Finite Group Databasebeta

← C29×#60331 #20355231

Subgroups — C29×#60331 #20355231

Order 7424.

1792 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3482C211yesmaximal, characteristic
2C29×#2994C216yesmaximal, complemented
3C29×#2991C211yesmaximal, characteristic, complemented
4C29×#2990C213yesmaximal, complemented
5C29×#2986C213yesmaximal, complemented
6C29×#2984C212yesmaximal, complemented
7C29×#2966C216yesmaximal, complemented
8C8×#41×C29C213yesmaximal, complemented
9C8×#41×C29C211yesmaximal, characteristic, complemented
10C29×#2960C213yesmaximal, complemented
11C2×C8×Q8×C29C212yesmaximal, complemented
12C29×#557C411yescharacteristic
13C29×#556C413yes—
14C29×#552C416yes—
15D4×Q8×C29C411yescharacteristic
16C29×#548C412yes—
17C29×#547C413yes—
18C29×#533C2213yes—
19C29×#529C2216yes—
20C4×#41×C29C2213yes—
21C4×#41×C29C2211yescharacteristic
22C2×C4×Q8×C29C2212yes—
23C29×#446C2216yes—
24C29×#446C2216yes—
25C29×#446C2216yes—
26C8×Q8×C29C2211yescharacteristic
27C8×Q8×C29C2216yes—
28C8×Q8×C29C2212yes—
29C8×Q8×C29C2216yes—
30C8×Q8×C29C2213yes—
31C8×Q8×C29C2211yescharacteristic
32C8×Q8×C29C2213yes—
33C29×#436C2216yes—
34C29×#435C22112yes—
35C8×D4×C29C2211yescharacteristic
36C8×D4×C29C2216yes—
37C8×D4×C29C2213yes—
38C8×D4×C29C2213yes—
39C8×D4×C29C2216yes—
40C8×D4×C29C2213yes—
41C29×#433C22112yes—
42C29×#432C2216yes—
43C29×#431C2216yes—
44C29×#431C2213yes—
45C29×#431C2213yes—
46C29×#424C2216yes—
47C29×#423C2213yes—
48C2×C29×C4⋊C8C2216yes—
49C29×#405C2216yes—
50C2×C4×C8×C29C2216yes—
51C2×C4×C8×C29C2213yes—
52C2×#41×C29C2×C413yes—
53C2×#41×C29C2×C411yescharacteristic
54C22×Q8×C29C2×C412yes—
55C2×M16×C29C2316yes—
56C22×C8×C29C2312yes—
57C22×C8×C29C2313yes—
58C22×C8×C29C2313yes—
59C22×C8×C29C2316yes—
60C29×C4⋊Q8C2×C413yes—
61C29×C4⋊Q8C2×C413yes—
62C29×#126C2×C4112yes—
63C29×#125C2×C416yes—
64C29×#125C2×C416yes—
65C29×#124C2×C416yes—
66C29×#123C2×C4112yes—
67C29×C22⋊Q8C2×C416yes—
68C29×C22⋊Q8C2×C416yes—
69C29×C22⋊Q8C2×C416yes—
70C29×#121C2×C416yes—
71C4×Q8×C29C2×C412yes—
72C4×Q8×C29C2×C416yes—
73C4×Q8×C29C2×C411yescharacteristic
74C4×Q8×C29C2×C413yes—
75C4×Q8×C29C2311yescharacteristic
76C4×Q8×C29C2316yes—
77C4×Q8×C29C2313yes—
78C4×D4×C29C2×C413yes—
79C4×D4×C29C2×C413yes—
80C4×D4×C29C2×C416yes—
81C4×D4×C29C2311yescharacteristic
82C4×D4×C29C2316yes—
83C4×D4×C29C2313yes—
84C29×#117C2×C413yes—
85C29×#117C2×C416yes—
86C29×#117C2×C413yes—
87C29×#117C2316yes—
88C2×C4⋊C4×C29C2×C416yes—
89C2×C42×C29C2313yes—
90C2×C42×C29C2316yes—
91C29×C4⋊C8C2311yescharacteristic
92C29×C4⋊C8C2313yes—
93C29×C4⋊C8C2316yes—
94C29×C4⋊C8C2313yes—
95C29×C4⋊C8C2313yes—
96C29×C4⋊C8C2316yes—
97C29×C4⋊C8C2316yes—
98C29×C4⋊C8C23112yes—
99C29×C22⋊C8C2312yes—
100C29×C22⋊C8C2316yes—
101C29×C22⋊C8C2316yes—
102C29×C22⋊C8C2316yes—
103C29×#97C23112yes—
104C4×C8×C29C2313yes—
105C4×C8×C29C2313yes—
106C4×C8×C29C2316yes—
107C4×C8×C29C2316yes—
