Finite Group Databasebeta

← C29×#25481 #20320381

Subgroups — C29×#25481 #20320381

Order 7424.

770 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#474C211yesmaximal, characteristic
2C2×C29×#446C211yesmaximal, characteristic, complemented
3C29×#2580C211yesmaximal, characteristic
4C29×#2567C211yesmaximal, characteristic, complemented
5C29×#2087C211yesmaximal, characteristic, complemented
6C29×#2086C211yesmaximal, characteristic, complemented
7C29×#2067C211yesmaximal, characteristic
8C29×#2065C211yesmaximal, characteristic
9C29×#1993C211yesmaximal, characteristic, complemented
10C29×#1949C211yesmaximal, characteristic, complemented
11C29×#1944C211yesmaximal, characteristic, complemented
12C29×#1942C211yesmaximal, characteristic, complemented
13C29×#1936C211yesmaximal, characteristic
14C29×#1934C211yesmaximal, characteristic
15C29×#1762C211yesmaximal, characteristic
16C2×C29×C4⋊Q8C2211yescharacteristic
17C2×C4×Q8×C29C2211yescharacteristic
18C2×C4×D4×C29C2211yescharacteristic
19C29×#474—24no—
20C29×#446—24no—
21C2×C29×#107C2211yescharacteristic
22C2×C29×#107C2211yescharacteristic
23C2×C29×#107C2211yescharacteristic
24C2×C29×#106C2211yescharacteristic
25C2×C29×C4⋊C8C2211yescharacteristic
26C2×C29×C4⋊C8C2211yescharacteristic
27C2×C29×C4⋊C8C2211yescharacteristic
28C2×C29×#102C2211yescharacteristic
29C2×C29×#102C2211yescharacteristic
30C2×C29×#102C2211yescharacteristic
31C2×C29×#102C2211yescharacteristic
32C2×C29×#97C2211yescharacteristic
33C2×C29×#97C2211yescharacteristic
34C2×C4×C8×C29C2211yescharacteristic
35C29×#399—21no—
36C29×#395—21no—
37C29×#395—21no—
38C29×#393—21no—
39C29×#391—21no—
40C29×#390C2211yescharacteristic
41C29×#390C2211yescharacteristic
42C29×#389C2211yescharacteristic
43C29×#389C2211yescharacteristic
44C29×#389C2211yescharacteristic
45C29×#389C2211yescharacteristic
46C29×#389C2211yescharacteristic
47C29×#389C2211yescharacteristic
48C29×#385—21no—
49C29×#385—21no—
50C29×#384—21no—
51C29×#382C2211yescharacteristic
52C4×C4⋊C4×C29C2211yescharacteristic
53C29×#340C2211yescharacteristic
54C29×#340C2211yescharacteristic
55C29×#340C2211yescharacteristic
56C29×#340C2211yescharacteristic
57C29×#340C2211yescharacteristic
58C29×#340C2211yescharacteristic
59C29×#340C2211yescharacteristic
60C29×#340C2211yescharacteristic
61C22×Q8×C29—21no—
62C22×Q8×C29D411yescharacteristic
63C22×D4×C29C2311yescharacteristic
64C23×C4×C29—21no—
65C22×C8×C29C2311yescharacteristic
66C22×C8×C29C2311yescharacteristic
67C22×C8×C29C2311yescharacteristic
68C22×C8×C29C2311yescharacteristic
69C29×C4⋊Q8—22no—
70C29×C4⋊Q8—22no—
71C4×Q8×C29—22no—
72C4×Q8×C29—22no—
73C4×D4×C29—22no—
74C4×D4×C29—22no—
75C2×C4⋊C4×C29—21no—
76C2×C4⋊C4×C29—21no—
77C2×C4⋊C4×C29—21no—
78C2×C4⋊C4×C29—21no—
79C2×C4⋊C4×C29—21no—
80C2×C4⋊C4×C29—21no—
81C2×C4⋊C4×C29—21no—
82C2×C4⋊C4×C29D411yescharacteristic
83C2×C4⋊C4×C29D411yescharacteristic
