Finite Group Databasebeta

← C29×#34594 #20329494

Subgroups — C29×#34594 #20329494

Order 7424.

2362 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#529C212yesmaximal, complemented
2C29×#2664C214yesmaximal, complemented
3C29×#2662C214yesmaximal, complemented
4C29×#2659C211yesmaximal, characteristic, complemented
5C29×#2656C211yesmaximal, characteristic
6C29×#2639C212yesmaximal, complemented
7C29×#2618C214yesmaximal, complemented
8C29×#2396C214yesmaximal, complemented
9C29×#2392C214yesmaximal, complemented
10C4×C29×#121C214yesmaximal, complemented
11C2×C4×C4⋊C4×C29C211yesmaximal, characteristic, complemented
12C29×#529—216no—
13C2×C29×#126C2214yes—
14C2×C29×#125C2212yes—
15C2×C29×#124C2212yes—
16C2×C29×#123C2214yes—
17C2×C29×C22⋊Q8C2212yes—
18C2×C29×#121C2212yes—
19C2×C29×#121C2214yes—
20C2×C4×Q8×C29C2212yes—
21C2×C4×D4×C29C2214yes—
22C2×C4×D4×C29C2212yes—
23C2×C4×D4×C29C2214yes—
24C2×C29×#117C2214yes—
25C22×C4⋊C4×C29C2212yes—
26C22×C42×C29C2212yes—
27C22×C42×C29C2211yescharacteristic
28C29×#400C2214yes—
29C29×#399C2214yes—
30C29×#398C2218yes—
31C29×#398C2214yes—
32C29×#397C2214yes—
33C29×#396C2218yes—
34C29×#396C2218yes—
35C29×#395C2214yes—
36C29×#394C2218yes—
37C29×#394C2214yes—
38C29×#393C2214yes—
39C29×#392C2214yes—
40C29×#390C2214yes—
41C29×#389C2214yes—
42C29×#388C2218yes—
43C29×#386C2218yes—
44C29×#380C2214yes—
45C4×C4⋊C4×C29C2214yes—
46C4×C4⋊C4×C29C2214yes—
47C4×C4⋊C4×C29C2214yes—
48C4×C22⋊C4×C29C2218yes—
49C2×C29×#95C2211yescharacteristic
50C2×C29×#95C2211yescharacteristic
51C22×Q8×C29C2312yes—
52C22×D4×C29C2314yes—
53C22×D4×C29C2312yes—
54C22×D4×C29C2314yes—
55C23×C4×C29C2314yes—
56C23×C4×C29C2311yescharacteristic
57C23×C4×C29C2311yescharacteristic
58C23×C4×C29C2312yes—
59C23×C4×C29C2311yescharacteristic
60C23×C4×C29C2312yes—
61C29×#126—216no—
62C29×#125—28no—
63C29×#124—28no—
64C29×#123—216no—
65C29×C22⋊Q8—28no—
66C29×#121—28no—
67C29×#121—216no—
68C4×Q8×C29—28no—
69C4×D4×C29—216no—
70C4×D4×C29—28no—
71C4×D4×C29—48no—
72C29×#117—216no—
73C2×C4⋊C4×C29—28no—
74C2×C4⋊C4×C29C2318yes—
75C2×C4⋊C4×C29C2314yes—
76C2×C4⋊C4×C29C2314yes—
77C2×C4⋊C4×C29C2312yes—
78C2×C4⋊C4×C29C2314yes—
79C2×C4⋊C4×C29C2312yes—
80C2×C4⋊C4×C29C2314yes—
81C2×C4⋊C4×C29C2314yes—
82C2×C4⋊C4×C29C2314yes—
83C2×C4⋊C4×C29C2314yes—
84C2×C22⋊C4×C29C2314yes—
85C2×C22⋊C4×C29C2314yes—
86C2×C22⋊C4×C29C2314yes—
87C2×C22⋊C4×C29C2314yes—
88C2×C22⋊C4×C29C2314yes—
89C2×C22⋊C4×C29C2318yes—
90C2×C22⋊C4×C29C2318yes—
91C2×C22⋊C4×C29C2318yes—
92C2×C42×C29—44no—
93C2×C42×C29D418yescomplemented
94C2×C42×C29C2314yes—
95C2×C42×C29C2314yes—
96C2×C42×C29C2314yes—
97C2×C42×C29C2312yes—
98C2×C42×C29C2312yes—
99C29×#95C2314yes—
100C29×#95C2314yes—
101C29×#95C2318yes—
102C29×#95C2318yes—
103C29×#95C2318yes—
104C24×C29C2414yes—
105C24×C29C2411yescharacteristic
106C2×Q8×C29—24no—
107C2×Q8×C29—44no—
108C2×D4×C29—28no—
109C2×D4×C29—216no—
110C2×D4×C29—24no—
111C2×D4×C29—28no—
