Finite Group Databasebeta

← C29×#11087 #20305987

Subgroups — C29×#11087 #20305987

Order 7424.

1478 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C29×#99C211yesmaximal, characteristic
2C29×#2308C211yesmaximal, characteristic
3C2×C29×#386C211yesmaximal, characteristic
4C2×C29×#385C211yesmaximal, characteristic, complemented
5C2×C29×#342C211yesmaximal, characteristic, complemented
6C2×C29×#342C211yesmaximal, characteristic, complemented
7C29×C22⋊#95C211yesmaximal, characteristic, complemented
8C23×D4×C29C2211yescharacteristic
9C24×C4×C29C2211yescharacteristic
10C22×C4⋊C4×C29—21no—
11C22×C22⋊C4×C29—21no—
12C22×C22⋊C4×C29C2211yescharacteristic
13C22×C22⋊C4×C29C2211yescharacteristic
14C22×C22⋊C4×C29C2211yescharacteristic
15C22×C22⋊C4×C29C2211yescharacteristic
16C22×C22⋊C4×C29C2211yescharacteristic
17C2×C29×#99—22no—
18C2×C29×#99—22no—
19C2×C29×#99C414yescomplemented
20C29×#386—22no—
21C29×#386—21no—
22C29×#386—21no—
23C29×#386—22no—
24C29×#386—22no—
25C29×#385—22no—
26C29×#385—22no—
27C29×#381—21no—
28C29×#379—21no—
29C2×C29×#95—21no—
30C2×C29×#95—21no—
31C2×C29×#95—22no—
32C29×#342—22no—
33C29×#342—22no—
34C25×C29D411yescharacteristic
35C25×C29C2311yescharacteristic
36C22×D4×C29—21no—
37C22×D4×C29—21no—
38C22×D4×C29—21no—
39C22×D4×C29—21no—
40C22×D4×C29—21no—
41C22×D4×C29—21no—
42C22×D4×C29—21no—
43C22×D4×C29—21no—
44C22×D4×C29—21no—
45C22×D4×C29—21no—
46C22×D4×C29—21no—
47C22×D4×C29—21no—
48C22×D4×C29C2×C412yes—
49C22×D4×C29Q812yes—
50C23×C4×C29—21no—
51C23×C4×C29—21no—
52C23×C4×C29—21no—
53C23×C4×C29—21no—
54C23×C4×C29—21no—
55C23×C4×C29—21no—
56C23×C4×C29—21no—
57C23×C4×C29—21no—
58C23×C4×C29—21no—
59C23×C4×C29—44no—
60C23×C4×C29D411yescharacteristic
61C23×C4×C29D411yescharacteristic
62C23×C4×C29D411yescharacteristic
63C23×C4×C29D412yes—
64C23×C4×C29D412yes—
65C2×C4⋊C4×C29—24no—
66C2×C4⋊C4×C29—44no—
67C2×C22⋊C4×C29—21no—
68C2×C22⋊C4×C29—21no—
69C2×C22⋊C4×C29—21no—
70C2×C22⋊C4×C29—21no—
71C2×C22⋊C4×C29—21no—
72C2×C22⋊C4×C29—21no—
73C2×C22⋊C4×C29—21no—
74C2×C22⋊C4×C29—21no—
75C2×C22⋊C4×C29—21no—
76C2×C22⋊C4×C29—21no—
77C2×C22⋊C4×C29—21no—
78C2×C22⋊C4×C29—24no—
79C2×C22⋊C4×C29—21no—
80C2×C22⋊C4×C29—21no—
81C2×C22⋊C4×C29—21no—
82C2×C22⋊C4×C29—21no—
83C2×C22⋊C4×C29—21no—
84C2×C22⋊C4×C29—21no—
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×C22⋊C4×C29—21no—
92C2×C22⋊C4×C29—21no—
93C2×C22⋊C4×C29—22no—
94C2×C22⋊C4×C29—22no—
95C2×C22⋊C4×C29—44no—
96C2×C22⋊C4×C29C2×C412yes—
97C2×C22⋊C4×C29C2×C412yes—
98C2×C22⋊C4×C29D412yes—
99C2×C22⋊C4×C29D412yes—
100C2×C22⋊C4×C29D412yes—
101C29×#99—28no—
102C29×#95—24no—
103C29×#95—24no—
104C29×#95—22no—
105C29×#95—22no—
