Finite Group Databasebeta

← C2×C29×#1867 #20315787

Subgroups — C2×C29×#1867 #20315787

Order 7424.

1994 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
1C2×C29×#518C211yesmaximal, characteristic
2C22×C29×#99C211yesmaximal, characteristic
3C2×C29×#386C211yesmaximal, characteristic
4C2×C29×#385C212yesmaximal, complemented
5C29×#1867C218yesmaximal, direct product factor
6C2×C29×#342C212yesmaximal, complemented
7C23×D4×C29C2211yescharacteristic
8C24×C4×C29C2211yescharacteristic
9C29×#518—22no—
10C29×#518—24no—
11C29×#518C2214yes—
12C2×C4×D4×C29—22no—
13C2×C4×D4×C29—22no—
14C2×C29×#117—21no—
15C22×C4⋊C4×C29—22no—
16C22×C22⋊C4×C29—21no—
17C22×C22⋊C4×C29—21no—
18C22×C22⋊C4×C29C2211yescharacteristic
19C22×C22⋊C4×C29C2212yes—
20C22×C22⋊C4×C29C2212yes—
21C2×C29×#99C418yescomplemented
22C2×C29×#99C2214yes—
23C29×#386—22no—
24C29×#386C2214yes—
25C29×#385—24no—
26C29×#385C2218yescomplemented
27C2×C29×#95—22no—
28C2×C29×#95—21no—
29C29×#342C2218yescomplemented
30C25×C29D411yescharacteristic
31C25×C29C2311yescharacteristic
32C22×D4×C29—22no—
33C22×D4×C29—22no—
34C22×D4×C29—24no—
35C22×D4×C29C2×C414yes—
36C22×D4×C29D412yes—
37C22×D4×C29Q814yes—
38C22×D4×C29C2312yes—
39C23×C4×C29—21no—
40C23×C4×C29—22no—
41C23×C4×C29—22no—
42C23×C4×C29—21no—
43C23×C4×C29—21no—
44C23×C4×C29—21no—
45C23×C4×C29—22no—
46C23×C4×C29—21no—
47C23×C4×C29—44no—
48C23×C4×C29D411yescharacteristic
49C23×C4×C29D412yes—
50C23×C4×C29D412yes—
51C23×C4×C29C2312yes—
52C4×D4×C29—28no—
53C4×D4×C29—28no—
54C4×D4×C29—28no—
55C4×D4×C29—28no—
56C29×#117—24no—
57C29×#117—24no—
58C2×C4⋊C4×C29—21no—
59C2×C4⋊C4×C29—21no—
60C2×C4⋊C4×C29—28no—
61C2×C4⋊C4×C29—48no—
62C2×C22⋊C4×C29—22no—
63C2×C22⋊C4×C29—24no—
64C2×C22⋊C4×C29—22no—
65C2×C22⋊C4×C29—24no—
66C2×C22⋊C4×C29—22no—
67C2×C22⋊C4×C29—22no—
68C2×C22⋊C4×C29—22no—
69C2×C22⋊C4×C29—22no—
70C2×C22⋊C4×C29—24no—
71C2×C22⋊C4×C29—24no—
72C2×C22⋊C4×C29—24no—
73C2×C22⋊C4×C29—21no—
74C2×C22⋊C4×C29—44no—
75C2×C22⋊C4×C29C2×C418yescomplemented
76C2×C22⋊C4×C29D414yes—
77C2×C22⋊C4×C29C2312yes—
78C2×C22⋊C4×C29C2314yes—
79C2×C22⋊C4×C29C2314yes—
80C2×C42×C29—22no—
81C29×#99C2×C4116yescomplemented
82C29×#95—28no—
83C29×#95—24no—
84C24×C29—21no—
85C24×C29—21no—
86C24×C29—22no—
87C24×C29—42no—
88C24×C29—42no—
89C24×C29—42no—
90C24×C29—42no—
91C24×C29C4⋊C414yescomplemented
92C24×C29C22×C412yes—
93C24×C29C2×D411yescharacteristic
94C24×C29C2×D412yes—
95C24×C29C2×D412yes—
96C24×C29C2×D411yescharacteristic
97C24×C29C2×D412yes—
98C24×C29C2×Q812yes—
99C24×C29#4114yes—
100C24×C29C2411yescharacteristic
101C2×D4×C29—28no—
102C2×D4×C29—28no—
103C2×D4×C29—24no—
104C2×D4×C29—28no—
105C2×D4×C29—28no—
