Finite Group Databasebeta

← C29×#33913 #20328813

Subgroups — C29×#33913 #20328813

Order 7424.

484 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3339C211yesmaximal, characteristic
2C29×#3338C211yesmaximal, characteristic, complemented
3C29×#2255C211yesmaximal, characteristic, complemented
4C29×#2237C211yesmaximal, characteristic, complemented
5C29×#2236C211yesmaximal, characteristic, complemented
6C29×#2233C211yesmaximal, characteristic, complemented
7C29×#2232C211yesmaximal, characteristic, complemented
8C29×#2229C211yesmaximal, characteristic, complemented
9C29×#2224C211yesmaximal, characteristic, complemented
10C29×#2220C211yesmaximal, characteristic, complemented
11C29×#2217C211yesmaximal, characteristic, complemented
12C29×#2175C211yesmaximal, characteristic, complemented
13C29×#2168C211yesmaximal, characteristic, complemented
14C29×#2159C211yesmaximal, characteristic, complemented
15C2×C29×#366C211yesmaximal, characteristic, complemented
16C29×#554—21no—
17C29×#553—21no—
18C2×C29×SD32C2211yescharacteristic
19C2×C29×M32C2211yescharacteristic
20C22×C16×C29C2211yescharacteristic
21C29×#500C2211yescharacteristic
22C29×#499C2211yescharacteristic
23C29×#484—21no—
24C29×#484—21no—
25C29×#482—21no—
26C29×#481—21no—
27C29×#478—21no—
28C29×#477—21no—
29C29×#467C2211yescharacteristic
30C29×#467C2211yescharacteristic
31C29×#466C2211yescharacteristic
32C29×#466C2211yescharacteristic
33C4×Q16×C29C2211yescharacteristic
34C4×D8×C29C2211yescharacteristic
35C8×D4×C29C2211yescharacteristic
36C29×#427C2211yescharacteristic
37C2×C29×#107C2211yescharacteristic
38C2×C29×#107C2211yescharacteristic
39C2×C29×#107C2211yescharacteristic
40C29×#367C2211yescharacteristic
41C29×#367C2211yescharacteristic
42C29×#367C2211yescharacteristic
43C29×#366C2211yescharacteristic
44C29×#366C2211yescharacteristic
45C29×#366C2211yescharacteristic
46C29×#366C2211yescharacteristic
47C29×#366C2211yescharacteristic
48C29×#366C2211yescharacteristic
49C29×C4⋊C16C2211yescharacteristic
50C29×#358C2211yescharacteristic
51C29×#358C2211yescharacteristic
52C29×#358C2211yescharacteristic
53C29×#357C2211yescharacteristic
54C29×#357C2211yescharacteristic
55C29×#357C2211yescharacteristic
56C29×C22⋊C16C2211yescharacteristic
57C29×C22⋊C16C2211yescharacteristic
58C29×#346C2211yescharacteristic
59C2×Q16×C29C2311yescharacteristic
60C2×D8×C29C2311yescharacteristic
61C22×C8×C29C2311yescharacteristic
62C22×C8×C29C2311yescharacteristic
63C29×C4⋊Q8—21no—
64C29×#126—41no—
65C29×#125—21no—
66C29×#125—41no—
67C29×#123—41no—
68C29×C22⋊Q8—21no—
69C29×C22⋊Q8—21no—
70C29×C22⋊Q8—41no—
71C29×C22⋊Q8—41no—
72C29×#121—21no—
73C29×#121—21no—
74C29×#121—41no—
75C4×Q8×C29—21no—
76C4×D4×C29—21no—
77C4×D4×C29—41no—
78C4×D4×C29—41no—
79C4×D4×C29D411yescharacteristic
80C29×#117—21no—
81C2×C4⋊C4×C29—21no—
82C2×C4⋊C4×C29—21no—
83C2×C4⋊C4×C29—21no—
84C29×SD32—22no—
85C29×M32—22no—
86C2×C16×C29—22no—
87C2×C16×C29C2311yescharacteristic
88C2×C16×C29C2311yescharacteristic
89C2×C16×C29C2311yescharacteristic
90C2×C16×C29C2311yescharacteristic
91C29×#107—21no—
92C29×#107—21no—
93C29×#107—21no—
94C29×#107—21no—
95C29×#107C2311yescharacteristic
96C29×#107C2311yescharacteristic
97C29×#107C2311yescharacteristic
