C4×C2911yescharacteristic
587C22×D4C2×C4×C2911yescharacteristic, complemented
588C22×D4D4×C2911yescharacteristic
589C23×C4—21no—
590C23×C4C23×C2911yescharacteristic
591C23×C4C23×C2911yescharacteristic
592C2×M16—21no—
593C2×M16—21no—
594C22×C8—21no—
595C22×C8—21no—
596C4⋊Q8C2×C4×C2911yescharacteristic, complemented
597#127—21no—
598#127C2×C4×C2911yescharacteristic, complemented
599#126—21no—
600#126—21no—
601#126—21no—
602#125—21no—
603#125C2×C4×C2911yescharacteristic, complemented
604#124—21no—
605#124—21no—
606#124—21no—
607#124C2×C4×C2911yescharacteristic, complemented
608#123—21no—
609#123—21no—
610#123—21no—
611#123—21no—
612#123—21no—
613#123—21no—
614#123—21no—
615C22⋊Q8—21no—
616C22⋊Q8—21no—
617C22⋊Q8C2×C4×C2911yescharacteristic
618C22⋊Q8C2×C4×C2911yescharacteristic, complemented
619C22⋊Q8C23×C2911yescharacteristic
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121—21no—
625#121—21no—
626#121—21no—
627#121—21no—
628#121—21no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—21no—
633#121C2×C4×C2911yescharacteristic
634#121C2×C4×C2911yescharacteristic
635#121C2×C4×C2911yescharacteristic
636#121C2×C4×C2911yescharacteristic, complemented
637#121C2×C4×C2911yescharacteristic, complemented
638#121C2×C4×C2911yescharacteristic, complemented
639#121C23×C2911yescharacteristic
640#121C23×C2911yescharacteristic
641#121C23×C2911yescharacteristic
642#120—21no—
643#120—21no—
644#120—21no—
645#120—21no—
646#120—21no—
647#120—21no—
648C4×Q8C2×C4×C2911yescharacteristic, complemented
649C4×D4—21no—
650C4×D4—21no—
651C4×D4—21no—
652C4×D4—21no—
653C4×D4—21no—
654C4×D4—21no—
655C4×D4—21no—
656C4×D4—21no—
657C4×D4—21no—
658C4×D4—21no—
659C4×D4C2×C4×C2911yescharacteristic
660C4×D4C2×C4×C2911yescharacteristic
661C4×D4C2×C4×C2911yescharacteristic
662C4×D4C2×C4×C2911yescharacteristic
663C4×D4C2×C4×C2911yescharacteristic, complemented
664C4×D4C2×C4×C2911yescharacteristic, complemented
665C4×D4C2×C4×C2911yescharacteristic, complemented
666C4×D4D4×C2911yescharacteristic
667C4×D4D4×C2911yescharacteristic
668C4×D4D4×C2911yescharacteristic
669C4×D4D4×C2911yescharacteristic
670#117—21no—
671#117—21no—
672#117C2×C4×C2911yescharacteristic
673#117C2×C4×C2911yescharacteristic, complemented
674C2×C4⋊C4—21no—
675C2×C4⋊C4—21no—
676C2×C4⋊C4C2×C4×C2911yescharacteristic
677C2×C4⋊C4C2×C4×C2911yescharacteristic, complemented
678C2×C4⋊C4D4×C2911yescharacteristic
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4D4×C2911yescharacteristic
687C2×C22⋊C4D4×C2911yescharacteristic
688C2×C42—21no—
689C2×C42C23×C2911yescharacteristic
690C4⋊C8—21no—
691C4⋊C8—21no—
692C22⋊C8—21no—
693C22⋊C8—21no—
694C22⋊C8—21no—
695C22⋊C8—21no—
696C22⋊C8C23×C2911yescharacteristic
697C22⋊C8C23×C2911yescharacteristic
698C22⋊C8C23×C2911yescharacteristic
699C22⋊C8C23×C2911yescharacteristic
700#97—21no—
701C4×C8—21no—
702#95—21no—
703#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95C23×C2911yescharacteristic
