Finite Group Databasebeta

← C29×#34262 #20329162

Subgroups — C29×#34262 #20329162

Order 7424.

2198 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#519C211yesmaximal, characteristic
2C29×#2356C213yesmaximal, complemented
3C29×#2355C213yesmaximal, complemented
4C29×#2351C211yesmaximal, characteristic, complemented
5Q8×C4⋊C4×C29C211yesmaximal, characteristic, complemented
6C29×#2347C213yesmaximal
7C29×#2346C213yesmaximal
8Q8×C22⋊C4×C29C211yesmaximal, characteristic
9Q8×C22⋊C4×C29C211yesmaximal, characteristic
10C29×#2320C213yesmaximal, complemented
11C29×#2314C213yesmaximal
12C29×#2298C213yesmaximal
13C29×#2295C213yesmaximal, complemented
14C29×#2276C211yesmaximal, characteristic, complemented
15C42×Q8×C29C211yesmaximal, characteristic, complemented
16C23×Q8×C29C2211yescharacteristic
17C29×#519C4116yescomplemented
18C2×C4×Q8×C29C2211yescharacteristic
19C2×C4×Q8×C29C2211yescharacteristic
20C2×C4×Q8×C29C2211yescharacteristic
21C2×C4×Q8×C29C2211yescharacteristic
22C2×C4×Q8×C29C2211yescharacteristic
23C2×C4×Q8×C29C2213yes—
24C2×C4×Q8×C29C2211yescharacteristic
25C2×C4×Q8×C29C2213yes—
26C2×C29×#117C2213yes—
27C2×C29×#117C2213yes—
28C29×#391C2213yes—
29C29×#391C2213yes—
30C29×#391C2213yes—
31C29×#391C2213yes—
32C29×#389C2213yes—
33C29×#389C2213yes—
34C29×#389C2213yes—
35C29×#389C2213yes—
36C29×#388C2211yescharacteristic
37C29×#388C2213yes—
38C29×#388C2213yes—
39C29×#388C2213yes—
40C29×#388C2216yes—
41C29×#387C2213yes—
42C29×#387C2216yes—
43C29×#387C2213yes—
44C29×#387C2213yes—
45C29×#387C2213yes—
46C29×#387C2216yes—
47C29×#384C2213yes—
48C29×#383C2216yes—
49C29×#382C2213yes—
50C29×#382C2216yes—
51C29×#380C2213yes—
52C29×#380C2213yes—
53C4×C4⋊C4×C29C2213yes—
54C4×C4⋊C4×C29C2213yes—
55C4×C4⋊C4×C29C2213yes—
56C4×C4⋊C4×C29C2213yes—
57C4×C4⋊C4×C29C2213yes—
58C4×C4⋊C4×C29C2213yes—
59C4×C4⋊C4×C29C2216yes—
60C4×C4⋊C4×C29C2213yes—
61C4×C4⋊C4×C29C2213yes—
62C4×C22⋊C4×C29C2213yes—
63C4×C22⋊C4×C29C2213yes—
64C29×#376C2213yes—
65C29×#376C2216yes—
66C43×C29C2213yes—
67C22×Q8×C29—24no—
68C22×Q8×C29—24no—
69C22×Q8×C29C2×C418yes—
70C22×Q8×C29C2313yes—
71C22×Q8×C29C2311yescharacteristic
72C23×C4×C29C2313yes—
73C4×Q8×C29—24no—
74C4×Q8×C29—24no—
75C4×Q8×C29—24no—
76C4×Q8×C29—24no—
77C4×Q8×C29C2×C4124yes—
78C4×Q8×C29C2×C4124yes—
79C4×Q8×C29C2×C418yes—
80C4×Q8×C29C2×C418yes—
81C29×#117C2×C4124yes—
82C29×#117C2×C4124yes—
83C2×C4⋊C4×C29C2313yes—
84C2×C4⋊C4×C29C2313yes—
85C2×C4⋊C4×C29C2313yes—
86C2×C4⋊C4×C29C2313yes—
87C2×C4⋊C4×C29C2311yescharacteristic
88C2×C4⋊C4×C29C2313yes—
89C2×C4⋊C4×C29C2313yes—
90C2×C4⋊C4×C29C2316yes—
91C2×C4⋊C4×C29C2313yes—
92C2×C4⋊C4×C29C2313yes—
93C2×C4⋊C4×C29C2313yes—
94C2×C4⋊C4×C29C2313yes—
95C2×C4⋊C4×C29C2313yes—
96C2×C22⋊C4×C29C2311yescharacteristic
97C2×C22⋊C4×C29C2311yescharacteristic
98C2×C22⋊C4×C29C2313yes—
99C2×C22⋊C4×C29C2313yes—
