Finite Group Databasebeta

← C29×#9449 #20304349

Subgroups — C29×#9449 #20304349

Order 7424.

490 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#2973C211yesmaximal, characteristic
2C29×#2566C211yesmaximal, characteristic
3C29×#1534C212yesmaximal, complemented
4C29×#1466C211yesmaximal, characteristic
5C29×#1285C212yesmaximal, complemented
6C2×C29×#125C2211yescharacteristic
7C2×C4×D4×C29C2211yescharacteristic
8C29×#435—24no—
9C29×#432C2212yes—
10C29×#432C2212yes—
11C29×#407—21no—
12C2×C29×C22⋊C8—21no—
13C29×#396—21no—
14C29×#396—21no—
15C29×#390C411yescharacteristic
16C29×#390C411yescharacteristic
17C29×#385—21no—
18C29×#385—21no—
19C29×#384C411yescharacteristic
20C29×#382C411yescharacteristic
21C4×C4⋊C4×C29C2211yescharacteristic
22C29×#330—24no—
23C29×#323—21no—
24C29×#323—21no—
25C22×D4×C29C2×C411yescharacteristic
26C23×C4×C29D411yescharacteristic
27C23×C4×C29D411yescharacteristic
28C2×M16×C29—22no—
29C22×C8×C29—22no—
30C29×#125—22no—
31C29×#125—22no—
32C4×D4×C29—22no—
33C4×D4×C29—22no—
34C2×C4⋊C4×C29—21no—
35C2×C4⋊C4×C29—21no—
36C2×C4⋊C4×C29—21no—
37C2×C4⋊C4×C29—21no—
38C2×C4⋊C4×C29—21no—
39C2×C4⋊C4×C29C2×C411yescharacteristic
40C2×C4⋊C4×C29C2×C411yescharacteristic
41C2×C4⋊C4×C29C2×C411yescharacteristic
42C2×C22⋊C4×C29—21no—
43C2×C22⋊C4×C29—21no—
44C2×C22⋊C4×C29—21no—
45C2×C22⋊C4×C29—21no—
46C2×C22⋊C4×C29D411yescharacteristic
47C2×C22⋊C4×C29D411yescharacteristic
48C2×C42×C29C2×C411yescharacteristic
49C2×C42×C29C2×C411yescharacteristic
50C2×C42×C29C2311yescharacteristic
51C29×C4⋊C8—22no—
52C29×C4⋊C8—22no—
53C29×C22⋊C8—22no—
54C29×C22⋊C8—22no—
55C29×C22⋊C8—22no—
56C29×C22⋊C8—22no—
57C29×#97—22no—
58C29×#97D414yes—
59C29×#95—21no—
60C29×#95—21no—
61C29×#95—21no—
62C24×C29C22⋊C411yescharacteristic
63C24×C29C22⋊C411yescharacteristic
64C2×D4×C29—22no—
65C2×D4×C29—22no—
66C2×D4×C29—41no—
67C22×C4×C29—21no—
68C22×C4×C29—21no—
69C22×C4×C29—21no—
70C22×C4×C29—21no—
71C22×C4×C29—21no—
72C22×C4×C29—21no—
73C22×C4×C29—21no—
74C22×C4×C29—21no—
75C22×C4×C29—81no—
76C22×C4×C29—81no—
77C22×C4×C29C22⋊C411yescharacteristic
78C22×C4×C29C22⋊C411yescharacteristic
79C22×C4×C29C22×C411yescharacteristic
80C22×C4×C29C2×D411yescharacteristic
81C22×C4×C29C2×D411yescharacteristic
82M16×C29—82no—
83C2×C8×C29—24no—
84C2×C8×C29—42no—
85C2×C8×C29—82no—
86C4⋊C4×C29—22no—
87C4⋊C4×C29—22no—
88C4⋊C4×C29—22no—
89C4⋊C4×C29—42no—
90C4⋊C4×C29—41no—
91C4⋊C4×C29—42no—
92C4⋊C4×C29—41no—
93C4⋊C4×C29—81no—
94C4⋊C4×C29—81no—
95C22⋊C4×C29—22no—
96C22⋊C4×C29—22no—
97C22⋊C4×C29—42no—
98C22⋊C4×C29—42no—
99C22⋊C4×C29—81no—
100C22⋊C4×C29—81no—
