Finite Group Databasebeta

← C29×#17506 #20312406

Subgroups — C29×#17506 #20312406

Order 7424.

890 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3461C211yesmaximal, characteristic
2C29×#2989C211yesmaximal, characteristic, complemented
3C29×#2965C211yesmaximal, characteristic, complemented
4C29×#1497C211yesmaximal, characteristic, complemented
5C29×#1495C211yesmaximal, characteristic, complemented
6C29×#1494C211yesmaximal, characteristic, complemented
7C29×#1493C211yesmaximal, characteristic, complemented
8C29×#1491C211yesmaximal, characteristic, complemented
9C29×#1489C211yesmaximal, characteristic, complemented
10C29×#1488C211yesmaximal, characteristic, complemented
11C29×#1487C211yesmaximal, characteristic, complemented
12C29×#1485C211yesmaximal, characteristic, complemented
13C29×#1483C211yesmaximal, characteristic, complemented
14C29×#1482C211yesmaximal, characteristic, complemented
15C29×#1481C211yesmaximal, characteristic, complemented
16C29×#544C411yescharacteristic
17C29×#542—21no—
18C29×#542C411yescharacteristic
19C29×#542C411yescharacteristic
20C29×#541—21no—
21C29×#541C411yescharacteristic
22C29×#541C411yescharacteristic
23C29×#539—21no—
24C29×#539—21no—
25C29×#537C411yescharacteristic
26C29×#536C411yescharacteristic
27C29×#536C411yescharacteristic
28C29×#533—21no—
29C29×#533C2211yescharacteristic
30C29×#533C2211yescharacteristic
31C29×#529—21no—
32C29×#529—21no—
33C29×#529—21no—
34C29×#529C2211yescharacteristic
35C29×#529C2211yescharacteristic
36C4×#41×C29C2211yescharacteristic
37C4×#41×C29C2211yescharacteristic
38C2×C4×Q8×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
49C29×#431C2211yescharacteristic
50C29×#431C2211yescharacteristic
51C29×#431C2211yescharacteristic
52C29×#431C2211yescharacteristic
53C29×#423C2211yescharacteristic
54C29×#423C2211yescharacteristic
55C2×C29×C4⋊C8C2211yescharacteristic
56C4×M16×C29C2211yescharacteristic
57C4×M16×C29C2211yescharacteristic
58C2×C4×C8×C29C2211yescharacteristic
59C29×Q8⋊C8C2211yescharacteristic
60C29×Q8⋊C8C2211yescharacteristic
61C29×Q8⋊C8C2211yescharacteristic
62C29×Q8⋊C8C2211yescharacteristic
63C29×Q8⋊C8C2211yescharacteristic
64C29×Q8⋊C8C2211yescharacteristic
65C29×Q8⋊C8C2211yescharacteristic
66C29×Q8⋊C8C2211yescharacteristic
67C29×Q8⋊C8C2211yescharacteristic
68C29×Q8⋊C8C2211yescharacteristic
69C29×Q8⋊C8C2211yescharacteristic
70C29×Q8⋊C8C2211yescharacteristic
71C29×D4⋊C8C2211yescharacteristic
72C29×D4⋊C8C2211yescharacteristic
73C29×D4⋊C8C2211yescharacteristic
74C29×D4⋊C8C2211yescharacteristic
75C2×#41×C29C2×C411yescharacteristic
76C2×#41×C29C2×C411yescharacteristic
77C22×Q8×C29C2×C411yescharacteristic
78C2×M16×C29—21no—
79C2×M16×C29—21no—
80C2×M16×C29—21no—
81C2×M16×C29—21no—
82C22×C8×C29—21no—
83C22×C8×C29—21no—
84C29×C4⋊Q8—21no—
85C29×C4⋊Q8—21no—
86C29×C4⋊Q8C2×C411yescharacteristic
87C29×C4⋊Q8C2×C411yescharacteristic
88C29×C4⋊Q8C2×C411yescharacteristic
89C29×C4⋊Q8C2×C411yescharacteristic
