Finite Group Databasebeta

← C29×#60274 #20355174

Subgroups — C29×#60274 #20355174

Order 7424.

1862 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3480C211yesmaximal, characteristic
2C29×#2994C216yesmaximal, complemented
3C29×#2993C216yesmaximal, complemented
4C29×#2991C212yesmaximal, complemented
5C29×#2988C212yesmaximal, complemented
6Q8×M16×C29C211yesmaximal, characteristic, complemented
7C2×C8×Q8×C29C211yesmaximal, characteristic, complemented
8C29×#2935C213yesmaximal, complemented
9C29×#2931C213yesmaximal, complemented
10C29×#2922C213yesmaximal, complemented
11C29×#2906C213yesmaximal, complemented
12C2×C29×#131C2216yes—
13C29×#559C413yes—
14C29×#557C411yescharacteristic
15C29×#556C413yes—
16C29×#553C416yes—
17C29×#550C411yescharacteristic
18C29×#548C412yes—
19C29×#532C2213yes—
20C29×#529C2216yes—
21C4×#41×C29C2212yes—
22C4×#41×C29C2213yes—
23C2×C4×Q8×C29C2211yescharacteristic
24C29×#446C2216yes—
25C8×Q8×C29C2211yescharacteristic
26C8×Q8×C29C2211yescharacteristic
27C8×Q8×C29C2213yes—
28C8×Q8×C29C2213yes—
29C8×Q8×C29C2212yes—
30C29×#436C2216yes—
31C29×#436C2216yes—
32C29×#436C2216yes—
33C29×#435C22112yes—
34C8×D4×C29C2216yes—
35C8×D4×C29C2216yes—
36C8×D4×C29C2216yes—
37C29×#433C2216yes—
38C29×#433C2216yes—
39C29×#431C2216yes—
40C29×#431C2216yes—
41C29×#424C22112yes—
42C29×#424C2213yes—
43C29×#424C2211yescharacteristic
44C29×#423C2213yes—
45C29×#423C2216yes—
46C2×C29×C4⋊C8C2213yes—
47C2×C29×C4⋊C8C2216yes—
48C29×#408C2213yes—
49C29×#408C2213yes—
50C4×M16×C29C2213yes—
51C2×C4×C8×C29C2213yes—
52C2×#41×C29C2×C412yes—
53C2×#41×C29C2313yes—
54C22×Q8×C29C2×C411yescharacteristic
55C29×#131—412no—
56C2×M16×C29C2313yes—
57C2×M16×C29C2311yescharacteristic
58C2×M16×C29C23112yes—
59C22×C8×C29C2313yes—
60C22×C8×C29C2311yescharacteristic
61C22×C8×C29C23112yes—
62C29×C4⋊Q8C2×C413yes—
63C29×#127C2×C413yes—
64C29×#126C2×C4112yes—
65C29×#125C2×C416yes—
66C29×#124C2×C416yes—
67C29×#124C2×C416yes—
68C29×#123C2×C4112yes—
69C29×C22⋊Q8C2×C416yes—
70C29×#121C2×C416yes—
71C29×#121C2×C416yes—
72C29×#121C2×C416yes—
73C4×Q8×C29C2×C411yescharacteristic
74C4×Q8×C29C2×C413yes—
75C4×Q8×C29C2×C412yes—
76C4×Q8×C29C2×C413yes—
77C4×Q8×C29C2×C413yes—
78C4×Q8×C29C2311yescharacteristic
79C4×Q8×C29C2313yes—
80C4×D4×C29C2×C416yes—
81C4×D4×C29C2×C413yes—
82C4×D4×C29C2×C416yes—
83C4×D4×C29C2×C416yes—
84C4×D4×C29C2×C413yes—
85C4×D4×C29C2316yes—
86C4×D4×C29C2316yes—
87C29×#117C2×C416yes—
88C29×#117C2316yes—
89C29×#117C2311yescharacteristic
90C2×C4⋊C4×C29C2×C413yes—
91C2×C42×C29C2316yes—
92C2×C42×C29C2313yes—
93C29×C4⋊C8C2312yes—
94C29×C4⋊C8C2312yes—
95C29×C4⋊C8C2316yes—
96C29×C4⋊C8C2316yes—
97C29×C4⋊C8C2313yes—
98C29×C4⋊C8C2316yes—
99C29×C4⋊C8C2316yes—
100C29×C4⋊C8C2316yes—
101C29×C4⋊C8C2313yes—
102C29×C22⋊C8C2316yes—
103C29×C22⋊C8C2316yes—
104C29×C22⋊C8C2316yes—
105C29×C22⋊C8C2316yes—
106C29×#97C2316yes—
107C4×C8×C29C2313yes—
108C4×C8×C29C2316yes—
