Finite Group Databasebeta

← C29×#28973 #20323873

Subgroups — C29×#28973 #20323873

Order 7424.

670 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#2508C211yesmaximal, characteristic, complemented
2C29×#2454C211yesmaximal, characteristic
3C29×#2092C211yesmaximal, characteristic
4C29×#2086C211yesmaximal, characteristic, complemented
5C29×#2065C211yesmaximal, characteristic
6C29×#2059C211yesmaximal, characteristic, complemented
7C29×#1991C211yesmaximal, characteristic, complemented
8C29×#1943C211yesmaximal, characteristic, complemented
9C29×#1943C211yesmaximal, characteristic, complemented
10C29×#1936C211yesmaximal, characteristic
11C29×#1934C211yesmaximal, characteristic
12C29×#1919C211yesmaximal, characteristic, complemented
13C29×#1862C211yesmaximal, characteristic
14C29×#1771C211yesmaximal, characteristic, complemented
15C29×#1762C211yesmaximal, characteristic
16C2×C29×#125C2211yescharacteristic
17C2×C4×D4×C29C2211yescharacteristic
18C2×C29×#107C2211yescharacteristic
19C2×C29×#107C2211yescharacteristic
20C2×C29×#106C2211yescharacteristic
21C2×C29×#106C2211yescharacteristic
22C2×C29×C4⋊C8C2211yescharacteristic
23C2×C29×#102C2211yescharacteristic
24C2×C29×#102C2211yescharacteristic
25C2×C29×#102C2211yescharacteristic
26C2×C29×#102C2211yescharacteristic
27C2×C29×#97C2211yescharacteristic
28C2×C29×#97C2211yescharacteristic
29C2×C4×C8×C29C2211yescharacteristic
30C29×#400—21no—
31C29×#399—21no—
32C29×#398—21no—
33C29×#396—21no—
34C29×#390C2211yescharacteristic
35C29×#390C2211yescharacteristic
36C29×#389C2211yescharacteristic
37C29×#389C2211yescharacteristic
38C29×#389C2211yescharacteristic
39C29×#389C2211yescharacteristic
40C29×#389C2211yescharacteristic
41C29×#389C2211yescharacteristic
42C29×#387—21no—
43C29×#385—21no—
44C29×#382—21no—
45C29×#382C2211yescharacteristic
46C29×#380—21no—
47C4×C4⋊C4×C29C2211yescharacteristic
48C4×C4⋊C4×C29C2211yescharacteristic
49C29×#340C2211yescharacteristic
50C29×#340C2211yescharacteristic
51C29×#340C2211yescharacteristic
52C29×#340C2211yescharacteristic
53C29×#340C2211yescharacteristic
54C29×#340C2211yescharacteristic
55C29×#340C2211yescharacteristic
56C29×#340C2211yescharacteristic
57C29×#336C2211yescharacteristic
58C29×#336C2211yescharacteristic
59C22×D4×C29C2311yescharacteristic
60C23×C4×C29—21no—
61C22×C8×C29C2311yescharacteristic
62C22×C8×C29C2311yescharacteristic
63C22×C8×C29C2311yescharacteristic
64C22×C8×C29C2311yescharacteristic
65C29×#125—22no—
66C29×#125—41no—
67C4×D4×C29—22no—
68C4×D4×C29—41no—
69C2×C4⋊C4×C29—21no—
70C2×C4⋊C4×C29—21no—
71C2×C4⋊C4×C29—21no—
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×C4⋊C4×C29C2311yescharacteristic
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×C29C2311yescharacteristic
93C2×C42×C29C2311yescharacteristic
94C2×C42×C29C2311yescharacteristic
95C29×#107—22no—
96C29×#107—22no—
97C29×#106—22no—
98C29×#106—41no—
99C29×C4⋊C8—22no—
100C29×#102—22no—
101C29×#102—22no—
102C29×#102—41no—
103C29×#102Q814yes—
104C29×#97—22no—
105C29×#97—41no—
106C4×C8×C29—41no—
107C29×#95—21no—
108C29×#95—21no—
109C29×#95—21no—
110C29×#95—21no—
111C29×#95—21no—
112C29×#95—21no—
113C29×#95—21no—
114C29×#95—21no—
115C29×#95—21no—
116C29×#95D411yescharacteristic
117C29×#95D411yescharacteristic
118C24×C29—21no—
119C2×D4×C29—21no—
