Finite Group Databasebeta

← C29×#19176 #20314076

Subgroups — C29×#19176 #20314076

Order 7424.

618 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3141C211yesmaximal, characteristic
2C29×#3103C211yesmaximal, characteristic
3C2×C29×#477C211yesmaximal, characteristic, complemented
4Q8×M16×C29C211yesmaximal, characteristic, complemented
5C29×#1704C212yesmaximal, complemented
6C29×#1698C212yesmaximal, complemented
7C29×#1684C212yesmaximal, complemented
8C29×#1678C212yesmaximal, complemented
9C29×#1565C211yesmaximal, characteristic, complemented
10C29×#1548C211yesmaximal, characteristic, complemented
11C29×#1547C211yesmaximal, characteristic
12C29×#532C2211yescharacteristic
13C2×C29×C4⋊Q8C2211yescharacteristic
14C2×C4×Q8×C29C2211yescharacteristic
15C29×#489—22no—
16C29×#487C2212yes—
17C29×#486C2212yes—
18C29×#481—21no—
19C29×#477—21no—
20C29×#477—21no—
21C29×#477C2212yes—
22C29×#477C2212yes—
23C29×#475C2211yescharacteristic
24C29×#475C2211yescharacteristic
25C29×#460C2211yescharacteristic
26C29×#460C2211yescharacteristic
27C29×#448—21no—
28C29×#446—22no—
29C29×#446C2212yes—
30C8×Q8×C29C2212yes—
31C4×SD16×C29—21no—
32C4×SD16×C29—21no—
33C29×#431C2211yescharacteristic
34C2×C29×#107—21no—
35C29×#423—21no—
36C29×#423C2211yescharacteristic
37C2×C29×C4⋊C8C2211yescharacteristic
38C29×#417—21no—
39C29×#417—21no—
40C2×C29×#103—21no—
41C4×M16×C29—21no—
42C4×M16×C29C2211yescharacteristic
43C29×#335C2212yes—
44C29×#334C2212yes—
45C29×#333C2212yes—
46C29×#333C2212yes—
47C29×#332C2212yes—
48C29×#331C2212yes—
49C2×#41×C29—21no—
50C22×Q8×C29—21no—
51C22×Q8×C29D411yescharacteristic
52C2×SD16×C29—21no—
53C2×SD16×C29—21no—
54C2×M16×C29—21no—
55C2×M16×C29D411yescharacteristic
56C2×M16×C29D411yescharacteristic
57C22×C8×C29—21no—
58C29×C4⋊Q8—21no—
59C29×C4⋊Q8—21no—
60C29×C4⋊Q8—21no—
61C29×C4⋊Q8C2311yescharacteristic
62C29×C4⋊Q8C2312yes—
63C29×#127C2311yescharacteristic
64C29×#124—21no—
65C29×#121—21no—
66C29×#121—21no—
67C4×Q8×C29—21no—
68C4×Q8×C29—21no—
69C4×Q8×C29D411yescharacteristic
70C4×Q8×C29D411yescharacteristic
71C4×Q8×C29C2311yescharacteristic
72C4×Q8×C29C2311yescharacteristic
73C4×D4×C29—21no—
74C4×D4×C29—21no—
75C2×C4⋊C4×C29—21no—
76C2×C4⋊C4×C29—21no—
77C2×C4⋊C4×C29—21no—
78C2×C4⋊C4×C29D411yescharacteristic
79C2×C42×C29—21no—
80C2×C42×C29C2311yescharacteristic
81C29×#107—22no—
82C29×#107—22no—
83C29×#106—21no—
84C29×#106—21no—
85C29×C4⋊C8—22no—
86C29×C4⋊C8—22no—
87C29×C4⋊C8—21no—
88C29×C4⋊C8—21no—
89C29×C4⋊C8C2311yescharacteristic
90C29×C4⋊C8C2311yescharacteristic
91C29×C4⋊C8C2312yes—
92C29×C4⋊C8C2312yes—
93C29×#103—21no—
94C29×#103—21no—
95C29×#103—22no—
96C29×#103—22no—
97C29×#103—22no—
98C29×#103—22no—
99C29×#102—22no—
100C29×#102—22no—
101C29×#102—21no—
102C29×#102—21no—
103C29×C22⋊C8—21no—
104C29×#97—22no—
105C29×#97D412yes—
106C4×C8×C29—22no—
107C4×C8×C29—21no—