708#95C23×C2911yescharacteristic
709#95C23×C2911yescharacteristic
710#95C23×C2911yescharacteristic
711C29#1759711yescharacteristic, direct product factor, Sylow
712C24—21no—
713C24—21no—
714C24C2×D4×C2911yescharacteristic
715C24C2×D4×C2911yescharacteristic
716#41—81no—
717#41—81no—
718#41—81no—
719#41—81no—
720C2×Q8—21no—
721C2×Q8C22×C4×C2911yescharacteristic
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—42no—
738C2×D4—44no—
739C2×D4—81no—
740C2×D4—81no—
741C2×D4—81no—
742C2×D4—81no—
743C2×D4—81no—
744C2×D4—81no—
745C2×D4C22⋊C4×C2911yescharacteristic
746C2×D4C22⋊C4×C2911yescharacteristic
747C2×D4C22⋊C4×C2911yescharacteristic
748C2×D4C22⋊C4×C2911yescharacteristic
749C2×D4C22×C4×C2911yescharacteristic
750C2×D4C22×C4×C2911yescharacteristic
751C2×D4C22×C4×C2911yescharacteristic
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—21no—
763C22×C4—42no—
764C22×C4—81no—
765C22×C4—81no—
766C22×C4—81no—
767C22×C4—81no—
768C22×C4C22×C4×C2911yescharacteristic
769C22×C4C22×C4×C2911yescharacteristic
770C22×C4C22×C4×C2911yescharacteristic
771C22×C4C22×C4×C2911yescharacteristic
772C22×C4C2×D4×C2911yescharacteristic
773C22×C4C2×D4×C2911yescharacteristic
774C22×C4C2×D4×C2911yescharacteristic
775C22×C4C2×D4×C2911yescharacteristic
776C22×C4C2×D4×C2911yescharacteristic
777C22×C4C2×D4×C2911yescharacteristic
778C22×C4C2×D4×C2911yescharacteristic
779C22×C4C2×D4×C2911yescharacteristic
780C22×C4C24×C2911yescharacteristic
781M16—81no—
782M16—81no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—81no—
788C2×C8—81no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4—21no—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—21no—
798C4⋊C4—81no—
799C4⋊C4—81no—
800C4⋊C4C22⋊C4×C2911yescharacteristic
801C4⋊C4C22⋊C4×C2911yescharacteristic
802C4⋊C4C22⋊C4×C2911yescharacteristic
803C4⋊C4C22⋊C4×C2911yescharacteristic
804C4⋊C4C22×C4×C2911yescharacteristic
805C4⋊C4C22×C4×C2911yescharacteristic
806C4⋊C4C22×C4×C2911yescharacteristic
807C4⋊C4C22×C4×C2911yescharacteristic
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—42no—
828C22⋊C4—81no—
829C22⋊C4—81no—
830C22⋊C4C22⋊C4×C2911yescharacteristic
831C22⋊C4C22⋊C4×C2911yescharacteristic
832C22⋊C4C22⋊C4×C2911yescharacteristic
833C22⋊C4C22⋊C4×C2911yescharacteristic
834C22⋊C4C22⋊C4×C2911yescharacteristic
835C22⋊C4C22⋊C4×C2911yescharacteristic
836C22⋊C4C22⋊C4×C2911yescharacteristic
837C22⋊C4C22⋊C4×C2911yescharacteristic
838C42—21no—
839C42—21no—
840C42—21no—
841C42—81no—
842C42C22×C4×C2911yescharacteristic
843C42C22×C4×C2911yescharacteristic
844C42C2×D4×C2911yescharacteristic
845C42C2×D4×C2911yescharacteristic
846C23—21no—
847C23—21no—
848C23—22no—
849C23—21no—
850C23—21no—
851C23—21no—
852C23—21no—
853C23—21no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—42no—
858C23—42no—
859C23—81no—
860C23—81no—
861C23—81no—
862C23—81no—
863C23C2×C22⋊C4×C2911yescharacteristic
864C23C2×C22⋊C4×C2911yescharacteristic
865C23C2×C22⋊C4×C2911yescharacteristic
