Finite Group Databasebeta

← C2×C29×#2196 #20328443

Subgroups — C2×C29×#2196 #20328443

Order 7424.

1956 conjugacy classes of subgroups; only the 222 normal subgroups are shown.

normal subgroups only

This group has 1956 conjugacy classes of subgroups — too many to draw. Only its 222 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C29C211yesmaximal, characteristic, complemented
2C2×C29×B(4,𝔽2)C212yesmaximal, complemented
3C2×C29×#453C211yesmaximal, characteristic, complemented
4C29×#2196C218yesmaximal, direct product factor
5C2×C29×#353C211yesmaximal, characteristic, complemented
6C2×C29×AΣL(1,𝔽16)C212yesmaximal, complemented
7C2×C29×H(5,𝔽2)C2211yescharacteristic, complemented
8C23×D4×C29—22no—
9C2×C29×AGL(1,ℤ/8)—21no—
10D42×C29—22no—
11D42×C29—24no—
12D42×C29C2214yescomplemented
13C2×C29×#127C2211yescharacteristic
14C2×C29×#121—22no—
15C2×C29×#120—21no—
16C2×C29×#120—22no—
17C2×C29×#120C2212yes—
18C2×C4×D4×C29—21no—
19C29×B(4,𝔽2)—24no—
20C29×B(4,𝔽2)C2218yescomplemented
21C29×#453—22no—
22C29×#453C2214yescomplemented
23C2×C29×#104—21no—
24C2×C29×#100C2211yescharacteristic, complemented
25C2×C29×#99—22no—
26C2×C29×#99C2212yescomplemented
27C29×#353C2214yescomplemented
28C29×AΣL(1,𝔽16)C2218yescomplemented
29C25×C29—21no—
30C25×C29D412yescomplemented
31C29×H(5,𝔽2)—22no—
32C29×H(5,𝔽2)—21no—
33C29×H(5,𝔽2)—42no—
34C29×H(5,𝔽2)C2312yescomplemented
35C2×#41×C29—21no—
36C2×#41×C29—41no—
37C22×D4×C29—21no—
38C22×D4×C29—22no—
39C22×D4×C29—28no—
40C22×D4×C29—22no—
41C22×D4×C29—22no—
42C22×D4×C29—22no—
43C22×D4×C29—28no—
44C22×D4×C29—41no—
45C22×D4×C29—416no—
46C22×D4×C29—42no—
47C22×D4×C29D411yescharacteristic, complemented
48C22×D4×C29C2311yescharacteristic
49C23×C4×C29—22no—
50C29×AGL(1,ℤ/8)—24no—
51C29×AGL(1,ℤ/8)—42no—
52C2×SD16×C29—41no—
53C2×D8×C29—41no—
54C2×M16×C29—21no—
55C29×#127—22no—
56C29×#127D412yescomplemented
57C29×#127C2312yes—
58C29×#121—28no—
59C29×#121—28no—
60C29×#120—24no—
61C29×#120—22no—
62C29×#120—22no—
63C29×#120—24no—
64C29×#120—28no—
65C29×#120—44no—
66C29×#120D414yescomplemented
67C29×#120C2314yes—
68C4×D4×C29—24no—
69C4×D4×C29—24no—
70C2×C4⋊C4×C29—21no—
71C2×C22⋊C4×C29—21no—
72C2×C22⋊C4×C29—22no—
73C2×C22⋊C4×C29—22no—
74C2×C22⋊C4×C29—42no—
75C2×C22⋊C4×C29D412yescomplemented
76C2×C42×C29D411yescharacteristic, complemented
77C29×#104—24no—
78C29×#100—21no—
79C29×#100C2312yescomplemented
80C29×#99—22no—
81C29×#99—28no—
82C29×#99C2314yescomplemented
83C24×C29—22no—
84C24×C29—24no—
85C24×C29—22no—
86C24×C29—21no—
87C24×C29—22no—
88C24×C29—42no—
89C24×C29—48no—
90C24×C29—48no—
91C24×C29—42no—
92C24×C29—81no—
93C24×C29—81no—
94C24×C29C2×D412yes—
