Finite Group Databasebeta

← C29×#13005 #20307905

Subgroups — C29×#13005 #20307905

Order 7424.

492 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3067C211yesmaximal, characteristic
2C29×#2912C211yesmaximal, characteristic, complemented
3C29×#2145C211yesmaximal, characteristic, complemented
4C2×C29×#360C211yesmaximal, characteristic, complemented
5C29×#2117C211yesmaximal, characteristic, complemented
6C29×#1389C211yesmaximal, characteristic, complemented
7C29×#1383C211yesmaximal, characteristic, complemented
8C29×#575—21no—
9C2×C29×#135C2211yescharacteristic
10C2×C29×#131C2211yescharacteristic
11C29×#520—21no—
12C2×C29×M32C2211yescharacteristic
13C2×C29×M32C2211yescharacteristic
14C29×#473C412yescomplemented
15C29×#472C412yescomplemented
16C29×#471—22no—
17C2×C29×#108C2211yescharacteristic
18C29×#428—22no—
19C29×#428—21no—
20C29×#427—21no—
21C29×#427C2211yescharacteristic
22C2×C29×#106—21no—
23C2×C29×#106C2211yescharacteristic
24C29×#413—21no—
25C29×#360—22no—
26C29×#360—21no—
27C29×#360—21no—
28C29×#350—22no—
29C2×#41×C29—21no—
30C2×#41×C29D411yescharacteristic
31C29×#137—22no—
32C29×#137—41no—
33C29×AGL(1,ℤ/8)—22no—
34C29×AGL(1,ℤ/8)—41no—
35C29×#135—21no—
36C29×#135—21no—
37C29×#135—21no—
38C29×#135—21no—
39C29×#135—42no—
40C2×Q16×C29C2×C411yescharacteristic, complemented
41C2×SD16×C29—21no—
42C2×D8×C29C2×C411yescharacteristic, complemented
43C29×#131—21no—
44C29×#131—21no—
45C29×#131C2×C412yes—
46C29×#131D412yes—
47C2×M16×C29—21no—
48C2×M16×C29—21no—
49C2×M16×C29D411yescharacteristic
50C22×C8×C29—21no—
51C22×C8×C29C2311yescharacteristic
52C4×Q8×C29—41no—
53C4×D4×C29—42no—
54C4×D4×C29—41no—
55C29×#117—22no—
56C29×#117—21no—
57C2×C4⋊C4×C29—22no—
58C2×C4⋊C4×C29—21no—
59C29×M32—21no—
60C29×M32—21no—
61C29×M32—21no—
62C29×M32—21no—
63C2×C16×C29—21no—
64C2×C16×C29—21no—
65C29×#108—21no—
66C29×#108C2×C412yescomplemented
67C29×#107—22no—
68C29×#107—21no—
69C29×#106—22no—
70C29×#106—21no—
71C29×#106D411yescharacteristic
72C29×#106D412yes—
73C29×#106D411yescharacteristic
74C29×#101—22no—
75C29×#100—22no—
76#41×C29—21no—
77#41×C29—21no—
78#41×C29—41no—
79#41×C29—41no—
80#41×C29—41no—
81#41×C29—41no—
82#41×C29C22⋊C412yes—
83#41×C29SD1612yes—
84C2×Q8×C29—21no—
85C2×Q8×C29D811yescharacteristic
86C2×D4×C29—21no—
87C2×D4×C29—21no—
88C2×D4×C29—41no—
89C2×D4×C29D811yescharacteristic
90C22×C4×C29—21no—
91C22×C4×C29—42no—
92C22×C4×C29—41no—
93C22×C4×C29—41no—
94C22×C4×C29C2×D411yescharacteristic
95Q16×C29—21no—
96Q16×C29—21no—
97Q16×C29—42no—
98SD16×C29—42no—
99SD16×C29—42no—
100SD16×C29—41no—
101SD16×C29—41no—
102D8×C29—21no—
103D8×C29—21no—
104D8×C29—42no—
105M16×C29—21no—
106M16×C29—22no—
107M16×C29—22no—
108M16×C29—22no—
109M16×C29—41no—
110M16×C29C22⋊C412yes—
111C2×C8×C29—21no—
112C2×C8×C29—22no—
113C2×C8×C29—22no—
114C2×C8×C29—41no—
115C2×C8×C29C22×C411yescharacteristic
116C2×C8×C29C2×D411yescharacteristic
117C2×C8×C29C2×D411yescharacteristic
118C2×C8×C29C2×D411yescharacteristic
119C2×C8×C29#4111yescharacteristic
120C2×C8×C29#4111yescharacteristic
121C4⋊C4×C29—21no—
122C4⋊C4×C29—22no—
123C4⋊C4×C29—21no—
124C4⋊C4×C29—42no—
125C4⋊C4×C29—41no—
126C22⋊C4×C29—42no—
127C22⋊C4×C29—41no—
128C42×C29—42no—
129C42×C29—41no—
130C16×C29—41no—
131C16×C29—41no—
132#13005C2911yesmaximal, characteristic, direct product factor, Sylow
