Finite Group Databasebeta

← C29×#36684 #20331584

Subgroups — C29×#36684 #20331584

Order 7424.

2138 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#529C212yesmaximal, complemented
2C29×#2823C214yesmaximal, complemented
3C29×#2822C211yesmaximal, characteristic, complemented
4C29×#2820C212yesmaximal, complemented
5C29×#2819C211yesmaximal, characteristic, complemented
6C29×#2814C214yesmaximal, complemented
7C29×#2813C214yesmaximal, complemented
8C29×#2396C214yesmaximal, complemented
9C29×#2392C214yesmaximal, complemented
10C29×#2392C214yesmaximal, complemented
11C29×#2285C211yesmaximal, characteristic, complemented
12C29×#529—216no—
13C2×C29×#126C2214yes—
14C2×C29×#125C2212yes—
15C2×C29×#124C2212yes—
16C2×C29×#123C2214yes—
17C2×C29×C22⋊Q8C2212yes—
18C2×C29×#121C2212yes—
19C2×C4×Q8×C29C2212yes—
20C2×C4×D4×C29C2214yes—
21C2×C4×D4×C29C2212yes—
22C2×C4×D4×C29C2214yes—
23C2×C29×#117C2214yes—
24C2×C29×#117C2212yes—
25C22×C42×C29C2211yescharacteristic
26C29×#400C2214yes—
27C29×#399C2214yes—
28C29×#398C2214yes—
29C29×#398C2218yes—
30C29×#398C2214yes—
31C29×#397C2214yes—
32C29×#397C2214yes—
33C29×#396C2218yes—
34C29×#396C2218yes—
35C29×#396C2218yes—
36C29×#395C2214yes—
37C29×#394C2218yes—
38C29×#394C2214yes—
39C29×#394C2218yes—
40C29×#394C2214yes—
41C29×#393C2214yes—
42C29×#392C2214yes—
43C29×#392C2214yes—
44C29×#384C2212yes—
45C29×#382C2211yescharacteristic
46C29×#382C2211yescharacteristic
47C29×#380C2214yes—
48C4×C4⋊C4×C29C2214yes—
49C4×C4⋊C4×C29C2214yes—
50C4×C22⋊C4×C29C2218yes—
51C22×Q8×C29C2312yes—
52C22×D4×C29C2314yes—
53C22×D4×C29C2312yes—
54C22×D4×C29C2314yes—
55C23×C4×C29C2314yes—
56C23×C4×C29C2311yescharacteristic
57C23×C4×C29C2312yes—
58C29×#126—216no—
59C29×#125—28no—
60C29×#124—28no—
61C29×#123—216no—
62C29×C22⋊Q8—28no—
63C29×#121—28no—
64C4×Q8×C29—28no—
65C4×D4×C29—216no—
66C4×D4×C29—28no—
67C4×D4×C29—48no—
68C29×#117—216no—
69C29×#117—44no—
70C2×C4⋊C4×C29C2314yes—
71C2×C4⋊C4×C29C2314yes—
72C2×C4⋊C4×C29C2312yes—
73C2×C4⋊C4×C29C2314yes—
74C2×C4⋊C4×C29C2312yes—
75C2×C4⋊C4×C29C2314yes—
76C2×C4⋊C4×C29C2312yes—
77C2×C4⋊C4×C29C2312yes—
78C2×C4⋊C4×C29C2314yes—
79C2×C4⋊C4×C29C2318yes—
80C2×C4⋊C4×C29C2318yes—
81C2×C22⋊C4×C29C2314yes—
82C2×C22⋊C4×C29C2314yes—
83C2×C22⋊C4×C29C2314yes—
84C2×C22⋊C4×C29C2314yes—
85C2×C22⋊C4×C29C2314yes—
86C2×C22⋊C4×C29C2314yes—
87C2×C22⋊C4×C29C2318yes—
88C2×C22⋊C4×C29C2318yes—
89C2×C22⋊C4×C29C2318yes—
90C2×C42×C29D418yescomplemented
91C2×C42×C29C2314yes—
92C2×C42×C29C2314yes—
93C2×C42×C29C2311yescharacteristic
94C2×C42×C29C2311yescharacteristic
95C2×C42×C29C2312yes—
96C29×#95C2318yes—
97C29×#95C2318yes—
98C29×#95C2314yes—
99C29×#95C2314yes—
100C29×#95C2314yes—
101C29×#95C2314yes—
102C24×C29C2414yes—
