Finite Group Databasebeta

← C29×#9322 #20304222

Subgroups — C29×#9322 #20304222

Order 7424.

558 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3038C211yesmaximal, characteristic
2C29×#2989C211yesmaximal, characteristic, complemented
3C29×#1982C211yesmaximal, characteristic, complemented
4C29×#1806C211yesmaximal, characteristic, complemented
5C29×#1545C211yesmaximal, characteristic, complemented
6C29×#1303C211yesmaximal, characteristic, complemented
7C29×#1292C211yesmaximal, characteristic, complemented
8C2×C29×AGL(1,ℤ/8)—21no—
9C2×C29×#127C2211yescharacteristic
10C4×#41×C29C2211yescharacteristic
11C29×#460—21no—
12C29×#460C412yescomplemented
13C29×#459—21no—
14C29×#459C412yescomplemented
15C29×#446—21no—
16C29×#436—21no—
17C29×#435—22no—
18C29×#432—21no—
19C29×#431C2211yescharacteristic
20C29×#423—21no—
21C29×#423C2211yescharacteristic
22C29×#423C2211yescharacteristic
23C2×C29×C4⋊C8C2211yescharacteristic
24C2×C29×#104—21no—
25C29×#418—21no—
26C2×C29×#102—22no—
27C4×C4⋊C4×C29C2211yescharacteristic
28C29×#339—21no—
29C29×#331—21no—
30C29×#331—21no—
31C2×#41×C29D411yescharacteristic
32C22×D4×C29—21no—
33C22×D4×C29—21no—
34C22×D4×C29—21no—
35C29×AGL(1,ℤ/8)—42no—
36C29×AGL(1,ℤ/8)—42no—
37C2×SD16×C29—22no—
38C2×D8×C29—22no—
39C2×M16×C29—21no—
40C2×M16×C29—22no—
41C2×M16×C29—21no—
42C22×C8×C29D412yes—
43C29×#127—21no—
44C29×#127—21no—
45C29×#127—21no—
46C29×#127C2×C412yes—
47C4×Q8×C29C2×C411yescharacteristic
48C4×Q8×C29D411yescharacteristic
49C4×D4×C29—21no—
50C4×D4×C29—21no—
51C4×D4×C29C2×C411yescharacteristic
52C4×D4×C29D411yescharacteristic
53C29×#117—21no—
54C29×#117D411yescharacteristic
55C2×C4⋊C4×C29—21no—
56C2×C42×C29—21no—
57C2×C42×C29—21no—
58C2×C42×C29C2311yescharacteristic
59C29×C4⋊C8—22no—
60C29×C4⋊C8—21no—
61C29×C4⋊C8—21no—
62C29×C4⋊C8—21no—
63C29×C4⋊C8—21no—
64C29×C4⋊C8—21no—
65C29×C4⋊C8C2×C412yes—
66C29×C4⋊C8D411yescharacteristic
67C29×C4⋊C8D411yescharacteristic
68C29×#104—42no—
69C29×#102—22no—
70C29×#102—22no—
71C29×#102—44no—
72C29×C22⋊C8—22no—
73C29×C22⋊C8—21no—
74C29×#97—22no—
75C4×C8×C29—21no—
76C29×#95—21no—
77C24×C29—41no—
78#41×C29—21no—
79#41×C29—21no—
80#41×C29—21no—
81#41×C29—21no—
82C2×Q8×C29C22⋊C411yescharacteristic
83C2×D4×C29—21no—
84C2×D4×C29—22no—
85C2×D4×C29—22no—
86C2×D4×C29—22no—
87C2×D4×C29—42no—
88C2×D4×C29—42no—
89C2×D4×C29—41no—
90C2×D4×C29—41no—
91C2×D4×C29—41no—
92C2×D4×C29—41no—
93C2×D4×C29—41no—
94C2×D4×C29—41no—
95C2×D4×C29—41no—
96C2×D4×C29—82no—
97C2×D4×C29C22⋊C411yescharacteristic
98C22×C4×C29—21no—
99C22×C4×C29—21no—
100C22×C4×C29—21no—
101C22×C4×C29—41no—
102C22×C4×C29C2×D411yescharacteristic
103C22×C4×C29C2×D411yescharacteristic
104C22×C4×C29#4111yescharacteristic
105SD16×C29—44no—
106D8×C29—44no—
107M16×C29—41no—
108M16×C29—41no—
109M16×C29—41no—
110M16×C29—41no—
111M16×C29—82no—
112C2×C8×C29—22no—
113C2×C8×C29—22no—
114C2×C8×C29—21no—
115C2×C8×C29—21no—
116C2×C8×C29—42no—
117C2×C8×C29—41no—
118C4⋊C4×C29—21no—
119C4⋊C4×C29—21no—
120C4⋊C4×C29—22no—
121C4⋊C4×C29—41no—
122C4⋊C4×C29C22⋊C411yescharacteristic
123C4⋊C4×C29C22⋊C411yescharacteristic
124C22⋊C4×C29—21no—
125C22⋊C4×C29—21no—
126C22⋊C4×C29—21no—
127C42×C29—21no—
128C42×C29—21no—
129C42×C29—21no—
130C42×C29—41no—
131C42×C29—41no—
132C42×C29C22×C411yescharacteristic
133C42×C29C2×D411yescharacteristic
134C42×C29C2×D411yescharacteristic
135C42×C29#4111yescharacteristic
136#9322C2911yesmaximal, characteristic, direct product factor, Sylow
137C23×C29—21no—
138C23×C29—42no—
139C23×C29—82no—
140C23×C29—82no—
141C23×C29—81no—
142C23×C29—81no—
