Finite Group Databasebeta

← C29×#17680 #20312580

Subgroups — C29×#17680 #20312580

Order 7424.

878 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3515C211yesmaximal, characteristic
2C29×#2970C211yesmaximal, characteristic, complemented
3C29×#2923C211yesmaximal, characteristic, complemented
4C29×#1537C211yesmaximal, characteristic, complemented
5C29×#1535C211yesmaximal, characteristic, complemented
6C29×#1535C211yesmaximal, characteristic, complemented
7C29×#1534C211yesmaximal, characteristic, complemented
8C29×#1532C211yesmaximal, characteristic, complemented
9C29×#1532C211yesmaximal, characteristic, complemented
10C29×#1531C211yesmaximal, characteristic, complemented
11C29×#1529C211yesmaximal, characteristic, complemented
12C29×#1528C211yesmaximal, characteristic, complemented
13C29×#1528C211yesmaximal, characteristic, complemented
14C29×#1524C211yesmaximal, characteristic, complemented
15C2×C29×#330C211yesmaximal, characteristic, complemented
16C29×#557C411yescharacteristic
17C29×#554C411yescharacteristic
18C29×#554C411yescharacteristic
19C29×#553C411yescharacteristic
20C29×#553C411yescharacteristic
21C29×#552—21no—
22C29×#552—21no—
23C29×#552—21no—
24C29×#552C411yescharacteristic
25C29×#552C411yescharacteristic
26C29×#547—21no—
27C29×#547C411yescharacteristic
28C29×#541—21no—
29C29×#539—21no—
30C29×#539—21no—
31C29×#533C2211yescharacteristic
32C29×#529C2211yescharacteristic
33C29×#529C2211yescharacteristic
34C29×#529C2211yescharacteristic
35C2×C29×#125C2211yescharacteristic
36C2×C29×#125C2211yescharacteristic
37C29×#520—21no—
38C4×#41×C29C2211yescharacteristic
39C29×#446—21no—
40C29×#435—21no—
41C29×#435—21no—
42C8×D4×C29—21no—
43C29×#433—21no—
44C29×#433—21no—
45C29×#432C2211yescharacteristic
46C29×#432C2211yescharacteristic
47C29×#432C2211yescharacteristic
48C29×#432C2211yescharacteristic
49C29×#432C2211yescharacteristic
50C29×#432C2211yescharacteristic
51C29×#432C2211yescharacteristic
52C29×#424—21no—
53C29×#408—21no—
54C4×M16×C29C2211yescharacteristic
55C4×M16×C29C2211yescharacteristic
56C2×C29×#97C2211yescharacteristic
57C2×C29×#97C2211yescharacteristic
58C2×C29×#97C2211yescharacteristic
59C29×#330C2211yescharacteristic
60C29×#330C2211yescharacteristic
61C29×#330C2211yescharacteristic
62C29×#330C2211yescharacteristic
63C29×#330C2211yescharacteristic
64C29×#330C2211yescharacteristic
65C29×#330C2211yescharacteristic
66C29×#330C2211yescharacteristic
67C29×#330C2211yescharacteristic
68C29×#330C2211yescharacteristic
69C29×#330C2211yescharacteristic
70C29×#330C2211yescharacteristic
71C29×#329C2211yescharacteristic
72C29×#329C2211yescharacteristic
73C29×#329C2211yescharacteristic
74C29×#329C2211yescharacteristic
75C2×#41×C29—21no—
76C2×#41×C29D411yescharacteristic
77C2×M16×C29—21no—
78C2×M16×C29—21no—
79C22×C8×C29—21no—
80C22×C8×C29—21no—
81C22×C8×C29—21no—
82C29×C4⋊Q8—21no—