95C24×C29C2×D414yescomplemented
96#41×C29—22no—
97#41×C29—22no—
98#41×C29—42no—
99#41×C29—41no—
100#41×C29—44no—
101#41×C29—42no—
102#41×C29—41no—
103C2×Q8×C29—21no—
104C2×D4×C29—24no—
105C2×D4×C29—28no—
106C2×D4×C29—21no—
107C2×D4×C29—28no—
108C2×D4×C29—24no—
109C2×D4×C29—24no—
110C2×D4×C29—24no—
111C2×D4×C29—24no—
112C2×D4×C29—24no—
113C2×D4×C29—24no—
114C2×D4×C29—21no—
115C2×D4×C29—41no—
116C2×D4×C29—41no—
117C2×D4×C29—48no—
118C2×D4×C29—41no—
119C2×D4×C29—41no—
120C2×D4×C29—42no—
121C2×D4×C29—432no—
122C2×D4×C29—432no—
123C2×D4×C29—42no—
124C2×D4×C29—48no—
125C2×D4×C29—48no—
126C2×D4×C29—42no—
127C2×D4×C29—42no—
128C2×D4×C29—44no—
129C2×D4×C29—42no—
130C2×D4×C29—41no—
131C2×D4×C29—48no—
132C2×D4×C29—88no—
133C2×D4×C29C2×D412yes—
134C2×D4×C29C2×D411yescharacteristic
135C2×D4×C29C2×D412yescomplemented
136C2×D4×C29C2411yescharacteristic
137C22×C4×C29—21no—
138C22×C4×C29—22no—
139C22×C4×C29—28no—
140C22×C4×C29—22no—
141C22×C4×C29—48no—
142C22×C4×C29—41no—
143C22×C4×C29—42no—
144C22×C4×C29C2×D411yescharacteristic
145SD16×C29—44no—
146D8×C29—44no—
147M16×C29—22no—
148M16×C29—41no—
149C2×C8×C29—41no—
150C4⋊C4×C29—24no—
151C22⋊C4×C29—24no—
152C22⋊C4×C29—22no—
153C22⋊C4×C29—24no—
154C22⋊C4×C29—24no—
155C22⋊C4×C29—24no—
156C22⋊C4×C29—48no—
157C22⋊C4×C29—42no—
158C22⋊C4×C29C2×D414yescomplemented
159C42×C29—21no—
160C42×C29C2×D412yescomplemented
161C2×#2196C2911yesmaximal, characteristic, direct product factor, Sylow
162C23×C29—28no—
163C23×C29—24no—
164C23×C29—22no—
165C23×C29—22no—
166C23×C29—24no—
167C23×C29—22no—
168C23×C29—44no—
169C23×C29—44no—
170C23×C29—44no—
171C23×C29—48no—
172C23×C29—44no—
173C23×C29—48no—
174C23×C29—416no—
175C23×C29—42no—
176C23×C29—42no—
177C23×C29—42no—
178C23×C29—48no—
179C23×C29—41no—
180C23×C29—41no—
181C23×C29—41no—
182C23×C29—82no—
183C23×C29—84no—
184C23×C29—88no—
185C23×C29—84no—
186C23×C29—88no—
187C23×C29—88no—
188C23×C29—84no—
189C23×C29#12012yes—
190C23×C29#12011yescharacteristic
191C23×C29C22×D412yes—
192Q8×C29—22no—
193Q8×C29—41no—
194D4×C29—216no—
195D4×C29—22no—
196D4×C29—41no—
197D4×C29—42no—
198D4×C29—41no—
199D4×C29—42no—
200D4×C29—48no—
201D4×C29—48no—
202D4×C29—41no—
203D4×C29—48no—
204D4×C29—48no—
205D4×C29—416no—
206D4×C29—44no—
207D4×C29—44no—
208D4×C29—42no—
209D4×C29—42no—
210D4×C29—81no—
211D4×C29—816no—
212C2×C4×C29—24no—
213C2×C4×C29—22no—
214C2×C4×C29—21no—
215C2×C4×C29—21no—
216C2×C4×C29—24no—
217C2×C4×C29—24no—
218C2×C4×C29—416no—
219C2×C4×C29—42no—
220C2×C4×C29—42no—
221C2×C4×C29—44no—
222C2×C4×C29—42no—
223C2×C4×C29—41no—
224C2×C4×C29—44no—
225C2×C4×C29—84no—
226C2×C4×C29#12011yescharacteristic
