Finite Group Databasebeta

← C29×#9260 #20304160

Subgroups — C29×#9260 #20304160

Order 7424.

594 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#480C211yesmaximal, characteristic
2C29×#2344C211yesmaximal, characteristic, complemented
3C29×#1964C211yesmaximal, characteristic
4C29×#1823C211yesmaximal, characteristic, complemented
5C29×#1519C211yesmaximal, characteristic
6C29×#1289C211yesmaximal, characteristic, complemented
7C29×#1282C211yesmaximal, characteristic, complemented
8C2×C29×#121C2211yescharacteristic
9C2×C29×#117—21no—
10C22×C4⋊C4×C29C2211yescharacteristic
11C29×#480—22no—
12C29×#480—21no—
13C29×#480—21no—
14C2×C29×#107C412yescomplemented
15C2×C29×#102C412yescomplemented
16C2×C29×#99—21no—
17C2×C29×#99—21no—
18C2×C29×C22⋊C8C2211yescharacteristic
19C2×C29×C22⋊C8C2211yescharacteristic
20C29×#389—21no—
21C29×#387—22no—
22C29×#381—21no—
23C29×#380C2211yescharacteristic
24C29×#380C2211yescharacteristic
25C4×C4⋊C4×C29—21no—
26C4×C22⋊C4×C29C2211yescharacteristic
27C29×#340—22no—
28C29×#327—22no—
29C22×D4×C29—21no—
30C22×D4×C29C2×C411yescharacteristic
31C23×C4×C29—21no—
32C23×C4×C29C2311yescharacteristic
33C22×C8×C29—21no—
34C22×C8×C29C2×C412yes—
35C29×#121—21no—
36C29×#121—21no—
37C29×#121—21no—
38C29×#121—21no—
39C29×#117—42no—
40C29×#117—42no—
41C2×C4⋊C4×C29—21no—
42C2×C4⋊C4×C29—21no—
43C2×C4⋊C4×C29—21no—
44C2×C4⋊C4×C29—22no—
45C2×C4⋊C4×C29—21no—
46C2×C4⋊C4×C29—21no—
47C2×C4⋊C4×C29C2×C411yescharacteristic
48C2×C4⋊C4×C29C2×C412yes—
49C2×C4⋊C4×C29D412yes—
50C2×C4⋊C4×C29D411yescharacteristic
51C2×C4⋊C4×C29D411yescharacteristic
52C2×C22⋊C4×C29—21no—
53C2×C22⋊C4×C29—21no—
54C2×C22⋊C4×C29—21no—
55C2×C22⋊C4×C29D411yescharacteristic
56C2×C22⋊C4×C29D411yescharacteristic
57C2×C42×C29—22no—
58C2×C42×C29—21no—
59C29×#107—22no—
60C29×#107—22no—
61C29×#102—22no—
62C29×#102—22no—
63C29×#99—42no—
64C29×#99—42no—
65C29×C22⋊C8—21no—
66C29×C22⋊C8—21no—
67C29×C22⋊C8—21no—
68C29×C22⋊C8—21no—
69C29×#95—22no—
70C29×#95—22no—
71C29×#95—21no—
72C29×#95—21no—
73C29×#95D412yes—
74C24×C29—21no—
75C24×C29C2×D411yescharacteristic
76C2×D4×C29—21no—
77C2×D4×C29—21no—
78C2×D4×C29—42no—
79C2×D4×C29—41no—
80C2×D4×C29—41no—
81C2×D4×C29—41no—
82C2×D4×C29—41no—
83C2×D4×C29—41no—
84C2×D4×C29—41no—
85C22×C4×C29—22no—
86C22×C4×C29—21no—
87C22×C4×C29—21no—
88C22×C4×C29—21no—
89C22×C4×C29—22no—
90C22×C4×C29—21no—
91C22×C4×C29—22no—
92C22×C4×C29—21no—
93C22×C4×C29—42no—
94C22×C4×C29—41no—
95C22×C4×C29—41no—
96C22×C4×C29—41no—
97C22×C4×C29—41no—
98C22×C4×C29—41no—
99C22×C4×C29C22×C411yescharacteristic
100C22×C4×C29C2×D411yescharacteristic
101C22×C4×C29C2×D411yescharacteristic
102C22×C4×C29C2×D411yescharacteristic
103C22×C4×C29#4111yescharacteristic
104C22×C4×C29#4111yescharacteristic
105C2×C8×C29—22no—
106C2×C8×C29—42no—
107C2×C8×C29—42no—
108C2×C8×C29—41no—
109C4⋊C4×C29—22no—
110C4⋊C4×C29—22no—
111C4⋊C4×C29—21no—
112C4⋊C4×C29—21no—
113C4⋊C4×C29—21no—
114C4⋊C4×C29—21no—
115C4⋊C4×C29—42no—
116C4⋊C4×C29—44no—
117C4⋊C4×C29—42no—
118C4⋊C4×C29C22⋊C412yes—
119C4⋊C4×C29C22⋊C412yes—
120C22⋊C4×C29—21no—
121C22⋊C4×C29—21no—
122C22⋊C4×C29—21no—
123C22⋊C4×C29—41no—
124C22⋊C4×C29—41no—
125C22⋊C4×C29—41no—
126C22⋊C4×C29—41no—
127C22⋊C4×C29—41no—
128C22⋊C4×C29—41no—
129C22⋊C4×C29D812yes—
130C42×C29—42no—
131C42×C29—44no—
132#9260C2911yesmaximal, characteristic, direct product factor, Sylow
133C23×C29—41no—
134C23×C29—41no—
135C23×C29—41no—
136C23×C29—41no—
137C23×C29—41no—
