Finite Group Databasebeta

← C29×#19363 #20314263

Subgroups — C29×#19363 #20314263

Order 7424.

596 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3239C211yesmaximal, characteristic
2C29×#3218C211yesmaximal, characteristic
3C2×C29×#487C211yesmaximal, characteristic, complemented
4C29×#2966C211yesmaximal, characteristic
5C29×#1700C212yesmaximal, complemented
6C29×#1699C212yesmaximal, complemented
7C29×#1680C212yesmaximal, complemented
8C29×#1679C212yesmaximal, complemented
9C29×#1568C211yesmaximal, characteristic, complemented
10C29×#1556C211yesmaximal, characteristic, complemented
11C29×#1556C211yesmaximal, characteristic, complemented
12C2×C29×C4⋊Q8C2211yescharacteristic
13C2×C29×C4⋊Q8C2211yescharacteristic
14C29×#529C2211yescharacteristic
15C29×#501—21no—
16C29×#497—21no—
17C29×#491—21no—
18C29×#489—21no—
19C29×#487—21no—
20C29×#487—21no—
21C29×#487C2212yes—
22C29×#487C2212yes—
23C29×#484—21no—
24C29×#481—21no—
25C29×#475C2212yes—
26C29×#474C2212yes—
27C29×#462C2212yes—
28C29×#461C2212yes—
29C29×#451—21no—
30C29×#448—21no—
31C29×#446C2211yescharacteristic
32C8×Q8×C29C2211yescharacteristic
33C29×#436C2211yescharacteristic
34C29×#435—21no—
35C8×D4×C29—21no—
36C8×D4×C29C2211yescharacteristic
37C29×#433—21no—
38C29×#432C2211yescharacteristic
39C29×#432C2211yescharacteristic
40C29×#432C2211yescharacteristic
41C2×C29×#103—21no—
42C2×C29×#103—21no—
43C29×#405—21no—
44C2×C4×C8×C29C2211yescharacteristic
45C29×#335C2212yes—
46C29×#334C2212yes—
47C29×#332C2212yes—
48C29×#332C2212yes—
49C29×#332C2212yes—
50C29×#332C2212yes—
51C22×Q8×C29—21no—
52C22×Q8×C29—21no—
53C2×Q16×C29—22no—
54C2×SD16×C29—22no—
55C2×M16×C29—21no—
56C22×C8×C29—21no—
57C22×C8×C29D411yescharacteristic
58C22×C8×C29D411yescharacteristic
59C29×C4⋊Q8—21no—
60C29×C4⋊Q8—21no—
61C29×C4⋊Q8—21no—
62C29×C4⋊Q8—21no—
63C29×C4⋊Q8—21no—
64C29×C4⋊Q8—21no—
65C29×C4⋊Q8C2312yes—
66C29×C4⋊Q8C2312yes—
67C29×#126—21no—
68C29×#125D411yescharacteristic
69C29×#124D411yescharacteristic
70C29×#123—21no—
71C29×C22⋊Q8D411yescharacteristic
72C29×#121D411yescharacteristic
73C4×Q8×C29C2311yescharacteristic
74C4×D4×C29—21no—
75C4×D4×C29C2311yescharacteristic
76C29×#117—21no—
77C2×C4⋊C4×C29—21no—
78C2×C4⋊C4×C29—21no—
79C2×C4⋊C4×C29—21no—
80C2×C4⋊C4×C29—21no—
81C2×C42×C29C2311yescharacteristic
82C29×#107—22no—
83C29×#106—22no—
84C29×C4⋊C8—21no—
85C29×C4⋊C8—21no—
86C29×C4⋊C8C2311yescharacteristic
87C29×C4⋊C8C2311yescharacteristic
88C29×C4⋊C8C2312yes—
89C29×C4⋊C8C2312yes—
90C29×#103—22no—
91C29×#103—22no—
92C29×#103—22no—
93C29×#103—22no—
94C29×#103—22no—
95C29×#103—22no—
96C29×#103—22no—
97C29×#102—22no—
98C29×C22⋊C8—21no—
99C29×C22⋊C8—21no—
100C29×C22⋊C8—21no—
101C29×C22⋊C8—21no—
102C29×C22⋊C8—21no—
103C29×#97—21no—
104C29×#97—21no—
105C29×#97—21no—
106C29×#97—21no—
107C4×C8×C29—21no—