227C2×C4×C29C22×D411yescharacteristic
228C8×C29—42no—
229C2×D42C2×C2911yescharacteristic, complemented
230C2×B(4,𝔽2)C2×C2912yescomplemented
231C2×#453C2×C2911yescharacteristic, complemented
232#2196C2×C2918yesdirect product factor
233C2×#353C2×C2911yescharacteristic, complemented
234C2×AΣL(1,𝔽16)C2×C2912yescomplemented
235C22×C29—22no—
236C22×C29—28no—
237C22×C29—22no—
238C22×C29—22no—
239C22×C29—42no—
240C22×C29—42no—
241C22×C29—44no—
242C22×C29—48no—
243C22×C29—44no—
244C22×C29—48no—
245C22×C29—44no—
246C22×C29—48no—
247C22×C29—44no—
248C22×C29—42no—
249C22×C29—42no—
250C22×C29—82no—
251C22×C29—82no—
252C22×C29—84no—
253C22×C29—88no—
254C22×C29—816no—
255C22×C29—84no—
256C22×C29—82no—
257C22×C29—82no—
258C22×C29—162no—
259C22×C29B(4,𝔽2)11yescharacteristic
260C22×C29B(4,𝔽2)11yescharacteristic
261C22×C29C2×#12011yescharacteristic
262C4×C29—24no—
263C4×C29—21no—
264C4×C29—21no—
265C4×C29—44no—
266C4×C29—42no—
267C4×C29—84no—
268C2×H(5,𝔽2)C22×C2911yescharacteristic, complemented
269C23×D4—22no—
270C2×AGL(1,ℤ/8)—21no—
271D42—22no—
272D42—24no—
273D42C22×C2914yescomplemented
274C2×#127C22×C2911yescharacteristic
275C2×#121—22no—
276C2×#120—21no—
277C2×#120—22no—
278C2×#120C22×C2912yes—
279C2×C4×D4—21no—
280B(4,𝔽2)—24no—
281B(4,𝔽2)C22×C2918yescomplemented
282#453—22no—
283#453C22×C2914yescomplemented
284C2×#104—21no—
285C2×#100C22×C2911yescharacteristic, complemented
286C2×#99—22no—
287C2×#99C22×C2912yescomplemented
288#353C22×C2914yescomplemented
289AΣL(1,𝔽16)C22×C2918yescomplemented
290C2×C29—21no—
291C2×C29—21no—
292C2×C29—42no—
293C2×C29—48no—
294C2×C29—42no—
295C2×C29—82no—
296C2×C29—82no—
297C2×C29#219612yesdirect product factor
298C2×C29C2×B(4,𝔽2)11yescharacteristic
299C25—21no—
300C25D4×C2912yescomplemented
301H(5,𝔽2)—22no—
302H(5,𝔽2)—21no—
303H(5,𝔽2)—42no—
304H(5,𝔽2)C23×C2912yescomplemented
305C2×#41—21no—
306C2×#41—41no—
307C22×D4—21no—
308C22×D4—22no—
309C22×D4—28no—
310C22×D4—22no—
311C22×D4—22no—
312C22×D4—22no—
313C22×D4—28no—
314C22×D4—41no—
315C22×D4—416no—
316C22×D4—42no—
317C22×D4D4×C2911yescharacteristic, complemented
318C22×D4C23×C2911yescharacteristic
319C23×C4—22no—
320AGL(1,ℤ/8)—24no—
321AGL(1,ℤ/8)—42no—
322C2×SD16—41no—
323C2×D8—41no—
324C2×M16—21no—
325#127—22no—
326#127D4×C2912yescomplemented
327#127C23×C2912yes—
328#121—28no—
329#121—28no—
330#120—24no—
331#120—22no—
332#120—22no—
333#120—24no—
334#120—28no—
335#120—44no—
336#120D4×C2914yescomplemented
337#120C23×C2914yes—
338C4×D4—24no—
339C4×D4—24no—
340C2×C4⋊C4—21no—
341C2×C22⋊C4—21no—
342C2×C22⋊C4—22no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4D4×C2912yescomplemented
