Finite Group Databasebeta

← C29×#9359 #20304259

Subgroups — C29×#9359 #20304259

Order 7424.

540 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3038C211yesmaximal, characteristic
2C29×#2990C211yesmaximal, characteristic, complemented
3C29×#1965C211yesmaximal, characteristic, complemented
4C29×#1545C211yesmaximal, characteristic, complemented
5C29×#1489C211yesmaximal, characteristic, complemented
6C29×#1309C211yesmaximal, characteristic, complemented
7C29×#1299C211yesmaximal, characteristic, complemented
8C2×C29×AGL(1,ℤ/8)C412yes—
9C2×C29×#127C2211yescharacteristic
10C4×#41×C29C2211yescharacteristic
11C29×#460—21no—
12C29×#460—21no—
13C29×#459—21no—
14C29×#459—21no—
15C29×#446—21no—
16C29×#435—22no—
17C8×D4×C29—21no—
18C29×#432—21no—
19C29×#431C2211yescharacteristic
20C29×#423C2211yescharacteristic
21C29×#423C2211yescharacteristic
22C29×#423C2211yescharacteristic
23C2×C29×C4⋊C8—21no—
24C29×#418C412yes—
25C2×C29×#100—22no—
26C4×M16×C29C2211yescharacteristic
27C29×#331—21no—
28C29×#331—21no—
29C29×Q8⋊C8—21no—
30C29×D4⋊C8—21no—
31C2×#41×C29C2×C411yescharacteristic
32C22×D4×C29—21no—
33C22×D4×C29—21no—
34C22×D4×C29C2×C412yes—
35C29×AGL(1,ℤ/8)—44no—
36C2×SD16×C29—22no—
37C2×D8×C29—22no—
38C2×M16×C29—21no—
39C2×M16×C29—21no—
40C2×M16×C29C2×C412yes—
41C2×M16×C29D412yes—
42C22×C8×C29—22no—
43C29×#127—21no—
44C29×#127—21no—
45C29×#127—21no—
46C29×#127—21no—
47C4×Q8×C29D411yescharacteristic
48C4×Q8×C29D411yescharacteristic
49C4×D4×C29—21no—
50C4×D4×C29—21no—
51C4×D4×C29D411yescharacteristic
52C4×D4×C29D411yescharacteristic
53C29×#117—21no—
54C29×#117C2×C411yescharacteristic
55C2×C42×C29—21no—
56C2×C42×C29C2311yescharacteristic
57C29×C4⋊C8—22no—
58C29×C4⋊C8—21no—
59C29×C4⋊C8—21no—
60C29×C4⋊C8—21no—
61C29×C4⋊C8—21no—
62C29×C4⋊C8—21no—
63C29×C4⋊C8—21no—
64C29×C4⋊C8D411yescharacteristic
65C29×C4⋊C8D411yescharacteristic
66C29×#102—22no—
67C29×#102—22no—
68C29×#100—44no—
69C29×C22⋊C8—22no—
70C29×C22⋊C8—21no—
71C29×#97—22no—
72C29×#97—21no—
73C4×C8×C29—21no—
74C4×C8×C29—21no—
75C24×C29—22no—
76#41×C29—22no—
77#41×C29—41no—
78C2×Q8×C29C22⋊C411yescharacteristic
79C2×D4×C29—21no—
80C2×D4×C29—22no—
81C2×D4×C29—22no—
82C2×D4×C29—42no—
83C2×D4×C29—42no—
84C2×D4×C29—42no—
85C2×D4×C29—42no—
86C2×D4×C29—41no—
87C2×D4×C29—41no—
88C2×D4×C29—41no—
89C2×D4×C29—41no—
90C2×D4×C29—81no—
91C2×D4×C29—81no—
92C2×D4×C29C22⋊C411yescharacteristic
93C22×C4×C29—21no—
94C22×C4×C29—21no—
95C22×C4×C29—21no—
96C22×C4×C29C22×C411yescharacteristic
97C22×C4×C29C2×D411yescharacteristic
98C22×C4×C29#4111yescharacteristic
99SD16×C29—44no—
100D8×C29—44no—
101M16×C29—22no—
102M16×C29—41no—
103M16×C29—42no—
104M16×C29—42no—
105M16×C29—81no—
106C2×C8×C29—22no—
107C2×C8×C29—21no—
108C2×C8×C29—22no—
109C2×C8×C29—21no—
110C2×C8×C29—41no—
111C2×C8×C29—41no—
112C2×C8×C29—82no—
113C4⋊C4×C29—21no—
114C4⋊C4×C29—21no—
115C4⋊C4×C29C22⋊C411yescharacteristic
116C4⋊C4×C29C22⋊C411yescharacteristic
117C22⋊C4×C29—21no—
118C22⋊C4×C29—21no—
119C22⋊C4×C29—21no—
120C42×C29—21no—
121C42×C29—21no—
122C42×C29—21no—
123C42×C29C2×D411yescharacteristic
124C42×C29C2×D411yescharacteristic
125C42×C29C2×D411yescharacteristic
126C42×C29#4111yescharacteristic
127#9359C2911yesmaximal, characteristic, direct product factor, Sylow
