Finite Group Databasebeta

← C29×#9035 #20303935

Subgroups — C29×#9035 #20303935

Order 7424.

612 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#2905C211yesmaximal, characteristic, complemented
2C29×#2392C211yesmaximal, characteristic
3C29×#1486C212yesmaximal, complemented
4C29×#1458C211yesmaximal, characteristic, complemented
5C29×#1303C212yesmaximal, complemented
6C22×M16×C29—21no—
7C2×C4×D4×C29—21no—
8C2×C4×D4×C29C2211yescharacteristic
9C2×C29×#117C2211yescharacteristic
10C29×#431C2212yes—
11C29×#424—24no—
12C29×#423—21no—
13C29×#423C2212yes—
14C29×#398C411yescharacteristic
15C29×#397C411yescharacteristic
16C29×#396—21no—
17C29×#394—21no—
18C29×#394C411yescharacteristic
19C29×#392C411yescharacteristic
20C4×C4⋊C4×C29C2211yescharacteristic
21C4×C22⋊C4×C29—21no—
22C29×D4⋊C8—24no—
23C29×#324—21no—
24C29×#323—21no—
25C22×D4×C29—21no—
26C22×D4×C29C2×C411yescharacteristic
27C23×C4×C29—21no—
28C23×C4×C29D411yescharacteristic
29C2×M16×C29—22no—
30C2×M16×C29—22no—
31C2×M16×C29—42no—
32C2×M16×C29—42no—
33C22×C8×C29—22no—
34C4×D4×C29—22no—
35C4×D4×C29—22no—
36C4×D4×C29—42no—
37C4×D4×C29—42no—
38C29×#117—22no—
39C29×#117—22no—
40C2×C4⋊C4×C29—21no—
41C2×C4⋊C4×C29—21no—
42C2×C4⋊C4×C29C2×C411yescharacteristic
43C2×C4⋊C4×C29C2×C411yescharacteristic
44C2×C4⋊C4×C29D411yescharacteristic
45C2×C22⋊C4×C29—21no—
46C2×C22⋊C4×C29—21no—
47C2×C22⋊C4×C29—21no—
48C2×C22⋊C4×C29—21no—
49C2×C22⋊C4×C29—21no—
50C2×C22⋊C4×C29C2×C411yescharacteristic
51C2×C22⋊C4×C29D411yescharacteristic
52C2×C42×C29—21no—
53C2×C42×C29D411yescharacteristic
54C2×C42×C29C2311yescharacteristic
55C29×C4⋊C8—24no—
56C29×C4⋊C8—22no—
57C29×C4⋊C8—22no—
58C29×C4⋊C8D414yescomplemented
59C29×C22⋊C8—22no—
60C4×C8×C29—22no—
61C29×#95—21no—
62C29×#95—21no—
63C29×#95C2×C411yescharacteristic
64C29×#95C2×C411yescharacteristic
65C24×C29—21no—
66C24×C29C22⋊C411yescharacteristic
67C2×D4×C29—22no—
68C2×D4×C29—42no—
69C2×D4×C29—42no—
70C2×D4×C29—42no—
71C2×D4×C29—42no—
72C22×C4×C29—21no—
73C22×C4×C29—21no—
74C22×C4×C29—21no—
75C22×C4×C29—21no—
76C22×C4×C29—21no—
77C22×C4×C29—21no—
78C22×C4×C29—21no—
79C22×C4×C29—41no—
80C22×C4×C29—41no—
81C22×C4×C29—41no—
82C22×C4×C29—41no—
83C22×C4×C29—41no—
84C22×C4×C29—41no—
85C22×C4×C29C22⋊C411yescharacteristic
86C22×C4×C29C22⋊C411yescharacteristic
87C22×C4×C29C22⋊C411yescharacteristic
88C22×C4×C29D812yes—
89C22×C4×C29SD1612yes—
90C22×C4×C29C22×C411yescharacteristic
91C22×C4×C29C2×D411yescharacteristic
92C22×C4×C29C2×D411yescharacteristic
93M16×C29—44no—
94M16×C29—42no—
95M16×C29—42no—
96C2×C8×C29—24no—
97C2×C8×C29—44no—
98C2×C8×C29—42no—
99C4⋊C4×C29—22no—
100C4⋊C4×C29—22no—
101C4⋊C4×C29—22no—
102C4⋊C4×C29—42no—
103C4⋊C4×C29—42no—
104C22⋊C4×C29—22no—
105C22⋊C4×C29—22no—
106C22⋊C4×C29—42no—
107C22⋊C4×C29—42no—
108C22⋊C4×C29—42no—
109C22⋊C4×C29—42no—
110C22⋊C4×C29—42no—
111C42×C29—21no—
112C42×C29—21no—
113C42×C29—41no—
114C42×C29—41no—
115C42×C29C2×D412yes—
116C42×C29#4112yes—
117#9035C2911yesmaximal, characteristic, direct product factor, Sylow
118C23×C29—21no—
119C23×C29—21no—
120C23×C29—22no—
