Finite Group Databasebeta

← C29×#62147 #20357047

Subgroups — C29×#62147 #20357047

Order 7424.

1734 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3503C211yesmaximal, characteristic, complemented
2C29×#3482C211yesmaximal, characteristic
3Q8×SD16×C29C212yesmaximal, complemented
4C29×#3363C212yesmaximal, complemented
5C29×#3356C216yesmaximal, complemented
6C29×#3331C216yesmaximal, complemented
7C29×#3255C213yesmaximal, complemented
8C29×#3229C213yesmaximal, complemented
9C29×#3107C213yesmaximal, complemented
10C29×#3079C213yesmaximal, complemented
11C29×#2991C211yesmaximal, characteristic, complemented
12Q82×C29C2212yes—
13C29×#557—21no—
14C29×#557C2211yescharacteristic
15C29×#556C2213yes—
16C29×#554C2216yes—
17C29×#552—23no—
18D4×Q8×C29—23no—
19D4×Q8×C29C2211yescharacteristic
20C29×#548—21no—
21C29×#547C2213yes—
22C29×#544—23no—
23C29×#533C2213yes—
24C29×#533C2213yes—
25C2×C29×C4⋊Q8C2213yes—
26C29×#529—23no—
27C29×#520—21no—
28C4×#41×C29C2213yes—
29C4×#41×C29C2211yescharacteristic
30C2×C4×Q8×C29—21no—
31C29×#498C2216yes—
32C29×#487C2216yes—
33C29×#485C2216yes—
34C29×#483C22112yes—
35C29×#477C2216yes—
36C29×#476C2216yes—
37C29×#475C2213yes—
38C29×#475C2216yes—
39C29×#475C2216yes—
40C29×#474C2213yes—
41C29×#470C22112yes—
42C29×#462C2213yes—
43C29×#462C2216yes—
44C29×#461C2211yescharacteristic
45C29×#452C2216yes—
46C8×Q8×C29C2212yes—
47C4×Q16×C29C2216yes—
48C4×SD16×C29C2216yes—
49C29×#436C2216yes—
50C29×#431C2213yes—
51C29×#428C2216yes—
52C29×#423C2213yes—
53C29×#417C2216yes—
54C2×#41×C29D411yescharacteristic
55C2×#41×C29C2313yes—
56C22×Q8×C29—21no—
57C22×Q8×C29—23no—
58C2×Q16×C29C2316yes—
59C2×SD16×C29C2312yes—
60C2×M16×C29C2316yes—
61C29×C4⋊Q8—26no—
62C29×C4⋊Q8—23no—
63C29×C4⋊Q8—23no—
64C29×C4⋊Q8C2311yescharacteristic
65C29×C4⋊Q8C2313yes—
66C29×C4⋊Q8C2313yes—
67C29×C4⋊Q8C2313yes—
68C29×C4⋊Q8C2316yes—
69C29×#126—26no—
70C29×#125—23no—
71C29×#125—26no—
72C29×#125—23no—
73C29×#125—23no—
74C29×#124—23no—
75C29×#123—26no—
76C29×C22⋊Q8—23no—
77C29×C22⋊Q8—23no—
78C29×C22⋊Q8—23no—
79C29×C22⋊Q8—212no—
80C29×C22⋊Q8C2316yes—
81C29×C22⋊Q8C2316yes—
82C29×#121—23no—
83C4×Q8×C29—21no—
84C4×Q8×C29—22no—
85C4×Q8×C29—23no—
86C4×Q8×C29—23no—
87C4×Q8×C29—23no—
88C4×Q8×C29D411yescharacteristic
89C4×Q8×C29C2316yes—
90C4×Q8×C29C2313yes—
91C4×Q8×C29C2313yes—
92C4×Q8×C29C2311yescharacteristic
93C4×D4×C29—26no—
94C4×D4×C29—23no—
95C4×D4×C29—23no—
96C4×D4×C29D413yes—
97C4×D4×C29C2313yes—
98C4×D4×C29C2311yescharacteristic
99C4×D4×C29C2313yes—
100C29×#117—23no—
101C29×#117—23no—
102C29×#117—23no—
103C29×#117D413yes—
104C29×#117C2313yes—
105C2×C4⋊C4×C29—23no—
106C2×C4⋊C4×C29—23no—
107C2×C4⋊C4×C29C2316yes—
108C2×C42×C29—23no—
109C2×C42×C29C2313yes—
110C29×#107C2316yes—
111C29×#106C23112yes—
112C29×#106C2316yes—
113C29×C4⋊C8C2311yescharacteristic
114C29×C4⋊C8C2313yes—
115C29×C4⋊C8C2316yes—
