Finite Group Databasebeta

← C29×#60218 #20355118

Subgroups — C29×#60218 #20355118

Order 7424.

1950 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3480C211yesmaximal, characteristic
2C29×#2971C212yesmaximal, complemented
3C29×#2969C216yesmaximal, complemented
4C29×#2966C216yesmaximal, complemented
5C8×#41×C29C212yesmaximal, complemented
6Q8×M16×C29C211yesmaximal, characteristic, complemented
7C2×C8×Q8×C29C211yesmaximal, characteristic, complemented
8C29×#2935C213yesmaximal, complemented
9C29×#2931C213yesmaximal, complemented
10C29×#2925C213yesmaximal, complemented
11C4×C29×#131C213yesmaximal, complemented
12C2×C29×#131C2213yes—
13C2×C29×#131C2213yes—
14C29×#559C413yes—
15C29×#557C411yescharacteristic
16C29×#556C413yes—
17C29×#553C416yes—
18C29×#550C411yescharacteristic
19C29×#548C412yes—
20C29×#532C2213yes—
21C29×#529C2216yes—
22C4×#41×C29C2212yes—
23C4×#41×C29C2213yes—
24C2×C4×Q8×C29C2211yescharacteristic
25C29×#446C2216yes—
26C8×Q8×C29C2211yescharacteristic
27C8×Q8×C29C2213yes—
28C8×Q8×C29C2213yes—
29C8×Q8×C29C2211yescharacteristic
30C8×Q8×C29C2212yes—
31C29×#436C2216yes—
32C29×#436C2216yes—
33C29×#436C2216yes—
34C29×#435C22112yes—
35C8×D4×C29C2216yes—
36C8×D4×C29C2216yes—
37C8×D4×C29C2216yes—
38C29×#433C22112yes—
39C29×#432C2216yes—
40C29×#431C2216yes—
41C29×#423C2213yes—
42C2×C29×C4⋊C8C2213yes—
43C29×#408C2216yes—
44C29×#405C2216yes—
45C29×#405C2216yes—
46C29×#405C2211yescharacteristic
47C29×#405C2213yes—
48C4×M16×C29C2213yes—
49C4×M16×C29C2216yes—
50C2×C4×C8×C29C2213yes—
51C2×C4×C8×C29C2216yes—
52C2×#41×C29C2×C412yes—
53C2×#41×C29C2313yes—
54C22×Q8×C29C2×C411yescharacteristic
55C29×#131—212no—
56C29×#131—212no—
57C2×M16×C29C2316yes—
58C2×M16×C29C2316yes—
59C2×M16×C29C2313yes—
60C2×M16×C29C2311yescharacteristic
61C22×C8×C29C2316yes—
62C22×C8×C29C2313yes—
63C22×C8×C29C2316yes—
64C22×C8×C29C2311yescharacteristic
65C29×C4⋊Q8C2×C413yes—
66C29×#127C2×C413yes—
67C29×#126C2×C4112yes—
68C29×#125C2×C416yes—
69C29×#124C2×C416yes—
70C29×#124C2×C416yes—
71C29×#123C2×C4112yes—
72C29×C22⋊Q8C2×C416yes—
73C29×#121C2×C416yes—
74C29×#121C2×C416yes—
75C29×#121C2×C416yes—
76C4×Q8×C29C2×C411yescharacteristic
77C4×Q8×C29C2×C413yes—
78C4×Q8×C29C2×C412yes—
79C4×Q8×C29C2×C413yes—
80C4×Q8×C29C2×C413yes—
81C4×Q8×C29C2311yescharacteristic
82C4×Q8×C29C2313yes—
83C4×D4×C29C2×C416yes—
84C4×D4×C29C2×C413yes—
85C4×D4×C29C2×C416yes—
86C4×D4×C29C2×C416yes—
87C4×D4×C29C2×C413yes—
