Finite Group Databasebeta

← C29×#8997 #20303897

Subgroups — C29×#8997 #20303897

Order 7424.

452 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3171C211yesmaximal, characteristic
2C29×#2995C211yesmaximal, characteristic, complemented
3C29×#1963C211yesmaximal, characteristic, complemented
4C29×#1500C211yesmaximal, characteristic, complemented
5C29×#1496C211yesmaximal, characteristic, complemented
6C29×#1300C211yesmaximal, characteristic, complemented
7C29×#1299C211yesmaximal, characteristic, complemented
8C29×#532C2211yescharacteristic
9C29×#529C2211yescharacteristic
10C29×#501C411yescharacteristic, complemented
11C29×#496C411yescharacteristic, complemented
12C29×#490C411yescharacteristic, complemented
13C29×#489C411yescharacteristic, complemented
14C29×#469—21no—
15C29×#468—21no—
16C29×#446—21no—
17C4×SD16×C29—21no—
18C4×D8×C29—21no—
19C29×#436—21no—
20C29×#435—21no—
21C29×#435—21no—
22C29×#433—21no—
23C29×#432C2211yescharacteristic
24C29×#431C2211yescharacteristic
25C29×#424—21no—
26C29×#423C2211yescharacteristic
27C2×C29×#104—21no—
28C2×C29×#104—21no—
29C4×M16×C29C2211yescharacteristic
30C29×#376C2211yescharacteristic
31C29×#328—21no—
32C29×#327—21no—
33C29×D4⋊C8—21no—
34C29×D4⋊C8—21no—
35C2×#41×C29—21no—
36C2×SD16×C29—21no—
37C2×D8×C29—21no—
38C2×M16×C29—21no—
39C2×M16×C29—21no—
40C2×M16×C29D411yescharacteristic
41C2×M16×C29D411yescharacteristic
42C22×C8×C29—21no—
43C29×C4⋊Q8C2×C411yescharacteristic
44C29×#127C2×C411yescharacteristic
45C29×#126—21no—
46C29×#125C2×C411yescharacteristic
47C29×#124—21no—
48C29×#124C2×C411yescharacteristic
49C29×#123—21no—
50C29×C22⋊Q8D411yescharacteristic
51C29×#121—21no—
52C29×#121—21no—
53C29×#121D411yescharacteristic
54C4×Q8×C29D411yescharacteristic
55C4×D4×C29—21no—
56C4×D4×C29—21no—
57C4×D4×C29—21no—
58C4×D4×C29D411yescharacteristic
59C29×#117—21no—
60C2×C42×C29—21no—
61C2×C42×C29C2311yescharacteristic
62C29×#107—21no—
63C29×#106—21no—
64C29×C4⋊C8—21no—
65C29×C4⋊C8—21no—
66C29×C4⋊C8—21no—
67C29×C4⋊C8—21no—
68C29×C4⋊C8—21no—
69C29×C4⋊C8D411yescharacteristic
70C29×C4⋊C8D411yescharacteristic
71C29×#104—42no—
72C29×#104—42no—
73C29×#103—21no—
74C29×#102—21no—
75C29×#102—21no—
76C29×#102—21no—
77C29×C22⋊C8—21no—
78C29×C22⋊C8—21no—
79C29×C22⋊C8—21no—
80C29×C22⋊C8—21no—
81C29×#97—21no—
82C29×#97—21no—
83C29×#97C2×C411yescharacteristic
84C29×#97C2×C411yescharacteristic
85C4×C8×C29—21no—
86C4×C8×C29—21no—
87C4×C8×C29—21no—
88C29×#95—21no—
89C29×#95—21no—
90#41×C29—41no—
91#41×C29—41no—
92#41×C29—41no—
93#41×C29—41no—
94C2×Q8×C29—21no—
95C2×Q8×C29C22⋊C411yescharacteristic
96C2×D4×C29—21no—
97C2×D4×C29—21no—
98C2×D4×C29—21no—
99C2×D4×C29—21no—
100C2×D4×C29—41no—
101C2×D4×C29C22⋊C411yescharacteristic
102C22×C4×C29—21no—
103C22×C4×C29—41no—
104C22×C4×C29—41no—
105C22×C4×C29C2×D411yescharacteristic
106C22×C4×C29C2×D411yescharacteristic
107C22×C4×C29#4111yescharacteristic
108SD16×C29—42no—
109D8×C29—42no—
110M16×C29—42no—
111M16×C29—41no—
112M16×C29—41no—
113M16×C29—81no—
114C2×C8×C29—21no—
115C2×C8×C29—21no—
116C2×C8×C29—21no—
117C2×C8×C29—21no—
118C2×C8×C29—21no—
119C2×C8×C29—21no—
120C2×C8×C29—41no—
121C2×C8×C29—81no—
122C4⋊C4×C29—21no—
123C4⋊C4×C29—21no—
124C4⋊C4×C29—21no—
125C4⋊C4×C29—21no—
126C4⋊C4×C29—21no—
127C4⋊C4×C29—21no—
128C4⋊C4×C29C22⋊C411yescharacteristic
129C4⋊C4×C29C22⋊C411yescharacteristic
130C22⋊C4×C29—21no—
131C22⋊C4×C29—21no—
132C22⋊C4×C29—21no—
133C22⋊C4×C29—21no—
134C22⋊C4×C29—21no—
135C22⋊C4×C29—41no—