116C29×#103C2316yes—
117C29×#103C2312yes—
118C29×#103C2316yes—
119C29×#103C23112yes—
120C29×#102C2316yes—
121C29×C22⋊C8C2316yes—
122C4×C8×C29C2316yes—
123#41×C29—24no—
124#41×C29—26no—
125#41×C29—43no—
126C2×Q8×C29—23no—
127C2×Q8×C29—23no—
128C2×Q8×C29—26no—
129C2×Q8×C29—44no—
130C2×Q8×C29—86no—
131C2×Q8×C29C2×D411yescharacteristic
132C2×Q8×C29C2412yes—
133C2×Q8×C29C2413yes—
134C2×D4×C29—23no—
135C2×D4×C29C2×D413yes—
136C2×D4×C29C2411yescharacteristic
137C22×C4×C29—26no—
138C22×C4×C29—21no—
139C22×C4×C29—23no—
140C22×C4×C29—23no—
141C22×C4×C29C2×D413yes—
142C22×C4×C29C2×D413yes—
143C22×C4×C29C2413yes—
144Q16×C29—46no—
145SD16×C29—24no—
146M16×C29—46no—
147C2×C8×C29C2416yes—
148C2×C8×C29C2412yes—
149C4⋊C4×C29—23no—
150C4⋊C4×C29—26no—
151C4⋊C4×C29—23no—
152C4⋊C4×C29—26no—
153C4⋊C4×C29—26no—
154C4⋊C4×C29—21no—
155C4⋊C4×C29—23no—
156C4⋊C4×C29—23no—
157C4⋊C4×C29—23no—
158C4⋊C4×C29—23no—
159C4⋊C4×C29—21no—
160C4⋊C4×C29—26no—
161C4⋊C4×C29—26no—
162C4⋊C4×C29C2×D413yes—
163C4⋊C4×C29C2×D413yes—
164C4⋊C4×C29C2416yes—
165C4⋊C4×C29C2411yescharacteristic
166C4⋊C4×C29C2413yes—
167C22⋊C4×C29—26no—
168C22⋊C4×C29—26no—
169C22⋊C4×C29—23no—
170C22⋊C4×C29—21no—
171C22⋊C4×C29—23no—
172C22⋊C4×C29C2×D416yes—
173C42×C29—23no—
174C42×C29—23no—
175C42×C29—23no—
176C42×C29—26no—
177C42×C29C2×D413yes—
178C42×C29C2×D413yes—
179C42×C29C2411yescharacteristic
180C42×C29C2413yes—
181#62147C2911yesmaximal, characteristic, direct product factor, Sylow
182C23×C29—21no—
183C23×C29C22×D413yes—
184Q8×C29—22no—
185Q8×C29—23no—
186Q8×C29—22no—
187Q8×C29—23no—
188Q8×C29—46no—
189Q8×C29—46no—
190Q8×C29—86no—
191Q8×C29#13714yes—
192D4×C29—26no—
193D4×C29—21no—
194D4×C29—46no—
195D4×C292−1+412yes—
196C2×C4×C29—26no—
197C2×C4×C29—26no—
198C2×C4×C29—23no—
199C2×C4×C29—23no—
200C2×C4×C29—21no—
201C2×C4×C29—22no—
202C2×C4×C29—23no—
203C2×C4×C29—23no—
204C2×C4×C29—26no—
205C2×C4×C29—46no—
206C2×C4×C29—46no—
207C2×C4×C29—42no—
208C2×C4×C29—86no—
209C2×C4×C29C22×D413yes—
210C2×C4×C29C22×D411yescharacteristic
211C2×C4×C29C22×D413yes—
212C2×C4×C29C22×D413yes—
213C2×C4×C29C22×D411yescharacteristic
214C2×C4×C29C2511yescharacteristic
215C8×C29—22no—
216C8×C29—26no—
217#3503C2×C2911yescharacteristic, complemented
218#3482C2×C2911yescharacteristic
219Q8×SD16C2×C2912yescomplemented
220#3363C2×C2912yescomplemented
221#3356C2×C2916yescomplemented
222#3331C2×C2916yescomplemented
223#3255C2×C2913yescomplemented
224#3229C2×C2913yescomplemented
225#3107C2×C2913yescomplemented
226#3079C2×C2913yescomplemented
227#2991C2×C2911yescharacteristic, complemented
228C22×C29—23no—
229C22×C29—22no—
230C22×C29—23no—
231C22×C29—23no—
232C22×C29—41no—
233C22×C29—41no—
234C22×C29C23×D411yescharacteristic
235C4×C29—23no—
236C4×C29—21no—
237C4×C29—23no—
238C4×C29—43no—
239C4×C29—42no—
240C4×C29—43no—
241C4×C29—41no—
242C4×C29—46no—
243C4×C29C2×#13716yes—