88C4×D4×C29C2316yes—
89C4×D4×C29C2316yes—
90C29×#117C2×C416yes—
91C29×#117C2316yes—
92C29×#117C2311yescharacteristic
93C2×C4⋊C4×C29C2×C413yes—
94C2×C42×C29C2316yes—
95C2×C42×C29C2313yes—
96C29×C4⋊C8C2313yes—
97C29×C4⋊C8C2316yes—
98C29×C4⋊C8C2313yes—
99C29×C4⋊C8C2316yes—
100C29×C4⋊C8C2316yes—
101C29×C22⋊C8C23112yes—
102C29×C22⋊C8C23112yes—
103C29×#97C2316yes—
104C29×#97C2316yes—
105C29×#97C2312yes—
106C4×C8×C29C2316yes—
107C4×C8×C29C2316yes—
108C4×C8×C29C2313yes—
109C4×C8×C29C2313yes—
110C4×C8×C29C2313yes—
111C4×C8×C29C2313yes—
112C4×C8×C29C2312yes—
113#41×C29—28no—
114#41×C29—26no—
115#41×C29—26no—
116C2×Q8×C29—24no—
117C2×Q8×C29C22×C413yes—
118C2×Q8×C29C22×C413yes—
119C2×Q8×C29C22×C411yescharacteristic
120C2×D4×C29C22×C416yes—
121C2×D4×C29C22×C413yes—
122C2×D4×C29C22×C416yes—
123C2×D4×C29C22×C416yes—
124C22×C4×C29C22×C413yes—
125C22×C4×C29C22×C416yes—
126C22×C4×C29C22×C413yes—
127C22×C4×C29C22×C416yes—
128C22×C4×C29C2416yes—
129C22×C4×C29C2411yescharacteristic
130M16×C29—26no—
131M16×C29—212no—
132M16×C29—212no—
133M16×C29#4114yescomplemented
134C2×C8×C29—26no—
135C2×C8×C29—212no—
136C2×C8×C29—212no—
137C2×C8×C29#4114yescomplemented
138C2×C8×C29C2413yes—
139C2×C8×C29C2413yes—
140C2×C8×C29C2416yes—
141C2×C8×C29C2412yes—
142C2×C8×C29C2411yescharacteristic
143C2×C8×C29C2411yescharacteristic
144C4⋊C4×C29C22×C413yes—
145C4⋊C4×C29C22×C413yes—
146C4⋊C4×C29C22×C416yes—
147C4⋊C4×C29C22×C416yes—
148C4⋊C4×C29C22×C411yescharacteristic
149C4⋊C4×C29C22×C411yescharacteristic
150C4⋊C4×C29C22×C416yes—
151C4⋊C4×C29C22×C416yes—
152C4⋊C4×C29C22×C416yes—
153C22⋊C4×C29C22×C4112yes—
154C22⋊C4×C29C22×C412yes—
155C22⋊C4×C29C22×C416yes—
156C22⋊C4×C29C22×C416yes—
157C22⋊C4×C29C22×C4112yes—
158C42×C29C22×C416yes—
159C42×C29C22×C416yes—
160C42×C29C22×C413yes—
161C42×C29C22×C413yes—
162C42×C29C2412yes—
163C42×C29C2413yes—
164C42×C29C2413yes—
165#60218C2911yesmaximal, characteristic, direct product factor, Sylow
166C23×C29C23×C416yes—
167C23×C29C23×C411yescharacteristic
168Q8×C29—26no—
169Q8×C29—26no—
170Q8×C29#13114yescomplemented
171D4×C29—212no—
172D4×C29—26no—
173D4×C29—212no—
174D4×C29—46no—
175C2×C4×C29—26no—
176C2×C4×C29—212no—
177C2×C4×C29—26no—
178C2×C4×C29—26no—
179C2×C4×C29—46no—
180C2×C4×C29—43no—
181C2×C4×C29C23×C412yes—
182C2×C4×C29C23×C413yes—
183C2×C4×C29C23×C412yes—
184C2×C4×C29C23×C416yes—
185C2×C4×C29C23×C413yes—
186C2×C4×C29C23×C413yes—
