Finite Group Databasebeta

← C29×#26710 #20321610

Subgroups — C29×#26710 #20321610

Order 7424.

696 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#2448C211yesmaximal, characteristic
2C29×#2369C211yesmaximal, characteristic, complemented
3C29×#2088C211yesmaximal, characteristic, complemented
4C29×#2042C211yesmaximal, characteristic
5C29×#2024C211yesmaximal, characteristic, complemented
6C29×#2023C211yesmaximal, characteristic
7C29×#1983C211yesmaximal, characteristic
8C29×#1936C211yesmaximal, characteristic
9C29×#1928C211yesmaximal, characteristic, complemented
10C29×#1926C211yesmaximal, characteristic
11C29×#1925C211yesmaximal, characteristic
12C29×#1918C211yesmaximal, characteristic, complemented
13C29×#1917C211yesmaximal, characteristic, complemented
14C29×#1865C211yesmaximal, characteristic, complemented
15C29×#1763C211yesmaximal, characteristic, complemented
16C2×C29×C4⋊Q8C2211yescharacteristic
17C2×C29×#124C2211yescharacteristic
18C2×C4×Q8×C29C2211yescharacteristic
19C2×C29×#107C2211yescharacteristic
20C2×C29×#106C2211yescharacteristic
21C2×C29×C4⋊C8C2211yescharacteristic
22C2×C29×#103C2211yescharacteristic
23C2×C29×#103C2211yescharacteristic
24C2×C29×#103C2211yescharacteristic
25C2×C29×#103C2211yescharacteristic
26C2×C29×#102C2211yescharacteristic
27C2×C29×#102C2211yescharacteristic
28C2×C29×#102C2211yescharacteristic
29C2×C29×#102C2211yescharacteristic
30C2×C29×#97C2211yescharacteristic
31C29×#399—21no—
32C29×#397—21no—
33C29×#391—21no—
34C29×#391—21no—
35C29×#391C2211yescharacteristic
36C29×#390C2211yescharacteristic
37C29×#390C2211yescharacteristic
38C29×#389—21no—
39C29×#389C2211yescharacteristic
40C29×#389C2211yescharacteristic
41C29×#389C2211yescharacteristic
42C29×#388—21no—
43C29×#388—21no—
44C4×C4⋊C4×C29—21no—
45C4×C4⋊C4×C29C2211yescharacteristic
46C4×C4⋊C4×C29C2211yescharacteristic
47C4×C4⋊C4×C29C2211yescharacteristic
48C4×C4⋊C4×C29C2211yescharacteristic
49C29×#340C2211yescharacteristic
50C29×#340C2211yescharacteristic
51C29×#340C2211yescharacteristic
52C29×#340C2211yescharacteristic
53C29×#340C2211yescharacteristic
54C29×#340C2211yescharacteristic
55C29×#336C2211yescharacteristic
56C29×#336C2211yescharacteristic
57C29×#336C2211yescharacteristic
58C29×#336C2211yescharacteristic
59C22×Q8×C29—21no—
60C22×Q8×C29C2311yescharacteristic
61C22×D4×C29C2311yescharacteristic
62C22×C8×C29C2311yescharacteristic
63C22×C8×C29C2311yescharacteristic
64C22×C8×C29C2311yescharacteristic
65C22×C8×C29C2311yescharacteristic
66C29×C4⋊Q8—22no—
67C29×C4⋊Q8—22no—
68C29×#124—22no—
69C29×#124—41no—
70C4×Q8×C29—22no—
71C4×Q8×C29—41no—
72C2×C4⋊C4×C29—21no—
73C2×C4⋊C4×C29—21no—
74C2×C4⋊C4×C29—21no—
75C2×C4⋊C4×C29—21no—
76C2×C4⋊C4×C29—21no—
77C2×C4⋊C4×C29D411yescharacteristic
78C2×C4⋊C4×C29D411yescharacteristic
79C2×C4⋊C4×C29C2311yescharacteristic
80C2×C4⋊C4×C29C2311yescharacteristic
