Finite Group Databasebeta

← C29×C22⋊#401 #20309727

Subgroups — C29×C22⋊#401 #20309727

Order 7424.

1650 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#401C211yesmaximal, characteristic, complemented
2C22×C29×#95C211yesmaximal, characteristic
3C29×#1443C213yesmaximal, complemented
4C29×#1443C213yesmaximal, complemented
5C29×#1443C211yesmaximal, characteristic, complemented
6C29×C22⋊#95C213yesmaximal
7C29×C22⋊#95C213yesmaximal
8C24×C4×C29C2213yes—
9C22×C22⋊C4×C29C2213yes—
10C22×C22⋊C4×C29C2211yescharacteristic
11C29×#401—24no—
12C2×C29×#95—24no—
13C2×C29×#95C2213yes—
14C2×C29×#95C2213yes—
15C2×C29×#95C2213yes—
16C2×C29×#95C2213yes—
17C2×C29×#95C2213yes—
18C2×C29×#95C2213yes—
19C2×C29×#95C2213yes—
20C2×C29×#95C2213yes—
21C2×C29×#95C2213yes—
22C2×C29×#95C2211yescharacteristic
23C25×C29C2311yescharacteristic
24C23×C4×C29—26no—
25C23×C4×C29—26no—
26C23×C4×C29—26no—
27C23×C4×C29—26no—
28C23×C4×C29—26no—
29C23×C4×C29—43no—
30C23×C4×C29—43no—
31C23×C4×C29C2311yescharacteristic
32C23×C4×C29C2313yes—
33C23×C4×C29C2313yes—
34C23×C4×C29C2311yescharacteristic
35C23×C4×C29C2313yes—
36C23×C4×C29C2313yes—
37C2×C22⋊C4×C29—26no—
38C2×C22⋊C4×C29—26no—
39C2×C22⋊C4×C29—26no—
40C2×C22⋊C4×C29—26no—
41C29×#95—26no—
42C29×#95—26no—
43C29×#95—26no—
44C29×#95—26no—
45C29×#95—26no—
46C29×#95—43no—
47C29×#95—43no—
48C29×#95—43no—
49C29×#95—43no—
50C29×#95D414yes—
51C24×C29—21no—
52C24×C29—23no—
53C24×C29—23no—
54C24×C29—21no—
55C24×C29#4112yes—
56C24×C29#4116yes—
57C24×C29#4116yes—
58C24×C29C2411yescharacteristic
59C22×C4×C29—224no—
60C22×C4×C29—23no—
61C22×C4×C29—23no—
62C22×C4×C29—23no—
63C22×C4×C29—23no—
64C22×C4×C29—23no—
65C22×C4×C29—23no—
66C22×C4×C29—23no—
67C22×C4×C29—23no—
68C22×C4×C29—23no—
69C22×C4×C29—23no—
70C22×C4×C29—23no—
71C22×C4×C29—23no—
72C22×C4×C29—21no—
73C22×C4×C29—23no—
74C22×C4×C29—23no—
75C22×C4×C29—23no—
76C22×C4×C29—23no—
77C22×C4×C29—23no—
78C22×C4×C29—23no—
79C22×C4×C29—23no—
80C22×C4×C29—23no—
81C22×C4×C29—23no—
82C22×C4×C29—23no—
83C22×C4×C29—23no—
84C22×C4×C29—23no—
85C22×C4×C29—23no—
86C22×C4×C29—23no—
87C22×C4×C29—23no—
88C22×C4×C29—23no—
89C22×C4×C29—23no—
90C22×C4×C29—21no—
91C22×C4×C29—23no—
92C22×C4×C29—412no—
93C22×C4×C29—412no—
94C22×C4×C29—412no—
95C22×C4×C29—412no—
96C22×C4×C29—412no—
97C22×C4×C29—412no—
98C22×C4×C29C2×D416yes—
99C22×C4×C29#4116yes—
100C22⋊C4×C29—44no—
101C22⋊C4×C29—412no—
102C22⋊#401C2911yesmaximal, characteristic, direct product factor, Sylow
103C23×C29—26no—
104C23×C29—26no—
105C23×C29—26no—
106C23×C29—26no—
107C23×C29—26no—
108C23×C29—22no—
109C23×C29—26no—
110C23×C29—26no—
111C23×C29—26no—
112C23×C29—26no—
113C23×C29#12614yes—
114C23×C29#126112yes—
115C23×C29#126112yes—
116C23×C29C22×D411yescharacteristic
117C23×C29C2×#4113yes—
118C23×C29C2×#4113yes—
119C23×C29C2×#4113yes—
120C23×C29C2×#4111yescharacteristic
121C23×C29H(5,𝔽2)13yes—
122C23×C292−1+411yescharacteristic