187C2×C4×C29C23×C411yescharacteristic
188C2×C4×C29C23×C413yes—
189C2×C4×C29C2×#4112yes—
190C2×C4×C29C2×#4112yes—
191C2×C4×C29C2511yescharacteristic
192C8×C29—23no—
193C8×C29—23no—
194C8×C29—26no—
195C8×C29C2×#4112yes—
196C8×C29C2×#4114yes—
197C8×C29C2×#4112yes—
198#3480C2×C2911yescharacteristic
199#2971C2×C2912yescomplemented
200#2969C2×C2916yescomplemented
201#2966C2×C2916yescomplemented
202C8×#41C2×C2912yescomplemented
203Q8×M16C2×C2911yescharacteristic, complemented
204C2×C8×Q8C2×C2911yescharacteristic, complemented
205#2935C2×C2913yescomplemented
206#2931C2×C2913yescomplemented
207#2925C2×C2913yescomplemented
208C4×#131C2×C2913yescomplemented
209C22×C29—21no—
210C22×C29—21no—
211C22×C29—26no—
212C22×C29—26no—
213C22×C29—26no—
214C22×C29C4×#4112yes—
215C22×C29C24×C411yescharacteristic
216C4×C29—26no—
217C4×C29—22no—
218C4×C29—23no—
219C4×C29—22no—
220C4×C29—23no—
221C4×C29—23no—
222C4×C29C4×#4112yes—
223C4×C29C2×#13116yes—
224C4×C29C22×#4111yescharacteristic
225C4×C29C22×#4111yescharacteristic
226C2×#131C22×C2913yes—
227C2×#131C22×C2913yes—
228#559C4×C2913yes—
229#557C4×C2911yescharacteristic
230#556C4×C2913yes—
231#553C4×C2916yes—
232#550C4×C2911yescharacteristic
233#548C4×C2912yes—
234#532C22×C2913yes—
235#529C22×C2916yes—
236C4×#41C22×C2912yes—
237C4×#41C22×C2913yes—
238C2×C4×Q8C22×C2911yescharacteristic
239#446C22×C2916yes—
240C8×Q8C22×C2911yescharacteristic
241C8×Q8C22×C2913yes—
242C8×Q8C22×C2913yes—
243C8×Q8C22×C2911yescharacteristic
244C8×Q8C22×C2912yes—
245#436C22×C2916yes—
246#436C22×C2916yes—
247#436C22×C2916yes—
248#435C22×C29112yes—
249C8×D4C22×C2916yes—
250C8×D4C22×C2916yes—
251C8×D4C22×C2916yes—
252#433C22×C29112yes—
253#432C22×C2916yes—
254#431C22×C2916yes—
255#423C22×C2913yes—
256C2×C4⋊C8C22×C2913yes—
257#408C22×C2916yes—
258#405C22×C2911yescharacteristic
259#405C22×C2913yes—
260#405C22×C2916yes—
261#405C22×C2916yes—
262C4×M16C22×C2913yes—
263C4×M16C22×C2916yes—
264C2×C4×C8C22×C2913yes—
265C2×C4×C8C22×C2916yes—
266C2×C29—22no—
267C2×C29—46no—
268C2×C29C2×C4×#4111yescharacteristic
269C2×C29C22×#13111yescharacteristic
270C2×C29#357311yescharacteristic
271C2×#41C2×C4×C2912yes—
272C2×#41C23×C2913yes—
273C22×Q8C2×C4×C2911yescharacteristic
274#131—212no—
275#131—212no—
276C2×M16C23×C2913yes—
277C2×M16C23×C2916yes—
278C2×M16C23×C2916yes—
279C2×M16C23×C2911yescharacteristic
280C22×C8C23×C2913yes—
281C22×C8C23×C2916yes—
282C22×C8C23×C2916yes—