143C23×C29#12111yescharacteristic
144Q8×C29—21no—
145Q8×C29—21no—
146D4×C29—21no—
147D4×C29—21no—
148D4×C29—44no—
149D4×C29—41no—
150D4×C29—41no—
151D4×C29—42no—
152D4×C29—42no—
153D4×C29—82no—
154D4×C29—82no—
155D4×C29—81no—
156D4×C29—81no—
157D4×C29—81no—
158D4×C29—81no—
159C2×C4×C29—21no—
160C2×C4×C29—21no—
161C2×C4×C29—21no—
162C2×C4×C29—21no—
163C2×C4×C29—21no—
164C2×C4×C29—41no—
165C2×C4×C29—41no—
166C2×C4×C29—41no—
167C2×C4×C29—41no—
168C2×C4×C29—41no—
169C2×C4×C29—42no—
170C2×C4×C29—81no—
171C2×C4×C29—81no—
172C2×C4×C29—81no—
173C2×C4×C29C2×C22⋊C411yescharacteristic
174C2×C4×C29C4×D411yescharacteristic
175C2×C4×C29C4×D411yescharacteristic
176C2×C4×C29#12011yescharacteristic
177C2×C4×C29#12111yescharacteristic
178C2×C4×C29#12311yescharacteristic
179C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
180C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
181C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
182C2×C4×C29#13711yescharacteristic
183C8×C29—42no—
184C8×C29—42no—
185C8×C29—41no—
186C8×C29—41no—
187C8×C29—81no—
188#3038C2×C2911yescharacteristic
189#2989C2×C2911yescharacteristic, complemented
190#1982C2×C2911yescharacteristic, complemented
191#1806C2×C2911yescharacteristic, complemented
192#1545C2×C2911yescharacteristic, complemented
193#1303C2×C2911yescharacteristic, complemented
194#1292C2×C2911yescharacteristic, complemented
195C22×C29—21no—
196C22×C29—21no—
197C22×C29—41no—
198C22×C29—41no—
199C22×C29—41no—
200C22×C29—82no—
201C22×C29—82no—
202C22×C29—82no—
203C22×C29—162no—
204C22×C29—162no—
205C22×C29#38611yescharacteristic
206C22×C29#46811yescharacteristic
207C22×C29#46911yescharacteristic
208C4×C29—21no—
209C4×C29—21no—
210C4×C29—21no—
211C4×C29—41no—
212C4×C29—41no—
213C4×C29—41no—
214C4×C29—82no—
215C4×C29#41711yescharacteristic
216C4×C29#41811yescharacteristic
217C4×C29#45311yescharacteristic
218C4×C29#45411yescharacteristic
219C4×C29#46811yescharacteristic
220C4×C29#46911yescharacteristic
221C2×AGL(1,ℤ/8)—21no—
222C2×#127C22×C2911yescharacteristic
223C4×#41C22×C2911yescharacteristic
224#460—21no—
225#460C4×C2912yescomplemented
226#459—21no—
227#459C4×C2912yescomplemented
228#446—21no—
229#436—21no—
230#435—22no—
231#432—21no—
232#431C22×C2911yescharacteristic
233#423—21no—
234#423C22×C2911yescharacteristic
235#423C22×C2911yescharacteristic
236C2×C4⋊C8C22×C2911yescharacteristic
237C2×#104—21no—
238#418—21no—
239C2×#102—22no—
240C4×C4⋊C4C22×C2911yescharacteristic
241#339—21no—
242#331—21no—
243#331—21no—
244C2×C29—21no—
245C2×C29—21no—
246C2×C29—81no—
247C2×C29—162no—
248C2×C29#188311yescharacteristic
249C2×C29#189511yescharacteristic
250C2×C29#190311yescharacteristic
251C2×#41D4×C2911yescharacteristic
252C22×D4—21no—
253C22×D4—21no—
254C22×D4—21no—
255AGL(1,ℤ/8)—42no—
256AGL(1,ℤ/8)—42no—
257C2×SD16—22no—
258C2×D8—22no—
259C2×M16—21no—
260C2×M16—22no—
261C2×M16—21no—
262C22×C8D4×C2912yes—
263#127—21no—
264#127—21no—
265#127—21no—
266#127C2×C4×C2912yes—
267C4×Q8C2×C4×C2911yescharacteristic
268C4×Q8D4×C2911yescharacteristic
269C4×D4—21no—
270C4×D4—21no—
271C4×D4C2×C4×C2911yescharacteristic
272C4×D4D4×C2911yescharacteristic
273#117—21no—
274#117D4×C2911yescharacteristic
275C2×C4⋊C4—21no—
276C2×C42—21no—
277C2×C42—21no—
278C2×C42C23×C2911yescharacteristic
279C4⋊C8—22no—
280C4⋊C8—21no—
281C4⋊C8—21no—
282C4⋊C8—21no—
283C4⋊C8—21no—
284C4⋊C8—21no—
285C4⋊C8C2×C4×C2912yes—
286C4⋊C8D4×C2911yescharacteristic
287C4⋊C8D4×C2911yescharacteristic
288#104—42no—
289#102—22no—
290#102—22no—
291#102—44no—
292C22⋊C8—22no—
