Finite Group Databasebeta

← C29×#33063 #20327963

Subgroups — C29×#33063 #20327963

Order 7424.

772 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#489C211yesmaximal, characteristic, complemented
2C29×#3079C211yesmaximal, characteristic, complemented
3C29×#3040C211yesmaximal, characteristic
4C29×#2875C211yesmaximal, characteristic, complemented
5C29×#1997C211yesmaximal, characteristic, complemented
6C29×#1967C211yesmaximal, characteristic, complemented
7C29×#1931C212yesmaximal, complemented
8C29×#1930C212yesmaximal, complemented
9C29×#1908C212yesmaximal, complemented
10C29×#1907C212yesmaximal
11C29×#1838C211yesmaximal, characteristic, complemented
12C2×C29×#137C2211yescharacteristic
13C2×C29×AGL(1,ℤ/8)C2211yescharacteristic
14C2×C29×#131C2212yes—
15C2×C29×C4⋊Q8C2211yescharacteristic
16C2×C29×#124C2211yescharacteristic
17C4×#41×C29C2211yescharacteristic
18C29×#489—21no—
19C29×#489—21no—
20C29×#489—22no—
21C29×#477—21no—
22C29×#476—21no—
23C29×#475—21no—
24C29×#474—21no—
25C29×#464—21no—
26C29×#464—21no—
27C29×#463—21no—
28C29×#463—21no—
29C29×#428C2212yes—
30C29×#423C2211yescharacteristic
31C29×#423C2211yescharacteristic
32C29×#419C2211yescharacteristic
33C29×#418C2211yescharacteristic
34C29×#417C2212yes—
35C2×C29×#103C2212yes—
36C2×C29×#102C2212yes—
37C2×C29×#101C2212yes—
38C2×C29×#100C2212yes—
39C29×#405—22no—
40C29×#405C2212yes—
41C4×M16×C29—21no—
42C4×M16×C29C2211yescharacteristic
43C2×C29×#97—21no—
44C2×C29×#97C2211yescharacteristic
45C29×#343C2212yes—
46C29×#343C2212yes—
47C29×#341C2212yes—
48C29×#341C2212yes—
49C2×#41×C29C2311yescharacteristic
50C22×Q8×C29—21no—
51C22×Q8×C29C2311yescharacteristic
52C22×D4×C29C2311yescharacteristic
53C29×#137—24no—
54C29×AGL(1,ℤ/8)—24no—
55C2×Q16×C29—21no—
56C2×SD16×C29—21no—
57C2×SD16×C29—21no—
58C2×D8×C29—21no—
59C29×#131—24no—
60C29×#131—24no—
61C2×M16×C29—22no—
62C2×M16×C29C2312yes—
63C2×M16×C29C2311yescharacteristic
64C2×M16×C29C2311yescharacteristic
65C2×M16×C29C2312yes—
66C22×C8×C29—22no—
67C22×C8×C29C2312yes—
68C29×C4⋊Q8—21no—
69C29×C4⋊Q8—21no—
70C29×C4⋊Q8—21no—
71C29×C4⋊Q8—21no—
72C29×#124—21no—
73C29×#124—21no—
74C29×#124—21no—
75C29×#124—21no—
76C4×Q8×C29D411yescharacteristic
77C4×Q8×C29D411yescharacteristic
78C4×D4×C29—21no—
79C4×D4×C29—21no—
80C4×D4×C29D411yescharacteristic
81C4×D4×C29D411yescharacteristic
82C29×#117—21no—
83C29×#117C2311yescharacteristic
84C2×C4⋊C4×C29—21no—
85C2×C4⋊C4×C29C2312yes—
86C2×C22⋊C4×C29—21no—
87C2×C22⋊C4×C29—21no—
88C2×C42×C29—21no—
89C2×C42×C29C2311yescharacteristic
90C29×#107—22no—
91C29×#106—22no—
92C29×C4⋊C8—21no—
93C29×C4⋊C8—21no—
94C29×C4⋊C8—21no—
95C29×C4⋊C8—21no—
96C29×#103—22no—
97C29×#103—22no—
98C29×#103—22no—
99C29×#103—21no—
100C29×#103—21no—
101C29×#102—22no—
102C29×#102—22no—
103C29×#102—22no—
104C29×#102—21no—
105C29×#102—21no—
106C29×#101—24no—
107C29×#100—24no—
108C29×#97—22no—
109C29×#97—21no—
110C29×#97D411yescharacteristic
111C29×#97D411yescharacteristic
112C29×#97D412yes—
113C4×C8×C29—22no—