100C2×C22⋊C4×C29C2311yescharacteristic
101C2×C22⋊C4×C29C2313yes—
102C2×C42×C29C2313yes—
103C2×C42×C29C2313yes—
104C2×C42×C29C2313yes—
105C2×C42×C29C2313yes—
106C2×C42×C29C2311yescharacteristic
107C2×C42×C29C2313yes—
108C2×C42×C29C2313yes—
109C2×C42×C29C2313yes—
110C2×C42×C29C2316yes—
111C2×C42×C29C2313yes—
112C2×C42×C29C2316yes—
113C2×C42×C29C2313yes—
114C29×#95C2311yescharacteristic
115C29×#95C2313yes—
116C29×#95C2313yes—
117C29×#95C2313yes—
118C29×#95C2313yes—
119C29×#95C2313yes—
120C29×#95C2316yes—
121C29×#95C2316yes—
122C29×#95C2313yes—
123C29×#95C2313yes—
124C29×#95C2313yes—
125C29×#95C2316yes—
126C29×#95C2311yescharacteristic
127C29×#95C2316yes—
128C29×#95C2313yes—
129C29×#95C2313yes—
130C24×C29C2411yescharacteristic
131C2×Q8×C29—232no—
132C2×Q8×C29—26no—
133C2×Q8×C29—26no—
134C2×Q8×C29C22×C4112yes—
135C2×Q8×C29C22×C414yes—
136C2×Q8×C29#4114yes—
137C2×Q8×C29#4114yes—
138C22×C4×C29—26no—
139C22×C4×C29—26no—
140C22×C4×C29C22×C4112yes—
141C22×C4×C29C2413yes—
142C22×C4×C29C2413yes—
143C22×C4×C29C2411yescharacteristic
144C22×C4×C29C2413yes—
145C22×C4×C29C2413yes—
146C22×C4×C29C2411yescharacteristic
147C22×C4×C29C2411yescharacteristic
148C22×C4×C29C2413yes—
149C22×C4×C29C2413yes—
150C22×C4×C29C2411yescharacteristic
151C22×C4×C29C2413yes—
152C22×C4×C29C2411yescharacteristic
153C22×C4×C29C2411yescharacteristic
154C22×C4×C29C2413yes—
155C4⋊C4×C29—26no—
156C4⋊C4×C29—26no—
157C4⋊C4×C29—26no—
158C4⋊C4×C29—26no—
159C4⋊C4×C29—22no—
160C4⋊C4×C29—26no—
161C4⋊C4×C29—43no—
162C4⋊C4×C29—43no—
163C4⋊C4×C29—46no—
164C4⋊C4×C29C22×C4112yes—
165C4⋊C4×C29C22×C4112yes—
166C4⋊C4×C29C22×C4112yes—
167C4⋊C4×C29C22×C4112yes—
168C22⋊C4×C29—22no—
169C22⋊C4×C29—22no—
170C22⋊C4×C29—43no—
171C22⋊C4×C29—43no—
172C22⋊C4×C29C22×C414yes—
173C22⋊C4×C29C22×C4112yes—
174C42×C29—26no—
175C42×C29—26no—
176C42×C29—26no—
177C42×C29—26no—
178C42×C29—22no—
179C42×C29—26no—
180C42×C29—43no—
181C42×C29—46no—
182C42×C29—43no—
183C42×C29C22×C4124yes—
184C42×C29C22×C4112yes—
185C42×C29C22×C4112yes—
186#34262C2911yesmaximal, characteristic, direct product factor, Sylow
187C23×C29—21no—
188C23×C29—21no—
189C23×C29—21no—
190C23×C29—21no—
191C23×C29—21no—
192C23×C29—21no—
193C23×C29C23×C412yes—
194C23×C29C2511yescharacteristic
195Q8×C29—224no—
196Q8×C29#117116yes—
197C2×C4×C29—21no—
198C2×C4×C29—21no—
199C2×C4×C29—23no—
200C2×C4×C29—23no—
201C2×C4×C29—21no—
202C2×C4×C29—23no—
203C2×C4×C29—21no—
204C2×C4×C29—23no—
205C2×C4×C29—21no—
206C2×C4×C29—23no—
207C2×C4×C29—21no—
208C2×C4×C29—21no—
209C2×C4×C29—21no—
210C2×C4×C29—23no—
211C2×C4×C29—224no—
212C2×C4×C29—21no—
213C2×C4×C29—21no—
214C2×C4×C29—23no—
215C2×C4×C29—23no—
216C2×C4×C29—23no—
217C2×C4×C29—23no—
218C2×C4×C29—23no—
219C2×C4×C29—21no—
220C2×C4×C29—21no—
221C2×C4×C29—23no—
222C2×C4×C29—21no—
223C2×C4×C29—23no—
224C2×C4×C29—23no—
225C2×C4×C29—23no—
