Finite Group Databasebeta

← C29×#17521 #20312421

Subgroups — C29×#17521 #20312421

Order 7424.

1010 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3481C211yesmaximal, characteristic
2C29×#2990C211yesmaximal, characteristic, complemented
3C29×#2922C211yesmaximal, characteristic, complemented
4C29×#1496C211yesmaximal, characteristic, complemented
5C29×#1495C211yesmaximal, characteristic, complemented
6C29×#1494C211yesmaximal, characteristic, complemented
7C29×#1490C211yesmaximal, characteristic, complemented
8C29×#1488C211yesmaximal, characteristic, complemented
9C29×#1486C211yesmaximal, characteristic, complemented
10C29×#1483C211yesmaximal, characteristic, complemented
11C29×#1482C211yesmaximal, characteristic, complemented
12C29×#1480C211yesmaximal, characteristic, complemented
13C29×#1478C211yesmaximal, characteristic, complemented
14C29×#1477C211yesmaximal, characteristic, complemented
15C2×C29×D4⋊C8C211yesmaximal, characteristic, complemented
16C29×#559C411yescharacteristic
17C29×#554C411yescharacteristic
18C29×#554C411yescharacteristic
19C29×#553—21no—
20C29×#553C411yescharacteristic
21C29×#553C411yescharacteristic
22C29×#551—21no—
23C29×#551—21no—
24C29×#546—21no—
25C29×#546C411yescharacteristic
26C29×#546C411yescharacteristic
27D42×C29C411yescharacteristic
28C29×#532C2211yescharacteristic
29C29×#529—21no—
30C29×#529C2211yescharacteristic
31C29×#529C2211yescharacteristic
32C29×#525—21no—
33C29×#525—21no—
34C4×#41×C29C2211yescharacteristic
35C4×#41×C29C2211yescharacteristic
36C2×C4×D4×C29—21no—
37C2×C4×D4×C29C2211yescharacteristic
38C2×C4×D4×C29C2211yescharacteristic
39C29×#446—21no—
40C29×#435—21no—
41C29×#435—21no—
42C8×D4×C29—21no—
43C29×#433—21no—
44C29×#433—21no—
45C29×#432C2211yescharacteristic, complemented
46C29×#432C2211yescharacteristic, complemented
47C29×#431C2211yescharacteristic, complemented
48C29×#431C2211yescharacteristic, complemented
49C29×#431C2211yescharacteristic, complemented
50C29×#431C2211yescharacteristic, complemented
51C29×#431C2211yescharacteristic, complemented
52C29×#424—21no—
53C29×#423C2211yescharacteristic, complemented
54C2×C29×C4⋊C8C2211yescharacteristic, complemented
55C2×C29×C4⋊C8C2211yescharacteristic, complemented
56C29×#408—21no—
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, complemented
68C29×D4⋊C8C2211yescharacteristic, complemented
69C29×D4⋊C8C2211yescharacteristic, complemented
70C29×D4⋊C8C2211yescharacteristic, complemented
71C29×D4⋊C8C2211yescharacteristic, complemented
72C29×D4⋊C8C2211yescharacteristic, complemented
73C29×D4⋊C8C2211yescharacteristic, complemented
74C29×D4⋊C8C2211yescharacteristic, complemented
75C2×#41×C29—21no—
76C2×#41×C29C2×C411yescharacteristic
77C2×#41×C29D411yescharacteristic
78C22×D4×C29—21no—
79C22×D4×C29C2×C411yescharacteristic
80C22×D4×C29C2×C411yescharacteristic
81C23×C4×C29—21no—
82C23×C4×C29—21no—
83C2×M16×C29—21no—
