Finite Group Databasebeta

← C29×#9917 #20304817

Subgroups — C29×#9917 #20304817

Order 7424.

872 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#448C211yesmaximal, characteristic
2C29×#2618C211yesmaximal, characteristic
3C2×C29×#395C211yesmaximal, characteristic, complemented
4C29×#1787C211yesmaximal, characteristic, complemented
5C2×C29×#327C211yesmaximal, characteristic
6C2×C29×#324C211yesmaximal, characteristic, complemented
7C29×#1294C211yesmaximal, characteristic, complemented
8C23×Q8×C29C2211yescharacteristic
9C22×SD16×C29—21no—
10C2×C29×#123—21no—
11C2×C29×#121C2211yescharacteristic
12C22×C4⋊C4×C29—21no—
13C22×C4⋊C4×C29C2211yescharacteristic
14C29×#448—22no—
15C29×#448—22no—
16C2×C29×#103—21no—
17C2×C29×#103—22no—
18C2×C29×C22⋊C8C2211yescharacteristic
19C2×C29×C22⋊C8C2211yescharacteristic
20C29×#398—21no—
21C29×#396—22no—
22C29×#395—22no—
23C29×#395—22no—
24C29×#394—21no—
25C29×#386—21no—
26C29×#380C2211yescharacteristic
27C2×C29×#95—21no—
28C2×C29×#95C2211yescharacteristic
29C29×#327—22no—
30C29×#324—22no—
31C22×Q8×C29—21no—
32C22×Q8×C29—21no—
33C22×Q8×C29—21no—
34C22×Q8×C29—21no—
35C22×Q8×C29—21no—
36C22×Q8×C29—44no—
37C22×Q8×C29D412yes—
38C22×D4×C29—21no—
39C22×D4×C29D411yescharacteristic
40C23×C4×C29—21no—
41C23×C4×C29—21no—
42C23×C4×C29D411yescharacteristic
43C23×C4×C29D411yescharacteristic
44C23×C4×C29C2311yescharacteristic
45C2×SD16×C29—24no—
46C2×SD16×C29—44no—
47C22×C8×C29—21no—
48C22×C8×C29—21no—
49C29×#123—42no—
50C29×#123—42no—
51C29×#121—21no—
52C29×#121—21no—
53C29×#121—21no—
54C29×#121—21no—
55C2×C4⋊C4×C29—24no—
56C2×C4⋊C4×C29—22no—
57C2×C4⋊C4×C29—21no—
58C2×C4⋊C4×C29—21no—
59C2×C4⋊C4×C29—21no—
60C2×C4⋊C4×C29—21no—
61C2×C4⋊C4×C29—21no—
62C2×C4⋊C4×C29—21no—
63C2×C4⋊C4×C29—44no—
64C2×C4⋊C4×C29D411yescharacteristic
65C2×C4⋊C4×C29D412yes—
66C2×C22⋊C4×C29—22no—
67C2×C22⋊C4×C29—21no—
68C2×C22⋊C4×C29—21no—
69C2×C22⋊C4×C29—22no—
70C29×#103—24no—
71C29×#103—44no—
72C29×C22⋊C8—21no—
73C29×C22⋊C8—21no—
74C29×C22⋊C8—21no—
75C29×C22⋊C8D412yes—
76C29×#95—24no—
77C29×#95—22no—
78C29×#95—21no—
79C29×#95—21no—
80C29×#95D412yes—
81C24×C29—21no—
82C24×C29C2×D411yescharacteristic
83C2×Q8×C29—24no—
84C2×Q8×C29—24no—
85C2×Q8×C29—22no—
86C2×Q8×C29—22no—
87C2×Q8×C29—44no—
88C2×Q8×C29—42no—
89C2×Q8×C29—42no—
90C2×Q8×C29—44no—
91C2×Q8×C29—44no—
92C2×Q8×C29—44no—
93C2×Q8×C29—41no—
94C2×Q8×C29—41no—
95C2×D4×C29—21no—
96C2×D4×C29—21no—
97C2×D4×C29—42no—
98C2×D4×C29—41no—
99C2×D4×C29—41no—
100C2×D4×C29—41no—
101C2×D4×C29—41no—
102C2×D4×C29—41no—
103C2×D4×C29—41no—
104C22×C4×C29—24no—
105C22×C4×C29—24no—
106C22×C4×C29—22no—
107C22×C4×C29—22no—
108C22×C4×C29—21no—
109C22×C4×C29—21no—
110C22×C4×C29—21no—
111C22×C4×C29—21no—
112C22×C4×C29—21no—
113C22×C4×C29—21no—
114C22×C4×C29—21no—
115C22×C4×C29—22no—
116C22×C4×C29—21no—
117C22×C4×C29—21no—
118C22×C4×C29—21no—