81C2×C4⋊C4×C29C2311yescharacteristic
82C2×C4⋊C4×C29C2311yescharacteristic
83C2×C4⋊C4×C29C2311yescharacteristic
84C2×C4⋊C4×C29C2311yescharacteristic
85C2×C22⋊C4×C29—21no—
86C2×C22⋊C4×C29—21no—
87C2×C22⋊C4×C29—21no—
88C2×C22⋊C4×C29—21no—
89C2×C22⋊C4×C29—21no—
90C2×C22⋊C4×C29—21no—
91C2×C42×C29—21no—
92C2×C42×C29—21no—
93C2×C42×C29—21no—
94C2×C42×C29—21no—
95C2×C42×C29C2311yescharacteristic
96C2×C42×C29C2311yescharacteristic
97C2×C42×C29C2311yescharacteristic
98C29×#107—22no—
99C29×#106—41no—
100C29×C4⋊C8—41no—
101C29×#103—22no—
102C29×#103—22no—
103C29×#103—22no—
104C29×#103—22no—
105C29×#102—22no—
106C29×#102—22no—
107C29×#102—22no—
108C29×#102—41no—
109C29×#97—41no—
110C29×#95—21no—
111C29×#95—21no—
112C29×#95—21no—
113C29×#95—21no—
114C29×#95—21no—
115C29×#95—21no—
116C29×#95—21no—
117C29×#95—21no—
118C29×#95D411yescharacteristic
119C29×#95D411yescharacteristic
120C24×C29—21no—
121C2×Q8×C29—24no—
122C2×Q8×C29—21no—
123C2×Q8×C29—21no—
124C2×Q8×C29—21no—
125C2×Q8×C29—21no—
126C2×Q8×C29—21no—
127C2×Q8×C29—81no—
128C2×Q8×C29—81no—
129C2×Q8×C29#4112yes—
130C2×D4×C29—21no—
131C2×D4×C29—21no—
132C2×D4×C29—21no—
133C2×D4×C29—21no—
134C2×D4×C29—21no—
135C2×D4×C29—21no—
136C22×C4×C29—21no—
137C22×C4×C29—21no—
138C22×C4×C29—21no—
139C22×C4×C29—21no—
140C22×C4×C29—21no—
141C22×C4×C29—21no—
142C22×C4×C29—21no—
143C22×C4×C29C2×D411yescharacteristic
144C22×C4×C29C2×D411yescharacteristic
145C22×C4×C29C2×D411yescharacteristic
146C22×C4×C29C2×D411yescharacteristic
147C22×C4×C29C2×D411yescharacteristic
148C22×C4×C29C2×D411yescharacteristic
149C22×C4×C29C2411yescharacteristic
150C2×C8×C29—21no—
151C2×C8×C29—21no—
152C2×C8×C29—21no—
153C2×C8×C29—21no—
154C2×C8×C29—21no—
155C2×C8×C29—21no—
156C2×C8×C29—21no—
157C2×C8×C29—21no—
158C2×C8×C29—21no—
159C2×C8×C29—21no—
160C2×C8×C29—21no—
161C2×C8×C29—21no—
162C4⋊C4×C29—24no—
163C4⋊C4×C29—22no—
164C4⋊C4×C29—21no—
165C4⋊C4×C29—21no—
166C4⋊C4×C29—21no—
167C4⋊C4×C29—21no—
168C4⋊C4×C29—21no—
169C4⋊C4×C29—21no—
170C4⋊C4×C29—21no—
171C4⋊C4×C29—21no—
172C4⋊C4×C29—21no—
173C4⋊C4×C29—41no—
174C4⋊C4×C29—42no—
175C4⋊C4×C29—81no—
176C4⋊C4×C29—81no—
177C4⋊C4×C29—81no—
178C4⋊C4×C29#4112yes—
179C4⋊C4×C29#4112yes—
180C4⋊C4×C29#4112yes—
181C22⋊C4×C29—42no—
182C22⋊C4×C29—42no—
183C22⋊C4×C29—42no—
184C22⋊C4×C29—42no—
185C22⋊C4×C29—81no—
186C22⋊C4×C29—81no—
187C42×C29—21no—
188C42×C29—21no—
189C42×C29—21no—
190C42×C29—21no—
191C42×C29—21no—
192C42×C29—21no—
193C42×C29—42no—
194C42×C29—42no—
195C42×C29—81no—
196C42×C29—81no—
197#26710C2911yesmaximal, characteristic, direct product factor, Sylow
198C23×C29—41no—
199C23×C29—41no—
200C23×C29—41no—
201C23×C29—41no—
202C23×C29—41no—
203C23×C29—41no—
204C23×C29—41no—
205C23×C29C22×D411yescharacteristic
206Q8×C29—22no—
207Q8×C29—22no—
208Q8×C29—41no—
209Q8×C29—41no—
210Q8×C29—84no—
211D4×C29—41no—
212D4×C29—41no—
