Finite Group Databasebeta

← C29×#8424 #20303324

Subgroups — C29×#8424 #20303324

Order 7424.

734 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3503C211yesmaximal, characteristic
2C29×#1987C211yesmaximal, characteristic, complemented
3C29×#1806C211yesmaximal, characteristic
4C29×#1550C211yesmaximal, characteristic, complemented
5C29×#1549C211yesmaximal, characteristic, complemented
6C29×#1503C211yesmaximal, characteristic, complemented
7C29×#1477C211yesmaximal, characteristic
8Q82×C29—21no—
9C29×#557C412yescomplemented
10C29×#554—21no—
11C29×#554—22no—
12D4×Q8×C29—22no—
13D4×Q8×C29C412yescomplemented
14C29×#544—22no—
15C29×#544—21no—
16C29×#533—21no—
17C29×#533C2211yescharacteristic
18C2×C29×C4⋊Q8—21no—
19C2×C29×C4⋊Q8C2211yescharacteristic
20C29×#520—21no—
21C4×#41×C29C2211yescharacteristic
22C29×#431C2211yescharacteristic
23C29×#423C2211yescharacteristic
24C2×C29×C4⋊C8C2211yescharacteristic
25C2×C29×#104—21no—
26C4×C4⋊C4×C29C2211yescharacteristic
27C29×#340—22no—
28C29×#339—21no—
29C29×#333—21no—
30C29×#332—22no—
31C29×#332—21no—
32C29×#328—22no—
33C29×Q8⋊C8—21no—
34C29×D4⋊C8—21no—
35C2×#41×C29D411yescharacteristic
36C22×Q8×C29—22no—
37C22×Q8×C29—21no—
38C2×M16×C29—21no—
39C22×C8×C29—21no—
40C29×C4⋊Q8—22no—
41C29×C4⋊Q8—22no—
42C29×C4⋊Q8—24no—
43C29×C4⋊Q8—22no—
44C29×C4⋊Q8—22no—
45C29×C4⋊Q8—21no—
46C29×C4⋊Q8—21no—
47C29×C4⋊Q8C2×C412yes—
48C29×C4⋊Q8D411yescharacteristic
49C29×C4⋊Q8D412yes—
50C29×C4⋊Q8D411yescharacteristic
51C29×#125—22no—
52C29×#125—24no—
53C29×#125—22no—
54C29×#125—21no—
55C29×C22⋊Q8—22no—
56C29×C22⋊Q8—24no—
57C29×C22⋊Q8—24no—
58C29×C22⋊Q8—21no—
59C29×C22⋊Q8—22no—
60C29×C22⋊Q8—24no—
61C29×C22⋊Q8D412yes—
62C4×Q8×C29—22no—
63C4×Q8×C29—22no—
64C4×Q8×C29—22no—
65C4×Q8×C29—21no—
66C4×Q8×C29C2×C411yescharacteristic
67C4×Q8×C29C2×C412yes—
68C4×Q8×C29D411yescharacteristic
69C4×D4×C29—24no—
70C4×D4×C29—22no—
71C4×D4×C29—21no—
72C4×D4×C29—21no—
73C4×D4×C29C2×C411yescharacteristic
74C4×D4×C29D411yescharacteristic
75C29×#117—22no—
76C29×#117—21no—
77C29×#117—21no—
78C29×#117D411yescharacteristic
79C2×C4⋊C4×C29—22no—
80C2×C4⋊C4×C29—22no—
81C2×C4⋊C4×C29—21no—
82C2×C4⋊C4×C29—21no—
83C2×C4⋊C4×C29D412yes—
84C2×C42×C29—21no—
85C2×C42×C29—21no—
86C2×C42×C29C2311yescharacteristic
87C29×C4⋊C8—21no—
88C29×C4⋊C8—21no—
89C29×C4⋊C8—21no—
90C29×C4⋊C8—21no—
91C29×C4⋊C8—21no—
92C29×#104—42no—
93C29×C22⋊C8—21no—
94C4×C8×C29—21no—
95C29×#95—21no—
96#41×C29—21no—
97#41×C29—21no—
98#41×C29SD1612yes—
99#41×C29Q1612yes—
100C2×Q8×C29—24no—
101C2×Q8×C29—22no—
102C2×Q8×C29—21no—
103C2×Q8×C29—22no—
104C2×Q8×C29—82no—
105C2×Q8×C29—84no—
106C2×Q8×C29C22⋊C411yescharacteristic
107C2×Q8×C29C22⋊C412yes—
108C2×D4×C29—21no—
109C2×D4×C29C22⋊C411yescharacteristic
110C22×C4×C29—21no—
111C22×C4×C29—24no—
112C22×C4×C29—22no—
113C22×C4×C29—21no—
114C22×C4×C29—21no—