106C29×#95—44no—
107C24×C29—21no—
108C24×C29—21no—
109C24×C29—21no—
110C24×C29—21no—
111C24×C29—21no—
112C24×C29—21no—
113C24×C29—42no—
114C24×C29—42no—
115C24×C29—42no—
116C24×C29—42no—
117C24×C29C4⋊C412yescomplemented
118C24×C29C22×C411yescharacteristic
119C24×C29C2×D411yescharacteristic
120C24×C29C2×D411yescharacteristic
121C24×C29C2×D411yescharacteristic
122C24×C29C2×D411yescharacteristic
123C24×C29C2×D411yescharacteristic
124C24×C29C2×D411yescharacteristic
125C24×C29C2×D411yescharacteristic
126C24×C29C2×Q811yescharacteristic
127C24×C29#4111yescharacteristic
128C24×C29#4111yescharacteristic
129C24×C29#4111yescharacteristic
130C24×C29#4111yescharacteristic
131C24×C29#4111yescharacteristic
132C24×C29#4111yescharacteristic
133C2×D4×C29—22no—
134C2×D4×C29—22no—
135C2×D4×C29—22no—
136C2×D4×C29—22no—
137C2×D4×C29—22no—
138C2×D4×C29—22no—
139C2×D4×C29—22no—
140C2×D4×C29—22no—
141C2×D4×C29—22no—
142C2×D4×C29—22no—
143C2×D4×C29—22no—
144C2×D4×C29—22no—
145C2×D4×C29—41no—
146C2×D4×C29—41no—
147C2×D4×C29—41no—
148C2×D4×C29—41no—
149C2×D4×C29—41no—
150C2×D4×C29—41no—
151C2×D4×C29—41no—
152C2×D4×C29—41no—
153C2×D4×C29—41no—
154C2×D4×C29—41no—
155C2×D4×C29—41no—
156C2×D4×C29—41no—
157C2×D4×C29—41no—
158C2×D4×C29—41no—
159C2×D4×C29—41no—
160C2×D4×C29—41no—
161C22×C4×C29—24no—
162C22×C4×C29—24no—
163C22×C4×C29—24no—
164C22×C4×C29—22no—
165C22×C4×C29—22no—
166C22×C4×C29—22no—
167C22×C4×C29—22no—
168C22×C4×C29—21no—
169C22×C4×C29—21no—
170C22×C4×C29—22no—
171C22×C4×C29—22no—
172C22×C4×C29—21no—
173C22×C4×C29—21no—
174C22×C4×C29—21no—
175C22×C4×C29—21no—
176C22×C4×C29—22no—
177C22×C4×C29—22no—
178C22×C4×C29—21no—
179C22×C4×C29—21no—
180C22×C4×C29—21no—
181C22×C4×C29—21no—
182C22×C4×C29—22no—
183C22×C4×C29—22no—
184C22×C4×C29—21no—
185C22×C4×C29—21no—
186C22×C4×C29—22no—
187C22×C4×C29—44no—
188C22×C4×C29—44no—
189C22×C4×C29—44no—
190C22×C4×C29—44no—
191C22×C4×C29—42no—
192C22×C4×C29—42no—
193C22×C4×C29—42no—
194C22×C4×C29—42no—
195C22×C4×C29—42no—
196C22×C4×C29—41no—
197C22×C4×C29—41no—
198C22×C4×C29—41no—
199C22×C4×C29—41no—
200C22×C4×C29—42no—
201C22×C4×C29—42no—
202C22×C4×C29—42no—
203C22×C4×C29—42no—
204C22×C4×C29—42no—
205C22×C4×C29—42no—
206C22×C4×C29—42no—
207C22×C4×C29—42no—
208C22×C4×C29—41no—
209C22×C4×C29—41no—
210C22×C4×C29—41no—
211C22×C4×C29—41no—
212C22×C4×C29C4⋊C412yescomplemented
213C4⋊C4×C29—48no—
214C22⋊C4×C29—22no—
215C22⋊C4×C29—22no—
216C22⋊C4×C29—22no—
217C22⋊C4×C29—22no—
218C22⋊C4×C29—22no—
219C22⋊C4×C29—22no—
220C22⋊C4×C29—22no—
221C22⋊C4×C29—48no—
222C22⋊C4×C29—41no—
223C22⋊C4×C29—41no—
224C22⋊C4×C29—41no—
225C22⋊C4×C29—41no—
226C22⋊C4×C29—41no—
227C22⋊C4×C29—41no—