244C4×C29#57712yes—
245C4×C29C2×2−1+411yescharacteristic
246C4×C29#58511yescharacteristic
247Q82C22×C2912yes—
248#557—21no—
249#557C22×C2911yescharacteristic
250#556C22×C2913yes—
251#554C22×C2916yes—
252#552—23no—
253D4×Q8—23no—
254D4×Q8C22×C2911yescharacteristic
255#548—21no—
256#547C22×C2913yes—
257#544—23no—
258#533C22×C2913yes—
259#533C22×C2913yes—
260C2×C4⋊Q8C22×C2913yes—
261#529—23no—
262#520—21no—
263C4×#41C22×C2913yes—
264C4×#41C22×C2911yescharacteristic
265C2×C4×Q8—21no—
266#498C22×C2916yes—
267#487C22×C2916yes—
268#485C22×C2916yes—
269#483C22×C29112yes—
270#477C22×C2916yes—
271#476C22×C2916yes—
272#475C22×C2916yes—
273#475C22×C2916yes—
274#475C22×C2913yes—
275#474C22×C2913yes—
276#470C22×C29112yes—
277#462C22×C2916yes—
278#462C22×C2913yes—
279#461C22×C2911yescharacteristic
280#452C22×C2916yes—
281C8×Q8C22×C2912yes—
282C4×Q16C22×C2916yes—
283C4×SD16C22×C2916yes—
284#436C22×C2916yes—
285#431C22×C2913yes—
286#428C22×C2916yes—
287#423C22×C2913yes—
288#417C22×C2916yes—
289C2×C29—43no—
290C2×C29—42no—
291C2×C29#348911yescharacteristic
292C2×C29C22×#13711yescharacteristic
293C2×C29C2×#57711yescharacteristic
294C2×#41D4×C2911yescharacteristic
295C2×#41C23×C2913yes—
296C22×Q8—21no—
297C22×Q8—23no—
298C2×Q16C23×C2916yes—
299C2×SD16C23×C2912yes—
300C2×M16C23×C2916yes—
301C4⋊Q8—26no—
302C4⋊Q8—23no—
303C4⋊Q8—23no—
304C4⋊Q8C23×C2911yescharacteristic
305C4⋊Q8C23×C2913yes—
306C4⋊Q8C23×C2913yes—
307C4⋊Q8C23×C2916yes—
308C4⋊Q8C23×C2913yes—
309#126—26no—
310#125—23no—
311#125—26no—
312#125—23no—
313#125—23no—
314#124—23no—
315#123—26no—
316C22⋊Q8—23no—
317C22⋊Q8—23no—
318C22⋊Q8—23no—
319C22⋊Q8—212no—
320C22⋊Q8C23×C2916yes—
321C22⋊Q8C23×C2916yes—
322#121—23no—
323C4×Q8—21no—
324C4×Q8—22no—
325C4×Q8—23no—
326C4×Q8—23no—
327C4×Q8—23no—
328C4×Q8D4×C2911yescharacteristic
329C4×Q8C23×C2913yes—
330C4×Q8C23×C2913yes—
331C4×Q8C23×C2916yes—
332C4×Q8C23×C2911yescharacteristic
333C4×D4—26no—
334C4×D4—23no—
335C4×D4—23no—
336C4×D4D4×C2913yes—
337C4×D4C23×C2911yescharacteristic
338C4×D4C23×C2913yes—
339C4×D4C23×C2913yes—
340#117—23no—
341#117—23no—
342#117—23no—
343#117D4×C2913yes—
344#117C23×C2913yes—
345C2×C4⋊C4—23no—
346C2×C4⋊C4—23no—
347C2×C4⋊C4C23×C2916yes—
348C2×C42—23no—
349C2×C42C23×C2913yes—
350#107C23×C2916yes—
351#106C23×C29112yes—
352#106C23×C2916yes—
353C4⋊C8C23×C2913yes—
354C4⋊C8C23×C2916yes—
355C4⋊C8C23×C2911yescharacteristic
356#103C23×C29112yes—
357#103C23×C2916yes—
358#103C23×C2912yes—
359#103C23×C2916yes—
360#102C23×C2916yes—
361C22⋊C8C23×C2916yes—
362C4×C8C23×C2916yes—
363C29#6214711yescharacteristic, direct product factor, Sylow
364#41—24no—
365#41—26no—
366#41—43no—
367C2×Q8—23no—
368C2×Q8—23no—
369C2×Q8—26no—
370C2×Q8—44no—
371C2×Q8—86no—
372C2×Q8C2×D4×C2911yescharacteristic
373C2×Q8C24×C2913yes—
374C2×Q8C24×C2912yes—
375C2×D4—23no—
376C2×D4C2×D4×C2913yes—
377C2×D4C24×C2911yescharacteristic