90C29×#126—21no—
91C29×#126—21no—
92C29×#126—21no—
93C29×#126—21no—
94C29×#126—21no—
95C29×#126—21no—
96C29×#126—21no—
97C29×#126—21no—
98C29×#125—21no—
99C29×#125—21no—
100C29×#125—21no—
101C29×#125—21no—
102C29×#125—21no—
103C29×#125—21no—
104C29×#125—21no—
105C29×#125C2×C411yescharacteristic
106C29×#125C2×C411yescharacteristic
107C29×#124—21no—
108C29×#124—21no—
109C29×#124—21no—
110C29×#124C2×C411yescharacteristic
111C29×#124C2×C411yescharacteristic
112C29×#123—21no—
113C29×#123—21no—
114C29×#123—21no—
115C29×#123—21no—
116C29×#123—21no—
117C29×#123—21no—
118C29×#123—21no—
119C29×#123—21no—
120C29×C22⋊Q8—21no—
121C29×C22⋊Q8—21no—
122C29×C22⋊Q8—21no—
123C29×C22⋊Q8—21no—
124C29×C22⋊Q8—21no—
125C29×C22⋊Q8—21no—
126C29×C22⋊Q8—21no—
127C29×C22⋊Q8—21no—
128C29×C22⋊Q8—21no—
129C29×C22⋊Q8C2×C411yescharacteristic
130C29×C22⋊Q8C2×C411yescharacteristic
131C29×C22⋊Q8C2×C411yescharacteristic
132C29×C22⋊Q8C2×C411yescharacteristic
133C29×C22⋊Q8C2×C411yescharacteristic
134C29×C22⋊Q8C2×C411yescharacteristic
135C29×#121—21no—
136C29×#121—21no—
137C29×#121—21no—
138C29×#121C2×C411yescharacteristic
139C29×#121C2×C411yescharacteristic
140C4×Q8×C29—21no—
141C4×Q8×C29—21no—
142C4×Q8×C29—21no—
143C4×Q8×C29—21no—
144C4×Q8×C29C2×C411yescharacteristic
145C4×Q8×C29C2×C411yescharacteristic
146C4×Q8×C29C2×C411yescharacteristic
147C4×Q8×C29D411yescharacteristic
148C4×Q8×C29D411yescharacteristic
149C4×Q8×C29C2311yescharacteristic
150C4×Q8×C29C2311yescharacteristic
151C4×Q8×C29C2311yescharacteristic
152C4×D4×C29—21no—
153C4×D4×C29—21no—
154C4×D4×C29—21no—
155C4×D4×C29—21no—
156C4×D4×C29C2×C411yescharacteristic
157C4×D4×C29D411yescharacteristic
158C4×D4×C29D411yescharacteristic
159C4×D4×C29D411yescharacteristic
160C4×D4×C29D411yescharacteristic
161C4×D4×C29D411yescharacteristic
162C4×D4×C29D411yescharacteristic
163C4×D4×C29C2311yescharacteristic
164C29×#117—21no—
165C29×#117—21no—
166C29×#117—21no—
167C29×#117—21no—
168C29×#117—21no—
169C29×#117C2×C411yescharacteristic
170C29×#117C2×C411yescharacteristic
171C29×#117C2×C411yescharacteristic
172C29×#117C2×C411yescharacteristic
173C2×C4⋊C4×C29—21no—
174C2×C4⋊C4×C29C2×C411yescharacteristic
175C2×C42×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
206#41×C29—42no—
207#41×C29—42no—
208C2×Q8×C29—21no—
209C2×Q8×C29—21no—
210C2×Q8×C29—21no—
211C2×Q8×C29—42no—
212C2×Q8×C29C22⋊C411yescharacteristic
213C2×Q8×C29C22×C411yescharacteristic
214C2×Q8×C29C22×C411yescharacteristic
215C2×Q8×C29C22×C411yescharacteristic
216C2×D4×C29—21no—
217C2×D4×C29—21no—
218C2×D4×C29—21no—
219C2×D4×C29C22⋊C411yescharacteristic
220C2×D4×C29C22⋊C411yescharacteristic
221C2×D4×C29C22⋊C411yescharacteristic
222C2×D4×C29C22×C411yescharacteristic
223C22×C4×C29—21no—
224C22×C4×C29—21no—
225C22×C4×C29—21no—
226C22×C4×C29—21no—
227C22×C4×C29—21no—
228C22×C4×C29C22×C411yescharacteristic
229C22×C4×C29C22×C411yescharacteristic
230C22×C4×C29C22×C411yescharacteristic
231C22×C4×C29C2×D411yescharacteristic
