Finite Group Databasebeta

← C29×#13339 #20308239

Subgroups — C29×#13339 #20308239

Order 7424.

534 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#510C211yesmaximal, characteristic
2C22×C29×Q32C211yesmaximal, characteristic, complemented
3C29×#3156C211yesmaximal, characteristic
4C2×C29×#362C211yesmaximal, characteristic, complemented
5C2×C29×#359C211yesmaximal, characteristic
6C29×#1979C211yesmaximal, characteristic, complemented
7C29×#1379C211yesmaximal, characteristic, complemented
8C2×C29×#137—21no—
9C2×C29×#135C2211yescharacteristic
10C22×Q16×C29C2211yescharacteristic
11C22×Q16×C29C2211yescharacteristic
12C29×#536—21no—
13C29×#510—22no—
14C29×#510—22no—
15C2×C29×Q32—22no—
16C2×C29×Q32—22no—
17C2×C29×Q32—22no—
18C2×C29×Q32—21no—
19C2×C29×SD32—21no—
20C2×C29×M32C2211yescharacteristic
21C22×C16×C29C2211yescharacteristic
22C29×#497—22no—
23C29×#495—21no—
24C29×#494—21no—
25C2×C29×#108C2211yescharacteristic
26C29×#419—21no—
27C2×C29×#101—21no—
28C29×#405C2211yescharacteristic
29C29×#362—22no—
30C29×#359—22no—
31C2×#41×C29—21no—
32C22×Q8×C29—21no—
33C22×Q8×C29—21no—
34C29×#137—42no—
35C29×#137—42no—
36C29×#135—21no—
37C29×#135—21no—
38C29×#135—21no—
39C29×#135—21no—
40C2×Q16×C29—22no—
41C2×Q16×C29—21no—
42C2×Q16×C29—21no—
43C2×Q16×C29—21no—
44C2×Q16×C29—21no—
45C2×Q16×C29—21no—
46C2×Q16×C29—21no—
47C2×Q16×C29—21no—
48C2×Q16×C29—21no—
49C2×Q16×C29—21no—
50C2×Q16×C29—21no—
51C2×Q16×C29D411yescharacteristic
52C2×Q16×C29D412yes—
53C2×Q16×C29D412yes—
54C2×SD16×C29—22no—
55C2×SD16×C29—21no—
56C2×D8×C29D411yescharacteristic
57C2×M16×C29—21no—
58C2×M16×C29D411yescharacteristic
59C22×C8×C29C2311yescharacteristic
60C29×C4⋊Q8—22no—
61C29×#124—22no—
62C29×#123—42no—
63C29×C22⋊Q8—42no—
64C29×#117D411yescharacteristic
65C29×Q32—28no—
66C29×Q32—24no—
67C29×SD32—24no—
68C29×M32—21no—
69C29×M32D412yes—
70C2×C16×C29—21no—
71C2×C16×C29—21no—
72C2×C16×C29—21no—
73C2×C16×C29D412yes—
74C29×#108—21no—
75C29×#108—21no—
76C29×#103—42no—
77C29×#101—42no—
78C29×#97—21no—
79C4×C8×C29—21no—
80#41×C29—41no—
81#41×C29—41no—
82#41×C29—41no—
83#41×C29—41no—
84C2×Q8×C29—22no—
85C2×Q8×C29—21no—
86C2×Q8×C29—22no—
87C2×Q8×C29—41no—
88C2×Q8×C29—41no—
89C2×Q8×C29—41no—
90C2×Q8×C29—41no—
91C2×Q8×C29—41no—
92C2×Q8×C29—41no—
93C2×Q8×C29—41no—
94C2×Q8×C29—41no—
95C2×Q8×C29—41no—
96C2×Q8×C29—41no—
97C2×D4×C29—21no—
98C2×D4×C29—41no—
99C22×C4×C29—41no—
100C22×C4×C29—41no—
101C22×C4×C29—41no—
102C22×C4×C29C2×D411yescharacteristic
103Q16×C29—22no—
104Q16×C29—22no—
105Q16×C29—22no—
106Q16×C29—21no—
107Q16×C29—22no—
108Q16×C29—21no—
109Q16×C29—44no—
110Q16×C29—41no—
111Q16×C29—41no—
112Q16×C29—41no—
113Q16×C29—41no—
114SD16×C29—44no—
115SD16×C29—41no—
116SD16×C29—41no—
117D8×C29—21no—
118D8×C29—21no—
119M16×C29—21no—
120M16×C29—41no—
121M16×C29—41no—
122M16×C29D812yes—
123C2×C8×C29—21no—
124C2×C8×C29—41no—
125C2×C8×C29C2×D411yescharacteristic
126C2×C8×C29C2×D411yescharacteristic
127C2×C8×C29C2×D411yescharacteristic
128C2×C8×C29C2×D411yescharacteristic
129C2×C8×C29C2×D411yescharacteristic
