Finite Group Databasebeta

← C29×#10188 #20305088

Subgroups — C29×#10188 #20305088

Order 7424.

550 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3227C211yesmaximal, characteristic, complemented
2C2×C29×#474C211yesmaximal, characteristic, complemented
3C29×#3036C211yesmaximal, characteristic
4C29×#1548C211yesmaximal, characteristic, complemented
5C29×#1480C211yesmaximal, characteristic, complemented
6C29×#1460C211yesmaximal, characteristic, complemented
7C29×#1301C211yesmaximal, characteristic, complemented
8C2×C29×AGL(1,ℤ/8)—21no—
9C29×#532C2211yescharacteristic
10C2×C29×C4⋊Q8C2211yescharacteristic
11C2×C4×D4×C29C2211yescharacteristic
12C29×#498—21no—
13C29×#486—21no—
14C29×#481—22no—
15C29×#476—22no—
16C29×#474—22no—
17C29×#474—22no—
18C29×#463—22no—
19C29×#461—21no—
20C29×#459—21no—
21C29×#431C2211yescharacteristic
22C29×#431C2211yescharacteristic
23C2×C29×#107—21no—
24C29×#423C2211yescharacteristic
25C2×C29×C4⋊C8C2211yescharacteristic
26C29×#417—21no—
27C2×C29×#102—21no—
28C29×#333—22no—
29C29×D4⋊C8—22no—
30C29×#323—22no—
31C2×#41×C29—21no—
32C22×Q8×C29—21no—
33C22×D4×C29D411yescharacteristic
34C23×C4×C29—21no—
35C29×AGL(1,ℤ/8)—42no—
36C29×AGL(1,ℤ/8)—42no—
37C2×SD16×C29—22no—
38C2×D8×C29—22no—
39C2×M16×C29—21no—
40C22×C8×C29—21no—
41C29×C4⋊Q8—21no—
42C29×C4⋊Q8—21no—
43C29×C4⋊Q8—21no—
44C29×C4⋊Q8D411yescharacteristic
45C29×C4⋊Q8D412yes—
46C29×#127D411yescharacteristic
47C29×#124—21no—
48C29×#121—21no—
49C29×#121—21no—
50C4×D4×C29—21no—
51C4×D4×C29—21no—
52C4×D4×C29—21no—
53C4×D4×C29—21no—
54C4×D4×C29—21no—
55C4×D4×C29—21no—
56C2×C4⋊C4×C29—21no—
57C2×C4⋊C4×C29—21no—
58C2×C4⋊C4×C29D411yescharacteristic
59C2×C22⋊C4×C29—21no—
60C2×C42×C29C2311yescharacteristic
61C29×#107—24no—
62C29×#106—24no—
63C29×C4⋊C8—21no—
64C29×C4⋊C8—21no—
65C29×C4⋊C8—21no—
66C29×C4⋊C8—21no—
67C29×C4⋊C8D412yes—
68C29×C4⋊C8D412yes—
69C29×#103—22no—
70C29×#102—22no—
71C29×#102—24no—
72C29×#102—24no—
73C29×C22⋊C8—21no—
74C29×C22⋊C8D412yes—
75C4×C8×C29—21no—
76C4×C8×C29—21no—
77C24×C29—21no—
78#41×C29—41no—
79#41×C29—41no—
80#41×C29—41no—
81#41×C29—41no—
82C2×Q8×C29—21no—
83C2×Q8×C29—22no—
84C2×Q8×C29—41no—
85C2×Q8×C29—82no—
86C2×D4×C29—21no—
87C2×D4×C29—21no—
88C2×D4×C29—21no—
89C2×D4×C29—21no—
90C2×D4×C29—21no—
91C2×D4×C29—21no—
92C2×D4×C29—21no—
93C2×D4×C29—21no—
94C2×D4×C29—41no—
95C2×D4×C29SD1612yes—
96C22×C4×C29—21no—
97C22×C4×C29—41no—
98C22×C4×C29—41no—
99C22×C4×C29—41no—
100C22×C4×C29—41no—
101C22×C4×C29—82no—
102C22×C4×C29C2×D411yescharacteristic
103C22×C4×C29C2×D411yescharacteristic
104C22×C4×C29#4111yescharacteristic
105SD16×C29—44no—
106D8×C29—44no—
107M16×C29—41no—
108M16×C29—41no—
109C2×C8×C29—22no—
110C2×C8×C29—22no—
111C2×C8×C29—22no—
112C2×C8×C29—41no—
113C2×C8×C29—41no—
114C2×C8×C29—41no—
115C4⋊C4×C29—22no—
116C4⋊C4×C29—22no—
117C4⋊C4×C29—21no—
118C4⋊C4×C29—21no—
119C4⋊C4×C29—21no—
120C4⋊C4×C29—21no—
121C4⋊C4×C29—41no—
122C4⋊C4×C29—41no—
123C22⋊C4×C29—41no—
124C22⋊C4×C29—41no—
125C22⋊C4×C29—41no—
126C22⋊C4×C29—41no—
127C42×C29C2×D411yescharacteristic
128C42×C29C2×D411yescharacteristic
129C42×C29C2×D411yescharacteristic
130C42×C29C2×D411yescharacteristic
131#10188C2911yesmaximal, characteristic, direct product factor, Sylow
