Finite Group Databasebeta

← C29×#33916 #20328816

Subgroups — C29×#33916 #20328816

Order 7424.

464 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3342C211yesmaximal, characteristic
2C29×#3336C211yesmaximal, characteristic
3C29×#2255C211yesmaximal, characteristic, complemented
4C29×#2237C211yesmaximal, characteristic, complemented
5C29×#2237C211yesmaximal, characteristic, complemented
6C29×#2237C211yesmaximal, characteristic, complemented
7C29×#2236C211yesmaximal, characteristic, complemented
8C29×#2229C211yesmaximal, characteristic, complemented
9C29×#2227C211yesmaximal, characteristic, complemented
10C29×#2219C211yesmaximal, characteristic, complemented
11C29×#2216C211yesmaximal, characteristic, complemented
12C29×#2176C211yesmaximal, characteristic, complemented
13C29×#2168C211yesmaximal, characteristic
14C29×#2159C211yesmaximal, characteristic, complemented
15C29×#2158C211yesmaximal, characteristic, complemented
16C29×#556—21no—
17C29×#552—21no—
18C2×C29×Q32C2211yescharacteristic
19C2×C29×M32C2211yescharacteristic
20C22×C16×C29C2211yescharacteristic
21C29×#500C2211yescharacteristic
22C29×#499C2211yescharacteristic
23C29×#485—21no—
24C29×#485—21no—
25C29×#485—21no—
26C29×#483—21no—
27C29×#479—21no—
28C29×#475—21no—
29C29×#467C2211yescharacteristic
30C29×#467C2211yescharacteristic
31C29×#467C2211yescharacteristic
32C29×#467C2211yescharacteristic
33C4×Q16×C29C2211yescharacteristic
34C4×Q16×C29C2211yescharacteristic
35C8×D4×C29C2211yescharacteristic
36C29×#427C2211yescharacteristic
37C29×#427C2211yescharacteristic
38C29×#427C2211yescharacteristic
39C2×C29×#107C2211yescharacteristic
40C29×#367C2211yescharacteristic
41C29×#367C2211yescharacteristic
42C29×#367C2211yescharacteristic
43C29×#367C2211yescharacteristic
44C29×#366C2211yescharacteristic
45C29×#366C2211yescharacteristic
46C29×#366C2211yescharacteristic
47C29×#366C2211yescharacteristic
48C29×#366C2211yescharacteristic
49C29×C4⋊C16C2211yescharacteristic
50C29×#358C2211yescharacteristic
51C29×#358C2211yescharacteristic
52C29×#358C2211yescharacteristic
53C29×#358C2211yescharacteristic
54C29×#358C2211yescharacteristic
55C29×#358C2211yescharacteristic
56C29×C22⋊C16C2211yescharacteristic
57C29×C22⋊C16C2211yescharacteristic
58C29×#346C2211yescharacteristic
59C2×Q16×C29C2311yescharacteristic
60C2×Q16×C29C2311yescharacteristic
61C22×C8×C29C2311yescharacteristic
62C22×C8×C29C2311yescharacteristic
63C29×C4⋊Q8—21no—
64C29×#126—41no—
65C29×#126—41no—
66C29×#126—41no—
67C29×#125—21no—
68C29×#125—41no—
69C29×#124—41no—
70C29×#123—41no—
71C29×C22⋊Q8—21no—
72C29×C22⋊Q8—21no—
73C29×C22⋊Q8—21no—
74C29×C22⋊Q8—21no—
75C4×Q8×C29—21no—
76C4×Q8×C29—21no—
77C4×Q8×C29—41no—
78C4×D4×C29D411yescharacteristic
79C29×#117—21no—
80C29×#117—21no—
81C29×#117—21no—
82C29×#117—41no—
83C2×C4⋊C4×C29—21no—
84C29×Q32—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×#107C2311yescharacteristic
94C29×#107C2311yescharacteristic
95C29×#107C2311yescharacteristic
96C29×#107C2311yescharacteristic
97C29×#107C2311yescharacteristic
