Finite Group Databasebeta

← C29×#10456 #20305356

Subgroups — C29×#10456 #20305356

Order 7424.

460 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3036C211yesmaximal, characteristic
2C29×#1800C211yesmaximal, characteristic, complemented
3C29×#1567C211yesmaximal, characteristic, complemented
4C29×#1547C211yesmaximal, characteristic, complemented
5C29×#1492C211yesmaximal, characteristic, complemented
6C2×C29×D4⋊C8C211yesmaximal, characteristic, complemented
7C29×#1292C211yesmaximal, characteristic, complemented
8C2×C29×AGL(1,ℤ/8)—21no—
9C29×#532C2211yescharacteristic
10C2×C4×D4×C29C2211yescharacteristic
11C29×#463—22no—
12C29×#461—21no—
13C29×#459—21no—
14C29×#423C2211yescharacteristic
15C29×#423C2211yescharacteristic
16C29×#423C2211yescharacteristic
17C2×C29×C4⋊C8C2211yescharacteristic
18C29×#417—21no—
19C2×C29×#100—21no—
20C2×C4×C8×C29C2211yescharacteristic
21C29×#343—21no—
22C29×#335—22no—
23C29×#332—21no—
24C29×#331—21no—
25C29×D4⋊C8—21no—
26C29×D4⋊C8—21no—
27C29×D4⋊C8—21no—
28C29×D4⋊C8—21no—
29C2×#41×C29—21no—
30C22×D4×C29D411yescharacteristic
31C23×C4×C29—21no—
32C29×AGL(1,ℤ/8)—42no—
33C29×AGL(1,ℤ/8)—42no—
34C2×SD16×C29—22no—
35C2×D8×C29—22no—
36C2×M16×C29—21no—
37C2×M16×C29—21no—
38C2×M16×C29—21no—
39C22×C8×C29—21no—
40C22×C8×C29—21no—
41C29×C4⋊Q8D411yescharacteristic
42C29×#127D411yescharacteristic
43C29×#124—21no—
44C29×#121—21no—
45C29×#121—21no—
46C4×D4×C29—21no—
47C4×D4×C29—21no—
48C4×D4×C29—21no—
49C4×D4×C29—21no—
50C4×D4×C29—21no—
51C4×D4×C29—21no—
52C2×C4⋊C4×C29D411yescharacteristic
53C2×C22⋊C4×C29—21no—
54C2×C42×C29C2311yescharacteristic
55C29×C4⋊C8—21no—
56C29×C4⋊C8—21no—
57C29×C4⋊C8—21no—
58C29×C4⋊C8—21no—
59C29×C4⋊C8—21no—
60C29×C4⋊C8—21no—
61C29×C4⋊C8—21no—
62C29×C4⋊C8D412yes—
63C29×#103—22no—
64C29×#102—22no—
65C29×#100—42no—
66C4×C8×C29—21no—
67C4×C8×C29D411yescharacteristic
68C4×C8×C29D411yescharacteristic
69C24×C29—21no—
70#41×C29—41no—
71#41×C29—41no—
72#41×C29—41no—
73#41×C29—41no—
74C2×Q8×C29—21no—
75C2×D4×C29—21no—
76C2×D4×C29—21no—
77C2×D4×C29—21no—
78C2×D4×C29—21no—
79C2×D4×C29—21no—
80C2×D4×C29—21no—
81C2×D4×C29—21no—
82C2×D4×C29—21no—
83C2×D4×C29—41no—
84C2×D4×C29D812yes—
85C22×C4×C29—21no—
86C22×C4×C29—41no—
87C22×C4×C29—41no—
88C22×C4×C29—41no—
89C22×C4×C29—81no—
90C22×C4×C29—81no—
91C22×C4×C29C2×D411yescharacteristic
92C22×C4×C29#4111yescharacteristic
93C22×C4×C29#4111yescharacteristic
94SD16×C29—44no—
95D8×C29—44no—
96M16×C29—41no—
97M16×C29—41no—
98M16×C29—41no—
99M16×C29—41no—
100M16×C29—41no—
101M16×C29—41no—
102C2×C8×C29—21no—
103C2×C8×C29—22no—
104C2×C8×C29—21no—
105C2×C8×C29—42no—
106C2×C8×C29—41no—
107C2×C8×C29—41no—
108C2×C8×C29—41no—
109C2×C8×C29—81no—
110C4⋊C4×C29—21no—
111C4⋊C4×C29—21no—
112C4⋊C4×C29—21no—
113C4⋊C4×C29—21no—
114C22⋊C4×C29—41no—
115C22⋊C4×C29—41no—
116C22⋊C4×C29—41no—
117C22⋊C4×C29—41no—
118C42×C29C2×D411yescharacteristic
119C42×C29C2×D411yescharacteristic
120C42×C29C2×D411yescharacteristic
121C42×C29#4111yescharacteristic
122#10456C2911yesmaximal, characteristic, direct product factor, Sylow
123C23×C29—22no—
124C23×C29—41no—
125C23×C29—41no—
126C23×C29—41no—
127C23×C29—81no—
128C23×C29—81no—
129C23×C29#12311yescharacteristic
