Finite Group Databasebeta

← C29×#9345 #20304245

Subgroups — C29×#9345 #20304245

Order 7424.

678 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3007C211yesmaximal, characteristic
2C29×#2880C211yesmaximal, characteristic
3C29×#1788C211yesmaximal, characteristic
4C29×#1520C211yesmaximal, characteristic, complemented
5C29×#1472C211yesmaximal, characteristic, complemented
6C29×#1305C211yesmaximal, characteristic, complemented
7C29×#1298C211yesmaximal, characteristic, complemented
8C22×#41×C29C2211yescharacteristic
9C2×C29×#137C411yescharacteristic, complemented
10C2×C29×#137C411yescharacteristic, complemented
11C2×C29×#131—21no—
12C2×C29×C22⋊Q8C2211yescharacteristic
13C29×#452—21no—
14C29×#452—21no—
15C29×#451—21no—
16C29×#450—21no—
17C29×#417C411yescharacteristic, complemented
18C29×#417C411yescharacteristic, complemented
19C2×C29×#103—21no—
20C2×C29×#102—21no—
21C29×#408—22no—
22C29×#408—21no—
23C29×#407—21no—
24C29×#407C2211yescharacteristic
25C29×#407C2211yescharacteristic
26C2×C29×C22⋊C8—21no—
27C2×C29×C22⋊C8C2211yescharacteristic
28C2×C29×C22⋊C8C2211yescharacteristic
29C29×#380C2211yescharacteristic
30C29×#328—21no—
31C29×#328—21no—
32C29×#324—22no—
33C2×#41×C29—21no—
34C2×#41×C29—21no—
35C2×#41×C29—42no—
36C2×#41×C29—42no—
37C2×#41×C29C2×C411yescharacteristic
38C2×#41×C29C2×C411yescharacteristic
39C2×#41×C29D411yescharacteristic
40C2×#41×C29D411yescharacteristic
41C22×Q8×C29C2×C411yescharacteristic
42C22×Q8×C29D411yescharacteristic
43C22×D4×C29—21no—
44C22×D4×C29D411yescharacteristic
45C23×C4×C29—21no—
46C23×C4×C29C2311yescharacteristic
47C29×#137—42no—
48C29×#137—42no—
49C2×Q16×C29—21no—
50C2×Q16×C29—21no—
51C2×SD16×C29—21no—
52C2×SD16×C29—21no—
53C29×#131—42no—
54C29×#131—42no—
55C2×M16×C29—22no—
56C2×M16×C29—21no—
57C2×M16×C29C2×C411yescharacteristic
58C2×M16×C29C2×C411yescharacteristic
59C22×C8×C29—22no—
60C22×C8×C29—21no—
61C22×C8×C29—21no—
62C29×C22⋊Q8—21no—
63C29×C22⋊Q8—21no—
64C29×C22⋊Q8—21no—
65C29×C22⋊Q8—21no—
66C2×C4⋊C4×C29—21no—
67C2×C4⋊C4×C29—21no—
68C2×C4⋊C4×C29C2×C411yescharacteristic
69C2×C22⋊C4×C29—21no—
70C2×C22⋊C4×C29—21no—
71C29×#103—21no—
72C29×#103—21no—
73C29×#103—42no—
74C29×#102—21no—
75C29×#102—21no—
76C29×#102—42no—
77C29×C22⋊C8—22no—
78C29×C22⋊C8—22no—
79C29×C22⋊C8—21no—
80C29×C22⋊C8—21no—
81C29×C22⋊C8—21no—
82C29×C22⋊C8—21no—
83C29×C22⋊C8—21no—
84C29×C22⋊C8—21no—
85C29×C22⋊C8D412yes—
86C29×C22⋊C8D411yescharacteristic
87C29×C22⋊C8D411yescharacteristic
88C29×#95—21no—
89C24×C29—21no—
90C24×C29#4111yescharacteristic
91#41×C29—22no—
92#41×C29—22no—
93#41×C29—22no—
94#41×C29—22no—
95#41×C29—41no—
96#41×C29—41no—
97#41×C29—41no—
98#41×C29—41no—
99#41×C29—44no—
100#41×C29—44no—
101C2×Q8×C29—21no—
102C2×Q8×C29—22no—
103C2×Q8×C29—21no—
104C2×Q8×C29—21no—
105C2×Q8×C29—41no—
106C2×Q8×C29—41no—
107C2×Q8×C29—41no—
108C2×Q8×C29C22⋊C411yescharacteristic
109C2×Q8×C29C22⋊C411yescharacteristic
110C2×D4×C29—21no—
111C2×D4×C29—22no—
112C2×D4×C29—21no—
113C2×D4×C29—21no—
114C2×D4×C29—21no—
115C2×D4×C29—21no—
