Finite Group Databasebeta

← C29×#12254 #20307154

Subgroups — C29×#12254 #20307154

Order 7424.

388 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 74 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×#2742C211yesmaximal, characteristic
2C29×#2062C211yesmaximal, characteristic
3C29×#1614C211yesmaximal, characteristic
4C29×#1602C211yesmaximal, characteristic
5C29×#1352C211yesmaximal, characteristic
6C29×#1351C211yesmaximal, characteristic
7C29×#1326C211yesmaximal, characteristic
8C29×#543C2211yescharacteristic
9C29×#484—21no—
10C29×#451—21no—
11C29×#400—21no—
12C29×#399C2211yescharacteristic
13C29×#395—21no—
14C29×#393C2211yescharacteristic
15C29×#389—21no—
16C29×#388—21no—
17C29×#387—21no—
18C29×#385—21no—
19C29×#385C2211yescharacteristic
20C29×#380—21no—
21C29×#342—21no—
22C29×#342C2211yescharacteristic
23C29×#328—21no—
24C29×#328—21no—
25C29×#323C2211yescharacteristic
26C29×#323C2211yescharacteristic
27C22×Q8×C29D411yescharacteristic
28C23×C4×C29D411yescharacteristic
29C2×Q16×C29—41no—
30C29×C22⋊Q8—21no—
31C29×C22⋊Q8—21no—
32C29×C22⋊Q8—41no—
33C29×C22⋊Q8—41no—
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×C29—41no—
40C2×C4⋊C4×C29D411yescharacteristic
41C2×C22⋊C4×C29—21no—
42C2×C22⋊C4×C29—21no—
43C2×C22⋊C4×C29—21no—
44C2×C22⋊C4×C29—21no—
45C2×C22⋊C4×C29D411yescharacteristic
46C2×C22⋊C4×C29C2311yescharacteristic
47C2×C42×C29—21no—
48C29×#107—41no—
49C29×#103—41no—
50C29×#103—41no—
51C29×C22⋊C8—21no—
52C29×C22⋊C8—21no—
53C29×#95—21no—
54C29×#95—21no—
55C29×#95—21no—
56C29×#95—21no—
57C29×#95—21no—
58C29×#95—21no—
59C29×#95—41no—
60C29×#95D411yescharacteristic
61C29×#95D411yescharacteristic
62C24×C29C2×D411yescharacteristic
63C2×Q8×C29—21no—
64C2×Q8×C29—21no—
65C2×Q8×C29—41no—
66C2×Q8×C29—81no—
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—42no—
76C22×C4×C29—41no—
77C22×C4×C29—41no—
78C22×C4×C29C2×D411yescharacteristic
79C22×C4×C29C2×D411yescharacteristic
80Q16×C29—82no—
81C2×C8×C29—41no—
82C2×C8×C29—41no—
83C4⋊C4×C29—21no—
84C4⋊C4×C29—21no—
85C4⋊C4×C29—41no—
86C4⋊C4×C29—42no—
87C4⋊C4×C29—42no—
88C4⋊C4×C29—41no—
89C4⋊C4×C29—41no—
90C4⋊C4×C29—81no—
91C4⋊C4×C29—81no—
92C4⋊C4×C29—81no—
93C4⋊C4×C29—82no—
94C22⋊C4×C29—21no—
95C22⋊C4×C29—22no—
96C22⋊C4×C29—41no—
97C22⋊C4×C29—41no—
98C22⋊C4×C29—41no—
99C22⋊C4×C29—41no—
100C22⋊C4×C29—81no—
101C22⋊C4×C29—81no—
102C22⋊C4×C29Q1612yescomplemented
103C42×C29—81no—
104#12254C2911yesmaximal, characteristic, direct product factor, Sylow
105C23×C29—21no—
106C23×C29—21no—
107C23×C29—41no—
108C23×C29—41no—
109C23×C29#12011yescharacteristic
110C23×C29C2×Q1611yescharacteristic
111C23×C29#13711yescharacteristic
112Q8×C29—42no—
113Q8×C29—81no—
114Q8×C29—81no—
115Q8×C29—81no—
116C2×C4×C29—22no—
117C2×C4×C29—22no—
118C2×C4×C29—21no—
119C2×C4×C29—21no—
120C2×C4×C29—41no—
121C2×C4×C29—41no—
122C2×C4×C29—41no—
123C2×C4×C29—41no—
124C2×C4×C29—41no—
125C2×C4×C29—41no—
126C2×C4×C29—42no—
127C2×C4×C29—41no—
128C2×C4×C29—41no—
129C2×C4×C29—42no—
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—41no—
141C2×C4×C29—41no—
142C2×C4×C29—81no—
143C2×C4×C29—81no—
144C2×C4×C29—81no—
145C2×C4×C29—81no—
146C2×C4×C29—81no—
147C8×C29—81no—
148C8×C29—81no—
149#2742C2×C2911yescharacteristic
150#2062C2×C2911yescharacteristic
151#1614C2×C2911yescharacteristic
152#1602C2×C2911yescharacteristic
153#1352C2×C2911yescharacteristic
154#1351C2×C2911yescharacteristic
155#1326C2×C2911yescharacteristic
156C22×C29—21no—
157C22×C29—21no—
158C22×C29—21no—
159C22×C29—21no—
160C22×C29—41no—
161C22×C29—41no—
162C22×C29—41no—
163C22×C29—41no—
164C22×C29—81no—
165C22×C29#45111yescharacteristic
166C22×C29#45611yescharacteristic
