Finite Group Databasebeta

← C29×#8435 #20303335

Subgroups — C29×#8435 #20303335

Order 7424.

696 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3507C211yesmaximal, characteristic
2C29×#1805C211yesmaximal, characteristic, complemented
3C29×#1542C211yesmaximal, characteristic, complemented
4C29×#1518C211yesmaximal, characteristic, complemented
5C29×#1517C211yesmaximal, characteristic
6C29×#1480C211yesmaximal, characteristic
7C29×#1479C211yesmaximal, characteristic, complemented
8C29×#559C412yescomplemented
9C29×#557C412yescomplemented
10C29×#556—21no—
11C29×#556—22no—
12C29×#554—21no—
13C29×#552—22no—
14C29×#539—22no—
15C29×#536—21no—
16C29×#533C2211yescharacteristic
17C29×#532C2211yescharacteristic
18C29×#529—22no—
19C29×#520—21no—
20C2×C4×Q8×C29C2211yescharacteristic
21C29×#431C2211yescharacteristic
22C29×#431C2211yescharacteristic
23C2×C29×C4⋊C8C2211yescharacteristic
24C2×C29×#103—21no—
25C29×#382C2211yescharacteristic
26C29×#340—21no—
27C29×#333—21no—
28C29×#332—21no—
29C29×#328—22no—
30C29×#327—22no—
31C29×Q8⋊C8—22no—
32C29×D4⋊C8—22no—
33C2×#41×C29—21no—
34C22×Q8×C29D411yescharacteristic
35C22×C8×C29—21no—
36C29×C4⋊Q8—22no—
37C29×C4⋊Q8C2×C411yescharacteristic
38C29×C4⋊Q8D411yescharacteristic
39C29×C4⋊Q8D411yescharacteristic
40C29×#127C2×C411yescharacteristic
41C29×#126—24no—
42C29×#126—24no—
43C29×#125—22no—
44C29×#125—24no—
45C29×#125—21no—
46C29×#124—22no—
47C29×#124—22no—
48C29×#124—21no—
49C29×#123—24no—
50C29×#123—24no—
51C29×C22⋊Q8—22no—
52C29×C22⋊Q8—22no—
53C29×C22⋊Q8—24no—
54C29×C22⋊Q8—21no—
55C29×C22⋊Q8D412yes—
56C29×#121—21no—
57C29×#121D412yes—
58C4×Q8×C29—22no—
59C4×Q8×C29—22no—
60C4×Q8×C29—21no—
61C4×Q8×C29—21no—
62C4×Q8×C29—21no—
63C4×Q8×C29C2×C412yes—
64C4×Q8×C29C2×C412yes—
65C4×Q8×C29D412yes—
66C4×D4×C29—24no—
67C4×D4×C29—22no—
68C4×D4×C29—22no—
69C4×D4×C29—21no—
70C4×D4×C29D412yes—
71C29×#117—22no—
72C29×#117—24no—
73C29×#117—21no—
74C2×C4⋊C4×C29—22no—
75C2×C4⋊C4×C29—21no—
76C2×C4⋊C4×C29—21no—
77C2×C4⋊C4×C29D411yescharacteristic
78C2×C42×C29—21no—
79C2×C42×C29C2311yescharacteristic
80C29×C4⋊C8—21no—
81C29×C4⋊C8—21no—
82C29×C4⋊C8—21no—
83C29×C4⋊C8—21no—
84C29×#103—42no—
85C29×C22⋊C8—21no—
86C29×C22⋊C8—21no—
87C4×C8×C29—21no—
88C4×C8×C29—21no—
89C29×#95—21no—
90C29×#95—21no—
91#41×C29—41no—
92#41×C29—41no—
93#41×C29—41no—
94#41×C29—41no—
95C2×Q8×C29—21no—
96C2×Q8×C29—21no—
97C2×Q8×C29—21no—
98C2×Q8×C29—21no—
99C2×Q8×C29—21no—
100C2×Q8×C29—21no—
101C2×Q8×C29—21no—
102C2×Q8×C29C22⋊C412yes—
103C2×Q8×C29C22⋊C412yes—
104C2×D4×C29—22no—
105C2×D4×C29—21no—
106C2×D4×C29—21no—
107C2×D4×C29C22⋊C412yes—