116C2×D4×C29—41no—
117C2×D4×C29—44no—
118C2×D4×C29C22⋊C411yescharacteristic
119C2×D4×C29C22⋊C411yescharacteristic
120C22×C4×C29—21no—
121C22×C4×C29—21no—
122C22×C4×C29—21no—
123C22×C4×C29—21no—
124C22×C4×C29—21no—
125C22×C4×C29—21no—
126C22×C4×C29—21no—
127C22×C4×C29—41no—
128C22×C4×C29—41no—
129C22×C4×C29—44no—
130C22×C4×C29—41no—
131C22×C4×C29C22×C411yescharacteristic
132C22×C4×C29C2×D411yescharacteristic
133C22×C4×C29C2×D411yescharacteristic
134C22×C4×C29C2×D411yescharacteristic
135C22×C4×C29C2×D411yescharacteristic
136C22×C4×C29#4111yescharacteristic
137Q16×C29—42no—
138Q16×C29—42no—
139SD16×C29—42no—
140SD16×C29—42no—
141M16×C29—44no—
142M16×C29—41no—
143M16×C29—41no—
144M16×C29—41no—
145M16×C29—41no—
146C2×C8×C29—21no—
147C2×C8×C29—21no—
148C2×C8×C29—21no—
149C2×C8×C29—22no—
150C2×C8×C29—21no—
151C2×C8×C29—44no—
152C2×C8×C29—41no—
153C2×C8×C29—41no—
154C2×C8×C29—41no—
155C2×C8×C29—41no—
156C2×C8×C29—41no—
157C4⋊C4×C29—21no—
158C4⋊C4×C29—21no—
159C4⋊C4×C29—41no—
160C4⋊C4×C29—41no—
161C4⋊C4×C29—41no—
162C4⋊C4×C29—41no—
163C22⋊C4×C29—41no—
164C22⋊C4×C29—41no—
165C22⋊C4×C29—81no—
166#9345C2911yesmaximal, characteristic, direct product factor, Sylow
167C23×C29—21no—
168C23×C29—21no—
169C23×C29—21no—
170C23×C29—21no—
171C23×C29—41no—
172C23×C29—41no—
173C23×C29—42no—
174C23×C29—41no—
175C23×C29—41no—
176C23×C29—81no—
177C23×C29C4×D411yescharacteristic
178C23×C29#12111yescharacteristic
179C23×C29#12311yescharacteristic
180Q8×C29—21no—
181Q8×C29—21no—
182Q8×C29—21no—
183Q8×C29—42no—
184Q8×C29—41no—
185Q8×C29—41no—
186Q8×C29—81no—
187Q8×C29#9912yes—
188D4×C29—24no—
189D4×C29—21no—
190D4×C29—21no—
191D4×C29—21no—
192D4×C29—42no—
193D4×C29—42no—
194D4×C29—42no—
195D4×C29—42no—
196D4×C29#9912yes—
197C2×C4×C29—24no—
198C2×C4×C29—21no—
199C2×C4×C29—21no—
200C2×C4×C29—21no—
201C2×C4×C29—21no—
202C2×C4×C29—21no—
203C2×C4×C29—21no—
204C2×C4×C29—21no—
205C2×C4×C29—21no—
206C2×C4×C29—41no—
207C2×C4×C29—41no—
208C2×C4×C29—41no—
209C2×C4×C29—42no—
210C2×C4×C29—42no—
211C2×C4×C29—42no—
212C2×C4×C29—42no—
213C2×C4×C29—42no—
214C2×C4×C29—41no—
215C2×C4×C29—41no—
216C2×C4×C29—81no—
217C2×C4×C29—81no—
218C2×C4×C29—81no—
219C2×C4×C29—81no—
220C2×C4×C29C2×C22⋊C411yescharacteristic
221C2×C4×C29C4×D411yescharacteristic
222C2×C4×C29#12011yescharacteristic
223C2×C4×C29#12111yescharacteristic
224C8×C29—41no—
225C8×C29—42no—
226C8×C29—41no—
227C8×C29—41no—
228C8×C29—41no—
229C8×C29—81no—
230#3007C2×C2911yescharacteristic
231#2880C2×C2911yescharacteristic
232#1788C2×C2911yescharacteristic
233#1520C2×C2911yescharacteristic, complemented
234#1472C2×C2911yescharacteristic, complemented
235#1305C2×C2911yescharacteristic, complemented
236#1298C2×C2911yescharacteristic, complemented
237C22×C29—21no—
238C22×C29—21no—
239C22×C29—21no—
240C22×C29—21no—
241C22×C29—21no—
242C22×C29—21no—
243C22×C29—22no—
244C22×C29—21no—
245C22×C29—21no—
246C22×C29—41no—
247C22×C29—41no—
248C22×C29—41no—
249C22×C29—41no—
250C22×C29—41no—
251C22×C29—81no—
252C22×C29—81no—
