Finite Group Databasebeta

← C29×#33875 #20328775

Subgroups — C29×#33875 #20328775

Order 7424.

580 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3334C211yesmaximal, characteristic, complemented
2C29×#3285C211yesmaximal, characteristic, complemented
3C29×#2243C211yesmaximal, characteristic, complemented
4C29×#2236C211yesmaximal, characteristic, complemented
5C29×#2232C211yesmaximal, characteristic, complemented
6C29×#2227C211yesmaximal, characteristic, complemented
7C29×#2220C211yesmaximal, characteristic, complemented
8C29×#2215C211yesmaximal, characteristic, complemented
9C29×#2210C211yesmaximal, characteristic, complemented
10C29×#2186C211yesmaximal, characteristic, complemented
11C29×#2185C211yesmaximal, characteristic, complemented
12C29×#2175C211yesmaximal, characteristic, complemented
13C29×#2168C211yesmaximal, characteristic, complemented
14C29×#2139C211yesmaximal, characteristic, complemented
15C2×C29×#358C211yesmaximal, characteristic, complemented
16C2×C29×#135C2211yescharacteristic
17C22×Q16×C29C2211yescharacteristic
18C29×#548—21no—
19C29×#547—21no—
20C2×C29×SD32C2211yescharacteristic
21C2×C29×SD32C2211yescharacteristic
22C2×C29×D16C2211yescharacteristic
23C2×C29×M32C2211yescharacteristic
24C22×C16×C29C2211yescharacteristic
25C29×#500C2211yescharacteristic
26C29×#495C2211yescharacteristic
27C29×#480—21no—
28C29×#480—21no—
29C29×#474—21no—
30C29×#467C2211yescharacteristic
31C29×#466C2211yescharacteristic
32C29×#466C2211yescharacteristic
33C29×#466C2211yescharacteristic
34C29×#464—21no—
35C29×#452—21no—
36C29×#448—21no—
37C4×Q16×C29C2211yescharacteristic
38C4×D8×C29C2211yescharacteristic
39C8×D4×C29C2211yescharacteristic
40C2×C29×#107C2211yescharacteristic
41C2×C29×#107C2211yescharacteristic
42C29×#366C2211yescharacteristic
43C29×#366C2211yescharacteristic
44C29×#366C2211yescharacteristic
45C29×C4⋊C16C2211yescharacteristic
46C29×#358C2211yescharacteristic
47C29×#358C2211yescharacteristic
48C29×#358C2211yescharacteristic
49C29×#358C2211yescharacteristic
50C29×#358C2211yescharacteristic
51C29×#358C2211yescharacteristic
52C29×#357C2211yescharacteristic
53C29×#357C2211yescharacteristic
54C29×#357C2211yescharacteristic
55C29×#357C2211yescharacteristic
56C29×C22⋊C16C2211yescharacteristic
57C29×C22⋊C16C2211yescharacteristic
58C29×#346C2211yescharacteristic
59C2×#41×C29—21no—
60C2×#41×C29—41no—
61C22×Q8×C29—21no—
62C29×#135—22no—
63C29×#135—41no—
64C2×Q16×C29—22no—
65C2×Q16×C29—21no—
66C2×Q16×C29—41no—
67C2×Q16×C29C2311yescharacteristic
68C2×Q16×C29C2311yescharacteristic
69C2×SD16×C29—21no—
70C2×SD16×C29—21no—
71C2×D8×C29C2311yescharacteristic
72C2×D8×C29C2311yescharacteristic
73C22×C8×C29C2311yescharacteristic
74C22×C8×C29C2311yescharacteristic
75C29×C4⋊Q8—21no—
76C29×#124—21no—
77C29×#124—41no—
78C29×#123—41no—
