Finite Group Databasebeta

← C29×#33671 #20328571

Subgroups — C29×#33671 #20328571

Order 7424.

554 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3168C211yesmaximal, characteristic, complemented
2C4×C29×#135C211yesmaximal, characteristic, complemented
3C29×#2237C211yesmaximal, characteristic, complemented
4C29×#2234C211yesmaximal, characteristic, complemented
5C29×#2229C211yesmaximal, characteristic, complemented
6C29×#2228C211yesmaximal, characteristic, complemented
7C29×#2211C211yesmaximal, characteristic, complemented
8C29×#2210C211yesmaximal, characteristic, complemented
9C29×#2189C211yesmaximal, characteristic, complemented
10C29×#2186C211yesmaximal, characteristic
11C29×#2177C211yesmaximal, characteristic, complemented
12C29×#2176C211yesmaximal, characteristic, complemented
13C29×#2175C211yesmaximal, characteristic, complemented
14C29×#2175C211yesmaximal, characteristic, complemented
15C29×#2163C211yesmaximal, characteristic, complemented
16C2×C29×#135C2211yescharacteristic
17C29×#529—21no—
18C4×#41×C29—21no—
19C2×C29×Q32C2211yescharacteristic
20C2×C29×SD32C2211yescharacteristic
21C2×C29×SD32C2211yescharacteristic
22C2×C29×D16C2211yescharacteristic
23C29×#499C2211yescharacteristic
24C29×#495C2211yescharacteristic
25C29×#488—21no—
26C29×#467C2211yescharacteristic
27C29×#466C2211yescharacteristic
28C29×#465—21no—
29C4×Q16×C29C2211yescharacteristic
30C4×Q16×C29C2211yescharacteristic
31C4×Q16×C29C2211yescharacteristic
32C4×SD16×C29—21no—
33C4×SD16×C29—21no—
34C4×SD16×C29—21no—
35C4×D8×C29C2211yescharacteristic
36C4×D8×C29C2211yescharacteristic
37C4×D8×C29C2211yescharacteristic
38C29×#427C2211yescharacteristic
39C29×#416—21no—
40C2×C4×C8×C29C2211yescharacteristic
41C29×#367C2211yescharacteristic
42C29×#367C2211yescharacteristic
43C29×#366C2211yescharacteristic
44C29×#366C2211yescharacteristic
45C29×C4⋊C16C2211yescharacteristic
46C29×C4⋊C16C2211yescharacteristic
47C29×#358C2211yescharacteristic
48C29×#358C2211yescharacteristic
49C29×#358C2211yescharacteristic
50C29×#358C2211yescharacteristic
51C29×#357C2211yescharacteristic
52C29×#357C2211yescharacteristic
53C29×#357C2211yescharacteristic
54C29×#357C2211yescharacteristic
55C29×C22⋊C16C2211yescharacteristic
56C29×C22⋊C16C2211yescharacteristic
57C29×#346C2211yescharacteristic
58C29×#346C2211yescharacteristic
59C2×#41×C29—21no—
60C29×#135—22no—
61C29×#135—22no—
62C2×Q16×C29C2311yescharacteristic
63C2×Q16×C29C2311yescharacteristic
64C2×SD16×C29—21no—
65C2×SD16×C29—21no—
66C2×D8×C29C2311yescharacteristic
67C2×D8×C29C2311yescharacteristic
68C22×C8×C29D411yescharacteristic
69C22×C8×C29C2311yescharacteristic
70C29×#126—41no—
71C29×#125—21no—
72C29×#124—21no—
73C29×#123—41no—
74C29×C22⋊Q8—21no—
75C29×#121—21no—
76C4×Q8×C29—21no—
77C4×Q8×C29—21no—
78C4×Q8×C29—21no—
79C4×D4×C29—21no—
80C4×D4×C29—21no—
81C4×D4×C29—21no—
82C4×D4×C29—41no—
83C4×D4×C29—41no—
84C4×D4×C29—41no—
85C29×#117—21no—
86C29×#117—41no—
87C29×#117—41no—
88C2×C42×C29—41no—
89C2×C42×C29D411yescharacteristic
90C29×Q32—22no—
91C29×SD32—22no—
92C29×SD32—22no—
93C29×D16—22no—
94C2×C16×C29C2311yescharacteristic
95C2×C16×C29C2311yescharacteristic
96C2×C16×C29C2311yescharacteristic
97C2×C16×C29C2311yescharacteristic
98C29×#107C2311yescharacteristic
99C29×#107C2311yescharacteristic
100C29×#107C2311yescharacteristic
101C29×#107C2311yescharacteristic
