Finite Group Databasebeta

← C29×#17513 #20312413

Subgroups — C29×#17513 #20312413

Order 7424.

958 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3475C211yesmaximal, characteristic
2C29×#2965C211yesmaximal, characteristic, complemented
3C29×#2925C211yesmaximal, characteristic, complemented
4C29×#1497C211yesmaximal, characteristic, complemented
5C29×#1495C211yesmaximal, characteristic, complemented
6C29×#1494C211yesmaximal, characteristic, complemented
7C29×#1490C211yesmaximal, characteristic, complemented
8C29×#1489C211yesmaximal, characteristic, complemented
9C29×#1488C211yesmaximal, characteristic, complemented
10C29×#1485C211yesmaximal, characteristic, complemented
11C29×#1483C211yesmaximal, characteristic, complemented
12C29×#1482C211yesmaximal, characteristic, complemented
13C29×#1478C211yesmaximal, characteristic, complemented
14C29×#1477C211yesmaximal, characteristic, complemented
15C29×#1476C211yesmaximal, characteristic, complemented
16C29×#556C411yescharacteristic
17C29×#555C411yescharacteristic
18C29×#554C411yescharacteristic
19C29×#553—21no—
20C29×#552—21no—
21C29×#552C411yescharacteristic
22C29×#552C411yescharacteristic
23C29×#551—21no—
24C29×#551—21no—
25C29×#547C411yescharacteristic
26C29×#546C411yescharacteristic
27C29×#546C411yescharacteristic
28C29×#533C2211yescharacteristic
29C29×#529—21no—
30C29×#529—21no—
31C29×#529C2211yescharacteristic
32C29×#529C2211yescharacteristic
33C29×#525—21no—
34C4×#41×C29C2211yescharacteristic
35C4×#41×C29C2211yescharacteristic
36C4×#41×C29C2211yescharacteristic
37C2×C4×D4×C29C2211yescharacteristic
38C2×C29×#117—21no—
39C29×#446—21no—
40C29×#436—21no—
41C29×#435—21no—
42C29×#435—21no—
43C29×#433—21no—
44C29×#433—21no—
45C29×#432C2211yescharacteristic
46C29×#432C2211yescharacteristic, complemented
47C29×#431C2211yescharacteristic
48C29×#431C2211yescharacteristic
49C29×#431C2211yescharacteristic, complemented
50C29×#431C2211yescharacteristic, complemented
51C29×#431C2211yescharacteristic, complemented
52C29×#423C2211yescharacteristic, complemented
53C2×C29×C4⋊C8C2211yescharacteristic, complemented
54C29×#408—21no—
55C29×#405—21no—
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×Q8⋊C8C2211yescharacteristic, complemented
64C29×Q8⋊C8C2211yescharacteristic, complemented
65C29×Q8⋊C8C2211yescharacteristic, complemented
66C29×Q8⋊C8C2211yescharacteristic, complemented
67C29×D4⋊C8C2211yescharacteristic
68C29×D4⋊C8C2211yescharacteristic
69C29×D4⋊C8C2211yescharacteristic
70C29×D4⋊C8C2211yescharacteristic
71C29×D4⋊C8C2211yescharacteristic
72C29×D4⋊C8C2211yescharacteristic
73C29×D4⋊C8C2211yescharacteristic
74C29×D4⋊C8C2211yescharacteristic
75C2×#41×C29C2×C411yescharacteristic
76C2×#41×C29C2×C411yescharacteristic
77C2×#41×C29D411yescharacteristic
78C22×D4×C29C2×C411yescharacteristic
79C23×C4×C29—21no—
80C2×M16×C29—21no—
81C2×M16×C29—21no—
82C2×M16×C29—21no—
83C22×C8×C29—21no—
84C22×C8×C29—21no—
85C29×C4⋊Q8C2×C411yescharacteristic
86C29×C4⋊Q8C2×C411yescharacteristic
87C29×#126—21no—
88C29×#126—21no—
89C29×#126—21no—
90C29×#126—21no—
