Finite Group Databasebeta

← C29×#60205 #20355105

Subgroups — C29×#60205 #20355105

Order 7424.

1950 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3444C211yesmaximal, characteristic
2C29×#2967C218yesmaximal, complemented
3C29×#2965C218yesmaximal, complemented
4C29×#2961C212yesmaximal, complemented
5C29×#2932C212yesmaximal, complemented
6C29×#2930C214yesmaximal, complemented
7C29×#2922C212yesmaximal, complemented
8C29×#2920C211yesmaximal, characteristic, complemented
9C4×C29×#131C212yesmaximal, complemented
10C2×C4×M16×C29C211yesmaximal, characteristic, complemented
11C2×C29×#131C2214yes—
12C22×M16×C29C2212yes—
13C29×#533C412yes—
14C29×#533C2211yescharacteristic
15C29×#532C412yes—
16C29×#532C2211yescharacteristic
17C29×#529C414yes—
18C29×#529C414yes—
19C29×#529C2214yes—
20C29×#525C414yes—
21C29×#525C2212yes—
22C4×#41×C29C2214yes—
23C4×#41×C29C2212yes—
24C22×C42×C29C2211yescharacteristic
25C29×#446C22116yescomplemented
26C29×#436C22116yes—
27C29×#435C22116yes—
28C29×#435C22116yescomplemented
29C29×#433C2218yescomplemented
30C29×#432C2214yes—
31C29×#431C2214yes—
32C29×#431C2218yescomplemented
33C29×#424C2214yes—
34C29×#423C2212yes—
35C29×#408C2214yes—
36C29×#407C2212yes—
37C29×#405C2214yes—
38C29×#405C2218yescomplemented
39C4×M16×C29C2214yes—
40C4×M16×C29C2214yes—
41C4×M16×C29C2212yes—
42C4×M16×C29C2214yescomplemented
43C2×C29×#97C2212yes—
44C2×C4×C8×C29C2211yescharacteristic
45C2×C4×C8×C29C2211yescharacteristic
46C2×C4×C8×C29C2214yescomplemented
47C2×#41×C29C2×C414yes—
48C2×#41×C29C2312yes—
49C23×C4×C29C2×C412yes—
50C23×C4×C29C2311yescharacteristic
51C29×#131—216no—
52C2×M16×C29—28no—
53C2×M16×C29C2318yes—
54C2×M16×C29C2318yes—
55C2×M16×C29C2314yes—
56C22×C8×C29C2318yes—
57C22×C8×C29C2312yes—
58C22×C8×C29C2312yes—
59C29×C4⋊Q8C2×C412yes—
60C29×C4⋊Q8C2×C411yescharacteristic
61C29×#127C2×C411yescharacteristic
62C29×#126C2×C418yes—
63C29×#125C2×C412yes—
64C29×#125C2×C414yes—
65C29×#124C2×C412yes—
66C29×#124C2×C414yes—
67C29×#123C2×C418yes—
68C29×#123C2×C414yes—
69C29×C22⋊Q8C2×C414yes—
70C29×C22⋊Q8C2×C414yes—
71C29×C22⋊Q8C2×C414yes—
72C29×#121C2×C414yes—
73C29×#121C2×C414yes—
74C29×#121C2×C414yes—
75C29×#120C2×C414yes—
76C4×Q8×C29C2×C414yes—
77C4×Q8×C29C2×C414yes—
78C4×Q8×C29C2314yes—
79C4×D4×C29C2×C418yes—
80C4×D4×C29C2×C418yes—
81C4×D4×C29C2×C414yes—
82C4×D4×C29C2×C414yes—
83C4×D4×C29C2318yes—
84C4×D4×C29C2314yes—
85C29×#117C2×C414yes—
86C29×#117C2×C418yes—
87C29×#117C2314yes—
88C29×#117C2312yes—