108C4×C8×C29C2311yescharacteristic
109C4×C8×C29C2313yes—
110C4×C8×C29C2316yes—
111#41×C29—24no—
112#41×C29—212no—
113C2×Q8×C29—28no—
114C2×Q8×C29C22×C416yes—
115C2×Q8×C29C22×C413yes—
116C2×Q8×C29C22×C411yescharacteristic
117C2×D4×C29C22×C416yes—
118C2×D4×C29C22×C413yes—
119C2×D4×C29C22×C411yescharacteristic
120C22×C4×C29C22×C416yes—
121C22×C4×C29C22×C416yes—
122C22×C4×C29C22×C413yes—
123C22×C4×C29C22×C413yes—
124C22×C4×C29C2412yes—
125C22×C4×C29C2413yes—
126M16×C29—46no—
127C2×C8×C29—24no—
128C2×C8×C29—26no—
129C2×C8×C29—43no—
130C2×C8×C29—46no—
131C2×C8×C29C2411yescharacteristic
132C2×C8×C29C2413yes—
133C2×C8×C29C2416yes—
134C2×C8×C29C2412yes—
135C2×C8×C29C2413yes—
136C2×C8×C29C2411yescharacteristic
137C4⋊C4×C29C22×C413yes—
138C4⋊C4×C29C22×C416yes—
139C4⋊C4×C29C22×C4112yes—
140C4⋊C4×C29C22×C411yescharacteristic
141C4⋊C4×C29C22×C416yes—
142C4⋊C4×C29C22×C413yes—
143C4⋊C4×C29C22×C413yes—
144C4⋊C4×C29C22×C416yes—
145C4⋊C4×C29C22×C416yes—
146C4⋊C4×C29C22×C416yes—
147C22⋊C4×C29C22×C412yes—
148C22⋊C4×C29C22×C416yes—
149C22⋊C4×C29C22×C416yes—
150C22⋊C4×C29C22×C416yes—
151C22⋊C4×C29C22×C4112yes—
152C42×C29C22×C413yes—
153C42×C29C22×C416yes—
154C42×C29C22×C413yes—
155C42×C29C22×C416yes—
156C42×C29C2411yescharacteristic
157C42×C29C2413yes—
158C42×C29C2416yes—
159#60331C2911yesmaximal, characteristic, direct product factor, Sylow
160C23×C29C23×C413yes—
161C23×C29C23×C412yes—
162Q8×C29—212no—
163Q8×C29—26no—
164Q8×C29#13114yes—
165D4×C29—212no—
166D4×C29—26no—
167D4×C29#13114yes—
168C2×C4×C29—212no—
169C2×C4×C29—212no—
170C2×C4×C29—26no—
171C2×C4×C29—26no—
172C2×C4×C29—22no—
173C2×C4×C29—23no—
174C2×C4×C29—22no—
175C2×C4×C29—23no—
176C2×C4×C29C23×C412yes—
177C2×C4×C29C23×C411yescharacteristic
178C2×C4×C29C23×C413yes—
179C2×C4×C29C23×C413yes—
180C2×C4×C29C23×C416yes—
181C2×C4×C29C23×C416yes—
182C2×C4×C29C23×C413yes—
183C2×C4×C29C23×C411yescharacteristic
184C2×C4×C29C2511yescharacteristic
185C8×C29—22no—
186C8×C29—23no—
187C8×C29—21no—
188C8×C29—23no—
189C8×C29—26no—
190C8×C292−1+412yes—
191#3482C2×C2911yescharacteristic
192#2994C2×C2916yescomplemented
193#2991C2×C2911yescharacteristic, complemented
194#2990C2×C2913yescomplemented
195#2986C2×C2913yescomplemented
196#2984C2×C2912yescomplemented
197#2966C2×C2916yescomplemented
198C8×#41C2×C2913yescomplemented
199C8×#41C2×C2911yescharacteristic, complemented
200#2960C2×C2913yescomplemented
201C2×C8×Q8C2×C2912yescomplemented
202C22×C29—22no—
203C22×C29—22no—
204C22×C29—23no—
205C22×C29—23no—
206C22×C29—23no—
207C22×C29C2×#13114yes—
208C22×C29C24×C411yescharacteristic
209C4×C29—22no—
210C4×C29—23no—
211C4×C29—23no—
212C4×C29—21no—
213C4×C29—26no—
214C4×C29—26no—
215C4×C29C2×#13116yes—
216C4×C29C2×#13112yes—
217C4×C29C2×2−1+411yescharacteristic
218C4×C29#58511yescharacteristic
219#557C4×C2911yescharacteristic
220#556C4×C2913yes—
221#552C4×C2916yes—
222D4×Q8C4×C2911yescharacteristic
