Finite Group Databasebeta

← C29×#9716 #20304616

Subgroups — C29×#9716 #20304616

Order 7424.

650 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#2850C211yesmaximal, characteristic
2C29×#1797C211yesmaximal, characteristic, complemented
3C2×C29×#328C212yesmaximal, complemented
4C2×C29×#327C212yesmaximal
5C29×#1434C211yesmaximal, characteristic, complemented
6C2×C29×#124C411yescharacteristic, complemented
7C2×C29×C22⋊Q8C2211yescharacteristic
8C2×C29×#121C2211yescharacteristic
9C22×C42×C29C2211yescharacteristic
10C2×C29×C4⋊C8—21no—
11C2×C29×C22⋊C8C2212yes—
12C29×#391C411yescharacteristic, complemented
13C29×#390C411yescharacteristic, complemented
14C29×#388—21no—
15C29×#388—21no—
16C29×#386—21no—
17C29×#386—21no—
18C29×#382C411yescharacteristic, complemented
19C2×C29×#95—21no—
20C2×C29×#95—21no—
21C2×C29×#95C2212yes—
22C29×#336—21no—
23C29×#328—24no—
24C29×#327—24no—
25C22×Q8×C29C2×C411yescharacteristic
26C22×D4×C29—21no—
27C22×D4×C29C2×C411yescharacteristic
28C23×C4×C29—22no—
29C23×C4×C29D411yescharacteristic
30C23×C4×C29D411yescharacteristic
31C23×C4×C29C2311yescharacteristic
32C22×C8×C29—22no—
33C29×#124—42no—
34C29×C22⋊Q8—22no—
35C29×C22⋊Q8—22no—
36C29×#121—22no—
37C29×#121—22no—
38C2×C4⋊C4×C29—21no—
39C2×C4⋊C4×C29C2×C411yescharacteristic
40C2×C4⋊C4×C29C2×C411yescharacteristic
41C2×C22⋊C4×C29—21no—
42C2×C22⋊C4×C29—21no—
43C2×C22⋊C4×C29—21no—
44C2×C22⋊C4×C29—21no—
45C2×C22⋊C4×C29—21no—
46C2×C22⋊C4×C29—21no—
47C2×C42×C29—42no—
48C2×C42×C29C2×C411yescharacteristic
49C2×C42×C29C2×C411yescharacteristic
50C2×C42×C29D411yescharacteristic
51C2×C42×C29D411yescharacteristic
52C29×C4⋊C8—42no—
53C29×C22⋊C8—22no—
54C29×C22⋊C8—22no—
55C29×#95—21no—
56C29×#95—21no—
57C29×#95—21no—
58C29×#95—21no—
59C29×#95—22no—
60C29×#95—42no—
61C29×#95—42no—
62C29×#95D414yes—
63C24×C29—21no—
64C24×C29C2×D411yescharacteristic
65C2×Q8×C29—22no—
66C2×Q8×C29—41no—
67C2×Q8×C29—41no—
68C2×D4×C29—22no—
69C2×D4×C29—41no—
70C2×D4×C29—41no—
71C2×D4×C29—42no—
72C2×D4×C29—42no—
73C2×D4×C29—41no—
74C2×D4×C29—41no—
75C22×C4×C29—22no—
76C22×C4×C29—21no—
77C22×C4×C29—21no—
78C22×C4×C29—22no—
79C22×C4×C29—21no—
80C22×C4×C29—21no—
81C22×C4×C29—21no—
82C22×C4×C29—24no—
83C22×C4×C29—41no—
84C22×C4×C29—41no—
85C22×C4×C29—41no—
86C22×C4×C29—41no—
87C22×C4×C29—41no—
88C22×C4×C29—42no—
89C22×C4×C29—42no—
90C22×C4×C29—42no—
91C22×C4×C29—42no—
92C22×C4×C29—42no—
93C22×C4×C29—42no—
94C22×C4×C29C22⋊C411yescharacteristic
95C22×C4×C29C22⋊C411yescharacteristic
96C22×C4×C29C22⋊C411yescharacteristic
97C22×C4×C29C22⋊C411yescharacteristic
98C22×C4×C29C22×C411yescharacteristic
99C22×C4×C29C2×D411yescharacteristic
100C22×C4×C29C2×D412yes—
101C22×C4×C29#4112yes—
102C2×C8×C29—42no—
103C2×C8×C29—42no—
104C2×C8×C29—42no—
105C4⋊C4×C29—22no—
106C4⋊C4×C29—22no—
107C4⋊C4×C29—41no—
108C4⋊C4×C29—41no—
109C22⋊C4×C29—42no—
110C22⋊C4×C29—42no—
111C22⋊C4×C29—42no—
112C22⋊C4×C29—42no—
113C22⋊C4×C29—42no—
114C22⋊C4×C29—41no—
115C22⋊C4×C29—41no—
116C42×C29—22no—
117C42×C29—22no—
118C42×C29—41no—
119C42×C29—41no—
120#9716C2911yesmaximal, characteristic, direct product factor, Sylow
121C23×C29—21no—
122C23×C29—21no—
123C23×C29—21no—
124C23×C29—21no—
125C23×C29—41no—
126C23×C29—41no—
127C23×C29—41no—
128C23×C29—41no—
129C23×C29—41no—
130C23×C29—41no—
131C23×C29—41no—
132C23×C29C2×C22⋊C411yescharacteristic
133C23×C29#12112yes—
134C23×C29#13512yes—
135C23×C29AGL(1,ℤ/8)11yescharacteristic
136C23×C29#13711yescharacteristic
