Finite Group Databasebeta

← C29×#9293 #20304193

Subgroups — C29×#9293 #20304193

Order 7424.

558 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
1C29×#3205C211yesmaximal, characteristic
2C29×#2932C211yesmaximal, characteristic, complemented
3C29×#1961C211yesmaximal, characteristic, complemented
4C29×#1545C211yesmaximal, characteristic, complemented
5C29×#1517C211yesmaximal, characteristic, complemented
6C29×#1286C211yesmaximal, characteristic, complemented
7C29×#1275C211yesmaximal, characteristic, complemented
8C2×C29×#131—21no—
9C29×#532C2211yescharacteristic
10C2×C29×#127C2211yescharacteristic
11C29×#493C412yescomplemented
12C29×#486C412yescomplemented
13C29×#459—22no—
14C29×#447—22no—
15C29×#435—22no—
16C29×#435—22no—
17C29×#431C2211yescharacteristic
18C29×#431C2211yescharacteristic
19C29×#423C2211yescharacteristic
20C2×C29×#102—21no—
21C2×C29×#102—21no—
22C29×#408—21no—
23C2×C29×#97C2211yescharacteristic
24C29×#382C2211yescharacteristic
25C29×#331—22no—
26C29×#327—22no—
27C2×#41×C29—21no—
28C22×D4×C29—21no—
29C22×D4×C29—21no—
30C22×D4×C29—21no—
31C2×D8×C29—24no—
32C29×#131—42no—
33C29×#131—42no—
34C2×M16×C29—22no—
35C2×M16×C29—21no—
36C22×C8×C29—22no—
37C22×C8×C29D411yescharacteristic
38C22×C8×C29D411yescharacteristic
39C29×C4⋊Q8C2×C411yescharacteristic
40C29×#127—21no—
41C29×#127—21no—
42C29×#127—21no—
43C29×#127C2×C412yes—
44C29×#127C2×C411yescharacteristic
45C29×#124—21no—
46C29×#121—21no—
47C29×#121D412yes—
48C4×D4×C29—21no—
49C4×D4×C29D412yes—
50C2×C4⋊C4×C29—21no—
51C2×C42×C29C2311yescharacteristic
52C29×C4⋊C8—21no—
53C29×C4⋊C8—21no—
54C29×C4⋊C8—21no—
55C29×C4⋊C8D412yes—
56C29×#102—24no—
57C29×#102—42no—
58C29×#102—42no—
59C29×C22⋊C8—24no—
60C29×C22⋊C8—21no—
61C29×C22⋊C8—21no—
62C29×#97—21no—
63C29×#97—21no—
64C4×C8×C29—21no—
65C4×C8×C29C2×C412yes—
66C29×#95—21no—
67C29×#95—21no—
68C24×C29—41no—
69#41×C29—41no—
70#41×C29—41no—
71#41×C29—41no—
72#41×C29—41no—
73C2×Q8×C29—21no—
74C2×D4×C29—22no—
75C2×D4×C29—22no—
76C2×D4×C29—21no—
77C2×D4×C29—22no—
78C2×D4×C29—21no—
79C2×D4×C29—22no—
80C2×D4×C29—41no—
81C2×D4×C29—41no—
82C2×D4×C29—41no—
83C2×D4×C29—41no—
84C2×D4×C29—41no—
85C2×D4×C29—41no—
86C2×D4×C29—41no—
87C2×D4×C29—82no—
88C2×D4×C29—82no—
89C2×D4×C29C22⋊C412yes—
90C22×C4×C29—22no—
91C22×C4×C29—41no—
92C22×C4×C29C2×D411yescharacteristic
93C22×C4×C29C2×D411yescharacteristic
94C22×C4×C29#4111yescharacteristic
95D8×C29—84no—
96M16×C29—44no—
97M16×C29—41no—
98M16×C29—41no—
99C2×C8×C29—21no—
100C2×C8×C29—21no—
101C2×C8×C29—22no—
102C2×C8×C29—22no—
103C2×C8×C29—21no—
104C2×C8×C29—21no—
105C2×C8×C29—21no—
106C2×C8×C29—44no—
107C2×C8×C29—41no—
108C2×C8×C29D812yescomplemented
109C4⋊C4×C29—21no—
110C4⋊C4×C29—41no—
111C4⋊C4×C29—41no—
112C4⋊C4×C29C22⋊C412yes—
113C22⋊C4×C29—22no—
114C22⋊C4×C29—22no—
115C42×C29C22×C411yescharacteristic
116C42×C29C2×D411yescharacteristic
117C42×C29C2×D411yescharacteristic
118C42×C29#4111yescharacteristic
119#9293C2911yesmaximal, characteristic, direct product factor, Sylow
120C23×C29—22no—
121C23×C29—42no—
122C23×C29—82no—
123C23×C29—82no—
124C23×C29—81no—
125C23×C29—81no—
126C23×C29#12111yescharacteristic
127Q8×C29—41no—
128Q8×C29—41no—
129D4×C29—42no—
130D4×C29—44no—