228C22⋊C4×C29—41no—
229C22⋊C4×C29—41no—
230C22⋊C4×C29—41no—
231C22⋊C4×C29—41no—
232C22⋊C4×C29—41no—
233C22⋊C4×C29—41no—
234C22⋊C4×C29—82no—
235C22⋊C4×C29—82no—
236C22⋊C4×C29C22⋊C414yescomplemented
237#11087C2911yesmaximal, characteristic, direct product factor, Sylow
238C23×C29—22no—
239C23×C29—22no—
240C23×C29—22no—
241C23×C29—22no—
242C23×C29—22no—
243C23×C29—22no—
244C23×C29—22no—
245C23×C29—22no—
246C23×C29—22no—
247C23×C29—41no—
248C23×C29—41no—
249C23×C29—41no—
250C23×C29—41no—
251C23×C29—42no—
252C23×C29—41no—
253C23×C29—41no—
254C23×C29—41no—
255C23×C29—42no—
256C23×C29—42no—
257C23×C29—42no—
258C23×C29—42no—
259C23×C29—41no—
260C23×C29—42no—
261C23×C29—42no—
262C23×C29—42no—
263C23×C29—44no—
264C23×C29—42no—
265C23×C29—42no—
266C23×C29—44no—
267C23×C29—41no—
268C23×C29—41no—
269C23×C29—41no—
270C23×C29—41no—
271C23×C29—42no—
272C23×C29—42no—
273C23×C29—82no—
274C23×C29—81no—
275C23×C29—81no—
276C23×C29—82no—
277C23×C29C2×C22⋊C411yescharacteristic
278C23×C29C2×C4⋊C411yescharacteristic
279C23×C29#11711yescharacteristic
280C23×C29C4×D411yescharacteristic
281C23×C29C4×D411yescharacteristic
282C23×C29C4×D411yescharacteristic
283C23×C29C4×D411yescharacteristic
284C23×C29#12011yescharacteristic
285C23×C29#12011yescharacteristic
286C23×C29#12011yescharacteristic
287C23×C29#12111yescharacteristic
288C23×C29#12111yescharacteristic
289C23×C29#12111yescharacteristic
290C23×C29#12111yescharacteristic
291C23×C29#12111yescharacteristic
292C23×C29#12111yescharacteristic
293C23×C29#12111yescharacteristic
294C23×C29#12111yescharacteristic
295C23×C29C22⋊Q811yescharacteristic
296C23×C29C22⋊Q811yescharacteristic
297C23×C29C22⋊Q811yescharacteristic
298C23×C29C22⋊Q811yescharacteristic
299C23×C29C22⋊Q811yescharacteristic
300C23×C29C22⋊Q811yescharacteristic
301C23×C29#12311yescharacteristic
302C23×C29#12311yescharacteristic
303C23×C29#12311yescharacteristic
304C23×C29#12311yescharacteristic
305C23×C29#12311yescharacteristic
306C23×C29#12411yescharacteristic
307C23×C29#12411yescharacteristic
308C23×C29#12411yescharacteristic
309C23×C29#12611yescharacteristic
310C23×C29#12611yescharacteristic
311C23×C29#12711yescharacteristic
312D4×C29—42no—
313D4×C29—42no—
314D4×C29—42no—
315D4×C29—42no—
316D4×C29—42no—
317D4×C29—42no—
318D4×C29—42no—
319D4×C29—42no—
320C2×C4×C29—24no—
321C2×C4×C29—24no—
322C2×C4×C29—24no—
323C2×C4×C29—22no—
324C2×C4×C29—22no—
325C2×C4×C29—22no—
326C2×C4×C29—24no—
327C2×C4×C29—42no—
328C2×C4×C29—44no—
329C2×C4×C29—42no—
330C2×C4×C29—44no—
331C2×C4×C29—42no—
332C2×C4×C29—42no—
333C2×C4×C29—42no—
334C2×C4×C29—44no—
335C2×C4×C29—44no—
336C2×C4×C29—44no—
337C2×C4×C29—42no—
