Finite Group Databasebeta

← C4×C29×#578 #20355073

Subgroups — C4×C29×#578 #20355073

Order 7424.

2658 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#578C211yesmaximal, characteristic
2C4×C29×2−1+4C212yesmaximal, complemented
3C29×#2951C213yesmaximal, complemented
4C29×#2950C213yesmaximal, complemented
5C29×#2947C216yesmaximal, complemented
6C4×C29×#137C216yesmaximal, complemented
7C4×C29×#135C213yesmaximal, complemented
8C2×C4×Q16×C29C213yesmaximal, complemented
9C29×#2913C211yesmaximal, characteristic, complemented
10C29×#2898C212yesmaximal, complemented
11C4×C29×#131C211yesmaximal, characteristic, complemented
12C2×C29×2−1+4C2212yes—
13C29×#578C4116yesdirect product factor
14C2×C29×#137C2216yes—
15C2×C29×#135C2213yes—
16C22×Q16×C29C2213yes—
17C2×C29×#131C2211yescharacteristic
18C2×C29×#131C2211yescharacteristic
19C29×#520—26no—
20C29×#520C2216yes—
21C29×#520C2212yes—
22C29×#519—22no—
23C29×#519C2216yes—
24C4×#41×C29—26no—
25C4×#41×C29C2216yes—
26C4×#41×C29C2211yescharacteristic
27C2×C4×Q8×C29—22no—
28C2×C4×Q8×C29C2216yes—
29C29×#441C22112yes—
30C29×#440C22112yes—
31C4×Q16×C29C2213yes—
32C4×Q16×C29C2216yes—
33C4×Q16×C29C2216yes—
34C4×Q16×C29C2216yes—
35C4×Q16×C29C2213yes—
36C4×SD16×C29C2216yes—
37C4×SD16×C29C2216yes—
38C4×D8×C29C2211yescharacteristic
39C4×D8×C29C2213yes—
40C29×#428C2216yes—
41C29×#427C2213yes—
42C2×C29×#107C2213yes—
43C29×#419C2216yes—
44C29×#417C2216yes—
45C29×#416C2216yes—
46C2×C29×#103C2216yes—
47C29×#405C2213yes—
48C29×#405C2213yes—
49C4×M16×C29C2213yes—
50C2×C4×C8×C29C2213yes—
51C29×2−1+4—28no—
52C29×2−1+4C2×C4116yescomplemented
53C2×#41×C29—26no—
54C2×#41×C29C2316yes—
55C2×#41×C29C2311yescharacteristic
56C22×Q8×C29—22no—
57C22×Q8×C29C2316yes—
58C29×#137C2×C4148yescomplemented
59C29×#135C2×C4124yescomplemented
60C2×Q16×C29C2×C4124yescomplemented
61C2×Q16×C29C2313yes—
62C2×Q16×C29C2316yes—
63C2×SD16×C29C2316yes—
64C2×D8×C29C2311yescharacteristic
65C29×#131—24no—
66C29×#131C2×C418yescomplemented
67C2×M16×C29C2313yes—
68C2×M16×C29C2313yes—
69C22×C8×C29C2313yes—
70C22×C8×C29C2313yes—
71C4×Q8×C29—22no—
72C4×Q8×C29—26no—
73C4×Q8×C29—26no—
74C4×Q8×C29—26no—
75C4×Q8×C29—26no—
76C4×Q8×C29D411yescharacteristic
77C4×Q8×C29D411yescharacteristic
78C4×Q8×C29C2316yes—
79C4×Q8×C29C2316yes—
80C4×Q8×C29C23112yes—
81C4×D4×C29—26no—
82C4×D4×C29—26no—
83C4×D4×C29—26no—
84C4×D4×C29—212no—
85C4×D4×C29D413yes—
86C4×D4×C29D413yes—