83C29×C4⋊Q8C2×C411yescharacteristic
84C29×C4⋊Q8C2×C411yescharacteristic
85C29×#126—21no—
86C29×#126—21no—
87C29×#126—21no—
88C29×#126—21no—
89C29×#126—21no—
90C29×#126—21no—
91C29×#126—21no—
92C29×#125—21no—
93C29×#125—21no—
94C29×#125—21no—
95C29×#125—21no—
96C29×#125—21no—
97C29×#125—21no—
98C29×#125—21no—
99C29×#125—21no—
100C29×#125—21no—
101C29×#125C2×C411yescharacteristic
102C29×#125C2×C411yescharacteristic
103C29×#125C2×C411yescharacteristic
104C29×#125C2×C411yescharacteristic
105C29×#125C2311yescharacteristic
106C29×#125C2311yescharacteristic
107C29×#125C2311yescharacteristic
108C29×#124C2311yescharacteristic
109C29×#123—21no—
110C29×#123—21no—
111C29×#123—21no—
112C29×#123—21no—
113C29×#123—21no—
114C29×#123—21no—
115C29×#123—21no—
116C29×#123—21no—
117C29×#123—21no—
118C29×C22⋊Q8—21no—
119C29×C22⋊Q8—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⋊Q8C2×C411yescharacteristic
127C29×C22⋊Q8C2×C411yescharacteristic
128C29×C22⋊Q8C2×C411yescharacteristic
129C29×#121—21no—
130C29×#121—21no—
131C29×#121C2×C411yescharacteristic
132C29×#121C2×C411yescharacteristic
133C29×#121C2×C411yescharacteristic
134C4×Q8×C29—21no—
135C4×Q8×C29—21no—
136C4×Q8×C29—21no—
137C4×Q8×C29C2×C411yescharacteristic
138C4×Q8×C29C2×C411yescharacteristic
139C4×Q8×C29C2×C411yescharacteristic
140C4×Q8×C29C2×C411yescharacteristic
141C4×Q8×C29D411yescharacteristic
142C4×D4×C29—21no—
143C4×D4×C29—21no—
144C4×D4×C29—21no—
145C4×D4×C29—21no—
146C4×D4×C29—21no—
147C4×D4×C29—21no—
148C4×D4×C29C2×C411yescharacteristic
149C4×D4×C29C2×C411yescharacteristic
150C4×D4×C29C2×C411yescharacteristic
151C4×D4×C29C2×C411yescharacteristic
152C4×D4×C29C2×C411yescharacteristic
153C4×D4×C29C2×C411yescharacteristic
154C4×D4×C29D411yescharacteristic
155C4×D4×C29D411yescharacteristic
156C4×D4×C29D411yescharacteristic
157C29×#117—21no—
158C29×#117—21no—
159C29×#117—21no—
160C29×#117—21no—
161C29×#117—21no—
162C29×#117C2×C411yescharacteristic
163C29×#117C2×C411yescharacteristic
164C29×#117D411yescharacteristic
165C29×#117D411yescharacteristic
166C29×#117D411yescharacteristic
167C2×C4⋊C4×C29—21no—
168C2×C4⋊C4×C29—21no—
169C2×C4⋊C4×C29—21no—
170C2×C4⋊C4×C29—21no—
171C2×C4⋊C4×C29—21no—
172C2×C4⋊C4×C29C2×C411yescharacteristic
173C2×C4⋊C4×C29C2×C411yescharacteristic
174C2×C4⋊C4×C29C2×C411yescharacteristic
175C2×C4⋊C4×C29C2×C411yescharacteristic
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⋊C8—21no—
185C29×C4⋊C8—21no—
186C29×C22⋊C8—21no—
187C29×C22⋊C8—21no—
188C29×C22⋊C8—21no—
189C29×C22⋊C8—21no—
190C29×C22⋊C8—21no—
191C29×C22⋊C8—21no—
192C29×C22⋊C8—21no—
193C29×#97—21no—
194C29×#97—21no—
195C29×#97—21no—
196C29×#97C2311yescharacteristic
197C29×#97C2311yescharacteristic
198C29×#97C2311yescharacteristic
199C29×#97C2311yescharacteristic
200C29×#97C2311yescharacteristic
201C29×#97C2311yescharacteristic
202C29×#97C2311yescharacteristic
203C29×#97C2311yescharacteristic
