Finite Group Databasebeta

← C29×#61844 #20356744

Subgroups — C29×#61844 #20356744

Order 7424.

1756 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3522C211yesmaximal, characteristic
2C2×Q82×C29C211yesmaximal, characteristic, complemented
3C29×#3385C216yesmaximal, complemented
4Q8×Q16×C29C212yesmaximal, complemented
5C29×#3375C216yesmaximal, complemented
6C29×#3362C212yesmaximal, complemented
7C29×#3238C213yesmaximal, complemented
8C29×#3226C213yesmaximal, complemented
9C29×#3112C213yesmaximal, complemented
10C29×#3108C213yesmaximal, complemented
11C29×#2984C211yesmaximal, characteristic, complemented
12C29×#559C2213yes—
13Q82×C29—21no—
14Q82×C29—23no—
15Q82×C29C2212yes—
16Q82×C29C2216yes—
17Q82×C29C2211yescharacteristic
18C29×#554C2213yes—
19C29×#550C2211yescharacteristic
20C29×#548—21no—
21C29×#547—23no—
22C29×#542—23no—
23C29×#532C2213yes—
24C2×C29×C4⋊Q8—23no—
25C2×C29×C4⋊Q8C2213yes—
26C29×#529C2213yes—
27C29×#520—21no—
28C2×C4×Q8×C29—21no—
29C2×C4×Q8×C29C2213yes—
30C2×C4×Q8×C29C2211yescharacteristic
31C29×#501C2216yes—
32C29×#500C2216yes—
33C29×#489C2216yes—
34C29×#486C2216yes—
35C29×#483C2213yes—
36C29×#480C2213yes—
37C29×#480C2216yes—
38C29×#479C2216yes—
39C29×#477C2216yes—
40C29×#477C2216yes—
41C29×#476C2216yes—
42C29×#474C22112yes—
43C29×#464C2216yes—
44C29×#460C2216yes—
45C29×#451C2211yescharacteristic
46C29×#448C2213yes—
47C29×#446C2216yes—
48C8×Q8×C29C2212yes—
49C29×#440C22112yes—
50C4×Q16×C29C2216yes—
51C4×SD16×C29C2216yes—
52C29×#432C2213yes—
53C29×#431C2213yes—
54C2×#41×C29—21no—
55C2×#41×C29—23no—
56C22×Q8×C29—23no—
57C22×Q8×C29D411yescharacteristic
58C22×Q8×C29C2311yescharacteristic
59C2×Q16×C29C2312yes—
60C2×SD16×C29C2316yes—
61C29×C4⋊Q8—26no—
62C29×C4⋊Q8—26no—
63C29×C4⋊Q8—212no—
64C29×C4⋊Q8—23no—
65C29×C4⋊Q8—23no—
66C29×C4⋊Q8—23no—
67C29×C4⋊Q8C2316yes—
68C29×C4⋊Q8C2316yes—
69C29×C4⋊Q8C2313yes—
70C29×#127C2313yes—
71C29×#126—23no—
72C29×#125C2313yes—
73C29×#124—23no—
74C29×#124—23no—
75C29×#124C2313yes—
76C29×#123—23no—
77C29×#123—26no—
78C29×C22⋊Q8—23no—
79C29×C22⋊Q8—26no—
80C29×C22⋊Q8C2311yescharacteristic
81C29×#121—23no—
82C29×#121—23no—
83C29×#121C2313yes—
84C4×Q8×C29—26no—
85C4×Q8×C29—22no—
86C4×Q8×C29—21no—
87C4×Q8×C29—23no—
88C4×Q8×C29—23no—
89C4×Q8×C29D411yescharacteristic
90C4×Q8×C29D413yes—
91C4×Q8×C29C2316yes—
92C4×Q8×C29C2313yes—
93C4×Q8×C29C2316yes—
94C4×Q8×C29C2311yescharacteristic
95C4×Q8×C29C2313yes—
96C4×D4×C29—23no—
97C4×D4×C29—23no—
98C4×D4×C29—23no—
99C4×D4×C29C2313yes—
100C4×D4×C29C2316yes—
101C29×#117—23no—
102C2×C4⋊C4×C29—23no—
103C2×C4⋊C4×C29—23no—
104C2×C4⋊C4×C29—23no—
105C2×C4⋊C4×C29D413yes—
106C2×C4⋊C4×C29C2313yes—
107C2×C42×C29—23no—
108C2×C42×C29C2313yes—
109C29×#107C2316yes—
110C29×#107C23112yes—
111C29×#106C2316yes—
112C29×C4⋊C8C2316yes—
113C29×C4⋊C8C2316yes—
114C29×#103C2312yes—
115C29×#103C2316yes—