98C29×#107C2311yescharacteristic
99C29×#106—21no—
100C29×#106—21no—
101C29×#106—21no—
102C29×#106—21no—
103C29×C4⋊C8D411yescharacteristic
104C29×#103—21no—
105C29×#103—21no—
106C29×#103—21no—
107C29×#103—21no—
108C29×#103—21no—
109C29×#103—21no—
110C29×C22⋊C8D411yescharacteristic
111C29×C22⋊C8D411yescharacteristic
112C4×C8×C29C2311yescharacteristic
113C2×Q8×C29—21no—
114C2×Q8×C29—21no—
115C2×Q8×C29—41no—
116C2×D4×C29D811yescharacteristic
117C22×C4×C29—41no—
118C22×C4×C29C2×D411yescharacteristic
119C22×C4×C29C2×D411yescharacteristic
120Q16×C29—21no—
121Q16×C29—21no—
122Q16×C29—21no—
123Q16×C29—21no—
124C2×C8×C29—21no—
125C2×C8×C29—21no—
126C2×C8×C29—21no—
127C2×C8×C29—21no—
128C2×C8×C29C2×D411yescharacteristic
129C2×C8×C29C2×D411yescharacteristic
130C2×C8×C29C2×D411yescharacteristic
131C2×C8×C29C2411yescharacteristic
132C4⋊C4×C29—21no—
133C4⋊C4×C29—21no—
134C4⋊C4×C29—21no—
135C4⋊C4×C29—21no—
136C4⋊C4×C29—21no—
137C4⋊C4×C29—21no—
138C4⋊C4×C29—41no—
139C4⋊C4×C29—41no—
140C4⋊C4×C29—41no—
141C4⋊C4×C29—41no—
142C4⋊C4×C29—41no—
143C4⋊C4×C29—41no—
144C4⋊C4×C29—41no—
145C4⋊C4×C29—41no—
146C4⋊C4×C29—41no—
147C4⋊C4×C29—41no—
148C4⋊C4×C29D811yescharacteristic
149C22⋊C4×C29—41no—
150C22⋊C4×C29—41no—
151C22⋊C4×C29—41no—
152C22⋊C4×C29—41no—
153C22⋊C4×C29—41no—
154C22⋊C4×C29—41no—
155C22⋊C4×C29—41no—
156C22⋊C4×C29D811yescharacteristic
157C22⋊C4×C29D811yescharacteristic
158C42×C29—41no—
159C42×C29—41no—
160C42×C29—41no—
161C42×C29—41no—
162C42×C29—41no—
163C42×C29C2×D411yescharacteristic
164C16×C29—21no—
165C16×C29—21no—
166C16×C29—21no—
167C16×C29#4112yes—
168#33916C2911yesmaximal, characteristic, direct product factor, Sylow
169C23×C29C2×D811yescharacteristic
170C23×C29C2×D811yescharacteristic
171Q8×C29—41no—
172Q8×C29—41no—
173Q8×C29—41no—
174Q8×C29—41no—
175Q8×C29—82no—
176D4×C29—41no—
177C2×C4×C29—21no—
178C2×C4×C29—21no—
179C2×C4×C29—21no—
180C2×C4×C29—21no—
181C2×C4×C29—41no—
182C2×C4×C29—41no—
183C2×C4×C29—41no—
184C2×C4×C29—41no—
185C2×C4×C29—41no—
186C2×C4×C29—41no—
187C2×C4×C29—41no—
188C2×C4×C29—41no—
189C2×C4×C29—82no—
190C2×C4×C29C2×D811yescharacteristic
191C2×C4×C29C2×D811yescharacteristic
192C2×C4×C29C2×D811yescharacteristic
193C2×C4×C29C2×D811yescharacteristic
194C2×C4×C29C22×D411yescharacteristic
195C8×C29—21no—
196C8×C29—21no—
197C8×C29—21no—
198C8×C29C2×#4111yescharacteristic
199C8×C292−1+411yescharacteristic
200#3342C2×C2911yescharacteristic
201#3336C2×C2911yescharacteristic
202#2255C2×C2911yescharacteristic, complemented
203#2237C2×C2911yescharacteristic, complemented
204#2237C2×C2911yescharacteristic, complemented
205#2237C2×C2911yescharacteristic, complemented
206#2236C2×C2911yescharacteristic, complemented
207#2229C2×C2911yescharacteristic, complemented
208#2227C2×C2911yescharacteristic, complemented
209#2219C2×C2911yescharacteristic, complemented
210#2216C2×C2911yescharacteristic, complemented
211#2176C2×C2911yescharacteristic, complemented
212#2168C2×C2911yescharacteristic
213#2159C2×C2911yescharacteristic, complemented