108C4×C8×C29D411yescharacteristic
109C4×C8×C29D411yescharacteristic
110C4×C8×C29C2311yescharacteristic
111C4×C8×C29C2311yescharacteristic
112C2×Q8×C29—22no—
113C2×Q8×C29—22no—
114C2×Q8×C29—42no—
115C2×Q8×C29—42no—
116C2×Q8×C29—41no—
117C2×Q8×C29—41no—
118C2×Q8×C29—82no—
119C2×Q8×C29C2×D411yescharacteristic
120C2×D4×C29—21no—
121C2×D4×C29C2×D411yescharacteristic
122C22×C4×C29—21no—
123C22×C4×C29—41no—
124C22×C4×C29—41no—
125C22×C4×C29C2×D411yescharacteristic
126C22×C4×C29C2×D411yescharacteristic
127C22×C4×C29#4111yescharacteristic
128Q16×C29—82no—
129SD16×C29—82no—
130M16×C29—42no—
131C2×C8×C29—21no—
132C2×C8×C29—21no—
133C2×C8×C29—22no—
134C2×C8×C29—22no—
135C2×C8×C29—41no—
136C2×C8×C29—41no—
137C2×C8×C29—42no—
138C2×C8×C29C2×D411yescharacteristic
139C2×C8×C29C2×D411yescharacteristic
140C2×C8×C29C2×D411yescharacteristic
141C2×C8×C29C2×D411yescharacteristic
142C4⋊C4×C29—21no—
143C4⋊C4×C29—21no—
144C4⋊C4×C29—21no—
145C4⋊C4×C29—21no—
146C4⋊C4×C29—22no—
147C4⋊C4×C29—22no—
148C4⋊C4×C29—22no—
149C4⋊C4×C29—22no—
150C4⋊C4×C29—41no—
151C4⋊C4×C29—41no—
152C4⋊C4×C29—41no—
153C4⋊C4×C29—41no—
154C4⋊C4×C29C2×D411yescharacteristic
155C4⋊C4×C29C2×D411yescharacteristic
156C22⋊C4×C29—21no—
157C22⋊C4×C29—21no—
158C22⋊C4×C29—21no—
159C22⋊C4×C29—21no—
160C22⋊C4×C29—21no—
161C42×C29—21no—
162C42×C29C2×D411yescharacteristic
163C42×C29C2×D411yescharacteristic
164C42×C29#4111yescharacteristic
165C42×C29C2411yescharacteristic
166#19363C2911yesmaximal, characteristic, direct product factor, Sylow
167C23×C29—21no—
168C23×C29#12111yescharacteristic
169Q8×C29—22no—
170Q8×C29—42no—
171Q8×C29—42no—
172Q8×C29—42no—
173Q8×C29—42no—
174Q8×C29—82no—
175Q8×C29—82no—
176D4×C29—22no—
177D4×C29—42no—
178C2×C4×C29—22no—
179C2×C4×C29—21no—
180C2×C4×C29—21no—
181C2×C4×C29—22no—
182C2×C4×C29—21no—
183C2×C4×C29—21no—
184C2×C4×C29—21no—
185C2×C4×C29—41no—
186C2×C4×C29—41no—
187C2×C4×C29—42no—
188C2×C4×C29—42no—
189C2×C4×C29—82no—
190C2×C4×C29—82no—
191C2×C4×C29#12111yescharacteristic
192C2×C4×C29#12111yescharacteristic
193C2×C4×C29#12111yescharacteristic
194C2×C4×C29C22×D411yescharacteristic
195C2×C4×C29C22×D411yescharacteristic
196C2×C4×C29C2×#4111yescharacteristic
197C8×C29—21no—
198C8×C29—21no—
199C8×C29—21no—
200C8×C29—21no—
201C8×C29—41no—
202C8×C29—41no—
203C8×C29—42no—
204C8×C29—42no—
205#3239C2×C2911yescharacteristic
206#3218C2×C2911yescharacteristic
207C2×#487C2×C2911yescharacteristic, complemented
208#2966C2×C2911yescharacteristic
209#1700C2×C2912yescomplemented
210#1699C2×C2912yescomplemented
211#1680C2×C2912yescomplemented
212#1679C2×C2912yescomplemented
213#1568C2×C2911yescharacteristic, complemented
214#1556C2×C2911yescharacteristic, complemented
215#1556C2×C2911yescharacteristic, complemented
216C22×C29—21no—
217C22×C29—21no—
218C22×C29—41no—
