Finite Group Databasebeta

← C29×#8427 #20303327

Subgroups — C29×#8427 #20303327

Order 7424.

700 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3509C211yesmaximal, characteristic
2C29×#1988C211yesmaximal, characteristic, complemented
3C29×#1806C211yesmaximal, characteristic
4C29×#1550C211yesmaximal, characteristic, complemented
5C29×#1546C211yesmaximal, characteristic, complemented
6C29×#1503C211yesmaximal, characteristic, complemented
7C29×#1477C211yesmaximal, characteristic
8C29×#557—21no—
9C29×#557C412yescomplemented
10C29×#556—21no—
11C29×#556C412yescomplemented
12C29×#552—22no—
13C29×#552—22no—
14C29×#541—22no—
15C29×#536—21no—
16C29×#533—21no—
17C29×#533—21no—
18C29×#533C2211yescharacteristic
19C2×C29×C4⋊Q8C2211yescharacteristic
20C29×#519—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—21no—
37C2×M16×C29—21no—
38C22×C8×C29—21no—
39C29×C4⋊Q8—22no—
40C29×C4⋊Q8—21no—
41C29×C4⋊Q8—21no—
42C29×C4⋊Q8C2×C412yes—
43C29×C4⋊Q8D411yescharacteristic
44C29×C4⋊Q8D412yes—
45C29×C4⋊Q8D411yescharacteristic
46C29×#126—24no—
47C29×#126—24no—
48C29×#125—22no—
49C29×#125—24no—
50C29×#125—22no—
51C29×#125—24no—
52C29×#125—21no—
53C29×#124—22no—
54C29×#123—24no—
55C29×C22⋊Q8—22no—
56C29×C22⋊Q8—22no—
57C29×C22⋊Q8—22no—
58C29×C22⋊Q8—22no—
59C29×C22⋊Q8—21no—
60C29×C22⋊Q8D412yes—
61C4×Q8×C29—22no—
62C4×Q8×C29—22no—
63C4×Q8×C29—22no—
64C4×Q8×C29—22no—
65C4×Q8×C29—22no—
66C4×Q8×C29—22no—
67C4×Q8×C29—21no—
68C4×Q8×C29C2×C411yescharacteristic
69C4×Q8×C29C2×C412yes—
70C4×Q8×C29D411yescharacteristic
71C4×D4×C29—21no—
72C4×D4×C29—21no—
73C4×D4×C29C2×C411yescharacteristic
74C4×D4×C29D411yescharacteristic
75C29×#117—24no—
76C29×#117—22no—
77C29×#117—21no—
78C29×#117—22no—
79C29×#117—21no—
80C29×#117D411yescharacteristic
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×C29—21no—
99#41×C29—21no—
100C2×Q8×C29—22no—
101C2×Q8×C29—21no—
102C2×Q8×C29—22no—
103C2×Q8×C29—41no—
104C2×Q8×C29—41no—
105C2×Q8×C29—41no—
106C2×Q8×C29—41no—
107C2×Q8×C29C22⋊C411yescharacteristic
108C2×Q8×C29C22⋊C412yes—
109C2×D4×C29—21no—
110C2×D4×C29C22⋊C411yescharacteristic
111C22×C4×C29—22no—
112C22×C4×C29—21no—
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—22no—
133C4⋊C4×C29—22no—
134C4⋊C4×C29—21no—
135C4⋊C4×C29—21no—
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⋊C412yes—
143C4⋊C4×C29C22⋊C411yescharacteristic
144C4⋊C4×C29C22⋊C411yescharacteristic
145C22⋊C4×C29—24no—
146C22⋊C4×C29—24no—
147C22⋊C4×C29—21no—
148C22⋊C4×C29—22no—
149C22⋊C4×C29—21no—
150C22⋊C4×C29—21no—
151C42×C29—24no—
152C42×C29—24no—
153C42×C29—21no—
154C42×C29—22no—
155C42×C29—21no—
156C42×C29—21no—
157C42×C29—41no—
158C42×C29—41no—
159C42×C29C22×C411yescharacteristic
160C42×C29C2×D411yescharacteristic
161C42×C29C2×D411yescharacteristic
162C42×C29C2×D411yescharacteristic
163#8427C2911yesmaximal, characteristic, direct product factor, Sylow
164C23×C29—21no—
165C23×C29#12011yescharacteristic
166Q8×C29—21no—
167Q8×C29—21no—
168Q8×C29—42no—
169Q8×C29—42no—
170Q8×C29—42no—
171Q8×C29—42no—
172Q8×C29—42no—
173Q8×C29—41no—
174Q8×C29—41no—
175D4×C29—21no—
176D4×C29—21no—
177D4×C29—41no—
178D4×C29—41no—
179C2×C4×C29—21no—
180C2×C4×C29—21no—
181C2×C4×C29—21no—
182C2×C4×C29—21no—
183C2×C4×C29—22no—
184C2×C4×C29—22no—
185C2×C4×C29—24no—
186C2×C4×C29—21no—
187C2×C4×C29—41no—
188C2×C4×C29—42no—
189C2×C4×C29—42no—
