Finite Group Databasebeta

← C29×#12233 #20307133

Subgroups — C29×#12233 #20307133

Order 7424.

370 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 70 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×#2835C211yesmaximal, characteristic
2C29×#2062C211yesmaximal, characteristic
3C29×#1608C211yesmaximal, characteristic
4C29×#1602C211yesmaximal, characteristic
5C29×#1351C211yesmaximal, characteristic
6C29×#1344C211yesmaximal, characteristic
7C29×#1326C211yesmaximal, characteristic
8C29×#543C2211yescharacteristic
9C29×#483—21no—
10C29×#451—21no—
11C29×#400—21no—
12C29×#400—21no—
13C29×#400—21no—
14C29×#397—21no—
15C29×#397C2211yescharacteristic
16C29×#395—21no—
17C29×#393C2211yescharacteristic
18C29×#385—21no—
19C29×#385—21no—
20C29×#385C2211yescharacteristic
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—41no—
39C2×C4⋊C4×C29D411yescharacteristic
40C2×C22⋊C4×C29—21no—
41C2×C22⋊C4×C29—21no—
42C2×C22⋊C4×C29—21no—
43C2×C22⋊C4×C29—21no—
44C2×C22⋊C4×C29D411yescharacteristic
45C2×C22⋊C4×C29C2311yescharacteristic
46C29×#106—41no—
47C29×#103—41no—
48C29×#103—41no—
49C29×C22⋊C8—21no—
50C29×C22⋊C8—21no—
51C29×#95—21no—
52C29×#95—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—41no—
76C22×C4×C29—41no—
77C22×C4×C29—81no—
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—41no—
87C4⋊C4×C29—41no—
88C4⋊C4×C29—81no—
89C4⋊C4×C29—81no—
90C4⋊C4×C29—81no—
91C4⋊C4×C29—81no—
92C4⋊C4×C29—82no—
93C22⋊C4×C29—22no—
94C22⋊C4×C29—21no—
95C22⋊C4×C29—21no—
96C22⋊C4×C29—41no—
97C22⋊C4×C29—41no—
98C22⋊C4×C29—41no—
99C22⋊C4×C29—41no—
100C22⋊C4×C29—41no—
101C22⋊C4×C29—41no—
102C22⋊C4×C29—81no—
103#12233C2911yesmaximal, characteristic, direct product factor, Sylow
104C23×C29—21no—
105C23×C29—21no—
106C23×C29—41no—
107C23×C29—41no—
108C23×C29#12011yescharacteristic
109C23×C29#13511yescharacteristic
110C23×C29#13711yescharacteristic
111Q8×C29—42no—
112Q8×C29—81no—
113Q8×C29—81no—
114Q8×C29—81no—
115C2×C4×C29—21no—
116C2×C4×C29—21no—
117C2×C4×C29—41no—
118C2×C4×C29—41no—
119C2×C4×C29—42no—
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—41no—
127C2×C4×C29—41no—
128C2×C4×C29—41no—
129C2×C4×C29—41no—
130C2×C4×C29—42no—
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—81no—
142C2×C4×C29—81no—
143C2×C4×C29—81no—
144C2×C4×C29—81no—
145C2×C4×C29—81no—
146C8×C29—81no—
147C8×C29—81no—
148#2835C2×C2911yescharacteristic
149#2062C2×C2911yescharacteristic
150#1608C2×C2911yescharacteristic
151#1602C2×C2911yescharacteristic
152#1351C2×C2911yescharacteristic
153#1344C2×C2911yescharacteristic
154#1326C2×C2911yescharacteristic
155C22×C29—21no—
156C22×C29—21no—
157C22×C29—21no—
158C22×C29—21no—
159C22×C29—41no—
160C22×C29—41no—
161C22×C29—41no—
162C22×C29—41no—
163C22×C29—81no—
164C22×C29#45211yescharacteristic
165C22×C29#45611yescharacteristic
166C22×C29B(4,𝔽2)11yescharacteristic
167C4×C29—41no—
168C4×C29—41no—
169C4×C29—81no—
170C4×C29—81no—
171C4×C29—81no—
172C4×C29—82no—
173C4×C29—81no—
174C4×C29—81no—
175C4×C29—81no—
176C4×C29—81no—
177C4×C29—81no—
178#543C22×C2911yescharacteristic