91C29×#126—21no—
92C29×#126—21no—
93C29×#125—21no—
94C29×#125—21no—
95C29×#125—21no—
96C29×#125C2×C411yescharacteristic
97C29×#125C2×C411yescharacteristic
98C29×#124—21no—
99C29×#124—21no—
100C29×#124C2×C411yescharacteristic
101C29×#124C2×C411yescharacteristic
102C29×#123—21no—
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⋊Q8—21no—
113C29×C22⋊Q8—21no—
114C29×C22⋊Q8—21no—
115C29×C22⋊Q8C2×C411yescharacteristic
116C29×C22⋊Q8C2×C411yescharacteristic
117C29×C22⋊Q8C2×C411yescharacteristic
118C29×C22⋊Q8C2×C411yescharacteristic
119C29×#121—21no—
120C29×#121—21no—
121C29×#121—21no—
122C29×#121—21no—
123C29×#121C2×C411yescharacteristic
124C29×#121C2×C411yescharacteristic
125C29×#120—21no—
126C29×#120—21no—
127C4×Q8×C29—21no—
128C4×Q8×C29C2×C411yescharacteristic
129C4×Q8×C29C2×C411yescharacteristic
130C4×Q8×C29C2×C411yescharacteristic
131C4×Q8×C29D411yescharacteristic
132C4×Q8×C29C2311yescharacteristic
133C4×Q8×C29C2311yescharacteristic
134C4×D4×C29—21no—
135C4×D4×C29—21no—
136C4×D4×C29—21no—
137C4×D4×C29—21no—
138C4×D4×C29—21no—
139C4×D4×C29—21no—
140C4×D4×C29—21no—
141C4×D4×C29—21no—
142C4×D4×C29C2×C411yescharacteristic
143C4×D4×C29C2×C411yescharacteristic
144C4×D4×C29C2×C411yescharacteristic
145C4×D4×C29C2×C411yescharacteristic
146C4×D4×C29C2×C411yescharacteristic
147C4×D4×C29C2×C411yescharacteristic
148C4×D4×C29C2×C411yescharacteristic
149C4×D4×C29D411yescharacteristic
150C4×D4×C29D411yescharacteristic
151C4×D4×C29D411yescharacteristic
152C4×D4×C29C2311yescharacteristic
153C4×D4×C29C2311yescharacteristic
154C29×#117—21no—
155C29×#117—21no—
156C29×#117—21no—
157C29×#117—21no—
158C29×#117—21no—
159C29×#117—21no—
160C29×#117—21no—
161C29×#117—21no—
162C29×#117—21no—
163C29×#117C2×C411yescharacteristic
164C29×#117C2×C411yescharacteristic
165C29×#117D411yescharacteristic
166C29×#117D411yescharacteristic
167C29×#117D411yescharacteristic
168C2×C4⋊C4×C29—21no—
169C2×C4⋊C4×C29—21no—
170C2×C4⋊C4×C29C2×C411yescharacteristic
171C2×C22⋊C4×C29—21no—
172C2×C22⋊C4×C29—21no—
173C2×C22⋊C4×C29—21no—
174C2×C42×C29—21no—
175C2×C42×C29—21no—
176C2×C42×C29C2311yescharacteristic
177C2×C42×C29C2311yescharacteristic
178C2×C42×C29C2311yescharacteristic
179C29×C4⋊C8—21no—
180C29×C4⋊C8—21no—
181C29×C4⋊C8—21no—
182C29×C4⋊C8—21no—
183C29×C4⋊C8—21no—
184C29×C4⋊C8C2311yescharacteristic
185C29×C4⋊C8C2311yescharacteristic
186C29×C4⋊C8C2311yescharacteristic
187C29×C4⋊C8C2311yescharacteristic
188C29×C22⋊C8—21no—
189C29×C22⋊C8—21no—
190C29×C22⋊C8—21no—
191C29×C22⋊C8—21no—
192C29×C22⋊C8—21no—
193C29×C22⋊C8—21no—
194C29×C22⋊C8—21no—
195C29×#97—21no—
196C29×#97—21no—
197C29×#97—21no—
198C29×#97—21no—
199C4×C8×C29—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—22no—
208#41×C29—22no—
209#41×C29—41no—
210#41×C29—41no—
211#41×C29—41no—
212#41×C29—41no—
213C2×Q8×C29—21no—
214C2×Q8×C29C22⋊C411yescharacteristic
215C2×Q8×C29C22×C411yescharacteristic
216C2×Q8×C29C22×C411yescharacteristic
217C2×D4×C29—22no—
218C2×D4×C29—21no—
219C2×D4×C29—21no—
220C2×D4×C29—21no—
221C2×D4×C29—21no—
222C2×D4×C29—21no—
223C2×D4×C29—41no—
