Finite Group Databasebeta

← C29×#12140 #20307040

Subgroups — C29×#12140 #20307040

Order 7424.

478 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#2680C211yesmaximal, characteristic, complemented
2C29×#2039C211yesmaximal, characteristic, complemented
3C29×#1604C211yesmaximal, characteristic, complemented
4C29×#1598C211yesmaximal, characteristic
5C29×#1354C211yesmaximal, characteristic, complemented
6C29×#1345C211yesmaximal, characteristic, complemented
7C29×#1325C211yesmaximal, characteristic, complemented
8C29×#537C2211yescharacteristic
9C2×C29×#123—21no—
10C2×C29×C22⋊Q8—21no—
11C29×#448—21no—
12C29×#447—21no—
13C2×C29×#104—21no—
14C29×#417—21no—
15C29×#398—21no—
16C29×#397—21no—
17C29×#395C2211yescharacteristic
18C29×#394C2211yescharacteristic
19C29×#388—21no—
20C29×#385—21no—
21C29×#384C2211yescharacteristic
22C29×#343C2211yescharacteristic
23C29×#327—21no—
24C29×#327—21no—
25C29×#324C2211yescharacteristic
26C29×#324C2211yescharacteristic
27C2×#41×C29—21no—
28C22×Q8×C29D411yescharacteristic
29C22×D4×C29D411yescharacteristic
30C23×C4×C29—21no—
31C2×SD16×C29—41no—
32C2×D8×C29—41no—
33C2×M16×C29—21no—
34C29×#123—44no—
35C29×C22⋊Q8—44no—
36C29×C22⋊Q8—41no—
37C29×#121—21no—
38C29×#121—21no—
39C29×#121—41no—
40C2×C4⋊C4×C29—21no—
41C2×C4⋊C4×C29—21no—
42C2×C4⋊C4×C29—21no—
43C2×C4⋊C4×C29—21no—
44C2×C4⋊C4×C29—21no—
45C2×C4⋊C4×C29D411yescharacteristic
46C2×C4⋊C4×C29C2311yescharacteristic
47C2×C22⋊C4×C29—21no—
48C2×C22⋊C4×C29—21no—
49C2×C22⋊C4×C29—21no—
50C2×C22⋊C4×C29—21no—
51C2×C22⋊C4×C29—21no—
52C2×C42×C29D411yescharacteristic
53C29×#104—42no—
54C29×#103—41no—
55C29×#103—41no—
56C29×#102—41no—
57C29×#102—41no—
58C29×C22⋊C8—21no—
59C29×C22⋊C8—21no—
60C29×#95—21no—
61C29×#95—21no—
62C29×#95—21no—
63C29×#95D411yescharacteristic
64C29×#95D411yescharacteristic
65C24×C29—21no—
66#41×C29—41no—
67#41×C29—41no—
68#41×C29—41no—
69#41×C29—41no—
70C2×Q8×C29—21no—
71C2×Q8×C29—42no—
72C2×Q8×C29—41no—
73C2×D4×C29—21no—
74C2×D4×C29—21no—
75C2×D4×C29—21no—
76C2×D4×C29—41no—
77C2×D4×C29—42no—
78C2×D4×C29—41no—
79C22×C4×C29—21no—
80C22×C4×C29—21no—
81C22×C4×C29—21no—
82C22×C4×C29—21no—
83C22×C4×C29—21no—
84C22×C4×C29—41no—
85C22×C4×C29—42no—
86C22×C4×C29—42no—
87C22×C4×C29—81no—
88C22×C4×C29C2×D411yescharacteristic
89C22×C4×C29C2×D411yescharacteristic
90C22×C4×C29C2×D411yescharacteristic
91SD16×C29—82no—
92D8×C29—82no—
93M16×C29—41no—
94M16×C29—41no—
95C2×C8×C29—41no—
96C2×C8×C29—41no—
97C2×C8×C29—41no—
98C4⋊C4×C29—21no—
99C4⋊C4×C29—21no—
100C4⋊C4×C29—41no—
101C4⋊C4×C29—41no—
102C4⋊C4×C29—42no—
103C4⋊C4×C29—42no—
104C4⋊C4×C29—42no—
105C4⋊C4×C29—42no—
106C4⋊C4×C29—42no—
107C22⋊C4×C29—24no—
108C22⋊C4×C29—42no—
109C22⋊C4×C29—41no—
110C22⋊C4×C29—41no—
111C22⋊C4×C29—42no—
112C22⋊C4×C29—42no—
113C22⋊C4×C29—41no—
114C22⋊C4×C29—41no—
115C42×C29—21no—
116C42×C29—21no—
