Finite Group Databasebeta

← C29×#8501 #20303401

Subgroups — C29×#8501 #20303401

Order 7424.

616 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3555C211yesmaximal, characteristic
2C29×#1554C211yesmaximal, characteristic, complemented
3C29×#1535C211yesmaximal, characteristic
4C29×#1521C211yesmaximal, characteristic
5C29×#1515C211yesmaximal, characteristic, complemented
6C29×#1515C211yesmaximal, characteristic, complemented
7C29×#1497C211yesmaximal, characteristic, complemented
8C29×#563—22no—
9Q82×C29C411yescharacteristic, complemented
10C29×#557—21no—
11C29×#557C411yescharacteristic, complemented
12C29×#556—21no—
13C29×#556—21no—
14C29×#556C411yescharacteristic, complemented
15C29×#554C411yescharacteristic, complemented
16C29×#552—21no—
17C29×#544—21no—
18C29×#542—21no—
19C29×#541—21no—
20C29×#541—21no—
21C29×#541—22no—
22C29×#533C2211yescharacteristic
23C29×#533C2211yescharacteristic
24C29×#529C2211yescharacteristic
25C29×#432C2211yescharacteristic
26C29×#432C2211yescharacteristic
27C29×#431C2211yescharacteristic
28C29×#383C2211yescharacteristic
29C29×#333—21no—
30C29×#332—21no—
31C29×#330—21no—
32C29×#329—21no—
33C29×#328—21no—
34C29×#328—21no—
35C29×#328—22no—
36C29×#328—21no—
37C29×#327—21no—
38C29×Q8⋊C8—22no—
39C29×C4⋊Q8—22no—
40C29×C4⋊Q8—21no—
41C29×C4⋊Q8—22no—
42C29×C4⋊Q8—21no—
43C29×C4⋊Q8—21no—
44C29×C4⋊Q8C2×C411yescharacteristic
45C29×C4⋊Q8C2×C411yescharacteristic
46C29×C4⋊Q8D411yescharacteristic
47C29×C4⋊Q8D411yescharacteristic
48C29×#126—22no—
49C29×#126—22no—
50C29×#126—22no—
51C29×#126—22no—
52C29×#126—22no—
53C29×#126—22no—
54C29×#126—21no—
55C29×#125—22no—
56C29×#125—22no—
57C29×#125—22no—
58C29×#125—22no—
59C29×#125—21no—
60C29×#125—22no—
61C29×#125—21no—
62C29×#125—21no—
63C29×#125—21no—
64C29×#125D411yescharacteristic
65C29×#124—22no—
66C29×#124—21no—
67C29×#124D411yescharacteristic
68C29×#123—22no—
69C29×#123—21no—
70C29×C22⋊Q8—22no—
71C29×C22⋊Q8—22no—
72C29×C22⋊Q8—21no—
73C29×C22⋊Q8—21no—
74C29×C22⋊Q8—22no—
75C29×C22⋊Q8—21no—
76C29×C22⋊Q8—21no—
77C29×C22⋊Q8D411yescharacteristic
78C29×C22⋊Q8D411yescharacteristic
79C29×C22⋊Q8D411yescharacteristic
80C29×C22⋊Q8D412yes—
81C29×#121D411yescharacteristic
82C4×Q8×C29—22no—
83C4×Q8×C29—21no—
84C4×Q8×C29—21no—
85C4×Q8×C29—21no—
86C4×Q8×C29—21no—
87C4×Q8×C29—21no—
88C4×Q8×C29—21no—
89C4×Q8×C29—21no—
90C4×Q8×C29C2×C411yescharacteristic
91C4×Q8×C29C2×C411yescharacteristic
92C4×Q8×C29C2×C411yescharacteristic
93C4×Q8×C29D412yes—
94C4×D4×C29—21no—
95C4×D4×C29—21no—
96C4×D4×C29C2×C411yescharacteristic
97C29×#117—22no—
98C29×#117—21no—
99C29×#117—21no—
100C29×#117—21no—
101C29×#117—21no—
102C2×C4⋊C4×C29—21no—
103C2×C42×C29C2311yescharacteristic
104C29×C4⋊C8—21no—
105C29×C4⋊C8—21no—
106C29×C4⋊C8—21no—
107C29×C22⋊C8—21no—
108C29×C22⋊C8—21no—
109C29×C22⋊C8—21no—
110C29×#97—21no—
111C29×#97—21no—
112C4×C8×C29—21no—
113C29×#95—21no—
114C29×#95—21no—
115C29×#95—21no—