253C22×C29—82no—
254C22×C29—82no—
255C22×C29#38611yescharacteristic
256C22×C29#47111yescharacteristic
257C22×C29#47311yescharacteristic
258C4×C29—21no—
259C4×C29—21no—
260C4×C29—22no—
261C4×C29—21no—
262C4×C29—41no—
263C4×C29—81no—
264C4×C29—81no—
265C4×C29—161no—
266C4×C29C2×#9911yescharacteristic
267C4×C29C2×#9911yescharacteristic
268C22×#41C22×C2911yescharacteristic
269C2×#137C4×C2911yescharacteristic, complemented
270C2×#137C4×C2911yescharacteristic, complemented
271C2×#131—21no—
272C2×C22⋊Q8C22×C2911yescharacteristic
273#452—21no—
274#452—21no—
275#451—21no—
276#450—21no—
277#417C4×C2911yescharacteristic, complemented
278#417C4×C2911yescharacteristic, complemented
279C2×#103—21no—
280C2×#102—21no—
281#408—21no—
282#408—22no—
283#407—21no—
284#407C22×C2911yescharacteristic
285#407C22×C2911yescharacteristic
286C2×C22⋊C8—21no—
287C2×C22⋊C8C22×C2911yescharacteristic
288C2×C22⋊C8C22×C2911yescharacteristic
289#380C22×C2911yescharacteristic
290#328—21no—
291#328—21no—
292#324—22no—
293C2×C29—21no—
294C2×C29—21no—
295C2×C29—41no—
296C2×C29—41no—
297C2×C29—42no—
298C2×C29—81no—
299C2×C29#188111yescharacteristic
300C2×C29#189811yescharacteristic
301C2×C29#190811yescharacteristic
302C2×#41—21no—
303C2×#41—21no—
304C2×#41—42no—
305C2×#41—42no—
306C2×#41C2×C4×C2911yescharacteristic
307C2×#41C2×C4×C2911yescharacteristic
308C2×#41D4×C2911yescharacteristic
309C2×#41D4×C2911yescharacteristic
310C22×Q8C2×C4×C2911yescharacteristic
311C22×Q8D4×C2911yescharacteristic
312C22×D4—21no—
313C22×D4D4×C2911yescharacteristic
314C23×C4—21no—
315C23×C4C23×C2911yescharacteristic
316#137—42no—
317#137—42no—
318C2×Q16—21no—
319C2×Q16—21no—
320C2×SD16—21no—
321C2×SD16—21no—
322#131—42no—
323#131—42no—
324C2×M16—22no—
325C2×M16—21no—
326C2×M16C2×C4×C2911yescharacteristic
327C2×M16C2×C4×C2911yescharacteristic
328C22×C8—22no—
329C22×C8—21no—
330C22×C8—21no—
331C22⋊Q8—21no—
332C22⋊Q8—21no—
333C22⋊Q8—21no—
334C22⋊Q8—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4C2×C4×C2911yescharacteristic
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340#103—21no—
341#103—21no—
342#103—42no—
343#102—21no—
344#102—21no—
345#102—42no—
346C22⋊C8—22no—
347C22⋊C8—22no—
348C22⋊C8—21no—
349C22⋊C8—21no—
350C22⋊C8—21no—
351C22⋊C8—21no—
352C22⋊C8—21no—
353C22⋊C8—21no—
354C22⋊C8D4×C2912yes—
355C22⋊C8D4×C2911yescharacteristic
356C22⋊C8D4×C2911yescharacteristic
357#95—21no—
358C29#934511yescharacteristic, direct product factor, Sylow
359C24—21no—
360C24#41×C2911yescharacteristic
361#41—22no—
362#41—22no—
363#41—22no—
364#41—22no—
365#41—41no—
366#41—41no—
367#41—41no—
368#41—41no—
369#41—44no—
370#41—44no—
371C2×Q8—21no—
372C2×Q8—22no—
373C2×Q8—21no—
374C2×Q8—21no—
375C2×Q8—41no—
376C2×Q8—41no—
377C2×Q8—41no—
378C2×Q8C22⋊C4×C2911yescharacteristic
379C2×Q8C22⋊C4×C2911yescharacteristic
380C2×D4—21no—
381C2×D4—22no—
382C2×D4—21no—
383C2×D4—21no—
384C2×D4—21no—
385C2×D4—21no—
386C2×D4—41no—
387C2×D4—44no—
388C2×D4C22⋊C4×C2911yescharacteristic
389C2×D4C22⋊C4×C2911yescharacteristic