137Q8×C29—82no—
138D4×C29—82no—
139D4×C29—82no—
140D4×C29—82no—
141C2×C4×C29—21no—
142C2×C4×C29—21no—
143C2×C4×C29—21no—
144C2×C4×C29—21no—
145C2×C4×C29—21no—
146C2×C4×C29—21no—
147C2×C4×C29—21no—
148C2×C4×C29—21no—
149C2×C4×C29—21no—
150C2×C4×C29—21no—
151C2×C4×C29—21no—
152C2×C4×C29—21no—
153C2×C4×C29—21no—
154C2×C4×C29—21no—
155C2×C4×C29—21no—
156C2×C4×C29—42no—
157C2×C4×C29—42no—
158C2×C4×C29—44no—
159C2×C4×C29—42no—
160C2×C4×C29—42no—
161C2×C4×C29—44no—
162C2×C4×C29—44no—
163C2×C4×C29—41no—
164C2×C4×C29—41no—
165C2×C4×C29—41no—
166C2×C4×C29—41no—
167C2×C4×C29—41no—
168C2×C4×C29—41no—
169C2×C4×C29—41no—
170C2×C4×C29—41no—
171C2×C4×C29—41no—
172C2×C4×C29—44no—
173C2×C4×C29—82no—
174C2×C4×C29—82no—
175C2×C4×C29—82no—
176C2×C4×C29—82no—
177C2×C4×C29#9912yes—
178C2×C4×C29C4×D412yes—
179C2×C4×C29#12411yescharacteristic
180C2×C4×C29#12711yescharacteristic
181C8×C29—82no—
182#2850C2×C2911yescharacteristic
183#1797C2×C2911yescharacteristic, complemented
184C2×#328C2×C2912yescomplemented
185C2×#327C2×C2912yes—
186#1434C2×C2911yescharacteristic, complemented
187C22×C29—22no—
188C22×C29—22no—
189C22×C29—21no—
190C22×C29—21no—
191C22×C29—21no—
192C22×C29—21no—
193C22×C29—22no—
194C22×C29—22no—
195C22×C29—81no—
196C22×C29—81no—
197C22×C29—81no—
198C22×C29—81no—
199C22×C29—81no—
200C22×C29—81no—
201C22×C29—81no—
202C22×C29#39011yescharacteristic
203C22×C29C2×#9911yescharacteristic
204C22×C29#41011yescharacteristic
205C22×C29#41611yescharacteristic
206C22×C29#41711yescharacteristic
207C22×C29#42111yescharacteristic
208C22×C29#42111yescharacteristic
209C22×C29#46312yes—
210C22×C29#46412yes—
211C4×C29—21no—
212C4×C29—22no—
213C4×C29—21no—
214C4×C29—22no—
215C4×C29—41no—
216C4×C29—41no—
217C4×C29—41no—
218C4×C29—84no—
219C4×C29—81no—
220C4×C29—81no—
221C4×C29—81no—
222C2×#124C4×C2911yescharacteristic, complemented
223C2×C22⋊Q8C22×C2911yescharacteristic
224C2×#121C22×C2911yescharacteristic
225C22×C42C22×C2911yescharacteristic
226C2×C4⋊C8—21no—
227C2×C22⋊C8C22×C2912yes—
228#391C4×C2911yescharacteristic, complemented
229#390C4×C2911yescharacteristic, complemented
230#388—21no—
231#388—21no—
232#386—21no—
233#386—21no—
234#382C4×C2911yescharacteristic, complemented
235C2×#95—21no—
236C2×#95—21no—
237C2×#95C22×C2912yes—
238#336—21no—
239#328—24no—
240#327—24no—
241C2×C29—22no—
242C2×C29—22no—
243C2×C29—161no—
244C2×C29#151211yescharacteristic
245C2×C29#151311yescharacteristic
246C2×C29#151611yescharacteristic
247C2×C29#152111yescharacteristic
248C2×C29#196311yescharacteristic
249C2×C29#196411yescharacteristic
250C2×C29#198311yescharacteristic
251C22×Q8C2×C4×C2911yescharacteristic
252C22×D4—21no—
253C22×D4C2×C4×C2911yescharacteristic
254C23×C4—22no—
255C23×C4D4×C2911yescharacteristic
256C23×C4D4×C2911yescharacteristic
257C23×C4C23×C2911yescharacteristic
258C22×C8—22no—
259#124—42no—
260C22⋊Q8—22no—
261C22⋊Q8—22no—
262#121—22no—
263#121—22no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4C2×C4×C2911yescharacteristic
266C2×C4⋊C4C2×C4×C2911yescharacteristic
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—21no—
273C2×C42—42no—
274C2×C42C2×C4×C2911yescharacteristic
275C2×C42C2×C4×C2911yescharacteristic
276C2×C42D4×C2911yescharacteristic
277C2×C42D4×C2911yescharacteristic
278C4⋊C8—42no—
279C22⋊C8—22no—
280C22⋊C8—22no—
281#95—21no—
282#95—21no—
283#95—21no—
284#95—21no—
285#95—22no—
286#95—42no—
287#95—42no—
288#95D4×C2914yes—