232C22×C4×C29C2×D411yescharacteristic
233C22×C4×C29C2×D411yescharacteristic
234C22×C4×C29C2×D411yescharacteristic
235C22×C4×C29C2×D411yescharacteristic
236C22×C4×C29C2×D411yescharacteristic
237M16×C29—42no—
238M16×C29—42no—
239M16×C29—81no—
240M16×C29—81no—
241C2×C8×C29—21no—
242C2×C8×C29—21no—
243C2×C8×C29—21no—
244C2×C8×C29—21no—
245C2×C8×C29—21no—
246C2×C8×C29—21no—
247C2×C8×C29—21no—
248C2×C8×C29—21no—
249C2×C8×C29—42no—
250C2×C8×C29—81no—
251C4⋊C4×C29—21no—
252C4⋊C4×C29—21no—
253C4⋊C4×C29—21no—
254C4⋊C4×C29—21no—
255C4⋊C4×C29—21no—
256C4⋊C4×C29—21no—
257C4⋊C4×C29—21no—
258C4⋊C4×C29—21no—
259C4⋊C4×C29—21no—
260C4⋊C4×C29—21no—
261C4⋊C4×C29—21no—
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×C29C22⋊C411yescharacteristic
275C4⋊C4×C29C22⋊C411yescharacteristic
276C4⋊C4×C29C22⋊C411yescharacteristic
277C4⋊C4×C29C22⋊C411yescharacteristic
278C4⋊C4×C29C22⋊C411yescharacteristic
279C4⋊C4×C29C22⋊C411yescharacteristic
280C4⋊C4×C29C22×C411yescharacteristic
281C4⋊C4×C29C22×C411yescharacteristic
282C4⋊C4×C29C22×C411yescharacteristic
283C4⋊C4×C29C22×C411yescharacteristic
284C22⋊C4×C29—21no—
285C22⋊C4×C29—21no—
286C22⋊C4×C29—21no—
287C22⋊C4×C29—21no—
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×C29C22⋊C411yescharacteristic
300C22⋊C4×C29C22⋊C411yescharacteristic
301C22⋊C4×C29C22⋊C411yescharacteristic
302C22⋊C4×C29C22⋊C411yescharacteristic
303C22⋊C4×C29C22⋊C411yescharacteristic
304C22⋊C4×C29C22⋊C411yescharacteristic
305C42×C29—21no—
306C42×C29—21no—
307C42×C29—21no—
308C42×C29—21no—
309C42×C29—21no—
310C42×C29—21no—
311C42×C29—21no—
312C42×C29C22×C411yescharacteristic
313C42×C29C22×C411yescharacteristic
314C42×C29C22×C411yescharacteristic
315C42×C29C2×D411yescharacteristic
316C42×C29C2×D411yescharacteristic
317C42×C29C2×D411yescharacteristic
318C42×C29C2×D411yescharacteristic
319C42×C29C2×D411yescharacteristic
320C42×C29C2×D411yescharacteristic
321C42×C29C2411yescharacteristic
322#17506C2911yesmaximal, characteristic, direct product factor, Sylow
323C23×C29—21no—
324C23×C29C2×C22⋊C411yescharacteristic
325C23×C29C2×C22⋊C411yescharacteristic
326C23×C29C2×C22⋊C411yescharacteristic
327Q8×C29—22no—
328Q8×C29—22no—
329Q8×C29—22no—
330Q8×C29—41no—
331Q8×C29—42no—
332Q8×C29—81no—
333Q8×C29—81no—
334D4×C29—22no—
335D4×C29—41no—
336D4×C29—41no—
337D4×C29—41no—
338D4×C29—42no—
339D4×C29—81no—
340D4×C29—81no—
341C2×C4×C29—22no—
342C2×C4×C29—22no—
343C2×C4×C29—22no—
344C2×C4×C29—21no—
345C2×C4×C29—21no—
346C2×C4×C29—21no—
347C2×C4×C29—21no—
348C2×C4×C29—21no—
349C2×C4×C29—21no—
350C2×C4×C29—21no—
351C2×C4×C29—21no—
352C2×C4×C29—21no—
353C2×C4×C29—21no—
354C2×C4×C29—21no—
355C2×C4×C29—21no—
356C2×C4×C29—21no—
357C2×C4×C29—41no—
358C2×C4×C29—41no—
359C2×C4×C29—41no—
360C2×C4×C29—42no—
361C2×C4×C29—42no—
362C2×C4×C29—41no—
363C2×C4×C29—41no—
364C2×C4×C29—81no—
365C2×C4×C29—81no—
366C2×C4×C29C2×C22⋊C411yescharacteristic
367C2×C4×C29C2×C22⋊C411yescharacteristic
368C2×C4×C29C2×C22⋊C411yescharacteristic
