Finite Group Databasebeta

← C29×#33880 #20328780

Subgroups — C29×#33880 #20328780

Order 7424.

540 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3342C211yesmaximal, characteristic, complemented
2C29×#3285C211yesmaximal, characteristic
3C29×#2243C211yesmaximal, characteristic, complemented
4C29×#2237C211yesmaximal, characteristic, complemented
5C29×#2234C211yesmaximal, characteristic, complemented
6C29×#2227C211yesmaximal, characteristic, complemented
7C29×#2220C211yesmaximal, characteristic, complemented
8C29×#2216C211yesmaximal, characteristic, complemented
9C29×#2211C211yesmaximal, characteristic, complemented
10C29×#2189C211yesmaximal, characteristic, complemented
11C29×#2188C211yesmaximal, characteristic, complemented
12C29×#2176C211yesmaximal, characteristic, complemented
13C29×#2168C211yesmaximal, characteristic, complemented
14C29×#2141C211yesmaximal, characteristic, complemented
15C29×#2138C211yesmaximal, characteristic, complemented
16C2×C29×#135C2211yescharacteristic
17C22×Q16×C29C2211yescharacteristic
18C29×#556—21no—
19C29×#548—21no—
20C2×C29×Q32C2211yescharacteristic
21C2×C29×Q32C2211yescharacteristic
22C2×C29×SD32C2211yescharacteristic
23C2×C29×M32C2211yescharacteristic
24C22×C16×C29C2211yescharacteristic
25C29×#500C2211yescharacteristic
26C29×#495C2211yescharacteristic
27C29×#485—21no—
28C29×#485—21no—
29C29×#475—21no—
30C29×#467C2211yescharacteristic
31C29×#467C2211yescharacteristic
32C29×#467C2211yescharacteristic
33C29×#466C2211yescharacteristic
34C29×#464—21no—
35C29×#452—21no—
36C29×#448—21no—
37C4×Q16×C29C2211yescharacteristic
38C4×Q16×C29C2211yescharacteristic
39C8×D4×C29C2211yescharacteristic
40C29×#427C2211yescharacteristic
41C29×#427C2211yescharacteristic
42C29×#367C2211yescharacteristic
43C29×#366C2211yescharacteristic
44C29×#366C2211yescharacteristic
45C29×C4⋊C16C2211yescharacteristic
46C29×#358C2211yescharacteristic
47C29×#358C2211yescharacteristic
48C29×#358C2211yescharacteristic
49C29×#358C2211yescharacteristic
50C29×#358C2211yescharacteristic
51C29×#358C2211yescharacteristic
52C29×#358C2211yescharacteristic
53C29×#357C2211yescharacteristic
54C29×#357C2211yescharacteristic
55C29×#357C2211yescharacteristic
56C29×C22⋊C16C2211yescharacteristic
57C29×C22⋊C16C2211yescharacteristic
58C29×#346C2211yescharacteristic
59C2×#41×C29—21no—
60C22×Q8×C29—21no—
61C29×#135—22no—
62C29×#135—41no—
63C2×Q16×C29—22no—
64C2×Q16×C29—21no—
65C2×Q16×C29—41no—
66C2×Q16×C29C2311yescharacteristic
67C2×Q16×C29C2311yescharacteristic
68C2×Q16×C29C2311yescharacteristic
69C2×SD16×C29—21no—
70C2×SD16×C29—21no—
71C2×D8×C29C2311yescharacteristic
72C22×C8×C29C2311yescharacteristic
73C22×C8×C29C2311yescharacteristic