204C4×C8×C29—21no—
205C4×C8×C29—21no—
206#41×C29—42no—
207#41×C29—44no—
208C2×Q8×C29—21no—
209C2×Q8×C29—21no—
210C2×Q8×C29C22⋊C411yescharacteristic
211C2×Q8×C29C22×C411yescharacteristic
212C2×D4×C29—21no—
213C2×D4×C29—21no—
214C2×D4×C29—21no—
215C2×D4×C29C22⋊C411yescharacteristic
216C2×D4×C29C22⋊C411yescharacteristic
217C2×D4×C29C22⋊C411yescharacteristic
218C2×D4×C29C22×C411yescharacteristic
219C22×C4×C29—21no—
220C22×C4×C29—21no—
221C22×C4×C29—21no—
222C22×C4×C29—21no—
223C22×C4×C29—21no—
224C22×C4×C29—21no—
225C22×C4×C29—21no—
226C22×C4×C29C22×C411yescharacteristic
227C22×C4×C29C22×C411yescharacteristic
228C22×C4×C29C22×C411yescharacteristic
229C22×C4×C29C2×D411yescharacteristic
230C22×C4×C29C2×D411yescharacteristic
231C22×C4×C29C2×D411yescharacteristic
232C22×C4×C29C2×D411yescharacteristic
233C22×C4×C29C2×D411yescharacteristic
234C22×C4×C29C2×D411yescharacteristic
235M16×C29—42no—
236M16×C29—42no—
237C2×C8×C29—21no—
238C2×C8×C29—21no—
239C2×C8×C29—21no—
240C2×C8×C29—21no—
241C2×C8×C29—21no—
242C2×C8×C29—21no—
243C2×C8×C29—21no—
244C2×C8×C29—21no—
245C2×C8×C29—42no—
246C2×C8×C29—42no—
247C2×C8×C29—42no—
248C4⋊C4×C29—21no—
249C4⋊C4×C29—21no—
250C4⋊C4×C29—21no—
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
284C4⋊C4×C29C22×C411yescharacteristic
285C4⋊C4×C29C22×C411yescharacteristic
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×C29C22×C411yescharacteristic
311C42×C29C22×C411yescharacteristic
312C42×C29C22×C411yescharacteristic
313C42×C29C2×D411yescharacteristic
314C42×C29C2×D411yescharacteristic
315C42×C29C2×D411yescharacteristic
316C42×C29C2×D411yescharacteristic
317C42×C29C2×D411yescharacteristic
318C42×C29C2×D411yescharacteristic
319C42×C29C2411yescharacteristic
320#17680C2911yesmaximal, characteristic, direct product factor, Sylow
321C23×C29—21no—
322C23×C29C2×C22⋊C411yescharacteristic
323C23×C29C2×C22⋊C411yescharacteristic
324C23×C29C2×C22⋊C411yescharacteristic
325Q8×C29—41no—
326Q8×C29—41no—
327Q8×C29—42no—
328Q8×C29—81no—
329D4×C29—22no—
330D4×C29—22no—
331D4×C29—41no—
332D4×C29—41no—
333D4×C29—42no—
334D4×C29—42no—
335D4×C29—81no—
336C2×C4×C29—22no—
337C2×C4×C29—21no—
338C2×C4×C29—21no—
339C2×C4×C29—21no—
340C2×C4×C29—21no—
341C2×C4×C29—21no—
342C2×C4×C29—21no—
343C2×C4×C29—21no—
344C2×C4×C29—41no—
345C2×C4×C29—41no—
346C2×C4×C29—41no—
347C2×C4×C29—41no—
348C2×C4×C29—41no—
349C2×C4×C29—41no—
350C2×C4×C29—41no—
351C2×C4×C29—41no—
352C2×C4×C29—42no—
353C2×C4×C29—42no—
354C2×C4×C29—42no—
355C2×C4×C29—81no—
356C2×C4×C29—81no—
357C2×C4×C29—81no—
358C2×C4×C29—81no—
359C2×C4×C29C2×C22⋊C411yescharacteristic
360C2×C4×C29C2×C22⋊C411yescharacteristic
361C2×C4×C29C2×C22⋊C411yescharacteristic
362C2×C4×C29C2×C22⋊C411yescharacteristic
363C2×C4×C29C2×C22⋊C411yescharacteristic
364C2×C4×C29C2×C22⋊C411yescharacteristic
365C2×C4×C29C2×C22⋊C411yescharacteristic
366C2×C4×C29C2×C22⋊C411yescharacteristic