102C29×#106—21no—
103C29×#106—21no—
104C29×#103—21no—
105C29×#103—21no—
106C29×#103—21no—
107C29×#103—21no—
108C29×#102—21no—
109C29×#102—21no—
110C29×#102—21no—
111C29×#102—21no—
112C4×C8×C29D411yescharacteristic
113C4×C8×C29D411yescharacteristic
114C4×C8×C29C2311yescharacteristic
115C4×C8×C29C2311yescharacteristic
116#41×C29—24no—
117#41×C29—42no—
118C2×Q8×C29—21no—
119C2×Q8×C29—21no—
120C2×D4×C29—21no—
121C2×D4×C29—21no—
122C2×D4×C29—41no—
123C2×D4×C29—41no—
124C22×C4×C29—41no—
125C22×C4×C29—41no—
126C22×C4×C29—41no—
127C22×C4×C29—41no—
128C22×C4×C29D811yescharacteristic
129C22×C4×C29D811yescharacteristic
130C22×C4×C29C2×D411yescharacteristic
131Q16×C29—21no—
132Q16×C29—21no—
133Q16×C29—21no—
134Q16×C29#4112yes—
135SD16×C29—24no—
136SD16×C29—42no—
137D8×C29—21no—
138D8×C29—21no—
139D8×C29—21no—
140D8×C29#4112yes—
141C2×C8×C29—21no—
142C2×C8×C29—21no—
143C2×C8×C29—41no—
144C2×C8×C29C2×D411yescharacteristic
145C2×C8×C29C2×D411yescharacteristic
146C2×C8×C29C2×D411yescharacteristic
147C2×C8×C29C2411yescharacteristic
148C4⋊C4×C29—21no—
149C4⋊C4×C29—21no—
150C4⋊C4×C29—21no—
151C4⋊C4×C29—21no—
152C4⋊C4×C29—41no—
153C4⋊C4×C29—41no—
154C4⋊C4×C29—41no—
155C4⋊C4×C29—41no—
156C4⋊C4×C29—41no—
157C4⋊C4×C29—41no—
158C22⋊C4×C29—41no—
159C22⋊C4×C29—41no—
160C22⋊C4×C29—41no—
161C22⋊C4×C29—41no—
162C22⋊C4×C29—41no—
163C22⋊C4×C29—41no—
164C22⋊C4×C29—41no—
165C22⋊C4×C29—41no—
166C42×C29—41no—
167C42×C29—41no—
168C42×C29—41no—
169C42×C29—41no—
170C42×C29D811yescharacteristic
171C42×C29D811yescharacteristic
172C42×C29C2×D411yescharacteristic
173C42×C29C2×D411yescharacteristic
174C16×C29—21no—
175C16×C29—21no—
176C16×C29—21no—
177C16×C29—21no—
178#33671C2911yesmaximal, characteristic, direct product factor, Sylow
179C23×C29—41no—
180C23×C29—41no—
181C23×C29C2×D811yescharacteristic
182Q8×C29—22no—
183Q8×C29—41no—
184Q8×C29—41no—
185Q8×C29—41no—
186D4×C29—22no—
187D4×C29—44no—
188D4×C29—41no—
189D4×C29—41no—
190D4×C29—41no—
191D4×C29—82no—
192C2×C4×C29—21no—
193C2×C4×C29—21no—
194C2×C4×C29—41no—
195C2×C4×C29—41no—
196C2×C4×C29—44no—
197C2×C4×C29—41no—
198C2×C4×C29—41no—
199C2×C4×C29—41no—
200C2×C4×C29—41no—
201C2×C4×C29—41no—
202C2×C4×C29—41no—
203C2×C4×C29—82no—
204C2×C4×C29—82no—
205C2×C4×C29—82no—
206C2×C4×C29C2×D811yescharacteristic
207C2×C4×C29C2×D811yescharacteristic
208C2×C4×C29C2×D811yescharacteristic
209C2×C4×C29C2×D811yescharacteristic
210C2×C4×C29C2×D811yescharacteristic
211C2×C4×C29C22×D411yescharacteristic
212C8×C29—21no—
213C8×C29—21no—
214C8×C29—21no—
215C8×C29C2×#4111yescharacteristic
216C8×C29C2×#4111yescharacteristic
217#3168C2×C2911yescharacteristic, complemented
218C4×#135C2×C2911yescharacteristic, complemented
219#2237C2×C2911yescharacteristic, complemented
220#2234C2×C2911yescharacteristic, complemented
221#2229C2×C2911yescharacteristic, complemented
222#2228C2×C2911yescharacteristic, complemented
223#2211C2×C2911yescharacteristic, complemented
224#2210C2×C2911yescharacteristic, complemented
225#2189C2×C2911yescharacteristic, complemented
226#2186C2×C2911yescharacteristic
227#2177C2×C2911yescharacteristic, complemented
228#2176C2×C2911yescharacteristic, complemented
229#2175C2×C2911yescharacteristic, complemented
230#2175C2×C2911yescharacteristic, complemented
231#2163C2×C2911yescharacteristic, complemented
232C22×C29—21no—
233C22×C29—21no—
234C22×C29—21no—
235C22×C29—42no—