114C4×C8×C29—21no—
115C24×C29—21no—
116#41×C29—22no—
117#41×C29#4114yes—
118C2×Q8×C29—21no—
119C2×Q8×C29—21no—
120C2×Q8×C29—22no—
121C2×Q8×C29—22no—
122C2×Q8×C29—41no—
123C2×Q8×C29—41no—
124C2×Q8×C29—82no—
125C2×Q8×C29C2×D411yescharacteristic
126C2×D4×C29—21no—
127C2×D4×C29—21no—
128C2×D4×C29—21no—
129C2×D4×C29—22no—
130C2×D4×C29—22no—
131C2×D4×C29C2×D411yescharacteristic
132C22×C4×C29—21no—
133C22×C4×C29—21no—
134C22×C4×C29—21no—
135C22×C4×C29—21no—
136C22×C4×C29—22no—
137C22×C4×C29#4111yescharacteristic
138C22×C4×C29#4111yescharacteristic
139C22×C4×C29C2411yescharacteristic
140Q16×C29—42no—
141SD16×C29—42no—
142SD16×C29—42no—
143D8×C29—42no—
144M16×C29—28no—
145M16×C29—22no—
146M16×C29—22no—
147M16×C29—22no—
148M16×C29—22no—
149M16×C29—22no—
150M16×C29#4114yes—
151C2×C8×C29—28no—
152C2×C8×C29—22no—
153C2×C8×C29—22no—
154C2×C8×C29—22no—
155C2×C8×C29—21no—
156C2×C8×C29—21no—
157C2×C8×C29—22no—
158C2×C8×C29C2×D412yes—
159C2×C8×C29C2×D412yes—
160C4⋊C4×C29—21no—
161C4⋊C4×C29—21no—
162C4⋊C4×C29—22no—
163C4⋊C4×C29—22no—
164C4⋊C4×C29—41no—
165C4⋊C4×C29—41no—
166C4⋊C4×C29C2×D411yescharacteristic
167C4⋊C4×C29C2×D411yescharacteristic
168C22⋊C4×C29—21no—
169C22⋊C4×C29—21no—
170C22⋊C4×C29—21no—
171C22⋊C4×C29—41no—
172C22⋊C4×C29—41no—
173C22⋊C4×C29—41no—
174C22⋊C4×C29—41no—
175C42×C29—21no—
176C42×C29—21no—
177C42×C29—21no—
178C42×C29C2×D411yescharacteristic
179C42×C29C2×D411yescharacteristic
180C42×C29C2×D411yescharacteristic
181C42×C29C2×D411yescharacteristic
182#33063C2911yesmaximal, characteristic, direct product factor, Sylow
183C23×C29—21no—
184C23×C29—41no—
185C23×C29—42no—
186C23×C29—81no—
187C23×C29—81no—
188C23×C29C2×#4111yescharacteristic
189Q8×C29—21no—
190Q8×C29—42no—
191Q8×C29—41no—
192Q8×C29—41no—
193Q8×C29—82no—
194Q8×C29—82no—
195Q8×C29#12412yes—
196D4×C29—24no—
197D4×C29—21no—
198D4×C29—42no—
199D4×C29—41no—
200D4×C29—41no—
201D4×C29#12412yes—
202C2×C4×C29—21no—
203C2×C4×C29—24no—
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—81no—
212C2×C4×C29—81no—
213C2×C4×C29—82no—
214C2×C4×C29#12111yescharacteristic
215C2×C4×C29#12111yescharacteristic
216C2×C4×C29#12111yescharacteristic
217C2×C4×C29#12111yescharacteristic
218C2×C4×C29C22×D411yescharacteristic
219C2×C4×C29C22×D411yescharacteristic
220C2×C4×C29C2×#4112yes—
221C2×C4×C29C2×#4112yes—
222C8×C29—22no—
223C8×C29—24no—
224C8×C29—22no—
225C8×C29—41no—
226C8×C29—41no—
227C8×C29—42no—
228C2×#489C2×C2911yescharacteristic, complemented
229#3079C2×C2911yescharacteristic, complemented
230#3040C2×C2911yescharacteristic
231#2875C2×C2911yescharacteristic, complemented
232#1997C2×C2911yescharacteristic, complemented
233#1967C2×C2911yescharacteristic, complemented
234#1931C2×C2912yescomplemented
235#1930C2×C2912yescomplemented
236#1908C2×C2912yescomplemented
237#1907C2×C2912yes—
238#1838C2×C2911yescharacteristic, complemented
239C22×C29—21no—
240C22×C29—21no—
241C22×C29—22no—
242C22×C29—41no—
243C22×C29—41no—
244C22×C29—81no—
245C22×C29—81no—
246C22×C29—81no—