84C2×M16×C29—21no—
85C22×C8×C29—21no—
86C22×C8×C29—21no—
87C22×C8×C29—21no—
88C29×C4⋊Q8C2×C411yescharacteristic
89C29×#127C2×C411yescharacteristic
90C29×#126—21no—
91C29×#126—21no—
92C29×#126—21no—
93C29×#126—21no—
94C29×#125—21no—
95C29×#125C2×C411yescharacteristic
96C29×#125C2×C411yescharacteristic
97C29×#124—21no—
98C29×#124—21no—
99C29×#124C2×C411yescharacteristic
100C29×#124C2×C411yescharacteristic
101C29×#123—21no—
102C29×#123—21no—
103C29×#123—21no—
104C29×#123—21no—
105C29×#123—21no—
106C29×#123—21no—
107C29×#123—21no—
108C29×#123—21no—
109C29×C22⋊Q8—21no—
110C29×C22⋊Q8—21no—
111C29×C22⋊Q8—21no—
112C29×C22⋊Q8—21no—
113C29×C22⋊Q8—21no—
114C29×C22⋊Q8C2×C411yescharacteristic
115C29×C22⋊Q8C2×C411yescharacteristic
116C29×#121—21no—
117C29×#121—21no—
118C29×#121—21no—
119C29×#121—21no—
120C29×#121—21no—
121C29×#121—21no—
122C29×#121C2×C411yescharacteristic
123C29×#121C2×C411yescharacteristic
124C29×#121C2×C411yescharacteristic
125C29×#121C2×C411yescharacteristic
126C29×#120—21no—
127C29×#120—21no—
128C29×#120—21no—
129C29×#120—21no—
130C4×Q8×C29C2×C411yescharacteristic
131C4×Q8×C29C2×C411yescharacteristic
132C4×Q8×C29D411yescharacteristic
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×C29—21no—
143C4×D4×C29—21no—
144C4×D4×C29—21no—
145C4×D4×C29—21no—
146C4×D4×C29—21no—
147C4×D4×C29C2×C411yescharacteristic
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×C29C2×C411yescharacteristic
155C4×D4×C29D411yescharacteristic
156C4×D4×C29D411yescharacteristic
157C4×D4×C29D411yescharacteristic
158C4×D4×C29C2311yescharacteristic
159C4×D4×C29C2311yescharacteristic
160C4×D4×C29C2311yescharacteristic
161C29×#117—21no—
162C29×#117—21no—
163C29×#117—21no—
164C29×#117C2×C411yescharacteristic
165C29×#117D411yescharacteristic
166C29×#117D411yescharacteristic
167C29×#117D411yescharacteristic
168C2×C4⋊C4×C29—21no—
169C2×C4⋊C4×C29C2×C411yescharacteristic
170C2×C4⋊C4×C29C2×C411yescharacteristic
171C2×C22⋊C4×C29—21no—
172C2×C22⋊C4×C29—21no—
173C2×C22⋊C4×C29—21no—
174C2×C22⋊C4×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⋊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×C22⋊C8—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—
207C24×C29—21no—
208#41×C29—22no—
209#41×C29—42no—
210#41×C29—41no—
211#41×C29—81no—
212#41×C29—81no—
213C2×Q8×C29—21no—
214C2×Q8×C29C22⋊C411yescharacteristic
215C2×Q8×C29C22×C411yescharacteristic
216C2×D4×C29—22no—
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—21no—
224C2×D4×C29—21no—
225C2×D4×C29—21no—
226C2×D4×C29—21no—
227C2×D4×C29—41no—
228C2×D4×C29—41no—
229C2×D4×C29—44no—
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—21no—
245C22×C4×C29—21no—
246C22×C4×C29—21no—
247C22×C4×C29—81no—
248C22×C4×C29—81no—
249C22×C4×C29—81no—
250C22×C4×C29—81no—
251C22×C4×C29C22×C411yescharacteristic
252C22×C4×C29C22×C411yescharacteristic
253C22×C4×C29C22×C411yescharacteristic