74C29×C4⋊Q8—21no—
75C29×#126—41no—
76C29×#126—41no—
77C29×#124—21no—
78C29×#124—41no—
79C29×#124—41no—
80C29×C22⋊Q8—21no—
81C29×C22⋊Q8—21no—
82C29×C22⋊Q8—21no—
83C29×C22⋊Q8—41no—
84C29×#121—21no—
85C29×#121—41no—
86C4×Q8×C29—21no—
87C4×Q8×C29—21no—
88C4×Q8×C29—41no—
89C4×D4×C29—41no—
90C4×D4×C29D411yescharacteristic
91C29×#117—21no—
92C29×#117—21no—
93C29×Q32—22no—
94C29×Q32—41no—
95C29×SD32—41no—
96C29×M32—41no—
97C2×C16×C29—41no—
98C2×C16×C29C2311yescharacteristic
99C2×C16×C29C2311yescharacteristic
100C2×C16×C29C2311yescharacteristic
101C2×C16×C29C2311yescharacteristic
102C29×#107—21no—
103C29×#107C2311yescharacteristic
104C29×#107C2311yescharacteristic
105C29×#107C2311yescharacteristic
106C29×#107C2311yescharacteristic
107C29×#106—21no—
108C29×#106—21no—
109C29×C4⋊C8D411yescharacteristic
110C29×#103—21no—
111C29×#103—21no—
112C29×#103—21no—
113C29×#103—21no—
114C29×#103—21no—
115C29×#102—21no—
116C29×C22⋊C8D411yescharacteristic
117C29×C22⋊C8D411yescharacteristic
118C4×C8×C29C2311yescharacteristic
119#41×C29—42no—
120#41×C29—81no—
121C2×Q8×C29—21no—
122C2×Q8×C29—21no—
123C2×Q8×C29—21no—
124C2×Q8×C29—42no—
125C2×Q8×C29—41no—
126C2×Q8×C29—41no—
127C2×Q8×C29—81no—
128C2×D4×C29—21no—
129C2×D4×C29—41no—
130C2×D4×C29—41no—
131C2×D4×C29D811yescharacteristic
132C22×C4×C29—41no—
133C22×C4×C29—41no—
134C22×C4×C29C2×D411yescharacteristic
135C22×C4×C29C2×D411yescharacteristic
136Q16×C29—21no—
137Q16×C29—21no—
138Q16×C29—21no—
139Q16×C29—21no—
140Q16×C29—21no—
141Q16×C29—42no—
142Q16×C29#4112yes—
143SD16×C29—42no—
144SD16×C29—81no—
145D8×C29—21no—
146D8×C29—21no—
147C2×C8×C29—21no—
148C2×C8×C29—21no—
149C2×C8×C29—21no—
150C2×C8×C29—21no—
151C2×C8×C29C2×D411yescharacteristic
152C2×C8×C29C2×D411yescharacteristic
153C2×C8×C29C2×D411yescharacteristic
154C2×C8×C29C2411yescharacteristic
155C4⋊C4×C29—21no—
156C4⋊C4×C29—21no—
157C4⋊C4×C29—21no—
158C4⋊C4×C29—21no—
159C4⋊C4×C29—41no—
160C4⋊C4×C29—41no—
161C4⋊C4×C29—41no—
162C4⋊C4×C29—41no—
163C4⋊C4×C29—41no—
164C4⋊C4×C29—41no—
165C4⋊C4×C29D811yescharacteristic
166C22⋊C4×C29—41no—
167C22⋊C4×C29—41no—
168C22⋊C4×C29—41no—
169C22⋊C4×C29—41no—
170C22⋊C4×C29—41no—
171C22⋊C4×C29—41no—
172C22⋊C4×C29—41no—
173C22⋊C4×C29—41no—
174C22⋊C4×C29D811yescharacteristic
175C22⋊C4×C29D811yescharacteristic
176C42×C29—41no—
177C42×C29—41no—
178C42×C29—41no—
179C42×C29—41no—
180C42×C29C2×D411yescharacteristic
181C16×C29—21no—
182C16×C29—21no—
183C16×C29—21no—
184C16×C29—21no—
185#33880C2911yesmaximal, characteristic, direct product factor, Sylow
186C23×C29—41no—
187C23×C29C2×D811yescharacteristic
188C23×C29C2×D811yescharacteristic
189Q8×C29—22no—
190Q8×C29—41no—
191Q8×C29—41no—
192Q8×C29—41no—
193Q8×C29—41no—
194Q8×C29—41no—