213D4×C29—41no—
214D4×C29—41no—
215C2×C4×C29—21no—
216C2×C4×C29—21no—
217C2×C4×C29—21no—
218C2×C4×C29—22no—
219C2×C4×C29—22no—
220C2×C4×C29—21no—
221C2×C4×C29—21no—
222C2×C4×C29—21no—
223C2×C4×C29—21no—
224C2×C4×C29—22no—
225C2×C4×C29—22no—
226C2×C4×C29—21no—
227C2×C4×C29—21no—
228C2×C4×C29—21no—
229C2×C4×C29—21no—
230C2×C4×C29—21no—
231C2×C4×C29—21no—
232C2×C4×C29—21no—
233C2×C4×C29—21no—
234C2×C4×C29—21no—
235C2×C4×C29—21no—
236C2×C4×C29—41no—
237C2×C4×C29—41no—
238C2×C4×C29—41no—
239C2×C4×C29—41no—
240C2×C4×C29—41no—
241C2×C4×C29—41no—
242C2×C4×C29—41no—
243C2×C4×C29—41no—
244C2×C4×C29—41no—
245C2×C4×C29—41no—
246C2×C4×C29—41no—
247C2×C4×C29—41no—
248C2×C4×C29—41no—
249C2×C4×C29—41no—
250C2×C4×C29—41no—
251C2×C4×C29—41no—
252C2×C4×C29—41no—
253C2×C4×C29#13712yes—
254C2×C4×C29C2×#4111yescharacteristic
255C2×C4×C29C2×#4111yescharacteristic
256C2×C4×C29C2×#4111yescharacteristic
257C2×C4×C29C2×#4111yescharacteristic
258C2×C4×C29H(5,𝔽2)11yescharacteristic
259C2×C4×C292−1+411yescharacteristic
260C8×C29—41no—
261C8×C29—41no—
262C8×C29—41no—
263C8×C29—41no—
264#2448C2×C2911yescharacteristic
265#2369C2×C2911yescharacteristic, complemented
266#2088C2×C2911yescharacteristic, complemented
267#2042C2×C2911yescharacteristic
268#2024C2×C2911yescharacteristic, complemented
269#2023C2×C2911yescharacteristic
270#1983C2×C2911yescharacteristic
271#1936C2×C2911yescharacteristic
272#1928C2×C2911yescharacteristic, complemented
273#1926C2×C2911yescharacteristic
274#1925C2×C2911yescharacteristic
275#1918C2×C2911yescharacteristic, complemented
276#1917C2×C2911yescharacteristic, complemented
277#1865C2×C2911yescharacteristic, complemented
278#1763C2×C2911yescharacteristic, complemented
279C22×C29—81no—
280C22×C29—81no—
281C22×C29—81no—
282C22×C29—81no—
283C22×C29—81no—
284C22×C29—81no—
285C22×C29—81no—
286C22×C29#52511yescharacteristic
287C22×C29#54611yescharacteristic
288C22×C29#54811yescharacteristic
289C22×C29C2×#13711yescharacteristic
290C22×C29#57511yescharacteristic
291C22×C29#57611yescharacteristic
292C22×C29#57711yescharacteristic
293C4×C29—22no—
294C4×C29—41no—
295C4×C29—41no—
296C4×C29—42no—
297C4×C29—41no—
298C4×C29—42no—
299C4×C29—42no—
300C4×C29—42no—
301C4×C29—41no—
302C4×C29—41no—
303C4×C29—81no—
304C4×C29—81no—
305C4×C29—81no—
306C4×C29#52911yescharacteristic
307C4×C29#54211yescharacteristic
308C4×C29#55211yescharacteristic
309C4×C29#55911yescharacteristic
310C2×C4⋊Q8C22×C2911yescharacteristic
311C2×#124C22×C2911yescharacteristic
312C2×C4×Q8C22×C2911yescharacteristic
313C2×#107C22×C2911yescharacteristic
314C2×#106C22×C2911yescharacteristic
315C2×C4⋊C8C22×C2911yescharacteristic
316C2×#103C22×C2911yescharacteristic
317C2×#103C22×C2911yescharacteristic
318C2×#103C22×C2911yescharacteristic
319C2×#103C22×C2911yescharacteristic
320C2×#102C22×C2911yescharacteristic
321C2×#102C22×C2911yescharacteristic