101C42×C29—41no—
102C42×C29—41no—
103C42×C29C2×D412yes—
104C42×C29#4112yes—
105#9449C2911yesmaximal, characteristic, direct product factor, Sylow
106C23×C29—21no—
107C23×C29—21no—
108C23×C29—21no—
109C23×C29—21no—
110C23×C29—21no—
111C23×C29—41no—
112C23×C29—41no—
113C23×C29—41no—
114C23×C29—41no—
115C23×C29#10112yes—
116C23×C29C2×C22⋊C411yescharacteristic
117D4×C29—44no—
118C2×C4×C29—21no—
119C2×C4×C29—21no—
120C2×C4×C29—22no—
121C2×C4×C29—21no—
122C2×C4×C29—21no—
123C2×C4×C29—41no—
124C2×C4×C29—41no—
125C2×C4×C29—42no—
126C2×C4×C29—42no—
127C2×C4×C29—41no—
128C2×C4×C29—41no—
129C2×C4×C29—41no—
130C2×C4×C29—41no—
131C2×C4×C29—41no—
132C2×C4×C29—41no—
133C2×C4×C29—41no—
134C2×C4×C29—41no—
135C2×C4×C29—41no—
136C2×C4×C29—41no—
137C2×C4×C29—41no—
138C2×C4×C29—41no—
139C2×C4×C29—41no—
140C2×C4×C29—81no—
141C2×C4×C29—81no—
142C2×C4×C29C4×D412yes—
143C2×C4×C29#12011yescharacteristic
144C2×C4×C29#12112yes—
145C2×C4×C29#12311yescharacteristic
146C8×C29—44no—
147C8×C29—82no—
148#2973C2×C2911yescharacteristic
149#2566C2×C2911yescharacteristic
150#1534C2×C2912yescomplemented
151#1466C2×C2911yescharacteristic
152#1285C2×C2912yescomplemented
153C22×C29—21no—
154C22×C29—21no—
155C22×C29—22no—
156C22×C29—42no—
157C22×C29—42no—
158C22×C29—41no—
159C22×C29—41no—
160C22×C29—41no—
161C22×C29—41no—
162C22×C29—41no—
163C22×C29—81no—
164C22×C29—81no—
165C22×C29#38611yescharacteristic
166C22×C29C2×#10111yescharacteristic
167C22×C29#41311yescharacteristic
168C4×C29—22no—
169C4×C29—22no—
170C4×C29—21no—
171C4×C29—21no—
172C4×C29—42no—
173C4×C29—41no—
174C4×C29—41no—
175C4×C29—81no—
176C4×C29—81no—
177C4×C29—81no—
178C2×#125C22×C2911yescharacteristic
179C2×C4×D4C22×C2911yescharacteristic
180#435—24no—
181#432C22×C2912yes—
182#432C22×C2912yes—
183#407—21no—
184C2×C22⋊C8—21no—
185#396—21no—
186#396—21no—
187#390C4×C2911yescharacteristic
188#390C4×C2911yescharacteristic
189#385—21no—
190#385—21no—
191#384C4×C2911yescharacteristic
192#382C4×C2911yescharacteristic
193C4×C4⋊C4C22×C2911yescharacteristic
194#330—24no—
195#323—21no—
196#323—21no—
197C2×C29—21no—
198C2×C29—21no—
199C2×C29—42no—
200C2×C29—81no—
201C2×C29#188411yescharacteristic
202C2×C29#190111yescharacteristic
203C2×C29#191111yescharacteristic
204C22×D4C2×C4×C2911yescharacteristic
205C23×C4D4×C2911yescharacteristic
206C23×C4D4×C2911yescharacteristic
207C2×M16—22no—
208C22×C8—22no—
209#125—22no—
210#125—22no—
211C4×D4—22no—
212C4×D4—22no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4C2×C4×C2911yescharacteristic
219C2×C4⋊C4C2×C4×C2911yescharacteristic