89C2×C42×C29C2×C412yes—
90C2×C42×C29C2×C412yes—
91C2×C42×C29C2×C412yes—
92C2×C42×C29C2312yes—
93C2×C42×C29C2311yescharacteristic
94C2×C42×C29C2312yes—
95C2×C42×C29C2314yes—
96C2×C42×C29C2311yescharacteristic
97C29×C4⋊C8C2318yes—
98C29×C4⋊C8C23116yes—
99C29×C22⋊C8C2318yes—
100C29×C22⋊C8C23116yes—
101C29×#97C2314yes—
102C29×#97C2318yes—
103C29×#97C2318yes—
104C4×C8×C29C2312yes—
105C4×C8×C29C2318yes—
106C4×C8×C29C2312yes—
107C4×C8×C29C2314yes—
108C4×C8×C29C2312yes—
109C4×C8×C29C2312yes—
110C24×C29C22×C411yescharacteristic
111#41×C29—28no—
112#41×C29—48no—
113C2×Q8×C29C22×C412yes—
114C2×Q8×C29C22×C414yes—
115C2×D4×C29C22×C414yes—
116C2×D4×C29C22×C412yes—
117C2×D4×C29C22×C418yes—
118C2×D4×C29C22×C414yes—
119C22×C4×C29—24no—
120C22×C4×C29—44no—
121C22×C4×C29C22×C412yes—
122C22×C4×C29C22×C411yescharacteristic
123C22×C4×C29C22×C412yes—
124C22×C4×C29C22×C412yes—
125C22×C4×C29C22×C412yes—
126C22×C4×C29C22×C418yes—
127C22×C4×C29C22×C412yes—
128C22×C4×C29C22×C412yes—
129C22×C4×C29C22×C412yes—
130C22×C4×C29C2412yes—
131C22×C4×C29C2414yes—
132C22×C4×C29C2411yescharacteristic
133M16×C29—28no—
134M16×C29—216no—
135M16×C29—216no—
136C2×C8×C29—24no—
137C2×C8×C29—216no—
138C2×C8×C29#4118yescomplemented
139C2×C8×C29C2418yes—
140C2×C8×C29C2414yes—
141C2×C8×C29C2414yes—
142C4⋊C4×C29C22×C414yes—
143C4⋊C4×C29C22×C418yes—
144C4⋊C4×C29C22×C414yes—
145C4⋊C4×C29C22×C418yes—
146C4⋊C4×C29C22×C414yes—
147C4⋊C4×C29C22×C418yes—
148C22⋊C4×C29C22×C418yes—
149C22⋊C4×C29C22×C418yes—
150C22⋊C4×C29C22×C418yes—
151C22⋊C4×C29C22×C414yes—
152C22⋊C4×C29C22×C418yes—
153C42×C29C22×C412yes—
154C42×C29C22×C412yes—
155C42×C29C22×C412yes—
156C42×C29C22×C412yes—
157C42×C29C22×C411yescharacteristic
158C42×C29C22×C412yes—
159C42×C29C22×C411yescharacteristic
160C42×C29C22×C418yes—
161C42×C29C2411yescharacteristic
162C42×C29C2412yes—
163C42×C29C2414yes—
164C42×C29C2411yescharacteristic
165#60205C2911yesmaximal, characteristic, direct product factor, Sylow
166C23×C29—22no—
167C23×C29—42no—
168C23×C29C23×C414yes—
169C23×C29C23×C412yes—
170C23×C29C23×C411yescharacteristic
171Q8×C29—24no—
172Q8×C29—44no—
173D4×C29—28no—
174D4×C29—24no—
175D4×C29—44no—
176D4×C29—48no—
177C2×C4×C29—22no—
178C2×C4×C29—24no—
179C2×C4×C29—24no—
180C2×C4×C29—24no—
181C2×C4×C29—24no—
182C2×C4×C29—216no—
183C2×C4×C29—28no—
184C2×C4×C29—24no—
185C2×C4×C29—42no—
186C2×C4×C29—42no—
187C2×C4×C29—42no—
188C2×C4×C29C23×C412yes—
189C2×C4×C29C23×C412yes—
190C2×C4×C29C23×C412yes—