369C2×C4×C29C2×C22⋊C411yescharacteristic
370C2×C4×C29C2×C22⋊C411yescharacteristic
371C2×C4×C29C2×C22⋊C411yescharacteristic
372C2×C4×C29C2×C22⋊C411yescharacteristic
373C2×C4×C29C2×C22⋊C411yescharacteristic
374C2×C4×C29C2×C22⋊C411yescharacteristic
375C2×C4×C29C23×C411yescharacteristic
376C2×C4×C29C22×D411yescharacteristic
377C2×C4×C29C22×D411yescharacteristic
378C8×C29—22no—
379C8×C29—41no—
380C8×C29—41no—
381C8×C29—41no—
382C8×C29—41no—
383C8×C29—41no—
384C8×C29—41no—
385C8×C29—41no—
386#3461C2×C2911yescharacteristic
387#2989C2×C2911yescharacteristic, complemented
388#2965C2×C2911yescharacteristic, complemented
389#1497C2×C2911yescharacteristic, complemented
390#1495C2×C2911yescharacteristic, complemented
391#1494C2×C2911yescharacteristic, complemented
392#1493C2×C2911yescharacteristic, complemented
393#1491C2×C2911yescharacteristic, complemented
394#1489C2×C2911yescharacteristic, complemented
395#1488C2×C2911yescharacteristic, complemented
396#1487C2×C2911yescharacteristic, complemented
397#1485C2×C2911yescharacteristic, complemented
398#1483C2×C2911yescharacteristic, complemented
399#1482C2×C2911yescharacteristic, complemented
400#1481C2×C2911yescharacteristic, complemented
401C22×C29—21no—
402C22×C29—21no—
403C22×C29—21no—
404C22×C29—21no—
405C22×C29—21no—
406C22×C29—21no—
407C22×C29—21no—
408C22×C29—21no—
409C22×C29—21no—
410C22×C29—41no—
411C22×C29—41no—
412C22×C29—41no—
413C22×C29C22×C22⋊C411yescharacteristic
414C4×C29—21no—
415C4×C29—21no—
416C4×C29—21no—
417C4×C29—21no—
418C4×C29—21no—
419C4×C29—21no—
420C4×C29—21no—
421C4×C29—21no—
422C4×C29—21no—
423C4×C29—21no—
424C4×C29—41no—
425C4×C29—41no—
426C4×C29—41no—
427C4×C29—41no—
428C4×C29—41no—
429C4×C29—41no—
430C4×C29—41no—
431C4×C29#56812yes—
432C4×C29#57711yescharacteristic
433C4×C29#57811yescharacteristic
434#544C4×C2911yescharacteristic
435#542—21no—
436#542C4×C2911yescharacteristic
437#542C4×C2911yescharacteristic
438#541—21no—
439#541C4×C2911yescharacteristic
440#541C4×C2911yescharacteristic
441#539—21no—
442#539—21no—
443#537C4×C2911yescharacteristic
444#536C4×C2911yescharacteristic
445#536C4×C2911yescharacteristic
446#533—21no—
447#533C22×C2911yescharacteristic
448#533C22×C2911yescharacteristic
449#529—21no—
450#529—21no—
451#529—21no—
452#529C22×C2911yescharacteristic
453#529C22×C2911yescharacteristic
454C4×#41C22×C2911yescharacteristic
455C4×#41C22×C2911yescharacteristic
456C2×C4×Q8C22×C2911yescharacteristic
457#446—21no—
458#446—21no—
459#436—21no—
460#436—21no—
461#435—21no—
462#435—21no—
463#435—21no—
464#435—21no—
465#432C22×C2911yescharacteristic
466#432C22×C2911yescharacteristic
467#431C22×C2911yescharacteristic
468#431C22×C2911yescharacteristic
469#431C22×C2911yescharacteristic
470#431C22×C2911yescharacteristic
471#423C22×C2911yescharacteristic
472#423C22×C2911yescharacteristic
473C2×C4⋊C8C22×C2911yescharacteristic
474C4×M16C22×C2911yescharacteristic
475C4×M16C22×C2911yescharacteristic