220C2×C4⋊C4C2×C4×C2911yescharacteristic
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4D4×C2911yescharacteristic
226C2×C22⋊C4D4×C2911yescharacteristic
227C2×C42C2×C4×C2911yescharacteristic
228C2×C42C2×C4×C2911yescharacteristic
229C2×C42C23×C2911yescharacteristic
230C4⋊C8—22no—
231C4⋊C8—22no—
232C22⋊C8—22no—
233C22⋊C8—22no—
234C22⋊C8—22no—
235C22⋊C8—22no—
236#97—22no—
237#97D4×C2914yes—
238#95—21no—
239#95—21no—
240#95—21no—
241C29#944911yescharacteristic, direct product factor, Sylow
242C24C22⋊C4×C2911yescharacteristic
243C24C22⋊C4×C2911yescharacteristic
244C2×D4—22no—
245C2×D4—22no—
246C2×D4—41no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—81no—
256C22×C4—81no—
257C22×C4C22⋊C4×C2911yescharacteristic
258C22×C4C22⋊C4×C2911yescharacteristic
259C22×C4C22×C4×C2911yescharacteristic
260C22×C4C2×D4×C2911yescharacteristic
261C22×C4C2×D4×C2911yescharacteristic
262M16—82no—
263C2×C8—24no—
264C2×C8—42no—
265C2×C8—82no—
266C4⋊C4—22no—
267C4⋊C4—22no—
268C4⋊C4—22no—
269C4⋊C4—42no—
270C4⋊C4—41no—
271C4⋊C4—42no—
272C4⋊C4—41no—
273C4⋊C4—81no—
274C4⋊C4—81no—
275C22⋊C4—22no—
276C22⋊C4—22no—
277C22⋊C4—42no—
278C22⋊C4—42no—
279C22⋊C4—81no—
280C22⋊C4—81no—
281C42—41no—
282C42—41no—
283C42C2×D4×C2912yes—
284C42#41×C2912yes—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23C29×#10112yes—
295C23C2×C22⋊C4×C2911yescharacteristic
296D4—44no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—22no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4C4×D4×C2912yes—
322C2×C4C29×#12011yescharacteristic
323C2×C4C29×#12112yes—
324C2×C4C29×#12311yescharacteristic
325C8—44no—
326C8—82no—
327C22—21no—
328C22—21no—
329C22—22no—
330C22—42no—
331C22—42no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—81no—
338C22—81no—
339C22C29×#38611yescharacteristic
340C22C2×C29×#10111yescharacteristic
341C22C29×#41311yescharacteristic
342C4—21no—
343C4—21no—
344C4—22no—
345C4—22no—
346C4—42no—
347C4—41no—
348C4—41no—
349C4—81no—
350C4—81no—
351C4—81no—
352C2—21no—
353C2—21no—
354C2—42no—
355C2—81no—
356C2C29×#188411yescharacteristic
357C2C29×#190111yescharacteristic
358C2C29×#191111yescharacteristic
subgroupG/H
center, socleC22×C29#386
commutatorC22×C4C22×C4×C29
Frattini, cosocleC2×C42C23×C29
prime radicalC22×D4×C29C2×C4
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
3. C29×#1534C2semidirect
5. C29×#1285C2semidirect
105. #9449C29direct (N × H)
150. #1534C2×C29semidirect
152. #1285C2×C29semidirect
241. C29#9449direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#29732
C29×#25662
C29×#15342
C29×#14662
C29×#12852
#944929