Finite Group Databasebeta

← C29×#9332 #20304232

Subgroups — C29×#9332 #20304232

Order 7424.

464 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3194C211yesmaximal, characteristic
2C29×#2978C211yesmaximal, characteristic, complemented
3C29×#1516C211yesmaximal, characteristic, complemented
4C29×#1510C211yesmaximal, characteristic, complemented
5C29×#1471C211yesmaximal, characteristic, complemented
6C29×#1306C211yesmaximal, characteristic, complemented
7C29×#1293C211yesmaximal, characteristic, complemented
8C29×#525C2211yescharacteristic
9C2×C29×#121C2211yescharacteristic
10C29×#483C411yescharacteristic, complemented
11C29×#482—21no—
12C29×#480C411yescharacteristic, complemented
13C29×#469—21no—
14C29×#468—21no—
15C29×#450C411yescharacteristic, complemented
16C29×#449—21no—
17C29×#447C411yescharacteristic, complemented
18C29×#436—21no—
19C29×#436—21no—
20C29×#435—21no—
21C29×#435—21no—
22C29×#433—21no—
23C29×#408—21no—
24C29×#407C2211yescharacteristic
25C29×#407C2211yescharacteristic
26C29×#407C2211yescharacteristic
27C2×C29×C22⋊C8C2211yescharacteristic
28C29×#381C2211yescharacteristic
29C29×#328—21no—
30C29×#327—21no—
31C29×#327—21no—
32C29×#327—21no—
33C29×#323—21no—
34C29×#323—21no—
35C2×#41×C29D411yescharacteristic
36C22×D4×C29—21no—
37C22×D4×C29C2×C411yescharacteristic
38C23×C4×C29C2311yescharacteristic
39C2×SD16×C29—21no—
40C2×D8×C29—21no—
41C2×M16×C29—21no—
42C2×M16×C29—21no—
43C2×M16×C29—21no—
44C2×M16×C29—21no—
45C22×C8×C29—21no—
46C22×C8×C29—21no—
47C29×#123—21no—
48C29×C22⋊Q8C2×C411yescharacteristic
49C29×C22⋊Q8D411yescharacteristic
50C29×#121—21no—
51C29×#121—21no—
52C29×#121—21no—
53C29×#121—21no—
54C29×#121C2×C411yescharacteristic
55C29×#121D411yescharacteristic
56C29×#120—21no—
57C4×D4×C29—21no—
58C4×D4×C29—21no—
59C29×#117D411yescharacteristic
60C2×C4⋊C4×C29C2×C411yescharacteristic
61C2×C22⋊C4×C29—21no—
62C2×C22⋊C4×C29—21no—
63C29×#107—21no—
64C29×#106—21no—
65C29×C4⋊C8—21no—
66C29×C4⋊C8—21no—
67C29×#103—21no—
68C29×#102—21no—
69C29×#102—21no—
70C29×#102—21no—
71C29×C22⋊C8—21no—
72C29×C22⋊C8—21no—
73C29×C22⋊C8—21no—
74C29×C22⋊C8—21no—
75C29×C22⋊C8—21no—
76C29×C22⋊C8—21no—
77C29×C22⋊C8—21no—
78C29×C22⋊C8C2×C411yescharacteristic
79C29×C22⋊C8C2×C411yescharacteristic
80C29×C22⋊C8D411yescharacteristic
81C29×C22⋊C8D411yescharacteristic
82C29×C22⋊C8D411yescharacteristic
83C29×C22⋊C8D411yescharacteristic
84C29×#97—21no—
85C4×C8×C29—21no—
86C29×#95—21no—
87C29×#95—21no—
88C24×C29—21no—
89C24×C29#4111yescharacteristic
90#41×C29—81no—
91C2×Q8×C29C22⋊C411yescharacteristic
92C2×D4×C29—21no—
93C2×D4×C29—21no—
94C2×D4×C29—21no—
95C2×D4×C29—21no—
96C2×D4×C29—21no—
97C2×D4×C29—41no—