112C2×D4×C29—44no—
113C2×D4×C29—44no—
114C2×D4×C29—44no—
115C22×C4×C29—24no—
116C22×C4×C29—22no—
117C22×C4×C29—22no—
118C22×C4×C29—24no—
119C22×C4×C29—28no—
120C22×C4×C29—28no—
121C22×C4×C29—28no—
122C22×C4×C29—42no—
123C22×C4×C29—42no—
124C22×C4×C29—42no—
125C22×C4×C29—42no—
126C22×C4×C29—42no—
127C22×C4×C29C2×D414yes—
128C22×C4×C29C2×D414yes—
129C22×C4×C29C2×D414yes—
130C22×C4×C29#4118yes—
131C22×C4×C29C2414yes—
132C22×C4×C29C2414yes—
133C22×C4×C29C2414yes—
134C22×C4×C29C2414yes—
135C22×C4×C29C2411yescharacteristic
136C22×C4×C29C2412yes—
137C22×C4×C29C2412yes—
138C22×C4×C29C2414yes—
139C22×C4×C29C2411yescharacteristic
140C4⋊C4×C29—28no—
141C4⋊C4×C29—28no—
142C4⋊C4×C29—24no—
143C4⋊C4×C29—28no—
144C4⋊C4×C29—24no—
145C4⋊C4×C29—28no—
146C4⋊C4×C29—216no—
147C4⋊C4×C29—28no—
148C4⋊C4×C29—44no—
149C4⋊C4×C29—44no—
150C22⋊C4×C29—28no—
151C22⋊C4×C29—28no—
152C22⋊C4×C29—28no—
153C22⋊C4×C29—28no—
154C22⋊C4×C29—28no—
155C22⋊C4×C29—216no—
156C22⋊C4×C29—48no—
157C22⋊C4×C29—48no—
158C42×C29—28no—
159C42×C29—28no—
160C42×C29—44no—
161C42×C29C2×D418yes—
162C42×C29C2×D418yes—
163#34594C2911yesmaximal, characteristic, direct product factor, Sylow
164C23×C29—21no—
165C23×C29—21no—
166C23×C29—22no—
167C23×C29—24no—
168C23×C29—28no—
169C23×C29—24no—
170C23×C29—24no—
171C23×C29—28no—
172C23×C29C22×D412yes—
173C23×C29C2×#4114yes—
174C23×C29C2511yescharacteristic
175Q8×C29—48no—
176D4×C29—48no—
177D4×C29—416no—
178D4×C29—416no—
179C2×C4×C29—28no—
180C2×C4×C29—24no—
181C2×C4×C29—24no—
182C2×C4×C29—21no—
183C2×C4×C29—21no—
184C2×C4×C29—24no—
185C2×C4×C29—24no—
186C2×C4×C29—28no—
187C2×C4×C29—24no—
188C2×C4×C29—24no—
189C2×C4×C29—24no—
190C2×C4×C29—28no—
191C2×C4×C29—24no—
192C2×C4×C29—24no—
193C2×C4×C29—24no—
194C2×C4×C29—24no—
195C2×C4×C29—24no—
196C2×C4×C29—28no—
197C2×C4×C29—44no—
198C2×C4×C29—48no—
199C2×C4×C29—48no—
200C2×C4×C29—416no—
201C2×C4×C29C22×D414yes—
202C2×C4×C29C22×D412yes—
203C2×C4×C29C22×D414yes—
204C2×C4×C29C22×D412yes—
205C2×C4×C29C2×#4118yes—
206C2×C4×C29H(5,𝔽2)12yes—
207C2×C4×C292−1+412yes—
208C2×#529C2×C2912yescomplemented
209#2664C2×C2914yescomplemented
210#2662C2×C2914yescomplemented
211#2659C2×C2911yescharacteristic, complemented
212#2656C2×C2911yescharacteristic
213#2639C2×C2912yescomplemented
214#2618C2×C2914yescomplemented
215#2396C2×C2914yescomplemented
216#2392C2×C2914yescomplemented
217C4×#121C2×C2914yescomplemented
218C2×C4×C4⋊C4C2×C2911yescharacteristic, complemented
219C22×C29—22no—
220C22×C29—22no—
221C22×C29—24no—
222C22×C29—24no—
223C22×C29—44no—
224C22×C29—44no—
225C22×C29—44no—
226C22×C29—48no—
227C22×C29—48no—
228C22×C29#53214yes—
229C22×C29C23×D411yescharacteristic
230C22×C29C22×#4112yes—
231C22×C29C2×H(5,𝔽2)11yescharacteristic
232C22×C29C2×2−1+411yescharacteristic
233C22×C29#58512yes—
234C4×C29—24no—
235C4×C29—22no—
236C4×C29—24no—
237C4×C29—28no—
238C4×C29—44no—
239C4×C29—44no—
240C4×C29—44no—
241C4×C29—44no—
242C4×C29#53714yes—