109C4×C8×C29C2313yes—
110C4×C8×C29C2313yes—
111C4×C8×C29C2313yes—
112#41×C29—28no—
113#41×C29—26no—
114#41×C29—26no—
115C2×Q8×C29—24no—
116C2×Q8×C29C22×C413yes—
117C2×Q8×C29C22×C413yes—
118C2×Q8×C29C22×C411yescharacteristic
119C2×D4×C29C22×C416yes—
120C2×D4×C29C22×C413yes—
121C2×D4×C29C22×C416yes—
122C2×D4×C29C22×C416yes—
123C22×C4×C29C22×C413yes—
124C22×C4×C29C22×C416yes—
125C22×C4×C29C22×C413yes—
126C22×C4×C29C22×C416yes—
127C22×C4×C29C2416yes—
128C22×C4×C29C2411yescharacteristic
129M16×C29—26no—
130M16×C29—22no—
131M16×C29—412no—
132C2×C8×C29—26no—
133C2×C8×C29—22no—
134C2×C8×C29—412no—
135C2×C8×C29C2413yes—
136C2×C8×C29C2416yes—
137C2×C8×C29C2413yes—
138C2×C8×C29C2411yescharacteristic
139C2×C8×C29C2411yescharacteristic
140C2×C8×C29C2412yes—
141C4⋊C4×C29C22×C413yes—
142C4⋊C4×C29C22×C413yes—
143C4⋊C4×C29C22×C416yes—
144C4⋊C4×C29C22×C416yes—
145C4⋊C4×C29C22×C411yescharacteristic
146C4⋊C4×C29C22×C411yescharacteristic
147C4⋊C4×C29C22×C416yes—
148C4⋊C4×C29C22×C416yes—
149C4⋊C4×C29C22×C416yes—
150C22⋊C4×C29C22×C4112yes—
151C22⋊C4×C29C22×C412yes—
152C22⋊C4×C29C22×C416yes—
153C22⋊C4×C29C22×C416yes—
154C22⋊C4×C29C22×C4112yes—
155C42×C29C22×C416yes—
156C42×C29C22×C416yes—
157C42×C29C22×C413yes—
158C42×C29C22×C413yes—
159C42×C29C2412yes—
160C42×C29C2413yes—
161C42×C29C2413yes—
162#60274C2911yesmaximal, characteristic, direct product factor, Sylow
163C23×C29C23×C416yes—
164C23×C29C23×C411yescharacteristic
165Q8×C29—26no—
166Q8×C29—26no—
167Q8×C29#13114yescomplemented
168D4×C29—212no—
169D4×C29—26no—
170D4×C29—212no—
171D4×C29—46no—
172C2×C4×C29—26no—
173C2×C4×C29—212no—
174C2×C4×C29—26no—
175C2×C4×C29—26no—
176C2×C4×C29—46no—
177C2×C4×C29—43no—
178C2×C4×C29C23×C412yes—
179C2×C4×C29C23×C413yes—
180C2×C4×C29C23×C412yes—
181C2×C4×C29C23×C416yes—
182C2×C4×C29C23×C413yes—
183C2×C4×C29C23×C413yes—
184C2×C4×C29C23×C411yescharacteristic
185C2×C4×C29C23×C413yes—
186C2×C4×C29H(5,𝔽2)12yes—
187C2×C4×C292−1+412yes—
188C2×C4×C29C2511yescharacteristic
189C8×C29—23no—
190C8×C29—23no—
191C8×C29—26no—
192C8×C29—21no—
193C8×C29—21no—
194C8×C29—22no—
195#3480C2×C2911yescharacteristic
196#2994C2×C2916yescomplemented
197#2993C2×C2916yescomplemented
198#2991C2×C2912yescomplemented
199#2988C2×C2912yescomplemented
200Q8×M16C2×C2911yescharacteristic, complemented
201C2×C8×Q8C2×C2911yescharacteristic, complemented
202#2935C2×C2913yescomplemented
203#2931C2×C2913yescomplemented
204#2922C2×C2913yescomplemented
205#2906C2×C2913yescomplemented
206C22×C29—21no—
207C22×C29—21no—
208C22×C29—26no—
209C22×C29—26no—
210C22×C29—26no—
211C22×C29#52012yes—
212C22×C29C24×C411yescharacteristic
213C4×C29—26no—
214C4×C29—22no—
215C4×C29—23no—
216C4×C29—22no—
217C4×C29—23no—
218C4×C29—23no—
219C4×C29#52012yes—
220C4×C29C2×#13116yes—
221C4×C29C2×H(5,𝔽2)11yescharacteristic
222C4×C29C2×2−1+411yescharacteristic
223C2×#131C22×C2916yes—
224#559C4×C2913yes—
225#557C4×C2911yescharacteristic