195Q8×C29—82no—
196Q8×C29—82no—
197D4×C29—41no—
198D4×C29—41no—
199D4×C29—41no—
200D4×C29—82no—
201D4×C29—82no—
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—41no—
210C2×C4×C29—41no—
211C2×C4×C29—41no—
212C2×C4×C29—41no—
213C2×C4×C29—82no—
214C2×C4×C29—82no—
215C2×C4×C29C2×D811yescharacteristic
216C2×C4×C29C2×D811yescharacteristic
217C2×C4×C29C2×D811yescharacteristic
218C2×C4×C29C2×D811yescharacteristic
219C2×C4×C29C22×D411yescharacteristic
220C8×C29—21no—
221C8×C29—21no—
222C8×C29—21no—
223C8×C29C2×#4111yescharacteristic
224C8×C29H(5,𝔽2)11yescharacteristic
225#3342C2×C2911yescharacteristic, complemented
226#3285C2×C2911yescharacteristic
227#2243C2×C2911yescharacteristic, complemented
228#2237C2×C2911yescharacteristic, complemented
229#2234C2×C2911yescharacteristic, complemented
230#2227C2×C2911yescharacteristic, complemented
231#2220C2×C2911yescharacteristic, complemented
232#2216C2×C2911yescharacteristic, complemented
233#2211C2×C2911yescharacteristic, complemented
234#2189C2×C2911yescharacteristic, complemented
235#2188C2×C2911yescharacteristic, complemented
236#2176C2×C2911yescharacteristic, complemented
237#2168C2×C2911yescharacteristic, complemented
238#2141C2×C2911yescharacteristic, complemented
239#2138C2×C2911yescharacteristic, complemented
240C22×C29—21no—
241C22×C29—21no—
242C22×C29—21no—
243C22×C29—21no—
244C22×C29—21no—
245C22×C29—21no—
246C22×C29—81no—
247C22×C29—81no—
248C22×C29—81no—
249C22×C29C22×D811yescharacteristic
250C4×C29—21no—
251C4×C29—21no—
252C4×C29—21no—
253C4×C29—21no—
254C4×C29—42no—
255C4×C29—81no—
256C4×C29—81no—
257C4×C29—81no—
258C4×C29—81no—
259C4×C29—81no—
260C4×C29—81no—
261C4×C29#54611yescharacteristic
262C4×C29#57711yescharacteristic
263C2×#135C22×C2911yescharacteristic
264C22×Q16C22×C2911yescharacteristic
265#556—21no—
266#548—21no—
267C2×Q32C22×C2911yescharacteristic
268C2×Q32C22×C2911yescharacteristic
269C2×SD32C22×C2911yescharacteristic
270C2×M32C22×C2911yescharacteristic
271C22×C16C22×C2911yescharacteristic
272#500C22×C2911yescharacteristic
273#495C22×C2911yescharacteristic
274#485—21no—
275#485—21no—
276#475—21no—
277#467C22×C2911yescharacteristic
278#467C22×C2911yescharacteristic
279#467C22×C2911yescharacteristic
280#466C22×C2911yescharacteristic
281#464—21no—
282#452—21no—
283#448—21no—
284C4×Q16C22×C2911yescharacteristic
285C4×Q16C22×C2911yescharacteristic
286C8×D4C22×C2911yescharacteristic
287#427C22×C2911yescharacteristic
288#427C22×C2911yescharacteristic
289#367C22×C2911yescharacteristic
290#366C22×C2911yescharacteristic
291#366C22×C2911yescharacteristic
292C4⋊C16C22×C2911yescharacteristic
293#358C22×C2911yescharacteristic
294#358C22×C2911yescharacteristic