128C23×C29—21no—
129C23×C29—44no—
130C23×C29—42no—
131C23×C29—82no—
132C23×C29—82no—
133C23×C29C4×D411yescharacteristic
134Q8×C29—21no—
135Q8×C29—21no—
136D4×C29—21no—
137D4×C29—42no—
138D4×C29—42no—
139D4×C29—42no—
140D4×C29—82no—
141D4×C29—82no—
142D4×C29—82no—
143D4×C29—81no—
144D4×C29—81no—
145D4×C29—81no—
146D4×C29—81no—
147D4×C29#10012yescomplemented
148C2×C4×C29—21no—
149C2×C4×C29—21no—
150C2×C4×C29—21no—
151C2×C4×C29—21no—
152C2×C4×C29—21no—
153C2×C4×C29—21no—
154C2×C4×C29—21no—
155C2×C4×C29—21no—
156C2×C4×C29—21no—
157C2×C4×C29—42no—
158C2×C4×C29—41no—
159C2×C4×C29—41no—
160C2×C4×C29—41no—
161C2×C4×C29—41no—
162C2×C4×C29C2×C22⋊C411yescharacteristic
163C2×C4×C29C4×D411yescharacteristic
164C2×C4×C29#12011yescharacteristic
165C2×C4×C29#12111yescharacteristic
166C2×C4×C29#12111yescharacteristic
167C2×C4×C29#12311yescharacteristic
168C8×C29—42no—
169C8×C29—42no—
170C8×C29—41no—
171C8×C29—42no—
172C8×C29—41no—
173C8×C29—81no—
174#3038C2×C2911yescharacteristic
175#2990C2×C2911yescharacteristic, complemented
176#1965C2×C2911yescharacteristic, complemented
177#1545C2×C2911yescharacteristic, complemented
178#1489C2×C2911yescharacteristic, complemented
179#1309C2×C2911yescharacteristic, complemented
180#1299C2×C2911yescharacteristic, complemented
181C22×C29—21no—
182C22×C29—21no—
183C22×C29—22no—
184C22×C29—21no—
185C22×C29—41no—
186C22×C29—41no—
187C22×C29—82no—
188C22×C29—82no—
189C22×C29—82no—
190C22×C29—164no—
191C22×C29#38611yescharacteristic
192C4×C29—21no—
193C4×C29—21no—
194C4×C29—21no—
195C4×C29—41no—
196C4×C29—41no—
197C4×C29—41no—
198C4×C29C2×#10011yescharacteristic
199C4×C29#41311yescharacteristic
200C4×C29#45311yescharacteristic
201C4×C29#45411yescharacteristic
202C4×C29#47111yescharacteristic
203C4×C29#47211yescharacteristic
204C2×AGL(1,ℤ/8)C4×C2912yes—
205C2×#127C22×C2911yescharacteristic
206C4×#41C22×C2911yescharacteristic
207#460—21no—
208#460—21no—
209#459—21no—
210#459—21no—
211#446—21no—
212#435—22no—
213C8×D4—21no—
214#432—21no—
215#431C22×C2911yescharacteristic
216#423C22×C2911yescharacteristic
217#423C22×C2911yescharacteristic
218#423C22×C2911yescharacteristic
219C2×C4⋊C8—21no—
220#418C4×C2912yes—
221C2×#100—22no—
222C4×M16C22×C2911yescharacteristic
223#331—21no—
224#331—21no—
225Q8⋊C8—21no—
226D4⋊C8—21no—
227C2×C29—41no—
228C2×C29—42no—
229C2×C29—162no—
230C2×C29#188311yescharacteristic
231C2×C29#190011yescharacteristic
232C2×C29#190711yescharacteristic
233C2×#41C2×C4×C2911yescharacteristic
234C22×D4—21no—
235C22×D4—21no—
236C22×D4C2×C4×C2912yes—
237AGL(1,ℤ/8)—44no—
238C2×SD16—22no—
239C2×D8—22no—
240C2×M16—21no—
241C2×M16—21no—
242C2×M16C2×C4×C2912yes—
243C2×M16D4×C2912yes—
244C22×C8—22no—
245#127—21no—
246#127—21no—
247#127—21no—
248#127—21no—
249C4×Q8D4×C2911yescharacteristic
250C4×Q8D4×C2911yescharacteristic
251C4×D4—21no—
252C4×D4—21no—
253C4×D4D4×C2911yescharacteristic
254C4×D4D4×C2911yescharacteristic
255#117—21no—
256#117C2×C4×C2911yescharacteristic
257C2×C42—21no—
258C2×C42C23×C2911yescharacteristic
259C4⋊C8—22no—
260C4⋊C8—21no—
261C4⋊C8—21no—
262C4⋊C8—21no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8D4×C2911yescharacteristic
267C4⋊C8D4×C2911yescharacteristic
268#102—22no—
269#102—22no—
270#100—44no—
271C22⋊C8—22no—
272C22⋊C8—21no—