123C2×C4×C29—26no—
124C2×C4×C29—26no—
125C2×C4×C29—26no—
126C2×C4×C29—26no—
127C2×C4×C29—26no—
128C2×C4×C29—26no—
129C2×C4×C29—448no—
130C2×C4×C29—43no—
131C2×C4×C29—43no—
132C2×C4×C29—43no—
133C2×C4×C29—43no—
134C2×C4×C29—43no—
135C2×C4×C29—43no—
136C2×C4×C29—43no—
137C2×C4×C29—43no—
138C2×C4×C29—43no—
139C2×C4×C29—43no—
140C2×C4×C29—41no—
141C2×C4×C29—41no—
142C2×C4×C29—43no—
143C2×C4×C29—43no—
144C2×C4×C29—43no—
145C2×C4×C29—43no—
146C2×C4×C29—43no—
147C2×C4×C29—43no—
148C2×C4×C29—43no—
149C2×C4×C29—43no—
150C2×C4×C29—43no—
151C2×C4×C29—43no—
152C2×C4×C29—43no—
153C2×C4×C29—43no—
154C2×C4×C29—43no—
155C2×C4×C29—43no—
156C2×C4×C29—43no—
157C2×C4×C29—43no—
158C2×#401C2×C2911yescharacteristic, complemented
159C22×#95C2×C2911yescharacteristic
160#1443C2×C2913yescomplemented
161#1443C2×C2913yescomplemented
162#1443C2×C2911yescharacteristic, complemented
163C22⋊#95C2×C2913yes—
164C22⋊#95C2×C2913yes—
165C22×C29—24no—
166C22×C29—24no—
167C22×C29—212no—
168C22×C29—212no—
169C22×C29—212no—
170C22×C29—212no—
171C22×C29#40118yescomplemented
172C22×C29#52513yes—
173C22×C29C2×#12611yescharacteristic
174C22×C29C2×#12613yes—
175C22×C29C2×#12613yes—
176C22×C29#52913yes—
177C22×C29#53813yes—
178C22×C29#53913yes—
179C22×C29#54613yes—
180C22×C29#54811yescharacteristic
181C22×C29#55113yes—
182C22×C29#55113yes—
183C22×C29#55213yes—
184C22×C29#55313yes—
185C4×C29—46no—
186C4×C29—46no—
187C4×C29—81no—
188C4×C29—81no—
189C4×C29—83no—
190C4×C29—83no—
191C24×C4C22×C2913yes—
192C22×C22⋊C4C22×C2913yes—
193C22×C22⋊C4C22×C2911yescharacteristic
194#401—24no—
195C2×#95—24no—
196C2×#95C22×C2913yes—
197C2×#95C22×C2913yes—
198C2×#95C22×C2913yes—
199C2×#95C22×C2913yes—
200C2×#95C22×C2913yes—
201C2×#95C22×C2913yes—
202C2×#95C22×C2913yes—
203C2×#95C22×C2913yes—
204C2×#95C22×C2913yes—
205C2×#95C22×C2911yescharacteristic
206C2×C29—28no—
207C2×C29C2×#40111yescharacteristic
208C2×C29#248013yes—
209C2×C29#248113yes—
210C2×C29#249313yes—
211C2×C29#251013yes—
212C2×C29#264311yescharacteristic
213C2×C29#285211yescharacteristic
214C25C23×C2911yescharacteristic
215C23×C4—26no—
216C23×C4—26no—
217C23×C4—26no—
218C23×C4—26no—
219C23×C4—26no—
220C23×C4—43no—
221C23×C4—43no—
222C23×C4C23×C2911yescharacteristic
223C23×C4C23×C2913yes—
224C23×C4C23×C2913yes—
225C23×C4C23×C2911yescharacteristic
226C23×C4C23×C2913yes—
227C23×C4C23×C2913yes—
228C2×C22⋊C4—26no—
229C2×C22⋊C4—26no—
230C2×C22⋊C4—26no—
231C2×C22⋊C4—26no—
232#95—26no—
233#95—26no—
234#95—26no—
235#95—26no—
236#95—26no—
237#95—43no—
238#95—43no—
239#95—43no—
240#95—43no—
241#95D4×C2914yes—
242C29C22⋊#40111yescharacteristic, direct product factor, Sylow
243C24—21no—
244C24—23no—
245C24—23no—
246C24—21no—
247C24#41×C2912yes—
248C24#41×C2916yes—
249C24#41×C2916yes—
250C24C24×C2911yescharacteristic
251C22×C4—224no—
252C22×C4—23no—
253C22×C4—23no—
254C22×C4—23no—
255C22×C4—23no—
256C22×C4—23no—