226#556C4×C2913yes—
227#553C4×C2916yes—
228#550C4×C2911yescharacteristic
229#548C4×C2912yes—
230#532C22×C2913yes—
231#529C22×C2916yes—
232C4×#41C22×C2912yes—
233C4×#41C22×C2913yes—
234C2×C4×Q8C22×C2911yescharacteristic
235#446C22×C2916yes—
236C8×Q8C22×C2911yescharacteristic
237C8×Q8C22×C2911yescharacteristic
238C8×Q8C22×C2913yes—
239C8×Q8C22×C2913yes—
240C8×Q8C22×C2912yes—
241#436C22×C2916yes—
242#436C22×C2916yes—
243#436C22×C2916yes—
244#435C22×C29112yes—
245C8×D4C22×C2916yes—
246C8×D4C22×C2916yes—
247C8×D4C22×C2916yes—
248#433C22×C2916yes—
249#433C22×C2916yes—
250#431C22×C2916yes—
251#431C22×C2916yes—
252#424C22×C2913yes—
253#424C22×C29112yes—
254#424C22×C2911yescharacteristic
255#423C22×C2913yes—
256#423C22×C2916yes—
257C2×C4⋊C8C22×C2913yes—
258C2×C4⋊C8C22×C2916yes—
259#408C22×C2913yes—
260#408C22×C2913yes—
261C4×M16C22×C2913yes—
262C2×C4×C8C22×C2913yes—
263C2×C29—22no—
264C2×C29—46no—
265C2×C29C2×#52011yescharacteristic
266C2×C29C22×#13111yescharacteristic
267C2×C29#357311yescharacteristic
268C2×#41C2×C4×C2912yes—
269C2×#41C23×C2913yes—
270C22×Q8C2×C4×C2911yescharacteristic
271#131—412no—
272C2×M16C23×C2913yes—
273C2×M16C23×C2911yescharacteristic
274C2×M16C23×C29112yes—
275C22×C8C23×C2913yes—
276C22×C8C23×C2911yescharacteristic
277C22×C8C23×C29112yes—
278C4⋊Q8C2×C4×C2913yes—
279#127C2×C4×C2913yes—
280#126C2×C4×C29112yes—
281#125C2×C4×C2916yes—
282#124C2×C4×C2916yes—
283#124C2×C4×C2916yes—
284#123C2×C4×C29112yes—
285C22⋊Q8C2×C4×C2916yes—
286#121C2×C4×C2916yes—
287#121C2×C4×C2916yes—
288#121C2×C4×C2916yes—
289C4×Q8C2×C4×C2911yescharacteristic
290C4×Q8C2×C4×C2913yes—
291C4×Q8C2×C4×C2912yes—
292C4×Q8C2×C4×C2913yes—
293C4×Q8C2×C4×C2913yes—
294C4×Q8C23×C2911yescharacteristic
295C4×Q8C23×C2913yes—
296C4×D4C2×C4×C2916yes—
297C4×D4C2×C4×C2913yes—
298C4×D4C2×C4×C2916yes—
299C4×D4C2×C4×C2916yes—
300C4×D4C2×C4×C2913yes—
301C4×D4C23×C2916yes—
302C4×D4C23×C2916yes—
303#117C2×C4×C2916yes—
304#117C23×C2911yescharacteristic
305#117C23×C2916yes—
306C2×C4⋊C4C2×C4×C2913yes—
307C2×C42C23×C2913yes—
308C2×C42C23×C2916yes—
309C4⋊C8C23×C2913yes—
310C4⋊C8C23×C2916yes—
311C4⋊C8C23×C2916yes—
312C4⋊C8C23×C2913yes—
313C4⋊C8C23×C2916yes—
314C4⋊C8C23×C2916yes—
315C4⋊C8C23×C2916yes—
316C4⋊C8C23×C2912yes—
317C4⋊C8C23×C2912yes—
318C22⋊C8C23×C2916yes—
319C22⋊C8C23×C2916yes—
320C22⋊C8C23×C2916yes—
321C22⋊C8C23×C2916yes—
322#97C23×C2916yes—
323C4×C8C23×C2913yes—
324C4×C8C23×C2913yes—
325C4×C8C23×C2913yes—
326C4×C8C23×C2913yes—
327C4×C8C23×C2916yes—
328C29#6027411yescharacteristic, direct product factor, Sylow
329#41—28no—
330#41—26no—
331#41—26no—
332C2×Q8—24no—
333C2×Q8C22×C4×C2913yes—
334C2×Q8C22×C4×C2913yes—
335C2×Q8C22×C4×C2911yescharacteristic
336C2×D4C22×C4×C2916yes—
337C2×D4C22×C4×C2913yes—
338C2×D4C22×C4×C2916yes—
339C2×D4C22×C4×C2916yes—
340C22×C4C22×C4×C2913yes—
341C22×C4C22×C4×C2916yes—
342C22×C4C22×C4×C2913yes—
343C22×C4C22×C4×C2916yes—
