Finite Group Databasebeta

← C29×#9339 #20304239

Subgroups — C29×#9339 #20304239

Order 7424.

416 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3239C211yesmaximal, characteristic
2C29×#2995C211yesmaximal, characteristic
3C29×#1966C211yesmaximal, characteristic, complemented
4C29×#1556C211yesmaximal, characteristic, complemented
5C29×#1529C211yesmaximal, characteristic
6C29×#1307C211yesmaximal, characteristic, complemented
7C29×#1291C211yesmaximal, characteristic, complemented
8C2×C29×C4⋊Q8C2211yescharacteristic
9C29×#529C2211yescharacteristic
10C29×#501—21no—
11C29×#489—21no—
12C29×#484C412yes—
13C29×#481C412yes—
14C29×#475—21no—
15C29×#474—21no—
16C29×#446—21no—
17C29×#436—21no—
18C29×#435—21no—
19C29×#435—21no—
20C29×#433—21no—
21C29×#432C2211yescharacteristic
22C29×#432C2211yescharacteristic
23C29×#432C2211yescharacteristic
24C29×#424—21no—
25C29×#423C2211yescharacteristic
26C2×C29×#101—21no—
27C2×C29×#101—21no—
28C4×M16×C29C2211yescharacteristic
29C29×#332—21no—
30C29×#332—21no—
31C29×#330—21no—
32C29×#329—21no—
33C22×Q8×C29—21no—
34C2×M16×C29—21no—
35C2×M16×C29—21no—
36C2×M16×C29D411yescharacteristic
37C2×M16×C29D411yescharacteristic
38C22×C8×C29—21no—
39C29×C4⋊Q8—21no—
40C29×C4⋊Q8—21no—
41C29×C4⋊Q8—21no—
42C29×C4⋊Q8—21no—
43C29×#126—21no—
44C29×#125D411yescharacteristic
45C29×#124D411yescharacteristic
46C29×#123—21no—
47C29×C22⋊Q8C2×C411yescharacteristic
48C29×#121C2×C411yescharacteristic
49C4×Q8×C29D411yescharacteristic
50C4×D4×C29—21no—
51C4×D4×C29D411yescharacteristic
52C29×#117—21no—
53C2×C4⋊C4×C29—21no—
54C2×C4⋊C4×C29C2×C412yes—
55C2×C42×C29C2311yescharacteristic
56C29×#107—22no—
57C29×#106—22no—
58C29×C4⋊C8—21no—
59C29×C4⋊C8—21no—
60C29×C4⋊C8—21no—
61C29×C4⋊C8—21no—
62C29×C4⋊C8—21no—
63C29×C4⋊C8—21no—
64C29×C4⋊C8D411yescharacteristic
65C29×C4⋊C8D411yescharacteristic
66C29×#103—22no—
67C29×#102—22no—
68C29×#101—42no—
69C29×#101—42no—
70C29×C22⋊C8—21no—
71C29×C22⋊C8—21no—
72C29×C22⋊C8—21no—
73C29×C22⋊C8—21no—
74C29×C22⋊C8C2×C412yes—
75C29×#97—21no—
76C29×#97—21no—
77C29×#97—21no—
78C29×#97—21no—
79C29×#97—21no—
80C4×C8×C29—21no—
81C4×C8×C29—21no—
82C2×Q8×C29—41no—
83C2×Q8×C29—41no—
84C2×Q8×C29—41no—
85C2×Q8×C29—41no—
86C2×Q8×C29—41no—
87C2×Q8×C29—41no—
88C2×Q8×C29C22⋊C411yescharacteristic
89C2×D4×C29—21no—
90C2×D4×C29C22⋊C411yescharacteristic
91C22×C4×C29—21no—
92C22×C4×C29—22no—
93C22×C4×C29C22×C411yescharacteristic
94C22×C4×C29C2×D411yescharacteristic
95C22×C4×C29#4111yescharacteristic
96M16×C29—22no—
97M16×C29—41no—
98M16×C29—41no—
99M16×C29—41no—
100M16×C29—81no—
101C2×C8×C29—22no—
102C2×C8×C29—21no—
103C2×C8×C29—21no—
104C2×C8×C29—21no—
105C2×C8×C29—21no—
106C2×C8×C29—41no—
107C2×C8×C29—41no—
108C2×C8×C29—81no—
109C4⋊C4×C29—21no—
110C4⋊C4×C29—21no—
111C4⋊C4×C29—21no—
112C4⋊C4×C29—21no—
113C4⋊C4×C29—22no—
114C4⋊C4×C29—22no—
115C4⋊C4×C29—41no—
116C4⋊C4×C29—41no—
117C4⋊C4×C29C22⋊C411yescharacteristic