84C2×C4⋊C4×C29D411yescharacteristic
85C2×C4⋊C4×C29C2311yescharacteristic
86C2×C4⋊C4×C29C2311yescharacteristic
87C2×C4⋊C4×C29C2311yescharacteristic
88C2×C4⋊C4×C29C2311yescharacteristic
89C2×C4⋊C4×C29C2311yescharacteristic
90C2×C4⋊C4×C29C2311yescharacteristic
91C2×C4⋊C4×C29C2311yescharacteristic
92C2×C22⋊C4×C29—21no—
93C2×C22⋊C4×C29—21no—
94C2×C22⋊C4×C29—21no—
95C2×C22⋊C4×C29—21no—
96C2×C22⋊C4×C29—21no—
97C2×C42×C29—21no—
98C2×C42×C29C2311yescharacteristic
99C2×C42×C29C2311yescharacteristic
100C2×C42×C29C2311yescharacteristic
101C29×#107—22no—
102C29×#107—22no—
103C29×#107—22no—
104C29×#106—22no—
105C29×C4⋊C8—22no—
106C29×C4⋊C8—22no—
107C29×C4⋊C8D414yes—
108C29×#102—22no—
109C29×#102—22no—
110C29×#102—22no—
111C29×#102Q814yescomplemented
112C29×#97—22no—
113C29×#97—22no—
114C4×C8×C29—22no—
115C29×#95—21no—
116C29×#95—21no—
117C29×#95—21no—
118C29×#95—21no—
119C29×#95—21no—
120C29×#95—21no—
121C29×#95—21no—
122C29×#95—21no—
123C29×#95—21no—
124C24×C29—21no—
125C2×Q8×C29—22no—
126C2×Q8×C29—22no—
127C2×Q8×C29—41no—
128C2×Q8×C29—42no—
129C2×Q8×C29—81no—
130C2×Q8×C29—81no—
131C2×D4×C29—21no—
132C2×D4×C29—21no—
133C2×D4×C29—21no—
134C2×D4×C29—21no—
135C2×D4×C29—21no—
136C2×D4×C29C2×Q812yes—
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×C29—21no—
144C22×C4×C29—42no—
145C22×C4×C29—81no—
146C22×C4×C29—81no—
147C22×C4×C29C2×D411yescharacteristic
148C22×C4×C29C2×D411yescharacteristic
149C22×C4×C29C2×D411yescharacteristic
150C22×C4×C29C2×D411yescharacteristic
151C22×C4×C29C2×D411yescharacteristic
152C22×C4×C29C2×D411yescharacteristic
153C22×C4×C29C2411yescharacteristic
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—
162C2×C8×C29—21no—
163C2×C8×C29C2×D412yes—
164C2×C8×C29C2×D412yes—
165C2×C8×C29C2×Q812yes—
166C4⋊C4×C29—22no—
167C4⋊C4×C29—22no—
168C4⋊C4×C29—22no—
169C4⋊C4×C29—21no—
170C4⋊C4×C29—21no—
171C4⋊C4×C29—21no—
172C4⋊C4×C29—21no—
173C4⋊C4×C29—21no—
174C4⋊C4×C29—21no—
175C4⋊C4×C29—21no—
176C4⋊C4×C29—21no—
177C4⋊C4×C29—21no—
178C4⋊C4×C29—21no—
179C4⋊C4×C29—21no—
180C4⋊C4×C29—21no—
181C4⋊C4×C29—42no—
182C4⋊C4×C29—81no—
183C4⋊C4×C29—81no—
184C4⋊C4×C29—81no—
185C4⋊C4×C29—81no—
186C4⋊C4×C29—81no—
187C4⋊C4×C29—81no—
188C4⋊C4×C29C2×Q812yes—
189C4⋊C4×C29#4112yes—
190C22⋊C4×C29—42no—
191C22⋊C4×C29—42no—
192C22⋊C4×C29—42no—
193C22⋊C4×C29—81no—
194C22⋊C4×C29—81no—
195C42×C29—21no—
196C42×C29—21no—
197C42×C29—21no—
198C42×C29—21no—
199C42×C29—42no—
200C42×C29C2×D412yes—
201C42×C29#4112yes—
202#25481C2911yesmaximal, characteristic, direct product factor, Sylow
203C23×C29—22no—
204C23×C29—41no—
205C23×C29—41no—
206C23×C29—41no—
207C23×C29—41no—
208C23×C29—41no—
209C23×C29—41no—
210C23×C29C22×D411yescharacteristic
211Q8×C29—44no—
212Q8×C29—84no—
213D4×C29—22no—
214D4×C29—22no—
215D4×C29—41no—
216D4×C29—41no—
217C2×C4×C29—21no—
218C2×C4×C29—21no—
219C2×C4×C29—21no—
220C2×C4×C29—21no—