346C2×C42D4×C2911yescharacteristic, complemented
347#104—24no—
348#100—21no—
349#100C23×C2912yescomplemented
350#99—22no—
351#99—28no—
352#99C23×C2914yescomplemented
353C29C2×#219611yescharacteristic, direct product factor, Sylow
354C24—22no—
355C24—24no—
356C24—22no—
357C24—21no—
358C24—22no—
359C24—42no—
360C24—48no—
361C24—48no—
362C24—42no—
363C24—81no—
364C24—81no—
365C24C2×D4×C2912yes—
366C24C2×D4×C2914yescomplemented
367#41—22no—
368#41—22no—
369#41—42no—
370#41—41no—
371#41—44no—
372#41—42no—
373#41—41no—
374C2×Q8—21no—
375C2×D4—24no—
376C2×D4—28no—
377C2×D4—21no—
378C2×D4—28no—
379C2×D4—24no—
380C2×D4—24no—
381C2×D4—24no—
382C2×D4—24no—
383C2×D4—24no—
384C2×D4—24no—
385C2×D4—21no—
386C2×D4—41no—
387C2×D4—41no—
388C2×D4—48no—
389C2×D4—41no—
390C2×D4—41no—
391C2×D4—42no—
392C2×D4—432no—
393C2×D4—432no—
394C2×D4—42no—
395C2×D4—48no—
396C2×D4—48no—
397C2×D4—42no—
398C2×D4—42no—
399C2×D4—44no—
400C2×D4—41no—
401C2×D4—42no—
402C2×D4—48no—
403C2×D4—88no—
404C2×D4C2×D4×C2912yes—
405C2×D4C2×D4×C2911yescharacteristic
406C2×D4C2×D4×C2912yescomplemented
407C2×D4C24×C2911yescharacteristic
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—28no—
411C22×C4—22no—
412C22×C4—48no—
413C22×C4—41no—
414C22×C4—42no—
415C22×C4C2×D4×C2911yescharacteristic
416SD16—44no—
417D8—44no—
418M16—22no—
419M16—41no—
420C2×C8—41no—
421C4⋊C4—24no—
422C22⋊C4—24no—
423C22⋊C4—22no—
424C22⋊C4—24no—
425C22⋊C4—24no—
426C22⋊C4—24no—
427C22⋊C4—48no—
428C22⋊C4—42no—
429C22⋊C4C2×D4×C2914yescomplemented
430C42—21no—
431C42C2×D4×C2912yescomplemented
432C23—28no—
433C23—22no—
434C23—24no—
435C23—22no—
436C23—24no—
437C23—22no—
438C23—44no—
439C23—44no—
440C23—44no—
441C23—48no—
442C23—44no—
443C23—48no—
444C23—416no—
445C23—42no—
446C23—42no—
447C23—42no—
448C23—48no—
449C23—41no—
450C23—41no—
451C23—41no—
452C23—82no—
453C23—84no—
454C23—88no—
455C23—84no—
456C23—88no—
457C23—88no—
458C23—84no—
459C23C29×#12011yescharacteristic
460C23C29×#12012yes—
461C23C22×D4×C2912yes—
462Q8—22no—
463Q8—41no—
464D4—216no—
465D4—22no—
466D4—41no—
467D4—42no—
468D4—41no—
469D4—42no—
470D4—48no—
471D4—48no—
472D4—41no—
473D4—48no—
474D4—48no—
475D4—416no—
476D4—44no—
477D4—44no—
478D4—42no—
479D4—42no—
480D4—81no—
481D4—816no—
482C2×C4—24no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—22no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—416no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—44no—
492C2×C4—42no—
493C2×C4—41no—
494C2×C4—44no—
495C2×C4—84no—
496C2×C4C29×#12011yescharacteristic
497C2×C4C22×D4×C2911yescharacteristic
498C8—42no—
499C22—22no—
500C22—28no—
501C22—22no—
502C22—22no—