115C22×C4×C29—41no—
116C22×C4×C29C2×D411yescharacteristic
117C22×C4×C29C2×D411yescharacteristic
118C22×C4×C29C2×D411yescharacteristic
119M16×C29—41no—
120M16×C29—41no—
121C2×C8×C29—42no—
122C2×C8×C29—41no—
123C2×C8×C29—41no—
124C2×C8×C29—41no—
125C4⋊C4×C29—24no—
126C4⋊C4×C29—24no—
127C4⋊C4×C29—24no—
128C4⋊C4×C29—24no—
129C4⋊C4×C29—22no—
130C4⋊C4×C29—21no—
131C4⋊C4×C29—22no—
132C4⋊C4×C29—21no—
133C4⋊C4×C29—22no—
134C4⋊C4×C29—21no—
135C4⋊C4×C29—22no—
136C4⋊C4×C29—21no—
137C4⋊C4×C29—21no—
138C4⋊C4×C29—22no—
139C4⋊C4×C29—22no—
140C4⋊C4×C29—41no—
141C4⋊C4×C29C22⋊C414yes—
142C4⋊C4×C29C22⋊C411yescharacteristic
143C4⋊C4×C29C22⋊C411yescharacteristic
144C4⋊C4×C29C22⋊C412yes—
145C22⋊C4×C29—24no—
146C22⋊C4×C29—22no—
147C22⋊C4×C29—21no—
148C22⋊C4×C29—21no—
149C22⋊C4×C29—21no—
150C42×C29—24no—
151C42×C29—21no—
152C42×C29—22no—
153C42×C29—21no—
154C42×C29—21no—
155C42×C29—41no—
156C42×C29—41no—
157C42×C29C22×C411yescharacteristic
158C42×C29C2×D411yescharacteristic
159C42×C29C2×D411yescharacteristic
160C42×C29C2×D411yescharacteristic
161#8424C2911yesmaximal, characteristic, direct product factor, Sylow
162C23×C29—21no—
163C23×C29#12011yescharacteristic
164Q8×C29—21no—
165Q8×C29—42no—
166Q8×C29—44no—
167Q8×C29—41no—
168Q8×C29—41no—
169Q8×C29—82no—
170Q8×C29—84no—
171Q8×C29#10312yes—
172D4×C29—22no—
173D4×C29—22no—
174D4×C29—21no—
175D4×C29#10312yes—
176C2×C4×C29—21no—
177C2×C4×C29—22no—
178C2×C4×C29—22no—
179C2×C4×C29—21no—
180C2×C4×C29—21no—
181C2×C4×C29—22no—
182C2×C4×C29—21no—
183C2×C4×C29—21no—
184C2×C4×C29—22no—
185C2×C4×C29—24no—
186C2×C4×C29—41no—
187C2×C4×C29—42no—
188C2×C4×C29—41no—
189C2×C4×C29—41no—
190C2×C4×C29—42no—
191C2×C4×C29—82no—
192C2×C4×C29—84no—
193C2×C4×C29—81no—
194C2×C4×C29—81no—
195C2×C4×C29C2×C22⋊C411yescharacteristic
196C2×C4×C29C2×C22⋊C411yescharacteristic
197C2×C4×C29C2×C22⋊C411yescharacteristic
198C2×C4×C29#12011yescharacteristic
199C2×C4×C29#12011yescharacteristic
200C2×C4×C29#12011yescharacteristic
201C2×C4×C29C2×SD1611yescharacteristic
202C2×C4×C29C2×Q1611yescharacteristic
203C2×C4×C29#13711yescharacteristic
204C2×C4×C29#13711yescharacteristic
205C8×C29—81no—
206C8×C29—81no—
207C8×C29—81no—
208#3503C2×C2911yescharacteristic
209#1987C2×C2911yescharacteristic, complemented
210#1806C2×C2911yescharacteristic
211#1550C2×C2911yescharacteristic, complemented
212#1549C2×C2911yescharacteristic, complemented
213#1503C2×C2911yescharacteristic, complemented
214#1477C2×C2911yescharacteristic
215C22×C29—21no—
216C22×C29—21no—
217C22×C29—22no—
218C22×C29—41no—
219C22×C29—41no—
220C22×C29#37911yescharacteristic
221C22×C29#44811yescharacteristic
222C22×C29#45111yescharacteristic
223C4×C29—21no—
224C4×C29—21no—
225C4×C29—21no—
226C4×C29—22no—
227C4×C29—41no—
228C4×C29—42no—
229C4×C29—41no—
230C4×C29—44no—
231C4×C29—42no—