106C2×D4×C29—24no—
107C2×D4×C29—24no—
108C2×D4×C29—24no—
109C2×D4×C29C4⋊C418yescomplemented
110C2×D4×C29C22×C414yes—
111C2×D4×C29C2×Q814yes—
112C22×C4×C29—21no—
113C22×C4×C29—21no—
114C22×C4×C29—22no—
115C22×C4×C29—24no—
116C22×C4×C29—28no—
117C22×C4×C29—28no—
118C22×C4×C29—22no—
119C22×C4×C29—22no—
120C22×C4×C29—22no—
121C22×C4×C29—24no—
122C22×C4×C29—24no—
123C22×C4×C29—24no—
124C22×C4×C29—24no—
125C22×C4×C29—22no—
126C22×C4×C29—22no—
127C22×C4×C29—22no—
128C22×C4×C29—44no—
129C22×C4×C29—44no—
130C22×C4×C29—48no—
131C22×C4×C29—44no—
132C22×C4×C29—44no—
133C22×C4×C29—44no—
134C22×C4×C29—42no—
135C22×C4×C29—41no—
136C22×C4×C29—42no—
137C22×C4×C29—41no—
138C22×C4×C29—44no—
139C22×C4×C29—44no—
140C22×C4×C29—42no—
141C22×C4×C29—42no—
142C22×C4×C29—42no—
143C22×C4×C29—82no—
144C22×C4×C29—82no—
145C22×C4×C29C4⋊C414yescomplemented
146C22×C4×C29C2×D412yes—
147C22×C4×C29C2×D414yes—
148C22×C4×C29C2×D414yes—
149C4⋊C4×C29—24no—
150C4⋊C4×C29—24no—
151C4⋊C4×C29—416no—
152C22⋊C4×C29—28no—
153C22⋊C4×C29—28no—
154C22⋊C4×C29—24no—
155C22⋊C4×C29—24no—
156C22⋊C4×C29—24no—
157C22⋊C4×C29—24no—
158C22⋊C4×C29—24no—
159C22⋊C4×C29—24no—
160C22⋊C4×C29—48no—
161C22⋊C4×C29—42no—
162C22⋊C4×C29C22×C418yescomplemented
163C42×C29—28no—
164C2×#1867C2911yesmaximal, characteristic, direct product factor, Sylow
165C23×C29—24no—
166C23×C29—22no—
167C23×C29—24no—
168C23×C29—22no—
169C23×C29—22no—
170C23×C29—24no—
171C23×C29—22no—
172C23×C29—24no—
173C23×C29—42no—
174C23×C29—41no—
175C23×C29—41no—
176C23×C29—44no—
177C23×C29—42no—
178C23×C29—41no—
179C23×C29—44no—
180C23×C29—48no—
181C23×C29—41no—
182C23×C29—42no—
183C23×C29—48no—
184C23×C29—42no—
185C23×C29—42no—
186C23×C29—42no—
187C23×C29—84no—
188C23×C29—81no—
189C23×C29—81no—
190C23×C29C2×C4⋊C412yes—
191C23×C29C2×C4⋊C412yes—
192C23×C29C2×C4⋊C414yescomplemented
193C23×C29C4×D414yes—
194C23×C29C4×D414yes—
195C23×C29#12011yescharacteristic
196C23×C29#12012yes—
197C23×C29#12011yescharacteristic
198C23×C29C22⋊Q814yes—
199C23×C29C22⋊Q814yes—
200C23×C29#12312yes—
201C23×C29#12312yes—
202C23×C29C23×C411yescharacteristic
203C23×C29C22×D411yescharacteristic
204C23×C29C22×D412yes—
205C23×C29C22×Q811yescharacteristic
206C23×C29C2×#4112yes—
207D4×C29—28no—
208D4×C29—28no—
209D4×C29—216no—
210C2×C4×C29—22no—
211C2×C4×C29—22no—
212C2×C4×C29—24no—
213C2×C4×C29—24no—
214C2×C4×C29—24no—
215C2×C4×C29—28no—
216C2×C4×C29—28no—
217C2×C4×C29—24no—
218C2×C4×C29—24no—
219C2×C4×C29—44no—
220C2×C4×C29—416no—
221C2×C4×C29—44no—
222C2×C4×C29—44no—
223C2×C4×C29—42no—
224C2×C4×C29—48no—
225C2×C4×C29—44no—
226C2×C4×C29—42no—
227C2×C4×C29—44no—
228C2×C4×C29—44no—
229C2×C4×C29—44no—
230C2×C4×C29—44no—