214#2158C2×C2911yescharacteristic, complemented
215C22×C29—21no—
216C22×C29—21no—
217C22×C29—21no—
218C22×C29—21no—
219C22×C29—21no—
220C22×C29—21no—
221C22×C29C22×D811yescharacteristic
222C4×C29—21no—
223C4×C29—21no—
224C4×C29—21no—
225C4×C29—21no—
226C4×C29—81no—
227C4×C29—81no—
228C4×C29—81no—
229C4×C29—81no—
230C4×C29—81no—
231C4×C29—81no—
232C4×C29—81no—
233C4×C29—81no—
234C4×C29#54711yescharacteristic
235C4×C29#57811yescharacteristic
236#556—21no—
237#552—21no—
238C2×Q32C22×C2911yescharacteristic
239C2×M32C22×C2911yescharacteristic
240C22×C16C22×C2911yescharacteristic
241#500C22×C2911yescharacteristic
242#499C22×C2911yescharacteristic
243#485—21no—
244#485—21no—
245#485—21no—
246#483—21no—
247#479—21no—
248#475—21no—
249#467C22×C2911yescharacteristic
250#467C22×C2911yescharacteristic
251#467C22×C2911yescharacteristic
252#467C22×C2911yescharacteristic
253C4×Q16C22×C2911yescharacteristic
254C4×Q16C22×C2911yescharacteristic
255C8×D4C22×C2911yescharacteristic
256#427C22×C2911yescharacteristic
257#427C22×C2911yescharacteristic
258#427C22×C2911yescharacteristic
259C2×#107C22×C2911yescharacteristic
260#367C22×C2911yescharacteristic
261#367C22×C2911yescharacteristic
262#367C22×C2911yescharacteristic
263#367C22×C2911yescharacteristic
264#366C22×C2911yescharacteristic
265#366C22×C2911yescharacteristic
266#366C22×C2911yescharacteristic
267#366C22×C2911yescharacteristic
268#366C22×C2911yescharacteristic
269C4⋊C16C22×C2911yescharacteristic
270#358C22×C2911yescharacteristic
271#358C22×C2911yescharacteristic
272#358C22×C2911yescharacteristic
273#358C22×C2911yescharacteristic
274#358C22×C2911yescharacteristic
275#358C22×C2911yescharacteristic
276C22⋊C16C22×C2911yescharacteristic
277C22⋊C16C22×C2911yescharacteristic
278#346C22×C2911yescharacteristic
279C2×C29—41no—
280C2×C29—41no—
281C2×C29#333411yescharacteristic
282C2×C29#341411yescharacteristic
283C2×C29#341711yescharacteristic
284C2×Q16C23×C2911yescharacteristic
285C2×Q16C23×C2911yescharacteristic
286C22×C8C23×C2911yescharacteristic
287C22×C8C23×C2911yescharacteristic
288C4⋊Q8—21no—
289#126—41no—
290#126—41no—
291#126—41no—
292#125—21no—
293#125—41no—
294#124—41no—
295#123—41no—
296C22⋊Q8—21no—
297C22⋊Q8—21no—
298C22⋊Q8—21no—
299C22⋊Q8—21no—
300C4×Q8—21no—
301C4×Q8—21no—
302C4×Q8—41no—
303C4×D4D4×C2911yescharacteristic
304#117—21no—
305#117—21no—
306#117—21no—
307#117—41no—
308C2×C4⋊C4—21no—
309Q32—22no—
310M32—22no—
311C2×C16—22no—
312C2×C16C23×C2911yescharacteristic
313C2×C16C23×C2911yescharacteristic
314C2×C16C23×C2911yescharacteristic
315C2×C16C23×C2911yescharacteristic
316#107—21no—
317#107—21no—
318#107C23×C2911yescharacteristic
319#107C23×C2911yescharacteristic
320#107C23×C2911yescharacteristic
321#107C23×C2911yescharacteristic
322#107C23×C2911yescharacteristic
323#107C23×C2911yescharacteristic
324#106—21no—
325#106—21no—
326#106—21no—
327#106—21no—
328C4⋊C8D4×C2911yescharacteristic
329#103—21no—
330#103—21no—
331#103—21no—
332#103—21no—
333#103—21no—
334#103—21no—
