Finite Group Databasebeta

← C29×#9789 #20304689

Subgroups — C29×#9789 #20304689

Order 7424.

392 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#488C211yesmaximal, characteristic
2C29×#1568C211yesmaximal, characteristic, complemented
3C29×#1528C211yesmaximal, characteristic, complemented
4C29×#1527C211yesmaximal, characteristic
5C29×#1470C211yesmaximal, characteristic, complemented
6C29×#1469C211yesmaximal, characteristic
7C8×M16×C29C211yesmaximal, characteristic, complemented
8C2×C29×#125C2211yescharacteristic
9C2×C29×#124C2211yescharacteristic
10C29×#488—21no—
11C29×#488—21no—
12C29×#488—21no—
13C29×#488—21no—
14C29×#432C2211yescharacteristic
15C29×#432C2211yescharacteristic
16C29×#431C2211yescharacteristic
17C2×C29×#103C411yescharacteristic
18C2×C29×#103C411yescharacteristic
19C2×C29×#102C411yescharacteristic
20C2×C29×#102C411yescharacteristic
21C4×M16×C29C2211yescharacteristic
22C2×C4×C8×C29C2211yescharacteristic
23C29×#335—21no—
24C29×#334—21no—
25C29×#330—22no—
26C29×#329—22no—
27C29×#324—22no—
28C29×#323—22no—
29C29×#322—21no—
30C82×C29—21no—
31C22×Q8×C29C2×C411yescharacteristic
32C22×D4×C29C2×C411yescharacteristic
33C2×M16×C29—21no—
34C22×C8×C29C2×C411yescharacteristic
35C22×C8×C29C2×C411yescharacteristic
36C29×#125—21no—
37C29×#125—21no—
38C29×#125—21no—
39C29×#125—21no—
40C29×#124—21no—
41C29×#124—21no—
42C29×#124—21no—
43C29×#124—21no—
44C2×C4⋊C4×C29—21no—
45C2×C4⋊C4×C29—21no—
46C2×C4⋊C4×C29C2×C411yescharacteristic
47C2×C4⋊C4×C29C2×C411yescharacteristic
48C2×C22⋊C4×C29—21no—
49C2×C22⋊C4×C29—21no—
50C2×C42×C29C2311yescharacteristic
51C29×C4⋊C8—21no—
52C29×C4⋊C8—21no—
53C29×C4⋊C8—21no—
54C29×#103—21no—
55C29×#103—21no—
56C29×#103—21no—
57C29×#103—21no—
58C29×#102—21no—
59C29×#102—21no—
60C29×#102—21no—
61C29×#102—21no—
62C29×C22⋊C8—21no—
63C29×C22⋊C8—21no—
64C29×C22⋊C8D412yes—
65C29×#97—21no—
66C29×#97—21no—
67C29×#97D412yes—
68C4×C8×C29—21no—
69C4×C8×C29—21no—
70C4×C8×C29D411yescharacteristic
71C4×C8×C29D411yescharacteristic
72C4×C8×C29D411yescharacteristic
73C4×C8×C29D411yescharacteristic
74C24×C29—21no—
75C2×Q8×C29—21no—
76C2×Q8×C29—21no—
77C2×Q8×C29—41no—
78C2×Q8×C29—41no—
79C2×D4×C29—21no—
80C2×D4×C29—21no—
81C2×D4×C29—41no—
82C2×D4×C29—41no—
83C22×C4×C29—21no—
84C22×C4×C29—21no—
85C22×C4×C29—21no—
86C22×C4×C29C22×C411yescharacteristic
87C22×C4×C29C2×D411yescharacteristic
88C22×C4×C29#4111yescharacteristic
89M16×C29—24no—
90C2×C8×C29—22no—
91C2×C8×C29—22no—
92C2×C8×C29—41no—
93C2×C8×C29—41no—
94C2×C8×C29—41no—
95C2×C8×C29—41no—
96C2×C8×C29C22⋊C411yescharacteristic
97C2×C8×C29C22⋊C411yescharacteristic
98C2×C8×C29C22⋊C411yescharacteristic
99C2×C8×C29C22⋊C411yescharacteristic
100C4⋊C4×C29—21no—
101C4⋊C4×C29—21no—
102C4⋊C4×C29—21no—
103C4⋊C4×C29—21no—
104C4⋊C4×C29—41no—
105C4⋊C4×C29—41no—
106C4⋊C4×C29—41no—
107C4⋊C4×C29—41no—
108C22⋊C4×C29—41no—