219C22×C29—41no—
220C22×C29—41no—
221C22×C29#47312yes—
222C22×C29C2×#12111yescharacteristic
223C4×C29—21no—
224C4×C29—21no—
225C4×C29—21no—
226C4×C29—21no—
227C4×C29—41no—
228C4×C29—41no—
229C4×C29—41no—
230C4×C29—82no—
231C4×C29—82no—
232C4×C29#57511yescharacteristic
233C4×C29#57511yescharacteristic
234C4×C29#57712yes—
235C2×C4⋊Q8C22×C2911yescharacteristic
236C2×C4⋊Q8C22×C2911yescharacteristic
237#529C22×C2911yescharacteristic
238#501—21no—
239#497—21no—
240#491—21no—
241#489—21no—
242#487—21no—
243#487—21no—
244#487C22×C2912yes—
245#487C22×C2912yes—
246#484—21no—
247#481—21no—
248#475C22×C2912yes—
249#474C22×C2912yes—
250#462C22×C2912yes—
251#461C22×C2912yes—
252#451—21no—
253#448—21no—
254#446C22×C2911yescharacteristic
255C8×Q8C22×C2911yescharacteristic
256#436C22×C2911yescharacteristic
257#435—21no—
258C8×D4—21no—
259C8×D4C22×C2911yescharacteristic
260#433—21no—
261#432C22×C2911yescharacteristic
262#432C22×C2911yescharacteristic
263#432C22×C2911yescharacteristic
264C2×#103—21no—
265C2×#103—21no—
266#405—21no—
267C2×C4×C8C22×C2911yescharacteristic
268#335C22×C2912yes—
269#334C22×C2912yes—
270#332C22×C2912yes—
271#332C22×C2912yes—
272#332C22×C2912yes—
273#332C22×C2912yes—
274C2×C29—22no—
275C2×C29—81no—
276C2×C29#304011yescharacteristic
277C2×C29#305711yescharacteristic
278C2×C29C2×#47311yescharacteristic
279C22×Q8—21no—
280C22×Q8—21no—
281C2×Q16—22no—
282C2×SD16—22no—
283C2×M16—21no—
284C22×C8—21no—
285C22×C8D4×C2911yescharacteristic
286C22×C8D4×C2911yescharacteristic
287C4⋊Q8—21no—
288C4⋊Q8—21no—
289C4⋊Q8—21no—
290C4⋊Q8—21no—
291C4⋊Q8—21no—
292C4⋊Q8—21no—
293C4⋊Q8C23×C2912yes—
294C4⋊Q8C23×C2912yes—
295#126—21no—
296#125D4×C2911yescharacteristic
297#124D4×C2911yescharacteristic
298#123—21no—
299C22⋊Q8D4×C2911yescharacteristic
300#121D4×C2911yescharacteristic
301C4×Q8C23×C2911yescharacteristic
302C4×D4—21no—
303C4×D4C23×C2911yescharacteristic
304#117—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C42C23×C2911yescharacteristic
310#107—22no—
311#106—22no—
312C4⋊C8—21no—
313C4⋊C8—21no—
314C4⋊C8C23×C2911yescharacteristic
315C4⋊C8C23×C2911yescharacteristic
316C4⋊C8C23×C2912yes—
317C4⋊C8C23×C2912yes—
318#103—22no—
319#103—22no—
320#103—22no—
321#103—22no—
322#103—22no—
323#103—22no—
324#103—22no—
325#102—22no—
326C22⋊C8—21no—
327C22⋊C8—21no—
328C22⋊C8—21no—
329C22⋊C8—21no—
330C22⋊C8—21no—
331#97—21no—
332#97—21no—
333#97—21no—
334#97—21no—
335C4×C8—21no—
336C4×C8D4×C2911yescharacteristic
337C4×C8D4×C2911yescharacteristic
338C4×C8C23×C2911yescharacteristic
339C4×C8C23×C2911yescharacteristic
340C29#1936311yescharacteristic, direct product factor, Sylow
341C2×Q8—22no—
342C2×Q8—22no—
343C2×Q8—42no—
344C2×Q8—42no—
345C2×Q8—41no—
346C2×Q8—41no—
347C2×Q8—82no—
348C2×Q8C2×D4×C2911yescharacteristic
349C2×D4—21no—