119C22×C4×C29—42no—
120C22×C4×C29—42no—
121C22×C4×C29—42no—
122C22×C4×C29—41no—
123C22×C4×C29—41no—
124C22×C4×C29—41no—
125C22×C4×C29—41no—
126C22×C4×C29—42no—
127C22×C4×C29SD1612yescomplemented
128C22×C4×C29C2×D411yescharacteristic
129C22×C4×C29C2×D411yescharacteristic
130C22×C4×C29C2×D411yescharacteristic
131C22×C4×C29C2×D411yescharacteristic
132C22×C4×C29C2×D411yescharacteristic
133C22×C4×C29#4111yescharacteristic
134SD16×C29—48no—
135C2×C8×C29—22no—
136C2×C8×C29—42no—
137C2×C8×C29—42no—
138C2×C8×C29—41no—
139C4⋊C4×C29—21no—
140C4⋊C4×C29—21no—
141C4⋊C4×C29—42no—
142C4⋊C4×C29—48no—
143C4⋊C4×C29—44no—
144C4⋊C4×C29—41no—
145C4⋊C4×C29—41no—
146C4⋊C4×C29—41no—
147C4⋊C4×C29—41no—
148C22⋊C4×C29—44no—
149C22⋊C4×C29—41no—
150C22⋊C4×C29—41no—
151C22⋊C4×C29—41no—
152C22⋊C4×C29—41no—
153C22⋊C4×C29—82no—
154#9917C2911yesmaximal, characteristic, direct product factor, Sylow
155C23×C29—22no—
156C23×C29—22no—
157C23×C29—41no—
158C23×C29—41no—
159C23×C29—41no—
160C23×C29—42no—
161C23×C29—42no—
162C23×C29#12011yescharacteristic
163C23×C29#12011yescharacteristic
164C23×C29#12111yescharacteristic
165C23×C29C2×SD1611yescharacteristic
166C23×C29#13511yescharacteristic
167C23×C29AGL(1,ℤ/8)11yescharacteristic
168C23×C29#13711yescharacteristic
169Q8×C29—24no—
170Q8×C29—24no—
171Q8×C29—42no—
172Q8×C29—44no—
173Q8×C29—44no—
174Q8×C29—42no—
175D4×C29—42no—
176D4×C29—81no—
177D4×C29—81no—
178D4×C29—81no—
179D4×C29—81no—
180D4×C29—81no—
181C2×C4×C29—22no—
182C2×C4×C29—22no—
183C2×C4×C29—24no—
184C2×C4×C29—24no—
185C2×C4×C29—22no—
186C2×C4×C29—22no—
187C2×C4×C29—22no—
188C2×C4×C29—41no—
189C2×C4×C29—41no—
190C2×C4×C29—41no—
191C2×C4×C29—41no—
192C2×C4×C29—42no—
193C2×C4×C29—44no—
194C2×C4×C29—44no—
195C2×C4×C29—42no—
196C2×C4×C29—44no—
197C2×C4×C29—41no—
198C2×C4×C29—42no—
199C2×C4×C29—41no—
200C2×C4×C29—42no—
201C2×C4×C29—41no—
202C2×C4×C29—44no—
203C2×C4×C29—41no—
204C2×C4×C29—42no—
205C2×C4×C29—41no—
206C2×C4×C29—41no—
207C2×C4×C29—42no—
208C2×C4×C29—41no—
209C2×C4×C29—41no—
210C2×C4×C29—42no—
211C2×C4×C29—42no—
212C2×C4×C29—42no—
213C2×C4×C29—81no—
214C2×C4×C29#12011yescharacteristic
215C2×C4×C29#12111yescharacteristic
216C2×C4×C29#12111yescharacteristic
217C2×C4×C29#12711yescharacteristic
218C8×C29—42no—
219C8×C29—81no—
220C2×#448C2×C2911yescharacteristic
221#2618C2×C2911yescharacteristic
222C2×#395C2×C2911yescharacteristic, complemented
223#1787C2×C2911yescharacteristic, complemented
224C2×#327C2×C2911yescharacteristic
225C2×#324C2×C2911yescharacteristic, complemented
226#1294C2×C2911yescharacteristic, complemented
227C22×C29—22no—
228C22×C29—22no—
229C22×C29—22no—
230C22×C29—22no—
231C22×C29—21no—
232C22×C29—21no—
233C22×C29—21no—
234C22×C29—21no—
235C22×C29—82no—
236C22×C29—82no—
237C22×C29—81no—
238C22×C29—81no—
239C22×C29—81no—
240C22×C29#39211yescharacteristic
