Finite Group Databasebeta

← C29×#33680 #20328580

Subgroups — C29×#33680 #20328580

Order 7424.

534 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3177C211yesmaximal, characteristic, complemented
2C29×#2951C211yesmaximal, characteristic
3C29×#2236C211yesmaximal, characteristic, complemented
4C29×#2235C211yesmaximal, characteristic, complemented
5C29×#2229C211yesmaximal, characteristic, complemented
6C29×#2228C211yesmaximal, characteristic, complemented
7C29×#2209C211yesmaximal, characteristic, complemented
8C29×#2208C211yesmaximal, characteristic, complemented
9C29×#2189C211yesmaximal, characteristic
10C29×#2189C211yesmaximal, characteristic
11C29×#2176C211yesmaximal, characteristic, complemented
12C29×#2175C211yesmaximal, characteristic, complemented
13C4×C29×Q32C211yesmaximal, characteristic, complemented
14C4×C29×SD32C211yesmaximal, characteristic, complemented
15C29×#2164C211yesmaximal, characteristic, complemented
16C2×C29×#135C2211yescharacteristic
17C29×#541—21no—
18C29×#520—21no—
19C2×C29×Q32C2211yescharacteristic
20C2×C29×Q32C2211yescharacteristic
21C2×C29×SD32C2211yescharacteristic
22C2×C29×SD32C2211yescharacteristic
23C29×#499C2211yescharacteristic
24C29×#494C2211yescharacteristic
25C29×#491—21no—
26C29×#470—21no—
27C29×#467C2211yescharacteristic
28C29×#467C2211yescharacteristic
29C29×#441—21no—
30C29×#440—21no—
31C29×#440—21no—
32C4×Q16×C29C2211yescharacteristic
33C4×Q16×C29C2211yescharacteristic
34C4×Q16×C29C2211yescharacteristic
35C4×Q16×C29C2211yescharacteristic
36C4×D8×C29C2211yescharacteristic
37C4×D8×C29C2211yescharacteristic
38C2×C29×#107C2211yescharacteristic
39C29×#417—21no—
40C29×#405C2211yescharacteristic
41C29×#367C2211yescharacteristic
42C29×#367C2211yescharacteristic
43C29×#366C2211yescharacteristic
44C29×#366C2211yescharacteristic
45C29×C4⋊C16C2211yescharacteristic
46C29×C4⋊C16C2211yescharacteristic
47C29×#358C2211yescharacteristic
48C29×#358C2211yescharacteristic
49C29×#358C2211yescharacteristic
50C29×#358C2211yescharacteristic
51C29×#358C2211yescharacteristic
52C29×#358C2211yescharacteristic
53C29×#357C2211yescharacteristic
54C29×#357C2211yescharacteristic
55C29×C22⋊C16C2211yescharacteristic
56C29×C22⋊C16C2211yescharacteristic
57C29×#346C2211yescharacteristic
58C4×C16×C29C2211yescharacteristic
59C2×#41×C29—21no—
60C29×#135—22no—
61C29×#135—22no—
62C2×Q16×C29—21no—
63C2×Q16×C29C2311yescharacteristic
64C2×Q16×C29C2311yescharacteristic
65C2×Q16×C29C2311yescharacteristic
66C2×SD16×C29—21no—
67C2×D8×C29C2311yescharacteristic
68C2×M16×C29D411yescharacteristic
69C22×C8×C29C2311yescharacteristic
70C29×C4⋊Q8—21no—
71C29×#126—41no—
72C29×#126—41no—
73C29×#125—21no—
74C29×#125—41no—
75C29×#125—41no—
76C29×C22⋊Q8—21no—
77C29×C22⋊Q8—21no—
78C4×Q8×C29—21no—
79C4×Q8×C29—21no—
80C4×Q8×C29—21no—
81C4×Q8×C29—21no—
82C4×D4×C29—21no—
83C4×D4×C29—21no—
84C4×D4×C29—41no—
85C4×D4×C29—41no—
86C29×#117—41no—
87C29×#117D411yescharacteristic
88C2×C4⋊C4×C29—21no—
89C2×C4⋊C4×C29—41no—
90C29×Q32—22no—
91C29×Q32—22no—
92C29×SD32—22no—
93C29×SD32—22no—
94C2×C16×C29C2311yescharacteristic
95C2×C16×C29C2311yescharacteristic
96C2×C16×C29C2311yescharacteristic
97C2×C16×C29C2311yescharacteristic
98C29×#107—21no—
99C29×#107C2311yescharacteristic
100C29×#107C2311yescharacteristic