191C2×C4×C29C23×C412yes—
192C2×C4×C29C23×C414yes—
193C2×C4×C29C23×C418yes—
194C2×C4×C29C23×C411yescharacteristic
195C2×C4×C29C23×C412yes—
196C2×C4×C29C2×#4114yes—
197C2×C4×C29C2511yescharacteristic
198C8×C29—24no—
199C8×C29—28no—
200C8×C29C2×#4118yes—
201#3444C2×C2911yescharacteristic
202#2967C2×C2918yescomplemented
203#2965C2×C2918yescomplemented
204#2961C2×C2912yescomplemented
205#2932C2×C2912yescomplemented
206#2930C2×C2914yescomplemented
207#2922C2×C2912yescomplemented
208#2920C2×C2911yescharacteristic, complemented
209C4×#131C2×C2912yescomplemented
210C2×C4×M16C2×C2911yescharacteristic, complemented
211C22×C29—22no—
212C22×C29—22no—
213C22×C29—24no—
214C22×C29—22no—
215C22×C29—22no—
216C22×C29—28no—
217C22×C29—44no—
218C22×C29C4×#4112yes—
219C22×C29C24×C411yescharacteristic
220C4×C29—22no—
221C4×C29—24no—
222C4×C29—22no—
223C4×C29—22no—
224C4×C29—22no—
225C4×C29—28no—
226C4×C29C4×#4112yes—
227C4×C29#56814yes—
228C4×C29C22×#4112yes—
229C2×#131C22×C2914yes—
230C22×M16C22×C2912yes—
231#533C4×C2912yes—
232#533C22×C2911yescharacteristic
233#532C4×C2912yes—
234#532C22×C2911yescharacteristic
235#529C4×C2914yes—
236#529C4×C2914yes—
237#529C22×C2914yes—
238#525C4×C2914yes—
239#525C22×C2912yes—
240C4×#41C22×C2914yes—
241C4×#41C22×C2912yes—
242C22×C42C22×C2911yescharacteristic
243#446C22×C29116yescomplemented
244#436C22×C29116yes—
245#435C22×C29116yes—
246#435C22×C29116yescomplemented
247#433C22×C2918yescomplemented
248#432C22×C2914yes—
249#431C22×C2914yes—
250#431C22×C2918yescomplemented
251#424C22×C2914yes—
252#423C22×C2912yes—
253#408C22×C2914yes—
254#407C22×C2912yes—
255#405C22×C2914yes—
256#405C22×C2918yescomplemented
257C4×M16C22×C2914yes—
258C4×M16C22×C2914yes—
259C4×M16C22×C2912yes—
260C4×M16C22×C2914yescomplemented
261C2×#97C22×C2912yes—
262C2×C4×C8C22×C2911yescharacteristic
263C2×C4×C8C22×C2911yescharacteristic
264C2×C4×C8C22×C2914yescomplemented
265C2×C29—22no—
266C2×C29—44no—
267C2×C29—42no—
268C2×C29C2×C4×#4111yescharacteristic
269C2×C29C2×#56812yes—
270C2×#41C2×C4×C2914yes—
271C2×#41C23×C2912yes—
272C23×C4C2×C4×C2912yes—
273C23×C4C23×C2911yescharacteristic
274#131—216no—
275C2×M16—28no—
276C2×M16C23×C2918yes—
277C2×M16C23×C2914yes—
278C2×M16C23×C2918yes—
279C22×C8C23×C2912yes—
280C22×C8C23×C2918yes—
281C22×C8C23×C2912yes—
282C4⋊Q8C2×C4×C2912yes—
283C4⋊Q8C2×C4×C2911yescharacteristic
284#127C2×C4×C2911yescharacteristic
285#126C2×C4×C2918yes—
286#125C2×C4×C2912yes—
287#125C2×C4×C2914yes—