367C2×C4×C29C2×C22⋊C411yescharacteristic
368C2×C4×C29C23×C411yescharacteristic
369C2×C4×C29C22×D411yescharacteristic
370C2×C4×C29C22×D411yescharacteristic
371C8×C29—22no—
372C8×C29—41no—
373C8×C29—41no—
374C8×C29—41no—
375C8×C29—41no—
376C8×C29—41no—
377C8×C29—41no—
378C8×C29—41no—
379#3515C2×C2911yescharacteristic
380#2970C2×C2911yescharacteristic, complemented
381#2923C2×C2911yescharacteristic, complemented
382#1537C2×C2911yescharacteristic, complemented
383#1535C2×C2911yescharacteristic, complemented
384#1535C2×C2911yescharacteristic, complemented
385#1534C2×C2911yescharacteristic, complemented
386#1532C2×C2911yescharacteristic, complemented
387#1532C2×C2911yescharacteristic, complemented
388#1531C2×C2911yescharacteristic, complemented
389#1529C2×C2911yescharacteristic, complemented
390#1528C2×C2911yescharacteristic, complemented
391#1528C2×C2911yescharacteristic, complemented
392#1524C2×C2911yescharacteristic, complemented
393C2×#330C2×C2911yescharacteristic, complemented
394C22×C29—21no—
395C22×C29—21no—
396C22×C29—21no—
397C22×C29—21no—
398C22×C29—21no—
399C22×C29—21no—
400C22×C29—21no—
401C22×C29—21no—
402C22×C29—41no—
403C22×C29—41no—
404C22×C29—41no—
405C22×C29#42112yes—
406C22×C29C22×C22⋊C411yescharacteristic
407C4×C29—21no—
408C4×C29—21no—
409C4×C29—21no—
410C4×C29—21no—
411C4×C29—21no—
412C4×C29—21no—
413C4×C29—21no—
414C4×C29—21no—
415C4×C29—21no—
416C4×C29—21no—
417C4×C29—21no—
418C4×C29—21no—
419C4×C29—41no—
420C4×C29—41no—
421C4×C29—41no—
422C4×C29—41no—
423C4×C29—41no—
424C4×C29—41no—
425C4×C29—41no—
426#557C4×C2911yescharacteristic
427#554C4×C2911yescharacteristic
428#554C4×C2911yescharacteristic
429#553C4×C2911yescharacteristic
430#553C4×C2911yescharacteristic
431#552—21no—
432#552—21no—
433#552—21no—
434#552C4×C2911yescharacteristic
435#552C4×C2911yescharacteristic
436#547—21no—
437#547C4×C2911yescharacteristic
438#541—21no—
439#539—21no—
440#539—21no—
441#533C22×C2911yescharacteristic
442#529C22×C2911yescharacteristic
443#529C22×C2911yescharacteristic
444#529C22×C2911yescharacteristic
445C2×#125C22×C2911yescharacteristic
446C2×#125C22×C2911yescharacteristic
447#520—21no—
448C4×#41C22×C2911yescharacteristic
449#446—21no—
450#435—21no—
451#435—21no—
452C8×D4—21no—
453#433—21no—
454#433—21no—
455#432C22×C2911yescharacteristic
456#432C22×C2911yescharacteristic
457#432C22×C2911yescharacteristic
458#432C22×C2911yescharacteristic
459#432C22×C2911yescharacteristic
460#432C22×C2911yescharacteristic
461#432C22×C2911yescharacteristic
462#424—21no—
463#408—21no—
464C4×M16C22×C2911yescharacteristic
465C4×M16C22×C2911yescharacteristic
466C2×#97C22×C2911yescharacteristic
467C2×#97C22×C2911yescharacteristic
468C2×#97C22×C2911yescharacteristic
469#330C22×C2911yescharacteristic
470#330C22×C2911yescharacteristic
471#330C22×C2911yescharacteristic
472#330C22×C2911yescharacteristic