295#358C22×C2911yescharacteristic
296#358C22×C2911yescharacteristic
297#358C22×C2911yescharacteristic
298#358C22×C2911yescharacteristic
299#358C22×C2911yescharacteristic
300#357C22×C2911yescharacteristic
301#357C22×C2911yescharacteristic
302#357C22×C2911yescharacteristic
303C22⋊C16C22×C2911yescharacteristic
304C22⋊C16C22×C2911yescharacteristic
305#346C22×C2911yescharacteristic
306C2×C29—41no—
307C2×C29—41no—
308C2×C29—161no—
309C2×C29#329411yescharacteristic
310C2×C29#341411yescharacteristic
311C2×C29#341711yescharacteristic
312C2×#41—21no—
313C22×Q8—21no—
314#135—22no—
315#135—41no—
316C2×Q16—22no—
317C2×Q16—21no—
318C2×Q16—41no—
319C2×Q16C23×C2911yescharacteristic
320C2×Q16C23×C2911yescharacteristic
321C2×Q16C23×C2911yescharacteristic
322C2×SD16—21no—
323C2×SD16—21no—
324C2×D8C23×C2911yescharacteristic
325C22×C8C23×C2911yescharacteristic
326C22×C8C23×C2911yescharacteristic
327C4⋊Q8—21no—
328#126—41no—
329#126—41no—
330#124—21no—
331#124—41no—
332#124—41no—
333C22⋊Q8—21no—
334C22⋊Q8—21no—
335C22⋊Q8—21no—
336C22⋊Q8—41no—
337#121—21no—
338#121—41no—
339C4×Q8—21no—
340C4×Q8—21no—
341C4×Q8—41no—
342C4×D4—41no—
343C4×D4D4×C2911yescharacteristic
344#117—21no—
345#117—21no—
346Q32—22no—
347Q32—41no—
348SD32—41no—
349M32—41no—
350C2×C16—41no—
351C2×C16C23×C2911yescharacteristic
352C2×C16C23×C2911yescharacteristic
353C2×C16C23×C2911yescharacteristic
354C2×C16C23×C2911yescharacteristic
355#107—21no—
356#107C23×C2911yescharacteristic
357#107C23×C2911yescharacteristic
358#107C23×C2911yescharacteristic
359#107C23×C2911yescharacteristic
360#106—21no—
361#106—21no—
362C4⋊C8D4×C2911yescharacteristic
363#103—21no—
364#103—21no—
365#103—21no—
366#103—21no—
367#103—21no—
368#102—21no—
369C22⋊C8D4×C2911yescharacteristic
370C22⋊C8D4×C2911yescharacteristic
371C4×C8C23×C2911yescharacteristic
372C29#3388011yescharacteristic, direct product factor, Sylow
373#41—42no—
374#41—81no—
375C2×Q8—21no—
376C2×Q8—21no—
377C2×Q8—21no—
378C2×Q8—42no—
379C2×Q8—41no—
380C2×Q8—41no—
381C2×Q8—81no—
382C2×D4—21no—
383C2×D4—41no—
384C2×D4—41no—
385C2×D4D8×C2911yescharacteristic
386C22×C4—41no—
387C22×C4—41no—
388C22×C4C2×D4×C2911yescharacteristic
389C22×C4C2×D4×C2911yescharacteristic
390Q16—21no—
391Q16—21no—
392Q16—21no—
393Q16—21no—
394Q16—21no—
395Q16—42no—
396Q16#41×C2912yes—
397SD16—42no—
398SD16—81no—
399D8—21no—
400D8—21no—
401C2×C8—21no—
402C2×C8—21no—
403C2×C8—21no—
404C2×C8—21no—
405C2×C8C2×D4×C2911yescharacteristic
406C2×C8C2×D4×C2911yescharacteristic
407C2×C8C2×D4×C2911yescharacteristic
408C2×C8C24×C2911yescharacteristic
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—41no—
414C4⋊C4—41no—
415C4⋊C4—41no—
416C4⋊C4—41no—
417C4⋊C4—41no—
418C4⋊C4—41no—
