Finite Group Databasebeta

← C29×#17505 #20312405

Subgroups — C29×#17505 #20312405

Order 7424.

954 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3460C211yesmaximal, characteristic
2C29×#2989C211yesmaximal, characteristic, complemented
3C29×#2965C211yesmaximal, characteristic, complemented
4C29×#1496C211yesmaximal, characteristic, complemented
5C29×#1495C211yesmaximal, characteristic, complemented
6C29×#1494C211yesmaximal, characteristic, complemented
7C29×#1492C211yesmaximal, characteristic, complemented
8C29×#1490C211yesmaximal, characteristic, complemented
9C29×#1489C211yesmaximal, characteristic, complemented
10C29×#1488C211yesmaximal, characteristic, complemented
11C29×#1486C211yesmaximal, characteristic, complemented
12C29×#1484C211yesmaximal, characteristic, complemented
13C29×#1483C211yesmaximal, characteristic, complemented
14C29×#1482C211yesmaximal, characteristic, complemented
15C29×#1480C211yesmaximal, characteristic, complemented
16C29×#544C411yescharacteristic
17C29×#542—21no—
18C29×#542C411yescharacteristic
19C29×#542C411yescharacteristic
20C29×#540—21no—
21C29×#540C411yescharacteristic
22C29×#540C411yescharacteristic
23C29×#538—21no—
24C29×#538—21no—
25C29×#537C411yescharacteristic
26C29×#535C411yescharacteristic
27C29×#535C411yescharacteristic
28C29×#532—21no—
29C29×#532C2211yescharacteristic
30C29×#532C2211yescharacteristic
31C29×#529—21no—
32C29×#529C2211yescharacteristic
33C29×#529C2211yescharacteristic
34C29×#525—21no—
35C29×#525—21no—
36C4×#41×C29C2211yescharacteristic
37C4×#41×C29C2211yescharacteristic
38C2×C4×D4×C29C2211yescharacteristic
39C29×#446—21no—
40C29×#446—21no—
41C29×#436—21no—
42C29×#436—21no—
43C29×#435—21no—
44C29×#435—21no—
45C29×#435—21no—
46C29×#435—21no—
47C29×#432C2211yescharacteristic
48C29×#432C2211yescharacteristic, complemented
49C29×#431C2211yescharacteristic
50C29×#431C2211yescharacteristic, complemented
51C29×#431C2211yescharacteristic, complemented
52C29×#431C2211yescharacteristic, complemented
53C29×#423C2211yescharacteristic
54C29×#423C2211yescharacteristic, complemented
55C2×C29×C4⋊C8C2211yescharacteristic, complemented
56C4×M16×C29C2211yescharacteristic
57C4×M16×C29C2211yescharacteristic, complemented
58C2×C4×C8×C29C2211yescharacteristic, complemented
59C29×Q8⋊C8C2211yescharacteristic, complemented
60C29×Q8⋊C8C2211yescharacteristic, complemented
61C29×Q8⋊C8C2211yescharacteristic, complemented
62C29×Q8⋊C8C2211yescharacteristic, complemented
63C29×D4⋊C8C2211yescharacteristic
64C29×D4⋊C8C2211yescharacteristic
65C29×D4⋊C8C2211yescharacteristic
66C29×D4⋊C8C2211yescharacteristic
67C29×D4⋊C8C2211yescharacteristic
68C29×D4⋊C8C2211yescharacteristic
69C29×D4⋊C8C2211yescharacteristic
70C29×D4⋊C8C2211yescharacteristic
71C29×D4⋊C8C2211yescharacteristic, complemented
72C29×D4⋊C8C2211yescharacteristic, complemented
73C29×D4⋊C8C2211yescharacteristic, complemented
74C29×D4⋊C8C2211yescharacteristic, complemented
75C2×#41×C29—21no—
76C2×#41×C29—21no—