87C4×D4×C29C2312yes—
88C4×D4×C29C2316yes—
89C29×#117—26no—
90C29×#117—212no—
91C29×#117—26no—
92C29×#117C2316yes—
93C29×#117C2313yes—
94C2×C4⋊C4×C29—26no—
95C2×C4⋊C4×C29—26no—
96C2×C4⋊C4×C29C2316yes—
97C2×C42×C29—26no—
98C2×C42×C29—26no—
99C2×C42×C29C2313yes—
100C29×#107C2313yes—
101C29×#107C2316yes—
102C29×#107C2311yescharacteristic
103C29×#106C2316yes—
104C29×#103C2316yes—
105C29×#103C2316yes—
106C29×#103C23112yes—
107C29×#102C2312yes—
108C29×#102C2316yes—
109C29×#97C2316yes—
110C4×C8×C29C2311yescharacteristic
111C4×C8×C29C2313yes—
112C4×C8×C29C2313yes—
113C4×C8×C29C2313yes—
114#41×C29—248no—
115#41×C29—212no—
116#41×C29C22×C4124yes—
117#41×C29C22×C414yes—
118#41×C29#4114yes—
119C2×Q8×C29—216no—
120C2×Q8×C29—26no—
121C2×Q8×C29—212no—
122C2×Q8×C29C22×C4124yes—
123C2×Q8×C29C2×D411yescharacteristic
124C2×Q8×C29C2416yes—
125C2×D4×C29—26no—
126C2×D4×C29C2×D413yes—
127C2×D4×C29C2412yes—
128C22×C4×C29—26no—
129C22×C4×C29—26no—
130C22×C4×C29—26no—
131C22×C4×C29—22no—
132C22×C4×C29—26no—
133C22×C4×C29C2×D413yes—
134C22×C4×C29C2×D413yes—
135C22×C4×C29C2413yes—
136Q16×C29C22×C4112yes—
137Q16×C29C22×C4124yes—
138SD16×C29C22×C4124yes—
139D8×C29C22×C414yes—
140M16×C29—26no—
141M16×C29C22×C4112yes—
142C2×C8×C29—26no—
143C2×C8×C29C22×C4112yes—
144C2×C8×C29C2411yescharacteristic
145C2×C8×C29C2413yes—
146C2×C8×C29C2411yescharacteristic
147C2×C8×C29C2413yes—
148C4⋊C4×C29—212no—
149C4⋊C4×C29—26no—
150C4⋊C4×C29—26no—
151C4⋊C4×C29—26no—
152C4⋊C4×C29C2×D413yes—
153C4⋊C4×C29C2×D413yes—
154C4⋊C4×C29C2416yes—
155C4⋊C4×C29C2412yes—
156C22⋊C4×C29—26no—
157C22⋊C4×C29—22no—
158C22⋊C4×C29—26no—
159C22⋊C4×C29C2×D416yes—
160C42×C29—26no—
161C42×C29—212no—
162C42×C29—26no—
163C42×C29—26no—
164C42×C29C2×D413yes—
165C42×C29C2×D413yes—
166C42×C29C2413yes—
167C42×C29C2411yescharacteristic
168C4×#578C2911yesmaximal, characteristic, direct product factor, Sylow
169C23×C29—22no—
170C23×C29C22×D413yes—
171Q8×C29—224no—
172Q8×C29—26no—
173Q8×C29C4×D414yes—
174Q8×C29C23×C4112yes—
175D4×C29—224no—
176D4×C29—22no—
177D4×C29C4×D4112yes—
178D4×C29C23×C414yes—
179C2×C4×C29—224no—
180C2×C4×C29—26no—
181C2×C4×C29—224no—
182C2×C4×C29—26no—
183C2×C4×C29—22no—
184C2×C4×C29—26no—
185C2×C4×C29—43no—
186C2×C4×C29—44no—
187C2×C4×C29—86no—
188C2×C4×C29—86no—
189C2×C4×C29C23×C416yes—
190C2×C4×C29C22×D413yes—
191C2×C4×C29C22×D413yes—
192C2×C4×C29C22×D411yescharacteristic
193C2×C4×C29C22×D413yes—