476C2×C4×C8C22×C2911yescharacteristic
477Q8⋊C8C22×C2911yescharacteristic
478Q8⋊C8C22×C2911yescharacteristic
479Q8⋊C8C22×C2911yescharacteristic
480Q8⋊C8C22×C2911yescharacteristic
481Q8⋊C8C22×C2911yescharacteristic
482Q8⋊C8C22×C2911yescharacteristic
483Q8⋊C8C22×C2911yescharacteristic
484Q8⋊C8C22×C2911yescharacteristic
485Q8⋊C8C22×C2911yescharacteristic
486Q8⋊C8C22×C2911yescharacteristic
487Q8⋊C8C22×C2911yescharacteristic
488Q8⋊C8C22×C2911yescharacteristic
489D4⋊C8C22×C2911yescharacteristic
490D4⋊C8C22×C2911yescharacteristic
491D4⋊C8C22×C2911yescharacteristic
492D4⋊C8C22×C2911yescharacteristic
493C2×C29—41no—
494C2×C29—41no—
495C2×C29—41no—
496C2×C29—81no—
497C2×C29#287911yescharacteristic
498C2×C29#289811yescharacteristic
499C2×C29#290111yescharacteristic
500C2×#41C2×C4×C2911yescharacteristic
501C2×#41C2×C4×C2911yescharacteristic
502C22×Q8C2×C4×C2911yescharacteristic
503C2×M16—21no—
504C2×M16—21no—
505C2×M16—21no—
506C2×M16—21no—
507C22×C8—21no—
508C22×C8—21no—
509C4⋊Q8—21no—
510C4⋊Q8—21no—
511C4⋊Q8C2×C4×C2911yescharacteristic
512C4⋊Q8C2×C4×C2911yescharacteristic
513C4⋊Q8C2×C4×C2911yescharacteristic
514C4⋊Q8C2×C4×C2911yescharacteristic
515#126—21no—
516#126—21no—
517#126—21no—
518#126—21no—
519#126—21no—
520#126—21no—
521#126—21no—
522#126—21no—
523#125—21no—
524#125—21no—
525#125—21no—
526#125—21no—
527#125—21no—
528#125—21no—
529#125—21no—
530#125C2×C4×C2911yescharacteristic
531#125C2×C4×C2911yescharacteristic
532#124—21no—
533#124—21no—
534#124—21no—
535#124C2×C4×C2911yescharacteristic
536#124C2×C4×C2911yescharacteristic
537#123—21no—
538#123—21no—
539#123—21no—
540#123—21no—
541#123—21no—
542#123—21no—
543#123—21no—
544#123—21no—
545C22⋊Q8—21no—
546C22⋊Q8—21no—
547C22⋊Q8—21no—
548C22⋊Q8—21no—
549C22⋊Q8—21no—
550C22⋊Q8—21no—
551C22⋊Q8—21no—
552C22⋊Q8—21no—
553C22⋊Q8—21no—
554C22⋊Q8C2×C4×C2911yescharacteristic
555C22⋊Q8C2×C4×C2911yescharacteristic
556C22⋊Q8C2×C4×C2911yescharacteristic
557C22⋊Q8C2×C4×C2911yescharacteristic
558C22⋊Q8C2×C4×C2911yescharacteristic
559C22⋊Q8C2×C4×C2911yescharacteristic
560#121—21no—
561#121—21no—
562#121—21no—
563#121C2×C4×C2911yescharacteristic
564#121C2×C4×C2911yescharacteristic
565C4×Q8—21no—
566C4×Q8—21no—
567C4×Q8—21no—
568C4×Q8—21no—
569C4×Q8C2×C4×C2911yescharacteristic
570C4×Q8C2×C4×C2911yescharacteristic
571C4×Q8C2×C4×C2911yescharacteristic
572C4×Q8D4×C2911yescharacteristic
573C4×Q8D4×C2911yescharacteristic
574C4×Q8C23×C2911yescharacteristic
575C4×Q8C23×C2911yescharacteristic
576C4×Q8C23×C2911yescharacteristic
577C4×D4—21no—
578C4×D4—21no—
579C4×D4—21no—
580C4×D4—21no—
581C4×D4C2×C4×C2911yescharacteristic
582C4×D4D4×C2911yescharacteristic
583C4×D4D4×C2911yescharacteristic
584C4×D4D4×C2911yescharacteristic
585C4×D4D4×C2911yescharacteristic
586C4×D4D4×C2911yescharacteristic
587C4×D4D4×C2911yescharacteristic
588C4×D4C23×C2911yescharacteristic
589#117—21no—
590#117—21no—
591#117—21no—
592#117—21no—
593#117—21no—
594#117C2×C4×C2911yescharacteristic