77C2×#41×C29C2×C411yescharacteristic
78C2×#41×C29C2×C411yescharacteristic
79C22×D4×C29C2×C411yescharacteristic
80C23×C4×C29—21no—
81C2×M16×C29—21no—
82C2×M16×C29—21no—
83C2×M16×C29—21no—
84C2×M16×C29—21no—
85C22×C8×C29—21no—
86C22×C8×C29—21no—
87C29×C4⋊Q8—21no—
88C29×C4⋊Q8C2×C411yescharacteristic
89C29×C4⋊Q8C2×C411yescharacteristic
90C29×#127—21no—
91C29×#127C2×C411yescharacteristic
92C29×#127C2×C411yescharacteristic
93C29×#126—21no—
94C29×#126—21no—
95C29×#126—21no—
96C29×#126—21no—
97C29×#125—21no—
98C29×#125C2×C411yescharacteristic
99C29×#125C2×C411yescharacteristic
100C29×#124—21no—
101C29×#124—21no—
102C29×#124—21no—
103C29×#124—21no—
104C29×#124—21no—
105C29×#124C2×C411yescharacteristic
106C29×#124C2×C411yescharacteristic
107C29×#123—21no—
108C29×#123—21no—
109C29×#123—21no—
110C29×#123—21no—
111C29×#123—21no—
112C29×#123—21no—
113C29×#123—21no—
114C29×#123—21no—
115C29×C22⋊Q8—21no—
116C29×C22⋊Q8—21no—
117C29×C22⋊Q8—21no—
118C29×C22⋊Q8—21no—
119C29×C22⋊Q8—21no—
120C29×C22⋊Q8C2×C411yescharacteristic
121C29×C22⋊Q8C2×C411yescharacteristic
122C29×#121—21no—
123C29×#121—21no—
124C29×#121—21no—
125C29×#121—21no—
126C29×#121—21no—
127C29×#121—21no—
128C29×#121—21no—
129C29×#121—21no—
130C29×#121—21no—
131C29×#121—21no—
132C29×#121—21no—
133C29×#121C2×C411yescharacteristic
134C29×#121C2×C411yescharacteristic
135C29×#121C2×C411yescharacteristic
136C29×#121C2×C411yescharacteristic
137C29×#121C2×C411yescharacteristic
138C29×#121C2×C411yescharacteristic
139C29×#120—21no—
140C29×#120—21no—
141C29×#120—21no—
142C29×#120—21no—
143C4×Q8×C29C2×C411yescharacteristic
144C4×Q8×C29D411yescharacteristic
145C4×Q8×C29D411yescharacteristic
146C4×Q8×C29C2311yescharacteristic
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×C29—21no—
155C4×D4×C29C2×C411yescharacteristic
156C4×D4×C29C2×C411yescharacteristic
157C4×D4×C29C2×C411yescharacteristic
158C4×D4×C29D411yescharacteristic
159C4×D4×C29D411yescharacteristic
160C4×D4×C29D411yescharacteristic
161C4×D4×C29D411yescharacteristic
162C4×D4×C29D411yescharacteristic
163C4×D4×C29D411yescharacteristic
164C4×D4×C29C2311yescharacteristic
165C4×D4×C29C2311yescharacteristic
166C4×D4×C29C2311yescharacteristic
167C29×#117—21no—
168C29×#117—21no—
169C29×#117—21no—
170C29×#117C2×C411yescharacteristic
171C29×#117C2×C411yescharacteristic
172C29×#117C2×C411yescharacteristic
173C29×#117C2×C411yescharacteristic
174C2×C4⋊C4×C29C2×C411yescharacteristic
175C2×C22⋊C4×C29—21no—
176C2×C42×C29—21no—
177C2×C42×C29C2311yescharacteristic
178C2×C42×C29C2311yescharacteristic
179C2×C42×C29C2311yescharacteristic
180C29×C4⋊C8—21no—
181C29×C4⋊C8—21no—
182C29×C4⋊C8—21no—
183C29×C4⋊C8—21no—
184C29×C4⋊C8—21no—
185C29×C4⋊C8—21no—
186C29×C4⋊C8C2311yescharacteristic
187C29×C4⋊C8C2311yescharacteristic
188C29×C4⋊C8C2311yescharacteristic
189C29×C4⋊C8C2311yescharacteristic
190C29×C22⋊C8—21no—
191C29×C22⋊C8—21no—
192C29×C22⋊C8—21no—
193C29×C22⋊C8—21no—
194C29×C22⋊C8—21no—
195C29×C22⋊C8—21no—