254C22×C4×C29C2×D411yescharacteristic
255C22×C4×C29C2×D411yescharacteristic
256C22×C4×C29C2×D411yescharacteristic
257C22×C4×C29C2×D411yescharacteristic
258C22×C4×C29C2×D411yescharacteristic
259C22×C4×C29C2×D411yescharacteristic
260M16×C29—42no—
261M16×C29—81no—
262C2×C8×C29—21no—
263C2×C8×C29—21no—
264C2×C8×C29—21no—
265C2×C8×C29—21no—
266C2×C8×C29—21no—
267C2×C8×C29—21no—
268C2×C8×C29—21no—
269C2×C8×C29—21no—
270C2×C8×C29—42no—
271C2×C8×C29—81no—
272C2×C8×C29—81no—
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×C29—21no—
281C4⋊C4×C29—21no—
282C4⋊C4×C29—21no—
283C4⋊C4×C29—21no—
284C4⋊C4×C29C22⋊C411yescharacteristic
285C4⋊C4×C29C22⋊C411yescharacteristic
286C4⋊C4×C29C22⋊C411yescharacteristic
287C4⋊C4×C29C22⋊C411yescharacteristic
288C4⋊C4×C29C22⋊C411yescharacteristic
289C4⋊C4×C29C22⋊C411yescharacteristic
290C4⋊C4×C29C22×C411yescharacteristic
291C4⋊C4×C29C22×C411yescharacteristic
292C4⋊C4×C29C22×C411yescharacteristic
293C4⋊C4×C29C22×C411yescharacteristic
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×C29—21no—
310C22⋊C4×C29—21no—
311C22⋊C4×C29—21no—
312C22⋊C4×C29—21no—
313C22⋊C4×C29C22⋊C411yescharacteristic
314C22⋊C4×C29C22⋊C411yescharacteristic
315C22⋊C4×C29C22⋊C411yescharacteristic
316C22⋊C4×C29C22⋊C411yescharacteristic
317C22⋊C4×C29C22⋊C411yescharacteristic
318C22⋊C4×C29C22⋊C411yescharacteristic
319C42×C29—21no—
320C42×C29—21no—
321C42×C29—21no—
322C42×C29C22×C411yescharacteristic
323C42×C29C22×C411yescharacteristic
324C42×C29C22×C411yescharacteristic
325C42×C29C2×D411yescharacteristic
326C42×C29C2×D411yescharacteristic
327C42×C29C2×D411yescharacteristic
328C42×C29C2×D411yescharacteristic
329C42×C29C2×D411yescharacteristic
330C42×C29C2×D411yescharacteristic
331C42×C29C2411yescharacteristic
332#17521C2911yesmaximal, characteristic, direct product factor, Sylow
333C23×C29—21no—
334C23×C29—21no—
335C23×C29—21no—
336C23×C29—42no—
337C23×C29—42no—
338C23×C29—42no—
339C23×C29—42no—
340C23×C29—81no—
341C23×C29—81no—
342C23×C29C2×C22⋊C411yescharacteristic
343C23×C29C2×C22⋊C411yescharacteristic
344C23×C29C2×C22⋊C411yescharacteristic
345Q8×C29—21no—
346Q8×C29—21no—
347Q8×C29—41no—
348Q8×C29—81no—
349D4×C29—22no—
350D4×C29—22no—
351D4×C29—21no—
352D4×C29—21no—
353D4×C29—21no—
354D4×C29—21no—
355D4×C29—21no—
356D4×C29—41no—
357D4×C29—42no—
358D4×C29—42no—
359D4×C29—42no—
360D4×C29—42no—
361D4×C29—42no—
362D4×C29—42no—
363D4×C29—81no—
364D4×C29—81no—
365D4×C29—81no—
366D4×C29#13112yes—
367C2×C4×C29—22no—
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—21no—
375C2×C4×C29—21no—
376C2×C4×C29—21no—
377C2×C4×C29—21no—
378C2×C4×C29—21no—
379C2×C4×C29—21no—
380C2×C4×C29—21no—
381C2×C4×C29—21no—
382C2×C4×C29—21no—
383C2×C4×C29—21no—
384C2×C4×C29—21no—
385C2×C4×C29—41no—
386C2×C4×C29—41no—
387C2×C4×C29—42no—
388C2×C4×C29—42no—
389C2×C4×C29—41no—
390C2×C4×C29—41no—
391C2×C4×C29—41no—
392C2×C4×C29—41no—
393C2×C4×C29—41no—