338C2×C4×C29—41no—
339C2×C4×C29—41no—
340C2×C4×C29—41no—
341C2×C4×C29—41no—
342C2×C4×C29—44no—
343C2×C4×C29—42no—
344C2×C4×C29—42no—
345C2×C4×C29—44no—
346C2×C4×C29—42no—
347C2×C4×C29—42no—
348C2×C4×C29—44no—
349C2×C4×C29—42no—
350C2×C4×C29—41no—
351C2×C4×C29—41no—
352C2×C4×C29—42no—
353C2×C4×C29—42no—
354C2×C4×C29—42no—
355C2×C4×C29—42no—
356C2×C4×C29—42no—
357C2×C4×C29—42no—
358C2×C4×C29—82no—
359C2×C4×C29—81no—
360C2×C4×C29—81no—
361C2×C4×C29—82no—
362C2×C4×C29—82no—
363C2×C4×C29—81no—
364C2×C4×C29—81no—
365C2×C4×C29—82no—
366C22×#99C2×C2911yescharacteristic
367#2308C2×C2911yescharacteristic
368C2×#386C2×C2911yescharacteristic
369C2×#385C2×C2911yescharacteristic, complemented
370C2×#342C2×C2911yescharacteristic, complemented
371C2×#342C2×C2911yescharacteristic, complemented
372C22⋊#95C2×C2911yescharacteristic, complemented
373C22×C29—22no—
374C22×C29—22no—
375C22×C29—22no—
376C22×C29—22no—
377C22×C29—22no—
378C22×C29—22no—
379C22×C29—21no—
380C22×C29—21no—
381C22×C29—21no—
382C22×C29—21no—
383C22×C29—21no—
384C22×C29—21no—
385C22×C29—21no—
386C22×C29—21no—
387C22×C29—21no—
388C22×C29—21no—
389C22×C29—21no—
390C22×C29—21no—
391C22×C29—22no—
392C22×C29—22no—
393C22×C29—22no—
394C22×C29—22no—
395C22×C29—22no—
396C22×C29—22no—
397C22×C29—41no—
398C22×C29—41no—
399C22×C29—41no—
400C22×C29—41no—
401C22×C29—41no—
402C22×C29—41no—
403C22×C29—41no—
404C22×C29—41no—
405C22×C29—41no—
406C22×C29—41no—
407C22×C29—41no—
408C22×C29—41no—
409C22×C29—41no—
410C22×C29—41no—
411C22×C29—41no—
412C22×C29—41no—
413C22×C29—44no—
414C22×C29—44no—
415C22×C29—42no—
416C22×C29—82no—
417C22×C29—82no—
418C22×C29—82no—
419C22×C29—81no—
420C22×C29—81no—
421C22×C29—82no—
422C22×C29#38011yescharacteristic
423C22×C29#38511yescharacteristic
424C22×C29#38511yescharacteristic
425C22×C29#38611yescharacteristic
426C22×C29#38811yescharacteristic
427C22×C29#38811yescharacteristic
428C22×C29#39011yescharacteristic
429C22×C29#39211yescharacteristic
430C22×C29#39311yescharacteristic
431C22×C29#39411yescharacteristic
432C22×C29#39411yescharacteristic
433C22×C29#39611yescharacteristic
434C22×C29#39611yescharacteristic
435C22×C29#39711yescharacteristic
436C22×C29#39911yescharacteristic
437C22×C29B(4,𝔽2)12yes—
438C22×C29#45812yes—
439C4×C29—44no—
440C4×C29—42no—
441C4×C29—44no—
442C4×C29—82no—
443C4×C29—82no—
444C4×C29—81no—
445C4×C29—81no—
446C4×C29—82no—
447C23×D4C22×C2911yescharacteristic
448C24×C4C22×C2911yescharacteristic
449C22×C4⋊C4—21no—
450C22×C22⋊C4—21no—
451C22×C22⋊C4C22×C2911yescharacteristic
452C22×C22⋊C4C22×C2911yescharacteristic
453C22×C22⋊C4C22×C2911yescharacteristic
454C22×C22⋊C4C22×C2911yescharacteristic
