Finite Group Databasebeta

← C29×#27027 #20321927

Subgroups — C29×#27027 #20321927

Order 7424.

690 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#2454C211yesmaximal, characteristic
2C29×#2370C211yesmaximal, characteristic, complemented
3C29×#2067C211yesmaximal, characteristic
4C29×#2059C211yesmaximal, characteristic, complemented
5C29×#2059C211yesmaximal, characteristic, complemented
6C29×#2025C211yesmaximal, characteristic
7C29×#1989C211yesmaximal, characteristic, complemented
8C29×#1944C211yesmaximal, characteristic, complemented
9C29×#1926C211yesmaximal, characteristic
10C29×#1925C211yesmaximal, characteristic
11C29×#1919C211yesmaximal, characteristic, complemented
12C29×#1918C211yesmaximal, characteristic, complemented
13C29×#1917C211yesmaximal, characteristic, complemented
14C29×#1864C211yesmaximal, characteristic
15C29×#1762C211yesmaximal, characteristic
16C2×C29×#125C2211yescharacteristic
17C2×C29×#125C2211yescharacteristic
18C2×C4×D4×C29C2211yescharacteristic
19C2×C29×#107C2211yescharacteristic
20C2×C29×#107C2211yescharacteristic
21C2×C29×#106C2211yescharacteristic
22C2×C29×#106C2211yescharacteristic
23C2×C29×C4⋊C8C2211yescharacteristic
24C2×C29×#102C2211yescharacteristic
25C2×C29×#102C2211yescharacteristic
26C2×C29×#102C2211yescharacteristic
27C2×C29×#102C2211yescharacteristic
28C2×C29×#97C2211yescharacteristic
29C29×#399—21no—
30C29×#396—21no—
31C29×#390C2211yescharacteristic
32C29×#390C2211yescharacteristic
33C29×#389—21no—
34C29×#389C2211yescharacteristic
35C29×#389C2211yescharacteristic
36C29×#389C2211yescharacteristic
37C29×#389C2211yescharacteristic
38C29×#387—21no—
39C29×#387—21no—
40C29×#385—21no—
41C29×#380—21no—
42C4×C4⋊C4×C29—21no—
43C4×C4⋊C4×C29C2211yescharacteristic
44C4×C4⋊C4×C29C2211yescharacteristic
45C4×C4⋊C4×C29C2211yescharacteristic
46C4×C4⋊C4×C29C2211yescharacteristic
47C29×#340C2211yescharacteristic
48C29×#340C2211yescharacteristic
49C29×#340C2211yescharacteristic
50C29×#340C2211yescharacteristic
51C29×#340C2211yescharacteristic
52C29×#340C2211yescharacteristic
53C29×#340C2211yescharacteristic
54C29×#340C2211yescharacteristic
55C29×#336C2211yescharacteristic
56C29×#336C2211yescharacteristic
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—22no—
67C29×#125—22no—
68C29×#125—41no—
69C4×D4×C29—22no—
70C4×D4×C29—41no—
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×C29—21no—
78C2×C4⋊C4×C29—21no—
79C2×C4⋊C4×C29D411yescharacteristic
80C2×C4⋊C4×C29D411yescharacteristic
81C2×C4⋊C4×C29C2311yescharacteristic
82C2×C4⋊C4×C29C2311yescharacteristic
83C2×C4⋊C4×C29C2311yescharacteristic
84C2×C4⋊C4×C29C2311yescharacteristic
85C2×C4⋊C4×C29C2311yescharacteristic
86C2×C4⋊C4×C29C2311yescharacteristic
87C2×C4⋊C4×C29C2311yescharacteristic
88C2×C22⋊C4×C29—21no—
89C2×C22⋊C4×C29—21no—
90C2×C22⋊C4×C29—21no—
91C2×C22⋊C4×C29—21no—
92C2×C22⋊C4×C29—21no—
93C2×C42×C29—21no—
94C2×C42×C29—21no—
95C2×C42×C29—21no—
96C2×C42×C29C2311yescharacteristic
97C2×C42×C29C2311yescharacteristic
98C2×C42×C29C2311yescharacteristic
99C29×#107—22no—
100C29×#107—41no—
101C29×#106—22no—
102C29×#106—22no—
103C29×C4⋊C8—41no—
104C29×#102—22no—
105C29×#102—22no—
106C29×#102—41no—
107C29×#102Q814yes—
108C29×#97—41no—
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×C29—21no—
152C2×C8×C29—21no—
153C2×C8×C29C2×Q812yes—
154C4⋊C4×C29—24no—
155C4⋊C4×C29—24no—
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×C29C2×Q812yes—
175C4⋊C4×C29#4112yes—
176C4⋊C4×C29#4112yes—
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—
190C42×C29—81no—
191C42×C29—81no—
192#27027C2911yesmaximal, characteristic, direct product factor, Sylow
193C23×C29—22no—
194C23×C29—41no—
195C23×C29—41no—
196C23×C29—41no—
197C23×C29—41no—
198C23×C29—41no—
199C23×C29—41no—
200C23×C29C22×D411yescharacteristic
201D4×C29—22no—
202D4×C29—22no—
203D4×C29—41no—
204D4×C29—41no—
205C2×C4×C29—21no—
206C2×C4×C29—21no—
