Finite Group Databasebeta

← C29×#61721 #20356621

Subgroups — C29×#61721 #20356621

Order 7424.

1798 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3501C211yesmaximal, characteristic, complemented
2C2×C29×#555C211yesmaximal, characteristic
3C29×#3357C218yesmaximal, complemented
4C29×#3329C218yesmaximal, complemented
5C29×#3230C212yesmaximal, complemented
6C29×#3193C214yesmaximal, complemented
7C29×#3101C212yesmaximal, complemented
8C29×#3095C214yesmaximal, complemented
9C29×#2975C211yesmaximal, characteristic, complemented
10C29×#555—24no—
11C29×#555C2218yes—
12C29×#554—24no—
13C29×#554C2214yescomplemented
14D4×Q8×C29C2214yescomplemented
15C29×#544—21no—
16C29×#543—22no—
17C29×#533C2212yes—
18C2×C29×C4⋊Q8C2211yescharacteristic
19C2×C29×#124—22no—
20C2×C29×C22⋊Q8C2214yes—
21C2×C29×#121—21no—
22C2×C29×#121C2212yes—
23C29×#518—21no—
24C2×C4×D4×C29C2211yescharacteristic
25C2×C4×D4×C29C2211yescharacteristic
26C2×C29×#117—21no—
27C2×C29×#117C2212yes—
28C29×#500C2214yescomplemented
29C29×#487C2214yescomplemented
30C29×#485C22116yescomplemented
31C29×#484C2218yes—
32C29×#483C2214yes—
33C29×#480C2218yescomplemented
34C29×#477C2218yescomplemented
35C29×#476C2214yescomplemented
36C29×#468C22116yescomplemented
37C29×#461C2214yescomplemented
38C29×#450C2214yes—
39C29×#448C2218yescomplemented
40C4×SD16×C29C2218yescomplemented
41C29×#436C2218yescomplemented
42C29×#431C2212yes—
43C29×#428C2218yescomplemented
44C29×#419C2218yescomplemented
45C29×#407C2214yes—
46C22×Q8×C29—21no—
47C22×Q8×C29C2314yes—
48C22×D4×C29—22no—
49C22×D4×C29D411yescharacteristic
50C22×D4×C29C2311yescharacteristic
51C23×C4×C29—21no—
52C23×C4×C29C2312yes—
53C2×SD16×C29C2318yes—
54C2×M16×C29C2318yes—
55C29×C4⋊Q8—24no—
56C29×C4⋊Q8—22no—
57C29×C4⋊Q8C2312yes—
58C29×C4⋊Q8C2312yes—
59C29×C4⋊Q8C2314yes—
60C29×#125—24no—
61C29×#125—22no—
62C29×#124—216no—
63C29×C22⋊Q8—24no—
64C29×C22⋊Q8—24no—
65C29×C22⋊Q8—22no—
66C29×C22⋊Q8—28no—
67C29×C22⋊Q8—28no—
68C29×C22⋊Q8C2314yes—
69C29×C22⋊Q8C2318yes—
70C29×#121—28no—
71C29×#121—24no—
72C29×#121C2318yes—
73C4×Q8×C29—22no—
74C4×Q8×C29C2314yes—
75C4×D4×C29—24no—
76C4×D4×C29—24no—
77C4×D4×C29—22no—
78C4×D4×C29D414yes—
79C4×D4×C29C2314yes—
80C4×D4×C29C2314yes—
81C29×#117—24no—
82C29×#117—22no—
83C29×#117—28no—
84C29×#117C2318yes—
85C2×C4⋊C4×C29—21no—
86C2×C4⋊C4×C29—24no—
87C2×C4⋊C4×C29D411yescharacteristic
88C2×C4⋊C4×C29C2314yes—
89C2×C4⋊C4×C29C2311yescharacteristic
90C2×C4⋊C4×C29C2312yes—
91C2×C22⋊C4×C29—22no—
92C2×C22⋊C4×C29—24no—
93C2×C22⋊C4×C29—22no—
94C2×C22⋊C4×C29—21no—
95C2×C22⋊C4×C29D412yes—
96C2×C42×C29—22no—
97C2×C42×C29C2311yescharacteristic
98C29×#107C23116yes—
99C29×#106C2318yes—
100C29×C4⋊C8C2314yes—
101C29×#103C2318yes—
102C29×#103C23116yes—
103C29×#102C2318yes—
104C29×C22⋊C8C2314yes—
105C29×C22⋊C8C2318yes—
106C4×C8×C29C2314yes—
107C24×C29—21no—
108C24×C29C2×D412yes—
109C2×Q8×C29—22no—
110C2×Q8×C29—24no—
111C2×Q8×C29—24no—
112C2×Q8×C29—48no—
113C2×Q8×C29—82no—