132C23×C29—22no—
133C23×C29—41no—
134C23×C29—41no—
135C23×C29—41no—
136C23×C29—81no—
137C23×C29—81no—
138C23×C29#12111yescharacteristic
139Q8×C29—41no—
140Q8×C29—41no—
141Q8×C29—82no—
142Q8×C29—82no—
143D4×C29—22no—
144D4×C29—22no—
145D4×C29—42no—
146D4×C29—41no—
147D4×C29—41no—
148D4×C29—41no—
149D4×C29—41no—
150D4×C29—42no—
151D4×C29—81no—
152D4×C29—81no—
153C2×C4×C29—22no—
154C2×C4×C29—41no—
155C2×C4×C29—41no—
156C2×C4×C29—41no—
157C2×C4×C29—42no—
158C2×C4×C29—82no—
159C2×C4×C29—82no—
160C2×C4×C29—81no—
161C2×C4×C29—81no—
162C2×C4×C29—82no—
163C2×C4×C29—81no—
164C2×C4×C29#12011yescharacteristic
165C2×C4×C29#12011yescharacteristic
166C2×C4×C29#12011yescharacteristic
167C2×C4×C29#12111yescharacteristic
168C2×C4×C29#12111yescharacteristic
169C2×C4×C29#12711yescharacteristic
170C2×C4×C29C2×SD1611yescharacteristic
171C2×C4×C29#13511yescharacteristic
172C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C29#13711yescharacteristic
174C8×C29—42no—
175C8×C29—42no—
176C8×C29—42no—
177C8×C29—81no—
178#3227C2×C2911yescharacteristic, complemented
179C2×#474C2×C2911yescharacteristic, complemented
180#3036C2×C2911yescharacteristic
181#1548C2×C2911yescharacteristic, complemented
182#1480C2×C2911yescharacteristic, complemented
183#1460C2×C2911yescharacteristic, complemented
184#1301C2×C2911yescharacteristic, complemented
185C22×C29—21no—
186C22×C29—21no—
187C22×C29—42no—
188C22×C29—82no—
189C22×C29—82no—
190C22×C29—81no—
191C22×C29—81no—
192C22×C29—81no—
193C22×C29—81no—
194C22×C29—81no—
195C22×C29#39211yescharacteristic
196C22×C29#46511yescharacteristic
197C22×C29#46811yescharacteristic
198C4×C29—21no—
199C4×C29—21no—
200C4×C29—21no—
201C4×C29—81no—
202C4×C29—81no—
203C4×C29—82no—
204C4×C29#44811yescharacteristic
205C4×C29#44911yescharacteristic
206C4×C29#45011yescharacteristic
207C4×C29#45211yescharacteristic
208C4×C29#47212yes—
209C2×AGL(1,ℤ/8)—21no—
210#532C22×C2911yescharacteristic
211C2×C4⋊Q8C22×C2911yescharacteristic
212C2×C4×D4C22×C2911yescharacteristic
213#498—21no—
214#486—21no—
215#481—22no—
216#476—22no—
217#474—22no—
218#474—22no—
219#463—22no—
220#461—21no—
221#459—21no—
222#431C22×C2911yescharacteristic
223#431C22×C2911yescharacteristic
224C2×#107—21no—
225#423C22×C2911yescharacteristic
226C2×C4⋊C8C22×C2911yescharacteristic
227#417—21no—
228C2×#102—21no—
229#333—22no—
230D4⋊C8—22no—
231#323—22no—
232C2×C29—21no—
233C2×C29—21no—
234C2×C29—82no—
235C2×C29—161no—
236C2×C29#200011yescharacteristic
237C2×C29#200911yescharacteristic
238C2×C29#201811yescharacteristic
239C2×#41—21no—
240C22×Q8—21no—
241C22×D4D4×C2911yescharacteristic
242C23×C4—21no—
243AGL(1,ℤ/8)—42no—
244AGL(1,ℤ/8)—42no—
245C2×SD16—22no—
246C2×D8—22no—
247C2×M16—21no—
248C22×C8—21no—
249C4⋊Q8—21no—
250C4⋊Q8—21no—
251C4⋊Q8—21no—
252C4⋊Q8D4×C2912yes—
253C4⋊Q8D4×C2911yescharacteristic
254#127D4×C2911yescharacteristic
255#124—21no—
256#121—21no—
257#121—21no—
258C4×D4—21no—
259C4×D4—21no—
260C4×D4—21no—
261C4×D4—21no—
262C4×D4—21no—
263C4×D4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4D4×C2911yescharacteristic
267C2×C22⋊C4—21no—
268C2×C42C23×C2911yescharacteristic
269#107—24no—
270#106—24no—
271C4⋊C8—21no—
272C4⋊C8—21no—
273C4⋊C8—21no—