207C2×C4×C29—22no—
208C2×C4×C29—22no—
209C2×C4×C29—21no—
210C2×C4×C29—21no—
211C2×C4×C29—21no—
212C2×C4×C29—21no—
213C2×C4×C29—22no—
214C2×C4×C29—22no—
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—21no—
224C2×C4×C29—21no—
225C2×C4×C29—21no—
226C2×C4×C29—21no—
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—41no—
243C2×C4×C29—41no—
244C2×C4×C29—84no—
245C2×C4×C29C22×Q811yescharacteristic
246C2×C4×C29C2×#4111yescharacteristic
247C2×C4×C29C2×#4111yescharacteristic
248C2×C4×C29C2×#4111yescharacteristic
249C2×C4×C29H(5,𝔽2)11yescharacteristic
250C2×C4×C292−1+411yescharacteristic
251C8×C29—22no—
252C8×C29—41no—
253C8×C29—41no—
254C8×C29—41no—
255#2454C2×C2911yescharacteristic
256#2370C2×C2911yescharacteristic, complemented
257#2067C2×C2911yescharacteristic
258#2059C2×C2911yescharacteristic, complemented
259#2059C2×C2911yescharacteristic, complemented
260#2025C2×C2911yescharacteristic
261#1989C2×C2911yescharacteristic, complemented
262#1944C2×C2911yescharacteristic, complemented
263#1926C2×C2911yescharacteristic
264#1925C2×C2911yescharacteristic
265#1919C2×C2911yescharacteristic, complemented
266#1918C2×C2911yescharacteristic, complemented
267#1917C2×C2911yescharacteristic, complemented
268#1864C2×C2911yescharacteristic
269#1762C2×C2911yescharacteristic
270C22×C29—42no—
271C22×C29—42no—
272C22×C29—42no—
273C22×C29—81no—
274C22×C29—81no—
275C22×C29—81no—
276C22×C29—81no—
277C22×C29#52511yescharacteristic
278C22×C29#54611yescharacteristic
279C22×C29D4×Q811yescharacteristic
280C22×C29#57511yescharacteristic
281C22×C29#57511yescharacteristic
282C22×C29#57611yescharacteristic
283C22×C29#57711yescharacteristic
284C4×C29—41no—
285C4×C29—42no—
286C4×C29—41no—
287C4×C29—42no—
288C4×C29—42no—
289C4×C29—41no—
290C4×C29—41no—
291C4×C29—41no—
292C4×C29—41no—
293C4×C29—42no—
294C4×C29—81no—
295C4×C29—81no—
296C4×C29—81no—
297C4×C29#53311yescharacteristic
298C4×C29#54211yescharacteristic
299C4×C29#55411yescharacteristic
300C4×C29#55611yescharacteristic
301C2×#125C22×C2911yescharacteristic
302C2×#125C22×C2911yescharacteristic
303C2×C4×D4C22×C2911yescharacteristic
304C2×#107C22×C2911yescharacteristic
305C2×#107C22×C2911yescharacteristic
306C2×#106C22×C2911yescharacteristic
307C2×#106C22×C2911yescharacteristic
308C2×C4⋊C8C22×C2911yescharacteristic
309C2×#102C22×C2911yescharacteristic
310C2×#102C22×C2911yescharacteristic
311C2×#102C22×C2911yescharacteristic
312C2×#102C22×C2911yescharacteristic
313C2×#97C22×C2911yescharacteristic
314#399—21no—
315#396—21no—
316#390C22×C2911yescharacteristic
317#390C22×C2911yescharacteristic
318#389—21no—
319#389C22×C2911yescharacteristic
320#389C22×C2911yescharacteristic
321#389C22×C2911yescharacteristic
322#389C22×C2911yescharacteristic
323#387—21no—
324#387—21no—
325#385—21no—
326#380—21no—
327C4×C4⋊C4—21no—
328C4×C4⋊C4C22×C2911yescharacteristic
329C4×C4⋊C4C22×C2911yescharacteristic
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
342#336C22×C2911yescharacteristic
343#336C22×C2911yescharacteristic
344C2×C29—82no—
345C2×C29#246511yescharacteristic
346C2×C29#311111yescharacteristic
347C2×C29#311911yescharacteristic
348C2×C29#330911yescharacteristic
349C2×C29#332311yescharacteristic
350C2×C29#338811yescharacteristic
351C2×C29#338911yescharacteristic
352C22×D4C23×C2911yescharacteristic
353C23×C4—21no—
354C22×C8C23×C2911yescharacteristic
355C22×C8C23×C2911yescharacteristic
356C22×C8C23×C2911yescharacteristic
357C22×C8C23×C2911yescharacteristic
358#125—22no—
359#125—22no—
360#125—22no—
361#125—41no—
362C4×D4—22no—
363C4×D4—41no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4D4×C2911yescharacteristic
373C2×C4⋊C4D4×C2911yescharacteristic
374C2×C4⋊C4C23×C2911yescharacteristic
375C2×C4⋊C4C23×C2911yescharacteristic
376C2×C4⋊C4C23×C2911yescharacteristic
377C2×C4⋊C4C23×C2911yescharacteristic
378C2×C4⋊C4C23×C2911yescharacteristic
379C2×C4⋊C4C23×C2911yescharacteristic