236C22×C29—81no—
237C22×C29—81no—
238C22×C29—81no—
239C22×C29—81no—
240C22×C29—81no—
241C22×C29C22×D811yescharacteristic
242C4×C29—21no—
243C4×C29—21no—
244C4×C29—21no—
245C4×C29—21no—
246C4×C29—21no—
247C4×C29—42no—
248C4×C29—81no—
249C4×C29—81no—
250C4×C29—81no—
251C4×C29—81no—
252C4×C29—81no—
253C4×C29#52511yescharacteristic
254C4×C29#57511yescharacteristic
255C2×#135C22×C2911yescharacteristic
256#529—21no—
257C4×#41—21no—
258C2×Q32C22×C2911yescharacteristic
259C2×SD32C22×C2911yescharacteristic
260C2×SD32C22×C2911yescharacteristic
261C2×D16C22×C2911yescharacteristic
262#499C22×C2911yescharacteristic
263#495C22×C2911yescharacteristic
264#488—21no—
265#467C22×C2911yescharacteristic
266#466C22×C2911yescharacteristic
267#465—21no—
268C4×Q16C22×C2911yescharacteristic
269C4×Q16C22×C2911yescharacteristic
270C4×Q16C22×C2911yescharacteristic
271C4×SD16—21no—
272C4×SD16—21no—
273C4×SD16—21no—
274C4×D8C22×C2911yescharacteristic
275C4×D8C22×C2911yescharacteristic
276C4×D8C22×C2911yescharacteristic
277#427C22×C2911yescharacteristic
278#416—21no—
279C2×C4×C8C22×C2911yescharacteristic
280#367C22×C2911yescharacteristic
281#367C22×C2911yescharacteristic
282#366C22×C2911yescharacteristic
283#366C22×C2911yescharacteristic
284C4⋊C16C22×C2911yescharacteristic
285C4⋊C16C22×C2911yescharacteristic
286#358C22×C2911yescharacteristic
287#358C22×C2911yescharacteristic
288#358C22×C2911yescharacteristic
289#358C22×C2911yescharacteristic
290#357C22×C2911yescharacteristic
291#357C22×C2911yescharacteristic
292#357C22×C2911yescharacteristic
293#357C22×C2911yescharacteristic
294C22⋊C16C22×C2911yescharacteristic
295C22⋊C16C22×C2911yescharacteristic
296#346C22×C2911yescharacteristic
297#346C22×C2911yescharacteristic
298C2×C29—41no—
299C2×C29—82no—
300C2×C29—161no—
301C2×C29#310011yescharacteristic
302C2×C29#341411yescharacteristic
303C2×C29#341411yescharacteristic
304C2×#41—21no—
305#135—22no—
306#135—22no—
307C2×Q16C23×C2911yescharacteristic
308C2×Q16C23×C2911yescharacteristic
309C2×SD16—21no—
310C2×SD16—21no—
311C2×D8C23×C2911yescharacteristic
312C2×D8C23×C2911yescharacteristic
313C22×C8D4×C2911yescharacteristic
314C22×C8C23×C2911yescharacteristic
315#126—41no—
316#125—21no—
317#124—21no—
318#123—41no—
319C22⋊Q8—21no—
320#121—21no—
321C4×Q8—21no—
322C4×Q8—21no—
323C4×Q8—21no—
324C4×D4—21no—
325C4×D4—21no—
326C4×D4—21no—
327C4×D4—41no—
328C4×D4—41no—
329C4×D4—41no—
330#117—21no—
331#117—41no—
332#117—41no—
333C2×C42—41no—
334C2×C42D4×C2911yescharacteristic
335Q32—22no—
336SD32—22no—
337SD32—22no—
338D16—22no—
339C2×C16C23×C2911yescharacteristic
340C2×C16C23×C2911yescharacteristic
341C2×C16C23×C2911yescharacteristic
342C2×C16C23×C2911yescharacteristic
343#107C23×C2911yescharacteristic
344#107C23×C2911yescharacteristic
345#107C23×C2911yescharacteristic
346#107C23×C2911yescharacteristic
347#106—21no—
348#106—21no—
349#103—21no—
350#103—21no—
351#103—21no—
352#103—21no—
353#102—21no—
354#102—21no—
355#102—21no—
356#102—21no—
357C4×C8D4×C2911yescharacteristic
358C4×C8D4×C2911yescharacteristic
359C4×C8C23×C2911yescharacteristic
360C4×C8C23×C2911yescharacteristic
361C29#3367111yescharacteristic, direct product factor, Sylow
362#41—24no—
363#41—42no—
364C2×Q8—21no—
365C2×Q8—21no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4—41no—
369C2×D4—41no—
370C22×C4—41no—
371C22×C4—41no—
372C22×C4—41no—