133C23×C29—21no—
134C23×C29—41no—
135C23×C29AGL(1,ℤ/8)11yescharacteristic
136Q8×C29—21no—
137Q8×C29—41no—
138Q8×C29—41no—
139Q8×C29#10212yes—
140D4×C29—22no—
141D4×C29—22no—
142D4×C29—21no—
143D4×C29—41no—
144D4×C29—41no—
145D4×C29—81no—
146D4×C29—81no—
147D4×C29#10212yes—
148C2×C4×C29—21no—
149C2×C4×C29—22no—
150C2×C4×C29—22no—
151C2×C4×C29—41no—
152C2×C4×C29—41no—
153C2×C4×C29—42no—
154C2×C4×C29—41no—
155C2×C4×C29—81no—
156C2×C4×C29—81no—
157C2×C4×C29—161no—
158C2×C4×C29—162no—
159C2×C4×C29C2×C22⋊C411yescharacteristic
160C2×C4×C29#12011yescharacteristic
161C2×C4×C29#12311yescharacteristic
162C2×C4×C29C2×D811yescharacteristic
163C2×C4×C29C2×SD1611yescharacteristic
164C2×C4×C29#13711yescharacteristic
165C8×C29—22no—
166C8×C29—42no—
167C8×C29C4×D411yescharacteristic
168C8×C29C4×D411yescharacteristic
169C8×C29#12111yescharacteristic
170C8×C29#12111yescharacteristic
171#3067C2×C2911yescharacteristic
172#2912C2×C2911yescharacteristic, complemented
173#2145C2×C2911yescharacteristic, complemented
174C2×#360C2×C2911yescharacteristic, complemented
175#2117C2×C2911yescharacteristic, complemented
176#1389C2×C2911yescharacteristic, complemented
177#1383C2×C2911yescharacteristic, complemented
178C22×C29—22no—
179C22×C29—41no—
180C22×C29—42no—
181C22×C29—81no—
182C22×C29—161no—
183C22×C29#41711yescharacteristic
184C22×C29#44711yescharacteristic
185C22×C29#48111yescharacteristic
186C4×C29—22no—
187C4×C29—81no—
188C4×C29—82no—
189C4×C29—81no—
190C4×C29—81no—
191C4×C29#38611yescharacteristic
192C4×C29C2×#10211yescharacteristic
193C4×C29#44811yescharacteristic
194C4×C29#48011yescharacteristic
195#575—21no—
196C2×#135C22×C2911yescharacteristic
197C2×#131C22×C2911yescharacteristic
198#520—21no—
199C2×M32C22×C2911yescharacteristic
200C2×M32C22×C2911yescharacteristic
201#473C4×C2912yescomplemented
202#472C4×C2912yescomplemented
203#471—22no—
204C2×#108C22×C2911yescharacteristic
205#428—21no—
206#428—22no—
207#427—21no—
208#427C22×C2911yescharacteristic
209C2×#106—21no—
210C2×#106C22×C2911yescharacteristic
211#413—21no—
212#360—22no—
213#360—21no—
214#360—21no—
215#350—22no—
216C2×C29—21no—
217C2×C29—21no—
218C2×C29—21no—
219C2×C29—42no—
220C2×C29—161no—
221C2×C29#187411yescharacteristic
222C2×#41—21no—
223C2×#41D4×C2911yescharacteristic
224#137—22no—
225#137—41no—
226AGL(1,ℤ/8)—22no—
227AGL(1,ℤ/8)—41no—
228#135—21no—
229#135—21no—
230#135—21no—
231#135—21no—
232#135—42no—
233C2×Q16C2×C4×C2911yescharacteristic, complemented
234C2×SD16—21no—
235C2×D8C2×C4×C2911yescharacteristic, complemented
236#131—21no—
237#131—21no—
238#131C2×C4×C2912yes—
239#131D4×C2912yes—
240C2×M16—21no—
241C2×M16—21no—
242C2×M16D4×C2911yescharacteristic
243C22×C8—21no—
244C22×C8C23×C2911yescharacteristic
245C4×Q8—41no—
246C4×D4—42no—
247C4×D4—41no—
248#117—22no—
249#117—21no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—21no—
252M32—21no—
253M32—21no—
254M32—21no—
255M32—21no—
256C2×C16—21no—
257C2×C16—21no—
258#108—21no—
259#108C2×C4×C2912yescomplemented
260#107—22no—
261#107—21no—
262#106—22no—
263#106—21no—
264#106D4×C2911yescharacteristic
265#106D4×C2912yes—
266#106D4×C2911yescharacteristic
267#101—22no—
268#100—22no—
269C29#1300511yescharacteristic, direct product factor, Sylow
270#41—21no—
271#41—21no—
272#41—41no—
273#41—41no—