101C29×#107C2311yescharacteristic
102C29×#107C2311yescharacteristic
103C29×#106—21no—
104C29×#103—21no—
105C29×#103—21no—
106C29×#103—21no—
107C29×#103—21no—
108C29×#103—21no—
109C29×#103—21no—
110C29×#102—21no—
111C29×#102—21no—
112C29×#97D411yescharacteristic
113C29×#97D411yescharacteristic
114C4×C8×C29C2311yescharacteristic
115C4×C8×C29C2311yescharacteristic
116#41×C29—24no—
117#41×C29—42no—
118C2×Q8×C29—21no—
119C2×Q8×C29—21no—
120C2×Q8×C29—21no—
121C2×D4×C29—21no—
122C2×D4×C29—41no—
123C22×C4×C29—41no—
124C22×C4×C29—41no—
125C22×C4×C29—41no—
126C22×C4×C29—41no—
127C22×C4×C29C2×D411yescharacteristic
128Q16×C29—21no—
129Q16×C29—21no—
130Q16×C29—21no—
131Q16×C29—21no—
132Q16×C29—21no—
133Q16×C29—42no—
134Q16×C29#4112yes—
135SD16×C29—24no—
136D8×C29—21no—
137D8×C29#4112yes—
138M16×C29—41no—
139C2×C8×C29—21no—
140C2×C8×C29—21no—
141C2×C8×C29C2×D411yescharacteristic
142C2×C8×C29C2×D411yescharacteristic
143C2×C8×C29C2×D411yescharacteristic
144C2×C8×C29C2411yescharacteristic
145C4⋊C4×C29—21no—
146C4⋊C4×C29—21no—
147C4⋊C4×C29—21no—
148C4⋊C4×C29—21no—
149C4⋊C4×C29—41no—
150C4⋊C4×C29—41no—
151C4⋊C4×C29—41no—
152C4⋊C4×C29—41no—
153C4⋊C4×C29—41no—
154C4⋊C4×C29—41no—
155C4⋊C4×C29—41no—
156C4⋊C4×C29—41no—
157C4⋊C4×C29—41no—
158C4⋊C4×C29—41no—
159C4⋊C4×C29—41no—
160C4⋊C4×C29D811yescharacteristic
161C4⋊C4×C29D811yescharacteristic
162C22⋊C4×C29—41no—
163C22⋊C4×C29—41no—
164C22⋊C4×C29—41no—
165C22⋊C4×C29—41no—
166C22⋊C4×C29D811yescharacteristic
167C22⋊C4×C29D811yescharacteristic
168C42×C29—41no—
169C42×C29—41no—
170C42×C29—41no—
171C42×C29—41no—
172C42×C29C2×D411yescharacteristic
173C42×C29C2×D411yescharacteristic
174C16×C29—21no—
175C16×C29—21no—
176C16×C29—21no—
177C16×C29—21no—
178#33680C2911yesmaximal, characteristic, direct product factor, Sylow
179C23×C29—41no—
180C23×C29C2×D811yescharacteristic
181Q8×C29—22no—
182Q8×C29—41no—
183Q8×C29—41no—
184Q8×C29—41no—
185Q8×C29—41no—
186Q8×C29—41no—
187D4×C29—22no—
188D4×C29—44no—
189D4×C29—41no—
190C2×C4×C29—21no—
191C2×C4×C29—21no—
192C2×C4×C29—44no—
193C2×C4×C29—41no—
194C2×C4×C29—41no—
195C2×C4×C29—41no—
196C2×C4×C29—41no—
197C2×C4×C29—41no—
198C2×C4×C29—41no—
199C2×C4×C29—41no—
200C2×C4×C29—161no—
201C2×C4×C29—161no—
202C2×C4×C29—161no—
203C2×C4×C29C2×D811yescharacteristic
204C2×C4×C29C2×D811yescharacteristic
205C2×C4×C29C2×D811yescharacteristic
206C2×C4×C29C2×D811yescharacteristic
207C2×C4×C29C2×D811yescharacteristic
208C2×C4×C29C22×D411yescharacteristic
209C8×C29—21no—
210C8×C29—21no—
211C8×C29—21no—
212C8×C29C2×#4111yescharacteristic
213C8×C29C2×#4111yescharacteristic
214#3177C2×C2911yescharacteristic, complemented
215#2951C2×C2911yescharacteristic
216#2236C2×C2911yescharacteristic, complemented
217#2235C2×C2911yescharacteristic, complemented
218#2229C2×C2911yescharacteristic, complemented
219#2228C2×C2911yescharacteristic, complemented
220#2209C2×C2911yescharacteristic, complemented
221#2208C2×C2911yescharacteristic, complemented
222#2189C2×C2911yescharacteristic
223#2189C2×C2911yescharacteristic
224#2176C2×C2911yescharacteristic, complemented
225#2175C2×C2911yescharacteristic, complemented
226C4×Q32C2×C2911yescharacteristic, complemented
227C4×SD32C2×C2911yescharacteristic, complemented
228#2164C2×C2911yescharacteristic, complemented