131D4×C29—42no—
132D4×C29—42no—
133D4×C29—41no—
134D4×C29—42no—
135D4×C29—41no—
136D4×C29—42no—
137D4×C29—81no—
138D4×C29—82no—
139D4×C29—82no—
140D4×C29—82no—
141D4×C29—81no—
142D4×C29—81no—
143C2×C4×C29—22no—
144C2×C4×C29—41no—
145C2×C4×C29—41no—
146C2×C4×C29—42no—
147C2×C4×C29—42no—
148C2×C4×C29—81no—
149C2×C4×C29—81no—
150C2×C4×C29—81no—
151C2×C4×C29C2×C22⋊C411yescharacteristic
152C2×C4×C29C4×D411yescharacteristic
153C2×C4×C29C4×D411yescharacteristic
154C2×C4×C29#12011yescharacteristic
155C2×C4×C29#12111yescharacteristic
156C2×C4×C29#12311yescharacteristic
157C2×C4×C29C2×D811yescharacteristic
158C2×C4×C29#13511yescharacteristic
159C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
160C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
161C8×C29—22no—
162C8×C29—42no—
163C8×C29—42no—
164C8×C29—41no—
165C8×C29—81no—
166#3205C2×C2911yescharacteristic
167#2932C2×C2911yescharacteristic, complemented
168#1961C2×C2911yescharacteristic, complemented
169#1545C2×C2911yescharacteristic, complemented
170#1517C2×C2911yescharacteristic, complemented
171#1286C2×C2911yescharacteristic, complemented
172#1275C2×C2911yescharacteristic, complemented
173C22×C29—21no—
174C22×C29—21no—
175C22×C29—42no—
176C22×C29—42no—
177C22×C29—42no—
178C22×C29—82no—
179C22×C29—82no—
180C22×C29—82no—
181C22×C29—162no—
182C22×C29—162no—
183C22×C29#38611yescharacteristic
184C22×C29#45911yescharacteristic
185C22×C29#46311yescharacteristic
186C4×C29—21no—
187C4×C29—21no—
188C4×C29—21no—
189C4×C29—21no—
190C4×C29—42no—
191C4×C29—161no—
192C4×C29C4×D811yescharacteristic
193C4×C29#44211yescharacteristic
194C4×C29#44711yescharacteristic
195C4×C29#44911yescharacteristic
196C2×#131—21no—
197#532C22×C2911yescharacteristic
198C2×#127C22×C2911yescharacteristic
199#493C4×C2912yescomplemented
200#486C4×C2912yescomplemented
201#459—22no—
202#447—22no—
203#435—22no—
204#435—22no—
205#431C22×C2911yescharacteristic
206#431C22×C2911yescharacteristic
207#423C22×C2911yescharacteristic
208C2×#102—21no—
209C2×#102—21no—
210#408—21no—
211C2×#97C22×C2911yescharacteristic
212#382C22×C2911yescharacteristic
213#331—22no—
214#327—22no—
215C2×C29—21no—
216C2×C29—21no—
217C2×C29—82no—
218C2×C29—162no—
219C2×C29#187911yescharacteristic
220C2×C29#190311yescharacteristic
221C2×C29#191011yescharacteristic
222C2×#41—21no—
223C22×D4—21no—
224C22×D4—21no—
225C22×D4—21no—
226C2×D8—24no—
227#131—42no—
228#131—42no—
229C2×M16—22no—
230C2×M16—21no—
231C22×C8—22no—
232C22×C8D4×C2911yescharacteristic
233C22×C8D4×C2911yescharacteristic
234C4⋊Q8C2×C4×C2911yescharacteristic
235#127—21no—
236#127—21no—
237#127—21no—
238#127C2×C4×C2912yes—
239#127C2×C4×C2911yescharacteristic
240#124—21no—
241#121—21no—
242#121D4×C2912yes—
243C4×D4—21no—
244C4×D4D4×C2912yes—
245C2×C4⋊C4—21no—
246C2×C42C23×C2911yescharacteristic
247C4⋊C8—21no—
248C4⋊C8—21no—
249C4⋊C8—21no—
250C4⋊C8D4×C2912yes—
251#102—24no—
252#102—42no—
253#102—42no—
254C22⋊C8—24no—
255C22⋊C8—21no—
256C22⋊C8—21no—
257#97—21no—
258#97—21no—
259C4×C8—21no—
260C4×C8C2×C4×C2912yes—
261#95—21no—
262#95—21no—
263C29#929311yescharacteristic, direct product factor, Sylow
264C24—41no—
265#41—41no—
266#41—41no—
267#41—41no—