114C2×Q8×C29C2414yes—
115C2×D4×C29—28no—
116C2×D4×C29—24no—
117C2×D4×C29—21no—
118C2×D4×C29—42no—
119C2×D4×C29—84no—
120C2×D4×C29C2×D414yes—
121C2×D4×C29C2412yes—
122C22×C4×C29—21no—
123C22×C4×C29—22no—
124C22×C4×C29—24no—
125C22×C4×C29—24no—
126C22×C4×C29—24no—
127C22×C4×C29—44no—
128C22×C4×C29—44no—
129C22×C4×C29C2×D412yes—
130C22×C4×C29C2×D411yescharacteristic
131C22×C4×C29C2×D414yes—
132C22×C4×C29C2×D411yescharacteristic
133C22×C4×C29C2411yescharacteristic
134C22×C4×C29C2414yes—
135SD16×C29—48no—
136M16×C29—48no—
137C2×C8×C29C2418yes—
138C4⋊C4×C29—24no—
139C4⋊C4×C29—24no—
140C4⋊C4×C29—28no—
141C4⋊C4×C29—21no—
142C4⋊C4×C29—22no—
143C4⋊C4×C29—24no—
144C4⋊C4×C29—22no—
145C4⋊C4×C29—22no—
146C4⋊C4×C29—22no—
147C4⋊C4×C29—24no—
148C4⋊C4×C29C2×D414yes—
149C4⋊C4×C29C2414yes—
150C4⋊C4×C29C2412yes—
151C4⋊C4×C29C2414yes—
152C22⋊C4×C29—24no—
153C22⋊C4×C29—28no—
154C22⋊C4×C29—28no—
155C22⋊C4×C29—28no—
156C22⋊C4×C29—24no—
157C22⋊C4×C29C2×D418yes—
158C42×C29—28no—
159C42×C29—24no—
160C42×C29C2×D412yes—
161C42×C29C2412yes—
162#61721C2911yesmaximal, characteristic, direct product factor, Sylow
163C23×C29—24no—
164C23×C29—22no—
165C23×C29—42no—
166C23×C29—42no—
167C23×C29—42no—
168C23×C29—42no—
169C23×C29—42no—
170C23×C29C22×D414yes—
171C23×C29C22×D411yescharacteristic
172Q8×C29—28no—
173Q8×C29—82no—
174Q8×C29—84no—
175Q8×C29—84no—
176D4×C29—28no—
177D4×C29—24no—
178D4×C29—42no—
179D4×C29—88no—
180C2×C4×C29—28no—
181C2×C4×C29—22no—
182C2×C4×C29—22no—
183C2×C4×C29—24no—
184C2×C4×C29—24no—
185C2×C4×C29—24no—
186C2×C4×C29—44no—
187C2×C4×C29—42no—
188C2×C4×C29—41no—
189C2×C4×C29—44no—
190C2×C4×C29—42no—
191C2×C4×C29—48no—
192C2×C4×C29—84no—
193C2×C4×C29—84no—
194C2×C4×C29#13714yes—
195C2×C4×C29C22×D414yes—
196C2×C4×C29C22×D411yescharacteristic
197C2×C4×C29C22×D412yes—
198C2×C4×C29C22×D412yes—
199C2×C4×C29C2511yescharacteristic
200C8×C29—28no—
201#3501C2×C2911yescharacteristic, complemented
202C2×#555C2×C2911yescharacteristic
203#3357C2×C2918yescomplemented
204#3329C2×C2918yescomplemented
205#3230C2×C2912yescomplemented
206#3193C2×C2914yescomplemented
207#3101C2×C2912yescomplemented
208#3095C2×C2914yescomplemented
209#2975C2×C2911yescharacteristic, complemented
210C22×C29—21no—
211C22×C29—21no—
212C22×C29—24no—
213C22×C29—24no—
214C22×C29—24no—
215C22×C29—42no—
216C22×C29—42no—
217C22×C29—42no—
218C22×C29—84no—
219C22×C29—84no—
220C22×C29C2×#13712yes—
221C22×C29C23×D411yescharacteristic
222C4×C29—22no—
223C4×C29—21no—
224C4×C29—24no—
225C4×C29—44no—
226C4×C29—44no—
227C4×C29—44no—
228C4×C29—42no—
229C4×C29C2×#13714yes—
230C4×C29#58512yes—
231#555—24no—
232#555C22×C2918yes—
233#554—24no—
234#554C22×C2914yescomplemented
235D4×Q8C22×C2914yescomplemented
236#544—21no—
237#543—22no—
238#533C22×C2912yes—
239C2×C4⋊Q8C22×C2911yescharacteristic
240C2×#124—22no—
241C2×C22⋊Q8C22×C2914yes—
242C2×#121—21no—
243C2×#121C22×C2912yes—
244#518—21no—
245C2×C4×D4C22×C2911yescharacteristic