229C22×C29—21no—
230C22×C29—21no—
231C22×C29—21no—
232C22×C29—42no—
233C22×C29—81no—
234C22×C29—81no—
235C22×C29C22×D811yescharacteristic
236C4×C29—21no—
237C4×C29—21no—
238C4×C29—21no—
239C4×C29—21no—
240C4×C29—21no—
241C4×C29—42no—
242C4×C29—81no—
243C4×C29—81no—
244C4×C29—81no—
245C4×C29—81no—
246C4×C29—81no—
247C4×C29—81no—
248C4×C29#52511yescharacteristic
249C4×C29#57511yescharacteristic
250C2×#135C22×C2911yescharacteristic
251#541—21no—
252#520—21no—
253C2×Q32C22×C2911yescharacteristic
254C2×Q32C22×C2911yescharacteristic
255C2×SD32C22×C2911yescharacteristic
256C2×SD32C22×C2911yescharacteristic
257#499C22×C2911yescharacteristic
258#494C22×C2911yescharacteristic
259#491—21no—
260#470—21no—
261#467C22×C2911yescharacteristic
262#467C22×C2911yescharacteristic
263#441—21no—
264#440—21no—
265#440—21no—
266C4×Q16C22×C2911yescharacteristic
267C4×Q16C22×C2911yescharacteristic
268C4×Q16C22×C2911yescharacteristic
269C4×Q16C22×C2911yescharacteristic
270C4×D8C22×C2911yescharacteristic
271C4×D8C22×C2911yescharacteristic
272C2×#107C22×C2911yescharacteristic
273#417—21no—
274#405C22×C2911yescharacteristic
275#367C22×C2911yescharacteristic
276#367C22×C2911yescharacteristic
277#366C22×C2911yescharacteristic
278#366C22×C2911yescharacteristic
279C4⋊C16C22×C2911yescharacteristic
280C4⋊C16C22×C2911yescharacteristic
281#358C22×C2911yescharacteristic
282#358C22×C2911yescharacteristic
283#358C22×C2911yescharacteristic
284#358C22×C2911yescharacteristic
285#358C22×C2911yescharacteristic
286#358C22×C2911yescharacteristic
287#357C22×C2911yescharacteristic
288#357C22×C2911yescharacteristic
289C22⋊C16C22×C2911yescharacteristic
290C22⋊C16C22×C2911yescharacteristic
291#346C22×C2911yescharacteristic
292C4×C16C22×C2911yescharacteristic
293C2×C29—41no—
294C2×C29—82no—
295C2×C29#310011yescharacteristic
296C2×C29#341611yescharacteristic
297C2×C29#341711yescharacteristic
298C2×#41—21no—
299#135—22no—
300#135—22no—
301C2×Q16—21no—
302C2×Q16C23×C2911yescharacteristic
303C2×Q16C23×C2911yescharacteristic
304C2×Q16C23×C2911yescharacteristic
305C2×SD16—21no—
306C2×D8C23×C2911yescharacteristic
307C2×M16D4×C2911yescharacteristic
308C22×C8C23×C2911yescharacteristic
309C4⋊Q8—21no—
310#126—41no—
311#126—41no—
312#125—21no—
313#125—41no—
314#125—41no—
315C22⋊Q8—21no—
316C22⋊Q8—21no—
317C4×Q8—21no—
318C4×Q8—21no—
319C4×Q8—21no—
320C4×Q8—21no—
321C4×D4—21no—
322C4×D4—21no—
323C4×D4—41no—
324C4×D4—41no—
325#117—41no—
326#117D4×C2911yescharacteristic
327C2×C4⋊C4—21no—
328C2×C4⋊C4—41no—
329Q32—22no—
330Q32—22no—
331SD32—22no—
332SD32—22no—
333C2×C16C23×C2911yescharacteristic
334C2×C16C23×C2911yescharacteristic
335C2×C16C23×C2911yescharacteristic
336C2×C16C23×C2911yescharacteristic
337#107—21no—
338#107C23×C2911yescharacteristic
339#107C23×C2911yescharacteristic
340#107C23×C2911yescharacteristic
341#107C23×C2911yescharacteristic
342#106—21no—
343#103—21no—
344#103—21no—
345#103—21no—
346#103—21no—
347#103—21no—
348#103—21no—
349#102—21no—
350#102—21no—
351#97D4×C2911yescharacteristic
352#97D4×C2911yescharacteristic
353C4×C8C23×C2911yescharacteristic
354C4×C8C23×C2911yescharacteristic
355C29#3368011yescharacteristic, direct product factor, Sylow
356#41—24no—
357#41—42no—
358C2×Q8—21no—
359C2×Q8—21no—
360C2×Q8—21no—
361C2×D4—21no—
