Finite Group Databasebeta

← C29×#18998 #20313898

Subgroups — C29×#18998 #20313898

Order 7424.

926 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#562C211yesmaximal, characteristic
2C29×#3236C211yesmaximal, characteristic, complemented
3C29×#3215C211yesmaximal, characteristic, complemented
4C29×#3140C211yesmaximal, characteristic, complemented
5C29×#1662C214yesmaximal, complemented
6C29×#1661C214yesmaximal, complemented
7C29×#1533C211yesmaximal, characteristic, complemented
8C29×#1528C211yesmaximal, characteristic, complemented
9C29×#1527C211yesmaximal, characteristic, complemented
10C29×#562—22no—
11C29×#562—22no—
12C29×#562—22no—
13C29×#562C2214yes—
14C29×#533C2211yescharacteristic
15C2×C29×#125C2211yescharacteristic
16C2×C29×#124C2211yescharacteristic
17C2×C29×#124C2211yescharacteristic
18C2×C29×#123—21no—
19C2×C29×#123—21no—
20C2×C29×C22⋊Q8—21no—
21C2×C29×C22⋊Q8—21no—
22C2×C29×#121—21no—
23C2×C29×#121—21no—
24C29×#501C2212yescomplemented
25C29×#497C2212yescomplemented
26C29×#491C2212yescomplemented
27C29×#489C2212yescomplemented
28C29×#489C2212yescomplemented
29C29×#489C2212yescomplemented
30C29×#488—22no—
31C29×#484—21no—
32C29×#483—21no—
33C29×#479—22no—
34C29×#464—22no—
35C29×#451—21no—
36C29×#450—21no—
37C29×#432C2211yescharacteristic
38C29×#432C2211yescharacteristic
39C29×#419—21no—
40C29×#418—21no—
41C4×M16×C29C2211yescharacteristic
42C29×#330C2214yescomplemented
43C29×#329C2214yescomplemented
44C29×#329C2214yescomplemented
45C22×Q8×C29D411yescharacteristic
46C22×Q8×C29D411yescharacteristic
47C22×D4×C29—21no—
48C22×D4×C29—21no—
49C22×D4×C29D411yescharacteristic
50C22×D4×C29D411yescharacteristic
51C23×C4×C29—21no—
52C23×C4×C29—21no—
53C2×Q16×C29—22no—
54C2×SD16×C29—22no—
55C2×M16×C29—21no—
56C29×C4⋊Q8C2311yescharacteristic
57C29×C4⋊Q8C2311yescharacteristic
58C29×#125—21no—
59C29×#125—21no—
60C29×#125—21no—
61C29×#125D412yes—
62C29×#125C2312yes—
63C29×#124—21no—
64C29×#124—21no—
65C29×#124—21no—
66C29×#124—21no—
67C29×#124D412yes—
68C29×#124D412yes—
69C29×#124C2312yes—
70C29×#124C2312yes—
71C29×#123—24no—
72C29×#123—24no—
73C29×#123—24no—
74C29×#123—24no—
75C29×C22⋊Q8—24no—
76C29×C22⋊Q8—24no—
77C29×C22⋊Q8—24no—
78C29×C22⋊Q8—24no—
79C29×C22⋊Q8—21no—
80C29×C22⋊Q8—21no—
81C29×#121—24no—
82C29×#121—24no—
83C29×#121—24no—
84C29×#121—24no—
85C4×Q8×C29—21no—
86C4×Q8×C29—21no—
87C29×#117—21no—
88C2×C4⋊C4×C29—21no—
89C2×C4⋊C4×C29—21no—
90C2×C4⋊C4×C29—21no—
91C2×C4⋊C4×C29—21no—
92C2×C4⋊C4×C29D411yescharacteristic
93C2×C4⋊C4×C29D411yescharacteristic
94C2×C22⋊C4×C29—21no—
95C2×C22⋊C4×C29—21no—
96C2×C22⋊C4×C29—21no—
97C2×C22⋊C4×C29—21no—
98C2×C22⋊C4×C29—21no—
99C2×C22⋊C4×C29—21no—
100C2×C42×C29C2311yescharacteristic
101C29×#107—22no—
102C29×#106—22no—
103C29×C4⋊C8—21no—
104C29×C4⋊C8—21no—
105C29×#103—22no—
106C29×#103—22no—
107C29×#103—22no—
108C29×#103—22no—
109C29×#103—22no—
110C29×#102—22no—
111C29×#102—22no—
112C29×#102—22no—
113C29×C22⋊C8—21no—
114C29×C22⋊C8—21no—
115C29×#97C2312yes—
116C29×#97C2312yes—
117C29×#97C2312yes—
118C4×C8×C29—21no—
