Finite Group Databasebeta

← C29×#19245 #20314145

Subgroups — C29×#19245 #20314145

Order 7424.

606 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3246C211yesmaximal, characteristic
2C29×#3209C211yesmaximal, characteristic, complemented
3C29×#3141C211yesmaximal, characteristic
4C29×#2962C211yesmaximal, characteristic, complemented
5C29×#1702C212yesmaximal, complemented
6C29×#1700C212yesmaximal, complemented
7C29×#1682C212yesmaximal, complemented
8C29×#1680C212yesmaximal, complemented
9C29×#1565C211yesmaximal, characteristic, complemented
10C29×#1540C211yesmaximal, characteristic
11C2×C29×#332C211yesmaximal, characteristic, complemented
12C29×#533C2211yescharacteristic
13C29×#532C2211yescharacteristic
14C2×C29×C4⋊Q8C2211yescharacteristic
15C29×#494—21no—
16C29×#489—22no—
17C29×#487—21no—
18C29×#487C2212yes—
19C29×#486C2212yes—
20C29×#476—21no—
21C29×#475C2212yes—
22C29×#465—22no—
23C29×#462C2212yes—
24C29×#462C2212yes—
25C29×#461—21no—
26C29×#460C2212yes—
27C29×#451—22no—
28C29×#446—22no—
29C29×#446C2212yes—
30C8×Q8×C29C2212yes—
31C29×#431C2211yescharacteristic
32C29×#424—21no—
33C2×C29×C4⋊C8C2211yescharacteristic
34C2×C29×C4⋊C8C2211yescharacteristic
35C29×#417—21no—
36C29×#417—21no—
37C29×#405—21no—
38C4×M16×C29C2211yescharacteristic
39C29×#335C2212yes—
40C29×#334C2212yes—
41C29×#332C2211yescharacteristic
42C29×#332C2212yes—
43C29×#332C2211yescharacteristic
44C29×#332C2212yes—
45C29×#331C2211yescharacteristic
46C29×#331C2211yescharacteristic
47C2×#41×C29—21no—
48C22×Q8×C29—21no—
49C2×Q16×C29—22no—
50C2×Q16×C29—22no—
51C2×SD16×C29—22no—
52C2×M16×C29D411yescharacteristic
53C2×M16×C29D411yescharacteristic
54C22×C8×C29—21no—
55C22×C8×C29—21no—
56C29×C4⋊Q8—21no—
57C29×C4⋊Q8—21no—
58C29×C4⋊Q8—21no—
59C29×C4⋊Q8D411yescharacteristic
60C29×C4⋊Q8D411yescharacteristic
61C29×C4⋊Q8C2312yes—
62C29×C4⋊Q8C2311yescharacteristic
63C29×#127C2311yescharacteristic
64C29×#125—21no—
65C29×#124—21no—
66C29×C22⋊Q8—21no—
67C29×C22⋊Q8D412yes—
68C29×#121—21no—
69C29×#121—21no—
70C4×Q8×C29—21no—
71C4×Q8×C29C2312yes—
72C4×D4×C29—21no—
73C4×D4×C29—21no—
74C29×#117—21no—
75C2×C4⋊C4×C29—21no—
76C2×C4⋊C4×C29—21no—
77C2×C42×C29C2311yescharacteristic
78C29×#106—22no—
79C29×C4⋊C8—22no—
80C29×C4⋊C8—22no—
81C29×C4⋊C8—21no—
82C29×C4⋊C8—21no—
83C29×C4⋊C8C2311yescharacteristic
84C29×C4⋊C8C2311yescharacteristic
85C29×C4⋊C8C2311yescharacteristic
86C29×C4⋊C8C2311yescharacteristic
87C29×C4⋊C8C2312yes—
88C29×#103—22no—
89C29×#103—22no—
90C29×#103—22no—
91C29×#103—22no—
92C29×#103—22no—
93C29×#102—22no—
94C29×#102—22no—
95C29×#102—22no—
96C29×C22⋊C8—21no—
97C29×#97—22no—
98C29×#97D412yes—
