Finite Group Databasebeta

← C29×#9275 #20304175

Subgroups — C29×#9275 #20304175

Order 7424.

606 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3187C211yesmaximal, characteristic
2C29×#2364C211yesmaximal, characteristic
3C29×#1996C211yesmaximal, characteristic, complemented
4C29×#1519C211yesmaximal, characteristic
5C2×C29×#328C211yesmaximal, characteristic, complemented
6C29×#1294C211yesmaximal, characteristic, complemented
7C29×#1282C211yesmaximal, characteristic, complemented
8C2×C29×C22⋊Q8C2211yescharacteristic
9C2×C29×#121C2211yescharacteristic
10C2×C4×D4×C29—21no—
11C29×#483—21no—
12C29×#481C412yescomplemented
13C29×#465—22no—
14C29×#450—21no—
15C29×#448C412yescomplemented
16C2×C29×C22⋊C8C2211yescharacteristic
17C2×C29×C22⋊C8C2211yescharacteristic
18C29×#388—21no—
19C29×#387—21no—
20C29×#386—21no—
21C29×#386—21no—
22C29×#380C2211yescharacteristic
23C4×C22⋊C4×C29—21no—
24C4×C22⋊C4×C29C2211yescharacteristic
25C2×C29×#95C2211yescharacteristic
26C29×#342—21no—
27C29×#342—21no—
28C29×#328—21no—
29C29×#328—21no—
30C29×#327—22no—
31C22×Q8×C29C2×C411yescharacteristic, complemented
32C22×D4×C29—21no—
33C22×D4×C29D411yescharacteristic
34C23×C4×C29—21no—
35C23×C4×C29—21no—
36C23×C4×C29C2311yescharacteristic
37C2×SD16×C29—22no—
38C22×C8×C29—21no—
39C22×C8×C29—21no—
40C29×C22⋊Q8—21no—
41C29×C22⋊Q8—21no—
42C29×C22⋊Q8—21no—
43C29×C22⋊Q8—21no—
44C29×#121—21no—
45C29×#121—21no—
46C29×#121C2×C412yes—
47C29×#121D412yes—
48C4×D4×C29—42no—
49C4×D4×C29—42no—
50C2×C4⋊C4×C29—21no—
51C2×C4⋊C4×C29—21no—
52C2×C4⋊C4×C29—21no—
53C2×C4⋊C4×C29C2×C411yescharacteristic, complemented
54C2×C4⋊C4×C29D411yescharacteristic
55C2×C22⋊C4×C29—21no—
56C2×C22⋊C4×C29—21no—
57C2×C22⋊C4×C29—21no—
58C2×C22⋊C4×C29—21no—
59C2×C22⋊C4×C29—21no—
60C2×C22⋊C4×C29—21no—
61C2×C22⋊C4×C29D411yescharacteristic
62C2×C22⋊C4×C29D411yescharacteristic
63C2×C42×C29—21no—
64C2×C42×C29—21no—
65C29×#106—22no—
66C29×#103—22no—
67C29×#102—22no—
68C29×C22⋊C8—21no—
69C29×C22⋊C8—21no—
70C29×C22⋊C8—21no—
71C29×C22⋊C8C2×C412yescomplemented
72C29×#95—21no—
73C29×#95—21no—
74C29×#95—21no—
75C29×#95—21no—
76C29×#95—21no—
77C29×#95D411yescharacteristic
78C29×#95D411yescharacteristic
79C24×C29—21no—
80C24×C29C2×D411yescharacteristic
81C2×Q8×C29—21no—
82C2×Q8×C29—21no—
83C2×Q8×C29—81no—
84C2×D4×C29—22no—
85C2×D4×C29—22no—
86C2×D4×C29—21no—
87C2×D4×C29—41no—
88C2×D4×C29—41no—
89C2×D4×C29—41no—
90C2×D4×C29—41no—
91C2×D4×C29—81no—
92C2×D4×C29C22⋊C412yes—
93C22×C4×C29—21no—
94C22×C4×C29—21no—
95C22×C4×C29—21no—
96C22×C4×C29—21no—
97C22×C4×C29—21no—
98C22×C4×C29—21no—
99C22×C4×C29—21no—
100C22×C4×C29—42no—
101C22×C4×C29—42no—
102C22×C4×C29—42no—
103C22×C4×C29—41no—
104C22×C4×C29—41no—
105C22×C4×C29—41no—
106C22×C4×C29—81no—
107C22×C4×C29—81no—
108C22×C4×C29—81no—
109C22×C4×C29C22×C411yescharacteristic
110C22×C4×C29C2×D411yescharacteristic