231C2×C4×C29—44no—
232C2×C4×C29—42no—
233C2×C4×C29—42no—
234C2×C4×C29—42no—
235C2×C4×C29—82no—
236C2×C4×C29—82no—
237C2×C4×C29—84no—
238C2×C4×C29—84no—
239C2×C4×C29—84no—
240C2×C4×C29C2×C4⋊C414yescomplemented
241C2×#518C2×C2911yescharacteristic
242C22×#99C2×C2911yescharacteristic
243C2×#386C2×C2911yescharacteristic
244C2×#385C2×C2912yescomplemented
245#1867C2×C2918yesdirect product factor
246C2×#342C2×C2912yescomplemented
247C22×C29—28no—
248C22×C29—24no—
249C22×C29—24no—
250C22×C29—28no—
251C22×C29—22no—
252C22×C29—21no—
253C22×C29—22no—
254C22×C29—21no—
255C22×C29—22no—
256C22×C29—21no—
257C22×C29—22no—
258C22×C29—21no—
259C22×C29—24no—
260C22×C29—42no—
261C22×C29—44no—
262C22×C29—44no—
263C22×C29—42no—
264C22×C29—41no—
265C22×C29—41no—
266C22×C29—42no—
267C22×C29—44no—
268C22×C29—48no—
269C22×C29—42no—
270C22×C29—42no—
271C22×C29—82no—
272C22×C29—84no—
273C22×C29#38512yes—
274C22×C29#38514yes—
275C22×C29#38512yes—
276C22×C29B(4,𝔽2)12yes—
277C22×C29#45812yes—
278C22×C29C22×C4⋊C411yescharacteristic
279C22×C29C2×C4×D412yes—
280C22×C29C2×#12011yescharacteristic
281C22×C29C2×C22⋊Q812yes—
282C22×C29C2×#12311yescharacteristic
283C4×C29—24no—
284C4×C29—48no—
285C4×C29—44no—
286C4×C29—44no—
287C4×C29—44no—
288C4×C29—82no—
289C23×D4C22×C2911yescharacteristic
290C24×C4C22×C2911yescharacteristic
291#518—22no—
292#518—24no—
293#518C22×C2914yes—
294C2×C4×D4—22no—
295C2×C4×D4—22no—
296C2×#117—21no—
297C22×C4⋊C4—22no—
298C22×C22⋊C4—21no—
299C22×C22⋊C4—21no—
300C22×C22⋊C4C22×C2911yescharacteristic
301C22×C22⋊C4C22×C2912yes—
302C22×C22⋊C4C22×C2912yes—
303C2×#99C4×C2918yescomplemented
304C2×#99C22×C2914yes—
305#386—22no—
306#386C22×C2914yes—
307#385—24no—
308#385C22×C2918yescomplemented
309C2×#95—22no—
310C2×#95—21no—
311#342C22×C2918yescomplemented
312C2×C29—22no—
313C2×C29—21no—
314C2×C29—21no—
315C2×C29—22no—
316C2×C29—22no—
317C2×C29—24no—
318C2×C29—44no—
319C2×C29#186714yesdirect product factor
320C2×C29C2×#38511yescharacteristic
321C2×C29C2×B(4,𝔽2)11yescharacteristic
322C2×C29C2×#45811yescharacteristic
323C25D4×C2911yescharacteristic
324C25C23×C2911yescharacteristic
325C22×D4—22no—
326C22×D4—22no—
327C22×D4—24no—
328C22×D4C2×C4×C2914yes—
329C22×D4D4×C2912yes—
330C22×D4Q8×C2914yes—
331C22×D4C23×C2912yes—
332C23×C4—21no—
333C23×C4—22no—
334C23×C4—22no—
335C23×C4—21no—
336C23×C4—21no—
337C23×C4—21no—
338C23×C4—22no—
339C23×C4—21no—
340C23×C4—44no—
341C23×C4D4×C2911yescharacteristic
342C23×C4D4×C2912yes—
343C23×C4D4×C2912yes—
344C23×C4C23×C2912yes—
345C4×D4—28no—
346C4×D4—28no—
347C4×D4—28no—
348C4×D4—28no—
349#117—24no—
350#117—24no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—28no—