99C4×C8×C29—22no—
100C4×C8×C29—21no—
101C4×C8×C29C2312yes—
102#41×C29—42no—
103#41×C29—42no—
104C2×Q8×C29—21no—
105C2×Q8×C29—21no—
106C2×Q8×C29—22no—
107C2×Q8×C29—41no—
108C2×Q8×C29—81no—
109C2×Q8×C29—81no—
110C2×Q8×C29C2×D412yes—
111C2×D4×C29—21no—
112C2×D4×C29—21no—
113C2×D4×C29—21no—
114C2×D4×C29—41no—
115C22×C4×C29—41no—
116C22×C4×C29—41no—
117C22×C4×C29C2×D411yescharacteristic
118C22×C4×C29C2×D411yescharacteristic
119C22×C4×C29#4111yescharacteristic
120Q16×C29—82no—
121Q16×C29—82no—
122SD16×C29—82no—
123M16×C29—22no—
124M16×C29—22no—
125C2×C8×C29—22no—
126C2×C8×C29—21no—
127C2×C8×C29—21no—
128C2×C8×C29—21no—
129C2×C8×C29—21no—
130C2×C8×C29—42no—
131C2×C8×C29—81no—
132C2×C8×C29C2×D412yes—
133C2×C8×C29C2×D412yes—
134C4⋊C4×C29—21no—
135C4⋊C4×C29—21no—
136C4⋊C4×C29—21no—
137C4⋊C4×C29—22no—
138C4⋊C4×C29—22no—
139C4⋊C4×C29—22no—
140C4⋊C4×C29—21no—
141C4⋊C4×C29—22no—
142C4⋊C4×C29—21no—
143C4⋊C4×C29—41no—
144C4⋊C4×C29—41no—
145C4⋊C4×C29C2×D412yes—
146C22⋊C4×C29—22no—
147C22⋊C4×C29—41no—
148C22⋊C4×C29—41no—
149C42×C29—22no—
150C42×C29C2×D411yescharacteristic
151C42×C29C2×D411yescharacteristic
152C42×C29#4111yescharacteristic
153C42×C29C2411yescharacteristic
154#19245C2911yesmaximal, characteristic, direct product factor, Sylow
155C23×C29—41no—
156C23×C29#12111yescharacteristic
157Q8×C29—22no—
158Q8×C29—22no—
159Q8×C29—41no—
160Q8×C29—41no—
161Q8×C29—42no—
162Q8×C29—42no—
163Q8×C29—81no—
164Q8×C29—82no—
165D4×C29—41no—
166D4×C29—41no—
167D4×C29—41no—
168D4×C29—41no—
169D4×C29—81no—
170D4×C29—82no—
171C2×C4×C29—21no—
172C2×C4×C29—21no—
173C2×C4×C29—22no—
174C2×C4×C29—22no—
175C2×C4×C29—41no—
176C2×C4×C29—41no—
177C2×C4×C29—42no—
178C2×C4×C29—82no—
179C2×C4×C29—82no—
180C2×C4×C29#12111yescharacteristic
181C2×C4×C29#12111yescharacteristic
182C2×C4×C29#12111yescharacteristic
183C2×C4×C29#13512yes—
184C2×C4×C29#13712yes—
185C2×C4×C29C22×D411yescharacteristic
186C2×C4×C29C22×D411yescharacteristic
187C2×C4×C29C2×#4111yescharacteristic
188C8×C29—22no—
189C8×C29—22no—
190C8×C29—41no—
191C8×C29—41no—
192C8×C29—42no—
193C8×C29—41no—
194C8×C29—41no—
195#3246C2×C2911yescharacteristic
196#3209C2×C2911yescharacteristic, complemented
197#3141C2×C2911yescharacteristic
198#2962C2×C2911yescharacteristic, complemented
199#1702C2×C2912yescomplemented
200#1700C2×C2912yescomplemented
201#1682C2×C2912yescomplemented
202#1680C2×C2912yescomplemented
203#1565C2×C2911yescharacteristic, complemented
204#1540C2×C2911yescharacteristic
205C2×#332C2×C2911yescharacteristic, complemented
206C22×C29—21no—
207C22×C29—21no—
208C22×C29—81no—
209C22×C29—81no—
210C22×C29—81no—
211C22×C29#46412yes—