866C23C2×C22⋊C4×C2911yescharacteristic
867C23C22×D4×C2911yescharacteristic
868Q8—41no—
869Q8—81no—
870D4—22no—
871D4—22no—
872D4—41no—
873D4—41no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—42no—
878D4—42no—
879D4—41no—
880D4—41no—
881D4—41no—
882D4—41no—
883D4—41no—
884D4—41no—
885D4—42no—
886D4—81no—
887D4—81no—
888D4—81no—
889D4—81no—
890D4—81no—
891D4—81no—
892D4—81no—
893D4—81no—
894D4—81no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
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—42no—
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—81no—
928C2×C4—81no—
929C2×C4—81no—
930C2×C4—81no—
931C2×C4—81no—
932C2×C4—81no—
933C2×C4—84no—
934C2×C4C2×C22⋊C4×C2911yescharacteristic
935C2×C4C2×C22⋊C4×C2911yescharacteristic
936C2×C4C2×C22⋊C4×C2911yescharacteristic
937C2×C4C2×C22⋊C4×C2911yescharacteristic
938C2×C4C2×C22⋊C4×C2911yescharacteristic
939C2×C4C2×C22⋊C4×C2911yescharacteristic
940C2×C4C2×C22⋊C4×C2911yescharacteristic
941C2×C4C2×C22⋊C4×C2911yescharacteristic
942C2×C4C23×C4×C2911yescharacteristic
943C2×C4C22×D4×C2911yescharacteristic
944C8—41no—
945C8—41no—
946C8—41no—
947C8—41no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—21no—
961C22—42no—
962C22—42no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—41no—
967C22—41no—
968C22—41no—
969C22—41no—
970C22—41no—
971C22—41no—
972C22—81no—
973C22—81no—
974C22—162no—
975C22—162no—
976C22C29×#42112yes—
977C22C22×C22⋊C4×C2911yescharacteristic
978C22C29×#57611yescharacteristic
979C22C29×#57711yescharacteristic
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—21no—
987C4—21no—
988C4—21no—
989C4—21no—
990C4—41no—
991C4—41no—
992C4—41no—
993C4—41no—
994C4—41no—
995C4—81no—
996C4—81no—
997C4—81no—
998C4—81no—
999C2—21no—
1000C2—21no—
1001C2—22no—
1002C2—41no—
1003C2—41no—
1004C2—41no—
1005C2—81no—
1006C2—81no—
1007C2—81no—
1008C2C29×#288311yescharacteristic
1009C2C29×#289711yescharacteristic
1010C2C2×C29×#42111yescharacteristic
subgroupG/H
center, socleC22×C29C22×C22⋊C4
commutatorC2×C4C23×C4×C29
Frattini, cosocleC22×C4C24×C29
prime radicalC29×#3519C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C4×D4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#2974C2semidirect
3. C29×#2318C2semidirect
4. C29×#1521C2semidirect
5. C29×#1519C2semidirect
6. C29×#1517C2semidirect
7. C29×#1516C2semidirect
8. C29×#1514C2semidirect
9. C29×#1513C2semidirect
10. C29×#1512C2semidirect
11. C29×#1510C2semidirect
12. C29×#1507C2semidirect
13. C29×#1504C2semidirect
14. C29×#1501C2semidirect
15. C2×C29×#327C2semidirect
16. C29×#555C4semidirect
17. C29×#554C4semidirect
19. C29×#553C4semidirect
20. C29×#553C4semidirect
21. C29×#550C4semidirect
24. C29×#546C4semidirect
25. C29×#546C4semidirect
27. D42×C29C4semidirect
43. C29×#432C22semidirect
44. C29×#431C22semidirect
45. C29×#407C22semidirect
46. C29×#407C22semidirect
47. C2×C29×C22⋊C8C22semidirect
48. C2×C29×C22⋊C8C22semidirect
53. C29×#383C22semidirect