190C2×C4×C29—42no—
191C2×C4×C29—41no—
192C2×C4×C29—41no—
193C2×C4×C29—41no—
194C2×C4×C29—41no—
195C2×C4×C29—42no—
196C2×C4×C29—81no—
197C2×C4×C29—81no—
198C2×C4×C29C2×C22⋊C411yescharacteristic
199C2×C4×C29C2×C22⋊C411yescharacteristic
200C2×C4×C29C2×C22⋊C411yescharacteristic
201C2×C4×C29#12011yescharacteristic
202C2×C4×C29#12011yescharacteristic
203C2×C4×C29#12011yescharacteristic
204C2×C4×C29#13511yescharacteristic
205C2×C4×C29#13511yescharacteristic
206C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
207C2×C4×C29#13711yescharacteristic
208C8×C29—81no—
209C8×C29—81no—
210C8×C29—81no—
211#3509C2×C2911yescharacteristic
212#1988C2×C2911yescharacteristic, complemented
213#1806C2×C2911yescharacteristic
214#1550C2×C2911yescharacteristic, complemented
215#1546C2×C2911yescharacteristic, complemented
216#1503C2×C2911yescharacteristic, complemented
217#1477C2×C2911yescharacteristic
218C22×C29—21no—
219C22×C29—21no—
220C22×C29—41no—
221C22×C29—41no—
222C22×C29—41no—
223C22×C29#37911yescharacteristic
224C22×C29#44911yescharacteristic
225C22×C29#45211yescharacteristic
226C4×C29—21no—
227C4×C29—21no—
228C4×C29—21no—
229C4×C29—41no—
230C4×C29—42no—
231C4×C29—41no—
232C4×C29—42no—
233C4×C29—41no—
234C4×C29—44no—
235C4×C29—82no—
236C4×C29#41611yescharacteristic
237C4×C29#41711yescharacteristic
238C4×C29#44911yescharacteristic
239C4×C29#45211yescharacteristic
240C4×C29#45411yescharacteristic
241C4×C29#45611yescharacteristic
242#557—21no—
243#557C4×C2912yescomplemented
244#556—21no—
245#556C4×C2912yescomplemented
246#552—22no—
247#552—22no—
248#541—22no—
249#536—21no—
250#533—21no—
251#533—21no—
252#533C22×C2911yescharacteristic
253C2×C4⋊Q8C22×C2911yescharacteristic
254#519—21no—
255C4×#41C22×C2911yescharacteristic
256#431C22×C2911yescharacteristic
257#423C22×C2911yescharacteristic
258C2×C4⋊C8C22×C2911yescharacteristic
259C2×#104—21no—
260C4×C4⋊C4C22×C2911yescharacteristic
261#340—22no—
262#339—21no—
263#333—21no—
264#332—22no—
265#332—21no—
266#328—22no—
267Q8⋊C8—21no—
268D4⋊C8—21no—
269C2×C29—21no—
270C2×C29—21no—
271C2×C29—81no—
272C2×C29#178811yescharacteristic
273C2×C29#179311yescharacteristic
274C2×C29#179611yescharacteristic
275C2×#41D4×C2911yescharacteristic
276C22×Q8—21no—
277C2×M16—21no—
278C22×C8—21no—
279C4⋊Q8—22no—
280C4⋊Q8—21no—
281C4⋊Q8—21no—
282C4⋊Q8C2×C4×C2912yes—
283C4⋊Q8D4×C2911yescharacteristic
284C4⋊Q8D4×C2912yes—
285C4⋊Q8D4×C2911yescharacteristic
286#126—24no—
287#126—24no—
288#125—22no—
289#125—24no—
290#125—22no—
291#125—24no—
292#125—21no—
293#124—22no—
294#123—24no—
295C22⋊Q8—22no—
296C22⋊Q8—22no—
297C22⋊Q8—22no—
298C22⋊Q8—22no—
299C22⋊Q8—21no—
300C22⋊Q8D4×C2912yes—
301C4×Q8—22no—
302C4×Q8—22no—
303C4×Q8—22no—
304C4×Q8—22no—
305C4×Q8—22no—
306C4×Q8—22no—
307C4×Q8—21no—
308C4×Q8C2×C4×C2911yescharacteristic
309C4×Q8C2×C4×C2912yes—
310C4×Q8D4×C2911yescharacteristic
311C4×D4—21no—
312C4×D4—21no—
313C4×D4C2×C4×C2911yescharacteristic
314C4×D4D4×C2911yescharacteristic
315#117—24no—
316#117—22no—
317#117—21no—
318#117—22no—
319#117—21no—
320#117D4×C2911yescharacteristic
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4D4×C2912yes—
324C2×C42—21no—
325C2×C42—21no—
326C2×C42C23×C2911yescharacteristic
327C4⋊C8—21no—
328C4⋊C8—21no—
329C4⋊C8—21no—
330C4⋊C8—21no—
331C4⋊C8—21no—
332#104—42no—
333C22⋊C8—21no—
334C4×C8—21no—
