Finite Group Databasebeta

← C29×#33879 #20328779

Subgroups — C29×#33879 #20328779

Order 7424.

536 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3336C211yesmaximal, characteristic
2D4×Q16×C29C211yesmaximal, characteristic
3C29×#2245C211yesmaximal, characteristic, complemented
4C29×#2237C211yesmaximal, characteristic, complemented
5C29×#2235C211yesmaximal, characteristic, complemented
6C29×#2229C211yesmaximal, characteristic, complemented
7C29×#2219C211yesmaximal, characteristic, complemented
8C29×#2216C211yesmaximal, characteristic, complemented
9C29×#2209C211yesmaximal, characteristic, complemented
10C29×#2188C211yesmaximal, characteristic, complemented
11C29×#2188C211yesmaximal, characteristic, complemented
12C29×#2176C211yesmaximal, characteristic, complemented
13C29×#2168C211yesmaximal, characteristic
14C29×#2141C211yesmaximal, characteristic, complemented
15C2×C29×#358C211yesmaximal, characteristic, complemented
16C22×Q16×C29C2211yescharacteristic
17C22×Q16×C29C2211yescharacteristic
18C29×#552—21no—
19D4×Q8×C29—21no—
20C2×C29×Q32C2211yescharacteristic
21C2×C29×Q32C2211yescharacteristic
22C2×C29×Q32C2211yescharacteristic
23C2×C29×M32C2211yescharacteristic
24C22×C16×C29C2211yescharacteristic
25C29×#499C2211yescharacteristic
26C29×#494C2211yescharacteristic
27C29×#485—21no—
28C29×#483—21no—
29C29×#479—21no—
30C29×#467C2211yescharacteristic
31C29×#467C2211yescharacteristic
32C29×#467C2211yescharacteristic
33C29×#467C2211yescharacteristic
34C29×#462—21no—
35C29×#451—21no—
36C29×#451—21no—
37C4×Q16×C29C2211yescharacteristic
38C4×Q16×C29C2211yescharacteristic
39C8×D4×C29C2211yescharacteristic
40C29×#427C2211yescharacteristic
41C2×C29×#107C2211yescharacteristic
42C29×#367C2211yescharacteristic
43C29×#367C2211yescharacteristic
44C29×#366C2211yescharacteristic
45C29×C4⋊C16C2211yescharacteristic
46C29×#358C2211yescharacteristic
47C29×#358C2211yescharacteristic
48C29×#358C2211yescharacteristic
49C29×#358C2211yescharacteristic
50C29×#358C2211yescharacteristic
51C29×#358C2211yescharacteristic
52C29×#358C2211yescharacteristic
53C29×#358C2211yescharacteristic
54C29×#358C2211yescharacteristic
55C29×#358C2211yescharacteristic
56C29×C22⋊C16C2211yescharacteristic
57C29×C22⋊C16C2211yescharacteristic
58C29×#346C2211yescharacteristic
59C22×Q8×C29—21no—
60C22×Q8×C29—21no—
61C2×Q16×C29—22no—
62C2×Q16×C29—22no—
63C2×Q16×C29—21no—
64C2×Q16×C29—21no—
65C2×Q16×C29—21no—
66C2×Q16×C29—41no—
67C2×Q16×C29—41no—
68C2×Q16×C29C2311yescharacteristic
69C2×Q16×C29C2311yescharacteristic
70C2×Q16×C29C2311yescharacteristic
71C2×Q16×C29C2311yescharacteristic
72C22×C8×C29C2311yescharacteristic
73C22×C8×C29C2311yescharacteristic
74C29×C4⋊Q8—21no—
75C29×C4⋊Q8—41no—
76C29×#126—41no—
77C29×#125—21no—
78C29×#125—41no—
79C29×#123—41no—
80C29×C22⋊Q8—21no—
81C29×C22⋊Q8—21no—
82C29×C22⋊Q8—21no—
83C29×C22⋊Q8—21no—
84C29×C22⋊Q8—41no—
85C29×C22⋊Q8—41no—
86C4×Q8×C29—21no—
87C4×Q8×C29—21no—
88C4×D4×C29—41no—
89C4×D4×C29D411yescharacteristic
90C29×#117—21no—
91C29×#117—41no—
92C2×C4⋊C4×C29—21no—
93C29×Q32—22no—
94C29×Q32—41no—
95C29×Q32—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×#103—21no—