108C22×C4×C29—21no—
109C22×C4×C29—24no—
110C22×C4×C29—21no—
111C22×C4×C29—22no—
112C22×C4×C29—41no—
113C22×C4×C29C2×D411yescharacteristic
114C22×C4×C29C2×D411yescharacteristic
115C22×C4×C29C2×D411yescharacteristic
116C2×C8×C29—41no—
117C2×C8×C29—41no—
118C2×C8×C29—41no—
119C2×C8×C29—41no—
120C2×C8×C29—41no—
121C4⋊C4×C29—24no—
122C4⋊C4×C29—24no—
123C4⋊C4×C29—24no—
124C4⋊C4×C29—22no—
125C4⋊C4×C29—21no—
126C4⋊C4×C29—22no—
127C4⋊C4×C29—21no—
128C4⋊C4×C29—21no—
129C4⋊C4×C29—22no—
130C4⋊C4×C29—21no—
131C4⋊C4×C29—22no—
132C4⋊C4×C29—21no—
133C4⋊C4×C29—41no—
134C4⋊C4×C29—41no—
135C4⋊C4×C29C22⋊C412yes—
136C4⋊C4×C29C22⋊C412yes—
137C4⋊C4×C29C22⋊C412yes—
138C22⋊C4×C29—24no—
139C22⋊C4×C29—24no—
140C22⋊C4×C29—24no—
141C22⋊C4×C29—22no—
142C22⋊C4×C29—22no—
143C22⋊C4×C29—22no—
144C42×C29—24no—
145C42×C29—22no—
146C42×C29—22no—
147C42×C29—22no—
148C42×C29C22×C411yescharacteristic
149C42×C29C2×D411yescharacteristic
150C42×C29C2×D411yescharacteristic
151C42×C29C2×D411yescharacteristic
152#8435C2911yesmaximal, characteristic, direct product factor, Sylow
153C23×C29—22no—
154C23×C29#12011yescharacteristic
155Q8×C29—22no—
156Q8×C29—22no—
157Q8×C29—42no—
158Q8×C29—41no—
159Q8×C29—41no—
160Q8×C29—41no—
161Q8×C29—41no—
162Q8×C29—81no—
163D4×C29—42no—
164D4×C29—42no—
165D4×C29—42no—
166D4×C29—42no—
167D4×C29—41no—
168D4×C29—41no—
169C2×C4×C29—22no—
170C2×C4×C29—22no—
171C2×C4×C29—22no—
172C2×C4×C29—22no—
173C2×C4×C29—22no—
174C2×C4×C29—41no—
175C2×C4×C29—41no—
176C2×C4×C29—41no—
177C2×C4×C29—41no—
178C2×C4×C29—42no—
179C2×C4×C29—42no—
180C2×C4×C29—81no—
181C2×C4×C29—84no—
182C2×C4×C29—81no—
183C2×C4×C29—81no—
184C2×C4×C29—81no—
185C2×C4×C29C2×C22⋊C411yescharacteristic
186C2×C4×C29C2×C22⋊C411yescharacteristic
187C2×C4×C29C2×C22⋊C411yescharacteristic
188C2×C4×C29#12011yescharacteristic
189C2×C4×C29#12011yescharacteristic
190C2×C4×C29#12011yescharacteristic
191C2×C4×C29#13511yescharacteristic
192C2×C4×C29#13511yescharacteristic
193C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
194C2×C4×C29#13711yescharacteristic
195C8×C29—81no—
196C8×C29—81no—
197C8×C29—81no—
198#3507C2×C2911yescharacteristic
199#1805C2×C2911yescharacteristic, complemented
200#1542C2×C2911yescharacteristic, complemented
201#1518C2×C2911yescharacteristic, complemented
202#1517C2×C2911yescharacteristic
203#1480C2×C2911yescharacteristic
204#1479C2×C2911yescharacteristic, complemented
205C22×C29—21no—
206C22×C29—21no—
207C22×C29—42no—
208C22×C29—42no—
209C22×C29—42no—
210C22×C29#37911yescharacteristic
211C22×C29#44911yescharacteristic
212C22×C29#45211yescharacteristic
213C4×C29—21no—