136C22⋊C4×C29—41no—
137C42×C29—21no—
138C42×C29—22no—
139C42×C29—41no—
140C42×C29C22×C411yescharacteristic
141C42×C29C2×D411yescharacteristic
142C42×C29C2×D411yescharacteristic
143C42×C29#4111yescharacteristic
144#8997C2911yesmaximal, characteristic, direct product factor, Sylow
145C23×C29—21no—
146C23×C29—41no—
147C23×C29#12111yescharacteristic
148Q8×C29—41no—
149Q8×C29—41no—
150Q8×C29—41no—
151D4×C29—41no—
152D4×C29—41no—
153D4×C29—41no—
154D4×C29—42no—
155D4×C29—41no—
156D4×C29—41no—
157D4×C29—81no—
158D4×C29—81no—
159D4×C29—81no—
160C2×C4×C29—21no—
161C2×C4×C29—21no—
162C2×C4×C29—21no—
163C2×C4×C29—21no—
164C2×C4×C29—21no—
165C2×C4×C29—41no—
166C2×C4×C29—41no—
167C2×C4×C29—41no—
168C2×C4×C29—41no—
169C2×C4×C29—42no—
170C2×C4×C29—41no—
171C2×C4×C29—81no—
172C2×C4×C29—81no—
173C2×C4×C29—81no—
174C2×C4×C29—81no—
175C2×C4×C29C2×C22⋊C411yescharacteristic
176C2×C4×C29C4×D411yescharacteristic
177C2×C4×C29C4×D411yescharacteristic
178C2×C4×C29#12011yescharacteristic
179C2×C4×C29#12111yescharacteristic
180C2×C4×C29#12311yescharacteristic
181C8×C29—22no—
182C8×C29—41no—
183C8×C29—41no—
184C8×C29—41no—
185C8×C29—41no—
186C8×C29—41no—
187C8×C29—81no—
188#3171C2×C2911yescharacteristic
189#2995C2×C2911yescharacteristic, complemented
190#1963C2×C2911yescharacteristic, complemented
191#1500C2×C2911yescharacteristic, complemented
192#1496C2×C2911yescharacteristic, complemented
193#1300C2×C2911yescharacteristic, complemented
194#1299C2×C2911yescharacteristic, complemented
195C22×C29—21no—
196C22×C29—21no—
197C22×C29—21no—
198C22×C29—41no—
199C22×C29—41no—
200C22×C29—41no—
201C22×C29—81no—
202C22×C29—81no—
203C22×C29—81no—
204C22×C29#38611yescharacteristic
205C4×C29—21no—
206C4×C29—21no—
207C4×C29—21no—
208C4×C29—21no—
209C4×C29—21no—
210C4×C29—41no—
211C4×C29—41no—
212C4×C29—41no—
213C4×C29—82no—
214C4×C29—81no—
215C4×C29#45311yescharacteristic
216C4×C29#45411yescharacteristic
217#532C22×C2911yescharacteristic
218#529C22×C2911yescharacteristic
219#501C4×C2911yescharacteristic, complemented
220#496C4×C2911yescharacteristic, complemented
221#490C4×C2911yescharacteristic, complemented
222#489C4×C2911yescharacteristic, complemented
223#469—21no—
224#468—21no—
225#446—21no—
226C4×SD16—21no—
227C4×D8—21no—
228#436—21no—
229#435—21no—
230#435—21no—
231#433—21no—
232#432C22×C2911yescharacteristic
233#431C22×C2911yescharacteristic
234#424—21no—
235#423C22×C2911yescharacteristic
236C2×#104—21no—
237C2×#104—21no—
238C4×M16C22×C2911yescharacteristic
239#376C22×C2911yescharacteristic
240#328—21no—
241#327—21no—
242D4⋊C8—21no—
243D4⋊C8—21no—
244C2×C29—41no—
245C2×C29—81no—
246C2×C29—161no—
247C2×C29#188111yescharacteristic
248C2×C29#188311yescharacteristic
249C2×C29#188411yescharacteristic
250C2×#41—21no—
251C2×SD16—21no—
252C2×D8—21no—
253C2×M16—21no—
254C2×M16—21no—
255C2×M16D4×C2911yescharacteristic
256C2×M16D4×C2911yescharacteristic
257C22×C8—21no—
258C4⋊Q8C2×C4×C2911yescharacteristic
259#127C2×C4×C2911yescharacteristic
260#126—21no—
261#125C2×C4×C2911yescharacteristic
262#124—21no—
263#124C2×C4×C2911yescharacteristic
264#123—21no—
265C22⋊Q8D4×C2911yescharacteristic
266#121—21no—
267#121—21no—
268#121D4×C2911yescharacteristic
269C4×Q8D4×C2911yescharacteristic
270C4×D4—21no—
271C4×D4—21no—
272C4×D4—21no—
273C4×D4D4×C2911yescharacteristic
274#117—21no—
275C2×C42—21no—
276C2×C42C23×C2911yescharacteristic
277#107—21no—
278#106—21no—
279C4⋊C8—21no—
280C4⋊C8—21no—
281C4⋊C8—21no—