196C29×#97—21no—
197C29×#97—21no—
198C29×#97—21no—
199C29×#97—21no—
200C4×C8×C29—21no—
201C4×C8×C29—21no—
202C4×C8×C29C2311yescharacteristic
203C4×C8×C29C2311yescharacteristic
204C4×C8×C29C2311yescharacteristic
205C4×C8×C29C2311yescharacteristic
206C24×C29—21no—
207#41×C29—42no—
208#41×C29—42no—
209#41×C29—81no—
210#41×C29—81no—
211#41×C29—81no—
212#41×C29—81no—
213C2×Q8×C29—21no—
214C2×Q8×C29—21no—
215C2×Q8×C29C22⋊C411yescharacteristic
216C2×Q8×C29C22×C411yescharacteristic
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—42no—
230C2×D4×C29C22⋊C411yescharacteristic
231C2×D4×C29C22⋊C411yescharacteristic
232C2×D4×C29C22⋊C411yescharacteristic
233C2×D4×C29C22×C411yescharacteristic
234C2×D4×C29C22×C411yescharacteristic
235C2×D4×C29C22×C411yescharacteristic
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—81no—
245C22×C4×C29—81no—
246C22×C4×C29C22×C411yescharacteristic
247C22×C4×C29C22×C411yescharacteristic
248C22×C4×C29C22×C411yescharacteristic
249C22×C4×C29C2×D411yescharacteristic
250C22×C4×C29C2×D411yescharacteristic
251C22×C4×C29C2×D411yescharacteristic
252C22×C4×C29C2×D411yescharacteristic
253C22×C4×C29C2×D411yescharacteristic
254C22×C4×C29C2×D411yescharacteristic
255M16×C29—42no—
256M16×C29—42no—
257M16×C29—81no—
258M16×C29—81no—
259C2×C8×C29—21no—
260C2×C8×C29—21no—
261C2×C8×C29—21no—
262C2×C8×C29—21no—
263C2×C8×C29—21no—
264C2×C8×C29—21no—
265C2×C8×C29—21no—
266C2×C8×C29—21no—
267C2×C8×C29—42no—
268C2×C8×C29—81no—
269C4⋊C4×C29—21no—
270C4⋊C4×C29—21no—
271C4⋊C4×C29—21no—
272C4⋊C4×C29—21no—
273C4⋊C4×C29—21no—
274C4⋊C4×C29—21no—
275C4⋊C4×C29—21no—
276C4⋊C4×C29—21no—
277C4⋊C4×C29—21no—
278C4⋊C4×C29—21no—
279C4⋊C4×C29—21no—
280C4⋊C4×C29C22⋊C411yescharacteristic
281C4⋊C4×C29C22⋊C411yescharacteristic
282C4⋊C4×C29C22⋊C411yescharacteristic
283C4⋊C4×C29C22⋊C411yescharacteristic
284C4⋊C4×C29C22⋊C411yescharacteristic
285C4⋊C4×C29C22⋊C411yescharacteristic
286C4⋊C4×C29C22×C411yescharacteristic
287C4⋊C4×C29C22×C411yescharacteristic
288C4⋊C4×C29C22×C411yescharacteristic
289C4⋊C4×C29C22×C411yescharacteristic
290C22⋊C4×C29—21no—
291C22⋊C4×C29—21no—
292C22⋊C4×C29—21no—
293C22⋊C4×C29—21no—
294C22⋊C4×C29—21no—
295C22⋊C4×C29—21no—
296C22⋊C4×C29—21no—
297C22⋊C4×C29—21no—
298C22⋊C4×C29—21no—
299C22⋊C4×C29—21no—
300C22⋊C4×C29—21no—
301C22⋊C4×C29—21no—
302C22⋊C4×C29—21no—
303C22⋊C4×C29—21no—
304C22⋊C4×C29—21no—
305C22⋊C4×C29—21no—
306C22⋊C4×C29—21no—
307C22⋊C4×C29—21no—
308C22⋊C4×C29—21no—
309C22⋊C4×C29C22⋊C411yescharacteristic
310C22⋊C4×C29C22⋊C411yescharacteristic
311C22⋊C4×C29C22⋊C411yescharacteristic
312C22⋊C4×C29C22⋊C411yescharacteristic
313C22⋊C4×C29C22⋊C411yescharacteristic
314C22⋊C4×C29C22⋊C411yescharacteristic
315C42×C29—21no—
316C42×C29—21no—
317C42×C29—21no—
318C42×C29C22×C411yescharacteristic
319C42×C29C22×C411yescharacteristic
320C42×C29C22×C411yescharacteristic
321C42×C29C2×D411yescharacteristic
322C42×C29C2×D411yescharacteristic
323C42×C29C2×D411yescharacteristic
324C42×C29C2×D411yescharacteristic