130Q8×C29—41no—
131Q8×C29—41no—
132D4×C29—22no—
133D4×C29—22no—
134D4×C29—41no—
135D4×C29—41no—
136D4×C29—41no—
137D4×C29—41no—
138D4×C29—41no—
139D4×C29—41no—
140D4×C29—81no—
141D4×C29—81no—
142D4×C29—81no—
143C2×C4×C29—21no—
144C2×C4×C29—21no—
145C2×C4×C29—41no—
146C2×C4×C29—41no—
147C2×C4×C29—41no—
148C2×C4×C29—82no—
149C2×C4×C29—81no—
150C2×C4×C29—81no—
151C2×C4×C29—81no—
152C2×C4×C29—81no—
153C2×C4×C29—81no—
154C2×C4×C29#12011yescharacteristic
155C2×C4×C29#12111yescharacteristic
156C2×C4×C29#12111yescharacteristic
157C2×C4×C29#12111yescharacteristic
158C2×C4×C29#12311yescharacteristic
159C2×C4×C29#12411yescharacteristic
160C2×C4×C29C2×D811yescharacteristic
161C2×C4×C29#13511yescharacteristic
162C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
163C2×C4×C29#13711yescharacteristic
164C8×C29—22no—
165C8×C29—41no—
166C8×C29—42no—
167C8×C29—81no—
168C8×C29—81no—
169C8×C29—81no—
170#3036C2×C2911yescharacteristic
171#1800C2×C2911yescharacteristic, complemented
172#1567C2×C2911yescharacteristic, complemented
173#1547C2×C2911yescharacteristic, complemented
174#1492C2×C2911yescharacteristic, complemented
175C2×D4⋊C8C2×C2911yescharacteristic, complemented
176#1292C2×C2911yescharacteristic, complemented
177C22×C29—21no—
178C22×C29—21no—
179C22×C29—42no—
180C22×C29—82no—
181C22×C29—82no—
182C22×C29—81no—
183C22×C29—81no—
184C22×C29—81no—
185C22×C29—81no—
186C22×C29—81no—
187C22×C29#39411yescharacteristic
188C22×C29#48011yescharacteristic
189C22×C29#48211yescharacteristic
190C4×C29—21no—
191C4×C29—21no—
192C4×C29—21no—
193C4×C29—81no—
194C4×C29—81no—
195C4×C29#44711yescharacteristic
196C4×C29#45211yescharacteristic
197C4×C29#46611yescharacteristic
198C4×C29#46811yescharacteristic
199C4×C29#47111yescharacteristic
200C4×C29#47211yescharacteristic
201C2×AGL(1,ℤ/8)—21no—
202#532C22×C2911yescharacteristic
203C2×C4×D4C22×C2911yescharacteristic
204#463—22no—
205#461—21no—
206#459—21no—
207#423C22×C2911yescharacteristic
208#423C22×C2911yescharacteristic
209#423C22×C2911yescharacteristic
210C2×C4⋊C8C22×C2911yescharacteristic
211#417—21no—
212C2×#100—21no—
213C2×C4×C8C22×C2911yescharacteristic
214#343—21no—
215#335—22no—
216#332—21no—
217#331—21no—
218D4⋊C8—21no—
219D4⋊C8—21no—
220D4⋊C8—21no—
221D4⋊C8—21no—
222C2×C29—21no—
223C2×C29—21no—
224C2×C29—82no—
225C2×C29—161no—
226C2×C29#203311yescharacteristic
227C2×C29#205011yescharacteristic
228C2×C29#205111yescharacteristic
229C2×#41—21no—
230C22×D4D4×C2911yescharacteristic
231C23×C4—21no—
232AGL(1,ℤ/8)—42no—
233AGL(1,ℤ/8)—42no—
234C2×SD16—22no—
235C2×D8—22no—
236C2×M16—21no—
237C2×M16—21no—
238C2×M16—21no—
239C22×C8—21no—
240C22×C8—21no—
241C4⋊Q8D4×C2911yescharacteristic
242#127D4×C2911yescharacteristic
243#124—21no—
244#121—21no—
245#121—21no—
246C4×D4—21no—
247C4×D4—21no—
248C4×D4—21no—
249C4×D4—21no—
250C4×D4—21no—
251C4×D4—21no—
252C2×C4⋊C4D4×C2911yescharacteristic
253C2×C22⋊C4—21no—
254C2×C42C23×C2911yescharacteristic
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8—21no—
259C4⋊C8—21no—
260C4⋊C8—21no—
261C4⋊C8—21no—
262C4⋊C8D4×C2912yes—
263#103—22no—
264#102—22no—
265#100—42no—
266C4×C8—21no—
267C4×C8D4×C2911yescharacteristic