119C24×C29—21no—
120C24×C29—21no—
121C2×Q8×C29—21no—
122C2×Q8×C29—21no—
123C2×Q8×C29—21no—
124C2×Q8×C29—21no—
125C2×Q8×C29—42no—
126C2×Q8×C29—81no—
127C2×Q8×C29C2×D412yes—
128C2×Q8×C29C2×D412yes—
129C2×D4×C29—24no—
130C2×D4×C29—24no—
131C2×D4×C29—21no—
132C2×D4×C29—21no—
133C2×D4×C29—42no—
134C2×D4×C29—81no—
135C2×D4×C29—82no—
136C2×D4×C29—82no—
137C2×D4×C29C2×D412yes—
138C2×D4×C29C2×D412yes—
139C22×C4×C29—21no—
140C22×C4×C29—21no—
141C22×C4×C29—21no—
142C22×C4×C29—21no—
143C22×C4×C29—24no—
144C22×C4×C29—24no—
145C22×C4×C29—82no—
146C22×C4×C29—82no—
147C22×C4×C29C2×D411yescharacteristic
148C22×C4×C29C2×D411yescharacteristic
149C22×C4×C29C2×D411yescharacteristic
150Q16×C29—82no—
151SD16×C29—82no—
152M16×C29—42no—
153C2×C8×C29—22no—
154C2×C8×C29—22no—
155C2×C8×C29—22no—
156C4⋊C4×C29—24no—
157C4⋊C4×C29—24no—
158C4⋊C4×C29—22no—
159C4⋊C4×C29—22no—
160C4⋊C4×C29—21no—
161C4⋊C4×C29—21no—
162C4⋊C4×C29—22no—
163C4⋊C4×C29—22no—
164C4⋊C4×C29—21no—
165C4⋊C4×C29—21no—
166C4⋊C4×C29—21no—
167C4⋊C4×C29—21no—
168C4⋊C4×C29—41no—
169C4⋊C4×C29—41no—
170C4⋊C4×C29C2×D412yes—
171C4⋊C4×C29C2×D412yes—
172C22⋊C4×C29—24no—
173C22⋊C4×C29—24no—
174C22⋊C4×C29—22no—
175C22⋊C4×C29—22no—
176C22⋊C4×C29—22no—
177C22⋊C4×C29—22no—
178C22⋊C4×C29—22no—
179C22⋊C4×C29—22no—
180C22⋊C4×C29—22no—
181C22⋊C4×C29—22no—
182C22⋊C4×C29—41no—
183C42×C29—41no—
184C42×C29C2×D411yescharacteristic
185C42×C29C2×D411yescharacteristic
186C42×C29C2×D411yescharacteristic
187C42×C29C2411yescharacteristic
188#18998C2911yesmaximal, characteristic, direct product factor, Sylow
189C23×C29—22no—
190C23×C29—22no—
191C23×C29—42no—
192C23×C29—42no—
193C23×C29—42no—
194C23×C29—42no—
195C23×C29—42no—
196C23×C29—42no—
197C23×C29#12011yescharacteristic
198Q8×C29—42no—
199Q8×C29—42no—
200Q8×C29—42no—
201Q8×C29—42no—
202Q8×C29—81no—
203Q8×C29—81no—
204D4×C29—42no—
205D4×C29—42no—
206D4×C29—81no—
207D4×C29—81no—
208D4×C29—84no—
209D4×C29—84no—
210C2×C4×C29—22no—
211C2×C4×C29—22no—
212C2×C4×C29—22no—
213C2×C4×C29—22no—
214C2×C4×C29—22no—
215C2×C4×C29—41no—
216C2×C4×C29—41no—
217C2×C4×C29—42no—
218C2×C4×C29—42no—
219C2×C4×C29—42no—
220C2×C4×C29—42no—
221C2×C4×C29—41no—
222C2×C4×C29—41no—
223C2×C4×C29—84no—
224C2×C4×C29—84no—
225C2×C4×C29#12011yescharacteristic
226C2×C4×C29#12011yescharacteristic
227C2×C4×C29#12011yescharacteristic
228C2×C4×C29C22×D411yescharacteristic
229C2×C4×C29C22×D411yescharacteristic
230C2×C4×C29C22×D411yescharacteristic
231C8×C29—42no—
232C8×C29—42no—
233C8×C29—42no—
234C2×#562C2×C2911yescharacteristic
235#3236C2×C2911yescharacteristic, complemented
236#3215C2×C2911yescharacteristic, complemented
237#3140C2×C2911yescharacteristic, complemented
238#1662C2×C2914yescomplemented
239#1661C2×C2914yescomplemented
240#1533C2×C2911yescharacteristic, complemented
241#1528C2×C2911yescharacteristic, complemented
242#1527C2×C2911yescharacteristic, complemented
243C22×C29—21no—
244C22×C29—21no—
245C22×C29—42no—
246C22×C29—42no—
247C22×C29—42no—
248C22×C29—42no—
249C22×C29—42no—
250C22×C29—42no—
251C22×C29—84no—
252C22×C29—84no—