394C2×C4×C29—41no—
395C2×C4×C29—81no—
396C2×C4×C29—81no—
397C2×C4×C29—81no—
398C2×C4×C29—81no—
399C2×C4×C29—81no—
400C2×C4×C29—81no—
401C2×C4×C29C2×C22⋊C411yescharacteristic
402C2×C4×C29C2×C22⋊C411yescharacteristic
403C2×C4×C29C2×C22⋊C411yescharacteristic
404C2×C4×C29C2×C22⋊C411yescharacteristic
405C2×C4×C29C2×C22⋊C411yescharacteristic
406C2×C4×C29C2×C22⋊C411yescharacteristic
407C2×C4×C29C2×C22⋊C411yescharacteristic
408C2×C4×C29C2×C22⋊C411yescharacteristic
409C2×C4×C29C2×C22⋊C411yescharacteristic
410C2×C4×C29C23×C411yescharacteristic
411C2×C4×C29C22×D411yescharacteristic
412C2×C4×C29C22×D411yescharacteristic
413C8×C29—41no—
414C8×C29—41no—
415C8×C29—41no—
416C8×C29—41no—
417C8×C29—41no—
418C8×C29—41no—
419C8×C29—41no—
420C8×C29—41no—
421#3481C2×C2911yescharacteristic
422#2990C2×C2911yescharacteristic, complemented
423#2922C2×C2911yescharacteristic, complemented
424#1496C2×C2911yescharacteristic, complemented
425#1495C2×C2911yescharacteristic, complemented
426#1494C2×C2911yescharacteristic, complemented
427#1490C2×C2911yescharacteristic, complemented
428#1488C2×C2911yescharacteristic, complemented
429#1486C2×C2911yescharacteristic, complemented
430#1483C2×C2911yescharacteristic, complemented
431#1482C2×C2911yescharacteristic, complemented
432#1480C2×C2911yescharacteristic, complemented
433#1478C2×C2911yescharacteristic, complemented
434#1477C2×C2911yescharacteristic, complemented
435C2×D4⋊C8C2×C2911yescharacteristic, complemented
436C22×C29—21no—
437C22×C29—21no—
438C22×C29—21no—
439C22×C29—21no—
440C22×C29—22no—
441C22×C29—21no—
442C22×C29—21no—
443C22×C29—21no—
444C22×C29—21no—
445C22×C29—41no—
446C22×C29—41no—
447C22×C29—41no—
448C22×C29—41no—
449C22×C29—41no—
450C22×C29—41no—
451C22×C29—41no—
452C22×C29—41no—
453C22×C29—84no—
454C22×C29—84no—
455C22×C29#42112yes—
456C22×C29C22×C22⋊C411yescharacteristic
457C4×C29—21no—
458C4×C29—21no—
459C4×C29—21no—
460C4×C29—21no—
461C4×C29—21no—
462C4×C29—21no—
463C4×C29—21no—
464C4×C29—21no—
465C4×C29—21no—
466C4×C29—21no—
467C4×C29—41no—
468C4×C29—41no—
469C4×C29—41no—
470C4×C29—41no—
471C4×C29—41no—
472C4×C29C2×#13111yescharacteristic
473C4×C29#56811yescharacteristic
474C4×C29#57611yescharacteristic
475C4×C29#57711yescharacteristic
476#559C4×C2911yescharacteristic
477#554C4×C2911yescharacteristic
478#554C4×C2911yescharacteristic
479#553—21no—
480#553C4×C2911yescharacteristic
481#553C4×C2911yescharacteristic
482#551—21no—
483#551—21no—
484#546—21no—
485#546C4×C2911yescharacteristic
486#546C4×C2911yescharacteristic
487D42C4×C2911yescharacteristic
488#532C22×C2911yescharacteristic
489#529—21no—
490#529C22×C2911yescharacteristic
491#529C22×C2911yescharacteristic
492#525—21no—
493#525—21no—
494C4×#41C22×C2911yescharacteristic
495C4×#41C22×C2911yescharacteristic
496C2×C4×D4—21no—
497C2×C4×D4C22×C2911yescharacteristic
498C2×C4×D4C22×C2911yescharacteristic
499#446—21no—
500#435—21no—