293C22⋊C8—21no—
294#97—22no—
295C4×C8—21no—
296#95—21no—
297C29#932211yescharacteristic, direct product factor, Sylow
298C24—41no—
299#41—21no—
300#41—21no—
301#41—21no—
302#41—21no—
303C2×Q8C22⋊C4×C2911yescharacteristic
304C2×D4—21no—
305C2×D4—22no—
306C2×D4—22no—
307C2×D4—22no—
308C2×D4—42no—
309C2×D4—42no—
310C2×D4—41no—
311C2×D4—41no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—82no—
318C2×D4C22⋊C4×C2911yescharacteristic
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—41no—
323C22×C4C2×D4×C2911yescharacteristic
324C22×C4C2×D4×C2911yescharacteristic
325C22×C4#41×C2911yescharacteristic
326SD16—44no—
327D8—44no—
328M16—41no—
329M16—41no—
330M16—41no—
331M16—41no—
332M16—82no—
333C2×C8—22no—
334C2×C8—21no—
335C2×C8—21no—
336C2×C8—22no—
337C2×C8—42no—
338C2×C8—41no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—22no—
342C4⋊C4—41no—
343C4⋊C4C22⋊C4×C2911yescharacteristic
344C4⋊C4C22⋊C4×C2911yescharacteristic
345C22⋊C4—21no—
346C22⋊C4—21no—
347C22⋊C4—21no—
348C42—21no—
349C42—21no—
350C42—21no—
351C42—41no—
352C42—41no—
353C42C22×C4×C2911yescharacteristic
354C42C2×D4×C2911yescharacteristic
355C42C2×D4×C2911yescharacteristic
356C42#41×C2911yescharacteristic
357C23—21no—
358C23—42no—
359C23—82no—
360C23—82no—
361C23—81no—
362C23—81no—
363C23C29×#12111yescharacteristic
364Q8—21no—
365Q8—21no—
366D4—21no—
367D4—21no—
368D4—44no—
369D4—41no—
370D4—41no—
371D4—42no—
372D4—42no—
373D4—82no—
374D4—82no—
375D4—81no—
376D4—81no—
377D4—81no—
378D4—81no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—42no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4C2×C22⋊C4×C2911yescharacteristic
394C2×C4C4×D4×C2911yescharacteristic
395C2×C4C4×D4×C2911yescharacteristic
396C2×C4C29×#12011yescharacteristic
397C2×C4C29×#12111yescharacteristic
398C2×C4C29×#12311yescharacteristic
399C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
400C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
401C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
402C2×C4C29×#13711yescharacteristic
403C8—42no—
404C8—41no—
405C8—41no—
406C8—42no—
407C8—81no—
408C22—21no—
409C22—21no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—82no—
414C22—82no—
415C22—82no—
416C22—162no—
417C22—162no—
418C22C29×#38611yescharacteristic
419C22C29×#46811yescharacteristic
420C22C29×#46911yescharacteristic
421C4—21no—
422C4—21no—
423C4—21no—
424C4—41no—
425C4—41no—
426C4—41no—
427C4—82no—
428C4C29×#41711yescharacteristic
429C4C29×#41811yescharacteristic
430C4C29×#45311yescharacteristic
431C4C29×#45411yescharacteristic
432C4C29×#46811yescharacteristic
433C4C29×#46911yescharacteristic
434C2—21no—
435C2—21no—
436C2—81no—
437C2—162no—
438C2C29×#188311yescharacteristic
439C2C29×#189511yescharacteristic
440C2C29×#190311yescharacteristic
subgroupG/H
center, socleC22×C29#386
commutatorC42C22×C4×C29
Frattini, cosocleC2×C42C23×C29
prime radicalC29×#3038C2
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×#2989C2semidirect
3. C29×#1982C2semidirect
4. C29×#1806C2semidirect
5. C29×#1545C2semidirect
6. C29×#1303C2semidirect
7. C29×#1292C2semidirect
12. C29×#460C4semidirect
14. C29×#459C4semidirect
136. #9322C29direct (N × H)
189. #2989C2×C29semidirect
190. #1982C2×C29semidirect
191. #1806C2×C29semidirect
192. #1545C2×C29semidirect
193. #1303C2×C29semidirect
194. #1292C2×C29semidirect
225. #460C4×C29semidirect
227. #459C4×C29semidirect
297. C29#9322direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#30382
C29×#29892
C29×#19822
C29×#18062
C29×#15452
C29×#13032
C29×#12922
#932229