109C22⋊C4×C29—41no—
110C22⋊C4×C29—41no—
111C22⋊C4×C29—41no—
112C42×C29C2×D411yescharacteristic
113C42×C29C2×D411yescharacteristic
114C42×C29C2×D411yescharacteristic
115C42×C29#4111yescharacteristic
116#9789C2911yesmaximal, characteristic, direct product factor, Sylow
117C23×C29—41no—
118C23×C29—42no—
119C23×C29—81no—
120C23×C29—81no—
121C23×C29C4×D411yescharacteristic
122Q8×C29—41no—
123Q8×C29—41no—
124Q8×C29—81no—
125D4×C29—41no—
126D4×C29—41no—
127D4×C29—81no—
128C2×C4×C29—22no—
129C2×C4×C29—21no—
130C2×C4×C29—21no—
131C2×C4×C29—41no—
132C2×C4×C29—41no—
133C2×C4×C29—41no—
134C2×C4×C29—41no—
135C2×C4×C29—42no—
136C2×C4×C29—81no—
137C2×C4×C29—81no—
138C2×C4×C29C2×C22⋊C411yescharacteristic
139C2×C4×C29C4×D411yescharacteristic
140C2×C4×C29#12111yescharacteristic
141C2×C4×C29#12111yescharacteristic
142C2×C4×C29#12411yescharacteristic
143C2×C4×C29#12711yescharacteristic
144C8×C29—24no—
145C8×C29—21no—
146C8×C29—21no—
147C8×C29—21no—
148C8×C29—21no—
149C8×C29—42no—
150C8×C29—81no—
151C8×C29—81no—
152C2×#488C2×C2911yescharacteristic
153#1568C2×C2911yescharacteristic, complemented
154#1528C2×C2911yescharacteristic, complemented
155#1527C2×C2911yescharacteristic
156#1470C2×C2911yescharacteristic, complemented
157#1469C2×C2911yescharacteristic
158C8×M16C2×C2911yescharacteristic, complemented
159C22×C29—21no—
160C22×C29—21no—
161C22×C29—81no—
162C22×C29—81no—
163C22×C29—81no—
164C22×C29—162no—
165C22×C29#39011yescharacteristic
166C22×C29#44312yes—
167C4×C29—21no—
168C4×C29—21no—
169C4×C29—21no—
170C4×C29—21no—
171C4×C29—21no—
172C4×C29—81no—
173C4×C29—81no—
174C4×C29—81no—
175C4×C29#41311yescharacteristic
176C4×C29#41311yescharacteristic
177C2×#125C22×C2911yescharacteristic
178C2×#124C22×C2911yescharacteristic
179#488—21no—
180#488—21no—
181#488—21no—
182#488—21no—
183#432C22×C2911yescharacteristic
184#432C22×C2911yescharacteristic
185#431C22×C2911yescharacteristic
186C2×#103C4×C2911yescharacteristic
187C2×#103C4×C2911yescharacteristic
188C2×#102C4×C2911yescharacteristic
189C2×#102C4×C2911yescharacteristic
190C4×M16C22×C2911yescharacteristic
191C2×C4×C8C22×C2911yescharacteristic
192#335—21no—
193#334—21no—
194#330—22no—
195#329—22no—
196#324—22no—
197#323—22no—
198#322—21no—
199C82—21no—
200C2×C29—22no—
201C2×C29—161no—
202C2×C29#196711yescharacteristic
203C2×C29#197411yescharacteristic
204C2×C29#197611yescharacteristic
205C22×Q8C2×C4×C2911yescharacteristic
206C22×D4C2×C4×C2911yescharacteristic
207C2×M16—21no—
208C22×C8C2×C4×C2911yescharacteristic
209C22×C8C2×C4×C2911yescharacteristic
210#125—21no—
211#125—21no—
212#125—21no—
213#125—21no—
214#124—21no—
215#124—21no—
216#124—21no—
217#124—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4C2×C4×C2911yescharacteristic
221C2×C4⋊C4C2×C4×C2911yescharacteristic
222C2×C22⋊C4—21no—
223C2×C22⋊C4—21no—
224C2×C42C23×C2911yescharacteristic