501#435—21no—
502C8×D4—21no—
503#433—21no—
504#433—21no—
505#432C22×C2911yescharacteristic, complemented
506#432C22×C2911yescharacteristic, complemented
507#431C22×C2911yescharacteristic, complemented
508#431C22×C2911yescharacteristic, complemented
509#431C22×C2911yescharacteristic, complemented
510#431C22×C2911yescharacteristic, complemented
511#431C22×C2911yescharacteristic, complemented
512#424—21no—
513#423C22×C2911yescharacteristic, complemented
514C2×C4⋊C8C22×C2911yescharacteristic, complemented
515C2×C4⋊C8C22×C2911yescharacteristic, complemented
516#408—21no—
517C4×M16C22×C2911yescharacteristic, complemented
518C2×C4×C8C22×C2911yescharacteristic, complemented
519Q8⋊C8C22×C2911yescharacteristic, complemented
520Q8⋊C8C22×C2911yescharacteristic, complemented
521Q8⋊C8C22×C2911yescharacteristic, complemented
522Q8⋊C8C22×C2911yescharacteristic, complemented
523D4⋊C8C22×C2911yescharacteristic
524D4⋊C8C22×C2911yescharacteristic
525D4⋊C8C22×C2911yescharacteristic
526D4⋊C8C22×C2911yescharacteristic
527D4⋊C8C22×C2911yescharacteristic, complemented
528D4⋊C8C22×C2911yescharacteristic, complemented
529D4⋊C8C22×C2911yescharacteristic, complemented
530D4⋊C8C22×C2911yescharacteristic, complemented
531D4⋊C8C22×C2911yescharacteristic, complemented
532D4⋊C8C22×C2911yescharacteristic, complemented
533D4⋊C8C22×C2911yescharacteristic, complemented
534D4⋊C8C22×C2911yescharacteristic, complemented
535C2×C29—22no—
536C2×C29—41no—
537C2×C29—41no—
538C2×C29—42no—
539C2×C29—81no—
540C2×C29—81no—
541C2×C29#288011yescharacteristic
542C2×C29#289711yescharacteristic
543C2×C29C2×#42111yescharacteristic
544C2×#41—21no—
545C2×#41C2×C4×C2911yescharacteristic
546C2×#41D4×C2911yescharacteristic
547C22×D4—21no—
548C22×D4C2×C4×C2911yescharacteristic
549C22×D4C2×C4×C2911yescharacteristic
550C23×C4—21no—
551C23×C4—21no—
552C2×M16—21no—
553C2×M16—21no—
554C22×C8—21no—
555C22×C8—21no—
556C22×C8—21no—
557C4⋊Q8C2×C4×C2911yescharacteristic
558#127C2×C4×C2911yescharacteristic
559#126—21no—
560#126—21no—
561#126—21no—
562#126—21no—
563#125—21no—
564#125C2×C4×C2911yescharacteristic
565#125C2×C4×C2911yescharacteristic
566#124—21no—
567#124—21no—
568#124C2×C4×C2911yescharacteristic
569#124C2×C4×C2911yescharacteristic
570#123—21no—
571#123—21no—
572#123—21no—
573#123—21no—
574#123—21no—
575#123—21no—
576#123—21no—
577#123—21no—
578C22⋊Q8—21no—
579C22⋊Q8—21no—
580C22⋊Q8—21no—
581C22⋊Q8—21no—
582C22⋊Q8—21no—
583C22⋊Q8C2×C4×C2911yescharacteristic
584C22⋊Q8C2×C4×C2911yescharacteristic
585#121—21no—
586#121—21no—
587#121—21no—
588#121—21no—
589#121—21no—
590#121—21no—
591#121C2×C4×C2911yescharacteristic
592#121C2×C4×C2911yescharacteristic
593#121C2×C4×C2911yescharacteristic
594#121C2×C4×C2911yescharacteristic
595#120—21no—
596#120—21no—
597#120—21no—
598#120—21no—
599C4×Q8C2×C4×C2911yescharacteristic
600C4×Q8C2×C4×C2911yescharacteristic
601C4×Q8D4×C2911yescharacteristic