79C29×#123—41no—
80C29×C22⋊Q8—21no—
81C29×C22⋊Q8—41no—
82C29×C22⋊Q8—41no—
83C29×#121—21no—
84C29×#121—21no—
85C29×#121—21no—
86C29×#121—41no—
87C4×Q8×C29—21no—
88C4×D4×C29—21no—
89C4×D4×C29—41no—
90C4×D4×C29D411yescharacteristic
91C2×C4⋊C4×C29—21no—
92C2×C4⋊C4×C29—21no—
93C29×SD32—22no—
94C29×SD32—41no—
95C29×D16—41no—
96C29×M32—41no—
97C2×C16×C29—41no—
98C2×C16×C29C2311yescharacteristic
99C2×C16×C29C2311yescharacteristic
100C2×C16×C29C2311yescharacteristic
101C2×C16×C29C2311yescharacteristic
102C29×#107—21no—
103C29×#107—21no—
104C29×#107—21no—
105C29×#107C2311yescharacteristic
106C29×#107C2311yescharacteristic
107C29×#107C2311yescharacteristic
108C29×#107C2311yescharacteristic
109C29×C4⋊C8D411yescharacteristic
110C29×#103—21no—
111C29×#103—21no—
112C29×#102—21no—
113C29×#102—21no—
114C29×#102—21no—
115C29×#102—21no—
116C29×C22⋊C8D411yescharacteristic
117C29×C22⋊C8D411yescharacteristic
118C4×C8×C29C2311yescharacteristic
119#41×C29—42no—
120#41×C29—81no—
121#41×C29—84no—
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—21no—
130C2×D4×C29—41no—
131C2×D4×C29—41no—
132C2×D4×C29—41no—
133C2×D4×C29—41no—
134C2×D4×C29D811yescharacteristic
135C22×C4×C29—41no—
136C22×C4×C29—41no—
137C22×C4×C29—41no—
138C22×C4×C29—41no—
139C22×C4×C29—41no—
140C22×C4×C29C2×D411yescharacteristic
141C22×C4×C29C2×D411yescharacteristic
142Q16×C29—21no—
143Q16×C29—21no—
144Q16×C29—21no—
145Q16×C29—42no—
146Q16×C29#4112yescomplemented
147SD16×C29—42no—
148SD16×C29—81no—
149D8×C29—21no—
150D8×C29—21no—
151D8×C29—21no—
152D8×C29—21no—
153C2×C8×C29—21no—
154C2×C8×C29—21no—
155C2×C8×C29—21no—
156C2×C8×C29—21no—
157C2×C8×C29C2×D411yescharacteristic
158C2×C8×C29C2×D411yescharacteristic
159C2×C8×C29C2×D411yescharacteristic
160C2×C8×C29C2411yescharacteristic
161C4⋊C4×C29—21no—
162C4⋊C4×C29—21no—
163C4⋊C4×C29—21no—
164C4⋊C4×C29—21no—
165C4⋊C4×C29—41no—
166C4⋊C4×C29—41no—
167C4⋊C4×C29—41no—
168C4⋊C4×C29—41no—
169C4⋊C4×C29—41no—
170C4⋊C4×C29D811yescharacteristic
171C22⋊C4×C29—41no—
172C22⋊C4×C29—41no—
173C22⋊C4×C29—41no—
174C22⋊C4×C29—41no—
175C22⋊C4×C29—41no—
176C22⋊C4×C29—41no—
177C22⋊C4×C29—41no—
178C22⋊C4×C29D811yescharacteristic
179C22⋊C4×C29D811yescharacteristic
180C42×C29—41no—
181C42×C29C2×D411yescharacteristic
182C16×C29—21no—
183C16×C29—21no—
184C16×C29—21no—
185C16×C29—21no—
186#33875C2911yesmaximal, characteristic, direct product factor, Sylow
187C23×C29—41no—
188C23×C29—41no—
189C23×C29C2×D811yescharacteristic
190C23×C29C2×D811yescharacteristic
191Q8×C29—22no—
192Q8×C29—41no—
193Q8×C29—41no—
194Q8×C29—41no—
195Q8×C29—82no—
196Q8×C29—82no—
197D4×C29—22no—
198D4×C29—41no—
199D4×C29—41no—
200D4×C29—41no—
201D4×C29—41no—
202D4×C29—82no—
203D4×C29—82no—
204D4×C29—82no—
205D4×C29—82no—
206C2×C4×C29—21no—
207C2×C4×C29—21no—
208C2×C4×C29—21no—