224C2×D4×C29C22⋊C411yescharacteristic
225C2×D4×C29C22⋊C411yescharacteristic
226C2×D4×C29C22⋊C411yescharacteristic
227C2×D4×C29C22×C411yescharacteristic
228C2×D4×C29C22×C411yescharacteristic
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—42no—
239C22×C4×C29—42no—
240C22×C4×C29C22×C411yescharacteristic
241C22×C4×C29C22×C411yescharacteristic
242C22×C4×C29C22×C411yescharacteristic
243C22×C4×C29C2×D411yescharacteristic
244C22×C4×C29C2×D411yescharacteristic
245C22×C4×C29C2×D411yescharacteristic
246C22×C4×C29C2×D411yescharacteristic
247C22×C4×C29C2×D411yescharacteristic
248C22×C4×C29C2×D411yescharacteristic
249M16×C29—42no—
250M16×C29—42no—
251M16×C29—42no—
252C2×C8×C29—21no—
253C2×C8×C29—21no—
254C2×C8×C29—21no—
255C2×C8×C29—21no—
256C2×C8×C29—21no—
257C2×C8×C29—21no—
258C2×C8×C29—21no—
259C2×C8×C29—21no—
260C2×C8×C29—42no—
261C2×C8×C29—42no—
262C4⋊C4×C29—21no—
263C4⋊C4×C29—21no—
264C4⋊C4×C29—21no—
265C4⋊C4×C29—21no—
266C4⋊C4×C29—21no—
267C4⋊C4×C29—21no—
268C4⋊C4×C29—21no—
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×C29C22⋊C411yescharacteristic
279C4⋊C4×C29C22⋊C411yescharacteristic
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
288C22⋊C4×C29—21no—
289C22⋊C4×C29—21no—
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×C29C22⋊C411yescharacteristic
307C22⋊C4×C29C22⋊C411yescharacteristic
308C22⋊C4×C29C22⋊C411yescharacteristic
309C22⋊C4×C29C22⋊C411yescharacteristic
310C22⋊C4×C29C22⋊C411yescharacteristic
311C22⋊C4×C29C22⋊C411yescharacteristic
312C42×C29—21no—
313C42×C29—21no—
314C42×C29—21no—
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#17513C2911yesmaximal, characteristic, direct product factor, Sylow
329C23×C29—21no—
330C23×C29—21no—
331C23×C29—42no—
332C23×C29—42no—
333C23×C29—81no—
334C23×C29C2×C22⋊C411yescharacteristic
335C23×C29C2×C22⋊C411yescharacteristic
336C23×C29C2×C22⋊C411yescharacteristic
337Q8×C29—21no—
338Q8×C29—21no—
339Q8×C29—21no—
340Q8×C29—21no—
341Q8×C29—41no—
342Q8×C29—81no—
343D4×C29—21no—
344D4×C29—21no—
345D4×C29—21no—
346D4×C29—41no—
347D4×C29—41no—
348D4×C29—41no—
349D4×C29—42no—
350D4×C29—42no—
351D4×C29—42no—
352D4×C29—81no—
353D4×C29—81no—
354D4×C29#13112yes—
355C2×C4×C29—21no—
356C2×C4×C29—21no—
357C2×C4×C29—21no—
358C2×C4×C29—21no—
359C2×C4×C29—21no—
360C2×C4×C29—21no—
361C2×C4×C29—21no—
362C2×C4×C29—21no—
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—41no—
374C2×C4×C29—41no—
375C2×C4×C29—41no—
376C2×C4×C29—42no—
377C2×C4×C29—42no—
378C2×C4×C29—42no—
379C2×C4×C29—42no—
380C2×C4×C29—42no—
381C2×C4×C29—41no—
382C2×C4×C29—41no—
383C2×C4×C29—41no—
384C2×C4×C29—41no—
385C2×C4×C29—81no—
386C2×C4×C29—81no—
387C2×C4×C29C2×C22⋊C411yescharacteristic
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×C29C23×C411yescharacteristic
397C2×C4×C29C22×D411yescharacteristic
398C2×C4×C29C22×D411yescharacteristic
399C8×C29—22no—
400C8×C29—41no—
401C8×C29—41no—
402C8×C29—41no—
403C8×C29—41no—
404C8×C29—41no—
405C8×C29—41no—
406C8×C29—41no—
407#3475C2×C2911yescharacteristic
408#2965C2×C2911yescharacteristic, complemented
