Finite Group Databasebeta

← C29×#19521 #20314421

Subgroups — C29×#19521 #20314421

Order 7424.

582 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3229C211yesmaximal, characteristic, complemented
2C29×#3216C211yesmaximal, characteristic
3C29×#3206C211yesmaximal, characteristic
4C29×#2985C211yesmaximal, characteristic, complemented
5C29×#1700C212yesmaximal, complemented
6C29×#1686C212yesmaximal, complemented
7C29×#1680C212yesmaximal, complemented
8C29×#1666C212yesmaximal, complemented
9C29×#1572C211yesmaximal, characteristic, complemented
10C29×#1556C211yesmaximal, characteristic, complemented
11C29×#1553C211yesmaximal, characteristic
12C29×#533C2211yescharacteristic
13C29×#532C2211yescharacteristic
14C2×C29×C4⋊Q8C2211yescharacteristic
15C29×#498—21no—
16C29×#497—21no—
17C29×#492C2211yescharacteristic
18C29×#492C2211yescharacteristic
19C29×#489—21no—
20C29×#487—21no—
21C29×#487C2211yescharacteristic
22C29×#487C2211yescharacteristic
23C29×#483—22no—
24C29×#475C2212yes—
25C29×#475C2212yes—
26C29×#462C2212yes—
27C29×#461—22no—
28C29×#460C2212yes—
29C29×#452—22no—
30C29×#448—22no—
31C29×#446—22no—
32C29×#446C2212yes—
33C8×Q8×C29C2212yes—
34C29×#433—22no—
35C29×#432C2211yescharacteristic
36C29×#432C2211yescharacteristic
37C29×#431C2211yescharacteristic
38C29×#431C2211yescharacteristic
39C29×#335C2212yes—
40C29×#334C2212yes—
41C29×#332C2212yes—
42C29×#332C2212yes—
43C29×#332C2212yes—
44C29×#331C2212yes—
45C2×#41×C29—21no—
46C22×Q8×C29—21no—
47C2×Q16×C29—22no—
48C2×SD16×C29—22no—
49C2×SD16×C29—22no—
50C2×SD16×C29—22no—
51C29×C4⋊Q8—21no—
52C29×C4⋊Q8—21no—
53C29×C4⋊Q8—21no—
54C29×C4⋊Q8D411yescharacteristic
55C29×C4⋊Q8D411yescharacteristic
56C29×C4⋊Q8C2311yescharacteristic
57C29×C4⋊Q8C2311yescharacteristic
58C29×C4⋊Q8C2311yescharacteristic
59C29×#127C2311yescharacteristic
60C29×#125—21no—
61C29×#124—21no—
62C29×C22⋊Q8—21no—
63C29×C22⋊Q8D412yes—
64C29×#121—21no—
65C29×#121—21no—
66C4×Q8×C29—21no—
67C4×Q8×C29C2312yes—
68C4×D4×C29—21no—
69C4×D4×C29—21no—
70C29×#117—21no—
71C2×C4⋊C4×C29—21no—
72C2×C4⋊C4×C29—21no—
73C2×C42×C29C2311yescharacteristic
74C29×#106—22no—
75C29×#106—22no—
76C29×C4⋊C8—22no—
77C29×C4⋊C8—22no—
78C29×C4⋊C8D412yes—
79C29×C4⋊C8C2312yes—
80C29×C4⋊C8C2312yes—
81C29×C4⋊C8C2312yes—
82C29×#103—22no—
83C29×#103—22no—
84C29×#103—22no—
85C29×#103—22no—
86C29×#103—22no—
87C29×#102—22no—
88C29×C22⋊C8—21no—
89C29×C22⋊C8—21no—
90C29×C22⋊C8—21no—
91C29×C22⋊C8D412yes—
92C29×#97—22no—
93C29×#97—21no—
94C29×#97—21no—
95C4×C8×C29—22no—
96C4×C8×C29—21no—
97C4×C8×C29C2311yescharacteristic
98C4×C8×C29C2311yescharacteristic
99#41×C29—82no—
100C2×Q8×C29—21no—
101C2×Q8×C29—21no—
102C2×Q8×C29—21no—
103C2×Q8×C29—21no—
104C2×Q8×C29—41no—
105C2×Q8×C29—82no—
106C2×Q8×C29C2×D412yes—
107C2×D4×C29—21no—
108C2×D4×C29—21no—
109C2×D4×C29—21no—
110C2×D4×C29—41no—
111C22×C4×C29—41no—
112C22×C4×C29—41no—
113C22×C4×C29C2×D411yescharacteristic
114C22×C4×C29C2×D411yescharacteristic
115C22×C4×C29#4111yescharacteristic
116Q16×C29—82no—
117SD16×C29—82no—
118SD16×C29—82no—
119SD16×C29—82no—
120C2×C8×C29—22no—
121C2×C8×C29—22no—
122C2×C8×C29—22no—
123C2×C8×C29C2×D412yes—
124C2×C8×C29C2×D412yes—
125C4⋊C4×C29—21no—
126C4⋊C4×C29—21no—
127C4⋊C4×C29—21no—
128C4⋊C4×C29—22no—