335#95—21no—
336C29#842711yescharacteristic, direct product factor, Sylow
337#41—21no—
338#41—21no—
339#41—21no—
340#41—21no—
341C2×Q8—22no—
342C2×Q8—21no—
343C2×Q8—22no—
344C2×Q8—41no—
345C2×Q8—41no—
346C2×Q8—41no—
347C2×Q8—41no—
348C2×Q8C22⋊C4×C2911yescharacteristic
349C2×Q8C22⋊C4×C2912yes—
350C2×D4—21no—
351C2×D4C22⋊C4×C2911yescharacteristic
352C22×C4—22no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—41no—
357C22×C4C2×D4×C2911yescharacteristic
358C22×C4C2×D4×C2911yescharacteristic
359C22×C4C2×D4×C2911yescharacteristic
360M16—41no—
361M16—41no—
362C2×C8—42no—
363C2×C8—41no—
364C2×C8—41no—
365C2×C8—41no—
366C4⋊C4—24no—
367C4⋊C4—24no—
368C4⋊C4—24no—
369C4⋊C4—24no—
370C4⋊C4—22no—
371C4⋊C4—21no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—22no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—22no—
380C4⋊C4—22no—
381C4⋊C4—41no—
382C4⋊C4C22⋊C4×C2914yes—
383C4⋊C4C22⋊C4×C2912yes—
384C4⋊C4C22⋊C4×C2911yescharacteristic
385C4⋊C4C22⋊C4×C2911yescharacteristic
386C22⋊C4—24no—
387C22⋊C4—24no—
388C22⋊C4—21no—
389C22⋊C4—22no—
390C22⋊C4—21no—
391C22⋊C4—21no—
392C42—24no—
393C42—24no—
394C42—21no—
395C42—22no—
396C42—21no—
397C42—21no—
398C42—41no—
399C42—41no—
400C42C22×C4×C2911yescharacteristic
401C42C2×D4×C2911yescharacteristic
402C42C2×D4×C2911yescharacteristic
403C42C2×D4×C2911yescharacteristic
404C23—21no—
405C23C29×#12011yescharacteristic
406Q8—21no—
407Q8—21no—
408Q8—42no—
409Q8—42no—
410Q8—42no—
411Q8—41no—
412Q8—41no—
413Q8—42no—
414Q8—42no—
415D4—21no—
416D4—21no—
417D4—41no—
418D4—41no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—24no—
426C2×C4—21no—
427C2×C4—41no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—42no—
436C2×C4—81no—
437C2×C4—81no—
438C2×C4C2×C22⋊C4×C2911yescharacteristic
439C2×C4C2×C22⋊C4×C2911yescharacteristic
440C2×C4C2×C22⋊C4×C2911yescharacteristic
441C2×C4C29×#12011yescharacteristic
442C2×C4C29×#12011yescharacteristic
443C2×C4C29×#12011yescharacteristic
444C2×C4C29×#13511yescharacteristic
445C2×C4C29×#13511yescharacteristic
446C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
447C2×C4C29×#13711yescharacteristic
448C8—81no—
449C8—81no—
450C8—81no—
451C22—21no—
452C22—21no—
453C22—41no—
454C22—41no—
455C22—41no—
456C22C29×#37911yescharacteristic
457C22C29×#44911yescharacteristic
458C22C29×#45211yescharacteristic
459C4—21no—
460C4—21no—
461C4—21no—
462C4—41no—
463C4—44no—
464C4—41no—
465C4—42no—
466C4—41no—
467C4—42no—
468C4—82no—
469C4C29×#41611yescharacteristic
470C4C29×#41711yescharacteristic
471C4C29×#44911yescharacteristic
472C4C29×#45211yescharacteristic
473C4C29×#45411yescharacteristic
474C4C29×#45611yescharacteristic
475C2—21no—
476C2—21no—
477C2—81no—
478C2C29×#178811yescharacteristic
479C2C29×#179311yescharacteristic
480C2C29×#179611yescharacteristic
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×#1988C2semidirect
4. C29×#1550C2semidirect
5. C29×#1546C2semidirect
6. C29×#1503C2semidirect
9. C29×#557C4semidirect
11. C29×#556C4semidirect
163. #8427C29direct (N × H)
212. #1988C2×C29semidirect
214. #1550C2×C29semidirect
215. #1546C2×C29semidirect
216. #1503C2×C29semidirect
243. #557C4×C29semidirect
245. #556C4×C29semidirect
336. C29#8427direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35092
C29×#19882
C29×#18062
C29×#15502
C29×#15462
C29×#15032
C29×#14772
#842729