54. C29×#382C22semidirect
55. C29×#381C22semidirect
56. C29×#380C22semidirect
57. C4×C22⋊C4×C29C22semidirect
58. C2×C29×#95C22semidirect
59. C29×#328C22semidirect
60. C29×#328C22semidirect
61. C29×#328C22semidirect
62. C29×#328C22semidirect
67. C29×#327C22semidirect
68. C29×#327C22semidirect
69. C29×#327C22semidirect
70. C29×#327C22semidirect
71. C29×#327C22semidirect
72. C29×#327C22semidirect
73. C29×#327C22semidirect
74. C29×#327C22semidirect
77. C2×#41×C29C2×C4semidirect
82. C22×D4×C29C2×C4semidirect
91. C29×C4⋊Q8C2×C4semidirect
93. C29×#127C2×C4semidirect
98. C29×#125C2×C4semidirect
102. C29×#124C2×C4semidirect
113. C29×C22⋊Q8C2×C4semidirect
131. C29×#121C2×C4semidirect
132. C29×#121C2×C4semidirect
133. C29×#121C2×C4semidirect
143. C4×Q8×C29C2×C4semidirect
158. C4×D4×C29C2×C4semidirect
159. C4×D4×C29C2×C4semidirect
160. C4×D4×C29C2×C4semidirect
168. C29×#117C2×C4semidirect
172. C2×C4⋊C4×C29C2×C4semidirect
340. #17597C29direct (N × H)
444. #2974C2×C29semidirect
445. #2318C2×C29semidirect
446. #1521C2×C29semidirect
447. #1519C2×C29semidirect
448. #1517C2×C29semidirect
449. #1516C2×C29semidirect
450. #1514C2×C29semidirect
451. #1513C2×C29semidirect
452. #1512C2×C29semidirect
453. #1510C2×C29semidirect
454. #1507C2×C29semidirect
455. #1504C2×C29semidirect
456. #1501C2×C29semidirect
457. C2×#327C2×C29semidirect
509. #555C4×C29semidirect
510. #554C4×C29semidirect
512. #553C4×C29semidirect
513. #553C4×C29semidirect
514. #550C4×C29semidirect
517. #546C4×C29semidirect
518. #546C4×C29semidirect
520. D42C4×C29semidirect
536. #432C22×C29semidirect
537. #431C22×C29semidirect
538. #407C22×C29semidirect
539. #407C22×C29semidirect
540. C2×C22⋊C8C22×C29semidirect
541. C2×C22⋊C8C22×C29semidirect
546. #383C22×C29semidirect
547. #382C22×C29semidirect
548. #381C22×C29semidirect
549. #380C22×C29semidirect
550. C4×C22⋊C4C22×C29semidirect
551. C2×#95C22×C29semidirect
552. #328C22×C29semidirect
553. #328C22×C29semidirect
554. #328C22×C29semidirect
555. #328C22×C29semidirect
560. #327C22×C29semidirect
561. #327C22×C29semidirect
562. #327C22×C29semidirect
563. #327C22×C29semidirect
564. #327C22×C29semidirect
565. #327C22×C29semidirect
566. #327C22×C29semidirect
567. #327C22×C29semidirect
582. C2×#41C2×C4×C29semidirect
587. C22×D4C2×C4×C29semidirect
596. C4⋊Q8C2×C4×C29semidirect
598. #127C2×C4×C29semidirect
603. #125C2×C4×C29semidirect
607. #124C2×C4×C29semidirect
618. C22⋊Q8C2×C4×C29semidirect
636. #121C2×C4×C29semidirect
637. #121C2×C4×C29semidirect
638. #121C2×C4×C29semidirect
648. C4×Q8C2×C4×C29semidirect
663. C4×D4C2×C4×C29semidirect
664. C4×D4C2×C4×C29semidirect
665. C4×D4C2×C4×C29semidirect
673. #117C2×C4×C29semidirect
677. C2×C4⋊C4C2×C4×C29semidirect
711. C29#17597direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35192
C29×#29742
C29×#23182
C29×#15212
C29×#15192
C29×#15172
C29×#15162
C29×#15142
C29×#15132
C29×#15122
C29×#15102
C29×#15072
C29×#15042
C29×#15012
C2×C29×#3272
#1759729