116C29×C22⋊C8D411yescharacteristic
117C29×C22⋊C8D411yescharacteristic
118C4×C8×C29C2311yescharacteristic
119C2×Q8×C29—21no—
120C2×Q8×C29—21no—
121C2×Q8×C29—21no—
122C2×Q8×C29—21no—
123C2×Q8×C29—42no—
124C2×Q8×C29—42no—
125C2×Q8×C29—41no—
126C2×Q8×C29—41no—
127C2×Q8×C29—81no—
128C2×Q8×C29—81no—
129C2×D4×C29D811yescharacteristic
130C22×C4×C29—41no—
131C22×C4×C29—41no—
132C22×C4×C29—41no—
133C22×C4×C29C2×D411yescharacteristic
134C22×C4×C29C2×D411yescharacteristic
135Q16×C29—21no—
136Q16×C29—21no—
137Q16×C29—21no—
138Q16×C29—21no—
139Q16×C29—21no—
140Q16×C29—21no—
141Q16×C29—21no—
142Q16×C29—42no—
143Q16×C29—42no—
144Q16×C29—81no—
145Q16×C29#4112yes—
146C2×C8×C29—21no—
147C2×C8×C29—21no—
148C2×C8×C29—21no—
149C2×C8×C29—21no—
150C2×C8×C29C2×D411yescharacteristic
151C2×C8×C29C2×D411yescharacteristic
152C2×C8×C29C2×D411yescharacteristic
153C2×C8×C29C2411yescharacteristic
154C4⋊C4×C29—21no—
155C4⋊C4×C29—21no—
156C4⋊C4×C29—21no—
157C4⋊C4×C29—21no—
158C4⋊C4×C29—41no—
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×C29—41no—
166C4⋊C4×C29—41no—
167C4⋊C4×C29—41no—
168C4⋊C4×C29—41no—
169C4⋊C4×C29D811yescharacteristic
170C22⋊C4×C29—41no—
171C22⋊C4×C29—41no—
172C22⋊C4×C29—41no—
173C22⋊C4×C29—41no—
174C22⋊C4×C29—41no—
175C22⋊C4×C29D811yescharacteristic
176C22⋊C4×C29D811yescharacteristic
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#33879C2911yesmaximal, characteristic, direct product factor, Sylow
186C23×C29C2×D811yescharacteristic
187C23×C29C2×D811yescharacteristic
188Q8×C29—22no—
189Q8×C29—41no—
190Q8×C29—41no—
191Q8×C29—41no—
192Q8×C29—41no—
193Q8×C29—41no—
194Q8×C29—41no—
195Q8×C29—41no—
196Q8×C29—82no—
197Q8×C29—82no—
198D4×C29—22no—
199C2×C4×C29—21no—
200C2×C4×C29—21no—
201C2×C4×C29—21no—
202C2×C4×C29—21no—
203C2×C4×C29—41no—
204C2×C4×C29—41no—
205C2×C4×C29—41no—
206C2×C4×C29—41no—
207C2×C4×C29—41no—
208C2×C4×C29—41no—
209C2×C4×C29—41no—
210C2×C4×C29—41no—
211C2×C4×C29—82no—
212C2×C4×C29—82no—
213C2×C4×C29—82no—
214C2×C4×C29C2×D811yescharacteristic
215C2×C4×C29C2×D811yescharacteristic
216C2×C4×C29C2×D811yescharacteristic
217C2×C4×C29C2×D811yescharacteristic
218C2×C4×C29C22×D411yescharacteristic
219C8×C29—21no—
220C8×C29—21no—
221C8×C29—21no—
222C8×C29C2×#4111yescharacteristic
223C8×C29H(5,𝔽2)11yescharacteristic
224#3336C2×C2911yescharacteristic
225D4×Q16C2×C2911yescharacteristic
226#2245C2×C2911yescharacteristic, complemented
227#2237C2×C2911yescharacteristic, complemented
228#2235C2×C2911yescharacteristic, complemented
229#2229C2×C2911yescharacteristic, complemented
230#2219C2×C2911yescharacteristic, complemented
231#2216C2×C2911yescharacteristic, complemented
232#2209C2×C2911yescharacteristic, complemented
233#2188C2×C2911yescharacteristic, complemented
234#2188C2×C2911yescharacteristic, complemented
235#2176C2×C2911yescharacteristic, complemented
236#2168C2×C2911yescharacteristic
237#2141C2×C2911yescharacteristic, complemented
238C2×#358C2×C2911yescharacteristic, complemented
239C22×C29—21no—
240C22×C29—21no—
241C22×C29—21no—
242C22×C29—21no—
243C22×C29—21no—
244C22×C29#51012yes—
245C22×C29C22×D811yescharacteristic