354C2×C4⋊C4—48no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4C2×C4×C2918yescomplemented
369C2×C22⋊C4D4×C2914yes—
370C2×C22⋊C4C23×C2912yes—
371C2×C22⋊C4C23×C2914yes—
372C2×C22⋊C4C23×C2914yes—
373C2×C42—22no—
374#99C2×C4×C29116yescomplemented
375#95—28no—
376#95—24no—
377C29C2×#186711yescharacteristic, direct product factor, Sylow
378C24—21no—
379C24—21no—
380C24—22no—
381C24—42no—
382C24—42no—
383C24—42no—
384C24—42no—
385C24C4⋊C4×C2914yescomplemented
386C24C22×C4×C2912yes—
387C24C2×D4×C2911yescharacteristic
388C24C2×D4×C2912yes—
389C24C2×D4×C2912yes—
390C24C2×D4×C2911yescharacteristic
391C24C2×D4×C2912yes—
392C24C2×Q8×C2912yes—
393C24#41×C2914yes—
394C24C24×C2911yescharacteristic
395C2×D4—28no—
396C2×D4—28no—
397C2×D4—24no—
398C2×D4—28no—
399C2×D4—28no—
400C2×D4—24no—
401C2×D4—24no—
402C2×D4—24no—
403C2×D4C4⋊C4×C2918yescomplemented
404C2×D4C22×C4×C2914yes—
405C2×D4C2×Q8×C2914yes—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4—24no—
410C22×C4—28no—
411C22×C4—28no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—24no—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—24no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—44no—
423C22×C4—44no—
424C22×C4—48no—
425C22×C4—44no—
426C22×C4—44no—
427C22×C4—42no—
428C22×C4—44no—
429C22×C4—41no—
430C22×C4—42no—
431C22×C4—41no—
432C22×C4—44no—
433C22×C4—44no—
434C22×C4—42no—
435C22×C4—42no—
436C22×C4—42no—
437C22×C4—82no—
438C22×C4—82no—
439C22×C4C4⋊C4×C2914yescomplemented
440C22×C4C2×D4×C2912yes—
441C22×C4C2×D4×C2914yes—
442C22×C4C2×D4×C2914yes—
443C4⋊C4—24no—
444C4⋊C4—24no—
445C4⋊C4—416no—
446C22⋊C4—28no—
447C22⋊C4—28no—
448C22⋊C4—24no—
449C22⋊C4—24no—
450C22⋊C4—24no—
451C22⋊C4—24no—
452C22⋊C4—24no—
453C22⋊C4—24no—
454C22⋊C4—48no—
455C22⋊C4—42no—
456C22⋊C4C22×C4×C2918yescomplemented
457C42—28no—
458C23—24no—
459C23—22no—
460C23—24no—
461C23—22no—
462C23—22no—
463C23—24no—
464C23—22no—
465C23—24no—
466C23—42no—
467C23—41no—
468C23—41no—
469C23—44no—
470C23—42no—
471C23—41no—
472C23—44no—
473C23—48no—
474C23—41no—
475C23—42no—
476C23—48no—
477C23—42no—
478C23—42no—
479C23—42no—
480C23—81no—
481C23—81no—
482C23—84no—
483C23C2×C4⋊C4×C2912yes—
484C23C2×C4⋊C4×C2912yes—
485C23C2×C4⋊C4×C2914yescomplemented
486C23C4×D4×C2914yes—
487C23C4×D4×C2914yes—
488C23C29×#12011yescharacteristic
489C23C29×#12012yes—
490C23C29×#12011yescharacteristic
491C23C29×C22⋊Q814yes—
492C23C29×C22⋊Q814yes—
493C23C29×#12312yes—
494C23C29×#12312yes—
495C23C23×C4×C2911yescharacteristic
496C23C22×D4×C2911yescharacteristic
497C23C22×D4×C2912yes—
498C23C22×Q8×C2911yescharacteristic
499C23C2×#41×C2912yes—
500D4—28no—
501D4—28no—