108C4×C8×C29C2312yes—
109#41×C29—42no—
110#41×C29—42no—
111C2×Q8×C29—21no—
112C2×Q8×C29—22no—
113C2×Q8×C29—21no—
114C2×Q8×C29—22no—
115C2×Q8×C29—41no—
116C2×Q8×C29—41no—
117C2×Q8×C29—82no—
118C2×Q8×C29C2×D411yescharacteristic
119C2×Q8×C29C2×D411yescharacteristic
120C2×D4×C29—21no—
121C2×D4×C29—21no—
122C2×D4×C29—21no—
123C2×D4×C29—41no—
124C22×C4×C29—21no—
125C22×C4×C29—21no—
126C22×C4×C29—41no—
127C22×C4×C29—41no—
128C22×C4×C29C2×D411yescharacteristic
129C22×C4×C29C2×D411yescharacteristic
130C22×C4×C29#4111yescharacteristic
131SD16×C29—42no—
132SD16×C29—42no—
133M16×C29—22no—
134M16×C29—22no—
135M16×C29—42no—
136C2×C8×C29—22no—
137C2×C8×C29—22no—
138C2×C8×C29—21no—
139C2×C8×C29—21no—
140C2×C8×C29—42no—
141C2×C8×C29C2×D412yes—
142C2×C8×C29C2×D412yes—
143C4⋊C4×C29—21no—
144C4⋊C4×C29—21no—
145C4⋊C4×C29—21no—
146C4⋊C4×C29—21no—
147C4⋊C4×C29—21no—
148C4⋊C4×C29—22no—
149C4⋊C4×C29—22no—
150C4⋊C4×C29—21no—
151C4⋊C4×C29—21no—
152C4⋊C4×C29—41no—
153C4⋊C4×C29—41no—
154C4⋊C4×C29C2×D411yescharacteristic
155C4⋊C4×C29C2×D411yescharacteristic
156C22⋊C4×C29—41no—
157C22⋊C4×C29—41no—
158C42×C29—21no—
159C42×C29—21no—
160C42×C29—21no—
161C42×C29—21no—
162C42×C29C2×D411yescharacteristic
163C42×C29C2×D411yescharacteristic
164C42×C29#4111yescharacteristic
165C42×C29C2411yescharacteristic
166#19176C2911yesmaximal, characteristic, direct product factor, Sylow
167C23×C29—41no—
168C23×C29#12111yescharacteristic
169Q8×C29—21no—
170Q8×C29—21no—
171Q8×C29—21no—
172Q8×C29—42no—
173Q8×C29—41no—
174Q8×C29—41no—
175Q8×C29—82no—
176Q8×C29—82no—
177Q8×C29#13712yes—
178D4×C29—41no—
179D4×C29—41no—
180D4×C29—41no—
181D4×C29—41no—
182D4×C29—81no—
183D4×C29—82no—
184C2×C4×C29—21no—
185C2×C4×C29—21no—
186C2×C4×C29—21no—
187C2×C4×C29—21no—
188C2×C4×C29—21no—
189C2×C4×C29—21no—
190C2×C4×C29—41no—
191C2×C4×C29—42no—
192C2×C4×C29—41no—
193C2×C4×C29—42no—
194C2×C4×C29—81no—
195C2×C4×C29—82no—
196C2×C4×C29—82no—
197C2×C4×C29#12111yescharacteristic
198C2×C4×C29#12111yescharacteristic
199C2×C4×C29#12111yescharacteristic
200C2×C4×C29#13512yes—
201C2×C4×C29#13712yes—
202C2×C4×C29C22×D411yescharacteristic
203C2×C4×C29C22×D411yescharacteristic
204C2×C4×C29C2×#4111yescharacteristic
205C8×C29—22no—
206C8×C29—22no—
207C8×C29—42no—
208C8×C29—41no—
209C8×C29—42no—
210C8×C29—41no—
211#3141C2×C2911yescharacteristic
212#3103C2×C2911yescharacteristic
213C2×#477C2×C2911yescharacteristic, complemented
214Q8×M16C2×C2911yescharacteristic, complemented
215#1704C2×C2912yescomplemented
216#1698C2×C2912yescomplemented
217#1684C2×C2912yescomplemented
218#1678C2×C2912yescomplemented
219#1565C2×C2911yescharacteristic, complemented
220#1548C2×C2911yescharacteristic, complemented
221#1547C2×C2911yescharacteristic
222C22×C29—21no—
223C22×C29—21no—
224C22×C29—81no—
225C22×C29—81no—
226C22×C29—81no—
227C22×C29#46412yes—