103C24×C29C2411yescharacteristic
104C2×Q8×C29—24no—
105C2×Q8×C29—44no—
106C2×D4×C29—28no—
107C2×D4×C29—24no—
108C2×D4×C29—44no—
109C2×D4×C29—44no—
110C2×D4×C29—48no—
111C2×D4×C29—48no—
112C22×C4×C29—22no—
113C22×C4×C29—22no—
114C22×C4×C29—28no—
115C22×C4×C29—28no—
116C22×C4×C29—28no—
117C22×C4×C29—44no—
118C22×C4×C29C2×D414yes—
119C22×C4×C29C2×D418yes—
120C22×C4×C29C2414yes—
121C22×C4×C29C2414yes—
122C22×C4×C29C2414yes—
123C22×C4×C29C2414yes—
124C22×C4×C29C2414yes—
125C22×C4×C29C2411yescharacteristic
126C22×C4×C29C2412yes—
127C22×C4×C29C2412yes—
128C22×C4×C29C2411yescharacteristic
129C4⋊C4×C29—28no—
130C4⋊C4×C29—28no—
131C4⋊C4×C29—24no—
132C4⋊C4×C29—28no—
133C4⋊C4×C29—24no—
134C4⋊C4×C29—28no—
135C4⋊C4×C29—48no—
136C4⋊C4×C29—48no—
137C4⋊C4×C29—42no—
138C4⋊C4×C29—42no—
139C4⋊C4×C29—44no—
140C22⋊C4×C29—28no—
141C22⋊C4×C29—28no—
142C22⋊C4×C29—28no—
143C22⋊C4×C29—28no—
144C22⋊C4×C29—28no—
145C22⋊C4×C29—48no—
146C22⋊C4×C29—48no—
147C22⋊C4×C29—44no—
148C22⋊C4×C29—48no—
149C42×C29—28no—
150C42×C29—28no—
151C42×C29C2×D418yes—
152C42×C29C2×D414yes—
153C42×C29C2×D414yes—
154#36684C2911yesmaximal, characteristic, direct product factor, Sylow
155C23×C29—21no—
156C23×C29—21no—
157C23×C29—24no—
158C23×C29—24no—
159C23×C29—24no—
160C23×C29—24no—
161C23×C29—28no—
162C23×C29—28no—
163C23×C29C22×D412yes—
164C23×C29C2511yescharacteristic
165Q8×C29—48no—
166D4×C29—48no—
167D4×C29—416no—
168D4×C29—416no—
169C2×C4×C29—21no—
170C2×C4×C29—21no—
171C2×C4×C29—24no—
172C2×C4×C29—24no—
173C2×C4×C29—28no—
174C2×C4×C29—24no—
175C2×C4×C29—24no—
176C2×C4×C29—24no—
177C2×C4×C29—24no—
178C2×C4×C29—24no—
179C2×C4×C29—24no—
180C2×C4×C29—24no—
181C2×C4×C29—28no—
182C2×C4×C29—28no—
183C2×C4×C29—28no—
184C2×C4×C29—28no—
185C2×C4×C29—48no—
186C2×C4×C29—416no—
187C2×C4×C29C22×D412yes—
188C2×C4×C29C22×D414yes—
189C2×C4×C29C22×D414yes—
190C2×C4×C29C22×D412yes—
191C2×C4×C29H(5,𝔽2)12yes—
192C2×C4×C292−1+412yes—
193C2×#529C2×C2912yescomplemented
194#2823C2×C2914yescomplemented
195#2822C2×C2911yescharacteristic, complemented
196#2820C2×C2912yescomplemented
197#2819C2×C2911yescharacteristic, complemented
198#2814C2×C2914yescomplemented
199#2813C2×C2914yescomplemented
200#2396C2×C2914yescomplemented
201#2392C2×C2914yescomplemented
202#2392C2×C2914yescomplemented
203#2285C2×C2911yescharacteristic, complemented
204C22×C29—22no—
205C22×C29—24no—
206C22×C29—42no—
207C22×C29—42no—
208C22×C29—44no—
209C22×C29—44no—
210C22×C29—44no—
211C22×C29—48no—
212C22×C29—48no—
213C22×C29C23×D411yescharacteristic
214C22×C29C2×H(5,𝔽2)11yescharacteristic
215C22×C29C2×2−1+411yescharacteristic
216C22×C29#58514yes—
217C4×C29—22no—
218C4×C29—24no—
219C4×C29—24no—
220C4×C29—44no—
221C4×C29—44no—
222C4×C29—44no—
223C4×C29—44no—