325C42×C29C2×D411yescharacteristic
326C42×C29C2×D411yescharacteristic
327C42×C29C2411yescharacteristic
328#17505C2911yesmaximal, characteristic, direct product factor, Sylow
329C23×C29—21no—
330C23×C29—21no—
331C23×C29—21no—
332C23×C29—42no—
333C23×C29—81no—
334C23×C29—81no—
335C23×C29C2×C22⋊C411yescharacteristic
336C23×C29C2×C22⋊C411yescharacteristic
337C23×C29C2×C22⋊C411yescharacteristic
338Q8×C29—22no—
339Q8×C29—41no—
340Q8×C29—81no—
341Q8×C29—81no—
342D4×C29—22no—
343D4×C29—22no—
344D4×C29—22no—
345D4×C29—41no—
346D4×C29—41no—
347D4×C29—41no—
348D4×C29—42no—
349D4×C29—42no—
350D4×C29—81no—
351D4×C29—81no—
352D4×C29—81no—
353D4×C29—81no—
354D4×C29—81no—
355D4×C29—81no—
356D4×C29—81no—
357D4×C29—81no—
358D4×C29—81no—
359D4×C29—81no—
360C2×C4×C29—22no—
361C2×C4×C29—22no—
362C2×C4×C29—22no—
363C2×C4×C29—21no—
364C2×C4×C29—21no—
365C2×C4×C29—21no—
366C2×C4×C29—21no—
367C2×C4×C29—21no—
368C2×C4×C29—21no—
369C2×C4×C29—21no—
370C2×C4×C29—21no—
371C2×C4×C29—21no—
372C2×C4×C29—21no—
373C2×C4×C29—21no—
374C2×C4×C29—41no—
375C2×C4×C29—41no—
376C2×C4×C29—41no—
377C2×C4×C29—42no—
378C2×C4×C29—41no—
379C2×C4×C29—41no—
380C2×C4×C29—41no—
381C2×C4×C29—41no—
382C2×C4×C29—41no—
383C2×C4×C29—41no—
384C2×C4×C29—81no—
385C2×C4×C29—81no—
386C2×C4×C29—81no—
387C2×C4×C29—81no—
388C2×C4×C29C2×C22⋊C411yescharacteristic
389C2×C4×C29C2×C22⋊C411yescharacteristic
390C2×C4×C29C2×C22⋊C411yescharacteristic
391C2×C4×C29C2×C22⋊C411yescharacteristic
392C2×C4×C29C2×C22⋊C411yescharacteristic
393C2×C4×C29C2×C22⋊C411yescharacteristic
394C2×C4×C29C2×C22⋊C411yescharacteristic
395C2×C4×C29C2×C22⋊C411yescharacteristic
396C2×C4×C29C2×C22⋊C411yescharacteristic
397C2×C4×C29C23×C411yescharacteristic
398C2×C4×C29C22×D411yescharacteristic
399C2×C4×C29C22×D411yescharacteristic
400C8×C29—22no—
401C8×C29—41no—
402C8×C29—41no—
403C8×C29—41no—
404C8×C29—41no—
405C8×C29—41no—
406C8×C29—41no—
407C8×C29—41no—
408#3460C2×C2911yescharacteristic
409#2989C2×C2911yescharacteristic, complemented
410#2965C2×C2911yescharacteristic, complemented
411#1496C2×C2911yescharacteristic, complemented
412#1495C2×C2911yescharacteristic, complemented
413#1494C2×C2911yescharacteristic, complemented
414#1492C2×C2911yescharacteristic, complemented
415#1490C2×C2911yescharacteristic, complemented
416#1489C2×C2911yescharacteristic, complemented
417#1488C2×C2911yescharacteristic, complemented
418#1486C2×C2911yescharacteristic, complemented
419#1484C2×C2911yescharacteristic, complemented
420#1483C2×C2911yescharacteristic, complemented
421#1482C2×C2911yescharacteristic, complemented
422#1480C2×C2911yescharacteristic, complemented
423C22×C29—21no—
424C22×C29—21no—
425C22×C29—21no—
426C22×C29—21no—
427C22×C29—21no—
428C22×C29—21no—
429C22×C29—21no—
430C22×C29—21no—
431C22×C29—21no—
432C22×C29—41no—
433C22×C29—41no—
434C22×C29—41no—
435C22×C29—41no—
436C22×C29—41no—
437C22×C29—41no—
438C22×C29—41no—
439C22×C29—41no—
440C22×C29—41no—
441C22×C29—84no—
442C22×C29C22×C22⋊C411yescharacteristic