226C2×C4×C29—23no—
227C2×C4×C29—23no—
228C2×C4×C29—23no—
229C2×C4×C29—21no—
230C2×C4×C29C23×C416yes—
231C2×C4×C29C23×C412yes—
232C2×C4×C29C23×C416yes—
233C2×C4×C29C23×C412yes—
234C2×C4×C29C23×C416yes—
235C2×C4×C29C23×C416yes—
236C2×C4×C29C2×#4116yes—
237C2×C4×C29C2×#4116yes—
238C2×C4×C292−1+412yes—
239C2×C4×C292−1+412yes—
240C2×#519C2×C2911yescharacteristic
241#2356C2×C2913yescomplemented
242#2355C2×C2913yescomplemented
243#2351C2×C2911yescharacteristic, complemented
244Q8×C4⋊C4C2×C2911yescharacteristic, complemented
245#2347C2×C2913yes—
246#2346C2×C2913yes—
247Q8×C22⋊C4C2×C2911yescharacteristic
248Q8×C22⋊C4C2×C2911yescharacteristic
249#2320C2×C2913yescomplemented
250#2314C2×C2913yes—
251#2298C2×C2913yes—
252#2295C2×C2913yescomplemented
253#2276C2×C2911yescharacteristic, complemented
254C42×Q8C2×C2911yescharacteristic, complemented
255C22×C29—22no—
256C22×C29—22no—
257C22×C29—22no—
258C22×C29—41no—
259C22×C29—41no—
260C22×C29—41no—
261C22×C29—41no—
262C22×C29C24×C411yescharacteristic
263C22×C29C22×#4111yescharacteristic
264C22×C29C22×#4111yescharacteristic
265C22×C29C2×2−1+411yescharacteristic
266C22×C29C2×2−1+411yescharacteristic
267C22×C29#58511yescharacteristic
268C22×C29#58511yescharacteristic
269C4×C29—26no—
270C4×C29—22no—
271C4×C29—26no—
272C4×C29—26no—
273C4×C29—22no—
274C4×C29—22no—
275C4×C29—22no—
276C4×C29—43no—
277C4×C29—41no—
278C4×C29—43no—
279C4×C29—41no—
280C4×C29—43no—
281C4×C29—43no—
282C4×C29C2×#117112yes—
283C23×Q8C22×C2911yescharacteristic
284#519C4×C29116yescomplemented
285C2×C4×Q8C22×C2911yescharacteristic
286C2×C4×Q8C22×C2911yescharacteristic
287C2×C4×Q8C22×C2911yescharacteristic
288C2×C4×Q8C22×C2911yescharacteristic
289C2×C4×Q8C22×C2913yes—
290C2×C4×Q8C22×C2911yescharacteristic
291C2×C4×Q8C22×C2913yes—
292C2×C4×Q8C22×C2911yescharacteristic
293C2×#117C22×C2913yes—
294C2×#117C22×C2913yes—
295#391C22×C2913yes—
296#391C22×C2913yes—
297#391C22×C2913yes—
298#391C22×C2913yes—
299#389C22×C2913yes—
300#389C22×C2913yes—
301#389C22×C2913yes—
302#389C22×C2913yes—
303#388C22×C2913yes—
304#388C22×C2916yes—
305#388C22×C2913yes—
306#388C22×C2913yes—
307#388C22×C2911yescharacteristic
308#387C22×C2916yes—
309#387C22×C2916yes—
310#387C22×C2913yes—
311#387C22×C2913yes—
312#387C22×C2913yes—
313#387C22×C2913yes—
314#384C22×C2913yes—
315#383C22×C2916yes—
316#382C22×C2913yes—
317#382C22×C2916yes—
318#380C22×C2913yes—
319#380C22×C2913yes—
320C4×C4⋊C4C22×C2913yes—
321C4×C4⋊C4C22×C2913yes—
322C4×C4⋊C4C22×C2913yes—
323C4×C4⋊C4C22×C2913yes—
324C4×C4⋊C4C22×C2913yes—
325C4×C4⋊C4C22×C2916yes—
326C4×C4⋊C4C22×C2913yes—
327C4×C4⋊C4C22×C2913yes—
328C4×C4⋊C4C22×C2913yes—
329C4×C22⋊C4C22×C2913yes—
330C4×C22⋊C4C22×C2913yes—
331#376C22×C2913yes—
332#376C22×C2916yes—
333C43C22×C2913yes—
334C2×C29—42no—
335C2×C29C22×#11711yescharacteristic
336C2×C29C4×2−1+411yescharacteristic