455C22×C22⋊C4C22×C2911yescharacteristic
456C2×#99—22no—
457C2×#99—22no—
458C2×#99C4×C2914yescomplemented
459#386—21no—
460#386—21no—
461#386—22no—
462#386—22no—
463#386—22no—
464#385—22no—
465#385—22no—
466#381—21no—
467#379—21no—
468C2×#95—21no—
469C2×#95—21no—
470C2×#95—22no—
471#342—22no—
472#342—22no—
473C2×C29—21no—
474C2×C29—21no—
475C2×C29—21no—
476C2×C29—21no—
477C2×C29—21no—
478C2×C29—21no—
479C2×C29—21no—
480C2×C29—21no—
481C2×C29—21no—
482C2×C29—21no—
483C2×C29—21no—
484C2×C29—21no—
485C2×C29—82no—
486C2×C29#143911yescharacteristic
487C2×C29#186712yes—
488C2×C29#202111yescharacteristic
489C2×C29#202211yescharacteristic
490C2×C29#204412yes—
491C25D4×C2911yescharacteristic
492C25C23×C2911yescharacteristic
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4C2×C4×C2912yes—
506C22×D4Q8×C2912yes—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—44no—
517C23×C4D4×C2911yescharacteristic
518C23×C4D4×C2911yescharacteristic
519C23×C4D4×C2911yescharacteristic
520C23×C4D4×C2912yes—
521C23×C4D4×C2912yes—
522C2×C4⋊C4—24no—
523C2×C4⋊C4—44no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—24no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—22no—
552C2×C22⋊C4—44no—
553C2×C22⋊C4C2×C4×C2912yes—
554C2×C22⋊C4C2×C4×C2912yes—
555C2×C22⋊C4D4×C2912yes—
556C2×C22⋊C4D4×C2912yes—
557C2×C22⋊C4D4×C2912yes—
558#99—28no—
559#95—24no—
560#95—24no—
561#95—22no—
562#95—22no—
563#95—44no—
564C29#1108711yescharacteristic, direct product factor, Sylow
565C24—21no—
566C24—21no—
567C24—21no—
568C24—21no—
569C24—21no—
570C24—21no—
571C24—42no—
572C24—42no—
573C24—42no—
574C24—42no—
575C24C4⋊C4×C2912yescomplemented
576C24C22×C4×C2911yescharacteristic
577C24C2×D4×C2911yescharacteristic
578C24C2×D4×C2911yescharacteristic
579C24C2×D4×C2911yescharacteristic
580C24C2×D4×C2911yescharacteristic
581C24C2×D4×C2911yescharacteristic
582C24C2×D4×C2911yescharacteristic
583C24C2×D4×C2911yescharacteristic
584C24C2×Q8×C2911yescharacteristic
585C24#41×C2911yescharacteristic
586C24#41×C2911yescharacteristic
587C24#41×C2911yescharacteristic
588C24#41×C2911yescharacteristic
589C24#41×C2911yescharacteristic
590C24#41×C2911yescharacteristic
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—41no—
604C2×D4—41no—
605C2×D4—41no—
606C2×D4—41no—
607C2×D4—41no—
608C2×D4—41no—
609C2×D4—41no—
610C2×D4—41no—
611C2×D4—41no—
612C2×D4—41no—
613C2×D4—41no—
614C2×D4—41no—
615C2×D4—41no—
616C2×D4—41no—
617C2×D4—41no—
618C2×D4—41no—
619C22×C4—24no—
620C22×C4—24no—
621C22×C4—24no—
622C22×C4—22no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—22no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—22no—