443C4×C29—21no—
444C4×C29—21no—
445C4×C29—21no—
446C4×C29—21no—
447C4×C29—21no—
448C4×C29—21no—
449C4×C29—21no—
450C4×C29—21no—
451C4×C29—21no—
452C4×C29—21no—
453C4×C29—41no—
454C4×C29—41no—
455C4×C29—41no—
456C4×C29—41no—
457C4×C29—41no—
458C4×C29#56812yes—
459C4×C29#57611yescharacteristic
460C4×C29#57711yescharacteristic
461#544C4×C2911yescharacteristic
462#542—21no—
463#542C4×C2911yescharacteristic
464#542C4×C2911yescharacteristic
465#540—21no—
466#540C4×C2911yescharacteristic
467#540C4×C2911yescharacteristic
468#538—21no—
469#538—21no—
470#537C4×C2911yescharacteristic
471#535C4×C2911yescharacteristic
472#535C4×C2911yescharacteristic
473#532—21no—
474#532C22×C2911yescharacteristic
475#532C22×C2911yescharacteristic
476#529—21no—
477#529C22×C2911yescharacteristic
478#529C22×C2911yescharacteristic
479#525—21no—
480#525—21no—
481C4×#41C22×C2911yescharacteristic
482C4×#41C22×C2911yescharacteristic
483C2×C4×D4C22×C2911yescharacteristic
484#446—21no—
485#446—21no—
486#436—21no—
487#436—21no—
488#435—21no—
489#435—21no—
490#435—21no—
491#435—21no—
492#432C22×C2911yescharacteristic
493#432C22×C2911yescharacteristic, complemented
494#431C22×C2911yescharacteristic
495#431C22×C2911yescharacteristic, complemented
496#431C22×C2911yescharacteristic, complemented
497#431C22×C2911yescharacteristic, complemented
498#423C22×C2911yescharacteristic
499#423C22×C2911yescharacteristic, complemented
500C2×C4⋊C8C22×C2911yescharacteristic, complemented
501C4×M16C22×C2911yescharacteristic
502C4×M16C22×C2911yescharacteristic, complemented
503C2×C4×C8C22×C2911yescharacteristic, complemented
504Q8⋊C8C22×C2911yescharacteristic, complemented
505Q8⋊C8C22×C2911yescharacteristic, complemented
506Q8⋊C8C22×C2911yescharacteristic, complemented
507Q8⋊C8C22×C2911yescharacteristic, complemented
508D4⋊C8C22×C2911yescharacteristic
509D4⋊C8C22×C2911yescharacteristic
510D4⋊C8C22×C2911yescharacteristic
511D4⋊C8C22×C2911yescharacteristic
512D4⋊C8C22×C2911yescharacteristic
513D4⋊C8C22×C2911yescharacteristic
514D4⋊C8C22×C2911yescharacteristic
515D4⋊C8C22×C2911yescharacteristic
516D4⋊C8C22×C2911yescharacteristic, complemented
517D4⋊C8C22×C2911yescharacteristic, complemented
518D4⋊C8C22×C2911yescharacteristic, complemented
519D4⋊C8C22×C2911yescharacteristic, complemented
520C2×C29—41no—
521C2×C29—41no—
522C2×C29—41no—
523C2×C29—81no—
524C2×C29—81no—
525C2×C29—81no—
526C2×C29#287911yescharacteristic
527C2×C29#289711yescharacteristic
528C2×C29#290111yescharacteristic
529C2×#41—21no—
530C2×#41—21no—
531C2×#41C2×C4×C2911yescharacteristic
532C2×#41C2×C4×C2911yescharacteristic
533C22×D4C2×C4×C2911yescharacteristic
534C23×C4—21no—
535C2×M16—21no—
536C2×M16—21no—
537C2×M16—21no—
538C2×M16—21no—
539C22×C8—21no—
540C22×C8—21no—
541C4⋊Q8—21no—
542C4⋊Q8C2×C4×C2911yescharacteristic
543C4⋊Q8C2×C4×C2911yescharacteristic
544#127—21no—
545#127C2×C4×C2911yescharacteristic
546#127C2×C4×C2911yescharacteristic
547#126—21no—
548#126—21no—