243#529—216no—
244C2×#126C22×C2914yes—
245C2×#125C22×C2912yes—
246C2×#124C22×C2912yes—
247C2×#123C22×C2914yes—
248C2×C22⋊Q8C22×C2912yes—
249C2×#121C22×C2914yes—
250C2×#121C22×C2912yes—
251C2×C4×Q8C22×C2912yes—
252C2×C4×D4C22×C2912yes—
253C2×C4×D4C22×C2914yes—
254C2×C4×D4C22×C2914yes—
255C2×#117C22×C2914yes—
256C22×C4⋊C4C22×C2912yes—
257C22×C42C22×C2912yes—
258C22×C42C22×C2911yescharacteristic
259#400C22×C2914yes—
260#399C22×C2914yes—
261#398C22×C2918yes—
262#398C22×C2914yes—
263#397C22×C2914yes—
264#396C22×C2918yes—
265#396C22×C2918yes—
266#395C22×C2914yes—
267#394C22×C2918yes—
268#394C22×C2914yes—
269#393C22×C2914yes—
270#392C22×C2914yes—
271#390C22×C2914yes—
272#389C22×C2914yes—
273#388C22×C2918yes—
274#386C22×C2918yes—
275#380C22×C2914yes—
276C4×C4⋊C4C22×C2914yes—
277C4×C4⋊C4C22×C2914yes—
278C4×C4⋊C4C22×C2914yes—
279C4×C22⋊C4C22×C2918yes—
280C2×#95C22×C2911yescharacteristic
281C2×#95C22×C2911yescharacteristic
282C2×C29—24no—
283C2×C29—84no—
284C2×C29C2×#53211yescharacteristic
285C2×C29C2×#53711yescharacteristic
286C2×C29#344911yescharacteristic
287C2×C29#345912yes—
288C2×C29#346112yes—
289C22×Q8C23×C2912yes—
290C22×D4C23×C2914yes—
291C22×D4C23×C2912yes—
292C22×D4C23×C2914yes—
293C23×C4C23×C2914yes—
294C23×C4C23×C2911yescharacteristic
295C23×C4C23×C2911yescharacteristic
296C23×C4C23×C2912yes—
297C23×C4C23×C2911yescharacteristic
298C23×C4C23×C2912yes—
299#126—216no—
300#125—28no—
301#124—28no—
302#123—216no—
303C22⋊Q8—28no—
304#121—28no—
305#121—216no—
306C4×Q8—28no—
307C4×D4—216no—
308C4×D4—28no—
309C4×D4—48no—
310#117—216no—
311C2×C4⋊C4—28no—
312C2×C4⋊C4C23×C2918yes—
313C2×C4⋊C4C23×C2914yes—
314C2×C4⋊C4C23×C2914yes—
315C2×C4⋊C4C23×C2912yes—
316C2×C4⋊C4C23×C2914yes—
317C2×C4⋊C4C23×C2912yes—
318C2×C4⋊C4C23×C2914yes—
319C2×C4⋊C4C23×C2914yes—
320C2×C4⋊C4C23×C2914yes—
321C2×C4⋊C4C23×C2914yes—
322C2×C22⋊C4C23×C2914yes—
323C2×C22⋊C4C23×C2914yes—
324C2×C22⋊C4C23×C2914yes—
325C2×C22⋊C4C23×C2914yes—
326C2×C22⋊C4C23×C2914yes—
327C2×C22⋊C4C23×C2918yes—
328C2×C22⋊C4C23×C2918yes—
329C2×C22⋊C4C23×C2918yes—
330C2×C42—44no—
331C2×C42D4×C2918yescomplemented
332C2×C42C23×C2914yes—
333C2×C42C23×C2914yes—
334C2×C42C23×C2914yes—
335C2×C42C23×C2912yes—
336C2×C42C23×C2912yes—
337#95C23×C2914yes—
338#95C23×C2914yes—
339#95C23×C2918yes—
340#95C23×C2918yes—
341#95C23×C2918yes—
342C29#3459411yescharacteristic, direct product factor, Sylow
343C24C24×C2914yes—
344C24C24×C2911yescharacteristic
345C2×Q8—24no—
346C2×Q8—44no—
347C2×D4—28no—
348C2×D4—216no—
349C2×D4—24no—
350C2×D4—28no—
351C2×D4—44no—
352C2×D4—44no—
353C2×D4—44no—
354C22×C4—24no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—24no—
358C22×C4—28no—
359C22×C4—28no—
360C22×C4—28no—
361C22×C4—42no—
362C22×C4—42no—
363C22×C4—42no—
364C22×C4—42no—
365C22×C4—42no—
366C22×C4C2×D4×C2914yes—
367C22×C4C2×D4×C2914yes—
368C22×C4C2×D4×C2914yes—
369C22×C4#41×C2918yes—
370C22×C4C24×C2914yes—
371C22×C4C24×C2914yes—