194C2×C4×C29C22×D411yescharacteristic
195C2×C4×C29C2×#4116yes—
196C2×C4×C29C2511yescharacteristic
197C8×C29—21no—
198C8×C29—23no—
199C8×C29C23×C412yes—
200C8×C29C23×C416yes—
201C2×#578C2×C2911yescharacteristic
202C4×2−1+4C2×C2912yescomplemented
203#2951C2×C2913yescomplemented
204#2950C2×C2913yescomplemented
205#2947C2×C2916yescomplemented
206C4×#137C2×C2916yescomplemented
207C4×#135C2×C2913yescomplemented
208C2×C4×Q16C2×C2913yescomplemented
209#2913C2×C2911yescharacteristic, complemented
210#2898C2×C2912yescomplemented
211C4×#131C2×C2911yescharacteristic, complemented
212C22×C29—23no—
213C22×C29—23no—
214C22×C29—24no—
215C22×C29—42no—
216C22×C29—42no—
217C22×C29C2×C4×D416yes—
218C22×C29C23×D411yescharacteristic
219C4×C29—21no—
220C4×C29—23no—
221C4×C29—212no—
222C4×C29—23no—
223C4×C29—46no—
224C4×C29—42no—
225C4×C29C2×C4×D416yes—
226C4×C29#57812yesdirect product factor
227C4×C29C24×C411yescharacteristic
228C4×C29C22×#4111yescharacteristic
229C2×2−1+4C22×C2912yes—
230#578C4×C29116yesdirect product factor
231C2×#137C22×C2916yes—
232C2×#135C22×C2913yes—
233C22×Q16C22×C2913yes—
234C2×#131C22×C2911yescharacteristic
235C2×#131C22×C2911yescharacteristic
236#520—26no—
237#520C22×C2916yes—
238#520C22×C2912yes—
239#519—22no—
240#519C22×C2916yes—
241C4×#41—26no—
242C4×#41C22×C2916yes—
243C4×#41C22×C2911yescharacteristic
244C2×C4×Q8—22no—
245C2×C4×Q8C22×C2916yes—
246#441C22×C29112yes—
247#440C22×C29112yes—
248C4×Q16C22×C2913yes—
249C4×Q16C22×C2916yes—
250C4×Q16C22×C2916yes—
251C4×Q16C22×C2916yes—
252C4×Q16C22×C2913yes—
253C4×SD16C22×C2916yes—
254C4×SD16C22×C2916yes—
255C4×D8C22×C2911yescharacteristic
256C4×D8C22×C2913yes—
257#428C22×C2916yes—
258#427C22×C2913yes—
259C2×#107C22×C2913yes—
260#419C22×C2916yes—
261#417C22×C2916yes—
262#416C22×C2916yes—
263C2×#103C22×C2916yes—
264#405C22×C2913yes—
265#405C22×C2913yes—
266C4×M16C22×C2913yes—
267C2×C4×C8C22×C2913yes—
268C2×C29—26no—
269C2×C29—44no—
270C2×C29C22×C4×D411yescharacteristic
271C2×C29C2×#57811yescharacteristic
272C2×C29#358411yescharacteristic
2732−1+4—28no—
2742−1+4C2×C4×C29116yescomplemented
275C2×#41—26no—
276C2×#41C23×C2916yes—
277C2×#41C23×C2911yescharacteristic
278C22×Q8—22no—
279C22×Q8C23×C2916yes—
280#137C2×C4×C29148yescomplemented
281#135C2×C4×C29124yescomplemented
282C2×Q16C2×C4×C29124yescomplemented
283C2×Q16C23×C2913yes—
284C2×Q16C23×C2916yes—
285C2×SD16C23×C2916yes—