116C2×Q8×C29—22no—
117C2×Q8×C29—21no—
118C2×Q8×C29—21no—
119C2×Q8×C29C22⋊C411yescharacteristic
120C2×Q8×C29C22⋊C411yescharacteristic
121C2×Q8×C29C22⋊C411yescharacteristic
122C2×Q8×C29C22⋊C412yes—
123C2×D4×C29—21no—
124C2×D4×C29C22⋊C411yescharacteristic
125C22×C4×C29—22no—
126C22×C4×C29—21no—
127C22×C4×C29—41no—
128C22×C4×C29C2×D411yescharacteristic
129C22×C4×C29C2×D411yescharacteristic
130C22×C4×C29C2×D411yescharacteristic
131C2×C8×C29—41no—
132C2×C8×C29—41no—
133C2×C8×C29—41no—
134C4⋊C4×C29—22no—
135C4⋊C4×C29—22no—
136C4⋊C4×C29—22no—
137C4⋊C4×C29—22no—
138C4⋊C4×C29—22no—
139C4⋊C4×C29—22no—
140C4⋊C4×C29—22no—
141C4⋊C4×C29—22no—
142C4⋊C4×C29—21no—
143C4⋊C4×C29—21no—
144C4⋊C4×C29—21no—
145C4⋊C4×C29—21no—
146C4⋊C4×C29—21no—
147C4⋊C4×C29—21no—
148C4⋊C4×C29—21no—
149C4⋊C4×C29—21no—
150C4⋊C4×C29—21no—
151C4⋊C4×C29—21no—
152C4⋊C4×C29—21no—
153C4⋊C4×C29—21no—
154C4⋊C4×C29—21no—
155C4⋊C4×C29—22no—
156C4⋊C4×C29—21no—
157C4⋊C4×C29—22no—
158C4⋊C4×C29C22⋊C411yescharacteristic
159C4⋊C4×C29C22⋊C411yescharacteristic
160C4⋊C4×C29C22⋊C411yescharacteristic
161C4⋊C4×C29C22⋊C411yescharacteristic
162C4⋊C4×C29C22⋊C412yes—
163C22⋊C4×C29—22no—
164C22⋊C4×C29—22no—
165C22⋊C4×C29—22no—
166C22⋊C4×C29—21no—
167C22⋊C4×C29—22no—
168C22⋊C4×C29—21no—
169C22⋊C4×C29—21no—
170C22⋊C4×C29—21no—
171C22⋊C4×C29—21no—
172C22⋊C4×C29—21no—
173C22⋊C4×C29—21no—
174C42×C29—22no—
175C42×C29—22no—
176C42×C29—22no—
177C42×C29—21no—
178C42×C29—21no—
179C42×C29—21no—
180C42×C29—22no—
181C42×C29C22×C411yescharacteristic
182C42×C29C2×D411yescharacteristic
183C42×C29C2×D411yescharacteristic
184C42×C29C2×D411yescharacteristic
185#8501C2911yesmaximal, characteristic, direct product factor, Sylow
186C23×C29—21no—
187C23×C29#12011yescharacteristic
188Q8×C29—42no—
189Q8×C29—41no—
190Q8×C29—41no—
191Q8×C29—41no—
192Q8×C29—42no—
193Q8×C29—81no—
194Q8×C29—82no—
195D4×C29—41no—
196D4×C29—81no—
197C2×C4×C29—21no—
198C2×C4×C29—21no—
199C2×C4×C29—21no—
200C2×C4×C29—22no—
201C2×C4×C29—21no—
202C2×C4×C29—21no—
203C2×C4×C29—21no—
204C2×C4×C29—22no—
205C2×C4×C29—21no—
206C2×C4×C29—41no—
207C2×C4×C29—41no—
208C2×C4×C29—41no—
209C2×C4×C29—42no—
210C2×C4×C29—82no—
211C2×C4×C29—81no—
212C2×C4×C29—81no—
213C2×C4×C29—81no—
214C2×C4×C29C2×C22⋊C411yescharacteristic
215C2×C4×C29C2×C22⋊C411yescharacteristic
216C2×C4×C29C2×C22⋊C411yescharacteristic
217C2×C4×C29#12011yescharacteristic
218C2×C4×C29#12011yescharacteristic
219C2×C4×C29#12011yescharacteristic
220C8×C29—81no—
221C8×C29—81no—
222C8×C29—81no—
223#3555C2×C2911yescharacteristic
224#1554C2×C2911yescharacteristic, complemented
225#1535C2×C2911yescharacteristic
226#1521C2×C2911yescharacteristic
227#1515C2×C2911yescharacteristic, complemented
228#1515C2×C2911yescharacteristic, complemented
229#1497C2×C2911yescharacteristic, complemented
230C22×C29—21no—
231C22×C29—21no—
232C22×C29—21no—
233C22×C29—41no—
234C22×C29—41no—
235C22×C29—41no—
236C22×C29#37911yescharacteristic