246C4×C29—21no—
247C4×C29—21no—
248C4×C29—21no—
249C4×C29—21no—
250C4×C29—42no—
251C4×C29—81no—
252C4×C29—81no—
253C4×C29—81no—
254C4×C29—81no—
255C4×C29—81no—
256C4×C29—81no—
257C4×C29—81no—
258C4×C29#54611yescharacteristic
259C4×C29#57711yescharacteristic
260C22×Q16C22×C2911yescharacteristic
261C22×Q16C22×C2911yescharacteristic
262#552—21no—
263D4×Q8—21no—
264C2×Q32C22×C2911yescharacteristic
265C2×Q32C22×C2911yescharacteristic
266C2×Q32C22×C2911yescharacteristic
267C2×M32C22×C2911yescharacteristic
268C22×C16C22×C2911yescharacteristic
269#499C22×C2911yescharacteristic
270#494C22×C2911yescharacteristic
271#485—21no—
272#483—21no—
273#479—21no—
274#467C22×C2911yescharacteristic
275#467C22×C2911yescharacteristic
276#467C22×C2911yescharacteristic
277#467C22×C2911yescharacteristic
278#462—21no—
279#451—21no—
280#451—21no—
281C4×Q16C22×C2911yescharacteristic
282C4×Q16C22×C2911yescharacteristic
283C8×D4C22×C2911yescharacteristic
284#427C22×C2911yescharacteristic
285C2×#107C22×C2911yescharacteristic
286#367C22×C2911yescharacteristic
287#367C22×C2911yescharacteristic
288#366C22×C2911yescharacteristic
289C4⋊C16C22×C2911yescharacteristic
290#358C22×C2911yescharacteristic
291#358C22×C2911yescharacteristic
292#358C22×C2911yescharacteristic
293#358C22×C2911yescharacteristic
294#358C22×C2911yescharacteristic
295#358C22×C2911yescharacteristic
296#358C22×C2911yescharacteristic
297#358C22×C2911yescharacteristic
298#358C22×C2911yescharacteristic
299#358C22×C2911yescharacteristic
300C22⋊C16C22×C2911yescharacteristic
301C22⋊C16C22×C2911yescharacteristic
302#346C22×C2911yescharacteristic
303C2×C29—22no—
304C2×C29—41no—
305C2×C29#329411yescharacteristic
306C2×C29C2×#51011yescharacteristic
307C2×C29#341711yescharacteristic
308C22×Q8—21no—
309C22×Q8—21no—
310C2×Q16—22no—
311C2×Q16—22no—
312C2×Q16—21no—
313C2×Q16—21no—
314C2×Q16—21no—
315C2×Q16—41no—
316C2×Q16—41no—
317C2×Q16C23×C2911yescharacteristic
318C2×Q16C23×C2911yescharacteristic
319C2×Q16C23×C2911yescharacteristic
320C2×Q16C23×C2911yescharacteristic
321C22×C8C23×C2911yescharacteristic
322C22×C8C23×C2911yescharacteristic
323C4⋊Q8—21no—
324C4⋊Q8—41no—
325#126—41no—
326#125—21no—
327#125—41no—
328#123—41no—
329C22⋊Q8—21no—
330C22⋊Q8—21no—
331C22⋊Q8—21no—
332C22⋊Q8—21no—
333C22⋊Q8—41no—
334C22⋊Q8—41no—
335C4×Q8—21no—
336C4×Q8—21no—
337C4×D4—41no—
338C4×D4D4×C2911yescharacteristic
339#117—21no—
340#117—41no—
341C2×C4⋊C4—21no—
342Q32—22no—
343Q32—41no—
344Q32—41no—
345M32—41no—
346C2×C16—41no—
347C2×C16C23×C2911yescharacteristic
348C2×C16C23×C2911yescharacteristic
349C2×C16C23×C2911yescharacteristic
350C2×C16C23×C2911yescharacteristic
351#107—21no—
352#107C23×C2911yescharacteristic
353#107C23×C2911yescharacteristic
354#107C23×C2911yescharacteristic
355#107C23×C2911yescharacteristic
356#106—21no—
357#106—21no—
358C4⋊C8D4×C2911yescharacteristic
359#103—21no—
360#103—21no—
361#103—21no—
362#103—21no—
363#103—21no—
364#103—21no—
365C22⋊C8D4×C2911yescharacteristic
366C22⋊C8D4×C2911yescharacteristic
367C4×C8C23×C2911yescharacteristic
368C29#3387911yescharacteristic, direct product factor, Sylow
369C2×Q8—21no—
