Finite Group Databasebeta

← C29×#10402 #20305302

Subgroups — C29×#10402 #20305302

Order 7424.

760 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#2656C211yesmaximal, characteristic
2C29×#1874C212yesmaximal, complemented
3C2×C29×#327C212yesmaximal, complemented
4C29×#1444C211yesmaximal, characteristic, complemented
5C29×#1280C211yesmaximal, characteristic, complemented
6C2×C29×#121—21no—
7C2×C29×#121—21no—
8C2×C29×#121C2212yes—
9C22×C4⋊C4×C29—21no—
10C22×C4⋊C4×C29C2211yescharacteristic
11C2×C29×#102—22no—
12C2×C29×C22⋊C8C2212yes—
13C29×#399—22no—
14C29×#392—22no—
15C2×C29×#95—21no—
16C2×C29×#95C2211yescharacteristic
17C2×C29×#95C2211yescharacteristic
18C29×#340—22no—
19C29×#327—24no—
20C22×D4×C29—22no—
21C22×D4×C29—21no—
22C22×D4×C29—21no—
23C22×D4×C29D412yes—
24C23×C4×C29—21no—
25C23×C4×C29—21no—
26C23×C4×C29D411yescharacteristic
27C23×C4×C29D411yescharacteristic
28C23×C4×C29C2311yescharacteristic
29C22×C8×C29—22no—
30C29×#121—22no—
31C29×#121—22no—
32C29×#121—22no—
33C29×#121—22no—
34C29×#121—42no—
35C29×#121—42no—
36C29×#121—42no—
37C29×#121—42no—
38C2×C4⋊C4×C29—22no—
39C2×C4⋊C4×C29—21no—
40C2×C4⋊C4×C29—21no—
41C2×C4⋊C4×C29—42no—
42C2×C4⋊C4×C29—42no—
43C2×C4⋊C4×C29—42no—
44C2×C4⋊C4×C29—42no—
45C2×C4⋊C4×C29D412yes—
46C2×C22⋊C4×C29—22no—
47C2×C22⋊C4×C29—22no—
48C2×C22⋊C4×C29—22no—
49C29×#102—44no—
50C29×C22⋊C8—22no—
51C29×C22⋊C8—22no—
52C29×#95—22no—
53C29×#95—21no—
54C29×#95—42no—
55C29×#95D412yescomplemented
56C24×C29—22no—
57C24×C29C2×D411yescharacteristic
58C2×D4×C29—22no—
59C2×D4×C29—22no—
60C2×D4×C29—42no—
61C2×D4×C29—42no—
62C2×D4×C29—42no—
63C2×D4×C29—42no—
64C2×D4×C29—42no—
65C2×D4×C29—42no—
66C2×D4×C29—42no—
67C2×D4×C29—42no—
68C2×D4×C29—42no—
69C2×D4×C29—42no—
70C2×D4×C29—81no—
71C2×D4×C29—81no—
72C2×D4×C29—81no—
73C2×D4×C29—81no—
74C22×C4×C29—22no—
75C22×C4×C29—22no—
76C22×C4×C29—21no—
77C22×C4×C29—21no—
78C22×C4×C29—22no—
79C22×C4×C29—21no—
80C22×C4×C29—21no—
81C22×C4×C29—22no—
82C22×C4×C29—22no—
83C22×C4×C29—41no—
84C22×C4×C29—41no—
85C22×C4×C29—41no—
86C22×C4×C29—41no—
87C22×C4×C29—41no—
88C22×C4×C29—41no—
89C22×C4×C29—41no—
90C22×C4×C29—41no—
91C22×C4×C29—41no—
92C22×C4×C29—41no—
93C22×C4×C29—41no—
94C22×C4×C29—41no—
95C22×C4×C29—41no—
96C22×C4×C29—41no—
97C22×C4×C29—41no—
98C22×C4×C29—41no—
99C22×C4×C29D812yes—
100C22×C4×C29SD1612yes—
101C22×C4×C29C2×D412yes—
102C22×C4×C29C2×D411yescharacteristic
103C22×C4×C29#4112yes—
104C22×C4×C29#4111yescharacteristic
105C2×C8×C29—42no—
106C2×C8×C29—42no—
107C2×C8×C29—42no—
108C4⋊C4×C29—24no—
109C4⋊C4×C29—22no—
110C4⋊C4×C29—22no—
111C4⋊C4×C29—42no—
112C4⋊C4×C29—42no—
113C4⋊C4×C29—42no—
114C4⋊C4×C29—48no—
115C22⋊C4×C29—44no—
116C22⋊C4×C29—44no—
117C22⋊C4×C29—42no—
118C22⋊C4×C29—42no—
119#10402C2911yesmaximal, characteristic, direct product factor, Sylow
120C23×C29—21no—
121C23×C29—21no—
122C23×C29—21no—
123C23×C29—21no—
124C23×C29—42no—
125C23×C29—42no—
126C23×C29—42no—
127C23×C29—42no—
128C23×C29—42no—
129C23×C29—42no—
130C23×C29—42no—
131C23×C29#12011yescharacteristic
132C23×C29#12111yescharacteristic
133C23×C29#12411yescharacteristic
134C23×C29C2×D811yescharacteristic
135C23×C29C2×SD1611yescharacteristic