378C22×C4—26no—
379C22×C4—21no—
380C22×C4—23no—
381C22×C4—23no—
382C22×C4C2×D4×C2913yes—
383C22×C4C2×D4×C2913yes—
384C22×C4C24×C2913yes—
385Q16—46no—
386SD16—24no—
387M16—46no—
388C2×C8C24×C2912yes—
389C2×C8C24×C2916yes—
390C4⋊C4—23no—
391C4⋊C4—26no—
392C4⋊C4—23no—
393C4⋊C4—26no—
394C4⋊C4—26no—
395C4⋊C4—21no—
396C4⋊C4—23no—
397C4⋊C4—23no—
398C4⋊C4—23no—
399C4⋊C4—23no—
400C4⋊C4—21no—
401C4⋊C4—26no—
402C4⋊C4—26no—
403C4⋊C4C2×D4×C2913yes—
404C4⋊C4C2×D4×C2913yes—
405C4⋊C4C24×C2916yes—
406C4⋊C4C24×C2913yes—
407C4⋊C4C24×C2911yescharacteristic
408C22⋊C4—26no—
409C22⋊C4—26no—
410C22⋊C4—23no—
411C22⋊C4—21no—
412C22⋊C4—23no—
413C22⋊C4C2×D4×C2916yes—
414C42—23no—
415C42—23no—
416C42—23no—
417C42—26no—
418C42C2×D4×C2913yes—
419C42C2×D4×C2913yes—
420C42C24×C2913yes—
421C42C24×C2911yescharacteristic
422C23—21no—
423C23C22×D4×C2913yes—
424Q8—22no—
425Q8—23no—
426Q8—22no—
427Q8—23no—
428Q8—46no—
429Q8—46no—
430Q8—86no—
431Q8C29×#13714yes—
432D4—26no—
433D4—21no—
434D4—46no—
435D4C29×2−1+412yes—
436C2×C4—26no—
437C2×C4—26no—
438C2×C4—23no—
439C2×C4—23no—
440C2×C4—21no—
441C2×C4—22no—
442C2×C4—23no—
443C2×C4—23no—
444C2×C4—26no—
445C2×C4—46no—
446C2×C4—46no—
447C2×C4—42no—
448C2×C4—86no—
449C2×C4C22×D4×C2913yes—
450C2×C4C22×D4×C2911yescharacteristic
451C2×C4C22×D4×C2913yes—
452C2×C4C22×D4×C2913yes—
453C2×C4C22×D4×C2911yescharacteristic
454C2×C4C25×C2911yescharacteristic
455C8—22no—
456C8—26no—
457C22—23no—
458C22—22no—
459C22—23no—
460C22—23no—
461C22—41no—
462C22—41no—
463C22C23×D4×C2911yescharacteristic
464C4—23no—
465C4—21no—
466C4—23no—
467C4—43no—
468C4—42no—
469C4—43no—
470C4—41no—
471C4—46no—
472C4C2×C29×#13716yes—
473C4C29×#57712yes—
474C4C2×C29×2−1+411yescharacteristic
475C4C29×#58511yescharacteristic
476C2—43no—
477C2—42no—
478C2C29×#348911yescharacteristic
479C2C22×C29×#13711yescharacteristic
480C2C2×C29×#57711yescharacteristic
subgroupG/H
center, socleC22×C29C23×D4
commutator, Frattini, cosocleC2×C4C25×C29
prime radicalC29×#3482C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C4×#41×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#3503C2semidirect
3. Q8×SD16×C29C2semidirect
4. C29×#3363C2semidirect
5. C29×#3356C2semidirect
6. C29×#3331C2semidirect
7. C29×#3255C2semidirect
8. C29×#3229C2semidirect
9. C29×#3107C2semidirect
10. C29×#3079C2semidirect
11. C29×#2991C2semidirect
181. #62147C29direct (N × H)
217. #3503C2×C29semidirect
219. Q8×SD16C2×C29semidirect
220. #3363C2×C29semidirect
221. #3356C2×C29semidirect
222. #3331C2×C29semidirect
223. #3255C2×C29semidirect
224. #3229C2×C29semidirect
225. #3107C2×C29semidirect
226. #3079C2×C29semidirect
227. #2991C2×C29semidirect
363. C29#62147direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35032
C29×#34822
Q8×SD16×C292
C29×#33632
C29×#33562
C29×#33312
C29×#32552
C29×#32292
C29×#31072
C29×#30792
C29×#29912
#6214729