273#97—22no—
274#97—21no—
275C4×C8—21no—
276C4×C8—21no—
277C29#935911yescharacteristic, direct product factor, Sylow
278C24—22no—
279#41—22no—
280#41—41no—
281C2×Q8C22⋊C4×C2911yescharacteristic
282C2×D4—21no—
283C2×D4—22no—
284C2×D4—22no—
285C2×D4—42no—
286C2×D4—42no—
287C2×D4—42no—
288C2×D4—42no—
289C2×D4—41no—
290C2×D4—41no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—81no—
294C2×D4—81no—
295C2×D4C22⋊C4×C2911yescharacteristic
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4C22×C4×C2911yescharacteristic
300C22×C4C2×D4×C2911yescharacteristic
301C22×C4#41×C2911yescharacteristic
302SD16—44no—
303D8—44no—
304M16—22no—
305M16—41no—
306M16—42no—
307M16—42no—
308M16—81no—
309C2×C8—22no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—22no—
313C2×C8—41no—
314C2×C8—41no—
315C2×C8—82no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4C22⋊C4×C2911yescharacteristic
319C4⋊C4C22⋊C4×C2911yescharacteristic
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—21no—
323C42—21no—
324C42—21no—
325C42—21no—
326C42C2×D4×C2911yescharacteristic
327C42C2×D4×C2911yescharacteristic
328C42C2×D4×C2911yescharacteristic
329C42#41×C2911yescharacteristic
330C23—21no—
331C23—44no—
332C23—42no—
333C23—82no—
334C23—82no—
335C23C4×D4×C2911yescharacteristic
336Q8—21no—
337Q8—21no—
338D4—21no—
339D4—42no—
340D4—42no—
341D4—42no—
342D4—82no—
343D4—82no—
344D4—82no—
345D4—81no—
346D4—81no—
347D4—81no—
348D4—81no—
349D4C29×#10012yescomplemented
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—42no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4C2×C22⋊C4×C2911yescharacteristic
365C2×C4C4×D4×C2911yescharacteristic
366C2×C4C29×#12011yescharacteristic
367C2×C4C29×#12111yescharacteristic
368C2×C4C29×#12111yescharacteristic
369C2×C4C29×#12311yescharacteristic
370C8—42no—
371C8—41no—
372C8—42no—
373C8—41no—
374C8—42no—
375C8—81no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—22no—
380C22—41no—
381C22—41no—
382C22—82no—
383C22—82no—
384C22—82no—
385C22—164no—
386C22C29×#38611yescharacteristic
387C4—21no—
388C4—21no—
389C4—21no—
390C4—41no—
391C4—41no—
392C4—41no—
393C4C2×C29×#10011yescharacteristic
394C4C29×#41311yescharacteristic
395C4C29×#45311yescharacteristic
396C4C29×#45411yescharacteristic
397C4C29×#47111yescharacteristic
398C4C29×#47211yescharacteristic
399C2—41no—
400C2—42no—
401C2—162no—
402C2C29×#188311yescharacteristic
403C2C29×#190011yescharacteristic
404C2C29×#190711yescharacteristic
subgroupG/H
center, socleC22×C29#386
commutatorC22×C4C22×C4×C29
Frattini, cosocleC2×C42C23×C29
prime radicalC29×#3038C2
LCSG ▷ C22×C4 ▷ 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×#2990C2semidirect
3. C29×#1965C2semidirect
4. C29×#1545C2semidirect
5. C29×#1489C2semidirect
6. C29×#1309C2semidirect
7. C29×#1299C2semidirect
127. #9359C29direct (N × H)
147. D4×C29#100semidirect
175. #2990C2×C29semidirect
176. #1965C2×C29semidirect
177. #1545C2×C29semidirect
178. #1489C2×C29semidirect
179. #1309C2×C29semidirect
180. #1299C2×C29semidirect
277. C29#9359direct (N × H)
349. D4C29×#100semidirect

Maximal subgroups

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

subgroupindex
C29×#30382
C29×#29902
C29×#19652
C29×#15452
C29×#14892
C29×#13092
C29×#12992
#935929