111C22×C4×C29C2×D411yescharacteristic
112C22×C4×C29C2×D411yescharacteristic
113C22×C4×C29#4111yescharacteristic
114C22×C4×C29#4111yescharacteristic
115SD16×C29—82no—
116C2×C8×C29—22no—
117C2×C8×C29—41no—
118C2×C8×C29—81no—
119C2×C8×C29—81no—
120C4⋊C4×C29—21no—
121C4⋊C4×C29—21no—
122C4⋊C4×C29—21no—
123C4⋊C4×C29—42no—
124C4⋊C4×C29—41no—
125C4⋊C4×C29—41no—
126C4⋊C4×C29—81no—
127C4⋊C4×C29C22⋊C412yes—
128C22⋊C4×C29—21no—
129C22⋊C4×C29—22no—
130C22⋊C4×C29—22no—
131C22⋊C4×C29—21no—
132C22⋊C4×C29—21no—
133C22⋊C4×C29—42no—
134C22⋊C4×C29—42no—
135C22⋊C4×C29—41no—
136C22⋊C4×C29—41no—
137C22⋊C4×C29—41no—
138C22⋊C4×C29—41no—
139C22⋊C4×C29—81no—
140C22⋊C4×C29SD1612yescomplemented
141C42×C29—42no—
142C42×C29—81no—
143#9275C2911yesmaximal, characteristic, direct product factor, Sylow
144C23×C29—22no—
145C23×C29—41no—
146C23×C29—41no—
147C23×C29—41no—
148C23×C29—41no—
149C23×C29—41no—
150C23×C29—41no—
151C23×C29—41no—
152C23×C29—41no—
153C23×C29C4×D411yescharacteristic
154C23×C29#12011yescharacteristic
155C23×C29#12111yescharacteristic
156C23×C29C2×SD1611yescharacteristic
157C23×C29#13511yescharacteristic
158C23×C29AGL(1,ℤ/8)11yescharacteristic
159C23×C29#13711yescharacteristic
160Q8×C29—42no—
161Q8×C29—81no—
162D4×C29—42no—
163D4×C29—42no—
164D4×C29—42no—
165D4×C29—42no—
166D4×C29—42no—
167D4×C29—81no—
168C2×C4×C29—22no—
169C2×C4×C29—22no—
170C2×C4×C29—22no—
171C2×C4×C29—41no—
172C2×C4×C29—41no—
173C2×C4×C29—41no—
174C2×C4×C29—41no—
175C2×C4×C29—41no—
176C2×C4×C29—41no—
177C2×C4×C29—41no—
178C2×C4×C29—41no—
179C2×C4×C29—41no—
180C2×C4×C29—41no—
181C2×C4×C29—41no—
182C2×C4×C29—41no—
183C2×C4×C29—41no—
184C2×C4×C29—41no—
185C2×C4×C29—41no—
186C2×C4×C29—41no—
187C2×C4×C29—41no—
188C2×C4×C29—41no—
189C2×C4×C29—41no—
190C2×C4×C29—41no—
191C2×C4×C29—84no—
192C2×C4×C29—82no—
193C2×C4×C29—82no—
194C2×C4×C29—81no—
195C2×C4×C29—81no—
196C2×C4×C29—81no—
197C2×C4×C29—81no—
198C2×C4×C29—81no—
199C2×C4×C29C2×C22⋊C411yescharacteristic
200C2×C4×C29C4×D411yescharacteristic
201C2×C4×C29#12111yescharacteristic
202C2×C4×C29#12311yescharacteristic
203C8×C29—42no—
204C8×C29—81no—
205#3187C2×C2911yescharacteristic
206#2364C2×C2911yescharacteristic
207#1996C2×C2911yescharacteristic, complemented
208#1519C2×C2911yescharacteristic
209C2×#328C2×C2911yescharacteristic, complemented
210#1294C2×C2911yescharacteristic, complemented
211#1282C2×C2911yescharacteristic, complemented
212C22×C29—21no—
213C22×C29—21no—
214C22×C29—21no—
215C22×C29—21no—
216C22×C29—21no—
217C22×C29—21no—
218C22×C29—41no—
219C22×C29—41no—
220C22×C29—41no—
221C22×C29—41no—
222C22×C29—42no—
223C22×C29—42no—
224C22×C29—42no—
225C22×C29—81no—
226C22×C29—81no—
227C22×C29—81no—
228C22×C29—81no—
229C22×C29#38611yescharacteristic
230C22×C29C4×SD1611yescharacteristic
231C22×C29#44011yescharacteristic
232C22×C29#45011yescharacteristic
233C22×C29#45211yescharacteristic