117#12140C2911yesmaximal, characteristic, direct product factor, Sylow
118C23×C29—22no—
119C23×C29—41no—
120C23×C29—41no—
121C23×C29—41no—
122C23×C29—41no—
123C23×C29—41no—
124C23×C29—41no—
125C23×C29—41no—
126C23×C29#12011yescharacteristic
127Q8×C29—41no—
128Q8×C29—41no—
129Q8×C29—42no—
130Q8×C29—81no—
131D4×C29—41no—
132D4×C29—41no—
133D4×C29—42no—
134D4×C29—81no—
135D4×C29—81no—
136D4×C29—81no—
137D4×C29—81no—
138D4×C29—81no—
139C2×C4×C29—21no—
140C2×C4×C29—21no—
141C2×C4×C29—22no—
142C2×C4×C29—22no—
143C2×C4×C29—21no—
144C2×C4×C29—21no—
145C2×C4×C29—41no—
146C2×C4×C29—41no—
147C2×C4×C29—41no—
148C2×C4×C29—41no—
149C2×C4×C29—41no—
150C2×C4×C29—41no—
151C2×C4×C29—41no—
152C2×C4×C29—41no—
153C2×C4×C29—41no—
154C2×C4×C29—41no—
155C2×C4×C29—41no—
156C2×C4×C29—41no—
157C2×C4×C29—41no—
158C2×C4×C29—41no—
159C2×C4×C29—41no—
160C2×C4×C29—41no—
161C2×C4×C29—81no—
162C2×C4×C29—81no—
163C2×C4×C29—84no—
164C2×C4×C29#13511yescharacteristic
165C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
166C8×C29—81no—
167C8×C29—81no—
168C8×C29—81no—
169#2680C2×C2911yescharacteristic, complemented
170#2039C2×C2911yescharacteristic, complemented
171#1604C2×C2911yescharacteristic, complemented
172#1598C2×C2911yescharacteristic
173#1354C2×C2911yescharacteristic, complemented
174#1345C2×C2911yescharacteristic, complemented
175#1325C2×C2911yescharacteristic, complemented
176C22×C29—21no—
177C22×C29—21no—
178C22×C29—42no—
179C22×C29—42no—
180C22×C29—42no—
181C22×C29—81no—
182C22×C29—81no—
183C22×C29—81no—
184C22×C29—81no—
185C22×C29—81no—
186C22×C29—81no—
187C22×C29—81no—
188C22×C29#44911yescharacteristic
189C22×C29#45411yescharacteristic
190C22×C29B(4,𝔽2)11yescharacteristic
191C4×C29—21no—
192C4×C29—21no—
193C4×C29—42no—
194C4×C29—41no—
195C4×C29—41no—
196C4×C29—42no—
197C4×C29—81no—
198C4×C29—81no—
199C4×C29—81no—
200C4×C29—81no—
201#537C22×C2911yescharacteristic
202C2×#123—21no—
203C2×C22⋊Q8—21no—
204#448—21no—
205#447—21no—
206C2×#104—21no—
207#417—21no—
208#398—21no—
209#397—21no—
210#395C22×C2911yescharacteristic
211#394C22×C2911yescharacteristic
212#388—21no—
213#385—21no—
214#384C22×C2911yescharacteristic
215#343C22×C2911yescharacteristic
216#327—21no—
217#327—21no—
218#324C22×C2911yescharacteristic
219#324C22×C2911yescharacteristic
220C2×C29—21no—
221C2×C29—21no—
222C2×C29—82no—
223C2×C29—161no—
224C2×C29#159711yescharacteristic
225C2×C29#219611yescharacteristic
226C2×C29#220311yescharacteristic
227C2×#41—21no—
228C22×Q8D4×C2911yescharacteristic
229C22×D4D4×C2911yescharacteristic
230C23×C4—21no—
231C2×SD16—41no—
232C2×D8—41no—
233C2×M16—21no—
234#123—44no—
235C22⋊Q8—44no—
236C22⋊Q8—41no—
237#121—21no—
238#121—21no—
239#121—41no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4D4×C2911yescharacteristic
246C2×C4⋊C4C23×C2911yescharacteristic
247C2×C22⋊C4—21no—
248C2×C22⋊C4—21no—