98C29×#107C2311yescharacteristic
99C29×#107C2311yescharacteristic
100C29×#107C2311yescharacteristic
101C29×#106—21no—
102C29×#106—21no—
103C29×C4⋊C8D411yescharacteristic
104C29×#103—21no—
105C29×#103—21no—
106C29×#103—21no—
107C29×#102—21no—
108C29×#102—21no—
109C29×#102—21no—
110C29×C22⋊C8D411yescharacteristic
111C29×C22⋊C8D411yescharacteristic
112C4×C8×C29C2311yescharacteristic
113C2×Q8×C29—21no—
114C2×Q8×C29—41no—
115C2×D4×C29—21no—
116C2×D4×C29—41no—
117C2×D4×C29—41no—
118C2×D4×C29D811yescharacteristic
119C22×C4×C29—41no—
120C22×C4×C29—41no—
121C22×C4×C29—41no—
122C22×C4×C29—41no—
123C22×C4×C29C2×D411yescharacteristic
124C22×C4×C29C2×D411yescharacteristic
125Q16×C29—21no—
126Q16×C29—21no—
127D8×C29—21no—
128D8×C29—21no—
129C2×C8×C29—21no—
130C2×C8×C29—21no—
131C2×C8×C29—21no—
132C2×C8×C29—21no—
133C2×C8×C29C2×D411yescharacteristic
134C2×C8×C29C2×D411yescharacteristic
135C2×C8×C29C2×D411yescharacteristic
136C2×C8×C29C2411yescharacteristic
137C4⋊C4×C29—21no—
138C4⋊C4×C29—21no—
139C4⋊C4×C29—21no—
140C4⋊C4×C29—21no—
141C4⋊C4×C29—21no—
142C4⋊C4×C29—21no—
143C4⋊C4×C29—41no—
144C4⋊C4×C29—41no—
145C4⋊C4×C29—41no—
146C4⋊C4×C29—41no—
147C4⋊C4×C29—41no—
148C4⋊C4×C29—41no—
149C4⋊C4×C29—41no—
150C4⋊C4×C29—41no—
151C4⋊C4×C29—41no—
152C4⋊C4×C29D811yescharacteristic
153C22⋊C4×C29—41no—
154C22⋊C4×C29—41no—
155C22⋊C4×C29—41no—
156C22⋊C4×C29—41no—
157C22⋊C4×C29—41no—
158C22⋊C4×C29—41no—
159C22⋊C4×C29D811yescharacteristic
160C22⋊C4×C29D811yescharacteristic
161C42×C29—41no—
162C42×C29—41no—
163C42×C29C2×D411yescharacteristic
164C16×C29—21no—
165C16×C29—21no—
166C16×C29—21no—
167C16×C29#4112yes—
168#33913C2911yesmaximal, characteristic, direct product factor, Sylow
169C23×C29—41no—
170C23×C29C2×D811yescharacteristic
171C23×C29C2×D811yescharacteristic
172Q8×C29—41no—
173Q8×C29—41no—
174Q8×C29—161no—
175D4×C29—22no—
176D4×C29—41no—
177D4×C29—41no—
178D4×C29—82no—
179D4×C29—161no—
180C2×C4×C29—21no—
181C2×C4×C29—21no—
182C2×C4×C29—21no—
183C2×C4×C29—21no—
184C2×C4×C29—41no—
185C2×C4×C29—41no—
186C2×C4×C29—41no—
187C2×C4×C29—41no—
188C2×C4×C29—41no—
189C2×C4×C29—41no—
190C2×C4×C29—41no—
191C2×C4×C29—161no—
192C2×C4×C29—161no—
193C2×C4×C29—161no—
194C2×C4×C29—161no—
195C2×C4×C29C2×D811yescharacteristic
196C2×C4×C29C2×D811yescharacteristic
197C2×C4×C29C2×D811yescharacteristic
198C2×C4×C29C2×D811yescharacteristic
199C2×C4×C29C22×D411yescharacteristic
200C8×C29—21no—
201C8×C29—21no—
202C8×C29—21no—
203C8×C29C2×#4111yescharacteristic
204C8×C292−1+411yescharacteristic
205#3339C2×C2911yescharacteristic
206#3338C2×C2911yescharacteristic, complemented
207#2255C2×C2911yescharacteristic, complemented
208#2237C2×C2911yescharacteristic, complemented
209#2236C2×C2911yescharacteristic, complemented
210#2233C2×C2911yescharacteristic, complemented
211#2232C2×C2911yescharacteristic, complemented
212#2229C2×C2911yescharacteristic, complemented
213#2224C2×C2911yescharacteristic, complemented
214#2220C2×C2911yescharacteristic, complemented
215#2217C2×C2911yescharacteristic, complemented
216#2175C2×C2911yescharacteristic, complemented
217#2168C2×C2911yescharacteristic, complemented
218#2159C2×C2911yescharacteristic, complemented
219C2×#366C2×C2911yescharacteristic, complemented