118C4⋊C4×C29C22⋊C411yescharacteristic
119C22⋊C4×C29—21no—
120C22⋊C4×C29—21no—
121C22⋊C4×C29—21no—
122C22⋊C4×C29—21no—
123C22⋊C4×C29—21no—
124C42×C29—21no—
125C42×C29C2×D411yescharacteristic
126C42×C29C2×D411yescharacteristic
127C42×C29C2×D411yescharacteristic
128C42×C29#4111yescharacteristic
129#9339C2911yesmaximal, characteristic, direct product factor, Sylow
130C23×C29—21no—
131C23×C29C4×D411yescharacteristic
132Q8×C29—41no—
133Q8×C29—81no—
134Q8×C29—81no—
135Q8×C29—81no—
136Q8×C29—81no—
137D4×C29—41no—
138D4×C29—81no—
139C2×C4×C29—21no—
140C2×C4×C29—21no—
141C2×C4×C29—21no—
142C2×C4×C29—21no—
143C2×C4×C29—21no—
144C2×C4×C29—41no—
145C2×C4×C29—41no—
146C2×C4×C29—41no—
147C2×C4×C29—41no—
148C2×C4×C29—42no—
149C2×C4×C29—42no—
150C2×C4×C29—42no—
151C2×C4×C29C2×C22⋊C411yescharacteristic
152C2×C4×C29C4×D411yescharacteristic
153C2×C4×C29#12011yescharacteristic
154C2×C4×C29#12111yescharacteristic
155C2×C4×C29#12111yescharacteristic
156C2×C4×C29#12311yescharacteristic
157C8×C29—42no—
158C8×C29—42no—
159C8×C29—41no—
160C8×C29—41no—
161C8×C29—41no—
162C8×C29—41no—
163C8×C29—81no—
164#3239C2×C2911yescharacteristic
165#2995C2×C2911yescharacteristic
166#1966C2×C2911yescharacteristic, complemented
167#1556C2×C2911yescharacteristic, complemented
168#1529C2×C2911yescharacteristic
169#1307C2×C2911yescharacteristic, complemented
170#1291C2×C2911yescharacteristic, complemented
171C22×C29—21no—
172C22×C29—21no—
173C22×C29—21no—
174C22×C29—41no—
175C22×C29—41no—
176C22×C29—41no—
177C22×C29#38611yescharacteristic
178C4×C29—21no—
179C4×C29—21no—
180C4×C29—21no—
181C4×C29—21no—
182C4×C29—21no—
183C4×C29—41no—
184C4×C29—41no—
185C4×C29—41no—
186C4×C29—82no—
187C4×C29#45311yescharacteristic
188C4×C29#45411yescharacteristic
189C2×C4⋊Q8C22×C2911yescharacteristic
190#529C22×C2911yescharacteristic
191#501—21no—
192#489—21no—
193#484C4×C2912yes—
194#481C4×C2912yes—
195#475—21no—
196#474—21no—
197#446—21no—
198#436—21no—
199#435—21no—
200#435—21no—
201#433—21no—
202#432C22×C2911yescharacteristic
203#432C22×C2911yescharacteristic
204#432C22×C2911yescharacteristic
205#424—21no—
206#423C22×C2911yescharacteristic
207C2×#101—21no—
208C2×#101—21no—
209C4×M16C22×C2911yescharacteristic
210#332—21no—
211#332—21no—
212#330—21no—
213#329—21no—
214C2×C29—41no—
215C2×C29—81no—
216C2×C29#188311yescharacteristic
217C2×C29#190211yescharacteristic
218C2×C29#191511yescharacteristic
219C22×Q8—21no—
220C2×M16—21no—
221C2×M16—21no—
222C2×M16D4×C2911yescharacteristic
223C2×M16D4×C2911yescharacteristic
224C22×C8—21no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229#126—21no—
230#125D4×C2911yescharacteristic
231#124D4×C2911yescharacteristic
232#123—21no—
233C22⋊Q8C2×C4×C2911yescharacteristic
234#121C2×C4×C2911yescharacteristic
235C4×Q8D4×C2911yescharacteristic
236C4×D4—21no—
237C4×D4D4×C2911yescharacteristic
238#117—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4C2×C4×C2912yes—