283C22×C8C23×C2911yescharacteristic
284C4⋊Q8C2×C4×C2913yes—
285#127C2×C4×C2913yes—
286#126C2×C4×C29112yes—
287#125C2×C4×C2916yes—
288#124C2×C4×C2916yes—
289#124C2×C4×C2916yes—
290#123C2×C4×C29112yes—
291C22⋊Q8C2×C4×C2916yes—
292#121C2×C4×C2916yes—
293#121C2×C4×C2916yes—
294#121C2×C4×C2916yes—
295C4×Q8C2×C4×C2911yescharacteristic
296C4×Q8C2×C4×C2913yes—
297C4×Q8C2×C4×C2912yes—
298C4×Q8C2×C4×C2913yes—
299C4×Q8C2×C4×C2913yes—
300C4×Q8C23×C2911yescharacteristic
301C4×Q8C23×C2913yes—
302C4×D4C2×C4×C2916yes—
303C4×D4C2×C4×C2913yes—
304C4×D4C2×C4×C2916yes—
305C4×D4C2×C4×C2916yes—
306C4×D4C2×C4×C2913yes—
307C4×D4C23×C2916yes—
308C4×D4C23×C2916yes—
309#117C2×C4×C2916yes—
310#117C23×C2911yescharacteristic
311#117C23×C2916yes—
312C2×C4⋊C4C2×C4×C2913yes—
313C2×C42C23×C2913yes—
314C2×C42C23×C2916yes—
315C4⋊C8C23×C2913yes—
316C4⋊C8C23×C2913yes—
317C4⋊C8C23×C2916yes—
318C4⋊C8C23×C2916yes—
319C4⋊C8C23×C2916yes—
320C22⋊C8C23×C29112yes—
321C22⋊C8C23×C29112yes—
322#97C23×C2912yes—
323#97C23×C2916yes—
324#97C23×C2916yes—
325C4×C8C23×C2912yes—
326C4×C8C23×C2913yes—
327C4×C8C23×C2916yes—
328C4×C8C23×C2913yes—
329C4×C8C23×C2916yes—
330C4×C8C23×C2913yes—
331C4×C8C23×C2913yes—
332C29#6021811yescharacteristic, direct product factor, Sylow
333#41—28no—
334#41—26no—
335#41—26no—
336C2×Q8—24no—
337C2×Q8C22×C4×C2913yes—
338C2×Q8C22×C4×C2913yes—
339C2×Q8C22×C4×C2911yescharacteristic
340C2×D4C22×C4×C2916yes—
341C2×D4C22×C4×C2913yes—
342C2×D4C22×C4×C2916yes—
343C2×D4C22×C4×C2916yes—
344C22×C4C22×C4×C2913yes—
345C22×C4C22×C4×C2916yes—
346C22×C4C22×C4×C2913yes—
347C22×C4C22×C4×C2916yes—
348C22×C4C24×C2916yes—
349C22×C4C24×C2911yescharacteristic
350M16—26no—
351M16—212no—
352M16—212no—
353M16#41×C2914yescomplemented
354C2×C8—26no—
355C2×C8—212no—
356C2×C8—212no—
357C2×C8#41×C2914yescomplemented
358C2×C8C24×C2913yes—
359C2×C8C24×C2916yes—
360C2×C8C24×C2913yes—
361C2×C8C24×C2911yescharacteristic
362C2×C8C24×C2911yescharacteristic
363C2×C8C24×C2912yes—
364C4⋊C4C22×C4×C2913yes—
365C4⋊C4C22×C4×C2913yes—
366C4⋊C4C22×C4×C2916yes—
367C4⋊C4C22×C4×C2916yes—
368C4⋊C4C22×C4×C2911yescharacteristic
369C4⋊C4C22×C4×C2911yescharacteristic
370C4⋊C4C22×C4×C2916yes—
371C4⋊C4C22×C4×C2916yes—
372C4⋊C4C22×C4×C2916yes—
373C22⋊C4C22×C4×C29112yes—
374C22⋊C4C22×C4×C2912yes—
375C22⋊C4C22×C4×C2916yes—
376C22⋊C4C22×C4×C2916yes—
377C22⋊C4C22×C4×C29112yes—
378C42C22×C4×C2916yes—
379C42C22×C4×C2916yes—
380C42C22×C4×C2913yes—