282C4⋊C8—21no—
283C4⋊C8—21no—
284C4⋊C8D4×C2911yescharacteristic
285C4⋊C8D4×C2911yescharacteristic
286#104—42no—
287#104—42no—
288#103—21no—
289#102—21no—
290#102—21no—
291#102—21no—
292C22⋊C8—21no—
293C22⋊C8—21no—
294C22⋊C8—21no—
295C22⋊C8—21no—
296#97—21no—
297#97—21no—
298#97C2×C4×C2911yescharacteristic
299#97C2×C4×C2911yescharacteristic
300C4×C8—21no—
301C4×C8—21no—
302C4×C8—21no—
303#95—21no—
304#95—21no—
305C29#899711yescharacteristic, direct product factor, Sylow
306#41—41no—
307#41—41no—
308#41—41no—
309#41—41no—
310C2×Q8—21no—
311C2×Q8C22⋊C4×C2911yescharacteristic
312C2×D4—21no—
313C2×D4—21no—
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—41no—
317C2×D4C22⋊C4×C2911yescharacteristic
318C22×C4—21no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4C2×D4×C2911yescharacteristic
322C22×C4C2×D4×C2911yescharacteristic
323C22×C4#41×C2911yescharacteristic
324SD16—42no—
325D8—42no—
326M16—42no—
327M16—41no—
328M16—41no—
329M16—81no—
330C2×C8—21no—
331C2×C8—21no—
332C2×C8—21no—
333C2×C8—21no—
334C2×C8—21no—
335C2×C8—21no—
336C2×C8—41no—
337C2×C8—81no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4C22⋊C4×C2911yescharacteristic
345C4⋊C4C22⋊C4×C2911yescharacteristic
346C22⋊C4—21no—
347C22⋊C4—21no—
348C22⋊C4—21no—
349C22⋊C4—21no—
350C22⋊C4—21no—
351C22⋊C4—41no—
352C22⋊C4—41no—
353C42—21no—
354C42—22no—
355C42—41no—
356C42C22×C4×C2911yescharacteristic
357C42C2×D4×C2911yescharacteristic
358C42C2×D4×C2911yescharacteristic
359C42#41×C2911yescharacteristic
360C23—21no—
361C23—41no—
362C23C29×#12111yescharacteristic
363Q8—41no—
364Q8—41no—
365Q8—41no—
366D4—41no—
367D4—41no—
368D4—41no—
369D4—41no—
370D4—41no—
371D4—42no—
372D4—81no—
373D4—81no—
374D4—81no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—41no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4—81no—
390C2×C4C2×C22⋊C4×C2911yescharacteristic
391C2×C4C4×D4×C2911yescharacteristic
392C2×C4C4×D4×C2911yescharacteristic
393C2×C4C29×#12011yescharacteristic
394C2×C4C29×#12111yescharacteristic
395C2×C4C29×#12311yescharacteristic
396C8—22no—
397C8—41no—
398C8—41no—
399C8—41no—
400C8—41no—
401C8—41no—
402C8—81no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—81no—
410C22—81no—
411C22—81no—
412C22C29×#38611yescharacteristic
413C4—21no—
414C4—21no—
415C4—21no—
416C4—21no—
417C4—21no—
418C4—41no—
419C4—41no—
420C4—41no—
421C4—82no—
422C4—81no—
423C4C29×#45311yescharacteristic
424C4C29×#45411yescharacteristic
425C2—41no—
426C2—81no—
427C2—161no—
428C2C29×#188111yescharacteristic
429C2C29×#188311yescharacteristic
430C2C29×#188411yescharacteristic
subgroupG/H
centerC2×C4×C29#120
commutatorC42C22×C4×C29
Frattini, cosocleC2×C42C23×C29
socleC22×C29#386
prime radicalC29×#3171C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#2995C2semidirect
3. C29×#1963C2semidirect
4. C29×#1500C2semidirect
5. C29×#1496C2semidirect
6. C29×#1300C2semidirect
7. C29×#1299C2semidirect
10. C29×#501C4semidirect
11. C29×#496C4semidirect
12. C29×#490C4semidirect
13. C29×#489C4semidirect
144. #8997C29direct (N × H)
189. #2995C2×C29semidirect
190. #1963C2×C29semidirect
191. #1500C2×C29semidirect
192. #1496C2×C29semidirect
193. #1300C2×C29semidirect
194. #1299C2×C29semidirect
219. #501C4×C29semidirect
220. #496C4×C29semidirect
221. #490C4×C29semidirect
222. #489C4×C29semidirect
305. C29#8997direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#31712
C29×#29952
C29×#19632
C29×#15002
C29×#14962
C29×#13002
C29×#12992
#899729