602C4×Q8C23×C2911yescharacteristic
603C4×D4—21no—
604C4×D4—21no—
605C4×D4—21no—
606C4×D4—21no—
607C4×D4—21no—
608C4×D4—21no—
609C4×D4—21no—
610C4×D4—21no—
611C4×D4—21no—
612C4×D4—21no—
613C4×D4—21no—
614C4×D4—21no—
615C4×D4—21no—
616C4×D4C2×C4×C2911yescharacteristic
617C4×D4C2×C4×C2911yescharacteristic
618C4×D4C2×C4×C2911yescharacteristic
619C4×D4C2×C4×C2911yescharacteristic
620C4×D4C2×C4×C2911yescharacteristic
621C4×D4C2×C4×C2911yescharacteristic
622C4×D4C2×C4×C2911yescharacteristic
623C4×D4C2×C4×C2911yescharacteristic
624C4×D4D4×C2911yescharacteristic
625C4×D4D4×C2911yescharacteristic
626C4×D4D4×C2911yescharacteristic
627C4×D4C23×C2911yescharacteristic
628C4×D4C23×C2911yescharacteristic
629C4×D4C23×C2911yescharacteristic
630#117—21no—
631#117—21no—
632#117—21no—
633#117C2×C4×C2911yescharacteristic
634#117D4×C2911yescharacteristic
635#117D4×C2911yescharacteristic
636#117D4×C2911yescharacteristic
637C2×C4⋊C4—21no—
638C2×C4⋊C4C2×C4×C2911yescharacteristic
639C2×C4⋊C4C2×C4×C2911yescharacteristic
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C42—21no—
645C2×C42C23×C2911yescharacteristic
646C2×C42C23×C2911yescharacteristic
647C2×C42C23×C2911yescharacteristic
648C4⋊C8—21no—
649C4⋊C8—21no—
650C4⋊C8—21no—
651C4⋊C8—21no—
652C4⋊C8—21no—
653C4⋊C8—21no—
654C4⋊C8—21no—
655C4⋊C8C23×C2911yescharacteristic
656C4⋊C8C23×C2911yescharacteristic
657C4⋊C8C23×C2911yescharacteristic
658C4⋊C8C23×C2911yescharacteristic
659C22⋊C8—21no—
660C22⋊C8—21no—
661C22⋊C8—21no—
662C22⋊C8—21no—
663C22⋊C8—21no—
664C22⋊C8—21no—
665C22⋊C8—21no—
666#97—21no—
667#97—21no—
668#97—21no—
669C4×C8—21no—
670C4×C8—21no—
671C4×C8C23×C2911yescharacteristic
672C4×C8C23×C2911yescharacteristic
673C4×C8C23×C2911yescharacteristic
674C4×C8C23×C2911yescharacteristic
675C29#1752111yescharacteristic, direct product factor, Sylow
676C24—21no—
677C24—21no—
678#41—22no—
679#41—42no—
680#41—41no—
681#41—81no—
682#41—81no—
683C2×Q8—21no—
684C2×Q8C22⋊C4×C2911yescharacteristic
685C2×Q8C22×C4×C2911yescharacteristic
686C2×D4—22no—
687C2×D4—22no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—41no—
698C2×D4—41no—
699C2×D4—44no—
700C2×D4C22⋊C4×C2911yescharacteristic
701C2×D4C22⋊C4×C2911yescharacteristic
702C2×D4C22⋊C4×C2911yescharacteristic
703C2×D4C22×C4×C2911yescharacteristic
704C2×D4C22×C4×C2911yescharacteristic
705C2×D4C22×C4×C2911yescharacteristic
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×C4—81no—
718C22×C4—81no—
719C22×C4—81no—
720C22×C4—81no—
721C22×C4C22×C4×C2911yescharacteristic
722C22×C4C22×C4×C2911yescharacteristic
723C22×C4C22×C4×C2911yescharacteristic
724C22×C4C2×D4×C2911yescharacteristic
725C22×C4C2×D4×C2911yescharacteristic
726C22×C4C2×D4×C2911yescharacteristic
727C22×C4C2×D4×C2911yescharacteristic
728C22×C4C2×D4×C2911yescharacteristic
729C22×C4C2×D4×C2911yescharacteristic
730M16—42no—
731M16—81no—
732C2×C8—21no—
733C2×C8—21no—