214C4×C29—21no—
215C4×C29—21no—
216C4×C29—21no—
217C4×C29—42no—
218C4×C29—42no—
219C4×C29—42no—
220C4×C29—42no—
221C4×C29—42no—
222C4×C29—161no—
223C4×C29#41611yescharacteristic
224C4×C29#41711yescharacteristic
225C4×C29#44911yescharacteristic
226C4×C29#45211yescharacteristic
227#559C4×C2912yescomplemented
228#557C4×C2912yescomplemented
229#556—21no—
230#556—22no—
231#554—21no—
232#552—22no—
233#539—22no—
234#536—21no—
235#533C22×C2911yescharacteristic
236#532C22×C2911yescharacteristic
237#529—22no—
238#520—21no—
239C2×C4×Q8C22×C2911yescharacteristic
240#431C22×C2911yescharacteristic
241#431C22×C2911yescharacteristic
242C2×C4⋊C8C22×C2911yescharacteristic
243C2×#103—21no—
244#382C22×C2911yescharacteristic
245#340—21no—
246#333—21no—
247#332—21no—
248#328—22no—
249#327—22no—
250Q8⋊C8—22no—
251D4⋊C8—22no—
252C2×C29—21no—
253C2×C29—21no—
254C2×C29—82no—
255C2×C29#178811yescharacteristic
256C2×C29#179411yescharacteristic
257C2×C29#179611yescharacteristic
258C2×#41—21no—
259C22×Q8D4×C2911yescharacteristic
260C22×C8—21no—
261C4⋊Q8—22no—
262C4⋊Q8C2×C4×C2911yescharacteristic
263C4⋊Q8D4×C2911yescharacteristic
264C4⋊Q8D4×C2911yescharacteristic
265#127C2×C4×C2911yescharacteristic
266#126—24no—
267#126—24no—
268#125—22no—
269#125—24no—
270#125—21no—
271#124—22no—
272#124—22no—
273#124—21no—
274#123—24no—
275#123—24no—
276C22⋊Q8—22no—
277C22⋊Q8—22no—
278C22⋊Q8—24no—
279C22⋊Q8—21no—
280C22⋊Q8D4×C2912yes—
281#121—21no—
282#121D4×C2912yes—
283C4×Q8—22no—
284C4×Q8—22no—
285C4×Q8—21no—
286C4×Q8—21no—
287C4×Q8—21no—
288C4×Q8C2×C4×C2912yes—
289C4×Q8C2×C4×C2912yes—
290C4×Q8D4×C2912yes—
291C4×D4—24no—
292C4×D4—22no—
293C4×D4—22no—
294C4×D4—21no—
295C4×D4D4×C2912yes—
296#117—22no—
297#117—24no—
298#117—21no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4D4×C2911yescharacteristic
303C2×C42—21no—
304C2×C42C23×C2911yescharacteristic
305C4⋊C8—21no—
306C4⋊C8—21no—
307C4⋊C8—21no—
308C4⋊C8—21no—
309#103—42no—
310C22⋊C8—21no—
311C22⋊C8—21no—
312C4×C8—21no—
313C4×C8—21no—
314#95—21no—
315#95—21no—
316C29#843511yescharacteristic, direct product factor, Sylow
317#41—41no—
318#41—41no—
319#41—41no—
320#41—41no—
321C2×Q8—21no—
322C2×Q8—21no—
323C2×Q8—21no—
324C2×Q8—21no—
325C2×Q8—21no—
326C2×Q8—21no—
327C2×Q8—21no—
328C2×Q8C22⋊C4×C2912yes—
329C2×Q8C22⋊C4×C2912yes—
330C2×D4—22no—
331C2×D4—21no—
332C2×D4—21no—
333C2×D4C22⋊C4×C2912yes—
334C22×C4—21no—
335C22×C4—24no—
336C22×C4—21no—
337C22×C4—22no—
338C22×C4—41no—
339C22×C4C2×D4×C2911yescharacteristic
340C22×C4C2×D4×C2911yescharacteristic
341C22×C4C2×D4×C2911yescharacteristic
342C2×C8—41no—
343C2×C8—41no—