268#41—41no—
269C2×Q8—21no—
270C2×D4—22no—
271C2×D4—22no—
272C2×D4—21no—
273C2×D4—22no—
274C2×D4—21no—
275C2×D4—22no—
276C2×D4—41no—
277C2×D4—41no—
278C2×D4—41no—
279C2×D4—41no—
280C2×D4—41no—
281C2×D4—41no—
282C2×D4—41no—
283C2×D4—82no—
284C2×D4—82no—
285C2×D4C22⋊C4×C2912yes—
286C22×C4—22no—
287C22×C4—41no—
288C22×C4C2×D4×C2911yescharacteristic
289C22×C4C2×D4×C2911yescharacteristic
290C22×C4#41×C2911yescharacteristic
291D8—84no—
292M16—44no—
293M16—41no—
294M16—41no—
295C2×C8—21no—
296C2×C8—21no—
297C2×C8—22no—
298C2×C8—21no—
299C2×C8—22no—
300C2×C8—21no—
301C2×C8—21no—
302C2×C8—44no—
303C2×C8—41no—
304C2×C8D8×C2912yescomplemented
305C4⋊C4—21no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4C22⋊C4×C2912yes—
309C22⋊C4—22no—
310C22⋊C4—22no—
311C42C22×C4×C2911yescharacteristic
312C42C2×D4×C2911yescharacteristic
313C42C2×D4×C2911yescharacteristic
314C42#41×C2911yescharacteristic
315C23—22no—
316C23—42no—
317C23—82no—
318C23—82no—
319C23—81no—
320C23—81no—
321C23C29×#12111yescharacteristic
322Q8—41no—
323Q8—41no—
324D4—42no—
325D4—44no—
326D4—42no—
327D4—42no—
328D4—41no—
329D4—42no—
330D4—41no—
331D4—42no—
332D4—81no—
333D4—82no—
334D4—82no—
335D4—82no—
336D4—81no—
337D4—81no—
338C2×C4—22no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4C2×C22⋊C4×C2911yescharacteristic
347C2×C4C4×D4×C2911yescharacteristic
348C2×C4C4×D4×C2911yescharacteristic
349C2×C4C29×#12011yescharacteristic
350C2×C4C29×#12111yescharacteristic
351C2×C4C29×#12311yescharacteristic
352C2×C4C2×D8×C2911yescharacteristic
353C2×C4C29×#13511yescharacteristic
354C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
355C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
356C8—22no—
357C8—42no—
358C8—42no—
359C8—41no—
360C8—81no—
361C22—21no—
362C22—21no—
363C22—42no—
364C22—42no—
365C22—42no—
366C22—82no—
367C22—82no—
368C22—82no—
369C22—162no—
370C22—162no—
371C22C29×#38611yescharacteristic
372C22C29×#45911yescharacteristic
373C22C29×#46311yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—42no—
379C4—161no—
380C4C4×D8×C2911yescharacteristic
381C4C29×#44211yescharacteristic
382C4C29×#44711yescharacteristic
383C4C29×#44911yescharacteristic
384C2—21no—
385C2—21no—
386C2—82no—
387C2—162no—
388C2C29×#187911yescharacteristic
389C2C29×#190311yescharacteristic
390C2C29×#191011yescharacteristic
subgroupG/H
center, socleC22×C29#386
commutatorC42C22×C4×C29
Frattini, cosocleC2×C42C23×C29
prime radicalC29×#3205C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#2932C2semidirect
3. C29×#1961C2semidirect
4. C29×#1545C2semidirect
5. C29×#1517C2semidirect
6. C29×#1286C2semidirect
7. C29×#1275C2semidirect
11. C29×#493C4semidirect
12. C29×#486C4semidirect
108. C2×C8×C29D8semidirect
119. #9293C29direct (N × H)
167. #2932C2×C29semidirect
168. #1961C2×C29semidirect
169. #1545C2×C29semidirect
170. #1517C2×C29semidirect
171. #1286C2×C29semidirect
172. #1275C2×C29semidirect
199. #493C4×C29semidirect
200. #486C4×C29semidirect
263. C29#9293direct (N × H)
304. C2×C8D8×C29semidirect

Maximal subgroups

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

subgroupindex
C29×#32052
C29×#29322
C29×#19612
C29×#15452
C29×#15172
C29×#12862
C29×#12752
#929329