473#330C22×C2911yescharacteristic
474#330C22×C2911yescharacteristic
475#330C22×C2911yescharacteristic
476#330C22×C2911yescharacteristic
477#330C22×C2911yescharacteristic
478#330C22×C2911yescharacteristic
479#330C22×C2911yescharacteristic
480#330C22×C2911yescharacteristic
481#329C22×C2911yescharacteristic
482#329C22×C2911yescharacteristic
483#329C22×C2911yescharacteristic
484#329C22×C2911yescharacteristic
485C2×C29—22no—
486C2×C29—41no—
487C2×C29—41no—
488C2×C29—81no—
489C2×C29#288911yescharacteristic
490C2×C29C2×#42111yescharacteristic
491C2×C29#290111yescharacteristic
492C2×#41—21no—
493C2×#41D4×C2911yescharacteristic
494C2×M16—21no—
495C2×M16—21no—
496C22×C8—21no—
497C22×C8—21no—
498C22×C8—21no—
499C4⋊Q8—21no—
500C4⋊Q8C2×C4×C2911yescharacteristic
501C4⋊Q8C2×C4×C2911yescharacteristic
502#126—21no—
503#126—21no—
504#126—21no—
505#126—21no—
506#126—21no—
507#126—21no—
508#126—21no—
509#125—21no—
510#125—21no—
511#125—21no—
512#125—21no—
513#125—21no—
514#125—21no—
515#125—21no—
516#125—21no—
517#125—21no—
518#125C2×C4×C2911yescharacteristic
519#125C2×C4×C2911yescharacteristic
520#125C2×C4×C2911yescharacteristic
521#125C2×C4×C2911yescharacteristic
522#125C23×C2911yescharacteristic
523#125C23×C2911yescharacteristic
524#125C23×C2911yescharacteristic
525#124C23×C2911yescharacteristic
526#123—21no—
527#123—21no—
528#123—21no—
529#123—21no—
530#123—21no—
531#123—21no—
532#123—21no—
533#123—21no—
534#123—21no—
535C22⋊Q8—21no—
536C22⋊Q8—21no—
537C22⋊Q8—21no—
538C22⋊Q8—21no—
539C22⋊Q8—21no—
540C22⋊Q8—21no—
541C22⋊Q8—21no—
542C22⋊Q8—21no—
543C22⋊Q8C2×C4×C2911yescharacteristic
544C22⋊Q8C2×C4×C2911yescharacteristic
545C22⋊Q8C2×C4×C2911yescharacteristic
546#121—21no—
547#121—21no—
548#121C2×C4×C2911yescharacteristic
549#121C2×C4×C2911yescharacteristic
550#121C2×C4×C2911yescharacteristic
551C4×Q8—21no—
552C4×Q8—21no—
553C4×Q8—21no—
554C4×Q8C2×C4×C2911yescharacteristic
555C4×Q8C2×C4×C2911yescharacteristic
556C4×Q8C2×C4×C2911yescharacteristic
557C4×Q8C2×C4×C2911yescharacteristic
558C4×Q8D4×C2911yescharacteristic
559C4×D4—21no—
560C4×D4—21no—
561C4×D4—21no—
562C4×D4—21no—
563C4×D4—21no—
564C4×D4—21no—
565C4×D4C2×C4×C2911yescharacteristic
566C4×D4C2×C4×C2911yescharacteristic
567C4×D4C2×C4×C2911yescharacteristic
568C4×D4C2×C4×C2911yescharacteristic
569C4×D4C2×C4×C2911yescharacteristic
570C4×D4C2×C4×C2911yescharacteristic
571C4×D4D4×C2911yescharacteristic
572C4×D4D4×C2911yescharacteristic
573C4×D4D4×C2911yescharacteristic
574#117—21no—
575#117—21no—
576#117—21no—
577#117—21no—
578#117—21no—
579#117C2×C4×C2911yescharacteristic
580#117C2×C4×C2911yescharacteristic
581#117D4×C2911yescharacteristic
582#117D4×C2911yescharacteristic
583#117D4×C2911yescharacteristic
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4C2×C4×C2911yescharacteristic
590C2×C4⋊C4C2×C4×C2911yescharacteristic
591C2×C4⋊C4C2×C4×C2911yescharacteristic