228C22×C29C2×#12111yescharacteristic
229C4×C29—21no—
230C4×C29—22no—
231C4×C29—21no—
232C4×C29—21no—
233C4×C29—41no—
234C4×C29—41no—
235C4×C29—41no—
236C4×C29—81no—
237C4×C29—82no—
238C4×C29#46412yes—
239C4×C29C2×#13511yescharacteristic
240C4×C29C2×#13711yescharacteristic
241C4×C29C2×#13711yescharacteristic
242C4×C29#57511yescharacteristic
243#532C22×C2911yescharacteristic
244C2×C4⋊Q8C22×C2911yescharacteristic
245C2×C4×Q8C22×C2911yescharacteristic
246#489—22no—
247#487C22×C2912yes—
248#486C22×C2912yes—
249#481—21no—
250#477—21no—
251#477—21no—
252#477C22×C2912yes—
253#477C22×C2912yes—
254#475C22×C2911yescharacteristic
255#475C22×C2911yescharacteristic
256#460C22×C2911yescharacteristic
257#460C22×C2911yescharacteristic
258#448—21no—
259#446—22no—
260#446C22×C2912yes—
261C8×Q8C22×C2912yes—
262C4×SD16—21no—
263C4×SD16—21no—
264#431C22×C2911yescharacteristic
265C2×#107—21no—
266#423—21no—
267#423C22×C2911yescharacteristic
268C2×C4⋊C8C22×C2911yescharacteristic
269#417—21no—
270#417—21no—
271C2×#103—21no—
272C4×M16—21no—
273C4×M16C22×C2911yescharacteristic
274#335C22×C2912yes—
275#334C22×C2912yes—
276#333C22×C2912yes—
277#333C22×C2912yes—
278#332C22×C2912yes—
279#331C22×C2912yes—
280C2×C29—22no—
281C2×C29—161no—
282C2×C29C2×#46411yescharacteristic
283C2×C29#305611yescharacteristic
284C2×C29#306811yescharacteristic
285C2×#41—21no—
286C22×Q8—21no—
287C22×Q8D4×C2911yescharacteristic
288C2×SD16—21no—
289C2×SD16—21no—
290C2×M16—21no—
291C2×M16D4×C2911yescharacteristic
292C2×M16D4×C2911yescharacteristic
293C22×C8—21no—
294C4⋊Q8—21no—
295C4⋊Q8—21no—
296C4⋊Q8—21no—
297C4⋊Q8C23×C2912yes—
298C4⋊Q8C23×C2911yescharacteristic
299#127C23×C2911yescharacteristic
300#124—21no—
301#121—21no—
302#121—21no—
303C4×Q8—21no—
304C4×Q8—21no—
305C4×Q8D4×C2911yescharacteristic
306C4×Q8D4×C2911yescharacteristic
307C4×Q8C23×C2911yescharacteristic
308C4×Q8C23×C2911yescharacteristic
309C4×D4—21no—
310C4×D4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4D4×C2911yescharacteristic
315C2×C42—21no—
316C2×C42C23×C2911yescharacteristic
317#107—22no—
318#107—22no—
319#106—21no—
320#106—21no—
321C4⋊C8—22no—
322C4⋊C8—22no—
323C4⋊C8—21no—
324C4⋊C8—21no—
325C4⋊C8C23×C2912yes—
326C4⋊C8C23×C2912yes—
327C4⋊C8C23×C2911yescharacteristic
328C4⋊C8C23×C2911yescharacteristic
329#103—22no—
330#103—22no—
331#103—21no—
332#103—21no—
333#103—22no—
334#103—22no—
335#102—22no—
336#102—22no—
337#102—21no—
338#102—21no—
339C22⋊C8—21no—
340#97—22no—
341#97D4×C2912yes—
342C4×C8—22no—
343C4×C8—21no—
344C4×C8C23×C2912yes—
345C29#1917611yescharacteristic, direct product factor, Sylow
346#41—42no—
347#41—42no—
348C2×Q8—21no—
349C2×Q8—22no—
350C2×Q8—21no—
351C2×Q8—22no—
352C2×Q8—41no—
353C2×Q8—41no—
354C2×Q8—82no—
355C2×Q8C2×D4×C2911yescharacteristic
356C2×Q8C2×D4×C2911yescharacteristic