98C2×D4×C29—41no—
99C2×D4×C29—81no—
100C2×D4×C29—82no—
101C2×D4×C29C22⋊C411yescharacteristic
102C22×C4×C29—21no—
103C22×C4×C29—21no—
104C22×C4×C29—41no—
105C22×C4×C29—81no—
106C22×C4×C29C22×C411yescharacteristic
107C22×C4×C29C2×D411yescharacteristic
108C22×C4×C29C2×D411yescharacteristic
109C22×C4×C29C2×D411yescharacteristic
110C22×C4×C29C2×D411yescharacteristic
111C22×C4×C29#4111yescharacteristic
112SD16×C29—81no—
113D8×C29—81no—
114M16×C29—81no—
115M16×C29—81no—
116M16×C29—81no—
117M16×C29—81no—
118C2×C8×C29—21no—
119C2×C8×C29—21no—
120C2×C8×C29—21no—
121C2×C8×C29—21no—
122C2×C8×C29—21no—
123C2×C8×C29—21no—
124C2×C8×C29—41no—
125C2×C8×C29—81no—
126C2×C8×C29—81no—
127C4⋊C4×C29—21no—
128C4⋊C4×C29—21no—
129C4⋊C4×C29—21no—
130C4⋊C4×C29—21no—
131C4⋊C4×C29C22⋊C411yescharacteristic
132C4⋊C4×C29C22⋊C411yescharacteristic
133C22⋊C4×C29—21no—
134C22⋊C4×C29—21no—
135C22⋊C4×C29—21no—
136C22⋊C4×C29—21no—
137C22⋊C4×C29—21no—
138C22⋊C4×C29—41no—
139C22⋊C4×C29—41no—
140C22⋊C4×C29—81no—
141C42×C29—21no—
142#9332C2911yesmaximal, characteristic, direct product factor, Sylow
143C23×C29—21no—
144C23×C29—41no—
145C23×C29—41no—
146C23×C29—41no—
147C23×C29—42no—
148C23×C29—41no—
149C23×C29—81no—
150C23×C29—81no—
151C23×C29C4×D411yescharacteristic
152C23×C29#12111yescharacteristic
153C23×C29#12311yescharacteristic
154Q8×C29—41no—
155D4×C29—41no—
156D4×C29—41no—
157D4×C29—41no—
158D4×C29—81no—
159D4×C29—81no—
160D4×C29—81no—
161D4×C29—81no—
162D4×C29—82no—
163D4×C29—82no—
164C2×C4×C29—21no—
165C2×C4×C29—21no—
166C2×C4×C29—21no—
167C2×C4×C29—41no—
168C2×C4×C29—41no—
169C2×C4×C29—41no—
170C2×C4×C29—41no—
171C2×C4×C29—41no—
172C2×C4×C29—41no—
173C2×C4×C29—41no—
174C2×C4×C29—41no—
175C2×C4×C29—41no—
176C2×C4×C29—81no—
177C2×C4×C29—81no—
178C2×C4×C29—81no—
179C2×C4×C29—81no—
180C2×C4×C29C2×C22⋊C411yescharacteristic
181C2×C4×C29C4×D411yescharacteristic
182C2×C4×C29#12011yescharacteristic
183C2×C4×C29#12111yescharacteristic
184C8×C29—41no—
185C8×C29—41no—
186C8×C29—41no—
187C8×C29—41no—
188C8×C29—41no—
189C8×C29—41no—
190C8×C29—81no—
191#3194C2×C2911yescharacteristic
192#2978C2×C2911yescharacteristic, complemented
193#1516C2×C2911yescharacteristic, complemented
194#1510C2×C2911yescharacteristic, complemented
195#1471C2×C2911yescharacteristic, complemented
196#1306C2×C2911yescharacteristic, complemented
197#1293C2×C2911yescharacteristic, complemented
198C22×C29—21no—
199C22×C29—21no—
200C22×C29—21no—
201C22×C29—21no—
202C22×C29—21no—
203C22×C29—21no—
204C22×C29—21no—
205C22×C29—21no—
206C22×C29—21no—
207C22×C29—41no—
208C22×C29—41no—
209C22×C29—41no—
210C22×C29—82no—
211C22×C29—81no—
212C22×C29—81no—
213C22×C29—81no—