237C4×C29—21no—
238C4×C29—21no—
239C4×C29—21no—
240C4×C29—21no—
241C4×C29—21no—
242C4×C29—21no—
243C4×C29—41no—
244C4×C29—42no—
245C4×C29—41no—
246C4×C29—41no—
247C4×C29—41no—
248C4×C29—41no—
249C4×C29—41no—
250C4×C29—41no—
251C4×C29—42no—
252C4×C29—161no—
253#563—22no—
254Q82C4×C2911yescharacteristic, complemented
255#557—21no—
256#557C4×C2911yescharacteristic, complemented
257#556—21no—
258#556—21no—
259#556C4×C2911yescharacteristic, complemented
260#554C4×C2911yescharacteristic, complemented
261#552—21no—
262#544—21no—
263#542—21no—
264#541—21no—
265#541—21no—
266#541—22no—
267#533C22×C2911yescharacteristic
268#533C22×C2911yescharacteristic
269#529C22×C2911yescharacteristic
270#432C22×C2911yescharacteristic
271#432C22×C2911yescharacteristic
272#431C22×C2911yescharacteristic
273#383C22×C2911yescharacteristic
274#333—21no—
275#332—21no—
276#330—21no—
277#329—21no—
278#328—21no—
279#328—21no—
280#328—22no—
281#328—21no—
282#327—21no—
283Q8⋊C8—22no—
284C2×C29—41no—
285C2×C29—81no—
286C2×C29#179411yescharacteristic
287C2×C29#179611yescharacteristic
288C2×C29#179611yescharacteristic
289C4⋊Q8—22no—
290C4⋊Q8—21no—
291C4⋊Q8—22no—
292C4⋊Q8—21no—
293C4⋊Q8—21no—
294C4⋊Q8C2×C4×C2911yescharacteristic
295C4⋊Q8C2×C4×C2911yescharacteristic
296C4⋊Q8D4×C2911yescharacteristic
297C4⋊Q8D4×C2911yescharacteristic
298#126—22no—
299#126—22no—
300#126—22no—
301#126—22no—
302#126—22no—
303#126—22no—
304#126—21no—
305#125—22no—
306#125—22no—
307#125—22no—
308#125—22no—
309#125—21no—
310#125—22no—
311#125—21no—
312#125—21no—
313#125—21no—
314#125D4×C2911yescharacteristic
315#124—22no—
316#124—21no—
317#124D4×C2911yescharacteristic
318#123—22no—
319#123—21no—
320C22⋊Q8—22no—
321C22⋊Q8—22no—
322C22⋊Q8—21no—
323C22⋊Q8—21no—
324C22⋊Q8—22no—
325C22⋊Q8—21no—
326C22⋊Q8—21no—
327C22⋊Q8D4×C2911yescharacteristic
328C22⋊Q8D4×C2911yescharacteristic
329C22⋊Q8D4×C2911yescharacteristic
330C22⋊Q8D4×C2912yes—
331#121D4×C2911yescharacteristic
332C4×Q8—22no—
333C4×Q8—21no—
334C4×Q8—21no—
335C4×Q8—21no—
336C4×Q8—21no—
337C4×Q8—21no—
338C4×Q8—21no—
339C4×Q8—21no—
340C4×Q8C2×C4×C2911yescharacteristic
341C4×Q8C2×C4×C2911yescharacteristic
342C4×Q8C2×C4×C2911yescharacteristic
343C4×Q8D4×C2912yes—
344C4×D4—21no—
345C4×D4—21no—
346C4×D4C2×C4×C2911yescharacteristic
347#117—22no—
348#117—21no—
349#117—21no—
350#117—21no—
351#117—21no—
352C2×C4⋊C4—21no—
353C2×C42C23×C2911yescharacteristic
354C4⋊C8—21no—
355C4⋊C8—21no—
356C4⋊C8—21no—
357C22⋊C8—21no—
358C22⋊C8—21no—
359C22⋊C8—21no—
360#97—21no—
361#97—21no—
362C4×C8—21no—
363#95—21no—
364#95—21no—
365#95—21no—
366C29#850111yescharacteristic, direct product factor, Sylow
367C2×Q8—22no—
368C2×Q8—21no—
369C2×Q8—21no—
370C2×Q8C22⋊C4×C2911yescharacteristic
371C2×Q8C22⋊C4×C2911yescharacteristic
372C2×Q8C22⋊C4×C2911yescharacteristic
373C2×Q8C22⋊C4×C2912yes—
374C2×D4—21no—
375C2×D4C22⋊C4×C2911yescharacteristic
376C22×C4—22no—
377C22×C4—21no—