247C22×C29—162no—
248C22×C29C2×#12111yescharacteristic
249C22×C29#52912yes—
250C4×C29—22no—
251C4×C29—21no—
252C4×C29—21no—
253C4×C29—21no—
254C4×C29—21no—
255C4×C29—41no—
256C4×C29—41no—
257C4×C29—81no—
258C4×C29—82no—
259C4×C29#52512yes—
260C4×C29C2×#12411yescharacteristic
261C4×C29#53211yescharacteristic
262C2×#137C22×C2911yescharacteristic
263C2×AGL(1,ℤ/8)C22×C2911yescharacteristic
264C2×#131C22×C2912yes—
265C2×C4⋊Q8C22×C2911yescharacteristic
266C2×#124C22×C2911yescharacteristic
267C4×#41C22×C2911yescharacteristic
268#489—21no—
269#489—21no—
270#489—22no—
271#477—21no—
272#476—21no—
273#475—21no—
274#474—21no—
275#464—21no—
276#464—21no—
277#463—21no—
278#463—21no—
279#428C22×C2912yes—
280#423C22×C2911yescharacteristic
281#423C22×C2911yescharacteristic
282#419C22×C2911yescharacteristic
283#418C22×C2911yescharacteristic
284#417C22×C2912yes—
285C2×#103C22×C2912yes—
286C2×#102C22×C2912yes—
287C2×#101C22×C2912yes—
288C2×#100C22×C2912yes—
289#405—22no—
290#405C22×C2912yes—
291C4×M16—21no—
292C4×M16C22×C2911yescharacteristic
293C2×#97—21no—
294C2×#97C22×C2911yescharacteristic
295#343C22×C2912yes—
296#343C22×C2912yes—
297#341C22×C2912yes—
298#341C22×C2912yes—
299C2×C29—22no—
300C2×C29—42no—
301C2×C29—161no—
302C2×C29#285011yescharacteristic
303C2×C29#306811yescharacteristic
304C2×C29#306911yescharacteristic
305C2×#41C23×C2911yescharacteristic
306C22×Q8—21no—
307C22×Q8C23×C2911yescharacteristic
308C22×D4C23×C2911yescharacteristic
309#137—24no—
310AGL(1,ℤ/8)—24no—
311C2×Q16—21no—
312C2×SD16—21no—
313C2×SD16—21no—
314C2×D8—21no—
315#131—24no—
316#131—24no—
317C2×M16—22no—
318C2×M16C23×C2911yescharacteristic
319C2×M16C23×C2911yescharacteristic
320C2×M16C23×C2912yes—
321C2×M16C23×C2912yes—
322C22×C8—22no—
323C22×C8C23×C2912yes—
324C4⋊Q8—21no—
325C4⋊Q8—21no—
326C4⋊Q8—21no—
327C4⋊Q8—21no—
328#124—21no—
329#124—21no—
330#124—21no—
331#124—21no—
332C4×Q8D4×C2911yescharacteristic
333C4×Q8D4×C2911yescharacteristic
334C4×D4—21no—
335C4×D4—21no—
336C4×D4D4×C2911yescharacteristic
337C4×D4D4×C2911yescharacteristic
338#117—21no—
339#117C23×C2911yescharacteristic
340C2×C4⋊C4—21no—
341C2×C4⋊C4C23×C2912yes—
342C2×C22⋊C4—21no—
343C2×C22⋊C4—21no—
344C2×C42—21no—
345C2×C42C23×C2911yescharacteristic
346#107—22no—
347#106—22no—
348C4⋊C8—21no—
349C4⋊C8—21no—
350C4⋊C8—21no—
351C4⋊C8—21no—
352#103—22no—
353#103—22no—
354#103—22no—
355#103—21no—
356#103—21no—
357#102—22no—
358#102—22no—
359#102—22no—
360#102—21no—
361#102—21no—
362#101—24no—
363#100—24no—
364#97—22no—
365#97—21no—
366#97D4×C2911yescharacteristic
367#97D4×C2911yescharacteristic
368#97D4×C2912yes—
369C4×C8—22no—
370C4×C8—21no—
371C29#3306311yescharacteristic, direct product factor, Sylow
372C24—21no—
373#41—22no—
374#41#41×C2914yes—
375C2×Q8—21no—
376C2×Q8—21no—
377C2×Q8—22no—
378C2×Q8—22no—
379C2×Q8—41no—
380C2×Q8—41no—
381C2×Q8—82no—
382C2×Q8C2×D4×C2911yescharacteristic
383C2×D4—21no—
384C2×D4—21no—
385C2×D4—21no—
386C2×D4—22no—
387C2×D4—22no—
388C2×D4C2×D4×C2911yescharacteristic
