Finite Group Databasebeta

← C29×#10189 #20305089

Subgroups — C29×#10189 #20305089

Order 7424.

518 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3227C211yesmaximal, characteristic
2C2×C29×#475C211yesmaximal, characteristic, complemented
3C29×#3037C211yesmaximal, characteristic
4C29×#1548C211yesmaximal, characteristic, complemented
5C29×#1480C211yesmaximal, characteristic
6C29×#1461C211yesmaximal, characteristic, complemented
7C29×#1301C211yesmaximal, characteristic, complemented
8C2×C29×#137—21no—
9C29×#532C2211yescharacteristic
10C2×C29×C4⋊Q8C2211yescharacteristic
11C2×C4×Q8×C29C2211yescharacteristic
12C29×#498—21no—
13C29×#486—21no—
14C29×#481—22no—
15C29×#476—22no—
16C29×#475—22no—
17C29×#475—22no—
18C29×#464—22no—
19C29×#462—21no—
20C29×#460—21no—
21C29×#431C2211yescharacteristic
22C29×#431C2211yescharacteristic
23C2×C29×#106—21no—
24C29×#423C2211yescharacteristic
25C2×C29×C4⋊C8C2211yescharacteristic
26C29×#417—21no—
27C2×C29×#103—21no—
28C29×#333—22no—
29C29×D4⋊C8—22no—
30C29×#324—22no—
31C2×#41×C29—21no—
32C22×Q8×C29—21no—
33C22×Q8×C29D411yescharacteristic
34C29×#137—42no—
35C29×#137—42no—
36C2×Q16×C29—22no—
37C2×SD16×C29—22no—
38C2×M16×C29—21no—
39C22×C8×C29—21no—
40C29×C4⋊Q8—21no—
41C29×C4⋊Q8—21no—
42C29×C4⋊Q8—21no—
43C29×C4⋊Q8D411yescharacteristic
44C29×C4⋊Q8D412yes—
45C29×#127D411yescharacteristic
46C29×#124—21no—
47C29×#121—21no—
48C29×#121—21no—
49C4×Q8×C29—21no—
50C4×Q8×C29—21no—
51C4×Q8×C29—21no—
52C4×Q8×C29—21no—
53C4×D4×C29—21no—
54C4×D4×C29—21no—
55C2×C4⋊C4×C29—21no—
56C2×C4⋊C4×C29—21no—
57C2×C4⋊C4×C29—21no—
58C2×C4⋊C4×C29D411yescharacteristic
59C2×C42×C29—21no—
60C2×C42×C29C2311yescharacteristic
61C29×#106—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×#103—24no—
71C29×#102—22no—
72C29×#102—24no—
73C29×C22⋊C8—21no—
74C29×C22⋊C8D412yes—
75C4×C8×C29—21no—
76C4×C8×C29—21no—
77#41×C29—41no—
78#41×C29—41no—
79#41×C29—41no—
80#41×C29—41no—
81C2×Q8×C29—21no—
82C2×Q8×C29—21no—
83C2×Q8×C29—21no—
84C2×Q8×C29—21no—
85C2×Q8×C29—22no—
86C2×Q8×C29—21no—
87C2×Q8×C29—21no—
88C2×Q8×C29—41no—
89C2×Q8×C29—82no—
90C2×Q8×C29SD1612yes—
91C2×D4×C29—21no—
92C2×D4×C29—21no—
93C2×D4×C29—21no—
94C2×D4×C29—41no—
95C22×C4×C29—21no—
96C22×C4×C29—21no—
97C22×C4×C29—41no—
98C22×C4×C29—41no—
99C22×C4×C29C2×D411yescharacteristic
100C22×C4×C29C2×D411yescharacteristic
101C22×C4×C29#4111yescharacteristic
102Q16×C29—44no—
103SD16×C29—44no—
104M16×C29—41no—
105M16×C29—41no—
106C2×C8×C29—22no—
107C2×C8×C29—22no—
108C2×C8×C29—22no—
109C2×C8×C29—41no—
110C2×C8×C29—41no—
111C2×C8×C29—41no—
112C4⋊C4×C29—22no—
113C4⋊C4×C29—22no—
114C4⋊C4×C29—21no—
115C4⋊C4×C29—21no—
116C4⋊C4×C29—21no—
117C4⋊C4×C29—21no—
118C4⋊C4×C29—41no—
119C4⋊C4×C29—41no—
120C4⋊C4×C29—41no—
121C4⋊C4×C29—41no—
122C22⋊C4×C29—41no—
123C22⋊C4×C29—41no—
124C42×C29—41no—
125C42×C29—41no—
126C42×C29C2×D411yescharacteristic
127C42×C29C2×D411yescharacteristic
128C42×C29C2×D411yescharacteristic
129C42×C29C2×D411yescharacteristic
130#10189C2911yesmaximal, characteristic, direct product factor, Sylow