129C4⋊C4×C29—22no—
130C4⋊C4×C29—21no—
131C4⋊C4×C29—21no—
132C4⋊C4×C29—21no—
133C4⋊C4×C29—21no—
134C4⋊C4×C29—21no—
135C4⋊C4×C29—21no—
136C4⋊C4×C29—41no—
137C4⋊C4×C29—41no—
138C4⋊C4×C29C2×D412yes—
139C22⋊C4×C29—22no—
140C22⋊C4×C29—41no—
141C22⋊C4×C29—41no—
142C42×C29—22no—
143C42×C29C2×D411yescharacteristic
144C42×C29C2×D411yescharacteristic
145C42×C29#4111yescharacteristic
146C42×C29C2411yescharacteristic
147#19521C2911yesmaximal, characteristic, direct product factor, Sylow
148C23×C29—41no—
149C23×C29#12111yescharacteristic
150Q8×C29—22no—
151Q8×C29—22no—
152Q8×C29—42no—
153Q8×C29—42no—
154Q8×C29—42no—
155Q8×C29—81no—
156Q8×C29—82no—
157D4×C29—42no—
158D4×C29—42no—
159D4×C29—81no—
160D4×C29—82no—
161C2×C4×C29—22no—
162C2×C4×C29—22no—
163C2×C4×C29—22no—
164C2×C4×C29—22no—
165C2×C4×C29—41no—
166C2×C4×C29—41no—
167C2×C4×C29—41no—
168C2×C4×C29—41no—
169C2×C4×C29—82no—
170C2×C4×C29—82no—
171C2×C4×C29#12111yescharacteristic
172C2×C4×C29#12111yescharacteristic
173C2×C4×C29#12111yescharacteristic
174C2×C4×C29C22×D411yescharacteristic
175C2×C4×C29C22×D411yescharacteristic
176C2×C4×C29C2×#4111yescharacteristic
177C8×C29—22no—
178C8×C29—22no—
179C8×C29—42no—
180C8×C29—42no—
181C8×C29—42no—
182#3229C2×C2911yescharacteristic, complemented
183#3216C2×C2911yescharacteristic
184#3206C2×C2911yescharacteristic
185#2985C2×C2911yescharacteristic, complemented
186#1700C2×C2912yescomplemented
187#1686C2×C2912yescomplemented
188#1680C2×C2912yescomplemented
189#1666C2×C2912yescomplemented
190#1572C2×C2911yescharacteristic, complemented
191#1556C2×C2911yescharacteristic, complemented
192#1553C2×C2911yescharacteristic
193C22×C29—21no—
194C22×C29—21no—
195C22×C29—21no—
196C22×C29—81no—
197C22×C29—81no—
198C22×C29—81no—
199C22×C29C2×#12111yescharacteristic
200C4×C29—21no—
201C4×C29—21no—
202C4×C29—21no—
203C4×C29—21no—
204C4×C29—42no—
205C4×C29—42no—
206C4×C29—81no—
207C4×C29—81no—
208C4×C29—81no—
209C4×C29#57712yes—
210C4×C29#57712yes—
211#533C22×C2911yescharacteristic
212#532C22×C2911yescharacteristic
213C2×C4⋊Q8C22×C2911yescharacteristic
214#498—21no—
215#497—21no—
216#492C22×C2911yescharacteristic
217#492C22×C2911yescharacteristic
218#489—21no—
219#487—21no—
220#487C22×C2911yescharacteristic
221#487C22×C2911yescharacteristic
222#483—22no—
223#475C22×C2912yes—
224#475C22×C2912yes—
225#462C22×C2912yes—
226#461—22no—
227#460C22×C2912yes—
228#452—22no—
229#448—22no—
230#446—22no—
231#446C22×C2912yes—
232C8×Q8C22×C2912yes—
233#433—22no—
234#432C22×C2911yescharacteristic
235#432C22×C2911yescharacteristic
236#431C22×C2911yescharacteristic
237#431C22×C2911yescharacteristic
238#335C22×C2912yes—
239#334C22×C2912yes—
240#332C22×C2912yes—
241#332C22×C2912yes—
242#332C22×C2912yes—
243#331C22×C2912yes—
244C2×C29—41no—
245C2×C29—161no—
246C2×C29#304311yescharacteristic
247C2×C29#305711yescharacteristic
248C2×C29#306911yescharacteristic
249C2×#41—21no—
250C22×Q8—21no—
251C2×Q16—22no—
252C2×SD16—22no—
253C2×SD16—22no—
254C2×SD16—22no—
255C4⋊Q8—21no—
256C4⋊Q8—21no—
257C4⋊Q8—21no—
258C4⋊Q8D4×C2911yescharacteristic
259C4⋊Q8D4×C2911yescharacteristic
260C4⋊Q8C23×C2911yescharacteristic
261C4⋊Q8C23×C2911yescharacteristic
262C4⋊Q8C23×C2911yescharacteristic
263#127C23×C2911yescharacteristic