209C2×C4×C29—21no—
210C2×C4×C29—41no—
211C2×C4×C29—41no—
212C2×C4×C29—41no—
213C2×C4×C29—41no—
214C2×C4×C29—41no—
215C2×C4×C29—41no—
216C2×C4×C29—82no—
217C2×C4×C29—82no—
218C2×C4×C29—82no—
219C2×C4×C29—82no—
220C2×C4×C29—82no—
221C2×C4×C29C2×D811yescharacteristic
222C2×C4×C29C2×D811yescharacteristic
223C2×C4×C29C2×D811yescharacteristic
224C2×C4×C29C2×D811yescharacteristic
225C2×C4×C29C22×D411yescharacteristic
226C8×C29—21no—
227C8×C29—21no—
228C8×C29—21no—
229C8×C29C2×#4111yescharacteristic
230C8×C29H(5,𝔽2)11yescharacteristic
231#3334C2×C2911yescharacteristic, complemented
232#3285C2×C2911yescharacteristic, complemented
233#2243C2×C2911yescharacteristic, complemented
234#2236C2×C2911yescharacteristic, complemented
235#2232C2×C2911yescharacteristic, complemented
236#2227C2×C2911yescharacteristic, complemented
237#2220C2×C2911yescharacteristic, complemented
238#2215C2×C2911yescharacteristic, complemented
239#2210C2×C2911yescharacteristic, complemented
240#2186C2×C2911yescharacteristic, complemented
241#2185C2×C2911yescharacteristic, complemented
242#2175C2×C2911yescharacteristic, complemented
243#2168C2×C2911yescharacteristic, complemented
244#2139C2×C2911yescharacteristic, complemented
245C2×#358C2×C2911yescharacteristic, complemented
246C22×C29—21no—
247C22×C29—21no—
248C22×C29—21no—
249C22×C29—21no—
250C22×C29—21no—
251C22×C29—81no—
252C22×C29—81no—
253C22×C29—81no—
254C22×C29—81no—
255C22×C29—81no—
256C22×C29—81no—
257C22×C29#50912yes—
258C22×C29C22×D811yescharacteristic
259C4×C29—21no—
260C4×C29—21no—
261C4×C29—21no—
262C4×C29—21no—
263C4×C29—42no—
264C4×C29—81no—
265C4×C29—81no—
266C4×C29—81no—
267C4×C29—81no—
268C4×C29—81no—
269C4×C29#54611yescharacteristic
270C4×C29#57711yescharacteristic
271C2×#135C22×C2911yescharacteristic
272C22×Q16C22×C2911yescharacteristic
273#548—21no—
274#547—21no—
275C2×SD32C22×C2911yescharacteristic
276C2×SD32C22×C2911yescharacteristic
277C2×D16C22×C2911yescharacteristic
278C2×M32C22×C2911yescharacteristic
279C22×C16C22×C2911yescharacteristic
280#500C22×C2911yescharacteristic
281#495C22×C2911yescharacteristic
282#480—21no—
283#480—21no—
284#474—21no—
285#467C22×C2911yescharacteristic
286#466C22×C2911yescharacteristic
287#466C22×C2911yescharacteristic
288#466C22×C2911yescharacteristic
289#464—21no—
290#452—21no—
291#448—21no—
292C4×Q16C22×C2911yescharacteristic
293C4×D8C22×C2911yescharacteristic
294C8×D4C22×C2911yescharacteristic
295C2×#107C22×C2911yescharacteristic
296C2×#107C22×C2911yescharacteristic
297#366C22×C2911yescharacteristic
298#366C22×C2911yescharacteristic
299#366C22×C2911yescharacteristic
300C4⋊C16C22×C2911yescharacteristic
301#358C22×C2911yescharacteristic
302#358C22×C2911yescharacteristic
303#358C22×C2911yescharacteristic
304#358C22×C2911yescharacteristic
305#358C22×C2911yescharacteristic