378C22×C4—41no—
379C22×C4C2×D4×C2911yescharacteristic
380C22×C4C2×D4×C2911yescharacteristic
381C22×C4C2×D4×C2911yescharacteristic
382C2×C8—41no—
383C2×C8—41no—
384C2×C8—41no—
385C4⋊C4—22no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—22no—
389C4⋊C4—22no—
390C4⋊C4—22no—
391C4⋊C4—22no—
392C4⋊C4—22no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—21no—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—22no—
407C4⋊C4—21no—
408C4⋊C4—22no—
409C4⋊C4C22⋊C4×C2911yescharacteristic
410C4⋊C4C22⋊C4×C2911yescharacteristic
411C4⋊C4C22⋊C4×C2911yescharacteristic
412C4⋊C4C22⋊C4×C2911yescharacteristic
413C4⋊C4C22⋊C4×C2912yes—
414C22⋊C4—22no—
415C22⋊C4—22no—
416C22⋊C4—22no—
417C22⋊C4—21no—
418C22⋊C4—22no—
419C22⋊C4—21no—
420C22⋊C4—21no—
421C22⋊C4—21no—
422C22⋊C4—21no—
423C22⋊C4—21no—
424C22⋊C4—21no—
425C42—22no—
426C42—22no—
427C42—22no—
428C42—21no—
429C42—21no—
430C42—21no—
431C42—22no—
432C42C22×C4×C2911yescharacteristic
433C42C2×D4×C2911yescharacteristic
434C42C2×D4×C2911yescharacteristic
435C42C2×D4×C2911yescharacteristic
436C23—21no—
437C23C29×#12011yescharacteristic
438Q8—42no—
439Q8—41no—
440Q8—41no—
441Q8—41no—
442Q8—42no—
443Q8—81no—
444Q8—82no—
445D4—41no—
446D4—81no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—22no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—22no—
455C2×C4—21no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—42no—
460C2×C4—82no—
461C2×C4—81no—
462C2×C4—81no—
463C2×C4—81no—
464C2×C4C2×C22⋊C4×C2911yescharacteristic
465C2×C4C2×C22⋊C4×C2911yescharacteristic
466C2×C4C2×C22⋊C4×C2911yescharacteristic
467C2×C4C29×#12011yescharacteristic
468C2×C4C29×#12011yescharacteristic
469C2×C4C29×#12011yescharacteristic
470C8—81no—
471C8—81no—
472C8—81no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—41no—
477C22—41no—
478C22—41no—
479C22C29×#37911yescharacteristic
480C4—21no—
481C4—21no—
482C4—21no—
483C4—21no—
484C4—21no—
485C4—21no—
486C4—41no—
487C4—42no—
488C4—41no—
489C4—41no—
490C4—41no—
491C4—42no—
492C4—41no—
493C4—41no—
494C4—41no—
495C4—161no—
496C2—41no—
497C2—81no—
498C2C29×#179411yescharacteristic
499C2C29×#179611yescharacteristic
500C2C29×#179611yescharacteristic
subgroupG/H
center, socleC22×C29#379
commutatorC42C22×C4×C29
Frattini, cosocleC2×C42C23×C29
prime radicalC29×#121D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#1554C2semidirect
5. C29×#1515C2semidirect
6. C29×#1515C2semidirect
7. C29×#1497C2semidirect
9. Q82×C29C4semidirect
11. C29×#557C4semidirect
14. C29×#556C4semidirect
15. C29×#554C4semidirect
185. #8501C29direct (N × H)
224. #1554C2×C29semidirect
227. #1515C2×C29semidirect
228. #1515C2×C29semidirect
229. #1497C2×C29semidirect
254. Q82C4×C29semidirect
256. #557C4×C29semidirect
259. #556C4×C29semidirect
260. #554C4×C29semidirect
366. C29#8501direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35552
C29×#15542
C29×#15352
C29×#15212
C29×#15152
C29×#14972
#850129