373C22×C4—41no—
374C22×C4D8×C2911yescharacteristic
375C22×C4D8×C2911yescharacteristic
376C22×C4C2×D4×C2911yescharacteristic
377Q16—21no—
378Q16—21no—
379Q16—21no—
380Q16#41×C2912yes—
381SD16—24no—
382SD16—42no—
383D8—21no—
384D8—21no—
385D8—21no—
386D8#41×C2912yes—
387C2×C8—21no—
388C2×C8—21no—
389C2×C8—41no—
390C2×C8C2×D4×C2911yescharacteristic
391C2×C8C2×D4×C2911yescharacteristic
392C2×C8C2×D4×C2911yescharacteristic
393C2×C8C24×C2911yescharacteristic
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—41no—
399C4⋊C4—41no—
400C4⋊C4—41no—
401C4⋊C4—41no—
402C4⋊C4—41no—
403C4⋊C4—41no—
404C22⋊C4—41no—
405C22⋊C4—41no—
406C22⋊C4—41no—
407C22⋊C4—41no—
408C22⋊C4—41no—
409C22⋊C4—41no—
410C22⋊C4—41no—
411C22⋊C4—41no—
412C42—41no—
413C42—41no—
414C42—41no—
415C42—41no—
416C42D8×C2911yescharacteristic
417C42D8×C2911yescharacteristic
418C42C2×D4×C2911yescharacteristic
419C42C2×D4×C2911yescharacteristic
420C16—21no—
421C16—21no—
422C16—21no—
423C16—21no—
424C23—41no—
425C23—41no—
426C23C2×D8×C2911yescharacteristic
427Q8—22no—
428Q8—41no—
429Q8—41no—
430Q8—41no—
431D4—22no—
432D4—44no—
433D4—41no—
434D4—41no—
435D4—41no—
436D4—82no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—44no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—82no—
449C2×C4—82no—
450C2×C4—82no—
451C2×C4C2×D8×C2911yescharacteristic
452C2×C4C2×D8×C2911yescharacteristic
453C2×C4C2×D8×C2911yescharacteristic
454C2×C4C2×D8×C2911yescharacteristic
455C2×C4C2×D8×C2911yescharacteristic
456C2×C4C22×D4×C2911yescharacteristic
457C8—21no—
458C8—21no—
459C8—21no—
460C8C2×#41×C2911yescharacteristic
461C8C2×#41×C2911yescharacteristic
462C22—21no—
463C22—21no—
464C22—21no—
465C22—42no—
466C22—81no—
467C22—81no—
468C22—81no—
469C22—81no—
470C22—81no—
471C22C22×D8×C2911yescharacteristic
472C4—21no—
473C4—21no—
474C4—21no—
475C4—21no—
476C4—21no—
477C4—42no—
478C4—81no—
479C4—81no—
480C4—81no—
481C4—81no—
482C4—81no—
483C4C29×#52511yescharacteristic
484C4C29×#57511yescharacteristic
485C2—41no—
486C2—82no—
487C2—161no—
488C2C29×#310011yescharacteristic
489C2C29×#341411yescharacteristic
490C2C29×#341411yescharacteristic
subgroupG/H
center, socleC22×C29C22×D8
commutator, Frattini, cosocleC2×C8C24×C29
prime radicalC29×#2186C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C42×C29 ◁ C2×C4×C8×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#3168C2semidirect
2. C4×C29×#135C2semidirect
3. C29×#2237C2semidirect
4. C29×#2234C2semidirect
5. C29×#2229C2semidirect
6. C29×#2228C2semidirect
7. C29×#2211C2semidirect
8. C29×#2210C2semidirect
9. C29×#2189C2semidirect
11. C29×#2177C2semidirect
12. C29×#2176C2semidirect
13. C29×#2175C2semidirect
14. C29×#2175C2semidirect
15. C29×#2163C2semidirect
178. #33671C29direct (N × H)
217. #3168C2×C29semidirect
218. C4×#135C2×C29semidirect
219. #2237C2×C29semidirect
220. #2234C2×C29semidirect
221. #2229C2×C29semidirect
222. #2228C2×C29semidirect
223. #2211C2×C29semidirect
224. #2210C2×C29semidirect
225. #2189C2×C29semidirect
227. #2177C2×C29semidirect
228. #2176C2×C29semidirect
229. #2175C2×C29semidirect
230. #2175C2×C29semidirect
231. #2163C2×C29semidirect
361. C29#33671direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#31682
C4×C29×#1352
C29×#22372
C29×#22342
C29×#22292
C29×#22282
C29×#22112
C29×#22102
C29×#21892
C29×#21862
C29×#21772
C29×#21762
C29×#21752
C29×#21632
#3367129