409#2925C2×C2911yescharacteristic, complemented
410#1497C2×C2911yescharacteristic, complemented
411#1495C2×C2911yescharacteristic, complemented
412#1494C2×C2911yescharacteristic, complemented
413#1490C2×C2911yescharacteristic, complemented
414#1489C2×C2911yescharacteristic, complemented
415#1488C2×C2911yescharacteristic, complemented
416#1485C2×C2911yescharacteristic, complemented
417#1483C2×C2911yescharacteristic, complemented
418#1482C2×C2911yescharacteristic, complemented
419#1478C2×C2911yescharacteristic, complemented
420#1477C2×C2911yescharacteristic, complemented
421#1476C2×C2911yescharacteristic, complemented
422C22×C29—21no—
423C22×C29—21no—
424C22×C29—21no—
425C22×C29—22no—
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—84no—
438C22×C29C22×C22⋊C411yescharacteristic
439C4×C29—21no—
440C4×C29—21no—
441C4×C29—21no—
442C4×C29—21no—
443C4×C29—21no—
444C4×C29—21no—
445C4×C29—21no—
446C4×C29—21no—
447C4×C29—21no—
448C4×C29—21no—
449C4×C29—41no—
450C4×C29—41no—
451C4×C29—41no—
452C4×C29—41no—
453C4×C29—41no—
454C4×C29—41no—
455C4×C29C2×#13111yescharacteristic
456C4×C29#56811yescharacteristic
457C4×C29#57511yescharacteristic
458C4×C29#57511yescharacteristic
459#556C4×C2911yescharacteristic
460#555C4×C2911yescharacteristic
461#554C4×C2911yescharacteristic
462#553—21no—
463#552—21no—
464#552C4×C2911yescharacteristic
465#552C4×C2911yescharacteristic
466#551—21no—
467#551—21no—
468#547C4×C2911yescharacteristic
469#546C4×C2911yescharacteristic
470#546C4×C2911yescharacteristic
471#533C22×C2911yescharacteristic
472#529—21no—
473#529—21no—
474#529C22×C2911yescharacteristic
475#529C22×C2911yescharacteristic
476#525—21no—
477C4×#41C22×C2911yescharacteristic
478C4×#41C22×C2911yescharacteristic
479C4×#41C22×C2911yescharacteristic
480C2×C4×D4C22×C2911yescharacteristic
481C2×#117—21no—
482#446—21no—
483#436—21no—
484#435—21no—
485#435—21no—
486#433—21no—
487#433—21no—
488#432C22×C2911yescharacteristic
489#432C22×C2911yescharacteristic, complemented
490#431C22×C2911yescharacteristic
491#431C22×C2911yescharacteristic
492#431C22×C2911yescharacteristic, complemented
493#431C22×C2911yescharacteristic, complemented
494#431C22×C2911yescharacteristic, complemented
495#423C22×C2911yescharacteristic, complemented
496C2×C4⋊C8C22×C2911yescharacteristic, complemented
497#408—21no—
498#405—21no—
499C4×M16C22×C2911yescharacteristic
500C4×M16C22×C2911yescharacteristic, complemented
501C2×C4×C8C22×C2911yescharacteristic, complemented
502Q8⋊C8C22×C2911yescharacteristic, complemented
503Q8⋊C8C22×C2911yescharacteristic, complemented
504Q8⋊C8C22×C2911yescharacteristic, complemented
505Q8⋊C8C22×C2911yescharacteristic, complemented
506Q8⋊C8C22×C2911yescharacteristic, complemented
507Q8⋊C8C22×C2911yescharacteristic, complemented
508Q8⋊C8C22×C2911yescharacteristic, complemented
509Q8⋊C8C22×C2911yescharacteristic, complemented
510D4⋊C8C22×C2911yescharacteristic
511D4⋊C8C22×C2911yescharacteristic
512D4⋊C8C22×C2911yescharacteristic
513D4⋊C8C22×C2911yescharacteristic
514D4⋊C8C22×C2911yescharacteristic
