Finite Group Databasebeta

← C29×#10236 #20305136

Subgroups — C29×#10236 #20305136

Order 7424.

628 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#477C211yesmaximal, characteristic, complemented
2C2×C29×#476C211yesmaximal, characteristic
3C29×#2538C211yesmaximal, characteristic
4C29×#1956C211yesmaximal, characteristic, complemented
5C2×C29×Q8⋊C8C211yesmaximal, characteristic, complemented
6C2×C29×D4⋊C8C211yesmaximal, characteristic
7C29×#1296C211yesmaximal, characteristic, complemented
8C2×C29×C4⋊Q8C2211yescharacteristic
9C2×C29×C22⋊Q8—21no—
10C2×C4×Q8×C29C2211yescharacteristic
11C2×C4×D4×C29C2211yescharacteristic
12C29×#477—22no—
13C29×#477—22no—
14C29×#476—22no—
15C29×#476—22no—
16C2×C29×#107—21no—
17C2×C29×#106—21no—
18C2×C29×C4⋊C8C2211yescharacteristic
19C2×C29×C4⋊C8C2211yescharacteristic
20C2×C29×#103—21no—
21C2×C29×#103—22no—
22C2×C29×#102—21no—
23C2×C4×C8×C29C2211yescharacteristic
24C29×#396—22no—
25C29×#390—21no—
26C29×#389—21no—
27C29×#384C2211yescharacteristic
28C29×#380—21no—
29C29×Q8⋊C8—22no—
30C29×D4⋊C8—22no—
31C22×Q8×C29—21no—
32C22×Q8×C29D411yescharacteristic
33C22×D4×C29D411yescharacteristic
34C23×C4×C29—21no—
35C22×C8×C29—21no—
36C22×C8×C29—21no—
37C22×C8×C29—21no—
38C29×C4⋊Q8—21no—
39C29×C4⋊Q8—21no—
40C29×C4⋊Q8—21no—
41C29×C4⋊Q8D412yes—
42C29×C22⋊Q8—42no—
43C29×C22⋊Q8—42no—
44C4×Q8×C29—21no—
45C4×Q8×C29—21no—
46C4×Q8×C29—21no—
47C4×Q8×C29—21no—
48C4×D4×C29—21no—
49C4×D4×C29—21no—
50C4×D4×C29—21no—
51C4×D4×C29—21no—
52C2×C4⋊C4×C29—21no—
53C2×C4⋊C4×C29—21no—
54C2×C4⋊C4×C29—22no—
55C2×C4⋊C4×C29—21no—
56C2×C4⋊C4×C29—21no—
57C2×C4⋊C4×C29—21no—
58C2×C4⋊C4×C29D411yescharacteristic
59C2×C4⋊C4×C29D411yescharacteristic
60C2×C4⋊C4×C29D412yes—
61C2×C22⋊C4×C29—22no—
62C2×C22⋊C4×C29—21no—
63C2×C22⋊C4×C29—22no—
64C2×C42×C29—21no—
65C2×C42×C29C2311yescharacteristic
66C29×#107—24no—
67C29×#106—24no—
68C29×C4⋊C8—21no—
69C29×C4⋊C8—21no—
70C29×C4⋊C8D412yes—
71C29×C4⋊C8D412yes—
72C29×#103—24no—
73C29×#103—44no—
74C29×#102—24no—
75C4×C8×C29—21no—
76C4×C8×C29—21no—
77C29×#95—22no—
78C24×C29—21no—
79C2×Q8×C29—21no—
80C2×Q8×C29—21no—
81C2×Q8×C29—21no—
82C2×Q8×C29—22no—
83C2×Q8×C29—21no—
84C2×Q8×C29—21no—
85C2×Q8×C29—42no—
86C2×Q8×C29—42no—
87C2×Q8×C29—41no—
88C2×Q8×C29SD1612yes—
89C2×D4×C29—21no—
90C2×D4×C29—21no—
91C2×D4×C29—21no—
92C2×D4×C29—21no—
93C2×D4×C29—21no—
94C2×D4×C29Q1612yes—
95C22×C4×C29—21no—
96C22×C4×C29—21no—
97C22×C4×C29—22no—
98C22×C4×C29—21no—
99C22×C4×C29—41no—
100C22×C4×C29—41no—
101C22×C4×C29—41no—
102C22×C4×C29—41no—
103C22×C4×C29—41no—
104C22×C4×C29—41no—
105C22×C4×C29—41no—
106C22×C4×C29C2×D411yescharacteristic
107C22×C4×C29C2×D411yescharacteristic
108C22×C4×C29C2×D411yescharacteristic
109C2×C8×C29—22no—
110C2×C8×C29—22no—
111C2×C8×C29—22no—
112C2×C8×C29—41no—
113C2×C8×C29—41no—
114C2×C8×C29—41no—
115C2×C8×C29—41no—