638C22×C4—21no—
639C22×C4—22no—
640C22×C4—21no—
641C22×C4—22no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—22no—
645C22×C4—44no—
646C22×C4—44no—
647C22×C4—44no—
648C22×C4—44no—
649C22×C4—42no—
650C22×C4—42no—
651C22×C4—42no—
652C22×C4—42no—
653C22×C4—42no—
654C22×C4—41no—
655C22×C4—41no—
656C22×C4—41no—
657C22×C4—41no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—41no—
667C22×C4—41no—
668C22×C4—41no—
669C22×C4—41no—
670C22×C4C4⋊C4×C2912yescomplemented
671C4⋊C4—48no—
672C22⋊C4—22no—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—22no—
679C22⋊C4—48no—
680C22⋊C4—41no—
681C22⋊C4—41no—
682C22⋊C4—41no—
683C22⋊C4—41no—
684C22⋊C4—41no—
685C22⋊C4—41no—
686C22⋊C4—41no—
687C22⋊C4—41no—
688C22⋊C4—41no—
689C22⋊C4—41no—
690C22⋊C4—41no—
691C22⋊C4—41no—
692C22⋊C4—82no—
693C22⋊C4—82no—
694C22⋊C4C22⋊C4×C2914yescomplemented
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—42no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—42no—
713C23—42no—
714C23—41no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—44no—
721C23—42no—
722C23—42no—
723C23—44no—
724C23—42no—
725C23—42no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—82no—
731C23—81no—
732C23—81no—
733C23—82no—
734C23C2×C22⋊C4×C2911yescharacteristic
735C23C2×C4⋊C4×C2911yescharacteristic
736C23C29×#11711yescharacteristic
737C23C4×D4×C2911yescharacteristic
738C23C4×D4×C2911yescharacteristic
739C23C4×D4×C2911yescharacteristic
740C23C4×D4×C2911yescharacteristic
741C23C29×#12011yescharacteristic
742C23C29×#12011yescharacteristic
743C23C29×#12011yescharacteristic
744C23C29×#12111yescharacteristic
745C23C29×#12111yescharacteristic
746C23C29×#12111yescharacteristic
747C23C29×#12111yescharacteristic
748C23C29×#12111yescharacteristic
749C23C29×#12111yescharacteristic
750C23C29×#12111yescharacteristic
751C23C29×#12111yescharacteristic
752C23C29×C22⋊Q811yescharacteristic
753C23C29×C22⋊Q811yescharacteristic
754C23C29×C22⋊Q811yescharacteristic
755C23C29×C22⋊Q811yescharacteristic
756C23C29×C22⋊Q811yescharacteristic
757C23C29×C22⋊Q811yescharacteristic
758C23C29×#12311yescharacteristic
759C23C29×#12311yescharacteristic
760C23C29×#12311yescharacteristic
761C23C29×#12311yescharacteristic
762C23C29×#12311yescharacteristic
763C23C29×#12411yescharacteristic
764C23C29×#12411yescharacteristic
765C23C29×#12411yescharacteristic
766C23C29×#12611yescharacteristic
767C23C29×#12611yescharacteristic
768C23C29×#12711yescharacteristic
769D4—42no—
770D4—42no—
771D4—42no—
772D4—42no—
773D4—42no—
774D4—42no—
775D4—42no—