116C29×#103C2316yes—
117C29×#102C2316yes—
118C29×#102C23112yes—
119C29×C22⋊C8C2311yescharacteristic
120C29×C22⋊C8C2313yes—
121C29×#97C2316yes—
122C4×C8×C29C2316yes—
123#41×C29—44no—
124#41×C29—86no—
125C2×Q8×C29—24no—
126C2×Q8×C29—24no—
127C2×Q8×C29—21no—
128C2×Q8×C29—23no—
129C2×Q8×C29—26no—
130C2×Q8×C29—26no—
131C2×Q8×C29—86no—
132C2×Q8×C29C2×D413yes—
133C2×Q8×C29C2×D411yescharacteristic
134C2×Q8×C29C2411yescharacteristic
135C2×Q8×C29C2412yes—
136C2×D4×C29—23no—
137C2×D4×C29—23no—
138C2×D4×C29—23no—
139C2×D4×C29C2413yes—
140C22×C4×C29—21no—
141C22×C4×C29—23no—
142C22×C4×C29—23no—
143C22×C4×C29—26no—
144C22×C4×C29C2×D413yes—
145C22×C4×C29C2×D413yes—
146C22×C4×C29C2411yescharacteristic
147Q16×C29—24no—
148SD16×C29—212no—
149C2×C8×C29C2416yes—
150C2×C8×C29C2412yes—
151C4⋊C4×C29—23no—
152C4⋊C4×C29—23no—
153C4⋊C4×C29—26no—
154C4⋊C4×C29—26no—
155C4⋊C4×C29—26no—
156C4⋊C4×C29—26no—
157C4⋊C4×C29—23no—
158C4⋊C4×C29—21no—
159C4⋊C4×C29—23no—
160C4⋊C4×C29—23no—
161C4⋊C4×C29C2×D413yes—
162C4⋊C4×C29C2×D413yes—
163C4⋊C4×C29C2×D416yes—
164C4⋊C4×C29C2416yes—
165C4⋊C4×C29C2411yescharacteristic
166C4⋊C4×C29C2413yes—
167C22⋊C4×C29—21no—
168C22⋊C4×C29—23no—
169C22⋊C4×C29—23no—
170C22⋊C4×C29—23no—
171C22⋊C4×C29—23no—
172C22⋊C4×C29—26no—
173C42×C29—26no—
174C42×C29—26no—
175C42×C29—23no—
176C42×C29C2×D413yes—
177C42×C29C2×D413yes—
178C42×C29C2413yes—
179C42×C29C2413yes—
180#61844C2911yesmaximal, characteristic, direct product factor, Sylow
181C23×C29—23no—
182C23×C29C22×D411yescharacteristic
183Q8×C29—24no—
184Q8×C29—26no—
185Q8×C29—22no—
186Q8×C29—22no—
187Q8×C29—86no—
188Q8×C29—86no—
189Q8×C29—83no—
190Q8×C29#13714yes—
191Q8×C292−1+414yes—
192D4×C29—26no—
193D4×C29—46no—
194D4×C29—46no—
195D4×C29—83no—
196C2×C4×C29—24no—
197C2×C4×C29—26no—
198C2×C4×C29—22no—
199C2×C4×C29—26no—
200C2×C4×C29—22no—
201C2×C4×C29—21no—
202C2×C4×C29—26no—
203C2×C4×C29—23no—
204C2×C4×C29—21no—
205C2×C4×C29—46no—
206C2×C4×C29—46no—
207C2×C4×C29—86no—
208C2×C4×C29C22×D413yes—
209C2×C4×C29C22×D411yescharacteristic
210C2×C4×C29C22×D413yes—
211C2×C4×C29C22×D413yes—
212C2×C4×C29C22×D413yes—
213C2×C4×C29C2511yescharacteristic
214C8×C29—26no—
215C8×C29—22no—
216#3522C2×C2911yescharacteristic
217C2×Q82C2×C2911yescharacteristic, complemented
218#3385C2×C2916yescomplemented
219Q8×Q16C2×C2912yescomplemented
220#3375C2×C2916yescomplemented
221#3362C2×C2912yescomplemented
222#3238C2×C2913yescomplemented
223#3226C2×C2913yescomplemented
224#3112C2×C2913yescomplemented
225#3108C2×C2913yescomplemented
226#2984C2×C2911yescharacteristic, complemented
227C22×C29—21no—
228C22×C29—21no—
229C22×C29—43no—
230C22×C29—43no—
231C22×C29—43no—
232C22×C29#57612yes—
233C22×C29C23×D411yescharacteristic
234C4×C29—24no—
235C4×C29—21no—
236C4×C29—23no—
237C4×C29—23no—
238C4×C29—23no—
239C4×C29—41no—
240C4×C29—41no—