241C22×C29#44811yescharacteristic
242C22×C29#44911yescharacteristic
243C22×C29#45011yescharacteristic
244C22×C29#45211yescharacteristic
245C22×C29#45612yes—
246C22×C29B(4,𝔽2)12yes—
247C22×C29#46511yescharacteristic
248C22×C29#46811yescharacteristic
249C4×C29—21no—
250C4×C29—21no—
251C4×C29—21no—
252C4×C29—21no—
253C4×C29—44no—
254C4×C29—42no—
255C4×C29—44no—
256C4×C29—82no—
257C4×C29—81no—
258C4×C29—81no—
259C23×Q8C22×C2911yescharacteristic
260C22×SD16—21no—
261C2×#123—21no—
262C2×#121C22×C2911yescharacteristic
263C22×C4⋊C4—21no—
264C22×C4⋊C4C22×C2911yescharacteristic
265#448—22no—
266#448—22no—
267C2×#103—21no—
268C2×#103—22no—
269C2×C22⋊C8C22×C2911yescharacteristic
270C2×C22⋊C8C22×C2911yescharacteristic
271#398—21no—
272#396—22no—
273#395—22no—
274#395—22no—
275#394—21no—
276#386—21no—
277#380C22×C2911yescharacteristic
278C2×#95—21no—
279C2×#95C22×C2911yescharacteristic
280#327—22no—
281#324—22no—
282C2×C29—21no—
283C2×C29—21no—
284C2×C29—21no—
285C2×C29—21no—
286C2×C29—161no—
287C2×C29#160312yes—
288C2×C29#160412yes—
289C2×C29#200011yescharacteristic
290C2×C29#200511yescharacteristic
291C2×C29#202111yescharacteristic
292C22×Q8—21no—
293C22×Q8—21no—
294C22×Q8—21no—
295C22×Q8—21no—
296C22×Q8—21no—
297C22×Q8—44no—
298C22×Q8D4×C2912yes—
299C22×D4—21no—
300C22×D4D4×C2911yescharacteristic
301C23×C4—21no—
302C23×C4—21no—
303C23×C4D4×C2911yescharacteristic
304C23×C4D4×C2911yescharacteristic
305C23×C4C23×C2911yescharacteristic
306C2×SD16—24no—
307C2×SD16—44no—
308C22×C8—21no—
309C22×C8—21no—
310#123—42no—
311#123—42no—
312#121—21no—
313#121—21no—
314#121—21no—
315#121—21no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—44no—
325C2×C4⋊C4D4×C2911yescharacteristic
326C2×C4⋊C4D4×C2912yes—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—22no—
331#103—24no—
332#103—44no—
333C22⋊C8—21no—
334C22⋊C8—21no—
335C22⋊C8—21no—
336C22⋊C8D4×C2912yes—
337#95—24no—
338#95—22no—
339#95—21no—
340#95—21no—
341#95D4×C2912yes—
342C29#991711yescharacteristic, direct product factor, Sylow
343C24—21no—
344C24C2×D4×C2911yescharacteristic
345C2×Q8—24no—
346C2×Q8—24no—
347C2×Q8—22no—
348C2×Q8—22no—
349C2×Q8—44no—
350C2×Q8—42no—
351C2×Q8—42no—
352C2×Q8—44no—
353C2×Q8—44no—
354C2×Q8—44no—
355C2×Q8—41no—
356C2×Q8—41no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—42no—
360C2×D4—41no—
361C2×D4—41no—
362C2×D4—41no—
363C2×D4—41no—
364C2×D4—41no—
365C2×D4—41no—
366C22×C4—24no—
367C22×C4—24no—
368C22×C4—21no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—42no—
382C22×C4—42no—
383C22×C4—42no—
384C22×C4—41no—
385C22×C4—41no—
386C22×C4—41no—
387C22×C4—41no—
388C22×C4—42no—
389C22×C4SD16×C2912yescomplemented
390C22×C4C2×D4×C2911yescharacteristic
391C22×C4C2×D4×C2911yescharacteristic
392C22×C4C2×D4×C2911yescharacteristic
393C22×C4C2×D4×C2911yescharacteristic
394C22×C4C2×D4×C2911yescharacteristic