214C22×C29—162no—
215C22×C29#38611yescharacteristic
216C4×C29—21no—
217C4×C29—21no—
218C4×C29—21no—
219C4×C29—21no—
220C4×C29—41no—
221C4×C29—41no—
222C4×C29—41no—
223C4×C29—81no—
224C4×C29—161no—
225#525C22×C2911yescharacteristic
226C2×#121C22×C2911yescharacteristic
227#483C4×C2911yescharacteristic, complemented
228#482—21no—
229#480C4×C2911yescharacteristic, complemented
230#469—21no—
231#468—21no—
232#450C4×C2911yescharacteristic, complemented
233#449—21no—
234#447C4×C2911yescharacteristic, complemented
235#436—21no—
236#436—21no—
237#435—21no—
238#435—21no—
239#433—21no—
240#408—21no—
241#407C22×C2911yescharacteristic
242#407C22×C2911yescharacteristic
243#407C22×C2911yescharacteristic
244C2×C22⋊C8C22×C2911yescharacteristic
245#381C22×C2911yescharacteristic
246#328—21no—
247#327—21no—
248#327—21no—
249#327—21no—
250#323—21no—
251#323—21no—
252C2×C29—41no—
253C2×C29—41no—
254C2×C29—41no—
255C2×C29—81no—
256C2×C29—161no—
257C2×C29#188111yescharacteristic
258C2×C29#190311yescharacteristic
259C2×C29#191311yescharacteristic
260C2×#41D4×C2911yescharacteristic
261C22×D4—21no—
262C22×D4C2×C4×C2911yescharacteristic
263C23×C4C23×C2911yescharacteristic
264C2×SD16—21no—
265C2×D8—21no—
266C2×M16—21no—
267C2×M16—21no—
268C2×M16—21no—
269C2×M16—21no—
270C22×C8—21no—
271C22×C8—21no—
272#123—21no—
273C22⋊Q8C2×C4×C2911yescharacteristic
274C22⋊Q8D4×C2911yescharacteristic
275#121—21no—
276#121—21no—
277#121—21no—
278#121—21no—
279#121C2×C4×C2911yescharacteristic
280#121D4×C2911yescharacteristic
281#120—21no—
282C4×D4—21no—
283C4×D4—21no—
284#117D4×C2911yescharacteristic
285C2×C4⋊C4C2×C4×C2911yescharacteristic
286C2×C22⋊C4—21no—
287C2×C22⋊C4—21no—
288#107—21no—
289#106—21no—
290C4⋊C8—21no—
291C4⋊C8—21no—
292#103—21no—
293#102—21no—
294#102—21no—
295#102—21no—
296C22⋊C8—21no—
297C22⋊C8—21no—
298C22⋊C8—21no—
299C22⋊C8—21no—
300C22⋊C8—21no—
301C22⋊C8—21no—
302C22⋊C8—21no—
303C22⋊C8C2×C4×C2911yescharacteristic
304C22⋊C8C2×C4×C2911yescharacteristic
305C22⋊C8D4×C2911yescharacteristic
306C22⋊C8D4×C2911yescharacteristic
307C22⋊C8D4×C2911yescharacteristic
308C22⋊C8D4×C2911yescharacteristic
309#97—21no—
310C4×C8—21no—
311#95—21no—
312#95—21no—
313C29#933211yescharacteristic, direct product factor, Sylow
314C24—21no—
315C24#41×C2911yescharacteristic
316#41—81no—
317C2×Q8C22⋊C4×C2911yescharacteristic
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—21no—
322C2×D4—21no—
323C2×D4—41no—
324C2×D4—41no—
325C2×D4—81no—
326C2×D4—82no—
327C2×D4C22⋊C4×C2911yescharacteristic
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—41no—
331C22×C4—81no—
332C22×C4C22×C4×C2911yescharacteristic
333C22×C4C2×D4×C2911yescharacteristic