120C2×D4×C29—21no—
121C2×D4×C29—21no—
122C2×D4×C29—21no—
123C2×D4×C29—21no—
124C2×D4×C29C2×Q812yes—
125C22×C4×C29—21no—
126C22×C4×C29—21no—
127C22×C4×C29—21no—
128C22×C4×C29—21no—
129C22×C4×C29—21no—
130C22×C4×C29—21no—
131C22×C4×C29—21no—
132C22×C4×C29—42no—
133C22×C4×C29—42no—
134C22×C4×C29—81no—
135C22×C4×C29C2×D411yescharacteristic
136C22×C4×C29C2×D411yescharacteristic
137C22×C4×C29C2×D411yescharacteristic
138C22×C4×C29C2×D411yescharacteristic
139C22×C4×C29C2×D411yescharacteristic
140C22×C4×C29C2×D411yescharacteristic
141C22×C4×C29C2411yescharacteristic
142C2×C8×C29—21no—
143C2×C8×C29—21no—
144C2×C8×C29—21no—
145C2×C8×C29—21no—
146C2×C8×C29—21no—
147C2×C8×C29—21no—
148C2×C8×C29—21no—
149C2×C8×C29—21no—
150C2×C8×C29—21no—
151C2×C8×C29C2×Q812yes—
152C2×C8×C29#4112yes—
153C2×C8×C29#4112yes—
154C4⋊C4×C29—21no—
155C4⋊C4×C29—21no—
156C4⋊C4×C29—21no—
157C4⋊C4×C29—21no—
158C4⋊C4×C29—21no—
159C4⋊C4×C29—21no—
160C4⋊C4×C29—21no—
161C4⋊C4×C29—21no—
162C4⋊C4×C29—21no—
163C4⋊C4×C29—21no—
164C4⋊C4×C29—21no—
165C4⋊C4×C29—21no—
166C4⋊C4×C29—41no—
167C4⋊C4×C29—41no—
168C4⋊C4×C29—42no—
169C4⋊C4×C29—42no—
170C4⋊C4×C29—42no—
171C4⋊C4×C29—81no—
172C4⋊C4×C29—81no—
173C4⋊C4×C29—81no—
174C4⋊C4×C29—81no—
175C4⋊C4×C29—81no—
176C4⋊C4×C29C2×Q812yes—
177C4⋊C4×C29#4112yes—
178C22⋊C4×C29—42no—
179C22⋊C4×C29—42no—
180C22⋊C4×C29—81no—
181C22⋊C4×C29—81no—
182C22⋊C4×C29—81no—
183C42×C29—21no—
184C42×C29—21no—
185C42×C29—21no—
186C42×C29—21no—
187C42×C29—21no—
188C42×C29—21no—
189C42×C29—42no—
190#28973C2911yesmaximal, characteristic, direct product factor, Sylow
191C23×C29—22no—
192C23×C29—41no—
193C23×C29—41no—
194C23×C29—41no—
195C23×C29—41no—
196C23×C29—41no—
197C23×C29—41no—
198C23×C29C22×D411yescharacteristic
199D4×C29—22no—
200D4×C29—22no—
201D4×C29—41no—
202D4×C29—41no—
203C2×C4×C29—21no—
204C2×C4×C29—21no—
205C2×C4×C29—21no—
206C2×C4×C29—21no—
207C2×C4×C29—21no—
208C2×C4×C29—21no—
209C2×C4×C29—22no—
210C2×C4×C29—22no—
211C2×C4×C29—21no—
212C2×C4×C29—21no—
213C2×C4×C29—21no—
214C2×C4×C29—21no—
215C2×C4×C29—21no—
216C2×C4×C29—21no—
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—41no—
224C2×C4×C29—41no—
225C2×C4×C29—41no—
226C2×C4×C29—41no—
227C2×C4×C29—41no—
228C2×C4×C29—41no—
229C2×C4×C29—41no—
230C2×C4×C29—41no—
231C2×C4×C29—41no—
232C2×C4×C29—41no—
233C2×C4×C29—41no—
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—84no—
243C2×C4×C29C22×Q811yescharacteristic
244C2×C4×C29C2×#4111yescharacteristic
245C2×C4×C29C2×#4111yescharacteristic
246C2×C4×C29C2×#4111yescharacteristic
247C2×C4×C29H(5,𝔽2)11yescharacteristic
248C2×C4×C292−1+411yescharacteristic
249C8×C29—22no—
250C8×C29—22no—
251C8×C29—22no—
252C8×C29—41no—
253#2508C2×C2911yescharacteristic, complemented
254#2454C2×C2911yescharacteristic
255#2092C2×C2911yescharacteristic
256#2086C2×C2911yescharacteristic, complemented
257#2065C2×C2911yescharacteristic
258#2059C2×C2911yescharacteristic, complemented
259#1991C2×C2911yescharacteristic, complemented
260#1943C2×C2911yescharacteristic, complemented
261#1943C2×C2911yescharacteristic, complemented
262#1936C2×C2911yescharacteristic
263#1934C2×C2911yescharacteristic
264#1919C2×C2911yescharacteristic, complemented
265#1862C2×C2911yescharacteristic
266#1771C2×C2911yescharacteristic, complemented
267#1762C2×C2911yescharacteristic