322C2×#102C22×C2911yescharacteristic
323C2×#102C22×C2911yescharacteristic
324C2×#97C22×C2911yescharacteristic
325#399—21no—
326#397—21no—
327#391—21no—
328#391—21no—
329#391C22×C2911yescharacteristic
330#390C22×C2911yescharacteristic
331#390C22×C2911yescharacteristic
332#389—21no—
333#389C22×C2911yescharacteristic
334#389C22×C2911yescharacteristic
335#389C22×C2911yescharacteristic
336#388—21no—
337#388—21no—
338C4×C4⋊C4—21no—
339C4×C4⋊C4C22×C2911yescharacteristic
340C4×C4⋊C4C22×C2911yescharacteristic
341C4×C4⋊C4C22×C2911yescharacteristic
342C4×C4⋊C4C22×C2911yescharacteristic
343#340C22×C2911yescharacteristic
344#340C22×C2911yescharacteristic
345#340C22×C2911yescharacteristic
346#340C22×C2911yescharacteristic
347#340C22×C2911yescharacteristic
348#340C22×C2911yescharacteristic
349#336C22×C2911yescharacteristic
350#336C22×C2911yescharacteristic
351#336C22×C2911yescharacteristic
352#336C22×C2911yescharacteristic
353C2×C29—161no—
354C2×C29#245811yescharacteristic
355C2×C29#311711yescharacteristic
356C2×C29#311811yescharacteristic
357C2×C29#332111yescharacteristic
358C2×C29#333311yescharacteristic
359C2×C29#336911yescharacteristic
360C2×C29#337011yescharacteristic
361C22×Q8—21no—
362C22×Q8C23×C2911yescharacteristic
363C22×D4C23×C2911yescharacteristic
364C22×C8C23×C2911yescharacteristic
365C22×C8C23×C2911yescharacteristic
366C22×C8C23×C2911yescharacteristic
367C22×C8C23×C2911yescharacteristic
368C4⋊Q8—22no—
369C4⋊Q8—22no—
370#124—22no—
371#124—41no—
372C4×Q8—22no—
373C4×Q8—41no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4D4×C2911yescharacteristic
380C2×C4⋊C4D4×C2911yescharacteristic
381C2×C4⋊C4C23×C2911yescharacteristic
382C2×C4⋊C4C23×C2911yescharacteristic
383C2×C4⋊C4C23×C2911yescharacteristic
384C2×C4⋊C4C23×C2911yescharacteristic
385C2×C4⋊C4C23×C2911yescharacteristic
386C2×C4⋊C4C23×C2911yescharacteristic
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C42—21no—
394C2×C42—21no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42C23×C2911yescharacteristic
398C2×C42C23×C2911yescharacteristic
399C2×C42C23×C2911yescharacteristic
400#107—22no—
401#106—41no—
402C4⋊C8—41no—
403#103—22no—
404#103—22no—
405#103—22no—
406#103—22no—
407#102—22no—
408#102—22no—
409#102—22no—
410#102—41no—
411#97—41no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95D4×C2911yescharacteristic
421#95D4×C2911yescharacteristic
422C29#2671011yescharacteristic, direct product factor, Sylow
423C24—21no—
424C2×Q8—24no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—81no—
431C2×Q8—81no—
432C2×Q8#41×C2912yes—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4C2×D4×C2911yescharacteristic
447C22×C4C2×D4×C2911yescharacteristic
448C22×C4C2×D4×C2911yescharacteristic
449C22×C4C2×D4×C2911yescharacteristic
450C22×C4C2×D4×C2911yescharacteristic
451C22×C4C2×D4×C2911yescharacteristic