286C2×D8C23×C2911yescharacteristic
287#131—24no—
288#131C2×C4×C2918yescomplemented
289C2×M16C23×C2913yes—
290C2×M16C23×C2913yes—
291C22×C8C23×C2913yes—
292C22×C8C23×C2913yes—
293C4×Q8—22no—
294C4×Q8—26no—
295C4×Q8—26no—
296C4×Q8—26no—
297C4×Q8—26no—
298C4×Q8D4×C2911yescharacteristic
299C4×Q8D4×C2911yescharacteristic
300C4×Q8C23×C2916yes—
301C4×Q8C23×C29112yes—
302C4×Q8C23×C2916yes—
303C4×D4—26no—
304C4×D4—26no—
305C4×D4—26no—
306C4×D4—212no—
307C4×D4D4×C2913yes—
308C4×D4D4×C2913yes—
309C4×D4C23×C2912yes—
310C4×D4C23×C2916yes—
311#117—26no—
312#117—212no—
313#117—26no—
314#117C23×C2916yes—
315#117C23×C2913yes—
316C2×C4⋊C4—26no—
317C2×C4⋊C4—26no—
318C2×C4⋊C4C23×C2916yes—
319C2×C42—26no—
320C2×C42—26no—
321C2×C42C23×C2913yes—
322#107C23×C2913yes—
323#107C23×C2916yes—
324#107C23×C2911yescharacteristic
325#106C23×C2916yes—
326#103C23×C2916yes—
327#103C23×C29112yes—
328#103C23×C2916yes—
329#102C23×C2912yes—
330#102C23×C2916yes—
331#97C23×C2916yes—
332C4×C8C23×C2911yescharacteristic
333C4×C8C23×C2913yes—
334C4×C8C23×C2913yes—
335C4×C8C23×C2913yes—
336C29C4×#57811yescharacteristic, direct product factor, Sylow
337#41—248no—
338#41—212no—
339#41C22×C4×C29124yes—
340#41C22×C4×C2914yes—
341#41#41×C2914yes—
342C2×Q8—216no—
343C2×Q8—26no—
344C2×Q8—212no—
345C2×Q8C22×C4×C29124yes—
346C2×Q8C2×D4×C2911yescharacteristic
347C2×Q8C24×C2916yes—
348C2×D4—26no—
349C2×D4C2×D4×C2913yes—
350C2×D4C24×C2912yes—
351C22×C4—26no—
352C22×C4—26no—
353C22×C4—26no—
354C22×C4—22no—
355C22×C4—26no—
356C22×C4C2×D4×C2913yes—
357C22×C4C2×D4×C2913yes—
358C22×C4C24×C2913yes—
359Q16C22×C4×C29112yes—
360Q16C22×C4×C29124yes—
361SD16C22×C4×C29124yes—
362D8C22×C4×C2914yes—
363M16—26no—
364M16C22×C4×C29112yes—
365C2×C8—26no—
366C2×C8C22×C4×C29112yes—
367C2×C8C24×C2911yescharacteristic
368C2×C8C24×C2913yes—
369C2×C8C24×C2911yescharacteristic
370C2×C8C24×C2913yes—
371C4⋊C4—212no—
372C4⋊C4—26no—
373C4⋊C4—26no—
374C4⋊C4—26no—
375C4⋊C4C2×D4×C2913yes—
376C4⋊C4C2×D4×C2913yes—
377C4⋊C4C24×C2912yes—
378C4⋊C4C24×C2916yes—
379C22⋊C4—26no—
380C22⋊C4—22no—
381C22⋊C4—26no—
382C22⋊C4C2×D4×C2916yes—
383C42—26no—
384C42—26no—
385C42—212no—
386C42—26no—
387C42C2×D4×C2913yes—
388C42C2×D4×C2913yes—
389C42C24×C2911yescharacteristic
390C42C24×C2913yes—
391C23—22no—
392C23C22×D4×C2913yes—
393Q8—224no—
394Q8—26no—
395Q8C4×D4×C2914yes—
396Q8C23×C4×C29112yes—
397D4—224no—
398D4—22no—
399D4C4×D4×C29112yes—
400D4C23×C4×C2914yes—