592C2×C4⋊C4C2×C4×C2911yescharacteristic
593C2×C42C23×C2911yescharacteristic
594C2×C42C23×C2911yescharacteristic
595C2×C42C23×C2911yescharacteristic
596C4⋊C8—21no—
597C4⋊C8—21no—
598C4⋊C8—21no—
599C4⋊C8—21no—
600C4⋊C8—21no—
601C4⋊C8—21no—
602C4⋊C8—21no—
603C22⋊C8—21no—
604C22⋊C8—21no—
605C22⋊C8—21no—
606C22⋊C8—21no—
607C22⋊C8—21no—
608C22⋊C8—21no—
609C22⋊C8—21no—
610#97—21no—
611#97—21no—
612#97—21no—
613#97C23×C2911yescharacteristic
614#97C23×C2911yescharacteristic
615#97C23×C2911yescharacteristic
616#97C23×C2911yescharacteristic
617#97C23×C2911yescharacteristic
618#97C23×C2911yescharacteristic
619#97C23×C2911yescharacteristic
620#97C23×C2911yescharacteristic
621C4×C8—21no—
622C4×C8—21no—
623C29#1768011yescharacteristic, direct product factor, Sylow
624#41—42no—
625#41—44no—
626C2×Q8—21no—
627C2×Q8—21no—
628C2×Q8C22⋊C4×C2911yescharacteristic
629C2×Q8C22×C4×C2911yescharacteristic
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4C22⋊C4×C2911yescharacteristic
634C2×D4C22⋊C4×C2911yescharacteristic
635C2×D4C22⋊C4×C2911yescharacteristic
636C2×D4C22×C4×C2911yescharacteristic
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4C22×C4×C2911yescharacteristic
645C22×C4C22×C4×C2911yescharacteristic
646C22×C4C22×C4×C2911yescharacteristic
647C22×C4C2×D4×C2911yescharacteristic
648C22×C4C2×D4×C2911yescharacteristic
649C22×C4C2×D4×C2911yescharacteristic
650C22×C4C2×D4×C2911yescharacteristic
651C22×C4C2×D4×C2911yescharacteristic
652C22×C4C2×D4×C2911yescharacteristic
653M16—42no—
654M16—42no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—42no—
664C2×C8—42no—
665C2×C8—42no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
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⋊C4C22⋊C4×C2911yescharacteristic
693C4⋊C4C22⋊C4×C2911yescharacteristic
694C4⋊C4C22⋊C4×C2911yescharacteristic
695C4⋊C4C22⋊C4×C2911yescharacteristic
696C4⋊C4C22⋊C4×C2911yescharacteristic
697C4⋊C4C22⋊C4×C2911yescharacteristic
698C4⋊C4C22×C4×C2911yescharacteristic
699C4⋊C4C22×C4×C2911yescharacteristic
700C4⋊C4C22×C4×C2911yescharacteristic
701C4⋊C4C22×C4×C2911yescharacteristic
702C4⋊C4C22×C4×C2911yescharacteristic
703C4⋊C4C22×C4×C2911yescharacteristic
704C22⋊C4—21no—
705C22⋊C4—21no—
706C22⋊C4—21no—
707C22⋊C4—21no—
708C22⋊C4—21no—
709C22⋊C4—21no—
710C22⋊C4—21no—
711C22⋊C4—21no—
712C22⋊C4—21no—
713C22⋊C4—21no—
714C22⋊C4—21no—
715C22⋊C4—21no—
716C22⋊C4—21no—
717C22⋊C4C22⋊C4×C2911yescharacteristic
718C22⋊C4C22⋊C4×C2911yescharacteristic
719C22⋊C4C22⋊C4×C2911yescharacteristic
720C22⋊C4C22⋊C4×C2911yescharacteristic
721C22⋊C4C22⋊C4×C2911yescharacteristic
722C22⋊C4C22⋊C4×C2911yescharacteristic
723C42—21no—
724C42—21no—
725C42—21no—
726C42—21no—
727C42—21no—
728C42C22×C4×C2911yescharacteristic
729C42C22×C4×C2911yescharacteristic
730C42C22×C4×C2911yescharacteristic
731C42C2×D4×C2911yescharacteristic
732C42C2×D4×C2911yescharacteristic