288#124C2×C4×C2912yes—
289#124C2×C4×C2914yes—
290#123C2×C4×C2918yes—
291#123C2×C4×C2914yes—
292C22⋊Q8C2×C4×C2914yes—
293C22⋊Q8C2×C4×C2914yes—
294C22⋊Q8C2×C4×C2914yes—
295#121C2×C4×C2914yes—
296#121C2×C4×C2914yes—
297#121C2×C4×C2914yes—
298#120C2×C4×C2914yes—
299C4×Q8C2×C4×C2914yes—
300C4×Q8C2×C4×C2914yes—
301C4×Q8C23×C2914yes—
302C4×D4C2×C4×C2918yes—
303C4×D4C2×C4×C2918yes—
304C4×D4C2×C4×C2914yes—
305C4×D4C2×C4×C2914yes—
306C4×D4C23×C2918yes—
307C4×D4C23×C2914yes—
308#117C2×C4×C2914yes—
309#117C2×C4×C2918yes—
310#117C23×C2912yes—
311#117C23×C2914yes—
312C2×C42C2×C4×C2912yes—
313C2×C42C2×C4×C2912yes—
314C2×C42C2×C4×C2912yes—
315C2×C42C23×C2914yes—
316C2×C42C23×C2911yescharacteristic
317C2×C42C23×C2912yes—
318C2×C42C23×C2912yes—
319C2×C42C23×C2911yescharacteristic
320C4⋊C8C23×C2918yes—
321C4⋊C8C23×C29116yes—
322C22⋊C8C23×C2918yes—
323C22⋊C8C23×C29116yes—
324#97C23×C2918yes—
325#97C23×C2914yes—
326#97C23×C2918yes—
327C4×C8C23×C2912yes—
328C4×C8C23×C2912yes—
329C4×C8C23×C2912yes—
330C4×C8C23×C2912yes—
331C4×C8C23×C2914yes—
332C4×C8C23×C2918yes—
333C29#6020511yescharacteristic, direct product factor, Sylow
334C24C22×C4×C2911yescharacteristic
335#41—28no—
336#41—48no—
337C2×Q8C22×C4×C2912yes—
338C2×Q8C22×C4×C2914yes—
339C2×D4C22×C4×C2914yes—
340C2×D4C22×C4×C2912yes—
341C2×D4C22×C4×C2918yes—
342C2×D4C22×C4×C2914yes—
343C22×C4—24no—
344C22×C4—44no—
345C22×C4C22×C4×C2912yes—
346C22×C4C22×C4×C2911yescharacteristic
347C22×C4C22×C4×C2912yes—
348C22×C4C22×C4×C2912yes—
349C22×C4C22×C4×C2912yes—
350C22×C4C22×C4×C2918yes—
351C22×C4C22×C4×C2912yes—
352C22×C4C22×C4×C2912yes—
353C22×C4C22×C4×C2912yes—
354C22×C4C24×C2912yes—
355C22×C4C24×C2914yes—
356C22×C4C24×C2911yescharacteristic
357M16—28no—
358M16—216no—
359M16—216no—
360C2×C8—24no—
361C2×C8—216no—
362C2×C8#41×C2918yescomplemented
363C2×C8C24×C2914yes—
364C2×C8C24×C2918yes—
365C2×C8C24×C2914yes—
366C4⋊C4C22×C4×C2914yes—
367C4⋊C4C22×C4×C2918yes—
368C4⋊C4C22×C4×C2914yes—
369C4⋊C4C22×C4×C2918yes—
370C4⋊C4C22×C4×C2914yes—
371C4⋊C4C22×C4×C2918yes—
372C22⋊C4C22×C4×C2918yes—
373C22⋊C4C22×C4×C2918yes—
374C22⋊C4C22×C4×C2918yes—
375C22⋊C4C22×C4×C2914yes—
376C22⋊C4C22×C4×C2918yes—
377C42C22×C4×C2912yes—
378C42C22×C4×C2912yes—
379C42C22×C4×C2912yes—
380C42C22×C4×C2912yes—
381C42C22×C4×C2911yescharacteristic
382C42C22×C4×C2912yes—
383C42C22×C4×C2911yescharacteristic
384C42C22×C4×C2918yes—
385C42C24×C2911yescharacteristic
386C42C24×C2911yescharacteristic
387C42C24×C2914yes—