234C22×C29#46111yescharacteristic
235C22×C29#46311yescharacteristic
236C4×C29—21no—
237C4×C29—21no—
238C4×C29—21no—
239C4×C29—21no—
240C4×C29—42no—
241C4×C29—42no—
242C4×C29—42no—
243C4×C29—81no—
244C4×C29—81no—
245C4×C29—81no—
246C4×C29—81no—
247C4×C29—161no—
248C2×C22⋊Q8C22×C2911yescharacteristic
249C2×#121C22×C2911yescharacteristic
250C2×C4×D4—21no—
251#483—21no—
252#481C4×C2912yescomplemented
253#465—22no—
254#450—21no—
255#448C4×C2912yescomplemented
256C2×C22⋊C8C22×C2911yescharacteristic
257C2×C22⋊C8C22×C2911yescharacteristic
258#388—21no—
259#387—21no—
260#386—21no—
261#386—21no—
262#380C22×C2911yescharacteristic
263C4×C22⋊C4—21no—
264C4×C22⋊C4C22×C2911yescharacteristic
265C2×#95C22×C2911yescharacteristic
266#342—21no—
267#342—21no—
268#328—21no—
269#328—21no—
270#327—22no—
271C2×C29—21no—
272C2×C29—21no—
273C2×C29—21no—
274C2×C29—21no—
275C2×C29—21no—
276C2×C29—21no—
277C2×C29—82no—
278C2×C29#187711yescharacteristic
279C2×C29#190611yescharacteristic
280C2×C29#191311yescharacteristic
281C22×Q8C2×C4×C2911yescharacteristic, complemented
282C22×D4—21no—
283C22×D4D4×C2911yescharacteristic
284C23×C4—21no—
285C23×C4—21no—
286C23×C4C23×C2911yescharacteristic
287C2×SD16—22no—
288C22×C8—21no—
289C22×C8—21no—
290C22⋊Q8—21no—
291C22⋊Q8—21no—
292C22⋊Q8—21no—
293C22⋊Q8—21no—
294#121—21no—
295#121—21no—
296#121C2×C4×C2912yes—
297#121D4×C2912yes—
298C4×D4—42no—
299C4×D4—42no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4C2×C4×C2911yescharacteristic, complemented
304C2×C4⋊C4D4×C2911yescharacteristic
305C2×C22⋊C4—21no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—21no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—21no—
311C2×C22⋊C4D4×C2911yescharacteristic
312C2×C22⋊C4D4×C2911yescharacteristic
313C2×C42—21no—
314C2×C42—21no—
315#106—22no—
316#103—22no—
317#102—22no—
318C22⋊C8—21no—
319C22⋊C8—21no—
320C22⋊C8—21no—
321C22⋊C8C2×C4×C2912yescomplemented
322#95—21no—
323#95—21no—
324#95—21no—
325#95—21no—
326#95—21no—
327#95D4×C2911yescharacteristic
328#95D4×C2911yescharacteristic
329C29#927511yescharacteristic, direct product factor, Sylow
330C24—21no—
331C24C2×D4×C2911yescharacteristic
332C2×Q8—21no—
333C2×Q8—21no—
334C2×Q8—81no—
335C2×D4—22no—
336C2×D4—22no—
337C2×D4—21no—
338C2×D4—41no—
339C2×D4—41no—
340C2×D4—41no—
341C2×D4—41no—
342C2×D4—81no—
343C2×D4C22⋊C4×C2912yes—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—42no—
352C22×C4—42no—
353C22×C4—42no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—81no—
358C22×C4—81no—
359C22×C4—81no—
360C22×C4C22×C4×C2911yescharacteristic
361C22×C4C2×D4×C2911yescharacteristic
362C22×C4C2×D4×C2911yescharacteristic
363C22×C4C2×D4×C2911yescharacteristic
364C22×C4#41×C2911yescharacteristic
365C22×C4#41×C2911yescharacteristic
366SD16—82no—
367C2×C8—22no—
368C2×C8—41no—
369C2×C8—81no—
370C2×C8—81no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—42no—
