Finite Group Databasebeta

← C29×#9051 #20303951

Subgroups — C29×#9051 #20303951

Order 7424.

436 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3108C211yesmaximal, characteristic
2C29×#2992C211yesmaximal, characteristic
3C29×#1985C211yesmaximal, characteristic, complemented
4C29×#1524C211yesmaximal, characteristic
5C29×#1491C211yesmaximal, characteristic, complemented
6C29×#1302C211yesmaximal, characteristic, complemented
7C29×#1283C211yesmaximal, characteristic, complemented
8C29×#529C2211yescharacteristic
9C2×C4×Q8×C29C2211yescharacteristic
10C29×#483C411yescharacteristic
11C29×#480C411yescharacteristic
12C29×#479—21no—
13C29×#464—21no—
14C29×#451C411yescharacteristic
15C29×#448C411yescharacteristic
16C29×#446—21no—
17C4×Q16×C29—21no—
18C4×SD16×C29—21no—
19C29×#435—21no—
20C29×#435—21no—
21C8×D4×C29—21no—
22C29×#433—21no—
23C29×#432C2211yescharacteristic
24C29×#431C2211yescharacteristic
25C29×#424—21no—
26C2×C29×C4⋊C8C2211yescharacteristic
27C4×M16×C29C2211yescharacteristic
28C2×C29×#97C2211yescharacteristic
29C29×#336—21no—
30C29×#336—21no—
31C29×#330—21no—
32C29×#329—21no—
33C29×Q8⋊C8—21no—
34C29×Q8⋊C8—21no—
35C22×Q8×C29C2×C411yescharacteristic
36C2×Q16×C29—21no—
37C2×SD16×C29—21no—
38C2×M16×C29—21no—
39C2×M16×C29—21no—
40C22×C8×C29—21no—
41C22×C8×C29—21no—
42C22×C8×C29D411yescharacteristic
43C22×C8×C29D411yescharacteristic
44C29×#126—21no—
45C29×#125D411yescharacteristic
46C29×#124D411yescharacteristic
47C29×#123—21no—
48C29×C22⋊Q8C2×C411yescharacteristic
49C29×#121C2×C411yescharacteristic
50C4×Q8×C29—21no—
51C4×Q8×C29—21no—
52C4×Q8×C29—21no—
53C4×Q8×C29—21no—
54C4×Q8×C29D411yescharacteristic
55C4×D4×C29—21no—
56C4×D4×C29D411yescharacteristic
57C29×#117—21no—
58C2×C4⋊C4×C29—21no—
59C2×C4⋊C4×C29C2×C411yescharacteristic
60C2×C42×C29—21no—
61C2×C42×C29C2311yescharacteristic
62C29×#107—21no—
63C29×#106—21no—
64C29×C4⋊C8—21no—
65C29×C4⋊C8—21no—
66C29×C4⋊C8—21no—
67C29×C4⋊C8—21no—
68C29×C4⋊C8—21no—
69C29×C4⋊C8D411yescharacteristic
70C29×C4⋊C8D411yescharacteristic
71C29×#103—21no—
72C29×#103—21no—
73C29×#103—21no—
74C29×#102—21no—
75C29×C22⋊C8—21no—
76C29×C22⋊C8—21no—
77C29×C22⋊C8—21no—
78C29×C22⋊C8C2×C411yescharacteristic
79C29×C22⋊C8C2×C411yescharacteristic
80C29×#97—21no—
81C29×#97—21no—
82C29×#97—21no—
83C29×#97—21no—
84C29×#97—21no—
85C4×C8×C29—21no—
86C4×C8×C29—21no—
87C4×C8×C29—21no—
88C2×Q8×C29—21no—
89C2×Q8×C29—21no—
90C2×Q8×C29—42no—
91C2×Q8×C29C22⋊C411yescharacteristic
92C2×D4×C29—21no—
93C2×D4×C29C22⋊C411yescharacteristic
94C22×C4×C29—21no—
95C22×C4×C29—21no—
96C22×C4×C29—21no—
97C22×C4×C29C22×C411yescharacteristic
98C22×C4×C29C2×D411yescharacteristic
99C22×C4×C29#4111yescharacteristic
100Q16×C29—42no—
101SD16×C29—42no—
102M16×C29—22no—
103M16×C29—41no—
104M16×C29—81no—
105C2×C8×C29—22no—
106C2×C8×C29—21no—
107C2×C8×C29—21no—
108C2×C8×C29—21no—
109C2×C8×C29—21no—
110C2×C8×C29—21no—
111C2×C8×C29—21no—
112C2×C8×C29—41no—
113C2×C8×C29—41no—
114C2×C8×C29—41no—
115C2×C8×C29—41no—
116C2×C8×C29—41no—
117C2×C8×C29—81no—
118C4⋊C4×C29—21no—
119C4⋊C4×C29—21no—
120C4⋊C4×C29—21no—
121C4⋊C4×C29—21no—
122C4⋊C4×C29—21no—
123C4⋊C4×C29—21no—
124C4⋊C4×C29—41no—
125C4⋊C4×C29—41no—
126C4⋊C4×C29C22⋊C411yescharacteristic