734C2×C8—21no—
735C2×C8—21no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—42no—
741C2×C8—81no—
742C2×C8—81no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4C22⋊C4×C2911yescharacteristic
755C4⋊C4C22⋊C4×C2911yescharacteristic
756C4⋊C4C22⋊C4×C2911yescharacteristic
757C4⋊C4C22⋊C4×C2911yescharacteristic
758C4⋊C4C22⋊C4×C2911yescharacteristic
759C4⋊C4C22⋊C4×C2911yescharacteristic
760C4⋊C4C22×C4×C2911yescharacteristic
761C4⋊C4C22×C4×C2911yescharacteristic
762C4⋊C4C22×C4×C2911yescharacteristic
763C4⋊C4C22×C4×C2911yescharacteristic
764C22⋊C4—21no—
765C22⋊C4—21no—
766C22⋊C4—21no—
767C22⋊C4—21no—
768C22⋊C4—21no—
769C22⋊C4—21no—
770C22⋊C4—21no—
771C22⋊C4—21no—
772C22⋊C4—21no—
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4C22⋊C4×C2911yescharacteristic
784C22⋊C4C22⋊C4×C2911yescharacteristic
785C22⋊C4C22⋊C4×C2911yescharacteristic
786C22⋊C4C22⋊C4×C2911yescharacteristic
787C22⋊C4C22⋊C4×C2911yescharacteristic
788C22⋊C4C22⋊C4×C2911yescharacteristic
789C42—21no—
790C42—21no—
791C42—21no—
792C42C22×C4×C2911yescharacteristic
793C42C22×C4×C2911yescharacteristic
794C42C22×C4×C2911yescharacteristic
795C42C2×D4×C2911yescharacteristic
796C42C2×D4×C2911yescharacteristic
797C42C2×D4×C2911yescharacteristic
798C42C2×D4×C2911yescharacteristic
799C42C2×D4×C2911yescharacteristic
800C42C2×D4×C2911yescharacteristic
801C42C24×C2911yescharacteristic
802C23—21no—
803C23—21no—
804C23—21no—
805C23—42no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—81no—
810C23—81no—
811C23C2×C22⋊C4×C2911yescharacteristic
812C23C2×C22⋊C4×C2911yescharacteristic
813C23C2×C22⋊C4×C2911yescharacteristic
814Q8—21no—
815Q8—21no—
816Q8—41no—
817Q8—81no—
818D4—22no—
819D4—22no—
820D4—21no—
821D4—21no—
822D4—21no—
823D4—21no—
824D4—21no—
825D4—41no—
826D4—42no—
827D4—42no—
828D4—42no—
829D4—42no—
830D4—42no—
831D4—42no—
832D4—81no—
833D4—81no—
834D4—81no—
835D4C29×#13112yes—
836C2×C4—22no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—81no—
865C2×C4—81no—
866C2×C4—81no—
867C2×C4—81no—
868C2×C4—81no—
869C2×C4—81no—
870C2×C4C2×C22⋊C4×C2911yescharacteristic
871C2×C4C2×C22⋊C4×C2911yescharacteristic
872C2×C4C2×C22⋊C4×C2911yescharacteristic
873C2×C4C2×C22⋊C4×C2911yescharacteristic
874C2×C4C2×C22⋊C4×C2911yescharacteristic
875C2×C4C2×C22⋊C4×C2911yescharacteristic
876C2×C4C2×C22⋊C4×C2911yescharacteristic
877C2×C4C2×C22⋊C4×C2911yescharacteristic
878C2×C4C2×C22⋊C4×C2911yescharacteristic
879C2×C4C23×C4×C2911yescharacteristic
880C2×C4C22×D4×C2911yescharacteristic
881C2×C4C22×D4×C2911yescharacteristic
882C8—41no—
883C8—41no—
884C8—41no—
885C8—41no—
886C8—41no—
887C8—41no—
888C8—41no—
889C8—41no—
890C22—21no—
891C22—21no—
892C22—21no—
893C22—21no—
894C22—22no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—41no—
900C22—41no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—84no—
908C22—84no—
909C22C29×#42112yes—
910C22C22×C22⋊C4×C2911yescharacteristic