306#358C22×C2911yescharacteristic
307#357C22×C2911yescharacteristic
308#357C22×C2911yescharacteristic
309#357C22×C2911yescharacteristic
310#357C22×C2911yescharacteristic
311C22⋊C16C22×C2911yescharacteristic
312C22⋊C16C22×C2911yescharacteristic
313#346C22×C2911yescharacteristic
314C2×C29—22no—
315C2×C29—41no—
316C2×C29—161no—
317C2×C29—161no—
318C2×C29#329411yescharacteristic
319C2×C29C2×#50911yescharacteristic
320C2×C29#341711yescharacteristic
321C2×#41—21no—
322C2×#41—41no—
323C22×Q8—21no—
324#135—22no—
325#135—41no—
326C2×Q16—22no—
327C2×Q16—21no—
328C2×Q16—41no—
329C2×Q16C23×C2911yescharacteristic
330C2×Q16C23×C2911yescharacteristic
331C2×SD16—21no—
332C2×SD16—21no—
333C2×D8C23×C2911yescharacteristic
334C2×D8C23×C2911yescharacteristic
335C22×C8C23×C2911yescharacteristic
336C22×C8C23×C2911yescharacteristic
337C4⋊Q8—21no—
338#124—21no—
339#124—41no—
340#123—41no—
341#123—41no—
342C22⋊Q8—21no—
343C22⋊Q8—41no—
344C22⋊Q8—41no—
345#121—21no—
346#121—21no—
347#121—21no—
348#121—41no—
349C4×Q8—21no—
350C4×D4—21no—
351C4×D4—41no—
352C4×D4D4×C2911yescharacteristic
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355SD32—22no—
356SD32—41no—
357D16—41no—
358M32—41no—
359C2×C16—41no—
360C2×C16C23×C2911yescharacteristic
361C2×C16C23×C2911yescharacteristic
362C2×C16C23×C2911yescharacteristic
363C2×C16C23×C2911yescharacteristic
364#107—21no—
365#107—21no—
366#107—21no—
367#107C23×C2911yescharacteristic
368#107C23×C2911yescharacteristic
369#107C23×C2911yescharacteristic
370#107C23×C2911yescharacteristic
371C4⋊C8D4×C2911yescharacteristic
372#103—21no—
373#103—21no—
374#102—21no—
375#102—21no—
376#102—21no—
377#102—21no—
378C22⋊C8D4×C2911yescharacteristic
379C22⋊C8D4×C2911yescharacteristic
380C4×C8C23×C2911yescharacteristic
381C29#3387511yescharacteristic, direct product factor, Sylow
382#41—42no—
383#41—81no—
384#41—84no—
385C2×Q8—21no—
386C2×Q8—21no—
387C2×Q8—42no—
388C2×Q8—41no—
389C2×Q8—41no—
390C2×Q8—81no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—41no—
394C2×D4—41no—
395C2×D4—41no—
396C2×D4—41no—
397C2×D4D8×C2911yescharacteristic
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4—41no—
402C22×C4—41no—
403C22×C4C2×D4×C2911yescharacteristic
404C22×C4C2×D4×C2911yescharacteristic
405Q16—21no—
406Q16—21no—
407Q16—21no—
408Q16—42no—
409Q16#41×C2912yescomplemented
410SD16—42no—
411SD16—81no—
412D8—21no—
413D8—21no—
414D8—21no—
415D8—21no—
416C2×C8—21no—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8C2×D4×C2911yescharacteristic
421C2×C8C2×D4×C2911yescharacteristic
422C2×C8C2×D4×C2911yescharacteristic
423C2×C8C24×C2911yescharacteristic
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—41no—
429C4⋊C4—41no—
430C4⋊C4—41no—
431C4⋊C4—41no—
432C4⋊C4—41no—
433C4⋊C4D8×C2911yescharacteristic
434C22⋊C4—41no—