130C2×C8×C29#4111yescharacteristic
131C4⋊C4×C29—44no—
132C4⋊C4×C29D812yes—
133C22⋊C4×C29—21no—
134C22⋊C4×C29—44no—
135C42×C29—21no—
136C16×C29—22no—
137C16×C29—22no—
138#13339C2911yesmaximal, characteristic, direct product factor, Sylow
139C23×C29—41no—
140C23×C29AGL(1,ℤ/8)11yescharacteristic
141Q8×C29—41no—
142Q8×C29—42no—
143Q8×C29—42no—
144Q8×C29—42no—
145Q8×C29—41no—
146Q8×C29—42no—
147Q8×C29—81no—
148Q8×C29—81no—
149Q8×C29—81no—
150Q8×C29—81no—
151D4×C29—41no—
152D4×C29—41no—
153D4×C29—81no—
154D4×C29—81no—
155C2×C4×C29—22no—
156C2×C4×C29—42no—
157C2×C4×C29—41no—
158C2×C4×C29—42no—
159C2×C4×C29—81no—
160C2×C4×C29—81no—
161C2×C4×C29—81no—
162C2×C4×C29—81no—
163C2×C4×C29—81no—
164C2×C4×C29—81no—
165C2×C4×C29#12011yescharacteristic
166C2×C4×C29#12111yescharacteristic
167C2×C4×C29#12711yescharacteristic
168C2×C4×C29C2×D811yescharacteristic
169C2×C4×C29C2×D811yescharacteristic
170C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
171C8×C29—22no—
172C8×C29—81no—
173C8×C29#12011yescharacteristic
174C8×C29#12011yescharacteristic
175C8×C29#12111yescharacteristic
176C8×C29#12111yescharacteristic
177C2×#510C2×C2911yescharacteristic
178C22×Q32C2×C2911yescharacteristic, complemented
179#3156C2×C2911yescharacteristic
180C2×#362C2×C2911yescharacteristic, complemented
181C2×#359C2×C2911yescharacteristic
182#1979C2×C2911yescharacteristic, complemented
183#1379C2×C2911yescharacteristic, complemented
184C22×C29—22no—
185C22×C29—82no—
186C22×C29—81no—
187C22×C29#44711yescharacteristic
188C22×C29#45911yescharacteristic
189C22×C29#49611yescharacteristic
190C4×C29—42no—
191C4×C29—81no—
192C4×C29—82no—
193C4×C29—82no—
194C4×C29#39211yescharacteristic
195C4×C29#44711yescharacteristic
196C4×C29#45911yescharacteristic
197C4×C29#49311yescharacteristic
198C2×#137—21no—
199C2×#135C22×C2911yescharacteristic
200C22×Q16C22×C2911yescharacteristic
201C22×Q16C22×C2911yescharacteristic
202#536—21no—
203#510—22no—
204#510—22no—
205C2×Q32—22no—
206C2×Q32—22no—
207C2×Q32—21no—
208C2×Q32—22no—
209C2×SD32—21no—
210C2×M32C22×C2911yescharacteristic
211C22×C16C22×C2911yescharacteristic
212#497—22no—
213#495—21no—
214#494—21no—
215C2×#108C22×C2911yescharacteristic
216#419—21no—
217C2×#101—21no—
218#405C22×C2911yescharacteristic
219#362—22no—
220#359—22no—
221C2×C29—21no—
222C2×C29—21no—
223C2×C29—161no—
224C2×C29#201111yescharacteristic
225C2×C29#219512yes—
226C2×#41—21no—
227C22×Q8—21no—
228C22×Q8—21no—
229#137—42no—
230#137—42no—
231#135—21no—
232#135—21no—
233#135—21no—
234#135—21no—
235C2×Q16—22no—
236C2×Q16—21no—
237C2×Q16—21no—
238C2×Q16—21no—
239C2×Q16—21no—
240C2×Q16—21no—
241C2×Q16—21no—
242C2×Q16—21no—
243C2×Q16—21no—
244C2×Q16—21no—
245C2×Q16—21no—
246C2×Q16D4×C2912yes—
247C2×Q16D4×C2912yes—
248C2×Q16D4×C2911yescharacteristic
249C2×SD16—22no—
250C2×SD16—21no—
251C2×D8D4×C2911yescharacteristic
252C2×M16—21no—
253C2×M16D4×C2911yescharacteristic
254C22×C8C23×C2911yescharacteristic
255C4⋊Q8—22no—
256#124—22no—
257#123—42no—
258C22⋊Q8—42no—
259#117D4×C2911yescharacteristic
260Q32—28no—