121C23×C29—41no—
122C23×C29—41no—
123C23×C29—41no—
124C23×C29—41no—
125C23×C29—41no—
126C23×C29—41no—
127C23×C29—41no—
128C23×C29—41no—
129C23×C29#10212yes—
130C23×C29C2×C22⋊C411yescharacteristic
131D4×C29—24no—
132D4×C29—42no—
133D4×C29—48no—
134C2×C4×C29—21no—
135C2×C4×C29—21no—
136C2×C4×C29—22no—
137C2×C4×C29—22no—
138C2×C4×C29—22no—
139C2×C4×C29—22no—
140C2×C4×C29—22no—
141C2×C4×C29—21no—
142C2×C4×C29—21no—
143C2×C4×C29—41no—
144C2×C4×C29—41no—
145C2×C4×C29—41no—
146C2×C4×C29—41no—
147C2×C4×C29—41no—
148C2×C4×C29—41no—
149C2×C4×C29—41no—
150C2×C4×C29—41no—
151C2×C4×C29—41no—
152C2×C4×C29—41no—
153C2×C4×C29—41no—
154C2×C4×C29—41no—
155C2×C4×C29—81no—
156C2×C4×C29—81no—
157C2×C4×C29—81no—
158C2×C4×C29—81no—
159C2×C4×C29#10212yes—
160C2×C4×C29C4×D412yes—
161C2×C4×C29#12011yescharacteristic
162C2×C4×C29#12112yes—
163C2×C4×C29#12311yescharacteristic
164C2×C4×C29C2×D811yescharacteristic
165C2×C4×C29C2×SD1611yescharacteristic
166C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C29#13711yescharacteristic
168C8×C29—44no—
169C8×C29—82no—
170#2905C2×C2911yescharacteristic, complemented
171#2392C2×C2911yescharacteristic
172#1486C2×C2912yescomplemented
173#1458C2×C2911yescharacteristic, complemented
174#1303C2×C2912yescomplemented
175C22×C29—21no—
176C22×C29—21no—
177C22×C29—22no—
178C22×C29—42no—
179C22×C29—42no—
180C22×C29—42no—
181C22×C29—41no—
182C22×C29—41no—
183C22×C29—42no—
184C22×C29—81no—
185C22×C29—81no—
186C22×C29—81no—
187C22×C29—81no—
188C22×C29—81no—
189C22×C29#38611yescharacteristic
190C22×C29C2×#10211yescharacteristic
191C22×C29#41711yescharacteristic
192C4×C29—22no—
193C4×C29—22no—
194C4×C29—22no—
195C4×C29—42no—
196C4×C29—41no—
197C4×C29—41no—
198C4×C29—81no—
199C4×C29—81no—
200C4×C29#44711yescharacteristic
201C4×C29#44811yescharacteristic
202C4×C29#48011yescharacteristic
203C4×C29#48111yescharacteristic
204C22×M16—21no—
205C2×C4×D4—21no—
206C2×C4×D4C22×C2911yescharacteristic
207C2×#117C22×C2911yescharacteristic
208#431C22×C2912yes—
209#424—24no—
210#423—21no—
211#423C22×C2912yes—
212#398C4×C2911yescharacteristic
213#397C4×C2911yescharacteristic
214#396—21no—
215#394—21no—
216#394C4×C2911yescharacteristic
217#392C4×C2911yescharacteristic
218C4×C4⋊C4C22×C2911yescharacteristic
219C4×C22⋊C4—21no—
220D4⋊C8—24no—
221#324—21no—
222#323—21no—
223C2×C29—21no—
224C2×C29—21no—
225C2×C29—42no—
226C2×C29—82no—
227C2×C29#187411yescharacteristic
228C2×C29#188411yescharacteristic
229C2×C29#189111yescharacteristic
230C22×D4—21no—
231C22×D4C2×C4×C2911yescharacteristic
232C23×C4—21no—
233C23×C4D4×C2911yescharacteristic
234C2×M16—22no—
235C2×M16—22no—
236C2×M16—42no—
237C2×M16—42no—
238C22×C8—22no—
239C4×D4—22no—
240C4×D4—22no—
241C4×D4—42no—
242C4×D4—42no—
243#117—22no—
244#117—22no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4C2×C4×C2911yescharacteristic
248C2×C4⋊C4C2×C4×C2911yescharacteristic
249C2×C4⋊C4D4×C2911yescharacteristic
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—21no—
255C2×C22⋊C4C2×C4×C2911yescharacteristic
256C2×C22⋊C4D4×C2911yescharacteristic