401C2×C4—224no—
402C2×C4—26no—
403C2×C4—224no—
404C2×C4—26no—
405C2×C4—22no—
406C2×C4—26no—
407C2×C4—43no—
408C2×C4—44no—
409C2×C4—86no—
410C2×C4—86no—
411C2×C4C23×C4×C2916yes—
412C2×C4C22×D4×C2913yes—
413C2×C4C22×D4×C2913yes—
414C2×C4C22×D4×C2911yescharacteristic
415C2×C4C22×D4×C2913yes—
416C2×C4C22×D4×C2911yescharacteristic
417C2×C4C2×#41×C2916yes—
418C2×C4C25×C2911yescharacteristic
419C8—21no—
420C8—23no—
421C8C23×C4×C2912yes—
422C8C23×C4×C2916yes—
423C22—23no—
424C22—23no—
425C22—24no—
426C22—42no—
427C22—42no—
428C22C2×C4×D4×C2916yes—
429C22C23×D4×C2911yescharacteristic
430C4—23no—
431C4—21no—
432C4—23no—
433C4—212no—
434C4—42no—
435C4—46no—
436C4C2×C4×D4×C2916yes—
437C4C29×#57812yesdirect product factor
438C4C24×C4×C2911yescharacteristic
439C4C22×#41×C2911yescharacteristic
440C2—26no—
441C2—44no—
442C2C22×C4×D4×C2911yescharacteristic
443C2C2×C29×#57811yescharacteristic
444C2C29×#358411yescharacteristic
subgroupG/H
centerC2×C4×C29C22×D4
commutatorC4C24×C4×C29
Frattini, cosocleC2×C4C25×C29
socleC22×C29C23×D4
prime radicalC2×C29×#578C2
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C29 ◁ C4×#41×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×C29×2−1+4C2semidirect
3. C29×#2951C2semidirect
4. C29×#2950C2semidirect
5. C29×#2947C2semidirect
6. C4×C29×#137C2semidirect
7. C4×C29×#135C2semidirect
8. C2×C4×Q16×C29C2semidirect
9. C29×#2913C2semidirect
10. C29×#2898C2semidirect
11. C4×C29×#131C2semidirect
13. C29×#578C4direct (N × H)
52. C29×2−1+4C2×C4semidirect
58. C29×#137C2×C4semidirect
59. C29×#135C2×C4semidirect
60. C2×Q16×C29C2×C4semidirect
66. C29×#131C2×C4semidirect
168. C4×#578C29direct (N × H)
202. C4×2−1+4C2×C29semidirect
203. #2951C2×C29semidirect
204. #2950C2×C29semidirect
205. #2947C2×C29semidirect
206. C4×#137C2×C29semidirect
207. C4×#135C2×C29semidirect
208. C2×C4×Q16C2×C29semidirect
209. #2913C2×C29semidirect
210. #2898C2×C29semidirect
211. C4×#131C2×C29semidirect
226. C4×C29#578direct (N × H)
230. #578C4×C29direct (N × H)
274. 2−1+4C2×C4×C29semidirect
280. #137C2×C4×C29semidirect
281. #135C2×C4×C29semidirect
282. C2×Q16C2×C4×C29semidirect
288. #131C2×C4×C29semidirect
336. C29C4×#578direct (N × H)
437. C4C29×#578direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#5782
C4×C29×2−1+42
C29×#29512
C29×#29502
C29×#29472
C4×C29×#1372
C4×C29×#1352
C2×C4×Q16×C292
C29×#29132
C29×#28982
C4×C29×#1312
C4×#57829