167C22×C29B(4,𝔽2)11yescharacteristic
168C4×C29—42no—
169C4×C29—41no—
170C4×C29—42no—
171C4×C29—41no—
172C4×C29—81no—
173C4×C29—81no—
174C4×C29—82no—
175C4×C29—81no—
176C4×C29—81no—
177C4×C29—81no—
178C4×C29—81no—
179#543C22×C2911yescharacteristic
180#484—21no—
181#451—21no—
182#400—21no—
183#399C22×C2911yescharacteristic
184#395—21no—
185#393C22×C2911yescharacteristic
186#389—21no—
187#388—21no—
188#387—21no—
189#385—21no—
190#385C22×C2911yescharacteristic
191#380—21no—
192#342—21no—
193#342C22×C2911yescharacteristic
194#328—21no—
195#328—21no—
196#323C22×C2911yescharacteristic
197#323C22×C2911yescharacteristic
198C2×C29—21no—
199C2×C29—21no—
200C2×C29—41no—
201C2×C29—41no—
202C2×C29#160511yescharacteristic
203C2×C29#219711yescharacteristic
204C2×C29#220011yescharacteristic
205C22×Q8D4×C2911yescharacteristic
206C23×C4D4×C2911yescharacteristic
207C2×Q16—41no—
208C22⋊Q8—21no—
209C22⋊Q8—21no—
210C22⋊Q8—41no—
211C22⋊Q8—41no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—41no—
218C2×C4⋊C4D4×C2911yescharacteristic
219C2×C22⋊C4—21no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223C2×C22⋊C4D4×C2911yescharacteristic
224C2×C22⋊C4C23×C2911yescharacteristic
225C2×C42—21no—
226#107—41no—
227#103—41no—
228#103—41no—
229C22⋊C8—21no—
230C22⋊C8—21no—
231#95—21no—
232#95—21no—
233#95—21no—
234#95—21no—
235#95—21no—
236#95—21no—
237#95—41no—
238#95D4×C2911yescharacteristic
239#95D4×C2911yescharacteristic
240C29#1225411yescharacteristic, direct product factor, Sylow
241C24C2×D4×C2911yescharacteristic
242C2×Q8—21no—
243C2×Q8—21no—
244C2×Q8—41no—
245C2×Q8—81no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—42no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4C2×D4×C2911yescharacteristic
258C22×C4C2×D4×C2911yescharacteristic
259Q16—82no—
260C2×C8—41no—
261C2×C8—41no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—41no—
265C4⋊C4—42no—
266C4⋊C4—42no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—81no—
270C4⋊C4—81no—
271C4⋊C4—81no—
272C4⋊C4—82no—
273C22⋊C4—21no—
274C22⋊C4—22no—
275C22⋊C4—41no—
276C22⋊C4—41no—
277C22⋊C4—41no—
278C22⋊C4—41no—
279C22⋊C4—81no—
280C22⋊C4—81no—
281C22⋊C4Q16×C2912yescomplemented
282C42—81no—
283C23—21no—
284C23—21no—
285C23—41no—
286C23—41no—
287C23C29×#12011yescharacteristic
288C23C2×Q16×C2911yescharacteristic
289C23C29×#13711yescharacteristic
290Q8—42no—
291Q8—81no—
292Q8—81no—
293Q8—81no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—42no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—42no—
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—41no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—81no—
325C8—81no—
326C8—81no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—81no—
336C22C29×#45111yescharacteristic
337C22C29×#45611yescharacteristic
338C22C29×B(4,𝔽2)11yescharacteristic
339C4—42no—
340C4—41no—
341C4—42no—
342C4—41no—
343C4—81no—
344C4—81no—
345C4—82no—
346C4—81no—
347C4—81no—
348C4—81no—
349C4—81no—
350C2—21no—
351C2—21no—
352C2—41no—
353C2—41no—
354C2C29×#160511yescharacteristic
355C2C29×#219711yescharacteristic
356C2C29×#220011yescharacteristic
subgroupG/H
center, socleC22×C29B(4,𝔽2)
commutator, Frattini, cosocleC2×C22⋊C4C23×C29
prime radicalC24×C29C2×D4
LCSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C23×C29 ◁ C2×C22⋊C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
102. C22⋊C4×C29Q16semidirect
104. #12254C29direct (N × H)
240. C29#12254direct (N × H)
281. C22⋊C4Q16×C29semidirect

Maximal subgroups

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

subgroupindex
C29×#27422
C29×#20622
C29×#16142
C29×#16022
C29×#13522
C29×#13512
C29×#13262
#1225429