289C29#971611yescharacteristic, direct product factor, Sylow
290C24—21no—
291C24C2×D4×C2911yescharacteristic
292C2×Q8—22no—
293C2×Q8—41no—
294C2×Q8—41no—
295C2×D4—22no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—42no—
299C2×D4—42no—
300C2×D4—41no—
301C2×D4—41no—
302C22×C4—22no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—22no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—24no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—42no—
316C22×C4—42no—
317C22×C4—42no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4C22⋊C4×C2911yescharacteristic
322C22×C4C22⋊C4×C2911yescharacteristic
323C22×C4C22⋊C4×C2911yescharacteristic
324C22×C4C22⋊C4×C2911yescharacteristic
325C22×C4C22×C4×C2911yescharacteristic
326C22×C4C2×D4×C2911yescharacteristic
327C22×C4C2×D4×C2912yes—
328C22×C4#41×C2912yes—
329C2×C8—42no—
330C2×C8—42no—
331C2×C8—42no—
332C4⋊C4—22no—
333C4⋊C4—22no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C22⋊C4—42no—
337C22⋊C4—42no—
338C22⋊C4—42no—
339C22⋊C4—42no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C22⋊C4—42no—
343C42—22no—
344C42—22no—
345C42—41no—
346C42—41no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—21no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23C2×C22⋊C4×C2911yescharacteristic
359C23C29×#12112yes—
360C23C29×#13512yes—
361C23C29×AGL(1,ℤ/8)11yescharacteristic
362C23C29×#13711yescharacteristic
363Q8—82no—
364D4—82no—
365D4—82no—
366D4—82no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—44no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—44no—
388C2×C4—44no—
389C2×C4—44no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—82no—
400C2×C4—82no—
401C2×C4—82no—
402C2×C4—82no—
403C2×C4C29×#9912yes—
404C2×C4C4×D4×C2912yes—
405C2×C4C29×#12411yescharacteristic
406C2×C4C29×#12711yescharacteristic
407C8—82no—
408C22—22no—
409C22—22no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—22no—
415C22—22no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22—81no—
422C22—81no—
423C22C29×#39011yescharacteristic
424C22C2×C29×#9911yescharacteristic
425C22C29×#41011yescharacteristic
426C22C29×#41611yescharacteristic
427C22C29×#41711yescharacteristic
428C22C29×#42111yescharacteristic
429C22C29×#42111yescharacteristic
430C22C29×#46312yes—
431C22C29×#46412yes—
432C4—21no—
433C4—22no—
434C4—21no—
435C4—22no—
436C4—41no—
437C4—41no—
438C4—41no—
439C4—84no—
440C4—81no—
441C4—81no—
442C4—81no—
443C2—22no—
444C2—22no—
445C2—161no—
446C2C29×#151211yescharacteristic
447C2C29×#151311yescharacteristic
448C2C29×#151611yescharacteristic
449C2C29×#152111yescharacteristic
450C2C29×#196311yescharacteristic
451C2C29×#196411yescharacteristic
452C2C29×#198311yescharacteristic
subgroupG/H
center, socleC23×C29C2×C22⋊C4
commutatorC22×C4C22×C4×C29
Frattini, cosocleC23×C4C23×C29
prime radicalC2×C29×#121C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C29 ◁ C22×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#1797C2semidirect
3. C2×C29×#328C2semidirect
5. C29×#1434C2semidirect
6. C2×C29×#124C4semidirect
12. C29×#391C4semidirect
13. C29×#390C4semidirect
18. C29×#382C4semidirect
120. #9716C29direct (N × H)
183. #1797C2×C29semidirect
184. C2×#328C2×C29semidirect
186. #1434C2×C29semidirect
222. C2×#124C4×C29semidirect
228. #391C4×C29semidirect
229. #390C4×C29semidirect
234. #382C4×C29semidirect
289. C29#9716direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#28502
C29×#17972
C2×C29×#3282
C2×C29×#3272
C29×#14342
#971629