232C4×C29—82no—
233C4×C29C2×#10311yescharacteristic
234C4×C29#41911yescharacteristic
235C4×C29#44811yescharacteristic
236C4×C29#45111yescharacteristic
237C4×C29#45411yescharacteristic
238C4×C29#45611yescharacteristic
239Q82—21no—
240#557C4×C2912yescomplemented
241#554—21no—
242#554—22no—
243D4×Q8—22no—
244D4×Q8C4×C2912yescomplemented
245#544—22no—
246#544—21no—
247#533—21no—
248#533C22×C2911yescharacteristic
249C2×C4⋊Q8—21no—
250C2×C4⋊Q8C22×C2911yescharacteristic
251#520—21no—
252C4×#41C22×C2911yescharacteristic
253#431C22×C2911yescharacteristic
254#423C22×C2911yescharacteristic
255C2×C4⋊C8C22×C2911yescharacteristic
256C2×#104—21no—
257C4×C4⋊C4C22×C2911yescharacteristic
258#340—22no—
259#339—21no—
260#333—21no—
261#332—22no—
262#332—21no—
263#328—22no—
264Q8⋊C8—21no—
265D4⋊C8—21no—
266C2×C29—21no—
267C2×C29—21no—
268C2×C29—42no—
269C2×C29#178711yescharacteristic
270C2×C29#179311yescharacteristic
271C2×C29#179511yescharacteristic
272C2×#41D4×C2911yescharacteristic
273C22×Q8—22no—
274C22×Q8—21no—
275C2×M16—21no—
276C22×C8—21no—
277C4⋊Q8—22no—
278C4⋊Q8—22no—
279C4⋊Q8—24no—
280C4⋊Q8—22no—
281C4⋊Q8—22no—
282C4⋊Q8—21no—
283C4⋊Q8—21no—
284C4⋊Q8C2×C4×C2912yes—
285C4⋊Q8D4×C2911yescharacteristic
286C4⋊Q8D4×C2912yes—
287C4⋊Q8D4×C2911yescharacteristic
288#125—22no—
289#125—24no—
290#125—22no—
291#125—21no—
292C22⋊Q8—22no—
293C22⋊Q8—24no—
294C22⋊Q8—24no—
295C22⋊Q8—21no—
296C22⋊Q8—22no—
297C22⋊Q8—24no—
298C22⋊Q8D4×C2912yes—
299C4×Q8—22no—
300C4×Q8—22no—
301C4×Q8—22no—
302C4×Q8—21no—
303C4×Q8C2×C4×C2911yescharacteristic
304C4×Q8C2×C4×C2912yes—
305C4×Q8D4×C2911yescharacteristic
306C4×D4—24no—
307C4×D4—22no—
308C4×D4—21no—
309C4×D4—21no—
310C4×D4C2×C4×C2911yescharacteristic
311C4×D4D4×C2911yescharacteristic
312#117—22no—
313#117—21no—
314#117—21no—
315#117D4×C2911yescharacteristic
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4D4×C2912yes—
321C2×C42—21no—
322C2×C42—21no—
323C2×C42C23×C2911yescharacteristic
324C4⋊C8—21no—
325C4⋊C8—21no—
326C4⋊C8—21no—
327C4⋊C8—21no—
328C4⋊C8—21no—
329#104—42no—
330C22⋊C8—21no—
331C4×C8—21no—
332#95—21no—
333C29#842411yescharacteristic, direct product factor, Sylow
334#41—21no—
335#41—21no—
336#41SD16×C2912yes—
337#41Q16×C2912yes—
338C2×Q8—24no—
339C2×Q8—22no—
340C2×Q8—21no—
341C2×Q8—22no—
342C2×Q8—82no—
343C2×Q8—84no—
344C2×Q8C22⋊C4×C2911yescharacteristic
345C2×Q8C22⋊C4×C2912yes—
346C2×D4—21no—
347C2×D4C22⋊C4×C2911yescharacteristic
348C22×C4—21no—
349C22×C4—24no—
350C22×C4—22no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—41no—
354C22×C4C2×D4×C2911yescharacteristic
355C22×C4C2×D4×C2911yescharacteristic
356C22×C4C2×D4×C2911yescharacteristic
357M16—41no—
358M16—41no—
359C2×C8—42no—
360C2×C8—41no—
361C2×C8—41no—
362C2×C8—41no—
363C4⋊C4—24no—
364C4⋊C4—24no—
365C4⋊C4—24no—
366C4⋊C4—24no—
367C4⋊C4—22no—
368C4⋊C4—21no—