515D4⋊C8C22×C2911yescharacteristic
516D4⋊C8C22×C2911yescharacteristic
517D4⋊C8C22×C2911yescharacteristic
518C2×C29—41no—
519C2×C29—41no—
520C2×C29—41no—
521C2×C29—42no—
522C2×C29—81no—
523C2×C29#288011yescharacteristic
524C2×C29#289611yescharacteristic
525C2×C29#290111yescharacteristic
526C2×#41C2×C4×C2911yescharacteristic
527C2×#41C2×C4×C2911yescharacteristic
528C2×#41D4×C2911yescharacteristic
529C22×D4C2×C4×C2911yescharacteristic
530C23×C4—21no—
531C2×M16—21no—
532C2×M16—21no—
533C2×M16—21no—
534C22×C8—21no—
535C22×C8—21no—
536C4⋊Q8C2×C4×C2911yescharacteristic
537C4⋊Q8C2×C4×C2911yescharacteristic
538#126—21no—
539#126—21no—
540#126—21no—
541#126—21no—
542#126—21no—
543#126—21no—
544#125—21no—
545#125—21no—
546#125—21no—
547#125C2×C4×C2911yescharacteristic
548#125C2×C4×C2911yescharacteristic
549#124—21no—
550#124—21no—
551#124C2×C4×C2911yescharacteristic
552#124C2×C4×C2911yescharacteristic
553#123—21no—
554#123—21no—
555#123—21no—
556#123—21no—
557#123—21no—
558#123—21no—
559#123—21no—
560#123—21no—
561C22⋊Q8—21no—
562C22⋊Q8—21no—
563C22⋊Q8—21no—
564C22⋊Q8—21no—
565C22⋊Q8—21no—
566C22⋊Q8C2×C4×C2911yescharacteristic
567C22⋊Q8C2×C4×C2911yescharacteristic
568C22⋊Q8C2×C4×C2911yescharacteristic
569C22⋊Q8C2×C4×C2911yescharacteristic
570#121—21no—
571#121—21no—
572#121—21no—
573#121—21no—
574#121C2×C4×C2911yescharacteristic
575#121C2×C4×C2911yescharacteristic
576#120—21no—
577#120—21no—
578C4×Q8—21no—
579C4×Q8C2×C4×C2911yescharacteristic
580C4×Q8C2×C4×C2911yescharacteristic
581C4×Q8C2×C4×C2911yescharacteristic
582C4×Q8D4×C2911yescharacteristic
583C4×Q8C23×C2911yescharacteristic
584C4×Q8C23×C2911yescharacteristic
585C4×D4—21no—
586C4×D4—21no—
587C4×D4—21no—
588C4×D4—21no—
589C4×D4—21no—
590C4×D4—21no—
591C4×D4—21no—
592C4×D4—21no—
593C4×D4C2×C4×C2911yescharacteristic
594C4×D4C2×C4×C2911yescharacteristic
595C4×D4C2×C4×C2911yescharacteristic
596C4×D4C2×C4×C2911yescharacteristic
597C4×D4C2×C4×C2911yescharacteristic
598C4×D4C2×C4×C2911yescharacteristic
599C4×D4C2×C4×C2911yescharacteristic
600C4×D4D4×C2911yescharacteristic
601C4×D4D4×C2911yescharacteristic
602C4×D4D4×C2911yescharacteristic
603C4×D4C23×C2911yescharacteristic
604C4×D4C23×C2911yescharacteristic
605#117—21no—
606#117—21no—
607#117—21no—
608#117—21no—
609#117—21no—
610#117—21no—
611#117—21no—
612#117—21no—
613#117—21no—
614#117C2×C4×C2911yescharacteristic
615#117C2×C4×C2911yescharacteristic
616#117D4×C2911yescharacteristic
617#117D4×C2911yescharacteristic
618#117D4×C2911yescharacteristic
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4C2×C4×C2911yescharacteristic
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C42—21no—
626C2×C42—21no—
627C2×C42C23×C2911yescharacteristic
628C2×C42C23×C2911yescharacteristic
629C2×C42C23×C2911yescharacteristic
630C4⋊C8—21no—
631C4⋊C8—21no—
632C4⋊C8—21no—
633C4⋊C8—21no—
634C4⋊C8—21no—
635C4⋊C8C23×C2911yescharacteristic
636C4⋊C8C23×C2911yescharacteristic
637C4⋊C8C23×C2911yescharacteristic
638C4⋊C8C23×C2911yescharacteristic
639C22⋊C8—21no—
640C22⋊C8—21no—
641C22⋊C8—21no—
642C22⋊C8—21no—
