Finite Group Databasebeta

← C29×#10194 #20305094

Subgroups — C29×#10194 #20305094

Order 7424.

640 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3246C211yesmaximal, characteristic, complemented
2C29×#3208C211yesmaximal, characteristic, complemented
3C29×#3151C211yesmaximal, characteristic
4C29×#1986C211yesmaximal, characteristic, complemented
5C29×#1982C211yesmaximal, characteristic, complemented
6C29×#1502C211yesmaximal, characteristic, complemented
7C29×#1283C211yesmaximal, characteristic, complemented
8C2×C29×AGL(1,ℤ/8)—22no—
9C29×#533C2211yescharacteristic
10C29×#532C2211yescharacteristic
11C2×C29×#127C2211yescharacteristic
12C29×#496—22no—
13C29×#493—21no—
14C29×#492—21no—
15C29×#492—21no—
16C29×#486—21no—
17C29×#476—21no—
18C29×#475—21no—
19C29×#465—22no—
20C29×#461—21no—
21C29×#460—22no—
22C29×#460—21no—
23C29×#450—22no—
24C29×#431C2211yescharacteristic
25C2×C29×C4⋊C8C2211yescharacteristic
26C2×C29×#102—22no—
27C4×M16×C29C2211yescharacteristic
28C4×C4⋊C4×C29C2211yescharacteristic
29C29×#339—22no—
30C29×#327—22no—
31C2×#41×C29—21no—
32C22×D4×C29—21no—
33C22×D4×C29—21no—
34C22×D4×C29—21no—
35C29×AGL(1,ℤ/8)—44no—
36C29×AGL(1,ℤ/8)—44no—
37C2×SD16×C29—24no—
38C2×SD16×C29—24no—
39C2×SD16×C29—22no—
40C2×D8×C29—24no—
41C2×M16×C29D412yes—
42C22×C8×C29D412yes—
43C29×C4⋊Q8D411yescharacteristic
44C29×C4⋊Q8D411yescharacteristic
45C29×C4⋊Q8D411yescharacteristic
46C29×#127—21no—
47C29×#127—21no—
48C29×#127—21no—
49C29×#127D411yescharacteristic
50C29×#127D412yes—
51C29×#125—21no—
52C29×#124—21no—
53C29×C22⋊Q8—21no—
54C29×C22⋊Q8—21no—
55C29×#121—21no—
56C29×#121—21no—
57C4×Q8×C29—21no—
58C4×Q8×C29—21no—
59C4×D4×C29—21no—
60C4×D4×C29—21no—
61C29×#117—21no—
62C2×C4⋊C4×C29—21no—
63C2×C42×C29—21no—
64C2×C42×C29C2311yescharacteristic
65C29×#106—22no—
66C29×C4⋊C8—21no—
67C29×C4⋊C8—21no—
68C29×C4⋊C8—21no—
69C29×#103—22no—
70C29×#102—24no—
71C29×#102—22no—
72C29×#102—44no—
73C29×C22⋊C8D412yes—
74C29×#97—21no—
75C4×C8×C29—21no—
76C4×C8×C29—21no—
77C29×#95—21no—
78C24×C29—41no—
79#41×C29—42no—
80#41×C29—42no—
81C2×Q8×C29—21no—
82C2×Q8×C29—21no—
83C2×Q8×C29—21no—
84C2×D4×C29—21no—
85C2×D4×C29—21no—
86C2×D4×C29—22no—
87C2×D4×C29—22no—
88C2×D4×C29—22no—
89C2×D4×C29—21no—
90C2×D4×C29—42no—
91C2×D4×C29—42no—
92C2×D4×C29—41no—
93C2×D4×C29—41no—
94C2×D4×C29—41no—
95C2×D4×C29—41no—
96C2×D4×C29—42no—
97C2×D4×C29—42no—
98C2×D4×C29—82no—
99C22×C4×C29—41no—
100C22×C4×C29—41no—
101C22×C4×C29C2×D411yescharacteristic
102C22×C4×C29C2×D411yescharacteristic
103C22×C4×C29C2×D411yescharacteristic
104SD16×C29—48no—
105SD16×C29—84no—
106SD16×C29—82no—
107D8×C29—48no—
108M16×C29—22no—
109M16×C29SD1614yescomplemented
110C2×C8×C29—22no—
111C2×C8×C29—22no—
112C2×C8×C29—22no—
113C2×C8×C29—42no—
114C4⋊C4×C29—22no—
115C4⋊C4×C29—21no—
116C4⋊C4×C29—21no—
117C4⋊C4×C29—21no—
118C4⋊C4×C29—21no—
119C4⋊C4×C29—21no—
120C4⋊C4×C29—21no—
121C4⋊C4×C29—41no—
122C4⋊C4×C29—41no—
123C4⋊C4×C29—41no—
124C22⋊C4×C29—41no—
125C22⋊C4×C29—41no—
126C22⋊C4×C29—41no—
127C42×C29—41no—
128C42×C29—42no—
129C42×C29C2×D411yescharacteristic
130C42×C29C2×D411yescharacteristic
131C42×C29C2×D411yescharacteristic
132C42×C29#4111yescharacteristic