220C22×C29—21no—
221C22×C29—21no—
222C22×C29—21no—
223C22×C29—21no—
224C22×C29—21no—
225C22×C29—81no—
226C22×C29—81no—
227C22×C29—81no—
228C22×C29#51012yes—
229C22×C29C22×D811yescharacteristic
230C4×C29—21no—
231C4×C29—21no—
232C4×C29—21no—
233C4×C29—21no—
234C4×C29—81no—
235C4×C29—81no—
236C4×C29—81no—
237C4×C29—81no—
238C4×C29—81no—
239C4×C29—81no—
240C4×C29—81no—
241C4×C29#54711yescharacteristic
242C4×C29#57811yescharacteristic
243#554—21no—
244#553—21no—
245C2×SD32C22×C2911yescharacteristic
246C2×M32C22×C2911yescharacteristic
247C22×C16C22×C2911yescharacteristic
248#500C22×C2911yescharacteristic
249#499C22×C2911yescharacteristic
250#484—21no—
251#484—21no—
252#482—21no—
253#481—21no—
254#478—21no—
255#477—21no—
256#467C22×C2911yescharacteristic
257#467C22×C2911yescharacteristic
258#466C22×C2911yescharacteristic
259#466C22×C2911yescharacteristic
260C4×Q16C22×C2911yescharacteristic
261C4×D8C22×C2911yescharacteristic
262C8×D4C22×C2911yescharacteristic
263#427C22×C2911yescharacteristic
264C2×#107C22×C2911yescharacteristic
265C2×#107C22×C2911yescharacteristic
266C2×#107C22×C2911yescharacteristic
267#367C22×C2911yescharacteristic
268#367C22×C2911yescharacteristic
269#367C22×C2911yescharacteristic
270#366C22×C2911yescharacteristic
271#366C22×C2911yescharacteristic
272#366C22×C2911yescharacteristic
273#366C22×C2911yescharacteristic
274#366C22×C2911yescharacteristic
275#366C22×C2911yescharacteristic
276C4⋊C16C22×C2911yescharacteristic
277#358C22×C2911yescharacteristic
278#358C22×C2911yescharacteristic
279#358C22×C2911yescharacteristic
280#357C22×C2911yescharacteristic
281#357C22×C2911yescharacteristic
282#357C22×C2911yescharacteristic
283C22⋊C16C22×C2911yescharacteristic
284C22⋊C16C22×C2911yescharacteristic
285#346C22×C2911yescharacteristic
286C2×C29—22no—
287C2×C29—41no—
288C2×C29—161no—
289C2×C29#333411yescharacteristic
290C2×C29C2×#51011yescharacteristic
291C2×C29#341511yescharacteristic
292C2×Q16C23×C2911yescharacteristic
293C2×D8C23×C2911yescharacteristic
294C22×C8C23×C2911yescharacteristic
295C22×C8C23×C2911yescharacteristic
296C4⋊Q8—21no—
297#126—41no—
298#125—21no—
299#125—41no—
300#123—41no—
301C22⋊Q8—21no—
302C22⋊Q8—21no—
303C22⋊Q8—41no—
304C22⋊Q8—41no—
305#121—21no—
306#121—21no—
307#121—41no—
308C4×Q8—21no—
309C4×D4—21no—
310C4×D4—41no—
311C4×D4—41no—
312C4×D4D4×C2911yescharacteristic
313#117—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317SD32—22no—
318M32—22no—
319C2×C16—22no—
320C2×C16C23×C2911yescharacteristic
321C2×C16C23×C2911yescharacteristic
322C2×C16C23×C2911yescharacteristic
323C2×C16C23×C2911yescharacteristic
324#107—21no—
325#107—21no—
326#107—21no—
327#107—21no—
328#107C23×C2911yescharacteristic
329#107C23×C2911yescharacteristic
330#107C23×C2911yescharacteristic
331#107C23×C2911yescharacteristic
332#107C23×C2911yescharacteristic
333#107C23×C2911yescharacteristic
334#106—21no—
335#106—21no—
336C4⋊C8D4×C2911yescharacteristic
337#103—21no—
338#103—21no—
339#103—21no—
340#102—21no—
341#102—21no—
342#102—21no—
343C22⋊C8D4×C2911yescharacteristic
344C22⋊C8D4×C2911yescharacteristic
345C4×C8C23×C2911yescharacteristic
346C29#3391311yescharacteristic, direct product factor, Sylow
347C2×Q8—21no—
348C2×Q8—41no—
349C2×D4—21no—