369C4⋊C4—22no—
370C4⋊C4—21no—
371C4⋊C4—22no—
372C4⋊C4—21no—
373C4⋊C4—22no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—22no—
377C4⋊C4—22no—
378C4⋊C4—41no—
379C4⋊C4C22⋊C4×C2914yes—
380C4⋊C4C22⋊C4×C2911yescharacteristic
381C4⋊C4C22⋊C4×C2911yescharacteristic
382C4⋊C4C22⋊C4×C2912yes—
383C22⋊C4—24no—
384C22⋊C4—22no—
385C22⋊C4—21no—
386C22⋊C4—21no—
387C22⋊C4—21no—
388C42—24no—
389C42—21no—
390C42—22no—
391C42—21no—
392C42—21no—
393C42—41no—
394C42—41no—
395C42C22×C4×C2911yescharacteristic
396C42C2×D4×C2911yescharacteristic
397C42C2×D4×C2911yescharacteristic
398C42C2×D4×C2911yescharacteristic
399C23—21no—
400C23C29×#12011yescharacteristic
401Q8—21no—
402Q8—42no—
403Q8—44no—
404Q8—41no—
405Q8—41no—
406Q8—82no—
407Q8—84no—
408Q8C29×#10312yes—
409D4—22no—
410D4—22no—
411D4—21no—
412D4C29×#10312yes—
413C2×C4—21no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—22no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—22no—
422C2×C4—24no—
423C2×C4—41no—
424C2×C4—42no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—82no—
429C2×C4—84no—
430C2×C4—81no—
431C2×C4—81no—
432C2×C4C2×C22⋊C4×C2911yescharacteristic
433C2×C4C2×C22⋊C4×C2911yescharacteristic
434C2×C4C2×C22⋊C4×C2911yescharacteristic
435C2×C4C29×#12011yescharacteristic
436C2×C4C29×#12011yescharacteristic
437C2×C4C29×#12011yescharacteristic
438C2×C4C2×SD16×C2911yescharacteristic
439C2×C4C2×Q16×C2911yescharacteristic
440C2×C4C29×#13711yescharacteristic
441C2×C4C29×#13711yescharacteristic
442C8—81no—
443C8—81no—
444C8—81no—
445C22—21no—
446C22—21no—
447C22—22no—
448C22—41no—
449C22—41no—
450C22C29×#37911yescharacteristic
451C22C29×#44811yescharacteristic
452C22C29×#45111yescharacteristic
453C4—22no—
454C4—21no—
455C4—21no—
456C4—21no—
457C4—41no—
458C4—42no—
459C4—41no—
460C4—44no—
461C4—42no—
462C4—82no—
463C4C2×C29×#10311yescharacteristic
464C4C29×#41911yescharacteristic
465C4C29×#44811yescharacteristic
466C4C29×#45111yescharacteristic
467C4C29×#45411yescharacteristic
468C4C29×#45611yescharacteristic
469C2—21no—
470C2—21no—
471C2—42no—
472C2C29×#178711yescharacteristic
473C2C29×#179311yescharacteristic
474C2C29×#179511yescharacteristic
subgroupG/H
center, socleC22×C29#379
commutatorC42C22×C4×C29
Frattini, cosocleC2×C42C23×C29
prime radicalC2×#41×C29D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#1987C2semidirect
4. C29×#1550C2semidirect
5. C29×#1549C2semidirect
6. C29×#1503C2semidirect
9. C29×#557C4semidirect
13. D4×Q8×C29C4semidirect
161. #8424C29direct (N × H)
209. #1987C2×C29semidirect
211. #1550C2×C29semidirect
212. #1549C2×C29semidirect
213. #1503C2×C29semidirect
240. #557C4×C29semidirect
244. D4×Q8C4×C29semidirect
333. C29#8424direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35032
C29×#19872
C29×#18062
C29×#15502
C29×#15492
C29×#15032
C29×#14772
#842429