133#10194C2911yesmaximal, characteristic, direct product factor, Sylow
134C23×C29—41no—
135C23×C29—42no—
136C23×C29—82no—
137C23×C29—82no—
138C23×C29—81no—
139C23×C29—81no—
140C23×C29#12711yescharacteristic
141Q8×C29—42no—
142Q8×C29—42no—
143Q8×C29—41no—
144Q8×C29—41no—
145D4×C29—44no—
146D4×C29—44no—
147D4×C29—42no—
148D4×C29—44no—
149D4×C29—41no—
150D4×C29—41no—
151D4×C29—81no—
152D4×C29—82no—
153D4×C29—81no—
154D4×C29—81no—
155D4×C29—81no—
156D4×C29—81no—
157D4×C29—82no—
158C2×C4×C29—21no—
159C2×C4×C29—21no—
160C2×C4×C29—41no—
161C2×C4×C29—42no—
162C2×C4×C29—41no—
163C2×C4×C29—41no—
164C2×C4×C29—41no—
165C2×C4×C29—81no—
166C2×C4×C29—81no—
167C2×C4×C29—82no—
168C2×C4×C29#12011yescharacteristic
169C2×C4×C29#12011yescharacteristic
170C2×C4×C29#12011yescharacteristic
171C2×C4×C29#12111yescharacteristic
172C2×C4×C29#12111yescharacteristic
173C2×C4×C29#12111yescharacteristic
174C2×C4×C29C2×SD1612yes—
175C2×C4×C29AGL(1,ℤ/8)12yes—
176C8×C29—24no—
177C8×C29—42no—
178C8×C29—42no—
179#3246C2×C2911yescharacteristic, complemented
180#3208C2×C2911yescharacteristic, complemented
181#3151C2×C2911yescharacteristic
182#1986C2×C2911yescharacteristic, complemented
183#1982C2×C2911yescharacteristic, complemented
184#1502C2×C2911yescharacteristic, complemented
185#1283C2×C2911yescharacteristic, complemented
186C22×C29—21no—
187C22×C29—21no—
188C22×C29—82no—
189C22×C29—81no—
190C22×C29—82no—
191C22×C29—81no—
192C22×C29—81no—
193C22×C29—82no—
194C22×C29—162no—
195C22×C29—162no—
196C22×C29#39211yescharacteristic
197C22×C29#49211yescharacteristic
198C22×C29#49611yescharacteristic
199C4×C29—21no—
200C4×C29—21no—
201C4×C29—21no—
202C4×C29—82no—
203C4×C29—81no—
204C4×C29—81no—
205C4×C29—81no—
206C4×C29#45012yes—
207C4×C29#45311yescharacteristic
208C4×C29#45411yescharacteristic
209C4×C29#46012yes—
210C2×AGL(1,ℤ/8)—22no—
211#533C22×C2911yescharacteristic
212#532C22×C2911yescharacteristic
213C2×#127C22×C2911yescharacteristic
214#496—22no—
215#493—21no—
216#492—21no—
217#492—21no—
218#486—21no—
219#476—21no—
220#475—21no—
221#465—22no—
222#461—21no—
223#460—22no—
224#460—21no—
225#450—22no—
226#431C22×C2911yescharacteristic
227C2×C4⋊C8C22×C2911yescharacteristic
228C2×#102—22no—
229C4×M16C22×C2911yescharacteristic
230C4×C4⋊C4C22×C2911yescharacteristic
231#339—22no—
232#327—22no—
233C2×C29—21no—
234C2×C29—21no—
235C2×C29—161no—
236C2×C29—162no—
237C2×C29#200611yescharacteristic
238C2×C29#200811yescharacteristic
239C2×C29#201411yescharacteristic
240C2×#41—21no—
241C22×D4—21no—
242C22×D4—21no—
243C22×D4—21no—
244AGL(1,ℤ/8)—44no—
245AGL(1,ℤ/8)—44no—
246C2×SD16—24no—
247C2×SD16—24no—
248C2×SD16—22no—
249C2×D8—24no—
250C2×M16D4×C2912yes—
251C22×C8D4×C2912yes—
252C4⋊Q8D4×C2911yescharacteristic
253C4⋊Q8D4×C2911yescharacteristic
254C4⋊Q8D4×C2911yescharacteristic
255#127—21no—
256#127—21no—
257#127—21no—
258#127D4×C2912yes—
259#127D4×C2911yescharacteristic
260#125—21no—
261#124—21no—
262C22⋊Q8—21no—
263C22⋊Q8—21no—
264#121—21no—
265#121—21no—
266C4×Q8—21no—
267C4×Q8—21no—
268C4×D4—21no—
269C4×D4—21no—
270#117—21no—
271C2×C4⋊C4—21no—
272C2×C42—21no—
273C2×C42C23×C2911yescharacteristic
274#106—22no—