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C42D4×C2911yescharacteristic
253#104—42no—
254#103—41no—
255#103—41no—
256#102—41no—
257#102—41no—
258C22⋊C8—21no—
259C22⋊C8—21no—
260#95—21no—
261#95—21no—
262#95—21no—
263#95D4×C2911yescharacteristic
264#95D4×C2911yescharacteristic
265C29#1214011yescharacteristic, direct product factor, Sylow
266C24—21no—
267#41—41no—
268#41—41no—
269#41—41no—
270#41—41no—
271C2×Q8—21no—
272C2×Q8—42no—
273C2×Q8—41no—
274C2×D4—21no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—41no—
278C2×D4—42no—
279C2×D4—41no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—41no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—81no—
289C22×C4C2×D4×C2911yescharacteristic
290C22×C4C2×D4×C2911yescharacteristic
291C22×C4C2×D4×C2911yescharacteristic
292SD16—82no—
293D8—82no—
294M16—41no—
295M16—41no—
296C2×C8—41no—
297C2×C8—41no—
298C2×C8—41no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—42no—
304C4⋊C4—42no—
305C4⋊C4—42no—
306C4⋊C4—42no—
307C4⋊C4—42no—
308C22⋊C4—24no—
309C22⋊C4—42no—
310C22⋊C4—41no—
311C22⋊C4—41no—
312C22⋊C4—42no—
313C22⋊C4—42no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C42—21no—
317C42—21no—
318C23—22no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23C29×#12011yescharacteristic
327Q8—41no—
328Q8—41no—
329Q8—42no—
330Q8—81no—
331D4—41no—
332D4—41no—
333D4—42no—
334D4—81no—
335D4—81no—
336D4—81no—
337D4—81no—
338D4—81no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4—84no—
364C2×C4C29×#13511yescharacteristic
365C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
366C8—81no—
367C8—81no—
368C8—81no—
369C22—21no—
370C22—21no—
371C22—42no—
372C22—42no—
373C22—42no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22—81no—
378C22—81no—
379C22—81no—
380C22—81no—
381C22C29×#44911yescharacteristic
382C22C29×#45411yescharacteristic
383C22C29×B(4,𝔽2)11yescharacteristic
384C4—21no—
385C4—21no—
386C4—42no—
387C4—41no—
388C4—41no—
389C4—42no—
390C4—81no—
391C4—81no—
392C4—81no—
393C4—81no—
394C2—21no—
395C2—21no—
396C2—82no—
397C2—161no—
398C2C29×#159711yescharacteristic
399C2C29×#219611yescharacteristic
400C2C29×#220311yescharacteristic
subgroupG/H
center, socleC22×C29B(4,𝔽2)
commutator, Frattini, cosocleC2×C4⋊C4C23×C29
prime radicalC29×#1598C2
LCSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C23×C29 ◁ C2×C4⋊C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#2680C2semidirect
2. C29×#2039C2semidirect
3. C29×#1604C2semidirect
5. C29×#1354C2semidirect
6. C29×#1345C2semidirect
7. C29×#1325C2semidirect
117. #12140C29direct (N × H)
169. #2680C2×C29semidirect
170. #2039C2×C29semidirect
171. #1604C2×C29semidirect
173. #1354C2×C29semidirect
174. #1345C2×C29semidirect
175. #1325C2×C29semidirect
265. C29#12140direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#26802
C29×#20392
C29×#16042
C29×#15982
C29×#13542
C29×#13452
C29×#13252
#1214029