221C2×C4×C29—21no—
222C2×C4×C29—21no—
223C2×C4×C29—21no—
224C2×C4×C29—21no—
225C2×C4×C29—21no—
226C2×C4×C29—22no—
227C2×C4×C29—22no—
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—41no—
235C2×C4×C29—41no—
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—84no—
254C2×C4×C29#12112yes—
255C2×C4×C29#12112yes—
256C2×C4×C29#13712yes—
257C2×C4×C29C22×D411yescharacteristic
258C2×C4×C29C22×Q811yescharacteristic
259C2×C4×C29C2×#4111yescharacteristic
260C2×C4×C29C2×#4111yescharacteristic
261C2×C4×C292−1+411yescharacteristic
262C2×C4×C292−1+411yescharacteristic
263C8×C29—22no—
264C8×C29—22no—
265C8×C29—22no—
266C8×C29—41no—
267C2×#474C2×C2911yescharacteristic
268C2×#446C2×C2911yescharacteristic, complemented
269#2580C2×C2911yescharacteristic
270#2567C2×C2911yescharacteristic, complemented
271#2087C2×C2911yescharacteristic, complemented
272#2086C2×C2911yescharacteristic, complemented
273#2067C2×C2911yescharacteristic
274#2065C2×C2911yescharacteristic
275#1993C2×C2911yescharacteristic, complemented
276#1949C2×C2911yescharacteristic, complemented
277#1944C2×C2911yescharacteristic, complemented
278#1942C2×C2911yescharacteristic, complemented
279#1936C2×C2911yescharacteristic
280#1934C2×C2911yescharacteristic
281#1762C2×C2911yescharacteristic
282C22×C29—42no—
283C22×C29—42no—
284C22×C29—42no—
285C22×C29—81no—
286C22×C29—81no—
287C22×C29—81no—
288C22×C29—81no—
289C22×C29C2×#12111yescharacteristic
290C22×C29#54811yescharacteristic
291C22×C29D4×Q811yescharacteristic
292C22×C29C2×#13711yescharacteristic
293C22×C29#57511yescharacteristic
294C22×C29#57611yescharacteristic
295C22×C29#57611yescharacteristic
296C4×C29—22no—
297C4×C29—22no—
298C4×C29—22no—
299C4×C29—42no—
300C4×C29—42no—
301C4×C29—41no—
302C4×C29—41no—
303C4×C29—41no—
304C4×C29—81no—
305C4×C29—81no—
306C4×C29—81no—
307C4×C29—81no—
308C4×C29—81no—
309C4×C29#53311yescharacteristic
310C4×C29#54111yescharacteristic
311C4×C29#54711yescharacteristic
312C4×C29D4×Q811yescharacteristic
313C2×C4⋊Q8C22×C2911yescharacteristic
314C2×C4×Q8C22×C2911yescharacteristic
315C2×C4×D4C22×C2911yescharacteristic
316#474—24no—
317#446—24no—
318C2×#107C22×C2911yescharacteristic
319C2×#107C22×C2911yescharacteristic
320C2×#107C22×C2911yescharacteristic
321C2×#106C22×C2911yescharacteristic
322C2×C4⋊C8C22×C2911yescharacteristic
323C2×C4⋊C8C22×C2911yescharacteristic
324C2×C4⋊C8C22×C2911yescharacteristic
325C2×#102C22×C2911yescharacteristic
326C2×#102C22×C2911yescharacteristic
327C2×#102C22×C2911yescharacteristic
328C2×#102C22×C2911yescharacteristic
329C2×#97C22×C2911yescharacteristic
330C2×#97C22×C2911yescharacteristic
331C2×C4×C8C22×C2911yescharacteristic
332#399—21no—
333#395—21no—
334#395—21no—
335#393—21no—
336#391—21no—
337#390C22×C2911yescharacteristic
338#390C22×C2911yescharacteristic
339#389C22×C2911yescharacteristic
340#389C22×C2911yescharacteristic