337C2×C29C4×2−1+411yescharacteristic
338C2×C29#351611yescharacteristic
339C2×C29#351811yescharacteristic
340C2×C29#352311yescharacteristic
341C2×C29#352411yescharacteristic
342C22×Q8—24no—
343C22×Q8—24no—
344C22×Q8C2×C4×C2918yes—
345C22×Q8C23×C2913yes—
346C22×Q8C23×C2911yescharacteristic
347C23×C4C23×C2913yes—
348C4×Q8—24no—
349C4×Q8—24no—
350C4×Q8—24no—
351C4×Q8—24no—
352C4×Q8C2×C4×C29124yes—
353C4×Q8C2×C4×C29124yes—
354C4×Q8C2×C4×C2918yes—
355C4×Q8C2×C4×C2918yes—
356#117C2×C4×C29124yes—
357#117C2×C4×C29124yes—
358C2×C4⋊C4C23×C2913yes—
359C2×C4⋊C4C23×C2913yes—
360C2×C4⋊C4C23×C2913yes—
361C2×C4⋊C4C23×C2913yes—
362C2×C4⋊C4C23×C2911yescharacteristic
363C2×C4⋊C4C23×C2913yes—
364C2×C4⋊C4C23×C2913yes—
365C2×C4⋊C4C23×C2916yes—
366C2×C4⋊C4C23×C2913yes—
367C2×C4⋊C4C23×C2913yes—
368C2×C4⋊C4C23×C2913yes—
369C2×C4⋊C4C23×C2913yes—
370C2×C4⋊C4C23×C2913yes—
371C2×C22⋊C4C23×C2911yescharacteristic
372C2×C22⋊C4C23×C2911yescharacteristic
373C2×C22⋊C4C23×C2913yes—
374C2×C22⋊C4C23×C2913yes—
375C2×C22⋊C4C23×C2911yescharacteristic
376C2×C22⋊C4C23×C2913yes—
377C2×C42C23×C2913yes—
378C2×C42C23×C2913yes—
379C2×C42C23×C2913yes—
380C2×C42C23×C2913yes—
381C2×C42C23×C2911yescharacteristic
382C2×C42C23×C2913yes—
383C2×C42C23×C2913yes—
384C2×C42C23×C2913yes—
385C2×C42C23×C2916yes—
386C2×C42C23×C2913yes—
387C2×C42C23×C2916yes—
388C2×C42C23×C2913yes—
389#95C23×C2911yescharacteristic
390#95C23×C2913yes—
391#95C23×C2913yes—
392#95C23×C2913yes—
393#95C23×C2913yes—
394#95C23×C2913yes—
395#95C23×C2916yes—
396#95C23×C2916yes—
397#95C23×C2913yes—
398#95C23×C2913yes—
399#95C23×C2913yes—
400#95C23×C2916yes—
401#95C23×C2911yescharacteristic
402#95C23×C2916yes—
403#95C23×C2913yes—
404#95C23×C2913yes—
405C29#3426211yescharacteristic, direct product factor, Sylow
406C24C24×C2911yescharacteristic
407C2×Q8—232no—
408C2×Q8—26no—
409C2×Q8—26no—
410C2×Q8C22×C4×C29112yes—
411C2×Q8C22×C4×C2914yes—
412C2×Q8#41×C2914yes—
413C2×Q8#41×C2914yes—
414C22×C4—26no—
415C22×C4—26no—
416C22×C4C22×C4×C29112yes—
417C22×C4C24×C2911yescharacteristic
418C22×C4C24×C2911yescharacteristic
419C22×C4C24×C2913yes—
420C22×C4C24×C2913yes—
421C22×C4C24×C2913yes—
422C22×C4C24×C2913yes—
423C22×C4C24×C2913yes—
424C22×C4C24×C2911yescharacteristic
425C22×C4C24×C2913yes—
426C22×C4C24×C2913yes—
427C22×C4C24×C2911yescharacteristic
428C22×C4C24×C2911yescharacteristic
429C22×C4C24×C2911yescharacteristic
430C22×C4C24×C2913yes—
431C4⋊C4—26no—
432C4⋊C4—26no—
433C4⋊C4—26no—
434C4⋊C4—26no—
435C4⋊C4—22no—
436C4⋊C4—26no—
437C4⋊C4—43no—
438C4⋊C4—43no—
439C4⋊C4—46no—
440C4⋊C4C22×C4×C29112yes—
441C4⋊C4C22×C4×C29112yes—
442C4⋊C4C22×C4×C29112yes—
443C4⋊C4C22×C4×C29112yes—
444C22⋊C4—22no—
445C22⋊C4—22no—
446C22⋊C4—43no—
447C22⋊C4—43no—
448C22⋊C4C22×C4×C2914yes—
449C22⋊C4C22×C4×C29112yes—
450C42—26no—
451C42—26no—
452C42—26no—
453C42—26no—
454C42—22no—