241C4×C29—46no—
242C4×C29—43no—
243C4×C29C2×#13716yes—
244C4×C29C2×2−1+412yes—
245#559C22×C2913yes—
246Q82—21no—
247Q82—23no—
248Q82C22×C2912yes—
249Q82C22×C2916yes—
250Q82C22×C2911yescharacteristic
251#554C22×C2913yes—
252#550C22×C2911yescharacteristic
253#548—21no—
254#547—23no—
255#542—23no—
256#532C22×C2913yes—
257C2×C4⋊Q8—23no—
258C2×C4⋊Q8C22×C2913yes—
259#529C22×C2913yes—
260#520—21no—
261C2×C4×Q8—21no—
262C2×C4×Q8C22×C2913yes—
263C2×C4×Q8C22×C2911yescharacteristic
264#501C22×C2916yes—
265#500C22×C2916yes—
266#489C22×C2916yes—
267#486C22×C2916yes—
268#483C22×C2913yes—
269#480C22×C2913yes—
270#480C22×C2916yes—
271#479C22×C2916yes—
272#477C22×C2916yes—
273#477C22×C2916yes—
274#476C22×C2916yes—
275#474C22×C29112yes—
276#464C22×C2916yes—
277#460C22×C2916yes—
278#451C22×C2911yescharacteristic
279#448C22×C2913yes—
280#446C22×C2916yes—
281C8×Q8C22×C2912yes—
282#440C22×C29112yes—
283C4×Q16C22×C2916yes—
284C4×SD16C22×C2916yes—
285#432C22×C2913yes—
286#431C22×C2913yes—
287C2×C29—22no—
288C2×C29—83no—
289C2×C29#348611yescharacteristic
290C2×C29C22×#13711yescharacteristic
291C2×C29C2×#57611yescharacteristic
292C2×#41—21no—
293C2×#41—23no—
294C22×Q8—23no—
295C22×Q8D4×C2911yescharacteristic
296C22×Q8C23×C2911yescharacteristic
297C2×Q16C23×C2912yes—
298C2×SD16C23×C2916yes—
299C4⋊Q8—26no—
300C4⋊Q8—26no—
301C4⋊Q8—212no—
302C4⋊Q8—23no—
303C4⋊Q8—23no—
304C4⋊Q8—23no—
305C4⋊Q8C23×C2916yes—
306C4⋊Q8C23×C2916yes—
307C4⋊Q8C23×C2913yes—
308#127C23×C2913yes—
309#126—23no—
310#125C23×C2913yes—
311#124—23no—
312#124—23no—
313#124C23×C2913yes—
314#123—23no—
315#123—26no—
316C22⋊Q8—23no—
317C22⋊Q8—26no—
318C22⋊Q8C23×C2911yescharacteristic
319#121—23no—
320#121—23no—
321#121C23×C2913yes—
322C4×Q8—26no—
323C4×Q8—22no—
324C4×Q8—21no—
325C4×Q8—23no—
326C4×Q8—23no—
327C4×Q8D4×C2911yescharacteristic
328C4×Q8D4×C2913yes—
329C4×Q8C23×C2916yes—
330C4×Q8C23×C2916yes—
331C4×Q8C23×C2913yes—
332C4×Q8C23×C2911yescharacteristic
333C4×Q8C23×C2913yes—
334C4×D4—23no—
335C4×D4—23no—
336C4×D4—23no—
337C4×D4C23×C2913yes—
338C4×D4C23×C2916yes—
339#117—23no—
340C2×C4⋊C4—23no—
341C2×C4⋊C4—23no—
342C2×C4⋊C4—23no—
343C2×C4⋊C4D4×C2913yes—
344C2×C4⋊C4C23×C2913yes—
345C2×C42—23no—
346C2×C42C23×C2913yes—
347#107C23×C2916yes—
348#107C23×C29112yes—
349#106C23×C2916yes—
350C4⋊C8C23×C2916yes—
351C4⋊C8C23×C2916yes—
352#103C23×C2912yes—
353#103C23×C2916yes—
354#103C23×C2916yes—
355#102C23×C2916yes—
356#102C23×C29112yes—
357C22⋊C8C23×C2911yescharacteristic
358C22⋊C8C23×C2913yes—
359#97C23×C2916yes—
360C4×C8C23×C2916yes—
361C29#6184411yescharacteristic, direct product factor, Sylow
362#41—44no—
363#41—86no—
364C2×Q8—24no—
365C2×Q8—24no—
366C2×Q8—21no—
367C2×Q8—23no—
368C2×Q8—26no—
369C2×Q8—26no—
370C2×Q8—86no—
371C2×Q8C2×D4×C2913yes—
372C2×Q8C2×D4×C2911yescharacteristic
373C2×Q8C24×C2911yescharacteristic