116C2×C8×C29—41no—
117C2×C8×C29—41no—
118C4⋊C4×C29—22no—
119C4⋊C4×C29—22no—
120C4⋊C4×C29—21no—
121C4⋊C4×C29—21no—
122C4⋊C4×C29—21no—
123C4⋊C4×C29—21no—
124C4⋊C4×C29—42no—
125C4⋊C4×C29—44no—
126C4⋊C4×C29—41no—
127C4⋊C4×C29—41no—
128C4⋊C4×C29—41no—
129C4⋊C4×C29—41no—
130C4⋊C4×C29—41no—
131C4⋊C4×C29—41no—
132C4⋊C4×C29—41no—
133C4⋊C4×C29—41no—
134C22⋊C4×C29—44no—
135C22⋊C4×C29—41no—
136C22⋊C4×C29—41no—
137C22⋊C4×C29—82no—
138C42×C29—41no—
139C42×C29—41no—
140C42×C29C2×D411yescharacteristic
141C42×C29C2×D411yescharacteristic
142C42×C29C2×D411yescharacteristic
143C42×C29#4111yescharacteristic
144#10236C2911yesmaximal, characteristic, direct product factor, Sylow
145C23×C29—22no—
146C23×C29—41no—
147C23×C29—41no—
148C23×C29—41no—
149C23×C29—41no—
150C23×C29—41no—
151C23×C29—41no—
152C23×C29#12011yescharacteristic
153Q8×C29—22no—
154Q8×C29—22no—
155Q8×C29—44no—
156Q8×C29—41no—
157Q8×C29—41no—
158Q8×C29—82no—
159D4×C29—22no—
160D4×C29—22no—
161D4×C29—41no—
162D4×C29—41no—
163C2×C4×C29—21no—
164C2×C4×C29—21no—
165C2×C4×C29—22no—
166C2×C4×C29—41no—
167C2×C4×C29—41no—
168C2×C4×C29—41no—
169C2×C4×C29—41no—
170C2×C4×C29—42no—
171C2×C4×C29—42no—
172C2×C4×C29—41no—
173C2×C4×C29—42no—
174C2×C4×C29—41no—
175C2×C4×C29—41no—
176C2×C4×C29—42no—
177C2×C4×C29—41no—
178C2×C4×C29—81no—
179C2×C4×C29—81no—
180C2×C4×C29—81no—
181C2×C4×C29—81no—
182C2×C4×C29—81no—
183C2×C4×C29—81no—
184C2×C4×C29#12011yescharacteristic
185C2×C4×C29#12011yescharacteristic
186C2×C4×C29#12111yescharacteristic
187C2×C4×C29#12111yescharacteristic
188C2×C4×C29#12111yescharacteristic
189C2×C4×C29#12711yescharacteristic
190C2×C4×C29C2×SD1611yescharacteristic
191C2×C4×C29C2×Q1611yescharacteristic
192C2×C4×C29#13511yescharacteristic
193C2×C4×C29#13511yescharacteristic
194C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
195C2×C4×C29#13711yescharacteristic
196C2×C4×C29#13711yescharacteristic
197C2×C4×C29#13711yescharacteristic
198C8×C29—42no—
199C8×C29—42no—
200C8×C29—42no—
201C2×#477C2×C2911yescharacteristic, complemented
202C2×#476C2×C2911yescharacteristic
203#2538C2×C2911yescharacteristic
204#1956C2×C2911yescharacteristic, complemented
205C2×Q8⋊C8C2×C2911yescharacteristic, complemented
206C2×D4⋊C8C2×C2911yescharacteristic
207#1296C2×C2911yescharacteristic, complemented
208C22×C29—42no—
209C22×C29—42no—
210C22×C29—42no—
211C22×C29—81no—
212C22×C29—81no—
213C22×C29—81no—
214C22×C29—81no—
215C22×C29#39211yescharacteristic
216C22×C29#45011yescharacteristic
217C22×C29#45111yescharacteristic
218C22×C29#45211yescharacteristic
219C22×C29#45211yescharacteristic
220C22×C29#45311yescharacteristic
221C22×C29#45411yescharacteristic
222C4×C29—21no—
223C4×C29—21no—
224C4×C29—42no—
225C4×C29—82no—
226C4×C29—81no—
227C4×C29—81no—
228C4×C29—82no—
229C4×C29#44811yescharacteristic
230C4×C29#44911yescharacteristic