549#126—21no—
550#126—21no—
551#125—21no—
552#125C2×C4×C2911yescharacteristic
553#125C2×C4×C2911yescharacteristic
554#124—21no—
555#124—21no—
556#124—21no—
557#124—21no—
558#124—21no—
559#124C2×C4×C2911yescharacteristic
560#124C2×C4×C2911yescharacteristic
561#123—21no—
562#123—21no—
563#123—21no—
564#123—21no—
565#123—21no—
566#123—21no—
567#123—21no—
568#123—21no—
569C22⋊Q8—21no—
570C22⋊Q8—21no—
571C22⋊Q8—21no—
572C22⋊Q8—21no—
573C22⋊Q8—21no—
574C22⋊Q8C2×C4×C2911yescharacteristic
575C22⋊Q8C2×C4×C2911yescharacteristic
576#121—21no—
577#121—21no—
578#121—21no—
579#121—21no—
580#121—21no—
581#121—21no—
582#121—21no—
583#121—21no—
584#121—21no—
585#121—21no—
586#121—21no—
587#121C2×C4×C2911yescharacteristic
588#121C2×C4×C2911yescharacteristic
589#121C2×C4×C2911yescharacteristic
590#121C2×C4×C2911yescharacteristic
591#121C2×C4×C2911yescharacteristic
592#121C2×C4×C2911yescharacteristic
593#120—21no—
594#120—21no—
595#120—21no—
596#120—21no—
597C4×Q8C2×C4×C2911yescharacteristic
598C4×Q8D4×C2911yescharacteristic
599C4×Q8D4×C2911yescharacteristic
600C4×Q8C23×C2911yescharacteristic
601C4×D4—21no—
602C4×D4—21no—
603C4×D4—21no—
604C4×D4—21no—
605C4×D4—21no—
606C4×D4—21no—
607C4×D4—21no—
608C4×D4—21no—
609C4×D4C2×C4×C2911yescharacteristic
610C4×D4C2×C4×C2911yescharacteristic
611C4×D4C2×C4×C2911yescharacteristic
612C4×D4D4×C2911yescharacteristic
613C4×D4D4×C2911yescharacteristic
614C4×D4D4×C2911yescharacteristic
615C4×D4D4×C2911yescharacteristic
616C4×D4D4×C2911yescharacteristic
617C4×D4D4×C2911yescharacteristic
618C4×D4C23×C2911yescharacteristic
619C4×D4C23×C2911yescharacteristic
620C4×D4C23×C2911yescharacteristic
621#117—21no—
622#117—21no—
623#117—21no—
624#117C2×C4×C2911yescharacteristic
625#117C2×C4×C2911yescharacteristic
626#117C2×C4×C2911yescharacteristic
627#117C2×C4×C2911yescharacteristic
628C2×C4⋊C4C2×C4×C2911yescharacteristic
629C2×C22⋊C4—21no—
630C2×C42—21no—
631C2×C42C23×C2911yescharacteristic
632C2×C42C23×C2911yescharacteristic
633C2×C42C23×C2911yescharacteristic
634C4⋊C8—21no—
635C4⋊C8—21no—
636C4⋊C8—21no—
637C4⋊C8—21no—
638C4⋊C8—21no—
639C4⋊C8—21no—
640C4⋊C8C23×C2911yescharacteristic
641C4⋊C8C23×C2911yescharacteristic
642C4⋊C8C23×C2911yescharacteristic
643C4⋊C8C23×C2911yescharacteristic
644C22⋊C8—21no—
645C22⋊C8—21no—
646C22⋊C8—21no—
647C22⋊C8—21no—
648C22⋊C8—21no—
649C22⋊C8—21no—
650#97—21no—
651#97—21no—
652#97—21no—
653#97—21no—
654C4×C8—21no—
655C4×C8—21no—
656C4×C8C23×C2911yescharacteristic
657C4×C8C23×C2911yescharacteristic
658C4×C8C23×C2911yescharacteristic
659C4×C8C23×C2911yescharacteristic
660C29#1750511yescharacteristic, direct product factor, Sylow
661C24—21no—
662#41—42no—
663#41—42no—
664#41—81no—
665#41—81no—
666#41—81no—
667#41—81no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8C22⋊C4×C2911yescharacteristic
671C2×Q8C22×C4×C2911yescharacteristic
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—42no—
685C2×D4C22⋊C4×C2911yescharacteristic
686C2×D4C22⋊C4×C2911yescharacteristic