223#548C4×C2912yes—
224#547C4×C2913yes—
225#533C22×C2913yes—
226#529C22×C2916yes—
227C4×#41C22×C2913yes—
228C4×#41C22×C2911yescharacteristic
229C2×C4×Q8C22×C2912yes—
230#446C22×C2916yes—
231#446C22×C2916yes—
232#446C22×C2916yes—
233C8×Q8C22×C2911yescharacteristic
234C8×Q8C22×C2916yes—
235C8×Q8C22×C2912yes—
236C8×Q8C22×C2916yes—
237C8×Q8C22×C2913yes—
238C8×Q8C22×C2911yescharacteristic
239C8×Q8C22×C2913yes—
240#436C22×C2916yes—
241#435C22×C29112yes—
242C8×D4C22×C2911yescharacteristic
243C8×D4C22×C2913yes—
244C8×D4C22×C2916yes—
245C8×D4C22×C2913yes—
246C8×D4C22×C2913yes—
247C8×D4C22×C2916yes—
248#433C22×C29112yes—
249#432C22×C2916yes—
250#431C22×C2916yes—
251#431C22×C2913yes—
252#431C22×C2913yes—
253#424C22×C2916yes—
254#423C22×C2913yes—
255C2×C4⋊C8C22×C2916yes—
256#405C22×C2916yes—
257C2×C4×C8C22×C2916yes—
258C2×C4×C8C22×C2913yes—
259C2×C29—24no—
260C2×C29—43no—
261C2×C29C4×2−1+411yescharacteristic
262C2×C29C22×#13111yescharacteristic
263C2×C29C22×#13111yescharacteristic
264C2×#41C2×C4×C2913yes—
265C2×#41C2×C4×C2911yescharacteristic
266C22×Q8C2×C4×C2912yes—
267C2×M16C23×C2916yes—
268C22×C8C23×C2912yes—
269C22×C8C23×C2913yes—
270C22×C8C23×C2916yes—
271C22×C8C23×C2913yes—
272C4⋊Q8C2×C4×C2913yes—
273C4⋊Q8C2×C4×C2913yes—
274#126C2×C4×C29112yes—
275#125C2×C4×C2916yes—
276#125C2×C4×C2916yes—
277#124C2×C4×C2916yes—
278#123C2×C4×C29112yes—
279C22⋊Q8C2×C4×C2916yes—
280C22⋊Q8C2×C4×C2916yes—
281C22⋊Q8C2×C4×C2916yes—
282#121C2×C4×C2916yes—
283C4×Q8C2×C4×C2912yes—
284C4×Q8C2×C4×C2916yes—
285C4×Q8C2×C4×C2911yescharacteristic
286C4×Q8C2×C4×C2913yes—
287C4×Q8C23×C2911yescharacteristic
288C4×Q8C23×C2916yes—
289C4×Q8C23×C2913yes—
290C4×D4C2×C4×C2913yes—
291C4×D4C2×C4×C2913yes—
292C4×D4C2×C4×C2916yes—
293C4×D4C23×C2911yescharacteristic
294C4×D4C23×C2916yes—
295C4×D4C23×C2913yes—
296#117C2×C4×C2913yes—
297#117C2×C4×C2916yes—
298#117C2×C4×C2913yes—
299#117C23×C2916yes—
300C2×C4⋊C4C2×C4×C2916yes—
301C2×C42C23×C2916yes—
302C2×C42C23×C2913yes—
303C4⋊C8C23×C2913yes—
304C4⋊C8C23×C2916yes—
305C4⋊C8C23×C29112yes—
306C4⋊C8C23×C2913yes—
307C4⋊C8C23×C2916yes—
308C4⋊C8C23×C2911yescharacteristic
309C4⋊C8C23×C2913yes—
310C4⋊C8C23×C2916yes—
311C22⋊C8C23×C2912yes—
312C22⋊C8C23×C2916yes—
313C22⋊C8C23×C2916yes—
314C22⋊C8C23×C2916yes—
315#97C23×C29112yes—
316C4×C8C23×C2913yes—
317C4×C8C23×C2911yescharacteristic
318C4×C8C23×C2916yes—
319C4×C8C23×C2913yes—
320C4×C8C23×C2913yes—
321C4×C8C23×C2916yes—
322C4×C8C23×C2916yes—
323C29#6033111yescharacteristic, direct product factor, Sylow
324#41—24no—
325#41—212no—
326C2×Q8—28no—
327C2×Q8C22×C4×C2916yes—
328C2×Q8C22×C4×C2913yes—
329C2×Q8C22×C4×C2911yescharacteristic
330C2×D4C22×C4×C2916yes—
331C2×D4C22×C4×C2913yes—
332C2×D4C22×C4×C2911yescharacteristic
333C22×C4C22×C4×C2916yes—
334C22×C4C22×C4×C2916yes—
335C22×C4C22×C4×C2913yes—
336C22×C4C22×C4×C2913yes—
337C22×C4C24×C2912yes—