643C22⋊C8—21no—
644C22⋊C8—21no—
645C22⋊C8—21no—
646#97—21no—
647#97—21no—
648#97—21no—
649#97—21no—
650C4×C8—21no—
651C4×C8—21no—
652C4×C8—21no—
653C4×C8C23×C2911yescharacteristic
654C4×C8C23×C2911yescharacteristic
655C4×C8C23×C2911yescharacteristic
656C4×C8C23×C2911yescharacteristic
657C29#1751311yescharacteristic, direct product factor, Sylow
658C24—21no—
659#41—22no—
660#41—22no—
661#41—41no—
662#41—41no—
663#41—41no—
664#41—41no—
665C2×Q8—21no—
666C2×Q8C22⋊C4×C2911yescharacteristic
667C2×Q8C22×C4×C2911yescharacteristic
668C2×Q8C22×C4×C2911yescharacteristic
669C2×D4—22no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—41no—
676C2×D4C22⋊C4×C2911yescharacteristic
677C2×D4C22⋊C4×C2911yescharacteristic
678C2×D4C22⋊C4×C2911yescharacteristic
679C2×D4C22×C4×C2911yescharacteristic
680C2×D4C22×C4×C2911yescharacteristic
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4C22×C4×C2911yescharacteristic
693C22×C4C22×C4×C2911yescharacteristic
694C22×C4C22×C4×C2911yescharacteristic
695C22×C4C2×D4×C2911yescharacteristic
696C22×C4C2×D4×C2911yescharacteristic
697C22×C4C2×D4×C2911yescharacteristic
698C22×C4C2×D4×C2911yescharacteristic
699C22×C4C2×D4×C2911yescharacteristic
700C22×C4C2×D4×C2911yescharacteristic
701M16—42no—
702M16—42no—
703M16—42no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—42no—
713C2×C8—42no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4C22⋊C4×C2911yescharacteristic
731C4⋊C4C22⋊C4×C2911yescharacteristic
732C4⋊C4C22⋊C4×C2911yescharacteristic
733C4⋊C4C22⋊C4×C2911yescharacteristic
734C4⋊C4C22⋊C4×C2911yescharacteristic
735C4⋊C4C22⋊C4×C2911yescharacteristic
736C4⋊C4C22×C4×C2911yescharacteristic
737C4⋊C4C22×C4×C2911yescharacteristic
738C4⋊C4C22×C4×C2911yescharacteristic
739C4⋊C4C22×C4×C2911yescharacteristic
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—21no—
757C22⋊C4—21no—
758C22⋊C4C22⋊C4×C2911yescharacteristic
759C22⋊C4C22⋊C4×C2911yescharacteristic
760C22⋊C4C22⋊C4×C2911yescharacteristic
761C22⋊C4C22⋊C4×C2911yescharacteristic
762C22⋊C4C22⋊C4×C2911yescharacteristic
763C22⋊C4C22⋊C4×C2911yescharacteristic
764C42—21no—
765C42—21no—
766C42—21no—
767C42—21no—
768C42—21no—
769C42—21no—
770C42C22×C4×C2911yescharacteristic
771C42C22×C4×C2911yescharacteristic
772C42C22×C4×C2911yescharacteristic
773C42C2×D4×C2911yescharacteristic
774C42C2×D4×C2911yescharacteristic
775C42C2×D4×C2911yescharacteristic
776C42C2×D4×C2911yescharacteristic
777C42C2×D4×C2911yescharacteristic
778C42C2×D4×C2911yescharacteristic
779C42C24×C2911yescharacteristic
780C23—21no—
781C23—21no—
782C23—42no—
783C23—42no—
784C23—81no—
785C23C2×C22⋊C4×C2911yescharacteristic
786C23C2×C22⋊C4×C2911yescharacteristic
787C23C2×C22⋊C4×C2911yescharacteristic
788Q8—21no—
789Q8—21no—
790Q8—21no—
791Q8—21no—
792Q8—41no—
793Q8—81no—
794D4—21no—
795D4—21no—
796D4—21no—
797D4—41no—
798D4—41no—
799D4—41no—
800D4—42no—
801D4—42no—
802D4—42no—
803D4—81no—
804D4—81no—
805D4C29×#13112yes—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—81no—
837C2×C4—81no—
838C2×C4C2×C22⋊C4×C2911yescharacteristic