261Q32—24no—
262SD32—24no—
263M32—21no—
264M32D4×C2912yes—
265C2×C16—21no—
266C2×C16—21no—
267C2×C16—21no—
268C2×C16D4×C2912yes—
269#108—21no—
270#108—21no—
271#103—42no—
272#101—42no—
273#97—21no—
274C4×C8—21no—
275C29#1333911yescharacteristic, direct product factor, Sylow
276#41—41no—
277#41—41no—
278#41—41no—
279#41—41no—
280C2×Q8—22no—
281C2×Q8—21no—
282C2×Q8—22no—
283C2×Q8—41no—
284C2×Q8—41no—
285C2×Q8—41no—
286C2×Q8—41no—
287C2×Q8—41no—
288C2×Q8—41no—
289C2×Q8—41no—
290C2×Q8—41no—
291C2×Q8—41no—
292C2×Q8—41no—
293C2×D4—21no—
294C2×D4—41no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4—41no—
298C22×C4C2×D4×C2911yescharacteristic
299Q16—22no—
300Q16—22no—
301Q16—22no—
302Q16—21no—
303Q16—22no—
304Q16—21no—
305Q16—44no—
306Q16—41no—
307Q16—41no—
308Q16—41no—
309Q16—41no—
310SD16—44no—
311SD16—41no—
312SD16—41no—
313D8—21no—
314D8—21no—
315M16—21no—
316M16—41no—
317M16—41no—
318M16D8×C2912yes—
319C2×C8—21no—
320C2×C8—41no—
321C2×C8C2×D4×C2911yescharacteristic
322C2×C8C2×D4×C2911yescharacteristic
323C2×C8C2×D4×C2911yescharacteristic
324C2×C8C2×D4×C2911yescharacteristic
325C2×C8C2×D4×C2911yescharacteristic
326C2×C8#41×C2911yescharacteristic
327C4⋊C4—44no—
328C4⋊C4D8×C2912yes—
329C22⋊C4—21no—
330C22⋊C4—44no—
331C42—21no—
332C16—22no—
333C16—22no—
334C23—41no—
335C23C29×AGL(1,ℤ/8)11yescharacteristic
336Q8—42no—
337Q8—41no—
338Q8—42no—
339Q8—41no—
340Q8—42no—
341Q8—42no—
342Q8—81no—
343Q8—81no—
344Q8—81no—
345Q8—81no—
346D4—41no—
347D4—41no—
348D4—81no—
349D4—81no—
350C2×C4—22no—
351C2×C4—42no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4C29×#12011yescharacteristic
361C2×C4C29×#12111yescharacteristic
362C2×C4C29×#12711yescharacteristic
363C2×C4C2×D8×C2911yescharacteristic
364C2×C4C2×D8×C2911yescharacteristic
365C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
366C8—22no—
367C8—81no—
368C8C29×#12011yescharacteristic
369C8C29×#12011yescharacteristic
370C8C29×#12111yescharacteristic
371C8C29×#12111yescharacteristic
372C22—22no—
373C22—82no—
374C22—81no—
375C22C29×#44711yescharacteristic
376C22C29×#45911yescharacteristic
377C22C29×#49611yescharacteristic
378C4—42no—
379C4—81no—
380C4—82no—
381C4—82no—
382C4C29×#39211yescharacteristic
383C4C29×#44711yescharacteristic
384C4C29×#45911yescharacteristic
385C4C29×#49311yescharacteristic
386C2—21no—
387C2—21no—
388C2—161no—
389C2C29×#201111yescharacteristic
390C2C29×#219512yes—
subgroupG/H
center, socleC22×C29#447
commutator, Frattini, cosocleC22×C8C23×C29
prime radicalC2×C29×#135C22
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C22×C4×C29 ◁ C29×#405 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C29×Q32C2semidirect
4. C2×C29×#362C2semidirect
6. C29×#1979C2semidirect
7. C29×#1379C2semidirect
138. #13339C29direct (N × H)
178. C22×Q32C2×C29semidirect
180. C2×#362C2×C29semidirect
182. #1979C2×C29semidirect
183. #1379C2×C29semidirect
275. C29#13339direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#5102
C22×C29×Q322
C29×#31562
C2×C29×#3622
C2×C29×#3592
C29×#19792
C29×#13792
#1333929