375C4⋊C4—41no—
376C4⋊C4—41no—
377C4⋊C4—81no—
378C4⋊C4C22⋊C4×C2912yes—
379C22⋊C4—21no—
380C22⋊C4—22no—
381C22⋊C4—22no—
382C22⋊C4—21no—
383C22⋊C4—21no—
384C22⋊C4—42no—
385C22⋊C4—42no—
386C22⋊C4—41no—
387C22⋊C4—41no—
388C22⋊C4—41no—
389C22⋊C4—41no—
390C22⋊C4—81no—
391C22⋊C4SD16×C2912yescomplemented
392C42—42no—
393C42—81no—
394C23—22no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—41no—
402C23—41no—
403C23C4×D4×C2911yescharacteristic
404C23C29×#12011yescharacteristic
405C23C29×#12111yescharacteristic
406C23C2×SD16×C2911yescharacteristic
407C23C29×#13511yescharacteristic
408C23C29×AGL(1,ℤ/8)11yescharacteristic
409C23C29×#13711yescharacteristic
410Q8—42no—
411Q8—81no—
412D4—42no—
413D4—42no—
414D4—42no—
415D4—42no—
416D4—42no—
417D4—81no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—84no—
442C2×C4—82no—
443C2×C4—82no—
444C2×C4—81no—
445C2×C4—81no—
446C2×C4—81no—
447C2×C4—81no—
448C2×C4—81no—
449C2×C4C2×C22⋊C4×C2911yescharacteristic
450C2×C4C4×D4×C2911yescharacteristic
451C2×C4C29×#12111yescharacteristic
452C2×C4C29×#12311yescharacteristic
453C8—42no—
454C8—81no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—42no—
466C22—42no—
467C22—42no—
468C22—81no—
469C22—81no—
470C22—81no—
471C22—81no—
472C22C29×#38611yescharacteristic
473C22C4×SD16×C2911yescharacteristic
474C22C29×#44011yescharacteristic
475C22C29×#45011yescharacteristic
476C22C29×#45211yescharacteristic
477C22C29×#46111yescharacteristic
478C22C29×#46311yescharacteristic
479C4—21no—
480C4—21no—
481C4—21no—
482C4—21no—
483C4—42no—
484C4—42no—
485C4—42no—
486C4—81no—
487C4—81no—
488C4—81no—
489C4—81no—
490C4—161no—
491C2—21no—
492C2—21no—
493C2—21no—
494C2—21no—
495C2—21no—
496C2—21no—
497C2—82no—
498C2C29×#187711yescharacteristic
499C2C29×#190611yescharacteristic
500C2C29×#191311yescharacteristic
subgroupG/H
center, socleC22×C29#386
commutatorC22×C4C22×C4×C29
Frattini, cosocleC23×C4C23×C29
prime radicalC2×C29×#121C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C23×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
3. C29×#1996C2semidirect
5. C2×C29×#328C2semidirect
6. C29×#1294C2semidirect
7. C29×#1282C2semidirect
12. C29×#481C4semidirect
15. C29×#448C4semidirect
31. C22×Q8×C29C2×C4semidirect
53. C2×C4⋊C4×C29C2×C4semidirect
71. C29×C22⋊C8C2×C4semidirect
140. C22⋊C4×C29SD16semidirect
143. #9275C29direct (N × H)
207. #1996C2×C29semidirect
209. C2×#328C2×C29semidirect
210. #1294C2×C29semidirect
211. #1282C2×C29semidirect
252. #481C4×C29semidirect
255. #448C4×C29semidirect
281. C22×Q8C2×C4×C29semidirect
303. C2×C4⋊C4C2×C4×C29semidirect
321. C22⋊C8C2×C4×C29semidirect
329. C29#9275direct (N × H)
391. C22⋊C4SD16×C29semidirect

Maximal subgroups

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

subgroupindex
C29×#31872
C29×#23642
C29×#19962
C29×#15192
C2×C29×#3282
C29×#12942
C29×#12822
#927529