687C2×D4C22⋊C4×C2911yescharacteristic
688C2×D4C22×C4×C2911yescharacteristic
689C2×D4C22×C4×C2911yescharacteristic
690C2×D4C22×C4×C2911yescharacteristic
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—81no—
700C22×C4—81no—
701C22×C4C22×C4×C2911yescharacteristic
702C22×C4C22×C4×C2911yescharacteristic
703C22×C4C22×C4×C2911yescharacteristic
704C22×C4C2×D4×C2911yescharacteristic
705C22×C4C2×D4×C2911yescharacteristic
706C22×C4C2×D4×C2911yescharacteristic
707C22×C4C2×D4×C2911yescharacteristic
708C22×C4C2×D4×C2911yescharacteristic
709C22×C4C2×D4×C2911yescharacteristic
710M16—42no—
711M16—42no—
712M16—81no—
713M16—81no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—42no—
723C2×C8—81no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4C22⋊C4×C2911yescharacteristic
736C4⋊C4C22⋊C4×C2911yescharacteristic
737C4⋊C4C22⋊C4×C2911yescharacteristic
738C4⋊C4C22⋊C4×C2911yescharacteristic
739C4⋊C4C22⋊C4×C2911yescharacteristic
740C4⋊C4C22⋊C4×C2911yescharacteristic
741C4⋊C4C22×C4×C2911yescharacteristic
742C4⋊C4C22×C4×C2911yescharacteristic
743C4⋊C4C22×C4×C2911yescharacteristic
744C4⋊C4C22×C4×C2911yescharacteristic
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—21no—
763C22⋊C4—21no—
764C22⋊C4C22⋊C4×C2911yescharacteristic
765C22⋊C4C22⋊C4×C2911yescharacteristic
766C22⋊C4C22⋊C4×C2911yescharacteristic
767C22⋊C4C22⋊C4×C2911yescharacteristic
768C22⋊C4C22⋊C4×C2911yescharacteristic
769C22⋊C4C22⋊C4×C2911yescharacteristic
770C42—21no—
771C42—21no—
772C42—21no—
773C42C22×C4×C2911yescharacteristic
774C42C22×C4×C2911yescharacteristic
775C42C22×C4×C2911yescharacteristic
776C42C2×D4×C2911yescharacteristic
777C42C2×D4×C2911yescharacteristic
778C42C2×D4×C2911yescharacteristic
779C42C2×D4×C2911yescharacteristic
780C42C2×D4×C2911yescharacteristic
781C42C2×D4×C2911yescharacteristic
782C42C24×C2911yescharacteristic
783C23—21no—
784C23—21no—
785C23—21no—
786C23—42no—
787C23—81no—
788C23—81no—
789C23C2×C22⋊C4×C2911yescharacteristic
790C23C2×C22⋊C4×C2911yescharacteristic
791C23C2×C22⋊C4×C2911yescharacteristic
792Q8—22no—
793Q8—41no—
794Q8—81no—
795Q8—81no—
796D4—22no—
797D4—22no—
798D4—22no—
799D4—41no—
800D4—41no—
801D4—41no—
802D4—42no—
803D4—42no—
804D4—81no—
805D4—81no—
806D4—81no—
807D4—81no—
808D4—81no—
809D4—81no—
810D4—81no—
811D4—81no—
812D4—81no—
813D4—81no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—42no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—81no—
839C2×C4—81no—
840C2×C4—81no—
841C2×C4—81no—
842C2×C4C2×C22⋊C4×C2911yescharacteristic
843C2×C4C2×C22⋊C4×C2911yescharacteristic
844C2×C4C2×C22⋊C4×C2911yescharacteristic
845C2×C4C2×C22⋊C4×C2911yescharacteristic
846C2×C4C2×C22⋊C4×C2911yescharacteristic
847C2×C4C2×C22⋊C4×C2911yescharacteristic
848C2×C4C2×C22⋊C4×C2911yescharacteristic
849C2×C4C2×C22⋊C4×C2911yescharacteristic
850C2×C4C2×C22⋊C4×C2911yescharacteristic
851C2×C4C23×C4×C2911yescharacteristic
852C2×C4C22×D4×C2911yescharacteristic
853C2×C4C22×D4×C2911yescharacteristic
854C8—22no—