344C2×C8—41no—
345C2×C8—41no—
346C2×C8—41no—
347C4⋊C4—24no—
348C4⋊C4—24no—
349C4⋊C4—24no—
350C4⋊C4—22no—
351C4⋊C4—21no—
352C4⋊C4—22no—
353C4⋊C4—21no—
354C4⋊C4—21no—
355C4⋊C4—22no—
356C4⋊C4—21no—
357C4⋊C4—22no—
358C4⋊C4—21no—
359C4⋊C4—41no—
360C4⋊C4—41no—
361C4⋊C4C22⋊C4×C2912yes—
362C4⋊C4C22⋊C4×C2912yes—
363C4⋊C4C22⋊C4×C2912yes—
364C22⋊C4—24no—
365C22⋊C4—24no—
366C22⋊C4—24no—
367C22⋊C4—22no—
368C22⋊C4—22no—
369C22⋊C4—22no—
370C42—24no—
371C42—22no—
372C42—22no—
373C42—22no—
374C42C22×C4×C2911yescharacteristic
375C42C2×D4×C2911yescharacteristic
376C42C2×D4×C2911yescharacteristic
377C42C2×D4×C2911yescharacteristic
378C23—22no—
379C23C29×#12011yescharacteristic
380Q8—22no—
381Q8—22no—
382Q8—42no—
383Q8—41no—
384Q8—41no—
385Q8—41no—
386Q8—41no—
387Q8—81no—
388D4—42no—
389D4—42no—
390D4—42no—
391D4—42no—
392D4—41no—
393D4—41no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—81no—
406C2×C4—84no—
407C2×C4—81no—
408C2×C4—81no—
409C2×C4—81no—
410C2×C4C2×C22⋊C4×C2911yescharacteristic
411C2×C4C2×C22⋊C4×C2911yescharacteristic
412C2×C4C2×C22⋊C4×C2911yescharacteristic
413C2×C4C29×#12011yescharacteristic
414C2×C4C29×#12011yescharacteristic
415C2×C4C29×#12011yescharacteristic
416C2×C4C29×#13511yescharacteristic
417C2×C4C29×#13511yescharacteristic
418C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
419C2×C4C29×#13711yescharacteristic
420C8—81no—
421C8—81no—
422C8—81no—
423C22—21no—
424C22—21no—
425C22—42no—
426C22—42no—
427C22—42no—
428C22C29×#37911yescharacteristic
429C22C29×#44911yescharacteristic
430C22C29×#45211yescharacteristic
431C4—21no—
432C4—21no—
433C4—21no—
434C4—21no—
435C4—42no—
436C4—42no—
437C4—42no—
438C4—42no—
439C4—42no—
440C4—161no—
441C4C29×#41611yescharacteristic
442C4C29×#41711yescharacteristic
443C4C29×#44911yescharacteristic
444C4C29×#45211yescharacteristic
445C2—21no—
446C2—21no—
447C2—82no—
448C2C29×#178811yescharacteristic
449C2C29×#179411yescharacteristic
450C2C29×#179611yescharacteristic
subgroupG/H
center, socleC22×C29#379
commutatorC42C22×C4×C29
Frattini, cosocleC2×C42C23×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
2. C29×#1805C2semidirect
3. C29×#1542C2semidirect
4. C29×#1518C2semidirect
7. C29×#1479C2semidirect
8. C29×#559C4semidirect
9. C29×#557C4semidirect
152. #8435C29direct (N × H)
199. #1805C2×C29semidirect
200. #1542C2×C29semidirect
201. #1518C2×C29semidirect
204. #1479C2×C29semidirect
227. #559C4×C29semidirect
228. #557C4×C29semidirect
316. C29#8435direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35072
C29×#18052
C29×#15422
C29×#15182
C29×#15172
C29×#14802
C29×#14792
#843529