839C2×C4C2×C22⋊C4×C2911yescharacteristic
840C2×C4C2×C22⋊C4×C2911yescharacteristic
841C2×C4C2×C22⋊C4×C2911yescharacteristic
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×C4C23×C4×C2911yescharacteristic
848C2×C4C22×D4×C2911yescharacteristic
849C2×C4C22×D4×C2911yescharacteristic
850C8—22no—
851C8—41no—
852C8—41no—
853C8—41no—
854C8—41no—
855C8—41no—
856C8—41no—
857C8—41no—
858C22—21no—
859C22—21no—
860C22—21no—
861C22—22no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—21no—
867C22—21no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—41no—
872C22—41no—
873C22—84no—
874C22C22×C22⋊C4×C2911yescharacteristic
875C4—21no—
876C4—21no—
877C4—21no—
878C4—21no—
879C4—21no—
880C4—21no—
881C4—21no—
882C4—21no—
883C4—21no—
884C4—21no—
885C4—41no—
886C4—41no—
887C4—41no—
888C4—41no—
889C4—41no—
890C4—41no—
891C4C2×C29×#13111yescharacteristic
892C4C29×#56811yescharacteristic
893C4C29×#57511yescharacteristic
894C4C29×#57511yescharacteristic
895C2—41no—
896C2—41no—
897C2—41no—
898C2—42no—
899C2—81no—
900C2C29×#288011yescharacteristic
901C2C29×#289611yescharacteristic
902C2C29×#290111yescharacteristic
subgroupG/H
centerC2×C4×C29C22×D4
commutatorC2×C4C23×C4×C29
Frattini, cosocleC42C24×C29
socleC22×C29C22×C22⋊C4
prime radicalC29×#3475C2
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×#2965C2semidirect
3. C29×#2925C2semidirect
4. C29×#1497C2semidirect
5. C29×#1495C2semidirect
6. C29×#1494C2semidirect
7. C29×#1490C2semidirect
8. C29×#1489C2semidirect
9. C29×#1488C2semidirect
10. C29×#1485C2semidirect
11. C29×#1483C2semidirect
12. C29×#1482C2semidirect
13. C29×#1478C2semidirect
14. C29×#1477C2semidirect
15. C29×#1476C2semidirect
46. C29×#432C22semidirect
49. C29×#431C22semidirect
50. C29×#431C22semidirect
51. C29×#431C22semidirect
52. C29×#423C22semidirect
53. 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
63. C29×Q8⋊C8C22semidirect
64. C29×Q8⋊C8C22semidirect
65. C29×Q8⋊C8C22semidirect
66. C29×Q8⋊C8C22semidirect
328. #17513C29direct (N × H)
408. #2965C2×C29semidirect
409. #2925C2×C29semidirect
410. #1497C2×C29semidirect
411. #1495C2×C29semidirect
412. #1494C2×C29semidirect
413. #1490C2×C29semidirect
414. #1489C2×C29semidirect
415. #1488C2×C29semidirect
416. #1485C2×C29semidirect
417. #1483C2×C29semidirect
418. #1482C2×C29semidirect
419. #1478C2×C29semidirect
420. #1477C2×C29semidirect
421. #1476C2×C29semidirect
489. #432C22×C29semidirect
492. #431C22×C29semidirect
493. #431C22×C29semidirect
494. #431C22×C29semidirect
495. #423C22×C29semidirect
496. C2×C4⋊C8C22×C29semidirect
500. C4×M16C22×C29semidirect
501. C2×C4×C8C22×C29semidirect
502. Q8⋊C8C22×C29semidirect
503. Q8⋊C8C22×C29semidirect
504. Q8⋊C8C22×C29semidirect
505. Q8⋊C8C22×C29semidirect
506. Q8⋊C8C22×C29semidirect
507. Q8⋊C8C22×C29semidirect
508. Q8⋊C8C22×C29semidirect
509. Q8⋊C8C22×C29semidirect
657. C29#17513direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#34752
C29×#29652
C29×#29252
C29×#14972
C29×#14952
C29×#14942
C29×#14902
C29×#14892
C29×#14882
C29×#14852
C29×#14832
C29×#14822
C29×#14782
C29×#14772
C29×#14762
#1751329