268C22×C29—42no—
269C22×C29—42no—
270C22×C29—42no—
271C22×C29—81no—
272C22×C29—81no—
273C22×C29—81no—
274C22×C29—81no—
275C22×C29#53211yescharacteristic
276C22×C29#54611yescharacteristic
277C22×C29D4×Q811yescharacteristic
278C22×C29#57511yescharacteristic
279C22×C29#57511yescharacteristic
280C22×C29#57611yescharacteristic
281C22×C29#57711yescharacteristic
282C4×C29—42no—
283C4×C29—41no—
284C4×C29—41no—
285C4×C29—41no—
286C4×C29—41no—
287C4×C29—41no—
288C4×C29—41no—
289C4×C29—42no—
290C4×C29—81no—
291C4×C29—81no—
292C4×C29—81no—
293C4×C29—81no—
294C4×C29—81no—
295C4×C29#53311yescharacteristic
296C4×C29#53911yescharacteristic
297C4×C29#55211yescharacteristic
298C4×C29#55411yescharacteristic
299C2×#125C22×C2911yescharacteristic
300C2×C4×D4C22×C2911yescharacteristic
301C2×#107C22×C2911yescharacteristic
302C2×#107C22×C2911yescharacteristic
303C2×#106C22×C2911yescharacteristic
304C2×#106C22×C2911yescharacteristic
305C2×C4⋊C8C22×C2911yescharacteristic
306C2×#102C22×C2911yescharacteristic
307C2×#102C22×C2911yescharacteristic
308C2×#102C22×C2911yescharacteristic
309C2×#102C22×C2911yescharacteristic
310C2×#97C22×C2911yescharacteristic
311C2×#97C22×C2911yescharacteristic
312C2×C4×C8C22×C2911yescharacteristic
313#400—21no—
314#399—21no—
315#398—21no—
316#396—21no—
317#390C22×C2911yescharacteristic
318#390C22×C2911yescharacteristic
319#389C22×C2911yescharacteristic
320#389C22×C2911yescharacteristic
321#389C22×C2911yescharacteristic
322#389C22×C2911yescharacteristic
323#389C22×C2911yescharacteristic
324#389C22×C2911yescharacteristic
325#387—21no—
326#385—21no—
327#382—21no—
328#382C22×C2911yescharacteristic
329#380—21no—
330C4×C4⋊C4C22×C2911yescharacteristic
331C4×C4⋊C4C22×C2911yescharacteristic
332#340C22×C2911yescharacteristic
333#340C22×C2911yescharacteristic
334#340C22×C2911yescharacteristic
335#340C22×C2911yescharacteristic
336#340C22×C2911yescharacteristic
337#340C22×C2911yescharacteristic
338#340C22×C2911yescharacteristic
339#340C22×C2911yescharacteristic
340#336C22×C2911yescharacteristic
341#336C22×C2911yescharacteristic
342C2×C29—82no—
343C2×C29#255611yescharacteristic
344C2×C29#317911yescharacteristic
345C2×C29#318311yescharacteristic
346C2×C29#331711yescharacteristic
347C2×C29#331911yescharacteristic
348C2×C29#338811yescharacteristic
349C2×C29#338911yescharacteristic
350C22×D4C23×C2911yescharacteristic
351C23×C4—21no—
352C22×C8C23×C2911yescharacteristic
353C22×C8C23×C2911yescharacteristic
354C22×C8C23×C2911yescharacteristic
355C22×C8C23×C2911yescharacteristic
356#125—22no—
357#125—41no—
358C4×D4—22no—
359C4×D4—41no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4D4×C2911yescharacteristic
369C2×C4⋊C4D4×C2911yescharacteristic
370C2×C4⋊C4C23×C2911yescharacteristic
371C2×C4⋊C4C23×C2911yescharacteristic
372C2×C4⋊C4C23×C2911yescharacteristic
373C2×C4⋊C4C23×C2911yescharacteristic
374C2×C4⋊C4C23×C2911yescharacteristic
375C2×C4⋊C4C23×C2911yescharacteristic
376C2×C4⋊C4C23×C2911yescharacteristic
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C42—21no—
383C2×C42C23×C2911yescharacteristic
384C2×C42C23×C2911yescharacteristic
385C2×C42C23×C2911yescharacteristic
386#107—22no—
387#107—22no—
388#106—22no—
389#106—41no—
390C4⋊C8—22no—
391#102—22no—
392#102—22no—
393#102—41no—
394#102Q8×C2914yes—
395#97—22no—