212C22×C29C2×#12111yescharacteristic
213C4×C29—21no—
214C4×C29—21no—
215C4×C29—21no—
216C4×C29—42no—
217C4×C29—42no—
218C4×C29—81no—
219C4×C29—82no—
220C4×C29#46412yes—
221C4×C29C2×#13511yescharacteristic
222C4×C29C2×#13711yescharacteristic
223C4×C29#57611yescharacteristic
224C4×C29#57711yescharacteristic
225#533C22×C2911yescharacteristic
226#532C22×C2911yescharacteristic
227C2×C4⋊Q8C22×C2911yescharacteristic
228#494—21no—
229#489—22no—
230#487—21no—
231#487C22×C2912yes—
232#486C22×C2912yes—
233#476—21no—
234#475C22×C2912yes—
235#465—22no—
236#462C22×C2912yes—
237#462C22×C2912yes—
238#461—21no—
239#460C22×C2912yes—
240#451—22no—
241#446—22no—
242#446C22×C2912yes—
243C8×Q8C22×C2912yes—
244#431C22×C2911yescharacteristic
245#424—21no—
246C2×C4⋊C8C22×C2911yescharacteristic
247C2×C4⋊C8C22×C2911yescharacteristic
248#417—21no—
249#417—21no—
250#405—21no—
251C4×M16C22×C2911yescharacteristic
252#335C22×C2912yes—
253#334C22×C2912yes—
254#332C22×C2912yes—
255#332C22×C2912yes—
256#332C22×C2911yescharacteristic
257#332C22×C2911yescharacteristic
258#331C22×C2911yescharacteristic
259#331C22×C2911yescharacteristic
260C2×C29—22no—
261C2×C29—161no—
262C2×C29C2×#46411yescharacteristic
263C2×C29#306211yescharacteristic
264C2×C29#306911yescharacteristic
265C2×#41—21no—
266C22×Q8—21no—
267C2×Q16—22no—
268C2×Q16—22no—
269C2×SD16—22no—
270C2×M16D4×C2911yescharacteristic
271C2×M16D4×C2911yescharacteristic
272C22×C8—21no—
273C22×C8—21no—
274C4⋊Q8—21no—
275C4⋊Q8—21no—
276C4⋊Q8—21no—
277C4⋊Q8D4×C2911yescharacteristic
278C4⋊Q8D4×C2911yescharacteristic
279C4⋊Q8C23×C2912yes—
280C4⋊Q8C23×C2911yescharacteristic
281#127C23×C2911yescharacteristic
282#125—21no—
283#124—21no—
284C22⋊Q8—21no—
285C22⋊Q8D4×C2912yes—
286#121—21no—
287#121—21no—
288C4×Q8—21no—
289C4×Q8C23×C2912yes—
290C4×D4—21no—
291C4×D4—21no—
292#117—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C42C23×C2911yescharacteristic
296#106—22no—
297C4⋊C8—22no—
298C4⋊C8—22no—
299C4⋊C8—21no—
300C4⋊C8—21no—
301C4⋊C8C23×C2911yescharacteristic
302C4⋊C8C23×C2911yescharacteristic
303C4⋊C8C23×C2911yescharacteristic
304C4⋊C8C23×C2911yescharacteristic
305C4⋊C8C23×C2912yes—
306#103—22no—
307#103—22no—
308#103—22no—
309#103—22no—
310#103—22no—
311#102—22no—
312#102—22no—
313#102—22no—
314C22⋊C8—21no—
315#97—22no—
316#97D4×C2912yes—
317C4×C8—22no—
318C4×C8—21no—
319C4×C8C23×C2912yes—
320C29#1924511yescharacteristic, direct product factor, Sylow
321#41—42no—
322#41—42no—
323C2×Q8—21no—
324C2×Q8—21no—
325C2×Q8—22no—
326C2×Q8—41no—
327C2×Q8—81no—
328C2×Q8—81no—
329C2×Q8C2×D4×C2912yes—
330C2×D4—21no—
331C2×D4—21no—
332C2×D4—21no—