350C2×D4C2×D4×C2911yescharacteristic
351C22×C4—21no—
352C22×C4—41no—
353C22×C4—41no—
354C22×C4C2×D4×C2911yescharacteristic
355C22×C4C2×D4×C2911yescharacteristic
356C22×C4#41×C2911yescharacteristic
357Q16—82no—
358SD16—82no—
359M16—42no—
360C2×C8—21no—
361C2×C8—21no—
362C2×C8—22no—
363C2×C8—22no—
364C2×C8—41no—
365C2×C8—41no—
366C2×C8—42no—
367C2×C8C2×D4×C2911yescharacteristic
368C2×C8C2×D4×C2911yescharacteristic
369C2×C8C2×D4×C2911yescharacteristic
370C2×C8C2×D4×C2911yescharacteristic
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—22no—
376C4⋊C4—22no—
377C4⋊C4—22no—
378C4⋊C4—22no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4—41no—
382C4⋊C4—41no—
383C4⋊C4C2×D4×C2911yescharacteristic
384C4⋊C4C2×D4×C2911yescharacteristic
385C22⋊C4—21no—
386C22⋊C4—21no—
387C22⋊C4—21no—
388C22⋊C4—21no—
389C22⋊C4—21no—
390C42—21no—
391C42C2×D4×C2911yescharacteristic
392C42C2×D4×C2911yescharacteristic
393C42#41×C2911yescharacteristic
394C42C24×C2911yescharacteristic
395C23—21no—
396C23C29×#12111yescharacteristic
397Q8—22no—
398Q8—42no—
399Q8—42no—
400Q8—42no—
401Q8—42no—
402Q8—82no—
403Q8—82no—
404D4—22no—
405D4—42no—
406C2×C4—22no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—22no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—82no—
418C2×C4—82no—
419C2×C4C29×#12111yescharacteristic
420C2×C4C29×#12111yescharacteristic
421C2×C4C29×#12111yescharacteristic
422C2×C4C22×D4×C2911yescharacteristic
423C2×C4C22×D4×C2911yescharacteristic
424C2×C4C2×#41×C2911yescharacteristic
425C8—21no—
426C8—21no—
427C8—21no—
428C8—21no—
429C8—41no—
430C8—41no—
431C8—42no—
432C8—42no—
433C22—21no—
434C22—21no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22C29×#47312yes—
439C22C2×C29×#12111yescharacteristic
440C4—21no—
441C4—21no—
442C4—21no—
443C4—21no—
444C4—41no—
445C4—41no—
446C4—41no—
447C4—82no—
448C4—82no—
449C4C29×#57511yescharacteristic
450C4C29×#57511yescharacteristic
451C4C29×#57712yes—
452C2—22no—
453C2—81no—
454C2C29×#304011yescharacteristic
455C2C29×#305711yescharacteristic
456C2C2×C29×#47311yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#121D4
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
3. C2×C29×#487C2semidirect
5. C29×#1700C2semidirect
6. C29×#1699C2semidirect
7. C29×#1680C2semidirect
8. C29×#1679C2semidirect
9. C29×#1568C2semidirect
10. C29×#1556C2semidirect
11. C29×#1556C2semidirect
166. #19363C29direct (N × H)
207. C2×#487C2×C29semidirect
209. #1700C2×C29semidirect
210. #1699C2×C29semidirect
211. #1680C2×C29semidirect
212. #1679C2×C29semidirect
213. #1568C2×C29semidirect
214. #1556C2×C29semidirect
215. #1556C2×C29semidirect
340. C29#19363direct (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×#32182
C2×C29×#4872
C29×#29662
C29×#17002
C29×#16992
C29×#16802
C29×#16792
C29×#15682
C29×#15562
#1936329