179#483—21no—
180#451—21no—
181#400—21no—
182#400—21no—
183#400—21no—
184#397—21no—
185#397C22×C2911yescharacteristic
186#395—21no—
187#393C22×C2911yescharacteristic
188#385—21no—
189#385—21no—
190#385C22×C2911yescharacteristic
191#342—21no—
192#342C22×C2911yescharacteristic
193#328—21no—
194#328—21no—
195#323C22×C2911yescharacteristic
196#323C22×C2911yescharacteristic
197C2×C29—21no—
198C2×C29—21no—
199C2×C29—41no—
200C2×C29—41no—
201C2×C29#160311yescharacteristic
202C2×C29#219911yescharacteristic
203C2×C29#220111yescharacteristic
204C22×Q8D4×C2911yescharacteristic
205C23×C4D4×C2911yescharacteristic
206C2×Q16—41no—
207C22⋊Q8—21no—
208C22⋊Q8—21no—
209C22⋊Q8—41no—
210C22⋊Q8—41no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—41no—
216C2×C4⋊C4D4×C2911yescharacteristic
217C2×C22⋊C4—21no—
218C2×C22⋊C4—21no—
219C2×C22⋊C4—21no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4D4×C2911yescharacteristic
222C2×C22⋊C4C23×C2911yescharacteristic
223#106—41no—
224#103—41no—
225#103—41no—
226C22⋊C8—21no—
227C22⋊C8—21no—
228#95—21no—
229#95—21no—
230#95—21no—
231#95—21no—
232#95—21no—
233#95—21no—
234#95—21no—
235#95—21no—
236#95—41no—
237#95D4×C2911yescharacteristic
238#95D4×C2911yescharacteristic
239C29#1223311yescharacteristic, direct product factor, Sylow
240C24C2×D4×C2911yescharacteristic
241C2×Q8—21no—
242C2×Q8—21no—
243C2×Q8—41no—
244C2×Q8—81no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—81no—
256C22×C4C2×D4×C2911yescharacteristic
257C22×C4C2×D4×C2911yescharacteristic
258Q16—82no—
259C2×C8—41no—
260C2×C8—41no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—81no—
267C4⋊C4—81no—
268C4⋊C4—81no—
269C4⋊C4—81no—
270C4⋊C4—82no—
271C22⋊C4—22no—
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—41no—
275C22⋊C4—41no—
276C22⋊C4—41no—
277C22⋊C4—41no—
278C22⋊C4—41no—
279C22⋊C4—41no—
280C22⋊C4—81no—
281C23—21no—
282C23—21no—
283C23—41no—
284C23—41no—
285C23C29×#12011yescharacteristic
286C23C29×#13511yescharacteristic
287C23C29×#13711yescharacteristic
288Q8—42no—
289Q8—81no—
290Q8—81no—
291Q8—81no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—42no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
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—81no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—81no—
323C8—81no—
324C8—81no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—21no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—81no—
334C22C29×#45211yescharacteristic
335C22C29×#45611yescharacteristic
336C22C29×B(4,𝔽2)11yescharacteristic
337C4—41no—
338C4—41no—
339C4—81no—
340C4—81no—
341C4—81no—
342C4—82no—
343C4—81no—
344C4—81no—
345C4—81no—
346C4—81no—
347C4—81no—
348C2—21no—
349C2—21no—
350C2—41no—
351C2—41no—
352C2C29×#160311yescharacteristic
353C2C29×#219911yescharacteristic
354C2C29×#220111yescharacteristic
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
103. #12233C29direct (N × H)
239. C29#12233direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#28352
C29×#20622
C29×#16082
C29×#16022
C29×#13512
C29×#13442
C29×#13262
#1223329