503C22—42no—
504C22—42no—
505C22—44no—
506C22—48no—
507C22—44no—
508C22—48no—
509C22—44no—
510C22—48no—
511C22—44no—
512C22—42no—
513C22—42no—
514C22—82no—
515C22—82no—
516C22—84no—
517C22—88no—
518C22—816no—
519C22—84no—
520C22—82no—
521C22—82no—
522C22—162no—
523C22C29×B(4,𝔽2)11yescharacteristic
524C22C29×B(4,𝔽2)11yescharacteristic
525C22C2×C29×#12011yescharacteristic
526C4—24no—
527C4—21no—
528C4—21no—
529C4—44no—
530C4—42no—
531C4—84no—
532C2—21no—
533C2—21no—
534C2—42no—
535C2—48no—
536C2—42no—
537C2—82no—
538C2—82no—
539C2C29×#219612yesdirect product factor
540C2C2×C29×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C29B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C29
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C23×C29 ◁ C22×D4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×D42×C29C2semidirect
2. C2×C29×B(4,𝔽2)C2semidirect
3. C2×C29×#453C2semidirect
4. C29×#2196C2direct (N × H)
5. C2×C29×#353C2semidirect
6. C2×C29×AΣL(1,𝔽16)C2semidirect
7. C2×C29×H(5,𝔽2)C22semidirect
12. D42×C29C22semidirect
20. C29×B(4,𝔽2)C22semidirect
22. C29×#453C22semidirect
24. C2×C29×#100C22semidirect
26. C2×C29×#99C22semidirect
27. C29×#353C22semidirect
28. C29×AΣL(1,𝔽16)C22semidirect
30. C25×C29D4semidirect
34. C29×H(5,𝔽2)C23semidirect
47. C22×D4×C29D4semidirect
56. C29×#127D4semidirect
66. C29×#120D4semidirect
75. C2×C22⋊C4×C29D4semidirect
76. C2×C42×C29D4semidirect
79. C29×#100C23semidirect
82. C29×#99C23semidirect
95. C24×C29C2×D4semidirect
135. C2×D4×C29C2×D4semidirect
158. C22⋊C4×C29C2×D4semidirect
160. C42×C29C2×D4semidirect
161. C2×#2196C29direct (N × H)
229. C2×D42C2×C29semidirect
230. C2×B(4,𝔽2)C2×C29semidirect
231. C2×#453C2×C29semidirect
232. #2196C2×C29direct (N × H)
233. C2×#353C2×C29semidirect
234. C2×AΣL(1,𝔽16)C2×C29semidirect
268. C2×H(5,𝔽2)C22×C29semidirect
273. D42C22×C29semidirect
281. B(4,𝔽2)C22×C29semidirect
283. #453C22×C29semidirect
285. C2×#100C22×C29semidirect
287. C2×#99C22×C29semidirect
288. #353C22×C29semidirect
289. AΣL(1,𝔽16)C22×C29semidirect
297. C2×C29#2196direct (N × H)
300. C25D4×C29semidirect
304. H(5,𝔽2)C23×C29semidirect
317. C22×D4D4×C29semidirect
326. #127D4×C29semidirect
336. #120D4×C29semidirect
345. C2×C22⋊C4D4×C29semidirect
346. C2×C42D4×C29semidirect
349. #100C23×C29semidirect
352. #99C23×C29semidirect
353. C29C2×#2196direct (N × H)
366. C24C2×D4×C29semidirect
406. C2×D4C2×D4×C29semidirect
429. C22⋊C4C2×D4×C29semidirect
431. C42C2×D4×C29semidirect
539. C2C29×#2196direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D42×C292
C2×C29×B(4,𝔽2)2
C2×C29×#4532
C29×#21962
C2×C29×#3532
C2×C29×AΣL(1,𝔽16)2
C2×#219629