274C4⋊C8—21no—
275C4⋊C8D4×C2912yes—
276C4⋊C8D4×C2912yes—
277#103—22no—
278#102—24no—
279#102—22no—
280#102—24no—
281C22⋊C8—21no—
282C22⋊C8D4×C2912yes—
283C4×C8—21no—
284C4×C8—21no—
285C29#1018811yescharacteristic, direct product factor, Sylow
286C24—21no—
287#41—41no—
288#41—41no—
289#41—41no—
290#41—41no—
291C2×Q8—21no—
292C2×Q8—22no—
293C2×Q8—41no—
294C2×Q8—82no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4—21no—
302C2×D4—21no—
303C2×D4—41no—
304C2×D4SD16×C2912yes—
305C22×C4—21no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—82no—
311C22×C4C2×D4×C2911yescharacteristic
312C22×C4C2×D4×C2911yescharacteristic
313C22×C4#41×C2911yescharacteristic
314SD16—44no—
315D8—44no—
316M16—41no—
317M16—41no—
318C2×C8—22no—
319C2×C8—22no—
320C2×C8—22no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—41no—
324C4⋊C4—21no—
325C4⋊C4—22no—
326C4⋊C4—22no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C42C2×D4×C2911yescharacteristic
337C42C2×D4×C2911yescharacteristic
338C42C2×D4×C2911yescharacteristic
339C42C2×D4×C2911yescharacteristic
340C23—22no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—81no—
345C23—81no—
346C23C29×#12111yescharacteristic
347Q8—41no—
348Q8—41no—
349Q8—82no—
350Q8—82no—
351D4—22no—
352D4—22no—
353D4—42no—
354D4—41no—
355D4—41no—
356D4—41no—
357D4—41no—
358D4—42no—
359D4—81no—
360D4—81no—
361C2×C4—22no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—82no—
367C2×C4—82no—
368C2×C4—81no—
369C2×C4—81no—
370C2×C4—82no—
371C2×C4—81no—
372C2×C4C29×#12011yescharacteristic
373C2×C4C29×#12011yescharacteristic
374C2×C4C29×#12011yescharacteristic
375C2×C4C29×#12111yescharacteristic
376C2×C4C29×#12111yescharacteristic
377C2×C4C29×#12711yescharacteristic
378C2×C4C2×SD16×C2911yescharacteristic
379C2×C4C29×#13511yescharacteristic
380C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
381C2×C4C29×#13711yescharacteristic
382C8—42no—
383C8—42no—
384C8—42no—
385C8—81no—
386C22—21no—
387C22—21no—
388C22—42no—
389C22—82no—
390C22—82no—
391C22—81no—
392C22—81no—
393C22—81no—
394C22—81no—
395C22—81no—
396C22C29×#39211yescharacteristic
397C22C29×#46511yescharacteristic
398C22C29×#46811yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—81no—
403C4—81no—
404C4—82no—
405C4C29×#44811yescharacteristic
406C4C29×#44911yescharacteristic
407C4C29×#45011yescharacteristic
408C4C29×#45211yescharacteristic
409C4C29×#47212yes—
410C2—21no—
411C2—21no—
412C2—82no—
413C2—161no—
414C2C29×#200011yescharacteristic
415C2C29×#200911yescharacteristic
416C2C29×#201811yescharacteristic
subgroupG/H
center, socleC22×C29#392
commutator, Frattini, cosocleC2×C42C23×C29
prime radicalC29×#3036C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#3227C2semidirect
2. C2×C29×#474C2semidirect
4. C29×#1548C2semidirect
5. C29×#1480C2semidirect
6. C29×#1460C2semidirect
7. C29×#1301C2semidirect
131. #10188C29direct (N × H)
178. #3227C2×C29semidirect
179. C2×#474C2×C29semidirect
181. #1548C2×C29semidirect
182. #1480C2×C29semidirect
183. #1460C2×C29semidirect
184. #1301C2×C29semidirect
285. C29#10188direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32272
C2×C29×#4742
C29×#30362
C29×#15482
C29×#14802
C29×#14602
C29×#13012
#1018829