241C2×C42C23×C2911yescharacteristic
242#107—22no—
243#106—22no—
244C4⋊C8—21no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—21no—
249C4⋊C8—21no—
250C4⋊C8D4×C2911yescharacteristic
251C4⋊C8D4×C2911yescharacteristic
252#103—22no—
253#102—22no—
254#101—42no—
255#101—42no—
256C22⋊C8—21no—
257C22⋊C8—21no—
258C22⋊C8—21no—
259C22⋊C8—21no—
260C22⋊C8C2×C4×C2912yes—
261#97—21no—
262#97—21no—
263#97—21no—
264#97—21no—
265#97—21no—
266C4×C8—21no—
267C4×C8—21no—
268C29#933911yescharacteristic, direct product factor, Sylow
269C2×Q8—41no—
270C2×Q8—41no—
271C2×Q8—41no—
272C2×Q8—41no—
273C2×Q8—41no—
274C2×Q8—41no—
275C2×Q8C22⋊C4×C2911yescharacteristic
276C2×D4—21no—
277C2×D4C22⋊C4×C2911yescharacteristic
278C22×C4—21no—
279C22×C4—22no—
280C22×C4C22×C4×C2911yescharacteristic
281C22×C4C2×D4×C2911yescharacteristic
282C22×C4#41×C2911yescharacteristic
283M16—22no—
284M16—41no—
285M16—41no—
286M16—41no—
287M16—81no—
288C2×C8—22no—
289C2×C8—21no—
290C2×C8—21no—
291C2×C8—21no—
292C2×C8—21no—
293C2×C8—41no—
294C2×C8—41no—
295C2×C8—81no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—22no—
301C4⋊C4—22no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4C22⋊C4×C2911yescharacteristic
305C4⋊C4C22⋊C4×C2911yescharacteristic
306C22⋊C4—21no—
307C22⋊C4—21no—
308C22⋊C4—21no—
309C22⋊C4—21no—
310C22⋊C4—21no—
311C42—21no—
312C42C2×D4×C2911yescharacteristic
313C42C2×D4×C2911yescharacteristic
314C42C2×D4×C2911yescharacteristic
315C42#41×C2911yescharacteristic
316C23—21no—
317C23C4×D4×C2911yescharacteristic
318Q8—41no—
319Q8—81no—
320Q8—81no—
321Q8—81no—
322Q8—81no—
323D4—41no—
324D4—81no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4C2×C22⋊C4×C2911yescharacteristic
338C2×C4C4×D4×C2911yescharacteristic
339C2×C4C29×#12011yescharacteristic
340C2×C4C29×#12111yescharacteristic
341C2×C4C29×#12111yescharacteristic
342C2×C4C29×#12311yescharacteristic
343C8—42no—
344C8—42no—
345C8—41no—
346C8—41no—
347C8—41no—
348C8—41no—
349C8—81no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22C29×#38611yescharacteristic
357C4—21no—
358C4—21no—
359C4—21no—
360C4—21no—
361C4—21no—
362C4—41no—
363C4—41no—
364C4—41no—
365C4—82no—
366C4C29×#45311yescharacteristic
367C4C29×#45411yescharacteristic
368C2—41no—
369C2—81no—
370C2C29×#188311yescharacteristic
371C2C29×#190211yescharacteristic
372C2C29×#191511yescharacteristic
subgroupG/H
center, socleC22×C29#386
commutatorC22×C4C22×C4×C29
Frattini, cosocleC2×C42C23×C29
prime radicalC29×#121C2×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×#1966C2semidirect
4. C29×#1556C2semidirect
6. C29×#1307C2semidirect
7. C29×#1291C2semidirect
129. #9339C29direct (N × H)
166. #1966C2×C29semidirect
167. #1556C2×C29semidirect
169. #1307C2×C29semidirect
170. #1291C2×C29semidirect
268. C29#9339direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32392
C29×#29952
C29×#19662
C29×#15562
C29×#15292
C29×#13072
C29×#12912
#933929