253C22×C29#45512yes—
254C22×C29C2×#12011yescharacteristic
255C4×C29—21no—
256C4×C29—21no—
257C4×C29—21no—
258C4×C29—21no—
259C4×C29—21no—
260C4×C29—21no—
261C4×C29—42no—
262C4×C29—42no—
263C4×C29—42no—
264C4×C29—42no—
265C4×C29—81no—
266C4×C29—81no—
267#562—22no—
268#562—22no—
269#562—22no—
270#562C22×C2914yes—
271#533C22×C2911yescharacteristic
272C2×#125C22×C2911yescharacteristic
273C2×#124C22×C2911yescharacteristic
274C2×#124C22×C2911yescharacteristic
275C2×#123—21no—
276C2×#123—21no—
277C2×C22⋊Q8—21no—
278C2×C22⋊Q8—21no—
279C2×#121—21no—
280C2×#121—21no—
281#501C22×C2912yescomplemented
282#497C22×C2912yescomplemented
283#491C22×C2912yescomplemented
284#489C22×C2912yescomplemented
285#489C22×C2912yescomplemented
286#489C22×C2912yescomplemented
287#488—22no—
288#484—21no—
289#483—21no—
290#479—22no—
291#464—22no—
292#451—21no—
293#450—21no—
294#432C22×C2911yescharacteristic
295#432C22×C2911yescharacteristic
296#419—21no—
297#418—21no—
298C4×M16C22×C2911yescharacteristic
299#330C22×C2914yescomplemented
300#329C22×C2914yescomplemented
301#329C22×C2914yescomplemented
302C2×C29—22no—
303C2×C29—82no—
304C2×C29—82no—
305C2×C29C2×#45511yescharacteristic
306C2×C29#301911yescharacteristic
307C2×C29#302011yescharacteristic
308C22×Q8D4×C2911yescharacteristic
309C22×Q8D4×C2911yescharacteristic
310C22×D4—21no—
311C22×D4—21no—
312C22×D4D4×C2911yescharacteristic
313C22×D4D4×C2911yescharacteristic
314C23×C4—21no—
315C23×C4—21no—
316C2×Q16—22no—
317C2×SD16—22no—
318C2×M16—21no—
319C4⋊Q8C23×C2911yescharacteristic
320C4⋊Q8C23×C2911yescharacteristic
321#125—21no—
322#125—21no—
323#125—21no—
324#125D4×C2912yes—
325#125C23×C2912yes—
326#124—21no—
327#124—21no—
328#124—21no—
329#124—21no—
330#124D4×C2912yes—
331#124D4×C2912yes—
332#124C23×C2912yes—
333#124C23×C2912yes—
334#123—24no—
335#123—24no—
336#123—24no—
337#123—24no—
338C22⋊Q8—24no—
339C22⋊Q8—24no—
340C22⋊Q8—24no—
341C22⋊Q8—24no—
342C22⋊Q8—21no—
343C22⋊Q8—21no—
344#121—24no—
345#121—24no—
346#121—24no—
347#121—24no—
348C4×Q8—21no—
349C4×Q8—21no—
350#117—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4D4×C2911yescharacteristic
356C2×C4⋊C4D4×C2911yescharacteristic
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C42C23×C2911yescharacteristic
364#107—22no—
365#106—22no—
366C4⋊C8—21no—
367C4⋊C8—21no—
368#103—22no—
369#103—22no—
370#103—22no—
371#103—22no—
372#103—22no—
373#102—22no—
374#102—22no—
375#102—22no—
376C22⋊C8—21no—
377C22⋊C8—21no—
378#97C23×C2912yes—
379#97C23×C2912yes—
380#97C23×C2912yes—
381C4×C8—21no—
382C29#1899811yescharacteristic, direct product factor, Sylow
383C24—21no—
384C24—21no—
385C2×Q8—21no—
386C2×Q8—21no—
387C2×Q8—21no—
388C2×Q8—21no—
389C2×Q8—42no—
390C2×Q8—81no—
391C2×Q8C2×D4×C2912yes—
392C2×Q8C2×D4×C2912yes—
393C2×D4—24no—
394C2×D4—24no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4—42no—
398C2×D4—81no—
399C2×D4—82no—
400C2×D4—82no—
401C2×D4C2×D4×C2912yes—
402C2×D4C2×D4×C2912yes—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—24no—
408C22×C4—24no—
409C22×C4—82no—