138C23×C29—81no—
139C23×C29—81no—
140C23×C29C4×D411yescharacteristic
141C23×C29#12011yescharacteristic
142C23×C29#12111yescharacteristic
143C23×C29C2×D811yescharacteristic
144C23×C29#13511yescharacteristic
145C23×C29AGL(1,ℤ/8)11yescharacteristic
146C23×C29AGL(1,ℤ/8)11yescharacteristic
147D4×C29—42no—
148D4×C29—81no—
149D4×C29—81no—
150D4×C29—81no—
151D4×C29—81no—
152D4×C29—81no—
153C2×C4×C29—22no—
154C2×C4×C29—22no—
155C2×C4×C29—22no—
156C2×C4×C29—22no—
157C2×C4×C29—22no—
158C2×C4×C29—22no—
159C2×C4×C29—41no—
160C2×C4×C29—41no—
161C2×C4×C29—41no—
162C2×C4×C29—41no—
163C2×C4×C29—41no—
164C2×C4×C29—42no—
165C2×C4×C29—42no—
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—42no—
175C2×C4×C29—41no—
176C2×C4×C29—41no—
177C2×C4×C29—41no—
178C2×C4×C29—41no—
179C2×C4×C29—42no—
180C2×C4×C29—41no—
181C2×C4×C29—81no—
182C2×C4×C29—81no—
183C2×C4×C29—81no—
184C2×C4×C29C2×C22⋊C411yescharacteristic
185C2×C4×C29C4×D411yescharacteristic
186C2×C4×C29#12111yescharacteristic
187C2×C4×C29#12311yescharacteristic
188C8×C29—42no—
189C8×C29—81no—
190C2×#480C2×C2911yescharacteristic
191#2344C2×C2911yescharacteristic, complemented
192#1964C2×C2911yescharacteristic
193#1823C2×C2911yescharacteristic, complemented
194#1519C2×C2911yescharacteristic
195#1289C2×C2911yescharacteristic, complemented
196#1282C2×C2911yescharacteristic, complemented
197C22×C29—21no—
198C22×C29—21no—
199C22×C29—21no—
200C22×C29—21no—
201C22×C29—21no—
202C22×C29—21no—
203C22×C29—41no—
204C22×C29—41no—
205C22×C29—41no—
206C22×C29—41no—
207C22×C29—81no—
208C22×C29—81no—
209C22×C29—81no—
210C22×C29—161no—
211C22×C29—161no—
212C22×C29#38611yescharacteristic
213C22×C29C4×D811yescharacteristic
214C22×C29#44211yescharacteristic
215C22×C29#44711yescharacteristic
216C22×C29#44911yescharacteristic
217C22×C29#45911yescharacteristic
218C22×C29#46311yescharacteristic
219C4×C29—21no—
220C4×C29—21no—
221C4×C29—21no—
222C4×C29—42no—
223C4×C29—42no—
224C4×C29—42no—
225C4×C29—82no—
226C4×C29—81no—
227C4×C29—81no—
228C4×C29—161no—
229C4×C29#41012yes—
230C2×#121C22×C2911yescharacteristic
231C2×#117—21no—
232C22×C4⋊C4C22×C2911yescharacteristic
233#480—22no—
234#480—21no—
235#480—21no—
236C2×#107C4×C2912yescomplemented
237C2×#102C4×C2912yescomplemented
238C2×#99—21no—
239C2×#99—21no—
240C2×C22⋊C8C22×C2911yescharacteristic
241C2×C22⋊C8C22×C2911yescharacteristic
242#389—21no—
243#387—22no—
244#381—21no—
245#380C22×C2911yescharacteristic
246#380C22×C2911yescharacteristic
247C4×C4⋊C4—21no—
248C4×C22⋊C4C22×C2911yescharacteristic
249#340—22no—
250#327—22no—
251C2×C29—21no—
252C2×C29—21no—
253C2×C29—21no—
254C2×C29—21no—
255C2×C29—21no—
256C2×C29—21no—
257C2×C29—161no—
258C2×C29#187911yescharacteristic
259C2×C29#189911yescharacteristic
260C2×C29#190511yescharacteristic
261C22×D4—21no—
262C22×D4C2×C4×C2911yescharacteristic
263C23×C4—21no—
264C23×C4C23×C2911yescharacteristic
265C22×C8—21no—
266C22×C8C2×C4×C2912yes—
267#121—21no—
268#121—21no—
269#121—21no—
270#121—21no—
271#117—42no—
272#117—42no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4C2×C4×C2911yescharacteristic
280C2×C4⋊C4C2×C4×C2912yes—
281C2×C4⋊C4D4×C2912yes—
282C2×C4⋊C4D4×C2911yescharacteristic
283C2×C4⋊C4D4×C2911yescharacteristic
284C2×C22⋊C4—21no—
285C2×C22⋊C4—21no—
286C2×C22⋊C4—21no—
287C2×C22⋊C4D4×C2911yescharacteristic
288C2×C22⋊C4D4×C2911yescharacteristic
289C2×C42—22no—
290C2×C42—21no—
291#107—22no—
292#107—22no—
293#102—22no—
294#102—22no—