225C4⋊C8—21no—
226C4⋊C8—21no—
227C4⋊C8—21no—
228#103—21no—
229#103—21no—
230#103—21no—
231#103—21no—
232#102—21no—
233#102—21no—
234#102—21no—
235#102—21no—
236C22⋊C8—21no—
237C22⋊C8—21no—
238C22⋊C8D4×C2912yes—
239#97—21no—
240#97—21no—
241#97D4×C2912yes—
242C4×C8—21no—
243C4×C8—21no—
244C4×C8D4×C2911yescharacteristic
245C4×C8D4×C2911yescharacteristic
246C4×C8D4×C2911yescharacteristic
247C4×C8D4×C2911yescharacteristic
248C29#978911yescharacteristic, direct product factor, Sylow
249C24—21no—
250C2×Q8—21no—
251C2×Q8—21no—
252C2×Q8—41no—
253C2×Q8—41no—
254C2×D4—21no—
255C2×D4—21no—
256C2×D4—41no—
257C2×D4—41no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4C22×C4×C2911yescharacteristic
262C22×C4C2×D4×C2911yescharacteristic
263C22×C4#41×C2911yescharacteristic
264M16—24no—
265C2×C8—22no—
266C2×C8—22no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8—41no—
270C2×C8—41no—
271C2×C8C22⋊C4×C2911yescharacteristic
272C2×C8C22⋊C4×C2911yescharacteristic
273C2×C8C22⋊C4×C2911yescharacteristic
274C2×C8C22⋊C4×C2911yescharacteristic
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C22⋊C4—41no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C42C2×D4×C2911yescharacteristic
288C42C2×D4×C2911yescharacteristic
289C42C2×D4×C2911yescharacteristic
290C42#41×C2911yescharacteristic
291C23—41no—
292C23—42no—
293C23—81no—
294C23—81no—
295C23C4×D4×C2911yescharacteristic
296Q8—41no—
297Q8—41no—
298Q8—81no—
299D4—41no—
300D4—41no—
301D4—81no—
302C2×C4—22no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—41no—
306C2×C4—42no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4C2×C22⋊C4×C2911yescharacteristic
313C2×C4C4×D4×C2911yescharacteristic
314C2×C4C29×#12111yescharacteristic
315C2×C4C29×#12111yescharacteristic
316C2×C4C29×#12411yescharacteristic
317C2×C4C29×#12711yescharacteristic
318C8—24no—
319C8—21no—
320C8—21no—
321C8—21no—
322C8—21no—
323C8—42no—
324C8—81no—
325C8—81no—
326C22—21no—
327C22—21no—
328C22—81no—
329C22—81no—
330C22—81no—
331C22—162no—
332C22C29×#39011yescharacteristic
333C22C29×#44312yes—
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—21no—
339C4—81no—
340C4—81no—
341C4—81no—
342C4C29×#41311yescharacteristic
343C4C29×#41311yescharacteristic
344C2—22no—
345C2—161no—
346C2C29×#196711yescharacteristic
347C2C29×#197411yescharacteristic
348C2C29×#197611yescharacteristic
subgroupG/H
center, socleC22×C29#390
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
2. C29×#1568C2semidirect
3. C29×#1528C2semidirect
5. C29×#1470C2semidirect
7. C8×M16×C29C2semidirect
116. #9789C29direct (N × H)
153. #1568C2×C29semidirect
154. #1528C2×C29semidirect
156. #1470C2×C29semidirect
158. C8×M16C2×C29semidirect
248. C29#9789direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#4882
C29×#15682
C29×#15282
C29×#15272
C29×#14702
C29×#14692
C8×M16×C292
#978929