396#97—41no—
397C4×C8—41no—
398#95—21no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95D4×C2911yescharacteristic
408#95D4×C2911yescharacteristic
409C29#2897311yescharacteristic, direct product factor, Sylow
410C24—21no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4C2×Q8×C2912yes—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—42no—
425C22×C4—42no—
426C22×C4—81no—
427C22×C4C2×D4×C2911yescharacteristic
428C22×C4C2×D4×C2911yescharacteristic
429C22×C4C2×D4×C2911yescharacteristic
430C22×C4C2×D4×C2911yescharacteristic
431C22×C4C2×D4×C2911yescharacteristic
432C22×C4C2×D4×C2911yescharacteristic
433C22×C4C24×C2911yescharacteristic
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8C2×Q8×C2912yes—
444C2×C8#41×C2912yes—
445C2×C8#41×C2912yes—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—41no—
459C4⋊C4—41no—
460C4⋊C4—42no—
461C4⋊C4—42no—
462C4⋊C4—42no—
463C4⋊C4—81no—
464C4⋊C4—81no—
465C4⋊C4—81no—
466C4⋊C4—81no—
467C4⋊C4—81no—
468C4⋊C4C2×Q8×C2912yes—
469C4⋊C4#41×C2912yes—
470C22⋊C4—42no—
471C22⋊C4—42no—
472C22⋊C4—81no—
473C22⋊C4—81no—
474C22⋊C4—81no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—42no—
482C23—22no—
483C23—41no—
484C23—41no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23C22×D4×C2911yescharacteristic
490D4—22no—
491D4—22no—
492D4—41no—
493D4—41no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—84no—
534C2×C4C22×Q8×C2911yescharacteristic
535C2×C4C2×#41×C2911yescharacteristic
536C2×C4C2×#41×C2911yescharacteristic
537C2×C4C2×#41×C2911yescharacteristic
538C2×C4C29×H(5,𝔽2)11yescharacteristic
539C2×C4C29×2−1+411yescharacteristic
540C8—22no—
541C8—22no—
542C8—22no—
543C8—41no—
544C22—42no—
545C22—42no—
546C22—42no—
547C22—81no—
548C22—81no—
549C22—81no—
550C22—81no—
551C22C29×#53211yescharacteristic
552C22C29×#54611yescharacteristic
553C22D4×Q8×C2911yescharacteristic
554C22C29×#57511yescharacteristic
555C22C29×#57511yescharacteristic
556C22C29×#57611yescharacteristic
557C22C29×#57711yescharacteristic
558C4—41no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—41no—
563C4—42no—
564C4—42no—
565C4—41no—
566C4—81no—
567C4—81no—
568C4—81no—
569C4—81no—
570C4—81no—
571C4C29×#53311yescharacteristic
572C4C29×#53911yescharacteristic
573C4C29×#55211yescharacteristic
574C4C29×#55411yescharacteristic
575C2—82no—
576C2C29×#255611yescharacteristic
577C2C29×#317911yescharacteristic
578C2C29×#318311yescharacteristic
579C2C29×#331711yescharacteristic
580C2C29×#331911yescharacteristic
581C2C29×#338811yescharacteristic
582C2C29×#338911yescharacteristic
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
1. C29×#2508C2semidirect
4. C29×#2086C2semidirect
6. C29×#2059C2semidirect
7. C29×#1991C2semidirect
8. C29×#1943C2semidirect
9. C29×#1943C2semidirect
12. C29×#1919C2semidirect
14. C29×#1771C2semidirect
190. #28973C29direct (N × H)
253. #2508C2×C29semidirect
256. #2086C2×C29semidirect
258. #2059C2×C29semidirect
259. #1991C2×C29semidirect
260. #1943C2×C29semidirect
261. #1943C2×C29semidirect
264. #1919C2×C29semidirect
266. #1771C2×C29semidirect
409. C29#28973direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#25082
C29×#24542
C29×#20922
C29×#20862
C29×#20652
C29×#20592
C29×#19912
C29×#19432
C29×#19362
C29×#19342
C29×#19192
C29×#18622
C29×#17712
C29×#17622
#2897329