380C2×C4⋊C4C23×C2911yescharacteristic
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C42—21no—
387C2×C42—21no—
388C2×C42—21no—
389C2×C42C23×C2911yescharacteristic
390C2×C42C23×C2911yescharacteristic
391C2×C42C23×C2911yescharacteristic
392#107—22no—
393#107—41no—
394#106—22no—
395#106—22no—
396C4⋊C8—41no—
397#102—22no—
398#102—22no—
399#102—41no—
400#102Q8×C2914yes—
401#97—41no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95D4×C2911yescharacteristic
410#95D4×C2911yescharacteristic
411C29#2702711yescharacteristic, direct product factor, Sylow
412C24—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4C2×Q8×C2912yes—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—42no—
427C22×C4—42no—
428C22×C4—81no—
429C22×C4C2×D4×C2911yescharacteristic
430C22×C4C2×D4×C2911yescharacteristic
431C22×C4C2×D4×C2911yescharacteristic
432C22×C4C2×D4×C2911yescharacteristic
433C22×C4C2×D4×C2911yescharacteristic
434C22×C4C2×D4×C2911yescharacteristic
435C22×C4C24×C2911yescharacteristic
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8C2×Q8×C2912yes—
448C4⋊C4—24no—
449C4⋊C4—24no—
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—21no—
459C4⋊C4—21no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4—42no—
463C4⋊C4—42no—
464C4⋊C4—42no—
465C4⋊C4—81no—
466C4⋊C4—81no—
467C4⋊C4—81no—
468C4⋊C4C2×Q8×C2912yes—
469C4⋊C4#41×C2912yes—
470C4⋊C4#41×C2912yes—
471C4⋊C4#41×C2912yes—
472C22⋊C4—42no—
473C22⋊C4—42no—
474C22⋊C4—81no—
475C22⋊C4—81no—
476C22⋊C4—81no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—21no—
483C42—42no—
484C42—81no—
485C42—81no—
486C23—22no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23C22×D4×C2911yescharacteristic
494D4—22no—
495D4—22no—
496D4—41no—
497D4—41no—
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—22no—
507C2×C4—22no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
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—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—84no—
538C2×C4C22×Q8×C2911yescharacteristic
539C2×C4C2×#41×C2911yescharacteristic
540C2×C4C2×#41×C2911yescharacteristic
541C2×C4C2×#41×C2911yescharacteristic
542C2×C4C29×H(5,𝔽2)11yescharacteristic
543C2×C4C29×2−1+411yescharacteristic
544C8—22no—
545C8—41no—
546C8—41no—
547C8—41no—
548C22—42no—
549C22—42no—
550C22—42no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22—81no—
555C22C29×#52511yescharacteristic
556C22C29×#54611yescharacteristic
557C22D4×Q8×C2911yescharacteristic
558C22C29×#57511yescharacteristic
559C22C29×#57511yescharacteristic
560C22C29×#57611yescharacteristic
561C22C29×#57711yescharacteristic
562C4—41no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—42no—
567C4—41no—
568C4—42no—
569C4—41no—
570C4—42no—
571C4—42no—
572C4—81no—
573C4—81no—
574C4—81no—
575C4C29×#53311yescharacteristic
576C4C29×#54211yescharacteristic
577C4C29×#55411yescharacteristic
578C4C29×#55611yescharacteristic
579C2—82no—
580C2C29×#246511yescharacteristic
581C2C29×#311111yescharacteristic
582C2C29×#311911yescharacteristic
583C2C29×#330911yescharacteristic
584C2C29×#332311yescharacteristic
585C2C29×#338811yescharacteristic
586C2C29×#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
2. C29×#2370C2semidirect
4. C29×#2059C2semidirect
5. C29×#2059C2semidirect
7. C29×#1989C2semidirect
8. C29×#1944C2semidirect
11. C29×#1919C2semidirect
12. C29×#1918C2semidirect
13. C29×#1917C2semidirect
192. #27027C29direct (N × H)
256. #2370C2×C29semidirect
258. #2059C2×C29semidirect
259. #2059C2×C29semidirect
261. #1989C2×C29semidirect
262. #1944C2×C29semidirect
265. #1919C2×C29semidirect
266. #1918C2×C29semidirect
267. #1917C2×C29semidirect
411. C29#27027direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#24542
C29×#23702
C29×#20672
C29×#20592
C29×#20252
C29×#19892
C29×#19442
C29×#19262
C29×#19252
C29×#19192
C29×#19182
C29×#19172
C29×#18642
C29×#17622
#2702729