246C2×C4×D4C22×C2911yescharacteristic
247C2×#117—21no—
248C2×#117C22×C2912yes—
249#500C22×C2914yescomplemented
250#487C22×C2914yescomplemented
251#485C22×C29116yescomplemented
252#484C22×C2918yes—
253#483C22×C2914yes—
254#480C22×C2918yescomplemented
255#477C22×C2918yescomplemented
256#476C22×C2914yescomplemented
257#468C22×C29116yescomplemented
258#461C22×C2914yescomplemented
259#450C22×C2914yes—
260#448C22×C2918yescomplemented
261C4×SD16C22×C2918yescomplemented
262#436C22×C2918yescomplemented
263#431C22×C2912yes—
264#428C22×C2918yescomplemented
265#419C22×C2918yescomplemented
266#407C22×C2914yes—
267C2×C29—22no—
268C2×C29—44no—
269C2×C29—82no—
270C2×C29#348511yescharacteristic
271C2×C29C22×#13711yescharacteristic
272C2×C29#358511yescharacteristic
273C22×Q8—21no—
274C22×Q8C23×C2914yes—
275C22×D4—22no—
276C22×D4D4×C2911yescharacteristic
277C22×D4C23×C2911yescharacteristic
278C23×C4—21no—
279C23×C4C23×C2912yes—
280C2×SD16C23×C2918yes—
281C2×M16C23×C2918yes—
282C4⋊Q8—24no—
283C4⋊Q8—22no—
284C4⋊Q8C23×C2912yes—
285C4⋊Q8C23×C2914yes—
286C4⋊Q8C23×C2912yes—
287#125—24no—
288#125—22no—
289#124—216no—
290C22⋊Q8—24no—
291C22⋊Q8—24no—
292C22⋊Q8—22no—
293C22⋊Q8—28no—
294C22⋊Q8—28no—
295C22⋊Q8C23×C2914yes—
296C22⋊Q8C23×C2918yes—
297#121—28no—
298#121—24no—
299#121C23×C2918yes—
300C4×Q8—22no—
301C4×Q8C23×C2914yes—
302C4×D4—24no—
303C4×D4—24no—
304C4×D4—22no—
305C4×D4D4×C2914yes—
306C4×D4C23×C2914yes—
307C4×D4C23×C2914yes—
308#117—24no—
309#117—22no—
310#117—28no—
311#117C23×C2918yes—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4D4×C2911yescharacteristic
315C2×C4⋊C4C23×C2911yescharacteristic
316C2×C4⋊C4C23×C2912yes—
317C2×C4⋊C4C23×C2914yes—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—21no—
322C2×C22⋊C4D4×C2912yes—
323C2×C42—22no—
324C2×C42C23×C2911yescharacteristic
325#107C23×C29116yes—
326#106C23×C2918yes—
327C4⋊C8C23×C2914yes—
328#103C23×C2918yes—
329#103C23×C29116yes—
330#102C23×C2918yes—
331C22⋊C8C23×C2914yes—
332C22⋊C8C23×C2918yes—
333C4×C8C23×C2914yes—
334C29#6172111yescharacteristic, direct product factor, Sylow
335C24—21no—
336C24C2×D4×C2912yes—
337C2×Q8—22no—
338C2×Q8—24no—
339C2×Q8—24no—
340C2×Q8—48no—
341C2×Q8—82no—
342C2×Q8C24×C2914yes—
343C2×D4—28no—
344C2×D4—24no—
345C2×D4—21no—
346C2×D4—42no—
347C2×D4—84no—
348C2×D4C2×D4×C2914yes—
349C2×D4C24×C2912yes—
350C22×C4—21no—
351C22×C4—22no—
352C22×C4—24no—
353C22×C4—24no—
354C22×C4—24no—
355C22×C4—44no—
356C22×C4—44no—
357C22×C4C2×D4×C2912yes—
358C22×C4C2×D4×C2911yescharacteristic
359C22×C4C2×D4×C2914yes—
360C22×C4C2×D4×C2911yescharacteristic
361C22×C4C24×C2911yescharacteristic
362C22×C4C24×C2914yes—
363SD16—48no—
364M16—48no—
365C2×C8C24×C2918yes—
366C4⋊C4—24no—
367C4⋊C4—24no—
368C4⋊C4—28no—
369C4⋊C4—21no—
370C4⋊C4—22no—
371C4⋊C4—24no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—22no—
375C4⋊C4—24no—
376C4⋊C4C2×D4×C2914yes—
377C4⋊C4C24×C2914yes—
378C4⋊C4C24×C2912yes—
379C4⋊C4C24×C2914yes—