275C4⋊C8—21no—
276C4⋊C8—21no—
277C4⋊C8—21no—
278#103—22no—
279#102—24no—
280#102—22no—
281#102—44no—
282C22⋊C8D4×C2912yes—
283#97—21no—
284C4×C8—21no—
285C4×C8—21no—
286#95—21no—
287C29#1019411yescharacteristic, direct product factor, Sylow
288C24—41no—
289#41—42no—
290#41—42no—
291C2×Q8—21no—
292C2×Q8—21no—
293C2×Q8—21no—
294C2×D4—21no—
295C2×D4—22no—
296C2×D4—21no—
297C2×D4—22no—
298C2×D4—22no—
299C2×D4—21no—
300C2×D4—42no—
301C2×D4—42no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—42no—
307C2×D4—42no—
308C2×D4—82no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4C2×D4×C2911yescharacteristic
312C22×C4C2×D4×C2911yescharacteristic
313C22×C4C2×D4×C2911yescharacteristic
314SD16—48no—
315SD16—84no—
316SD16—82no—
317D8—48no—
318M16—22no—
319M16SD16×C2914yescomplemented
320C2×C8—22no—
321C2×C8—22no—
322C2×C8—22no—
323C2×C8—42no—
324C4⋊C4—22no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C42—41no—
338C42—42no—
339C42C2×D4×C2911yescharacteristic
340C42C2×D4×C2911yescharacteristic
341C42C2×D4×C2911yescharacteristic
342C42#41×C2911yescharacteristic
343C23—41no—
344C23—42no—
345C23—82no—
346C23—82no—
347C23—81no—
348C23—81no—
349C23C29×#12711yescharacteristic
350Q8—42no—
351Q8—42no—
352Q8—41no—
353Q8—41no—
354D4—44no—
355D4—44no—
356D4—42no—
357D4—44no—
358D4—41no—
359D4—41no—
360D4—81no—
361D4—82no—
362D4—81no—
363D4—81no—
364D4—81no—
365D4—81no—
366D4—82no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—81no—
375C2×C4—81no—
376C2×C4—82no—
377C2×C4C29×#12011yescharacteristic
378C2×C4C29×#12011yescharacteristic
379C2×C4C29×#12011yescharacteristic
380C2×C4C29×#12111yescharacteristic
381C2×C4C29×#12111yescharacteristic
382C2×C4C29×#12111yescharacteristic
383C2×C4C2×SD16×C2912yes—
384C2×C4C29×AGL(1,ℤ/8)12yes—
385C8—24no—
386C8—42no—
387C8—42no—
388C22—21no—
389C22—21no—
390C22—82no—
391C22—81no—
392C22—82no—
393C22—81no—
394C22—81no—
395C22—82no—
396C22—162no—
397C22—162no—
398C22C29×#39211yescharacteristic
399C22C29×#49211yescharacteristic
400C22C29×#49611yescharacteristic
401C4—21no—
402C4—21no—
403C4—21no—
404C4—82no—
405C4—81no—
406C4—81no—
407C4—81no—
408C4C29×#45012yes—
409C4C29×#45311yescharacteristic
410C4C29×#45411yescharacteristic
411C4C29×#46012yes—
412C2—21no—
413C2—21no—
414C2—162no—
415C2—161no—
416C2C29×#200611yescharacteristic
417C2C29×#200811yescharacteristic
418C2C29×#201411yescharacteristic
subgroupG/H
center, socleC22×C29#392
commutator, Frattini, cosocleC2×C42C23×C29
prime radicalC29×#3151C2
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×#3246C2semidirect
2. C29×#3208C2semidirect
4. C29×#1986C2semidirect
5. C29×#1982C2semidirect
6. C29×#1502C2semidirect
7. C29×#1283C2semidirect
109. M16×C29SD16semidirect
133. #10194C29direct (N × H)
179. #3246C2×C29semidirect
180. #3208C2×C29semidirect
182. #1986C2×C29semidirect
183. #1982C2×C29semidirect
184. #1502C2×C29semidirect
185. #1283C2×C29semidirect
287. C29#10194direct (N × H)
319. M16SD16×C29semidirect

Maximal subgroups

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

subgroupindex
C29×#32462
C29×#32082
C29×#31512
C29×#19862
C29×#19822
C29×#15022
C29×#12832
#1019429