435C22⋊C4—41no—
436C22⋊C4—41no—
437C22⋊C4—41no—
438C22⋊C4—41no—
439C22⋊C4—41no—
440C22⋊C4—41no—
441C22⋊C4D8×C2911yescharacteristic
442C22⋊C4D8×C2911yescharacteristic
443C42—41no—
444C42C2×D4×C2911yescharacteristic
445C16—21no—
446C16—21no—
447C16—21no—
448C16—21no—
449C23—41no—
450C23—41no—
451C23C2×D8×C2911yescharacteristic
452C23C2×D8×C2911yescharacteristic
453Q8—22no—
454Q8—41no—
455Q8—41no—
456Q8—41no—
457Q8—82no—
458Q8—82no—
459D4—22no—
460D4—41no—
461D4—41no—
462D4—41no—
463D4—41no—
464D4—82no—
465D4—82no—
466D4—82no—
467D4—82no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—82no—
479C2×C4—82no—
480C2×C4—82no—
481C2×C4—82no—
482C2×C4—82no—
483C2×C4C2×D8×C2911yescharacteristic
484C2×C4C2×D8×C2911yescharacteristic
485C2×C4C2×D8×C2911yescharacteristic
486C2×C4C2×D8×C2911yescharacteristic
487C2×C4C22×D4×C2911yescharacteristic
488C8—21no—
489C8—21no—
490C8—21no—
491C8C2×#41×C2911yescharacteristic
492C8C29×H(5,𝔽2)11yescharacteristic
493C22—21no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—81no—
499C22—81no—
500C22—81no—
501C22—81no—
502C22—81no—
503C22—81no—
504C22C29×#50912yes—
505C22C22×D8×C2911yescharacteristic
506C4—21no—
507C4—21no—
508C4—21no—
509C4—21no—
510C4—42no—
511C4—81no—
512C4—81no—
513C4—81no—
514C4—81no—
515C4—81no—
516C4C29×#54611yescharacteristic
517C4C29×#57711yescharacteristic
518C2—22no—
519C2—41no—
520C2—161no—
521C2—161no—
522C2C29×#329411yescharacteristic
523C2C2×C29×#50911yescharacteristic
524C2C29×#341711yescharacteristic
subgroupG/H
center, socleC22×C29C22×D8
commutator, Frattini, cosocleC2×C8C24×C29
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×#3334C2semidirect
2. C29×#3285C2semidirect
3. C29×#2243C2semidirect
4. C29×#2236C2semidirect
5. C29×#2232C2semidirect
6. C29×#2227C2semidirect
7. C29×#2220C2semidirect
8. C29×#2215C2semidirect
9. C29×#2210C2semidirect
10. C29×#2186C2semidirect
11. C29×#2185C2semidirect
12. C29×#2175C2semidirect
13. C29×#2168C2semidirect
14. C29×#2139C2semidirect
15. C2×C29×#358C2semidirect
146. Q16×C29#41semidirect
186. #33875C29direct (N × H)
231. #3334C2×C29semidirect
232. #3285C2×C29semidirect
233. #2243C2×C29semidirect
234. #2236C2×C29semidirect
235. #2232C2×C29semidirect
236. #2227C2×C29semidirect
237. #2220C2×C29semidirect
238. #2215C2×C29semidirect
239. #2210C2×C29semidirect
240. #2186C2×C29semidirect
241. #2185C2×C29semidirect
242. #2175C2×C29semidirect
243. #2168C2×C29semidirect
244. #2139C2×C29semidirect
245. C2×#358C2×C29semidirect
381. C29#33875direct (N × H)
409. Q16#41×C29semidirect

Maximal subgroups

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

subgroupindex
C29×#33342
C29×#32852
C29×#22432
C29×#22362
C29×#22322
C29×#22272
C29×#22202
C29×#22152
C29×#22102
C29×#21862
C29×#21852
C29×#21752
C29×#21682
C29×#21392
C2×C29×#3582
#3387529