911C4—21no—
912C4—21no—
913C4—21no—
914C4—21no—
915C4—21no—
916C4—21no—
917C4—21no—
918C4—21no—
919C4—21no—
920C4—21no—
921C4—41no—
922C4—41no—
923C4—41no—
924C4—41no—
925C4—41no—
926C4C2×C29×#13111yescharacteristic
927C4C29×#56811yescharacteristic
928C4C29×#57611yescharacteristic
929C4C29×#57711yescharacteristic
930C2—22no—
931C2—41no—
932C2—41no—
933C2—42no—
934C2—81no—
935C2—81no—
936C2C29×#288011yescharacteristic
937C2C29×#289711yescharacteristic
938C2C2×C29×#42111yescharacteristic
subgroupG/H
centerC2×C4×C29C22×D4
commutatorC2×C4C23×C4×C29
Frattini, cosocleC42C24×C29
socleC22×C29C22×C22⋊C4
prime radicalC29×#3481C2
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×#2990C2semidirect
3. C29×#2922C2semidirect
4. C29×#1496C2semidirect
5. C29×#1495C2semidirect
6. C29×#1494C2semidirect
7. C29×#1490C2semidirect
8. C29×#1488C2semidirect
9. C29×#1486C2semidirect
10. C29×#1483C2semidirect
11. C29×#1482C2semidirect
12. C29×#1480C2semidirect
13. C29×#1478C2semidirect
14. C29×#1477C2semidirect
15. C2×C29×D4⋊C8C2semidirect
45. C29×#432C22semidirect
46. C29×#432C22semidirect
47. C29×#431C22semidirect
48. C29×#431C22semidirect
49. C29×#431C22semidirect
50. C29×#431C22semidirect
51. C29×#431C22semidirect
53. C29×#423C22semidirect
54. C2×C29×C4⋊C8C22semidirect
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
67. C29×D4⋊C8C22semidirect
68. C29×D4⋊C8C22semidirect
69. C29×D4⋊C8C22semidirect
70. C29×D4⋊C8C22semidirect
71. C29×D4⋊C8C22semidirect
72. C29×D4⋊C8C22semidirect
73. C29×D4⋊C8C22semidirect
74. C29×D4⋊C8C22semidirect
332. #17521C29direct (N × H)
422. #2990C2×C29semidirect
423. #2922C2×C29semidirect
424. #1496C2×C29semidirect
425. #1495C2×C29semidirect
426. #1494C2×C29semidirect
427. #1490C2×C29semidirect
428. #1488C2×C29semidirect
429. #1486C2×C29semidirect
430. #1483C2×C29semidirect
431. #1482C2×C29semidirect
432. #1480C2×C29semidirect
433. #1478C2×C29semidirect
434. #1477C2×C29semidirect
435. C2×D4⋊C8C2×C29semidirect
505. #432C22×C29semidirect
506. #432C22×C29semidirect
507. #431C22×C29semidirect
508. #431C22×C29semidirect
509. #431C22×C29semidirect
510. #431C22×C29semidirect
511. #431C22×C29semidirect
513. #423C22×C29semidirect
514. C2×C4⋊C8C22×C29semidirect
515. C2×C4⋊C8C22×C29semidirect
517. C4×M16C22×C29semidirect
518. C2×C4×C8C22×C29semidirect
519. Q8⋊C8C22×C29semidirect
520. Q8⋊C8C22×C29semidirect
521. Q8⋊C8C22×C29semidirect
522. Q8⋊C8C22×C29semidirect
527. D4⋊C8C22×C29semidirect
528. D4⋊C8C22×C29semidirect
529. D4⋊C8C22×C29semidirect
530. D4⋊C8C22×C29semidirect
531. D4⋊C8C22×C29semidirect
532. D4⋊C8C22×C29semidirect
533. D4⋊C8C22×C29semidirect
534. D4⋊C8C22×C29semidirect
675. C29#17521direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#34812
C29×#29902
C29×#29222
C29×#14962
C29×#14952
C29×#14942
C29×#14902
C29×#14882
C29×#14862
C29×#14832
C29×#14822
C29×#14802
C29×#14782
C29×#14772
C2×C29×D4⋊C82
#1752129