264#125—21no—
265#124—21no—
266C22⋊Q8—21no—
267C22⋊Q8D4×C2912yes—
268#121—21no—
269#121—21no—
270C4×Q8—21no—
271C4×Q8C23×C2912yes—
272C4×D4—21no—
273C4×D4—21no—
274#117—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C42C23×C2911yescharacteristic
278#106—22no—
279#106—22no—
280C4⋊C8—22no—
281C4⋊C8—22no—
282C4⋊C8D4×C2912yes—
283C4⋊C8C23×C2912yes—
284C4⋊C8C23×C2912yes—
285C4⋊C8C23×C2912yes—
286#103—22no—
287#103—22no—
288#103—22no—
289#103—22no—
290#103—22no—
291#102—22no—
292C22⋊C8—21no—
293C22⋊C8—21no—
294C22⋊C8—21no—
295C22⋊C8D4×C2912yes—
296#97—22no—
297#97—21no—
298#97—21no—
299C4×C8—22no—
300C4×C8—21no—
301C4×C8C23×C2911yescharacteristic
302C4×C8C23×C2911yescharacteristic
303C29#1952111yescharacteristic, direct product factor, Sylow
304#41—82no—
305C2×Q8—21no—
306C2×Q8—21no—
307C2×Q8—21no—
308C2×Q8—21no—
309C2×Q8—41no—
310C2×Q8—82no—
311C2×Q8C2×D4×C2912yes—
312C2×D4—21no—
313C2×D4—21no—
314C2×D4—21no—
315C2×D4—41no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4C2×D4×C2911yescharacteristic
319C22×C4C2×D4×C2911yescharacteristic
320C22×C4#41×C2911yescharacteristic
321Q16—82no—
322SD16—82no—
323SD16—82no—
324SD16—82no—
325C2×C8—22no—
326C2×C8—22no—
327C2×C8—22no—
328C2×C8C2×D4×C2912yes—
329C2×C8C2×D4×C2912yes—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4—22no—
334C4⋊C4—22no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4C2×D4×C2912yes—
344C22⋊C4—22no—
345C22⋊C4—41no—
346C22⋊C4—41no—
347C42—22no—
348C42C2×D4×C2911yescharacteristic
349C42C2×D4×C2911yescharacteristic
350C42#41×C2911yescharacteristic
351C42C24×C2911yescharacteristic
352C23—41no—
353C23C29×#12111yescharacteristic
354Q8—22no—
355Q8—22no—
356Q8—42no—
357Q8—42no—
358Q8—42no—
359Q8—81no—
360Q8—82no—
361D4—42no—
362D4—42no—
363D4—81no—
364D4—82no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—82no—
374C2×C4—82no—
375C2×C4C29×#12111yescharacteristic
376C2×C4C29×#12111yescharacteristic
377C2×C4C29×#12111yescharacteristic
378C2×C4C22×D4×C2911yescharacteristic
379C2×C4C22×D4×C2911yescharacteristic
380C2×C4C2×#41×C2911yescharacteristic
381C8—22no—
382C8—22no—
383C8—42no—
384C8—42no—
385C8—42no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—81no—
390C22—81no—
391C22—81no—
392C22C2×C29×#12111yescharacteristic
393C4—21no—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—42no—
398C4—42no—
399C4—81no—
400C4—81no—
401C4—81no—
402C4C29×#57712yes—
403C4C29×#57712yes—
404C2—41no—
405C2—161no—
406C2C29×#304311yescharacteristic
407C2C29×#305711yescharacteristic
408C2C29×#306911yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#3229C2semidirect
4. C29×#2985C2semidirect
5. C29×#1700C2semidirect
6. C29×#1686C2semidirect
7. C29×#1680C2semidirect
8. C29×#1666C2semidirect
9. C29×#1572C2semidirect
10. C29×#1556C2semidirect
147. #19521C29direct (N × H)
182. #3229C2×C29semidirect
185. #2985C2×C29semidirect
186. #1700C2×C29semidirect
187. #1686C2×C29semidirect
188. #1680C2×C29semidirect
189. #1666C2×C29semidirect
190. #1572C2×C29semidirect
191. #1556C2×C29semidirect
303. C29#19521direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32292
C29×#32162
C29×#32062
C29×#29852
C29×#17002
C29×#16862
C29×#16802
C29×#16662
C29×#15722
C29×#15562
C29×#15532
#1952129