341#389C22×C2911yescharacteristic
342#389C22×C2911yescharacteristic
343#389C22×C2911yescharacteristic
344#389C22×C2911yescharacteristic
345#385—21no—
346#385—21no—
347#384—21no—
348#382C22×C2911yescharacteristic
349C4×C4⋊C4C22×C2911yescharacteristic
350#340C22×C2911yescharacteristic
351#340C22×C2911yescharacteristic
352#340C22×C2911yescharacteristic
353#340C22×C2911yescharacteristic
354#340C22×C2911yescharacteristic
355#340C22×C2911yescharacteristic
356#340C22×C2911yescharacteristic
357#340C22×C2911yescharacteristic
358C2×C29—82no—
359C2×C29#242911yescharacteristic
360C2×C29#305611yescharacteristic
361C2×C29#305811yescharacteristic
362C2×C29#337011yescharacteristic
363C2×C29#337511yescharacteristic
364C2×C29#338511yescharacteristic
365C2×C29#338911yescharacteristic
366C22×Q8—21no—
367C22×Q8D4×C2911yescharacteristic
368C22×D4C23×C2911yescharacteristic
369C23×C4—21no—
370C22×C8C23×C2911yescharacteristic
371C22×C8C23×C2911yescharacteristic
372C22×C8C23×C2911yescharacteristic
373C22×C8C23×C2911yescharacteristic
374C4⋊Q8—22no—
375C4⋊Q8—22no—
376C4×Q8—22no—
377C4×Q8—22no—
378C4×D4—22no—
379C4×D4—22no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4D4×C2911yescharacteristic
388C2×C4⋊C4D4×C2911yescharacteristic
389C2×C4⋊C4D4×C2911yescharacteristic
390C2×C4⋊C4C23×C2911yescharacteristic
391C2×C4⋊C4C23×C2911yescharacteristic
392C2×C4⋊C4C23×C2911yescharacteristic
393C2×C4⋊C4C23×C2911yescharacteristic
394C2×C4⋊C4C23×C2911yescharacteristic
395C2×C4⋊C4C23×C2911yescharacteristic
396C2×C4⋊C4C23×C2911yescharacteristic
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C42—21no—
403C2×C42C23×C2911yescharacteristic
404C2×C42C23×C2911yescharacteristic
405C2×C42C23×C2911yescharacteristic
406#107—22no—
407#107—22no—
408#107—22no—
409#106—22no—
410C4⋊C8—22no—
411C4⋊C8—22no—
412C4⋊C8D4×C2914yes—
413#102—22no—
414#102—22no—
415#102—22no—
416#102Q8×C2914yescomplemented
417#97—22no—
418#97—22no—
419C4×C8—22no—
420#95—21no—
421#95—21no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—21no—
429C29#2548111yescharacteristic, direct product factor, Sylow
430C24—21no—
431C2×Q8—22no—
432C2×Q8—22no—
433C2×Q8—41no—
434C2×Q8—42no—
435C2×Q8—81no—
436C2×Q8—81no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4C2×Q8×C2912yes—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—42no—
451C22×C4—81no—
452C22×C4—81no—
453C22×C4C2×D4×C2911yescharacteristic
454C22×C4C2×D4×C2911yescharacteristic
455C22×C4C2×D4×C2911yescharacteristic
456C22×C4C2×D4×C2911yescharacteristic
457C22×C4C2×D4×C2911yescharacteristic
458C22×C4C2×D4×C2911yescharacteristic
459C22×C4C24×C2911yescharacteristic
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8C2×D4×C2912yes—
470C2×C8C2×D4×C2912yes—
471C2×C8C2×Q8×C2912yes—
472C4⋊C4—22no—
473C4⋊C4—22no—
474C4⋊C4—22no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—42no—
488C4⋊C4—81no—
489C4⋊C4—81no—