136C23×C29AGL(1,ℤ/8)11yescharacteristic
137C23×C29AGL(1,ℤ/8)11yescharacteristic
138D4×C29—44no—
139D4×C29—82no—
140D4×C29—84no—
141D4×C29—84no—
142D4×C29—82no—
143D4×C29—82no—
144D4×C29—82no—
145D4×C29—82no—
146C2×C4×C29—22no—
147C2×C4×C29—22no—
148C2×C4×C29—24no—
149C2×C4×C29—22no—
150C2×C4×C29—22no—
151C2×C4×C29—41no—
152C2×C4×C29—42no—
153C2×C4×C29—41no—
154C2×C4×C29—42no—
155C2×C4×C29—42no—
156C2×C4×C29—42no—
157C2×C4×C29—42no—
158C2×C4×C29—42no—
159C2×C4×C29—41no—
160C2×C4×C29—41no—
161C2×C4×C29—41no—
162C2×C4×C29—41no—
163C2×C4×C29—42no—
164C2×C4×C29—42no—
165C2×C4×C29—42no—
166C2×C4×C29—42no—
167C2×C4×C29—42no—
168C2×C4×C29—42no—
169C2×C4×C29—42no—
170C2×C4×C29—42no—
171C2×C4×C29—42no—
172C2×C4×C29—81no—
173C2×C4×C29—81no—
174C2×C4×C29—81no—
175C2×C4×C29—81no—
176C2×C4×C29—81no—
177C2×C4×C29—81no—
178C2×C4×C29#12112yes—
179C2×C4×C29#12312yes—
180C8×C29—82no—
181#2656C2×C2911yescharacteristic
182#1874C2×C2912yescomplemented
183C2×#327C2×C2912yescomplemented
184#1444C2×C2911yescharacteristic, complemented
185#1280C2×C2911yescharacteristic, complemented
186C22×C29—21no—
187C22×C29—21no—
188C22×C29—21no—
189C22×C29—21no—
190C22×C29—21no—
191C22×C29—21no—
192C22×C29—21no—
193C22×C29—21no—
194C22×C29—21no—
195C22×C29—21no—
196C22×C29—21no—
197C22×C29—21no—
198C22×C29—82no—
199C22×C29—82no—
200C22×C29—82no—
201C22×C29—82no—
202C22×C29—82no—
203C22×C29—82no—
204C22×C29—82no—
205C22×C29#39411yescharacteristic
206C22×C29#44711yescharacteristic
207C22×C29#45011yescharacteristic
208C22×C29#45311yescharacteristic
209C22×C29#45611yescharacteristic
210C22×C29B(4,𝔽2)11yescharacteristic
211C22×C29#45811yescharacteristic
212C22×C29#45911yescharacteristic
213C22×C29#46011yescharacteristic
214C22×C29#48611yescharacteristic
215C22×C29#49011yescharacteristic
216C4×C29—22no—
217C4×C29—22no—
218C4×C29—44no—
219C4×C29—42no—
220C4×C29—42no—
221C4×C29—82no—
222C4×C29—82no—
223C2×#121—21no—
224C2×#121—21no—
225C2×#121C22×C2912yes—
226C22×C4⋊C4—21no—
227C22×C4⋊C4C22×C2911yescharacteristic
228C2×#102—22no—
229C2×C22⋊C8C22×C2912yes—
230#399—22no—
231#392—22no—
232C2×#95—21no—
233C2×#95C22×C2911yescharacteristic
234C2×#95C22×C2911yescharacteristic
235#340—22no—
236#327—24no—
237C2×C29—21no—
238C2×C29—21no—
239C2×C29—21no—
240C2×C29—21no—
241C2×C29—162no—
242C2×C29#159511yescharacteristic
243C2×C29#160411yescharacteristic
244C2×C29#161011yescharacteristic
245C2×C29#161311yescharacteristic
246C2×C29#203911yescharacteristic
247C2×C29#204111yescharacteristic
248C2×C29#204411yescharacteristic
249C22×D4—22no—
250C22×D4—21no—
251C22×D4—21no—
252C22×D4D4×C2912yes—
253C23×C4—21no—
254C23×C4—21no—
255C23×C4D4×C2911yescharacteristic
256C23×C4D4×C2911yescharacteristic
257C23×C4C23×C2911yescharacteristic
258C22×C8—22no—
259#121—22no—
260#121—22no—
261#121—22no—
262#121—22no—
263#121—42no—
264#121—42no—
265#121—42no—
266#121—42no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—42no—
271C2×C4⋊C4—42no—
272C2×C4⋊C4—42no—
273C2×C4⋊C4—42no—
274C2×C4⋊C4D4×C2912yes—
275C2×C22⋊C4—22no—
276C2×C22⋊C4—22no—
277C2×C22⋊C4—22no—
278#102—44no—
279C22⋊C8—22no—
280C22⋊C8—22no—
281#95—22no—
282#95—21no—