257C2×C42—21no—
258C2×C42D4×C2911yescharacteristic
259C2×C42C23×C2911yescharacteristic
260C4⋊C8—24no—
261C4⋊C8—22no—
262C4⋊C8—22no—
263C4⋊C8D4×C2914yescomplemented
264C22⋊C8—22no—
265C4×C8—22no—
266#95—21no—
267#95—21no—
268#95C2×C4×C2911yescharacteristic
269#95C2×C4×C2911yescharacteristic
270C29#903511yescharacteristic, direct product factor, Sylow
271C24—21no—
272C24C22⋊C4×C2911yescharacteristic
273C2×D4—22no—
274C2×D4—42no—
275C2×D4—42no—
276C2×D4—42no—
277C2×D4—42no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4C22⋊C4×C2911yescharacteristic
292C22×C4C22⋊C4×C2911yescharacteristic
293C22×C4C22⋊C4×C2911yescharacteristic
294C22×C4D8×C2912yes—
295C22×C4SD16×C2912yes—
296C22×C4C22×C4×C2911yescharacteristic
297C22×C4C2×D4×C2911yescharacteristic
298C22×C4C2×D4×C2911yescharacteristic
299M16—44no—
300M16—42no—
301M16—42no—
302C2×C8—24no—
303C2×C8—44no—
304C2×C8—42no—
305C4⋊C4—22no—
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4—42no—
309C4⋊C4—42no—
310C22⋊C4—22no—
311C22⋊C4—22no—
312C22⋊C4—42no—
313C22⋊C4—42no—
314C22⋊C4—42no—
315C22⋊C4—42no—
316C22⋊C4—42no—
317C42—21no—
318C42—21no—
319C42—41no—
320C42—41no—
321C42C2×D4×C2912yes—
322C42#41×C2912yes—
323C23—21no—
324C23—21no—
325C23—22no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23C29×#10212yes—
335C23C2×C22⋊C4×C2911yescharacteristic
336D4—24no—
337D4—42no—
338D4—48no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4—81no—
364C2×C4C29×#10212yes—
365C2×C4C4×D4×C2912yes—
366C2×C4C29×#12011yescharacteristic
367C2×C4C29×#12112yes—
368C2×C4C29×#12311yescharacteristic
369C2×C4C2×D8×C2911yescharacteristic
370C2×C4C2×SD16×C2911yescharacteristic
371C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
372C2×C4C29×#13711yescharacteristic
373C8—44no—
374C8—82no—
375C22—21no—
376C22—21no—
377C22—22no—
378C22—42no—
379C22—42no—
380C22—42no—
381C22—41no—
382C22—41no—
383C22—42no—
384C22—81no—
385C22—81no—
386C22—81no—
387C22—81no—
388C22—81no—
389C22C29×#38611yescharacteristic
390C22C2×C29×#10211yescharacteristic
391C22C29×#41711yescharacteristic
392C4—22no—
393C4—22no—
394C4—22no—
395C4—42no—
396C4—41no—
397C4—41no—
398C4—81no—
399C4—81no—
400C4C29×#44711yescharacteristic
401C4C29×#44811yescharacteristic
402C4C29×#48011yescharacteristic
403C4C29×#48111yescharacteristic
404C2—21no—
405C2—21no—
406C2—42no—
407C2—82no—
408C2C29×#187411yescharacteristic
409C2C29×#188411yescharacteristic
410C2C29×#189111yescharacteristic
subgroupG/H
centerC2×C4×C29#120
commutatorC22×C4C22×C4×C29
Frattini, cosocleC2×C42C23×C29
socleC22×C29#386
prime radicalC29×#392C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#2905C2semidirect
3. C29×#1486C2semidirect
4. C29×#1458C2semidirect
5. C29×#1303C2semidirect
58. C29×C4⋊C8D4semidirect
117. #9035C29direct (N × H)
170. #2905C2×C29semidirect
172. #1486C2×C29semidirect
173. #1458C2×C29semidirect
174. #1303C2×C29semidirect
263. C4⋊C8D4×C29semidirect
270. C29#9035direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#29052
C29×#23922
C29×#14862
C29×#14582
C29×#13032
#903529