131C23×C29—41no—
132C23×C29#12111yescharacteristic
133Q8×C29—22no—
134Q8×C29—22no—
135Q8×C29—41no—
136Q8×C29—41no—
137Q8×C29—41no—
138Q8×C29—41no—
139Q8×C29—82no—
140Q8×C29—82no—
141D4×C29—42no—
142D4×C29—41no—
143D4×C29—41no—
144D4×C29—42no—
145D4×C29—81no—
146D4×C29—81no—
147C2×C4×C29—22no—
148C2×C4×C29—22no—
149C2×C4×C29—41no—
150C2×C4×C29—41no—
151C2×C4×C29—41no—
152C2×C4×C29—41no—
153C2×C4×C29—41no—
154C2×C4×C29—42no—
155C2×C4×C29—82no—
156C2×C4×C29—81no—
157C2×C4×C29—81no—
158C2×C4×C29—81no—
159C2×C4×C29#12011yescharacteristic
160C2×C4×C29#12011yescharacteristic
161C2×C4×C29#12011yescharacteristic
162C2×C4×C29#12111yescharacteristic
163C2×C4×C29#12111yescharacteristic
164C2×C4×C29#12711yescharacteristic
165C2×C4×C29C2×SD1611yescharacteristic
166C2×C4×C29#13511yescharacteristic
167C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
168C2×C4×C29#13711yescharacteristic
169C8×C29—42no—
170C8×C29—42no—
171C8×C29—42no—
172C8×C29—81no—
173#3227C2×C2911yescharacteristic
174C2×#475C2×C2911yescharacteristic, complemented
175#3037C2×C2911yescharacteristic
176#1548C2×C2911yescharacteristic, complemented
177#1480C2×C2911yescharacteristic
178#1461C2×C2911yescharacteristic, complemented
179#1301C2×C2911yescharacteristic, complemented
180C22×C29—21no—
181C22×C29—21no—
182C22×C29—81no—
183C22×C29—81no—
184C22×C29—81no—
185C22×C29#39211yescharacteristic
186C22×C29#46511yescharacteristic
187C22×C29#46811yescharacteristic
188C4×C29—21no—
189C4×C29—21no—
190C4×C29—21no—
191C4×C29—42no—
192C4×C29—81no—
193C4×C29—81no—
194C4×C29—82no—
195C4×C29#44811yescharacteristic
196C4×C29#44911yescharacteristic
197C4×C29#45011yescharacteristic
198C4×C29#45211yescharacteristic
199C4×C29#47112yes—
200C2×#137—21no—
201#532C22×C2911yescharacteristic
202C2×C4⋊Q8C22×C2911yescharacteristic
203C2×C4×Q8C22×C2911yescharacteristic
204#498—21no—
205#486—21no—
206#481—22no—
207#476—22no—
208#475—22no—
209#475—22no—
210#464—22no—
211#462—21no—
212#460—21no—
213#431C22×C2911yescharacteristic
214#431C22×C2911yescharacteristic
215C2×#106—21no—
216#423C22×C2911yescharacteristic
217C2×C4⋊C8C22×C2911yescharacteristic
218#417—21no—
219C2×#103—21no—
220#333—22no—
221D4⋊C8—22no—
222#324—22no—
223C2×C29—21no—
224C2×C29—21no—
225C2×C29—161no—
226C2×C29#200011yescharacteristic
227C2×C29#200911yescharacteristic
228C2×C29#201911yescharacteristic
229C2×#41—21no—
230C22×Q8—21no—
231C22×Q8D4×C2911yescharacteristic
232#137—42no—
233#137—42no—
234C2×Q16—22no—
235C2×SD16—22no—
236C2×M16—21no—
237C22×C8—21no—
238C4⋊Q8—21no—
239C4⋊Q8—21no—
240C4⋊Q8—21no—
241C4⋊Q8D4×C2912yes—
242C4⋊Q8D4×C2911yescharacteristic
243#127D4×C2911yescharacteristic
244#124—21no—
245#121—21no—
246#121—21no—
247C4×Q8—21no—
248C4×Q8—21no—
249C4×Q8—21no—
250C4×Q8—21no—
251C4×D4—21no—
252C4×D4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4D4×C2911yescharacteristic
257C2×C42—21no—
258C2×C42C23×C2911yescharacteristic
259#106—24no—
260#106—24no—
261C4⋊C8—21no—