776D4—42no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—24no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—42no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—42no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—44no—
804C2×C4—42no—
805C2×C4—44no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—81no—
816C2×C4—81no—
817C2×C4—82no—
818C2×C4—82no—
819C2×C4—82no—
820C2×C4—81no—
821C2×C4—81no—
822C2×C4—82no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—21no—
829C22—21no—
830C22—21no—
831C22—21no—
832C22—21no—
833C22—21no—
834C22—21no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—22no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—41no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—44no—
864C22—42no—
865C22—44no—
866C22—82no—
867C22—82no—
868C22—82no—
869C22—81no—
870C22—81no—
871C22—82no—
872C22C29×#38011yescharacteristic
873C22C29×#38511yescharacteristic
874C22C29×#38511yescharacteristic
875C22C29×#38611yescharacteristic
876C22C29×#38811yescharacteristic
877C22C29×#38811yescharacteristic
878C22C29×#39011yescharacteristic
879C22C29×#39211yescharacteristic
880C22C29×#39311yescharacteristic
881C22C29×#39411yescharacteristic
882C22C29×#39411yescharacteristic
883C22C29×#39611yescharacteristic
884C22C29×#39611yescharacteristic
885C22C29×#39711yescharacteristic
886C22C29×#39911yescharacteristic
887C22C29×B(4,𝔽2)12yes—
888C22C29×#45812yes—
889C4—44no—
890C4—42no—
891C4—44no—
892C4—82no—
893C4—82no—
894C4—81no—
895C4—81no—
896C4—82no—
897C2—21no—
898C2—21no—
899C2—21no—
900C2—21no—
901C2—21no—
902C2—21no—
903C2—21no—
904C2—21no—
905C2—21no—
906C2—21no—
907C2—21no—
908C2—21no—
909C2—82no—
910C2C29×#143911yescharacteristic
911C2C29×#186712yes—
912C2C29×#202111yescharacteristic
913C2C29×#202211yescharacteristic
914C2C29×#204412yes—
subgroupG/H
center, socleC23×C29#120
commutatorC24C22×C4×C29
Frattini, cosocleC25C23×C29
prime radicalC23×D4×C29C22
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C29 ◁ C25×C29 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C29×#385C2semidirect
5. C2×C29×#342C2semidirect
6. C2×C29×#342C2semidirect
7. C29×C22⋊#95C2semidirect
19. C2×C29×#99C4semidirect
117. C24×C29C4⋊C4semidirect
212. C22×C4×C29C4⋊C4semidirect
236. C22⋊C4×C29C22⋊C4semidirect
237. #11087C29direct (N × H)
369. C2×#385C2×C29semidirect
370. C2×#342C2×C29semidirect
371. C2×#342C2×C29semidirect
372. C22⋊#95C2×C29semidirect
458. C2×#99C4×C29semidirect
564. C29#11087direct (N × H)
575. C24C4⋊C4×C29semidirect
670. C22×C4C4⋊C4×C29semidirect
694. C22⋊C4C22⋊C4×C29semidirect

Maximal subgroups

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

subgroupindex
C22×C29×#992
C29×#23082
C2×C29×#3862
C2×C29×#3852
C2×C29×#3422
C29×C22⋊#952
#1108729