502D4—216no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—28no—
509C2×C4—28no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—44no—
513C2×C4—44no—
514C2×C4—42no—
515C2×C4—48no—
516C2×C4—44no—
517C2×C4—44no—
518C2×C4—416no—
519C2×C4—44no—
520C2×C4—44no—
521C2×C4—44no—
522C2×C4—42no—
523C2×C4—44no—
524C2×C4—44no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—82no—
529C2×C4—82no—
530C2×C4—84no—
531C2×C4—84no—
532C2×C4—84no—
533C2×C4C2×C4⋊C4×C2914yescomplemented
534C22—22no—
535C22—21no—
536C22—22no—
537C22—21no—
538C22—22no—
539C22—21no—
540C22—22no—
541C22—21no—
542C22—28no—
543C22—24no—
544C22—24no—
545C22—28no—
546C22—24no—
547C22—42no—
548C22—44no—
549C22—44no—
550C22—42no—
551C22—41no—
552C22—41no—
553C22—42no—
554C22—44no—
555C22—42no—
556C22—42no—
557C22—48no—
558C22—82no—
559C22—84no—
560C22C29×#38512yes—
561C22C29×#38514yes—
562C22C29×#38512yes—
563C22C29×B(4,𝔽2)12yes—
564C22C29×#45812yes—
565C22C22×C4⋊C4×C2911yescharacteristic
566C22C2×C4×D4×C2912yes—
567C22C2×C29×#12011yescharacteristic
568C22C2×C29×C22⋊Q812yes—
569C22C2×C29×#12311yescharacteristic
570C4—24no—
571C4—48no—
572C4—44no—
573C4—44no—
574C4—44no—
575C4—82no—
576C2—22no—
577C2—21no—
578C2—21no—
579C2—22no—
580C2—22no—
581C2—24no—
582C2—44no—
583C2C29×#186714yesdirect product factor
584C2C2×C29×#38511yescharacteristic
585C2C2×C29×B(4,𝔽2)11yescharacteristic
586C2C2×C29×#45811yescharacteristic
subgroupG/H
center, socleC23×C29#120
commutatorC23C23×C4×C29
Frattini, cosocleC24C24×C29
prime radicalC23×D4×C29C22
LCSG ▷ C23 ▷ 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. C29×#1867C2direct (N × H)
6. C2×C29×#342C2semidirect
21. C2×C29×#99C4semidirect
26. C29×#385C22semidirect
29. C29×#342C22semidirect
75. C2×C22⋊C4×C29C2×C4semidirect
81. C29×#99C2×C4semidirect
91. C24×C29C4⋊C4semidirect
109. C2×D4×C29C4⋊C4semidirect
145. C22×C4×C29C4⋊C4semidirect
162. C22⋊C4×C29C22×C4semidirect
164. C2×#1867C29direct (N × H)
192. C23×C29C2×C4⋊C4semidirect
240. C2×C4×C29C2×C4⋊C4semidirect
244. C2×#385C2×C29semidirect
245. #1867C2×C29direct (N × H)
246. C2×#342C2×C29semidirect
303. C2×#99C4×C29semidirect
308. #385C22×C29semidirect
311. #342C22×C29semidirect
319. C2×C29#1867direct (N × H)
368. C2×C22⋊C4C2×C4×C29semidirect
374. #99C2×C4×C29semidirect
377. C29C2×#1867direct (N × H)
385. C24C4⋊C4×C29semidirect
403. C2×D4C4⋊C4×C29semidirect
439. C22×C4C4⋊C4×C29semidirect
456. C22⋊C4C22×C4×C29semidirect
485. C23C2×C4⋊C4×C29semidirect
533. C2×C4C2×C4⋊C4×C29semidirect
583. C2C29×#1867direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#5182
C22×C29×#992
C2×C29×#3862
C2×C29×#3852
C29×#18672
C2×C29×#3422
C2×#186729