380C22⋊C4—24no—
381C22⋊C4—28no—
382C22⋊C4—28no—
383C22⋊C4—28no—
384C22⋊C4—24no—
385C22⋊C4C2×D4×C2918yes—
386C42—28no—
387C42—24no—
388C42C2×D4×C2912yes—
389C42C24×C2912yes—
390C23—24no—
391C23—22no—
392C23—42no—
393C23—42no—
394C23—42no—
395C23—42no—
396C23—42no—
397C23C22×D4×C2914yes—
398C23C22×D4×C2911yescharacteristic
399Q8—28no—
400Q8—84no—
401Q8—84no—
402Q8—82no—
403D4—28no—
404D4—24no—
405D4—42no—
406D4—88no—
407C2×C4—28no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—24no—
411C2×C4—24no—
412C2×C4—24no—
413C2×C4—44no—
414C2×C4—42no—
415C2×C4—41no—
416C2×C4—44no—
417C2×C4—42no—
418C2×C4—48no—
419C2×C4—84no—
420C2×C4—84no—
421C2×C4C29×#13714yes—
422C2×C4C22×D4×C2914yes—
423C2×C4C22×D4×C2911yescharacteristic
424C2×C4C22×D4×C2912yes—
425C2×C4C22×D4×C2912yes—
426C2×C4C25×C2911yescharacteristic
427C8—28no—
428C22—21no—
429C22—21no—
430C22—24no—
431C22—24no—
432C22—24no—
433C22—42no—
434C22—42no—
435C22—42no—
436C22—84no—
437C22—84no—
438C22C2×C29×#13712yes—
439C22C23×D4×C2911yescharacteristic
440C4—21no—
441C4—24no—
442C4—22no—
443C4—44no—
444C4—42no—
445C4—44no—
446C4—44no—
447C4C2×C29×#13714yes—
448C4C29×#58512yes—
449C2—22no—
450C2—44no—
451C2—82no—
452C2C29×#348511yescharacteristic
453C2C22×C29×#13711yescharacteristic
454C2C29×#358511yescharacteristic
subgroupG/H
center, socleC22×C29C23×D4
commutator, Frattini, cosocleC2×C4C25×C29
prime radicalC2×C29×#555C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C4×D4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#3501C2semidirect
3. C29×#3357C2semidirect
4. C29×#3329C2semidirect
5. C29×#3230C2semidirect
6. C29×#3193C2semidirect
7. C29×#3101C2semidirect
8. C29×#3095C2semidirect
9. C29×#2975C2semidirect
13. C29×#554C22semidirect
14. D4×Q8×C29C22semidirect
28. C29×#500C22semidirect
29. C29×#487C22semidirect
30. C29×#485C22semidirect
33. C29×#480C22semidirect
34. C29×#477C22semidirect
35. C29×#476C22semidirect
36. C29×#468C22semidirect
37. C29×#461C22semidirect
39. C29×#448C22semidirect
40. C4×SD16×C29C22semidirect
41. C29×#436C22semidirect
43. C29×#428C22semidirect
44. C29×#419C22semidirect
162. #61721C29direct (N × H)
201. #3501C2×C29semidirect
203. #3357C2×C29semidirect
204. #3329C2×C29semidirect
205. #3230C2×C29semidirect
206. #3193C2×C29semidirect
207. #3101C2×C29semidirect
208. #3095C2×C29semidirect
209. #2975C2×C29semidirect
234. #554C22×C29semidirect
235. D4×Q8C22×C29semidirect
249. #500C22×C29semidirect
250. #487C22×C29semidirect
251. #485C22×C29semidirect
254. #480C22×C29semidirect
255. #477C22×C29semidirect
256. #476C22×C29semidirect
257. #468C22×C29semidirect
258. #461C22×C29semidirect
260. #448C22×C29semidirect
261. C4×SD16C22×C29semidirect
262. #436C22×C29semidirect
264. #428C22×C29semidirect
265. #419C22×C29semidirect
334. C29#61721direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35012
C2×C29×#5552
C29×#33572
C29×#33292
C29×#32302
C29×#31932
C29×#31012
C29×#30952
C29×#29752
#6172129