370C2×Q8—21no—
371C2×Q8—21no—
372C2×Q8—21no—
373C2×Q8—42no—
374C2×Q8—42no—
375C2×Q8—41no—
376C2×Q8—41no—
377C2×Q8—81no—
378C2×Q8—81no—
379C2×D4D8×C2911yescharacteristic
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4C2×D4×C2911yescharacteristic
384C22×C4C2×D4×C2911yescharacteristic
385Q16—21no—
386Q16—21no—
387Q16—21no—
388Q16—21no—
389Q16—21no—
390Q16—21no—
391Q16—21no—
392Q16—42no—
393Q16—42no—
394Q16—81no—
395Q16#41×C2912yes—
396C2×C8—21no—
397C2×C8—21no—
398C2×C8—21no—
399C2×C8—21no—
400C2×C8C2×D4×C2911yescharacteristic
401C2×C8C2×D4×C2911yescharacteristic
402C2×C8C2×D4×C2911yescharacteristic
403C2×C8C24×C2911yescharacteristic
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—41no—
409C4⋊C4—41no—
410C4⋊C4—41no—
411C4⋊C4—41no—
412C4⋊C4—41no—
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⋊C4D8×C2911yescharacteristic
426C22⋊C4D8×C2911yescharacteristic
427C42—41no—
428C42—41no—
429C42—41no—
430C42C2×D4×C2911yescharacteristic
431C16—21no—
432C16—21no—
433C16—21no—
434C16—21no—
435C23C2×D8×C2911yescharacteristic
436C23C2×D8×C2911yescharacteristic
437Q8—22no—
438Q8—41no—
439Q8—41no—
440Q8—41no—
441Q8—41no—
442Q8—41no—
443Q8—41no—
444Q8—41no—
445Q8—82no—
446Q8—82no—
447D4—22no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—82no—
461C2×C4—82no—
462C2×C4—82no—
463C2×C4C2×D8×C2911yescharacteristic
464C2×C4C2×D8×C2911yescharacteristic
465C2×C4C2×D8×C2911yescharacteristic
466C2×C4C2×D8×C2911yescharacteristic
467C2×C4C22×D4×C2911yescharacteristic
468C8—21no—
469C8—21no—
470C8—21no—
471C8C2×#41×C2911yescharacteristic
472C8C29×H(5,𝔽2)11yescharacteristic
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22C29×#51012yes—
479C22C22×D8×C2911yescharacteristic
480C4—21no—
481C4—21no—
482C4—21no—
483C4—21no—
484C4—42no—
485C4—81no—
486C4—81no—
487C4—81no—
488C4—81no—
489C4—81no—
490C4—81no—
491C4—81no—
492C4C29×#54611yescharacteristic
493C4C29×#57711yescharacteristic
494C2—22no—
495C2—41no—
496C2C29×#329411yescharacteristic
497C2C2×C29×#51011yescharacteristic
498C2C29×#341711yescharacteristic
subgroupG/H
center, socleC22×C29C22×D8
commutator, Frattini, cosocleC2×C8C24×C29
prime radicalC2×D4×C29D8
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
3. C29×#2245C2semidirect
4. C29×#2237C2semidirect
5. C29×#2235C2semidirect
6. C29×#2229C2semidirect
7. C29×#2219C2semidirect
8. C29×#2216C2semidirect
9. C29×#2209C2semidirect
10. C29×#2188C2semidirect
11. C29×#2188C2semidirect
12. C29×#2176C2semidirect
14. C29×#2141C2semidirect
15. C2×C29×#358C2semidirect
185. #33879C29direct (N × H)
226. #2245C2×C29semidirect
227. #2237C2×C29semidirect
228. #2235C2×C29semidirect
229. #2229C2×C29semidirect
230. #2219C2×C29semidirect
231. #2216C2×C29semidirect
232. #2209C2×C29semidirect
233. #2188C2×C29semidirect
234. #2188C2×C29semidirect
235. #2176C2×C29semidirect
237. #2141C2×C29semidirect
238. C2×#358C2×C29semidirect
368. C29#33879direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#33362
D4×Q16×C292
C29×#22452
C29×#22372
C29×#22352
C29×#22292
C29×#22192
C29×#22162
C29×#22092
C29×#21882
C29×#21762
C29×#21682
C29×#21412
C2×C29×#3582
#3387929