334C22×C4C2×D4×C2911yescharacteristic
335C22×C4C2×D4×C2911yescharacteristic
336C22×C4C2×D4×C2911yescharacteristic
337C22×C4#41×C2911yescharacteristic
338SD16—81no—
339D8—81no—
340M16—81no—
341M16—81no—
342M16—81no—
343M16—81no—
344C2×C8—21no—
345C2×C8—21no—
346C2×C8—21no—
347C2×C8—21no—
348C2×C8—21no—
349C2×C8—21no—
350C2×C8—41no—
351C2×C8—81no—
352C2×C8—81no—
353C4⋊C4—21no—
354C4⋊C4—21no—
355C4⋊C4—21no—
356C4⋊C4—21no—
357C4⋊C4C22⋊C4×C2911yescharacteristic
358C4⋊C4C22⋊C4×C2911yescharacteristic
359C22⋊C4—21no—
360C22⋊C4—21no—
361C22⋊C4—21no—
362C22⋊C4—21no—
363C22⋊C4—21no—
364C22⋊C4—41no—
365C22⋊C4—41no—
366C22⋊C4—81no—
367C42—21no—
368C23—21no—
369C23—41no—
370C23—41no—
371C23—41no—
372C23—42no—
373C23—41no—
374C23—81no—
375C23—81no—
376C23C4×D4×C2911yescharacteristic
377C23C29×#12111yescharacteristic
378C23C29×#12311yescharacteristic
379Q8—41no—
380D4—41no—
381D4—41no—
382D4—41no—
383D4—81no—
384D4—81no—
385D4—81no—
386D4—81no—
387D4—82no—
388D4—82no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—81no—
404C2×C4—81no—
405C2×C4C2×C22⋊C4×C2911yescharacteristic
406C2×C4C4×D4×C2911yescharacteristic
407C2×C4C29×#12011yescharacteristic
408C2×C4C29×#12111yescharacteristic
409C8—41no—
410C8—41no—
411C8—41no—
412C8—41no—
413C8—41no—
414C8—41no—
415C8—81no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—41no—
426C22—41no—
427C22—41no—
428C22—82no—
429C22—81no—
430C22—81no—
431C22—81no—
432C22—162no—
433C22C29×#38611yescharacteristic
434C4—21no—
435C4—21no—
436C4—21no—
437C4—21no—
438C4—41no—
439C4—41no—
440C4—41no—
441C4—81no—
442C4—161no—
443C2—41no—
444C2—41no—
445C2—41no—
446C2—81no—
447C2—161no—
448C2C29×#188111yescharacteristic
449C2C29×#190311yescharacteristic
450C2C29×#191311yescharacteristic
subgroupG/H
center, socleC22×C29#386
commutatorC22×C4C22×C4×C29
Frattini, cosocleC23×C4C23×C29
prime radicalC29×#3194C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C23×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#2978C2semidirect
3. C29×#1516C2semidirect
4. C29×#1510C2semidirect
5. C29×#1471C2semidirect
6. C29×#1306C2semidirect
7. C29×#1293C2semidirect
10. C29×#483C4semidirect
12. C29×#480C4semidirect
15. C29×#450C4semidirect
17. C29×#447C4semidirect
142. #9332C29direct (N × H)
192. #2978C2×C29semidirect
193. #1516C2×C29semidirect
194. #1510C2×C29semidirect
195. #1471C2×C29semidirect
196. #1306C2×C29semidirect
197. #1293C2×C29semidirect
227. #483C4×C29semidirect
229. #480C4×C29semidirect
232. #450C4×C29semidirect
234. #447C4×C29semidirect
313. C29#9332direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#31942
C29×#29782
C29×#15162
C29×#15102
C29×#14712
C29×#13062
C29×#12932
#933229