333C2×D4—41no—
334C22×C4—41no—
335C22×C4—41no—
336C22×C4C2×D4×C2911yescharacteristic
337C22×C4C2×D4×C2911yescharacteristic
338C22×C4#41×C2911yescharacteristic
339Q16—82no—
340Q16—82no—
341SD16—82no—
342M16—22no—
343M16—22no—
344C2×C8—21no—
345C2×C8—21no—
346C2×C8—21no—
347C2×C8—21no—
348C2×C8—22no—
349C2×C8—42no—
350C2×C8—81no—
351C2×C8C2×D4×C2912yes—
352C2×C8C2×D4×C2912yes—
353C4⋊C4—21no—
354C4⋊C4—21no—
355C4⋊C4—21no—
356C4⋊C4—22no—
357C4⋊C4—22no—
358C4⋊C4—22no—
359C4⋊C4—21no—
360C4⋊C4—22no—
361C4⋊C4—21no—
362C4⋊C4—41no—
363C4⋊C4—41no—
364C4⋊C4C2×D4×C2912yes—
365C22⋊C4—22no—
366C22⋊C4—41no—
367C22⋊C4—41no—
368C42—22no—
369C42C2×D4×C2911yescharacteristic
370C42C2×D4×C2911yescharacteristic
371C42#41×C2911yescharacteristic
372C42C24×C2911yescharacteristic
373C23—41no—
374C23C29×#12111yescharacteristic
375Q8—22no—
376Q8—22no—
377Q8—41no—
378Q8—41no—
379Q8—42no—
380Q8—42no—
381Q8—81no—
382Q8—82no—
383D4—41no—
384D4—41no—
385D4—41no—
386D4—41no—
387D4—81no—
388D4—82no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—42no—
396C2×C4—82no—
397C2×C4—82no—
398C2×C4C29×#12111yescharacteristic
399C2×C4C29×#12111yescharacteristic
400C2×C4C29×#12111yescharacteristic
401C2×C4C29×#13512yes—
402C2×C4C29×#13712yes—
403C2×C4C22×D4×C2911yescharacteristic
404C2×C4C22×D4×C2911yescharacteristic
405C2×C4C2×#41×C2911yescharacteristic
406C8—22no—
407C8—22no—
408C8—41no—
409C8—41no—
410C8—42no—
411C8—41no—
412C8—41no—
413C22—21no—
414C22—21no—
415C22—81no—
416C22—81no—
417C22—81no—
418C22C29×#46412yes—
419C22C2×C29×#12111yescharacteristic
420C4—21no—
421C4—21no—
422C4—21no—
423C4—42no—
424C4—42no—
425C4—81no—
426C4—82no—
427C4C29×#46412yes—
428C4C2×C29×#13511yescharacteristic
429C4C2×C29×#13711yescharacteristic
430C4C29×#57611yescharacteristic
431C4C29×#57711yescharacteristic
432C2—22no—
433C2—161no—
434C2C2×C29×#46411yescharacteristic
435C2C29×#306211yescharacteristic
436C2C29×#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
2. C29×#3209C2semidirect
4. C29×#2962C2semidirect
5. C29×#1702C2semidirect
6. C29×#1700C2semidirect
7. C29×#1682C2semidirect
8. C29×#1680C2semidirect
9. C29×#1565C2semidirect
11. C2×C29×#332C2semidirect
154. #19245C29direct (N × H)
196. #3209C2×C29semidirect
198. #2962C2×C29semidirect
199. #1702C2×C29semidirect
200. #1700C2×C29semidirect
201. #1682C2×C29semidirect
202. #1680C2×C29semidirect
203. #1565C2×C29semidirect
205. C2×#332C2×C29semidirect
320. C29#19245direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32462
C29×#32092
C29×#31412
C29×#29622
C29×#17022
C29×#17002
C29×#16822
C29×#16802
C29×#15652
C29×#15402
C2×C29×#3322
#1924529