362C2×D4—41no—
363C22×C4—41no—
364C22×C4—41no—
365C22×C4—41no—
366C22×C4—41no—
367C22×C4C2×D4×C2911yescharacteristic
368Q16—21no—
369Q16—21no—
370Q16—21no—
371Q16—21no—
372Q16—21no—
373Q16—42no—
374Q16#41×C2912yes—
375SD16—24no—
376D8—21no—
377D8#41×C2912yes—
378M16—41no—
379C2×C8—21no—
380C2×C8—21no—
381C2×C8C2×D4×C2911yescharacteristic
382C2×C8C2×D4×C2911yescharacteristic
383C2×C8C2×D4×C2911yescharacteristic
384C2×C8C24×C2911yescharacteristic
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—41no—
390C4⋊C4—41no—
391C4⋊C4—41no—
392C4⋊C4—41no—
393C4⋊C4—41no—
394C4⋊C4—41no—
395C4⋊C4—41no—
396C4⋊C4—41no—
397C4⋊C4—41no—
398C4⋊C4—41no—
399C4⋊C4—41no—
400C4⋊C4D8×C2911yescharacteristic
401C4⋊C4D8×C2911yescharacteristic
402C22⋊C4—41no—
403C22⋊C4—41no—
404C22⋊C4—41no—
405C22⋊C4—41no—
406C22⋊C4D8×C2911yescharacteristic
407C22⋊C4D8×C2911yescharacteristic
408C42—41no—
409C42—41no—
410C42—41no—
411C42—41no—
412C42C2×D4×C2911yescharacteristic
413C42C2×D4×C2911yescharacteristic
414C16—21no—
415C16—21no—
416C16—21no—
417C16—21no—
418C23—41no—
419C23C2×D8×C2911yescharacteristic
420Q8—22no—
421Q8—41no—
422Q8—41no—
423Q8—41no—
424Q8—41no—
425Q8—41no—
426D4—22no—
427D4—44no—
428D4—41no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—44no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—161no—
440C2×C4—161no—
441C2×C4—161no—
442C2×C4C2×D8×C2911yescharacteristic
443C2×C4C2×D8×C2911yescharacteristic
444C2×C4C2×D8×C2911yescharacteristic
445C2×C4C2×D8×C2911yescharacteristic
446C2×C4C2×D8×C2911yescharacteristic
447C2×C4C22×D4×C2911yescharacteristic
448C8—21no—
449C8—21no—
450C8—21no—
451C8C2×#41×C2911yescharacteristic
452C8C2×#41×C2911yescharacteristic
453C22—21no—
454C22—21no—
455C22—21no—
456C22—42no—
457C22—81no—
458C22—81no—
459C22C22×D8×C2911yescharacteristic
460C4—21no—
461C4—21no—
462C4—21no—
463C4—21no—
464C4—21no—
465C4—42no—
466C4—81no—
467C4—81no—
468C4—81no—
469C4—81no—
470C4—81no—
471C4—81no—
472C4C29×#52511yescharacteristic
473C4C29×#57511yescharacteristic
474C2—41no—
475C2—82no—
476C2C29×#310011yescharacteristic
477C2C29×#341611yescharacteristic
478C2C29×#341711yescharacteristic
subgroupG/H
center, socleC22×C29C22×D8
commutator, Frattini, cosocleC2×C8C24×C29
prime radicalC2×C29×#135C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C29×#117 ◁ C29×#405 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#3177C2semidirect
3. C29×#2236C2semidirect
4. C29×#2235C2semidirect
5. C29×#2229C2semidirect
6. C29×#2228C2semidirect
7. C29×#2209C2semidirect
8. C29×#2208C2semidirect
11. C29×#2176C2semidirect
12. C29×#2175C2semidirect
13. C4×C29×Q32C2semidirect
14. C4×C29×SD32C2semidirect
15. C29×#2164C2semidirect
178. #33680C29direct (N × H)
214. #3177C2×C29semidirect
216. #2236C2×C29semidirect
217. #2235C2×C29semidirect
218. #2229C2×C29semidirect
219. #2228C2×C29semidirect
220. #2209C2×C29semidirect
221. #2208C2×C29semidirect
224. #2176C2×C29semidirect
225. #2175C2×C29semidirect
226. C4×Q32C2×C29semidirect
227. C4×SD32C2×C29semidirect
228. #2164C2×C29semidirect
355. C29#33680direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#31772
C29×#29512
C29×#22362
C29×#22352
C29×#22292
C29×#22282
C29×#22092
C29×#22082
C29×#21892
C29×#21762
C29×#21752
C4×C29×Q322
C4×C29×SD322
C29×#21642
#3368029