224C4×C29—44no—
225C4×C29#53714yes—
226#529—216no—
227C2×#126C22×C2914yes—
228C2×#125C22×C2912yes—
229C2×#124C22×C2912yes—
230C2×#123C22×C2914yes—
231C2×C22⋊Q8C22×C2912yes—
232C2×#121C22×C2912yes—
233C2×C4×Q8C22×C2912yes—
234C2×C4×D4C22×C2914yes—
235C2×C4×D4C22×C2912yes—
236C2×C4×D4C22×C2914yes—
237C2×#117C22×C2914yes—
238C2×#117C22×C2912yes—
239C22×C42C22×C2911yescharacteristic
240#400C22×C2914yes—
241#399C22×C2914yes—
242#398C22×C2914yes—
243#398C22×C2914yes—
244#398C22×C2918yes—
245#397C22×C2914yes—
246#397C22×C2914yes—
247#396C22×C2918yes—
248#396C22×C2918yes—
249#396C22×C2918yes—
250#395C22×C2914yes—
251#394C22×C2914yes—
252#394C22×C2914yes—
253#394C22×C2918yes—
254#394C22×C2918yes—
255#393C22×C2914yes—
256#392C22×C2914yes—
257#392C22×C2914yes—
258#384C22×C2912yes—
259#382C22×C2911yescharacteristic
260#382C22×C2911yescharacteristic
261#380C22×C2914yes—
262C4×C4⋊C4C22×C2914yes—
263C4×C4⋊C4C22×C2914yes—
264C4×C22⋊C4C22×C2918yes—
265C2×C29—42no—
266C2×C29—84no—
267C2×C29C2×#53711yescharacteristic
268C2×C29#344912yes—
269C2×C29#352912yes—
270C2×C29#353112yes—
271C22×Q8C23×C2912yes—
272C22×D4C23×C2914yes—
273C22×D4C23×C2912yes—
274C22×D4C23×C2914yes—
275C23×C4C23×C2914yes—
276C23×C4C23×C2911yescharacteristic
277C23×C4C23×C2912yes—
278#126—216no—
279#125—28no—
280#124—28no—
281#123—216no—
282C22⋊Q8—28no—
283#121—28no—
284C4×Q8—28no—
285C4×D4—216no—
286C4×D4—28no—
287C4×D4—48no—
288#117—216no—
289#117—44no—
290C2×C4⋊C4C23×C2914yes—
291C2×C4⋊C4C23×C2914yes—
292C2×C4⋊C4C23×C2912yes—
293C2×C4⋊C4C23×C2914yes—
294C2×C4⋊C4C23×C2912yes—
295C2×C4⋊C4C23×C2914yes—
296C2×C4⋊C4C23×C2912yes—
297C2×C4⋊C4C23×C2912yes—
298C2×C4⋊C4C23×C2914yes—
299C2×C4⋊C4C23×C2918yes—
300C2×C4⋊C4C23×C2918yes—
301C2×C22⋊C4C23×C2914yes—
302C2×C22⋊C4C23×C2914yes—
303C2×C22⋊C4C23×C2914yes—
304C2×C22⋊C4C23×C2914yes—
305C2×C22⋊C4C23×C2914yes—
306C2×C22⋊C4C23×C2914yes—
307C2×C22⋊C4C23×C2918yes—
308C2×C22⋊C4C23×C2918yes—
309C2×C22⋊C4C23×C2918yes—
310C2×C42D4×C2918yescomplemented
311C2×C42C23×C2914yes—
312C2×C42C23×C2914yes—
313C2×C42C23×C2912yes—
314C2×C42C23×C2911yescharacteristic
315C2×C42C23×C2911yescharacteristic
316#95C23×C2918yes—
317#95C23×C2918yes—
318#95C23×C2914yes—
319#95C23×C2914yes—
320#95C23×C2914yes—
321#95C23×C2914yes—
322C29#3668411yescharacteristic, direct product factor, Sylow
323C24C24×C2914yes—
324C24C24×C2911yescharacteristic
325C2×Q8—24no—
326C2×Q8—44no—
327C2×D4—28no—
328C2×D4—24no—
329C2×D4—44no—
330C2×D4—44no—
331C2×D4—48no—
332C2×D4—48no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—28no—
336C22×C4—28no—
337C22×C4—28no—
338C22×C4—44no—
339C22×C4C2×D4×C2914yes—
340C22×C4C2×D4×C2918yes—
341C22×C4C24×C2914yes—
342C22×C4C24×C2914yes—
343C22×C4C24×C2914yes—