257C22×C4—23no—
258C22×C4—23no—
259C22×C4—23no—
260C22×C4—23no—
261C22×C4—23no—
262C22×C4—23no—
263C22×C4—23no—
264C22×C4—21no—
265C22×C4—23no—
266C22×C4—23no—
267C22×C4—23no—
268C22×C4—23no—
269C22×C4—23no—
270C22×C4—23no—
271C22×C4—23no—
272C22×C4—23no—
273C22×C4—23no—
274C22×C4—23no—
275C22×C4—23no—
276C22×C4—23no—
277C22×C4—23no—
278C22×C4—23no—
279C22×C4—23no—
280C22×C4—23no—
281C22×C4—23no—
282C22×C4—21no—
283C22×C4—23no—
284C22×C4—412no—
285C22×C4—412no—
286C22×C4—412no—
287C22×C4—412no—
288C22×C4—412no—
289C22×C4—412no—
290C22×C4C2×D4×C2916yes—
291C22×C4#41×C2916yes—
292C22⋊C4—412no—
293C22⋊C4—44no—
294C23—26no—
295C23—26no—
296C23—26no—
297C23—26no—
298C23—26no—
299C23—22no—
300C23—26no—
301C23—26no—
302C23—26no—
303C23—26no—
304C23C29×#126112yes—
305C23C29×#12614yes—
306C23C29×#126112yes—
307C23C22×D4×C2911yescharacteristic
308C23C2×#41×C2913yes—
309C23C2×#41×C2913yes—
310C23C2×#41×C2913yes—
311C23C2×#41×C2911yescharacteristic
312C23C29×H(5,𝔽2)13yes—
313C23C29×2−1+411yescharacteristic
314C2×C4—26no—
315C2×C4—26no—
316C2×C4—26no—
317C2×C4—26no—
318C2×C4—26no—
319C2×C4—26no—
320C2×C4—448no—
321C2×C4—43no—
322C2×C4—43no—
323C2×C4—43no—
324C2×C4—43no—
325C2×C4—43no—
326C2×C4—43no—
327C2×C4—43no—
328C2×C4—43no—
329C2×C4—43no—
330C2×C4—43no—
331C2×C4—43no—
332C2×C4—43no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—43no—
336C2×C4—43no—
337C2×C4—43no—
338C2×C4—43no—
339C2×C4—43no—
340C2×C4—43no—
341C2×C4—43no—
342C2×C4—43no—
343C2×C4—43no—
344C2×C4—43no—
345C2×C4—43no—
346C2×C4—43no—
347C2×C4—43no—
348C2×C4—43no—
349C22—212no—
350C22—212no—
351C22—212no—
352C22—212no—
353C22—24no—
354C22—24no—
355C22C29×#40118yescomplemented
356C22C29×#52513yes—
357C22C2×C29×#12613yes—
358C22C2×C29×#12613yes—
359C22C2×C29×#12611yescharacteristic
360C22C29×#52913yes—
361C22C29×#53813yes—
362C22C29×#53913yes—
363C22C29×#54613yes—
364C22C29×#54811yescharacteristic
365C22C29×#55113yes—
366C22C29×#55113yes—
367C22C29×#55213yes—
368C22C29×#55313yes—
369C4—46no—
370C4—46no—
371C4—83no—
372C4—83no—
373C4—81no—
374C4—81no—
375C2—28no—
376C2C2×C29×#40111yescharacteristic
377C2C29×#248013yes—
378C2C29×#248113yes—
379C2C29×#249313yes—
380C2C29×#251013yes—
381C2C29×#264311yescharacteristic
382C2C29×#285211yescharacteristic
subgroupG/H
center, socleC24×C29C24
commutator, Frattini, cosocleC24C24×C29
prime radicalC25×C29C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C29×#401C2semidirect
3. C29×#1443C2semidirect
4. C29×#1443C2semidirect
5. C29×#1443C2semidirect
102. C22⋊#401C29direct (N × H)
158. C2×#401C2×C29semidirect
160. #1443C2×C29semidirect
161. #1443C2×C29semidirect
162. #1443C2×C29semidirect
171. C22×C29#401semidirect
242. C29C22⋊#401direct (N × H)
355. C22C29×#401semidirect

Maximal subgroups

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

subgroupindex
C2×C29×#4012
C22×C29×#952
C29×#14432
C29×C22⋊#952
C22⋊#40129