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4—41no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—41no—
364C22×C4—41no—
365C22×C4C2×D4×C2911yescharacteristic
366C22×C4C2×D4×C2911yescharacteristic
367C22×C4#41×C2911yescharacteristic
368SD16—42no—
369SD16—42no—
370M16—22no—
371M16—22no—
372M16—42no—
373C2×C8—22no—
374C2×C8—21no—
375C2×C8—21no—
376C2×C8—22no—
377C2×C8—42no—
378C2×C8C2×D4×C2912yes—
379C2×C8C2×D4×C2912yes—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—22no—
386C4⋊C4—21no—
387C4⋊C4—22no—
388C4⋊C4—21no—
389C4⋊C4—41no—
390C4⋊C4—41no—
391C4⋊C4C2×D4×C2911yescharacteristic
392C4⋊C4C2×D4×C2911yescharacteristic
393C22⋊C4—41no—
394C22⋊C4—41no—
395C42—21no—
396C42—21no—
397C42—21no—
398C42—21no—
399C42C2×D4×C2911yescharacteristic
400C42C2×D4×C2911yescharacteristic
401C42#41×C2911yescharacteristic
402C42C24×C2911yescharacteristic
403C23—41no—
404C23C29×#12111yescharacteristic
405Q8—21no—
406Q8—21no—
407Q8—21no—
408Q8—42no—
409Q8—41no—
410Q8—41no—
411Q8—82no—
412Q8—82no—
413Q8C29×#13712yes—
414D4—41no—
415D4—41no—
416D4—41no—
417D4—41no—
418D4—81no—
419D4—82no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—41no—
429C2×C4—42no—
430C2×C4—81no—
431C2×C4—82no—
432C2×C4—82no—
433C2×C4C29×#12111yescharacteristic
434C2×C4C29×#12111yescharacteristic
435C2×C4C29×#12111yescharacteristic
436C2×C4C29×#13512yes—
437C2×C4C29×#13712yes—
438C2×C4C22×D4×C2911yescharacteristic
439C2×C4C22×D4×C2911yescharacteristic
440C2×C4C2×#41×C2911yescharacteristic
441C8—22no—
442C8—22no—
443C8—42no—
444C8—41no—
445C8—42no—
446C8—41no—
447C22—21no—
448C22—21no—
449C22—81no—
450C22—81no—
451C22—81no—
452C22C29×#46412yes—
453C22C2×C29×#12111yescharacteristic
454C4—21no—
455C4—22no—
456C4—21no—
457C4—21no—
458C4—41no—
459C4—41no—
460C4—41no—
461C4—81no—
462C4—82no—
463C4C29×#46412yes—
464C4C2×C29×#13511yescharacteristic
465C4C2×C29×#13711yescharacteristic
466C4C2×C29×#13711yescharacteristic
467C4C29×#57511yescharacteristic
468C2—22no—
469C2—161no—
470C2C2×C29×#46411yescharacteristic
471C2C29×#305611yescharacteristic
472C2C29×#306811yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#532C22
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
3. C2×C29×#477C2semidirect
4. Q8×M16×C29C2semidirect
5. C29×#1704C2semidirect
6. C29×#1698C2semidirect
7. C29×#1684C2semidirect
8. C29×#1678C2semidirect
9. C29×#1565C2semidirect
10. C29×#1548C2semidirect
166. #19176C29direct (N × H)
213. C2×#477C2×C29semidirect
214. Q8×M16C2×C29semidirect
215. #1704C2×C29semidirect
216. #1698C2×C29semidirect
217. #1684C2×C29semidirect
218. #1678C2×C29semidirect
219. #1565C2×C29semidirect
220. #1548C2×C29semidirect
345. C29#19176direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#31412
C29×#31032
C2×C29×#4772
Q8×M16×C292
C29×#17042
C29×#16982
C29×#16842
C29×#16782
C29×#15652
C29×#15482
C29×#15472
#1917629