372C22×C4C24×C2914yes—
373C22×C4C24×C2914yes—
374C22×C4C24×C2912yes—
375C22×C4C24×C2911yescharacteristic
376C22×C4C24×C2912yes—
377C22×C4C24×C2914yes—
378C22×C4C24×C2911yescharacteristic
379C4⋊C4—28no—
380C4⋊C4—28no—
381C4⋊C4—24no—
382C4⋊C4—28no—
383C4⋊C4—24no—
384C4⋊C4—28no—
385C4⋊C4—216no—
386C4⋊C4—28no—
387C4⋊C4—44no—
388C4⋊C4—44no—
389C22⋊C4—28no—
390C22⋊C4—28no—
391C22⋊C4—28no—
392C22⋊C4—28no—
393C22⋊C4—28no—
394C22⋊C4—216no—
395C22⋊C4—48no—
396C22⋊C4—48no—
397C42—28no—
398C42—28no—
399C42—44no—
400C42C2×D4×C2918yes—
401C42C2×D4×C2918yes—
402C23—21no—
403C23—21no—
404C23—22no—
405C23—24no—
406C23—28no—
407C23—24no—
408C23—24no—
409C23—28no—
410C23C22×D4×C2912yes—
411C23C2×#41×C2914yes—
412C23C25×C2911yescharacteristic
413Q8—48no—
414D4—48no—
415D4—416no—
416D4—416no—
417C2×C4—28no—
418C2×C4—24no—
419C2×C4—24no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—24no—
423C2×C4—24no—
424C2×C4—28no—
425C2×C4—24no—
426C2×C4—24no—
427C2×C4—24no—
428C2×C4—28no—
429C2×C4—24no—
430C2×C4—24no—
431C2×C4—24no—
432C2×C4—24no—
433C2×C4—24no—
434C2×C4—28no—
435C2×C4—44no—
436C2×C4—48no—
437C2×C4—48no—
438C2×C4—416no—
439C2×C4C22×D4×C2914yes—
440C2×C4C22×D4×C2912yes—
441C2×C4C22×D4×C2914yes—
442C2×C4C22×D4×C2912yes—
443C2×C4C2×#41×C2918yes—
444C2×C4C29×H(5,𝔽2)12yes—
445C2×C4C29×2−1+412yes—
446C22—22no—
447C22—22no—
448C22—24no—
449C22—24no—
450C22—44no—
451C22—44no—
452C22—44no—
453C22—48no—
454C22—48no—
455C22C29×#53214yes—
456C22C23×D4×C2911yescharacteristic
457C22C22×#41×C2912yes—
458C22C2×C29×H(5,𝔽2)11yescharacteristic
459C22C2×C29×2−1+411yescharacteristic
460C22C29×#58512yes—
461C4—24no—
462C4—22no—
463C4—24no—
464C4—28no—
465C4—44no—
466C4—44no—
467C4—44no—
468C4—44no—
469C4C29×#53714yes—
470C2—24no—
471C2—84no—
472C2C2×C29×#53211yescharacteristic
473C2C2×C29×#53711yescharacteristic
474C2C29×#344911yescharacteristic
475C2C29×#345912yes—
476C2C29×#346112yes—
subgroupG/H
centerC22×C4×C29C24
commutator, Frattini, cosocleC23C25×C29
socleC23×C29C25
prime radicalC29×#2656C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C29×#529C2semidirect
2. C29×#2664C2semidirect
3. C29×#2662C2semidirect
4. C29×#2659C2semidirect
6. C29×#2639C2semidirect
7. C29×#2618C2semidirect
8. C29×#2396C2semidirect
9. C29×#2392C2semidirect
10. C4×C29×#121C2semidirect
11. C2×C4×C4⋊C4×C29C2semidirect
93. C2×C42×C29D4semidirect
163. #34594C29direct (N × H)
208. C2×#529C2×C29semidirect
209. #2664C2×C29semidirect
210. #2662C2×C29semidirect
211. #2659C2×C29semidirect
213. #2639C2×C29semidirect
214. #2618C2×C29semidirect
215. #2396C2×C29semidirect
216. #2392C2×C29semidirect
217. C4×#121C2×C29semidirect
218. C2×C4×C4⋊C4C2×C29semidirect
331. C2×C42D4×C29semidirect
342. C29#34594direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#5292
C29×#26642
C29×#26622
C29×#26592
C29×#26562
C29×#26392
C29×#26182
C29×#23962
C29×#23922
C4×C29×#1212
C2×C4×C4⋊C4×C292
#3459429