855C8—41no—
856C8—41no—
857C8—41no—
858C8—41no—
859C8—41no—
860C8—41no—
861C8—41no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—21no—
867C22—21no—
868C22—21no—
869C22—21no—
870C22—21no—
871C22—41no—
872C22—41no—
873C22—41no—
874C22—41no—
875C22—41no—
876C22—41no—
877C22—41no—
878C22—41no—
879C22—41no—
880C22—84no—
881C22C22×C22⋊C4×C2911yescharacteristic
882C4—21no—
883C4—21no—
884C4—21no—
885C4—21no—
886C4—21no—
887C4—21no—
888C4—21no—
889C4—21no—
890C4—21no—
891C4—21no—
892C4—41no—
893C4—41no—
894C4—41no—
895C4—41no—
896C4—41no—
897C4C29×#56812yes—
898C4C29×#57611yescharacteristic
899C4C29×#57711yescharacteristic
900C2—41no—
901C2—41no—
902C2—41no—
903C2—81no—
904C2—81no—
905C2—81no—
906C2C29×#287911yescharacteristic
907C2C29×#289711yescharacteristic
908C2C29×#290111yescharacteristic
subgroupG/H
centerC2×C4×C29C22×D4
commutatorC2×C4C23×C4×C29
Frattini, cosocleC42C24×C29
socleC22×C29C22×C22⋊C4
prime radicalC29×#3460C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C29 ◁ C4×#41×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#2989C2semidirect
3. C29×#2965C2semidirect
4. C29×#1496C2semidirect
5. C29×#1495C2semidirect
6. C29×#1494C2semidirect
7. C29×#1492C2semidirect
8. C29×#1490C2semidirect
9. C29×#1489C2semidirect
10. C29×#1488C2semidirect
11. C29×#1486C2semidirect
12. C29×#1484C2semidirect
13. C29×#1483C2semidirect
14. C29×#1482C2semidirect
15. C29×#1480C2semidirect
48. C29×#432C22semidirect
50. C29×#431C22semidirect
51. C29×#431C22semidirect
52. C29×#431C22semidirect
54. C29×#423C22semidirect
55. C2×C29×C4⋊C8C22semidirect
57. C4×M16×C29C22semidirect
58. C2×C4×C8×C29C22semidirect
59. C29×Q8⋊C8C22semidirect
60. C29×Q8⋊C8C22semidirect
61. C29×Q8⋊C8C22semidirect
62. C29×Q8⋊C8C22semidirect
71. C29×D4⋊C8C22semidirect
72. C29×D4⋊C8C22semidirect
73. C29×D4⋊C8C22semidirect
74. C29×D4⋊C8C22semidirect
328. #17505C29direct (N × H)
409. #2989C2×C29semidirect
410. #2965C2×C29semidirect
411. #1496C2×C29semidirect
412. #1495C2×C29semidirect
413. #1494C2×C29semidirect
414. #1492C2×C29semidirect
415. #1490C2×C29semidirect
416. #1489C2×C29semidirect
417. #1488C2×C29semidirect
418. #1486C2×C29semidirect
419. #1484C2×C29semidirect
420. #1483C2×C29semidirect
421. #1482C2×C29semidirect
422. #1480C2×C29semidirect
493. #432C22×C29semidirect
495. #431C22×C29semidirect
496. #431C22×C29semidirect
497. #431C22×C29semidirect
499. #423C22×C29semidirect
500. C2×C4⋊C8C22×C29semidirect
502. C4×M16C22×C29semidirect
503. C2×C4×C8C22×C29semidirect
504. Q8⋊C8C22×C29semidirect
505. Q8⋊C8C22×C29semidirect
506. Q8⋊C8C22×C29semidirect
507. Q8⋊C8C22×C29semidirect
516. D4⋊C8C22×C29semidirect
517. D4⋊C8C22×C29semidirect
518. D4⋊C8C22×C29semidirect
519. D4⋊C8C22×C29semidirect
660. C29#17505direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#34602
C29×#29892
C29×#29652
C29×#14962
C29×#14952
C29×#14942
C29×#14922
C29×#14902
C29×#14892
C29×#14882
C29×#14862
C29×#14842
C29×#14832
C29×#14822
C29×#14802
#1750529