388C42C24×C2912yes—
389C23—22no—
390C23—42no—
391C23C23×C4×C2914yes—
392C23C23×C4×C2912yes—
393C23C23×C4×C2911yescharacteristic
394Q8—24no—
395Q8—44no—
396D4—28no—
397D4—24no—
398D4—44no—
399D4—48no—
400C2×C4—22no—
401C2×C4—24no—
402C2×C4—24no—
403C2×C4—24no—
404C2×C4—24no—
405C2×C4—216no—
406C2×C4—28no—
407C2×C4—24no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4C23×C4×C2912yes—
412C2×C4C23×C4×C2912yes—
413C2×C4C23×C4×C2912yes—
414C2×C4C23×C4×C2912yes—
415C2×C4C23×C4×C2914yes—
416C2×C4C23×C4×C2918yes—
417C2×C4C23×C4×C2911yescharacteristic
418C2×C4C23×C4×C2912yes—
419C2×C4C2×#41×C2914yes—
420C2×C4C25×C2911yescharacteristic
421C8—24no—
422C8—28no—
423C8C2×#41×C2918yes—
424C22—22no—
425C22—22no—
426C22—22no—
427C22—28no—
428C22—22no—
429C22—24no—
430C22—44no—
431C22C4×#41×C2912yes—
432C22C24×C4×C2911yescharacteristic
433C4—22no—
434C4—22no—
435C4—22no—
436C4—28no—
437C4—22no—
438C4—24no—
439C4C4×#41×C2912yes—
440C4C29×#56814yes—
441C4C22×#41×C2912yes—
442C2—22no—
443C2—42no—
444C2—44no—
445C2C2×C4×#41×C2911yescharacteristic
446C2C2×C29×#56812yes—
subgroupG/H
centerC42×C29C24
commutatorC22C24×C4×C29
Frattini, cosocleC2×C4C25×C29
socleC22×C29C24×C4
prime radicalC29×#3444C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#2967C2semidirect
3. C29×#2965C2semidirect
4. C29×#2961C2semidirect
5. C29×#2932C2semidirect
6. C29×#2930C2semidirect
7. C29×#2922C2semidirect
8. C29×#2920C2semidirect
9. C4×C29×#131C2semidirect
10. C2×C4×M16×C29C2semidirect
25. C29×#446C22semidirect
28. C29×#435C22semidirect
29. C29×#433C22semidirect
32. C29×#431C22semidirect
38. C29×#405C22semidirect
42. C4×M16×C29C22semidirect
46. C2×C4×C8×C29C22semidirect
138. C2×C8×C29#41semidirect
165. #60205C29direct (N × H)
202. #2967C2×C29semidirect
203. #2965C2×C29semidirect
204. #2961C2×C29semidirect
205. #2932C2×C29semidirect
206. #2930C2×C29semidirect
207. #2922C2×C29semidirect
208. #2920C2×C29semidirect
209. C4×#131C2×C29semidirect
210. C2×C4×M16C2×C29semidirect
243. #446C22×C29semidirect
246. #435C22×C29semidirect
247. #433C22×C29semidirect
250. #431C22×C29semidirect
256. #405C22×C29semidirect
260. C4×M16C22×C29semidirect
264. C2×C4×C8C22×C29semidirect
333. C29#60205direct (N × H)
362. C2×C8#41×C29semidirect

Maximal subgroups

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

subgroupindex
C29×#34442
C29×#29672
C29×#29652
C29×#29612
C29×#29322
C29×#29302
C29×#29222
C29×#29202
C4×C29×#1312
C2×C4×M16×C292
#6020529