455C42—26no—
456C42—43no—
457C42—46no—
458C42—43no—
459C42C22×C4×C29124yes—
460C42C22×C4×C29112yes—
461C42C22×C4×C29112yes—
462C23—21no—
463C23—21no—
464C23—21no—
465C23—21no—
466C23—21no—
467C23—21no—
468C23C23×C4×C2912yes—
469C23C25×C2911yescharacteristic
470Q8—224no—
471Q8C29×#117116yes—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—23no—
475C2×C4—23no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—23no—
479C2×C4—23no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—23no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—23no—
486C2×C4—224no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—23no—
490C2×C4—23no—
491C2×C4—23no—
492C2×C4—23no—
493C2×C4—23no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—23no—
497C2×C4—21no—
498C2×C4—23no—
499C2×C4—23no—
500C2×C4—23no—
501C2×C4—23no—
502C2×C4—23no—
503C2×C4—23no—
504C2×C4—21no—
505C2×C4C23×C4×C2916yes—
506C2×C4C23×C4×C2912yes—
507C2×C4C23×C4×C2916yes—
508C2×C4C23×C4×C2912yes—
509C2×C4C23×C4×C2916yes—
510C2×C4C23×C4×C2916yes—
511C2×C4C2×#41×C2916yes—
512C2×C4C2×#41×C2916yes—
513C2×C4C29×2−1+412yes—
514C2×C4C29×2−1+412yes—
515C22—22no—
516C22—22no—
517C22—22no—
518C22—41no—
519C22—41no—
520C22—41no—
521C22—41no—
522C22C24×C4×C2911yescharacteristic
523C22C22×#41×C2911yescharacteristic
524C22C22×#41×C2911yescharacteristic
525C22C2×C29×2−1+411yescharacteristic
526C22C2×C29×2−1+411yescharacteristic
527C22C29×#58511yescharacteristic
528C22C29×#58511yescharacteristic
529C4—22no—
530C4—22no—
531C4—26no—
532C4—22no—
533C4—26no—
534C4—26no—
535C4—22no—
536C4—43no—
537C4—41no—
538C4—43no—
539C4—41no—
540C4—43no—
541C4—43no—
542C4C2×C29×#117112yes—
543C2—42no—
544C2C22×C29×#11711yescharacteristic
545C2C4×C29×2−1+411yescharacteristic
546C2C4×C29×2−1+411yescharacteristic
547C2C29×#351611yescharacteristic
548C2C29×#351811yescharacteristic
549C2C29×#352311yescharacteristic
550C2C29×#352411yescharacteristic
subgroupG/H
center, socleC23×C29C25
commutatorC22C24×C4×C29
Frattini, cosocleC23C25×C29
prime radicalC24×C29C24
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#2356C2semidirect
3. C29×#2355C2semidirect
4. C29×#2351C2semidirect
5. Q8×C4⋊C4×C29C2semidirect
10. C29×#2320C2semidirect
13. C29×#2295C2semidirect
14. C29×#2276C2semidirect
15. C42×Q8×C29C2semidirect
17. C29×#519C4semidirect
186. #34262C29direct (N × H)
241. #2356C2×C29semidirect
242. #2355C2×C29semidirect
243. #2351C2×C29semidirect
244. Q8×C4⋊C4C2×C29semidirect
249. #2320C2×C29semidirect
252. #2295C2×C29semidirect
253. #2276C2×C29semidirect
254. C42×Q8C2×C29semidirect
284. #519C4×C29semidirect
405. C29#34262direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#5192
C29×#23562
C29×#23552
C29×#23512
Q8×C4⋊C4×C292
C29×#23472
C29×#23462
Q8×C22⋊C4×C292
C29×#23202
C29×#23142
C29×#22982
C29×#22952
C29×#22762
C42×Q8×C292
#3426229