262C4⋊C8—21no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8D4×C2912yes—
266C4⋊C8D4×C2912yes—
267#103—24no—
268#103—22no—
269#102—22no—
270#102—24no—
271C22⋊C8—21no—
272C22⋊C8D4×C2912yes—
273C4×C8—21no—
274C4×C8—21no—
275C29#1018911yescharacteristic, direct product factor, Sylow
276#41—41no—
277#41—41no—
278#41—41no—
279#41—41no—
280C2×Q8—21no—
281C2×Q8—21no—
282C2×Q8—21no—
283C2×Q8—21no—
284C2×Q8—22no—
285C2×Q8—21no—
286C2×Q8—21no—
287C2×Q8—41no—
288C2×Q8—82no—
289C2×Q8SD16×C2912yes—
290C2×D4—21no—
291C2×D4—21no—
292C2×D4—21no—
293C2×D4—41no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—41no—
297C22×C4—41no—
298C22×C4C2×D4×C2911yescharacteristic
299C22×C4C2×D4×C2911yescharacteristic
300C22×C4#41×C2911yescharacteristic
301Q16—44no—
302SD16—44no—
303M16—41no—
304M16—41no—
305C2×C8—22no—
306C2×C8—22no—
307C2×C8—22no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—41no—
311C4⋊C4—21no—
312C4⋊C4—22no—
313C4⋊C4—22no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C42—41no—
324C42—41no—
325C42C2×D4×C2911yescharacteristic
326C42C2×D4×C2911yescharacteristic
327C42C2×D4×C2911yescharacteristic
328C42C2×D4×C2911yescharacteristic
329C23—41no—
330C23C29×#12111yescharacteristic
331Q8—22no—
332Q8—22no—
333Q8—41no—
334Q8—41no—
335Q8—41no—
336Q8—41no—
337Q8—82no—
338Q8—82no—
339D4—42no—
340D4—41no—
341D4—41no—
342D4—42no—
343D4—81no—
344D4—81no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—42no—
353C2×C4—82no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4C29×#12011yescharacteristic
358C2×C4C29×#12011yescharacteristic
359C2×C4C29×#12011yescharacteristic
360C2×C4C29×#12111yescharacteristic
361C2×C4C29×#12111yescharacteristic
362C2×C4C29×#12711yescharacteristic
363C2×C4C2×SD16×C2911yescharacteristic
364C2×C4C29×#13511yescharacteristic
365C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
366C2×C4C29×#13711yescharacteristic
367C8—42no—
368C8—42no—
369C8—42no—
370C8—81no—
371C22—21no—
372C22—21no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22C29×#39211yescharacteristic
377C22C29×#46511yescharacteristic
378C22C29×#46811yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—42no—
383C4—81no—
384C4—81no—
385C4—82no—
386C4C29×#44811yescharacteristic
387C4C29×#44911yescharacteristic
388C4C29×#45011yescharacteristic
389C4C29×#45211yescharacteristic
390C4C29×#47112yes—
391C2—21no—
392C2—21no—
393C2—161no—
394C2C29×#200011yescharacteristic
395C2C29×#200911yescharacteristic
396C2C29×#201911yescharacteristic
subgroupG/H
center, socleC22×C29#392
commutator, Frattini, cosocleC2×C42C23×C29
prime radicalC29×#532C22
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
2. C2×C29×#475C2semidirect
4. C29×#1548C2semidirect
6. C29×#1461C2semidirect
7. C29×#1301C2semidirect
130. #10189C29direct (N × H)
174. C2×#475C2×C29semidirect
176. #1548C2×C29semidirect
178. #1461C2×C29semidirect
179. #1301C2×C29semidirect
275. C29#10189direct (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×#4752
C29×#30372
C29×#15482
C29×#14802
C29×#14612
C29×#13012
#1018929