381C42C22×C4×C2913yes—
382C42C24×C2912yes—
383C42C24×C2913yes—
384C42C24×C2913yes—
385C23C23×C4×C2916yes—
386C23C23×C4×C2911yescharacteristic
387Q8—26no—
388Q8—26no—
389Q8C29×#13114yescomplemented
390D4—212no—
391D4—26no—
392D4—212no—
393D4—46no—
394C2×C4—26no—
395C2×C4—212no—
396C2×C4—26no—
397C2×C4—26no—
398C2×C4—46no—
399C2×C4—43no—
400C2×C4C23×C4×C2912yes—
401C2×C4C23×C4×C2913yes—
402C2×C4C23×C4×C2912yes—
403C2×C4C23×C4×C2916yes—
404C2×C4C23×C4×C2913yes—
405C2×C4C23×C4×C2913yes—
406C2×C4C23×C4×C2911yescharacteristic
407C2×C4C23×C4×C2913yes—
408C2×C4C2×#41×C2912yes—
409C2×C4C2×#41×C2912yes—
410C2×C4C25×C2911yescharacteristic
411C8—23no—
412C8—23no—
413C8—26no—
414C8C2×#41×C2912yes—
415C8C2×#41×C2914yes—
416C8C2×#41×C2912yes—
417C22—21no—
418C22—21no—
419C22—26no—
420C22—26no—
421C22—26no—
422C22C4×#41×C2912yes—
423C22C24×C4×C2911yescharacteristic
424C4—22no—
425C4—23no—
426C4—22no—
427C4—23no—
428C4—23no—
429C4—26no—
430C4C4×#41×C2912yes—
431C4C2×C29×#13116yes—
432C4C22×#41×C2911yescharacteristic
433C4C22×#41×C2911yescharacteristic
434C2—22no—
435C2—46no—
436C2C2×C4×#41×C2911yescharacteristic
437C2C22×C29×#13111yescharacteristic
438C2C29×#357311yescharacteristic
subgroupG/H
centerC2×C8×C29C24
commutatorC22C24×C4×C29
Frattini, cosocleC2×C4C25×C29
socleC22×C29C24×C4
prime radicalC29×#3480C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C8×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#2971C2semidirect
3. C29×#2969C2semidirect
4. C29×#2966C2semidirect
5. C8×#41×C29C2semidirect
6. Q8×M16×C29C2semidirect
7. C2×C8×Q8×C29C2semidirect
8. C29×#2935C2semidirect
9. C29×#2931C2semidirect
10. C29×#2925C2semidirect
11. C4×C29×#131C2semidirect
133. M16×C29#41semidirect
137. C2×C8×C29#41semidirect
165. #60218C29direct (N × H)
170. Q8×C29#131semidirect
199. #2971C2×C29semidirect
200. #2969C2×C29semidirect
201. #2966C2×C29semidirect
202. C8×#41C2×C29semidirect
203. Q8×M16C2×C29semidirect
204. C2×C8×Q8C2×C29semidirect
205. #2935C2×C29semidirect
206. #2931C2×C29semidirect
207. #2925C2×C29semidirect
208. C4×#131C2×C29semidirect
332. C29#60218direct (N × H)
353. M16#41×C29semidirect
357. C2×C8#41×C29semidirect
389. Q8C29×#131semidirect

Maximal subgroups

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

subgroupindex
C29×#34802
C29×#29712
C29×#29692
C29×#29662
C8×#41×C292
Q8×M16×C292
C2×C8×Q8×C292
C29×#29352
C29×#29312
C29×#29252
C4×C29×#1312
#6021829