338C22×C4C24×C2913yes—
339M16—46no—
340C2×C8—24no—
341C2×C8—26no—
342C2×C8—43no—
343C2×C8—46no—
344C2×C8C24×C2912yes—
345C2×C8C24×C2911yescharacteristic
346C2×C8C24×C2913yes—
347C2×C8C24×C2913yes—
348C2×C8C24×C2916yes—
349C2×C8C24×C2911yescharacteristic
350C4⋊C4C22×C4×C2913yes—
351C4⋊C4C22×C4×C2916yes—
352C4⋊C4C22×C4×C29112yes—
353C4⋊C4C22×C4×C2911yescharacteristic
354C4⋊C4C22×C4×C2916yes—
355C4⋊C4C22×C4×C2913yes—
356C4⋊C4C22×C4×C2913yes—
357C4⋊C4C22×C4×C2916yes—
358C4⋊C4C22×C4×C2916yes—
359C4⋊C4C22×C4×C2916yes—
360C22⋊C4C22×C4×C2912yes—
361C22⋊C4C22×C4×C2916yes—
362C22⋊C4C22×C4×C2916yes—
363C22⋊C4C22×C4×C2916yes—
364C22⋊C4C22×C4×C29112yes—
365C42C22×C4×C2913yes—
366C42C22×C4×C2916yes—
367C42C22×C4×C2913yes—
368C42C22×C4×C2916yes—
369C42C24×C2911yescharacteristic
370C42C24×C2913yes—
371C42C24×C2916yes—
372C23C23×C4×C2913yes—
373C23C23×C4×C2912yes—
374Q8—212no—
375Q8—26no—
376Q8C29×#13114yes—
377D4—212no—
378D4—26no—
379D4C29×#13114yes—
380C2×C4—212no—
381C2×C4—212no—
382C2×C4—26no—
383C2×C4—26no—
384C2×C4—22no—
385C2×C4—23no—
386C2×C4—22no—
387C2×C4—23no—
388C2×C4C23×C4×C2912yes—
389C2×C4C23×C4×C2911yescharacteristic
390C2×C4C23×C4×C2913yes—
391C2×C4C23×C4×C2913yes—
392C2×C4C23×C4×C2916yes—
393C2×C4C23×C4×C2916yes—
394C2×C4C23×C4×C2913yes—
395C2×C4C23×C4×C2911yescharacteristic
396C2×C4C25×C2911yescharacteristic
397C8—22no—
398C8—23no—
399C8—21no—
400C8—23no—
401C8—26no—
402C8C29×2−1+412yes—
403C22—22no—
404C22—22no—
405C22—23no—
406C22—23no—
407C22—23no—
408C22C2×C29×#13114yes—
409C22C24×C4×C2911yescharacteristic
410C4—23no—
411C4—21no—
412C4—26no—
413C4—26no—
414C4—22no—
415C4—23no—
416C4C2×C29×#13116yes—
417C4C2×C29×#13112yes—
418C4C2×C29×2−1+411yescharacteristic
419C4C29×#58511yescharacteristic
420C2—24no—
421C2—43no—
422C2C4×C29×2−1+411yescharacteristic
423C2C22×C29×#13111yescharacteristic
424C2C22×C29×#13111yescharacteristic
subgroupG/H
centerC2×C8×C29C24
commutatorC22C24×C4×C29
Frattini, cosocleC2×C4C25×C29
socleC22×C29C24×C4
prime radicalC29×#3482C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C8×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#2994C2semidirect
3. C29×#2991C2semidirect
4. C29×#2990C2semidirect
5. C29×#2986C2semidirect
6. C29×#2984C2semidirect
7. C29×#2966C2semidirect
8. C8×#41×C29C2semidirect
9. C8×#41×C29C2semidirect
10. C29×#2960C2semidirect
11. C2×C8×Q8×C29C2semidirect
159. #60331C29direct (N × H)
192. #2994C2×C29semidirect
193. #2991C2×C29semidirect
194. #2990C2×C29semidirect
195. #2986C2×C29semidirect
196. #2984C2×C29semidirect
197. #2966C2×C29semidirect
198. C8×#41C2×C29semidirect
199. C8×#41C2×C29semidirect
200. #2960C2×C29semidirect
201. C2×C8×Q8C2×C29semidirect
323. C29#60331direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#34822
C29×#29942
C29×#29912
C29×#29902
C29×#29862
C29×#29842
C29×#29662
C8×#41×C292
C29×#29602
C2×C8×Q8×C292
#6033129