733C42C2×D4×C2911yescharacteristic
734C42C2×D4×C2911yescharacteristic
735C42C2×D4×C2911yescharacteristic
736C42C2×D4×C2911yescharacteristic
737C42C24×C2911yescharacteristic
738C23—21no—
739C23C2×C22⋊C4×C2911yescharacteristic
740C23C2×C22⋊C4×C2911yescharacteristic
741C23C2×C22⋊C4×C2911yescharacteristic
742Q8—41no—
743Q8—41no—
744Q8—42no—
745Q8—81no—
746D4—22no—
747D4—22no—
748D4—41no—
749D4—41no—
750D4—42no—
751D4—42no—
752D4—81no—
753C2×C4—22no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—81no—
773C2×C4—81no—
774C2×C4—81no—
775C2×C4—81no—
776C2×C4C2×C22⋊C4×C2911yescharacteristic
777C2×C4C2×C22⋊C4×C2911yescharacteristic
778C2×C4C2×C22⋊C4×C2911yescharacteristic
779C2×C4C2×C22⋊C4×C2911yescharacteristic
780C2×C4C2×C22⋊C4×C2911yescharacteristic
781C2×C4C2×C22⋊C4×C2911yescharacteristic
782C2×C4C2×C22⋊C4×C2911yescharacteristic
783C2×C4C2×C22⋊C4×C2911yescharacteristic
784C2×C4C2×C22⋊C4×C2911yescharacteristic
785C2×C4C23×C4×C2911yescharacteristic
786C2×C4C22×D4×C2911yescharacteristic
787C2×C4C22×D4×C2911yescharacteristic
788C8—22no—
789C8—41no—
790C8—41no—
791C8—41no—
792C8—41no—
793C8—41no—
794C8—41no—
795C8—41no—
796C22—21no—
797C22—21no—
798C22—21no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22C29×#42112yes—
808C22C22×C22⋊C4×C2911yescharacteristic
809C4—21no—
810C4—21no—
811C4—21no—
812C4—21no—
813C4—21no—
814C4—21no—
815C4—21no—
816C4—21no—
817C4—21no—
818C4—21no—
819C4—21no—
820C4—21no—
821C4—41no—
822C4—41no—
823C4—41no—
824C4—41no—
825C4—41no—
826C4—41no—
827C4—41no—
828C2—22no—
829C2—41no—
830C2—41no—
831C2—81no—
832C2C29×#288911yescharacteristic
833C2C2×C29×#42111yescharacteristic
834C2C29×#290111yescharacteristic
subgroupG/H
center, socleC22×C29C22×C22⋊C4
commutatorC2×C4C23×C4×C29
Frattini, cosocleC42C24×C29
prime radicalC29×#3515C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C4×#41×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#2970C2semidirect
3. C29×#2923C2semidirect
4. C29×#1537C2semidirect
5. C29×#1535C2semidirect
6. C29×#1535C2semidirect
7. C29×#1534C2semidirect
8. C29×#1532C2semidirect
9. C29×#1532C2semidirect
10. C29×#1531C2semidirect
11. C29×#1529C2semidirect
12. C29×#1528C2semidirect
13. C29×#1528C2semidirect
14. C29×#1524C2semidirect
15. C2×C29×#330C2semidirect
320. #17680C29direct (N × H)
380. #2970C2×C29semidirect
381. #2923C2×C29semidirect
382. #1537C2×C29semidirect
383. #1535C2×C29semidirect
384. #1535C2×C29semidirect
385. #1534C2×C29semidirect
386. #1532C2×C29semidirect
387. #1532C2×C29semidirect
388. #1531C2×C29semidirect
389. #1529C2×C29semidirect
390. #1528C2×C29semidirect
391. #1528C2×C29semidirect
392. #1524C2×C29semidirect
393. C2×#330C2×C29semidirect
623. C29#17680direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35152
C29×#29702
C29×#29232
C29×#15372
C29×#15352
C29×#15342
C29×#15322
C29×#15312
C29×#15292
C29×#15282
C29×#15242
C2×C29×#3302
#1768029