410C22×C4—82no—
411C22×C4C2×D4×C2911yescharacteristic
412C22×C4C2×D4×C2911yescharacteristic
413C22×C4C2×D4×C2911yescharacteristic
414Q16—82no—
415SD16—82no—
416M16—42no—
417C2×C8—22no—
418C2×C8—22no—
419C2×C8—22no—
420C4⋊C4—24no—
421C4⋊C4—24no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—41no—
433C4⋊C4—41no—
434C4⋊C4C2×D4×C2912yes—
435C4⋊C4C2×D4×C2912yes—
436C22⋊C4—24no—
437C22⋊C4—24no—
438C22⋊C4—22no—
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—22no—
442C22⋊C4—22no—
443C22⋊C4—22no—
444C22⋊C4—22no—
445C22⋊C4—22no—
446C22⋊C4—41no—
447C42—41no—
448C42C2×D4×C2911yescharacteristic
449C42C2×D4×C2911yescharacteristic
450C42C2×D4×C2911yescharacteristic
451C42C24×C2911yescharacteristic
452C23—22no—
453C23—22no—
454C23—42no—
455C23—42no—
456C23—42no—
457C23—42no—
458C23—42no—
459C23—42no—
460C23C29×#12011yescharacteristic
461Q8—42no—
462Q8—42no—
463Q8—42no—
464Q8—42no—
465Q8—81no—
466Q8—81no—
467D4—42no—
468D4—42no—
469D4—81no—
470D4—81no—
471D4—84no—
472D4—84no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—84no—
487C2×C4—84no—
488C2×C4C29×#12011yescharacteristic
489C2×C4C29×#12011yescharacteristic
490C2×C4C29×#12011yescharacteristic
491C2×C4C22×D4×C2911yescharacteristic
492C2×C4C22×D4×C2911yescharacteristic
493C2×C4C22×D4×C2911yescharacteristic
494C8—42no—
495C8—42no—
496C8—42no—
497C22—21no—
498C22—21no—
499C22—42no—
500C22—42no—
501C22—42no—
502C22—42no—
503C22—42no—
504C22—42no—
505C22—84no—
506C22—84no—
507C22C29×#45512yes—
508C22C2×C29×#12011yescharacteristic
509C4—21no—
510C4—21no—
511C4—21no—
512C4—21no—
513C4—21no—
514C4—21no—
515C4—42no—
516C4—42no—
517C4—42no—
518C4—42no—
519C4—81no—
520C4—81no—
521C2—22no—
522C2—82no—
523C2—82no—
524C2C2×C29×#45511yescharacteristic
525C2C29×#301911yescharacteristic
526C2C29×#302011yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC42C24×C29
prime radicalC2×C29×#562C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#3236C2semidirect
3. C29×#3215C2semidirect
4. C29×#3140C2semidirect
5. C29×#1662C2semidirect
6. C29×#1661C2semidirect
7. C29×#1533C2semidirect
8. C29×#1528C2semidirect
9. C29×#1527C2semidirect
24. C29×#501C22semidirect
25. C29×#497C22semidirect
26. C29×#491C22semidirect
27. C29×#489C22semidirect
28. C29×#489C22semidirect
29. C29×#489C22semidirect
42. C29×#330C22semidirect
43. C29×#329C22semidirect
44. C29×#329C22semidirect
188. #18998C29direct (N × H)
235. #3236C2×C29semidirect
236. #3215C2×C29semidirect
237. #3140C2×C29semidirect
238. #1662C2×C29semidirect
239. #1661C2×C29semidirect
240. #1533C2×C29semidirect
241. #1528C2×C29semidirect
242. #1527C2×C29semidirect
281. #501C22×C29semidirect
282. #497C22×C29semidirect
283. #491C22×C29semidirect
284. #489C22×C29semidirect
285. #489C22×C29semidirect
286. #489C22×C29semidirect
299. #330C22×C29semidirect
300. #329C22×C29semidirect
301. #329C22×C29semidirect
382. C29#18998direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#5622
C29×#32362
C29×#32152
C29×#31402
C29×#16622
C29×#16612
C29×#15332
C29×#15282
C29×#15272
#1899829