268C4×C8D4×C2911yescharacteristic
269C29#1045611yescharacteristic, direct product factor, Sylow
270C24—21no—
271#41—41no—
272#41—41no—
273#41—41no—
274#41—41no—
275C2×Q8—21no—
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—21no—
279C2×D4—21no—
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—41no—
285C2×D4D8×C2912yes—
286C22×C4—21no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—81no—
291C22×C4—81no—
292C22×C4C2×D4×C2911yescharacteristic
293C22×C4#41×C2911yescharacteristic
294C22×C4#41×C2911yescharacteristic
295SD16—44no—
296D8—44no—
297M16—41no—
298M16—41no—
299M16—41no—
300M16—41no—
301M16—41no—
302M16—41no—
303C2×C8—21no—
304C2×C8—22no—
305C2×C8—21no—
306C2×C8—42no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—81no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C22⋊C4—41no—
318C22⋊C4—41no—
319C42C2×D4×C2911yescharacteristic
320C42C2×D4×C2911yescharacteristic
321C42C2×D4×C2911yescharacteristic
322C42#41×C2911yescharacteristic
323C23—22no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23—81no—
328C23—81no—
329C23C29×#12311yescharacteristic
330Q8—41no—
331Q8—41no—
332D4—22no—
333D4—22no—
334D4—41no—
335D4—41no—
336D4—41no—
337D4—41no—
338D4—41no—
339D4—41no—
340D4—81no—
341D4—81no—
342D4—81no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—82no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4—81no—
353C2×C4—81no—
354C2×C4C29×#12011yescharacteristic
355C2×C4C29×#12111yescharacteristic
356C2×C4C29×#12111yescharacteristic
357C2×C4C29×#12111yescharacteristic
358C2×C4C29×#12311yescharacteristic
359C2×C4C29×#12411yescharacteristic
360C2×C4C2×D8×C2911yescharacteristic
361C2×C4C29×#13511yescharacteristic
362C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
363C2×C4C29×#13711yescharacteristic
364C8—22no—
365C8—41no—
366C8—42no—
367C8—81no—
368C8—81no—
369C8—81no—
370C22—21no—
371C22—21no—
372C22—42no—
373C22—82no—
374C22—82no—
375C22—81no—
376C22—81no—
377C22—81no—
378C22—81no—
379C22—81no—
380C22C29×#39411yescharacteristic
381C22C29×#48011yescharacteristic
382C22C29×#48211yescharacteristic
383C4—21no—
384C4—21no—
385C4—21no—
386C4—81no—
387C4—81no—
388C4C29×#44711yescharacteristic
389C4C29×#45211yescharacteristic
390C4C29×#46611yescharacteristic
391C4C29×#46811yescharacteristic
392C4C29×#47111yescharacteristic
393C4C29×#47211yescharacteristic
394C2—21no—
395C2—21no—
396C2—82no—
397C2—161no—
398C2C29×#203311yescharacteristic
399C2C29×#205011yescharacteristic
400C2C29×#205111yescharacteristic
subgroupG/H
center, socleC22×C29#394
commutator, Frattini, cosocleC2×C42C23×C29
prime radicalC29×#3036C2
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. C29×#1800C2semidirect
3. C29×#1567C2semidirect
4. C29×#1547C2semidirect
5. C29×#1492C2semidirect
6. C2×C29×D4⋊C8C2semidirect
7. C29×#1292C2semidirect
122. #10456C29direct (N × H)
171. #1800C2×C29semidirect
172. #1567C2×C29semidirect
173. #1547C2×C29semidirect
174. #1492C2×C29semidirect
175. C2×D4⋊C8C2×C29semidirect
176. #1292C2×C29semidirect
269. C29#10456direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#30362
C29×#18002
C29×#15672
C29×#15472
C29×#14922
C2×C29×D4⋊C82
C29×#12922
#1045629