419C4⋊C4D8×C2911yescharacteristic
420C22⋊C4—41no—
421C22⋊C4—41no—
422C22⋊C4—41no—
423C22⋊C4—41no—
424C22⋊C4—41no—
425C22⋊C4—41no—
426C22⋊C4—41no—
427C22⋊C4—41no—
428C22⋊C4D8×C2911yescharacteristic
429C22⋊C4D8×C2911yescharacteristic
430C42—41no—
431C42—41no—
432C42—41no—
433C42—41no—
434C42C2×D4×C2911yescharacteristic
435C16—21no—
436C16—21no—
437C16—21no—
438C16—21no—
439C23—41no—
440C23C2×D8×C2911yescharacteristic
441C23C2×D8×C2911yescharacteristic
442Q8—22no—
443Q8—41no—
444Q8—41no—
445Q8—41no—
446Q8—41no—
447Q8—41no—
448Q8—82no—
449Q8—82no—
450D4—41no—
451D4—41no—
452D4—41no—
453D4—82no—
454D4—82no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—82no—
467C2×C4—82no—
468C2×C4C2×D8×C2911yescharacteristic
469C2×C4C2×D8×C2911yescharacteristic
470C2×C4C2×D8×C2911yescharacteristic
471C2×C4C2×D8×C2911yescharacteristic
472C2×C4C22×D4×C2911yescharacteristic
473C8—21no—
474C8—21no—
475C8—21no—
476C8C2×#41×C2911yescharacteristic
477C8C29×H(5,𝔽2)11yescharacteristic
478C22—21no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22—21no—
484C22—81no—
485C22—81no—
486C22—81no—
487C22C22×D8×C2911yescharacteristic
488C4—21no—
489C4—21no—
490C4—21no—
491C4—21no—
492C4—42no—
493C4—81no—
494C4—81no—
495C4—81no—
496C4—81no—
497C4—81no—
498C4—81no—
499C4C29×#54611yescharacteristic
500C4C29×#57711yescharacteristic
501C2—41no—
502C2—41no—
503C2—161no—
504C2C29×#329411yescharacteristic
505C2C29×#341411yescharacteristic
506C2C29×#341711yescharacteristic
subgroupG/H
center, socleC22×C29C22×D8
commutator, Frattini, cosocleC2×C8C24×C29
prime radicalC29×#3285C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C4×D4×C29 ◁ C8×D4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#3342C2semidirect
3. C29×#2243C2semidirect
4. C29×#2237C2semidirect
5. C29×#2234C2semidirect
6. C29×#2227C2semidirect
7. C29×#2220C2semidirect
8. C29×#2216C2semidirect
9. C29×#2211C2semidirect
10. C29×#2189C2semidirect
11. C29×#2188C2semidirect
12. C29×#2176C2semidirect
13. C29×#2168C2semidirect
14. C29×#2141C2semidirect
15. C29×#2138C2semidirect
185. #33880C29direct (N × H)
225. #3342C2×C29semidirect
227. #2243C2×C29semidirect
228. #2237C2×C29semidirect
229. #2234C2×C29semidirect
230. #2227C2×C29semidirect
231. #2220C2×C29semidirect
232. #2216C2×C29semidirect
233. #2211C2×C29semidirect
234. #2189C2×C29semidirect
235. #2188C2×C29semidirect
236. #2176C2×C29semidirect
237. #2168C2×C29semidirect
238. #2141C2×C29semidirect
239. #2138C2×C29semidirect
372. C29#33880direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#33422
C29×#32852
C29×#22432
C29×#22372
C29×#22342
C29×#22272
C29×#22202
C29×#22162
C29×#22112
C29×#21892
C29×#21882
C29×#21762
C29×#21682
C29×#21412
C29×#21382
#3388029