344C22×C4C24×C2916yes—
345C22×C4C24×C2911yescharacteristic
346M16—26no—
347M16—22no—
348M16—412no—
349C2×C8—26no—
350C2×C8—22no—
351C2×C8—412no—
352C2×C8C24×C2911yescharacteristic
353C2×C8C24×C2911yescharacteristic
354C2×C8C24×C2912yes—
355C2×C8C24×C2913yes—
356C2×C8C24×C2913yes—
357C2×C8C24×C2916yes—
358C4⋊C4C22×C4×C2913yes—
359C4⋊C4C22×C4×C2913yes—
360C4⋊C4C22×C4×C2916yes—
361C4⋊C4C22×C4×C2916yes—
362C4⋊C4C22×C4×C2911yescharacteristic
363C4⋊C4C22×C4×C2911yescharacteristic
364C4⋊C4C22×C4×C2916yes—
365C4⋊C4C22×C4×C2916yes—
366C4⋊C4C22×C4×C2916yes—
367C22⋊C4C22×C4×C29112yes—
368C22⋊C4C22×C4×C2912yes—
369C22⋊C4C22×C4×C2916yes—
370C22⋊C4C22×C4×C2916yes—
371C22⋊C4C22×C4×C29112yes—
372C42C22×C4×C2916yes—
373C42C22×C4×C2916yes—
374C42C22×C4×C2913yes—
375C42C22×C4×C2913yes—
376C42C24×C2913yes—
377C42C24×C2913yes—
378C42C24×C2912yes—
379C23C23×C4×C2916yes—
380C23C23×C4×C2911yescharacteristic
381Q8—26no—
382Q8—26no—
383Q8C29×#13114yescomplemented
384D4—212no—
385D4—26no—
386D4—212no—
387D4—46no—
388C2×C4—26no—
389C2×C4—212no—
390C2×C4—26no—
391C2×C4—26no—
392C2×C4—46no—
393C2×C4—43no—
394C2×C4C23×C4×C2912yes—
395C2×C4C23×C4×C2913yes—
396C2×C4C23×C4×C2912yes—
397C2×C4C23×C4×C2916yes—
398C2×C4C23×C4×C2913yes—
399C2×C4C23×C4×C2913yes—
400C2×C4C23×C4×C2911yescharacteristic
401C2×C4C23×C4×C2913yes—
402C2×C4C29×H(5,𝔽2)12yes—
403C2×C4C29×2−1+412yes—
404C2×C4C25×C2911yescharacteristic
405C8—23no—
406C8—23no—
407C8—26no—
408C8—21no—
409C8—21no—
410C8—22no—
411C22—21no—
412C22—21no—
413C22—26no—
414C22—26no—
415C22—26no—
416C22C29×#52012yes—
417C22C24×C4×C2911yescharacteristic
418C4—22no—
419C4—23no—
420C4—22no—
421C4—23no—
422C4—23no—
423C4—26no—
424C4C29×#52012yes—
425C4C2×C29×#13116yes—
426C4C2×C29×H(5,𝔽2)11yescharacteristic
427C4C2×C29×2−1+411yescharacteristic
428C2—22no—
429C2—46no—
430C2C2×C29×#52011yescharacteristic
431C2C22×C29×#13111yescharacteristic
432C2C29×#357311yescharacteristic
subgroupG/H
centerC2×C4×C29C25
commutatorC22C24×C4×C29
Frattini, cosocleC2×C4C25×C29
socleC22×C29C24×C4
prime radicalC29×#3480C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#2994C2semidirect
3. C29×#2993C2semidirect
4. C29×#2991C2semidirect
5. C29×#2988C2semidirect
6. Q8×M16×C29C2semidirect
7. C2×C8×Q8×C29C2semidirect
8. C29×#2935C2semidirect
9. C29×#2931C2semidirect
10. C29×#2922C2semidirect
11. C29×#2906C2semidirect
162. #60274C29direct (N × H)
167. Q8×C29#131semidirect
196. #2994C2×C29semidirect
197. #2993C2×C29semidirect
198. #2991C2×C29semidirect
199. #2988C2×C29semidirect
200. Q8×M16C2×C29semidirect
201. C2×C8×Q8C2×C29semidirect
202. #2935C2×C29semidirect
203. #2931C2×C29semidirect
204. #2922C2×C29semidirect
205. #2906C2×C29semidirect
328. C29#60274direct (N × H)
383. 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×#29942
C29×#29932
C29×#29912
C29×#29882
Q8×M16×C292
C2×C8×Q8×C292
C29×#29352
C29×#29312
C29×#29222
C29×#29062
#6027429