595#117C2×C4×C2911yescharacteristic
596#117C2×C4×C2911yescharacteristic
597#117C2×C4×C2911yescharacteristic
598C2×C4⋊C4—21no—
599C2×C4⋊C4C2×C4×C2911yescharacteristic
600C2×C42—21no—
601C2×C42—21no—
602C2×C42C23×C2911yescharacteristic
603C2×C42C23×C2911yescharacteristic
604C2×C42C23×C2911yescharacteristic
605C4⋊C8—21no—
606C4⋊C8—21no—
607C4⋊C8—21no—
608C4⋊C8—21no—
609C4⋊C8—21no—
610C4⋊C8—21no—
611C4⋊C8C23×C2911yescharacteristic
612C4⋊C8C23×C2911yescharacteristic
613C4⋊C8C23×C2911yescharacteristic
614C4⋊C8C23×C2911yescharacteristic
615C22⋊C8—21no—
616C22⋊C8—21no—
617C22⋊C8—21no—
618C22⋊C8—21no—
619C22⋊C8—21no—
620C22⋊C8—21no—
621#97—21no—
622#97—21no—
623#97—21no—
624#97—21no—
625C4×C8—21no—
626C4×C8—21no—
627C4×C8C23×C2911yescharacteristic
628C4×C8C23×C2911yescharacteristic
629C4×C8C23×C2911yescharacteristic
630C4×C8C23×C2911yescharacteristic
631C29#1750611yescharacteristic, direct product factor, Sylow
632#41—42no—
633#41—42no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—42no—
638C2×Q8C22⋊C4×C2911yescharacteristic
639C2×Q8C22×C4×C2911yescharacteristic
640C2×Q8C22×C4×C2911yescharacteristic
641C2×Q8C22×C4×C2911yescharacteristic
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4C22⋊C4×C2911yescharacteristic
646C2×D4C22⋊C4×C2911yescharacteristic
647C2×D4C22⋊C4×C2911yescharacteristic
648C2×D4C22×C4×C2911yescharacteristic
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4C22×C4×C2911yescharacteristic
655C22×C4C22×C4×C2911yescharacteristic
656C22×C4C22×C4×C2911yescharacteristic
657C22×C4C2×D4×C2911yescharacteristic
658C22×C4C2×D4×C2911yescharacteristic
659C22×C4C2×D4×C2911yescharacteristic
660C22×C4C2×D4×C2911yescharacteristic
661C22×C4C2×D4×C2911yescharacteristic
662C22×C4C2×D4×C2911yescharacteristic
663M16—42no—
664M16—42no—
665M16—81no—
666M16—81no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—42no—
676C2×C8—81no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4C22⋊C4×C2911yescharacteristic
701C4⋊C4C22⋊C4×C2911yescharacteristic
702C4⋊C4C22⋊C4×C2911yescharacteristic
703C4⋊C4C22⋊C4×C2911yescharacteristic
704C4⋊C4C22⋊C4×C2911yescharacteristic
705C4⋊C4C22⋊C4×C2911yescharacteristic
706C4⋊C4C22×C4×C2911yescharacteristic
707C4⋊C4C22×C4×C2911yescharacteristic
708C4⋊C4C22×C4×C2911yescharacteristic
709C4⋊C4C22×C4×C2911yescharacteristic
710C22⋊C4—21no—
711C22⋊C4—21no—
712C22⋊C4—21no—
713C22⋊C4—21no—
714C22⋊C4—21no—
715C22⋊C4—21no—
716C22⋊C4—21no—
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—21no—
722C22⋊C4—21no—
723C22⋊C4—21no—
724C22⋊C4—21no—
725C22⋊C4C22⋊C4×C2911yescharacteristic
726C22⋊C4C22⋊C4×C2911yescharacteristic
727C22⋊C4C22⋊C4×C2911yescharacteristic
728C22⋊C4C22⋊C4×C2911yescharacteristic
729C22⋊C4C22⋊C4×C2911yescharacteristic
730C22⋊C4C22⋊C4×C2911yescharacteristic
731C42—21no—
732C42—21no—
733C42—21no—
734C42—21no—
735C42—21no—
736C42—21no—
737C42—21no—
738C42C22×C4×C2911yescharacteristic
739C42C22×C4×C2911yescharacteristic