374C2×Q8C24×C2912yes—
375C2×D4—23no—
376C2×D4—23no—
377C2×D4—23no—
378C2×D4C24×C2913yes—
379C22×C4—21no—
380C22×C4—23no—
381C22×C4—23no—
382C22×C4—26no—
383C22×C4C2×D4×C2913yes—
384C22×C4C2×D4×C2913yes—
385C22×C4C24×C2911yescharacteristic
386Q16—24no—
387SD16—212no—
388C2×C8C24×C2912yes—
389C2×C8C24×C2916yes—
390C4⋊C4—23no—
391C4⋊C4—23no—
392C4⋊C4—26no—
393C4⋊C4—26no—
394C4⋊C4—26no—
395C4⋊C4—26no—
396C4⋊C4—23no—
397C4⋊C4—21no—
398C4⋊C4—23no—
399C4⋊C4—23no—
400C4⋊C4C2×D4×C2913yes—
401C4⋊C4C2×D4×C2913yes—
402C4⋊C4C2×D4×C2916yes—
403C4⋊C4C24×C2916yes—
404C4⋊C4C24×C2911yescharacteristic
405C4⋊C4C24×C2913yes—
406C22⋊C4—21no—
407C22⋊C4—23no—
408C22⋊C4—23no—
409C22⋊C4—23no—
410C22⋊C4—23no—
411C22⋊C4—26no—
412C42—26no—
413C42—26no—
414C42—23no—
415C42C2×D4×C2913yes—
416C42C2×D4×C2913yes—
417C42C24×C2913yes—
418C42C24×C2913yes—
419C23—23no—
420C23C22×D4×C2911yescharacteristic
421Q8—24no—
422Q8—26no—
423Q8—22no—
424Q8—22no—
425Q8—86no—
426Q8—86no—
427Q8—83no—
428Q8C29×#13714yes—
429Q8C29×2−1+414yes—
430D4—26no—
431D4—46no—
432D4—46no—
433D4—83no—
434C2×C4—24no—
435C2×C4—26no—
436C2×C4—22no—
437C2×C4—26no—
438C2×C4—22no—
439C2×C4—21no—
440C2×C4—26no—
441C2×C4—23no—
442C2×C4—21no—
443C2×C4—46no—
444C2×C4—46no—
445C2×C4—86no—
446C2×C4C22×D4×C2913yes—
447C2×C4C22×D4×C2911yescharacteristic
448C2×C4C22×D4×C2913yes—
449C2×C4C22×D4×C2913yes—
450C2×C4C22×D4×C2913yes—
451C2×C4C25×C2911yescharacteristic
452C8—26no—
453C8—22no—
454C22—21no—
455C22—21no—
456C22—43no—
457C22—43no—
458C22—43no—
459C22C29×#57612yes—
460C22C23×D4×C2911yescharacteristic
461C4—24no—
462C4—21no—
463C4—23no—
464C4—23no—
465C4—23no—
466C4—41no—
467C4—41no—
468C4—46no—
469C4—43no—
470C4C2×C29×#13716yes—
471C4C2×C29×2−1+412yes—
472C2—22no—
473C2—83no—
474C2C29×#348611yescharacteristic
475C2C22×C29×#13711yescharacteristic
476C2C2×C29×#57611yescharacteristic
subgroupG/H
center, socleC22×C29C23×D4
commutator, Frattini, cosocleC2×C4C25×C29
prime radicalC29×#3522C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C4×Q8×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×Q82×C29C2semidirect
3. C29×#3385C2semidirect
4. Q8×Q16×C29C2semidirect
5. C29×#3375C2semidirect
6. C29×#3362C2semidirect
7. C29×#3238C2semidirect
8. C29×#3226C2semidirect
9. C29×#3112C2semidirect
10. C29×#3108C2semidirect
11. C29×#2984C2semidirect
180. #61844C29direct (N × H)
217. C2×Q82C2×C29semidirect
218. #3385C2×C29semidirect
219. Q8×Q16C2×C29semidirect
220. #3375C2×C29semidirect
221. #3362C2×C29semidirect
222. #3238C2×C29semidirect
223. #3226C2×C29semidirect
224. #3112C2×C29semidirect
225. #3108C2×C29semidirect
226. #2984C2×C29semidirect
361. C29#61844direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35222
C2×Q82×C292
C29×#33852
Q8×Q16×C292
C29×#33752
C29×#33622
C29×#32382
C29×#32262
C29×#31122
C29×#31082
C29×#29842
#6184429