395C22×C4#41×C2911yescharacteristic
396SD16—48no—
397C2×C8—22no—
398C2×C8—42no—
399C2×C8—42no—
400C2×C8—41no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—42no—
404C4⋊C4—48no—
405C4⋊C4—44no—
406C4⋊C4—41no—
407C4⋊C4—41no—
408C4⋊C4—41no—
409C4⋊C4—41no—
410C22⋊C4—44no—
411C22⋊C4—41no—
412C22⋊C4—41no—
413C22⋊C4—41no—
414C22⋊C4—41no—
415C22⋊C4—82no—
416C23—22no—
417C23—22no—
418C23—41no—
419C23—41no—
420C23—42no—
421C23—42no—
422C23—41no—
423C23C29×#12011yescharacteristic
424C23C29×#12011yescharacteristic
425C23C29×#12111yescharacteristic
426C23C2×SD16×C2911yescharacteristic
427C23C29×#13511yescharacteristic
428C23C29×AGL(1,ℤ/8)11yescharacteristic
429C23C29×#13711yescharacteristic
430Q8—24no—
431Q8—24no—
432Q8—42no—
433Q8—44no—
434Q8—44no—
435Q8—42no—
436D4—42no—
437D4—81no—
438D4—81no—
439D4—81no—
440D4—81no—
441D4—81no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—24no—
445C2×C4—24no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—44no—
456C2×C4—44no—
457C2×C4—44no—
458C2×C4—41no—
459C2×C4—42no—
460C2×C4—41no—
461C2×C4—44no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—81no—
475C2×C4C29×#12011yescharacteristic
476C2×C4C29×#12111yescharacteristic
477C2×C4C29×#12111yescharacteristic
478C2×C4C29×#12711yescharacteristic
479C8—42no—
480C8—81no—
481C22—21no—
482C22—21no—
483C22—21no—
484C22—21no—
485C22—22no—
486C22—22no—
487C22—22no—
488C22—22no—
489C22—81no—
490C22—81no—
491C22—81no—
492C22—82no—
493C22—82no—
494C22C29×#39211yescharacteristic
495C22C29×#44811yescharacteristic
496C22C29×#44911yescharacteristic
497C22C29×#45011yescharacteristic
498C22C29×#45211yescharacteristic
499C22C29×#45612yes—
500C22C29×B(4,𝔽2)12yes—
501C22C29×#46511yescharacteristic
502C22C29×#46811yescharacteristic
503C4—21no—
504C4—21no—
505C4—21no—
506C4—21no—
507C4—44no—
508C4—42no—
509C4—44no—
510C4—81no—
511C4—81no—
512C4—82no—
513C2—21no—
514C2—21no—
515C2—21no—
516C2—21no—
517C2—161no—
518C2C29×#160312yes—
519C2C29×#160412yes—
520C2C29×#200011yescharacteristic
521C2C29×#200511yescharacteristic
522C2C29×#202111yescharacteristic
subgroupG/H
center, socleC23×C29#120
commutator, Frattini, cosocleC23×C4C23×C29
prime radicalC2×C29×#121C22
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C29 ◁ C23×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C29×#395C2semidirect
4. C29×#1787C2semidirect
6. C2×C29×#324C2semidirect
7. C29×#1294C2semidirect
127. C22×C4×C29SD16semidirect
154. #9917C29direct (N × H)
222. C2×#395C2×C29semidirect
223. #1787C2×C29semidirect
225. C2×#324C2×C29semidirect
226. #1294C2×C29semidirect
342. C29#9917direct (N × H)
389. C22×C4SD16×C29semidirect

Maximal subgroups

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

subgroupindex
C2×C29×#4482
C29×#26182
C2×C29×#3952
C29×#17872
C2×C29×#3272
C2×C29×#3242
C29×#12942
#991729