344C22×C4C24×C2914yes—
345C22×C4C24×C2914yes—
346C22×C4C24×C2912yes—
347C22×C4C24×C2911yescharacteristic
348C22×C4C24×C2912yes—
349C22×C4C24×C2911yescharacteristic
350C4⋊C4—28no—
351C4⋊C4—28no—
352C4⋊C4—24no—
353C4⋊C4—28no—
354C4⋊C4—24no—
355C4⋊C4—28no—
356C4⋊C4—42no—
357C4⋊C4—42no—
358C4⋊C4—44no—
359C4⋊C4—48no—
360C4⋊C4—48no—
361C22⋊C4—28no—
362C22⋊C4—28no—
363C22⋊C4—28no—
364C22⋊C4—28no—
365C22⋊C4—28no—
366C22⋊C4—44no—
367C22⋊C4—48no—
368C22⋊C4—48no—
369C22⋊C4—48no—
370C42—28no—
371C42—28no—
372C42C2×D4×C2918yes—
373C42C2×D4×C2914yes—
374C42C2×D4×C2914yes—
375C23—21no—
376C23—21no—
377C23—24no—
378C23—24no—
379C23—24no—
380C23—24no—
381C23—28no—
382C23—28no—
383C23C22×D4×C2912yes—
384C23C25×C2911yescharacteristic
385Q8—48no—
386D4—48no—
387D4—416no—
388D4—416no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—24no—
392C2×C4—24no—
393C2×C4—28no—
394C2×C4—24no—
395C2×C4—24no—
396C2×C4—24no—
397C2×C4—24no—
398C2×C4—24no—
399C2×C4—24no—
400C2×C4—24no—
401C2×C4—28no—
402C2×C4—28no—
403C2×C4—28no—
404C2×C4—28no—
405C2×C4—48no—
406C2×C4—416no—
407C2×C4C22×D4×C2912yes—
408C2×C4C22×D4×C2914yes—
409C2×C4C22×D4×C2914yes—
410C2×C4C22×D4×C2912yes—
411C2×C4C29×H(5,𝔽2)12yes—
412C2×C4C29×2−1+412yes—
413C22—22no—
414C22—24no—
415C22—42no—
416C22—42no—
417C22—44no—
418C22—44no—
419C22—44no—
420C22—48no—
421C22—48no—
422C22C23×D4×C2911yescharacteristic
423C22C2×C29×H(5,𝔽2)11yescharacteristic
424C22C2×C29×2−1+411yescharacteristic
425C22C29×#58514yes—
426C4—22no—
427C4—24no—
428C4—24no—
429C4—44no—
430C4—44no—
431C4—44no—
432C4—44no—
433C4—44no—
434C4C29×#53714yes—
435C2—42no—
436C2—84no—
437C2C2×C29×#53711yescharacteristic
438C2C29×#344912yes—
439C2C29×#352912yes—
440C2C29×#353112yes—
subgroupG/H
centerC22×C4×C29C24
commutator, Frattini, cosocleC23C25×C29
socleC23×C29C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C29×#529C2semidirect
2. C29×#2823C2semidirect
3. C29×#2822C2semidirect
4. C29×#2820C2semidirect
5. C29×#2819C2semidirect
6. C29×#2814C2semidirect
7. C29×#2813C2semidirect
8. C29×#2396C2semidirect
9. C29×#2392C2semidirect
10. C29×#2392C2semidirect
11. C29×#2285C2semidirect
90. C2×C42×C29D4semidirect
154. #36684C29direct (N × H)
193. C2×#529C2×C29semidirect
194. #2823C2×C29semidirect
195. #2822C2×C29semidirect
196. #2820C2×C29semidirect
197. #2819C2×C29semidirect
198. #2814C2×C29semidirect
199. #2813C2×C29semidirect
200. #2396C2×C29semidirect
201. #2392C2×C29semidirect
202. #2392C2×C29semidirect
203. #2285C2×C29semidirect
310. C2×C42D4×C29semidirect
322. C29#36684direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#5292
C29×#28232
C29×#28222
C29×#28202
C29×#28192
C29×#28142
C29×#28132
C29×#23962
C29×#23922
C29×#22852
#3668429