231C4×C29#45111yescharacteristic
232C4×C29#45211yescharacteristic
233C4×C29#46511yescharacteristic
234C4×C29#46711yescharacteristic
235C4×C29#46811yescharacteristic
236C4×C29#47011yescharacteristic
237C2×C4⋊Q8C22×C2911yescharacteristic
238C2×C22⋊Q8—21no—
239C2×C4×Q8C22×C2911yescharacteristic
240C2×C4×D4C22×C2911yescharacteristic
241#477—22no—
242#477—22no—
243#476—22no—
244#476—22no—
245C2×#107—21no—
246C2×#106—21no—
247C2×C4⋊C8C22×C2911yescharacteristic
248C2×C4⋊C8C22×C2911yescharacteristic
249C2×#103—21no—
250C2×#103—22no—
251C2×#102—21no—
252C2×C4×C8C22×C2911yescharacteristic
253#396—22no—
254#390—21no—
255#389—21no—
256#384C22×C2911yescharacteristic
257#380—21no—
258Q8⋊C8—22no—
259D4⋊C8—22no—
260C2×C29—82no—
261C2×C29#163111yescharacteristic
262C2×C29#163211yescharacteristic
263C2×C29#163711yescharacteristic
264C2×C29#163811yescharacteristic
265C2×C29#200011yescharacteristic
266C2×C29#200111yescharacteristic
267C2×C29#200611yescharacteristic
268C22×Q8—21no—
269C22×Q8D4×C2911yescharacteristic
270C22×D4D4×C2911yescharacteristic
271C23×C4—21no—
272C22×C8—21no—
273C22×C8—21no—
274C22×C8—21no—
275C4⋊Q8—21no—
276C4⋊Q8—21no—
277C4⋊Q8—21no—
278C4⋊Q8D4×C2912yes—
279C22⋊Q8—42no—
280C22⋊Q8—42no—
281C4×Q8—21no—
282C4×Q8—21no—
283C4×Q8—21no—
284C4×Q8—21no—
285C4×D4—21no—
286C4×D4—21no—
287C4×D4—21no—
288C4×D4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4D4×C2911yescharacteristic
296C2×C4⋊C4D4×C2911yescharacteristic
297C2×C4⋊C4D4×C2912yes—
298C2×C22⋊C4—22no—
299C2×C22⋊C4—21no—
300C2×C22⋊C4—22no—
301C2×C42—21no—
302C2×C42C23×C2911yescharacteristic
303#107—24no—
304#106—24no—
305C4⋊C8—21no—
306C4⋊C8—21no—
307C4⋊C8D4×C2912yes—
308C4⋊C8D4×C2912yes—
309#103—24no—
310#103—44no—
311#102—24no—
312C4×C8—21no—
313C4×C8—21no—
314#95—22no—
315C29#1023611yescharacteristic, direct product factor, Sylow
316C24—21no—
317C2×Q8—21no—
318C2×Q8—21no—
319C2×Q8—21no—
320C2×Q8—22no—
321C2×Q8—21no—
322C2×Q8—21no—
323C2×Q8—42no—
324C2×Q8—42no—
325C2×Q8—41no—
326C2×Q8SD16×C2912yes—
327C2×D4—21no—
328C2×D4—21no—
329C2×D4—21no—
330C2×D4—21no—
331C2×D4—21no—
332C2×D4Q16×C2912yes—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—22no—
337C22×C4—41no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4—41no—
344C22×C4C2×D4×C2911yescharacteristic
345C22×C4C2×D4×C2911yescharacteristic
346C22×C4C2×D4×C2911yescharacteristic
347C2×C8—22no—
348C2×C8—22no—
349C2×C8—22no—
350C2×C8—41no—
351C2×C8—41no—
352C2×C8—41no—
353C2×C8—41no—
354C2×C8—41no—
355C2×C8—41no—
356C4⋊C4—22no—
357C4⋊C4—22no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—42no—
363C4⋊C4—44no—
364C4⋊C4—41no—
365C4⋊C4—41no—
366C4⋊C4—41no—
367C4⋊C4—41no—
368C4⋊C4—41no—
369C4⋊C4—41no—
370C4⋊C4—41no—
371C4⋊C4—41no—
372C22⋊C4—44no—
373C22⋊C4—41no—
374C22⋊C4—41no—
375C22⋊C4—82no—
376C42—41no—
377C42—41no—