283#95—42no—
284#95D4×C2912yescomplemented
285C29#1040211yescharacteristic, direct product factor, Sylow
286C24—22no—
287C24C2×D4×C2911yescharacteristic
288C2×D4—22no—
289C2×D4—22no—
290C2×D4—42no—
291C2×D4—42no—
292C2×D4—42no—
293C2×D4—42no—
294C2×D4—42no—
295C2×D4—42no—
296C2×D4—42no—
297C2×D4—42no—
298C2×D4—42no—
299C2×D4—42no—
300C2×D4—81no—
301C2×D4—81no—
302C2×D4—81no—
303C2×D4—81no—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—22no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4D8×C2912yes—
330C22×C4SD16×C2912yes—
331C22×C4C2×D4×C2912yes—
332C22×C4C2×D4×C2911yescharacteristic
333C22×C4#41×C2912yes—
334C22×C4#41×C2911yescharacteristic
335C2×C8—42no—
336C2×C8—42no—
337C2×C8—42no—
338C4⋊C4—24no—
339C4⋊C4—22no—
340C4⋊C4—22no—
341C4⋊C4—42no—
342C4⋊C4—42no—
343C4⋊C4—42no—
344C4⋊C4—48no—
345C22⋊C4—44no—
346C22⋊C4—44no—
347C22⋊C4—42no—
348C22⋊C4—42no—
349C23—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—42no—
354C23—42no—
355C23—42no—
356C23—42no—
357C23—42no—
358C23—42no—
359C23—42no—
360C23C29×#12011yescharacteristic
361C23C29×#12111yescharacteristic
362C23C29×#12411yescharacteristic
363C23C2×D8×C2911yescharacteristic
364C23C2×SD16×C2911yescharacteristic
365C23C29×AGL(1,ℤ/8)11yescharacteristic
366C23C29×AGL(1,ℤ/8)11yescharacteristic
367D4—44no—
368D4—82no—
369D4—84no—
370D4—84no—
371D4—82no—
372D4—82no—
373D4—82no—
374D4—82no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—24no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—41no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—81no—
404C2×C4—81no—
405C2×C4—81no—
406C2×C4—81no—
407C2×C4C29×#12112yes—
408C2×C4C29×#12312yes—
409C8—82no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—82no—
423C22—82no—
424C22—82no—
425C22—82no—
426C22—82no—
427C22—82no—
428C22—82no—
429C22C29×#39411yescharacteristic
430C22C29×#44711yescharacteristic
431C22C29×#45011yescharacteristic
432C22C29×#45311yescharacteristic
433C22C29×#45611yescharacteristic
434C22C29×B(4,𝔽2)11yescharacteristic
435C22C29×#45811yescharacteristic
436C22C29×#45911yescharacteristic
437C22C29×#46011yescharacteristic
438C22C29×#48611yescharacteristic
439C22C29×#49011yescharacteristic
440C4—22no—
441C4—22no—
442C4—44no—
443C4—42no—
444C4—42no—
445C4—82no—
446C4—82no—
447C2—21no—
448C2—21no—
449C2—21no—
450C2—21no—
451C2—162no—
452C2C29×#159511yescharacteristic
453C2C29×#160411yescharacteristic
454C2C29×#161011yescharacteristic
455C2C29×#161311yescharacteristic
456C2C29×#203911yescharacteristic
457C2C29×#204111yescharacteristic
458C2C29×#204411yescharacteristic
subgroupG/H
center, socleC23×C29#120
commutator, Frattini, cosocleC23×C4C23×C29
prime radicalC29×#2656C2
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
2. C29×#1874C2semidirect
3. C2×C29×#327C2semidirect
4. C29×#1444C2semidirect
5. C29×#1280C2semidirect
55. C29×#95D4semidirect
119. #10402C29direct (N × H)
182. #1874C2×C29semidirect
183. C2×#327C2×C29semidirect
184. #1444C2×C29semidirect
185. #1280C2×C29semidirect
284. #95D4×C29semidirect
285. C29#10402direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#26562
C29×#18742
C2×C29×#3272
C29×#14442
C29×#12802
#1040229