452C22×C4C24×C2911yescharacteristic
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C4⋊C4—24no—
466C4⋊C4—22no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—41no—
477C4⋊C4—42no—
478C4⋊C4—81no—
479C4⋊C4—81no—
480C4⋊C4—81no—
481C4⋊C4#41×C2912yes—
482C4⋊C4#41×C2912yes—
483C4⋊C4#41×C2912yes—
484C22⋊C4—42no—
485C22⋊C4—42no—
486C22⋊C4—42no—
487C22⋊C4—42no—
488C22⋊C4—81no—
489C22⋊C4—81no—
490C42—21no—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—42no—
497C42—42no—
498C42—81no—
499C42—81no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23C22×D4×C2911yescharacteristic
508Q8—22no—
509Q8—22no—
510Q8—41no—
511Q8—41no—
512Q8—84no—
513D4—41no—
514D4—41no—
515D4—41no—
516D4—41no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4C29×#13712yes—
556C2×C4C2×#41×C2911yescharacteristic
557C2×C4C2×#41×C2911yescharacteristic
558C2×C4C2×#41×C2911yescharacteristic
559C2×C4C2×#41×C2911yescharacteristic
560C2×C4C29×H(5,𝔽2)11yescharacteristic
561C2×C4C29×2−1+411yescharacteristic
562C8—41no—
563C8—41no—
564C8—41no—
565C8—41no—
566C22—81no—
567C22—81no—
568C22—81no—
569C22—81no—
570C22—81no—
571C22—81no—
572C22—81no—
573C22C29×#52511yescharacteristic
574C22C29×#54611yescharacteristic
575C22C29×#54811yescharacteristic
576C22C2×C29×#13711yescharacteristic
577C22C29×#57511yescharacteristic
578C22C29×#57611yescharacteristic
579C22C29×#57711yescharacteristic
580C4—22no—
581C4—42no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—41no—
586C4—42no—
587C4—41no—
588C4—42no—
589C4—42no—
590C4—81no—
591C4—81no—
592C4—81no—
593C4C29×#52911yescharacteristic
594C4C29×#54211yescharacteristic
595C4C29×#55211yescharacteristic
596C4C29×#55911yescharacteristic
597C2—161no—
598C2C29×#245811yescharacteristic
599C2C29×#311711yescharacteristic
600C2C29×#311811yescharacteristic
601C2C29×#332111yescharacteristic
602C2C29×#333311yescharacteristic
603C2C29×#336911yescharacteristic
604C2C29×#337011yescharacteristic
subgroupG/H
center, socleC23×C29C22×D4
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC22×D4×C29C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C29 ◁ C4×C4⋊C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#2369C2semidirect
3. C29×#2088C2semidirect
5. C29×#2024C2semidirect
9. C29×#1928C2semidirect
12. C29×#1918C2semidirect
13. C29×#1917C2semidirect
14. C29×#1865C2semidirect
15. C29×#1763C2semidirect
197. #26710C29direct (N × H)
265. #2369C2×C29semidirect
266. #2088C2×C29semidirect
268. #2024C2×C29semidirect
272. #1928C2×C29semidirect
275. #1918C2×C29semidirect
276. #1917C2×C29semidirect
277. #1865C2×C29semidirect
278. #1763C2×C29semidirect
422. C29#26710direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#24482
C29×#23692
C29×#20882
C29×#20422
C29×#20242
C29×#20232
C29×#19832
C29×#19362
C29×#19282
C29×#19262
C29×#19252
C29×#19182
C29×#19172
C29×#18652
C29×#17632
#2671029