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—41no—
398C22×C4—41no—
399C22×C4—44no—
400C22×C4—41no—
401C22×C4C22×C4×C2911yescharacteristic
402C22×C4C2×D4×C2911yescharacteristic
403C22×C4C2×D4×C2911yescharacteristic
404C22×C4C2×D4×C2911yescharacteristic
405C22×C4C2×D4×C2911yescharacteristic
406C22×C4#41×C2911yescharacteristic
407Q16—42no—
408Q16—42no—
409SD16—42no—
410SD16—42no—
411M16—44no—
412M16—41no—
413M16—41no—
414M16—41no—
415M16—41no—
416C2×C8—21no—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8—22no—
420C2×C8—21no—
421C2×C8—44no—
422C2×C8—41no—
423C2×C8—41no—
424C2×C8—41no—
425C2×C8—41no—
426C2×C8—41no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—41no—
430C4⋊C4—41no—
431C4⋊C4—41no—
432C4⋊C4—41no—
433C22⋊C4—41no—
434C22⋊C4—41no—
435C22⋊C4—81no—
436C23—21no—
437C23—21no—
438C23—21no—
439C23—21no—
440C23—41no—
441C23—41no—
442C23—42no—
443C23—41no—
444C23—41no—
445C23—81no—
446C23C4×D4×C2911yescharacteristic
447C23C29×#12111yescharacteristic
448C23C29×#12311yescharacteristic
449Q8—21no—
450Q8—21no—
451Q8—21no—
452Q8—42no—
453Q8—41no—
454Q8—41no—
455Q8—81no—
456Q8C29×#9912yes—
457D4—24no—
458D4—21no—
459D4—21no—
460D4—21no—
461D4—42no—
462D4—42no—
463D4—42no—
464D4—42no—
465D4C29×#9912yes—
466C2×C4—24no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—81no—
486C2×C4—81no—
487C2×C4—81no—
488C2×C4—81no—
489C2×C4C2×C22⋊C4×C2911yescharacteristic
490C2×C4C4×D4×C2911yescharacteristic
491C2×C4C29×#12011yescharacteristic
492C2×C4C29×#12111yescharacteristic
493C8—41no—
494C8—42no—
495C8—41no—
496C8—41no—
497C8—41no—
498C8—81no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—22no—
508C22—41no—
509C22—41no—
510C22—41no—
511C22—41no—
512C22—41no—
513C22—81no—
514C22—81no—
515C22—82no—
516C22—82no—
517C22C29×#38611yescharacteristic
518C22C29×#47111yescharacteristic
519C22C29×#47311yescharacteristic
520C4—21no—
521C4—21no—
522C4—22no—
523C4—21no—
524C4—41no—
525C4—81no—
526C4—81no—
527C4—161no—
528C4C2×C29×#9911yescharacteristic
529C4C2×C29×#9911yescharacteristic
530C2—21no—
531C2—21no—
532C2—41no—
533C2—41no—
534C2—42no—
535C2—81no—
536C2C29×#188111yescharacteristic
537C2C29×#189811yescharacteristic
538C2C29×#190811yescharacteristic
subgroupG/H
center, socleC22×C29#386
commutatorC22×C4C22×C4×C29
Frattini, cosocleC23×C4C23×C29
prime radicalC22×#41×C29C22
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
4. C29×#1520C2semidirect
5. C29×#1472C2semidirect
6. C29×#1305C2semidirect
7. C29×#1298C2semidirect
9. C2×C29×#137C4semidirect
10. C2×C29×#137C4semidirect
17. C29×#417C4semidirect
18. C29×#417C4semidirect
166. #9345C29direct (N × H)
233. #1520C2×C29semidirect
234. #1472C2×C29semidirect
235. #1305C2×C29semidirect
236. #1298C2×C29semidirect
269. C2×#137C4×C29semidirect
270. C2×#137C4×C29semidirect
277. #417C4×C29semidirect
278. #417C4×C29semidirect
358. C29#9345direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#30072
C29×#28802
C29×#17882
C29×#15202
C29×#14722
C29×#13052
C29×#12982
#934529