127C4⋊C4×C29C22⋊C411yescharacteristic
128C22⋊C4×C29—21no—
129C22⋊C4×C29—21no—
130C22⋊C4×C29—21no—
131C22⋊C4×C29—21no—
132C22⋊C4×C29—21no—
133C42×C29—21no—
134C42×C29—41no—
135C42×C29—41no—
136C42×C29C2×D411yescharacteristic
137C42×C29C2×D411yescharacteristic
138C42×C29C2×D411yescharacteristic
139C42×C29#4111yescharacteristic
140#9051C2911yesmaximal, characteristic, direct product factor, Sylow
141C23×C29—21no—
142C23×C29C4×D411yescharacteristic
143Q8×C29—22no—
144Q8×C29—22no—
145Q8×C29—41no—
146Q8×C29—41no—
147Q8×C29—41no—
148D4×C29—41no—
149D4×C29—41no—
150D4×C29—41no—
151C2×C4×C29—21no—
152C2×C4×C29—21no—
153C2×C4×C29—21no—
154C2×C4×C29—21no—
155C2×C4×C29—22no—
156C2×C4×C29—21no—
157C2×C4×C29—21no—
158C2×C4×C29—21no—
159C2×C4×C29—41no—
160C2×C4×C29—41no—
161C2×C4×C29—41no—
162C2×C4×C29—41no—
163C2×C4×C29—41no—
164C2×C4×C29—41no—
165C2×C4×C29—41no—
166C2×C4×C29—41no—
167C2×C4×C29C2×C22⋊C411yescharacteristic
168C2×C4×C29C4×D411yescharacteristic
169C2×C4×C29#12011yescharacteristic
170C2×C4×C29#12111yescharacteristic
171C2×C4×C29#12111yescharacteristic
172C2×C4×C29#12311yescharacteristic
173C8×C29—42no—
174C8×C29—41no—
175C8×C29—41no—
176C8×C29—42no—
177C8×C29—41no—
178C8×C29—41no—
179C8×C29—41no—
180C8×C29—41no—
181#3108C2×C2911yescharacteristic
182#2992C2×C2911yescharacteristic
183#1985C2×C2911yescharacteristic, complemented
184#1524C2×C2911yescharacteristic
185#1491C2×C2911yescharacteristic, complemented
186#1302C2×C2911yescharacteristic, complemented
187#1283C2×C2911yescharacteristic, complemented
188C22×C29—21no—
189C22×C29—21no—
190C22×C29—41no—
191C22×C29—41no—
192C22×C29—41no—
193C22×C29#38611yescharacteristic
194C22×C29#44311yescharacteristic
195C22×C29#44411yescharacteristic
196C4×C29—21no—
197C4×C29—21no—
198C4×C29—21no—
199C4×C29—21no—
200C4×C29—21no—
201C4×C29—41no—
202C4×C29—41no—
203C4×C29—42no—
204C4×C29—41no—
205C4×C29—81no—
206C4×C29#45511yescharacteristic
207C4×C29#45611yescharacteristic
208#529C22×C2911yescharacteristic
209C2×C4×Q8C22×C2911yescharacteristic
210#483C4×C2911yescharacteristic
211#480C4×C2911yescharacteristic
212#479—21no—
213#464—21no—
214#451C4×C2911yescharacteristic
215#448C4×C2911yescharacteristic
216#446—21no—
217C4×Q16—21no—
218C4×SD16—21no—
219#435—21no—
220#435—21no—
221C8×D4—21no—
222#433—21no—
223#432C22×C2911yescharacteristic
224#431C22×C2911yescharacteristic
225#424—21no—
226C2×C4⋊C8C22×C2911yescharacteristic
227C4×M16C22×C2911yescharacteristic
228C2×#97C22×C2911yescharacteristic
229#336—21no—
230#336—21no—
231#330—21no—
232#329—21no—
233Q8⋊C8—21no—
234Q8⋊C8—21no—
235C2×C29—21no—
236C2×C29—21no—
237C2×C29—81no—
238C2×C29#187611yescharacteristic
239C2×C29#188211yescharacteristic
240C2×C29#189111yescharacteristic
241C22×Q8C2×C4×C2911yescharacteristic
242C2×Q16—21no—
243C2×SD16—21no—
244C2×M16—21no—
245C2×M16—21no—
246C22×C8—21no—
247C22×C8—21no—
248C22×C8D4×C2911yescharacteristic
249C22×C8D4×C2911yescharacteristic
250#126—21no—
251#125D4×C2911yescharacteristic
252#124D4×C2911yescharacteristic
253#123—21no—
254C22⋊Q8C2×C4×C2911yescharacteristic
255#121C2×C4×C2911yescharacteristic
256C4×Q8—21no—
257C4×Q8—21no—
258C4×Q8—21no—
259C4×Q8—21no—
260C4×Q8D4×C2911yescharacteristic
261C4×D4—21no—
262C4×D4D4×C2911yescharacteristic