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—22no—
394C22×C4#41×C2911yescharacteristic
395C22×C4#41×C2911yescharacteristic
396C22×C4C24×C2911yescharacteristic
397Q16—42no—
398SD16—42no—
399SD16—42no—
400D8—42no—
401M16—28no—
402M16—22no—
403M16—22no—
404M16—22no—
405M16—22no—
406M16—22no—
407M16#41×C2914yes—
408C2×C8—28no—
409C2×C8—22no—
410C2×C8—22no—
411C2×C8—22no—
412C2×C8—21no—
413C2×C8—22no—
414C2×C8—21no—
415C2×C8C2×D4×C2912yes—
416C2×C8C2×D4×C2912yes—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—41no—
422C4⋊C4—41no—
423C4⋊C4C2×D4×C2911yescharacteristic
424C4⋊C4C2×D4×C2911yescharacteristic
425C22⋊C4—21no—
426C22⋊C4—21no—
427C22⋊C4—21no—
428C22⋊C4—41no—
429C22⋊C4—41no—
430C22⋊C4—41no—
431C22⋊C4—41no—
432C42—21no—
433C42—21no—
434C42—21no—
435C42C2×D4×C2911yescharacteristic
436C42C2×D4×C2911yescharacteristic
437C42C2×D4×C2911yescharacteristic
438C42C2×D4×C2911yescharacteristic
439C23—21no—
440C23—41no—
441C23—42no—
442C23—81no—
443C23—81no—
444C23C2×#41×C2911yescharacteristic
445Q8—21no—
446Q8—42no—
447Q8—41no—
448Q8—41no—
449Q8—82no—
450Q8—82no—
451Q8C29×#12412yes—
452D4—24no—
453D4—21no—
454D4—42no—
455D4—41no—
456D4—41no—
457D4C29×#12412yes—
458C2×C4—21no—
459C2×C4—24no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—81no—
468C2×C4—81no—
469C2×C4—82no—
470C2×C4C29×#12111yescharacteristic
471C2×C4C29×#12111yescharacteristic
472C2×C4C29×#12111yescharacteristic
473C2×C4C29×#12111yescharacteristic
474C2×C4C22×D4×C2911yescharacteristic
475C2×C4C22×D4×C2911yescharacteristic
476C2×C4C2×#41×C2912yes—
477C2×C4C2×#41×C2912yes—
478C8—22no—
479C8—24no—
480C8—22no—
481C8—41no—
482C8—41no—
483C8—42no—
484C22—21no—
485C22—21no—
486C22—22no—
487C22—41no—
488C22—41no—
489C22—81no—
490C22—81no—
491C22—81no—
492C22—162no—
493C22C2×C29×#12111yescharacteristic
494C22C29×#52912yes—
495C4—21no—
496C4—21no—
497C4—21no—
498C4—21no—
499C4—22no—
500C4—41no—
501C4—41no—
502C4—82no—
503C4—81no—
504C4C29×#52512yes—
505C4C2×C29×#12411yescharacteristic
506C4C29×#53211yescharacteristic
507C2—22no—
508C2—42no—
509C2—161no—
510C2C29×#285011yescharacteristic
511C2C29×#306811yescharacteristic
512C2C29×#306911yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC2×C29×AGL(1,ℤ/8)C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C29×#489C2semidirect
2. C29×#3079C2semidirect
4. C29×#2875C2semidirect
5. C29×#1997C2semidirect
6. C29×#1967C2semidirect
7. C29×#1931C2semidirect
8. C29×#1930C2semidirect
9. C29×#1908C2semidirect
11. C29×#1838C2semidirect
182. #33063C29direct (N × H)
228. C2×#489C2×C29semidirect
229. #3079C2×C29semidirect
231. #2875C2×C29semidirect
232. #1997C2×C29semidirect
233. #1967C2×C29semidirect
234. #1931C2×C29semidirect
235. #1930C2×C29semidirect
236. #1908C2×C29semidirect
238. #1838C2×C29semidirect
371. C29#33063direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#4892
C29×#30792
C29×#30402
C29×#28752
C29×#19972
C29×#19672
C29×#19312
C29×#19302
C29×#19082
C29×#19072
C29×#18382
#3306329