378C42C2×D4×C2911yescharacteristic
379C42C2×D4×C2911yescharacteristic
380C42C2×D4×C2911yescharacteristic
381C42#41×C2911yescharacteristic
382C23—22no—
383C23—41no—
384C23—41no—
385C23—41no—
386C23—41no—
387C23—41no—
388C23—41no—
389C23C29×#12011yescharacteristic
390Q8—22no—
391Q8—22no—
392Q8—44no—
393Q8—41no—
394Q8—41no—
395Q8—82no—
396D4—22no—
397D4—22no—
398D4—41no—
399D4—41no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—22no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—42no—
406C2×C4—41no—
407C2×C4—42no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—42no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—42no—
415C2×C4—81no—
416C2×C4—81no—
417C2×C4—81no—
418C2×C4—81no—
419C2×C4—81no—
420C2×C4—81no—
421C2×C4C29×#12011yescharacteristic
422C2×C4C29×#12011yescharacteristic
423C2×C4C29×#12111yescharacteristic
424C2×C4C29×#12111yescharacteristic
425C2×C4C29×#12111yescharacteristic
426C2×C4C29×#12711yescharacteristic
427C2×C4C2×SD16×C2911yescharacteristic
428C2×C4C2×Q16×C2911yescharacteristic
429C2×C4C29×#13511yescharacteristic
430C2×C4C29×#13511yescharacteristic
431C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
432C2×C4C29×#13711yescharacteristic
433C2×C4C29×#13711yescharacteristic
434C2×C4C29×#13711yescharacteristic
435C8—42no—
436C8—42no—
437C8—42no—
438C22—42no—
439C22—42no—
440C22—42no—
441C22—81no—
442C22—81no—
443C22—81no—
444C22—81no—
445C22C29×#39211yescharacteristic
446C22C29×#45011yescharacteristic
447C22C29×#45111yescharacteristic
448C22C29×#45211yescharacteristic
449C22C29×#45211yescharacteristic
450C22C29×#45311yescharacteristic
451C22C29×#45411yescharacteristic
452C4—21no—
453C4—21no—
454C4—42no—
455C4—81no—
456C4—81no—
457C4—82no—
458C4—82no—
459C4C29×#44811yescharacteristic
460C4C29×#44911yescharacteristic
461C4C29×#45111yescharacteristic
462C4C29×#45211yescharacteristic
463C4C29×#46511yescharacteristic
464C4C29×#46711yescharacteristic
465C4C29×#46811yescharacteristic
466C4C29×#47011yescharacteristic
467C2—82no—
468C2C29×#163111yescharacteristic
469C2C29×#163211yescharacteristic
470C2C29×#163711yescharacteristic
471C2C29×#163811yescharacteristic
472C2C29×#200011yescharacteristic
473C2C29×#200111yescharacteristic
474C2C29×#200611yescharacteristic
subgroupG/H
center, socleC23×C29#120
commutator, Frattini, cosocleC2×C42C23×C29
prime radicalC22×D4×C29D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C29×#477C2semidirect
4. C29×#1956C2semidirect
5. C2×C29×Q8⋊C8C2semidirect
7. C29×#1296C2semidirect
144. #10236C29direct (N × H)
201. C2×#477C2×C29semidirect
204. #1956C2×C29semidirect
205. C2×Q8⋊C8C2×C29semidirect
207. #1296C2×C29semidirect
315. C29#10236direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#4772
C2×C29×#4762
C29×#25382
C29×#19562
C2×C29×Q8⋊C82
C2×C29×D4⋊C82
C29×#12962
#1023629