295#99—42no—
296#99—42no—
297C22⋊C8—21no—
298C22⋊C8—21no—
299C22⋊C8—21no—
300C22⋊C8—21no—
301#95—22no—
302#95—22no—
303#95—21no—
304#95—21no—
305#95D4×C2912yes—
306C29#926011yescharacteristic, direct product factor, Sylow
307C24—21no—
308C24C2×D4×C2911yescharacteristic
309C2×D4—21no—
310C2×D4—21no—
311C2×D4—42no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C22×C4—22no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—22no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—22no—
326C22×C4—42no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4C22×C4×C2911yescharacteristic
333C22×C4C2×D4×C2911yescharacteristic
334C22×C4C2×D4×C2911yescharacteristic
335C22×C4C2×D4×C2911yescharacteristic
336C22×C4#41×C2911yescharacteristic
337C22×C4#41×C2911yescharacteristic
338C2×C8—22no—
339C2×C8—42no—
340C2×C8—42no—
341C2×C8—41no—
342C4⋊C4—22no—
343C4⋊C4—22no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—44no—
349C4⋊C4—42no—
350C4⋊C4—42no—
351C4⋊C4C22⋊C4×C2912yes—
352C4⋊C4C22⋊C4×C2912yes—
353C22⋊C4—21no—
354C22⋊C4—21no—
355C22⋊C4—21no—
356C22⋊C4—41no—
357C22⋊C4—41no—
358C22⋊C4—41no—
359C22⋊C4—41no—
360C22⋊C4—41no—
361C22⋊C4—41no—
362C22⋊C4D8×C2912yes—
363C42—44no—
364C42—42no—
365C23—41no—
366C23—41no—
367C23—41no—
368C23—41no—
369C23—41no—
370C23—81no—
371C23—81no—
372C23C4×D4×C2911yescharacteristic
373C23C29×#12011yescharacteristic
374C23C29×#12111yescharacteristic
375C23C2×D8×C2911yescharacteristic
376C23C29×#13511yescharacteristic
377C23C29×AGL(1,ℤ/8)11yescharacteristic
378C23C29×AGL(1,ℤ/8)11yescharacteristic
379D4—42no—
380D4—81no—
381D4—81no—
382D4—81no—
383D4—81no—
384D4—81no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—42no—
403C2×C4—42no—
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—81no—
414C2×C4—81no—
415C2×C4—81no—
416C2×C4C2×C22⋊C4×C2911yescharacteristic
417C2×C4C4×D4×C2911yescharacteristic
418C2×C4C29×#12111yescharacteristic
419C2×C4C29×#12311yescharacteristic
420C8—42no—
421C8—81no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—41no—
429C22—41no—
430C22—41no—
431C22—41no—
432C22—81no—
433C22—81no—
434C22—81no—
435C22—161no—
436C22—161no—
437C22C29×#38611yescharacteristic
438C22C4×D8×C2911yescharacteristic
439C22C29×#44211yescharacteristic
440C22C29×#44711yescharacteristic
441C22C29×#44911yescharacteristic
442C22C29×#45911yescharacteristic
443C22C29×#46311yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—42no—
448C4—42no—
449C4—42no—
450C4—82no—
451C4—81no—
452C4—81no—
453C4—161no—
454C4C29×#41012yes—
455C2—21no—
456C2—21no—
457C2—21no—
458C2—21no—
459C2—21no—
460C2—21no—
461C2—161no—
462C2C29×#187911yescharacteristic
463C2C29×#189911yescharacteristic
464C2C29×#190511yescharacteristic
subgroupG/H
center, socleC22×C29#386
commutatorC22×C4C22×C4×C29
Frattini, cosocleC23×C4C23×C29
prime radicalC2×C29×#121C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C23×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#2344C2semidirect
4. C29×#1823C2semidirect
6. C29×#1289C2semidirect
7. C29×#1282C2semidirect
14. C2×C29×#107C4semidirect
15. C2×C29×#102C4semidirect
132. #9260C29direct (N × H)
191. #2344C2×C29semidirect
193. #1823C2×C29semidirect
195. #1289C2×C29semidirect
196. #1282C2×C29semidirect
236. C2×#107C4×C29semidirect
237. C2×#102C4×C29semidirect
306. C29#9260direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#4802
C29×#23442
C29×#19642
C29×#18232
C29×#15192
C29×#12892
C29×#12822
#926029