350C2×D4—41no—
351C2×D4—41no—
352C2×D4D8×C2911yescharacteristic
353C22×C4—41no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4C2×D4×C2911yescharacteristic
358C22×C4C2×D4×C2911yescharacteristic
359Q16—21no—
360Q16—21no—
361D8—21no—
362D8—21no—
363C2×C8—21no—
364C2×C8—21no—
365C2×C8—21no—
366C2×C8—21no—
367C2×C8C2×D4×C2911yescharacteristic
368C2×C8C2×D4×C2911yescharacteristic
369C2×C8C2×D4×C2911yescharacteristic
370C2×C8C24×C2911yescharacteristic
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—41no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4—41no—
382C4⋊C4—41no—
383C4⋊C4—41no—
384C4⋊C4—41no—
385C4⋊C4—41no—
386C4⋊C4D8×C2911yescharacteristic
387C22⋊C4—41no—
388C22⋊C4—41no—
389C22⋊C4—41no—
390C22⋊C4—41no—
391C22⋊C4—41no—
392C22⋊C4—41no—
393C22⋊C4D8×C2911yescharacteristic
394C22⋊C4D8×C2911yescharacteristic
395C42—41no—
396C42—41no—
397C42C2×D4×C2911yescharacteristic
398C16—21no—
399C16—21no—
400C16—21no—
401C16#41×C2912yes—
402C23—41no—
403C23C2×D8×C2911yescharacteristic
404C23C2×D8×C2911yescharacteristic
405Q8—41no—
406Q8—41no—
407Q8—161no—
408D4—22no—
409D4—41no—
410D4—41no—
411D4—82no—
412D4—161no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—161no—
425C2×C4—161no—
426C2×C4—161no—
427C2×C4—161no—
428C2×C4C2×D8×C2911yescharacteristic
429C2×C4C2×D8×C2911yescharacteristic
430C2×C4C2×D8×C2911yescharacteristic
431C2×C4C2×D8×C2911yescharacteristic
432C2×C4C22×D4×C2911yescharacteristic
433C8—21no—
434C8—21no—
435C8—21no—
436C8C2×#41×C2911yescharacteristic
437C8C29×2−1+411yescharacteristic
438C22—21no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—81no—
444C22—81no—
445C22—81no—
446C22C29×#51012yes—
447C22C22×D8×C2911yescharacteristic
448C4—21no—
449C4—21no—
450C4—21no—
451C4—21no—
452C4—81no—
453C4—81no—
454C4—81no—
455C4—81no—
456C4—81no—
457C4—81no—
458C4—81no—
459C4C29×#54711yescharacteristic
460C4C29×#57811yescharacteristic
461C2—22no—
462C2—41no—
463C2—161no—
464C2C29×#333411yescharacteristic
465C2C2×C29×#51011yescharacteristic
466C2C29×#341511yescharacteristic
subgroupG/H
center, socleC22×C29C22×D8
commutator, Frattini, cosocleC2×C8C24×C29
prime radicalC29×#3339C2
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
2. C29×#3338C2semidirect
3. C29×#2255C2semidirect
4. C29×#2237C2semidirect
5. C29×#2236C2semidirect
6. C29×#2233C2semidirect
7. C29×#2232C2semidirect
8. C29×#2229C2semidirect
9. C29×#2224C2semidirect
10. C29×#2220C2semidirect
11. C29×#2217C2semidirect
12. C29×#2175C2semidirect
13. C29×#2168C2semidirect
14. C29×#2159C2semidirect
15. C2×C29×#366C2semidirect
168. #33913C29direct (N × H)
206. #3338C2×C29semidirect
207. #2255C2×C29semidirect
208. #2237C2×C29semidirect
209. #2236C2×C29semidirect
210. #2233C2×C29semidirect
211. #2232C2×C29semidirect
212. #2229C2×C29semidirect
213. #2224C2×C29semidirect
214. #2220C2×C29semidirect
215. #2217C2×C29semidirect
216. #2175C2×C29semidirect
217. #2168C2×C29semidirect
218. #2159C2×C29semidirect
219. C2×#366C2×C29semidirect
346. C29#33913direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#33392
C29×#33382
C29×#22552
C29×#22372
C29×#22362
C29×#22332
C29×#22322
C29×#22292
C29×#22242
C29×#22202
C29×#22172
C29×#21752
C29×#21682
C29×#21592
C2×C29×#3662
#3391329