263#117—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4C2×C4×C2911yescharacteristic
266C2×C42—21no—
267C2×C42C23×C2911yescharacteristic
268#107—21no—
269#106—21no—
270C4⋊C8—21no—
271C4⋊C8—21no—
272C4⋊C8—21no—
273C4⋊C8—21no—
274C4⋊C8—21no—
275C4⋊C8D4×C2911yescharacteristic
276C4⋊C8D4×C2911yescharacteristic
277#103—21no—
278#103—21no—
279#103—21no—
280#102—21no—
281C22⋊C8—21no—
282C22⋊C8—21no—
283C22⋊C8—21no—
284C22⋊C8C2×C4×C2911yescharacteristic
285C22⋊C8C2×C4×C2911yescharacteristic
286#97—21no—
287#97—21no—
288#97—21no—
289#97—21no—
290#97—21no—
291C4×C8—21no—
292C4×C8—21no—
293C4×C8—21no—
294C29#905111yescharacteristic, direct product factor, Sylow
295C2×Q8—21no—
296C2×Q8—21no—
297C2×Q8—42no—
298C2×Q8C22⋊C4×C2911yescharacteristic
299C2×D4—21no—
300C2×D4C22⋊C4×C2911yescharacteristic
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4C22×C4×C2911yescharacteristic
305C22×C4C2×D4×C2911yescharacteristic
306C22×C4#41×C2911yescharacteristic
307Q16—42no—
308SD16—42no—
309M16—22no—
310M16—41no—
311M16—81no—
312C2×C8—22no—
313C2×C8—21no—
314C2×C8—21no—
315C2×C8—21no—
316C2×C8—21no—
317C2×C8—21no—
318C2×C8—21no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8—81no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4C22⋊C4×C2911yescharacteristic
334C4⋊C4C22⋊C4×C2911yescharacteristic
335C22⋊C4—21no—
336C22⋊C4—21no—
337C22⋊C4—21no—
338C22⋊C4—21no—
339C22⋊C4—21no—
340C42—21no—
341C42—41no—
342C42—41no—
343C42C2×D4×C2911yescharacteristic
344C42C2×D4×C2911yescharacteristic
345C42C2×D4×C2911yescharacteristic
346C42#41×C2911yescharacteristic
347C23—21no—
348C23C4×D4×C2911yescharacteristic
349Q8—22no—
350Q8—22no—
351Q8—41no—
352Q8—41no—
353Q8—41no—
354D4—41no—
355D4—41no—
356D4—41no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—22no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4C2×C22⋊C4×C2911yescharacteristic
374C2×C4C4×D4×C2911yescharacteristic
375C2×C4C29×#12011yescharacteristic
376C2×C4C29×#12111yescharacteristic
377C2×C4C29×#12111yescharacteristic
378C2×C4C29×#12311yescharacteristic
379C8—42no—
380C8—41no—
381C8—41no—
382C8—42no—
383C8—41no—
384C8—41no—
385C8—41no—
386C8—41no—
387C22—21no—
388C22—21no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22C29×#38611yescharacteristic
393C22C29×#44311yescharacteristic
394C22C29×#44411yescharacteristic
395C4—21no—
396C4—21no—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—42no—
403C4—41no—
404C4—81no—
405C4C29×#45511yescharacteristic
406C4C29×#45611yescharacteristic
407C2—21no—
408C2—21no—
409C2—81no—
410C2C29×#187611yescharacteristic
411C2C29×#188211yescharacteristic
412C2C29×#189111yescharacteristic
subgroupG/H
centerC2×C4×C29#120
commutatorC22×C4C22×C4×C29
Frattini, cosocleC2×C42C23×C29
socleC22×C29#386
prime radicalC29×#121C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
3. C29×#1985C2semidirect
5. C29×#1491C2semidirect
6. C29×#1302C2semidirect
7. C29×#1283C2semidirect
140. #9051C29direct (N × H)
183. #1985C2×C29semidirect
185. #1491C2×C29semidirect
186. #1302C2×C29semidirect
187. #1283C2×C29semidirect
294. C29#9051direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#31082
C29×#29922
C29×#19852
C29×#15242
C29×#14912
C29×#13022
C29×#12832
#905129