490C4⋊C4—81no—
491C4⋊C4—81no—
492C4⋊C4—81no—
493C4⋊C4—81no—
494C4⋊C4C2×Q8×C2912yes—
495C4⋊C4#41×C2912yes—
496C22⋊C4—42no—
497C22⋊C4—42no—
498C22⋊C4—42no—
499C22⋊C4—81no—
500C22⋊C4—81no—
501C42—21no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—42no—
506C42C2×D4×C2912yes—
507C42#41×C2912yes—
508C23—22no—
509C23—41no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23C22×D4×C2911yescharacteristic
516Q8—44no—
517Q8—84no—
518D4—22no—
519D4—22no—
520D4—41no—
521D4—41no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
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×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—84no—
559C2×C4C29×#12112yes—
560C2×C4C29×#12112yes—
561C2×C4C29×#13712yes—
562C2×C4C22×D4×C2911yescharacteristic
563C2×C4C22×Q8×C2911yescharacteristic
564C2×C4C2×#41×C2911yescharacteristic
565C2×C4C2×#41×C2911yescharacteristic
566C2×C4C29×2−1+411yescharacteristic
567C2×C4C29×2−1+411yescharacteristic
568C8—22no—
569C8—22no—
570C8—22no—
571C8—41no—
572C22—42no—
573C22—42no—
574C22—42no—
575C22—81no—
576C22—81no—
577C22—81no—
578C22—81no—
579C22C2×C29×#12111yescharacteristic
580C22C29×#54811yescharacteristic
581C22D4×Q8×C2911yescharacteristic
582C22C2×C29×#13711yescharacteristic
583C22C29×#57511yescharacteristic
584C22C29×#57611yescharacteristic
585C22C29×#57611yescharacteristic
586C4—22no—
587C4—22no—
588C4—22no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4—42no—
593C4—42no—
594C4—81no—
595C4—81no—
596C4—81no—
597C4—81no—
598C4—81no—
599C4C29×#53311yescharacteristic
600C4C29×#54111yescharacteristic
601C4C29×#54711yescharacteristic
602C4D4×Q8×C2911yescharacteristic
603C2—82no—
604C2C29×#242911yescharacteristic
605C2C29×#305611yescharacteristic
606C2C29×#305811yescharacteristic
607C2C29×#337011yescharacteristic
608C2C29×#337511yescharacteristic
609C2C29×#338511yescharacteristic
610C2C29×#338911yescharacteristic
subgroupG/H
center, socleC23×C29C22×D4
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC22×D4×C29C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C29 ◁ C2×C4×Q8×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C29×#446C2semidirect
4. C29×#2567C2semidirect
5. C29×#2087C2semidirect
6. C29×#2086C2semidirect
9. C29×#1993C2semidirect
10. C29×#1949C2semidirect
11. C29×#1944C2semidirect
12. C29×#1942C2semidirect
111. C29×#102Q8semidirect
202. #25481C29direct (N × H)
268. C2×#446C2×C29semidirect
270. #2567C2×C29semidirect
271. #2087C2×C29semidirect
272. #2086C2×C29semidirect
275. #1993C2×C29semidirect
276. #1949C2×C29semidirect
277. #1944C2×C29semidirect
278. #1942C2×C29semidirect
416. #102Q8×C29semidirect
429. C29#25481direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#4742
C2×C29×#4462
C29×#25802
C29×#25672
C29×#20872
C29×#20862
C29×#20672
C29×#20652
C29×#19932
C29×#19492
C29×#19442
C29×#19422
C29×#19362
C29×#19342
C29×#17622
#2548129