335C22⋊C8D4×C2911yescharacteristic
336C22⋊C8D4×C2911yescharacteristic
337C4×C8C23×C2911yescharacteristic
338C29#3391611yescharacteristic, direct product factor, Sylow
339C2×Q8—21no—
340C2×Q8—21no—
341C2×Q8—41no—
342C2×D4D8×C2911yescharacteristic
343C22×C4—41no—
344C22×C4C2×D4×C2911yescharacteristic
345C22×C4C2×D4×C2911yescharacteristic
346Q16—21no—
347Q16—21no—
348Q16—21no—
349Q16—21no—
350C2×C8—21no—
351C2×C8—21no—
352C2×C8—21no—
353C2×C8—21no—
354C2×C8C2×D4×C2911yescharacteristic
355C2×C8C2×D4×C2911yescharacteristic
356C2×C8C2×D4×C2911yescharacteristic
357C2×C8C24×C2911yescharacteristic
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—41no—
365C4⋊C4—41no—
366C4⋊C4—41no—
367C4⋊C4—41no—
368C4⋊C4—41no—
369C4⋊C4—41no—
370C4⋊C4—41no—
371C4⋊C4—41no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4D8×C2911yescharacteristic
375C22⋊C4—41no—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C22⋊C4—41no—
379C22⋊C4—41no—
380C22⋊C4—41no—
381C22⋊C4—41no—
382C22⋊C4D8×C2911yescharacteristic
383C22⋊C4D8×C2911yescharacteristic
384C42—41no—
385C42—41no—
386C42—41no—
387C42—41no—
388C42—41no—
389C42C2×D4×C2911yescharacteristic
390C16—21no—
391C16—21no—
392C16—21no—
393C16#41×C2912yes—
394C23C2×D8×C2911yescharacteristic
395C23C2×D8×C2911yescharacteristic
396Q8—41no—
397Q8—41no—
398Q8—41no—
399Q8—41no—
400Q8—82no—
401D4—41no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—82no—
415C2×C4C2×D8×C2911yescharacteristic
416C2×C4C2×D8×C2911yescharacteristic
417C2×C4C2×D8×C2911yescharacteristic
418C2×C4C2×D8×C2911yescharacteristic
419C2×C4C22×D4×C2911yescharacteristic
420C8—21no—
421C8—21no—
422C8—21no—
423C8C2×#41×C2911yescharacteristic
424C8C29×2−1+411yescharacteristic
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22C22×D8×C2911yescharacteristic
432C4—21no—
433C4—21no—
434C4—21no—
435C4—21no—
436C4—81no—
437C4—81no—
438C4—81no—
439C4—81no—
440C4—81no—
441C4—81no—
442C4—81no—
443C4—81no—
444C4C29×#54711yescharacteristic
445C4C29×#57811yescharacteristic
446C2—41no—
447C2—41no—
448C2C29×#333411yescharacteristic
449C2C29×#341411yescharacteristic
450C2C29×#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×#2255C2semidirect
4. C29×#2237C2semidirect
5. C29×#2237C2semidirect
6. C29×#2237C2semidirect
7. C29×#2236C2semidirect
8. C29×#2229C2semidirect
9. C29×#2227C2semidirect
10. C29×#2219C2semidirect
11. C29×#2216C2semidirect
12. C29×#2176C2semidirect
14. C29×#2159C2semidirect
15. C29×#2158C2semidirect
168. #33916C29direct (N × H)
202. #2255C2×C29semidirect
203. #2237C2×C29semidirect
204. #2237C2×C29semidirect
205. #2237C2×C29semidirect
206. #2236C2×C29semidirect
207. #2229C2×C29semidirect
208. #2227C2×C29semidirect
209. #2219C2×C29semidirect
210. #2216C2×C29semidirect
211. #2176C2×C29semidirect
213. #2159C2×C29semidirect
214. #2158C2×C29semidirect
338. C29#33916direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#33422
C29×#33362
C29×#22552
C29×#22372
C29×#22362
C29×#22292
C29×#22272
C29×#22192
C29×#22162
C29×#21762
C29×#21682
C29×#21592
C29×#21582
#3391629