274#41—41no—
275#41—41no—
276#41C22⋊C4×C2912yes—
277#41SD16×C2912yes—
278C2×Q8—21no—
279C2×Q8D8×C2911yescharacteristic
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—41no—
283C2×D4D8×C2911yescharacteristic
284C22×C4—21no—
285C22×C4—42no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4C2×D4×C2911yescharacteristic
289Q16—21no—
290Q16—21no—
291Q16—42no—
292SD16—42no—
293SD16—42no—
294SD16—41no—
295SD16—41no—
296D8—21no—
297D8—21no—
298D8—42no—
299M16—21no—
300M16—22no—
301M16—22no—
302M16—22no—
303M16—41no—
304M16C22⋊C4×C2912yes—
305C2×C8—21no—
306C2×C8—22no—
307C2×C8—22no—
308C2×C8—41no—
309C2×C8C22×C4×C2911yescharacteristic
310C2×C8C2×D4×C2911yescharacteristic
311C2×C8C2×D4×C2911yescharacteristic
312C2×C8C2×D4×C2911yescharacteristic
313C2×C8#41×C2911yescharacteristic
314C2×C8#41×C2911yescharacteristic
315C4⋊C4—21no—
316C4⋊C4—22no—
317C4⋊C4—21no—
318C4⋊C4—42no—
319C4⋊C4—41no—
320C22⋊C4—42no—
321C22⋊C4—41no—
322C42—42no—
323C42—41no—
324C16—41no—
325C16—41no—
326C23—21no—
327C23—41no—
328C23C29×AGL(1,ℤ/8)11yescharacteristic
329Q8—21no—
330Q8—41no—
331Q8—41no—
332Q8C29×#10212yes—
333D4—22no—
334D4—22no—
335D4—21no—
336D4—41no—
337D4—41no—
338D4—81no—
339D4—81no—
340D4C29×#10212yes—
341C2×C4—21no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—41no—
345C2×C4—42no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—81no—
349C2×C4—81no—
350C2×C4—161no—
351C2×C4—162no—
352C2×C4C2×C22⋊C4×C2911yescharacteristic
353C2×C4C29×#12011yescharacteristic
354C2×C4C29×#12311yescharacteristic
355C2×C4C2×D8×C2911yescharacteristic
356C2×C4C2×SD16×C2911yescharacteristic
357C2×C4C29×#13711yescharacteristic
358C8—22no—
359C8—42no—
360C8C4×D4×C2911yescharacteristic
361C8C4×D4×C2911yescharacteristic
362C8C29×#12111yescharacteristic
363C8C29×#12111yescharacteristic
364C22—22no—
365C22—41no—
366C22—42no—
367C22—81no—
368C22—161no—
369C22C29×#41711yescharacteristic
370C22C29×#44711yescharacteristic
371C22C29×#48111yescharacteristic
372C4—22no—
373C4—82no—
374C4—81no—
375C4—81no—
376C4—81no—
377C4C29×#38611yescharacteristic
378C4C2×C29×#10211yescharacteristic
379C4C29×#44811yescharacteristic
380C4C29×#48011yescharacteristic
381C2—21no—
382C2—21no—
383C2—21no—
384C2—42no—
385C2—161no—
386C2C29×#187411yescharacteristic
subgroupG/H
center, socleC2×C29#1874
commutatorC2×C8C22×C4×C29
Frattini, cosocleC22×C8C23×C29
prime radicalC29×#3067C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C29 ◁ C22×C4×C29 ◁ C2×C29×#131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#2912C2semidirect
3. C29×#2145C2semidirect
4. C2×C29×#360C2semidirect
5. C29×#2117C2semidirect
6. C29×#1389C2semidirect
7. C29×#1383C2semidirect
14. C29×#473C4semidirect
15. C29×#472C4semidirect
40. C2×Q16×C29C2×C4semidirect
42. C2×D8×C29C2×C4semidirect
66. C29×#108C2×C4semidirect
132. #13005C29direct (N × H)
172. #2912C2×C29semidirect
173. #2145C2×C29semidirect
174. C2×#360C2×C29semidirect
175. #2117C2×C29semidirect
176. #1389C2×C29semidirect
177. #1383C2×C29semidirect
201. #473C4×C29semidirect
202. #472C4×C29semidirect
233. C2×Q16C2×C4×C29semidirect
235. C2×D8C2×C4×C29semidirect
259. #108C2×C4×C29semidirect
269. C29#13005direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#30672
C29×#29122
C29×#21452
C2×C29×#3602
C29×#21172
C29×#13892
C29×#13832
#1300529