740C42C22×C4×C2911yescharacteristic
741C42C2×D4×C2911yescharacteristic
742C42C2×D4×C2911yescharacteristic
743C42C2×D4×C2911yescharacteristic
744C42C2×D4×C2911yescharacteristic
745C42C2×D4×C2911yescharacteristic
746C42C2×D4×C2911yescharacteristic
747C42C24×C2911yescharacteristic
748C23—21no—
749C23C2×C22⋊C4×C2911yescharacteristic
750C23C2×C22⋊C4×C2911yescharacteristic
751C23C2×C22⋊C4×C2911yescharacteristic
752Q8—22no—
753Q8—22no—
754Q8—22no—
755Q8—41no—
756Q8—42no—
757Q8—81no—
758Q8—81no—
759D4—22no—
760D4—41no—
761D4—41no—
762D4—41no—
763D4—42no—
764D4—81no—
765D4—81no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—81no—
790C2×C4—81no—
791C2×C4C2×C22⋊C4×C2911yescharacteristic
792C2×C4C2×C22⋊C4×C2911yescharacteristic
793C2×C4C2×C22⋊C4×C2911yescharacteristic
794C2×C4C2×C22⋊C4×C2911yescharacteristic
795C2×C4C2×C22⋊C4×C2911yescharacteristic
796C2×C4C2×C22⋊C4×C2911yescharacteristic
797C2×C4C2×C22⋊C4×C2911yescharacteristic
798C2×C4C2×C22⋊C4×C2911yescharacteristic
799C2×C4C2×C22⋊C4×C2911yescharacteristic
800C2×C4C23×C4×C2911yescharacteristic
801C2×C4C22×D4×C2911yescharacteristic
802C2×C4C22×D4×C2911yescharacteristic
803C8—22no—
804C8—41no—
805C8—41no—
806C8—41no—
807C8—41no—
808C8—41no—
809C8—41no—
810C8—41no—
811C22—21no—
812C22—21no—
813C22—21no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22C22×C22⋊C4×C2911yescharacteristic
824C4—21no—
825C4—21no—
826C4—21no—
827C4—21no—
828C4—21no—
829C4—21no—
830C4—21no—
831C4—21no—
832C4—21no—
833C4—21no—
834C4—41no—
835C4—41no—
836C4—41no—
837C4—41no—
838C4—41no—
839C4—41no—
840C4—41no—
841C4C29×#56812yes—
842C4C29×#57711yescharacteristic
843C4C29×#57811yescharacteristic
844C2—41no—
845C2—41no—
846C2—41no—
847C2—81no—
848C2C29×#287911yescharacteristic
849C2C29×#289811yescharacteristic
850C2C29×#290111yescharacteristic
subgroupG/H
centerC2×C4×C29C22×D4
commutatorC2×C4C23×C4×C29
Frattini, cosocleC42C24×C29
socleC22×C29C22×C22⋊C4
prime radicalC29×#537C4
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×#1497C2semidirect
5. C29×#1495C2semidirect
6. C29×#1494C2semidirect
7. C29×#1493C2semidirect
8. C29×#1491C2semidirect
9. C29×#1489C2semidirect
10. C29×#1488C2semidirect
11. C29×#1487C2semidirect
12. C29×#1485C2semidirect
13. C29×#1483C2semidirect
14. C29×#1482C2semidirect
15. C29×#1481C2semidirect
322. #17506C29direct (N × H)
387. #2989C2×C29semidirect
388. #2965C2×C29semidirect
389. #1497C2×C29semidirect
390. #1495C2×C29semidirect
391. #1494C2×C29semidirect
392. #1493C2×C29semidirect
393. #1491C2×C29semidirect
394. #1489C2×C29semidirect
395. #1488C2×C29semidirect
396. #1487C2×C29semidirect
397. #1485C2×C29semidirect
398. #1483C2×C29semidirect
399. #1482C2×C29semidirect
400. #1481C2×C29semidirect
631. C29#17506direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#34612
C29×#29892
C29×#29652
C29×#14972
C29×#14952
C29×#14942
C29×#14932
C29×#14912
C29×#14892
C29×#14882
C29×#14872
C29×#14852
C29×#14832
C29×#14822
C29×#14812
#1750629